LMFDB - Embedded newform 160.6.n.c.127.3

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			127.3
Root			$3.47866i$ of defining polynomial
Character	$\chi$	$=$	160.127
Dual form			160.6.n.c.63.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.47866 - 4.47866i) q^{3} +(-49.0494 + 26.8170i) q^{5} +(-132.222 + 132.222i) q^{7} -202.883i q^{9} +O(q^{10})$	\(q+(-4.47866 - 4.47866i) q^{3} +(-49.0494 + 26.8170i) q^{5} +(-132.222 + 132.222i) q^{7} -202.883i q^{9} -364.650i q^{11} +(-530.900 + 530.900i) q^{13} +(339.780 + 99.5716i) q^{15} +(115.649 + 115.649i) q^{17} +1498.32 q^{19} +1184.35 q^{21} +(2630.46 + 2630.46i) q^{23} +(1686.70 - 2630.72i) q^{25} +(-1996.96 + 1996.96i) q^{27} -8089.88i q^{29} +1296.29i q^{31} +(-1633.14 + 1633.14i) q^{33} +(2939.61 - 10031.2i) q^{35} +(-5684.73 - 5684.73i) q^{37} +4755.44 q^{39} +10224.2 q^{41} +(11002.7 + 11002.7i) q^{43} +(5440.72 + 9951.31i) q^{45} +(11004.2 - 11004.2i) q^{47} -18158.1i q^{49} -1035.91i q^{51} +(23125.1 - 23125.1i) q^{53} +(9778.82 + 17885.9i) q^{55} +(-6710.47 - 6710.47i) q^{57} -6310.91 q^{59} -33090.5 q^{61} +(26825.5 + 26825.5i) q^{63} +(11803.2 - 40277.5i) q^{65} +(26821.8 - 26821.8i) q^{67} -23561.8i q^{69} +51803.3i q^{71} +(-5524.99 + 5524.99i) q^{73} +(-19336.2 + 4227.95i) q^{75} +(48214.6 + 48214.6i) q^{77} +79623.0 q^{79} -31413.2 q^{81} +(-59795.0 - 59795.0i) q^{83} +(-8773.88 - 2571.16i) q^{85} +(-36231.8 + 36231.8i) q^{87} +118466. i q^{89} -140393. i q^{91} +(5805.63 - 5805.63i) q^{93} +(-73491.8 + 40180.5i) q^{95} +(4680.48 + 4680.48i) q^{97} -73981.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

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

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
$3$	−4.47866	−	4.47866i	−0.287306	−	0.287306i	0.548708	−	0.836014i	$-0.315120\pi$
$3$	−4.47866	−	4.47866i	−0.287306	−	0.287306i	−0.836014	+	0.548708i	$0.815120\pi$
$4$		0			0
$5$	−49.0494	+	26.8170i	−0.877423	+	0.479717i
$5$	−49.0494	+	26.8170i	−0.877423	+	0.479717i
$6$		0			0
$7$	−132.222	+	132.222i	−1.01990	+	1.01990i	−0.0201008	+	0.999798i	$0.506399\pi$
$7$	−132.222	+	132.222i	−1.01990	+	1.01990i	−0.999798	+	0.0201008i	$0.993601\pi$
$8$		0			0
$9$		−	202.883i		−	0.834910i
$10$		0			0
$11$		−	364.650i		−	0.908646i	−0.890837	−	0.454323i	$-0.849881\pi$
$11$		−	364.650i		−	0.908646i	0.890837	−	0.454323i	$-0.150119\pi$
$12$		0			0
$13$	−530.900	+	530.900i	−0.871272	+	0.871272i	−0.992611	−	0.121339i	$-0.961281\pi$
$13$	−530.900	+	530.900i	−0.871272	+	0.871272i	0.121339	+	0.992611i	$0.461281\pi$
$14$		0			0
$15$	339.780	+	99.5716i	0.389915	+	0.114263i
$16$		0			0
$17$	115.649	+	115.649i	0.0970554	+	0.0970554i	0.753967	−	0.656912i	$-0.228138\pi$
$17$	115.649	+	115.649i	0.0970554	+	0.0970554i	−0.656912	+	0.753967i	$0.728138\pi$
$18$		0			0
$19$	1498.32			0.952184			0.476092	−	0.879395i	$-0.342053\pi$
$19$	1498.32			0.952184			0.476092	+	0.879395i	$0.342053\pi$
$20$		0			0
$21$	1184.35			0.586046
$22$		0			0
$23$	2630.46	+	2630.46i	1.03684	+	1.03684i	0.999295	+	0.0375445i	$0.0119536\pi$
$23$	2630.46	+	2630.46i	1.03684	+	1.03684i	0.0375445	+	0.999295i	$0.488046\pi$
$24$		0			0
$25$	1686.70	−	2630.72i	0.539743	−	0.841830i
$26$		0			0
$27$	−1996.96	+	1996.96i	−0.527181	+	0.527181i
$28$		0			0
$29$		−	8089.88i		−	1.78627i	−0.449788	−	0.893135i	$-0.648501\pi$
$29$		−	8089.88i		−	1.78627i	0.449788	−	0.893135i	$-0.351499\pi$
$30$		0			0
$31$			1296.29i			0.242269i	0.992636	+	0.121134i	$0.0386532\pi$
$31$			1296.29i			0.242269i	−0.992636	+	0.121134i	$0.961347\pi$
$32$		0			0
$33$	−1633.14	+	1633.14i	−0.261060	+	0.261060i
$34$		0			0
$35$	2939.61	−	10031.2i	0.405620	−	1.38415i
$36$		0			0
$37$	−5684.73	−	5684.73i	−0.682661	−	0.682661i	0.277938	−	0.960599i	$-0.410349\pi$
$37$	−5684.73	−	5684.73i	−0.682661	−	0.682661i	−0.960599	+	0.277938i	$0.910349\pi$
$38$		0			0
$39$	4755.44			0.500644
$40$		0			0
$41$	10224.2			0.949885			0.474942	−	0.880017i	$-0.342469\pi$
$41$	10224.2			0.949885			0.474942	+	0.880017i	$0.342469\pi$
$42$		0			0
$43$	11002.7	+	11002.7i	0.907462	+	0.907462i	0.996067	−	0.0886051i	$-0.0282409\pi$
$43$	11002.7	+	11002.7i	0.907462	+	0.907462i	−0.0886051	+	0.996067i	$0.528241\pi$
$44$		0			0
$45$	5440.72	+	9951.31i	0.400521	+	0.732570i
$46$		0			0
$47$	11004.2	−	11004.2i	0.726628	−	0.726628i	−0.243319	−	0.969946i	$-0.578236\pi$
$47$	11004.2	−	11004.2i	0.726628	−	0.726628i	0.969946	+	0.243319i	$0.0782361\pi$
$48$		0			0
$49$		−	18158.1i		−	1.08039i
$50$		0			0
$51$		−	1035.91i		−	0.0557692i
$52$		0			0
$53$	23125.1	−	23125.1i	1.13082	−	1.13082i	0.140779	−	0.990041i	$-0.455039\pi$
$53$	23125.1	−	23125.1i	1.13082	−	1.13082i	0.990041	−	0.140779i	$-0.0449606\pi$
$54$		0			0
$55$	9778.82	+	17885.9i	0.435893	+	0.797267i
$56$		0			0
$57$	−6710.47	−	6710.47i	−0.273568	−	0.273568i
$58$		0			0
$59$	−6310.91			−0.236027			−0.118014	−	0.993012i	$-0.537653\pi$
$59$	−6310.91			−0.236027			−0.118014	+	0.993012i	$0.537653\pi$
$60$		0			0
$61$	−33090.5			−1.13862			−0.569309	−	0.822124i	$-0.692789\pi$
$61$	−33090.5			−1.13862			−0.569309	+	0.822124i	$0.692789\pi$
$62$		0			0
$63$	26825.5	+	26825.5i	0.851524	+	0.851524i
$64$		0			0
$65$	11803.2	−	40277.5i	0.346510	−	1.18244i
$66$		0			0
$67$	26821.8	−	26821.8i	0.729962	−	0.729962i	−0.240650	−	0.970612i	$-0.577361\pi$
$67$	26821.8	−	26821.8i	0.729962	−	0.729962i	0.970612	+	0.240650i	$0.0773606\pi$
$68$		0			0
$69$		−	23561.8i		−	0.595781i
$70$		0			0
$71$			51803.3i			1.21958i	0.792562	+	0.609792i	$0.208747\pi$
$71$			51803.3i			1.21958i	−0.792562	+	0.609792i	$0.791253\pi$
$72$		0			0
$73$	−5524.99	+	5524.99i	−0.121346	+	0.121346i	−0.765172	−	0.643826i	$-0.777346\pi$
$73$	−5524.99	+	5524.99i	−0.121346	+	0.121346i	0.643826	+	0.765172i	$0.277346\pi$
$74$		0			0
$75$	−19336.2	+	4227.95i	−0.396934	+	0.0867914i
$76$		0			0
$77$	48214.6	+	48214.6i	0.926727	+	0.926727i
$78$		0			0
$79$	79623.0			1.43539			0.717697	−	0.696356i	$-0.245197\pi$
$79$	79623.0			1.43539			0.717697	+	0.696356i	$0.245197\pi$
$80$		0			0
$81$	−31413.2			−0.531986
$82$		0			0
$83$	−59795.0	−	59795.0i	−0.952730	−	0.952730i	0.0462022	−	0.998932i	$-0.485288\pi$
$83$	−59795.0	−	59795.0i	−0.952730	−	0.952730i	−0.998932	+	0.0462022i	$0.985288\pi$
$84$		0			0
$85$	−8773.88	−	2571.16i	−0.131718	−	0.0385995i
$86$		0			0
$87$	−36231.8	+	36231.8i	−0.513207	+	0.513207i
$88$		0			0
$89$			118466.i			1.58532i	0.609663	+	0.792660i	$0.291305\pi$
$89$			118466.i			1.58532i	−0.609663	+	0.792660i	$0.708695\pi$
$90$		0			0
$91$		−	140393.i		−	1.77722i
$92$		0			0
$93$	5805.63	−	5805.63i	0.0696052	−	0.0696052i
$94$		0			0
$95$	−73491.8	+	40180.5i	−0.835468	+	0.456779i
$96$		0			0
$97$	4680.48	+	4680.48i	0.0505081	+	0.0505081i	0.731910	−	0.681402i	$-0.238629\pi$
$97$	4680.48	+	4680.48i	0.0505081	+	0.0505081i	−0.681402	+	0.731910i	$0.738629\pi$
$98$		0			0
$99$	−73981.4			−0.758638
$100$		0			0
$101$	−54138.2			−0.528081			−0.264041	−	0.964512i	$-0.585055\pi$
$101$	−54138.2			−0.528081			−0.264041	+	0.964512i	$0.585055\pi$
$102$		0			0
$103$	19950.3	+	19950.3i	0.185292	+	0.185292i	0.793657	−	0.608365i	$-0.208174\pi$
$103$	19950.3	+	19950.3i	0.185292	+	0.185292i	−0.608365	+	0.793657i	$0.708174\pi$
$104$		0			0
$105$	−58091.7	+	31760.7i	−0.514211	+	0.281136i
$106$		0			0
$107$	10953.8	−	10953.8i	0.0924927	−	0.0924927i	−0.659347	−	0.751839i	$-0.729167\pi$
$107$	10953.8	−	10953.8i	0.0924927	−	0.0924927i	0.751839	+	0.659347i	$0.229167\pi$
$108$		0			0
$109$		−	63104.9i		−	0.508741i	−0.967107	−	0.254371i	$-0.918132\pi$
$109$		−	63104.9i		−	0.508741i	0.967107	−	0.254371i	$-0.0818683\pi$
$110$		0			0
$111$			50919.9i			0.392266i
$112$		0			0
$113$	24181.7	−	24181.7i	0.178152	−	0.178152i	−0.612398	−	0.790550i	$-0.709795\pi$
$113$	24181.7	−	24181.7i	0.178152	−	0.178152i	0.790550	+	0.612398i	$0.209795\pi$
$114$		0			0
$115$	−199563.	−	58481.5i	−1.40714	−	0.412357i
$116$		0			0
$117$	107711.	+	107711.i	0.727434	+	0.727434i
$118$		0			0
$119$	−30582.6			−0.197973
$120$		0			0
$121$	28081.3			0.174363
$122$		0			0
$123$	−45790.8	−	45790.8i	−0.272908	−	0.272908i
$124$		0			0
$125$	−12183.6	+	174267.i	−0.0697428	+	0.997565i
$126$		0			0
$127$	−61368.9	+	61368.9i	−0.337629	+	0.337629i	−0.855474	−	0.517845i	$-0.826734\pi$
$127$	−61368.9	+	61368.9i	−0.337629	+	0.337629i	0.517845	+	0.855474i	$0.326734\pi$
$128$		0			0
$129$		−	98554.7i		−	0.521439i
$130$		0			0
$131$			14768.9i			0.0751916i	0.999293	+	0.0375958i	$0.0119699\pi$
$131$			14768.9i			0.0751916i	−0.999293	+	0.0375958i	$0.988030\pi$
$132$		0			0
$133$	−198110.	+	198110.i	−0.971131	+	0.971131i
$134$		0			0
$135$	44397.3	−	151502.i	0.209663	−	0.715459i
$136$		0			0
$137$	62613.4	+	62613.4i	0.285014	+	0.285014i	0.835105	−	0.550091i	$-0.185407\pi$
$137$	62613.4	+	62613.4i	0.285014	+	0.285014i	−0.550091	+	0.835105i	$0.685407\pi$
$138$		0			0
$139$	−75635.9			−0.332040			−0.166020	−	0.986122i	$-0.553092\pi$
$139$	−75635.9			−0.332040			−0.166020	+	0.986122i	$0.553092\pi$
$140$		0			0
$141$	−98567.7			−0.417529
$142$		0			0
$143$	193593.	+	193593.i	0.791678	+	0.791678i
$144$		0			0
$145$	216946.	+	396804.i	0.856905	+	1.56732i
$146$		0			0
$147$	−81323.8	+	81323.8i	−0.310402	+	0.310402i
$148$		0			0
$149$			80926.3i			0.298624i	0.988790	+	0.149312i	$0.0477058\pi$
$149$			80926.3i			0.298624i	−0.988790	+	0.149312i	$0.952294\pi$
$150$		0			0
$151$		−	388022.i		−	1.38489i	−0.721472	−	0.692443i	$-0.756534\pi$
$151$		−	388022.i		−	1.38489i	0.721472	−	0.692443i	$-0.243466\pi$
$152$		0			0
$153$	23463.3	−	23463.3i	0.0810326	−	0.0810326i
$154$		0			0
$155$	−34762.5	−	63582.2i	−0.116220	−	0.212572i
$156$		0			0
$157$	−234782.	−	234782.i	−0.760179	−	0.760179i	0.216176	−	0.976354i	$-0.430642\pi$
$157$	−234782.	−	234782.i	−0.760179	−	0.760179i	−0.976354	+	0.216176i	$0.930642\pi$
$158$		0			0
$159$	−207139.			−0.649783
$160$		0			0
$161$	−695606.			−2.11494
$162$		0			0
$163$	−916.314	−	916.314i	−0.00270132	−	0.00270132i	0.705755	−	0.708456i	$-0.250608\pi$
$163$	−916.314	−	916.314i	−0.00270132	−	0.00270132i	−0.708456	+	0.705755i	$0.750608\pi$
$164$		0			0
$165$	36308.8	−	123901.i	0.103825	−	0.354294i
$166$		0			0
$167$	−363140.	+	363140.i	−1.00759	+	1.00759i	−0.00761789	+	0.999971i	$0.502425\pi$
$167$	−363140.	+	363140.i	−1.00759	+	1.00759i	−0.999971	+	0.00761789i	$0.997575\pi$
$168$		0			0
$169$		−	192416.i		−	0.518231i
$170$		0			0
$171$		−	303984.i		−	0.794988i
$172$		0			0
$173$	328481.	−	328481.i	0.834440	−	0.834440i	−0.153681	−	0.988121i	$-0.549113\pi$
$173$	328481.	−	328481.i	0.834440	−	0.834440i	0.988121	+	0.153681i	$0.0491128\pi$
$174$		0			0
$175$	124820.	+	570855.i	0.308098	+	1.40906i
$176$		0			0
$177$	28264.4	+	28264.4i	0.0678121	+	0.0678121i
$178$		0			0
$179$	655619.			1.52939			0.764696	−	0.644391i	$-0.222889\pi$
$179$	655619.			1.52939			0.764696	+	0.644391i	$0.222889\pi$
$180$		0			0
$181$	399723.			0.906906			0.453453	−	0.891280i	$-0.350192\pi$
$181$	399723.			0.906906			0.453453	+	0.891280i	$0.350192\pi$
$182$		0			0
$183$	148201.	+	148201.i	0.327132	+	0.327132i
$184$		0			0
$185$	431280.	+	126385.i	0.926467	+	0.271499i
$186$		0			0
$187$	42171.4	−	42171.4i	0.0881890	−	0.0881890i
$188$		0			0
$189$		−	528082.i		−	1.07534i
$190$		0			0
$191$		−	654090.i		−	1.29734i	−0.761070	−	0.648670i	$-0.775325\pi$
$191$		−	654090.i		−	1.29734i	0.761070	−	0.648670i	$-0.224675\pi$
$192$		0			0
$193$	562157.	−	562157.i	1.08634	−	1.08634i	0.0904339	−	0.995902i	$-0.471175\pi$
$193$	562157.	−	562157.i	1.08634	−	1.08634i	0.995902	−	0.0904339i	$-0.0288254\pi$
$194$		0			0
$195$	−233252.	+	127527.i	−0.439277	+	0.240167i
$196$		0			0
$197$	306725.	+	306725.i	0.563098	+	0.563098i	0.930186	−	0.367088i	$-0.119645\pi$
$197$	306725.	+	306725.i	0.563098	+	0.563098i	−0.367088	+	0.930186i	$0.619645\pi$
$198$		0			0
$199$	1.01174e6			1.81107			0.905535	−	0.424271i	$-0.139470\pi$
$199$	1.01174e6			1.81107			0.905535	+	0.424271i	$0.139470\pi$
$200$		0			0
$201$	−240251.			−0.419445
$202$		0			0
$203$	1.06966e6	+	1.06966e6i	1.82182	+	1.82182i
$204$		0			0
$205$	−501493.	+	274183.i	−0.833451	+	0.455676i
$206$		0			0
$207$	533675.	−	533675.i	0.865668	−	0.865668i
$208$		0			0
$209$		−	546363.i		−	0.865198i
$210$		0			0
$211$			45058.2i			0.0696735i	0.999393	+	0.0348368i	$0.0110911\pi$
$211$			45058.2i			0.0696735i	−0.999393	+	0.0348368i	$0.988909\pi$
$212$		0			0
$213$	232009.	−	232009.i	0.350394	−	0.350394i
$214$		0			0
$215$	−834736.	−	244617.i	−1.23155	−	0.360903i
$216$		0			0
$217$	−171397.	−	171397.i	−0.247089	−	0.247089i
$218$		0			0
$219$	49489.1			0.0697267
$220$		0			0
$221$	−122796.			−0.169123
$222$		0			0
$223$	−844061.	−	844061.i	−1.13661	−	1.13661i	−0.989053	−	0.147558i	$-0.952859\pi$
$223$	−844061.	−	844061.i	−1.13661	−	1.13661i	−0.147558	−	0.989053i	$-0.547141\pi$
$224$		0			0
$225$	−533729.	−	342202.i	−0.702852	−	0.450637i
$226$		0			0
$227$	−151574.	+	151574.i	−0.195236	+	0.195236i	−0.797954	−	0.602718i	$-0.794084\pi$
$227$	−151574.	+	151574.i	−0.195236	+	0.195236i	0.602718	+	0.797954i	$0.294084\pi$
$228$		0			0
$229$		−	10167.7i		−	0.0128125i	−0.999979	−	0.00640627i	$-0.997961\pi$
$229$		−	10167.7i		−	0.0128125i	0.999979	−	0.00640627i	$-0.00203919\pi$
$230$		0			0
$231$		−	431874.i		−	0.532509i
$232$		0			0
$233$	796132.	−	796132.i	0.960717	−	0.960717i	−0.0385399	−	0.999257i	$-0.512271\pi$
$233$	796132.	−	796132.i	0.960717	−	0.960717i	0.999257	+	0.0385399i	$0.0122707\pi$
$234$		0			0
$235$	−244649.	+	834846.i	−0.288984	+	0.986136i
$236$		0			0
$237$	−356604.	−	356604.i	−0.412397	−	0.412397i
$238$		0			0
$239$	825827.			0.935178			0.467589	−	0.883946i	$-0.345123\pi$
$239$	825827.			0.935178			0.467589	+	0.883946i	$0.345123\pi$
$240$		0			0
$241$	−725546.			−0.804678			−0.402339	−	0.915491i	$-0.631803\pi$
$241$	−725546.			−0.804678			−0.402339	+	0.915491i	$0.631803\pi$
$242$		0			0
$243$	625950.	+	625950.i	0.680024	+	0.680024i
$244$		0			0
$245$	486945.	+	890643.i	0.518280	+	0.947957i
$246$		0			0
$247$	−795458.	+	795458.i	−0.829612	+	0.829612i
$248$		0			0
$249$			535603.i			0.547450i
$250$		0			0
$251$			825003.i			0.826554i	0.910605	+	0.413277i	$0.135616\pi$
$251$			825003.i			0.826554i	−0.910605	+	0.413277i	$0.864384\pi$
$252$		0			0
$253$	959196.	−	959196.i	0.942120	−	0.942120i
$254$		0			0
$255$	27779.9	+	50810.6i	0.0267535	+	0.0489332i
$256$		0			0
$257$	432976.	+	432976.i	0.408913	+	0.408913i	0.881359	−	0.472446i	$-0.156629\pi$
$257$	432976.	+	432976.i	0.408913	+	0.408913i	−0.472446	+	0.881359i	$0.656629\pi$
$258$		0			0
$259$	1.50329e6			1.39249
$260$		0			0
$261$	−1.64130e6			−1.49138
$262$		0			0
$263$	−394606.	−	394606.i	−0.351783	−	0.351783i	0.508990	−	0.860773i	$-0.330019\pi$
$263$	−394606.	−	394606.i	−0.351783	−	0.351783i	−0.860773	+	0.508990i	$0.830019\pi$
$264$		0			0
$265$	−514127.	+	1.75442e6i	−0.449734	+	1.53468i
$266$		0			0
$267$	530567.	−	530567.i	0.455472	−	0.455472i
$268$		0			0
$269$		−	1.34502e6i		−	1.13331i	−0.823955	−	0.566655i	$-0.808237\pi$
$269$		−	1.34502e6i		−	1.13331i	0.823955	−	0.566655i	$-0.191763\pi$
$270$		0			0
$271$		−	2.08722e6i		−	1.72642i	−0.504847	−	0.863209i	$-0.668451\pi$
$271$		−	2.08722e6i		−	1.72642i	0.504847	−	0.863209i	$-0.331549\pi$
$272$		0			0
$273$	−628771.	+	628771.i	−0.510606	+	0.510606i
$274$		0			0
$275$	−959292.	−	615054.i	−0.764925	−	0.490435i
$276$		0			0
$277$	1.30227e6	+	1.30227e6i	1.01977	+	1.01977i	0.999801	+	0.0199682i	$0.00635651\pi$
$277$	1.30227e6	+	1.30227e6i	1.01977	+	1.01977i	0.0199682	+	0.999801i	$0.493643\pi$
$278$		0			0
$279$	262995.			0.202272
$280$		0			0
$281$	765832.			0.578586			0.289293	−	0.957241i	$-0.406580\pi$
$281$	765832.			0.578586			0.289293	+	0.957241i	$0.406580\pi$
$282$		0			0
$283$	829895.	+	829895.i	0.615967	+	0.615967i	0.944494	−	0.328528i	$-0.106552\pi$
$283$	829895.	+	829895.i	0.615967	+	0.615967i	−0.328528	+	0.944494i	$0.606552\pi$
$284$		0			0
$285$	509100.	+	149190.i	0.371271	+	0.108800i
$286$		0			0
$287$	−1.35186e6	+	1.35186e6i	−0.968786	+	0.968786i
$288$		0			0
$289$		−	1.39311e6i		−	0.981160i
$290$		0			0
$291$		−	41924.6i		−	0.0290226i
$292$		0			0
$293$	−506267.	+	506267.i	−0.344517	+	0.344517i	−0.858062	−	0.513545i	$-0.828332\pi$
$293$	−506267.	+	506267.i	−0.344517	+	0.344517i	0.513545	+	0.858062i	$0.328332\pi$
$294$		0			0
$295$	309547.	−	169240.i	0.207096	−	0.113226i
$296$		0			0
$297$	728191.	+	728191.i	0.479021	+	0.479021i
$298$		0			0
$299$	−2.79302e6			−1.80674
$300$		0			0
$301$	−2.90959e6			−1.85104
$302$		0			0
$303$	242467.	+	242467.i	0.151721	+	0.151721i
$304$		0			0
$305$	1.62307e6	−	887387.i	0.999050	−	0.546215i
$306$		0			0
$307$	−432884.	+	432884.i	−0.262135	+	0.262135i	−0.825921	−	0.563786i	$-0.809344\pi$
$307$	−432884.	+	432884.i	−0.262135	+	0.262135i	0.563786	+	0.825921i	$0.309344\pi$
$308$		0			0
$309$		−	178701.i		−	0.106471i
$310$		0			0
$311$		−	1.28163e6i		−	0.751383i	−0.926745	−	0.375692i	$-0.877405\pi$
$311$		−	1.28163e6i		−	0.751383i	0.926745	−	0.375692i	$-0.122595\pi$
$312$		0			0
$313$	−1.08747e6	+	1.08747e6i	−0.627416	+	0.627416i	−0.947417	−	0.320001i	$-0.896317\pi$
$313$	−1.08747e6	+	1.08747e6i	−0.627416	+	0.627416i	0.320001	+	0.947417i	$0.396317\pi$
$314$		0			0
$315$	−2.03516e6	−	596397.i	−1.15564	−	0.338656i
$316$		0			0
$317$	599568.	+	599568.i	0.335112	+	0.335112i	0.854524	−	0.519412i	$-0.173849\pi$
$317$	599568.	+	599568.i	0.335112	+	0.335112i	−0.519412	+	0.854524i	$0.673849\pi$
$318$		0			0
$319$	−2.94998e6			−1.62309
$320$		0			0
$321$	−98117.1			−0.0531474
$322$		0			0
$323$	173279.	+	173279.i	0.0924146	+	0.0924146i
$324$		0			0
$325$	501181.	+	2.29211e6i	0.263200	+	1.20373i
$326$		0			0
$327$	−282626.	+	282626.i	−0.146165	+	0.146165i
$328$		0			0
$329$			2.90997e6i			1.48217i
$330$		0			0
$331$		−	3.32067e6i		−	1.66592i	−0.553330	−	0.832962i	$-0.686643\pi$
$331$		−	3.32067e6i		−	1.66592i	0.553330	−	0.832962i	$-0.313357\pi$
$332$		0			0
$333$	−1.15334e6	+	1.15334e6i	−0.569961	+	0.569961i
$334$		0			0
$335$	−596313.	+	2.03487e6i	−0.290310	+	0.990661i
$336$		0			0
$337$	−2.67275e6	−	2.67275e6i	−1.28199	−	1.28199i	−0.939535	−	0.342454i	$-0.888742\pi$
$337$	−2.67275e6	−	2.67275e6i	−1.28199	−	1.28199i	−0.342454	−	0.939535i	$-0.611258\pi$
$338$		0			0
$339$	−216603.			−0.102368
$340$		0			0
$341$	472691.			0.220136
$342$		0			0
$343$	178640.	+	178640.i	0.0819866	+	0.0819866i
$344$		0			0
$345$	631858.	+	1.15570e6i	0.285806	+	0.522752i
$346$		0			0
$347$	941218.	−	941218.i	0.419630	−	0.419630i	−0.465446	−	0.885076i	$-0.654106\pi$
$347$	941218.	−	941218.i	0.419630	−	0.419630i	0.885076	+	0.465446i	$0.154106\pi$
$348$		0			0
$349$			1.16335e6i			0.511268i	0.966774	+	0.255634i	$0.0822841\pi$
$349$			1.16335e6i			0.511268i	−0.966774	+	0.255634i	$0.917716\pi$
$350$		0			0
$351$		−	2.12037e6i		−	0.918637i
$352$		0			0
$353$	112471.	−	112471.i	0.0480402	−	0.0480402i	−0.682679	−	0.730719i	$-0.739185\pi$
$353$	112471.	−	112471.i	0.0480402	−	0.0480402i	0.730719	+	0.682679i	$0.239185\pi$
$354$		0			0
$355$	−1.38921e6	−	2.54092e6i	−0.585055	−	1.07009i
$356$		0			0
$357$	136969.	+	136969.i	0.0568790	+	0.0568790i
$358$		0			0
$359$	2.33314e6			0.955443			0.477721	−	0.878511i	$-0.341463\pi$
$359$	2.33314e6			0.955443			0.477721	+	0.878511i	$0.341463\pi$
$360$		0			0
$361$	−231132.			−0.0933453
$362$		0			0
$363$	−125767.	−	125767.i	−0.0500955	−	0.0500955i
$364$		0			0
$365$	122834.	−	419161.i	0.0482599	−	0.164683i
$366$		0			0
$367$	−1.26022e6	+	1.26022e6i	−0.488408	+	0.488408i	−0.907803	−	0.419396i	$-0.862242\pi$
$367$	−1.26022e6	+	1.26022e6i	−0.488408	+	0.488408i	0.419396	+	0.907803i	$0.362242\pi$
$368$		0			0
$369$		−	2.07432e6i		−	0.793069i
$370$		0			0
$371$			6.11526e6i			2.30664i
$372$		0			0
$373$	2.30854e6	−	2.30854e6i	0.859143	−	0.859143i	−0.132094	−	0.991237i	$-0.542170\pi$
$373$	2.30854e6	−	2.30854e6i	0.859143	−	0.859143i	0.991237	+	0.132094i	$0.0421700\pi$
$374$		0			0
$375$	835051.	−	725918.i	0.306644	−	0.266569i
$376$		0			0
$377$	4.29492e6	+	4.29492e6i	1.55633	+	1.55633i
$378$		0			0
$379$	2.18445e6			0.781167			0.390584	−	0.920567i	$-0.372273\pi$
$379$	2.18445e6			0.781167			0.390584	+	0.920567i	$0.372273\pi$
$380$		0			0
$381$	549701.			0.194006
$382$		0			0
$383$	2.93246e6	+	2.93246e6i	1.02149	+	1.02149i	0.999764	+	0.0217295i	$0.00691727\pi$
$383$	2.93246e6	+	2.93246e6i	1.02149	+	1.02149i	0.0217295	+	0.999764i	$0.493083\pi$
$384$		0			0
$385$	−3.65787e6	−	1.07193e6i	−1.25770	−	0.368565i
$386$		0			0
$387$	2.23226e6	−	2.23226e6i	0.757649	−	0.757649i
$388$		0			0
$389$			746544.i			0.250139i	0.992148	+	0.125069i	$0.0399154\pi$
$389$			746544.i			0.250139i	−0.992148	+	0.125069i	$0.960085\pi$
$390$		0			0
$391$			608420.i			0.201262i
$392$		0			0
$393$	66144.8	−	66144.8i	0.0216030	−	0.0216030i
$394$		0			0
$395$	−3.90546e6	+	2.13525e6i	−1.25945	+	0.688583i
$396$		0			0
$397$	−3.79033e6	−	3.79033e6i	−1.20698	−	1.20698i	−0.972000	−	0.234981i	$-0.924497\pi$
$397$	−3.79033e6	−	3.79033e6i	−1.20698	−	1.20698i	−0.234981	−	0.972000i	$-0.575503\pi$
$398$		0			0
$399$	1.77454e6			0.558024
$400$		0			0
$401$	−1.98755e6			−0.617246			−0.308623	−	0.951184i	$-0.599868\pi$
$401$	−1.98755e6			−0.617246			−0.308623	+	0.951184i	$0.599868\pi$
$402$		0			0
$403$	−688198.	−	688198.i	−0.211082	−	0.211082i
$404$		0			0
$405$	1.54080e6	−	842408.i	0.466777	−	0.255203i
$406$		0			0
$407$	−2.07294e6	+	2.07294e6i	−0.620297	+	0.620297i
$408$		0			0
$409$		−	3.28485e6i		−	0.970973i	−0.874244	−	0.485486i	$-0.838643\pi$
$409$		−	3.28485e6i		−	0.970973i	0.874244	−	0.485486i	$-0.161357\pi$
$410$		0			0
$411$		−	560848.i		−	0.163772i
$412$		0			0
$413$	834439.	−	834439.i	0.240724	−	0.240724i
$414$		0			0
$415$	4.53644e6	+	1.32939e6i	1.29299	+	0.378907i
$416$		0			0
$417$	338747.	+	338747.i	0.0953972	+	0.0953972i
$418$		0			0
$419$	−3.88062e6			−1.07986			−0.539929	−	0.841711i	$-0.681549\pi$
$419$	−3.88062e6			−1.07986			−0.539929	+	0.841711i	$0.681549\pi$
$420$		0			0
$421$	493290.			0.135643			0.0678215	−	0.997697i	$-0.478395\pi$
$421$	493290.			0.135643			0.0678215	+	0.997697i	$0.478395\pi$
$422$		0			0
$423$	−2.23256e6	−	2.23256e6i	−0.606669	−	0.606669i
$424$		0			0
$425$	499305.	−	109175.i	0.134089	−	0.0293192i
$426$		0			0
$427$	4.37527e6	−	4.37527e6i	1.16128	−	1.16128i
$428$		0			0
$429$		−	1.73407e6i		−	0.454908i
$430$		0			0
$431$			4.45998e6i			1.15649i	0.815865	+	0.578243i	$0.196261\pi$
$431$			4.45998e6i			1.15649i	−0.815865	+	0.578243i	$0.803739\pi$
$432$		0			0
$433$	1.91271e6	−	1.91271e6i	0.490264	−	0.490264i	−0.418125	−	0.908389i	$-0.637313\pi$
$433$	1.91271e6	−	1.91271e6i	0.490264	−	0.490264i	0.908389	+	0.418125i	$0.137313\pi$
$434$		0			0
$435$	805522.	−	2.74878e6i	0.204105	−	0.696493i
$436$		0			0
$437$	3.94127e6	+	3.94127e6i	0.987262	+	0.987262i
$438$		0			0
$439$	7.34257e6			1.81839			0.909194	−	0.416372i	$-0.136699\pi$
$439$	7.34257e6			1.81839			0.909194	+	0.416372i	$0.136699\pi$
$440$		0			0
$441$	−3.68397e6			−0.902026
$442$		0			0
$443$	−1.09711e6	−	1.09711e6i	−0.265609	−	0.265609i	0.561719	−	0.827328i	$-0.310140\pi$
$443$	−1.09711e6	−	1.09711e6i	−0.265609	−	0.265609i	−0.827328	+	0.561719i	$0.810140\pi$
$444$		0			0
$445$	−3.17689e6	−	5.81067e6i	−0.760506	−	1.39100i
$446$		0			0
$447$	362441.	−	362441.i	0.0857964	−	0.0857964i
$448$		0			0
$449$		−	3.66093e6i		−	0.856989i	−0.903544	−	0.428494i	$-0.859044\pi$
$449$		−	3.66093e6i		−	0.856989i	0.903544	−	0.428494i	$-0.140956\pi$
$450$		0			0
$451$		−	3.72827e6i		−	0.863109i
$452$		0			0
$453$	−1.73782e6	+	1.73782e6i	−0.397886	+	0.397886i
$454$		0			0
$455$	3.76491e6	+	6.88618e6i	0.852563	+	1.55937i
$456$		0			0
$457$	1.99200e6	+	1.99200e6i	0.446168	+	0.446168i	0.894078	−	0.447911i	$-0.147832\pi$
$457$	1.99200e6	+	1.99200e6i	0.446168	+	0.446168i	−0.447911	+	0.894078i	$0.647832\pi$
$458$		0			0
$459$	−461893.			−0.102332
$460$		0			0
$461$	5.54414e6			1.21502			0.607508	−	0.794314i	$-0.292169\pi$
$461$	5.54414e6			1.21502			0.607508	+	0.794314i	$0.292169\pi$
$462$		0			0
$463$	−3.87266e6	−	3.87266e6i	−0.839570	−	0.839570i	0.149232	−	0.988802i	$-0.452320\pi$
$463$	−3.87266e6	−	3.87266e6i	−0.839570	−	0.839570i	−0.988802	+	0.149232i	$0.952320\pi$
$464$		0			0
$465$	−129073.	+	440452.i	−0.0276824	+	0.0944641i
$466$		0			0
$467$	2.85668e6	−	2.85668e6i	0.606134	−	0.606134i	−0.335799	−	0.941934i	$-0.609006\pi$
$467$	2.85668e6	−	2.85668e6i	0.606134	−	0.606134i	0.941934	+	0.335799i	$0.109006\pi$
$468$		0			0
$469$			7.09283e6i			1.48897i
$470$		0			0
$471$			2.10302e6i			0.436808i
$472$		0			0
$473$	4.01214e6	−	4.01214e6i	0.824561	−	0.824561i
$474$		0			0
$475$	2.52721e6	−	3.94166e6i	0.513935	−	0.801577i
$476$		0			0
$477$	−4.69169e6	−	4.69169e6i	−0.944133	−	0.944133i
$478$		0			0
$479$	4.76395e6			0.948700			0.474350	−	0.880336i	$-0.342683\pi$
$479$	4.76395e6			0.948700			0.474350	+	0.880336i	$0.342683\pi$
$480$		0			0
$481$	6.03604e6			1.18957
$482$		0			0
$483$	3.11538e6	+	3.11538e6i	0.607636	+	0.607636i
$484$		0			0
$485$	−355092.	−	104059.i	−0.0685466	−	0.0200874i
$486$		0			0
$487$	−5.82325e6	+	5.82325e6i	−1.11261	+	1.11261i	−0.119815	+	0.992796i	$0.538230\pi$
$487$	−5.82325e6	+	5.82325e6i	−1.11261	+	1.11261i	−0.992796	+	0.119815i	$0.961770\pi$
$488$		0			0
$489$			8207.72i			0.00155221i
$490$		0			0
$491$			6.32918e6i			1.18480i	0.805645	+	0.592398i	$0.201819\pi$
$491$			6.32918e6i			1.18480i	−0.805645	+	0.592398i	$0.798181\pi$
$492$		0			0
$493$	935587.	−	935587.i	0.173367	−	0.173367i
$494$		0			0
$495$	3.62875e6	−	1.98396e6i	0.665646	−	0.363932i
$496$		0			0
$497$	−6.84951e6	−	6.84951e6i	−1.24385	−	1.24385i
$498$		0			0
$499$	−5.12729e6			−0.921800			−0.460900	−	0.887452i	$-0.652473\pi$
$499$	−5.12729e6			−0.921800			−0.460900	+	0.887452i	$0.652473\pi$
$500$		0			0
$501$	3.25276e6			0.578973
$502$		0			0
$503$	392167.	+	392167.i	0.0691115	+	0.0691115i	0.740818	−	0.671706i	$-0.234438\pi$
$503$	392167.	+	392167.i	0.0691115	+	0.0691115i	−0.671706	+	0.740818i	$0.734438\pi$
$504$		0			0
$505$	2.65545e6	−	1.45183e6i	0.463351	−	0.253330i
$506$		0			0
$507$	−861764.	+	861764.i	−0.148891	+	0.148891i
$508$		0			0
$509$		−	5.56309e6i		−	0.951747i	−0.879514	−	0.475874i	$-0.842132\pi$
$509$		−	5.56309e6i		−	0.951747i	0.879514	−	0.475874i	$-0.157868\pi$
$510$		0			0
$511$		−	1.46104e6i		−	0.247521i
$512$		0			0
$513$	−2.99209e6	+	2.99209e6i	−0.501973	+	0.501973i
$514$		0			0
$515$	−1.51356e6	−	443543.i	−0.251467	−	0.0736916i
$516$		0			0
$517$	−4.01267e6	−	4.01267e6i	−0.660247	−	0.660247i
$518$		0			0
$519$	−2.94231e6			−0.479479
$520$		0			0
$521$	7.40625e6			1.19538			0.597688	−	0.801729i	$-0.296086\pi$
$521$	7.40625e6			1.19538			0.597688	+	0.801729i	$0.296086\pi$
$522$		0			0
$523$	3.98821e6	+	3.98821e6i	0.637564	+	0.637564i	0.949954	−	0.312390i	$-0.101130\pi$
$523$	3.98821e6	+	3.98821e6i	0.637564	+	0.637564i	−0.312390	+	0.949954i	$0.601130\pi$
$524$		0			0
$525$	1.99764e6	−	3.11569e6i	0.316314	−	0.493351i
$526$		0			0
$527$	−149914.	+	149914.i	−0.0235135	+	0.0235135i
$528$		0			0
$529$			7.40226e6i			1.15007i
$530$		0			0
$531$			1.28038e6i			0.197062i
$532$		0			0
$533$	−5.42804e6	+	5.42804e6i	−0.827608	+	0.827608i
$534$		0			0
$535$	−243531.	+	831030.i	−0.0367849	+	0.125526i
$536$		0			0
$537$	−2.93629e6	−	2.93629e6i	−0.439404	−	0.439404i
$538$		0			0
$539$	−6.62134e6			−0.981689
$540$		0			0
$541$	−6.55601e6			−0.963045			−0.481522	−	0.876434i	$-0.659916\pi$
$541$	−6.55601e6			−0.963045			−0.481522	+	0.876434i	$0.659916\pi$
$542$		0			0
$543$	−1.79022e6	−	1.79022e6i	−0.260560	−	0.260560i
$544$		0			0
$545$	1.69229e6	+	3.09526e6i	0.244052	+	0.446381i
$546$		0			0
$547$	5.50795e6	−	5.50795e6i	0.787085	−	0.787085i	−0.193931	−	0.981015i	$-0.562124\pi$
$547$	5.50795e6	−	5.50795e6i	0.787085	−	0.787085i	0.981015	+	0.193931i	$0.0621237\pi$
$548$		0			0
$549$			6.71350e6i			0.950644i
$550$		0			0
$551$		−	1.21212e7i		−	1.70086i
$552$		0			0
$553$	−1.05279e7	+	1.05279e7i	−1.46396	+	1.46396i
$554$		0			0
$555$	−1.36552e6	−	2.49759e6i	−0.188176	−	0.344183i
$556$		0			0
$557$	4.99989e6	+	4.99989e6i	0.682846	+	0.682846i	0.960640	−	0.277795i	$-0.0896035\pi$
$557$	4.99989e6	+	4.99989e6i	0.682846	+	0.682846i	−0.277795	+	0.960640i	$0.589604\pi$
$558$		0			0
$559$	−1.16827e7			−1.58129
$560$		0			0
$561$	−377743.			−0.0506745
$562$		0			0
$563$	774955.	+	774955.i	0.103040	+	0.103040i	0.756747	−	0.653707i	$-0.226787\pi$
$563$	774955.	+	774955.i	0.103040	+	0.103040i	−0.653707	+	0.756747i	$0.726787\pi$
$564$		0			0
$565$	−537617.	+	1.83458e6i	−0.0708520	+	0.241777i
$566$		0			0
$567$	4.15350e6	−	4.15350e6i	0.542571	−	0.542571i
$568$		0			0
$569$			1.51045e7i			1.95580i	0.209066	+	0.977902i	$0.432958\pi$
$569$			1.51045e7i			1.95580i	−0.209066	+	0.977902i	$0.567042\pi$
$570$		0			0
$571$			1.51926e7i			1.95003i	0.222133	+	0.975016i	$0.428698\pi$
$571$			1.51926e7i			1.95003i	−0.222133	+	0.975016i	$0.571302\pi$
$572$		0			0
$573$	−2.92945e6	+	2.92945e6i	−0.372734	+	0.372734i
$574$		0			0
$575$	1.13568e7	−	2.48321e6i	1.43247	−	0.313216i
$576$		0			0
$577$	633112.	+	633112.i	0.0791665	+	0.0791665i	0.745581	−	0.666415i	$-0.232172\pi$
$577$	633112.	+	633112.i	0.0791665	+	0.0791665i	−0.666415	+	0.745581i	$0.732172\pi$
$578$		0			0
$579$	−5.03542e6			−0.624222
$580$		0			0
$581$	1.58124e7			1.94338
$582$		0			0
$583$	−8.43256e6	−	8.43256e6i	−1.02751	−	1.02751i
$584$		0			0
$585$	−8.17162e6	−	2.39467e6i	−0.987231	−	0.289305i
$586$		0			0
$587$	−4.97005e6	+	4.97005e6i	−0.595341	+	0.595341i	−0.939069	−	0.343728i	$-0.888310\pi$
$587$	−4.97005e6	+	4.97005e6i	−0.595341	+	0.595341i	0.343728	+	0.939069i	$0.388310\pi$
$588$		0			0
$589$			1.94225e6i			0.230684i
$590$		0			0
$591$		−	2.74743e6i		−	0.323563i
$592$		0			0
$593$	1.17143e6	−	1.17143e6i	0.136798	−	0.136798i	−0.635392	−	0.772190i	$-0.719162\pi$
$593$	1.17143e6	−	1.17143e6i	0.136798	−	0.136798i	0.772190	+	0.635392i	$0.219162\pi$
$594$		0			0
$595$	1.50006e6	−	820133.i	0.173706	−	0.0949712i
$596$		0			0
$597$	−4.53123e6	−	4.53123e6i	−0.520332	−	0.520332i
$598$		0			0
$599$	−1.47865e7			−1.68384			−0.841918	−	0.539606i	$-0.818573\pi$
$599$	−1.47865e7			−1.68384			−0.841918	+	0.539606i	$0.818573\pi$
$600$		0			0
$601$	9.12282e6			1.03025			0.515125	−	0.857115i	$-0.327745\pi$
$601$	9.12282e6			1.03025			0.515125	+	0.857115i	$0.327745\pi$
$602$		0			0
$603$	−5.44168e6	−	5.44168e6i	−0.609453	−	0.609453i
$604$		0			0
$605$	−1.37737e6	+	753056.i	−0.152990	+	0.0836448i
$606$		0			0
$607$	−9.54466e6	+	9.54466e6i	−1.05145	+	1.05145i	−0.0528482	+	0.998603i	$0.516830\pi$
$607$	−9.54466e6	+	9.54466e6i	−1.05145	+	1.05145i	−0.998603	+	0.0528482i	$0.983170\pi$
$608$		0			0
$609$		−	9.58126e6i		−	1.04684i
$610$		0			0
$611$			1.16842e7i			1.26618i
$612$		0			0
$613$	−5.06559e6	+	5.06559e6i	−0.544476	+	0.544476i	−0.924838	−	0.380362i	$-0.875799\pi$
$613$	−5.06559e6	+	5.06559e6i	−0.544476	+	0.544476i	0.380362	+	0.924838i	$0.375799\pi$
$614$		0			0
$615$	3.47399e6	+	1.01804e6i	0.370374	+	0.108537i
$616$		0			0
$617$	126176.	+	126176.i	0.0133433	+	0.0133433i	0.713747	−	0.700404i	$-0.246997\pi$
$617$	126176.	+	126176.i	0.0133433	+	0.0133433i	−0.700404	+	0.713747i	$0.746997\pi$
$618$		0			0
$619$	1.26023e7			1.32198			0.660989	−	0.750396i	$-0.270137\pi$
$619$	1.26023e7			1.32198			0.660989	+	0.750396i	$0.270137\pi$
$620$		0			0
$621$	−1.05058e7			−1.09320
$622$		0			0
$623$	−1.56637e7	−	1.56637e7i	−1.61687	−	1.61687i
$624$		0			0
$625$	−4.07573e6	−	8.87445e6i	−0.417355	−	0.908744i
$626$		0			0
$627$	−2.44697e6	+	2.44697e6i	−0.248577	+	0.248577i
$628$		0			0
$629$		−	1.31487e6i		−	0.132512i
$630$		0			0
$631$		−	709073.i		−	0.0708953i	−0.999372	−	0.0354477i	$-0.988714\pi$
$631$		−	709073.i		−	0.0708953i	0.999372	−	0.0354477i	$-0.0112857\pi$
$632$		0			0
$633$	201800.	−	201800.i	0.0200176	−	0.0200176i
$634$		0			0
$635$	1.36438e6	−	4.65584e6i	0.134277	−	0.458209i
$636$		0			0
$637$	9.64011e6	+	9.64011e6i	0.941311	+	0.941311i
$638$		0			0
$639$	1.05100e7			1.01824
$640$		0			0
$641$	767242.			0.0737543			0.0368771	−	0.999320i	$-0.488259\pi$
$641$	767242.			0.0737543			0.0368771	+	0.999320i	$0.488259\pi$
$642$		0			0
$643$	−4.82695e6	−	4.82695e6i	−0.460411	−	0.460411i	0.438379	−	0.898790i	$-0.355553\pi$
$643$	−4.82695e6	−	4.82695e6i	−0.460411	−	0.460411i	−0.898790	+	0.438379i	$0.855553\pi$
$644$		0			0
$645$	2.64294e6	+	4.83406e6i	0.250143	+	0.457522i
$646$		0			0
$647$	−1.21492e6	+	1.21492e6i	−0.114100	+	0.114100i	−0.761852	−	0.647751i	$-0.775710\pi$
$647$	−1.21492e6	+	1.21492e6i	−0.114100	+	0.114100i	0.647751	+	0.761852i	$0.275710\pi$
$648$		0			0
$649$			2.30128e6i			0.214465i
$650$		0			0
$651$			1.53526e6i			0.141981i
$652$		0			0
$653$	3.39942e6	−	3.39942e6i	0.311977	−	0.311977i	−0.533698	−	0.845675i	$-0.679198\pi$
$653$	3.39942e6	−	3.39942e6i	0.311977	−	0.311977i	0.845675	+	0.533698i	$0.179198\pi$
$654$		0			0
$655$	−396057.	−	724405.i	−0.0360707	−	0.0659748i
$656$		0			0
$657$	1.12093e6	+	1.12093e6i	0.101313	+	0.101313i
$658$		0			0
$659$	−7.67897e6			−0.688794			−0.344397	−	0.938824i	$-0.611917\pi$
$659$	−7.67897e6			−0.688794			−0.344397	+	0.938824i	$0.611917\pi$
$660$		0			0
$661$	341343.			0.0303869			0.0151935	−	0.999885i	$-0.495164\pi$
$661$	341343.			0.0303869			0.0151935	+	0.999885i	$0.495164\pi$
$662$		0			0
$663$	549962.	+	549962.i	0.0485902	+	0.0485902i
$664$		0			0
$665$	4.40448e6	−	1.50299e7i	0.386225	−	1.31796i
$666$		0			0
$667$	2.12801e7	−	2.12801e7i	1.85208	−	1.85208i
$668$		0			0
$669$			7.56053e6i			0.653111i
$670$		0			0
$671$			1.20664e7i			1.03460i
$672$		0			0
$673$	−6.48305e6	+	6.48305e6i	−0.551750	+	0.551750i	−0.926946	−	0.375196i	$-0.877575\pi$
$673$	−6.48305e6	+	6.48305e6i	−0.551750	+	0.551750i	0.375196	+	0.926946i	$0.377575\pi$
$674$		0			0
$675$	1.88517e6	+	8.62170e6i	0.159254	+	0.728339i
$676$		0			0
$677$	1.36747e6	+	1.36747e6i	0.114669	+	0.114669i	0.762113	−	0.647444i	$-0.224162\pi$
$677$	1.36747e6	+	1.36747e6i	0.114669	+	0.114669i	−0.647444	+	0.762113i	$0.724162\pi$
$678$		0			0
$679$	−1.23772e6			−0.103026
$680$		0			0
$681$	1.35769e6			0.112185
$682$		0			0
$683$	9.62135e6	+	9.62135e6i	0.789195	+	0.789195i	0.981362	−	0.192167i	$-0.0615516\pi$
$683$	9.62135e6	+	9.62135e6i	0.789195	+	0.789195i	−0.192167	+	0.981362i	$0.561552\pi$
$684$		0			0
$685$	−4.75026e6	−	1.39205e6i	−0.386804	−	0.113352i
$686$		0			0
$687$	−45537.8	+	45537.8i	−0.00368112	+	0.00368112i
$688$		0			0
$689$			2.45542e7i			1.97050i
$690$		0			0
$691$			2.18218e7i			1.73859i	0.494297	+	0.869293i	$0.335425\pi$
$691$			2.18218e7i			1.73859i	−0.494297	+	0.869293i	$0.664575\pi$
$692$		0			0
$693$	9.78193e6	−	9.78193e6i	0.773734	−	0.773734i
$694$		0			0
$695$	3.70990e6	−	2.02833e6i	0.291340	−	0.159285i
$696$		0			0
$697$	1.18242e6	+	1.18242e6i	0.0921915	+	0.0921915i
$698$		0			0
$699$	−7.13121e6			−0.552040
$700$		0			0
$701$	6.79404e6			0.522195			0.261098	−	0.965312i	$-0.415916\pi$
$701$	6.79404e6			0.522195			0.261098	+	0.965312i	$0.415916\pi$
$702$		0			0
$703$	−8.51755e6	−	8.51755e6i	−0.650019	−	0.650019i
$704$		0			0
$705$	4.83469e6	−	2.64329e6i	0.366350	−	0.200296i
$706$		0			0
$707$	7.15824e6	−	7.15824e6i	0.538589	−	0.538589i
$708$		0			0
$709$		−	1.96118e7i		−	1.46521i	−0.680652	−	0.732607i	$-0.738303\pi$
$709$		−	1.96118e7i		−	1.46521i	0.680652	−	0.732607i	$-0.261697\pi$
$710$		0			0
$711$		−	1.61542e7i		−	1.19842i
$712$		0			0
$713$	−3.40983e6	+	3.40983e6i	−0.251194	+	0.251194i
$714$		0			0
$715$	−1.46872e7	−	4.30404e6i	−1.07442	−	0.314855i
$716$		0			0
$717$	−3.69860e6	−	3.69860e6i	−0.268682	−	0.268682i
$718$		0			0
$719$	1.15930e7			0.836321			0.418160	−	0.908373i	$-0.362675\pi$
$719$	1.15930e7			0.836321			0.418160	+	0.908373i	$0.362675\pi$
$720$		0			0
$721$	−5.27571e6			−0.377957
$722$		0			0
$723$	3.24947e6	+	3.24947e6i	0.231189	+	0.231189i
$724$		0			0
$725$	−2.12822e7	−	1.36452e7i	−1.50374	−	0.964127i
$726$		0			0
$727$	9.10769e6	−	9.10769e6i	0.639105	−	0.639105i	−0.311230	−	0.950335i	$-0.600741\pi$
$727$	9.10769e6	−	9.10769e6i	0.639105	−	0.639105i	0.950335	+	0.311230i	$0.100741\pi$
$728$		0			0
$729$			2.02658e6i			0.141236i
$730$		0			0
$731$			2.54490e6i			0.176148i
$732$		0			0
$733$	770955.	−	770955.i	0.0529992	−	0.0529992i	−0.680110	−	0.733110i	$-0.738068\pi$
$733$	770955.	−	770955.i	0.0529992	−	0.0529992i	0.733110	+	0.680110i	$0.238068\pi$
$734$		0			0
$735$	1.80803e6	−	6.16975e6i	0.123449	−	0.421259i
$736$		0			0
$737$	−9.78056e6	−	9.78056e6i	−0.663277	−	0.663277i
$738$		0			0
$739$	6.71284e6			0.452163			0.226081	−	0.974108i	$-0.427408\pi$
$739$	6.71284e6			0.452163			0.226081	+	0.974108i	$0.427408\pi$
$740$		0			0
$741$	7.12517e6			0.476705
$742$		0			0
$743$	8.86339e6	+	8.86339e6i	0.589017	+	0.589017i	0.937365	−	0.348348i	$-0.113257\pi$
$743$	8.86339e6	+	8.86339e6i	0.589017	+	0.589017i	−0.348348	+	0.937365i	$0.613257\pi$
$744$		0			0
$745$	−2.17020e6	−	3.96939e6i	−0.143255	−	0.262019i
$746$		0			0
$747$	−1.21314e7	+	1.21314e7i	−0.795444	+	0.795444i
$748$		0			0
$749$			2.89667e6i			0.188666i
$750$		0			0
$751$			1.43379e7i			0.927654i	0.885926	+	0.463827i	$0.153524\pi$
$751$			1.43379e7i			0.927654i	−0.885926	+	0.463827i	$0.846476\pi$
$752$		0			0
$753$	3.69491e6	−	3.69491e6i	0.237474	−	0.237474i
$754$		0			0
$755$	1.04056e7	+	1.90323e7i	0.664354	+	1.21513i
$756$		0			0
$757$	−6.93153e6	−	6.93153e6i	−0.439632	−	0.439632i	0.452256	−	0.891888i	$-0.350619\pi$
$757$	−6.93153e6	−	6.93153e6i	−0.439632	−	0.439632i	−0.891888	+	0.452256i	$0.850619\pi$
$758$		0			0
$759$	−8.59183e6			−0.541354
$760$		0			0
$761$	2.27072e6			0.142135			0.0710676	−	0.997472i	$-0.477359\pi$
$761$	2.27072e6			0.142135			0.0710676	+	0.997472i	$0.477359\pi$
$762$		0			0
$763$	8.34383e6	+	8.34383e6i	0.518865	+	0.518865i
$764$		0			0
$765$	−521645.	+	1.78007e6i	−0.0322271	+	0.109973i
$766$		0			0
$767$	3.35046e6	−	3.35046e6i	0.205644	−	0.205644i
$768$		0			0
$769$		−	2.99725e7i		−	1.82771i	−0.406040	−	0.913855i	$-0.633091\pi$
$769$		−	2.99725e7i		−	1.82771i	0.406040	−	0.913855i	$-0.366909\pi$
$770$		0			0
$771$		−	3.87830e6i		−	0.234966i
$772$		0			0
$773$	−6.19757e6	+	6.19757e6i	−0.373055	+	0.373055i	−0.868589	−	0.495534i	$-0.834972\pi$
$773$	−6.19757e6	+	6.19757e6i	−0.373055	+	0.373055i	0.495534	+	0.868589i	$0.334972\pi$
$774$		0			0
$775$	3.41017e6	+	2.18644e6i	0.203949	+	0.130763i
$776$		0			0
$777$	−6.73271e6	−	6.73271e6i	−0.400071	−	0.400071i
$778$		0			0
$779$	1.53192e7			0.904465
$780$		0			0
$781$	1.88901e7			1.10817
$782$		0			0
$783$	1.61552e7	+	1.61552e7i	0.941688	+	0.941688i
$784$		0			0
$785$	1.78121e7	+	5.21978e6i	1.03167	+	0.302328i
$786$		0			0
$787$	2.08578e7	−	2.08578e7i	1.20041	−	1.20041i	0.226374	−	0.974040i	$-0.427313\pi$
$787$	2.08578e7	−	2.08578e7i	1.20041	−	1.20041i	0.974040	−	0.226374i	$-0.0726872\pi$
$788$		0			0
$789$			3.53461e6i			0.202139i
$790$		0			0
$791$			6.39467e6i			0.363393i
$792$		0			0
$793$	1.75677e7	−	1.75677e7i	0.992047	−	0.992047i
$794$		0			0
$795$	1.01600e7	−	5.55484e6i	0.570135	−	0.311712i
$796$		0			0
$797$	−5.04266e6	−	5.04266e6i	−0.281199	−	0.281199i	0.552388	−	0.833587i	$-0.313717\pi$
$797$	−5.04266e6	−	5.04266e6i	−0.281199	−	0.281199i	−0.833587	+	0.552388i	$0.813717\pi$
$798$		0			0
$799$	2.54524e6			0.141046
$800$		0			0
$801$	2.40347e7			1.32360
$802$		0			0
$803$	2.01469e6	+	2.01469e6i	0.110260	+	0.110260i
$804$		0			0
$805$	3.41191e7	−	1.86541e7i	1.85570	−	1.01457i
$806$		0			0
$807$	−6.02390e6	+	6.02390e6i	−0.325607	+	0.325607i
$808$		0			0
$809$		−	6.96850e6i		−	0.374342i	−0.982327	−	0.187171i	$-0.940068\pi$
$809$		−	6.96850e6i		−	0.374342i	0.982327	−	0.187171i	$-0.0599318\pi$
$810$		0			0
$811$		−	1.97275e7i		−	1.05322i	−0.850107	−	0.526610i	$-0.823463\pi$
$811$		−	1.97275e7i		−	1.05322i	0.850107	−	0.526610i	$-0.176537\pi$
$812$		0			0
$813$	−9.34797e6	+	9.34797e6i	−0.496010	+	0.496010i
$814$		0			0
$815$	69517.5	+	20371.9i	0.00366607	+	0.00107433i
$816$		0			0
$817$	1.64856e7	+	1.64856e7i	0.864071	+	0.864071i
$818$		0			0
$819$	−2.84833e7			−1.48382
$820$		0			0
$821$	−3.14861e7			−1.63028			−0.815138	−	0.579267i	$-0.803339\pi$
$821$	−3.14861e7			−1.63028			−0.815138	+	0.579267i	$0.803339\pi$
$822$		0			0
$823$	1.04816e7	+	1.04816e7i	0.539420	+	0.539420i	0.923359	−	0.383938i	$-0.125432\pi$
$823$	1.04816e7	+	1.04816e7i	0.539420	+	0.539420i	−0.383938	+	0.923359i	$0.625432\pi$
$824$		0			0
$825$	1.54172e6	+	7.05096e6i	0.0788627	+	0.360673i
$826$		0			0
$827$	−1.90665e7	+	1.90665e7i	−0.969412	+	0.969412i	−0.999546	−	0.0301342i	$-0.990407\pi$
$827$	−1.90665e7	+	1.90665e7i	−0.969412	+	0.969412i	0.0301342	+	0.999546i	$0.490407\pi$
$828$		0			0
$829$			8.42335e6i			0.425695i	0.977085	+	0.212847i	$0.0682737\pi$
$829$			8.42335e6i			0.425695i	−0.977085	+	0.212847i	$0.931726\pi$
$830$		0			0
$831$		−	1.16649e7i		−	0.585972i
$832$		0			0
$833$	2.09996e6	−	2.09996e6i	0.104857	−	0.104857i
$834$		0			0
$835$	8.07350e6	−	2.75502e7i	0.400724	−	1.36744i
$836$		0			0
$837$	−2.58863e6	−	2.58863e6i	−0.127719	−	0.127719i
$838$		0			0
$839$	1.88805e7			0.925993			0.462997	−	0.886360i	$-0.346774\pi$
$839$	1.88805e7			0.925993			0.462997	+	0.886360i	$0.346774\pi$
$840$		0			0
$841$	−4.49351e7			−2.19076
$842$		0			0
$843$	−3.42990e6	−	3.42990e6i	−0.166231	−	0.166231i
$844$		0			0
$845$	5.16001e6	+	9.43788e6i	0.248604	+	0.454708i
$846$		0			0
$847$	−3.71295e6	+	3.71295e6i	−0.177832	+	0.177832i
$848$		0			0
$849$		−	7.43364e6i		−	0.353942i
$850$		0			0
$851$		−	2.99068e7i		−	1.41562i
$852$		0			0
$853$	−1.64158e7	+	1.64158e7i	−0.772486	+	0.772486i	−0.978541	−	0.206054i	$-0.933938\pi$
$853$	−1.64158e7	+	1.64158e7i	−0.772486	+	0.772486i	0.206054	+	0.978541i	$0.433938\pi$
$854$		0			0
$855$	8.15195e6	+	1.49103e7i	0.381370	+	0.697541i
$856$		0			0
$857$	−4.36397e6	−	4.36397e6i	−0.202969	−	0.202969i	0.598302	−	0.801271i	$-0.295842\pi$
$857$	−4.36397e6	−	4.36397e6i	−0.202969	−	0.202969i	−0.801271	+	0.598302i	$0.795842\pi$
$858$		0			0
$859$	−1.28095e7			−0.592309			−0.296155	−	0.955140i	$-0.595704\pi$
$859$	−1.28095e7			−0.592309			−0.296155	+	0.955140i	$0.595704\pi$
$860$		0			0
$861$	1.21091e7			0.556677
$862$		0			0
$863$	−1.52761e7	−	1.52761e7i	−0.698209	−	0.698209i	0.265815	−	0.964024i	$-0.414359\pi$
$863$	−1.52761e7	−	1.52761e7i	−0.698209	−	0.698209i	−0.964024	+	0.265815i	$0.914359\pi$
$864$		0			0
$865$	−7.30293e6	+	2.49207e7i	−0.331862	+	1.13245i
$866$		0			0
$867$	−6.23926e6	+	6.23926e6i	−0.281893	+	0.281893i
$868$		0			0
$869$		−	2.90345e7i		−	1.30426i
$870$		0			0
$871$			2.84793e7i			1.27199i
$872$		0			0
$873$	949591.	−	949591.i	0.0421698	−	0.0421698i
$874$		0			0
$875$	−2.14310e7	−	2.46528e7i	−0.946285	−	1.08855i
$876$		0			0
$877$	1.73235e7	+	1.73235e7i	0.760564	+	0.760564i	0.976424	−	0.215861i	$-0.0692557\pi$
$877$	1.73235e7	+	1.73235e7i	0.760564	+	0.760564i	−0.215861	+	0.976424i	$0.569256\pi$
$878$		0			0
$879$	4.53480e6			0.197964
$880$		0			0
$881$	−1.97411e7			−0.856905			−0.428452	−	0.903564i	$-0.640941\pi$
$881$	−1.97411e7			−0.856905			−0.428452	+	0.903564i	$0.640941\pi$
$882$		0			0
$883$	−1.28646e7	−	1.28646e7i	−0.555258	−	0.555258i	0.372695	−	0.927954i	$-0.378434\pi$
$883$	−1.28646e7	−	1.28646e7i	−0.555258	−	0.555258i	−0.927954	+	0.372695i	$0.878434\pi$
$884$		0			0
$885$	−2.14432e6	−	628388.i	−0.0920305	−	0.0269693i
$886$		0			0
$887$	2.64447e6	−	2.64447e6i	0.112857	−	0.112857i	−0.648423	−	0.761280i	$-0.724571\pi$
$887$	2.64447e6	−	2.64447e6i	0.112857	−	0.112857i	0.761280	+	0.648423i	$0.224571\pi$
$888$		0			0
$889$		−	1.62286e7i		−	0.688694i
$890$		0			0
$891$			1.14548e7i			0.483387i
$892$		0			0
$893$	1.64878e7	−	1.64878e7i	0.691883	−	0.691883i
$894$		0			0
$895$	−3.21577e7	+	1.75817e7i	−1.34192	+	0.733676i
$896$		0			0
$897$	1.25090e7	+	1.25090e7i	0.519087	+	0.519087i
$898$		0			0
$899$	1.04868e7			0.432757
$900$		0			0
$901$	5.34878e6			0.219504
$902$		0			0
$903$	1.30311e7	+	1.30311e7i	0.531815	+	0.531815i
$904$		0			0
$905$	−1.96062e7	+	1.07194e7i	−0.795741	+	0.435058i
$906$		0			0
$907$	−1.84989e7	+	1.84989e7i	−0.746668	+	0.746668i	−0.973852	−	0.227184i	$-0.927048\pi$
$907$	−1.84989e7	+	1.84989e7i	−0.746668	+	0.746668i	0.227184	+	0.973852i	$0.427048\pi$
$908$		0			0
$909$			1.09837e7i			0.440900i
$910$		0			0
$911$		−	3.51079e6i		−	0.140155i	−0.997542	−	0.0700775i	$-0.977675\pi$
$911$		−	3.51079e6i		−	0.140155i	0.997542	−	0.0700775i	$-0.0223247\pi$
$912$		0			0
$913$	−2.18043e7	+	2.18043e7i	−0.865694	+	0.865694i
$914$		0			0
$915$	−1.12435e7	−	3.29487e6i	−0.443964	−	0.130102i
$916$		0			0
$917$	−1.95276e6	−	1.95276e6i	−0.0766878	−	0.0766878i
$918$		0			0
$919$	−1.18671e7			−0.463506			−0.231753	−	0.972775i	$-0.574446\pi$
$919$	−1.18671e7			−0.463506			−0.231753	+	0.972775i	$0.574446\pi$
$920$		0			0
$921$	3.87748e6			0.150626
$922$		0			0
$923$	−2.75023e7	−	2.75023e7i	−1.06259	−	1.06259i
$924$		0			0
$925$	−2.45433e7	+	5.36650e6i	−0.943146	+	0.206223i
$926$		0			0
$927$	4.04757e6	−	4.04757e6i	0.154702	−	0.154702i
$928$		0			0
$929$			4.20018e7i			1.59672i	0.602181	+	0.798359i	$0.294298\pi$
$929$			4.20018e7i			1.59672i	−0.602181	+	0.798359i	$0.705702\pi$
$930$		0			0
$931$		−	2.72066e7i		−	1.02873i
$932$		0			0
$933$	−5.73998e6	+	5.73998e6i	−0.215877	+	0.215877i
$934$		0			0
$935$	−937574.	+	3.19940e6i	−0.0350733	+	0.119685i
$936$		0			0
$937$	−479102.	−	479102.i	−0.0178270	−	0.0178270i	0.698137	−	0.715964i	$-0.254013\pi$
$937$	−479102.	−	479102.i	−0.0178270	−	0.0178270i	−0.715964	+	0.698137i	$0.754013\pi$
$938$		0			0
$939$	9.74080e6			0.360521
$940$		0			0
$941$	−2.11465e6			−0.0778510			−0.0389255	−	0.999242i	$-0.512394\pi$
$941$	−2.11465e6			−0.0778510			−0.0389255	+	0.999242i	$0.512394\pi$
$942$		0			0
$943$	2.68944e7	+	2.68944e7i	0.984878	+	0.984878i
$944$		0			0
$945$	1.41616e7	+	2.59021e7i	0.515860	+	0.943531i
$946$		0			0
$947$	−5.10856e6	+	5.10856e6i	−0.185107	+	0.185107i	−0.793577	−	0.608470i	$-0.791784\pi$
$947$	−5.10856e6	+	5.10856e6i	−0.185107	+	0.185107i	0.608470	+	0.793577i	$0.291784\pi$
$948$		0			0
$949$		−	5.86643e6i		−	0.211450i
$950$		0			0
$951$		−	5.37052e6i		−	0.192560i
$952$		0			0
$953$	3.45103e7	−	3.45103e7i	1.23088	−	1.23088i	0.267255	−	0.963626i	$-0.413884\pi$
$953$	3.45103e7	−	3.45103e7i	1.23088	−	1.23088i	0.963626	−	0.267255i	$-0.0861165\pi$
$954$		0			0
$955$	1.75407e7	+	3.20827e7i	0.622357	+	1.13832i
$956$		0			0
$957$	1.32119e7	+	1.32119e7i	0.466323	+	0.466323i
$958$		0			0
$959$	−1.65577e7			−0.581370
$960$		0			0
$961$	2.69488e7			0.941306
$962$		0			0
$963$	−2.22235e6	−	2.22235e6i	−0.0772231	−	0.0772231i
$964$		0			0
$965$	−1.24981e7	+	4.26489e7i	−0.432043	+	1.47431i
$966$		0			0
$967$	−2.57989e7	+	2.57989e7i	−0.887228	+	0.887228i	−0.994256	−	0.107028i	$-0.965867\pi$
$967$	−2.57989e7	+	2.57989e7i	−0.887228	+	0.887228i	0.107028	+	0.994256i	$0.465867\pi$
$968$		0			0
$969$		−	1.55212e6i		−	0.0531026i
$970$		0			0
$971$		−	5.62810e7i		−	1.91564i	−0.287372	−	0.957819i	$-0.592782\pi$
$971$		−	5.62810e7i		−	1.91564i	0.287372	−	0.957819i	$-0.407218\pi$
$972$		0			0
$973$	1.00007e7	−	1.00007e7i	0.338647	−	0.338647i
$974$		0			0
$975$	8.02098e6	−	1.25102e7i	0.270219	−	0.421457i
$976$		0			0
$977$	−8.72864e6	−	8.72864e6i	−0.292557	−	0.292557i	0.545533	−	0.838089i	$-0.316327\pi$
$977$	−8.72864e6	−	8.72864e6i	−0.292557	−	0.292557i	−0.838089	+	0.545533i	$0.816327\pi$
$978$		0			0
$979$	4.31985e7			1.44050
$980$		0			0
$981$	−1.28029e7			−0.424753
$982$		0			0
$983$	−2.12428e6	−	2.12428e6i	−0.0701179	−	0.0701179i	0.671178	−	0.741296i	$-0.265789\pi$
$983$	−2.12428e6	−	2.12428e6i	−0.0701179	−	0.0701179i	−0.741296	+	0.671178i	$0.765789\pi$
$984$		0			0
$985$	−2.32701e7	−	6.81925e6i	−0.764202	−	0.223947i
$986$		0			0
$987$	1.30328e7	−	1.30328e7i	0.425838	−	0.425838i
$988$		0			0
$989$			5.78843e7i			1.88178i
$990$		0			0
$991$			1.56428e7i			0.505978i	0.967469	+	0.252989i	$0.0814137\pi$
$991$			1.56428e7i			0.505978i	−0.967469	+	0.252989i	$0.918586\pi$
$992$		0			0
$993$	−1.48721e7	+	1.48721e7i	−0.478630	+	0.478630i
$994$		0			0
$995$	−4.96252e7	+	2.71318e7i	−1.58908	+	0.868802i
$996$		0			0
$997$	−1.05485e6	−	1.05485e6i	−0.0336087	−	0.0336087i	0.690103	−	0.723711i	$-0.257565\pi$
$997$	−1.05485e6	−	1.05485e6i	−0.0336087	−	0.0336087i	−0.723711	+	0.690103i	$0.757565\pi$
$998$		0			0
$999$	2.27043e7			0.719772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.6.n.c.127.3	yes	16
4.3	odd	2		160.6.n.d.127.6	yes	16
5.3	odd	4		160.6.n.d.63.6	yes	16
20.3	even	4	inner	160.6.n.c.63.3	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.6.n.c.63.3	✓	16	20.3	even	4	inner
160.6.n.c.127.3	yes	16	1.1	even	1	trivial
160.6.n.d.63.6	yes	16	5.3	odd	4
160.6.n.d.127.6	yes	16	4.3	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-4.47866 - 4.47866i) q^{3} +(-49.0494 + 26.8170i) q^{5} +(-132.222 + 132.222i) q^{7} -202.883i q^{9} +O(q^{10})\)	\(q+(-4.47866 - 4.47866i) q^{3} +(-49.0494 + 26.8170i) q^{5} +(-132.222 + 132.222i) q^{7} -202.883i q^{9} -364.650i q^{11} +(-530.900 + 530.900i) q^{13} +(339.780 + 99.5716i) q^{15} +(115.649 + 115.649i) q^{17} +1498.32 q^{19} +1184.35 q^{21} +(2630.46 + 2630.46i) q^{23} +(1686.70 - 2630.72i) q^{25} +(-1996.96 + 1996.96i) q^{27} -8089.88i q^{29} +1296.29i q^{31} +(-1633.14 + 1633.14i) q^{33} +(2939.61 - 10031.2i) q^{35} +(-5684.73 - 5684.73i) q^{37} +4755.44 q^{39} +10224.2 q^{41} +(11002.7 + 11002.7i) q^{43} +(5440.72 + 9951.31i) q^{45} +(11004.2 - 11004.2i) q^{47} -18158.1i q^{49} -1035.91i q^{51} +(23125.1 - 23125.1i) q^{53} +(9778.82 + 17885.9i) q^{55} +(-6710.47 - 6710.47i) q^{57} -6310.91 q^{59} -33090.5 q^{61} +(26825.5 + 26825.5i) q^{63} +(11803.2 - 40277.5i) q^{65} +(26821.8 - 26821.8i) q^{67} -23561.8i q^{69} +51803.3i q^{71} +(-5524.99 + 5524.99i) q^{73} +(-19336.2 + 4227.95i) q^{75} +(48214.6 + 48214.6i) q^{77} +79623.0 q^{79} -31413.2 q^{81} +(-59795.0 - 59795.0i) q^{83} +(-8773.88 - 2571.16i) q^{85} +(-36231.8 + 36231.8i) q^{87} +118466. i q^{89} -140393. i q^{91} +(5805.63 - 5805.63i) q^{93} +(-73491.8 + 40180.5i) q^{95} +(4680.48 + 4680.48i) q^{97} -73981.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 10 q^{3} - 42 q^{5} + 86 q^{7}+O(q^{10}) \) 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