LMFDB - Embedded newform 128.8.e.a.33.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,8,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, 8, names="a")

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

chi := DirichletCharacter("128.33");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 8 $
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:	$39.9852832620$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			33.13
Character	$\chi$	$=$	128.33
Dual form			128.8.e.a.97.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(61.7547 + 61.7547i) q^{3} +(-160.824 + 160.824i) q^{5} +1202.46i q^{7} +5440.30i q^{9} +O(q^{10})$	\(q+(61.7547 + 61.7547i) q^{3} +(-160.824 + 160.824i) q^{5} +1202.46i q^{7} +5440.30i q^{9} +(313.790 - 313.790i) q^{11} +(2231.18 + 2231.18i) q^{13} -19863.3 q^{15} +21041.2 q^{17} +(-17903.6 - 17903.6i) q^{19} +(-74257.9 + 74257.9i) q^{21} -33619.9i q^{23} +26396.1i q^{25} +(-200907. + 200907. i) q^{27} +(4104.39 + 4104.39i) q^{29} -9133.16 q^{31} +38756.0 q^{33} +(-193385. - 193385. i) q^{35} +(104557. - 104557. i) q^{37} +275572. i q^{39} -599792. i q^{41} +(79842.5 - 79842.5i) q^{43} +(-874932. - 874932. i) q^{45} +1.24454e6 q^{47} -622377. q^{49} +(1.29939e6 + 1.29939e6i) q^{51} +(-274857. + 274857. i) q^{53} +100930. i q^{55} -2.21127e6i q^{57} +(-1.13722e6 + 1.13722e6i) q^{59} +(-984936. - 984936. i) q^{61} -6.54176e6 q^{63} -717657. q^{65} +(-2.25153e6 - 2.25153e6i) q^{67} +(2.07619e6 - 2.07619e6i) q^{69} +5.48968e6i q^{71} +4.23698e6i q^{73} +(-1.63008e6 + 1.63008e6i) q^{75} +(377321. + 377321. i) q^{77} -3.54577e6 q^{79} -1.29159e7 q^{81} +(179482. + 179482. i) q^{83} +(-3.38394e6 + 3.38394e6i) q^{85} +506931. i q^{87} +262425. i q^{89} +(-2.68292e6 + 2.68292e6i) q^{91} +(-564016. - 564016. i) q^{93} +5.75868e6 q^{95} +1.53573e7 q^{97} +(1.70711e6 + 1.70711e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 2 q^{3} + 2 q^{5}+O(q^{10}) $ 26 * q - 2 * q^3 + 2 * q^5	$ 26 q - 2 q^{3} + 2 q^{5} + 1202 q^{11} + 2 q^{13} + 27004 q^{15} - 4 q^{17} + 60582 q^{19} - 4372 q^{21} - 233672 q^{27} + 51690 q^{29} - 357488 q^{31} - 4 q^{33} - 252004 q^{35} - 415574 q^{37} + 569754 q^{43} - 151874 q^{45} + 2076464 q^{47} - 1647090 q^{49} + 2609508 q^{51} - 907814 q^{53} - 4865142 q^{59} - 2279886 q^{61} - 8295108 q^{63} - 1426892 q^{65} - 5564458 q^{67} + 4786076 q^{69} + 6212566 q^{75} - 7604308 q^{77} + 9598912 q^{79} - 5314414 q^{81} + 4531198 q^{83} - 7377748 q^{85} + 2587652 q^{91} + 14504144 q^{93} + 4900620 q^{95} - 4 q^{97} + 18815006 q^{99}+O(q^{100}) $ 26 * q - 2 * q^3 + 2 * q^5 + 1202 * q^11 + 2 * q^13 + 27004 * q^15 - 4 * q^17 + 60582 * q^19 - 4372 * q^21 - 233672 * q^27 + 51690 * q^29 - 357488 * q^31 - 4 * q^33 - 252004 * q^35 - 415574 * q^37 + 569754 * q^43 - 151874 * q^45 + 2076464 * q^47 - 1647090 * q^49 + 2609508 * q^51 - 907814 * q^53 - 4865142 * q^59 - 2279886 * q^61 - 8295108 * q^63 - 1426892 * q^65 - 5564458 * q^67 + 4786076 * q^69 + 6212566 * q^75 - 7604308 * q^77 + 9598912 * q^79 - 5314414 * q^81 + 4531198 * q^83 - 7377748 * q^85 + 2587652 * q^91 + 14504144 * q^93 + 4900620 * q^95 - 4 * q^97 + 18815006 * 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
$3$	61.7547	+	61.7547i	1.32052	+	1.32052i	0.913352	+	0.407171i	$0.133485\pi$
$3$	61.7547	+	61.7547i	1.32052	+	1.32052i	0.407171	+	0.913352i	$0.366515\pi$
$4$		0			0
$5$	−160.824	+	160.824i	−0.575383	+	0.575383i	−0.933628	−	0.358245i	$-0.883375\pi$
$5$	−160.824	+	160.824i	−0.575383	+	0.575383i	0.358245	+	0.933628i	$0.383375\pi$
$6$		0			0
$7$			1202.46i			1.32504i	0.749044	+	0.662520i	$0.230513\pi$
$7$			1202.46i			1.32504i	−0.749044	+	0.662520i	$0.769487\pi$
$8$		0			0
$9$			5440.30i			2.48756i
$10$		0			0
$11$	313.790	−	313.790i	0.0710827	−	0.0710827i	−0.670672	−	0.741754i	$-0.733994\pi$
$11$	313.790	−	313.790i	0.0710827	−	0.0710827i	0.741754	+	0.670672i	$0.233994\pi$
$12$		0			0
$13$	2231.18	+	2231.18i	0.281665	+	0.281665i	0.833773	−	0.552108i	$-0.186176\pi$
$13$	2231.18	+	2231.18i	0.281665	+	0.281665i	−0.552108	+	0.833773i	$0.686176\pi$
$14$		0			0
$15$	−19863.3			−1.51961
$16$		0			0
$17$	21041.2			1.03872			0.519361	−	0.854555i	$-0.326170\pi$
$17$	21041.2			1.03872			0.519361	+	0.854555i	$0.326170\pi$
$18$		0			0
$19$	−17903.6	−	17903.6i	−0.598830	−	0.598830i	0.341171	−	0.940001i	$-0.389177\pi$
$19$	−17903.6	−	17903.6i	−0.598830	−	0.598830i	−0.940001	+	0.341171i	$0.889177\pi$
$20$		0			0
$21$	−74257.9	+	74257.9i	−1.74975	+	1.74975i
$22$		0			0
$23$		−	33619.9i		−	0.576167i	−0.957605	−	0.288084i	$-0.906982\pi$
$23$		−	33619.9i		−	0.576167i	0.957605	−	0.288084i	$-0.0930181\pi$
$24$		0			0
$25$			26396.1i			0.337870i
$26$		0			0
$27$	−200907.	+	200907.i	−1.96436	+	1.96436i
$28$		0			0
$29$	4104.39	+	4104.39i	0.0312504	+	0.0312504i	0.722559	−	0.691309i	$-0.242966\pi$
$29$	4104.39	+	4104.39i	0.0312504	+	0.0312504i	−0.691309	+	0.722559i	$0.742966\pi$
$30$		0			0
$31$	−9133.16			−0.0550624			−0.0275312	−	0.999621i	$-0.508765\pi$
$31$	−9133.16			−0.0550624			−0.0275312	+	0.999621i	$0.508765\pi$
$32$		0			0
$33$	38756.0			0.187733
$34$		0			0
$35$	−193385.	−	193385.i	−0.762405	−	0.762405i
$36$		0			0
$37$	104557.	−	104557.i	0.339349	−	0.339349i	−0.516773	−	0.856122i	$-0.672867\pi$
$37$	104557.	−	104557.i	0.339349	−	0.339349i	0.856122	+	0.516773i	$0.172867\pi$
$38$		0			0
$39$			275572.i			0.743891i
$40$		0			0
$41$		−	599792.i		−	1.35912i	−0.733621	−	0.679559i	$-0.762171\pi$
$41$		−	599792.i		−	1.35912i	0.733621	−	0.679559i	$-0.237829\pi$
$42$		0			0
$43$	79842.5	−	79842.5i	0.153142	−	0.153142i	−0.626378	−	0.779520i	$-0.715463\pi$
$43$	79842.5	−	79842.5i	0.153142	−	0.153142i	0.779520	+	0.626378i	$0.215463\pi$
$44$		0			0
$45$	−874932.	−	874932.i	−1.43130	−	1.43130i
$46$		0			0
$47$	1.24454e6			1.74851			0.874254	−	0.485469i	$-0.161351\pi$
$47$	1.24454e6			1.74851			0.874254	+	0.485469i	$0.161351\pi$
$48$		0			0
$49$	−622377.			−0.755732
$50$		0			0
$51$	1.29939e6	+	1.29939e6i	1.37166	+	1.37166i
$52$		0			0
$53$	−274857.	+	274857.i	−0.253596	+	0.253596i	−0.822443	−	0.568847i	$-0.807390\pi$
$53$	−274857.	+	274857.i	−0.253596	+	0.253596i	0.568847	+	0.822443i	$0.307390\pi$
$54$		0			0
$55$			100930.i			0.0817995i
$56$		0			0
$57$		−	2.21127e6i		−	1.58154i
$58$		0			0
$59$	−1.13722e6	+	1.13722e6i	−0.720876	+	0.720876i	−0.968784	−	0.247908i	$-0.920257\pi$
$59$	−1.13722e6	+	1.13722e6i	−0.720876	+	0.720876i	0.247908	+	0.968784i	$0.420257\pi$
$60$		0			0
$61$	−984936.	−	984936.i	−0.555589	−	0.555589i	0.372459	−	0.928048i	$-0.378515\pi$
$61$	−984936.	−	984936.i	−0.555589	−	0.555589i	−0.928048	+	0.372459i	$0.878515\pi$
$62$		0			0
$63$	−6.54176e6			−3.29612
$64$		0			0
$65$	−717657.			−0.324131
$66$		0			0
$67$	−2.25153e6	−	2.25153e6i	−0.914570	−	0.914570i	0.0820580	−	0.996628i	$-0.473851\pi$
$67$	−2.25153e6	−	2.25153e6i	−0.914570	−	0.914570i	−0.996628	+	0.0820580i	$0.973851\pi$
$68$		0			0
$69$	2.07619e6	−	2.07619e6i	0.760842	−	0.760842i
$70$		0			0
$71$			5.48968e6i			1.82030i	0.414278	+	0.910150i	$0.364034\pi$
$71$			5.48968e6i			1.82030i	−0.414278	+	0.910150i	$0.635966\pi$
$72$		0			0
$73$			4.23698e6i			1.27476i	0.770552	+	0.637378i	$0.219981\pi$
$73$			4.23698e6i			1.27476i	−0.770552	+	0.637378i	$0.780019\pi$
$74$		0			0
$75$	−1.63008e6	+	1.63008e6i	−0.446165	+	0.446165i
$76$		0			0
$77$	377321.	+	377321.i	0.0941875	+	0.0941875i
$78$		0			0
$79$	−3.54577e6			−0.809125			−0.404563	−	0.914510i	$-0.632576\pi$
$79$	−3.54577e6			−0.809125			−0.404563	+	0.914510i	$0.632576\pi$
$80$		0			0
$81$	−1.29159e7			−2.70040
$82$		0			0
$83$	179482.	+	179482.i	0.0344546	+	0.0344546i	0.724124	−	0.689670i	$-0.242244\pi$
$83$	179482.	+	179482.i	0.0344546	+	0.0344546i	−0.689670	+	0.724124i	$0.742244\pi$
$84$		0			0
$85$	−3.38394e6	+	3.38394e6i	−0.597662	+	0.597662i
$86$		0			0
$87$			506931.i			0.0825337i
$88$		0			0
$89$			262425.i			0.0394584i	0.999805	+	0.0197292i	$0.00628041\pi$
$89$			262425.i			0.0394584i	−0.999805	+	0.0197292i	$0.993720\pi$
$90$		0			0
$91$	−2.68292e6	+	2.68292e6i	−0.373218	+	0.373218i
$92$		0			0
$93$	−564016.	−	564016.i	−0.0727112	−	0.0727112i
$94$		0			0
$95$	5.75868e6			0.689113
$96$		0			0
$97$	1.53573e7			1.70849			0.854247	−	0.519867i	$-0.174018\pi$
$97$	1.53573e7			1.70849			0.854247	+	0.519867i	$0.174018\pi$
$98$		0			0
$99$	1.70711e6	+	1.70711e6i	0.176823	+	0.176823i
$100$		0			0
$101$	4.25472e6	−	4.25472e6i	0.410910	−	0.410910i	−0.471146	−	0.882055i	$-0.656159\pi$
$101$	4.25472e6	−	4.25472e6i	0.410910	−	0.410910i	0.882055	+	0.471146i	$0.156159\pi$
$102$		0			0
$103$		−	1.37835e7i		−	1.24288i	−0.783463	−	0.621438i	$-0.786549\pi$
$103$		−	1.37835e7i		−	1.24288i	0.783463	−	0.621438i	$-0.213451\pi$
$104$		0			0
$105$		−	2.38849e7i		−	2.01355i
$106$		0			0
$107$	−4.13797e6	+	4.13797e6i	−0.326546	+	0.326546i	−0.851271	−	0.524726i	$-0.824168\pi$
$107$	−4.13797e6	+	4.13797e6i	−0.326546	+	0.326546i	0.524726	+	0.851271i	$0.324168\pi$
$108$		0			0
$109$	−5.14000e6	−	5.14000e6i	−0.380163	−	0.380163i	0.490998	−	0.871161i	$-0.336632\pi$
$109$	−5.14000e6	−	5.14000e6i	−0.380163	−	0.380163i	−0.871161	+	0.490998i	$0.836632\pi$
$110$		0			0
$111$	1.29138e7			0.896236
$112$		0			0
$113$	1.07199e7			0.698899			0.349449	−	0.936955i	$-0.386369\pi$
$113$	1.07199e7			0.698899			0.349449	+	0.936955i	$0.386369\pi$
$114$		0			0
$115$	5.40689e6	+	5.40689e6i	0.331516	+	0.331516i
$116$		0			0
$117$	−1.21383e7	+	1.21383e7i	−0.700660	+	0.700660i
$118$		0			0
$119$			2.53013e7i			1.37635i
$120$		0			0
$121$			1.92902e7i			0.989894i
$122$		0			0
$123$	3.70400e7	−	3.70400e7i	1.79475	−	1.79475i
$124$		0			0
$125$	−1.68095e7	−	1.68095e7i	−0.769787	−	0.769787i
$126$		0			0
$127$	2.14599e7			0.929640			0.464820	−	0.885405i	$-0.346119\pi$
$127$	2.14599e7			0.929640			0.464820	+	0.885405i	$0.346119\pi$
$128$		0			0
$129$	9.86131e6			0.404455
$130$		0			0
$131$	−1.95903e6	−	1.95903e6i	−0.0761361	−	0.0761361i	0.668013	−	0.744149i	$-0.267145\pi$
$131$	−1.95903e6	−	1.95903e6i	−0.0761361	−	0.0761361i	−0.744149	+	0.668013i	$0.767145\pi$
$132$		0			0
$133$	2.15285e7	−	2.15285e7i	0.793474	−	0.793474i
$134$		0			0
$135$		−	6.46213e7i		−	2.26052i
$136$		0			0
$137$			3.21454e6i			0.106806i	0.998573	+	0.0534031i	$0.0170068\pi$
$137$			3.21454e6i			0.106806i	−0.998573	+	0.0534031i	$0.982993\pi$
$138$		0			0
$139$	−2.99300e7	+	2.99300e7i	−0.945267	+	0.945267i	−0.998578	−	0.0533107i	$-0.983023\pi$
$139$	−2.99300e7	+	2.99300e7i	−0.945267	+	0.945267i	0.0533107	+	0.998578i	$0.483023\pi$
$140$		0			0
$141$	7.68565e7	+	7.68565e7i	2.30894	+	2.30894i
$142$		0			0
$143$	1.40024e6			0.0400431
$144$		0			0
$145$	−1.32017e6			−0.0359619
$146$		0			0
$147$	−3.84348e7	−	3.84348e7i	−0.997961	−	0.997961i
$148$		0			0
$149$	−3.53474e7	+	3.53474e7i	−0.875397	+	0.875397i	−0.993054	−	0.117657i	$-0.962462\pi$
$149$	−3.53474e7	+	3.53474e7i	−0.875397	+	0.875397i	0.117657	+	0.993054i	$0.462462\pi$
$150$		0			0
$151$		−	1.10574e7i		−	0.261356i	−0.991425	−	0.130678i	$-0.958285\pi$
$151$		−	1.10574e7i		−	0.261356i	0.991425	−	0.130678i	$-0.0417153\pi$
$152$		0			0
$153$			1.14470e8i			2.58388i
$154$		0			0
$155$	1.46883e6	−	1.46883e6i	0.0316819	−	0.0316819i
$156$		0			0
$157$	2.40003e7	+	2.40003e7i	0.494958	+	0.494958i	0.909864	−	0.414906i	$-0.136186\pi$
$157$	2.40003e7	+	2.40003e7i	0.494958	+	0.494958i	−0.414906	+	0.909864i	$0.636186\pi$
$158$		0			0
$159$	−3.39475e7			−0.669758
$160$		0			0
$161$	4.04267e7			0.763444
$162$		0			0
$163$	3.75312e7	+	3.75312e7i	0.678791	+	0.678791i	0.959727	−	0.280936i	$-0.0906447\pi$
$163$	3.75312e7	+	3.75312e7i	0.678791	+	0.678791i	−0.280936	+	0.959727i	$0.590645\pi$
$164$		0			0
$165$	−6.23291e6	+	6.23291e6i	−0.108018	+	0.108018i
$166$		0			0
$167$			9.47634e7i			1.57447i	0.616656	+	0.787233i	$0.288487\pi$
$167$			9.47634e7i			1.57447i	−0.616656	+	0.787233i	$0.711513\pi$
$168$		0			0
$169$		−	5.27922e7i		−	0.841329i
$170$		0			0
$171$	9.74012e7	−	9.74012e7i	1.48963	−	1.48963i
$172$		0			0
$173$	3.79692e7	+	3.79692e7i	0.557532	+	0.557532i	0.928604	−	0.371072i	$-0.121010\pi$
$173$	3.79692e7	+	3.79692e7i	0.557532	+	0.557532i	−0.371072	+	0.928604i	$0.621010\pi$
$174$		0			0
$175$	−3.17404e7			−0.447691
$176$		0			0
$177$	−1.40457e8			−1.90387
$178$		0			0
$179$	2.43266e7	+	2.43266e7i	0.317026	+	0.317026i	0.847624	−	0.530598i	$-0.178032\pi$
$179$	2.43266e7	+	2.43266e7i	0.317026	+	0.317026i	−0.530598	+	0.847624i	$0.678032\pi$
$180$		0			0
$181$	9.65728e7	−	9.65728e7i	1.21054	−	1.21054i	0.239693	−	0.970849i	$-0.422953\pi$
$181$	9.65728e7	−	9.65728e7i	1.21054	−	1.21054i	0.970849	−	0.239693i	$-0.0770467\pi$
$182$		0			0
$183$		−	1.21649e8i		−	1.46734i
$184$		0			0
$185$			3.36305e7i			0.390511i
$186$		0			0
$187$	6.60251e6	−	6.60251e6i	0.0738352	−	0.0738352i
$188$		0			0
$189$	−2.41583e8	−	2.41583e8i	−2.60285	−	2.60285i
$190$		0			0
$191$	−8.94372e6			−0.0928756			−0.0464378	−	0.998921i	$-0.514787\pi$
$191$	−8.94372e6			−0.0928756			−0.0464378	+	0.998921i	$0.514787\pi$
$192$		0			0
$193$	1.39431e8			1.39607			0.698037	−	0.716062i	$-0.254057\pi$
$193$	1.39431e8			1.39607			0.698037	+	0.716062i	$0.254057\pi$
$194$		0			0
$195$	−4.43187e7	−	4.43187e7i	−0.428022	−	0.428022i
$196$		0			0
$197$	1.05806e8	−	1.05806e8i	0.986004	−	0.986004i	−0.0138997	−	0.999903i	$-0.504425\pi$
$197$	1.05806e8	−	1.05806e8i	0.986004	−	0.986004i	0.999903	+	0.0138997i	$0.00442455\pi$
$198$		0			0
$199$			1.09713e8i			0.986899i	0.869774	+	0.493449i	$0.164264\pi$
$199$			1.09713e8i			0.986899i	−0.869774	+	0.493449i	$0.835736\pi$
$200$		0			0
$201$		−	2.78086e8i		−	2.41542i
$202$		0			0
$203$	−4.93538e6	+	4.93538e6i	−0.0414080	+	0.0414080i
$204$		0			0
$205$	9.64612e7	+	9.64612e7i	0.782013	+	0.782013i
$206$		0			0
$207$	1.82902e8			1.43325
$208$		0			0
$209$	−1.12360e7			−0.0851330
$210$		0			0
$211$	1.50429e8	+	1.50429e8i	1.10241	+	1.10241i	0.994120	+	0.108288i	$0.0345370\pi$
$211$	1.50429e8	+	1.50429e8i	1.10241	+	1.10241i	0.108288	+	0.994120i	$0.465463\pi$
$212$		0			0
$213$	−3.39014e8	+	3.39014e8i	−2.40375	+	2.40375i
$214$		0			0
$215$			2.56812e7i			0.176231i
$216$		0			0
$217$		−	1.09823e7i		−	0.0729599i
$218$		0			0
$219$	−2.61654e8	+	2.61654e8i	−1.68334	+	1.68334i
$220$		0			0
$221$	4.69467e7	+	4.69467e7i	0.292572	+	0.292572i
$222$		0			0
$223$	−2.61269e7			−0.157768			−0.0788842	−	0.996884i	$-0.525136\pi$
$223$	−2.61269e7			−0.157768			−0.0788842	+	0.996884i	$0.525136\pi$
$224$		0			0
$225$	−1.43603e8			−0.840472
$226$		0			0
$227$	−8.25829e7	−	8.25829e7i	−0.468597	−	0.468597i	0.432863	−	0.901460i	$-0.357504\pi$
$227$	−8.25829e7	−	8.25829e7i	−0.468597	−	0.468597i	−0.901460	+	0.432863i	$0.857504\pi$
$228$		0			0
$229$	6.46397e7	−	6.46397e7i	0.355693	−	0.355693i	−0.506530	−	0.862223i	$-0.669072\pi$
$229$	6.46397e7	−	6.46397e7i	0.355693	−	0.355693i	0.862223	+	0.506530i	$0.169072\pi$
$230$		0			0
$231$			4.66027e7i			0.248754i
$232$		0			0
$233$			1.31897e8i			0.683109i	0.939862	+	0.341555i	$0.110953\pi$
$233$			1.31897e8i			0.683109i	−0.939862	+	0.341555i	$0.889047\pi$
$234$		0			0
$235$	−2.00153e8	+	2.00153e8i	−1.00606	+	1.00606i
$236$		0			0
$237$	−2.18968e8	−	2.18968e8i	−1.06847	−	1.06847i
$238$		0			0
$239$	−1.29899e8			−0.615478			−0.307739	−	0.951471i	$-0.599572\pi$
$239$	−1.29899e8			−0.615478			−0.307739	+	0.951471i	$0.599572\pi$
$240$		0			0
$241$	−1.44120e8			−0.663233			−0.331616	−	0.943414i	$-0.607594\pi$
$241$	−1.44120e8			−0.663233			−0.331616	+	0.943414i	$0.607594\pi$
$242$		0			0
$243$	−3.58238e8	−	3.58238e8i	−1.60158	−	1.60158i
$244$		0			0
$245$	1.00093e8	−	1.00093e8i	0.434835	−	0.434835i
$246$		0			0
$247$		−	7.98926e7i		−	0.337339i
$248$		0			0
$249$			2.21677e7i			0.0909961i
$250$		0			0
$251$	3.49428e7	−	3.49428e7i	0.139476	−	0.139476i	−0.633921	−	0.773398i	$-0.718556\pi$
$251$	3.49428e7	−	3.49428e7i	0.139476	−	0.139476i	0.773398	+	0.633921i	$0.218556\pi$
$252$		0			0
$253$	−1.05496e7	−	1.05496e7i	−0.0409555	−	0.0409555i
$254$		0			0
$255$	−4.17948e8			−1.57845
$256$		0			0
$257$	3.00776e8			1.10529			0.552647	−	0.833416i	$-0.313618\pi$
$257$	3.00776e8			1.10529			0.552647	+	0.833416i	$0.313618\pi$
$258$		0			0
$259$	1.25726e8	+	1.25726e8i	0.449651	+	0.449651i
$260$		0			0
$261$	−2.23291e7	+	2.23291e7i	−0.0777373	+	0.0777373i
$262$		0			0
$263$			3.76784e8i			1.27716i	0.769553	+	0.638582i	$0.220479\pi$
$263$			3.76784e8i			1.27716i	−0.769553	+	0.638582i	$0.779521\pi$
$264$		0			0
$265$		−	8.84075e7i		−	0.291829i
$266$		0			0
$267$	−1.62060e7	+	1.62060e7i	−0.0521058	+	0.0521058i
$268$		0			0
$269$	−1.16914e8	−	1.16914e8i	−0.366214	−	0.366214i	0.499881	−	0.866094i	$-0.333377\pi$
$269$	−1.16914e8	−	1.16914e8i	−0.366214	−	0.366214i	−0.866094	+	0.499881i	$0.833377\pi$
$270$		0			0
$271$	−4.28052e8			−1.30648			−0.653242	−	0.757149i	$-0.726592\pi$
$271$	−4.28052e8			−1.30648			−0.653242	+	0.757149i	$0.726592\pi$
$272$		0			0
$273$	−3.31366e8			−0.985685
$274$		0			0
$275$	8.28282e6	+	8.28282e6i	0.0240167	+	0.0240167i
$276$		0			0
$277$	−2.81665e8	+	2.81665e8i	−0.796259	+	0.796259i	−0.982503	−	0.186245i	$-0.940368\pi$
$277$	−2.81665e8	+	2.81665e8i	−0.796259	+	0.796259i	0.186245	+	0.982503i	$0.440368\pi$
$278$		0			0
$279$		−	4.96871e7i		−	0.136971i
$280$		0			0
$281$			1.55429e7i			0.0417888i	0.999782	+	0.0208944i	$0.00665138\pi$
$281$			1.55429e7i			0.0417888i	−0.999782	+	0.0208944i	$0.993349\pi$
$282$		0			0
$283$	2.73861e8	−	2.73861e8i	0.718253	−	0.718253i	−0.249994	−	0.968247i	$-0.580429\pi$
$283$	2.73861e8	−	2.73861e8i	0.718253	−	0.718253i	0.968247	+	0.249994i	$0.0804287\pi$
$284$		0			0
$285$	3.55626e8	+	3.55626e8i	0.909990	+	0.909990i
$286$		0			0
$287$	7.21229e8			1.80089
$288$		0			0
$289$	3.23934e7			0.0789430
$290$		0			0
$291$	9.48386e8	+	9.48386e8i	2.25611	+	2.25611i
$292$		0			0
$293$	2.08481e8	−	2.08481e8i	0.484206	−	0.484206i	−0.422266	−	0.906472i	$-0.638765\pi$
$293$	2.08481e8	−	2.08481e8i	0.484206	−	0.484206i	0.906472	+	0.422266i	$0.138765\pi$
$294$		0			0
$295$		−	3.65784e8i		−	0.829559i
$296$		0			0
$297$			1.26085e8i			0.279264i
$298$		0			0
$299$	7.50120e7	−	7.50120e7i	0.162286	−	0.162286i
$300$		0			0
$301$	9.60078e7	+	9.60078e7i	0.202919	+	0.202919i
$302$		0			0
$303$	5.25499e8			1.08523
$304$		0			0
$305$	3.16803e8			0.639352
$306$		0			0
$307$	−6.18048e8	−	6.18048e8i	−1.21910	−	1.21910i	−0.967949	−	0.251148i	$-0.919192\pi$
$307$	−6.18048e8	−	6.18048e8i	−1.21910	−	1.21910i	−0.251148	−	0.967949i	$-0.580808\pi$
$308$		0			0
$309$	8.51194e8	−	8.51194e8i	1.64125	−	1.64125i
$310$		0			0
$311$			5.41827e7i			0.102141i	0.998695	+	0.0510704i	$0.0162633\pi$
$311$			5.41827e7i			0.102141i	−0.998695	+	0.0510704i	$0.983737\pi$
$312$		0			0
$313$		−	9.15920e8i		−	1.68831i	−0.536099	−	0.844155i	$-0.680102\pi$
$313$		−	9.15920e8i		−	1.68831i	0.536099	−	0.844155i	$-0.319898\pi$
$314$		0			0
$315$	1.05207e9	−	1.05207e9i	1.89653	−	1.89653i
$316$		0			0
$317$	−3.83951e8	−	3.83951e8i	−0.676968	−	0.676968i	0.282345	−	0.959313i	$-0.408888\pi$
$317$	−3.83951e8	−	3.83951e8i	−0.676968	−	0.676968i	−0.959313	+	0.282345i	$0.908888\pi$
$318$		0			0
$319$	2.57583e6			0.00444273
$320$		0			0
$321$	−5.11079e8			−0.862423
$322$		0			0
$323$	−3.76714e8	−	3.76714e8i	−0.622018	−	0.622018i
$324$		0			0
$325$	−5.88945e7	+	5.88945e7i	−0.0951662	+	0.0951662i
$326$		0			0
$327$		−	6.34838e8i		−	1.00403i
$328$		0			0
$329$			1.49652e9i			2.31684i
$330$		0			0
$331$	−1.82269e8	+	1.82269e8i	−0.276258	+	0.276258i	−0.831613	−	0.555355i	$-0.812582\pi$
$331$	−1.82269e8	+	1.82269e8i	−0.276258	+	0.276258i	0.555355	+	0.831613i	$0.312582\pi$
$332$		0			0
$333$	5.68820e8	+	5.68820e8i	0.844151	+	0.844151i
$334$		0			0
$335$	7.24203e8			1.05245
$336$		0			0
$337$	4.15826e8			0.591843			0.295921	−	0.955212i	$-0.404373\pi$
$337$	4.15826e8			0.591843			0.295921	+	0.955212i	$0.404373\pi$
$338$		0			0
$339$	6.62002e8	+	6.62002e8i	0.922912	+	0.922912i
$340$		0			0
$341$	−2.86589e6	+	2.86589e6i	−0.00391399	+	0.00391399i
$342$		0			0
$343$			2.41894e8i			0.323666i
$344$		0			0
$345$			6.67802e8i			0.875550i
$346$		0			0
$347$	−1.16993e8	+	1.16993e8i	−0.150316	+	0.150316i	−0.778259	−	0.627943i	$-0.783897\pi$
$347$	−1.16993e8	+	1.16993e8i	−0.150316	+	0.150316i	0.627943	+	0.778259i	$0.283897\pi$
$348$		0			0
$349$	9.43121e8	+	9.43121e8i	1.18762	+	1.18762i	0.977723	+	0.209900i	$0.0673138\pi$
$349$	9.43121e8	+	9.43121e8i	1.18762	+	1.18762i	0.209900	+	0.977723i	$0.432686\pi$
$350$		0			0
$351$	−8.96518e8			−1.10658
$352$		0			0
$353$	−2.66226e8			−0.322136			−0.161068	−	0.986943i	$-0.551494\pi$
$353$	−2.66226e8			−0.322136			−0.161068	+	0.986943i	$0.551494\pi$
$354$		0			0
$355$	−8.82875e8	−	8.82875e8i	−1.04737	−	1.04737i
$356$		0			0
$357$	−1.56247e9	+	1.56247e9i	−1.81750	+	1.81750i
$358$		0			0
$359$			6.82905e8i			0.778987i	0.921029	+	0.389493i	$0.127350\pi$
$359$			6.82905e8i			0.778987i	−0.921029	+	0.389493i	$0.872650\pi$
$360$		0			0
$361$		−	2.52791e8i		−	0.282804i
$362$		0			0
$363$	−1.19126e9	+	1.19126e9i	−1.30718	+	1.30718i
$364$		0			0
$365$	−6.81410e8	−	6.81410e8i	−0.733472	−	0.733472i
$366$		0			0
$367$	2.05790e8			0.217316			0.108658	−	0.994079i	$-0.465345\pi$
$367$	2.05790e8			0.217316			0.108658	+	0.994079i	$0.465345\pi$
$368$		0			0
$369$	3.26305e9			3.38089
$370$		0			0
$371$	−3.30506e8	−	3.30506e8i	−0.336025	−	0.336025i
$372$		0			0
$373$	−1.39903e8	+	1.39903e8i	−0.139588	+	0.139588i	−0.773448	−	0.633860i	$-0.781470\pi$
$373$	−1.39903e8	+	1.39903e8i	−0.139588	+	0.139588i	0.633860	+	0.773448i	$0.281470\pi$
$374$		0			0
$375$		−	2.07614e9i		−	2.03304i
$376$		0			0
$377$			1.83153e7i			0.0176043i
$378$		0			0
$379$	3.01841e7	−	3.01841e7i	0.0284801	−	0.0284801i	−0.692723	−	0.721203i	$-0.743589\pi$
$379$	3.01841e7	−	3.01841e7i	0.0284801	−	0.0284801i	0.721203	+	0.692723i	$0.243589\pi$
$380$		0			0
$381$	1.32525e9	+	1.32525e9i	1.22761	+	1.22761i
$382$		0			0
$383$	−1.42433e9			−1.29543			−0.647717	−	0.761881i	$-0.724276\pi$
$383$	−1.42433e9			−1.29543			−0.647717	+	0.761881i	$0.724276\pi$
$384$		0			0
$385$	−1.21365e8			−0.108388
$386$		0			0
$387$	4.34367e8	+	4.34367e8i	0.380950	+	0.380950i
$388$		0			0
$389$	−1.23137e9	+	1.23137e9i	−1.06063	+	1.06063i	−0.0625913	+	0.998039i	$0.519936\pi$
$389$	−1.23137e9	+	1.23137e9i	−1.06063	+	1.06063i	−0.998039	+	0.0625913i	$0.980064\pi$
$390$		0			0
$391$		−	7.07402e8i		−	0.598477i
$392$		0			0
$393$		−	2.41958e8i		−	0.201079i
$394$		0			0
$395$	5.70246e8	−	5.70246e8i	0.465557	−	0.465557i
$396$		0			0
$397$	−1.48636e9	−	1.48636e9i	−1.19223	−	1.19223i	−0.976441	−	0.215784i	$-0.930769\pi$
$397$	−1.48636e9	−	1.48636e9i	−1.19223	−	1.19223i	−0.215784	−	0.976441i	$-0.569231\pi$
$398$		0			0
$399$	2.65897e9			2.09560
$400$		0			0
$401$	−1.01690e9			−0.787544			−0.393772	−	0.919208i	$-0.628830\pi$
$401$	−1.01690e9			−0.787544			−0.393772	+	0.919208i	$0.628830\pi$
$402$		0			0
$403$	−2.03777e7	−	2.03777e7i	−0.0155092	−	0.0155092i
$404$		0			0
$405$	2.07720e9	−	2.07720e9i	1.55376	−	1.55376i
$406$		0			0
$407$		−	6.56177e7i		−	0.0482437i
$408$		0			0
$409$		−	5.67432e8i		−	0.410093i	−0.978752	−	0.205046i	$-0.934266\pi$
$409$		−	5.67432e8i		−	0.410093i	0.978752	−	0.205046i	$-0.0657345\pi$
$410$		0			0
$411$	−1.98513e8	+	1.98513e8i	−0.141040	+	0.141040i
$412$		0			0
$413$	−1.36746e9	−	1.36746e9i	−0.955190	−	0.955190i
$414$		0			0
$415$	−5.77300e7			−0.0396491
$416$		0			0
$417$	−3.69664e9			−2.49649
$418$		0			0
$419$	1.16751e9	+	1.16751e9i	0.775372	+	0.775372i	0.979040	−	0.203668i	$-0.0652863\pi$
$419$	1.16751e9	+	1.16751e9i	0.775372	+	0.775372i	−0.203668	+	0.979040i	$0.565286\pi$
$420$		0			0
$421$	1.41024e9	−	1.41024e9i	0.921096	−	0.921096i	−0.0760111	−	0.997107i	$-0.524218\pi$
$421$	1.41024e9	−	1.41024e9i	0.921096	−	0.921096i	0.997107	+	0.0760111i	$0.0242184\pi$
$422$		0			0
$423$			6.77069e9i			4.34952i
$424$		0			0
$425$			5.55405e8i			0.350953i
$426$		0			0
$427$	1.18435e9	−	1.18435e9i	0.736178	−	0.736178i
$428$		0			0
$429$	8.64717e7	+	8.64717e7i	0.0528778	+	0.0528778i
$430$		0			0
$431$	1.12113e9			0.674503			0.337252	−	0.941415i	$-0.390503\pi$
$431$	1.12113e9			0.674503			0.337252	+	0.941415i	$0.390503\pi$
$432$		0			0
$433$	2.87439e8			0.170153			0.0850763	−	0.996374i	$-0.472887\pi$
$433$	2.87439e8			0.170153			0.0850763	+	0.996374i	$0.472887\pi$
$434$		0			0
$435$	−8.15268e7	−	8.15268e7i	−0.0474885	−	0.0474885i
$436$		0			0
$437$	−6.01918e8	+	6.01918e8i	−0.345026	+	0.345026i
$438$		0			0
$439$		−	2.85117e9i		−	1.60841i	−0.594349	−	0.804207i	$-0.702590\pi$
$439$		−	2.85117e9i		−	1.60841i	0.594349	−	0.804207i	$-0.297410\pi$
$440$		0			0
$441$		−	3.38592e9i		−	1.87993i
$442$		0			0
$443$	4.04267e8	−	4.04267e8i	0.220930	−	0.220930i	−0.587960	−	0.808890i	$-0.700069\pi$
$443$	4.04267e8	−	4.04267e8i	0.220930	−	0.220930i	0.808890	+	0.587960i	$0.200069\pi$
$444$		0			0
$445$	−4.22043e7	−	4.22043e7i	−0.0227037	−	0.0227037i
$446$		0			0
$447$	−4.36573e9			−2.31196
$448$		0			0
$449$	−7.72327e8			−0.402660			−0.201330	−	0.979523i	$-0.564526\pi$
$449$	−7.72327e8			−0.402660			−0.201330	+	0.979523i	$0.564526\pi$
$450$		0			0
$451$	−1.88209e8	−	1.88209e8i	−0.0966099	−	0.0966099i
$452$		0			0
$453$	6.82844e8	−	6.82844e8i	0.345126	−	0.345126i
$454$		0			0
$455$		−	8.62956e8i		−	0.429486i
$456$		0			0
$457$		−	1.74188e9i		−	0.853714i	−0.904319	−	0.426857i	$-0.859621\pi$
$457$		−	1.74188e9i		−	0.853714i	0.904319	−	0.426857i	$-0.140379\pi$
$458$		0			0
$459$	−4.22731e9	+	4.22731e9i	−2.04042	+	2.04042i
$460$		0			0
$461$	−3.94690e8	−	3.94690e8i	−0.187630	−	0.187630i	0.607041	−	0.794671i	$-0.292356\pi$
$461$	−3.94690e8	−	3.94690e8i	−0.187630	−	0.187630i	−0.794671	+	0.607041i	$0.792356\pi$
$462$		0			0
$463$	−1.89577e9			−0.887671			−0.443835	−	0.896108i	$-0.646382\pi$
$463$	−1.89577e9			−0.887671			−0.443835	+	0.896108i	$0.646382\pi$
$464$		0			0
$465$	1.81415e8			0.0836735
$466$		0			0
$467$	−1.55488e9	−	1.55488e9i	−0.706459	−	0.706459i	0.259330	−	0.965789i	$-0.416498\pi$
$467$	−1.55488e9	−	1.55488e9i	−0.706459	−	0.706459i	−0.965789	+	0.259330i	$0.916498\pi$
$468$		0			0
$469$	2.70739e9	−	2.70739e9i	1.21184	−	1.21184i
$470$		0			0
$471$			2.96427e9i			1.30721i
$472$		0			0
$473$		−	5.01075e7i		−	0.0217715i
$474$		0			0
$475$	4.72586e8	−	4.72586e8i	0.202327	−	0.202327i
$476$		0			0
$477$	−1.49531e9	−	1.49531e9i	−0.630835	−	0.630835i
$478$		0			0
$479$	9.27374e8			0.385550			0.192775	−	0.981243i	$-0.438251\pi$
$479$	9.27374e8			0.385550			0.192775	+	0.981243i	$0.438251\pi$
$480$		0			0
$481$	4.66570e8			0.191165
$482$		0			0
$483$	2.49654e9	+	2.49654e9i	1.00815	+	1.00815i
$484$		0			0
$485$	−2.46983e9	+	2.46983e9i	−0.983038	+	0.983038i
$486$		0			0
$487$		−	3.35907e9i		−	1.31786i	−0.752206	−	0.658929i	$-0.771010\pi$
$487$		−	3.35907e9i		−	1.31786i	0.752206	−	0.658929i	$-0.228990\pi$
$488$		0			0
$489$			4.63546e9i			1.79272i
$490$		0			0
$491$	−6.58146e8	+	6.58146e8i	−0.250921	+	0.250921i	−0.821348	−	0.570427i	$-0.806778\pi$
$491$	−6.58146e8	+	6.58146e8i	−0.250921	+	0.250921i	0.570427	+	0.821348i	$0.306778\pi$
$492$		0			0
$493$	8.63613e7	+	8.63613e7i	0.0324605	+	0.0324605i
$494$		0			0
$495$	−5.49089e8			−0.203481
$496$		0			0
$497$	−6.60115e9			−2.41197
$498$		0			0
$499$	−1.16527e9	−	1.16527e9i	−0.419830	−	0.419830i	0.465315	−	0.885145i	$-0.345941\pi$
$499$	−1.16527e9	−	1.16527e9i	−0.419830	−	0.419830i	−0.885145	+	0.465315i	$0.845941\pi$
$500$		0			0
$501$	−5.85209e9	+	5.85209e9i	−2.07912	+	2.07912i
$502$		0			0
$503$			8.09330e8i			0.283555i	0.989899	+	0.141778i	$0.0452818\pi$
$503$			8.09330e8i			0.283555i	−0.989899	+	0.141778i	$0.954718\pi$
$504$		0			0
$505$			1.36853e9i			0.472861i
$506$		0			0
$507$	3.26017e9	−	3.26017e9i	1.11099	−	1.11099i
$508$		0			0
$509$	3.64859e9	+	3.64859e9i	1.22635	+	1.22635i	0.965336	+	0.261011i	$0.0840560\pi$
$509$	3.64859e9	+	3.64859e9i	1.22635	+	1.22635i	0.261011	+	0.965336i	$0.415944\pi$
$510$		0			0
$511$	−5.09482e9			−1.68910
$512$		0			0
$513$	7.19392e9			2.35264
$514$		0			0
$515$	2.21671e9	+	2.21671e9i	0.715129	+	0.715129i
$516$		0			0
$517$	3.90525e8	−	3.90525e8i	0.124289	−	0.124289i
$518$		0			0
$519$			4.68956e9i			1.47247i
$520$		0			0
$521$		−	5.31090e7i		−	0.0164527i	−0.999966	−	0.00822633i	$-0.997381\pi$
$521$		−	5.31090e7i		−	0.0164527i	0.999966	−	0.00822633i	$-0.00261855\pi$
$522$		0			0
$523$	−1.99031e9	+	1.99031e9i	−0.608364	+	0.608364i	−0.942518	−	0.334154i	$-0.891549\pi$
$523$	−1.99031e9	+	1.99031e9i	−0.608364	+	0.608364i	0.334154	+	0.942518i	$0.391549\pi$
$524$		0			0
$525$	−1.96012e9	−	1.96012e9i	−0.591187	−	0.591187i
$526$		0			0
$527$	−1.92173e8			−0.0571945
$528$		0			0
$529$	2.27453e9			0.668032
$530$		0			0
$531$	−6.18679e9	−	6.18679e9i	−1.79322	−	1.79322i
$532$		0			0
$533$	1.33825e9	−	1.33825e9i	0.382816	−	0.382816i
$534$		0			0
$535$		−	1.33097e9i		−	0.375778i
$536$		0			0
$537$			3.00456e9i			0.837281i
$538$		0			0
$539$	−1.95296e8	+	1.95296e8i	−0.0537195	+	0.0537195i
$540$		0			0
$541$	−1.46358e9	−	1.46358e9i	−0.397398	−	0.397398i	0.479916	−	0.877314i	$-0.340667\pi$
$541$	−1.46358e9	−	1.46358e9i	−0.397398	−	0.397398i	−0.877314	+	0.479916i	$0.840667\pi$
$542$		0			0
$543$	1.19277e10			3.19710
$544$		0			0
$545$	1.65327e9			0.437479
$546$		0			0
$547$	−1.11429e9	−	1.11429e9i	−0.291101	−	0.291101i	0.546414	−	0.837515i	$-0.315993\pi$
$547$	−1.11429e9	−	1.11429e9i	−0.291101	−	0.291101i	−0.837515	+	0.546414i	$0.815993\pi$
$548$		0			0
$549$	5.35835e9	−	5.35835e9i	1.38206	−	1.38206i
$550$		0			0
$551$		−	1.46967e8i		−	0.0374274i
$552$		0			0
$553$		−	4.26366e9i		−	1.07212i
$554$		0			0
$555$	−2.07685e9	+	2.07685e9i	−0.515678	+	0.515678i
$556$		0			0
$557$	4.33757e9	+	4.33757e9i	1.06354	+	1.06354i	0.997839	+	0.0656996i	$0.0209279\pi$
$557$	4.33757e9	+	4.33757e9i	1.06354	+	1.06354i	0.0656996	+	0.997839i	$0.479072\pi$
$558$		0			0
$559$	3.56286e8			0.0862696
$560$		0			0
$561$	8.15473e8			0.195002
$562$		0			0
$563$	1.49585e9	+	1.49585e9i	0.353271	+	0.353271i	0.861325	−	0.508054i	$-0.169635\pi$
$563$	1.49585e9	+	1.49585e9i	0.353271	+	0.353271i	−0.508054	+	0.861325i	$0.669635\pi$
$564$		0			0
$565$	−1.72401e9	+	1.72401e9i	−0.402134	+	0.402134i
$566$		0			0
$567$		−	1.55310e10i		−	3.57814i
$568$		0			0
$569$		−	5.13775e9i		−	1.16918i	−0.811330	−	0.584588i	$-0.801256\pi$
$569$		−	5.13775e9i		−	1.16918i	0.811330	−	0.584588i	$-0.198744\pi$
$570$		0			0
$571$	−1.26567e9	+	1.26567e9i	−0.284508	+	0.284508i	−0.834904	−	0.550396i	$-0.814477\pi$
$571$	−1.26567e9	+	1.26567e9i	−0.284508	+	0.284508i	0.550396	+	0.834904i	$0.314477\pi$
$572$		0			0
$573$	−5.52317e8	−	5.52317e8i	−0.122644	−	0.122644i
$574$		0			0
$575$	8.87433e8			0.194670
$576$		0			0
$577$	−5.72767e8			−0.124126			−0.0620630	−	0.998072i	$-0.519768\pi$
$577$	−5.72767e8			−0.124126			−0.0620630	+	0.998072i	$0.519768\pi$
$578$		0			0
$579$	8.61052e9	+	8.61052e9i	1.84355	+	1.84355i
$580$		0			0
$581$	−2.15820e8	+	2.15820e8i	−0.0456537	+	0.0456537i
$582$		0			0
$583$			1.72495e8i			0.0360526i
$584$		0			0
$585$		−	3.90426e9i		−	0.806295i
$586$		0			0
$587$	4.64216e9	−	4.64216e9i	0.947298	−	0.947298i	−0.0513812	−	0.998679i	$-0.516362\pi$
$587$	4.64216e9	−	4.64216e9i	0.947298	−	0.947298i	0.998679	+	0.0513812i	$0.0163624\pi$
$588$		0			0
$589$	1.63517e8	+	1.63517e8i	0.0329730	+	0.0329730i
$590$		0			0
$591$	1.30680e10			2.60408
$592$		0			0
$593$	6.95056e8			0.136876			0.0684382	−	0.997655i	$-0.478198\pi$
$593$	6.95056e8			0.136876			0.0684382	+	0.997655i	$0.478198\pi$
$594$		0			0
$595$	−4.06906e9	−	4.06906e9i	−0.791927	−	0.791927i
$596$		0			0
$597$	−6.77530e9	+	6.77530e9i	−1.30322	+	1.30322i
$598$		0			0
$599$			4.70981e9i			0.895384i	0.894188	+	0.447692i	$0.147754\pi$
$599$			4.70981e9i			0.895384i	−0.894188	+	0.447692i	$0.852246\pi$
$600$		0			0
$601$			7.02648e9i			1.32031i	0.751128	+	0.660157i	$0.229510\pi$
$601$			7.02648e9i			1.32031i	−0.751128	+	0.660157i	$0.770490\pi$
$602$		0			0
$603$	1.22490e10	−	1.22490e10i	2.27505	−	2.27505i
$604$		0			0
$605$	−3.10234e9	−	3.10234e9i	−0.569568	−	0.569568i
$606$		0			0
$607$	−8.10093e8			−0.147019			−0.0735096	−	0.997295i	$-0.523420\pi$
$607$	−8.10093e8			−0.147019			−0.0735096	+	0.997295i	$0.523420\pi$
$608$		0			0
$609$	−6.09567e8			−0.109361
$610$		0			0
$611$	2.77680e9	+	2.77680e9i	0.492494	+	0.492494i
$612$		0			0
$613$	7.64430e9	−	7.64430e9i	1.34037	−	1.34037i	0.444689	−	0.895685i	$-0.353314\pi$
$613$	7.64430e9	−	7.64430e9i	1.34037	−	1.34037i	0.895685	−	0.444689i	$-0.146686\pi$
$614$		0			0
$615$			1.19139e10i			2.06533i
$616$		0			0
$617$		−	1.76031e9i		−	0.301710i	−0.988556	−	0.150855i	$-0.951797\pi$
$617$		−	1.76031e9i		−	0.301710i	0.988556	−	0.150855i	$-0.0482027\pi$
$618$		0			0
$619$	5.28896e8	−	5.28896e8i	0.0896299	−	0.0896299i	−0.660870	−	0.750500i	$-0.729813\pi$
$619$	5.28896e8	−	5.28896e8i	0.0896299	−	0.0896299i	0.750500	+	0.660870i	$0.229813\pi$
$620$		0			0
$621$	6.75445e9	+	6.75445e9i	1.13180	+	1.13180i
$622$		0			0
$623$	−3.15557e8			−0.0522840
$624$		0			0
$625$	3.34457e9			0.547974
$626$		0			0
$627$	−6.93874e8	−	6.93874e8i	−0.112420	−	0.112420i
$628$		0			0
$629$	2.20000e9	−	2.20000e9i	0.352489	−	0.352489i
$630$		0			0
$631$		−	9.08344e9i		−	1.43929i	−0.694344	−	0.719644i	$-0.744305\pi$
$631$		−	9.08344e9i		−	1.43929i	0.694344	−	0.719644i	$-0.255695\pi$
$632$		0			0
$633$			1.85794e10i			2.91151i
$634$		0			0
$635$	−3.45128e9	+	3.45128e9i	−0.534899	+	0.534899i
$636$		0			0
$637$	−1.38864e9	−	1.38864e9i	−0.212863	−	0.212863i
$638$		0			0
$639$	−2.98655e10			−4.52811
$640$		0			0
$641$	9.60692e9			1.44073			0.720363	−	0.693598i	$-0.243975\pi$
$641$	9.60692e9			1.44073			0.720363	+	0.693598i	$0.243975\pi$
$642$		0			0
$643$	−9.22467e9	−	9.22467e9i	−1.36840	−	1.36840i	−0.862726	−	0.505672i	$-0.831245\pi$
$643$	−9.22467e9	−	9.22467e9i	−1.36840	−	1.36840i	−0.505672	−	0.862726i	$-0.668755\pi$
$644$		0			0
$645$	−1.58594e9	+	1.58594e9i	−0.232717	+	0.232717i
$646$		0			0
$647$		−	7.64371e9i		−	1.10953i	−0.832007	−	0.554765i	$-0.812808\pi$
$647$		−	7.64371e9i		−	1.10953i	0.832007	−	0.554765i	$-0.187192\pi$
$648$		0			0
$649$			7.13693e8i			0.102484i
$650$		0			0
$651$	6.78209e8	−	6.78209e8i	0.0963452	−	0.0963452i
$652$		0			0
$653$	9.00786e9	+	9.00786e9i	1.26598	+	1.26598i	0.948148	+	0.317828i	$0.102954\pi$
$653$	9.00786e9	+	9.00786e9i	1.26598	+	1.26598i	0.317828	+	0.948148i	$0.397046\pi$
$654$		0			0
$655$	6.30118e8			0.0876147
$656$		0			0
$657$	−2.30505e10			−3.17103
$658$		0			0
$659$	8.58058e9	+	8.58058e9i	1.16793	+	1.16793i	0.982693	+	0.185239i	$0.0593060\pi$
$659$	8.58058e9	+	8.58058e9i	1.16793	+	1.16793i	0.185239	+	0.982693i	$0.440694\pi$
$660$		0			0
$661$	3.98292e9	−	3.98292e9i	0.536410	−	0.536410i	−0.386063	−	0.922472i	$-0.626165\pi$
$661$	3.98292e9	−	3.98292e9i	0.536410	−	0.536410i	0.922472	+	0.386063i	$0.126165\pi$
$662$		0			0
$663$			5.79837e9i			0.772696i
$664$		0			0
$665$			6.92461e9i			0.913103i
$666$		0			0
$667$	1.37989e8	−	1.37989e8i	0.0180055	−	0.0180055i
$668$		0			0
$669$	−1.61346e9	−	1.61346e9i	−0.208337	−	0.208337i
$670$		0			0
$671$	−6.18126e8			−0.0789856
$672$		0			0
$673$	1.05739e10			1.33716			0.668580	−	0.743640i	$-0.266902\pi$
$673$	1.05739e10			1.33716			0.668580	+	0.743640i	$0.266902\pi$
$674$		0			0
$675$	−5.30315e9	−	5.30315e9i	−0.663698	−	0.663698i
$676$		0			0
$677$	−1.00400e10	+	1.00400e10i	−1.24358	+	1.24358i	−0.285078	+	0.958504i	$0.592019\pi$
$677$	−1.00400e10	+	1.00400e10i	−1.24358	+	1.24358i	−0.958504	+	0.285078i	$0.907981\pi$
$678$		0			0
$679$			1.84666e10i			2.26382i
$680$		0			0
$681$		−	1.01998e10i		−	1.23759i
$682$		0			0
$683$	−1.01009e10	+	1.01009e10i	−1.21307	+	1.21307i	−0.243059	+	0.970012i	$0.578151\pi$
$683$	−1.01009e10	+	1.01009e10i	−1.21307	+	1.21307i	−0.970012	+	0.243059i	$0.921849\pi$
$684$		0			0
$685$	−5.16976e8	−	5.16976e8i	−0.0614544	−	0.0614544i
$686$		0			0
$687$	7.98362e9			0.939401
$688$		0			0
$689$	−1.22651e9			−0.142858
$690$		0			0
$691$	8.49939e8	+	8.49939e8i	0.0979974	+	0.0979974i	0.754406	−	0.656408i	$-0.227925\pi$
$691$	8.49939e8	+	8.49939e8i	0.0979974	+	0.0979974i	−0.656408	+	0.754406i	$0.727925\pi$
$692$		0			0
$693$	−2.05274e9	+	2.05274e9i	−0.234297	+	0.234297i
$694$		0			0
$695$		−	9.62694e9i		−	1.08778i
$696$		0			0
$697$		−	1.26203e10i		−	1.41175i
$698$		0			0
$699$	−8.14528e9	+	8.14528e9i	−0.902061	+	0.902061i
$700$		0			0
$701$	−8.49362e9	−	8.49362e9i	−0.931278	−	0.931278i	0.0665075	−	0.997786i	$-0.478814\pi$
$701$	−8.49362e9	−	8.49362e9i	−0.931278	−	0.931278i	−0.997786	+	0.0665075i	$0.978814\pi$
$702$		0			0
$703$	−3.74390e9			−0.406425
$704$		0			0
$705$	−2.47208e10			−2.65705
$706$		0			0
$707$	5.11615e9	+	5.11615e9i	0.544472	+	0.544472i
$708$		0			0
$709$	4.58762e9	−	4.58762e9i	0.483421	−	0.483421i	−0.422801	−	0.906222i	$-0.638953\pi$
$709$	4.58762e9	−	4.58762e9i	0.483421	−	0.483421i	0.906222	+	0.422801i	$0.138953\pi$
$710$		0			0
$711$		−	1.92900e10i		−	2.01275i
$712$		0			0
$713$			3.07056e8i			0.0317251i
$714$		0			0
$715$	−2.25193e8	+	2.25193e8i	−0.0230401	+	0.0230401i
$716$		0			0
$717$	−8.02186e9	−	8.02186e9i	−0.812752	−	0.812752i
$718$		0			0
$719$	9.61133e9			0.964345			0.482172	−	0.876076i	$-0.339848\pi$
$719$	9.61133e9			0.964345			0.482172	+	0.876076i	$0.339848\pi$
$720$		0			0
$721$	1.65741e10			1.64686
$722$		0			0
$723$	−8.90012e9	−	8.90012e9i	−0.875814	−	0.875814i
$724$		0			0
$725$	−1.08340e8	+	1.08340e8i	−0.0105586	+	0.0105586i
$726$		0			0
$727$			1.34243e10i			1.29575i	0.761745	+	0.647877i	$0.224343\pi$
$727$			1.34243e10i			1.29575i	−0.761745	+	0.647877i	$0.775657\pi$
$728$		0			0
$729$		−	1.59986e10i		−	1.52945i
$730$		0			0
$731$	1.67998e9	−	1.67998e9i	0.159072	−	0.159072i
$732$		0			0
$733$	9.32912e8	+	9.32912e8i	0.0874937	+	0.0874937i	0.749499	−	0.662005i	$-0.230294\pi$
$733$	9.32912e8	+	9.32912e8i	0.0874937	+	0.0874937i	−0.662005	+	0.749499i	$0.730294\pi$
$734$		0			0
$735$	1.23625e10			1.14842
$736$		0			0
$737$	−1.41302e9			−0.130020
$738$		0			0
$739$	−1.69251e9	−	1.69251e9i	−0.154268	−	0.154268i	0.625753	−	0.780021i	$-0.284792\pi$
$739$	−1.69251e9	−	1.69251e9i	−0.154268	−	0.154268i	−0.780021	+	0.625753i	$0.784792\pi$
$740$		0			0
$741$	4.93375e9	−	4.93375e9i	0.445464	−	0.445464i
$742$		0			0
$743$			1.77397e10i			1.58666i	0.608791	+	0.793331i	$0.291655\pi$
$743$			1.77397e10i			1.58666i	−0.608791	+	0.793331i	$0.708345\pi$
$744$		0			0
$745$		−	1.13694e10i		−	1.00738i
$746$		0			0
$747$	−9.76433e8	+	9.76433e8i	−0.0857078	+	0.0857078i
$748$		0			0
$749$	−4.97576e9	−	4.97576e9i	−0.432686	−	0.432686i
$750$		0			0
$751$	−1.09851e10			−0.946375			−0.473188	−	0.880962i	$-0.656897\pi$
$751$	−1.09851e10			−0.946375			−0.473188	+	0.880962i	$0.656897\pi$
$752$		0			0
$753$	4.31577e9			0.368363
$754$		0			0
$755$	1.77829e9	+	1.77829e9i	0.150379	+	0.150379i
$756$		0			0
$757$	9.18198e9	−	9.18198e9i	0.769309	−	0.769309i	−0.208676	−	0.977985i	$-0.566915\pi$
$757$	9.18198e9	−	9.18198e9i	0.769309	−	0.769309i	0.977985	+	0.208676i	$0.0669153\pi$
$758$		0			0
$759$		−	1.30297e9i		−	0.108165i
$760$		0			0
$761$			1.19466e9i			0.0982647i	0.998792	+	0.0491324i	$0.0156456\pi$
$761$			1.19466e9i			0.0982647i	−0.998792	+	0.0491324i	$0.984354\pi$
$762$		0			0
$763$	6.18066e9	−	6.18066e9i	0.503732	−	0.503732i
$764$		0			0
$765$	−1.84096e10	−	1.84096e10i	−1.48672	−	1.48672i
$766$		0			0
$767$	−5.07467e9			−0.406091
$768$		0			0
$769$	8.71208e9			0.690844			0.345422	−	0.938448i	$-0.387736\pi$
$769$	8.71208e9			0.690844			0.345422	+	0.938448i	$0.387736\pi$
$770$		0			0
$771$	1.85744e10	+	1.85744e10i	1.45957	+	1.45957i
$772$		0			0
$773$	−3.31528e9	+	3.31528e9i	−0.258162	+	0.258162i	−0.824306	−	0.566144i	$-0.808434\pi$
$773$	−3.31528e9	+	3.31528e9i	−0.258162	+	0.258162i	0.566144	+	0.824306i	$0.308434\pi$
$774$		0			0
$775$		−	2.41080e8i		−	0.0186039i
$776$		0			0
$777$			1.55283e10i			1.18755i
$778$		0			0
$779$	−1.07385e10	+	1.07385e10i	−0.813882	+	0.813882i
$780$		0			0
$781$	1.72261e9	+	1.72261e9i	0.129392	+	0.129392i
$782$		0			0
$783$	−1.64920e9			−0.122774
$784$		0			0
$785$	−7.71968e9			−0.569581
$786$		0			0
$787$	2.66527e8	+	2.66527e8i	0.0194908	+	0.0194908i	0.716785	−	0.697294i	$-0.245613\pi$
$787$	2.66527e8	+	2.66527e8i	0.0194908	+	0.0194908i	−0.697294	+	0.716785i	$0.745613\pi$
$788$		0			0
$789$	−2.32682e10	+	2.32682e10i	−1.68653	+	1.68653i
$790$		0			0
$791$			1.28902e10i			0.926069i
$792$		0			0
$793$		−	4.39514e9i		−	0.312980i
$794$		0			0
$795$	5.45958e9	−	5.45958e9i	0.385367	−	0.385367i
$796$		0			0
$797$	1.91922e10	+	1.91922e10i	1.34283	+	1.34283i	0.893233	+	0.449593i	$0.148431\pi$
$797$	1.91922e10	+	1.91922e10i	1.34283	+	1.34283i	0.449593	+	0.893233i	$0.351569\pi$
$798$		0			0
$799$	2.61867e10			1.81621
$800$		0			0
$801$	−1.42767e9			−0.0981553
$802$		0			0
$803$	1.32952e9	+	1.32952e9i	0.0906131	+	0.0906131i
$804$		0			0
$805$	−6.50159e9	+	6.50159e9i	−0.439273	+	0.439273i
$806$		0			0
$807$		−	1.44400e10i		−	0.967187i
$808$		0			0
$809$			1.86279e9i			0.123692i	0.998086	+	0.0618462i	$0.0196988\pi$
$809$			1.86279e9i			0.123692i	−0.998086	+	0.0618462i	$0.980301\pi$
$810$		0			0
$811$	−1.60625e10	+	1.60625e10i	−1.05740	+	1.05740i	−0.0591547	+	0.998249i	$0.518841\pi$
$811$	−1.60625e10	+	1.60625e10i	−1.05740	+	1.05740i	−0.998249	+	0.0591547i	$0.981159\pi$
$812$		0			0
$813$	−2.64343e10	−	2.64343e10i	−1.72524	−	1.72524i
$814$		0			0
$815$	−1.20719e10			−0.781129
$816$		0			0
$817$	−2.85894e9			−0.183412
$818$		0			0
$819$	−1.45959e10	−	1.45959e10i	−0.928402	−	0.928402i
$820$		0			0
$821$	1.04505e10	−	1.04505e10i	0.659074	−	0.659074i	−0.296087	−	0.955161i	$-0.595682\pi$
$821$	1.04505e10	−	1.04505e10i	0.659074	−	0.659074i	0.955161	+	0.296087i	$0.0956819\pi$
$822$		0			0
$823$		−	2.02179e10i		−	1.26426i	−0.774863	−	0.632129i	$-0.782181\pi$
$823$		−	2.02179e10i		−	1.26426i	0.774863	−	0.632129i	$-0.217819\pi$
$824$		0			0
$825$			1.02301e9i			0.0634293i
$826$		0			0
$827$	3.41907e9	−	3.41907e9i	0.210203	−	0.210203i	−0.594151	−	0.804354i	$-0.702512\pi$
$827$	3.41907e9	−	3.41907e9i	0.210203	−	0.210203i	0.804354	+	0.594151i	$0.202512\pi$
$828$		0			0
$829$	1.87636e10	+	1.87636e10i	1.14387	+	1.14387i	0.987737	+	0.156130i	$0.0499018\pi$
$829$	1.87636e10	+	1.87636e10i	1.14387	+	1.14387i	0.156130	+	0.987737i	$0.450098\pi$
$830$		0			0
$831$	−3.47883e10			−2.10296
$832$		0			0
$833$	−1.30956e10			−0.784995
$834$		0			0
$835$	−1.52403e10	−	1.52403e10i	−0.905920	−	0.905920i
$836$		0			0
$837$	1.83491e9	−	1.83491e9i	0.108162	−	0.108162i
$838$		0			0
$839$		−	1.12631e10i		−	0.658401i	−0.944260	−	0.329201i	$-0.893221\pi$
$839$		−	1.12631e10i		−	0.658401i	0.944260	−	0.329201i	$-0.106779\pi$
$840$		0			0
$841$		−	1.72162e10i		−	0.998047i
$842$		0			0
$843$	−9.59848e8	+	9.59848e8i	−0.0551831	+	0.0551831i
$844$		0			0
$845$	8.49026e9	+	8.49026e9i	0.484086	+	0.484086i
$846$		0			0
$847$	−2.31958e10			−1.31165
$848$		0			0
$849$	3.38244e10			1.89694
$850$		0			0
$851$	−3.51518e9	−	3.51518e9i	−0.195522	−	0.195522i
$852$		0			0
$853$	8.00308e9	−	8.00308e9i	0.441505	−	0.441505i	−0.451012	−	0.892518i	$-0.648937\pi$
$853$	8.00308e9	−	8.00308e9i	0.441505	−	0.441505i	0.892518	+	0.451012i	$0.148937\pi$
$854$		0			0
$855$			3.13289e10i			1.71421i
$856$		0			0
$857$		−	8.36787e9i		−	0.454132i	−0.973879	−	0.227066i	$-0.927087\pi$
$857$		−	8.36787e9i		−	0.454132i	0.973879	−	0.227066i	$-0.0729133\pi$
$858$		0			0
$859$	1.16635e10	−	1.16635e10i	0.627847	−	0.627847i	−0.319679	−	0.947526i	$-0.603575\pi$
$859$	1.16635e10	−	1.16635e10i	0.627847	−	0.627847i	0.947526	+	0.319679i	$0.103575\pi$
$860$		0			0
$861$	4.45393e10	+	4.45393e10i	2.37811	+	2.37811i
$862$		0			0
$863$	8.94130e9			0.473547			0.236774	−	0.971565i	$-0.423910\pi$
$863$	8.94130e9			0.473547			0.236774	+	0.971565i	$0.423910\pi$
$864$		0			0
$865$	−1.22127e10			−0.641589
$866$		0			0
$867$	2.00045e9	+	2.00045e9i	0.104246	+	0.104246i
$868$		0			0
$869$	−1.11263e9	+	1.11263e9i	−0.0575149	+	0.0575149i
$870$		0			0
$871$		−	1.00472e10i		−	0.515205i
$872$		0			0
$873$			8.35483e10i			4.24999i
$874$		0			0
$875$	2.02129e10	−	2.02129e10i	1.02000	−	1.02000i
$876$		0			0
$877$	−7.31289e9	−	7.31289e9i	−0.366092	−	0.366092i	0.499958	−	0.866050i	$-0.333349\pi$
$877$	−7.31289e9	−	7.31289e9i	−0.366092	−	0.366092i	−0.866050	+	0.499958i	$0.833349\pi$
$878$		0			0
$879$	2.57494e10			1.27881
$880$		0			0
$881$	−3.54118e10			−1.74474			−0.872372	−	0.488842i	$-0.837419\pi$
$881$	−3.54118e10			−1.74474			−0.872372	+	0.488842i	$0.837419\pi$
$882$		0			0
$883$	9.77015e9	+	9.77015e9i	0.477572	+	0.477572i	0.904354	−	0.426782i	$-0.140353\pi$
$883$	9.77015e9	+	9.77015e9i	0.477572	+	0.477572i	−0.426782	+	0.904354i	$0.640353\pi$
$884$		0			0
$885$	2.25889e10	−	2.25889e10i	1.09545	−	1.09545i
$886$		0			0
$887$			5.27697e9i			0.253894i	0.991910	+	0.126947i	$0.0405178\pi$
$887$			5.27697e9i			0.253894i	−0.991910	+	0.126947i	$0.959482\pi$
$888$		0			0
$889$			2.58048e10i			1.23181i
$890$		0			0
$891$	−4.05289e9	+	4.05289e9i	−0.191952	+	0.191952i
$892$		0			0
$893$	−2.22819e10	−	2.22819e10i	−1.04706	−	1.04706i
$894$		0			0
$895$	−7.82461e9			−0.364823
$896$		0			0
$897$	9.26469e9			0.428605
$898$		0			0
$899$	−3.74860e7	−	3.74860e7i	−0.00172072	−	0.00172072i
$900$		0			0
$901$	−5.78333e9	+	5.78333e9i	−0.263415	+	0.263415i
$902$		0			0
$903$			1.18579e10i			0.535920i
$904$		0			0
$905$			3.10625e10i			1.39305i
$906$		0			0
$907$	1.84084e10	−	1.84084e10i	0.819203	−	0.819203i	−0.166789	−	0.985993i	$-0.553340\pi$
$907$	1.84084e10	−	1.84084e10i	0.819203	−	0.819203i	0.985993	+	0.166789i	$0.0533400\pi$
$908$		0			0
$909$	2.31470e10	+	2.31470e10i	1.02216	+	1.02216i
$910$		0			0
$911$	1.76557e10			0.773697			0.386848	−	0.922143i	$-0.373564\pi$
$911$	1.76557e10			0.773697			0.386848	+	0.922143i	$0.373564\pi$
$912$		0			0
$913$	1.12639e8			0.00489825
$914$		0			0
$915$	1.95641e10	+	1.95641e10i	0.844280	+	0.844280i
$916$		0			0
$917$	2.35566e9	−	2.35566e9i	0.100883	−	0.100883i
$918$		0			0
$919$		−	2.50780e10i		−	1.06583i	−0.846169	−	0.532915i	$-0.821097\pi$
$919$		−	2.50780e10i		−	1.06583i	0.846169	−	0.532915i	$-0.178903\pi$
$920$		0			0
$921$		−	7.63349e10i		−	3.21969i
$922$		0			0
$923$	−1.22485e10	+	1.22485e10i	−0.512715	+	0.512715i
$924$		0			0
$925$	2.75989e9	+	2.75989e9i	0.114656	+	0.114656i
$926$		0			0
$927$	7.49861e10			3.09173
$928$		0			0
$929$	1.46170e10			0.598140			0.299070	−	0.954231i	$-0.403324\pi$
$929$	1.46170e10			0.598140			0.299070	+	0.954231i	$0.403324\pi$
$930$		0			0
$931$	1.11428e10	+	1.11428e10i	0.452555	+	0.452555i
$932$		0			0
$933$	−3.34604e9	+	3.34604e9i	−0.134879	+	0.134879i
$934$		0			0
$935$			2.12369e9i			0.0849670i
$936$		0			0
$937$		−	1.58555e10i		−	0.629637i	−0.949152	−	0.314818i	$-0.898056\pi$
$937$		−	1.58555e10i		−	0.629637i	0.949152	−	0.314818i	$-0.101944\pi$
$938$		0			0
$939$	5.65624e10	−	5.65624e10i	2.22945	−	2.22945i
$940$		0			0
$941$	−1.71527e10	−	1.71527e10i	−0.671071	−	0.671071i	0.286892	−	0.957963i	$-0.407378\pi$
$941$	−1.71527e10	−	1.71527e10i	−0.671071	−	0.671071i	−0.957963	+	0.286892i	$0.907378\pi$
$942$		0			0
$943$	−2.01649e10			−0.783079
$944$		0			0
$945$	7.77048e10			2.99527
$946$		0			0
$947$	6.39507e9	+	6.39507e9i	0.244693	+	0.244693i	0.818788	−	0.574096i	$-0.194646\pi$
$947$	6.39507e9	+	6.39507e9i	0.244693	+	0.244693i	−0.574096	+	0.818788i	$0.694646\pi$
$948$		0			0
$949$	−9.45348e9	+	9.45348e9i	−0.359054	+	0.359054i
$950$		0			0
$951$		−	4.74216e10i		−	1.78790i
$952$		0			0
$953$		−	3.47793e10i		−	1.30165i	−0.759226	−	0.650827i	$-0.774422\pi$
$953$		−	3.47793e10i		−	1.30165i	0.759226	−	0.650827i	$-0.225578\pi$
$954$		0			0
$955$	1.43837e9	−	1.43837e9i	0.0534390	−	0.0534390i
$956$		0			0
$957$	1.59070e8	+	1.59070e8i	0.00586673	+	0.00586673i
$958$		0			0
$959$	−3.86537e9			−0.141522
$960$		0			0
$961$	−2.74292e10			−0.996968
$962$		0			0
$963$	−2.25118e10	−	2.25118e10i	−0.812303	−	0.812303i
$964$		0			0
$965$	−2.24239e10	+	2.24239e10i	−0.803276	+	0.803276i
$966$		0			0
$967$		−	1.12415e10i		−	0.399790i	−0.979817	−	0.199895i	$-0.935940\pi$
$967$		−	1.12415e10i		−	0.399790i	0.979817	−	0.199895i	$-0.0640602\pi$
$968$		0			0
$969$		−	4.65278e10i		−	1.64278i
$970$		0			0
$971$	1.71514e10	−	1.71514e10i	0.601219	−	0.601219i	−0.339417	−	0.940636i	$-0.610230\pi$
$971$	1.71514e10	−	1.71514e10i	0.601219	−	0.601219i	0.940636	+	0.339417i	$0.110230\pi$
$972$		0			0
$973$	−3.59897e10	−	3.59897e10i	−1.25252	−	1.25252i
$974$		0			0
$975$	−7.27403e9			−0.251338
$976$		0			0
$977$	4.79355e10			1.64447			0.822236	−	0.569147i	$-0.192726\pi$
$977$	4.79355e10			1.64447			0.822236	+	0.569147i	$0.192726\pi$
$978$		0			0
$979$	8.23462e7	+	8.23462e7i	0.00280481	+	0.00280481i
$980$		0			0
$981$	2.79631e10	−	2.79631e10i	0.945679	−	0.945679i
$982$		0			0
$983$		−	4.01721e9i		−	0.134892i	−0.997723	−	0.0674462i	$-0.978515\pi$
$983$		−	4.01721e9i		−	0.134892i	0.997723	−	0.0674462i	$-0.0214851\pi$
$984$		0			0
$985$			3.40324e10i			1.13466i
$986$		0			0
$987$	−9.24171e10	+	9.24171e10i	−3.05944	+	3.05944i
$988$		0			0
$989$	−2.68429e9	−	2.68429e9i	−0.0882354	−	0.0882354i
$990$		0			0
$991$	−6.76525e9			−0.220814			−0.110407	−	0.993886i	$-0.535215\pi$
$991$	−6.76525e9			−0.220814			−0.110407	+	0.993886i	$0.535215\pi$
$992$		0			0
$993$	−2.25120e10			−0.729610
$994$		0			0
$995$	−1.76445e10	−	1.76445e10i	−0.567844	−	0.567844i
$996$		0			0
$997$	−2.14103e10	+	2.14103e10i	−0.684212	+	0.684212i	−0.960946	−	0.276735i	$-0.910748\pi$
$997$	−2.14103e10	+	2.14103e10i	−0.684212	+	0.684212i	0.276735	+	0.960946i	$0.410748\pi$
$998$		0			0
$999$			4.20123e10i			1.33321i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.8.e.a.33.13		26
4.3	odd	2		128.8.e.b.33.1		26
8.3	odd	2		16.8.e.a.13.8	yes	26
8.5	even	2		64.8.e.a.17.1		26
16.3	odd	4		16.8.e.a.5.8	✓	26
16.5	even	4	inner	128.8.e.a.97.13		26
16.11	odd	4		128.8.e.b.97.1		26
16.13	even	4		64.8.e.a.49.1		26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.8.e.a.5.8	✓	26	16.3	odd	4
16.8.e.a.13.8	yes	26	8.3	odd	2
64.8.e.a.17.1		26	8.5	even	2
64.8.e.a.49.1		26	16.13	even	4
128.8.e.a.33.13		26	1.1	even	1	trivial
128.8.e.a.97.13		26	16.5	even	4	inner
128.8.e.b.33.1		26	4.3	odd	2
128.8.e.b.97.1		26	16.11	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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	128.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(61.7547 + 61.7547i) q^{3} +(-160.824 + 160.824i) q^{5} +1202.46i q^{7} +5440.30i q^{9} +O(q^{10})\)	\(q+(61.7547 + 61.7547i) q^{3} +(-160.824 + 160.824i) q^{5} +1202.46i q^{7} +5440.30i q^{9} +(313.790 - 313.790i) q^{11} +(2231.18 + 2231.18i) q^{13} -19863.3 q^{15} +21041.2 q^{17} +(-17903.6 - 17903.6i) q^{19} +(-74257.9 + 74257.9i) q^{21} -33619.9i q^{23} +26396.1i q^{25} +(-200907. + 200907. i) q^{27} +(4104.39 + 4104.39i) q^{29} -9133.16 q^{31} +38756.0 q^{33} +(-193385. - 193385. i) q^{35} +(104557. - 104557. i) q^{37} +275572. i q^{39} -599792. i q^{41} +(79842.5 - 79842.5i) q^{43} +(-874932. - 874932. i) q^{45} +1.24454e6 q^{47} -622377. q^{49} +(1.29939e6 + 1.29939e6i) q^{51} +(-274857. + 274857. i) q^{53} +100930. i q^{55} -2.21127e6i q^{57} +(-1.13722e6 + 1.13722e6i) q^{59} +(-984936. - 984936. i) q^{61} -6.54176e6 q^{63} -717657. q^{65} +(-2.25153e6 - 2.25153e6i) q^{67} +(2.07619e6 - 2.07619e6i) q^{69} +5.48968e6i q^{71} +4.23698e6i q^{73} +(-1.63008e6 + 1.63008e6i) q^{75} +(377321. + 377321. i) q^{77} -3.54577e6 q^{79} -1.29159e7 q^{81} +(179482. + 179482. i) q^{83} +(-3.38394e6 + 3.38394e6i) q^{85} +506931. i q^{87} +262425. i q^{89} +(-2.68292e6 + 2.68292e6i) q^{91} +(-564016. - 564016. i) q^{93} +5.75868e6 q^{95} +1.53573e7 q^{97} +(1.70711e6 + 1.70711e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 2 q^{3} + 2 q^{5}+O(q^{10}) \) 26 * q - 2 * q^3 + 2 * q^5	\( 26 q - 2 q^{3} + 2 q^{5} + 1202 q^{11} + 2 q^{13} + 27004 q^{15} - 4 q^{17} + 60582 q^{19} - 4372 q^{21} - 233672 q^{27} + 51690 q^{29} - 357488 q^{31} - 4 q^{33} - 252004 q^{35} - 415574 q^{37} + 569754 q^{43} - 151874 q^{45} + 2076464 q^{47} - 1647090 q^{49} + 2609508 q^{51} - 907814 q^{53} - 4865142 q^{59} - 2279886 q^{61} - 8295108 q^{63} - 1426892 q^{65} - 5564458 q^{67} + 4786076 q^{69} + 6212566 q^{75} - 7604308 q^{77} + 9598912 q^{79} - 5314414 q^{81} + 4531198 q^{83} - 7377748 q^{85} + 2587652 q^{91} + 14504144 q^{93} + 4900620 q^{95} - 4 q^{97} + 18815006 q^{99}+O(q^{100}) \) 26 * q - 2 * q^3 + 2 * q^5 + 1202 * q^11 + 2 * q^13 + 27004 * q^15 - 4 * q^17 + 60582 * q^19 - 4372 * q^21 - 233672 * q^27 + 51690 * q^29 - 357488 * q^31 - 4 * q^33 - 252004 * q^35 - 415574 * q^37 + 569754 * q^43 - 151874 * q^45 + 2076464 * q^47 - 1647090 * q^49 + 2609508 * q^51 - 907814 * q^53 - 4865142 * q^59 - 2279886 * q^61 - 8295108 * q^63 - 1426892 * q^65 - 5564458 * q^67 + 4786076 * q^69 + 6212566 * q^75 - 7604308 * q^77 + 9598912 * q^79 - 5314414 * q^81 + 4531198 * q^83 - 7377748 * q^85 + 2587652 * q^91 + 14504144 * q^93 + 4900620 * q^95 - 4 * q^97 + 18815006 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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