LMFDB - Embedded newform 4.31.b.a.3.5

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			3.5
Root			$0.500000 - 872651. i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.31.b.a.3.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-16991.5 - 28018.4i) q^{2} +1.39624e7i q^{3} +(-4.96318e8 + 9.52150e8i) q^{4} +8.38288e9 q^{5} +(3.91204e11 - 2.37243e11i) q^{6} -4.67445e12i q^{7} +(3.51109e13 - 2.27243e12i) q^{8} +1.09422e13 q^{9} +O(q^{10})$	\(q+(-16991.5 - 28018.4i) q^{2} +1.39624e7i q^{3} +(-4.96318e8 + 9.52150e8i) q^{4} +8.38288e9 q^{5} +(3.91204e11 - 2.37243e11i) q^{6} -4.67445e12i q^{7} +(3.51109e13 - 2.27243e12i) q^{8} +1.09422e13 q^{9} +(-1.42438e14 - 2.34875e14i) q^{10} +1.25880e15i q^{11} +(-1.32943e16 - 6.92980e15i) q^{12} -5.60336e16 q^{13} +(-1.30971e17 + 7.94260e16i) q^{14} +1.17045e17i q^{15} +(-6.60257e17 - 9.45139e17i) q^{16} +4.24738e18 q^{17} +(-1.85924e17 - 3.06582e17i) q^{18} +1.63419e19i q^{19} +(-4.16058e18 + 7.98175e18i) q^{20} +6.52666e19 q^{21} +(3.52695e19 - 2.13889e19i) q^{22} +1.14847e20i q^{23} +(3.17286e19 + 4.90233e20i) q^{24} -8.61050e20 q^{25} +(9.52096e20 + 1.56997e21i) q^{26} +3.02752e21i q^{27} +(4.45078e21 + 2.32002e21i) q^{28} +1.34840e22 q^{29} +(3.27942e21 - 1.98878e21i) q^{30} +2.16376e22i q^{31} +(-1.52625e22 + 3.45587e22i) q^{32} -1.75759e22 q^{33} +(-7.21694e22 - 1.19005e23i) q^{34} -3.91853e22i q^{35} +(-5.43079e21 + 1.04186e22i) q^{36} -2.27561e23 q^{37} +(4.57875e23 - 2.77674e23i) q^{38} -7.82364e23i q^{39} +(2.94330e23 - 1.90495e22i) q^{40} -9.64365e23 q^{41} +(-1.10898e24 - 1.82867e24i) q^{42} +3.63505e24i q^{43} +(-1.19857e24 - 6.24765e23i) q^{44} +9.17267e22 q^{45} +(3.21782e24 - 1.95142e24i) q^{46} +1.87075e25i q^{47} +(1.31964e25 - 9.21879e24i) q^{48} +6.88842e23 q^{49} +(1.46305e25 + 2.41252e25i) q^{50} +5.93036e25i q^{51} +(2.78105e25 - 5.33524e25i) q^{52} -9.96199e25 q^{53} +(8.48261e25 - 5.14421e25i) q^{54} +1.05524e25i q^{55} +(-1.06224e25 - 1.64124e26i) q^{56} -2.28173e26 q^{57} +(-2.29113e26 - 3.77799e26i) q^{58} +4.36473e26i q^{59} +(-1.11445e26 - 5.80917e25i) q^{60} +2.08449e26 q^{61} +(6.06250e26 - 3.67655e26i) q^{62} -5.11486e25i q^{63} +(1.22761e27 - 1.59574e26i) q^{64} -4.69723e26 q^{65} +(2.98641e26 + 4.92448e26i) q^{66} +2.05452e27i q^{67} +(-2.10805e27 + 4.04414e27i) q^{68} -1.60354e27 q^{69} +(-1.09791e27 + 6.65819e26i) q^{70} -4.38762e27i q^{71} +(3.84189e26 - 2.48653e25i) q^{72} +1.53240e28 q^{73} +(3.86661e27 + 6.37591e27i) q^{74} -1.20223e28i q^{75} +(-1.55600e28 - 8.11080e27i) q^{76} +5.88420e27 q^{77} +(-2.19206e28 + 1.32936e28i) q^{78} -3.41778e28i q^{79} +(-5.53486e27 - 7.92298e27i) q^{80} -4.00185e28 q^{81} +(1.63860e28 + 2.70200e28i) q^{82} -7.25366e28i q^{83} +(-3.23930e28 + 6.21436e28i) q^{84} +3.56052e28 q^{85} +(1.01848e29 - 6.17651e28i) q^{86} +1.88269e29i q^{87} +(2.86053e27 + 4.41976e28i) q^{88} +1.76311e29 q^{89} +(-1.55858e27 - 2.57004e27i) q^{90} +2.61926e29i q^{91} +(-1.09351e29 - 5.70006e28i) q^{92} -3.02113e29 q^{93} +(5.24154e29 - 3.17869e29i) q^{94} +1.36992e29i q^{95} +(-4.82523e29 - 2.13101e29i) q^{96} -4.97906e29 q^{97} +(-1.17045e28 - 1.93003e28i) q^{98} +1.37740e28i 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 $

$2$	−16991.5	−	28018.4i	−0.518540	−	0.855053i
$2$	−16991.5	−	28018.4i	−0.518540	−	0.855053i
$3$			1.39624e7i			0.973065i	0.873663	+	0.486532i	$0.161738\pi$
$3$			1.39624e7i			0.973065i	−0.873663	+	0.486532i	$0.838262\pi$
$4$	−4.96318e8	+	9.52150e8i	−0.462233	+	0.886759i
$5$	8.38288e9			0.274690			0.137345	−	0.990523i	$-0.456143\pi$
$5$	8.38288e9			0.274690			0.137345	+	0.990523i	$0.456143\pi$
$6$	3.91204e11	−	2.37243e11i	0.832022	−	0.504573i
$7$		−	4.67445e12i		−	0.984601i	−0.870425	−	0.492300i	$-0.836156\pi$
$7$		−	4.67445e12i		−	0.984601i	0.870425	−	0.492300i	$-0.163844\pi$
$8$	3.51109e13	−	2.27243e12i	0.997912	−	0.0645863i
$9$	1.09422e13			0.0531453
$10$	−1.42438e14	−	2.34875e14i	−0.142438	−	0.234875i
$11$			1.25880e15i			0.301347i	0.988584	+	0.150673i	$0.0481441\pi$
$11$			1.25880e15i			0.301347i	−0.988584	+	0.150673i	$0.951856\pi$
$12$	−1.32943e16	−	6.92980e15i	−0.862873	−	0.449782i
$13$	−5.60336e16			−1.09471			−0.547354	−	0.836901i	$-0.684365\pi$
$13$	−5.60336e16			−1.09471			−0.547354	+	0.836901i	$0.684365\pi$
$14$	−1.30971e17	+	7.94260e16i	−0.841886	+	0.510555i
$15$			1.17045e17i			0.267291i
$16$	−6.60257e17	−	9.45139e17i	−0.572682	−	0.819778i
$17$	4.24738e18			1.48384			0.741920	−	0.670489i	$-0.233916\pi$
$17$	4.24738e18			1.48384			0.741920	+	0.670489i	$0.233916\pi$
$18$	−1.85924e17	−	3.06582e17i	−0.0275580	−	0.0454421i
$19$			1.63419e19i			1.07646i	0.842797	+	0.538232i	$0.180908\pi$
$19$			1.63419e19i			1.07646i	−0.842797	+	0.538232i	$0.819092\pi$
$20$	−4.16058e18	+	7.98175e18i	−0.126971	+	0.243584i
$21$	6.52666e19			0.958080
$22$	3.52695e19	−	2.13889e19i	0.257667	−	0.156260i
$23$			1.14847e20i			0.430726i	0.976534	+	0.215363i	$0.0690935\pi$
$23$			1.14847e20i			0.430726i	−0.976534	+	0.215363i	$0.930906\pi$
$24$	3.17286e19	+	4.90233e20i	0.0628466	+	0.971033i
$25$	−8.61050e20			−0.924545
$26$	9.52096e20	+	1.56997e21i	0.567650	+	0.936034i
$27$			3.02752e21i			1.02478i
$28$	4.45078e21	+	2.32002e21i	0.873103	+	0.455114i
$29$	1.34840e22			1.56260			0.781300	−	0.624156i	$-0.214557\pi$
$29$	1.34840e22			1.56260			0.781300	+	0.624156i	$0.214557\pi$
$30$	3.27942e21	−	1.98878e21i	0.228548	−	0.138601i
$31$			2.16376e22i			0.922111i	0.887371	+	0.461055i	$0.152529\pi$
$31$			2.16376e22i			0.922111i	−0.887371	+	0.461055i	$0.847471\pi$
$32$	−1.52625e22	+	3.45587e22i	−0.403995	+	0.914761i
$33$	−1.75759e22			−0.293230
$34$	−7.21694e22	−	1.19005e23i	−0.769430	−	1.26876i
$35$		−	3.91853e22i		−	0.270460i
$36$	−5.43079e21	+	1.04186e22i	−0.0245655	+	0.0471271i
$37$	−2.27561e23			−0.682453			−0.341227	−	0.939981i	$-0.610842\pi$
$37$	−2.27561e23			−0.682453			−0.341227	+	0.939981i	$0.610842\pi$
$38$	4.57875e23	−	2.77674e23i	0.920434	−	0.558190i
$39$		−	7.82364e23i		−	1.06522i
$40$	2.94330e23	−	1.90495e22i	0.274117	−	0.0177412i
$41$	−9.64365e23			−0.620131			−0.310066	−	0.950715i	$-0.600351\pi$
$41$	−9.64365e23			−0.620131			−0.310066	+	0.950715i	$0.600351\pi$
$42$	−1.10898e24	−	1.82867e24i	−0.496803	−	0.819209i
$43$			3.63505e24i			1.14415i	0.820201	+	0.572076i	$0.193862\pi$
$43$			3.63505e24i			1.14415i	−0.820201	+	0.572076i	$0.806138\pi$
$44$	−1.19857e24	−	6.24765e23i	−0.267222	−	0.139292i
$45$	9.17267e22			0.0145985
$46$	3.21782e24	−	1.95142e24i	0.368294	−	0.223349i
$47$			1.87075e25i			1.55077i	0.631488	+	0.775386i	$0.282444\pi$
$47$			1.87075e25i			1.55077i	−0.631488	+	0.775386i	$0.717556\pi$
$48$	1.31964e25	−	9.21879e24i	0.797697	−	0.557257i
$49$	6.88842e23			0.0305618
$50$	1.46305e25	+	2.41252e25i	0.479414	+	0.790536i
$51$			5.93036e25i			1.44387i
$52$	2.78105e25	−	5.33524e25i	0.506010	−	0.970742i
$53$	−9.96199e25			−1.36210			−0.681049	−	0.732238i	$-0.738476\pi$
$53$	−9.96199e25			−1.36210			−0.681049	+	0.732238i	$0.738476\pi$
$54$	8.48261e25	−	5.14421e25i	0.876240	−	0.531389i
$55$			1.05524e25i			0.0827769i
$56$	−1.06224e25	−	1.64124e26i	−0.0635917	−	0.982545i
$57$	−2.28173e26			−1.04747
$58$	−2.29113e26	−	3.77799e26i	−0.810271	−	1.33611i
$59$			4.36473e26i			1.19448i	0.802064	+	0.597238i	$0.203735\pi$
$59$			4.36473e26i			1.19448i	−0.802064	+	0.597238i	$0.796265\pi$
$60$	−1.11445e26	−	5.80917e25i	−0.237023	−	0.123551i
$61$	2.08449e26			0.345982			0.172991	−	0.984923i	$-0.444657\pi$
$61$	2.08449e26			0.345982			0.172991	+	0.984923i	$0.444657\pi$
$62$	6.06250e26	−	3.67655e26i	0.788454	−	0.478151i
$63$		−	5.11486e25i		−	0.0523269i
$64$	1.22761e27	−	1.59574e26i	0.991657	−	0.128903i
$65$	−4.69723e26			−0.300705
$66$	2.98641e26	+	4.92448e26i	0.152051	+	0.250727i
$67$			2.05452e27i			0.834809i	0.908721	+	0.417405i	$0.137060\pi$
$67$			2.05452e27i			0.834809i	−0.908721	+	0.417405i	$0.862940\pi$
$68$	−2.10805e27	+	4.04414e27i	−0.685879	+	1.31581i
$69$	−1.60354e27			−0.419125
$70$	−1.09791e27	+	6.65819e26i	−0.231258	+	0.140244i
$71$		−	4.38762e27i		−	0.747056i	−0.927619	−	0.373528i	$-0.878148\pi$
$71$		−	4.38762e27i		−	0.747056i	0.927619	−	0.373528i	$-0.121852\pi$
$72$	3.84189e26	−	2.48653e25i	0.0530344	−	0.00343246i
$73$	1.53240e28			1.72001			0.860004	−	0.510287i	$-0.170461\pi$
$73$	1.53240e28			1.72001			0.860004	+	0.510287i	$0.170461\pi$
$74$	3.86661e27	+	6.37591e27i	0.353879	+	0.583534i
$75$		−	1.20223e28i		−	0.899642i
$76$	−1.55600e28	−	8.11080e27i	−0.954564	−	0.497577i
$77$	5.88420e27			0.296706
$78$	−2.19206e28	+	1.32936e28i	−0.910821	+	0.552360i
$79$		−	3.41778e28i		−	1.17311i	−0.809910	−	0.586554i	$-0.800484\pi$
$79$		−	3.41778e28i		−	1.17311i	0.809910	−	0.586554i	$-0.199516\pi$
$80$	−5.53486e27	−	7.92298e27i	−0.157310	−	0.225185i
$81$	−4.00185e28			−0.944030
$82$	1.63860e28	+	2.70200e28i	0.321563	+	0.530245i
$83$		−	7.25366e28i		−	1.18682i	−0.804899	−	0.593412i	$-0.797781\pi$
$83$		−	7.25366e28i		−	1.18682i	0.804899	−	0.593412i	$-0.202219\pi$
$84$	−3.23930e28	+	6.21436e28i	−0.442856	+	0.849586i
$85$	3.56052e28			0.407596
$86$	1.01848e29	−	6.17651e28i	0.978311	−	0.593289i
$87$			1.88269e29i			1.52051i
$88$	2.86053e27	+	4.41976e28i	0.0194629	+	0.300717i
$89$	1.76311e29			1.01258			0.506290	−	0.862363i	$-0.331017\pi$
$89$	1.76311e29			1.01258			0.506290	+	0.862363i	$0.331017\pi$
$90$	−1.55858e27	−	2.57004e27i	−0.00756991	−	0.0124825i
$91$			2.61926e29i			1.07785i
$92$	−1.09351e29	−	5.70006e28i	−0.381950	−	0.199096i
$93$	−3.02113e29			−0.897273
$94$	5.24154e29	−	3.17869e29i	1.32599	−	0.804137i
$95$			1.36992e29i			0.295694i
$96$	−4.82523e29	−	2.13101e29i	−0.890122	−	0.393113i
$97$	−4.97906e29			−0.786269			−0.393135	−	0.919481i	$-0.628609\pi$
$97$	−4.97906e29			−0.786269			−0.393135	+	0.919481i	$0.628609\pi$
$98$	−1.17045e28	−	1.93003e28i	−0.0158475	−	0.0261319i
$99$			1.37740e28i			0.0160152i
$100$	4.27355e29	−	8.19849e29i	0.427355	−	0.819849i
$101$	−9.95181e29			−0.857199			−0.428599	−	0.903495i	$-0.640993\pi$
$101$	−9.95181e29			−0.857199			−0.428599	+	0.903495i	$0.640993\pi$
$102$	1.66159e30	−	1.00766e30i	1.23459	−	0.748705i
$103$		−	6.85173e29i		−	0.439786i	−0.975524	−	0.219893i	$-0.929429\pi$
$103$		−	6.85173e29i		−	0.439786i	0.975524	−	0.219893i	$-0.0705709\pi$
$104$	−1.96739e30	+	1.27332e29i	−1.09242	+	0.0707031i
$105$	5.47122e29			0.263175
$106$	1.69269e30	+	2.79119e30i	0.706302	+	1.16467i
$107$			2.22566e30i			0.806682i	0.915050	+	0.403341i	$0.132151\pi$
$107$			2.22566e30i			0.806682i	−0.915050	+	0.403341i	$0.867849\pi$
$108$	−2.88265e30	−	1.50261e30i	−0.908731	−	0.473686i
$109$	5.07013e30			1.39194			0.695972	−	0.718069i	$-0.254974\pi$
$109$	5.07013e30			1.39194			0.695972	+	0.718069i	$0.254974\pi$
$110$	2.95660e29	−	1.79301e29i	0.0707787	−	0.0429231i
$111$		−	3.17731e30i		−	0.664071i
$112$	−4.41801e30	+	3.08634e30i	−0.807153	+	0.563863i
$113$	−1.17851e30			−0.188433			−0.0942164	−	0.995552i	$-0.530035\pi$
$113$	−1.17851e30			−0.188433			−0.0942164	+	0.995552i	$0.530035\pi$
$114$	3.87700e30	+	6.39304e30i	0.543155	+	0.895642i
$115$			9.62747e29i			0.118316i
$116$	−6.69234e30	+	1.28388e31i	−0.722285	+	1.38565i
$117$	−6.13128e29			−0.0581786
$118$	1.22293e31	−	7.41634e30i	1.02134	−	0.619384i
$119$		−	1.98542e31i		−	1.46099i
$120$	2.65977e29	+	4.10956e30i	0.0172633	+	0.266733i
$121$	1.58648e31			0.909190
$122$	−3.54187e30	−	5.84041e30i	−0.179405	−	0.295833i
$123$		−	1.34649e31i		−	0.603428i
$124$	−2.06022e31	−	1.07391e31i	−0.817690	−	0.426230i
$125$	−1.50252e31			−0.528654
$126$	−1.43310e30	+	8.69092e29i	−0.0447423	+	0.0271336i
$127$			1.01841e31i			0.282402i	0.989981	+	0.141201i	$0.0450964\pi$
$127$			1.01841e31i			0.282402i	−0.989981	+	0.141201i	$0.954904\pi$
$128$	−2.53300e31	−	3.16843e31i	−0.624433	−	0.781079i
$129$	−5.07541e31			−1.11333
$130$	7.98130e30	+	1.31609e31i	0.155928	+	0.257119i
$131$			7.76210e31i			1.35179i	0.736997	+	0.675896i	$0.236243\pi$
$131$			7.76210e31i			1.35179i	−0.736997	+	0.675896i	$0.763757\pi$
$132$	8.72323e30	−	1.67349e31i	0.135540	−	0.260024i
$133$	7.63896e31			1.05989
$134$	5.75642e31	−	3.49093e31i	0.713807	−	0.432882i
$135$			2.53793e31i			0.281496i
$136$	1.49129e32	−	9.65186e30i	1.48074	−	0.0958357i
$137$	−1.75935e31			−0.156511			−0.0782555	−	0.996933i	$-0.524935\pi$
$137$	−1.75935e31			−0.156511			−0.0782555	+	0.996933i	$0.524935\pi$
$138$	2.72466e31	+	4.49286e31i	0.217333	+	0.358374i
$139$			1.62070e32i			1.16006i	0.814594	+	0.580032i	$0.196960\pi$
$139$			1.62070e32i			1.16006i	−0.814594	+	0.580032i	$0.803040\pi$
$140$	3.73103e31	+	1.94484e31i	0.239833	+	0.125015i
$141$	−2.61202e32			−1.50900
$142$	−1.22934e32	+	7.45523e31i	−0.638773	+	0.387379i
$143$		−	7.05351e31i		−	0.329886i
$144$	−7.22464e30	−	1.03419e31i	−0.0304354	−	0.0435674i
$145$	1.13034e32			0.429231
$146$	−2.60379e32	−	4.29355e32i	−0.891893	−	1.47070i
$147$			9.61790e30i			0.0297386i
$148$	1.12943e32	−	2.16673e32i	0.315452	−	0.605171i
$149$	3.20051e32			0.808026			0.404013	−	0.914753i	$-0.367615\pi$
$149$	3.20051e32			0.808026			0.404013	+	0.914753i	$0.367615\pi$
$150$	−3.36846e32	+	2.04278e32i	−0.769242	+	0.466501i
$151$		−	8.35362e32i		−	1.72671i	−0.504593	−	0.863357i	$-0.668357\pi$
$151$		−	8.35362e32i		−	1.72671i	0.504593	−	0.863357i	$-0.331643\pi$
$152$	3.71359e31	+	5.73780e32i	0.0695248	+	1.07422i
$153$	4.64755e31			0.0788592
$154$	−9.99814e31	−	1.64866e32i	−0.153854	−	0.253699i
$155$			1.81385e32i			0.253295i
$156$	7.44928e32	+	3.88302e32i	0.944594	+	0.492380i
$157$	−3.20805e31			−0.0369612			−0.0184806	−	0.999829i	$-0.505883\pi$
$157$	−3.20805e31			−0.0369612			−0.0184806	+	0.999829i	$0.505883\pi$
$158$	−9.57608e32	+	5.80733e32i	−1.00307	+	0.608304i
$159$		−	1.39093e33i		−	1.32541i
$160$	−1.27944e32	+	2.89701e32i	−0.110973	+	0.251276i
$161$	5.36846e32			0.424093
$162$	6.79976e32	+	1.12125e33i	0.489517	+	0.807196i
$163$			1.64495e33i			1.07979i	0.841733	+	0.539893i	$0.181535\pi$
$163$			1.64495e33i			1.07979i	−0.841733	+	0.539893i	$0.818465\pi$
$164$	4.78632e32	−	9.18220e32i	0.286645	−	0.549907i
$165$	−1.47336e32			−0.0805473
$166$	−2.03236e33	+	1.23251e33i	−1.01480	+	0.615415i
$167$			4.58658e32i			0.209287i	0.994510	+	0.104643i	$0.0333701\pi$
$167$			4.58658e32i			0.209287i	−0.994510	+	0.104643i	$0.966630\pi$
$168$	2.29157e33	−	1.48314e32i	0.956080	−	0.0618788i
$169$	5.19769e32			0.198385
$170$	−6.04987e32	−	9.97601e32i	−0.211355	−	0.348516i
$171$			1.78816e32i			0.0572091i
$172$	−3.46111e33	−	1.80414e33i	−1.01459	−	0.528864i
$173$	1.68258e33			0.452152			0.226076	−	0.974110i	$-0.427410\pi$
$173$	1.68258e33			0.452152			0.226076	+	0.974110i	$0.427410\pi$
$174$	5.27499e33	−	3.19897e33i	1.30012	−	0.788446i
$175$			4.02494e33i			0.910308i
$176$	1.18974e33	−	8.31132e32i	0.247037	−	0.172576i
$177$	−6.09422e33			−1.16230
$178$	−2.99579e33	−	4.93995e33i	−0.525063	−	0.865810i
$179$		−	4.77742e33i		−	0.769836i	−0.922951	−	0.384918i	$-0.874230\pi$
$179$		−	4.77742e33i		−	0.769836i	0.922951	−	0.384918i	$-0.125770\pi$
$180$	−4.55257e31	+	8.73376e31i	−0.00674790	+	0.0129453i
$181$	−9.62456e33			−1.31281			−0.656406	−	0.754408i	$-0.727924\pi$
$181$	−9.62456e33			−1.31281			−0.656406	+	0.754408i	$0.727924\pi$
$182$	7.33875e33	−	4.45053e33i	0.921619	−	0.558908i
$183$			2.91046e33i			0.336662i
$184$	2.60981e32	+	4.03238e33i	0.0278190	+	0.429827i
$185$	−1.90762e33			−0.187463
$186$	5.13335e33	+	8.46471e33i	0.465272	+	0.767217i
$187$			5.34659e33i			0.447150i
$188$	−1.78123e34	−	9.28487e33i	−1.37516	−	0.716817i
$189$	1.41520e34			1.00900
$190$	3.83831e33	−	2.32771e33i	0.252834	−	0.153329i
$191$			1.04409e34i			0.635678i	0.948145	+	0.317839i	$0.102957\pi$
$191$			1.04409e34i			0.635678i	−0.948145	+	0.317839i	$0.897043\pi$
$192$	2.22804e33	+	1.71404e34i	0.125431	+	0.964947i
$193$	2.69535e34			1.40364			0.701821	−	0.712354i	$-0.252371\pi$
$193$	2.69535e34			1.40364			0.701821	+	0.712354i	$0.252371\pi$
$194$	8.46018e33	+	1.39505e34i	0.407712	+	0.672302i
$195$		−	6.55846e33i		−	0.292606i
$196$	−3.41885e32	+	6.55881e32i	−0.0141266	+	0.0271009i
$197$	4.58151e33			0.175394			0.0876972	−	0.996147i	$-0.472049\pi$
$197$	4.58151e33			0.175394			0.0876972	+	0.996147i	$0.472049\pi$
$198$	3.85925e32	−	2.34041e32i	0.0136938	−	0.00830450i
$199$		−	2.26691e34i		−	0.745827i	−0.927866	−	0.372913i	$-0.878359\pi$
$199$		−	2.26691e34i		−	0.745827i	0.927866	−	0.372913i	$-0.121641\pi$
$200$	−3.02322e34	+	1.95667e33i	−0.922615	+	0.0597130i
$201$	−2.86860e34			−0.812323
$202$	1.69096e34	+	2.78834e34i	0.444492	+	0.732951i
$203$		−	6.30302e34i		−	1.53854i
$204$	−5.64659e34	−	2.94335e34i	−1.28037	−	0.667404i
$205$	−8.08415e33			−0.170344
$206$	−1.91974e34	+	1.16421e34i	−0.376041	+	0.228047i
$207$			1.25667e33i			0.0228911i
$208$	3.69966e34	+	5.29596e34i	0.626920	+	0.897417i
$209$	−2.05712e34			−0.324389
$210$	−9.29643e33	−	1.53295e34i	−0.136467	−	0.225029i
$211$		−	3.34114e34i		−	0.456728i	−0.973576	−	0.228364i	$-0.926662\pi$
$211$		−	3.34114e34i		−	0.456728i	0.973576	−	0.228364i	$-0.0733376\pi$
$212$	4.94432e34	−	9.48531e34i	0.629606	−	1.20785i
$213$	6.12617e34			0.726934
$214$	6.23594e34	−	3.78174e34i	0.689756	−	0.418297i
$215$			3.04722e34i			0.314287i
$216$	6.87981e33	+	1.06299e35i	0.0661866	+	1.02264i
$217$	1.01144e35			0.907911
$218$	−8.61493e34	−	1.42057e35i	−0.721779	−	1.19019i
$219$			2.13961e35i			1.67368i
$220$	−1.00474e34	−	5.23733e33i	−0.0734031	−	0.0382622i
$221$	−2.37996e35			−1.62437
$222$	−8.90230e34	+	5.39873e34i	−0.567816	+	0.344347i
$223$			3.10505e35i			1.85138i	0.378280	+	0.925691i	$0.376516\pi$
$223$			3.10505e35i			1.85138i	−0.378280	+	0.925691i	$0.623484\pi$
$224$	1.61543e35	+	7.13438e34i	0.900674	+	0.397774i
$225$	−9.42174e33			−0.0491353
$226$	2.00247e34	+	3.30199e34i	0.0977099	+	0.161120i
$227$		−	3.31252e35i		−	1.51276i	−0.654132	−	0.756381i	$-0.726966\pi$
$227$		−	3.31252e35i		−	1.51276i	0.654132	−	0.756381i	$-0.273034\pi$
$228$	1.13246e35	−	2.17255e35i	0.484174	−	0.928852i
$229$	−1.95794e32			−0.000783913			−0.000391957	−	1.00000i	$-0.500125\pi$
$229$	−1.95794e32			−0.000783913			−0.000391957		1.00000i	$0.500125\pi$
$230$	2.69746e34	−	1.63585e34i	0.101167	−	0.0613517i
$231$			8.21576e34i			0.288714i
$232$	4.73434e35	−	3.06414e34i	1.55934	−	0.100923i
$233$	−2.72784e35			−0.842326			−0.421163	−	0.906985i	$-0.638378\pi$
$233$	−2.72784e35			−0.842326			−0.421163	+	0.906985i	$0.638378\pi$
$234$	1.04180e34	+	1.71789e34i	0.0301679	+	0.0497458i
$235$			1.56823e35i			0.425981i
$236$	−4.15588e35	−	2.16630e35i	−1.05921	−	0.552126i
$237$	4.77205e35			1.14151
$238$	−5.56281e35	+	3.37352e35i	−1.24922	+	0.757581i
$239$		−	6.70971e35i		−	1.41493i	−0.706748	−	0.707466i	$-0.749838\pi$
$239$		−	6.70971e35i		−	1.41493i	0.706748	−	0.707466i	$-0.250162\pi$
$240$	1.10624e35	−	7.72799e34i	0.219119	−	0.153073i
$241$	−1.78112e35			−0.331465			−0.165732	−	0.986171i	$-0.552999\pi$
$241$	−1.78112e35			−0.331465			−0.165732	+	0.986171i	$0.552999\pi$
$242$	−2.69567e35	−	4.44507e35i	−0.471451	−	0.777406i
$243$			6.45834e34i			0.106176i
$244$	−1.03457e35	+	1.98475e35i	−0.159924	+	0.306802i
$245$	5.77448e33			0.00839502
$246$	−3.77264e35	+	2.28788e35i	−0.515963	+	0.312901i
$247$		−	9.15698e35i		−	1.17841i
$248$	4.91698e34	+	7.59715e35i	0.0595557	+	0.920186i
$249$	1.01279e36			1.15486
$250$	2.55302e35	+	4.20983e35i	0.274128	+	0.452027i
$251$			2.27397e35i			0.229974i	0.993367	+	0.114987i	$0.0366827\pi$
$251$			2.27397e35i			0.229974i	−0.993367	+	0.114987i	$0.963317\pi$
$252$	4.87011e34	+	2.53860e34i	0.0464014	+	0.0241872i
$253$	−1.44569e35			−0.129798
$254$	2.85343e35	−	1.73044e35i	0.241469	−	0.146437i
$255$			4.97135e35i			0.396617i
$256$	−4.57348e35	+	1.24807e36i	−0.344071	+	0.938944i
$257$	−2.89993e34			−0.0205774			−0.0102887	−	0.999947i	$-0.503275\pi$
$257$	−2.89993e34			−0.0205774			−0.0102887	+	0.999947i	$0.503275\pi$
$258$	8.62389e35	+	1.42205e36i	0.577308	+	0.951960i
$259$			1.06373e36i			0.671944i
$260$	2.33132e35	−	4.47246e35i	0.138996	−	0.266653i
$261$	1.47544e35			0.0830449
$262$	2.17481e36	−	1.31890e36i	1.15585	−	0.700958i
$263$		−	2.67219e36i		−	1.34132i	−0.741766	−	0.670659i	$-0.766011\pi$
$263$		−	2.67219e36i		−	1.34132i	0.741766	−	0.670659i	$-0.233989\pi$
$264$	−6.17105e35	+	3.99399e34i	−0.292617	+	0.0189386i
$265$	−8.35101e35			−0.374155
$266$	−1.29798e36	−	2.14031e36i	−0.549594	−	0.906260i
$267$			2.46173e36i			0.985305i
$268$	−1.95621e36	−	1.01969e36i	−0.740275	−	0.385876i
$269$	−6.41952e34			−0.0229730			−0.0114865	−	0.999934i	$-0.503656\pi$
$269$	−6.41952e34			−0.0229730			−0.0114865	+	0.999934i	$0.503656\pi$
$270$	7.11087e35	−	4.31233e35i	0.240695	−	0.145967i
$271$			2.76863e36i			0.886597i	0.896374	+	0.443298i	$0.146192\pi$
$271$			2.76863e36i			0.886597i	−0.896374	+	0.443298i	$0.853808\pi$
$272$	−2.80436e36	−	4.01436e36i	−0.849768	−	1.21642i
$273$	−3.65712e36			−1.04882
$274$	2.98941e35	+	4.92943e35i	0.0811572	+	0.133825i
$275$		−	1.08389e36i		−	0.278609i
$276$	7.95866e35	−	1.52681e36i	0.193733	−	0.371662i
$277$	1.92913e35			0.0444799			0.0222400	−	0.999753i	$-0.492920\pi$
$277$	1.92913e35			0.0444799			0.0222400	+	0.999753i	$0.492920\pi$
$278$	4.54095e36	−	2.75382e36i	0.991916	−	0.601539i
$279$			2.36762e35i			0.0490059i
$280$	−8.90459e34	−	1.37583e36i	−0.0174680	−	0.269895i
$281$	−2.17810e35			−0.0405026			−0.0202513	−	0.999795i	$-0.506447\pi$
$281$	−2.17810e35			−0.0405026			−0.0202513	+	0.999795i	$0.506447\pi$
$282$	4.43821e36	+	7.31845e36i	0.782477	+	1.29028i
$283$			6.01039e35i			0.100486i	0.998737	+	0.0502430i	$0.0159996\pi$
$283$			6.01039e35i			0.100486i	−0.998737	+	0.0502430i	$0.984000\pi$
$284$	4.17767e36	+	2.17766e36i	0.662459	+	0.345314i
$285$	−1.91274e36			−0.287729
$286$	−1.97628e36	+	1.19850e36i	−0.282071	+	0.171059i
$287$			4.50788e36i			0.610581i
$288$	−1.67005e35	+	3.78147e35i	−0.0214705	+	0.0486153i
$289$	9.84674e36			1.20178
$290$	−1.92063e36	−	3.16704e36i	−0.222573	−	0.367015i
$291$		−	6.95197e36i		−	0.765091i
$292$	−7.60561e36	+	1.45908e37i	−0.795044	+	1.52523i
$293$	−1.54207e36			−0.153141			−0.0765704	−	0.997064i	$-0.524397\pi$
$293$	−1.54207e36			−0.153141			−0.0765704	+	0.997064i	$0.524397\pi$
$294$	2.69478e35	−	1.63423e35i	0.0254281	−	0.0154206i
$295$			3.65890e36i			0.328111i
$296$	−7.98989e36	+	5.17117e35i	−0.681028	+	0.0440771i
$297$	−3.81103e36			−0.308813
$298$	−5.43816e36	−	8.96732e36i	−0.418994	−	0.690906i
$299$		−	6.43528e36i		−	0.471520i
$300$	1.14471e37	+	5.96691e36i	0.797766	+	0.415844i
$301$	1.69919e37			1.12653
$302$	−2.34055e37	+	1.41941e37i	−1.47643	+	0.895371i
$303$		−	1.38951e37i		−	0.834110i
$304$	1.54454e37	−	1.07899e37i	0.882461	−	0.616472i
$305$	1.74740e36			0.0950377
$306$	−7.89688e35	−	1.30217e36i	−0.0408916	−	0.0674288i
$307$		−	2.08170e37i		−	1.02646i	−0.858250	−	0.513232i	$-0.828448\pi$
$307$		−	2.08170e37i		−	1.02646i	0.858250	−	0.513232i	$-0.171552\pi$
$308$	−2.92044e36	+	5.60264e36i	−0.137147	+	0.263107i
$309$	9.56667e36			0.427941
$310$	5.08212e36	−	3.08201e36i	0.216580	−	0.131343i
$311$			1.41901e36i			0.0576208i	0.999585	+	0.0288104i	$0.00917190\pi$
$311$			1.41901e36i			0.0576208i	−0.999585	+	0.0288104i	$0.990828\pi$
$312$	−1.77787e36	−	2.74695e37i	−0.0687987	−	1.06300i
$313$	−3.10590e37			−1.14557			−0.572785	−	0.819705i	$-0.694137\pi$
$313$	−3.10590e37			−1.14557			−0.572785	+	0.819705i	$0.694137\pi$
$314$	5.45096e35	+	8.98844e35i	0.0191659	+	0.0316038i
$315$		−	4.28772e35i		−	0.0143737i
$316$	3.25424e37	+	1.69631e37i	1.04026	+	0.542249i
$317$	−2.72735e37			−0.831482			−0.415741	−	0.909483i	$-0.636478\pi$
$317$	−2.72735e37			−0.831482			−0.415741	+	0.909483i	$0.636478\pi$
$318$	−3.89717e37	+	2.36341e37i	−1.13330	+	0.687277i
$319$			1.69736e37i			0.470884i
$320$	1.02909e37	−	1.33769e36i	0.272398	−	0.0354083i
$321$	−3.10756e37			−0.784954
$322$	−9.12183e36	−	1.50416e37i	−0.219909	−	0.362623i
$323$			6.94103e37i			1.59730i
$324$	1.98619e37	−	3.81036e37i	0.436362	−	0.837127i
$325$	4.82477e37			1.01211
$326$	4.60888e37	−	2.79502e37i	0.923275	−	0.559912i
$327$			7.07913e37i			1.35445i
$328$	−3.38597e37	+	2.19145e36i	−0.618836	+	0.0400520i
$329$	8.74473e37			1.52689
$330$	2.50347e36	+	4.12813e36i	0.0417670	+	0.0688722i
$331$		−	3.05550e37i		−	0.487149i	−0.969882	−	0.243574i	$-0.921680\pi$
$331$		−	3.05550e37i		−	0.487149i	0.969882	−	0.243574i	$-0.0783200\pi$
$332$	6.90657e37	+	3.60013e37i	1.05243	+	0.548588i
$333$	−2.49001e36			−0.0362692
$334$	1.28509e37	−	7.79330e36i	0.178952	−	0.108524i
$335$			1.72227e37i			0.229314i
$336$	−4.30928e37	−	6.16860e37i	−0.548675	−	0.785412i
$337$	−1.59151e38			−1.93803			−0.969014	−	0.247005i	$-0.920554\pi$
$337$	−1.59151e38			−1.93803			−0.969014	+	0.247005i	$0.920554\pi$
$338$	−8.83166e36	−	1.45631e37i	−0.102871	−	0.169630i
$339$		−	1.64548e37i		−	0.183357i
$340$	−1.76715e37	+	3.39015e37i	−0.188404	+	0.361439i
$341$	−2.72374e37			−0.277875
$342$	5.01014e36	−	3.03836e36i	0.0489168	−	0.0296652i
$343$		−	1.08579e38i		−	1.01469i
$344$	8.26040e36	+	1.27630e38i	0.0738966	+	1.14176i
$345$	−1.34423e37			−0.115129
$346$	−2.85896e37	−	4.71432e37i	−0.234459	−	0.386614i
$347$		−	7.96396e37i		−	0.625442i	−0.949845	−	0.312721i	$-0.898759\pi$
$347$		−	7.96396e37i		−	0.625442i	0.949845	−	0.312721i	$-0.101241\pi$
$348$	−1.79260e38	−	9.34413e37i	−1.34833	−	0.702830i
$349$	9.03439e37			0.650905			0.325453	−	0.945558i	$-0.394483\pi$
$349$	9.03439e37			0.650905			0.325453	+	0.945558i	$0.394483\pi$
$350$	1.12772e38	−	6.83898e37i	0.778362	−	0.472031i
$351$		−	1.69643e38i		−	1.12183i
$352$	−4.35025e37	−	1.92124e37i	−0.275660	−	0.121743i
$353$	3.23720e37			0.196585			0.0982923	−	0.995158i	$-0.468662\pi$
$353$	3.23720e37			0.196585			0.0982923	+	0.995158i	$0.468662\pi$
$354$	1.03550e38	+	1.70750e38i	0.602700	+	0.993831i
$355$		−	3.67808e37i		−	0.205209i
$356$	−8.75064e37	+	1.67874e38i	−0.468047	+	0.897914i
$357$	2.77212e38			1.42164
$358$	−1.33856e38	+	8.11757e37i	−0.658251	+	0.399191i
$359$			2.02318e38i			0.954154i	0.878862	+	0.477077i	$0.158304\pi$
$359$			2.02318e38i			0.954154i	−0.878862	+	0.477077i	$0.841696\pi$
$360$	3.22061e36	−	2.08442e35i	0.0145680	−	0.000942863i
$361$	−3.65923e37			−0.158775
$362$	1.63536e38	+	2.69665e38i	0.680745	+	1.12252i
$363$			2.21511e38i			0.884701i
$364$	−2.49393e38	−	1.29999e38i	−0.955793	−	0.498217i
$365$	1.28460e38			0.472469
$366$	8.15463e37	−	4.94531e37i	0.287864	−	0.174573i
$367$		−	4.11768e38i		−	1.39528i	−0.716448	−	0.697641i	$-0.754233\pi$
$367$		−	4.11768e38i		−	1.39528i	0.716448	−	0.697641i	$-0.245767\pi$
$368$	1.08546e38	−	7.58285e37i	0.353100	−	0.246669i
$369$	−1.05522e37			−0.0329571
$370$	3.24134e37	+	5.34484e37i	0.0972071	+	0.160291i
$371$			4.65668e38i			1.34112i
$372$	1.49944e38	−	2.87657e38i	0.414749	−	0.795665i
$373$	−1.93745e38			−0.514752			−0.257376	−	0.966311i	$-0.582858\pi$
$373$	−1.93745e38			−0.514752			−0.257376	+	0.966311i	$0.582858\pi$
$374$	1.49803e38	−	9.08467e37i	0.382337	−	0.231865i
$375$		−	2.09789e38i		−	0.514414i
$376$	4.25114e37	+	6.56837e38i	0.100159	+	1.54753i
$377$	−7.55555e38			−1.71059
$378$	−2.40464e38	−	3.96516e38i	−0.523205	−	0.862747i
$379$			5.31736e37i			0.111201i	0.998453	+	0.0556004i	$0.0177073\pi$
$379$			5.31736e37i			0.111201i	−0.998453	+	0.0556004i	$0.982293\pi$
$380$	−1.30437e38	−	6.79919e37i	−0.262209	−	0.136679i
$381$	−1.42195e38			−0.274796
$382$	2.92537e38	−	1.77407e38i	0.543538	−	0.329624i
$383$			1.88520e38i			0.336804i	0.985718	+	0.168402i	$0.0538606\pi$
$383$			1.88520e38i			0.336804i	−0.985718	+	0.168402i	$0.946139\pi$
$384$	4.42389e38	−	3.53668e38i	0.760040	−	0.607613i
$385$	4.93265e37			0.0815022
$386$	−4.57982e38	−	7.55195e38i	−0.727844	−	1.20019i
$387$			3.97753e37i			0.0608064i
$388$	2.47120e38	−	4.74081e38i	0.363439	−	0.697231i
$389$	1.18512e39			1.67694			0.838469	−	0.544949i	$-0.183451\pi$
$389$	1.18512e39			1.67694			0.838469	+	0.544949i	$0.183451\pi$
$390$	−1.83758e38	+	1.11438e38i	−0.250194	+	0.151728i
$391$			4.87798e38i			0.639129i
$392$	2.41859e37	−	1.56534e36i	0.0304980	−	0.00197387i
$393$	−1.08378e39			−1.31538
$394$	−7.78469e37	−	1.28367e38i	−0.0909490	−	0.149971i
$395$		−	2.86509e38i		−	0.322241i
$396$	−1.31149e37	−	6.83628e36i	−0.0142016	−	0.00740273i
$397$	1.03584e39			1.08003			0.540013	−	0.841657i	$-0.318419\pi$
$397$	1.03584e39			1.08003			0.540013	+	0.841657i	$0.318419\pi$
$398$	−6.35152e38	+	3.85182e38i	−0.637722	+	0.386741i
$399$			1.06658e39i			1.03134i
$400$	5.68515e38	+	8.13812e38i	0.529471	+	0.757922i
$401$	−1.54634e39			−1.38720			−0.693602	−	0.720358i	$-0.743977\pi$
$401$	−1.54634e39			−1.38720			−0.693602	+	0.720358i	$0.743977\pi$
$402$	4.87419e38	+	8.03735e38i	0.421222	+	0.694580i
$403$		−	1.21243e39i		−	1.00944i
$404$	4.93927e38	−	9.47562e38i	0.396225	−	0.760129i
$405$	−3.35470e38			−0.259316
$406$	−1.76600e39	+	1.07098e39i	−1.31553	+	0.797793i
$407$		−	2.86454e38i		−	0.205655i
$408$	1.34763e38	+	2.08220e39i	0.0932543	+	1.44086i
$409$	2.15390e39			1.43673			0.718366	−	0.695665i	$-0.244890\pi$
$409$	2.15390e39			1.43673			0.718366	+	0.695665i	$0.244890\pi$
$410$	1.37362e38	+	2.26505e38i	0.0883301	+	0.145653i
$411$		−	2.45648e38i		−	0.152295i
$412$	6.52387e38	+	3.40064e38i	0.389984	+	0.203284i
$413$	2.04027e39			1.17608
$414$	3.52099e37	−	2.13528e37i	0.0195731	−	0.0118700i
$415$		−	6.08066e38i		−	0.326009i
$416$	8.55213e38	−	1.93645e39i	0.442257	−	1.00140i
$417$	−2.26289e39			−1.12882
$418$	3.49536e38	+	5.76372e38i	0.168209	+	0.277370i
$419$		−	2.23916e39i		−	1.03962i	−0.854282	−	0.519810i	$-0.826003\pi$
$419$		−	2.23916e39i		−	1.03962i	0.854282	−	0.519810i	$-0.173997\pi$
$420$	−2.71547e38	+	5.20942e38i	−0.121648	+	0.233373i
$421$	3.29127e39			1.42276			0.711381	−	0.702806i	$-0.248070\pi$
$421$	3.29127e39			1.42276			0.711381	+	0.702806i	$0.248070\pi$
$422$	−9.36132e38	+	5.67710e38i	−0.390526	+	0.236831i
$423$			2.04700e38i			0.0824163i
$424$	−3.49775e39	+	2.26379e38i	−1.35925	+	0.0879728i
$425$	−3.65720e39			−1.37188
$426$	−1.04093e39	−	1.71645e39i	−0.376944	−	0.621568i
$427$		−	9.74386e38i		−	0.340654i
$428$	−2.11916e39	−	1.10464e39i	−0.715332	−	0.372875i
$429$	9.84840e38			0.321001
$430$	8.53782e38	−	5.17769e38i	0.268732	−	0.162971i
$431$			7.91827e38i			0.240697i	0.992732	+	0.120349i	$0.0384013\pi$
$431$			7.91827e38i			0.240697i	−0.992732	+	0.120349i	$0.961599\pi$
$432$	2.86142e39	−	1.99894e39i	0.840090	−	0.586872i
$433$	−1.60137e39			−0.454123			−0.227061	−	0.973880i	$-0.572912\pi$
$433$	−1.60137e39			−0.454123			−0.227061	+	0.973880i	$0.572912\pi$
$434$	−1.71859e39	−	2.83389e39i	−0.470788	−	0.776312i
$435$			1.57823e39i			0.417669i
$436$	−2.51640e39	+	4.82753e39i	−0.643402	+	1.23432i
$437$	−1.87682e39			−0.463661
$438$	5.99483e39	−	3.63552e39i	1.43108	−	0.867869i
$439$		−	9.54562e36i		−	0.00220210i	−0.999999	−	0.00110105i	$-0.999650\pi$
$439$		−	9.54562e36i		−	0.00220210i	0.999999	−	0.00110105i	$-0.000350475\pi$
$440$	2.39795e37	+	3.70503e38i	0.00534625	+	0.0826041i
$441$	7.53742e36			0.00162422
$442$	4.04391e39	+	6.66826e39i	0.842301	+	1.38892i
$443$			6.17978e39i			1.24428i	0.782907	+	0.622139i	$0.213736\pi$
$443$			6.17978e39i			1.24428i	−0.782907	+	0.622139i	$0.786264\pi$
$444$	3.02527e39	+	1.57696e39i	0.588871	+	0.306955i
$445$	1.47799e39			0.278146
$446$	8.69986e39	−	5.27596e39i	1.58303	−	0.960016i
$447$			4.46869e39i			0.786262i
$448$	−7.45921e38	−	5.73841e39i	−0.126918	−	0.976386i
$449$	−5.92678e39			−0.975267			−0.487633	−	0.873048i	$-0.662140\pi$
$449$	−5.92678e39			−0.975267			−0.487633	+	0.873048i	$0.662140\pi$
$450$	1.60090e38	+	2.63982e38i	0.0254786	+	0.0420133i
$451$		−	1.21394e39i		−	0.186874i
$452$	5.84916e38	−	1.12212e39i	0.0870997	−	0.167094i
$453$	1.16637e40			1.68020
$454$	−9.28114e39	+	5.62847e39i	−1.29349	+	0.784427i
$455$			2.19570e39i			0.296075i
$456$	−8.01136e39	+	5.18506e38i	−1.04528	+	0.0676521i
$457$	−1.24203e40			−1.56815			−0.784077	−	0.620664i	$-0.786863\pi$
$457$	−1.24203e40			−1.56815			−0.784077	+	0.620664i	$0.786863\pi$
$458$	3.32684e36	+	5.48584e36i	0.000406490	+	0.000670288i
$459$			1.28590e40i			1.52061i
$460$	−9.16679e38	−	4.77829e38i	−0.104918	−	0.0546896i
$461$	5.75349e39			0.637408			0.318704	−	0.947854i	$-0.396752\pi$
$461$	5.75349e39			0.637408			0.318704	+	0.947854i	$0.396752\pi$
$462$	2.30192e39	−	1.39598e39i	0.246866	−	0.149710i
$463$		−	1.68459e40i		−	1.74896i	−0.485059	−	0.874481i	$-0.661202\pi$
$463$		−	1.68459e40i		−	1.74896i	0.485059	−	0.874481i	$-0.338798\pi$
$464$	−8.90289e39	−	1.27442e40i	−0.894873	−	1.28098i
$465$	−2.53257e39			−0.246472
$466$	4.63501e39	+	7.64297e39i	0.436780	+	0.720234i
$467$		−	1.65246e40i		−	1.50792i	−0.656920	−	0.753960i	$-0.728141\pi$
$467$		−	1.65246e40i		−	1.50792i	0.656920	−	0.753960i	$-0.271859\pi$
$468$	3.04307e38	−	5.83790e38i	0.0268921	−	0.0515904i
$469$	9.60373e39			0.821954
$470$	4.39392e39	−	2.66465e39i	0.364237	−	0.220888i
$471$		−	4.47921e38i		−	0.0359657i
$472$	9.91854e38	+	1.53250e40i	0.0771468	+	1.19198i
$473$	−4.57580e39			−0.344786
$474$	−8.10844e39	−	1.33705e40i	−0.591919	−	0.976052i
$475$		−	1.40712e40i		−	0.995240i
$476$	1.89041e40	+	9.85398e39i	1.29554	+	0.675317i
$477$	−1.09006e39			−0.0723891
$478$	−1.87995e40	+	1.14008e40i	−1.20984	+	0.733699i
$479$			8.38353e38i			0.0522870i	0.999658	+	0.0261435i	$0.00832269\pi$
$479$			8.38353e38i			0.0522870i	−0.999658	+	0.0261435i	$0.991677\pi$
$480$	−4.04493e39	−	1.78640e39i	−0.244508	−	0.107984i
$481$	1.27511e40			0.747087
$482$	3.02639e39	+	4.99041e39i	0.171878	+	0.283420i
$483$			7.49566e39i			0.412670i
$484$	−7.87401e39	+	1.51057e40i	−0.420257	+	0.806232i
$485$	−4.17388e39			−0.215980
$486$	1.80952e39	−	1.09737e39i	0.0907862	−	0.0550565i
$487$		−	1.96799e40i		−	0.957391i	−0.877981	−	0.478695i	$-0.841110\pi$
$487$		−	1.96799e40i		−	0.957391i	0.877981	−	0.478695i	$-0.158890\pi$
$488$	7.31884e39	−	4.73686e38i	0.345259	−	0.0223457i
$489$	−2.29674e40			−1.05070
$490$	−9.81172e37	−	1.61792e38i	−0.00435315	−	0.00717819i
$491$			3.08710e40i			1.32840i	0.747555	+	0.664199i	$0.231227\pi$
$491$			3.08710e40i			1.32840i	−0.747555	+	0.664199i	$0.768773\pi$
$492$	1.28206e40	+	6.68286e39i	0.535095	+	0.278924i
$493$	5.72715e40			2.31865
$494$	−2.56564e40	+	1.55591e40i	−1.00761	+	0.611055i
$495$			1.15466e38i			0.00439921i
$496$	2.04505e40	−	1.42864e40i	0.755926	−	0.528076i
$497$	−2.05097e40			−0.735552
$498$	−1.72088e40	−	2.83766e40i	−0.598839	−	0.987463i
$499$			8.17690e39i			0.276109i	0.990425	+	0.138055i	$0.0440849\pi$
$499$			8.17690e39i			0.276109i	−0.990425	+	0.138055i	$0.955915\pi$
$500$	7.45730e39	−	1.43063e40i	0.244361	−	0.468788i
$501$	−6.40398e39			−0.203650
$502$	6.37130e39	−	3.86382e39i	0.196640	−	0.119251i
$503$			6.13130e40i			1.83668i	0.395796	+	0.918338i	$0.370469\pi$
$503$			6.13130e40i			1.83668i	−0.395796	+	0.918338i	$0.629531\pi$
$504$	−1.16231e38	−	1.79587e39i	−0.00337960	−	0.0522177i
$505$	−8.34248e39			−0.235464
$506$	2.45645e39	+	4.05059e39i	0.0673054	+	0.110984i
$507$			7.25723e39i			0.193042i
$508$	−9.69682e39	−	5.05457e39i	−0.250423	−	0.130536i
$509$	−9.18713e39			−0.230363			−0.115182	−	0.993344i	$-0.536745\pi$
$509$	−9.18713e39			−0.230363			−0.115182	+	0.993344i	$0.536745\pi$
$510$	1.39289e40	−	8.44708e39i	0.339129	−	0.205662i
$511$		−	7.16315e40i		−	1.69352i
$512$	4.27400e40	−	8.39245e39i	0.981261	−	0.192681i
$513$	−4.94755e40			−1.10314
$514$	4.92742e38	+	8.12514e38i	0.0106702	+	0.0175948i
$515$		−	5.74372e39i		−	0.120805i
$516$	2.51902e40	−	4.83255e40i	0.514619	−	0.987259i
$517$	−2.35490e40			−0.467319
$518$	2.98039e40	−	1.80743e40i	0.574548	−	0.348430i
$519$			2.34929e40i			0.439973i
$520$	−1.64924e40	+	1.06741e39i	−0.300078	+	0.0194214i
$521$	1.96725e40			0.347770			0.173885	−	0.984766i	$-0.444368\pi$
$521$	1.96725e40			0.347770			0.173885	+	0.984766i	$0.444368\pi$
$522$	−2.50699e39	−	4.13394e39i	−0.0430621	−	0.0710078i
$523$		−	5.68743e40i		−	0.949271i	−0.880182	−	0.474636i	$-0.842580\pi$
$523$		−	5.68743e40i		−	0.949271i	0.880182	−	0.474636i	$-0.157420\pi$
$524$	−7.39068e40	−	3.85247e40i	−1.19871	−	0.624842i
$525$	−5.61978e40			−0.885788
$526$	−7.48706e40	+	4.54046e40i	−1.14690	+	0.695527i
$527$			9.19029e40i			1.36826i
$528$	1.16046e40	+	1.66116e40i	0.167927	+	0.240383i
$529$	5.79046e40			0.814475
$530$	1.41896e40	+	2.33982e40i	0.194014	+	0.319922i
$531$			4.77596e39i			0.0634808i
$532$	−3.79136e40	+	7.27343e40i	−0.489914	+	0.939864i
$533$	5.40368e40			0.678862
$534$	6.89736e40	−	4.18285e40i	0.842489	−	0.510920i
$535$			1.86574e40i			0.221588i
$536$	4.66874e39	+	7.21359e40i	0.0539173	+	0.833066i
$537$	6.67043e40			0.749100
$538$	1.09077e39	+	1.79865e39i	0.0119124	+	0.0196432i
$539$			8.67114e38i			0.00920968i
$540$	−2.41649e40	−	1.25962e40i	−0.249619	−	0.130117i
$541$	9.27534e40			0.931903			0.465952	−	0.884810i	$-0.345712\pi$
$541$	9.27534e40			0.931903			0.465952	+	0.884810i	$0.345712\pi$
$542$	7.75727e40	−	4.70433e40i	0.758088	−	0.459736i
$543$		−	1.34382e41i		−	1.27745i
$544$	−6.48256e40	+	1.46784e41i	−0.599464	+	1.35736i
$545$	4.25023e40			0.382353
$546$	6.21401e40	+	1.02467e41i	0.543854	+	0.896795i
$547$		−	1.72931e41i		−	1.47252i	−0.676697	−	0.736261i	$-0.736589\pi$
$547$		−	1.72931e41i		−	1.47252i	0.676697	−	0.736261i	$-0.263411\pi$
$548$	8.73200e39	−	1.67517e40i	0.0723445	−	0.138787i
$549$	2.28088e39			0.0183873
$550$	−3.03688e40	+	1.84169e40i	−0.238225	+	0.144470i
$551$			2.20354e41i			1.68208i
$552$	−5.63017e40	+	3.64393e39i	−0.418249	+	0.0270697i
$553$	−1.59763e41			−1.15504
$554$	−3.27788e39	−	5.40510e39i	−0.0230646	−	0.0380327i
$555$		−	2.66350e40i		−	0.182414i
$556$	−1.54315e41	−	8.04386e40i	−1.02870	−	0.536219i
$557$	−1.41490e41			−0.918115			−0.459057	−	0.888407i	$-0.651813\pi$
$557$	−1.41490e41			−0.918115			−0.459057	+	0.888407i	$0.651813\pi$
$558$	6.63368e39	−	4.02294e39i	0.0419027	−	0.0254115i
$559$		−	2.03685e41i		−	1.25251i
$560$	−3.70356e40	+	2.58724e40i	−0.221717	+	0.154888i
$561$	−7.46514e40			−0.435106
$562$	3.70092e39	+	6.10269e39i	0.0210022	+	0.0346319i
$563$		−	2.18121e41i		−	1.20523i	−0.798031	−	0.602616i	$-0.794125\pi$
$563$		−	2.18121e41i		−	1.20523i	0.798031	−	0.602616i	$-0.205875\pi$
$564$	1.29639e41	−	2.48703e41i	0.697509	−	1.33812i
$565$	−9.87930e39			−0.0517606
$566$	1.68401e40	−	1.02126e40i	0.0859210	−	0.0521061i
$567$			1.87065e41i			0.929493i
$568$	−9.97054e39	−	1.54053e41i	−0.0482496	−	0.745497i
$569$	2.82112e41			1.32965			0.664826	−	0.746999i	$-0.268506\pi$
$569$	2.82112e41			1.32965			0.664826	+	0.746999i	$0.268506\pi$
$570$	3.25004e40	+	5.35920e40i	0.149199	+	0.246024i
$571$			4.11821e41i			1.84148i	0.390178	+	0.920740i	$0.372414\pi$
$571$			4.11821e41i			1.84148i	−0.390178	+	0.920740i	$0.627586\pi$
$572$	6.71599e40	+	3.50079e40i	0.292530	+	0.152484i
$573$	−1.45780e41			−0.618555
$574$	1.26303e41	−	7.65957e40i	0.522080	−	0.316611i
$575$		−	9.88889e40i		−	0.398226i
$576$	1.34327e40	−	1.74608e39i	0.0527020	−	0.00685059i
$577$	3.78670e41			1.44752			0.723758	−	0.690054i	$-0.242413\pi$
$577$	3.78670e41			1.44752			0.723758	+	0.690054i	$0.242413\pi$
$578$	−1.67311e41	−	2.75890e41i	−0.623171	−	1.02759i
$579$			3.76336e41i			1.36583i
$580$	−5.61011e40	+	1.07626e41i	−0.198404	+	0.380624i
$581$	−3.39069e41			−1.16855
$582$	−1.94783e41	+	1.18124e41i	−0.654193	+	0.396730i
$583$		−	1.25401e41i		−	0.410463i
$584$	5.38041e41	−	3.48228e40i	1.71642	−	0.111089i
$585$	−5.13978e39			−0.0159811
$586$	2.62022e40	+	4.32064e40i	0.0794096	+	0.130944i
$587$			3.89769e41i			1.15142i	0.817652	+	0.575712i	$0.195275\pi$
$587$			3.89769e41i			1.15142i	−0.817652	+	0.575712i	$0.804725\pi$
$588$	−9.15768e39	−	4.77354e39i	−0.0263709	−	0.0137461i
$589$	−3.53600e41			−0.992619
$590$	1.02517e41	−	6.21703e40i	0.280552	−	0.170139i
$591$			6.39690e40i			0.170670i
$592$	1.50249e41	+	2.15077e41i	0.390829	+	0.559460i
$593$	−4.91606e41			−1.24680			−0.623400	−	0.781903i	$-0.714249\pi$
$593$	−4.91606e41			−1.24680			−0.623400	+	0.781903i	$0.714249\pi$
$594$	6.47553e40	+	1.06779e41i	0.160132	+	0.264052i
$595$		−	1.66435e41i		−	0.401319i
$596$	−1.58847e41	+	3.04737e41i	−0.373496	+	0.716524i
$597$	3.16515e41			0.725738
$598$	−1.80306e41	+	1.09345e41i	−0.403174	+	0.244502i
$599$		−	4.46553e41i		−	0.973802i	−0.873457	−	0.486901i	$-0.838127\pi$
$599$		−	4.46553e41i		−	0.973802i	0.873457	−	0.486901i	$-0.161873\pi$
$600$	−2.73199e40	−	4.22115e41i	−0.0581046	−	0.897764i
$601$	5.32487e41			1.10457			0.552283	−	0.833657i	$-0.313757\pi$
$601$	5.32487e41			1.10457			0.552283	+	0.833657i	$0.313757\pi$
$602$	−2.88718e41	−	4.76085e41i	−0.584152	−	0.963246i
$603$			2.24808e40i			0.0443662i
$604$	7.95390e41	+	4.14606e41i	1.53118	+	0.798144i
$605$	1.32993e41			0.249746
$606$	−3.89319e41	+	2.36099e41i	−0.713208	+	0.432519i
$607$		−	6.91015e40i		−	0.123497i	−0.998092	−	0.0617486i	$-0.980332\pi$
$607$		−	6.91015e40i		−	0.123497i	0.998092	−	0.0617486i	$-0.0196677\pi$
$608$	−5.64756e41	−	2.49419e41i	−0.984707	−	0.434886i
$609$	8.80053e41			1.49710
$610$	−2.96911e40	−	4.89595e40i	−0.0492808	−	0.0812623i
$611$		−	1.04825e42i		−	1.69764i
$612$	−2.30666e40	+	4.42516e40i	−0.0364513	+	0.0699290i
$613$	−8.81634e41			−1.35951			−0.679753	−	0.733441i	$-0.737913\pi$
$613$	−8.81634e41			−1.35951			−0.679753	+	0.733441i	$0.737913\pi$
$614$	−5.83260e41	+	3.53713e41i	−0.877681	+	0.532262i
$615$		−	1.12874e41i		−	0.165756i
$616$	2.06599e41	−	1.33714e40i	0.296086	−	0.0191631i
$617$	3.42006e41			0.478361			0.239181	−	0.970975i	$-0.423121\pi$
$617$	3.42006e41			0.478361			0.239181	+	0.970975i	$0.423121\pi$
$618$	−1.62552e41	−	2.68043e41i	−0.221904	−	0.365912i
$619$			4.16624e41i			0.555116i	0.960709	+	0.277558i	$0.0895251\pi$
$619$			4.16624e41i			0.555116i	−0.960709	+	0.277558i	$0.910475\pi$
$620$	−1.72706e41	−	9.00248e40i	−0.224611	−	0.117081i
$621$	−3.47701e41			−0.441399
$622$	3.97583e40	−	2.41111e40i	0.0492688	−	0.0298787i
$623$		−	8.24157e41i		−	0.996987i
$624$	−7.39443e41	+	5.16562e41i	−0.873245	+	0.610033i
$625$	6.75961e41			0.779329
$626$	5.27739e41	+	8.70222e41i	0.594024	+	0.979524i
$627$		−	2.87224e41i		−	0.315651i
$628$	1.59221e40	−	3.05454e40i	0.0170847	−	0.0327757i
$629$	−9.66539e41			−1.01265
$630$	−1.20135e40	+	7.28549e39i	−0.0122903	+	0.00745333i
$631$			1.39378e42i			1.39237i	0.717865	+	0.696183i	$0.245120\pi$
$631$			1.39378e42i			1.39237i	−0.717865	+	0.696183i	$0.754880\pi$
$632$	−7.76667e40	−	1.20002e42i	−0.0757667	−	1.17066i
$633$	4.66503e41			0.444425
$634$	4.63419e41	+	7.64161e41i	0.431156	+	0.710961i
$635$			8.53723e40i			0.0775731i
$636$	1.32438e42	+	6.90346e41i	1.17532	+	0.612647i
$637$	−3.85983e40			−0.0334562
$638$	4.75573e41	−	2.88407e41i	0.402631	−	0.244172i
$639$		−	4.80100e40i		−	0.0397026i
$640$	−2.12338e41	−	2.65606e41i	−0.171525	−	0.214555i
$641$	3.52136e41			0.277869			0.138935	−	0.990302i	$-0.455632\pi$
$641$	3.52136e41			0.277869			0.138935	+	0.990302i	$0.455632\pi$
$642$	5.28022e41	+	8.70688e41i	0.407030	+	0.671177i
$643$		−	8.12328e40i		−	0.0611740i	−0.999532	−	0.0305870i	$-0.990262\pi$
$643$		−	8.12328e40i		−	0.0611740i	0.999532	−	0.0305870i	$-0.00973766\pi$
$644$	−2.66447e41	+	5.11158e41i	−0.196030	+	0.376069i
$645$	−4.25465e41			−0.305822
$646$	1.94477e42	−	1.17939e42i	1.36578	−	0.828264i
$647$			2.24550e42i			1.54081i	0.637555	+	0.770405i	$0.279946\pi$
$647$			2.24550e42i			1.54081i	−0.637555	+	0.770405i	$0.720054\pi$
$648$	−1.40509e42	+	9.09393e40i	−0.942059	+	0.0609714i
$649$	−5.49432e41			−0.359951
$650$	−8.19802e41	−	1.35182e42i	−0.524818	−	0.865406i
$651$			1.41221e42i			0.883456i
$652$	−1.56624e42	−	8.16418e41i	−0.957510	−	0.499113i
$653$	−3.45568e41			−0.206460			−0.103230	−	0.994658i	$-0.532918\pi$
$653$	−3.45568e41			−0.206460			−0.103230	+	0.994658i	$0.532918\pi$
$654$	1.98346e42	−	1.20285e42i	1.15813	−	0.702337i
$655$			6.50687e41i			0.371324i
$656$	6.36729e41	+	9.11459e41i	0.355138	+	0.508370i
$657$	1.67678e41			0.0914104
$658$	−1.48586e42	−	2.45013e42i	−0.791754	−	1.30557i
$659$		−	1.28448e42i		−	0.669031i	−0.942390	−	0.334516i	$-0.891427\pi$
$659$		−	1.28448e42i		−	0.669031i	0.942390	−	0.334516i	$-0.108573\pi$
$660$	7.31258e40	−	1.40286e41i	0.0372316	−	0.0714260i
$661$	3.84251e41			0.191246			0.0956232	−	0.995418i	$-0.469516\pi$
$661$	3.84251e41			0.191246			0.0956232	+	0.995418i	$0.469516\pi$
$662$	−8.56101e41	+	5.19175e41i	−0.416538	+	0.252606i
$663$		−	3.32300e42i		−	1.58062i
$664$	−1.64834e41	−	2.54683e42i	−0.0766525	−	1.18435i
$665$	6.40364e41			0.291140
$666$	4.23091e40	+	6.97662e40i	0.0188070	+	0.0310121i
$667$			1.54859e42i			0.673053i
$668$	−4.36711e41	−	2.27641e41i	−0.185587	−	0.0967392i
$669$	−4.33540e42			−1.80151
$670$	4.82554e41	−	2.92641e41i	0.196076	−	0.118908i
$671$			2.62396e41i			0.104260i
$672$	−9.96132e41	+	2.25553e42i	−0.387060	+	0.876414i
$673$	−3.42472e42			−1.30137			−0.650683	−	0.759350i	$-0.725517\pi$
$673$	−3.42472e42			−1.30137			−0.650683	+	0.759350i	$0.725517\pi$
$674$	2.70421e42	+	4.45915e42i	1.00495	+	1.65712i
$675$		−	2.60684e42i		−	0.947454i
$676$	−2.57971e41	+	4.94898e41i	−0.0917002	+	0.175920i
$677$	4.10779e42			1.42816			0.714082	−	0.700063i	$-0.246845\pi$
$677$	4.10779e42			1.42816			0.714082	+	0.700063i	$0.246845\pi$
$678$	−4.61038e41	+	2.79593e41i	−0.156780	+	0.0950780i
$679$			2.32744e42i			0.774161i
$680$	1.25013e42	−	8.09103e40i	0.406745	−	0.0263251i
$681$	4.62507e42			1.47201
$682$	4.62804e41	+	7.63147e41i	0.144089	+	0.237598i
$683$		−	4.01147e42i		−	1.22178i	−0.791715	−	0.610890i	$-0.790812\pi$
$683$		−	4.01147e42i		−	1.22178i	0.791715	−	0.610890i	$-0.209188\pi$
$684$	−1.70260e41	−	8.87497e40i	−0.0507306	−	0.0264439i
$685$	−1.47484e41			−0.0429920
$686$	−3.04221e42	+	1.84492e42i	−0.867616	+	0.526158i
$687$		−	2.73376e39i		−	0.000762798i
$688$	3.43563e42	−	2.40007e42i	0.937950	−	0.655235i
$689$	5.58206e42			1.49110
$690$	2.28405e41	+	3.76631e41i	0.0596992	+	0.0984417i
$691$			3.05232e42i			0.780655i	0.920676	+	0.390327i	$0.127638\pi$
$691$			3.05232e42i			0.780655i	−0.920676	+	0.390327i	$0.872362\pi$
$692$	−8.35096e41	+	1.60207e42i	−0.208999	+	0.400950i
$693$	6.43858e40			0.0157685
$694$	−2.23137e42	+	1.35320e42i	−0.534786	+	0.324317i
$695$			1.35862e42i			0.318658i
$696$	4.27827e41	+	6.61029e42i	0.0982042	+	1.51734i
$697$	−4.09602e42			−0.920175
$698$	−1.53508e42	−	2.53129e42i	−0.337520	−	0.556559i
$699$		−	3.80872e42i		−	0.819637i
$700$	−3.83234e42	−	1.99765e42i	−0.807223	−	0.420774i
$701$	2.77612e42			0.572359			0.286180	−	0.958176i	$-0.407615\pi$
$701$	2.77612e42			0.572359			0.286180	+	0.958176i	$0.407615\pi$
$702$	−4.75311e42	+	2.88249e42i	−0.959227	+	0.581715i
$703$		−	3.71880e42i		−	0.734636i
$704$	2.00872e41	+	1.54532e42i	0.0388444	+	0.298832i
$705$	−2.18962e42			−0.414507
$706$	−5.50050e41	−	9.07012e41i	−0.101937	−	0.168090i
$707$			4.65193e42i			0.843998i
$708$	3.02467e42	−	5.80261e42i	0.537254	−	1.03068i
$709$	−3.47146e42			−0.603697			−0.301849	−	0.953356i	$-0.597604\pi$
$709$	−3.47146e42			−0.603697			−0.301849	+	0.953356i	$0.597604\pi$
$710$	−1.03054e42	+	6.24962e41i	−0.175465	+	0.106409i
$711$		−	3.73979e41i		−	0.0623453i
$712$	6.19044e42	−	4.00654e41i	1.01047	−	0.0653988i
$713$	−2.48501e42			−0.397177
$714$	−4.71025e42	−	7.76703e42i	−0.737175	−	1.21558i
$715$		−	5.91287e41i		−	0.0906165i
$716$	4.54882e42	+	2.37112e42i	0.682659	+	0.355843i
$717$	9.36838e42			1.37682
$718$	5.66863e42	−	3.43769e42i	0.815852	−	0.494767i
$719$		−	4.93391e42i		−	0.695438i	−0.937599	−	0.347719i	$-0.886956\pi$
$719$		−	4.93391e42i		−	0.695438i	0.937599	−	0.347719i	$-0.113044\pi$
$720$	−6.05633e40	−	8.66945e40i	−0.00836030	−	0.0119675i
$721$	−3.20281e42			−0.433014
$722$	6.21758e41	+	1.02526e42i	0.0823310	+	0.135761i
$723$		−	2.48687e42i		−	0.322536i
$724$	4.77685e42	−	9.16403e42i	0.606824	−	1.16415i
$725$	−1.16104e43			−1.44469
$726$	6.20639e42	−	3.76381e42i	0.756466	−	0.458753i
$727$			4.88682e42i			0.583459i	0.956501	+	0.291730i	$0.0942307\pi$
$727$			4.88682e42i			0.583459i	−0.956501	+	0.291730i	$0.905769\pi$
$728$	5.95209e41	+	9.19647e42i	0.0696143	+	1.07560i
$729$	−9.14120e42			−1.04735
$730$	−2.18272e42	−	3.59923e42i	−0.244994	−	0.403986i
$731$			1.54394e43i			1.69774i
$732$	−2.77119e42	−	1.44451e42i	−0.298538	−	0.155616i
$733$	3.94249e42			0.416113			0.208056	−	0.978117i	$-0.433286\pi$
$733$	3.94249e42			0.416113			0.208056	+	0.978117i	$0.433286\pi$
$734$	−1.15371e43	+	6.99657e42i	−1.19304	+	0.723509i
$735$			8.06257e40i			0.00816889i
$736$	−3.96896e42	−	1.75285e42i	−0.394012	−	0.174011i
$737$	−2.58622e42			−0.251567
$738$	1.79298e41	+	2.95657e41i	0.0170896	+	0.0281801i
$739$			1.52611e43i			1.42535i	0.701497	+	0.712673i	$0.252515\pi$
$739$			1.52611e43i			1.42535i	−0.701497	+	0.712673i	$0.747485\pi$
$740$	9.46787e41	−	1.81634e42i	0.0866516	−	0.166235i
$741$	1.27853e43			1.14667
$742$	1.30473e43	−	7.91241e42i	1.14673	−	0.695425i
$743$		−	8.51767e42i		−	0.733650i	−0.930290	−	0.366825i	$-0.880445\pi$
$743$		−	8.51767e42i		−	0.733650i	0.930290	−	0.366825i	$-0.119555\pi$
$744$	−1.06075e43	+	6.86529e41i	−0.895400	+	0.0579516i
$745$	2.68295e42			0.221957
$746$	3.29202e42	+	5.42842e42i	0.266920	+	0.440141i
$747$		−	7.93707e41i		−	0.0630741i
$748$	−5.09076e42	−	2.65361e42i	−0.396514	−	0.206687i
$749$	1.04037e43			0.794259
$750$	−5.87794e42	+	3.56463e42i	−0.439851	+	0.266744i
$751$			8.39445e42i			0.615734i	0.951429	+	0.307867i	$0.0996152\pi$
$751$			8.39445e42i			0.615734i	−0.951429	+	0.307867i	$0.900385\pi$
$752$	1.76812e43	−	1.23518e43i	1.27129	−	0.888099i
$753$	−3.17501e42			−0.223780
$754$	1.28380e43	+	2.11694e43i	0.887010	+	1.46265i
$755$		−	7.00274e42i		−	0.474311i
$756$	−7.02389e42	+	1.34748e43i	−0.466391	+	0.894737i
$757$	6.12800e42			0.398915			0.199458	−	0.979906i	$-0.436082\pi$
$757$	6.12800e42			0.398915			0.199458	+	0.979906i	$0.436082\pi$
$758$	1.48984e42	−	9.03501e41i	0.0950827	−	0.0576621i
$759$		−	2.01853e42i		−	0.126302i
$760$	3.11305e41	+	4.80993e42i	0.0190978	+	0.295077i
$761$	−1.12440e43			−0.676319			−0.338159	−	0.941089i	$-0.609804\pi$
$761$	−1.12440e43			−0.676319			−0.338159	+	0.941089i	$0.609804\pi$
$762$	2.41611e42	+	3.98408e42i	0.142493	+	0.234965i
$763$		−	2.37001e43i		−	1.37051i
$764$	−9.94129e42	−	5.18201e42i	−0.563693	−	0.293831i
$765$	3.89598e41			0.0216618
$766$	5.28204e42	−	3.20325e42i	0.287985	−	0.174646i
$767$		−	2.44572e43i		−	1.30760i
$768$	−1.74261e43	−	6.38568e42i	−0.913653	−	0.334803i
$769$	−1.20627e43			−0.620225			−0.310113	−	0.950700i	$-0.600367\pi$
$769$	−1.20627e43			−0.620225			−0.310113	+	0.950700i	$0.600367\pi$
$770$	−8.38132e41	−	1.38205e42i	−0.0422621	−	0.0696887i
$771$		−	4.04901e41i		−	0.0200232i
$772$	−1.33775e43	+	2.56638e43i	−0.648809	+	1.24469i
$773$	1.88559e43			0.896921			0.448460	−	0.893803i	$-0.351973\pi$
$773$	1.88559e43			0.896921			0.448460	+	0.893803i	$0.351973\pi$
$774$	1.11444e42	−	6.75843e41i	0.0519927	−	0.0315305i
$775$		−	1.86310e43i		−	0.852533i
$776$	−1.74819e43	+	1.13146e42i	−0.784628	+	0.0507822i
$777$	−1.48522e43			−0.653845
$778$	−2.01369e43	−	3.32051e43i	−0.869559	−	1.43387i
$779$		−	1.57596e43i		−	0.667549i
$780$	6.24464e42	+	3.25509e42i	0.259471	+	0.135252i
$781$	5.52313e42			0.225123
$782$	1.36673e43	−	8.28842e42i	0.546489	−	0.331414i
$783$			4.08229e43i			1.60132i
$784$	−4.54813e41	−	6.51052e41i	−0.0175022	−	0.0250539i
$785$	−2.68927e41			−0.0101529
$786$	1.84150e43	+	3.03657e43i	0.682077	+	1.12472i
$787$		−	1.37457e42i		−	0.0499513i	−0.999688	−	0.0249756i	$-0.992049\pi$
$787$		−	1.37457e42i		−	0.0499513i	0.999688	−	0.0249756i	$-0.00795082\pi$
$788$	−2.27389e42	+	4.36229e42i	−0.0810730	+	0.155532i
$789$	3.73103e43			1.30519
$790$	−8.02751e42	+	4.86822e42i	−0.275534	+	0.167095i
$791$			5.50888e42i			0.185531i
$792$	3.13004e40	+	4.83617e41i	0.00103436	+	0.0159817i
$793$	−1.16802e43			−0.378749
$794$	−1.76005e43	−	2.90225e43i	−0.560037	−	0.923480i
$795$		−	1.16600e43i		−	0.364077i
$796$	2.15844e43	+	1.12511e43i	0.661369	+	0.344746i
$797$	−3.28530e42			−0.0987869			−0.0493935	−	0.998779i	$-0.515729\pi$
$797$	−3.28530e42			−0.0987869			−0.0493935	+	0.998779i	$0.515729\pi$
$798$	2.98839e43	−	1.81229e43i	0.881849	−	0.534790i
$799$			7.94578e43i			2.30110i
$800$	1.31418e43	−	2.97568e43i	0.373512	−	0.845738i
$801$	1.92922e42			0.0538139
$802$	2.62747e43	+	4.33261e43i	0.719321	+	1.18613i
$803$			1.92899e43i			0.518318i
$804$	1.42374e43	−	2.73134e43i	0.375482	−	0.720335i
$805$	4.50031e42			0.116494
$806$	−3.39704e43	+	2.06010e43i	−0.863127	+	0.523436i
$807$		−	8.96320e41i		−	0.0223542i
$808$	−3.49417e43	+	2.26148e42i	−0.855409	+	0.0553633i
$809$	−1.93552e43			−0.465125			−0.232562	−	0.972581i	$-0.574711\pi$
$809$	−1.93552e43			−0.465125			−0.232562	+	0.972581i	$0.574711\pi$
$810$	5.70015e42	+	9.39934e42i	0.134466	+	0.221729i
$811$		−	1.29622e43i		−	0.300169i	−0.988673	−	0.150084i	$-0.952045\pi$
$811$		−	1.29622e43i		−	0.300169i	0.988673	−	0.150084i	$-0.0479545\pi$
$812$	6.00142e43	+	3.12830e43i	1.36431	+	0.711162i
$813$	−3.86568e43			−0.862716
$814$	−8.02599e42	+	4.86729e42i	−0.175846	+	0.106640i
$815$			1.37894e43i			0.296607i
$816$	5.60502e43	−	3.91557e43i	1.18365	−	0.826879i
$817$	−5.94038e43			−1.23164
$818$	−3.65980e43	−	6.03488e43i	−0.745003	−	1.22848i
$819$			2.86604e42i			0.0572827i
$820$	4.01231e42	−	7.69732e42i	0.0787385	−	0.151054i
$821$	−3.12666e43			−0.602467			−0.301234	−	0.953550i	$-0.597398\pi$
$821$	−3.12666e43			−0.602467			−0.301234	+	0.953550i	$0.597398\pi$
$822$	−6.88267e42	+	4.17394e42i	−0.130221	+	0.0789712i
$823$		−	6.51858e43i		−	1.21103i	−0.795833	−	0.605516i	$-0.792967\pi$
$823$		−	6.51858e43i		−	1.21103i	0.795833	−	0.605516i	$-0.207033\pi$
$824$	−1.55701e42	−	2.40570e43i	−0.0284042	−	0.438868i
$825$	1.51337e43			0.271104
$826$	−3.46673e43	−	5.71652e43i	−0.609845	−	1.00561i
$827$			3.16396e43i			0.546573i	0.961933	+	0.273286i	$0.0881107\pi$
$827$			3.16396e43i			0.546573i	−0.961933	+	0.273286i	$0.911889\pi$
$828$	−1.19654e42	−	6.23709e41i	−0.0202989	−	0.0105810i
$829$	1.12226e44			1.86972			0.934859	−	0.355020i	$-0.115526\pi$
$829$	1.12226e44			1.86972			0.934859	+	0.355020i	$0.115526\pi$
$830$	−1.70370e43	+	1.03320e43i	−0.278755	+	0.169048i
$831$			2.69353e42i			0.0432818i
$832$	−6.87875e43	+	8.94151e42i	−1.08557	+	0.141111i
$833$	2.92577e42			0.0453488
$834$	3.84500e43	+	6.34027e43i	0.585337	+	0.965199i
$835$			3.84487e42i			0.0574890i
$836$	1.02099e43	−	1.95869e43i	0.149943	−	0.287654i
$837$	−6.55081e43			−0.944959
$838$	−6.27376e43	+	3.80467e43i	−0.888930	+	0.539084i
$839$		−	4.66312e43i		−	0.649004i	−0.945885	−	0.324502i	$-0.894803\pi$
$839$		−	4.66312e43i		−	0.649004i	0.945885	−	0.324502i	$-0.105197\pi$
$840$	1.92100e43	−	1.24330e42i	0.262626	−	0.0169975i
$841$	1.07355e44			1.44172
$842$	−5.59237e43	−	9.22161e43i	−0.737759	−	1.21654i
$843$		−	3.04115e42i		−	0.0394117i
$844$	3.18126e43	+	1.65827e43i	0.405007	+	0.211114i
$845$	4.35716e42			0.0544945
$846$	5.73537e42	−	3.47817e42i	0.0704703	−	0.0427361i
$847$		−	7.41594e43i		−	0.895189i
$848$	6.57748e43	+	9.41547e43i	0.780049	+	1.11662i
$849$	−8.39195e42			−0.0977795
$850$	6.21414e43	+	1.02469e44i	0.711373	+	1.17303i
$851$		−	2.61347e43i		−	0.293951i
$852$	−3.04053e43	+	5.83303e43i	−0.336013	+	0.644615i
$853$	7.53883e43			0.818594			0.409297	−	0.912401i	$-0.365774\pi$
$853$	7.53883e43			0.818594			0.409297	+	0.912401i	$0.365774\pi$
$854$	−2.73007e43	+	1.65563e43i	−0.291277	+	0.176643i
$855$			1.49899e42i			0.0157148i
$856$	5.05765e42	+	7.81450e43i	0.0521006	+	0.804998i
$857$	−6.76652e43			−0.684941			−0.342470	−	0.939529i	$-0.611264\pi$
$857$	−6.76652e43			−0.684941			−0.342470	+	0.939529i	$0.611264\pi$
$858$	−1.67339e43	−	2.75936e43i	−0.166452	−	0.274473i
$859$		−	6.60720e43i		−	0.645832i	−0.946428	−	0.322916i	$-0.895337\pi$
$859$		−	6.60720e43i		−	0.645832i	0.946428	−	0.322916i	$-0.104663\pi$
$860$	−2.90141e43	−	1.51239e43i	−0.278697	−	0.145274i
$861$	−6.29408e43			−0.594135
$862$	2.21857e43	−	1.34543e43i	0.205809	−	0.124811i
$863$			8.22474e43i			0.749825i	0.927060	+	0.374913i	$0.122327\pi$
$863$			8.22474e43i			0.749825i	−0.927060	+	0.374913i	$0.877673\pi$
$864$	−1.04627e44	−	4.62075e43i	−0.937428	−	0.414005i
$865$	1.41049e43			0.124202
$866$	2.72097e43	+	4.48678e43i	0.235481	+	0.388299i
$867$			1.37484e44i			1.16941i
$868$	−5.01995e43	+	9.63040e43i	−0.419666	+	0.805098i
$869$	4.30230e43			0.353512
$870$	4.42196e43	−	2.68166e43i	0.357129	−	0.216578i
$871$		−	1.15122e44i		−	0.913872i
$872$	1.78017e44	−	1.15215e43i	1.38904	−	0.0899005i
$873$	−5.44816e42			−0.0417866
$874$	3.18900e43	+	5.25855e43i	0.240427	+	0.396455i
$875$			7.02347e43i			0.520513i
$876$	−2.03723e44	−	1.06193e44i	−1.48415	−	0.773629i
$877$	−6.90260e42			−0.0494332			−0.0247166	−	0.999694i	$-0.507868\pi$
$877$	−6.90260e42			−0.0494332			−0.0247166	+	0.999694i	$0.507868\pi$
$878$	−2.67453e41	+	1.62195e41i	−0.00188291	+	0.00114187i
$879$		−	2.15311e43i		−	0.149016i
$880$	9.97345e42	−	6.96727e42i	0.0678586	−	0.0474048i
$881$	1.52523e44			1.02022			0.510112	−	0.860108i	$-0.329604\pi$
$881$	1.52523e44			1.02022			0.510112	+	0.860108i	$0.329604\pi$
$882$	−1.28072e41	−	2.11186e41i	−0.000842221	−	0.00138879i
$883$		−	5.64141e43i		−	0.364735i	−0.983230	−	0.182368i	$-0.941624\pi$
$883$		−	5.64141e43i		−	0.364735i	0.983230	−	0.182368i	$-0.0583761\pi$
$884$	1.18122e44	−	2.26608e44i	0.750837	−	1.44042i
$885$	−5.10871e43			−0.319273
$886$	1.73148e44	−	1.05004e44i	1.06392	−	0.645208i
$887$			8.90466e43i			0.537976i	0.963144	+	0.268988i	$0.0866892\pi$
$887$			8.90466e43i			0.537976i	−0.963144	+	0.268988i	$0.913311\pi$
$888$	−7.22020e42	−	1.11558e44i	−0.0428899	−	0.662685i
$889$	4.76052e43			0.278053
$890$	−2.51133e43	−	4.14110e43i	−0.144230	−	0.237829i
$891$		−	5.03753e43i		−	0.284480i
$892$	−2.95648e44	−	1.54110e44i	−1.64173	−	0.855769i
$893$	−3.05717e44			−1.66935
$894$	1.25205e44	−	7.59298e43i	0.672296	−	0.407708i
$895$		−	4.00485e43i		−	0.211466i
$896$	−1.48107e44	+	1.18404e44i	−0.769050	+	0.614817i
$897$	8.98521e43			0.458819
$898$	1.00705e44	+	1.66059e44i	0.505715	+	0.833905i
$899$			2.91760e44i			1.44089i
$900$	4.67618e42	−	8.97091e42i	0.0227119	−	0.0435711i
$901$	−4.23123e44			−2.02113
$902$	−3.40127e43	+	2.06267e43i	−0.159788	+	0.0969018i
$903$			2.37248e44i			1.09619i
$904$	−4.13785e43	+	2.67808e42i	−0.188039	+	0.0121702i
$905$	−8.06815e43			−0.360616
$906$	−1.98183e44	−	3.26797e44i	−0.871253	−	1.43666i
$907$		−	2.53886e44i		−	1.09782i	−0.835883	−	0.548908i	$-0.815044\pi$
$907$		−	2.53886e44i		−	1.09782i	0.835883	−	0.548908i	$-0.184956\pi$
$908$	3.15401e44	+	1.64406e44i	1.34145	+	0.699248i
$909$	−1.08894e43			−0.0455561
$910$	6.15199e43	−	3.73082e43i	0.253160	−	0.153527i
$911$		−	4.74136e43i		−	0.191923i	−0.995385	−	0.0959615i	$-0.969407\pi$
$911$		−	4.74136e43i		−	0.191923i	0.995385	−	0.0959615i	$-0.0305926\pi$
$912$	1.50653e44	+	2.15655e44i	0.599867	+	0.858692i
$913$	9.13091e43			0.357645
$914$	2.11039e44	+	3.47996e44i	0.813150	+	1.34085i
$915$			2.43980e43i			0.0924778i
$916$	9.71764e40	−	1.86426e41i	0.000362350	−	0.000695142i
$917$	3.62835e44			1.33097
$918$	3.60288e44	−	2.18494e44i	1.30020	−	0.788495i
$919$		−	1.24217e44i		−	0.441009i	−0.975386	−	0.220505i	$-0.929230\pi$
$919$		−	1.24217e44i		−	0.441009i	0.975386	−	0.220505i	$-0.0707704\pi$
$920$	2.18777e42	+	3.38029e43i	0.00764161	+	0.118069i
$921$	2.90656e44			0.998815
$922$	−9.77605e43	−	1.61203e44i	−0.330521	−	0.545018i
$923$			2.45854e44i			0.817809i
$924$	−7.82263e43	−	4.07763e43i	−0.256020	−	0.133453i
$925$	1.95942e44			0.630959
$926$	−4.71996e44	+	2.86238e44i	−1.49546	+	0.906907i
$927$		−	7.49727e42i		−	0.0233726i
$928$	−2.05799e44	+	4.65988e44i	−0.631283	+	1.42941i
$929$	−1.67838e43			−0.0506587			−0.0253294	−	0.999679i	$-0.508063\pi$
$929$	−1.67838e43			−0.0506587			−0.0253294	+	0.999679i	$0.508063\pi$
$930$	4.30323e43	+	7.09586e43i	0.127806	+	0.210747i
$931$			1.12570e43i			0.0328986i
$932$	1.35388e44	−	2.59731e44i	0.389350	−	0.746940i
$933$	−1.98128e43			−0.0560687
$934$	−4.62993e44	+	2.80778e44i	−1.28935	+	0.781917i
$935$			4.48198e43i			0.122828i
$936$	−2.15275e43	+	1.39329e42i	−0.0580572	+	0.00375754i
$937$	3.31179e44			0.878960			0.439480	−	0.898252i	$-0.355163\pi$
$937$	3.31179e44			0.878960			0.439480	+	0.898252i	$0.355163\pi$
$938$	−1.63182e44	−	2.69081e44i	−0.426216	−	0.702814i
$939$		−	4.33658e44i		−	1.11471i
$940$	−1.49319e44	−	7.78339e43i	−0.377743	−	0.196902i
$941$	−5.54669e44			−1.38099			−0.690493	−	0.723339i	$-0.742606\pi$
$941$	−5.54669e44			−1.38099			−0.690493	+	0.723339i	$0.742606\pi$
$942$	−1.25500e43	+	7.61086e42i	−0.0307526	+	0.0186496i
$943$		−	1.10754e44i		−	0.267107i
$944$	4.12528e44	−	2.88185e44i	0.979205	−	0.684055i
$945$	1.18634e44			0.277162
$946$	7.77498e43	+	1.28207e44i	0.178785	+	0.294811i
$947$		−	7.06492e44i		−	1.59903i	−0.600644	−	0.799517i	$-0.705089\pi$
$947$		−	7.06492e44i		−	1.59903i	0.600644	−	0.799517i	$-0.294911\pi$
$948$	−2.36846e44	+	4.54371e44i	−0.527643	+	1.01224i
$949$	−8.58661e44			−1.88291
$950$	−3.94253e44	+	2.39091e44i	−0.850983	+	0.516072i
$951$		−	3.80804e44i		−	0.809085i
$952$	−4.51171e43	−	6.97097e44i	−0.0943599	−	1.45794i
$953$	9.23198e44			1.90065			0.950323	−	0.311265i	$-0.100753\pi$
$953$	9.23198e44			1.90065			0.950323	+	0.311265i	$0.100753\pi$
$954$	1.85217e43	+	3.05416e43i	0.0375367	+	0.0618966i
$955$			8.75247e43i			0.174614i
$956$	6.38865e44	+	3.33015e44i	1.25470	+	0.654027i
$957$	−2.36993e44			−0.458201
$958$	2.34893e43	−	1.42449e43i	0.0447082	−	0.0271129i
$959$			8.22402e43i			0.154101i
$960$	1.86774e43	+	1.43686e44i	0.0344546	+	0.265061i
$961$	8.24340e43			0.149712
$962$	−2.16660e44	−	3.57265e44i	−0.387394	−	0.638799i
$963$			2.43535e43i			0.0428714i
$964$	8.84002e43	−	1.69589e44i	0.153214	−	0.293929i
$965$	2.25948e44			0.385566
$966$	2.10016e44	−	1.27363e44i	0.352855	−	0.213986i
$967$			9.55994e44i			1.58146i	0.612166	+	0.790729i	$0.290298\pi$
$967$			9.55994e44i			1.58146i	−0.612166	+	0.790729i	$0.709702\pi$
$968$	5.57029e44	−	3.60517e43i	0.907292	−	0.0587212i
$969$	−9.69136e44			−1.55428
$970$	7.09206e43	+	1.16945e44i	0.111994	+	0.184675i
$971$		−	3.57541e44i		−	0.555952i	−0.960588	−	0.277976i	$-0.910336\pi$
$971$		−	3.57541e44i		−	0.555952i	0.960588	−	0.277976i	$-0.0896635\pi$
$972$	−6.14931e43	−	3.20539e43i	−0.0941525	−	0.0490780i
$973$	7.57591e44			1.14220
$974$	−5.51400e44	+	3.34392e44i	−0.818620	+	0.496445i
$975$			6.73655e44i			0.984846i
$976$	−1.37630e44	−	1.97014e44i	−0.198137	−	0.283628i
$977$	−2.78888e44			−0.395377			−0.197688	−	0.980265i	$-0.563343\pi$
$977$	−2.78888e44			−0.395377			−0.197688	+	0.980265i	$0.563343\pi$
$978$	3.90252e44	+	6.43510e44i	0.544831	+	0.898406i
$979$			2.21940e44i			0.305137i
$980$	−2.86598e42	+	5.49817e42i	−0.00388045	+	0.00744435i
$981$	5.54782e43			0.0739754
$982$	8.64956e44	−	5.24545e44i	1.13585	−	0.688828i
$983$			9.78416e44i			1.26538i	0.774405	+	0.632690i	$0.218049\pi$
$983$			9.78416e44i			1.26538i	−0.774405	+	0.632690i	$0.781951\pi$
$984$	−3.05979e43	−	4.72764e44i	−0.0389732	−	0.602168i
$985$	3.84063e43			0.0481791
$986$	−9.73130e44	−	1.60466e45i	−1.20231	−	1.98257i
$987$			1.22097e45i			1.48576i
$988$	8.71881e44	+	4.54478e44i	1.04497	+	0.544701i
$989$	−4.17474e44			−0.492817
$990$	3.23516e42	−	1.96193e42i	0.00376156	−	0.00228116i
$991$		−	6.97508e44i		−	0.798812i	−0.916774	−	0.399406i	$-0.869216\pi$
$991$		−	6.97508e44i		−	0.798812i	0.916774	−	0.399406i	$-0.130784\pi$
$992$	−7.47766e44	−	3.30243e44i	−0.843511	−	0.372528i
$993$	4.26621e44			0.474027
$994$	3.48491e44	+	5.74649e44i	0.381413	+	0.628936i
$995$		−	1.90032e44i		−	0.204871i
$996$	−5.02665e44	+	9.64324e44i	−0.533812	+	1.02408i
$997$	−9.97750e43			−0.104375			−0.0521873	−	0.998637i	$-0.516619\pi$
$997$	−9.97750e43			−0.104375			−0.0521873	+	0.998637i	$0.516619\pi$
$998$	2.29104e44	−	1.38938e44i	0.236088	−	0.143174i
$999$		−	6.88946e44i		−	0.699363i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.31.b.a.3.5	✓	14
3.2	odd	2		36.31.d.c.19.10		14
4.3	odd	2	inner	4.31.b.a.3.6	yes	14
12.11	even	2		36.31.d.c.19.9		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.31.b.a.3.5	✓	14	1.1	even	1	trivial
4.31.b.a.3.6	yes	14	4.3	odd	2	inner
36.31.d.c.19.9		14	12.11	even	2
36.31.d.c.19.10		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)

\(f(q)\)	\(=\)	\(q+(-16991.5 - 28018.4i) q^{2} +1.39624e7i q^{3} +(-4.96318e8 + 9.52150e8i) q^{4} +8.38288e9 q^{5} +(3.91204e11 - 2.37243e11i) q^{6} -4.67445e12i q^{7} +(3.51109e13 - 2.27243e12i) q^{8} +1.09422e13 q^{9} +O(q^{10})\)	\(q+(-16991.5 - 28018.4i) q^{2} +1.39624e7i q^{3} +(-4.96318e8 + 9.52150e8i) q^{4} +8.38288e9 q^{5} +(3.91204e11 - 2.37243e11i) q^{6} -4.67445e12i q^{7} +(3.51109e13 - 2.27243e12i) q^{8} +1.09422e13 q^{9} +(-1.42438e14 - 2.34875e14i) q^{10} +1.25880e15i q^{11} +(-1.32943e16 - 6.92980e15i) q^{12} -5.60336e16 q^{13} +(-1.30971e17 + 7.94260e16i) q^{14} +1.17045e17i q^{15} +(-6.60257e17 - 9.45139e17i) q^{16} +4.24738e18 q^{17} +(-1.85924e17 - 3.06582e17i) q^{18} +1.63419e19i q^{19} +(-4.16058e18 + 7.98175e18i) q^{20} +6.52666e19 q^{21} +(3.52695e19 - 2.13889e19i) q^{22} +1.14847e20i q^{23} +(3.17286e19 + 4.90233e20i) q^{24} -8.61050e20 q^{25} +(9.52096e20 + 1.56997e21i) q^{26} +3.02752e21i q^{27} +(4.45078e21 + 2.32002e21i) q^{28} +1.34840e22 q^{29} +(3.27942e21 - 1.98878e21i) q^{30} +2.16376e22i q^{31} +(-1.52625e22 + 3.45587e22i) q^{32} -1.75759e22 q^{33} +(-7.21694e22 - 1.19005e23i) q^{34} -3.91853e22i q^{35} +(-5.43079e21 + 1.04186e22i) q^{36} -2.27561e23 q^{37} +(4.57875e23 - 2.77674e23i) q^{38} -7.82364e23i q^{39} +(2.94330e23 - 1.90495e22i) q^{40} -9.64365e23 q^{41} +(-1.10898e24 - 1.82867e24i) q^{42} +3.63505e24i q^{43} +(-1.19857e24 - 6.24765e23i) q^{44} +9.17267e22 q^{45} +(3.21782e24 - 1.95142e24i) q^{46} +1.87075e25i q^{47} +(1.31964e25 - 9.21879e24i) q^{48} +6.88842e23 q^{49} +(1.46305e25 + 2.41252e25i) q^{50} +5.93036e25i q^{51} +(2.78105e25 - 5.33524e25i) q^{52} -9.96199e25 q^{53} +(8.48261e25 - 5.14421e25i) q^{54} +1.05524e25i q^{55} +(-1.06224e25 - 1.64124e26i) q^{56} -2.28173e26 q^{57} +(-2.29113e26 - 3.77799e26i) q^{58} +4.36473e26i q^{59} +(-1.11445e26 - 5.80917e25i) q^{60} +2.08449e26 q^{61} +(6.06250e26 - 3.67655e26i) q^{62} -5.11486e25i q^{63} +(1.22761e27 - 1.59574e26i) q^{64} -4.69723e26 q^{65} +(2.98641e26 + 4.92448e26i) q^{66} +2.05452e27i q^{67} +(-2.10805e27 + 4.04414e27i) q^{68} -1.60354e27 q^{69} +(-1.09791e27 + 6.65819e26i) q^{70} -4.38762e27i q^{71} +(3.84189e26 - 2.48653e25i) q^{72} +1.53240e28 q^{73} +(3.86661e27 + 6.37591e27i) q^{74} -1.20223e28i q^{75} +(-1.55600e28 - 8.11080e27i) q^{76} +5.88420e27 q^{77} +(-2.19206e28 + 1.32936e28i) q^{78} -3.41778e28i q^{79} +(-5.53486e27 - 7.92298e27i) q^{80} -4.00185e28 q^{81} +(1.63860e28 + 2.70200e28i) q^{82} -7.25366e28i q^{83} +(-3.23930e28 + 6.21436e28i) q^{84} +3.56052e28 q^{85} +(1.01848e29 - 6.17651e28i) q^{86} +1.88269e29i q^{87} +(2.86053e27 + 4.41976e28i) q^{88} +1.76311e29 q^{89} +(-1.55858e27 - 2.57004e27i) q^{90} +2.61926e29i q^{91} +(-1.09351e29 - 5.70006e28i) q^{92} -3.02113e29 q^{93} +(5.24154e29 - 3.17869e29i) q^{94} +1.36992e29i q^{95} +(-4.82523e29 - 2.13101e29i) q^{96} -4.97906e29 q^{97} +(-1.17045e28 - 1.93003e28i) q^{98} +1.37740e28i 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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