LMFDB - Embedded newform 320.6.l.a.81.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,6,Mod(81,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("320.81");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	320.l (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:	$51.3228223402$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			81.3
Character	$\chi$	$=$	320.81
Dual form			320.6.l.a.241.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-19.6483 - 19.6483i) q^{3} +(-17.6777 + 17.6777i) q^{5} -152.043i q^{7} +529.109i q^{9} +O(q^{10})$	\(q+(-19.6483 - 19.6483i) q^{3} +(-17.6777 + 17.6777i) q^{5} -152.043i q^{7} +529.109i q^{9} +(11.6148 - 11.6148i) q^{11} +(-337.401 - 337.401i) q^{13} +694.671 q^{15} +1971.39 q^{17} +(1675.04 + 1675.04i) q^{19} +(-2987.39 + 2987.39i) q^{21} -2713.65i q^{23} -625.000i q^{25} +(5621.55 - 5621.55i) q^{27} +(2271.81 + 2271.81i) q^{29} +9252.07 q^{31} -456.423 q^{33} +(2687.77 + 2687.77i) q^{35} +(2728.98 - 2728.98i) q^{37} +13258.7i q^{39} +9698.90i q^{41} +(-7983.39 + 7983.39i) q^{43} +(-9353.41 - 9353.41i) q^{45} +12393.3 q^{47} -6310.14 q^{49} +(-38734.4 - 38734.4i) q^{51} +(779.013 - 779.013i) q^{53} +410.646i q^{55} -65823.4i q^{57} +(2779.17 - 2779.17i) q^{59} +(16149.2 + 16149.2i) q^{61} +80447.4 q^{63} +11928.9 q^{65} +(-27196.6 - 27196.6i) q^{67} +(-53318.6 + 53318.6i) q^{69} -61737.5i q^{71} -18521.1i q^{73} +(-12280.2 + 12280.2i) q^{75} +(-1765.96 - 1765.96i) q^{77} -54765.8 q^{79} -92333.9 q^{81} +(-76036.0 - 76036.0i) q^{83} +(-34849.5 + 34849.5i) q^{85} -89274.2i q^{87} -60590.0i q^{89} +(-51299.5 + 51299.5i) q^{91} +(-181787. - 181787. i) q^{93} -59221.7 q^{95} +80405.2 q^{97} +(6145.52 + 6145.52i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q+O(q^{10}) $ 80 * q	$ 80 q - 1208 q^{11} + 1800 q^{15} - 2360 q^{19} + 7464 q^{27} - 8144 q^{29} + 21296 q^{37} - 32072 q^{43} + 88360 q^{47} - 192080 q^{49} + 5920 q^{51} - 49456 q^{53} - 44984 q^{59} + 48080 q^{61} - 158760 q^{63} - 61160 q^{67} - 22320 q^{69} - 14896 q^{77} - 177680 q^{79} - 524880 q^{81} + 329240 q^{83} + 132400 q^{85} - 364832 q^{91} - 362352 q^{93} - 288800 q^{95} - 659000 q^{99}+O(q^{100}) $ 80 * q - 1208 * q^11 + 1800 * q^15 - 2360 * q^19 + 7464 * q^27 - 8144 * q^29 + 21296 * q^37 - 32072 * q^43 + 88360 * q^47 - 192080 * q^49 + 5920 * q^51 - 49456 * q^53 - 44984 * q^59 + 48080 * q^61 - 158760 * q^63 - 61160 * q^67 - 22320 * q^69 - 14896 * q^77 - 177680 * q^79 - 524880 * q^81 + 329240 * q^83 + 132400 * q^85 - 364832 * q^91 - 362352 * q^93 - 288800 * q^95 - 659000 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−19.6483	−	19.6483i	−1.26044	−	1.26044i	−0.950881	−	0.309556i	$-0.899820\pi$
$3$	−19.6483	−	19.6483i	−1.26044	−	1.26044i	−0.309556	−	0.950881i	$-0.600180\pi$
$4$		0			0
$5$	−17.6777	+	17.6777i	−0.316228	+	0.316228i
$5$	−17.6777	+	17.6777i	−0.316228	+	0.316228i
$6$		0			0
$7$		−	152.043i		−	1.17279i	−0.810024	−	0.586397i	$-0.800546\pi$
$7$		−	152.043i		−	1.17279i	0.810024	−	0.586397i	$-0.199454\pi$
$8$		0			0
$9$			529.109i			2.17740i
$10$		0			0
$11$	11.6148	−	11.6148i	0.0289422	−	0.0289422i	−0.692488	−	0.721430i	$-0.743485\pi$
$11$	11.6148	−	11.6148i	0.0289422	−	0.0289422i	0.721430	+	0.692488i	$0.243485\pi$
$12$		0			0
$13$	−337.401	−	337.401i	−0.553717	−	0.553717i	0.373795	−	0.927511i	$-0.378056\pi$
$13$	−337.401	−	337.401i	−0.553717	−	0.553717i	−0.927511	+	0.373795i	$0.878056\pi$
$14$		0			0
$15$	694.671			0.797170
$16$		0			0
$17$	1971.39			1.65443			0.827217	−	0.561882i	$-0.189922\pi$
$17$	1971.39			1.65443			0.827217	+	0.561882i	$0.189922\pi$
$18$		0			0
$19$	1675.04	+	1675.04i	1.06449	+	1.06449i	0.997772	+	0.0667196i	$0.0212533\pi$
$19$	1675.04	+	1675.04i	1.06449	+	1.06449i	0.0667196	+	0.997772i	$0.478747\pi$
$20$		0			0
$21$	−2987.39	+	2987.39i	−1.47823	+	1.47823i
$22$		0			0
$23$		−	2713.65i		−	1.06963i	−0.844968	−	0.534816i	$-0.820381\pi$
$23$		−	2713.65i		−	1.06963i	0.844968	−	0.534816i	$-0.179619\pi$
$24$		0			0
$25$		−	625.000i		−	0.200000i
$26$		0			0
$27$	5621.55	−	5621.55i	1.48404	−	1.48404i
$28$		0			0
$29$	2271.81	+	2271.81i	0.501622	+	0.501622i	0.911942	−	0.410320i	$-0.134583\pi$
$29$	2271.81	+	2271.81i	0.501622	+	0.501622i	−0.410320	+	0.911942i	$0.634583\pi$
$30$		0			0
$31$	9252.07			1.72916			0.864579	−	0.502497i	$-0.167585\pi$
$31$	9252.07			1.72916			0.864579	+	0.502497i	$0.167585\pi$
$32$		0			0
$33$	−456.423			−0.0729596
$34$		0			0
$35$	2687.77	+	2687.77i	0.370870	+	0.370870i
$36$		0			0
$37$	2728.98	−	2728.98i	0.327715	−	0.327715i	−0.524002	−	0.851717i	$-0.675562\pi$
$37$	2728.98	−	2728.98i	0.327715	−	0.327715i	0.851717	+	0.524002i	$0.175562\pi$
$38$		0			0
$39$			13258.7i			1.39585i
$40$		0			0
$41$			9698.90i			0.901079i	0.892757	+	0.450539i	$0.148768\pi$
$41$			9698.90i			0.901079i	−0.892757	+	0.450539i	$0.851232\pi$
$42$		0			0
$43$	−7983.39	+	7983.39i	−0.658440	+	0.658440i	−0.955011	−	0.296571i	$-0.904157\pi$
$43$	−7983.39	+	7983.39i	−0.658440	+	0.658440i	0.296571	+	0.955011i	$0.404157\pi$
$44$		0			0
$45$	−9353.41	−	9353.41i	−0.688555	−	0.688555i
$46$		0			0
$47$	12393.3			0.818359			0.409179	−	0.912454i	$-0.365815\pi$
$47$	12393.3			0.818359			0.409179	+	0.912454i	$0.365815\pi$
$48$		0			0
$49$	−6310.14			−0.375447
$50$		0			0
$51$	−38734.4	−	38734.4i	−2.08531	−	2.08531i
$52$		0			0
$53$	779.013	−	779.013i	0.0380939	−	0.0380939i	−0.687803	−	0.725897i	$-0.741425\pi$
$53$	779.013	−	779.013i	0.0380939	−	0.0380939i	0.725897	+	0.687803i	$0.241425\pi$
$54$		0			0
$55$			410.646i			0.0183046i
$56$		0			0
$57$		−	65823.4i		−	2.68345i
$58$		0			0
$59$	2779.17	−	2779.17i	0.103940	−	0.103940i	−0.653224	−	0.757165i	$-0.726584\pi$
$59$	2779.17	−	2779.17i	0.103940	−	0.103940i	0.757165	+	0.653224i	$0.226584\pi$
$60$		0			0
$61$	16149.2	+	16149.2i	0.555682	+	0.555682i	0.928075	−	0.372393i	$-0.121463\pi$
$61$	16149.2	+	16149.2i	0.555682	+	0.555682i	−0.372393	+	0.928075i	$0.621463\pi$
$62$		0			0
$63$	80447.4			2.55365
$64$		0			0
$65$	11928.9			0.350201
$66$		0			0
$67$	−27196.6	−	27196.6i	−0.740164	−	0.740164i	0.232445	−	0.972609i	$-0.425327\pi$
$67$	−27196.6	−	27196.6i	−0.740164	−	0.740164i	−0.972609	+	0.232445i	$0.925327\pi$
$68$		0			0
$69$	−53318.6	+	53318.6i	−1.34820	+	1.34820i
$70$		0			0
$71$		−	61737.5i		−	1.45346i	−0.686923	−	0.726730i	$-0.741039\pi$
$71$		−	61737.5i		−	1.45346i	0.686923	−	0.726730i	$-0.258961\pi$
$72$		0			0
$73$		−	18521.1i		−	0.406780i	−0.979098	−	0.203390i	$-0.934804\pi$
$73$		−	18521.1i		−	0.406780i	0.979098	−	0.203390i	$-0.0651960\pi$
$74$		0			0
$75$	−12280.2	+	12280.2i	−0.252087	+	0.252087i
$76$		0			0
$77$	−1765.96	−	1765.96i	−0.0339432	−	0.0339432i
$78$		0			0
$79$	−54765.8			−0.987284			−0.493642	−	0.869665i	$-0.664335\pi$
$79$	−54765.8			−0.987284			−0.493642	+	0.869665i	$0.664335\pi$
$80$		0			0
$81$	−92333.9			−1.56368
$82$		0			0
$83$	−76036.0	−	76036.0i	−1.21150	−	1.21150i	−0.970533	−	0.240969i	$-0.922535\pi$
$83$	−76036.0	−	76036.0i	−1.21150	−	1.21150i	−0.240969	−	0.970533i	$-0.577465\pi$
$84$		0			0
$85$	−34849.5	+	34849.5i	−0.523178	+	0.523178i
$86$		0			0
$87$		−	89274.2i		−	1.26453i
$88$		0			0
$89$		−	60590.0i		−	0.810823i	−0.914134	−	0.405412i	$-0.867128\pi$
$89$		−	60590.0i		−	0.810823i	0.914134	−	0.405412i	$-0.132872\pi$
$90$		0			0
$91$	−51299.5	+	51299.5i	−0.649396	+	0.649396i
$92$		0			0
$93$	−181787.	−	181787.i	−2.17949	−	2.17949i
$94$		0			0
$95$	−59221.7			−0.673243
$96$		0			0
$97$	80405.2			0.867670			0.433835	−	0.900992i	$-0.357160\pi$
$97$	80405.2			0.867670			0.433835	+	0.900992i	$0.357160\pi$
$98$		0			0
$99$	6145.52	+	6145.52i	0.0630188	+	0.0630188i
$100$		0			0
$101$	−19812.4	+	19812.4i	−0.193256	+	0.193256i	−0.797102	−	0.603845i	$-0.793634\pi$
$101$	−19812.4	+	19812.4i	−0.193256	+	0.193256i	0.603845	+	0.797102i	$0.293634\pi$
$102$		0			0
$103$			130085.i			1.20819i	0.796912	+	0.604095i	$0.206465\pi$
$103$			130085.i			1.20819i	−0.796912	+	0.604095i	$0.793535\pi$
$104$		0			0
$105$		−	105620.i		−	0.934917i
$106$		0			0
$107$	−141881.	+	141881.i	−1.19802	+	1.19802i	−0.223260	+	0.974759i	$0.571670\pi$
$107$	−141881.	+	141881.i	−1.19802	+	1.19802i	−0.974759	+	0.223260i	$0.928330\pi$
$108$		0			0
$109$	9250.02	+	9250.02i	0.0745721	+	0.0745721i	0.743409	−	0.668837i	$-0.233208\pi$
$109$	9250.02	+	9250.02i	0.0745721	+	0.0745721i	−0.668837	+	0.743409i	$0.733208\pi$
$110$		0			0
$111$	−107240.			−0.826128
$112$		0			0
$113$	46485.0			0.342466			0.171233	−	0.985231i	$-0.445225\pi$
$113$	46485.0			0.342466			0.171233	+	0.985231i	$0.445225\pi$
$114$		0			0
$115$	47971.0	+	47971.0i	0.338247	+	0.338247i
$116$		0			0
$117$	178522.	−	178522.i	1.20566	−	1.20566i
$118$		0			0
$119$		−	299736.i		−	1.94031i
$120$		0			0
$121$			160781.i			0.998325i
$122$		0			0
$123$	190567.	−	190567.i	1.13575	−	1.13575i
$124$		0			0
$125$	11048.5	+	11048.5i	0.0632456	+	0.0632456i
$126$		0			0
$127$	286357.			1.57543			0.787714	−	0.616041i	$-0.211264\pi$
$127$	286357.			1.57543			0.787714	+	0.616041i	$0.211264\pi$
$128$		0			0
$129$	313719.			1.65984
$130$		0			0
$131$	−117828.	−	117828.i	−0.599887	−	0.599887i	0.340396	−	0.940282i	$-0.389439\pi$
$131$	−117828.	−	117828.i	−0.599887	−	0.599887i	−0.940282	+	0.340396i	$0.889439\pi$
$132$		0			0
$133$	254679.	−	254679.i	1.24843	−	1.24843i
$134$		0			0
$135$			198752.i			0.938591i
$136$		0			0
$137$			82337.9i			0.374799i	0.982284	+	0.187400i	$0.0600059\pi$
$137$			82337.9i			0.374799i	−0.982284	+	0.187400i	$0.939994\pi$
$138$		0			0
$139$	214865.	−	214865.i	0.943255	−	0.943255i	−0.0552189	−	0.998474i	$-0.517586\pi$
$139$	214865.	−	214865.i	0.943255	−	0.943255i	0.998474	+	0.0552189i	$0.0175857\pi$
$140$		0			0
$141$	−243508.	−	243508.i	−1.03149	−	1.03149i
$142$		0			0
$143$	−7837.71			−0.0320515
$144$		0			0
$145$	−80320.5			−0.317254
$146$		0			0
$147$	123983.	+	123983.i	0.473227	+	0.473227i
$148$		0			0
$149$	359536.	−	359536.i	1.32671	−	1.32671i	0.418494	−	0.908220i	$-0.362558\pi$
$149$	359536.	−	359536.i	1.32671	−	1.32671i	0.908220	−	0.418494i	$-0.137442\pi$
$150$		0			0
$151$		−	89139.5i		−	0.318147i	−0.987267	−	0.159073i	$-0.949149\pi$
$151$		−	89139.5i		−	0.318147i	0.987267	−	0.159073i	$-0.0508507\pi$
$152$		0			0
$153$			1.04308e6i			3.60237i
$154$		0			0
$155$	−163555.	+	163555.i	−0.546808	+	0.546808i
$156$		0			0
$157$	41880.8	+	41880.8i	0.135602	+	0.135602i	0.771650	−	0.636048i	$-0.219432\pi$
$157$	41880.8	+	41880.8i	0.135602	+	0.135602i	−0.636048	+	0.771650i	$0.719432\pi$
$158$		0			0
$159$	−30612.5			−0.0960298
$160$		0			0
$161$	−412592.			−1.25446
$162$		0			0
$163$	−119285.	−	119285.i	−0.351654	−	0.351654i	0.509070	−	0.860725i	$-0.329989\pi$
$163$	−119285.	−	119285.i	−0.351654	−	0.351654i	−0.860725	+	0.509070i	$0.829989\pi$
$164$		0			0
$165$	8068.49	−	8068.49i	0.0230719	−	0.0230719i
$166$		0			0
$167$		−	121470.i		−	0.337036i	−0.985699	−	0.168518i	$-0.946102\pi$
$167$		−	121470.i		−	0.337036i	0.985699	−	0.168518i	$-0.0538982\pi$
$168$		0			0
$169$		−	143615.i		−	0.386796i
$170$		0			0
$171$	−886281.	+	886281.i	−2.31783	+	2.31783i
$172$		0			0
$173$	219318.	+	219318.i	0.557134	+	0.557134i	0.928490	−	0.371356i	$-0.121107\pi$
$173$	219318.	+	219318.i	0.557134	+	0.557134i	−0.371356	+	0.928490i	$0.621107\pi$
$174$		0			0
$175$	−95027.0			−0.234559
$176$		0			0
$177$	−109212.			−0.262021
$178$		0			0
$179$	481512.	+	481512.i	1.12325	+	1.12325i	0.991250	+	0.131996i	$0.0421385\pi$
$179$	481512.	+	481512.i	1.12325	+	1.12325i	0.131996	+	0.991250i	$0.457862\pi$
$180$		0			0
$181$	−185016.	+	185016.i	−0.419772	+	0.419772i	−0.885125	−	0.465353i	$-0.845927\pi$
$181$	−185016.	+	185016.i	−0.419772	+	0.419772i	0.465353	+	0.885125i	$0.345927\pi$
$182$		0			0
$183$		−	634607.i		−	1.40080i
$184$		0			0
$185$			96484.1i			0.207265i
$186$		0			0
$187$	22897.3	−	22897.3i	0.0478830	−	0.0478830i
$188$		0			0
$189$	−854718.	−	854718.i	−1.74048	−	1.74048i
$190$		0			0
$191$	−144475.			−0.286556			−0.143278	−	0.989682i	$-0.545764\pi$
$191$	−144475.			−0.286556			−0.143278	+	0.989682i	$0.545764\pi$
$192$		0			0
$193$	573446.			1.10815			0.554076	−	0.832466i	$-0.313072\pi$
$193$	573446.			1.10815			0.554076	+	0.832466i	$0.313072\pi$
$194$		0			0
$195$	−234383.	−	234383.i	−0.441406	−	0.441406i
$196$		0			0
$197$	228983.	−	228983.i	0.420376	−	0.420376i	−0.464957	−	0.885333i	$-0.653930\pi$
$197$	228983.	−	228983.i	0.420376	−	0.420376i	0.885333	+	0.464957i	$0.153930\pi$
$198$		0			0
$199$			455416.i			0.815221i	0.913156	+	0.407611i	$0.133638\pi$
$199$			455416.i			0.815221i	−0.913156	+	0.407611i	$0.866362\pi$
$200$		0			0
$201$			1.06873e6i			1.86586i
$202$		0			0
$203$	345413.	−	345413.i	0.588300	−	0.588300i
$204$		0			0
$205$	−171454.	−	171454.i	−0.284946	−	0.284946i
$206$		0			0
$207$	1.43582e6			2.32902
$208$		0			0
$209$	38910.7			0.0616174
$210$		0			0
$211$	375836.	+	375836.i	0.581156	+	0.581156i	0.935221	−	0.354065i	$-0.115201\pi$
$211$	375836.	+	375836.i	0.581156	+	0.581156i	−0.354065	+	0.935221i	$0.615201\pi$
$212$		0			0
$213$	−1.21304e6	+	1.21304e6i	−1.83200	+	1.83200i
$214$		0			0
$215$		−	282255.i		−	0.416434i
$216$		0			0
$217$		−	1.40671e6i		−	2.02795i
$218$		0			0
$219$	−363908.	+	363908.i	−0.512721	+	0.512721i
$220$		0			0
$221$	−665147.	−	665147.i	−0.916088	−	0.916088i
$222$		0			0
$223$	372759.			0.501956			0.250978	−	0.967993i	$-0.419248\pi$
$223$	372759.			0.501956			0.250978	+	0.967993i	$0.419248\pi$
$224$		0			0
$225$	330693.			0.435481
$226$		0			0
$227$	−603192.	−	603192.i	−0.776946	−	0.776946i	0.202365	−	0.979310i	$-0.435137\pi$
$227$	−603192.	−	603192.i	−0.776946	−	0.776946i	−0.979310	+	0.202365i	$0.935137\pi$
$228$		0			0
$229$	578307.	−	578307.i	0.728736	−	0.728736i	−0.241632	−	0.970368i	$-0.577683\pi$
$229$	578307.	−	578307.i	0.728736	−	0.728736i	0.970368	+	0.241632i	$0.0776828\pi$
$230$		0			0
$231$			69396.0i			0.0855666i
$232$		0			0
$233$			815767.i			0.984410i	0.870479	+	0.492205i	$0.163809\pi$
$233$			815767.i			0.984410i	−0.870479	+	0.492205i	$0.836191\pi$
$234$		0			0
$235$	−219085.	+	219085.i	−0.258788	+	0.258788i
$236$		0			0
$237$	1.07605e6	+	1.07605e6i	1.24441	+	1.24441i
$238$		0			0
$239$	−255220.			−0.289015			−0.144507	−	0.989504i	$-0.546160\pi$
$239$	−255220.			−0.289015			−0.144507	+	0.989504i	$0.546160\pi$
$240$		0			0
$241$	−1.21711e6			−1.34986			−0.674928	−	0.737883i	$-0.735825\pi$
$241$	−1.21711e6			−1.34986			−0.674928	+	0.737883i	$0.735825\pi$
$242$		0			0
$243$	448165.	+	448165.i	0.486880	+	0.486880i
$244$		0			0
$245$	111549.	−	111549.i	0.118727	−	0.118727i
$246$		0			0
$247$		−	1.13032e6i		−	1.17885i
$248$		0			0
$249$			2.98795e6i			3.05404i
$250$		0			0
$251$	711568.	−	711568.i	0.712906	−	0.712906i	−0.254236	−	0.967142i	$-0.581824\pi$
$251$	711568.	−	711568.i	0.712906	−	0.712906i	0.967142	+	0.254236i	$0.0818241\pi$
$252$		0			0
$253$	−31518.6	−	31518.6i	−0.0309575	−	0.0309575i
$254$		0			0
$255$	1.36947e6			1.31887
$256$		0			0
$257$	−394842.			−0.372899			−0.186449	−	0.982465i	$-0.559698\pi$
$257$	−394842.			−0.372899			−0.186449	+	0.982465i	$0.559698\pi$
$258$		0			0
$259$	−414923.	−	414923.i	−0.384342	−	0.384342i
$260$		0			0
$261$	−1.20203e6	+	1.20203e6i	−1.09223	+	1.09223i
$262$		0			0
$263$			446751.i			0.398269i	0.979972	+	0.199134i	$0.0638130\pi$
$263$			446751.i			0.398269i	−0.979972	+	0.199134i	$0.936187\pi$
$264$		0			0
$265$			27542.3i			0.0240927i
$266$		0			0
$267$	−1.19049e6	+	1.19049e6i	−1.02199	+	1.02199i
$268$		0			0
$269$	−616974.	−	616974.i	−0.519860	−	0.519860i	0.397669	−	0.917529i	$-0.369819\pi$
$269$	−616974.	−	616974.i	−0.519860	−	0.519860i	−0.917529	+	0.397669i	$0.869819\pi$
$270$		0			0
$271$	302965.			0.250593			0.125297	−	0.992119i	$-0.460012\pi$
$271$	302965.			0.250593			0.125297	+	0.992119i	$0.460012\pi$
$272$		0			0
$273$	2.01589e6			1.63705
$274$		0			0
$275$	−7259.27	−	7259.27i	−0.00578844	−	0.00578844i
$276$		0			0
$277$	−754020.	+	754020.i	−0.590450	+	0.590450i	−0.937753	−	0.347303i	$-0.887098\pi$
$277$	−754020.	+	754020.i	−0.590450	+	0.590450i	0.347303	+	0.937753i	$0.387098\pi$
$278$		0			0
$279$			4.89535e6i			3.76507i
$280$		0			0
$281$		−	1.82778e6i		−	1.38088i	−0.723388	−	0.690442i	$-0.757416\pi$
$281$		−	1.82778e6i		−	1.38088i	0.723388	−	0.690442i	$-0.242584\pi$
$282$		0			0
$283$	−112611.	+	112611.i	−0.0835825	+	0.0835825i	−0.747662	−	0.664079i	$-0.768824\pi$
$283$	−112611.	+	112611.i	−0.0835825	+	0.0835825i	0.664079	+	0.747662i	$0.268824\pi$
$284$		0			0
$285$	1.16360e6	+	1.16360e6i	0.848581	+	0.848581i
$286$		0			0
$287$	1.47465e6			1.05678
$288$		0			0
$289$	2.46651e6			1.73716
$290$		0			0
$291$	−1.57982e6	−	1.57982e6i	−1.09364	−	1.09364i
$292$		0			0
$293$	1.02302e6	−	1.02302e6i	0.696168	−	0.696168i	−0.267414	−	0.963582i	$-0.586169\pi$
$293$	1.02302e6	−	1.02302e6i	0.696168	−	0.696168i	0.963582	+	0.267414i	$0.0861691\pi$
$294$		0			0
$295$			98258.4i			0.0657377i
$296$		0			0
$297$		−	130587.i		−	0.0859029i
$298$		0			0
$299$	−915588.	+	915588.i	−0.592273	+	0.592273i
$300$		0			0
$301$	1.21382e6	+	1.21382e6i	0.772215	+	0.772215i
$302$		0			0
$303$	778559.			0.487175
$304$		0			0
$305$	−570960.			−0.351444
$306$		0			0
$307$	−712045.	−	712045.i	−0.431183	−	0.431183i	0.457848	−	0.889031i	$-0.348621\pi$
$307$	−712045.	−	712045.i	−0.431183	−	0.431183i	−0.889031	+	0.457848i	$0.848621\pi$
$308$		0			0
$309$	2.55595e6	−	2.55595e6i	1.52285	−	1.52285i
$310$		0			0
$311$		−	459793.i		−	0.269564i	−0.990875	−	0.134782i	$-0.956967\pi$
$311$		−	459793.i		−	0.269564i	0.990875	−	0.134782i	$-0.0430334\pi$
$312$		0			0
$313$		−	2.11774e6i		−	1.22183i	−0.791696	−	0.610915i	$-0.790802\pi$
$313$		−	2.11774e6i		−	1.22183i	0.791696	−	0.610915i	$-0.209198\pi$
$314$		0			0
$315$	−1.42212e6	+	1.42212e6i	−0.807534	+	0.807534i
$316$		0			0
$317$	818417.	+	818417.i	0.457432	+	0.457432i	0.897812	−	0.440380i	$-0.145156\pi$
$317$	818417.	+	818417.i	0.457432	+	0.457432i	−0.440380	+	0.897812i	$0.645156\pi$
$318$		0			0
$319$	52773.3			0.0290361
$320$		0			0
$321$	5.57542e6			3.02006
$322$		0			0
$323$	3.30216e6	+	3.30216e6i	1.76113	+	1.76113i
$324$		0			0
$325$	−210875.	+	210875.i	−0.110743	+	0.110743i
$326$		0			0
$327$		−	363494.i		−	0.187987i
$328$		0			0
$329$		−	1.88432e6i		−	0.959766i
$330$		0			0
$331$	930448.	−	930448.i	0.466790	−	0.466790i	−0.434083	−	0.900873i	$-0.642927\pi$
$331$	930448.	−	930448.i	0.466790	−	0.466790i	0.900873	+	0.434083i	$0.142927\pi$
$332$		0			0
$333$	1.44393e6	+	1.44393e6i	0.713568	+	0.713568i
$334$		0			0
$335$	961546.			0.468121
$336$		0			0
$337$	−1.66985e6			−0.800946			−0.400473	−	0.916308i	$-0.631154\pi$
$337$	−1.66985e6			−0.800946			−0.400473	+	0.916308i	$0.631154\pi$
$338$		0			0
$339$	−913350.	−	913350.i	−0.431656	−	0.431656i
$340$		0			0
$341$	107461.	−	107461.i	0.0500456	−	0.0500456i
$342$		0			0
$343$		−	1.59598e6i		−	0.732472i
$344$		0			0
$345$		−	1.88510e6i		−	0.852679i
$346$		0			0
$347$	−2.96486e6	+	2.96486e6i	−1.32185	+	1.32185i	−0.409565	+	0.912281i	$0.634320\pi$
$347$	−2.96486e6	+	2.96486e6i	−1.32185	+	1.32185i	−0.912281	+	0.409565i	$0.865680\pi$
$348$		0			0
$349$	−2.89685e6	−	2.89685e6i	−1.27310	−	1.27310i	−0.944452	−	0.328650i	$-0.893406\pi$
$349$	−2.89685e6	−	2.89685e6i	−1.27310	−	1.27310i	−0.328650	−	0.944452i	$-0.606594\pi$
$350$		0			0
$351$	−3.79343e6			−1.64348
$352$		0			0
$353$	−2.14860e6			−0.917740			−0.458870	−	0.888503i	$-0.651746\pi$
$353$	−2.14860e6			−0.917740			−0.458870	+	0.888503i	$0.651746\pi$
$354$		0			0
$355$	1.09138e6	+	1.09138e6i	0.459625	+	0.459625i
$356$		0			0
$357$	−5.88930e6	+	5.88930e6i	−2.44564	+	2.44564i
$358$		0			0
$359$		−	2.61006e6i		−	1.06884i	−0.845218	−	0.534421i	$-0.820530\pi$
$359$		−	2.61006e6i		−	1.06884i	0.845218	−	0.534421i	$-0.179470\pi$
$360$		0			0
$361$			3.13544e6i			1.26628i
$362$		0			0
$363$	3.15907e6	−	3.15907e6i	1.25833	−	1.25833i
$364$		0			0
$365$	327410.	+	327410.i	0.128635	+	0.128635i
$366$		0			0
$367$	7255.03			0.00281173			0.00140587	−	0.999999i	$-0.499552\pi$
$367$	7255.03			0.00281173			0.00140587	+	0.999999i	$0.499552\pi$
$368$		0			0
$369$	−5.13177e6			−1.96201
$370$		0			0
$371$	−118444.	−	118444.i	−0.0446763	−	0.0446763i
$372$		0			0
$373$	3.28076e6	−	3.28076e6i	1.22096	−	1.22096i	0.253675	−	0.967290i	$-0.418361\pi$
$373$	3.28076e6	−	3.28076e6i	1.22096	−	1.22096i	0.967290	−	0.253675i	$-0.0816393\pi$
$374$		0			0
$375$		−	434170.i		−	0.159434i
$376$		0			0
$377$		−	1.53302e6i		−	0.555513i
$378$		0			0
$379$	1.97719e6	−	1.97719e6i	0.707051	−	0.707051i	−0.258863	−	0.965914i	$-0.583348\pi$
$379$	1.97719e6	−	1.97719e6i	0.707051	−	0.707051i	0.965914	+	0.258863i	$0.0833477\pi$
$380$		0			0
$381$	−5.62642e6	−	5.62642e6i	−1.98573	−	1.98573i
$382$		0			0
$383$	−925457.			−0.322374			−0.161187	−	0.986924i	$-0.551532\pi$
$383$	−925457.			−0.322374			−0.161187	+	0.986924i	$0.551532\pi$
$384$		0			0
$385$	62436.0			0.0214676
$386$		0			0
$387$	−4.22408e6	−	4.22408e6i	−1.43369	−	1.43369i
$388$		0			0
$389$	−1.44312e6	+	1.44312e6i	−0.483536	+	0.483536i	−0.906259	−	0.422723i	$-0.861074\pi$
$389$	−1.44312e6	+	1.44312e6i	−0.483536	+	0.483536i	0.422723	+	0.906259i	$0.361074\pi$
$390$		0			0
$391$		−	5.34966e6i		−	1.76964i
$392$		0			0
$393$			4.63022e6i			1.51224i
$394$		0			0
$395$	968132.	−	968132.i	0.312207	−	0.312207i
$396$		0			0
$397$	2.24787e6	+	2.24787e6i	0.715807	+	0.715807i	0.967744	−	0.251937i	$-0.0810676\pi$
$397$	2.24787e6	+	2.24787e6i	0.715807	+	0.715807i	−0.251937	+	0.967744i	$0.581068\pi$
$398$		0			0
$399$	−1.00080e7			−3.14713
$400$		0			0
$401$	−2.69259e6			−0.836200			−0.418100	−	0.908401i	$-0.637304\pi$
$401$	−2.69259e6			−0.836200			−0.418100	+	0.908401i	$0.637304\pi$
$402$		0			0
$403$	−3.12165e6	−	3.12165e6i	−0.957463	−	0.957463i
$404$		0			0
$405$	1.63225e6	−	1.63225e6i	0.494480	−	0.494480i
$406$		0			0
$407$		−	63393.3i		−	0.0189696i
$408$		0			0
$409$		−	625505.i		−	0.184894i	−0.995718	−	0.0924470i	$-0.970531\pi$
$409$		−	625505.i		−	0.184894i	0.995718	−	0.0924470i	$-0.0294689\pi$
$410$		0			0
$411$	1.61780e6	−	1.61780e6i	0.472411	−	0.472411i
$412$		0			0
$413$	−422553.	−	422553.i	−0.121901	−	0.121901i
$414$		0			0
$415$	2.68828e6			0.766221
$416$		0			0
$417$	−8.44346e6			−2.37783
$418$		0			0
$419$	3.97089e6	+	3.97089e6i	1.10497	+	1.10497i	0.993801	+	0.111174i	$0.0354610\pi$
$419$	3.97089e6	+	3.97089e6i	1.10497	+	1.10497i	0.111174	+	0.993801i	$0.464539\pi$
$420$		0			0
$421$	4.47822e6	−	4.47822e6i	1.23140	−	1.23140i	0.267979	−	0.963425i	$-0.413644\pi$
$421$	4.47822e6	−	4.47822e6i	1.23140	−	1.23140i	0.963425	−	0.267979i	$-0.0863558\pi$
$422$		0			0
$423$			6.55743e6i			1.78190i
$424$		0			0
$425$		−	1.23212e6i		−	0.330887i
$426$		0			0
$427$	2.45537e6	−	2.45537e6i	0.651701	−	0.651701i
$428$		0			0
$429$	153997.	+	153997.i	0.0403989	+	0.0403989i
$430$		0			0
$431$	3.93764e6			1.02104			0.510521	−	0.859865i	$-0.329453\pi$
$431$	3.93764e6			1.02104			0.510521	+	0.859865i	$0.329453\pi$
$432$		0			0
$433$	−3.83172e6			−0.982141			−0.491071	−	0.871120i	$-0.663394\pi$
$433$	−3.83172e6			−0.982141			−0.491071	+	0.871120i	$0.663394\pi$
$434$		0			0
$435$	1.57816e6	+	1.57816e6i	0.399878	+	0.399878i
$436$		0			0
$437$	4.54548e6	−	4.54548e6i	1.13861	−	1.13861i
$438$		0			0
$439$			1.34172e6i			0.332278i	0.986102	+	0.166139i	$0.0531301\pi$
$439$			1.34172e6i			0.332278i	−0.986102	+	0.166139i	$0.946870\pi$
$440$		0			0
$441$		−	3.33875e6i		−	0.817500i
$442$		0			0
$443$	655716.	−	655716.i	0.158747	−	0.158747i	−0.623264	−	0.782011i	$-0.714194\pi$
$443$	655716.	−	655716.i	0.158747	−	0.158747i	0.782011	+	0.623264i	$0.214194\pi$
$444$		0			0
$445$	1.07109e6	+	1.07109e6i	0.256405	+	0.256405i
$446$		0			0
$447$	−1.41285e7			−3.34448
$448$		0			0
$449$	3.17602e6			0.743476			0.371738	−	0.928338i	$-0.378762\pi$
$449$	3.17602e6			0.743476			0.371738	+	0.928338i	$0.378762\pi$
$450$		0			0
$451$	112651.	+	112651.i	0.0260792	+	0.0260792i
$452$		0			0
$453$	−1.75144e6	+	1.75144e6i	−0.401004	+	0.401004i
$454$		0			0
$455$		−	1.81371e6i		−	0.410714i
$456$		0			0
$457$		−	4.41310e6i		−	0.988447i	−0.869335	−	0.494224i	$-0.835452\pi$
$457$		−	4.41310e6i		−	0.988447i	0.869335	−	0.494224i	$-0.164548\pi$
$458$		0			0
$459$	1.10822e7	−	1.10822e7i	2.45525	−	2.45525i
$460$		0			0
$461$	−2.80445e6	−	2.80445e6i	−0.614604	−	0.614604i	0.329539	−	0.944142i	$-0.393107\pi$
$461$	−2.80445e6	−	2.80445e6i	−0.614604	−	0.614604i	−0.944142	+	0.329539i	$0.893107\pi$
$462$		0			0
$463$	2.47795e6			0.537205			0.268603	−	0.963251i	$-0.413438\pi$
$463$	2.47795e6			0.537205			0.268603	+	0.963251i	$0.413438\pi$
$464$		0			0
$465$	6.42714e6			1.37843
$466$		0			0
$467$	1.18173e6	+	1.18173e6i	0.250742	+	0.250742i	0.821275	−	0.570533i	$-0.193263\pi$
$467$	1.18173e6	+	1.18173e6i	0.250742	+	0.250742i	−0.570533	+	0.821275i	$0.693263\pi$
$468$		0			0
$469$	−4.13506e6	+	4.13506e6i	−0.868060	+	0.868060i
$470$		0			0
$471$		−	1.64577e6i		−	0.341835i
$472$		0			0
$473$			185451.i			0.0381134i
$474$		0			0
$475$	1.04690e6	−	1.04690e6i	0.212898	−	0.212898i
$476$		0			0
$477$	412183.	+	412183.i	0.0829457	+	0.0829457i
$478$		0			0
$479$	−9.82296e6			−1.95616			−0.978078	−	0.208240i	$-0.933227\pi$
$479$	−9.82296e6			−1.95616			−0.978078	+	0.208240i	$0.933227\pi$
$480$		0			0
$481$	−1.84152e6			−0.362922
$482$		0			0
$483$	8.10672e6	+	8.10672e6i	1.58117	+	1.58117i
$484$		0			0
$485$	−1.42138e6	+	1.42138e6i	−0.274381	+	0.274381i
$486$		0			0
$487$			2.05462e6i			0.392562i	0.980548	+	0.196281i	$0.0628865\pi$
$487$			2.05462e6i			0.392562i	−0.980548	+	0.196281i	$0.937114\pi$
$488$		0			0
$489$			4.68748e6i			0.886476i
$490$		0			0
$491$	−4.27455e6	+	4.27455e6i	−0.800178	+	0.800178i	−0.983123	−	0.182945i	$-0.941437\pi$
$491$	−4.27455e6	+	4.27455e6i	−0.800178	+	0.800178i	0.182945	+	0.983123i	$0.441437\pi$
$492$		0			0
$493$	4.47861e6	+	4.47861e6i	0.829901	+	0.829901i
$494$		0			0
$495$	−217277.			−0.0398566
$496$		0			0
$497$	−9.38677e6			−1.70461
$498$		0			0
$499$	2.64763e6	+	2.64763e6i	0.475999	+	0.475999i	0.903850	−	0.427850i	$-0.140729\pi$
$499$	2.64763e6	+	2.64763e6i	0.475999	+	0.475999i	−0.427850	+	0.903850i	$0.640729\pi$
$500$		0			0
$501$	−2.38667e6	+	2.38667e6i	−0.424813	+	0.424813i
$502$		0			0
$503$			475460.i			0.0837904i	0.999122	+	0.0418952i	$0.0133396\pi$
$503$			475460.i			0.0837904i	−0.999122	+	0.0418952i	$0.986660\pi$
$504$		0			0
$505$		−	700474.i		−	0.122226i
$506$		0			0
$507$	−2.82178e6	+	2.82178e6i	−0.487532	+	0.487532i
$508$		0			0
$509$	2.26623e6	+	2.26623e6i	0.387712	+	0.387712i	0.873870	−	0.486159i	$-0.161602\pi$
$509$	2.26623e6	+	2.26623e6i	0.387712	+	0.387712i	−0.486159	+	0.873870i	$0.661602\pi$
$510$		0			0
$511$	−2.81601e6			−0.477070
$512$		0			0
$513$	1.88327e7			3.15950
$514$		0			0
$515$	−2.29961e6	−	2.29961e6i	−0.382063	−	0.382063i
$516$		0			0
$517$	143947.	−	143947.i	0.0236851	−	0.0236851i
$518$		0			0
$519$		−	8.61845e6i		−	1.40447i
$520$		0			0
$521$		−	5.50679e6i		−	0.888801i	−0.895828	−	0.444401i	$-0.853417\pi$
$521$		−	5.50679e6i		−	0.888801i	0.895828	−	0.444401i	$-0.146583\pi$
$522$		0			0
$523$	−4.02488e6	+	4.02488e6i	−0.643426	+	0.643426i	−0.951396	−	0.307970i	$-0.900350\pi$
$523$	−4.02488e6	+	4.02488e6i	−0.643426	+	0.643426i	0.307970	+	0.951396i	$0.400350\pi$
$524$		0			0
$525$	1.86712e6	+	1.86712e6i	0.295647	+	0.295647i
$526$		0			0
$527$	1.82394e7			2.86078
$528$		0			0
$529$	−927561.			−0.144113
$530$		0			0
$531$	1.47048e6	+	1.47048e6i	0.226320	+	0.226320i
$532$		0			0
$533$	3.27241e6	−	3.27241e6i	0.498942	−	0.498942i
$534$		0			0
$535$		−	5.01624e6i		−	0.757694i
$536$		0			0
$537$		−	1.89218e7i		−	2.83156i
$538$		0			0
$539$	−73291.2	+	73291.2i	−0.0108663	+	0.0108663i
$540$		0			0
$541$	7.20318e6	+	7.20318e6i	1.05811	+	1.05811i	0.998204	+	0.0599075i	$0.0190806\pi$
$541$	7.20318e6	+	7.20318e6i	1.05811	+	1.05811i	0.0599075	+	0.998204i	$0.480919\pi$
$542$		0			0
$543$	7.27049e6			1.05819
$544$		0			0
$545$	−327038.			−0.0471635
$546$		0			0
$547$	−579264.	−	579264.i	−0.0827767	−	0.0827767i	0.664506	−	0.747283i	$-0.268642\pi$
$547$	−579264.	−	579264.i	−0.0827767	−	0.0827767i	−0.747283	+	0.664506i	$0.768642\pi$
$548$		0			0
$549$	−8.54468e6	+	8.54468e6i	−1.20994	+	1.20994i
$550$		0			0
$551$			7.61075e6i			1.06794i
$552$		0			0
$553$			8.32677e6i			1.15788i
$554$		0			0
$555$	1.89574e6	−	1.89574e6i	0.261245	−	0.261245i
$556$		0			0
$557$	1.06112e6	+	1.06112e6i	0.144920	+	0.144920i	0.775844	−	0.630925i	$-0.217324\pi$
$557$	1.06112e6	+	1.06112e6i	0.144920	+	0.144920i	−0.630925	+	0.775844i	$0.717324\pi$
$558$		0			0
$559$	5.38720e6			0.729178
$560$		0			0
$561$	−899786.			−0.120707
$562$		0			0
$563$	−5.65144e6	−	5.65144e6i	−0.751429	−	0.751429i	0.223317	−	0.974746i	$-0.428312\pi$
$563$	−5.65144e6	−	5.65144e6i	−0.751429	−	0.751429i	−0.974746	+	0.223317i	$0.928312\pi$
$564$		0			0
$565$	−821747.	+	821747.i	−0.108297	+	0.108297i
$566$		0			0
$567$			1.40387e7i			1.83388i
$568$		0			0
$569$		−	5.69200e6i		−	0.737028i	−0.929622	−	0.368514i	$-0.879867\pi$
$569$		−	5.69200e6i		−	0.737028i	0.929622	−	0.368514i	$-0.120133\pi$
$570$		0			0
$571$	500996.	−	500996.i	0.0643049	−	0.0643049i	−0.674223	−	0.738528i	$-0.735521\pi$
$571$	500996.	−	500996.i	0.0643049	−	0.0643049i	0.738528	+	0.674223i	$0.235521\pi$
$572$		0			0
$573$	2.83869e6	+	2.83869e6i	0.361186	+	0.361186i
$574$		0			0
$575$	−1.69603e6			−0.213926
$576$		0			0
$577$	4.96081e6			0.620316			0.310158	−	0.950685i	$-0.399618\pi$
$577$	4.96081e6			0.620316			0.310158	+	0.950685i	$0.399618\pi$
$578$		0			0
$579$	−1.12672e7	−	1.12672e7i	−1.39676	−	1.39676i
$580$		0			0
$581$	−1.15608e7	+	1.15608e7i	−1.42084	+	1.42084i
$582$		0			0
$583$		−	18096.2i		−	0.00220504i
$584$		0			0
$585$			6.31170e6i			0.762529i
$586$		0			0
$587$	2.22699e6	−	2.22699e6i	0.266761	−	0.266761i	−0.561032	−	0.827794i	$-0.689596\pi$
$587$	2.22699e6	−	2.22699e6i	0.266761	−	0.266761i	0.827794	+	0.561032i	$0.189596\pi$
$588$		0			0
$589$	1.54976e7	+	1.54976e7i	1.84067	+	1.84067i
$590$		0			0
$591$	−8.99824e6			−1.05971
$592$		0			0
$593$	−749550.			−0.0875314			−0.0437657	−	0.999042i	$-0.513936\pi$
$593$	−749550.			−0.0875314			−0.0437657	+	0.999042i	$0.513936\pi$
$594$		0			0
$595$	5.29864e6	+	5.29864e6i	0.613581	+	0.613581i
$596$		0			0
$597$	8.94814e6	−	8.94814e6i	1.02754	−	1.02754i
$598$		0			0
$599$			1.24336e7i			1.41589i	0.706267	+	0.707946i	$0.250378\pi$
$599$			1.24336e7i			1.41589i	−0.706267	+	0.707946i	$0.749622\pi$
$600$		0			0
$601$		−	1.06573e7i		−	1.20354i	−0.798668	−	0.601772i	$-0.794462\pi$
$601$		−	1.06573e7i		−	1.20354i	0.798668	−	0.601772i	$-0.205538\pi$
$602$		0			0
$603$	1.43900e7	−	1.43900e7i	1.61164	−	1.61164i
$604$		0			0
$605$	−2.84224e6	−	2.84224e6i	−0.315698	−	0.315698i
$606$		0			0
$607$	−1.21466e7			−1.33808			−0.669039	−	0.743228i	$-0.733294\pi$
$607$	−1.21466e7			−1.33808			−0.669039	+	0.743228i	$0.733294\pi$
$608$		0			0
$609$	−1.35735e7			−1.48303
$610$		0			0
$611$	−4.18152e6	−	4.18152e6i	−0.453139	−	0.453139i
$612$		0			0
$613$	189949.	−	189949.i	0.0204168	−	0.0204168i	−0.696825	−	0.717241i	$-0.745404\pi$
$613$	189949.	−	189949.i	0.0204168	−	0.0204168i	0.717241	+	0.696825i	$0.245404\pi$
$614$		0			0
$615$			6.73755e6i			0.718313i
$616$		0			0
$617$			1.08751e7i			1.15006i	0.818133	+	0.575028i	$0.195009\pi$
$617$			1.08751e7i			1.15006i	−0.818133	+	0.575028i	$0.804991\pi$
$618$		0			0
$619$	−1.32235e7	+	1.32235e7i	−1.38714	+	1.38714i	−0.555859	+	0.831277i	$0.687611\pi$
$619$	−1.32235e7	+	1.32235e7i	−1.38714	+	1.38714i	−0.831277	+	0.555859i	$0.812389\pi$
$620$		0			0
$621$	−1.52549e7	−	1.52549e7i	−1.58738	−	1.58738i
$622$		0			0
$623$	−9.21230e6			−0.950929
$624$		0			0
$625$	−390625.			−0.0400000
$626$		0			0
$627$	−764528.	−	764528.i	−0.0776649	−	0.0776649i
$628$		0			0
$629$	5.37988e6	−	5.37988e6i	0.542183	−	0.542183i
$630$		0			0
$631$		−	1.12988e7i		−	1.12969i	−0.825197	−	0.564845i	$-0.808936\pi$
$631$		−	1.12988e7i		−	1.12969i	0.825197	−	0.564845i	$-0.191064\pi$
$632$		0			0
$633$		−	1.47691e7i		−	1.46502i
$634$		0			0
$635$	−5.06213e6	+	5.06213e6i	−0.498194	+	0.498194i
$636$		0			0
$637$	2.12904e6	+	2.12904e6i	0.207891	+	0.207891i
$638$		0			0
$639$	3.26659e7			3.16477
$640$		0			0
$641$	−1.29242e7			−1.24239			−0.621195	−	0.783656i	$-0.713352\pi$
$641$	−1.29242e7			−1.24239			−0.621195	+	0.783656i	$0.713352\pi$
$642$		0			0
$643$	816087.	+	816087.i	0.0778411	+	0.0778411i	0.744955	−	0.667114i	$-0.232471\pi$
$643$	816087.	+	816087.i	0.0778411	+	0.0778411i	−0.667114	+	0.744955i	$0.732471\pi$
$644$		0			0
$645$	−5.54583e6	+	5.54583e6i	−0.524889	+	0.524889i
$646$		0			0
$647$			1.14750e7i			1.07769i	0.842406	+	0.538844i	$0.181139\pi$
$647$			1.14750e7i			1.07769i	−0.842406	+	0.538844i	$0.818861\pi$
$648$		0			0
$649$		−	64559.1i		−	0.00601653i
$650$		0			0
$651$	−2.76395e7	+	2.76395e7i	−2.55610	+	2.55610i
$652$		0			0
$653$	5.60167e6	+	5.60167e6i	0.514084	+	0.514084i	0.915775	−	0.401691i	$-0.131577\pi$
$653$	5.60167e6	+	5.60167e6i	0.514084	+	0.514084i	−0.401691	+	0.915775i	$0.631577\pi$
$654$		0			0
$655$	4.16584e6			0.379402
$656$		0			0
$657$	9.79969e6			0.885725
$658$		0			0
$659$	−3.61020e6	−	3.61020e6i	−0.323831	−	0.323831i	0.526404	−	0.850235i	$-0.323540\pi$
$659$	−3.61020e6	−	3.61020e6i	−0.323831	−	0.323831i	−0.850235	+	0.526404i	$0.823540\pi$
$660$		0			0
$661$	4.16305e6	−	4.16305e6i	0.370602	−	0.370602i	−0.497094	−	0.867696i	$-0.665600\pi$
$661$	4.16305e6	−	4.16305e6i	0.370602	−	0.370602i	0.867696	+	0.497094i	$0.165600\pi$
$662$		0			0
$663$			2.61380e7i			2.30934i
$664$		0			0
$665$			9.00426e6i			0.789576i
$666$		0			0
$667$	6.16489e6	−	6.16489e6i	0.536551	−	0.536551i
$668$		0			0
$669$	−7.32406e6	−	7.32406e6i	−0.632684	−	0.632684i
$670$		0			0
$671$	375140.			0.0321653
$672$		0			0
$673$	2.21199e7			1.88255			0.941273	−	0.337645i	$-0.109630\pi$
$673$	2.21199e7			1.88255			0.941273	+	0.337645i	$0.109630\pi$
$674$		0			0
$675$	−3.51347e6	−	3.51347e6i	−0.296809	−	0.296809i
$676$		0			0
$677$	−5.09252e6	+	5.09252e6i	−0.427033	+	0.427033i	−0.887616	−	0.460584i	$-0.847640\pi$
$677$	−5.09252e6	+	5.09252e6i	−0.427033	+	0.427033i	0.460584	+	0.887616i	$0.347640\pi$
$678$		0			0
$679$		−	1.22251e7i		−	1.01760i
$680$		0			0
$681$			2.37033e7i			1.95858i
$682$		0			0
$683$	−5.69497e6	+	5.69497e6i	−0.467132	+	0.467132i	−0.900984	−	0.433852i	$-0.857154\pi$
$683$	−5.69497e6	+	5.69497e6i	−0.467132	+	0.467132i	0.433852	+	0.900984i	$0.357154\pi$
$684$		0			0
$685$	−1.45554e6	−	1.45554e6i	−0.118522	−	0.118522i
$686$		0			0
$687$	−2.27255e7			−1.83705
$688$		0			0
$689$	−525679.			−0.0421864
$690$		0			0
$691$	2.98475e6	+	2.98475e6i	0.237801	+	0.237801i	0.815939	−	0.578138i	$-0.196221\pi$
$691$	2.98475e6	+	2.98475e6i	0.237801	+	0.237801i	−0.578138	+	0.815939i	$0.696221\pi$
$692$		0			0
$693$	934384.	−	934384.i	0.0739081	−	0.0739081i
$694$		0			0
$695$			7.59664e6i			0.596567i
$696$		0			0
$697$			1.91203e7i			1.49078i
$698$		0			0
$699$	1.60284e7	−	1.60284e7i	1.24079	−	1.24079i
$700$		0			0
$701$	−9.70805e6	−	9.70805e6i	−0.746169	−	0.746169i	0.227589	−	0.973757i	$-0.426916\pi$
$701$	−9.70805e6	−	9.70805e6i	−0.746169	−	0.746169i	−0.973757	+	0.227589i	$0.926916\pi$
$702$		0			0
$703$	9.14233e6			0.697699
$704$		0			0
$705$	8.60929e6			0.652371
$706$		0			0
$707$	3.01234e6	+	3.01234e6i	0.226650	+	0.226650i
$708$		0			0
$709$	1.00421e7	−	1.00421e7i	0.750256	−	0.750256i	−0.224270	−	0.974527i	$-0.572000\pi$
$709$	1.00421e7	−	1.00421e7i	0.750256	−	0.750256i	0.974527	+	0.224270i	$0.0719999\pi$
$710$		0			0
$711$		−	2.89771e7i		−	2.14972i
$712$		0			0
$713$		−	2.51069e7i		−	1.84956i
$714$		0			0
$715$	138552.	−	138552.i	0.0101356	−	0.0101356i
$716$		0			0
$717$	5.01463e6	+	5.01463e6i	0.364285	+	0.364285i
$718$		0			0
$719$	3.73707e6			0.269593			0.134796	−	0.990873i	$-0.456962\pi$
$719$	3.73707e6			0.269593			0.134796	+	0.990873i	$0.456962\pi$
$720$		0			0
$721$	1.97786e7			1.41696
$722$		0			0
$723$	2.39141e7	+	2.39141e7i	1.70141	+	1.70141i
$724$		0			0
$725$	1.41988e6	−	1.41988e6i	0.100324	−	0.100324i
$726$		0			0
$727$		−	2.73870e7i		−	1.92180i	−0.276894	−	0.960900i	$-0.589305\pi$
$727$		−	2.73870e7i		−	1.92180i	0.276894	−	0.960900i	$-0.410695\pi$
$728$		0			0
$729$			4.82580e6i			0.336318i
$730$		0			0
$731$	−1.57383e7	+	1.57383e7i	−1.08935	+	1.08935i
$732$		0			0
$733$	−1.05278e6	−	1.05278e6i	−0.0723728	−	0.0723728i	0.669994	−	0.742367i	$-0.266297\pi$
$733$	−1.05278e6	−	1.05278e6i	−0.0723728	−	0.0723728i	−0.742367	+	0.669994i	$0.766297\pi$
$734$		0			0
$735$	−4.38347e6			−0.299295
$736$		0			0
$737$	−631769.			−0.0428439
$738$		0			0
$739$	1.09564e6	+	1.09564e6i	0.0737998	+	0.0737998i	0.743043	−	0.669243i	$-0.233382\pi$
$739$	1.09564e6	+	1.09564e6i	0.0737998	+	0.0737998i	−0.669243	+	0.743043i	$0.733382\pi$
$740$		0			0
$741$	−2.22089e7	+	2.22089e7i	−1.48587	+	1.48587i
$742$		0			0
$743$		−	4.23113e6i		−	0.281180i	−0.990068	−	0.140590i	$-0.955100\pi$
$743$		−	4.23113e6i		−	0.281180i	0.990068	−	0.140590i	$-0.0448999\pi$
$744$		0			0
$745$			1.27115e7i			0.839087i
$746$		0			0
$747$	4.02313e7	−	4.02313e7i	2.63793	−	2.63793i
$748$		0			0
$749$	2.15720e7	+	2.15720e7i	1.40503	+	1.40503i
$750$		0			0
$751$	−1.15236e7			−0.745568			−0.372784	−	0.927918i	$-0.621597\pi$
$751$	−1.15236e7			−0.745568			−0.372784	+	0.927918i	$0.621597\pi$
$752$		0			0
$753$	−2.79622e7			−1.79715
$754$		0			0
$755$	1.57578e6	+	1.57578e6i	0.100607	+	0.100607i
$756$		0			0
$757$	−3.45229e6	+	3.45229e6i	−0.218962	+	0.218962i	−0.808061	−	0.589099i	$-0.799483\pi$
$757$	−3.45229e6	+	3.45229e6i	−0.218962	+	0.218962i	0.589099	+	0.808061i	$0.299483\pi$
$758$		0			0
$759$			1.23857e6i			0.0780400i
$760$		0			0
$761$			1.60302e7i			1.00341i	0.865040	+	0.501703i	$0.167293\pi$
$761$			1.60302e7i			1.00341i	−0.865040	+	0.501703i	$0.832707\pi$
$762$		0			0
$763$	1.40640e6	−	1.40640e6i	0.0874578	−	0.0874578i
$764$		0			0
$765$	−1.84392e7	−	1.84392e7i	−1.13917	−	1.13917i
$766$		0			0
$767$	−1.87538e6			−0.115107
$768$		0			0
$769$	−1.30895e7			−0.798189			−0.399095	−	0.916910i	$-0.630675\pi$
$769$	−1.30895e7			−0.798189			−0.399095	+	0.916910i	$0.630675\pi$
$770$		0			0
$771$	7.75797e6	+	7.75797e6i	0.470015	+	0.470015i
$772$		0			0
$773$	4.93181e6	−	4.93181e6i	0.296864	−	0.296864i	−0.542920	−	0.839784i	$-0.682681\pi$
$773$	4.93181e6	−	4.93181e6i	0.296864	−	0.296864i	0.839784	+	0.542920i	$0.182681\pi$
$774$		0			0
$775$		−	5.78254e6i		−	0.345831i
$776$		0			0
$777$			1.63050e7i			0.968879i
$778$		0			0
$779$	−1.62461e7	+	1.62461e7i	−0.959191	+	0.959191i
$780$		0			0
$781$	−717071.	−	717071.i	−0.0420663	−	0.0420663i
$782$		0			0
$783$	2.55422e7			1.48886
$784$		0			0
$785$	−1.48071e6			−0.0857622
$786$		0			0
$787$	2.31058e7	+	2.31058e7i	1.32979	+	1.32979i	0.905549	+	0.424242i	$0.139460\pi$
$787$	2.31058e7	+	2.31058e7i	1.32979	+	1.32979i	0.424242	+	0.905549i	$0.360540\pi$
$788$		0			0
$789$	8.77788e6	−	8.77788e6i	0.501993	−	0.501993i
$790$		0			0
$791$		−	7.06773e6i		−	0.401642i
$792$		0			0
$793$		−	1.08975e7i		−	0.615380i
$794$		0			0
$795$	541158.	−	541158.i	0.0303673	−	0.0303673i
$796$		0			0
$797$	−9.91730e6	−	9.91730e6i	−0.553029	−	0.553029i	0.374285	−	0.927314i	$-0.377888\pi$
$797$	−9.91730e6	−	9.91730e6i	−0.553029	−	0.553029i	−0.927314	+	0.374285i	$0.877888\pi$
$798$		0			0
$799$	2.44321e7			1.35392
$800$		0			0
$801$	3.20587e7			1.76549
$802$		0			0
$803$	−215120.	−	215120.i	−0.0117731	−	0.0117731i
$804$		0			0
$805$	7.29367e6	−	7.29367e6i	0.396695	−	0.396695i
$806$		0			0
$807$			2.42450e7i			1.31050i
$808$		0			0
$809$			1.84026e7i			0.988569i	0.869300	+	0.494284i	$0.164570\pi$
$809$			1.84026e7i			0.988569i	−0.869300	+	0.494284i	$0.835430\pi$
$810$		0			0
$811$	−6.67819e6	+	6.67819e6i	−0.356539	+	0.356539i	−0.862535	−	0.505997i	$-0.831125\pi$
$811$	−6.67819e6	+	6.67819e6i	−0.356539	+	0.356539i	0.505997	+	0.862535i	$0.331125\pi$
$812$		0			0
$813$	−5.95274e6	−	5.95274e6i	−0.315857	−	0.315857i
$814$		0			0
$815$	4.21735e6			0.222406
$816$		0			0
$817$	−2.67450e7			−1.40181
$818$		0			0
$819$	−2.71430e7	−	2.71430e7i	−1.41400	−	1.41400i
$820$		0			0
$821$	4.76725e6	−	4.76725e6i	0.246837	−	0.246837i	−0.572834	−	0.819671i	$-0.694156\pi$
$821$	4.76725e6	−	4.76725e6i	0.246837	−	0.246837i	0.819671	+	0.572834i	$0.194156\pi$
$822$		0			0
$823$		−	1.24864e7i		−	0.642593i	−0.946979	−	0.321297i	$-0.895881\pi$
$823$		−	1.24864e7i		−	0.642593i	0.946979	−	0.321297i	$-0.104119\pi$
$824$		0			0
$825$			285264.i			0.0145919i
$826$		0			0
$827$	1.97584e7	−	1.97584e7i	1.00459	−	1.00459i	0.00459995	−	0.999989i	$-0.498536\pi$
$827$	1.97584e7	−	1.97584e7i	1.00459	−	1.00459i	0.999989	−	0.00459995i	$-0.00146421\pi$
$828$		0			0
$829$	−1.04021e7	−	1.04021e7i	−0.525695	−	0.525695i	0.393591	−	0.919286i	$-0.371233\pi$
$829$	−1.04021e7	−	1.04021e7i	−0.525695	−	0.525695i	−0.919286	+	0.393591i	$0.871233\pi$
$830$		0			0
$831$	2.96304e7			1.48845
$832$		0			0
$833$	−1.24397e7			−0.621153
$834$		0			0
$835$	2.14730e6	+	2.14730e6i	0.106580	+	0.106580i
$836$		0			0
$837$	5.20109e7	−	5.20109e7i	2.56614	−	2.56614i
$838$		0			0
$839$		−	5.97699e6i		−	0.293142i	−0.989200	−	0.146571i	$-0.953176\pi$
$839$		−	5.97699e6i		−	0.293142i	0.989200	−	0.146571i	$-0.0468237\pi$
$840$		0			0
$841$		−	1.01889e7i		−	0.496751i
$842$		0			0
$843$	−3.59126e7	+	3.59126e7i	−1.74052	+	1.74052i
$844$		0			0
$845$	2.53877e6	+	2.53877e6i	0.122316	+	0.122316i
$846$		0			0
$847$	2.44457e7			1.17083
$848$		0			0
$849$	4.42523e6			0.210701
$850$		0			0
$851$	−7.40550e6	−	7.40550e6i	−0.350534	−	0.350534i
$852$		0			0
$853$	17875.4	−	17875.4i	0.000841170	−	0.000841170i	−0.706686	−	0.707527i	$-0.749811\pi$
$853$	17875.4	−	17875.4i	0.000841170	−	0.000841170i	0.707527	+	0.706686i	$0.249811\pi$
$854$		0			0
$855$		−	3.13348e7i		−	1.46592i
$856$		0			0
$857$			1.76443e7i			0.820640i	0.911942	+	0.410320i	$0.134583\pi$
$857$			1.76443e7i			0.820640i	−0.911942	+	0.410320i	$0.865417\pi$
$858$		0			0
$859$	−920994.	+	920994.i	−0.0425867	+	0.0425867i	−0.728079	−	0.685493i	$-0.759587\pi$
$859$	−920994.	+	920994.i	−0.0425867	+	0.0425867i	0.685493	+	0.728079i	$0.259587\pi$
$860$		0			0
$861$	−2.89744e7	−	2.89744e7i	−1.33201	−	1.33201i
$862$		0			0
$863$	−1.98421e7			−0.906901			−0.453450	−	0.891281i	$-0.649807\pi$
$863$	−1.98421e7			−0.906901			−0.453450	+	0.891281i	$0.649807\pi$
$864$		0			0
$865$	−7.75408e6			−0.352363
$866$		0			0
$867$	−4.84627e7	−	4.84627e7i	−2.18957	−	2.18957i
$868$		0			0
$869$	−636096.	+	636096.i	−0.0285742	+	0.0285742i
$870$		0			0
$871$			1.83523e7i			0.819682i
$872$		0			0
$873$			4.25431e7i			1.88927i
$874$		0			0
$875$	1.67986e6	−	1.67986e6i	0.0741740	−	0.0741740i
$876$		0			0
$877$	−2.55034e7	−	2.55034e7i	−1.11969	−	1.11969i	−0.991786	−	0.127905i	$-0.959175\pi$
$877$	−2.55034e7	−	2.55034e7i	−1.11969	−	1.11969i	−0.127905	−	0.991786i	$-0.540825\pi$
$878$		0			0
$879$	−4.02010e7			−1.75495
$880$		0			0
$881$	−3.12202e7			−1.35518			−0.677588	−	0.735442i	$-0.736975\pi$
$881$	−3.12202e7			−1.35518			−0.677588	+	0.735442i	$0.736975\pi$
$882$		0			0
$883$	751066.	+	751066.i	0.0324173	+	0.0324173i	0.723130	−	0.690712i	$-0.242703\pi$
$883$	751066.	+	751066.i	0.0324173	+	0.0324173i	−0.690712	+	0.723130i	$0.742703\pi$
$884$		0			0
$885$	1.93061e6	−	1.93061e6i	0.0828582	−	0.0828582i
$886$		0			0
$887$			1.33534e6i			0.0569878i	0.999594	+	0.0284939i	$0.00907112\pi$
$887$			1.33534e6i			0.0569878i	−0.999594	+	0.0284939i	$0.990929\pi$
$888$		0			0
$889$		−	4.35387e7i		−	1.84765i
$890$		0			0
$891$	−1.07244e6	+	1.07244e6i	−0.0452564	+	0.0452564i
$892$		0			0
$893$	2.07594e7	+	2.07594e7i	0.871136	+	0.871136i
$894$		0			0
$895$	−1.70240e7			−0.710403
$896$		0			0
$897$	3.59794e7			1.49305
$898$		0			0
$899$	2.10189e7	+	2.10189e7i	0.867383	+	0.867383i
$900$		0			0
$901$	1.53574e6	−	1.53574e6i	0.0630238	−	0.0630238i
$902$		0			0
$903$		−	4.76989e7i		−	1.94666i
$904$		0			0
$905$		−	6.54131e6i		−	0.265487i
$906$		0			0
$907$	1.98474e7	−	1.98474e7i	0.801098	−	0.801098i	−0.182169	−	0.983267i	$-0.558312\pi$
$907$	1.98474e7	−	1.98474e7i	0.801098	−	0.801098i	0.983267	+	0.182169i	$0.0583119\pi$
$908$		0			0
$909$	−1.04829e7	−	1.04829e7i	−0.420797	−	0.420797i
$910$		0			0
$911$	−1.80547e7			−0.720767			−0.360383	−	0.932804i	$-0.617354\pi$
$911$	−1.80547e7			−0.720767			−0.360383	+	0.932804i	$0.617354\pi$
$912$		0			0
$913$	−1.76629e6			−0.0701270
$914$		0			0
$915$	1.12184e7	+	1.12184e7i	0.442973	+	0.442973i
$916$		0			0
$917$	−1.79149e7	+	1.79149e7i	−0.703544	+	0.703544i
$918$		0			0
$919$			2.96410e7i			1.15772i	0.815426	+	0.578861i	$0.196503\pi$
$919$			2.96410e7i			1.15772i	−0.815426	+	0.578861i	$0.803497\pi$
$920$		0			0
$921$			2.79809e7i			1.08696i
$922$		0			0
$923$	−2.08303e7	+	2.08303e7i	−0.804805	+	0.804805i
$924$		0			0
$925$	−1.70561e6	−	1.70561e6i	−0.0655430	−	0.0655430i
$926$		0			0
$927$	−6.88294e7			−2.63072
$928$		0			0
$929$	−8.63963e6			−0.328440			−0.164220	−	0.986424i	$-0.552511\pi$
$929$	−8.63963e6			−0.328440			−0.164220	+	0.986424i	$0.552511\pi$
$930$		0			0
$931$	−1.05698e7	−	1.05698e7i	−0.399660	−	0.399660i
$932$		0			0
$933$	−9.03414e6	+	9.03414e6i	−0.339768	+	0.339768i
$934$		0			0
$935$			809543.i			0.0302838i
$936$		0			0
$937$		−	1.12375e7i		−	0.418138i	−0.977901	−	0.209069i	$-0.932957\pi$
$937$		−	1.12375e7i		−	0.418138i	0.977901	−	0.209069i	$-0.0670434\pi$
$938$		0			0
$939$	−4.16098e7	+	4.16098e7i	−1.54004	+	1.54004i
$940$		0			0
$941$	−2.30935e7	−	2.30935e7i	−0.850190	−	0.850190i	0.139966	−	0.990156i	$-0.455301\pi$
$941$	−2.30935e7	−	2.30935e7i	−0.850190	−	0.850190i	−0.990156	+	0.139966i	$0.955301\pi$
$942$		0			0
$943$	2.63194e7			0.963823
$944$		0			0
$945$	3.02189e7			1.10077
$946$		0			0
$947$	−1.68224e7	−	1.68224e7i	−0.609557	−	0.609557i	0.333274	−	0.942830i	$-0.391847\pi$
$947$	−1.68224e7	−	1.68224e7i	−0.609557	−	0.609557i	−0.942830	+	0.333274i	$0.891847\pi$
$948$		0			0
$949$	−6.24904e6	+	6.24904e6i	−0.225241	+	0.225241i
$950$		0			0
$951$		−	3.21610e7i		−	1.15313i
$952$		0			0
$953$			2.32202e7i			0.828199i	0.910232	+	0.414099i	$0.135903\pi$
$953$			2.32202e7i			0.828199i	−0.910232	+	0.414099i	$0.864097\pi$
$954$		0			0
$955$	2.55398e6	−	2.55398e6i	0.0906170	−	0.0906170i
$956$		0			0
$957$	−1.03691e6	−	1.03691e6i	−0.0365981	−	0.0365981i
$958$		0			0
$959$	1.25189e7			0.439562
$960$		0			0
$961$	5.69716e7			1.98999
$962$		0			0
$963$	−7.50703e7	−	7.50703e7i	−2.60857	−	2.60857i
$964$		0			0
$965$	−1.01372e7	+	1.01372e7i	−0.350428	+	0.350428i
$966$		0			0
$967$			4.77137e7i			1.64088i	0.571731	+	0.820441i	$0.306272\pi$
$967$			4.77137e7i			1.64088i	−0.571731	+	0.820441i	$0.693728\pi$
$968$		0			0
$969$		−	1.29763e8i		−	4.43959i
$970$		0			0
$971$	2.29107e7	−	2.29107e7i	0.779813	−	0.779813i	−0.199986	−	0.979799i	$-0.564090\pi$
$971$	2.29107e7	−	2.29107e7i	0.779813	−	0.779813i	0.979799	+	0.199986i	$0.0640895\pi$
$972$		0			0
$973$	−3.26688e7	−	3.26688e7i	−1.10624	−	1.10624i
$974$		0			0
$975$	8.28667e6			0.279170
$976$		0			0
$977$	−5.07357e7			−1.70050			−0.850251	−	0.526377i	$-0.823550\pi$
$977$	−5.07357e7			−1.70050			−0.850251	+	0.526377i	$0.823550\pi$
$978$		0			0
$979$	−703743.	−	703743.i	−0.0234670	−	0.0234670i
$980$		0			0
$981$	−4.89427e6	+	4.89427e6i	−0.162374	+	0.162374i
$982$		0			0
$983$		−	6.51198e6i		−	0.214946i	−0.994208	−	0.107473i	$-0.965724\pi$
$983$		−	6.51198e6i		−	0.214946i	0.994208	−	0.107473i	$-0.0342759\pi$
$984$		0			0
$985$			8.09577e6i			0.265869i
$986$		0			0
$987$	−3.70237e7	+	3.70237e7i	−1.20973	+	1.20973i
$988$		0			0
$989$	2.16641e7	+	2.16641e7i	0.704288	+	0.704288i
$990$		0			0
$991$	5.04162e7			1.63074			0.815372	−	0.578938i	$-0.196533\pi$
$991$	5.04162e7			1.63074			0.815372	+	0.578938i	$0.196533\pi$
$992$		0			0
$993$	−3.65634e7			−1.17672
$994$		0			0
$995$	−8.05069e6	−	8.05069e6i	−0.257796	−	0.257796i
$996$		0			0
$997$	1.83995e7	−	1.83995e7i	0.586229	−	0.586229i	−0.350379	−	0.936608i	$-0.613947\pi$
$997$	1.83995e7	−	1.83995e7i	0.586229	−	0.586229i	0.936608	+	0.350379i	$0.113947\pi$
$998$		0			0
$999$		−	3.06822e7i		−	0.972686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.6.l.a.81.3		80
4.3	odd	2		80.6.l.a.61.2	yes	80
16.5	even	4	inner	320.6.l.a.241.3		80
16.11	odd	4		80.6.l.a.21.2	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.2	✓	80	16.11	odd	4
80.6.l.a.61.2	yes	80	4.3	odd	2
320.6.l.a.81.3		80	1.1	even	1	trivial
320.6.l.a.241.3		80	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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	320.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-19.6483 - 19.6483i) q^{3} +(-17.6777 + 17.6777i) q^{5} -152.043i q^{7} +529.109i q^{9} +O(q^{10})\)	\(q+(-19.6483 - 19.6483i) q^{3} +(-17.6777 + 17.6777i) q^{5} -152.043i q^{7} +529.109i q^{9} +(11.6148 - 11.6148i) q^{11} +(-337.401 - 337.401i) q^{13} +694.671 q^{15} +1971.39 q^{17} +(1675.04 + 1675.04i) q^{19} +(-2987.39 + 2987.39i) q^{21} -2713.65i q^{23} -625.000i q^{25} +(5621.55 - 5621.55i) q^{27} +(2271.81 + 2271.81i) q^{29} +9252.07 q^{31} -456.423 q^{33} +(2687.77 + 2687.77i) q^{35} +(2728.98 - 2728.98i) q^{37} +13258.7i q^{39} +9698.90i q^{41} +(-7983.39 + 7983.39i) q^{43} +(-9353.41 - 9353.41i) q^{45} +12393.3 q^{47} -6310.14 q^{49} +(-38734.4 - 38734.4i) q^{51} +(779.013 - 779.013i) q^{53} +410.646i q^{55} -65823.4i q^{57} +(2779.17 - 2779.17i) q^{59} +(16149.2 + 16149.2i) q^{61} +80447.4 q^{63} +11928.9 q^{65} +(-27196.6 - 27196.6i) q^{67} +(-53318.6 + 53318.6i) q^{69} -61737.5i q^{71} -18521.1i q^{73} +(-12280.2 + 12280.2i) q^{75} +(-1765.96 - 1765.96i) q^{77} -54765.8 q^{79} -92333.9 q^{81} +(-76036.0 - 76036.0i) q^{83} +(-34849.5 + 34849.5i) q^{85} -89274.2i q^{87} -60590.0i q^{89} +(-51299.5 + 51299.5i) q^{91} +(-181787. - 181787. i) q^{93} -59221.7 q^{95} +80405.2 q^{97} +(6145.52 + 6145.52i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q+O(q^{10}) \) 80 * q	\( 80 q - 1208 q^{11} + 1800 q^{15} - 2360 q^{19} + 7464 q^{27} - 8144 q^{29} + 21296 q^{37} - 32072 q^{43} + 88360 q^{47} - 192080 q^{49} + 5920 q^{51} - 49456 q^{53} - 44984 q^{59} + 48080 q^{61} - 158760 q^{63} - 61160 q^{67} - 22320 q^{69} - 14896 q^{77} - 177680 q^{79} - 524880 q^{81} + 329240 q^{83} + 132400 q^{85} - 364832 q^{91} - 362352 q^{93} - 288800 q^{95} - 659000 q^{99}+O(q^{100}) \) 80 * q - 1208 * q^11 + 1800 * q^15 - 2360 * q^19 + 7464 * q^27 - 8144 * q^29 + 21296 * q^37 - 32072 * q^43 + 88360 * q^47 - 192080 * q^49 + 5920 * q^51 - 49456 * q^53 - 44984 * q^59 + 48080 * q^61 - 158760 * q^63 - 61160 * q^67 - 22320 * q^69 - 14896 * q^77 - 177680 * q^79 - 524880 * q^81 + 329240 * q^83 + 132400 * q^85 - 364832 * q^91 - 362352 * q^93 - 288800 * q^95 - 659000 * q^99

Introduction

L-functions

Modular forms

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Database

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