LMFDB - Embedded newform 8.22.b.a.5.1

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			5.1
Root			$0.500000 + 19382.6i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.22.b.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1394.30 - 391.258i) q^{2} -77530.5i q^{3} +(1.79099e6 + 1.09106e6i) q^{4} -2.27953e7i q^{5} +(-3.03344e7 + 1.08101e8i) q^{6} +1.10984e9 q^{7} +(-2.07029e9 - 2.22200e9i) q^{8} +4.44938e9 q^{9} +O(q^{10})$	\(q+(-1394.30 - 391.258i) q^{2} -77530.5i q^{3} +(1.79099e6 + 1.09106e6i) q^{4} -2.27953e7i q^{5} +(-3.03344e7 + 1.08101e8i) q^{6} +1.10984e9 q^{7} +(-2.07029e9 - 2.22200e9i) q^{8} +4.44938e9 q^{9} +(-8.91883e9 + 3.17834e10i) q^{10} +1.60961e11i q^{11} +(8.45904e10 - 1.38856e11i) q^{12} +2.43539e11i q^{13} +(-1.54745e12 - 4.34235e11i) q^{14} -1.76733e12 q^{15} +(2.01722e12 + 3.90815e12i) q^{16} +8.96622e12 q^{17} +(-6.20377e12 - 1.74085e12i) q^{18} +2.58938e13i q^{19} +(2.48710e13 - 4.08261e13i) q^{20} -8.60467e13i q^{21} +(6.29773e13 - 2.24428e14i) q^{22} +2.80432e14 q^{23} +(-1.72273e14 + 1.60510e14i) q^{24} -4.27879e13 q^{25} +(9.52863e13 - 3.39566e14i) q^{26} -1.15596e15i q^{27} +(1.98772e15 + 1.21091e15i) q^{28} -1.04492e15i q^{29} +(2.46418e15 + 6.91481e14i) q^{30} -1.15584e15 q^{31} +(-1.28352e15 - 6.23838e15i) q^{32} +1.24794e16 q^{33} +(-1.25016e16 - 3.50810e15i) q^{34} -2.52992e16i q^{35} +(7.96879e15 + 4.85454e15i) q^{36} +4.43260e16i q^{37} +(1.01311e16 - 3.61037e16i) q^{38} +1.88817e16 q^{39} +(-5.06511e16 + 4.71928e16i) q^{40} -4.51196e16 q^{41} +(-3.36664e16 + 1.19975e17i) q^{42} +6.04472e16i q^{43} +(-1.75618e17 + 2.88279e17i) q^{44} -1.01425e17i q^{45} +(-3.91007e17 - 1.09721e17i) q^{46} -3.69037e15 q^{47} +(3.03001e17 - 1.56396e17i) q^{48} +6.73207e17 q^{49} +(5.96591e16 + 1.67411e16i) q^{50} -6.95155e17i q^{51} +(-2.65715e17 + 4.36175e17i) q^{52} -1.54786e18i q^{53} +(-4.52277e17 + 1.61175e18i) q^{54} +3.66916e18 q^{55} +(-2.29769e18 - 2.46607e18i) q^{56} +2.00756e18 q^{57} +(-4.08834e17 + 1.45694e18i) q^{58} -1.30533e18i q^{59} +(-3.16526e18 - 1.92826e18i) q^{60} -9.47359e17i q^{61} +(1.61159e18 + 4.52233e17i) q^{62} +4.93812e18 q^{63} +(-6.51204e17 + 9.20035e18i) q^{64} +5.55153e18 q^{65} +(-1.74000e19 - 4.88266e18i) q^{66} -1.17614e17i q^{67} +(1.60584e19 + 9.78268e18i) q^{68} -2.17421e19i q^{69} +(-9.89850e18 + 3.52746e19i) q^{70} -1.21820e19 q^{71} +(-9.21149e18 - 9.88653e18i) q^{72} -3.88562e19 q^{73} +(1.73429e19 - 6.18036e19i) q^{74} +3.31737e18i q^{75} +(-2.82517e19 + 4.63755e19i) q^{76} +1.78642e20i q^{77} +(-2.63267e19 - 7.38759e18i) q^{78} +4.17704e19 q^{79} +(8.90874e19 - 4.59832e19i) q^{80} -4.30799e19 q^{81} +(6.29102e19 + 1.76534e19i) q^{82} -1.10207e20i q^{83} +(9.38821e19 - 1.54108e20i) q^{84} -2.04388e20i q^{85} +(2.36504e19 - 8.42815e19i) q^{86} -8.10134e19 q^{87} +(3.57656e20 - 3.33236e20i) q^{88} -3.49128e20 q^{89} +(-3.96833e19 + 1.41417e20i) q^{90} +2.70290e20i q^{91} +(5.02251e20 + 3.05969e20i) q^{92} +8.96132e19i q^{93} +(5.14548e18 + 1.44389e18i) q^{94} +5.90257e20 q^{95} +(-4.83665e20 + 9.95118e19i) q^{96} -1.04936e21 q^{97} +(-9.38652e20 - 2.63397e20i) q^{98} +7.16178e20i 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}+O(q^{10}) $ 20 * q + 286 * q^2 + 409876 * q^4 + 118236748 * q^6 + 564950496 * q^7 + 3649699336 * q^8 - 62762119220 * q^9	$ 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} - 16\!\cdots\!04 q^{25}+ \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

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1394.30	−	391.258i	−0.962811	−	0.270177i
$2$	−1394.30	−	391.258i	−0.962811	−	0.270177i
$3$		−	77530.5i		−	0.758052i	−0.925386	−	0.379026i	$-0.876259\pi$
$3$		−	77530.5i		−	0.758052i	0.925386	−	0.379026i	$-0.123741\pi$
$4$	1.79099e6	+	1.09106e6i	0.854009	+	0.520258i
$5$		−	2.27953e7i		−	1.04390i	−0.852975	−	0.521951i	$-0.825204\pi$
$5$		−	2.27953e7i		−	1.04390i	0.852975	−	0.521951i	$-0.174796\pi$
$6$	−3.03344e7	+	1.08101e8i	−0.204808	+	0.729861i
$7$	1.10984e9			1.48502			0.742510	−	0.669835i	$-0.233635\pi$
$7$	1.10984e9			1.48502			0.742510	+	0.669835i	$0.233635\pi$
$8$	−2.07029e9	−	2.22200e9i	−0.681688	−	0.731643i
$9$	4.44938e9			0.425357
$10$	−8.91883e9	+	3.17834e10i	−0.282038	+	1.00508i
$11$			1.60961e11i			1.87110i	0.353188	+	0.935552i	$0.385098\pi$
$11$			1.60961e11i			1.87110i	−0.353188	+	0.935552i	$0.614902\pi$
$12$	8.45904e10	−	1.38856e11i	0.394383	−	0.647384i
$13$			2.43539e11i			0.489962i	0.969528	+	0.244981i	$0.0787818\pi$
$13$			2.43539e11i			0.489962i	−0.969528	+	0.244981i	$0.921218\pi$
$14$	−1.54745e12	−	4.34235e11i	−1.42979	−	0.401218i
$15$	−1.76733e12			−0.791333
$16$	2.01722e12	+	3.90815e12i	0.458663	+	0.888610i
$17$	8.96622e12			1.07869			0.539344	−	0.842086i	$-0.318672\pi$
$17$	8.96622e12			1.07869			0.539344	+	0.842086i	$0.318672\pi$
$18$	−6.20377e12	−	1.74085e12i	−0.409538	−	0.114921i
$19$			2.58938e13i			0.968909i	0.874816	+	0.484455i	$0.160982\pi$
$19$			2.58938e13i			0.968909i	−0.874816	+	0.484455i	$0.839018\pi$
$20$	2.48710e13	−	4.08261e13i	0.543099	−	0.891502i
$21$		−	8.60467e13i		−	1.12572i
$22$	6.29773e13	−	2.24428e14i	0.505529	−	1.80152i
$23$	2.80432e14			1.41152			0.705758	−	0.708453i	$-0.250606\pi$
$23$	2.80432e14			1.41152			0.705758	+	0.708453i	$0.250606\pi$
$24$	−1.72273e14	+	1.60510e14i	−0.554624	+	0.516755i
$25$	−4.27879e13			−0.0897327
$26$	9.52863e13	−	3.39566e14i	0.132376	−	0.471741i
$27$		−	1.15596e15i		−	1.08049i
$28$	1.98772e15	+	1.21091e15i	1.26822	+	0.772593i
$29$		−	1.04492e15i		−	0.461217i	−0.973047	−	0.230609i	$-0.925928\pi$
$29$		−	1.04492e15i		−	0.461217i	0.973047	−	0.230609i	$-0.0740717\pi$
$30$	2.46418e15	+	6.91481e14i	0.761904	+	0.213800i
$31$	−1.15584e15			−0.253280			−0.126640	−	0.991949i	$-0.540419\pi$
$31$	−1.15584e15			−0.253280			−0.126640	+	0.991949i	$0.540419\pi$
$32$	−1.28352e15	−	6.23838e15i	−0.201524	−	0.979483i
$33$	1.24794e16			1.41840
$34$	−1.25016e16	−	3.50810e15i	−1.03857	−	0.291436i
$35$		−	2.52992e16i		−	1.55022i
$36$	7.96879e15	+	4.85454e15i	0.363259	+	0.221295i
$37$			4.43260e16i			1.51544i	0.652577	+	0.757722i	$0.273688\pi$
$37$			4.43260e16i			1.51544i	−0.652577	+	0.757722i	$0.726312\pi$
$38$	1.01311e16	−	3.61037e16i	0.261777	−	0.932876i
$39$	1.88817e16			0.371417
$40$	−5.06511e16	+	4.71928e16i	−0.763764	+	0.711616i
$41$	−4.51196e16			−0.524970			−0.262485	−	0.964936i	$-0.584542\pi$
$41$	−4.51196e16			−0.524970			−0.262485	+	0.964936i	$0.584542\pi$
$42$	−3.36664e16	+	1.19975e17i	−0.304144	+	1.08386i
$43$			6.04472e16i			0.426538i	0.976994	+	0.213269i	$0.0684110\pi$
$43$			6.04472e16i			0.426538i	−0.976994	+	0.213269i	$0.931589\pi$
$44$	−1.75618e17	+	2.88279e17i	−0.973457	+	1.59794i
$45$		−	1.01425e17i		−	0.444031i
$46$	−3.91007e17	−	1.09721e17i	−1.35902	−	0.381359i
$47$	−3.69037e15			−0.0102339			−0.00511696	−	0.999987i	$-0.501629\pi$
$47$	−3.69037e15			−0.0102339			−0.00511696	+	0.999987i	$0.501629\pi$
$48$	3.03001e17	−	1.56396e17i	0.673613	−	0.347691i
$49$	6.73207e17			1.20528
$50$	5.96591e16	+	1.67411e16i	0.0863956	+	0.0242437i
$51$		−	6.95155e17i		−	0.817702i
$52$	−2.65715e17	+	4.36175e17i	−0.254907	+	0.418432i
$53$		−	1.54786e18i		−	1.21572i	−0.794044	−	0.607860i	$-0.792028\pi$
$53$		−	1.54786e18i		−	1.21572i	0.794044	−	0.607860i	$-0.207972\pi$
$54$	−4.52277e17	+	1.61175e18i	−0.291924	+	1.04031i
$55$	3.66916e18			1.95325
$56$	−2.29769e18	−	2.46607e18i	−1.01232	−	1.08650i
$57$	2.00756e18			0.734484
$58$	−4.08834e17	+	1.45694e18i	−0.124610	+	0.444065i
$59$		−	1.30533e18i		−	0.332486i	−0.986085	−	0.166243i	$-0.946836\pi$
$59$		−	1.30533e18i		−	0.332486i	0.986085	−	0.166243i	$-0.0531637\pi$
$60$	−3.16526e18	−	1.92826e18i	−0.675805	−	0.411697i
$61$		−	9.47359e17i		−	0.170040i	−0.996379	−	0.0850201i	$-0.972905\pi$
$61$		−	9.47359e17i		−	0.170040i	0.996379	−	0.0850201i	$-0.0270954\pi$
$62$	1.61159e18	+	4.52233e17i	0.243861	+	0.0684305i
$63$	4.93812e18			0.631663
$64$	−6.51204e17	+	9.20035e18i	−0.0706037	+	0.997504i
$65$	5.55153e18			0.511473
$66$	−1.74000e19	−	4.88266e18i	−1.36565	−	0.383217i
$67$		−	1.17614e17i		−	0.00788269i	−0.999992	−	0.00394134i	$-0.998745\pi$
$67$		−	1.17614e17i		−	0.00788269i	0.999992	−	0.00394134i	$-0.00125457\pi$
$68$	1.60584e19	+	9.78268e18i	0.921209	+	0.561196i
$69$		−	2.17421e19i		−	1.07000i
$70$	−9.89850e18	+	3.52746e19i	−0.418832	+	1.49257i
$71$	−1.21820e19			−0.444125			−0.222062	−	0.975032i	$-0.571279\pi$
$71$	−1.21820e19			−0.444125			−0.222062	+	0.975032i	$0.571279\pi$
$72$	−9.21149e18	−	9.88653e18i	−0.289960	−	0.311209i
$73$	−3.88562e19			−1.05821			−0.529104	−	0.848557i	$-0.677472\pi$
$73$	−3.88562e19			−1.05821			−0.529104	+	0.848557i	$0.677472\pi$
$74$	1.73429e19	−	6.18036e19i	0.409438	−	1.45909i
$75$			3.31737e18i			0.0680221i
$76$	−2.82517e19	+	4.63755e19i	−0.504083	+	0.827458i
$77$			1.78642e20i			2.77863i
$78$	−2.63267e19	−	7.38759e18i	−0.357604	−	0.100348i
$79$	4.17704e19			0.496346			0.248173	−	0.968716i	$-0.420170\pi$
$79$	4.17704e19			0.496346			0.248173	+	0.968716i	$0.420170\pi$
$80$	8.90874e19	−	4.59832e19i	0.927622	−	0.478800i
$81$	−4.30799e19			−0.393715
$82$	6.29102e19	+	1.76534e19i	0.505447	+	0.141835i
$83$		−	1.10207e20i		−	0.779628i	−0.920894	−	0.389814i	$-0.872539\pi$
$83$		−	1.10207e20i		−	0.779628i	0.920894	−	0.389814i	$-0.127461\pi$
$84$	9.38821e19	−	1.54108e20i	0.585666	−	0.961378i
$85$		−	2.04388e20i		−	1.12604i
$86$	2.36504e19	−	8.42815e19i	0.115241	−	0.410675i
$87$	−8.10134e19			−0.349627
$88$	3.57656e20	−	3.33236e20i	1.36898	−	1.27551i
$89$	−3.49128e20			−1.18683			−0.593416	−	0.804896i	$-0.702221\pi$
$89$	−3.49128e20			−1.18683			−0.593416	+	0.804896i	$0.702221\pi$
$90$	−3.96833e19	+	1.41417e20i	−0.119967	+	0.427518i
$91$			2.70290e20i			0.727604i
$92$	5.02251e20	+	3.05969e20i	1.20545	+	0.734353i
$93$			8.96132e19i			0.192000i
$94$	5.14548e18	+	1.44389e18i	0.00985334	+	0.00276497i
$95$	5.90257e20			1.01145
$96$	−4.83665e20	+	9.95118e19i	−0.742500	+	0.152766i
$97$	−1.04936e21			−1.44485			−0.722425	−	0.691449i	$-0.756973\pi$
$97$	−1.04936e21			−1.44485			−0.722425	+	0.691449i	$0.756973\pi$
$98$	−9.38652e20	−	2.63397e20i	−1.16046	−	0.325640i
$99$			7.16178e20i			0.795887i
$100$	−7.66326e19	−	4.66842e19i	−0.0766326	−	0.0466842i
$101$			6.53785e20i			0.588926i	0.955663	+	0.294463i	$0.0951407\pi$
$101$			6.53785e20i			0.588926i	−0.955663	+	0.294463i	$0.904859\pi$
$102$	−2.71985e20	+	9.69254e20i	−0.220924	+	0.787292i
$103$	1.60521e21			1.17690			0.588450	−	0.808534i	$-0.299738\pi$
$103$	1.60521e21			1.17690			0.588450	+	0.808534i	$0.299738\pi$
$104$	5.41143e20	−	5.04195e20i	0.358478	−	0.334001i
$105$	−1.96146e21			−1.17515
$106$	−6.05610e20	+	2.15817e21i	−0.328459	+	1.17051i
$107$		−	2.99930e21i		−	1.47397i	−0.675907	−	0.736987i	$-0.736248\pi$
$107$		−	2.99930e21i		−	1.47397i	0.675907	−	0.736987i	$-0.263752\pi$
$108$	1.26122e21	−	2.07031e21i	0.562136	−	0.922753i
$109$			6.09163e20i			0.246465i	0.992378	+	0.123233i	$0.0393261\pi$
$109$			6.09163e20i			0.246465i	−0.992378	+	0.123233i	$0.960674\pi$
$110$	−5.11590e21	−	1.43559e21i	−1.88061	−	0.527723i
$111$	3.43661e21			1.14879
$112$	2.23880e21	+	4.33743e21i	0.681124	+	1.31960i
$113$	5.51064e21			1.52714			0.763569	−	0.645726i	$-0.223445\pi$
$113$	5.51064e21			1.52714			0.763569	+	0.645726i	$0.223445\pi$
$114$	−2.79914e21	−	7.85473e20i	−0.707169	−	0.198440i
$115$		−	6.39254e21i		−	1.47349i
$116$	1.14007e21	−	1.87144e21i	0.239952	−	0.393884i
$117$			1.08360e21i			0.208409i
$118$	−5.10720e20	+	1.82002e21i	−0.0898301	+	0.320121i
$119$	9.95110e21			1.60187
$120$	3.65888e21	+	3.92701e21i	0.539442	+	0.578973i
$121$	−1.85083e22			−2.50103
$122$	−3.70662e20	+	1.32090e21i	−0.0459409	+	0.163717i
$123$			3.49814e21i			0.397955i
$124$	−2.07010e21	−	1.26110e21i	−0.216304	−	0.131771i
$125$		−	9.89428e21i		−	0.950230i
$126$	−6.88521e21	−	1.93208e21i	−0.608172	−	0.170661i
$127$	1.64796e22			1.33970			0.669849	−	0.742497i	$-0.266359\pi$
$127$	1.64796e22			1.33970			0.669849	+	0.742497i	$0.266359\pi$
$128$	4.50768e21	−	1.25733e22i	0.337480	−	0.941333i
$129$	4.68650e21			0.323338
$130$	−7.74050e21	−	2.17208e21i	−0.492452	−	0.138188i
$131$			1.02357e21i			0.0600852i	0.999549	+	0.0300426i	$0.00956430\pi$
$131$			1.02357e21i			0.0600852i	−0.999549	+	0.0300426i	$0.990436\pi$
$132$	2.23504e22	+	1.36158e22i	1.21132	+	0.737931i
$133$			2.87381e22i			1.43885i
$134$	−4.60174e19	+	1.63989e20i	−0.00212972	+	0.00758954i
$135$	−2.63504e22			−1.12793
$136$	−1.85626e22	−	1.99229e22i	−0.735328	−	0.789214i
$137$	−3.69679e22			−1.35600			−0.677998	−	0.735064i	$-0.737152\pi$
$137$	−3.69679e22			−1.35600			−0.677998	+	0.735064i	$0.737152\pi$
$138$	−8.50674e21	+	3.03149e22i	−0.289090	+	1.03021i
$139$			3.92514e22i			1.23652i	0.785975	+	0.618258i	$0.212161\pi$
$139$			3.92514e22i			1.23652i	−0.785975	+	0.618258i	$0.787839\pi$
$140$	2.76029e22	−	4.53105e22i	0.806512	−	1.32390i
$141$			2.86116e20i			0.00775785i
$142$	1.69853e22	+	4.76629e21i	0.427608	+	0.119992i
$143$	−3.92003e22			−0.916771
$144$	8.97540e21	+	1.73888e22i	0.195096	+	0.377976i
$145$	−2.38193e22			−0.481466
$146$	5.41772e22	+	1.52028e22i	1.01885	+	0.285903i
$147$		−	5.21940e22i		−	0.913669i
$148$	−4.83623e22	+	7.93872e22i	−0.788422	+	1.29420i
$149$		−	2.53583e22i		−	0.385181i	−0.981279	−	0.192590i	$-0.938311\pi$
$149$		−	2.53583e22i		−	0.385181i	0.981279	−	0.192590i	$-0.0616889\pi$
$150$	1.29794e21	−	4.62540e21i	0.0183780	−	0.0654924i
$151$	6.61629e22			0.873688			0.436844	−	0.899537i	$-0.356096\pi$
$151$	6.61629e22			0.873688			0.436844	+	0.899537i	$0.356096\pi$
$152$	5.75361e22	−	5.36076e22i	0.708896	−	0.660494i
$153$	3.98941e22			0.458827
$154$	6.98949e22	−	2.49080e23i	0.750720	−	2.67529i
$155$			2.63478e22i			0.264400i
$156$	3.38168e22	+	2.06010e22i	0.317194	+	0.193233i
$157$			6.02174e22i			0.528172i	0.964499	+	0.264086i	$0.0850704\pi$
$157$			6.02174e22i			0.528172i	−0.964499	+	0.264086i	$0.914930\pi$
$158$	−5.82404e22	−	1.63430e22i	−0.477887	−	0.134101i
$159$	−1.20006e23			−0.921580
$160$	−1.42206e23	+	2.92582e22i	−1.02249	+	0.210372i
$161$	3.11236e23			2.09613
$162$	6.00662e22	+	1.68553e22i	0.379073	+	0.106373i
$163$		−	2.95203e22i		−	0.174643i	−0.996180	−	0.0873216i	$-0.972169\pi$
$163$		−	2.95203e22i		−	0.174643i	0.996180	−	0.0873216i	$-0.0278308\pi$
$164$	−8.08086e22	−	4.92282e22i	−0.448329	−	0.273120i
$165$		−	2.84471e23i		−	1.48067i
$166$	−4.31192e22	+	1.53661e23i	−0.210637	+	0.750635i
$167$	−1.88348e23			−0.863850			−0.431925	−	0.901910i	$-0.642165\pi$
$167$	−1.88348e23			−0.863850			−0.431925	+	0.901910i	$0.642165\pi$
$168$	−1.91196e23	+	1.78141e23i	−0.823628	+	0.767391i
$169$	1.87753e23			0.759937
$170$	−7.99682e22	+	2.84977e23i	−0.304231	+	1.08417i
$171$			1.15211e23i			0.412132i
$172$	−6.59515e22	+	1.08260e23i	−0.221910	+	0.364267i
$173$			3.51171e23i			1.11182i	0.831243	+	0.555910i	$0.187630\pi$
$173$			3.51171e23i			1.11182i	−0.831243	+	0.555910i	$0.812370\pi$
$174$	1.12957e23	+	3.16971e22i	0.336624	+	0.0944610i
$175$	−4.74879e22			−0.133255
$176$	−6.29060e23	+	3.24695e23i	−1.66268	+	0.858207i
$177$	−1.01203e23			−0.252042
$178$	4.86788e23	+	1.36599e23i	1.14269	+	0.320654i
$179$		−	4.28950e23i		−	0.949401i	−0.880147	−	0.474701i	$-0.842556\pi$
$179$		−	4.28950e23i		−	0.949401i	0.880147	−	0.474701i	$-0.157444\pi$
$180$	1.10661e23	−	1.81651e23i	0.231011	−	0.379207i
$181$		−	4.66195e23i		−	0.918210i	−0.888382	−	0.459105i	$-0.848170\pi$
$181$		−	4.66195e23i		−	0.918210i	0.888382	−	0.459105i	$-0.151830\pi$
$182$	1.05753e23	−	3.76865e23i	0.196582	−	0.700545i
$183$	−7.34492e22			−0.128899
$184$	−5.80575e23	−	6.23121e23i	−0.962214	−	1.03273i
$185$	1.01042e24			1.58198
$186$	3.50618e22	−	1.24948e23i	0.0518739	−	0.184860i
$187$			1.44321e24i			2.01834i
$188$	−6.60940e21	−	4.02641e21i	−0.00873987	−	0.00532428i
$189$		−	1.28293e24i		−	1.60456i
$190$	−8.22995e23	−	2.30942e23i	−0.973832	−	0.273269i
$191$	−1.73189e23			−0.193941			−0.0969707	−	0.995287i	$-0.530915\pi$
$191$	−1.73189e23			−0.193941			−0.0969707	+	0.995287i	$0.530915\pi$
$192$	7.13308e23	+	5.04881e22i	0.756161	+	0.0535213i
$193$	−4.94526e23			−0.496406			−0.248203	−	0.968708i	$-0.579840\pi$
$193$	−4.94526e23			−0.496406			−0.248203	+	0.968708i	$0.579840\pi$
$194$	1.46313e24	+	4.10572e23i	1.39112	+	0.390365i
$195$		−	4.30413e23i		−	0.387723i
$196$	1.20570e24	+	7.34509e23i	1.02932	+	0.627059i
$197$			2.03740e24i			1.64885i	0.565972	+	0.824425i	$0.308501\pi$
$197$			2.03740e24i			1.64885i	−0.565972	+	0.824425i	$0.691499\pi$
$198$	2.80210e23	−	9.98566e23i	0.215030	−	0.766289i
$199$	−1.41903e24			−1.03284			−0.516421	−	0.856335i	$-0.672736\pi$
$199$	−1.41903e24			−1.03284			−0.516421	+	0.856335i	$0.672736\pi$
$200$	8.85832e22	+	9.50748e22i	0.0611697	+	0.0656523i
$201$	−9.11868e21			−0.00597549
$202$	2.55798e23	−	9.11572e23i	0.159114	−	0.567024i
$203$		−	1.15970e24i		−	0.684917i
$204$	7.58456e23	−	1.24501e24i	0.425416	−	0.698325i
$205$			1.02851e24i			0.548018i
$206$	−2.23814e24	−	6.28049e23i	−1.13313	−	0.317971i
$207$	1.24775e24			0.600398
$208$	−9.51785e23	+	4.91272e23i	−0.435385	+	0.224728i
$209$	−4.16790e24			−1.81293
$210$	2.73486e24	+	7.67435e23i	1.13144	+	0.317497i
$211$		−	1.40265e24i		−	0.552057i	−0.961149	−	0.276029i	$-0.910982\pi$
$211$		−	1.40265e24i		−	0.552057i	0.961149	−	0.276029i	$-0.0890185\pi$
$212$	1.68880e24	−	2.77219e24i	0.632488	−	1.03824i
$213$			9.44474e23i			0.336670i
$214$	−1.17350e24	+	4.18192e24i	−0.398233	+	1.41916i
$215$	1.37791e24			0.445264
$216$	−2.56854e24	+	2.39316e24i	−0.790537	+	0.736560i
$217$	−1.28281e24			−0.376127
$218$	2.38340e23	−	8.49355e23i	0.0665891	−	0.237299i
$219$			3.01254e24i			0.802176i
$220$	6.57141e24	+	4.00327e24i	1.66809	+	1.01619i
$221$			2.18362e24i			0.528516i
$222$	−4.79166e24	−	1.34460e24i	−1.10606	−	0.310375i
$223$	−9.22558e23			−0.203139			−0.101569	−	0.994828i	$-0.532386\pi$
$223$	−9.22558e23			−0.203139			−0.101569	+	0.994828i	$0.532386\pi$
$224$	−1.42451e24	−	6.92363e24i	−0.299268	−	1.45455i
$225$	−1.90380e23			−0.0381684
$226$	−7.68348e24	−	2.15608e24i	−1.47034	−	0.412597i
$227$		−	3.79551e23i		−	0.0693424i	−0.999399	−	0.0346712i	$-0.988962\pi$
$227$		−	3.79551e23i		−	0.0693424i	0.999399	−	0.0346712i	$-0.0110384\pi$
$228$	3.59551e24	+	2.19037e24i	0.627256	+	0.382121i
$229$		−	6.08316e24i		−	1.01358i	−0.862070	−	0.506789i	$-0.830832\pi$
$229$		−	6.08316e24i		−	1.01358i	0.862070	−	0.506789i	$-0.169168\pi$
$230$	−2.50113e24	+	8.91311e24i	−0.398101	+	1.41869i
$231$	1.38502e25			2.10635
$232$	−2.32182e24	+	2.16329e24i	−0.337446	+	0.314406i
$233$	−2.00859e24			−0.279032			−0.139516	−	0.990220i	$-0.544555\pi$
$233$	−2.00859e24			−0.279032			−0.139516	+	0.990220i	$0.544555\pi$
$234$	4.23965e23	−	1.51086e24i	0.0563072	−	0.200658i
$235$			8.41230e22i			0.0106832i
$236$	1.42419e24	−	2.33783e24i	0.172979	−	0.283946i
$237$		−	3.23848e24i		−	0.376256i
$238$	−1.38748e25	−	3.89344e24i	−1.54230	−	0.432789i
$239$	1.53589e25			1.63373			0.816866	−	0.576827i	$-0.195710\pi$
$239$	1.53589e25			1.63373			0.816866	+	0.576827i	$0.195710\pi$
$240$	−3.56510e24	−	6.90698e24i	−0.362955	−	0.703186i
$241$	1.53732e24			0.149825			0.0749125	−	0.997190i	$-0.476132\pi$
$241$	1.53732e24			0.149825			0.0749125	+	0.997190i	$0.476132\pi$
$242$	2.58061e25	+	7.24150e24i	2.40802	+	0.675720i
$243$		−	8.75173e24i		−	0.782038i
$244$	1.03363e24	−	1.69671e24i	0.0884647	−	0.145216i
$245$		−	1.53459e25i		−	1.25820i
$246$	1.36867e24	−	4.87746e24i	0.107518	−	0.383155i
$247$	−6.30614e24			−0.474729
$248$	2.39293e24	+	2.56829e24i	0.172658	+	0.185311i
$249$	−8.54437e24			−0.590999
$250$	−3.87121e24	+	1.37956e25i	−0.256730	+	0.914892i
$251$		−	3.10657e25i		−	1.97564i	−0.155611	−	0.987818i	$-0.549734\pi$
$251$		−	3.10657e25i		−	1.97564i	0.155611	−	0.987818i	$-0.450266\pi$
$252$	8.84410e24	+	5.38778e24i	0.539446	+	0.328628i
$253$			4.51387e25i			2.64110i
$254$	−2.29775e25	−	6.44776e24i	−1.28988	−	0.361955i
$255$	−1.58463e25			−0.853601
$256$	−1.12044e25	+	1.57672e25i	−0.579256	+	0.815146i
$257$	2.74249e25			1.36096			0.680482	−	0.732764i	$-0.261770\pi$
$257$	2.74249e25			1.36096			0.680482	+	0.732764i	$0.261770\pi$
$258$	−6.53438e24	−	1.83363e24i	−0.311313	−	0.0873583i
$259$			4.91949e25i			2.25047i
$260$	9.94272e24	+	6.05706e24i	0.436803	+	0.266098i
$261$		−	4.64926e24i		−	0.196182i
$262$	4.00478e23	−	1.42716e24i	0.0162336	−	0.0578507i
$263$	−2.54321e25			−0.990481			−0.495240	−	0.868756i	$-0.664920\pi$
$263$	−2.54321e25			−0.990481			−0.495240	+	0.868756i	$0.664920\pi$
$264$	−2.58359e25	−	2.77292e25i	−0.966903	−	1.03776i
$265$	−3.52838e25			−1.26909
$266$	1.12440e25	−	4.00695e25i	0.388744	−	1.38534i
$267$			2.70680e25i			0.899681i
$268$	1.28324e23	−	2.10645e23i	0.00410103	−	0.00673189i
$269$		−	4.64238e24i		−	0.142673i	−0.997452	−	0.0713365i	$-0.977274\pi$
$269$		−	4.64238e24i		−	0.142673i	0.997452	−	0.0713365i	$-0.0227264\pi$
$270$	3.67403e25	+	1.03098e25i	1.08598	+	0.304741i
$271$	−2.75633e25			−0.783708			−0.391854	−	0.920028i	$-0.628166\pi$
$271$	−2.75633e25			−0.783708			−0.391854	+	0.920028i	$0.628166\pi$
$272$	1.80869e25	+	3.50413e25i	0.494754	+	0.958533i
$273$	2.09557e25			0.551562
$274$	5.15443e25	+	1.44640e25i	1.30557	+	0.366358i
$275$		−	6.88719e24i		−	0.167899i
$276$	2.37219e25	−	3.89397e25i	0.556678	−	0.913793i
$277$		−	1.95684e25i		−	0.442097i	−0.975263	−	0.221048i	$-0.929052\pi$
$277$		−	1.95684e25i		−	0.442097i	0.975263	−	0.221048i	$-0.0709479\pi$
$278$	1.53574e25	−	5.47282e25i	0.334078	−	1.19053i
$279$	−5.14280e24			−0.107735
$280$	−5.62148e25	+	5.23766e25i	−1.13421	+	1.05676i
$281$	2.27437e25			0.442023			0.221011	−	0.975271i	$-0.429064\pi$
$281$	2.27437e25			0.442023			0.221011	+	0.975271i	$0.429064\pi$
$282$	1.11945e23	−	3.98931e23i	0.00209599	−	0.00746934i
$283$		−	5.57861e25i		−	1.00640i	−0.864171	−	0.503198i	$-0.832157\pi$
$283$		−	5.57861e25i		−	1.00640i	0.864171	−	0.503198i	$-0.167843\pi$
$284$	−2.18178e25	−	1.32913e25i	−0.379287	−	0.231060i
$285$		−	4.57629e25i		−	0.766730i
$286$	5.46569e25	+	1.53374e25i	0.882677	+	0.247690i
$287$	−5.00757e25			−0.779591
$288$	−5.71087e24	−	2.77569e25i	−0.0857198	−	0.416630i
$289$	1.13011e25			0.163567
$290$	3.32113e25	+	9.31949e24i	0.463560	+	0.130081i
$291$			8.13577e25i			1.09527i
$292$	−6.95910e25	−	4.23945e25i	−0.903719	−	0.550541i
$293$		−	1.20185e25i		−	0.150570i	−0.997162	−	0.0752850i	$-0.976013\pi$
$293$		−	1.20185e25i		−	0.150570i	0.997162	−	0.0752850i	$-0.0239867\pi$
$294$	−2.04213e25	+	7.27741e25i	−0.246852	+	0.879690i
$295$	−2.97553e25			−0.347083
$296$	9.84923e25	−	9.17674e25i	1.10876	−	1.03306i
$297$	1.86064e26			2.02172
$298$	−9.92163e24	+	3.53571e25i	−0.104067	+	0.370856i
$299$			6.82961e25i			0.691590i
$300$	−3.61944e24	+	5.94136e24i	−0.0353890	+	0.0580915i
$301$			6.70869e25i			0.633417i
$302$	−9.22508e25	−	2.58867e25i	−0.841196	−	0.236050i
$303$	5.06882e25			0.446436
$304$	−1.01197e26	+	5.22336e25i	−0.860983	+	0.444403i
$305$	−2.15953e25			−0.177505
$306$	−5.56243e25	−	1.56089e25i	−0.441764	−	0.123964i
$307$		−	1.61739e26i		−	1.24125i	−0.784106	−	0.620627i	$-0.786878\pi$
$307$		−	1.61739e26i		−	1.24125i	0.784106	−	0.620627i	$-0.213122\pi$
$308$	−1.94909e26	+	3.19945e26i	−1.44560	+	2.37297i
$309$		−	1.24452e26i		−	0.892152i
$310$	1.03088e25	−	3.67367e25i	0.0714347	−	0.254567i
$311$	1.63077e25			0.109247			0.0546233	−	0.998507i	$-0.482604\pi$
$311$	1.63077e25			0.109247			0.0546233	+	0.998507i	$0.482604\pi$
$312$	−3.90904e25	−	4.19551e25i	−0.253190	−	0.271745i
$313$	−1.80717e25			−0.113184			−0.0565918	−	0.998397i	$-0.518023\pi$
$313$	−1.80717e25			−0.113184			−0.0565918	+	0.998397i	$0.518023\pi$
$314$	2.35605e25	−	8.39611e25i	0.142700	−	0.508530i
$315$		−	1.12566e26i		−	0.659395i
$316$	7.48103e25	+	4.55740e25i	0.423884	+	0.258228i
$317$			1.06034e26i			0.581198i	0.956845	+	0.290599i	$0.0938546\pi$
$317$			1.06034e26i			0.581198i	−0.956845	+	0.290599i	$0.906145\pi$
$318$	1.67324e26	+	4.69532e25i	0.887307	+	0.248989i
$319$	1.68192e26			0.862986
$320$	2.09725e26	+	1.48444e25i	1.04130	+	0.0737034i
$321$	−2.32537e26			−1.11735
$322$	−4.33956e26	−	1.21773e26i	−2.01818	−	0.566325i
$323$			2.32170e26i			1.04515i
$324$	−7.71555e25	−	4.70027e25i	−0.336236	−	0.204833i
$325$		−	1.04205e25i		−	0.0439657i
$326$	−1.15501e25	+	4.11602e25i	−0.0471845	+	0.168148i
$327$	4.72287e25			0.186833
$328$	9.34105e25	+	1.00256e26i	0.357866	+	0.384091i
$329$	−4.09573e24			−0.0151976
$330$	−1.11302e26	+	3.96638e26i	−0.400041	+	1.42560i
$331$		−	1.38816e26i		−	0.483332i	−0.970359	−	0.241666i	$-0.922306\pi$
$331$		−	1.38816e26i		−	0.483332i	0.970359	−	0.241666i	$-0.0776938\pi$
$332$	1.20242e26	−	1.97379e26i	0.405608	−	0.665810i
$333$			1.97223e26i			0.644604i
$334$	2.62613e26	+	7.36926e25i	0.831724	+	0.233392i
$335$	−2.68105e24			−0.00822876
$336$	3.36283e26	−	1.73575e26i	1.00033	−	0.516328i
$337$	8.42702e25			0.242974			0.121487	−	0.992593i	$-0.461234\pi$
$337$	8.42702e25			0.242974			0.121487	+	0.992593i	$0.461234\pi$
$338$	−2.61784e26	−	7.34600e25i	−0.731675	−	0.205317i
$339$		−	4.27242e26i		−	1.15765i
$340$	2.22999e26	−	3.66055e26i	0.585834	−	0.961653i
$341$		−	1.86046e26i		−	0.473914i
$342$	4.50774e25	−	1.60639e26i	0.111348	−	0.396805i
$343$	1.27256e26			0.304852
$344$	1.34314e26	−	1.25143e26i	0.312073	−	0.290766i
$345$	−4.95616e26			−1.11698
$346$	1.37398e26	−	4.89637e26i	0.300388	−	1.07047i
$347$			3.15434e26i			0.669035i	0.942389	+	0.334518i	$0.108573\pi$
$347$			3.15434e26i			0.669035i	−0.942389	+	0.334518i	$0.891427\pi$
$348$	−1.45094e26	−	8.83905e25i	−0.298584	−	0.181896i
$349$			5.55602e26i			1.10942i	0.832043	+	0.554711i	$0.187171\pi$
$349$			5.55602e26i			1.10942i	−0.832043	+	0.554711i	$0.812829\pi$
$350$	6.62123e25	+	1.85800e25i	0.128299	+	0.0360024i
$351$	2.81521e26			0.529402
$352$	1.00414e27	−	2.06597e26i	1.83272	−	0.377073i
$353$	−1.07638e27			−1.90692			−0.953461	−	0.301515i	$-0.902508\pi$
$353$	−1.07638e27			−1.90692			−0.953461	+	0.301515i	$0.902508\pi$
$354$	1.41107e26	+	3.95963e25i	0.242669	+	0.0680959i
$355$			2.77692e26i			0.463623i
$356$	−6.25283e26	−	3.80919e26i	−1.01357	−	0.617459i
$357$		−	7.71513e26i		−	1.21430i
$358$	−1.67830e26	+	5.98084e26i	−0.256506	+	0.914094i
$359$	5.85797e26			0.869471			0.434736	−	0.900558i	$-0.356842\pi$
$359$	5.85797e26			0.869471			0.434736	+	0.900558i	$0.356842\pi$
$360$	−2.25366e26	+	2.09979e26i	−0.324872	+	0.302691i
$361$	4.37199e25			0.0612144
$362$	−1.82402e26	+	6.50015e26i	−0.248079	+	0.884063i
$363$			1.43495e27i			1.89591i
$364$	−2.94902e26	+	4.84086e26i	−0.378542	+	0.621380i
$365$			8.85739e26i			1.10467i
$366$	1.02410e26	+	2.87376e25i	0.124106	+	0.0348256i
$367$	−6.87699e26			−0.809850			−0.404925	−	0.914350i	$-0.632702\pi$
$367$	−6.87699e26			−0.809850			−0.404925	+	0.914350i	$0.632702\pi$
$368$	5.65695e26	+	1.09597e27i	0.647411	+	1.25429i
$369$	−2.00754e26			−0.223300
$370$	−1.40883e27	−	3.95336e26i	−1.52314	−	0.427413i
$371$		−	1.71788e27i		−	1.80537i
$372$	−9.77733e25	+	1.60496e26i	−0.0998894	+	0.163970i
$373$		−	9.23247e25i		−	0.0917013i	−0.998948	−	0.0458506i	$-0.985400\pi$
$373$		−	9.23247e25i		−	0.0917013i	0.998948	−	0.0458506i	$-0.0145998\pi$
$374$	5.64668e26	−	2.01227e27i	0.545308	−	1.94328i
$375$	−7.67108e26			−0.720324
$376$	7.64012e24	+	8.20001e24i	0.00697634	+	0.00748758i
$377$	2.54479e26			0.225979
$378$	−5.01957e26	+	1.78879e27i	−0.433514	+	1.54488i
$379$		−	8.93084e26i		−	0.750206i	−0.926983	−	0.375103i	$-0.877607\pi$
$379$		−	8.93084e26i		−	0.750206i	0.926983	−	0.375103i	$-0.122393\pi$
$380$	1.05714e27	+	6.44006e26i	0.863785	+	0.526213i
$381$		−	1.27767e27i		−	1.01556i
$382$	2.41478e26	+	6.77616e25i	0.186729	+	0.0523985i
$383$	−6.66372e26			−0.501337			−0.250669	−	0.968073i	$-0.580650\pi$
$383$	−6.66372e26			−0.501337			−0.250669	+	0.968073i	$0.580650\pi$
$384$	−9.74810e26	−	3.49483e26i	−0.713579	−	0.255828i
$385$	4.07219e27			2.90062
$386$	6.89517e26	+	1.93487e26i	0.477945	+	0.134117i
$387$			2.68953e26i			0.181431i
$388$	−1.87940e27	−	1.14492e27i	−1.23392	−	0.751695i
$389$			2.51717e27i			1.60858i	0.594239	+	0.804288i	$0.297453\pi$
$389$			2.51717e27i			1.60858i	−0.594239	+	0.804288i	$0.702547\pi$
$390$	−1.68402e26	+	6.00124e26i	−0.104754	+	0.373304i
$391$	2.51442e27			1.52259
$392$	−1.39373e27	−	1.49587e27i	−0.821628	−	0.881838i
$393$	7.93576e25			0.0455477
$394$	7.97148e26	−	2.84074e27i	0.445480	−	1.58753i
$395$		−	9.52168e26i		−	0.518137i
$396$	−7.81393e26	+	1.28267e27i	−0.414067	+	0.679695i
$397$		−	3.62413e27i		−	1.87026i	−0.354300	−	0.935132i	$-0.615281\pi$
$397$		−	3.62413e27i		−	1.87026i	0.354300	−	0.935132i	$-0.384719\pi$
$398$	1.97855e27	+	5.55206e26i	0.994432	+	0.279050i
$399$	2.22808e27			1.09072
$400$	−8.63127e25	−	1.67221e26i	−0.0411571	−	0.0797374i
$401$	9.22349e26			0.428429			0.214215	−	0.976787i	$-0.431281\pi$
$401$	9.22349e26			0.428429			0.214215	+	0.976787i	$0.431281\pi$
$402$	1.27142e25	+	3.56775e24i	0.00575326	+	0.00161444i
$403$		−	2.81493e26i		−	0.124098i
$404$	−7.13318e26	+	1.17092e27i	−0.306393	+	0.502948i
$405$			9.82018e26i			0.411000i
$406$	−4.53742e26	+	1.61697e27i	−0.185048	+	0.659445i
$407$	−7.13476e27			−2.83555
$408$	−1.54464e27	+	1.43917e27i	−0.598266	+	0.557417i
$409$	−1.34833e27			−0.508979			−0.254490	−	0.967076i	$-0.581907\pi$
$409$	−1.34833e27			−0.508979			−0.254490	+	0.967076i	$0.581907\pi$
$410$	4.02414e26	−	1.43406e27i	0.148062	−	0.527637i
$411$			2.86614e27i			1.02792i
$412$	2.87490e27	+	1.75137e27i	1.00508	+	0.612292i
$413$		−	1.44871e27i		−	0.493749i
$414$	−1.73974e27	−	4.88192e26i	−0.578070	−	0.162214i
$415$	−2.51219e27			−0.813856
$416$	1.51929e27	−	3.12587e26i	0.479910	−	0.0987394i
$417$	3.04318e27			0.937343
$418$	5.81130e27	+	1.63072e27i	1.74551	+	0.489812i
$419$			5.06368e27i			1.48327i	0.670805	+	0.741634i	$0.265949\pi$
$419$			5.06368e27i			1.48327i	−0.670805	+	0.741634i	$0.734051\pi$
$420$	−3.51295e27	−	2.14007e27i	−1.00358	−	0.611379i
$421$		−	3.91945e27i		−	1.09210i	−0.837752	−	0.546051i	$-0.816131\pi$
$421$		−	3.91945e27i		−	1.09210i	0.837752	−	0.546051i	$-0.183869\pi$
$422$	−5.48798e26	+	1.95572e27i	−0.149153	+	0.531527i
$423$	−1.64199e25			−0.00435307
$424$	−3.43934e27	+	3.20450e27i	−0.889474	+	0.828742i
$425$	−3.83646e26			−0.0967936
$426$	3.69533e26	−	1.31688e27i	0.0909603	−	0.324149i
$427$		−	1.05142e27i		−	0.252513i
$428$	3.27241e27	−	5.37170e27i	0.766846	−	1.25879i
$429$			3.03922e27i			0.694960i
$430$	−1.92122e27	−	5.39118e26i	−0.428705	−	0.120300i
$431$	−2.77199e27			−0.603642			−0.301821	−	0.953365i	$-0.597595\pi$
$431$	−2.77199e27			−0.603642			−0.301821	+	0.953365i	$0.597595\pi$
$432$	4.51766e27	−	2.33183e27i	0.960139	−	0.495583i
$433$	−6.32717e27			−1.31246			−0.656230	−	0.754561i	$-0.727850\pi$
$433$	−6.32717e27			−1.31246			−0.656230	+	0.754561i	$0.727850\pi$
$434$	1.78862e27	+	5.01908e26i	0.362139	+	0.101621i
$435$			1.84672e27i			0.364976i
$436$	−6.64633e26	+	1.09100e27i	−0.128225	+	0.210483i
$437$			7.26147e27i			1.36763i
$438$	1.17868e27	−	4.20038e27i	0.216729	−	0.772344i
$439$	2.90516e27			0.521546			0.260773	−	0.965400i	$-0.416023\pi$
$439$	2.90516e27			0.521546			0.260773	+	0.965400i	$0.416023\pi$
$440$	−7.59620e27	−	8.15287e27i	−1.33151	−	1.42908i
$441$	2.99535e27			0.512676
$442$	8.54358e26	−	3.04462e27i	0.142793	−	0.508861i
$443$		−	4.43788e27i		−	0.724330i	−0.932114	−	0.362165i	$-0.882038\pi$
$443$		−	4.43788e27i		−	0.724330i	0.932114	−	0.362165i	$-0.117962\pi$
$444$	6.15493e27	+	3.74955e27i	0.981074	+	0.597665i
$445$			7.95847e27i			1.23894i
$446$	1.28632e27	+	3.60958e26i	0.195584	+	0.0548833i
$447$	−1.96604e27			−0.291987
$448$	−7.22735e26	+	1.02110e28i	−0.104848	+	1.48131i
$449$	−9.60802e27			−1.36159			−0.680796	−	0.732473i	$-0.738366\pi$
$449$	−9.60802e27			−1.36159			−0.680796	+	0.732473i	$0.738366\pi$
$450$	2.65446e26	+	7.44875e25i	0.0367490	+	0.0103122i
$451$		−	7.26250e27i		−	0.982274i
$452$	9.86948e27	+	6.01244e27i	1.30419	+	0.794506i
$453$		−	5.12964e27i		−	0.662301i
$454$	−1.48502e26	+	5.29208e26i	−0.0187347	+	0.0667636i
$455$	6.16133e27			0.759548
$456$	−4.15622e27	−	4.46080e27i	−0.500689	−	0.537380i
$457$	8.86135e27			1.04323			0.521615	−	0.853181i	$-0.325330\pi$
$457$	8.86135e27			1.04323			0.521615	+	0.853181i	$0.325330\pi$
$458$	−2.38008e27	+	8.48175e27i	−0.273845	+	0.975883i
$459$		−	1.03646e28i		−	1.16552i
$460$	6.97464e27	−	1.14490e28i	0.766593	−	1.25837i
$461$		−	1.19350e28i		−	1.28222i	−0.767450	−	0.641108i	$-0.778475\pi$
$461$		−	1.19350e28i		−	1.28222i	0.767450	−	0.641108i	$-0.221525\pi$
$462$	−1.93113e28	−	5.41899e27i	−2.02801	−	0.569085i
$463$	1.20448e28			1.23651			0.618255	−	0.785978i	$-0.287840\pi$
$463$	1.20448e28			1.23651			0.618255	+	0.785978i	$0.287840\pi$
$464$	4.08372e27	−	2.10784e27i	0.409842	−	0.211543i
$465$	2.04276e27			0.200429
$466$	2.80057e27	+	7.85875e26i	0.268655	+	0.0753879i
$467$			1.87848e28i			1.76189i	0.473219	+	0.880945i	$0.343092\pi$
$467$			1.87848e28i			1.76189i	−0.473219	+	0.880945i	$0.656908\pi$
$468$	−1.18227e27	+	1.94071e27i	−0.108426	+	0.177983i
$469$		−	1.30533e26i		−	0.0117059i
$470$	3.29138e25	−	1.17293e26i	0.00288636	−	0.0102859i
$471$	4.66868e27			0.400382
$472$	−2.90044e27	+	2.70240e27i	−0.243261	+	0.226652i
$473$	−9.72966e27			−0.798097
$474$	−1.26708e27	+	4.51541e27i	−0.101656	+	0.362263i
$475$		−	1.10794e27i		−	0.0869429i
$476$	1.78223e28	+	1.08572e28i	1.36801	+	0.833387i
$477$		−	6.88700e27i		−	0.517115i
$478$	−2.14148e28	−	6.00927e27i	−1.57297	−	0.441396i
$479$	2.46039e27			0.176799			0.0883997	−	0.996085i	$-0.471825\pi$
$479$	2.46039e27			0.176799			0.0883997	+	0.996085i	$0.471825\pi$
$480$	2.26840e27	+	1.10253e28i	0.159473	+	0.775097i
$481$	−1.07951e28			−0.742511
$482$	−2.14348e27	−	6.01486e26i	−0.144253	−	0.0404792i
$483$		−	2.41303e28i		−	1.58898i
$484$	−3.31481e28	−	2.01936e28i	−2.13590	−	1.30118i
$485$			2.39206e28i			1.50828i
$486$	−3.42418e27	+	1.22025e28i	−0.211289	+	0.752955i
$487$	2.24901e28			1.35812			0.679058	−	0.734084i	$-0.262388\pi$
$487$	2.24901e28			1.35812			0.679058	+	0.734084i	$0.262388\pi$
$488$	−2.10503e27	+	1.96130e27i	−0.124409	+	0.115914i
$489$	−2.28873e27			−0.132389
$490$	−6.00422e27	+	2.13968e28i	−0.339936	+	1.21141i
$491$			1.20477e28i			0.667649i	0.942635	+	0.333825i	$0.108339\pi$
$491$			1.20477e28i			0.667649i	−0.942635	+	0.333825i	$0.891661\pi$
$492$	−3.81668e27	+	6.26513e27i	−0.207039	+	0.339857i
$493$		−	9.36901e27i		−	0.497509i
$494$	8.79265e27	+	2.46733e27i	0.457074	+	0.128261i
$495$	1.63255e28			0.830829
$496$	−2.33160e27	−	4.51721e27i	−0.116170	−	0.225068i
$497$	−1.35201e28			−0.659534
$498$	1.19134e28	+	3.34305e27i	0.569020	+	0.159674i
$499$			3.02192e28i			1.41328i	0.707575	+	0.706638i	$0.249789\pi$
$499$			3.02192e28i			1.41328i	−0.707575	+	0.706638i	$0.750211\pi$
$500$	1.07952e28	−	1.77205e28i	0.494365	−	0.811506i
$501$			1.46027e28i			0.654843i
$502$	−1.21547e28	+	4.33149e28i	−0.533771	+	1.90216i
$503$	−3.30201e28			−1.42009			−0.710043	−	0.704159i	$-0.751324\pi$
$503$	−3.30201e28			−1.42009			−0.710043	+	0.704159i	$0.751324\pi$
$504$	−1.02233e28	−	1.09725e28i	−0.430597	−	0.462152i
$505$	1.49032e28			0.614781
$506$	1.76609e28	−	6.29369e28i	0.713562	−	2.54287i
$507$		−	1.45566e28i		−	0.576072i
$508$	2.95147e28	+	1.79802e28i	1.14412	+	0.696989i
$509$		−	2.21692e28i		−	0.841810i	−0.907105	−	0.420905i	$-0.861713\pi$
$509$		−	2.21692e28i		−	0.841810i	0.907105	−	0.420905i	$-0.138287\pi$
$510$	2.20944e28	+	6.19997e27i	0.821856	+	0.230623i
$511$	−4.31244e28			−1.57146
$512$	2.17914e28	−	1.76004e28i	0.777947	−	0.628330i
$513$	2.99322e28			1.04690
$514$	−3.82385e28	−	1.07302e28i	−1.31035	−	0.367701i
$515$		−	3.65911e28i		−	1.22857i
$516$	8.39346e27	+	5.11325e27i	0.276134	+	0.168219i
$517$		−	5.94006e26i		−	0.0191488i
$518$	1.92479e28	−	6.85924e28i	0.608023	−	2.16677i
$519$	2.72264e28			0.842817
$520$	−1.14933e28	−	1.23355e28i	−0.348665	−	0.374216i
$521$	−2.99139e28			−0.889358			−0.444679	−	0.895690i	$-0.646682\pi$
$521$	−2.99139e28			−0.889358			−0.444679	+	0.895690i	$0.646682\pi$
$522$	−1.81906e27	+	6.48246e27i	−0.0530037	+	0.188886i
$523$			8.60630e27i			0.245781i	0.992420	+	0.122891i	$0.0392165\pi$
$523$			8.60630e27i			0.245781i	−0.992420	+	0.122891i	$0.960784\pi$
$524$	−1.11677e27	+	1.83320e27i	−0.0312598	+	0.0513133i
$525$			3.68176e27i			0.101014i
$526$	3.54599e28	+	9.95048e27i	0.953646	+	0.267605i
$527$	−1.03636e28			−0.273211
$528$	2.51737e28	+	4.87713e28i	0.650566	+	1.26040i
$529$	3.91708e28			0.992379
$530$	4.91962e28	+	1.38051e28i	1.22190	+	0.342880i
$531$		−	5.80791e27i		−	0.141425i
$532$	−3.13550e28	+	5.14695e28i	−0.748573	+	1.22879i
$533$		−	1.09884e28i		−	0.257216i
$534$	1.05906e28	−	3.77409e28i	0.243073	−	0.866222i
$535$	−6.83698e28			−1.53868
$536$	−2.61339e26	+	2.43495e26i	−0.00576731	+	0.00537353i
$537$	−3.32567e28			−0.719696
$538$	−1.81637e27	+	6.47287e27i	−0.0385469	+	0.137367i
$539$			1.08360e29i			2.25521i
$540$	−4.71932e28	−	2.87499e28i	−0.963264	−	0.586815i
$541$			5.48447e28i			1.09790i	0.835855	+	0.548951i	$0.184973\pi$
$541$			5.48447e28i			1.09790i	−0.835855	+	0.548951i	$0.815027\pi$
$542$	3.84315e28	+	1.07844e28i	0.754562	+	0.211739i
$543$	−3.61443e28			−0.696051
$544$	−1.15083e28	−	5.59347e28i	−0.217382	−	1.05656i
$545$	1.38860e28			0.257286
$546$	−2.92185e28	−	8.19907e27i	−0.531050	−	0.149019i
$547$			1.26984e28i			0.226403i	0.993572	+	0.113201i	$0.0361105\pi$
$547$			1.26984e28i			0.226403i	−0.993572	+	0.113201i	$0.963889\pi$
$548$	−6.62090e28	−	4.03342e28i	−1.15803	−	0.705468i
$549$		−	4.21516e27i		−	0.0723277i
$550$	−2.69467e27	+	9.60281e27i	−0.0453625	+	0.161655i
$551$	2.70570e28			0.446878
$552$	−4.83109e28	+	4.50123e28i	−0.782861	+	0.729408i
$553$	4.63586e28			0.737083
$554$	−7.65628e27	+	2.72842e28i	−0.119444	+	0.425655i
$555$		−	7.83385e28i		−	1.19922i
$556$	−4.28256e28	+	7.02987e28i	−0.643307	+	1.05600i
$557$			5.91846e27i			0.0872427i	0.999048	+	0.0436214i	$0.0138895\pi$
$557$			5.91846e27i			0.0872427i	−0.999048	+	0.0436214i	$0.986110\pi$
$558$	7.17059e27	+	2.01216e27i	0.103728	+	0.0291074i
$559$	−1.47212e28			−0.208987
$560$	9.88730e28	−	5.10341e28i	1.37754	−	0.711028i
$561$	1.11893e29			1.53001
$562$	−3.17115e28	−	8.89864e27i	−0.425584	−	0.119424i
$563$		−	2.87457e28i		−	0.378647i	−0.981915	−	0.189323i	$-0.939371\pi$
$563$		−	2.87457e28i		−	0.378647i	0.981915	−	0.189323i	$-0.0606294\pi$
$564$	−3.12170e26	+	5.12430e26i	−0.00403608	+	0.00662528i
$565$		−	1.25617e29i		−	1.59418i
$566$	−2.18267e28	+	7.77825e28i	−0.271904	+	0.968968i
$567$	−4.78119e28			−0.584675
$568$	2.52202e28	+	2.70684e28i	0.302755	+	0.324941i
$569$	2.34982e28			0.276921			0.138461	−	0.990368i	$-0.455785\pi$
$569$	2.34982e28			0.276921			0.138461	+	0.990368i	$0.455785\pi$
$570$	−1.79051e28	+	6.38071e28i	−0.207152	+	0.738216i
$571$			2.01511e27i			0.0228886i	0.999935	+	0.0114443i	$0.00364292\pi$
$571$			2.01511e27i			0.0228886i	−0.999935	+	0.0114443i	$0.996357\pi$
$572$	−7.02072e28	−	4.27699e28i	−0.782931	−	0.476957i
$573$			1.34274e28i			0.147018i
$574$	6.98205e28	+	1.95925e28i	0.750599	+	0.210627i
$575$	−1.19991e28			−0.126659
$576$	−2.89746e27	+	4.09359e28i	−0.0300318	+	0.424295i
$577$	−7.56626e28			−0.770079			−0.385039	−	0.922900i	$-0.625812\pi$
$577$	−7.56626e28			−0.770079			−0.385039	+	0.922900i	$0.625812\pi$
$578$	−1.57572e28	−	4.42166e27i	−0.157484	−	0.0441919i
$579$			3.83408e28i			0.376302i
$580$	−4.26601e28	−	2.59883e28i	−0.411176	−	0.250486i
$581$		−	1.22312e29i		−	1.15776i
$582$	3.18318e28	−	1.13437e29i	0.295917	−	1.05454i
$583$	2.49145e29			2.27474
$584$	8.04435e28	+	8.63386e28i	0.721367	+	0.774230i
$585$	2.47009e28			0.217558
$586$	−4.70231e27	+	1.67573e28i	−0.0406805	+	0.144970i
$587$			9.25532e28i			0.786486i	0.919434	+	0.393243i	$0.128647\pi$
$587$			9.25532e28i			0.786486i	−0.919434	+	0.393243i	$0.871353\pi$
$588$	5.69468e28	−	9.34788e28i	0.475343	−	0.780282i
$589$		−	2.99292e28i		−	0.245406i
$590$	4.14879e28	+	1.16420e28i	0.334176	+	0.0937738i
$591$	1.57961e29			1.24991
$592$	−1.73232e29	+	8.94153e28i	−1.34664	+	0.695079i
$593$	−1.15554e29			−0.882492			−0.441246	−	0.897386i	$-0.645463\pi$
$593$	−1.15554e29			−0.882492			−0.441246	+	0.897386i	$0.645463\pi$
$594$	−2.59430e29	−	7.27991e28i	−1.94653	−	0.546221i
$595$		−	2.26838e29i		−	1.67220i
$596$	2.76674e28	−	4.54164e28i	0.200393	−	0.328948i
$597$			1.10018e29i			0.782948i
$598$	2.67214e28	−	9.52252e28i	0.186851	−	0.665870i
$599$	−1.49063e29			−1.02421			−0.512106	−	0.858922i	$-0.671134\pi$
$599$	−1.49063e29			−1.02421			−0.512106	+	0.858922i	$0.671134\pi$
$600$	7.37119e27	−	6.86790e27i	0.0497679	−	0.0463698i
$601$	9.42768e28			0.625494			0.312747	−	0.949837i	$-0.398751\pi$
$601$	9.42768e28			0.625494			0.312747	+	0.949837i	$0.398751\pi$
$602$	2.62483e28	−	9.35393e28i	0.171135	−	0.609861i
$603$		−	5.23310e26i		−	0.00335295i
$604$	1.18497e29	+	7.21877e28i	0.746138	+	0.454543i
$605$			4.21901e29i			2.61083i
$606$	−7.06746e28	−	1.98322e28i	−0.429834	−	0.120617i
$607$	−1.64280e27			−0.00981979			−0.00490989	−	0.999988i	$-0.501563\pi$
$607$	−1.64280e27			−0.00981979			−0.00490989	+	0.999988i	$0.501563\pi$
$608$	1.61535e29	−	3.32352e28i	0.949031	−	0.195259i
$609$	−8.99122e28			−0.519203
$610$	3.01103e28	+	8.44934e27i	0.170904	+	0.0479578i
$611$		−	8.98748e26i		−	0.00501424i
$612$	7.14499e28	+	4.35269e28i	0.391842	+	0.238708i
$613$		−	5.93094e28i		−	0.319734i	−0.987139	−	0.159867i	$-0.948893\pi$
$613$		−	5.93094e28i		−	0.319734i	0.987139	−	0.159867i	$-0.0511065\pi$
$614$	−6.32814e28	+	2.25512e29i	−0.335358	+	1.19509i
$615$	7.97412e28			0.415426
$616$	3.96942e29	−	3.69840e29i	2.03296	−	1.89416i
$617$	−2.96236e29			−1.49157			−0.745785	−	0.666187i	$-0.767925\pi$
$617$	−2.96236e29			−1.49157			−0.745785	+	0.666187i	$0.767925\pi$
$618$	−4.86929e28	+	1.73524e29i	−0.241039	+	0.858973i
$619$		−	8.60651e28i		−	0.418866i	−0.977823	−	0.209433i	$-0.932838\pi$
$619$		−	8.60651e28i		−	0.418866i	0.977823	−	0.209433i	$-0.0671618\pi$
$620$	−2.87470e28	+	4.71886e28i	−0.137556	+	0.225800i
$621$		−	3.24168e29i		−	1.52514i
$622$	−2.27378e28	−	6.38050e27i	−0.105184	−	0.0295159i
$623$	−3.87477e29			−1.76247
$624$	3.80885e28	+	7.37923e28i	0.170355	+	0.330045i
$625$	−2.45946e29			−1.08168
$626$	2.51974e28	+	7.07070e27i	0.108974	+	0.0305796i
$627$			3.23139e29i			1.37430i
$628$	−6.57008e28	+	1.07849e29i	−0.274786	+	0.451064i
$629$			3.97436e29i			1.63469i
$630$	−4.40422e28	+	1.56950e29i	−0.178153	+	0.634873i
$631$	3.25638e29			1.29547			0.647735	−	0.761866i	$-0.275717\pi$
$631$	3.25638e29			1.29547			0.647735	+	0.761866i	$0.275717\pi$
$632$	−8.64767e28	−	9.28139e28i	−0.338353	−	0.363148i
$633$	−1.08748e29			−0.418488
$634$	4.14867e28	−	1.47844e29i	0.157026	−	0.559584i
$635$		−	3.75657e29i		−	1.39852i
$636$	−2.14929e29	−	1.30934e29i	−0.787038	−	0.479459i
$637$			1.63952e29i			0.590544i
$638$	−2.34510e29	−	6.58064e28i	−0.830892	−	0.233159i
$639$	−5.42023e28			−0.188912
$640$	−2.86611e29	−	1.02754e29i	−0.982660	−	0.352297i
$641$	−1.26230e29			−0.425749			−0.212874	−	0.977080i	$-0.568283\pi$
$641$	−1.26230e29			−0.425749			−0.212874	+	0.977080i	$0.568283\pi$
$642$	3.24226e29	+	9.09818e28i	1.07580	+	0.301882i
$643$			4.92343e29i			1.60714i	0.595213	+	0.803568i	$0.297068\pi$
$643$			4.92343e29i			1.60714i	−0.595213	+	0.803568i	$0.702932\pi$
$644$	5.57420e29	+	3.39577e29i	1.79011	+	1.09053i
$645$		−	1.06830e29i		−	0.337533i
$646$	9.08381e28	−	3.23714e29i	0.282375	−	1.00628i
$647$	3.75642e29			1.14889			0.574447	−	0.818542i	$-0.305217\pi$
$647$	3.75642e29			1.14889			0.574447	+	0.818542i	$0.305217\pi$
$648$	8.91877e28	+	9.57235e28i	0.268391	+	0.288059i
$649$	2.10107e29			0.622117
$650$	−4.07710e27	+	1.45293e28i	−0.0118785	+	0.0423306i
$651$			9.94566e28i			0.285124i
$652$	3.22085e28	−	5.28706e28i	0.0908595	−	0.149147i
$653$		−	3.65957e29i		−	1.01588i	−0.861393	−	0.507939i	$-0.830407\pi$
$653$		−	3.65957e29i		−	1.01588i	0.861393	−	0.507939i	$-0.169593\pi$
$654$	−6.58509e28	−	1.84786e28i	−0.179885	−	0.0504780i
$655$	2.33325e28			0.0627231
$656$	−9.10163e28	−	1.76334e29i	−0.240785	−	0.466494i
$657$	−1.72886e29			−0.450116
$658$	5.71068e27	+	1.60249e27i	0.0146324	+	0.00410603i
$659$		−	2.28709e29i		−	0.576749i	−0.957518	−	0.288375i	$-0.906885\pi$
$659$		−	2.28709e29i		−	0.576749i	0.957518	−	0.288375i	$-0.0931148\pi$
$660$	3.10375e29	−	5.09485e29i	0.770328	−	1.26450i
$661$		−	6.81720e29i		−	1.66529i	−0.553805	−	0.832646i	$-0.686825\pi$
$661$		−	6.81720e29i		−	1.66529i	0.553805	−	0.832646i	$-0.313175\pi$
$662$	−5.43128e28	+	1.93551e29i	−0.130585	+	0.465357i
$663$	1.69297e29			0.400643
$664$	−2.44879e29	+	2.28159e29i	−0.570410	+	0.531463i
$665$	6.55093e29			1.50202
$666$	7.71650e28	−	2.74988e29i	0.174157	−	0.620632i
$667$		−	2.93030e29i		−	0.651016i
$668$	−3.37329e29	−	2.05499e29i	−0.737735	−	0.449425i
$669$			7.15264e28i			0.153990i
$670$	3.73818e27	+	1.04898e27i	0.00792274	+	0.00222322i
$671$	1.52488e29			0.318163
$672$	−5.36792e29	+	1.10443e29i	−1.10263	+	0.226861i
$673$	9.26117e29			1.87287			0.936435	−	0.350841i	$-0.114104\pi$
$673$	9.26117e29			1.87287			0.936435	+	0.350841i	$0.114104\pi$
$674$	−1.17498e29	−	3.29713e28i	−0.233938	−	0.0656459i
$675$			4.94610e28i			0.0969558i
$676$	3.36264e29	+	2.04850e29i	0.648993	+	0.395363i
$677$		−	1.07428e29i		−	0.204145i	−0.994777	−	0.102072i	$-0.967453\pi$
$677$		−	1.07428e29i		−	0.204145i	0.994777	−	0.102072i	$-0.0325473\pi$
$678$	−1.67162e29	+	5.95703e29i	−0.312770	+	1.11460i
$679$	−1.16463e30			−2.14563
$680$	−4.54149e29	+	4.23141e29i	−0.823863	+	0.767611i
$681$	−2.94268e28			−0.0525652
$682$	−7.27920e28	+	2.59404e29i	−0.128041	+	0.456290i
$683$			1.77787e28i			0.0307951i	0.999881	+	0.0153976i	$0.00490139\pi$
$683$			1.77787e28i			0.0307951i	−0.999881	+	0.0153976i	$0.995099\pi$
$684$	−1.25703e29	+	2.06342e29i	−0.214415	+	0.351965i
$685$			8.42693e29i			1.41553i
$686$	−1.77432e29	−	4.97898e28i	−0.293515	−	0.0823639i
$687$	−4.71631e29			−0.768345
$688$	−2.36237e29	+	1.21936e29i	−0.379026	+	0.195637i
$689$	3.76963e29			0.595657
$690$	6.91037e29	+	1.93914e29i	1.07544	+	0.301782i
$691$		−	7.13999e29i		−	1.09440i	−0.837000	−	0.547202i	$-0.815693\pi$
$691$		−	7.13999e29i		−	1.09440i	0.837000	−	0.547202i	$-0.184307\pi$
$692$	−3.83148e29	+	6.28942e29i	−0.578433	+	0.949504i
$693$			7.94845e29i			1.18191i
$694$	1.23416e29	−	4.39809e29i	0.180758	−	0.644154i
$695$	8.94746e29			1.29080
$696$	1.67721e29	+	1.80012e29i	0.238336	+	0.255802i
$697$	−4.04552e29			−0.566279
$698$	2.17384e29	−	7.74676e29i	0.299740	−	1.06816i
$699$			1.55727e29i			0.211521i
$700$	−8.50502e28	−	5.18121e28i	−0.113801	−	0.0693269i
$701$		−	3.07844e29i		−	0.405781i	−0.979201	−	0.202890i	$-0.934966\pi$
$701$		−	3.07844e29i		−	0.405781i	0.979201	−	0.202890i	$-0.0650335\pi$
$702$	−3.92524e29	−	1.10147e29i	−0.509714	−	0.143032i
$703$	−1.14777e30			−1.46833
$704$	−1.48090e30	−	1.04819e29i	−1.86644	−	0.132107i
$705$	6.52210e27			0.00809844
$706$	1.50080e30	+	4.21144e29i	1.83601	+	0.515206i
$707$			7.25599e29i			0.874566i
$708$	−1.81253e29	−	1.10418e29i	−0.215246	−	0.131127i
$709$		−	9.13833e29i		−	1.06925i	−0.845088	−	0.534627i	$-0.820452\pi$
$709$		−	9.13833e29i		−	1.06925i	0.845088	−	0.534627i	$-0.179548\pi$
$710$	1.08649e29	−	3.87185e29i	0.125260	−	0.446381i
$711$	1.85853e29			0.211124
$712$	7.22794e29	+	7.75762e29i	0.809049	+	0.868338i
$713$	−3.24136e29			−0.357510
$714$	−3.01860e29	+	1.07572e30i	−0.328076	+	1.16914i
$715$			8.93582e29i			0.957019i
$716$	4.68010e29	−	7.68244e29i	0.493934	−	0.810797i
$717$		−	1.19078e30i		−	1.23845i
$718$	−8.16776e29	−	2.29197e29i	−0.837136	−	0.234911i
$719$	−3.76524e29			−0.380311			−0.190155	−	0.981754i	$-0.560899\pi$
$719$	−3.76524e29			−0.380311			−0.190155	+	0.981754i	$0.560899\pi$
$720$	3.96384e29	−	2.04597e29i	0.394570	−	0.203661i
$721$	1.78153e30			1.74772
$722$	−6.09587e28	−	1.71058e28i	−0.0589379	−	0.0165387i
$723$		−	1.19189e29i		−	0.113575i
$724$	5.08646e29	−	8.34949e29i	0.477706	−	0.784160i
$725$			4.47101e28i			0.0413863i
$726$	5.61437e29	−	2.00076e30i	0.512231	−	1.82541i
$727$	−2.42270e29			−0.217866			−0.108933	−	0.994049i	$-0.534743\pi$
$727$	−2.42270e29			−0.217866			−0.108933	+	0.994049i	$0.534743\pi$
$728$	6.00584e29	−	5.59577e29i	0.532346	−	0.495999i
$729$	−1.12916e30			−0.986541
$730$	3.46552e29	−	1.23499e30i	0.298455	−	1.06358i
$731$			5.41983e29i			0.460101i
$732$	−1.31547e29	−	8.01375e28i	−0.110081	−	0.0670609i
$733$			1.97789e30i			1.63159i	0.578341	+	0.815795i	$0.303700\pi$
$733$			1.97789e30i			1.63159i	−0.578341	+	0.815795i	$0.696300\pi$
$734$	9.58858e29	+	2.69067e29i	0.779733	+	0.218803i
$735$	−1.18978e30			−0.953781
$736$	−3.59940e29	−	1.74944e30i	−0.284455	−	1.38256i
$737$	1.89313e28			0.0147493
$738$	2.79912e29	+	7.85466e28i	0.214995	+	0.0603303i
$739$			2.13243e29i			0.161476i	0.996735	+	0.0807381i	$0.0257277\pi$
$739$			2.13243e29i			0.161476i	−0.996735	+	0.0807381i	$0.974272\pi$
$740$	1.80965e30	+	1.10243e30i	1.35102	+	0.823036i
$741$			4.88918e29i			0.359869i
$742$	−6.72133e29	+	2.39524e30i	−0.487769	+	1.73823i
$743$	1.56953e30			1.12302			0.561509	−	0.827470i	$-0.310221\pi$
$743$	1.56953e30			1.12302			0.561509	+	0.827470i	$0.310221\pi$
$744$	1.99121e29	−	1.85525e29i	0.140475	−	0.130884i
$745$	−5.78050e29			−0.402091
$746$	−3.61227e28	+	1.28728e29i	−0.0247755	+	0.0882910i
$747$		−	4.90351e29i		−	0.331620i
$748$	−1.57463e30	+	2.58478e30i	−1.05006	+	1.72368i
$749$		−	3.32875e30i		−	2.18888i
$750$	1.06958e30	+	3.00137e29i	0.693536	+	0.194615i
$751$	−1.04794e30			−0.670068			−0.335034	−	0.942206i	$-0.608748\pi$
$751$	−1.04794e30			−0.670068			−0.335034	+	0.942206i	$0.608748\pi$
$752$	−7.44430e27	−	1.44225e28i	−0.00469393	−	0.00909397i
$753$	−2.40854e30			−1.49764
$754$	−3.54820e29	−	9.95669e28i	−0.217575	−	0.0610542i
$755$		−	1.50820e30i		−	0.912045i
$756$	1.39976e30	−	2.29772e30i	0.834783	−	1.37031i
$757$			2.85700e30i			1.68036i	0.542306	+	0.840181i	$0.317551\pi$
$757$			2.85700e30i			1.68036i	−0.542306	+	0.840181i	$0.682449\pi$
$758$	−3.49426e29	+	1.24523e30i	−0.202688	+	0.722307i
$759$	3.49963e30			2.00209
$760$	−1.22200e30	−	1.31155e30i	−0.689491	−	0.740018i
$761$	2.38724e29			0.132849			0.0664244	−	0.997791i	$-0.478841\pi$
$761$	2.38724e29			0.132849			0.0664244	+	0.997791i	$0.478841\pi$
$762$	−4.99898e29	+	1.78145e30i	−0.274381	+	0.977794i
$763$			6.76076e29i			0.366006i
$764$	−3.10180e29	−	1.88960e29i	−0.165628	−	0.100900i
$765$		−	9.09398e29i		−	0.478971i
$766$	9.29122e29	+	2.60723e29i	0.482693	+	0.135450i
$767$	3.17898e29			0.162906
$768$	1.22244e30	+	8.68685e29i	0.617923	+	0.439106i
$769$	−3.78810e30			−1.88884			−0.944419	−	0.328743i	$-0.893375\pi$
$769$	−3.78810e30			−1.88884			−0.944419	+	0.328743i	$0.893375\pi$
$770$	−5.67785e30	−	1.59328e30i	−2.79275	−	0.783679i
$771$		−	2.12626e30i		−	1.03168i
$772$	−8.85690e29	−	5.39558e29i	−0.423936	−	0.258259i
$773$			3.45371e30i			1.63080i	0.578896	+	0.815401i	$0.303484\pi$
$773$			3.45371e30i			1.63080i	−0.578896	+	0.815401i	$0.696516\pi$
$774$	1.05230e29	−	3.75000e29i	0.0490183	−	0.174683i
$775$	4.94562e28			0.0227276
$776$	2.17248e30	+	2.33169e30i	0.984937	+	1.05712i
$777$	3.81410e30			1.70597
$778$	9.84862e29	−	3.50969e30i	0.434600	−	1.54875i
$779$		−	1.16832e30i		−	0.508649i
$780$	4.69606e29	−	7.70864e29i	0.201716	−	0.331119i
$781$		−	1.96083e30i		−	0.831004i
$782$	−3.50585e30	−	9.83785e29i	−1.46596	−	0.411367i
$783$	−1.20789e30			−0.498343
$784$	1.35801e30	+	2.63099e30i	0.552820	+	1.07103i
$785$	1.37267e30			0.551361
$786$	−1.10648e29	−	3.10493e28i	−0.0438539	−	0.0123059i
$787$			3.28648e30i			1.28528i	0.766170	+	0.642638i	$0.222160\pi$
$787$			3.28648e30i			1.28528i	−0.766170	+	0.642638i	$0.777840\pi$
$788$	−2.22293e30	+	3.64896e30i	−0.857827	+	1.40813i
$789$			1.97176e30i			0.750836i
$790$	−3.72543e29	+	1.32761e30i	−0.139988	+	0.498868i
$791$	6.11595e30			2.26783
$792$	1.59135e30	−	1.48269e30i	0.582305	−	0.542546i
$793$	2.30719e29			0.0833133
$794$	−1.41797e30	+	5.05311e30i	−0.505302	+	1.80071i
$795$			2.73557e30i			0.962040i
$796$	−2.54146e30	−	1.54825e30i	−0.882057	−	0.537344i
$797$			1.48318e29i			0.0508022i	0.999677	+	0.0254011i	$0.00808630\pi$
$797$			1.48318e29i			0.0508022i	−0.999677	+	0.0254011i	$0.991914\pi$
$798$	−3.10660e30	−	8.71752e29i	−1.05016	−	0.294688i
$799$	−3.30887e28			−0.0110392
$800$	5.49191e28	+	2.66927e29i	0.0180833	+	0.0878917i
$801$	−1.55340e30			−0.504827
$802$	−1.28603e30	−	3.60876e29i	−0.412496	−	0.115752i
$803$		−	6.25435e30i		−	1.98002i
$804$	−1.63314e28	−	9.94903e27i	−0.00510312	−	0.00310880i
$805$		−	7.09472e30i		−	2.18816i
$806$	−1.10136e29	+	3.92485e29i	−0.0335284	+	0.119483i
$807$	−3.59926e29			−0.108154
$808$	1.45271e30	−	1.35352e30i	0.430883	−	0.401463i
$809$	−1.73067e30			−0.506705			−0.253352	−	0.967374i	$-0.581533\pi$
$809$	−1.73067e30			−0.506705			−0.253352	+	0.967374i	$0.581533\pi$
$810$	3.84222e29	−	1.36923e30i	0.111043	−	0.395715i
$811$		−	3.04306e30i		−	0.868145i	−0.900878	−	0.434072i	$-0.857076\pi$
$811$		−	3.04306e30i		−	0.868145i	0.900878	−	0.434072i	$-0.142924\pi$
$812$	1.26530e30	−	2.07701e30i	0.356333	−	0.584925i
$813$			2.13700e30i			0.594091i
$814$	9.94799e30	+	2.79153e30i	2.73010	+	0.766101i
$815$	−6.72925e29			−0.182310
$816$	2.71677e30	−	1.40228e30i	0.726618	−	0.375050i
$817$	−1.56521e30			−0.413276
$818$	1.87997e30	+	5.27542e29i	0.490051	+	0.137514i
$819$			1.20262e30i			0.309491i
$820$	−1.12217e30	+	1.84206e30i	−0.285111	+	0.468012i
$821$		−	3.76870e30i		−	0.945340i	−0.881239	−	0.472670i	$-0.843290\pi$
$821$		−	3.76870e30i		−	0.945340i	0.881239	−	0.472670i	$-0.156710\pi$
$822$	1.12140e30	−	3.99625e30i	0.277719	−	0.989689i
$823$	2.83769e30			0.693853			0.346926	−	0.937892i	$-0.387225\pi$
$823$	2.83769e30			0.693853			0.346926	+	0.937892i	$0.387225\pi$
$824$	−3.32323e30	−	3.56677e30i	−0.802278	−	0.861071i
$825$	−5.33967e29			−0.127276
$826$	−5.66819e29	+	2.01994e30i	−0.133399	+	0.475387i
$827$			5.52943e29i			0.128491i	0.997934	+	0.0642455i	$0.0204641\pi$
$827$			5.52943e29i			0.128491i	−0.997934	+	0.0642455i	$0.979536\pi$
$828$	2.23471e30	+	1.36137e30i	0.512745	+	0.312362i
$829$			8.01599e30i			1.81608i	0.418885	+	0.908039i	$0.362421\pi$
$829$			8.01599e30i			1.81608i	−0.418885	+	0.908039i	$0.637579\pi$
$830$	3.50275e30	+	9.82914e29i	0.783590	+	0.219885i
$831$	−1.51715e30			−0.335132
$832$	−2.24064e30	−	1.58593e29i	−0.488740	−	0.0345931i
$833$	6.03612e30			1.30013
$834$	−4.24310e30	−	1.19067e30i	−0.902484	−	0.253248i
$835$			4.29345e30i			0.901775i
$836$	−7.46465e30	−	4.54743e30i	−1.54826	−	0.943192i
$837$			1.33611e30i			0.273668i
$838$	1.98120e30	−	7.06029e30i	0.400744	−	1.42811i
$839$	−9.36879e29			−0.187147			−0.0935735	−	0.995612i	$-0.529829\pi$
$839$	−9.36879e29			−0.187147			−0.0935735	+	0.995612i	$0.529829\pi$
$840$	4.06078e30	+	4.35836e30i	0.801082	+	0.859787i
$841$	4.04098e30			0.787279
$842$	−1.53351e30	+	5.46488e30i	−0.295060	+	1.05149i
$843$		−	1.76333e30i		−	0.335076i
$844$	1.53038e30	−	2.51213e30i	0.287212	−	0.471462i
$845$		−	4.27989e30i		−	0.793300i
$846$	2.28942e28	+	6.42440e27i	0.00419118	+	0.00117610i
$847$	−2.05413e31			−3.71408
$848$	6.04925e30	−	3.12237e30i	1.08030	−	0.557607i
$849$	−4.32512e30			−0.762900
$850$	5.34917e29	+	1.50104e29i	0.0931939	+	0.0261514i
$851$			1.24304e31i			2.13907i
$852$	−1.03048e30	+	1.69154e30i	−0.175155	+	0.287519i
$853$		−	3.37231e30i		−	0.566191i	−0.959092	−	0.283096i	$-0.908639\pi$
$853$		−	3.37231e30i		−	0.566191i	0.959092	−	0.283096i	$-0.0913614\pi$
$854$	−4.11376e29	+	1.46599e30i	−0.0682231	+	0.243122i
$855$	2.62628e30			0.430226
$856$	−6.66444e30	+	6.20940e30i	−1.07842	+	1.00479i
$857$	−5.41852e30			−0.866129			−0.433064	−	0.901363i	$-0.642568\pi$
$857$	−5.41852e30			−0.866129			−0.433064	+	0.901363i	$0.642568\pi$
$858$	1.18912e30	−	4.23757e30i	0.187762	−	0.669115i
$859$			6.68437e30i			1.04264i	0.853363	+	0.521318i	$0.174559\pi$
$859$			6.68437e30i			1.04264i	−0.853363	+	0.521318i	$0.825441\pi$
$860$	2.46782e30	+	1.50338e30i	0.380259	+	0.231652i
$861$			3.88239e30i			0.590971i
$862$	3.86498e30	+	1.08456e30i	0.581193	+	0.163090i
$863$	−4.77207e30			−0.708914			−0.354457	−	0.935072i	$-0.615334\pi$
$863$	−4.77207e30			−0.708914			−0.354457	+	0.935072i	$0.615334\pi$
$864$	−7.21131e30	+	1.48370e30i	−1.05833	+	0.217746i
$865$	8.00504e30			1.16063
$866$	8.82196e30	+	2.47555e30i	1.26365	+	0.354596i
$867$		−	8.76183e29i		−	0.123992i
$868$	−2.29749e30	−	1.39962e30i	−0.321216	−	0.195683i
$869$			6.72342e30i			0.928715i
$870$	7.22544e29	−	2.57488e30i	0.0986080	−	0.351403i
$871$	2.86436e28			0.00386222
$872$	1.35356e30	−	1.26114e30i	0.180324	−	0.168012i
$873$	−4.66902e30			−0.614577
$874$	2.84110e30	−	1.01247e31i	0.369502	−	1.31677i
$875$		−	1.09811e31i		−	1.41111i
$876$	−3.28686e30	+	5.39542e30i	−0.417339	+	0.685066i
$877$		−	6.83283e30i		−	0.857244i	−0.903484	−	0.428622i	$-0.858999\pi$
$877$		−	6.83283e30i		−	0.857244i	0.903484	−	0.428622i	$-0.141001\pi$
$878$	−4.05066e30	−	1.13667e30i	−0.502150	−	0.140909i
$879$	−9.31796e29			−0.114140
$880$	7.40151e30	+	1.43396e31i	0.895885	+	1.73568i
$881$	3.22002e30			0.385133			0.192567	−	0.981284i	$-0.438319\pi$
$881$	3.22002e30			0.385133			0.192567	+	0.981284i	$0.438319\pi$
$882$	−4.17642e30	−	1.17195e30i	−0.493610	−	0.138513i
$883$		−	9.73367e30i		−	1.13681i	−0.822748	−	0.568407i	$-0.807560\pi$
$883$		−	9.73367e30i		−	1.13681i	0.822748	−	0.568407i	$-0.192440\pi$
$884$	−2.38246e30	+	3.91084e30i	−0.274965	+	0.451358i
$885$			2.30695e30i			0.263107i
$886$	−1.73635e30	+	6.18773e30i	−0.195697	+	0.697393i
$887$	1.49942e31			1.67004			0.835019	−	0.550220i	$-0.185456\pi$
$887$	1.49942e31			1.67004			0.835019	+	0.550220i	$0.185456\pi$
$888$	−7.11477e30	−	7.63615e30i	−0.783113	−	0.840501i
$889$	1.82898e31			1.98948
$890$	3.11381e30	−	1.10965e31i	0.334732	−	1.19286i
$891$		−	6.93419e30i		−	0.736682i
$892$	−1.65229e30	−	1.00657e30i	−0.173482	−	0.105685i
$893$		−	9.55577e28i		−	0.00991575i
$894$	2.74125e30	+	7.69229e29i	0.281128	+	0.0788881i
$895$	−9.77804e30			−0.991083
$896$	5.00282e30	−	1.39543e31i	0.501165	−	1.39790i
$897$	5.29503e30			0.524261
$898$	1.33964e31	+	3.75921e30i	1.31096	+	0.367870i
$899$			1.20777e30i			0.116817i
$900$	−3.40968e29	−	2.07716e29i	−0.0325962	−	0.0198574i
$901$		−	1.38784e31i		−	1.31138i
$902$	−2.84151e30	+	1.01261e31i	−0.265388	+	0.945744i
$903$	5.20128e30			0.480163
$904$	−1.14086e31	−	1.22446e31i	−1.04103	−	1.11732i
$905$	−1.06270e31			−0.958522
$906$	−2.00701e30	+	7.15225e30i	−0.178938	+	0.637671i
$907$			5.18389e30i			0.456856i	0.973561	+	0.228428i	$0.0733585\pi$
$907$			5.18389e30i			0.456856i	−0.973561	+	0.228428i	$0.926641\pi$
$908$	4.14113e29	−	6.79771e29i	0.0360759	−	0.0592190i
$909$			2.90894e30i			0.250503i
$910$	−8.59074e30	−	2.41067e30i	−0.731301	−	0.205212i
$911$	−2.70091e30			−0.227283			−0.113642	−	0.993522i	$-0.536252\pi$
$911$	−2.70091e30			−0.227283			−0.113642	+	0.993522i	$0.536252\pi$
$912$	4.04969e30	+	7.84584e30i	0.336881	+	0.652670i
$913$	1.77390e31			1.45877
$914$	−1.23554e31	−	3.46707e30i	−1.00443	−	0.281856i
$915$			1.67430e30i			0.134558i
$916$	6.63710e30	−	1.08949e31i	0.527322	−	0.865605i
$917$			1.13600e30i			0.0892278i
$918$	−4.05522e30	+	1.44513e31i	−0.314895	+	1.12217i
$919$	6.06788e30			0.465826			0.232913	−	0.972498i	$-0.425174\pi$
$919$	6.06788e30			0.465826			0.232913	+	0.972498i	$0.425174\pi$
$920$	−1.42042e31	+	1.32344e31i	−1.07807	+	1.00446i
$921$	−1.25397e31			−0.940935
$922$	−4.66965e30	+	1.66409e31i	−0.346425	+	1.23453i
$923$		−	2.96678e30i		−	0.217604i
$924$	2.48055e31	+	1.51114e31i	1.79884	+	1.09584i
$925$		−	1.89661e30i		−	0.135985i
$926$	−1.67940e31	−	4.71260e30i	−1.19053	−	0.334076i
$927$	7.14217e30			0.500602
$928$	−6.51863e30	+	1.34118e30i	−0.451755	+	0.0929465i
$929$	−1.24254e31			−0.851421			−0.425711	−	0.904859i	$-0.639976\pi$
$929$	−1.24254e31			−0.851421			−0.425711	+	0.904859i	$0.639976\pi$
$930$	−2.84822e30	−	7.99244e29i	−0.192975	−	0.0541513i
$931$			1.74319e31i			1.16781i
$932$	−3.59735e30	−	2.19149e30i	−0.238296	−	0.145168i
$933$		−	1.26434e30i		−	0.0828147i
$934$	7.34968e30	−	2.61916e31i	0.476021	−	1.69637i
$935$	3.28985e31			2.10695
$936$	2.40775e30	−	2.24335e30i	0.152481	−	0.142070i
$937$	5.59647e30			0.350468			0.175234	−	0.984527i	$-0.443932\pi$
$937$	5.59647e30			0.350468			0.175234	+	0.984527i	$0.443932\pi$
$938$	−5.10722e28	+	1.82002e29i	−0.00316267	+	0.0112706i
$939$			1.40111e30i			0.0857992i
$940$	−9.17833e28	+	1.50663e29i	−0.00555803	+	0.00912357i
$941$			1.65017e31i			0.988181i	0.869411	+	0.494090i	$0.164499\pi$
$941$			1.65017e31i			0.988181i	−0.869411	+	0.494090i	$0.835501\pi$
$942$	−6.50954e30	−	1.82666e30i	−0.385492	−	0.108174i
$943$	−1.26530e31			−0.741004
$944$	5.10142e30	−	2.63314e30i	0.295451	−	0.152499i
$945$	−2.92448e31			−1.67500
$946$	1.35661e31	+	3.80680e30i	0.768416	+	0.215627i
$947$		−	9.88562e30i		−	0.553770i	−0.960903	−	0.276885i	$-0.910698\pi$
$947$		−	9.88562e30i		−	0.553770i	0.960903	−	0.276885i	$-0.0893021\pi$
$948$	3.53337e30	−	5.80007e30i	0.195750	−	0.321326i
$949$		−	9.46300e30i		−	0.518482i
$950$	−4.33491e29	+	1.54480e30i	−0.0234899	+	0.0837096i
$951$	8.22089e30			0.440579
$952$	−2.06016e31	−	2.21114e31i	−1.09198	−	1.17200i
$953$	−2.98273e31			−1.56365			−0.781823	−	0.623500i	$-0.785710\pi$
$953$	−2.98273e31			−1.56365			−0.781823	+	0.623500i	$0.785710\pi$
$954$	−2.69459e30	+	9.60254e30i	−0.139712	+	0.497884i
$955$			3.94790e30i			0.202456i
$956$	2.75075e31	+	1.67574e31i	1.39522	+	0.849962i
$957$		−	1.30400e31i		−	0.654188i
$958$	−3.43052e30	−	9.62646e29i	−0.170224	−	0.0477671i
$959$	−4.10286e31			−2.01368
$960$	1.15089e30	−	1.62601e31i	0.0558710	−	0.789358i
$961$	−1.94895e31			−0.935849
$962$	1.50516e31	+	4.22366e30i	0.714897	+	0.200609i
$963$		−	1.33450e31i		−	0.626965i
$964$	2.75331e30	+	1.67730e30i	0.127952	+	0.0779476i
$965$			1.12729e31i			0.518200i
$966$	−9.44115e30	+	3.36448e31i	−0.429304	+	1.52988i
$967$	3.99806e31			1.79834			0.899169	−	0.437602i	$-0.144172\pi$
$967$	3.99806e31			1.79834			0.899169	+	0.437602i	$0.144172\pi$
$968$	3.83174e31	+	4.11254e31i	1.70492	+	1.82986i
$969$	1.80002e31			0.792279
$970$	9.35910e30	−	3.33524e31i	0.407503	−	1.45219i
$971$			2.38423e31i			1.02694i	0.858106	+	0.513472i	$0.171641\pi$
$971$			2.38423e31i			1.02694i	−0.858106	+	0.513472i	$0.828359\pi$
$972$	9.54866e30	−	1.56742e31i	0.406862	−	0.667868i
$973$			4.35629e31i			1.83625i
$974$	−3.13579e31	−	8.79942e30i	−1.30761	−	0.366931i
$975$	−8.07907e29			−0.0333283
$976$	3.70242e30	−	1.91104e30i	0.151099	−	0.0779912i
$977$	−3.63637e30			−0.146816			−0.0734082	−	0.997302i	$-0.523388\pi$
$977$	−3.63637e30			−0.146816			−0.0734082	+	0.997302i	$0.523388\pi$
$978$	3.19117e30	+	8.95481e29i	0.127465	+	0.0357683i
$979$		−	5.61960e31i		−	2.22069i
$980$	1.67433e31	−	2.74844e31i	0.654588	−	1.07451i
$981$			2.71040e30i			0.104836i
$982$	4.71375e30	−	1.67981e31i	0.180383	−	0.642820i
$983$	−1.92855e31			−0.730161			−0.365081	−	0.930976i	$-0.618959\pi$
$983$	−1.92855e31			−0.730161			−0.365081	+	0.930976i	$0.618959\pi$
$984$	7.77288e30	−	7.24216e30i	0.291161	−	0.271281i
$985$	4.64431e31			1.72124
$986$	−3.66570e30	+	1.30632e31i	−0.134415	+	0.479007i
$987$			3.17544e29i			0.0115206i
$988$	−1.12942e31	−	6.88038e30i	−0.405423	−	0.246982i
$989$			1.69514e31i			0.602065i
$990$	−2.27626e31	−	6.38747e30i	−0.799931	−	0.224470i
$991$	−4.06700e31			−1.41417			−0.707084	−	0.707129i	$-0.749990\pi$
$991$	−4.06700e31			−1.41417			−0.707084	+	0.707129i	$0.749990\pi$
$992$	1.48355e30	+	7.21060e30i	0.0510422	+	0.248084i
$993$	−1.07625e31			−0.366391
$994$	1.88510e31	+	5.28984e30i	0.635007	+	0.178191i
$995$			3.23472e31i			1.07819i
$996$	−1.53029e31	−	9.32242e30i	−0.504719	−	0.307472i
$997$		−	1.09446e31i		−	0.357192i	−0.983922	−	0.178596i	$-0.942845\pi$
$997$		−	1.09446e31i		−	0.357192i	0.983922	−	0.178596i	$-0.0571555\pi$
$998$	1.18235e31	−	4.21346e31i	0.381834	−	1.36072i
$999$	5.12390e31			1.63743

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.22.b.a.5.1	✓	20
4.3	odd	2		32.22.b.a.17.14		20
8.3	odd	2		32.22.b.a.17.7		20
8.5	even	2	inner	8.22.b.a.5.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.22.b.a.5.1	✓	20	1.1	even	1	trivial
8.22.b.a.5.2	yes	20	8.5	even	2	inner
32.22.b.a.17.7		20	8.3	odd	2
32.22.b.a.17.14		20	4.3	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)

\(f(q)\)	\(=\)	\(q+(-1394.30 - 391.258i) q^{2} -77530.5i q^{3} +(1.79099e6 + 1.09106e6i) q^{4} -2.27953e7i q^{5} +(-3.03344e7 + 1.08101e8i) q^{6} +1.10984e9 q^{7} +(-2.07029e9 - 2.22200e9i) q^{8} +4.44938e9 q^{9} +O(q^{10})\)	\(q+(-1394.30 - 391.258i) q^{2} -77530.5i q^{3} +(1.79099e6 + 1.09106e6i) q^{4} -2.27953e7i q^{5} +(-3.03344e7 + 1.08101e8i) q^{6} +1.10984e9 q^{7} +(-2.07029e9 - 2.22200e9i) q^{8} +4.44938e9 q^{9} +(-8.91883e9 + 3.17834e10i) q^{10} +1.60961e11i q^{11} +(8.45904e10 - 1.38856e11i) q^{12} +2.43539e11i q^{13} +(-1.54745e12 - 4.34235e11i) q^{14} -1.76733e12 q^{15} +(2.01722e12 + 3.90815e12i) q^{16} +8.96622e12 q^{17} +(-6.20377e12 - 1.74085e12i) q^{18} +2.58938e13i q^{19} +(2.48710e13 - 4.08261e13i) q^{20} -8.60467e13i q^{21} +(6.29773e13 - 2.24428e14i) q^{22} +2.80432e14 q^{23} +(-1.72273e14 + 1.60510e14i) q^{24} -4.27879e13 q^{25} +(9.52863e13 - 3.39566e14i) q^{26} -1.15596e15i q^{27} +(1.98772e15 + 1.21091e15i) q^{28} -1.04492e15i q^{29} +(2.46418e15 + 6.91481e14i) q^{30} -1.15584e15 q^{31} +(-1.28352e15 - 6.23838e15i) q^{32} +1.24794e16 q^{33} +(-1.25016e16 - 3.50810e15i) q^{34} -2.52992e16i q^{35} +(7.96879e15 + 4.85454e15i) q^{36} +4.43260e16i q^{37} +(1.01311e16 - 3.61037e16i) q^{38} +1.88817e16 q^{39} +(-5.06511e16 + 4.71928e16i) q^{40} -4.51196e16 q^{41} +(-3.36664e16 + 1.19975e17i) q^{42} +6.04472e16i q^{43} +(-1.75618e17 + 2.88279e17i) q^{44} -1.01425e17i q^{45} +(-3.91007e17 - 1.09721e17i) q^{46} -3.69037e15 q^{47} +(3.03001e17 - 1.56396e17i) q^{48} +6.73207e17 q^{49} +(5.96591e16 + 1.67411e16i) q^{50} -6.95155e17i q^{51} +(-2.65715e17 + 4.36175e17i) q^{52} -1.54786e18i q^{53} +(-4.52277e17 + 1.61175e18i) q^{54} +3.66916e18 q^{55} +(-2.29769e18 - 2.46607e18i) q^{56} +2.00756e18 q^{57} +(-4.08834e17 + 1.45694e18i) q^{58} -1.30533e18i q^{59} +(-3.16526e18 - 1.92826e18i) q^{60} -9.47359e17i q^{61} +(1.61159e18 + 4.52233e17i) q^{62} +4.93812e18 q^{63} +(-6.51204e17 + 9.20035e18i) q^{64} +5.55153e18 q^{65} +(-1.74000e19 - 4.88266e18i) q^{66} -1.17614e17i q^{67} +(1.60584e19 + 9.78268e18i) q^{68} -2.17421e19i q^{69} +(-9.89850e18 + 3.52746e19i) q^{70} -1.21820e19 q^{71} +(-9.21149e18 - 9.88653e18i) q^{72} -3.88562e19 q^{73} +(1.73429e19 - 6.18036e19i) q^{74} +3.31737e18i q^{75} +(-2.82517e19 + 4.63755e19i) q^{76} +1.78642e20i q^{77} +(-2.63267e19 - 7.38759e18i) q^{78} +4.17704e19 q^{79} +(8.90874e19 - 4.59832e19i) q^{80} -4.30799e19 q^{81} +(6.29102e19 + 1.76534e19i) q^{82} -1.10207e20i q^{83} +(9.38821e19 - 1.54108e20i) q^{84} -2.04388e20i q^{85} +(2.36504e19 - 8.42815e19i) q^{86} -8.10134e19 q^{87} +(3.57656e20 - 3.33236e20i) q^{88} -3.49128e20 q^{89} +(-3.96833e19 + 1.41417e20i) q^{90} +2.70290e20i q^{91} +(5.02251e20 + 3.05969e20i) q^{92} +8.96132e19i q^{93} +(5.14548e18 + 1.44389e18i) q^{94} +5.90257e20 q^{95} +(-4.83665e20 + 9.95118e19i) q^{96} -1.04936e21 q^{97} +(-9.38652e20 - 2.63397e20i) q^{98} +7.16178e20i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 286 q^{2} + 409876 q^{4} + 118236748 q^{6} + 564950496 q^{7} + 3649699336 q^{8} - 62762119220 q^{9}+O(q^{10}) \) 20 * q + 286 * q^2 + 409876 * q^4 + 118236748 * q^6 + 564950496 * q^7 + 3649699336 * q^8 - 62762119220 * q^9	\( 20 q + 286 q^{2} + 409876 q^{4} + 118236748 q^{6} + 564950496 q^{7} + 3649699336 q^{8} - 62762119220 q^{9} - 51269339528 q^{10} + 65316900136 q^{12} - 1924309104464 q^{14} - 2285680856096 q^{15} + 7793508571920 q^{16} + 1740714497000 q^{17} - 41325344023822 q^{18} - 78999934156016 q^{20} + 294957216952508 q^{22} + 335749622520224 q^{23} + 786737698607504 q^{24} - 16\!\cdots\!04 q^{25}+ \cdots + 13\!\cdots\!30 q^{98}+O(q^{100}) \) 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

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