LMFDB - Embedded newform 240.5.bg.b.193.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,5,Mod(97,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("240.97");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	240.bg (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.8087911401$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			193.2
Root			$-1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	240.193
Dual form			240.5.bg.b.97.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.67423 + 3.67423i) q^{3} +(24.6742 - 4.02270i) q^{5} +(-44.4393 + 44.4393i) q^{7} +27.0000i q^{9} +O(q^{10})$	\(q+(3.67423 + 3.67423i) q^{3} +(24.6742 - 4.02270i) q^{5} +(-44.4393 + 44.4393i) q^{7} +27.0000i q^{9} -167.439 q^{11} +(-223.621 - 223.621i) q^{13} +(105.439 + 75.8786i) q^{15} +(-71.0148 + 71.0148i) q^{17} -272.211i q^{19} -326.561 q^{21} +(-87.6821 - 87.6821i) q^{23} +(592.636 - 198.514i) q^{25} +(-99.2043 + 99.2043i) q^{27} +839.832i q^{29} -403.787 q^{31} +(-615.211 - 615.211i) q^{33} +(-917.739 + 1275.27i) q^{35} +(-207.589 + 207.589i) q^{37} -1643.27i q^{39} -1386.39 q^{41} +(-568.393 - 568.393i) q^{43} +(108.613 + 666.204i) q^{45} +(2642.77 - 2642.77i) q^{47} -1548.70i q^{49} -521.850 q^{51} +(-1378.64 - 1378.64i) q^{53} +(-4131.44 + 673.559i) q^{55} +(1000.17 - 1000.17i) q^{57} -327.503i q^{59} -4205.66 q^{61} +(-1199.86 - 1199.86i) q^{63} +(-6417.24 - 4618.11i) q^{65} +(-2832.99 + 2832.99i) q^{67} -644.330i q^{69} -5339.03 q^{71} +(6865.24 + 6865.24i) q^{73} +(2906.87 + 1448.09i) q^{75} +(7440.88 - 7440.88i) q^{77} +4666.69i q^{79} -729.000 q^{81} +(-4111.98 - 4111.98i) q^{83} +(-1466.56 + 2037.91i) q^{85} +(-3085.74 + 3085.74i) q^{87} +9911.62i q^{89} +19875.1 q^{91} +(-1483.61 - 1483.61i) q^{93} +(-1095.03 - 6716.60i) q^{95} +(-10688.9 + 10688.9i) q^{97} -4520.86i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 84 q^{5} + 28 q^{7}+O(q^{10}) $ 4 * q + 84 * q^5 + 28 * q^7	$ 4 q + 84 q^{5} + 28 q^{7} - 464 q^{11} - 336 q^{13} + 216 q^{15} + 392 q^{17} - 1512 q^{21} - 968 q^{23} + 1136 q^{25} + 560 q^{31} - 756 q^{33} + 2296 q^{35} + 2256 q^{37} + 392 q^{41} - 216 q^{43} - 756 q^{45} + 9072 q^{47} - 4968 q^{51} - 4280 q^{53} - 10500 q^{55} + 6264 q^{57} - 4536 q^{61} + 756 q^{63} - 12912 q^{65} + 2248 q^{67} - 18064 q^{71} + 20524 q^{73} + 10584 q^{75} + 7336 q^{77} - 2916 q^{81} + 336 q^{83} + 15944 q^{85} - 8316 q^{87} + 52752 q^{91} - 7992 q^{93} - 23104 q^{95} - 40404 q^{97}+O(q^{100}) $ 4 * q + 84 * q^5 + 28 * q^7 - 464 * q^11 - 336 * q^13 + 216 * q^15 + 392 * q^17 - 1512 * q^21 - 968 * q^23 + 1136 * q^25 + 560 * q^31 - 756 * q^33 + 2296 * q^35 + 2256 * q^37 + 392 * q^41 - 216 * q^43 - 756 * q^45 + 9072 * q^47 - 4968 * q^51 - 4280 * q^53 - 10500 * q^55 + 6264 * q^57 - 4536 * q^61 + 756 * q^63 - 12912 * q^65 + 2248 * q^67 - 18064 * q^71 + 20524 * q^73 + 10584 * q^75 + 7336 * q^77 - 2916 * q^81 + 336 * q^83 + 15944 * q^85 - 8316 * q^87 + 52752 * q^91 - 7992 * q^93 - 23104 * q^95 - 40404 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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
$3$	3.67423	+	3.67423i	0.408248	+	0.408248i
$3$	3.67423	+	3.67423i	0.408248	+	0.408248i
$4$		0			0
$5$	24.6742	−	4.02270i	0.986969	−	0.160908i
$5$	24.6742	−	4.02270i	0.986969	−	0.160908i
$6$		0			0
$7$	−44.4393	+	44.4393i	−0.906924	+	0.906924i	−0.996023	−	0.0890986i	$-0.971601\pi$
$7$	−44.4393	+	44.4393i	−0.906924	+	0.906924i	0.0890986	+	0.996023i	$0.471601\pi$
$8$		0			0
$9$			27.0000i			0.333333i
$10$		0			0
$11$	−167.439			−1.38380			−0.691898	−	0.721995i	$-0.743225\pi$
$11$	−167.439			−1.38380			−0.691898	+	0.721995i	$0.743225\pi$
$12$		0			0
$13$	−223.621	−	223.621i	−1.32320	−	1.32320i	−0.911170	−	0.412031i	$-0.864820\pi$
$13$	−223.621	−	223.621i	−1.32320	−	1.32320i	−0.412031	−	0.911170i	$-0.635180\pi$
$14$		0			0
$15$	105.439	+	75.8786i	0.468619	+	0.337238i
$16$		0			0
$17$	−71.0148	+	71.0148i	−0.245726	+	0.245726i	−0.819214	−	0.573488i	$-0.805590\pi$
$17$	−71.0148	+	71.0148i	−0.245726	+	0.245726i	0.573488	+	0.819214i	$0.305590\pi$
$18$		0			0
$19$		−	272.211i		−	0.754048i	−0.926204	−	0.377024i	$-0.876947\pi$
$19$		−	272.211i		−	0.754048i	0.926204	−	0.377024i	$-0.123053\pi$
$20$		0			0
$21$	−326.561			−0.740500
$22$		0			0
$23$	−87.6821	−	87.6821i	−0.165751	−	0.165751i	0.619358	−	0.785109i	$-0.287393\pi$
$23$	−87.6821	−	87.6821i	−0.165751	−	0.165751i	−0.785109	+	0.619358i	$0.787393\pi$
$24$		0			0
$25$	592.636	−	198.514i	0.948217	−	0.317623i
$26$		0			0
$27$	−99.2043	+	99.2043i	−0.136083	+	0.136083i
$28$		0			0
$29$			839.832i			0.998611i	0.866426	+	0.499306i	$0.166412\pi$
$29$			839.832i			0.998611i	−0.866426	+	0.499306i	$0.833588\pi$
$30$		0			0
$31$	−403.787			−0.420173			−0.210087	−	0.977683i	$-0.567375\pi$
$31$	−403.787			−0.420173			−0.210087	+	0.977683i	$0.567375\pi$
$32$		0			0
$33$	−615.211	−	615.211i	−0.564932	−	0.564932i
$34$		0			0
$35$	−917.739	+	1275.27i	−0.749175	+	1.04104i
$36$		0			0
$37$	−207.589	+	207.589i	−0.151636	+	0.151636i	−0.778848	−	0.627212i	$-0.784196\pi$
$37$	−207.589	+	207.589i	−0.151636	+	0.151636i	0.627212	+	0.778848i	$0.284196\pi$
$38$		0			0
$39$		−	1643.27i		−	1.08039i
$40$		0			0
$41$	−1386.39			−0.824742			−0.412371	−	0.911016i	$-0.635299\pi$
$41$	−1386.39			−0.824742			−0.412371	+	0.911016i	$0.635299\pi$
$42$		0			0
$43$	−568.393	−	568.393i	−0.307406	−	0.307406i	0.536497	−	0.843902i	$-0.319747\pi$
$43$	−568.393	−	568.393i	−0.307406	−	0.307406i	−0.843902	+	0.536497i	$0.819747\pi$
$44$		0			0
$45$	108.613	+	666.204i	0.0536361	+	0.328990i
$46$		0			0
$47$	2642.77	−	2642.77i	1.19637	−	1.19637i	0.221119	−	0.975247i	$-0.429029\pi$
$47$	2642.77	−	2642.77i	1.19637	−	1.19637i	0.975247	−	0.221119i	$-0.0709709\pi$
$48$		0			0
$49$		−	1548.70i		−	0.645023i
$50$		0			0
$51$	−521.850			−0.200634
$52$		0			0
$53$	−1378.64	−	1378.64i	−0.490792	−	0.490792i	0.417763	−	0.908556i	$-0.362814\pi$
$53$	−1378.64	−	1378.64i	−0.490792	−	0.490792i	−0.908556	+	0.417763i	$0.862814\pi$
$54$		0			0
$55$	−4131.44	+	673.559i	−1.36576	+	0.222664i
$56$		0			0
$57$	1000.17	−	1000.17i	0.307839	−	0.307839i
$58$		0			0
$59$		−	327.503i		−	0.0940829i	−0.998893	−	0.0470415i	$-0.985021\pi$
$59$		−	327.503i		−	0.0940829i	0.998893	−	0.0470415i	$-0.0149793\pi$
$60$		0			0
$61$	−4205.66			−1.13025			−0.565125	−	0.825005i	$-0.691172\pi$
$61$	−4205.66			−1.13025			−0.565125	+	0.825005i	$0.691172\pi$
$62$		0			0
$63$	−1199.86	−	1199.86i	−0.302308	−	0.302308i
$64$		0			0
$65$	−6417.24	−	4618.11i	−1.51887	−	1.09304i
$66$		0			0
$67$	−2832.99	+	2832.99i	−0.631097	+	0.631097i	−0.948343	−	0.317246i	$-0.897242\pi$
$67$	−2832.99	+	2832.99i	−0.631097	+	0.631097i	0.317246	+	0.948343i	$0.397242\pi$
$68$		0			0
$69$		−	644.330i		−	0.135335i
$70$		0			0
$71$	−5339.03			−1.05912			−0.529560	−	0.848272i	$-0.677643\pi$
$71$	−5339.03			−1.05912			−0.529560	+	0.848272i	$0.677643\pi$
$72$		0			0
$73$	6865.24	+	6865.24i	1.28828	+	1.28828i	0.935832	+	0.352447i	$0.114650\pi$
$73$	6865.24	+	6865.24i	1.28828	+	1.28828i	0.352447	+	0.935832i	$0.385350\pi$
$74$		0			0
$75$	2906.87	+	1448.09i	0.516777	+	0.257439i
$76$		0			0
$77$	7440.88	−	7440.88i	1.25500	−	1.25500i
$78$		0			0
$79$			4666.69i			0.747748i	0.927480	+	0.373874i	$0.121971\pi$
$79$			4666.69i			0.747748i	−0.927480	+	0.373874i	$0.878029\pi$
$80$		0			0
$81$	−729.000			−0.111111
$82$		0			0
$83$	−4111.98	−	4111.98i	−0.596890	−	0.596890i	0.342594	−	0.939484i	$-0.388695\pi$
$83$	−4111.98	−	4111.98i	−0.596890	−	0.596890i	−0.939484	+	0.342594i	$0.888695\pi$
$84$		0			0
$85$	−1466.56	+	2037.91i	−0.202985	+	0.282063i
$86$		0			0
$87$	−3085.74	+	3085.74i	−0.407681	+	0.407681i
$88$		0			0
$89$			9911.62i			1.25131i	0.780100	+	0.625654i	$0.215168\pi$
$89$			9911.62i			1.25131i	−0.780100	+	0.625654i	$0.784832\pi$
$90$		0			0
$91$	19875.1			2.40009
$92$		0			0
$93$	−1483.61	−	1483.61i	−0.171535	−	0.171535i
$94$		0			0
$95$	−1095.03	−	6716.60i	−0.121332	−	0.744222i
$96$		0			0
$97$	−10688.9	+	10688.9i	−1.13603	+	1.13603i	−0.146871	+	0.989156i	$0.546920\pi$
$97$	−10688.9	+	10688.9i	−1.13603	+	1.13603i	−0.989156	+	0.146871i	$0.953080\pi$
$98$		0			0
$99$		−	4520.86i		−	0.461265i
$100$		0			0
$101$	−1763.09			−0.172835			−0.0864177	−	0.996259i	$-0.527542\pi$
$101$	−1763.09			−0.172835			−0.0864177	+	0.996259i	$0.527542\pi$
$102$		0			0
$103$	2414.27	+	2414.27i	0.227568	+	0.227568i	0.811676	−	0.584108i	$-0.198556\pi$
$103$	2414.27	+	2414.27i	0.227568	+	0.227568i	−0.584108	+	0.811676i	$0.698556\pi$
$104$		0			0
$105$	−8057.64	+	1313.66i	−0.730851	+	0.119153i
$106$		0			0
$107$	−4279.03	+	4279.03i	−0.373747	+	0.373747i	−0.868840	−	0.495093i	$-0.835134\pi$
$107$	−4279.03	+	4279.03i	−0.373747	+	0.373747i	0.495093	+	0.868840i	$0.335134\pi$
$108$		0			0
$109$		−	11819.5i		−	0.994827i	−0.867514	−	0.497413i	$-0.834283\pi$
$109$		−	11819.5i		−	0.994827i	0.867514	−	0.497413i	$-0.165717\pi$
$110$		0			0
$111$	−1525.46			−0.123810
$112$		0			0
$113$	1620.60	+	1620.60i	0.126917	+	0.126917i	0.767712	−	0.640795i	$-0.221395\pi$
$113$	1620.60	+	1620.60i	0.126917	+	0.126917i	−0.640795	+	0.767712i	$0.721395\pi$
$114$		0			0
$115$	−2516.21	−	1810.77i	−0.190262	−	0.136920i
$116$		0			0
$117$	6037.76	−	6037.76i	0.441067	−	0.441067i
$118$		0			0
$119$		−	6311.69i		−	0.445710i
$120$		0			0
$121$	13394.9			0.914891
$122$		0			0
$123$	−5093.93	−	5093.93i	−0.336699	−	0.336699i
$124$		0			0
$125$	13824.3	−	7282.19i	0.884753	−	0.466060i
$126$		0			0
$127$	11572.5	−	11572.5i	0.717494	−	0.717494i	−0.250597	−	0.968091i	$-0.580627\pi$
$127$	11572.5	−	11572.5i	0.717494	−	0.717494i	0.968091	+	0.250597i	$0.0806270\pi$
$128$		0			0
$129$		−	4176.82i		−	0.250996i
$130$		0			0
$131$	−65.6230			−0.00382396			−0.00191198	−	0.999998i	$-0.500609\pi$
$131$	−65.6230			−0.00382396			−0.00191198	+	0.999998i	$0.500609\pi$
$132$		0			0
$133$	12096.9	+	12096.9i	0.683864	+	0.683864i
$134$		0			0
$135$	−2048.72	+	2846.86i	−0.112413	+	0.156206i
$136$		0			0
$137$	579.439	−	579.439i	0.0308721	−	0.0308721i	−0.691502	−	0.722374i	$-0.743051\pi$
$137$	579.439	−	579.439i	0.0308721	−	0.0308721i	0.722374	+	0.691502i	$0.243051\pi$
$138$		0			0
$139$			36158.2i			1.87145i	0.352734	+	0.935724i	$0.385252\pi$
$139$			36158.2i			1.87145i	−0.352734	+	0.935724i	$0.614748\pi$
$140$		0			0
$141$	19420.3			0.976829
$142$		0			0
$143$	37442.9	+	37442.9i	1.83104	+	1.83104i
$144$		0			0
$145$	3378.40	+	20722.2i	0.160685	+	0.985599i
$146$		0			0
$147$	5690.29	−	5690.29i	0.263330	−	0.263330i
$148$		0			0
$149$			2143.94i			0.0965695i	0.998834	+	0.0482847i	$0.0153755\pi$
$149$			2143.94i			0.0965695i	−0.998834	+	0.0482847i	$0.984625\pi$
$150$		0			0
$151$	8940.59			0.392114			0.196057	−	0.980593i	$-0.437186\pi$
$151$	8940.59			0.392114			0.196057	+	0.980593i	$0.437186\pi$
$152$		0			0
$153$	−1917.40	−	1917.40i	−0.0819086	−	0.0819086i
$154$		0			0
$155$	−9963.13	+	1624.31i	−0.414698	+	0.0676093i
$156$		0			0
$157$	18032.9	−	18032.9i	0.731586	−	0.731586i	−0.239348	−	0.970934i	$-0.576934\pi$
$157$	18032.9	−	18032.9i	0.731586	−	0.731586i	0.970934	+	0.239348i	$0.0769337\pi$
$158$		0			0
$159$		−	10130.9i		−	0.400730i
$160$		0			0
$161$	7793.06			0.300647
$162$		0			0
$163$	6859.00	+	6859.00i	0.258158	+	0.258158i	0.824305	−	0.566147i	$-0.191566\pi$
$163$	6859.00	+	6859.00i	0.258158	+	0.258158i	−0.566147	+	0.824305i	$0.691566\pi$
$164$		0			0
$165$	−17654.7	−	12705.1i	−0.648473	−	0.466669i
$166$		0			0
$167$	37439.2	−	37439.2i	1.34244	−	1.34244i	0.448811	−	0.893627i	$-0.351848\pi$
$167$	37439.2	−	37439.2i	1.34244	−	1.34244i	0.893627	−	0.448811i	$-0.148152\pi$
$168$		0			0
$169$			71451.6i			2.50172i
$170$		0			0
$171$	7349.70			0.251349
$172$		0			0
$173$	−32638.2	−	32638.2i	−1.09052	−	1.09052i	−0.995472	−	0.0950500i	$-0.969699\pi$
$173$	−32638.2	−	32638.2i	−1.09052	−	1.09052i	−0.0950500	−	0.995472i	$-0.530301\pi$
$174$		0			0
$175$	−17514.5	+	35158.1i	−0.571901	+	1.14802i
$176$		0			0
$177$	1203.32	−	1203.32i	0.0384092	−	0.0384092i
$178$		0			0
$179$		−	6396.19i		−	0.199625i	−0.995006	−	0.0998126i	$-0.968176\pi$
$179$		−	6396.19i		−	0.199625i	0.995006	−	0.0998126i	$-0.0318243\pi$
$180$		0			0
$181$	49025.9			1.49647			0.748236	−	0.663432i	$-0.230901\pi$
$181$	49025.9			1.49647			0.748236	+	0.663432i	$0.230901\pi$
$182$		0			0
$183$	−15452.6	−	15452.6i	−0.461423	−	0.461423i
$184$		0			0
$185$	−4287.04	+	5957.18i	−0.125260	+	0.174059i
$186$		0			0
$187$	11890.7	−	11890.7i	0.340034	−	0.340034i
$188$		0			0
$189$		−	8817.14i		−	0.246833i
$190$		0			0
$191$	−39949.0			−1.09506			−0.547531	−	0.836785i	$-0.684432\pi$
$191$	−39949.0			−1.09506			−0.547531	+	0.836785i	$0.684432\pi$
$192$		0			0
$193$	−23749.1	−	23749.1i	−0.637577	−	0.637577i	0.312380	−	0.949957i	$-0.398874\pi$
$193$	−23749.1	−	23749.1i	−0.637577	−	0.637577i	−0.949957	+	0.312380i	$0.898874\pi$
$194$		0			0
$195$	−6610.39	−	40546.5i	−0.173843	−	1.06631i
$196$		0			0
$197$	−2725.09	+	2725.09i	−0.0702181	+	0.0702181i	−0.741344	−	0.671126i	$-0.765811\pi$
$197$	−2725.09	+	2725.09i	−0.0702181	+	0.0702181i	0.671126	+	0.741344i	$0.265811\pi$
$198$		0			0
$199$			63212.5i			1.59624i	0.602502	+	0.798118i	$0.294171\pi$
$199$			63212.5i			1.59624i	−0.602502	+	0.798118i	$0.705829\pi$
$200$		0			0
$201$	−20818.2			−0.515288
$202$		0			0
$203$	−37321.5	−	37321.5i	−0.905665	−	0.905665i
$204$		0			0
$205$	−34208.1	+	5577.04i	−0.813995	+	0.132708i
$206$		0			0
$207$	2367.42	−	2367.42i	0.0552502	−	0.0552502i
$208$		0			0
$209$			45578.9i			1.04345i
$210$		0			0
$211$	−15470.2			−0.347480			−0.173740	−	0.984792i	$-0.555585\pi$
$211$	−15470.2			−0.347480			−0.173740	+	0.984792i	$0.555585\pi$
$212$		0			0
$213$	−19616.8	−	19616.8i	−0.432384	−	0.432384i
$214$		0			0
$215$	−16311.1	−	11738.2i	−0.352864	−	0.253936i
$216$		0			0
$217$	17944.0	−	17944.0i	0.381065	−	0.381065i
$218$		0			0
$219$			50449.0i			1.05188i
$220$		0			0
$221$	31760.8			0.650289
$222$		0			0
$223$	−28817.8	−	28817.8i	−0.579496	−	0.579496i	0.355268	−	0.934764i	$-0.384389\pi$
$223$	−28817.8	−	28817.8i	−0.579496	−	0.579496i	−0.934764	+	0.355268i	$0.884389\pi$
$224$		0			0
$225$	5359.89	+	16001.2i	0.105874	+	0.316072i
$226$		0			0
$227$	−884.237	+	884.237i	−0.0171600	+	0.0171600i	−0.715635	−	0.698475i	$-0.753862\pi$
$227$	−884.237	+	884.237i	−0.0171600	+	0.0171600i	0.698475	+	0.715635i	$0.253862\pi$
$228$		0			0
$229$			12076.4i			0.230285i	0.993349	+	0.115143i	$0.0367325\pi$
$229$			12076.4i			0.230285i	−0.993349	+	0.115143i	$0.963268\pi$
$230$		0			0
$231$	54679.1			1.02470
$232$		0			0
$233$	−24695.8	−	24695.8i	−0.454894	−	0.454894i	0.442081	−	0.896975i	$-0.354240\pi$
$233$	−24695.8	−	24695.8i	−0.454894	−	0.454894i	−0.896975	+	0.442081i	$0.854240\pi$
$234$		0			0
$235$	54577.3	−	75839.5i	0.988271	−	1.37328i
$236$		0			0
$237$	−17146.5	+	17146.5i	−0.305267	+	0.305267i
$238$		0			0
$239$			48187.8i			0.843608i	0.906687	+	0.421804i	$0.138603\pi$
$239$			48187.8i			0.843608i	−0.906687	+	0.421804i	$0.861397\pi$
$240$		0			0
$241$	−55184.2			−0.950125			−0.475062	−	0.879952i	$-0.657574\pi$
$241$	−55184.2			−0.950125			−0.475062	+	0.879952i	$0.657574\pi$
$242$		0			0
$243$	−2678.52	−	2678.52i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	−6229.96	−	38213.0i	−0.103789	−	0.636618i
$246$		0			0
$247$	−60872.1	+	60872.1i	−0.997756	+	0.997756i
$248$		0			0
$249$		−	30216.7i		−	0.487359i
$250$		0			0
$251$	69667.8			1.10582			0.552910	−	0.833241i	$-0.313517\pi$
$251$	69667.8			1.10582			0.552910	+	0.833241i	$0.313517\pi$
$252$		0			0
$253$	14681.4	+	14681.4i	0.229365	+	0.229365i
$254$		0			0
$255$	−12876.2	+	2099.25i	−0.198020	+	0.0322837i
$256$		0			0
$257$	−11614.4	+	11614.4i	−0.175846	+	0.175846i	−0.789542	−	0.613696i	$-0.789682\pi$
$257$	−11614.4	+	11614.4i	−0.175846	+	0.175846i	0.613696	+	0.789542i	$0.289682\pi$
$258$		0			0
$259$		−	18450.2i		−	0.275044i
$260$		0			0
$261$	−22675.5			−0.332870
$262$		0			0
$263$	−86811.6	−	86811.6i	−1.25507	−	1.25507i	−0.953420	−	0.301646i	$-0.902464\pi$
$263$	−86811.6	−	86811.6i	−1.25507	−	1.25507i	−0.301646	−	0.953420i	$-0.597536\pi$
$264$		0			0
$265$	−39562.6	−	28470.9i	−0.563370	−	0.405425i
$266$		0			0
$267$	−36417.6	+	36417.6i	−0.510845	+	0.510845i
$268$		0			0
$269$		−	93439.3i		−	1.29129i	−0.763636	−	0.645647i	$-0.776588\pi$
$269$		−	93439.3i		−	1.29129i	0.763636	−	0.645647i	$-0.223412\pi$
$270$		0			0
$271$	10856.5			0.147826			0.0739131	−	0.997265i	$-0.476451\pi$
$271$	10856.5			0.147826			0.0739131	+	0.997265i	$0.476451\pi$
$272$		0			0
$273$	73025.8	+	73025.8i	0.979831	+	0.979831i
$274$		0			0
$275$	−99230.5	+	33239.1i	−1.31214	+	0.439525i
$276$		0			0
$277$	65214.7	−	65214.7i	0.849935	−	0.849935i	−0.140189	−	0.990125i	$-0.544771\pi$
$277$	65214.7	−	65214.7i	0.849935	−	0.849935i	0.990125	+	0.140189i	$0.0447711\pi$
$278$		0			0
$279$		−	10902.2i		−	0.140058i
$280$		0			0
$281$	−8669.34			−0.109793			−0.0548963	−	0.998492i	$-0.517483\pi$
$281$	−8669.34			−0.109793			−0.0548963	+	0.998492i	$0.517483\pi$
$282$		0			0
$283$	23747.0	+	23747.0i	0.296508	+	0.296508i	0.839645	−	0.543136i	$-0.182763\pi$
$283$	23747.0	+	23747.0i	0.296508	+	0.296508i	−0.543136	+	0.839645i	$0.682763\pi$
$284$		0			0
$285$	20655.0	−	28701.8i	0.254294	−	0.353361i
$286$		0			0
$287$	61610.2	−	61610.2i	0.747978	−	0.747978i
$288$		0			0
$289$			73434.8i			0.879238i
$290$		0			0
$291$	−78546.9			−0.927562
$292$		0			0
$293$	−55077.2	−	55077.2i	−0.641559	−	0.641559i	0.309380	−	0.950939i	$-0.399879\pi$
$293$	−55077.2	−	55077.2i	−0.641559	−	0.641559i	−0.950939	+	0.309380i	$0.899879\pi$
$294$		0			0
$295$	−1317.45	−	8080.88i	−0.0151387	−	0.0928569i
$296$		0			0
$297$	16610.7	−	16610.7i	0.188311	−	0.188311i
$298$		0			0
$299$			39215.1i			0.438643i
$300$		0			0
$301$	50517.9			0.557587
$302$		0			0
$303$	−6478.02	−	6478.02i	−0.0705597	−	0.0705597i
$304$		0			0
$305$	−103771.	+	16918.1i	−1.11552	+	0.181866i
$306$		0			0
$307$	−11961.1	+	11961.1i	−0.126910	+	0.126910i	−0.767709	−	0.640799i	$-0.778603\pi$
$307$	−11961.1	+	11961.1i	−0.126910	+	0.126910i	0.640799	+	0.767709i	$0.278603\pi$
$308$		0			0
$309$			17741.2i			0.185808i
$310$		0			0
$311$	65284.5			0.674977			0.337489	−	0.941330i	$-0.390423\pi$
$311$	65284.5			0.674977			0.337489	+	0.941330i	$0.390423\pi$
$312$		0			0
$313$	−6418.45	−	6418.45i	−0.0655151	−	0.0655151i	0.673590	−	0.739105i	$-0.264751\pi$
$313$	−6418.45	−	6418.45i	−0.0655151	−	0.0655151i	−0.739105	+	0.673590i	$0.764751\pi$
$314$		0			0
$315$	−34432.3	−	24779.0i	−0.347013	−	0.249725i
$316$		0			0
$317$	22100.1	−	22100.1i	0.219926	−	0.219926i	−0.588541	−	0.808467i	$-0.700298\pi$
$317$	22100.1	−	22100.1i	0.219926	−	0.219926i	0.808467	+	0.588541i	$0.200298\pi$
$318$		0			0
$319$		−	140621.i		−	1.38187i
$320$		0			0
$321$	−31444.3			−0.305163
$322$		0			0
$323$	19331.0	+	19331.0i	0.185289	+	0.185289i
$324$		0			0
$325$	−176918.	−	88133.8i	−1.67496	−	0.834403i
$326$		0			0
$327$	43427.7	−	43427.7i	0.406136	−	0.406136i
$328$		0			0
$329$			234886.i			2.17003i
$330$		0			0
$331$	49108.7			0.448231			0.224116	−	0.974563i	$-0.428051\pi$
$331$	49108.7			0.448231			0.224116	+	0.974563i	$0.428051\pi$
$332$		0			0
$333$	−5604.91	−	5604.91i	−0.0505452	−	0.0505452i
$334$		0			0
$335$	−58505.6	+	81298.2i	−0.521324	+	0.724422i
$336$		0			0
$337$	−142816.	+	142816.i	−1.25753	+	1.25753i	−0.305260	+	0.952269i	$0.598743\pi$
$337$	−142816.	+	142816.i	−1.25753	+	1.25753i	−0.952269	+	0.305260i	$0.901257\pi$
$338$		0			0
$339$			11909.0i			0.103627i
$340$		0			0
$341$	67609.8			0.581434
$342$		0			0
$343$	−37875.6	−	37875.6i	−0.321937	−	0.321937i
$344$		0			0
$345$	−2591.95	−	15898.3i	−0.0217765	−	0.133571i
$346$		0			0
$347$	21400.3	−	21400.3i	0.177730	−	0.177730i	−0.612635	−	0.790366i	$-0.709891\pi$
$347$	21400.3	−	21400.3i	0.177730	−	0.177730i	0.790366	+	0.612635i	$0.209891\pi$
$348$		0			0
$349$			34091.2i			0.279893i	0.990159	+	0.139946i	$0.0446930\pi$
$349$			34091.2i			0.279893i	−0.990159	+	0.139946i	$0.955307\pi$
$350$		0			0
$351$	44368.3			0.360130
$352$		0			0
$353$	28.7539	+	28.7539i	0.000230753	+	0.000230753i	0.707222	−	0.706991i	$-0.249948\pi$
$353$	28.7539	+	28.7539i	0.000230753	+	0.000230753i	−0.706991	+	0.707222i	$0.749948\pi$
$354$		0			0
$355$	−131736.	+	21477.3i	−1.04532	+	0.170421i
$356$		0			0
$357$	23190.6	−	23190.6i	0.181960	−	0.181960i
$358$		0			0
$359$			173943.i			1.34964i	0.737984	+	0.674818i	$0.235778\pi$
$359$			173943.i			1.34964i	−0.737984	+	0.674818i	$0.764222\pi$
$360$		0			0
$361$	56222.1			0.431412
$362$		0			0
$363$	49216.1	+	49216.1i	0.373503	+	0.373503i
$364$		0			0
$365$	197011.	+	141778.i	1.47879	+	1.06420i
$366$		0			0
$367$	41954.1	−	41954.1i	0.311489	−	0.311489i	−0.533997	−	0.845486i	$-0.679311\pi$
$367$	41954.1	−	41954.1i	0.311489	−	0.311489i	0.845486	+	0.533997i	$0.179311\pi$
$368$		0			0
$369$		−	37432.6i		−	0.274914i
$370$		0			0
$371$	122531.			0.890223
$372$		0			0
$373$	−65875.2	−	65875.2i	−0.473483	−	0.473483i	0.429557	−	0.903040i	$-0.358670\pi$
$373$	−65875.2	−	65875.2i	−0.473483	−	0.473483i	−0.903040	+	0.429557i	$0.858670\pi$
$374$		0			0
$375$	77550.1	+	24037.1i	0.551467	+	0.170931i
$376$		0			0
$377$	187804.	−	187804.i	1.32136	−	1.32136i
$378$		0			0
$379$		−	10837.0i		−	0.0754448i	−0.999288	−	0.0377224i	$-0.987990\pi$
$379$		−	10837.0i		−	0.0754448i	0.999288	−	0.0377224i	$-0.0120103\pi$
$380$		0			0
$381$	85039.9			0.585831
$382$		0			0
$383$	−22327.5	−	22327.5i	−0.152210	−	0.152210i	0.626894	−	0.779104i	$-0.284326\pi$
$383$	−22327.5	−	22327.5i	−0.152210	−	0.152210i	−0.779104	+	0.626894i	$0.784326\pi$
$384$		0			0
$385$	153666.	−	213531.i	1.03671	−	1.44058i
$386$		0			0
$387$	15346.6	−	15346.6i	0.102469	−	0.102469i
$388$		0			0
$389$			203884.i			1.34736i	0.739023	+	0.673680i	$0.235287\pi$
$389$			203884.i			1.34736i	−0.739023	+	0.673680i	$0.764713\pi$
$390$		0			0
$391$	12453.5			0.0814585
$392$		0			0
$393$	−241.114	−	241.114i	−0.00156113	−	0.00156113i
$394$		0			0
$395$	18772.7	+	115147.i	0.120319	+	0.738004i
$396$		0			0
$397$	117299.	−	117299.i	0.744238	−	0.744238i	−0.229153	−	0.973390i	$-0.573596\pi$
$397$	117299.	−	117299.i	0.744238	−	0.744238i	0.973390	+	0.229153i	$0.0735955\pi$
$398$		0			0
$399$			88893.5i			0.558373i
$400$		0			0
$401$	43093.1			0.267990			0.133995	−	0.990982i	$-0.457219\pi$
$401$	43093.1			0.267990			0.133995	+	0.990982i	$0.457219\pi$
$402$		0			0
$403$	90295.2	+	90295.2i	0.555974	+	0.555974i
$404$		0			0
$405$	−17987.5	+	2932.55i	−0.109663	+	0.0178787i
$406$		0			0
$407$	34758.6	−	34758.6i	0.209833	−	0.209833i
$408$		0			0
$409$		−	186090.i		−	1.11244i	−0.831036	−	0.556219i	$-0.812252\pi$
$409$		−	186090.i		−	1.11244i	0.831036	−	0.556219i	$-0.187748\pi$
$410$		0			0
$411$	4257.99			0.0252070
$412$		0			0
$413$	14554.0	+	14554.0i	0.0853261	+	0.0853261i
$414$		0			0
$415$	−118001.	−	84918.6i	−0.685157	−	0.493068i
$416$		0			0
$417$	−132854.	+	132854.i	−0.764015	+	0.764015i
$418$		0			0
$419$		−	101699.i		−	0.579278i	−0.957136	−	0.289639i	$-0.906465\pi$
$419$		−	101699.i		−	0.579278i	0.957136	−	0.289639i	$-0.0935352\pi$
$420$		0			0
$421$	−22533.0			−0.127132			−0.0635659	−	0.997978i	$-0.520247\pi$
$421$	−22533.0			−0.127132			−0.0635659	+	0.997978i	$0.520247\pi$
$422$		0			0
$423$	71354.8	+	71354.8i	0.398789	+	0.398789i
$424$		0			0
$425$	−27988.5	+	56183.4i	−0.154953	+	0.311050i
$426$		0			0
$427$	186897.	−	186897.i	1.02505	−	1.02505i
$428$		0			0
$429$			275148.i			1.49504i
$430$		0			0
$431$	−210598.			−1.13370			−0.566852	−	0.823820i	$-0.691839\pi$
$431$	−210598.			−1.13370			−0.566852	+	0.823820i	$0.691839\pi$
$432$		0			0
$433$	123405.	+	123405.i	0.658201	+	0.658201i	0.954954	−	0.296754i	$-0.0959040\pi$
$433$	123405.	+	123405.i	0.658201	+	0.658201i	−0.296754	+	0.954954i	$0.595904\pi$
$434$		0			0
$435$	−63725.3	+	88551.3i	−0.336770	+	0.467968i
$436$		0			0
$437$	−23868.1	+	23868.1i	−0.124984	+	0.124984i
$438$		0			0
$439$			265180.i			1.37598i	0.725721	+	0.687989i	$0.241506\pi$
$439$			265180.i			1.37598i	−0.725721	+	0.687989i	$0.758494\pi$
$440$		0			0
$441$	41814.9			0.215008
$442$		0			0
$443$	99815.9	+	99815.9i	0.508619	+	0.508619i	0.914102	−	0.405484i	$-0.132897\pi$
$443$	99815.9	+	99815.9i	0.508619	+	0.508619i	−0.405484	+	0.914102i	$0.632897\pi$
$444$		0			0
$445$	39871.5	+	244562.i	0.201346	+	1.23500i
$446$		0			0
$447$	−7877.34	+	7877.34i	−0.0394243	+	0.0394243i
$448$		0			0
$449$		−	182934.i		−	0.907408i	−0.891152	−	0.453704i	$-0.850102\pi$
$449$		−	182934.i		−	0.907408i	0.891152	−	0.453704i	$-0.149898\pi$
$450$		0			0
$451$	232136.			1.14127
$452$		0			0
$453$	32849.8	+	32849.8i	0.160080	+	0.160080i
$454$		0			0
$455$	490403.	−	79951.7i	2.36881	−	0.386193i
$456$		0			0
$457$	147497.	−	147497.i	0.706239	−	0.706239i	−0.259503	−	0.965742i	$-0.583559\pi$
$457$	147497.	−	147497.i	0.706239	−	0.706239i	0.965742	+	0.259503i	$0.0835588\pi$
$458$		0			0
$459$		−	14090.0i		−	0.0668781i
$460$		0			0
$461$	−354912.			−1.67001			−0.835006	−	0.550241i	$-0.814536\pi$
$461$	−354912.			−1.67001			−0.835006	+	0.550241i	$0.814536\pi$
$462$		0			0
$463$	−182475.	−	182475.i	−0.851221	−	0.851221i	0.139063	−	0.990284i	$-0.455591\pi$
$463$	−182475.	−	182475.i	−0.851221	−	0.851221i	−0.990284	+	0.139063i	$0.955591\pi$
$464$		0			0
$465$	−42575.0	−	30638.8i	−0.196901	−	0.141699i
$466$		0			0
$467$	−4348.30	+	4348.30i	−0.0199382	+	0.0199382i	−0.717006	−	0.697067i	$-0.754488\pi$
$467$	−4348.30	+	4348.30i	−0.0199382	+	0.0199382i	0.697067	+	0.717006i	$0.254488\pi$
$468$		0			0
$469$		−	251792.i		−	1.14471i
$470$		0			0
$471$	132514.			0.597337
$472$		0			0
$473$	95171.3	+	95171.3i	0.425386	+	0.425386i
$474$		0			0
$475$	−54037.8	−	161322.i	−0.239503	−	0.715001i
$476$		0			0
$477$	37223.2	−	37223.2i	0.163597	−	0.163597i
$478$		0			0
$479$		−	77346.0i		−	0.337106i	−0.985693	−	0.168553i	$-0.946091\pi$
$479$		−	77346.0i		−	0.337106i	0.985693	−	0.168553i	$-0.0539095\pi$
$480$		0			0
$481$	92842.6			0.401289
$482$		0			0
$483$	28633.5	+	28633.5i	0.122739	+	0.122739i
$484$		0			0
$485$	−220742.	+	306738.i	−0.938428	+	1.30402i
$486$		0			0
$487$	−77225.6	+	77225.6i	−0.325614	+	0.325614i	−0.850916	−	0.525302i	$-0.823952\pi$
$487$	−77225.6	+	77225.6i	−0.325614	+	0.325614i	0.525302	+	0.850916i	$0.323952\pi$
$488$		0			0
$489$			50403.1i			0.210785i
$490$		0			0
$491$	−340217.			−1.41121			−0.705607	−	0.708603i	$-0.749326\pi$
$491$	−340217.			−1.41121			−0.705607	+	0.708603i	$0.749326\pi$
$492$		0			0
$493$	−59640.5	−	59640.5i	−0.245385	−	0.245385i
$494$		0			0
$495$	−18186.1	−	111549.i	−0.0742213	−	0.455255i
$496$		0			0
$497$	237263.	−	237263.i	0.960542	−	0.960542i
$498$		0			0
$499$		−	331024.i		−	1.32941i	−0.747108	−	0.664703i	$-0.768558\pi$
$499$		−	331024.i		−	1.32941i	0.747108	−	0.664703i	$-0.231442\pi$
$500$		0			0
$501$	275121.			1.09610
$502$		0			0
$503$	123301.	+	123301.i	0.487338	+	0.487338i	0.907465	−	0.420127i	$-0.138015\pi$
$503$	123301.	+	123301.i	0.487338	+	0.487338i	−0.420127	+	0.907465i	$0.638015\pi$
$504$		0			0
$505$	−43503.0	+	7092.40i	−0.170583	+	0.0278106i
$506$		0			0
$507$	−262530.	+	262530.i	−1.02132	+	1.02132i
$508$		0			0
$509$		−	364729.i		−	1.40778i	−0.710309	−	0.703890i	$-0.751445\pi$
$509$		−	364729.i		−	1.40778i	0.710309	−	0.703890i	$-0.248555\pi$
$510$		0			0
$511$	−610173.			−2.33674
$512$		0			0
$513$	27004.5	+	27004.5i	0.102613	+	0.102613i
$514$		0			0
$515$	69282.1	+	49858.3i	0.261220	+	0.187985i
$516$		0			0
$517$	−442504.	+	442504.i	−1.65553	+	1.65553i
$518$		0			0
$519$		−	239841.i		−	0.890408i
$520$		0			0
$521$	−203461.			−0.749560			−0.374780	−	0.927114i	$-0.622282\pi$
$521$	−203461.			−0.749560			−0.374780	+	0.927114i	$0.622282\pi$
$522$		0			0
$523$	−72655.5	−	72655.5i	−0.265623	−	0.265623i	0.561711	−	0.827334i	$-0.310143\pi$
$523$	−72655.5	−	72655.5i	−0.265623	−	0.265623i	−0.827334	+	0.561711i	$0.810143\pi$
$524$		0			0
$525$	−193532.	+	64827.0i	−0.702155	+	0.235200i
$526$		0			0
$527$	28674.8	−	28674.8i	0.103248	−	0.103248i
$528$		0			0
$529$		−	264465.i		−	0.945053i
$530$		0			0
$531$	8842.57			0.0313610
$532$		0			0
$533$	310026.	+	310026.i	1.09130	+	1.09130i
$534$		0			0
$535$	−88368.4	+	122795.i	−0.308738	+	0.429015i
$536$		0			0
$537$	23501.1	−	23501.1i	0.0814966	−	0.0814966i
$538$		0			0
$539$			259313.i			0.892580i
$540$		0			0
$541$	−91367.2			−0.312173			−0.156087	−	0.987743i	$-0.549888\pi$
$541$	−91367.2			−0.312173			−0.156087	+	0.987743i	$0.549888\pi$
$542$		0			0
$543$	180133.	+	180133.i	0.610932	+	0.610932i
$544$		0			0
$545$	−47546.5	−	291638.i	−0.160076	−	0.981863i
$546$		0			0
$547$	9895.50	−	9895.50i	0.0330722	−	0.0330722i	−0.690377	−	0.723450i	$-0.742555\pi$
$547$	9895.50	−	9895.50i	0.0330722	−	0.0330722i	0.723450	+	0.690377i	$0.242555\pi$
$548$		0			0
$549$		−	113553.i		−	0.376750i
$550$		0			0
$551$	228612.			0.753001
$552$		0			0
$553$	−207384.	−	207384.i	−0.678150	−	0.678150i
$554$		0			0
$555$	−37639.6	+	6136.49i	−0.122197	+	0.0199220i
$556$		0			0
$557$	−306800.	+	306800.i	−0.988883	+	0.988883i	−0.999939	−	0.0110558i	$-0.996481\pi$
$557$	−306800.	+	306800.i	−0.988883	+	0.988883i	0.0110558	+	0.999939i	$0.496481\pi$
$558$		0			0
$559$			254209.i			0.813518i
$560$		0			0
$561$	87378.2			0.277637
$562$		0			0
$563$	−331132.	−	331132.i	−1.04468	−	1.04468i	−0.998954	−	0.0457279i	$-0.985439\pi$
$563$	−331132.	−	331132.i	−1.04468	−	1.04468i	−0.0457279	−	0.998954i	$-0.514561\pi$
$564$		0			0
$565$	46506.4	+	33467.9i	0.145685	+	0.104841i
$566$		0			0
$567$	32396.2	−	32396.2i	0.100769	−	0.100769i
$568$		0			0
$569$			257399.i			0.795028i	0.917596	+	0.397514i	$0.130127\pi$
$569$			257399.i			0.795028i	−0.917596	+	0.397514i	$0.869873\pi$
$570$		0			0
$571$	622495.			1.90925			0.954626	−	0.297807i	$-0.0962552\pi$
$571$	622495.			1.90925			0.954626	+	0.297807i	$0.0962552\pi$
$572$		0			0
$573$	−146782.	−	146782.i	−0.447057	−	0.447057i
$574$		0			0
$575$	−69369.7	−	34557.4i	−0.209814	−	0.104521i
$576$		0			0
$577$	−23928.8	+	23928.8i	−0.0718736	+	0.0718736i	−0.742130	−	0.670256i	$-0.766184\pi$
$577$	−23928.8	+	23928.8i	−0.0718736	+	0.0718736i	0.670256	+	0.742130i	$0.266184\pi$
$578$		0			0
$579$		−	174520.i		−	0.520580i
$580$		0			0
$581$	365467.			1.08267
$582$		0			0
$583$	230838.	+	230838.i	0.679156	+	0.679156i
$584$		0			0
$585$	124689.	−	173265.i	0.364348	−	0.506291i
$586$		0			0
$587$	−181136.	+	181136.i	−0.525690	+	0.525690i	−0.919284	−	0.393595i	$-0.871231\pi$
$587$	−181136.	+	181136.i	−0.525690	+	0.525690i	0.393595	+	0.919284i	$0.371231\pi$
$588$		0			0
$589$			109915.i			0.316831i
$590$		0			0
$591$	−20025.3			−0.0573328
$592$		0			0
$593$	−235890.	−	235890.i	−0.670812	−	0.670812i	0.287091	−	0.957903i	$-0.407312\pi$
$593$	−235890.	−	235890.i	−0.670812	−	0.670812i	−0.957903	+	0.287091i	$0.907312\pi$
$594$		0			0
$595$	−25390.1	−	155736.i	−0.0717183	−	0.439902i
$596$		0			0
$597$	−232258.	+	232258.i	−0.651660	+	0.651660i
$598$		0			0
$599$			141629.i			0.394728i	0.980330	+	0.197364i	$0.0632381\pi$
$599$			141629.i			0.394728i	−0.980330	+	0.197364i	$0.936762\pi$
$600$		0			0
$601$	−564417.			−1.56261			−0.781306	−	0.624148i	$-0.785446\pi$
$601$	−564417.			−1.56261			−0.781306	+	0.624148i	$0.785446\pi$
$602$		0			0
$603$	−76490.8	−	76490.8i	−0.210366	−	0.210366i
$604$		0			0
$605$	330509.	−	53883.8i	0.902969	−	0.147213i
$606$		0			0
$607$	−247253.	+	247253.i	−0.671064	+	0.671064i	−0.957961	−	0.286898i	$-0.907376\pi$
$607$	−247253.	+	247253.i	−0.671064	+	0.671064i	0.286898	+	0.957961i	$0.407376\pi$
$608$		0			0
$609$		−	274256.i		−	0.739472i
$610$		0			0
$611$	−1.18196e6			−3.16606
$612$		0			0
$613$	−163758.	−	163758.i	−0.435794	−	0.435794i	0.454800	−	0.890594i	$-0.349711\pi$
$613$	−163758.	−	163758.i	−0.435794	−	0.435794i	−0.890594	+	0.454800i	$0.849711\pi$
$614$		0			0
$615$	−146180.	−	105197.i	−0.386490	−	0.278134i
$616$		0			0
$617$	273782.	−	273782.i	0.719176	−	0.719176i	−0.249260	−	0.968437i	$-0.580188\pi$
$617$	273782.	−	273782.i	0.719176	−	0.719176i	0.968437	+	0.249260i	$0.0801875\pi$
$618$		0			0
$619$		−	428345.i		−	1.11792i	−0.829194	−	0.558962i	$-0.811200\pi$
$619$		−	428345.i		−	1.11792i	0.829194	−	0.558962i	$-0.188800\pi$
$620$		0			0
$621$	17396.9			0.0451116
$622$		0			0
$623$	−440465.	−	440465.i	−1.13484	−	1.13484i
$624$		0			0
$625$	311809.	−	235293.i	0.798231	−	0.602351i
$626$		0			0
$627$	−167467.	+	167467.i	−0.425986	+	0.425986i
$628$		0			0
$629$		−	29483.8i		−	0.0745216i
$630$		0			0
$631$	−108870.			−0.273432			−0.136716	−	0.990610i	$-0.543655\pi$
$631$	−108870.			−0.273432			−0.136716	+	0.990610i	$0.543655\pi$
$632$		0			0
$633$	−56841.0	−	56841.0i	−0.141858	−	0.141858i
$634$		0			0
$635$	238989.	−	332094.i	0.592694	−	0.823595i
$636$		0			0
$637$	−346322.	+	346322.i	−0.853495	+	0.853495i
$638$		0			0
$639$		−	144154.i		−	0.353040i
$640$		0			0
$641$	−501643.			−1.22090			−0.610448	−	0.792056i	$-0.709011\pi$
$641$	−501643.			−1.22090			−0.610448	+	0.792056i	$0.709011\pi$
$642$		0			0
$643$	117251.	+	117251.i	0.283592	+	0.283592i	0.834540	−	0.550948i	$-0.185734\pi$
$643$	117251.	+	117251.i	0.283592	+	0.283592i	−0.550948	+	0.834540i	$0.685734\pi$
$644$		0			0
$645$	−16802.1	−	103060.i	−0.0403872	−	0.247725i
$646$		0			0
$647$	362031.	−	362031.i	0.864843	−	0.864843i	−0.127053	−	0.991896i	$-0.540552\pi$
$647$	362031.	−	362031.i	0.864843	−	0.864843i	0.991896	+	0.127053i	$0.0405519\pi$
$648$		0			0
$649$			54836.8i			0.130192i
$650$		0			0
$651$	131861.			0.311139
$652$		0			0
$653$	−411293.	−	411293.i	−0.964552	−	0.964552i	0.0348413	−	0.999393i	$-0.488907\pi$
$653$	−411293.	−	411293.i	−0.964552	−	0.964552i	−0.999393	+	0.0348413i	$0.988907\pi$
$654$		0			0
$655$	−1619.20	+	263.982i	−0.00377413	+	0.000615306i
$656$		0			0
$657$	−185361.	+	185361.i	−0.429426	+	0.429426i
$658$		0			0
$659$			291952.i			0.672265i	0.941815	+	0.336133i	$0.109119\pi$
$659$			291952.i			0.672265i	−0.941815	+	0.336133i	$0.890881\pi$
$660$		0			0
$661$	757270.			1.73320			0.866599	−	0.499006i	$-0.166301\pi$
$661$	757270.			1.73320			0.866599	+	0.499006i	$0.166301\pi$
$662$		0			0
$663$	116697.	+	116697.i	0.265480	+	0.265480i
$664$		0			0
$665$	347143.	+	249819.i	0.784992	+	0.564914i
$666$		0			0
$667$	73638.3	−	73638.3i	0.165521	−	0.165521i
$668$		0			0
$669$		−	211766.i		−	0.473156i
$670$		0			0
$671$	704193.			1.56404
$672$		0			0
$673$	310335.	+	310335.i	0.685173	+	0.685173i	0.961161	−	0.275988i	$-0.0890050\pi$
$673$	310335.	+	310335.i	0.685173	+	0.685173i	−0.275988	+	0.961161i	$0.589005\pi$
$674$		0			0
$675$	−39098.6	+	78485.5i	−0.0858130	+	0.172259i
$676$		0			0
$677$	9203.97	−	9203.97i	0.0200816	−	0.0200816i	−0.696995	−	0.717076i	$-0.745480\pi$
$677$	9203.97	−	9203.97i	0.0200816	−	0.0200816i	0.717076	+	0.696995i	$0.245480\pi$
$678$		0			0
$679$		−	950012.i		−	2.06058i
$680$		0			0
$681$	−6497.79			−0.0140111
$682$		0			0
$683$	421590.	+	421590.i	0.903750	+	0.903750i	0.995758	−	0.0920080i	$-0.0293285\pi$
$683$	421590.	+	421590.i	0.903750	+	0.903750i	−0.0920080	+	0.995758i	$0.529329\pi$
$684$		0			0
$685$	11966.3	−	16628.1i	0.0255023	−	0.0354374i
$686$		0			0
$687$	−44371.4	+	44371.4i	−0.0940135	+	0.0940135i
$688$		0			0
$689$			616584.i			1.29883i
$690$		0			0
$691$	−102275.			−0.214197			−0.107098	−	0.994248i	$-0.534156\pi$
$691$	−102275.			−0.214197			−0.107098	+	0.994248i	$0.534156\pi$
$692$		0			0
$693$	200904.	+	200904.i	0.418333	+	0.418333i
$694$		0			0
$695$	145454.	+	892177.i	0.301131	+	1.84706i
$696$		0			0
$697$	98454.3	−	98454.3i	0.202660	−	0.202660i
$698$		0			0
$699$		−	181476.i		−	0.371420i
$700$		0			0
$701$	−685359.			−1.39471			−0.697353	−	0.716728i	$-0.745639\pi$
$701$	−685359.			−1.39471			−0.697353	+	0.716728i	$0.745639\pi$
$702$		0			0
$703$	56508.1	+	56508.1i	0.114341	+	0.114341i
$704$		0			0
$705$	479182.	−	78122.2i	0.964100	−	0.157180i
$706$		0			0
$707$	78350.6	−	78350.6i	0.156749	−	0.156749i
$708$		0			0
$709$			164715.i			0.327673i	0.986487	+	0.163837i	$0.0523870\pi$
$709$			164715.i			0.327673i	−0.986487	+	0.163837i	$0.947613\pi$
$710$		0			0
$711$	−126001.			−0.249249
$712$		0			0
$713$	35404.9	+	35404.9i	0.0696441	+	0.0696441i
$714$		0			0
$715$	1.07450e6	+	773254.i	2.10181	+	1.51255i
$716$		0			0
$717$	−177053.	+	177053.i	−0.344402	+	0.344402i
$718$		0			0
$719$		−	782798.i		−	1.51423i	−0.653282	−	0.757115i	$-0.726608\pi$
$719$		−	782798.i		−	1.51423i	0.653282	−	0.757115i	$-0.273392\pi$
$720$		0			0
$721$	−214577.			−0.412774
$722$		0			0
$723$	−202760.	−	202760.i	−0.387887	−	0.387887i
$724$		0			0
$725$	166719.	+	497715.i	0.317182	+	0.946900i
$726$		0			0
$727$	−659110.	+	659110.i	−1.24706	+	1.24706i	−0.290054	+	0.957010i	$0.593673\pi$
$727$	−659110.	+	659110.i	−1.24706	+	1.24706i	−0.957010	+	0.290054i	$0.906327\pi$
$728$		0			0
$729$		−	19683.0i		−	0.0370370i
$730$		0			0
$731$	80728.6			0.151075
$732$		0			0
$733$	356952.	+	356952.i	0.664358	+	0.664358i	0.956404	−	0.292046i	$-0.0943361\pi$
$733$	356952.	+	356952.i	0.664358	+	0.664358i	−0.292046	+	0.956404i	$0.594336\pi$
$734$		0			0
$735$	117513.	−	163294.i	0.217526	−	0.302270i
$736$		0			0
$737$	474354.	−	474354.i	0.873309	−	0.873309i
$738$		0			0
$739$			231725.i			0.424311i	0.977236	+	0.212156i	$0.0680483\pi$
$739$			231725.i			0.424311i	−0.977236	+	0.212156i	$0.931952\pi$
$740$		0			0
$741$	−447317.			−0.814665
$742$		0			0
$743$	35964.9	+	35964.9i	0.0651480	+	0.0651480i	0.738930	−	0.673782i	$-0.235331\pi$
$743$	35964.9	+	35964.9i	0.0651480	+	0.0651480i	−0.673782	+	0.738930i	$0.735331\pi$
$744$		0			0
$745$	8624.43	+	52900.1i	0.0155388	+	0.0953111i
$746$		0			0
$747$	111023.	−	111023.i	0.198963	−	0.198963i
$748$		0			0
$749$		−	380314.i		−	0.677920i
$750$		0			0
$751$	−702045.			−1.24476			−0.622379	−	0.782716i	$-0.713834\pi$
$751$	−702045.			−1.24476			−0.622379	+	0.782716i	$0.713834\pi$
$752$		0			0
$753$	255976.	+	255976.i	0.451449	+	0.451449i
$754$		0			0
$755$	220602.	−	35965.3i	0.387004	−	0.0630943i
$756$		0			0
$757$	−111880.	+	111880.i	−0.195236	+	0.195236i	−0.797954	−	0.602718i	$-0.794084\pi$
$757$	−111880.	+	111880.i	−0.195236	+	0.195236i	0.602718	+	0.797954i	$0.294084\pi$
$758$		0			0
$759$			107886.i			0.187276i
$760$		0			0
$761$	−579015.			−0.999817			−0.499908	−	0.866078i	$-0.666633\pi$
$761$	−579015.			−0.999817			−0.499908	+	0.866078i	$0.666633\pi$
$762$		0			0
$763$	525252.	+	525252.i	0.902232	+	0.902232i
$764$		0			0
$765$	−55023.5	−	39597.2i	−0.0940211	−	0.0676616i
$766$		0			0
$767$	−73236.4	+	73236.4i	−0.124491	+	0.124491i
$768$		0			0
$769$		−	472110.i		−	0.798344i	−0.916876	−	0.399172i	$-0.869298\pi$
$769$		−	472110.i		−	0.798344i	0.916876	−	0.399172i	$-0.130702\pi$
$770$		0			0
$771$	−85348.4			−0.143578
$772$		0			0
$773$	−20353.7	−	20353.7i	−0.0340631	−	0.0340631i	0.689870	−	0.723933i	$-0.257668\pi$
$773$	−20353.7	−	20353.7i	−0.0340631	−	0.0340631i	−0.723933	+	0.689870i	$0.757668\pi$
$774$		0			0
$775$	−239298.	+	80157.4i	−0.398416	+	0.133457i
$776$		0			0
$777$	67790.5	−	67790.5i	0.112286	−	0.112286i
$778$		0			0
$779$			377391.i			0.621895i
$780$		0			0
$781$	893963.			1.46561
$782$		0			0
$783$	−83315.0	−	83315.0i	−0.135894	−	0.135894i
$784$		0			0
$785$	372406.	−	517488.i	0.604335	−	0.839771i
$786$		0			0
$787$	−640630.	+	640630.i	−1.03433	+	1.03433i	−0.0349373	+	0.999390i	$0.511123\pi$
$787$	−640630.	+	640630.i	−1.03433	+	1.03433i	−0.999390	+	0.0349373i	$0.988877\pi$
$788$		0			0
$789$		−	637933.i		−	1.02476i
$790$		0			0
$791$	−144037.			−0.230208
$792$		0			0
$793$	940474.	+	940474.i	1.49555	+	1.49555i
$794$		0			0
$795$	−40753.5	−	249971.i	−0.0644808	−	0.395509i
$796$		0			0
$797$	542782.	−	542782.i	0.854494	−	0.854494i	−0.136189	−	0.990683i	$-0.543485\pi$
$797$	542782.	−	542782.i	0.854494	−	0.854494i	0.990683	+	0.136189i	$0.0434854\pi$
$798$		0			0
$799$			375352.i			0.587956i
$800$		0			0
$801$	−267614.			−0.417103
$802$		0			0
$803$	−1.14951e6	−	1.14951e6i	−1.78271	−	1.78271i
$804$		0			0
$805$	192288.	−	31349.2i	0.296729	−	0.0483765i
$806$		0			0
$807$	343318.	−	343318.i	0.527168	−	0.527168i
$808$		0			0
$809$		−	1.09699e6i		−	1.67613i	−0.545571	−	0.838065i	$-0.683687\pi$
$809$		−	1.09699e6i		−	1.67613i	0.545571	−	0.838065i	$-0.316313\pi$
$810$		0			0
$811$	711398.			1.08161			0.540805	−	0.841148i	$-0.318120\pi$
$811$	711398.			1.08161			0.540805	+	0.841148i	$0.318120\pi$
$812$		0			0
$813$	39889.3	+	39889.3i	0.0603498	+	0.0603498i
$814$		0			0
$815$	196832.	+	141649.i	0.296334	+	0.213254i
$816$		0			0
$817$	−154723.	+	154723.i	−0.231798	+	0.231798i
$818$		0			0
$819$			536628.i			0.800028i
$820$		0			0
$821$	−566243.			−0.840071			−0.420036	−	0.907508i	$-0.637982\pi$
$821$	−566243.			−0.840071			−0.420036	+	0.907508i	$0.637982\pi$
$822$		0			0
$823$	678523.	+	678523.i	1.00176	+	1.00176i	0.999998	+	0.00176504i	$0.000561830\pi$
$823$	678523.	+	678523.i	1.00176	+	1.00176i	0.00176504	+	0.999998i	$0.499438\pi$
$824$		0			0
$825$	−486724.	−	242468.i	−0.715114	−	0.356243i
$826$		0			0
$827$	822466.	−	822466.i	1.20256	−	1.20256i	0.229174	−	0.973385i	$-0.426397\pi$
$827$	822466.	−	822466.i	1.20256	−	1.20256i	0.973385	−	0.229174i	$-0.0736026\pi$
$828$		0			0
$829$			1.26805e6i			1.84514i	0.385832	+	0.922569i	$0.373914\pi$
$829$			1.26805e6i			1.84514i	−0.385832	+	0.922569i	$0.626086\pi$
$830$		0			0
$831$	479228.			0.693969
$832$		0			0
$833$	109981.	+	109981.i	0.158499	+	0.158499i
$834$		0			0
$835$	773178.	−	1.07439e6i	1.10894	−	1.54095i
$836$		0			0
$837$	40057.4	−	40057.4i	0.0571784	−	0.0571784i
$838$		0			0
$839$		−	487091.i		−	0.691968i	−0.938240	−	0.345984i	$-0.887545\pi$
$839$		−	487091.i		−	0.691968i	0.938240	−	0.345984i	$-0.112455\pi$
$840$		0			0
$841$	1962.99			0.00277541
$842$		0			0
$843$	−31853.2	−	31853.2i	−0.0448227	−	0.0448227i
$844$		0			0
$845$	287429.	+	1.76301e6i	0.402547	+	2.46912i
$846$		0			0
$847$	−595260.	+	595260.i	−0.829736	+	0.829736i
$848$		0			0
$849$			174504.i			0.242098i
$850$		0			0
$851$	36403.7			0.0502675
$852$		0			0
$853$	10645.4	+	10645.4i	0.0146307	+	0.0146307i	0.714384	−	0.699754i	$-0.246707\pi$
$853$	10645.4	+	10645.4i	0.0146307	+	0.0146307i	−0.699754	+	0.714384i	$0.746707\pi$
$854$		0			0
$855$	181348.	−	29565.7i	0.248074	−	0.0404441i
$856$		0			0
$857$	−692563.	+	692563.i	−0.942970	+	0.942970i	−0.998459	−	0.0554896i	$-0.982328\pi$
$857$	−692563.	+	692563.i	−0.942970	+	0.942970i	0.0554896	+	0.998459i	$0.482328\pi$
$858$		0			0
$859$			745974.i			1.01097i	0.862836	+	0.505484i	$0.168686\pi$
$859$			745974.i			1.01097i	−0.862836	+	0.505484i	$0.831314\pi$
$860$		0			0
$861$	452741.			0.610722
$862$		0			0
$863$	−259362.	−	259362.i	−0.348245	−	0.348245i	0.511211	−	0.859456i	$-0.329197\pi$
$863$	−259362.	−	259362.i	−0.348245	−	0.348245i	−0.859456	+	0.511211i	$0.829197\pi$
$864$		0			0
$865$	−936618.	−	674030.i	−1.25179	−	0.900838i
$866$		0			0
$867$	−269817.	+	269817.i	−0.358947	+	0.358947i
$868$		0			0
$869$		−	781388.i		−	1.03473i
$870$		0			0
$871$	1.26703e6			1.67013
$872$		0			0
$873$	−288600.	−	288600.i	−0.378676	−	0.378676i
$874$		0			0
$875$	−290725.	+	937956.i	−0.379723	+	1.22509i
$876$		0			0
$877$	−191986.	+	191986.i	−0.249615	+	0.249615i	−0.820813	−	0.571197i	$-0.806479\pi$
$877$	−191986.	+	191986.i	−0.249615	+	0.249615i	0.571197	+	0.820813i	$0.306479\pi$
$878$		0			0
$879$		−	404733.i		−	0.523830i
$880$		0			0
$881$	1.08074e6			1.39241			0.696207	−	0.717841i	$-0.254870\pi$
$881$	1.08074e6			1.39241			0.696207	+	0.717841i	$0.254870\pi$
$882$		0			0
$883$	−294604.	−	294604.i	−0.377848	−	0.377848i	0.492477	−	0.870325i	$-0.336091\pi$
$883$	−294604.	−	294604.i	−0.377848	−	0.377848i	−0.870325	+	0.492477i	$0.836091\pi$
$884$		0			0
$885$	24850.4	−	34531.6i	0.0317283	−	0.0440890i
$886$		0			0
$887$	373328.	−	373328.i	0.474507	−	0.474507i	−0.428862	−	0.903370i	$-0.641085\pi$
$887$	373328.	−	373328.i	0.474507	−	0.474507i	0.903370	+	0.428862i	$0.141085\pi$
$888$		0			0
$889$			1.02854e6i			1.30143i
$890$		0			0
$891$	122063.			0.153755
$892$		0			0
$893$	−719392.	−	719392.i	−0.902117	−	0.902117i
$894$		0			0
$895$	−25730.0	−	157821.i	−0.0321213	−	0.197024i
$896$		0			0
$897$	−144086.	+	144086.i	−0.179075	+	0.179075i
$898$		0			0
$899$		−	339113.i		−	0.419590i
$900$		0			0
$901$	195807.			0.241201
$902$		0			0
$903$	185615.	+	185615.i	0.227634	+	0.227634i
$904$		0			0
$905$	1.20968e6	−	197217.i	1.47697	−	0.240795i
$906$		0			0
$907$	342694.	−	342694.i	0.416574	−	0.416574i	−0.467447	−	0.884021i	$-0.654826\pi$
$907$	342694.	−	342694.i	0.416574	−	0.416574i	0.884021	+	0.467447i	$0.154826\pi$
$908$		0			0
$909$		−	47603.5i		−	0.0576118i
$910$		0			0
$911$	−653388.			−0.787290			−0.393645	−	0.919263i	$-0.628786\pi$
$911$	−653388.			−0.787290			−0.393645	+	0.919263i	$0.628786\pi$
$912$		0			0
$913$	688506.	+	688506.i	0.825974	+	0.825974i
$914$		0			0
$915$	−443442.	−	319119.i	−0.529657	−	0.381163i
$916$		0			0
$917$	2916.24	−	2916.24i	0.00346804	−	0.00346804i
$918$		0			0
$919$		−	316752.i		−	0.375050i	−0.982260	−	0.187525i	$-0.939953\pi$
$919$		−	316752.i		−	0.375050i	0.982260	−	0.187525i	$-0.0600465\pi$
$920$		0			0
$921$	−87896.0			−0.103621
$922$		0			0
$923$	1.19392e6	+	1.19392e6i	1.40143	+	1.40143i
$924$		0			0
$925$	−81815.4	+	164234.i	−0.0956206	+	0.191947i
$926$		0			0
$927$	−65185.2	+	65185.2i	−0.0758560	+	0.0758560i
$928$		0			0
$929$			1.39646e6i			1.61807i	0.587759	+	0.809036i	$0.300010\pi$
$929$			1.39646e6i			1.61807i	−0.587759	+	0.809036i	$0.699990\pi$
$930$		0			0
$931$	−421574.			−0.486378
$932$		0			0
$933$	239870.	+	239870.i	0.275558	+	0.275558i
$934$		0			0
$935$	245560.	−	341226.i	0.280889	−	0.390318i
$936$		0			0
$937$	81884.2	−	81884.2i	0.0932655	−	0.0932655i	−0.658935	−	0.752200i	$-0.728993\pi$
$937$	81884.2	−	81884.2i	0.0932655	−	0.0932655i	0.752200	+	0.658935i	$0.228993\pi$
$938$		0			0
$939$		−	47165.7i		−	0.0534928i
$940$		0			0
$941$	1.67094e6			1.88705			0.943524	−	0.331305i	$-0.107489\pi$
$941$	1.67094e6			1.88705			0.943524	+	0.331305i	$0.107489\pi$
$942$		0			0
$943$	121562.	+	121562.i	0.136702	+	0.136702i
$944$		0			0
$945$	−35468.7	−	217556.i	−0.0397175	−	0.243617i
$946$		0			0
$947$	−689602.	+	689602.i	−0.768950	+	0.768950i	−0.977922	−	0.208971i	$-0.932988\pi$
$947$	−689602.	+	689602.i	−0.768950	+	0.768950i	0.208971	+	0.977922i	$0.432988\pi$
$948$		0			0
$949$		−	3.07042e6i		−	3.40930i
$950$		0			0
$951$	162402.			0.179569
$952$		0			0
$953$	150337.	+	150337.i	0.165532	+	0.165532i	0.785012	−	0.619480i	$-0.212657\pi$
$953$	150337.	+	150337.i	0.165532	+	0.165532i	−0.619480	+	0.785012i	$0.712657\pi$
$954$		0			0
$955$	−985710.	+	160703.i	−1.08079	+	0.176204i
$956$		0			0
$957$	516674.	−	516674.i	0.564148	−	0.564148i
$958$		0			0
$959$			51499.7i			0.0559974i
$960$		0			0
$961$	−760477.			−0.823454
$962$		0			0
$963$	−115534.	−	115534.i	−0.124582	−	0.124582i
$964$		0			0
$965$	−681527.	−	490456.i	−0.731861	−	0.526678i
$966$		0			0
$967$	312723.	−	312723.i	0.334432	−	0.334432i	−0.519835	−	0.854267i	$-0.674007\pi$
$967$	312723.	−	312723.i	0.334432	−	0.334432i	0.854267	+	0.519835i	$0.174007\pi$
$968$		0			0
$969$			142053.i			0.151288i
$970$		0			0
$971$	−1.16534e6			−1.23598			−0.617992	−	0.786185i	$-0.712054\pi$
$971$	−1.16534e6			−1.23598			−0.617992	+	0.786185i	$0.712054\pi$
$972$		0			0
$973$	−1.60685e6	−	1.60685e6i	−1.69726	−	1.69726i
$974$		0			0
$975$	−326213.	−	973861.i	−0.343156	−	1.02444i
$976$		0			0
$977$	−748461.	+	748461.i	−0.784115	+	0.784115i	−0.980522	−	0.196407i	$-0.937073\pi$
$977$	−748461.	+	748461.i	−0.784115	+	0.784115i	0.196407	+	0.980522i	$0.437073\pi$
$978$		0			0
$979$		−	1.65959e6i		−	1.73156i
$980$		0			0
$981$	319127.			0.331609
$982$		0			0
$983$	542812.	+	542812.i	0.561749	+	0.561749i	0.929804	−	0.368055i	$-0.119976\pi$
$983$	542812.	+	542812.i	0.561749	+	0.561749i	−0.368055	+	0.929804i	$0.619976\pi$
$984$		0			0
$985$	−56277.3	+	78201.8i	−0.0580044	+	0.0806017i
$986$		0			0
$987$	−863025.	+	863025.i	−0.885909	+	0.885909i
$988$		0			0
$989$			99675.8i			0.101905i
$990$		0			0
$991$	−1.08269e6			−1.10245			−0.551224	−	0.834357i	$-0.685839\pi$
$991$	−1.08269e6			−1.10245			−0.551224	+	0.834357i	$0.685839\pi$
$992$		0			0
$993$	180437.	+	180437.i	0.182990	+	0.182990i
$994$		0			0
$995$	254285.	+	1.55972e6i	0.256847	+	1.57544i
$996$		0			0
$997$	25593.2	−	25593.2i	0.0257475	−	0.0257475i	−0.694116	−	0.719863i	$-0.744204\pi$
$997$	25593.2	−	25593.2i	0.0257475	−	0.0257475i	0.719863	+	0.694116i	$0.244204\pi$
$998$		0			0
$999$		−	41187.5i		−	0.0412700i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.5.bg.b.193.2		4
4.3	odd	2		30.5.f.a.13.1	yes	4
5.2	odd	4	inner	240.5.bg.b.97.2		4
12.11	even	2		90.5.g.e.73.1		4
20.3	even	4		150.5.f.e.7.2		4
20.7	even	4		30.5.f.a.7.1	✓	4
20.19	odd	2		150.5.f.e.43.2		4
60.23	odd	4		450.5.g.f.307.1		4
60.47	odd	4		90.5.g.e.37.1		4
60.59	even	2		450.5.g.f.343.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.5.f.a.7.1	✓	4	20.7	even	4
30.5.f.a.13.1	yes	4	4.3	odd	2
90.5.g.e.37.1		4	60.47	odd	4
90.5.g.e.73.1		4	12.11	even	2
150.5.f.e.7.2		4	20.3	even	4
150.5.f.e.43.2		4	20.19	odd	2
240.5.bg.b.97.2		4	5.2	odd	4	inner
240.5.bg.b.193.2		4	1.1	even	1	trivial
450.5.g.f.307.1		4	60.23	odd	4
450.5.g.f.343.1		4	60.59	even	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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	240.bg (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.67423 + 3.67423i) q^{3} +(24.6742 - 4.02270i) q^{5} +(-44.4393 + 44.4393i) q^{7} +27.0000i q^{9} +O(q^{10})\)	\(q+(3.67423 + 3.67423i) q^{3} +(24.6742 - 4.02270i) q^{5} +(-44.4393 + 44.4393i) q^{7} +27.0000i q^{9} -167.439 q^{11} +(-223.621 - 223.621i) q^{13} +(105.439 + 75.8786i) q^{15} +(-71.0148 + 71.0148i) q^{17} -272.211i q^{19} -326.561 q^{21} +(-87.6821 - 87.6821i) q^{23} +(592.636 - 198.514i) q^{25} +(-99.2043 + 99.2043i) q^{27} +839.832i q^{29} -403.787 q^{31} +(-615.211 - 615.211i) q^{33} +(-917.739 + 1275.27i) q^{35} +(-207.589 + 207.589i) q^{37} -1643.27i q^{39} -1386.39 q^{41} +(-568.393 - 568.393i) q^{43} +(108.613 + 666.204i) q^{45} +(2642.77 - 2642.77i) q^{47} -1548.70i q^{49} -521.850 q^{51} +(-1378.64 - 1378.64i) q^{53} +(-4131.44 + 673.559i) q^{55} +(1000.17 - 1000.17i) q^{57} -327.503i q^{59} -4205.66 q^{61} +(-1199.86 - 1199.86i) q^{63} +(-6417.24 - 4618.11i) q^{65} +(-2832.99 + 2832.99i) q^{67} -644.330i q^{69} -5339.03 q^{71} +(6865.24 + 6865.24i) q^{73} +(2906.87 + 1448.09i) q^{75} +(7440.88 - 7440.88i) q^{77} +4666.69i q^{79} -729.000 q^{81} +(-4111.98 - 4111.98i) q^{83} +(-1466.56 + 2037.91i) q^{85} +(-3085.74 + 3085.74i) q^{87} +9911.62i q^{89} +19875.1 q^{91} +(-1483.61 - 1483.61i) q^{93} +(-1095.03 - 6716.60i) q^{95} +(-10688.9 + 10688.9i) q^{97} -4520.86i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 84 q^{5} + 28 q^{7}+O(q^{10}) \) 4 * q + 84 * q^5 + 28 * q^7	\( 4 q + 84 q^{5} + 28 q^{7} - 464 q^{11} - 336 q^{13} + 216 q^{15} + 392 q^{17} - 1512 q^{21} - 968 q^{23} + 1136 q^{25} + 560 q^{31} - 756 q^{33} + 2296 q^{35} + 2256 q^{37} + 392 q^{41} - 216 q^{43} - 756 q^{45} + 9072 q^{47} - 4968 q^{51} - 4280 q^{53} - 10500 q^{55} + 6264 q^{57} - 4536 q^{61} + 756 q^{63} - 12912 q^{65} + 2248 q^{67} - 18064 q^{71} + 20524 q^{73} + 10584 q^{75} + 7336 q^{77} - 2916 q^{81} + 336 q^{83} + 15944 q^{85} - 8316 q^{87} + 52752 q^{91} - 7992 q^{93} - 23104 q^{95} - 40404 q^{97}+O(q^{100}) \) 4 * q + 84 * q^5 + 28 * q^7 - 464 * q^11 - 336 * q^13 + 216 * q^15 + 392 * q^17 - 1512 * q^21 - 968 * q^23 + 1136 * q^25 + 560 * q^31 - 756 * q^33 + 2296 * q^35 + 2256 * q^37 + 392 * q^41 - 216 * q^43 - 756 * q^45 + 9072 * q^47 - 4968 * q^51 - 4280 * q^53 - 10500 * q^55 + 6264 * q^57 - 4536 * q^61 + 756 * q^63 - 12912 * q^65 + 2248 * q^67 - 18064 * q^71 + 20524 * q^73 + 10584 * q^75 + 7336 * q^77 - 2916 * q^81 + 336 * q^83 + 15944 * q^85 - 8316 * q^87 + 52752 * q^91 - 7992 * q^93 - 23104 * q^95 - 40404 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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