LMFDB - Embedded newform 75.12.e.d.32.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,12,Mod(32,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, 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("75.32");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	75.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:	$57.6257385420$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			32.7
Character	$\chi$	$=$	75.32
Dual form			75.12.e.d.68.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-26.1390 + 26.1390i) q^{2} +(-389.593 - 159.262i) q^{3} +681.505i q^{4} +(14346.5 - 6020.60i) q^{6} +(-5513.09 - 5513.09i) q^{7} +(-71346.5 - 71346.5i) q^{8} +(126418. + 124095. i) q^{9} +O(q^{10})$	\(q+(-26.1390 + 26.1390i) q^{2} +(-389.593 - 159.262i) q^{3} +681.505i q^{4} +(14346.5 - 6020.60i) q^{6} +(-5513.09 - 5513.09i) q^{7} +(-71346.5 - 71346.5i) q^{8} +(126418. + 124095. i) q^{9} +213111. i q^{11} +(108538. - 265509. i) q^{12} +(-1.40784e6 + 1.40784e6i) q^{13} +288214. q^{14} +2.33413e6 q^{16} +(2.24338e6 - 2.24338e6i) q^{17} +(-6.54816e6 + 60720.1i) q^{18} -1.02378e7i q^{19} +(1.26983e6 + 3.02589e6i) q^{21} +(-5.57051e6 - 5.57051e6i) q^{22} +(-1.46579e7 - 1.46579e7i) q^{23} +(1.64333e7 + 3.91589e7i) q^{24} -7.35989e7i q^{26} +(-2.94878e7 - 6.84801e7i) q^{27} +(3.75720e6 - 3.75720e6i) q^{28} -1.52840e8 q^{29} -2.64198e8 q^{31} +(8.51058e7 - 8.51058e7i) q^{32} +(3.39406e7 - 8.30265e7i) q^{33} +1.17279e8i q^{34} +(-8.45713e7 + 8.61545e7i) q^{36} +(-2.07043e8 - 2.07043e8i) q^{37} +(2.67607e8 + 2.67607e8i) q^{38} +(7.72699e8 - 3.24268e8i) q^{39} +1.29665e8i q^{41} +(-1.12286e8 - 4.59016e7i) q^{42} +(2.00424e8 - 2.00424e8i) q^{43} -1.45236e8 q^{44} +7.66285e8 q^{46} +(9.40322e8 - 9.40322e8i) q^{47} +(-9.09361e8 - 3.71740e8i) q^{48} -1.91654e9i q^{49} +(-1.23129e9 + 5.16718e8i) q^{51} +(-9.59448e8 - 9.59448e8i) q^{52} +(3.25209e9 + 3.25209e9i) q^{53} +(2.56079e9 + 1.01922e9i) q^{54} +7.86680e8i q^{56} +(-1.63050e9 + 3.98859e9i) q^{57} +(3.99508e9 - 3.99508e9i) q^{58} +4.71394e9 q^{59} -4.47029e9 q^{61} +(6.90587e9 - 6.90587e9i) q^{62} +(-1.28067e7 - 1.38110e9i) q^{63} +9.22947e9i q^{64} +(1.28306e9 + 3.05740e9i) q^{66} +(1.40139e10 + 1.40139e10i) q^{67} +(1.52887e9 + 1.52887e9i) q^{68} +(3.37615e9 + 8.04505e9i) q^{69} +9.83456e9i q^{71} +(-1.65736e8 - 1.78732e10i) q^{72} +(-2.37754e10 + 2.37754e10i) q^{73} +1.08238e10 q^{74} +6.97714e9 q^{76} +(1.17490e9 - 1.17490e9i) q^{77} +(-1.17215e10 + 2.86736e10i) q^{78} +6.03538e9i q^{79} +(5.81934e8 + 3.13757e10i) q^{81} +(-3.38931e9 - 3.38931e9i) q^{82} +(-3.18619e10 - 3.18619e10i) q^{83} +(-2.06216e9 + 8.65397e8i) q^{84} +1.04777e10i q^{86} +(5.95453e10 + 2.43416e10i) q^{87} +(1.52047e10 - 1.52047e10i) q^{88} +9.38732e10 q^{89} +1.55231e10 q^{91} +(9.98942e9 - 9.98942e9i) q^{92} +(1.02930e11 + 4.20768e10i) q^{93} +4.91582e10i q^{94} +(-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} + 1714188 q^{12} + 3448472 q^{13} - 43202180 q^{16} - 3729120 q^{18} + 33570840 q^{21} + 21743260 q^{22} - 113282712 q^{27} - 253355948 q^{28} + 67990880 q^{31} + 563443560 q^{33} + 1116103980 q^{36} - 1292573224 q^{37} + 5132304780 q^{42} - 4012128208 q^{43} - 8170829920 q^{46} + 13847034876 q^{48} + 5424535440 q^{51} - 10287332704 q^{52} + 10576855656 q^{57} - 56277468420 q^{58} - 24994982320 q^{61} + 50371112832 q^{63} + 56311074600 q^{66} - 37314988144 q^{67} + 92983114440 q^{72} - 51361482568 q^{73} - 121004023440 q^{76} + 104085843000 q^{78} - 22936122360 q^{81} + 56747065840 q^{82} - 84564024000 q^{87} - 148338843420 q^{88} + 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 + 1714188 * q^12 + 3448472 * q^13 - 43202180 * q^16 - 3729120 * q^18 + 33570840 * q^21 + 21743260 * q^22 - 113282712 * q^27 - 253355948 * q^28 + 67990880 * q^31 + 563443560 * q^33 + 1116103980 * q^36 - 1292573224 * q^37 + 5132304780 * q^42 - 4012128208 * q^43 - 8170829920 * q^46 + 13847034876 * q^48 + 5424535440 * q^51 - 10287332704 * q^52 + 10576855656 * q^57 - 56277468420 * q^58 - 24994982320 * q^61 + 50371112832 * q^63 + 56311074600 * q^66 - 37314988144 * q^67 + 92983114440 * q^72 - 51361482568 * q^73 - 121004023440 * q^76 + 104085843000 * q^78 - 22936122360 * q^81 + 56747065840 * q^82 - 84564024000 * q^87 - 148338843420 * q^88 + 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 $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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	$0.383921\pi$
$3$	−389.593	−	159.262i	−0.925644	−	0.378396i
$3$	−389.593	−	159.262i	−0.925644	−	0.378396i
$4$			681.505i			0.332766i
$5$		0			0
$5$		0			0
$6$	14346.5	−	6020.60i	0.753208	−	0.316088i
$7$	−5513.09	−	5513.09i	−0.123981	−	0.123981i	0.642394	−	0.766375i	$-0.277941\pi$
$7$	−5513.09	−	5513.09i	−0.123981	−	0.123981i	−0.766375	+	0.642394i	$0.777941\pi$
$8$	−71346.5	−	71346.5i	−0.769800	−	0.769800i
$9$	126418.	+	124095.i	0.713633	+	0.700520i
$10$		0			0
$11$			213111.i			0.398975i	0.979900	+	0.199488i	$0.0639278\pi$
$11$			213111.i			0.398975i	−0.979900	+	0.199488i	$0.936072\pi$
$12$	108538.	−	265509.i	0.125917	−	0.308023i
$13$	−1.40784e6	+	1.40784e6i	−1.05163	+	1.05163i	−0.0530403	+	0.998592i	$0.516891\pi$
$13$	−1.40784e6	+	1.40784e6i	−1.05163	+	1.05163i	−0.998592	+	0.0530403i	$0.983109\pi$
$14$	288214.			0.143222
$15$		0			0
$16$	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	$0.162656\pi$
$18$	−6.54816e6	+	60720.1i	−0.816809	+	0.00757415i
$19$		−	1.02378e7i		−	0.948557i	−0.880375	−	0.474279i	$-0.842709\pi$
$19$		−	1.02378e7i		−	0.948557i	0.880375	−	0.474279i	$-0.157291\pi$
$20$		0			0
$21$	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
$25$		0			0
$26$		−	7.35989e7i		−	1.21484i
$27$	−2.94878e7	−	6.84801e7i	−0.395496	−	0.918468i
$28$	3.75720e6	−	3.75720e6i	0.0412568	−	0.0412568i
$29$	−1.52840e8			−1.38372			−0.691859	−	0.722033i	$-0.743208\pi$
$29$	−1.52840e8			−1.38372			−0.691859	+	0.722033i	$0.743208\pi$
$30$		0			0
$31$	−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
$33$	3.39406e7	−	8.30265e7i	0.150971	−	0.369309i
$34$			1.17279e8i			0.442677i
$35$		0			0
$36$	−8.45713e7	+	8.61545e7i	−0.233109	+	0.237473i
$37$	−2.07043e8	−	2.07043e8i	−0.490853	−	0.490853i	0.417722	−	0.908575i	$-0.362829\pi$
$37$	−2.07043e8	−	2.07043e8i	−0.490853	−	0.490853i	−0.908575	+	0.417722i	$0.862829\pi$
$38$	2.67607e8	+	2.67607e8i	0.547883	+	0.547883i
$39$	7.72699e8	−	3.24268e8i	1.37137	−	0.575504i
$40$		0			0
$41$			1.29665e8i			0.174788i	0.996174	+	0.0873939i	$0.0278539\pi$
$41$			1.29665e8i			0.174788i	−0.996174	+	0.0873939i	$0.972146\pi$
$42$	−1.12286e8	−	4.59016e7i	−0.132573	−	0.0541947i
$43$	2.00424e8	−	2.00424e8i	0.207909	−	0.207909i	−0.595469	−	0.803378i	$-0.703034\pi$
$43$	2.00424e8	−	2.00424e8i	0.207909	−	0.207909i	0.803378	+	0.595469i	$0.203034\pi$
$44$	−1.45236e8			−0.132765
$45$		0			0
$46$	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	$0.111017\pi$
$48$	−9.09361e8	−	3.71740e8i	−0.515121	−	0.210578i
$49$		−	1.91654e9i		−	0.969257i
$50$		0			0
$51$	−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
$55$		0			0
$56$			7.86680e8i			0.190882i
$57$	−1.63050e9	+	3.98859e9i	−0.358930	+	0.878026i
$58$	3.99508e9	−	3.99508e9i	0.799230	−	0.799230i
$59$	4.71394e9			0.858417			0.429208	−	0.903206i	$-0.358793\pi$
$59$	4.71394e9			0.858417			0.429208	+	0.903206i	$0.358793\pi$
$60$		0			0
$61$	−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
$63$	−1.28067e7	−	1.38110e9i	−0.00162580	−	0.175328i
$64$			9.22947e9i			1.07445i
$65$		0			0
$66$	1.28306e9	+	3.05740e9i	0.126111	+	0.300511i
$67$	1.40139e10	+	1.40139e10i	1.26808	+	1.26808i	0.947076	+	0.321008i	$0.104022\pi$
$67$	1.40139e10	+	1.40139e10i	1.26808	+	1.26808i	0.321008	+	0.947076i	$0.395978\pi$
$68$	1.52887e9	+	1.52887e9i	0.127518	+	0.127518i
$69$	3.37615e9	+	8.04505e9i	0.259868	+	0.619240i
$70$		0			0
$71$			9.83456e9i			0.646895i	0.946246	+	0.323448i	$0.104842\pi$
$71$			9.83456e9i			0.646895i	−0.946246	+	0.323448i	$0.895158\pi$
$72$	−1.65736e8	−	1.78732e10i	−0.0100946	−	1.08862i
$73$	−2.37754e10	+	2.37754e10i	−1.34231	+	1.34231i	−0.448545	+	0.893760i	$0.648058\pi$
$73$	−2.37754e10	+	2.37754e10i	−1.34231	+	1.34231i	−0.893760	+	0.448545i	$0.851942\pi$
$74$	1.08238e10			0.567030
$75$		0			0
$76$	6.97714e9			0.315648
$77$	1.17490e9	−	1.17490e9i	0.0494655	−	0.0494655i
$78$	−1.17215e10	+	2.86736e10i	−0.459690	+	1.12451i
$79$			6.03538e9i			0.220676i	0.993894	+	0.110338i	$0.0351934\pi$
$79$			6.03538e9i			0.220676i	−0.993894	+	0.110338i	$0.964807\pi$
$80$		0			0
$81$	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
$85$		0			0
$86$			1.04777e10i			0.240174i
$87$	5.95453e10	+	2.43416e10i	1.28083	+	0.523593i
$88$	1.52047e10	−	1.52047e10i	0.307131	−	0.307131i
$89$	9.38732e10			1.78195			0.890977	−	0.454049i	$-0.150021\pi$
$89$	9.38732e10			1.78195			0.890977	+	0.454049i	$0.150021\pi$
$90$		0			0
$91$	1.55231e10			0.260766
$92$	9.98942e9	−	9.98942e9i	0.158018	−	0.158018i
$93$	1.02930e11	+	4.20768e10i	1.53421	+	0.627172i
$94$			4.91582e10i			0.690864i
$95$		0			0
$96$	−4.67108e10	+	1.96024e10i	−0.584689	+	0.245368i
$97$	1.56778e10	+	1.56778e10i	0.185371	+	0.185371i	0.793691	−	0.608321i	$-0.208157\pi$
$97$	1.56778e10	+	1.56778e10i	0.185371	+	0.185371i	−0.608321	+	0.793691i	$0.708157\pi$
$98$	5.00964e10	+	5.00964e10i	0.559839	+	0.559839i
$99$	−2.64460e10	+	2.69410e10i	−0.279490	+	0.284722i
$100$		0			0
$101$		−	2.76599e9i		−	0.0261869i	−0.999914	−	0.0130934i	$-0.995832\pi$
$101$		−	2.76599e9i		−	0.0261869i	0.999914	−	0.0130934i	$-0.00416789\pi$
$102$	1.86782e10	−	4.56912e10i	0.167507	−	0.409762i
$103$	3.71254e10	−	3.71254e10i	0.315549	−	0.315549i	−0.531506	−	0.847055i	$-0.678374\pi$
$103$	3.71254e10	−	3.71254e10i	0.315549	−	0.315549i	0.847055	+	0.531506i	$0.178374\pi$
$104$	2.00889e11			1.61909
$105$		0			0
$106$	−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	$0.129924\pi$
$108$	4.66695e10	−	2.00961e10i	0.305635	−	0.131608i
$109$		−	2.26559e10i		−	0.141038i	−0.997510	−	0.0705189i	$-0.977534\pi$
$109$		−	2.26559e10i		−	0.141038i	0.997510	−	0.0705189i	$-0.0224655\pi$
$110$		0			0
$111$	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
$115$		0			0
$116$		−	1.04161e11i		−	0.460454i
$117$	−3.52681e11	+	3.27036e9i	−1.48717	+	0.0137903i
$118$	−1.23218e11	+	1.23218e11i	−0.495818	+	0.495818i
$119$	−2.47359e10			−0.0950209
$120$		0			0
$121$	2.39895e11			0.840819
$122$	1.16849e11	−	1.16849e11i	0.391422	−	0.391422i
$123$	2.06508e10	−	5.05165e10i	0.0661390	−	0.161791i
$124$		−	1.80052e11i		−	0.551543i
$125$		0			0
$126$	3.64354e10	+	3.57658e10i	0.102208	+	0.100330i
$127$	−1.39533e10	−	1.39533e10i	−0.0374762	−	0.0374762i	0.688120	−	0.725597i	$-0.258436\pi$
$127$	−1.39533e10	−	1.39533e10i	−0.0374762	−	0.0374762i	−0.725597	+	0.688120i	$0.758436\pi$
$128$	−6.69523e10	−	6.69523e10i	−0.172231	−	0.172231i
$129$	−1.10004e11	+	4.61636e10i	−0.271121	+	0.113778i
$130$		0			0
$131$		−	2.87714e11i		−	0.651582i	−0.945442	−	0.325791i	$-0.894369\pi$
$131$		−	2.87714e11i		−	0.651582i	0.945442	−	0.325791i	$-0.105631\pi$
$132$	5.65830e10	+	2.31307e10i	0.122894	+	0.0502379i
$133$	−5.64422e10	+	5.64422e10i	−0.117603	+	0.117603i
$134$	−7.32620e11			−1.46488
$135$		0			0
$136$	−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	$0.247382\pi$
$138$	−2.98539e11	−	1.22040e11i	−0.507769	−	0.207572i
$139$			4.58263e11i			0.749089i	0.927209	+	0.374544i	$0.122201\pi$
$139$			4.58263e11i			0.749089i	−0.927209	+	0.374544i	$0.877799\pi$
$140$		0			0
$141$	−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
$145$		0			0
$146$		−	1.24293e12i		−	1.55062i
$147$	−3.05233e11	+	7.46669e11i	−0.366763	+	0.897187i
$148$	1.41101e11	−	1.41101e11i	0.163339	−	0.163339i
$149$	−8.85563e11			−0.987859			−0.493929	−	0.869502i	$-0.664440\pi$
$149$	−8.85563e11			−0.987859			−0.493929	+	0.869502i	$0.664440\pi$
$150$		0			0
$151$	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
$153$	5.61995e11	−	5.21130e9i	0.541913	−	0.00502508i
$154$			6.14214e10i			0.0571421i
$155$		0			0
$156$	2.20990e11	+	5.26598e11i	0.191508	+	0.456346i
$157$	1.32762e12	+	1.32762e12i	1.11078	+	1.11078i	0.993046	+	0.117731i	$0.0375621\pi$
$157$	1.32762e12	+	1.32762e12i	1.11078	+	1.11078i	0.117731	+	0.993046i	$0.462438\pi$
$158$	−1.57759e11	−	1.57759e11i	−0.127462	−	0.127462i
$159$	−7.49055e11	−	1.78493e12i	−0.584561	−	1.39295i
$160$		0			0
$161$			1.61620e11i			0.117748i
$162$	−8.35340e11	−	8.04917e11i	−0.588208	−	0.566786i
$163$	2.03428e11	−	2.03428e11i	0.138477	−	0.138477i	−0.634470	−	0.772947i	$-0.718782\pi$
$163$	2.03428e11	−	2.03428e11i	0.138477	−	0.138477i	0.772947	+	0.634470i	$0.218782\pi$
$164$	−8.83673e10			−0.0581635
$165$		0			0
$166$	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	$0.329792\pi$
$168$	1.25289e11	−	3.06485e11i	0.0722288	−	0.176688i
$169$		−	2.17185e12i		−	1.21186i
$170$		0			0
$171$	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
$175$		0			0
$176$			4.97429e11i			0.222030i
$177$	−1.83652e12	−	7.50754e11i	−0.794588	−	0.324821i
$178$	−2.45375e12	+	2.45375e12i	−1.02925	+	1.02925i
$179$	2.93207e12			1.19257			0.596283	−	0.802774i	$-0.296644\pi$
$179$	2.93207e12			1.19257			0.596283	+	0.802774i	$0.296644\pi$
$180$		0			0
$181$	−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
$183$	1.74159e12	+	7.11949e11i	0.627286	+	0.256430i
$184$			2.09158e12i			0.731099i
$185$		0			0
$186$	−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
$190$		0			0
$191$			2.71574e11i			0.0773046i	0.999253	+	0.0386523i	$0.0123065\pi$
$191$			2.71574e11i			0.0773046i	−0.999253	+	0.0386523i	$0.987694\pi$
$192$	1.46991e12	−	3.59573e12i	0.406568	−	0.994559i
$193$	4.02711e12	−	4.02711e12i	1.08250	−	1.08250i	0.0862264	−	0.996276i	$-0.472519\pi$
$193$	4.02711e12	−	4.02711e12i	1.08250	−	1.08250i	0.996276	−	0.0862264i	$-0.0274808\pi$
$194$	−8.19605e11			−0.214139
$195$		0			0
$196$	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	$0.0990828\pi$
$198$	−1.29401e10	−	1.39548e12i	−0.00302190	−	0.325886i
$199$			9.81048e11i			0.222843i	0.993773	+	0.111421i	$0.0355403\pi$
$199$			9.81048e11i			0.222843i	−0.993773	+	0.111421i	$0.964460\pi$
$200$		0			0
$201$	−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
$205$		0			0
$206$			1.94084e12i			0.364519i
$207$	−3.40498e10	−	3.67199e12i	−0.00622699	−	0.671528i
$208$	−3.28608e12	+	3.28608e12i	−0.585234	+	0.585234i
$209$	2.18180e12			0.378451
$210$		0			0
$211$	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
$213$	1.56628e12	−	3.83147e12i	0.244783	−	0.598795i
$214$			3.95094e12i			0.601762i
$215$		0			0
$216$	−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
$220$		0			0
$221$			6.31662e12i			0.805986i
$222$	−4.21688e12	−	1.72383e12i	−0.524867	−	0.214562i
$223$	−1.03012e13	+	1.03012e13i	−1.25086	+	1.25086i	−0.295529	+	0.955334i	$0.595496\pi$
$223$	−1.03012e13	+	1.03012e13i	−1.25086	+	1.25086i	−0.955334	+	0.295529i	$0.904504\pi$
$224$	−9.38392e11			−0.111178
$225$		0			0
$226$	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	$0.00657128\pi$
$228$	−2.71824e12	−	1.11120e12i	−0.292177	−	0.119440i
$229$			1.14466e13i			1.20110i	0.799587	+	0.600551i	$0.205052\pi$
$229$			1.14466e13i			1.20110i	−0.799587	+	0.600551i	$0.794948\pi$
$230$		0			0
$231$	−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
$235$		0			0
$236$			3.21257e12i			0.285652i
$237$	9.61209e11	−	2.35134e12i	0.0835030	−	0.204268i
$238$	6.46572e11	−	6.46572e11i	0.0548837	−	0.0548837i
$239$	−1.69963e12			−0.140983			−0.0704915	−	0.997512i	$-0.522457\pi$
$239$	−1.69963e12			−0.140983			−0.0704915	+	0.997512i	$0.522457\pi$
$240$		0			0
$241$	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
$243$	4.77025e12	−	1.23164e13i	0.361166	−	0.932502i
$244$		−	3.04652e12i		−	0.225507i
$245$		0			0
$246$	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
$250$		0			0
$251$			1.94310e13i			1.23109i	0.788103	+	0.615543i	$0.211063\pi$
$251$			1.94310e13i			1.23109i	−0.788103	+	0.615543i	$0.788937\pi$
$252$	9.41227e11	−	8.72786e9i	0.0583434	−	0.000541010i
$253$	3.12375e12	−	3.12375e12i	0.189458	−	0.189458i
$254$	7.29449e11			0.0432922
$255$		0			0
$256$	−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	$0.275405\pi$
$258$	1.66871e12	−	4.08205e12i	0.0908810	−	0.222316i
$259$			2.28290e12i			0.121713i
$260$		0			0
$261$	−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
$265$		0			0
$266$		−	2.95068e12i		−	0.135854i
$267$	−3.65723e13	−	1.49505e13i	−1.64945	−	0.674284i
$268$	−9.55056e12	+	9.55056e12i	−0.421976	+	0.421976i
$269$	−7.65520e12			−0.331374			−0.165687	−	0.986178i	$-0.552984\pi$
$269$	−7.65520e12			−0.331374			−0.165687	+	0.986178i	$0.552984\pi$
$270$		0			0
$271$	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
$273$	−6.04768e12	−	2.47224e12i	−0.241376	−	0.0986726i
$274$			3.43505e11i			0.0134371i
$275$		0			0
$276$	−5.48274e12	+	2.30086e12i	−0.206062	+	0.0864751i
$277$	−4.52314e12	−	4.52314e12i	−0.166648	−	0.166648i	0.618856	−	0.785504i	$-0.287596\pi$
$277$	−4.52314e12	−	4.52314e12i	−0.166648	−	0.166648i	−0.785504	+	0.618856i	$0.787596\pi$
$278$	−1.19785e13	−	1.19785e13i	−0.432670	−	0.432670i
$279$	−3.33994e13	−	3.27857e13i	−1.18281	−	1.16108i
$280$		0			0
$281$		−	4.20421e13i		−	1.43153i	−0.698343	−	0.715763i	$-0.746079\pi$
$281$		−	4.20421e13i		−	1.43153i	0.698343	−	0.715763i	$-0.253921\pi$
$282$	7.82905e12	−	1.91517e13i	0.261420	−	0.639494i
$283$	−2.84577e13	+	2.84577e13i	−0.931911	+	0.931911i	−0.997825	−	0.0659139i	$-0.979004\pi$
$283$	−2.84577e13	+	2.84577e13i	−0.931911	+	0.931911i	0.0659139	+	0.997825i	$0.479004\pi$
$284$	−6.70230e12			−0.215265
$285$		0			0
$286$	1.56847e13			0.484690
$287$	7.14855e11	−	7.14855e11i	0.0216704	−	0.0216704i
$288$	2.13201e13	−	1.97698e11i	0.634060	−	0.00587955i
$289$			2.42064e13i			0.706305i
$290$		0			0
$291$	−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
$295$		0			0
$296$			2.95436e13i			0.755718i
$297$	1.45939e13	−	6.28418e12i	0.366446	−	0.157793i
$298$	2.31477e13	−	2.31477e13i	0.570583	−	0.570583i
$299$	4.12718e13			0.998762
$300$		0			0
$301$	−2.20991e12			−0.0515535
$302$	−3.73816e13	+	3.73816e13i	−0.856287	+	0.856287i
$303$	−4.40519e11	+	1.07761e12i	−0.00990901	+	0.0242397i
$304$		−	2.38965e13i		−	0.527873i
$305$		0			0
$306$	−1.45538e13	+	1.48262e13i	−0.310104	+	0.315909i
$307$	2.20819e13	+	2.20819e13i	0.462141	+	0.462141i	0.899357	−	0.437216i	$-0.144035\pi$
$307$	2.20819e13	+	2.20819e13i	0.462141	+	0.462141i	−0.437216	+	0.899357i	$0.644035\pi$
$308$	8.00700e11	+	8.00700e11i	0.0164604	+	0.0164604i
$309$	−2.03765e13	+	8.55110e12i	−0.411488	+	0.172683i
$310$		0			0
$311$		−	8.99308e13i		−	1.75278i	−0.481606	−	0.876388i	$-0.659946\pi$
$311$		−	8.99308e13i		−	1.75278i	0.481606	−	0.876388i	$-0.340054\pi$
$312$	−7.82648e13	−	3.19940e13i	−1.49870	−	0.612659i
$313$	2.91430e13	−	2.91430e13i	0.548328	−	0.548328i	−0.377629	−	0.925957i	$-0.623261\pi$
$313$	2.91430e13	−	2.91430e13i	0.548328	−	0.548328i	0.925957	+	0.377629i	$0.123261\pi$
$314$	−6.94055e13			−1.28316
$315$		0			0
$316$	−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	$0.314619\pi$
$318$	6.62358e13	+	2.70767e13i	1.14220	+	0.466924i
$319$		−	3.25718e13i		−	0.552069i
$320$		0			0
$321$	−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
$325$		0			0
$326$			1.06348e13i			0.159968i
$327$	−3.60823e12	+	8.82657e12i	−0.0533681	+	0.130551i
$328$	9.25114e12	−	9.25114e12i	0.134552	−	0.134552i
$329$	−1.03682e13			−0.148294
$330$		0			0
$331$	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
$333$	−4.80955e11	−	5.18670e13i	−0.00643667	−	0.694141i
$334$		−	3.07840e13i		−	0.405247i
$335$		0			0
$336$	2.96396e12	+	7.06283e12i	0.0377577	+	0.0899731i
$337$	3.22426e13	+	3.22426e13i	0.404078	+	0.404078i	0.879667	−	0.475589i	$-0.157765\pi$
$337$	3.22426e13	+	3.22426e13i	0.404078	+	0.404078i	−0.475589	+	0.879667i	$0.657765\pi$
$338$	5.67700e13	+	5.67700e13i	0.699967	+	0.699967i
$339$	1.07850e13	+	2.56996e13i	0.130834	+	0.311766i
$340$		0			0
$341$		−	5.63035e13i		−	0.661281i
$342$	6.21643e11	+	6.70390e13i	0.00718452	+	0.774790i
$343$	−2.14672e13	+	2.14672e13i	−0.244151	+	0.244151i
$344$	−2.85991e13			−0.320096
$345$		0			0
$346$	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	$0.310613\pi$
$348$	−1.65890e13	+	4.05804e13i	−0.174234	+	0.426217i
$349$			5.77981e13i			0.597549i	0.954324	+	0.298774i	$0.0965778\pi$
$349$			5.77981e13i			0.597549i	−0.954324	+	0.298774i	$0.903422\pi$
$350$		0			0
$351$	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
$355$		0			0
$356$			6.39750e13i			0.592974i
$357$	9.63692e12	+	3.93950e12i	0.0879556	+	0.0359555i
$358$	−7.66413e13	+	7.66413e13i	−0.688821	+	0.688821i
$359$	1.26366e14			1.11843			0.559217	−	0.829021i	$-0.311102\pi$
$359$	1.26366e14			1.11843			0.559217	+	0.829021i	$0.311102\pi$
$360$		0			0
$361$	1.16768e13			0.100239
$362$	7.04817e13	−	7.04817e13i	0.595908	−	0.595908i
$363$	−9.34615e13	−	3.82063e13i	−0.778299	−	0.318162i
$364$			1.05791e13i			0.0867739i
$365$		0			0
$366$	−6.41331e13	+	2.69138e13i	−0.510430	+	0.214205i
$367$	1.12492e13	+	1.12492e13i	0.0881983	+	0.0881983i	0.749829	−	0.661631i	$-0.230136\pi$
$367$	1.12492e13	+	1.12492e13i	0.0881983	+	0.0881983i	−0.661631	+	0.749829i	$0.730136\pi$
$368$	−3.42134e13	−	3.42134e13i	−0.264261	−	0.264261i
$369$	−1.60908e13	+	1.63920e13i	−0.122442	+	0.124734i
$370$		0			0
$371$		−	3.58582e13i		−	0.264869i
$372$	−2.86756e13	+	7.01471e13i	−0.208702	+	0.510532i
$373$	−7.82605e13	+	7.82605e13i	−0.561234	+	0.561234i	−0.929658	−	0.368424i	$-0.879898\pi$
$373$	−7.82605e13	+	7.82605e13i	−0.561234	+	0.561234i	0.368424	+	0.929658i	$0.379898\pi$
$374$	−2.49935e13			−0.176617
$375$		0			0
$376$	−1.34177e14			−0.920760
$377$	2.15174e14	−	2.15174e14i	1.45516	−	1.45516i
$378$	−8.49879e12	−	1.97369e13i	−0.0566438	−	0.131545i
$379$			1.35574e14i			0.890556i	0.895392	+	0.445278i	$0.146895\pi$
$379$			1.35574e14i			0.890556i	−0.895392	+	0.445278i	$0.853105\pi$
$380$		0			0
$381$	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
$385$		0			0
$386$			2.10529e14i			1.25050i
$387$	5.02087e13	−	4.65578e11i	0.294014	−	0.00272635i
$388$	−1.06845e13	+	1.06845e13i	−0.0616851	+	0.0616851i
$389$	5.35695e13			0.304926			0.152463	−	0.988309i	$-0.451279\pi$
$389$	5.35695e13			0.304926			0.152463	+	0.988309i	$0.451279\pi$
$390$		0			0
$391$	−6.57663e13			−0.363941
$392$	−1.36738e14	+	1.36738e14i	−0.746134	+	0.746134i
$393$	−4.58220e13	+	1.12091e14i	−0.246556	+	0.603133i
$394$			1.40570e14i			0.745870i
$395$		0			0
$396$	−1.83605e13	−	1.80231e13i	−0.0947458	−	0.0930048i
$397$	−2.12579e14	−	2.12579e14i	−1.08186	−	1.08186i	−0.996336	−	0.0855292i	$-0.972742\pi$
$397$	−2.12579e14	−	2.12579e14i	−1.08186	−	1.08186i	−0.0855292	−	0.996336i	$-0.527258\pi$
$398$	−2.56436e13	−	2.56436e13i	−0.128713	−	0.128713i
$399$	3.09786e13	−	1.30003e13i	0.153359	−	0.0643582i
$400$		0			0
$401$		−	2.56873e14i		−	1.23715i	−0.785724	−	0.618577i	$-0.787709\pi$
$401$		−	2.56873e14i		−	1.23715i	0.785724	−	0.618577i	$-0.212291\pi$
$402$	2.85423e14	+	1.16679e14i	1.35596	+	0.554305i
$403$	3.71948e14	−	3.71948e14i	1.74303	−	1.74303i
$404$	1.88504e12			0.00871410
$405$		0			0
$406$	−4.40505e13			−0.198179
$407$	4.41232e13	−	4.41232e13i	0.195838	−	0.195838i
$408$	1.24714e14	+	5.09822e13i	0.546116	+	0.223248i
$409$		−	1.44694e14i		−	0.625133i	−0.949896	−	0.312567i	$-0.898811\pi$
$409$		−	1.44694e14i		−	0.625133i	0.949896	−	0.312567i	$-0.101189\pi$
$410$		0			0
$411$	−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
$415$		0			0
$416$			2.39630e14i			0.943036i
$417$	7.29841e13	−	1.78536e14i	0.283452	−	0.693389i
$418$	−5.70300e13	+	5.70300e13i	−0.218592	+	0.218592i
$419$	4.52097e14			1.71023			0.855115	−	0.518439i	$-0.173487\pi$
$419$	4.52097e14			1.71023			0.855115	+	0.518439i	$0.173487\pi$
$420$		0			0
$421$	−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
$423$	2.35563e14	−	2.18434e12i	0.845736	−	0.00784239i
$424$		−	4.64051e14i		−	1.64457i
$425$		0			0
$426$	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
$430$		0			0
$431$			4.20038e14i			1.36039i	0.733031	+	0.680195i	$0.238105\pi$
$431$			4.20038e14i			1.36039i	−0.733031	+	0.680195i	$0.761895\pi$
$432$	−6.88285e13	−	1.59842e14i	−0.220094	−	0.511128i
$433$	−5.30911e13	+	5.30911e13i	−0.167625	+	0.167625i	−0.785935	−	0.618310i	$-0.787818\pi$
$433$	−5.30911e13	+	5.30911e13i	−0.167625	+	0.167625i	0.618310	+	0.785935i	$0.287818\pi$
$434$	−7.61455e13			−0.237383
$435$		0			0
$436$	1.54401e13			0.0469326
$437$	−1.50065e14	+	1.50065e14i	−0.450434	+	0.450434i
$438$	−1.97952e14	+	4.84236e14i	−0.586748	+	1.43532i
$439$		−	2.43794e14i		−	0.713623i	−0.934176	−	0.356812i	$-0.883864\pi$
$439$		−	2.43794e14i		−	0.713623i	0.934176	−	0.356812i	$-0.116136\pi$
$440$		0			0
$441$	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
$445$		0			0
$446$		−	5.38525e14i		−	1.44499i
$447$	3.45009e14	+	1.41037e14i	0.914405	+	0.373802i
$448$	5.08829e13	−	5.08829e13i	0.133212	−	0.133212i
$449$	−1.97963e13			−0.0511953			−0.0255976	−	0.999672i	$-0.508149\pi$
$449$	−1.97963e13			−0.0511953			−0.0255976	+	0.999672i	$0.508149\pi$
$450$		0			0
$451$	−2.76330e13			−0.0697360
$452$	3.19108e13	−	3.19108e13i	0.0795567	−	0.0795567i
$453$	−5.57159e14	−	2.27762e14i	−1.37227	−	0.560973i
$454$			4.64845e14i			1.13110i
$455$		0			0
$456$	4.00903e14	−	1.68241e14i	0.952209	−	0.399600i
$457$	−6.24954e13	−	6.24954e13i	−0.146659	−	0.146659i	0.629965	−	0.776624i	$-0.283069\pi$
$457$	−6.24954e13	−	6.24954e13i	−0.146659	−	0.146659i	−0.776624	+	0.629965i	$0.783069\pi$
$458$	−2.99201e14	−	2.99201e14i	−0.693751	−	0.693751i
$459$	−2.19779e14	−	8.74744e13i	−0.503520	−	0.200406i
$460$		0			0
$461$			4.69410e14i			1.05002i	0.851096	+	0.525010i	$0.175938\pi$
$461$			4.69410e14i			1.05002i	−0.851096	+	0.525010i	$0.824062\pi$
$462$	9.78213e12	−	2.39293e13i	0.0216223	−	0.0528932i
$463$	3.67034e14	−	3.67034e14i	0.801699	−	0.801699i	−0.181662	−	0.983361i	$-0.558148\pi$
$463$	3.67034e14	−	3.67034e14i	0.801699	−	0.801699i	0.983361	+	0.181662i	$0.0581478\pi$
$464$	−3.56748e14			−0.770040
$465$		0			0
$466$	−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	$0.275700\pi$
$468$	−2.22877e12	−	2.40354e14i	−0.00458895	−	0.494880i
$469$		−	1.54520e14i		−	0.314437i
$470$		0			0
$471$	−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
$475$		0			0
$476$		−	1.68576e13i		−	0.0316198i
$477$	7.55451e12	+	8.14691e14i	0.0140073	+	1.51057i
$478$	4.44267e13	−	4.44267e13i	0.0814312	−	0.0814312i
$479$	−6.43240e14			−1.16554			−0.582771	−	0.812636i	$-0.698032\pi$
$479$	−6.43240e14			−1.16554			−0.582771	+	0.812636i	$0.698032\pi$
$480$		0			0
$481$	5.82967e14			1.03239
$482$	−3.62966e14	+	3.62966e14i	−0.635487	+	0.635487i
$483$	2.57401e13	−	6.29662e13i	0.0445554	−	0.108993i
$484$			1.63490e14i			0.279796i
$485$		0			0
$486$	1.97249e14	+	4.46628e14i	0.330001	+	0.747217i
$487$	4.58342e13	+	4.58342e13i	0.0758194	+	0.0758194i	0.744000	−	0.668180i	$-0.232926\pi$
$487$	4.58342e13	+	4.58342e13i	0.0758194	+	0.0758194i	−0.668180	+	0.744000i	$0.732926\pi$
$488$	3.18940e14	+	3.18940e14i	0.521674	+	0.521674i
$489$	−1.11652e14	+	4.68556e13i	−0.180580	+	0.0757814i
$490$		0			0
$491$		−	6.98254e14i		−	1.10424i	−0.833763	−	0.552122i	$-0.813818\pi$
$491$		−	6.98254e14i		−	1.10424i	0.833763	−	0.552122i	$-0.186182\pi$
$492$	3.44273e13	+	1.40736e13i	0.0538387	+	0.0220088i
$493$	−3.42877e14	+	3.42877e14i	−0.530250	+	0.530250i
$494$	−7.53494e14			−1.15234
$495$		0			0
$496$	−6.16673e14			−0.922372
$497$	5.42188e13	−	5.42188e13i	0.0802029	−	0.0802029i
$498$	−6.48935e14	−	2.65279e14i	−0.949379	−	0.388099i
$499$		−	5.35718e14i		−	0.775146i	−0.921839	−	0.387573i	$-0.873313\pi$
$499$		−	5.35718e14i		−	0.775146i	0.921839	−	0.387573i	$-0.126687\pi$
$500$		0			0
$501$	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
$505$		0			0
$506$			1.63304e14i			0.218861i
$507$	−3.45894e14	+	8.46138e14i	−0.458564	+	1.12175i
$508$	9.50923e12	−	9.50923e12i	0.0124708	−	0.0124708i
$509$	−5.02829e14			−0.652338			−0.326169	−	0.945311i	$-0.605758\pi$
$509$	−5.02829e14			−0.652338			−0.326169	+	0.945311i	$0.605758\pi$
$510$		0			0
$511$	2.62151e14			0.332841
$512$	5.39706e14	−	5.39706e14i	0.677911	−	0.677911i
$513$	−7.01089e14	+	3.01892e14i	−0.871219	+	0.375151i
$514$		−	1.05945e14i		−	0.130252i
$515$		0			0
$516$	−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
$520$		0			0
$521$			8.42723e14i			0.961783i	0.876780	+	0.480892i	$0.159687\pi$
$521$			8.42723e14i			0.961783i	−0.876780	+	0.480892i	$0.840313\pi$
$522$	1.00082e15	−	9.28045e12i	1.13023	−	0.0104805i
$523$	3.08210e14	−	3.08210e14i	0.344419	−	0.344419i	−0.513607	−	0.858026i	$-0.671691\pi$
$523$	3.08210e14	−	3.08210e14i	0.344419	−	0.344419i	0.858026	+	0.513607i	$0.171691\pi$
$524$	1.96079e14			0.216824
$525$		0			0
$526$	9.52798e14			1.03176
$527$	−5.92696e14	+	5.92696e14i	−0.635146	+	0.635146i
$528$	7.92218e13	−	1.93795e14i	0.0840152	−	0.205521i
$529$		−	5.23103e14i		−	0.549011i
$530$		0			0
$531$	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
$535$		0			0
$536$		−	1.99969e15i		−	1.95234i
$537$	−1.14231e15	−	4.66968e14i	−1.10389	−	0.451262i
$538$	2.00099e14	−	2.00099e14i	0.191401	−	0.191401i
$539$	4.08435e14			0.386710
$540$		0			0
$541$	−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
$543$	1.05051e15	+	4.29438e14i	0.954991	+	0.390393i
$544$		−	3.81849e14i		−	0.343635i
$545$		0			0
$546$	2.22702e14	−	9.34583e13i	0.196411	−	0.0824249i
$547$	−3.85557e14	−	3.85557e14i	−0.336634	−	0.336634i	0.518465	−	0.855099i	$-0.326504\pi$
$547$	−3.85557e14	−	3.85557e14i	−0.336634	−	0.336634i	−0.855099	+	0.518465i	$0.826504\pi$
$548$	4.47799e12	+	4.47799e12i	0.00387070	+	0.00387070i
$549$	−5.65125e14	−	5.54740e14i	−0.483611	−	0.474725i
$550$		0			0
$551$			1.56475e15i			1.31254i
$552$	3.33110e14	−	8.14863e14i	0.276645	−	0.676737i
$553$	3.32736e13	−	3.32736e13i	0.0273597	−	0.0273597i
$554$	2.36461e14			0.192511
$555$		0			0
$556$	−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	$0.0439731\pi$
$558$	1.73001e15	−	1.60421e13i	1.35382	−	0.0125538i
$559$			5.64328e14i			0.437287i
$560$		0			0
$561$	−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
$565$		0			0
$566$		−	1.48771e15i		−	1.07654i
$567$	1.69769e14	−	1.76185e14i	0.121661	−	0.126259i
$568$	7.01662e14	−	7.01662e14i	0.497980	−	0.497980i
$569$	−2.48247e13			−0.0174488			−0.00872440	−	0.999962i	$-0.502777\pi$
$569$	−2.48247e13			−0.0174488			−0.00872440	+	0.999962i	$0.502777\pi$
$570$		0			0
$571$	−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
$573$	4.32516e13	−	1.05803e14i	0.0292517	−	0.0715565i
$574$			3.73712e13i			0.0250335i
$575$		0			0
$576$	−1.14533e15	+	1.16677e15i	−0.752674	+	0.766764i
$577$	−8.40047e14	−	8.40047e14i	−0.546810	−	0.546810i	0.378707	−	0.925517i	$-0.376369\pi$
$577$	−8.40047e14	−	8.40047e14i	−0.546810	−	0.546810i	−0.925517	+	0.378707i	$0.876369\pi$
$578$	−6.32731e14	−	6.32731e14i	−0.407959	−	0.407959i
$579$	−2.21030e15	+	9.27566e14i	−1.41163	+	0.592397i
$580$		0			0
$581$			3.51315e14i			0.220155i
$582$	3.19312e14	+	1.30532e14i	0.198216	+	0.0810292i
$583$	−6.93056e14	+	6.93056e14i	−0.426178	+	0.426178i
$584$	3.39258e15			2.06661
$585$		0			0
$586$	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	$0.0989889\pi$
$588$	−5.08859e14	−	2.08018e14i	−0.298553	−	0.122046i
$589$			2.70482e15i			1.57219i
$590$		0			0
$591$	−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
$595$		0			0
$596$		−	6.03515e14i		−	0.328726i
$597$	1.56244e14	−	3.82209e14i	0.0843227	−	0.206273i
$598$	−1.07880e15	+	1.07880e15i	−0.576881	+	0.576881i
$599$	3.59256e15			1.90352			0.951759	−	0.306846i	$-0.0992736\pi$
$599$	3.59256e15			1.90352			0.951759	+	0.306846i	$0.0992736\pi$
$600$		0			0
$601$	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
$603$	3.25539e13	+	3.51067e15i	0.0166287	+	1.79327i
$604$			9.74625e14i			0.493326i
$605$		0			0
$606$	−1.66529e13	−	3.96824e13i	−0.00827736	−	0.0197242i
$607$	−3.75195e13	−	3.75195e13i	−0.0184807	−	0.0184807i	0.697806	−	0.716287i	$-0.254160\pi$
$607$	−3.75195e13	−	3.75195e13i	−0.0184807	−	0.0184807i	−0.716287	+	0.697806i	$0.754160\pi$
$608$	−8.71300e14	−	8.71300e14i	−0.425303	−	0.425303i
$609$	−1.94081e14	−	4.62476e14i	−0.0938832	−	0.223715i
$610$		0			0
$611$			2.64764e15i			1.25786i
$612$	3.55153e12	+	3.83002e14i	0.00167218	+	0.180330i
$613$	−5.32610e14	+	5.32610e14i	−0.248529	+	0.248529i	−0.820367	−	0.571838i	$-0.806231\pi$
$613$	−5.32610e14	+	5.32610e14i	−0.248529	+	0.248529i	0.571838	+	0.820367i	$0.306231\pi$
$614$	−1.15440e15			−0.533862
$615$		0			0
$616$	−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	$0.163542\pi$
$618$	3.09103e14	−	7.56137e14i	0.137933	−	0.337415i
$619$		−	2.24348e15i		−	0.992258i	−0.868249	−	0.496129i	$-0.834754\pi$
$619$		−	2.24348e15i		−	0.992258i	0.868249	−	0.496129i	$-0.165246\pi$
$620$		0			0
$621$	−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
$625$		0			0
$626$			1.52354e15i			0.633424i
$627$	−8.50012e14	−	3.47478e14i	−0.350311	−	0.143204i
$628$	−9.04782e14	+	9.04782e14i	−0.369629	+	0.369629i
$629$	−9.28952e14			−0.376197
$630$		0			0
$631$	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
$633$	−9.05284e14	−	3.70073e14i	−0.354050	−	0.144733i
$634$		−	8.49537e14i		−	0.329375i
$635$		0			0
$636$	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
$640$		0			0
$641$		−	3.15822e15i		−	1.15272i	−0.817197	−	0.576359i	$-0.804473\pi$
$641$		−	3.15822e15i		−	1.15272i	0.817197	−	0.576359i	$-0.195527\pi$
$642$	6.29236e14	−	1.53926e15i	0.227704	−	0.557017i
$643$	−5.77831e14	+	5.77831e14i	−0.207320	+	0.207320i	−0.803127	−	0.595807i	$-0.796832\pi$
$643$	−5.77831e14	+	5.77831e14i	−0.207320	+	0.207320i	0.595807	+	0.803127i	$0.296832\pi$
$644$	−1.10145e14			−0.0391826
$645$		0			0
$646$	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	$0.349919\pi$
$648$	2.19703e15	−	2.28006e15i	0.755393	−	0.783943i
$649$			1.00459e15i			0.342487i
$650$		0			0
$651$	−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
$655$		0			0
$656$			3.02655e14i			0.0972696i
$657$	−5.95603e15	+	5.52294e13i	−1.89822	+	0.0176020i
$658$	2.71014e14	−	2.71014e14i	0.0856542	−	0.0856542i
$659$	1.27064e14			0.0398248			0.0199124	−	0.999802i	$-0.493661\pi$
$659$	1.27064e14			0.0398248			0.0199124	+	0.999802i	$0.493661\pi$
$660$		0			0
$661$	−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
$663$	1.00600e15	−	2.46091e15i	0.304982	−	0.746056i
$664$			4.54647e15i			1.36694i
$665$		0			0
$666$	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
$670$		0			0
$671$		−	9.52668e14i		−	0.270376i
$672$	3.65591e14	+	1.49451e14i	0.102912	+	0.0420695i
$673$	1.77621e15	−	1.77621e15i	0.495920	−	0.495920i	−0.414245	−	0.910165i	$-0.635954\pi$
$673$	1.77621e15	−	1.77621e15i	0.495920	−	0.495920i	0.910165	+	0.414245i	$0.135954\pi$
$674$	−1.68558e15			−0.466788
$675$		0			0
$676$	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	$0.328473\pi$
$678$	−9.53672e14	−	3.89854e14i	−0.255644	−	0.104505i
$679$		−	1.72867e14i		−	0.0459650i
$680$		0			0
$681$	−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
$685$		0			0
$686$		−	1.12226e15i		−	0.282041i
$687$	1.82301e15	−	4.45949e15i	0.454492	−	1.11179i
$688$	4.67815e14	−	4.67815e14i	0.115701	−	0.115701i
$689$	−9.15683e15			−2.24667
$690$		0			0
$691$	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
$693$	2.94328e14	−	2.72926e12i	0.0699517	−	0.000648652i
$694$		−	1.31141e15i		−	0.309215i
$695$		0			0
$696$	−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
$700$		0			0
$701$			8.81518e12i			0.00196690i	1.00000		0.000983450i	$0.000313042\pi$
$701$			8.81518e12i			0.00196690i	−1.00000		0.000983450i	$0.999687\pi$
$702$	−5.04006e15	+	2.17027e15i	−1.11579	+	0.480463i
$703$	−2.11968e15	+	2.11968e15i	−0.465602	+	0.465602i
$704$	−1.96690e15			−0.428679
$705$		0			0
$706$	3.41691e15			0.733174
$707$	−1.52492e13	+	1.52492e13i	−0.00324668	+	0.00324668i
$708$	5.11643e14	−	1.25160e15i	0.108090	−	0.264412i
$709$		−	6.16528e15i		−	1.29240i	−0.763166	−	0.646202i	$-0.776356\pi$
$709$		−	6.16528e15i		−	1.29240i	0.763166	−	0.646202i	$-0.223644\pi$
$710$		0			0
$711$	−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
$715$		0			0
$716$			1.99822e15i			0.396845i
$717$	6.62165e14	+	2.70688e14i	0.130500	+	0.0533474i
$718$	−3.30308e15	+	3.30308e15i	−0.646003	+	0.646003i
$719$	2.03645e15			0.395243			0.197622	−	0.980278i	$-0.436678\pi$
$719$	2.03645e15			0.395243			0.197622	+	0.980278i	$0.436678\pi$
$720$		0			0
$721$	−4.09351e14			−0.0782442
$722$	−3.05221e14	+	3.05221e14i	−0.0578975	+	0.0578975i
$723$	−5.40988e15	−	2.21152e15i	−1.01842	−	0.416322i
$724$		−	1.83762e15i		−	0.343316i
$725$		0			0
$726$	3.44167e15	−	1.44432e15i	0.633311	−	0.265773i
$727$	−2.70789e15	−	2.70789e15i	−0.494529	−	0.494529i	0.415201	−	0.909730i	$-0.363711\pi$
$727$	−2.70789e15	−	2.70789e15i	−0.494529	−	0.494529i	−0.909730	+	0.415201i	$0.863711\pi$
$728$	−1.10752e15	−	1.10752e15i	−0.200737	−	0.200737i
$729$	−3.82000e15	+	4.03866e15i	−0.687166	+	0.726501i
$730$		0			0
$731$		−	8.99252e14i		−	0.159344i
$732$	−4.85197e14	+	1.18690e15i	−0.0853311	+	0.208739i
$733$	1.39822e15	−	1.39822e15i	0.244063	−	0.244063i	−0.574466	−	0.818529i	$-0.694790\pi$
$733$	1.39822e15	−	1.39822e15i	0.244063	−	0.244063i	0.818529	+	0.574466i	$0.194790\pi$
$734$	−5.88088e14			−0.101886
$735$		0			0
$736$	−2.49494e15			−0.425826
$737$	−2.98652e15	+	2.98652e15i	−0.505934	+	0.505934i
$738$	−7.87327e12	−	8.49067e14i	−0.00132387	−	0.142768i
$739$			3.48541e15i			0.581714i	0.956767	+	0.290857i	$0.0939403\pi$
$739$			3.48541e15i			0.581714i	−0.956767	+	0.290857i	$0.906060\pi$
$740$		0			0
$741$	−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
$745$		0			0
$746$		−	4.09131e15i		−	0.648333i
$747$	−7.40142e13	−	7.98181e15i	−0.0116426	−	1.25556i
$748$	−3.25820e14	+	3.25820e14i	−0.0508766	+	0.0508766i
$749$	−8.33310e14			−0.129168
$750$		0			0
$751$	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
$753$	3.09462e15	−	7.57016e15i	0.465838	−	1.13955i
$754$			1.12488e16i			1.68099i
$755$		0			0
$756$	−3.68085e14	−	1.46502e14i	−0.0542099	−	0.0215761i
$757$	1.60133e15	+	1.60133e15i	0.234128	+	0.234128i	0.814413	−	0.580285i	$-0.197059\pi$
$757$	1.60133e15	+	1.60133e15i	0.234128	+	0.234128i	−0.580285	+	0.814413i	$0.697059\pi$
$758$	−3.54377e15	−	3.54377e15i	−0.514381	−	0.514381i
$759$	−1.71449e15	+	7.19495e14i	−0.247061	+	0.103681i
$760$		0			0
$761$			7.42244e15i			1.05422i	0.849797	+	0.527110i	$0.176724\pi$
$761$			7.42244e15i			1.05422i	−0.849797	+	0.527110i	$0.823276\pi$
$762$	−2.84188e14	−	1.16174e14i	−0.0400732	−	0.0163816i
$763$	−1.24904e14	+	1.24904e14i	−0.0174860	+	0.0174860i
$764$	−1.85079e14			−0.0257244
$765$		0			0
$766$	−9.32882e15			−1.27811
$767$	−6.63646e15	+	6.63646e15i	−0.902739	+	0.902739i
$768$	6.00043e15	+	2.45293e15i	0.810393	+	0.331282i
$769$		−	2.88608e15i		−	0.387002i	−0.981100	−	0.193501i	$-0.938016\pi$
$769$		−	2.88608e15i		−	0.387002i	0.981100	−	0.193501i	$-0.0619843\pi$
$770$		0			0
$771$	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
$775$		0			0
$776$		−	2.23712e15i		−	0.285397i
$777$	3.63580e14	−	8.89400e14i	0.0460558	−	0.112663i
$778$	−1.40025e15	+	1.40025e15i	−0.176124	+	0.176124i
$779$	1.32749e15			0.165796
$780$		0			0
$781$	−2.09585e15			−0.258095
$782$	1.71907e15	−	1.71907e15i	0.210211	−	0.210211i
$783$	4.50692e15	+	1.04665e16i	0.547255	+	1.27090i
$784$		−	4.47345e15i		−	0.539392i
$785$		0			0
$786$	−1.73221e15	−	4.12770e15i	−0.205957	−	0.490777i
$787$	7.49129e15	+	7.49129e15i	0.884495	+	0.884495i	0.993988	−	0.109493i	$-0.0349226\pi$
$787$	7.49129e15	+	7.49129e15i	0.884495	+	0.884495i	−0.109493	+	0.993988i	$0.534923\pi$
$788$	1.83249e15	+	1.83249e15i	0.214856	+	0.214856i
$789$	4.19791e15	+	1.00032e16i	0.488775	+	1.16470i
$790$		0			0
$791$			5.16291e14i			0.0592821i
$792$	3.80898e15	−	3.53201e13i	0.434330	−	0.00402748i
$793$	6.29344e15	−	6.29344e15i	0.712665	−	0.712665i
$794$	1.11132e16			1.24976
$795$		0			0
$796$	−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	$0.298054\pi$
$798$	−4.69933e14	+	1.14957e15i	−0.0514068	+	0.125753i
$799$		−	4.21900e15i		−	0.458355i
$800$		0			0
$801$	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
$805$		0			0
$806$			1.94447e16i			2.01353i
$807$	2.98241e15	+	1.21919e15i	0.306735	+	0.125391i
$808$	−1.97344e14	+	1.97344e14i	−0.0201587	+	0.0201587i
$809$	4.76769e15			0.483717			0.241858	−	0.970312i	$-0.422243\pi$
$809$	4.76769e15			0.483717			0.241858	+	0.970312i	$0.422243\pi$
$810$		0			0
$811$	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
$813$	−1.21093e16	−	4.95017e15i	−1.19569	−	0.488789i
$814$			2.30667e15i			0.226231i
$815$		0			0
$816$	−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
$820$		0			0
$821$		−	1.37691e16i		−	1.28831i	−0.764897	−	0.644153i	$-0.777210\pi$
$821$		−	1.37691e16i		−	1.28831i	0.764897	−	0.644153i	$-0.222790\pi$
$822$	5.47074e13	−	1.33827e14i	0.00508453	−	0.0124379i
$823$	−3.41704e15	+	3.41704e15i	−0.315464	+	0.315464i	−0.847022	−	0.531558i	$-0.821607\pi$
$823$	−3.41704e15	+	3.41704e15i	−0.315464	+	0.315464i	0.531558	+	0.847022i	$0.321607\pi$
$824$	−5.29753e15			−0.485819
$825$		0			0
$826$	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	$0.161571\pi$
$828$	2.50248e15	−	2.32051e13i	0.223462	−	0.00207213i
$829$		−	4.82944e15i		−	0.428398i	−0.976790	−	0.214199i	$-0.931286\pi$
$829$		−	4.82944e15i		−	0.428398i	0.976790	−	0.214199i	$-0.0687141\pi$
$830$		0			0
$831$	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
$835$		0			0
$836$			1.48690e15i			0.125936i
$837$	7.79063e15	+	1.80923e16i	0.655515	+	1.52231i
$838$	−1.18174e16	+	1.18174e16i	−0.987821	+	0.987821i
$839$	−4.02227e14			−0.0334026			−0.0167013	−	0.999861i	$-0.505316\pi$
$839$	−4.02227e14			−0.0334026			−0.0167013	+	0.999861i	$0.505316\pi$
$840$		0			0
$841$	1.11595e16			0.914675
$842$	5.40134e15	−	5.40134e15i	0.439830	−	0.439830i
$843$	−6.69572e15	+	1.63793e16i	−0.541684	+	1.32508i
$844$			1.58359e15i			0.127280i
$845$		0			0
$846$	−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
$850$		0			0
$851$			6.06963e15i			0.466176i
$852$	2.61117e15	+	1.06742e15i	0.199259	+	0.0814553i
$853$	1.37262e16	−	1.37262e16i	1.04071	−	1.04071i	0.0415739	−	0.999135i	$-0.486763\pi$
$853$	1.37262e16	−	1.37262e16i	1.04071	−	1.04071i	0.999135	−	0.0415739i	$-0.0132372\pi$
$854$	−1.28840e15			−0.0970581
$855$		0			0
$856$	−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	$0.0999928\pi$
$858$	−6.11066e15	−	2.49799e15i	−0.448650	−	0.183405i
$859$			1.77808e16i			1.29714i	0.761154	+	0.648571i	$0.224633\pi$
$859$			1.77808e16i			1.29714i	−0.761154	+	0.648571i	$0.775367\pi$
$860$		0			0
$861$	−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
$865$		0			0
$866$		−	2.77550e15i		−	0.193639i
$867$	3.85517e15	−	9.43064e15i	0.267263	−	0.653787i
$868$	−9.92645e14	+	9.92645e14i	−0.0683810	+	0.0683810i
$869$	−1.28621e15			−0.0880443
$870$		0			0
$871$	−3.94586e16			−2.66712
$872$	−1.61642e15	+	1.61642e15i	−0.108571	+	0.108571i
$873$	3.64191e13	+	3.92750e15i	0.00243081	+	0.262142i
$874$		−	7.84510e15i		−	0.520338i
$875$		0			0
$876$	3.73205e15	+	8.89311e15i	0.244441	+	0.582480i
$877$	8.91823e15	+	8.91823e15i	0.580471	+	0.580471i	0.935033	−	0.354561i	$-0.115370\pi$
$877$	8.91823e15	+	8.91823e15i	0.580471	+	0.580471i	−0.354561	+	0.935033i	$0.615370\pi$
$878$	6.37254e15	+	6.37254e15i	0.412186	+	0.412186i
$879$	5.37792e15	+	1.28151e16i	0.345681	+	0.823725i
$880$		0			0
$881$		−	1.56283e16i		−	0.992076i	−0.868301	−	0.496038i	$-0.834788\pi$
$881$		−	1.56283e16i		−	0.992076i	0.868301	−	0.496038i	$-0.165212\pi$
$882$	1.16372e14	+	1.25498e16i	0.00734130	+	0.791698i
$883$	1.35585e16	−	1.35585e16i	0.850019	−	0.850019i	−0.140116	−	0.990135i	$-0.544747\pi$
$883$	1.35585e16	−	1.35585e16i	0.850019	−	0.850019i	0.990135	+	0.140116i	$0.0447475\pi$
$884$	−4.30481e15			−0.268205
$885$		0			0
$886$	−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	$-0.0635303\pi$
$888$	4.70519e15	−	1.15100e16i	0.285961	−	0.699526i
$889$			1.53851e14i			0.00929270i
$890$		0			0
$891$	−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
$895$		0			0
$896$			7.38229e14i			0.0427068i
$897$	−1.60792e16	−	6.57305e15i	−0.924498	−	0.377928i
$898$	5.17457e14	−	5.17457e14i	0.0295702	−	0.0295702i
$899$	4.03800e16			2.29344
$900$		0			0
$901$	1.45913e16			0.818670
$902$	7.22300e14	−	7.22300e14i	0.0402793	−	0.0402793i
$903$	8.60964e14	+	3.51955e14i	0.0477202	+	0.0195077i
$904$			6.68147e15i			0.368083i
$905$		0			0
$906$	2.05171e16	−	8.61010e15i	1.11663	−	0.468601i
$907$	2.67667e15	+	2.67667e15i	0.144796	+	0.144796i	0.775789	−	0.630993i	$-0.217352\pi$
$907$	2.67667e15	+	2.67667e15i	0.144796	+	0.144796i	−0.630993	+	0.775789i	$0.717352\pi$
$908$	6.05979e15	+	6.05979e15i	0.325826	+	0.325826i
$909$	3.43246e14	−	3.49671e14i	0.0183444	−	0.0186878i
$910$		0			0
$911$		−	1.46086e16i		−	0.771360i	−0.922633	−	0.385680i	$-0.873967\pi$
$911$		−	1.46086e16i		−	0.771360i	0.922633	−	0.385680i	$-0.126033\pi$
$912$	−3.80581e15	+	9.30990e15i	−0.199745	+	0.488622i
$913$	6.79011e15	−	6.79011e15i	0.354232	−	0.354232i
$914$	3.26713e15			0.169419
$915$		0			0
$916$	−7.80088e15			−0.399686
$917$	−1.58619e15	+	1.58619e15i	−0.0807839	+	0.0807839i
$918$	8.03130e15	−	3.45831e15i	0.406585	−	0.175077i
$919$		−	1.66108e16i		−	0.835901i	−0.908470	−	0.417950i	$-0.862749\pi$
$919$		−	1.66108e16i		−	0.835901i	0.908470	−	0.417950i	$-0.137251\pi$
$920$		0			0
$921$	−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
$925$		0			0
$926$			1.91878e16i			0.926116i
$927$	9.30039e15	−	8.62412e13i	0.446234	−	0.00413786i
$928$	−1.30076e16	+	1.30076e16i	−0.620414	+	0.620414i
$929$	−3.86131e16			−1.83083			−0.915416	−	0.402510i	$-0.868138\pi$
$929$	−3.86131e16			−1.83083			−0.915416	+	0.402510i	$0.868138\pi$
$930$		0			0
$931$	−1.96212e16			−0.919396
$932$	−5.46666e15	+	5.46666e15i	−0.254644	+	0.254644i
$933$	−1.43226e16	+	3.50364e16i	−0.663243	+	1.62245i
$934$		−	2.86215e15i		−	0.131760i
$935$		0			0
$936$	2.53959e16	+	2.49293e16i	1.15544	+	1.13421i
$937$	−2.13328e16	−	2.13328e16i	−0.964895	−	0.964895i	0.0345091	−	0.999404i	$-0.489013\pi$
$937$	−2.13328e16	−	2.13328e16i	−0.964895	−	0.964895i	−0.999404	+	0.0345091i	$0.989013\pi$
$938$	4.03900e15	+	4.03900e15i	0.181618	+	0.181618i
$939$	−1.59953e16	+	6.71251e15i	−0.715041	+	0.300071i
$940$		0			0
$941$		−	1.40599e16i		−	0.621213i	−0.950539	−	0.310606i	$-0.899468\pi$
$941$		−	1.40599e16i		−	0.621213i	0.950539	−	0.310606i	$-0.100532\pi$
$942$	2.70399e16	+	1.10537e16i	1.18775	+	0.485543i
$943$	1.90061e15	−	1.90061e15i	0.0830002	−	0.0830002i
$944$	1.10030e16			0.477709
$945$		0			0
$946$	−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	$0.985738\pi$
$948$	1.60245e15	+	6.55069e14i	0.0679733	+	0.0277870i
$949$		−	6.69437e16i		−	2.82322i
$950$		0			0
$951$	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
$955$		0			0
$956$		−	1.15831e15i		−	0.0469144i
$957$	−5.18747e15	+	1.26897e16i	−0.208901	+	0.511019i
$958$	1.68137e16	−	1.68137e16i	0.673212	−	0.673212i
$959$	−7.24501e13			−0.00288428
$960$		0			0
$961$	4.43921e16			1.74714
$962$	−1.52382e16	+	1.52382e16i	−0.596307	+	0.596307i
$963$	1.89326e16	−	1.75560e14i	0.736659	−	0.00683094i
$964$			9.46337e15i			0.366119i
$965$		0			0
$966$	9.73053e14	+	2.31869e15i	0.0372188	+	0.0886888i
$967$	−9.28422e15	−	9.28422e15i	−0.353102	−	0.353102i	0.508161	−	0.861262i	$-0.330326\pi$
$967$	−9.28422e15	−	9.28422e15i	−0.353102	−	0.353102i	−0.861262	+	0.508161i	$0.830326\pi$
$968$	−1.71157e16	−	1.71157e16i	−0.647262	−	0.647262i
$969$	5.29007e15	+	1.26057e16i	0.198921	+	0.474010i
$970$		0			0
$971$		−	4.65625e15i		−	0.173113i	−0.996247	−	0.0865567i	$-0.972414\pi$
$971$		−	4.65625e15i		−	0.173113i	0.996247	−	0.0865567i	$-0.0275864\pi$
$972$	8.39369e15	+	3.25095e15i	0.310305	+	0.120184i
$973$	2.52645e15	−	2.52645e15i	0.0928730	−	0.0928730i
$974$	−2.39612e15			−0.0875860
$975$		0			0
$976$	−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	$0.311204\pi$
$978$	1.69372e15	−	4.14324e15i	0.0605311	−	0.148073i
$979$			2.00054e16i			0.710956i
$980$		0			0
$981$	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
$985$		0			0
$986$		−	1.79249e16i		−	0.612541i
$987$	4.03936e15	+	1.65126e15i	0.137268	+	0.0561140i
$988$	−9.82268e15	+	9.82268e15i	−0.331946	+	0.331946i
$989$	−5.87557e15			−0.197456
$990$		0			0
$991$	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
$993$	−8.74718e15	−	3.57578e15i	−0.287506	−	0.117530i
$994$			2.83445e15i			0.0926497i
$995$		0			0
$996$	−1.19178e16	+	5.00139e15i	−0.385276	+	0.161683i
$997$	1.28655e15	+	1.28655e15i	0.0413621	+	0.0413621i	0.727485	−	0.686123i	$-0.240689\pi$
$997$	1.28655e15	+	1.28655e15i	0.0413621	+	0.0413621i	−0.686123	+	0.727485i	$0.740689\pi$
$998$	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	75.12.e.d.32.7		40
3.2	odd	2	inner	75.12.e.d.32.14		40
5.2	odd	4		15.12.e.a.8.7	yes	40
5.3	odd	4	inner	75.12.e.d.68.14		40
5.4	even	2		15.12.e.a.2.14	yes	40
15.2	even	4		15.12.e.a.8.14	yes	40
15.8	even	4	inner	75.12.e.d.68.7		40
15.14	odd	2		15.12.e.a.2.7	✓	40

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	75.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-26.1390 + 26.1390i) q^{2} +(-389.593 - 159.262i) q^{3} +681.505i q^{4} +(14346.5 - 6020.60i) q^{6} +(-5513.09 - 5513.09i) q^{7} +(-71346.5 - 71346.5i) q^{8} +(126418. + 124095. i) q^{9} +O(q^{10})\)	\(q+(-26.1390 + 26.1390i) q^{2} +(-389.593 - 159.262i) q^{3} +681.505i q^{4} +(14346.5 - 6020.60i) q^{6} +(-5513.09 - 5513.09i) q^{7} +(-71346.5 - 71346.5i) q^{8} +(126418. + 124095. i) q^{9} +213111. i q^{11} +(108538. - 265509. i) q^{12} +(-1.40784e6 + 1.40784e6i) q^{13} +288214. q^{14} +2.33413e6 q^{16} +(2.24338e6 - 2.24338e6i) q^{17} +(-6.54816e6 + 60720.1i) q^{18} -1.02378e7i q^{19} +(1.26983e6 + 3.02589e6i) q^{21} +(-5.57051e6 - 5.57051e6i) q^{22} +(-1.46579e7 - 1.46579e7i) q^{23} +(1.64333e7 + 3.91589e7i) q^{24} -7.35989e7i q^{26} +(-2.94878e7 - 6.84801e7i) q^{27} +(3.75720e6 - 3.75720e6i) q^{28} -1.52840e8 q^{29} -2.64198e8 q^{31} +(8.51058e7 - 8.51058e7i) q^{32} +(3.39406e7 - 8.30265e7i) q^{33} +1.17279e8i q^{34} +(-8.45713e7 + 8.61545e7i) q^{36} +(-2.07043e8 - 2.07043e8i) q^{37} +(2.67607e8 + 2.67607e8i) q^{38} +(7.72699e8 - 3.24268e8i) q^{39} +1.29665e8i q^{41} +(-1.12286e8 - 4.59016e7i) q^{42} +(2.00424e8 - 2.00424e8i) q^{43} -1.45236e8 q^{44} +7.66285e8 q^{46} +(9.40322e8 - 9.40322e8i) q^{47} +(-9.09361e8 - 3.71740e8i) q^{48} -1.91654e9i q^{49} +(-1.23129e9 + 5.16718e8i) q^{51} +(-9.59448e8 - 9.59448e8i) q^{52} +(3.25209e9 + 3.25209e9i) q^{53} +(2.56079e9 + 1.01922e9i) q^{54} +7.86680e8i q^{56} +(-1.63050e9 + 3.98859e9i) q^{57} +(3.99508e9 - 3.99508e9i) q^{58} +4.71394e9 q^{59} -4.47029e9 q^{61} +(6.90587e9 - 6.90587e9i) q^{62} +(-1.28067e7 - 1.38110e9i) q^{63} +9.22947e9i q^{64} +(1.28306e9 + 3.05740e9i) q^{66} +(1.40139e10 + 1.40139e10i) q^{67} +(1.52887e9 + 1.52887e9i) q^{68} +(3.37615e9 + 8.04505e9i) q^{69} +9.83456e9i q^{71} +(-1.65736e8 - 1.78732e10i) q^{72} +(-2.37754e10 + 2.37754e10i) q^{73} +1.08238e10 q^{74} +6.97714e9 q^{76} +(1.17490e9 - 1.17490e9i) q^{77} +(-1.17215e10 + 2.86736e10i) q^{78} +6.03538e9i q^{79} +(5.81934e8 + 3.13757e10i) q^{81} +(-3.38931e9 - 3.38931e9i) q^{82} +(-3.18619e10 - 3.18619e10i) q^{83} +(-2.06216e9 + 8.65397e8i) q^{84} +1.04777e10i q^{86} +(5.95453e10 + 2.43416e10i) q^{87} +(1.52047e10 - 1.52047e10i) q^{88} +9.38732e10 q^{89} +1.55231e10 q^{91} +(9.98942e9 - 9.98942e9i) q^{92} +(1.02930e11 + 4.20768e10i) q^{93} +4.91582e10i q^{94} +(-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	\( 40 q - 504 q^{3} + 2940 q^{6} - 31504 q^{7} + 1714188 q^{12} + 3448472 q^{13} - 43202180 q^{16} - 3729120 q^{18} + 33570840 q^{21} + 21743260 q^{22} - 113282712 q^{27} - 253355948 q^{28} + 67990880 q^{31} + 563443560 q^{33} + 1116103980 q^{36} - 1292573224 q^{37} + 5132304780 q^{42} - 4012128208 q^{43} - 8170829920 q^{46} + 13847034876 q^{48} + 5424535440 q^{51} - 10287332704 q^{52} + 10576855656 q^{57} - 56277468420 q^{58} - 24994982320 q^{61} + 50371112832 q^{63} + 56311074600 q^{66} - 37314988144 q^{67} + 92983114440 q^{72} - 51361482568 q^{73} - 121004023440 q^{76} + 104085843000 q^{78} - 22936122360 q^{81} + 56747065840 q^{82} - 84564024000 q^{87} - 148338843420 q^{88} + 230876677280 q^{91} - 38932525008 q^{93} - 437860137180 q^{96} + 294950050616 q^{97}+O(q^{100}) \) 40 * q - 504 * q^3 + 2940 * q^6 - 31504 * q^7 + 1714188 * q^12 + 3448472 * q^13 - 43202180 * q^16 - 3729120 * q^18 + 33570840 * q^21 + 21743260 * q^22 - 113282712 * q^27 - 253355948 * q^28 + 67990880 * q^31 + 563443560 * q^33 + 1116103980 * q^36 - 1292573224 * q^37 + 5132304780 * q^42 - 4012128208 * q^43 - 8170829920 * q^46 + 13847034876 * q^48 + 5424535440 * q^51 - 10287332704 * q^52 + 10576855656 * q^57 - 56277468420 * q^58 - 24994982320 * q^61 + 50371112832 * q^63 + 56311074600 * q^66 - 37314988144 * q^67 + 92983114440 * q^72 - 51361482568 * q^73 - 121004023440 * q^76 + 104085843000 * q^78 - 22936122360 * q^81 + 56747065840 * q^82 - 84564024000 * q^87 - 148338843420 * q^88 + 230876677280 * q^91 - 38932525008 * q^93 - 437860137180 * q^96 + 294950050616 * q^97

Introduction

L-functions

Modular forms

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Database

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