LMFDB - Embedded newform 64.22.e.a.17.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,22,Mod(17,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("64.17");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	64.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:	$178.865500344$
Analytic rank:	$0$
Dimension:	$82$
Relative dimension:	$41$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.8
Character	$\chi$	$=$	64.17
Dual form			64.22.e.a.49.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-80161.3 - 80161.3i) q^{3} +(-2.92075e7 + 2.92075e7i) q^{5} +9.19049e8i q^{7} +2.39133e9i q^{9} +O(q^{10})$	\(q+(-80161.3 - 80161.3i) q^{3} +(-2.92075e7 + 2.92075e7i) q^{5} +9.19049e8i q^{7} +2.39133e9i q^{9} +(-8.07921e10 + 8.07921e10i) q^{11} +(2.85246e11 + 2.85246e11i) q^{13} +4.68262e12 q^{15} +2.16585e12 q^{17} +(-1.42419e13 - 1.42419e13i) q^{19} +(7.36722e13 - 7.36722e13i) q^{21} +2.48194e13i q^{23} -1.22932e15i q^{25} +(-6.46824e14 + 6.46824e14i) q^{27} +(1.64531e15 + 1.64531e15i) q^{29} +6.36937e15 q^{31} +1.29528e16 q^{33} +(-2.68431e16 - 2.68431e16i) q^{35} +(1.90454e16 - 1.90454e16i) q^{37} -4.57314e16i q^{39} -1.04111e17i q^{41} +(1.09613e17 - 1.09613e17i) q^{43} +(-6.98447e16 - 6.98447e16i) q^{45} -1.74861e17 q^{47} -2.86106e17 q^{49} +(-1.73617e17 - 1.73617e17i) q^{51} +(-3.51842e17 + 3.51842e17i) q^{53} -4.71947e18i q^{55} +2.28330e18i q^{57} +(-2.18059e18 + 2.18059e18i) q^{59} +(2.13605e18 + 2.13605e18i) q^{61} -2.19775e18 q^{63} -1.66626e19 q^{65} +(5.18581e18 + 5.18581e18i) q^{67} +(1.98956e18 - 1.98956e18i) q^{69} -2.16084e19i q^{71} +6.31848e19i q^{73} +(-9.85438e19 + 9.85438e19i) q^{75} +(-7.42519e19 - 7.42519e19i) q^{77} -5.28580e19 q^{79} +1.28715e20 q^{81} +(-1.28459e20 - 1.28459e20i) q^{83} +(-6.32590e19 + 6.32590e19i) q^{85} -2.63781e20i q^{87} -3.76038e20i q^{89} +(-2.62155e20 + 2.62155e20i) q^{91} +(-5.10577e20 - 5.10577e20i) q^{93} +8.31941e20 q^{95} +1.20427e21 q^{97} +(-1.93200e20 - 1.93200e20i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 2 q^{3} - 2 q^{5}+O(q^{10}) $ 82 * q + 2 * q^3 - 2 * q^5	$ 82 q + 2 q^{3} - 2 q^{5} - 67333320738 q^{11} - 2 q^{13} - 4613203124996 q^{15} - 4 q^{17} + 46007763621434 q^{19} + 20920706404 q^{21} - 11\!\cdots\!20 q^{27}+ \cdots - 27\!\cdots\!38 q^{99}+O(q^{100}) $ 82 * q + 2 * q^3 - 2 * q^5 - 67333320738 * q^11 - 2 * q^13 - 4613203124996 * q^15 - 4 * q^17 + 46007763621434 * q^19 + 20920706404 * q^21 - 1147760716556920 * q^27 - 2433173450216602 * q^29 + 9835539443769616 * q^31 - 4 * q^33 + 19253478556034884 * q^35 - 7245708527119386 * q^37 - 215332019803969386 * q^43 + 953653395699842 * q^45 - 1051982644716600976 * q^47 - 5585458640832840074 * q^49 - 3238772068175213124 * q^51 + 1889987679210147606 * q^53 - 3631979197965016922 * q^59 + 10385362452353654062 * q^61 + 17464422381302680956 * q^63 - 9364161130572538716 * q^65 + 17102217044572669130 * q^67 - 3951842785111207532 * q^69 - 145960939174166395366 * q^75 - 82041801652678580764 * q^77 - 204448210818924484480 * q^79 - 802405920297757300870 * q^81 - 317463236552669319678 * q^83 + 323656241286464843748 * q^85 - 144326756239046079748 * q^91 - 669717759565183008560 * q^93 + 1411330138695550130700 * q^95 - 4 * q^97 - 2710306841526615010238 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	−80161.3	−	80161.3i	−0.783776	−	0.783776i	0.196690	−	0.980466i	$-0.436981\pi$
$3$	−80161.3	−	80161.3i	−0.783776	−	0.783776i	−0.980466	+	0.196690i	$0.936981\pi$
$4$		0			0
$5$	−2.92075e7	+	2.92075e7i	−1.33755	+	1.33755i	−0.439118	+	0.898429i	$0.644709\pi$
$5$	−2.92075e7	+	2.92075e7i	−1.33755	+	1.33755i	−0.898429	+	0.439118i	$0.855291\pi$
$6$		0			0
$7$			9.19049e8i			1.22973i	0.788633	+	0.614864i	$0.210789\pi$
$7$			9.19049e8i			1.22973i	−0.788633	+	0.614864i	$0.789211\pi$
$8$		0			0
$9$			2.39133e9i			0.228609i
$10$		0			0
$11$	−8.07921e10	+	8.07921e10i	−0.939173	+	0.939173i	−0.998253	−	0.0590805i	$-0.981183\pi$
$11$	−8.07921e10	+	8.07921e10i	−0.939173	+	0.939173i	0.0590805	+	0.998253i	$0.481183\pi$
$12$		0			0
$13$	2.85246e11	+	2.85246e11i	0.573871	+	0.573871i	0.933208	−	0.359337i	$-0.116997\pi$
$13$	2.85246e11	+	2.85246e11i	0.573871	+	0.573871i	−0.359337	+	0.933208i	$0.616997\pi$
$14$		0			0
$15$	4.68262e12			2.09667
$16$		0			0
$17$	2.16585e12			0.260564			0.130282	−	0.991477i	$-0.458412\pi$
$17$	2.16585e12			0.260564			0.130282	+	0.991477i	$0.458412\pi$
$18$		0			0
$19$	−1.42419e13	−	1.42419e13i	−0.532912	−	0.532912i	0.388526	−	0.921438i	$-0.372984\pi$
$19$	−1.42419e13	−	1.42419e13i	−0.532912	−	0.532912i	−0.921438	+	0.388526i	$0.872984\pi$
$20$		0			0
$21$	7.36722e13	−	7.36722e13i	0.963832	−	0.963832i
$22$		0			0
$23$			2.48194e13i			0.124925i	0.998047	+	0.0624625i	$0.0198954\pi$
$23$			2.48194e13i			0.124925i	−0.998047	+	0.0624625i	$0.980105\pi$
$24$		0			0
$25$		−	1.22932e15i		−	2.57807i
$26$		0			0
$27$	−6.46824e14	+	6.46824e14i	−0.604598	+	0.604598i
$28$		0			0
$29$	1.64531e15	+	1.64531e15i	0.726222	+	0.726222i	0.969865	−	0.243643i	$-0.0783425\pi$
$29$	1.64531e15	+	1.64531e15i	0.726222	+	0.726222i	−0.243643	+	0.969865i	$0.578342\pi$
$30$		0			0
$31$	6.36937e15			1.39572			0.697860	−	0.716234i	$-0.254136\pi$
$31$	6.36937e15			1.39572			0.697860	+	0.716234i	$0.254136\pi$
$32$		0			0
$33$	1.29528e16			1.47220
$34$		0			0
$35$	−2.68431e16	−	2.68431e16i	−1.64482	−	1.64482i
$36$		0			0
$37$	1.90454e16	−	1.90454e16i	0.651136	−	0.651136i	−0.302130	−	0.953267i	$-0.597698\pi$
$37$	1.90454e16	−	1.90454e16i	0.651136	−	0.651136i	0.953267	+	0.302130i	$0.0976978\pi$
$38$		0			0
$39$		−	4.57314e16i		−	0.899572i
$40$		0			0
$41$		−	1.04111e17i		−	1.21134i	−0.795716	−	0.605670i	$-0.792905\pi$
$41$		−	1.04111e17i		−	1.21134i	0.795716	−	0.605670i	$-0.207095\pi$
$42$		0			0
$43$	1.09613e17	−	1.09613e17i	0.773467	−	0.773467i	−0.205244	−	0.978711i	$-0.565799\pi$
$43$	1.09613e17	−	1.09613e17i	0.773467	−	0.773467i	0.978711	+	0.205244i	$0.0657988\pi$
$44$		0			0
$45$	−6.98447e16	−	6.98447e16i	−0.305775	−	0.305775i
$46$		0			0
$47$	−1.74861e17			−0.484914			−0.242457	−	0.970162i	$-0.577953\pi$
$47$	−1.74861e17			−0.484914			−0.242457	+	0.970162i	$0.577953\pi$
$48$		0			0
$49$	−2.86106e17			−0.512233
$50$		0			0
$51$	−1.73617e17	−	1.73617e17i	−0.204224	−	0.204224i
$52$		0			0
$53$	−3.51842e17	+	3.51842e17i	−0.276345	+	0.276345i	−0.831648	−	0.555303i	$-0.812602\pi$
$53$	−3.51842e17	+	3.51842e17i	−0.276345	+	0.276345i	0.555303	+	0.831648i	$0.312602\pi$
$54$		0			0
$55$		−	4.71947e18i		−	2.51238i
$56$		0			0
$57$			2.28330e18i			0.835367i
$58$		0			0
$59$	−2.18059e18	+	2.18059e18i	−0.555428	+	0.555428i	−0.928002	−	0.372574i	$-0.878475\pi$
$59$	−2.18059e18	+	2.18059e18i	−0.555428	+	0.555428i	0.372574	+	0.928002i	$0.378475\pi$
$60$		0			0
$61$	2.13605e18	+	2.13605e18i	0.383396	+	0.383396i	0.872324	−	0.488928i	$-0.162612\pi$
$61$	2.13605e18	+	2.13605e18i	0.383396	+	0.383396i	−0.488928	+	0.872324i	$0.662612\pi$
$62$		0			0
$63$	−2.19775e18			−0.281127
$64$		0			0
$65$	−1.66626e19			−1.53516
$66$		0			0
$67$	5.18581e18	+	5.18581e18i	0.347561	+	0.347561i	0.859200	−	0.511639i	$-0.170962\pi$
$67$	5.18581e18	+	5.18581e18i	0.347561	+	0.347561i	−0.511639	+	0.859200i	$0.670962\pi$
$68$		0			0
$69$	1.98956e18	−	1.98956e18i	0.0979132	−	0.0979132i
$70$		0			0
$71$		−	2.16084e19i		−	0.787788i	−0.919156	−	0.393894i	$-0.871128\pi$
$71$		−	2.16084e19i		−	0.787788i	0.919156	−	0.393894i	$-0.128872\pi$
$72$		0			0
$73$			6.31848e19i			1.72077i	0.509645	+	0.860385i	$0.329777\pi$
$73$			6.31848e19i			1.72077i	−0.509645	+	0.860385i	$0.670223\pi$
$74$		0			0
$75$	−9.85438e19	+	9.85438e19i	−2.02063	+	2.02063i
$76$		0			0
$77$	−7.42519e19	−	7.42519e19i	−1.15493	−	1.15493i
$78$		0			0
$79$	−5.28580e19			−0.628096			−0.314048	−	0.949407i	$-0.601685\pi$
$79$	−5.28580e19			−0.628096			−0.314048	+	0.949407i	$0.601685\pi$
$80$		0			0
$81$	1.28715e20			1.17635
$82$		0			0
$83$	−1.28459e20	−	1.28459e20i	−0.908750	−	0.908750i	0.0874210	−	0.996171i	$-0.472137\pi$
$83$	−1.28459e20	−	1.28459e20i	−0.908750	−	0.908750i	−0.996171	+	0.0874210i	$0.972137\pi$
$84$		0			0
$85$	−6.32590e19	+	6.32590e19i	−0.348517	+	0.348517i
$86$		0			0
$87$		−	2.63781e20i		−	1.13839i
$88$		0			0
$89$		−	3.76038e20i		−	1.27831i	−0.769077	−	0.639156i	$-0.779284\pi$
$89$		−	3.76038e20i		−	1.27831i	0.769077	−	0.639156i	$-0.220716\pi$
$90$		0			0
$91$	−2.62155e20	+	2.62155e20i	−0.705706	+	0.705706i
$92$		0			0
$93$	−5.10577e20	−	5.10577e20i	−1.09393	−	1.09393i
$94$		0			0
$95$	8.31941e20			1.42559
$96$		0			0
$97$	1.20427e21			1.65814			0.829069	−	0.559147i	$-0.188871\pi$
$97$	1.20427e21			1.65814			0.829069	+	0.559147i	$0.188871\pi$
$98$		0			0
$99$	−1.93200e20	−	1.93200e20i	−0.214703	−	0.214703i
$100$		0			0
$101$	3.43226e20	−	3.43226e20i	0.309176	−	0.309176i	−0.535414	−	0.844590i	$-0.679844\pi$
$101$	3.43226e20	−	3.43226e20i	0.309176	−	0.309176i	0.844590	+	0.535414i	$0.179844\pi$
$102$		0			0
$103$		−	1.64265e21i		−	1.20435i	−0.798364	−	0.602175i	$-0.794301\pi$
$103$		−	1.64265e21i		−	1.20435i	0.798364	−	0.602175i	$-0.205699\pi$
$104$		0			0
$105$			4.30356e21i			2.57834i
$106$		0			0
$107$	−5.91432e20	+	5.91432e20i	−0.290653	+	0.290653i	−0.837338	−	0.546685i	$-0.815889\pi$
$107$	−5.91432e20	+	5.91432e20i	−0.290653	+	0.290653i	0.546685	+	0.837338i	$0.315889\pi$
$108$		0			0
$109$	2.84946e21	+	2.84946e21i	1.15288	+	1.15288i	0.985973	+	0.166907i	$0.0533780\pi$
$109$	2.84946e21	+	2.84946e21i	1.15288	+	1.15288i	0.166907	+	0.985973i	$0.446622\pi$
$110$		0			0
$111$	−3.05341e21			−1.02069
$112$		0			0
$113$	4.01941e21			1.11388			0.556940	−	0.830553i	$-0.311975\pi$
$113$	4.01941e21			1.11388			0.556940	+	0.830553i	$0.311975\pi$
$114$		0			0
$115$	−7.24913e20	−	7.24913e20i	−0.167093	−	0.167093i
$116$		0			0
$117$	−6.82117e20	+	6.82117e20i	−0.131192	+	0.131192i
$118$		0			0
$119$			1.99052e21i			0.320423i
$120$		0			0
$121$		−	5.65446e21i		−	0.764091i
$122$		0			0
$123$	−8.34567e21	+	8.34567e21i	−0.949419	+	0.949419i
$124$		0			0
$125$	2.19781e22	+	2.19781e22i	2.11074	+	2.11074i
$126$		0			0
$127$	1.24109e22			1.00894			0.504468	−	0.863430i	$-0.331689\pi$
$127$	1.24109e22			1.00894			0.504468	+	0.863430i	$0.331689\pi$
$128$		0			0
$129$	−1.75734e22			−1.21245
$130$		0			0
$131$	−2.46972e21	−	2.46972e21i	−0.144977	−	0.144977i	0.630893	−	0.775870i	$-0.282689\pi$
$131$	−2.46972e21	−	2.46972e21i	−0.144977	−	0.144977i	−0.775870	+	0.630893i	$0.782689\pi$
$132$		0			0
$133$	1.30890e22	−	1.30890e22i	0.655338	−	0.655338i
$134$		0			0
$135$		−	3.77842e22i		−	1.61736i
$136$		0			0
$137$		−	4.54651e22i		−	1.66768i	−0.552008	−	0.833839i	$-0.686138\pi$
$137$		−	4.54651e22i		−	1.66768i	0.552008	−	0.833839i	$-0.313862\pi$
$138$		0			0
$139$	3.66977e22	−	3.66977e22i	1.15607	−	1.15607i	0.170755	−	0.985314i	$-0.445379\pi$
$139$	3.66977e22	−	3.66977e22i	1.15607	−	1.15607i	0.985314	−	0.170755i	$-0.0546205\pi$
$140$		0			0
$141$	1.40171e22	+	1.40171e22i	0.380064	+	0.380064i
$142$		0			0
$143$	−4.60912e22			−1.07793
$144$		0			0
$145$	−9.61109e22			−1.94271
$146$		0			0
$147$	2.29346e22	+	2.29346e22i	0.401476	+	0.401476i
$148$		0			0
$149$	3.40355e22	−	3.40355e22i	0.516983	−	0.516983i	−0.399674	−	0.916657i	$-0.630877\pi$
$149$	3.40355e22	−	3.40355e22i	0.516983	−	0.516983i	0.916657	+	0.399674i	$0.130877\pi$
$150$		0			0
$151$			1.28075e23i			1.69124i	0.533783	+	0.845622i	$0.320770\pi$
$151$			1.28075e23i			1.69124i	−0.533783	+	0.845622i	$0.679230\pi$
$152$		0			0
$153$			5.17926e21i			0.0595672i
$154$		0			0
$155$	−1.86033e23	+	1.86033e23i	−1.86684	+	1.86684i
$156$		0			0
$157$	6.40535e22	+	6.40535e22i	0.561819	+	0.561819i	0.929824	−	0.368005i	$-0.119959\pi$
$157$	6.40535e22	+	6.40535e22i	0.561819	+	0.561819i	−0.368005	+	0.929824i	$0.619959\pi$
$158$		0			0
$159$	5.64083e22			0.433185
$160$		0			0
$161$	−2.28103e22			−0.153624
$162$		0			0
$163$	−6.01465e21	−	6.01465e21i	−0.0355828	−	0.0355828i	0.689092	−	0.724674i	$-0.258010\pi$
$163$	−6.01465e21	−	6.01465e21i	−0.0355828	−	0.0355828i	−0.724674	+	0.689092i	$0.758010\pi$
$164$		0			0
$165$	−3.78319e23	+	3.78319e23i	−1.96914	+	1.96914i
$166$		0			0
$167$		−	1.49347e23i		−	0.684972i	−0.939523	−	0.342486i	$-0.888731\pi$
$167$		−	1.49347e23i		−	0.684972i	0.939523	−	0.342486i	$-0.111269\pi$
$168$		0			0
$169$		−	8.43341e22i		−	0.341344i
$170$		0			0
$171$	3.40571e22	−	3.40571e22i	0.121828	−	0.121828i
$172$		0			0
$173$	3.10899e22	+	3.10899e22i	0.0984318	+	0.0984318i	0.754608	−	0.656176i	$-0.227827\pi$
$173$	3.10899e22	+	3.10899e22i	0.0984318	+	0.0984318i	−0.656176	+	0.754608i	$0.727827\pi$
$174$		0			0
$175$	1.12980e24			3.17032
$176$		0			0
$177$	3.49598e23			0.870663
$178$		0			0
$179$	4.26228e23	+	4.26228e23i	0.943376	+	0.943376i	0.998481	−	0.0551042i	$-0.0175491\pi$
$179$	4.26228e23	+	4.26228e23i	0.943376	+	0.943376i	−0.0551042	+	0.998481i	$0.517549\pi$
$180$		0			0
$181$	4.78329e23	−	4.78329e23i	0.942110	−	0.942110i	−0.0563040	−	0.998414i	$-0.517932\pi$
$181$	4.78329e23	−	4.78329e23i	0.942110	−	0.942110i	0.998414	+	0.0563040i	$0.0179316\pi$
$182$		0			0
$183$		−	3.42457e23i		−	0.600993i
$184$		0			0
$185$			1.11254e24i			1.74185i
$186$		0			0
$187$	−1.74983e23	+	1.74983e23i	−0.244715	+	0.244715i
$188$		0			0
$189$	−5.94463e23	−	5.94463e23i	−0.743491	−	0.743491i
$190$		0			0
$191$	5.43341e22			0.0608446			0.0304223	−	0.999537i	$-0.490315\pi$
$191$	5.43341e22			0.0608446			0.0304223	+	0.999537i	$0.490315\pi$
$192$		0			0
$193$	4.54499e22			0.0456227			0.0228113	−	0.999740i	$-0.492738\pi$
$193$	4.54499e22			0.0456227			0.0228113	+	0.999740i	$0.492738\pi$
$194$		0			0
$195$	1.33570e24	+	1.33570e24i	1.20322	+	1.20322i
$196$		0			0
$197$	7.16258e23	−	7.16258e23i	0.579661	−	0.579661i	−0.355149	−	0.934810i	$-0.615570\pi$
$197$	7.16258e23	−	7.16258e23i	0.579661	−	0.579661i	0.934810	+	0.355149i	$0.115570\pi$
$198$		0			0
$199$			4.03347e23i			0.293576i	0.989168	+	0.146788i	$0.0468936\pi$
$199$			4.03347e23i			0.293576i	−0.989168	+	0.146788i	$0.953106\pi$
$200$		0			0
$201$		−	8.31403e23i		−	0.544820i
$202$		0			0
$203$	−1.51212e24	+	1.51212e24i	−0.893056	+	0.893056i
$204$		0			0
$205$	3.04082e24	+	3.04082e24i	1.62022	+	1.62022i
$206$		0			0
$207$	−5.93514e22			−0.0285589
$208$		0			0
$209$	2.30127e24			1.00099
$210$		0			0
$211$	1.98547e23	+	1.98547e23i	0.0781444	+	0.0781444i	0.745099	−	0.666954i	$-0.232402\pi$
$211$	1.98547e23	+	1.98547e23i	0.0781444	+	0.0781444i	−0.666954	+	0.745099i	$0.732402\pi$
$212$		0			0
$213$	−1.73215e24	+	1.73215e24i	−0.617449	+	0.617449i
$214$		0			0
$215$			6.40302e24i			2.06910i
$216$		0			0
$217$			5.85376e24i			1.71636i
$218$		0			0
$219$	5.06498e24	−	5.06498e24i	1.34870	−	1.34870i
$220$		0			0
$221$	6.17800e23	+	6.17800e23i	0.149530	+	0.149530i
$222$		0			0
$223$	−6.86989e24			−1.51268			−0.756342	−	0.654176i	$-0.773016\pi$
$223$	−6.86989e24			−1.51268			−0.756342	+	0.654176i	$0.773016\pi$
$224$		0			0
$225$	2.93970e24			0.589369
$226$		0			0
$227$	−1.50643e24	−	1.50643e24i	−0.275218	−	0.275218i	0.555978	−	0.831197i	$-0.312344\pi$
$227$	−1.50643e24	−	1.50643e24i	−0.275218	−	0.275218i	−0.831197	+	0.555978i	$0.812344\pi$
$228$		0			0
$229$	−5.45180e24	+	5.45180e24i	−0.908380	+	0.908380i	−0.996142	−	0.0877615i	$-0.972029\pi$
$229$	−5.45180e24	+	5.45180e24i	−0.908380	+	0.908380i	0.0877615	+	0.996142i	$0.472029\pi$
$230$		0			0
$231$			1.19043e25i			1.81041i
$232$		0			0
$233$			1.59871e24i			0.222092i	0.993815	+	0.111046i	$0.0354200\pi$
$233$			1.59871e24i			0.222092i	−0.993815	+	0.111046i	$0.964580\pi$
$234$		0			0
$235$	5.10724e24	−	5.10724e24i	0.648595	−	0.648595i
$236$		0			0
$237$	4.23717e24	+	4.23717e24i	0.492287	+	0.492287i
$238$		0			0
$239$	−2.79790e24			−0.297615			−0.148807	−	0.988866i	$-0.547543\pi$
$239$	−2.79790e24			−0.297615			−0.148807	+	0.988866i	$0.547543\pi$
$240$		0			0
$241$	9.27715e24			0.904140			0.452070	−	0.891983i	$-0.350686\pi$
$241$	9.27715e24			0.904140			0.452070	+	0.891983i	$0.350686\pi$
$242$		0			0
$243$	−3.55193e24	−	3.55193e24i	−0.317394	−	0.317394i
$244$		0			0
$245$	8.35643e24	−	8.35643e24i	0.685136	−	0.685136i
$246$		0			0
$247$		−	8.12490e24i		−	0.611646i
$248$		0			0
$249$			2.05949e25i			1.42451i
$250$		0			0
$251$	4.26684e23	−	4.26684e23i	0.0271351	−	0.0271351i	−0.693409	−	0.720544i	$-0.743892\pi$
$251$	4.26684e23	−	4.26684e23i	0.0271351	−	0.0271351i	0.720544	+	0.693409i	$0.243892\pi$
$252$		0			0
$253$	−2.00521e24	−	2.00521e24i	−0.117326	−	0.117326i
$254$		0			0
$255$	1.01419e25			0.546318
$256$		0			0
$257$	6.31907e24			0.313585			0.156793	−	0.987632i	$-0.449885\pi$
$257$	6.31907e24			0.313585			0.156793	+	0.987632i	$0.449885\pi$
$258$		0			0
$259$	1.75037e25	+	1.75037e25i	0.800721	+	0.800721i
$260$		0			0
$261$	−3.93448e24	+	3.93448e24i	−0.166021	+	0.166021i
$262$		0			0
$263$		−	1.27751e24i		−	0.0497540i	−0.999691	−	0.0248770i	$-0.992081\pi$
$263$		−	1.27751e24i		−	0.0497540i	0.999691	−	0.0248770i	$-0.00791940\pi$
$264$		0			0
$265$		−	2.05528e25i		−	0.739248i
$266$		0			0
$267$	−3.01437e25	+	3.01437e25i	−1.00191	+	1.00191i
$268$		0			0
$269$	1.08945e25	+	1.08945e25i	0.334818	+	0.334818i	0.854413	−	0.519595i	$-0.173917\pi$
$269$	1.08945e25	+	1.08945e25i	0.334818	+	0.334818i	−0.519595	+	0.854413i	$0.673917\pi$
$270$		0			0
$271$	4.30945e25			1.22531			0.612653	−	0.790352i	$-0.290102\pi$
$271$	4.30945e25			1.22531			0.612653	+	0.790352i	$0.290102\pi$
$272$		0			0
$273$	4.20294e25			1.10623
$274$		0			0
$275$	9.93191e25	+	9.93191e25i	2.42125	+	2.42125i
$276$		0			0
$277$	1.34871e24	−	1.34871e24i	0.0304706	−	0.0304706i	−0.691707	−	0.722178i	$-0.743141\pi$
$277$	1.34871e24	−	1.34871e24i	0.0304706	−	0.0304706i	0.722178	+	0.691707i	$0.243141\pi$
$278$		0			0
$279$			1.52312e25i			0.319074i
$280$		0			0
$281$			6.44651e25i			1.25288i	0.779471	+	0.626439i	$0.215488\pi$
$281$			6.44651e25i			1.25288i	−0.779471	+	0.626439i	$0.784512\pi$
$282$		0			0
$283$	−4.13691e25	+	4.13691e25i	−0.746309	+	0.746309i	−0.973784	−	0.227475i	$-0.926953\pi$
$283$	−4.13691e25	+	4.13691e25i	−0.746309	+	0.746309i	0.227475	+	0.973784i	$0.426953\pi$
$284$		0			0
$285$	−6.66895e25	−	6.66895e25i	−1.11734	−	1.11734i
$286$		0			0
$287$	9.56831e25			1.48962
$288$		0			0
$289$	−6.44010e25			−0.932106
$290$		0			0
$291$	−9.65359e25	−	9.65359e25i	−1.29961	−	1.29961i
$292$		0			0
$293$	−2.65949e25	+	2.65949e25i	−0.333187	+	0.333187i	−0.853795	−	0.520609i	$-0.825705\pi$
$293$	−2.65949e25	+	2.65949e25i	−0.333187	+	0.333187i	0.520609	+	0.853795i	$0.325705\pi$
$294$		0			0
$295$		−	1.27379e26i		−	1.48582i
$296$		0			0
$297$		−	1.04516e26i		−	1.13564i
$298$		0			0
$299$	−7.07964e24	+	7.07964e24i	−0.0716908	+	0.0716908i
$300$		0			0
$301$	1.00739e26	+	1.00739e26i	0.951154	+	0.951154i
$302$		0			0
$303$	−5.50269e25			−0.484649
$304$		0			0
$305$	−1.24777e26			−1.02562
$306$		0			0
$307$	−3.92095e25	−	3.92095e25i	−0.300911	−	0.300911i	0.540459	−	0.841370i	$-0.318251\pi$
$307$	−3.92095e25	−	3.92095e25i	−0.300911	−	0.300911i	−0.841370	+	0.540459i	$0.818251\pi$
$308$		0			0
$309$	−1.31677e26	+	1.31677e26i	−0.943941	+	0.943941i
$310$		0			0
$311$		−	7.04338e24i		−	0.0471843i	−0.999722	−	0.0235921i	$-0.992490\pi$
$311$		−	7.04338e24i		−	0.0471843i	0.999722	−	0.0235921i	$-0.00751030\pi$
$312$		0			0
$313$		−	2.26438e26i		−	1.41819i	−0.705115	−	0.709093i	$-0.749104\pi$
$313$		−	2.26438e26i		−	1.41819i	0.705115	−	0.709093i	$-0.250896\pi$
$314$		0			0
$315$	6.41907e25	−	6.41907e25i	0.376020	−	0.376020i
$316$		0			0
$317$	−1.40120e26	−	1.40120e26i	−0.768028	−	0.768028i	0.209731	−	0.977759i	$-0.432741\pi$
$317$	−1.40120e26	−	1.40120e26i	−0.768028	−	0.768028i	−0.977759	+	0.209731i	$0.932741\pi$
$318$		0			0
$319$	−2.65856e26			−1.36410
$320$		0			0
$321$	9.48200e25			0.455614
$322$		0			0
$323$	−3.08458e25	−	3.08458e25i	−0.138858	−	0.138858i
$324$		0			0
$325$	3.50658e26	−	3.50658e26i	1.47948	−	1.47948i
$326$		0			0
$327$		−	4.56833e26i		−	1.80720i
$328$		0			0
$329$		−	1.60705e26i		−	0.596312i
$330$		0			0
$331$	1.50104e25	−	1.50104e25i	0.0522637	−	0.0522637i	−0.680492	−	0.732756i	$-0.738234\pi$
$331$	1.50104e25	−	1.50104e25i	0.0522637	−	0.0522637i	0.732756	+	0.680492i	$0.238234\pi$
$332$		0			0
$333$	4.55438e25	+	4.55438e25i	0.148855	+	0.148855i
$334$		0			0
$335$	−3.02929e26			−0.929759
$336$		0			0
$337$	−2.78165e26			−0.802027			−0.401014	−	0.916072i	$-0.631342\pi$
$337$	−2.78165e26			−0.802027			−0.401014	+	0.916072i	$0.631342\pi$
$338$		0			0
$339$	−3.22201e26	−	3.22201e26i	−0.873033	−	0.873033i
$340$		0			0
$341$	−5.14594e26	+	5.14594e26i	−1.31082	+	1.31082i
$342$		0			0
$343$			2.50386e26i			0.599821i
$344$		0			0
$345$			1.16220e26i			0.261927i
$346$		0			0
$347$	−1.80086e26	+	1.80086e26i	−0.381963	+	0.381963i	−0.871809	−	0.489846i	$-0.837053\pi$
$347$	−1.80086e26	+	1.80086e26i	−0.381963	+	0.381963i	0.489846	+	0.871809i	$0.337053\pi$
$348$		0			0
$349$	3.65356e26	+	3.65356e26i	0.729540	+	0.729540i	0.970528	−	0.240988i	$-0.0774715\pi$
$349$	3.65356e26	+	3.65356e26i	0.729540	+	0.729540i	−0.240988	+	0.970528i	$0.577471\pi$
$350$		0			0
$351$	−3.69008e26			−0.693922
$352$		0			0
$353$	8.49307e26			1.50463			0.752316	−	0.658802i	$-0.228937\pi$
$353$	8.49307e26			1.50463			0.752316	+	0.658802i	$0.228937\pi$
$354$		0			0
$355$	6.31126e26	+	6.31126e26i	1.05370	+	1.05370i
$356$		0			0
$357$	1.59563e26	−	1.59563e26i	0.251140	−	0.251140i
$358$		0			0
$359$		−	1.74641e26i		−	0.259211i	−0.991566	−	0.129606i	$-0.958629\pi$
$359$		−	1.74641e26i		−	0.259211i	0.991566	−	0.129606i	$-0.0413711\pi$
$360$		0			0
$361$		−	3.08545e26i		−	0.432009i
$362$		0			0
$363$	−4.53269e26	+	4.53269e26i	−0.598876	+	0.598876i
$364$		0			0
$365$	−1.84547e27	−	1.84547e27i	−2.30161	−	2.30161i
$366$		0			0
$367$	1.25335e27			1.47598			0.737988	−	0.674814i	$-0.235776\pi$
$367$	1.25335e27			1.47598			0.737988	+	0.674814i	$0.235776\pi$
$368$		0			0
$369$	2.48963e26			0.276923
$370$		0			0
$371$	−3.23360e26	−	3.23360e26i	−0.339829	−	0.339829i
$372$		0			0
$373$	−5.26985e25	+	5.26985e25i	−0.0523426	+	0.0523426i	−0.732794	−	0.680451i	$-0.761784\pi$
$373$	−5.26985e25	+	5.26985e25i	−0.0523426	+	0.0523426i	0.680451	+	0.732794i	$0.261784\pi$
$374$		0			0
$375$		−	3.52358e27i		−	3.30869i
$376$		0			0
$377$			9.38637e26i			0.833516i
$378$		0			0
$379$	2.32096e26	−	2.32096e26i	0.194964	−	0.194964i	−0.602873	−	0.797837i	$-0.705977\pi$
$379$	2.32096e26	−	2.32096e26i	0.194964	−	0.194964i	0.797837	+	0.602873i	$0.205977\pi$
$380$		0			0
$381$	−9.94873e26	−	9.94873e26i	−0.790780	−	0.790780i
$382$		0			0
$383$	−1.43936e27			−1.08289			−0.541444	−	0.840737i	$-0.682122\pi$
$383$	−1.43936e27			−1.08289			−0.541444	+	0.840737i	$0.682122\pi$
$384$		0			0
$385$	4.33742e27			3.08954
$386$		0			0
$387$	2.62120e26	+	2.62120e26i	0.176821	+	0.176821i
$388$		0			0
$389$	5.48710e25	−	5.48710e25i	0.0350648	−	0.0350648i	−0.689357	−	0.724422i	$-0.742107\pi$
$389$	5.48710e25	−	5.48710e25i	0.0350648	−	0.0350648i	0.724422	+	0.689357i	$0.242107\pi$
$390$		0			0
$391$			5.37551e25i			0.0325510i
$392$		0			0
$393$			3.95952e26i			0.227259i
$394$		0			0
$395$	1.54385e27	−	1.54385e27i	0.840109	−	0.840109i
$396$		0			0
$397$	−1.75345e27	−	1.75345e27i	−0.904882	−	0.904882i	0.0909715	−	0.995853i	$-0.471003\pi$
$397$	−1.75345e27	−	1.75345e27i	−0.904882	−	0.904882i	−0.995853	+	0.0909715i	$0.971003\pi$
$398$		0			0
$399$	−2.09847e27			−1.02728
$400$		0			0
$401$	3.11816e26			0.144838			0.0724190	−	0.997374i	$-0.476928\pi$
$401$	3.11816e26			0.144838			0.0724190	+	0.997374i	$0.476928\pi$
$402$		0			0
$403$	1.81684e27	+	1.81684e27i	0.800963	+	0.800963i
$404$		0			0
$405$	−3.75943e27	+	3.75943e27i	−1.57342	+	1.57342i
$406$		0			0
$407$			3.07743e27i			1.22306i
$408$		0			0
$409$		−	4.64107e26i		−	0.175196i	−0.996156	−	0.0875978i	$-0.972081\pi$
$409$		−	4.64107e26i		−	0.175196i	0.996156	−	0.0875978i	$-0.0279190\pi$
$410$		0			0
$411$	−3.64454e27	+	3.64454e27i	−1.30709	+	1.30709i
$412$		0			0
$413$	−2.00407e27	−	2.00407e27i	−0.683026	−	0.683026i
$414$		0			0
$415$	7.50393e27			2.43099
$416$		0			0
$417$	−5.88347e27			−1.81220
$418$		0			0
$419$	7.37634e25	+	7.37634e25i	0.0216070	+	0.0216070i	0.717828	−	0.696221i	$-0.245137\pi$
$419$	7.37634e25	+	7.37634e25i	0.0216070	+	0.0216070i	−0.696221	+	0.717828i	$0.745137\pi$
$420$		0			0
$421$	−4.01806e27	+	4.01806e27i	−1.11958	+	1.11958i	−0.127775	+	0.991803i	$0.540783\pi$
$421$	−4.01806e27	+	4.01806e27i	−1.11958	+	1.11958i	−0.991803	+	0.127775i	$0.959217\pi$
$422$		0			0
$423$		−	4.18149e26i		−	0.110855i
$424$		0			0
$425$		−	2.66252e27i		−	0.671752i
$426$		0			0
$427$	−1.96313e27	+	1.96313e27i	−0.471473	+	0.471473i
$428$		0			0
$429$	3.69473e27	+	3.69473e27i	0.844854	+	0.844854i
$430$		0			0
$431$	−5.32506e27			−1.15961			−0.579806	−	0.814754i	$-0.696872\pi$
$431$	−5.32506e27			−1.15961			−0.579806	+	0.814754i	$0.696872\pi$
$432$		0			0
$433$	8.50464e27			1.76414			0.882070	−	0.471118i	$-0.156149\pi$
$433$	8.50464e27			1.76414			0.882070	+	0.471118i	$0.156149\pi$
$434$		0			0
$435$	7.70438e27	+	7.70438e27i	1.52265	+	1.52265i
$436$		0			0
$437$	3.53476e26	−	3.53476e26i	0.0665740	−	0.0665740i
$438$		0			0
$439$		−	2.95325e27i		−	0.530180i	−0.964224	−	0.265090i	$-0.914598\pi$
$439$		−	2.95325e27i		−	0.530180i	0.964224	−	0.265090i	$-0.0854017\pi$
$440$		0			0
$441$		−	6.84173e26i		−	0.117101i
$442$		0			0
$443$	−2.57086e26	+	2.57086e26i	−0.0419603	+	0.0419603i	−0.727776	−	0.685815i	$-0.759446\pi$
$443$	−2.57086e26	+	2.57086e26i	−0.0419603	+	0.0419603i	0.685815	+	0.727776i	$0.259446\pi$
$444$		0			0
$445$	1.09831e28	+	1.09831e28i	1.70980	+	1.70980i
$446$		0			0
$447$	−5.45666e27			−0.810397
$448$		0			0
$449$	−4.15085e27			−0.588235			−0.294117	−	0.955769i	$-0.595026\pi$
$449$	−4.15085e27			−0.588235			−0.294117	+	0.955769i	$0.595026\pi$
$450$		0			0
$451$	8.41134e27	+	8.41134e27i	1.13766	+	1.13766i
$452$		0			0
$453$	1.02667e28	−	1.02667e28i	1.32556	−	1.32556i
$454$		0			0
$455$		−	1.53138e28i		−	1.88783i
$456$		0			0
$457$		−	2.85653e27i		−	0.336293i	−0.985762	−	0.168147i	$-0.946222\pi$
$457$		−	2.85653e27i		−	0.336293i	0.985762	−	0.168147i	$-0.0537782\pi$
$458$		0			0
$459$	−1.40092e27	+	1.40092e27i	−0.157536	+	0.157536i
$460$		0			0
$461$	−3.21762e27	−	3.21762e27i	−0.345681	−	0.345681i	0.512817	−	0.858498i	$-0.328602\pi$
$461$	−3.21762e27	−	3.21762e27i	−0.345681	−	0.345681i	−0.858498	+	0.512817i	$0.828602\pi$
$462$		0			0
$463$	1.00327e28			1.02996			0.514978	−	0.857204i	$-0.327800\pi$
$463$	1.00327e28			1.02996			0.514978	+	0.857204i	$0.327800\pi$
$464$		0			0
$465$	2.98253e28			2.92637
$466$		0			0
$467$	1.63052e27	+	1.63052e27i	0.152932	+	0.152932i	0.779426	−	0.626494i	$-0.215511\pi$
$467$	1.63052e27	+	1.63052e27i	0.152932	+	0.152932i	−0.626494	+	0.779426i	$0.715511\pi$
$468$		0			0
$469$	−4.76602e27	+	4.76602e27i	−0.427406	+	0.427406i
$470$		0			0
$471$		−	1.02692e28i		−	0.880680i
$472$		0			0
$473$			1.77117e28i			1.45284i
$474$		0			0
$475$	−1.75078e28	+	1.75078e28i	−1.37388	+	1.37388i
$476$		0			0
$477$	−8.41370e26	−	8.41370e26i	−0.0631748	−	0.0631748i
$478$		0			0
$479$	1.74255e28			1.25217			0.626083	−	0.779756i	$-0.284657\pi$
$479$	1.74255e28			1.25217			0.626083	+	0.779756i	$0.284657\pi$
$480$		0			0
$481$	1.08652e28			0.747336
$482$		0			0
$483$	1.82850e27	+	1.82850e27i	0.120407	+	0.120407i
$484$		0			0
$485$	−3.51737e28	+	3.51737e28i	−2.21784	+	2.21784i
$486$		0			0
$487$		−	1.24418e28i		−	0.751327i	−0.926756	−	0.375664i	$-0.877415\pi$
$487$		−	1.24418e28i		−	0.751327i	0.926756	−	0.375664i	$-0.122585\pi$
$488$		0			0
$489$			9.64284e26i			0.0557779i
$490$		0			0
$491$	−1.09926e28	+	1.09926e28i	−0.609181	+	0.609181i	−0.942732	−	0.333551i	$-0.891753\pi$
$491$	−1.09926e28	+	1.09926e28i	−0.609181	+	0.609181i	0.333551	+	0.942732i	$0.391753\pi$
$492$		0			0
$493$	3.56350e27	+	3.56350e27i	0.189227	+	0.189227i
$494$		0			0
$495$	1.12858e28			0.574351
$496$		0			0
$497$	1.98591e28			0.968765
$498$		0			0
$499$	−1.33639e28	−	1.33639e28i	−0.624999	−	0.624999i	0.321807	−	0.946805i	$-0.395710\pi$
$499$	−1.33639e28	−	1.33639e28i	−0.624999	−	0.624999i	−0.946805	+	0.321807i	$0.895710\pi$
$500$		0			0
$501$	−1.19718e28	+	1.19718e28i	−0.536864	+	0.536864i
$502$		0			0
$503$			5.26378e27i			0.226378i	0.993573	+	0.113189i	$0.0361065\pi$
$503$			5.26378e27i			0.226378i	−0.993573	+	0.113189i	$0.963894\pi$
$504$		0			0
$505$			2.00495e28i			0.827075i
$506$		0			0
$507$	−6.76033e27	+	6.76033e27i	−0.267537	+	0.267537i
$508$		0			0
$509$	−2.53350e28	−	2.53350e28i	−0.962019	−	0.962019i	0.0372860	−	0.999305i	$-0.488129\pi$
$509$	−2.53350e28	−	2.53350e28i	−0.962019	−	0.962019i	−0.999305	+	0.0372860i	$0.988129\pi$
$510$		0			0
$511$	−5.80700e28			−2.11608
$512$		0			0
$513$	1.84240e28			0.644395
$514$		0			0
$515$	4.79776e28	+	4.79776e28i	1.61088	+	1.61088i
$516$		0			0
$517$	1.41273e28	−	1.41273e28i	0.455418	−	0.455418i
$518$		0			0
$519$		−	4.98442e27i		−	0.154297i
$520$		0			0
$521$		−	1.82409e28i		−	0.542315i	−0.962535	−	0.271157i	$-0.912594\pi$
$521$		−	1.82409e28i		−	0.542315i	0.962535	−	0.271157i	$-0.0874063\pi$
$522$		0			0
$523$	−2.06424e27	+	2.06424e27i	−0.0589511	+	0.0589511i	−0.735968	−	0.677017i	$-0.763273\pi$
$523$	−2.06424e27	+	2.06424e27i	−0.0589511	+	0.0589511i	0.677017	+	0.735968i	$0.263273\pi$
$524$		0			0
$525$	−9.05666e28	−	9.05666e28i	−2.48482	−	2.48482i
$526$		0			0
$527$	1.37951e28			0.363675
$528$		0			0
$529$	3.88556e28			0.984394
$530$		0			0
$531$	−5.21451e27	−	5.21451e27i	−0.126976	−	0.126976i
$532$		0			0
$533$	2.96972e28	−	2.96972e28i	0.695153	−	0.695153i
$534$		0			0
$535$		−	3.45485e28i		−	0.777525i
$536$		0			0
$537$		−	6.83340e28i		−	1.47879i
$538$		0			0
$539$	2.31151e28	−	2.31151e28i	0.481076	−	0.481076i
$540$		0			0
$541$	3.14767e28	+	3.14767e28i	0.630111	+	0.630111i	0.948096	−	0.317985i	$-0.103006\pi$
$541$	3.14767e28	+	3.14767e28i	0.630111	+	0.630111i	−0.317985	+	0.948096i	$0.603006\pi$
$542$		0			0
$543$	−7.66870e28			−1.47681
$544$		0			0
$545$	−1.66451e29			−3.08406
$546$		0			0
$547$	−2.15773e28	−	2.15773e28i	−0.384707	−	0.384707i	0.488088	−	0.872795i	$-0.337695\pi$
$547$	−2.15773e28	−	2.15773e28i	−0.384707	−	0.384707i	−0.872795	+	0.488088i	$0.837695\pi$
$548$		0			0
$549$	−5.10799e27	+	5.10799e27i	−0.0876477	+	0.0876477i
$550$		0			0
$551$		−	4.68648e28i		−	0.774025i
$552$		0			0
$553$		−	4.85791e28i		−	0.772388i
$554$		0			0
$555$	8.91824e28	−	8.91824e28i	1.36522	−	1.36522i
$556$		0			0
$557$	1.53200e28	+	1.53200e28i	0.225829	+	0.225829i	0.810948	−	0.585119i	$-0.198952\pi$
$557$	1.53200e28	+	1.53200e28i	0.225829	+	0.225829i	−0.585119	+	0.810948i	$0.698952\pi$
$558$		0			0
$559$	6.25331e28			0.887740
$560$		0			0
$561$	2.80538e28			0.383603
$562$		0			0
$563$	−1.91473e28	−	1.91473e28i	−0.252214	−	0.252214i	0.569664	−	0.821878i	$-0.307073\pi$
$563$	−1.91473e28	−	1.91473e28i	−0.252214	−	0.252214i	−0.821878	+	0.569664i	$0.807073\pi$
$564$		0			0
$565$	−1.17397e29	+	1.17397e29i	−1.48987	+	1.48987i
$566$		0			0
$567$			1.18295e29i			1.44659i
$568$		0			0
$569$			9.68610e28i			1.14148i	0.821129	+	0.570742i	$0.193344\pi$
$569$			9.68610e28i			1.14148i	−0.821129	+	0.570742i	$0.806656\pi$
$570$		0			0
$571$	−1.33585e28	+	1.33585e28i	−0.151732	+	0.151732i	−0.778891	−	0.627159i	$-0.784218\pi$
$571$	−1.33585e28	+	1.33585e28i	−0.151732	+	0.151732i	0.627159	+	0.778891i	$0.284218\pi$
$572$		0			0
$573$	−4.35550e27	−	4.35550e27i	−0.0476886	−	0.0476886i
$574$		0			0
$575$	3.05110e28			0.322065
$576$		0			0
$577$	2.95525e28			0.300779			0.150390	−	0.988627i	$-0.451947\pi$
$577$	2.95525e28			0.300779			0.150390	+	0.988627i	$0.451947\pi$
$578$		0			0
$579$	−3.64332e27	−	3.64332e27i	−0.0357579	−	0.0357579i
$580$		0			0
$581$	1.18060e29	−	1.18060e29i	1.11752	−	1.11752i
$582$		0			0
$583$		−	5.68521e28i		−	0.519071i
$584$		0			0
$585$		−	3.98458e28i		−	0.350951i
$586$		0			0
$587$	3.03571e28	−	3.03571e28i	0.257965	−	0.257965i	−0.566261	−	0.824226i	$-0.691611\pi$
$587$	3.03571e28	−	3.03571e28i	0.257965	−	0.257965i	0.824226	+	0.566261i	$0.191611\pi$
$588$		0			0
$589$	−9.07120e28	−	9.07120e28i	−0.743796	−	0.743796i
$590$		0			0
$591$	−1.14832e29			−0.908649
$592$		0			0
$593$	7.56081e28			0.577423			0.288712	−	0.957416i	$-0.406773\pi$
$593$	7.56081e28			0.577423			0.288712	+	0.957416i	$0.406773\pi$
$594$		0			0
$595$	−5.81382e28	−	5.81382e28i	−0.428581	−	0.428581i
$596$		0			0
$597$	3.23328e28	−	3.23328e28i	0.230098	−	0.230098i
$598$		0			0
$599$			1.44460e29i			0.992584i	0.868156	+	0.496292i	$0.165306\pi$
$599$			1.44460e29i			0.992584i	−0.868156	+	0.496292i	$0.834694\pi$
$600$		0			0
$601$		−	1.23945e29i		−	0.822333i	−0.911560	−	0.411166i	$-0.865122\pi$
$601$		−	1.23945e29i		−	0.822333i	0.911560	−	0.411166i	$-0.134878\pi$
$602$		0			0
$603$	−1.24010e28	+	1.24010e28i	−0.0794555	+	0.0794555i
$604$		0			0
$605$	1.65153e29	+	1.65153e29i	1.02201	+	1.02201i
$606$		0			0
$607$	−1.39669e29			−0.834871			−0.417436	−	0.908706i	$-0.637071\pi$
$607$	−1.39669e29			−0.834871			−0.417436	+	0.908706i	$0.637071\pi$
$608$		0			0
$609$	2.42428e29			1.39991
$610$		0			0
$611$	−4.98783e28	−	4.98783e28i	−0.278278	−	0.278278i
$612$		0			0
$613$	−3.90372e28	+	3.90372e28i	−0.210448	+	0.210448i	−0.804458	−	0.594010i	$-0.797544\pi$
$613$	−3.90372e28	+	3.90372e28i	−0.210448	+	0.210448i	0.594010	+	0.804458i	$0.297544\pi$
$614$		0			0
$615$		−	4.87512e29i		−	2.53979i
$616$		0			0
$617$			1.77921e29i			0.895846i	0.894072	+	0.447923i	$0.147836\pi$
$617$			1.77921e29i			0.895846i	−0.894072	+	0.447923i	$0.852164\pi$
$618$		0			0
$619$	−2.23851e29	+	2.23851e29i	−1.08945	+	1.08945i	−0.0938642	+	0.995585i	$0.529922\pi$
$619$	−2.23851e29	+	2.23851e29i	−1.08945	+	1.08945i	−0.995585	+	0.0938642i	$0.970078\pi$
$620$		0			0
$621$	−1.60538e28	−	1.60538e28i	−0.0755294	−	0.0755294i
$622$		0			0
$623$	3.45597e29			1.57198
$624$		0			0
$625$	−6.97664e29			−3.06836
$626$		0			0
$627$	−1.84473e29	−	1.84473e29i	−0.784554	−	0.784554i
$628$		0			0
$629$	4.12495e28	−	4.12495e28i	0.169663	−	0.169663i
$630$		0			0
$631$			6.81505e28i			0.271120i	0.990769	+	0.135560i	$0.0432833\pi$
$631$			6.81505e28i			0.271120i	−0.990769	+	0.135560i	$0.956717\pi$
$632$		0			0
$633$		−	3.18316e28i		−	0.122495i
$634$		0			0
$635$	−3.62491e29	+	3.62491e29i	−1.34950	+	1.34950i
$636$		0			0
$637$	−8.16105e28	−	8.16105e28i	−0.293956	−	0.293956i
$638$		0			0
$639$	5.16727e28			0.180095
$640$		0			0
$641$	2.33327e28			0.0786967			0.0393483	−	0.999226i	$-0.487472\pi$
$641$	2.33327e28			0.0786967			0.0393483	+	0.999226i	$0.487472\pi$
$642$		0			0
$643$	−2.09563e28	−	2.09563e28i	−0.0684068	−	0.0684068i	0.672076	−	0.740482i	$-0.265403\pi$
$643$	−2.09563e28	−	2.09563e28i	−0.0684068	−	0.0684068i	−0.740482	+	0.672076i	$0.765403\pi$
$644$		0			0
$645$	5.13274e29	−	5.13274e29i	1.62171	−	1.62171i
$646$		0			0
$647$			3.64215e29i			1.11394i	0.830532	+	0.556971i	$0.188037\pi$
$647$			3.64215e29i			1.11394i	−0.830532	+	0.556971i	$0.811963\pi$
$648$		0			0
$649$		−	3.52349e29i		−	1.04329i
$650$		0			0
$651$	4.69245e29	−	4.69245e29i	1.34524	−	1.34524i
$652$		0			0
$653$	2.00728e29	+	2.00728e29i	0.557212	+	0.557212i	0.928513	−	0.371301i	$-0.121088\pi$
$653$	2.00728e29	+	2.00728e29i	0.557212	+	0.557212i	−0.371301	+	0.928513i	$0.621088\pi$
$654$		0			0
$655$	1.44269e29			0.387827
$656$		0			0
$657$	−1.51096e29			−0.393383
$658$		0			0
$659$	−1.15322e29	−	1.15322e29i	−0.290813	−	0.290813i	0.546588	−	0.837401i	$-0.315926\pi$
$659$	−1.15322e29	−	1.15322e29i	−0.290813	−	0.290813i	−0.837401	+	0.546588i	$0.815926\pi$
$660$		0			0
$661$	−4.07738e29	+	4.07738e29i	−0.996016	+	0.996016i	−0.999992	−	0.00397614i	$-0.998734\pi$
$661$	−4.07738e29	+	4.07738e29i	−0.996016	+	0.996016i	0.00397614	+	0.999992i	$0.498734\pi$
$662$		0			0
$663$		−	9.90473e28i		−	0.234396i
$664$		0			0
$665$			7.64595e29i			1.75309i
$666$		0			0
$667$	−4.08357e28	+	4.08357e28i	−0.0907233	+	0.0907233i
$668$		0			0
$669$	5.50699e29	+	5.50699e29i	1.18561	+	1.18561i
$670$		0			0
$671$	−3.45151e29			−0.720151
$672$		0			0
$673$	−4.56792e29			−0.923762			−0.461881	−	0.886942i	$-0.652825\pi$
$673$	−4.56792e29			−0.923762			−0.461881	+	0.886942i	$0.652825\pi$
$674$		0			0
$675$	7.95152e29	+	7.95152e29i	1.55869	+	1.55869i
$676$		0			0
$677$	1.96277e29	−	1.96277e29i	0.372982	−	0.372982i	−0.495580	−	0.868562i	$-0.665045\pi$
$677$	1.96277e29	−	1.96277e29i	0.372982	−	0.372982i	0.868562	+	0.495580i	$0.165045\pi$
$678$		0			0
$679$			1.10678e30i			2.03906i
$680$		0			0
$681$			2.41515e29i			0.431419i
$682$		0			0
$683$	6.93637e29	−	6.93637e29i	1.20148	−	1.20148i	0.227758	−	0.973718i	$-0.426861\pi$
$683$	6.93637e29	−	6.93637e29i	1.20148	−	1.20148i	0.973718	−	0.227758i	$-0.0731394\pi$
$684$		0			0
$685$	1.32792e30	+	1.32792e30i	2.23060	+	2.23060i
$686$		0			0
$687$	8.74048e29			1.42393
$688$		0			0
$689$	−2.00723e29			−0.317172
$690$		0			0
$691$	−5.74606e29	−	5.74606e29i	−0.880747	−	0.880747i	0.112864	−	0.993610i	$-0.463998\pi$
$691$	−5.74606e29	−	5.74606e29i	−0.880747	−	0.880747i	−0.993610	+	0.112864i	$0.963998\pi$
$692$		0			0
$693$	1.77561e29	−	1.77561e29i	0.264027	−	0.264027i
$694$		0			0
$695$			2.14370e30i			3.09259i
$696$		0			0
$697$		−	2.25489e29i		−	0.315632i
$698$		0			0
$699$	1.28155e29	−	1.28155e29i	0.174070	−	0.174070i
$700$		0			0
$701$	−8.59856e29	−	8.59856e29i	−1.13341	−	1.13341i	−0.989606	−	0.143802i	$-0.954067\pi$
$701$	−8.59856e29	−	8.59856e29i	−1.13341	−	1.13341i	−0.143802	−	0.989606i	$-0.545933\pi$
$702$		0			0
$703$	−5.42486e29			−0.693997
$704$		0			0
$705$	−8.18806e29			−1.01671
$706$		0			0
$707$	3.15441e29	+	3.15441e29i	0.380203	+	0.380203i
$708$		0			0
$709$	−4.70532e29	+	4.70532e29i	−0.550559	+	0.550559i	−0.926602	−	0.376043i	$-0.877284\pi$
$709$	−4.70532e29	+	4.70532e29i	−0.550559	+	0.550559i	0.376043	+	0.926602i	$0.377284\pi$
$710$		0			0
$711$		−	1.26401e29i		−	0.143588i
$712$		0			0
$713$			1.58084e29i			0.174360i
$714$		0			0
$715$	1.34621e30	−	1.34621e30i	1.44178	−	1.44178i
$716$		0			0
$717$	2.24284e29	+	2.24284e29i	0.233263	+	0.233263i
$718$		0			0
$719$	9.16893e29			0.926116			0.463058	−	0.886328i	$-0.346752\pi$
$719$	9.16893e29			0.926116			0.463058	+	0.886328i	$0.346752\pi$
$720$		0			0
$721$	1.50967e30			1.48103
$722$		0			0
$723$	−7.43669e29	−	7.43669e29i	−0.708643	−	0.708643i
$724$		0			0
$725$	2.02261e30	−	2.02261e30i	1.87225	−	1.87225i
$726$		0			0
$727$			1.55768e30i			1.40077i	0.713766	+	0.700384i	$0.246988\pi$
$727$			1.55768e30i			1.40077i	−0.713766	+	0.700384i	$0.753012\pi$
$728$		0			0
$729$		−	7.76945e29i		−	0.678815i
$730$		0			0
$731$	2.37404e29	−	2.37404e29i	0.201538	−	0.201538i
$732$		0			0
$733$	−1.15479e30	−	1.15479e30i	−0.952600	−	0.952600i	0.0463265	−	0.998926i	$-0.485249\pi$
$733$	−1.15479e30	−	1.15479e30i	−0.952600	−	0.952600i	−0.998926	+	0.0463265i	$0.985249\pi$
$734$		0			0
$735$	−1.33973e30			−1.07399
$736$		0			0
$737$	−8.37945e29			−0.652840
$738$		0			0
$739$	1.54853e30	+	1.54853e30i	1.17261	+	1.17261i	0.981585	+	0.191024i	$0.0611809\pi$
$739$	1.54853e30	+	1.54853e30i	1.17261	+	1.17261i	0.191024	+	0.981585i	$0.438819\pi$
$740$		0			0
$741$	−6.51303e29	+	6.51303e29i	−0.479393	+	0.479393i
$742$		0			0
$743$		−	1.39830e29i		−	0.100050i	−0.998748	−	0.0500251i	$-0.984070\pi$
$743$		−	1.39830e29i		−	0.100050i	0.998748	−	0.0500251i	$-0.0159301\pi$
$744$		0			0
$745$			1.98818e30i			1.38298i
$746$		0			0
$747$	3.07188e29	−	3.07188e29i	0.207748	−	0.207748i
$748$		0			0
$749$	−5.43555e29	−	5.43555e29i	−0.357425	−	0.357425i
$750$		0			0
$751$	1.38587e30			0.886144			0.443072	−	0.896486i	$-0.353889\pi$
$751$	1.38587e30			0.886144			0.443072	+	0.896486i	$0.353889\pi$
$752$		0			0
$753$	−6.84071e28			−0.0425357
$754$		0			0
$755$	−3.74075e30	−	3.74075e30i	−2.26212	−	2.26212i
$756$		0			0
$757$	−2.36907e29	+	2.36907e29i	−0.139338	+	0.139338i	−0.773335	−	0.633997i	$-0.781413\pi$
$757$	−2.36907e29	+	2.36907e29i	−0.139338	+	0.139338i	0.633997	+	0.773335i	$0.281413\pi$
$758$		0			0
$759$			3.21481e29i			0.183915i
$760$		0			0
$761$			1.39283e30i			0.775105i	0.921848	+	0.387553i	$0.126679\pi$
$761$			1.39283e30i			0.775105i	−0.921848	+	0.387553i	$0.873321\pi$
$762$		0			0
$763$	−2.61879e30	+	2.61879e30i	−1.41773	+	1.41773i
$764$		0			0
$765$	−1.51273e29	−	1.51273e29i	−0.0796740	−	0.0796740i
$766$		0			0
$767$	−1.24401e30			−0.637488
$768$		0			0
$769$	1.69828e30			0.846803			0.423402	−	0.905942i	$-0.360836\pi$
$769$	1.69828e30			0.846803			0.423402	+	0.905942i	$0.360836\pi$
$770$		0			0
$771$	−5.06545e29	−	5.06545e29i	−0.245780	−	0.245780i
$772$		0			0
$773$	−5.28755e29	+	5.28755e29i	−0.249672	+	0.249672i	−0.820836	−	0.571164i	$-0.806492\pi$
$773$	−5.28755e29	+	5.28755e29i	−0.249672	+	0.249672i	0.571164	+	0.820836i	$0.306492\pi$
$774$		0			0
$775$		−	7.82997e30i		−	3.59826i
$776$		0			0
$777$		−	2.80623e30i		−	1.25517i
$778$		0			0
$779$	−1.48274e30	+	1.48274e30i	−0.645538	+	0.645538i
$780$		0			0
$781$	1.74578e30	+	1.74578e30i	0.739869	+	0.739869i
$782$		0			0
$783$	−2.12846e30			−0.878145
$784$		0			0
$785$	−3.74168e30			−1.50292
$786$		0			0
$787$	3.30268e30	+	3.30268e30i	1.29161	+	1.29161i	0.933790	+	0.357822i	$0.116480\pi$
$787$	3.30268e30	+	3.30268e30i	1.29161	+	1.29161i	0.357822	+	0.933790i	$0.383520\pi$
$788$		0			0
$789$	−1.02407e29	+	1.02407e29i	−0.0389959	+	0.0389959i
$790$		0			0
$791$			3.69404e30i			1.36977i
$792$		0			0
$793$			1.21860e30i			0.440040i
$794$		0			0
$795$	−1.64754e30	+	1.64754e30i	−0.579405	+	0.579405i
$796$		0			0
$797$	1.06437e30	+	1.06437e30i	0.364569	+	0.364569i	0.865492	−	0.500923i	$-0.167006\pi$
$797$	1.06437e30	+	1.06437e30i	0.364569	+	0.364569i	−0.500923	+	0.865492i	$0.667006\pi$
$798$		0			0
$799$	−3.78722e29			−0.126351
$800$		0			0
$801$	8.99230e29			0.292233
$802$		0			0
$803$	−5.10483e30	−	5.10483e30i	−1.61610	−	1.61610i
$804$		0			0
$805$	6.66231e29	−	6.66231e29i	0.205479	−	0.205479i
$806$		0			0
$807$		−	1.74664e30i		−	0.524845i
$808$		0			0
$809$			4.26353e30i			1.24827i	0.781315	+	0.624137i	$0.214549\pi$
$809$			4.26353e30i			1.24827i	−0.781315	+	0.624137i	$0.785451\pi$
$810$		0			0
$811$	4.43321e30	−	4.43321e30i	1.26473	−	1.26473i	0.315964	−	0.948771i	$-0.397672\pi$
$811$	4.43321e30	−	4.43321e30i	1.26473	−	1.26473i	0.948771	−	0.315964i	$-0.102328\pi$
$812$		0			0
$813$	−3.45452e30	−	3.45452e30i	−0.960365	−	0.960365i
$814$		0			0
$815$	3.51345e29			0.0951874
$816$		0			0
$817$	−3.12219e30			−0.824380
$818$		0			0
$819$	−6.26899e29	−	6.26899e29i	−0.161330	−	0.161330i
$820$		0			0
$821$	5.12281e30	−	5.12281e30i	1.28501	−	1.28501i	0.347225	−	0.937782i	$-0.387124\pi$
$821$	5.12281e30	−	5.12281e30i	1.28501	−	1.28501i	0.937782	−	0.347225i	$-0.112876\pi$
$822$		0			0
$823$		−	5.21863e30i		−	1.27602i	−0.770027	−	0.638011i	$-0.779758\pi$
$823$		−	5.21863e30i		−	1.27602i	0.770027	−	0.638011i	$-0.220242\pi$
$824$		0			0
$825$		−	1.59231e31i		−	3.79543i
$826$		0			0
$827$	−6.01616e29	+	6.01616e29i	−0.139802	+	0.139802i	−0.773544	−	0.633743i	$-0.781518\pi$
$827$	−6.01616e29	+	6.01616e29i	−0.139802	+	0.139802i	0.633743	+	0.773544i	$0.281518\pi$
$828$		0			0
$829$	2.20876e30	+	2.20876e30i	0.500410	+	0.500410i	0.911565	−	0.411155i	$-0.134875\pi$
$829$	2.20876e30	+	2.20876e30i	0.500410	+	0.500410i	−0.411155	+	0.911565i	$0.634875\pi$
$830$		0			0
$831$	−2.16229e29			−0.0477642
$832$		0			0
$833$	−6.19662e29			−0.133470
$834$		0			0
$835$	4.36204e30	+	4.36204e30i	0.916182	+	0.916182i
$836$		0			0
$837$	−4.11986e30	+	4.11986e30i	−0.843849	+	0.843849i
$838$		0			0
$839$			4.68996e29i			0.0936847i	0.998902	+	0.0468423i	$0.0149158\pi$
$839$			4.68996e29i			0.0936847i	−0.998902	+	0.0468423i	$0.985084\pi$
$840$		0			0
$841$			2.81265e29i			0.0547972i
$842$		0			0
$843$	5.16761e30	−	5.16761e30i	0.981975	−	0.981975i
$844$		0			0
$845$	2.46319e30	+	2.46319e30i	0.456564	+	0.456564i
$846$		0			0
$847$	5.19673e30			0.939624
$848$		0			0
$849$	6.63241e30			1.16988
$850$		0			0
$851$	4.72696e29	+	4.72696e29i	0.0813432	+	0.0813432i
$852$		0			0
$853$	−7.01358e30	+	7.01358e30i	−1.17754	+	1.17754i	−0.197168	+	0.980370i	$0.563174\pi$
$853$	−7.01358e30	+	7.01358e30i	−1.17754	+	1.17754i	−0.980370	+	0.197168i	$0.936826\pi$
$854$		0			0
$855$			1.98944e30i			0.325902i
$856$		0			0
$857$		−	1.05935e31i		−	1.69333i	−0.532129	−	0.846663i	$-0.678608\pi$
$857$		−	1.05935e31i		−	1.69333i	0.532129	−	0.846663i	$-0.321392\pi$
$858$		0			0
$859$	3.04930e30	−	3.04930e30i	0.475634	−	0.475634i	−0.428099	−	0.903732i	$-0.640816\pi$
$859$	3.04930e30	−	3.04930e30i	0.475634	−	0.475634i	0.903732	+	0.428099i	$0.140816\pi$
$860$		0			0
$861$	−7.67009e30	−	7.67009e30i	−1.16753	−	1.16753i
$862$		0			0
$863$	1.56977e30			0.233197			0.116598	−	0.993179i	$-0.462801\pi$
$863$	1.56977e30			0.233197			0.116598	+	0.993179i	$0.462801\pi$
$864$		0			0
$865$	−1.81612e30			−0.263314
$866$		0			0
$867$	5.16247e30	+	5.16247e30i	0.730562	+	0.730562i
$868$		0			0
$869$	4.27051e30	−	4.27051e30i	0.589891	−	0.589891i
$870$		0			0
$871$			2.95846e30i			0.398910i
$872$		0			0
$873$			2.87980e30i			0.379065i
$874$		0			0
$875$	−2.01989e31	+	2.01989e31i	−2.59564	+	2.59564i
$876$		0			0
$877$	−4.23095e30	−	4.23095e30i	−0.530813	−	0.530813i	0.390001	−	0.920814i	$-0.372475\pi$
$877$	−4.23095e30	−	4.23095e30i	−0.530813	−	0.530813i	−0.920814	+	0.390001i	$0.872475\pi$
$878$		0			0
$879$	4.26376e30			0.522287
$880$		0			0
$881$	−1.85214e30			−0.221527			−0.110764	−	0.993847i	$-0.535330\pi$
$881$	−1.85214e30			−0.221527			−0.110764	+	0.993847i	$0.535330\pi$
$882$		0			0
$883$	−3.58670e30	−	3.58670e30i	−0.418897	−	0.418897i	0.465927	−	0.884823i	$-0.345721\pi$
$883$	−3.58670e30	−	3.58670e30i	−0.418897	−	0.418897i	−0.884823	+	0.465927i	$0.845721\pi$
$884$		0			0
$885$	−1.02109e31	+	1.02109e31i	−1.16455	+	1.16455i
$886$		0			0
$887$		−	3.04532e30i		−	0.339183i	−0.985514	−	0.169592i	$-0.945755\pi$
$887$		−	3.04532e30i		−	0.339183i	0.985514	−	0.169592i	$-0.0542449\pi$
$888$		0			0
$889$			1.14062e31i			1.24072i
$890$		0			0
$891$	−1.03991e31	+	1.03991e31i	−1.10479	+	1.10479i
$892$		0			0
$893$	2.49035e30	+	2.49035e30i	0.258416	+	0.258416i
$894$		0			0
$895$	−2.48981e31			−2.52362
$896$		0			0
$897$	1.13503e30			0.112379
$898$		0			0
$899$	1.04796e31	+	1.04796e31i	1.01360	+	1.01360i
$900$		0			0
$901$	−7.62037e29	+	7.62037e29i	−0.0720055	+	0.0720055i
$902$		0			0
$903$		−	1.61508e31i		−	1.49098i
$904$		0			0
$905$			2.79416e31i			2.52023i
$906$		0			0
$907$	1.54021e31	−	1.54021e31i	1.35738	−	1.35738i	0.480256	−	0.877128i	$-0.340544\pi$
$907$	1.54021e31	−	1.54021e31i	1.35738	−	1.35738i	0.877128	−	0.480256i	$-0.159456\pi$
$908$		0			0
$909$	8.20766e29	+	8.20766e29i	0.0706803	+	0.0706803i
$910$		0			0
$911$	8.74875e30			0.736212			0.368106	−	0.929784i	$-0.380006\pi$
$911$	8.74875e30			0.736212			0.368106	+	0.929784i	$0.380006\pi$
$912$		0			0
$913$	2.07569e31			1.70695
$914$		0			0
$915$	1.00023e31	+	1.00023e31i	0.803857	+	0.803857i
$916$		0			0
$917$	2.26979e30	−	2.26979e30i	0.178282	−	0.178282i
$918$		0			0
$919$		−	1.75964e31i		−	1.35086i	−0.737422	−	0.675432i	$-0.763957\pi$
$919$		−	1.75964e31i		−	1.35086i	0.737422	−	0.675432i	$-0.236043\pi$
$920$		0			0
$921$			6.28618e30i			0.471694i
$922$		0			0
$923$	6.16370e30	−	6.16370e30i	0.452088	−	0.452088i
$924$		0			0
$925$	−2.34128e31	−	2.34128e31i	−1.67867	−	1.67867i
$926$		0			0
$927$	3.92810e30			0.275325
$928$		0			0
$929$	1.75316e31			1.20131			0.600657	−	0.799507i	$-0.294906\pi$
$929$	1.75316e31			1.20131			0.600657	+	0.799507i	$0.294906\pi$
$930$		0			0
$931$	4.07470e30	+	4.07470e30i	0.272975	+	0.272975i
$932$		0			0
$933$	−5.64607e29	+	5.64607e29i	−0.0369819	+	0.0369819i
$934$		0			0
$935$		−	1.02217e31i		−	0.654635i
$936$		0			0
$937$		−	1.54029e31i		−	0.964576i	−0.876013	−	0.482288i	$-0.839806\pi$
$937$		−	1.54029e31i		−	0.964576i	0.876013	−	0.482288i	$-0.160194\pi$
$938$		0			0
$939$	−1.81516e31	+	1.81516e31i	−1.11154	+	1.11154i
$940$		0			0
$941$	−1.11426e31	−	1.11426e31i	−0.667260	−	0.667260i	0.289821	−	0.957081i	$-0.406404\pi$
$941$	−1.11426e31	−	1.11426e31i	−0.667260	−	0.667260i	−0.957081	+	0.289821i	$0.906404\pi$
$942$		0			0
$943$	2.58397e30			0.151327
$944$		0			0
$945$	3.47255e31			1.98891
$946$		0			0
$947$	−1.19203e31	−	1.19203e31i	−0.667749	−	0.667749i	0.289445	−	0.957195i	$-0.406529\pi$
$947$	−1.19203e31	−	1.19203e31i	−0.667749	−	0.667749i	−0.957195	+	0.289445i	$0.906529\pi$
$948$		0			0
$949$	−1.80232e31	+	1.80232e31i	−0.987500	+	0.987500i
$950$		0			0
$951$			2.24644e31i			1.20392i
$952$		0			0
$953$		−	8.43189e30i		−	0.442028i	−0.975271	−	0.221014i	$-0.929063\pi$
$953$		−	8.43189e30i		−	0.442028i	0.975271	−	0.221014i	$-0.0709366\pi$
$954$		0			0
$955$	−1.58696e30	+	1.58696e30i	−0.0813826	+	0.0813826i
$956$		0			0
$957$	2.13114e31	+	2.13114e31i	1.06915	+	1.06915i
$958$		0			0
$959$	4.17847e31			2.05079
$960$		0			0
$961$	1.97433e31			0.948035
$962$		0			0
$963$	−1.41431e30	−	1.41431e30i	−0.0664459	−	0.0664459i
$964$		0			0
$965$	−1.32748e30	+	1.32748e30i	−0.0610225	+	0.0610225i
$966$		0			0
$967$			2.35052e31i			1.05727i	0.848849	+	0.528635i	$0.177296\pi$
$967$			2.35052e31i			1.05727i	−0.848849	+	0.528635i	$0.822704\pi$
$968$		0			0
$969$			4.94529e30i			0.217667i
$970$		0			0
$971$	1.74073e31	−	1.74073e31i	0.749771	−	0.749771i	−0.224665	−	0.974436i	$-0.572129\pi$
$971$	1.74073e31	−	1.74073e31i	0.749771	−	0.749771i	0.974436	+	0.224665i	$0.0721289\pi$
$972$		0			0
$973$	3.37270e31	+	3.37270e31i	1.42165	+	1.42165i
$974$		0			0
$975$	−5.62184e31			−2.31916
$976$		0			0
$977$	7.49187e30			0.302480			0.151240	−	0.988497i	$-0.451673\pi$
$977$	7.49187e30			0.302480			0.151240	+	0.988497i	$0.451673\pi$
$978$		0			0
$979$	3.03809e31	+	3.03809e31i	1.20056	+	1.20056i
$980$		0			0
$981$	−6.81399e30	+	6.81399e30i	−0.263558	+	0.263558i
$982$		0			0
$983$			2.94913e31i			1.11656i	0.829653	+	0.558279i	$0.188538\pi$
$983$			2.94913e31i			1.11656i	−0.829653	+	0.558279i	$0.811462\pi$
$984$		0			0
$985$			4.18402e31i			1.55065i
$986$		0			0
$987$	−1.28824e31	+	1.28824e31i	−0.467375	+	0.467375i
$988$		0			0
$989$	2.72052e30	+	2.72052e30i	0.0966253	+	0.0966253i
$990$		0			0
$991$	−2.76494e31			−0.961419			−0.480710	−	0.876880i	$-0.659621\pi$
$991$	−2.76494e31			−0.961419			−0.480710	+	0.876880i	$0.659621\pi$
$992$		0			0
$993$	−2.40652e30			−0.0819260
$994$		0			0
$995$	−1.17807e31	−	1.17807e31i	−0.392672	−	0.392672i
$996$		0			0
$997$	2.13839e31	−	2.13839e31i	0.697892	−	0.697892i	−0.266063	−	0.963956i	$-0.585723\pi$
$997$	2.13839e31	−	2.13839e31i	0.697892	−	0.697892i	0.963956	+	0.266063i	$0.0857231\pi$
$998$		0			0
$999$			2.46380e31i			0.787351i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.22.e.a.17.8		82
4.3	odd	2		16.22.e.a.13.15	yes	82
16.5	even	4	inner	64.22.e.a.49.8		82
16.11	odd	4		16.22.e.a.5.15	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.22.e.a.5.15	✓	82	16.11	odd	4
16.22.e.a.13.15	yes	82	4.3	odd	2
64.22.e.a.17.8		82	1.1	even	1	trivial
64.22.e.a.49.8		82	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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	64.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-80161.3 - 80161.3i) q^{3} +(-2.92075e7 + 2.92075e7i) q^{5} +9.19049e8i q^{7} +2.39133e9i q^{9} +O(q^{10})\)	\(q+(-80161.3 - 80161.3i) q^{3} +(-2.92075e7 + 2.92075e7i) q^{5} +9.19049e8i q^{7} +2.39133e9i q^{9} +(-8.07921e10 + 8.07921e10i) q^{11} +(2.85246e11 + 2.85246e11i) q^{13} +4.68262e12 q^{15} +2.16585e12 q^{17} +(-1.42419e13 - 1.42419e13i) q^{19} +(7.36722e13 - 7.36722e13i) q^{21} +2.48194e13i q^{23} -1.22932e15i q^{25} +(-6.46824e14 + 6.46824e14i) q^{27} +(1.64531e15 + 1.64531e15i) q^{29} +6.36937e15 q^{31} +1.29528e16 q^{33} +(-2.68431e16 - 2.68431e16i) q^{35} +(1.90454e16 - 1.90454e16i) q^{37} -4.57314e16i q^{39} -1.04111e17i q^{41} +(1.09613e17 - 1.09613e17i) q^{43} +(-6.98447e16 - 6.98447e16i) q^{45} -1.74861e17 q^{47} -2.86106e17 q^{49} +(-1.73617e17 - 1.73617e17i) q^{51} +(-3.51842e17 + 3.51842e17i) q^{53} -4.71947e18i q^{55} +2.28330e18i q^{57} +(-2.18059e18 + 2.18059e18i) q^{59} +(2.13605e18 + 2.13605e18i) q^{61} -2.19775e18 q^{63} -1.66626e19 q^{65} +(5.18581e18 + 5.18581e18i) q^{67} +(1.98956e18 - 1.98956e18i) q^{69} -2.16084e19i q^{71} +6.31848e19i q^{73} +(-9.85438e19 + 9.85438e19i) q^{75} +(-7.42519e19 - 7.42519e19i) q^{77} -5.28580e19 q^{79} +1.28715e20 q^{81} +(-1.28459e20 - 1.28459e20i) q^{83} +(-6.32590e19 + 6.32590e19i) q^{85} -2.63781e20i q^{87} -3.76038e20i q^{89} +(-2.62155e20 + 2.62155e20i) q^{91} +(-5.10577e20 - 5.10577e20i) q^{93} +8.31941e20 q^{95} +1.20427e21 q^{97} +(-1.93200e20 - 1.93200e20i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 2 q^{3} - 2 q^{5}+O(q^{10}) \) 82 * q + 2 * q^3 - 2 * q^5	\( 82 q + 2 q^{3} - 2 q^{5} - 67333320738 q^{11} - 2 q^{13} - 4613203124996 q^{15} - 4 q^{17} + 46007763621434 q^{19} + 20920706404 q^{21} - 11\!\cdots\!20 q^{27}+ \cdots - 27\!\cdots\!38 q^{99}+O(q^{100}) \) 82 * q + 2 * q^3 - 2 * q^5 - 67333320738 * q^11 - 2 * q^13 - 4613203124996 * q^15 - 4 * q^17 + 46007763621434 * q^19 + 20920706404 * q^21 - 1147760716556920 * q^27 - 2433173450216602 * q^29 + 9835539443769616 * q^31 - 4 * q^33 + 19253478556034884 * q^35 - 7245708527119386 * q^37 - 215332019803969386 * q^43 + 953653395699842 * q^45 - 1051982644716600976 * q^47 - 5585458640832840074 * q^49 - 3238772068175213124 * q^51 + 1889987679210147606 * q^53 - 3631979197965016922 * q^59 + 10385362452353654062 * q^61 + 17464422381302680956 * q^63 - 9364161130572538716 * q^65 + 17102217044572669130 * q^67 - 3951842785111207532 * q^69 - 145960939174166395366 * q^75 - 82041801652678580764 * q^77 - 204448210818924484480 * q^79 - 802405920297757300870 * q^81 - 317463236552669319678 * q^83 + 323656241286464843748 * q^85 - 144326756239046079748 * q^91 - 669717759565183008560 * q^93 + 1411330138695550130700 * q^95 - 4 * q^97 - 2710306841526615010238 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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