LMFDB - Embedded newform 128.12.e.b.33.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,12,Mod(33,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("128.33");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	128.e (of order $4$, degree $2$, not 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:	$98.3479271116$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			33.1
Character	$\chi$	$=$	128.33
Dual form			128.12.e.b.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-585.540 - 585.540i) q^{3} +(6859.07 - 6859.07i) q^{5} -19914.8i q^{7} +508568. i q^{9} +O(q^{10})$	\(q+(-585.540 - 585.540i) q^{3} +(6859.07 - 6859.07i) q^{5} -19914.8i q^{7} +508568. i q^{9} +(96496.9 - 96496.9i) q^{11} +(674561. + 674561. i) q^{13} -8.03253e6 q^{15} +3.70861e6 q^{17} +(2.61985e6 + 2.61985e6i) q^{19} +(-1.16609e7 + 1.16609e7i) q^{21} -2.97611e7i q^{23} -4.52657e7i q^{25} +(1.94060e8 - 1.94060e8i) q^{27} +(-4.14366e7 - 4.14366e7i) q^{29} +6.07925e7 q^{31} -1.13006e8 q^{33} +(-1.36597e8 - 1.36597e8i) q^{35} +(4.37984e8 - 4.37984e8i) q^{37} -7.89965e8i q^{39} +1.20680e9i q^{41} +(1.45559e8 - 1.45559e8i) q^{43} +(3.48830e9 + 3.48830e9i) q^{45} +1.52664e9 q^{47} +1.58073e9 q^{49} +(-2.17154e9 - 2.17154e9i) q^{51} +(2.52787e9 - 2.52787e9i) q^{53} -1.32376e9i q^{55} -3.06806e9i q^{57} +(4.54873e9 - 4.54873e9i) q^{59} +(-9.96512e7 - 9.96512e7i) q^{61} +1.01280e10 q^{63} +9.25373e9 q^{65} +(-7.32144e9 - 7.32144e9i) q^{67} +(-1.74263e10 + 1.74263e10i) q^{69} +1.31476e9i q^{71} -2.59505e9i q^{73} +(-2.65049e10 + 2.65049e10i) q^{75} +(-1.92171e9 - 1.92171e9i) q^{77} -4.08802e9 q^{79} -1.37169e11 q^{81} +(-3.03277e10 - 3.03277e10i) q^{83} +(2.54376e10 - 2.54376e10i) q^{85} +4.85256e10i q^{87} -5.68675e10i q^{89} +(1.34337e10 - 1.34337e10i) q^{91} +(-3.55964e10 - 3.55964e10i) q^{93} +3.59395e10 q^{95} -5.73135e10 q^{97} +(4.90752e10 + 4.90752e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 2 q^{3} + 2 q^{5}+O(q^{10}) $ 42 * q + 2 * q^3 + 2 * q^5	$ 42 q + 2 q^{3} + 2 q^{5} + 540846 q^{11} + 2 q^{13} - 6075004 q^{15} - 4 q^{17} + 11291290 q^{19} - 354292 q^{21} + 66463304 q^{27} - 77673206 q^{29} + 343549808 q^{31} - 4 q^{33} + 434731684 q^{35} + 522762058 q^{37} - 3824193658 q^{43} - 97301954 q^{45} - 4586900144 q^{47} - 8474257474 q^{49} - 7074245796 q^{51} + 2100608058 q^{53} - 955824746 q^{59} - 2150827022 q^{61} + 27758037828 q^{63} - 1884965292 q^{65} + 3186519018 q^{67} + 16193060732 q^{69} - 28890034486 q^{75} + 22711870540 q^{77} + 48011833792 q^{79} - 90656394430 q^{81} - 55713221118 q^{83} + 84575506252 q^{85} + 147369662716 q^{91} + 69689773328 q^{93} + 375702304500 q^{95} - 4 q^{97} + 286271331106 q^{99}+O(q^{100}) $ 42 * q + 2 * q^3 + 2 * q^5 + 540846 * q^11 + 2 * q^13 - 6075004 * q^15 - 4 * q^17 + 11291290 * q^19 - 354292 * q^21 + 66463304 * q^27 - 77673206 * q^29 + 343549808 * q^31 - 4 * q^33 + 434731684 * q^35 + 522762058 * q^37 - 3824193658 * q^43 - 97301954 * q^45 - 4586900144 * q^47 - 8474257474 * q^49 - 7074245796 * q^51 + 2100608058 * q^53 - 955824746 * q^59 - 2150827022 * q^61 + 27758037828 * q^63 - 1884965292 * q^65 + 3186519018 * q^67 + 16193060732 * q^69 - 28890034486 * q^75 + 22711870540 * q^77 + 48011833792 * q^79 - 90656394430 * q^81 - 55713221118 * q^83 + 84575506252 * q^85 + 147369662716 * q^91 + 69689773328 * q^93 + 375702304500 * q^95 - 4 * q^97 + 286271331106 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−585.540	−	585.540i	−1.39120	−	1.39120i	−0.822644	−	0.568557i	$-0.807502\pi$
$3$	−585.540	−	585.540i	−1.39120	−	1.39120i	−0.568557	−	0.822644i	$-0.692498\pi$
$4$		0			0
$5$	6859.07	−	6859.07i	0.981591	−	0.981591i	−0.0182428	−	0.999834i	$-0.505807\pi$
$5$	6859.07	−	6859.07i	0.981591	−	0.981591i	0.999834	+	0.0182428i	$0.00580719\pi$
$6$		0			0
$7$		−	19914.8i		−	0.447854i	−0.974606	−	0.223927i	$-0.928112\pi$
$7$		−	19914.8i		−	0.447854i	0.974606	−	0.223927i	$-0.0718877\pi$
$8$		0			0
$9$			508568.i			2.87088i
$10$		0			0
$11$	96496.9	−	96496.9i	0.180656	−	0.180656i	−0.610985	−	0.791642i	$-0.709227\pi$
$11$	96496.9	−	96496.9i	0.180656	−	0.180656i	0.791642	+	0.610985i	$0.209227\pi$
$12$		0			0
$13$	674561.	+	674561.i	0.503887	+	0.503887i	0.912643	−	0.408757i	$-0.134038\pi$
$13$	674561.	+	674561.i	0.503887	+	0.503887i	−0.408757	+	0.912643i	$0.634038\pi$
$14$		0			0
$15$	−8.03253e6			−2.73118
$16$		0			0
$17$	3.70861e6			0.633494			0.316747	−	0.948510i	$-0.397409\pi$
$17$	3.70861e6			0.633494			0.316747	+	0.948510i	$0.397409\pi$
$18$		0			0
$19$	2.61985e6	+	2.61985e6i	0.242735	+	0.242735i	0.817981	−	0.575246i	$-0.195094\pi$
$19$	2.61985e6	+	2.61985e6i	0.242735	+	0.242735i	−0.575246	+	0.817981i	$0.695094\pi$
$20$		0			0
$21$	−1.16609e7	+	1.16609e7i	−0.623055	+	0.623055i
$22$		0			0
$23$		−	2.97611e7i		−	0.964153i	−0.876129	−	0.482077i	$-0.839883\pi$
$23$		−	2.97611e7i		−	0.964153i	0.876129	−	0.482077i	$-0.160117\pi$
$24$		0			0
$25$		−	4.52657e7i		−	0.927041i
$26$		0			0
$27$	1.94060e8	−	1.94060e8i	2.60277	−	2.60277i
$28$		0			0
$29$	−4.14366e7	−	4.14366e7i	−0.375142	−	0.375142i	0.494204	−	0.869346i	$-0.335459\pi$
$29$	−4.14366e7	−	4.14366e7i	−0.375142	−	0.375142i	−0.869346	+	0.494204i	$0.835459\pi$
$30$		0			0
$31$	6.07925e7			0.381382			0.190691	−	0.981650i	$-0.438927\pi$
$31$	6.07925e7			0.381382			0.190691	+	0.981650i	$0.438927\pi$
$32$		0			0
$33$	−1.13006e8			−0.502659
$34$		0			0
$35$	−1.36597e8	−	1.36597e8i	−0.439609	−	0.439609i
$36$		0			0
$37$	4.37984e8	−	4.37984e8i	1.03836	−	1.03836i	0.0391281	−	0.999234i	$-0.487542\pi$
$37$	4.37984e8	−	4.37984e8i	1.03836	−	1.03836i	0.999234	−	0.0391281i	$-0.0124580\pi$
$38$		0			0
$39$		−	7.89965e8i		−	1.40201i
$40$		0			0
$41$			1.20680e9i			1.62677i	0.581729	+	0.813383i	$0.302376\pi$
$41$			1.20680e9i			1.62677i	−0.581729	+	0.813383i	$0.697624\pi$
$42$		0			0
$43$	1.45559e8	−	1.45559e8i	0.150995	−	0.150995i	−0.627567	−	0.778562i	$-0.715949\pi$
$43$	1.45559e8	−	1.45559e8i	0.150995	−	0.150995i	0.778562	+	0.627567i	$0.215949\pi$
$44$		0			0
$45$	3.48830e9	+	3.48830e9i	2.81803	+	2.81803i
$46$		0			0
$47$	1.52664e9			0.970953			0.485476	−	0.874250i	$-0.338646\pi$
$47$	1.52664e9			0.970953			0.485476	+	0.874250i	$0.338646\pi$
$48$		0			0
$49$	1.58073e9			0.799427
$50$		0			0
$51$	−2.17154e9	−	2.17154e9i	−0.881317	−	0.881317i
$52$		0			0
$53$	2.52787e9	−	2.52787e9i	0.830306	−	0.830306i	−0.157252	−	0.987558i	$-0.550264\pi$
$53$	2.52787e9	−	2.52787e9i	0.830306	−	0.830306i	0.987558	+	0.157252i	$0.0502636\pi$
$54$		0			0
$55$		−	1.32376e9i		−	0.354661i
$56$		0			0
$57$		−	3.06806e9i		−	0.675386i
$58$		0			0
$59$	4.54873e9	−	4.54873e9i	0.828332	−	0.828332i	−0.158954	−	0.987286i	$-0.550812\pi$
$59$	4.54873e9	−	4.54873e9i	0.828332	−	0.828332i	0.987286	+	0.158954i	$0.0508121\pi$
$60$		0			0
$61$	−9.96512e7	−	9.96512e7i	−0.0151067	−	0.0151067i	0.699513	−	0.714620i	$-0.253400\pi$
$61$	−9.96512e7	−	9.96512e7i	−0.0151067	−	0.0151067i	−0.714620	+	0.699513i	$0.753400\pi$
$62$		0			0
$63$	1.01280e10			1.28573
$64$		0			0
$65$	9.25373e9			0.989221
$66$		0			0
$67$	−7.32144e9	−	7.32144e9i	−0.662498	−	0.662498i	0.293470	−	0.955968i	$-0.405190\pi$
$67$	−7.32144e9	−	7.32144e9i	−0.662498	−	0.662498i	−0.955968	+	0.293470i	$0.905190\pi$
$68$		0			0
$69$	−1.74263e10	+	1.74263e10i	−1.34133	+	1.34133i
$70$		0			0
$71$			1.31476e9i			0.0864822i	0.999065	+	0.0432411i	$0.0137684\pi$
$71$			1.31476e9i			0.0864822i	−0.999065	+	0.0432411i	$0.986232\pi$
$72$		0			0
$73$		−	2.59505e9i		−	0.146511i	−0.997313	−	0.0732556i	$-0.976661\pi$
$73$		−	2.59505e9i		−	0.146511i	0.997313	−	0.0732556i	$-0.0233389\pi$
$74$		0			0
$75$	−2.65049e10	+	2.65049e10i	−1.28970	+	1.28970i
$76$		0			0
$77$	−1.92171e9	−	1.92171e9i	−0.0809077	−	0.0809077i
$78$		0			0
$79$	−4.08802e9			−0.149473			−0.0747367	−	0.997203i	$-0.523812\pi$
$79$	−4.08802e9			−0.149473			−0.0747367	+	0.997203i	$0.523812\pi$
$80$		0			0
$81$	−1.37169e11			−4.37107
$82$		0			0
$83$	−3.03277e10	−	3.03277e10i	−0.845103	−	0.845103i	0.144415	−	0.989517i	$-0.453870\pi$
$83$	−3.03277e10	−	3.03277e10i	−0.845103	−	0.845103i	−0.989517	+	0.144415i	$0.953870\pi$
$84$		0			0
$85$	2.54376e10	−	2.54376e10i	0.621832	−	0.621832i
$86$		0			0
$87$			4.85256e10i			1.04379i
$88$		0			0
$89$		−	5.68675e10i		−	1.07949i	−0.841828	−	0.539746i	$-0.818520\pi$
$89$		−	5.68675e10i		−	1.07949i	0.841828	−	0.539746i	$-0.181480\pi$
$90$		0			0
$91$	1.34337e10	−	1.34337e10i	0.225668	−	0.225668i
$92$		0			0
$93$	−3.55964e10	−	3.55964e10i	−0.530579	−	0.530579i
$94$		0			0
$95$	3.59395e10			0.476532
$96$		0			0
$97$	−5.73135e10			−0.677661			−0.338830	−	0.940847i	$-0.610031\pi$
$97$	−5.73135e10			−0.677661			−0.338830	+	0.940847i	$0.610031\pi$
$98$		0			0
$99$	4.90752e10	+	4.90752e10i	0.518643	+	0.518643i
$100$		0			0
$101$	−3.62044e10	+	3.62044e10i	−0.342763	+	0.342763i	−0.857405	−	0.514642i	$-0.827925\pi$
$101$	−3.62044e10	+	3.62044e10i	−0.342763	+	0.342763i	0.514642	+	0.857405i	$0.327925\pi$
$102$		0			0
$103$		−	9.12485e10i		−	0.775570i	−0.921750	−	0.387785i	$-0.873240\pi$
$103$		−	9.12485e10i		−	0.775570i	0.921750	−	0.387785i	$-0.126760\pi$
$104$		0			0
$105$			1.59966e11i			1.22317i
$106$		0			0
$107$	−7.80580e10	+	7.80580e10i	−0.538030	+	0.538030i	−0.922950	−	0.384920i	$-0.874229\pi$
$107$	−7.80580e10	+	7.80580e10i	−0.538030	+	0.538030i	0.384920	+	0.922950i	$0.374229\pi$
$108$		0			0
$109$	−3.50084e9	−	3.50084e9i	−0.0217935	−	0.0217935i	0.696126	−	0.717920i	$-0.254905\pi$
$109$	−3.50084e9	−	3.50084e9i	−0.0217935	−	0.0217935i	−0.717920	+	0.696126i	$0.754905\pi$
$110$		0			0
$111$	−5.12915e11			−2.88914
$112$		0			0
$113$	3.13967e11			1.60307			0.801534	−	0.597949i	$-0.204018\pi$
$113$	3.13967e11			1.60307			0.801534	+	0.597949i	$0.204018\pi$
$114$		0			0
$115$	−2.04134e11	−	2.04134e11i	−0.946404	−	0.946404i
$116$		0			0
$117$	−3.43060e11	+	3.43060e11i	−1.44660	+	1.44660i
$118$		0			0
$119$		−	7.38562e10i		−	0.283713i
$120$		0			0
$121$			2.66688e11i			0.934727i
$122$		0			0
$123$	7.06631e11	−	7.06631e11i	2.26316	−	2.26316i
$124$		0			0
$125$	2.44352e10	+	2.44352e10i	0.0716160	+	0.0716160i
$126$		0			0
$127$	6.20048e11			1.66535			0.832673	−	0.553765i	$-0.186809\pi$
$127$	6.20048e11			1.66535			0.832673	+	0.553765i	$0.186809\pi$
$128$		0			0
$129$	−1.70462e11			−0.420130
$130$		0			0
$131$	−1.33237e9	−	1.33237e9i	−0.00301739	−	0.00301739i	0.705596	−	0.708614i	$-0.250679\pi$
$131$	−1.33237e9	−	1.33237e9i	−0.00301739	−	0.00301739i	−0.708614	+	0.705596i	$0.750679\pi$
$132$		0			0
$133$	5.21738e10	−	5.21738e10i	0.108710	−	0.108710i
$134$		0			0
$135$		−	2.66215e12i		−	5.10971i
$136$		0			0
$137$		−	2.80780e11i		−	0.497054i	−0.968625	−	0.248527i	$-0.920054\pi$
$137$		−	2.80780e11i		−	0.497054i	0.968625	−	0.248527i	$-0.0799464\pi$
$138$		0			0
$139$	−1.98123e11	+	1.98123e11i	−0.323857	+	0.323857i	−0.850245	−	0.526388i	$-0.823546\pi$
$139$	−1.98123e11	+	1.98123e11i	−0.323857	+	0.323857i	0.526388	+	0.850245i	$0.323546\pi$
$140$		0			0
$141$	−8.93909e11	−	8.93909e11i	−1.35079	−	1.35079i
$142$		0			0
$143$	1.30186e11			0.182061
$144$		0			0
$145$	−5.68434e11			−0.736471
$146$		0			0
$147$	−9.25580e11	−	9.25580e11i	−1.11216	−	1.11216i
$148$		0			0
$149$	−6.80120e11	+	6.80120e11i	−0.758685	+	0.758685i	−0.976083	−	0.217398i	$-0.930243\pi$
$149$	−6.80120e11	+	6.80120e11i	−0.758685	+	0.758685i	0.217398	+	0.976083i	$0.430243\pi$
$150$		0			0
$151$			1.24483e12i			1.29044i	0.763996	+	0.645221i	$0.223235\pi$
$151$			1.24483e12i			1.29044i	−0.763996	+	0.645221i	$0.776765\pi$
$152$		0			0
$153$			1.88608e12i			1.81868i
$154$		0			0
$155$	4.16980e11	−	4.16980e11i	0.374361	−	0.374361i
$156$		0			0
$157$	5.32516e11	+	5.32516e11i	0.445538	+	0.445538i	0.893868	−	0.448330i	$-0.147981\pi$
$157$	5.32516e11	+	5.32516e11i	0.445538	+	0.445538i	−0.448330	+	0.893868i	$0.647981\pi$
$158$		0			0
$159$	−2.96035e12			−2.31025
$160$		0			0
$161$	−5.92686e11			−0.431800
$162$		0			0
$163$	2.47550e9	+	2.47550e9i	0.00168512	+	0.00168512i	0.707949	−	0.706264i	$-0.249621\pi$
$163$	2.47550e9	+	2.47550e9i	0.00168512	+	0.00168512i	−0.706264	+	0.707949i	$0.749621\pi$
$164$		0			0
$165$	−7.75114e11	+	7.75114e11i	−0.493405	+	0.493405i
$166$		0			0
$167$			1.98829e12i			1.18451i	0.805751	+	0.592254i	$0.201762\pi$
$167$			1.98829e12i			1.18451i	−0.805751	+	0.592254i	$0.798238\pi$
$168$		0			0
$169$		−	8.82095e11i		−	0.492197i
$170$		0			0
$171$	−1.33237e12	+	1.33237e12i	−0.696862	+	0.696862i
$172$		0			0
$173$	−2.52033e11	−	2.52033e11i	−0.123653	−	0.123653i	0.642572	−	0.766225i	$-0.277867\pi$
$173$	−2.52033e11	−	2.52033e11i	−0.123653	−	0.123653i	−0.766225	+	0.642572i	$0.777867\pi$
$174$		0			0
$175$	−9.01456e11			−0.415179
$176$		0			0
$177$	−5.32693e12			−2.30475
$178$		0			0
$179$	1.45805e12	+	1.45805e12i	0.593037	+	0.593037i	0.938451	−	0.345414i	$-0.112261\pi$
$179$	1.45805e12	+	1.45805e12i	0.593037	+	0.593037i	−0.345414	+	0.938451i	$0.612261\pi$
$180$		0			0
$181$	−1.35746e12	+	1.35746e12i	−0.519392	+	0.519392i	−0.917387	−	0.397996i	$-0.869706\pi$
$181$	−1.35746e12	+	1.35746e12i	−0.519392	+	0.519392i	0.397996	+	0.917387i	$0.369706\pi$
$182$		0			0
$183$			1.16700e11i			0.0420328i
$184$		0			0
$185$		−	6.00833e12i		−	2.03849i
$186$		0			0
$187$	3.57869e11	−	3.57869e11i	0.114445	−	0.114445i
$188$		0			0
$189$	−3.86467e12	−	3.86467e12i	−1.16566	−	1.16566i
$190$		0			0
$191$	2.60506e12			0.741539			0.370770	−	0.928725i	$-0.379094\pi$
$191$	2.60506e12			0.741539			0.370770	+	0.928725i	$0.379094\pi$
$192$		0			0
$193$	−2.54172e12			−0.683222			−0.341611	−	0.939841i	$-0.610973\pi$
$193$	−2.54172e12			−0.683222			−0.341611	+	0.939841i	$0.610973\pi$
$194$		0			0
$195$	−5.41843e12	−	5.41843e12i	−1.37620	−	1.37620i
$196$		0			0
$197$	2.85642e12	−	2.85642e12i	0.685896	−	0.685896i	−0.275426	−	0.961322i	$-0.588819\pi$
$197$	2.85642e12	−	2.85642e12i	0.685896	−	0.685896i	0.961322	+	0.275426i	$0.0888190\pi$
$198$		0			0
$199$		−	3.66476e12i		−	0.832442i	−0.909263	−	0.416221i	$-0.863354\pi$
$199$		−	3.66476e12i		−	0.832442i	0.909263	−	0.416221i	$-0.136646\pi$
$200$		0			0
$201$			8.57399e12i			1.84334i
$202$		0			0
$203$	−8.25201e11	+	8.25201e11i	−0.168009	+	0.168009i
$204$		0			0
$205$	8.27755e12	+	8.27755e12i	1.59682	+	1.59682i
$206$		0			0
$207$	1.51355e13			2.76797
$208$		0			0
$209$	5.05615e11			0.0877032
$210$		0			0
$211$	−1.86773e12	−	1.86773e12i	−0.307441	−	0.307441i	0.536475	−	0.843916i	$-0.319755\pi$
$211$	−1.86773e12	−	1.86773e12i	−0.307441	−	0.307441i	−0.843916	+	0.536475i	$0.819755\pi$
$212$		0			0
$213$	7.69847e11	−	7.69847e11i	0.120314	−	0.120314i
$214$		0			0
$215$		−	1.99680e12i		−	0.296431i
$216$		0			0
$217$		−	1.21067e12i		−	0.170804i
$218$		0			0
$219$	−1.51951e12	+	1.51951e12i	−0.203826	+	0.203826i
$220$		0			0
$221$	2.50168e12	+	2.50168e12i	0.319209	+	0.319209i
$222$		0			0
$223$	−1.26372e13			−1.53453			−0.767263	−	0.641332i	$-0.778382\pi$
$223$	−1.26372e13			−1.53453			−0.767263	+	0.641332i	$0.778382\pi$
$224$		0			0
$225$	2.30207e13			2.66142
$226$		0			0
$227$	−6.38980e12	−	6.38980e12i	−0.703632	−	0.703632i	0.261557	−	0.965188i	$-0.415764\pi$
$227$	−6.38980e12	−	6.38980e12i	−0.703632	−	0.703632i	−0.965188	+	0.261557i	$0.915764\pi$
$228$		0			0
$229$	−1.21476e12	+	1.21476e12i	−0.127466	+	0.127466i	−0.767962	−	0.640496i	$-0.778729\pi$
$229$	−1.21476e12	+	1.21476e12i	−0.127466	+	0.127466i	0.640496	+	0.767962i	$0.278729\pi$
$230$		0			0
$231$			2.25048e12i			0.225118i
$232$		0			0
$233$		−	1.65378e13i		−	1.57769i	−0.614595	−	0.788843i	$-0.710681\pi$
$233$		−	1.65378e13i		−	1.57769i	0.614595	−	0.788843i	$-0.289319\pi$
$234$		0			0
$235$	1.04713e13	−	1.04713e13i	0.953078	−	0.953078i
$236$		0			0
$237$	2.39370e12	+	2.39370e12i	0.207948	+	0.207948i
$238$		0			0
$239$	9.34650e12			0.775283			0.387642	−	0.921810i	$-0.373290\pi$
$239$	9.34650e12			0.775283			0.387642	+	0.921810i	$0.373290\pi$
$240$		0			0
$241$	1.11589e13			0.884150			0.442075	−	0.896978i	$-0.354243\pi$
$241$	1.11589e13			0.884150			0.442075	+	0.896978i	$0.354243\pi$
$242$		0			0
$243$	4.59407e13	+	4.59407e13i	3.47827	+	3.47827i
$244$		0			0
$245$	1.08423e13	−	1.08423e13i	0.784710	−	0.784710i
$246$		0			0
$247$			3.53450e12i			0.244622i
$248$		0			0
$249$			3.55161e13i			2.35142i
$250$		0			0
$251$	8.13313e12	−	8.13313e12i	0.515291	−	0.515291i	−0.400852	−	0.916143i	$-0.631286\pi$
$251$	8.13313e12	−	8.13313e12i	0.515291	−	0.515291i	0.916143	+	0.400852i	$0.131286\pi$
$252$		0			0
$253$	−2.87185e12	−	2.87185e12i	−0.174180	−	0.174180i
$254$		0			0
$255$	−2.97895e13			−1.73019
$256$		0			0
$257$	1.40965e13			0.784294			0.392147	−	0.919903i	$-0.371732\pi$
$257$	1.40965e13			0.784294			0.392147	+	0.919903i	$0.371732\pi$
$258$		0			0
$259$	−8.72236e12	−	8.72236e12i	−0.465035	−	0.465035i
$260$		0			0
$261$	2.10733e13	−	2.10733e13i	1.07699	−	1.07699i
$262$		0			0
$263$			3.74224e13i			1.83390i	0.399003	+	0.916950i	$0.369356\pi$
$263$			3.74224e13i			1.83390i	−0.399003	+	0.916950i	$0.630644\pi$
$264$		0			0
$265$		−	3.46778e13i		−	1.63004i
$266$		0			0
$267$	−3.32982e13	+	3.32982e13i	−1.50179	+	1.50179i
$268$		0			0
$269$	−6.31416e12	−	6.31416e12i	−0.273324	−	0.273324i	0.557113	−	0.830437i	$-0.311909\pi$
$269$	−6.31416e12	−	6.31416e12i	−0.273324	−	0.273324i	−0.830437	+	0.557113i	$0.811909\pi$
$270$		0			0
$271$	−3.31124e12			−0.137613			−0.0688064	−	0.997630i	$-0.521919\pi$
$271$	−3.31124e12			−0.137613			−0.0688064	+	0.997630i	$0.521919\pi$
$272$		0			0
$273$	−1.57320e13			−0.627898
$274$		0			0
$275$	−4.36799e12	−	4.36799e12i	−0.167476	−	0.167476i
$276$		0			0
$277$	−3.06698e13	+	3.06698e13i	−1.12998	+	1.12998i	−0.139803	+	0.990179i	$0.544647\pi$
$277$	−3.06698e13	+	3.06698e13i	−1.12998	+	1.12998i	−0.990179	+	0.139803i	$0.955353\pi$
$278$		0			0
$279$			3.09171e13i			1.09490i
$280$		0			0
$281$			1.12496e13i			0.383046i	0.981488	+	0.191523i	$0.0613427\pi$
$281$			1.12496e13i			0.383046i	−0.981488	+	0.191523i	$0.938657\pi$
$282$		0			0
$283$	−3.47187e13	+	3.47187e13i	−1.13694	+	1.13694i	−0.147946	+	0.988995i	$0.547266\pi$
$283$	−3.47187e13	+	3.47187e13i	−1.13694	+	1.13694i	−0.988995	+	0.147946i	$0.952734\pi$
$284$		0			0
$285$	−2.10440e13	−	2.10440e13i	−0.662952	−	0.662952i
$286$		0			0
$287$	2.40332e13			0.728553
$288$		0			0
$289$	−2.05181e13			−0.598686
$290$		0			0
$291$	3.35594e13	+	3.35594e13i	0.942763	+	0.942763i
$292$		0			0
$293$	4.28304e13	−	4.28304e13i	1.15873	−	1.15873i	0.173975	−	0.984750i	$-0.444339\pi$
$293$	4.28304e13	−	4.28304e13i	1.15873	−	1.15873i	0.984750	−	0.173975i	$-0.0556613\pi$
$294$		0			0
$295$		−	6.24002e13i		−	1.62617i
$296$		0			0
$297$		−	3.74524e13i		−	0.940414i
$298$		0			0
$299$	2.00757e13	−	2.00757e13i	0.485824	−	0.485824i
$300$		0			0
$301$	−2.89878e12	−	2.89878e12i	−0.0676238	−	0.0676238i
$302$		0			0
$303$	4.23983e13			0.953705
$304$		0			0
$305$	−1.36703e12			−0.0296571
$306$		0			0
$307$	−5.00993e11	−	5.00993e11i	−0.0104851	−	0.0104851i	0.701845	−	0.712330i	$-0.252360\pi$
$307$	−5.00993e11	−	5.00993e11i	−0.0104851	−	0.0104851i	−0.712330	+	0.701845i	$0.752360\pi$
$308$		0			0
$309$	−5.34297e13	+	5.34297e13i	−1.07897	+	1.07897i
$310$		0			0
$311$			6.71357e13i			1.30849i	0.756282	+	0.654246i	$0.227014\pi$
$311$			6.71357e13i			1.30849i	−0.756282	+	0.654246i	$0.772986\pi$
$312$		0			0
$313$		−	1.16967e13i		−	0.220075i	−0.993927	−	0.110037i	$-0.964903\pi$
$313$		−	1.16967e13i		−	0.220075i	0.993927	−	0.110037i	$-0.0350971\pi$
$314$		0			0
$315$	6.94688e13	−	6.94688e13i	1.26207	−	1.26207i
$316$		0			0
$317$	−5.42552e13	−	5.42552e13i	−0.951952	−	0.951952i	0.0469451	−	0.998897i	$-0.485051\pi$
$317$	−5.42552e13	−	5.42552e13i	−0.951952	−	0.951952i	−0.998897	+	0.0469451i	$0.985051\pi$
$318$		0			0
$319$	−7.99701e12			−0.135543
$320$		0			0
$321$	9.14122e13			1.49702
$322$		0			0
$323$	9.71601e12	+	9.71601e12i	0.153771	+	0.153771i
$324$		0			0
$325$	3.05345e13	−	3.05345e13i	0.467123	−	0.467123i
$326$		0			0
$327$			4.09976e12i			0.0606381i
$328$		0			0
$329$		−	3.04027e13i		−	0.434845i
$330$		0			0
$331$	−9.47342e13	+	9.47342e13i	−1.31055	+	1.31055i	−0.389537	+	0.921011i	$0.627365\pi$
$331$	−9.47342e13	+	9.47342e13i	−1.31055	+	1.31055i	−0.921011	+	0.389537i	$0.872635\pi$
$332$		0			0
$333$	2.22745e14	+	2.22745e14i	2.98101	+	2.98101i
$334$		0			0
$335$	−1.00437e14			−1.30060
$336$		0			0
$337$	−2.48393e13			−0.311298			−0.155649	−	0.987812i	$-0.549747\pi$
$337$	−2.48393e13			−0.311298			−0.155649	+	0.987812i	$0.549747\pi$
$338$		0			0
$339$	−1.83840e14	−	1.83840e14i	−2.23019	−	2.23019i
$340$		0			0
$341$	5.86628e12	−	5.86628e12i	0.0688992	−	0.0688992i
$342$		0			0
$343$		−	7.08579e13i		−	0.805880i
$344$		0			0
$345$			2.39057e14i			2.63328i
$346$		0			0
$347$	4.05821e13	−	4.05821e13i	0.433035	−	0.433035i	−0.456625	−	0.889659i	$-0.650942\pi$
$347$	4.05821e13	−	4.05821e13i	0.433035	−	0.433035i	0.889659	+	0.456625i	$0.150942\pi$
$348$		0			0
$349$	5.40864e13	+	5.40864e13i	0.559175	+	0.559175i	0.929073	−	0.369897i	$-0.120607\pi$
$349$	5.40864e13	+	5.40864e13i	0.559175	+	0.559175i	−0.369897	+	0.929073i	$0.620607\pi$
$350$		0			0
$351$	2.61811e14			2.62300
$352$		0			0
$353$	1.19115e14			1.15666			0.578328	−	0.815805i	$-0.303706\pi$
$353$	1.19115e14			1.15666			0.578328	+	0.815805i	$0.303706\pi$
$354$		0			0
$355$	9.01806e12	+	9.01806e12i	0.0848901	+	0.0848901i
$356$		0			0
$357$	−4.32458e13	+	4.32458e13i	−0.394701	+	0.394701i
$358$		0			0
$359$		−	1.67025e14i		−	1.47830i	−0.673541	−	0.739150i	$-0.735228\pi$
$359$		−	1.67025e14i		−	1.47830i	0.673541	−	0.739150i	$-0.264772\pi$
$360$		0			0
$361$		−	1.02763e14i		−	0.882160i
$362$		0			0
$363$	1.56157e14	−	1.56157e14i	1.30039	−	1.30039i
$364$		0			0
$365$	−1.77997e13	−	1.77997e13i	−0.143814	−	0.143814i
$366$		0			0
$367$	−1.32967e14			−1.04251			−0.521255	−	0.853401i	$-0.674536\pi$
$367$	−1.32967e14			−1.04251			−0.521255	+	0.853401i	$0.674536\pi$
$368$		0			0
$369$	−6.13741e14			−4.67025
$370$		0			0
$371$	−5.03421e13	−	5.03421e13i	−0.371856	−	0.371856i
$372$		0			0
$373$	1.58936e14	−	1.58936e14i	1.13979	−	1.13979i	0.151297	−	0.988488i	$-0.451655\pi$
$373$	1.58936e14	−	1.58936e14i	1.13979	−	1.13979i	0.988488	−	0.151297i	$-0.0483450\pi$
$374$		0			0
$375$		−	2.86156e13i		−	0.199265i
$376$		0			0
$377$		−	5.59030e13i		−	0.378058i
$378$		0			0
$379$	−2.82445e12	+	2.82445e12i	−0.0185532	+	0.0185532i	−0.716323	−	0.697769i	$-0.754176\pi$
$379$	−2.82445e12	+	2.82445e12i	−0.0185532	+	0.0185532i	0.697769	+	0.716323i	$0.254176\pi$
$380$		0			0
$381$	−3.63063e14	−	3.63063e14i	−2.31683	−	2.31683i
$382$		0			0
$383$	−5.92249e13			−0.367207			−0.183604	−	0.983000i	$-0.558776\pi$
$383$	−5.92249e13			−0.367207			−0.183604	+	0.983000i	$0.558776\pi$
$384$		0			0
$385$	−2.63624e13			−0.158836
$386$		0			0
$387$	7.40268e13	+	7.40268e13i	0.433489	+	0.433489i
$388$		0			0
$389$	−2.33475e13	+	2.33475e13i	−0.132898	+	0.132898i	−0.770427	−	0.637529i	$-0.779957\pi$
$389$	−2.33475e13	+	2.33475e13i	−0.132898	+	0.132898i	0.637529	+	0.770427i	$0.279957\pi$
$390$		0			0
$391$		−	1.10372e14i		−	0.610785i
$392$		0			0
$393$			1.56031e12i			0.00839560i
$394$		0			0
$395$	−2.80400e13	+	2.80400e13i	−0.146722	+	0.146722i
$396$		0			0
$397$	−2.18990e13	−	2.18990e13i	−0.111449	−	0.111449i	0.649183	−	0.760632i	$-0.275111\pi$
$397$	−2.18990e13	−	2.18990e13i	−0.111449	−	0.111449i	−0.760632	+	0.649183i	$0.775111\pi$
$398$		0			0
$399$	−6.10997e13			−0.302474
$400$		0			0
$401$	7.84224e13			0.377699			0.188850	−	0.982006i	$-0.439524\pi$
$401$	7.84224e13			0.377699			0.188850	+	0.982006i	$0.439524\pi$
$402$		0			0
$403$	4.10082e13	+	4.10082e13i	0.192173	+	0.192173i
$404$		0			0
$405$	−9.40851e14	+	9.40851e14i	−4.29060	+	4.29060i
$406$		0			0
$407$		−	8.45282e13i		−	0.375174i
$408$		0			0
$409$			5.44125e13i			0.235083i	0.993068	+	0.117541i	$0.0375013\pi$
$409$			5.44125e13i			0.235083i	−0.993068	+	0.117541i	$0.962499\pi$
$410$		0			0
$411$	−1.64408e14	+	1.64408e14i	−0.691502	+	0.691502i
$412$		0			0
$413$	−9.05871e13	−	9.05871e13i	−0.370972	−	0.370972i
$414$		0			0
$415$	−4.16039e14			−1.65909
$416$		0			0
$417$	2.32018e14			0.901100
$418$		0			0
$419$	−2.47223e14	−	2.47223e14i	−0.935214	−	0.935214i	0.0628113	−	0.998025i	$-0.479993\pi$
$419$	−2.47223e14	−	2.47223e14i	−0.935214	−	0.935214i	−0.998025	+	0.0628113i	$0.979993\pi$
$420$		0			0
$421$	3.01416e14	−	3.01416e14i	1.11074	−	1.11074i	0.117695	−	0.993050i	$-0.462449\pi$
$421$	3.01416e14	−	3.01416e14i	1.11074	−	1.11074i	0.993050	−	0.117695i	$-0.0375505\pi$
$422$		0			0
$423$			7.76399e14i			2.78749i
$424$		0			0
$425$		−	1.67873e14i		−	0.587274i
$426$		0			0
$427$	−1.98453e12	+	1.98453e12i	−0.00676557	+	0.00676557i
$428$		0			0
$429$	−7.62292e13	−	7.62292e13i	−0.253283	−	0.253283i
$430$		0			0
$431$	−4.56713e14			−1.47917			−0.739586	−	0.673062i	$-0.764979\pi$
$431$	−4.56713e14			−1.47917			−0.739586	+	0.673062i	$0.764979\pi$
$432$		0			0
$433$	1.87325e14			0.591443			0.295721	−	0.955274i	$-0.404440\pi$
$433$	1.87325e14			0.591443			0.295721	+	0.955274i	$0.404440\pi$
$434$		0			0
$435$	3.32841e14	+	3.32841e14i	1.02458	+	1.02458i
$436$		0			0
$437$	7.79697e13	−	7.79697e13i	0.234033	−	0.234033i
$438$		0			0
$439$		−	6.17945e14i		−	1.80882i	−0.426667	−	0.904409i	$-0.640312\pi$
$439$		−	6.17945e14i		−	1.80882i	0.426667	−	0.904409i	$-0.359688\pi$
$440$		0			0
$441$			8.03907e14i			2.29506i
$442$		0			0
$443$	−3.84254e14	+	3.84254e14i	−1.07004	+	1.07004i	−0.0726803	+	0.997355i	$0.523155\pi$
$443$	−3.84254e14	+	3.84254e14i	−1.07004	+	1.07004i	−0.997355	+	0.0726803i	$0.976845\pi$
$444$		0			0
$445$	−3.90058e14	−	3.90058e14i	−1.05962	−	1.05962i
$446$		0			0
$447$	7.96476e14			2.11097
$448$		0			0
$449$	3.39135e12			0.00877037			0.00438518	−	0.999990i	$-0.498604\pi$
$449$	3.39135e12			0.00877037			0.00438518	+	0.999990i	$0.498604\pi$
$450$		0			0
$451$	1.16453e14	+	1.16453e14i	0.293886	+	0.293886i
$452$		0			0
$453$	7.28901e14	−	7.28901e14i	1.79526	−	1.79526i
$454$		0			0
$455$		−	1.84286e14i		−	0.443026i
$456$		0			0
$457$		−	6.33305e14i		−	1.48619i	−0.669187	−	0.743094i	$-0.733357\pi$
$457$		−	6.33305e14i		−	1.48619i	0.669187	−	0.743094i	$-0.266643\pi$
$458$		0			0
$459$	7.19694e14	−	7.19694e14i	1.64884	−	1.64884i
$460$		0			0
$461$	4.96950e14	+	4.96950e14i	1.11162	+	1.11162i	0.992931	+	0.118692i	$0.0378701\pi$
$461$	4.96950e14	+	4.96950e14i	1.11162	+	1.11162i	0.118692	+	0.992931i	$0.462130\pi$
$462$		0			0
$463$	6.46594e14			1.41233			0.706165	−	0.708047i	$-0.250424\pi$
$463$	6.46594e14			1.41233			0.706165	+	0.708047i	$0.250424\pi$
$464$		0			0
$465$	−4.88317e14			−1.04162
$466$		0			0
$467$	−2.80275e14	−	2.80275e14i	−0.583904	−	0.583904i	0.352070	−	0.935974i	$-0.385478\pi$
$467$	−2.80275e14	−	2.80275e14i	−0.583904	−	0.583904i	−0.935974	+	0.352070i	$0.885478\pi$
$468$		0			0
$469$	−1.45805e14	+	1.45805e14i	−0.296702	+	0.296702i
$470$		0			0
$471$		−	6.23619e14i		−	1.23967i
$472$		0			0
$473$		−	2.80920e13i		−	0.0545566i
$474$		0			0
$475$	1.18589e14	−	1.18589e14i	0.225025	−	0.225025i
$476$		0			0
$477$	1.28560e15	+	1.28560e15i	2.38371	+	2.38371i
$478$		0			0
$479$	−7.99937e14			−1.44947			−0.724737	−	0.689025i	$-0.758039\pi$
$479$	−7.99937e14			−1.44947			−0.724737	+	0.689025i	$0.758039\pi$
$480$		0			0
$481$	5.90894e14			1.04643
$482$		0			0
$483$	3.47042e14	+	3.47042e14i	0.600720	+	0.600720i
$484$		0			0
$485$	−3.93118e14	+	3.93118e14i	−0.665186	+	0.665186i
$486$		0			0
$487$			5.92515e14i			0.980145i	0.871682	+	0.490072i	$0.163030\pi$
$487$			5.92515e14i			0.980145i	−0.871682	+	0.490072i	$0.836970\pi$
$488$		0			0
$489$		−	2.89902e12i		−	0.00468869i
$490$		0			0
$491$	3.01153e14	−	3.01153e14i	0.476254	−	0.476254i	−0.427677	−	0.903932i	$-0.640668\pi$
$491$	3.01153e14	−	3.01153e14i	0.476254	−	0.476254i	0.903932	+	0.427677i	$0.140668\pi$
$492$		0			0
$493$	−1.53672e14	−	1.53672e14i	−0.237650	−	0.237650i
$494$		0			0
$495$	6.73221e14			1.01819
$496$		0			0
$497$	2.61832e13			0.0387314
$498$		0			0
$499$	−4.74558e14	−	4.74558e14i	−0.686651	−	0.686651i	0.274839	−	0.961490i	$-0.411375\pi$
$499$	−4.74558e14	−	4.74558e14i	−0.686651	−	0.686651i	−0.961490	+	0.274839i	$0.911375\pi$
$500$		0			0
$501$	1.16422e15	−	1.16422e15i	1.64789	−	1.64789i
$502$		0			0
$503$			8.88794e14i			1.23077i	0.788226	+	0.615385i	$0.211000\pi$
$503$			8.88794e14i			1.23077i	−0.788226	+	0.615385i	$0.789000\pi$
$504$		0			0
$505$			4.96658e14i			0.672907i
$506$		0			0
$507$	−5.16502e14	+	5.16502e14i	−0.684744	+	0.684744i
$508$		0			0
$509$	−6.54049e14	−	6.54049e14i	−0.848521	−	0.848521i	0.141428	−	0.989949i	$-0.454831\pi$
$509$	−6.54049e14	−	6.54049e14i	−0.848521	−	0.848521i	−0.989949	+	0.141428i	$0.954831\pi$
$510$		0			0
$511$	−5.16799e13			−0.0656156
$512$		0			0
$513$	1.01682e15			1.26357
$514$		0			0
$515$	−6.25880e14	−	6.25880e14i	−0.761292	−	0.761292i
$516$		0			0
$517$	1.47316e14	−	1.47316e14i	0.175409	−	0.175409i
$518$		0			0
$519$			2.95151e14i			0.344052i
$520$		0			0
$521$		−	6.02759e14i		−	0.687918i	−0.938985	−	0.343959i	$-0.888232\pi$
$521$		−	6.02759e14i		−	0.687918i	0.938985	−	0.343959i	$-0.111768\pi$
$522$		0			0
$523$	1.41456e14	−	1.41456e14i	0.158075	−	0.158075i	−0.623638	−	0.781713i	$-0.714346\pi$
$523$	1.41456e14	−	1.41456e14i	0.158075	−	0.158075i	0.781713	+	0.623638i	$0.214346\pi$
$524$		0			0
$525$	5.27839e14	+	5.27839e14i	0.577597	+	0.577597i
$526$		0			0
$527$	2.25456e14			0.241603
$528$		0			0
$529$	6.70861e13			0.0704087
$530$		0			0
$531$	2.31334e15	+	2.31334e15i	2.37804	+	2.37804i
$532$		0			0
$533$	−8.14062e14	+	8.14062e14i	−0.819705	+	0.819705i
$534$		0			0
$535$			1.07081e15i			1.05625i
$536$		0			0
$537$		−	1.70750e15i		−	1.65007i
$538$		0			0
$539$	1.52535e14	−	1.52535e14i	0.144422	−	0.144422i
$540$		0			0
$541$	−3.03750e14	−	3.03750e14i	−0.281794	−	0.281794i	0.552030	−	0.833824i	$-0.313853\pi$
$541$	−3.03750e14	−	3.03750e14i	−0.281794	−	0.281794i	−0.833824	+	0.552030i	$0.813853\pi$
$542$		0			0
$543$	1.58970e15			1.44516
$544$		0			0
$545$	−4.80250e13			−0.0427845
$546$		0			0
$547$	−3.85320e14	−	3.85320e14i	−0.336427	−	0.336427i	0.518594	−	0.855021i	$-0.326456\pi$
$547$	−3.85320e14	−	3.85320e14i	−0.336427	−	0.336427i	−0.855021	+	0.518594i	$0.826456\pi$
$548$		0			0
$549$	5.06794e13	−	5.06794e13i	0.0433694	−	0.0433694i
$550$		0			0
$551$		−	2.17116e14i		−	0.182120i
$552$		0			0
$553$			8.14121e13i			0.0669423i
$554$		0			0
$555$	−3.51812e15	+	3.51812e15i	−2.83595	+	2.83595i
$556$		0			0
$557$	7.16583e14	+	7.16583e14i	0.566321	+	0.566321i	0.931096	−	0.364775i	$-0.118854\pi$
$557$	7.16583e14	+	7.16583e14i	0.566321	+	0.566321i	−0.364775	+	0.931096i	$0.618854\pi$
$558$		0			0
$559$	1.96377e14			0.152169
$560$		0			0
$561$	−4.19094e14			−0.318431
$562$		0			0
$563$	−8.55321e14	−	8.55321e14i	−0.637284	−	0.637284i	0.312600	−	0.949885i	$-0.398800\pi$
$563$	−8.55321e14	−	8.55321e14i	−0.637284	−	0.637284i	−0.949885	+	0.312600i	$0.898800\pi$
$564$		0			0
$565$	2.15352e15	−	2.15352e15i	1.57356	−	1.57356i
$566$		0			0
$567$			2.73169e15i			1.95760i
$568$		0			0
$569$		−	1.81588e15i		−	1.27635i	−0.769891	−	0.638175i	$-0.779689\pi$
$569$		−	1.81588e15i		−	1.27635i	0.769891	−	0.638175i	$-0.220311\pi$
$570$		0			0
$571$	−1.13410e15	+	1.13410e15i	−0.781901	+	0.781901i	−0.980151	−	0.198251i	$-0.936474\pi$
$571$	−1.13410e15	+	1.13410e15i	−0.781901	+	0.781901i	0.198251	+	0.980151i	$0.436474\pi$
$572$		0			0
$573$	−1.52537e15	−	1.52537e15i	−1.03163	−	1.03163i
$574$		0			0
$575$	−1.34716e15			−0.893809
$576$		0			0
$577$	−2.48933e15			−1.62038			−0.810188	−	0.586170i	$-0.800635\pi$
$577$	−2.48933e15			−1.62038			−0.810188	+	0.586170i	$0.800635\pi$
$578$		0			0
$579$	1.48828e15	+	1.48828e15i	0.950499	+	0.950499i
$580$		0			0
$581$	−6.03969e14	+	6.03969e14i	−0.378483	+	0.378483i
$582$		0			0
$583$		−	4.87864e14i		−	0.300000i
$584$		0			0
$585$			4.70615e15i			2.83993i
$586$		0			0
$587$	1.17168e15	−	1.17168e15i	0.693903	−	0.693903i	−0.269185	−	0.963088i	$-0.586754\pi$
$587$	1.17168e15	−	1.17168e15i	0.693903	−	0.693903i	0.963088	+	0.269185i	$0.0867543\pi$
$588$		0			0
$589$	1.59267e14	+	1.59267e14i	0.0925747	+	0.0925747i
$590$		0			0
$591$	−3.34510e15			−1.90844
$592$		0			0
$593$	2.16626e15			1.21314			0.606569	−	0.795031i	$-0.292545\pi$
$593$	2.16626e15			1.21314			0.606569	+	0.795031i	$0.292545\pi$
$594$		0			0
$595$	−5.06585e14	−	5.06585e14i	−0.278490	−	0.278490i
$596$		0			0
$597$	−2.14587e15	+	2.14587e15i	−1.15809	+	1.15809i
$598$		0			0
$599$			2.29916e15i			1.21821i	0.793089	+	0.609105i	$0.208471\pi$
$599$			2.29916e15i			1.21821i	−0.793089	+	0.609105i	$0.791529\pi$
$600$		0			0
$601$			7.60944e14i			0.395861i	0.980216	+	0.197931i	$0.0634221\pi$
$601$			7.60944e14i			0.395861i	−0.980216	+	0.197931i	$0.936578\pi$
$602$		0			0
$603$	3.72345e15	−	3.72345e15i	1.90195	−	1.90195i
$604$		0			0
$605$	1.82924e15	+	1.82924e15i	0.917519	+	0.917519i
$606$		0			0
$607$	1.83671e15			0.904694			0.452347	−	0.891842i	$-0.350587\pi$
$607$	1.83671e15			0.904694			0.452347	+	0.891842i	$0.350587\pi$
$608$		0			0
$609$	9.66377e14			0.467467
$610$		0			0
$611$	1.02981e15	+	1.02981e15i	0.489250	+	0.489250i
$612$		0			0
$613$	−8.30874e14	+	8.30874e14i	−0.387706	+	0.387706i	−0.873868	−	0.486162i	$-0.838396\pi$
$613$	−8.30874e14	+	8.30874e14i	−0.387706	+	0.387706i	0.486162	+	0.873868i	$0.338396\pi$
$614$		0			0
$615$		−	9.69367e15i		−	4.44299i
$616$		0			0
$617$		−	2.95927e15i		−	1.33234i	−0.745799	−	0.666171i	$-0.767932\pi$
$617$		−	2.95927e15i		−	1.33234i	0.745799	−	0.666171i	$-0.232068\pi$
$618$		0			0
$619$	1.00184e15	−	1.00184e15i	0.443100	−	0.443100i	−0.449953	−	0.893052i	$-0.648559\pi$
$619$	1.00184e15	−	1.00184e15i	0.443100	−	0.443100i	0.893052	+	0.449953i	$0.148559\pi$
$620$		0			0
$621$	−5.77545e15	−	5.77545e15i	−2.50947	−	2.50947i
$622$		0			0
$623$	−1.13250e15			−0.483454
$624$		0			0
$625$	2.54544e15			1.06764
$626$		0			0
$627$	−2.96058e14	−	2.96058e14i	−0.122013	−	0.122013i
$628$		0			0
$629$	1.62431e15	−	1.62431e15i	0.657796	−	0.657796i
$630$		0			0
$631$		−	2.54047e15i		−	1.01100i	−0.862825	−	0.505502i	$-0.831307\pi$
$631$		−	2.54047e15i		−	1.01100i	0.862825	−	0.505502i	$-0.168693\pi$
$632$		0			0
$633$			2.18727e15i			0.855423i
$634$		0			0
$635$	4.25295e15	−	4.25295e15i	1.63469	−	1.63469i
$636$		0			0
$637$	1.06630e15	+	1.06630e15i	0.402820	+	0.402820i
$638$		0			0
$639$	−6.68646e14			−0.248280
$640$		0			0
$641$	−2.18928e15			−0.799064			−0.399532	−	0.916719i	$-0.630827\pi$
$641$	−2.18928e15			−0.799064			−0.399532	+	0.916719i	$0.630827\pi$
$642$		0			0
$643$	−1.65718e15	−	1.65718e15i	−0.594577	−	0.594577i	0.344287	−	0.938864i	$-0.388121\pi$
$643$	−1.65718e15	−	1.65718e15i	−0.594577	−	0.594577i	−0.938864	+	0.344287i	$0.888121\pi$
$644$		0			0
$645$	−1.16921e15	+	1.16921e15i	−0.412395	+	0.412395i
$646$		0			0
$647$			1.95252e15i			0.677051i	0.940957	+	0.338526i	$0.109928\pi$
$647$			1.95252e15i			0.677051i	−0.940957	+	0.338526i	$0.890072\pi$
$648$		0			0
$649$		−	8.77877e14i		−	0.299287i
$650$		0			0
$651$	−7.08895e14	+	7.08895e14i	−0.237622	+	0.237622i
$652$		0			0
$653$	1.59179e15	+	1.59179e15i	0.524642	+	0.524642i	0.918970	−	0.394328i	$-0.129022\pi$
$653$	1.59179e15	+	1.59179e15i	0.524642	+	0.524642i	−0.394328	+	0.918970i	$0.629022\pi$
$654$		0			0
$655$	−1.82776e13			−0.00592369
$656$		0			0
$657$	1.31976e15			0.420616
$658$		0			0
$659$	1.25231e15	+	1.25231e15i	0.392502	+	0.392502i	0.875578	−	0.483077i	$-0.160481\pi$
$659$	1.25231e15	+	1.25231e15i	0.392502	+	0.392502i	−0.483077	+	0.875578i	$0.660481\pi$
$660$		0			0
$661$	1.31167e15	−	1.31167e15i	0.404311	−	0.404311i	−0.475438	−	0.879749i	$-0.657710\pi$
$661$	1.31167e15	−	1.31167e15i	0.404311	−	0.404311i	0.879749	+	0.475438i	$0.157710\pi$
$662$		0			0
$663$		−	2.92967e15i		−	0.888168i
$664$		0			0
$665$		−	7.15728e14i		−	0.213417i
$666$		0			0
$667$	−1.23320e15	+	1.23320e15i	−0.361694	+	0.361694i
$668$		0			0
$669$	7.39959e15	+	7.39959e15i	2.13483	+	2.13483i
$670$		0			0
$671$	−1.92320e13			−0.00545823
$672$		0			0
$673$	−4.42717e15			−1.23607			−0.618035	−	0.786151i	$-0.712071\pi$
$673$	−4.42717e15			−1.23607			−0.618035	+	0.786151i	$0.712071\pi$
$674$		0			0
$675$	−8.78426e15	−	8.78426e15i	−2.41287	−	2.41287i
$676$		0			0
$677$	−4.02631e15	+	4.02631e15i	−1.08810	+	1.08810i	−0.0923785	+	0.995724i	$0.529447\pi$
$677$	−4.02631e15	+	4.02631e15i	−1.08810	+	1.08810i	−0.995724	+	0.0923785i	$0.970553\pi$
$678$		0			0
$679$			1.14139e15i			0.303493i
$680$		0			0
$681$			7.48297e15i			1.95779i
$682$		0			0
$683$	−1.78162e15	+	1.78162e15i	−0.458671	+	0.458671i	−0.898219	−	0.439548i	$-0.855139\pi$
$683$	−1.78162e15	+	1.78162e15i	−0.458671	+	0.458671i	0.439548	+	0.898219i	$0.355139\pi$
$684$		0			0
$685$	−1.92589e15	−	1.92589e15i	−0.487903	−	0.487903i
$686$		0			0
$687$	1.42258e15			0.354662
$688$		0			0
$689$	3.41041e15			0.836760
$690$		0			0
$691$	2.83219e15	+	2.83219e15i	0.683902	+	0.683902i	0.960877	−	0.276975i	$-0.0893321\pi$
$691$	2.83219e15	+	2.83219e15i	0.683902	+	0.683902i	−0.276975	+	0.960877i	$0.589332\pi$
$692$		0			0
$693$	9.77322e14	−	9.77322e14i	0.232276	−	0.232276i
$694$		0			0
$695$			2.71788e15i			0.635790i
$696$		0			0
$697$			4.47556e15i			1.03055i
$698$		0			0
$699$	−9.68356e15	+	9.68356e15i	−2.19488	+	2.19488i
$700$		0			0
$701$	−2.66761e15	−	2.66761e15i	−0.595214	−	0.595214i	0.343821	−	0.939035i	$-0.388279\pi$
$701$	−2.66761e15	−	2.66761e15i	−0.595214	−	0.595214i	−0.939035	+	0.343821i	$0.888279\pi$
$702$		0			0
$703$	2.29491e15			0.504093
$704$		0			0
$705$	−1.22628e16			−2.65185
$706$		0			0
$707$	7.21004e14	+	7.21004e14i	0.153508	+	0.153508i
$708$		0			0
$709$	−2.91989e15	+	2.91989e15i	−0.612085	+	0.612085i	−0.943489	−	0.331404i	$-0.892478\pi$
$709$	−2.91989e15	+	2.91989e15i	−0.612085	+	0.612085i	0.331404	+	0.943489i	$0.392478\pi$
$710$		0			0
$711$		−	2.07904e15i		−	0.429120i
$712$		0			0
$713$		−	1.80925e15i		−	0.367711i
$714$		0			0
$715$	8.92956e14	−	8.92956e14i	0.178709	−	0.178709i
$716$		0			0
$717$	−5.47275e15	−	5.47275e15i	−1.07857	−	1.07857i
$718$		0			0
$719$	7.46765e15			1.44935			0.724677	−	0.689088i	$-0.241989\pi$
$719$	7.46765e15			1.44935			0.724677	+	0.689088i	$0.241989\pi$
$720$		0			0
$721$	−1.81719e15			−0.347342
$722$		0			0
$723$	−6.53396e15	−	6.53396e15i	−1.23003	−	1.23003i
$724$		0			0
$725$	−1.87566e15	+	1.87566e15i	−0.347772	+	0.347772i
$726$		0			0
$727$			8.34141e13i			0.0152335i	0.999971	+	0.00761676i	$0.00242451\pi$
$727$			8.34141e13i			0.0152335i	−0.999971	+	0.00761676i	$0.997575\pi$
$728$		0			0
$729$		−	2.95012e16i		−	5.30687i
$730$		0			0
$731$	5.39823e14	−	5.39823e14i	0.0956546	−	0.0956546i
$732$		0			0
$733$	−7.73562e15	−	7.73562e15i	−1.35028	−	1.35028i	−0.885346	−	0.464933i	$-0.846079\pi$
$733$	−7.73562e15	−	7.73562e15i	−1.35028	−	1.35028i	−0.464933	−	0.885346i	$-0.653921\pi$
$734$		0			0
$735$	−1.26972e16			−2.18338
$736$		0			0
$737$	−1.41299e15			−0.239369
$738$		0			0
$739$	2.34299e15	+	2.34299e15i	0.391044	+	0.391044i	0.875060	−	0.484015i	$-0.160822\pi$
$739$	2.34299e15	+	2.34299e15i	0.391044	+	0.391044i	−0.484015	+	0.875060i	$0.660822\pi$
$740$		0			0
$741$	2.06959e15	−	2.06959e15i	0.340318	−	0.340318i
$742$		0			0
$743$			7.38859e15i			1.19708i	0.801093	+	0.598540i	$0.204252\pi$
$743$			7.38859e15i			1.19708i	−0.801093	+	0.598540i	$0.795748\pi$
$744$		0			0
$745$			9.32999e15i			1.48944i
$746$		0			0
$747$	1.54237e16	−	1.54237e16i	2.42619	−	2.42619i
$748$		0			0
$749$	1.55451e15	+	1.55451e15i	0.240959	+	0.240959i
$750$		0			0
$751$	2.74146e14			0.0418758			0.0209379	−	0.999781i	$-0.493335\pi$
$751$	2.74146e14			0.0418758			0.0209379	+	0.999781i	$0.493335\pi$
$752$		0			0
$753$	−9.52455e15			−1.43375
$754$		0			0
$755$	8.53841e15	+	8.53841e15i	1.26669	+	1.26669i
$756$		0			0
$757$	−1.20145e15	+	1.20145e15i	−0.175662	+	0.175662i	−0.789462	−	0.613800i	$-0.789640\pi$
$757$	−1.20145e15	+	1.20145e15i	−0.175662	+	0.175662i	0.613800	+	0.789462i	$0.289640\pi$
$758$		0			0
$759$			3.36317e15i			0.484640i
$760$		0			0
$761$			5.15297e15i			0.731883i	0.930638	+	0.365942i	$0.119253\pi$
$761$			5.15297e15i			0.731883i	−0.930638	+	0.365942i	$0.880747\pi$
$762$		0			0
$763$	−6.97184e13	+	6.97184e13i	−0.00976028	+	0.00976028i
$764$		0			0
$765$	1.29368e16	+	1.29368e16i	1.78520	+	1.78520i
$766$		0			0
$767$	6.13680e15			0.834771
$768$		0			0
$769$	−8.26093e14			−0.110773			−0.0553866	−	0.998465i	$-0.517639\pi$
$769$	−8.26093e14			−0.110773			−0.0553866	+	0.998465i	$0.517639\pi$
$770$		0			0
$771$	−8.25407e15	−	8.25407e15i	−1.09111	−	1.09111i
$772$		0			0
$773$	−5.16962e15	+	5.16962e15i	−0.673707	+	0.673707i	−0.958569	−	0.284861i	$-0.908052\pi$
$773$	−5.16962e15	+	5.16962e15i	−0.673707	+	0.673707i	0.284861	+	0.958569i	$0.408052\pi$
$774$		0			0
$775$		−	2.75181e15i		−	0.353557i
$776$		0			0
$777$			1.02146e16i			1.29391i
$778$		0			0
$779$	−3.16164e15	+	3.16164e15i	−0.394873	+	0.394873i
$780$		0			0
$781$	1.26871e14	+	1.26871e14i	0.0156236	+	0.0156236i
$782$		0			0
$783$	−1.60824e16			−1.95281
$784$		0			0
$785$	7.30513e15			0.874672
$786$		0			0
$787$	5.98784e15	+	5.98784e15i	0.706983	+	0.706983i	0.965900	−	0.258917i	$-0.0833655\pi$
$787$	5.98784e15	+	5.98784e15i	0.706983	+	0.706983i	−0.258917	+	0.965900i	$0.583365\pi$
$788$		0			0
$789$	2.19123e16	−	2.19123e16i	2.55132	−	2.55132i
$790$		0			0
$791$		−	6.25258e15i		−	0.717940i
$792$		0			0
$793$		−	1.34442e14i		−	0.0152241i
$794$		0			0
$795$	−2.03052e16	+	2.03052e16i	−2.26772	+	2.26772i
$796$		0			0
$797$	1.83817e15	+	1.83817e15i	0.202472	+	0.202472i	0.801058	−	0.598586i	$-0.204271\pi$
$797$	1.83817e15	+	1.83817e15i	0.202472	+	0.202472i	−0.598586	+	0.801058i	$0.704271\pi$
$798$		0			0
$799$	5.66171e15			0.615092
$800$		0			0
$801$	2.89210e16			3.09909
$802$		0			0
$803$	−2.50415e14	−	2.50415e14i	−0.0264682	−	0.0264682i
$804$		0			0
$805$	−4.06528e15	+	4.06528e15i	−0.423851	+	0.423851i
$806$		0			0
$807$			7.39439e15i			0.760498i
$808$		0			0
$809$		−	7.03952e14i		−	0.0714211i	−0.999362	−	0.0357105i	$-0.988631\pi$
$809$		−	7.03952e14i		−	0.0714211i	0.999362	−	0.0357105i	$-0.0113694\pi$
$810$		0			0
$811$	7.23162e15	−	7.23162e15i	0.723804	−	0.723804i	−0.245574	−	0.969378i	$-0.578977\pi$
$811$	7.23162e15	−	7.23162e15i	0.723804	−	0.723804i	0.969378	+	0.245574i	$0.0789765\pi$
$812$		0			0
$813$	1.93886e15	+	1.93886e15i	0.191447	+	0.191447i
$814$		0			0
$815$	3.39593e13			0.00330821
$816$		0			0
$817$	7.62688e14			0.0733036
$818$		0			0
$819$	6.83196e15	+	6.83196e15i	0.647864	+	0.647864i
$820$		0			0
$821$	−3.15400e15	+	3.15400e15i	−0.295103	+	0.295103i	−0.839092	−	0.543989i	$-0.816913\pi$
$821$	−3.15400e15	+	3.15400e15i	−0.295103	+	0.295103i	0.543989	+	0.839092i	$0.316913\pi$
$822$		0			0
$823$		−	7.95562e15i		−	0.734471i	−0.930128	−	0.367236i	$-0.880304\pi$
$823$		−	7.95562e15i		−	0.734471i	0.930128	−	0.367236i	$-0.119696\pi$
$824$		0			0
$825$			5.11527e15i			0.465985i
$826$		0			0
$827$	7.06259e15	−	7.06259e15i	0.634869	−	0.634869i	−0.314417	−	0.949285i	$-0.601809\pi$
$827$	7.06259e15	−	7.06259e15i	0.634869	−	0.634869i	0.949285	+	0.314417i	$0.101809\pi$
$828$		0			0
$829$	7.83457e15	+	7.83457e15i	0.694969	+	0.694969i	0.963321	−	0.268352i	$-0.0864791\pi$
$829$	7.83457e15	+	7.83457e15i	0.694969	+	0.694969i	−0.268352	+	0.963321i	$0.586479\pi$
$830$		0			0
$831$	3.59168e16			3.14406
$832$		0			0
$833$	5.86231e15			0.506432
$834$		0			0
$835$	1.36378e16	+	1.36378e16i	1.16270	+	1.16270i
$836$		0			0
$837$	1.17974e16	−	1.17974e16i	0.992650	−	0.992650i
$838$		0			0
$839$		−	5.19905e15i		−	0.431751i	−0.976421	−	0.215876i	$-0.930739\pi$
$839$		−	5.19905e15i		−	0.431751i	0.976421	−	0.215876i	$-0.0692606\pi$
$840$		0			0
$841$		−	8.76652e15i		−	0.718538i
$842$		0			0
$843$	6.58707e15	−	6.58707e15i	0.532894	−	0.532894i
$844$		0			0
$845$	−6.05036e15	−	6.05036e15i	−0.483136	−	0.483136i
$846$		0			0
$847$	5.31104e15			0.418621
$848$		0			0
$849$	4.06584e16			3.16343
$850$		0			0
$851$	−1.30349e16	−	1.30349e16i	−1.00114	−	1.00114i
$852$		0			0
$853$	6.77512e15	−	6.77512e15i	0.513686	−	0.513686i	−0.401968	−	0.915654i	$-0.631674\pi$
$853$	6.77512e15	−	6.77512e15i	0.513686	−	0.513686i	0.915654	+	0.401968i	$0.131674\pi$
$854$		0			0
$855$			1.82777e16i			1.36807i
$856$		0			0
$857$			1.61172e16i			1.19095i	0.803372	+	0.595477i	$0.203037\pi$
$857$			1.61172e16i			1.19095i	−0.803372	+	0.595477i	$0.796963\pi$
$858$		0			0
$859$	2.67447e15	−	2.67447e15i	0.195108	−	0.195108i	−0.602791	−	0.797899i	$-0.705945\pi$
$859$	2.67447e15	−	2.67447e15i	0.195108	−	0.195108i	0.797899	+	0.602791i	$0.205945\pi$
$860$		0			0
$861$	−1.40724e16	−	1.40724e16i	−1.01356	−	1.01356i
$862$		0			0
$863$	−1.60361e16			−1.14036			−0.570178	−	0.821521i	$-0.693126\pi$
$863$	−1.60361e16			−1.14036			−0.570178	+	0.821521i	$0.693126\pi$
$864$		0			0
$865$	−3.45743e15			−0.242753
$866$		0			0
$867$	1.20142e16	+	1.20142e16i	0.832892	+	0.832892i
$868$		0			0
$869$	−3.94481e14	+	3.94481e14i	−0.0270033	+	0.0270033i
$870$		0			0
$871$		−	9.87751e15i		−	0.667648i
$872$		0			0
$873$		−	2.91478e16i		−	1.94548i
$874$		0			0
$875$	4.86621e14	−	4.86621e14i	0.0320735	−	0.0320735i
$876$		0			0
$877$	9.67974e15	+	9.67974e15i	0.630037	+	0.630037i	0.948077	−	0.318041i	$-0.103025\pi$
$877$	9.67974e15	+	9.67974e15i	0.630037	+	0.630037i	−0.318041	+	0.948077i	$0.603025\pi$
$878$		0			0
$879$	−5.01579e16			−3.22404
$880$		0			0
$881$	−5.86163e15			−0.372093			−0.186046	−	0.982541i	$-0.559567\pi$
$881$	−5.86163e15			−0.372093			−0.186046	+	0.982541i	$0.559567\pi$
$882$		0			0
$883$	7.35372e15	+	7.35372e15i	0.461024	+	0.461024i	0.898991	−	0.437967i	$-0.144301\pi$
$883$	7.35372e15	+	7.35372e15i	0.461024	+	0.461024i	−0.437967	+	0.898991i	$0.644301\pi$
$884$		0			0
$885$	−3.65378e16	+	3.65378e16i	−2.26232	+	2.26232i
$886$		0			0
$887$			2.65254e16i			1.62211i	0.584967	+	0.811057i	$0.301108\pi$
$887$			2.65254e16i			1.62211i	−0.584967	+	0.811057i	$0.698892\pi$
$888$		0			0
$889$		−	1.23481e16i		−	0.745832i
$890$		0			0
$891$	−1.32364e16	+	1.32364e16i	−0.789662	+	0.789662i
$892$		0			0
$893$	3.99957e15	+	3.99957e15i	0.235684	+	0.235684i
$894$		0			0
$895$	2.00018e16			1.16424
$896$		0			0
$897$	−2.35102e16			−1.35176
$898$		0			0
$899$	−2.51903e15	−	2.51903e15i	−0.143072	−	0.143072i
$900$		0			0
$901$	9.37491e15	−	9.37491e15i	0.525994	−	0.525994i
$902$		0			0
$903$			3.39471e15i			0.188157i
$904$		0			0
$905$			1.86218e16i			1.01966i
$906$		0			0
$907$	−1.45137e16	+	1.45137e16i	−0.785124	+	0.785124i	−0.980690	−	0.195567i	$-0.937345\pi$
$907$	−1.45137e16	+	1.45137e16i	−0.785124	+	0.785124i	0.195567	+	0.980690i	$0.437345\pi$
$908$		0			0
$909$	−1.84124e16	−	1.84124e16i	−0.984032	−	0.984032i
$910$		0			0
$911$	−2.74199e16			−1.44782			−0.723910	−	0.689895i	$-0.757657\pi$
$911$	−2.74199e16			−1.44782			−0.723910	+	0.689895i	$0.757657\pi$
$912$		0			0
$913$	−5.85305e15			−0.305346
$914$		0			0
$915$	8.00451e14	+	8.00451e14i	0.0412590	+	0.0412590i
$916$		0			0
$917$	−2.65338e13	+	2.65338e13i	−0.00135135	+	0.00135135i
$918$		0			0
$919$		−	1.55320e16i		−	0.781612i	−0.920473	−	0.390806i	$-0.872196\pi$
$919$		−	1.55320e16i		−	0.781612i	0.920473	−	0.390806i	$-0.127804\pi$
$920$		0			0
$921$			5.86704e14i			0.0291737i
$922$		0			0
$923$	−8.86888e14	+	8.86888e14i	−0.0435772	+	0.0435772i
$924$		0			0
$925$	−1.98256e16	−	1.98256e16i	−0.962604	−	0.962604i
$926$		0			0
$927$	4.64060e16			2.22657
$928$		0			0
$929$	−1.93944e16			−0.919579			−0.459790	−	0.888028i	$-0.652075\pi$
$929$	−1.93944e16			−0.919579			−0.459790	+	0.888028i	$0.652075\pi$
$930$		0			0
$931$	4.14127e15	+	4.14127e15i	0.194049	+	0.194049i
$932$		0			0
$933$	3.93106e16	−	3.93106e16i	1.82038	−	1.82038i
$934$		0			0
$935$		−	4.90931e15i		−	0.224676i
$936$		0			0
$937$		−	2.03964e16i		−	0.922543i	−0.887259	−	0.461272i	$-0.847393\pi$
$937$		−	2.03964e16i		−	0.922543i	0.887259	−	0.461272i	$-0.152607\pi$
$938$		0			0
$939$	−6.84890e15	+	6.84890e15i	−0.306168	+	0.306168i
$940$		0			0
$941$	2.84300e16	+	2.84300e16i	1.25613	+	1.25613i	0.952926	+	0.303204i	$0.0980565\pi$
$941$	2.84300e16	+	2.84300e16i	1.25613	+	1.25613i	0.303204	+	0.952926i	$0.401944\pi$
$942$		0			0
$943$	3.59158e16			1.56845
$944$		0			0
$945$	−5.30161e16			−2.28840
$946$		0			0
$947$	−1.73191e15	−	1.73191e15i	−0.0738925	−	0.0738925i	0.669195	−	0.743087i	$-0.266639\pi$
$947$	−1.73191e15	−	1.73191e15i	−0.0738925	−	0.0738925i	−0.743087	+	0.669195i	$0.766639\pi$
$948$		0			0
$949$	1.75052e15	−	1.75052e15i	0.0738250	−	0.0738250i
$950$		0			0
$951$			6.35372e16i			2.64871i
$952$		0			0
$953$			2.78400e16i			1.14725i	0.819118	+	0.573625i	$0.194463\pi$
$953$			2.78400e16i			1.14725i	−0.819118	+	0.573625i	$0.805537\pi$
$954$		0			0
$955$	1.78683e16	−	1.78683e16i	0.727888	−	0.727888i
$956$		0			0
$957$	4.68257e15	+	4.68257e15i	0.188568	+	0.188568i
$958$		0			0
$959$	−5.59168e15			−0.222607
$960$		0			0
$961$	−2.17128e16			−0.854548
$962$		0			0
$963$	−3.96978e16	−	3.96978e16i	−1.54462	−	1.54462i
$964$		0			0
$965$	−1.74338e16	+	1.74338e16i	−0.670645	+	0.670645i
$966$		0			0
$967$			1.07368e16i			0.408348i	0.978935	+	0.204174i	$0.0654508\pi$
$967$			1.07368e16i			0.408348i	−0.978935	+	0.204174i	$0.934549\pi$
$968$		0			0
$969$		−	1.13782e16i		−	0.427852i
$970$		0			0
$971$	−2.12051e15	+	2.12051e15i	−0.0788377	+	0.0788377i	−0.745426	−	0.666588i	$-0.767754\pi$
$971$	−2.12051e15	+	2.12051e15i	−0.0788377	+	0.0788377i	0.666588	+	0.745426i	$0.267754\pi$
$972$		0			0
$973$	3.94558e15	+	3.94558e15i	0.145041	+	0.145041i
$974$		0			0
$975$	−3.57583e16			−1.29973
$976$		0			0
$977$	−2.75619e16			−0.990579			−0.495289	−	0.868728i	$-0.664938\pi$
$977$	−2.75619e16			−0.990579			−0.495289	+	0.868728i	$0.664938\pi$
$978$		0			0
$979$	−5.48754e15	−	5.48754e15i	−0.195017	−	0.195017i
$980$		0			0
$981$	1.78041e15	−	1.78041e15i	0.0625664	−	0.0625664i
$982$		0			0
$983$			7.69115e15i			0.267268i	0.991031	+	0.133634i	$0.0426646\pi$
$983$			7.69115e15i			0.267268i	−0.991031	+	0.133634i	$0.957335\pi$
$984$		0			0
$985$		−	3.91848e16i		−	1.34654i
$986$		0			0
$987$	−1.78020e16	+	1.78020e16i	−0.604957	+	0.604957i
$988$		0			0
$989$	−4.33201e15	−	4.33201e15i	−0.145583	−	0.145583i
$990$		0			0
$991$	5.13881e14			0.0170788			0.00853939	−	0.999964i	$-0.497282\pi$
$991$	5.13881e14			0.0170788			0.00853939	+	0.999964i	$0.497282\pi$
$992$		0			0
$993$	1.10941e17			3.64647
$994$		0			0
$995$	−2.51369e16	−	2.51369e16i	−0.817118	−	0.817118i
$996$		0			0
$997$	−2.49674e16	+	2.49674e16i	−0.802693	+	0.802693i	−0.983516	−	0.180822i	$-0.942124\pi$
$997$	−2.49674e16	+	2.49674e16i	−0.802693	+	0.802693i	0.180822	+	0.983516i	$0.442124\pi$
$998$		0			0
$999$		−	1.69991e17i		−	5.40524i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.12.e.b.33.1		42
4.3	odd	2		128.12.e.a.33.21		42
8.3	odd	2		64.12.e.a.17.1		42
8.5	even	2		16.12.e.a.13.7	yes	42
16.3	odd	4		64.12.e.a.49.1		42
16.5	even	4	inner	128.12.e.b.97.1		42
16.11	odd	4		128.12.e.a.97.21		42
16.13	even	4		16.12.e.a.5.7	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.12.e.a.5.7	✓	42	16.13	even	4
16.12.e.a.13.7	yes	42	8.5	even	2
64.12.e.a.17.1		42	8.3	odd	2
64.12.e.a.49.1		42	16.3	odd	4
128.12.e.a.33.21		42	4.3	odd	2
128.12.e.a.97.21		42	16.11	odd	4
128.12.e.b.33.1		42	1.1	even	1	trivial
128.12.e.b.97.1		42	16.5	even	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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	128.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-585.540 - 585.540i) q^{3} +(6859.07 - 6859.07i) q^{5} -19914.8i q^{7} +508568. i q^{9} +O(q^{10})\)	\(q+(-585.540 - 585.540i) q^{3} +(6859.07 - 6859.07i) q^{5} -19914.8i q^{7} +508568. i q^{9} +(96496.9 - 96496.9i) q^{11} +(674561. + 674561. i) q^{13} -8.03253e6 q^{15} +3.70861e6 q^{17} +(2.61985e6 + 2.61985e6i) q^{19} +(-1.16609e7 + 1.16609e7i) q^{21} -2.97611e7i q^{23} -4.52657e7i q^{25} +(1.94060e8 - 1.94060e8i) q^{27} +(-4.14366e7 - 4.14366e7i) q^{29} +6.07925e7 q^{31} -1.13006e8 q^{33} +(-1.36597e8 - 1.36597e8i) q^{35} +(4.37984e8 - 4.37984e8i) q^{37} -7.89965e8i q^{39} +1.20680e9i q^{41} +(1.45559e8 - 1.45559e8i) q^{43} +(3.48830e9 + 3.48830e9i) q^{45} +1.52664e9 q^{47} +1.58073e9 q^{49} +(-2.17154e9 - 2.17154e9i) q^{51} +(2.52787e9 - 2.52787e9i) q^{53} -1.32376e9i q^{55} -3.06806e9i q^{57} +(4.54873e9 - 4.54873e9i) q^{59} +(-9.96512e7 - 9.96512e7i) q^{61} +1.01280e10 q^{63} +9.25373e9 q^{65} +(-7.32144e9 - 7.32144e9i) q^{67} +(-1.74263e10 + 1.74263e10i) q^{69} +1.31476e9i q^{71} -2.59505e9i q^{73} +(-2.65049e10 + 2.65049e10i) q^{75} +(-1.92171e9 - 1.92171e9i) q^{77} -4.08802e9 q^{79} -1.37169e11 q^{81} +(-3.03277e10 - 3.03277e10i) q^{83} +(2.54376e10 - 2.54376e10i) q^{85} +4.85256e10i q^{87} -5.68675e10i q^{89} +(1.34337e10 - 1.34337e10i) q^{91} +(-3.55964e10 - 3.55964e10i) q^{93} +3.59395e10 q^{95} -5.73135e10 q^{97} +(4.90752e10 + 4.90752e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 2 q^{5}+O(q^{10}) \) 42 * q + 2 * q^3 + 2 * q^5	\( 42 q + 2 q^{3} + 2 q^{5} + 540846 q^{11} + 2 q^{13} - 6075004 q^{15} - 4 q^{17} + 11291290 q^{19} - 354292 q^{21} + 66463304 q^{27} - 77673206 q^{29} + 343549808 q^{31} - 4 q^{33} + 434731684 q^{35} + 522762058 q^{37} - 3824193658 q^{43} - 97301954 q^{45} - 4586900144 q^{47} - 8474257474 q^{49} - 7074245796 q^{51} + 2100608058 q^{53} - 955824746 q^{59} - 2150827022 q^{61} + 27758037828 q^{63} - 1884965292 q^{65} + 3186519018 q^{67} + 16193060732 q^{69} - 28890034486 q^{75} + 22711870540 q^{77} + 48011833792 q^{79} - 90656394430 q^{81} - 55713221118 q^{83} + 84575506252 q^{85} + 147369662716 q^{91} + 69689773328 q^{93} + 375702304500 q^{95} - 4 q^{97} + 286271331106 q^{99}+O(q^{100}) \) 42 * q + 2 * q^3 + 2 * q^5 + 540846 * q^11 + 2 * q^13 - 6075004 * q^15 - 4 * q^17 + 11291290 * q^19 - 354292 * q^21 + 66463304 * q^27 - 77673206 * q^29 + 343549808 * q^31 - 4 * q^33 + 434731684 * q^35 + 522762058 * q^37 - 3824193658 * q^43 - 97301954 * q^45 - 4586900144 * q^47 - 8474257474 * q^49 - 7074245796 * q^51 + 2100608058 * q^53 - 955824746 * q^59 - 2150827022 * q^61 + 27758037828 * q^63 - 1884965292 * q^65 + 3186519018 * q^67 + 16193060732 * q^69 - 28890034486 * q^75 + 22711870540 * q^77 + 48011833792 * q^79 - 90656394430 * q^81 - 55713221118 * q^83 + 84575506252 * q^85 + 147369662716 * q^91 + 69689773328 * q^93 + 375702304500 * q^95 - 4 * q^97 + 286271331106 * q^99

Introduction

L-functions

Modular forms

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