LMFDB - Embedded newform 36.23.d.c.19.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,23,Mod(19,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("36.19");

S:= CuspForms(chi, 23);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 23 $
Character orbit:	$[\chi]$	$=$	36.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:	$110.414676543$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{90}\cdot 3^{16} $
Twist minimal:	no (minimal twist has level 4)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.7
Root			$-313.209 - 431.746i$ of defining polynomial
Character	$\chi$	$=$	36.19
Dual form			36.23.d.c.19.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1100.83 - 1726.98i) q^{2} +(-1.77063e6 - 3.80224e6i) q^{4} +6.05072e7 q^{5} +1.97415e9i q^{7} +(-8.51558e9 - 1.12779e9i) q^{8} +O(q^{10})$	\(q+(1100.83 - 1726.98i) q^{2} +(-1.77063e6 - 3.80224e6i) q^{4} +6.05072e7 q^{5} +1.97415e9i q^{7} +(-8.51558e9 - 1.12779e9i) q^{8} +(6.66084e10 - 1.04495e11i) q^{10} -7.57457e10i q^{11} +1.29303e12 q^{13} +(3.40931e12 + 2.17321e12i) q^{14} +(-1.13219e13 + 1.34647e13i) q^{16} -3.32190e13 q^{17} +1.76447e13i q^{19} +(-1.07136e14 - 2.30063e14i) q^{20} +(-1.30811e14 - 8.33835e13i) q^{22} -1.87369e14i q^{23} +1.27693e15 q^{25} +(1.42342e15 - 2.23305e15i) q^{26} +(7.50618e15 - 3.49548e15i) q^{28} +1.78471e16 q^{29} -2.82708e16i q^{31} +(1.07898e16 + 3.43752e16i) q^{32} +(-3.65686e16 + 5.73686e16i) q^{34} +1.19450e17i q^{35} +8.79279e16 q^{37} +(3.04722e16 + 1.94239e16i) q^{38} +(-5.15254e17 - 6.82397e16i) q^{40} +8.41341e17 q^{41} +4.07059e17i q^{43} +(-2.88003e17 + 1.34118e17i) q^{44} +(-3.23584e17 - 2.06263e17i) q^{46} +1.09278e18i q^{47} +1.25682e16 q^{49} +(1.40569e18 - 2.20524e18i) q^{50} +(-2.28949e18 - 4.91643e18i) q^{52} +8.43782e18 q^{53} -4.58316e18i q^{55} +(2.22643e18 - 1.68110e19i) q^{56} +(1.96467e19 - 3.08216e19i) q^{58} +2.97106e19i q^{59} +2.50406e19 q^{61} +(-4.88232e19 - 3.11215e19i) q^{62} +(7.12431e19 + 1.92076e19i) q^{64} +7.82379e19 q^{65} +1.87547e20i q^{67} +(5.88185e19 + 1.26307e20i) q^{68} +(2.06288e20 + 1.31495e20i) q^{70} -1.30739e20i q^{71} +4.17001e20 q^{73} +(9.67941e19 - 1.51850e20i) q^{74} +(6.70896e19 - 3.12423e19i) q^{76} +1.49533e20 q^{77} -9.62025e20i q^{79} +(-6.85058e20 + 8.14713e20i) q^{80} +(9.26177e20 - 1.45298e21i) q^{82} -2.47144e21i q^{83} -2.00999e21 q^{85} +(7.02984e20 + 4.48105e20i) q^{86} +(-8.54255e19 + 6.45018e20i) q^{88} +2.99090e21 q^{89} +2.55264e21i q^{91} +(-7.12424e20 + 3.31762e20i) q^{92} +(1.88721e21 + 1.20297e21i) q^{94} +1.06763e21i q^{95} -1.35826e22 q^{97} +(1.38355e19 - 2.17051e19i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 1540 q^{2} + 2264464 q^{4} + 17091100 q^{5} - 9804431680 q^{8}+O(q^{10}) $ 10 * q - 1540 * q^2 + 2264464 * q^4 + 17091100 * q^5 - 9804431680 * q^8	$ 10 q - 1540 q^{2} + 2264464 q^{4} + 17091100 q^{5} - 9804431680 q^{8} + 159414035240 q^{10} - 531230356540 q^{13} + 5894008940736 q^{14} - 27717620084480 q^{16} - 14058178115540 q^{17} - 233643631625120 q^{20} + 120589650366240 q^{22} + 77\!\cdots\!70 q^{25}+ \cdots + 23\!\cdots\!20 q^{98}+O(q^{100}) $ 10 * q - 1540 * q^2 + 2264464 * q^4 + 17091100 * q^5 - 9804431680 * q^8 + 159414035240 * q^10 - 531230356540 * q^13 + 5894008940736 * q^14 - 27717620084480 * q^16 - 14058178115540 * q^17 - 233643631625120 * q^20 + 120589650366240 * q^22 + 7710175817606670 * q^25 + 3953973318046744 * q^26 + 1177952265288960 * q^28 + 14464474185570172 * q^29 + 73831192092953600 * q^32 - 26625976920357496 * q^34 + 324587767823538020 * q^37 - 369140808808591200 * q^38 - 1158049295468479360 * q^40 + 1355457345814233100 * q^41 + 1919761520625210240 * q^44 + 6132624002565203904 * q^46 + 183553700661552298 * q^49 - 29084394113996178540 * q^50 - 38492433127521128800 * q^52 + 11424344766226018780 * q^53 + 102844865827678657536 * q^56 + 173059696836432320360 * q^58 + 58241718146183220740 * q^61 - 317897221476923285760 * q^62 - 412080172429987966976 * q^64 + 121531695066047433560 * q^65 + 667890522330713878240 * q^68 + 1014396282552321513600 * q^70 + 83030422224875883380 * q^73 - 801906083011176262184 * q^74 + 286747421140990627200 * q^76 + 704201825495570814720 * q^77 - 1509611955050789726720 * q^80 - 2389572513290905036600 * q^82 - 1796890366112110859960 * q^85 + 8221838255181360278496 * q^86 + 11178210842814940531200 * q^88 - 3420669206528505615668 * q^89 - 21476264197983864733440 * q^92 - 20874543047091388369536 * q^94 - 20429910746446196146540 * q^97 + 23110416876469762175420 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$1$

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 $

$2$	1100.83	−	1726.98i	0.537517	−	0.843253i
$2$	1100.83	−	1726.98i	0.537517	−	0.843253i
$3$		0			0
$3$		0			0
$4$	−1.77063e6	−	3.80224e6i	−0.422151	−	0.906525i
$5$	6.05072e7			1.23919			0.619594	−	0.784923i	$-0.287297\pi$
$5$	6.05072e7			1.23919			0.619594	+	0.784923i	$0.287297\pi$
$6$		0			0
$7$			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
$9$		0			0
$10$	6.66084e10	−	1.04495e11i	0.666084	−	1.04495i
$11$		−	7.57457e10i		−	0.265484i	−0.991151	−	0.132742i	$-0.957622\pi$
$11$		−	7.57457e10i		−	0.265484i	0.991151	−	0.132742i	$-0.0423782\pi$
$12$		0			0
$13$	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
$15$		0			0
$16$	−1.13219e13	+	1.34647e13i	−0.643577	+	0.765382i
$17$	−3.32190e13			−0.969278			−0.484639	−	0.874714i	$-0.661049\pi$
$17$	−3.32190e13			−0.969278			−0.484639	+	0.874714i	$0.661049\pi$
$18$		0			0
$19$			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
$21$		0			0
$22$	−1.30811e14	−	8.33835e13i	−0.223870	−	0.142702i
$23$		−	1.87369e14i		−	0.196649i	−0.995154	−	0.0983247i	$-0.968652\pi$
$23$		−	1.87369e14i		−	0.196649i	0.995154	−	0.0983247i	$-0.0313484\pi$
$24$		0			0
$25$	1.27693e15			0.535585
$26$	1.42342e15	−	2.23305e15i	0.387816	−	0.608403i
$27$		0			0
$28$	7.50618e15	−	3.49548e15i	0.905067	−	0.421472i
$29$	1.78471e16			1.46282			0.731408	−	0.681940i	$-0.238863\pi$
$29$	1.78471e16			1.46282			0.731408	+	0.681940i	$0.238863\pi$
$30$		0			0
$31$		−	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
$33$		0			0
$34$	−3.65686e16	+	5.73686e16i	−0.521003	+	0.817346i
$35$			1.19450e17i			1.23719i
$36$		0			0
$37$	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
$39$		0			0
$40$	−5.15254e17	−	6.82397e16i	−1.22846	−	0.162696i
$41$	8.41341e17			1.52880			0.764398	−	0.644744i	$-0.223036\pi$
$41$	8.41341e17			1.52880			0.764398	+	0.644744i	$0.223036\pi$
$42$		0			0
$43$			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
$45$		0			0
$46$	−3.23584e17	−	2.06263e17i	−0.165825	−	0.105702i
$47$			1.09278e18i			0.442035i	0.975270	+	0.221018i	$0.0709378\pi$
$47$			1.09278e18i			0.442035i	−0.975270	+	0.221018i	$0.929062\pi$
$48$		0			0
$49$	1.25682e16			0.00321453
$50$	1.40569e18	−	2.20524e18i	0.287886	−	0.451634i
$51$		0			0
$52$	−2.28949e18	−	4.91643e18i	−0.304580	−	0.654053i
$53$	8.43782e18			0.910323			0.455162	−	0.890409i	$-0.349581\pi$
$53$	8.43782e18			0.910323			0.455162	+	0.890409i	$0.349581\pi$
$54$		0			0
$55$		−	4.58316e18i		−	0.328984i
$56$	2.22643e18	−	1.68110e19i	0.131081	−	0.989749i
$57$		0			0
$58$	1.96467e19	−	3.08216e19i	0.786289	−	1.23352i
$59$			2.97106e19i			0.985235i	0.870246	+	0.492618i	$0.163960\pi$
$59$			2.97106e19i			0.985235i	−0.870246	+	0.492618i	$0.836040\pi$
$60$		0			0
$61$	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
$63$		0			0
$64$	7.12431e19	+	1.92076e19i	0.965525	+	0.260312i
$65$	7.82379e19			0.894067
$66$		0			0
$67$			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
$69$		0			0
$70$	2.06288e20	+	1.31495e20i	1.04327	+	0.665013i
$71$		−	1.30739e20i		−	0.565671i	−0.959168	−	0.282835i	$-0.908725\pi$
$71$		−	1.30739e20i		−	0.565671i	0.959168	−	0.282835i	$-0.0912750\pi$
$72$		0			0
$73$	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
$75$		0			0
$76$	6.70896e19	−	3.12423e19i	0.137311	−	0.0639431i
$77$	1.49533e20			0.265057
$78$		0			0
$79$		−	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
$81$		0			0
$82$	9.26177e20	−	1.45298e21i	0.821754	−	1.28916i
$83$		−	2.47144e21i		−	1.91907i	−0.281588	−	0.959535i	$-0.590861\pi$
$83$		−	2.47144e21i		−	1.91907i	0.281588	−	0.959535i	$-0.409139\pi$
$84$		0			0
$85$	−2.00999e21			−1.20112
$86$	7.02984e20	+	4.48105e20i	0.369371	+	0.235449i
$87$		0			0
$88$	−8.54255e19	+	6.45018e20i	−0.0348561	+	0.263186i
$89$	2.99090e21			1.07774			0.538868	−	0.842391i	$-0.318852\pi$
$89$	2.99090e21			1.07774			0.538868	+	0.842391i	$0.318852\pi$
$90$		0			0
$91$			2.55264e21i			0.720334i
$92$	−7.12424e20	+	3.31762e20i	−0.178268	+	0.0830158i
$93$		0			0
$94$	1.88721e21	+	1.20297e21i	0.372747	+	0.237601i
$95$			1.06763e21i			0.187699i
$96$		0			0
$97$	−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
$99$		0			0
$100$	−2.26098e21	−	4.85522e21i	−0.226098	−	0.485522i
$101$	3.15304e21			0.282614			0.141307	−	0.989966i	$-0.454870\pi$
$101$	3.15304e21			0.282614			0.141307	+	0.989966i	$0.454870\pi$
$102$		0			0
$103$			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
$105$		0			0
$106$	9.28864e21	−	1.45720e22i	0.489314	−	0.767633i
$107$		−	9.44020e21i		−	0.448497i	−0.974532	−	0.224249i	$-0.928007\pi$
$107$		−	9.44020e21i		−	0.448497i	0.974532	−	0.224249i	$-0.0719928\pi$
$108$		0			0
$109$	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
$111$		0			0
$112$	−2.65814e22	−	2.23511e22i	−0.764150	−	0.642542i
$113$	3.00212e22			0.782646			0.391323	−	0.920253i	$-0.372017\pi$
$113$	3.00212e22			0.782646			0.391323	+	0.920253i	$0.372017\pi$
$114$		0			0
$115$		−	1.13372e22i		−	0.243685i
$116$	−3.16006e22	−	6.78591e22i	−0.617530	−	1.32608i
$117$		0			0
$118$	5.13098e22	+	3.27065e22i	0.830803	+	0.529581i
$119$		−	6.55791e22i		−	0.967719i
$120$		0			0
$121$	7.56653e22			0.929518
$122$	2.75655e22	−	4.32446e22i	0.309320	−	0.485260i
$123$		0			0
$124$	−1.07493e23	+	5.00572e22i	−1.00865	+	0.469708i
$125$	−6.69967e22			−0.575497
$126$		0			0
$127$		−	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
$129$		0			0
$130$	8.61270e22	−	1.35115e23i	0.480576	−	0.753925i
$131$		−	1.57071e23i		−	0.805585i	−0.915291	−	0.402793i	$-0.868040\pi$
$131$		−	1.57071e23i		−	0.805585i	0.915291	−	0.402793i	$-0.131960\pi$
$132$		0			0
$133$	−3.48333e22			−0.151226
$134$	3.23891e23	+	2.06459e23i	1.29493	+	0.825431i
$135$		0			0
$136$	2.82879e23	+	3.74642e22i	0.960887	+	0.127259i
$137$	2.57501e23			0.806962			0.403481	−	0.914988i	$-0.367800\pi$
$137$	2.57501e23			0.806962			0.403481	+	0.914988i	$0.367800\pi$
$138$		0			0
$139$		−	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
$141$		0			0
$142$	−2.25784e23	−	1.43922e23i	−0.477003	−	0.304058i
$143$		−	9.79418e22i		−	0.191545i
$144$		0			0
$145$	1.07988e24			1.81270
$146$	4.59049e23	−	7.20153e23i	0.714460	−	1.12084i
$147$		0			0
$148$	−1.55688e23	−	3.34323e23i	−0.208629	−	0.448010i
$149$	−2.27575e23			−0.283188			−0.141594	−	0.989925i	$-0.545223\pi$
$149$	−2.27575e23			−0.283188			−0.141594	+	0.989925i	$0.545223\pi$
$150$		0			0
$151$		−	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
$153$		0			0
$154$	1.64611e23	−	2.58241e23i	0.142473	−	0.223510i
$155$		−	1.71059e24i		−	1.37879i
$156$		0			0
$157$	−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
$159$		0			0
$160$	6.52860e23	+	2.07995e24i	0.371108	+	1.18231i
$161$	3.69895e23			0.196333
$162$		0			0
$163$			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
$165$		0			0
$166$	−4.26813e24	−	2.72065e24i	−1.61826	−	1.03153i
$167$			3.11720e24i			1.10633i	0.833073	+	0.553163i	$0.186579\pi$
$167$			3.11720e24i			1.10633i	−0.833073	+	0.553163i	$0.813421\pi$
$168$		0			0
$169$	−1.53990e24			−0.479445
$170$	−2.21266e24	+	3.47121e24i	−0.645621	+	1.01285i
$171$		0			0
$172$	1.54774e24	−	7.20751e23i	0.397086	−	0.184915i
$173$	1.66796e24			0.401493			0.200747	−	0.979643i	$-0.435663\pi$
$173$	1.66796e24			0.401493			0.200747	+	0.979643i	$0.435663\pi$
$174$		0			0
$175$			2.52086e24i			0.534724i
$176$	1.01990e24	+	8.57587e23i	0.203197	+	0.170859i
$177$		0			0
$178$	3.29249e24	−	5.16523e24i	0.579301	−	0.908803i
$179$		−	2.60509e24i		−	0.430962i	−0.976508	−	0.215481i	$-0.930868\pi$
$179$		−	2.60509e24i		−	0.430962i	0.976508	−	0.215481i	$-0.0691319\pi$
$180$		0			0
$181$	−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
$183$		0			0
$184$	−2.11314e23	+	1.59556e24i	−0.0258186	+	0.194947i
$185$	5.32027e24			0.612413
$186$		0			0
$187$			2.51619e24i			0.257328i
$188$	4.15502e24	−	1.93491e24i	0.400716	−	0.186606i
$189$		0			0
$190$	1.84378e24	+	1.17529e24i	0.158278	+	0.100892i
$191$		−	3.05525e24i		−	0.247559i	−0.992310	−	0.123780i	$-0.960498\pi$
$191$		−	3.05525e24i		−	0.247559i	0.992310	−	0.123780i	$-0.0395016\pi$
$192$		0			0
$193$	−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
$195$		0			0
$196$	−2.22537e22	−	4.77875e22i	−0.00135702	−	0.00291405i
$197$	−8.09195e24			−0.466579			−0.233289	−	0.972407i	$-0.574949\pi$
$197$	−8.09195e24			−0.466579			−0.233289	+	0.972407i	$0.574949\pi$
$198$		0			0
$199$			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
$201$		0			0
$202$	3.47097e24	−	5.44524e24i	0.151910	−	0.238315i
$203$			3.52328e25i			1.46046i
$204$		0			0
$205$	5.09072e25			1.89447
$206$	1.36272e25	+	8.68642e24i	0.480692	+	0.306409i
$207$		0			0
$208$	−1.46396e25	+	1.74104e25i	−0.464337	+	0.552219i
$209$	1.33651e24			0.0402128
$210$		0			0
$211$		−	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
$213$		0			0
$214$	−1.63031e25	−	1.03921e25i	−0.378197	−	0.241075i
$215$			2.46300e25i			0.542802i
$216$		0			0
$217$	5.58108e25			1.11086
$218$	1.17337e25	−	1.84078e25i	0.222032	−	0.348322i
$219$		0			0
$220$	−1.74263e25	+	8.11508e24i	−0.298233	+	0.138881i
$221$	−4.29533e25			−0.699329
$222$		0			0
$223$			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
$225$		0			0
$226$	3.30484e25	−	5.18461e25i	0.420686	−	0.659969i
$227$			1.00157e26i			1.21450i	0.794511	+	0.607250i	$0.207727\pi$
$227$			1.00157e26i			1.21450i	−0.794511	+	0.607250i	$0.792273\pi$
$228$		0			0
$229$	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
$231$		0			0
$232$	−1.51978e26	−	2.01279e25i	−1.45015	−	0.192057i
$233$	3.39103e25			0.308614			0.154307	−	0.988023i	$-0.450685\pi$
$233$	3.39103e25			0.308614			0.154307	+	0.988023i	$0.450685\pi$
$234$		0			0
$235$			6.61211e25i			0.547764i
$236$	1.12967e26	−	5.26066e25i	0.893141	−	0.415918i
$237$		0			0
$238$	−1.13254e26	−	7.21918e25i	−0.816032	−	0.520165i
$239$			2.54233e26i			1.74927i	0.484786	+	0.874633i	$0.338898\pi$
$239$			2.54233e26i			1.74927i	−0.484786	+	0.874633i	$0.661102\pi$
$240$		0			0
$241$	−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
$243$		0			0
$244$	−4.43376e25	−	9.52104e25i	−0.242932	−	0.521670i
$245$	7.60468e23			0.00398340
$246$		0			0
$247$			2.28153e25i			0.109285i
$248$	−3.18837e25	+	2.40742e26i	−0.146083	+	1.10302i
$249$		0			0
$250$	−7.37522e25	+	1.15702e26i	−0.309339	+	0.485289i
$251$		−	3.78088e26i		−	1.51769i	−0.651273	−	0.758843i	$-0.725765\pi$
$251$		−	3.78088e26i		−	1.51769i	0.651273	−	0.758843i	$-0.274235\pi$
$252$		0			0
$253$	−1.41924e25			−0.0522073
$254$	−2.82489e26	−	1.80068e26i	−0.995019	−	0.634257i
$255$		0			0
$256$	−5.31131e25	−	3.04893e26i	−0.171618	−	0.985164i
$257$	3.92889e25			0.121620			0.0608101	−	0.998149i	$-0.480632\pi$
$257$	3.92889e25			0.121620			0.0608101	+	0.998149i	$0.480632\pi$
$258$		0			0
$259$			1.73583e26i			0.493411i
$260$	−1.38530e26	−	2.97479e26i	−0.377432	−	0.810495i
$261$		0			0
$262$	−2.71259e26	−	1.72909e26i	−0.679312	−	0.433016i
$263$		−	4.70959e26i		−	1.13102i	−0.824742	−	0.565510i	$-0.808679\pi$
$263$		−	4.70959e26i		−	1.13102i	0.824742	−	0.565510i	$-0.191321\pi$
$264$		0			0
$265$	5.10549e26			1.12806
$266$	−3.83457e25	+	6.01565e25i	−0.0812866	+	0.127522i
$267$		0			0
$268$	7.13101e26	−	3.32077e26i	1.39209	−	0.648271i
$269$	7.64721e26			1.43294			0.716470	−	0.697618i	$-0.245757\pi$
$269$	7.64721e26			1.43294			0.716470	+	0.697618i	$0.245757\pi$
$270$		0			0
$271$			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
$273$		0			0
$274$	2.83466e26	−	4.44700e26i	0.433756	−	0.680473i
$275$		−	9.67223e25i		−	0.142189i
$276$		0			0
$277$	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
$279$		0			0
$280$	1.34715e26	−	1.01719e27i	0.162434	−	1.22648i
$281$	8.40763e26			0.974774			0.487387	−	0.873186i	$-0.337950\pi$
$281$	8.40763e26			0.974774			0.487387	+	0.873186i	$0.337950\pi$
$282$		0			0
$283$			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
$285$		0			0
$286$	−1.69144e26	−	1.07818e26i	−0.161521	−	0.102959i
$287$			1.66093e27i			1.52634i
$288$		0			0
$289$	−7.10618e25			−0.0605006
$290$	1.18877e27	−	1.86493e27i	0.974359	−	1.52857i
$291$		0			0
$292$	−7.38355e26	−	1.58554e27i	−0.561117	−	1.20494i
$293$	3.74295e26			0.273949			0.136975	−	0.990575i	$-0.456262\pi$
$293$	3.74295e26			0.273949			0.136975	+	0.990575i	$0.456262\pi$
$294$		0			0
$295$			1.79771e27i			1.22089i
$296$	−7.48757e26	−	9.91646e25i	−0.489928	−	0.0648855i
$297$		0			0
$298$	−2.50522e26	+	3.93017e26i	−0.152218	+	0.238799i
$299$		−	2.42275e26i		−	0.141882i
$300$		0			0
$301$	−8.03594e26			−0.437326
$302$	−1.56029e27	−	9.94581e26i	−0.818709	−	0.521872i
$303$		0			0
$304$	−2.37582e26	−	1.99772e26i	−0.115932	−	0.0974824i
$305$	1.51514e27			0.713104
$306$		0			0
$307$		−	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
$309$		0			0
$310$	−2.95416e27	−	1.88308e27i	−1.16267	−	0.741121i
$311$			1.58500e27i			0.602096i	0.953609	+	0.301048i	$0.0973364\pi$
$311$			1.58500e27i			0.602096i	−0.953609	+	0.301048i	$0.902664\pi$
$312$		0			0
$313$	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
$315$		0			0
$316$	−3.65785e27	+	1.70339e27i	−1.16592	+	0.542946i
$317$	−5.25906e27			−1.61904			−0.809518	−	0.587095i	$-0.800272\pi$
$317$	−5.25906e27			−1.61904			−0.809518	+	0.587095i	$0.800272\pi$
$318$		0			0
$319$		−	1.35184e27i		−	0.388354i
$320$	4.31072e27	+	1.16220e27i	1.19647	+	0.322575i
$321$		0			0
$322$	4.07193e26	−	6.38802e26i	0.105532	−	0.165558i
$323$		−	5.86141e26i		−	0.146816i
$324$		0			0
$325$	1.65112e27			0.386422
$326$	3.12840e27	+	1.99414e27i	0.707829	+	0.451193i
$327$		0			0
$328$	−7.16451e27	−	9.48860e26i	−1.51556	−	0.200720i
$329$	−2.15731e27			−0.441324
$330$		0			0
$331$			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
$333$		0			0
$334$	5.38335e27	+	3.43152e27i	0.932913	+	0.594669i
$335$			1.13480e28i			1.90294i
$336$		0			0
$337$	−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
$339$		0			0
$340$	3.55895e27	+	7.64246e27i	0.507053	+	1.08884i
$341$	−2.14139e27			−0.295392
$342$		0			0
$343$			7.74337e27i			1.00160i
$344$	4.59079e26	−	3.46634e27i	0.0575102	−	0.434239i
$345$		0			0
$346$	1.83615e27	−	2.88053e27i	0.215809	−	0.338560i
$347$		−	1.65711e27i		−	0.188680i	−0.995540	−	0.0943401i	$-0.969926\pi$
$347$		−	1.65711e27i		−	0.188680i	0.995540	−	0.0943401i	$-0.0300741\pi$
$348$		0			0
$349$	−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
$351$		0			0
$352$	2.60377e27	−	8.17280e26i	0.253299	−	0.0795063i
$353$	−4.91291e27			−0.463252			−0.231626	−	0.972805i	$-0.574405\pi$
$353$	−4.91291e27			−0.463252			−0.231626	+	0.972805i	$0.574405\pi$
$354$		0			0
$355$		−	7.91066e27i		−	0.700972i
$356$	−5.29578e27	−	1.13721e28i	−0.454967	−	0.976994i
$357$		0			0
$358$	−4.49894e27	−	2.86777e27i	−0.363410	−	0.231649i
$359$		−	5.07949e27i		−	0.397906i	−0.980009	−	0.198953i	$-0.936246\pi$
$359$		−	5.07949e27i		−	0.397906i	0.980009	−	0.198953i	$-0.0637542\pi$
$360$		0			0
$361$	1.32586e28			0.977057
$362$	−4.57590e27	+	7.17865e27i	−0.327101	+	0.513155i
$363$		0			0
$364$	9.70575e27	−	4.51978e27i	0.653001	−	0.304090i
$365$	2.52316e28			1.64711
$366$		0			0
$367$			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
$369$		0			0
$370$	5.85674e27	−	9.18801e27i	0.329183	−	0.516419i
$371$			1.66575e28i			0.908859i
$372$		0			0
$373$	−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
$375$		0			0
$376$	1.23243e27	−	9.30566e27i	0.0580359	−	0.438209i
$377$	2.30769e28			1.05541
$378$		0			0
$379$		−	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
$381$		0			0
$382$	−5.27636e27	−	3.36332e27i	−0.208755	−	0.133067i
$383$		−	3.19313e28i		−	1.22752i	−0.789491	−	0.613762i	$-0.789656\pi$
$383$		−	3.19313e28i		−	1.22752i	0.789491	−	0.613762i	$-0.210344\pi$
$384$		0			0
$385$	9.04782e27			0.328455
$386$	−1.56141e28	+	2.44953e28i	−0.550880	+	0.864217i
$387$		0			0
$388$	2.40497e28	+	5.16443e28i	0.801606	+	1.72137i
$389$	−3.58810e28			−1.16257			−0.581285	−	0.813700i	$-0.697450\pi$
$389$	−3.58810e28			−1.16257			−0.581285	+	0.813700i	$0.697450\pi$
$390$		0			0
$391$			6.22422e27i			0.190608i
$392$	−1.07026e26	−	1.41744e25i	−0.00318670	−	0.000422043i
$393$		0			0
$394$	−8.90790e27	+	1.39747e28i	−0.250794	+	0.393444i
$395$		−	5.82094e28i		−	1.59377i
$396$		0			0
$397$	−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
$399$		0			0
$400$	−1.44574e28	+	1.71936e28i	−0.344690	+	0.409927i
$401$	−5.32831e27			−0.123595			−0.0617976	−	0.998089i	$-0.519683\pi$
$401$	−5.32831e27			−0.123595			−0.0617976	+	0.998089i	$0.519683\pi$
$402$		0			0
$403$		−	3.65552e28i		−	0.802774i
$404$	−5.58286e27	−	1.19886e28i	−0.119306	−	0.256197i
$405$		0			0
$406$	6.08464e28	+	3.87855e28i	1.23154	+	0.785024i
$407$		−	6.66016e27i		−	0.131204i
$408$		0			0
$409$	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
$411$		0			0
$412$	3.00026e28	−	1.39716e28i	0.516760	−	0.240645i
$413$	−5.86532e28			−0.983651
$414$		0			0
$415$		−	1.49540e29i		−	2.37809i
$416$	1.39516e28	+	4.44483e28i	0.216071	+	0.688381i
$417$		0			0
$418$	1.47128e27	−	2.30813e27i	0.0216150	−	0.0339095i
$419$		−	7.13763e28i		−	1.02141i	−0.859756	−	0.510705i	$-0.829385\pi$
$419$		−	7.13763e28i		−	1.02141i	0.859756	−	0.510705i	$-0.170615\pi$
$420$		0			0
$421$	−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
$423$		0			0
$424$	−7.18529e28	−	9.51613e27i	−0.902443	−	0.119519i
$425$	−4.24185e28			−0.519131
$426$		0			0
$427$			4.94338e28i			0.574536i
$428$	−3.58939e28	+	1.67151e28i	−0.406574	+	0.189334i
$429$		0			0
$430$	4.25356e28	+	2.71136e28i	0.457720	+	0.291765i
$431$		−	6.77466e26i		−	0.00710620i	−0.999994	−	0.00355310i	$-0.998869\pi$
$431$		−	6.77466e26i		−	0.00710620i	0.999994	−	0.00355310i	$-0.00113099\pi$
$432$		0			0
$433$	−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
$435$		0			0
$436$	−1.88731e28	−	4.05279e28i	−0.174378	−	0.374458i
$437$	3.30609e27			0.0297864
$438$		0			0
$439$		−	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
$441$		0			0
$442$	−4.72845e28	+	7.41796e28i	−0.375901	+	0.589711i
$443$			7.32468e27i			0.0567999i	0.999597	+	0.0284000i	$0.00904120\pi$
$443$			7.32468e27i			0.0567999i	−0.999597	+	0.0284000i	$0.990959\pi$
$444$		0			0
$445$	1.80971e29			1.33552
$446$	1.98954e29	+	1.26820e29i	1.43242	+	0.913070i
$447$		0			0
$448$	−3.79187e28	+	1.40644e29i	−0.259893	+	0.963971i
$449$	9.02131e28			0.603337			0.301668	−	0.953413i	$-0.402456\pi$
$449$	9.02131e28			0.603337			0.301668	+	0.953413i	$0.402456\pi$
$450$		0			0
$451$		−	6.37279e28i		−	0.405871i
$452$	−5.31565e28	−	1.14148e29i	−0.330395	−	0.709489i
$453$		0			0
$454$	1.72970e29	+	1.10256e29i	1.02413	+	0.652814i
$455$			1.54453e29i			0.892629i
$456$		0			0
$457$	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
$459$		0			0
$460$	−4.31068e28	+	2.00740e28i	−0.220907	+	0.102872i
$461$	1.65157e29			0.826395			0.413198	−	0.910641i	$-0.364412\pi$
$461$	1.65157e29			0.826395			0.413198	+	0.910641i	$0.364412\pi$
$462$		0			0
$463$			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
$465$		0			0
$466$	3.73296e28	−	5.85624e28i	0.165885	−	0.260240i
$467$			2.71594e29i			1.17879i	0.807847	+	0.589393i	$0.200633\pi$
$467$			2.71594e29i			1.17879i	−0.807847	+	0.589393i	$0.799367\pi$
$468$		0			0
$469$	−3.70246e29			−1.53317
$470$	1.14190e29	+	7.27884e28i	0.461904	+	0.294433i
$471$		0			0
$472$	3.35075e28	−	2.53003e29i	0.129354	−	0.976707i
$473$	3.08330e28			0.116290
$474$		0			0
$475$			2.25312e28i			0.0811249i
$476$	−2.49348e29	+	1.16116e29i	−0.877262	+	0.408524i
$477$		0			0
$478$	4.39057e29	+	2.79869e29i	1.47507	+	0.940260i
$479$		−	5.94621e29i		−	1.95231i	−0.217065	−	0.976157i	$-0.569648\pi$
$479$		−	5.94621e29i		−	1.95231i	0.217065	−	0.976157i	$-0.430352\pi$
$480$		0			0
$481$	1.13694e29			0.356567
$482$	−5.81059e28	+	9.11561e28i	−0.178116	+	0.279427i
$483$		0			0
$484$	−1.33975e29	−	2.87698e29i	−0.392397	−	0.842632i
$485$	−8.21844e29			−2.35304
$486$		0			0
$487$		−	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
$489$		0			0
$490$	8.37150e26	−	1.31331e27i	0.00214115	−	0.00335902i
$491$			1.49100e29i			0.372891i	0.982465	+	0.186445i	$0.0596967\pi$
$491$			1.49100e29i			0.372891i	−0.982465	+	0.186445i	$0.940303\pi$
$492$		0			0
$493$	−5.92863e29			−1.41788
$494$	3.94015e28	+	2.51158e28i	0.0921546	+	0.0587423i
$495$		0			0
$496$	3.80659e29	+	3.20080e29i	0.851605	+	0.716078i
$497$	2.58098e29			0.564761
$498$		0			0
$499$			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
$501$		0			0
$502$	−6.52951e29	−	4.16212e29i	−1.27979	−	0.815782i
$503$			1.68225e29i			0.322583i	0.986907	+	0.161292i	$0.0515660\pi$
$503$			1.68225e29i			0.322583i	−0.986907	+	0.161292i	$0.948434\pi$
$504$		0			0
$505$	1.90781e29			0.350212
$506$	−1.56235e28	+	2.45101e28i	−0.0280623	+	0.0440239i
$507$		0			0
$508$	−6.21948e29	+	2.89629e29i	−1.06968	+	0.498128i
$509$	9.63042e28			0.162088			0.0810438	−	0.996711i	$-0.474175\pi$
$509$	9.63042e28			0.162088			0.0810438	+	0.996711i	$0.474175\pi$
$510$		0			0
$511$			8.23221e29i			1.32705i
$512$	−5.85014e29	−	2.43912e29i	−0.922990	−	0.384825i
$513$		0			0
$514$	4.32506e28	−	6.78513e28i	0.0653729	−	0.102557i
$515$			4.77448e29i			0.706393i
$516$		0			0
$517$	8.27734e28			0.117353
$518$	2.99774e29	+	1.91086e29i	0.416070	+	0.265217i
$519$		0			0
$520$	−6.66241e29	−	8.82362e28i	−0.886328	−	0.117384i
$521$	4.46922e29			0.582126			0.291063	−	0.956704i	$-0.405991\pi$
$521$	4.46922e29			0.582126			0.291063	+	0.956704i	$0.405991\pi$
$522$		0			0
$523$		−	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
$525$		0			0
$526$	−8.13338e29	−	5.18448e29i	−0.953736	−	0.607942i
$527$			9.39129e29i			1.07847i
$528$		0			0
$529$	8.72739e29			0.961329
$530$	5.62030e29	−	8.81709e29i	0.606352	−	0.951241i
$531$		0			0
$532$	6.16769e28	+	1.32445e29i	0.0638402	+	0.137090i
$533$	1.08788e30			1.10302
$534$		0			0
$535$		−	5.71200e29i		−	0.555772i
$536$	2.11515e29	−	1.59708e30i	0.201618	−	1.52234i
$537$		0			0
$538$	8.41831e29	−	1.32066e30i	0.770229	−	1.20833i
$539$		−	9.51989e26i		−	0.000853405i
$540$		0			0
$541$	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
$543$		0			0
$544$	−3.58426e29	−	1.14191e30i	−0.290276	−	0.924791i
$545$	6.44943e29			0.511871
$546$		0			0
$547$			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
$549$		0			0
$550$	−1.67038e29	−	1.06475e29i	−0.119902	−	0.0764291i
$551$			3.14908e29i			0.221572i
$552$		0			0
$553$	1.89918e30			1.28407
$554$	1.33566e30	−	2.09537e30i	0.885295	−	1.38884i
$555$		0			0
$556$	−6.74315e29	+	3.14015e29i	−0.429576	+	0.200045i
$557$	−2.81931e30			−1.76090			−0.880451	−	0.474138i	$-0.842760\pi$
$557$	−2.81931e30			−1.76090			−0.880451	+	0.474138i	$0.842760\pi$
$558$		0			0
$559$			5.26342e29i			0.316037i
$560$	−1.60836e30	−	1.35240e30i	−0.946925	−	0.796229i
$561$		0			0
$562$	9.25541e29	−	1.45198e30i	0.523958	−	0.821981i
$563$		−	2.40066e30i		−	1.33272i	−0.745631	−	0.666359i	$-0.767852\pi$
$563$		−	2.40066e30i		−	1.33272i	0.745631	−	0.666359i	$-0.232148\pi$
$564$		0			0
$565$	1.81650e30			0.969845
$566$	1.80731e30	+	1.15204e30i	0.946349	+	0.603233i
$567$		0			0
$568$	−1.47447e29	+	1.11332e30i	−0.0742683	+	0.560774i
$569$	1.95203e29			0.0964385			0.0482193	−	0.998837i	$-0.484645\pi$
$569$	1.95203e29			0.0964385			0.0482193	+	0.998837i	$0.484645\pi$
$570$		0			0
$571$			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
$573$		0			0
$574$	2.86840e30	+	1.82841e30i	1.28709	+	0.820432i
$575$		−	2.39259e29i		−	0.105323i
$576$		0			0
$577$	−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
$579$		0			0
$580$	−1.91207e30	−	4.10596e30i	−0.765235	−	1.64326i
$581$	4.87898e30			1.91598
$582$		0			0
$583$		−	6.39128e29i		−	0.241676i
$584$	−3.55101e30	−	4.70291e29i	−1.31768	−	0.174512i
$585$		0			0
$586$	4.12037e29	−	6.46401e29i	0.147252	−	0.231009i
$587$		−	2.14924e30i		−	0.753818i	−0.926250	−	0.376909i	$-0.876987\pi$
$587$		−	2.14924e30i		−	0.753818i	0.926250	−	0.376909i	$-0.123013\pi$
$588$		0			0
$589$	4.98832e29			0.168533
$590$	3.10461e30	+	1.97898e30i	1.02952	+	0.656250i
$591$		0			0
$592$	−9.95513e29	+	1.18393e30i	−0.318059	+	0.378256i
$593$	−5.02543e30			−1.57606			−0.788028	−	0.615639i	$-0.788898\pi$
$593$	−5.02543e30			−1.57606			−0.788028	+	0.615639i	$0.788898\pi$
$594$		0			0
$595$		−	3.96801e30i		−	1.19918i
$596$	4.02950e29	+	8.65294e29i	0.119548	+	0.256717i
$597$		0			0
$598$	−4.18405e29	−	2.66705e29i	−0.119642	−	0.0762637i
$599$			2.64248e30i			0.741852i	0.928662	+	0.370926i	$0.120960\pi$
$599$			2.64248e30i			0.741852i	−0.928662	+	0.370926i	$0.879040\pi$
$600$		0			0
$601$	−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
$603$		0			0
$604$	−3.43525e30	+	1.59973e30i	−0.880140	+	0.409864i
$605$	4.57830e30			1.15185
$606$		0			0
$607$		−	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
$609$		0			0
$610$	1.66791e30	−	2.61661e30i	0.383306	−	0.601327i
$611$			1.41300e30i			0.318926i
$612$		0			0
$613$	−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
$615$		0			0
$616$	−1.27336e30	−	1.68642e29i	−0.262762	−	0.0348000i
$617$	4.82474e30			0.977997			0.488998	−	0.872285i	$-0.337362\pi$
$617$	4.82474e30			0.977997			0.488998	+	0.872285i	$0.337362\pi$
$618$		0			0
$619$			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
$621$		0			0
$622$	2.73727e30	+	1.74483e30i	0.507719	+	0.323637i
$623$			5.90448e30i			1.07600i
$624$		0			0
$625$	−7.09823e30			−1.24873
$626$	3.49276e30	−	5.47942e30i	0.603742	−	0.947147i
$627$		0			0
$628$	2.91027e29	+	6.24950e29i	0.0485710	+	0.104301i
$629$	−2.92088e30			−0.479023
$630$		0			0
$631$			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
$633$		0			0
$634$	−5.78936e30	+	9.08231e30i	−0.870259	+	1.36526i
$635$		−	9.89740e30i		−	1.46221i
$636$		0			0
$637$	1.62512e28			0.00231927
$638$	−2.33461e30	−	1.48815e30i	−0.327481	−	0.208747i
$639$		0			0
$640$	6.75249e30	−	6.16515e30i	0.915133	−	0.835534i
$641$	−1.26491e31			−1.68508			−0.842542	−	0.538631i	$-0.818942\pi$
$641$	−1.26491e31			−1.68508			−0.842542	+	0.538631i	$0.818942\pi$
$642$		0			0
$643$		−	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
$645$		0			0
$646$	−1.01225e30	−	6.45244e29i	−0.123803	−	0.0789162i
$647$			1.20144e31i			1.44462i	0.691569	+	0.722310i	$0.256920\pi$
$647$			1.20144e31i			1.44462i	−0.691569	+	0.722310i	$0.743080\pi$
$648$		0			0
$649$	2.25045e30			0.261564
$650$	1.81761e30	−	2.85146e30i	0.207708	−	0.325851i
$651$		0			0
$652$	6.88770e30	−	3.20747e30i	0.760940	−	0.354355i
$653$	−4.64890e30			−0.505016			−0.252508	−	0.967595i	$-0.581255\pi$
$653$	−4.64890e30			−0.505016			−0.252508	+	0.967595i	$0.581255\pi$
$654$		0			0
$655$		−	9.50392e30i		−	0.998271i
$656$	−9.52560e30	+	1.13284e31i	−0.983898	+	1.17011i
$657$		0			0
$658$	−2.37484e30	+	3.72564e30i	−0.237219	+	0.372148i
$659$			1.56134e30i			0.153377i	0.997055	+	0.0766883i	$0.0244346\pi$
$659$			1.56134e30i			0.153377i	−0.997055	+	0.0766883i	$0.975565\pi$
$660$		0			0
$661$	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
$663$		0			0
$664$	−2.78728e30	+	2.10457e31i	−0.251960	+	1.90246i
$665$	−2.10767e30			−0.187397
$666$		0			0
$667$		−	3.34400e30i		−	0.287662i
$668$	1.18523e31	−	5.51941e30i	1.00291	−	0.467037i
$669$		0			0
$670$	1.95977e31	+	1.24922e31i	1.60466	+	1.02286i
$671$		−	1.89672e30i		−	0.152776i
$672$		0			0
$673$	−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
$675$		0			0
$676$	2.72659e30	+	5.85508e30i	0.202398	+	0.434629i
$677$	−2.99574e29			−0.0218791			−0.0109395	−	0.999940i	$-0.503482\pi$
$677$	−2.99574e29			−0.0218791			−0.0109395	+	0.999940i	$0.503482\pi$
$678$		0			0
$679$		−	2.68140e31i		−	1.89581i
$680$	1.71162e31	+	2.26685e30i	1.19072	+	0.157698i
$681$		0			0
$682$	−2.35732e30	+	3.69815e30i	−0.158778	+	0.249090i
$683$		−	1.95084e31i		−	1.29298i	−0.762921	−	0.646492i	$-0.776235\pi$
$683$		−	1.95084e31i		−	1.29298i	0.762921	−	0.646492i	$-0.223765\pi$
$684$		0			0
$685$	1.55807e31			0.999977
$686$	1.33727e31	+	8.52417e30i	0.844603	+	0.538377i
$687$		0			0
$688$	−5.48095e30	−	4.60869e30i	−0.335261	−	0.281906i
$689$	1.09104e31			0.656794
$690$		0			0
$691$		−	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
$693$		0			0
$694$	−2.86179e30	−	1.82420e30i	−0.159105	−	0.101419i
$695$		−	1.07307e31i		−	0.587215i
$696$		0			0
$697$	−2.79485e31			−1.48183
$698$	−7.52275e30	+	1.18016e31i	−0.392615	+	0.615932i
$699$		0			0
$700$	9.58491e30	−	4.46350e30i	0.484741	−	0.225734i
$701$	−1.73956e31			−0.866045			−0.433022	−	0.901383i	$-0.642553\pi$
$701$	−1.73956e31			−0.866045			−0.433022	+	0.901383i	$0.642553\pi$
$702$		0			0
$703$			1.55147e30i			0.0748572i
$704$	1.45490e30	−	5.39636e30i	0.0691087	−	0.256331i
$705$		0			0
$706$	−5.40830e30	+	8.48451e30i	−0.249006	+	0.390638i
$707$			6.22456e30i			0.282160i
$708$		0			0
$709$	−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
$711$		0			0
$712$	−2.54693e31	−	3.37312e30i	−1.06841	−	0.141499i
$713$	−5.29709e30			−0.218803
$714$		0			0
$715$		−	5.92618e30i		−	0.237361i
$716$	−9.90518e30	+	4.61265e30i	−0.390678	+	0.181931i
$717$		0			0
$718$	−8.77218e30	−	5.59167e30i	−0.335536	−	0.213881i
$719$		−	1.22766e31i		−	0.462445i	−0.972901	−	0.231222i	$-0.925727\pi$
$719$		−	1.22766e31i		−	0.462445i	0.972901	−	0.231222i	$-0.0742725\pi$
$720$		0			0
$721$	−1.55775e31			−0.569128
$722$	1.45956e31	−	2.28974e31i	0.525185	−	0.823906i
$723$		0			0
$724$	7.36008e30	+	1.58050e31i	0.256897	+	0.551659i
$725$	2.27896e31			0.783463
$726$		0			0
$727$		−	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
$729$		0			0
$730$	2.77758e31	−	4.35745e31i	0.885350	−	1.38893i
$731$		−	1.35221e31i		−	0.424574i
$732$		0			0
$733$	−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
$735$		0			0
$736$	6.44086e30	−	2.02168e30i	0.187624	−	0.0588919i
$737$	1.42059e31			0.407687
$738$		0			0
$739$			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
$741$		0			0
$742$	2.87672e31	+	1.83371e31i	0.766398	+	0.488527i
$743$			5.69328e30i			0.149446i	0.997204	+	0.0747232i	$0.0238073\pi$
$743$			5.69328e30i			0.149446i	−0.997204	+	0.0747232i	$0.976193\pi$
$744$		0			0
$745$	−1.37699e31			−0.350923
$746$	−2.38276e31	+	3.73806e31i	−0.598347	+	0.938683i
$747$		0			0
$748$	9.56718e30	−	4.45525e30i	0.233274	−	0.108631i
$749$	1.86363e31			0.447776
$750$		0			0
$751$		−	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
$753$		0			0
$754$	2.54039e31	−	3.98534e31i	0.567303	−	0.889982i
$755$		−	5.46670e31i		−	1.20312i
$756$		0			0
$757$	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
$759$		0			0
$760$	1.20407e30	−	9.09152e30i	0.0246435	−	0.186075i
$761$	6.82212e29			0.0137622			0.00688110	−	0.999976i	$-0.497810\pi$
$761$	6.82212e29			0.0137622			0.00688110	+	0.999976i	$0.497810\pi$
$762$		0			0
$763$			2.10423e31i			0.412405i
$764$	−1.16168e31	+	5.40972e30i	−0.224419	+	0.104508i
$765$		0			0
$766$	−5.51447e31	−	3.51511e31i	−1.03511	−	0.659815i
$767$			3.84169e31i			0.710842i
$768$		0			0
$769$	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
$771$		0			0
$772$	2.51144e31	+	5.39306e31i	0.432646	+	0.929063i
$773$	2.00705e31			0.340865			0.170433	−	0.985369i	$-0.445483\pi$
$773$	2.00705e31			0.340865			0.170433	+	0.985369i	$0.445483\pi$
$774$		0			0
$775$		−	3.61000e31i		−	0.595921i
$776$	1.15664e32	+	1.53184e31i	1.88242	+	0.249306i
$777$		0			0
$778$	−3.94991e31	+	6.19659e31i	−0.624901	+	0.980341i
$779$			1.48452e31i			0.231566i
$780$		0			0
$781$	−9.90292e30			−0.150176
$782$	1.07491e31	+	6.85184e30i	0.160731	+	0.102455i
$783$		0			0
$784$	−1.42297e29	+	1.69228e29i	−0.00206880	+	0.00246034i
$785$	−9.94517e30			−0.142576
$786$		0			0
$787$			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
$789$		0			0
$790$	−1.00527e32	−	6.40790e31i	−1.34395	−	0.856678i
$791$			5.92663e31i			0.781387i
$792$		0			0
$793$	3.23783e31			0.415192
$794$	−7.81242e31	+	1.22561e32i	−0.988007	+	1.54998i
$795$		0			0
$796$	7.10130e31	−	3.30694e31i	0.873562	−	0.406801i
$797$	−2.66122e31			−0.322878			−0.161439	−	0.986883i	$-0.551614\pi$
$797$	−2.66122e31			−0.322878			−0.161439	+	0.986883i	$0.551614\pi$
$798$		0			0
$799$		−	3.63011e31i		−	0.428455i
$800$	1.37779e31	+	4.38949e31i	0.160395	+	0.511004i
$801$		0			0
$802$	−5.86559e30	+	9.20190e30i	−0.0664345	+	0.104222i
$803$		−	3.15860e31i		−	0.352878i
$804$		0			0
$805$	2.23813e31			0.243293
$806$	−6.31301e31	−	4.02412e31i	−0.676941	−	0.431505i
$807$		0			0
$808$	−2.68499e31	−	3.55598e30i	−0.280168	−	0.0371051i
$809$	−5.54943e31			−0.571235			−0.285617	−	0.958344i	$-0.592199\pi$
$809$	−5.54943e31			−0.571235			−0.285617	+	0.958344i	$0.592199\pi$
$810$		0			0
$811$			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
$813$		0			0
$814$	−1.15020e31	−	7.33173e30i	−0.110638	−	0.0705242i
$815$			1.09608e32i			1.04018i
$816$		0			0
$817$	−7.18246e30			−0.0663484
$818$	5.53788e31	−	8.68779e31i	0.504728	−	0.791814i
$819$		0			0
$820$	−9.01378e31	−	1.93562e32i	−0.799751	−	1.71738i
$821$	1.67649e31			0.146766			0.0733832	−	0.997304i	$-0.476620\pi$
$821$	1.67649e31			0.146766			0.0733832	+	0.997304i	$0.476620\pi$
$822$		0			0
$823$			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
$825$		0			0
$826$	−6.45674e31	+	1.01293e32i	−0.528729	+	0.829466i
$827$			2.30009e32i			1.85859i	0.369338	+	0.929295i	$0.379584\pi$
$827$			2.30009e32i			1.85859i	−0.369338	+	0.929295i	$0.620416\pi$
$828$		0			0
$829$	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
$831$		0			0
$832$	9.21198e31	+	2.48361e31i	0.696621	+	0.187814i
$833$	−4.17504e29			−0.00311577
$834$		0			0
$835$			1.88613e32i			1.37095i
$836$	−2.36647e30	−	5.08175e30i	−0.0169759	−	0.0364539i
$837$		0			0
$838$	−1.23266e32	−	7.85735e31i	−0.861306	−	0.549025i
$839$			8.56056e31i			0.590365i	0.955441	+	0.295183i	$0.0953805\pi$
$839$			8.56056e31i			0.590365i	−0.955441	+	0.295183i	$0.904620\pi$
$840$		0			0
$841$	1.69667e32			1.13983
$842$	−5.49084e31	+	8.61400e31i	−0.364088	+	0.571178i
$843$		0			0
$844$	−3.21966e31	+	1.49933e31i	−0.207990	+	0.0968569i
$845$	−9.31751e31			−0.594122
$846$		0			0
$847$			1.49374e32i			0.928023i
$848$	−9.55323e31	+	1.13613e32i	−0.585863	+	0.696745i
$849$		0			0
$850$	−4.66957e31	+	7.32560e31i	−0.279042	+	0.437759i
$851$		−	1.64750e31i		−	0.0971852i
$852$		0			0
$853$	−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
$855$		0			0
$856$	−1.06466e31	+	8.03888e31i	−0.0588843	+	0.444615i
$857$	9.96835e31			0.544295			0.272147	−	0.962256i	$-0.412266\pi$
$857$	9.96835e31			0.544295			0.272147	+	0.962256i	$0.412266\pi$
$858$		0			0
$859$		−	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
$861$		0			0
$862$	−1.16997e30	−	7.45778e29i	−0.00599233	−	0.00381970i
$863$			5.62172e31i			0.284283i	0.989846	+	0.142141i	$0.0453988\pi$
$863$			5.62172e31i			0.284283i	−0.989846	+	0.142141i	$0.954601\pi$
$864$		0			0
$865$	1.00923e32			0.497525
$866$	−9.92591e31	+	1.55717e32i	−0.483141	+	0.757948i
$867$		0			0
$868$	−9.88202e31	−	2.12206e32i	−0.468952	−	1.00703i
$869$	−7.28692e31			−0.341450
$870$		0			0
$871$			2.42505e32i			1.10795i
$872$	−9.07672e31	−	1.20211e31i	−0.409494	−	0.0542330i
$873$		0			0
$874$	3.63945e30	−	5.70955e30i	0.0160107	−	0.0251175i
$875$		−	1.32261e32i		−	0.574571i
$876$		0			0
$877$	−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
$879$		0			0
$880$	6.17110e31	+	5.18902e31i	0.251799	+	0.211727i
$881$	3.96579e32			1.59807			0.799033	−	0.601287i	$-0.205345\pi$
$881$	3.96579e32			1.59807			0.799033	+	0.601287i	$0.205345\pi$
$882$		0			0
$883$		−	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
$885$		0			0
$886$	1.26496e31	+	8.06326e30i	0.0478967	+	0.0305309i
$887$		−	4.60675e32i		−	1.72280i	−0.507929	−	0.861399i	$-0.669589\pi$
$887$		−	4.60675e32i		−	1.72280i	0.507929	−	0.861399i	$-0.330411\pi$
$888$		0			0
$889$	3.22919e32			1.17808
$890$	1.99219e32	−	3.12534e32i	0.717862	−	1.12618i
$891$		0			0
$892$	4.38032e32	−	2.03983e32i	1.53990	−	0.717100i
$893$	−1.92818e31			−0.0669549
$894$		0			0
$895$		−	1.57627e32i		−	0.534043i
$896$	2.01148e32	+	2.20311e32i	0.673175	+	0.737307i
$897$		0			0
$898$	9.93097e31	−	1.55796e32i	0.324304	−	0.508765i
$899$		−	5.04553e32i		−	1.62761i
$900$		0			0
$901$	−2.80296e32			−0.882356
$902$	−1.10057e32	−	7.01539e31i	−0.342252	−	0.218162i
$903$		0			0
$904$	−2.55648e32	−	3.38578e31i	−0.775871	−	0.102756i
$905$	−2.51514e32			−0.754097
$906$		0			0
$907$			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
$909$		0			0
$910$	2.66738e32	+	1.70027e32i	0.752712	+	0.479803i
$911$			2.04125e32i			0.569107i	0.958660	+	0.284553i	$0.0918453\pi$
$911$			2.04125e32i			0.569107i	−0.958660	+	0.284553i	$0.908155\pi$
$912$		0			0
$913$	−1.87201e32			−0.509482
$914$	1.22342e32	−	1.91929e32i	0.328978	−	0.516098i
$915$		0			0
$916$	−3.61668e30	−	7.76645e30i	−0.00949424	−	0.0203879i
$917$	3.10081e32			0.804289
$918$		0			0
$919$		−	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
$921$		0			0
$922$	1.81811e32	−	2.85224e32i	0.444201	−	0.696860i
$923$		−	1.69050e32i		−	0.408128i
$924$		0			0
$925$	1.12278e32			0.264689
$926$	4.99316e32	+	3.18280e32i	1.16320	+	0.741461i
$927$		0			0
$928$	1.92567e32	+	6.13498e32i	0.438080	+	1.39568i
$929$	2.04352e32			0.459415			0.229708	−	0.973260i	$-0.426223\pi$
$929$	2.04352e32			0.459415			0.229708	+	0.973260i	$0.426223\pi$
$930$		0			0
$931$			2.21763e29i			0.000486904i
$932$	−6.00425e31	−	1.28935e32i	−0.130282	−	0.279767i
$933$		0			0
$934$	4.69038e32	+	2.98980e32i	0.994014	+	0.633617i
$935$			1.52248e32i			0.318877i
$936$		0			0
$937$	−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
$939$		0			0
$940$	2.51409e32	−	1.17076e32i	0.496562	−	0.231239i
$941$	−3.09258e31			−0.0603719			−0.0301860	−	0.999544i	$-0.509610\pi$
$941$	−3.09258e31			−0.0603719			−0.0301860	+	0.999544i	$0.509610\pi$
$942$		0			0
$943$		−	1.57642e32i		−	0.300637i
$944$	−4.00046e32	−	3.36382e32i	−0.754081	−	0.634075i
$945$		0			0
$946$	3.39420e31	−	5.32480e31i	0.0625079	−	0.0980620i
$947$		−	1.85469e32i		−	0.337614i	−0.985649	−	0.168807i	$-0.946009\pi$
$947$		−	1.85469e32i		−	0.337614i	0.985649	−	0.168807i	$-0.0539915\pi$
$948$		0			0
$949$	5.39197e32			0.959001
$950$	3.89110e31	+	2.48031e31i	0.0684088	+	0.0436060i
$951$		0			0
$952$	−7.39598e31	+	5.58444e32i	−0.127054	+	0.959342i
$953$	−5.98563e31			−0.101645			−0.0508227	−	0.998708i	$-0.516184\pi$
$953$	−5.98563e31			−0.101645			−0.0508227	+	0.998708i	$0.516184\pi$
$954$		0			0
$955$		−	1.84865e32i		−	0.306773i
$956$	9.66657e32	−	4.50153e32i	1.58575	−	0.738455i
$957$		0			0
$958$	−1.02690e33	−	6.54580e32i	−1.64629	−	1.04940i
$959$			5.08345e32i			0.805664i
$960$		0			0
$961$	−1.53649e32			−0.237998
$962$	1.25158e32	−	1.96347e32i	0.191661	−	0.300676i
$963$		0			0
$964$	9.34600e31	+	2.00696e32i	0.139887	+	0.300393i
$965$	−8.58228e32			−1.27000
$966$		0			0
$967$			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
$969$		0			0
$970$	−9.04714e32	+	1.41931e33i	−1.26480	+	1.98421i
$971$		−	2.51375e32i		−	0.347465i	−0.984793	−	0.173733i	$-0.944417\pi$
$971$		−	2.51375e32i		−	0.347465i	0.984793	−	0.173733i	$-0.0555828\pi$
$972$		0			0
$973$	3.50108e32			0.473108
$974$	−6.91529e32	−	4.40803e32i	−0.923978	−	0.588974i
$975$		0			0
$976$	−2.83508e32	+	3.37165e32i	−0.370354	+	0.440448i
$977$	−1.27159e33			−1.64250			−0.821250	−	0.570568i	$-0.806723\pi$
$977$	−1.27159e33			−1.64250			−0.821250	+	0.570568i	$0.806723\pi$
$978$		0			0
$979$		−	2.26548e32i		−	0.286121i
$980$	−1.34651e30	−	2.89149e30i	−0.00168160	−	0.00361106i
$981$		0			0
$982$	2.57493e32	+	1.64135e32i	0.314441	+	0.200435i
$983$		−	7.15765e32i		−	0.864334i	−0.901794	−	0.432167i	$-0.857749\pi$
$983$		−	7.15765e32i		−	0.864334i	0.901794	−	0.432167i	$-0.142251\pi$
$984$		0			0
$985$	−4.89621e32			−0.578178
$986$	−6.52644e32	+	1.02386e33i	−0.762132	+	1.19563i
$987$		0			0
$988$	8.67492e31	−	4.03974e31i	0.0990693	−	0.0461346i
$989$	7.62705e31			0.0861385
$990$		0			0
$991$		−	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
$993$		0			0
$994$	2.84123e32	−	4.45731e32i	0.303568	−	0.476236i
$995$			1.13007e33i			1.19413i
$996$		0			0
$997$	−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
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.23.b.a.3.3	✓	10	12.11	even	2
4.23.b.a.3.4	yes	10	3.2	odd	2
36.23.d.c.19.7		10	1.1	even	1	trivial
36.23.d.c.19.8		10	4.3	odd	2	inner
64.23.c.e.63.1		10	24.5	odd	2
64.23.c.e.63.10		10	24.11	even	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:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 23 \)
Character orbit:	\([\chi]\)	\(=\)	36.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1100.83 - 1726.98i) q^{2} +(-1.77063e6 - 3.80224e6i) q^{4} +6.05072e7 q^{5} +1.97415e9i q^{7} +(-8.51558e9 - 1.12779e9i) q^{8} +O(q^{10})\)	\(q+(1100.83 - 1726.98i) q^{2} +(-1.77063e6 - 3.80224e6i) q^{4} +6.05072e7 q^{5} +1.97415e9i q^{7} +(-8.51558e9 - 1.12779e9i) q^{8} +(6.66084e10 - 1.04495e11i) q^{10} -7.57457e10i q^{11} +1.29303e12 q^{13} +(3.40931e12 + 2.17321e12i) q^{14} +(-1.13219e13 + 1.34647e13i) q^{16} -3.32190e13 q^{17} +1.76447e13i q^{19} +(-1.07136e14 - 2.30063e14i) q^{20} +(-1.30811e14 - 8.33835e13i) q^{22} -1.87369e14i q^{23} +1.27693e15 q^{25} +(1.42342e15 - 2.23305e15i) q^{26} +(7.50618e15 - 3.49548e15i) q^{28} +1.78471e16 q^{29} -2.82708e16i q^{31} +(1.07898e16 + 3.43752e16i) q^{32} +(-3.65686e16 + 5.73686e16i) q^{34} +1.19450e17i q^{35} +8.79279e16 q^{37} +(3.04722e16 + 1.94239e16i) q^{38} +(-5.15254e17 - 6.82397e16i) q^{40} +8.41341e17 q^{41} +4.07059e17i q^{43} +(-2.88003e17 + 1.34118e17i) q^{44} +(-3.23584e17 - 2.06263e17i) q^{46} +1.09278e18i q^{47} +1.25682e16 q^{49} +(1.40569e18 - 2.20524e18i) q^{50} +(-2.28949e18 - 4.91643e18i) q^{52} +8.43782e18 q^{53} -4.58316e18i q^{55} +(2.22643e18 - 1.68110e19i) q^{56} +(1.96467e19 - 3.08216e19i) q^{58} +2.97106e19i q^{59} +2.50406e19 q^{61} +(-4.88232e19 - 3.11215e19i) q^{62} +(7.12431e19 + 1.92076e19i) q^{64} +7.82379e19 q^{65} +1.87547e20i q^{67} +(5.88185e19 + 1.26307e20i) q^{68} +(2.06288e20 + 1.31495e20i) q^{70} -1.30739e20i q^{71} +4.17001e20 q^{73} +(9.67941e19 - 1.51850e20i) q^{74} +(6.70896e19 - 3.12423e19i) q^{76} +1.49533e20 q^{77} -9.62025e20i q^{79} +(-6.85058e20 + 8.14713e20i) q^{80} +(9.26177e20 - 1.45298e21i) q^{82} -2.47144e21i q^{83} -2.00999e21 q^{85} +(7.02984e20 + 4.48105e20i) q^{86} +(-8.54255e19 + 6.45018e20i) q^{88} +2.99090e21 q^{89} +2.55264e21i q^{91} +(-7.12424e20 + 3.31762e20i) q^{92} +(1.88721e21 + 1.20297e21i) q^{94} +1.06763e21i q^{95} -1.35826e22 q^{97} +(1.38355e19 - 2.17051e19i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 1540 q^{2} + 2264464 q^{4} + 17091100 q^{5} - 9804431680 q^{8}+O(q^{10}) \) 10 * q - 1540 * q^2 + 2264464 * q^4 + 17091100 * q^5 - 9804431680 * q^8	\( 10 q - 1540 q^{2} + 2264464 q^{4} + 17091100 q^{5} - 9804431680 q^{8} + 159414035240 q^{10} - 531230356540 q^{13} + 5894008940736 q^{14} - 27717620084480 q^{16} - 14058178115540 q^{17} - 233643631625120 q^{20} + 120589650366240 q^{22} + 77\!\cdots\!70 q^{25}+ \cdots + 23\!\cdots\!20 q^{98}+O(q^{100}) \) 10 * q - 1540 * q^2 + 2264464 * q^4 + 17091100 * q^5 - 9804431680 * q^8 + 159414035240 * q^10 - 531230356540 * q^13 + 5894008940736 * q^14 - 27717620084480 * q^16 - 14058178115540 * q^17 - 233643631625120 * q^20 + 120589650366240 * q^22 + 7710175817606670 * q^25 + 3953973318046744 * q^26 + 1177952265288960 * q^28 + 14464474185570172 * q^29 + 73831192092953600 * q^32 - 26625976920357496 * q^34 + 324587767823538020 * q^37 - 369140808808591200 * q^38 - 1158049295468479360 * q^40 + 1355457345814233100 * q^41 + 1919761520625210240 * q^44 + 6132624002565203904 * q^46 + 183553700661552298 * q^49 - 29084394113996178540 * q^50 - 38492433127521128800 * q^52 + 11424344766226018780 * q^53 + 102844865827678657536 * q^56 + 173059696836432320360 * q^58 + 58241718146183220740 * q^61 - 317897221476923285760 * q^62 - 412080172429987966976 * q^64 + 121531695066047433560 * q^65 + 667890522330713878240 * q^68 + 1014396282552321513600 * q^70 + 83030422224875883380 * q^73 - 801906083011176262184 * q^74 + 286747421140990627200 * q^76 + 704201825495570814720 * q^77 - 1509611955050789726720 * q^80 - 2389572513290905036600 * q^82 - 1796890366112110859960 * q^85 + 8221838255181360278496 * q^86 + 11178210842814940531200 * q^88 - 3420669206528505615668 * q^89 - 21476264197983864733440 * q^92 - 20874543047091388369536 * q^94 - 20429910746446196146540 * q^97 + 23110416876469762175420 * q^98

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