LMFDB - Embedded newform 128.12.e.b.33.15

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			33.15
Character	$\chi$	$=$	128.33
Dual form			128.12.e.b.97.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(199.508 + 199.508i) q^{3} +(-8937.54 + 8937.54i) q^{5} -55653.3i q^{7} -97540.0i q^{9} +O(q^{10})$	\(q+(199.508 + 199.508i) q^{3} +(-8937.54 + 8937.54i) q^{5} -55653.3i q^{7} -97540.0i q^{9} +(146129. - 146129. i) q^{11} +(-1.33136e6 - 1.33136e6i) q^{13} -3.56623e6 q^{15} -2.92311e6 q^{17} +(1.11550e7 + 1.11550e7i) q^{19} +(1.11033e7 - 1.11033e7i) q^{21} +2.12560e7i q^{23} -1.10931e8i q^{25} +(5.48023e7 - 5.48023e7i) q^{27} +(1.31742e7 + 1.31742e7i) q^{29} +1.84262e8 q^{31} +5.83078e7 q^{33} +(4.97404e8 + 4.97404e8i) q^{35} +(-6.58484e7 + 6.58484e7i) q^{37} -5.31233e8i q^{39} +7.48317e8i q^{41} +(3.10180e8 - 3.10180e8i) q^{43} +(8.71768e8 + 8.71768e8i) q^{45} -1.85656e9 q^{47} -1.11996e9 q^{49} +(-5.83185e8 - 5.83185e8i) q^{51} +(-3.45179e9 + 3.45179e9i) q^{53} +2.61207e9i q^{55} +4.45104e9i q^{57} +(-8.57741e8 + 8.57741e8i) q^{59} +(-6.80487e9 - 6.80487e9i) q^{61} -5.42842e9 q^{63} +2.37981e10 q^{65} +(5.85461e9 + 5.85461e9i) q^{67} +(-4.24075e9 + 4.24075e9i) q^{69} +1.15906e8i q^{71} -1.23316e9i q^{73} +(2.21317e10 - 2.21317e10i) q^{75} +(-8.13256e9 - 8.13256e9i) q^{77} -1.66808e9 q^{79} +4.58810e9 q^{81} +(1.21868e10 + 1.21868e10i) q^{83} +(2.61254e10 - 2.61254e10i) q^{85} +5.25674e9i q^{87} -3.35444e10i q^{89} +(-7.40944e10 + 7.40944e10i) q^{91} +(3.67618e10 + 3.67618e10i) q^{93} -1.99397e11 q^{95} +2.49231e10 q^{97} +(-1.42534e10 - 1.42534e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	199.508	+	199.508i	0.474017	+	0.474017i	0.903212	−	0.429195i	$-0.141203\pi$
$3$	199.508	+	199.508i	0.474017	+	0.474017i	−0.429195	+	0.903212i	$0.641203\pi$
$4$		0			0
$5$	−8937.54	+	8937.54i	−1.27904	+	1.27904i	−0.337830	+	0.941207i	$0.609693\pi$
$5$	−8937.54	+	8937.54i	−1.27904	+	1.27904i	−0.941207	+	0.337830i	$0.890307\pi$
$6$		0			0
$7$		−	55653.3i		−	1.25156i	−0.780000	−	0.625780i	$-0.784781\pi$
$7$		−	55653.3i		−	1.25156i	0.780000	−	0.625780i	$-0.215219\pi$
$8$		0			0
$9$		−	97540.0i		−	0.550616i
$10$		0			0
$11$	146129.	−	146129.i	0.273575	−	0.273575i	−0.556963	−	0.830538i	$-0.688033\pi$
$11$	146129.	−	146129.i	0.273575	−	0.273575i	0.830538	+	0.556963i	$0.188033\pi$
$12$		0			0
$13$	−1.33136e6	−	1.33136e6i	−0.994502	−	0.994502i	0.00548268	−	0.999985i	$-0.498255\pi$
$13$	−1.33136e6	−	1.33136e6i	−0.994502	−	0.994502i	−0.999985	+	0.00548268i	$0.998255\pi$
$14$		0			0
$15$	−3.56623e6			−1.21257
$16$		0			0
$17$	−2.92311e6			−0.499317			−0.249659	−	0.968334i	$-0.580318\pi$
$17$	−2.92311e6			−0.499317			−0.249659	+	0.968334i	$0.580318\pi$
$18$		0			0
$19$	1.11550e7	+	1.11550e7i	1.03354	+	1.03354i	0.999418	+	0.0341197i	$0.0108627\pi$
$19$	1.11550e7	+	1.11550e7i	1.03354	+	1.03354i	0.0341197	+	0.999418i	$0.489137\pi$
$20$		0			0
$21$	1.11033e7	−	1.11033e7i	0.593261	−	0.593261i
$22$		0			0
$23$			2.12560e7i			0.688619i	0.938856	+	0.344309i	$0.111887\pi$
$23$			2.12560e7i			0.688619i	−0.938856	+	0.344309i	$0.888113\pi$
$24$		0			0
$25$		−	1.10931e8i		−	2.27187i
$26$		0			0
$27$	5.48023e7	−	5.48023e7i	0.735018	−	0.735018i
$28$		0			0
$29$	1.31742e7	+	1.31742e7i	0.119271	+	0.119271i	0.764223	−	0.644952i	$-0.223123\pi$
$29$	1.31742e7	+	1.31742e7i	0.119271	+	0.119271i	−0.644952	+	0.764223i	$0.723123\pi$
$30$		0			0
$31$	1.84262e8			1.15597			0.577986	−	0.816047i	$-0.303839\pi$
$31$	1.84262e8			1.15597			0.577986	+	0.816047i	$0.303839\pi$
$32$		0			0
$33$	5.83078e7			0.259358
$34$		0			0
$35$	4.97404e8	+	4.97404e8i	1.60079	+	1.60079i
$36$		0			0
$37$	−6.58484e7	+	6.58484e7i	−0.156112	+	0.156112i	−0.780841	−	0.624729i	$-0.785209\pi$
$37$	−6.58484e7	+	6.58484e7i	−0.156112	+	0.156112i	0.624729	+	0.780841i	$0.285209\pi$
$38$		0			0
$39$		−	5.31233e8i		−	0.942822i
$40$		0			0
$41$			7.48317e8i			1.00873i	0.863491	+	0.504364i	$0.168273\pi$
$41$			7.48317e8i			1.00873i	−0.863491	+	0.504364i	$0.831727\pi$
$42$		0			0
$43$	3.10180e8	−	3.10180e8i	0.321764	−	0.321764i	−0.527680	−	0.849443i	$-0.676938\pi$
$43$	3.10180e8	−	3.10180e8i	0.321764	−	0.321764i	0.849443	+	0.527680i	$0.176938\pi$
$44$		0			0
$45$	8.71768e8	+	8.71768e8i	0.704258	+	0.704258i
$46$		0			0
$47$	−1.85656e9			−1.18078			−0.590392	−	0.807117i	$-0.701027\pi$
$47$	−1.85656e9			−1.18078			−0.590392	+	0.807117i	$0.701027\pi$
$48$		0			0
$49$	−1.11996e9			−0.566403
$50$		0			0
$51$	−5.83185e8	−	5.83185e8i	−0.236685	−	0.236685i
$52$		0			0
$53$	−3.45179e9	+	3.45179e9i	−1.13378	+	1.13378i	−0.144232	+	0.989544i	$0.546071\pi$
$53$	−3.45179e9	+	3.45179e9i	−1.13378	+	1.13378i	−0.989544	+	0.144232i	$0.953929\pi$
$54$		0			0
$55$			2.61207e9i			0.699825i
$56$		0			0
$57$			4.45104e9i			0.979828i
$58$		0			0
$59$	−8.57741e8	+	8.57741e8i	−0.156196	+	0.156196i	−0.780879	−	0.624683i	$-0.785228\pi$
$59$	−8.57741e8	+	8.57741e8i	−0.156196	+	0.156196i	0.624683	+	0.780879i	$0.285228\pi$
$60$		0			0
$61$	−6.80487e9	−	6.80487e9i	−1.03159	−	1.03159i	−0.999485	−	0.0321015i	$-0.989780\pi$
$61$	−6.80487e9	−	6.80487e9i	−1.03159	−	1.03159i	−0.0321015	−	0.999485i	$-0.510220\pi$
$62$		0			0
$63$	−5.42842e9			−0.689129
$64$		0			0
$65$	2.37981e10			2.54401
$66$		0			0
$67$	5.85461e9	+	5.85461e9i	0.529769	+	0.529769i	0.920503	−	0.390735i	$-0.127779\pi$
$67$	5.85461e9	+	5.85461e9i	0.529769	+	0.529769i	−0.390735	+	0.920503i	$0.627779\pi$
$68$		0			0
$69$	−4.24075e9	+	4.24075e9i	−0.326417	+	0.326417i
$70$		0			0
$71$			1.15906e8i			0.00762402i	0.999993	+	0.00381201i	$0.00121340\pi$
$71$			1.15906e8i			0.00762402i	−0.999993	+	0.00381201i	$0.998787\pi$
$72$		0			0
$73$		−	1.23316e9i		−	0.0696213i	−0.999394	−	0.0348106i	$-0.988917\pi$
$73$		−	1.23316e9i		−	0.0696213i	0.999394	−	0.0348106i	$-0.0110828\pi$
$74$		0			0
$75$	2.21317e10	−	2.21317e10i	1.07691	−	1.07691i
$76$		0			0
$77$	−8.13256e9	−	8.13256e9i	−0.342396	−	0.342396i
$78$		0			0
$79$	−1.66808e9			−0.0609914			−0.0304957	−	0.999535i	$-0.509709\pi$
$79$	−1.66808e9			−0.0609914			−0.0304957	+	0.999535i	$0.509709\pi$
$80$		0			0
$81$	4.58810e9			0.146206
$82$		0			0
$83$	1.21868e10	+	1.21868e10i	0.339593	+	0.339593i	0.856214	−	0.516621i	$-0.172810\pi$
$83$	1.21868e10	+	1.21868e10i	0.339593	+	0.339593i	−0.516621	+	0.856214i	$0.672810\pi$
$84$		0			0
$85$	2.61254e10	−	2.61254e10i	0.638645	−	0.638645i
$86$		0			0
$87$			5.25674e9i			0.113073i
$88$		0			0
$89$		−	3.35444e10i		−	0.636759i	−0.947963	−	0.318379i	$-0.896861\pi$
$89$		−	3.35444e10i		−	0.636759i	0.947963	−	0.318379i	$-0.103139\pi$
$90$		0			0
$91$	−7.40944e10	+	7.40944e10i	−1.24468	+	1.24468i
$92$		0			0
$93$	3.67618e10	+	3.67618e10i	0.547950	+	0.547950i
$94$		0			0
$95$	−1.99397e11			−2.64387
$96$		0			0
$97$	2.49231e10			0.294685			0.147342	−	0.989086i	$-0.452928\pi$
$97$	2.49231e10			0.294685			0.147342	+	0.989086i	$0.452928\pi$
$98$		0			0
$99$	−1.42534e10	−	1.42534e10i	−0.150635	−	0.150635i
$100$		0			0
$101$	−7.39401e10	+	7.39401e10i	−0.700023	+	0.700023i	−0.964415	−	0.264392i	$-0.914829\pi$
$101$	−7.39401e10	+	7.39401e10i	−0.700023	+	0.700023i	0.264392	+	0.964415i	$0.414829\pi$
$102$		0			0
$103$		−	1.55937e10i		−	0.132539i	−0.997802	−	0.0662694i	$-0.978890\pi$
$103$		−	1.55937e10i		−	0.132539i	0.997802	−	0.0662694i	$-0.0211097\pi$
$104$		0			0
$105$			1.98472e11i			1.51760i
$106$		0			0
$107$	−6.52098e10	+	6.52098e10i	−0.449471	+	0.449471i	−0.895179	−	0.445707i	$-0.852952\pi$
$107$	−6.52098e10	+	6.52098e10i	−0.449471	+	0.449471i	0.445707	+	0.895179i	$0.352952\pi$
$108$		0			0
$109$	1.02657e11	+	1.02657e11i	0.639061	+	0.639061i	0.950324	−	0.311263i	$-0.100752\pi$
$109$	1.02657e11	+	1.02657e11i	0.639061	+	0.639061i	−0.311263	+	0.950324i	$0.600752\pi$
$110$		0			0
$111$	−2.62746e10			−0.147999
$112$		0			0
$113$	−2.05501e10			−0.104926			−0.0524630	−	0.998623i	$-0.516707\pi$
$113$	−2.05501e10			−0.104926			−0.0524630	+	0.998623i	$0.516707\pi$
$114$		0			0
$115$	−1.89977e11	−	1.89977e11i	−0.880769	−	0.880769i
$116$		0			0
$117$	−1.29860e11	+	1.29860e11i	−0.547589	+	0.547589i
$118$		0			0
$119$			1.62681e11i			0.624925i
$120$		0			0
$121$			2.42604e11i			0.850313i
$122$		0			0
$123$	−1.49295e11	+	1.49295e11i	−0.478154	+	0.478154i
$124$		0			0
$125$	5.55050e11	+	5.55050e11i	1.62677	+	1.62677i
$126$		0			0
$127$	6.09498e11			1.63701			0.818506	−	0.574498i	$-0.194803\pi$
$127$	6.09498e11			1.63701			0.818506	+	0.574498i	$0.194803\pi$
$128$		0			0
$129$	1.23767e11			0.305043
$130$		0			0
$131$	9.65459e10	+	9.65459e10i	0.218646	+	0.218646i	0.807928	−	0.589282i	$-0.200589\pi$
$131$	9.65459e10	+	9.65459e10i	0.218646	+	0.218646i	−0.589282	+	0.807928i	$0.700589\pi$
$132$		0			0
$133$	6.20815e11	−	6.20815e11i	1.29353	−	1.29353i
$134$		0			0
$135$			9.79596e11i			1.88023i
$136$		0			0
$137$			4.17036e11i			0.738262i	0.929377	+	0.369131i	$0.120345\pi$
$137$			4.17036e11i			0.738262i	−0.929377	+	0.369131i	$0.879655\pi$
$138$		0			0
$139$	−4.11704e11	+	4.11704e11i	−0.672982	+	0.672982i	−0.958403	−	0.285420i	$-0.907867\pi$
$139$	−4.11704e11	+	4.11704e11i	−0.672982	+	0.672982i	0.285420	+	0.958403i	$0.407867\pi$
$140$		0			0
$141$	−3.70399e11	−	3.70399e11i	−0.559711	−	0.559711i
$142$		0			0
$143$	−3.89099e11			−0.544142
$144$		0			0
$145$	−2.35491e11			−0.305105
$146$		0			0
$147$	−2.23442e11	−	2.23442e11i	−0.268484	−	0.268484i
$148$		0			0
$149$	−5.89614e11	+	5.89614e11i	−0.657724	+	0.657724i	−0.954841	−	0.297117i	$-0.903975\pi$
$149$	−5.89614e11	+	5.89614e11i	−0.657724	+	0.657724i	0.297117	+	0.954841i	$0.403975\pi$
$150$		0			0
$151$		−	1.16918e12i		−	1.21201i	−0.795459	−	0.606007i	$-0.792770\pi$
$151$		−	1.16918e12i		−	1.21201i	0.795459	−	0.606007i	$-0.207230\pi$
$152$		0			0
$153$			2.85120e11i			0.274932i
$154$		0			0
$155$	−1.64685e12	+	1.64685e12i	−1.47853	+	1.47853i
$156$		0			0
$157$	1.50102e12	+	1.50102e12i	1.25585	+	1.25585i	0.953057	+	0.302791i	$0.0979186\pi$
$157$	1.50102e12	+	1.50102e12i	1.25585	+	1.25585i	0.302791	+	0.953057i	$0.402081\pi$
$158$		0			0
$159$	−1.37732e12			−1.07486
$160$		0			0
$161$	1.18297e12			0.861848
$162$		0			0
$163$	−1.05489e12	−	1.05489e12i	−0.718085	−	0.718085i	0.250128	−	0.968213i	$-0.419527\pi$
$163$	−1.05489e12	−	1.05489e12i	−0.718085	−	0.718085i	−0.968213	+	0.250128i	$0.919527\pi$
$164$		0			0
$165$	−5.21129e11	+	5.21129e11i	−0.331729	+	0.331729i
$166$		0			0
$167$			2.19763e12i			1.30923i	0.755965	+	0.654613i	$0.227168\pi$
$167$			2.19763e12i			1.30923i	−0.755965	+	0.654613i	$0.772832\pi$
$168$		0			0
$169$			1.75286e12i			0.978070i
$170$		0			0
$171$	1.08806e12	−	1.08806e12i	0.569082	−	0.569082i
$172$		0			0
$173$	2.08631e12	+	2.08631e12i	1.02359	+	1.02359i	0.999715	+	0.0238746i	$0.00760024\pi$
$173$	2.08631e12	+	2.08631e12i	1.02359	+	1.02359i	0.0238746	+	0.999715i	$0.492400\pi$
$174$		0			0
$175$	−6.17369e12			−2.84339
$176$		0			0
$177$	−3.42253e11			−0.148079
$178$		0			0
$179$	7.81494e11	+	7.81494e11i	0.317859	+	0.317859i	0.847944	−	0.530086i	$-0.177840\pi$
$179$	7.81494e11	+	7.81494e11i	0.317859	+	0.317859i	−0.530086	+	0.847944i	$0.677840\pi$
$180$		0			0
$181$	−1.08737e12	+	1.08737e12i	−0.416052	+	0.416052i	−0.883840	−	0.467789i	$-0.845051\pi$
$181$	−1.08737e12	+	1.08737e12i	−0.416052	+	0.416052i	0.467789	+	0.883840i	$0.345051\pi$
$182$		0			0
$183$		−	2.71525e12i		−	0.977978i
$184$		0			0
$185$		−	1.17705e12i		−	0.399346i
$186$		0			0
$187$	−4.27151e11	+	4.27151e11i	−0.136601	+	0.136601i
$188$		0			0
$189$	−3.04993e12	−	3.04993e12i	−0.919919	−	0.919919i
$190$		0			0
$191$	2.35610e12			0.670672			0.335336	−	0.942099i	$-0.391150\pi$
$191$	2.35610e12			0.670672			0.335336	+	0.942099i	$0.391150\pi$
$192$		0			0
$193$	5.05945e12			1.36000			0.679999	−	0.733213i	$-0.261980\pi$
$193$	5.05945e12			1.36000			0.679999	+	0.733213i	$0.261980\pi$
$194$		0			0
$195$	4.74792e12	+	4.74792e12i	1.20590	+	1.20590i
$196$		0			0
$197$	2.28419e12	−	2.28419e12i	0.548490	−	0.548490i	−0.377514	−	0.926004i	$-0.623221\pi$
$197$	2.28419e12	−	2.28419e12i	0.548490	−	0.548490i	0.926004	+	0.377514i	$0.123221\pi$
$198$		0			0
$199$			1.32865e12i			0.301799i	0.988549	+	0.150899i	$0.0482170\pi$
$199$			1.32865e12i			0.301799i	−0.988549	+	0.150899i	$0.951783\pi$
$200$		0			0
$201$			2.33608e12i			0.502239i
$202$		0			0
$203$	7.33190e11	−	7.33190e11i	0.149275	−	0.149275i
$204$		0			0
$205$	−6.68812e12	−	6.68812e12i	−1.29020	−	1.29020i
$206$		0			0
$207$	2.07331e12			0.379165
$208$		0			0
$209$	3.26015e12			0.565500
$210$		0			0
$211$	−7.82026e12	−	7.82026e12i	−1.28726	−	1.28726i	−0.936442	−	0.350823i	$-0.885902\pi$
$211$	−7.82026e12	−	7.82026e12i	−1.28726	−	1.28726i	−0.350823	−	0.936442i	$-0.614098\pi$
$212$		0			0
$213$	−2.31242e10	+	2.31242e10i	−0.00361392	+	0.00361392i
$214$		0			0
$215$			5.54449e12i			0.823096i
$216$		0			0
$217$		−	1.02548e13i		−	1.44677i
$218$		0			0
$219$	2.46025e11	−	2.46025e11i	0.0330017	−	0.0330017i
$220$		0			0
$221$	3.89170e12	+	3.89170e12i	0.496572	+	0.496572i
$222$		0			0
$223$	1.45466e13			1.76638			0.883190	−	0.469015i	$-0.155391\pi$
$223$	1.45466e13			1.76638			0.883190	+	0.469015i	$0.155391\pi$
$224$		0			0
$225$	−1.08202e13			−1.25093
$226$		0			0
$227$	1.14517e13	+	1.14517e13i	1.26104	+	1.26104i	0.950591	+	0.310446i	$0.100478\pi$
$227$	1.14517e13	+	1.14517e13i	1.26104	+	1.26104i	0.310446	+	0.950591i	$0.399522\pi$
$228$		0			0
$229$	−8.19588e12	+	8.19588e12i	−0.860004	+	0.860004i	−0.991338	−	0.131335i	$-0.958074\pi$
$229$	−8.19588e12	+	8.19588e12i	−0.860004	+	0.860004i	0.131335	+	0.991338i	$0.458074\pi$
$230$		0			0
$231$		−	3.24502e12i		−	0.324603i
$232$		0			0
$233$			1.19894e13i			1.14378i	0.820332	+	0.571888i	$0.193789\pi$
$233$			1.19894e13i			1.14378i	−0.820332	+	0.571888i	$0.806211\pi$
$234$		0			0
$235$	1.65931e13	−	1.65931e13i	1.51027	−	1.51027i
$236$		0			0
$237$	−3.32796e11	−	3.32796e11i	−0.0289109	−	0.0289109i
$238$		0			0
$239$	−1.05045e13			−0.871339			−0.435669	−	0.900107i	$-0.643488\pi$
$239$	−1.05045e13			−0.871339			−0.435669	+	0.900107i	$0.643488\pi$
$240$		0			0
$241$	−4.17569e12			−0.330853			−0.165426	−	0.986222i	$-0.552900\pi$
$241$	−4.17569e12			−0.330853			−0.165426	+	0.986222i	$0.552900\pi$
$242$		0			0
$243$	−8.79270e12	−	8.79270e12i	−0.665714	−	0.665714i
$244$		0			0
$245$	1.00097e13	−	1.00097e13i	0.724450	−	0.724450i
$246$		0			0
$247$		−	2.97027e13i		−	2.05571i
$248$		0			0
$249$			4.86271e12i			0.321945i
$250$		0			0
$251$	−1.23422e13	+	1.23422e13i	−0.781962	+	0.781962i	−0.980162	−	0.198199i	$-0.936491\pi$
$251$	−1.23422e13	+	1.23422e13i	−0.781962	+	0.781962i	0.198199	+	0.980162i	$0.436491\pi$
$252$		0			0
$253$	3.10612e12	+	3.10612e12i	0.188389	+	0.188389i
$254$		0			0
$255$	1.04245e13			0.605457
$256$		0			0
$257$	−1.61488e13			−0.898477			−0.449238	−	0.893412i	$-0.648305\pi$
$257$	−1.61488e13			−0.898477			−0.449238	+	0.893412i	$0.648305\pi$
$258$		0			0
$259$	3.66468e12	+	3.66468e12i	0.195383	+	0.195383i
$260$		0			0
$261$	1.28501e12	−	1.28501e12i	0.0656728	−	0.0656728i
$262$		0			0
$263$			2.33354e13i			1.14356i	0.820407	+	0.571780i	$0.193747\pi$
$263$			2.33354e13i			1.14356i	−0.820407	+	0.571780i	$0.806253\pi$
$264$		0			0
$265$		−	6.17011e13i		−	2.90028i
$266$		0			0
$267$	6.69238e12	−	6.69238e12i	0.301834	−	0.301834i
$268$		0			0
$269$	−2.23132e12	−	2.23132e12i	−0.0965881	−	0.0965881i	0.657162	−	0.753750i	$-0.271757\pi$
$269$	−2.23132e12	−	2.23132e12i	−0.0965881	−	0.0965881i	−0.753750	+	0.657162i	$0.771757\pi$
$270$		0			0
$271$	3.01445e13			1.25279			0.626393	−	0.779508i	$-0.284531\pi$
$271$	3.01445e13			1.25279			0.626393	+	0.779508i	$0.284531\pi$
$272$		0			0
$273$	−2.95649e13			−1.18000
$274$		0			0
$275$	−1.62103e13	−	1.62103e13i	−0.621528	−	0.621528i
$276$		0			0
$277$	1.38774e13	−	1.38774e13i	0.511292	−	0.511292i	−0.403630	−	0.914922i	$-0.632252\pi$
$277$	1.38774e13	−	1.38774e13i	0.511292	−	0.511292i	0.914922	+	0.403630i	$0.132252\pi$
$278$		0			0
$279$		−	1.79729e13i		−	0.636497i
$280$		0			0
$281$		−	1.23343e13i		−	0.419981i	−0.977703	−	0.209990i	$-0.932657\pi$
$281$		−	1.23343e13i		−	0.419981i	0.977703	−	0.209990i	$-0.0673433\pi$
$282$		0			0
$283$	−5.76116e12	+	5.76116e12i	−0.188662	+	0.188662i	−0.795118	−	0.606455i	$-0.792591\pi$
$283$	−5.76116e12	+	5.76116e12i	−0.188662	+	0.188662i	0.606455	+	0.795118i	$0.292591\pi$
$284$		0			0
$285$	−3.97814e13	−	3.97814e13i	−1.25324	−	1.25324i
$286$		0			0
$287$	4.16463e13			1.26248
$288$		0			0
$289$	−2.57273e13			−0.750683
$290$		0			0
$291$	4.97237e12	+	4.97237e12i	0.139686	+	0.139686i
$292$		0			0
$293$	3.65192e13	−	3.65192e13i	0.987982	−	0.987982i	−0.0119465	−	0.999929i	$-0.503803\pi$
$293$	3.65192e13	−	3.65192e13i	0.987982	−	0.987982i	0.999929	+	0.0119465i	$0.00380279\pi$
$294$		0			0
$295$		−	1.53322e13i		−	0.399561i
$296$		0			0
$297$		−	1.60164e13i		−	0.402165i
$298$		0			0
$299$	2.82993e13	−	2.82993e13i	0.684833	−	0.684833i
$300$		0			0
$301$	−1.72625e13	−	1.72625e13i	−0.402707	−	0.402707i
$302$		0			0
$303$	−2.95033e13			−0.663646
$304$		0			0
$305$	1.21638e14			2.63887
$306$		0			0
$307$	3.86138e13	+	3.86138e13i	0.808131	+	0.808131i	0.984351	−	0.176220i	$-0.0563871\pi$
$307$	3.86138e13	+	3.86138e13i	0.808131	+	0.808131i	−0.176220	+	0.984351i	$0.556387\pi$
$308$		0			0
$309$	3.11106e12	−	3.11106e12i	0.0628256	−	0.0628256i
$310$		0			0
$311$			2.21250e13i			0.431221i	0.976479	+	0.215611i	$0.0691742\pi$
$311$			2.21250e13i			0.431221i	−0.976479	+	0.215611i	$0.930826\pi$
$312$		0			0
$313$			4.91648e13i			0.925039i	0.886609	+	0.462520i	$0.153055\pi$
$313$			4.91648e13i			0.925039i	−0.886609	+	0.462520i	$0.846945\pi$
$314$		0			0
$315$	4.85168e13	−	4.85168e13i	0.881422	−	0.881422i
$316$		0			0
$317$	2.50121e13	+	2.50121e13i	0.438858	+	0.438858i	0.891627	−	0.452770i	$-0.149564\pi$
$317$	2.50121e13	+	2.50121e13i	0.438858	+	0.438858i	−0.452770	+	0.891627i	$0.649564\pi$
$318$		0			0
$319$	3.85027e12			0.0652594
$320$		0			0
$321$	−2.60198e13			−0.426114
$322$		0			0
$323$	−3.26074e13	−	3.26074e13i	−0.516063	−	0.516063i
$324$		0			0
$325$	−1.47689e14	+	1.47689e14i	−2.25938	+	2.25938i
$326$		0			0
$327$			4.09618e13i			0.605852i
$328$		0			0
$329$			1.03324e14i			1.47782i
$330$		0			0
$331$	−6.15855e13	+	6.15855e13i	−0.851970	+	0.851970i	−0.990376	−	0.138405i	$-0.955802\pi$
$331$	−6.15855e13	+	6.15855e13i	−0.851970	+	0.851970i	0.138405	+	0.990376i	$0.455802\pi$
$332$		0			0
$333$	6.42285e12	+	6.42285e12i	0.0859577	+	0.0859577i
$334$		0			0
$335$	−1.04652e14			−1.35519
$336$		0			0
$337$	−1.50805e11			−0.00188996			−0.000944980	−	1.00000i	$-0.500301\pi$
$337$	−1.50805e11			−0.00188996			−0.000944980		1.00000i	$0.500301\pi$
$338$		0			0
$339$	−4.09992e12	−	4.09992e12i	−0.0497367	−	0.0497367i
$340$		0			0
$341$	2.69261e13	−	2.69261e13i	0.316245	−	0.316245i
$342$		0			0
$343$		−	4.77151e13i		−	0.542673i
$344$		0			0
$345$		−	7.58038e13i		−	0.834999i
$346$		0			0
$347$	−1.74401e13	+	1.74401e13i	−0.186096	+	0.186096i	−0.794006	−	0.607910i	$-0.792008\pi$
$347$	−1.74401e13	+	1.74401e13i	−0.186096	+	0.186096i	0.607910	+	0.794006i	$0.292008\pi$
$348$		0			0
$349$	3.25744e13	+	3.25744e13i	0.336773	+	0.336773i	0.855151	−	0.518378i	$-0.173464\pi$
$349$	3.25744e13	+	3.25744e13i	0.336773	+	0.336773i	−0.518378	+	0.855151i	$0.673464\pi$
$350$		0			0
$351$	−1.45923e14			−1.46195
$352$		0			0
$353$	−1.61148e12			−0.0156481			−0.00782407	−	0.999969i	$-0.502491\pi$
$353$	−1.61148e12			−0.0156481			−0.00782407	+	0.999969i	$0.502491\pi$
$354$		0			0
$355$	−1.03591e12	−	1.03591e12i	−0.00975141	−	0.00975141i
$356$		0			0
$357$	−3.24562e13	+	3.24562e13i	−0.296225	+	0.296225i
$358$		0			0
$359$		−	5.33566e13i		−	0.472246i	−0.971723	−	0.236123i	$-0.924123\pi$
$359$		−	5.33566e13i		−	0.472246i	0.971723	−	0.236123i	$-0.0758769\pi$
$360$		0			0
$361$			1.32379e14i			1.13640i
$362$		0			0
$363$	−4.84015e13	+	4.84015e13i	−0.403063	+	0.403063i
$364$		0			0
$365$	1.10214e13	+	1.10214e13i	0.0890482	+	0.0890482i
$366$		0			0
$367$	9.63988e13			0.755802			0.377901	−	0.925846i	$-0.376646\pi$
$367$	9.63988e13			0.755802			0.377901	+	0.925846i	$0.376646\pi$
$368$		0			0
$369$	7.29908e13			0.555422
$370$		0			0
$371$	1.92104e14	+	1.92104e14i	1.41899	+	1.41899i
$372$		0			0
$373$	6.67716e13	−	6.67716e13i	0.478843	−	0.478843i	−0.425919	−	0.904761i	$-0.640049\pi$
$373$	6.67716e13	−	6.67716e13i	0.478843	−	0.478843i	0.904761	+	0.425919i	$0.140049\pi$
$374$		0			0
$375$			2.21474e14i			1.54224i
$376$		0			0
$377$		−	3.50792e13i		−	0.237231i
$378$		0			0
$379$	−3.97407e13	+	3.97407e13i	−0.261048	+	0.261048i	−0.825480	−	0.564432i	$-0.809095\pi$
$379$	−3.97407e13	+	3.97407e13i	−0.261048	+	0.261048i	0.564432	+	0.825480i	$0.309095\pi$
$380$		0			0
$381$	1.21600e14	+	1.21600e14i	0.775971	+	0.775971i
$382$		0			0
$383$	−1.57401e14			−0.975918			−0.487959	−	0.872866i	$-0.662259\pi$
$383$	−1.57401e14			−0.975918			−0.487959	+	0.872866i	$0.662259\pi$
$384$		0			0
$385$	1.45370e14			0.875873
$386$		0			0
$387$	−3.02549e13	−	3.02549e13i	−0.177168	−	0.177168i
$388$		0			0
$389$	1.16568e14	−	1.16568e14i	0.663525	−	0.663525i	−0.292684	−	0.956209i	$-0.594548\pi$
$389$	1.16568e14	−	1.16568e14i	0.663525	−	0.663525i	0.956209	+	0.292684i	$0.0945485\pi$
$390$		0			0
$391$		−	6.21337e13i		−	0.343839i
$392$		0			0
$393$			3.85234e13i			0.207284i
$394$		0			0
$395$	1.49086e13	−	1.49086e13i	0.0780102	−	0.0780102i
$396$		0			0
$397$	6.93873e13	+	6.93873e13i	0.353128	+	0.353128i	0.861272	−	0.508144i	$-0.169668\pi$
$397$	6.93873e13	+	6.93873e13i	0.353128	+	0.353128i	−0.508144	+	0.861272i	$0.669668\pi$
$398$		0			0
$399$	2.47715e14			1.22631
$400$		0			0
$401$	−1.22810e14			−0.591482			−0.295741	−	0.955268i	$-0.595566\pi$
$401$	−1.22810e14			−0.591482			−0.295741	+	0.955268i	$0.595566\pi$
$402$		0			0
$403$	−2.45319e14	−	2.45319e14i	−1.14962	−	1.14962i
$404$		0			0
$405$	−4.10063e13	+	4.10063e13i	−0.187003	+	0.187003i
$406$		0			0
$407$			1.92447e13i			0.0854166i
$408$		0			0
$409$		−	7.71261e13i		−	0.333214i	−0.986023	−	0.166607i	$-0.946719\pi$
$409$		−	7.71261e13i		−	0.333214i	0.986023	−	0.166607i	$-0.0532811\pi$
$410$		0			0
$411$	−8.32021e13	+	8.32021e13i	−0.349948	+	0.349948i
$412$		0			0
$413$	4.77361e13	+	4.77361e13i	0.195489	+	0.195489i
$414$		0			0
$415$	−2.17839e14			−0.868704
$416$		0			0
$417$	−1.64277e14			−0.638010
$418$		0			0
$419$	−3.70961e14	−	3.70961e14i	−1.40330	−	1.40330i	−0.789314	−	0.613989i	$-0.789564\pi$
$419$	−3.70961e14	−	3.70961e14i	−1.40330	−	1.40330i	−0.613989	−	0.789314i	$-0.710436\pi$
$420$		0			0
$421$	−1.97013e13	+	1.97013e13i	−0.0726011	+	0.0726011i	−0.742475	−	0.669874i	$-0.766348\pi$
$421$	−1.97013e13	+	1.97013e13i	−0.0726011	+	0.0726011i	0.669874	+	0.742475i	$0.266348\pi$
$422$		0			0
$423$			1.81089e14i			0.650159i
$424$		0			0
$425$			3.24265e14i			1.13438i
$426$		0			0
$427$	−3.78713e14	+	3.78713e14i	−1.29109	+	1.29109i
$428$		0			0
$429$	−7.76285e13	−	7.76285e13i	−0.257932	−	0.257932i
$430$		0			0
$431$	8.37088e13			0.271110			0.135555	−	0.990770i	$-0.456718\pi$
$431$	8.37088e13			0.271110			0.135555	+	0.990770i	$0.456718\pi$
$432$		0			0
$433$	3.95547e14			1.24886			0.624431	−	0.781080i	$-0.285331\pi$
$433$	3.95547e14			1.24886			0.624431	+	0.781080i	$0.285331\pi$
$434$		0			0
$435$	−4.69823e13	−	4.69823e13i	−0.144625	−	0.144625i
$436$		0			0
$437$	−2.37112e14	+	2.37112e14i	−0.711713	+	0.711713i
$438$		0			0
$439$			4.95762e14i			1.45117i	0.688132	+	0.725586i	$0.258431\pi$
$439$			4.95762e14i			1.45117i	−0.688132	+	0.725586i	$0.741569\pi$
$440$		0			0
$441$			1.09241e14i			0.311871i
$442$		0			0
$443$	−9.47829e13	+	9.47829e13i	−0.263943	+	0.263943i	−0.826654	−	0.562711i	$-0.809758\pi$
$443$	−9.47829e13	+	9.47829e13i	−0.263943	+	0.263943i	0.562711	+	0.826654i	$0.309758\pi$
$444$		0			0
$445$	2.99805e14	+	2.99805e14i	0.814438	+	0.814438i
$446$		0			0
$447$	−2.35266e14			−0.623544
$448$		0			0
$449$	−3.01226e14			−0.779001			−0.389500	−	0.921026i	$-0.627352\pi$
$449$	−3.01226e14			−0.779001			−0.389500	+	0.921026i	$0.627352\pi$
$450$		0			0
$451$	1.09351e14	+	1.09351e14i	0.275963	+	0.275963i
$452$		0			0
$453$	2.33261e14	−	2.33261e14i	0.574515	−	0.574515i
$454$		0			0
$455$		−	1.32444e15i		−	3.18398i
$456$		0			0
$457$		−	1.00211e14i		−	0.235166i	−0.993063	−	0.117583i	$-0.962485\pi$
$457$		−	1.00211e14i		−	0.235166i	0.993063	−	0.117583i	$-0.0375146\pi$
$458$		0			0
$459$	−1.60193e14	+	1.60193e14i	−0.367007	+	0.367007i
$460$		0			0
$461$	−3.90890e14	−	3.90890e14i	−0.874377	−	0.874377i	0.118568	−	0.992946i	$-0.462169\pi$
$461$	−3.90890e14	−	3.90890e14i	−0.874377	−	0.874377i	−0.992946	+	0.118568i	$0.962169\pi$
$462$		0			0
$463$	−7.10495e13			−0.155191			−0.0775953	−	0.996985i	$-0.524724\pi$
$463$	−7.10495e13			−0.155191			−0.0775953	+	0.996985i	$0.524724\pi$
$464$		0			0
$465$	−6.57121e14			−1.40170
$466$		0			0
$467$	4.92262e14	+	4.92262e14i	1.02554	+	1.02554i	0.999665	+	0.0258775i	$0.00823799\pi$
$467$	4.92262e14	+	4.92262e14i	1.02554	+	1.02554i	0.0258775	+	0.999665i	$0.491762\pi$
$468$		0			0
$469$	3.25828e14	−	3.25828e14i	0.663037	−	0.663037i
$470$		0			0
$471$			5.98930e14i			1.19059i
$472$		0			0
$473$		−	9.06525e13i		−	0.176053i
$474$		0			0
$475$	1.23744e15	−	1.23744e15i	2.34807	−	2.34807i
$476$		0			0
$477$	3.36688e14	+	3.36688e14i	0.624275	+	0.624275i
$478$		0			0
$479$	1.05196e15			1.90614			0.953069	−	0.302752i	$-0.0979053\pi$
$479$	1.05196e15			1.90614			0.953069	+	0.302752i	$0.0979053\pi$
$480$		0			0
$481$	1.75335e14			0.310507
$482$		0			0
$483$	2.36012e14	+	2.36012e14i	0.408530	+	0.408530i
$484$		0			0
$485$	−2.22752e14	+	2.22752e14i	−0.376913	+	0.376913i
$486$		0			0
$487$			1.75551e14i			0.290398i	0.989403	+	0.145199i	$0.0463822\pi$
$487$			1.75551e14i			0.290398i	−0.989403	+	0.145199i	$0.953618\pi$
$488$		0			0
$489$		−	4.20919e14i		−	0.680769i
$490$		0			0
$491$	3.90969e14	−	3.90969e14i	0.618293	−	0.618293i	−0.326800	−	0.945093i	$-0.605970\pi$
$491$	3.90969e14	−	3.90969e14i	0.618293	−	0.618293i	0.945093	+	0.326800i	$0.105970\pi$
$492$		0			0
$493$	−3.85098e13	−	3.85098e13i	−0.0595543	−	0.0595543i
$494$		0			0
$495$	2.54781e14			0.385335
$496$		0			0
$497$	6.45054e12			0.00954192
$498$		0			0
$499$	4.65711e14	+	4.65711e14i	0.673851	+	0.673851i	0.958602	−	0.284751i	$-0.0919109\pi$
$499$	4.65711e14	+	4.65711e14i	0.673851	+	0.673851i	−0.284751	+	0.958602i	$0.591911\pi$
$500$		0			0
$501$	−4.38445e14	+	4.38445e14i	−0.620595	+	0.620595i
$502$		0			0
$503$		−	1.00596e15i		−	1.39302i	−0.717546	−	0.696511i	$-0.754735\pi$
$503$		−	1.00596e15i		−	1.39302i	0.717546	−	0.696511i	$-0.245265\pi$
$504$		0			0
$505$		−	1.32169e15i		−	1.79071i
$506$		0			0
$507$	−3.49709e14	+	3.49709e14i	−0.463621	+	0.463621i
$508$		0			0
$509$	−9.28220e14	−	9.28220e14i	−1.20421	−	1.20421i	−0.972873	−	0.231339i	$-0.925690\pi$
$509$	−9.28220e14	−	9.28220e14i	−1.20421	−	1.20421i	−0.231339	−	0.972873i	$-0.574310\pi$
$510$		0			0
$511$	−6.86292e13			−0.0871352
$512$		0			0
$513$	1.22264e15			1.51934
$514$		0			0
$515$	1.39369e14	+	1.39369e14i	0.169522	+	0.169522i
$516$		0			0
$517$	−2.71297e14	+	2.71297e14i	−0.323033	+	0.323033i
$518$		0			0
$519$			8.32473e14i			0.970397i
$520$		0			0
$521$			3.89954e14i			0.445047i	0.974927	+	0.222523i	$0.0714294\pi$
$521$			3.89954e14i			0.445047i	−0.974927	+	0.222523i	$0.928571\pi$
$522$		0			0
$523$	8.43298e14	−	8.43298e14i	0.942370	−	0.942370i	−0.0560573	−	0.998428i	$-0.517853\pi$
$523$	8.43298e14	−	8.43298e14i	0.942370	−	0.942370i	0.998428	+	0.0560573i	$0.0178530\pi$
$524$		0			0
$525$	−1.23170e15	−	1.23170e15i	−1.34781	−	1.34781i
$526$		0			0
$527$	−5.38619e14			−0.577196
$528$		0			0
$529$	5.00991e14			0.525804
$530$		0			0
$531$	8.36641e13	+	8.36641e13i	0.0860041	+	0.0860041i
$532$		0			0
$533$	9.96276e14	−	9.96276e14i	1.00318	−	1.00318i
$534$		0			0
$535$		−	1.16563e15i		−	1.14978i
$536$		0			0
$537$			3.11829e14i			0.301341i
$538$		0			0
$539$	−1.63659e14	+	1.63659e14i	−0.154954	+	0.154954i
$540$		0			0
$541$	−7.75321e14	−	7.75321e14i	−0.719277	−	0.719277i	0.249180	−	0.968457i	$-0.419839\pi$
$541$	−7.75321e14	−	7.75321e14i	−0.719277	−	0.719277i	−0.968457	+	0.249180i	$0.919839\pi$
$542$		0			0
$543$	−4.33880e14			−0.394431
$544$		0			0
$545$	−1.83500e15			−1.63477
$546$		0			0
$547$	−1.27728e15	−	1.27728e15i	−1.11521	−	1.11521i	−0.992435	−	0.122774i	$-0.960821\pi$
$547$	−1.27728e15	−	1.27728e15i	−1.11521	−	1.11521i	−0.122774	−	0.992435i	$-0.539179\pi$
$548$		0			0
$549$	−6.63747e14	+	6.63747e14i	−0.568008	+	0.568008i
$550$		0			0
$551$			2.93918e14i			0.246543i
$552$		0			0
$553$			9.28343e13i			0.0763344i
$554$		0			0
$555$	2.34830e14	−	2.34830e14i	0.189297	−	0.189297i
$556$		0			0
$557$	6.89209e14	+	6.89209e14i	0.544687	+	0.544687i	0.924899	−	0.380212i	$-0.124149\pi$
$557$	6.89209e14	+	6.89209e14i	0.544687	+	0.544687i	−0.380212	+	0.924899i	$0.624149\pi$
$558$		0			0
$559$	−8.25920e14			−0.639990
$560$		0			0
$561$	−1.70440e14			−0.129502
$562$		0			0
$563$	−7.63745e14	−	7.63745e14i	−0.569052	−	0.569052i	0.362811	−	0.931863i	$-0.381817\pi$
$563$	−7.63745e14	−	7.63745e14i	−0.569052	−	0.569052i	−0.931863	+	0.362811i	$0.881817\pi$
$564$		0			0
$565$	1.83668e14	−	1.83668e14i	0.134204	−	0.134204i
$566$		0			0
$567$		−	2.55343e14i		−	0.182985i
$568$		0			0
$569$		−	1.49261e14i		−	0.104913i	−0.998623	−	0.0524563i	$-0.983295\pi$
$569$		−	1.49261e14i		−	0.104913i	0.998623	−	0.0524563i	$-0.0167050\pi$
$570$		0			0
$571$	−1.12561e15	+	1.12561e15i	−0.776052	+	0.776052i	−0.979157	−	0.203105i	$-0.934897\pi$
$571$	−1.12561e15	+	1.12561e15i	−0.776052	+	0.776052i	0.203105	+	0.979157i	$0.434897\pi$
$572$		0			0
$573$	4.70061e14	+	4.70061e14i	0.317910	+	0.317910i
$574$		0			0
$575$	2.35796e15			1.56445
$576$		0			0
$577$	−1.10552e15			−0.719615			−0.359807	−	0.933027i	$-0.617158\pi$
$577$	−1.10552e15			−0.719615			−0.359807	+	0.933027i	$0.617158\pi$
$578$		0			0
$579$	1.00940e15	+	1.00940e15i	0.644662	+	0.644662i
$580$		0			0
$581$	6.78233e14	−	6.78233e14i	0.425021	−	0.425021i
$582$		0			0
$583$			1.00881e15i			0.620345i
$584$		0			0
$585$		−	2.32127e15i		−	1.40077i
$586$		0			0
$587$	5.74857e14	−	5.74857e14i	0.340448	−	0.340448i	−0.516088	−	0.856536i	$-0.672612\pi$
$587$	5.74857e14	−	5.74857e14i	0.340448	−	0.340448i	0.856536	+	0.516088i	$0.172612\pi$
$588$		0			0
$589$	2.05545e15	+	2.05545e15i	1.19474	+	1.19474i
$590$		0			0
$591$	9.11431e14			0.519987
$592$		0			0
$593$	1.70041e15			0.952252			0.476126	−	0.879377i	$-0.342041\pi$
$593$	1.70041e15			0.952252			0.476126	+	0.879377i	$0.342041\pi$
$594$		0			0
$595$	−1.45397e15	−	1.45397e15i	−0.799303	−	0.799303i
$596$		0			0
$597$	−2.65076e14	+	2.65076e14i	−0.143058	+	0.143058i
$598$		0			0
$599$		−	9.06284e14i		−	0.480194i	−0.970749	−	0.240097i	$-0.922821\pi$
$599$		−	9.06284e14i		−	0.480194i	0.970749	−	0.240097i	$-0.0771792\pi$
$600$		0			0
$601$			3.33138e15i			1.73306i	0.499124	+	0.866531i	$0.333655\pi$
$601$			3.33138e15i			1.73306i	−0.499124	+	0.866531i	$0.666345\pi$
$602$		0			0
$603$	5.71058e14	−	5.71058e14i	0.291699	−	0.291699i
$604$		0			0
$605$	−2.16829e15	−	2.16829e15i	−1.08758	−	1.08758i
$606$		0			0
$607$	1.62819e15			0.801986			0.400993	−	0.916081i	$-0.368665\pi$
$607$	1.62819e15			0.801986			0.400993	+	0.916081i	$0.368665\pi$
$608$		0			0
$609$	2.92555e14			0.141518
$610$		0			0
$611$	2.47174e15	+	2.47174e15i	1.17429	+	1.17429i
$612$		0			0
$613$	1.39720e15	−	1.39720e15i	0.651968	−	0.651968i	−0.301499	−	0.953467i	$-0.597487\pi$
$613$	1.39720e15	−	1.39720e15i	0.651968	−	0.651968i	0.953467	+	0.301499i	$0.0974868\pi$
$614$		0			0
$615$		−	2.66867e15i		−	1.22315i
$616$		0			0
$617$		−	1.42742e15i		−	0.642661i	−0.946967	−	0.321331i	$-0.895870\pi$
$617$		−	1.42742e15i		−	0.642661i	0.946967	−	0.321331i	$-0.104130\pi$
$618$		0			0
$619$	5.96980e14	−	5.96980e14i	0.264035	−	0.264035i	−0.562656	−	0.826691i	$-0.690220\pi$
$619$	5.96980e14	−	5.96980e14i	0.264035	−	0.264035i	0.826691	+	0.562656i	$0.190220\pi$
$620$		0			0
$621$	1.16488e15	+	1.16488e15i	0.506147	+	0.506147i
$622$		0			0
$623$	−1.86686e15			−0.796942
$624$		0			0
$625$	−4.50500e15			−1.88953
$626$		0			0
$627$	6.50426e14	+	6.50426e14i	0.268057	+	0.268057i
$628$		0			0
$629$	1.92482e14	−	1.92482e14i	0.0779493	−	0.0779493i
$630$		0			0
$631$			3.18386e15i			1.26704i	0.773724	+	0.633522i	$0.218392\pi$
$631$			3.18386e15i			1.26704i	−0.773724	+	0.633522i	$0.781608\pi$
$632$		0			0
$633$		−	3.12041e15i		−	1.22037i
$634$		0			0
$635$	−5.44742e15	+	5.44742e15i	−2.09380	+	2.09380i
$636$		0			0
$637$	1.49107e15	+	1.49107e15i	0.563289	+	0.563289i
$638$		0			0
$639$	1.13054e13			0.00419791
$640$		0			0
$641$	3.07527e15			1.12244			0.561222	−	0.827665i	$-0.310331\pi$
$641$	3.07527e15			1.12244			0.561222	+	0.827665i	$0.310331\pi$
$642$		0			0
$643$	2.71246e14	+	2.71246e14i	0.0973203	+	0.0973203i	0.754091	−	0.656770i	$-0.228078\pi$
$643$	2.71246e14	+	2.71246e14i	0.0973203	+	0.0973203i	−0.656770	+	0.754091i	$0.728078\pi$
$644$		0			0
$645$	−1.10617e15	+	1.10617e15i	−0.390161	+	0.390161i
$646$		0			0
$647$			4.50034e15i			1.56053i	0.625451	+	0.780264i	$0.284915\pi$
$647$			4.50034e15i			1.56053i	−0.625451	+	0.780264i	$0.715085\pi$
$648$		0			0
$649$			2.50682e14i			0.0854627i
$650$		0			0
$651$	2.04592e15	−	2.04592e15i	0.685792	−	0.685792i
$652$		0			0
$653$	2.95719e15	+	2.95719e15i	0.974668	+	0.974668i	0.999687	−	0.0250186i	$-0.00796451\pi$
$653$	2.95719e15	+	2.95719e15i	0.974668	+	0.974668i	−0.0250186	+	0.999687i	$0.507965\pi$
$654$		0			0
$655$	−1.72577e15			−0.559313
$656$		0			0
$657$	−1.20282e14			−0.0383346
$658$		0			0
$659$	−2.05647e15	−	2.05647e15i	−0.644545	−	0.644545i	0.307124	−	0.951669i	$-0.400633\pi$
$659$	−2.05647e15	−	2.05647e15i	−0.644545	−	0.644545i	−0.951669	+	0.307124i	$0.900633\pi$
$660$		0			0
$661$	−2.94861e15	+	2.94861e15i	−0.908887	+	0.908887i	−0.996182	−	0.0872957i	$-0.972177\pi$
$661$	−2.94861e15	+	2.94861e15i	−0.908887	+	0.908887i	0.0872957	+	0.996182i	$0.472177\pi$
$662$		0			0
$663$			1.55285e15i			0.470767i
$664$		0			0
$665$			1.10971e16i			3.30896i
$666$		0			0
$667$	−2.80032e14	+	2.80032e14i	−0.0821326	+	0.0821326i
$668$		0			0
$669$	2.90216e15	+	2.90216e15i	0.837294	+	0.837294i
$670$		0			0
$671$	−1.98878e15			−0.564432
$672$		0			0
$673$	−3.67663e15			−1.02652			−0.513259	−	0.858234i	$-0.671562\pi$
$673$	−3.67663e15			−1.02652			−0.513259	+	0.858234i	$0.671562\pi$
$674$		0			0
$675$	−6.07929e15	−	6.07929e15i	−1.66987	−	1.66987i
$676$		0			0
$677$	1.77059e15	−	1.77059e15i	0.478499	−	0.478499i	−0.426152	−	0.904651i	$-0.640131\pi$
$677$	1.77059e15	−	1.77059e15i	0.478499	−	0.478499i	0.904651	+	0.426152i	$0.140131\pi$
$678$		0			0
$679$		−	1.38705e15i		−	0.368816i
$680$		0			0
$681$			4.56942e15i			1.19551i
$682$		0			0
$683$	−2.83214e15	+	2.83214e15i	−0.729124	+	0.729124i	−0.970445	−	0.241321i	$-0.922419\pi$
$683$	−2.83214e15	+	2.83214e15i	−0.729124	+	0.729124i	0.241321	+	0.970445i	$0.422419\pi$
$684$		0			0
$685$	−3.72728e15	−	3.72728e15i	−0.944264	−	0.944264i
$686$		0			0
$687$	−3.27029e15			−0.815312
$688$		0			0
$689$	9.19112e15			2.25508
$690$		0			0
$691$	2.15938e15	+	2.15938e15i	0.521435	+	0.521435i	0.918005	−	0.396570i	$-0.129800\pi$
$691$	2.15938e15	+	2.15938e15i	0.521435	+	0.521435i	−0.396570	+	0.918005i	$0.629800\pi$
$692$		0			0
$693$	−7.93250e14	+	7.93250e14i	−0.188529	+	0.188529i
$694$		0			0
$695$		−	7.35925e15i		−	1.72154i
$696$		0			0
$697$		−	2.18741e15i		−	0.503675i
$698$		0			0
$699$	−2.39199e15	+	2.39199e15i	−0.542169	+	0.542169i
$700$		0			0
$701$	2.82397e14	+	2.82397e14i	0.0630102	+	0.0630102i	0.737910	−	0.674900i	$-0.235813\pi$
$701$	2.82397e14	+	2.82397e14i	0.0630102	+	0.0630102i	−0.674900	+	0.737910i	$0.735813\pi$
$702$		0			0
$703$	−1.46908e15			−0.322695
$704$		0			0
$705$	6.62091e15			1.43178
$706$		0			0
$707$	4.11501e15	+	4.11501e15i	0.876121	+	0.876121i
$708$		0			0
$709$	−5.08406e15	+	5.08406e15i	−1.06575	+	1.06575i	−0.0680718	+	0.997680i	$0.521685\pi$
$709$	−5.08406e15	+	5.08406e15i	−1.06575	+	1.06575i	−0.997680	+	0.0680718i	$0.978315\pi$
$710$		0			0
$711$			1.62705e14i			0.0335828i
$712$		0			0
$713$			3.91668e15i			0.796024i
$714$		0			0
$715$	3.47759e15	−	3.47759e15i	0.695978	−	0.695978i
$716$		0			0
$717$	−2.09573e15	−	2.09573e15i	−0.413029	−	0.413029i
$718$		0			0
$719$	−5.28231e15			−1.02522			−0.512608	−	0.858623i	$-0.671321\pi$
$719$	−5.28231e15			−1.02522			−0.512608	+	0.858623i	$0.671321\pi$
$720$		0			0
$721$	−8.67838e14			−0.165880
$722$		0			0
$723$	−8.33084e14	−	8.33084e14i	−0.156830	−	0.156830i
$724$		0			0
$725$	1.46144e15	−	1.46144e15i	0.270970	−	0.270970i
$726$		0			0
$727$			1.04603e16i			1.91032i	0.296087	+	0.955161i	$0.404318\pi$
$727$			1.04603e16i			1.91032i	−0.296087	+	0.955161i	$0.595682\pi$
$728$		0			0
$729$		−	4.32120e15i		−	0.777325i
$730$		0			0
$731$	−9.06691e14	+	9.06691e14i	−0.160662	+	0.160662i
$732$		0			0
$733$	−2.63519e15	−	2.63519e15i	−0.459982	−	0.459982i	0.438668	−	0.898649i	$-0.355451\pi$
$733$	−2.63519e15	−	2.63519e15i	−0.459982	−	0.459982i	−0.898649	+	0.438668i	$0.855451\pi$
$734$		0			0
$735$	3.99404e15			0.686803
$736$		0			0
$737$	1.71105e15			0.289863
$738$		0			0
$739$	−1.96675e15	−	1.96675e15i	−0.328250	−	0.328250i	0.523671	−	0.851921i	$-0.324562\pi$
$739$	−1.96675e15	−	1.96675e15i	−0.328250	−	0.328250i	−0.851921	+	0.523671i	$0.824562\pi$
$740$		0			0
$741$	5.92592e15	−	5.92592e15i	0.974442	−	0.974442i
$742$		0			0
$743$			3.54440e15i			0.574255i	0.957892	+	0.287127i	$0.0927003\pi$
$743$			3.54440e15i			0.574255i	−0.957892	+	0.287127i	$0.907300\pi$
$744$		0			0
$745$		−	1.05394e16i		−	1.68251i
$746$		0			0
$747$	1.18870e15	−	1.18870e15i	0.186985	−	0.186985i
$748$		0			0
$749$	3.62914e15	+	3.62914e15i	0.562541	+	0.562541i
$750$		0			0
$751$	−7.22921e15			−1.10426			−0.552130	−	0.833758i	$-0.686185\pi$
$751$	−7.22921e15			−1.10426			−0.552130	+	0.833758i	$0.686185\pi$
$752$		0			0
$753$	−4.92473e15			−0.741327
$754$		0			0
$755$	1.04496e16	+	1.04496e16i	1.55021	+	1.55021i
$756$		0			0
$757$	−1.87506e15	+	1.87506e15i	−0.274150	+	0.274150i	−0.830768	−	0.556618i	$-0.812099\pi$
$757$	−1.87506e15	+	1.87506e15i	−0.274150	+	0.274150i	0.556618	+	0.830768i	$0.312099\pi$
$758$		0			0
$759$			1.23939e15i			0.178599i
$760$		0			0
$761$		−	1.29960e16i		−	1.84584i	−0.384994	−	0.922919i	$-0.625796\pi$
$761$		−	1.29960e16i		−	1.84584i	0.384994	−	0.922919i	$-0.374204\pi$
$762$		0			0
$763$	5.71320e15	−	5.71320e15i	0.799824	−	0.799824i
$764$		0			0
$765$	−2.54828e15	−	2.54828e15i	−0.351648	−	0.351648i
$766$		0			0
$767$	2.28392e15			0.310675
$768$		0			0
$769$	1.09185e16			1.46408			0.732042	−	0.681259i	$-0.238567\pi$
$769$	1.09185e16			1.46408			0.732042	+	0.681259i	$0.238567\pi$
$770$		0			0
$771$	−3.22181e15	−	3.22181e15i	−0.425893	−	0.425893i
$772$		0			0
$773$	7.36281e15	−	7.36281e15i	0.959526	−	0.959526i	−0.0396865	−	0.999212i	$-0.512636\pi$
$773$	7.36281e15	−	7.36281e15i	0.959526	−	0.959526i	0.999212	+	0.0396865i	$0.0126359\pi$
$774$		0			0
$775$		−	2.04405e16i		−	2.62622i
$776$		0			0
$777$			1.46227e15i			0.185230i
$778$		0			0
$779$	−8.34750e15	+	8.34750e15i	−1.04256	+	1.04256i
$780$		0			0
$781$	1.69372e13	+	1.69372e13i	0.00208574	+	0.00208574i
$782$		0			0
$783$	1.44396e15			0.175333
$784$		0			0
$785$	−2.68308e16			−3.21255
$786$		0			0
$787$	−2.03453e15	−	2.03453e15i	−0.240216	−	0.240216i	0.576723	−	0.816940i	$-0.304331\pi$
$787$	−2.03453e15	−	2.03453e15i	−0.240216	−	0.240216i	−0.816940	+	0.576723i	$0.804331\pi$
$788$		0			0
$789$	−4.65561e15	+	4.65561e15i	−0.542067	+	0.542067i
$790$		0			0
$791$			1.14368e15i			0.131321i
$792$		0			0
$793$			1.81194e16i			2.05183i
$794$		0			0
$795$	1.23099e16	−	1.23099e16i	1.37478	−	1.37478i
$796$		0			0
$797$	−1.65013e15	−	1.65013e15i	−0.181760	−	0.181760i	0.610363	−	0.792122i	$-0.291024\pi$
$797$	−1.65013e15	−	1.65013e15i	−0.181760	−	0.181760i	−0.792122	+	0.610363i	$0.791024\pi$
$798$		0			0
$799$	5.42693e15			0.589585
$800$		0			0
$801$	−3.27192e15			−0.350610
$802$		0			0
$803$	−1.80200e14	−	1.80200e14i	−0.0190466	−	0.0190466i
$804$		0			0
$805$	−1.05728e16	+	1.05728e16i	−1.10234	+	1.10234i
$806$		0			0
$807$		−	8.90332e14i		−	0.0915688i
$808$		0			0
$809$			8.91512e15i			0.904504i	0.891890	+	0.452252i	$0.149379\pi$
$809$			8.91512e15i			0.904504i	−0.891890	+	0.452252i	$0.850621\pi$
$810$		0			0
$811$	−1.44005e15	+	1.44005e15i	−0.144133	+	0.144133i	−0.775491	−	0.631358i	$-0.782498\pi$
$811$	−1.44005e15	+	1.44005e15i	−0.144133	+	0.144133i	0.631358	+	0.775491i	$0.282498\pi$
$812$		0			0
$813$	6.01407e15	+	6.01407e15i	0.593841	+	0.593841i
$814$		0			0
$815$	1.88563e16			1.83691
$816$		0			0
$817$	6.92014e15			0.665110
$818$		0			0
$819$	7.22716e15	+	7.22716e15i	0.685341	+	0.685341i
$820$		0			0
$821$	2.49954e15	−	2.49954e15i	0.233869	−	0.233869i	−0.580437	−	0.814305i	$-0.697118\pi$
$821$	2.49954e15	−	2.49954e15i	0.233869	−	0.233869i	0.814305	+	0.580437i	$0.197118\pi$
$822$		0			0
$823$			7.96258e15i			0.735114i	0.930001	+	0.367557i	$0.119806\pi$
$823$			7.96258e15i			0.735114i	−0.930001	+	0.367557i	$0.880194\pi$
$824$		0			0
$825$		−	6.46816e15i		−	0.589229i
$826$		0			0
$827$	−4.10254e15	+	4.10254e15i	−0.368784	+	0.368784i	−0.867034	−	0.498249i	$-0.833976\pi$
$827$	−4.10254e15	+	4.10254e15i	−0.368784	+	0.368784i	0.498249	+	0.867034i	$0.333976\pi$
$828$		0			0
$829$	2.13377e15	+	2.13377e15i	0.189277	+	0.189277i	0.795383	−	0.606107i	$-0.207270\pi$
$829$	2.13377e15	+	2.13377e15i	0.189277	+	0.189277i	−0.606107	+	0.795383i	$0.707270\pi$
$830$		0			0
$831$	5.53730e15			0.484722
$832$		0			0
$833$	3.27378e15			0.282815
$834$		0			0
$835$	−1.96414e16	−	1.96414e16i	−1.67455	−	1.67455i
$836$		0			0
$837$	1.00980e16	−	1.00980e16i	0.849660	−	0.849660i
$838$		0			0
$839$		−	1.44656e16i		−	1.20128i	−0.799519	−	0.600641i	$-0.794912\pi$
$839$		−	1.44656e16i		−	1.20128i	0.799519	−	0.600641i	$-0.205088\pi$
$840$		0			0
$841$		−	1.18534e16i		−	0.971549i
$842$		0			0
$843$	2.46079e15	−	2.46079e15i	0.199078	−	0.199078i
$844$		0			0
$845$	−1.56662e16	−	1.56662e16i	−1.25099	−	1.25099i
$846$		0			0
$847$	1.35017e16			1.06422
$848$		0			0
$849$	−2.29880e15			−0.178858
$850$		0			0
$851$	−1.39968e15	−	1.39968e15i	−0.107502	−	0.107502i
$852$		0			0
$853$	1.03276e14	−	1.03276e14i	0.00783032	−	0.00783032i	−0.703181	−	0.711011i	$-0.748238\pi$
$853$	1.03276e14	−	1.03276e14i	0.00783032	−	0.00783032i	0.711011	+	0.703181i	$0.248238\pi$
$854$		0			0
$855$			1.94492e16i			1.45576i
$856$		0			0
$857$			4.13417e14i			0.0305488i	0.999883	+	0.0152744i	$0.00486218\pi$
$857$			4.13417e14i			0.0305488i	−0.999883	+	0.0152744i	$0.995138\pi$
$858$		0			0
$859$	−1.18177e16	+	1.18177e16i	−0.862124	+	0.862124i	−0.991585	−	0.129461i	$-0.958675\pi$
$859$	−1.18177e16	+	1.18177e16i	−0.862124	+	0.862124i	0.129461	+	0.991585i	$0.458675\pi$
$860$		0			0
$861$	8.30878e15	+	8.30878e15i	0.598439	+	0.598439i
$862$		0			0
$863$	2.93105e15			0.208432			0.104216	−	0.994555i	$-0.466767\pi$
$863$	2.93105e15			0.208432			0.104216	+	0.994555i	$0.466767\pi$
$864$		0			0
$865$	−3.72930e16			−2.61842
$866$		0			0
$867$	−5.13281e15	−	5.13281e15i	−0.355836	−	0.355836i
$868$		0			0
$869$	−2.43755e14	+	2.43755e14i	−0.0166857	+	0.0166857i
$870$		0			0
$871$		−	1.55891e16i		−	1.05371i
$872$		0			0
$873$		−	2.43100e15i		−	0.162258i
$874$		0			0
$875$	3.08904e16	−	3.08904e16i	2.03600	−	2.03600i
$876$		0			0
$877$	−1.13600e16	−	1.13600e16i	−0.739402	−	0.739402i	0.233060	−	0.972462i	$-0.425126\pi$
$877$	−1.13600e16	−	1.13600e16i	−0.739402	−	0.739402i	−0.972462	+	0.233060i	$0.925126\pi$
$878$		0			0
$879$	1.45717e16			0.936640
$880$		0			0
$881$	1.42576e16			0.905062			0.452531	−	0.891749i	$-0.350521\pi$
$881$	1.42576e16			0.905062			0.452531	+	0.891749i	$0.350521\pi$
$882$		0			0
$883$	1.57729e16	+	1.57729e16i	0.988842	+	0.988842i	0.999938	−	0.0110969i	$-0.00353232\pi$
$883$	1.57729e16	+	1.57729e16i	0.988842	+	0.988842i	−0.0110969	+	0.999938i	$0.503532\pi$
$884$		0			0
$885$	3.05890e15	−	3.05890e15i	0.189399	−	0.189399i
$886$		0			0
$887$			1.79870e16i			1.09997i	0.835175	+	0.549984i	$0.185366\pi$
$887$			1.79870e16i			1.09997i	−0.835175	+	0.549984i	$0.814634\pi$
$888$		0			0
$889$		−	3.39206e16i		−	2.04882i
$890$		0			0
$891$	6.70453e14	−	6.70453e14i	0.0399983	−	0.0399983i
$892$		0			0
$893$	−2.07100e16	−	2.07100e16i	−1.22038	−	1.22038i
$894$		0			0
$895$	−1.39693e16			−0.813106
$896$		0			0
$897$	1.12919e16			0.649245
$898$		0			0
$899$	2.42752e15	+	2.42752e15i	0.137874	+	0.137874i
$900$		0			0
$901$	1.00900e16	−	1.00900e16i	0.566113	−	0.566113i
$902$		0			0
$903$		−	6.88804e15i		−	0.381780i
$904$		0			0
$905$		−	1.94369e16i		−	1.06429i
$906$		0			0
$907$	−1.21117e15	+	1.21117e15i	−0.0655186	+	0.0655186i	−0.739107	−	0.673588i	$-0.764752\pi$
$907$	−1.21117e15	+	1.21117e15i	−0.0655186	+	0.0655186i	0.673588	+	0.739107i	$0.264752\pi$
$908$		0			0
$909$	7.21212e15	+	7.21212e15i	0.385444	+	0.385444i
$910$		0			0
$911$	−2.23895e16			−1.18221			−0.591104	−	0.806595i	$-0.701308\pi$
$911$	−2.23895e16			−1.18221			−0.591104	+	0.806595i	$0.701308\pi$
$912$		0			0
$913$	3.56167e15			0.185808
$914$		0			0
$915$	2.42677e16	+	2.42677e16i	1.25087	+	1.25087i
$916$		0			0
$917$	5.37310e15	−	5.37310e15i	0.273649	−	0.273649i
$918$		0			0
$919$		−	2.32306e16i		−	1.16903i	−0.811384	−	0.584514i	$-0.801285\pi$
$919$		−	2.32306e16i		−	1.16903i	0.811384	−	0.584514i	$-0.198715\pi$
$920$		0			0
$921$			1.54075e16i			0.766135i
$922$		0			0
$923$	1.54312e14	−	1.54312e14i	0.00758211	−	0.00758211i
$924$		0			0
$925$	7.30465e15	+	7.30465e15i	0.354666	+	0.354666i
$926$		0			0
$927$	−1.52100e15			−0.0729780
$928$		0			0
$929$	−1.44121e16			−0.683345			−0.341673	−	0.939819i	$-0.610993\pi$
$929$	−1.44121e16			−0.683345			−0.341673	+	0.939819i	$0.610993\pi$
$930$		0			0
$931$	−1.24932e16	−	1.24932e16i	−0.585399	−	0.585399i
$932$		0			0
$933$	−4.41411e15	+	4.41411e15i	−0.204406	+	0.204406i
$934$		0			0
$935$		−	7.63537e15i		−	0.349435i
$936$		0			0
$937$			2.81562e16i			1.27352i	0.771061	+	0.636762i	$0.219727\pi$
$937$			2.81562e16i			1.27352i	−0.771061	+	0.636762i	$0.780273\pi$
$938$		0			0
$939$	−9.80877e15	+	9.80877e15i	−0.438484	+	0.438484i
$940$		0			0
$941$	6.14074e15	+	6.14074e15i	0.271318	+	0.271318i	0.829631	−	0.558313i	$-0.188551\pi$
$941$	6.14074e15	+	6.14074e15i	0.271318	+	0.271318i	−0.558313	+	0.829631i	$0.688551\pi$
$942$		0			0
$943$	−1.59062e16			−0.694630
$944$		0			0
$945$	5.45178e16			2.35322
$946$		0			0
$947$	−1.03061e16	−	1.03061e16i	−0.439714	−	0.439714i	0.452202	−	0.891916i	$-0.350639\pi$
$947$	−1.03061e16	−	1.03061e16i	−0.439714	−	0.439714i	−0.891916	+	0.452202i	$0.850639\pi$
$948$		0			0
$949$	−1.64177e15	+	1.64177e15i	−0.0692385	+	0.0692385i
$950$		0			0
$951$			9.98022e15i			0.416052i
$952$		0			0
$953$			9.28274e15i			0.382530i	0.981538	+	0.191265i	$0.0612589\pi$
$953$			9.28274e15i			0.382530i	−0.981538	+	0.191265i	$0.938741\pi$
$954$		0			0
$955$	−2.10578e16	+	2.10578e16i	−0.857815	+	0.857815i
$956$		0			0
$957$	7.68161e14	+	7.68161e14i	0.0309340	+	0.0309340i
$958$		0			0
$959$	2.32094e16			0.923979
$960$		0			0
$961$	8.54412e15			0.336271
$962$		0			0
$963$	6.36056e15	+	6.36056e15i	0.247486	+	0.247486i
$964$		0			0
$965$	−4.52191e16	+	4.52191e16i	−1.73949	+	1.73949i
$966$		0			0
$967$		−	1.09617e16i		−	0.416901i	−0.978033	−	0.208451i	$-0.933158\pi$
$967$		−	1.09617e16i		−	0.416901i	0.978033	−	0.208451i	$-0.0668421\pi$
$968$		0			0
$969$		−	1.30109e16i		−	0.489245i
$970$		0			0
$971$	2.45150e16	−	2.45150e16i	0.911436	−	0.911436i	−0.0849489	−	0.996385i	$-0.527073\pi$
$971$	2.45150e16	−	2.45150e16i	0.911436	−	0.911436i	0.996385	+	0.0849489i	$0.0270727\pi$
$972$		0			0
$973$	2.29127e16	+	2.29127e16i	0.842278	+	0.842278i
$974$		0			0
$975$	−5.89303e16			−2.14197
$976$		0			0
$977$	−3.81818e16			−1.37226			−0.686130	−	0.727479i	$-0.740692\pi$
$977$	−3.81818e16			−1.37226			−0.686130	+	0.727479i	$0.740692\pi$
$978$		0			0
$979$	−4.90181e15	−	4.90181e15i	−0.174201	−	0.174201i
$980$		0			0
$981$	1.00132e16	−	1.00132e16i	0.351877	−	0.351877i
$982$		0			0
$983$			2.94742e16i			1.02423i	0.858917	+	0.512115i	$0.171138\pi$
$983$			2.94742e16i			1.02423i	−0.858917	+	0.512115i	$0.828862\pi$
$984$		0			0
$985$			4.08302e16i			1.40308i
$986$		0			0
$987$	−2.06139e16	+	2.06139e16i	−0.700512	+	0.700512i
$988$		0			0
$989$	6.59319e15	+	6.59319e15i	0.221573	+	0.221573i
$990$		0			0
$991$	2.13654e15			0.0710077			0.0355038	−	0.999370i	$-0.488696\pi$
$991$	2.13654e15			0.0710077			0.0355038	+	0.999370i	$0.488696\pi$
$992$		0			0
$993$	−2.45736e16			−0.807696
$994$		0			0
$995$	−1.18748e16	−	1.18748e16i	−0.386012	−	0.386012i
$996$		0			0
$997$	−2.64209e16	+	2.64209e16i	−0.849423	+	0.849423i	−0.990061	−	0.140638i	$-0.955085\pi$
$997$	−2.64209e16	+	2.64209e16i	−0.849423	+	0.849423i	0.140638	+	0.990061i	$0.455085\pi$
$998$		0			0
$999$			7.21729e15i			0.229490i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.12.e.b.33.15		42
4.3	odd	2		128.12.e.a.33.7		42
8.3	odd	2		64.12.e.a.17.15		42
8.5	even	2		16.12.e.a.13.8	yes	42
16.3	odd	4		64.12.e.a.49.15		42
16.5	even	4	inner	128.12.e.b.97.15		42
16.11	odd	4		128.12.e.a.97.7		42
16.13	even	4		16.12.e.a.5.8	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.12.e.a.5.8	✓	42	16.13	even	4
16.12.e.a.13.8	yes	42	8.5	even	2
64.12.e.a.17.15		42	8.3	odd	2
64.12.e.a.49.15		42	16.3	odd	4
128.12.e.a.33.7		42	4.3	odd	2
128.12.e.a.97.7		42	16.11	odd	4
128.12.e.b.33.15		42	1.1	even	1	trivial
128.12.e.b.97.15		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)

\(f(q)\)	\(=\)	\(q+(199.508 + 199.508i) q^{3} +(-8937.54 + 8937.54i) q^{5} -55653.3i q^{7} -97540.0i q^{9} +O(q^{10})\)	\(q+(199.508 + 199.508i) q^{3} +(-8937.54 + 8937.54i) q^{5} -55653.3i q^{7} -97540.0i q^{9} +(146129. - 146129. i) q^{11} +(-1.33136e6 - 1.33136e6i) q^{13} -3.56623e6 q^{15} -2.92311e6 q^{17} +(1.11550e7 + 1.11550e7i) q^{19} +(1.11033e7 - 1.11033e7i) q^{21} +2.12560e7i q^{23} -1.10931e8i q^{25} +(5.48023e7 - 5.48023e7i) q^{27} +(1.31742e7 + 1.31742e7i) q^{29} +1.84262e8 q^{31} +5.83078e7 q^{33} +(4.97404e8 + 4.97404e8i) q^{35} +(-6.58484e7 + 6.58484e7i) q^{37} -5.31233e8i q^{39} +7.48317e8i q^{41} +(3.10180e8 - 3.10180e8i) q^{43} +(8.71768e8 + 8.71768e8i) q^{45} -1.85656e9 q^{47} -1.11996e9 q^{49} +(-5.83185e8 - 5.83185e8i) q^{51} +(-3.45179e9 + 3.45179e9i) q^{53} +2.61207e9i q^{55} +4.45104e9i q^{57} +(-8.57741e8 + 8.57741e8i) q^{59} +(-6.80487e9 - 6.80487e9i) q^{61} -5.42842e9 q^{63} +2.37981e10 q^{65} +(5.85461e9 + 5.85461e9i) q^{67} +(-4.24075e9 + 4.24075e9i) q^{69} +1.15906e8i q^{71} -1.23316e9i q^{73} +(2.21317e10 - 2.21317e10i) q^{75} +(-8.13256e9 - 8.13256e9i) q^{77} -1.66808e9 q^{79} +4.58810e9 q^{81} +(1.21868e10 + 1.21868e10i) q^{83} +(2.61254e10 - 2.61254e10i) q^{85} +5.25674e9i q^{87} -3.35444e10i q^{89} +(-7.40944e10 + 7.40944e10i) q^{91} +(3.67618e10 + 3.67618e10i) q^{93} -1.99397e11 q^{95} +2.49231e10 q^{97} +(-1.42534e10 - 1.42534e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 2 q^{5}+O(q^{10}) \) 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

Varieties

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Representations

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Database

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