LMFDB - Embedded newform 8.21.d.b.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,21,Mod(3,8)]

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([1, 1]))

N = Newforms(chi, 21, names="a")

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

chi := DirichletCharacter("8.3");

S:= CuspForms(chi, 21);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 21 $
Character orbit:	$[\chi]$	$=$	8.d (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:	$20.2811012082$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 66008406614424 x^{16} + \cdots + 53\!\cdots\!00 $ x^18 + 66008406614424x^16 - 170362825164232872x^15 + 1756210031321623676418457398x^14 - 8143876994687623666322842711032x^13 + 24350477750271510634494454384791667990404x^12 - 150098892256302975432925342820456817156772440x^11 + 191202710428210659782696002203561503780870353303759377x^10 - 1295069212697340229160215370735662134952032297259046562056x^9 + 870944882856087336674875277000277878990405713083632292121165358076x^8 - 4812915841402167440171875831348280575634953635256498021616060003579520x^7 + 2268474737024234177226752378807914883078144887754356976399017987196241603311520x^6 - 4757172104321022064833287336478952531807855909655138781977813255912131556348455680x^5 + 3199222078336759259493497095495346495581808310744107378246303720899215796326992176238102400x^4 + 8929774272757329376425833321340788600302219356646171490279817057245825930569313705998374604800x^3 + 2186805491439153577309421324561832859804177633153493793273223699303415894069647268007263015677943481600x^2 + 13250359115341501288916746421398415873922554950681918855831714718905060696192946493864164248007740533504000x + 531754461748673811827664952573861209640978431708236170453755006606958174478016712983511620954972201107600928640000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{153}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.1
Root			$16622.8 - 2.05933e6i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.21.d.b.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-998.751 - 225.992i) q^{2} +60145.3 q^{3} +(946431. + 451420. i) q^{4} +8.23733e6i q^{5} +(-6.00701e7 - 1.35924e7i) q^{6} +5.26995e8i q^{7} +(-8.43231e8 - 6.64742e8i) q^{8} +1.30668e8 q^{9} +O(q^{10})$	\(q+(-998.751 - 225.992i) q^{2} +60145.3 q^{3} +(946431. + 451420. i) q^{4} +8.23733e6i q^{5} +(-6.00701e7 - 1.35924e7i) q^{6} +5.26995e8i q^{7} +(-8.43231e8 - 6.64742e8i) q^{8} +1.30668e8 q^{9} +(1.86157e9 - 8.22704e9i) q^{10} +6.02652e9 q^{11} +(5.69233e10 + 2.71508e10i) q^{12} -1.38203e11i q^{13} +(1.19097e11 - 5.26337e11i) q^{14} +4.95436e11i q^{15} +(6.91951e11 + 8.54476e11i) q^{16} -1.98685e12 q^{17} +(-1.30505e11 - 2.95300e10i) q^{18} -8.88192e12 q^{19} +(-3.71850e12 + 7.79606e12i) q^{20} +3.16963e13i q^{21} +(-6.01899e12 - 1.36195e12i) q^{22} -2.01771e13i q^{23} +(-5.07164e13 - 3.99811e13i) q^{24} +2.75139e13 q^{25} +(-3.12327e13 + 1.38030e14i) q^{26} -2.01854e14 q^{27} +(-2.37896e14 + 4.98765e14i) q^{28} -2.99333e14i q^{29} +(1.11965e14 - 4.94817e14i) q^{30} +1.39233e15i q^{31} +(-4.97982e14 - 1.00978e15i) q^{32} +3.62466e14 q^{33} +(1.98437e15 + 4.49014e14i) q^{34} -4.34103e15 q^{35} +(1.23668e14 + 5.89862e13i) q^{36} +1.32225e15i q^{37} +(8.87083e15 + 2.00725e15i) q^{38} -8.31223e15i q^{39} +(5.47570e15 - 6.94597e15i) q^{40} +1.06415e16 q^{41} +(7.16311e15 - 3.16567e16i) q^{42} -1.54318e15 q^{43} +(5.70368e15 + 2.72049e15i) q^{44} +1.07636e15i q^{45} +(-4.55987e15 + 2.01519e16i) q^{46} +6.01114e16i q^{47} +(4.16176e16 + 5.13927e16i) q^{48} -1.97932e17 q^{49} +(-2.74795e16 - 6.21792e15i) q^{50} -1.19500e17 q^{51} +(6.23874e16 - 1.30799e17i) q^{52} +2.12573e17i q^{53} +(2.01602e17 + 4.56176e16i) q^{54} +4.96424e16i q^{55} +(3.50316e17 - 4.44379e17i) q^{56} -5.34206e17 q^{57} +(-6.76469e16 + 2.98959e17i) q^{58} +4.77160e15 q^{59} +(-2.23650e17 + 4.68896e17i) q^{60} -3.65093e16i q^{61} +(3.14655e17 - 1.39059e18i) q^{62} +6.88615e16i q^{63} +(2.69157e17 + 1.12106e18i) q^{64} +1.13842e18 q^{65} +(-3.62014e17 - 8.19146e16i) q^{66} +6.78003e17 q^{67} +(-1.88042e18 - 8.96906e17i) q^{68} -1.21356e18i q^{69} +(4.33561e18 + 9.81040e17i) q^{70} -2.60562e18i q^{71} +(-1.10183e17 - 8.68606e16i) q^{72} +2.08057e18 q^{73} +(2.98817e17 - 1.32059e18i) q^{74} +1.65483e18 q^{75} +(-8.40613e18 - 4.00948e18i) q^{76} +3.17595e18i q^{77} +(-1.87850e18 + 8.30185e18i) q^{78} +4.99331e18i q^{79} +(-7.03860e18 + 5.69983e18i) q^{80} -1.25962e19 q^{81} +(-1.06282e19 - 2.40489e18i) q^{82} +2.79468e19 q^{83} +(-1.43083e19 + 2.99983e19i) q^{84} -1.63664e19i q^{85} +(1.54125e18 + 3.48747e17i) q^{86} -1.80034e19i q^{87} +(-5.08175e18 - 4.00608e18i) q^{88} -2.07280e19 q^{89} +(2.43248e17 - 1.07501e18i) q^{90} +7.28321e19 q^{91} +(9.10834e18 - 1.90962e19i) q^{92} +8.37419e19i q^{93} +(1.35847e19 - 6.00363e19i) q^{94} -7.31633e19i q^{95} +(-2.99513e19 - 6.07337e19i) q^{96} -9.97818e19 q^{97} +(1.97685e20 + 4.47311e19i) q^{98} +7.87473e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 398 q^{2} - 114228 q^{3} + 724980 q^{4} - 91643748 q^{6} - 3105291368 q^{8} + 10197650262 q^{9}+O(q^{10}) $ 18 * q - 398 * q^2 - 114228 * q^3 + 724980 * q^4 - 91643748 * q^6 - 3105291368 * q^8 + 10197650262 * q^9	$ 18 q - 398 q^{2} - 114228 q^{3} + 724980 q^{4} - 91643748 q^{6} - 3105291368 q^{8} + 10197650262 q^{9} + 742754160 q^{10} + 27862395020 q^{11} - 212292734088 q^{12} - 431248136928 q^{14} - 958534870512 q^{16} + 4343925139172 q^{17} - 4517494524426 q^{18} - 360681653556 q^{19} - 32520172742880 q^{20} - 66275482922148 q^{22} + 22289322475152 q^{24} - 395727477008910 q^{25} + 154289718058128 q^{26} - 12\!\cdots\!64 q^{27}+ \cdots + 62\!\cdots\!84 q^{99}+O(q^{100}) $ 18 * q - 398 * q^2 - 114228 * q^3 + 724980 * q^4 - 91643748 * q^6 - 3105291368 * q^8 + 10197650262 * q^9 + 742754160 * q^10 + 27862395020 * q^11 - 212292734088 * q^12 - 431248136928 * q^14 - 958534870512 * q^16 + 4343925139172 * q^17 - 4517494524426 * q^18 - 360681653556 * q^19 - 32520172742880 * q^20 - 66275482922148 * q^22 + 22289322475152 * q^24 - 395727477008910 * q^25 + 154289718058128 * q^26 - 1208398438889064 * q^27 - 394619539621440 * q^28 + 223250517248160 * q^30 - 2833814588985248 * q^32 + 4461969540487176 * q^33 - 939462769526748 * q^34 + 3615863153468160 * q^35 + 1560521174396700 * q^36 + 12905383833568412 * q^38 + 11813880412973760 * q^40 + 16990829756398820 * q^41 + 38127588900300480 * q^42 - 27498466356753396 * q^43 + 33178844343953144 * q^44 - 21739818881100192 * q^46 + 28364131397385312 * q^48 - 252965388018862638 * q^49 + 41705619584456530 * q^50 - 34182574557901800 * q^51 - 44583718369992480 * q^52 - 579400710808894920 * q^54 - 505574909383001472 * q^56 - 522453489061123704 * q^57 - 677523738697093680 * q^58 + 93112194700366220 * q^59 + 1631640690429240000 * q^60 + 1780090172849178240 * q^62 + 175441813011570240 * q^64 + 1575343920200472960 * q^65 + 8001047667731567880 * q^66 - 1452645642074335668 * q^67 + 1153770320813215592 * q^68 - 6151558949299572480 * q^70 - 5306529204268842936 * q^72 + 9882821313863175972 * q^73 - 5642095430673385488 * q^74 + 13414715768769378060 * q^75 - 8416781249057544840 * q^76 - 14599907290310144160 * q^78 - 22104885212702947200 * q^80 - 32315102667184036518 * q^81 + 10320950271478847652 * q^82 - 46425529968268557748 * q^83 + 17095266896298568320 * q^84 + 33555485282446075868 * q^86 + 32344350945394345872 * q^88 - 28075170672250840156 * q^89 - 33204348719592139440 * q^90 + 161045136122144660736 * q^91 - 932896292396925120 * q^92 - 107259275077774974528 * q^94 + 68580843917215697472 * q^96 + 127276645173366650724 * q^97 + 154837385163137764402 * q^98 + 62802542261652714084 * q^99

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 $

$2$	−998.751	−	225.992i	−0.975343	−	0.220696i
$2$	−998.751	−	225.992i	−0.975343	−	0.220696i
$3$	60145.3			1.01857			0.509283	−	0.860599i	$-0.329911\pi$
$3$	60145.3			1.01857			0.509283	+	0.860599i	$0.329911\pi$
$4$	946431.	+	451420.i	0.902587	+	0.430508i
$5$			8.23733e6i			0.843502i	0.906712	+	0.421751i	$0.138584\pi$
$5$			8.23733e6i			0.843502i	−0.906712	+	0.421751i	$0.861416\pi$
$6$	−6.00701e7	−	1.35924e7i	−0.993450	−	0.224793i
$7$			5.26995e8i			1.86563i	0.360351	+	0.932817i	$0.382657\pi$
$7$			5.26995e8i			1.86563i	−0.360351	+	0.932817i	$0.617343\pi$
$8$	−8.43231e8	−	6.64742e8i	−0.785320	−	0.619090i
$9$	1.30668e8			0.0374752
$10$	1.86157e9	−	8.22704e9i	0.186157	−	0.822704i
$11$	6.02652e9			0.232348			0.116174	−	0.993229i	$-0.462937\pi$
$11$	6.02652e9			0.232348			0.116174	+	0.993229i	$0.462937\pi$
$12$	5.69233e10	+	2.71508e10i	0.919344	+	0.438500i
$13$		−	1.38203e11i		−	1.00250i	−0.865304	−	0.501248i	$-0.832874\pi$
$13$		−	1.38203e11i		−	1.00250i	0.865304	−	0.501248i	$-0.167126\pi$
$14$	1.19097e11	−	5.26337e11i	0.411737	−	1.81963i
$15$			4.95436e11i			0.859162i
$16$	6.91951e11	+	8.54476e11i	0.629326	+	0.777141i
$17$	−1.98685e12			−0.985546			−0.492773	−	0.870158i	$-0.664017\pi$
$17$	−1.98685e12			−0.985546			−0.492773	+	0.870158i	$0.664017\pi$
$18$	−1.30505e11	−	2.95300e10i	−0.0365512	−	0.00827062i
$19$	−8.88192e12			−1.44867			−0.724337	−	0.689446i	$-0.757854\pi$
$19$	−8.88192e12			−1.44867			−0.724337	+	0.689446i	$0.757854\pi$
$20$	−3.71850e12	+	7.79606e12i	−0.363134	+	0.761334i
$21$			3.16963e13i			1.90027i
$22$	−6.01899e12	−	1.36195e12i	−0.226619	−	0.0512783i
$23$		−	2.01771e13i		−	0.487057i	−0.969894	−	0.243529i	$-0.921695\pi$
$23$		−	2.01771e13i		−	0.487057i	0.969894	−	0.243529i	$-0.0783050\pi$
$24$	−5.07164e13	−	3.99811e13i	−0.799900	−	0.630583i
$25$	2.75139e13			0.288504
$26$	−3.12327e13	+	1.38030e14i	−0.221246	+	0.977777i
$27$	−2.01854e14			−0.980394
$28$	−2.37896e14	+	4.98765e14i	−0.803170	+	1.68390i
$29$		−	2.99333e14i		−	0.711499i	−0.934581	−	0.355749i	$-0.884226\pi$
$29$		−	2.99333e14i		−	0.711499i	0.934581	−	0.355749i	$-0.115774\pi$
$30$	1.11965e14	−	4.94817e14i	0.189613	−	0.837978i
$31$			1.39233e15i			1.69873i	0.527805	+	0.849366i	$0.323015\pi$
$31$			1.39233e15i			1.69873i	−0.527805	+	0.849366i	$0.676985\pi$
$32$	−4.97982e14	−	1.00978e15i	−0.442297	−	0.896869i
$33$	3.62466e14			0.236662
$34$	1.98437e15	+	4.49014e14i	0.961245	+	0.217506i
$35$	−4.34103e15			−1.57367
$36$	1.23668e14	+	5.89862e13i	0.0338246	+	0.0161334i
$37$			1.32225e15i			0.274976i	0.990503	+	0.137488i	$0.0439029\pi$
$37$			1.32225e15i			0.274976i	−0.990503	+	0.137488i	$0.956097\pi$
$38$	8.87083e15	+	2.00725e15i	1.41295	+	0.319716i
$39$		−	8.31223e15i		−	1.02111i
$40$	5.47570e15	−	6.94597e15i	0.522204	−	0.662420i
$41$	1.06415e16			0.792798			0.396399	−	0.918078i	$-0.370260\pi$
$41$	1.06415e16			0.792798			0.396399	+	0.918078i	$0.370260\pi$
$42$	7.16311e15	−	3.16567e16i	0.419381	−	1.85341i
$43$	−1.54318e15			−0.0714056			−0.0357028	−	0.999362i	$-0.511367\pi$
$43$	−1.54318e15			−0.0714056			−0.0357028	+	0.999362i	$0.511367\pi$
$44$	5.70368e15	+	2.72049e15i	0.209715	+	0.100028i
$45$			1.07636e15i			0.0316104i
$46$	−4.55987e15	+	2.01519e16i	−0.107491	+	0.475048i
$47$			6.01114e16i			1.14282i	0.820664	+	0.571411i	$0.193604\pi$
$47$			6.01114e16i			1.14282i	−0.820664	+	0.571411i	$0.806396\pi$
$48$	4.16176e16	+	5.13927e16i	0.641010	+	0.791569i
$49$	−1.97932e17			−2.48059
$50$	−2.74795e16	−	6.21792e15i	−0.281390	−	0.0636715i
$51$	−1.19500e17			−1.00384
$52$	6.23874e16	−	1.30799e17i	0.431582	−	0.904840i
$53$			2.12573e17i			1.21549i	0.794134	+	0.607743i	$0.207925\pi$
$53$			2.12573e17i			1.21549i	−0.794134	+	0.607743i	$0.792075\pi$
$54$	2.01602e17	+	4.56176e16i	0.956220	+	0.216369i
$55$			4.96424e16i			0.195986i
$56$	3.50316e17	−	4.44379e17i	1.15499	−	1.46512i
$57$	−5.34206e17			−1.47557
$58$	−6.76469e16	+	2.98959e17i	−0.157025	+	0.693955i
$59$	4.77160e15			0.00933563			0.00466782	−	0.999989i	$-0.498514\pi$
$59$	4.77160e15			0.00933563			0.00466782	+	0.999989i	$0.498514\pi$
$60$	−2.23650e17	+	4.68896e17i	−0.369876	+	0.775469i
$61$		−	3.65093e16i		−	0.0511805i	−0.999673	−	0.0255903i	$-0.991853\pi$
$61$		−	3.65093e16i		−	0.0511805i	0.999673	−	0.0255903i	$-0.00814652\pi$
$62$	3.14655e17	−	1.39059e18i	0.374903	−	1.65685i
$63$			6.88615e16i			0.0699151i
$64$	2.69157e17	+	1.12106e18i	0.233456	+	0.972367i
$65$	1.13842e18			0.845608
$66$	−3.62014e17	−	8.19146e16i	−0.230826	−	0.0522303i
$67$	6.78003e17			0.371949			0.185975	−	0.982555i	$-0.440456\pi$
$67$	6.78003e17			0.371949			0.185975	+	0.982555i	$0.440456\pi$
$68$	−1.88042e18	−	8.96906e17i	−0.889541	−	0.424285i
$69$		−	1.21356e18i		−	0.496100i
$70$	4.33561e18	+	9.81040e17i	1.53486	+	0.347301i
$71$		−	2.60562e18i		−	0.800439i	−0.916419	−	0.400220i	$-0.868934\pi$
$71$		−	2.60562e18i		−	0.800439i	0.916419	−	0.400220i	$-0.131066\pi$
$72$	−1.10183e17	−	8.68606e16i	−0.0294301	−	0.0232005i
$73$	2.08057e18			0.484121			0.242061	−	0.970261i	$-0.422177\pi$
$73$	2.08057e18			0.484121			0.242061	+	0.970261i	$0.422177\pi$
$74$	2.98817e17	−	1.32059e18i	0.0606860	−	0.268196i
$75$	1.65483e18			0.293860
$76$	−8.40613e18	−	4.00948e18i	−1.30756	−	0.623666i
$77$			3.17595e18i			0.433477i
$78$	−1.87850e18	+	8.30185e18i	−0.225354	+	0.995930i
$79$			4.99331e18i			0.527372i	0.964609	+	0.263686i	$0.0849383\pi$
$79$			4.99331e18i			0.527372i	−0.964609	+	0.263686i	$0.915062\pi$
$80$	−7.03860e18	+	5.69983e18i	−0.655520	+	0.530838i
$81$	−1.25962e19			−1.03607
$82$	−1.06282e19	−	2.40489e18i	−0.773250	−	0.174967i
$83$	2.79468e19			1.80115			0.900577	−	0.434696i	$-0.143144\pi$
$83$	2.79468e19			1.80115			0.900577	+	0.434696i	$0.143144\pi$
$84$	−1.43083e19	+	2.99983e19i	−0.818081	+	1.71516i
$85$		−	1.63664e19i		−	0.831310i
$86$	1.54125e18	+	3.48747e17i	0.0696449	+	0.0157589i
$87$		−	1.80034e19i		−	0.724708i
$88$	−5.08175e18	−	4.00608e18i	−0.182468	−	0.143844i
$89$	−2.07280e19			−0.664748			−0.332374	−	0.943148i	$-0.607850\pi$
$89$	−2.07280e19			−0.664748			−0.332374	+	0.943148i	$0.607850\pi$
$90$	2.43248e17	−	1.07501e18i	0.00697629	−	0.0308310i
$91$	7.28321e19			1.87029
$92$	9.10834e18	−	1.90962e19i	0.209682	−	0.439611i
$93$			8.37419e19i			1.73027i
$94$	1.35847e19	−	6.00363e19i	0.252216	−	1.11464i
$95$		−	7.31633e19i		−	1.22196i
$96$	−2.99513e19	−	6.07337e19i	−0.450508	−	0.913519i
$97$	−9.97818e19			−1.35311			−0.676557	−	0.736391i	$-0.736529\pi$
$97$	−9.97818e19			−1.35311			−0.676557	+	0.736391i	$0.736529\pi$
$98$	1.97685e20	+	4.47311e19i	2.41942	+	0.547455i
$99$	7.87473e17			0.00870731
$100$	2.60400e19	+	1.24203e19i	0.260400	+	0.124203i
$101$		−	1.23930e20i		−	1.12192i	−0.827843	−	0.560960i	$-0.810432\pi$
$101$		−	1.23930e20i		−	1.12192i	0.827843	−	0.560960i	$-0.189568\pi$
$102$	1.19351e20	+	2.70060e19i	0.979091	+	0.221544i
$103$			1.90114e20i			1.41463i	0.706901	+	0.707313i	$0.250093\pi$
$103$			1.90114e20i			1.41463i	−0.706901	+	0.707313i	$0.749907\pi$
$104$	−9.18691e19	+	1.16537e20i	−0.620635	+	0.787280i
$105$	−2.61093e20			−1.60288
$106$	4.80399e19	−	2.12308e20i	0.268252	−	1.18551i
$107$	−2.21231e18			−0.0112463			−0.00562314	−	0.999984i	$-0.501790\pi$
$107$	−2.21231e18			−0.0112463			−0.00562314	+	0.999984i	$0.501790\pi$
$108$	−1.91041e20	−	9.11212e19i	−0.884891	−	0.422067i
$109$			2.92007e20i			1.23347i	0.787171	+	0.616734i	$0.211545\pi$
$109$			2.92007e20i			1.23347i	−0.787171	+	0.616734i	$0.788455\pi$
$110$	1.12188e19	−	4.95804e19i	0.0432533	−	0.191154i
$111$			7.95268e19i			0.280081i
$112$	−4.50305e20	+	3.64655e20i	−1.44986	+	1.17409i
$113$	−1.48679e20			−0.437990			−0.218995	−	0.975726i	$-0.570278\pi$
$113$	−1.48679e20			−0.437990			−0.218995	+	0.975726i	$0.570278\pi$
$114$	5.33538e20	+	1.20726e20i	1.43919	+	0.325652i
$115$	1.66205e20			0.410834
$116$	1.35125e20	−	2.83298e20i	0.306306	−	0.642189i
$117$		−	1.80587e19i		−	0.0375688i
$118$	−4.76564e18	−	1.07834e18i	−0.00910544	−	0.00206033i
$119$		−	1.04706e21i		−	1.83867i
$120$	3.29337e20	−	4.17767e20i	0.531898	−	0.674718i
$121$	−6.36431e20			−0.946014
$122$	−8.25081e18	+	3.64637e19i	−0.0112953	+	0.0499185i
$123$	6.40033e20			0.807516
$124$	−6.28525e20	+	1.31774e21i	−0.731317	+	1.53325i
$125$			1.01221e21i			1.08686i
$126$	1.55622e19	−	6.87754e19i	0.0154299	−	0.0681911i
$127$			1.29687e21i			1.18812i	0.804422	+	0.594058i	$0.202475\pi$
$127$			1.29687e21i			1.18812i	−0.804422	+	0.594058i	$0.797525\pi$
$128$	−1.54688e19	−	1.18049e21i	−0.0131026	−	0.999914i
$129$	−9.28150e19			−0.0727313
$130$	−1.13700e21	−	2.57274e20i	−0.824757	−	0.186622i
$131$	2.73520e21			1.83770			0.918852	−	0.394603i	$-0.129118\pi$
$131$	2.73520e21			1.83770			0.918852	+	0.394603i	$0.129118\pi$
$132$	3.43049e20	+	1.63625e20i	0.213608	+	0.101885i
$133$		−	4.68073e21i		−	2.70270i
$134$	−6.77156e20	−	1.53223e20i	−0.362778	−	0.0820875i
$135$		−	1.66274e21i		−	0.826965i
$136$	1.67538e21	+	1.32075e21i	0.773969	+	0.610141i
$137$	3.47180e21			1.49056			0.745279	−	0.666753i	$-0.232316\pi$
$137$	3.47180e21			1.49056			0.745279	+	0.666753i	$0.232316\pi$
$138$	−2.74254e20	+	1.21204e21i	−0.109487	+	0.483867i
$139$	−2.01290e19			−0.00747607			−0.00373804	−	0.999993i	$-0.501190\pi$
$139$	−2.01290e19			−0.00747607			−0.00373804	+	0.999993i	$0.501190\pi$
$140$	−4.10849e21	−	1.95963e21i	−1.42037	−	0.677476i
$141$			3.61542e21i			1.16404i
$142$	−5.88851e20	+	2.60237e21i	−0.176653	+	0.780703i
$143$		−	8.32880e20i		−	0.232928i
$144$	9.04159e19	+	1.11653e20i	0.0235841	+	0.0291235i
$145$	2.46570e21			0.600151
$146$	−2.07797e21	−	4.70193e20i	−0.472184	−	0.106843i
$147$	−1.19047e22			−2.52664
$148$	−5.96888e20	+	1.25141e21i	−0.118379	+	0.248190i
$149$			4.96578e21i			0.920714i	0.887734	+	0.460357i	$0.152279\pi$
$149$			4.96578e21i			0.920714i	−0.887734	+	0.460357i	$0.847721\pi$
$150$	−1.65276e21	−	3.73979e20i	−0.286614	−	0.0648536i
$151$			5.02251e21i			0.814988i	0.913208	+	0.407494i	$0.133597\pi$
$151$			5.02251e21i			0.814988i	−0.913208	+	0.407494i	$0.866403\pi$
$152$	7.48952e21	+	5.90419e21i	1.13767	+	0.896860i
$153$	−2.59618e20			−0.0369335
$154$	7.17740e20	−	3.17198e21i	0.0956664	−	0.422789i
$155$	−1.14691e22			−1.43288
$156$	3.75231e21	−	7.86695e21i	0.439595	−	0.921638i
$157$		−	1.25764e22i		−	1.38216i	−0.722777	−	0.691081i	$-0.757135\pi$
$157$		−	1.25764e22i		−	1.38216i	0.722777	−	0.691081i	$-0.242865\pi$
$158$	1.12845e21	−	4.98707e21i	0.116389	−	0.514369i
$159$			1.27853e22i			1.23805i
$160$	8.31792e21	−	4.10204e21i	0.756511	−	0.373079i
$161$	1.06332e22			0.908670
$162$	1.25805e22	+	2.84664e21i	1.01052	+	0.228656i
$163$	−5.79110e20			−0.0437406			−0.0218703	−	0.999761i	$-0.506962\pi$
$163$	−5.79110e20			−0.0437406			−0.0218703	+	0.999761i	$0.506962\pi$
$164$	1.00714e22	+	4.80377e21i	0.715569	+	0.341306i
$165$			2.98575e21i			0.199625i
$166$	−2.79119e22	−	6.31576e21i	−1.75674	−	0.397507i
$167$		−	2.14950e22i		−	1.27401i	−0.770861	−	0.637004i	$-0.780174\pi$
$167$		−	2.14950e22i		−	1.27401i	0.770861	−	0.637004i	$-0.219826\pi$
$168$	2.10699e22	−	2.67273e22i	1.17644	−	1.49232i
$169$	−9.49847e19			−0.00499789
$170$	−3.69867e21	+	1.63459e22i	−0.183466	+	0.810812i
$171$	−1.16058e21			−0.0542894
$172$	−1.46051e21	−	6.96623e20i	−0.0644498	−	0.0307407i
$173$		−	7.43145e21i		−	0.309466i	−0.987956	−	0.154733i	$-0.950548\pi$
$173$		−	7.43145e21i		−	0.309466i	0.987956	−	0.154733i	$-0.0494517\pi$
$174$	−4.06864e21	+	1.79810e22i	−0.159940	+	0.706839i
$175$			1.44997e22i			0.538242i
$176$	4.17006e21	+	5.14951e21i	0.146223	+	0.180567i
$177$	2.86989e20			0.00950895
$178$	2.07021e22	+	4.68437e21i	0.648357	+	0.146707i
$179$	−3.33062e21			−0.0986267			−0.0493134	−	0.998783i	$-0.515703\pi$
$179$	−3.33062e21			−0.0986267			−0.0493134	+	0.998783i	$0.515703\pi$
$180$	−4.85888e20	+	1.01870e21i	−0.0136085	+	0.0285312i
$181$			5.92307e22i			1.56950i	0.619813	+	0.784750i	$0.287209\pi$
$181$			5.92307e22i			1.56950i	−0.619813	+	0.784750i	$0.712791\pi$
$182$	−7.27411e22	−	1.64595e22i	−1.82417	−	0.412765i
$183$		−	2.19586e21i		−	0.0521307i
$184$	−1.34126e22	+	1.70139e22i	−0.301532	+	0.382496i
$185$	−1.08918e22			−0.231943
$186$	1.89250e22	−	8.36373e22i	0.381863	−	1.68760i
$187$	−1.19738e22			−0.228990
$188$	−2.71355e22	+	5.68913e22i	−0.491994	+	1.03150i
$189$		−	1.06376e23i		−	1.82906i
$190$	−1.65343e22	+	7.30719e22i	−0.269681	+	1.19183i
$191$			1.05814e22i			0.163761i	0.996642	+	0.0818806i	$0.0260926\pi$
$191$			1.05814e22i			0.163761i	−0.996642	+	0.0818806i	$0.973907\pi$
$192$	1.61885e22	+	6.74266e22i	0.237790	+	0.990420i
$193$	4.43070e22			0.617873			0.308937	−	0.951083i	$-0.400027\pi$
$193$	4.43070e22			0.617873			0.308937	+	0.951083i	$0.400027\pi$
$194$	9.96572e22	+	2.25499e22i	1.31975	+	0.298626i
$195$	6.84706e22			0.861307
$196$	−1.87329e23	−	8.93504e22i	−2.23895	−	1.06791i
$197$			2.36624e22i			0.268779i	0.990929	+	0.134390i	$0.0429074\pi$
$197$			2.36624e22i			0.268779i	−0.990929	+	0.134390i	$0.957093\pi$
$198$	−7.86490e20	−	1.77963e20i	−0.00849261	−	0.00192166i
$199$		−	7.89983e22i		−	0.811123i	−0.914068	−	0.405562i	$-0.867076\pi$
$199$		−	7.89983e22i		−	0.811123i	0.914068	−	0.405562i	$-0.132924\pi$
$200$	−2.32006e22	−	1.82896e22i	−0.226568	−	0.178610i
$201$	4.07787e22			0.378854
$202$	−2.80072e22	+	1.23775e23i	−0.247603	+	1.09426i
$203$	1.57747e23			1.32740
$204$	−1.13098e23	−	5.39446e22i	−0.906055	−	0.432162i
$205$			8.76572e22i			0.668727i
$206$	4.29643e22	−	1.89876e23i	0.312202	−	1.37974i
$207$		−	2.63650e21i		−	0.0182526i
$208$	1.18091e23	−	9.56295e22i	0.779081	−	0.630897i
$209$	−5.35271e22			−0.336597
$210$	2.60766e23	+	5.90049e22i	1.56336	+	0.353749i
$211$	1.91400e22			0.109425			0.0547127	−	0.998502i	$-0.482576\pi$
$211$	1.91400e22			0.109425			0.0547127	+	0.998502i	$0.482576\pi$
$212$	−9.59598e22	+	2.01186e23i	−0.523276	+	1.09708i
$213$		−	1.56716e23i		−	0.815300i
$214$	2.20955e21	+	4.99966e20i	0.0109690	+	0.00248200i
$215$		−	1.27117e22i		−	0.0602308i
$216$	1.70210e23	+	1.34181e23i	0.769924	+	0.606952i
$217$	−7.33751e23			−3.16921
$218$	6.59913e22	−	2.91642e23i	0.272221	−	1.20305i
$219$	1.25137e23			0.493109
$220$	−2.24096e22	+	4.69831e22i	−0.0843736	+	0.176895i
$221$			2.74588e23i			0.988005i
$222$	1.79725e22	−	7.94275e22i	0.0618127	−	0.273175i
$223$			5.23366e22i			0.172090i	0.996291	+	0.0860452i	$0.0274230\pi$
$223$			5.23366e22i			0.172090i	−0.996291	+	0.0860452i	$0.972577\pi$
$224$	5.32152e23	−	2.62434e23i	1.67323	−	0.825164i
$225$	3.59518e21			0.0108117
$226$	1.48493e23	+	3.36003e22i	0.427191	+	0.0966626i
$227$	8.58318e22			0.236260			0.118130	−	0.992998i	$-0.462310\pi$
$227$	8.58318e22			0.236260			0.118130	+	0.992998i	$0.462310\pi$
$228$	−5.05589e23	−	2.41151e23i	−1.33183	−	0.635244i
$229$			3.17833e23i			0.801391i	0.916211	+	0.400695i	$0.131231\pi$
$229$			3.17833e23i			0.801391i	−0.916211	+	0.400695i	$0.868769\pi$
$230$	−1.65998e23	−	3.75611e22i	−0.400704	−	0.0906692i
$231$			1.91018e23i			0.441525i
$232$	−1.98979e23	+	2.52407e23i	−0.440481	+	0.558754i
$233$	−3.29360e23			−0.698411			−0.349206	−	0.937046i	$-0.613549\pi$
$233$	−3.29360e23			−0.698411			−0.349206	+	0.937046i	$0.613549\pi$
$234$	−4.08112e21	+	1.80361e22i	−0.00829126	+	0.0366424i
$235$	−4.95158e23			−0.963973
$236$	4.51599e21	+	2.15400e21i	0.00842622	+	0.00401906i
$237$			3.00324e23i			0.537163i
$238$	−2.36628e23	+	1.04576e24i	−0.405786	+	1.79333i
$239$		−	5.66048e23i		−	0.930839i	−0.885090	−	0.465419i	$-0.845904\pi$
$239$		−	5.66048e23i		−	0.930839i	0.885090	−	0.465419i	$-0.154096\pi$
$240$	−4.23338e23	+	3.42818e23i	−0.667690	+	0.540693i
$241$	3.83872e23			0.580786			0.290393	−	0.956907i	$-0.406214\pi$
$241$	3.83872e23			0.580786			0.290393	+	0.956907i	$0.406214\pi$
$242$	6.35636e23	+	1.43829e23i	0.922688	+	0.208781i
$243$	−5.37788e22			−0.0749115
$244$	1.64810e22	−	3.45535e22i	0.0220336	−	0.0461949i
$245$		−	1.63043e24i		−	2.09238i
$246$	−6.39234e23	−	1.44643e23i	−0.787605	−	0.178215i
$247$			1.22750e24i			1.45229i
$248$	9.25540e23	−	1.17405e24i	1.05167	−	1.33405i
$249$	1.68087e24			1.83459
$250$	2.28752e23	−	1.01095e24i	0.239864	−	1.06006i
$251$	1.74402e23			0.175717			0.0878586	−	0.996133i	$-0.471998\pi$
$251$	1.74402e23			0.175717			0.0878586	+	0.996133i	$0.471998\pi$
$252$	−3.10854e22	+	6.51726e22i	−0.0300990	+	0.0631044i
$253$		−	1.21598e23i		−	0.113167i
$254$	2.93082e23	−	1.29525e24i	0.262212	−	1.15882i
$255$		−	9.84359e23i		−	0.846744i
$256$	−2.51332e23	+	1.18251e24i	−0.207897	+	0.978151i
$257$	2.21521e24			1.76231			0.881157	−	0.472824i	$-0.156765\pi$
$257$	2.21521e24			1.76231			0.881157	+	0.472824i	$0.156765\pi$
$258$	9.26991e22	+	2.09755e22i	0.0709379	+	0.0160515i
$259$	−6.96818e23			−0.513005
$260$	1.07744e24	+	5.13906e23i	0.763234	+	0.364041i
$261$		−	3.91132e22i		−	0.0266636i
$262$	−2.73178e24	−	6.18133e23i	−1.79239	−	0.405573i
$263$		−	5.35900e23i		−	0.338475i	−0.985575	−	0.169237i	$-0.945870\pi$
$263$		−	5.35900e23i		−	0.338475i	0.985575	−	0.169237i	$-0.0541305\pi$
$264$	−3.05643e23	−	2.40947e23i	−0.185855	−	0.146515i
$265$	−1.75103e24			−1.02526
$266$	−1.05781e24	+	4.67489e24i	−0.596473	+	2.63606i
$267$	−1.24669e24			−0.677089
$268$	6.41683e23	+	3.06064e23i	0.335716	+	0.160127i
$269$			1.60976e24i			0.811408i	0.914004	+	0.405704i	$0.132974\pi$
$269$			1.60976e24i			0.811408i	−0.914004	+	0.405704i	$0.867026\pi$
$270$	−3.75767e23	+	1.66066e24i	−0.182508	+	0.806574i
$271$			2.62551e22i			0.0122891i	0.999981	+	0.00614457i	$0.00195589\pi$
$271$			2.62551e22i			0.0122891i	−0.999981	+	0.00614457i	$0.998044\pi$
$272$	−1.37481e24	−	1.69772e24i	−0.620230	−	0.765908i
$273$	4.38051e24			1.90501
$274$	−3.46746e24	−	7.84600e23i	−1.45380	−	0.328960i
$275$	1.65813e23			0.0670334
$276$	5.47823e23	−	1.14855e24i	0.213575	−	0.447773i
$277$		−	5.84599e22i		−	0.0219817i	−0.999940	−	0.0109908i	$-0.996501\pi$
$277$		−	5.84599e22i		−	0.0219817i	0.999940	−	0.0109908i	$-0.00349856\pi$
$278$	2.01038e22	+	4.54899e21i	0.00729173	+	0.00164994i
$279$			1.81933e23i			0.0636603i
$280$	3.66050e24	+	2.88567e24i	1.23583	+	0.974241i
$281$	−5.61456e24			−1.82916			−0.914581	−	0.404402i	$-0.867480\pi$
$281$	−5.61456e24			−1.82916			−0.914581	+	0.404402i	$0.867480\pi$
$282$	8.17057e23	−	3.61090e24i	0.256898	−	1.13534i
$283$	1.26250e24			0.383149			0.191574	−	0.981478i	$-0.438641\pi$
$283$	1.26250e24			0.383149			0.191574	+	0.981478i	$0.438641\pi$
$284$	1.17623e24	−	2.46604e24i	0.344595	−	0.722466i
$285$		−	4.40043e24i		−	1.24465i
$286$	−1.88225e23	+	8.31840e23i	−0.0514062	+	0.227185i
$287$			5.60800e24i			1.47907i
$288$	−6.50704e22	−	1.31947e23i	−0.0165752	−	0.0336104i
$289$	−1.16643e23			−0.0286998
$290$	−2.46262e24	−	5.57230e23i	−0.585353	−	0.132451i
$291$	−6.00141e24			−1.37823
$292$	1.96912e24	+	9.39212e23i	0.436962	+	0.208418i
$293$			4.18336e24i			0.897117i	0.893753	+	0.448559i	$0.148062\pi$
$293$			4.18336e24i			0.897117i	−0.893753	+	0.448559i	$0.851938\pi$
$294$	1.18898e25	+	2.69036e24i	2.46434	+	0.557619i
$295$			3.93052e22i			0.00787463i
$296$	8.78953e23	−	1.11496e24i	0.170235	−	0.215944i
$297$	−1.21648e24			−0.227793
$298$	1.12223e24	−	4.95958e24i	0.203198	−	0.898012i
$299$	−2.78852e24			−0.488273
$300$	1.56618e24	+	7.47023e23i	0.265234	+	0.126509i
$301$		−	8.13249e23i		−	0.133217i
$302$	1.13505e24	−	5.01624e24i	0.179864	−	0.794893i
$303$		−	7.45378e24i		−	1.14275i
$304$	−6.14586e24	−	7.58939e24i	−0.911689	−	1.12583i
$305$	3.00739e23			0.0431709
$306$	2.59294e23	+	5.86717e22i	0.0360229	+	0.00815107i
$307$	7.79220e24			1.04780			0.523898	−	0.851781i	$-0.324477\pi$
$307$	7.79220e24			1.04780			0.523898	+	0.851781i	$0.324477\pi$
$308$	−1.43369e24	+	3.00581e24i	−0.186615	+	0.391251i
$309$			1.14344e25i			1.44089i
$310$	1.14547e25	+	2.59192e24i	1.39755	+	0.316231i
$311$		−	3.44553e24i		−	0.407054i	−0.979069	−	0.203527i	$-0.934760\pi$
$311$		−	3.44553e24i		−	0.407054i	0.979069	−	0.203527i	$-0.0652404\pi$
$312$	−5.52549e24	+	7.00913e24i	−0.632157	+	0.801896i
$313$	1.01897e24			0.112906			0.0564531	−	0.998405i	$-0.482021\pi$
$313$	1.01897e24			0.112906			0.0564531	+	0.998405i	$0.482021\pi$
$314$	−2.84217e24	+	1.25607e25i	−0.305037	+	1.34808i
$315$	−5.67234e23			−0.0589735
$316$	−2.25408e24	+	4.72582e24i	−0.227038	+	0.475999i
$317$		−	1.18213e25i		−	1.15365i	−0.816868	−	0.576825i	$-0.804292\pi$
$317$		−	1.18213e25i		−	1.15365i	0.816868	−	0.576825i	$-0.195708\pi$
$318$	2.88937e24	−	1.27693e25i	0.273232	−	1.20752i
$319$		−	1.80393e24i		−	0.165316i
$320$	−9.23456e24	+	2.21713e24i	−0.820194	+	0.196921i
$321$	−1.33060e23			−0.0114551
$322$	−1.06199e25	−	2.40303e24i	−0.886265	−	0.200540i
$323$	1.76471e25			1.42774
$324$	−1.19214e25	−	5.68618e24i	−0.935144	−	0.446037i
$325$		−	3.80249e24i		−	0.289224i
$326$	5.78387e23	+	1.30874e23i	0.0426621	+	0.00965336i
$327$			1.75628e25i			1.25637i
$328$	−8.97321e24	−	7.07383e24i	−0.622600	−	0.490813i
$329$	−3.16784e25			−2.13209
$330$	6.74758e23	−	2.98203e24i	0.0440563	−	0.194703i
$331$	2.48437e25			1.57375			0.786877	−	0.617110i	$-0.211697\pi$
$331$	2.48437e25			1.57375			0.786877	+	0.617110i	$0.211697\pi$
$332$	2.64497e25	+	1.26157e25i	1.62570	+	0.775411i
$333$			1.72775e23i			0.0103048i
$334$	−4.85770e24	+	2.14681e25i	−0.281168	+	1.24259i
$335$			5.58493e24i			0.313740i
$336$	−2.70837e25	+	2.19323e25i	−1.47678	+	1.19589i
$337$	−2.67940e24			−0.141821			−0.0709103	−	0.997483i	$-0.522590\pi$
$337$	−2.67940e24			−0.141821			−0.0709103	+	0.997483i	$0.522590\pi$
$338$	9.48661e22	+	2.14658e22i	0.00487466	+	0.00110301i
$339$	−8.94233e24			−0.446122
$340$	7.38811e24	−	1.54896e25i	0.357885	−	0.750330i
$341$			8.39089e24i			0.394697i
$342$	1.15913e24	+	2.62283e23i	0.0529508	+	0.0119814i
$343$		−	6.22590e25i		−	2.76224i
$344$	1.30126e24	+	1.02582e24i	0.0560763	+	0.0442065i
$345$	9.99646e24			0.418461
$346$	−1.67945e24	+	7.42216e24i	−0.0682977	+	0.301835i
$347$	9.41337e24			0.371921			0.185960	−	0.982557i	$-0.440460\pi$
$347$	9.41337e24			0.371921			0.185960	+	0.982557i	$0.440460\pi$
$348$	8.12712e24	−	1.70390e25i	0.311992	−	0.654112i
$349$			3.63487e25i			1.35592i	0.735098	+	0.677960i	$0.237136\pi$
$349$			3.63487e25i			1.35592i	−0.735098	+	0.677960i	$0.762864\pi$
$350$	3.27682e24	−	1.44816e25i	0.118788	−	0.524971i
$351$			2.78968e25i			0.982841i
$352$	−3.00110e24	−	6.08548e24i	−0.102767	−	0.208386i
$353$	1.59639e25			0.531364			0.265682	−	0.964061i	$-0.414403\pi$
$353$	1.59639e25			0.531364			0.265682	+	0.964061i	$0.414403\pi$
$354$	−2.86631e23	−	6.48573e22i	−0.00927449	−	0.00209858i
$355$	2.14634e25			0.675172
$356$	−1.96176e25	−	9.35703e24i	−0.599993	−	0.286179i
$357$		−	6.29759e25i		−	1.87280i
$358$	3.32646e24	+	7.52694e23i	0.0961949	+	0.0217665i
$359$		−	3.25820e24i		−	0.0916292i	−0.998950	−	0.0458146i	$-0.985412\pi$
$359$		−	3.25820e24i		−	0.0916292i	0.998950	−	0.0458146i	$-0.0145883\pi$
$360$	7.15499e23	−	9.07617e23i	0.0195697	−	0.0248243i
$361$	4.12986e25			1.09866
$362$	1.33857e25	−	5.91567e25i	0.346382	−	1.53080i
$363$	−3.82783e25			−0.963577
$364$	6.89306e25	+	3.28779e25i	1.68810	+	0.805174i
$365$			1.71384e25i			0.408358i
$366$	−4.96247e23	+	2.19312e24i	−0.0115050	+	0.0508453i
$367$			2.00995e25i			0.453445i	0.973959	+	0.226722i	$0.0728010\pi$
$367$			2.00995e25i			0.453445i	−0.973959	+	0.226722i	$0.927199\pi$
$368$	1.72408e25	−	1.39616e25i	0.378512	−	0.306518i
$369$	1.39050e24			0.0297103
$370$	1.08782e25	+	2.46146e24i	0.226224	+	0.0511888i
$371$	−1.12025e26			−2.26765
$372$	−3.78028e25	+	7.92560e25i	−0.744894	+	1.56172i
$373$		−	5.49354e25i		−	1.05381i	−0.849923	−	0.526907i	$-0.823352\pi$
$373$		−	5.49354e25i		−	1.05381i	0.849923	−	0.526907i	$-0.176648\pi$
$374$	1.19589e25	+	2.70599e24i	0.223344	+	0.0505371i
$375$			6.08798e25i			1.10703i
$376$	3.99586e25	−	5.06878e25i	0.707509	−	0.897481i
$377$	−4.13685e25			−0.713275
$378$	−2.40402e25	+	1.06244e26i	−0.403665	+	1.78396i
$379$	−8.50762e25			−1.39129			−0.695643	−	0.718388i	$-0.744880\pi$
$379$	−8.50762e25			−1.39129			−0.695643	+	0.718388i	$0.744880\pi$
$380$	3.30274e25	−	6.92440e25i	0.526064	−	1.10293i
$381$			7.80005e25i			1.21017i
$382$	2.39132e24	−	1.05682e25i	0.0361414	−	0.159723i
$383$			4.26912e25i			0.628565i	0.949330	+	0.314282i	$0.101764\pi$
$383$			4.26912e25i			0.628565i	−0.949330	+	0.314282i	$0.898236\pi$
$384$	−9.30377e23	−	7.10009e25i	−0.0133459	−	1.01848i
$385$	−2.61613e25			−0.365639
$386$	−4.42517e25	−	1.00130e25i	−0.602638	−	0.136362i
$387$	−2.01644e23			−0.00267594
$388$	−9.44366e25	−	4.50435e25i	−1.22130	−	0.582526i
$389$			1.17009e26i			1.47477i	0.675472	+	0.737386i	$0.263940\pi$
$389$			1.17009e26i			1.47477i	−0.675472	+	0.737386i	$0.736060\pi$
$390$	−6.83850e25	−	1.54738e25i	−0.840069	−	0.190087i
$391$			4.00889e25i			0.480017i
$392$	1.66902e26	+	1.31574e26i	1.94806	+	1.53571i
$393$	1.64509e26			1.87182
$394$	5.34751e24	−	2.36328e25i	0.0593184	−	0.262152i
$395$	−4.11315e25			−0.444840
$396$	7.45289e23	+	3.55481e23i	0.00785910	+	0.00374856i
$397$		−	1.54508e26i		−	1.58872i	−0.607450	−	0.794358i	$-0.707807\pi$
$397$		−	1.54508e26i		−	1.58872i	0.607450	−	0.794358i	$-0.292193\pi$
$398$	−1.78530e25	+	7.88996e25i	−0.179011	+	0.791123i
$399$		−	2.81524e26i		−	2.75287i
$400$	1.90383e25	+	2.35099e25i	0.181563	+	0.224208i
$401$	−6.14125e25			−0.571232			−0.285616	−	0.958344i	$-0.592198\pi$
$401$	−6.14125e25			−0.571232			−0.285616	+	0.958344i	$0.592198\pi$
$402$	−4.07277e25	−	9.21566e24i	−0.369513	−	0.0836115i
$403$	1.92423e26			1.70297
$404$	5.59443e25	−	1.17291e26i	0.482995	−	1.01263i
$405$		−	1.03759e26i		−	0.873928i
$406$	−1.57550e26	−	3.56496e25i	−1.29467	−	0.292951i
$407$			7.96854e24i			0.0638903i
$408$	1.00766e26	+	7.94366e25i	0.788338	+	0.621468i
$409$	1.42600e26			1.08865			0.544323	−	0.838876i	$-0.316787\pi$
$409$	1.42600e26			1.08865			0.544323	+	0.838876i	$0.316787\pi$
$410$	1.98098e25	−	8.75477e25i	0.147585	−	0.652238i
$411$	2.08812e26			1.51823
$412$	−8.58212e25	+	1.79930e26i	−0.609007	+	1.27682i
$413$			2.51461e24i			0.0174169i
$414$	−5.95829e23	+	2.63321e24i	−0.00402826	+	0.0178025i
$415$			2.30207e26i			1.51928i
$416$	−1.39555e26	+	6.88224e25i	−0.899107	+	0.443401i
$417$	−1.21066e24			−0.00761487
$418$	5.34602e25	+	1.20967e25i	0.328298	+	0.0742855i
$419$	−1.80660e26			−1.08323			−0.541616	−	0.840626i	$-0.682187\pi$
$419$	−1.80660e26			−1.08323			−0.541616	+	0.840626i	$0.682187\pi$
$420$	−2.47106e26	−	1.17862e26i	−1.44674	−	0.690053i
$421$			8.46001e25i			0.483671i	0.970317	+	0.241835i	$0.0777494\pi$
$421$			8.46001e25i			0.483671i	−0.970317	+	0.241835i	$0.922251\pi$
$422$	−1.91161e25	−	4.32550e24i	−0.106727	−	0.0241497i
$423$			7.85464e24i			0.0428275i
$424$	1.41306e26	−	1.79248e26i	0.752494	−	0.954546i
$425$	−5.46660e25			−0.284334
$426$	−3.54166e25	+	1.56520e26i	−0.179933	+	0.795197i
$427$	1.92402e25			0.0954841
$428$	−2.09380e24	−	9.98682e23i	−0.0101507	−	0.00484161i
$429$		−	5.00938e25i		−	0.237253i
$430$	−2.87274e24	+	1.26958e25i	−0.0132927	+	0.0587457i
$431$		−	2.88333e26i		−	1.30353i	−0.758420	−	0.651766i	$-0.774028\pi$
$431$		−	2.88333e26i		−	1.30353i	0.758420	−	0.651766i	$-0.225972\pi$
$432$	−1.39674e26	−	1.72480e26i	−0.616988	−	0.761905i
$433$	−9.66878e25			−0.417343			−0.208671	−	0.977986i	$-0.566914\pi$
$433$	−9.66878e25			−0.417343			−0.208671	+	0.977986i	$0.566914\pi$
$434$	7.32834e26	+	1.65822e26i	3.09107	+	0.699431i
$435$	1.48300e26			0.611293
$436$	−1.31818e26	+	2.76364e26i	−0.531018	+	1.11331i
$437$			1.79211e26i			0.705588i
$438$	−1.24980e26	−	2.82799e25i	−0.480951	−	0.108827i
$439$		−	6.67083e25i		−	0.250920i	−0.992099	−	0.125460i	$-0.959959\pi$
$439$		−	6.67083e25i		−	0.250920i	0.992099	−	0.125460i	$-0.0400406\pi$
$440$	3.29994e25	−	4.18600e25i	0.121333	−	0.153912i
$441$	−2.58634e25			−0.0929607
$442$	6.20548e25	−	2.74245e26i	0.218048	−	0.963644i
$443$	−2.09664e26			−0.720257			−0.360129	−	0.932903i	$-0.617267\pi$
$443$	−2.09664e26			−0.720257			−0.360129	+	0.932903i	$0.617267\pi$
$444$	−3.59000e25	+	7.52667e25i	−0.120577	+	0.252798i
$445$		−	1.70743e26i		−	0.560717i
$446$	1.18277e25	−	5.22712e25i	0.0379796	−	0.167847i
$447$			2.98668e26i			0.937808i
$448$	−5.90795e26	+	1.41844e26i	−1.81408	+	0.435544i
$449$	−5.39396e26			−1.61974			−0.809868	−	0.586613i	$-0.800461\pi$
$449$	−5.39396e26			−1.61974			−0.809868	+	0.586613i	$0.800461\pi$
$450$	−3.59069e24	−	8.12484e23i	−0.0105452	−	0.00238610i
$451$	6.41309e25			0.184205
$452$	−1.40714e26	−	6.71166e25i	−0.395324	−	0.188558i
$453$			3.02080e26i			0.830118i
$454$	−8.57246e25	−	1.93973e25i	−0.230434	−	0.0521415i
$455$			5.99942e26i			1.57759i
$456$	4.50459e26	+	3.55109e26i	1.15880	+	0.913510i
$457$	1.14132e25			0.0287240			0.0143620	−	0.999897i	$-0.495428\pi$
$457$	1.14132e25			0.0287240			0.0143620	+	0.999897i	$0.495428\pi$
$458$	7.18278e25	−	3.17436e26i	0.176863	−	0.781631i
$459$	4.01055e26			0.966223
$460$	1.57302e26	+	7.50284e25i	0.370813	+	0.176867i
$461$		−	4.34604e25i		−	0.100250i	−0.998743	−	0.0501250i	$-0.984038\pi$
$461$		−	4.34604e25i		−	0.100250i	0.998743	−	0.0501250i	$-0.0159620\pi$
$462$	4.31686e25	−	1.90780e26i	0.0974425	−	0.430638i
$463$		−	7.99415e26i		−	1.76588i	−0.469482	−	0.882942i	$-0.655559\pi$
$463$		−	7.99415e26i		−	1.76588i	0.469482	−	0.882942i	$-0.344441\pi$
$464$	2.55773e26	−	2.07124e26i	0.552935	−	0.447765i
$465$	−6.89810e26			−1.45949
$466$	3.28948e26	+	7.44328e25i	0.681191	+	0.154136i
$467$	2.20079e26			0.446077			0.223039	−	0.974810i	$-0.428402\pi$
$467$	2.20079e26			0.446077			0.223039	+	0.974810i	$0.428402\pi$
$468$	8.15204e24	−	1.70913e25i	0.0161736	−	0.0339091i
$469$			3.57304e26i			0.693921i
$470$	4.94539e26	+	1.11902e26i	0.940204	+	0.212745i
$471$		−	7.56410e26i		−	1.40782i
$472$	−4.02356e24	−	3.17188e24i	−0.00733146	−	0.00577959i
$473$	−9.30001e24			−0.0165910
$474$	6.78709e25	−	2.99949e26i	0.118550	−	0.523918i
$475$	−2.44376e26			−0.417948
$476$	4.72665e26	−	9.90973e26i	0.791560	−	1.65956i
$477$			2.77765e25i			0.0455506i
$478$	−1.27923e26	+	5.65341e26i	−0.205432	+	0.907887i
$479$			1.06198e27i			1.67017i	0.550122	+	0.835084i	$0.314581\pi$
$479$			1.06198e27i			1.67017i	−0.550122	+	0.835084i	$0.685419\pi$
$480$	5.00284e26	−	2.46718e26i	0.770556	−	0.380005i
$481$	1.82738e26			0.275662
$482$	−3.83393e26	−	8.67522e25i	−0.566466	−	0.128177i
$483$	6.39538e26			0.925540
$484$	−6.02338e26	−	2.87298e26i	−0.853860	−	0.407266i
$485$		−	8.21936e26i		−	1.14135i
$486$	5.37116e25	+	1.21536e25i	0.0730644	+	0.0165326i
$487$		−	2.80248e26i		−	0.373468i	−0.982411	−	0.186734i	$-0.940210\pi$
$487$		−	2.80248e26i		−	0.373468i	0.982411	−	0.186734i	$-0.0597902\pi$
$488$	−2.42693e25	+	3.07858e25i	−0.0316853	+	0.0401931i
$489$	−3.48307e25			−0.0445527
$490$	−3.68465e26	+	1.62839e27i	−0.461780	+	2.04079i
$491$	−5.74718e26			−0.705732			−0.352866	−	0.935674i	$-0.614793\pi$
$491$	−5.74718e26			−0.705732			−0.352866	+	0.935674i	$0.614793\pi$
$492$	6.05747e26	+	2.88924e26i	0.728854	+	0.347642i
$493$			5.94730e26i			0.701215i
$494$	2.77407e26	−	1.22597e27i	0.320514	−	1.41648i
$495$			6.48667e24i			0.00734463i
$496$	−1.18971e27	+	9.63424e26i	−1.32015	+	1.06906i
$497$	1.37315e27			1.49333
$498$	−1.67877e27	−	3.79863e26i	−1.78936	−	0.404887i
$499$	−5.06644e26			−0.529295			−0.264648	−	0.964345i	$-0.585256\pi$
$499$	−5.06644e26			−0.529295			−0.264648	+	0.964345i	$0.585256\pi$
$500$	−4.56934e26	+	9.57990e26i	−0.467900	+	0.980982i
$501$		−	1.29282e27i		−	1.29766i
$502$	−1.74184e26	−	3.94135e25i	−0.171385	−	0.0387800i
$503$			2.15458e26i			0.207818i	0.994587	+	0.103909i	$0.0331351\pi$
$503$			2.15458e26i			0.207818i	−0.994587	+	0.103909i	$0.966865\pi$
$504$	4.57751e25	−	5.80661e25i	0.0432837	−	0.0549057i
$505$	1.02085e27			0.946342
$506$	−2.74801e25	+	1.21446e26i	−0.0249754	+	0.110377i
$507$	−5.71288e24			−0.00509068
$508$	−5.85432e26	+	1.22740e27i	−0.511493	+	1.07238i
$509$			2.11869e26i			0.181506i	0.995873	+	0.0907528i	$0.0289273\pi$
$509$			2.11869e26i			0.181506i	−0.995873	+	0.0907528i	$0.971073\pi$
$510$	−2.22458e26	+	9.83130e26i	−0.186873	+	0.825865i
$511$			1.09645e27i			0.903193i
$512$	5.18257e26	−	1.12424e27i	0.418645	−	0.908150i
$513$	1.79286e27			1.42027
$514$	−2.21244e27	−	5.00620e26i	−1.71886	−	0.388935i
$515$	−1.56603e27			−1.19324
$516$	−8.78430e25	−	4.18986e25i	−0.0656463	−	0.0313114i
$517$			3.62263e26i			0.265533i
$518$	6.95947e26	+	1.57475e26i	0.500356	+	0.113218i
$519$		−	4.46966e26i		−	0.315211i
$520$	−9.59951e26	−	7.56756e26i	−0.664073	−	0.523507i
$521$	−4.14659e26			−0.281393			−0.140697	−	0.990053i	$-0.544934\pi$
$521$	−4.14659e26			−0.281393			−0.140697	+	0.990053i	$0.544934\pi$
$522$	−8.83929e24	+	3.90644e25i	−0.00588453	+	0.0260061i
$523$	−8.08616e26			−0.528111			−0.264056	−	0.964507i	$-0.585060\pi$
$523$	−8.08616e26			−0.528111			−0.264056	+	0.964507i	$0.585060\pi$
$524$	2.58867e27	+	1.23472e27i	1.65869	+	0.791145i
$525$			8.72087e26i			0.548235i
$526$	−1.21109e26	+	5.35231e26i	−0.0746999	+	0.330129i
$527$		−	2.76635e27i		−	1.67418i
$528$	2.50809e26	+	3.09719e26i	0.148938	+	0.183920i
$529$	1.30904e27			0.762775
$530$	1.74885e27	+	3.95720e26i	0.999985	+	0.226271i
$531$	6.23495e23			0.000349855
$532$	2.11298e27	−	4.42999e27i	1.16353	−	2.43942i
$533$		−	1.47068e27i		−	0.794777i
$534$	1.24513e27	+	2.81742e26i	0.660394	+	0.149431i
$535$		−	1.82235e25i		−	0.00948626i
$536$	−5.71713e26	−	4.50697e26i	−0.292099	−	0.230270i
$537$	−2.00321e26			−0.100458
$538$	3.63794e26	−	1.60775e27i	0.179074	−	0.791401i
$539$	−1.19284e27			−0.576361
$540$	7.50595e26	−	1.57367e27i	0.356015	−	0.746408i
$541$		−	3.78702e26i		−	0.176330i	−0.996106	−	0.0881648i	$-0.971900\pi$
$541$		−	3.78702e26i		−	0.176330i	0.996106	−	0.0881648i	$-0.0281002\pi$
$542$	5.93346e24	−	2.62223e25i	0.00271216	−	0.0119861i
$543$			3.56245e27i			1.59864i
$544$	9.89418e26	+	2.00629e27i	0.435904	+	0.883905i
$545$	−2.40536e27			−1.04043
$546$	−4.37503e27	−	9.89961e26i	−1.85804	−	0.420428i
$547$	3.78029e27			1.57635			0.788173	−	0.615453i	$-0.211027\pi$
$547$	3.78029e27			1.57635			0.788173	+	0.615453i	$0.211027\pi$
$548$	3.28582e27	+	1.56724e27i	1.34536	+	0.641697i
$549$		−	4.77059e24i		−	0.00191800i
$550$	−1.65606e26	−	3.74724e25i	−0.0653805	−	0.0147940i
$551$			2.65865e27i			1.03073i
$552$	−8.06702e26	+	1.02331e27i	−0.307130	+	0.389597i
$553$	−2.63145e27			−0.983884
$554$	−1.32115e25	+	5.83869e25i	−0.00485126	+	0.0214397i
$555$	−6.55089e26			−0.236249
$556$	−1.90507e25	−	9.08662e24i	−0.00674781	−	0.00321851i
$557$			1.66373e27i			0.578803i	0.957208	+	0.289401i	$0.0934563\pi$
$557$			1.66373e27i			0.578803i	−0.957208	+	0.289401i	$0.906544\pi$
$558$	4.11154e25	−	1.81706e26i	0.0140496	−	0.0620907i
$559$			2.13272e26i			0.0715838i
$560$	−3.00378e27	−	3.70931e27i	−0.990350	−	1.22296i
$561$	−7.20168e26			−0.233241
$562$	5.60754e27	+	1.26885e27i	1.78406	+	0.403688i
$563$	−1.91718e27			−0.599211			−0.299606	−	0.954063i	$-0.596855\pi$
$563$	−1.91718e27			−0.599211			−0.299606	+	0.954063i	$0.596855\pi$
$564$	−1.63207e27	+	3.42174e27i	−0.501128	+	1.05065i
$565$		−	1.22472e27i		−	0.369446i
$566$	−1.26092e27	−	2.85316e26i	−0.373701	−	0.0845593i
$567$		−	6.63814e27i		−	1.93293i
$568$	−1.73207e27	+	2.19714e27i	−0.495544	+	0.628601i
$569$	−4.08427e27			−1.14813			−0.574066	−	0.818809i	$-0.694635\pi$
$569$	−4.08427e27			−1.14813			−0.574066	+	0.818809i	$0.694635\pi$
$570$	−9.94462e26	+	4.39493e27i	−0.274688	+	1.21396i
$571$	−5.81506e26			−0.157831			−0.0789157	−	0.996881i	$-0.525146\pi$
$571$	−5.81506e26			−0.157831			−0.0789157	+	0.996881i	$0.525146\pi$
$572$	3.75979e26	−	7.88264e26i	0.100277	−	0.210238i
$573$			6.36423e26i			0.166801i
$574$	1.26736e27	−	5.60099e27i	0.326424	−	1.44260i
$575$		−	5.55150e26i		−	0.140518i
$576$	3.51702e25	+	1.46487e26i	0.00874883	+	0.0364397i
$577$	2.69062e27			0.657801			0.328901	−	0.944365i	$-0.393322\pi$
$577$	2.69062e27			0.657801			0.328901	+	0.944365i	$0.393322\pi$
$578$	1.16497e26	+	2.63603e25i	0.0279921	+	0.00633392i
$579$	2.66486e27			0.629344
$580$	2.33362e27	+	1.11307e27i	0.541688	+	0.258370i
$581$			1.47278e28i			3.36030i
$582$	5.99391e27	+	1.35627e27i	1.34425	+	0.304170i
$583$			1.28108e27i			0.282416i
$584$	−1.75440e27	−	1.38304e27i	−0.380190	−	0.299715i
$585$	1.48755e26			0.0316893
$586$	9.45408e26	−	4.17814e27i	0.197990	−	0.874997i
$587$	−8.87574e26			−0.182736			−0.0913678	−	0.995817i	$-0.529124\pi$
$587$	−8.87574e26			−0.182736			−0.0913678	+	0.995817i	$0.529124\pi$
$588$	−1.12669e28	−	5.37400e27i	−2.28051	−	1.08774i
$589$		−	1.23666e28i		−	2.46091i
$590$	8.88268e24	−	3.92561e25i	0.00173790	−	0.00768046i
$591$			1.42318e27i			0.273769i
$592$	−1.12983e27	+	9.14930e26i	−0.213695	+	0.173050i
$593$	2.28118e27			0.424241			0.212120	−	0.977244i	$-0.431963\pi$
$593$	2.28118e27			0.424241			0.212120	+	0.977244i	$0.431963\pi$
$594$	1.21496e27	+	2.74915e26i	0.222176	+	0.0502729i
$595$	8.62500e27			1.55092
$596$	−2.24165e27	+	4.69977e27i	−0.396375	+	0.831025i
$597$		−	4.75137e27i		−	0.826182i
$598$	2.78504e27	+	6.30185e26i	0.476233	+	0.107760i
$599$			4.01414e27i			0.675032i	0.941320	+	0.337516i	$0.109587\pi$
$599$			4.01414e27i			0.675032i	−0.941320	+	0.337516i	$0.890413\pi$
$600$	−1.39540e27	−	1.10003e27i	−0.230774	−	0.181926i
$601$	−9.03918e27			−1.47023			−0.735114	−	0.677944i	$-0.762871\pi$
$601$	−9.03918e27			−1.47023			−0.735114	+	0.677944i	$0.762871\pi$
$602$	−1.83788e26	+	8.12234e26i	−0.0294003	+	0.129932i
$603$	8.85933e25			0.0139389
$604$	−2.26726e27	+	4.75346e27i	−0.350859	+	0.735597i
$605$		−	5.24249e27i		−	0.797965i
$606$	−1.68450e27	+	7.44447e27i	−0.252199	+	1.11457i
$607$		−	9.64789e27i		−	1.42084i	−0.703777	−	0.710421i	$-0.748505\pi$
$607$		−	9.64789e27i		−	1.42084i	0.703777	−	0.710421i	$-0.251495\pi$
$608$	4.42304e27	+	8.96883e27i	0.640745	+	1.29927i
$609$	9.48773e27			1.35204
$610$	−3.00363e26	−	6.79646e25i	−0.0421064	−	0.00952763i
$611$	8.30755e27			1.14567
$612$	−2.45711e26	−	1.17197e26i	−0.0333357	−	0.0159002i
$613$			3.72539e26i			0.0497241i	0.999691	+	0.0248620i	$0.00791465\pi$
$613$			3.72539e26i			0.0497241i	−0.999691	+	0.0248620i	$0.992085\pi$
$614$	−7.78247e27	−	1.76098e27i	−1.02196	−	0.231244i
$615$			5.27216e27i			0.681142i
$616$	2.11119e27	−	2.67806e27i	0.268361	−	0.340418i
$617$	4.15904e27			0.520165			0.260083	−	0.965586i	$-0.416250\pi$
$617$	4.15904e27			0.520165			0.260083	+	0.965586i	$0.416250\pi$
$618$	2.58410e27	−	1.14202e28i	0.317998	−	1.40536i
$619$	1.08544e28			1.31431			0.657154	−	0.753756i	$-0.271760\pi$
$619$	1.08544e28			1.31431			0.657154	+	0.753756i	$0.271760\pi$
$620$	−1.08547e28	−	5.17737e27i	−1.29330	−	0.616868i
$621$			4.07283e27i			0.477508i
$622$	−7.78662e26	+	3.44122e27i	−0.0898349	+	0.397017i
$623$		−	1.09236e28i		−	1.24018i
$624$	7.10260e27	−	5.75166e27i	0.793545	−	0.642610i
$625$	−5.71401e27			−0.628262
$626$	−1.01770e27	−	2.30279e26i	−0.110122	−	0.0249179i
$627$	−3.21940e27			−0.342846
$628$	5.67723e27	−	1.19027e28i	0.595032	−	1.24752i
$629$		−	2.62711e27i		−	0.271002i
$630$	5.66526e26	+	1.28191e26i	0.0575194	+	0.0130152i
$631$			3.07267e27i			0.307060i	0.988144	+	0.153530i	$0.0490641\pi$
$631$			3.07267e27i			0.307060i	−0.988144	+	0.153530i	$0.950936\pi$
$632$	3.31926e27	−	4.21051e27i	0.326491	−	0.414156i
$633$	1.15118e27			0.111457
$634$	−2.67153e27	+	1.18066e28i	−0.254605	+	1.12520i
$635$	−1.06827e28			−1.00218
$636$	−5.77153e27	+	1.21004e28i	−0.532991	+	1.11745i
$637$			2.73547e28i			2.48678i
$638$	−4.07675e26	+	1.80168e27i	−0.0364844	+	0.161239i
$639$		−	3.40472e26i		−	0.0299966i
$640$	9.72409e27	−	1.27422e26i	0.843430	−	0.0110521i
$641$	−1.90529e28			−1.62697			−0.813485	−	0.581586i	$-0.802433\pi$
$641$	−1.90529e28			−1.62697			−0.813485	+	0.581586i	$0.802433\pi$
$642$	1.32894e26	+	3.00706e25i	0.0111726	+	0.00252808i
$643$	−1.05796e28			−0.875711			−0.437856	−	0.899045i	$-0.644262\pi$
$643$	−1.05796e28			−0.875711			−0.437856	+	0.899045i	$0.644262\pi$
$644$	1.00636e28	+	4.80005e27i	0.820154	+	0.391190i
$645$		−	7.64548e26i		−	0.0613490i
$646$	−1.76250e28	−	3.98810e27i	−1.39253	−	0.315095i
$647$			3.30511e27i			0.257124i	0.991701	+	0.128562i	$0.0410361\pi$
$647$			3.30511e27i			0.257124i	−0.991701	+	0.128562i	$0.958964\pi$
$648$	1.06215e28	+	8.37323e27i	0.813648	+	0.641421i
$649$	2.87561e25			0.00216912
$650$	−8.59333e26	+	3.79774e27i	−0.0638304	+	0.282092i
$651$	−4.41316e28			−3.22805
$652$	−5.48087e26	−	2.61422e26i	−0.0394797	−	0.0188307i
$653$		−	1.75915e28i		−	1.24787i	−0.781475	−	0.623937i	$-0.785532\pi$
$653$		−	1.75915e28i		−	1.24787i	0.781475	−	0.623937i	$-0.214468\pi$
$654$	3.96906e27	−	1.75409e28i	0.277275	−	1.22539i
$655$			2.25307e28i			1.55011i
$656$	7.36337e27	+	9.09287e27i	0.498928	+	0.616116i
$657$	2.71864e26			0.0181426
$658$	3.16389e28	+	7.15909e27i	2.07952	+	0.470542i
$659$	1.99713e28			1.29287			0.646433	−	0.762971i	$-0.276260\pi$
$659$	1.99713e28			1.29287			0.646433	+	0.762971i	$0.276260\pi$
$660$	−1.34783e27	+	2.82581e27i	−0.0859401	+	0.180179i
$661$		−	9.97708e27i		−	0.626598i	−0.949655	−	0.313299i	$-0.898566\pi$
$661$		−	9.97708e27i		−	0.626598i	0.949655	−	0.313299i	$-0.101434\pi$
$662$	−2.48127e28	−	5.61449e27i	−1.53495	−	0.347320i
$663$			1.65152e28i			1.00635i
$664$	−2.35656e28	−	1.85774e28i	−1.41448	−	1.11508i
$665$	3.85567e28			2.27973
$666$	3.90459e25	−	1.72560e26i	0.00227422	−	0.0100507i
$667$	−6.03966e27			−0.346541
$668$	9.70326e27	−	2.03435e28i	0.548470	−	1.14990i
$669$			3.14780e27i			0.175285i
$670$	1.26215e27	−	5.57796e27i	0.0692410	−	0.306004i
$671$		−	2.20024e26i		−	0.0118917i
$672$	3.20064e28	−	1.57842e28i	1.70429	−	0.840484i
$673$	1.56242e28			0.819683			0.409841	−	0.912157i	$-0.365584\pi$
$673$	1.56242e28			0.819683			0.409841	+	0.912157i	$0.365584\pi$
$674$	2.67606e27	+	6.05525e26i	0.138324	+	0.0312992i
$675$	−5.55380e27			−0.282847
$676$	−8.98965e25	−	4.28780e25i	−0.00451103	−	0.00215163i
$677$		−	2.96609e28i		−	1.46655i	−0.679932	−	0.733275i	$-0.737991\pi$
$677$		−	2.96609e28i		−	1.46655i	0.679932	−	0.733275i	$-0.262009\pi$
$678$	8.93116e27	+	2.02090e27i	0.435122	+	0.0984571i
$679$		−	5.25846e28i		−	2.52441i
$680$	−1.08794e28	+	1.38006e28i	−0.514655	+	0.652845i
$681$	5.16238e27			0.240646
$682$	1.89628e27	−	8.38041e27i	0.0871080	−	0.384965i
$683$	−8.85063e27			−0.400652			−0.200326	−	0.979729i	$-0.564200\pi$
$683$	−8.85063e27			−0.400652			−0.200326	+	0.979729i	$0.564200\pi$
$684$	−1.09841e27	−	5.23911e26i	−0.0490009	−	0.0233720i
$685$			2.85983e28i			1.25729i
$686$	−1.40701e28	+	6.21813e28i	−0.609614	+	2.69413i
$687$			1.91162e28i			0.816269i
$688$	−1.06781e27	−	1.31861e27i	−0.0449374	−	0.0554923i
$689$	2.93782e28			1.21852
$690$	−9.98397e27	−	2.25912e27i	−0.408143	−	0.0923525i
$691$	2.99742e27			0.120772			0.0603862	−	0.998175i	$-0.480767\pi$
$691$	2.99742e27			0.120772			0.0603862	+	0.998175i	$0.480767\pi$
$692$	3.35470e27	−	7.03335e27i	0.133227	−	0.279320i
$693$			4.14995e26i			0.0162446i
$694$	−9.40161e27	−	2.12735e27i	−0.362750	−	0.0820813i
$695$		−	1.65809e26i		−	0.00630609i
$696$	−1.19677e28	+	1.51811e28i	−0.448659	+	0.569128i
$697$	−2.11430e28			−0.781339
$698$	8.21452e27	−	3.63033e28i	0.299246	−	1.32249i
$699$	−1.98094e28			−0.711378
$700$	−6.54545e27	+	1.37229e28i	−0.231718	+	0.485811i
$701$			3.99234e26i			0.0139331i	0.999976	+	0.00696655i	$0.00221754\pi$
$701$			3.99234e26i			0.0139331i	−0.999976	+	0.00696655i	$0.997782\pi$
$702$	6.30446e27	−	2.78620e28i	0.216909	−	0.958607i
$703$		−	1.17441e28i		−	0.398351i
$704$	1.62208e27	+	6.75611e27i	0.0542432	+	0.225928i
$705$	−2.97814e28			−0.981869
$706$	−1.59440e28	−	3.60772e27i	−0.518262	−	0.117270i
$707$	6.53104e28			2.09309
$708$	2.71615e26	+	1.29553e26i	0.00858265	+	0.00409368i
$709$			2.52620e28i			0.787055i	0.919313	+	0.393528i	$0.128745\pi$
$709$			2.52620e28i			0.787055i	−0.919313	+	0.393528i	$0.871255\pi$
$710$	−2.14366e28	−	4.85056e27i	−0.658524	−	0.149008i
$711$			6.52466e26i			0.0197634i
$712$	1.74785e28	+	1.37788e28i	0.522040	+	0.411539i
$713$	2.80931e28			0.827379
$714$	−1.42321e28	+	6.28972e28i	−0.413319	+	1.82662i
$715$	6.86071e27			0.196476
$716$	−3.15220e27	−	1.50351e27i	−0.0890192	−	0.0424596i
$717$		−	3.40451e28i		−	0.948120i
$718$	−7.36329e26	+	3.25413e27i	−0.0202222	+	0.0893699i
$719$			2.54621e28i			0.689612i	0.938674	+	0.344806i	$0.112055\pi$
$719$			2.54621e28i			0.689612i	−0.938674	+	0.344806i	$0.887945\pi$
$720$	−9.19720e26	+	7.44786e26i	−0.0245658	+	0.0198933i
$721$	−1.00189e29			−2.63917
$722$	−4.12470e28	−	9.33316e27i	−1.07157	−	0.242469i
$723$	2.30881e28			0.591569
$724$	−2.67379e28	+	5.60578e28i	−0.675682	+	1.41661i
$725$		−	8.23580e27i		−	0.205270i
$726$	3.82305e28	+	8.65060e27i	0.939818	+	0.212657i
$727$			4.09725e28i			0.993455i	0.867907	+	0.496728i	$0.165465\pi$
$727$			4.09725e28i			0.993455i	−0.867907	+	0.496728i	$0.834535\pi$
$728$	−6.14143e28	−	4.84146e28i	−1.46878	−	1.15788i
$729$	4.06857e28			0.959769
$730$	3.87314e27	−	1.71170e28i	0.0901227	−	0.398289i
$731$	3.06608e27			0.0703735
$732$	9.91255e26	−	2.07823e27i	0.0224427	−	0.0470525i
$733$		−	1.43241e28i		−	0.319911i	−0.987124	−	0.159955i	$-0.948865\pi$
$733$		−	1.43241e28i		−	0.319911i	0.987124	−	0.159955i	$-0.0511350\pi$
$734$	4.54233e27	−	2.00744e28i	0.100073	−	0.442264i
$735$		−	9.80626e28i		−	2.13123i
$736$	−2.03745e28	+	1.00478e28i	−0.436826	+	0.215424i
$737$	4.08600e27			0.0864217
$738$	−1.38876e27	−	3.14242e26i	−0.0289777	−	0.00655693i
$739$	7.87579e28			1.62125			0.810624	−	0.585567i	$-0.199128\pi$
$739$	7.87579e28			1.62125			0.810624	+	0.585567i	$0.199128\pi$
$740$	−1.03083e28	−	4.91677e27i	−0.209349	−	0.0998533i
$741$			7.38286e28i			1.47925i
$742$	1.11885e29	+	2.53168e28i	2.21174	+	0.500461i
$743$		−	5.32560e28i		−	1.03868i	−0.854569	−	0.519338i	$-0.826178\pi$
$743$		−	5.32560e28i		−	1.03868i	0.854569	−	0.519338i	$-0.173822\pi$
$744$	5.56668e28	−	7.06138e28i	1.07119	−	1.35882i
$745$	−4.09048e28			−0.776625
$746$	−1.24150e28	+	5.48668e28i	−0.232572	+	1.02783i
$747$	3.65175e27			0.0674987
$748$	−1.13324e28	−	5.40522e27i	−0.206683	−	0.0985819i
$749$		−	1.16588e27i		−	0.0209814i
$750$	1.37584e28	−	6.08038e28i	0.244318	−	1.07974i
$751$			9.40055e28i			1.64723i	0.567151	+	0.823614i	$0.308046\pi$
$751$			9.40055e28i			1.64723i	−0.567151	+	0.823614i	$0.691954\pi$
$752$	−5.13638e28	+	4.15942e28i	−0.888134	+	0.719208i
$753$	1.04895e28			0.178979
$754$	4.13169e28	+	9.34897e27i	0.695687	+	0.157417i
$755$	−4.13720e28			−0.687444
$756$	4.80204e28	−	1.00678e29i	0.787423	−	1.65088i
$757$		−	5.34938e28i		−	0.865654i	−0.901477	−	0.432827i	$-0.857516\pi$
$757$		−	5.34938e28i		−	0.865654i	0.901477	−	0.432827i	$-0.142484\pi$
$758$	8.49700e28	+	1.92266e28i	1.35698	+	0.307051i
$759$		−	7.31352e27i		−	0.115268i
$760$	−4.86347e28	+	6.16936e28i	−0.756503	+	0.959631i
$761$	−2.22827e28			−0.342074			−0.171037	−	0.985265i	$-0.554712\pi$
$761$	−2.22827e28			−0.342074			−0.171037	+	0.985265i	$0.554712\pi$
$762$	1.76275e28	−	7.79031e28i	0.267080	−	1.18033i
$763$	−1.53886e29			−2.30120
$764$	−4.77667e27	+	1.00146e28i	−0.0705004	+	0.147809i
$765$		−	2.13856e27i		−	0.0311535i
$766$	9.64787e27	−	4.26378e28i	0.138722	−	0.613066i
$767$		−	6.59447e26i		−	0.00935893i
$768$	−1.51164e28	+	7.11225e28i	−0.211757	+	0.996310i
$769$	−8.54432e28			−1.18145			−0.590723	−	0.806874i	$-0.701157\pi$
$769$	−8.54432e28			−1.18145			−0.590723	+	0.806874i	$0.701157\pi$
$770$	2.61286e28	+	5.91226e27i	0.356623	+	0.0806949i
$771$	1.33234e29			1.79503
$772$	4.19335e28	+	2.00011e28i	0.557684	+	0.265999i
$773$			1.08746e29i			1.42764i	0.700330	+	0.713819i	$0.253036\pi$
$773$			1.08746e29i			1.42764i	−0.700330	+	0.713819i	$0.746964\pi$
$774$	2.01393e26	+	4.55701e25i	0.00260996	+	0.000590569i
$775$			3.83083e28i			0.490090i
$776$	8.41392e28	+	6.63292e28i	1.06263	+	0.837698i
$777$	−4.19103e28			−0.522529
$778$	2.64432e28	−	1.16863e29i	0.325476	−	1.43841i
$779$	−9.45166e28			−1.14851
$780$	6.48027e28	+	3.09090e28i	0.777404	+	0.370799i
$781$		−	1.57028e28i		−	0.185981i
$782$	9.05979e27	−	4.00388e28i	0.105938	−	0.468181i
$783$			6.04216e28i			0.697549i
$784$	−1.36959e29	−	1.69128e29i	−1.56110	−	1.92777i
$785$	1.03596e29			1.16586
$786$	−1.64304e29	−	3.71778e28i	−1.82567	−	0.413103i
$787$	1.07439e29			1.17873			0.589364	−	0.807867i	$-0.299378\pi$
$787$	1.07439e29			1.17873			0.589364	+	0.807867i	$0.299378\pi$
$788$	−1.06817e28	+	2.23948e28i	−0.115712	+	0.242597i
$789$		−	3.22319e28i		−	0.344759i
$790$	4.10801e28	+	9.29540e27i	0.433871	+	0.0981742i
$791$		−	7.83530e28i		−	0.817130i
$792$	−6.64022e26	−	5.23467e26i	−0.00683803	−	0.00539060i
$793$	−5.04567e27			−0.0513083
$794$	−3.49177e28	+	1.54315e29i	−0.350623	+	1.54954i
$795$	−1.05316e29			−1.04430
$796$	3.56614e28	−	7.47664e28i	0.349195	−	0.732109i
$797$		−	7.13483e28i		−	0.689923i	−0.938617	−	0.344961i	$-0.887892\pi$
$797$		−	7.13483e28i		−	0.689923i	0.938617	−	0.344961i	$-0.112108\pi$
$798$	−6.36222e28	+	2.81172e29i	−0.607547	+	2.68499i
$799$		−	1.19433e29i		−	1.12630i
$800$	−1.37014e28	−	2.77831e28i	−0.127604	−	0.258750i
$801$	−2.70849e27			−0.0249116
$802$	6.13358e28	+	1.38787e28i	0.557147	+	0.126068i
$803$	1.25386e28			0.112485
$804$	3.85942e28	+	1.84083e28i	0.341949	+	0.163100i
$805$			8.75894e28i			0.766466i
$806$	−1.92183e29	−	4.34862e28i	−1.66098	−	0.375838i
$807$			9.68197e28i			0.826472i
$808$	−8.23813e28	+	1.04501e29i	−0.694569	+	0.881066i
$809$	6.54964e28			0.545422			0.272711	−	0.962096i	$-0.412080\pi$
$809$	6.54964e28			0.545422			0.272711	+	0.962096i	$0.412080\pi$
$810$	−2.34487e28	+	1.03629e29i	−0.192872	+	0.852379i
$811$	9.88172e28			0.802831			0.401415	−	0.915896i	$-0.368518\pi$
$811$	9.88172e28			0.802831			0.401415	+	0.915896i	$0.368518\pi$
$812$	1.49297e29	+	7.12101e28i	1.19809	+	0.571454i
$813$			1.57912e27i			0.0125173i
$814$	1.80083e27	−	7.95859e27i	0.0141003	−	0.0623149i
$815$		−	4.77032e27i		−	0.0368953i
$816$	−8.26881e28	−	1.02110e29i	−0.631744	−	0.780127i
$817$	1.37064e28			0.103444
$818$	−1.42422e29	−	3.22265e28i	−1.06180	−	0.240259i
$819$	9.51683e27			0.0700895
$820$	−3.95702e28	+	8.29615e28i	−0.287892	+	0.603584i
$821$		−	9.44155e28i		−	0.678596i	−0.940679	−	0.339298i	$-0.889810\pi$
$821$		−	9.44155e28i		−	0.678596i	0.940679	−	0.339298i	$-0.110190\pi$
$822$	−2.08551e29	−	4.71899e28i	−1.48079	−	0.335067i
$823$			8.48654e28i			0.595295i	0.954676	+	0.297647i	$0.0962020\pi$
$823$			8.48654e28i			0.595295i	−0.954676	+	0.297647i	$0.903798\pi$
$824$	1.26377e29	−	1.60310e29i	0.875780	−	1.11093i
$825$	9.97285e27			0.0682779
$826$	5.68283e26	−	2.51147e27i	0.00384383	−	0.0169874i
$827$	−1.42055e29			−0.949296			−0.474648	−	0.880176i	$-0.657425\pi$
$827$	−1.42055e29			−0.949296			−0.474648	+	0.880176i	$0.657425\pi$
$828$	1.19017e27	−	2.49526e27i	0.00785788	−	0.0164745i
$829$			5.53248e28i			0.360890i	0.983585	+	0.180445i	$0.0577537\pi$
$829$			5.53248e28i			0.360890i	−0.983585	+	0.180445i	$0.942246\pi$
$830$	5.20250e28	−	2.29919e29i	0.335298	−	1.48182i
$831$		−	3.51609e27i		−	0.0223898i
$832$	1.54934e29	−	3.71981e28i	0.974794	−	0.234039i
$833$	3.93262e29			2.44473
$834$	1.20915e27	+	2.73600e26i	0.00742711	+	0.00168057i
$835$	1.77061e29			1.07463
$836$	−5.06597e28	−	2.41632e28i	−0.303808	−	0.144908i
$837$		−	2.81048e29i		−	1.66543i
$838$	1.80434e29	+	4.08277e28i	1.05652	+	0.239064i
$839$			6.58676e28i			0.381111i	0.981676	+	0.190556i	$0.0610290\pi$
$839$			6.58676e28i			0.381111i	−0.981676	+	0.190556i	$0.938971\pi$
$840$	2.20161e29	+	1.73559e29i	1.25878	+	0.992328i
$841$	8.73945e28			0.493770
$842$	1.91190e28	−	8.44944e28i	0.106744	−	0.471745i
$843$	−3.37689e29			−1.86312
$844$	1.81147e28	+	8.64020e27i	0.0987660	+	0.0471085i
$845$		−	7.82420e26i		−	0.00421573i
$846$	1.77509e27	−	7.84483e27i	0.00945184	−	0.0417715i
$847$		−	3.35396e29i		−	1.76492i
$848$	−1.81639e29	+	1.47090e29i	−0.944604	+	0.764937i
$849$	7.59335e28			0.390262
$850$	5.45978e28	+	1.23541e28i	0.277323	+	0.0627512i
$851$	2.66791e28			0.133929
$852$	7.07447e28	−	1.48321e29i	0.350993	−	0.735879i
$853$		−	9.95133e28i		−	0.487968i	−0.969779	−	0.243984i	$-0.921546\pi$
$853$		−	9.95133e28i		−	0.487968i	0.969779	−	0.243984i	$-0.0784544\pi$
$854$	−1.92162e28	−	4.34814e27i	−0.0931297	−	0.0210729i
$855$		−	9.56011e27i		−	0.0457933i
$856$	1.86549e27	+	1.47062e27i	0.00883193	+	0.00696245i
$857$	−1.09474e29			−0.512275			−0.256138	−	0.966640i	$-0.582450\pi$
$857$	−1.09474e29			−0.512275			−0.256138	+	0.966640i	$0.582450\pi$
$858$	−1.13208e28	+	5.00312e28i	−0.0523606	+	0.231403i
$859$	−1.09959e29			−0.502690			−0.251345	−	0.967898i	$-0.580873\pi$
$859$	−1.09959e29			−0.502690			−0.251345	+	0.967898i	$0.580873\pi$
$860$	5.73831e27	−	1.20307e28i	0.0259298	−	0.0543635i
$861$			3.37295e29i			1.50653i
$862$	−6.51611e28	+	2.87973e29i	−0.287684	+	1.27139i
$863$			2.72249e29i			1.18811i	0.804423	+	0.594057i	$0.202475\pi$
$863$			2.72249e29i			1.18811i	−0.804423	+	0.594057i	$0.797525\pi$
$864$	1.00520e29	+	2.03830e29i	0.433625	+	0.879285i
$865$	6.12153e28			0.261035
$866$	9.65670e28	+	2.18507e28i	0.407052	+	0.0921057i
$867$	−7.01550e27			−0.0292326
$868$	−6.94444e29	−	3.31230e29i	−2.86049	−	1.36437i
$869$			3.00922e28i			0.122534i
$870$	−1.48115e29	−	3.35147e28i	−0.596220	−	0.134910i
$871$		−	9.37017e28i		−	0.372877i
$872$	1.94109e29	−	2.46229e29i	0.763628	−	0.968668i
$873$	−1.30383e28			−0.0507082
$874$	4.05004e28	−	1.78987e29i	0.155720	−	0.688190i
$875$	−5.33432e29			−2.02768
$876$	1.18433e29	+	5.64892e28i	0.445074	+	0.212287i
$877$			4.13929e29i			1.53791i	0.639305	+	0.768953i	$0.279222\pi$
$877$			4.13929e29i			1.53791i	−0.639305	+	0.768953i	$0.720778\pi$
$878$	−1.50756e28	+	6.66250e28i	−0.0553769	+	0.244733i
$879$			2.51609e29i			0.913772i
$880$	−4.24182e28	+	3.43501e28i	−0.152309	+	0.123339i
$881$	−2.41396e29			−0.856979			−0.428489	−	0.903547i	$-0.640954\pi$
$881$	−2.41396e29			−0.856979			−0.428489	+	0.903547i	$0.640954\pi$
$882$	2.58311e28	+	5.84492e27i	0.0906685	+	0.0205160i
$883$	4.40744e29			1.52960			0.764802	−	0.644265i	$-0.222837\pi$
$883$	4.40744e29			1.52960			0.764802	+	0.644265i	$0.222837\pi$
$884$	−1.23955e29	+	2.59879e29i	−0.425344	+	0.891761i
$885$			2.36402e27i			0.00802082i
$886$	2.09403e29	+	4.73826e28i	0.702498	+	0.158958i
$887$			2.33752e29i			0.775387i	0.921788	+	0.387693i	$0.126728\pi$
$887$			2.33752e29i			0.775387i	−0.921788	+	0.387693i	$0.873272\pi$
$888$	5.28649e28	−	6.70595e28i	0.173395	−	0.219953i
$889$	−6.83444e29			−2.21659
$890$	−3.85867e28	+	1.70530e29i	−0.123748	+	0.546891i
$891$	−7.59112e28			−0.240729
$892$	−2.36258e28	+	4.95330e28i	−0.0740863	+	0.155327i
$893$		−	5.33905e29i		−	1.65558i
$894$	6.74967e28	−	2.98295e29i	0.206970	−	0.914684i
$895$		−	2.74354e28i		−	0.0831919i
$896$	6.22113e29	−	8.15201e27i	1.86547	−	0.0244447i
$897$	−1.67717e29			−0.497338
$898$	5.38722e29	+	1.21899e29i	1.57980	+	0.357469i
$899$	4.16769e29			1.20865
$900$	3.40259e27	+	1.62294e27i	0.00975854	+	0.00465454i
$901$		−	4.22352e29i		−	1.19792i
$902$	−6.40508e28	−	1.44931e28i	−0.179663	−	0.0406533i
$903$		−	4.89131e28i		−	0.135690i
$904$	1.25371e29	+	9.88331e28i	0.343963	+	0.271155i
$905$	−4.87903e29			−1.32388
$906$	6.82678e28	−	3.01703e29i	0.183204	−	0.809650i
$907$	4.46010e29			1.18378			0.591891	−	0.806018i	$-0.298382\pi$
$907$	4.46010e29			1.18378			0.591891	+	0.806018i	$0.298382\pi$
$908$	8.12339e28	+	3.87462e28i	0.213245	+	0.101712i
$909$		−	1.61936e28i		−	0.0420442i
$910$	1.35582e29	−	5.99193e29i	0.348168	−	1.53869i
$911$		−	4.01750e29i		−	1.02040i	−0.860054	−	0.510202i	$-0.829570\pi$
$911$		−	4.01750e29i		−	1.02040i	0.860054	−	0.510202i	$-0.170430\pi$
$912$	−3.69644e29	−	4.56466e29i	−0.928615	−	1.14673i
$913$	1.68422e29			0.418495
$914$	−1.13989e28	−	2.57929e27i	−0.0280158	−	0.00633927i
$915$	1.80880e28			0.0439724
$916$	−1.43476e29	+	3.00807e29i	−0.345005	+	0.723325i
$917$			1.44144e30i			3.42848i
$918$	−4.00554e29	−	9.06354e28i	−0.942399	−	0.213241i
$919$		−	4.30423e29i		−	1.00171i	−0.865532	−	0.500854i	$-0.833020\pi$
$919$		−	4.30423e29i		−	1.00171i	0.865532	−	0.500854i	$-0.166980\pi$
$920$	−1.40149e29	−	1.10484e29i	−0.322636	−	0.254343i
$921$	4.68664e29			1.06725
$922$	−9.82172e27	+	4.34061e28i	−0.0221247	+	0.0977781i
$923$	−3.60104e29			−0.802437
$924$	−8.62294e28	+	1.80785e29i	−0.190080	+	0.398514i
$925$			3.63801e28i			0.0793317i
$926$	−1.80662e29	+	7.98416e29i	−0.389723	+	1.72234i
$927$			2.48418e28i			0.0530134i
$928$	−3.02261e29	+	1.49062e29i	−0.638121	+	0.314694i
$929$	−5.72927e28			−0.119658			−0.0598291	−	0.998209i	$-0.519056\pi$
$929$	−5.72927e28			−0.119658			−0.0598291	+	0.998209i	$0.519056\pi$
$930$	6.88948e29	+	1.55892e29i	1.42350	+	0.322102i
$931$	1.75802e30			3.59357
$932$	−3.11716e29	−	1.48680e29i	−0.630377	−	0.300672i
$933$		−	2.07232e29i		−	0.414611i
$934$	−2.19804e29	−	4.97362e28i	−0.435078	−	0.0984473i
$935$		−	9.86322e28i		−	0.193153i
$936$	−1.20044e28	+	1.52276e28i	−0.0232584	+	0.0295035i
$937$	−4.30339e29			−0.824926			−0.412463	−	0.910974i	$-0.635331\pi$
$937$	−4.30339e29			−0.824926			−0.412463	+	0.910974i	$0.635331\pi$
$938$	8.07480e28	−	3.56858e29i	0.153145	−	0.676811i
$939$	6.12861e28			0.115002
$940$	−4.68632e29	−	2.23524e29i	−0.870069	−	0.414998i
$941$		−	9.52735e29i		−	1.75015i	−0.483985	−	0.875076i	$-0.660811\pi$
$941$		−	9.52735e29i		−	1.75015i	0.483985	−	0.875076i	$-0.339189\pi$
$942$	−1.70943e29	+	7.55465e29i	−0.310700	+	1.37311i
$943$		−	2.14714e29i		−	0.386138i
$944$	3.30171e27	+	4.07722e27i	0.00587516	+	0.00725511i
$945$	8.76257e29			1.54281
$946$	9.28839e27	+	2.10173e27i	0.0161819	+	0.00366156i
$947$	−9.71257e29			−1.67430			−0.837152	−	0.546970i	$-0.815781\pi$
$947$	−9.71257e29			−1.67430			−0.837152	+	0.546970i	$0.815781\pi$
$948$	−1.35572e29	+	2.84236e29i	−0.231253	+	0.484836i
$949$		−	2.87541e29i		−	0.485330i
$950$	2.44071e29	+	5.52271e28i	0.407643	+	0.0922393i
$951$		−	7.10997e29i		−	1.17507i
$952$	−6.96027e29	+	8.82916e29i	−1.13830	+	1.44394i
$953$	8.45826e29			1.36884			0.684419	−	0.729089i	$-0.260056\pi$
$953$	8.45826e29			1.36884			0.684419	+	0.729089i	$0.260056\pi$
$954$	6.27728e27	−	2.77418e28i	0.0100528	−	0.0444274i
$955$	−8.71627e28			−0.138133
$956$	2.55526e29	−	5.35726e29i	0.400733	−	0.840163i
$957$		−	1.08498e29i		−	0.168385i
$958$	2.39999e29	−	1.06065e30i	0.368599	−	1.62899i
$959$			1.82962e30i			2.78083i
$960$	−5.55415e29	+	1.33350e29i	−0.835421	+	0.200577i
$961$	−1.26679e30			−1.88569
$962$	−1.82510e29	−	4.12973e28i	−0.268865	−	0.0608375i
$963$	−2.89079e26			−0.000421457
$964$	3.63309e29	+	1.73288e29i	0.524210	+	0.250033i
$965$			3.64971e29i			0.521177i
$966$	−6.38740e29	−	1.44531e29i	−0.902719	−	0.204263i
$967$			5.87774e29i			0.822140i	0.911604	+	0.411070i	$0.134845\pi$
$967$			5.87774e29i			0.822140i	−0.911604	+	0.411070i	$0.865155\pi$
$968$	5.36659e29	+	4.23063e29i	0.742924	+	0.585668i
$969$	1.06139e30			1.45424
$970$	−1.85751e29	+	8.20909e29i	−0.251892	+	1.11321i
$971$	−2.67719e29			−0.359324			−0.179662	−	0.983728i	$-0.557500\pi$
$971$	−2.67719e29			−0.359324			−0.179662	+	0.983728i	$0.557500\pi$
$972$	−5.08979e28	−	2.42768e28i	−0.0676141	−	0.0322500i
$973$		−	1.06079e28i		−	0.0139476i
$974$	−6.33339e28	+	2.79898e29i	−0.0824227	+	0.364259i
$975$		−	2.28702e29i		−	0.294593i
$976$	3.11963e28	−	2.52626e28i	0.0397745	−	0.0322092i
$977$	−1.25089e30			−1.57860			−0.789301	−	0.614006i	$-0.789557\pi$
$977$	−1.25089e30			−1.57860			−0.789301	+	0.614006i	$0.789557\pi$
$978$	3.47872e28	+	7.87147e27i	0.0434541	+	0.00983258i
$979$	−1.24918e29			−0.154453
$980$	7.36009e29	−	1.54309e30i	0.900787	−	1.88856i
$981$			3.81560e28i			0.0462245i
$982$	5.74000e29	+	1.29882e29i	0.688330	+	0.155752i
$983$		−	5.43017e29i		−	0.644582i	−0.946641	−	0.322291i	$-0.895547\pi$
$983$		−	5.43017e29i		−	0.644582i	0.946641	−	0.322291i	$-0.104453\pi$
$984$	−5.39696e29	−	4.25457e29i	−0.634159	−	0.499925i
$985$	−1.94915e29			−0.226716
$986$	1.34404e29	−	5.93987e29i	0.154755	−	0.683924i
$987$	−1.90531e30			−2.17167
$988$	−5.54120e29	+	1.16175e30i	−0.625222	+	1.31082i
$989$			3.11369e28i			0.0347786i
$990$	1.46594e27	−	6.47857e27i	0.00162093	−	0.00716353i
$991$			1.86839e29i			0.204518i	0.994758	+	0.102259i	$0.0326070\pi$
$991$			1.86839e29i			0.204518i	−0.994758	+	0.102259i	$0.967393\pi$
$992$	1.40595e30	−	6.93355e29i	1.52354	−	0.751344i
$993$	1.49423e30			1.60297
$994$	−1.37144e30	−	3.10322e29i	−1.45651	−	0.329571i
$995$	6.50735e29			0.684184
$996$	1.59082e30	+	7.58777e29i	1.65588	+	0.789807i
$997$			9.13788e29i			0.941659i	0.882224	+	0.470830i	$0.156045\pi$
$997$			9.13788e29i			0.941659i	−0.882224	+	0.470830i	$0.843955\pi$
$998$	5.06012e29	+	1.14498e29i	0.516244	+	0.116813i
$999$		−	2.66901e29i		−	0.269585i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.21.d.b.3.1	✓	18
3.2	odd	2		72.21.b.b.19.18		18
4.3	odd	2		32.21.d.b.15.4		18
8.3	odd	2	inner	8.21.d.b.3.2	yes	18
8.5	even	2		32.21.d.b.15.3		18
24.11	even	2		72.21.b.b.19.17		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.21.d.b.3.1	✓	18	1.1	even	1	trivial
8.21.d.b.3.2	yes	18	8.3	odd	2	inner
32.21.d.b.15.3		18	8.5	even	2
32.21.d.b.15.4		18	4.3	odd	2
72.21.b.b.19.17		18	24.11	even	2
72.21.b.b.19.18		18	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-998.751 - 225.992i) q^{2} +60145.3 q^{3} +(946431. + 451420. i) q^{4} +8.23733e6i q^{5} +(-6.00701e7 - 1.35924e7i) q^{6} +5.26995e8i q^{7} +(-8.43231e8 - 6.64742e8i) q^{8} +1.30668e8 q^{9} +O(q^{10})\)	\(q+(-998.751 - 225.992i) q^{2} +60145.3 q^{3} +(946431. + 451420. i) q^{4} +8.23733e6i q^{5} +(-6.00701e7 - 1.35924e7i) q^{6} +5.26995e8i q^{7} +(-8.43231e8 - 6.64742e8i) q^{8} +1.30668e8 q^{9} +(1.86157e9 - 8.22704e9i) q^{10} +6.02652e9 q^{11} +(5.69233e10 + 2.71508e10i) q^{12} -1.38203e11i q^{13} +(1.19097e11 - 5.26337e11i) q^{14} +4.95436e11i q^{15} +(6.91951e11 + 8.54476e11i) q^{16} -1.98685e12 q^{17} +(-1.30505e11 - 2.95300e10i) q^{18} -8.88192e12 q^{19} +(-3.71850e12 + 7.79606e12i) q^{20} +3.16963e13i q^{21} +(-6.01899e12 - 1.36195e12i) q^{22} -2.01771e13i q^{23} +(-5.07164e13 - 3.99811e13i) q^{24} +2.75139e13 q^{25} +(-3.12327e13 + 1.38030e14i) q^{26} -2.01854e14 q^{27} +(-2.37896e14 + 4.98765e14i) q^{28} -2.99333e14i q^{29} +(1.11965e14 - 4.94817e14i) q^{30} +1.39233e15i q^{31} +(-4.97982e14 - 1.00978e15i) q^{32} +3.62466e14 q^{33} +(1.98437e15 + 4.49014e14i) q^{34} -4.34103e15 q^{35} +(1.23668e14 + 5.89862e13i) q^{36} +1.32225e15i q^{37} +(8.87083e15 + 2.00725e15i) q^{38} -8.31223e15i q^{39} +(5.47570e15 - 6.94597e15i) q^{40} +1.06415e16 q^{41} +(7.16311e15 - 3.16567e16i) q^{42} -1.54318e15 q^{43} +(5.70368e15 + 2.72049e15i) q^{44} +1.07636e15i q^{45} +(-4.55987e15 + 2.01519e16i) q^{46} +6.01114e16i q^{47} +(4.16176e16 + 5.13927e16i) q^{48} -1.97932e17 q^{49} +(-2.74795e16 - 6.21792e15i) q^{50} -1.19500e17 q^{51} +(6.23874e16 - 1.30799e17i) q^{52} +2.12573e17i q^{53} +(2.01602e17 + 4.56176e16i) q^{54} +4.96424e16i q^{55} +(3.50316e17 - 4.44379e17i) q^{56} -5.34206e17 q^{57} +(-6.76469e16 + 2.98959e17i) q^{58} +4.77160e15 q^{59} +(-2.23650e17 + 4.68896e17i) q^{60} -3.65093e16i q^{61} +(3.14655e17 - 1.39059e18i) q^{62} +6.88615e16i q^{63} +(2.69157e17 + 1.12106e18i) q^{64} +1.13842e18 q^{65} +(-3.62014e17 - 8.19146e16i) q^{66} +6.78003e17 q^{67} +(-1.88042e18 - 8.96906e17i) q^{68} -1.21356e18i q^{69} +(4.33561e18 + 9.81040e17i) q^{70} -2.60562e18i q^{71} +(-1.10183e17 - 8.68606e16i) q^{72} +2.08057e18 q^{73} +(2.98817e17 - 1.32059e18i) q^{74} +1.65483e18 q^{75} +(-8.40613e18 - 4.00948e18i) q^{76} +3.17595e18i q^{77} +(-1.87850e18 + 8.30185e18i) q^{78} +4.99331e18i q^{79} +(-7.03860e18 + 5.69983e18i) q^{80} -1.25962e19 q^{81} +(-1.06282e19 - 2.40489e18i) q^{82} +2.79468e19 q^{83} +(-1.43083e19 + 2.99983e19i) q^{84} -1.63664e19i q^{85} +(1.54125e18 + 3.48747e17i) q^{86} -1.80034e19i q^{87} +(-5.08175e18 - 4.00608e18i) q^{88} -2.07280e19 q^{89} +(2.43248e17 - 1.07501e18i) q^{90} +7.28321e19 q^{91} +(9.10834e18 - 1.90962e19i) q^{92} +8.37419e19i q^{93} +(1.35847e19 - 6.00363e19i) q^{94} -7.31633e19i q^{95} +(-2.99513e19 - 6.07337e19i) q^{96} -9.97818e19 q^{97} +(1.97685e20 + 4.47311e19i) q^{98} +7.87473e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 398 q^{2} - 114228 q^{3} + 724980 q^{4} - 91643748 q^{6} - 3105291368 q^{8} + 10197650262 q^{9}+O(q^{10}) \) 18 * q - 398 * q^2 - 114228 * q^3 + 724980 * q^4 - 91643748 * q^6 - 3105291368 * q^8 + 10197650262 * q^9	\( 18 q - 398 q^{2} - 114228 q^{3} + 724980 q^{4} - 91643748 q^{6} - 3105291368 q^{8} + 10197650262 q^{9} + 742754160 q^{10} + 27862395020 q^{11} - 212292734088 q^{12} - 431248136928 q^{14} - 958534870512 q^{16} + 4343925139172 q^{17} - 4517494524426 q^{18} - 360681653556 q^{19} - 32520172742880 q^{20} - 66275482922148 q^{22} + 22289322475152 q^{24} - 395727477008910 q^{25} + 154289718058128 q^{26} - 12\!\cdots\!64 q^{27}+ \cdots + 62\!\cdots\!84 q^{99}+O(q^{100}) \) 18 * q - 398 * q^2 - 114228 * q^3 + 724980 * q^4 - 91643748 * q^6 - 3105291368 * q^8 + 10197650262 * q^9 + 742754160 * q^10 + 27862395020 * q^11 - 212292734088 * q^12 - 431248136928 * q^14 - 958534870512 * q^16 + 4343925139172 * q^17 - 4517494524426 * q^18 - 360681653556 * q^19 - 32520172742880 * q^20 - 66275482922148 * q^22 + 22289322475152 * q^24 - 395727477008910 * q^25 + 154289718058128 * q^26 - 1208398438889064 * q^27 - 394619539621440 * q^28 + 223250517248160 * q^30 - 2833814588985248 * q^32 + 4461969540487176 * q^33 - 939462769526748 * q^34 + 3615863153468160 * q^35 + 1560521174396700 * q^36 + 12905383833568412 * q^38 + 11813880412973760 * q^40 + 16990829756398820 * q^41 + 38127588900300480 * q^42 - 27498466356753396 * q^43 + 33178844343953144 * q^44 - 21739818881100192 * q^46 + 28364131397385312 * q^48 - 252965388018862638 * q^49 + 41705619584456530 * q^50 - 34182574557901800 * q^51 - 44583718369992480 * q^52 - 579400710808894920 * q^54 - 505574909383001472 * q^56 - 522453489061123704 * q^57 - 677523738697093680 * q^58 + 93112194700366220 * q^59 + 1631640690429240000 * q^60 + 1780090172849178240 * q^62 + 175441813011570240 * q^64 + 1575343920200472960 * q^65 + 8001047667731567880 * q^66 - 1452645642074335668 * q^67 + 1153770320813215592 * q^68 - 6151558949299572480 * q^70 - 5306529204268842936 * q^72 + 9882821313863175972 * q^73 - 5642095430673385488 * q^74 + 13414715768769378060 * q^75 - 8416781249057544840 * q^76 - 14599907290310144160 * q^78 - 22104885212702947200 * q^80 - 32315102667184036518 * q^81 + 10320950271478847652 * q^82 - 46425529968268557748 * q^83 + 17095266896298568320 * q^84 + 33555485282446075868 * q^86 + 32344350945394345872 * q^88 - 28075170672250840156 * q^89 - 33204348719592139440 * q^90 + 161045136122144660736 * q^91 - 932896292396925120 * q^92 - 107259275077774974528 * q^94 + 68580843917215697472 * q^96 + 127276645173366650724 * q^97 + 154837385163137764402 * q^98 + 62802542261652714084 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more