LMFDB - Embedded newform 36.15.d.c.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,15,Mod(19,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 15, names="a")

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

chi := DirichletCharacter("36.19");

S:= CuspForms(chi, 15);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	36.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$44.7584285347$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 88x^{4} - 1824x^{3} + 325632x^{2} + 21572352x + 982333440 $ x^6 - x^5 + 88x^4 - 1824x^3 + 325632x^2 + 21572352x + 982333440
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{30}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 4)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.6
Root			$-24.5778 + 14.3983i$ of defining polynomial
Character	$\chi$	$=$	36.19
Dual form			36.15.d.c.19.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(114.311 + 57.5931i) q^{2} +(9750.07 + 13167.1i) q^{4} +81680.5 q^{5} +1.09921e6i q^{7} +(356209. + 2.06668e6i) q^{8} +O(q^{10})$	\(q+(114.311 + 57.5931i) q^{2} +(9750.07 + 13167.1i) q^{4} +81680.5 q^{5} +1.09921e6i q^{7} +(356209. + 2.06668e6i) q^{8} +(9.33699e6 + 4.70423e6i) q^{10} +4.90926e6i q^{11} -7.29644e7 q^{13} +(-6.33071e7 + 1.25652e8i) q^{14} +(-7.83078e7 + 2.56760e8i) q^{16} +4.69361e8 q^{17} -6.82881e8i q^{19} +(7.96390e8 + 1.07549e9i) q^{20} +(-2.82739e8 + 5.61183e8i) q^{22} +9.17041e8i q^{23} +5.68188e8 q^{25} +(-8.34064e9 - 4.20224e9i) q^{26} +(-1.44734e10 + 1.07174e10i) q^{28} +1.00105e10 q^{29} +3.41422e10i q^{31} +(-2.37390e10 + 2.48405e10i) q^{32} +(5.36532e10 + 2.70320e10i) q^{34} +8.97842e10i q^{35} -4.99005e10 q^{37} +(3.93292e10 - 7.80609e10i) q^{38} +(2.90953e10 + 1.68807e11i) q^{40} -1.91904e11 q^{41} -3.10023e11i q^{43} +(-6.46405e10 + 4.78656e10i) q^{44} +(-5.28152e10 + 1.04828e11i) q^{46} +4.62878e11i q^{47} -5.30046e11 q^{49} +(6.49503e10 + 3.27237e10i) q^{50} +(-7.11407e11 - 9.60726e11i) q^{52} +5.28568e11 q^{53} +4.00991e11i q^{55} +(-2.27172e12 + 3.91549e11i) q^{56} +(1.14431e12 + 5.76534e11i) q^{58} +8.92307e11i q^{59} +3.16992e12 q^{61} +(-1.96636e12 + 3.90284e12i) q^{62} +(-4.14428e12 + 1.47234e12i) q^{64} -5.95976e12 q^{65} +5.43679e12i q^{67} +(4.57630e12 + 6.18011e12i) q^{68} +(-5.17095e12 + 1.02633e13i) q^{70} +2.22157e12i q^{71} -8.53427e12 q^{73} +(-5.70419e12 - 2.87393e12i) q^{74} +(8.99154e12 - 6.65813e12i) q^{76} -5.39632e12 q^{77} +1.09319e13i q^{79} +(-6.39622e12 + 2.09723e13i) q^{80} +(-2.19368e13 - 1.10524e13i) q^{82} +8.13058e12i q^{83} +3.83377e13 q^{85} +(1.78552e13 - 3.54390e13i) q^{86} +(-1.01459e13 + 1.74872e12i) q^{88} +6.18420e13 q^{89} -8.02033e13i q^{91} +(-1.20747e13 + 8.94121e12i) q^{92} +(-2.66586e13 + 5.29121e13i) q^{94} -5.57781e13i q^{95} +7.86895e13 q^{97} +(-6.05901e13 - 3.05270e13i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 92 q^{2} - 1392 q^{4} - 8060 q^{5} - 446272 q^{8}+O(q^{10}) $ 6 * q + 92 * q^2 - 1392 * q^4 - 8060 * q^5 - 446272 * q^8	\( 6 q + 92 q^{2} - 1392 q^{4} - 8060 q^{5} - 446272 q^{8} + 5796840 q^{10} - 80775396 q^{13} - 175232064 q^{14} - 353013504 q^{16} + 120131764 q^{17} + 5047343200 q^{20} + 9916985760 q^{22} + 3942973410 q^{25} - 39549467048 q^{26} - 65094731520 q^{28} + 8035796644 q^{29} + 85711465472 q^{32} + 98089165512 q^{34} + 31334118396 q^{37} + 165268841760 q^{38} + 435607171200 q^{40} - 83362750892 q^{41} - 915657452160 q^{44} - 1712365889856 q^{46} - 551978693658 q^{49} + 1639579094580 q^{50} + 1057159118496 q^{52} - 76712275004 q^{53} + 560223046656 q^{56} + 4483777382184 q^{58} + 6210000787932 q^{61} - 10375644284160 q^{62} - 14398852657152 q^{64} + 7189912943720 q^{65} + 18507298307296 q^{68} + 12679529923200 q^{70} - 29882649313236 q^{73} + 1536652566808 q^{74} + 21457134000000 q^{76} - 37339673521920 q^{77} - 57843429624320 q^{80} - 71900577251064 q^{82} + 151199882653560 q^{85} + 100164269733216 q^{86} + 51557990330880 q^{88} + 180966014731924 q^{89} - 82241452266240 q^{92} - 40381697410176 q^{94} - 345459072299124 q^{97} - 121406102961892 q^{98}+O(q^{100}) \) 6 * q + 92 * q^2 - 1392 * q^4 - 8060 * q^5 - 446272 * q^8 + 5796840 * q^10 - 80775396 * q^13 - 175232064 * q^14 - 353013504 * q^16 + 120131764 * q^17 + 5047343200 * q^20 + 9916985760 * q^22 + 3942973410 * q^25 - 39549467048 * q^26 - 65094731520 * q^28 + 8035796644 * q^29 + 85711465472 * q^32 + 98089165512 * q^34 + 31334118396 * q^37 + 165268841760 * q^38 + 435607171200 * q^40 - 83362750892 * q^41 - 915657452160 * q^44 - 1712365889856 * q^46 - 551978693658 * q^49 + 1639579094580 * q^50 + 1057159118496 * q^52 - 76712275004 * q^53 + 560223046656 * q^56 + 4483777382184 * q^58 + 6210000787932 * q^61 - 10375644284160 * q^62 - 14398852657152 * q^64 + 7189912943720 * q^65 + 18507298307296 * q^68 + 12679529923200 * q^70 - 29882649313236 * q^73 + 1536652566808 * q^74 + 21457134000000 * q^76 - 37339673521920 * q^77 - 57843429624320 * q^80 - 71900577251064 * q^82 + 151199882653560 * q^85 + 100164269733216 * q^86 + 51557990330880 * q^88 + 180966014731924 * q^89 - 82241452266240 * q^92 - 40381697410176 * q^94 - 345459072299124 * q^97 - 121406102961892 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	114.311	+	57.5931i	0.893056	+	0.449946i
$2$	114.311	+	57.5931i	0.893056	+	0.449946i
$3$		0			0
$3$		0			0
$4$	9750.07	+	13167.1i	0.595097	+	0.803654i
$5$	81680.5			1.04551			0.522755	−	0.852483i	$-0.324904\pi$
$5$	81680.5			1.04551			0.522755	+	0.852483i	$0.324904\pi$
$6$		0			0
$7$			1.09921e6i			1.33474i	0.744728	+	0.667368i	$0.232579\pi$
$7$			1.09921e6i			1.33474i	−0.744728	+	0.667368i	$0.767421\pi$
$8$	356209.	+	2.06668e6i	0.169854	+	0.985469i
$9$		0			0
$10$	9.33699e6	+	4.70423e6i	0.933699	+	0.470423i
$11$			4.90926e6i			0.251923i	0.992035	+	0.125961i	$0.0402015\pi$
$11$			4.90926e6i			0.251923i	−0.992035	+	0.125961i	$0.959798\pi$
$12$		0			0
$13$	−7.29644e7			−1.16281			−0.581403	−	0.813616i	$-0.697496\pi$
$13$	−7.29644e7			−1.16281			−0.581403	+	0.813616i	$0.697496\pi$
$14$	−6.33071e7	+	1.25652e8i	−0.600559	+	1.19199i
$15$		0			0
$16$	−7.83078e7	+	2.56760e8i	−0.291719	+	0.956504i
$17$	4.69361e8			1.14384			0.571919	−	0.820310i	$-0.306199\pi$
$17$	4.69361e8			1.14384			0.571919	+	0.820310i	$0.306199\pi$
$18$		0			0
$19$		−	6.82881e8i		−	0.763958i	−0.924171	−	0.381979i	$-0.875243\pi$
$19$		−	6.82881e8i		−	0.763958i	0.924171	−	0.381979i	$-0.124757\pi$
$20$	7.96390e8	+	1.07549e9i	0.622180	+	0.840229i
$21$		0			0
$22$	−2.82739e8	+	5.61183e8i	−0.113352	+	0.224981i
$23$			9.17041e8i			0.269336i	0.990891	+	0.134668i	$0.0429967\pi$
$23$			9.17041e8i			0.269336i	−0.990891	+	0.134668i	$0.957003\pi$
$24$		0			0
$25$	5.68188e8			0.0930920
$26$	−8.34064e9	−	4.20224e9i	−1.03845	−	0.523200i
$27$		0			0
$28$	−1.44734e10	+	1.07174e10i	−1.07267	+	0.794297i
$29$	1.00105e10			0.580321			0.290161	−	0.956978i	$-0.406291\pi$
$29$	1.00105e10			0.580321			0.290161	+	0.956978i	$0.406291\pi$
$30$		0			0
$31$			3.41422e10i			1.24097i	0.784220	+	0.620483i	$0.213063\pi$
$31$			3.41422e10i			1.24097i	−0.784220	+	0.620483i	$0.786937\pi$
$32$	−2.37390e10	+	2.48405e10i	−0.690897	+	0.722953i
$33$		0			0
$34$	5.36532e10	+	2.70320e10i	1.02151	+	0.514666i
$35$			8.97842e10i			1.39548i
$36$		0			0
$37$	−4.99005e10			−0.525646			−0.262823	−	0.964844i	$-0.584653\pi$
$37$	−4.99005e10			−0.525646			−0.262823	+	0.964844i	$0.584653\pi$
$38$	3.93292e10	−	7.80609e10i	0.343740	−	0.682257i
$39$		0			0
$40$	2.90953e10	+	1.68807e11i	0.177584	+	1.03032i
$41$	−1.91904e11			−0.985366			−0.492683	−	0.870209i	$-0.663984\pi$
$41$	−1.91904e11			−0.985366			−0.492683	+	0.870209i	$0.663984\pi$
$42$		0			0
$43$		−	3.10023e11i		−	1.14055i	−0.821454	−	0.570275i	$-0.806837\pi$
$43$		−	3.10023e11i		−	1.14055i	0.821454	−	0.570275i	$-0.193163\pi$
$44$	−6.46405e10	+	4.78656e10i	−0.202459	+	0.149918i
$45$		0			0
$46$	−5.28152e10	+	1.04828e11i	−0.121187	+	0.240532i
$47$			4.62878e11i			0.913654i	0.889556	+	0.456827i	$0.151014\pi$
$47$			4.62878e11i			0.913654i	−0.889556	+	0.456827i	$0.848986\pi$
$48$		0			0
$49$	−5.30046e11			−0.781521
$50$	6.49503e10	+	3.27237e10i	0.0831363	+	0.0418864i
$51$		0			0
$52$	−7.11407e11	−	9.60726e11i	−0.691982	−	0.934494i
$53$	5.28568e11			0.449956			0.224978	−	0.974364i	$-0.427769\pi$
$53$	5.28568e11			0.449956			0.224978	+	0.974364i	$0.427769\pi$
$54$		0			0
$55$			4.00991e11i			0.263388i
$56$	−2.27172e12	+	3.91549e11i	−1.31534	+	0.226710i
$57$		0			0
$58$	1.14431e12	+	5.76534e11i	0.518259	+	0.261113i
$59$			8.92307e11i			0.358550i	0.983799	+	0.179275i	$0.0573753\pi$
$59$			8.92307e11i			0.358550i	−0.983799	+	0.179275i	$0.942625\pi$
$60$		0			0
$61$	3.16992e12			1.00865			0.504324	−	0.863514i	$-0.331742\pi$
$61$	3.16992e12			1.00865			0.504324	+	0.863514i	$0.331742\pi$
$62$	−1.96636e12	+	3.90284e12i	−0.558368	+	1.10825i
$63$		0			0
$64$	−4.14428e12	+	1.47234e12i	−0.942299	+	0.334771i
$65$	−5.95976e12			−1.21573
$66$		0			0
$67$			5.43679e12i			0.897055i	0.893769	+	0.448528i	$0.148051\pi$
$67$			5.43679e12i			0.897055i	−0.893769	+	0.448528i	$0.851949\pi$
$68$	4.57630e12	+	6.18011e12i	0.680695	+	0.919250i
$69$		0			0
$70$	−5.17095e12	+	1.02633e13i	−0.627891	+	1.24624i
$71$			2.22157e12i			0.244260i	0.992514	+	0.122130i	$0.0389725\pi$
$71$			2.22157e12i			0.244260i	−0.992514	+	0.122130i	$0.961028\pi$
$72$		0			0
$73$	−8.53427e12			−0.772514			−0.386257	−	0.922391i	$-0.626232\pi$
$73$	−8.53427e12			−0.772514			−0.386257	+	0.922391i	$0.626232\pi$
$74$	−5.70419e12	−	2.87393e12i	−0.469431	−	0.236512i
$75$		0			0
$76$	8.99154e12	−	6.65813e12i	0.613958	−	0.454629i
$77$	−5.39632e12			−0.336250
$78$		0			0
$79$			1.09319e13i			0.569252i	0.958639	+	0.284626i	$0.0918694\pi$
$79$			1.09319e13i			0.569252i	−0.958639	+	0.284626i	$0.908131\pi$
$80$	−6.39622e12	+	2.09723e13i	−0.304996	+	1.00003i
$81$		0			0
$82$	−2.19368e13	−	1.10524e13i	−0.879987	−	0.443362i
$83$			8.13058e12i			0.299623i	0.988715	+	0.149811i	$0.0478667\pi$
$83$			8.13058e12i			0.299623i	−0.988715	+	0.149811i	$0.952133\pi$
$84$		0			0
$85$	3.83377e13			1.19590
$86$	1.78552e13	−	3.54390e13i	0.513186	−	1.01857i
$87$		0			0
$88$	−1.01459e13	+	1.74872e12i	−0.248262	+	0.0427900i
$89$	6.18420e13			1.39815			0.699075	−	0.715049i	$-0.253595\pi$
$89$	6.18420e13			1.39815			0.699075	+	0.715049i	$0.253595\pi$
$90$		0			0
$91$		−	8.02033e13i		−	1.55204i
$92$	−1.20747e13	+	8.94121e12i	−0.216453	+	0.160281i
$93$		0			0
$94$	−2.66586e13	+	5.29121e13i	−0.411095	+	0.815943i
$95$		−	5.57781e13i		−	0.798726i
$96$		0			0
$97$	7.86895e13			0.973900			0.486950	−	0.873430i	$-0.338109\pi$
$97$	7.86895e13			0.973900			0.486950	+	0.873430i	$0.338109\pi$
$98$	−6.05901e13	−	3.05270e13i	−0.697942	−	0.351642i
$99$		0			0
$100$	5.53988e12	+	7.48137e12i	0.0553988	+	0.0748137i
$101$	6.76553e13			0.631034			0.315517	−	0.948920i	$-0.397822\pi$
$101$	6.76553e13			0.631034			0.315517	+	0.948920i	$0.397822\pi$
$102$		0			0
$103$		−	2.12142e14i		−	1.72491i	−0.506132	−	0.862456i	$-0.668925\pi$
$103$		−	2.12142e14i		−	1.72491i	0.506132	−	0.862456i	$-0.331075\pi$
$104$	−2.59906e13	−	1.50794e14i	−0.197507	−	1.14591i
$105$		0			0
$106$	6.04212e13	+	3.04419e13i	0.401836	+	0.202456i
$107$		−	2.80059e14i		−	1.74406i	−0.489449	−	0.872032i	$-0.662802\pi$
$107$		−	2.80059e14i		−	1.74406i	0.489449	−	0.872032i	$-0.337198\pi$
$108$		0			0
$109$	1.85065e14			1.01237			0.506183	−	0.862426i	$-0.331056\pi$
$109$	1.85065e14			1.01237			0.506183	+	0.862426i	$0.331056\pi$
$110$	−2.30943e13	+	4.58377e13i	−0.118510	+	0.235220i
$111$		0			0
$112$	−2.82233e14	−	8.60769e13i	−1.27668	−	0.389368i
$113$	3.29356e14			1.39996			0.699981	−	0.714162i	$-0.253192\pi$
$113$	3.29356e14			1.39996			0.699981	+	0.714162i	$0.253192\pi$
$114$		0			0
$115$			7.49044e13i			0.281593i
$116$	9.76027e13	+	1.31808e14i	0.345347	+	0.466377i
$117$		0			0
$118$	−5.13907e13	+	1.02001e14i	−0.161328	+	0.320206i
$119$			5.15928e14i			1.52672i
$120$		0			0
$121$	3.55649e14			0.936535
$122$	3.62358e14	+	1.82566e14i	0.900780	+	0.453838i
$123$		0			0
$124$	−4.49553e14	+	3.32889e14i	−0.997307	+	0.738495i
$125$	−4.52128e14			−0.948182
$126$		0			0
$127$			5.08059e14i			0.953429i	0.879058	+	0.476715i	$0.158172\pi$
$127$			5.08059e14i			0.953429i	−0.879058	+	0.476715i	$0.841828\pi$
$128$	−5.58534e14	−	7.03770e13i	−0.992155	−	0.125015i
$129$		0			0
$130$	−6.81267e14	−	3.43241e14i	−1.08571	−	0.547011i
$131$		−	8.76324e14i		−	1.32363i	−0.749668	−	0.661814i	$-0.769787\pi$
$131$		−	8.76324e14i		−	1.32363i	0.749668	−	0.661814i	$-0.230213\pi$
$132$		0			0
$133$	7.50631e14			1.01968
$134$	−3.13122e14	+	6.21486e14i	−0.403627	+	0.801120i
$135$		0			0
$136$	1.67191e14	+	9.70019e14i	0.194285	+	1.12722i
$137$	7.70700e14			0.850827			0.425414	−	0.904999i	$-0.360129\pi$
$137$	7.70700e14			0.850827			0.425414	+	0.904999i	$0.360129\pi$
$138$		0			0
$139$		−	1.67539e15i		−	1.67113i	−0.549388	−	0.835567i	$-0.685139\pi$
$139$		−	1.67539e15i		−	1.67113i	0.549388	−	0.835567i	$-0.314861\pi$
$140$	−1.18220e15	+	8.75402e14i	−1.12148	+	0.830446i
$141$		0			0
$142$	−1.27947e14	+	2.53951e14i	−0.109904	+	0.218138i
$143$		−	3.58201e14i		−	0.292937i
$144$		0			0
$145$	8.17660e14			0.606732
$146$	−9.75562e14	−	4.91515e14i	−0.689898	−	0.347590i
$147$		0			0
$148$	−4.86534e14	−	6.57044e14i	−0.312810	−	0.422437i
$149$	−6.40824e13			−0.0393038			−0.0196519	−	0.999807i	$-0.506256\pi$
$149$	−6.40824e13			−0.0393038			−0.0196519	+	0.999807i	$0.506256\pi$
$150$		0			0
$151$			3.11313e14i			0.173924i	0.996212	+	0.0869618i	$0.0277158\pi$
$151$			3.11313e14i			0.173924i	−0.996212	+	0.0869618i	$0.972284\pi$
$152$	1.41130e15	−	2.43248e14i	0.752858	−	0.129761i
$153$		0			0
$154$	−6.16859e14	−	3.10791e14i	−0.300290	−	0.151295i
$155$			2.78875e15i			1.29744i
$156$		0			0
$157$	−1.13617e15			−0.483222			−0.241611	−	0.970373i	$-0.577676\pi$
$157$	−1.13617e15			−0.483222			−0.241611	+	0.970373i	$0.577676\pi$
$158$	−6.29600e14	+	1.24963e15i	−0.256133	+	0.508374i
$159$		0			0
$160$	−1.93902e15	+	2.02898e15i	−0.722340	+	0.755855i
$161$	−1.00802e15			−0.359492
$162$		0			0
$163$		−	1.63279e13i		−	0.00534092i	−0.999996	−	0.00267046i	$-0.999150\pi$
$163$		−	1.63279e13i		−	0.00534092i	0.999996	−	0.00267046i	$-0.000850035\pi$
$164$	−1.87108e15	−	2.52682e15i	−0.586388	−	0.791893i
$165$		0			0
$166$	−4.68265e14	+	9.29416e14i	−0.134814	+	0.267580i
$167$			4.16001e15i			1.14836i	0.818728	+	0.574181i	$0.194680\pi$
$167$			4.16001e15i			1.14836i	−0.818728	+	0.574181i	$0.805320\pi$
$168$		0			0
$169$	1.38642e15			0.352118
$170$	4.38242e15	+	2.20799e15i	1.06800	+	0.538088i
$171$		0			0
$172$	4.08209e15	−	3.02274e15i	0.916608	−	0.678738i
$173$	1.71620e15			0.370036			0.185018	−	0.982735i	$-0.440766\pi$
$173$	1.71620e15			0.370036			0.185018	+	0.982735i	$0.440766\pi$
$174$		0			0
$175$			6.24560e14i			0.124253i
$176$	−1.26050e15	−	3.84433e14i	−0.240965	−	0.0734907i
$177$		0			0
$178$	7.06923e15	+	3.56167e15i	1.24863	+	0.629092i
$179$		−	9.91848e15i		−	1.68451i	−0.539078	−	0.842256i	$-0.681227\pi$
$179$		−	9.91848e15i		−	1.68451i	0.539078	−	0.842256i	$-0.318773\pi$
$180$		0			0
$181$	−1.24532e16			−1.95673			−0.978366	−	0.206884i	$-0.933668\pi$
$181$	−1.24532e16			−1.95673			−0.978366	+	0.206884i	$0.933668\pi$
$182$	4.61916e15	−	9.16813e15i	0.698334	−	1.38606i
$183$		0			0
$184$	−1.89523e15	+	3.26658e14i	−0.265422	+	0.0457477i
$185$	−4.07590e15			−0.549568
$186$		0			0
$187$			2.30422e15i			0.288159i
$188$	−6.09475e15	+	4.51309e15i	−0.734261	+	0.543712i
$189$		0			0
$190$	3.21243e15	−	6.37605e15i	0.359384	−	0.713307i
$191$		−	5.36016e15i		−	0.578021i	−0.957326	−	0.289011i	$-0.906674\pi$
$191$		−	5.36016e15i		−	0.578021i	0.957326	−	0.289011i	$-0.0933263\pi$
$192$		0			0
$193$	1.72612e16			1.73049			0.865245	−	0.501349i	$-0.167163\pi$
$193$	1.72612e16			1.73049			0.865245	+	0.501349i	$0.167163\pi$
$194$	8.99508e15	+	4.53197e15i	0.869747	+	0.438203i
$195$		0			0
$196$	−5.16798e15	−	6.97914e15i	−0.465081	−	0.628072i
$197$	3.83258e15			0.332834			0.166417	−	0.986055i	$-0.446780\pi$
$197$	3.83258e15			0.332834			0.166417	+	0.986055i	$0.446780\pi$
$198$		0			0
$199$			8.15094e15i			0.659532i	0.944063	+	0.329766i	$0.106970\pi$
$199$			8.15094e15i			0.659532i	−0.944063	+	0.329766i	$0.893030\pi$
$200$	2.02394e14	+	1.17426e15i	0.0158120	+	0.0917393i
$201$		0			0
$202$	7.73376e15	+	3.89648e15i	0.563548	+	0.283931i
$203$			1.10036e16i			0.774576i
$204$		0			0
$205$	−1.56748e16			−1.03021
$206$	1.22179e16	−	2.42502e16i	0.776118	−	1.54044i
$207$		0			0
$208$	5.71368e15	−	1.87343e16i	0.339213	−	1.11223i
$209$	3.35244e15			0.192458
$210$		0			0
$211$		−	5.93713e14i		−	0.0318859i	−0.999873	−	0.0159430i	$-0.994925\pi$
$211$		−	5.93713e14i		−	0.0318859i	0.999873	−	0.0159430i	$-0.00507502\pi$
$212$	5.15357e15	+	6.95969e15i	0.267767	+	0.361609i
$213$		0			0
$214$	1.61294e16	−	3.20138e16i	0.784735	−	1.55755i
$215$		−	2.53228e16i		−	1.19246i
$216$		0			0
$217$	−3.75296e16			−1.65636
$218$	2.11549e16	+	1.06584e16i	0.904100	+	0.455510i
$219$		0			0
$220$	−5.27987e15	+	3.90969e15i	−0.211673	+	0.156741i
$221$	−3.42466e16			−1.33006
$222$		0			0
$223$		−	1.54317e16i		−	0.562704i	−0.959605	−	0.281352i	$-0.909217\pi$
$223$		−	1.54317e16i		−	0.562704i	0.959605	−	0.281352i	$-0.0907828\pi$
$224$	−2.73050e16	−	2.60942e16i	−0.964952	−	0.922165i
$225$		0			0
$226$	3.76490e16	+	1.89686e16i	1.25024	+	0.629907i
$227$			4.44026e16i			1.42964i	0.699308	+	0.714820i	$0.253492\pi$
$227$			4.44026e16i			1.42964i	−0.699308	+	0.714820i	$0.746508\pi$
$228$		0			0
$229$	−1.37801e16			−0.417257			−0.208628	−	0.977995i	$-0.566900\pi$
$229$	−1.37801e16			−0.417257			−0.208628	+	0.977995i	$0.566900\pi$
$230$	−4.31397e15	+	8.56240e15i	−0.126702	+	0.251478i
$231$		0			0
$232$	3.56582e15	+	2.06884e16i	0.0985697	+	0.571889i
$233$	−5.96868e15			−0.160098			−0.0800492	−	0.996791i	$-0.525508\pi$
$233$	−5.96868e15			−0.160098			−0.0800492	+	0.996791i	$0.525508\pi$
$234$		0			0
$235$			3.78081e16i			0.955234i
$236$	−1.17491e16	+	8.70005e15i	−0.288150	+	0.213372i
$237$		0			0
$238$	−2.97139e16	+	5.89763e16i	−0.686943	+	1.36345i
$239$			4.38433e16i			0.984278i	0.870517	+	0.492139i	$0.163785\pi$
$239$			4.38433e16i			0.984278i	−0.870517	+	0.492139i	$0.836215\pi$
$240$		0			0
$241$	9.28157e15			0.196563			0.0982816	−	0.995159i	$-0.468665\pi$
$241$	9.28157e15			0.196563			0.0982816	+	0.995159i	$0.468665\pi$
$242$	4.06546e16	+	2.04829e16i	0.836378	+	0.421390i
$243$		0			0
$244$	3.09070e16	+	4.17386e16i	0.600244	+	0.810605i
$245$	−4.32944e16			−0.817088
$246$		0			0
$247$			4.98260e16i			0.888335i
$248$	−7.05610e16	+	1.21618e16i	−1.22293	+	0.210783i
$249$		0			0
$250$	−5.16833e16	−	2.60395e16i	−0.846779	−	0.426631i
$251$			5.86421e16i			0.934316i	0.884174	+	0.467158i	$0.154722\pi$
$251$			5.86421e16i			0.934316i	−0.884174	+	0.467158i	$0.845278\pi$
$252$		0			0
$253$	−4.50199e15			−0.0678517
$254$	−2.92607e16	+	5.80768e16i	−0.428992	+	0.851465i
$255$		0			0
$256$	−5.97934e16	−	4.02126e16i	−0.829800	−	0.558061i
$257$	1.04285e17			1.40828			0.704141	−	0.710060i	$-0.251332\pi$
$257$	1.04285e17			1.40828			0.704141	+	0.710060i	$0.251332\pi$
$258$		0			0
$259$		−	5.48513e16i		−	0.701598i
$260$	−5.81081e16	−	7.84726e16i	−0.723475	−	0.977023i
$261$		0			0
$262$	5.04702e16	−	1.00174e17i	0.595561	−	1.18207i
$263$		−	1.40742e17i		−	1.61709i	−0.588434	−	0.808545i	$-0.700255\pi$
$263$		−	1.40742e17i		−	1.61709i	0.588434	−	0.808545i	$-0.299745\pi$
$264$		0			0
$265$	4.31737e16			0.470433
$266$	8.58055e16	+	4.32312e16i	0.910634	+	0.458802i
$267$		0			0
$268$	−7.15866e16	+	5.30091e16i	−0.720922	+	0.533835i
$269$	3.96167e16			0.388698			0.194349	−	0.980932i	$-0.437741\pi$
$269$	3.96167e16			0.388698			0.194349	+	0.980932i	$0.437741\pi$
$270$		0			0
$271$		−	2.85994e16i		−	0.266423i	−0.991088	−	0.133212i	$-0.957471\pi$
$271$		−	2.85994e16i		−	0.266423i	0.991088	−	0.133212i	$-0.0425290\pi$
$272$	−3.67546e16	+	1.20513e17i	−0.333680	+	1.09409i
$273$		0			0
$274$	8.80996e16	+	4.43870e16i	0.759836	+	0.382826i
$275$			2.78938e15i			0.0234520i
$276$		0			0
$277$	1.26075e17			1.00756			0.503781	−	0.863832i	$-0.331942\pi$
$277$	1.26075e17			1.00756			0.503781	+	0.863832i	$0.331942\pi$
$278$	9.64907e16	−	1.91515e17i	0.751921	−	1.49242i
$279$		0			0
$280$	−1.85555e17	+	3.19820e16i	−1.37520	+	0.237028i
$281$	−1.24455e17			−0.899635			−0.449818	−	0.893120i	$-0.648511\pi$
$281$	−1.24455e17			−0.899635			−0.449818	+	0.893120i	$0.648511\pi$
$282$		0			0
$283$		−	1.96560e17i		−	1.35205i	−0.736881	−	0.676023i	$-0.763702\pi$
$283$		−	1.96560e17i		−	1.35205i	0.736881	−	0.676023i	$-0.236298\pi$
$284$	−2.92516e16	+	2.16605e16i	−0.196300	+	0.145358i
$285$		0			0
$286$	2.06299e16	−	4.09464e16i	0.131806	−	0.261609i
$287$		−	2.10944e17i		−	1.31520i
$288$		0			0
$289$	5.19222e16			0.308367
$290$	9.34676e16	+	4.70916e16i	0.541845	+	0.272997i
$291$		0			0
$292$	−8.32097e16	−	1.12371e17i	−0.459721	−	0.620834i
$293$	8.68418e16			0.468442			0.234221	−	0.972183i	$-0.424746\pi$
$293$	8.68418e16			0.468442			0.234221	+	0.972183i	$0.424746\pi$
$294$		0			0
$295$			7.28841e16i			0.374868i
$296$	−1.77750e16	−	1.03128e17i	−0.0892829	−	0.518008i
$297$		0			0
$298$	−7.32533e15	−	3.69070e15i	−0.0351005	−	0.0176846i
$299$		−	6.69113e16i		−	0.313185i
$300$		0			0
$301$	3.40781e17			1.52233
$302$	−1.79295e16	+	3.55865e16i	−0.0782563	+	0.155323i
$303$		0			0
$304$	1.75336e17	+	5.34749e16i	0.730729	+	0.222861i
$305$	2.58921e17			1.05455
$306$		0			0
$307$		−	3.44813e16i		−	0.134158i	−0.997748	−	0.0670788i	$-0.978632\pi$
$307$		−	3.44813e16i		−	0.134158i	0.997748	−	0.0670788i	$-0.0213679\pi$
$308$	−5.26145e16	−	7.10537e16i	−0.200102	−	0.270229i
$309$		0			0
$310$	−1.60613e17	+	3.18786e17i	−0.583779	+	1.15869i
$311$			2.33238e17i			0.828851i	0.910083	+	0.414426i	$0.136018\pi$
$311$			2.33238e17i			0.828851i	−0.910083	+	0.414426i	$0.863982\pi$
$312$		0			0
$313$	4.09151e16			0.139019			0.0695094	−	0.997581i	$-0.477857\pi$
$313$	4.09151e16			0.139019			0.0695094	+	0.997581i	$0.477857\pi$
$314$	−1.29877e17	−	6.54358e16i	−0.431545	−	0.217424i
$315$		0			0
$316$	−1.43941e17	+	1.06586e17i	−0.457482	+	0.338760i
$317$	5.10326e17			1.58647			0.793237	−	0.608913i	$-0.208394\pi$
$317$	5.10326e17			1.58647			0.793237	+	0.608913i	$0.208394\pi$
$318$		0			0
$319$			4.91440e16i			0.146196i
$320$	−3.38507e17	+	1.20261e17i	−0.985184	+	0.350007i
$321$		0			0
$322$	−1.15228e17	−	5.80552e16i	−0.321046	−	0.161752i
$323$		−	3.20518e17i		−	0.873845i
$324$		0			0
$325$	−4.14575e16			−0.108248
$326$	9.40372e14	−	1.86646e15i	0.00240313	−	0.00476974i
$327$		0			0
$328$	−6.83580e16	−	3.96604e17i	−0.167368	−	0.971048i
$329$	−5.08801e17			−1.21949
$330$		0			0
$331$		−	4.46968e17i		−	1.02679i	−0.858153	−	0.513394i	$-0.828388\pi$
$331$		−	4.46968e17i		−	1.02679i	0.858153	−	0.513394i	$-0.171612\pi$
$332$	−1.07056e17	+	7.92737e16i	−0.240793	+	0.178305i
$333$		0			0
$334$	−2.39588e17	+	4.75535e17i	−0.516701	+	1.02555i
$335$			4.44080e17i			0.937881i
$336$		0			0
$337$	−6.42271e17			−1.30109			−0.650547	−	0.759466i	$-0.725460\pi$
$337$	−6.42271e17			−1.30109			−0.650547	+	0.759466i	$0.725460\pi$
$338$	1.58483e17	+	7.98483e16i	0.314461	+	0.158434i
$339$		0			0
$340$	3.73795e17	+	5.04795e17i	0.711674	+	0.961086i
$341$	−1.67613e17			−0.312627
$342$		0			0
$343$			1.62879e17i			0.291612i
$344$	6.40717e17	−	1.10433e17i	1.12398	−	0.193727i
$345$		0			0
$346$	1.96180e17	+	9.88410e16i	0.330463	+	0.166496i
$347$			6.78908e17i			1.12074i	0.828243	+	0.560370i	$0.189341\pi$
$347$			6.78908e17i			1.12074i	−0.828243	+	0.560370i	$0.810659\pi$
$348$		0			0
$349$	1.59374e17			0.252720			0.126360	−	0.991984i	$-0.459671\pi$
$349$	1.59374e17			0.252720			0.126360	+	0.991984i	$0.459671\pi$
$350$	−3.59703e16	+	7.13942e16i	−0.0559073	+	0.110965i
$351$		0			0
$352$	−1.21948e17	−	1.16541e17i	−0.182128	−	0.174053i
$353$	−4.20198e17			−0.615220			−0.307610	−	0.951512i	$-0.599529\pi$
$353$	−4.20198e17			−0.615220			−0.307610	+	0.951512i	$0.599529\pi$
$354$		0			0
$355$			1.81459e17i			0.255376i
$356$	6.02964e17	+	8.14278e17i	0.832035	+	1.12363i
$357$		0			0
$358$	5.71236e17	−	1.13379e18i	0.757940	−	1.50436i
$359$		−	6.81761e17i		−	0.887097i	−0.896250	−	0.443549i	$-0.853719\pi$
$359$		−	6.81761e17i		−	0.887097i	0.896250	−	0.443549i	$-0.146281\pi$
$360$		0			0
$361$	3.32680e17			0.416367
$362$	−1.42354e18	−	7.17219e17i	−1.74747	−	0.880424i
$363$		0			0
$364$	1.05604e18	−	7.81988e17i	1.24730	−	0.923614i
$365$	−6.97084e17			−0.807672
$366$		0			0
$367$			1.31363e18i			1.46491i	0.680814	+	0.732457i	$0.261626\pi$
$367$			1.31363e18i			1.46491i	−0.680814	+	0.732457i	$0.738374\pi$
$368$	−2.35459e17	−	7.18115e16i	−0.257621	−	0.0785704i
$369$		0			0
$370$	−4.65921e17	−	2.34744e17i	−0.490795	−	0.247276i
$371$			5.81009e17i			0.600572i
$372$		0			0
$373$	−1.80553e18			−1.79739			−0.898695	−	0.438575i	$-0.855483\pi$
$373$	−1.80553e18			−1.79739			−0.898695	+	0.438575i	$0.855483\pi$
$374$	−1.32707e17	+	2.63398e17i	−0.129656	+	0.257342i
$375$		0			0
$376$	−9.56620e17	+	1.64881e17i	−0.900378	+	0.155187i
$377$	−7.30407e17			−0.674801
$378$		0			0
$379$			5.56600e17i			0.495528i	0.968820	+	0.247764i	$0.0796958\pi$
$379$			5.56600e17i			0.495528i	−0.968820	+	0.247764i	$0.920304\pi$
$380$	7.34433e17	−	5.43840e17i	0.641900	−	0.475320i
$381$		0			0
$382$	3.08708e17	−	6.12725e17i	0.260078	−	0.516205i
$383$		−	6.77328e17i		−	0.560283i	−0.959959	−	0.280141i	$-0.909619\pi$
$383$		−	6.77328e17i		−	0.560283i	0.959959	−	0.280141i	$-0.0903814\pi$
$384$		0			0
$385$	−4.40774e17			−0.351553
$386$	1.97314e18	+	9.94124e17i	1.54542	+	0.778627i
$387$		0			0
$388$	7.67228e17	+	1.03611e18i	0.579565	+	0.782679i
$389$	3.94973e17			0.293035			0.146518	−	0.989208i	$-0.453193\pi$
$389$	3.94973e17			0.293035			0.146518	+	0.989208i	$0.453193\pi$
$390$		0			0
$391$			4.30423e17i			0.308077i
$392$	−1.88807e17	−	1.09543e18i	−0.132744	−	0.770165i
$393$		0			0
$394$	4.38107e17	+	2.20730e17i	0.297240	+	0.149757i
$395$			8.92920e17i			0.595159i
$396$		0			0
$397$	4.50573e17			0.289889			0.144945	−	0.989440i	$-0.453700\pi$
$397$	4.50573e17			0.289889			0.144945	+	0.989440i	$0.453700\pi$
$398$	−4.69438e17	+	9.31743e17i	−0.296754	+	0.588999i
$399$		0			0
$400$	−4.44936e16	+	1.45888e17i	−0.0271567	+	0.0890429i
$401$	1.76006e18			1.05564			0.527820	−	0.849356i	$-0.323009\pi$
$401$	1.76006e18			1.05564			0.527820	+	0.849356i	$0.323009\pi$
$402$		0			0
$403$		−	2.49116e18i		−	1.44300i
$404$	6.59644e17	+	8.90822e17i	0.375526	+	0.507133i
$405$		0			0
$406$	−6.33733e17	+	1.25784e18i	−0.348517	+	0.691739i
$407$		−	2.44975e17i		−	0.132422i
$408$		0			0
$409$	−1.15236e18			−0.601901			−0.300950	−	0.953640i	$-0.597304\pi$
$409$	−1.15236e18			−0.601901			−0.300950	+	0.953640i	$0.597304\pi$
$410$	−1.79181e18	−	9.02762e17i	−0.920035	−	0.463539i
$411$		0			0
$412$	2.79329e18	−	2.06840e18i	1.38623	−	1.02649i
$413$	−9.80835e17			−0.478570
$414$		0			0
$415$			6.64110e17i			0.313259i
$416$	1.73210e18	−	1.81247e18i	0.803379	−	0.840654i
$417$		0			0
$418$	3.83221e17	+	1.93077e17i	0.171876	+	0.0865959i
$419$		−	1.51013e18i		−	0.666066i	−0.942915	−	0.333033i	$-0.891928\pi$
$419$		−	1.51013e18i		−	0.666066i	0.942915	−	0.333033i	$-0.108072\pi$
$420$		0			0
$421$	−4.01385e16			−0.0171233			−0.00856163	−	0.999963i	$-0.502725\pi$
$421$	−4.01385e16			−0.0171233			−0.00856163	+	0.999963i	$0.502725\pi$
$422$	3.41938e16	−	6.78680e16i	0.0143470	−	0.0284759i
$423$		0			0
$424$	1.88281e17	+	1.09238e18i	0.0764266	+	0.443418i
$425$	2.66686e17			0.106482
$426$		0			0
$427$			3.48442e18i			1.34628i
$428$	3.68755e18	−	2.73059e18i	1.40162	−	1.03789i
$429$		0			0
$430$	1.45842e18	−	2.89468e18i	0.536541	−	1.06493i
$431$			1.79163e18i			0.648496i	0.945972	+	0.324248i	$0.105111\pi$
$431$			1.79163e18i			0.648496i	−0.945972	+	0.324248i	$0.894889\pi$
$432$		0			0
$433$	−2.26536e18			−0.793820			−0.396910	−	0.917858i	$-0.629917\pi$
$433$	−2.26536e18			−0.793820			−0.396910	+	0.917858i	$0.629917\pi$
$434$	−4.29005e18	−	2.16144e18i	−1.47922	−	0.745274i
$435$		0			0
$436$	1.80439e18	+	2.43676e18i	0.602456	+	0.813592i
$437$	6.26230e17			0.205761
$438$		0			0
$439$		−	5.73841e18i		−	1.82616i	−0.407776	−	0.913082i	$-0.633696\pi$
$439$		−	5.73841e18i		−	1.82616i	0.407776	−	0.913082i	$-0.366304\pi$
$440$	−8.28719e17	+	1.42837e17i	−0.259561	+	0.0447374i
$441$		0			0
$442$	−3.91477e18	−	1.97237e18i	−1.18782	−	0.598457i
$443$			1.37351e16i			0.00410209i	0.999998	+	0.00205104i	$0.000652868\pi$
$443$			1.37351e16i			0.00410209i	−0.999998	+	0.00205104i	$0.999347\pi$
$444$		0			0
$445$	5.05129e18			1.46178
$446$	8.88759e17	−	1.76401e18i	0.253186	−	0.502526i
$447$		0			0
$448$	−1.61841e18	−	4.55544e18i	−0.446831	−	1.25772i
$449$	1.04253e17			0.0283378			0.0141689	−	0.999900i	$-0.495490\pi$
$449$	1.04253e17			0.0283378			0.0141689	+	0.999900i	$0.495490\pi$
$450$		0			0
$451$		−	9.42108e17i		−	0.248236i
$452$	3.21124e18	+	4.33665e18i	0.833113	+	1.12508i
$453$		0			0
$454$	−2.55728e18	+	5.07571e18i	−0.643261	+	1.27675i
$455$		−	6.55105e18i		−	1.62267i
$456$		0			0
$457$	6.06077e18			1.45584			0.727921	−	0.685661i	$-0.240487\pi$
$457$	6.06077e18			1.45584			0.727921	+	0.685661i	$0.240487\pi$
$458$	−1.57522e18	−	7.93637e17i	−0.372633	−	0.187743i
$459$		0			0
$460$	−9.86271e17	+	7.30323e17i	−0.226304	+	0.167575i
$461$	−9.53265e17			−0.215430			−0.107715	−	0.994182i	$-0.534353\pi$
$461$	−9.53265e17			−0.215430			−0.107715	+	0.994182i	$0.534353\pi$
$462$		0			0
$463$		−	1.80388e18i		−	0.395495i	−0.980253	−	0.197748i	$-0.936637\pi$
$463$		−	1.80388e18i		−	0.395495i	0.980253	−	0.197748i	$-0.0633627\pi$
$464$	−7.83898e17	+	2.57028e18i	−0.169291	+	0.555079i
$465$		0			0
$466$	−6.82286e17	−	3.43755e17i	−0.142977	−	0.0720356i
$467$			4.98642e18i			1.02937i	0.857380	+	0.514684i	$0.172091\pi$
$467$			4.98642e18i			1.02937i	−0.857380	+	0.514684i	$0.827909\pi$
$468$		0			0
$469$	−5.97619e18			−1.19733
$470$	−2.17749e18	+	4.32189e18i	−0.429804	+	0.853077i
$471$		0			0
$472$	−1.84411e18	+	3.17848e17i	−0.353340	+	0.0609011i
$473$	1.52198e18			0.287330
$474$		0			0
$475$		−	3.88005e17i		−	0.0711184i
$476$	−6.79326e18	+	5.03033e18i	−1.22696	+	0.908548i
$477$		0			0
$478$	−2.52507e18	+	5.01178e18i	−0.442872	+	0.879015i
$479$		−	7.81614e17i		−	0.135096i	−0.997716	−	0.0675482i	$-0.978482\pi$
$479$		−	7.81614e17i		−	0.135096i	0.997716	−	0.0675482i	$-0.0215176\pi$
$480$		0			0
$481$	3.64096e18			0.611224
$482$	1.06099e18	+	5.34555e17i	0.175542	+	0.0884429i
$483$		0			0
$484$	3.46760e18	+	4.68285e18i	0.557329	+	0.752650i
$485$	6.42739e18			1.01822
$486$		0			0
$487$			1.09338e19i			1.68294i	0.540307	+	0.841468i	$0.318308\pi$
$487$			1.09338e19i			1.68294i	−0.540307	+	0.841468i	$0.681692\pi$
$488$	1.12916e18	+	6.55121e18i	0.171323	+	0.993992i
$489$		0			0
$490$	−4.94903e18	−	2.49346e18i	−0.729705	−	0.367646i
$491$			2.12840e18i			0.309373i	0.987964	+	0.154686i	$0.0494367\pi$
$491$			2.12840e18i			0.309373i	−0.987964	+	0.154686i	$0.950563\pi$
$492$		0			0
$493$	4.69852e18			0.663794
$494$	−2.86963e18	+	5.69566e18i	−0.399703	+	0.793333i
$495$		0			0
$496$	−8.76634e18	−	2.67360e18i	−1.18699	−	0.362014i
$497$	−2.44198e18			−0.326023
$498$		0			0
$499$			2.24625e18i			0.291577i	0.989316	+	0.145789i	$0.0465719\pi$
$499$			2.24625e18i			0.291577i	−0.989316	+	0.145789i	$0.953428\pi$
$500$	−4.40828e18	−	5.95320e18i	−0.564260	−	0.762010i
$501$		0			0
$502$	−3.37738e18	+	6.70345e18i	−0.420392	+	0.834396i
$503$			8.51955e18i			1.04578i	0.852400	+	0.522891i	$0.175146\pi$
$503$			8.51955e18i			1.04578i	−0.852400	+	0.522891i	$0.824854\pi$
$504$		0			0
$505$	5.52612e18			0.659752
$506$	−5.14628e17	−	2.59284e17i	−0.0605954	−	0.0305296i
$507$		0			0
$508$	−6.68965e18	+	4.95361e18i	−0.766227	+	0.567383i
$509$	−1.21923e19			−1.37740			−0.688699	−	0.725047i	$-0.741818\pi$
$509$	−1.21923e19			−1.37740			−0.688699	+	0.725047i	$0.741818\pi$
$510$		0			0
$511$		−	9.38098e18i		−	1.03110i
$512$	−4.51908e18	−	8.04043e18i	−0.489960	−	0.871745i
$513$		0			0
$514$	1.19209e19	+	6.00609e18i	1.25767	+	0.633651i
$515$		−	1.73279e19i		−	1.80341i
$516$		0			0
$517$	−2.27239e18			−0.230170
$518$	3.15906e18	−	6.27012e18i	0.315682	−	0.626567i
$519$		0			0
$520$	−2.12292e18	−	1.23169e19i	−0.206496	−	1.19806i
$521$	−2.24317e18			−0.215277			−0.107639	−	0.994190i	$-0.534329\pi$
$521$	−2.24317e18			−0.215277			−0.107639	+	0.994190i	$0.534329\pi$
$522$		0			0
$523$			4.84461e18i			0.452633i	0.974054	+	0.226317i	$0.0726684\pi$
$523$			4.84461e18i			0.452633i	−0.974054	+	0.226317i	$0.927332\pi$
$524$	1.15386e19	−	8.54422e18i	1.06374	−	0.787687i
$525$		0			0
$526$	8.10578e18	−	1.60884e19i	0.727603	−	1.44415i
$527$			1.60250e19i			1.41946i
$528$		0			0
$529$	1.07519e19			0.927458
$530$	4.93523e18	+	2.48651e18i	0.420123	+	0.211670i
$531$		0			0
$532$	7.31871e18	+	9.88361e18i	0.606810	+	0.819472i
$533$	1.40022e19			1.14579
$534$		0			0
$535$		−	2.28753e19i		−	1.82344i
$536$	−1.12361e19	+	1.93663e18i	−0.884020	+	0.152368i
$537$		0			0
$538$	4.52863e18	+	2.28165e18i	0.347129	+	0.174893i
$539$		−	2.60213e18i		−	0.196883i
$540$		0			0
$541$	−2.44277e19			−1.80095			−0.900475	−	0.434908i	$-0.856781\pi$
$541$	−2.44277e19			−1.80095			−0.900475	+	0.434908i	$0.856781\pi$
$542$	1.64713e18	−	3.26923e18i	0.119876	−	0.237931i
$543$		0			0
$544$	−1.11422e19	+	1.16592e19i	−0.790275	+	0.826942i
$545$	1.51162e19			1.05844
$546$		0			0
$547$		−	1.61060e19i		−	1.09920i	−0.835429	−	0.549599i	$-0.814781\pi$
$547$		−	1.61060e19i		−	1.09920i	0.835429	−	0.549599i	$-0.185219\pi$
$548$	7.51438e18	+	1.01479e19i	0.506325	+	0.683771i
$549$		0			0
$550$	−1.60649e17	+	3.18858e17i	−0.0105521	+	0.0209439i
$551$		−	6.83596e18i		−	0.443341i
$552$		0			0
$553$	−1.20164e19			−0.759801
$554$	1.44118e19	+	7.26107e18i	0.899809	+	0.453348i
$555$		0			0
$556$	2.20599e19	−	1.63351e19i	1.34301	−	0.994487i
$557$	1.12923e19			0.678884			0.339442	−	0.940627i	$-0.389762\pi$
$557$	1.12923e19			0.678884			0.339442	+	0.940627i	$0.389762\pi$
$558$		0			0
$559$			2.26206e19i			1.32624i
$560$	−2.30530e19	−	7.03081e18i	−1.33478	−	0.407089i
$561$		0			0
$562$	−1.42265e19	−	7.16772e18i	−0.803424	−	0.404787i
$563$		−	2.32051e19i		−	1.29427i	−0.762376	−	0.647135i	$-0.775967\pi$
$563$		−	2.32051e19i		−	1.29427i	0.762376	−	0.647135i	$-0.224033\pi$
$564$		0			0
$565$	2.69019e19			1.46367
$566$	1.13205e19	−	2.24691e19i	0.608347	−	1.20745i
$567$		0			0
$568$	−4.59128e18	+	7.91344e17i	−0.240711	+	0.0414885i
$569$	−2.03393e19			−1.05330			−0.526648	−	0.850083i	$-0.676552\pi$
$569$	−2.03393e19			−1.05330			−0.526648	+	0.850083i	$0.676552\pi$
$570$		0			0
$571$			8.30855e18i			0.419829i	0.977720	+	0.209914i	$0.0673185\pi$
$571$			8.30855e18i			0.419829i	−0.977720	+	0.209914i	$0.932681\pi$
$572$	4.71646e18	−	3.49248e18i	0.235420	−	0.174326i
$573$		0			0
$574$	1.21489e19	−	2.41132e19i	0.591771	−	1.17455i
$575$			5.21052e17i			0.0250730i
$576$		0			0
$577$	−2.07299e19			−0.973567			−0.486784	−	0.873523i	$-0.661830\pi$
$577$	−2.07299e19			−0.973567			−0.486784	+	0.873523i	$0.661830\pi$
$578$	5.93528e18	+	2.99036e18i	0.275389	+	0.138749i
$579$		0			0
$580$	7.97224e18	+	1.07662e19i	0.361064	+	0.487602i
$581$	−8.93724e18			−0.399917
$582$		0			0
$583$			2.59488e18i			0.113354i
$584$	−3.03998e18	−	1.76376e19i	−0.131214	−	0.761289i
$585$		0			0
$586$	9.92699e18	+	5.00149e18i	0.418345	+	0.210774i
$587$			1.91370e19i			0.796908i	0.917188	+	0.398454i	$0.130453\pi$
$587$			1.91370e19i			0.796908i	−0.917188	+	0.398454i	$0.869547\pi$
$588$		0			0
$589$	2.33151e19			0.948046
$590$	−4.19762e18	+	8.33146e18i	−0.168671	+	0.334778i
$591$		0			0
$592$	3.90760e18	−	1.28124e19i	0.153341	−	0.502782i
$593$	−3.66977e19			−1.42317			−0.711584	−	0.702601i	$-0.752022\pi$
$593$	−3.66977e19			−1.42317			−0.711584	+	0.702601i	$0.752022\pi$
$594$		0			0
$595$			4.21412e19i			1.59620i
$596$	−6.24808e17	−	8.43777e17i	−0.0233896	−	0.0315867i
$597$		0			0
$598$	3.85363e18	−	7.64871e18i	0.140916	−	0.279692i
$599$			1.40056e19i			0.506191i	0.967441	+	0.253095i	$0.0814486\pi$
$599$			1.40056e19i			0.506191i	−0.967441	+	0.253095i	$0.918551\pi$
$600$		0			0
$601$	−4.92264e19			−1.73811			−0.869054	−	0.494717i	$-0.835272\pi$
$601$	−4.92264e19			−1.73811			−0.869054	+	0.494717i	$0.835272\pi$
$602$	3.89551e19	+	1.96266e19i	1.35953	+	0.684968i
$603$		0			0
$604$	−4.09908e18	+	3.03532e18i	−0.139774	+	0.103501i
$605$	2.90496e19			0.979157
$606$		0			0
$607$			3.01738e19i			0.993823i	0.867801	+	0.496912i	$0.165533\pi$
$607$			3.01738e19i			0.993823i	−0.867801	+	0.496912i	$0.834467\pi$
$608$	1.69631e19	+	1.62109e19i	0.552306	+	0.527816i
$609$		0			0
$610$	2.95975e19	+	1.49121e19i	0.941774	+	0.474492i
$611$		−	3.37736e19i		−	1.06240i
$612$		0			0
$613$	−2.74397e19			−0.843637			−0.421818	−	0.906680i	$-0.638608\pi$
$613$	−2.74397e19			−0.843637			−0.421818	+	0.906680i	$0.638608\pi$
$614$	1.98589e18	−	3.94160e18i	0.0603637	−	0.119810i
$615$		0			0
$616$	−1.92222e18	−	1.11525e19i	−0.0571134	−	0.331364i
$617$	−4.38772e19			−1.28897			−0.644485	−	0.764617i	$-0.722928\pi$
$617$	−4.38772e19			−1.28897			−0.644485	+	0.764617i	$0.722928\pi$
$618$		0			0
$619$		−	4.15587e18i		−	0.119351i	−0.998218	−	0.0596757i	$-0.980993\pi$
$619$		−	4.15587e18i		−	0.119351i	0.998218	−	0.0596757i	$-0.0190067\pi$
$620$	−3.67197e19	+	2.71905e19i	−1.04270	+	0.772104i
$621$		0			0
$622$	−1.34329e19	+	2.66617e19i	−0.372938	+	0.740210i
$623$			6.79775e19i			1.86616i
$624$		0			0
$625$	−4.03980e19			−1.08443
$626$	4.67706e18	+	2.35643e18i	0.124152	+	0.0625510i
$627$		0			0
$628$	−1.10778e19	−	1.49601e19i	−0.287564	−	0.388344i
$629$	−2.34214e19			−0.601254
$630$		0			0
$631$		−	4.77489e19i		−	1.19883i	−0.800438	−	0.599416i	$-0.795400\pi$
$631$		−	4.77489e19i		−	1.19883i	0.800438	−	0.599416i	$-0.204600\pi$
$632$	−2.25927e19	+	3.89403e18i	−0.560980	+	0.0966896i
$633$		0			0
$634$	5.83359e19	+	2.93913e19i	1.41681	+	0.713828i
$635$			4.14985e19i			0.996820i
$636$		0			0
$637$	3.86744e19			0.908757
$638$	−2.83035e18	+	5.61770e18i	−0.0657803	+	0.130561i
$639$		0			0
$640$	−4.56213e19	−	5.74843e18i	−1.03731	−	0.130704i
$641$	2.76966e19			0.622903			0.311452	−	0.950262i	$-0.399185\pi$
$641$	2.76966e19			0.622903			0.311452	+	0.950262i	$0.399185\pi$
$642$		0			0
$643$			7.06912e18i			0.155557i	0.996971	+	0.0777783i	$0.0247826\pi$
$643$			7.06912e18i			0.155557i	−0.996971	+	0.0777783i	$0.975217\pi$
$644$	−9.82829e18	−	1.32727e19i	−0.213933	−	0.288907i
$645$		0			0
$646$	1.84596e19	−	3.66388e19i	0.393183	−	0.780392i
$647$		−	7.95252e19i		−	1.67562i	−0.545964	−	0.837808i	$-0.683837\pi$
$647$		−	7.95252e19i		−	1.67562i	0.545964	−	0.837808i	$-0.316163\pi$
$648$		0			0
$649$	−4.38057e18			−0.0903270
$650$	−4.73905e18	−	2.38767e18i	−0.0966714	−	0.0487057i
$651$		0			0
$652$	2.14990e17	−	1.59198e17i	0.00429225	−	0.00317836i
$653$	1.09740e19			0.216757			0.108379	−	0.994110i	$-0.465434\pi$
$653$	1.09740e19			0.216757			0.108379	+	0.994110i	$0.465434\pi$
$654$		0			0
$655$		−	7.15786e19i		−	1.38387i
$656$	1.50276e19	−	4.92732e19i	0.287450	−	0.942506i
$657$		0			0
$658$	−5.81617e19	−	2.93035e19i	−1.08907	−	0.548703i
$659$			3.69518e19i			0.684601i	0.939590	+	0.342301i	$0.111206\pi$
$659$			3.69518e19i			0.684601i	−0.939590	+	0.342301i	$0.888794\pi$
$660$		0			0
$661$	1.34638e19			0.244206			0.122103	−	0.992517i	$-0.461036\pi$
$661$	1.34638e19			0.244206			0.122103	+	0.992517i	$0.461036\pi$
$662$	2.57423e19	−	5.10934e19i	0.461999	−	0.916979i
$663$		0			0
$664$	−1.68033e19	+	2.89619e18i	−0.295269	+	0.0508920i
$665$	6.13119e19			1.06609
$666$		0			0
$667$			9.18001e18i			0.156301i
$668$	−5.47751e19	+	4.05604e19i	−0.922886	+	0.683387i
$669$		0			0
$670$	−2.55759e19	+	5.07633e19i	−0.421996	+	0.837580i
$671$			1.55620e19i			0.254101i
$672$		0			0
$673$	8.10738e19			1.29651			0.648253	−	0.761425i	$-0.275500\pi$
$673$	8.10738e19			1.29651			0.648253	+	0.761425i	$0.275500\pi$
$674$	−7.34187e19	−	3.69904e19i	−1.16195	−	0.585423i
$675$		0			0
$676$	1.35177e19	+	1.82551e19i	0.209544	+	0.282981i
$677$	−1.44487e19			−0.221671			−0.110836	−	0.993839i	$-0.535353\pi$
$677$	−1.44487e19			−0.221671			−0.110836	+	0.993839i	$0.535353\pi$
$678$		0			0
$679$			8.64965e19i			1.29990i
$680$	1.36562e19	+	7.92316e19i	0.203127	+	1.17852i
$681$		0			0
$682$	−1.91600e19	−	9.65335e18i	−0.279194	−	0.140666i
$683$		−	3.56963e17i		−	0.00514848i	−0.999997	−	0.00257424i	$-0.999181\pi$
$683$		−	3.56963e17i		−	0.00514848i	0.999997	−	0.00257424i	$-0.000819407\pi$
$684$		0			0
$685$	6.29511e19			0.889549
$686$	−9.38069e18	+	1.86188e19i	−0.131210	+	0.260426i
$687$		0			0
$688$	7.96013e19	+	2.42772e19i	1.09094	+	0.332720i
$689$	−3.85666e19			−0.523211
$690$		0			0
$691$		−	8.28163e19i		−	1.10096i	−0.834850	−	0.550478i	$-0.814446\pi$
$691$		−	8.28163e19i		−	1.10096i	0.834850	−	0.550478i	$-0.185554\pi$
$692$	1.67330e19	+	2.25973e19i	0.220207	+	0.297381i
$693$		0			0
$694$	−3.91004e19	+	7.76067e19i	−0.504272	+	1.00088i
$695$		−	1.36846e20i		−	1.74719i
$696$		0			0
$697$	−9.00724e19			−1.12710
$698$	1.82182e19	+	9.17883e18i	0.225693	+	0.113710i
$699$		0			0
$700$	−8.22362e18	+	6.08950e18i	−0.0998566	+	0.0739427i
$701$	1.09189e20			1.31266			0.656331	−	0.754473i	$-0.272108\pi$
$701$	1.09189e20			1.31266			0.656331	+	0.754473i	$0.272108\pi$
$702$		0			0
$703$			3.40761e19i			0.401572i
$704$	−7.22810e18	−	2.03453e19i	−0.0843364	−	0.237387i
$705$		0			0
$706$	−4.80333e19	−	2.42005e19i	−0.549426	−	0.276816i
$707$			7.43676e19i			0.842263i
$708$		0			0
$709$	−3.15046e19			−0.349825			−0.174913	−	0.984584i	$-0.555964\pi$
$709$	−3.15046e19			−0.349825			−0.174913	+	0.984584i	$0.555964\pi$
$710$	−1.04508e19	+	2.07428e19i	−0.114906	+	0.228065i
$711$		0			0
$712$	2.20287e19	+	1.27808e20i	0.237481	+	1.37783i
$713$	−3.13098e19			−0.334236
$714$		0			0
$715$		−	2.92580e19i		−	0.306269i
$716$	1.30597e20	−	9.67059e19i	1.35376	−	1.00245i
$717$		0			0
$718$	3.92647e19	−	7.79329e19i	0.399146	−	0.792227i
$719$		−	3.86358e19i		−	0.388945i	−0.980908	−	0.194472i	$-0.937701\pi$
$719$		−	3.86358e19i		−	0.388945i	0.980908	−	0.194472i	$-0.0622995\pi$
$720$		0			0
$721$	2.33190e20			2.30230
$722$	3.80291e19	+	1.91601e19i	0.371839	+	0.187343i
$723$		0			0
$724$	−1.21420e20	−	1.63972e20i	−1.16444	−	1.57253i
$725$	5.68783e18			0.0540232
$726$		0			0
$727$		−	4.69779e19i		−	0.437676i	−0.975761	−	0.218838i	$-0.929773\pi$
$727$		−	4.69779e19i		−	0.437676i	0.975761	−	0.218838i	$-0.0702266\pi$
$728$	1.65755e20	−	2.85692e19i	1.52949	−	0.263620i
$729$		0			0
$730$	−7.96844e19	−	4.01472e19i	−0.721296	−	0.363409i
$731$		−	1.45513e20i		−	1.30461i
$732$		0			0
$733$	9.92861e19			0.873294			0.436647	−	0.899633i	$-0.356166\pi$
$733$	9.92861e19			0.873294			0.436647	+	0.899633i	$0.356166\pi$
$734$	−7.56563e19	+	1.50163e20i	−0.659132	+	1.30825i
$735$		0			0
$736$	−2.27797e19	−	2.17697e19i	−0.194717	−	0.186083i
$737$	−2.66906e19			−0.225989
$738$		0			0
$739$		−	3.72308e19i		−	0.309308i	−0.987969	−	0.154654i	$-0.950574\pi$
$739$		−	3.72308e19i		−	0.309308i	0.987969	−	0.154654i	$-0.0494262\pi$
$740$	−3.97403e19	−	5.36677e19i	−0.327046	−	0.441663i
$741$		0			0
$742$	−3.34621e19	+	6.64158e19i	−0.270225	+	0.536344i
$743$		−	6.07429e18i		−	0.0485930i	−0.999705	−	0.0242965i	$-0.992265\pi$
$743$		−	6.07429e18i		−	0.0485930i	0.999705	−	0.0242965i	$-0.00773457\pi$
$744$		0			0
$745$	−5.23428e18			−0.0410926
$746$	−2.06392e20	−	1.03986e20i	−1.60517	−	0.808729i
$747$		0			0
$748$	−3.03398e19	+	2.24663e19i	−0.231580	+	0.171482i
$749$	3.07844e20			2.32787
$750$		0			0
$751$		−	1.15626e20i		−	0.858172i	−0.903264	−	0.429086i	$-0.858836\pi$
$751$		−	1.15626e20i		−	0.858172i	0.903264	−	0.429086i	$-0.141164\pi$
$752$	−1.18848e20	−	3.62470e19i	−0.873913	−	0.266530i
$753$		0			0
$754$	−8.34937e19	−	4.20664e19i	−0.602635	−	0.303624i
$755$			2.54282e19i			0.181839i
$756$		0			0
$757$	−9.31288e19			−0.653752			−0.326876	−	0.945067i	$-0.605996\pi$
$757$	−9.31288e19			−0.653752			−0.326876	+	0.945067i	$0.605996\pi$
$758$	−3.20563e19	+	6.36255e19i	−0.222961	+	0.442534i
$759$		0			0
$760$	1.15275e20	−	1.98686e19i	0.787120	−	0.135667i
$761$	−1.85510e20			−1.25509			−0.627546	−	0.778579i	$-0.715941\pi$
$761$	−1.85510e20			−1.25509			−0.627546	+	0.778579i	$0.715941\pi$
$762$		0			0
$763$			2.03425e20i			1.35124i
$764$	7.05775e19	−	5.22619e19i	0.464529	−	0.343979i
$765$		0			0
$766$	3.90094e19	−	7.74261e19i	0.252097	−	0.500364i
$767$		−	6.51066e19i		−	0.416925i
$768$		0			0
$769$	2.13193e19			0.134057			0.0670283	−	0.997751i	$-0.478648\pi$
$769$	2.13193e19			0.134057			0.0670283	+	0.997751i	$0.478648\pi$
$770$	−5.03854e19	−	2.53856e19i	−0.313957	−	0.158180i
$771$		0			0
$772$	1.68298e20	+	2.27279e20i	1.02981	+	1.39072i
$773$	−4.44231e17			−0.00269372			−0.00134686	−	0.999999i	$-0.500429\pi$
$773$	−4.44231e17			−0.00269372			−0.00134686	+	0.999999i	$0.500429\pi$
$774$		0			0
$775$			1.93992e19i			0.115524i
$776$	2.80299e19	+	1.62626e20i	0.165421	+	0.959749i
$777$		0			0
$778$	4.51498e19	+	2.27477e19i	0.261697	+	0.131850i
$779$			1.31048e20i			0.752779i
$780$		0			0
$781$	−1.09063e19			−0.0615346
$782$	−2.47894e19	+	4.92022e19i	−0.138618	+	0.275130i
$783$		0			0
$784$	4.15067e19	−	1.36094e20i	0.227985	−	0.747528i
$785$	−9.28032e19			−0.505214
$786$		0			0
$787$		−	2.32384e20i		−	1.24275i	−0.783513	−	0.621375i	$-0.786574\pi$
$787$		−	2.32384e20i		−	1.24275i	0.783513	−	0.621375i	$-0.213426\pi$
$788$	3.73679e19	+	5.04639e19i	0.198069	+	0.267484i
$789$		0			0
$790$	−5.14261e19	+	1.02071e20i	−0.267790	+	0.531510i
$791$			3.62032e20i			1.86858i
$792$		0			0
$793$	−2.31291e20			−1.17286
$794$	5.15056e19	+	2.59499e19i	0.258887	+	0.130435i
$795$		0			0
$796$	−1.07324e20	+	7.94722e19i	−0.530036	+	0.392486i
$797$	−6.26695e19			−0.306795			−0.153397	−	0.988165i	$-0.549021\pi$
$797$	−6.26695e19			−0.306795			−0.153397	+	0.988165i	$0.549021\pi$
$798$		0			0
$799$			2.17257e20i			1.04507i
$800$	−1.34882e19	+	1.41141e19i	−0.0643170	+	0.0673012i
$801$		0			0
$802$	2.01194e20	+	1.01367e20i	0.942746	+	0.474981i
$803$		−	4.18970e19i		−	0.194614i
$804$		0			0
$805$	−8.23358e19			−0.375853
$806$	1.43474e20	−	2.84768e20i	0.649274	−	1.28868i
$807$		0			0
$808$	2.40994e19	+	1.39822e20i	0.107183	+	0.621864i
$809$	−1.83746e20			−0.810172			−0.405086	−	0.914279i	$-0.632758\pi$
$809$	−1.83746e20			−0.810172			−0.405086	+	0.914279i	$0.632758\pi$
$810$		0			0
$811$		−	2.96921e20i		−	1.28675i	−0.765551	−	0.643375i	$-0.777533\pi$
$811$		−	2.96921e20i		−	1.28675i	0.765551	−	0.643375i	$-0.222467\pi$
$812$	−1.44886e20	+	1.07286e20i	−0.622491	+	0.460948i
$813$		0			0
$814$	1.41089e19	−	2.80033e19i	0.0595828	−	0.118260i
$815$		−	1.33367e18i		−	0.00558399i
$816$		0			0
$817$	−2.11709e20			−0.871333
$818$	−1.31727e20	−	6.63680e19i	−0.537531	−	0.270823i
$819$		0			0
$820$	−1.52831e20	−	2.06392e20i	−0.613075	−	0.827932i
$821$	−1.21912e20			−0.484891			−0.242445	−	0.970165i	$-0.577950\pi$
$821$	−1.21912e20			−0.484891			−0.242445	+	0.970165i	$0.577950\pi$
$822$		0			0
$823$			4.76822e20i			1.86448i	0.361844	+	0.932239i	$0.382147\pi$
$823$			4.76822e20i			1.86448i	−0.361844	+	0.932239i	$0.617853\pi$
$824$	4.38430e20	−	7.55671e19i	1.69985	−	0.292983i
$825$		0			0
$826$	−1.12120e20	−	5.64894e19i	−0.427390	−	0.215331i
$827$			1.90780e20i			0.721098i	0.932740	+	0.360549i	$0.117411\pi$
$827$			1.90780e20i			0.721098i	−0.932740	+	0.360549i	$0.882589\pi$
$828$		0			0
$829$	−2.09950e20			−0.780249			−0.390125	−	0.920762i	$-0.627568\pi$
$829$	−2.09950e20			−0.780249			−0.390125	+	0.920762i	$0.627568\pi$
$830$	−3.82481e19	+	7.59151e19i	−0.140950	+	0.279758i
$831$		0			0
$832$	3.02384e20	−	1.07428e20i	1.09571	−	0.389274i
$833$	−2.48783e20			−0.893934
$834$		0			0
$835$			3.39792e20i			1.20062i
$836$	3.26865e19	+	4.41418e19i	0.114531	+	0.154670i
$837$		0			0
$838$	8.69732e19	−	1.72625e20i	0.299694	−	0.594834i
$839$			2.14640e20i			0.733462i	0.930327	+	0.366731i	$0.119523\pi$
$839$			2.14640e20i			0.733462i	−0.930327	+	0.366731i	$0.880477\pi$
$840$		0			0
$841$	−1.97349e20			−0.663228
$842$	−4.58828e18	−	2.31170e18i	−0.0152920	−	0.00770454i
$843$		0			0
$844$	7.81746e18	−	5.78874e18i	0.0256253	−	0.0189752i
$845$	1.13244e20			0.368143
$846$		0			0
$847$			3.90934e20i			1.25003i
$848$	−4.13910e19	+	1.35715e20i	−0.131261	+	0.430384i
$849$		0			0
$850$	3.04851e19	+	1.53593e19i	0.0950946	+	0.0479113i
$851$		−	4.57608e19i		−	0.141575i
$852$		0			0
$853$	1.18167e20			0.359629			0.179814	−	0.983701i	$-0.442450\pi$
$853$	1.18167e20			0.359629			0.179814	+	0.983701i	$0.442450\pi$
$854$	−2.00679e20	+	3.98308e20i	−0.605754	+	1.20230i
$855$		0			0
$856$	5.78791e20	−	9.97594e19i	1.71872	−	0.296236i
$857$	4.17254e20			1.22895			0.614475	−	0.788936i	$-0.289368\pi$
$857$	4.17254e20			1.22895			0.614475	+	0.788936i	$0.289368\pi$
$858$		0			0
$859$		−	1.19956e20i		−	0.347591i	−0.984782	−	0.173796i	$-0.944397\pi$
$859$		−	1.19956e20i		−	0.347591i	0.984782	−	0.173796i	$-0.0556032\pi$
$860$	3.33427e20	−	2.46899e20i	0.958323	−	0.709627i
$861$		0			0
$862$	−1.03186e20	+	2.04803e20i	−0.291788	+	0.579143i
$863$		−	5.57748e20i		−	1.56445i	−0.622994	−	0.782226i	$-0.714084\pi$
$863$		−	5.57748e20i		−	1.56445i	0.622994	−	0.782226i	$-0.285916\pi$
$864$		0			0
$865$	1.40180e20			0.386876
$866$	−2.58956e20	−	1.30469e20i	−0.708925	−	0.357176i
$867$		0			0
$868$	−3.65916e20	−	4.94154e20i	−0.985696	−	1.33114i
$869$	−5.36674e19			−0.143407
$870$		0			0
$871$		−	3.96692e20i		−	1.04310i
$872$	6.59217e19	+	3.82469e20i	0.171954	+	0.997656i
$873$		0			0
$874$	7.15850e19	+	3.60665e19i	0.183756	+	0.0925815i
$875$		−	4.96985e20i		−	1.26557i
$876$		0			0
$877$	5.81992e20			1.45855			0.729273	−	0.684223i	$-0.239859\pi$
$877$	5.81992e20			1.45855			0.729273	+	0.684223i	$0.239859\pi$
$878$	3.30493e20	−	6.55964e20i	0.821675	−	1.63087i
$879$		0			0
$880$	−1.02958e20	−	3.14007e19i	−0.251931	−	0.0768353i
$881$	−9.64672e19			−0.234179			−0.117090	−	0.993121i	$-0.537356\pi$
$881$	−9.64672e19			−0.234179			−0.117090	+	0.993121i	$0.537356\pi$
$882$		0			0
$883$		−	3.24016e20i		−	0.774178i	−0.922042	−	0.387089i	$-0.873481\pi$
$883$		−	3.24016e20i		−	0.774178i	0.922042	−	0.387089i	$-0.126519\pi$
$884$	−3.33907e20	−	4.50928e20i	−0.791516	−	1.06891i
$885$		0			0
$886$	−7.91046e17	+	1.57007e18i	−0.00184572	+	0.00366339i
$887$		−	3.43357e20i		−	0.794842i	−0.917636	−	0.397421i	$-0.869905\pi$
$887$		−	3.43357e20i		−	0.794842i	0.917636	−	0.397421i	$-0.130095\pi$
$888$		0			0
$889$	−5.58465e20			−1.27258
$890$	5.77418e20	+	2.90919e20i	1.30545	+	0.657722i
$891$		0			0
$892$	2.03190e20	−	1.50460e20i	0.452219	−	0.334863i
$893$	3.16091e20			0.697993
$894$		0			0
$895$		−	8.10147e20i		−	1.76117i
$896$	7.73593e19	−	6.13947e20i	0.166862	−	1.32427i
$897$		0			0
$898$	1.19173e19	+	6.00428e18i	0.0253072	+	0.0127505i
$899$			3.41780e20i			0.720159i
$900$		0			0
$901$	2.48089e20			0.514677
$902$	5.42589e19	−	1.07693e20i	0.111693	−	0.221689i
$903$		0			0
$904$	1.17319e20	+	6.80672e20i	0.237789	+	1.37962i
$905$	−1.01718e21			−2.04578
$906$		0			0
$907$			5.62078e20i			1.11313i	0.830804	+	0.556565i	$0.187881\pi$
$907$			5.62078e20i			1.11313i	−0.830804	+	0.556565i	$0.812119\pi$
$908$	−5.84651e20	+	4.32928e20i	−1.14894	+	0.850775i
$909$		0			0
$910$	3.77295e20	−	7.48858e20i	0.730116	−	1.44914i
$911$			1.30865e20i			0.251301i	0.992075	+	0.125650i	$0.0401017\pi$
$911$			1.30865e20i			0.251301i	−0.992075	+	0.125650i	$0.959898\pi$
$912$		0			0
$913$	−3.99151e19			−0.0754818
$914$	6.92813e20	+	3.49058e20i	1.30015	+	0.655051i
$915$		0			0
$916$	−1.34357e20	−	1.81443e20i	−0.248308	−	0.335330i
$917$	9.63267e20			1.76669
$918$		0			0
$919$			3.30567e19i			0.0597105i	0.999554	+	0.0298553i	$0.00950464\pi$
$919$			3.30567e19i			0.0597105i	−0.999554	+	0.0298553i	$0.990495\pi$
$920$	−1.54803e20	+	2.66816e19i	−0.277501	+	0.0478297i
$921$		0			0
$922$	−1.08969e20	−	5.49015e19i	−0.192391	−	0.0969321i
$923$		−	1.62096e20i		−	0.284027i
$924$		0			0
$925$	−2.83529e19			−0.0489334
$926$	1.03891e20	−	2.06204e20i	0.177952	−	0.353199i
$927$		0			0
$928$	−2.37639e20	+	2.48665e20i	−0.400942	+	0.419545i
$929$	4.74648e20			0.794807			0.397403	−	0.917644i	$-0.369911\pi$
$929$	4.74648e20			0.794807			0.397403	+	0.917644i	$0.369911\pi$
$930$		0			0
$931$			3.61958e20i			0.597050i
$932$	−5.81950e19	−	7.85900e19i	−0.0952740	−	0.128664i
$933$		0			0
$934$	−2.87183e20	+	5.70003e20i	−0.463160	+	0.919283i
$935$			1.88210e20i			0.301273i
$936$		0			0
$937$	−2.04422e20			−0.322367			−0.161183	−	0.986924i	$-0.551531\pi$
$937$	−2.04422e20			−0.322367			−0.161183	+	0.986924i	$0.551531\pi$
$938$	−6.83145e20	−	3.44187e20i	−1.06928	−	0.538735i
$939$		0			0
$940$	−4.97822e20	+	3.68632e20i	−0.767678	+	0.568457i
$941$	4.27194e20			0.653880			0.326940	−	0.945045i	$-0.393982\pi$
$941$	4.27194e20			0.653880			0.326940	+	0.945045i	$0.393982\pi$
$942$		0			0
$943$		−	1.75984e20i		−	0.265394i
$944$	−2.29108e20	−	6.98746e19i	−0.342955	−	0.104596i
$945$		0			0
$946$	1.73979e20	+	8.76557e19i	0.256602	+	0.129283i
$947$			9.72640e20i			1.42397i	0.702192	+	0.711987i	$0.252205\pi$
$947$			9.72640e20i			1.42397i	−0.702192	+	0.711987i	$0.747795\pi$
$948$		0			0
$949$	6.22698e20			0.898284
$950$	2.23464e19	−	4.43533e19i	0.0319995	−	0.0635127i
$951$		0			0
$952$	−1.06626e21	+	1.83778e20i	−1.50454	+	0.259320i
$953$	−1.18544e21			−1.66046			−0.830231	−	0.557419i	$-0.811792\pi$
$953$	−1.18544e21			−1.66046			−0.830231	+	0.557419i	$0.811792\pi$
$954$		0			0
$955$		−	4.37820e20i		−	0.604327i
$956$	−5.77287e20	+	4.27475e20i	−0.791019	+	0.585741i
$957$		0			0
$958$	4.50156e19	−	8.93472e19i	0.0607861	−	0.120649i
$959$			8.47163e20i			1.13563i
$960$		0			0
$961$	−4.08747e20			−0.539997
$962$	4.16202e20	+	2.09694e20i	0.545857	+	0.275018i
$963$		0			0
$964$	9.04960e19	+	1.22211e20i	0.116974	+	0.157969i
$965$	1.40990e21			1.80925
$966$		0			0
$967$			3.18444e20i			0.402761i	0.979513	+	0.201381i	$0.0645428\pi$
$967$			3.18444e20i			0.402761i	−0.979513	+	0.201381i	$0.935457\pi$
$968$	1.26685e20	+	7.35012e20i	0.159074	+	0.922926i
$969$		0			0
$970$	7.34723e20	+	3.70174e20i	0.909330	+	0.458145i
$971$		−	6.49048e20i		−	0.797521i	−0.917055	−	0.398760i	$-0.869441\pi$
$971$		−	6.49048e20i		−	0.797521i	0.917055	−	0.398760i	$-0.130559\pi$
$972$		0			0
$973$	1.84161e21			2.23052
$974$	−6.29710e20	+	1.24985e21i	−0.757230	+	1.50295i
$975$		0			0
$976$	−2.48230e20	+	8.13908e20i	−0.294242	+	0.964777i
$977$	−1.58212e21			−1.86199			−0.930997	−	0.365026i	$-0.881060\pi$
$977$	−1.58212e21			−1.86199			−0.930997	+	0.365026i	$0.881060\pi$
$978$		0			0
$979$			3.03599e20i			0.352226i
$980$	−4.22123e20	−	5.70060e20i	−0.486247	−	0.656656i
$981$		0			0
$982$	−1.22581e20	+	2.43299e20i	−0.139201	+	0.276287i
$983$		−	1.41267e21i		−	1.59282i	−0.604757	−	0.796410i	$-0.706730\pi$
$983$		−	1.41267e21i		−	1.59282i	0.604757	−	0.796410i	$-0.293270\pi$
$984$		0			0
$985$	3.13047e20			0.347982
$986$	5.37094e20	+	2.70603e20i	0.592805	+	0.298671i
$987$		0			0
$988$	−6.56062e20	+	4.85807e20i	−0.713914	+	0.528646i
$989$	2.84304e20			0.307191
$990$		0			0
$991$		−	1.47183e21i		−	1.56798i	−0.620771	−	0.783992i	$-0.713180\pi$
$991$		−	1.47183e21i		−	1.56798i	0.620771	−	0.783992i	$-0.286820\pi$
$992$	−8.48109e20	−	8.10503e20i	−0.897161	−	0.857380i
$993$		0			0
$994$	−2.79146e20	−	1.40641e20i	−0.291156	−	0.146693i
$995$			6.65773e20i			0.689548i
$996$		0			0
$997$	−1.75970e20			−0.179710			−0.0898549	−	0.995955i	$-0.528640\pi$
$997$	−1.75970e20			−0.179710			−0.0898549	+	0.995955i	$0.528640\pi$
$998$	−1.29368e20	+	2.56771e20i	−0.131194	+	0.260395i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.15.d.c.19.6		6
3.2	odd	2		4.15.b.a.3.1	✓	6
4.3	odd	2	inner	36.15.d.c.19.5		6
12.11	even	2		4.15.b.a.3.2	yes	6
24.5	odd	2		64.15.c.d.63.6		6
24.11	even	2		64.15.c.d.63.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.15.b.a.3.1	✓	6	3.2	odd	2
4.15.b.a.3.2	yes	6	12.11	even	2
36.15.d.c.19.5		6	4.3	odd	2	inner
36.15.d.c.19.6		6	1.1	even	1	trivial
64.15.c.d.63.1		6	24.11	even	2
64.15.c.d.63.6		6	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	36.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(114.311 + 57.5931i) q^{2} +(9750.07 + 13167.1i) q^{4} +81680.5 q^{5} +1.09921e6i q^{7} +(356209. + 2.06668e6i) q^{8} +O(q^{10})\)	\(q+(114.311 + 57.5931i) q^{2} +(9750.07 + 13167.1i) q^{4} +81680.5 q^{5} +1.09921e6i q^{7} +(356209. + 2.06668e6i) q^{8} +(9.33699e6 + 4.70423e6i) q^{10} +4.90926e6i q^{11} -7.29644e7 q^{13} +(-6.33071e7 + 1.25652e8i) q^{14} +(-7.83078e7 + 2.56760e8i) q^{16} +4.69361e8 q^{17} -6.82881e8i q^{19} +(7.96390e8 + 1.07549e9i) q^{20} +(-2.82739e8 + 5.61183e8i) q^{22} +9.17041e8i q^{23} +5.68188e8 q^{25} +(-8.34064e9 - 4.20224e9i) q^{26} +(-1.44734e10 + 1.07174e10i) q^{28} +1.00105e10 q^{29} +3.41422e10i q^{31} +(-2.37390e10 + 2.48405e10i) q^{32} +(5.36532e10 + 2.70320e10i) q^{34} +8.97842e10i q^{35} -4.99005e10 q^{37} +(3.93292e10 - 7.80609e10i) q^{38} +(2.90953e10 + 1.68807e11i) q^{40} -1.91904e11 q^{41} -3.10023e11i q^{43} +(-6.46405e10 + 4.78656e10i) q^{44} +(-5.28152e10 + 1.04828e11i) q^{46} +4.62878e11i q^{47} -5.30046e11 q^{49} +(6.49503e10 + 3.27237e10i) q^{50} +(-7.11407e11 - 9.60726e11i) q^{52} +5.28568e11 q^{53} +4.00991e11i q^{55} +(-2.27172e12 + 3.91549e11i) q^{56} +(1.14431e12 + 5.76534e11i) q^{58} +8.92307e11i q^{59} +3.16992e12 q^{61} +(-1.96636e12 + 3.90284e12i) q^{62} +(-4.14428e12 + 1.47234e12i) q^{64} -5.95976e12 q^{65} +5.43679e12i q^{67} +(4.57630e12 + 6.18011e12i) q^{68} +(-5.17095e12 + 1.02633e13i) q^{70} +2.22157e12i q^{71} -8.53427e12 q^{73} +(-5.70419e12 - 2.87393e12i) q^{74} +(8.99154e12 - 6.65813e12i) q^{76} -5.39632e12 q^{77} +1.09319e13i q^{79} +(-6.39622e12 + 2.09723e13i) q^{80} +(-2.19368e13 - 1.10524e13i) q^{82} +8.13058e12i q^{83} +3.83377e13 q^{85} +(1.78552e13 - 3.54390e13i) q^{86} +(-1.01459e13 + 1.74872e12i) q^{88} +6.18420e13 q^{89} -8.02033e13i q^{91} +(-1.20747e13 + 8.94121e12i) q^{92} +(-2.66586e13 + 5.29121e13i) q^{94} -5.57781e13i q^{95} +7.86895e13 q^{97} +(-6.05901e13 - 3.05270e13i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 92 q^{2} - 1392 q^{4} - 8060 q^{5} - 446272 q^{8}+O(q^{10}) \) 6 * q + 92 * q^2 - 1392 * q^4 - 8060 * q^5 - 446272 * q^8	\( 6 q + 92 q^{2} - 1392 q^{4} - 8060 q^{5} - 446272 q^{8} + 5796840 q^{10} - 80775396 q^{13} - 175232064 q^{14} - 353013504 q^{16} + 120131764 q^{17} + 5047343200 q^{20} + 9916985760 q^{22} + 3942973410 q^{25} - 39549467048 q^{26} - 65094731520 q^{28} + 8035796644 q^{29} + 85711465472 q^{32} + 98089165512 q^{34} + 31334118396 q^{37} + 165268841760 q^{38} + 435607171200 q^{40} - 83362750892 q^{41} - 915657452160 q^{44} - 1712365889856 q^{46} - 551978693658 q^{49} + 1639579094580 q^{50} + 1057159118496 q^{52} - 76712275004 q^{53} + 560223046656 q^{56} + 4483777382184 q^{58} + 6210000787932 q^{61} - 10375644284160 q^{62} - 14398852657152 q^{64} + 7189912943720 q^{65} + 18507298307296 q^{68} + 12679529923200 q^{70} - 29882649313236 q^{73} + 1536652566808 q^{74} + 21457134000000 q^{76} - 37339673521920 q^{77} - 57843429624320 q^{80} - 71900577251064 q^{82} + 151199882653560 q^{85} + 100164269733216 q^{86} + 51557990330880 q^{88} + 180966014731924 q^{89} - 82241452266240 q^{92} - 40381697410176 q^{94} - 345459072299124 q^{97} - 121406102961892 q^{98}+O(q^{100}) \) 6 * q + 92 * q^2 - 1392 * q^4 - 8060 * q^5 - 446272 * q^8 + 5796840 * q^10 - 80775396 * q^13 - 175232064 * q^14 - 353013504 * q^16 + 120131764 * q^17 + 5047343200 * q^20 + 9916985760 * q^22 + 3942973410 * q^25 - 39549467048 * q^26 - 65094731520 * q^28 + 8035796644 * q^29 + 85711465472 * q^32 + 98089165512 * q^34 + 31334118396 * q^37 + 165268841760 * q^38 + 435607171200 * q^40 - 83362750892 * q^41 - 915657452160 * q^44 - 1712365889856 * q^46 - 551978693658 * q^49 + 1639579094580 * q^50 + 1057159118496 * q^52 - 76712275004 * q^53 + 560223046656 * q^56 + 4483777382184 * q^58 + 6210000787932 * q^61 - 10375644284160 * q^62 - 14398852657152 * q^64 + 7189912943720 * q^65 + 18507298307296 * q^68 + 12679529923200 * q^70 - 29882649313236 * q^73 + 1536652566808 * q^74 + 21457134000000 * q^76 - 37339673521920 * q^77 - 57843429624320 * q^80 - 71900577251064 * q^82 + 151199882653560 * q^85 + 100164269733216 * q^86 + 51557990330880 * q^88 + 180966014731924 * q^89 - 82241452266240 * q^92 - 40381697410176 * q^94 - 345459072299124 * q^97 - 121406102961892 * q^98

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