LMFDB - Embedded newform 60.12.h.b.59.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,12,Mod(59,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("60.59");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	60.h (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:	$46.1005908336$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			59.1
Root			$0.809017 + 1.40126i$ of defining polynomial
Character	$\chi$	$=$	60.59
Dual form			60.12.h.b.59.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-25.7148 - 37.2391i) q^{2} -420.888i q^{3} +(-725.500 + 1915.19i) q^{4} +6987.71 q^{5} +(-15673.5 + 10823.1i) q^{6} +(89976.0 - 22231.7i) q^{8} -177147. q^{9} +O(q^{10})$	\(q+(-25.7148 - 37.2391i) q^{2} -420.888i q^{3} +(-725.500 + 1915.19i) q^{4} +6987.71 q^{5} +(-15673.5 + 10823.1i) q^{6} +(89976.0 - 22231.7i) q^{8} -177147. q^{9} +(-179687. - 260216. i) q^{10} +(806081. + 305354. i) q^{12} -2.94105e6i q^{15} +(-3.14160e6 - 2.77894e6i) q^{16} +258163. q^{17} +(4.55530e6 + 6.59679e6i) q^{18} +1.09327e7i q^{19} +(-5.06959e6 + 1.33828e7i) q^{20} +4.92288e7i q^{23} +(-9.35708e6 - 3.78699e7i) q^{24} +4.88281e7 q^{25} +7.45591e7i q^{27} +(-1.09522e8 + 7.56284e7i) q^{30} +2.61679e8i q^{31} +(-2.26996e7 + 1.88450e8i) q^{32} +(-6.63860e6 - 9.61376e6i) q^{34} +(1.28520e8 - 3.39270e8i) q^{36} +(4.07125e8 - 2.81133e8i) q^{38} +(6.28727e8 - 1.55349e8i) q^{40} -1.23785e9 q^{45} +(1.83324e9 - 1.26591e9i) q^{46} -1.15727e8i q^{47} +(-1.16962e9 + 1.32226e9i) q^{48} -1.97733e9 q^{49} +(-1.25560e9 - 1.81832e9i) q^{50} -1.08658e8i q^{51} +1.75601e9 q^{53} +(2.77651e9 - 1.91727e9i) q^{54} +4.60146e9 q^{57} +(5.63266e9 + 2.13373e9i) q^{60} +1.30276e10 q^{61} +(9.74467e9 - 6.72901e9i) q^{62} +(7.60143e9 - 4.00065e9i) q^{64} +(-1.87297e8 + 4.94431e8i) q^{68} +2.07198e10 q^{69} +(-1.59390e10 + 3.93829e9i) q^{72} -2.05512e10i q^{75} +(-2.09383e10 - 7.93170e9i) q^{76} -5.30371e10i q^{79} +(-2.19526e10 - 1.94184e10i) q^{80} +3.13811e10 q^{81} +6.18059e10i q^{83} +1.80397e9 q^{85} +(3.18311e10 + 4.60965e10i) q^{90} +(-9.42826e10 - 3.57155e10i) q^{92} +1.10137e11 q^{93} +(-4.30956e9 + 2.97589e9i) q^{94} +7.63949e10i q^{95} +(7.93165e10 + 9.55400e9i) q^{96} +(5.08465e10 + 7.36339e10i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2902 q^{4} - 62694 q^{6} - 708588 q^{9}+O(q^{10}) $ 4 * q - 2902 * q^4 - 62694 * q^6 - 708588 * q^9	$ 4 q - 2902 q^{4} - 62694 q^{6} - 708588 q^{9} - 718750 q^{10} - 12566414 q^{16} - 37428318 q^{24} + 195312500 q^{25} - 26554420 q^{34} + 514080594 q^{36} + 2514906250 q^{40} + 7332949788 q^{46} - 7909306972 q^{49} + 11106054018 q^{54} + 22530656250 q^{60} + 52110458392 q^{61} + 30405736922 q^{64} + 82879385976 q^{69} - 83753128740 q^{76} + 125524238436 q^{81} + 7215875000 q^{85} + 127324406250 q^{90} - 17238229236 q^{94} + 317266184394 q^{96}+O(q^{100}) $ 4 * q - 2902 * q^4 - 62694 * q^6 - 708588 * q^9 - 718750 * q^10 - 12566414 * q^16 - 37428318 * q^24 + 195312500 * q^25 - 26554420 * q^34 + 514080594 * q^36 + 2514906250 * q^40 + 7332949788 * q^46 - 7909306972 * q^49 + 11106054018 * q^54 + 22530656250 * q^60 + 52110458392 * q^61 + 30405736922 * q^64 + 82879385976 * q^69 - 83753128740 * q^76 + 125524238436 * q^81 + 7215875000 * q^85 + 127324406250 * q^90 - 17238229236 * q^94 + 317266184394 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−25.7148	−	37.2391i	−0.568222	−	0.822875i
$2$	−25.7148	−	37.2391i	−0.568222	−	0.822875i
$3$		−	420.888i		−	1.00000i
$3$		−	420.888i		−	1.00000i
$4$	−725.500	+	1915.19i	−0.354248	+	0.935151i
$5$	6987.71			1.00000
$5$	6987.71			1.00000
$6$	−15673.5	+	10823.1i	−0.822875	+	0.568222i
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$	89976.0	−	22231.7i	0.970805	−	0.239871i
$9$	−177147.			−1.00000
$10$	−179687.	−	260216.i	−0.568222	−	0.822875i
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$	806081.	+	305354.i	0.935151	+	0.354248i
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$		0			0
$15$		−	2.94105e6i		−	1.00000i
$16$	−3.14160e6	−	2.77894e6i	−0.749017	−	0.662551i
$17$	258163.			0.0440986			0.0220493	−	0.999757i	$-0.492981\pi$
$17$	258163.			0.0440986			0.0220493	+	0.999757i	$0.492981\pi$
$18$	4.55530e6	+	6.59679e6i	0.568222	+	0.822875i
$19$			1.09327e7i			1.01294i	0.862257	+	0.506471i	$0.169050\pi$
$19$			1.09327e7i			1.01294i	−0.862257	+	0.506471i	$0.830950\pi$
$20$	−5.06959e6	+	1.33828e7i	−0.354248	+	0.935151i
$21$		0			0
$22$		0			0
$23$			4.92288e7i			1.59484i	0.603426	+	0.797419i	$0.293802\pi$
$23$			4.92288e7i			1.59484i	−0.603426	+	0.797419i	$0.706198\pi$
$24$	−9.35708e6	−	3.78699e7i	−0.239871	−	0.970805i
$25$	4.88281e7			1.00000
$26$		0			0
$27$			7.45591e7i			1.00000i
$28$		0			0
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$	−1.09522e8	+	7.56284e7i	−0.822875	+	0.568222i
$31$			2.61679e8i			1.64164i	0.571184	+	0.820822i	$0.306484\pi$
$31$			2.61679e8i			1.64164i	−0.571184	+	0.820822i	$0.693516\pi$
$32$	−2.26996e7	+	1.88450e8i	−0.119590	+	0.992823i
$33$		0			0
$34$	−6.63860e6	−	9.61376e6i	−0.0250578	−	0.0362877i
$35$		0			0
$36$	1.28520e8	−	3.39270e8i	0.354248	−	0.935151i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	4.07125e8	−	2.81133e8i	0.833525	−	0.575575i
$39$		0			0
$40$	6.28727e8	−	1.55349e8i	0.970805	−	0.239871i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$		0			0
$45$	−1.23785e9			−1.00000
$46$	1.83324e9	−	1.26591e9i	1.31235	−	0.906222i
$47$		−	1.15727e8i		−	0.0736030i	−0.999323	−	0.0368015i	$-0.988283\pi$
$47$		−	1.15727e8i		−	0.0736030i	0.999323	−	0.0368015i	$-0.0117169\pi$
$48$	−1.16962e9	+	1.32226e9i	−0.662551	+	0.749017i
$49$	−1.97733e9			−1.00000
$50$	−1.25560e9	−	1.81832e9i	−0.568222	−	0.822875i
$51$		−	1.08658e8i		−	0.0440986i
$52$		0			0
$53$	1.75601e9			0.576778			0.288389	−	0.957513i	$-0.406880\pi$
$53$	1.75601e9			0.576778			0.288389	+	0.957513i	$0.406880\pi$
$54$	2.77651e9	−	1.91727e9i	0.822875	−	0.568222i
$55$		0			0
$56$		0			0
$57$	4.60146e9			1.01294
$58$		0			0
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$	5.63266e9	+	2.13373e9i	0.935151	+	0.354248i
$61$	1.30276e10			1.97493			0.987463	−	0.157851i	$-0.0504565\pi$
$61$	1.30276e10			1.97493			0.987463	+	0.157851i	$0.0504565\pi$
$62$	9.74467e9	−	6.72901e9i	1.35087	−	0.932818i
$63$		0			0
$64$	7.60143e9	−	4.00065e9i	0.884923	−	0.465737i
$65$		0			0
$66$		0			0
$67$		0			0			−	1.00000i	$-0.5\pi$
$67$		0			0				1.00000i	$0.5\pi$
$68$	−1.87297e8	+	4.94431e8i	−0.0156218	+	0.0412389i
$69$	2.07198e10			1.59484
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	−1.59390e10	+	3.93829e9i	−0.970805	+	0.239871i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$		0			0
$75$		−	2.05512e10i		−	1.00000i
$76$	−2.09383e10	−	7.93170e9i	−0.947254	−	0.358833i
$77$		0			0
$78$		0			0
$79$		−	5.30371e10i		−	1.93924i	−0.244623	−	0.969618i	$-0.578664\pi$
$79$		−	5.30371e10i		−	1.93924i	0.244623	−	0.969618i	$-0.421336\pi$
$80$	−2.19526e10	−	1.94184e10i	−0.749017	−	0.662551i
$81$	3.13811e10			1.00000
$82$		0			0
$83$			6.18059e10i			1.72227i	0.508379	+	0.861133i	$0.330245\pi$
$83$			6.18059e10i			1.72227i	−0.508379	+	0.861133i	$0.669755\pi$
$84$		0			0
$85$	1.80397e9			0.0440986
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$	3.18311e10	+	4.60965e10i	0.568222	+	0.822875i
$91$		0			0
$92$	−9.42826e10	−	3.57155e10i	−1.49142	−	0.564968i
$93$	1.10137e11			1.64164
$94$	−4.30956e9	+	2.97589e9i	−0.0605661	+	0.0418228i
$95$			7.63949e10i			1.01294i
$96$	7.93165e10	+	9.55400e9i	0.992823	+	0.119590i
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	5.08465e10	+	7.36339e10i	0.568222	+	0.822875i
$99$		0			0
$100$	−3.54248e10	+	9.35151e10i	−0.354248	+	0.935151i
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$	−4.04632e9	+	2.79411e9i	−0.0362877	+	0.0250578i
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$		0			0
$105$		0			0
$106$	−4.51553e10	−	6.53921e10i	−0.327738	−	0.474617i
$107$			1.37573e11i			0.948246i	0.880459	+	0.474123i	$0.157235\pi$
$107$			1.37573e11i			0.948246i	−0.880459	+	0.474123i	$0.842765\pi$
$108$	−1.42795e11	−	5.40926e10i	−0.935151	−	0.354248i
$109$	−3.12857e11			−1.94760			−0.973802	−	0.227399i	$-0.926978\pi$
$109$	−3.12857e11			−1.94760			−0.973802	+	0.227399i	$0.926978\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.83793e11			1.44901			0.724503	−	0.689272i	$-0.242070\pi$
$113$	2.83793e11			1.44901			0.724503	+	0.689272i	$0.242070\pi$
$114$	−1.18326e11	−	1.71354e11i	−0.575575	−	0.833525i
$115$			3.43997e11i			1.59484i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−6.53846e10	−	2.64624e11i	−0.239871	−	0.970805i
$121$	−2.85312e11			−1.00000
$122$	−3.35002e11	−	4.85137e11i	−1.12220	−	1.62512i
$123$		0			0
$124$	−5.01164e11	−	1.89848e11i	−1.53519	−	0.581549i
$125$	3.41197e11			1.00000
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	−3.44450e11	−	1.80195e11i	−0.886076	−	0.463540i
$129$		0			0
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$			5.20998e11i			1.00000i
$136$	2.32285e10	−	5.73941e9i	0.0428111	−	0.0105780i
$137$	1.11472e12			1.97334			0.986672	−	0.162724i	$-0.0520279\pi$
$137$	1.11472e12			1.97334			0.986672	+	0.162724i	$0.0520279\pi$
$138$	−5.32806e11	−	7.71588e11i	−0.906222	−	1.31235i
$139$			3.66583e11i			0.599226i	0.954061	+	0.299613i	$0.0968575\pi$
$139$			3.66583e11i			0.599226i	−0.954061	+	0.299613i	$0.903142\pi$
$140$		0			0
$141$	−4.87080e10			−0.0736030
$142$		0			0
$143$		0			0
$144$	5.56526e11	+	4.92281e11i	0.749017	+	0.662551i
$145$		0			0
$146$		0			0
$147$			8.32234e11i			1.00000i
$148$		0			0
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$	−7.65308e11	+	5.28469e11i	−0.822875	+	0.568222i
$151$		−	1.68799e12i		−	1.74983i	−0.484273	−	0.874917i	$-0.660916\pi$
$151$		−	1.68799e12i		−	1.74983i	0.484273	−	0.874917i	$-0.339084\pi$
$152$	2.43054e11	+	9.83685e11i	0.242976	+	0.983368i
$153$	−4.57328e10			−0.0440986
$154$		0			0
$155$			1.82853e12i			1.64164i
$156$		0			0
$157$		0			0		1.00000			$0$
$157$		0			0		−1.00000			$\pi$
$158$	−1.97505e12	+	1.36384e12i	−1.59575	+	1.10192i
$159$		−	7.39083e11i		−	0.576778i
$160$	−1.58618e11	+	1.31684e12i	−0.119590	+	0.992823i
$161$		0			0
$162$	−8.06957e11	−	1.16860e12i	−0.568222	−	0.822875i
$163$		0			0			−	1.00000i	$-0.5\pi$
$163$		0			0				1.00000i	$0.5\pi$
$164$		0			0
$165$		0			0
$166$	2.30160e12	−	1.58933e12i	1.41721	−	0.978630i
$167$			2.46664e12i			1.46948i	0.678346	+	0.734742i	$0.262697\pi$
$167$			2.46664e12i			1.46948i	−0.678346	+	0.734742i	$0.737303\pi$
$168$		0			0
$169$	1.79216e12			1.00000
$170$	−4.63887e10	−	6.71782e10i	−0.0250578	−	0.0362877i
$171$		−	1.93670e12i		−	1.01294i
$172$		0			0
$173$	4.01002e12			1.96740			0.983701	−	0.179813i	$-0.0575493\pi$
$173$	4.01002e12			1.96740			0.983701	+	0.179813i	$0.0575493\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	8.98062e11	−	2.37072e12i	0.354248	−	0.935151i
$181$	4.67073e12			1.78711			0.893557	−	0.448950i	$-0.148202\pi$
$181$	4.67073e12			1.78711			0.893557	+	0.448950i	$0.148202\pi$
$182$		0			0
$183$		−	5.48317e12i		−	1.97493i
$184$	1.09444e12	+	4.42942e12i	0.382556	+	1.54828i
$185$		0			0
$186$	−2.83216e12	−	4.10142e12i	−0.932818	−	1.35087i
$187$		0			0
$188$	2.21639e11	+	8.39597e10i	0.0688299	+	0.0260737i
$189$		0			0
$190$	2.84488e12	−	1.96448e12i	0.833525	−	0.575575i
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$	−1.68383e12	−	3.19936e12i	−0.465737	−	0.884923i
$193$		0			0		1.00000			$0$
$193$		0			0		−1.00000			$\pi$
$194$		0			0
$195$		0			0
$196$	1.43455e12	−	3.78696e12i	0.354248	−	0.935151i
$197$	−8.18048e12			−1.96433			−0.982165	−	0.188023i	$-0.939792\pi$
$197$	−8.18048e12			−1.96433			−0.982165	+	0.188023i	$0.939792\pi$
$198$		0			0
$199$			8.27204e12i			1.87897i	0.342586	+	0.939486i	$0.388697\pi$
$199$			8.27204e12i			1.87897i	−0.342586	+	0.939486i	$0.611303\pi$
$200$	4.39336e12	−	1.08553e12i	0.970805	−	0.239871i
$201$		0			0
$202$		0			0
$203$		0			0
$204$	2.08100e11	+	7.88312e10i	0.0412389	+	0.0156218i
$205$		0			0
$206$		0			0
$207$		−	8.72074e12i		−	1.59484i
$208$		0			0
$209$		0			0
$210$		0			0
$211$		−	2.08891e12i		−	0.343849i	−0.985110	−	0.171924i	$-0.945002\pi$
$211$		−	2.08891e12i		−	0.343849i	0.985110	−	0.171924i	$-0.0549984\pi$
$212$	−1.27398e12	+	3.36309e12i	−0.204323	+	0.539375i
$213$		0			0
$214$	5.12308e12	−	3.53765e12i	0.780289	−	0.538814i
$215$		0			0
$216$	1.65758e12	+	6.70853e12i	0.239871	+	0.970805i
$217$		0			0
$218$	8.04506e12	+	1.16505e13i	1.10667	+	1.60264i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0			−	1.00000i	$-0.5\pi$
$223$		0			0				1.00000i	$0.5\pi$
$224$		0			0
$225$	−8.64976e12			−1.00000
$226$	−7.29767e12	−	1.05682e13i	−0.823356	−	1.19235i
$227$			1.37937e13i			1.51894i	0.650545	+	0.759468i	$0.274541\pi$
$227$			1.37937e13i			1.51894i	−0.650545	+	0.759468i	$0.725459\pi$
$228$	−3.33836e12	+	8.81268e12i	−0.358833	+	0.947254i
$229$	−1.77547e13			−1.86302			−0.931511	−	0.363713i	$-0.881509\pi$
$229$	−1.77547e13			−1.86302			−0.931511	+	0.363713i	$0.881509\pi$
$230$	1.28101e13	−	8.84581e12i	1.31235	−	0.906222i
$231$		0			0
$232$		0			0
$233$	7.84924e12			0.748808			0.374404	−	0.927266i	$-0.377847\pi$
$233$	7.84924e12			0.748808			0.374404	+	0.927266i	$0.377847\pi$
$234$		0			0
$235$		−	8.08665e11i		−	0.0736030i
$236$		0			0
$237$	−2.23227e13			−1.93924
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$	−8.17300e12	+	9.23960e12i	−0.662551	+	0.749017i
$241$	−1.64356e13			−1.30225			−0.651123	−	0.758972i	$-0.725702\pi$
$241$	−1.64356e13			−1.30225			−0.651123	+	0.758972i	$0.725702\pi$
$242$	7.33673e12	+	1.06247e13i	0.568222	+	0.822875i
$243$		−	1.32079e13i		−	1.00000i
$244$	−9.45153e12	+	2.49504e13i	−0.699614	+	1.84685i
$245$	−1.38170e13			−1.00000
$246$		0			0
$247$		0			0
$248$	5.81757e12	+	2.35448e13i	0.393783	+	1.59372i
$249$	2.60134e13			1.72227
$250$	−8.77380e12	−	1.27059e13i	−0.568222	−	0.822875i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		−	7.59269e11i		−	0.0440986i
$256$	2.14716e12	+	1.74607e13i	0.122052	+	0.992524i
$257$	−2.64056e13			−1.46914			−0.734570	−	0.678533i	$-0.762616\pi$
$257$	−2.64056e13			−1.46914			−0.734570	+	0.678533i	$0.762616\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		−	4.07165e13i		−	1.99533i	−0.0683139	−	0.997664i	$-0.521762\pi$
$263$		−	4.07165e13i		−	1.99533i	0.0683139	−	0.997664i	$-0.478238\pi$
$264$		0			0
$265$	1.22705e13			0.576778
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$	1.94015e13	−	1.33973e13i	0.822875	−	0.568222i
$271$			2.42937e13i			1.00963i	0.863228	+	0.504814i	$0.168439\pi$
$271$			2.42937e13i			1.00963i	−0.863228	+	0.504814i	$0.831561\pi$
$272$	−8.11046e11	−	7.17420e11i	−0.0330306	−	0.0292176i
$273$		0			0
$274$	−2.86648e13	−	4.15112e13i	−1.12130	−	1.62382i
$275$		0			0
$276$	−1.50322e13	+	3.96824e13i	−0.564968	+	1.49142i
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$	1.36512e13	−	9.42659e12i	0.493088	−	0.340493i
$279$		−	4.63556e13i		−	1.64164i
$280$		0			0
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	1.25252e12	+	1.81384e12i	0.0418228	+	0.0605661i
$283$		0			0			−	1.00000i	$-0.5\pi$
$283$		0			0				1.00000i	$0.5\pi$
$284$		0			0
$285$	3.21537e13			1.01294
$286$		0			0
$287$		0			0
$288$	4.02117e12	−	3.33834e13i	0.119590	−	0.992823i
$289$	−3.42052e13			−0.998055
$290$		0			0
$291$		0			0
$292$		0			0
$293$	9.48300e12			0.256551			0.128276	−	0.991739i	$-0.459056\pi$
$293$	9.48300e12			0.256551			0.128276	+	0.991739i	$0.459056\pi$
$294$	3.09916e13	−	2.14007e13i	0.822875	−	0.568222i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	3.93594e13	+	1.49099e13i	0.935151	+	0.354248i
$301$		0			0
$302$	−6.28593e13	+	4.34063e13i	−1.43990	+	0.994294i
$303$		0			0
$304$	3.03814e13	−	3.43463e13i	0.671126	−	0.758710i
$305$	9.10332e13			1.97493
$306$	1.17601e12	+	1.70305e12i	0.0250578	+	0.0362877i
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$		0			0
$309$		0			0
$310$	6.80930e13	−	4.70204e13i	1.35087	−	0.932818i
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$		0			0
$315$		0			0
$316$	1.01576e14	+	3.84784e13i	1.81348	+	0.686971i
$317$	−1.05605e14			−1.85292			−0.926462	−	0.376389i	$-0.877165\pi$
$317$	−1.05605e14			−1.85292			−0.926462	+	0.376389i	$0.877165\pi$
$318$	−2.75228e13	+	1.90054e13i	−0.474617	+	0.327738i
$319$		0			0
$320$	5.31166e13	−	2.79554e13i	0.884923	−	0.465737i
$321$	5.79027e13			0.948246
$322$		0			0
$323$			2.82243e12i			0.0446693i
$324$	−2.27670e13	+	6.01007e13i	−0.354248	+	0.935151i
$325$		0			0
$326$		0			0
$327$			1.31678e14i			1.94760i
$328$		0			0
$329$		0			0
$330$		0			0
$331$			1.40631e14i			1.94548i	0.231894	+	0.972741i	$0.425508\pi$
$331$			1.40631e14i			1.94548i	−0.231894	+	0.972741i	$0.574492\pi$
$332$	−1.18370e14	−	4.48402e13i	−1.61058	−	0.610110i
$333$		0			0
$334$	9.18554e13	−	6.34291e13i	1.20920	−	0.834993i
$335$		0			0
$336$		0			0
$337$		0			0		1.00000			$0$
$337$		0			0		−1.00000			$\pi$
$338$	−4.60850e13	−	6.67384e13i	−0.568222	−	0.822875i
$339$		−	1.19445e14i		−	1.44901i
$340$	−1.30878e12	+	3.45494e12i	−0.0156218	+	0.0412389i
$341$		0			0
$342$	−7.21210e13	+	4.98019e13i	−0.833525	+	0.575575i
$343$		0			0
$344$		0			0
$345$	1.44784e14			1.59484
$346$	−1.03117e14	−	1.49330e14i	−1.11792	−	1.61893i
$347$		−	5.98828e12i		−	0.0638984i	−0.999489	−	0.0319492i	$-0.989829\pi$
$347$		−	5.98828e12i		−	0.0638984i	0.999489	−	0.0319492i	$-0.0101715\pi$
$348$		0			0
$349$	1.83115e12			0.0189314			0.00946572	−	0.999955i	$-0.496987\pi$
$349$	1.83115e12			0.0189314			0.00946572	+	0.999955i	$0.496987\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	2.03198e14			1.97315			0.986574	−	0.163318i	$-0.0522196\pi$
$353$	2.03198e14			1.97315			0.986574	+	0.163318i	$0.0522196\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$	−1.11377e14	+	2.75196e13i	−0.970805	+	0.239871i
$361$	−3.03460e12			−0.0260503
$362$	−1.20107e14	−	1.73934e14i	−1.01548	−	1.47057i
$363$			1.20084e14i			1.00000i
$364$		0			0
$365$		0			0
$366$	−2.04188e14	+	1.40999e14i	−1.62512	+	1.12220i
$367$		0			0			−	1.00000i	$-0.5\pi$
$367$		0			0				1.00000i	$0.5\pi$
$368$	1.36804e14	−	1.54658e14i	1.05666	−	1.19456i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−7.99047e13	+	2.10934e14i	−0.581549	+	1.53519i
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$		0			0
$375$		−	1.43606e14i		−	1.00000i
$376$	−2.57281e12	−	1.04126e13i	−0.0176552	−	0.0714541i
$377$		0			0
$378$		0			0
$379$			1.29338e14i			0.849589i	0.905290	+	0.424795i	$0.139654\pi$
$379$			1.29338e14i			0.849589i	−0.905290	+	0.424795i	$0.860346\pi$
$380$	−1.46311e14	−	5.54245e13i	−0.947254	−	0.358833i
$381$		0			0
$382$		0			0
$383$			2.65220e14i			1.64442i	0.569185	+	0.822209i	$0.307259\pi$
$383$			2.65220e14i			1.64442i	−0.569185	+	0.822209i	$0.692741\pi$
$384$	−7.58419e13	+	1.44975e14i	−0.463540	+	0.886076i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		1.00000			$0$
$389$		0			0		−1.00000			$\pi$
$390$		0			0
$391$			1.27091e13i			0.0703301i
$392$	−1.77912e14	+	4.39594e13i	−0.970805	+	0.239871i
$393$		0			0
$394$	2.10359e14	+	3.04633e14i	1.11617	+	1.61640i
$395$		−	3.70608e14i		−	1.93924i
$396$		0			0
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$	3.08043e14	−	2.12714e14i	1.54616	−	1.06767i
$399$		0			0
$400$	−1.53399e14	−	1.35690e14i	−0.749017	−	0.662551i
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	2.19282e14			1.00000
$406$		0			0
$407$		0			0
$408$	−2.41565e12	−	9.77660e12i	−0.0105780	−	0.0428111i
$409$	−4.55914e14			−1.96972			−0.984860	−	0.173351i	$-0.944541\pi$
$409$	−4.55914e14			−1.96972			−0.984860	+	0.173351i	$0.944541\pi$
$410$		0			0
$411$		−	4.69173e14i		−	1.97334i
$412$		0			0
$413$		0			0
$414$	−3.24753e14	+	2.24252e14i	−1.31235	+	0.906222i
$415$			4.31882e14i			1.72227i
$416$		0			0
$417$	1.54290e14			0.599226
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−2.38099e14			−0.877418			−0.438709	−	0.898629i	$-0.644564\pi$
$421$	−2.38099e14			−0.877418			−0.438709	+	0.898629i	$0.644564\pi$
$422$	−7.77893e13	+	5.37160e13i	−0.282945	+	0.195382i
$423$			2.05006e13i			0.0736030i
$424$	1.57999e14	−	3.90391e13i	0.559939	−	0.138353i
$425$	1.26056e13			0.0440986
$426$		0			0
$427$		0			0
$428$	−2.63478e14	−	9.98089e13i	−0.886754	−	0.335914i
$429$		0			0
$430$		0			0
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$	2.07195e14	−	2.34235e14i	0.662551	−	0.749017i
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		0			0
$435$		0			0
$436$	2.26978e14	−	5.99181e14i	0.689935	−	1.82130i
$437$	−5.38206e14			−1.61548
$438$		0			0
$439$			2.67952e14i			0.784336i	0.919894	+	0.392168i	$0.128275\pi$
$439$			2.67952e14i			0.784336i	−0.919894	+	0.392168i	$0.871725\pi$
$440$		0			0
$441$	3.50278e14			1.00000
$442$		0			0
$443$			8.28737e13i			0.230779i	0.993320	+	0.115390i	$0.0368116\pi$
$443$			8.28737e13i			0.230779i	−0.993320	+	0.115390i	$0.963188\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	2.22427e14	+	3.22109e14i	0.568222	+	0.822875i
$451$		0			0
$452$	−2.05892e14	+	5.43517e14i	−0.513307	+	1.35504i
$453$	−7.10456e14			−1.74983
$454$	5.13666e14	−	3.54703e14i	1.24989	−	0.863092i
$455$		0			0
$456$	4.14021e14	−	1.02299e14i	0.983368	−	0.242976i
$457$		0			0		1.00000			$0$
$457$		0			0		−1.00000			$\pi$
$458$	4.56558e14	+	6.61169e14i	1.05861	+	1.53304i
$459$			1.92484e13i			0.0440986i
$460$	−6.58820e14	−	2.49570e14i	−1.49142	−	0.564968i
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$		0			0			−	1.00000i	$-0.5\pi$
$463$		0			0				1.00000i	$0.5\pi$
$464$		0			0
$465$	7.69609e14			1.64164
$466$	−2.01842e14	−	2.92299e14i	−0.425489	−	0.616175i
$467$		−	2.55122e14i		−	0.531501i	−0.964042	−	0.265751i	$-0.914380\pi$
$467$		−	2.55122e14i		−	0.531501i	0.964042	−	0.265751i	$-0.0856198\pi$
$468$		0			0
$469$		0			0
$470$	−3.01139e13	+	2.07946e13i	−0.0605661	+	0.0418228i
$471$		0			0
$472$		0			0
$473$		0			0
$474$	5.74023e14	+	8.31277e14i	1.10192	+	1.59575i
$475$			5.33825e14i			1.01294i
$476$		0			0
$477$	−3.11071e14			−0.576778
$478$		0			0
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$	5.54241e14	+	6.67606e13i	0.992823	+	0.119590i
$481$		0			0
$482$	4.22639e14	+	6.12049e14i	0.739965	+	1.07159i
$483$		0			0
$484$	2.06994e14	−	5.46426e14i	0.354248	−	0.935151i
$485$		0			0
$486$	−4.91851e14	+	3.39639e14i	−0.822875	+	0.568222i
$487$		0			0			−	1.00000i	$-0.5\pi$
$487$		0			0				1.00000i	$0.5\pi$
$488$	1.17217e15	−	2.89627e14i	1.91727	−	0.473728i
$489$		0			0
$490$	3.55301e14	+	5.14532e14i	0.568222	+	0.822875i
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	7.27189e14	−	8.22090e14i	1.08767	−	1.22962i
$497$		0			0
$498$	−6.68929e14	−	9.68715e14i	−0.978630	−	1.41721i
$499$		−	1.30030e15i		−	1.88144i	−0.339189	−	0.940718i	$-0.610152\pi$
$499$		−	1.30030e15i		−	1.88144i	0.339189	−	0.940718i	$-0.389848\pi$
$500$	−2.47538e14	+	6.53457e14i	−0.354248	+	0.935151i
$501$	1.03818e15			1.46948
$502$		0			0
$503$		−	1.08541e15i		−	1.50303i	−0.659714	−	0.751517i	$-0.729323\pi$
$503$		−	1.08541e15i		−	1.50303i	0.659714	−	0.751517i	$-0.270677\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		−	7.54299e14i		−	1.00000i
$508$		0			0
$509$		0			0		1.00000			$0$
$509$		0			0		−1.00000			$\pi$
$510$	−2.82745e13	+	1.95244e13i	−0.0362877	+	0.0250578i
$511$		0			0
$512$	5.95005e14	−	5.28955e14i	0.747371	−	0.664407i
$513$	−8.15136e14			−1.01294
$514$	6.79013e14	+	9.83319e14i	0.834797	+	1.20892i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		−	1.68777e15i		−	1.96740i
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$		0			0
$523$		0			0			−	1.00000i	$-0.5\pi$
$523$		0			0				1.00000i	$0.5\pi$
$524$		0			0
$525$		0			0
$526$	−1.51625e15	+	1.04702e15i	−1.64191	+	1.13379i
$527$			6.75557e13i			0.0723942i
$528$		0			0
$529$	−1.47067e15			−1.54351
$530$	−3.15532e14	−	4.56941e14i	−0.327738	−	0.474617i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$			9.61318e14i			0.948246i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$	−9.97810e14	−	3.77984e14i	−0.935151	−	0.354248i
$541$	9.82248e14			0.911247			0.455624	−	0.890172i	$-0.349416\pi$
$541$	9.82248e14			0.911247			0.455624	+	0.890172i	$0.349416\pi$
$542$	9.04673e14	−	6.24706e14i	0.830799	−	0.573693i
$543$		−	1.96585e15i		−	1.78711i
$544$	−5.86020e12	+	4.86509e13i	−0.00527373	+	0.0437821i
$545$	−2.18616e15			−1.94760
$546$		0			0
$547$		0			0			−	1.00000i	$-0.5\pi$
$547$		0			0				1.00000i	$0.5\pi$
$548$	−8.08729e14	+	2.13490e15i	−0.699053	+	1.84537i
$549$	−2.30780e15			−1.97493
$550$		0			0
$551$		0			0
$552$	1.86429e15	−	4.60638e14i	1.54828	−	0.382556i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−7.02076e14	−	2.65956e14i	−0.560367	−	0.212275i
$557$	1.90873e15			1.50848			0.754241	−	0.656598i	$-0.228005\pi$
$557$	1.90873e15			1.50848			0.754241	+	0.656598i	$0.228005\pi$
$558$	−1.72624e15	+	1.19202e15i	−1.35087	+	0.932818i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$			2.68300e15i			1.99905i	0.0308080	+	0.999525i	$0.490192\pi$
$563$			2.68300e15i			1.99905i	−0.0308080	+	0.999525i	$0.509808\pi$
$564$	3.53377e13	−	9.32851e13i	0.0260737	−	0.0688299i
$565$	1.98306e15			1.44901
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		1.00000			$0$
$569$		0			0		−1.00000			$\pi$
$570$	−8.26826e14	−	1.19737e15i	−0.575575	−	0.833525i
$571$			2.39016e15i			1.64789i	0.566671	+	0.823944i	$0.308231\pi$
$571$			2.39016e15i			1.64789i	−0.566671	+	0.823944i	$0.691769\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			2.40375e15i			1.59484i
$576$	−1.34657e15	+	7.08703e14i	−0.884923	+	0.465737i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	8.79580e14	+	1.27377e15i	0.567117	+	0.821275i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−2.43853e14	−	3.53138e14i	−0.145778	−	0.211110i
$587$			1.77412e15i			1.05069i	0.850890	+	0.525345i	$0.176064\pi$
$587$			1.77412e15i			1.05069i	−0.850890	+	0.525345i	$0.823936\pi$
$588$	−1.59389e15	−	6.03786e14i	−0.935151	−	0.354248i
$589$	−2.86086e15			−1.66289
$590$		0			0
$591$			3.44307e15i			1.96433i
$592$		0			0
$593$	3.02715e15			1.69525			0.847625	−	0.530596i	$-0.178032\pi$
$593$	3.02715e15			1.69525			0.847625	+	0.530596i	$0.178032\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	3.48160e15			1.87897
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	−4.56889e14	−	1.84911e15i	−0.239871	−	0.970805i
$601$	−1.24412e15			−0.647222			−0.323611	−	0.946190i	$-0.604897\pi$
$601$	−1.24412e15			−0.647222			−0.323611	+	0.946190i	$0.604897\pi$
$602$		0			0
$603$		0			0
$604$	3.23282e15	+	1.22464e15i	1.63636	+	0.619875i
$605$	−1.99368e15			−1.00000
$606$		0			0
$607$		0			0			−	1.00000i	$-0.5\pi$
$607$		0			0				1.00000i	$0.5\pi$
$608$	−2.06028e15	−	2.48169e14i	−1.00567	−	0.121137i
$609$		0			0
$610$	−2.34090e15	−	3.38999e15i	−1.12220	−	1.62512i
$611$		0			0
$612$	3.31791e13	−	8.75870e13i	0.0156218	−	0.0412389i
$613$		0			0		1.00000			$0$
$613$		0			0		−1.00000			$\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.40907e14			0.0634401			0.0317201	−	0.999497i	$-0.489901\pi$
$617$	1.40907e14			0.0634401			0.0317201	+	0.999497i	$0.489901\pi$
$618$		0			0
$619$		−	3.64716e15i		−	1.61308i	−0.591178	−	0.806541i	$-0.701337\pi$
$619$		−	3.64716e15i		−	1.61308i	0.591178	−	0.806541i	$-0.298663\pi$
$620$	−3.50199e15	−	1.32660e15i	−1.53519	−	0.581549i
$621$	−3.67046e15			−1.59484
$622$		0			0
$623$		0			0
$624$		0			0
$625$	2.38419e15			1.00000
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		−	1.28273e15i		−	0.510475i	−0.966878	−	0.255237i	$-0.917846\pi$
$631$		−	1.28273e15i		−	0.510475i	0.966878	−	0.255237i	$-0.0821536\pi$
$632$	−1.17911e15	−	4.77207e15i	−0.465167	−	1.88262i
$633$	−8.79200e14			−0.343849
$634$	2.71560e15	+	3.93262e15i	1.05287	+	1.52472i
$635$		0			0
$636$	1.41548e15	+	5.36205e14i	0.539375	+	0.204323i
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−2.40692e15	−	1.25915e15i	−0.886076	−	0.463540i
$641$		0			0		1.00000			$0$
$641$		0			0		−1.00000			$\pi$
$642$	−1.48896e15	−	2.15624e15i	−0.538814	−	0.780289i
$643$		0			0			−	1.00000i	$-0.5\pi$
$643$		0			0				1.00000i	$0.5\pi$
$644$		0			0
$645$		0			0
$646$	1.05105e14	−	7.25782e13i	0.0367573	−	0.0253821i
$647$		−	4.20857e15i		−	1.45935i	−0.683792	−	0.729677i	$-0.739670\pi$
$647$		−	4.20857e15i		−	1.45935i	0.683792	−	0.729677i	$-0.260330\pi$
$648$	2.82354e15	−	6.97655e14i	0.970805	−	0.239871i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	6.02340e15			1.98527			0.992633	−	0.121156i	$-0.0386601\pi$
$653$	6.02340e15			1.98527			0.992633	+	0.121156i	$0.0386601\pi$
$654$	4.90357e15	−	3.38607e15i	1.60264	−	1.10667i
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	6.41472e15			1.97729			0.988643	−	0.150284i	$-0.0480189\pi$
$661$	6.41472e15			1.97729			0.988643	+	0.150284i	$0.0480189\pi$
$662$	5.23697e15	−	3.61630e15i	1.60089	−	1.10547i
$663$		0			0
$664$	1.37405e15	+	5.56105e15i	0.413123	+	1.67198i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−4.72408e15	−	1.78955e15i	−1.37419	−	0.520562i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		1.00000			$0$
$673$		0			0		−1.00000			$\pi$
$674$		0			0
$675$			3.64058e15i			1.00000i
$676$	−1.30021e15	+	3.43233e15i	−0.354248	+	0.935151i
$677$	5.39565e15			1.45816			0.729081	−	0.684427i	$-0.239948\pi$
$677$	5.39565e15			1.45816			0.729081	+	0.684427i	$0.239948\pi$
$678$	−4.44803e15	+	3.07150e15i	−1.19235	+	0.823356i
$679$		0			0
$680$	1.62314e14	−	4.01054e13i	0.0428111	−	0.0105780i
$681$	5.80562e15			1.51894
$682$		0			0
$683$		−	3.30125e15i		−	0.849893i	−0.905219	−	0.424946i	$-0.860293\pi$
$683$		−	3.30125e15i		−	0.849893i	0.905219	−	0.424946i	$-0.139707\pi$
$684$	3.70915e15	+	1.40508e15i	0.947254	+	0.358833i
$685$	7.78934e15			1.97334
$686$		0			0
$687$			7.47274e15i			1.86302i
$688$		0			0
$689$		0			0
$690$	−3.72310e15	−	5.39164e15i	−0.906222	−	1.31235i
$691$		−	8.26956e15i		−	1.99689i	−0.0557838	−	0.998443i	$-0.517766\pi$
$691$		−	8.26956e15i		−	1.99689i	0.0557838	−	0.998443i	$-0.482234\pi$
$692$	−2.90927e15	+	7.67995e15i	−0.696948	+	1.83982i
$693$		0			0
$694$	−2.22998e14	+	1.53987e14i	−0.0525804	+	0.0363085i
$695$			2.56157e15i			0.599226i
$696$		0			0
$697$		0			0
$698$	−4.70876e13	−	6.81903e13i	−0.0107573	−	0.0155782i
$699$		−	3.30366e15i		−	0.748808i
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−3.40358e14			−0.0736030
$706$	−5.22520e15	−	7.56692e15i	−1.12119	−	1.62365i
$707$		0			0
$708$		0			0
$709$	−5.94397e15			−1.24601			−0.623006	−	0.782217i	$-0.714089\pi$
$709$	−5.94397e15			−1.24601			−0.623006	+	0.782217i	$0.714089\pi$
$710$		0			0
$711$			9.39536e15i			1.93924i
$712$		0			0
$713$	−1.28821e16			−2.61816
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$	3.88884e15	+	3.43992e15i	0.749017	+	0.662551i
$721$		0			0
$722$	7.80341e13	+	1.13006e14i	0.0148023	+	0.0214361i
$723$			6.91757e15i			1.30225i
$724$	−3.38861e15	+	8.94533e15i	−0.633082	+	1.67122i
$725$		0			0
$726$	4.47183e15	−	3.08794e15i	0.822875	−	0.568222i
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$		0			0
$729$	−5.55906e15			−1.00000
$730$		0			0
$731$		0			0
$732$	1.05013e16	+	3.97804e15i	1.84685	+	0.699614i
$733$		0			0		1.00000			$0$
$733$		0			0		−1.00000			$\pi$
$734$		0			0
$735$			5.81541e15i			1.00000i
$736$	−9.27719e15	−	1.11747e15i	−1.58339	−	0.190726i
$737$		0			0
$738$		0			0
$739$		−	8.26230e15i		−	1.37898i	−0.724297	−	0.689488i	$-0.757836\pi$
$739$		−	8.26230e15i		−	1.37898i	0.724297	−	0.689488i	$-0.242164\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	4.96170e15i		−	0.803882i	−0.915666	−	0.401941i	$-0.868336\pi$
$743$		−	4.96170e15i		−	0.803882i	0.915666	−	0.401941i	$-0.131664\pi$
$744$	9.90973e15	−	2.44855e15i	1.59372	−	0.393783i
$745$		0			0
$746$		0			0
$747$		−	1.09487e16i		−	1.72227i
$748$		0			0
$749$		0			0
$750$	−5.34775e15	+	3.69279e15i	−0.822875	+	0.568222i
$751$		−	5.30697e14i		−	0.0810637i	−0.999178	−	0.0405319i	$-0.987095\pi$
$751$		−	5.30697e14i		−	0.0810637i	0.999178	−	0.0405319i	$-0.0129052\pi$
$752$	−3.21598e14	+	3.63567e14i	−0.0487657	+	0.0551299i
$753$		0			0
$754$		0			0
$755$		−	1.17952e16i		−	1.74983i
$756$		0			0
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$	4.81641e15	−	3.32589e15i	0.699106	−	0.482755i
$759$		0			0
$760$	1.69839e15	+	6.87371e15i	0.242976	+	0.983368i
$761$		0			0		1.00000			$0$
$761$		0			0		−1.00000			$\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−3.19568e14			−0.0440986
$766$	9.87654e15	−	6.82006e15i	1.35315	−	0.934394i
$767$		0			0
$768$	7.34899e15	−	9.03714e14i	0.992524	−	0.122052i
$769$	−1.44975e16			−1.94400			−0.972002	−	0.234972i	$-0.924500\pi$
$769$	−1.44975e16			−1.94400			−0.972002	+	0.234972i	$0.924500\pi$
$770$		0			0
$771$			1.11138e16i			1.46914i
$772$		0			0
$773$	−1.18833e16			−1.54864			−0.774320	−	0.632794i	$-0.781908\pi$
$773$	−1.18833e16			−1.54864			−0.774320	+	0.632794i	$0.781908\pi$
$774$		0			0
$775$			1.27773e16i			1.64164i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	4.73274e14	−	3.26811e14i	0.0578729	−	0.0399631i
$783$		0			0
$784$	6.21198e15	+	5.49487e15i	0.749017	+	0.662551i
$785$		0			0
$786$		0			0
$787$		0			0			−	1.00000i	$-0.5\pi$
$787$		0			0				1.00000i	$0.5\pi$
$788$	5.93494e15	−	1.56672e16i	0.695860	−	1.83695i
$789$	−1.71371e16			−1.99533
$790$	−1.38011e16	+	9.53010e15i	−1.59575	+	1.10192i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		−	5.16450e15i		−	0.576778i
$796$	−1.58425e16	−	6.00136e15i	−1.75712	−	0.665622i
$797$	−1.45654e16			−1.60436			−0.802180	−	0.597083i	$-0.796326\pi$
$797$	−1.45654e16			−1.60436			−0.802180	+	0.597083i	$0.796326\pi$
$798$		0			0
$799$		−	2.98764e13i		−	0.00324579i
$800$	−1.10838e15	+	9.20168e15i	−0.119590	+	0.992823i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		1.00000			$0$
$809$		0			0		−1.00000			$\pi$
$810$	−5.63878e15	−	8.16586e15i	−0.568222	−	0.822875i
$811$		−	1.99022e16i		−	1.99199i	−0.0894253	−	0.995994i	$-0.528503\pi$
$811$		−	1.99022e16i		−	1.99199i	0.0894253	−	0.995994i	$-0.471497\pi$
$812$		0			0
$813$	1.02249e16			1.00963
$814$		0			0
$815$		0			0
$816$	−3.01954e14	+	3.41360e14i	−0.0292176	+	0.0330306i
$817$		0			0
$818$	1.17237e16	+	1.69778e16i	1.11924	+	1.62083i
$819$		0			0
$820$		0			0
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$	−1.74716e16	+	1.20647e16i	−1.62382	+	1.12130i
$823$		0			0			−	1.00000i	$-0.5\pi$
$823$		0			0				1.00000i	$0.5\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	1.00585e16i		−	0.904173i	−0.891974	−	0.452086i	$-0.850680\pi$
$827$		−	1.00585e16i		−	0.904173i	0.891974	−	0.452086i	$-0.149320\pi$
$828$	1.67019e16	+	6.32690e15i	1.49142	+	0.564968i
$829$	1.39016e16			1.23314			0.616572	−	0.787298i	$-0.288521\pi$
$829$	1.39016e16			1.23314			0.616572	+	0.787298i	$0.288521\pi$
$830$	1.60829e16	−	1.11057e16i	1.41721	−	0.978630i
$831$		0			0
$832$		0			0
$833$	−5.10473e14			−0.0440986
$834$	−3.96754e15	−	5.74563e15i	−0.340493	−	0.493088i
$835$			1.72362e16i			1.46948i
$836$		0			0
$837$	−1.95105e16			−1.64164
$838$		0			0
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	1.22005e16			1.00000
$842$	6.12267e15	+	8.86660e15i	0.498568	+	0.722006i
$843$		0			0
$844$	4.00067e15	+	1.51551e15i	0.321550	+	0.121808i
$845$	1.25231e16			1.00000
$846$	7.63425e14	−	5.27169e14i	0.0605661	−	0.0418228i
$847$		0			0
$848$	−5.51668e15	−	4.87984e15i	−0.432017	−	0.382145i
$849$		0			0
$850$	−3.24151e14	−	4.69422e14i	−0.0250578	−	0.0362877i
$851$		0			0
$852$		0			0
$853$		0			0		1.00000			$0$
$853$		0			0		−1.00000			$\pi$
$854$		0			0
$855$		−	1.35331e16i		−	1.01294i
$856$	3.05848e15	+	1.23782e16i	0.227457	+	0.920562i
$857$	−7.11740e15			−0.525929			−0.262964	−	0.964806i	$-0.584700\pi$
$857$	−7.11740e15			−0.525929			−0.262964	+	0.964806i	$0.584700\pi$
$858$		0			0
$859$		−	2.73149e16i		−	1.99268i	−0.0855025	−	0.996338i	$-0.527250\pi$
$859$		−	2.73149e16i		−	1.99268i	0.0855025	−	0.996338i	$-0.472750\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			2.80073e16i			1.99165i	0.0913010	+	0.995823i	$0.470897\pi$
$863$			2.80073e16i			1.99165i	−0.0913010	+	0.995823i	$0.529103\pi$
$864$	−1.40507e16	−	1.69246e15i	−0.992823	−	0.119590i
$865$	2.80209e16			1.96740
$866$		0			0
$867$			1.43966e16i			0.998055i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−2.81497e16	+	6.95536e15i	−1.89074	+	0.467174i
$873$		0			0
$874$	1.38399e16	+	2.00423e16i	0.917949	+	1.32934i
$875$		0			0
$876$		0			0
$877$		0			0		1.00000			$0$
$877$		0			0		−1.00000			$\pi$
$878$	9.97829e15	−	6.89033e15i	0.645411	−	0.445677i
$879$		−	3.99128e15i		−	0.256551i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−9.00731e15	−	1.30440e16i	−0.568222	−	0.822875i
$883$		0			0			−	1.00000i	$-0.5\pi$
$883$		0			0				1.00000i	$0.5\pi$
$884$		0			0
$885$		0			0
$886$	3.08614e15	−	2.13108e15i	0.189902	−	0.131134i
$887$		−	2.84924e15i		−	0.174240i	−0.996198	−	0.0871201i	$-0.972234\pi$
$887$		−	2.84924e15i		−	0.174240i	0.996198	−	0.0871201i	$-0.0277664\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.26521e15			0.0745555
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	6.27540e15	−	1.65659e16i	0.354248	−	0.935151i
$901$	4.53336e14			0.0254351
$902$		0			0
$903$		0			0
$904$	2.55345e16	−	6.30921e15i	1.40670	−	0.347575i
$905$	3.26377e16			1.78711
$906$	1.82692e16	+	2.64567e16i	0.994294	+	1.43990i
$907$		0			0			−	1.00000i	$-0.5\pi$
$907$		0			0				1.00000i	$0.5\pi$
$908$	−2.64176e16	−	1.00073e16i	−1.42044	−	0.538080i
$909$		0			0
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$	−1.44560e16	−	1.27872e16i	−0.758710	−	0.671126i
$913$		0			0
$914$		0			0
$915$		−	3.83148e16i		−	1.97493i
$916$	1.28810e16	−	3.40036e16i	0.659972	−	1.74221i
$917$		0			0
$918$	7.16793e14	−	4.94968e14i	0.0362877	−	0.0250578i
$919$			3.68242e16i			1.85309i	0.376179	+	0.926547i	$0.377238\pi$
$919$			3.68242e16i			1.85309i	−0.376179	+	0.926547i	$0.622762\pi$
$920$	7.64765e15	+	3.09515e16i	0.382556	+	1.54828i
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		1.00000			$0$
$929$		0			0		−1.00000			$\pi$
$930$	−1.97903e16	−	2.86595e16i	−0.932818	−	1.35087i
$931$		−	2.16176e16i		−	1.01294i
$932$	−5.69463e15	+	1.50328e16i	−0.265264	+	0.700249i
$933$		0			0
$934$	−9.50049e15	+	6.56039e15i	−0.437359	+	0.302011i
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$		0			0
$940$	1.54875e15	+	5.86686e14i	0.0688299	+	0.0260737i
$941$		0			0		1.00000			$0$
$941$		0			0		−1.00000			$\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$			4.66310e16i			1.98953i	0.102193	+	0.994765i	$0.467414\pi$
$947$			4.66310e16i			1.98953i	−0.102193	+	0.994765i	$0.532586\pi$
$948$	1.61951e16	−	4.27522e16i	0.686971	−	1.81348i
$949$		0			0
$950$	1.98792e16	−	1.37272e16i	0.833525	−	0.575575i
$951$			4.44478e16i			1.85292i
$952$		0			0
$953$	3.90667e16			1.60989			0.804944	−	0.593350i	$-0.202195\pi$
$953$	3.90667e16			1.60989			0.804944	+	0.593350i	$0.202195\pi$
$954$	7.99913e15	+	1.15840e16i	0.327738	+	0.474617i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−1.17661e16	−	2.23562e16i	−0.465737	−	0.884923i
$961$	−4.30672e16			−1.69499
$962$		0			0
$963$		−	2.43706e16i		−	0.948246i
$964$	1.19241e16	−	3.14774e16i	0.461318	−	1.21780i
$965$		0			0
$966$		0			0
$967$		0			0			−	1.00000i	$-0.5\pi$
$967$		0			0				1.00000i	$0.5\pi$
$968$	−2.56712e16	+	6.34297e15i	−0.970805	+	0.239871i
$969$	1.18793e15			0.0446693
$970$		0			0
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$	2.52957e16	+	9.58235e15i	0.935151	+	0.354248i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−4.09276e16	−	3.62030e16i	−1.47925	−	1.30849i
$977$	3.94354e16			1.41731			0.708657	−	0.705553i	$-0.249302\pi$
$977$	3.94354e16			1.41731			0.708657	+	0.705553i	$0.249302\pi$
$978$		0			0
$979$		0			0
$980$	1.00242e16	−	2.64622e16i	0.354248	−	0.935151i
$981$	5.54217e16			1.94760
$982$		0			0
$983$		−	3.28759e16i		−	1.14244i	−0.820797	−	0.571220i	$-0.806470\pi$
$983$		−	3.28759e16i		−	1.14244i	0.820797	−	0.571220i	$-0.193530\pi$
$984$		0			0
$985$	−5.71628e16			−1.96433
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$			5.49859e16i			1.82745i	0.406328	+	0.913727i	$0.366809\pi$
$991$			5.49859e16i			1.82745i	−0.406328	+	0.913727i	$0.633191\pi$
$992$	−4.93134e16	−	5.94000e15i	−1.62986	−	0.196323i
$993$	5.91900e16			1.94548
$994$		0			0
$995$			5.78026e16i			1.87897i
$996$	−1.88727e16	+	4.98206e16i	−0.610110	+	1.61058i
$997$		0			0		1.00000			$0$
$997$		0			0		−1.00000			$\pi$
$998$	−4.84219e16	+	3.34369e16i	−1.54819	+	1.06907i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.12.h.b.59.1	✓	4
3.2	odd	2	inner	60.12.h.b.59.4	yes	4
4.3	odd	2	inner	60.12.h.b.59.2	yes	4
5.4	even	2	inner	60.12.h.b.59.4	yes	4
12.11	even	2	inner	60.12.h.b.59.3	yes	4
15.14	odd	2	CM	60.12.h.b.59.1	✓	4
20.19	odd	2	inner	60.12.h.b.59.3	yes	4
60.59	even	2	inner	60.12.h.b.59.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.12.h.b.59.1	✓	4	1.1	even	1	trivial
60.12.h.b.59.1	✓	4	15.14	odd	2	CM
60.12.h.b.59.2	yes	4	4.3	odd	2	inner
60.12.h.b.59.2	yes	4	60.59	even	2	inner
60.12.h.b.59.3	yes	4	12.11	even	2	inner
60.12.h.b.59.3	yes	4	20.19	odd	2	inner
60.12.h.b.59.4	yes	4	3.2	odd	2	inner
60.12.h.b.59.4	yes	4	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	60.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-25.7148 - 37.2391i) q^{2} -420.888i q^{3} +(-725.500 + 1915.19i) q^{4} +6987.71 q^{5} +(-15673.5 + 10823.1i) q^{6} +(89976.0 - 22231.7i) q^{8} -177147. q^{9} +O(q^{10})\)	\(q+(-25.7148 - 37.2391i) q^{2} -420.888i q^{3} +(-725.500 + 1915.19i) q^{4} +6987.71 q^{5} +(-15673.5 + 10823.1i) q^{6} +(89976.0 - 22231.7i) q^{8} -177147. q^{9} +(-179687. - 260216. i) q^{10} +(806081. + 305354. i) q^{12} -2.94105e6i q^{15} +(-3.14160e6 - 2.77894e6i) q^{16} +258163. q^{17} +(4.55530e6 + 6.59679e6i) q^{18} +1.09327e7i q^{19} +(-5.06959e6 + 1.33828e7i) q^{20} +4.92288e7i q^{23} +(-9.35708e6 - 3.78699e7i) q^{24} +4.88281e7 q^{25} +7.45591e7i q^{27} +(-1.09522e8 + 7.56284e7i) q^{30} +2.61679e8i q^{31} +(-2.26996e7 + 1.88450e8i) q^{32} +(-6.63860e6 - 9.61376e6i) q^{34} +(1.28520e8 - 3.39270e8i) q^{36} +(4.07125e8 - 2.81133e8i) q^{38} +(6.28727e8 - 1.55349e8i) q^{40} -1.23785e9 q^{45} +(1.83324e9 - 1.26591e9i) q^{46} -1.15727e8i q^{47} +(-1.16962e9 + 1.32226e9i) q^{48} -1.97733e9 q^{49} +(-1.25560e9 - 1.81832e9i) q^{50} -1.08658e8i q^{51} +1.75601e9 q^{53} +(2.77651e9 - 1.91727e9i) q^{54} +4.60146e9 q^{57} +(5.63266e9 + 2.13373e9i) q^{60} +1.30276e10 q^{61} +(9.74467e9 - 6.72901e9i) q^{62} +(7.60143e9 - 4.00065e9i) q^{64} +(-1.87297e8 + 4.94431e8i) q^{68} +2.07198e10 q^{69} +(-1.59390e10 + 3.93829e9i) q^{72} -2.05512e10i q^{75} +(-2.09383e10 - 7.93170e9i) q^{76} -5.30371e10i q^{79} +(-2.19526e10 - 1.94184e10i) q^{80} +3.13811e10 q^{81} +6.18059e10i q^{83} +1.80397e9 q^{85} +(3.18311e10 + 4.60965e10i) q^{90} +(-9.42826e10 - 3.57155e10i) q^{92} +1.10137e11 q^{93} +(-4.30956e9 + 2.97589e9i) q^{94} +7.63949e10i q^{95} +(7.93165e10 + 9.55400e9i) q^{96} +(5.08465e10 + 7.36339e10i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2902 q^{4} - 62694 q^{6} - 708588 q^{9}+O(q^{10}) \) 4 * q - 2902 * q^4 - 62694 * q^6 - 708588 * q^9	\( 4 q - 2902 q^{4} - 62694 q^{6} - 708588 q^{9} - 718750 q^{10} - 12566414 q^{16} - 37428318 q^{24} + 195312500 q^{25} - 26554420 q^{34} + 514080594 q^{36} + 2514906250 q^{40} + 7332949788 q^{46} - 7909306972 q^{49} + 11106054018 q^{54} + 22530656250 q^{60} + 52110458392 q^{61} + 30405736922 q^{64} + 82879385976 q^{69} - 83753128740 q^{76} + 125524238436 q^{81} + 7215875000 q^{85} + 127324406250 q^{90} - 17238229236 q^{94} + 317266184394 q^{96}+O(q^{100}) \) 4 * q - 2902 * q^4 - 62694 * q^6 - 708588 * q^9 - 718750 * q^10 - 12566414 * q^16 - 37428318 * q^24 + 195312500 * q^25 - 26554420 * q^34 + 514080594 * q^36 + 2514906250 * q^40 + 7332949788 * q^46 - 7909306972 * q^49 + 11106054018 * q^54 + 22530656250 * q^60 + 52110458392 * q^61 + 30405736922 * q^64 + 82879385976 * q^69 - 83753128740 * q^76 + 125524238436 * q^81 + 7215875000 * q^85 + 127324406250 * q^90 - 17238229236 * q^94 + 317266184394 * q^96

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