LMFDB - Embedded newform 160.6.n.d.63.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,6,Mod(63,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("160.63");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	160.n (of order $4$, degree $2$, 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:	$25.6614111701$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 1375 x^{14} + 743087 x^{12} + 198706725 x^{10} + 26872635188 x^{8} + 1612811892960 x^{6} + \cdots + 177426662425600 $ x^16 + 1375x^14 + 743087x^12 + 198706725x^10 + 26872635188x^8 + 1612811892960x^6 + 24971013117824x^4 + 124211190826240*x^2 + 177426662425600
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{41}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			63.7
Root			$15.6412i$ of defining polynomial
Character	$\chi$	$=$	160.63
Dual form			160.6.n.d.127.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(16.6412 - 16.6412i) q^{3} +(53.0700 + 17.5663i) q^{5} +(76.6521 + 76.6521i) q^{7} -310.861i q^{9} +O(q^{10})$	\(q+(16.6412 - 16.6412i) q^{3} +(53.0700 + 17.5663i) q^{5} +(76.6521 + 76.6521i) q^{7} -310.861i q^{9} -711.961i q^{11} +(467.264 + 467.264i) q^{13} +(1175.48 - 590.825i) q^{15} +(-836.650 + 836.650i) q^{17} +2320.28 q^{19} +2551.17 q^{21} +(-1734.68 + 1734.68i) q^{23} +(2507.85 + 1864.49i) q^{25} +(-1129.29 - 1129.29i) q^{27} -4876.54i q^{29} -3489.29i q^{31} +(-11847.9 - 11847.9i) q^{33} +(2721.43 + 5414.42i) q^{35} +(4903.89 - 4903.89i) q^{37} +15551.7 q^{39} -18926.0 q^{41} +(-737.882 + 737.882i) q^{43} +(5460.68 - 16497.4i) q^{45} +(9021.42 + 9021.42i) q^{47} -5055.91i q^{49} +27845.8i q^{51} +(-6487.29 - 6487.29i) q^{53} +(12506.5 - 37783.8i) q^{55} +(38612.3 - 38612.3i) q^{57} +7291.98 q^{59} -27205.5 q^{61} +(23828.2 - 23828.2i) q^{63} +(16589.6 + 33005.8i) q^{65} +(-23546.8 - 23546.8i) q^{67} +57734.3i q^{69} +1000.88i q^{71} +(7721.57 + 7721.57i) q^{73} +(72761.1 - 10706.4i) q^{75} +(54573.3 - 54573.3i) q^{77} +72708.3 q^{79} +37953.6 q^{81} +(-51919.4 + 51919.4i) q^{83} +(-59097.8 + 29704.2i) q^{85} +(-81151.6 - 81151.6i) q^{87} -61693.6i q^{89} +71633.5i q^{91} +(-58066.1 - 58066.1i) q^{93} +(123137. + 40758.8i) q^{95} +(-65468.6 + 65468.6i) q^{97} -221321. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 10 q^{3} - 42 q^{5} - 86 q^{7}+O(q^{10}) $ 16 * q + 10 * q^3 - 42 * q^5 - 86 * q^7	$ 16 q + 10 q^{3} - 42 q^{5} - 86 q^{7} + 536 q^{13} - 698 q^{15} - 1828 q^{17} + 2512 q^{19} - 4284 q^{21} - 7642 q^{23} + 9140 q^{25} - 12272 q^{27} + 11876 q^{33} + 10518 q^{35} - 7620 q^{37} + 11244 q^{39} - 21284 q^{41} + 20002 q^{43} + 686 q^{45} + 25298 q^{47} + 12852 q^{53} - 10584 q^{55} + 55848 q^{57} - 142704 q^{59} - 20564 q^{61} - 115282 q^{63} - 38256 q^{65} - 10506 q^{67} + 15432 q^{73} + 256226 q^{75} + 133852 q^{77} - 159344 q^{79} - 236116 q^{81} - 61222 q^{83} + 7056 q^{85} + 162176 q^{87} + 122180 q^{93} + 267512 q^{95} - 17344 q^{97} + 107332 q^{99}+O(q^{100}) $ 16 * q + 10 * q^3 - 42 * q^5 - 86 * q^7 + 536 * q^13 - 698 * q^15 - 1828 * q^17 + 2512 * q^19 - 4284 * q^21 - 7642 * q^23 + 9140 * q^25 - 12272 * q^27 + 11876 * q^33 + 10518 * q^35 - 7620 * q^37 + 11244 * q^39 - 21284 * q^41 + 20002 * q^43 + 686 * q^45 + 25298 * q^47 + 12852 * q^53 - 10584 * q^55 + 55848 * q^57 - 142704 * q^59 - 20564 * q^61 - 115282 * q^63 - 38256 * q^65 - 10506 * q^67 + 15432 * q^73 + 256226 * q^75 + 133852 * q^77 - 159344 * q^79 - 236116 * q^81 - 61222 * q^83 + 7056 * q^85 + 162176 * q^87 + 122180 * q^93 + 267512 * q^95 - 17344 * q^97 + 107332 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	16.6412	−	16.6412i	1.06754	−	1.06754i	0.0699876	−	0.997548i	$-0.477704\pi$
$3$	16.6412	−	16.6412i	1.06754	−	1.06754i	0.997548	−	0.0699876i	$-0.0222960\pi$
$4$		0			0
$5$	53.0700	+	17.5663i	0.949345	+	0.314236i
$5$	53.0700	+	17.5663i	0.949345	+	0.314236i
$6$		0			0
$7$	76.6521	+	76.6521i	0.591261	+	0.591261i	0.937972	−	0.346711i	$-0.112702\pi$
$7$	76.6521	+	76.6521i	0.591261	+	0.591261i	−0.346711	+	0.937972i	$0.612702\pi$
$8$		0			0
$9$		−	310.861i		−	1.27926i
$10$		0			0
$11$		−	711.961i		−	1.77408i	−0.461688	−	0.887042i	$-0.652756\pi$
$11$		−	711.961i		−	1.77408i	0.461688	−	0.887042i	$-0.347244\pi$
$12$		0			0
$13$	467.264	+	467.264i	0.766838	+	0.766838i	0.977549	−	0.210710i	$-0.0675777\pi$
$13$	467.264	+	467.264i	0.766838	+	0.766838i	−0.210710	+	0.977549i	$0.567578\pi$
$14$		0			0
$15$	1175.48	−	590.825i	1.34892	−	0.678002i
$16$		0			0
$17$	−836.650	+	836.650i	−0.702136	+	0.702136i	−0.964869	−	0.262732i	$-0.915376\pi$
$17$	−836.650	+	836.650i	−0.702136	+	0.702136i	0.262732	+	0.964869i	$0.415376\pi$
$18$		0			0
$19$	2320.28			1.47454			0.737270	−	0.675598i	$-0.236115\pi$
$19$	2320.28			1.47454			0.737270	+	0.675598i	$0.236115\pi$
$20$		0			0
$21$	2551.17			1.26238
$22$		0			0
$23$	−1734.68	+	1734.68i	−0.683753	+	0.683753i	−0.960844	−	0.277091i	$-0.910630\pi$
$23$	−1734.68	+	1734.68i	−0.683753	+	0.683753i	0.277091	+	0.960844i	$0.410630\pi$
$24$		0			0
$25$	2507.85	+	1864.49i	0.802512	+	0.596636i
$26$		0			0
$27$	−1129.29	−	1129.29i	−0.298124	−	0.298124i
$28$		0			0
$29$		−	4876.54i		−	1.07675i	−0.842704	−	0.538377i	$-0.819038\pi$
$29$		−	4876.54i		−	1.07675i	0.842704	−	0.538377i	$-0.180962\pi$
$30$		0			0
$31$		−	3489.29i		−	0.652128i	−0.945348	−	0.326064i	$-0.894277\pi$
$31$		−	3489.29i		−	0.652128i	0.945348	−	0.326064i	$-0.105723\pi$
$32$		0			0
$33$	−11847.9	−	11847.9i	−1.89390	−	1.89390i
$34$		0			0
$35$	2721.43	+	5414.42i	0.375515	+	0.747105i
$36$		0			0
$37$	4903.89	−	4903.89i	0.588893	−	0.588893i	−0.348439	−	0.937332i	$-0.613288\pi$
$37$	4903.89	−	4903.89i	0.588893	−	0.588893i	0.937332	+	0.348439i	$0.113288\pi$
$38$		0			0
$39$	15551.7			1.63725
$40$		0			0
$41$	−18926.0			−1.75833			−0.879163	−	0.476521i	$-0.841898\pi$
$41$	−18926.0			−1.75833			−0.879163	+	0.476521i	$0.841898\pi$
$42$		0			0
$43$	−737.882	+	737.882i	−0.0608578	+	0.0608578i	−0.736881	−	0.676023i	$-0.763702\pi$
$43$	−737.882	+	737.882i	−0.0608578	+	0.0608578i	0.676023	+	0.736881i	$0.263702\pi$
$44$		0			0
$45$	5460.68	−	16497.4i	0.401990	−	1.21446i
$46$		0			0
$47$	9021.42	+	9021.42i	0.595704	+	0.595704i	0.939166	−	0.343462i	$-0.111600\pi$
$47$	9021.42	+	9021.42i	0.595704	+	0.595704i	−0.343462	+	0.939166i	$0.611600\pi$
$48$		0			0
$49$		−	5055.91i		−	0.300822i
$50$		0			0
$51$			27845.8i			1.49911i
$52$		0			0
$53$	−6487.29	−	6487.29i	−0.317230	−	0.317230i	0.530472	−	0.847702i	$-0.322015\pi$
$53$	−6487.29	−	6487.29i	−0.317230	−	0.317230i	−0.847702	+	0.530472i	$0.822015\pi$
$54$		0			0
$55$	12506.5	−	37783.8i	0.557481	−	1.68422i
$56$		0			0
$57$	38612.3	−	38612.3i	1.57412	−	1.57412i
$58$		0			0
$59$	7291.98			0.272719			0.136359	−	0.990659i	$-0.456460\pi$
$59$	7291.98			0.272719			0.136359	+	0.990659i	$0.456460\pi$
$60$		0			0
$61$	−27205.5			−0.936121			−0.468060	−	0.883697i	$-0.655047\pi$
$61$	−27205.5			−0.936121			−0.468060	+	0.883697i	$0.655047\pi$
$62$		0			0
$63$	23828.2	−	23828.2i	0.756378	−	0.756378i
$64$		0			0
$65$	16589.6	+	33005.8i	0.487026	+	0.968962i
$66$		0			0
$67$	−23546.8	−	23546.8i	−0.640833	−	0.640833i	0.309928	−	0.950760i	$-0.399695\pi$
$67$	−23546.8	−	23546.8i	−0.640833	−	0.640833i	−0.950760	+	0.309928i	$0.899695\pi$
$68$		0			0
$69$			57734.3i			1.45986i
$70$		0			0
$71$			1000.88i			0.0235633i	0.999931	+	0.0117816i	$0.00375030\pi$
$71$			1000.88i			0.0235633i	−0.999931	+	0.0117816i	$0.996250\pi$
$72$		0			0
$73$	7721.57	+	7721.57i	0.169589	+	0.169589i	0.786799	−	0.617209i	$-0.211737\pi$
$73$	7721.57	+	7721.57i	0.169589	+	0.169589i	−0.617209	+	0.786799i	$0.711737\pi$
$74$		0			0
$75$	72761.1	−	10706.4i	1.49364	−	0.219780i
$76$		0			0
$77$	54573.3	−	54573.3i	1.04895	−	1.04895i
$78$		0			0
$79$	72708.3			1.31074			0.655370	−	0.755308i	$-0.272513\pi$
$79$	72708.3			1.31074			0.655370	+	0.755308i	$0.272513\pi$
$80$		0			0
$81$	37953.6			0.642748
$82$		0			0
$83$	−51919.4	+	51919.4i	−0.827246	+	0.827246i	−0.987135	−	0.159889i	$-0.948886\pi$
$83$	−51919.4	+	51919.4i	−0.827246	+	0.827246i	0.159889	+	0.987135i	$0.448886\pi$
$84$		0			0
$85$	−59097.8	+	29704.2i	−0.887206	+	0.445933i
$86$		0			0
$87$	−81151.6	−	81151.6i	−1.14947	−	1.14947i
$88$		0			0
$89$		−	61693.6i		−	0.825591i	−0.910824	−	0.412796i	$-0.864552\pi$
$89$		−	61693.6i		−	0.825591i	0.910824	−	0.412796i	$-0.135448\pi$
$90$		0			0
$91$			71633.5i			0.906802i
$92$		0			0
$93$	−58066.1	−	58066.1i	−0.696170	−	0.696170i
$94$		0			0
$95$	123137.	+	40758.8i	1.39985	+	0.463353i
$96$		0			0
$97$	−65468.6	+	65468.6i	−0.706486	+	0.706486i	−0.965794	−	0.259309i	$-0.916505\pi$
$97$	−65468.6	+	65468.6i	−0.706486	+	0.706486i	0.259309	+	0.965794i	$0.416505\pi$
$98$		0			0
$99$	−221321.			−2.26952
$100$		0			0
$101$	−138726.			−1.35318			−0.676590	−	0.736360i	$-0.736543\pi$
$101$	−138726.			−1.35318			−0.676590	+	0.736360i	$0.736543\pi$
$102$		0			0
$103$	−81295.3	+	81295.3i	−0.755044	+	0.755044i	−0.975416	−	0.220372i	$-0.929273\pi$
$103$	−81295.3	+	81295.3i	−0.755044	+	0.755044i	0.220372	+	0.975416i	$0.429273\pi$
$104$		0			0
$105$	135391.	+	44814.6i	1.19844	+	0.396686i
$106$		0			0
$107$	−6315.87	−	6315.87i	−0.0533302	−	0.0533302i	0.679939	−	0.733269i	$-0.262006\pi$
$107$	−6315.87	−	6315.87i	−0.0533302	−	0.0533302i	−0.733269	+	0.679939i	$0.762006\pi$
$108$		0			0
$109$			166944.i			1.34588i	0.739699	+	0.672938i	$0.234968\pi$
$109$			166944.i			1.34588i	−0.739699	+	0.672938i	$0.765032\pi$
$110$		0			0
$111$		−	163214.i		−	1.25733i
$112$		0			0
$113$	67328.6	+	67328.6i	0.496025	+	0.496025i	0.910198	−	0.414173i	$-0.135929\pi$
$113$	67328.6	+	67328.6i	0.496025	+	0.496025i	−0.414173	+	0.910198i	$0.635929\pi$
$114$		0			0
$115$	−122531.	+	61587.5i	−0.863977	+	0.434258i
$116$		0			0
$117$	145254.	−	145254.i	0.980988	−	0.980988i
$118$		0			0
$119$	−128262.			−0.830291
$120$		0			0
$121$	−345837.			−2.14738
$122$		0			0
$123$	−314952.	+	314952.i	−1.87708	+	1.87708i
$124$		0			0
$125$	100339.	+	143002.i	0.574377	+	0.818591i
$126$		0			0
$127$	−28653.2	−	28653.2i	−0.157639	−	0.157639i	0.623881	−	0.781520i	$-0.285555\pi$
$127$	−28653.2	−	28653.2i	−0.157639	−	0.157639i	−0.781520	+	0.623881i	$0.785555\pi$
$128$		0			0
$129$			24558.5i			0.129936i
$130$		0			0
$131$			69183.5i			0.352228i	0.984370	+	0.176114i	$0.0563528\pi$
$131$			69183.5i			0.352228i	−0.984370	+	0.176114i	$0.943647\pi$
$132$		0			0
$133$	177854.	+	177854.i	0.871837	+	0.871837i
$134$		0			0
$135$	−40094.1	−	79769.1i	−0.189341	−	0.376704i
$136$		0			0
$137$	−214967.	+	214967.i	−0.978522	+	0.978522i	−0.999774	−	0.0212523i	$-0.993235\pi$
$137$	−214967.	+	214967.i	−0.978522	+	0.978522i	0.0212523	+	0.999774i	$0.493235\pi$
$138$		0			0
$139$	373349.			1.63900			0.819498	−	0.573083i	$-0.194253\pi$
$139$	373349.			1.63900			0.819498	+	0.573083i	$0.194253\pi$
$140$		0			0
$141$	300255.			1.27187
$142$		0			0
$143$	332673.	−	332673.i	1.36044	−	1.36044i
$144$		0			0
$145$	85662.7	−	258798.i	0.338354	−	1.02221i
$146$		0			0
$147$	−84136.6	−	84136.6i	−0.321138	−	0.321138i
$148$		0			0
$149$			528106.i			1.94875i	0.224936	+	0.974374i	$0.427783\pi$
$149$			528106.i			1.94875i	−0.224936	+	0.974374i	$0.572217\pi$
$150$		0			0
$151$		−	181007.i		−	0.646032i	−0.946394	−	0.323016i	$-0.895303\pi$
$151$		−	181007.i		−	0.646032i	0.946394	−	0.323016i	$-0.104697\pi$
$152$		0			0
$153$	260082.	+	260082.i	0.898218	+	0.898218i
$154$		0			0
$155$	61293.9	−	185177.i	0.204922	−	0.619095i
$156$		0			0
$157$	114655.	−	114655.i	0.371232	−	0.371232i	−0.496694	−	0.867926i	$-0.665453\pi$
$157$	114655.	−	114655.i	0.371232	−	0.371232i	0.867926	+	0.496694i	$0.165453\pi$
$158$		0			0
$159$	−215913.			−0.677308
$160$		0			0
$161$	−265933.			−0.808552
$162$		0			0
$163$	20298.8	−	20298.8i	0.0598414	−	0.0598414i	−0.676553	−	0.736394i	$-0.736527\pi$
$163$	20298.8	−	20298.8i	0.0598414	−	0.0598414i	0.736394	+	0.676553i	$0.236527\pi$
$164$		0			0
$165$	−420644.	−	836892.i	−1.20283	−	2.39309i
$166$		0			0
$167$	436568.	+	436568.i	1.21133	+	1.21133i	0.970591	+	0.240735i	$0.0773885\pi$
$167$	436568.	+	436568.i	1.21133	+	1.21133i	0.240735	+	0.970591i	$0.422611\pi$
$168$		0			0
$169$			65377.7i			0.176081i
$170$		0			0
$171$		−	721285.i		−	1.88633i
$172$		0			0
$173$	−244030.	−	244030.i	−0.619909	−	0.619909i	0.325599	−	0.945508i	$-0.394434\pi$
$173$	−244030.	−	244030.i	−0.619909	−	0.619909i	−0.945508	+	0.325599i	$0.894434\pi$
$174$		0			0
$175$	49315.1	+	335149.i	0.121726	+	0.827261i
$176$		0			0
$177$	121347.	−	121347.i	0.291137	−	0.291137i
$178$		0			0
$179$	−675955.			−1.57683			−0.788416	−	0.615142i	$-0.789099\pi$
$179$	−675955.			−1.57683			−0.788416	+	0.615142i	$0.789099\pi$
$180$		0			0
$181$	582873.			1.32245			0.661223	−	0.750190i	$-0.270038\pi$
$181$	582873.			1.32245			0.661223	+	0.750190i	$0.270038\pi$
$182$		0			0
$183$	−452733.	+	452733.i	−0.999342	+	0.999342i
$184$		0			0
$185$	346393.	−	174106.i	0.744114	−	0.374012i
$186$		0			0
$187$	595662.	+	595662.i	1.24565	+	1.24565i
$188$		0			0
$189$		−	173125.i		−	0.352538i
$190$		0			0
$191$		−	35415.3i		−	0.0702437i	−0.999383	−	0.0351219i	$-0.988818\pi$
$191$		−	35415.3i		−	0.0702437i	0.999383	−	0.0351219i	$-0.0111819\pi$
$192$		0			0
$193$	228876.	+	228876.i	0.442291	+	0.442291i	0.892781	−	0.450491i	$-0.148751\pi$
$193$	228876.	+	228876.i	0.442291	+	0.442291i	−0.450491	+	0.892781i	$0.648751\pi$
$194$		0			0
$195$	825328.	+	273186.i	1.55432	+	0.514483i
$196$		0			0
$197$	−603414.	+	603414.i	−1.10777	+	1.10777i	−0.114328	+	0.993443i	$0.536471\pi$
$197$	−603414.	+	603414.i	−1.10777	+	1.10777i	−0.993443	+	0.114328i	$0.963529\pi$
$198$		0			0
$199$	−600185.			−1.07437			−0.537183	−	0.843466i	$-0.680512\pi$
$199$	−600185.			−1.07437			−0.537183	+	0.843466i	$0.680512\pi$
$200$		0			0
$201$	−783695.			−1.36822
$202$		0			0
$203$	373797.	−	373797.i	0.636642	−	0.636642i
$204$		0			0
$205$	−1.00440e6	−	332460.i	−1.66926	−	0.552529i
$206$		0			0
$207$	539244.	+	539244.i	0.874700	+	0.874700i
$208$		0			0
$209$		−	1.65195e6i		−	2.61596i
$210$		0			0
$211$		−	410548.i		−	0.634831i	−0.948287	−	0.317415i	$-0.897185\pi$
$211$		−	410548.i		−	0.634831i	0.948287	−	0.317415i	$-0.102815\pi$
$212$		0			0
$213$	16655.8	+	16655.8i	0.0251546	+	0.0251546i
$214$		0			0
$215$	−52121.3	+	26197.6i	−0.0768987	+	0.0386513i
$216$		0			0
$217$	267462.	−	267462.i	0.385578	−	0.385578i
$218$		0			0
$219$	256993.			0.362085
$220$		0			0
$221$	−781872.			−1.07685
$222$		0			0
$223$	−109519.	+	109519.i	−0.147478	+	0.147478i	−0.776991	−	0.629512i	$-0.783255\pi$
$223$	−109519.	+	109519.i	−0.147478	+	0.147478i	0.629512	+	0.776991i	$0.283255\pi$
$224$		0			0
$225$	579597.	−	779593.i	0.763255	−	1.02662i
$226$		0			0
$227$	−120.761	−	120.761i	−0.000155547	−	0.000155547i	0.707029	−	0.707185i	$-0.250035\pi$
$227$	−120.761	−	120.761i	−0.000155547	−	0.000155547i	−0.707185	+	0.707029i	$0.750035\pi$
$228$		0			0
$229$		−	274947.i		−	0.346466i	−0.984881	−	0.173233i	$-0.944579\pi$
$229$		−	274947.i		−	0.346466i	0.984881	−	0.173233i	$-0.0554213\pi$
$230$		0			0
$231$		−	1.81633e6i		−	2.23958i
$232$		0			0
$233$	271323.	+	271323.i	0.327414	+	0.327414i	0.851602	−	0.524189i	$-0.175631\pi$
$233$	271323.	+	271323.i	0.327414	+	0.327414i	−0.524189	+	0.851602i	$0.675631\pi$
$234$		0			0
$235$	320294.	+	637240.i	0.378337	+	0.752720i
$236$		0			0
$237$	1.20996e6	−	1.20996e6i	1.39926	−	1.39926i
$238$		0			0
$239$	286352.			0.324269			0.162135	−	0.986769i	$-0.448162\pi$
$239$	286352.			0.324269			0.162135	+	0.986769i	$0.448162\pi$
$240$		0			0
$241$	836510.			0.927745			0.463872	−	0.885902i	$-0.346460\pi$
$241$	836510.			0.927745			0.463872	+	0.885902i	$0.346460\pi$
$242$		0			0
$243$	906013.	−	906013.i	0.984280	−	0.984280i
$244$		0			0
$245$	88813.7	−	268317.i	0.0945289	−	0.285584i
$246$		0			0
$247$	1.08418e6	+	1.08418e6i	1.13073	+	1.13073i
$248$		0			0
$249$			1.72801e6i			1.76623i
$250$		0			0
$251$		−	1.24436e6i		−	1.24670i	−0.781943	−	0.623350i	$-0.785771\pi$
$251$		−	1.24436e6i		−	1.24670i	0.781943	−	0.623350i	$-0.214229\pi$
$252$		0			0
$253$	1.23502e6	+	1.23502e6i	1.21304	+	1.21304i
$254$		0			0
$255$	−489147.	+	1.47777e6i	−0.471074	+	1.42317i
$256$		0			0
$257$	−600458.	+	600458.i	−0.567087	+	0.567087i	−0.931311	−	0.364224i	$-0.881334\pi$
$257$	−600458.	+	600458.i	−0.567087	+	0.567087i	0.364224	+	0.931311i	$0.381334\pi$
$258$		0			0
$259$	751787.			0.696378
$260$		0			0
$261$	−1.51593e6			−1.37745
$262$		0			0
$263$	−256770.	+	256770.i	−0.228904	+	0.228904i	−0.812235	−	0.583330i	$-0.801749\pi$
$263$	−256770.	+	256770.i	−0.228904	+	0.228904i	0.583330	+	0.812235i	$0.301749\pi$
$264$		0			0
$265$	−230323.	−	458238.i	−0.201476	−	0.400845i
$266$		0			0
$267$	−1.02666e6	−	1.02666e6i	−0.881348	−	0.881348i
$268$		0			0
$269$			1.30320e6i			1.09807i	0.835799	+	0.549035i	$0.185005\pi$
$269$			1.30320e6i			1.09807i	−0.835799	+	0.549035i	$0.814995\pi$
$270$		0			0
$271$		−	91415.8i		−	0.0756133i	−0.999285	−	0.0378066i	$-0.987963\pi$
$271$		−	91415.8i		−	0.0756133i	0.999285	−	0.0378066i	$-0.0120371\pi$
$272$		0			0
$273$	1.19207e6	+	1.19207e6i	0.968044	+	0.968044i
$274$		0			0
$275$	1.32744e6	−	1.78549e6i	1.05848	−	1.42372i
$276$		0			0
$277$	−254664.	+	254664.i	−0.199420	+	0.199420i	−0.799751	−	0.600331i	$-0.795035\pi$
$277$	−254664.	+	254664.i	−0.199420	+	0.199420i	0.600331	+	0.799751i	$0.295035\pi$
$278$		0			0
$279$	−1.08469e6			−0.834244
$280$		0			0
$281$	−2.07524e6			−1.56784			−0.783920	−	0.620862i	$-0.786783\pi$
$281$	−2.07524e6			−1.56784			−0.783920	+	0.620862i	$0.786783\pi$
$282$		0			0
$283$	−1.34648e6	+	1.34648e6i	−0.999387	+	0.999387i	−1.00000		0.000612960i	$-0.999805\pi$
$283$	−1.34648e6	+	1.34648e6i	−0.999387	+	0.999387i	0.000612960		1.00000i	$0.499805\pi$
$284$		0			0
$285$	2.72743e6	−	1.37088e6i	1.98903	−	0.999741i
$286$		0			0
$287$	−1.45072e6	−	1.45072e6i	−1.03963	−	1.03963i
$288$		0			0
$289$			19891.3i			0.0140094i
$290$		0			0
$291$			2.17895e6i			1.50840i
$292$		0			0
$293$	299974.	+	299974.i	0.204134	+	0.204134i	0.801768	−	0.597635i	$-0.203893\pi$
$293$	299974.	+	299974.i	0.204134	+	0.204134i	−0.597635	+	0.801768i	$0.703893\pi$
$294$		0			0
$295$	386985.	+	128093.i	0.258904	+	0.0856980i
$296$		0			0
$297$	−804012.	+	804012.i	−0.528897	+	0.528897i
$298$		0			0
$299$	−1.62110e6			−1.04866
$300$		0			0
$301$	−113120.			−0.0719656
$302$		0			0
$303$	−2.30858e6	+	2.30858e6i	−1.44457	+	1.44457i
$304$		0			0
$305$	−1.44379e6	−	477900.i	−0.888701	−	0.294162i
$306$		0			0
$307$	−570825.	−	570825.i	−0.345667	−	0.345667i	0.512826	−	0.858493i	$-0.328599\pi$
$307$	−570825.	−	570825.i	−0.345667	−	0.345667i	−0.858493	+	0.512826i	$0.828599\pi$
$308$		0			0
$309$			2.70571e6i			1.61207i
$310$		0			0
$311$			556022.i			0.325980i	0.986628	+	0.162990i	$0.0521138\pi$
$311$			556022.i			0.325980i	−0.986628	+	0.162990i	$0.947886\pi$
$312$		0			0
$313$	−1.54884e6	−	1.54884e6i	−0.893604	−	0.893604i	0.101256	−	0.994860i	$-0.467714\pi$
$313$	−1.54884e6	−	1.54884e6i	−0.893604	−	0.893604i	−0.994860	+	0.101256i	$0.967714\pi$
$314$		0			0
$315$	1.68313e6	−	845988.i	0.955745	−	0.480383i
$316$		0			0
$317$	1.89893e6	−	1.89893e6i	1.06135	−	1.06135i	0.0633644	−	0.997990i	$-0.479817\pi$
$317$	1.89893e6	−	1.89893e6i	1.06135	−	1.06135i	0.997990	−	0.0633644i	$-0.0201830\pi$
$318$		0			0
$319$	−3.47190e6			−1.91025
$320$		0			0
$321$	−210208.			−0.113864
$322$		0			0
$323$	−1.94126e6	+	1.94126e6i	−1.03533	+	1.03533i
$324$		0			0
$325$	300620.	+	2.04303e6i	0.157874	+	1.07292i
$326$		0			0
$327$	2.77816e6	+	2.77816e6i	1.43677	+	1.43677i
$328$		0			0
$329$			1.38302e6i			0.704433i
$330$		0			0
$331$		−	1.09843e6i		−	0.551066i	−0.961292	−	0.275533i	$-0.911146\pi$
$331$		−	1.09843e6i		−	0.551066i	0.961292	−	0.275533i	$-0.0888543\pi$
$332$		0			0
$333$	−1.52443e6	−	1.52443e6i	−0.753350	−	0.753350i
$334$		0			0
$335$	−835998.	−	1.66326e6i	−0.406999	−	0.809744i
$336$		0			0
$337$	2.19408e6	−	2.19408e6i	1.05239	−	1.05239i	0.0538452	−	0.998549i	$-0.482852\pi$
$337$	2.19408e6	−	2.19408e6i	1.05239	−	1.05239i	0.998549	−	0.0538452i	$-0.0171478\pi$
$338$		0			0
$339$	2.24086e6			1.05905
$340$		0			0
$341$	−2.48424e6			−1.15693
$342$		0			0
$343$	1.67584e6	−	1.67584e6i	0.769125	−	0.769125i
$344$		0			0
$345$	−1.01418e6	+	3.06396e6i	−0.458740	+	1.38591i
$346$		0			0
$347$	−1.85528e6	−	1.85528e6i	−0.827151	−	0.827151i	0.159971	−	0.987122i	$-0.448860\pi$
$347$	−1.85528e6	−	1.85528e6i	−0.827151	−	0.827151i	−0.987122	+	0.159971i	$0.948860\pi$
$348$		0			0
$349$		−	1.39518e6i		−	0.613152i	−0.951846	−	0.306576i	$-0.900817\pi$
$349$		−	1.39518e6i		−	0.613152i	0.951846	−	0.306576i	$-0.0991833\pi$
$350$		0			0
$351$		−	1.05535e6i		−	0.457226i
$352$		0			0
$353$	−941786.	−	941786.i	−0.402268	−	0.402268i	0.476764	−	0.879032i	$-0.341810\pi$
$353$	−941786.	−	941786.i	−0.402268	−	0.402268i	−0.879032	+	0.476764i	$0.841810\pi$
$354$		0			0
$355$	−17581.7	+	53116.6i	−0.00740441	+	0.0223697i
$356$		0			0
$357$	−2.13444e6	+	2.13444e6i	−0.886365	+	0.886365i
$358$		0			0
$359$	−914355.			−0.374437			−0.187218	−	0.982318i	$-0.559947\pi$
$359$	−914355.			−0.374437			−0.187218	+	0.982318i	$0.559947\pi$
$360$		0			0
$361$	2.90760e6			1.17427
$362$		0			0
$363$	−5.75516e6	+	5.75516e6i	−2.29240	+	2.29240i
$364$		0			0
$365$	274144.	+	545423.i	0.107708	+	0.214290i
$366$		0			0
$367$	−856168.	−	856168.i	−0.331814	−	0.331814i	0.521461	−	0.853275i	$-0.325387\pi$
$367$	−856168.	−	856168.i	−0.331814	−	0.331814i	−0.853275	+	0.521461i	$0.825387\pi$
$368$		0			0
$369$			5.88336e6i			2.24936i
$370$		0			0
$371$		−	994529.i		−	0.375131i
$372$		0			0
$373$	2.56774e6	+	2.56774e6i	0.955607	+	0.955607i	0.999056	−	0.0434490i	$-0.0138346\pi$
$373$	2.56774e6	+	2.56774e6i	0.955607	+	0.955607i	−0.0434490	+	0.999056i	$0.513835\pi$
$374$		0			0
$375$	4.04950e6	+	709957.i	1.48704	+	0.260708i
$376$		0			0
$377$	2.27863e6	−	2.27863e6i	0.825696	−	0.825696i
$378$		0			0
$379$	−1.53848e6			−0.550167			−0.275083	−	0.961420i	$-0.588705\pi$
$379$	−1.53848e6			−0.550167			−0.275083	+	0.961420i	$0.588705\pi$
$380$		0			0
$381$	−953650.			−0.336571
$382$		0			0
$383$	3.94723e6	−	3.94723e6i	1.37498	−	1.37498i	0.522080	−	0.852897i	$-0.325156\pi$
$383$	3.94723e6	−	3.94723e6i	1.37498	−	1.37498i	0.852897	−	0.522080i	$-0.174844\pi$
$384$		0			0
$385$	3.85486e6	−	1.93755e6i	1.32543	−	0.666196i
$386$		0			0
$387$	229379.	+	229379.i	0.0778531	+	0.0778531i
$388$		0			0
$389$		−	1.61781e6i		−	0.542068i	−0.962570	−	0.271034i	$-0.912634\pi$
$389$		−	1.61781e6i		−	0.542068i	0.962570	−	0.271034i	$-0.0873656\pi$
$390$		0			0
$391$		−	2.90263e6i		−	0.960175i
$392$		0			0
$393$	1.15130e6	+	1.15130e6i	0.376016	+	0.376016i
$394$		0			0
$395$	3.85863e6	+	1.27722e6i	1.24434	+	0.411881i
$396$		0			0
$397$	−245425.	+	245425.i	−0.0781524	+	0.0781524i	−0.745102	−	0.666950i	$-0.767599\pi$
$397$	−245425.	+	245425.i	−0.0781524	+	0.0781524i	0.666950	+	0.745102i	$0.267599\pi$
$398$		0			0
$399$	5.91943e6			1.86143
$400$		0			0
$401$	−1.40652e6			−0.436802			−0.218401	−	0.975859i	$-0.570084\pi$
$401$	−1.40652e6			−0.436802			−0.218401	+	0.975859i	$0.570084\pi$
$402$		0			0
$403$	1.63042e6	−	1.63042e6i	0.500077	−	0.500077i
$404$		0			0
$405$	2.01420e6	+	666705.i	0.610189	+	0.201974i
$406$		0			0
$407$	−3.49138e6	−	3.49138e6i	−1.04475	−	1.04475i
$408$		0			0
$409$			1.53093e6i			0.452528i	0.974066	+	0.226264i	$0.0726513\pi$
$409$			1.53093e6i			0.452528i	−0.974066	+	0.226264i	$0.927349\pi$
$410$		0			0
$411$			7.15463e6i			2.08921i
$412$		0			0
$413$	558945.	+	558945.i	0.161248	+	0.161248i
$414$		0			0
$415$	−3.66740e6	+	1.84333e6i	−1.04529	+	0.525392i
$416$		0			0
$417$	6.21298e6	−	6.21298e6i	1.74969	−	1.74969i
$418$		0			0
$419$	3.16210e6			0.879915			0.439958	−	0.898019i	$-0.354993\pi$
$419$	3.16210e6			0.879915			0.439958	+	0.898019i	$0.354993\pi$
$420$		0			0
$421$	−5.21415e6			−1.43377			−0.716883	−	0.697194i	$-0.754432\pi$
$421$	−5.21415e6			−1.43377			−0.716883	+	0.697194i	$0.754432\pi$
$422$		0			0
$423$	2.80441e6	−	2.80441e6i	0.762063	−	0.762063i
$424$		0			0
$425$	−3.65812e6	+	538269.i	−0.982392	+	0.144553i
$426$		0			0
$427$	−2.08536e6	−	2.08536e6i	−0.553491	−	0.553491i
$428$		0			0
$429$		−	1.10722e7i		−	2.90463i
$430$		0			0
$431$		−	3.75600e6i		−	0.973940i	−0.873419	−	0.486970i	$-0.838102\pi$
$431$		−	3.75600e6i		−	0.973940i	0.873419	−	0.486970i	$-0.161898\pi$
$432$		0			0
$433$	−2.97050e6	−	2.97050e6i	−0.761396	−	0.761396i	0.215179	−	0.976575i	$-0.430967\pi$
$433$	−2.97050e6	−	2.97050e6i	−0.761396	−	0.761396i	−0.976575	+	0.215179i	$0.930967\pi$
$434$		0			0
$435$	−2.88118e6	−	5.73225e6i	−0.730041	−	1.45245i
$436$		0			0
$437$	−4.02494e6	+	4.02494e6i	−1.00822	+	1.00822i
$438$		0			0
$439$	−802291.			−0.198687			−0.0993437	−	0.995053i	$-0.531674\pi$
$439$	−802291.			−0.198687			−0.0993437	+	0.995053i	$0.531674\pi$
$440$		0			0
$441$	−1.57169e6			−0.384831
$442$		0			0
$443$	2.89117e6	−	2.89117e6i	0.699946	−	0.699946i	−0.264453	−	0.964399i	$-0.585191\pi$
$443$	2.89117e6	−	2.89117e6i	0.699946	−	0.699946i	0.964399	+	0.264453i	$0.0851913\pi$
$444$		0			0
$445$	1.08373e6	−	3.27408e6i	0.259430	−	0.783771i
$446$		0			0
$447$	8.78833e6	+	8.78833e6i	2.08036	+	2.08036i
$448$		0			0
$449$		−	5.59736e6i		−	1.31029i	−0.755503	−	0.655146i	$-0.772607\pi$
$449$		−	5.59736e6i		−	1.31029i	0.755503	−	0.655146i	$-0.227393\pi$
$450$		0			0
$451$			1.34746e7i			3.11942i
$452$		0			0
$453$	−3.01219e6	−	3.01219e6i	−0.689662	−	0.689662i
$454$		0			0
$455$	−1.25834e6	+	3.80159e6i	−0.284949	+	0.860868i
$456$		0			0
$457$	−4.35384e6	+	4.35384e6i	−0.975174	+	0.975174i	−0.999699	−	0.0245252i	$-0.992193\pi$
$457$	−4.35384e6	+	4.35384e6i	−0.975174	+	0.975174i	0.0245252	+	0.999699i	$0.492193\pi$
$458$		0			0
$459$	1.88964e6			0.418647
$460$		0			0
$461$	3.11913e6			0.683567			0.341783	−	0.939779i	$-0.388969\pi$
$461$	3.11913e6			0.683567			0.341783	+	0.939779i	$0.388969\pi$
$462$		0			0
$463$	1.35302e6	−	1.35302e6i	0.293327	−	0.293327i	−0.545066	−	0.838393i	$-0.683495\pi$
$463$	1.35302e6	−	1.35302e6i	0.293327	−	0.293327i	0.838393	+	0.545066i	$0.183495\pi$
$464$		0			0
$465$	−2.06156e6	−	4.10157e6i	−0.442144	−	0.879667i
$466$		0			0
$467$	−5.34775e6	−	5.34775e6i	−1.13470	−	1.13470i	−0.989386	−	0.145309i	$-0.953582\pi$
$467$	−5.34775e6	−	5.34775e6i	−1.13470	−	1.13470i	−0.145309	−	0.989386i	$-0.546418\pi$
$468$		0			0
$469$		−	3.60982e6i		−	0.757798i
$470$		0			0
$471$		−	3.81601e6i		−	0.792607i
$472$		0			0
$473$	525343.	+	525343.i	0.107967	+	0.107967i
$474$		0			0
$475$	5.81892e6	+	4.32613e6i	1.18334	+	0.879764i
$476$		0			0
$477$	−2.01665e6	+	2.01665e6i	−0.405820	+	0.405820i
$478$		0			0
$479$	5.60363e6			1.11591			0.557957	−	0.829870i	$-0.311585\pi$
$479$	5.60363e6			1.11591			0.557957	+	0.829870i	$0.311585\pi$
$480$		0			0
$481$	4.58282e6			0.903171
$482$		0			0
$483$	−4.42546e6	+	4.42546e6i	−0.863158	+	0.863158i
$484$		0			0
$485$	−4.62446e6	+	2.32438e6i	−0.892702	+	0.448696i
$486$		0			0
$487$	4.44597e6	+	4.44597e6i	0.849463	+	0.849463i	0.990066	−	0.140603i	$-0.0449042\pi$
$487$	4.44597e6	+	4.44597e6i	0.849463	+	0.849463i	−0.140603	+	0.990066i	$0.544904\pi$
$488$		0			0
$489$		−	675595.i		−	0.127766i
$490$		0			0
$491$		−	7.72866e6i		−	1.44677i	−0.690443	−	0.723387i	$-0.742584\pi$
$491$		−	7.72866e6i		−	1.44677i	0.690443	−	0.723387i	$-0.257416\pi$
$492$		0			0
$493$	4.07995e6	+	4.07995e6i	0.756028	+	0.756028i
$494$		0			0
$495$	−1.17455e7	−	3.88779e6i	−2.15456	−	0.713165i
$496$		0			0
$497$	−76719.4	+	76719.4i	−0.0139320	+	0.0139320i
$498$		0			0
$499$	−2.00470e6			−0.360410			−0.180205	−	0.983629i	$-0.557676\pi$
$499$	−2.00470e6			−0.360410			−0.180205	+	0.983629i	$0.557676\pi$
$500$		0			0
$501$	1.45301e7			2.58627
$502$		0			0
$503$	−757927.	+	757927.i	−0.133569	+	0.133569i	−0.770731	−	0.637161i	$-0.780109\pi$
$503$	−757927.	+	757927.i	−0.133569	+	0.133569i	0.637161	+	0.770731i	$0.280109\pi$
$504$		0			0
$505$	−7.36220e6	−	2.43691e6i	−1.28463	−	0.425217i
$506$		0			0
$507$	1.08797e6	+	1.08797e6i	0.187973	+	0.187973i
$508$		0			0
$509$			3.95906e6i			0.677326i	0.940908	+	0.338663i	$0.109975\pi$
$509$			3.95906e6i			0.677326i	−0.940908	+	0.338663i	$0.890025\pi$
$510$		0			0
$511$			1.18375e6i			0.200543i
$512$		0			0
$513$	−2.62028e6	−	2.62028e6i	−0.439596	−	0.439596i
$514$		0			0
$515$	−5.74240e6	+	2.88628e6i	−0.954059	+	0.479536i
$516$		0			0
$517$	6.42290e6	−	6.42290e6i	1.05683	−	1.05683i
$518$		0			0
$519$	−8.12192e6			−1.32355
$520$		0			0
$521$	−1.39986e6			−0.225938			−0.112969	−	0.993599i	$-0.536036\pi$
$521$	−1.39986e6			−0.225938			−0.112969	+	0.993599i	$0.536036\pi$
$522$		0			0
$523$	5.33392e6	−	5.33392e6i	0.852693	−	0.852693i	−0.137771	−	0.990464i	$-0.543994\pi$
$523$	5.33392e6	−	5.33392e6i	0.852693	−	0.852693i	0.990464	+	0.137771i	$0.0439939\pi$
$524$		0			0
$525$	6.39795e6	+	4.75662e6i	1.01308	+	0.753183i
$526$		0			0
$527$	2.91931e6	+	2.91931e6i	0.457883	+	0.457883i
$528$		0			0
$529$			418135.i			0.0649647i
$530$		0			0
$531$		−	2.26679e6i		−	0.348879i
$532$		0			0
$533$	−8.84344e6	−	8.84344e6i	−1.34835	−	1.34835i
$534$		0			0
$535$	−224237.	−	446130.i	−0.0338705	−	0.0673871i
$536$		0			0
$537$	−1.12487e7	+	1.12487e7i	−1.68332	+	1.68332i
$538$		0			0
$539$	−3.59961e6			−0.533683
$540$		0			0
$541$	7.01214e6			1.03005			0.515024	−	0.857176i	$-0.327783\pi$
$541$	7.01214e6			1.03005			0.515024	+	0.857176i	$0.327783\pi$
$542$		0			0
$543$	9.69973e6	−	9.69973e6i	1.41176	−	1.41176i
$544$		0			0
$545$	−2.93259e6	+	8.85972e6i	−0.422922	+	1.27770i
$546$		0			0
$547$	5.71824e6	+	5.71824e6i	0.817136	+	0.817136i	0.985692	−	0.168556i	$-0.0539104\pi$
$547$	5.71824e6	+	5.71824e6i	0.817136	+	0.817136i	−0.168556	+	0.985692i	$0.553910\pi$
$548$		0			0
$549$			8.45713e6i			1.19755i
$550$		0			0
$551$		−	1.13149e7i		−	1.58772i
$552$		0			0
$553$	5.57324e6	+	5.57324e6i	0.774988	+	0.774988i
$554$		0			0
$555$	2.86706e6	−	8.66174e6i	0.395097	−	1.19364i
$556$		0			0
$557$	−3.19122e6	+	3.19122e6i	−0.435832	+	0.435832i	−0.890606	−	0.454775i	$-0.849720\pi$
$557$	−3.19122e6	+	3.19122e6i	−0.435832	+	0.435832i	0.454775	+	0.890606i	$0.349720\pi$
$558$		0			0
$559$	−689571.			−0.0933361
$560$		0			0
$561$	1.98251e7			2.65955
$562$		0			0
$563$	3.41590e6	−	3.41590e6i	0.454186	−	0.454186i	−0.442555	−	0.896741i	$-0.645928\pi$
$563$	3.41590e6	−	3.41590e6i	0.454186	−	0.454186i	0.896741	+	0.442555i	$0.145928\pi$
$564$		0			0
$565$	2.39041e6	+	4.75584e6i	0.315030	+	0.626767i
$566$		0			0
$567$	2.90922e6	+	2.90922e6i	0.380031	+	0.380031i
$568$		0			0
$569$			453370.i			0.0587046i	0.999569	+	0.0293523i	$0.00934448\pi$
$569$			453370.i			0.0587046i	−0.999569	+	0.0293523i	$0.990656\pi$
$570$		0			0
$571$			6.91185e6i			0.887164i	0.896234	+	0.443582i	$0.146293\pi$
$571$			6.91185e6i			0.887164i	−0.896234	+	0.443582i	$0.853707\pi$
$572$		0			0
$573$	−589354.	−	589354.i	−0.0749877	−	0.0749877i
$574$		0			0
$575$	−7.58459e6	+	1.11603e6i	−0.956671	+	0.140768i
$576$		0			0
$577$	−4.87226e6	+	4.87226e6i	−0.609244	+	0.609244i	−0.942748	−	0.333505i	$-0.891769\pi$
$577$	−4.87226e6	+	4.87226e6i	−0.609244	+	0.609244i	0.333505	+	0.942748i	$0.391769\pi$
$578$		0			0
$579$	7.61757e6			0.944322
$580$		0			0
$581$	−7.95946e6			−0.978236
$582$		0			0
$583$	−4.61870e6	+	4.61870e6i	−0.562792	+	0.562792i
$584$		0			0
$585$	1.02602e7	−	5.15706e6i	1.23956	−	0.623035i
$586$		0			0
$587$	−3.96751e6	−	3.96751e6i	−0.475250	−	0.475250i	0.428359	−	0.903609i	$-0.359092\pi$
$587$	−3.96751e6	−	3.96751e6i	−0.475250	−	0.475250i	−0.903609	+	0.428359i	$0.859092\pi$
$588$		0			0
$589$		−	8.09614e6i		−	0.961589i
$590$		0			0
$591$			2.00831e7i			2.36517i
$592$		0			0
$593$	215888.	+	215888.i	0.0252111	+	0.0252111i	0.719600	−	0.694389i	$-0.244325\pi$
$593$	215888.	+	215888.i	0.0252111	+	0.0252111i	−0.694389	+	0.719600i	$0.744325\pi$
$594$		0			0
$595$	−6.80686e6	−	2.25309e6i	−0.788233	−	0.260907i
$596$		0			0
$597$	−9.98781e6	+	9.98781e6i	−1.14692	+	1.14692i
$598$		0			0
$599$	−1.09794e7			−1.25030			−0.625149	−	0.780506i	$-0.714962\pi$
$599$	−1.09794e7			−1.25030			−0.625149	+	0.780506i	$0.714962\pi$
$600$		0			0
$601$	6.90506e6			0.779796			0.389898	−	0.920858i	$-0.372510\pi$
$601$	6.90506e6			0.779796			0.389898	+	0.920858i	$0.372510\pi$
$602$		0			0
$603$	−7.31978e6	+	7.31978e6i	−0.819794	+	0.819794i
$604$		0			0
$605$	−1.83536e7	−	6.07508e6i	−2.03860	−	0.674782i
$606$		0			0
$607$	−7.70491e6	−	7.70491e6i	−0.848782	−	0.848782i	0.141199	−	0.989981i	$-0.454904\pi$
$607$	−7.70491e6	−	7.70491e6i	−0.848782	−	0.848782i	−0.989981	+	0.141199i	$0.954904\pi$
$608$		0			0
$609$		−	1.24409e7i		−	1.35928i
$610$		0			0
$611$			8.43077e6i			0.913617i
$612$		0			0
$613$	9.79354e6	+	9.79354e6i	1.05266	+	1.05266i	0.998534	+	0.0541272i	$0.0172377\pi$
$613$	9.79354e6	+	9.79354e6i	1.05266	+	1.05266i	0.0541272	+	0.998534i	$0.482762\pi$
$614$		0			0
$615$	−2.22471e7	+	1.11820e7i	−2.37184	+	1.19215i
$616$		0			0
$617$	−3.05140e6	+	3.05140e6i	−0.322690	+	0.322690i	−0.849798	−	0.527108i	$-0.823276\pi$
$617$	−3.05140e6	+	3.05140e6i	−0.322690	+	0.322690i	0.527108	+	0.849798i	$0.323276\pi$
$618$		0			0
$619$	9.70734e6			1.01829			0.509147	−	0.860679i	$-0.329961\pi$
$619$	9.70734e6			1.01829			0.509147	+	0.860679i	$0.329961\pi$
$620$		0			0
$621$	3.91792e6			0.407686
$622$		0			0
$623$	4.72894e6	−	4.72894e6i	0.488140	−	0.488140i
$624$		0			0
$625$	2.81300e6	+	9.35171e6i	0.288051	+	0.957615i
$626$		0			0
$627$	−2.74905e7	−	2.74905e7i	−2.79263	−	2.79263i
$628$		0			0
$629$			8.20568e6i			0.826966i
$630$		0			0
$631$			5.70040e6i			0.569944i	0.958536	+	0.284972i	$0.0919843\pi$
$631$			5.70040e6i			0.569944i	−0.958536	+	0.284972i	$0.908016\pi$
$632$		0			0
$633$	−6.83203e6	−	6.83203e6i	−0.677704	−	0.677704i
$634$		0			0
$635$	−1.01730e6	−	2.02396e6i	−0.100118	−	0.199190i
$636$		0			0
$637$	2.36244e6	−	2.36244e6i	0.230682	−	0.230682i
$638$		0			0
$639$	311134.			0.0301436
$640$		0			0
$641$	−1.38342e7			−1.32987			−0.664936	−	0.746901i	$-0.731541\pi$
$641$	−1.38342e7			−1.32987			−0.664936	+	0.746901i	$0.731541\pi$
$642$		0			0
$643$	2.12369e6	−	2.12369e6i	0.202565	−	0.202565i	−0.598533	−	0.801098i	$-0.704249\pi$
$643$	2.12369e6	−	2.12369e6i	0.202565	−	0.202565i	0.801098	+	0.598533i	$0.204249\pi$
$644$		0			0
$645$	−431403.	+	1.30332e6i	−0.0408304	+	0.123354i
$646$		0			0
$647$	8.72755e6	+	8.72755e6i	0.819656	+	0.819656i	0.986058	−	0.166402i	$-0.0532148\pi$
$647$	8.72755e6	+	8.72755e6i	0.819656	+	0.819656i	−0.166402	+	0.986058i	$0.553215\pi$
$648$		0			0
$649$		−	5.19160e6i		−	0.483826i
$650$		0			0
$651$		−	8.90178e6i		−	0.823236i
$652$		0			0
$653$	1.72641e6	+	1.72641e6i	0.158439	+	0.158439i	0.781874	−	0.623436i	$-0.214264\pi$
$653$	1.72641e6	+	1.72641e6i	0.158439	+	0.158439i	−0.623436	+	0.781874i	$0.714264\pi$
$654$		0			0
$655$	−1.21530e6	+	3.67157e6i	−0.110683	+	0.334386i
$656$		0			0
$657$	2.40034e6	−	2.40034e6i	0.216950	−	0.216950i
$658$		0			0
$659$	1.83652e7			1.64733			0.823666	−	0.567075i	$-0.191925\pi$
$659$	1.83652e7			1.64733			0.823666	+	0.567075i	$0.191925\pi$
$660$		0			0
$661$	−1.33765e7			−1.19080			−0.595399	−	0.803430i	$-0.703006\pi$
$661$	−1.33765e7			−1.19080			−0.595399	+	0.803430i	$0.703006\pi$
$662$		0			0
$663$	−1.30113e7	+	1.30113e7i	−1.14958	+	1.14958i
$664$		0			0
$665$	6.31449e6	+	1.25630e7i	0.553712	+	1.10164i
$666$		0			0
$667$	8.45922e6	+	8.45922e6i	0.736234	+	0.736234i
$668$		0			0
$669$			3.64507e6i			0.314877i
$670$		0			0
$671$			1.93692e7i			1.66076i
$672$		0			0
$673$	3.67918e6	+	3.67918e6i	0.313122	+	0.313122i	0.846118	−	0.532996i	$-0.178934\pi$
$673$	3.67918e6	+	3.67918e6i	0.313122	+	0.313122i	−0.532996	+	0.846118i	$0.678934\pi$
$674$		0			0
$675$	−726545.	−	4.93765e6i	−0.0613766	−	0.417120i
$676$		0			0
$677$	8.21030e6	−	8.21030e6i	0.688474	−	0.688474i	−0.273421	−	0.961895i	$-0.588155\pi$
$677$	8.21030e6	−	8.21030e6i	0.688474	−	0.688474i	0.961895	+	0.273421i	$0.0881551\pi$
$678$		0			0
$679$	−1.00366e7			−0.835434
$680$		0			0
$681$	−4019.21			−0.000332103
$682$		0			0
$683$	2.62244e6	−	2.62244e6i	0.215107	−	0.215107i	−0.591326	−	0.806433i	$-0.701395\pi$
$683$	2.62244e6	−	2.62244e6i	0.215107	−	0.215107i	0.806433	+	0.591326i	$0.201395\pi$
$684$		0			0
$685$	−1.51845e7	+	7.63213e6i	−1.23644	+	0.621469i
$686$		0			0
$687$	−4.57546e6	−	4.57546e6i	−0.369864	−	0.369864i
$688$		0			0
$689$		−	6.06255e6i		−	0.486528i
$690$		0			0
$691$			1.75172e7i			1.39562i	0.716281	+	0.697812i	$0.245843\pi$
$691$			1.75172e7i			1.39562i	−0.716281	+	0.697812i	$0.754157\pi$
$692$		0			0
$693$	−1.69647e7	−	1.69647e7i	−1.34188	−	1.34188i
$694$		0			0
$695$	1.98136e7	+	6.55836e6i	1.55597	+	0.515031i
$696$		0			0
$697$	1.58344e7	−	1.58344e7i	1.23458	−	1.23458i
$698$		0			0
$699$	9.03029e6			0.699051
$700$		0			0
$701$	1.66768e7			1.28180			0.640898	−	0.767626i	$-0.278562\pi$
$701$	1.66768e7			1.28180			0.640898	+	0.767626i	$0.278562\pi$
$702$		0			0
$703$	1.13784e7	−	1.13784e7i	0.868346	−	0.868346i
$704$		0			0
$705$	1.59345e7	+	5.27437e6i	1.20744	+	0.399667i
$706$		0			0
$707$	−1.06337e7	−	1.06337e7i	−0.800082	−	0.800082i
$708$		0			0
$709$			5.43469e6i			0.406031i	0.979176	+	0.203015i	$0.0650742\pi$
$709$			5.43469e6i			0.406031i	−0.979176	+	0.203015i	$0.934926\pi$
$710$		0			0
$711$		−	2.26022e7i		−	1.67678i
$712$		0			0
$713$	6.05279e6	+	6.05279e6i	0.445894	+	0.445894i
$714$		0			0
$715$	2.34988e7	−	1.18111e7i	1.71902	−	0.864026i
$716$		0			0
$717$	4.76525e6	−	4.76525e6i	0.346169	−	0.346169i
$718$		0			0
$719$	3.72831e6			0.268962			0.134481	−	0.990916i	$-0.457063\pi$
$719$	3.72831e6			0.268962			0.134481	+	0.990916i	$0.457063\pi$
$720$		0			0
$721$	−1.24629e7			−0.892856
$722$		0			0
$723$	1.39206e7	−	1.39206e7i	0.990401	−	0.990401i
$724$		0			0
$725$	9.09224e6	−	1.22296e7i	0.642430	−	0.864108i
$726$		0			0
$727$	−1.32677e7	−	1.32677e7i	−0.931024	−	0.931024i	0.0667459	−	0.997770i	$-0.478738\pi$
$727$	−1.32677e7	−	1.32677e7i	−0.931024	−	0.931024i	−0.997770	+	0.0667459i	$0.978738\pi$
$728$		0			0
$729$		−	2.09316e7i		−	1.45876i
$730$		0			0
$731$		−	1.23470e6i		−	0.0854609i
$732$		0			0
$733$	−1.97327e7	−	1.97327e7i	−1.35652	−	1.35652i	−0.878168	−	0.478353i	$-0.841234\pi$
$733$	−1.97327e7	−	1.97327e7i	−1.35652	−	1.35652i	−0.478353	−	0.878168i	$-0.658766\pi$
$734$		0			0
$735$	−2.98716e6	−	5.94310e6i	−0.203958	−	0.405784i
$736$		0			0
$737$	−1.67644e7	+	1.67644e7i	−1.13689	+	1.13689i
$738$		0			0
$739$	5.66235e6			0.381404			0.190702	−	0.981648i	$-0.438924\pi$
$739$	5.66235e6			0.381404			0.190702	+	0.981648i	$0.438924\pi$
$740$		0			0
$741$	3.60843e7			2.41420
$742$		0			0
$743$	1.31264e7	−	1.31264e7i	0.872314	−	0.872314i	−0.120411	−	0.992724i	$-0.538421\pi$
$743$	1.31264e7	−	1.31264e7i	0.872314	−	0.872314i	0.992724	+	0.120411i	$0.0384211\pi$
$744$		0			0
$745$	−9.27687e6	+	2.80266e7i	−0.612366	+	1.85003i
$746$		0			0
$747$	1.61397e7	+	1.61397e7i	1.05827	+	1.05827i
$748$		0			0
$749$		−	968249.i		−	0.0630641i
$750$		0			0
$751$		−	1.61237e6i		−	0.104320i	−0.998639	−	0.0521598i	$-0.983389\pi$
$751$		−	1.61237e6i		−	0.104320i	0.998639	−	0.0521598i	$-0.0166105\pi$
$752$		0			0
$753$	−2.07077e7	−	2.07077e7i	−1.33090	−	1.33090i
$754$		0			0
$755$	3.17963e6	−	9.60606e6i	0.203006	−	0.613307i
$756$		0			0
$757$	1.06901e7	−	1.06901e7i	0.678016	−	0.678016i	−0.281535	−	0.959551i	$-0.590843\pi$
$757$	1.06901e7	−	1.06901e7i	0.678016	−	0.678016i	0.959551	+	0.281535i	$0.0908435\pi$
$758$		0			0
$759$	4.11046e7			2.58992
$760$		0			0
$761$	−7.43314e6			−0.465276			−0.232638	−	0.972563i	$-0.574736\pi$
$761$	−7.43314e6			−0.465276			−0.232638	+	0.972563i	$0.574736\pi$
$762$		0			0
$763$	−1.27966e7	+	1.27966e7i	−0.795763	+	0.795763i
$764$		0			0
$765$	9.23387e6	+	1.83712e7i	0.570467	+	1.13497i
$766$		0			0
$767$	3.40728e6	+	3.40728e6i	0.209131	+	0.209131i
$768$		0			0
$769$			6.59786e6i			0.402335i	0.979557	+	0.201167i	$0.0644735\pi$
$769$			6.59786e6i			0.402335i	−0.979557	+	0.201167i	$0.935526\pi$
$770$		0			0
$771$			1.99847e7i			1.21077i
$772$		0			0
$773$	1.28485e7	+	1.28485e7i	0.773397	+	0.773397i	0.978699	−	0.205302i	$-0.0658176\pi$
$773$	1.28485e7	+	1.28485e7i	0.773397	+	0.773397i	−0.205302	+	0.978699i	$0.565818\pi$
$774$		0			0
$775$	6.50574e6	−	8.75062e6i	0.389083	−	0.523341i
$776$		0			0
$777$	1.25107e7	−	1.25107e7i	0.743409	−	0.743409i
$778$		0			0
$779$	−4.39137e7			−2.59272
$780$		0			0
$781$	712586.			0.0418032
$782$		0			0
$783$	−5.50704e6	+	5.50704e6i	−0.321006	+	0.321006i
$784$		0			0
$785$	8.09883e6	−	4.07069e6i	0.469081	−	0.235773i
$786$		0			0
$787$	6.95126e6	+	6.95126e6i	0.400061	+	0.400061i	0.878255	−	0.478193i	$-0.158708\pi$
$787$	6.95126e6	+	6.95126e6i	0.400061	+	0.400061i	−0.478193	+	0.878255i	$0.658708\pi$
$788$		0			0
$789$			8.54593e6i			0.488727i
$790$		0			0
$791$			1.03218e7i			0.586560i
$792$		0			0
$793$	−1.27121e7	−	1.27121e7i	−0.717853	−	0.717853i
$794$		0			0
$795$	−1.14585e7	−	3.79279e6i	−0.642999	−	0.212834i
$796$		0			0
$797$	1.79190e7	−	1.79190e7i	0.999238	−	0.999238i	−0.000761608	−	1.00000i	$-0.500242\pi$
$797$	1.79190e7	−	1.79190e7i	0.999238	−	0.999238i	1.00000		0.000761608i	$0.000242427\pi$
$798$		0			0
$799$	−1.50955e7			−0.836531
$800$		0			0
$801$	−1.91781e7			−1.05615
$802$		0			0
$803$	5.49746e6	−	5.49746e6i	0.300866	−	0.300866i
$804$		0			0
$805$	−1.41131e7	−	4.67146e6i	−0.767595	−	0.254076i
$806$		0			0
$807$	2.16868e7	+	2.16868e7i	1.17223	+	1.17223i
$808$		0			0
$809$		−	1.42932e7i		−	0.767819i	−0.923371	−	0.383909i	$-0.874577\pi$
$809$		−	1.42932e7i		−	0.767819i	0.923371	−	0.383909i	$-0.125423\pi$
$810$		0			0
$811$		−	1.02478e7i		−	0.547113i	−0.961856	−	0.273557i	$-0.911800\pi$
$811$		−	1.02478e7i		−	0.547113i	0.961856	−	0.273557i	$-0.0882001\pi$
$812$		0			0
$813$	−1.52127e6	−	1.52127e6i	−0.0807198	−	0.0807198i
$814$		0			0
$815$	1.43383e6	−	720684.i	0.0756145	−	0.0380059i
$816$		0			0
$817$	−1.71209e6	+	1.71209e6i	−0.0897372	+	0.0897372i
$818$		0			0
$819$	2.22681e7			1.16004
$820$		0			0
$821$	−1.09640e7			−0.567687			−0.283844	−	0.958871i	$-0.591610\pi$
$821$	−1.09640e7			−0.567687			−0.283844	+	0.958871i	$0.591610\pi$
$822$		0			0
$823$	−1.50404e7	+	1.50404e7i	−0.774032	+	0.774032i	−0.978809	−	0.204777i	$-0.934353\pi$
$823$	−1.50404e7	+	1.50404e7i	−0.774032	+	0.774032i	0.204777	+	0.978809i	$0.434353\pi$
$824$		0			0
$825$	−7.62250e6	−	5.18030e7i	−0.389909	−	2.64984i
$826$		0			0
$827$	−1.94638e7	−	1.94638e7i	−0.989608	−	0.989608i	0.0103388	−	0.999947i	$-0.496709\pi$
$827$	−1.94638e7	−	1.94638e7i	−0.989608	−	0.989608i	−0.999947	+	0.0103388i	$0.996709\pi$
$828$		0			0
$829$			1.47941e7i			0.747658i	0.927498	+	0.373829i	$0.121955\pi$
$829$			1.47941e7i			0.747658i	−0.927498	+	0.373829i	$0.878045\pi$
$830$		0			0
$831$			8.47586e6i			0.425776i
$832$		0			0
$833$	4.23003e6	+	4.23003e6i	0.211218	+	0.211218i
$834$		0			0
$835$	1.54998e7	+	3.08376e7i	0.769325	+	1.53061i
$836$		0			0
$837$	−3.94043e6	+	3.94043e6i	−0.194415	+	0.194415i
$838$		0			0
$839$	2.09516e7			1.02757			0.513785	−	0.857919i	$-0.328243\pi$
$839$	2.09516e7			1.02757			0.513785	+	0.857919i	$0.328243\pi$
$840$		0			0
$841$	−3.26947e6			−0.159400
$842$		0			0
$843$	−3.45345e7	+	3.45345e7i	−1.67372	+	1.67372i
$844$		0			0
$845$	−1.14844e6	+	3.46960e6i	−0.0553310	+	0.167162i
$846$		0			0
$847$	−2.65091e7	−	2.65091e7i	−1.26966	−	1.26966i
$848$		0			0
$849$			4.48141e7i			2.13376i
$850$		0			0
$851$			1.70133e7i			0.805314i
$852$		0			0
$853$	−2.03458e7	−	2.03458e7i	−0.957418	−	0.957418i	0.0417118	−	0.999130i	$-0.486719\pi$
$853$	−2.03458e7	−	2.03458e7i	−0.957418	−	0.957418i	−0.999130	+	0.0417118i	$0.986719\pi$
$854$		0			0
$855$	1.26703e7	−	3.82786e7i	0.592751	−	1.79077i
$856$		0			0
$857$	−4.00445e6	+	4.00445e6i	−0.186247	+	0.186247i	−0.794072	−	0.607824i	$-0.792043\pi$
$857$	−4.00445e6	+	4.00445e6i	−0.186247	+	0.186247i	0.607824	+	0.794072i	$0.292043\pi$
$858$		0			0
$859$	1.26736e7			0.586025			0.293012	−	0.956109i	$-0.405342\pi$
$859$	1.26736e7			0.586025			0.293012	+	0.956109i	$0.405342\pi$
$860$		0			0
$861$	−4.82835e7			−2.21968
$862$		0			0
$863$	−1.29179e6	+	1.29179e6i	−0.0590426	+	0.0590426i	−0.736012	−	0.676969i	$-0.763293\pi$
$863$	−1.29179e6	+	1.29179e6i	−0.0590426	+	0.0590426i	0.676969	+	0.736012i	$0.263293\pi$
$864$		0			0
$865$	−8.66397e6	−	1.72374e7i	−0.393710	−	0.783305i
$866$		0			0
$867$	331016.	+	331016.i	0.0149555	+	0.0149555i
$868$		0			0
$869$		−	5.17655e7i		−	2.32536i
$870$		0			0
$871$		−	2.20051e7i		−	0.982830i
$872$		0			0
$873$	2.03516e7	+	2.03516e7i	0.903782	+	0.903782i
$874$		0			0
$875$	−3.27017e6	+	1.86526e7i	−0.144394	+	0.823607i
$876$		0			0
$877$	−2.45246e6	+	2.45246e6i	−0.107672	+	0.107672i	−0.758890	−	0.651218i	$-0.774258\pi$
$877$	−2.45246e6	+	2.45246e6i	−0.107672	+	0.107672i	0.651218	+	0.758890i	$0.274258\pi$
$878$		0			0
$879$	9.98388e6			0.435840
$880$		0			0
$881$	3.44091e7			1.49360			0.746798	−	0.665050i	$-0.231590\pi$
$881$	3.44091e7			1.49360			0.746798	+	0.665050i	$0.231590\pi$
$882$		0			0
$883$	1.49795e7	−	1.49795e7i	0.646540	−	0.646540i	−0.305615	−	0.952155i	$-0.598862\pi$
$883$	1.49795e7	−	1.49795e7i	0.646540	−	0.646540i	0.952155	+	0.305615i	$0.0988620\pi$
$884$		0			0
$885$	8.57154e6	−	4.30828e6i	0.367875	−	0.184904i
$886$		0			0
$887$	7.56428e6	+	7.56428e6i	0.322819	+	0.322819i	0.849847	−	0.527029i	$-0.176694\pi$
$887$	7.56428e6	+	7.56428e6i	0.322819	+	0.322819i	−0.527029	+	0.849847i	$0.676694\pi$
$888$		0			0
$889$		−	4.39266e6i		−	0.186412i
$890$		0			0
$891$		−	2.70215e7i		−	1.14029i
$892$		0			0
$893$	2.09322e7	+	2.09322e7i	0.878389	+	0.878389i
$894$		0			0
$895$	−3.58730e7	−	1.18740e7i	−1.49696	−	0.495497i
$896$		0			0
$897$	−2.69772e7	+	2.69772e7i	−1.11948	+	1.11948i
$898$		0			0
$899$	−1.70157e7			−0.702182
$900$		0			0
$901$	1.08552e7			0.445477
$902$		0			0
$903$	−1.88246e6	+	1.88246e6i	−0.0768258	+	0.0768258i
$904$		0			0
$905$	3.09331e7	+	1.02389e7i	1.25546	+	0.415559i
$906$		0			0
$907$	−9.75108e6	−	9.75108e6i	−0.393581	−	0.393581i	0.482380	−	0.875962i	$-0.339772\pi$
$907$	−9.75108e6	−	9.75108e6i	−0.393581	−	0.393581i	−0.875962	+	0.482380i	$0.839772\pi$
$908$		0			0
$909$			4.31246e7i			1.73107i
$910$		0			0
$911$			2.71934e6i			0.108559i	0.998526	+	0.0542796i	$0.0172862\pi$
$911$			2.71934e6i			0.108559i	−0.998526	+	0.0542796i	$0.982714\pi$
$912$		0			0
$913$	3.69646e7	+	3.69646e7i	1.46760	+	1.46760i
$914$		0			0
$915$	−3.19794e7	+	1.60737e7i	−1.26275	+	0.634692i
$916$		0			0
$917$	−5.30306e6	+	5.30306e6i	−0.208259	+	0.208259i
$918$		0			0
$919$	−2.42332e7			−0.946502			−0.473251	−	0.880928i	$-0.656920\pi$
$919$	−2.42332e7			−0.946502			−0.473251	+	0.880928i	$0.656920\pi$
$920$		0			0
$921$	−1.89985e7			−0.738023
$922$		0			0
$923$	−467674.	+	467674.i	−0.0180692	+	0.0180692i
$924$		0			0
$925$	2.14415e7	−	3.15498e6i	0.823948	−	0.121239i
$926$		0			0
$927$	2.52715e7	+	2.52715e7i	0.965901	+	0.965901i
$928$		0			0
$929$		−	2.31300e7i		−	0.879300i	−0.898169	−	0.439650i	$-0.855103\pi$
$929$		−	2.31300e7i		−	0.879300i	0.898169	−	0.439650i	$-0.144897\pi$
$930$		0			0
$931$		−	1.17311e7i		−	0.443574i
$932$		0			0
$933$	9.25289e6	+	9.25289e6i	0.347995	+	0.347995i
$934$		0			0
$935$	2.11482e7	+	4.20754e7i	0.791124	+	1.57398i
$936$		0			0
$937$	2.75206e7	−	2.75206e7i	1.02402	−	1.02402i	0.0243173	−	0.999704i	$-0.492259\pi$
$937$	2.75206e7	−	2.75206e7i	1.02402	−	1.02402i	0.999704	−	0.0243173i	$-0.00774119\pi$
$938$		0			0
$939$	−5.15492e7			−1.90791
$940$		0			0
$941$	−3.85324e7			−1.41857			−0.709287	−	0.704920i	$-0.750983\pi$
$941$	−3.85324e7			−1.41857			−0.709287	+	0.704920i	$0.750983\pi$
$942$		0			0
$943$	3.28305e7	−	3.28305e7i	1.20226	−	1.20226i
$944$		0			0
$945$	3.04117e6	−	9.18776e6i	0.110780	−	0.334680i
$946$		0			0
$947$	2.80112e7	+	2.80112e7i	1.01498	+	1.01498i	0.999886	+	0.0150913i	$0.00480388\pi$
$947$	2.80112e7	+	2.80112e7i	1.01498	+	1.01498i	0.0150913	+	0.999886i	$0.495196\pi$
$948$		0			0
$949$			7.21602e6i			0.260095i
$950$		0			0
$951$		−	6.32010e7i		−	2.26607i
$952$		0			0
$953$	2.35368e7	+	2.35368e7i	0.839489	+	0.839489i	0.988791	−	0.149303i	$-0.0477030\pi$
$953$	2.35368e7	+	2.35368e7i	0.839489	+	0.839489i	−0.149303	+	0.988791i	$0.547703\pi$
$954$		0			0
$955$	622116.	−	1.87949e6i	0.0220731	−	0.0666856i
$956$		0			0
$957$	−5.77768e7	+	5.77768e7i	−2.03926	+	2.03926i
$958$		0			0
$959$	−3.29554e7			−1.15712
$960$		0			0
$961$	1.64540e7			0.574729
$962$		0			0
$963$	−1.96336e6	+	1.96336e6i	−0.0682235	+	0.0682235i
$964$		0			0
$965$	8.12596e6	+	1.61670e7i	0.280903	+	0.558870i
$966$		0			0
$967$	−1.33576e7	−	1.33576e7i	−0.459369	−	0.459369i	0.439079	−	0.898448i	$-0.355305\pi$
$967$	−1.33576e7	−	1.33576e7i	−0.459369	−	0.459369i	−0.898448	+	0.439079i	$0.855305\pi$
$968$		0			0
$969$			6.46100e7i			2.21050i
$970$		0			0
$971$			9.48454e6i			0.322826i	0.986887	+	0.161413i	$0.0516051\pi$
$971$			9.48454e6i			0.322826i	−0.986887	+	0.161413i	$0.948395\pi$
$972$		0			0
$973$	2.86180e7	+	2.86180e7i	0.969073	+	0.969073i
$974$		0			0
$975$	3.90013e7	+	2.89959e7i	1.31392	+	0.976844i
$976$		0			0
$977$	−4.72089e6	+	4.72089e6i	−0.158230	+	0.158230i	−0.781782	−	0.623552i	$-0.785689\pi$
$977$	−4.72089e6	+	4.72089e6i	−0.158230	+	0.158230i	0.623552	+	0.781782i	$0.285689\pi$
$978$		0			0
$979$	−4.39234e7			−1.46467
$980$		0			0
$981$	5.18964e7			1.72173
$982$		0			0
$983$	−7.18879e6	+	7.18879e6i	−0.237286	+	0.237286i	−0.815725	−	0.578439i	$-0.803662\pi$
$983$	−7.18879e6	+	7.18879e6i	−0.237286	+	0.237286i	0.578439	+	0.815725i	$0.303662\pi$
$984$		0			0
$985$	−4.26229e7	+	2.14234e7i	−1.39976	+	0.703556i
$986$		0			0
$987$	2.30152e7	+	2.30152e7i	0.752007	+	0.752007i
$988$		0			0
$989$		−	2.55997e6i		−	0.0832233i
$990$		0			0
$991$		−	4.01764e7i		−	1.29953i	−0.760135	−	0.649765i	$-0.774867\pi$
$991$		−	4.01764e7i		−	1.29953i	0.760135	−	0.649765i	$-0.225133\pi$
$992$		0			0
$993$	−1.82793e7	−	1.82793e7i	−0.588282	−	0.588282i
$994$		0			0
$995$	−3.18518e7	−	1.05430e7i	−1.01994	−	0.337604i
$996$		0			0
$997$	−6.24232e6	+	6.24232e6i	−0.198888	+	0.198888i	−0.799523	−	0.600635i	$-0.794914\pi$
$997$	−6.24232e6	+	6.24232e6i	−0.198888	+	0.198888i	0.600635	+	0.799523i	$0.294914\pi$
$998$		0			0
$999$	−1.10759e7			−0.351126

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.6.n.d.63.7	yes	16
4.3	odd	2		160.6.n.c.63.2	✓	16
5.2	odd	4		160.6.n.c.127.2	yes	16
20.7	even	4	inner	160.6.n.d.127.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.6.n.c.63.2	✓	16	4.3	odd	2
160.6.n.c.127.2	yes	16	5.2	odd	4
160.6.n.d.63.7	yes	16	1.1	even	1	trivial
160.6.n.d.127.7	yes	16	20.7	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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	160.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(16.6412 - 16.6412i) q^{3} +(53.0700 + 17.5663i) q^{5} +(76.6521 + 76.6521i) q^{7} -310.861i q^{9} +O(q^{10})\)	\(q+(16.6412 - 16.6412i) q^{3} +(53.0700 + 17.5663i) q^{5} +(76.6521 + 76.6521i) q^{7} -310.861i q^{9} -711.961i q^{11} +(467.264 + 467.264i) q^{13} +(1175.48 - 590.825i) q^{15} +(-836.650 + 836.650i) q^{17} +2320.28 q^{19} +2551.17 q^{21} +(-1734.68 + 1734.68i) q^{23} +(2507.85 + 1864.49i) q^{25} +(-1129.29 - 1129.29i) q^{27} -4876.54i q^{29} -3489.29i q^{31} +(-11847.9 - 11847.9i) q^{33} +(2721.43 + 5414.42i) q^{35} +(4903.89 - 4903.89i) q^{37} +15551.7 q^{39} -18926.0 q^{41} +(-737.882 + 737.882i) q^{43} +(5460.68 - 16497.4i) q^{45} +(9021.42 + 9021.42i) q^{47} -5055.91i q^{49} +27845.8i q^{51} +(-6487.29 - 6487.29i) q^{53} +(12506.5 - 37783.8i) q^{55} +(38612.3 - 38612.3i) q^{57} +7291.98 q^{59} -27205.5 q^{61} +(23828.2 - 23828.2i) q^{63} +(16589.6 + 33005.8i) q^{65} +(-23546.8 - 23546.8i) q^{67} +57734.3i q^{69} +1000.88i q^{71} +(7721.57 + 7721.57i) q^{73} +(72761.1 - 10706.4i) q^{75} +(54573.3 - 54573.3i) q^{77} +72708.3 q^{79} +37953.6 q^{81} +(-51919.4 + 51919.4i) q^{83} +(-59097.8 + 29704.2i) q^{85} +(-81151.6 - 81151.6i) q^{87} -61693.6i q^{89} +71633.5i q^{91} +(-58066.1 - 58066.1i) q^{93} +(123137. + 40758.8i) q^{95} +(-65468.6 + 65468.6i) q^{97} -221321. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 10 q^{3} - 42 q^{5} - 86 q^{7}+O(q^{10}) \) 16 * q + 10 * q^3 - 42 * q^5 - 86 * q^7	\( 16 q + 10 q^{3} - 42 q^{5} - 86 q^{7} + 536 q^{13} - 698 q^{15} - 1828 q^{17} + 2512 q^{19} - 4284 q^{21} - 7642 q^{23} + 9140 q^{25} - 12272 q^{27} + 11876 q^{33} + 10518 q^{35} - 7620 q^{37} + 11244 q^{39} - 21284 q^{41} + 20002 q^{43} + 686 q^{45} + 25298 q^{47} + 12852 q^{53} - 10584 q^{55} + 55848 q^{57} - 142704 q^{59} - 20564 q^{61} - 115282 q^{63} - 38256 q^{65} - 10506 q^{67} + 15432 q^{73} + 256226 q^{75} + 133852 q^{77} - 159344 q^{79} - 236116 q^{81} - 61222 q^{83} + 7056 q^{85} + 162176 q^{87} + 122180 q^{93} + 267512 q^{95} - 17344 q^{97} + 107332 q^{99}+O(q^{100}) \) 16 * q + 10 * q^3 - 42 * q^5 - 86 * q^7 + 536 * q^13 - 698 * q^15 - 1828 * q^17 + 2512 * q^19 - 4284 * q^21 - 7642 * q^23 + 9140 * q^25 - 12272 * q^27 + 11876 * q^33 + 10518 * q^35 - 7620 * q^37 + 11244 * q^39 - 21284 * q^41 + 20002 * q^43 + 686 * q^45 + 25298 * q^47 + 12852 * q^53 - 10584 * q^55 + 55848 * q^57 - 142704 * q^59 - 20564 * q^61 - 115282 * q^63 - 38256 * q^65 - 10506 * q^67 + 15432 * q^73 + 256226 * q^75 + 133852 * q^77 - 159344 * q^79 - 236116 * q^81 - 61222 * q^83 + 7056 * q^85 + 162176 * q^87 + 122180 * q^93 + 267512 * q^95 - 17344 * q^97 + 107332 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more