LMFDB - Embedded newform 64.12.e.a.17.5

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			17.5
Character	$\chi$	$=$	64.17
Dual form			64.12.e.a.49.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-367.824 - 367.824i) q^{3} +(-502.344 + 502.344i) q^{5} -33063.2i q^{7} +93442.1i q^{9} +O(q^{10})$	\(q+(-367.824 - 367.824i) q^{3} +(-502.344 + 502.344i) q^{5} -33063.2i q^{7} +93442.1i q^{9} +(-335681. + 335681. i) q^{11} +(568061. + 568061. i) q^{13} +369548. q^{15} -6.78457e6 q^{17} +(-1.33879e6 - 1.33879e6i) q^{19} +(-1.21614e7 + 1.21614e7i) q^{21} +1.07133e6i q^{23} +4.83234e7i q^{25} +(-3.07887e7 + 3.07887e7i) q^{27} +(5.01359e7 + 5.01359e7i) q^{29} -2.95969e8 q^{31} +2.46943e8 q^{33} +(1.66091e7 + 1.66091e7i) q^{35} +(5.11883e8 - 5.11883e8i) q^{37} -4.17893e8i q^{39} +9.31803e8i q^{41} +(1.27362e9 - 1.27362e9i) q^{43} +(-4.69401e7 - 4.69401e7i) q^{45} +1.80739e7 q^{47} +8.84154e8 q^{49} +(2.49553e9 + 2.49553e9i) q^{51} +(2.29607e9 - 2.29607e9i) q^{53} -3.37255e8i q^{55} +9.84878e8i q^{57} +(4.81453e8 - 4.81453e8i) q^{59} +(1.30887e9 + 1.30887e9i) q^{61} +3.08949e9 q^{63} -5.70724e8 q^{65} +(9.42251e9 + 9.42251e9i) q^{67} +(3.94062e8 - 3.94062e8i) q^{69} +1.74203e10i q^{71} -8.91310e9i q^{73} +(1.77745e10 - 1.77745e10i) q^{75} +(1.10987e10 + 1.10987e10i) q^{77} +4.07466e10 q^{79} +3.92026e10 q^{81} +(-1.16461e10 - 1.16461e10i) q^{83} +(3.40819e9 - 3.40819e9i) q^{85} -3.68824e10i q^{87} -7.96706e10i q^{89} +(1.87819e10 - 1.87819e10i) q^{91} +(1.08864e11 + 1.08864e11i) q^{93} +1.34507e9 q^{95} -1.03397e10 q^{97} +(-3.13667e10 - 3.13667e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−367.824	−	367.824i	−0.873923	−	0.873923i	0.118974	−	0.992897i	$-0.462039\pi$
$3$	−367.824	−	367.824i	−0.873923	−	0.873923i	−0.992897	+	0.118974i	$0.962039\pi$
$4$		0			0
$5$	−502.344	+	502.344i	−0.0718896	+	0.0718896i	−0.742137	−	0.670248i	$-0.766188\pi$
$5$	−502.344	+	502.344i	−0.0718896	+	0.0718896i	0.670248	+	0.742137i	$0.266188\pi$
$6$		0			0
$7$		−	33063.2i		−	0.743542i	−0.928325	−	0.371771i	$-0.878751\pi$
$7$		−	33063.2i		−	0.743542i	0.928325	−	0.371771i	$-0.121249\pi$
$8$		0			0
$9$			93442.1i			0.527483i
$10$		0			0
$11$	−335681.	+	335681.i	−0.628444	+	0.628444i	−0.947677	−	0.319232i	$-0.896575\pi$
$11$	−335681.	+	335681.i	−0.628444	+	0.628444i	0.319232	+	0.947677i	$0.396575\pi$
$12$		0			0
$13$	568061.	+	568061.i	0.424333	+	0.424333i	0.886692	−	0.462360i	$-0.152997\pi$
$13$	568061.	+	568061.i	0.424333	+	0.424333i	−0.462360	+	0.886692i	$0.652997\pi$
$14$		0			0
$15$	369548.			0.125652
$16$		0			0
$17$	−6.78457e6			−1.15892			−0.579460	−	0.815001i	$-0.696736\pi$
$17$	−6.78457e6			−1.15892			−0.579460	+	0.815001i	$0.696736\pi$
$18$		0			0
$19$	−1.33879e6	−	1.33879e6i	−0.124042	−	0.124042i	0.642361	−	0.766402i	$-0.277955\pi$
$19$	−1.33879e6	−	1.33879e6i	−0.124042	−	0.124042i	−0.766402	+	0.642361i	$0.777955\pi$
$20$		0			0
$21$	−1.21614e7	+	1.21614e7i	−0.649798	+	0.649798i
$22$		0			0
$23$			1.07133e6i			0.0347074i	0.999849	+	0.0173537i	$0.00552412\pi$
$23$			1.07133e6i			0.0347074i	−0.999849	+	0.0173537i	$0.994476\pi$
$24$		0			0
$25$			4.83234e7i			0.989664i
$26$		0			0
$27$	−3.07887e7	+	3.07887e7i	−0.412943	+	0.412943i
$28$		0			0
$29$	5.01359e7	+	5.01359e7i	0.453899	+	0.453899i	0.896647	−	0.442747i	$-0.145996\pi$
$29$	5.01359e7	+	5.01359e7i	0.453899	+	0.453899i	−0.442747	+	0.896647i	$0.645996\pi$
$30$		0			0
$31$	−2.95969e8			−1.85676			−0.928382	−	0.371628i	$-0.878800\pi$
$31$	−2.95969e8			−1.85676			−0.928382	+	0.371628i	$0.878800\pi$
$32$		0			0
$33$	2.46943e8			1.09842
$34$		0			0
$35$	1.66091e7	+	1.66091e7i	0.0534529	+	0.0534529i
$36$		0			0
$37$	5.11883e8	−	5.11883e8i	1.21356	−	1.21356i	0.243711	−	0.969848i	$-0.421635\pi$
$37$	5.11883e8	−	5.11883e8i	1.21356	−	1.21356i	0.969848	−	0.243711i	$-0.0783649\pi$
$38$		0			0
$39$		−	4.17893e8i		−	0.741669i
$40$		0			0
$41$			9.31803e8i			1.25607i	0.778186	+	0.628034i	$0.216140\pi$
$41$			9.31803e8i			1.25607i	−0.778186	+	0.628034i	$0.783860\pi$
$42$		0			0
$43$	1.27362e9	−	1.27362e9i	1.32118	−	1.32118i	0.408358	−	0.912822i	$-0.366101\pi$
$43$	1.27362e9	−	1.27362e9i	1.32118	−	1.32118i	0.912822	−	0.408358i	$-0.133899\pi$
$44$		0			0
$45$	−4.69401e7	−	4.69401e7i	−0.0379206	−	0.0379206i
$46$		0			0
$47$	1.80739e7			0.0114951			0.00574756	−	0.999983i	$-0.498170\pi$
$47$	1.80739e7			0.0114951			0.00574756	+	0.999983i	$0.498170\pi$
$48$		0			0
$49$	8.84154e8			0.447146
$50$		0			0
$51$	2.49553e9	+	2.49553e9i	1.01281	+	1.01281i
$52$		0			0
$53$	2.29607e9	−	2.29607e9i	0.754168	−	0.754168i	−0.221086	−	0.975254i	$-0.570960\pi$
$53$	2.29607e9	−	2.29607e9i	0.754168	−	0.754168i	0.975254	+	0.221086i	$0.0709602\pi$
$54$		0			0
$55$		−	3.37255e8i		−	0.0903572i
$56$		0			0
$57$			9.84878e8i			0.216806i
$58$		0			0
$59$	4.81453e8	−	4.81453e8i	0.0876734	−	0.0876734i	−0.661910	−	0.749583i	$-0.730254\pi$
$59$	4.81453e8	−	4.81453e8i	0.0876734	−	0.0876734i	0.749583	+	0.661910i	$0.230254\pi$
$60$		0			0
$61$	1.30887e9	+	1.30887e9i	0.198419	+	0.198419i	0.799322	−	0.600903i	$-0.205192\pi$
$61$	1.30887e9	+	1.30887e9i	0.198419	+	0.198419i	−0.600903	+	0.799322i	$0.705192\pi$
$62$		0			0
$63$	3.08949e9			0.392206
$64$		0			0
$65$	−5.70724e8			−0.0610103
$66$		0			0
$67$	9.42251e9	+	9.42251e9i	0.852619	+	0.852619i	0.990455	−	0.137836i	$-0.0440147\pi$
$67$	9.42251e9	+	9.42251e9i	0.852619	+	0.852619i	−0.137836	+	0.990455i	$0.544015\pi$
$68$		0			0
$69$	3.94062e8	−	3.94062e8i	0.0303316	−	0.0303316i
$70$		0			0
$71$			1.74203e10i			1.14587i	0.819601	+	0.572934i	$0.194195\pi$
$71$			1.74203e10i			1.14587i	−0.819601	+	0.572934i	$0.805805\pi$
$72$		0			0
$73$		−	8.91310e9i		−	0.503215i	−0.967829	−	0.251607i	$-0.919041\pi$
$73$		−	8.91310e9i		−	0.503215i	0.967829	−	0.251607i	$-0.0809591\pi$
$74$		0			0
$75$	1.77745e10	−	1.77745e10i	0.864890	−	0.864890i
$76$		0			0
$77$	1.10987e10	+	1.10987e10i	0.467274	+	0.467274i
$78$		0			0
$79$	4.07466e10			1.48985			0.744924	−	0.667149i	$-0.232486\pi$
$79$	4.07466e10			1.48985			0.744924	+	0.667149i	$0.232486\pi$
$80$		0			0
$81$	3.92026e10			1.24924
$82$		0			0
$83$	−1.16461e10	−	1.16461e10i	−0.324527	−	0.324527i	0.525974	−	0.850501i	$-0.323701\pi$
$83$	−1.16461e10	−	1.16461e10i	−0.324527	−	0.324527i	−0.850501	+	0.525974i	$0.823701\pi$
$84$		0			0
$85$	3.40819e9	−	3.40819e9i	0.0833143	−	0.0833143i
$86$		0			0
$87$		−	3.68824e10i		−	0.793346i
$88$		0			0
$89$		−	7.96706e10i		−	1.51235i	−0.654368	−	0.756176i	$-0.727065\pi$
$89$		−	7.96706e10i		−	1.51235i	0.654368	−	0.756176i	$-0.272935\pi$
$90$		0			0
$91$	1.87819e10	−	1.87819e10i	0.315509	−	0.315509i
$92$		0			0
$93$	1.08864e11	+	1.08864e11i	1.62267	+	1.62267i
$94$		0			0
$95$	1.34507e9			0.0178346
$96$		0			0
$97$	−1.03397e10			−0.122254			−0.0611269	−	0.998130i	$-0.519469\pi$
$97$	−1.03397e10			−0.122254			−0.0611269	+	0.998130i	$0.519469\pi$
$98$		0			0
$99$	−3.13667e10	−	3.13667e10i	−0.331494	−	0.331494i
$100$		0			0
$101$	−3.36018e10	+	3.36018e10i	−0.318123	+	0.318123i	−0.848046	−	0.529923i	$-0.822221\pi$
$101$	−3.36018e10	+	3.36018e10i	−0.318123	+	0.318123i	0.529923	+	0.848046i	$0.322221\pi$
$102$		0			0
$103$			9.27041e10i			0.787942i	0.919123	+	0.393971i	$0.128899\pi$
$103$			9.27041e10i			0.787942i	−0.919123	+	0.393971i	$0.871101\pi$
$104$		0			0
$105$		−	1.22184e10i		−	0.0934275i
$106$		0			0
$107$	−2.88146e10	+	2.88146e10i	−0.198610	+	0.198610i	−0.799404	−	0.600794i	$-0.794851\pi$
$107$	−2.88146e10	+	2.88146e10i	−0.198610	+	0.198610i	0.600794	+	0.799404i	$0.294851\pi$
$108$		0			0
$109$	−2.21468e10	−	2.21468e10i	−0.137868	−	0.137868i	0.634804	−	0.772673i	$-0.281081\pi$
$109$	−2.21468e10	−	2.21468e10i	−0.137868	−	0.137868i	−0.772673	+	0.634804i	$0.781081\pi$
$110$		0			0
$111$	−3.76565e11			−2.12111
$112$		0			0
$113$	−1.71538e11			−0.875849			−0.437924	−	0.899012i	$-0.644286\pi$
$113$	−1.71538e11			−0.875849			−0.437924	+	0.899012i	$0.644286\pi$
$114$		0			0
$115$	−5.38178e8	−	5.38178e8i	−0.00249510	−	0.00249510i
$116$		0			0
$117$	−5.30808e10	+	5.30808e10i	−0.223829	+	0.223829i
$118$		0			0
$119$			2.24319e11i			0.861705i
$120$		0			0
$121$			5.99484e10i			0.210116i
$122$		0			0
$123$	3.42740e11	−	3.42740e11i	1.09771	−	1.09771i
$124$		0			0
$125$	−4.88035e10	−	4.88035e10i	−0.143036	−	0.143036i
$126$		0			0
$127$	−5.54635e11			−1.48966			−0.744830	−	0.667254i	$-0.767469\pi$
$127$	−5.54635e11			−1.48966			−0.744830	+	0.667254i	$0.767469\pi$
$128$		0			0
$129$	−9.36933e11			−2.30922
$130$		0			0
$131$	4.50085e11	+	4.50085e11i	1.01930	+	1.01930i	0.999810	+	0.0194915i	$0.00620473\pi$
$131$	4.50085e11	+	4.50085e11i	1.01930	+	1.01930i	0.0194915	+	0.999810i	$0.493795\pi$
$132$		0			0
$133$	−4.42646e10	+	4.42646e10i	−0.0922301	+	0.0922301i
$134$		0			0
$135$		−	3.09330e10i		−	0.0593727i
$136$		0			0
$137$		−	7.75745e11i		−	1.37327i	−0.727002	−	0.686635i	$-0.759087\pi$
$137$		−	7.75745e11i		−	1.37327i	0.727002	−	0.686635i	$-0.240913\pi$
$138$		0			0
$139$	3.80649e11	−	3.80649e11i	0.622219	−	0.622219i	−0.323880	−	0.946098i	$-0.604987\pi$
$139$	3.80649e11	−	3.80649e11i	0.622219	−	0.622219i	0.946098	+	0.323880i	$0.104987\pi$
$140$		0			0
$141$	−6.64802e9	−	6.64802e9i	−0.0100459	−	0.0100459i
$142$		0			0
$143$	−3.81374e11			−0.533339
$144$		0			0
$145$	−5.03709e10			−0.0652613
$146$		0			0
$147$	−3.25213e11	−	3.25213e11i	−0.390771	−	0.390771i
$148$		0			0
$149$	−1.21482e11	+	1.21482e11i	−0.135515	+	0.135515i	−0.771610	−	0.636095i	$-0.780549\pi$
$149$	−1.21482e11	+	1.21482e11i	−0.135515	+	0.135515i	0.636095	+	0.771610i	$0.280549\pi$
$150$		0			0
$151$			4.18981e11i			0.434331i	0.976135	+	0.217166i	$0.0696812\pi$
$151$			4.18981e11i			0.434331i	−0.976135	+	0.217166i	$0.930319\pi$
$152$		0			0
$153$		−	6.33965e11i		−	0.611311i
$154$		0			0
$155$	1.48678e11	−	1.48678e11i	0.133482	−	0.133482i
$156$		0			0
$157$	1.64950e12	+	1.64950e12i	1.38008	+	1.38008i	0.844456	+	0.535626i	$0.179924\pi$
$157$	1.64950e12	+	1.64950e12i	1.38008	+	1.38008i	0.535626	+	0.844456i	$0.320076\pi$
$158$		0			0
$159$	−1.68910e12			−1.31817
$160$		0			0
$161$	3.54217e10			0.0258064
$162$		0			0
$163$	−1.07698e12	−	1.07698e12i	−0.733121	−	0.733121i	0.238116	−	0.971237i	$-0.423470\pi$
$163$	−1.07698e12	−	1.07698e12i	−0.733121	−	0.733121i	−0.971237	+	0.238116i	$0.923470\pi$
$164$		0			0
$165$	−1.24050e11	+	1.24050e11i	−0.0789653	+	0.0789653i
$166$		0			0
$167$			1.59845e12i			0.952268i	0.879373	+	0.476134i	$0.157962\pi$
$167$			1.59845e12i			0.952268i	−0.879373	+	0.476134i	$0.842038\pi$
$168$		0			0
$169$		−	1.14677e12i		−	0.639883i
$170$		0			0
$171$	1.25099e11	−	1.25099e11i	0.0654299	−	0.0654299i
$172$		0			0
$173$	1.45486e12	+	1.45486e12i	0.713785	+	0.713785i	0.967325	−	0.253540i	$-0.0815949\pi$
$173$	1.45486e12	+	1.45486e12i	0.713785	+	0.713785i	−0.253540	+	0.967325i	$0.581595\pi$
$174$		0			0
$175$	1.59773e12			0.735856
$176$		0			0
$177$	−3.54180e11			−0.153240
$178$		0			0
$179$	1.30891e12	+	1.30891e12i	0.532376	+	0.532376i	0.921279	−	0.388903i	$-0.127146\pi$
$179$	1.30891e12	+	1.30891e12i	0.532376	+	0.532376i	−0.388903	+	0.921279i	$0.627146\pi$
$180$		0			0
$181$	−2.38152e12	+	2.38152e12i	−0.911219	+	0.911219i	−0.996368	−	0.0851488i	$-0.972863\pi$
$181$	−2.38152e12	+	2.38152e12i	−0.911219	+	0.911219i	0.0851488	+	0.996368i	$0.472863\pi$
$182$		0			0
$183$		−	9.62869e11i		−	0.346806i
$184$		0			0
$185$			5.14282e11i			0.174485i
$186$		0			0
$187$	2.27745e12	−	2.27745e12i	0.728316	−	0.728316i
$188$		0			0
$189$	1.01797e12	+	1.01797e12i	0.307040	+	0.307040i
$190$		0			0
$191$	3.52280e12			1.00278			0.501388	−	0.865223i	$-0.332823\pi$
$191$	3.52280e12			1.00278			0.501388	+	0.865223i	$0.332823\pi$
$192$		0			0
$193$	4.01739e12			1.07989			0.539944	−	0.841701i	$-0.318445\pi$
$193$	4.01739e12			1.07989			0.539944	+	0.841701i	$0.318445\pi$
$194$		0			0
$195$	2.09926e11	+	2.09926e11i	0.0533183	+	0.0533183i
$196$		0			0
$197$	3.98851e12	−	3.98851e12i	0.957737	−	0.957737i	−0.0414057	−	0.999142i	$-0.513184\pi$
$197$	3.98851e12	−	3.98851e12i	0.957737	−	0.957737i	0.999142	+	0.0414057i	$0.0131836\pi$
$198$		0			0
$199$			1.41250e11i			0.0320846i	0.999871	+	0.0160423i	$0.00510665\pi$
$199$			1.41250e11i			0.0320846i	−0.999871	+	0.0160423i	$0.994893\pi$
$200$		0			0
$201$		−	6.93165e12i		−	1.49025i
$202$		0			0
$203$	1.65765e12	−	1.65765e12i	0.337493	−	0.337493i
$204$		0			0
$205$	−4.68086e11	−	4.68086e11i	−0.0902982	−	0.0902982i
$206$		0			0
$207$	−1.00108e11			−0.0183076
$208$		0			0
$209$	8.98812e11			0.155907
$210$		0			0
$211$	3.64182e12	+	3.64182e12i	0.599466	+	0.599466i	0.940170	−	0.340704i	$-0.110666\pi$
$211$	3.64182e12	+	3.64182e12i	0.599466	+	0.599466i	−0.340704	+	0.940170i	$0.610666\pi$
$212$		0			0
$213$	6.40761e12	−	6.40761e12i	1.00140	−	1.00140i
$214$		0			0
$215$			1.27959e12i			0.189958i
$216$		0			0
$217$			9.78567e12i			1.38058i
$218$		0			0
$219$	−3.27845e12	+	3.27845e12i	−0.439771	+	0.439771i
$220$		0			0
$221$	−3.85405e12	−	3.85405e12i	−0.491768	−	0.491768i
$222$		0			0
$223$	5.31451e12			0.645337			0.322668	−	0.946512i	$-0.395420\pi$
$223$	5.31451e12			0.645337			0.322668	+	0.946512i	$0.395420\pi$
$224$		0			0
$225$	−4.51544e12			−0.522031
$226$		0			0
$227$	4.88964e12	+	4.88964e12i	0.538437	+	0.538437i	0.923070	−	0.384633i	$-0.125672\pi$
$227$	4.88964e12	+	4.88964e12i	0.538437	+	0.538437i	−0.384633	+	0.923070i	$0.625672\pi$
$228$		0			0
$229$	−7.07133e12	+	7.07133e12i	−0.742003	+	0.742003i	−0.972963	−	0.230960i	$-0.925813\pi$
$229$	−7.07133e12	+	7.07133e12i	−0.742003	+	0.742003i	0.230960	+	0.972963i	$0.425813\pi$
$230$		0			0
$231$		−	8.16472e12i		−	0.816724i
$232$		0			0
$233$			1.54810e13i			1.47687i	0.674324	+	0.738435i	$0.264435\pi$
$233$			1.54810e13i			1.47687i	−0.674324	+	0.738435i	$0.735565\pi$
$234$		0			0
$235$	−9.07932e9	+	9.07932e9i	−0.000826380	+	0.000826380i
$236$		0			0
$237$	−1.49876e13	−	1.49876e13i	−1.30201	−	1.30201i
$238$		0			0
$239$	−1.47869e13			−1.22656			−0.613280	−	0.789866i	$-0.710150\pi$
$239$	−1.47869e13			−1.22656			−0.613280	+	0.789866i	$0.710150\pi$
$240$		0			0
$241$	−3.70990e12			−0.293946			−0.146973	−	0.989140i	$-0.546953\pi$
$241$	−3.70990e12			−0.293946			−0.146973	+	0.989140i	$0.546953\pi$
$242$		0			0
$243$	−8.96555e12	−	8.96555e12i	−0.678801	−	0.678801i
$244$		0			0
$245$	−4.44149e11	+	4.44149e11i	−0.0321452	+	0.0321452i
$246$		0			0
$247$		−	1.52103e12i		−	0.105270i
$248$		0			0
$249$			8.56743e12i			0.567223i
$250$		0			0
$251$	−1.64619e13	+	1.64619e13i	−1.04297	+	1.04297i	−0.0439391	+	0.999034i	$0.513991\pi$
$251$	−1.64619e13	+	1.64619e13i	−1.04297	+	1.04297i	−0.999034	+	0.0439391i	$0.986009\pi$
$252$		0			0
$253$	−3.59626e11	−	3.59626e11i	−0.0218116	−	0.0218116i
$254$		0			0
$255$	−2.50723e12			−0.145621
$256$		0			0
$257$	2.20187e13			1.22506			0.612532	−	0.790446i	$-0.290151\pi$
$257$	2.20187e13			1.22506			0.612532	+	0.790446i	$0.290151\pi$
$258$		0			0
$259$	−1.69245e13	−	1.69245e13i	−0.902331	−	0.902331i
$260$		0			0
$261$	−4.68480e12	+	4.68480e12i	−0.239424	+	0.239424i
$262$		0			0
$263$		−	4.64085e12i		−	0.227426i	−0.993514	−	0.113713i	$-0.963726\pi$
$263$		−	4.64085e12i		−	0.227426i	0.993514	−	0.113713i	$-0.0362745\pi$
$264$		0			0
$265$			2.30684e12i			0.108434i
$266$		0			0
$267$	−2.93047e13	+	2.93047e13i	−1.32168	+	1.32168i
$268$		0			0
$269$	−3.23177e12	−	3.23177e12i	−0.139895	−	0.139895i	0.633691	−	0.773586i	$-0.281539\pi$
$269$	−3.23177e12	−	3.23177e12i	−0.139895	−	0.139895i	−0.773586	+	0.633691i	$0.781539\pi$
$270$		0			0
$271$	3.04462e13			1.26533			0.632663	−	0.774427i	$-0.281962\pi$
$271$	3.04462e13			1.26533			0.632663	+	0.774427i	$0.281962\pi$
$272$		0			0
$273$	−1.38169e13			−0.551461
$274$		0			0
$275$	−1.62212e13	−	1.62212e13i	−0.621949	−	0.621949i
$276$		0			0
$277$	1.12987e13	−	1.12987e13i	0.416282	−	0.416282i	−0.467638	−	0.883920i	$-0.654895\pi$
$277$	1.12987e13	−	1.12987e13i	0.416282	−	0.416282i	0.883920	+	0.467638i	$0.154895\pi$
$278$		0			0
$279$		−	2.76559e13i		−	0.979412i
$280$		0			0
$281$		−	2.01696e13i		−	0.686772i	−0.939194	−	0.343386i	$-0.888426\pi$
$281$		−	2.01696e13i		−	0.686772i	0.939194	−	0.343386i	$-0.111574\pi$
$282$		0			0
$283$	2.67176e12	−	2.67176e12i	0.0874929	−	0.0874929i	−0.662006	−	0.749499i	$-0.730295\pi$
$283$	2.67176e12	−	2.67176e12i	0.0874929	−	0.0874929i	0.749499	+	0.662006i	$0.230295\pi$
$284$		0			0
$285$	−4.94748e11	−	4.94748e11i	−0.0155861	−	0.0155861i
$286$		0			0
$287$	3.08084e13			0.933938
$288$		0			0
$289$	1.17585e13			0.343095
$290$		0			0
$291$	3.80318e12	+	3.80318e12i	0.106840	+	0.106840i
$292$		0			0
$293$	−3.85320e13	+	3.85320e13i	−1.04244	+	1.04244i	−0.0433791	+	0.999059i	$0.513812\pi$
$293$	−3.85320e13	+	3.85320e13i	−1.04244	+	1.04244i	−0.999059	+	0.0433791i	$0.986188\pi$
$294$		0			0
$295$			4.83710e11i			0.0126056i
$296$		0			0
$297$		−	2.06703e13i		−	0.519024i
$298$		0			0
$299$	−6.08583e11	+	6.08583e11i	−0.0147275	+	0.0147275i
$300$		0			0
$301$	−4.21098e13	−	4.21098e13i	−0.982352	−	0.982352i
$302$		0			0
$303$	2.47191e13			0.556031
$304$		0			0
$305$	−1.31501e12			−0.0285285
$306$		0			0
$307$	3.24055e13	+	3.24055e13i	0.678199	+	0.678199i	0.959593	−	0.281393i	$-0.0907966\pi$
$307$	3.24055e13	+	3.24055e13i	0.678199	+	0.678199i	−0.281393	+	0.959593i	$0.590797\pi$
$308$		0			0
$309$	3.40988e13	−	3.40988e13i	0.688601	−	0.688601i
$310$		0			0
$311$			5.32038e13i			1.03696i	0.855091	+	0.518478i	$0.173501\pi$
$311$			5.32038e13i			1.03696i	−0.855091	+	0.518478i	$0.826499\pi$
$312$		0			0
$313$			7.41435e13i			1.39502i	0.716577	+	0.697508i	$0.245708\pi$
$313$			7.41435e13i			1.39502i	−0.716577	+	0.697508i	$0.754292\pi$
$314$		0			0
$315$	−1.55199e12	+	1.55199e12i	−0.0281955	+	0.0281955i
$316$		0			0
$317$	6.45432e12	+	6.45432e12i	0.113246	+	0.113246i	0.761459	−	0.648213i	$-0.224483\pi$
$317$	6.45432e12	+	6.45432e12i	0.113246	+	0.113246i	−0.648213	+	0.761459i	$0.724483\pi$
$318$		0			0
$319$	−3.36593e13			−0.570501
$320$		0			0
$321$	2.11974e13			0.347140
$322$		0			0
$323$	9.08312e12	+	9.08312e12i	0.143754	+	0.143754i
$324$		0			0
$325$	−2.74507e13	+	2.74507e13i	−0.419947	+	0.419947i
$326$		0			0
$327$			1.62922e13i			0.240973i
$328$		0			0
$329$		−	5.97580e11i		−	0.00854710i
$330$		0			0
$331$	5.80148e13	−	5.80148e13i	0.802574	−	0.802574i	−0.180923	−	0.983497i	$-0.557909\pi$
$331$	5.80148e13	−	5.80148e13i	0.802574	−	0.802574i	0.983497	+	0.180923i	$0.0579085\pi$
$332$		0			0
$333$	4.78314e13	+	4.78314e13i	0.640132	+	0.640132i
$334$		0			0
$335$	−9.46668e12			−0.122589
$336$		0			0
$337$	−7.30225e13			−0.915150			−0.457575	−	0.889171i	$-0.651282\pi$
$337$	−7.30225e13			−0.915150			−0.457575	+	0.889171i	$0.651282\pi$
$338$		0			0
$339$	6.30958e13	+	6.30958e13i	0.765425	+	0.765425i
$340$		0			0
$341$	9.93510e13	−	9.93510e13i	1.16687	−	1.16687i
$342$		0			0
$343$		−	9.46096e13i		−	1.07601i
$344$		0			0
$345$			3.95910e11i			0.00436105i
$346$		0			0
$347$	4.07174e13	−	4.07174e13i	0.434478	−	0.434478i	−0.455670	−	0.890149i	$-0.650600\pi$
$347$	4.07174e13	−	4.07174e13i	0.434478	−	0.434478i	0.890149	+	0.455670i	$0.150600\pi$
$348$		0			0
$349$	7.50423e13	+	7.50423e13i	0.775829	+	0.775829i	0.979119	−	0.203290i	$-0.0651633\pi$
$349$	7.50423e13	+	7.50423e13i	0.775829	+	0.775829i	−0.203290	+	0.979119i	$0.565163\pi$
$350$		0			0
$351$	−3.49797e13			−0.350451
$352$		0			0
$353$	1.92000e14			1.86441			0.932205	−	0.361931i	$-0.117882\pi$
$353$	1.92000e14			1.86441			0.932205	+	0.361931i	$0.117882\pi$
$354$		0			0
$355$	−8.75099e12	−	8.75099e12i	−0.0823761	−	0.0823761i
$356$		0			0
$357$	8.25101e13	−	8.25101e13i	0.753064	−	0.753064i
$358$		0			0
$359$			6.04811e13i			0.535304i	0.963516	+	0.267652i	$0.0862477\pi$
$359$			6.04811e13i			0.535304i	−0.963516	+	0.267652i	$0.913752\pi$
$360$		0			0
$361$		−	1.12906e14i		−	0.969227i
$362$		0			0
$363$	2.20505e13	−	2.20505e13i	0.183625	−	0.183625i
$364$		0			0
$365$	4.47744e12	+	4.47744e12i	0.0361759	+	0.0361759i
$366$		0			0
$367$	−7.73489e13			−0.606444			−0.303222	−	0.952920i	$-0.598062\pi$
$367$	−7.73489e13			−0.606444			−0.303222	+	0.952920i	$0.598062\pi$
$368$		0			0
$369$	−8.70696e13			−0.662555
$370$		0			0
$371$	−7.59154e13	−	7.59154e13i	−0.560755	−	0.560755i
$372$		0			0
$373$	−7.33207e13	+	7.33207e13i	−0.525809	+	0.525809i	−0.919320	−	0.393511i	$-0.871260\pi$
$373$	−7.33207e13	+	7.33207e13i	−0.525809	+	0.525809i	0.393511	+	0.919320i	$0.371260\pi$
$374$		0			0
$375$			3.59022e13i			0.250005i
$376$		0			0
$377$			5.69605e13i			0.385209i
$378$		0			0
$379$	1.92106e14	−	1.92106e14i	1.26190	−	1.26190i	0.311734	−	0.950169i	$-0.399090\pi$
$379$	1.92106e14	−	1.92106e14i	1.26190	−	1.26190i	0.950169	−	0.311734i	$-0.100910\pi$
$380$		0			0
$381$	2.04008e14	+	2.04008e14i	1.30185	+	1.30185i
$382$		0			0
$383$	−1.28679e14			−0.797836			−0.398918	−	0.916987i	$-0.630614\pi$
$383$	−1.28679e14			−0.797836			−0.398918	+	0.916987i	$0.630614\pi$
$384$		0			0
$385$	−1.11507e13			−0.0671844
$386$		0			0
$387$	1.19009e14	+	1.19009e14i	0.696900	+	0.696900i
$388$		0			0
$389$	−2.00352e14	+	2.00352e14i	−1.14044	+	1.14044i	−0.152068	+	0.988370i	$0.548593\pi$
$389$	−2.00352e14	+	2.00352e14i	−1.14044	+	1.14044i	−0.988370	+	0.152068i	$0.951407\pi$
$390$		0			0
$391$		−	7.26854e12i		−	0.0402230i
$392$		0			0
$393$		−	3.31104e14i		−	1.78158i
$394$		0			0
$395$	−2.04688e13	+	2.04688e13i	−0.107105	+	0.107105i
$396$		0			0
$397$	−1.54966e14	−	1.54966e14i	−0.788657	−	0.788657i	0.192617	−	0.981274i	$-0.438303\pi$
$397$	−1.54966e14	−	1.54966e14i	−0.788657	−	0.788657i	−0.981274	+	0.192617i	$0.938303\pi$
$398$		0			0
$399$	3.25632e13			0.161204
$400$		0			0
$401$	−3.58680e14			−1.72748			−0.863740	−	0.503938i	$-0.831884\pi$
$401$	−3.58680e14			−1.72748			−0.863740	+	0.503938i	$0.831884\pi$
$402$		0			0
$403$	−1.68128e14	−	1.68128e14i	−0.787886	−	0.787886i
$404$		0			0
$405$	−1.96932e13	+	1.96932e13i	−0.0898077	+	0.0898077i
$406$		0			0
$407$			3.43658e14i			1.52531i
$408$		0			0
$409$			4.56728e13i			0.197324i	0.995121	+	0.0986618i	$0.0314562\pi$
$409$			4.56728e13i			0.197324i	−0.995121	+	0.0986618i	$0.968544\pi$
$410$		0			0
$411$	−2.85338e14	+	2.85338e14i	−1.20013	+	1.20013i
$412$		0			0
$413$	−1.59184e13	−	1.59184e13i	−0.0651888	−	0.0651888i
$414$		0			0
$415$	1.17007e13			0.0466602
$416$		0			0
$417$	−2.80024e14			−1.08754
$418$		0			0
$419$	−2.11630e13	−	2.11630e13i	−0.0800572	−	0.0800572i	0.665944	−	0.746001i	$-0.268029\pi$
$419$	−2.11630e13	−	2.11630e13i	−0.0800572	−	0.0800572i	−0.746001	+	0.665944i	$0.768029\pi$
$420$		0			0
$421$	−1.92706e14	+	1.92706e14i	−0.710138	+	0.710138i	−0.966564	−	0.256426i	$-0.917455\pi$
$421$	−1.92706e14	+	1.92706e14i	−0.710138	+	0.710138i	0.256426	+	0.966564i	$0.417455\pi$
$422$		0			0
$423$			1.68886e12i			0.00606349i
$424$		0			0
$425$		−	3.27854e14i		−	1.14694i
$426$		0			0
$427$	4.32754e13	−	4.32754e13i	0.147533	−	0.147533i
$428$		0			0
$429$	1.40279e14	+	1.40279e14i	0.466097	+	0.466097i
$430$		0			0
$431$	−3.15533e14			−1.02193			−0.510964	−	0.859602i	$-0.670711\pi$
$431$	−3.15533e14			−1.02193			−0.510964	+	0.859602i	$0.670711\pi$
$432$		0			0
$433$	9.43423e13			0.297867			0.148934	−	0.988847i	$-0.452416\pi$
$433$	9.43423e13			0.297867			0.148934	+	0.988847i	$0.452416\pi$
$434$		0			0
$435$	1.85276e13	+	1.85276e13i	0.0570334	+	0.0570334i
$436$		0			0
$437$	1.43429e12	−	1.43429e12i	0.00430516	−	0.00430516i
$438$		0			0
$439$			4.26118e12i			0.0124731i	0.999981	+	0.00623655i	$0.00198517\pi$
$439$			4.26118e12i			0.0124731i	−0.999981	+	0.00623655i	$0.998015\pi$
$440$		0			0
$441$			8.26172e13i			0.235862i
$442$		0			0
$443$	−1.07675e13	+	1.07675e13i	−0.0299843	+	0.0299843i	−0.721940	−	0.691956i	$-0.756749\pi$
$443$	−1.07675e13	+	1.07675e13i	−0.0299843	+	0.0299843i	0.691956	+	0.721940i	$0.256749\pi$
$444$		0			0
$445$	4.00220e13	+	4.00220e13i	0.108722	+	0.108722i
$446$		0			0
$447$	8.93681e13			0.236860
$448$		0			0
$449$	1.49573e14			0.386811			0.193405	−	0.981119i	$-0.438047\pi$
$449$	1.49573e14			0.386811			0.193405	+	0.981119i	$0.438047\pi$
$450$		0			0
$451$	−3.12788e14	−	3.12788e14i	−0.789368	−	0.789368i
$452$		0			0
$453$	1.54111e14	−	1.54111e14i	0.379572	−	0.379572i
$454$		0			0
$455$			1.88700e13i			0.0453637i
$456$		0			0
$457$		−	5.73073e13i		−	0.134484i	−0.997737	−	0.0672420i	$-0.978580\pi$
$457$		−	5.73073e13i		−	0.134484i	0.997737	−	0.0672420i	$-0.0214200\pi$
$458$		0			0
$459$	2.08888e14	−	2.08888e14i	0.478568	−	0.478568i
$460$		0			0
$461$	−5.04689e14	−	5.04689e14i	−1.12893	−	1.12893i	−0.990351	−	0.138583i	$-0.955745\pi$
$461$	−5.04689e14	−	5.04689e14i	−1.12893	−	1.12893i	−0.138583	−	0.990351i	$-0.544255\pi$
$462$		0			0
$463$	1.04606e14			0.228487			0.114243	−	0.993453i	$-0.463556\pi$
$463$	1.04606e14			0.228487			0.114243	+	0.993453i	$0.463556\pi$
$464$		0			0
$465$	−1.09375e14			−0.233306
$466$		0			0
$467$	5.83143e14	+	5.83143e14i	1.21488	+	1.21488i	0.969404	+	0.245472i	$0.0789430\pi$
$467$	5.83143e14	+	5.83143e14i	1.21488	+	1.21488i	0.245472	+	0.969404i	$0.421057\pi$
$468$		0			0
$469$	3.11538e14	−	3.11538e14i	0.633958	−	0.633958i
$470$		0			0
$471$		−	1.21345e15i		−	2.41217i
$472$		0			0
$473$			8.55057e14i			1.66058i
$474$		0			0
$475$	6.46949e13	−	6.46949e13i	0.122760	−	0.122760i
$476$		0			0
$477$	2.14550e14	+	2.14550e14i	0.397811	+	0.397811i
$478$		0			0
$479$	9.29337e12			0.0168394			0.00841972	−	0.999965i	$-0.497320\pi$
$479$	9.29337e12			0.0168394			0.00841972	+	0.999965i	$0.497320\pi$
$480$		0			0
$481$	5.81561e14			1.02991
$482$		0			0
$483$	−1.30289e13	−	1.30289e13i	−0.0225528	−	0.0225528i
$484$		0			0
$485$	5.19407e12	−	5.19407e12i	0.00878878	−	0.00878878i
$486$		0			0
$487$			2.67485e14i			0.442477i	0.975220	+	0.221238i	$0.0710099\pi$
$487$			2.67485e14i			0.442477i	−0.975220	+	0.221238i	$0.928990\pi$
$488$		0			0
$489$			7.92278e14i			1.28138i
$490$		0			0
$491$	−3.39834e13	+	3.39834e13i	−0.0537425	+	0.0537425i	−0.733467	−	0.679725i	$-0.762099\pi$
$491$	−3.39834e13	+	3.39834e13i	−0.0537425	+	0.0537425i	0.679725	+	0.733467i	$0.262099\pi$
$492$		0			0
$493$	−3.40150e14	−	3.40150e14i	−0.526033	−	0.526033i
$494$		0			0
$495$	3.15138e13			0.0476619
$496$		0			0
$497$	5.75970e14			0.852001
$498$		0			0
$499$	−1.03300e14	−	1.03300e14i	−0.149468	−	0.149468i	0.628412	−	0.777880i	$-0.283705\pi$
$499$	−1.03300e14	−	1.03300e14i	−0.149468	−	0.149468i	−0.777880	+	0.628412i	$0.783705\pi$
$500$		0			0
$501$	5.87949e14	−	5.87949e14i	0.832209	−	0.832209i
$502$		0			0
$503$			1.03966e15i			1.43969i	0.694136	+	0.719843i	$0.255786\pi$
$503$			1.03966e15i			1.43969i	−0.694136	+	0.719843i	$0.744214\pi$
$504$		0			0
$505$		−	3.37594e13i		−	0.0457395i
$506$		0			0
$507$	−4.21811e14	+	4.21811e14i	−0.559209	+	0.559209i
$508$		0			0
$509$	5.30191e14	+	5.30191e14i	0.687835	+	0.687835i	0.961753	−	0.273918i	$-0.0883196\pi$
$509$	5.30191e14	+	5.30191e14i	0.687835	+	0.687835i	−0.273918	+	0.961753i	$0.588320\pi$
$510$		0			0
$511$	−2.94695e14			−0.374161
$512$		0			0
$513$	8.24391e13			0.102444
$514$		0			0
$515$	−4.65693e13	−	4.65693e13i	−0.0566448	−	0.0566448i
$516$		0			0
$517$	−6.06706e12	+	6.06706e12i	−0.00722405	+	0.00722405i
$518$		0			0
$519$		−	1.07026e15i		−	1.24759i
$520$		0			0
$521$			7.25048e14i			0.827484i	0.910394	+	0.413742i	$0.135778\pi$
$521$			7.25048e14i			0.827484i	−0.910394	+	0.413742i	$0.864222\pi$
$522$		0			0
$523$	−6.35477e14	+	6.35477e14i	−0.710134	+	0.710134i	−0.966563	−	0.256429i	$-0.917454\pi$
$523$	−6.35477e14	+	6.35477e14i	−0.710134	+	0.710134i	0.256429	+	0.966563i	$0.417454\pi$
$524$		0			0
$525$	−5.87682e14	−	5.87682e14i	−0.643082	−	0.643082i
$526$		0			0
$527$	2.00802e15			2.15184
$528$		0			0
$529$	9.51662e14			0.998795
$530$		0			0
$531$	4.49880e13	+	4.49880e13i	0.0462463	+	0.0462463i
$532$		0			0
$533$	−5.29321e14	+	5.29321e14i	−0.532991	+	0.532991i
$534$		0			0
$535$		−	2.89497e13i		−	0.0285560i
$536$		0			0
$537$		−	9.62898e14i		−	0.930511i
$538$		0			0
$539$	−2.96793e14	+	2.96793e14i	−0.281006	+	0.281006i
$540$		0			0
$541$	−1.14149e15	−	1.14149e15i	−1.05898	−	1.05898i	−0.998148	−	0.0608311i	$-0.980625\pi$
$541$	−1.14149e15	−	1.14149e15i	−1.05898	−	1.05898i	−0.0608311	−	0.998148i	$-0.519375\pi$
$542$		0			0
$543$	1.75196e15			1.59267
$544$		0			0
$545$	2.22506e13			0.0198226
$546$		0			0
$547$	7.92097e14	+	7.92097e14i	0.691589	+	0.691589i	0.962581	−	0.270993i	$-0.0873519\pi$
$547$	7.92097e14	+	7.92097e14i	0.691589	+	0.691589i	−0.270993	+	0.962581i	$0.587352\pi$
$548$		0			0
$549$	−1.22304e14	+	1.22304e14i	−0.104663	+	0.104663i
$550$		0			0
$551$		−	1.34243e14i		−	0.112605i
$552$		0			0
$553$		−	1.34721e15i		−	1.10776i
$554$		0			0
$555$	1.89165e14	−	1.89165e14i	0.152486	−	0.152486i
$556$		0			0
$557$	1.32985e15	+	1.32985e15i	1.05099	+	1.05099i	0.998628	+	0.0523642i	$0.0166757\pi$
$557$	1.32985e15	+	1.32985e15i	1.05099	+	1.05099i	0.0523642	+	0.998628i	$0.483324\pi$
$558$		0			0
$559$	1.44698e15			1.12124
$560$		0			0
$561$	−1.67540e15			−1.27299
$562$		0			0
$563$	−6.09588e14	−	6.09588e14i	−0.454193	−	0.454193i	0.442551	−	0.896743i	$-0.354074\pi$
$563$	−6.09588e14	−	6.09588e14i	−0.454193	−	0.454193i	−0.896743	+	0.442551i	$0.854074\pi$
$564$		0			0
$565$	8.61711e13	−	8.61711e13i	0.0629644	−	0.0629644i
$566$		0			0
$567$		−	1.29616e15i		−	0.928865i
$568$		0			0
$569$			1.37610e15i			0.967234i	0.875280	+	0.483617i	$0.160677\pi$
$569$			1.37610e15i			0.967234i	−0.875280	+	0.483617i	$0.839323\pi$
$570$		0			0
$571$	4.57011e14	−	4.57011e14i	0.315085	−	0.315085i	−0.531790	−	0.846876i	$-0.678481\pi$
$571$	4.57011e14	−	4.57011e14i	0.315085	−	0.315085i	0.846876	+	0.531790i	$0.178481\pi$
$572$		0			0
$573$	−1.29577e15	−	1.29577e15i	−0.876349	−	0.876349i
$574$		0			0
$575$	−5.17705e13			−0.0343486
$576$		0			0
$577$	1.10753e15			0.720921			0.360460	−	0.932775i	$-0.382620\pi$
$577$	1.10753e15			0.720921			0.360460	+	0.932775i	$0.382620\pi$
$578$		0			0
$579$	−1.47769e15	−	1.47769e15i	−0.943740	−	0.943740i
$580$		0			0
$581$	−3.85057e14	+	3.85057e14i	−0.241299	+	0.241299i
$582$		0			0
$583$			1.54149e15i			0.947905i
$584$		0			0
$585$		−	5.33297e13i		−	0.0321819i
$586$		0			0
$587$	−7.20142e14	+	7.20142e14i	−0.426490	+	0.426490i	−0.887431	−	0.460941i	$-0.847512\pi$
$587$	−7.20142e14	+	7.20142e14i	−0.426490	+	0.426490i	0.460941	+	0.887431i	$0.347512\pi$
$588$		0			0
$589$	3.96240e14	+	3.96240e14i	0.230316	+	0.230316i
$590$		0			0
$591$	−2.93414e15			−1.67398
$592$		0			0
$593$	1.05889e15			0.592996			0.296498	−	0.955034i	$-0.404181\pi$
$593$	1.05889e15			0.592996			0.296498	+	0.955034i	$0.404181\pi$
$594$		0			0
$595$	−1.12686e14	−	1.12686e14i	−0.0619476	−	0.0619476i
$596$		0			0
$597$	5.19552e13	−	5.19552e13i	0.0280395	−	0.0280395i
$598$		0			0
$599$			8.03403e14i			0.425682i	0.977087	+	0.212841i	$0.0682717\pi$
$599$			8.03403e14i			0.425682i	−0.977087	+	0.212841i	$0.931728\pi$
$600$		0			0
$601$		−	1.38624e15i		−	0.721155i	−0.932729	−	0.360578i	$-0.882580\pi$
$601$		−	1.38624e15i		−	0.721155i	0.932729	−	0.360578i	$-0.117420\pi$
$602$		0			0
$603$	−8.80459e14	+	8.80459e14i	−0.449742	+	0.449742i
$604$		0			0
$605$	−3.01147e13	−	3.01147e13i	−0.0151051	−	0.0151051i
$606$		0			0
$607$	−3.18636e15			−1.56948			−0.784742	−	0.619823i	$-0.787204\pi$
$607$	−3.18636e15			−1.56948			−0.784742	+	0.619823i	$0.787204\pi$
$608$		0			0
$609$	−1.21945e15			−0.589886
$610$		0			0
$611$	1.02671e13	+	1.02671e13i	0.00487776	+	0.00487776i
$612$		0			0
$613$	1.13972e15	−	1.13972e15i	0.531820	−	0.531820i	−0.389294	−	0.921114i	$-0.627281\pi$
$613$	1.13972e15	−	1.13972e15i	0.531820	−	0.531820i	0.921114	+	0.389294i	$0.127281\pi$
$614$		0			0
$615$			3.44346e14i			0.157827i
$616$		0			0
$617$			4.02609e15i			1.81265i	0.422578	+	0.906326i	$0.361125\pi$
$617$			4.02609e15i			1.81265i	−0.422578	+	0.906326i	$0.638875\pi$
$618$		0			0
$619$	−1.12455e14	+	1.12455e14i	−0.0497370	+	0.0497370i	−0.731538	−	0.681801i	$-0.761197\pi$
$619$	−1.12455e14	+	1.12455e14i	−0.0497370	+	0.0497370i	0.681801	+	0.731538i	$0.261197\pi$
$620$		0			0
$621$	−3.29849e13	−	3.29849e13i	−0.0143322	−	0.0143322i
$622$		0			0
$623$	−2.63416e15			−1.12450
$624$		0			0
$625$	−2.31051e15			−0.969098
$626$		0			0
$627$	−3.30605e14	−	3.30605e14i	−0.136250	−	0.136250i
$628$		0			0
$629$	−3.47290e15	+	3.47290e15i	−1.40642	+	1.40642i
$630$		0			0
$631$		−	3.54561e15i		−	1.41101i	−0.708706	−	0.705504i	$-0.750721\pi$
$631$		−	3.54561e15i		−	1.41101i	0.708706	−	0.705504i	$-0.249279\pi$
$632$		0			0
$633$		−	2.67910e15i		−	1.04777i
$634$		0			0
$635$	2.78618e14	−	2.78618e14i	0.107091	−	0.107091i
$636$		0			0
$637$	5.02253e14	+	5.02253e14i	0.189739	+	0.189739i
$638$		0			0
$639$	−1.62779e15			−0.604427
$640$		0			0
$641$	−3.99466e15			−1.45801			−0.729005	−	0.684509i	$-0.760017\pi$
$641$	−3.99466e15			−1.45801			−0.729005	+	0.684509i	$0.760017\pi$
$642$		0			0
$643$	7.20860e14	+	7.20860e14i	0.258637	+	0.258637i	0.824500	−	0.565863i	$-0.191457\pi$
$643$	7.20860e14	+	7.20860e14i	0.258637	+	0.258637i	−0.565863	+	0.824500i	$0.691457\pi$
$644$		0			0
$645$	4.70663e14	−	4.70663e14i	0.166009	−	0.166009i
$646$		0			0
$647$			2.38050e15i			0.825458i	0.910854	+	0.412729i	$0.135424\pi$
$647$			2.38050e15i			0.825458i	−0.910854	+	0.412729i	$0.864576\pi$
$648$		0			0
$649$			3.23229e14i			0.110196i
$650$		0			0
$651$	3.59940e15	−	3.59940e15i	1.20652	−	1.20652i
$652$		0			0
$653$	3.05366e15	+	3.05366e15i	1.00646	+	1.00646i	0.999979	+	0.00648374i	$0.00206385\pi$
$653$	3.05366e15	+	3.05366e15i	1.00646	+	1.00646i	0.00648374	+	0.999979i	$0.497936\pi$
$654$		0			0
$655$	−4.52195e14			−0.146554
$656$		0			0
$657$	8.32859e14			0.265437
$658$		0			0
$659$	3.38786e15	+	3.38786e15i	1.06183	+	1.06183i	0.997958	+	0.0638750i	$0.0203459\pi$
$659$	3.38786e15	+	3.38786e15i	1.06183	+	1.06183i	0.0638750	+	0.997958i	$0.479654\pi$
$660$		0			0
$661$	2.17225e15	−	2.17225e15i	0.669580	−	0.669580i	−0.288039	−	0.957619i	$-0.593003\pi$
$661$	2.17225e15	−	2.17225e15i	0.669580	−	0.669580i	0.957619	+	0.288039i	$0.0930032\pi$
$662$		0			0
$663$			2.83523e15i			0.859534i
$664$		0			0
$665$		−	4.44722e13i		−	0.0132608i
$666$		0			0
$667$	−5.37122e13	+	5.37122e13i	−0.0157536	+	0.0157536i
$668$		0			0
$669$	−1.95480e15	−	1.95480e15i	−0.563975	−	0.563975i
$670$		0			0
$671$	−8.78726e14			−0.249390
$672$		0			0
$673$	−2.38223e14			−0.0665121			−0.0332561	−	0.999447i	$-0.510588\pi$
$673$	−2.38223e14			−0.0665121			−0.0332561	+	0.999447i	$0.510588\pi$
$674$		0			0
$675$	−1.48781e15	−	1.48781e15i	−0.408675	−	0.408675i
$676$		0			0
$677$	1.90659e15	−	1.90659e15i	0.515252	−	0.515252i	−0.400879	−	0.916131i	$-0.631295\pi$
$677$	1.90659e15	−	1.90659e15i	0.515252	−	0.515252i	0.916131	+	0.400879i	$0.131295\pi$
$678$		0			0
$679$			3.41862e14i			0.0909007i
$680$		0			0
$681$		−	3.59706e15i		−	0.941106i
$682$		0			0
$683$	2.55329e15	−	2.55329e15i	0.657334	−	0.657334i	−0.297415	−	0.954748i	$-0.596124\pi$
$683$	2.55329e15	−	2.55329e15i	0.657334	−	0.657334i	0.954748	+	0.297415i	$0.0961243\pi$
$684$		0			0
$685$	3.89691e14	+	3.89691e14i	0.0987239	+	0.0987239i
$686$		0			0
$687$	5.20201e15			1.29691
$688$		0			0
$689$	2.60862e15			0.640037
$690$		0			0
$691$	4.73213e14	+	4.73213e14i	0.114269	+	0.114269i	0.761929	−	0.647660i	$-0.224252\pi$
$691$	4.73213e14	+	4.73213e14i	0.114269	+	0.114269i	−0.647660	+	0.761929i	$0.724252\pi$
$692$		0			0
$693$	−1.03708e15	+	1.03708e15i	−0.246479	+	0.246479i
$694$		0			0
$695$			3.82433e14i			0.0894621i
$696$		0			0
$697$		−	6.32188e15i		−	1.45568i
$698$		0			0
$699$	5.69430e15	−	5.69430e15i	1.29067	−	1.29067i
$700$		0			0
$701$	4.29380e14	+	4.29380e14i	0.0958061	+	0.0958061i	0.753385	−	0.657579i	$-0.228420\pi$
$701$	4.29380e14	+	4.29380e14i	0.0958061	+	0.0958061i	−0.657579	+	0.753385i	$0.728420\pi$
$702$		0			0
$703$	−1.37061e15			−0.301064
$704$		0			0
$705$	6.67918e12			0.00144439
$706$		0			0
$707$	1.11098e15	+	1.11098e15i	0.236538	+	0.236538i
$708$		0			0
$709$	−1.83229e14	+	1.83229e14i	−0.0384097	+	0.0384097i	−0.726051	−	0.687641i	$-0.758646\pi$
$709$	−1.83229e14	+	1.83229e14i	−0.0384097	+	0.0384097i	0.687641	+	0.726051i	$0.258646\pi$
$710$		0			0
$711$			3.80744e15i			0.785870i
$712$		0			0
$713$		−	3.17081e14i		−	0.0644433i
$714$		0			0
$715$	1.91581e14	−	1.91581e14i	0.0383415	−	0.0383415i
$716$		0			0
$717$	5.43898e15	+	5.43898e15i	1.07192	+	1.07192i
$718$		0			0
$719$	4.63852e15			0.900265			0.450133	−	0.892962i	$-0.351377\pi$
$719$	4.63852e15			0.900265			0.450133	+	0.892962i	$0.351377\pi$
$720$		0			0
$721$	3.06509e15			0.585867
$722$		0			0
$723$	1.36459e15	+	1.36459e15i	0.256887	+	0.256887i
$724$		0			0
$725$	−2.42274e15	+	2.42274e15i	−0.449208	+	0.449208i
$726$		0			0
$727$		−	3.43021e15i		−	0.626442i	−0.949680	−	0.313221i	$-0.898592\pi$
$727$		−	3.43021e15i		−	0.626442i	0.949680	−	0.313221i	$-0.101408\pi$
$728$		0			0
$729$		−	3.49140e14i		−	0.0628055i
$730$		0			0
$731$	−8.64094e15	+	8.64094e15i	−1.53114	+	1.53114i
$732$		0			0
$733$	4.05712e15	+	4.05712e15i	0.708184	+	0.708184i	0.966153	−	0.257969i	$-0.0830534\pi$
$733$	4.05712e15	+	4.05712e15i	0.708184	+	0.708184i	−0.257969	+	0.966153i	$0.583053\pi$
$734$		0			0
$735$	3.26738e14			0.0561848
$736$		0			0
$737$	−6.32591e15			−1.07165
$738$		0			0
$739$	−1.67030e15	−	1.67030e15i	−0.278772	−	0.278772i	0.553846	−	0.832619i	$-0.313159\pi$
$739$	−1.67030e15	−	1.67030e15i	−0.278772	−	0.278772i	−0.832619	+	0.553846i	$0.813159\pi$
$740$		0			0
$741$	−5.59471e14	+	5.59471e14i	−0.0919978	+	0.0919978i
$742$		0			0
$743$			4.61265e15i			0.747330i	0.927564	+	0.373665i	$0.121899\pi$
$743$			4.61265e15i			0.747330i	−0.927564	+	0.373665i	$0.878101\pi$
$744$		0			0
$745$		−	1.22052e14i		−	0.0194843i
$746$		0			0
$747$	1.08824e15	−	1.08824e15i	0.171183	−	0.171183i
$748$		0			0
$749$	9.52701e14	+	9.52701e14i	0.147675	+	0.147675i
$750$		0			0
$751$	6.38439e14			0.0975214			0.0487607	−	0.998810i	$-0.484473\pi$
$751$	6.38439e14			0.0975214			0.0487607	+	0.998810i	$0.484473\pi$
$752$		0			0
$753$	1.21101e16			1.82296
$754$		0			0
$755$	−2.10473e14	−	2.10473e14i	−0.0312239	−	0.0312239i
$756$		0			0
$757$	−3.03835e15	+	3.03835e15i	−0.444232	+	0.444232i	−0.893432	−	0.449199i	$-0.851709\pi$
$757$	−3.03835e15	+	3.03835e15i	−0.444232	+	0.444232i	0.449199	+	0.893432i	$0.351709\pi$
$758$		0			0
$759$			2.64558e14i			0.0381234i
$760$		0			0
$761$		−	2.97530e15i		−	0.422586i	−0.977423	−	0.211293i	$-0.932233\pi$
$761$		−	2.97530e15i		−	0.422586i	0.977423	−	0.211293i	$-0.0677674\pi$
$762$		0			0
$763$	−7.32242e14	+	7.32242e14i	−0.102511	+	0.102511i
$764$		0			0
$765$	3.18468e14	+	3.18468e14i	0.0439469	+	0.0439469i
$766$		0			0
$767$	5.46989e14			0.0744054
$768$		0			0
$769$	−4.50036e15			−0.603465			−0.301733	−	0.953393i	$-0.597565\pi$
$769$	−4.50036e15			−0.603465			−0.301733	+	0.953393i	$0.597565\pi$
$770$		0			0
$771$	−8.09899e15	−	8.09899e15i	−1.07061	−	1.07061i
$772$		0			0
$773$	6.33340e15	−	6.33340e15i	0.825372	−	0.825372i	−0.161500	−	0.986873i	$-0.551633\pi$
$773$	6.33340e15	−	6.33340e15i	0.825372	−	0.825372i	0.986873	+	0.161500i	$0.0516333\pi$
$774$		0			0
$775$		−	1.43022e16i		−	1.83757i
$776$		0			0
$777$			1.24504e16i			1.57714i
$778$		0			0
$779$	1.24749e15	−	1.24749e15i	0.155805	−	0.155805i
$780$		0			0
$781$	−5.84766e15	−	5.84766e15i	−0.720115	−	0.720115i
$782$		0			0
$783$	−3.08723e15			−0.374869
$784$		0			0
$785$	−1.65723e15			−0.198427
$786$		0			0
$787$	3.25291e15	+	3.25291e15i	0.384071	+	0.384071i	0.872566	−	0.488496i	$-0.162454\pi$
$787$	3.25291e15	+	3.25291e15i	0.384071	+	0.384071i	−0.488496	+	0.872566i	$0.662454\pi$
$788$		0			0
$789$	−1.70702e15	+	1.70702e15i	−0.198753	+	0.198753i
$790$		0			0
$791$			5.67159e15i			0.651230i
$792$		0			0
$793$			1.48704e15i			0.168391i
$794$		0			0
$795$	8.48510e14	−	8.48510e14i	0.0947628	−	0.0947628i
$796$		0			0
$797$	−2.11952e15	−	2.11952e15i	−0.233462	−	0.233462i	0.580674	−	0.814136i	$-0.302789\pi$
$797$	−2.11952e15	−	2.11952e15i	−0.233462	−	0.233462i	−0.814136	+	0.580674i	$0.802789\pi$
$798$		0			0
$799$	−1.22624e14			−0.0133219
$800$		0			0
$801$	7.44458e15			0.797740
$802$		0			0
$803$	2.99196e15	+	2.99196e15i	0.316242	+	0.316242i
$804$		0			0
$805$	−1.77939e13	+	1.77939e13i	−0.00185521	+	0.00185521i
$806$		0			0
$807$			2.37745e15i			0.244515i
$808$		0			0
$809$			6.90043e15i			0.700098i	0.936731	+	0.350049i	$0.113835\pi$
$809$			6.90043e15i			0.700098i	−0.936731	+	0.350049i	$0.886165\pi$
$810$		0			0
$811$	1.16275e15	−	1.16275e15i	0.116378	−	0.116378i	−0.646519	−	0.762898i	$-0.723776\pi$
$811$	1.16275e15	−	1.16275e15i	0.116378	−	0.116378i	0.762898	+	0.646519i	$0.223776\pi$
$812$		0			0
$813$	−1.11989e16	−	1.11989e16i	−1.10580	−	1.10580i
$814$		0			0
$815$	1.08203e15			0.105408
$816$		0			0
$817$	−3.41021e15			−0.327763
$818$		0			0
$819$	1.75502e15	+	1.75502e15i	0.166426	+	0.166426i
$820$		0			0
$821$	8.05348e15	−	8.05348e15i	0.753523	−	0.753523i	−0.221612	−	0.975135i	$-0.571132\pi$
$821$	8.05348e15	−	8.05348e15i	0.753523	−	0.753523i	0.975135	+	0.221612i	$0.0711319\pi$
$822$		0			0
$823$		−	1.72899e16i		−	1.59622i	−0.602510	−	0.798111i	$-0.705833\pi$
$823$		−	1.72899e16i		−	1.59622i	0.602510	−	0.798111i	$-0.294167\pi$
$824$		0			0
$825$			1.19331e16i			1.08707i
$826$		0			0
$827$	−1.23292e16	+	1.23292e16i	−1.10829	+	1.10829i	−0.114913	+	0.993376i	$0.536659\pi$
$827$	−1.23292e16	+	1.23292e16i	−1.10829	+	1.10829i	−0.993376	+	0.114913i	$0.963341\pi$
$828$		0			0
$829$	−1.23351e16	−	1.23351e16i	−1.09419	−	1.09419i	−0.995076	−	0.0991110i	$-0.968400\pi$
$829$	−1.23351e16	−	1.23351e16i	−1.09419	−	1.09419i	−0.0991110	−	0.995076i	$-0.531600\pi$
$830$		0			0
$831$	−8.31183e15			−0.727598
$832$		0			0
$833$	−5.99860e15			−0.518206
$834$		0			0
$835$	−8.02973e14	−	8.02973e14i	−0.0684582	−	0.0684582i
$836$		0			0
$837$	9.11249e15	−	9.11249e15i	0.766738	−	0.766738i
$838$		0			0
$839$			5.85813e15i			0.486484i	0.969966	+	0.243242i	$0.0782109\pi$
$839$			5.85813e15i			0.486484i	−0.969966	+	0.243242i	$0.921789\pi$
$840$		0			0
$841$		−	7.17330e15i		−	0.587951i
$842$		0			0
$843$	−7.41886e15	+	7.41886e15i	−0.600186	+	0.600186i
$844$		0			0
$845$	5.76075e14	+	5.76075e14i	0.0460010	+	0.0460010i
$846$		0			0
$847$	1.98209e15			0.156230
$848$		0			0
$849$	−1.96548e15			−0.152924
$850$		0			0
$851$	5.48397e14	+	5.48397e14i	0.0421194	+	0.0421194i
$852$		0			0
$853$	−1.14683e16	+	1.14683e16i	−0.869522	+	0.869522i	−0.992419	−	0.122898i	$-0.960781\pi$
$853$	−1.14683e16	+	1.14683e16i	−0.869522	+	0.869522i	0.122898	+	0.992419i	$0.460781\pi$
$854$		0			0
$855$			1.25686e14i			0.00940747i
$856$		0			0
$857$			3.71190e15i			0.274285i	0.990551	+	0.137142i	$0.0437918\pi$
$857$			3.71190e15i			0.274285i	−0.990551	+	0.137142i	$0.956208\pi$
$858$		0			0
$859$	−1.20180e15	+	1.20180e15i	−0.0876735	+	0.0876735i	−0.749583	−	0.661910i	$-0.769746\pi$
$859$	−1.20180e15	+	1.20180e15i	−0.0876735	+	0.0876735i	0.661910	+	0.749583i	$0.269746\pi$
$860$		0			0
$861$	−1.13321e16	−	1.13321e16i	−0.816190	−	0.816190i
$862$		0			0
$863$	−4.89836e15			−0.348331			−0.174165	−	0.984716i	$-0.555723\pi$
$863$	−4.89836e15			−0.348331			−0.174165	+	0.984716i	$0.555723\pi$
$864$		0			0
$865$	−1.46168e15			−0.102627
$866$		0			0
$867$	−4.32506e15	−	4.32506e15i	−0.299839	−	0.299839i
$868$		0			0
$869$	−1.36778e16	+	1.36778e16i	−0.936287	+	0.936287i
$870$		0			0
$871$			1.07051e16i			0.723589i
$872$		0			0
$873$		−	9.66161e14i		−	0.0644868i
$874$		0			0
$875$	−1.61360e15	+	1.61360e15i	−0.106353	+	0.106353i
$876$		0			0
$877$	3.94432e15	+	3.94432e15i	0.256729	+	0.256729i	0.823722	−	0.566993i	$-0.191894\pi$
$877$	3.94432e15	+	3.94432e15i	0.256729	+	0.256729i	−0.566993	+	0.823722i	$0.691894\pi$
$878$		0			0
$879$	2.83460e16			1.82202
$880$		0			0
$881$	−8.41637e15			−0.534266			−0.267133	−	0.963660i	$-0.586076\pi$
$881$	−8.41637e15			−0.534266			−0.267133	+	0.963660i	$0.586076\pi$
$882$		0			0
$883$	4.32184e15	+	4.32184e15i	0.270947	+	0.270947i	0.829482	−	0.558534i	$-0.188636\pi$
$883$	4.32184e15	+	4.32184e15i	0.270947	+	0.270947i	−0.558534	+	0.829482i	$0.688636\pi$
$884$		0			0
$885$	1.77920e14	−	1.77920e14i	0.0110163	−	0.0110163i
$886$		0			0
$887$		−	2.87494e16i		−	1.75812i	−0.476707	−	0.879062i	$-0.658170\pi$
$887$		−	2.87494e16i		−	1.75812i	0.476707	−	0.879062i	$-0.341830\pi$
$888$		0			0
$889$			1.83380e16i			1.10762i
$890$		0			0
$891$	−1.31596e16	+	1.31596e16i	−0.785081	+	0.785081i
$892$		0			0
$893$	−2.41972e13	−	2.41972e13i	−0.00142587	−	0.00142587i
$894$		0			0
$895$	−1.31505e15			−0.0765446
$896$		0			0
$897$	4.47703e14			0.0257414
$898$		0			0
$899$	−1.48387e16	−	1.48387e16i	−0.842784	−	0.842784i
$900$		0			0
$901$	−1.55779e16	+	1.55779e16i	−0.874020	+	0.874020i
$902$		0			0
$903$			3.09780e16i			1.71700i
$904$		0			0
$905$		−	2.39269e15i		−	0.131014i
$906$		0			0
$907$	5.17663e15	−	5.17663e15i	0.280031	−	0.280031i	−0.553090	−	0.833121i	$-0.686551\pi$
$907$	5.17663e15	−	5.17663e15i	0.280031	−	0.280031i	0.833121	+	0.553090i	$0.186551\pi$
$908$		0			0
$909$	−3.13983e15	−	3.13983e15i	−0.167805	−	0.167805i
$910$		0			0
$911$	2.22340e16			1.17400			0.586998	−	0.809588i	$-0.300310\pi$
$911$	2.22340e16			1.17400			0.586998	+	0.809588i	$0.300310\pi$
$912$		0			0
$913$	7.81874e15			0.407894
$914$		0			0
$915$	4.83691e14	+	4.83691e14i	0.0249317	+	0.0249317i
$916$		0			0
$917$	1.48812e16	−	1.48812e16i	0.757893	−	0.757893i
$918$		0			0
$919$		−	1.58068e16i		−	0.795444i	−0.917506	−	0.397722i	$-0.869801\pi$
$919$		−	1.58068e16i		−	0.795444i	0.917506	−	0.397722i	$-0.130199\pi$
$920$		0			0
$921$		−	2.38390e16i		−	1.18539i
$922$		0			0
$923$	−9.89580e15	+	9.89580e15i	−0.486230	+	0.486230i
$924$		0			0
$925$	2.47359e16	+	2.47359e16i	1.20102	+	1.20102i
$926$		0			0
$927$	−8.66246e15			−0.415626
$928$		0			0
$929$	3.46893e16			1.64479			0.822393	−	0.568920i	$-0.192639\pi$
$929$	3.46893e16			1.64479			0.822393	+	0.568920i	$0.192639\pi$
$930$		0			0
$931$	−1.18370e15	−	1.18370e15i	−0.0554647	−	0.0554647i
$932$		0			0
$933$	1.95696e16	−	1.95696e16i	0.906220	−	0.906220i
$934$		0			0
$935$			2.28813e15i			0.104717i
$936$		0			0
$937$		−	2.05502e16i		−	0.929496i	−0.885443	−	0.464748i	$-0.846145\pi$
$937$		−	2.05502e16i		−	0.929496i	0.885443	−	0.464748i	$-0.153855\pi$
$938$		0			0
$939$	2.72718e16	−	2.72718e16i	1.21914	−	1.21914i
$940$		0			0
$941$	1.82034e16	+	1.82034e16i	0.804286	+	0.804286i	0.983762	−	0.179476i	$-0.0574402\pi$
$941$	1.82034e16	+	1.82034e16i	0.804286	+	0.804286i	−0.179476	+	0.983762i	$0.557440\pi$
$942$		0			0
$943$	−9.98271e14			−0.0435948
$944$		0			0
$945$	−1.02274e15			−0.0441460
$946$		0			0
$947$	−2.56323e15	−	2.56323e15i	−0.109361	−	0.109361i	0.650309	−	0.759670i	$-0.274640\pi$
$947$	−2.56323e15	−	2.56323e15i	−0.109361	−	0.109361i	−0.759670	+	0.650309i	$0.774640\pi$
$948$		0			0
$949$	5.06319e15	−	5.06319e15i	0.213530	−	0.213530i
$950$		0			0
$951$		−	4.74811e15i		−	0.197937i
$952$		0			0
$953$			7.68907e15i			0.316857i	0.987370	+	0.158428i	$0.0506427\pi$
$953$			7.68907e15i			0.316857i	−0.987370	+	0.158428i	$0.949357\pi$
$954$		0			0
$955$	−1.76966e15	+	1.76966e15i	−0.0720892	+	0.0720892i
$956$		0			0
$957$	1.23807e16	+	1.23807e16i	0.498574	+	0.498574i
$958$		0			0
$959$	−2.56486e16			−1.02108
$960$		0			0
$961$	6.21890e16			2.44757
$962$		0			0
$963$	−2.69249e15	−	2.69249e15i	−0.104764	−	0.104764i
$964$		0			0
$965$	−2.01811e15	+	2.01811e15i	−0.0776328	+	0.0776328i
$966$		0			0
$967$		−	2.35131e16i		−	0.894260i	−0.894469	−	0.447130i	$-0.852446\pi$
$967$		−	2.35131e16i		−	0.894260i	0.894469	−	0.447130i	$-0.147554\pi$
$968$		0			0
$969$		−	6.68198e15i		−	0.251261i
$970$		0			0
$971$	2.96572e16	−	2.96572e16i	1.10262	−	1.10262i	0.108522	−	0.994094i	$-0.465388\pi$
$971$	2.96572e16	−	2.96572e16i	1.10262	−	1.10262i	0.994094	−	0.108522i	$-0.0346117\pi$
$972$		0			0
$973$	−1.25855e16	−	1.25855e16i	−0.462645	−	0.462645i
$974$		0			0
$975$	2.01940e16			0.734003
$976$		0			0
$977$	−3.19671e16			−1.14890			−0.574450	−	0.818539i	$-0.694784\pi$
$977$	−3.19671e16			−1.14890			−0.574450	+	0.818539i	$0.694784\pi$
$978$		0			0
$979$	2.67439e16	+	2.67439e16i	0.950429	+	0.950429i
$980$		0			0
$981$	2.06944e15	−	2.06944e15i	0.0727233	−	0.0727233i
$982$		0			0
$983$			3.59807e16i			1.25033i	0.780492	+	0.625166i	$0.214969\pi$
$983$			3.59807e16i			1.25033i	−0.780492	+	0.625166i	$0.785031\pi$
$984$		0			0
$985$			4.00721e15i			0.137703i
$986$		0			0
$987$	−2.19804e14	+	2.19804e14i	−0.00746951	+	0.00746951i
$988$		0			0
$989$	1.36447e15	+	1.36447e15i	0.0458547	+	0.0458547i
$990$		0			0
$991$	2.28338e16			0.758881			0.379441	−	0.925216i	$-0.376116\pi$
$991$	2.28338e16			0.758881			0.379441	+	0.925216i	$0.376116\pi$
$992$		0			0
$993$	−4.26785e16			−1.40278
$994$		0			0
$995$	−7.09562e13	−	7.09562e13i	−0.00230655	−	0.00230655i
$996$		0			0
$997$	−2.26548e16	+	2.26548e16i	−0.728346	+	0.728346i	−0.970290	−	0.241945i	$-0.922215\pi$
$997$	−2.26548e16	+	2.26548e16i	−0.728346	+	0.728346i	0.241945	+	0.970290i	$0.422215\pi$
$998$		0			0
$999$			3.15204e16i			1.00226i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.12.e.a.17.5		42
4.3	odd	2		16.12.e.a.13.14	yes	42
8.3	odd	2		128.12.e.b.33.5		42
8.5	even	2		128.12.e.a.33.17		42
16.3	odd	4		128.12.e.b.97.5		42
16.5	even	4	inner	64.12.e.a.49.5		42
16.11	odd	4		16.12.e.a.5.14	✓	42
16.13	even	4		128.12.e.a.97.17		42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.12.e.a.5.14	✓	42	16.11	odd	4
16.12.e.a.13.14	yes	42	4.3	odd	2
64.12.e.a.17.5		42	1.1	even	1	trivial
64.12.e.a.49.5		42	16.5	even	4	inner
128.12.e.a.33.17		42	8.5	even	2
128.12.e.a.97.17		42	16.13	even	4
128.12.e.b.33.5		42	8.3	odd	2
128.12.e.b.97.5		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)

\(f(q)\)	\(=\)	\(q+(-367.824 - 367.824i) q^{3} +(-502.344 + 502.344i) q^{5} -33063.2i q^{7} +93442.1i q^{9} +O(q^{10})\)	\(q+(-367.824 - 367.824i) q^{3} +(-502.344 + 502.344i) q^{5} -33063.2i q^{7} +93442.1i q^{9} +(-335681. + 335681. i) q^{11} +(568061. + 568061. i) q^{13} +369548. q^{15} -6.78457e6 q^{17} +(-1.33879e6 - 1.33879e6i) q^{19} +(-1.21614e7 + 1.21614e7i) q^{21} +1.07133e6i q^{23} +4.83234e7i q^{25} +(-3.07887e7 + 3.07887e7i) q^{27} +(5.01359e7 + 5.01359e7i) q^{29} -2.95969e8 q^{31} +2.46943e8 q^{33} +(1.66091e7 + 1.66091e7i) q^{35} +(5.11883e8 - 5.11883e8i) q^{37} -4.17893e8i q^{39} +9.31803e8i q^{41} +(1.27362e9 - 1.27362e9i) q^{43} +(-4.69401e7 - 4.69401e7i) q^{45} +1.80739e7 q^{47} +8.84154e8 q^{49} +(2.49553e9 + 2.49553e9i) q^{51} +(2.29607e9 - 2.29607e9i) q^{53} -3.37255e8i q^{55} +9.84878e8i q^{57} +(4.81453e8 - 4.81453e8i) q^{59} +(1.30887e9 + 1.30887e9i) q^{61} +3.08949e9 q^{63} -5.70724e8 q^{65} +(9.42251e9 + 9.42251e9i) q^{67} +(3.94062e8 - 3.94062e8i) q^{69} +1.74203e10i q^{71} -8.91310e9i q^{73} +(1.77745e10 - 1.77745e10i) q^{75} +(1.10987e10 + 1.10987e10i) q^{77} +4.07466e10 q^{79} +3.92026e10 q^{81} +(-1.16461e10 - 1.16461e10i) q^{83} +(3.40819e9 - 3.40819e9i) q^{85} -3.68824e10i q^{87} -7.96706e10i q^{89} +(1.87819e10 - 1.87819e10i) q^{91} +(1.08864e11 + 1.08864e11i) q^{93} +1.34507e9 q^{95} -1.03397e10 q^{97} +(-3.13667e10 - 3.13667e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} - 2 q^{5}+O(q^{10}) \) 42 * q + 2 * q^3 - 2 * q^5	\( 42 q + 2 q^{3} - 2 q^{5} + 540846 q^{11} - 2 q^{13} + 6075004 q^{15} - 4 q^{17} + 11291290 q^{19} + 354292 q^{21} + 66463304 q^{27} + 77673206 q^{29} - 343549808 q^{31} - 4 q^{33} + 434731684 q^{35} - 522762058 q^{37} - 3824193658 q^{43} + 97301954 q^{45} + 4586900144 q^{47} - 8474257474 q^{49} - 7074245796 q^{51} - 2100608058 q^{53} - 955824746 q^{59} + 2150827022 q^{61} - 27758037828 q^{63} - 1884965292 q^{65} + 3186519018 q^{67} - 16193060732 q^{69} - 28890034486 q^{75} - 22711870540 q^{77} - 48011833792 q^{79} - 90656394430 q^{81} - 55713221118 q^{83} - 84575506252 q^{85} + 147369662716 q^{91} - 69689773328 q^{93} - 375702304500 q^{95} - 4 q^{97} + 286271331106 q^{99}+O(q^{100}) \) 42 * q + 2 * q^3 - 2 * q^5 + 540846 * q^11 - 2 * q^13 + 6075004 * q^15 - 4 * q^17 + 11291290 * q^19 + 354292 * q^21 + 66463304 * q^27 + 77673206 * q^29 - 343549808 * q^31 - 4 * q^33 + 434731684 * q^35 - 522762058 * q^37 - 3824193658 * q^43 + 97301954 * q^45 + 4586900144 * q^47 - 8474257474 * q^49 - 7074245796 * q^51 - 2100608058 * q^53 - 955824746 * q^59 + 2150827022 * q^61 - 27758037828 * q^63 - 1884965292 * q^65 + 3186519018 * q^67 - 16193060732 * q^69 - 28890034486 * q^75 - 22711870540 * q^77 - 48011833792 * q^79 - 90656394430 * q^81 - 55713221118 * q^83 - 84575506252 * q^85 + 147369662716 * q^91 - 69689773328 * q^93 - 375702304500 * q^95 - 4 * q^97 + 286271331106 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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