LMFDB - Embedded newform 4.23.b.a.3.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,23,Mod(3,4)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 23, names="a")

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

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 23);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 23 $
Character orbit:	$[\chi]$	$=$	4.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.2682973937$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 5 x^{9} - 63342 x^{8} - 45742928 x^{7} + 34835133568 x^{6} + 12622768560288 x^{5} + \cdots + 11\!\cdots\!40 $ x^10 - 5x^9 - 63342x^8 - 45742928x^7 + 34835133568x^6 + 12622768560288x^5 + 13335465927292608x^4 - 404504858109047040x^3 - 95573988251584922880x^2 - 1820809561188275535801600*x + 1168838172864011361183920640
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{90}\cdot 3^{11} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.4
Root			$-313.209 - 431.746i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.23.b.a.3.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1100.83 + 1726.98i) q^{2} +308212. i q^{3} +(-1.77063e6 - 3.80224e6i) q^{4} -6.05072e7 q^{5} +(-5.32276e8 - 3.39290e8i) q^{6} +1.97415e9i q^{7} +(8.51558e9 + 1.12779e9i) q^{8} -6.36133e10 q^{9} +O(q^{10})$	\(q+(-1100.83 + 1726.98i) q^{2} +308212. i q^{3} +(-1.77063e6 - 3.80224e6i) q^{4} -6.05072e7 q^{5} +(-5.32276e8 - 3.39290e8i) q^{6} +1.97415e9i q^{7} +(8.51558e9 + 1.12779e9i) q^{8} -6.36133e10 q^{9} +(6.66084e10 - 1.04495e11i) q^{10} +7.57457e10i q^{11} +(1.17190e12 - 5.45729e11i) q^{12} +1.29303e12 q^{13} +(-3.40931e12 - 2.17321e12i) q^{14} -1.86490e13i q^{15} +(-1.13219e13 + 1.34647e13i) q^{16} +3.32190e13 q^{17} +(7.00277e13 - 1.09859e14i) q^{18} +1.76447e13i q^{19} +(1.07136e14 + 2.30063e14i) q^{20} -6.08455e14 q^{21} +(-1.30811e14 - 8.33835e13i) q^{22} +1.87369e14i q^{23} +(-3.47599e14 + 2.62460e15i) q^{24} +1.27693e15 q^{25} +(-1.42342e15 + 2.23305e15i) q^{26} -9.93436e15i q^{27} +(7.50618e15 - 3.49548e15i) q^{28} -1.78471e16 q^{29} +(3.22065e16 + 2.05295e16i) q^{30} -2.82708e16i q^{31} +(-1.07898e16 - 3.43752e16i) q^{32} -2.33457e16 q^{33} +(-3.65686e16 + 5.73686e16i) q^{34} -1.19450e17i q^{35} +(1.12636e17 + 2.41873e17i) q^{36} +8.79279e16 q^{37} +(-3.04722e16 - 1.94239e16i) q^{38} +3.98528e17i q^{39} +(-5.15254e17 - 6.82397e16i) q^{40} -8.41341e17 q^{41} +(6.69808e17 - 1.05079e18i) q^{42} +4.07059e17i q^{43} +(2.88003e17 - 1.34118e17i) q^{44} +3.84906e18 q^{45} +(-3.23584e17 - 2.06263e17i) q^{46} -1.09278e18i q^{47} +(-4.14999e18 - 3.48955e18i) q^{48} +1.25682e16 q^{49} +(-1.40569e18 + 2.20524e18i) q^{50} +1.02385e19i q^{51} +(-2.28949e18 - 4.91643e18i) q^{52} -8.43782e18 q^{53} +(1.71565e19 + 1.09361e19i) q^{54} -4.58316e18i q^{55} +(-2.22643e18 + 1.68110e19i) q^{56} -5.43831e18 q^{57} +(1.96467e19 - 3.08216e19i) q^{58} -2.97106e19i q^{59} +(-7.09081e19 + 3.30205e19i) q^{60} +2.50406e19 q^{61} +(4.88232e19 + 3.11215e19i) q^{62} -1.25582e20i q^{63} +(7.12431e19 + 1.92076e19i) q^{64} -7.82379e19 q^{65} +(2.56997e19 - 4.03176e19i) q^{66} +1.87547e20i q^{67} +(-5.88185e19 - 1.26307e20i) q^{68} -5.77494e19 q^{69} +(2.06288e20 + 1.31495e20i) q^{70} +1.30739e20i q^{71} +(-5.41704e20 - 7.17427e19i) q^{72} +4.17001e20 q^{73} +(-9.67941e19 + 1.51850e20i) q^{74} +3.93566e20i q^{75} +(6.70896e19 - 3.12423e19i) q^{76} -1.49533e20 q^{77} +(-6.88251e20 - 4.38714e20i) q^{78} -9.62025e20i q^{79} +(6.85058e20 - 8.14713e20i) q^{80} +1.06563e21 q^{81} +(9.26177e20 - 1.45298e21i) q^{82} +2.47144e21i q^{83} +(1.07735e21 + 2.31349e21i) q^{84} -2.00999e21 q^{85} +(-7.02984e20 - 4.48105e20i) q^{86} -5.50069e21i q^{87} +(-8.54255e19 + 6.45018e20i) q^{88} -2.99090e21 q^{89} +(-4.23718e21 + 6.64726e21i) q^{90} +2.55264e21i q^{91} +(7.12424e20 - 3.31762e20i) q^{92} +8.71340e21 q^{93} +(1.88721e21 + 1.20297e21i) q^{94} -1.06763e21i q^{95} +(1.05948e22 - 3.32554e21i) q^{96} -1.35826e22 q^{97} +(-1.38355e19 + 2.17051e19i) q^{98} -4.81843e21i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 1540 q^{2} + 2264464 q^{4} - 17091100 q^{5} - 791935776 q^{6} + 9804431680 q^{8} - 104309613702 q^{9}+O(q^{10}) $ 10 * q + 1540 * q^2 + 2264464 * q^4 - 17091100 * q^5 - 791935776 * q^6 + 9804431680 * q^8 - 104309613702 * q^9	$ 10 q + 1540 q^{2} + 2264464 q^{4} - 17091100 q^{5} - 791935776 q^{6} + 9804431680 q^{8} - 104309613702 q^{9} + 159414035240 q^{10} + 519021175680 q^{12} - 531230356540 q^{13} - 5894008940736 q^{14} - 27717620084480 q^{16} + 14058178115540 q^{17} + 16283956279140 q^{18} + 233643631625120 q^{20} - 313135665760512 q^{21} + 120589650366240 q^{22} - 20\!\cdots\!36 q^{24}+ \cdots - 23\!\cdots\!20 q^{98}+O(q^{100}) $ 10 * q + 1540 * q^2 + 2264464 * q^4 - 17091100 * q^5 - 791935776 * q^6 + 9804431680 * q^8 - 104309613702 * q^9 + 159414035240 * q^10 + 519021175680 * q^12 - 531230356540 * q^13 - 5894008940736 * q^14 - 27717620084480 * q^16 + 14058178115540 * q^17 + 16283956279140 * q^18 + 233643631625120 * q^20 - 313135665760512 * q^21 + 120589650366240 * q^22 - 2007619616180736 * q^24 + 7710175817606670 * q^25 - 3953973318046744 * q^26 + 1177952265288960 * q^28 - 14464474185570172 * q^29 + 10252783730669760 * q^30 - 73831192092953600 * q^32 + 72906957628179840 * q^33 - 26625976920357496 * q^34 - 36609276067793136 * q^36 + 324587767823538020 * q^37 + 369140808808591200 * q^38 - 1158049295468479360 * q^40 - 1355457345814233100 * q^41 + 2644455724909770240 * q^42 - 1919761520625210240 * q^44 + 9367295763131460 * q^45 + 6132624002565203904 * q^46 - 18374169355003791360 * q^48 + 183553700661552298 * q^49 + 29084394113996178540 * q^50 - 38492433127521128800 * q^52 - 11424344766226018780 * q^53 + 79182840955393027008 * q^54 - 102844865827678657536 * q^56 + 30188516183231506560 * q^57 + 173059696836432320360 * q^58 - 377769459746631548160 * q^60 + 58241718146183220740 * q^61 + 317897221476923285760 * q^62 - 412080172429987966976 * q^64 - 121531695066047433560 * q^65 + 700585278654050000640 * q^66 - 667890522330713878240 * q^68 + 54497497397908094208 * q^69 + 1014396282552321513600 * q^70 - 1244773253376491901120 * q^72 + 83030422224875883380 * q^73 + 801906083011176262184 * q^74 + 286747421140990627200 * q^76 - 704201825495570814720 * q^77 - 964412732782594923840 * q^78 + 1509611955050789726720 * q^80 + 251577744224553978858 * q^81 - 2389572513290905036600 * q^82 + 6185640644326191863808 * q^84 - 1796890366112110859960 * q^85 - 8221838255181360278496 * q^86 + 11178210842814940531200 * q^88 + 3420669206528505615668 * q^89 - 24782809563337507735320 * q^90 + 21476264197983864733440 * q^92 + 15493754050318100597760 * q^93 - 20874543047091388369536 * q^94 + 29250284502468708163584 * q^96 - 20429910746446196146540 * q^97 - 23110416876469762175420 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

Coefficient data

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

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

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

$2$	−1100.83	+	1726.98i	−0.537517	+	0.843253i
$2$	−1100.83	+	1726.98i	−0.537517	+	0.843253i
$3$			308212.i			1.73986i	0.493172	+	0.869932i	$0.335837\pi$
$3$			308212.i			1.73986i	−0.493172	+	0.869932i	$0.664163\pi$
$4$	−1.77063e6	−	3.80224e6i	−0.422151	−	0.906525i
$5$	−6.05072e7			−1.23919			−0.619594	−	0.784923i	$-0.712703\pi$
$5$	−6.05072e7			−1.23919			−0.619594	+	0.784923i	$0.712703\pi$
$6$	−5.32276e8	−	3.39290e8i	−1.46714	−	0.935206i
$7$			1.97415e9i			0.998391i	0.866489	+	0.499196i	$0.166371\pi$
$7$			1.97415e9i			0.998391i	−0.866489	+	0.499196i	$0.833629\pi$
$8$	8.51558e9	+	1.12779e9i	0.991344	+	0.131293i
$9$	−6.36133e10			−2.02712
$10$	6.66084e10	−	1.04495e11i	0.666084	−	1.04495i
$11$			7.57457e10i			0.265484i	0.991151	+	0.132742i	$0.0423782\pi$
$11$			7.57457e10i			0.265484i	−0.991151	+	0.132742i	$0.957622\pi$
$12$	1.17190e12	−	5.45729e11i	1.57723	−	0.734485i
$13$	1.29303e12			0.721495			0.360747	−	0.932664i	$-0.382522\pi$
$13$	1.29303e12			0.721495			0.360747	+	0.932664i	$0.382522\pi$
$14$	−3.40931e12	−	2.17321e12i	−0.841897	−	0.536652i
$15$		−	1.86490e13i		−	2.15602i
$16$	−1.13219e13	+	1.34647e13i	−0.643577	+	0.765382i
$17$	3.32190e13			0.969278			0.484639	−	0.874714i	$-0.338951\pi$
$17$	3.32190e13			0.969278			0.484639	+	0.874714i	$0.338951\pi$
$18$	7.00277e13	−	1.09859e14i	1.08961	−	1.70938i
$19$			1.76447e13i			0.151470i	0.997128	+	0.0757348i	$0.0241303\pi$
$19$			1.76447e13i			0.151470i	−0.997128	+	0.0757348i	$0.975870\pi$
$20$	1.07136e14	+	2.30063e14i	0.523124	+	1.12335i
$21$	−6.08455e14			−1.73706
$22$	−1.30811e14	−	8.33835e13i	−0.223870	−	0.142702i
$23$			1.87369e14i			0.196649i	0.995154	+	0.0983247i	$0.0313484\pi$
$23$			1.87369e14i			0.196649i	−0.995154	+	0.0983247i	$0.968652\pi$
$24$	−3.47599e14	+	2.62460e15i	−0.228431	+	1.72480i
$25$	1.27693e15			0.535585
$26$	−1.42342e15	+	2.23305e15i	−0.387816	+	0.608403i
$27$		−	9.93436e15i		−	1.78706i
$28$	7.50618e15	−	3.49548e15i	0.905067	−	0.421472i
$29$	−1.78471e16			−1.46282			−0.731408	−	0.681940i	$-0.761137\pi$
$29$	−1.78471e16			−1.46282			−0.731408	+	0.681940i	$0.761137\pi$
$30$	3.22065e16	+	2.05295e16i	1.81807	+	1.15890i
$31$		−	2.82708e16i		−	1.11265i	−0.830964	−	0.556327i	$-0.812210\pi$
$31$		−	2.82708e16i		−	1.11265i	0.830964	−	0.556327i	$-0.187790\pi$
$32$	−1.07898e16	−	3.43752e16i	−0.299477	−	0.954104i
$33$	−2.33457e16			−0.461906
$34$	−3.65686e16	+	5.73686e16i	−0.521003	+	0.817346i
$35$		−	1.19450e17i		−	1.23719i
$36$	1.12636e17	+	2.41873e17i	0.855753	+	1.83764i
$37$	8.79279e16			0.494206			0.247103	−	0.968989i	$-0.420521\pi$
$37$	8.79279e16			0.494206			0.247103	+	0.968989i	$0.420521\pi$
$38$	−3.04722e16	−	1.94239e16i	−0.127727	−	0.0814175i
$39$			3.98528e17i			1.25530i
$40$	−5.15254e17	−	6.82397e16i	−1.22846	−	0.162696i
$41$	−8.41341e17			−1.52880			−0.764398	−	0.644744i	$-0.776964\pi$
$41$	−8.41341e17			−1.52880			−0.764398	+	0.644744i	$0.776964\pi$
$42$	6.69808e17	−	1.05079e18i	0.933702	−	1.46478i
$43$			4.07059e17i			0.438031i	0.975721	+	0.219015i	$0.0702845\pi$
$43$			4.07059e17i			0.438031i	−0.975721	+	0.219015i	$0.929716\pi$
$44$	2.88003e17	−	1.34118e17i	0.240668	−	0.112074i
$45$	3.84906e18			2.51199
$46$	−3.23584e17	−	2.06263e17i	−0.165825	−	0.105702i
$47$		−	1.09278e18i		−	0.442035i	−0.975270	−	0.221018i	$-0.929062\pi$
$47$		−	1.09278e18i		−	0.442035i	0.975270	−	0.221018i	$-0.0709378\pi$
$48$	−4.14999e18	−	3.48955e18i	−1.33166	−	1.11974i
$49$	1.25682e16			0.00321453
$50$	−1.40569e18	+	2.20524e18i	−0.287886	+	0.451634i
$51$			1.02385e19i			1.68641i
$52$	−2.28949e18	−	4.91643e18i	−0.304580	−	0.654053i
$53$	−8.43782e18			−0.910323			−0.455162	−	0.890409i	$-0.650419\pi$
$53$	−8.43782e18			−0.910323			−0.455162	+	0.890409i	$0.650419\pi$
$54$	1.71565e19	+	1.09361e19i	1.50694	+	0.960573i
$55$		−	4.58316e18i		−	0.328984i
$56$	−2.22643e18	+	1.68110e19i	−0.131081	+	0.989749i
$57$	−5.43831e18			−0.263537
$58$	1.96467e19	−	3.08216e19i	0.786289	−	1.23352i
$59$		−	2.97106e19i		−	0.985235i	−0.870246	−	0.492618i	$-0.836040\pi$
$59$		−	2.97106e19i		−	0.985235i	0.870246	−	0.492618i	$-0.163960\pi$
$60$	−7.09081e19	+	3.30205e19i	−1.95448	+	0.910165i
$61$	2.50406e19			0.575461			0.287731	−	0.957711i	$-0.407099\pi$
$61$	2.50406e19			0.575461			0.287731	+	0.957711i	$0.407099\pi$
$62$	4.88232e19	+	3.11215e19i	0.938249	+	0.598070i
$63$		−	1.25582e20i		−	2.02386i
$64$	7.12431e19	+	1.92076e19i	0.965525	+	0.260312i
$65$	−7.82379e19			−0.894067
$66$	2.56997e19	−	4.03176e19i	0.248282	−	0.389503i
$67$			1.87547e20i			1.53564i	0.640668	+	0.767818i	$0.278658\pi$
$67$			1.87547e20i			1.53564i	−0.640668	+	0.767818i	$0.721342\pi$
$68$	−5.88185e19	−	1.26307e20i	−0.409182	−	0.878675i
$69$	−5.77494e19			−0.342143
$70$	2.06288e20	+	1.31495e20i	1.04327	+	0.665013i
$71$			1.30739e20i			0.565671i	0.959168	+	0.282835i	$0.0912750\pi$
$71$			1.30739e20i			0.565671i	−0.959168	+	0.282835i	$0.908725\pi$
$72$	−5.41704e20	−	7.17427e19i	−2.00958	−	0.266146i
$73$	4.17001e20			1.32919			0.664593	−	0.747206i	$-0.268605\pi$
$73$	4.17001e20			1.32919			0.664593	+	0.747206i	$0.268605\pi$
$74$	−9.67941e19	+	1.51850e20i	−0.265644	+	0.416740i
$75$			3.93566e20i			0.931845i
$76$	6.70896e19	−	3.12423e19i	0.137311	−	0.0639431i
$77$	−1.49533e20			−0.265057
$78$	−6.88251e20	−	4.38714e20i	−1.05854	−	0.674746i
$79$		−	9.62025e20i		−	1.28614i	−0.765807	−	0.643070i	$-0.777660\pi$
$79$		−	9.62025e20i		−	1.28614i	0.765807	−	0.643070i	$-0.222340\pi$
$80$	6.85058e20	−	8.14713e20i	0.797512	−	0.948451i
$81$	1.06563e21			1.08211
$82$	9.26177e20	−	1.45298e21i	0.821754	−	1.28916i
$83$			2.47144e21i			1.91907i	0.281588	+	0.959535i	$0.409139\pi$
$83$			2.47144e21i			1.91907i	−0.281588	+	0.959535i	$0.590861\pi$
$84$	1.07735e21	+	2.31349e21i	0.733304	+	1.57469i
$85$	−2.00999e21			−1.20112
$86$	−7.02984e20	−	4.48105e20i	−0.369371	−	0.235449i
$87$		−	5.50069e21i		−	2.54510i
$88$	−8.54255e19	+	6.45018e20i	−0.0348561	+	0.263186i
$89$	−2.99090e21			−1.07774			−0.538868	−	0.842391i	$-0.681148\pi$
$89$	−2.99090e21			−1.07774			−0.538868	+	0.842391i	$0.681148\pi$
$90$	−4.23718e21	+	6.64726e21i	−1.35024	+	2.11824i
$91$			2.55264e21i			0.720334i
$92$	7.12424e20	−	3.31762e20i	0.178268	−	0.0830158i
$93$	8.71340e21			1.93587
$94$	1.88721e21	+	1.20297e21i	0.372747	+	0.237601i
$95$		−	1.06763e21i		−	0.187699i
$96$	1.05948e22	−	3.32554e21i	1.66001	−	0.521049i
$97$	−1.35826e22			−1.89886			−0.949431	−	0.313977i	$-0.898338\pi$
$97$	−1.35826e22			−1.89886			−0.949431	+	0.313977i	$0.898338\pi$
$98$	−1.38355e19	+	2.17051e19i	−0.00172786	+	0.00271066i
$99$		−	4.81843e21i		−	0.538169i
$100$	−2.26098e21	−	4.85522e21i	−0.226098	−	0.485522i
$101$	−3.15304e21			−0.282614			−0.141307	−	0.989966i	$-0.545130\pi$
$101$	−3.15304e21			−0.282614			−0.141307	+	0.989966i	$0.545130\pi$
$102$	−1.76817e22	−	1.12709e22i	−1.42207	−	0.906474i
$103$			7.89076e21i			0.570045i	0.958521	+	0.285023i	$0.0920011\pi$
$103$			7.89076e21i			0.570045i	−0.958521	+	0.285023i	$0.907999\pi$
$104$	1.10109e22	+	1.45828e21i	0.715249	+	0.0947269i
$105$	3.68159e22			2.15255
$106$	9.28864e21	−	1.45720e22i	0.489314	−	0.767633i
$107$			9.44020e21i			0.448497i	0.974532	+	0.224249i	$0.0719928\pi$
$107$			9.44020e21i			0.448497i	−0.974532	+	0.224249i	$0.928007\pi$
$108$	−3.77728e22	+	1.75901e22i	−1.62001	+	0.754408i
$109$	1.06590e22			0.413070			0.206535	−	0.978439i	$-0.433781\pi$
$109$	1.06590e22			0.413070			0.206535	+	0.978439i	$0.433781\pi$
$110$	7.91503e21	+	5.04530e21i	0.277417	+	0.176835i
$111$			2.71004e22i			0.859850i
$112$	−2.65814e22	−	2.23511e22i	−0.764150	−	0.642542i
$113$	−3.00212e22			−0.782646			−0.391323	−	0.920253i	$-0.627983\pi$
$113$	−3.00212e22			−0.782646			−0.391323	+	0.920253i	$0.627983\pi$
$114$	5.98668e21	−	9.39187e21i	0.141655	−	0.222228i
$115$		−	1.13372e22i		−	0.243685i
$116$	3.16006e22	+	6.78591e22i	0.617530	+	1.32608i
$117$	−8.22542e22			−1.46256
$118$	5.13098e22	+	3.27065e22i	0.830803	+	0.529581i
$119$			6.55791e22i			0.967719i
$120$	2.10323e22	−	1.58807e23i	0.283069	−	2.13735i
$121$	7.56653e22			0.929518
$122$	−2.75655e22	+	4.32446e22i	−0.309320	+	0.485260i
$123$		−	2.59311e23i		−	2.65990i
$124$	−1.07493e23	+	5.00572e22i	−1.00865	+	0.469708i
$125$	6.69967e22			0.575497
$126$	2.16878e23	+	1.38245e23i	1.70663	+	1.08786i
$127$		−	1.63574e23i		−	1.17998i	−0.807412	−	0.589988i	$-0.799132\pi$
$127$		−	1.63574e23i		−	1.17998i	0.807412	−	0.589988i	$-0.200868\pi$
$128$	−1.11598e23	+	1.01891e23i	−0.738495	+	0.674259i
$129$	−1.25460e23			−0.762114
$130$	8.61270e22	−	1.35115e23i	0.480576	−	0.753925i
$131$			1.57071e23i			0.805585i	0.915291	+	0.402793i	$0.131960\pi$
$131$			1.57071e23i			0.805585i	−0.915291	+	0.402793i	$0.868040\pi$
$132$	4.13366e22	+	8.87660e22i	0.194994	+	0.418729i
$133$	−3.48333e22			−0.151226
$134$	−3.23891e23	−	2.06459e23i	−1.29493	−	0.825431i
$135$			6.01100e23i			2.21450i
$136$	2.82879e23	+	3.74642e22i	0.960887	+	0.127259i
$137$	−2.57501e23			−0.806962			−0.403481	−	0.914988i	$-0.632200\pi$
$137$	−2.57501e23			−0.806962			−0.403481	+	0.914988i	$0.632200\pi$
$138$	6.35726e22	−	9.97322e22i	0.183908	−	0.288513i
$139$		−	1.77347e23i		−	0.473871i	−0.971525	−	0.236935i	$-0.923857\pi$
$139$		−	1.77347e23i		−	0.473871i	0.971525	−	0.236935i	$-0.0761430\pi$
$140$	−4.54178e23	+	2.11502e23i	−1.12155	+	0.522283i
$141$	3.36808e23			0.769081
$142$	−2.25784e23	−	1.43922e23i	−0.477003	−	0.304058i
$143$			9.79418e22i			0.191545i
$144$	7.20225e23	−	8.56536e23i	1.30461	−	1.55152i
$145$	1.07988e24			1.81270
$146$	−4.59049e23	+	7.20153e23i	−0.714460	+	1.12084i
$147$			3.87367e21i			0.00559284i
$148$	−1.55688e23	−	3.34323e23i	−0.208629	−	0.448010i
$149$	2.27575e23			0.283188			0.141594	−	0.989925i	$-0.454777\pi$
$149$	2.27575e23			0.283188			0.141594	+	0.989925i	$0.454777\pi$
$150$	−6.79682e23	−	4.33251e23i	−0.785781	−	0.500883i
$151$		−	9.03479e23i		−	0.970894i	−0.874266	−	0.485447i	$-0.838657\pi$
$151$		−	9.03479e23i		−	0.970894i	0.874266	−	0.485447i	$-0.161343\pi$
$152$	−1.98996e22	+	1.50255e23i	−0.0198868	+	0.150159i
$153$	−2.11317e24			−1.96485
$154$	1.64611e23	−	2.58241e23i	0.142473	−	0.223510i
$155$			1.71059e24i			1.37879i
$156$	1.51530e24	−	7.05646e23i	1.13796	−	0.529927i
$157$	−1.64363e23			−0.115056			−0.0575280	−	0.998344i	$-0.518322\pi$
$157$	−1.64363e23			−0.115056			−0.0575280	+	0.998344i	$0.518322\pi$
$158$	1.66140e24	+	1.05903e24i	1.08454	+	0.691322i
$159$		−	2.60063e24i		−	1.58384i
$160$	6.52860e23	+	2.07995e24i	0.371108	+	1.18231i
$161$	−3.69895e23			−0.196333
$162$	−1.17308e24	+	1.84032e24i	−0.581652	+	0.912492i
$163$			1.81148e24i			0.839403i	0.907662	+	0.419702i	$0.137865\pi$
$163$			1.81148e24i			0.839403i	−0.907662	+	0.419702i	$0.862135\pi$
$164$	1.48970e24	+	3.19898e24i	0.645383	+	1.38589i
$165$	1.41258e24			0.572388
$166$	−4.26813e24	−	2.72065e24i	−1.61826	−	1.03153i
$167$		−	3.11720e24i		−	1.10633i	−0.833073	−	0.553163i	$-0.813421\pi$
$167$		−	3.11720e24i		−	1.10633i	0.833073	−	0.553163i	$-0.186579\pi$
$168$	−5.18134e24	−	6.86212e23i	−1.72203	−	0.228064i
$169$	−1.53990e24			−0.479445
$170$	2.21266e24	−	3.47121e24i	0.645621	−	1.01285i
$171$		−	1.12244e24i		−	0.307048i
$172$	1.54774e24	−	7.20751e23i	0.397086	−	0.184915i
$173$	−1.66796e24			−0.401493			−0.200747	−	0.979643i	$-0.564337\pi$
$173$	−1.66796e24			−0.401493			−0.200747	+	0.979643i	$0.564337\pi$
$174$	9.49959e24	+	6.05535e24i	2.14616	+	1.36804i
$175$			2.52086e24i			0.534724i
$176$	−1.01990e24	−	8.57587e23i	−0.203197	−	0.170859i
$177$	9.15717e24			1.71417
$178$	3.29249e24	−	5.16523e24i	0.579301	−	0.908803i
$179$			2.60509e24i			0.430962i	0.976508	+	0.215481i	$0.0691319\pi$
$179$			2.60509e24i			0.430962i	−0.976508	+	0.215481i	$0.930868\pi$
$180$	−6.81527e24	−	1.46351e25i	−1.06044	−	2.27718i
$181$	−4.15676e24			−0.608542			−0.304271	−	0.952586i	$-0.598413\pi$
$181$	−4.15676e24			−0.608542			−0.304271	+	0.952586i	$0.598413\pi$
$182$	−4.40836e24	−	2.81003e24i	−0.607424	−	0.387192i
$183$			7.71780e24i			1.00122i
$184$	−2.11314e23	+	1.59556e24i	−0.0258186	+	0.194947i
$185$	−5.32027e24			−0.612413
$186$	−9.59201e24	+	1.50479e25i	−1.04056	+	1.63242i
$187$			2.51619e24i			0.257328i
$188$	−4.15502e24	+	1.93491e24i	−0.400716	+	0.186606i
$189$	1.96119e25			1.78418
$190$	1.84378e24	+	1.17529e24i	0.158278	+	0.100892i
$191$			3.05525e24i			0.247559i	0.992310	+	0.123780i	$0.0395016\pi$
$191$			3.05525e24i			0.247559i	−0.992310	+	0.123780i	$0.960498\pi$
$192$	−5.92002e24	+	2.19580e25i	−0.452907	+	1.67988i
$193$	−1.41839e25			−1.02486			−0.512431	−	0.858729i	$-0.671255\pi$
$193$	−1.41839e25			−1.02486			−0.512431	+	0.858729i	$0.671255\pi$
$194$	1.49522e25	−	2.34569e25i	1.02067	−	1.60122i
$195$		−	2.41138e25i		−	1.55555i
$196$	−2.22537e22	−	4.77875e22i	−0.00135702	−	0.00291405i
$197$	8.09195e24			0.466579			0.233289	−	0.972407i	$-0.425051\pi$
$197$	8.09195e24			0.466579			0.233289	+	0.972407i	$0.425051\pi$
$198$	8.32135e24	+	5.30430e24i	0.453813	+	0.289275i
$199$			1.86766e25i			0.963638i	0.876271	+	0.481819i	$0.160024\pi$
$199$			1.86766e25i			0.963638i	−0.876271	+	0.481819i	$0.839976\pi$
$200$	1.08738e25	+	1.44012e24i	0.530949	+	0.0703183i
$201$	−5.78043e25			−2.67180
$202$	3.47097e24	−	5.44524e24i	0.151910	−	0.238315i
$203$		−	3.52328e25i		−	1.46046i
$204$	3.89292e25	−	1.81286e25i	1.52877	−	0.711920i
$205$	5.09072e25			1.89447
$206$	−1.36272e25	−	8.68642e24i	−0.480692	−	0.306409i
$207$		−	1.19192e25i		−	0.398633i
$208$	−1.46396e25	+	1.74104e25i	−0.464337	+	0.552219i
$209$	−1.33651e24			−0.0402128
$210$	−4.05282e25	+	6.35804e25i	−1.15703	+	1.81514i
$211$		−	8.46778e24i		−	0.229437i	−0.993398	−	0.114718i	$-0.963403\pi$
$211$		−	8.46778e24i		−	0.229437i	0.993398	−	0.114718i	$-0.0365965\pi$
$212$	1.49403e25	+	3.20826e25i	0.384294	+	0.825231i
$213$	−4.02953e25			−0.984190
$214$	−1.63031e25	−	1.03921e25i	−0.378197	−	0.241075i
$215$		−	2.46300e25i		−	0.542802i
$216$	1.12039e25	−	8.45968e25i	0.234627	−	1.77159i
$217$	5.58108e25			1.11086
$218$	−1.17337e25	+	1.84078e25i	−0.222032	+	0.348322i
$219$			1.28525e26i			2.31260i
$220$	−1.74263e25	+	8.11508e24i	−0.298233	+	0.138881i
$221$	4.29533e25			0.699329
$222$	−4.68019e25	−	2.98331e25i	−0.725071	−	0.462184i
$223$			1.15203e26i			1.69868i	0.527845	+	0.849341i	$0.323000\pi$
$223$			1.15203e26i			1.69868i	−0.527845	+	0.849341i	$0.677000\pi$
$224$	6.78617e25	−	2.13006e25i	0.952569	−	0.298995i
$225$	−8.12301e25			−1.08570
$226$	3.30484e25	−	5.18461e25i	0.420686	−	0.659969i
$227$		−	1.00157e26i		−	1.21450i	−0.794511	−	0.607250i	$-0.792273\pi$
$227$		−	1.00157e26i		−	1.21450i	0.794511	−	0.607250i	$-0.207727\pi$
$228$	9.62924e24	+	2.06778e25i	0.111252	+	0.238903i
$229$	2.04260e24			0.0224902			0.0112451	−	0.999937i	$-0.496421\pi$
$229$	2.04260e24			0.0224902			0.0112451	+	0.999937i	$0.496421\pi$
$230$	1.95791e25	+	1.24804e25i	0.205488	+	0.130985i
$231$		−	4.60878e25i		−	0.461163i
$232$	−1.51978e26	−	2.01279e25i	−1.45015	−	0.192057i
$233$	−3.39103e25			−0.308614			−0.154307	−	0.988023i	$-0.549315\pi$
$233$	−3.39103e25			−0.308614			−0.154307	+	0.988023i	$0.549315\pi$
$234$	9.05483e25	−	1.42052e26i	0.786151	−	1.23331i
$235$			6.61211e25i			0.547764i
$236$	−1.12967e26	+	5.26066e25i	−0.893141	+	0.415918i
$237$	2.96507e26			2.23771
$238$	−1.13254e26	−	7.21918e25i	−0.816032	−	0.520165i
$239$		−	2.54233e26i		−	1.74927i	−0.484786	−	0.874633i	$-0.661102\pi$
$239$		−	2.54233e26i		−	1.74927i	0.484786	−	0.874633i	$-0.338898\pi$
$240$	2.51104e26	+	2.11143e26i	1.65018	+	1.38756i
$241$	−5.27835e25			−0.331368			−0.165684	−	0.986179i	$-0.552983\pi$
$241$	−5.27835e25			−0.331368			−0.165684	+	0.986179i	$0.552983\pi$
$242$	−8.32950e25	+	1.30673e26i	−0.499632	+	0.783819i
$243$			1.66889e25i			0.0956662i
$244$	−4.43376e25	−	9.52104e25i	−0.242932	−	0.521670i
$245$	−7.60468e23			−0.00398340
$246$	4.47826e26	+	2.85459e26i	2.24297	+	1.42974i
$247$			2.28153e25i			0.109285i
$248$	3.18837e25	−	2.40742e26i	0.146083	−	1.10302i
$249$	−7.61726e26			−3.33892
$250$	−7.37522e25	+	1.15702e26i	−0.309339	+	0.485289i
$251$			3.78088e26i			1.51769i	0.651273	+	0.758843i	$0.274235\pi$
$251$			3.78088e26i			1.51769i	−0.651273	+	0.758843i	$0.725765\pi$
$252$	−4.77493e26	+	2.22359e26i	−1.83468	+	0.854376i
$253$	−1.41924e25			−0.0522073
$254$	2.82489e26	+	1.80068e26i	0.995019	+	0.634257i
$255$		−	6.19501e26i		−	2.08978i
$256$	−5.31131e25	−	3.04893e26i	−0.171618	−	0.985164i
$257$	−3.92889e25			−0.121620			−0.0608101	−	0.998149i	$-0.519368\pi$
$257$	−3.92889e25			−0.121620			−0.0608101	+	0.998149i	$0.519368\pi$
$258$	1.38111e26	−	2.16668e26i	0.409649	−	0.642655i
$259$			1.73583e26i			0.493411i
$260$	1.38530e26	+	2.97479e26i	0.377432	+	0.810495i
$261$	1.13531e27			2.96531
$262$	−2.71259e26	−	1.72909e26i	−0.679312	−	0.433016i
$263$			4.70959e26i			1.13102i	0.824742	+	0.565510i	$0.191321\pi$
$263$			4.70959e26i			1.13102i	−0.824742	+	0.565510i	$0.808679\pi$
$264$	−1.98802e26	−	2.63291e25i	−0.457907	−	0.0606448i
$265$	5.10549e26			1.12806
$266$	3.83457e25	−	6.01565e25i	0.0812866	−	0.127522i
$267$		−	9.21830e26i		−	1.87511i
$268$	7.13101e26	−	3.32077e26i	1.39209	−	0.648271i
$269$	−7.64721e26			−1.43294			−0.716470	−	0.697618i	$-0.754243\pi$
$269$	−7.64721e26			−1.43294			−0.716470	+	0.697618i	$0.754243\pi$
$270$	−1.03809e27	−	6.61712e26i	−1.86738	−	1.19033i
$271$			4.92729e26i			0.851032i	0.904951	+	0.425516i	$0.139907\pi$
$271$			4.92729e26i			0.851032i	−0.904951	+	0.425516i	$0.860093\pi$
$272$	−3.76103e26	+	4.47285e26i	−0.623805	+	0.741867i
$273$	−7.86753e26			−1.25328
$274$	2.83466e26	−	4.44700e26i	0.433756	−	0.680473i
$275$			9.67223e25i			0.142189i
$276$	1.02253e26	+	2.19577e26i	0.144436	+	0.310161i
$277$	1.21331e27			1.64701			0.823504	−	0.567310i	$-0.192016\pi$
$277$	1.21331e27			1.64701			0.823504	+	0.567310i	$0.192016\pi$
$278$	3.06274e26	+	1.95229e26i	0.399593	+	0.254714i
$279$			1.79840e27i			2.25549i
$280$	1.34715e26	−	1.01719e27i	0.162434	−	1.22648i
$281$	−8.40763e26			−0.974774			−0.487387	−	0.873186i	$-0.662050\pi$
$281$	−8.40763e26			−0.974774			−0.487387	+	0.873186i	$0.662050\pi$
$282$	−3.70770e26	+	5.81661e26i	−0.413394	+	0.648530i
$283$			1.04651e27i			1.12226i	0.827728	+	0.561130i	$0.189633\pi$
$283$			1.04651e27i			1.12226i	−0.827728	+	0.561130i	$0.810367\pi$
$284$	4.97102e26	−	2.31491e26i	0.512795	−	0.238799i
$285$	3.29057e26			0.326571
$286$	−1.69144e26	−	1.07818e26i	−0.161521	−	0.102959i
$287$		−	1.66093e27i		−	1.52634i
$288$	6.86374e26	+	2.18672e27i	0.607077	+	1.93409i
$289$	−7.10618e25			−0.0605006
$290$	−1.18877e27	+	1.86493e27i	−0.974359	+	1.52857i
$291$		−	4.18631e27i		−	3.30376i
$292$	−7.38355e26	−	1.58554e27i	−0.561117	−	1.20494i
$293$	−3.74295e26			−0.273949			−0.136975	−	0.990575i	$-0.543738\pi$
$293$	−3.74295e26			−0.273949			−0.136975	+	0.990575i	$0.543738\pi$
$294$	−6.68976e24	−	4.26427e24i	−0.00471618	−	0.00300625i
$295$			1.79771e27i			1.22089i
$296$	7.48757e26	+	9.91646e25i	0.489928	+	0.0648855i
$297$	7.52484e26			0.474435
$298$	−2.50522e26	+	3.93017e26i	−0.152218	+	0.238799i
$299$			2.42275e26i			0.141882i
$300$	1.49643e27	−	6.96860e26i	0.844741	−	0.393380i
$301$	−8.03594e26			−0.437326
$302$	1.56029e27	+	9.94581e26i	0.818709	+	0.521872i
$303$		−	9.71803e26i		−	0.491710i
$304$	−2.37582e26	−	1.99772e26i	−0.115932	−	0.0974824i
$305$	−1.51514e27			−0.713104
$306$	2.32625e27	−	3.64941e27i	1.05614	−	1.65686i
$307$		−	5.58595e26i		−	0.244667i	−0.992489	−	0.122333i	$-0.960962\pi$
$307$		−	5.58595e26i		−	0.244667i	0.992489	−	0.122333i	$-0.0390377\pi$
$308$	2.64768e26	+	5.68561e26i	0.111894	+	0.240281i
$309$	−2.43202e27			−0.991801
$310$	−2.95416e27	−	1.88308e27i	−1.16267	−	0.741121i
$311$		−	1.58500e27i		−	0.602096i	−0.953609	−	0.301048i	$-0.902664\pi$
$311$		−	1.58500e27i		−	0.602096i	0.953609	−	0.301048i	$-0.0973364\pi$
$312$	−4.49458e26	+	3.39370e27i	−0.164812	+	1.24444i
$313$	3.17283e27			1.12321			0.561603	−	0.827407i	$-0.310185\pi$
$313$	3.17283e27			1.12321			0.561603	+	0.827407i	$0.310185\pi$
$314$	1.80937e26	−	2.83853e26i	0.0618445	−	0.0970213i
$315$			7.59861e27i			2.50795i
$316$	−3.65785e27	+	1.70339e27i	−1.16592	+	0.542946i
$317$	5.25906e27			1.61904			0.809518	−	0.587095i	$-0.199728\pi$
$317$	5.25906e27			1.61904			0.809518	+	0.587095i	$0.199728\pi$
$318$	4.49125e27	+	2.86287e27i	1.33558	+	0.851340i
$319$		−	1.35184e27i		−	0.388354i
$320$	−4.31072e27	−	1.16220e27i	−1.19647	−	0.322575i
$321$	−2.90958e27			−0.780324
$322$	4.07193e26	−	6.38802e26i	0.105532	−	0.165558i
$323$			5.86141e26i			0.146816i
$324$	−1.88684e27	−	4.05178e27i	−0.456814	−	0.980960i
$325$	1.65112e27			0.386422
$326$	−3.12840e27	−	1.99414e27i	−0.707829	−	0.451193i
$327$			3.28521e27i			0.718685i
$328$	−7.16451e27	−	9.48860e26i	−1.51556	−	0.200720i
$329$	2.15731e27			0.441324
$330$	−1.55502e27	+	2.43950e27i	−0.307668	+	0.482668i
$331$			6.20093e27i			1.18672i	0.804937	+	0.593361i	$0.202199\pi$
$331$			6.20093e27i			1.18672i	−0.804937	+	0.593361i	$0.797801\pi$
$332$	9.39702e27	−	4.37601e27i	1.73969	−	0.810138i
$333$	−5.59339e27			−1.00182
$334$	5.38335e27	+	3.43152e27i	0.932913	+	0.594669i
$335$		−	1.13480e28i		−	1.90294i
$336$	6.88888e27	−	8.19268e27i	1.11793	−	1.32952i
$337$	−1.04431e27			−0.164022			−0.0820109	−	0.996631i	$-0.526134\pi$
$337$	−1.04431e27			−0.164022			−0.0820109	+	0.996631i	$0.526134\pi$
$338$	1.69518e27	−	2.65938e27i	0.257710	−	0.404294i
$339$		−	9.25289e27i		−	1.36170i
$340$	3.55895e27	+	7.64246e27i	0.507053	+	1.08884i
$341$	2.14139e27			0.295392
$342$	1.93843e27	+	1.23562e27i	0.258919	+	0.165043i
$343$			7.74337e27i			1.00160i
$344$	−4.59079e26	+	3.46634e27i	−0.0575102	+	0.434239i
$345$	3.49426e27			0.423979
$346$	1.83615e27	−	2.88053e27i	0.215809	−	0.338560i
$347$			1.65711e27i			0.188680i	0.995540	+	0.0943401i	$0.0300741\pi$
$347$			1.65711e27i			0.188680i	−0.995540	+	0.0943401i	$0.969926\pi$
$348$	−2.09149e28	+	9.73968e27i	−2.30720	+	1.07442i
$349$	−6.83368e27			−0.730424			−0.365212	−	0.930924i	$-0.619004\pi$
$349$	−6.83368e27			−0.730424			−0.365212	+	0.930924i	$0.619004\pi$
$350$	−4.35347e27	−	2.77505e27i	−0.450907	−	0.287423i
$351$		−	1.28455e28i		−	1.28935i
$352$	2.60377e27	−	8.17280e26i	0.253299	−	0.0795063i
$353$	4.91291e27			0.463252			0.231626	−	0.972805i	$-0.425595\pi$
$353$	4.91291e27			0.463252			0.231626	+	0.972805i	$0.425595\pi$
$354$	−1.00805e28	+	1.58143e28i	−0.921398	+	1.44548i
$355$		−	7.91066e27i		−	0.700972i
$356$	5.29578e27	+	1.13721e28i	0.454967	+	0.976994i
$357$	−2.02122e28			−1.68370
$358$	−4.49894e27	−	2.86777e27i	−0.363410	−	0.231649i
$359$			5.07949e27i			0.397906i	0.980009	+	0.198953i	$0.0637542\pi$
$359$			5.07949e27i			0.397906i	−0.980009	+	0.198953i	$0.936246\pi$
$360$	3.27770e28	+	4.34095e27i	2.49024	+	0.329805i
$361$	1.32586e28			0.977057
$362$	4.57590e27	−	7.17865e27i	0.327101	−	0.513155i
$363$			2.33209e28i			1.61723i
$364$	9.70575e27	−	4.51978e27i	0.653001	−	0.304090i
$365$	−2.52316e28			−1.64711
$366$	−1.33285e28	−	8.49602e27i	−0.844285	−	0.538175i
$367$			5.06222e27i			0.311182i	0.987822	+	0.155591i	$0.0497281\pi$
$367$			5.06222e27i			0.311182i	−0.987822	+	0.155591i	$0.950272\pi$
$368$	−2.52288e27	−	2.12138e27i	−0.150512	−	0.126559i
$369$	5.35205e28			3.09906
$370$	5.85674e27	−	9.18801e27i	0.329183	−	0.516419i
$371$		−	1.66575e28i		−	0.908859i
$372$	−1.54282e28	−	3.31305e28i	−0.817228	−	1.75491i
$373$	−2.16450e28			−1.11317			−0.556584	−	0.830791i	$-0.687888\pi$
$373$	−2.16450e28			−1.11317			−0.556584	+	0.830791i	$0.687888\pi$
$374$	−4.34542e27	−	2.76991e27i	−0.216992	−	0.138318i
$375$			2.06491e28i			1.00129i
$376$	1.23243e27	−	9.30566e27i	0.0580359	−	0.438209i
$377$	−2.30769e28			−1.05541
$378$	−2.15894e28	+	3.38693e28i	−0.959028	+	1.50452i
$379$		−	2.84238e28i		−	1.22645i	−0.789907	−	0.613227i	$-0.789871\pi$
$379$		−	2.84238e28i		−	1.22645i	0.789907	−	0.613227i	$-0.210129\pi$
$380$	−4.05940e27	+	1.89038e27i	−0.170154	+	0.0792375i
$381$	5.04154e28			2.05300
$382$	−5.27636e27	−	3.36332e27i	−0.208755	−	0.133067i
$383$			3.19313e28i			1.22752i	0.789491	+	0.613762i	$0.210344\pi$
$383$			3.19313e28i			1.22752i	−0.789491	+	0.613762i	$0.789656\pi$
$384$	−3.14040e28	−	3.43958e28i	−1.17312	−	1.28488i
$385$	9.04782e27			0.328455
$386$	1.56141e28	−	2.44953e28i	0.550880	−	0.864217i
$387$		−	2.58944e28i		−	0.887943i
$388$	2.40497e28	+	5.16443e28i	0.801606	+	1.72137i
$389$	3.58810e28			1.16257			0.581285	−	0.813700i	$-0.302550\pi$
$389$	3.58810e28			1.16257			0.581285	+	0.813700i	$0.302550\pi$
$390$	4.16441e28	+	2.65453e28i	1.31173	+	0.836137i
$391$			6.22422e27i			0.190608i
$392$	1.07026e26	+	1.41744e25i	0.00318670	+	0.000422043i
$393$	−4.84111e28			−1.40161
$394$	−8.90790e27	+	1.39747e28i	−0.250794	+	0.393444i
$395$			5.82094e28i			1.59377i
$396$	−1.83209e28	+	8.53166e27i	−0.487864	+	0.227189i
$397$	−7.09681e28			−1.83809			−0.919047	−	0.394148i	$-0.871040\pi$
$397$	−7.09681e28			−1.83809			−0.919047	+	0.394148i	$0.871040\pi$
$398$	−3.22542e28	−	2.05598e28i	−0.812591	−	0.517972i
$399$		−	1.07360e28i		−	0.263113i
$400$	−1.44574e28	+	1.71936e28i	−0.344690	+	0.409927i
$401$	5.32831e27			0.123595			0.0617976	−	0.998089i	$-0.480317\pi$
$401$	5.32831e27			0.123595			0.0617976	+	0.998089i	$0.480317\pi$
$402$	6.36330e28	−	9.98270e28i	1.43614	−	2.25300i
$403$		−	3.65552e28i		−	0.802774i
$404$	5.58286e27	+	1.19886e28i	0.119306	+	0.256197i
$405$	−6.44783e28			−1.34094
$406$	6.08464e28	+	3.87855e28i	1.23154	+	0.785024i
$407$			6.66016e27i			0.131204i
$408$	−1.15469e28	+	8.71865e28i	−0.221413	+	1.67181i
$409$	5.03062e28			0.938999			0.469500	−	0.882933i	$-0.344434\pi$
$409$	5.03062e28			0.938999			0.469500	+	0.882933i	$0.344434\pi$
$410$	−5.60404e28	+	8.79158e28i	−1.01831	+	1.59751i
$411$		−	7.93649e28i		−	1.40400i
$412$	3.00026e28	−	1.39716e28i	0.516760	−	0.240645i
$413$	5.86532e28			0.983651
$414$	2.05842e28	+	1.31211e28i	0.336148	+	0.214272i
$415$		−	1.49540e29i		−	2.37809i
$416$	−1.39516e28	−	4.44483e28i	−0.216071	−	0.688381i
$417$	5.46602e28			0.824470
$418$	1.47128e27	−	2.30813e27i	0.0216150	−	0.0339095i
$419$			7.13763e28i			1.02141i	0.859756	+	0.510705i	$0.170615\pi$
$419$			7.13763e28i			1.02141i	−0.859756	+	0.510705i	$0.829385\pi$
$420$	−6.51873e28	−	1.39983e29i	−0.908701	−	1.95134i
$421$	−4.98789e28			−0.677351			−0.338676	−	0.940903i	$-0.609979\pi$
$421$	−4.98789e28			−0.677351			−0.338676	+	0.940903i	$0.609979\pi$
$422$	1.46237e28	+	9.32163e27i	0.193473	+	0.123326i
$423$			6.95154e28i			0.896060i
$424$	−7.18529e28	−	9.51613e27i	−0.902443	−	0.119519i
$425$	4.24185e28			0.519131
$426$	4.43585e28	−	6.95893e28i	0.529019	−	0.829921i
$427$			4.94338e28i			0.574536i
$428$	3.58939e28	−	1.67151e28i	0.406574	−	0.189334i
$429$	−3.01868e28			−0.333263
$430$	4.25356e28	+	2.71136e28i	0.457720	+	0.291765i
$431$			6.77466e26i			0.00710620i	0.999994	+	0.00355310i	$0.00113099\pi$
$431$			6.77466e26i			0.00710620i	−0.999994	+	0.00355310i	$0.998869\pi$
$432$	1.33763e29	+	1.12476e29i	1.36778	+	1.15011i
$433$	−9.01672e28			−0.898838			−0.449419	−	0.893321i	$-0.648369\pi$
$433$	−9.01672e28			−0.898838			−0.449419	+	0.893321i	$0.648369\pi$
$434$	−6.14384e28	+	9.63842e28i	−0.597108	+	0.936739i
$435$			3.32831e29i			3.15386i
$436$	−1.88731e28	−	4.05279e28i	−0.174378	−	0.374458i
$437$	−3.30609e27			−0.0297864
$438$	−2.21960e29	−	1.41484e29i	−1.95011	−	1.24306i
$439$		−	1.57112e29i		−	1.34617i	−0.739564	−	0.673086i	$-0.764968\pi$
$439$		−	1.57112e29i		−	1.34617i	0.739564	−	0.673086i	$-0.235032\pi$
$440$	5.16886e27	−	3.90282e28i	0.0431932	−	0.326137i
$441$	−7.99507e26			−0.00651625
$442$	−4.72845e28	+	7.41796e28i	−0.375901	+	0.589711i
$443$		−	7.32468e27i		−	0.0567999i	−0.999597	−	0.0284000i	$-0.990959\pi$
$443$		−	7.32468e27i		−	0.0567999i	0.999597	−	0.0284000i	$-0.00904120\pi$
$444$	1.03042e29	−	4.79848e28i	0.779476	−	0.362987i
$445$	1.80971e29			1.33552
$446$	−1.98954e29	−	1.26820e29i	−1.43242	−	0.913070i
$447$			7.01411e28i			0.492708i
$448$	−3.79187e28	+	1.40644e29i	−0.259893	+	0.963971i
$449$	−9.02131e28			−0.603337			−0.301668	−	0.953413i	$-0.597544\pi$
$449$	−9.02131e28			−0.603337			−0.301668	+	0.953413i	$0.597544\pi$
$450$	8.94209e28	−	1.40283e29i	0.583581	−	0.915518i
$451$		−	6.37279e28i		−	0.405871i
$452$	5.31565e28	+	1.14148e29i	0.330395	+	0.709489i
$453$	2.78463e29			1.68922
$454$	1.72970e29	+	1.10256e29i	1.02413	+	0.652814i
$455$		−	1.54453e29i		−	0.892629i
$456$	−4.63104e28	−	6.13330e27i	−0.261255	−	0.0346004i
$457$	1.11136e29			0.612033			0.306016	−	0.952026i	$-0.401004\pi$
$457$	1.11136e29			0.612033			0.306016	+	0.952026i	$0.401004\pi$
$458$	−2.24856e27	+	3.52753e27i	−0.0120888	+	0.0189649i
$459$		−	3.30009e29i		−	1.73215i
$460$	−4.31068e28	+	2.00740e28i	−0.220907	+	0.102872i
$461$	−1.65157e29			−0.826395			−0.413198	−	0.910641i	$-0.635588\pi$
$461$	−1.65157e29			−0.826395			−0.413198	+	0.910641i	$0.635588\pi$
$462$	7.95928e28	+	5.07351e28i	0.388877	+	0.247883i
$463$			2.89126e29i			1.37942i	0.724086	+	0.689710i	$0.242262\pi$
$463$			2.89126e29i			1.37942i	−0.724086	+	0.689710i	$0.757738\pi$
$464$	2.02064e29	−	2.40307e29i	0.941435	−	1.11961i
$465$	−5.27223e29			−2.39890
$466$	3.73296e28	−	5.85624e28i	0.165885	−	0.260240i
$467$		−	2.71594e29i		−	1.17879i	−0.807847	−	0.589393i	$-0.799367\pi$
$467$		−	2.71594e29i		−	1.17879i	0.807847	−	0.589393i	$-0.200633\pi$
$468$	1.45642e29	+	3.12751e29i	0.617421	+	1.32585i
$469$	−3.70246e29			−1.53317
$470$	−1.14190e29	−	7.27884e28i	−0.461904	−	0.294433i
$471$		−	5.06587e28i		−	0.200182i
$472$	3.35075e28	−	2.53003e29i	0.129354	−	0.976707i
$473$	−3.08330e28			−0.116290
$474$	−3.26405e29	+	5.12063e29i	−1.20281	+	1.88695i
$475$			2.25312e28i			0.0811249i
$476$	2.49348e29	−	1.16116e29i	0.877262	−	0.408524i
$477$	5.36758e29			1.84534
$478$	4.39057e29	+	2.79869e29i	1.47507	+	0.940260i
$479$			5.94621e29i			1.95231i	0.217065	+	0.976157i	$0.430352\pi$
$479$			5.94621e29i			1.95231i	−0.217065	+	0.976157i	$0.569648\pi$
$480$	−6.41064e29	+	2.01219e29i	−2.05706	+	0.645677i
$481$	1.13694e29			0.356567
$482$	5.81059e28	−	9.11561e28i	0.178116	−	0.279427i
$483$		−	1.14006e29i		−	0.341593i
$484$	−1.33975e29	−	2.87698e29i	−0.392397	−	0.842632i
$485$	8.21844e29			2.35304
$486$	−2.88214e28	−	1.83717e28i	−0.0806708	−	0.0514222i
$487$		−	4.00426e29i		−	1.09573i	−0.836567	−	0.547865i	$-0.815441\pi$
$487$		−	4.00426e29i		−	1.09573i	0.836567	−	0.547865i	$-0.184559\pi$
$488$	2.13235e29	+	2.82406e28i	0.570480	+	0.0755538i
$489$	−5.58320e29			−1.46045
$490$	8.37150e26	−	1.31331e27i	0.00214115	−	0.00335902i
$491$		−	1.49100e29i		−	0.372891i	−0.982465	−	0.186445i	$-0.940303\pi$
$491$		−	1.49100e29i		−	0.372891i	0.982465	−	0.186445i	$-0.0596967\pi$
$492$	−9.85964e29	+	4.59144e29i	−2.41126	+	1.12288i
$493$	−5.92863e29			−1.41788
$494$	−3.94015e28	−	2.51158e28i	−0.0921546	−	0.0587423i
$495$			2.91550e29i			0.666892i
$496$	3.80659e29	+	3.20080e29i	0.851605	+	0.716078i
$497$	−2.58098e29			−0.564761
$498$	8.38535e29	−	1.31549e30i	1.79473	−	2.81556i
$499$			9.19079e29i			1.92419i	0.272722	+	0.962093i	$0.412076\pi$
$499$			9.19079e29i			1.92419i	−0.272722	+	0.962093i	$0.587924\pi$
$500$	−1.18626e29	−	2.54738e29i	−0.242947	−	0.521703i
$501$	9.60757e29			1.92486
$502$	−6.52951e29	−	4.16212e29i	−1.27979	−	0.815782i
$503$		−	1.68225e29i		−	0.322583i	−0.986907	−	0.161292i	$-0.948434\pi$
$503$		−	1.68225e29i		−	0.322583i	0.986907	−	0.161292i	$-0.0515660\pi$
$504$	1.41631e29	−	1.06940e30i	0.265718	−	2.00634i
$505$	1.90781e29			0.350212
$506$	1.56235e28	−	2.45101e28i	0.0280623	−	0.0440239i
$507$		−	4.74615e29i		−	0.834169i
$508$	−6.21948e29	+	2.89629e29i	−1.06968	+	0.498128i
$509$	−9.63042e28			−0.162088			−0.0810438	−	0.996711i	$-0.525825\pi$
$509$	−9.63042e28			−0.162088			−0.0810438	+	0.996711i	$0.525825\pi$
$510$	1.06987e30	+	6.81969e29i	1.76221	+	1.12329i
$511$			8.23221e29i			1.32705i
$512$	5.85014e29	+	2.43912e29i	0.922990	+	0.384825i
$513$	1.75289e29			0.270685
$514$	4.32506e28	−	6.78513e28i	0.0653729	−	0.102557i
$515$		−	4.77448e29i		−	0.706393i
$516$	2.22144e29	+	4.77031e29i	0.321727	+	0.690876i
$517$	8.27734e28			0.117353
$518$	−2.99774e29	−	1.91086e29i	−0.416070	−	0.265217i
$519$		−	5.14084e29i		−	0.698543i
$520$	−6.66241e29	−	8.82362e28i	−0.886328	−	0.117384i
$521$	−4.46922e29			−0.582126			−0.291063	−	0.956704i	$-0.594009\pi$
$521$	−4.46922e29			−0.582126			−0.291063	+	0.956704i	$0.594009\pi$
$522$	−1.24979e30	+	1.96067e30i	−1.59391	+	2.50051i
$523$		−	3.55590e29i		−	0.444050i	−0.975041	−	0.222025i	$-0.928733\pi$
$523$		−	3.55590e29i		−	0.444050i	0.975041	−	0.222025i	$-0.0712666\pi$
$524$	5.97222e29	−	2.78115e29i	0.730284	−	0.340079i
$525$	−7.76957e29			−0.930346
$526$	−8.13338e29	−	5.18448e29i	−0.953736	−	0.607942i
$527$		−	9.39129e29i		−	1.07847i
$528$	2.64318e29	−	3.14344e29i	0.297272	−	0.353534i
$529$	8.72739e29			0.961329
$530$	−5.62030e29	+	8.81709e29i	−0.606352	+	0.951241i
$531$			1.88999e30i			1.99719i
$532$	6.16769e28	+	1.32445e29i	0.0638402	+	0.137090i
$533$	−1.08788e30			−1.10302
$534$	1.59198e30	+	1.01478e30i	1.58119	+	1.00790i
$535$		−	5.71200e29i		−	0.555772i
$536$	−2.11515e29	+	1.59708e30i	−0.201618	+	1.52234i
$537$	−8.02918e29			−0.749815
$538$	8.41831e29	−	1.32066e30i	0.770229	−	1.20833i
$539$			9.51989e26i			0.000853405i
$540$	2.28553e30	−	1.06433e30i	2.00750	−	0.934853i
$541$	1.10806e30			0.953658			0.476829	−	0.878996i	$-0.341786\pi$
$541$	1.10806e30			0.953658			0.476829	+	0.878996i	$0.341786\pi$
$542$	−8.50935e29	−	5.42413e29i	−0.717636	−	0.457444i
$543$		−	1.28116e30i		−	1.05878i
$544$	−3.58426e29	−	1.14191e30i	−0.290276	−	0.924791i
$545$	−6.44943e29			−0.511871
$546$	8.66085e29	−	1.35871e30i	0.673661	−	1.05683i
$547$			3.06639e29i			0.233758i	0.993146	+	0.116879i	$0.0372890\pi$
$547$			3.06639e29i			0.233758i	−0.993146	+	0.116879i	$0.962711\pi$
$548$	4.55939e29	+	9.79082e29i	0.340660	+	0.731532i
$549$	−1.59291e30			−1.16653
$550$	−1.67038e29	−	1.06475e29i	−0.119902	−	0.0764291i
$551$		−	3.14908e29i		−	0.221572i
$552$	−4.91770e29	−	6.51295e28i	−0.339181	−	0.0449208i
$553$	1.89918e30			1.28407
$554$	−1.33566e30	+	2.09537e30i	−0.885295	+	1.38884i
$555$		−	1.63977e30i		−	1.06552i
$556$	−6.74315e29	+	3.14015e29i	−0.429576	+	0.200045i
$557$	2.81931e30			1.76090			0.880451	−	0.474138i	$-0.157240\pi$
$557$	2.81931e30			1.76090			0.880451	+	0.474138i	$0.157240\pi$
$558$	−3.10581e30	−	1.97974e30i	−1.90195	−	1.21236i
$559$			5.26342e29i			0.316037i
$560$	1.60836e30	+	1.35240e30i	0.946925	+	0.796229i
$561$	−7.75520e29			−0.447715
$562$	9.25541e29	−	1.45198e30i	0.523958	−	0.821981i
$563$			2.40066e30i			1.33272i	0.745631	+	0.666359i	$0.232148\pi$
$563$			2.40066e30i			1.33272i	−0.745631	+	0.666359i	$0.767852\pi$
$564$	−5.96362e29	−	1.28063e30i	−0.324668	−	0.697191i
$565$	1.81650e30			0.969845
$566$	−1.80731e30	−	1.15204e30i	−0.946349	−	0.603233i
$567$			2.10371e30i			1.08037i
$568$	−1.47447e29	+	1.11332e30i	−0.0742683	+	0.560774i
$569$	−1.95203e29			−0.0964385			−0.0482193	−	0.998837i	$-0.515355\pi$
$569$	−1.95203e29			−0.0964385			−0.0482193	+	0.998837i	$0.515355\pi$
$570$	−3.62237e29	+	5.68276e29i	−0.175538	+	0.275382i
$571$			3.39571e30i			1.61411i	0.590477	+	0.807055i	$0.298940\pi$
$571$			3.39571e30i			1.61411i	−0.590477	+	0.807055i	$0.701060\pi$
$572$	3.72398e29	−	1.73419e29i	0.173641	−	0.0808611i
$573$	−9.41663e29			−0.430720
$574$	2.86840e30	+	1.82841e30i	1.28709	+	0.820432i
$575$			2.39259e29i			0.105323i
$576$	−4.53201e30	−	1.22186e30i	−1.95724	−	0.527685i
$577$	−2.27695e30			−0.964762			−0.482381	−	0.875961i	$-0.660228\pi$
$577$	−2.27695e30			−0.964762			−0.482381	+	0.875961i	$0.660228\pi$
$578$	7.82272e28	−	1.22722e29i	0.0325201	−	0.0510173i
$579$		−	4.37164e30i		−	1.78312i
$580$	−1.91207e30	−	4.10596e30i	−0.765235	−	1.64326i
$581$	−4.87898e30			−1.91598
$582$	7.22968e30	+	4.60843e30i	2.78590	+	1.77583i
$583$		−	6.39128e29i		−	0.241676i
$584$	3.55101e30	+	4.70291e29i	1.31768	+	0.174512i
$585$	4.97697e30			1.81239
$586$	4.12037e29	−	6.46401e29i	0.147252	−	0.231009i
$587$			2.14924e30i			0.753818i	0.926250	+	0.376909i	$0.123013\pi$
$587$			2.14924e30i			0.753818i	−0.926250	+	0.376909i	$0.876987\pi$
$588$	1.47286e28	−	6.85884e27i	0.00507005	−	0.00236102i
$589$	4.98832e29			0.168533
$590$	−3.10461e30	−	1.97898e30i	−1.02952	−	0.656250i
$591$			2.49403e30i			0.811783i
$592$	−9.95513e29	+	1.18393e30i	−0.318059	+	0.378256i
$593$	5.02543e30			1.57606			0.788028	−	0.615639i	$-0.211102\pi$
$593$	5.02543e30			1.57606			0.788028	+	0.615639i	$0.211102\pi$
$594$	−8.28361e29	+	1.29953e30i	−0.255017	+	0.400069i
$595$		−	3.96801e30i		−	1.19918i
$596$	−4.02950e29	−	8.65294e29i	−0.119548	−	0.256717i
$597$	−5.75634e30			−1.67660
$598$	−4.18405e29	−	2.66705e29i	−0.119642	−	0.0762637i
$599$		−	2.64248e30i		−	0.741852i	−0.928662	−	0.370926i	$-0.879040\pi$
$599$		−	2.64248e30i		−	0.741852i	0.928662	−	0.370926i	$-0.120960\pi$
$600$	−4.43862e29	+	3.35144e30i	−0.122344	+	0.923779i
$601$	−1.06264e30			−0.287586			−0.143793	−	0.989608i	$-0.545930\pi$
$601$	−1.06264e30			−0.287586			−0.143793	+	0.989608i	$0.545930\pi$
$602$	8.84625e29	−	1.38779e30i	0.235070	−	0.368777i
$603$		−	1.19305e31i		−	3.11293i
$604$	−3.43525e30	+	1.59973e30i	−0.880140	+	0.409864i
$605$	−4.57830e30			−1.15185
$606$	1.67829e30	+	1.06979e30i	0.414636	+	0.264302i
$607$		−	1.19158e30i		−	0.289100i	−0.989497	−	0.144550i	$-0.953827\pi$
$607$		−	1.19158e30i		−	0.289100i	0.989497	−	0.144550i	$-0.0461735\pi$
$608$	6.06542e29	−	1.90383e29i	0.144518	−	0.0453617i
$609$	1.08592e31			2.54101
$610$	1.66791e30	−	2.61661e30i	0.383306	−	0.601327i
$611$		−	1.41300e30i		−	0.318926i
$612$	3.74164e30	+	8.03479e30i	0.829462	+	1.78118i
$613$	−3.85606e30			−0.839612			−0.419806	−	0.907614i	$-0.637902\pi$
$613$	−3.85606e30			−0.839612			−0.419806	+	0.907614i	$0.637902\pi$
$614$	9.64684e29	+	6.14921e29i	0.206316	+	0.131513i
$615$			1.56902e31i			3.29611i
$616$	−1.27336e30	−	1.68642e29i	−0.262762	−	0.0348000i
$617$	−4.82474e30			−0.977997			−0.488998	−	0.872285i	$-0.662638\pi$
$617$	−4.82474e30			−0.977997			−0.488998	+	0.872285i	$0.662638\pi$
$618$	2.67726e30	−	4.20006e30i	0.533110	−	0.836339i
$619$			8.42305e30i			1.64768i	0.566824	+	0.823839i	$0.308172\pi$
$619$			8.42305e30i			1.64768i	−0.566824	+	0.823839i	$0.691828\pi$
$620$	6.50408e30	−	3.02882e30i	1.24990	−	0.582056i
$621$	1.86139e30			0.351424
$622$	2.73727e30	+	1.74483e30i	0.507719	+	0.323637i
$623$		−	5.90448e30i		−	1.07600i
$624$	−5.36608e30	−	4.51211e30i	−0.960785	−	0.807884i
$625$	−7.09823e30			−1.24873
$626$	−3.49276e30	+	5.47942e30i	−0.603742	+	0.947147i
$627$		−	4.11929e29i		−	0.0699647i
$628$	2.91027e29	+	6.24950e29i	0.0485710	+	0.104301i
$629$	2.92088e30			0.479023
$630$	−1.31227e31	−	8.36482e30i	−2.11483	−	1.34806i
$631$			3.17567e30i			0.502936i	0.967866	+	0.251468i	$0.0809133\pi$
$631$			3.17567e30i			0.502936i	−0.967866	+	0.251468i	$0.919087\pi$
$632$	1.08497e30	−	8.19220e30i	0.168861	−	1.27501i
$633$	2.60987e30			0.399188
$634$	−5.78936e30	+	9.08231e30i	−0.870259	+	1.36526i
$635$			9.89740e30i			1.46221i
$636$	−9.88824e30	+	4.60476e30i	−1.43579	+	0.668619i
$637$	1.62512e28			0.00231927
$638$	2.33461e30	+	1.48815e30i	0.327481	+	0.208747i
$639$		−	8.31675e30i		−	1.14668i
$640$	6.75249e30	−	6.16515e30i	0.915133	−	0.835534i
$641$	1.26491e31			1.68508			0.842542	−	0.538631i	$-0.181058\pi$
$641$	1.26491e31			1.68508			0.842542	+	0.538631i	$0.181058\pi$
$642$	3.20297e30	−	5.02479e30i	0.419437	−	0.658010i
$643$		−	3.84411e30i		−	0.494852i	−0.968907	−	0.247426i	$-0.920415\pi$
$643$		−	3.84411e30i		−	0.494852i	0.968907	−	0.247426i	$-0.0795848\pi$
$644$	6.54947e29	+	1.40643e30i	0.0828822	+	0.177981i
$645$	7.59126e30			0.944402
$646$	−1.01225e30	−	6.45244e29i	−0.123803	−	0.0789162i
$647$		−	1.20144e31i		−	1.44462i	−0.691569	−	0.722310i	$-0.743080\pi$
$647$		−	1.20144e31i		−	1.44462i	0.691569	−	0.722310i	$-0.256920\pi$
$648$	9.07445e30	+	1.20181e30i	1.07274	+	0.142073i
$649$	2.25045e30			0.261564
$650$	−1.81761e30	+	2.85146e30i	−0.207708	+	0.325851i
$651$			1.72015e31i			1.93275i
$652$	6.88770e30	−	3.20747e30i	0.760940	−	0.354355i
$653$	4.64890e30			0.505016			0.252508	−	0.967595i	$-0.418745\pi$
$653$	4.64890e30			0.505016			0.252508	+	0.967595i	$0.418745\pi$
$654$	−5.67350e30	−	3.61648e30i	−0.606033	−	0.386305i
$655$		−	9.50392e30i		−	0.998271i
$656$	9.52560e30	−	1.13284e31i	0.983898	−	1.17011i
$657$	−2.65268e31			−2.69443
$658$	−2.37484e30	+	3.72564e30i	−0.237219	+	0.372148i
$659$		−	1.56134e30i		−	0.153377i	−0.997055	−	0.0766883i	$-0.975565\pi$
$659$		−	1.56134e30i		−	0.153377i	0.997055	−	0.0766883i	$-0.0244346\pi$
$660$	−2.50116e30	−	5.37098e30i	−0.241634	−	0.518884i
$661$	6.57725e30			0.624925			0.312463	−	0.949930i	$-0.398846\pi$
$661$	6.57725e30			0.624925			0.312463	+	0.949930i	$0.398846\pi$
$662$	−1.07089e31	−	6.82619e30i	−1.00071	−	0.637883i
$663$			1.32387e31i			1.21674i
$664$	−2.78728e30	+	2.10457e31i	−0.251960	+	1.90246i
$665$	2.10767e30			0.187397
$666$	6.15739e30	−	9.65968e30i	0.538493	−	0.844785i
$667$		−	3.34400e30i		−	0.287662i
$668$	−1.18523e31	+	5.51941e30i	−1.00291	+	0.467037i
$669$	−3.55070e31			−2.95547
$670$	1.95977e31	+	1.24922e31i	1.60466	+	1.02286i
$671$			1.89672e30i			0.152776i
$672$	6.56510e30	+	2.09158e31i	0.520211	+	1.65734i
$673$	−3.90846e29			−0.0304677			−0.0152339	−	0.999884i	$-0.504849\pi$
$673$	−3.90846e29			−0.0304677			−0.0152339	+	0.999884i	$0.504849\pi$
$674$	1.14962e30	−	1.80351e30i	0.0881645	−	0.138312i
$675$		−	1.26855e31i		−	0.957121i
$676$	2.72659e30	+	5.85508e30i	0.202398	+	0.434629i
$677$	2.99574e29			0.0218791			0.0109395	−	0.999940i	$-0.496518\pi$
$677$	2.99574e29			0.0218791			0.0109395	+	0.999940i	$0.496518\pi$
$678$	1.59796e31	+	1.01859e31i	1.14826	+	0.731935i
$679$		−	2.68140e31i		−	1.89581i
$680$	−1.71162e31	−	2.26685e30i	−1.19072	−	0.157698i
$681$	3.08696e31			2.11306
$682$	−2.35732e30	+	3.69815e30i	−0.158778	+	0.249090i
$683$			1.95084e31i			1.29298i	0.762921	+	0.646492i	$0.223765\pi$
$683$			1.95084e31i			1.29298i	−0.762921	+	0.646492i	$0.776235\pi$
$684$	−4.26779e30	+	1.98743e30i	−0.278347	+	0.129621i
$685$	1.55807e31			0.999977
$686$	−1.33727e31	−	8.52417e30i	−0.844603	−	0.538377i
$687$			6.29552e29i			0.0391298i
$688$	−5.48095e30	−	4.60869e30i	−0.335261	−	0.281906i
$689$	−1.09104e31			−0.656794
$690$	−3.84660e30	+	6.03452e30i	−0.227896	+	0.357522i
$691$		−	7.57560e30i		−	0.441732i	−0.975304	−	0.220866i	$-0.929112\pi$
$691$		−	7.57560e30i		−	0.441732i	0.975304	−	0.220866i	$-0.0708883\pi$
$692$	2.95334e30	+	6.34198e30i	0.169491	+	0.363964i
$693$	9.51229e30			0.537303
$694$	−2.86179e30	−	1.82420e30i	−0.159105	−	0.101419i
$695$			1.07307e31i			0.587215i
$696$	6.20364e30	−	4.68415e31i	0.334153	−	2.52307i
$697$	−2.79485e31			−1.48183
$698$	7.52275e30	−	1.18016e31i	0.392615	−	0.615932i
$699$		−	1.04515e31i		−	0.536947i
$700$	9.58491e30	−	4.46350e30i	0.484741	−	0.225734i
$701$	1.73956e31			0.866045			0.433022	−	0.901383i	$-0.357447\pi$
$701$	1.73956e31			0.866045			0.433022	+	0.901383i	$0.357447\pi$
$702$	2.21839e31	+	1.41407e31i	1.08725	+	0.693049i
$703$			1.55147e30i			0.0748572i
$704$	−1.45490e30	+	5.39636e30i	−0.0691087	+	0.256331i
$705$	−2.03793e31			−0.953035
$706$	−5.40830e30	+	8.48451e30i	−0.249006	+	0.390638i
$707$		−	6.22456e30i		−	0.282160i
$708$	−1.62140e31	−	3.48178e31i	−0.723641	−	1.55394i
$709$	−1.27965e31			−0.562319			−0.281159	−	0.959661i	$-0.590719\pi$
$709$	−1.27965e31			−0.562319			−0.281159	+	0.959661i	$0.590719\pi$
$710$	1.36616e31	+	8.70832e30i	0.591097	+	0.376784i
$711$			6.11976e31i			2.60717i
$712$	−2.54693e31	−	3.37312e30i	−1.06841	−	0.141499i
$713$	5.29709e30			0.218803
$714$	2.22503e31	−	3.49062e31i	0.905016	−	1.41978i
$715$		−	5.92618e30i		−	0.237361i
$716$	9.90518e30	−	4.61265e30i	0.390678	−	0.181931i
$717$	7.83577e31			3.04348
$718$	−8.77218e30	−	5.59167e30i	−0.335536	−	0.213881i
$719$			1.22766e31i			0.462445i	0.972901	+	0.231222i	$0.0742725\pi$
$719$			1.22766e31i			0.462445i	−0.972901	+	0.231222i	$0.925727\pi$
$720$	−4.35788e31	+	5.18266e31i	−1.61666	+	1.92263i
$721$	−1.55775e31			−0.569128
$722$	−1.45956e31	+	2.28974e31i	−0.525185	+	0.823906i
$723$		−	1.62685e31i		−	0.576535i
$724$	7.36008e30	+	1.58050e31i	0.256897	+	0.551659i
$725$	−2.27896e31			−0.783463
$726$	−4.02748e31	−	2.56725e31i	−1.36374	−	0.869291i
$727$		−	1.95008e31i		−	0.650390i	−0.945647	−	0.325195i	$-0.894570\pi$
$727$		−	1.95008e31i		−	0.650390i	0.945647	−	0.325195i	$-0.105430\pi$
$728$	−2.87885e30	+	2.17372e31i	−0.0945745	+	0.714099i
$729$	2.82969e31			0.915663
$730$	2.77758e31	−	4.35745e31i	0.885350	−	1.38893i
$731$			1.35221e31i			0.424574i
$732$	2.93449e31	−	1.36654e31i	0.907635	−	0.422668i
$733$	−1.57706e31			−0.480512			−0.240256	−	0.970710i	$-0.577231\pi$
$733$	−1.57706e31			−0.480512			−0.240256	+	0.970710i	$0.577231\pi$
$734$	−8.74236e30	−	5.57266e30i	−0.262405	−	0.167265i
$735$		−	2.34385e29i		−	0.00693058i
$736$	6.44086e30	−	2.02168e30i	0.187624	−	0.0588919i
$737$	−1.42059e31			−0.407687
$738$	−5.89172e31	+	9.24289e31i	−1.66580	+	2.61329i
$739$			5.56868e31i			1.55118i	0.631235	+	0.775592i	$0.282548\pi$
$739$			5.56868e31i			1.55118i	−0.631235	+	0.775592i	$0.717452\pi$
$740$	9.42023e30	+	2.02290e31i	0.258531	+	0.555168i
$741$	−7.03193e30			−0.190140
$742$	2.87672e31	+	1.83371e31i	0.766398	+	0.488527i
$743$		−	5.69328e30i		−	0.149446i	−0.997204	−	0.0747232i	$-0.976193\pi$
$743$		−	5.69328e30i		−	0.149446i	0.997204	−	0.0747232i	$-0.0238073\pi$
$744$	7.41996e31	+	9.82692e30i	1.91911	+	0.254165i
$745$	−1.37699e31			−0.350923
$746$	2.38276e31	−	3.73806e31i	0.598347	−	0.938683i
$747$		−	1.57216e32i		−	3.89020i
$748$	9.56718e30	−	4.45525e30i	0.233274	−	0.108631i
$749$	−1.86363e31			−0.447776
$750$	−3.56607e31	−	2.27313e31i	−0.844337	−	0.538208i
$751$		−	1.65979e31i		−	0.387270i	−0.981074	−	0.193635i	$-0.937972\pi$
$751$		−	1.65979e31i		−	0.387270i	0.981074	−	0.193635i	$-0.0620278\pi$
$752$	1.47140e31	+	1.23724e31i	0.338326	+	0.284484i
$753$	−1.16531e32			−2.64057
$754$	2.54039e31	−	3.98534e31i	0.567303	−	0.889982i
$755$			5.46670e31i			1.20312i
$756$	−3.47254e31	−	7.45691e31i	−0.753194	−	1.61741i
$757$	5.52834e31			1.18179			0.590895	−	0.806748i	$-0.298775\pi$
$757$	5.52834e31			1.18179			0.590895	+	0.806748i	$0.298775\pi$
$758$	4.90874e31	+	3.12899e31i	1.03421	+	0.659240i
$759$		−	4.37427e30i		−	0.0908335i
$760$	1.20407e30	−	9.09152e30i	0.0246435	−	0.186075i
$761$	−6.82212e29			−0.0137622			−0.00688110	−	0.999976i	$-0.502190\pi$
$761$	−6.82212e29			−0.0137622			−0.00688110	+	0.999976i	$0.502190\pi$
$762$	−5.54990e31	+	8.70665e31i	−1.10352	+	1.73120i
$763$			2.10423e31i			0.412405i
$764$	1.16168e31	−	5.40972e30i	0.224419	−	0.104508i
$765$	1.27862e32			2.43481
$766$	−5.51447e31	−	3.51511e31i	−1.03511	−	0.659815i
$767$		−	3.84169e31i		−	0.710842i
$768$	9.39717e31	−	1.63701e31i	1.71405	−	0.298592i
$769$	5.03093e31			0.904605			0.452302	−	0.891865i	$-0.350603\pi$
$769$	5.03093e31			0.904605			0.452302	+	0.891865i	$0.350603\pi$
$770$	−9.96016e30	+	1.56254e31i	−0.176550	+	0.276971i
$771$		−	1.21093e31i		−	0.211603i
$772$	2.51144e31	+	5.39306e31i	0.432646	+	0.929063i
$773$	−2.00705e31			−0.340865			−0.170433	−	0.985369i	$-0.554517\pi$
$773$	−2.00705e31			−0.340865			−0.170433	+	0.985369i	$0.554517\pi$
$774$	4.47191e31	+	2.85054e31i	0.748761	+	0.477284i
$775$		−	3.61000e31i		−	0.595921i
$776$	−1.15664e32	−	1.53184e31i	−1.88242	−	0.249306i
$777$	−5.35001e31			−0.858467
$778$	−3.94991e31	+	6.19659e31i	−0.624901	+	0.980341i
$779$		−	1.48452e31i		−	0.231566i
$780$	−9.16866e31	+	4.26967e31i	−1.41015	+	0.656679i
$781$	−9.90292e30			−0.150176
$782$	−1.07491e31	−	6.85184e30i	−0.160731	−	0.102455i
$783$			1.77300e32i			2.61414i
$784$	−1.42297e29	+	1.69228e29i	−0.00206880	+	0.00246034i
$785$	9.94517e30			0.142576
$786$	5.32926e31	−	8.36051e31i	0.753388	−	1.18191i
$787$			9.79608e31i			1.36562i	0.730595	+	0.682811i	$0.239243\pi$
$787$			9.79608e31i			1.36562i	−0.730595	+	0.682811i	$0.760757\pi$
$788$	−1.43279e31	−	3.07676e31i	−0.196967	−	0.422965i
$789$	−1.45155e32			−1.96782
$790$	−1.00527e32	−	6.40790e31i	−1.34395	−	0.856678i
$791$		−	5.92663e31i		−	0.781387i
$792$	5.43420e30	−	4.10317e31i	0.0706576	−	0.533510i
$793$	3.23783e31			0.415192
$794$	7.81242e31	−	1.22561e32i	0.988007	−	1.54998i
$795$			1.57357e32i			1.96267i
$796$	7.10130e31	−	3.30694e31i	0.873562	−	0.406801i
$797$	2.66122e31			0.322878			0.161439	−	0.986883i	$-0.448386\pi$
$797$	2.66122e31			0.322878			0.161439	+	0.986883i	$0.448386\pi$
$798$	1.85409e31	+	1.18186e31i	0.221871	+	0.141428i
$799$		−	3.63011e31i		−	0.428455i
$800$	−1.37779e31	−	4.38949e31i	−0.160395	−	0.511004i
$801$	1.90261e32			2.18470
$802$	−5.86559e30	+	9.20190e30i	−0.0664345	+	0.104222i
$803$			3.15860e31i			0.352878i
$804$	1.02350e32	+	2.19786e32i	1.12790	+	2.42205i
$805$	2.23813e31			0.243293
$806$	6.31301e31	+	4.02412e31i	0.676941	+	0.431505i
$807$		−	2.35696e32i		−	2.49312i
$808$	−2.68499e31	−	3.55598e30i	−0.280168	−	0.0371051i
$809$	5.54943e31			0.571235			0.285617	−	0.958344i	$-0.407801\pi$
$809$	5.54943e31			0.571235			0.285617	+	0.958344i	$0.407801\pi$
$810$	7.09799e31	−	1.11353e32i	0.720776	−	1.13075i
$811$			8.78289e31i			0.879849i	0.898035	+	0.439925i	$0.144995\pi$
$811$			8.78289e31i			0.879849i	−0.898035	+	0.439925i	$0.855005\pi$
$812$	−1.33964e32	+	6.23843e31i	−1.32395	+	0.616536i
$813$	−1.51865e32			−1.48068
$814$	−1.15020e31	−	7.33173e30i	−0.110638	−	0.0705242i
$815$		−	1.09608e32i		−	1.04018i
$816$	−1.37858e32	−	1.15919e32i	−1.29075	−	1.08533i
$817$	−7.18246e30			−0.0663484
$818$	−5.53788e31	+	8.68779e31i	−0.504728	+	0.791814i
$819$		−	1.62382e32i		−	1.46021i
$820$	−9.01378e31	−	1.93562e32i	−0.799751	−	1.71738i
$821$	−1.67649e31			−0.146766			−0.0733832	−	0.997304i	$-0.523380\pi$
$821$	−1.67649e31			−0.146766			−0.0733832	+	0.997304i	$0.523380\pi$
$822$	1.37062e32	+	8.73676e31i	1.18393	+	0.754676i
$823$			1.11241e30i			0.00948129i	0.999989	+	0.00474065i	$0.00150900\pi$
$823$			1.11241e30i			0.00948129i	−0.999989	+	0.00474065i	$0.998491\pi$
$824$	−8.89915e30	+	6.71944e31i	−0.0748427	+	0.565111i
$825$	−2.98109e31			−0.247390
$826$	−6.45674e31	+	1.01293e32i	−0.528729	+	0.829466i
$827$		−	2.30009e32i		−	1.85859i	−0.369338	−	0.929295i	$-0.620416\pi$
$827$		−	2.30009e32i		−	1.85859i	0.369338	−	0.929295i	$-0.379584\pi$
$828$	−4.53197e31	+	2.11045e31i	−0.361371	+	0.168283i
$829$	3.81296e31			0.300028			0.150014	−	0.988684i	$-0.452068\pi$
$829$	3.81296e31			0.300028			0.150014	+	0.988684i	$0.452068\pi$
$830$	2.58253e32	+	1.64619e32i	2.00533	+	1.27826i
$831$			3.73957e32i			2.86557i
$832$	9.21198e31	+	2.48361e31i	0.696621	+	0.187814i
$833$	4.17504e29			0.00311577
$834$	−6.01719e31	+	9.43973e31i	−0.443167	+	0.695237i
$835$			1.88613e32i			1.37095i
$836$	2.36647e30	+	5.08175e30i	0.0169759	+	0.0364539i
$837$	−2.80853e32			−1.98837
$838$	−1.23266e32	−	7.85735e31i	−0.861306	−	0.549025i
$839$		−	8.56056e31i		−	0.590365i	−0.955441	−	0.295183i	$-0.904620\pi$
$839$		−	8.56056e31i		−	0.590365i	0.955441	−	0.295183i	$-0.0953805\pi$
$840$	3.13509e32	+	4.15207e31i	2.13392	+	0.282614i
$841$	1.69667e32			1.13983
$842$	5.49084e31	−	8.61400e31i	0.364088	−	0.571178i
$843$		−	2.59133e32i		−	1.69597i
$844$	−3.21966e31	+	1.49933e31i	−0.207990	+	0.0968569i
$845$	9.31751e31			0.594122
$846$	−1.20052e32	−	7.65250e31i	−0.755606	−	0.481648i
$847$			1.49374e32i			0.928023i
$848$	9.55323e31	−	1.13613e32i	0.585863	−	0.696745i
$849$	−3.22547e32			−1.95258
$850$	−4.66957e31	+	7.32560e31i	−0.279042	+	0.437759i
$851$			1.64750e31i			0.0971852i
$852$	7.13481e31	+	1.53213e32i	0.415477	+	0.892193i
$853$	−1.14707e32			−0.659400			−0.329700	−	0.944086i	$-0.606948\pi$
$853$	−1.14707e32			−0.659400			−0.329700	+	0.944086i	$0.606948\pi$
$854$	−8.53712e31	−	5.44184e31i	−0.484479	−	0.308823i
$855$			6.79157e31i			0.380490i
$856$	−1.06466e31	+	8.03888e31i	−0.0588843	+	0.444615i
$857$	−9.96835e31			−0.544295			−0.272147	−	0.962256i	$-0.587734\pi$
$857$	−9.96835e31			−0.544295			−0.272147	+	0.962256i	$0.587734\pi$
$858$	3.32307e31	−	5.21320e31i	0.179134	−	0.281025i
$859$		−	1.24614e32i		−	0.663199i	−0.943420	−	0.331599i	$-0.892412\pi$
$859$		−	1.24614e32i		−	0.663199i	0.943420	−	0.331599i	$-0.107588\pi$
$860$	−9.36493e31	+	4.36106e31i	−0.492064	+	0.229145i
$861$	5.11918e32			2.65562
$862$	−1.16997e30	−	7.45778e29i	−0.00599233	−	0.00381970i
$863$		−	5.62172e31i		−	0.284283i	−0.989846	−	0.142141i	$-0.954601\pi$
$863$		−	5.62172e31i		−	0.284283i	0.989846	−	0.142141i	$-0.0453988\pi$
$864$	−3.41495e32	+	1.07190e32i	−1.70504	+	0.535182i
$865$	1.00923e32			0.497525
$866$	9.92591e31	−	1.55717e32i	0.483141	−	0.757948i
$867$		−	2.19021e31i		−	0.105263i
$868$	−9.88202e31	−	2.12206e32i	−0.468952	−	1.00703i
$869$	7.28692e31			0.341450
$870$	−5.74793e32	−	3.66392e32i	−2.65950	−	1.69525i
$871$			2.42505e32i			1.10795i
$872$	9.07672e31	+	1.20211e31i	0.409494	+	0.0542330i
$873$	8.64033e32			3.84923
$874$	3.63945e30	−	5.70955e30i	0.0160107	−	0.0251175i
$875$			1.32261e32i			0.574571i
$876$	4.88682e32	−	2.27569e32i	2.09643	−	0.976268i
$877$	−3.81151e32			−1.61474			−0.807369	−	0.590047i	$-0.799109\pi$
$877$	−3.81151e32			−1.61474			−0.807369	+	0.590047i	$0.799109\pi$
$878$	2.71330e32	+	1.72955e32i	1.13516	+	0.723591i
$879$		−	1.15362e32i		−	0.476634i
$880$	6.17110e31	+	5.18902e31i	0.251799	+	0.211727i
$881$	−3.96579e32			−1.59807			−0.799033	−	0.601287i	$-0.794655\pi$
$881$	−3.96579e32			−1.59807			−0.799033	+	0.601287i	$0.794655\pi$
$882$	8.80125e29	−	1.38073e30i	0.00350259	−	0.00549485i
$883$		−	2.86427e32i		−	1.12576i	−0.826538	−	0.562881i	$-0.809693\pi$
$883$		−	2.86427e32i		−	1.12576i	0.826538	−	0.562881i	$-0.190307\pi$
$884$	−7.60544e31	−	1.63319e32i	−0.295223	−	0.633959i
$885$	−5.54074e32			−2.12418
$886$	1.26496e31	+	8.06326e30i	0.0478967	+	0.0305309i
$887$			4.60675e32i			1.72280i	0.507929	+	0.861399i	$0.330411\pi$
$887$			4.60675e32i			1.72280i	−0.507929	+	0.861399i	$0.669589\pi$
$888$	−3.05637e31	+	2.30776e32i	−0.112892	+	0.852407i
$889$	3.22919e32			1.17808
$890$	−1.99219e32	+	3.12534e32i	−0.717862	+	1.12618i
$891$			8.07169e31i			0.287283i
$892$	4.38032e32	−	2.03983e32i	1.53990	−	0.717100i
$893$	1.92818e31			0.0669549
$894$	−1.21132e32	−	7.72137e31i	−0.415478	−	0.264839i
$895$		−	1.57627e32i		−	0.534043i
$896$	−2.01148e32	−	2.20311e32i	−0.673175	−	0.737307i
$897$	−7.46720e31			−0.246854
$898$	9.93097e31	−	1.55796e32i	0.324304	−	0.508765i
$899$			5.04553e32i			1.62761i
$900$	1.43828e32	+	3.08856e32i	0.458329	+	0.984213i
$901$	−2.80296e32			−0.882356
$902$	1.10057e32	+	7.01539e31i	0.342252	+	0.218162i
$903$		−	2.47677e32i		−	0.760888i
$904$	−2.55648e32	−	3.38578e31i	−0.775871	−	0.102756i
$905$	2.51514e32			0.754097
$906$	−3.06541e32	+	4.80900e32i	−0.907985	+	1.42444i
$907$			8.61347e31i			0.252057i	0.992027	+	0.126028i	$0.0402230\pi$
$907$			8.61347e31i			0.252057i	−0.992027	+	0.126028i	$0.959777\pi$
$908$	−3.80822e32	+	1.77341e32i	−1.10098	+	0.512703i
$909$	2.00575e32			0.572894
$910$	2.66738e32	+	1.70027e32i	0.752712	+	0.479803i
$911$		−	2.04125e32i		−	0.569107i	−0.958660	−	0.284553i	$-0.908155\pi$
$911$		−	2.04125e32i		−	0.569107i	0.958660	−	0.284553i	$-0.0918453\pi$
$912$	6.15722e31	−	7.32255e31i	0.169606	−	0.201706i
$913$	−1.87201e32			−0.509482
$914$	−1.22342e32	+	1.91929e32i	−0.328978	+	0.516098i
$915$		−	4.66982e32i		−	1.24070i
$916$	−3.61668e30	−	7.76645e30i	−0.00949424	−	0.0203879i
$917$	−3.10081e32			−0.804289
$918$	5.69920e32	+	3.63286e32i	1.46064	+	0.931062i
$919$		−	6.73645e32i		−	1.70593i	−0.521969	−	0.852964i	$-0.674803\pi$
$919$		−	6.73645e32i		−	1.70593i	0.521969	−	0.852964i	$-0.325197\pi$
$920$	1.27860e31	−	9.65428e31i	0.0319941	−	0.241576i
$921$	1.72166e32			0.425687
$922$	1.81811e32	−	2.85224e32i	0.444201	−	0.696860i
$923$			1.69050e32i			0.408128i
$924$	−1.75237e32	+	8.16045e31i	−0.418056	+	0.194680i
$925$	1.12278e32			0.264689
$926$	−4.99316e32	−	3.18280e32i	−1.16320	−	0.741461i
$927$		−	5.01957e32i		−	1.15555i
$928$	1.92567e32	+	6.13498e32i	0.438080	+	1.39568i
$929$	−2.04352e32			−0.459415			−0.229708	−	0.973260i	$-0.573777\pi$
$929$	−2.04352e32			−0.459415			−0.229708	+	0.973260i	$0.573777\pi$
$930$	5.80386e32	−	9.10505e32i	1.28945	−	2.02288i
$931$			2.21763e29i			0.000486904i
$932$	6.00425e31	+	1.28935e32i	0.130282	+	0.279767i
$933$	4.88516e32			1.04756
$934$	4.69038e32	+	2.98980e32i	0.994014	+	0.633617i
$935$		−	1.52248e32i		−	0.318877i
$936$	−7.00442e32	−	9.27658e31i	−1.44990	−	0.192023i
$937$	−7.88652e31			−0.161343			−0.0806715	−	0.996741i	$-0.525706\pi$
$937$	−7.88652e31			−0.161343			−0.0806715	+	0.996741i	$0.525706\pi$
$938$	4.07580e32	−	6.39408e32i	0.824103	−	1.29285i
$939$			9.77904e32i			1.95422i
$940$	2.51409e32	−	1.17076e32i	0.496562	−	0.231239i
$941$	3.09258e31			0.0603719			0.0301860	−	0.999544i	$-0.490390\pi$
$941$	3.09258e31			0.0603719			0.0301860	+	0.999544i	$0.490390\pi$
$942$	8.74867e31	+	5.57669e31i	0.168804	+	0.107601i
$943$		−	1.57642e32i		−	0.300637i
$944$	4.00046e32	+	3.36382e32i	0.754081	+	0.634075i
$945$	−1.18666e33			−2.21094
$946$	3.39420e31	−	5.32480e31i	0.0625079	−	0.0980620i
$947$			1.85469e32i			0.337614i	0.985649	+	0.168807i	$0.0539915\pi$
$947$			1.85469e32i			0.337614i	−0.985649	+	0.168807i	$0.946009\pi$
$948$	−5.25005e32	−	1.12739e33i	−0.944651	−	2.02854i
$949$	5.39197e32			0.959001
$950$	−3.89110e31	−	2.48031e31i	−0.0684088	−	0.0436060i
$951$			1.62090e33i			2.81690i
$952$	−7.39598e31	+	5.58444e32i	−0.127054	+	0.959342i
$953$	5.98563e31			0.101645			0.0508227	−	0.998708i	$-0.483816\pi$
$953$	5.98563e31			0.101645			0.0508227	+	0.998708i	$0.483816\pi$
$954$	−5.90881e32	+	9.26971e32i	−0.991901	+	1.55609i
$955$		−	1.84865e32i		−	0.306773i
$956$	−9.66657e32	+	4.50153e32i	−1.58575	+	0.738455i
$957$	4.16653e32			0.675684
$958$	−1.02690e33	−	6.54580e32i	−1.64629	−	1.04940i
$959$		−	5.08345e32i		−	0.805664i
$960$	3.58204e32	−	1.32861e33i	0.561237	−	2.08169i
$961$	−1.53649e32			−0.237998
$962$	−1.25158e32	+	1.96347e32i	−0.191661	+	0.300676i
$963$		−	6.00523e32i		−	0.909160i
$964$	9.34600e31	+	2.00696e32i	0.139887	+	0.300393i
$965$	8.58228e32			1.27000
$966$	1.96886e32	+	1.25502e32i	0.288049	+	0.183612i
$967$			2.70972e32i			0.391953i	0.980609	+	0.195976i	$0.0627876\pi$
$967$			2.70972e32i			0.391953i	−0.980609	+	0.195976i	$0.937212\pi$
$968$	6.44334e32	+	8.53349e31i	0.921472	+	0.122039i
$969$	−1.80655e32			−0.255440
$970$	−9.04714e32	+	1.41931e33i	−1.26480	+	1.98421i
$971$			2.51375e32i			0.347465i	0.984793	+	0.173733i	$0.0555828\pi$
$971$			2.51375e32i			0.347465i	−0.984793	+	0.173733i	$0.944417\pi$
$972$	6.34553e31	−	2.95499e31i	0.0867239	−	0.0403856i
$973$	3.50108e32			0.473108
$974$	6.91529e32	+	4.40803e32i	0.923978	+	0.588974i
$975$			5.08894e32i			0.672321i
$976$	−2.83508e32	+	3.37165e32i	−0.370354	+	0.440448i
$977$	1.27159e33			1.64250			0.821250	−	0.570568i	$-0.193277\pi$
$977$	1.27159e33			1.64250			0.821250	+	0.570568i	$0.193277\pi$
$978$	6.14618e32	−	9.64209e32i	0.785015	−	1.23153i
$979$		−	2.26548e32i		−	0.286121i
$980$	1.34651e30	+	2.89149e30i	0.00168160	+	0.00361106i
$981$	−6.78052e32			−0.837343
$982$	2.57493e32	+	1.64135e32i	0.314441	+	0.200435i
$983$			7.15765e32i			0.864334i	0.901794	+	0.432167i	$0.142251\pi$
$983$			7.15765e32i			0.864334i	−0.901794	+	0.432167i	$0.857749\pi$
$984$	2.92450e32	−	2.20818e33i	0.349225	−	2.63687i
$985$	−4.89621e32			−0.578178
$986$	6.52644e32	−	1.02386e33i	0.762132	−	1.19563i
$987$			6.64908e32i			0.767844i
$988$	8.67492e31	−	4.03974e31i	0.0990693	−	0.0461346i
$989$	−7.62705e31			−0.0861385
$990$	−5.03501e32	−	3.20948e32i	−0.562359	−	0.358466i
$991$		−	1.49459e33i		−	1.65087i	−0.564496	−	0.825436i	$-0.690929\pi$
$991$		−	1.49459e33i		−	1.65087i	0.564496	−	0.825436i	$-0.309071\pi$
$992$	−9.71816e32	+	3.05036e32i	−1.06159	+	0.333214i
$993$	−1.91120e33			−2.06473
$994$	2.84123e32	−	4.45731e32i	0.303568	−	0.476236i
$995$		−	1.13007e33i		−	1.19413i
$996$	1.34874e33	+	2.89627e33i	1.40953	+	3.02682i
$997$	−1.87106e33			−1.93393			−0.966964	−	0.254912i	$-0.917953\pi$
$997$	−1.87106e33			−1.93393			−0.966964	+	0.254912i	$0.917953\pi$
$998$	−1.58723e33	−	1.01175e33i	−1.62258	−	1.03428i
$999$		−	8.73507e32i		−	0.883173i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.23.b.a.3.4	yes	10
3.2	odd	2		36.23.d.c.19.7		10
4.3	odd	2	inner	4.23.b.a.3.3	✓	10
8.3	odd	2		64.23.c.e.63.10		10
8.5	even	2		64.23.c.e.63.1		10
12.11	even	2		36.23.d.c.19.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.23.b.a.3.3	✓	10	4.3	odd	2	inner
4.23.b.a.3.4	yes	10	1.1	even	1	trivial
36.23.d.c.19.7		10	3.2	odd	2
36.23.d.c.19.8		10	12.11	even	2
64.23.c.e.63.1		10	8.5	even	2
64.23.c.e.63.10		10	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 23 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1100.83 + 1726.98i) q^{2} +308212. i q^{3} +(-1.77063e6 - 3.80224e6i) q^{4} -6.05072e7 q^{5} +(-5.32276e8 - 3.39290e8i) q^{6} +1.97415e9i q^{7} +(8.51558e9 + 1.12779e9i) q^{8} -6.36133e10 q^{9} +O(q^{10})\)	\(q+(-1100.83 + 1726.98i) q^{2} +308212. i q^{3} +(-1.77063e6 - 3.80224e6i) q^{4} -6.05072e7 q^{5} +(-5.32276e8 - 3.39290e8i) q^{6} +1.97415e9i q^{7} +(8.51558e9 + 1.12779e9i) q^{8} -6.36133e10 q^{9} +(6.66084e10 - 1.04495e11i) q^{10} +7.57457e10i q^{11} +(1.17190e12 - 5.45729e11i) q^{12} +1.29303e12 q^{13} +(-3.40931e12 - 2.17321e12i) q^{14} -1.86490e13i q^{15} +(-1.13219e13 + 1.34647e13i) q^{16} +3.32190e13 q^{17} +(7.00277e13 - 1.09859e14i) q^{18} +1.76447e13i q^{19} +(1.07136e14 + 2.30063e14i) q^{20} -6.08455e14 q^{21} +(-1.30811e14 - 8.33835e13i) q^{22} +1.87369e14i q^{23} +(-3.47599e14 + 2.62460e15i) q^{24} +1.27693e15 q^{25} +(-1.42342e15 + 2.23305e15i) q^{26} -9.93436e15i q^{27} +(7.50618e15 - 3.49548e15i) q^{28} -1.78471e16 q^{29} +(3.22065e16 + 2.05295e16i) q^{30} -2.82708e16i q^{31} +(-1.07898e16 - 3.43752e16i) q^{32} -2.33457e16 q^{33} +(-3.65686e16 + 5.73686e16i) q^{34} -1.19450e17i q^{35} +(1.12636e17 + 2.41873e17i) q^{36} +8.79279e16 q^{37} +(-3.04722e16 - 1.94239e16i) q^{38} +3.98528e17i q^{39} +(-5.15254e17 - 6.82397e16i) q^{40} -8.41341e17 q^{41} +(6.69808e17 - 1.05079e18i) q^{42} +4.07059e17i q^{43} +(2.88003e17 - 1.34118e17i) q^{44} +3.84906e18 q^{45} +(-3.23584e17 - 2.06263e17i) q^{46} -1.09278e18i q^{47} +(-4.14999e18 - 3.48955e18i) q^{48} +1.25682e16 q^{49} +(-1.40569e18 + 2.20524e18i) q^{50} +1.02385e19i q^{51} +(-2.28949e18 - 4.91643e18i) q^{52} -8.43782e18 q^{53} +(1.71565e19 + 1.09361e19i) q^{54} -4.58316e18i q^{55} +(-2.22643e18 + 1.68110e19i) q^{56} -5.43831e18 q^{57} +(1.96467e19 - 3.08216e19i) q^{58} -2.97106e19i q^{59} +(-7.09081e19 + 3.30205e19i) q^{60} +2.50406e19 q^{61} +(4.88232e19 + 3.11215e19i) q^{62} -1.25582e20i q^{63} +(7.12431e19 + 1.92076e19i) q^{64} -7.82379e19 q^{65} +(2.56997e19 - 4.03176e19i) q^{66} +1.87547e20i q^{67} +(-5.88185e19 - 1.26307e20i) q^{68} -5.77494e19 q^{69} +(2.06288e20 + 1.31495e20i) q^{70} +1.30739e20i q^{71} +(-5.41704e20 - 7.17427e19i) q^{72} +4.17001e20 q^{73} +(-9.67941e19 + 1.51850e20i) q^{74} +3.93566e20i q^{75} +(6.70896e19 - 3.12423e19i) q^{76} -1.49533e20 q^{77} +(-6.88251e20 - 4.38714e20i) q^{78} -9.62025e20i q^{79} +(6.85058e20 - 8.14713e20i) q^{80} +1.06563e21 q^{81} +(9.26177e20 - 1.45298e21i) q^{82} +2.47144e21i q^{83} +(1.07735e21 + 2.31349e21i) q^{84} -2.00999e21 q^{85} +(-7.02984e20 - 4.48105e20i) q^{86} -5.50069e21i q^{87} +(-8.54255e19 + 6.45018e20i) q^{88} -2.99090e21 q^{89} +(-4.23718e21 + 6.64726e21i) q^{90} +2.55264e21i q^{91} +(7.12424e20 - 3.31762e20i) q^{92} +8.71340e21 q^{93} +(1.88721e21 + 1.20297e21i) q^{94} -1.06763e21i q^{95} +(1.05948e22 - 3.32554e21i) q^{96} -1.35826e22 q^{97} +(-1.38355e19 + 2.17051e19i) q^{98} -4.81843e21i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 1540 q^{2} + 2264464 q^{4} - 17091100 q^{5} - 791935776 q^{6} + 9804431680 q^{8} - 104309613702 q^{9}+O(q^{10}) \) 10 * q + 1540 * q^2 + 2264464 * q^4 - 17091100 * q^5 - 791935776 * q^6 + 9804431680 * q^8 - 104309613702 * q^9	\( 10 q + 1540 q^{2} + 2264464 q^{4} - 17091100 q^{5} - 791935776 q^{6} + 9804431680 q^{8} - 104309613702 q^{9} + 159414035240 q^{10} + 519021175680 q^{12} - 531230356540 q^{13} - 5894008940736 q^{14} - 27717620084480 q^{16} + 14058178115540 q^{17} + 16283956279140 q^{18} + 233643631625120 q^{20} - 313135665760512 q^{21} + 120589650366240 q^{22} - 20\!\cdots\!36 q^{24}+ \cdots - 23\!\cdots\!20 q^{98}+O(q^{100}) \) 10 * q + 1540 * q^2 + 2264464 * q^4 - 17091100 * q^5 - 791935776 * q^6 + 9804431680 * q^8 - 104309613702 * q^9 + 159414035240 * q^10 + 519021175680 * q^12 - 531230356540 * q^13 - 5894008940736 * q^14 - 27717620084480 * q^16 + 14058178115540 * q^17 + 16283956279140 * q^18 + 233643631625120 * q^20 - 313135665760512 * q^21 + 120589650366240 * q^22 - 2007619616180736 * q^24 + 7710175817606670 * q^25 - 3953973318046744 * q^26 + 1177952265288960 * q^28 - 14464474185570172 * q^29 + 10252783730669760 * q^30 - 73831192092953600 * q^32 + 72906957628179840 * q^33 - 26625976920357496 * q^34 - 36609276067793136 * q^36 + 324587767823538020 * q^37 + 369140808808591200 * q^38 - 1158049295468479360 * q^40 - 1355457345814233100 * q^41 + 2644455724909770240 * q^42 - 1919761520625210240 * q^44 + 9367295763131460 * q^45 + 6132624002565203904 * q^46 - 18374169355003791360 * q^48 + 183553700661552298 * q^49 + 29084394113996178540 * q^50 - 38492433127521128800 * q^52 - 11424344766226018780 * q^53 + 79182840955393027008 * q^54 - 102844865827678657536 * q^56 + 30188516183231506560 * q^57 + 173059696836432320360 * q^58 - 377769459746631548160 * q^60 + 58241718146183220740 * q^61 + 317897221476923285760 * q^62 - 412080172429987966976 * q^64 - 121531695066047433560 * q^65 + 700585278654050000640 * q^66 - 667890522330713878240 * q^68 + 54497497397908094208 * q^69 + 1014396282552321513600 * q^70 - 1244773253376491901120 * q^72 + 83030422224875883380 * q^73 + 801906083011176262184 * q^74 + 286747421140990627200 * q^76 - 704201825495570814720 * q^77 - 964412732782594923840 * q^78 + 1509611955050789726720 * q^80 + 251577744224553978858 * q^81 - 2389572513290905036600 * q^82 + 6185640644326191863808 * q^84 - 1796890366112110859960 * q^85 - 8221838255181360278496 * q^86 + 11178210842814940531200 * q^88 + 3420669206528505615668 * q^89 - 24782809563337507735320 * q^90 + 21476264197983864733440 * q^92 + 15493754050318100597760 * q^93 - 20874543047091388369536 * q^94 + 29250284502468708163584 * q^96 - 20429910746446196146540 * q^97 - 23110416876469762175420 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more