LMFDB - Embedded newform 128.12.e.b.33.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("128.33");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	128.e (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$98.3479271116$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			33.17
Character	$\chi$	$=$	128.33
Dual form			128.12.e.b.97.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(296.568 + 296.568i) q^{3} +(2867.98 - 2867.98i) q^{5} +8380.90i q^{7} -1242.24i q^{9} +O(q^{10})$	\(q+(296.568 + 296.568i) q^{3} +(2867.98 - 2867.98i) q^{5} +8380.90i q^{7} -1242.24i q^{9} +(-84515.5 + 84515.5i) q^{11} +(385486. + 385486. i) q^{13} +1.70110e6 q^{15} +1.56551e6 q^{17} +(-9.59253e6 - 9.59253e6i) q^{19} +(-2.48550e6 + 2.48550e6i) q^{21} +3.88214e7i q^{23} +3.23775e7i q^{25} +(5.29045e7 - 5.29045e7i) q^{27} +(8.81048e7 + 8.81048e7i) q^{29} -7.23333e7 q^{31} -5.01291e7 q^{33} +(2.40363e7 + 2.40363e7i) q^{35} +(9.98585e7 - 9.98585e7i) q^{37} +2.28645e8i q^{39} +1.13304e9i q^{41} +(1.05585e9 - 1.05585e9i) q^{43} +(-3.56273e6 - 3.56273e6i) q^{45} +1.33450e9 q^{47} +1.90709e9 q^{49} +(4.64281e8 + 4.64281e8i) q^{51} +(-2.50213e9 + 2.50213e9i) q^{53} +4.84778e8i q^{55} -5.68967e9i q^{57} +(3.81835e9 - 3.81835e9i) q^{59} +(7.73084e9 + 7.73084e9i) q^{61} +1.04111e7 q^{63} +2.21114e9 q^{65} +(-2.91020e9 - 2.91020e9i) q^{67} +(-1.15132e10 + 1.15132e10i) q^{69} +1.77198e10i q^{71} -2.04116e10i q^{73} +(-9.60211e9 + 9.60211e9i) q^{75} +(-7.08316e8 - 7.08316e8i) q^{77} -3.60858e10 q^{79} +3.11595e10 q^{81} +(-5.73137e9 - 5.73137e9i) q^{83} +(4.48987e9 - 4.48987e9i) q^{85} +5.22581e10i q^{87} +1.07134e10i q^{89} +(-3.23072e9 + 3.23072e9i) q^{91} +(-2.14517e10 - 2.14517e10i) q^{93} -5.50224e10 q^{95} -7.36209e9 q^{97} +(1.04989e8 + 1.04989e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 2 q^{3} + 2 q^{5}+O(q^{10}) $ 42 * q + 2 * q^3 + 2 * q^5	$ 42 q + 2 q^{3} + 2 q^{5} + 540846 q^{11} + 2 q^{13} - 6075004 q^{15} - 4 q^{17} + 11291290 q^{19} - 354292 q^{21} + 66463304 q^{27} - 77673206 q^{29} + 343549808 q^{31} - 4 q^{33} + 434731684 q^{35} + 522762058 q^{37} - 3824193658 q^{43} - 97301954 q^{45} - 4586900144 q^{47} - 8474257474 q^{49} - 7074245796 q^{51} + 2100608058 q^{53} - 955824746 q^{59} - 2150827022 q^{61} + 27758037828 q^{63} - 1884965292 q^{65} + 3186519018 q^{67} + 16193060732 q^{69} - 28890034486 q^{75} + 22711870540 q^{77} + 48011833792 q^{79} - 90656394430 q^{81} - 55713221118 q^{83} + 84575506252 q^{85} + 147369662716 q^{91} + 69689773328 q^{93} + 375702304500 q^{95} - 4 q^{97} + 286271331106 q^{99}+O(q^{100}) $ 42 * q + 2 * q^3 + 2 * q^5 + 540846 * q^11 + 2 * q^13 - 6075004 * q^15 - 4 * q^17 + 11291290 * q^19 - 354292 * q^21 + 66463304 * q^27 - 77673206 * q^29 + 343549808 * q^31 - 4 * q^33 + 434731684 * q^35 + 522762058 * q^37 - 3824193658 * q^43 - 97301954 * q^45 - 4586900144 * q^47 - 8474257474 * q^49 - 7074245796 * q^51 + 2100608058 * q^53 - 955824746 * q^59 - 2150827022 * q^61 + 27758037828 * q^63 - 1884965292 * q^65 + 3186519018 * q^67 + 16193060732 * q^69 - 28890034486 * q^75 + 22711870540 * q^77 + 48011833792 * q^79 - 90656394430 * q^81 - 55713221118 * q^83 + 84575506252 * q^85 + 147369662716 * q^91 + 69689773328 * q^93 + 375702304500 * q^95 - 4 * q^97 + 286271331106 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	296.568	+	296.568i	0.704623	+	0.704623i	0.965399	−	0.260776i	$-0.0839785\pi$
$3$	296.568	+	296.568i	0.704623	+	0.704623i	−0.260776	+	0.965399i	$0.583978\pi$
$4$		0			0
$5$	2867.98	−	2867.98i	0.410432	−	0.410432i	−0.471457	−	0.881889i	$-0.656272\pi$
$5$	2867.98	−	2867.98i	0.410432	−	0.410432i	0.881889	+	0.471457i	$0.156272\pi$
$6$		0			0
$7$			8380.90i			0.188474i	0.995550	+	0.0942370i	$0.0300411\pi$
$7$			8380.90i			0.188474i	−0.995550	+	0.0942370i	$0.969959\pi$
$8$		0			0
$9$		−	1242.24i		−	0.00701249i
$10$		0			0
$11$	−84515.5	+	84515.5i	−0.158226	+	0.158226i	−0.781780	−	0.623554i	$-0.785688\pi$
$11$	−84515.5	+	84515.5i	−0.158226	+	0.158226i	0.623554	+	0.781780i	$0.285688\pi$
$12$		0			0
$13$	385486.	+	385486.i	0.287952	+	0.287952i	0.836270	−	0.548318i	$-0.184732\pi$
$13$	385486.	+	385486.i	0.287952	+	0.287952i	−0.548318	+	0.836270i	$0.684732\pi$
$14$		0			0
$15$	1.70110e6			0.578400
$16$		0			0
$17$	1.56551e6			0.267416			0.133708	−	0.991021i	$-0.457311\pi$
$17$	1.56551e6			0.267416			0.133708	+	0.991021i	$0.457311\pi$
$18$		0			0
$19$	−9.59253e6	−	9.59253e6i	−0.888768	−	0.888768i	0.105637	−	0.994405i	$-0.466312\pi$
$19$	−9.59253e6	−	9.59253e6i	−0.888768	−	0.888768i	−0.994405	+	0.105637i	$0.966312\pi$
$20$		0			0
$21$	−2.48550e6	+	2.48550e6i	−0.132803	+	0.132803i
$22$		0			0
$23$			3.88214e7i			1.25767i	0.777537	+	0.628837i	$0.216469\pi$
$23$			3.88214e7i			1.25767i	−0.777537	+	0.628837i	$0.783531\pi$
$24$		0			0
$25$			3.23775e7i			0.663091i
$26$		0			0
$27$	5.29045e7	−	5.29045e7i	0.709564	−	0.709564i
$28$		0			0
$29$	8.81048e7	+	8.81048e7i	0.797647	+	0.797647i	0.982724	−	0.185077i	$-0.0592535\pi$
$29$	8.81048e7	+	8.81048e7i	0.797647	+	0.797647i	−0.185077	+	0.982724i	$0.559254\pi$
$30$		0			0
$31$	−7.23333e7			−0.453784			−0.226892	−	0.973920i	$-0.572856\pi$
$31$	−7.23333e7			−0.453784			−0.226892	+	0.973920i	$0.572856\pi$
$32$		0			0
$33$	−5.01291e7			−0.222979
$34$		0			0
$35$	2.40363e7	+	2.40363e7i	0.0773558	+	0.0773558i
$36$		0			0
$37$	9.98585e7	−	9.98585e7i	0.236742	−	0.236742i	−0.578758	−	0.815500i	$-0.696462\pi$
$37$	9.98585e7	−	9.98585e7i	0.236742	−	0.236742i	0.815500	+	0.578758i	$0.196462\pi$
$38$		0			0
$39$			2.28645e8i			0.405795i
$40$		0			0
$41$			1.13304e9i			1.52733i	0.645611	+	0.763667i	$0.276603\pi$
$41$			1.13304e9i			1.52733i	−0.645611	+	0.763667i	$0.723397\pi$
$42$		0			0
$43$	1.05585e9	−	1.05585e9i	1.09528	−	1.09528i	0.100329	−	0.994954i	$-0.468010\pi$
$43$	1.05585e9	−	1.05585e9i	1.09528	−	1.09528i	0.994954	−	0.100329i	$-0.0319897\pi$
$44$		0			0
$45$	−3.56273e6	−	3.56273e6i	−0.00287815	−	0.00287815i
$46$		0			0
$47$	1.33450e9			0.848750			0.424375	−	0.905486i	$-0.360494\pi$
$47$	1.33450e9			0.848750			0.424375	+	0.905486i	$0.360494\pi$
$48$		0			0
$49$	1.90709e9			0.964478
$50$		0			0
$51$	4.64281e8	+	4.64281e8i	0.188428	+	0.188428i
$52$		0			0
$53$	−2.50213e9	+	2.50213e9i	−0.821850	+	0.821850i	−0.986373	−	0.164523i	$-0.947392\pi$
$53$	−2.50213e9	+	2.50213e9i	−0.821850	+	0.821850i	0.164523	+	0.986373i	$0.447392\pi$
$54$		0			0
$55$			4.84778e8i			0.129882i
$56$		0			0
$57$		−	5.68967e9i		−	1.25249i
$58$		0			0
$59$	3.81835e9	−	3.81835e9i	0.695329	−	0.695329i	−0.268071	−	0.963399i	$-0.586386\pi$
$59$	3.81835e9	−	3.81835e9i	0.695329	−	0.695329i	0.963399	+	0.268071i	$0.0863861\pi$
$60$		0			0
$61$	7.73084e9	+	7.73084e9i	1.17196	+	1.17196i	0.981742	+	0.190218i	$0.0609193\pi$
$61$	7.73084e9	+	7.73084e9i	1.17196	+	1.17196i	0.190218	+	0.981742i	$0.439081\pi$
$62$		0			0
$63$	1.04111e7			0.00132167
$64$		0			0
$65$	2.21114e9			0.236370
$66$		0			0
$67$	−2.91020e9	−	2.91020e9i	−0.263337	−	0.263337i	0.563071	−	0.826408i	$-0.309620\pi$
$67$	−2.91020e9	−	2.91020e9i	−0.263337	−	0.263337i	−0.826408	+	0.563071i	$0.809620\pi$
$68$		0			0
$69$	−1.15132e10	+	1.15132e10i	−0.886186	+	0.886186i
$70$		0			0
$71$			1.77198e10i			1.16557i	0.812628	+	0.582783i	$0.198036\pi$
$71$			1.77198e10i			1.16557i	−0.812628	+	0.582783i	$0.801964\pi$
$72$		0			0
$73$		−	2.04116e10i		−	1.15239i	−0.817311	−	0.576197i	$-0.804536\pi$
$73$		−	2.04116e10i		−	1.15239i	0.817311	−	0.576197i	$-0.195464\pi$
$74$		0			0
$75$	−9.60211e9	+	9.60211e9i	−0.467229	+	0.467229i
$76$		0			0
$77$	−7.08316e8	−	7.08316e8i	−0.0298214	−	0.0298214i
$78$		0			0
$79$	−3.60858e10			−1.31943			−0.659717	−	0.751514i	$-0.729324\pi$
$79$	−3.60858e10			−1.31943			−0.659717	+	0.751514i	$0.729324\pi$
$80$		0			0
$81$	3.11595e10			0.992938
$82$		0			0
$83$	−5.73137e9	−	5.73137e9i	−0.159709	−	0.159709i	0.622729	−	0.782438i	$-0.286024\pi$
$83$	−5.73137e9	−	5.73137e9i	−0.159709	−	0.159709i	−0.782438	+	0.622729i	$0.786024\pi$
$84$		0			0
$85$	4.48987e9	−	4.48987e9i	0.109756	−	0.109756i
$86$		0			0
$87$			5.22581e10i			1.12408i
$88$		0			0
$89$			1.07134e10i			0.203367i	0.994817	+	0.101684i	$0.0324230\pi$
$89$			1.07134e10i			0.203367i	−0.994817	+	0.101684i	$0.967577\pi$
$90$		0			0
$91$	−3.23072e9	+	3.23072e9i	−0.0542715	+	0.0542715i
$92$		0			0
$93$	−2.14517e10	−	2.14517e10i	−0.319746	−	0.319746i
$94$		0			0
$95$	−5.50224e10			−0.729558
$96$		0			0
$97$	−7.36209e9			−0.0870475			−0.0435238	−	0.999052i	$-0.513858\pi$
$97$	−7.36209e9			−0.0870475			−0.0435238	+	0.999052i	$0.513858\pi$
$98$		0			0
$99$	1.04989e8	+	1.04989e8i	0.00110956	+	0.00110956i
$100$		0			0
$101$	8.80812e10	−	8.80812e10i	0.833903	−	0.833903i	−0.154145	−	0.988048i	$-0.549262\pi$
$101$	8.80812e10	−	8.80812e10i	0.833903	−	0.833903i	0.988048	+	0.154145i	$0.0492623\pi$
$102$		0			0
$103$			1.00874e11i			0.857383i	0.903451	+	0.428691i	$0.141025\pi$
$103$			1.00874e11i			0.857383i	−0.903451	+	0.428691i	$0.858975\pi$
$104$		0			0
$105$			1.42568e10i			0.109013i
$106$		0			0
$107$	−3.90961e10	+	3.90961e10i	−0.269478	+	0.269478i	−0.828890	−	0.559412i	$-0.811027\pi$
$107$	−3.90961e10	+	3.90961e10i	−0.269478	+	0.269478i	0.559412	+	0.828890i	$0.311027\pi$
$108$		0			0
$109$	1.52858e11	+	1.52858e11i	0.951576	+	0.951576i	0.998881	−	0.0473045i	$-0.0150631\pi$
$109$	1.52858e11	+	1.52858e11i	0.951576	+	0.951576i	−0.0473045	+	0.998881i	$0.515063\pi$
$110$		0			0
$111$	5.92296e10			0.333628
$112$		0			0
$113$	8.86408e10			0.452587			0.226293	−	0.974059i	$-0.427339\pi$
$113$	8.86408e10			0.452587			0.226293	+	0.974059i	$0.427339\pi$
$114$		0			0
$115$	1.11339e11	+	1.11339e11i	0.516190	+	0.516190i
$116$		0			0
$117$	4.78867e8	−	4.78867e8i	0.00201926	−	0.00201926i
$118$		0			0
$119$			1.31204e10i			0.0504011i
$120$		0			0
$121$			2.71026e11i			0.949929i
$122$		0			0
$123$	−3.36023e11	+	3.36023e11i	−1.07619	+	1.07619i
$124$		0			0
$125$	2.32896e11	+	2.32896e11i	0.682586	+	0.682586i
$126$		0			0
$127$	1.85470e11			0.498142			0.249071	−	0.968485i	$-0.419875\pi$
$127$	1.85470e11			0.498142			0.249071	+	0.968485i	$0.419875\pi$
$128$		0			0
$129$	6.26263e11			1.54352
$130$		0			0
$131$	1.99872e11	+	1.99872e11i	0.452646	+	0.452646i	0.896232	−	0.443586i	$-0.146294\pi$
$131$	1.99872e11	+	1.99872e11i	0.452646	+	0.452646i	−0.443586	+	0.896232i	$0.646294\pi$
$132$		0			0
$133$	8.03940e10	−	8.03940e10i	0.167510	−	0.167510i
$134$		0			0
$135$		−	3.03458e11i		−	0.582456i
$136$		0			0
$137$			1.03458e12i			1.83147i	0.401786	+	0.915734i	$0.368390\pi$
$137$			1.03458e12i			1.83147i	−0.401786	+	0.915734i	$0.631610\pi$
$138$		0			0
$139$	−7.75928e11	+	7.75928e11i	−1.26835	+	1.26835i	−0.321415	+	0.946938i	$0.604158\pi$
$139$	−7.75928e11	+	7.75928e11i	−1.26835	+	1.26835i	−0.946938	+	0.321415i	$0.895842\pi$
$140$		0			0
$141$	3.95769e11	+	3.95769e11i	0.598049	+	0.598049i
$142$		0			0
$143$	−6.51591e10			−0.0911228
$144$		0			0
$145$	5.05366e11			0.654760
$146$		0			0
$147$	5.65580e11	+	5.65580e11i	0.679593	+	0.679593i
$148$		0			0
$149$	8.48328e11	−	8.48328e11i	0.946323	−	0.946323i	−0.0523077	−	0.998631i	$-0.516658\pi$
$149$	8.48328e11	−	8.48328e11i	0.946323	−	0.946323i	0.998631	+	0.0523077i	$0.0166577\pi$
$150$		0			0
$151$			8.18468e11i			0.848454i	0.905556	+	0.424227i	$0.139454\pi$
$151$			8.18468e11i			0.848454i	−0.905556	+	0.424227i	$0.860546\pi$
$152$		0			0
$153$		−	1.94475e9i		−	0.00187526i
$154$		0			0
$155$	−2.07451e11	+	2.07451e11i	−0.186247	+	0.186247i
$156$		0			0
$157$	5.92527e11	+	5.92527e11i	0.495747	+	0.495747i	0.910111	−	0.414364i	$-0.135996\pi$
$157$	5.92527e11	+	5.92527e11i	0.495747	+	0.495747i	−0.414364	+	0.910111i	$0.635996\pi$
$158$		0			0
$159$	−1.48410e12			−1.15819
$160$		0			0
$161$	−3.25358e11			−0.237039
$162$		0			0
$163$	−2.74040e11	−	2.74040e11i	−0.186544	−	0.186544i	0.607656	−	0.794200i	$-0.292110\pi$
$163$	−2.74040e11	−	2.74040e11i	−0.186544	−	0.186544i	−0.794200	+	0.607656i	$0.792110\pi$
$164$		0			0
$165$	−1.43770e11	+	1.43770e11i	−0.0915177	+	0.0915177i
$166$		0			0
$167$			2.53745e12i			1.51167i	0.654762	+	0.755836i	$0.272769\pi$
$167$			2.53745e12i			1.51167i	−0.654762	+	0.755836i	$0.727231\pi$
$168$		0			0
$169$		−	1.49496e12i		−	0.834167i
$170$		0			0
$171$	−1.19162e10	+	1.19162e10i	−0.00623247	+	0.00623247i
$172$		0			0
$173$	−5.71348e11	−	5.71348e11i	−0.280315	−	0.280315i	0.552919	−	0.833235i	$-0.313514\pi$
$173$	−5.71348e11	−	5.71348e11i	−0.280315	−	0.280315i	−0.833235	+	0.552919i	$0.813514\pi$
$174$		0			0
$175$	−2.71352e11			−0.124975
$176$		0			0
$177$	2.26480e12			0.979889
$178$		0			0
$179$	−1.62660e12	−	1.62660e12i	−0.661592	−	0.661592i	0.294163	−	0.955755i	$-0.404959\pi$
$179$	−1.62660e12	−	1.62660e12i	−0.661592	−	0.661592i	−0.955755	+	0.294163i	$0.904959\pi$
$180$		0			0
$181$	5.16199e11	−	5.16199e11i	0.197508	−	0.197508i	−0.601423	−	0.798931i	$-0.705399\pi$
$181$	5.16199e11	−	5.16199e11i	0.197508	−	0.197508i	0.798931	+	0.601423i	$0.205399\pi$
$182$		0			0
$183$			4.58543e12i			1.65158i
$184$		0			0
$185$		−	5.72785e11i		−	0.194333i
$186$		0			0
$187$	−1.32310e11	+	1.32310e11i	−0.0423121	+	0.0423121i
$188$		0			0
$189$	4.43387e11	+	4.43387e11i	0.133734	+	0.133734i
$190$		0			0
$191$	−2.22938e12			−0.634602			−0.317301	−	0.948325i	$-0.602776\pi$
$191$	−2.22938e12			−0.634602			−0.317301	+	0.948325i	$0.602776\pi$
$192$		0			0
$193$	1.44625e11			0.0388758			0.0194379	−	0.999811i	$-0.493812\pi$
$193$	1.44625e11			0.0388758			0.0194379	+	0.999811i	$0.493812\pi$
$194$		0			0
$195$	6.55751e11	+	6.55751e11i	0.166552	+	0.166552i
$196$		0			0
$197$	−2.27490e12	+	2.27490e12i	−0.546257	+	0.546257i	−0.925356	−	0.379099i	$-0.876234\pi$
$197$	−2.27490e12	+	2.27490e12i	−0.546257	+	0.546257i	0.379099	+	0.925356i	$0.376234\pi$
$198$		0			0
$199$		−	3.80350e12i		−	0.863956i	−0.901884	−	0.431978i	$-0.857816\pi$
$199$		−	3.80350e12i		−	0.863956i	0.901884	−	0.431978i	$-0.142184\pi$
$200$		0			0
$201$		−	1.72614e12i		−	0.371106i
$202$		0			0
$203$	−7.38398e11	+	7.38398e11i	−0.150336	+	0.150336i
$204$		0			0
$205$	3.24954e12	+	3.24954e12i	0.626867	+	0.626867i
$206$		0			0
$207$	4.82255e10			0.00881942
$208$		0			0
$209$	1.62143e12			0.281252
$210$		0			0
$211$	4.90777e12	+	4.90777e12i	0.807849	+	0.807849i	0.984308	−	0.176459i	$-0.0564642\pi$
$211$	4.90777e12	+	4.90777e12i	0.807849	+	0.807849i	−0.176459	+	0.984308i	$0.556464\pi$
$212$		0			0
$213$	−5.25511e12	+	5.25511e12i	−0.821285	+	0.821285i
$214$		0			0
$215$		−	6.05633e12i		−	0.899080i
$216$		0			0
$217$		−	6.06218e11i		−	0.0855264i
$218$		0			0
$219$	6.05341e12	−	6.05341e12i	0.812003	−	0.812003i
$220$		0			0
$221$	6.03484e11	+	6.03484e11i	0.0770031	+	0.0770031i
$222$		0			0
$223$	4.65341e12			0.565060			0.282530	−	0.959259i	$-0.408826\pi$
$223$	4.65341e12			0.565060			0.282530	+	0.959259i	$0.408826\pi$
$224$		0			0
$225$	4.02206e10			0.00464992
$226$		0			0
$227$	−7.96621e12	−	7.96621e12i	−0.877222	−	0.877222i	0.116024	−	0.993246i	$-0.462985\pi$
$227$	−7.96621e12	−	7.96621e12i	−0.877222	−	0.877222i	−0.993246	+	0.116024i	$0.962985\pi$
$228$		0			0
$229$	1.29670e12	−	1.29670e12i	0.136064	−	0.136064i	−0.635794	−	0.771858i	$-0.719327\pi$
$229$	1.29670e12	−	1.29670e12i	0.136064	−	0.136064i	0.771858	+	0.635794i	$0.219327\pi$
$230$		0			0
$231$		−	4.20127e11i		−	0.0420257i
$232$		0			0
$233$			4.73649e12i			0.451855i	0.974144	+	0.225928i	$0.0725413\pi$
$233$			4.73649e12i			0.451855i	−0.974144	+	0.225928i	$0.927459\pi$
$234$		0			0
$235$	3.82732e12	−	3.82732e12i	0.348355	−	0.348355i
$236$		0			0
$237$	−1.07019e13	−	1.07019e13i	−0.929704	−	0.929704i
$238$		0			0
$239$	1.73692e13			1.44076			0.720381	−	0.693578i	$-0.243967\pi$
$239$	1.73692e13			1.44076			0.720381	+	0.693578i	$0.243967\pi$
$240$		0			0
$241$	−1.51130e13			−1.19745			−0.598725	−	0.800955i	$-0.704326\pi$
$241$	−1.51130e13			−1.19745			−0.598725	+	0.800955i	$0.704326\pi$
$242$		0			0
$243$	−1.30983e11	−	1.30983e11i	−0.00991697	−	0.00991697i
$244$		0			0
$245$	5.46949e12	−	5.46949e12i	0.395853	−	0.395853i
$246$		0			0
$247$		−	7.39557e12i		−	0.511845i
$248$		0			0
$249$		−	3.39948e12i		−	0.225069i
$250$		0			0
$251$	7.55409e12	−	7.55409e12i	0.478604	−	0.478604i	−0.426081	−	0.904685i	$-0.640106\pi$
$251$	7.55409e12	−	7.55409e12i	0.478604	−	0.478604i	0.904685	+	0.426081i	$0.140106\pi$
$252$		0			0
$253$	−3.28101e12	−	3.28101e12i	−0.198996	−	0.198996i
$254$		0			0
$255$	2.66310e12			0.154674
$256$		0			0
$257$	−2.57756e13			−1.43409			−0.717045	−	0.697027i	$-0.754506\pi$
$257$	−2.57756e13			−1.43409			−0.717045	+	0.697027i	$0.754506\pi$
$258$		0			0
$259$	8.36904e11	+	8.36904e11i	0.0446197	+	0.0446197i
$260$		0			0
$261$	1.09447e11	−	1.09447e11i	0.00559349	−	0.00559349i
$262$		0			0
$263$		−	3.41102e13i		−	1.67158i	−0.549047	−	0.835791i	$-0.685009\pi$
$263$		−	3.41102e13i		−	1.67158i	0.549047	−	0.835791i	$-0.314991\pi$
$264$		0			0
$265$			1.43521e13i			0.674628i
$266$		0			0
$267$	−3.17724e12	+	3.17724e12i	−0.143297	+	0.143297i
$268$		0			0
$269$	−2.71092e13	−	2.71092e13i	−1.17349	−	1.17349i	−0.981372	−	0.192117i	$-0.938465\pi$
$269$	−2.71092e13	−	2.71092e13i	−1.17349	−	1.17349i	−0.192117	−	0.981372i	$-0.561535\pi$
$270$		0			0
$271$	−2.37221e13			−0.985876			−0.492938	−	0.870065i	$-0.664077\pi$
$271$	−2.37221e13			−0.985876			−0.492938	+	0.870065i	$0.664077\pi$
$272$		0			0
$273$	−1.91625e12			−0.0764819
$274$		0			0
$275$	−2.73640e12	−	2.73640e12i	−0.104918	−	0.104918i
$276$		0			0
$277$	2.86303e13	−	2.86303e13i	1.05484	−	1.05484i	0.0564356	−	0.998406i	$-0.482026\pi$
$277$	2.86303e13	−	2.86303e13i	1.05484	−	1.05484i	0.998406	−	0.0564356i	$-0.0179736\pi$
$278$		0			0
$279$			8.98554e10i			0.00318215i
$280$		0			0
$281$		−	1.73419e13i		−	0.590488i	−0.955422	−	0.295244i	$-0.904599\pi$
$281$		−	1.73419e13i		−	0.590488i	0.955422	−	0.295244i	$-0.0954010\pi$
$282$		0			0
$283$	−3.78495e12	+	3.78495e12i	−0.123947	+	0.123947i	−0.766359	−	0.642412i	$-0.777934\pi$
$283$	−3.78495e12	+	3.78495e12i	−0.123947	+	0.123947i	0.642412	+	0.766359i	$0.277934\pi$
$284$		0			0
$285$	−1.63179e13	−	1.63179e13i	−0.514063	−	0.514063i
$286$		0			0
$287$	−9.49589e12			−0.287863
$288$		0			0
$289$	−3.18211e13			−0.928488
$290$		0			0
$291$	−2.18336e12	−	2.18336e12i	−0.0613357	−	0.0613357i
$292$		0			0
$293$	−3.44335e13	+	3.44335e13i	−0.931556	+	0.931556i	−0.997803	−	0.0662477i	$-0.978897\pi$
$293$	−3.44335e13	+	3.44335e13i	−0.931556	+	0.931556i	0.0662477	+	0.997803i	$0.478897\pi$
$294$		0			0
$295$		−	2.19020e13i		−	0.570771i
$296$		0			0
$297$			8.94250e12i			0.224542i
$298$		0			0
$299$	−1.49651e13	+	1.49651e13i	−0.362150	+	0.362150i
$300$		0			0
$301$	8.84899e12	+	8.84899e12i	0.206433	+	0.206433i
$302$		0			0
$303$	5.22441e13			1.17518
$304$		0			0
$305$	4.43438e13			0.962020
$306$		0			0
$307$	−1.03299e13	−	1.03299e13i	−0.216190	−	0.216190i	0.590701	−	0.806891i	$-0.298851\pi$
$307$	−1.03299e13	−	1.03299e13i	−0.216190	−	0.216190i	−0.806891	+	0.590701i	$0.798851\pi$
$308$		0			0
$309$	−2.99160e13	+	2.99160e13i	−0.604132	+	0.604132i
$310$		0			0
$311$		−	7.78955e12i		−	0.151820i	−0.997115	−	0.0759102i	$-0.975814\pi$
$311$		−	7.78955e12i		−	0.151820i	0.997115	−	0.0759102i	$-0.0241862\pi$
$312$		0			0
$313$		−	9.37500e13i		−	1.76391i	−0.471330	−	0.881957i	$-0.656226\pi$
$313$		−	9.37500e13i		−	1.76391i	0.471330	−	0.881957i	$-0.343774\pi$
$314$		0			0
$315$	2.98589e10	−	2.98589e10i	0.000542457	−	0.000542457i
$316$		0			0
$317$	2.94124e13	+	2.94124e13i	0.516065	+	0.516065i	0.916378	−	0.400313i	$-0.131099\pi$
$317$	2.94124e13	+	2.94124e13i	0.516065	+	0.516065i	−0.400313	+	0.916378i	$0.631099\pi$
$318$		0			0
$319$	−1.48924e13			−0.252416
$320$		0			0
$321$	−2.31893e13			−0.379761
$322$		0			0
$323$	−1.50172e13	−	1.50172e13i	−0.237671	−	0.237671i
$324$		0			0
$325$	−1.24811e13	+	1.24811e13i	−0.190938	+	0.190938i
$326$		0			0
$327$			9.06657e13i			1.34100i
$328$		0			0
$329$			1.11843e13i			0.159967i
$330$		0			0
$331$	8.90138e13	−	8.90138e13i	1.23141	−	1.23141i	0.267990	−	0.963422i	$-0.413640\pi$
$331$	8.90138e13	−	8.90138e13i	1.23141	−	1.23141i	0.963422	−	0.267990i	$-0.0863596\pi$
$332$		0			0
$333$	−1.24048e11	−	1.24048e11i	−0.00166015	−	0.00166015i
$334$		0			0
$335$	−1.66928e13			−0.216164
$336$		0			0
$337$	4.94592e13			0.619844			0.309922	−	0.950762i	$-0.399697\pi$
$337$	4.94592e13			0.619844			0.309922	+	0.950762i	$0.399697\pi$
$338$		0			0
$339$	2.62880e13	+	2.62880e13i	0.318903	+	0.318903i
$340$		0			0
$341$	6.11328e12	−	6.11328e12i	0.0718002	−	0.0718002i
$342$		0			0
$343$			3.25549e13i			0.370253i
$344$		0			0
$345$			6.60392e13i			0.727439i
$346$		0			0
$347$	4.93186e13	−	4.93186e13i	0.526258	−	0.526258i	−0.393197	−	0.919454i	$-0.628631\pi$
$347$	4.93186e13	−	4.93186e13i	0.526258	−	0.526258i	0.919454	+	0.393197i	$0.128631\pi$
$348$		0			0
$349$	1.31044e14	+	1.31044e14i	1.35481	+	1.35481i	0.880196	+	0.474610i	$0.157411\pi$
$349$	1.31044e14	+	1.31044e14i	1.35481	+	1.35481i	0.474610	+	0.880196i	$0.342589\pi$
$350$		0			0
$351$	4.07879e13			0.408641
$352$		0			0
$353$	1.16944e14			1.13558			0.567791	−	0.823173i	$-0.307798\pi$
$353$	1.16944e14			1.13558			0.567791	+	0.823173i	$0.307798\pi$
$354$		0			0
$355$	5.08200e13	+	5.08200e13i	0.478386	+	0.478386i
$356$		0			0
$357$	−3.89109e12	+	3.89109e12i	−0.0355137	+	0.0355137i
$358$		0			0
$359$			4.01208e13i			0.355100i	0.984112	+	0.177550i	$0.0568171\pi$
$359$			4.01208e13i			0.355100i	−0.984112	+	0.177550i	$0.943183\pi$
$360$		0			0
$361$			6.75428e13i			0.579815i
$362$		0			0
$363$	−8.03775e13	+	8.03775e13i	−0.669342	+	0.669342i
$364$		0			0
$365$	−5.85401e13	−	5.85401e13i	−0.472980	−	0.472980i
$366$		0			0
$367$	−1.48808e14			−1.16671			−0.583354	−	0.812218i	$-0.698260\pi$
$367$	−1.48808e14			−1.16671			−0.583354	+	0.812218i	$0.698260\pi$
$368$		0			0
$369$	1.40751e12			0.0107104
$370$		0			0
$371$	−2.09701e13	−	2.09701e13i	−0.154897	−	0.154897i
$372$		0			0
$373$	9.75473e13	−	9.75473e13i	0.699547	−	0.699547i	−0.264766	−	0.964313i	$-0.585295\pi$
$373$	9.75473e13	−	9.75473e13i	0.699547	−	0.699547i	0.964313	+	0.264766i	$0.0852948\pi$
$374$		0			0
$375$			1.38139e14i			0.961932i
$376$		0			0
$377$			6.79263e13i			0.459368i
$378$		0			0
$379$	−1.24977e14	+	1.24977e14i	−0.820944	+	0.820944i	−0.986243	−	0.165299i	$-0.947141\pi$
$379$	−1.24977e14	+	1.24977e14i	−0.820944	+	0.820944i	0.165299	+	0.986243i	$0.447141\pi$
$380$		0			0
$381$	5.50044e13	+	5.50044e13i	0.351002	+	0.351002i
$382$		0			0
$383$	−4.86299e13			−0.301516			−0.150758	−	0.988571i	$-0.548171\pi$
$383$	−4.86299e13			−0.301516			−0.150758	+	0.988571i	$0.548171\pi$
$384$		0			0
$385$	−4.06288e12			−0.0244793
$386$		0			0
$387$	−1.31162e12	−	1.31162e12i	−0.00768067	−	0.00768067i
$388$		0			0
$389$	−8.60395e12	+	8.60395e12i	−0.0489751	+	0.0489751i	−0.731170	−	0.682195i	$-0.761025\pi$
$389$	−8.60395e12	+	8.60395e12i	−0.0489751	+	0.0489751i	0.682195	+	0.731170i	$0.261025\pi$
$390$		0			0
$391$			6.07755e13i			0.336323i
$392$		0			0
$393$			1.18551e14i			0.637890i
$394$		0			0
$395$	−1.03494e14	+	1.03494e14i	−0.541539	+	0.541539i
$396$		0			0
$397$	4.00648e13	+	4.00648e13i	0.203899	+	0.203899i	0.801668	−	0.597769i	$-0.203946\pi$
$397$	4.00648e13	+	4.00648e13i	0.203899	+	0.203899i	−0.597769	+	0.801668i	$0.703946\pi$
$398$		0			0
$399$	4.76845e13			0.236062
$400$		0			0
$401$	3.93054e14			1.89304			0.946518	−	0.322652i	$-0.104574\pi$
$401$	3.93054e14			1.89304			0.946518	+	0.322652i	$0.104574\pi$
$402$		0			0
$403$	−2.78835e13	−	2.78835e13i	−0.130668	−	0.130668i
$404$		0			0
$405$	8.93648e13	−	8.93648e13i	0.407534	−	0.407534i
$406$		0			0
$407$			1.68792e13i			0.0749173i
$408$		0			0
$409$		−	3.20804e14i		−	1.38599i	−0.720941	−	0.692997i	$-0.756290\pi$
$409$		−	3.20804e14i		−	1.38599i	0.720941	−	0.692997i	$-0.243710\pi$
$410$		0			0
$411$	−3.06822e14	+	3.06822e14i	−1.29049	+	1.29049i
$412$		0			0
$413$	3.20012e13	+	3.20012e13i	0.131051	+	0.131051i
$414$		0			0
$415$	−3.28750e13			−0.131099
$416$		0			0
$417$	−4.60231e14			−1.78742
$418$		0			0
$419$	1.19903e14	+	1.19903e14i	0.453580	+	0.453580i	0.896541	−	0.442961i	$-0.146072\pi$
$419$	1.19903e14	+	1.19903e14i	0.453580	+	0.453580i	−0.442961	+	0.896541i	$0.646072\pi$
$420$		0			0
$421$	−6.87949e13	+	6.87949e13i	−0.253516	+	0.253516i	−0.822410	−	0.568895i	$-0.807371\pi$
$421$	−6.87949e13	+	6.87949e13i	−0.253516	+	0.253516i	0.568895	+	0.822410i	$0.307371\pi$
$422$		0			0
$423$		−	1.65777e12i		−	0.00595185i
$424$		0			0
$425$			5.06874e13i			0.177321i
$426$		0			0
$427$	−6.47914e13	+	6.47914e13i	−0.220884	+	0.220884i
$428$		0			0
$429$	−1.93241e13	−	1.93241e13i	−0.0642072	−	0.0642072i
$430$		0			0
$431$	−2.48651e14			−0.805314			−0.402657	−	0.915351i	$-0.631913\pi$
$431$	−2.48651e14			−0.805314			−0.402657	+	0.915351i	$0.631913\pi$
$432$		0			0
$433$	7.94573e13			0.250871			0.125435	−	0.992102i	$-0.459967\pi$
$433$	7.94573e13			0.250871			0.125435	+	0.992102i	$0.459967\pi$
$434$		0			0
$435$	1.49875e14	+	1.49875e14i	0.461359	+	0.461359i
$436$		0			0
$437$	3.72395e14	−	3.72395e14i	1.11778	−	1.11778i
$438$		0			0
$439$		−	5.46704e14i		−	1.60029i	−0.599809	−	0.800143i	$-0.704757\pi$
$439$		−	5.46704e14i		−	1.60029i	0.599809	−	0.800143i	$-0.295243\pi$
$440$		0			0
$441$		−	2.36906e12i		−	0.00676339i
$442$		0			0
$443$	7.74563e13	−	7.74563e13i	0.215693	−	0.215693i	−0.590988	−	0.806681i	$-0.701262\pi$
$443$	7.74563e13	−	7.74563e13i	0.215693	−	0.215693i	0.806681	+	0.590988i	$0.201262\pi$
$444$		0			0
$445$	3.07258e13	+	3.07258e13i	0.0834686	+	0.0834686i
$446$		0			0
$447$	5.03174e14			1.33360
$448$		0			0
$449$	1.23108e14			0.318369			0.159184	−	0.987249i	$-0.449114\pi$
$449$	1.23108e14			0.318369			0.159184	+	0.987249i	$0.449114\pi$
$450$		0			0
$451$	−9.57594e13	−	9.57594e13i	−0.241663	−	0.241663i
$452$		0			0
$453$	−2.42731e14	+	2.42731e14i	−0.597841	+	0.597841i
$454$		0			0
$455$			1.85313e13i			0.0445495i
$456$		0			0
$457$			5.91954e14i			1.38915i	0.719421	+	0.694574i	$0.244407\pi$
$457$			5.91954e14i			1.38915i	−0.719421	+	0.694574i	$0.755593\pi$
$458$		0			0
$459$	8.28228e13	−	8.28228e13i	0.189749	−	0.189749i
$460$		0			0
$461$	−3.14114e14	−	3.14114e14i	−0.702639	−	0.702639i	0.262337	−	0.964976i	$-0.415507\pi$
$461$	−3.14114e14	−	3.14114e14i	−0.702639	−	0.702639i	−0.964976	+	0.262337i	$0.915507\pi$
$462$		0			0
$463$	2.18707e14			0.477713			0.238857	−	0.971055i	$-0.423227\pi$
$463$	2.18707e14			0.477713			0.238857	+	0.971055i	$0.423227\pi$
$464$		0			0
$465$	−1.23046e14			−0.262469
$466$		0			0
$467$	1.13426e13	+	1.13426e13i	0.0236304	+	0.0236304i	0.718823	−	0.695193i	$-0.244681\pi$
$467$	1.13426e13	+	1.13426e13i	0.0236304	+	0.0236304i	−0.695193	+	0.718823i	$0.744681\pi$
$468$		0			0
$469$	2.43901e13	−	2.43901e13i	0.0496322	−	0.0496322i
$470$		0			0
$471$			3.51449e14i			0.698629i
$472$		0			0
$473$			1.78472e14i			0.346604i
$474$		0			0
$475$	3.10582e14	−	3.10582e14i	0.589333	−	0.589333i
$476$		0			0
$477$	3.10825e12	+	3.10825e12i	0.00576322	+	0.00576322i
$478$		0			0
$479$	−2.93567e14			−0.531939			−0.265969	−	0.963981i	$-0.585692\pi$
$479$	−2.93567e14			−0.531939			−0.265969	+	0.963981i	$0.585692\pi$
$480$		0			0
$481$	7.69881e13			0.136341
$482$		0			0
$483$	−9.64907e13	−	9.64907e13i	−0.167023	−	0.167023i
$484$		0			0
$485$	−2.11143e13	+	2.11143e13i	−0.0357271	+	0.0357271i
$486$		0			0
$487$			2.66029e13i			0.0440069i	0.999758	+	0.0220034i	$0.00700448\pi$
$487$			2.66029e13i			0.0440069i	−0.999758	+	0.0220034i	$0.992996\pi$
$488$		0			0
$489$		−	1.62543e14i		−	0.262887i
$490$		0			0
$491$	8.66005e14	−	8.66005e14i	1.36953	−	1.36953i	0.508428	−	0.861104i	$-0.330227\pi$
$491$	8.66005e14	−	8.66005e14i	1.36953	−	1.36953i	0.861104	−	0.508428i	$-0.169773\pi$
$492$		0			0
$493$	1.37929e14	+	1.37929e14i	0.213304	+	0.213304i
$494$		0			0
$495$	6.02212e11			0.000910795
$496$		0			0
$497$	−1.48508e14			−0.219679
$498$		0			0
$499$	−5.86185e14	−	5.86185e14i	−0.848168	−	0.848168i	0.141736	−	0.989904i	$-0.454732\pi$
$499$	−5.86185e14	−	5.86185e14i	−0.848168	−	0.848168i	−0.989904	+	0.141736i	$0.954732\pi$
$500$		0			0
$501$	−7.52526e14	+	7.52526e14i	−1.06516	+	1.06516i
$502$		0			0
$503$		−	1.63209e14i		−	0.226006i	−0.993595	−	0.113003i	$-0.963953\pi$
$503$		−	1.63209e14i		−	0.226006i	0.993595	−	0.113003i	$-0.0360470\pi$
$504$		0			0
$505$		−	5.05231e14i		−	0.684522i
$506$		0			0
$507$	4.43357e14	−	4.43357e14i	0.587774	−	0.587774i
$508$		0			0
$509$	2.22280e14	+	2.22280e14i	0.288372	+	0.288372i	0.836436	−	0.548065i	$-0.184635\pi$
$509$	2.22280e14	+	2.22280e14i	0.288372	+	0.288372i	−0.548065	+	0.836436i	$0.684635\pi$
$510$		0			0
$511$	1.71067e14			0.217196
$512$		0			0
$513$	−1.01498e15			−1.26128
$514$		0			0
$515$	2.89305e14	+	2.89305e14i	0.351898	+	0.351898i
$516$		0			0
$517$	−1.12786e14	+	1.12786e14i	−0.134294	+	0.134294i
$518$		0			0
$519$		−	3.38886e14i		−	0.395033i
$520$		0			0
$521$		−	1.24751e15i		−	1.42375i	−0.702304	−	0.711877i	$-0.747845\pi$
$521$		−	1.24751e15i		−	1.42375i	0.702304	−	0.711877i	$-0.252155\pi$
$522$		0			0
$523$	4.96253e13	−	4.96253e13i	0.0554555	−	0.0554555i	−0.678835	−	0.734291i	$-0.737515\pi$
$523$	4.96253e13	−	4.96253e13i	0.0554555	−	0.0554555i	0.734291	+	0.678835i	$0.237515\pi$
$524$		0			0
$525$	−8.04743e13	−	8.04743e13i	−0.0880605	−	0.0880605i
$526$		0			0
$527$	−1.13239e14			−0.121349
$528$		0			0
$529$	−5.54291e14			−0.581744
$530$		0			0
$531$	−4.74332e12	−	4.74332e12i	−0.00487598	−	0.00487598i
$532$		0			0
$533$	−4.36771e14	+	4.36771e14i	−0.439799	+	0.439799i
$534$		0			0
$535$			2.24254e14i			0.221205i
$536$		0			0
$537$		−	9.64796e14i		−	0.932346i
$538$		0			0
$539$	−1.61178e14	+	1.61178e14i	−0.152605	+	0.152605i
$540$		0			0
$541$	−9.45723e14	−	9.45723e14i	−0.877363	−	0.877363i	0.115898	−	0.993261i	$-0.463025\pi$
$541$	−9.45723e14	−	9.45723e14i	−0.877363	−	0.877363i	−0.993261	+	0.115898i	$0.963025\pi$
$542$		0			0
$543$	3.06176e14			0.278338
$544$		0			0
$545$	8.76790e14			0.781115
$546$		0			0
$547$	−1.14467e15	−	1.14467e15i	−0.999428	−	0.999428i	0.000571894	−	1.00000i	$-0.499818\pi$
$547$	−1.14467e15	−	1.14467e15i	−0.999428	−	0.999428i	−1.00000		0.000571894i	$0.999818\pi$
$548$		0			0
$549$	9.60357e12	−	9.60357e12i	0.00821835	−	0.00821835i
$550$		0			0
$551$		−	1.69030e15i		−	1.41785i
$552$		0			0
$553$		−	3.02432e14i		−	0.248679i
$554$		0			0
$555$	1.69870e14	−	1.69870e14i	0.136932	−	0.136932i
$556$		0			0
$557$	−1.26785e15	−	1.26785e15i	−1.00199	−	1.00199i	−0.999998	−	0.00199459i	$-0.999365\pi$
$557$	−1.26785e15	−	1.26785e15i	−1.00199	−	1.00199i	−0.00199459	−	0.999998i	$-0.500635\pi$
$558$		0			0
$559$	8.14033e14			0.630778
$560$		0			0
$561$	−7.84779e13			−0.0596282
$562$		0			0
$563$	9.53526e14	+	9.53526e14i	0.710455	+	0.710455i	0.966630	−	0.256175i	$-0.0824624\pi$
$563$	9.53526e14	+	9.53526e14i	0.710455	+	0.710455i	−0.256175	+	0.966630i	$0.582462\pi$
$564$		0			0
$565$	2.54220e14	−	2.54220e14i	0.185756	−	0.185756i
$566$		0			0
$567$			2.61144e14i			0.187143i
$568$		0			0
$569$			5.93700e14i			0.417301i	0.977990	+	0.208650i	$0.0669071\pi$
$569$			5.93700e14i			0.417301i	−0.977990	+	0.208650i	$0.933093\pi$
$570$		0			0
$571$	−3.83062e14	+	3.83062e14i	−0.264101	+	0.264101i	−0.826718	−	0.562617i	$-0.809795\pi$
$571$	−3.83062e14	+	3.83062e14i	−0.264101	+	0.264101i	0.562617	+	0.826718i	$0.309795\pi$
$572$		0			0
$573$	−6.61163e14	−	6.61163e14i	−0.447155	−	0.447155i
$574$		0			0
$575$	−1.25694e15			−0.833952
$576$		0			0
$577$	−1.21498e15			−0.790867			−0.395434	−	0.918495i	$-0.629406\pi$
$577$	−1.21498e15			−0.790867			−0.395434	+	0.918495i	$0.629406\pi$
$578$		0			0
$579$	4.28912e13	+	4.28912e13i	0.0273928	+	0.0273928i
$580$		0			0
$581$	4.80341e13	−	4.80341e13i	0.0301010	−	0.0301010i
$582$		0			0
$583$		−	4.22938e14i		−	0.260076i
$584$		0			0
$585$		−	2.74676e12i		−	0.00165754i
$586$		0			0
$587$	−8.85634e14	+	8.85634e14i	−0.524499	+	0.524499i	−0.918927	−	0.394428i	$-0.870943\pi$
$587$	−8.85634e14	+	8.85634e14i	−0.524499	+	0.524499i	0.394428	+	0.918927i	$0.370943\pi$
$588$		0			0
$589$	6.93859e14	+	6.93859e14i	0.403308	+	0.403308i
$590$		0			0
$591$	−1.34932e15			−0.769811
$592$		0			0
$593$	−2.11099e14			−0.118218			−0.0591092	−	0.998252i	$-0.518826\pi$
$593$	−2.11099e14			−0.118218			−0.0591092	+	0.998252i	$0.518826\pi$
$594$		0			0
$595$	3.76292e13	+	3.76292e13i	0.0206862	+	0.0206862i
$596$		0			0
$597$	1.12800e15	−	1.12800e15i	0.608763	−	0.608763i
$598$		0			0
$599$		−	1.04958e15i		−	0.556122i	−0.960563	−	0.278061i	$-0.910308\pi$
$599$		−	1.04958e15i		−	0.556122i	0.960563	−	0.278061i	$-0.0896917\pi$
$600$		0			0
$601$			1.43484e15i			0.746436i	0.927744	+	0.373218i	$0.121746\pi$
$601$			1.43484e15i			0.746436i	−0.927744	+	0.373218i	$0.878254\pi$
$602$		0			0
$603$	−3.61517e12	+	3.61517e12i	−0.00184665	+	0.00184665i
$604$		0			0
$605$	7.77298e14	+	7.77298e14i	0.389882	+	0.389882i
$606$		0			0
$607$	2.30297e15			1.13436			0.567181	−	0.823593i	$-0.308034\pi$
$607$	2.30297e15			1.13436			0.567181	+	0.823593i	$0.308034\pi$
$608$		0			0
$609$	−4.37970e14			−0.211860
$610$		0			0
$611$	5.14431e14	+	5.14431e14i	0.244399	+	0.244399i
$612$		0			0
$613$	1.01165e15	−	1.01165e15i	0.472058	−	0.472058i	−0.430522	−	0.902580i	$-0.641670\pi$
$613$	1.01165e15	−	1.01165e15i	0.472058	−	0.472058i	0.902580	+	0.430522i	$0.141670\pi$
$614$		0			0
$615$			1.92742e15i			0.883410i
$616$		0			0
$617$			2.46635e15i			1.11042i	0.831711	+	0.555209i	$0.187362\pi$
$617$			2.46635e15i			1.11042i	−0.831711	+	0.555209i	$0.812638\pi$
$618$		0			0
$619$	−4.54673e14	+	4.54673e14i	−0.201095	+	0.201095i	−0.800469	−	0.599374i	$-0.795416\pi$
$619$	−4.54673e14	+	4.54673e14i	−0.201095	+	0.201095i	0.599374	+	0.800469i	$0.295416\pi$
$620$		0			0
$621$	2.05383e15	+	2.05383e15i	0.892400	+	0.892400i
$622$		0			0
$623$	−8.97878e13			−0.0383295
$624$		0			0
$625$	−2.45046e14			−0.102780
$626$		0			0
$627$	4.80865e14	+	4.80865e14i	0.198176	+	0.198176i
$628$		0			0
$629$	1.56330e14	−	1.56330e14i	0.0633088	−	0.0633088i
$630$		0			0
$631$			2.74681e15i			1.09312i	0.837420	+	0.546560i	$0.184063\pi$
$631$			2.74681e15i			1.09312i	−0.837420	+	0.546560i	$0.815937\pi$
$632$		0			0
$633$			2.91097e15i			1.13846i
$634$		0			0
$635$	5.31925e14	−	5.31925e14i	0.204454	−	0.204454i
$636$		0			0
$637$	7.35156e14	+	7.35156e14i	0.277723	+	0.277723i
$638$		0			0
$639$	2.20122e13			0.00817352
$640$		0			0
$641$	4.33345e15			1.58167			0.790833	−	0.612032i	$-0.209648\pi$
$641$	4.33345e15			1.58167			0.790833	+	0.612032i	$0.209648\pi$
$642$		0			0
$643$	−2.47930e15	−	2.47930e15i	−0.889545	−	0.889545i	0.104934	−	0.994479i	$-0.466537\pi$
$643$	−2.47930e15	−	2.47930e15i	−0.889545	−	0.889545i	−0.994479	+	0.104934i	$0.966537\pi$
$644$		0			0
$645$	1.79611e15	−	1.79611e15i	0.633512	−	0.633512i
$646$		0			0
$647$		−	1.92897e15i		−	0.668885i	−0.942416	−	0.334443i	$-0.891452\pi$
$647$		−	1.92897e15i		−	0.668885i	0.942416	−	0.334443i	$-0.108548\pi$
$648$		0			0
$649$			6.45420e14i			0.220038i
$650$		0			0
$651$	1.79785e14	−	1.79785e14i	0.0602639	−	0.0602639i
$652$		0			0
$653$	−6.57083e14	−	6.57083e14i	−0.216570	−	0.216570i	0.590481	−	0.807051i	$-0.298938\pi$
$653$	−6.57083e14	−	6.57083e14i	−0.216570	−	0.216570i	−0.807051	+	0.590481i	$0.798938\pi$
$654$		0			0
$655$	1.14646e15			0.371561
$656$		0			0
$657$	−2.53561e13			−0.00808115
$658$		0			0
$659$	3.43636e15	+	3.43636e15i	1.07703	+	1.07703i	0.996774	+	0.0802587i	$0.0255747\pi$
$659$	3.43636e15	+	3.43636e15i	1.07703	+	1.07703i	0.0802587	+	0.996774i	$0.474425\pi$
$660$		0			0
$661$	−2.46547e15	+	2.46547e15i	−0.759963	+	0.759963i	−0.976315	−	0.216353i	$-0.930584\pi$
$661$	−2.46547e15	+	2.46547e15i	−0.759963	+	0.759963i	0.216353	+	0.976315i	$0.430584\pi$
$662$		0			0
$663$			3.57948e14i			0.108516i
$664$		0			0
$665$		−	4.61137e14i		−	0.137503i
$666$		0			0
$667$	−3.42035e15	+	3.42035e15i	−1.00318	+	1.00318i
$668$		0			0
$669$	1.38005e15	+	1.38005e15i	0.398154	+	0.398154i
$670$		0			0
$671$	−1.30675e15			−0.370868
$672$		0			0
$673$	5.59870e15			1.56316			0.781581	−	0.623803i	$-0.214413\pi$
$673$	5.59870e15			1.56316			0.781581	+	0.623803i	$0.214413\pi$
$674$		0			0
$675$	1.71291e15	+	1.71291e15i	0.470505	+	0.470505i
$676$		0			0
$677$	−9.69257e14	+	9.69257e14i	−0.261940	+	0.261940i	−0.825842	−	0.563902i	$-0.809300\pi$
$677$	−9.69257e14	+	9.69257e14i	−0.261940	+	0.261940i	0.563902	+	0.825842i	$0.309300\pi$
$678$		0			0
$679$		−	6.17009e13i		−	0.0164062i
$680$		0			0
$681$		−	4.72504e15i		−	1.23622i
$682$		0			0
$683$	−6.09310e14	+	6.09310e14i	−0.156864	+	0.156864i	−0.781176	−	0.624311i	$-0.785380\pi$
$683$	−6.09310e14	+	6.09310e14i	−0.156864	+	0.156864i	0.624311	+	0.781176i	$0.285380\pi$
$684$		0			0
$685$	2.96715e15	+	2.96715e15i	0.751693	+	0.751693i
$686$		0			0
$687$	7.69116e14			0.191748
$688$		0			0
$689$	−1.92907e15			−0.473307
$690$		0			0
$691$	2.63310e14	+	2.63310e14i	0.0635826	+	0.0635826i	0.738183	−	0.674600i	$-0.235684\pi$
$691$	2.63310e14	+	2.63310e14i	0.0635826	+	0.0635826i	−0.674600	+	0.738183i	$0.735684\pi$
$692$		0			0
$693$	−8.79900e11	+	8.79900e11i	−0.000209122	+	0.000209122i
$694$		0			0
$695$			4.45070e15i			1.04115i
$696$		0			0
$697$			1.77379e15i			0.408434i
$698$		0			0
$699$	−1.40469e15	+	1.40469e15i	−0.318388	+	0.318388i
$700$		0			0
$701$	−3.81857e15	−	3.81857e15i	−0.852024	−	0.852024i	0.138358	−	0.990382i	$-0.455818\pi$
$701$	−3.81857e15	−	3.81857e15i	−0.852024	−	0.852024i	−0.990382	+	0.138358i	$0.955818\pi$
$702$		0			0
$703$	−1.91579e15			−0.420817
$704$		0			0
$705$	2.27012e15			0.490918
$706$		0			0
$707$	7.38200e14	+	7.38200e14i	0.157169	+	0.157169i
$708$		0			0
$709$	2.06573e15	−	2.06573e15i	0.433031	−	0.433031i	−0.456627	−	0.889658i	$-0.650943\pi$
$709$	2.06573e15	−	2.06573e15i	0.433031	−	0.433031i	0.889658	+	0.456627i	$0.150943\pi$
$710$		0			0
$711$			4.48273e13i			0.00925252i
$712$		0			0
$713$		−	2.80808e15i		−	0.570712i
$714$		0			0
$715$	−1.86875e14	+	1.86875e14i	−0.0373997	+	0.0373997i
$716$		0			0
$717$	5.15116e15	+	5.15116e15i	1.01519	+	1.01519i
$718$		0			0
$719$	−9.28686e15			−1.80244			−0.901218	−	0.433366i	$-0.857326\pi$
$719$	−9.28686e15			−1.80244			−0.901218	+	0.433366i	$0.857326\pi$
$720$		0			0
$721$	−8.45416e14			−0.161594
$722$		0			0
$723$	−4.48203e15	−	4.48203e15i	−0.843751	−	0.843751i
$724$		0			0
$725$	−2.85261e15	+	2.85261e15i	−0.528912	+	0.528912i
$726$		0			0
$727$			7.23879e15i			1.32198i	0.750393	+	0.660992i	$0.229864\pi$
$727$			7.23879e15i			1.32198i	−0.750393	+	0.660992i	$0.770136\pi$
$728$		0			0
$729$		−	5.59749e15i		−	1.00691i
$730$		0			0
$731$	1.65295e15	−	1.65295e15i	0.292897	−	0.292897i
$732$		0			0
$733$	−1.06411e15	−	1.06411e15i	−0.185743	−	0.185743i	0.608110	−	0.793853i	$-0.291928\pi$
$733$	−1.06411e15	−	1.06411e15i	−0.185743	−	0.185743i	−0.793853	+	0.608110i	$0.791928\pi$
$734$		0			0
$735$	3.24415e15			0.557854
$736$		0			0
$737$	4.91914e14			0.0833333
$738$		0			0
$739$	−2.11437e15	−	2.11437e15i	−0.352887	−	0.352887i	0.508295	−	0.861183i	$-0.330276\pi$
$739$	−2.11437e15	−	2.11437e15i	−0.352887	−	0.352887i	−0.861183	+	0.508295i	$0.830276\pi$
$740$		0			0
$741$	2.19329e15	−	2.19329e15i	0.360658	−	0.360658i
$742$		0			0
$743$			5.36629e15i			0.869432i	0.900568	+	0.434716i	$0.143151\pi$
$743$			5.36629e15i			0.869432i	−0.900568	+	0.434716i	$0.856849\pi$
$744$		0			0
$745$		−	4.86598e15i		−	0.776803i
$746$		0			0
$747$	−7.11975e12	+	7.11975e12i	−0.00111996	+	0.00111996i
$748$		0			0
$749$	−3.27661e14	−	3.27661e14i	−0.0507896	−	0.0507896i
$750$		0			0
$751$	−6.27521e15			−0.958536			−0.479268	−	0.877669i	$-0.659098\pi$
$751$	−6.27521e15			−0.958536			−0.479268	+	0.877669i	$0.659098\pi$
$752$		0			0
$753$	4.48060e15			0.674471
$754$		0			0
$755$	2.34735e15	+	2.34735e15i	0.348233	+	0.348233i
$756$		0			0
$757$	−5.57647e15	+	5.57647e15i	−0.815327	+	0.815327i	−0.985427	−	0.170100i	$-0.945591\pi$
$757$	−5.57647e15	+	5.57647e15i	−0.815327	+	0.815327i	0.170100	+	0.985427i	$0.445591\pi$
$758$		0			0
$759$		−	1.94608e15i		−	0.280435i
$760$		0			0
$761$			9.13565e15i			1.29755i	0.760981	+	0.648775i	$0.224718\pi$
$761$			9.13565e15i			1.29755i	−0.760981	+	0.648775i	$0.775282\pi$
$762$		0			0
$763$	−1.28109e15	+	1.28109e15i	−0.179347	+	0.179347i
$764$		0			0
$765$	−5.57750e12	−	5.57750e12i	−0.000769665	−	0.000769665i
$766$		0			0
$767$	2.94384e15			0.400443
$768$		0			0
$769$	−1.05572e16			−1.41564			−0.707822	−	0.706390i	$-0.750322\pi$
$769$	−1.05572e16			−1.41564			−0.707822	+	0.706390i	$0.750322\pi$
$770$		0			0
$771$	−7.64420e15	−	7.64420e15i	−1.01049	−	1.01049i
$772$		0			0
$773$	−4.20745e14	+	4.20745e14i	−0.0548317	+	0.0548317i	−0.733991	−	0.679159i	$-0.762345\pi$
$773$	−4.20745e14	+	4.20745e14i	−0.0548317	+	0.0548317i	0.679159	+	0.733991i	$0.262345\pi$
$774$		0			0
$775$		−	2.34197e15i		−	0.300900i
$776$		0			0
$777$			4.96397e14i			0.0628802i
$778$		0			0
$779$	1.08687e16	−	1.08687e16i	1.35744	−	1.35744i
$780$		0			0
$781$	−1.49760e15	−	1.49760e15i	−0.184422	−	0.184422i
$782$		0			0
$783$	9.32228e15			1.13196
$784$		0			0
$785$	3.39871e15			0.406941
$786$		0			0
$787$	6.07370e15	+	6.07370e15i	0.717121	+	0.717121i	0.968015	−	0.250894i	$-0.0807246\pi$
$787$	6.07370e15	+	6.07370e15i	0.717121	+	0.717121i	−0.250894	+	0.968015i	$0.580725\pi$
$788$		0			0
$789$	1.01160e16	−	1.01160e16i	1.17784	−	1.17784i
$790$		0			0
$791$			7.42889e14i			0.0853009i
$792$		0			0
$793$			5.96026e15i			0.674936i
$794$		0			0
$795$	−4.25638e15	+	4.25638e15i	−0.475358	+	0.475358i
$796$		0			0
$797$	−7.43572e15	−	7.43572e15i	−0.819034	−	0.819034i	0.166934	−	0.985968i	$-0.446613\pi$
$797$	−7.43572e15	−	7.43572e15i	−0.819034	−	0.819034i	−0.985968	+	0.166934i	$0.946613\pi$
$798$		0			0
$799$	2.08918e15			0.226970
$800$		0			0
$801$	1.33086e13			0.00142611
$802$		0			0
$803$	1.72510e15	+	1.72510e15i	0.182338	+	0.182338i
$804$		0			0
$805$	−9.33122e14	+	9.33122e14i	−0.0972884	+	0.0972884i
$806$		0			0
$807$		−	1.60794e16i		−	1.65374i
$808$		0			0
$809$			3.62426e15i			0.367708i	0.982954	+	0.183854i	$0.0588573\pi$
$809$			3.62426e15i			0.367708i	−0.982954	+	0.183854i	$0.941143\pi$
$810$		0			0
$811$	5.45703e15	−	5.45703e15i	0.546187	−	0.546187i	−0.379149	−	0.925336i	$-0.623783\pi$
$811$	5.45703e15	−	5.45703e15i	0.546187	−	0.546187i	0.925336	+	0.379149i	$0.123783\pi$
$812$		0			0
$813$	−7.03521e15	−	7.03521e15i	−0.694671	−	0.694671i
$814$		0			0
$815$	−1.57188e15			−0.153128
$816$		0			0
$817$	−2.02566e16			−1.94691
$818$		0			0
$819$	4.01333e12	+	4.01333e12i	0.000380578	+	0.000380578i
$820$		0			0
$821$	−7.79173e14	+	7.79173e14i	−0.0729032	+	0.0729032i	−0.742618	−	0.669715i	$-0.766416\pi$
$821$	−7.79173e14	+	7.79173e14i	−0.0729032	+	0.0729032i	0.669715	+	0.742618i	$0.266416\pi$
$822$		0			0
$823$		−	1.87740e16i		−	1.73323i	−0.498975	−	0.866616i	$-0.666290\pi$
$823$		−	1.87740e16i		−	1.73323i	0.498975	−	0.866616i	$-0.333710\pi$
$824$		0			0
$825$		−	1.62305e15i		−	0.147855i
$826$		0			0
$827$	−3.96952e15	+	3.96952e15i	−0.356827	+	0.356827i	−0.862642	−	0.505815i	$-0.831192\pi$
$827$	−3.96952e15	+	3.96952e15i	−0.356827	+	0.356827i	0.505815	+	0.862642i	$0.331192\pi$
$828$		0			0
$829$	8.56186e15	+	8.56186e15i	0.759483	+	0.759483i	0.976228	−	0.216745i	$-0.0695440\pi$
$829$	8.56186e15	+	8.56186e15i	0.759483	+	0.759483i	−0.216745	+	0.976228i	$0.569544\pi$
$830$		0			0
$831$	1.69816e16			1.48653
$832$		0			0
$833$	2.98557e15			0.257917
$834$		0			0
$835$	7.27737e15	+	7.27737e15i	0.620439	+	0.620439i
$836$		0			0
$837$	−3.82675e15	+	3.82675e15i	−0.321989	+	0.321989i
$838$		0			0
$839$		−	1.76310e16i		−	1.46415i	−0.681224	−	0.732075i	$-0.738552\pi$
$839$		−	1.76310e16i		−	1.46415i	0.681224	−	0.732075i	$-0.261448\pi$
$840$		0			0
$841$			3.32441e15i			0.272481i
$842$		0			0
$843$	5.14304e15	−	5.14304e15i	0.416072	−	0.416072i
$844$		0			0
$845$	−4.28752e15	−	4.28752e15i	−0.342369	−	0.342369i
$846$		0			0
$847$	−2.27144e15			−0.179037
$848$		0			0
$849$	−2.24499e15			−0.174671
$850$		0			0
$851$	3.87665e15	+	3.87665e15i	0.297744	+	0.297744i
$852$		0			0
$853$	−8.96322e15	+	8.96322e15i	−0.679586	+	0.679586i	−0.959907	−	0.280320i	$-0.909559\pi$
$853$	−8.96322e15	+	8.96322e15i	−0.679586	+	0.679586i	0.280320	+	0.959907i	$0.409559\pi$
$854$		0			0
$855$			6.83511e13i			0.00511602i
$856$		0			0
$857$		−	1.38540e16i		−	1.02372i	−0.859069	−	0.511859i	$-0.828957\pi$
$857$		−	1.38540e16i		−	1.02372i	0.859069	−	0.511859i	$-0.171043\pi$
$858$		0			0
$859$	9.36023e14	−	9.36023e14i	0.0682848	−	0.0682848i	−0.672140	−	0.740424i	$-0.734625\pi$
$859$	9.36023e14	−	9.36023e14i	0.0682848	−	0.0682848i	0.740424	+	0.672140i	$0.234625\pi$
$860$		0			0
$861$	−2.81617e15	−	2.81617e15i	−0.202835	−	0.202835i
$862$		0			0
$863$	2.24799e16			1.59858			0.799291	−	0.600945i	$-0.205209\pi$
$863$	2.24799e16			1.59858			0.799291	+	0.600945i	$0.205209\pi$
$864$		0			0
$865$	−3.27723e15			−0.230101
$866$		0			0
$867$	−9.43710e15	−	9.43710e15i	−0.654234	−	0.654234i
$868$		0			0
$869$	3.04981e15	−	3.04981e15i	0.208768	−	0.208768i
$870$		0			0
$871$		−	2.24368e15i		−	0.151657i
$872$		0			0
$873$			9.14549e12i			0.000610420i
$874$		0			0
$875$	−1.95188e15	+	1.95188e15i	−0.128650	+	0.128650i
$876$		0			0
$877$	−4.07874e14	−	4.07874e14i	−0.0265478	−	0.0265478i	0.693708	−	0.720256i	$-0.255976\pi$
$877$	−4.07874e14	−	4.07874e14i	−0.0265478	−	0.0265478i	−0.720256	+	0.693708i	$0.755976\pi$
$878$		0			0
$879$	−2.04237e16			−1.31279
$880$		0			0
$881$	−1.29668e15			−0.0823122			−0.0411561	−	0.999153i	$-0.513104\pi$
$881$	−1.29668e15			−0.0823122			−0.0411561	+	0.999153i	$0.513104\pi$
$882$		0			0
$883$	−1.46438e16	−	1.46438e16i	−0.918056	−	0.918056i	0.0788318	−	0.996888i	$-0.474881\pi$
$883$	−1.46438e16	−	1.46438e16i	−0.918056	−	0.918056i	−0.996888	+	0.0788318i	$0.974881\pi$
$884$		0			0
$885$	6.49541e15	−	6.49541e15i	0.402178	−	0.402178i
$886$		0			0
$887$			1.45969e16i			0.892648i	0.894871	+	0.446324i	$0.147267\pi$
$887$			1.45969e16i			0.892648i	−0.894871	+	0.446324i	$0.852733\pi$
$888$		0			0
$889$			1.55441e15i			0.0938869i
$890$		0			0
$891$	−2.63346e15	+	2.63346e15i	−0.157108	+	0.157108i
$892$		0			0
$893$	−1.28012e16	−	1.28012e16i	−0.754342	−	0.754342i
$894$		0			0
$895$	−9.33014e15			−0.543077
$896$		0			0
$897$	−8.87633e15			−0.510358
$898$		0			0
$899$	−6.37291e15	−	6.37291e15i	−0.361959	−	0.361959i
$900$		0			0
$901$	−3.91712e15	+	3.91712e15i	−0.219776	+	0.219776i
$902$		0			0
$903$			5.24865e15i			0.290914i
$904$		0			0
$905$		−	2.96090e15i		−	0.162128i
$906$		0			0
$907$	1.79943e14	−	1.79943e14i	0.00973408	−	0.00973408i	−0.702223	−	0.711957i	$-0.747809\pi$
$907$	1.79943e14	−	1.79943e14i	0.00973408	−	0.00973408i	0.711957	+	0.702223i	$0.247809\pi$
$908$		0			0
$909$	−1.09418e14	−	1.09418e14i	−0.00584774	−	0.00584774i
$910$		0			0
$911$	4.66120e15			0.246120			0.123060	−	0.992399i	$-0.460729\pi$
$911$	4.66120e15			0.246120			0.123060	+	0.992399i	$0.460729\pi$
$912$		0			0
$913$	9.68780e14			0.0505401
$914$		0			0
$915$	1.31509e16	+	1.31509e16i	0.677862	+	0.677862i
$916$		0			0
$917$	−1.67510e15	+	1.67510e15i	−0.0853120	+	0.0853120i
$918$		0			0
$919$			7.32403e15i			0.368565i	0.982873	+	0.184283i	$0.0589962\pi$
$919$			7.32403e15i			0.368565i	−0.982873	+	0.184283i	$0.941004\pi$
$920$		0			0
$921$		−	6.12703e15i		−	0.304665i
$922$		0			0
$923$	−6.83072e15	+	6.83072e15i	−0.335627	+	0.335627i
$924$		0			0
$925$	3.23317e15	+	3.23317e15i	0.156981	+	0.156981i
$926$		0			0
$927$	1.25310e14			0.00601239
$928$		0			0
$929$	3.83734e15			0.181946			0.0909732	−	0.995853i	$-0.471002\pi$
$929$	3.83734e15			0.181946			0.0909732	+	0.995853i	$0.471002\pi$
$930$		0			0
$931$	−1.82938e16	−	1.82938e16i	−0.857196	−	0.857196i
$932$		0			0
$933$	2.31013e15	−	2.31013e15i	0.106976	−	0.106976i
$934$		0			0
$935$			7.58928e14i			0.0347325i
$936$		0			0
$937$			3.42166e15i			0.154764i	0.997002	+	0.0773818i	$0.0246560\pi$
$937$			3.42166e15i			0.154764i	−0.997002	+	0.0773818i	$0.975344\pi$
$938$		0			0
$939$	2.78032e16	−	2.78032e16i	1.24289	−	1.24289i
$940$		0			0
$941$	4.01665e15	+	4.01665e15i	0.177468	+	0.177468i	0.790251	−	0.612783i	$-0.209950\pi$
$941$	4.01665e15	+	4.01665e15i	0.177468	+	0.177468i	−0.612783	+	0.790251i	$0.709950\pi$
$942$		0			0
$943$	−4.39862e16			−1.92089
$944$		0			0
$945$	2.54325e15			0.109778
$946$		0			0
$947$	2.64810e16	+	2.64810e16i	1.12982	+	1.12982i	0.990206	+	0.139617i	$0.0445870\pi$
$947$	2.64810e16	+	2.64810e16i	1.12982	+	1.12982i	0.139617	+	0.990206i	$0.455413\pi$
$948$		0			0
$949$	7.86838e15	−	7.86838e15i	0.331834	−	0.331834i
$950$		0			0
$951$			1.74455e16i			0.727263i
$952$		0			0
$953$		−	1.46484e16i		−	0.603640i	−0.953365	−	0.301820i	$-0.902406\pi$
$953$		−	1.46484e16i		−	0.603640i	0.953365	−	0.301820i	$-0.0975942\pi$
$954$		0			0
$955$	−6.39383e15	+	6.39383e15i	−0.260461	+	0.260461i
$956$		0			0
$957$	−4.41662e15	−	4.41662e15i	−0.177858	−	0.177858i
$958$		0			0
$959$	−8.67068e15			−0.345184
$960$		0			0
$961$	−2.01764e16			−0.794080
$962$		0			0
$963$	4.85668e13	+	4.85668e13i	0.00188971	+	0.00188971i
$964$		0			0
$965$	4.14783e14	−	4.14783e14i	0.0159559	−	0.0159559i
$966$		0			0
$967$			5.90633e15i			0.224632i	0.993673	+	0.112316i	$0.0358270\pi$
$967$			5.90633e15i			0.224632i	−0.993673	+	0.112316i	$0.964173\pi$
$968$		0			0
$969$		−	8.90726e15i		−	0.334937i
$970$		0			0
$971$	−4.00686e15	+	4.00686e15i	−0.148970	+	0.148970i	−0.777658	−	0.628688i	$-0.783592\pi$
$971$	−4.00686e15	+	4.00686e15i	−0.148970	+	0.148970i	0.628688	+	0.777658i	$0.283592\pi$
$972$		0			0
$973$	−6.50298e15	−	6.50298e15i	−0.239052	−	0.239052i
$974$		0			0
$975$	−7.40296e15			−0.269079
$976$		0			0
$977$	3.72683e16			1.33943			0.669714	−	0.742619i	$-0.266417\pi$
$977$	3.72683e16			1.33943			0.669714	+	0.742619i	$0.266417\pi$
$978$		0			0
$979$	−9.05447e14	−	9.05447e14i	−0.0321779	−	0.0321779i
$980$		0			0
$981$	1.89887e14	−	1.89887e14i	0.00667292	−	0.00667292i
$982$		0			0
$983$			4.32496e16i			1.50293i	0.659776	+	0.751463i	$0.270651\pi$
$983$			4.32496e16i			1.50293i	−0.659776	+	0.751463i	$0.729349\pi$
$984$		0			0
$985$			1.30487e16i			0.448403i
$986$		0			0
$987$	−3.31690e15	+	3.31690e15i	−0.112717	+	0.112717i
$988$		0			0
$989$	4.09897e16	+	4.09897e16i	1.37751	+	1.37751i
$990$		0			0
$991$	3.69777e16			1.22895			0.614476	−	0.788936i	$-0.289368\pi$
$991$	3.69777e16			1.22895			0.614476	+	0.788936i	$0.289368\pi$
$992$		0			0
$993$	5.27972e16			1.73536
$994$		0			0
$995$	−1.09084e16	−	1.09084e16i	−0.354595	−	0.354595i
$996$		0			0
$997$	−3.76589e16	+	3.76589e16i	−1.21072	+	1.21072i	−0.239932	+	0.970790i	$0.577125\pi$
$997$	−3.76589e16	+	3.76589e16i	−1.21072	+	1.21072i	−0.970790	+	0.239932i	$0.922875\pi$
$998$		0			0
$999$		−	1.05659e16i		−	0.335968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.12.e.b.33.17		42
4.3	odd	2		128.12.e.a.33.5		42
8.3	odd	2		64.12.e.a.17.17		42
8.5	even	2		16.12.e.a.13.12	yes	42
16.3	odd	4		64.12.e.a.49.17		42
16.5	even	4	inner	128.12.e.b.97.17		42
16.11	odd	4		128.12.e.a.97.5		42
16.13	even	4		16.12.e.a.5.12	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.12.e.a.5.12	✓	42	16.13	even	4
16.12.e.a.13.12	yes	42	8.5	even	2
64.12.e.a.17.17		42	8.3	odd	2
64.12.e.a.49.17		42	16.3	odd	4
128.12.e.a.33.5		42	4.3	odd	2
128.12.e.a.97.5		42	16.11	odd	4
128.12.e.b.33.17		42	1.1	even	1	trivial
128.12.e.b.97.17		42	16.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	128.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(296.568 + 296.568i) q^{3} +(2867.98 - 2867.98i) q^{5} +8380.90i q^{7} -1242.24i q^{9} +O(q^{10})\)	\(q+(296.568 + 296.568i) q^{3} +(2867.98 - 2867.98i) q^{5} +8380.90i q^{7} -1242.24i q^{9} +(-84515.5 + 84515.5i) q^{11} +(385486. + 385486. i) q^{13} +1.70110e6 q^{15} +1.56551e6 q^{17} +(-9.59253e6 - 9.59253e6i) q^{19} +(-2.48550e6 + 2.48550e6i) q^{21} +3.88214e7i q^{23} +3.23775e7i q^{25} +(5.29045e7 - 5.29045e7i) q^{27} +(8.81048e7 + 8.81048e7i) q^{29} -7.23333e7 q^{31} -5.01291e7 q^{33} +(2.40363e7 + 2.40363e7i) q^{35} +(9.98585e7 - 9.98585e7i) q^{37} +2.28645e8i q^{39} +1.13304e9i q^{41} +(1.05585e9 - 1.05585e9i) q^{43} +(-3.56273e6 - 3.56273e6i) q^{45} +1.33450e9 q^{47} +1.90709e9 q^{49} +(4.64281e8 + 4.64281e8i) q^{51} +(-2.50213e9 + 2.50213e9i) q^{53} +4.84778e8i q^{55} -5.68967e9i q^{57} +(3.81835e9 - 3.81835e9i) q^{59} +(7.73084e9 + 7.73084e9i) q^{61} +1.04111e7 q^{63} +2.21114e9 q^{65} +(-2.91020e9 - 2.91020e9i) q^{67} +(-1.15132e10 + 1.15132e10i) q^{69} +1.77198e10i q^{71} -2.04116e10i q^{73} +(-9.60211e9 + 9.60211e9i) q^{75} +(-7.08316e8 - 7.08316e8i) q^{77} -3.60858e10 q^{79} +3.11595e10 q^{81} +(-5.73137e9 - 5.73137e9i) q^{83} +(4.48987e9 - 4.48987e9i) q^{85} +5.22581e10i q^{87} +1.07134e10i q^{89} +(-3.23072e9 + 3.23072e9i) q^{91} +(-2.14517e10 - 2.14517e10i) q^{93} -5.50224e10 q^{95} -7.36209e9 q^{97} +(1.04989e8 + 1.04989e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 2 q^{5}+O(q^{10}) \) 42 * q + 2 * q^3 + 2 * q^5	\( 42 q + 2 q^{3} + 2 q^{5} + 540846 q^{11} + 2 q^{13} - 6075004 q^{15} - 4 q^{17} + 11291290 q^{19} - 354292 q^{21} + 66463304 q^{27} - 77673206 q^{29} + 343549808 q^{31} - 4 q^{33} + 434731684 q^{35} + 522762058 q^{37} - 3824193658 q^{43} - 97301954 q^{45} - 4586900144 q^{47} - 8474257474 q^{49} - 7074245796 q^{51} + 2100608058 q^{53} - 955824746 q^{59} - 2150827022 q^{61} + 27758037828 q^{63} - 1884965292 q^{65} + 3186519018 q^{67} + 16193060732 q^{69} - 28890034486 q^{75} + 22711870540 q^{77} + 48011833792 q^{79} - 90656394430 q^{81} - 55713221118 q^{83} + 84575506252 q^{85} + 147369662716 q^{91} + 69689773328 q^{93} + 375702304500 q^{95} - 4 q^{97} + 286271331106 q^{99}+O(q^{100}) \) 42 * q + 2 * q^3 + 2 * q^5 + 540846 * q^11 + 2 * q^13 - 6075004 * q^15 - 4 * q^17 + 11291290 * q^19 - 354292 * q^21 + 66463304 * q^27 - 77673206 * q^29 + 343549808 * q^31 - 4 * q^33 + 434731684 * q^35 + 522762058 * q^37 - 3824193658 * q^43 - 97301954 * q^45 - 4586900144 * q^47 - 8474257474 * q^49 - 7074245796 * q^51 + 2100608058 * q^53 - 955824746 * q^59 - 2150827022 * q^61 + 27758037828 * q^63 - 1884965292 * q^65 + 3186519018 * q^67 + 16193060732 * q^69 - 28890034486 * q^75 + 22711870540 * q^77 + 48011833792 * q^79 - 90656394430 * q^81 - 55713221118 * q^83 + 84575506252 * q^85 + 147369662716 * q^91 + 69689773328 * q^93 + 375702304500 * q^95 - 4 * q^97 + 286271331106 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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