LMFDB - Embedded newform 15.12.e.a.2.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,12,Mod(2,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("15.2");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	15.e (of order $4$, degree $2$, 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:	$11.5251477084$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2.7
Character	$\chi$	$=$	15.2
Dual form			15.12.e.a.8.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-26.1390 + 26.1390i) q^{2} +(-159.262 - 389.593i) q^{3} +681.505i q^{4} +(-2800.46 + 6402.00i) q^{5} +(14346.5 + 6020.60i) q^{6} +(5513.09 + 5513.09i) q^{7} +(-71346.5 - 71346.5i) q^{8} +(-126418. + 124095. i) q^{9} +O(q^{10})$	\(q+(-26.1390 + 26.1390i) q^{2} +(-159.262 - 389.593i) q^{3} +681.505i q^{4} +(-2800.46 + 6402.00i) q^{5} +(14346.5 + 6020.60i) q^{6} +(5513.09 + 5513.09i) q^{7} +(-71346.5 - 71346.5i) q^{8} +(-126418. + 124095. i) q^{9} +(-94140.6 - 240543. i) q^{10} -213111. i q^{11} +(265509. - 108538. i) q^{12} +(1.40784e6 - 1.40784e6i) q^{13} -288214. q^{14} +(2.94018e6 + 71441.2i) q^{15} +2.33413e6 q^{16} +(2.24338e6 - 2.24338e6i) q^{17} +(60720.1 - 6.54816e6i) q^{18} -1.02378e7i q^{19} +(-4.36299e6 - 1.90853e6i) q^{20} +(1.26983e6 - 3.02589e6i) q^{21} +(5.57051e6 + 5.57051e6i) q^{22} +(-1.46579e7 - 1.46579e7i) q^{23} +(-1.64333e7 + 3.91589e7i) q^{24} +(-3.31430e7 - 3.58571e7i) q^{25} +7.35989e7i q^{26} +(6.84801e7 + 2.94878e7i) q^{27} +(-3.75720e6 + 3.75720e6i) q^{28} +1.52840e8 q^{29} +(-7.87207e7 + 7.49859e7i) q^{30} -2.64198e8 q^{31} +(8.51058e7 - 8.51058e7i) q^{32} +(-8.30265e7 + 3.39406e7i) q^{33} +1.17279e8i q^{34} +(-5.07340e7 + 1.98556e7i) q^{35} +(-8.45713e7 - 8.61545e7i) q^{36} +(2.07043e8 + 2.07043e8i) q^{37} +(2.67607e8 + 2.67607e8i) q^{38} +(-7.72699e8 - 3.24268e8i) q^{39} +(6.56563e8 - 2.56957e8i) q^{40} -1.29665e8i q^{41} +(4.59016e7 + 1.12286e8i) q^{42} +(-2.00424e8 + 2.00424e8i) q^{43} +1.45236e8 q^{44} +(-4.40427e8 - 1.15685e9i) q^{45} +7.66285e8 q^{46} +(9.40322e8 - 9.40322e8i) q^{47} +(-3.71740e8 - 9.09361e8i) q^{48} -1.91654e9i q^{49} +(1.80359e9 + 7.09436e7i) q^{50} +(-1.23129e9 - 5.16718e8i) q^{51} +(9.59448e8 + 9.59448e8i) q^{52} +(3.25209e9 + 3.25209e9i) q^{53} +(-2.56079e9 + 1.01922e9i) q^{54} +(1.36434e9 + 5.96809e8i) q^{55} -7.86680e8i q^{56} +(-3.98859e9 + 1.63050e9i) q^{57} +(-3.99508e9 + 3.99508e9i) q^{58} -4.71394e9 q^{59} +(-4.86876e7 + 2.00375e9i) q^{60} -4.47029e9 q^{61} +(6.90587e9 - 6.90587e9i) q^{62} +(-1.38110e9 - 1.28067e7i) q^{63} +9.22947e9i q^{64} +(5.07038e9 + 1.29556e10i) q^{65} +(1.28306e9 - 3.05740e9i) q^{66} +(-1.40139e10 - 1.40139e10i) q^{67} +(1.52887e9 + 1.52887e9i) q^{68} +(-3.37615e9 + 8.04505e9i) q^{69} +(8.07130e8 - 1.84514e9i) q^{70} -9.83456e9i q^{71} +(1.78732e10 + 1.65736e8i) q^{72} +(2.37754e10 - 2.37754e10i) q^{73} -1.08238e10 q^{74} +(-8.69122e9 + 1.86229e10i) q^{75} +6.97714e9 q^{76} +(1.17490e9 - 1.17490e9i) q^{77} +(2.86736e10 - 1.17215e10i) q^{78} +6.03538e9i q^{79} +(-6.53665e9 + 1.49431e10i) q^{80} +(5.81934e8 - 3.13757e10i) q^{81} +(3.38931e9 + 3.38931e9i) q^{82} +(-3.18619e10 - 3.18619e10i) q^{83} +(2.06216e9 + 8.65397e8i) q^{84} +(8.07960e9 + 2.06446e10i) q^{85} -1.04777e10i q^{86} +(-2.43416e10 - 5.95453e10i) q^{87} +(-1.52047e10 + 1.52047e10i) q^{88} -9.38732e10 q^{89} +(4.17512e10 + 1.87266e10i) q^{90} +1.55231e10 q^{91} +(9.98942e9 - 9.98942e9i) q^{92} +(4.20768e10 + 1.02930e11i) q^{93} +4.91582e10i q^{94} +(6.55426e10 + 2.86707e10i) q^{95} +(-4.67108e10 - 1.96024e10i) q^{96} +(-1.56778e10 - 1.56778e10i) q^{97} +(5.00964e10 + 5.00964e10i) q^{98} +(2.64460e10 + 2.69410e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 504 q^{3} + 2940 q^{6} + 31504 q^{7}+O(q^{10}) $ 40 * q + 504 * q^3 + 2940 * q^6 + 31504 * q^7	$ 40 q + 504 q^{3} + 2940 q^{6} + 31504 q^{7} + 305140 q^{10} - 1714188 q^{12} - 3448472 q^{13} - 6075120 q^{15} - 43202180 q^{16} + 3729120 q^{18} + 33570840 q^{21} - 21743260 q^{22} - 68969000 q^{25} + 113282712 q^{27} + 253355948 q^{28} + 536094300 q^{30} + 67990880 q^{31} - 563443560 q^{33} + 1116103980 q^{36} + 1292573224 q^{37} - 2754089880 q^{40} - 5132304780 q^{42} + 4012128208 q^{43} + 4994447400 q^{45} - 8170829920 q^{46} - 13847034876 q^{48} + 5424535440 q^{51} + 10287332704 q^{52} - 23061806800 q^{55} - 10576855656 q^{57} + 56277468420 q^{58} + 66297294060 q^{60} - 24994982320 q^{61} - 50371112832 q^{63} + 56311074600 q^{66} + 37314988144 q^{67} - 90895488900 q^{70} - 92983114440 q^{72} + 51361482568 q^{73} + 96079968600 q^{75} - 121004023440 q^{76} - 104085843000 q^{78} - 22936122360 q^{81} - 56747065840 q^{82} + 5885083240 q^{85} + 84564024000 q^{87} + 148338843420 q^{88} + 17247857160 q^{90} + 230876677280 q^{91} + 38932525008 q^{93} - 437860137180 q^{96} - 294950050616 q^{97}+O(q^{100}) $ 40 * q + 504 * q^3 + 2940 * q^6 + 31504 * q^7 + 305140 * q^10 - 1714188 * q^12 - 3448472 * q^13 - 6075120 * q^15 - 43202180 * q^16 + 3729120 * q^18 + 33570840 * q^21 - 21743260 * q^22 - 68969000 * q^25 + 113282712 * q^27 + 253355948 * q^28 + 536094300 * q^30 + 67990880 * q^31 - 563443560 * q^33 + 1116103980 * q^36 + 1292573224 * q^37 - 2754089880 * q^40 - 5132304780 * q^42 + 4012128208 * q^43 + 4994447400 * q^45 - 8170829920 * q^46 - 13847034876 * q^48 + 5424535440 * q^51 + 10287332704 * q^52 - 23061806800 * q^55 - 10576855656 * q^57 + 56277468420 * q^58 + 66297294060 * q^60 - 24994982320 * q^61 - 50371112832 * q^63 + 56311074600 * q^66 + 37314988144 * q^67 - 90895488900 * q^70 - 92983114440 * q^72 + 51361482568 * q^73 + 96079968600 * q^75 - 121004023440 * q^76 - 104085843000 * q^78 - 22936122360 * q^81 - 56747065840 * q^82 + 5885083240 * q^85 + 84564024000 * q^87 + 148338843420 * q^88 + 17247857160 * q^90 + 230876677280 * q^91 + 38932525008 * q^93 - 437860137180 * q^96 - 294950050616 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−26.1390	+	26.1390i	−0.577596	+	0.577596i	−0.934240	−	0.356644i	$-0.883921\pi$
$2$	−26.1390	+	26.1390i	−0.577596	+	0.577596i	0.356644	+	0.934240i	$0.383921\pi$
$3$	−159.262	−	389.593i	−0.378396	−	0.925644i
$3$	−159.262	−	389.593i	−0.378396	−	0.925644i
$4$			681.505i			0.332766i
$5$	−2800.46	+	6402.00i	−0.400769	+	0.916179i
$5$	−2800.46	+	6402.00i	−0.400769	+	0.916179i
$6$	14346.5	+	6020.60i	0.753208	+	0.316088i
$7$	5513.09	+	5513.09i	0.123981	+	0.123981i	0.766375	−	0.642394i	$-0.222059\pi$
$7$	5513.09	+	5513.09i	0.123981	+	0.123981i	−0.642394	+	0.766375i	$0.722059\pi$
$8$	−71346.5	−	71346.5i	−0.769800	−	0.769800i
$9$	−126418.	+	124095.i	−0.713633	+	0.700520i
$10$	−94140.6	−	240543.i	−0.297699	−	0.760664i
$11$		−	213111.i		−	0.398975i	−0.979900	−	0.199488i	$-0.936072\pi$
$11$		−	213111.i		−	0.398975i	0.979900	−	0.199488i	$-0.0639278\pi$
$12$	265509.	−	108538.i	0.308023	−	0.125917i
$13$	1.40784e6	−	1.40784e6i	1.05163	−	1.05163i	0.0530403	−	0.998592i	$-0.483109\pi$
$13$	1.40784e6	−	1.40784e6i	1.05163	−	1.05163i	0.998592	−	0.0530403i	$-0.0168912\pi$
$14$	−288214.			−0.143222
$15$	2.94018e6	+	71441.2i	0.999705	+	0.0242911i
$16$	2.33413e6			0.556501
$17$	2.24338e6	−	2.24338e6i	0.383207	−	0.383207i	−0.489049	−	0.872256i	$-0.662656\pi$
$17$	2.24338e6	−	2.24338e6i	0.383207	−	0.383207i	0.872256	+	0.489049i	$0.162656\pi$
$18$	60720.1	−	6.54816e6i	0.00757415	−	0.816809i
$19$		−	1.02378e7i		−	0.948557i	−0.880375	−	0.474279i	$-0.842709\pi$
$19$		−	1.02378e7i		−	0.948557i	0.880375	−	0.474279i	$-0.157291\pi$
$20$	−4.36299e6	−	1.90853e6i	−0.304873	−	0.133362i
$21$	1.26983e6	−	3.02589e6i	0.0678485	−	0.161677i
$22$	5.57051e6	+	5.57051e6i	0.230446	+	0.230446i
$23$	−1.46579e7	−	1.46579e7i	−0.474863	−	0.474863i	0.428622	−	0.903484i	$-0.358999\pi$
$23$	−1.46579e7	−	1.46579e7i	−0.474863	−	0.474863i	−0.903484	+	0.428622i	$0.858999\pi$
$24$	−1.64333e7	+	3.91589e7i	−0.421271	+	1.00385i
$25$	−3.31430e7	−	3.58571e7i	−0.678768	−	0.734353i
$26$			7.35989e7i			1.21484i
$27$	6.84801e7	+	2.94878e7i	0.918468	+	0.395496i
$28$	−3.75720e6	+	3.75720e6i	−0.0412568	+	0.0412568i
$29$	1.52840e8			1.38372			0.691859	−	0.722033i	$-0.256792\pi$
$29$	1.52840e8			1.38372			0.691859	+	0.722033i	$0.256792\pi$
$30$	−7.87207e7	+	7.49859e7i	−0.591456	+	0.563395i
$31$	−2.64198e8			−1.65745			−0.828725	−	0.559656i	$-0.810933\pi$
$31$	−2.64198e8			−1.65745			−0.828725	+	0.559656i	$0.810933\pi$
$32$	8.51058e7	−	8.51058e7i	0.448368	−	0.448368i
$33$	−8.30265e7	+	3.39406e7i	−0.369309	+	0.150971i
$34$			1.17279e8i			0.442677i
$35$	−5.07340e7	+	1.98556e7i	−0.163277	+	0.0639012i
$36$	−8.45713e7	−	8.61545e7i	−0.233109	−	0.237473i
$37$	2.07043e8	+	2.07043e8i	0.490853	+	0.490853i	0.908575	−	0.417722i	$-0.137171\pi$
$37$	2.07043e8	+	2.07043e8i	0.490853	+	0.490853i	−0.417722	+	0.908575i	$0.637171\pi$
$38$	2.67607e8	+	2.67607e8i	0.547883	+	0.547883i
$39$	−7.72699e8	−	3.24268e8i	−1.37137	−	0.575504i
$40$	6.56563e8	−	2.56957e8i	1.01379	−	0.396763i
$41$		−	1.29665e8i		−	0.174788i	−0.996174	−	0.0873939i	$-0.972146\pi$
$41$		−	1.29665e8i		−	0.174788i	0.996174	−	0.0873939i	$-0.0278539\pi$
$42$	4.59016e7	+	1.12286e8i	0.0541947	+	0.132573i
$43$	−2.00424e8	+	2.00424e8i	−0.207909	+	0.207909i	−0.803378	−	0.595469i	$-0.796966\pi$
$43$	−2.00424e8	+	2.00424e8i	−0.207909	+	0.207909i	0.595469	+	0.803378i	$0.296966\pi$
$44$	1.45236e8			0.132765
$45$	−4.40427e8	−	1.15685e9i	−0.355799	−	0.934562i
$46$	7.66285e8			0.548557
$47$	9.40322e8	−	9.40322e8i	0.598051	−	0.598051i	−0.341742	−	0.939794i	$-0.611017\pi$
$47$	9.40322e8	−	9.40322e8i	0.598051	−	0.598051i	0.939794	+	0.341742i	$0.111017\pi$
$48$	−3.71740e8	−	9.09361e8i	−0.210578	−	0.515121i
$49$		−	1.91654e9i		−	0.969257i
$50$	1.80359e9	+	7.09436e7i	0.816213	+	0.0321054i
$51$	−1.23129e9	−	5.16718e8i	−0.499717	−	0.209709i
$52$	9.59448e8	+	9.59448e8i	0.349948	+	0.349948i
$53$	3.25209e9	+	3.25209e9i	1.06818	+	1.06818i	0.997499	+	0.0706837i	$0.0225181\pi$
$53$	3.25209e9	+	3.25209e9i	1.06818	+	1.06818i	0.0706837	+	0.997499i	$0.477482\pi$
$54$	−2.56079e9	+	1.01922e9i	−0.758940	+	0.302066i
$55$	1.36434e9	+	5.96809e8i	0.365533	+	0.159897i
$56$		−	7.86680e8i		−	0.190882i
$57$	−3.98859e9	+	1.63050e9i	−0.878026	+	0.358930i
$58$	−3.99508e9	+	3.99508e9i	−0.799230	+	0.799230i
$59$	−4.71394e9			−0.858417			−0.429208	−	0.903206i	$-0.641207\pi$
$59$	−4.71394e9			−0.858417			−0.429208	+	0.903206i	$0.641207\pi$
$60$	−4.86876e7	+	2.00375e9i	−0.00808325	+	0.332668i
$61$	−4.47029e9			−0.677675			−0.338838	−	0.940845i	$-0.610034\pi$
$61$	−4.47029e9			−0.677675			−0.338838	+	0.940845i	$0.610034\pi$
$62$	6.90587e9	−	6.90587e9i	0.957336	−	0.957336i
$63$	−1.38110e9	−	1.28067e7i	−0.175328	−	0.00162580i
$64$			9.22947e9i			1.07445i
$65$	5.07038e9	+	1.29556e10i	0.542022	+	1.38495i
$66$	1.28306e9	−	3.05740e9i	0.126111	−	0.300511i
$67$	−1.40139e10	−	1.40139e10i	−1.26808	−	1.26808i	−0.947076	−	0.321008i	$-0.895978\pi$
$67$	−1.40139e10	−	1.40139e10i	−1.26808	−	1.26808i	−0.321008	−	0.947076i	$-0.604022\pi$
$68$	1.52887e9	+	1.52887e9i	0.127518	+	0.127518i
$69$	−3.37615e9	+	8.04505e9i	−0.259868	+	0.619240i
$70$	8.07130e8	−	1.84514e9i	0.0573990	−	0.131217i
$71$		−	9.83456e9i		−	0.646895i	−0.946246	−	0.323448i	$-0.895158\pi$
$71$		−	9.83456e9i		−	0.646895i	0.946246	−	0.323448i	$-0.104842\pi$
$72$	1.78732e10	+	1.65736e8i	1.08862	+	0.0100946i
$73$	2.37754e10	−	2.37754e10i	1.34231	−	1.34231i	0.448545	−	0.893760i	$-0.351942\pi$
$73$	2.37754e10	−	2.37754e10i	1.34231	−	1.34231i	0.893760	−	0.448545i	$-0.148058\pi$
$74$	−1.08238e10			−0.567030
$75$	−8.69122e9	+	1.86229e10i	−0.422906	+	0.906174i
$76$	6.97714e9			0.315648
$77$	1.17490e9	−	1.17490e9i	0.0494655	−	0.0494655i
$78$	2.86736e10	−	1.17215e10i	1.12451	−	0.459690i
$79$			6.03538e9i			0.220676i	0.993894	+	0.110338i	$0.0351934\pi$
$79$			6.03538e9i			0.220676i	−0.993894	+	0.110338i	$0.964807\pi$
$80$	−6.53665e9	+	1.49431e10i	−0.223028	+	0.509854i
$81$	5.81934e8	−	3.13757e10i	0.0185441	−	0.999828i
$82$	3.38931e9	+	3.38931e9i	0.100957	+	0.100957i
$83$	−3.18619e10	−	3.18619e10i	−0.887854	−	0.887854i	0.106463	−	0.994317i	$-0.466048\pi$
$83$	−3.18619e10	−	3.18619e10i	−0.887854	−	0.887854i	−0.994317	+	0.106463i	$0.966048\pi$
$84$	2.06216e9	+	8.65397e8i	0.0538005	+	0.0225777i
$85$	8.07960e9	+	2.06446e10i	0.197509	+	0.504664i
$86$		−	1.04777e10i		−	0.240174i
$87$	−2.43416e10	−	5.95453e10i	−0.523593	−	1.28083i
$88$	−1.52047e10	+	1.52047e10i	−0.307131	+	0.307131i
$89$	−9.38732e10			−1.78195			−0.890977	−	0.454049i	$-0.849979\pi$
$89$	−9.38732e10			−1.78195			−0.890977	+	0.454049i	$0.849979\pi$
$90$	4.17512e10	+	1.87266e10i	0.745308	+	0.334291i
$91$	1.55231e10			0.260766
$92$	9.98942e9	−	9.98942e9i	0.158018	−	0.158018i
$93$	4.20768e10	+	1.02930e11i	0.627172	+	1.53421i
$94$			4.91582e10i			0.690864i
$95$	6.55426e10	+	2.86707e10i	0.869048	+	0.380153i
$96$	−4.67108e10	−	1.96024e10i	−0.584689	−	0.245368i
$97$	−1.56778e10	−	1.56778e10i	−0.185371	−	0.185371i	0.608321	−	0.793691i	$-0.291843\pi$
$97$	−1.56778e10	−	1.56778e10i	−0.185371	−	0.185371i	−0.793691	+	0.608321i	$0.791843\pi$
$98$	5.00964e10	+	5.00964e10i	0.559839	+	0.559839i
$99$	2.64460e10	+	2.69410e10i	0.279490	+	0.284722i
$100$	2.44368e10	−	2.25871e10i	0.244368	−	0.225871i
$101$			2.76599e9i			0.0261869i	0.999914	+	0.0130934i	$0.00416789\pi$
$101$			2.76599e9i			0.0261869i	−0.999914	+	0.0130934i	$0.995832\pi$
$102$	4.56912e10	−	1.86782e10i	0.409762	−	0.167507i
$103$	−3.71254e10	+	3.71254e10i	−0.315549	+	0.315549i	−0.847055	−	0.531506i	$-0.821626\pi$
$103$	−3.71254e10	+	3.71254e10i	−0.315549	+	0.315549i	0.531506	+	0.847055i	$0.321626\pi$
$104$	−2.00889e11			−1.61909
$105$	1.58156e10	+	1.66033e10i	0.120933	+	0.126956i
$106$	−1.70013e11			−1.23396
$107$	7.55755e10	−	7.55755e10i	0.520919	−	0.520919i	−0.396930	−	0.917849i	$-0.629924\pi$
$107$	7.55755e10	−	7.55755e10i	0.520919	−	0.520919i	0.917849	+	0.396930i	$0.129924\pi$
$108$	−2.00961e10	+	4.66695e10i	−0.131608	+	0.305635i
$109$		−	2.26559e10i		−	0.141038i	−0.997510	−	0.0705189i	$-0.977534\pi$
$109$		−	2.26559e10i		−	0.141038i	0.997510	−	0.0705189i	$-0.0224655\pi$
$110$	−5.12623e10	+	2.00624e10i	−0.303486	+	0.118774i
$111$	4.76883e10	−	1.13637e11i	0.268618	−	0.640092i
$112$	1.28683e10	+	1.28683e10i	0.0689957	+	0.0689957i
$113$	−4.68241e10	−	4.68241e10i	−0.239077	−	0.239077i	0.577391	−	0.816468i	$-0.304071\pi$
$113$	−4.68241e10	−	4.68241e10i	−0.239077	−	0.239077i	−0.816468	+	0.577391i	$0.804071\pi$
$114$	6.16380e10	−	1.46877e11i	0.299828	−	0.714461i
$115$	1.34888e11	−	5.27909e10i	0.625370	−	0.244749i
$116$			1.04161e11i			0.460454i
$117$	−3.27036e9	+	3.52681e11i	−0.0137903	+	1.48717i
$118$	1.23218e11	−	1.23218e11i	0.495818	−	0.495818i
$119$	2.47359e10			0.0950209
$120$	−2.04675e11	−	2.14869e11i	−0.750874	−	0.788272i
$121$	2.39895e11			0.840819
$122$	1.16849e11	−	1.16849e11i	0.391422	−	0.391422i
$123$	−5.05165e10	+	2.06508e10i	−0.161791	+	0.0661390i
$124$		−	1.80052e11i		−	0.551543i
$125$	3.22372e11	−	1.11765e11i	0.944828	−	0.327567i
$126$	3.64354e10	−	3.57658e10i	0.102208	−	0.100330i
$127$	1.39533e10	+	1.39533e10i	0.0374762	+	0.0374762i	0.725597	−	0.688120i	$-0.241564\pi$
$127$	1.39533e10	+	1.39533e10i	0.0374762	+	0.0374762i	−0.688120	+	0.725597i	$0.741564\pi$
$128$	−6.69523e10	−	6.69523e10i	−0.172231	−	0.172231i
$129$	1.10004e11	+	4.61636e10i	0.271121	+	0.113778i
$130$	−4.71180e11	−	2.06111e11i	−1.11301	−	0.486869i
$131$			2.87714e11i			0.651582i	0.945442	+	0.325791i	$0.105631\pi$
$131$			2.87714e11i			0.651582i	−0.945442	+	0.325791i	$0.894369\pi$
$132$	−2.31307e10	−	5.65830e10i	−0.0502379	−	0.122894i
$133$	5.64422e10	−	5.64422e10i	0.117603	−	0.117603i
$134$	7.32620e11			1.46488
$135$	−3.80557e11	+	3.55830e11i	−0.730439	+	0.682978i
$136$	−3.20114e11			−0.589985
$137$	6.57073e9	−	6.57073e9i	0.0116319	−	0.0116319i	−0.701267	−	0.712899i	$-0.747382\pi$
$137$	6.57073e9	−	6.57073e9i	0.0116319	−	0.0116319i	0.712899	+	0.701267i	$0.247382\pi$
$138$	−1.22040e11	−	2.98539e11i	−0.207572	−	0.507769i
$139$			4.58263e11i			0.749089i	0.927209	+	0.374544i	$0.122201\pi$
$139$			4.58263e11i			0.749089i	−0.927209	+	0.374544i	$0.877799\pi$
$140$	−1.35317e10	−	3.45755e10i	−0.0212641	−	0.0543330i
$141$	−5.16101e11	−	2.16585e11i	−0.779883	−	0.327282i
$142$	2.57066e11	+	2.57066e11i	0.373644	+	0.373644i
$143$	−3.00026e11	−	3.00026e11i	−0.419575	−	0.419575i
$144$	−2.95076e11	+	2.89654e11i	−0.397137	+	0.389840i
$145$	−4.28022e11	+	9.78480e11i	−0.554551	+	1.26773i
$146$			1.24293e12i			1.55062i
$147$	−7.46669e11	+	3.05233e11i	−0.897187	+	0.366763i
$148$	−1.41101e11	+	1.41101e11i	−0.163339	+	0.163339i
$149$	8.85563e11			0.987859			0.493929	−	0.869502i	$-0.335560\pi$
$149$	8.85563e11			0.987859			0.493929	+	0.869502i	$0.335560\pi$
$150$	−2.59605e11	−	7.13965e11i	−0.279133	−	0.767671i
$151$	1.43011e12			1.48250			0.741251	−	0.671228i	$-0.234233\pi$
$151$	1.43011e12			1.48250			0.741251	+	0.671228i	$0.234233\pi$
$152$	−7.30435e11	+	7.30435e11i	−0.730200	+	0.730200i
$153$	−5.21130e9	+	5.61995e11i	−0.00502508	+	0.541913i
$154$			6.14214e10i			0.0571421i
$155$	7.39876e11	−	1.69139e12i	0.664255	−	1.51852i
$156$	2.20990e11	−	5.26598e11i	0.191508	−	0.456346i
$157$	−1.32762e12	−	1.32762e12i	−1.11078	−	1.11078i	−0.993046	−	0.117731i	$-0.962438\pi$
$157$	−1.32762e12	−	1.32762e12i	−1.11078	−	1.11078i	−0.117731	−	0.993046i	$-0.537562\pi$
$158$	−1.57759e11	−	1.57759e11i	−0.127462	−	0.127462i
$159$	7.49055e11	−	1.78493e12i	0.584561	−	1.39295i
$160$	3.06512e11	+	7.83182e11i	0.231093	+	0.590477i
$161$		−	1.61620e11i		−	0.117748i
$162$	8.04917e11	+	8.35340e11i	0.566786	+	0.588208i
$163$	−2.03428e11	+	2.03428e11i	−0.138477	+	0.138477i	−0.772947	−	0.634470i	$-0.781218\pi$
$163$	−2.03428e11	+	2.03428e11i	−0.138477	+	0.138477i	0.634470	+	0.772947i	$0.281218\pi$
$164$	8.83673e10			0.0581635
$165$	1.52249e10	−	6.26584e11i	0.00969154	−	0.398858i
$166$	1.66567e12			1.02564
$167$	−5.88852e11	+	5.88852e11i	−0.350805	+	0.350805i	−0.860409	−	0.509604i	$-0.829792\pi$
$167$	−5.88852e11	+	5.88852e11i	−0.350805	+	0.350805i	0.509604	+	0.860409i	$0.329792\pi$
$168$	−3.06485e11	+	1.25289e11i	−0.176688	+	0.0722288i
$169$		−	2.17185e12i		−	1.21186i
$170$	−7.50822e11	−	3.28436e11i	−0.405572	−	0.177411i
$171$	1.27046e12	+	1.29425e12i	0.664483	+	0.676922i
$172$	−1.36590e11	−	1.36590e11i	−0.0691849	−	0.0691849i
$173$	−9.94474e11	−	9.94474e11i	−0.487910	−	0.487910i	0.419736	−	0.907646i	$-0.362123\pi$
$173$	−9.94474e11	−	9.94474e11i	−0.487910	−	0.487910i	−0.907646	+	0.419736i	$0.862123\pi$
$174$	2.19272e12	+	9.20188e11i	1.04223	+	0.437377i
$175$	1.49630e10	−	3.80404e11i	0.00689145	−	0.175201i
$176$		−	4.97429e11i		−	0.222030i
$177$	7.50754e11	+	1.83652e12i	0.324821	+	0.794588i
$178$	2.45375e12	−	2.45375e12i	1.02925	−	1.02925i
$179$	−2.93207e12			−1.19257			−0.596283	−	0.802774i	$-0.703356\pi$
$179$	−2.93207e12			−1.19257			−0.596283	+	0.802774i	$0.703356\pi$
$180$	7.88399e11	−	3.00153e11i	0.310991	−	0.118398i
$181$	−2.69642e12			−1.03170			−0.515852	−	0.856678i	$-0.672525\pi$
$181$	−2.69642e12			−1.03170			−0.515852	+	0.856678i	$0.672525\pi$
$182$	−4.05758e11	+	4.05758e11i	−0.150617	+	0.150617i
$183$	7.11949e11	+	1.74159e12i	0.256430	+	0.627286i
$184$			2.09158e12i			0.731099i
$185$	−1.90531e12	+	7.45674e11i	−0.646428	+	0.252991i
$186$	−3.79032e12	−	1.59063e12i	−1.24840	−	0.523900i
$187$	−4.78088e11	−	4.78088e11i	−0.152890	−	0.152890i
$188$	6.40834e11	+	6.40834e11i	0.199011	+	0.199011i
$189$	2.14968e11	+	5.40106e11i	0.0648387	+	0.162907i
$190$	−2.46264e12	+	9.63796e11i	−0.721533	+	0.282384i
$191$		−	2.71574e11i		−	0.0773046i	−0.999253	−	0.0386523i	$-0.987694\pi$
$191$		−	2.71574e11i		−	0.0773046i	0.999253	−	0.0386523i	$-0.0123065\pi$
$192$	3.59573e12	−	1.46991e12i	0.994559	−	0.406568i
$193$	−4.02711e12	+	4.02711e12i	−1.08250	+	1.08250i	−0.0862264	+	0.996276i	$0.527481\pi$
$193$	−4.02711e12	+	4.02711e12i	−1.08250	+	1.08250i	−0.996276	+	0.0862264i	$0.972519\pi$
$194$	8.19605e11			0.214139
$195$	4.23987e12	−	4.03872e12i	1.07687	−	1.02578i
$196$	1.30613e12			0.322536
$197$	2.68889e12	−	2.68889e12i	0.645668	−	0.645668i	−0.306275	−	0.951943i	$-0.599083\pi$
$197$	2.68889e12	−	2.68889e12i	0.645668	−	0.645668i	0.951943	+	0.306275i	$0.0990828\pi$
$198$	−1.39548e12	−	1.29401e10i	−0.325886	−	0.00302190i
$199$			9.81048e11i			0.222843i	0.993773	+	0.111421i	$0.0355403\pi$
$199$			9.81048e11i			0.222843i	−0.993773	+	0.111421i	$0.964460\pi$
$200$	−1.93641e11	+	4.92291e12i	−0.0427890	+	1.08782i
$201$	−3.22783e12	+	7.69161e12i	−0.693957	+	1.65363i
$202$	−7.23003e10	−	7.23003e10i	−0.0151254	−	0.0151254i
$203$	8.42620e11	+	8.42620e11i	0.171555	+	0.171555i
$204$	3.52146e11	−	8.39130e11i	0.0697841	−	0.166289i
$205$	8.30114e11	+	3.63121e11i	0.160137	+	0.0700496i
$206$		−	1.94084e12i		−	0.364519i
$207$	3.67199e12	+	3.40498e10i	0.671528	+	0.00622699i
$208$	3.28608e12	−	3.28608e12i	0.585234	−	0.585234i
$209$	−2.18180e12			−0.378451
$210$	−8.47399e11	−	2.05903e10i	−0.143180	−	0.00347902i
$211$	2.32367e12			0.382490			0.191245	−	0.981542i	$-0.438747\pi$
$211$	2.32367e12			0.382490			0.191245	+	0.981542i	$0.438747\pi$
$212$	−2.21632e12	+	2.21632e12i	−0.355455	+	0.355455i
$213$	−3.83147e12	+	1.56628e12i	−0.598795	+	0.244783i
$214$			3.95094e12i			0.601762i
$215$	−7.21833e11	−	1.84439e12i	−0.107158	−	0.273805i
$216$	−2.78196e12	−	6.98968e12i	−0.402584	−	1.01149i
$217$	−1.45655e12	−	1.45655e12i	−0.205493	−	0.205493i
$218$	5.92202e11	+	5.92202e11i	0.0814628	+	0.0814628i
$219$	−1.30492e13	−	5.47618e12i	−1.75042	−	0.734574i
$220$	−4.06728e11	+	9.29801e11i	−0.0532083	+	0.121637i
$221$		−	6.31662e12i		−	0.805986i
$222$	1.72383e12	+	4.21688e12i	0.214562	+	0.524867i
$223$	1.03012e13	−	1.03012e13i	1.25086	−	1.25086i	0.295529	−	0.955334i	$-0.404504\pi$
$223$	1.03012e13	−	1.03012e13i	1.25086	−	1.25086i	0.955334	−	0.295529i	$-0.0954960\pi$
$224$	9.38392e11			0.111178
$225$	8.63955e12	+	4.20100e11i	0.998820	+	0.0485678i
$226$	2.44787e12			0.276180
$227$	8.89178e12	−	8.89178e12i	0.979144	−	0.979144i	−0.0206428	−	0.999787i	$-0.506571\pi$
$227$	8.89178e12	−	8.89178e12i	0.979144	−	0.979144i	0.999787	+	0.0206428i	$0.00657128\pi$
$228$	−1.11120e12	−	2.71824e12i	−0.119440	−	0.292177i
$229$			1.14466e13i			1.20110i	0.799587	+	0.600551i	$0.205052\pi$
$229$			1.14466e13i			1.20110i	−0.799587	+	0.600551i	$0.794948\pi$
$230$	−2.14595e12	+	4.90575e12i	−0.219845	+	0.502577i
$231$	−6.44850e11	−	2.70615e11i	−0.0645049	−	0.0270699i
$232$	−1.09046e13	−	1.09046e13i	−1.06519	−	1.06519i
$233$	8.02145e12	+	8.02145e12i	0.765235	+	0.765235i	0.977264	−	0.212028i	$-0.0680068\pi$
$233$	8.02145e12	+	8.02145e12i	0.765235	+	0.765235i	−0.212028	+	0.977264i	$0.568007\pi$
$234$	−9.13326e12	−	9.30423e12i	−0.851018	−	0.866948i
$235$	3.38660e12	+	8.65327e12i	0.308242	+	0.787603i
$236$		−	3.21257e12i		−	0.285652i
$237$	2.35134e12	−	9.61209e11i	0.204268	−	0.0835030i
$238$	−6.46572e11	+	6.46572e11i	−0.0548837	+	0.0548837i
$239$	1.69963e12			0.140983			0.0704915	−	0.997512i	$-0.477543\pi$
$239$	1.69963e12			0.140983			0.0704915	+	0.997512i	$0.477543\pi$
$240$	6.86277e12	+	1.66753e11i	0.556336	+	0.0135180i
$241$	1.38860e13			1.10023			0.550114	−	0.835089i	$-0.314584\pi$
$241$	1.38860e13			1.10023			0.550114	+	0.835089i	$0.314584\pi$
$242$	−6.27063e12	+	6.27063e12i	−0.485653	+	0.485653i
$243$	−1.23164e13	+	4.77025e12i	−0.932502	+	0.361166i
$244$		−	3.04652e12i		−	0.225507i
$245$	1.22697e13	+	5.36719e12i	0.888013	+	0.388448i
$246$	7.80661e11	−	1.86024e12i	0.0552484	−	0.131652i
$247$	−1.44132e13	−	1.44132e13i	−0.997534	−	0.997534i
$248$	1.88496e13	+	1.88496e13i	1.27590	+	1.27590i
$249$	−7.33875e12	+	1.74875e13i	−0.485876	+	1.15780i
$250$	−5.50507e12	+	1.13479e13i	−0.356527	+	0.734930i
$251$		−	1.94310e13i		−	1.23109i	−0.788103	−	0.615543i	$-0.788937\pi$
$251$		−	1.94310e13i		−	1.23109i	0.788103	−	0.615543i	$-0.211063\pi$
$252$	8.72786e9	−	9.41227e11i	0.000541010	−	0.0583434i
$253$	−3.12375e12	+	3.12375e12i	−0.189458	+	0.189458i
$254$	−7.29449e11			−0.0432922
$255$	6.75620e12	−	6.43566e12i	0.392402	−	0.373785i
$256$	−1.54018e13			−0.875492
$257$	−2.02657e12	+	2.02657e12i	−0.112753	+	0.112753i	−0.761232	−	0.648479i	$-0.775405\pi$
$257$	−2.02657e12	+	2.02657e12i	−0.112753	+	0.112753i	0.648479	+	0.761232i	$0.275405\pi$
$258$	−4.08205e12	+	1.66871e12i	−0.222316	+	0.0908810i
$259$			2.28290e12i			0.121713i
$260$	−8.82928e12	+	3.45549e12i	−0.460863	+	0.180366i
$261$	−1.93217e13	+	1.89667e13i	−0.987467	+	0.969322i
$262$	−7.52056e12	−	7.52056e12i	−0.376351	−	0.376351i
$263$	−1.82256e13	−	1.82256e13i	−0.893151	−	0.893151i	0.101667	−	0.994818i	$-0.467582\pi$
$263$	−1.82256e13	−	1.82256e13i	−0.893151	−	0.893151i	−0.994818	+	0.101667i	$0.967582\pi$
$264$	8.34519e12	+	3.50211e12i	0.400511	+	0.168077i
$265$	−2.99272e13	+	1.17125e13i	−1.40674	+	0.550552i
$266$			2.95068e12i			0.135854i
$267$	1.49505e13	+	3.65723e13i	0.674284	+	1.64945i
$268$	9.55056e12	−	9.55056e12i	0.421976	−	0.421976i
$269$	7.65520e12			0.331374			0.165687	−	0.986178i	$-0.447016\pi$
$269$	7.65520e12			0.331374			0.165687	+	0.986178i	$0.447016\pi$
$270$	6.46336e11	−	1.92484e13i	0.0274131	−	0.816384i
$271$	3.10818e13			1.29174			0.645870	−	0.763447i	$-0.276495\pi$
$271$	3.10818e13			1.29174			0.645870	+	0.763447i	$0.276495\pi$
$272$	5.23634e12	−	5.23634e12i	0.213255	−	0.213255i
$273$	−2.47224e12	−	6.04768e12i	−0.0986726	−	0.241376i
$274$			3.43505e11i			0.0134371i
$275$	−7.64153e12	+	7.06313e12i	−0.292989	+	0.270812i
$276$	−5.48274e12	−	2.30086e12i	−0.206062	−	0.0864751i
$277$	4.52314e12	+	4.52314e12i	0.166648	+	0.166648i	0.785504	−	0.618856i	$-0.212404\pi$
$277$	4.52314e12	+	4.52314e12i	0.166648	+	0.166648i	−0.618856	+	0.785504i	$0.712404\pi$
$278$	−1.19785e13	−	1.19785e13i	−0.432670	−	0.432670i
$279$	3.33994e13	−	3.27857e13i	1.18281	−	1.16108i
$280$	5.03632e12	+	2.20307e12i	0.174882	+	0.0764995i
$281$			4.20421e13i			1.43153i	0.698343	+	0.715763i	$0.253921\pi$
$281$			4.20421e13i			1.43153i	−0.698343	+	0.715763i	$0.746079\pi$
$282$	1.91517e13	−	7.82905e12i	0.639494	−	0.261420i
$283$	2.84577e13	−	2.84577e13i	0.931911	−	0.931911i	−0.0659139	−	0.997825i	$-0.520996\pi$
$283$	2.84577e13	−	2.84577e13i	0.931911	−	0.931911i	0.997825	+	0.0659139i	$0.0209963\pi$
$284$	6.70230e12			0.215265
$285$	7.31404e11	−	3.01011e13i	0.0230415	−	0.948278i
$286$	1.56847e13			0.484690
$287$	7.14855e11	−	7.14855e11i	0.0216704	−	0.0216704i
$288$	−1.97698e11	+	2.13201e13i	−0.00587955	+	0.634060i
$289$			2.42064e13i			0.706305i
$290$	−1.43884e13	−	3.67646e13i	−0.411931	−	1.05254i
$291$	−3.61108e12	+	8.60485e12i	−0.101444	+	0.241731i
$292$	1.62030e13	+	1.62030e13i	0.446674	+	0.446674i
$293$	−2.33487e13	−	2.33487e13i	−0.631672	−	0.631672i	0.316815	−	0.948487i	$-0.397386\pi$
$293$	−2.33487e13	−	2.33487e13i	−0.631672	−	0.631672i	−0.948487	+	0.316815i	$0.897386\pi$
$294$	1.15387e13	−	2.74957e13i	0.306371	−	0.730052i
$295$	1.32012e13	−	3.01786e13i	0.344027	−	0.786463i
$296$		−	2.95436e13i		−	0.755718i
$297$	6.28418e12	−	1.45939e13i	0.157793	−	0.366446i
$298$	−2.31477e13	+	2.31477e13i	−0.570583	+	0.570583i
$299$	−4.12718e13			−0.998762
$300$	−1.26916e13	−	5.92311e12i	−0.301544	−	0.140729i
$301$	−2.20991e12			−0.0515535
$302$	−3.73816e13	+	3.73816e13i	−0.856287	+	0.856287i
$303$	1.07761e12	−	4.40519e11i	0.0242397	−	0.00990901i
$304$		−	2.38965e13i		−	0.527873i
$305$	1.25189e13	−	2.86188e13i	0.271591	−	0.620872i
$306$	−1.45538e13	−	1.48262e13i	−0.310104	−	0.315909i
$307$	−2.20819e13	−	2.20819e13i	−0.462141	−	0.462141i	0.437216	−	0.899357i	$-0.355965\pi$
$307$	−2.20819e13	−	2.20819e13i	−0.462141	−	0.462141i	−0.899357	+	0.437216i	$0.855965\pi$
$308$	8.00700e11	+	8.00700e11i	0.0164604	+	0.0164604i
$309$	2.03765e13	+	8.55110e12i	0.411488	+	0.172683i
$310$	2.48718e13	+	6.35510e13i	0.493420	+	1.26076i
$311$			8.99308e13i			1.75278i	0.481606	+	0.876388i	$0.340054\pi$
$311$			8.99308e13i			1.75278i	−0.481606	+	0.876388i	$0.659946\pi$
$312$	3.19940e13	+	7.82648e13i	0.612659	+	1.49870i
$313$	−2.91430e13	+	2.91430e13i	−0.548328	+	0.548328i	−0.925957	−	0.377629i	$-0.876739\pi$
$313$	−2.91430e13	+	2.91430e13i	−0.548328	+	0.548328i	0.377629	+	0.925957i	$0.376739\pi$
$314$	6.94055e13			1.28316
$315$	3.94971e12	−	8.80594e12i	0.0717558	−	0.159981i
$316$	−4.11314e12			−0.0734336
$317$	−1.62504e13	+	1.62504e13i	−0.285126	+	0.285126i	−0.835149	−	0.550023i	$-0.814619\pi$
$317$	−1.62504e13	+	1.62504e13i	−0.285126	+	0.285126i	0.550023	+	0.835149i	$0.314619\pi$
$318$	2.70767e13	+	6.62358e13i	0.466924	+	1.14220i
$319$		−	3.25718e13i		−	0.552069i
$320$	−5.90870e13	−	2.58467e13i	−0.984390	−	0.430607i
$321$	−4.14800e13	−	1.74073e13i	−0.679299	−	0.285072i
$322$	4.22460e12	+	4.22460e12i	0.0680108	+	0.0680108i
$323$	−2.29673e13	−	2.29673e13i	−0.363494	−	0.363494i
$324$	2.13827e13	+	3.96591e11i	0.332709	+	0.00617085i
$325$	−9.71408e13	−	3.82100e12i	−1.48608	−	0.0584546i
$326$		−	1.06348e13i		−	0.159968i
$327$	−8.82657e12	+	3.60823e12i	−0.130551	+	0.0533681i
$328$	−9.25114e12	+	9.25114e12i	−0.134552	+	0.134552i
$329$	1.03682e13			0.148294
$330$	1.59803e13	+	1.67763e13i	0.224781	+	0.235976i
$331$	2.24521e13			0.310601			0.155301	−	0.987867i	$-0.450365\pi$
$331$	2.24521e13			0.310601			0.155301	+	0.987867i	$0.450365\pi$
$332$	2.17140e13	−	2.17140e13i	0.295448	−	0.295448i
$333$	−5.18670e13	−	4.80955e11i	−0.694141	−	0.00643667i
$334$		−	3.07840e13i		−	0.405247i
$335$	1.28962e14	−	5.04716e13i	1.67000	−	0.653583i
$336$	2.96396e12	−	7.06283e12i	0.0377577	−	0.0899731i
$337$	−3.22426e13	−	3.22426e13i	−0.404078	−	0.404078i	0.475589	−	0.879667i	$-0.342235\pi$
$337$	−3.22426e13	−	3.22426e13i	−0.404078	−	0.404078i	−0.879667	+	0.475589i	$0.842235\pi$
$338$	5.67700e13	+	5.67700e13i	0.699967	+	0.699967i
$339$	−1.07850e13	+	2.56996e13i	−0.130834	+	0.311766i
$340$	−1.40694e13	+	5.50629e12i	−0.167935	+	0.0657242i
$341$			5.63035e13i			0.661281i
$342$	−6.70390e13	−	6.21643e11i	−0.774790	−	0.00718452i
$343$	2.14672e13	−	2.14672e13i	0.244151	−	0.244151i
$344$	2.85991e13			0.320096
$345$	−4.20496e13	−	4.41440e13i	−0.463188	−	0.486257i
$346$	5.19891e13			0.563630
$347$	−2.50852e13	+	2.50852e13i	−0.267674	+	0.267674i	−0.828162	−	0.560488i	$-0.810613\pi$
$347$	−2.50852e13	+	2.50852e13i	−0.267674	+	0.267674i	0.560488	+	0.828162i	$0.310613\pi$
$348$	4.05804e13	−	1.65890e13i	0.426217	−	0.174234i
$349$			5.77981e13i			0.597549i	0.954324	+	0.298774i	$0.0965778\pi$
$349$			5.77981e13i			0.597549i	−0.954324	+	0.298774i	$0.903422\pi$
$350$	9.55225e12	+	1.03345e13i	0.0972146	+	0.105176i
$351$	1.37923e14	−	5.48948e13i	1.38181	−	0.549974i
$352$	−1.81370e13	−	1.81370e13i	−0.178888	−	0.178888i
$353$	−6.53603e13	−	6.53603e13i	−0.634677	−	0.634677i	0.314560	−	0.949238i	$-0.398143\pi$
$353$	−6.53603e13	−	6.53603e13i	−0.634677	−	0.634677i	−0.949238	+	0.314560i	$0.898143\pi$
$354$	−6.76287e13	−	2.83808e13i	−0.646566	−	0.271335i
$355$	6.29608e13	+	2.75413e13i	0.592672	+	0.259256i
$356$		−	6.39750e13i		−	0.592974i
$357$	−3.93950e12	−	9.63692e12i	−0.0359555	−	0.0879556i
$358$	7.66413e13	−	7.66413e13i	0.688821	−	0.688821i
$359$	−1.26366e14			−1.11843			−0.559217	−	0.829021i	$-0.688898\pi$
$359$	−1.26366e14			−1.11843			−0.559217	+	0.829021i	$0.688898\pi$
$360$	−5.11143e13	+	1.13960e14i	−0.445532	+	0.993321i
$361$	1.16768e13			0.100239
$362$	7.04817e13	−	7.04817e13i	0.595908	−	0.595908i
$363$	−3.82063e13	−	9.34615e13i	−0.318162	−	0.778299i
$364$			1.05791e13i			0.0867739i
$365$	8.56278e13	+	2.18792e14i	0.691837	+	1.76775i
$366$	−6.41331e13	−	2.69138e13i	−0.510430	−	0.214205i
$367$	−1.12492e13	−	1.12492e13i	−0.0881983	−	0.0881983i	0.661631	−	0.749829i	$-0.269864\pi$
$367$	−1.12492e13	−	1.12492e13i	−0.0881983	−	0.0881983i	−0.749829	+	0.661631i	$0.769864\pi$
$368$	−3.42134e13	−	3.42134e13i	−0.264261	−	0.264261i
$369$	1.60908e13	+	1.63920e13i	0.122442	+	0.124734i
$370$	3.03116e13	−	6.92940e13i	0.227248	−	0.519501i
$371$			3.58582e13i			0.264869i
$372$	−7.01471e13	+	2.86756e13i	−0.510532	+	0.208702i
$373$	7.82605e13	−	7.82605e13i	0.561234	−	0.561234i	−0.368424	−	0.929658i	$-0.620102\pi$
$373$	7.82605e13	−	7.82605e13i	0.561234	−	0.561234i	0.929658	+	0.368424i	$0.120102\pi$
$374$	2.49935e13			0.176617
$375$	−9.48846e13	−	1.07794e14i	−0.660730	−	0.750624i
$376$	−1.34177e14			−0.920760
$377$	2.15174e14	−	2.15174e14i	1.45516	−	1.45516i
$378$	−1.97369e13	−	8.49879e12i	−0.131545	−	0.0566438i
$379$			1.35574e14i			0.890556i	0.895392	+	0.445278i	$0.146895\pi$
$379$			1.35574e14i			0.890556i	−0.895392	+	0.445278i	$0.853105\pi$
$380$	−1.95392e13	+	4.46676e13i	−0.126502	+	0.289190i
$381$	3.21386e12	−	7.65833e12i	0.0205088	−	0.0488705i
$382$	7.09869e12	+	7.09869e12i	0.0446508	+	0.0446508i
$383$	1.78446e14	+	1.78446e14i	1.10641	+	1.10641i	0.993619	+	0.112786i	$0.0359776\pi$
$383$	1.78446e14	+	1.78446e14i	1.10641	+	1.10641i	0.112786	+	0.993619i	$0.464022\pi$
$384$	−1.54212e13	+	3.67471e13i	−0.0942530	+	0.224596i
$385$	4.23145e12	+	1.08120e13i	0.0254950	+	0.0651435i
$386$		−	2.10529e14i		−	1.25050i
$387$	4.65578e11	−	5.02087e13i	0.00272635	−	0.294014i
$388$	1.06845e13	−	1.06845e13i	0.0616851	−	0.0616851i
$389$	−5.35695e13			−0.304926			−0.152463	−	0.988309i	$-0.548721\pi$
$389$	−5.35695e13			−0.304926			−0.152463	+	0.988309i	$0.548721\pi$
$390$	−5.25800e12	+	2.16394e14i	−0.0295097	+	1.21448i
$391$	−6.57663e13			−0.363941
$392$	−1.36738e14	+	1.36738e14i	−0.746134	+	0.746134i
$393$	1.12091e14	−	4.58220e13i	0.603133	−	0.246556i
$394$			1.40570e14i			0.745870i
$395$	−3.86385e13	−	1.69018e13i	−0.202179	−	0.0884402i
$396$	−1.83605e13	+	1.80231e13i	−0.0947458	+	0.0930048i
$397$	2.12579e14	+	2.12579e14i	1.08186	+	1.08186i	0.996336	+	0.0855292i	$0.0272581\pi$
$397$	2.12579e14	+	2.12579e14i	1.08186	+	1.08186i	0.0855292	+	0.996336i	$0.472742\pi$
$398$	−2.56436e13	−	2.56436e13i	−0.128713	−	0.128713i
$399$	−3.09786e13	−	1.30003e13i	−0.153359	−	0.0643582i
$400$	−7.73601e13	−	8.36951e13i	−0.377735	−	0.408668i
$401$			2.56873e14i			1.23715i	0.785724	+	0.618577i	$0.212291\pi$
$401$			2.56873e14i			1.23715i	−0.785724	+	0.618577i	$0.787709\pi$
$402$	−1.16679e14	−	2.85423e14i	−0.554305	−	1.35596i
$403$	−3.71948e14	+	3.71948e14i	−1.74303	+	1.74303i
$404$	−1.88504e12			−0.00871410
$405$	1.99237e14	+	9.15918e13i	0.908590	+	0.417690i
$406$	−4.40505e13			−0.198179
$407$	4.41232e13	−	4.41232e13i	0.195838	−	0.195838i
$408$	5.09822e13	+	1.24714e14i	0.223248	+	0.546116i
$409$		−	1.44694e14i		−	0.625133i	−0.949896	−	0.312567i	$-0.898811\pi$
$409$		−	1.44694e14i		−	0.625133i	0.949896	−	0.312567i	$-0.101189\pi$
$410$	−3.11900e13	+	1.22067e13i	−0.132955	+	0.0520341i
$411$	−3.60638e12	−	1.51344e12i	−0.0151685	−	0.00636553i
$412$	−2.53011e13	−	2.53011e13i	−0.105004	−	0.105004i
$413$	−2.59884e13	−	2.59884e13i	−0.106428	−	0.106428i
$414$	−9.68721e13	+	9.50921e13i	−0.391469	+	0.384275i
$415$	2.93207e14	−	1.14752e14i	1.16926	−	0.457609i
$416$		−	2.39630e14i		−	0.943036i
$417$	1.78536e14	−	7.29841e13i	0.693389	−	0.283452i
$418$	5.70300e13	−	5.70300e13i	0.218592	−	0.218592i
$419$	−4.52097e14			−1.71023			−0.855115	−	0.518439i	$-0.826513\pi$
$419$	−4.52097e14			−1.71023			−0.855115	+	0.518439i	$0.826513\pi$
$420$	−1.13153e13	+	1.07784e13i	−0.0422468	+	0.0402424i
$421$	−2.06639e14			−0.761484			−0.380742	−	0.924681i	$-0.624331\pi$
$421$	−2.06639e14			−0.761484			−0.380742	+	0.924681i	$0.624331\pi$
$422$	−6.07383e13	+	6.07383e13i	−0.220925	+	0.220925i
$423$	−2.18434e12	+	2.35563e14i	−0.00784239	+	0.845736i
$424$		−	4.64051e14i		−	1.64457i
$425$	−1.54793e14	−	6.08873e12i	−0.541518	−	0.0213004i
$426$	5.92100e13	−	1.41092e14i	0.204476	−	0.487247i
$427$	−2.46451e13	−	2.46451e13i	−0.0840190	−	0.0840190i
$428$	5.15051e13	+	5.15051e13i	0.173344	+	0.173344i
$429$	−6.91050e13	+	1.64671e14i	−0.229612	+	0.547143i
$430$	6.70785e13	+	2.93425e13i	0.220043	+	0.0962544i
$431$		−	4.20038e14i		−	1.36039i	−0.733031	−	0.680195i	$-0.761895\pi$
$431$		−	4.20038e14i		−	1.36039i	0.733031	−	0.680195i	$-0.238105\pi$
$432$	1.59842e14	+	6.88285e13i	0.511128	+	0.220094i
$433$	5.30911e13	−	5.30911e13i	0.167625	−	0.167625i	−0.618310	−	0.785935i	$-0.712182\pi$
$433$	5.30911e13	−	5.30911e13i	0.167625	−	0.167625i	0.785935	+	0.618310i	$0.212182\pi$
$434$	7.61455e13			0.237383
$435$	4.49376e14	+	1.09191e13i	1.38331	+	0.0336120i
$436$	1.54401e13			0.0469326
$437$	−1.50065e14	+	1.50065e14i	−0.450434	+	0.450434i
$438$	4.84236e14	−	1.97952e14i	1.43532	−	0.586748i
$439$		−	2.43794e14i		−	0.713623i	−0.934176	−	0.356812i	$-0.883864\pi$
$439$		−	2.43794e14i		−	0.713623i	0.934176	−	0.356812i	$-0.116136\pi$
$440$	−5.47604e13	−	1.39921e14i	−0.158298	−	0.404476i
$441$	2.37833e14	+	2.42285e14i	0.678984	+	0.691694i
$442$	1.65110e14	+	1.65110e14i	0.465534	+	0.465534i
$443$	7.36944e13	+	7.36944e13i	0.205217	+	0.205217i	0.802231	−	0.597014i	$-0.203646\pi$
$443$	7.36944e13	+	7.36944e13i	0.205217	+	0.205217i	−0.597014	+	0.802231i	$0.703646\pi$
$444$	7.74440e13	+	3.24998e13i	0.213001	+	0.0893871i
$445$	2.62888e14	−	6.00976e14i	0.714152	−	1.63259i
$446$			5.38525e14i			1.44499i
$447$	−1.41037e14	−	3.45009e14i	−0.373802	−	0.914405i
$448$	−5.08829e13	+	5.08829e13i	−0.133212	+	0.133212i
$449$	1.97963e13			0.0511953			0.0255976	−	0.999672i	$-0.491851\pi$
$449$	1.97963e13			0.0511953			0.0255976	+	0.999672i	$0.491851\pi$
$450$	−2.36810e14	+	2.14848e14i	−0.604967	+	0.548862i
$451$	−2.76330e13			−0.0697360
$452$	3.19108e13	−	3.19108e13i	0.0795567	−	0.0795567i
$453$	−2.27762e14	−	5.57159e14i	−0.560973	−	1.37227i
$454$			4.64845e14i			1.13110i
$455$	−4.34718e13	+	9.93787e13i	−0.104507	+	0.238908i
$456$	4.00903e14	+	1.68241e14i	0.952209	+	0.399600i
$457$	6.24954e13	+	6.24954e13i	0.146659	+	0.146659i	0.776624	−	0.629965i	$-0.216931\pi$
$457$	6.24954e13	+	6.24954e13i	0.146659	+	0.146659i	−0.629965	+	0.776624i	$0.716931\pi$
$458$	−2.99201e14	−	2.99201e14i	−0.693751	−	0.693751i
$459$	2.19779e14	−	8.74744e13i	0.503520	−	0.200406i
$460$	3.59772e13	+	9.19272e13i	0.0814441	+	0.208102i
$461$		−	4.69410e14i		−	1.05002i	−0.851096	−	0.525010i	$-0.824062\pi$
$461$		−	4.69410e14i		−	1.05002i	0.851096	−	0.525010i	$-0.175938\pi$
$462$	2.39293e13	−	9.78213e12i	0.0528932	−	0.0216223i
$463$	−3.67034e14	+	3.67034e14i	−0.801699	+	0.801699i	−0.983361	−	0.181662i	$-0.941852\pi$
$463$	−3.67034e14	+	3.67034e14i	−0.801699	+	0.801699i	0.181662	+	0.983361i	$0.441852\pi$
$464$	3.56748e14			0.770040
$465$	−7.76790e14	−	1.88746e13i	−1.65696	−	0.0402613i
$466$	−4.19345e14			−0.883994
$467$	−5.47486e13	+	5.47486e13i	−0.114059	+	0.114059i	−0.761833	−	0.647774i	$-0.775700\pi$
$467$	−5.47486e13	+	5.47486e13i	−0.114059	+	0.114059i	0.647774	+	0.761833i	$0.275700\pi$
$468$	−2.40354e14	−	2.22877e12i	−0.494880	−	0.00458895i
$469$		−	1.54520e14i		−	0.314437i
$470$	−3.14710e14	−	1.37665e14i	−0.632955	−	0.276877i
$471$	−3.05792e14	+	7.28673e14i	−0.607870	+	1.44850i
$472$	3.36323e14	+	3.36323e14i	0.660809	+	0.660809i
$473$	4.27125e13	+	4.27125e13i	0.0829504	+	0.0829504i
$474$	−3.63366e13	+	8.65867e13i	−0.0697531	+	0.166215i
$475$	−3.67099e14	+	3.39313e14i	−0.696576	+	0.643851i
$476$			1.68576e13i			0.0316198i
$477$	−8.14691e14	−	7.55451e12i	−1.51057	−	0.0140073i
$478$	−4.44267e13	+	4.44267e13i	−0.0814312	+	0.0814312i
$479$	6.43240e14			1.16554			0.582771	−	0.812636i	$-0.301968\pi$
$479$	6.43240e14			1.16554			0.582771	+	0.812636i	$0.301968\pi$
$480$	2.56306e14	−	2.44146e14i	0.459127	−	0.437344i
$481$	5.82967e14			1.03239
$482$	−3.62966e14	+	3.62966e14i	−0.635487	+	0.635487i
$483$	−6.29662e13	+	2.57401e13i	−0.108993	+	0.0445554i
$484$			1.63490e14i			0.279796i
$485$	1.44274e14	−	5.64642e13i	0.244124	−	0.0955419i
$486$	1.97249e14	−	4.46628e14i	0.330001	−	0.747217i
$487$	−4.58342e13	−	4.58342e13i	−0.0758194	−	0.0758194i	0.668180	−	0.744000i	$-0.267074\pi$
$487$	−4.58342e13	−	4.58342e13i	−0.0758194	−	0.0758194i	−0.744000	+	0.668180i	$0.767074\pi$
$488$	3.18940e14	+	3.18940e14i	0.521674	+	0.521674i
$489$	1.11652e14	+	4.68556e13i	0.180580	+	0.0757814i
$490$	−4.61010e14	+	1.80424e14i	−0.737279	+	0.288547i
$491$			6.98254e14i			1.10424i	0.833763	+	0.552122i	$0.186182\pi$
$491$			6.98254e14i			1.10424i	−0.833763	+	0.552122i	$0.813818\pi$
$492$	−1.40736e13	−	3.44273e13i	−0.0220088	−	0.0538387i
$493$	3.42877e14	−	3.42877e14i	0.530250	−	0.530250i
$494$	7.53494e14			1.15234
$495$	−2.46537e14	+	9.38598e13i	−0.372867	+	0.141955i
$496$	−6.16673e14			−0.922372
$497$	5.42188e13	−	5.42188e13i	0.0802029	−	0.0802029i
$498$	−2.65279e14	−	6.48935e14i	−0.388099	−	0.949379i
$499$		−	5.35718e14i		−	0.775146i	−0.921839	−	0.387573i	$-0.873313\pi$
$499$		−	5.35718e14i		−	0.775146i	0.921839	−	0.387573i	$-0.126687\pi$
$500$	7.61683e13	+	2.19698e14i	0.109003	+	0.314407i
$501$	3.23194e14	+	1.35630e14i	0.457463	+	0.191977i
$502$	5.07906e14	+	5.07906e14i	0.711070	+	0.711070i
$503$	−1.54622e13	−	1.54622e13i	−0.0214115	−	0.0214115i	0.696320	−	0.717731i	$-0.254819\pi$
$503$	−1.54622e13	−	1.54622e13i	−0.0214115	−	0.0214115i	−0.717731	+	0.696320i	$0.754819\pi$
$504$	9.76231e13	+	9.94505e13i	0.133716	+	0.136219i
$505$	−1.77079e13	−	7.74605e12i	−0.0239919	−	0.0104949i
$506$		−	1.63304e14i		−	0.218861i
$507$	−8.46138e14	+	3.45894e14i	−1.12175	+	0.458564i
$508$	−9.50923e12	+	9.50923e12i	−0.0124708	+	0.0124708i
$509$	5.02829e14			0.652338			0.326169	−	0.945311i	$-0.394242\pi$
$509$	5.02829e14			0.652338			0.326169	+	0.945311i	$0.394242\pi$
$510$	−8.37858e12	+	3.44822e14i	−0.0107531	+	0.442547i
$511$	2.62151e14			0.332841
$512$	5.39706e14	−	5.39706e14i	0.677911	−	0.677911i
$513$	3.01892e14	−	7.01089e14i	0.375151	−	0.871219i
$514$		−	1.05945e14i		−	0.130252i
$515$	−1.33708e14	−	3.41645e14i	−0.162637	−	0.415561i
$516$	−3.14607e13	+	7.49680e13i	−0.0378613	+	0.0902199i
$517$	−2.00393e14	−	2.00393e14i	−0.238608	−	0.238608i
$518$	−5.96727e13	−	5.96727e13i	−0.0703010	−	0.0703010i
$519$	−2.29057e14	+	5.45822e14i	−0.267008	+	0.636254i
$520$	5.62581e14	−	1.28609e15i	0.648883	−	1.48338i
$521$		−	8.42723e14i		−	0.961783i	−0.876780	−	0.480892i	$-0.840313\pi$
$521$		−	8.42723e14i		−	0.961783i	0.876780	−	0.480892i	$-0.159687\pi$
$522$	9.28045e12	−	1.00082e15i	0.0104805	−	1.13023i
$523$	−3.08210e14	+	3.08210e14i	−0.344419	+	0.344419i	−0.858026	−	0.513607i	$-0.828309\pi$
$523$	−3.08210e14	+	3.08210e14i	−0.344419	+	0.344419i	0.513607	+	0.858026i	$0.328309\pi$
$524$	−1.96079e14			−0.216824
$525$	−1.50586e14	+	5.47545e13i	−0.164781	+	0.0599161i
$526$	9.52798e14			1.03176
$527$	−5.92696e14	+	5.92696e14i	−0.635146	+	0.635146i
$528$	−1.93795e14	+	7.92218e13i	−0.205521	+	0.0840152i
$529$		−	5.23103e14i		−	0.549011i
$530$	4.76114e14	−	1.08842e15i	0.494531	−	1.13052i
$531$	5.95927e14	−	5.84976e14i	0.612594	−	0.601338i
$532$	3.84656e13	+	3.84656e13i	0.0391344	+	0.0391344i
$533$	−1.82547e14	−	1.82547e14i	−0.183813	−	0.183813i
$534$	−1.34675e15	−	5.65173e14i	−1.34218	−	0.563254i
$535$	2.72188e14	+	6.95480e14i	0.268487	+	0.686024i
$536$			1.99969e15i			1.95234i
$537$	4.66968e14	+	1.14231e15i	0.451262	+	1.10389i
$538$	−2.00099e14	+	2.00099e14i	−0.191401	+	0.191401i
$539$	−4.08435e14			−0.386710
$540$	−2.42500e14	−	2.59351e14i	−0.227272	−	0.243065i
$541$	−1.05800e15			−0.981521			−0.490760	−	0.871295i	$-0.663281\pi$
$541$	−1.05800e15			−0.981521			−0.490760	+	0.871295i	$0.663281\pi$
$542$	−8.12448e14	+	8.12448e14i	−0.746104	+	0.746104i
$543$	4.29438e14	+	1.05051e15i	0.390393	+	0.954991i
$544$		−	3.81849e14i		−	0.343635i
$545$	1.45043e14	+	6.34469e13i	0.129216	+	0.0565236i
$546$	2.22702e14	+	9.34583e13i	0.196411	+	0.0824249i
$547$	3.85557e14	+	3.85557e14i	0.336634	+	0.336634i	0.855099	−	0.518465i	$-0.173496\pi$
$547$	3.85557e14	+	3.85557e14i	0.336634	+	0.336634i	−0.518465	+	0.855099i	$0.673496\pi$
$548$	4.47799e12	+	4.47799e12i	0.00387070	+	0.00387070i
$549$	5.65125e14	−	5.54740e14i	0.483611	−	0.474725i
$550$	1.51189e13	−	3.84365e14i	0.0128093	−	0.325649i
$551$		−	1.56475e15i		−	1.31254i
$552$	8.14863e14	−	3.33110e14i	0.676737	−	0.276645i
$553$	−3.32736e13	+	3.32736e13i	−0.0273597	+	0.0273597i
$554$	−2.36461e14			−0.192511
$555$	5.93953e14	+	6.23536e14i	0.478785	+	0.502632i
$556$	−3.12308e14			−0.249271
$557$	1.07903e15	−	1.07903e15i	0.852767	−	0.852767i	−0.137707	−	0.990473i	$-0.543973\pi$
$557$	1.07903e15	−	1.07903e15i	0.852767	−	0.852767i	0.990473	+	0.137707i	$0.0439731\pi$
$558$	−1.60421e13	+	1.73001e15i	−0.0125538	+	1.35382i
$559$			5.64328e14i			0.437287i
$560$	−1.18420e14	+	4.63456e13i	−0.0908637	+	0.0355610i
$561$	−1.10118e14	+	2.62401e14i	−0.0836688	+	0.199375i
$562$	−1.09894e15	−	1.09894e15i	−0.826844	−	0.826844i
$563$	4.67312e14	+	4.67312e14i	0.348186	+	0.348186i	0.859433	−	0.511248i	$-0.170817\pi$
$563$	4.67312e14	+	4.67312e14i	0.348186	+	0.348186i	−0.511248	+	0.859433i	$0.670817\pi$
$564$	1.47604e14	−	3.51725e14i	0.108908	−	0.259519i
$565$	4.30896e14	−	1.68639e14i	0.314852	−	0.123223i
$566$			1.48771e15i			1.07654i
$567$	1.76185e14	−	1.69769e14i	0.126259	−	0.121661i
$568$	−7.01662e14	+	7.01662e14i	−0.497980	+	0.497980i
$569$	2.48247e13			0.0174488			0.00872440	−	0.999962i	$-0.497223\pi$
$569$	2.48247e13			0.0174488			0.00872440	+	0.999962i	$0.497223\pi$
$570$	7.67694e14	+	8.05931e14i	0.534412	+	0.561030i
$571$	−2.27029e15			−1.56525			−0.782624	−	0.622495i	$-0.786119\pi$
$571$	−2.27029e15			−1.56525			−0.782624	+	0.622495i	$0.786119\pi$
$572$	2.04469e14	−	2.04469e14i	0.139620	−	0.139620i
$573$	−1.05803e14	+	4.32516e13i	−0.0715565	+	0.0292517i
$574$			3.73712e13i			0.0250335i
$575$	−3.97828e13	+	1.01139e15i	−0.0263950	+	0.671038i
$576$	−1.14533e15	−	1.16677e15i	−0.752674	−	0.766764i
$577$	8.40047e14	+	8.40047e14i	0.546810	+	0.546810i	0.925517	−	0.378707i	$-0.123631\pi$
$577$	8.40047e14	+	8.40047e14i	0.546810	+	0.546810i	−0.378707	+	0.925517i	$0.623631\pi$
$578$	−6.32731e14	−	6.32731e14i	−0.407959	−	0.407959i
$579$	2.21030e15	+	9.27566e14i	1.41163	+	0.592397i
$580$	−6.66839e14	−	2.91699e14i	−0.421859	−	0.184536i
$581$		−	3.51315e14i		−	0.220155i
$582$	−1.30532e14	−	3.19312e14i	−0.0810292	−	0.198216i
$583$	6.93056e14	−	6.93056e14i	0.426178	−	0.426178i
$584$	−3.39258e15			−2.06661
$585$	−2.24871e15	−	1.00861e15i	−1.35699	−	0.608646i
$586$	1.22063e15			0.729702
$587$	1.09086e15	−	1.09086e15i	0.646039	−	0.646039i	−0.305994	−	0.952033i	$-0.598989\pi$
$587$	1.09086e15	−	1.09086e15i	0.646039	−	0.646039i	0.952033	+	0.305994i	$0.0989889\pi$
$588$	−2.08018e14	−	5.08859e14i	−0.122046	−	0.298553i
$589$			2.70482e15i			1.57219i
$590$	4.43773e14	+	1.13391e15i	0.255549	+	0.652966i
$591$	−1.47581e15	−	6.19333e14i	−0.841976	−	0.353340i
$592$	4.83266e14	+	4.83266e14i	0.273160	+	0.273160i
$593$	−2.77594e14	−	2.77594e14i	−0.155456	−	0.155456i	0.625093	−	0.780550i	$-0.285061\pi$
$593$	−2.77594e14	−	2.77594e14i	−0.155456	−	0.155456i	−0.780550	+	0.625093i	$0.785061\pi$
$594$	2.17207e14	+	5.45731e14i	0.120517	+	0.302798i
$595$	−6.92719e13	+	1.58359e14i	−0.0380815	+	0.0870562i
$596$			6.03515e14i			0.328726i
$597$	3.82209e14	−	1.56244e14i	0.206273	−	0.0843227i
$598$	1.07880e15	−	1.07880e15i	0.576881	−	0.576881i
$599$	−3.59256e15			−1.90352			−0.951759	−	0.306846i	$-0.900726\pi$
$599$	−3.59256e15			−1.90352			−0.951759	+	0.306846i	$0.900726\pi$
$600$	1.94877e15	−	7.08594e14i	1.02313	−	0.372020i
$601$	2.15962e15			1.12348			0.561742	−	0.827312i	$-0.310131\pi$
$601$	2.15962e15			1.12348			0.561742	+	0.827312i	$0.310131\pi$
$602$	5.77648e13	−	5.77648e13i	0.0297771	−	0.0297771i
$603$	3.51067e15	+	3.25539e13i	1.79327	+	0.0166287i
$604$			9.74625e14i			0.493326i
$605$	−6.71817e14	+	1.53581e15i	−0.336974	+	0.770341i
$606$	−1.66529e13	+	3.96824e13i	−0.00827736	+	0.0197242i
$607$	3.75195e13	+	3.75195e13i	0.0184807	+	0.0184807i	0.716287	−	0.697806i	$-0.245840\pi$
$607$	3.75195e13	+	3.75195e13i	0.0184807	+	0.0184807i	−0.697806	+	0.716287i	$0.745840\pi$
$608$	−8.71300e14	−	8.71300e14i	−0.425303	−	0.425303i
$609$	1.94081e14	−	4.62476e14i	0.0938832	−	0.223715i
$610$	4.20836e14	+	1.07530e15i	0.201743	+	0.515483i
$611$		−	2.64764e15i		−	1.25786i
$612$	−3.83002e14	−	3.55153e12i	−0.180330	−	0.00167218i
$613$	5.32610e14	−	5.32610e14i	0.248529	−	0.248529i	−0.571838	−	0.820367i	$-0.693769\pi$
$613$	5.32610e14	−	5.32610e14i	0.248529	−	0.248529i	0.820367	+	0.571838i	$0.193769\pi$
$614$	1.15440e15			0.533862
$615$	9.26342e12	−	3.81238e14i	0.00424579	−	0.174736i
$616$	−1.67650e14			−0.0761570
$617$	8.42728e14	−	8.42728e14i	0.379419	−	0.379419i	−0.491474	−	0.870892i	$-0.663542\pi$
$617$	8.42728e14	−	8.42728e14i	0.379419	−	0.379419i	0.870892	+	0.491474i	$0.163542\pi$
$618$	−7.56137e14	+	3.09103e14i	−0.337415	+	0.137933i
$619$		−	2.24348e15i		−	0.992258i	−0.868249	−	0.496129i	$-0.834754\pi$
$619$		−	2.24348e15i		−	0.992258i	0.868249	−	0.496129i	$-0.165246\pi$
$620$	1.15269e15	+	5.04229e14i	0.505312	+	0.221041i
$621$	−5.71544e14	−	1.43600e15i	−0.248340	−	0.623952i
$622$	−2.35070e15	−	2.35070e15i	−1.01240	−	1.01240i
$623$	−5.17532e14	−	5.17532e14i	−0.220929	−	0.220929i
$624$	−1.80358e15	−	7.56883e14i	−0.763169	−	0.320268i
$625$	−1.87272e14	+	2.37682e15i	−0.0785477	+	0.996910i
$626$		−	1.52354e15i		−	0.633424i
$627$	3.47478e14	+	8.50012e14i	0.143204	+	0.350311i
$628$	9.04782e14	−	9.04782e14i	0.369629	−	0.369629i
$629$	9.28952e14			0.376197
$630$	1.26937e14	+	3.33420e14i	0.0509583	+	0.133850i
$631$	1.63111e15			0.649114			0.324557	−	0.945866i	$-0.394785\pi$
$631$	1.63111e15			0.649114			0.324557	+	0.945866i	$0.394785\pi$
$632$	4.30603e14	−	4.30603e14i	0.169877	−	0.169877i
$633$	−3.70073e14	−	9.05284e14i	−0.144733	−	0.354050i
$634$		−	8.49537e14i		−	0.329375i
$635$	−1.28404e14	+	5.02532e13i	−0.0493542	+	0.0193156i
$636$	1.21644e15	+	5.10485e14i	0.463527	+	0.194522i
$637$	−2.69817e15	−	2.69817e15i	−1.01930	−	1.01930i
$638$	8.51395e14	+	8.51395e14i	0.318873	+	0.318873i
$639$	1.22042e15	+	1.24326e15i	0.453163	+	0.461646i
$640$	6.16126e14	−	2.41131e14i	0.226819	−	0.0887695i
$641$			3.15822e15i			1.15272i	0.817197	+	0.576359i	$0.195527\pi$
$641$			3.15822e15i			1.15272i	−0.817197	+	0.576359i	$0.804473\pi$
$642$	1.53926e15	−	6.29236e14i	0.557017	−	0.227704i
$643$	5.77831e14	−	5.77831e14i	0.207320	−	0.207320i	−0.595807	−	0.803127i	$-0.703168\pi$
$643$	5.77831e14	−	5.77831e14i	0.207320	−	0.207320i	0.803127	+	0.595807i	$0.203168\pi$
$644$	1.10145e14			0.0391826
$645$	−6.03600e14	+	5.74963e14i	−0.212898	+	0.202797i
$646$	1.20069e15			0.419905
$647$	−1.25931e15	+	1.25931e15i	−0.436675	+	0.436675i	−0.890891	−	0.454217i	$-0.849919\pi$
$647$	−1.25931e15	+	1.25931e15i	−0.436675	+	0.436675i	0.454217	+	0.890891i	$0.349919\pi$
$648$	−2.28006e15	+	2.19703e15i	−0.783943	+	0.755393i
$649$			1.00459e15i			0.342487i
$650$	2.63904e15	−	2.43929e15i	0.892119	−	0.824593i
$651$	−3.35487e14	+	7.99434e14i	−0.112455	+	0.267971i
$652$	−1.38637e14	−	1.38637e14i	−0.0460805	−	0.0460805i
$653$	2.52424e15	+	2.52424e15i	0.831970	+	0.831970i	0.987786	−	0.155816i	$-0.0498008\pi$
$653$	2.52424e15	+	2.52424e15i	0.831970	+	0.831970i	−0.155816	+	0.987786i	$0.549801\pi$
$654$	1.36402e14	−	3.25033e14i	0.0445804	−	0.106231i
$655$	−1.84194e15	−	8.05732e14i	−0.596966	−	0.261134i
$656$		−	3.02655e14i		−	0.0972696i
$657$	−5.52294e13	+	5.95603e15i	−0.0176020	+	1.89822i
$658$	−2.71014e14	+	2.71014e14i	−0.0856542	+	0.0856542i
$659$	−1.27064e14			−0.0398248			−0.0199124	−	0.999802i	$-0.506339\pi$
$659$	−1.27064e14			−0.0398248			−0.0199124	+	0.999802i	$0.506339\pi$
$660$	4.27020e14	+	1.03758e13i	0.132726	+	0.00322502i
$661$	−2.03628e15			−0.627666			−0.313833	−	0.949478i	$-0.601613\pi$
$661$	−2.03628e15			−0.627666			−0.313833	+	0.949478i	$0.601613\pi$
$662$	−5.86876e14	+	5.86876e14i	−0.179402	+	0.179402i
$663$	−2.46091e15	+	1.00600e15i	−0.746056	+	0.304982i
$664$			4.54647e15i			1.36694i
$665$	2.03279e14	+	5.19407e14i	0.0606139	+	0.154878i
$666$	1.36832e15	−	1.34318e15i	0.404651	−	0.397215i
$667$	−2.24031e15	−	2.24031e15i	−0.657076	−	0.657076i
$668$	−4.01305e14	−	4.01305e14i	−0.116736	−	0.116736i
$669$	−5.65385e15	−	2.37267e15i	−1.63118	−	0.684532i
$670$	−2.05167e15	+	4.69023e15i	−0.587079	+	1.34209i
$671$			9.52668e14i			0.270376i
$672$	−1.49451e14	−	3.65591e14i	−0.0420695	−	0.102912i
$673$	−1.77621e15	+	1.77621e15i	−0.495920	+	0.495920i	−0.910165	−	0.414245i	$-0.864046\pi$
$673$	−1.77621e15	+	1.77621e15i	−0.495920	+	0.495920i	0.414245	+	0.910165i	$0.364046\pi$
$674$	1.68558e15			0.466788
$675$	−1.21229e15	−	3.43281e15i	−0.332993	−	0.942929i
$676$	1.48013e15			0.403267
$677$	−1.27707e15	+	1.27707e15i	−0.345126	+	0.345126i	−0.858291	−	0.513164i	$-0.828473\pi$
$677$	−1.27707e15	+	1.27707e15i	−0.345126	+	0.345126i	0.513164	+	0.858291i	$0.328473\pi$
$678$	−3.89854e14	−	9.53672e14i	−0.104505	−	0.255644i
$679$		−	1.72867e14i		−	0.0459650i
$680$	8.96468e14	−	2.04937e15i	0.236448	−	0.540532i
$681$	−4.88030e15	−	2.04805e15i	−1.27684	−	0.535835i
$682$	−1.47172e15	−	1.47172e15i	−0.381953	−	0.381953i
$683$	−1.34259e14	−	1.34259e14i	−0.0345645	−	0.0345645i	0.689613	−	0.724178i	$-0.257781\pi$
$683$	−1.34259e14	−	1.34259e14i	−0.0345645	−	0.0345645i	−0.724178	+	0.689613i	$0.757781\pi$
$684$	−8.82036e14	+	8.65828e14i	−0.225257	+	0.221117i
$685$	2.36647e13	+	6.04669e13i	0.00599520	+	0.0153186i
$686$			1.12226e15i			0.282041i
$687$	4.45949e15	−	1.82301e15i	1.11179	−	0.454492i
$688$	−4.67815e14	+	4.67815e14i	−0.115701	+	0.115701i
$689$	9.15683e15			2.24667
$690$	2.25301e15	+	5.47443e13i	0.548395	+	0.0133251i
$691$	2.47271e15			0.597095			0.298548	−	0.954395i	$-0.403498\pi$
$691$	2.47271e15			0.597095			0.298548	+	0.954395i	$0.403498\pi$
$692$	6.77739e14	−	6.77739e14i	0.162360	−	0.162360i
$693$	−2.72926e12	+	2.94328e14i	−0.000648652	+	0.0699517i
$694$		−	1.31141e15i		−	0.309215i
$695$	−2.93380e15	−	1.28335e15i	−0.686299	−	0.300212i
$696$	−2.51166e15	+	5.98504e15i	−0.582921	+	1.38905i
$697$	−2.90887e14	−	2.90887e14i	−0.0669799	−	0.0669799i
$698$	−1.51078e15	−	1.51078e15i	−0.345142	−	0.345142i
$699$	1.84758e15	−	4.40261e15i	0.418773	−	0.997897i
$700$	2.59247e14	+	1.01974e13i	0.0583008	+	0.00229324i
$701$		−	8.81518e12i		−	0.00196690i	−1.00000		0.000983450i	$-0.999687\pi$
$701$		−	8.81518e12i		−	0.00196690i	1.00000		0.000983450i	$-0.000313042\pi$
$702$	−2.17027e15	+	5.04006e15i	−0.480463	+	1.11579i
$703$	2.11968e15	−	2.11968e15i	0.465602	−	0.465602i
$704$	1.96690e15			0.428679
$705$	2.83189e15	−	2.69754e15i	0.612402	−	0.583348i
$706$	3.41691e15			0.733174
$707$	−1.52492e13	+	1.52492e13i	−0.00324668	+	0.00324668i
$708$	−1.25160e15	+	5.11643e14i	−0.264412	+	0.108090i
$709$		−	6.16528e15i		−	1.29240i	−0.763166	−	0.646202i	$-0.776356\pi$
$709$		−	6.16528e15i		−	1.29240i	0.763166	−	0.646202i	$-0.223644\pi$
$710$	−2.36563e15	+	9.25831e14i	−0.492070	+	0.192580i
$711$	−7.48960e14	−	7.62980e14i	−0.154588	−	0.157482i
$712$	6.69753e15	+	6.69753e15i	1.37175	+	1.37175i
$713$	3.87258e15	+	3.87258e15i	0.787061	+	0.787061i
$714$	3.54874e14	+	1.48925e14i	0.0715705	+	0.0300350i
$715$	2.76097e15	−	1.08055e15i	0.552559	−	0.216253i
$716$		−	1.99822e15i		−	0.396845i
$717$	−2.70688e14	−	6.62165e14i	−0.0533474	−	0.130500i
$718$	3.30308e15	−	3.30308e15i	0.646003	−	0.646003i
$719$	−2.03645e15			−0.395243			−0.197622	−	0.980278i	$-0.563322\pi$
$719$	−2.03645e15			−0.395243			−0.197622	+	0.980278i	$0.563322\pi$
$720$	−1.02802e15	−	2.70024e15i	−0.198003	−	0.520085i
$721$	−4.09351e14			−0.0782442
$722$	−3.05221e14	+	3.05221e14i	−0.0578975	+	0.0578975i
$723$	−2.21152e15	−	5.40988e15i	−0.416322	−	1.01842i
$724$		−	1.83762e15i		−	0.343316i
$725$	−5.06557e15	−	5.48039e15i	−0.939223	−	1.01614i
$726$	3.44167e15	+	1.44432e15i	0.633311	+	0.265773i
$727$	2.70789e15	+	2.70789e15i	0.494529	+	0.494529i	0.909730	−	0.415201i	$-0.136289\pi$
$727$	2.70789e15	+	2.70789e15i	0.494529	+	0.494529i	−0.415201	+	0.909730i	$0.636289\pi$
$728$	−1.10752e15	−	1.10752e15i	−0.200737	−	0.200737i
$729$	3.82000e15	+	4.03866e15i	0.687166	+	0.726501i
$730$	−7.95722e15	−	3.48077e15i	−1.42065	−	0.621441i
$731$			8.99252e14i			0.159344i
$732$	−1.18690e15	+	4.85197e14i	−0.208739	+	0.0853311i
$733$	−1.39822e15	+	1.39822e15i	−0.244063	+	0.244063i	−0.818529	−	0.574466i	$-0.805210\pi$
$733$	−1.39822e15	+	1.39822e15i	−0.244063	+	0.244063i	0.574466	+	0.818529i	$0.305210\pi$
$734$	5.88088e14			0.101886
$735$	1.36920e14	−	5.63497e15i	0.0235443	−	0.968971i
$736$	−2.49494e15			−0.425826
$737$	−2.98652e15	+	2.98652e15i	−0.505934	+	0.505934i
$738$	−8.49067e14	−	7.87327e12i	−0.142768	−	0.00132387i
$739$			3.48541e15i			0.581714i	0.956767	+	0.290857i	$0.0939403\pi$
$739$			3.48541e15i			0.581714i	−0.956767	+	0.290857i	$0.906060\pi$
$740$	−5.08180e14	−	1.29848e15i	−0.0841867	−	0.215109i
$741$	−3.31980e15	+	7.91077e15i	−0.545898	+	1.30082i
$742$	−9.37297e14	−	9.37297e14i	−0.152987	−	0.152987i
$743$	−6.05827e15	−	6.05827e15i	−0.981545	−	0.981545i	0.0182882	−	0.999833i	$-0.494178\pi$
$743$	−6.05827e15	−	6.05827e15i	−0.981545	−	0.981545i	−0.999833	+	0.0182882i	$0.994178\pi$
$744$	4.34164e15	−	1.03457e16i	0.698236	−	1.66383i
$745$	−2.47998e15	+	5.66937e15i	−0.395903	+	0.905056i
$746$			4.09131e15i			0.648333i
$747$	7.98181e15	+	7.40142e13i	1.25556	+	0.0116426i
$748$	3.25820e14	−	3.25820e14i	0.0508766	−	0.0508766i
$749$	8.33310e14			0.129168
$750$	5.29782e15	+	3.37438e14i	0.815192	+	0.0519226i
$751$	6.92061e15			1.05712			0.528560	−	0.848896i	$-0.322732\pi$
$751$	6.92061e15			1.05712			0.528560	+	0.848896i	$0.322732\pi$
$752$	2.19484e15	−	2.19484e15i	0.332816	−	0.332816i
$753$	−7.57016e15	+	3.09462e15i	−1.13955	+	0.465838i
$754$			1.12488e16i			1.68099i
$755$	−4.00496e15	+	9.15554e15i	−0.594141	+	1.35824i
$756$	−3.68085e14	+	1.46502e14i	−0.0542099	+	0.0215761i
$757$	−1.60133e15	−	1.60133e15i	−0.234128	−	0.234128i	0.580285	−	0.814413i	$-0.302941\pi$
$757$	−1.60133e15	−	1.60133e15i	−0.234128	−	0.234128i	−0.814413	+	0.580285i	$0.802941\pi$
$758$	−3.54377e15	−	3.54377e15i	−0.514381	−	0.514381i
$759$	1.71449e15	+	7.19495e14i	0.247061	+	0.103681i
$760$	−2.63069e15	−	6.72179e15i	−0.376352	−	0.961635i
$761$		−	7.42244e15i		−	1.05422i	−0.849797	−	0.527110i	$-0.823276\pi$
$761$		−	7.42244e15i		−	1.05422i	0.849797	−	0.527110i	$-0.176724\pi$
$762$	1.16174e14	+	2.84188e14i	0.0163816	+	0.0400732i
$763$	1.24904e14	−	1.24904e14i	0.0174860	−	0.0174860i
$764$	1.85079e14			0.0257244
$765$	−3.58330e15	−	1.60721e15i	−0.494475	−	0.221786i
$766$	−9.32882e15			−1.27811
$767$	−6.63646e15	+	6.63646e15i	−0.902739	+	0.902739i
$768$	2.45293e15	+	6.00043e15i	0.331282	+	0.810393i
$769$		−	2.88608e15i		−	0.387002i	−0.981100	−	0.193501i	$-0.938016\pi$
$769$		−	2.88608e15i		−	0.387002i	0.981100	−	0.193501i	$-0.0619843\pi$
$770$	−3.93220e14	−	1.72008e14i	−0.0523524	−	0.0229008i
$771$	1.11229e15	+	4.66780e14i	0.147035	+	0.0617040i
$772$	−2.74450e15	−	2.74450e15i	−0.360220	−	0.360220i
$773$	9.13270e15	+	9.13270e15i	1.19018	+	1.19018i	0.977017	+	0.213162i	$0.0683761\pi$
$773$	9.13270e15	+	9.13270e15i	1.19018	+	1.19018i	0.213162	+	0.977017i	$0.431624\pi$
$774$	1.30024e15	+	1.32458e15i	0.168247	+	0.171396i
$775$	8.75631e15	+	9.47337e15i	1.12502	+	1.21715i
$776$			2.23712e15i			0.285397i
$777$	8.89400e14	−	3.63580e14i	0.112663	−	0.0460558i
$778$	1.40025e15	−	1.40025e15i	0.176124	−	0.176124i
$779$	−1.32749e15			−0.165796
$780$	2.75241e15	+	2.88949e15i	0.341344	+	0.358345i
$781$	−2.09585e15			−0.258095
$782$	1.71907e15	−	1.71907e15i	0.210211	−	0.210211i
$783$	1.04665e16	+	4.50692e15i	1.27090	+	0.547255i
$784$		−	4.47345e15i		−	0.539392i
$785$	1.22174e16	−	4.78148e15i	1.46284	−	0.572505i
$786$	−1.73221e15	+	4.12770e15i	−0.205957	+	0.490777i
$787$	−7.49129e15	−	7.49129e15i	−0.884495	−	0.884495i	0.109493	−	0.993988i	$-0.465077\pi$
$787$	−7.49129e15	−	7.49129e15i	−0.884495	−	0.884495i	−0.993988	+	0.109493i	$0.965077\pi$
$788$	1.83249e15	+	1.83249e15i	0.214856	+	0.214856i
$789$	−4.19791e15	+	1.00032e16i	−0.488775	+	1.16470i
$790$	1.45177e15	−	5.68174e14i	0.167860	−	0.0656950i
$791$		−	5.16291e14i		−	0.0592821i
$792$	3.53201e13	−	3.80898e15i	0.00402748	−	0.434330i
$793$	−6.29344e15	+	6.29344e15i	−0.712665	+	0.712665i
$794$	−1.11132e16			−1.24976
$795$	9.32940e15	+	9.79406e15i	1.04192	+	1.09381i
$796$	−6.68589e14			−0.0741545
$797$	−1.93093e15	+	1.93093e15i	−0.212690	+	0.212690i	−0.805409	−	0.592719i	$-0.798054\pi$
$797$	−1.93093e15	+	1.93093e15i	−0.212690	+	0.212690i	0.592719	+	0.805409i	$0.298054\pi$
$798$	1.14957e15	−	4.69933e14i	0.125753	−	0.0514068i
$799$		−	4.21900e15i		−	0.458355i
$800$	−5.87230e15	−	2.30985e14i	−0.633598	−	0.0249223i
$801$	1.18673e16	−	1.16492e16i	1.27166	−	1.24829i
$802$	−6.71440e15	−	6.71440e15i	−0.714575	−	0.714575i
$803$	−5.06679e15	−	5.06679e15i	−0.535547	−	0.535547i
$804$	−5.24187e15	−	2.19978e15i	−0.550273	−	0.230925i
$805$	1.03469e15	+	4.52612e14i	0.107878	+	0.0471898i
$806$		−	1.94447e16i		−	2.01353i
$807$	−1.21919e15	−	2.98241e15i	−0.125391	−	0.306735i
$808$	1.97344e14	−	1.97344e14i	0.0201587	−	0.0201587i
$809$	−4.76769e15			−0.483717			−0.241858	−	0.970312i	$-0.577757\pi$
$809$	−4.76769e15			−0.483717			−0.241858	+	0.970312i	$0.577757\pi$
$810$	−7.60198e15	+	2.81374e15i	−0.766054	+	0.283542i
$811$	9.81433e15			0.982304			0.491152	−	0.871074i	$-0.336576\pi$
$811$	9.81433e15			0.982304			0.491152	+	0.871074i	$0.336576\pi$
$812$	−5.74250e14	+	5.74250e14i	−0.0570877	+	0.0570877i
$813$	−4.95017e15	−	1.21093e16i	−0.488789	−	1.19569i
$814$			2.30667e15i			0.226231i
$815$	−7.32652e14	−	1.87203e15i	−0.0713725	−	0.182367i
$816$	−2.87399e15	−	1.20609e15i	−0.278093	−	0.116703i
$817$	2.05191e15	+	2.05191e15i	0.197213	+	0.197213i
$818$	3.78216e15	+	3.78216e15i	0.361074	+	0.361074i
$819$	−1.96240e15	+	1.92634e15i	−0.186091	+	0.182671i
$820$	−2.47469e14	+	5.65727e14i	−0.0233101	+	0.0532882i
$821$			1.37691e16i			1.28831i	0.764897	+	0.644153i	$0.222790\pi$
$821$			1.37691e16i			1.28831i	−0.764897	+	0.644153i	$0.777210\pi$
$822$	1.33827e14	−	5.47074e13i	0.0124379	−	0.00508453i
$823$	3.41704e15	−	3.41704e15i	0.315464	−	0.315464i	−0.531558	−	0.847022i	$-0.678393\pi$
$823$	3.41704e15	−	3.41704e15i	0.315464	−	0.315464i	0.847022	+	0.531558i	$0.178393\pi$
$824$	5.29753e15			0.485819
$825$	3.96875e15	+	1.85219e15i	0.361541	+	0.168729i
$826$	1.35862e15			0.122944
$827$	4.31458e15	−	4.31458e15i	0.387845	−	0.387845i	−0.486073	−	0.873918i	$-0.661571\pi$
$827$	4.31458e15	−	4.31458e15i	0.387845	−	0.387845i	0.873918	+	0.486073i	$0.161571\pi$
$828$	−2.32051e13	+	2.50248e15i	−0.00207213	+	0.223462i
$829$		−	4.82944e15i		−	0.428398i	−0.976790	−	0.214199i	$-0.931286\pi$
$829$		−	4.82944e15i		−	0.428398i	0.976790	−	0.214199i	$-0.0687141\pi$
$830$	−4.66465e15	+	1.06636e16i	−0.411046	+	0.939671i
$831$	1.04182e15	−	2.48255e15i	0.0911980	−	0.217316i
$832$	1.29936e16	+	1.29936e16i	1.12993	+	1.12993i
$833$	−4.29952e15	−	4.29952e15i	−0.371426	−	0.371426i
$834$	−2.75902e15	+	6.57448e15i	−0.236778	+	0.564220i
$835$	−2.12077e15	−	5.41888e15i	−0.180808	−	0.461992i
$836$		−	1.48690e15i		−	0.125936i
$837$	−1.80923e16	−	7.79063e15i	−1.52231	−	0.655515i
$838$	1.18174e16	−	1.18174e16i	0.987821	−	0.987821i
$839$	4.02227e14			0.0334026			0.0167013	−	0.999861i	$-0.494684\pi$
$839$	4.02227e14			0.0334026			0.0167013	+	0.999861i	$0.494684\pi$
$840$	5.62014e13	−	2.31298e15i	0.00463672	−	0.190825i
$841$	1.11595e16			0.914675
$842$	5.40134e15	−	5.40134e15i	0.439830	−	0.439830i
$843$	1.63793e16	−	6.69572e15i	1.32508	−	0.541684i
$844$			1.58359e15i			0.127280i
$845$	1.39042e16	+	6.08218e15i	1.11028	+	0.485677i
$846$	−6.10028e15	−	6.21447e15i	−0.483964	−	0.493023i
$847$	1.32257e15	+	1.32257e15i	0.104246	+	0.104246i
$848$	7.59081e15	+	7.59081e15i	0.594444	+	0.594444i
$849$	−1.56192e16	−	6.55467e15i	−1.21525	−	0.509987i
$850$	4.20529e15	−	3.88698e15i	0.325081	−	0.300475i
$851$		−	6.06963e15i		−	0.466176i
$852$	−1.06742e15	−	2.61117e15i	−0.0814553	−	0.199259i
$853$	−1.37262e16	+	1.37262e16i	−1.04071	+	1.04071i	−0.0415739	+	0.999135i	$0.513237\pi$
$853$	−1.37262e16	+	1.37262e16i	−1.04071	+	1.04071i	−0.999135	+	0.0415739i	$0.986763\pi$
$854$	1.28840e15			0.0970581
$855$	−1.18436e16	+	4.50902e15i	−0.886486	+	0.337496i
$856$	−1.07841e16			−0.802007
$857$	8.68912e15	−	8.68912e15i	0.642068	−	0.642068i	−0.308995	−	0.951064i	$-0.599993\pi$
$857$	8.68912e15	−	8.68912e15i	0.642068	−	0.642068i	0.951064	+	0.308995i	$0.0999928\pi$
$858$	−2.49799e15	−	6.11066e15i	−0.183405	−	0.448650i
$859$			1.77808e16i			1.29714i	0.761154	+	0.648571i	$0.224633\pi$
$859$			1.77808e16i			1.29714i	−0.761154	+	0.648571i	$0.775367\pi$
$860$	1.25696e15	−	4.91933e14i	0.0911130	−	0.0356586i
$861$	−3.92352e14	−	1.64653e14i	−0.0282591	−	0.0118591i
$862$	1.09794e16	+	1.09794e16i	0.785755	+	0.785755i
$863$	1.59266e15	+	1.59266e15i	0.113257	+	0.113257i	0.761464	−	0.648207i	$-0.224481\pi$
$863$	1.59266e15	+	1.59266e15i	0.113257	+	0.113257i	−0.648207	+	0.761464i	$0.724481\pi$
$864$	8.33764e15	−	3.31847e15i	0.589139	−	0.234484i
$865$	9.15160e15	−	3.58163e15i	0.642552	−	0.251474i
$866$			2.77550e15i			0.193639i
$867$	9.43064e15	−	3.85517e15i	0.653787	−	0.267263i
$868$	9.92645e14	−	9.92645e14i	0.0683810	−	0.0683810i
$869$	1.28621e15			0.0880443
$870$	−1.20317e16	+	1.14608e16i	−0.818408	+	0.779580i
$871$	−3.94586e16			−2.66712
$872$	−1.61642e15	+	1.61642e15i	−0.108571	+	0.108571i
$873$	3.92750e15	+	3.64191e13i	0.262142	+	0.00243081i
$874$		−	7.84510e15i		−	0.520338i
$875$	2.39344e15	+	1.16110e15i	0.157753	+	0.0765288i
$876$	3.73205e15	−	8.89311e15i	0.244441	−	0.582480i
$877$	−8.91823e15	−	8.91823e15i	−0.580471	−	0.580471i	0.354561	−	0.935033i	$-0.384630\pi$
$877$	−8.91823e15	−	8.91823e15i	−0.580471	−	0.580471i	−0.935033	+	0.354561i	$0.884630\pi$
$878$	6.37254e15	+	6.37254e15i	0.412186	+	0.412186i
$879$	−5.37792e15	+	1.28151e16i	−0.345681	+	0.823725i
$880$	3.18454e15	+	1.39303e15i	0.203419	+	0.0889828i
$881$			1.56283e16i			0.992076i	0.868301	+	0.496038i	$0.165212\pi$
$881$			1.56283e16i			0.992076i	−0.868301	+	0.496038i	$0.834788\pi$
$882$	−1.25498e16	−	1.16372e14i	−0.791698	−	0.00734130i
$883$	−1.35585e16	+	1.35585e16i	−0.850019	+	0.850019i	−0.990135	−	0.140116i	$-0.955253\pi$
$883$	−1.35585e16	+	1.35585e16i	−0.850019	+	0.850019i	0.140116	+	0.990135i	$0.455253\pi$
$884$	4.30481e15			0.268205
$885$	−1.38598e16	−	3.36770e14i	−0.858163	−	0.0208519i
$886$	−3.85260e15			−0.237065
$887$	1.92698e16	−	1.92698e16i	1.17841	−	1.17841i	0.198264	−	0.980149i	$-0.436470\pi$
$887$	1.92698e16	−	1.92698e16i	1.17841	−	1.17841i	0.980149	−	0.198264i	$-0.0635303\pi$
$888$	−1.15100e16	+	4.70519e15i	−0.699526	+	0.285961i
$889$			1.53851e14i			0.00929270i
$890$	8.83727e15	+	2.25805e16i	0.530485	+	1.35547i
$891$	−6.68650e15	−	1.24017e14i	−0.398907	−	0.00739864i
$892$	7.02030e15	+	7.02030e15i	0.416245	+	0.416245i
$893$	−9.62687e15	−	9.62687e15i	−0.567286	−	0.567286i
$894$	1.27047e16	+	5.33162e15i	0.744063	+	0.312250i
$895$	8.21114e15	−	1.87711e16i	0.477944	−	1.09260i
$896$		−	7.38229e14i		−	0.0427068i
$897$	6.57305e15	+	1.60792e16i	0.377928	+	0.924498i
$898$	−5.17457e14	+	5.17457e14i	−0.0295702	+	0.0295702i
$899$	−4.03800e16			−2.29344
$900$	−2.86300e14	+	5.88790e15i	−0.0161617	+	0.332373i
$901$	1.45913e16			0.818670
$902$	7.22300e14	−	7.22300e14i	0.0402793	−	0.0402793i
$903$	3.51955e14	+	8.60964e14i	0.0195077	+	0.0477202i
$904$			6.68147e15i			0.368083i
$905$	7.55121e15	−	1.72625e16i	0.413475	−	0.945226i
$906$	2.05171e16	+	8.61010e15i	1.11663	+	0.468601i
$907$	−2.67667e15	−	2.67667e15i	−0.144796	−	0.144796i	0.630993	−	0.775789i	$-0.282648\pi$
$907$	−2.67667e15	−	2.67667e15i	−0.144796	−	0.144796i	−0.775789	+	0.630993i	$0.782648\pi$
$908$	6.05979e15	+	6.05979e15i	0.325826	+	0.325826i
$909$	−3.43246e14	−	3.49671e14i	−0.0183444	−	0.0186878i
$910$	−1.46135e15	−	3.73397e15i	−0.0776295	−	0.198355i
$911$			1.46086e16i			0.771360i	0.922633	+	0.385680i	$0.126033\pi$
$911$			1.46086e16i			0.771360i	−0.922633	+	0.385680i	$0.873967\pi$
$912$	−9.30990e15	+	3.80581e15i	−0.488622	+	0.199745i
$913$	−6.79011e15	+	6.79011e15i	−0.354232	+	0.354232i
$914$	−3.26713e15			−0.169419
$915$	−1.31435e16	−	3.19363e14i	−0.677475	−	0.0164615i
$916$	−7.80088e15			−0.399686
$917$	−1.58619e15	+	1.58619e15i	−0.0807839	+	0.0807839i
$918$	−3.45831e15	+	8.03130e15i	−0.175077	+	0.406585i
$919$		−	1.66108e16i		−	0.835901i	−0.908470	−	0.417950i	$-0.862749\pi$
$919$		−	1.66108e16i		−	0.835901i	0.908470	−	0.417950i	$-0.137251\pi$
$920$	−1.33903e16	−	5.85738e15i	−0.669817	−	0.293002i
$921$	−5.08612e15	+	1.21197e16i	−0.252906	+	0.602650i
$922$	1.22699e16	+	1.22699e16i	0.606487	+	0.606487i
$923$	−1.38455e16	−	1.38455e16i	−0.680296	−	0.680296i
$924$	1.84426e14	−	4.39469e14i	0.00900793	−	0.0214651i
$925$	5.61934e14	−	1.42860e16i	0.0272839	−	0.693635i
$926$		−	1.91878e16i		−	0.926116i
$927$	8.62412e13	−	9.30039e15i	0.00413786	−	0.446234i
$928$	1.30076e16	−	1.30076e16i	0.620414	−	0.620414i
$929$	3.86131e16			1.83083			0.915416	−	0.402510i	$-0.131862\pi$
$929$	3.86131e16			1.83083			0.915416	+	0.402510i	$0.131862\pi$
$930$	2.07979e16	−	1.98111e16i	0.980308	−	0.933799i
$931$	−1.96212e16			−0.919396
$932$	−5.46666e15	+	5.46666e15i	−0.254644	+	0.254644i
$933$	3.50364e16	−	1.43226e16i	1.62245	−	0.663243i
$934$		−	2.86215e15i		−	0.131760i
$935$	4.39959e15	−	1.72185e15i	0.201348	−	0.0788010i
$936$	2.53959e16	−	2.49293e16i	1.15544	−	1.13421i
$937$	2.13328e16	+	2.13328e16i	0.964895	+	0.964895i	0.999404	−	0.0345091i	$-0.0109868\pi$
$937$	2.13328e16	+	2.13328e16i	0.964895	+	0.964895i	−0.0345091	+	0.999404i	$0.510987\pi$
$938$	4.03900e15	+	4.03900e15i	0.181618	+	0.181618i
$939$	1.59953e16	+	6.71251e15i	0.715041	+	0.300071i
$940$	−5.89725e15	+	2.30799e15i	−0.262087	+	0.102572i
$941$			1.40599e16i			0.621213i	0.950539	+	0.310606i	$0.100532\pi$
$941$			1.40599e16i			0.621213i	−0.950539	+	0.310606i	$0.899468\pi$
$942$	−1.10537e16	−	2.70399e16i	−0.485543	−	1.18775i
$943$	−1.90061e15	+	1.90061e15i	−0.0830002	+	0.0830002i
$944$	−1.10030e16			−0.477709
$945$	−4.05977e15	−	1.36322e14i	−0.175237	−	0.00588423i
$946$	−2.23292e15			−0.0958236
$947$	−2.44645e16	+	2.44645e16i	−1.04379	+	1.04379i	−0.0447891	+	0.998996i	$0.514262\pi$
$947$	−2.44645e16	+	2.44645e16i	−1.04379	+	1.04379i	−0.998996	+	0.0447891i	$0.985738\pi$
$948$	6.55069e14	+	1.60245e15i	0.0277870	+	0.0679733i
$949$		−	6.69437e16i		−	2.82322i
$950$	7.26310e14	−	1.84649e16i	0.0304538	−	0.774225i
$951$	8.91910e15	+	3.74295e15i	0.371816	+	0.156035i
$952$	−1.76482e15	−	1.76482e15i	−0.0731471	−	0.0731471i
$953$	−8.65090e15	−	8.65090e15i	−0.356492	−	0.356492i	0.506026	−	0.862518i	$-0.331114\pi$
$953$	−8.65090e15	−	8.65090e15i	−0.356492	−	0.356492i	−0.862518	+	0.506026i	$0.831114\pi$
$954$	2.14927e16	−	2.10977e16i	0.880591	−	0.864410i
$955$	1.73862e15	+	7.60533e14i	0.0708249	+	0.0309813i
$956$			1.15831e15i			0.0469144i
$957$	−1.26897e16	+	5.18747e15i	−0.511019	+	0.208901i
$958$	−1.68137e16	+	1.68137e16i	−0.673212	+	0.673212i
$959$	7.24501e13			0.00288428
$960$	−6.59364e14	+	2.71363e16i	−0.0260996	+	1.07413i
$961$	4.43921e16			1.74714
$962$	−1.52382e16	+	1.52382e16i	−0.596307	+	0.596307i
$963$	−1.75560e14	+	1.89326e16i	−0.00683094	+	0.736659i
$964$			9.46337e15i			0.366119i
$965$	−1.45038e16	−	3.70593e16i	−0.557932	−	1.42560i
$966$	9.73053e14	−	2.31869e15i	0.0372188	−	0.0886888i
$967$	9.28422e15	+	9.28422e15i	0.353102	+	0.353102i	0.861262	−	0.508161i	$-0.169674\pi$
$967$	9.28422e15	+	9.28422e15i	0.353102	+	0.353102i	−0.508161	+	0.861262i	$0.669674\pi$
$968$	−1.71157e16	−	1.71157e16i	−0.647262	−	0.647262i
$969$	−5.29007e15	+	1.26057e16i	−0.198921	+	0.474010i
$970$	−2.29527e15	+	5.24711e15i	−0.0858202	+	0.196189i
$971$			4.65625e15i			0.173113i	0.996247	+	0.0865567i	$0.0275864\pi$
$971$			4.65625e15i			0.173113i	−0.996247	+	0.0865567i	$0.972414\pi$
$972$	−3.25095e15	−	8.39369e15i	−0.120184	−	0.310305i
$973$	−2.52645e15	+	2.52645e15i	−0.0928730	+	0.0928730i
$974$	2.39612e15			0.0875860
$975$	1.39823e16	+	3.84539e16i	0.508220	+	1.39770i
$976$	−1.04342e16			−0.377127
$977$	−7.51949e15	+	7.51949e15i	−0.270252	+	0.270252i	−0.829201	−	0.558950i	$-0.811204\pi$
$977$	−7.51949e15	+	7.51949e15i	−0.270252	+	0.270252i	0.558950	+	0.829201i	$0.311204\pi$
$978$	−4.14324e15	+	1.69372e15i	−0.148073	+	0.0605311i
$979$			2.00054e16i			0.710956i
$980$	−3.65777e15	+	8.36184e15i	−0.129262	+	0.295501i
$981$	2.81148e15	+	2.86411e15i	0.0987997	+	0.100649i
$982$	−1.82517e16	−	1.82517e16i	−0.637807	−	0.637807i
$983$	−3.59894e15	−	3.59894e15i	−0.125063	−	0.125063i	0.641805	−	0.766868i	$-0.278186\pi$
$983$	−3.59894e15	−	3.59894e15i	−0.125063	−	0.125063i	−0.766868	+	0.641805i	$0.778186\pi$
$984$	5.07754e15	+	2.13082e15i	0.175461	+	0.0736332i
$985$	9.68414e15	+	2.47444e16i	0.332783	+	0.850311i
$986$			1.79249e16i			0.612541i
$987$	−1.65126e15	−	4.03936e15i	−0.0561140	−	0.137268i
$988$	9.82268e15	−	9.82268e15i	0.331946	−	0.331946i
$989$	5.87557e15			0.197456
$990$	3.99084e15	−	8.89765e15i	0.133374	−	0.297359i
$991$	5.31043e15			0.176492			0.0882459	−	0.996099i	$-0.471874\pi$
$991$	5.31043e15			0.176492			0.0882459	+	0.996099i	$0.471874\pi$
$992$	−2.24848e16	+	2.24848e16i	−0.743147	+	0.743147i
$993$	−3.57578e15	−	8.74718e15i	−0.117530	−	0.287506i
$994$			2.83445e15i			0.0926497i
$995$	−6.28066e15	−	2.74738e15i	−0.204164	−	0.0893084i
$996$	−1.19178e16	−	5.00139e15i	−0.385276	−	0.161683i
$997$	−1.28655e15	−	1.28655e15i	−0.0413621	−	0.0413621i	0.686123	−	0.727485i	$-0.259311\pi$
$997$	−1.28655e15	−	1.28655e15i	−0.0413621	−	0.0413621i	−0.727485	+	0.686123i	$0.759311\pi$
$998$	1.40031e16	+	1.40031e16i	0.447721	+	0.447721i
$999$	8.07309e15	+	2.02836e16i	0.256702	+	0.644963i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.12.e.a.2.7	✓	40
3.2	odd	2	inner	15.12.e.a.2.14	yes	40
5.2	odd	4		75.12.e.d.68.7		40
5.3	odd	4	inner	15.12.e.a.8.14	yes	40
5.4	even	2		75.12.e.d.32.14		40
15.2	even	4		75.12.e.d.68.14		40
15.8	even	4	inner	15.12.e.a.8.7	yes	40
15.14	odd	2		75.12.e.d.32.7		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.12.e.a.2.7	✓	40	1.1	even	1	trivial
15.12.e.a.2.14	yes	40	3.2	odd	2	inner
15.12.e.a.8.7	yes	40	15.8	even	4	inner
15.12.e.a.8.14	yes	40	5.3	odd	4	inner
75.12.e.d.32.7		40	15.14	odd	2
75.12.e.d.32.14		40	5.4	even	2
75.12.e.d.68.7		40	5.2	odd	4
75.12.e.d.68.14		40	15.2	even	4

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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	15.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-26.1390 + 26.1390i) q^{2} +(-159.262 - 389.593i) q^{3} +681.505i q^{4} +(-2800.46 + 6402.00i) q^{5} +(14346.5 + 6020.60i) q^{6} +(5513.09 + 5513.09i) q^{7} +(-71346.5 - 71346.5i) q^{8} +(-126418. + 124095. i) q^{9} +O(q^{10})\)	\(q+(-26.1390 + 26.1390i) q^{2} +(-159.262 - 389.593i) q^{3} +681.505i q^{4} +(-2800.46 + 6402.00i) q^{5} +(14346.5 + 6020.60i) q^{6} +(5513.09 + 5513.09i) q^{7} +(-71346.5 - 71346.5i) q^{8} +(-126418. + 124095. i) q^{9} +(-94140.6 - 240543. i) q^{10} -213111. i q^{11} +(265509. - 108538. i) q^{12} +(1.40784e6 - 1.40784e6i) q^{13} -288214. q^{14} +(2.94018e6 + 71441.2i) q^{15} +2.33413e6 q^{16} +(2.24338e6 - 2.24338e6i) q^{17} +(60720.1 - 6.54816e6i) q^{18} -1.02378e7i q^{19} +(-4.36299e6 - 1.90853e6i) q^{20} +(1.26983e6 - 3.02589e6i) q^{21} +(5.57051e6 + 5.57051e6i) q^{22} +(-1.46579e7 - 1.46579e7i) q^{23} +(-1.64333e7 + 3.91589e7i) q^{24} +(-3.31430e7 - 3.58571e7i) q^{25} +7.35989e7i q^{26} +(6.84801e7 + 2.94878e7i) q^{27} +(-3.75720e6 + 3.75720e6i) q^{28} +1.52840e8 q^{29} +(-7.87207e7 + 7.49859e7i) q^{30} -2.64198e8 q^{31} +(8.51058e7 - 8.51058e7i) q^{32} +(-8.30265e7 + 3.39406e7i) q^{33} +1.17279e8i q^{34} +(-5.07340e7 + 1.98556e7i) q^{35} +(-8.45713e7 - 8.61545e7i) q^{36} +(2.07043e8 + 2.07043e8i) q^{37} +(2.67607e8 + 2.67607e8i) q^{38} +(-7.72699e8 - 3.24268e8i) q^{39} +(6.56563e8 - 2.56957e8i) q^{40} -1.29665e8i q^{41} +(4.59016e7 + 1.12286e8i) q^{42} +(-2.00424e8 + 2.00424e8i) q^{43} +1.45236e8 q^{44} +(-4.40427e8 - 1.15685e9i) q^{45} +7.66285e8 q^{46} +(9.40322e8 - 9.40322e8i) q^{47} +(-3.71740e8 - 9.09361e8i) q^{48} -1.91654e9i q^{49} +(1.80359e9 + 7.09436e7i) q^{50} +(-1.23129e9 - 5.16718e8i) q^{51} +(9.59448e8 + 9.59448e8i) q^{52} +(3.25209e9 + 3.25209e9i) q^{53} +(-2.56079e9 + 1.01922e9i) q^{54} +(1.36434e9 + 5.96809e8i) q^{55} -7.86680e8i q^{56} +(-3.98859e9 + 1.63050e9i) q^{57} +(-3.99508e9 + 3.99508e9i) q^{58} -4.71394e9 q^{59} +(-4.86876e7 + 2.00375e9i) q^{60} -4.47029e9 q^{61} +(6.90587e9 - 6.90587e9i) q^{62} +(-1.38110e9 - 1.28067e7i) q^{63} +9.22947e9i q^{64} +(5.07038e9 + 1.29556e10i) q^{65} +(1.28306e9 - 3.05740e9i) q^{66} +(-1.40139e10 - 1.40139e10i) q^{67} +(1.52887e9 + 1.52887e9i) q^{68} +(-3.37615e9 + 8.04505e9i) q^{69} +(8.07130e8 - 1.84514e9i) q^{70} -9.83456e9i q^{71} +(1.78732e10 + 1.65736e8i) q^{72} +(2.37754e10 - 2.37754e10i) q^{73} -1.08238e10 q^{74} +(-8.69122e9 + 1.86229e10i) q^{75} +6.97714e9 q^{76} +(1.17490e9 - 1.17490e9i) q^{77} +(2.86736e10 - 1.17215e10i) q^{78} +6.03538e9i q^{79} +(-6.53665e9 + 1.49431e10i) q^{80} +(5.81934e8 - 3.13757e10i) q^{81} +(3.38931e9 + 3.38931e9i) q^{82} +(-3.18619e10 - 3.18619e10i) q^{83} +(2.06216e9 + 8.65397e8i) q^{84} +(8.07960e9 + 2.06446e10i) q^{85} -1.04777e10i q^{86} +(-2.43416e10 - 5.95453e10i) q^{87} +(-1.52047e10 + 1.52047e10i) q^{88} -9.38732e10 q^{89} +(4.17512e10 + 1.87266e10i) q^{90} +1.55231e10 q^{91} +(9.98942e9 - 9.98942e9i) q^{92} +(4.20768e10 + 1.02930e11i) q^{93} +4.91582e10i q^{94} +(6.55426e10 + 2.86707e10i) q^{95} +(-4.67108e10 - 1.96024e10i) q^{96} +(-1.56778e10 - 1.56778e10i) q^{97} +(5.00964e10 + 5.00964e10i) q^{98} +(2.64460e10 + 2.69410e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 504 q^{3} + 2940 q^{6} + 31504 q^{7}+O(q^{10}) \) 40 * q + 504 * q^3 + 2940 * q^6 + 31504 * q^7	\( 40 q + 504 q^{3} + 2940 q^{6} + 31504 q^{7} + 305140 q^{10} - 1714188 q^{12} - 3448472 q^{13} - 6075120 q^{15} - 43202180 q^{16} + 3729120 q^{18} + 33570840 q^{21} - 21743260 q^{22} - 68969000 q^{25} + 113282712 q^{27} + 253355948 q^{28} + 536094300 q^{30} + 67990880 q^{31} - 563443560 q^{33} + 1116103980 q^{36} + 1292573224 q^{37} - 2754089880 q^{40} - 5132304780 q^{42} + 4012128208 q^{43} + 4994447400 q^{45} - 8170829920 q^{46} - 13847034876 q^{48} + 5424535440 q^{51} + 10287332704 q^{52} - 23061806800 q^{55} - 10576855656 q^{57} + 56277468420 q^{58} + 66297294060 q^{60} - 24994982320 q^{61} - 50371112832 q^{63} + 56311074600 q^{66} + 37314988144 q^{67} - 90895488900 q^{70} - 92983114440 q^{72} + 51361482568 q^{73} + 96079968600 q^{75} - 121004023440 q^{76} - 104085843000 q^{78} - 22936122360 q^{81} - 56747065840 q^{82} + 5885083240 q^{85} + 84564024000 q^{87} + 148338843420 q^{88} + 17247857160 q^{90} + 230876677280 q^{91} + 38932525008 q^{93} - 437860137180 q^{96} - 294950050616 q^{97}+O(q^{100}) \) 40 * q + 504 * q^3 + 2940 * q^6 + 31504 * q^7 + 305140 * q^10 - 1714188 * q^12 - 3448472 * q^13 - 6075120 * q^15 - 43202180 * q^16 + 3729120 * q^18 + 33570840 * q^21 - 21743260 * q^22 - 68969000 * q^25 + 113282712 * q^27 + 253355948 * q^28 + 536094300 * q^30 + 67990880 * q^31 - 563443560 * q^33 + 1116103980 * q^36 + 1292573224 * q^37 - 2754089880 * q^40 - 5132304780 * q^42 + 4012128208 * q^43 + 4994447400 * q^45 - 8170829920 * q^46 - 13847034876 * q^48 + 5424535440 * q^51 + 10287332704 * q^52 - 23061806800 * q^55 - 10576855656 * q^57 + 56277468420 * q^58 + 66297294060 * q^60 - 24994982320 * q^61 - 50371112832 * q^63 + 56311074600 * q^66 + 37314988144 * q^67 - 90895488900 * q^70 - 92983114440 * q^72 + 51361482568 * q^73 + 96079968600 * q^75 - 121004023440 * q^76 - 104085843000 * q^78 - 22936122360 * q^81 - 56747065840 * q^82 + 5885083240 * q^85 + 84564024000 * q^87 + 148338843420 * q^88 + 17247857160 * q^90 + 230876677280 * q^91 + 38932525008 * q^93 - 437860137180 * q^96 - 294950050616 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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