LMFDB - Embedded newform 64.12.e.a.17.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,12,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, 12, names="a")

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

chi := DirichletCharacter("64.17");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 12 $
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:	$49.1739635558$
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			17.16
Character	$\chi$	$=$	64.17
Dual form			64.12.e.a.49.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(291.167 + 291.167i) q^{3} +(-9753.88 + 9753.88i) q^{5} -16447.0i q^{7} -7590.38i q^{9} +O(q^{10})$	\(q+(291.167 + 291.167i) q^{3} +(-9753.88 + 9753.88i) q^{5} -16447.0i q^{7} -7590.38i q^{9} +(-477540. + 477540. i) q^{11} +(665864. + 665864. i) q^{13} -5.68002e6 q^{15} -5.80462e6 q^{17} +(-1.91371e6 - 1.91371e6i) q^{19} +(4.78882e6 - 4.78882e6i) q^{21} +1.46860e7i q^{23} -1.41448e8i q^{25} +(5.37895e7 - 5.37895e7i) q^{27} +(5.83665e7 + 5.83665e7i) q^{29} -8.50845e7 q^{31} -2.78088e8 q^{33} +(1.60422e8 + 1.60422e8i) q^{35} +(2.52847e7 - 2.52847e7i) q^{37} +3.87755e8i q^{39} -9.24887e8i q^{41} +(-1.00305e9 + 1.00305e9i) q^{43} +(7.40356e7 + 7.40356e7i) q^{45} +2.86182e9 q^{47} +1.70682e9 q^{49} +(-1.69011e9 - 1.69011e9i) q^{51} +(2.34993e9 - 2.34993e9i) q^{53} -9.31574e9i q^{55} -1.11442e9i q^{57} +(5.55716e8 - 5.55716e8i) q^{59} +(-2.31483e9 - 2.31483e9i) q^{61} -1.24839e8 q^{63} -1.29895e10 q^{65} +(-1.02227e10 - 1.02227e10i) q^{67} +(-4.27609e9 + 4.27609e9i) q^{69} -1.39591e9i q^{71} -2.22133e10i q^{73} +(4.11850e10 - 4.11850e10i) q^{75} +(7.85409e9 + 7.85409e9i) q^{77} -3.84124e10 q^{79} +2.99788e10 q^{81} +(4.10961e9 + 4.10961e9i) q^{83} +(5.66175e10 - 5.66175e10i) q^{85} +3.39888e10i q^{87} -1.47623e10i q^{89} +(1.09514e10 - 1.09514e10i) q^{91} +(-2.47738e10 - 2.47738e10i) q^{93} +3.73322e10 q^{95} -9.56623e10 q^{97} +(3.62471e9 + 3.62471e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

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

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
$3$	291.167	+	291.167i	0.691792	+	0.691792i	0.962626	−	0.270834i	$-0.0872995\pi$
$3$	291.167	+	291.167i	0.691792	+	0.691792i	−0.270834	+	0.962626i	$0.587299\pi$
$4$		0			0
$5$	−9753.88	+	9753.88i	−1.39586	+	1.39586i	−0.584384	+	0.811477i	$0.698664\pi$
$5$	−9753.88	+	9753.88i	−1.39586	+	1.39586i	−0.811477	+	0.584384i	$0.801336\pi$
$6$		0			0
$7$		−	16447.0i		−	0.369868i	−0.982751	−	0.184934i	$-0.940793\pi$
$7$		−	16447.0i		−	0.369868i	0.982751	−	0.184934i	$-0.0592071\pi$
$8$		0			0
$9$		−	7590.38i		−	0.0428479i
$10$		0			0
$11$	−477540.	+	477540.i	−0.894026	+	0.894026i	−0.994899	−	0.100873i	$-0.967836\pi$
$11$	−477540.	+	477540.i	−0.894026	+	0.894026i	0.100873	+	0.994899i	$0.467836\pi$
$12$		0			0
$13$	665864.	+	665864.i	0.497390	+	0.497390i	0.910625	−	0.413235i	$-0.135601\pi$
$13$	665864.	+	665864.i	0.497390	+	0.497390i	−0.413235	+	0.910625i	$0.635601\pi$
$14$		0			0
$15$	−5.68002e6			−1.93129
$16$		0			0
$17$	−5.80462e6			−0.991527			−0.495764	−	0.868457i	$-0.665112\pi$
$17$	−5.80462e6			−0.991527			−0.495764	+	0.868457i	$0.665112\pi$
$18$		0			0
$19$	−1.91371e6	−	1.91371e6i	−0.177309	−	0.177309i	0.612873	−	0.790182i	$-0.290014\pi$
$19$	−1.91371e6	−	1.91371e6i	−0.177309	−	0.177309i	−0.790182	+	0.612873i	$0.790014\pi$
$20$		0			0
$21$	4.78882e6	−	4.78882e6i	0.255872	−	0.255872i
$22$		0			0
$23$			1.46860e7i			0.475775i	0.971293	+	0.237888i	$0.0764550\pi$
$23$			1.46860e7i			0.475775i	−0.971293	+	0.237888i	$0.923545\pi$
$24$		0			0
$25$		−	1.41448e8i		−	2.89686i
$26$		0			0
$27$	5.37895e7	−	5.37895e7i	0.721434	−	0.721434i
$28$		0			0
$29$	5.83665e7	+	5.83665e7i	0.528414	+	0.528414i	0.920099	−	0.391685i	$-0.128108\pi$
$29$	5.83665e7	+	5.83665e7i	0.528414	+	0.528414i	−0.391685	+	0.920099i	$0.628108\pi$
$30$		0			0
$31$	−8.50845e7			−0.533778			−0.266889	−	0.963727i	$-0.585996\pi$
$31$	−8.50845e7			−0.533778			−0.266889	+	0.963727i	$0.585996\pi$
$32$		0			0
$33$	−2.78088e8			−1.23696
$34$		0			0
$35$	1.60422e8	+	1.60422e8i	0.516284	+	0.516284i
$36$		0			0
$37$	2.52847e7	−	2.52847e7i	0.0599443	−	0.0599443i	−0.676499	−	0.736443i	$-0.736504\pi$
$37$	2.52847e7	−	2.52847e7i	0.0599443	−	0.0599443i	0.736443	+	0.676499i	$0.236504\pi$
$38$		0			0
$39$			3.87755e8i			0.688180i
$40$		0			0
$41$		−	9.24887e8i		−	1.24674i	−0.781925	−	0.623372i	$-0.785762\pi$
$41$		−	9.24887e8i		−	1.24674i	0.781925	−	0.623372i	$-0.214238\pi$
$42$		0			0
$43$	−1.00305e9	+	1.00305e9i	−1.04051	+	1.04051i	−0.0413672	+	0.999144i	$0.513171\pi$
$43$	−1.00305e9	+	1.00305e9i	−1.04051	+	1.04051i	−0.999144	+	0.0413672i	$0.986829\pi$
$44$		0			0
$45$	7.40356e7	+	7.40356e7i	0.0598097	+	0.0598097i
$46$		0			0
$47$	2.86182e9			1.82014			0.910068	−	0.414459i	$-0.136029\pi$
$47$	2.86182e9			1.82014			0.910068	+	0.414459i	$0.136029\pi$
$48$		0			0
$49$	1.70682e9			0.863198
$50$		0			0
$51$	−1.69011e9	−	1.69011e9i	−0.685931	−	0.685931i
$52$		0			0
$53$	2.34993e9	−	2.34993e9i	0.771858	−	0.771858i	−0.206574	−	0.978431i	$-0.566231\pi$
$53$	2.34993e9	−	2.34993e9i	0.771858	−	0.771858i	0.978431	+	0.206574i	$0.0662313\pi$
$54$		0			0
$55$		−	9.31574e9i		−	2.49587i
$56$		0			0
$57$		−	1.11442e9i		−	0.245322i
$58$		0			0
$59$	5.55716e8	−	5.55716e8i	0.101197	−	0.101197i	−0.654696	−	0.755893i	$-0.727203\pi$
$59$	5.55716e8	−	5.55716e8i	0.101197	−	0.101197i	0.755893	+	0.654696i	$0.227203\pi$
$60$		0			0
$61$	−2.31483e9	−	2.31483e9i	−0.350918	−	0.350918i	0.509533	−	0.860451i	$-0.329818\pi$
$61$	−2.31483e9	−	2.31483e9i	−0.350918	−	0.350918i	−0.860451	+	0.509533i	$0.829818\pi$
$62$		0			0
$63$	−1.24839e8			−0.0158481
$64$		0			0
$65$	−1.29895e10			−1.38857
$66$		0			0
$67$	−1.02227e10	−	1.02227e10i	−0.925025	−	0.925025i	0.0723539	−	0.997379i	$-0.476949\pi$
$67$	−1.02227e10	−	1.02227e10i	−0.925025	−	0.925025i	−0.997379	+	0.0723539i	$0.976949\pi$
$68$		0			0
$69$	−4.27609e9	+	4.27609e9i	−0.329137	+	0.329137i
$70$		0			0
$71$		−	1.39591e9i		−	0.0918200i	−0.998946	−	0.0459100i	$-0.985381\pi$
$71$		−	1.39591e9i		−	0.0918200i	0.998946	−	0.0459100i	$-0.0146187\pi$
$72$		0			0
$73$		−	2.22133e10i		−	1.25411i	−0.778974	−	0.627057i	$-0.784259\pi$
$73$		−	2.22133e10i		−	1.25411i	0.778974	−	0.627057i	$-0.215741\pi$
$74$		0			0
$75$	4.11850e10	−	4.11850e10i	2.00402	−	2.00402i
$76$		0			0
$77$	7.85409e9	+	7.85409e9i	0.330671	+	0.330671i
$78$		0			0
$79$	−3.84124e10			−1.40450			−0.702251	−	0.711929i	$-0.747822\pi$
$79$	−3.84124e10			−1.40450			−0.702251	+	0.711929i	$0.747822\pi$
$80$		0			0
$81$	2.99788e10			0.955316
$82$		0			0
$83$	4.10961e9	+	4.10961e9i	0.114517	+	0.114517i	0.762043	−	0.647526i	$-0.224196\pi$
$83$	4.10961e9	+	4.10961e9i	0.114517	+	0.114517i	−0.647526	+	0.762043i	$0.724196\pi$
$84$		0			0
$85$	5.66175e10	−	5.66175e10i	1.38403	−	1.38403i
$86$		0			0
$87$			3.39888e10i			0.731106i
$88$		0			0
$89$		−	1.47623e10i		−	0.280227i	−0.990135	−	0.140114i	$-0.955253\pi$
$89$		−	1.47623e10i		−	0.280227i	0.990135	−	0.140114i	$-0.0447468\pi$
$90$		0			0
$91$	1.09514e10	−	1.09514e10i	0.183968	−	0.183968i
$92$		0			0
$93$	−2.47738e10	−	2.47738e10i	−0.369263	−	0.369263i
$94$		0			0
$95$	3.73322e10			0.494998
$96$		0			0
$97$	−9.56623e10			−1.13109			−0.565544	−	0.824718i	$-0.691334\pi$
$97$	−9.56623e10			−1.13109			−0.565544	+	0.824718i	$0.691334\pi$
$98$		0			0
$99$	3.62471e9	+	3.62471e9i	0.0383071	+	0.0383071i
$100$		0			0
$101$	−6.71598e9	+	6.71598e9i	−0.0635831	+	0.0635831i	−0.738183	−	0.674600i	$-0.764316\pi$
$101$	−6.71598e9	+	6.71598e9i	−0.0635831	+	0.0635831i	0.674600	+	0.738183i	$0.264316\pi$
$102$		0			0
$103$			1.06230e11i			0.902908i	0.892294	+	0.451454i	$0.149095\pi$
$103$			1.06230e11i			0.902908i	−0.892294	+	0.451454i	$0.850905\pi$
$104$		0			0
$105$			9.34190e10i			0.714322i
$106$		0			0
$107$	−7.29036e10	+	7.29036e10i	−0.502502	+	0.502502i	−0.912215	−	0.409712i	$-0.865629\pi$
$107$	−7.29036e10	+	7.29036e10i	−0.502502	+	0.502502i	0.409712	+	0.912215i	$0.365629\pi$
$108$		0			0
$109$	−8.14448e10	−	8.14448e10i	−0.507011	−	0.507011i	0.406596	−	0.913608i	$-0.366716\pi$
$109$	−8.14448e10	−	8.14448e10i	−0.507011	−	0.507011i	−0.913608	+	0.406596i	$0.866716\pi$
$110$		0			0
$111$	1.47241e10			0.0829379
$112$		0			0
$113$	−7.80734e10			−0.398631			−0.199316	−	0.979935i	$-0.563872\pi$
$113$	−7.80734e10			−0.398631			−0.199316	+	0.979935i	$0.563872\pi$
$114$		0			0
$115$	−1.43246e11	−	1.43246e11i	−0.664116	−	0.664116i
$116$		0			0
$117$	5.05415e9	−	5.05415e9i	0.0213121	−	0.0213121i
$118$		0			0
$119$			9.54684e10i			0.366734i
$120$		0			0
$121$		−	1.70778e11i		−	0.598565i
$122$		0			0
$123$	2.69297e11	−	2.69297e11i	0.862488	−	0.862488i
$124$		0			0
$125$	9.03404e11	+	9.03404e11i	2.64775	+	2.64775i
$126$		0			0
$127$	−9.32872e10			−0.250554			−0.125277	−	0.992122i	$-0.539982\pi$
$127$	−9.32872e10			−0.250554			−0.125277	+	0.992122i	$0.539982\pi$
$128$		0			0
$129$	−5.84111e11			−1.43963
$130$		0			0
$131$	−7.57223e10	−	7.57223e10i	−0.171487	−	0.171487i	0.616145	−	0.787632i	$-0.288693\pi$
$131$	−7.57223e10	−	7.57223e10i	−0.171487	−	0.171487i	−0.787632	+	0.616145i	$0.788693\pi$
$132$		0			0
$133$	−3.14747e10	+	3.14747e10i	−0.0655809	+	0.0655809i
$134$		0			0
$135$			1.04931e12i			2.01404i
$136$		0			0
$137$			2.64100e11i			0.467525i	0.972294	+	0.233762i	$0.0751038\pi$
$137$			2.64100e11i			0.467525i	−0.972294	+	0.233762i	$0.924896\pi$
$138$		0			0
$139$	−2.24899e10	+	2.24899e10i	−0.0367625	+	0.0367625i	−0.725249	−	0.688487i	$-0.758275\pi$
$139$	−2.24899e10	+	2.24899e10i	−0.0367625	+	0.0367625i	0.688487	+	0.725249i	$0.258275\pi$
$140$		0			0
$141$	8.33267e11	+	8.33267e11i	1.25916	+	1.25916i
$142$		0			0
$143$	−6.35953e11			−0.889359
$144$		0			0
$145$	−1.13860e12			−1.47519
$146$		0			0
$147$	4.96971e11	+	4.96971e11i	0.597153	+	0.597153i
$148$		0			0
$149$	−5.86301e11	+	5.86301e11i	−0.654028	+	0.654028i	−0.953960	−	0.299933i	$-0.903036\pi$
$149$	−5.86301e11	+	5.86301e11i	−0.654028	+	0.654028i	0.299933	+	0.953960i	$0.403036\pi$
$150$		0			0
$151$			9.25928e11i			0.959852i	0.877309	+	0.479926i	$0.159336\pi$
$151$			9.25928e11i			0.959852i	−0.877309	+	0.479926i	$0.840664\pi$
$152$		0			0
$153$			4.40592e10i			0.0424849i
$154$		0			0
$155$	8.29903e11	−	8.29903e11i	0.745080	−	0.745080i
$156$		0			0
$157$	−6.13818e11	−	6.13818e11i	−0.513560	−	0.513560i	0.402055	−	0.915615i	$-0.368296\pi$
$157$	−6.13818e11	−	6.13818e11i	−0.513560	−	0.513560i	−0.915615	+	0.402055i	$0.868296\pi$
$158$		0			0
$159$	1.36844e12			1.06793
$160$		0			0
$161$	2.41541e11			0.175974
$162$		0			0
$163$	−1.92844e12	−	1.92844e12i	−1.31272	−	1.31272i	−0.919399	−	0.393325i	$-0.871325\pi$
$163$	−1.92844e12	−	1.92844e12i	−1.31272	−	1.31272i	−0.393325	−	0.919399i	$-0.628675\pi$
$164$		0			0
$165$	2.71244e12	−	2.71244e12i	1.72662	−	1.72662i
$166$		0			0
$167$			5.92600e11i			0.353038i	0.984297	+	0.176519i	$0.0564837\pi$
$167$			5.92600e11i			0.353038i	−0.984297	+	0.176519i	$0.943516\pi$
$168$		0			0
$169$		−	9.05412e11i		−	0.505207i
$170$		0			0
$171$	−1.45258e10	+	1.45258e10i	−0.00759732	+	0.00759732i
$172$		0			0
$173$	−1.88219e12	−	1.88219e12i	−0.923441	−	0.923441i	0.0738298	−	0.997271i	$-0.476478\pi$
$173$	−1.88219e12	−	1.88219e12i	−0.923441	−	0.923441i	−0.997271	+	0.0738298i	$0.976478\pi$
$174$		0			0
$175$	−2.32639e12			−1.07145
$176$		0			0
$177$	3.23613e11			0.140014
$178$		0			0
$179$	1.56075e12	+	1.56075e12i	0.634806	+	0.634806i	0.949270	−	0.314463i	$-0.101825\pi$
$179$	1.56075e12	+	1.56075e12i	0.634806	+	0.634806i	−0.314463	+	0.949270i	$0.601825\pi$
$180$		0			0
$181$	1.26985e12	−	1.26985e12i	0.485869	−	0.485869i	−0.421131	−	0.907000i	$-0.638367\pi$
$181$	1.26985e12	−	1.26985e12i	0.485869	−	0.485869i	0.907000	+	0.421131i	$0.138367\pi$
$182$		0			0
$183$		−	1.34801e12i		−	0.485524i
$184$		0			0
$185$			4.93247e11i			0.167348i
$186$		0			0
$187$	2.77194e12	−	2.77194e12i	0.886451	−	0.886451i
$188$		0			0
$189$	−8.84673e11	−	8.84673e11i	−0.266835	−	0.266835i
$190$		0			0
$191$	−9.87202e11			−0.281011			−0.140505	−	0.990080i	$-0.544873\pi$
$191$	−9.87202e11			−0.281011			−0.140505	+	0.990080i	$0.544873\pi$
$192$		0			0
$193$	−2.65642e12			−0.714056			−0.357028	−	0.934094i	$-0.616210\pi$
$193$	−2.65642e12			−0.714056			−0.357028	+	0.934094i	$0.616210\pi$
$194$		0			0
$195$	−3.78212e12	−	3.78212e12i	−0.960604	−	0.960604i
$196$		0			0
$197$	−2.91004e12	+	2.91004e12i	−0.698771	+	0.698771i	−0.964145	−	0.265375i	$-0.914504\pi$
$197$	−2.91004e12	+	2.91004e12i	−0.698771	+	0.698771i	0.265375	+	0.964145i	$0.414504\pi$
$198$		0			0
$199$			4.90265e12i			1.11363i	0.830638	+	0.556813i	$0.187976\pi$
$199$			4.90265e12i			1.11363i	−0.830638	+	0.556813i	$0.812024\pi$
$200$		0			0
$201$		−	5.95302e12i		−	1.27985i
$202$		0			0
$203$	9.59952e11	−	9.59952e11i	0.195443	−	0.195443i
$204$		0			0
$205$	9.02123e12	+	9.02123e12i	1.74028	+	1.74028i
$206$		0			0
$207$	1.11473e11			0.0203860
$208$		0			0
$209$	1.82775e12			0.317038
$210$		0			0
$211$	2.11785e12	+	2.11785e12i	0.348611	+	0.348611i	0.859592	−	0.510981i	$-0.170718\pi$
$211$	2.11785e12	+	2.11785e12i	0.348611	+	0.348611i	−0.510981	+	0.859592i	$0.670718\pi$
$212$		0			0
$213$	4.06444e11	−	4.06444e11i	0.0635203	−	0.0635203i
$214$		0			0
$215$		−	1.95673e13i		−	2.90482i
$216$		0			0
$217$			1.39938e12i			0.197427i
$218$		0			0
$219$	6.46777e12	−	6.46777e12i	0.867585	−	0.867585i
$220$		0			0
$221$	−3.86508e12	−	3.86508e12i	−0.493175	−	0.493175i
$222$		0			0
$223$	1.24041e13			1.50622			0.753110	−	0.657894i	$-0.228553\pi$
$223$	1.24041e13			1.50622			0.753110	+	0.657894i	$0.228553\pi$
$224$		0			0
$225$	−1.07364e12			−0.124124
$226$		0			0
$227$	2.26312e12	+	2.26312e12i	0.249210	+	0.249210i	0.820646	−	0.571436i	$-0.193614\pi$
$227$	2.26312e12	+	2.26312e12i	0.249210	+	0.249210i	−0.571436	+	0.820646i	$0.693614\pi$
$228$		0			0
$229$	2.38743e12	−	2.38743e12i	0.250516	−	0.250516i	−0.570666	−	0.821182i	$-0.693315\pi$
$229$	2.38743e12	−	2.38743e12i	0.250516	−	0.250516i	0.821182	+	0.570666i	$0.193315\pi$
$230$		0			0
$231$			4.57370e12i			0.457512i
$232$		0			0
$233$			3.00078e12i			0.286271i	0.989703	+	0.143135i	$0.0457184\pi$
$233$			3.00078e12i			0.286271i	−0.989703	+	0.143135i	$0.954282\pi$
$234$		0			0
$235$	−2.79138e13	+	2.79138e13i	−2.54066	+	2.54066i
$236$		0			0
$237$	−1.11844e13	−	1.11844e13i	−0.971624	−	0.971624i
$238$		0			0
$239$	−1.56710e13			−1.29989			−0.649947	−	0.759980i	$-0.725209\pi$
$239$	−1.56710e13			−1.29989			−0.649947	+	0.759980i	$0.725209\pi$
$240$		0			0
$241$	1.45177e13			1.15029			0.575143	−	0.818053i	$-0.304947\pi$
$241$	1.45177e13			1.15029			0.575143	+	0.818053i	$0.304947\pi$
$242$		0			0
$243$	−7.99789e11	−	7.99789e11i	−0.0605537	−	0.0605537i
$244$		0			0
$245$	−1.66482e13	+	1.66482e13i	−1.20490	+	1.20490i
$246$		0			0
$247$		−	2.54854e12i		−	0.176383i
$248$		0			0
$249$			2.39317e12i			0.158444i
$250$		0			0
$251$	−1.54759e13	+	1.54759e13i	−0.980507	+	0.980507i	−0.999814	−	0.0193070i	$-0.993854\pi$
$251$	−1.54759e13	+	1.54759e13i	−0.980507	+	0.980507i	0.0193070	+	0.999814i	$0.493854\pi$
$252$		0			0
$253$	−7.01318e12	−	7.01318e12i	−0.425355	−	0.425355i
$254$		0			0
$255$	3.29703e13			1.91493
$256$		0			0
$257$	1.62238e13			0.902654			0.451327	−	0.892359i	$-0.350951\pi$
$257$	1.62238e13			0.902654			0.451327	+	0.892359i	$0.350951\pi$
$258$		0			0
$259$	−4.15856e11	−	4.15856e11i	−0.0221715	−	0.0221715i
$260$		0			0
$261$	4.43024e11	−	4.43024e11i	0.0226414	−	0.0226414i
$262$		0			0
$263$			3.73684e12i			0.183125i	0.995799	+	0.0915626i	$0.0291862\pi$
$263$			3.73684e12i			0.183125i	−0.995799	+	0.0915626i	$0.970814\pi$
$264$		0			0
$265$			4.58418e13i			2.15481i
$266$		0			0
$267$	4.29831e12	−	4.29831e12i	0.193859	−	0.193859i
$268$		0			0
$269$	−9.41768e12	−	9.41768e12i	−0.407668	−	0.407668i	0.473257	−	0.880925i	$-0.343078\pi$
$269$	−9.41768e12	−	9.41768e12i	−0.407668	−	0.407668i	−0.880925	+	0.473257i	$0.843078\pi$
$270$		0			0
$271$	−2.56747e13			−1.06703			−0.533513	−	0.845792i	$-0.679128\pi$
$271$	−2.56747e13			−1.06703			−0.533513	+	0.845792i	$0.679128\pi$
$272$		0			0
$273$	6.37740e12			0.254536
$274$		0			0
$275$	6.75472e13	+	6.75472e13i	2.58987	+	2.58987i
$276$		0			0
$277$	5.89614e12	−	5.89614e12i	0.217235	−	0.217235i	−0.590097	−	0.807332i	$-0.700911\pi$
$277$	5.89614e12	−	5.89614e12i	0.217235	−	0.217235i	0.807332	+	0.590097i	$0.200911\pi$
$278$		0			0
$279$			6.45823e11i			0.0228713i
$280$		0			0
$281$		−	4.45719e13i		−	1.51767i	−0.651285	−	0.758833i	$-0.725770\pi$
$281$		−	4.45719e13i		−	1.51767i	0.651285	−	0.758833i	$-0.274230\pi$
$282$		0			0
$283$	2.16962e13	−	2.16962e13i	0.710490	−	0.710490i	−0.256147	−	0.966638i	$-0.582453\pi$
$283$	2.16962e13	−	2.16962e13i	0.710490	−	0.710490i	0.966638	+	0.256147i	$0.0824533\pi$
$284$		0			0
$285$	1.08699e13	+	1.08699e13i	0.342435	+	0.342435i
$286$		0			0
$287$	−1.52116e13			−0.461131
$288$		0			0
$289$	−5.78287e11			−0.0168735
$290$		0			0
$291$	−2.78537e13	−	2.78537e13i	−0.782477	−	0.782477i
$292$		0			0
$293$	−2.92892e13	+	2.92892e13i	−0.792383	+	0.792383i	−0.981881	−	0.189498i	$-0.939314\pi$
$293$	−2.92892e13	+	2.92892e13i	−0.792383	+	0.792383i	0.189498	+	0.981881i	$0.439314\pi$
$294$		0			0
$295$			1.08408e13i			0.282514i
$296$		0			0
$297$			5.13733e13i			1.28996i
$298$		0			0
$299$	−9.77890e12	+	9.77890e12i	−0.236646	+	0.236646i
$300$		0			0
$301$	1.64972e13	+	1.64972e13i	0.384852	+	0.384852i
$302$		0			0
$303$	−3.91094e12			−0.0879725
$304$		0			0
$305$	4.51571e13			0.979664
$306$		0			0
$307$	−6.21960e13	−	6.21960e13i	−1.30167	−	1.30167i	−0.927265	−	0.374406i	$-0.877847\pi$
$307$	−6.21960e13	−	6.21960e13i	−1.30167	−	1.30167i	−0.374406	−	0.927265i	$-0.622153\pi$
$308$		0			0
$309$	−3.09308e13	+	3.09308e13i	−0.624625	+	0.624625i
$310$		0			0
$311$		−	6.41499e13i		−	1.25030i	−0.780505	−	0.625150i	$-0.785038\pi$
$311$		−	6.41499e13i		−	1.25030i	0.780505	−	0.625150i	$-0.214962\pi$
$312$		0			0
$313$		−	1.54374e13i		−	0.290456i	−0.989398	−	0.145228i	$-0.953608\pi$
$313$		−	1.54374e13i		−	0.290456i	0.989398	−	0.145228i	$-0.0463916\pi$
$314$		0			0
$315$	1.21766e12	−	1.21766e12i	0.0221217	−	0.0221217i
$316$		0			0
$317$	−5.18012e13	−	5.18012e13i	−0.908895	−	0.908895i	0.0872885	−	0.996183i	$-0.472180\pi$
$317$	−5.18012e13	−	5.18012e13i	−0.908895	−	0.908895i	−0.996183	+	0.0872885i	$0.972180\pi$
$318$		0			0
$319$	−5.57447e13			−0.944832
$320$		0			0
$321$	−4.24542e13			−0.695254
$322$		0			0
$323$	1.11083e13	+	1.11083e13i	0.175807	+	0.175807i
$324$		0			0
$325$	9.41851e13	−	9.41851e13i	1.44087	−	1.44087i
$326$		0			0
$327$		−	4.74281e13i		−	0.701493i
$328$		0			0
$329$		−	4.70682e13i		−	0.673210i
$330$		0			0
$331$	−3.29569e12	+	3.29569e12i	−0.0455924	+	0.0455924i	−0.729535	−	0.683943i	$-0.760264\pi$
$331$	−3.29569e12	+	3.29569e12i	−0.0455924	+	0.0455924i	0.683943	+	0.729535i	$0.260264\pi$
$332$		0			0
$333$	−1.91920e11	−	1.91920e11i	−0.00256849	−	0.00256849i
$334$		0			0
$335$	1.99422e14			2.58241
$336$		0			0
$337$	−3.67883e12			−0.0461048			−0.0230524	−	0.999734i	$-0.507338\pi$
$337$	−3.67883e12			−0.0461048			−0.0230524	+	0.999734i	$0.507338\pi$
$338$		0			0
$339$	−2.27324e13	−	2.27324e13i	−0.275770	−	0.275770i
$340$		0			0
$341$	4.06312e13	−	4.06312e13i	0.477212	−	0.477212i
$342$		0			0
$343$		−	6.05931e13i		−	0.689137i
$344$		0			0
$345$		−	8.34170e13i		−	0.918860i
$346$		0			0
$347$	6.36528e11	−	6.36528e11i	0.00679212	−	0.00679212i	−0.703703	−	0.710495i	$-0.748471\pi$
$347$	6.36528e11	−	6.36528e11i	0.00679212	−	0.00679212i	0.710495	+	0.703703i	$0.248471\pi$
$348$		0			0
$349$	−3.62572e13	−	3.62572e13i	−0.374847	−	0.374847i	0.494392	−	0.869239i	$-0.335391\pi$
$349$	−3.62572e13	−	3.62572e13i	−0.374847	−	0.374847i	−0.869239	+	0.494392i	$0.835391\pi$
$350$		0			0
$351$	7.16329e13			0.717667
$352$		0			0
$353$	−1.11210e14			−1.07990			−0.539949	−	0.841698i	$-0.681557\pi$
$353$	−1.11210e14			−1.07990			−0.539949	+	0.841698i	$0.681557\pi$
$354$		0			0
$355$	1.36156e13	+	1.36156e13i	0.128168	+	0.128168i
$356$		0			0
$357$	−2.77973e13	+	2.77973e13i	−0.253704	+	0.253704i
$358$		0			0
$359$			4.35968e13i			0.385865i	0.981212	+	0.192933i	$0.0617999\pi$
$359$			4.35968e13i			0.385865i	−0.981212	+	0.192933i	$0.938200\pi$
$360$		0			0
$361$		−	1.09166e14i		−	0.937123i
$362$		0			0
$363$	4.97248e13	−	4.97248e13i	0.414083	−	0.414083i
$364$		0			0
$365$	2.16665e14	+	2.16665e14i	1.75057	+	1.75057i
$366$		0			0
$367$	−2.04459e14			−1.60304			−0.801519	−	0.597970i	$-0.795974\pi$
$367$	−2.04459e14			−1.60304			−0.801519	+	0.597970i	$0.795974\pi$
$368$		0			0
$369$	−7.02024e12			−0.0534204
$370$		0			0
$371$	−3.86492e13	−	3.86492e13i	−0.285485	−	0.285485i
$372$		0			0
$373$	8.29755e12	−	8.29755e12i	0.0595047	−	0.0595047i	−0.676728	−	0.736233i	$-0.736603\pi$
$373$	8.29755e12	−	8.29755e12i	0.0595047	−	0.0595047i	0.736233	+	0.676728i	$0.236603\pi$
$374$		0			0
$375$			5.26083e14i			3.66338i
$376$		0			0
$377$			7.77282e13i			0.525656i
$378$		0			0
$379$	−1.44461e13	+	1.44461e13i	−0.0948932	+	0.0948932i	−0.752960	−	0.658067i	$-0.771375\pi$
$379$	−1.44461e13	+	1.44461e13i	−0.0948932	+	0.0948932i	0.658067	+	0.752960i	$0.271375\pi$
$380$		0			0
$381$	−2.71622e13	−	2.71622e13i	−0.173331	−	0.173331i
$382$		0			0
$383$	−2.01776e14			−1.25105			−0.625526	−	0.780203i	$-0.715116\pi$
$383$	−2.01776e14			−1.25105			−0.625526	+	0.780203i	$0.715116\pi$
$384$		0			0
$385$	−1.53216e14			−0.923143
$386$		0			0
$387$	7.61354e12	+	7.61354e12i	0.0445837	+	0.0445837i
$388$		0			0
$389$	1.86952e14	−	1.86952e14i	1.06416	−	1.06416i	0.0663626	−	0.997796i	$-0.478861\pi$
$389$	1.86952e14	−	1.86952e14i	1.06416	−	1.06416i	0.997796	−	0.0663626i	$-0.0211394\pi$
$390$		0			0
$391$		−	8.52469e13i		−	0.471744i
$392$		0			0
$393$		−	4.40957e13i		−	0.237267i
$394$		0			0
$395$	3.74670e14	−	3.74670e14i	1.96049	−	1.96049i
$396$		0			0
$397$	1.42061e14	+	1.42061e14i	0.722980	+	0.722980i	0.969211	−	0.246231i	$-0.0791923\pi$
$397$	1.42061e14	+	1.42061e14i	0.722980	+	0.722980i	−0.246231	+	0.969211i	$0.579192\pi$
$398$		0			0
$399$	−1.83288e13			−0.0907367
$400$		0			0
$401$	−8.14768e13			−0.392410			−0.196205	−	0.980563i	$-0.562862\pi$
$401$	−8.14768e13			−0.392410			−0.196205	+	0.980563i	$0.562862\pi$
$402$		0			0
$403$	−5.66546e13	−	5.66546e13i	−0.265496	−	0.265496i
$404$		0			0
$405$	−2.92410e14	+	2.92410e14i	−1.33349	+	1.33349i
$406$		0			0
$407$			2.41489e13i			0.107183i
$408$		0			0
$409$		−	1.78053e13i		−	0.0769254i	−0.999260	−	0.0384627i	$-0.987754\pi$
$409$		−	1.78053e13i		−	0.0769254i	0.999260	−	0.0384627i	$-0.0122461\pi$
$410$		0			0
$411$	−7.68971e13	+	7.68971e13i	−0.323430	+	0.323430i
$412$		0			0
$413$	−9.13984e12	−	9.13984e12i	−0.0374295	−	0.0374295i
$414$		0			0
$415$	−8.01692e13			−0.319700
$416$		0			0
$417$	−1.30966e13			−0.0508640
$418$		0			0
$419$	1.09139e14	+	1.09139e14i	0.412860	+	0.412860i	0.882734	−	0.469874i	$-0.155701\pi$
$419$	1.09139e14	+	1.09139e14i	0.412860	+	0.412860i	−0.469874	+	0.882734i	$0.655701\pi$
$420$		0			0
$421$	1.20556e14	−	1.20556e14i	0.444259	−	0.444259i	−0.449182	−	0.893440i	$-0.648284\pi$
$421$	1.20556e14	−	1.20556e14i	0.444259	−	0.444259i	0.893440	+	0.449182i	$0.148284\pi$
$422$		0			0
$423$		−	2.17223e13i		−	0.0779890i
$424$		0			0
$425$			8.21053e14i			2.87231i
$426$		0			0
$427$	−3.80719e13	+	3.80719e13i	−0.129793	+	0.129793i
$428$		0			0
$429$	−1.85169e14	−	1.85169e14i	−0.615251	−	0.615251i
$430$		0			0
$431$	4.25147e14			1.37694			0.688469	−	0.725265i	$-0.258283\pi$
$431$	4.25147e14			1.37694			0.688469	+	0.725265i	$0.258283\pi$
$432$		0			0
$433$	1.11943e14			0.353439			0.176719	−	0.984261i	$-0.443452\pi$
$433$	1.11943e14			0.353439			0.176719	+	0.984261i	$0.443452\pi$
$434$		0			0
$435$	−3.31523e14	−	3.31523e14i	−1.02052	−	1.02052i
$436$		0			0
$437$	2.81048e13	−	2.81048e13i	0.0843593	−	0.0843593i
$438$		0			0
$439$			1.95428e14i			0.572048i	0.958222	+	0.286024i	$0.0923337\pi$
$439$			1.95428e14i			0.572048i	−0.958222	+	0.286024i	$0.907666\pi$
$440$		0			0
$441$		−	1.29554e13i		−	0.0369862i
$442$		0			0
$443$	−2.58061e14	+	2.58061e14i	−0.718624	+	0.718624i	−0.968323	−	0.249699i	$-0.919668\pi$
$443$	−2.58061e14	+	2.58061e14i	−0.718624	+	0.718624i	0.249699	+	0.968323i	$0.419668\pi$
$444$		0			0
$445$	1.43990e14	+	1.43990e14i	0.391158	+	0.391158i
$446$		0			0
$447$	−3.41423e14			−0.904902
$448$		0			0
$449$	−2.05485e14			−0.531404			−0.265702	−	0.964055i	$-0.585604\pi$
$449$	−2.05485e14			−0.531404			−0.265702	+	0.964055i	$0.585604\pi$
$450$		0			0
$451$	4.41671e14	+	4.41671e14i	1.11462	+	1.11462i
$452$		0			0
$453$	−2.69600e14	+	2.69600e14i	−0.664018	+	0.664018i
$454$		0			0
$455$			2.13638e14i			0.513589i
$456$		0			0
$457$			1.38601e14i			0.325259i	0.986687	+	0.162629i	$0.0519975\pi$
$457$			1.38601e14i			0.325259i	−0.986687	+	0.162629i	$0.948003\pi$
$458$		0			0
$459$	−3.12227e14	+	3.12227e14i	−0.715321	+	0.715321i
$460$		0			0
$461$	1.43453e14	+	1.43453e14i	0.320888	+	0.320888i	0.849108	−	0.528219i	$-0.177140\pi$
$461$	1.43453e14	+	1.43453e14i	0.320888	+	0.320888i	−0.528219	+	0.849108i	$0.677140\pi$
$462$		0			0
$463$	4.65737e14			1.01729			0.508646	−	0.860976i	$-0.330146\pi$
$463$	4.65737e14			1.01729			0.508646	+	0.860976i	$0.330146\pi$
$464$		0			0
$465$	4.83281e14			1.03088
$466$		0			0
$467$	−5.02083e13	−	5.02083e13i	−0.104600	−	0.104600i	0.652870	−	0.757470i	$-0.273565\pi$
$467$	−5.02083e13	−	5.02083e13i	−0.104600	−	0.104600i	−0.757470	+	0.652870i	$0.773565\pi$
$468$		0			0
$469$	−1.68132e14	+	1.68132e14i	−0.342137	+	0.342137i
$470$		0			0
$471$		−	3.57447e14i		−	0.710553i
$472$		0			0
$473$		−	9.57995e14i		−	1.86049i
$474$		0			0
$475$	−2.70690e14	+	2.70690e14i	−0.513639	+	0.513639i
$476$		0			0
$477$	−1.78368e13	−	1.78368e13i	−0.0330725	−	0.0330725i
$478$		0			0
$479$	−2.16318e13			−0.0391966			−0.0195983	−	0.999808i	$-0.506239\pi$
$479$	−2.16318e13			−0.0391966			−0.0195983	+	0.999808i	$0.506239\pi$
$480$		0			0
$481$	3.36723e13			0.0596313
$482$		0			0
$483$	7.03288e13	+	7.03288e13i	0.121737	+	0.121737i
$484$		0			0
$485$	9.33078e14	−	9.33078e14i	1.57884	−	1.57884i
$486$		0			0
$487$		−	5.85834e14i		−	0.969092i	−0.874766	−	0.484546i	$-0.838985\pi$
$487$		−	5.85834e14i		−	0.969092i	0.874766	−	0.484546i	$-0.161015\pi$
$488$		0			0
$489$		−	1.12299e15i		−	1.81626i
$490$		0			0
$491$	6.67345e14	−	6.67345e14i	1.05536	−	1.05536i	0.0569895	−	0.998375i	$-0.481850\pi$
$491$	6.67345e14	−	6.67345e14i	1.05536	−	1.05536i	0.998375	−	0.0569895i	$-0.0181501\pi$
$492$		0			0
$493$	−3.38795e14	−	3.38795e14i	−0.523937	−	0.523937i
$494$		0			0
$495$	−7.07099e13			−0.106943
$496$		0			0
$497$	−2.29585e13			−0.0339612
$498$		0			0
$499$	5.33147e14	+	5.33147e14i	0.771426	+	0.771426i	0.978356	−	0.206930i	$-0.0663473\pi$
$499$	5.33147e14	+	5.33147e14i	0.771426	+	0.771426i	−0.206930	+	0.978356i	$0.566347\pi$
$500$		0			0
$501$	−1.72546e14	+	1.72546e14i	−0.244229	+	0.244229i
$502$		0			0
$503$		−	1.51395e14i		−	0.209646i	−0.994491	−	0.104823i	$-0.966572\pi$
$503$		−	1.51395e14i		−	0.209646i	0.994491	−	0.104823i	$-0.0334277\pi$
$504$		0			0
$505$		−	1.31014e14i		−	0.177506i
$506$		0			0
$507$	2.63626e14	−	2.63626e14i	0.349498	−	0.349498i
$508$		0			0
$509$	−1.31667e14	−	1.31667e14i	−0.170816	−	0.170816i	0.616522	−	0.787338i	$-0.288541\pi$
$509$	−1.31667e14	−	1.31667e14i	−0.170816	−	0.170816i	−0.787338	+	0.616522i	$0.788541\pi$
$510$		0			0
$511$	−3.65341e14			−0.463856
$512$		0			0
$513$	−2.05875e14			−0.255833
$514$		0			0
$515$	−1.03616e15	−	1.03616e15i	−1.26033	−	1.26033i
$516$		0			0
$517$	−1.36663e15	+	1.36663e15i	−1.62725	+	1.62725i
$518$		0			0
$519$		−	1.09606e15i		−	1.27766i
$520$		0			0
$521$			6.24091e14i			0.712263i	0.934436	+	0.356131i	$0.115904\pi$
$521$			6.24091e14i			0.712263i	−0.934436	+	0.356131i	$0.884096\pi$
$522$		0			0
$523$	−6.36730e14	+	6.36730e14i	−0.711535	+	0.711535i	−0.966856	−	0.255321i	$-0.917819\pi$
$523$	−6.36730e14	+	6.36730e14i	−0.711535	+	0.711535i	0.255321	+	0.966856i	$0.417819\pi$
$524$		0			0
$525$	−6.77369e14	−	6.77369e14i	−0.741223	−	0.741223i
$526$		0			0
$527$	4.93883e14			0.529256
$528$		0			0
$529$	7.37130e14			0.773638
$530$		0			0
$531$	−4.21809e12	−	4.21809e12i	−0.00433607	−	0.00433607i
$532$		0			0
$533$	6.15848e14	−	6.15848e14i	0.620118	−	0.620118i
$534$		0			0
$535$		−	1.42218e15i		−	1.40285i
$536$		0			0
$537$			9.08877e14i			0.878308i
$538$		0			0
$539$	−8.15077e14	+	8.15077e14i	−0.771721	+	0.771721i
$540$		0			0
$541$	−1.39317e15	−	1.39317e15i	−1.29247	−	1.29247i	−0.933257	−	0.359209i	$-0.883046\pi$
$541$	−1.39317e15	−	1.39317e15i	−1.29247	−	1.29247i	−0.359209	−	0.933257i	$-0.616954\pi$
$542$		0			0
$543$	7.39475e14			0.672240
$544$		0			0
$545$	1.58881e15			1.41544
$546$		0			0
$547$	−1.56662e12	−	1.56662e12i	−0.00136783	−	0.00136783i	0.706423	−	0.707790i	$-0.250308\pi$
$547$	−1.56662e12	−	1.56662e12i	−0.00136783	−	0.00136783i	−0.707790	+	0.706423i	$0.750308\pi$
$548$		0			0
$549$	−1.75704e13	+	1.75704e13i	−0.0150361	+	0.0150361i
$550$		0			0
$551$		−	2.23393e14i		−	0.187385i
$552$		0			0
$553$			6.31768e14i			0.519480i
$554$		0			0
$555$	−1.43617e14	+	1.43617e14i	−0.115770	+	0.115770i
$556$		0			0
$557$	6.08001e14	+	6.08001e14i	0.480508	+	0.480508i	0.905294	−	0.424786i	$-0.139651\pi$
$557$	6.08001e14	+	6.08001e14i	0.480508	+	0.480508i	−0.424786	+	0.905294i	$0.639651\pi$
$558$		0			0
$559$	−1.33579e15			−1.03508
$560$		0			0
$561$	1.61420e15			1.22648
$562$		0			0
$563$	1.87402e15	+	1.87402e15i	1.39630	+	1.39630i	0.810340	+	0.585960i	$0.199283\pi$
$563$	1.87402e15	+	1.87402e15i	1.39630	+	1.39630i	0.585960	+	0.810340i	$0.300717\pi$
$564$		0			0
$565$	7.61518e14	−	7.61518e14i	0.556434	−	0.556434i
$566$		0			0
$567$		−	4.93061e14i		−	0.353341i
$568$		0			0
$569$			2.24491e15i			1.57791i	0.614453	+	0.788953i	$0.289377\pi$
$569$			2.24491e15i			1.57791i	−0.614453	+	0.788953i	$0.710623\pi$
$570$		0			0
$571$	1.65127e15	−	1.65127e15i	1.13846	−	1.13846i	0.149739	−	0.988726i	$-0.452157\pi$
$571$	1.65127e15	−	1.65127e15i	1.13846	−	1.13846i	0.988726	−	0.149739i	$-0.0478434\pi$
$572$		0			0
$573$	−2.87441e14	−	2.87441e14i	−0.194401	−	0.194401i
$574$		0			0
$575$	2.07731e15			1.37825
$576$		0			0
$577$	−1.13891e15			−0.741349			−0.370674	−	0.928763i	$-0.620873\pi$
$577$	−1.13891e15			−0.741349			−0.370674	+	0.928763i	$0.620873\pi$
$578$		0			0
$579$	−7.73463e14	−	7.73463e14i	−0.493978	−	0.493978i
$580$		0			0
$581$	6.75906e13	−	6.75906e13i	0.0423562	−	0.0423562i
$582$		0			0
$583$			2.24437e15i			1.38012i
$584$		0			0
$585$			9.85952e13i			0.0594975i
$586$		0			0
$587$	−1.23197e15	+	1.23197e15i	−0.729609	+	0.729609i	−0.970542	−	0.240933i	$-0.922547\pi$
$587$	−1.23197e15	+	1.23197e15i	−0.729609	+	0.729609i	0.240933	+	0.970542i	$0.422547\pi$
$588$		0			0
$589$	1.62827e14	+	1.62827e14i	0.0946437	+	0.0946437i
$590$		0			0
$591$	−1.69462e15			−0.966808
$592$		0			0
$593$	2.95839e14			0.165674			0.0828371	−	0.996563i	$-0.473602\pi$
$593$	2.95839e14			0.165674			0.0828371	+	0.996563i	$0.473602\pi$
$594$		0			0
$595$	−9.31187e14	−	9.31187e14i	−0.511910	−	0.511910i
$596$		0			0
$597$	−1.42749e15	+	1.42749e15i	−0.770398	+	0.770398i
$598$		0			0
$599$			8.24594e14i			0.436911i	0.975847	+	0.218455i	$0.0701018\pi$
$599$			8.24594e14i			0.436911i	−0.975847	+	0.218455i	$0.929898\pi$
$600$		0			0
$601$		−	2.17617e15i		−	1.13210i	−0.824372	−	0.566048i	$-0.808472\pi$
$601$		−	2.17617e15i		−	1.13210i	0.824372	−	0.566048i	$-0.191528\pi$
$602$		0			0
$603$	−7.75940e13	+	7.75940e13i	−0.0396354	+	0.0396354i
$604$		0			0
$605$	1.66574e15	+	1.66574e15i	0.835514	+	0.835514i
$606$		0			0
$607$	−1.27606e15			−0.628540			−0.314270	−	0.949334i	$-0.601760\pi$
$607$	−1.27606e15			−0.628540			−0.314270	+	0.949334i	$0.601760\pi$
$608$		0			0
$609$	5.59013e14			0.270412
$610$		0			0
$611$	1.90558e15	+	1.90558e15i	0.905317	+	0.905317i
$612$		0			0
$613$	−2.29249e15	+	2.29249e15i	−1.06973	+	1.06973i	−0.0723525	+	0.997379i	$0.523051\pi$
$613$	−2.29249e15	+	2.29249e15i	−1.06973	+	1.06973i	−0.997379	+	0.0723525i	$0.976949\pi$
$614$		0			0
$615$			5.25337e15i			2.40783i
$616$		0			0
$617$		−	3.32955e15i		−	1.49905i	−0.661974	−	0.749527i	$-0.730281\pi$
$617$		−	3.32955e15i		−	1.49905i	0.661974	−	0.749527i	$-0.269719\pi$
$618$		0			0
$619$	−5.88044e14	+	5.88044e14i	−0.260083	+	0.260083i	−0.825088	−	0.565005i	$-0.808874\pi$
$619$	−5.88044e14	+	5.88044e14i	−0.260083	+	0.260083i	0.565005	+	0.825088i	$0.308874\pi$
$620$		0			0
$621$	7.89954e14	+	7.89954e14i	0.343240	+	0.343240i
$622$		0			0
$623$	−2.42796e14			−0.103647
$624$		0			0
$625$	−1.07167e16			−4.49493
$626$		0			0
$627$	5.32179e14	+	5.32179e14i	0.219324	+	0.219324i
$628$		0			0
$629$	−1.46768e14	+	1.46768e14i	−0.0594364	+	0.0594364i
$630$		0			0
$631$		−	2.51383e15i		−	1.00040i	−0.865909	−	0.500201i	$-0.833259\pi$
$631$		−	2.51383e15i		−	1.00040i	0.865909	−	0.500201i	$-0.166741\pi$
$632$		0			0
$633$			1.23329e15i			0.482332i
$634$		0			0
$635$	9.09912e14	−	9.09912e14i	0.349739	−	0.349739i
$636$		0			0
$637$	1.13651e15	+	1.13651e15i	0.429346	+	0.429346i
$638$		0			0
$639$	−1.05955e13			−0.00393429
$640$		0			0
$641$	3.20773e15			1.17079			0.585394	−	0.810749i	$-0.300940\pi$
$641$	3.20773e15			1.17079			0.585394	+	0.810749i	$0.300940\pi$
$642$		0			0
$643$	−1.86386e15	−	1.86386e15i	−0.668733	−	0.668733i	0.288689	−	0.957423i	$-0.406781\pi$
$643$	−1.86386e15	−	1.86386e15i	−0.668733	−	0.668733i	−0.957423	+	0.288689i	$0.906781\pi$
$644$		0			0
$645$	5.69735e15	−	5.69735e15i	2.00953	−	2.00953i
$646$		0			0
$647$			1.87463e15i			0.650044i	0.945707	+	0.325022i	$0.105372\pi$
$647$			1.87463e15i			0.650044i	−0.945707	+	0.325022i	$0.894628\pi$
$648$		0			0
$649$			5.30754e14i			0.180945i
$650$		0			0
$651$	−4.07454e14	+	4.07454e14i	−0.136579	+	0.136579i
$652$		0			0
$653$	8.43485e14	+	8.43485e14i	0.278006	+	0.278006i	0.832313	−	0.554306i	$-0.187016\pi$
$653$	8.43485e14	+	8.43485e14i	0.278006	+	0.278006i	−0.554306	+	0.832313i	$0.687016\pi$
$654$		0			0
$655$	1.47717e15			0.478745
$656$		0			0
$657$	−1.68607e14			−0.0537361
$658$		0			0
$659$	2.31013e15	+	2.31013e15i	0.724046	+	0.724046i	0.969427	−	0.245381i	$-0.0789129\pi$
$659$	2.31013e15	+	2.31013e15i	0.724046	+	0.724046i	−0.245381	+	0.969427i	$0.578913\pi$
$660$		0			0
$661$	1.26148e15	−	1.26148e15i	0.388843	−	0.388843i	−0.485432	−	0.874274i	$-0.661338\pi$
$661$	1.26148e15	−	1.26148e15i	0.388843	−	0.388843i	0.874274	+	0.485432i	$0.161338\pi$
$662$		0			0
$663$		−	2.25077e15i		−	0.682350i
$664$		0			0
$665$		−	6.14001e14i		−	0.183084i
$666$		0			0
$667$	−8.57173e14	+	8.57173e14i	−0.251406	+	0.251406i
$668$		0			0
$669$	3.61167e15	+	3.61167e15i	1.04199	+	1.04199i
$670$		0			0
$671$	2.21085e15			0.627459
$672$		0			0
$673$	4.56547e15			1.27468			0.637342	−	0.770581i	$-0.280034\pi$
$673$	4.56547e15			1.27468			0.637342	+	0.770581i	$0.280034\pi$
$674$		0			0
$675$	−7.60842e15	−	7.60842e15i	−2.08989	−	2.08989i
$676$		0			0
$677$	−3.62225e15	+	3.62225e15i	−0.978905	+	0.978905i	−0.999782	−	0.0208774i	$-0.993354\pi$
$677$	−3.62225e15	+	3.62225e15i	−0.978905	+	0.978905i	0.0208774	+	0.999782i	$0.493354\pi$
$678$		0			0
$679$			1.57335e15i			0.418353i
$680$		0			0
$681$			1.31789e15i			0.344803i
$682$		0			0
$683$	3.69656e15	−	3.69656e15i	0.951664	−	0.951664i	−0.0472205	−	0.998884i	$-0.515036\pi$
$683$	3.69656e15	−	3.69656e15i	0.951664	−	0.951664i	0.998884	+	0.0472205i	$0.0150363\pi$
$684$		0			0
$685$	−2.57600e15	−	2.57600e15i	−0.652600	−	0.652600i
$686$		0			0
$687$	1.39028e15			0.346609
$688$		0			0
$689$	3.12946e15			0.767828
$690$		0			0
$691$	−8.90107e13	−	8.90107e13i	−0.0214938	−	0.0214938i	0.696278	−	0.717772i	$-0.254838\pi$
$691$	−8.90107e13	−	8.90107e13i	−0.0214938	−	0.0214938i	−0.717772	+	0.696278i	$0.754838\pi$
$692$		0			0
$693$	5.96155e13	−	5.96155e13i	0.0141686	−	0.0141686i
$694$		0			0
$695$		−	4.38727e14i		−	0.102631i
$696$		0			0
$697$			5.36862e15i			1.23618i
$698$		0			0
$699$	−8.73729e14	+	8.73729e14i	−0.198040	+	0.198040i
$700$		0			0
$701$	−3.34215e14	−	3.34215e14i	−0.0745721	−	0.0745721i	0.668837	−	0.743409i	$-0.266792\pi$
$701$	−3.34215e14	−	3.34215e14i	−0.0745721	−	0.0745721i	−0.743409	+	0.668837i	$0.766792\pi$
$702$		0			0
$703$	−9.67749e13			−0.0212573
$704$		0			0
$705$	−1.62552e16			−3.51521
$706$		0			0
$707$	1.10457e14	+	1.10457e14i	0.0235173	+	0.0235173i
$708$		0			0
$709$	−1.45448e15	+	1.45448e15i	−0.304897	+	0.304897i	−0.842926	−	0.538029i	$-0.819169\pi$
$709$	−1.45448e15	+	1.45448e15i	−0.304897	+	0.304897i	0.538029	+	0.842926i	$0.319169\pi$
$710$		0			0
$711$			2.91565e14i			0.0601800i
$712$		0			0
$713$		−	1.24955e15i		−	0.253958i
$714$		0			0
$715$	6.20301e15	−	6.20301e15i	1.24142	−	1.24142i
$716$		0			0
$717$	−4.56287e15	−	4.56287e15i	−0.899256	−	0.899256i
$718$		0			0
$719$	−5.51626e15			−1.07062			−0.535311	−	0.844655i	$-0.679805\pi$
$719$	−5.51626e15			−1.07062			−0.535311	+	0.844655i	$0.679805\pi$
$720$		0			0
$721$	1.74717e15			0.333957
$722$		0			0
$723$	4.22709e15	+	4.22709e15i	0.795758	+	0.795758i
$724$		0			0
$725$	8.25583e15	−	8.25583e15i	1.53074	−	1.53074i
$726$		0			0
$727$			5.66188e15i			1.03400i	0.855985	+	0.517001i	$0.172952\pi$
$727$			5.66188e15i			1.03400i	−0.855985	+	0.517001i	$0.827048\pi$
$728$		0			0
$729$		−	5.77641e15i		−	1.03910i
$730$		0			0
$731$	5.82233e15	−	5.82233e15i	1.03170	−	1.03170i
$732$		0			0
$733$	2.12425e15	+	2.12425e15i	0.370794	+	0.370794i	0.867766	−	0.496972i	$-0.165555\pi$
$733$	2.12425e15	+	2.12425e15i	0.370794	+	0.370794i	−0.496972	+	0.867766i	$0.665555\pi$
$734$		0			0
$735$	−9.69479e15			−1.66709
$736$		0			0
$737$	9.76349e15			1.65399
$738$		0			0
$739$	−5.43075e14	−	5.43075e14i	−0.0906391	−	0.0906391i	0.660333	−	0.750973i	$-0.270415\pi$
$739$	−5.43075e14	−	5.43075e14i	−0.0906391	−	0.0906391i	−0.750973	+	0.660333i	$0.770415\pi$
$740$		0			0
$741$	7.42050e14	−	7.42050e14i	0.122021	−	0.122021i
$742$		0			0
$743$		−	8.27772e15i		−	1.34113i	−0.741849	−	0.670567i	$-0.766051\pi$
$743$		−	8.27772e15i		−	1.34113i	0.741849	−	0.670567i	$-0.233949\pi$
$744$		0			0
$745$		−	1.14374e16i		−	1.82586i
$746$		0			0
$747$	3.11935e13	−	3.11935e13i	0.00490682	−	0.00490682i
$748$		0			0
$749$	1.19904e15	+	1.19904e15i	0.185859	+	0.185859i
$750$		0			0
$751$	4.14454e15			0.633077			0.316538	−	0.948580i	$-0.397479\pi$
$751$	4.14454e15			0.633077			0.316538	+	0.948580i	$0.397479\pi$
$752$		0			0
$753$	−9.01215e15			−1.35661
$754$		0			0
$755$	−9.03139e15	−	9.03139e15i	−1.33982	−	1.33982i
$756$		0			0
$757$	2.94822e15	−	2.94822e15i	0.431055	−	0.431055i	−0.457932	−	0.888987i	$-0.651410\pi$
$757$	2.94822e15	−	2.94822e15i	0.431055	−	0.431055i	0.888987	+	0.457932i	$0.151410\pi$
$758$		0			0
$759$		−	4.08401e15i		−	0.588515i
$760$		0			0
$761$			9.46505e14i			0.134433i	0.997738	+	0.0672167i	$0.0214119\pi$
$761$			9.46505e14i			0.134433i	−0.997738	+	0.0672167i	$0.978588\pi$
$762$		0			0
$763$	−1.33952e15	+	1.33952e15i	−0.187527	+	0.187527i
$764$		0			0
$765$	−4.29748e14	−	4.29748e14i	−0.0593030	−	0.0593030i
$766$		0			0
$767$	7.40062e14			0.100669
$768$		0			0
$769$	2.12353e15			0.284750			0.142375	−	0.989813i	$-0.454526\pi$
$769$	2.12353e15			0.284750			0.142375	+	0.989813i	$0.454526\pi$
$770$		0			0
$771$	4.72385e15	+	4.72385e15i	0.624449	+	0.624449i
$772$		0			0
$773$	−6.39086e15	+	6.39086e15i	−0.832860	+	0.832860i	−0.987907	−	0.155047i	$-0.950447\pi$
$773$	−6.39086e15	+	6.39086e15i	−0.832860	+	0.832860i	0.155047	+	0.987907i	$0.450447\pi$
$774$		0			0
$775$			1.20350e16i			1.54628i
$776$		0			0
$777$		−	2.42167e14i		−	0.0306761i
$778$		0			0
$779$	−1.76996e15	+	1.76996e15i	−0.221059	+	0.221059i
$780$		0			0
$781$	6.66604e14	+	6.66604e14i	0.0820894	+	0.0820894i
$782$		0			0
$783$	6.27900e15			0.762432
$784$		0			0
$785$	1.19742e16			1.43372
$786$		0			0
$787$	4.46749e15	+	4.46749e15i	0.527476	+	0.527476i	0.919819	−	0.392343i	$-0.128335\pi$
$787$	4.46749e15	+	4.46749e15i	0.527476	+	0.527476i	−0.392343	+	0.919819i	$0.628335\pi$
$788$		0			0
$789$	−1.08805e15	+	1.08805e15i	−0.126685	+	0.126685i
$790$		0			0
$791$			1.28407e15i			0.147441i
$792$		0			0
$793$		−	3.08272e15i		−	0.349086i
$794$		0			0
$795$	−1.33476e16	+	1.33476e16i	−1.49068	+	1.49068i
$796$		0			0
$797$	−5.72078e15	−	5.72078e15i	−0.630136	−	0.630136i	0.317966	−	0.948102i	$-0.397000\pi$
$797$	−5.72078e15	−	5.72078e15i	−0.630136	−	0.630136i	−0.948102	+	0.317966i	$0.897000\pi$
$798$		0			0
$799$	−1.66118e16			−1.80471
$800$		0			0
$801$	−1.12052e14			−0.0120071
$802$		0			0
$803$	1.06077e16	+	1.06077e16i	1.12121	+	1.12121i
$804$		0			0
$805$	−2.35596e15	+	2.35596e15i	−0.245635	+	0.245635i
$806$		0			0
$807$		−	5.48424e15i		−	0.564043i
$808$		0			0
$809$			1.21732e16i			1.23506i	0.786547	+	0.617530i	$0.211867\pi$
$809$			1.21732e16i			1.23506i	−0.786547	+	0.617530i	$0.788133\pi$
$810$		0			0
$811$	−8.59740e15	+	8.59740e15i	−0.860503	+	0.860503i	−0.991396	−	0.130894i	$-0.958215\pi$
$811$	−8.59740e15	+	8.59740e15i	−0.860503	+	0.860503i	0.130894	+	0.991396i	$0.458215\pi$
$812$		0			0
$813$	−7.47564e15	−	7.47564e15i	−0.738160	−	0.738160i
$814$		0			0
$815$	3.76195e16			3.66476
$816$		0			0
$817$	3.83910e15			0.368984
$818$		0			0
$819$	−8.31255e13	−	8.31255e13i	−0.00788266	−	0.00788266i
$820$		0			0
$821$	−8.03811e15	+	8.03811e15i	−0.752084	+	0.752084i	−0.974868	−	0.222784i	$-0.928486\pi$
$821$	−8.03811e15	+	8.03811e15i	−0.752084	+	0.752084i	0.222784	+	0.974868i	$0.428486\pi$
$822$		0			0
$823$		−	1.13075e16i		−	1.04392i	−0.852969	−	0.521961i	$-0.825200\pi$
$823$		−	1.13075e16i		−	1.04392i	0.852969	−	0.521961i	$-0.174800\pi$
$824$		0			0
$825$			3.93350e16i			3.58330i
$826$		0			0
$827$	−1.51446e16	+	1.51446e16i	−1.36137	+	1.36137i	−0.489205	+	0.872169i	$0.662713\pi$
$827$	−1.51446e16	+	1.51446e16i	−1.36137	+	1.36137i	−0.872169	+	0.489205i	$0.837287\pi$
$828$		0			0
$829$	7.61387e15	+	7.61387e15i	0.675392	+	0.675392i	0.958954	−	0.283562i	$-0.0915162\pi$
$829$	7.61387e15	+	7.61387e15i	0.675392	+	0.675392i	−0.283562	+	0.958954i	$0.591516\pi$
$830$		0			0
$831$	3.43353e15			0.300562
$832$		0			0
$833$	−9.90746e15			−0.855884
$834$		0			0
$835$	−5.78015e15	−	5.78015e15i	−0.492792	−	0.492792i
$836$		0			0
$837$	−4.57665e15	+	4.57665e15i	−0.385086	+	0.385086i
$838$		0			0
$839$		−	1.36580e16i		−	1.13422i	−0.823642	−	0.567109i	$-0.808062\pi$
$839$		−	1.36580e16i		−	1.13422i	0.823642	−	0.567109i	$-0.191938\pi$
$840$		0			0
$841$		−	5.38721e15i		−	0.441556i
$842$		0			0
$843$	1.29779e16	−	1.29779e16i	1.04991	−	1.04991i
$844$		0			0
$845$	8.83128e15	+	8.83128e15i	0.705199	+	0.705199i
$846$		0			0
$847$	−2.80877e15			−0.221390
$848$		0			0
$849$	1.26344e16			0.983023
$850$		0			0
$851$	3.71332e14	+	3.71332e14i	0.0285200	+	0.0285200i
$852$		0			0
$853$	−1.28698e16	+	1.28698e16i	−0.975782	+	0.975782i	−0.999714	−	0.0239316i	$-0.992382\pi$
$853$	−1.28698e16	+	1.28698e16i	−0.975782	+	0.975782i	0.0239316	+	0.999714i	$0.492382\pi$
$854$		0			0
$855$		−	2.83365e14i		−	0.0212096i
$856$		0			0
$857$		−	2.63583e16i		−	1.94770i	−0.227185	−	0.973852i	$-0.572952\pi$
$857$		−	2.63583e16i		−	1.94770i	0.227185	−	0.973852i	$-0.427048\pi$
$858$		0			0
$859$	−1.14396e16	+	1.14396e16i	−0.834544	+	0.834544i	−0.988135	−	0.153591i	$-0.950916\pi$
$859$	−1.14396e16	+	1.14396e16i	−0.834544	+	0.834544i	0.153591	+	0.988135i	$0.450916\pi$
$860$		0			0
$861$	−4.42911e15	−	4.42911e15i	−0.319006	−	0.319006i
$862$		0			0
$863$	−2.32764e15			−0.165522			−0.0827610	−	0.996569i	$-0.526374\pi$
$863$	−2.32764e15			−0.165522			−0.0827610	+	0.996569i	$0.526374\pi$
$864$		0			0
$865$	3.67172e16			2.57799
$866$		0			0
$867$	−1.68378e14	−	1.68378e14i	−0.0116729	−	0.0116729i
$868$		0			0
$869$	1.83435e16	−	1.83435e16i	1.25566	−	1.25566i
$870$		0			0
$871$		−	1.36138e16i		−	0.920196i
$872$		0			0
$873$			7.26113e14i			0.0484647i
$874$		0			0
$875$	1.48583e16	−	1.48583e16i	0.979318	−	0.979318i
$876$		0			0
$877$	−5.37423e15	−	5.37423e15i	−0.349799	−	0.349799i	0.510236	−	0.860035i	$-0.329558\pi$
$877$	−5.37423e15	−	5.37423e15i	−0.349799	−	0.349799i	−0.860035	+	0.510236i	$0.829558\pi$
$878$		0			0
$879$	−1.70561e16			−1.09633
$880$		0			0
$881$	−2.90790e16			−1.84591			−0.922957	−	0.384902i	$-0.874235\pi$
$881$	−2.90790e16			−1.84591			−0.922957	+	0.384902i	$0.874235\pi$
$882$		0			0
$883$	8.53623e15	+	8.53623e15i	0.535158	+	0.535158i	0.922103	−	0.386945i	$-0.126470\pi$
$883$	8.53623e15	+	8.53623e15i	0.535158	+	0.535158i	−0.386945	+	0.922103i	$0.626470\pi$
$884$		0			0
$885$	−3.15648e15	+	3.15648e15i	−0.195441	+	0.195441i
$886$		0			0
$887$			2.47422e16i			1.51307i	0.653955	+	0.756534i	$0.273109\pi$
$887$			2.47422e16i			1.51307i	−0.653955	+	0.756534i	$0.726891\pi$
$888$		0			0
$889$			1.53429e15i			0.0926719i
$890$		0			0
$891$	−1.43161e16	+	1.43161e16i	−0.854078	+	0.854078i
$892$		0			0
$893$	−5.47669e15	−	5.47669e15i	−0.322727	−	0.322727i
$894$		0			0
$895$	−3.04467e16			−1.77220
$896$		0			0
$897$	−5.69459e15			−0.327419
$898$		0			0
$899$	−4.96608e15	−	4.96608e15i	−0.282056	−	0.282056i
$900$		0			0
$901$	−1.36404e16	+	1.36404e16i	−0.765318	+	0.765318i
$902$		0			0
$903$			9.60686e15i			0.532474i
$904$		0			0
$905$			2.47719e16i			1.35641i
$906$		0			0
$907$	1.96865e16	−	1.96865e16i	1.06495	−	1.06495i	0.0672110	−	0.997739i	$-0.478590\pi$
$907$	1.96865e16	−	1.96865e16i	1.06495	−	1.06495i	0.997739	−	0.0672110i	$-0.0214101\pi$
$908$		0			0
$909$	5.09768e13	+	5.09768e13i	0.00272440	+	0.00272440i
$910$		0			0
$911$	1.02147e16			0.539354			0.269677	−	0.962951i	$-0.413083\pi$
$911$	1.02147e16			0.539354			0.269677	+	0.962951i	$0.413083\pi$
$912$		0			0
$913$	−3.92501e15			−0.204763
$914$		0			0
$915$	1.31483e16	+	1.31483e16i	0.677724	+	0.677724i
$916$		0			0
$917$	−1.24540e15	+	1.24540e15i	−0.0634276	+	0.0634276i
$918$		0			0
$919$		−	3.12625e16i		−	1.57322i	−0.617453	−	0.786608i	$-0.711835\pi$
$919$		−	3.12625e16i		−	1.57322i	0.617453	−	0.786608i	$-0.288165\pi$
$920$		0			0
$921$		−	3.62188e16i		−	1.80097i
$922$		0			0
$923$	9.29487e14	−	9.29487e14i	0.0456703	−	0.0456703i
$924$		0			0
$925$	−3.57647e15	−	3.57647e15i	−0.173650	−	0.173650i
$926$		0			0
$927$	8.06328e14			0.0386877
$928$		0			0
$929$	6.31662e15			0.299501			0.149751	−	0.988724i	$-0.452153\pi$
$929$	6.31662e15			0.299501			0.149751	+	0.988724i	$0.452153\pi$
$930$		0			0
$931$	−3.26636e15	−	3.26636e15i	−0.153053	−	0.153053i
$932$		0			0
$933$	1.86783e16	−	1.86783e16i	0.864947	−	0.864947i
$934$		0			0
$935$			5.40743e16i			2.47473i
$936$		0			0
$937$		−	2.25279e16i		−	1.01895i	−0.860486	−	0.509475i	$-0.829840\pi$
$937$		−	2.25279e16i		−	1.01895i	0.860486	−	0.509475i	$-0.170160\pi$
$938$		0			0
$939$	4.49487e15	−	4.49487e15i	0.200935	−	0.200935i
$940$		0			0
$941$	−6.01225e15	−	6.01225e15i	−0.265640	−	0.265640i	0.561700	−	0.827341i	$-0.310147\pi$
$941$	−6.01225e15	−	6.01225e15i	−0.265640	−	0.265640i	−0.827341	+	0.561700i	$0.810147\pi$
$942$		0			0
$943$	1.35829e16			0.593170
$944$		0			0
$945$	1.72580e16			0.744930
$946$		0			0
$947$	−1.01304e16	−	1.01304e16i	−0.432218	−	0.432218i	0.457164	−	0.889382i	$-0.348865\pi$
$947$	−1.01304e16	−	1.01304e16i	−0.432218	−	0.432218i	−0.889382	+	0.457164i	$0.848865\pi$
$948$		0			0
$949$	1.47910e16	−	1.47910e16i	0.623783	−	0.623783i
$950$		0			0
$951$		−	3.01656e16i		−	1.25753i
$952$		0			0
$953$			4.21276e16i			1.73602i	0.496543	+	0.868012i	$0.334603\pi$
$953$			4.21276e16i			1.73602i	−0.496543	+	0.868012i	$0.665397\pi$
$954$		0			0
$955$	9.62905e15	−	9.62905e15i	0.392252	−	0.392252i
$956$		0			0
$957$	−1.62310e16	−	1.62310e16i	−0.653627	−	0.653627i
$958$		0			0
$959$	4.34364e15			0.172922
$960$		0			0
$961$	−1.81691e16			−0.715081
$962$		0			0
$963$	5.53365e14	+	5.53365e14i	0.0215312	+	0.0215312i
$964$		0			0
$965$	2.59104e16	−	2.59104e16i	0.996723	−	0.996723i
$966$		0			0
$967$			2.33377e15i			0.0887589i	0.999015	+	0.0443795i	$0.0141311\pi$
$967$			2.33377e15i			0.0887589i	−0.999015	+	0.0443795i	$0.985869\pi$
$968$		0			0
$969$			6.46877e15i			0.243243i
$970$		0			0
$971$	−5.65037e15	+	5.65037e15i	−0.210073	+	0.210073i	−0.804299	−	0.594225i	$-0.797459\pi$
$971$	−5.65037e15	+	5.65037e15i	−0.210073	+	0.210073i	0.594225	+	0.804299i	$0.297459\pi$
$972$		0			0
$973$	3.69890e14	+	3.69890e14i	0.0135973	+	0.0135973i
$974$		0			0
$975$	5.48472e16			1.99356
$976$		0			0
$977$	2.13934e16			0.768882			0.384441	−	0.923150i	$-0.374394\pi$
$977$	2.13934e16			0.768882			0.384441	+	0.923150i	$0.374394\pi$
$978$		0			0
$979$	7.04961e15	+	7.04961e15i	0.250530	+	0.250530i
$980$		0			0
$981$	−6.18197e14	+	6.18197e14i	−0.0217244	+	0.0217244i
$982$		0			0
$983$		−	3.06868e16i		−	1.06637i	−0.845999	−	0.533184i	$-0.820995\pi$
$983$		−	3.06868e16i		−	1.06637i	0.845999	−	0.533184i	$-0.179005\pi$
$984$		0			0
$985$		−	5.67684e16i		−	1.95077i
$986$		0			0
$987$	1.37047e16	−	1.37047e16i	0.465721	−	0.465721i
$988$		0			0
$989$	−1.47309e16	−	1.47309e16i	−0.495049	−	0.495049i
$990$		0			0
$991$	−4.22930e16			−1.40561			−0.702803	−	0.711384i	$-0.748069\pi$
$991$	−4.22930e16			−1.40561			−0.702803	+	0.711384i	$0.748069\pi$
$992$		0			0
$993$	−1.91920e15			−0.0630810
$994$		0			0
$995$	−4.78199e16	−	4.78199e16i	−1.55447	−	1.55447i
$996$		0			0
$997$	−3.17389e16	+	3.17389e16i	−1.02040	+	1.02040i	−0.0206085	+	0.999788i	$0.506560\pi$
$997$	−3.17389e16	+	3.17389e16i	−1.02040	+	1.02040i	−0.999788	+	0.0206085i	$0.993440\pi$
$998$		0			0
$999$		−	2.72010e15i		−	0.0864916i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.12.e.a.17.16		42
4.3	odd	2		16.12.e.a.13.9	yes	42
8.3	odd	2		128.12.e.b.33.16		42
8.5	even	2		128.12.e.a.33.6		42
16.3	odd	4		128.12.e.b.97.16		42
16.5	even	4	inner	64.12.e.a.49.16		42
16.11	odd	4		16.12.e.a.5.9	✓	42
16.13	even	4		128.12.e.a.97.6		42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.12.e.a.5.9	✓	42	16.11	odd	4
16.12.e.a.13.9	yes	42	4.3	odd	2
64.12.e.a.17.16		42	1.1	even	1	trivial
64.12.e.a.49.16		42	16.5	even	4	inner
128.12.e.a.33.6		42	8.5	even	2
128.12.e.a.97.6		42	16.13	even	4
128.12.e.b.33.16		42	8.3	odd	2
128.12.e.b.97.16		42	16.3	odd	4

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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	64.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(291.167 + 291.167i) q^{3} +(-9753.88 + 9753.88i) q^{5} -16447.0i q^{7} -7590.38i q^{9} +O(q^{10})\)	\(q+(291.167 + 291.167i) q^{3} +(-9753.88 + 9753.88i) q^{5} -16447.0i q^{7} -7590.38i q^{9} +(-477540. + 477540. i) q^{11} +(665864. + 665864. i) q^{13} -5.68002e6 q^{15} -5.80462e6 q^{17} +(-1.91371e6 - 1.91371e6i) q^{19} +(4.78882e6 - 4.78882e6i) q^{21} +1.46860e7i q^{23} -1.41448e8i q^{25} +(5.37895e7 - 5.37895e7i) q^{27} +(5.83665e7 + 5.83665e7i) q^{29} -8.50845e7 q^{31} -2.78088e8 q^{33} +(1.60422e8 + 1.60422e8i) q^{35} +(2.52847e7 - 2.52847e7i) q^{37} +3.87755e8i q^{39} -9.24887e8i q^{41} +(-1.00305e9 + 1.00305e9i) q^{43} +(7.40356e7 + 7.40356e7i) q^{45} +2.86182e9 q^{47} +1.70682e9 q^{49} +(-1.69011e9 - 1.69011e9i) q^{51} +(2.34993e9 - 2.34993e9i) q^{53} -9.31574e9i q^{55} -1.11442e9i q^{57} +(5.55716e8 - 5.55716e8i) q^{59} +(-2.31483e9 - 2.31483e9i) q^{61} -1.24839e8 q^{63} -1.29895e10 q^{65} +(-1.02227e10 - 1.02227e10i) q^{67} +(-4.27609e9 + 4.27609e9i) q^{69} -1.39591e9i q^{71} -2.22133e10i q^{73} +(4.11850e10 - 4.11850e10i) q^{75} +(7.85409e9 + 7.85409e9i) q^{77} -3.84124e10 q^{79} +2.99788e10 q^{81} +(4.10961e9 + 4.10961e9i) q^{83} +(5.66175e10 - 5.66175e10i) q^{85} +3.39888e10i q^{87} -1.47623e10i q^{89} +(1.09514e10 - 1.09514e10i) q^{91} +(-2.47738e10 - 2.47738e10i) q^{93} +3.73322e10 q^{95} -9.56623e10 q^{97} +(3.62471e9 + 3.62471e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} - 2 q^{5}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more