LMFDB - Embedded newform 8.22.b.a.5.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,22,Mod(5,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("8.5");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	8.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$22.3581875430$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 10 x^{19} + 8499037025 x^{18} - 76491332940 x^{17} + \cdots + 35\!\cdots\!00 $ x^20 - 10x^19 + 8499037025x^18 - 76491332940x^17 + 29917993634631504354x^16 - 239343947343248489484x^15 + 56735124423752018369174556138x^14 - 397145866777745056145685733776x^13 + 63238887245213577325916647519604926269x^12 - 379433318308385206734963736802075208922x^11 + 42482893644148833600712851037696291113731507797x^10 - 212414464742605426308676323132417376601509837748x^9 + 16991149511760794392812139094660185274650292829286304832x^8 - 67964596772556393289382483692574713665819457865324101248x^7 + 3856070948945815855551883712975066709737139564290759222840809728x^6 - 11568212608961359754849022371262813346960834248571059910113653760x^5 + 447495609895006687050069424346090867517835281773807292283716383294251008x^4 - 894991200509659105123235067097342555549602100555628271172491492140580864x^3 + 21617394414514960541269362233298250396222492191038308122525553887833389622886400x^2 - 21617393967019362214475233171141277620661834650156142656637432362426234096844800*x + 356285834965428012369716852146922959222876595571555882248526187687502452643625697280000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{190}\cdot 3^{14}\cdot 5^{4}\cdot 7^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.20
Root			$0.500000 - 29091.7i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.22.b.a.5.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1444.36 + 104.758i) q^{2} +116367. i q^{3} +(2.07520e6 + 302616. i) q^{4} +3.48989e7i q^{5} +(-1.21903e7 + 1.68076e8i) q^{6} -1.26580e9 q^{7} +(2.96564e9 + 6.54481e8i) q^{8} -3.08088e9 q^{9} +(-3.65593e9 + 5.04066e10i) q^{10} -3.61925e10i q^{11} +(-3.52145e10 + 2.41485e11i) q^{12} -5.83952e11i q^{13} +(-1.82827e12 - 1.32602e11i) q^{14} -4.06107e12 q^{15} +(4.21489e12 + 1.25598e12i) q^{16} +3.71123e12 q^{17} +(-4.44990e12 - 3.22746e11i) q^{18} +1.39188e13i q^{19} +(-1.05610e13 + 7.24223e13i) q^{20} -1.47297e14i q^{21} +(3.79144e12 - 5.22750e13i) q^{22} +6.23488e12 q^{23} +(-7.61598e13 + 3.45102e14i) q^{24} -7.41095e14 q^{25} +(6.11735e13 - 8.43438e14i) q^{26} +8.58726e14i q^{27} +(-2.62679e15 - 3.83051e14i) q^{28} +3.96616e15i q^{29} +(-5.86565e15 - 4.25429e14i) q^{30} -5.98822e15 q^{31} +(5.95625e15 + 2.25563e15i) q^{32} +4.21160e15 q^{33} +(5.36036e15 + 3.88781e14i) q^{34} -4.41750e16i q^{35} +(-6.39345e15 - 9.32324e14i) q^{36} +3.67235e16i q^{37} +(-1.45810e15 + 2.01037e16i) q^{38} +6.79526e16 q^{39} +(-2.28406e16 + 1.03498e17i) q^{40} +4.32347e16 q^{41} +(1.54305e16 - 2.12750e17i) q^{42} +1.55834e16i q^{43} +(1.09524e16 - 7.51068e16i) q^{44} -1.07519e17i q^{45} +(9.00542e15 + 6.53153e14i) q^{46} +2.82812e17 q^{47} +(-1.46154e17 + 4.90474e17i) q^{48} +1.04370e18 q^{49} +(-1.07041e18 - 7.76355e16i) q^{50} +4.31864e17i q^{51} +(1.76713e17 - 1.21182e18i) q^{52} -3.04645e17i q^{53} +(-8.99582e16 + 1.24031e18i) q^{54} +1.26308e18 q^{55} +(-3.75391e18 - 8.28441e17i) q^{56} -1.61968e18 q^{57} +(-4.15486e17 + 5.72857e18i) q^{58} -2.15723e18i q^{59} +(-8.42755e18 - 1.22895e18i) q^{60} -4.15297e18i q^{61} +(-8.64915e18 - 6.27313e17i) q^{62} +3.89977e18 q^{63} +(8.36668e18 + 3.88191e18i) q^{64} +2.03793e19 q^{65} +(6.08307e18 + 4.41198e17i) q^{66} +2.12477e19i q^{67} +(7.70157e18 + 1.12308e18i) q^{68} +7.25533e17i q^{69} +(4.62767e18 - 6.38046e19i) q^{70} +1.05682e19 q^{71} +(-9.13678e18 - 2.01638e18i) q^{72} +1.19343e19 q^{73} +(-3.84708e18 + 5.30420e19i) q^{74} -8.62388e19i q^{75} +(-4.21204e18 + 2.88843e19i) q^{76} +4.58124e19i q^{77} +(9.81481e19 + 7.11857e18i) q^{78} -1.10112e20 q^{79} +(-4.38323e19 + 1.47095e20i) q^{80} -1.32154e20 q^{81} +(6.24465e19 + 4.52917e18i) q^{82} -4.07937e19i q^{83} +(4.45744e19 - 3.05671e20i) q^{84} +1.29518e20i q^{85} +(-1.63248e18 + 2.25080e19i) q^{86} -4.61530e20 q^{87} +(2.36873e19 - 1.07334e20i) q^{88} +3.12189e20 q^{89} +(1.12635e19 - 1.55297e20i) q^{90} +7.39166e20i q^{91} +(1.29387e19 + 1.88678e18i) q^{92} -6.96830e20i q^{93} +(4.08483e20 + 2.96268e19i) q^{94} -4.85749e20 q^{95} +(-2.62481e20 + 6.93110e20i) q^{96} -3.40413e20 q^{97} +(1.50748e21 + 1.09336e20i) q^{98} +1.11505e20i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 286 q^{2} + 409876 q^{4} + 118236748 q^{6} + 564950496 q^{7} + 3649699336 q^{8} - 62762119220 q^{9} - 51269339528 q^{10} + 65316900136 q^{12} - 1924309104464 q^{14} - 2285680856096 q^{15} + 7793508571920 q^{16}+ \cdots + 13\!\cdots\!30 q^{98}+O(q^{100}) $ 20 * q + 286 * q^2 + 409876 * q^4 + 118236748 * q^6 + 564950496 * q^7 + 3649699336 * q^8 - 62762119220 * q^9 - 51269339528 * q^10 + 65316900136 * q^12 - 1924309104464 * q^14 - 2285680856096 * q^15 + 7793508571920 * q^16 + 1740714497000 * q^17 - 41325344023822 * q^18 - 78999934156016 * q^20 + 294957216952508 * q^22 + 335749622520224 * q^23 + 786737698607504 * q^24 - 1665114591247004 * q^25 - 2772669922448408 * q^26 - 4284340177681888 * q^28 + 3807691030523312 * q^30 - 8989263821171840 * q^31 - 9127378177656544 * q^32 + 5359113021386256 * q^33 + 19124803780998044 * q^34 + 39378114498954828 * q^36 - 41860137429498580 * q^38 + 121743910075345312 * q^39 - 160007944946664288 * q^40 - 84626460793452344 * q^41 + 178614544452770272 * q^42 - 27785097292304568 * q^44 + 184220935820050448 * q^46 + 149908985865280320 * q^47 + 1509829480382701344 * q^48 + 477689401234988532 * q^49 - 1722157324053237098 * q^50 - 1640429312330235856 * q^52 + 785391046636854392 * q^54 - 1936239868862269088 * q^55 - 3751496032099552448 * q^56 + 409355502574547024 * q^57 + 3182351472522780872 * q^58 + 2751731248604508192 * q^60 - 13336157978726113600 * q^62 - 8780950644120846560 * q^63 - 9021637553716933568 * q^64 + 6302857570713584320 * q^65 + 5291575090585638744 * q^66 + 40891724357029299816 * q^68 + 18077776609913587392 * q^70 + 96451291685825247456 * q^71 + 49841566955976579512 * q^72 - 21461290229157072184 * q^73 - 42953490504627871688 * q^74 - 206966483397015363224 * q^76 + 163869164384378609168 * q^78 - 284214874786393231680 * q^79 - 49904712513208125120 * q^80 + 1291808332257012164 * q^81 + 112698322843931711404 * q^82 + 178681601993395676224 * q^84 - 523293212085532715396 * q^86 + 517213147301817170208 * q^87 - 124028902608265335088 * q^88 + 17316387144455013640 * q^89 + 171098967229297148360 * q^90 + 827091233447044225632 * q^92 - 165060487582514765280 * q^94 - 2333725338330109674784 * q^95 - 715448174391177540544 * q^96 + 9560220979460741928 * q^97 + 137273120368488603630 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1444.36	+	104.758i	0.997380	+	0.0723388i
$2$	1444.36	+	104.758i	0.997380	+	0.0723388i
$3$			116367.i			1.13777i	0.822416	+	0.568887i	$0.192626\pi$
$3$			116367.i			1.13777i	−0.822416	+	0.568887i	$0.807374\pi$
$4$	2.07520e6	+	302616.i	0.989534	+	0.144299i
$5$			3.48989e7i			1.59818i	0.601209	+	0.799091i	$0.294686\pi$
$5$			3.48989e7i			1.59818i	−0.601209	+	0.799091i	$0.705314\pi$
$6$	−1.21903e7	+	1.68076e8i	−0.0823052	+	1.13479i
$7$	−1.26580e9			−1.69370			−0.846848	−	0.531835i	$-0.821502\pi$
$7$	−1.26580e9			−1.69370			−0.846848	+	0.531835i	$0.821502\pi$
$8$	2.96564e9	+	6.54481e8i	0.976503	+	0.215502i
$9$	−3.08088e9			−0.294529
$10$	−3.65593e9	+	5.04066e10i	−0.115611	+	1.59400i
$11$		−	3.61925e10i		−	0.420722i	−0.977624	−	0.210361i	$-0.932536\pi$
$11$		−	3.61925e10i		−	0.420722i	0.977624	−	0.210361i	$-0.0674639\pi$
$12$	−3.52145e10	+	2.41485e11i	−0.164179	+	1.12587i
$13$		−	5.83952e11i		−	1.17482i	−0.809289	−	0.587411i	$-0.800147\pi$
$13$		−	5.83952e11i		−	1.17482i	0.809289	−	0.587411i	$-0.199853\pi$
$14$	−1.82827e12	−	1.32602e11i	−1.68926	−	0.122520i
$15$	−4.06107e12			−1.81837
$16$	4.21489e12	+	1.25598e12i	0.958356	+	0.285577i
$17$	3.71123e12			0.446483			0.223241	−	0.974763i	$-0.428336\pi$
$17$	3.71123e12			0.446483			0.223241	+	0.974763i	$0.428336\pi$
$18$	−4.44990e12	−	3.22746e11i	−0.293758	−	0.0213059i
$19$			1.39188e13i			0.520820i	0.965498	+	0.260410i	$0.0838578\pi$
$19$			1.39188e13i			0.520820i	−0.965498	+	0.260410i	$0.916142\pi$
$20$	−1.05610e13	+	7.24223e13i	−0.230616	+	1.58146i
$21$		−	1.47297e14i		−	1.92704i
$22$	3.79144e12	−	5.22750e13i	0.0304345	−	0.419620i
$23$	6.23488e12			0.0313824			0.0156912	−	0.999877i	$-0.495005\pi$
$23$	6.23488e12			0.0313824			0.0156912	+	0.999877i	$0.495005\pi$
$24$	−7.61598e13	+	3.45102e14i	−0.245193	+	1.11104i
$25$	−7.41095e14			−1.55419
$26$	6.11735e13	−	8.43438e14i	0.0849852	−	1.17174i
$27$			8.58726e14i			0.802666i
$28$	−2.62679e15	−	3.83051e14i	−1.67597	−	0.244398i
$29$			3.96616e15i			1.75062i	0.483564	+	0.875309i	$0.339342\pi$
$29$			3.96616e15i			1.75062i	−0.483564	+	0.875309i	$0.660658\pi$
$30$	−5.86565e15	−	4.25429e14i	−1.81361	−	0.131539i
$31$	−5.98822e15			−1.31220			−0.656100	−	0.754674i	$-0.727795\pi$
$31$	−5.98822e15			−1.31220			−0.656100	+	0.754674i	$0.727795\pi$
$32$	5.95625e15	+	2.25563e15i	0.935187	+	0.354155i
$33$	4.21160e15			0.478686
$34$	5.36036e15	+	3.88781e14i	0.445313	+	0.0322980i
$35$		−	4.41750e16i		−	2.70684i
$36$	−6.39345e15	−	9.32324e14i	−0.291447	−	0.0425002i
$37$			3.67235e16i			1.25553i	0.778404	+	0.627764i	$0.216030\pi$
$37$			3.67235e16i			1.25553i	−0.778404	+	0.627764i	$0.783970\pi$
$38$	−1.45810e15	+	2.01037e16i	−0.0376755	+	0.519456i
$39$	6.79526e16			1.33668
$40$	−2.28406e16	+	1.03498e17i	−0.344412	+	1.56063i
$41$	4.32347e16			0.503039			0.251520	−	0.967852i	$-0.419070\pi$
$41$	4.32347e16			0.503039			0.251520	+	0.967852i	$0.419070\pi$
$42$	1.54305e16	−	2.12750e17i	0.139400	−	1.92199i
$43$			1.55834e16i			0.109962i	0.998487	+	0.0549811i	$0.0175098\pi$
$43$			1.55834e16i			0.109962i	−0.998487	+	0.0549811i	$0.982490\pi$
$44$	1.09524e16	−	7.51068e16i	0.0607096	−	0.416319i
$45$		−	1.07519e17i		−	0.470712i
$46$	9.00542e15	+	6.53153e14i	0.0313002	+	0.00227017i
$47$	2.82812e17			0.784280			0.392140	−	0.919906i	$-0.371735\pi$
$47$	2.82812e17			0.784280			0.392140	+	0.919906i	$0.371735\pi$
$48$	−1.46154e17	+	4.90474e17i	−0.324922	+	1.09039i
$49$	1.04370e18			1.86860
$50$	−1.07041e18	−	7.76355e16i	−1.55012	−	0.112428i
$51$			4.31864e17i			0.507996i
$52$	1.76713e17	−	1.21182e18i	0.169525	−	1.16253i
$53$		−	3.04645e17i		−	0.239275i	−0.992818	−	0.119638i	$-0.961827\pi$
$53$		−	3.04645e17i		−	0.239275i	0.992818	−	0.119638i	$-0.0381733\pi$
$54$	−8.99582e16	+	1.24031e18i	−0.0580639	+	0.800563i
$55$	1.26308e18			0.672391
$56$	−3.75391e18	−	8.28441e17i	−1.65390	−	0.364995i
$57$	−1.61968e18			−0.592576
$58$	−4.15486e17	+	5.72857e18i	−0.126638	+	1.74603i
$59$		−	2.15723e18i		−	0.549477i	−0.961519	−	0.274739i	$-0.911409\pi$
$59$		−	2.15723e18i		−	0.549477i	0.961519	−	0.274739i	$-0.0885913\pi$
$60$	−8.42755e18	−	1.22895e18i	−1.79934	−	0.262388i
$61$		−	4.15297e18i		−	0.745410i	−0.927950	−	0.372705i	$-0.878430\pi$
$61$		−	4.15297e18i		−	0.745410i	0.927950	−	0.372705i	$-0.121570\pi$
$62$	−8.64915e18	−	6.27313e17i	−1.30876	−	0.0949230i
$63$	3.89977e18			0.498843
$64$	8.36668e18	+	3.88191e18i	0.907118	+	0.420877i
$65$	2.03793e19			1.87758
$66$	6.08307e18	+	4.41198e17i	0.477432	+	0.0346276i
$67$			2.12477e19i			1.42405i	0.702152	+	0.712027i	$0.252223\pi$
$67$			2.12477e19i			1.42405i	−0.702152	+	0.712027i	$0.747777\pi$
$68$	7.70157e18	+	1.12308e18i	0.441810	+	0.0644268i
$69$			7.25533e17i			0.0357061i
$70$	4.62767e18	−	6.38046e19i	0.195809	−	2.69974i
$71$	1.05682e19			0.385290			0.192645	−	0.981269i	$-0.438293\pi$
$71$	1.05682e19			0.385290			0.192645	+	0.981269i	$0.438293\pi$
$72$	−9.13678e18	−	2.01638e18i	−0.287609	−	0.0634717i
$73$	1.19343e19			0.325018			0.162509	−	0.986707i	$-0.448041\pi$
$73$	1.19343e19			0.325018			0.162509	+	0.986707i	$0.448041\pi$
$74$	−3.84708e18	+	5.30420e19i	−0.0908234	+	1.25224i
$75$		−	8.62388e19i		−	1.76832i
$76$	−4.21204e18	+	2.88843e19i	−0.0751536	+	0.515370i
$77$			4.58124e19i			0.712575i
$78$	9.81481e19	+	7.11857e18i	1.33318	+	0.0966940i
$79$	−1.10112e20			−1.30843			−0.654213	−	0.756310i	$-0.727000\pi$
$79$	−1.10112e20			−1.30843			−0.654213	+	0.756310i	$0.727000\pi$
$80$	−4.38323e19	+	1.47095e20i	−0.456404	+	1.53163i
$81$	−1.32154e20			−1.20778
$82$	6.24465e19	+	4.52917e18i	0.501721	+	0.0363893i
$83$		−	4.07937e19i		−	0.288585i	−0.989535	−	0.144292i	$-0.953909\pi$
$83$		−	4.07937e19i		−	0.288585i	0.989535	−	0.144292i	$-0.0460906\pi$
$84$	4.45744e19	−	3.05671e20i	0.278069	−	1.90687i
$85$			1.29518e20i			0.713561i
$86$	−1.63248e18	+	2.25080e19i	−0.00795453	+	0.109674i
$87$	−4.61530e20			−1.99181
$88$	2.36873e19	−	1.07334e20i	0.0906665	−	0.410836i
$89$	3.12189e20			1.06126			0.530630	−	0.847603i	$-0.321955\pi$
$89$	3.12189e20			1.06126			0.530630	+	0.847603i	$0.321955\pi$
$90$	1.12635e19	−	1.55297e20i	0.0340507	−	0.469478i
$91$			7.39166e20i			1.98979i
$92$	1.29387e19	+	1.88678e18i	0.0310540	+	0.00452844i
$93$		−	6.96830e20i		−	1.49299i
$94$	4.08483e20	+	2.96268e19i	0.782225	+	0.0567339i
$95$	−4.85749e20			−0.832366
$96$	−2.62481e20	+	6.93110e20i	−0.402948	+	1.06403i
$97$	−3.40413e20			−0.468709			−0.234355	−	0.972151i	$-0.575298\pi$
$97$	−3.40413e20			−0.468709			−0.234355	+	0.972151i	$0.575298\pi$
$98$	1.50748e21	+	1.09336e20i	1.86371	+	0.135173i
$99$			1.11505e20i			0.123915i
$100$	−1.53792e21	−	2.24267e20i	−1.53792	−	0.224267i
$101$		−	6.23301e20i		−	0.561466i	−0.959786	−	0.280733i	$-0.909423\pi$
$101$		−	6.23301e20i		−	0.561466i	0.959786	−	0.280733i	$-0.0905775\pi$
$102$	−4.52412e19	+	6.23768e20i	−0.0367478	+	0.506665i
$103$	4.80970e20			0.352637			0.176318	−	0.984333i	$-0.443581\pi$
$103$	4.80970e20			0.352637			0.176318	+	0.984333i	$0.443581\pi$
$104$	3.82185e20	−	1.73179e21i	0.253177	−	1.14722i
$105$	5.14050e21			3.07977
$106$	3.19140e19	−	4.40018e20i	0.0173089	−	0.238648i
$107$		−	2.85277e21i		−	1.40196i	−0.713180	−	0.700981i	$-0.752746\pi$
$107$		−	2.85277e21i		−	1.40196i	0.713180	−	0.700981i	$-0.247254\pi$
$108$	−2.59864e20	+	1.78203e21i	−0.115824	+	0.794266i
$109$			3.01847e21i			1.22126i	0.791915	+	0.610632i	$0.209084\pi$
$109$			3.01847e21i			1.22126i	−0.791915	+	0.610632i	$0.790916\pi$
$110$	1.82434e21	+	1.32317e20i	0.670629	+	0.0486399i
$111$	−4.27340e21			−1.42851
$112$	−5.33521e21	−	1.58982e21i	−1.62316	−	0.483680i
$113$	3.95772e21			1.09678			0.548392	−	0.836221i	$-0.315240\pi$
$113$	3.95772e21			1.09678			0.548392	+	0.836221i	$0.315240\pi$
$114$	−2.33941e21	−	1.69674e20i	−0.591023	−	0.0428662i
$115$			2.17590e20i			0.0501548i
$116$	−1.20022e21	+	8.23059e21i	−0.252612	+	1.73230i
$117$			1.79909e21i			0.346019i
$118$	2.25986e20	−	3.11581e21i	0.0397485	−	0.548038i
$119$	−4.69768e21			−0.756206
$120$	−1.20437e22	−	2.65789e21i	−1.77565	−	0.391863i
$121$	6.09035e21			0.822993
$122$	4.35056e20	−	5.99839e21i	0.0539221	−	0.743458i
$123$			5.03108e21i			0.572345i
$124$	−1.24268e22	−	1.81213e21i	−1.29847	−	0.189349i
$125$		−	9.22230e21i		−	0.885695i
$126$	5.63268e21	+	4.08532e20i	0.497536	+	0.0360857i
$127$	−2.93164e20			−0.0238326			−0.0119163	−	0.999929i	$-0.503793\pi$
$127$	−2.93164e20			−0.0238326			−0.0119163	+	0.999929i	$0.503793\pi$
$128$	1.16778e22	+	6.48335e21i	0.874295	+	0.485395i
$129$	−1.81339e21			−0.125112
$130$	2.94350e22	+	2.13489e21i	1.87266	+	0.135822i
$131$			8.08973e21i			0.474882i	0.971402	+	0.237441i	$0.0763086\pi$
$131$			8.08973e21i			0.474882i	−0.971402	+	0.237441i	$0.923691\pi$
$132$	8.73993e21	+	1.27450e21i	0.473677	+	0.0690738i
$133$		−	1.76184e22i		−	0.882111i
$134$	−2.22586e21	+	3.06893e22i	−0.103014	+	1.42032i
$135$	−2.99686e22			−1.28281
$136$	1.10062e22	+	2.42893e21i	0.435992	+	0.0962180i
$137$	5.33440e22			1.95668			0.978341	−	0.207002i	$-0.0663707\pi$
$137$	5.33440e22			1.95668			0.978341	+	0.207002i	$0.0663707\pi$
$138$	−7.60053e19	+	1.04793e21i	−0.00258293	+	0.0356125i
$139$		−	3.30872e22i		−	1.04233i	−0.853456	−	0.521164i	$-0.825498\pi$
$139$		−	3.30872e22i		−	1.04233i	0.853456	−	0.521164i	$-0.174502\pi$
$140$	1.33681e22	−	9.16721e22i	0.390592	−	2.67851i
$141$			3.29100e22i			0.892333i
$142$	1.52643e22	+	1.10710e21i	0.384280	+	0.0278714i
$143$	−2.11347e22			−0.494273
$144$	−1.29856e22	−	3.86952e21i	−0.282264	−	0.0841107i
$145$	−1.38415e23			−2.79781
$146$	1.72375e22	+	1.25021e21i	0.324167	+	0.0235115i
$147$			1.21452e23i			2.12605i
$148$	−1.11131e22	+	7.62088e22i	−0.181171	+	1.24239i
$149$			4.27336e22i			0.649103i	0.945868	+	0.324551i	$0.105213\pi$
$149$			4.27336e22i			0.649103i	−0.945868	+	0.324551i	$0.894787\pi$
$150$	9.03419e21	−	1.24560e23i	0.127918	−	1.76368i
$151$	4.47213e22			0.590550			0.295275	−	0.955412i	$-0.404589\pi$
$151$	4.47213e22			0.590550			0.295275	+	0.955412i	$0.404589\pi$
$152$	−9.10956e21	+	4.12781e22i	−0.112238	+	0.508583i
$153$	−1.14339e22			−0.131502
$154$	−4.79921e21	+	6.61696e22i	−0.0515468	+	0.710708i
$155$		−	2.08982e23i		−	2.09714i
$156$	1.41016e23	+	2.05636e22i	1.32269	+	0.192881i
$157$		−	1.28304e23i		−	1.12536i	−0.826673	−	0.562682i	$-0.809769\pi$
$157$		−	1.28304e23i		−	1.12536i	0.826673	−	0.562682i	$-0.190231\pi$
$158$	−1.59041e23	−	1.15351e22i	−1.30500	−	0.0946500i
$159$	3.54506e22			0.272241
$160$	−7.87190e22	+	2.07867e23i	−0.566004	+	1.49460i
$161$	−7.89211e21			−0.0531522
$162$	−1.90878e23	−	1.38442e22i	−1.20462	−	0.0873695i
$163$			4.69745e22i			0.277902i	0.990299	+	0.138951i	$0.0443731\pi$
$163$			4.69745e22i			0.277902i	−0.990299	+	0.138951i	$0.955627\pi$
$164$	8.97208e22	+	1.30835e22i	0.497775	+	0.0725879i
$165$			1.46980e23i			0.765028i
$166$	4.27346e21	−	5.89209e22i	0.0208759	−	0.287829i
$167$	2.00344e23			0.918870			0.459435	−	0.888211i	$-0.348052\pi$
$167$	2.00344e23			0.918870			0.459435	+	0.888211i	$0.348052\pi$
$168$	9.64030e22	−	4.36830e23i	0.415282	−	1.88176i
$169$	−9.39356e22			−0.380207
$170$	−1.35680e22	+	1.87071e23i	−0.0516182	+	0.711692i
$171$		−	4.28821e22i		−	0.153397i
$172$	−4.71578e21	+	3.23387e22i	−0.0158674	+	0.108811i
$173$			2.89286e23i			0.915889i	0.888981	+	0.457944i	$0.151414\pi$
$173$			2.89286e23i			0.915889i	−0.888981	+	0.457944i	$0.848586\pi$
$174$	−6.66615e23	−	4.83488e22i	−1.98659	−	0.144085i
$175$	9.38077e23			2.63232
$176$	4.54570e22	−	1.52547e23i	0.120148	−	0.403201i
$177$	2.51030e23			0.625181
$178$	4.50913e23	+	3.27042e22i	1.05848	+	0.0767703i
$179$			1.16861e23i			0.258651i	0.991602	+	0.129325i	$0.0412811\pi$
$179$			1.16861e23i			0.258651i	−0.991602	+	0.129325i	$0.958719\pi$
$180$	3.25371e22	−	2.23124e23i	0.0679230	−	0.465785i
$181$		−	6.16947e23i		−	1.21513i	−0.794270	−	0.607565i	$-0.792146\pi$
$181$		−	6.16947e23i		−	1.21513i	0.794270	−	0.607565i	$-0.207854\pi$
$182$	−7.74334e22	+	1.06762e24i	−0.143939	+	1.98458i
$183$	4.83268e23			0.848108
$184$	1.84904e22	+	4.08061e21i	0.0306450	+	0.00676298i
$185$	−1.28161e24			−2.00656
$186$	7.29984e22	−	1.00647e24i	0.108001	−	1.48908i
$187$		−	1.34319e23i		−	0.187845i
$188$	5.86893e23	+	8.55836e22i	0.776071	+	0.113170i
$189$		−	1.08697e24i		−	1.35947i
$190$	−7.01597e23	−	5.08860e22i	−0.830186	−	0.0602124i
$191$	−1.50576e24			−1.68618			−0.843091	−	0.537771i	$-0.819267\pi$
$191$	−1.50576e24			−1.68618			−0.843091	+	0.537771i	$0.819267\pi$
$192$	−4.51725e23	+	9.73604e23i	−0.478863	+	1.03209i
$193$	8.19140e23			0.822255			0.411127	−	0.911578i	$-0.365135\pi$
$193$	8.19140e23			0.822255			0.411127	+	0.911578i	$0.365135\pi$
$194$	−4.91680e23	−	3.56610e22i	−0.467481	−	0.0339059i
$195$			2.37147e24i			2.13626i
$196$	2.16589e24	+	3.15841e23i	1.84905	+	0.269637i
$197$			1.76115e24i			1.42528i	0.701530	+	0.712640i	$0.252501\pi$
$197$			1.76115e24i			1.42528i	−0.701530	+	0.712640i	$0.747499\pi$
$198$	−1.16810e22	+	1.61053e23i	−0.00896386	+	0.123590i
$199$	−1.06899e24			−0.778067			−0.389033	−	0.921224i	$-0.627191\pi$
$199$	−1.06899e24			−0.778067			−0.389033	+	0.921224i	$0.627191\pi$
$200$	−2.19782e24	−	4.85032e23i	−1.51767	−	0.334931i
$201$	−2.47253e24			−1.62025
$202$	6.52956e22	−	9.00271e23i	0.0406158	−	0.559995i
$203$		−	5.02036e24i		−	2.96501i
$204$	−1.30689e23	+	8.96207e23i	−0.0733031	+	0.502680i
$205$			1.50884e24i			0.803949i
$206$	6.94694e23	+	5.03854e22i	0.351713	+	0.0255093i
$207$	−1.92089e22			−0.00924303
$208$	7.33432e23	−	2.46130e24i	0.335502	−	1.12590i
$209$	5.03755e23			0.219121
$210$	7.42474e24	+	5.38507e23i	3.07170	+	0.222787i
$211$			1.29339e24i			0.509056i	0.967065	+	0.254528i	$0.0819200\pi$
$211$			1.29339e24i			0.509056i	−0.967065	+	0.254528i	$0.918080\pi$
$212$	9.21905e22	−	6.32201e23i	0.0345271	−	0.236771i
$213$			1.22978e24i			0.438372i
$214$	2.98849e23	−	4.12042e24i	0.101416	−	1.39829i
$215$	−5.43843e23			−0.175740
$216$	−5.62019e23	+	2.54667e24i	−0.172976	+	0.783806i
$217$	7.57989e24			2.22247
$218$	−3.16209e23	+	4.35977e24i	−0.0883447	+	1.21806i
$219$			1.38876e24i			0.369798i
$220$	2.62114e24	+	3.82227e23i	0.665353	+	0.0970250i
$221$		−	2.16718e24i		−	0.524538i
$222$	−6.17233e24	−	4.47672e23i	−1.42476	−	0.103337i
$223$	−4.03079e24			−0.887543			−0.443771	−	0.896140i	$-0.646360\pi$
$223$	−4.03079e24			−0.887543			−0.443771	+	0.896140i	$0.646360\pi$
$224$	−7.53942e24	−	2.85518e24i	−1.58392	−	0.599831i
$225$	2.28322e24			0.457754
$226$	5.71637e24	+	4.14602e23i	1.09391	+	0.0793401i
$227$			7.81965e23i			0.142862i	0.997446	+	0.0714309i	$0.0227565\pi$
$227$			7.81965e23i			0.142862i	−0.997446	+	0.0714309i	$0.977243\pi$
$228$	−3.36117e24	−	4.90142e23i	−0.586374	−	0.0855079i
$229$		−	8.55580e24i		−	1.42557i	−0.701384	−	0.712784i	$-0.747434\pi$
$229$		−	8.55580e24i		−	1.42557i	0.701384	−	0.712784i	$-0.252566\pi$
$230$	−2.27943e22	+	3.14279e23i	−0.00362814	+	0.0500234i
$231$	−5.33104e24			−0.810749
$232$	−2.59578e24	+	1.17622e25i	−0.377262	+	1.70948i
$233$	3.05921e24			0.424983			0.212491	−	0.977163i	$-0.431842\pi$
$233$	3.05921e24			0.424983			0.212491	+	0.977163i	$0.431842\pi$
$234$	−1.88468e23	+	2.59853e24i	−0.0250306	+	0.345113i
$235$			9.86984e24i			1.25342i
$236$	6.52812e23	−	4.47669e24i	0.0792888	−	0.543727i
$237$		−	1.28134e25i		−	1.48869i
$238$	−6.78514e24	−	4.92118e23i	−0.754224	−	0.0547030i
$239$	5.15515e24			0.548357			0.274178	−	0.961679i	$-0.411594\pi$
$239$	5.15515e24			0.548357			0.274178	+	0.961679i	$0.411594\pi$
$240$	−1.71170e25	−	5.10062e24i	−1.74265	−	0.519284i
$241$	6.86441e24			0.668997			0.334499	−	0.942396i	$-0.391433\pi$
$241$	6.86441e24			0.668997			0.334499	+	0.942396i	$0.391433\pi$
$242$	8.79667e24	+	6.38012e23i	0.820837	+	0.0595343i
$243$		−	6.39579e24i		−	0.571516i
$244$	1.25676e24	−	8.61826e24i	0.107562	−	0.737609i
$245$			3.64240e25i			2.98637i
$246$	−5.27045e23	+	7.26670e24i	−0.0414028	+	0.570846i
$247$	8.12789e24			0.611871
$248$	−1.77589e25	−	3.91918e24i	−1.28137	−	0.282782i
$249$	4.74704e24			0.328344
$250$	9.66108e23	−	1.33203e25i	0.0640701	−	0.883374i
$251$		−	8.35468e23i		−	0.0531319i	−0.999647	−	0.0265660i	$-0.991543\pi$
$251$		−	8.35468e23i		−	0.0531319i	0.999647	−	0.0265660i	$-0.00845720\pi$
$252$	8.09283e24	+	1.18013e24i	0.493622	+	0.0719823i
$253$		−	2.25656e23i		−	0.0132033i
$254$	−4.23435e23	−	3.07112e22i	−0.0237702	−	0.00172402i
$255$	−1.50716e25			−0.811871
$256$	1.61878e25	+	1.05876e25i	0.836892	+	0.547368i
$257$	−1.18113e25			−0.586140			−0.293070	−	0.956091i	$-0.594677\pi$
$257$	−1.18113e25			−0.586140			−0.293070	+	0.956091i	$0.594677\pi$
$258$	−2.61919e24	−	1.89967e23i	−0.124784	−	0.00905046i
$259$		−	4.64846e25i		−	2.12648i
$260$	4.22912e25	+	6.16710e24i	1.85793	+	0.270932i
$261$		−	1.22193e25i		−	0.515608i
$262$	−8.47463e23	+	1.16845e25i	−0.0343524	+	0.473638i
$263$	−1.55635e25			−0.606138			−0.303069	−	0.952969i	$-0.598011\pi$
$263$	−1.55635e25			−0.606138			−0.303069	+	0.952969i	$0.598011\pi$
$264$	1.24901e25	+	2.75641e24i	0.467439	+	0.103158i
$265$	1.06318e25			0.382406
$266$	1.84566e24	−	2.54473e25i	0.0638109	−	0.879800i
$267$			3.63284e25i			1.20747i
$268$	−6.42990e24	+	4.40933e25i	−0.205489	+	1.40915i
$269$		−	3.30880e25i		−	1.01689i	−0.861096	−	0.508443i	$-0.830221\pi$
$269$		−	3.30880e25i		−	1.01689i	0.861096	−	0.508443i	$-0.169779\pi$
$270$	−4.32854e25	−	3.13944e24i	−1.27945	−	0.0927968i
$271$	5.93487e25			1.68746			0.843731	−	0.536767i	$-0.180355\pi$
$271$	5.93487e25			1.68746			0.843731	+	0.536767i	$0.180355\pi$
$272$	1.56425e25	+	4.66123e24i	0.427889	+	0.127505i
$273$	−8.60144e25			−2.26393
$274$	7.70480e25	+	5.58821e24i	1.95155	+	0.141544i
$275$			2.68221e25i			0.653881i
$276$	−2.19558e23	+	1.50563e24i	−0.00515234	+	0.0353324i
$277$			7.26699e25i			1.64179i	0.571080	+	0.820894i	$0.306525\pi$
$277$			7.26699e25i			1.64179i	−0.571080	+	0.820894i	$0.693475\pi$
$278$	3.46614e24	−	4.77899e25i	0.0754008	−	1.03960i
$279$	1.84490e25			0.386481
$280$	2.89117e25	−	1.31007e26i	0.583329	−	2.64323i
$281$	−4.74175e25			−0.921557			−0.460778	−	0.887515i	$-0.652430\pi$
$281$	−4.74175e25			−0.921557			−0.460778	+	0.887515i	$0.652430\pi$
$282$	−3.44758e24	+	4.75339e25i	−0.0645503	+	0.889995i
$283$			3.08734e25i			0.556964i	0.960441	+	0.278482i	$0.0898312\pi$
$283$			3.08734e25i			0.556964i	−0.960441	+	0.278482i	$0.910169\pi$
$284$	2.19311e25	+	3.19810e24i	0.381257	+	0.0555968i
$285$		−	5.65251e25i		−	0.947045i
$286$	−3.05261e25	−	2.21402e24i	−0.492978	−	0.0357551i
$287$	−5.47264e25			−0.851996
$288$	−1.83505e25	−	6.94933e24i	−0.275440	−	0.104309i
$289$	−5.53187e25			−0.800653
$290$	−1.99921e26	−	1.45000e25i	−2.79048	−	0.202390i
$291$		−	3.96128e25i		−	0.533285i
$292$	2.47662e25	+	3.61152e24i	0.321617	+	0.0468997i
$293$			1.20855e25i			0.151410i	0.997130	+	0.0757050i	$0.0241207\pi$
$293$			1.20855e25i			0.151410i	−0.997130	+	0.0757050i	$0.975879\pi$
$294$	−1.27231e25	+	1.75421e26i	−0.153796	+	2.12048i
$295$	7.52848e25			0.878165
$296$	−2.40348e25	+	1.08909e26i	−0.270569	+	1.22603i
$297$	3.10794e25			0.337699
$298$	−4.47668e24	+	6.17227e25i	−0.0469553	+	0.647402i
$299$		−	3.64087e24i		−	0.0368687i
$300$	2.60973e25	−	1.78963e26i	0.255165	−	1.74981i
$301$		−	1.97254e25i		−	0.186242i
$302$	6.45937e25	+	4.68491e24i	0.589003	+	0.0427197i
$303$	7.25315e25			0.638821
$304$	−1.74817e25	+	5.86661e25i	−0.148734	+	0.499131i
$305$	1.44934e26			1.19130
$306$	−1.65146e25	−	1.19779e24i	−0.131158	−	0.00951271i
$307$		−	1.35933e26i		−	1.04321i	−0.853186	−	0.521607i	$-0.825333\pi$
$307$		−	1.35933e26i		−	1.04321i	0.853186	−	0.521607i	$-0.174667\pi$
$308$	−1.38636e25	+	9.50701e25i	−0.102824	+	0.705117i
$309$			5.59690e25i			0.401221i
$310$	2.18925e25	−	3.01846e26i	0.151704	−	2.09164i
$311$	1.63215e26			1.09339			0.546695	−	0.837332i	$-0.315886\pi$
$311$	1.63215e26			1.09339			0.546695	+	0.837332i	$0.315886\pi$
$312$	2.01523e26	+	4.44737e25i	1.30527	+	0.288058i
$313$	−3.17530e25			−0.198870			−0.0994349	−	0.995044i	$-0.531703\pi$
$313$	−3.17530e25			−0.198870			−0.0994349	+	0.995044i	$0.531703\pi$
$314$	1.34408e25	−	1.85317e26i	0.0814075	−	1.12242i
$315$			1.36098e26i			0.797242i
$316$	−2.28504e26	−	3.33216e25i	−1.29473	−	0.188804i
$317$		−	2.32784e26i		−	1.27594i	−0.770061	−	0.637971i	$-0.779774\pi$
$317$		−	2.32784e26i		−	1.27594i	0.770061	−	0.637971i	$-0.220226\pi$
$318$	5.12034e25	+	3.71373e24i	0.271528	+	0.0196936i
$319$	1.43545e26			0.736523
$320$	−1.35474e26	+	2.91988e26i	−0.672639	+	1.44974i
$321$	3.31967e26			1.59512
$322$	−1.13991e25	−	8.26760e23i	−0.0530130	−	0.00384497i
$323$			5.16558e25i			0.232537i
$324$	−2.74247e26	−	3.99920e25i	−1.19514	−	0.174281i
$325$			4.32764e26i			1.82590i
$326$	−4.92094e24	+	6.78481e25i	−0.0201031	+	0.277174i
$327$	−3.51250e26			−1.38952
$328$	1.28219e26	+	2.82963e25i	0.491220	+	0.108406i
$329$	−3.57984e26			−1.32833
$330$	−1.53973e25	+	2.12292e26i	−0.0553412	+	0.763024i
$331$		−	3.56656e26i		−	1.24181i	−0.783885	−	0.620906i	$-0.786765\pi$
$331$		−	3.56656e26i		−	1.24181i	0.783885	−	0.620906i	$-0.213235\pi$
$332$	1.23448e25	−	8.46553e25i	0.0416424	−	0.285565i
$333$		−	1.13141e26i		−	0.369790i
$334$	2.89369e26	+	2.09876e25i	0.916462	+	0.0664700i
$335$	−7.41521e26			−2.27590
$336$	1.85002e26	−	6.20841e26i	0.550319	−	1.84679i
$337$	4.72337e26			1.36188			0.680938	−	0.732341i	$-0.261572\pi$
$337$	4.72337e26			1.36188			0.680938	+	0.732341i	$0.261572\pi$
$338$	−1.35677e26	−	9.84049e24i	−0.379211	−	0.0275037i
$339$			4.60547e26i			1.24789i
$340$	−3.91942e25	+	2.68776e26i	−0.102966	+	0.706093i
$341$			2.16729e26i			0.552071i
$342$	4.49223e24	−	6.19372e25i	0.0110965	−	0.152995i
$343$	−6.14109e26			−1.47115
$344$	−1.01990e25	+	4.62147e25i	−0.0236971	+	0.107378i
$345$	−2.53203e25			−0.0570648
$346$	−3.03049e25	+	4.17833e26i	−0.0662543	+	0.913489i
$347$		−	2.88810e26i		−	0.612566i	−0.951940	−	0.306283i	$-0.900915\pi$
$347$		−	2.88810e26i		−	0.612566i	0.951940	−	0.306283i	$-0.0990854\pi$
$348$	−9.57768e26	−	1.39666e26i	−1.97096	−	0.287415i
$349$		−	6.64002e26i		−	1.32587i	−0.748675	−	0.662937i	$-0.769310\pi$
$349$		−	6.64002e26i		−	1.32587i	0.748675	−	0.662937i	$-0.230690\pi$
$350$	1.35492e27	+	9.82709e25i	2.62543	+	0.190419i
$351$	5.01455e26			0.942990
$352$	8.16369e25	−	2.15572e26i	0.149001	−	0.393454i
$353$	−5.10078e26			−0.903655			−0.451827	−	0.892105i	$-0.649228\pi$
$353$	−5.10078e26			−0.903655			−0.451827	+	0.892105i	$0.649228\pi$
$354$	3.62577e26	+	2.62973e25i	0.623543	+	0.0452248i
$355$			3.68818e26i			0.615763i
$356$	6.47855e26	+	9.44733e25i	1.05015	+	0.153138i
$357$		−	5.46653e26i		−	0.860391i
$358$	−1.22421e25	+	1.68790e26i	−0.0187105	+	0.257973i
$359$	1.14599e26			0.170095			0.0850474	−	0.996377i	$-0.472896\pi$
$359$	1.14599e26			0.170095			0.0850474	+	0.996377i	$0.472896\pi$
$360$	7.03693e25	−	3.18864e26i	0.101439	−	0.459651i
$361$	5.20477e26			0.728746
$362$	6.46300e25	−	8.91094e26i	0.0879011	−	1.21195i
$363$			7.08715e26i			0.936380i
$364$	−2.23684e26	+	1.53392e27i	−0.287124	+	1.96897i
$365$			4.16495e26i			0.519439i
$366$	6.98013e26	+	5.06261e25i	0.845886	+	0.0613512i
$367$	−1.17521e27			−1.38395			−0.691976	−	0.721920i	$-0.743260\pi$
$367$	−1.17521e27			−1.38395			−0.691976	+	0.721920i	$0.743260\pi$
$368$	2.62794e25	+	7.83089e24i	0.0300755	+	0.00896208i
$369$	−1.33201e26			−0.148160
$370$	−1.85111e27	−	1.34259e26i	−2.00131	−	0.145152i
$371$			3.85620e26i			0.405259i
$372$	2.10872e26	−	1.44606e27i	0.215436	−	1.47736i
$373$			6.90947e26i			0.686281i	0.939284	+	0.343141i	$0.111491\pi$
$373$			6.90947e26i			0.686281i	−0.939284	+	0.343141i	$0.888509\pi$
$374$	1.40709e25	−	1.94005e26i	0.0135885	−	0.187353i
$375$	1.07317e27			1.00772
$376$	8.38720e26	+	1.85095e26i	0.765852	+	0.169014i
$377$	2.31605e27			2.05666
$378$	1.13869e26	−	1.56998e27i	0.0983426	−	1.35591i
$379$		−	2.25252e27i		−	1.89216i	−0.323938	−	0.946078i	$-0.605007\pi$
$379$		−	2.25252e27i		−	1.89216i	0.323938	−	0.946078i	$-0.394993\pi$
$380$	−1.00803e27	−	1.46996e26i	−0.823655	−	0.120109i
$381$		−	3.41146e25i		−	0.0271161i
$382$	−2.17486e27	−	1.57740e26i	−1.68176	−	0.121976i
$383$	1.60978e27			1.21110			0.605549	−	0.795808i	$-0.292953\pi$
$383$	1.60978e27			1.21110			0.605549	+	0.795808i	$0.292953\pi$
$384$	−7.54447e26	+	1.35891e27i	−0.552269	+	0.994750i
$385$	−1.59880e27			−1.13882
$386$	1.18313e27	+	8.58113e25i	0.820101	+	0.0594810i
$387$		−	4.80106e25i		−	0.0323871i
$388$	−7.06427e26	−	1.03015e26i	−0.463804	−	0.0676341i
$389$			1.52357e27i			0.973627i	0.873506	+	0.486814i	$0.161841\pi$
$389$			1.52357e27i			0.973627i	−0.873506	+	0.486814i	$0.838159\pi$
$390$	−2.48430e26	+	3.42526e27i	−0.154535	+	2.13067i
$391$	2.31391e25			0.0140117
$392$	3.09524e27	+	6.83082e26i	1.82470	+	0.402688i
$393$	−9.41376e26			−0.540308
$394$	−1.84494e26	+	2.54373e27i	−0.103103	+	1.42155i
$395$		−	3.84278e27i		−	2.09111i
$396$	−3.37431e25	+	2.31395e26i	−0.0178807	+	0.122618i
$397$			4.24807e26i			0.219225i	0.993974	+	0.109613i	$0.0349611\pi$
$397$			4.24807e26i			0.219225i	−0.993974	+	0.109613i	$0.965039\pi$
$398$	−1.54401e27	−	1.11985e26i	−0.776028	−	0.0562844i
$399$	2.05019e27			1.00364
$400$	−3.12364e27	−	9.30800e26i	−1.48947	−	0.443840i
$401$	−2.90975e27			−1.35157			−0.675787	−	0.737097i	$-0.736196\pi$
$401$	−2.90975e27			−1.35157			−0.675787	+	0.737097i	$0.736196\pi$
$402$	−3.57122e27	−	2.59016e26i	−1.61601	−	0.117207i
$403$			3.49684e27i			1.54160i
$404$	1.88621e26	−	1.29348e27i	0.0810187	−	0.555590i
$405$		−	4.61204e27i		−	1.93026i
$406$	5.25922e26	−	7.25121e27i	0.214486	−	2.95725i
$407$	1.32912e27			0.528228
$408$	−2.82647e26	+	1.28075e27i	−0.109474	+	0.496060i
$409$	−1.94788e27			−0.735304			−0.367652	−	0.929963i	$-0.619838\pi$
$409$	−1.94788e27			−0.735304			−0.367652	+	0.929963i	$0.619838\pi$
$410$	−1.58063e26	+	2.17931e27i	−0.0581567	+	0.801843i
$411$			6.20748e27i			2.22626i
$412$	9.98111e26	+	1.45549e26i	0.348946	+	0.0508850i
$413$			2.73062e27i			0.930647i
$414$	−2.77446e25	−	2.01228e24i	−0.00921882	−	0.000668630i
$415$	1.42366e27			0.461211
$416$	1.31718e27	−	3.47817e27i	0.416069	−	1.09868i
$417$	3.85025e27			1.18593
$418$	7.27603e26	+	5.27722e25i	0.218546	+	0.0158509i
$419$		−	1.80593e27i		−	0.528997i	−0.964386	−	0.264498i	$-0.914794\pi$
$419$		−	1.80593e27i		−	0.528997i	0.964386	−	0.264498i	$-0.0852064\pi$
$420$	1.06676e28	+	1.55560e27i	3.04753	+	0.444406i
$421$		−	1.98240e27i		−	0.552370i	−0.961105	−	0.276185i	$-0.910930\pi$
$421$		−	1.98240e27i		−	0.552370i	0.961105	−	0.276185i	$-0.0890702\pi$
$422$	−1.35493e26	+	1.86813e27i	−0.0368245	+	0.507722i
$423$	−8.71311e26			−0.230993
$424$	1.99384e26	−	9.03468e26i	0.0515643	−	0.233653i
$425$	−2.75038e27			−0.693918
$426$	−1.28830e26	+	1.77625e27i	−0.0317113	+	0.437224i
$427$			5.25682e27i			1.26250i
$428$	8.63293e26	−	5.92007e27i	0.202301	−	1.38729i
$429$		−	2.45937e27i		−	0.562371i
$430$	−7.85505e26	−	5.69718e25i	−0.175279	−	0.0127128i
$431$	−5.89168e27			−1.28300			−0.641501	−	0.767122i	$-0.721688\pi$
$431$	−5.89168e27			−1.28300			−0.641501	+	0.767122i	$0.721688\pi$
$432$	−1.07854e27	+	3.61944e27i	−0.229223	+	0.769240i
$433$	−2.46636e27			−0.511604			−0.255802	−	0.966729i	$-0.582340\pi$
$433$	−2.46636e27			−0.511604			−0.255802	+	0.966729i	$0.582340\pi$
$434$	1.09481e28	+	7.94052e26i	2.21665	+	0.160771i
$435$		−	1.61069e28i		−	3.18327i
$436$	−9.13439e26	+	6.26395e27i	−0.176227	+	1.20848i
$437$			8.67819e25i			0.0163446i
$438$	−1.45483e26	+	2.00587e27i	−0.0267507	+	0.368829i
$439$	9.97270e27			1.79034			0.895170	−	0.445726i	$-0.147054\pi$
$439$	9.97270e27			1.79034			0.895170	+	0.445726i	$0.147054\pi$
$440$	3.74583e27	+	8.26659e26i	0.656592	+	0.144902i
$441$	−3.21552e27			−0.550359
$442$	2.27029e26	−	3.13019e27i	0.0379444	−	0.523163i
$443$			2.72703e27i			0.445092i	0.974922	+	0.222546i	$0.0714368\pi$
$443$			2.72703e27i			0.445092i	−0.974922	+	0.222546i	$0.928563\pi$
$444$	−8.86818e27	−	1.29320e27i	−1.41356	−	0.206132i
$445$			1.08950e28i			1.69609i
$446$	−5.82192e27	−	4.22257e26i	−0.885217	−	0.0642038i
$447$	−4.97277e27			−0.738532
$448$	−1.05905e28	−	4.91372e27i	−1.53638	−	0.712838i
$449$	−5.09946e27			−0.722665			−0.361333	−	0.932437i	$-0.617678\pi$
$449$	−5.09946e27			−0.722665			−0.361333	+	0.932437i	$0.617678\pi$
$450$	3.29780e27	+	2.39186e26i	0.456555	+	0.0331134i
$451$		−	1.56477e27i		−	0.211640i
$452$	8.21307e27	+	1.19767e27i	1.08531	+	0.158264i
$453$			5.20408e27i			0.671912i
$454$	−8.19170e25	+	1.12944e27i	−0.0103345	+	0.142487i
$455$	−2.57961e28			−3.18005
$456$	−4.80340e27	−	1.06005e27i	−0.578652	−	0.127701i
$457$	9.11592e27			1.07320			0.536600	−	0.843837i	$-0.319709\pi$
$457$	9.11592e27			1.07320			0.536600	+	0.843837i	$0.319709\pi$
$458$	8.96286e26	−	1.23577e28i	0.103124	−	1.42183i
$459$			3.18693e27i			0.358377i
$460$	−6.58464e25	+	4.51545e26i	−0.00723727	+	0.0496299i
$461$			3.48173e27i			0.374055i	0.982355	+	0.187027i	$0.0598853\pi$
$461$			3.48173e27i			0.374055i	−0.982355	+	0.187027i	$0.940115\pi$
$462$	−7.69995e27	−	5.58468e26i	−0.808625	−	0.0586486i
$463$	4.82435e27			0.495266			0.247633	−	0.968854i	$-0.420347\pi$
$463$	4.82435e27			0.495266			0.247633	+	0.968854i	$0.420347\pi$
$464$	−4.98142e27	+	1.67169e28i	−0.499936	+	1.67771i
$465$	2.43186e28			2.38607
$466$	4.41860e27	+	3.20476e26i	0.423869	+	0.0307428i
$467$			1.47014e28i			1.37890i	0.724335	+	0.689448i	$0.242147\pi$
$467$			1.47014e28i			1.37890i	−0.724335	+	0.689448i	$0.757853\pi$
$468$	−5.44433e26	+	3.73347e27i	−0.0499301	+	0.342398i
$469$		−	2.68953e28i		−	2.41191i
$470$	−1.03394e27	+	1.42556e28i	−0.0906711	+	1.25014i
$471$	1.49303e28			1.28041
$472$	1.41186e27	−	6.39756e27i	0.118414	−	0.536566i
$473$	5.64001e26			0.0462635
$474$	1.34230e27	−	1.85071e28i	0.107690	−	1.48479i
$475$		−	1.03151e28i		−	0.809453i
$476$	−9.74863e27	−	1.42159e27i	−0.748291	−	0.109119i
$477$			9.38575e26i			0.0704735i
$478$	7.44590e27	+	5.40042e26i	0.546920	+	0.0396675i
$479$	1.31443e27			0.0944530			0.0472265	−	0.998884i	$-0.484962\pi$
$479$	1.31443e27			0.0944530			0.0472265	+	0.998884i	$0.484962\pi$
$480$	−2.41888e28	−	9.16028e27i	−1.70052	−	0.643985i
$481$	2.14448e28			1.47502
$482$	9.91469e27	+	7.19101e26i	0.667245	+	0.0483945i
$483$		−	9.18380e26i		−	0.0604752i
$484$	1.26387e28	+	1.84304e27i	0.814380	+	0.118757i
$485$		−	1.18801e28i		−	0.749083i
$486$	6.70009e26	−	9.23783e27i	0.0413428	−	0.570019i
$487$	−4.46244e27			−0.269475			−0.134737	−	0.990881i	$-0.543019\pi$
$487$	−4.46244e27			−0.269475			−0.134737	+	0.990881i	$0.543019\pi$
$488$	2.71804e27	−	1.23162e28i	0.160638	−	0.727896i
$489$	−5.46627e27			−0.316190
$490$	−3.81570e27	+	5.26094e28i	−0.216031	+	2.97855i
$491$			1.58826e28i			0.880167i	0.897957	+	0.440084i	$0.145051\pi$
$491$			1.58826e28i			0.880167i	−0.897957	+	0.440084i	$0.854949\pi$
$492$	−1.52249e27	+	1.04405e28i	−0.0825886	+	0.566355i
$493$			1.47194e28i			0.781621i
$494$	1.17396e28	+	8.51460e26i	0.610268	+	0.0442620i
$495$	−3.89139e27			−0.198039
$496$	−2.52397e28	−	7.52109e27i	−1.25756	−	0.374734i
$497$	−1.33772e28			−0.652563
$498$	6.85643e27	+	4.97289e26i	0.327484	+	0.0237520i
$499$		−	1.96729e28i		−	0.920052i	−0.887905	−	0.460026i	$-0.847840\pi$
$499$		−	1.96729e28i		−	0.920052i	0.887905	−	0.460026i	$-0.152160\pi$
$500$	2.79082e27	−	1.91382e28i	0.127805	−	0.876425i
$501$			2.33134e28i			1.04547i
$502$	8.75217e25	−	1.20672e27i	0.00384350	−	0.0529927i
$503$	6.10929e27			0.262740			0.131370	−	0.991333i	$-0.458062\pi$
$503$	6.10929e27			0.262740			0.131370	+	0.991333i	$0.458062\pi$
$504$	1.15653e28	+	2.55233e27i	0.487122	+	0.107502i
$505$	2.17525e28			0.897325
$506$	2.36392e25	−	3.25928e26i	0.000955108	−	0.0131687i
$507$		−	1.09310e28i		−	0.432589i
$508$	−6.08375e26	−	8.87162e25i	−0.0235832	−	0.00343901i
$509$		−	3.64801e28i		−	1.38522i	−0.721312	−	0.692611i	$-0.756460\pi$
$509$		−	3.64801e28i		−	1.38522i	0.721312	−	0.692611i	$-0.243540\pi$
$510$	−2.17688e28	−	1.57887e27i	−0.809744	−	0.0587298i
$511$	−1.51065e28			−0.550482
$512$	2.22719e28	+	1.69882e28i	0.795103	+	0.606474i
$513$	−1.19524e28			−0.418045
$514$	−1.70598e28	−	1.23733e27i	−0.584605	−	0.0424007i
$515$			1.67853e28i			0.563578i
$516$	−3.76315e27	−	5.48761e26i	−0.123803	−	0.0180535i
$517$		−	1.02357e28i		−	0.329964i
$518$	4.86963e27	−	6.71406e28i	0.153827	−	2.12091i
$519$	−3.36632e28			−1.04207
$520$	6.04376e28	+	1.33378e28i	1.83346	+	0.404623i
$521$	−5.93755e28			−1.76527			−0.882636	−	0.470058i	$-0.844233\pi$
$521$	−5.93755e28			−1.76527			−0.882636	+	0.470058i	$0.844233\pi$
$522$	1.28006e27	−	1.76490e28i	0.0372985	−	0.514257i
$523$			1.38164e28i			0.394574i	0.980346	+	0.197287i	$0.0632131\pi$
$523$			1.38164e28i			0.394574i	−0.980346	+	0.197287i	$0.936787\pi$
$524$	−2.44808e27	+	1.67878e28i	−0.0685248	+	0.469912i
$525$			1.09161e29i			2.99499i
$526$	−2.24793e28	−	1.63040e27i	−0.604550	−	0.0438473i
$527$	−2.22237e28			−0.585875
$528$	1.77515e28	+	5.28969e27i	0.458752	+	0.136702i
$529$	−3.94327e28			−0.999015
$530$	1.53561e28	+	1.11376e27i	0.381404	+	0.0276628i
$531$			6.64616e27i			0.161837i
$532$	5.33160e27	−	3.65617e28i	0.127287	−	0.872879i
$533$		−	2.52470e28i		−	0.590982i
$534$	−3.80568e27	+	5.24713e28i	−0.0873473	+	1.20431i
$535$	9.95583e28			2.24059
$536$	−1.39062e28	+	6.30130e28i	−0.306887	+	1.39059i
$537$	−1.35988e28			−0.294286
$538$	3.46623e27	−	4.77911e28i	0.0735603	−	1.01422i
$539$		−	3.77741e28i		−	0.786163i
$540$	−6.21909e28	−	9.06897e27i	−1.26938	−	0.185107i
$541$		−	8.42470e28i		−	1.68649i	−0.537531	−	0.843244i	$-0.680643\pi$
$541$		−	8.42470e28i		−	1.68649i	0.537531	−	0.843244i	$-0.319357\pi$
$542$	8.57210e28	+	6.21724e27i	1.68304	+	0.122069i
$543$	7.17921e28			1.38254
$544$	2.21050e28	+	8.37117e27i	0.417545	+	0.158124i
$545$	−1.05341e29			−1.95180
$546$	−1.24236e29	−	9.01068e27i	−2.25800	−	0.163770i
$547$			1.62906e28i			0.290449i	0.989399	+	0.145224i	$0.0463904\pi$
$547$			1.62906e28i			0.290449i	−0.989399	+	0.145224i	$0.953610\pi$
$548$	1.10700e29	+	1.61428e28i	1.93620	+	0.282346i
$549$			1.27948e28i			0.219545i
$550$	−2.80982e27	+	3.87407e28i	−0.0473010	+	0.652168i
$551$	−5.52041e28			−0.911758
$552$	−4.74848e26	+	2.15167e27i	−0.00769474	+	0.0348671i
$553$	1.39379e29			2.21608
$554$	−7.61274e27	+	1.04962e29i	−0.118765	+	1.63749i
$555$		−	1.49137e29i		−	2.28302i
$556$	1.00127e28	−	6.86627e28i	0.150407	−	1.03142i
$557$		−	7.01874e27i		−	0.103462i	−0.998661	−	0.0517308i	$-0.983526\pi$
$557$		−	7.01874e27i		−	0.103462i	0.998661	−	0.0517308i	$-0.0164738\pi$
$558$	2.66470e28	+	1.93268e27i	0.385469	+	0.0279576i
$559$	9.09995e27			0.129186
$560$	5.54829e28	−	1.86193e29i	0.773009	−	2.59411i
$561$	1.56302e28			0.213725
$562$	−6.84879e28	−	4.96735e27i	−0.919142	−	0.0666643i
$563$			1.19005e29i			1.56757i	0.621030	+	0.783786i	$0.286714\pi$
$563$			1.19005e29i			1.56757i	−0.621030	+	0.783786i	$0.713286\pi$
$564$	−9.95909e27	+	6.82949e28i	−0.128762	+	0.882994i
$565$			1.38120e29i			1.75286i
$566$	−3.23423e27	+	4.45923e28i	−0.0402901	+	0.555505i
$567$	1.67281e29			2.04561
$568$	3.13414e28	+	6.91666e27i	0.376237	+	0.0830308i
$569$	5.15637e28			0.607667			0.303833	−	0.952725i	$-0.401733\pi$
$569$	5.15637e28			0.607667			0.303833	+	0.952725i	$0.401733\pi$
$570$	5.92145e27	−	8.16426e28i	0.0685081	−	0.944563i
$571$			1.05374e29i			1.19689i	0.801163	+	0.598447i	$0.204215\pi$
$571$			1.05374e29i			1.19689i	−0.801163	+	0.598447i	$0.795785\pi$
$572$	−4.38588e28	−	6.39569e27i	−0.489100	−	0.0713229i
$573$		−	1.75220e29i		−	1.91849i
$574$	−7.90447e28	−	5.73302e27i	−0.849763	−	0.0616323i
$575$	−4.62064e27			−0.0487742
$576$	−2.57767e28	−	1.19597e28i	−0.267173	−	0.123961i
$577$	−3.49991e28			−0.356214			−0.178107	−	0.984011i	$-0.556997\pi$
$577$	−3.49991e28			−0.356214			−0.178107	+	0.984011i	$0.556997\pi$
$578$	−7.99001e28	−	5.79506e27i	−0.798556	−	0.0579183i
$579$			9.53207e28i			0.935540i
$580$	−2.87238e29	−	4.18865e28i	−2.76853	−	0.403720i
$581$			5.16367e28i			0.488775i
$582$	4.14975e27	−	5.72152e28i	0.0385772	−	0.531888i
$583$	−1.10259e28			−0.100668
$584$	3.53929e28	+	7.81079e27i	0.317382	+	0.0700422i
$585$	−6.27861e28			−0.553002
$586$	−1.26605e27	+	1.74558e28i	−0.0109528	+	0.151013i
$587$		−	5.23823e28i		−	0.445127i	−0.974918	−	0.222564i	$-0.928557\pi$
$587$		−	5.23823e28i		−	0.445127i	0.974918	−	0.222564i	$-0.0714425\pi$
$588$	−3.67534e28	+	2.52038e29i	−0.306786	+	2.10380i
$589$		−	8.33487e28i		−	0.683421i
$590$	1.08738e29	+	7.88667e27i	0.875864	+	0.0635254i
$591$	−2.04939e29			−1.62165
$592$	−4.61240e28	+	1.54786e29i	−0.358550	+	1.20324i
$593$	7.14627e28			0.545765			0.272882	−	0.962047i	$-0.412023\pi$
$593$	7.14627e28			0.545765			0.272882	+	0.962047i	$0.412023\pi$
$594$	4.48899e28	+	3.25581e27i	0.336814	+	0.0244288i
$595$		−	1.63944e29i		−	1.20855i
$596$	−1.29319e28	+	8.86809e28i	−0.0936646	+	0.642309i
$597$		−	1.24395e29i		−	0.885264i
$598$	3.81410e26	−	5.25874e27i	0.00266704	−	0.0367721i
$599$	−1.02973e29			−0.707522			−0.353761	−	0.935336i	$-0.615097\pi$
$599$	−1.02973e29			−0.707522			−0.353761	+	0.935336i	$0.615097\pi$
$600$	5.64416e28	−	2.55753e29i	0.381076	−	1.72677i
$601$	−2.50060e29			−1.65906			−0.829530	−	0.558463i	$-0.811391\pi$
$601$	−2.50060e29			−1.65906			−0.829530	+	0.558463i	$0.811391\pi$
$602$	2.06639e27	−	2.84906e28i	0.0134726	−	0.185754i
$603$		−	6.54616e28i		−	0.419426i
$604$	9.28058e28	+	1.35334e28i	0.584369	+	0.0852155i
$605$			2.12547e29i			1.31529i
$606$	1.04762e29	+	7.59824e27i	0.637147	+	0.0462116i
$607$	1.41619e29			0.846524			0.423262	−	0.906007i	$-0.360885\pi$
$607$	1.41619e29			0.846524			0.423262	+	0.906007i	$0.360885\pi$
$608$	−3.13956e28	+	8.29037e28i	−0.184451	+	0.487064i
$609$	5.84204e29			3.37351
$610$	2.09337e29	+	1.51830e28i	1.18818	+	0.0861774i
$611$		−	1.65149e29i		−	0.921389i
$612$	−2.37276e28	−	3.46007e27i	−0.130126	−	0.0189756i
$613$			2.69483e29i			1.45277i	0.687289	+	0.726385i	$0.258801\pi$
$613$			2.69483e29i			1.45277i	−0.687289	+	0.726385i	$0.741199\pi$
$614$	1.42401e28	−	1.96337e29i	0.0754648	−	1.04048i
$615$	−1.75579e29			−0.914712
$616$	−2.99833e28	+	1.35863e29i	−0.153561	+	0.695832i
$617$	9.76041e28			0.491444			0.245722	−	0.969340i	$-0.420975\pi$
$617$	9.76041e28			0.491444			0.245722	+	0.969340i	$0.420975\pi$
$618$	−5.86319e27	+	8.08394e28i	−0.0290238	+	0.400169i
$619$			2.22921e29i			1.08492i	0.840081	+	0.542461i	$0.182508\pi$
$619$			2.22921e29i			1.08492i	−0.840081	+	0.542461i	$0.817492\pi$
$620$	6.32414e28	−	4.33681e29i	0.302614	−	2.07519i
$621$			5.35405e27i			0.0251896i
$622$	2.35741e29	+	1.70980e28i	1.09053	+	0.0790945i
$623$	−3.95168e29			−1.79745
$624$	2.86413e29	+	8.53472e28i	1.28102	+	0.381725i
$625$	−3.15336e28			−0.138686
$626$	−4.58627e28	−	3.32637e27i	−0.198349	−	0.0143860i
$627$			5.86203e28i			0.249310i
$628$	3.88268e28	−	2.66257e29i	0.162389	−	1.11359i
$629$			1.36290e29i			0.560572i
$630$	−1.42573e28	+	1.96574e29i	−0.0576715	+	0.795153i
$631$	−1.06630e29			−0.424200			−0.212100	−	0.977248i	$-0.568030\pi$
$631$	−1.06630e29			−0.424200			−0.212100	+	0.977248i	$0.568030\pi$
$632$	−3.26552e29	−	7.20660e28i	−1.27768	−	0.281969i
$633$	−1.50508e29			−0.579190
$634$	2.43859e28	−	3.36224e29i	0.0923001	−	1.27260i
$635$		−	1.02311e28i		−	0.0380889i
$636$	7.35672e28	+	1.07279e28i	0.269392	+	0.0392840i
$637$		−	6.09472e29i		−	2.19528i
$638$	2.07331e29	+	1.50375e28i	0.734594	+	0.0532792i
$639$	−3.25593e28			−0.113479
$640$	−2.26262e29	+	4.07544e29i	−0.775749	+	1.39728i
$641$	−2.20432e29			−0.743472			−0.371736	−	0.928339i	$-0.621237\pi$
$641$	−2.20432e29			−0.743472			−0.371736	+	0.928339i	$0.621237\pi$
$642$	4.79480e29	+	3.47762e28i	1.59094	+	0.115389i
$643$		−	1.92753e29i		−	0.629197i	−0.949225	−	0.314599i	$-0.898130\pi$
$643$		−	1.92753e29i		−	0.629197i	0.949225	−	0.314599i	$-0.101870\pi$
$644$	−1.63777e28	−	2.38828e27i	−0.0525959	−	0.00766979i
$645$		−	6.32853e28i		−	0.199952i
$646$	−5.41135e27	+	7.46096e28i	−0.0168215	+	0.231928i
$647$	4.56666e29			1.39670			0.698352	−	0.715755i	$-0.253917\pi$
$647$	4.56666e29			1.39670			0.698352	+	0.715755i	$0.253917\pi$
$648$	−3.91922e29	−	8.64924e28i	−1.17940	−	0.260280i
$649$	−7.80754e28			−0.231177
$650$	−4.53354e28	+	6.25067e29i	−0.132083	+	1.82111i
$651$			8.82047e29i			2.52867i
$652$	−1.42152e28	+	9.74816e28i	−0.0401009	+	0.274994i
$653$			9.77360e28i			0.271310i	0.990756	+	0.135655i	$0.0433139\pi$
$653$			9.77360e28i			0.271310i	−0.990756	+	0.135655i	$0.956686\pi$
$654$	−5.07332e29	−	3.67962e28i	−1.38588	−	0.100516i
$655$	−2.82323e29			−0.758948
$656$	1.82230e29	+	5.43019e28i	0.482091	+	0.143656i
$657$	−3.67682e28			−0.0957275
$658$	−5.17057e29	−	3.75016e28i	−1.32485	−	0.0960899i
$659$		−	1.12411e29i		−	0.283473i	−0.989904	−	0.141736i	$-0.954731\pi$
$659$		−	1.12411e29i		−	0.283473i	0.989904	−	0.141736i	$-0.0452685\pi$
$660$	−4.44786e28	+	3.05014e29i	−0.110393	+	0.757022i
$661$		−	3.28483e29i		−	0.802412i	−0.915988	−	0.401206i	$-0.868591\pi$
$661$		−	3.28483e29i		−	0.802412i	0.915988	−	0.401206i	$-0.131409\pi$
$662$	3.73625e28	−	5.15140e29i	0.0898312	−	1.23856i
$663$	2.52188e29			0.596805
$664$	2.66987e28	−	1.20980e29i	0.0621907	−	0.281804i
$665$	6.14861e29			1.40977
$666$	1.18524e28	−	1.63416e29i	0.0267502	−	0.368821i
$667$			2.47286e28i			0.0549386i
$668$	4.15755e29	+	6.06274e28i	0.909253	+	0.132592i
$669$		−	4.69050e29i		−	1.00982i
$670$	−1.07102e30	−	7.76801e28i	−2.26994	−	0.164636i
$671$	−1.50306e29			−0.313610
$672$	3.32248e29	−	8.77338e29i	0.682472	−	1.80214i
$673$	−2.43465e29			−0.492355			−0.246177	−	0.969225i	$-0.579175\pi$
$673$	−2.43465e29			−0.492355			−0.246177	+	0.969225i	$0.579175\pi$
$674$	6.82224e29	+	4.94809e28i	1.35831	+	0.0985165i
$675$		−	6.36397e29i		−	1.24749i
$676$	−1.94936e29	−	2.84264e28i	−0.376228	−	0.0548633i
$677$			6.05441e29i			1.15051i	0.817974	+	0.575256i	$0.195097\pi$
$677$			6.05441e29i			1.15051i	−0.817974	+	0.575256i	$0.804903\pi$
$678$	−4.82459e28	+	6.65196e29i	−0.0902711	+	1.24462i
$679$	4.30895e29			0.793851
$680$	−8.47669e28	+	3.84104e29i	−0.153774	+	0.696795i
$681$	−9.09948e28			−0.162544
$682$	−2.27040e28	+	3.13034e29i	−0.0399362	+	0.550625i
$683$		−	8.55320e29i		−	1.48153i	−0.671763	−	0.740766i	$-0.734463\pi$
$683$		−	8.55320e29i		−	1.48153i	0.671763	−	0.740766i	$-0.265537\pi$
$684$	1.29768e28	−	8.89890e28i	0.0221349	−	0.151791i
$685$			1.86165e30i			3.12713i
$686$	−8.86995e29	−	6.43327e28i	−1.46730	−	0.106421i
$687$	9.95611e29			1.62197
$688$	−1.95724e28	+	6.56823e28i	−0.0314026	+	0.105383i
$689$	−1.77898e29			−0.281106
$690$	−3.65717e28	−	2.65250e27i	−0.0569153	−	0.00412800i
$691$		−	1.40587e29i		−	0.215489i	−0.994179	−	0.107744i	$-0.965637\pi$
$691$		−	1.40587e29i		−	0.215489i	0.994179	−	0.107744i	$-0.0343628\pi$
$692$	−8.75425e28	+	6.00326e29i	−0.132161	+	0.906303i
$693$		−	1.41142e29i		−	0.209874i
$694$	3.02551e28	−	4.17146e29i	0.0443123	−	0.610961i
$695$	1.15471e30			1.66583
$696$	−1.36873e30	−	3.02062e29i	−1.94501	−	0.429239i
$697$	1.60454e29			0.224598
$698$	6.95594e28	−	9.59059e29i	0.0959122	−	1.32240i
$699$			3.55990e29i			0.483534i
$700$	1.94670e30	+	2.83877e29i	2.60477	+	0.379840i
$701$		−	1.36147e30i		−	1.79461i	−0.441412	−	0.897305i	$-0.645522\pi$
$701$		−	1.36147e30i		−	1.79461i	0.441412	−	0.897305i	$-0.354478\pi$
$702$	7.24282e29	+	5.25313e28i	0.940519	+	0.0682148i
$703$	−5.11146e29			−0.653905
$704$	1.40496e29	−	3.02811e29i	0.177072	−	0.381644i
$705$	−1.14852e30			−1.42611
$706$	−7.36737e29	−	5.34347e28i	−0.901287	−	0.0653693i
$707$			7.88973e29i			0.950952i
$708$	5.20938e29	+	7.59656e28i	0.618638	+	0.0902127i
$709$			4.07199e29i			0.476454i	0.971210	+	0.238227i	$0.0765662\pi$
$709$			4.07199e29i			0.476454i	−0.971210	+	0.238227i	$0.923434\pi$
$710$	−3.86365e28	+	5.32706e29i	−0.0445436	+	0.614150i
$711$	3.39241e29			0.385370
$712$	9.25839e29	+	2.04321e29i	1.03632	+	0.228704i
$713$	−3.73359e28			−0.0411800
$714$	5.72662e28	−	7.89565e29i	0.0622397	−	0.858137i
$715$		−	7.37577e29i		−	0.789939i
$716$	−3.53641e28	+	2.42511e29i	−0.0373229	+	0.255944i
$717$			5.99888e29i			0.623906i
$718$	1.65523e29	+	1.20052e28i	0.169649	+	0.0123044i
$719$	1.60726e29			0.162343			0.0811713	−	0.996700i	$-0.474134\pi$
$719$	1.60726e29			0.162343			0.0811713	+	0.996700i	$0.474134\pi$
$720$	1.35042e29	−	4.53182e29i	0.134424	−	0.451109i
$721$	−6.08812e29			−0.597259
$722$	7.51757e29	+	5.45241e28i	0.726837	+	0.0527166i
$723$			7.98790e29i			0.761168i
$724$	1.86698e29	−	1.28029e30i	0.175342	−	1.20241i
$725$		−	2.93930e30i		−	2.72079i
$726$	−7.42434e28	+	1.02364e30i	−0.0677366	+	0.933927i
$727$	−6.61860e29			−0.595189			−0.297594	−	0.954692i	$-0.596184\pi$
$727$	−6.61860e29			−0.595189			−0.297594	+	0.954692i	$0.596184\pi$
$728$	−4.83770e29	+	2.19210e30i	−0.428804	+	1.94304i
$729$	−6.38122e29			−0.557525
$730$	−4.36311e28	+	6.01569e29i	−0.0375756	+	0.518078i
$731$			5.78336e28i			0.0490962i
$732$	1.00288e30	+	1.46245e29i	0.839232	+	0.122381i
$733$		−	2.30207e29i		−	0.189900i	−0.995482	−	0.0949502i	$-0.969731\pi$
$733$		−	2.30207e29i		−	0.189900i	0.995482	−	0.0949502i	$-0.0302692\pi$
$734$	−1.69742e30	−	1.23112e29i	−1.38033	−	0.100113i
$735$	−4.23854e30			−3.39781
$736$	3.71365e28	+	1.40636e28i	0.0293484	+	0.0111142i
$737$	7.69007e29			0.599131
$738$	−1.92390e29	−	1.39538e28i	−0.147772	−	0.0107177i
$739$			1.02374e30i			0.775214i	0.921825	+	0.387607i	$0.126698\pi$
$739$			1.02374e30i			0.775214i	−0.921825	+	0.387607i	$0.873302\pi$
$740$	−2.65960e30	−	3.87836e29i	−1.98556	−	0.289544i
$741$			9.45817e29i			0.696171i
$742$	−4.03967e28	+	5.56974e29i	−0.0293160	+	0.404198i
$743$	1.16628e30			0.834492			0.417246	−	0.908794i	$-0.362995\pi$
$743$	1.16628e30			0.834492			0.417246	+	0.908794i	$0.362995\pi$
$744$	4.56062e29	−	2.06655e30i	0.321742	−	1.45791i
$745$	−1.49135e30			−1.03739
$746$	−7.23821e28	+	9.97977e29i	−0.0496448	+	0.684483i
$747$			1.25681e29i			0.0849967i
$748$	4.06470e28	−	2.78739e29i	0.0271058	−	0.185879i
$749$			3.61103e30i			2.37450i
$750$	1.55004e30	+	1.12423e29i	1.00508	+	0.0728973i
$751$	8.81536e29			0.563664			0.281832	−	0.959464i	$-0.409058\pi$
$751$	8.81536e29			0.563664			0.281832	+	0.959464i	$0.409058\pi$
$752$	1.19202e30	+	3.55207e29i	0.751619	+	0.223972i
$753$	9.72207e28			0.0604521
$754$	3.34521e30	+	2.42624e29i	2.05128	+	0.148777i
$755$			1.56072e30i			0.943807i
$756$	3.28936e29	−	2.25569e30i	0.196170	−	1.34524i
$757$		−	1.17925e30i		−	0.693584i	−0.937942	−	0.346792i	$-0.887271\pi$
$757$		−	1.17925e30i		−	0.693584i	0.937942	−	0.346792i	$-0.112729\pi$
$758$	2.35969e29	−	3.25345e30i	0.136876	−	1.88720i
$759$	2.62589e28			0.0150223
$760$	−1.44056e30	−	3.17914e29i	−0.812808	−	0.179377i
$761$	1.38198e30			0.769063			0.384532	−	0.923112i	$-0.374363\pi$
$761$	1.38198e30			0.769063			0.384532	+	0.923112i	$0.374363\pi$
$762$	3.57377e27	−	4.92737e28i	0.00196155	−	0.0270451i
$763$		−	3.82078e30i		−	2.06845i
$764$	−3.12475e30	−	4.55666e29i	−1.66853	−	0.243314i
$765$		−	3.99029e29i		−	0.210165i
$766$	2.32510e30	+	1.68637e29i	1.20793	+	0.0876094i
$767$	−1.25972e30			−0.645538
$768$	−1.23205e30	+	1.88373e30i	−0.622781	+	0.952194i
$769$	1.56974e30			0.782709			0.391354	−	0.920240i	$-0.372007\pi$
$769$	1.56974e30			0.782709			0.391354	+	0.920240i	$0.372007\pi$
$770$	−2.30925e30	−	1.67487e29i	−1.13584	−	0.0823812i
$771$		−	1.37445e30i		−	0.666895i
$772$	1.69988e30	+	2.47885e29i	0.813649	+	0.118650i
$773$		−	3.88908e29i		−	0.183638i	−0.995776	−	0.0918189i	$-0.970732\pi$
$773$		−	3.88908e29i		−	0.183638i	0.995776	−	0.0918189i	$-0.0292681\pi$
$774$	5.02948e27	−	6.93446e28i	0.00234284	−	0.0323022i
$775$	4.43784e30			2.03941
$776$	−1.00954e30	−	2.22794e29i	−0.457696	−	0.101008i
$777$	5.40927e30			2.41946
$778$	−1.59606e29	+	2.20059e30i	−0.0704310	+	0.971076i
$779$			6.01774e29i			0.261993i
$780$	−7.17645e29	+	4.92129e30i	−0.308260	+	2.11390i
$781$		−	3.82488e29i		−	0.162100i
$782$	3.34212e28	+	2.42400e27i	0.0139750	+	0.00101359i
$783$	−3.40584e30			−1.40516
$784$	4.39909e30	+	1.31087e30i	1.79079	+	0.533630i
$785$	4.47766e30			1.79854
$786$	−1.35969e30	−	9.86165e28i	−0.538893	−	0.0390853i
$787$		−	2.75242e29i		−	0.107641i	−0.998551	−	0.0538207i	$-0.982860\pi$
$787$		−	2.75242e29i		−	0.107641i	0.998551	−	0.0538207i	$-0.0171400\pi$
$788$	−5.32952e29	+	3.65474e30i	−0.205666	+	1.41036i
$789$		−	1.81107e30i		−	0.689648i
$790$	4.02561e29	−	5.55036e30i	0.151268	−	2.08563i
$791$	−5.00968e30			−1.85762
$792$	−7.29776e28	+	3.30683e29i	−0.0267039	+	0.121003i
$793$	−2.42514e30			−0.875725
$794$	−4.45018e28	+	6.13574e29i	−0.0158585	+	0.218651i
$795$			1.23719e30i			0.435091i
$796$	−2.21837e30	−	3.23494e29i	−0.769924	−	0.112274i
$797$		−	8.59681e29i		−	0.294459i	−0.989102	−	0.147230i	$-0.952964\pi$
$797$		−	8.59681e29i		−	0.294459i	0.989102	−	0.147230i	$-0.0470356\pi$
$798$	2.96122e30	+	2.14774e29i	1.00101	+	0.0726023i
$799$	1.04958e30			0.350167
$800$	−4.41415e30	−	1.67164e30i	−1.45346	−	0.550424i
$801$	−9.61815e29			−0.312572
$802$	−4.20273e30	−	3.04819e29i	−1.34803	−	0.0977712i
$803$		−	4.31933e29i		−	0.136742i
$804$	−5.13100e30	−	7.48226e29i	−1.60329	−	0.233800i
$805$		−	2.75426e29i		−	0.0849470i
$806$	−3.66321e29	+	5.05069e30i	−0.111518	+	1.53756i
$807$	3.85035e30			1.15699
$808$	4.07938e29	−	1.84849e30i	0.120997	−	0.548273i
$809$	−2.12602e30			−0.622454			−0.311227	−	0.950336i	$-0.600740\pi$
$809$	−2.12602e30			−0.622454			−0.311227	+	0.950336i	$0.600740\pi$
$810$	4.83147e29	−	6.66144e30i	0.139632	−	1.92520i
$811$			4.96211e30i			1.41562i	0.706402	+	0.707811i	$0.250317\pi$
$811$			4.96211e30i			1.41562i	−0.706402	+	0.707811i	$0.749683\pi$
$812$	1.51924e30	−	1.04183e31i	0.427847	−	2.93398i
$813$			6.90622e30i			1.91995i
$814$	1.91972e30	+	1.39235e29i	0.526844	+	0.0382114i
$815$	−1.63936e30			−0.444139
$816$	−5.42413e29	+	1.82026e30i	−0.145072	+	0.486841i
$817$	−2.16902e29			−0.0572705
$818$	−2.81344e30	−	2.04055e29i	−0.733377	−	0.0531910i
$819$		−	2.27728e30i		−	0.586052i
$820$	−4.56600e29	+	3.13116e30i	−0.116009	+	0.795535i
$821$			1.94153e30i			0.487013i	0.969899	+	0.243507i	$0.0782978\pi$
$821$			1.94153e30i			0.487013i	−0.969899	+	0.243507i	$0.921702\pi$
$822$	−6.50282e29	+	8.96584e30i	−0.161045	+	2.22043i
$823$	4.47697e30			1.09468			0.547339	−	0.836911i	$-0.315641\pi$
$823$	4.47697e30			1.09468			0.547339	+	0.836911i	$0.315641\pi$
$824$	1.42639e30	+	3.14786e29i	0.344351	+	0.0759940i
$825$	−3.12120e30			−0.743969
$826$	−2.86053e29	+	3.94399e30i	−0.0673219	+	0.928209i
$827$		−	3.96513e30i		−	0.921404i	−0.887555	−	0.460702i	$-0.847598\pi$
$827$		−	3.96513e30i		−	0.921404i	0.887555	−	0.460702i	$-0.152402\pi$
$828$	−3.98624e28	−	5.81293e27i	−0.00914630	−	0.00133376i
$829$		−	4.99122e30i		−	1.13080i	−0.824819	−	0.565398i	$-0.808723\pi$
$829$		−	4.99122e30i		−	1.13080i	0.824819	−	0.565398i	$-0.191277\pi$
$830$	2.05627e30	+	1.49139e29i	0.460003	+	0.0333635i
$831$	−8.45637e30			−1.86798
$832$	2.26685e30	−	4.88574e30i	0.494456	−	1.06570i
$833$	3.87342e30			0.834299
$834$	5.56115e30	+	4.03344e29i	1.18283	+	0.0857891i
$835$			6.99179e30i			1.46852i
$836$	1.04539e30	+	1.52444e29i	0.216827	+	0.0316188i
$837$		−	5.14224e30i		−	1.05326i
$838$	1.89185e29	−	2.60841e30i	0.0382670	−	0.527611i
$839$	8.90907e30			1.77964			0.889819	−	0.456313i	$-0.150830\pi$
$839$	8.90907e30			1.77964			0.889819	+	0.456313i	$0.150830\pi$
$840$	1.52449e31	+	3.36436e30i	3.00740	+	0.663697i
$841$	−1.05976e31			−2.06466
$842$	2.07672e29	−	2.86331e30i	0.0399578	−	0.550923i
$843$		−	5.51782e30i		−	1.04852i
$844$	−3.91402e29	+	2.68406e30i	−0.0734560	+	0.503728i
$845$		−	3.27825e30i		−	0.607640i
$846$	−1.25849e30	−	9.12766e28i	−0.230388	−	0.0167098i
$847$	−7.70916e30			−1.39390
$848$	3.82628e29	−	1.28405e30i	0.0683314	−	0.229311i
$849$	−3.59264e30			−0.633699
$850$	−3.97254e30	−	2.88123e29i	−0.692100	−	0.0501972i
$851$			2.28967e29i			0.0394015i
$852$	−3.72153e29	+	2.55205e30i	−0.0632565	+	0.433785i
$853$			8.10797e30i			1.36128i	0.732618	+	0.680640i	$0.238298\pi$
$853$			8.10797e30i			1.36128i	−0.732618	+	0.680640i	$0.761702\pi$
$854$	−5.50693e29	+	7.59275e30i	−0.0913276	+	1.25919i
$855$	1.49654e30			0.245156
$856$	1.86708e30	−	8.46028e30i	0.302126	−	1.36902i
$857$	7.83011e30			1.25161			0.625805	−	0.779979i	$-0.284770\pi$
$857$	7.83011e30			1.25161			0.625805	+	0.779979i	$0.284770\pi$
$858$	2.57639e29	−	3.55222e30i	0.0406813	−	0.560898i
$859$			5.58068e30i			0.870480i	0.900315	+	0.435240i	$0.143336\pi$
$859$			5.58068e30i			0.870480i	−0.900315	+	0.435240i	$0.856664\pi$
$860$	−1.12858e30	−	1.64576e29i	−0.173900	−	0.0253590i
$861$		−	6.36834e30i		−	0.969378i
$862$	−8.50971e30	−	6.17199e29i	−1.27964	−	0.0928109i
$863$	4.00476e30			0.594926			0.297463	−	0.954733i	$-0.403859\pi$
$863$	4.00476e30			0.594926			0.297463	+	0.954733i	$0.403859\pi$
$864$	−1.93697e30	+	5.11479e30i	−0.284268	+	0.750643i
$865$	−1.00957e31			−1.46376
$866$	−3.56232e30	−	2.58371e29i	−0.510264	−	0.0370089i
$867$		−	6.43726e30i		−	0.910962i
$868$	1.57298e31	+	2.29380e30i	2.19921	+	0.320699i
$869$			3.98522e30i			0.550484i
$870$	1.68732e30	−	2.32641e31i	0.230274	−	3.17493i
$871$	1.24076e31			1.67301
$872$	−1.97553e30	+	8.95171e30i	−0.263185	+	1.19257i
$873$	1.04877e30			0.138049
$874$	−9.09108e27	+	1.25344e29i	−0.00118235	+	0.0163018i
$875$			1.16736e31i			1.50010i
$876$	−4.20261e29	+	2.88196e30i	−0.0533613	+	0.365927i
$877$			2.67352e30i			0.335419i	0.985836	+	0.167710i	$0.0536371\pi$
$877$			2.67352e30i			0.335419i	−0.985836	+	0.167710i	$0.946363\pi$
$878$	1.44042e31	+	1.04472e30i	1.78565	+	0.129511i
$879$	−1.40635e30			−0.172270
$880$	5.32374e30	+	1.58640e30i	0.644389	+	0.192019i
$881$	−1.19745e31			−1.43222			−0.716112	−	0.697985i	$-0.754080\pi$
$881$	−1.19745e31			−1.43222			−0.716112	+	0.697985i	$0.754080\pi$
$882$	−4.64437e30	−	3.36851e29i	−0.548917	−	0.0398123i
$883$		−	1.60841e31i		−	1.87849i	−0.343245	−	0.939246i	$-0.611526\pi$
$883$		−	1.60841e31i		−	1.87849i	0.343245	−	0.939246i	$-0.388474\pi$
$884$	6.55824e29	−	4.49735e30i	0.0756900	−	0.519048i
$885$			8.76065e30i			0.999153i
$886$	−2.85677e29	+	3.93881e30i	−0.0321975	+	0.443926i
$887$	9.03823e30			1.00667			0.503333	−	0.864093i	$-0.332107\pi$
$887$	9.03823e30			1.00667			0.503333	+	0.864093i	$0.332107\pi$
$888$	−1.26734e31	−	2.79686e30i	−1.39494	−	0.307847i
$889$	3.71087e29			0.0403652
$890$	−1.14134e30	+	1.57364e31i	−0.122693	+	1.69164i
$891$			4.78299e30i			0.508140i
$892$	−8.36471e30	−	1.21978e30i	−0.878254	−	0.128071i
$893$			3.93640e30i			0.408469i
$894$	−7.18247e30	−	5.20936e29i	−0.736597	−	0.0534245i
$895$	−4.07832e30			−0.413371
$896$	−1.47818e31	−	8.20662e30i	−1.48079	−	0.822111i
$897$	4.23677e29			0.0419483
$898$	−7.36545e30	−	5.34208e29i	−0.720772	−	0.0522768i
$899$		−	2.37503e31i		−	2.29716i
$900$	4.73816e30	+	6.90940e29i	0.452963	+	0.0660533i
$901$		−	1.13061e30i		−	0.106832i
$902$	1.63922e29	−	2.26009e30i	0.0153098	−	0.211085i
$903$	2.29539e30			0.211902
$904$	1.17372e31	+	2.59025e30i	1.07101	+	0.236360i
$905$	2.15308e31			1.94200
$906$	−5.45168e29	+	7.51656e30i	−0.0486053	+	0.670152i
$907$			1.14372e31i			1.00796i	0.863715	+	0.503981i	$0.168132\pi$
$907$			1.14372e31i			1.00796i	−0.863715	+	0.503981i	$0.831868\pi$
$908$	−2.36635e29	+	1.62274e30i	−0.0206148	+	0.141367i
$909$			1.92031e30i			0.165368i
$910$	−3.72588e31	−	2.70234e30i	−3.17172	−	0.230041i
$911$	−1.76545e31			−1.48563			−0.742817	−	0.669494i	$-0.766511\pi$
$911$	−1.76545e31			−1.48563			−0.742817	+	0.669494i	$0.766511\pi$
$912$	−6.82679e30	−	2.03429e30i	−0.567898	−	0.169226i
$913$	−1.47643e30			−0.121414
$914$	1.31667e31	+	9.54964e29i	1.07039	+	0.0776340i
$915$			1.68655e31i			1.35543i
$916$	2.58912e30	−	1.77550e31i	0.205707	−	1.41065i
$917$		−	1.02400e31i		−	0.804305i
$918$	−3.33856e29	+	4.60308e30i	−0.0259245	+	0.357438i
$919$	5.44409e30			0.417939			0.208969	−	0.977922i	$-0.432989\pi$
$919$	5.44409e30			0.417939			0.208969	+	0.977922i	$0.432989\pi$
$920$	−1.42409e29	+	6.45295e29i	−0.0108085	+	0.0489763i
$921$	1.58181e31			1.18694
$922$	−3.64738e29	+	5.02887e30i	−0.0270587	+	0.373075i
$923$		−	6.17131e30i		−	0.452647i
$924$	−1.10630e31	−	1.61326e30i	−0.802264	−	0.116990i
$925$		−	2.72156e31i		−	1.95133i
$926$	6.96811e30	+	5.05389e29i	0.493969	+	0.0358270i
$927$	−1.48181e30			−0.103862
$928$	−8.94620e30	+	2.36235e31i	−0.619990	+	1.63715i
$929$	−3.07142e30			−0.210462			−0.105231	−	0.994448i	$-0.533558\pi$
$929$	−3.07142e30			−0.210462			−0.105231	+	0.994448i	$0.533558\pi$
$930$	3.51248e31	+	2.54756e30i	2.37982	+	0.172605i
$931$			1.45270e31i			0.973207i
$932$	6.34847e30	+	9.25765e29i	0.420535	+	0.0613244i
$933$			1.89928e31i			1.24403i
$934$	−1.54009e30	+	2.12341e31i	−0.0997477	+	1.37528i
$935$	4.68757e30			0.300211
$936$	−1.17747e30	+	5.33545e30i	−0.0745680	+	0.337889i
$937$	−1.73830e31			−1.08857			−0.544287	−	0.838899i	$-0.683200\pi$
$937$	−1.73830e31			−1.08857			−0.544287	+	0.838899i	$0.683200\pi$
$938$	2.81749e30	−	3.88465e31i	0.174475	−	2.40559i
$939$		−	3.69499e30i		−	0.226269i
$940$	−2.98677e30	+	2.04819e31i	−0.180867	+	1.24030i
$941$		−	2.83336e31i		−	1.69672i	−0.529420	−	0.848360i	$-0.677590\pi$
$941$		−	2.83336e31i		−	1.69672i	0.529420	−	0.848360i	$-0.322410\pi$
$942$	2.15647e31	+	1.56407e30i	1.27706	+	0.0926234i
$943$	2.69563e29			0.0157866
$944$	2.70943e30	−	9.09248e30i	0.156918	−	0.526595i
$945$	3.79342e31			2.17268
$946$	8.14622e29	+	5.90836e28i	0.0461423	+	0.00334665i
$947$			3.56217e31i			1.99545i	0.0674371	+	0.997724i	$0.478518\pi$
$947$			3.56217e31i			1.99545i	−0.0674371	+	0.997724i	$0.521482\pi$
$948$	3.87753e30	−	2.65903e31i	0.214816	−	1.47311i
$949$		−	6.96908e30i		−	0.381839i
$950$	1.08059e30	−	1.48988e31i	0.0585549	−	0.807332i
$951$	2.70883e31			1.45173
$952$	−1.39316e31	−	3.07454e30i	−0.738437	−	0.162964i
$953$	−4.09398e30			−0.214620			−0.107310	−	0.994226i	$-0.534224\pi$
$953$	−4.09398e30			−0.214620			−0.107310	+	0.994226i	$0.534224\pi$
$954$	−9.83231e28	+	1.35564e30i	−0.00509797	+	0.0702889i
$955$		−	5.25492e31i		−	2.69483i
$956$	1.06980e31	+	1.56003e30i	0.542618	+	0.0791271i
$957$			1.67039e31i			0.837997i
$958$	1.89852e30	+	1.37697e29i	0.0942055	+	0.00683262i
$959$	−6.75228e31			−3.31402
$960$	−3.39777e31	−	1.57647e31i	−1.64948	−	0.765311i
$961$	1.50333e31			0.721870
$962$	3.09740e31	+	2.24651e30i	1.47116	+	0.106701i
$963$			8.78903e30i			0.412919i
$964$	1.42451e31	+	2.07728e30i	0.661996	+	0.0965354i
$965$			2.85871e31i			1.31411i
$966$	9.62074e28	−	1.32647e30i	0.00437470	−	0.0603168i
$967$	8.68171e29			0.0390506			0.0195253	−	0.999809i	$-0.493785\pi$
$967$	8.68171e29			0.0390506			0.0195253	+	0.999809i	$0.493785\pi$
$968$	1.80618e31	+	3.98602e30i	0.803656	+	0.177357i
$969$	−6.01102e30			−0.264575
$970$	1.24453e30	−	1.71591e31i	0.0541878	−	0.747121i
$971$			2.42616e31i			1.04500i	0.852639	+	0.522501i	$0.175001\pi$
$971$			2.42616e31i			1.04500i	−0.852639	+	0.522501i	$0.824999\pi$
$972$	1.93547e30	−	1.32726e31i	0.0824690	−	0.565535i
$973$			4.18818e31i			1.76539i
$974$	−6.44537e30	−	4.67475e29i	−0.268769	−	0.0194935i
$975$	−5.03594e31			−2.07746
$976$	5.21605e30	−	1.75043e31i	0.212872	−	0.714368i
$977$	−1.05813e31			−0.427216			−0.213608	−	0.976919i	$-0.568522\pi$
$977$	−1.05813e31			−0.427216			−0.213608	+	0.976919i	$0.568522\pi$
$978$	−7.89527e30	−	5.72635e29i	−0.315362	−	0.0228728i
$979$		−	1.12989e31i		−	0.446495i
$980$	−1.10225e31	+	7.55872e31i	−0.430929	+	2.95512i
$981$		−	9.29956e30i		−	0.359698i
$982$	−1.66382e30	+	2.29402e31i	−0.0636703	+	0.877861i
$983$	−2.80237e31			−1.06099			−0.530497	−	0.847687i	$-0.677995\pi$
$983$	−2.80237e31			−1.06099			−0.530497	+	0.847687i	$0.677995\pi$
$984$	−3.29275e30	+	1.49204e31i	−0.123342	+	0.558897i
$985$	−6.14621e31			−2.27786
$986$	−1.54197e30	+	2.12601e31i	−0.0565415	+	0.779573i
$987$		−	4.16574e31i		−	1.51134i
$988$	1.68670e31	+	2.45963e30i	0.605468	+	0.0882922i
$989$			9.71606e28i			0.00345088i
$990$	−5.62057e30	−	4.07653e29i	−0.197520	−	0.0143259i
$991$	3.61409e31			1.25668			0.628341	−	0.777938i	$-0.283734\pi$
$991$	3.61409e31			1.25668			0.628341	+	0.777938i	$0.283734\pi$
$992$	−3.56674e31	−	1.35072e31i	−1.22715	−	0.464722i
$993$	4.15030e31			1.41290
$994$	−1.93215e31	−	1.40136e30i	−0.650854	−	0.0472057i
$995$		−	3.73066e31i		−	1.24349i
$996$	9.85107e30	+	1.43653e30i	0.324908	+	0.0473796i
$997$			6.57334e30i			0.214529i	0.994230	+	0.107265i	$0.0342092\pi$
$997$			6.57334e30i			0.214529i	−0.994230	+	0.107265i	$0.965791\pi$
$998$	2.06089e30	−	2.84147e31i	0.0665555	−	0.917642i
$999$	−3.15354e31			−1.00777

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.22.b.a.5.20	yes	20
4.3	odd	2		32.22.b.a.17.5		20
8.3	odd	2		32.22.b.a.17.16		20
8.5	even	2	inner	8.22.b.a.5.19	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.22.b.a.5.19	✓	20	8.5	even	2	inner
8.22.b.a.5.20	yes	20	1.1	even	1	trivial
32.22.b.a.17.5		20	4.3	odd	2
32.22.b.a.17.16		20	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1444.36 + 104.758i) q^{2} +116367. i q^{3} +(2.07520e6 + 302616. i) q^{4} +3.48989e7i q^{5} +(-1.21903e7 + 1.68076e8i) q^{6} -1.26580e9 q^{7} +(2.96564e9 + 6.54481e8i) q^{8} -3.08088e9 q^{9} +(-3.65593e9 + 5.04066e10i) q^{10} -3.61925e10i q^{11} +(-3.52145e10 + 2.41485e11i) q^{12} -5.83952e11i q^{13} +(-1.82827e12 - 1.32602e11i) q^{14} -4.06107e12 q^{15} +(4.21489e12 + 1.25598e12i) q^{16} +3.71123e12 q^{17} +(-4.44990e12 - 3.22746e11i) q^{18} +1.39188e13i q^{19} +(-1.05610e13 + 7.24223e13i) q^{20} -1.47297e14i q^{21} +(3.79144e12 - 5.22750e13i) q^{22} +6.23488e12 q^{23} +(-7.61598e13 + 3.45102e14i) q^{24} -7.41095e14 q^{25} +(6.11735e13 - 8.43438e14i) q^{26} +8.58726e14i q^{27} +(-2.62679e15 - 3.83051e14i) q^{28} +3.96616e15i q^{29} +(-5.86565e15 - 4.25429e14i) q^{30} -5.98822e15 q^{31} +(5.95625e15 + 2.25563e15i) q^{32} +4.21160e15 q^{33} +(5.36036e15 + 3.88781e14i) q^{34} -4.41750e16i q^{35} +(-6.39345e15 - 9.32324e14i) q^{36} +3.67235e16i q^{37} +(-1.45810e15 + 2.01037e16i) q^{38} +6.79526e16 q^{39} +(-2.28406e16 + 1.03498e17i) q^{40} +4.32347e16 q^{41} +(1.54305e16 - 2.12750e17i) q^{42} +1.55834e16i q^{43} +(1.09524e16 - 7.51068e16i) q^{44} -1.07519e17i q^{45} +(9.00542e15 + 6.53153e14i) q^{46} +2.82812e17 q^{47} +(-1.46154e17 + 4.90474e17i) q^{48} +1.04370e18 q^{49} +(-1.07041e18 - 7.76355e16i) q^{50} +4.31864e17i q^{51} +(1.76713e17 - 1.21182e18i) q^{52} -3.04645e17i q^{53} +(-8.99582e16 + 1.24031e18i) q^{54} +1.26308e18 q^{55} +(-3.75391e18 - 8.28441e17i) q^{56} -1.61968e18 q^{57} +(-4.15486e17 + 5.72857e18i) q^{58} -2.15723e18i q^{59} +(-8.42755e18 - 1.22895e18i) q^{60} -4.15297e18i q^{61} +(-8.64915e18 - 6.27313e17i) q^{62} +3.89977e18 q^{63} +(8.36668e18 + 3.88191e18i) q^{64} +2.03793e19 q^{65} +(6.08307e18 + 4.41198e17i) q^{66} +2.12477e19i q^{67} +(7.70157e18 + 1.12308e18i) q^{68} +7.25533e17i q^{69} +(4.62767e18 - 6.38046e19i) q^{70} +1.05682e19 q^{71} +(-9.13678e18 - 2.01638e18i) q^{72} +1.19343e19 q^{73} +(-3.84708e18 + 5.30420e19i) q^{74} -8.62388e19i q^{75} +(-4.21204e18 + 2.88843e19i) q^{76} +4.58124e19i q^{77} +(9.81481e19 + 7.11857e18i) q^{78} -1.10112e20 q^{79} +(-4.38323e19 + 1.47095e20i) q^{80} -1.32154e20 q^{81} +(6.24465e19 + 4.52917e18i) q^{82} -4.07937e19i q^{83} +(4.45744e19 - 3.05671e20i) q^{84} +1.29518e20i q^{85} +(-1.63248e18 + 2.25080e19i) q^{86} -4.61530e20 q^{87} +(2.36873e19 - 1.07334e20i) q^{88} +3.12189e20 q^{89} +(1.12635e19 - 1.55297e20i) q^{90} +7.39166e20i q^{91} +(1.29387e19 + 1.88678e18i) q^{92} -6.96830e20i q^{93} +(4.08483e20 + 2.96268e19i) q^{94} -4.85749e20 q^{95} +(-2.62481e20 + 6.93110e20i) q^{96} -3.40413e20 q^{97} +(1.50748e21 + 1.09336e20i) q^{98} +1.11505e20i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 286 q^{2} + 409876 q^{4} + 118236748 q^{6} + 564950496 q^{7} + 3649699336 q^{8} - 62762119220 q^{9} - 51269339528 q^{10} + 65316900136 q^{12} - 1924309104464 q^{14} - 2285680856096 q^{15} + 7793508571920 q^{16}+ \cdots + 13\!\cdots\!30 q^{98}+O(q^{100}) \) 20 * q + 286 * q^2 + 409876 * q^4 + 118236748 * q^6 + 564950496 * q^7 + 3649699336 * q^8 - 62762119220 * q^9 - 51269339528 * q^10 + 65316900136 * q^12 - 1924309104464 * q^14 - 2285680856096 * q^15 + 7793508571920 * q^16 + 1740714497000 * q^17 - 41325344023822 * q^18 - 78999934156016 * q^20 + 294957216952508 * q^22 + 335749622520224 * q^23 + 786737698607504 * q^24 - 1665114591247004 * q^25 - 2772669922448408 * q^26 - 4284340177681888 * q^28 + 3807691030523312 * q^30 - 8989263821171840 * q^31 - 9127378177656544 * q^32 + 5359113021386256 * q^33 + 19124803780998044 * q^34 + 39378114498954828 * q^36 - 41860137429498580 * q^38 + 121743910075345312 * q^39 - 160007944946664288 * q^40 - 84626460793452344 * q^41 + 178614544452770272 * q^42 - 27785097292304568 * q^44 + 184220935820050448 * q^46 + 149908985865280320 * q^47 + 1509829480382701344 * q^48 + 477689401234988532 * q^49 - 1722157324053237098 * q^50 - 1640429312330235856 * q^52 + 785391046636854392 * q^54 - 1936239868862269088 * q^55 - 3751496032099552448 * q^56 + 409355502574547024 * q^57 + 3182351472522780872 * q^58 + 2751731248604508192 * q^60 - 13336157978726113600 * q^62 - 8780950644120846560 * q^63 - 9021637553716933568 * q^64 + 6302857570713584320 * q^65 + 5291575090585638744 * q^66 + 40891724357029299816 * q^68 + 18077776609913587392 * q^70 + 96451291685825247456 * q^71 + 49841566955976579512 * q^72 - 21461290229157072184 * q^73 - 42953490504627871688 * q^74 - 206966483397015363224 * q^76 + 163869164384378609168 * q^78 - 284214874786393231680 * q^79 - 49904712513208125120 * q^80 + 1291808332257012164 * q^81 + 112698322843931711404 * q^82 + 178681601993395676224 * q^84 - 523293212085532715396 * q^86 + 517213147301817170208 * q^87 - 124028902608265335088 * q^88 + 17316387144455013640 * q^89 + 171098967229297148360 * q^90 + 827091233447044225632 * q^92 - 165060487582514765280 * q^94 - 2333725338330109674784 * q^95 - 715448174391177540544 * q^96 + 9560220979460741928 * q^97 + 137273120368488603630 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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