LMFDB - Embedded newform 230.5.c.a.229.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,5,Mod(229,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("230.229");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	230.c (of order $2$, degree $1$, 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:	$23.7750915093$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.8
Character	$\chi$	$=$	230.229
Dual form			230.5.c.a.229.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.82843i q^{2} +0.832711i q^{3} -8.00000 q^{4} +(19.4576 + 15.6972i) q^{5} -2.35526 q^{6} +66.8572 q^{7} -22.6274i q^{8} +80.3066 q^{9} +O(q^{10})$	\(q+2.82843i q^{2} +0.832711i q^{3} -8.00000 q^{4} +(19.4576 + 15.6972i) q^{5} -2.35526 q^{6} +66.8572 q^{7} -22.6274i q^{8} +80.3066 q^{9} +(-44.3985 + 55.0343i) q^{10} -65.0740i q^{11} -6.66169i q^{12} -269.615i q^{13} +189.101i q^{14} +(-13.0713 + 16.2025i) q^{15} +64.0000 q^{16} +87.9174 q^{17} +227.141i q^{18} -708.415i q^{19} +(-155.661 - 125.578i) q^{20} +55.6727i q^{21} +184.057 q^{22} +(-507.336 - 149.839i) q^{23} +18.8421 q^{24} +(132.194 + 610.860i) q^{25} +762.586 q^{26} +134.322i q^{27} -534.857 q^{28} +84.5700 q^{29} +(-45.8277 - 36.9711i) q^{30} +1611.43 q^{31} +181.019i q^{32} +54.1878 q^{33} +248.668i q^{34} +(1300.88 + 1049.47i) q^{35} -642.453 q^{36} +1015.63 q^{37} +2003.70 q^{38} +224.511 q^{39} +(355.188 - 440.274i) q^{40} -879.723 q^{41} -157.466 q^{42} -899.776 q^{43} +520.592i q^{44} +(1562.57 + 1260.59i) q^{45} +(423.807 - 1434.96i) q^{46} +2264.87i q^{47} +53.2935i q^{48} +2068.88 q^{49} +(-1727.77 + 373.900i) q^{50} +73.2098i q^{51} +2156.92i q^{52} -3444.29 q^{53} -379.919 q^{54} +(1021.48 - 1266.18i) q^{55} -1512.81i q^{56} +589.905 q^{57} +239.200i q^{58} +4781.22 q^{59} +(104.570 - 129.620i) q^{60} -316.058i q^{61} +4557.81i q^{62} +5369.07 q^{63} -512.000 q^{64} +(4232.21 - 5246.05i) q^{65} +153.266i q^{66} -4010.12 q^{67} -703.339 q^{68} +(124.772 - 422.464i) q^{69} +(-2968.36 + 3679.44i) q^{70} -7480.16 q^{71} -1817.13i q^{72} +9429.75i q^{73} +2872.63i q^{74} +(-508.670 + 110.079i) q^{75} +5667.32i q^{76} -4350.66i q^{77} +635.014i q^{78} +6602.25i q^{79} +(1245.28 + 1004.62i) q^{80} +6392.98 q^{81} -2488.23i q^{82} -7557.25 q^{83} -445.382i q^{84} +(1710.66 + 1380.06i) q^{85} -2544.95i q^{86} +70.4224i q^{87} -1472.46 q^{88} +8915.39i q^{89} +(-3565.49 + 4419.62i) q^{90} -18025.7i q^{91} +(4058.68 + 1198.71i) q^{92} +1341.85i q^{93} -6406.01 q^{94} +(11120.2 - 13784.0i) q^{95} -150.737 q^{96} +5318.88 q^{97} +5851.68i q^{98} -5225.87i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9}+O(q^{10}) $ 48 * q - 384 * q^4 - 64 * q^6 - 1608 * q^9	$ 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9} + 3072 q^{16} + 512 q^{24} + 1488 q^{25} - 384 q^{26} - 2940 q^{29} + 4732 q^{31} + 2556 q^{35} + 12864 q^{36} + 2736 q^{39} + 828 q^{41} - 64 q^{46} + 32572 q^{49} - 3264 q^{50} + 10112 q^{54} + 12824 q^{55} + 7092 q^{59} - 24576 q^{64} + 14000 q^{69} - 6592 q^{70} - 12708 q^{71} + 24728 q^{75} - 13040 q^{81} - 15700 q^{85} - 9728 q^{94} - 46608 q^{95} - 4096 q^{96}+O(q^{100}) $ 48 * q - 384 * q^4 - 64 * q^6 - 1608 * q^9 + 3072 * q^16 + 512 * q^24 + 1488 * q^25 - 384 * q^26 - 2940 * q^29 + 4732 * q^31 + 2556 * q^35 + 12864 * q^36 + 2736 * q^39 + 828 * q^41 - 64 * q^46 + 32572 * q^49 - 3264 * q^50 + 10112 * q^54 + 12824 * q^55 + 7092 * q^59 - 24576 * q^64 + 14000 * q^69 - 6592 * q^70 - 12708 * q^71 + 24728 * q^75 - 13040 * q^81 - 15700 * q^85 - 9728 * q^94 - 46608 * q^95 - 4096 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$-1$

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 $

$2$			2.82843i			0.707107i
$2$			2.82843i			0.707107i
$3$			0.832711i			0.0925234i	0.998929	+	0.0462617i	$0.0147308\pi$
$3$			0.832711i			0.0925234i	−0.998929	+	0.0462617i	$0.985269\pi$
$4$	−8.00000			−0.500000
$5$	19.4576	+	15.6972i	0.778303	+	0.627889i
$5$	19.4576	+	15.6972i	0.778303	+	0.627889i
$6$	−2.35526			−0.0654239
$7$	66.8572			1.36443			0.682216	−	0.731151i	$-0.261016\pi$
$7$	66.8572			1.36443			0.682216	+	0.731151i	$0.261016\pi$
$8$		−	22.6274i		−	0.353553i
$9$	80.3066			0.991439
$10$	−44.3985	+	55.0343i	−0.443985	+	0.550343i
$11$		−	65.0740i		−	0.537801i	−0.963168	−	0.268901i	$-0.913340\pi$
$11$		−	65.0740i		−	0.537801i	0.963168	−	0.268901i	$-0.0866604\pi$
$12$		−	6.66169i		−	0.0462617i
$13$		−	269.615i		−	1.59535i	−0.603085	−	0.797677i	$-0.706062\pi$
$13$		−	269.615i		−	1.59535i	0.603085	−	0.797677i	$-0.293938\pi$
$14$			189.101i			0.964799i
$15$	−13.0713	+	16.2025i	−0.0580945	+	0.0720112i
$16$	64.0000			0.250000
$17$	87.9174			0.304212			0.152106	−	0.988364i	$-0.451394\pi$
$17$	87.9174			0.304212			0.152106	+	0.988364i	$0.451394\pi$
$18$			227.141i			0.701054i
$19$		−	708.415i		−	1.96237i	−0.193072	−	0.981185i	$-0.561845\pi$
$19$		−	708.415i		−	1.96237i	0.193072	−	0.981185i	$-0.438155\pi$
$20$	−155.661	−	125.578i	−0.389151	−	0.313945i
$21$			55.6727i			0.126242i
$22$	184.057			0.380283
$23$	−507.336	−	149.839i	−0.959047	−	0.283249i
$23$	−507.336	−	149.839i	−0.959047	−	0.283249i
$24$	18.8421			0.0327120
$25$	132.194	+	610.860i	0.211510	+	0.977376i
$26$	762.586			1.12809
$27$			134.322i			0.184255i
$28$	−534.857			−0.682216
$29$	84.5700			0.100559			0.0502795	−	0.998735i	$-0.483989\pi$
$29$	84.5700			0.100559			0.0502795	+	0.998735i	$0.483989\pi$
$30$	−45.8277	−	36.9711i	−0.0509196	−	0.0410790i
$31$	1611.43			1.67682			0.838412	−	0.545037i	$-0.183484\pi$
$31$	1611.43			1.67682			0.838412	+	0.545037i	$0.183484\pi$
$32$			181.019i			0.176777i
$33$	54.1878			0.0497592
$34$			248.668i			0.215111i
$35$	1300.88	+	1049.47i	1.06194	+	0.856712i
$36$	−642.453			−0.495720
$37$	1015.63			0.741877			0.370938	−	0.928658i	$-0.379036\pi$
$37$	1015.63			0.741877			0.370938	+	0.928658i	$0.379036\pi$
$38$	2003.70			1.38760
$39$	224.511			0.147608
$40$	355.188	−	440.274i	0.221992	−	0.275172i
$41$	−879.723			−0.523333			−0.261667	−	0.965158i	$-0.584272\pi$
$41$	−879.723			−0.523333			−0.261667	+	0.965158i	$0.584272\pi$
$42$	−157.466			−0.0892665
$43$	−899.776			−0.486629			−0.243314	−	0.969947i	$-0.578235\pi$
$43$	−899.776			−0.486629			−0.243314	+	0.969947i	$0.578235\pi$
$44$			520.592i			0.268901i
$45$	1562.57	+	1260.59i	0.771640	+	0.622514i
$46$	423.807	−	1434.96i	0.200287	−	0.678148i
$47$			2264.87i			1.02529i	0.858600	+	0.512645i	$0.171334\pi$
$47$			2264.87i			1.02529i	−0.858600	+	0.512645i	$0.828666\pi$
$48$			53.2935i			0.0231309i
$49$	2068.88			0.861675
$50$	−1727.77	+	373.900i	−0.691109	+	0.149560i
$51$			73.2098i			0.0281468i
$52$			2156.92i			0.797677i
$53$	−3444.29			−1.22616			−0.613081	−	0.790020i	$-0.710070\pi$
$53$	−3444.29			−1.22616			−0.613081	+	0.790020i	$0.710070\pi$
$54$	−379.919			−0.130288
$55$	1021.48	−	1266.18i	0.337680	−	0.418572i
$56$		−	1512.81i		−	0.482400i
$57$	589.905			0.181565
$58$			239.200i			0.0711059i
$59$	4781.22			1.37352			0.686760	−	0.726884i	$-0.259032\pi$
$59$	4781.22			1.37352			0.686760	+	0.726884i	$0.259032\pi$
$60$	104.570	−	129.620i	0.0290472	−	0.0360056i
$61$		−	316.058i		−	0.0849390i	−0.999098	−	0.0424695i	$-0.986477\pi$
$61$		−	316.058i		−	0.0849390i	0.999098	−	0.0424695i	$-0.0135225\pi$
$62$			4557.81i			1.18569i
$63$	5369.07			1.35275
$64$	−512.000			−0.125000
$65$	4232.21	−	5246.05i	1.00171	−	1.24167i
$66$			153.266i			0.0351851i
$67$	−4010.12			−0.893321			−0.446661	−	0.894703i	$-0.647387\pi$
$67$	−4010.12			−0.893321			−0.446661	+	0.894703i	$0.647387\pi$
$68$	−703.339			−0.152106
$69$	124.772	−	422.464i	0.0262071	−	0.0887343i
$70$	−2968.36	+	3679.44i	−0.605787	+	0.750906i
$71$	−7480.16			−1.48386			−0.741932	−	0.670475i	$-0.766090\pi$
$71$	−7480.16			−1.48386			−0.741932	+	0.670475i	$0.766090\pi$
$72$		−	1817.13i		−	0.350527i
$73$			9429.75i			1.76952i	0.466052	+	0.884758i	$0.345676\pi$
$73$			9429.75i			1.76952i	−0.466052	+	0.884758i	$0.654324\pi$
$74$			2872.63i			0.524586i
$75$	−508.670	+	110.079i	−0.0904302	+	0.0195696i
$76$			5667.32i			0.981185i
$77$		−	4350.66i		−	0.733794i
$78$			635.014i			0.104374i
$79$			6602.25i			1.05788i	0.848658	+	0.528941i	$0.177411\pi$
$79$			6602.25i			1.05788i	−0.848658	+	0.528941i	$0.822589\pi$
$80$	1245.28	+	1004.62i	0.194576	+	0.156972i
$81$	6392.98			0.974392
$82$		−	2488.23i		−	0.370052i
$83$	−7557.25			−1.09700			−0.548501	−	0.836150i	$-0.684801\pi$
$83$	−7557.25			−1.09700			−0.548501	+	0.836150i	$0.684801\pi$
$84$		−	445.382i		−	0.0631210i
$85$	1710.66	+	1380.06i	0.236769	+	0.191012i
$86$		−	2544.95i		−	0.344098i
$87$			70.4224i			0.00930406i
$88$	−1472.46			−0.190142
$89$			8915.39i			1.12554i	0.826614	+	0.562769i	$0.190264\pi$
$89$			8915.39i			1.12554i	−0.826614	+	0.562769i	$0.809736\pi$
$90$	−3565.49	+	4419.62i	−0.440184	+	0.545632i
$91$		−	18025.7i		−	2.17675i
$92$	4058.68	+	1198.71i	0.479523	+	0.141624i
$93$			1341.85i			0.155146i
$94$	−6406.01			−0.724990
$95$	11120.2	−	13784.0i	1.23215	−	1.52732i
$96$	−150.737			−0.0163560
$97$	5318.88			0.565297			0.282648	−	0.959224i	$-0.408787\pi$
$97$	5318.88			0.565297			0.282648	+	0.959224i	$0.408787\pi$
$98$			5851.68i			0.609296i
$99$		−	5225.87i		−	0.533198i
$100$	−1057.55	−	4886.88i	−0.105755	−	0.488688i
$101$	537.769			0.0527173			0.0263586	−	0.999653i	$-0.491609\pi$
$101$	537.769			0.0527173			0.0263586	+	0.999653i	$0.491609\pi$
$102$	−207.068			−0.0199028
$103$	1937.52			0.182630			0.0913150	−	0.995822i	$-0.470893\pi$
$103$	1937.52			0.182630			0.0913150	+	0.995822i	$0.470893\pi$
$104$	−6100.69			−0.564043
$105$	−873.907	+	1083.26i	−0.0792660	+	0.0982544i
$106$		−	9741.92i		−	0.867027i
$107$	4131.20			0.360835			0.180418	−	0.983590i	$-0.442255\pi$
$107$	4131.20			0.360835			0.180418	+	0.983590i	$0.442255\pi$
$108$		−	1074.57i		−	0.0921274i
$109$		−	45.0710i		−	0.00379353i	−0.999998	−	0.00189677i	$-0.999396\pi$
$109$		−	45.0710i		−	0.00379353i	0.999998	−	0.00189677i	$-0.000603760\pi$
$110$	3581.30	+	2889.19i	0.295975	+	0.238776i
$111$			845.725i			0.0686410i
$112$	4278.86			0.341108
$113$	−15075.2			−1.18061			−0.590305	−	0.807180i	$-0.700993\pi$
$113$	−15075.2			−1.18061			−0.590305	+	0.807180i	$0.700993\pi$
$114$			1668.50i			0.128386i
$115$	−7519.47	−	10879.3i	−0.568580	−	0.822628i
$116$	−676.560			−0.0502795
$117$		−	21651.8i		−	1.58170i
$118$			13523.3i			0.971225i
$119$	5877.91			0.415077
$120$	366.621	+	295.769i	0.0254598	+	0.0205395i
$121$	10406.4			0.710770
$122$	893.947			0.0600609
$123$		−	732.555i		−	0.0484206i
$124$	−12891.4			−0.838412
$125$	−7016.64	+	13960.9i	−0.449065	+	0.893499i
$126$			15186.0i			0.956540i
$127$		−	2022.65i		−	0.125405i	−0.998032	−	0.0627024i	$-0.980028\pi$
$127$		−	2022.65i		−	0.125405i	0.998032	−	0.0627024i	$-0.0199719\pi$
$128$		−	1448.15i		−	0.0883883i
$129$		−	749.254i		−	0.0450246i
$130$	14838.1	+	11970.5i	0.877992	+	0.708313i
$131$	−21418.4			−1.24808			−0.624041	−	0.781391i	$-0.714510\pi$
$131$	−21418.4			−1.24808			−0.624041	+	0.781391i	$0.714510\pi$
$132$	−433.502			−0.0248796
$133$		−	47362.6i		−	2.67752i
$134$		−	11342.3i		−	0.631674i
$135$	−2108.48	+	2613.57i	−0.115692	+	0.143406i
$136$		−	1989.34i		−	0.107555i
$137$	−15475.0			−0.824499			−0.412250	−	0.911071i	$-0.635257\pi$
$137$	−15475.0			−0.824499			−0.412250	+	0.911071i	$0.635257\pi$
$138$	1194.91	+	352.909i	0.0627446	+	0.0185312i
$139$	15690.9			0.812118			0.406059	−	0.913847i	$-0.366903\pi$
$139$	15690.9			0.812118			0.406059	+	0.913847i	$0.366903\pi$
$140$	−10407.0	−	8395.78i	−0.530971	−	0.428356i
$141$	−1885.98			−0.0948634
$142$		−	21157.1i		−	1.04925i
$143$	−17544.9			−0.857984
$144$	5139.62			0.247860
$145$	1645.53	+	1327.52i	0.0782653	+	0.0631399i
$146$	−26671.4			−1.25124
$147$			1722.78i			0.0797252i
$148$	−8125.03			−0.370938
$149$		−	7299.23i		−	0.328779i	−0.986395	−	0.164390i	$-0.947435\pi$
$149$		−	7299.23i		−	0.328779i	0.986395	−	0.164390i	$-0.0525654\pi$
$150$	−311.351	−	1438.74i	−0.0138378	−	0.0639438i
$151$	21694.6			0.951476			0.475738	−	0.879587i	$-0.342181\pi$
$151$	21694.6			0.951476			0.475738	+	0.879587i	$0.342181\pi$
$152$	−16029.6			−0.693802
$153$	7060.35			0.301608
$154$	12305.5			0.518870
$155$	31354.5	+	25295.0i	1.30508	+	1.05286i
$156$	−1796.09			−0.0738038
$157$	−15040.2			−0.610176			−0.305088	−	0.952324i	$-0.598686\pi$
$157$	−15040.2			−0.610176			−0.305088	+	0.952324i	$0.598686\pi$
$158$	−18674.0			−0.748036
$159$		−	2868.10i		−	0.113449i
$160$	−2841.50	+	3522.20i	−0.110996	+	0.137586i
$161$	−33919.0	−	10017.8i	−1.30855	−	0.386474i
$162$			18082.1i			0.688999i
$163$		−	31863.7i		−	1.19928i	−0.800269	−	0.599641i	$-0.795310\pi$
$163$		−	31863.7i		−	1.19928i	0.800269	−	0.599641i	$-0.204690\pi$
$164$	7037.78			0.261667
$165$	1054.36	+	850.599i	0.0387277	+	0.0312433i
$166$		−	21375.1i		−	0.775698i
$167$			4796.28i			0.171978i	0.996296	+	0.0859888i	$0.0274049\pi$
$167$			4796.28i			0.171978i	−0.996296	+	0.0859888i	$0.972595\pi$
$168$	1259.73			0.0446333
$169$	−44131.1			−1.54515
$170$	−3903.40	+	4838.47i	−0.135066	+	0.167421i
$171$		−	56890.4i		−	1.94557i
$172$	7198.21			0.243314
$173$			44966.8i			1.50245i	0.660046	+	0.751225i	$0.270537\pi$
$173$			44966.8i			1.50245i	−0.660046	+	0.751225i	$0.729463\pi$
$174$	−199.185			−0.00657896
$175$	8838.10	+	40840.4i	0.288591	+	1.33356i
$176$		−	4164.73i		−	0.134450i
$177$			3981.38i			0.127083i
$178$	−25216.5			−0.795876
$179$	−524.809			−0.0163793			−0.00818965	−	0.999966i	$-0.502607\pi$
$179$	−524.809			−0.0163793			−0.00818965	+	0.999966i	$0.502607\pi$
$180$	−12500.6	−	10084.7i	−0.385820	−	0.311257i
$181$			33361.4i			1.01833i	0.860670	+	0.509163i	$0.170045\pi$
$181$			33361.4i			1.01833i	−0.860670	+	0.509163i	$0.829955\pi$
$182$	50984.3			1.53920
$183$	263.185			0.00785884
$184$	−3390.46	+	11479.7i	−0.100144	+	0.339074i
$185$	19761.7	+	15942.6i	0.577404	+	0.465816i
$186$	−3795.34			−0.109704
$187$		−	5721.13i		−	0.163606i
$188$		−	18118.9i		−	0.512645i
$189$			8980.37i			0.251403i
$190$	38987.1	+	31452.6i	1.07998	+	0.871262i
$191$		−	33501.8i		−	0.918334i	−0.888350	−	0.459167i	$-0.848148\pi$
$191$		−	33501.8i		−	0.918334i	0.888350	−	0.459167i	$-0.151852\pi$
$192$		−	426.348i		−	0.0115654i
$193$		−	14762.8i		−	0.396328i	−0.980169	−	0.198164i	$-0.936502\pi$
$193$		−	14762.8i		−	0.396328i	0.980169	−	0.198164i	$-0.0634979\pi$
$194$			15044.1i			0.399725i
$195$	4368.44	+	3524.20i	0.114883	+	0.0926813i
$196$	−16551.1			−0.430838
$197$			40053.6i			1.03207i	0.856568	+	0.516034i	$0.172592\pi$
$197$			40053.6i			1.03207i	−0.856568	+	0.516034i	$0.827408\pi$
$198$	14781.0			0.377028
$199$			28014.0i			0.707406i	0.935358	+	0.353703i	$0.115078\pi$
$199$			28014.0i			0.707406i	−0.935358	+	0.353703i	$0.884922\pi$
$200$	13822.2	−	2991.20i	0.345555	−	0.0747801i
$201$		−	3339.27i		−	0.0826532i
$202$			1521.04i			0.0372768i
$203$	5654.11			0.137206
$204$		−	585.678i		−	0.0140734i
$205$	−17117.3	−	13809.2i	−0.407312	−	0.328595i
$206$			5480.14i			0.129139i
$207$	−40742.4	−	12033.0i	−0.950837	−	0.280824i
$208$		−	17255.3i		−	0.398838i
$209$	−46099.4			−1.05536
$210$	−3063.91	−	2471.78i	−0.0694764	−	0.0560495i
$211$	40550.5			0.910817			0.455408	−	0.890283i	$-0.349493\pi$
$211$	40550.5			0.910817			0.455408	+	0.890283i	$0.349493\pi$
$212$	27554.3			0.613081
$213$		−	6228.81i		−	0.137292i
$214$			11684.8i			0.255149i
$215$	−17507.5	−	14124.0i	−0.378744	−	0.305549i
$216$	3039.35			0.0651439
$217$	107736.			2.28791
$218$	127.480			0.00268243
$219$	−7852.25			−0.163722
$220$	−8171.85	+	10129.4i	−0.168840	+	0.209286i
$221$		−	23703.8i		−	0.485326i
$222$	−2392.07			−0.0485365
$223$			58125.9i			1.16885i	0.811446	+	0.584427i	$0.198681\pi$
$223$			58125.9i			1.16885i	−0.811446	+	0.584427i	$0.801319\pi$
$224$			12102.4i			0.241200i
$225$	10616.0	+	49056.1i	0.209699	+	0.969009i
$226$		−	42639.2i		−	0.834818i
$227$	78881.1			1.53081			0.765405	−	0.643549i	$-0.222539\pi$
$227$	78881.1			1.53081			0.765405	+	0.643549i	$0.222539\pi$
$228$	−4719.24			−0.0907826
$229$			32596.4i			0.621582i	0.950478	+	0.310791i	$0.100594\pi$
$229$			32596.4i			0.621582i	−0.950478	+	0.310791i	$0.899406\pi$
$230$	30771.2	−	21268.3i	0.581686	−	0.402046i
$231$	3622.84			0.0678931
$232$		−	1913.60i		−	0.0355529i
$233$			60197.4i			1.10883i	0.832239	+	0.554416i	$0.187058\pi$
$233$			60197.4i			1.10883i	−0.832239	+	0.554416i	$0.812942\pi$
$234$	61240.7			1.11843
$235$	−35552.2	+	44068.8i	−0.643769	+	0.797987i
$236$	−38249.8			−0.686760
$237$	−5497.76			−0.0978789
$238$			16625.2i			0.293504i
$239$	70024.5			1.22590			0.612949	−	0.790123i	$-0.289983\pi$
$239$	70024.5			1.22590			0.612949	+	0.790123i	$0.289983\pi$
$240$	−836.561	+	1036.96i	−0.0145236	+	0.0180028i
$241$		−	83558.0i		−	1.43865i	−0.694675	−	0.719323i	$-0.744452\pi$
$241$		−	83558.0i		−	1.43865i	0.694675	−	0.719323i	$-0.255548\pi$
$242$			29433.7i			0.502590i
$243$			16203.6i			0.274409i
$244$			2528.46i			0.0424695i
$245$	40255.4	+	32475.7i	0.670644	+	0.541037i
$246$	2071.98			0.0342385
$247$	−190999.			−3.13067
$248$		−	36462.5i		−	0.592847i
$249$		−	6293.00i		−	0.101498i
$250$	−39487.5	−	19846.1i	−0.631799	−	0.317537i
$251$		−	62834.3i		−	0.997354i	−0.866788	−	0.498677i	$-0.833819\pi$
$251$		−	62834.3i		−	0.997354i	0.866788	−	0.498677i	$-0.166181\pi$
$252$	−42952.6			−0.676376
$253$	−9750.59	+	33014.3i	−0.152332	+	0.515777i
$254$	5720.93			0.0886745
$255$	−1149.19	+	1424.48i	−0.0176731	+	0.0219067i
$256$	4096.00			0.0625000
$257$			80190.7i			1.21411i	0.794660	+	0.607054i	$0.207649\pi$
$257$			80190.7i			1.21411i	−0.794660	+	0.607054i	$0.792351\pi$
$258$	2119.21			0.0318372
$259$	67902.1			1.01224
$260$	−33857.7	+	41968.4i	−0.500853	+	0.620834i
$261$	6791.53			0.0996981
$262$		−	60580.2i		−	0.882528i
$263$	30694.9			0.443767			0.221884	−	0.975073i	$-0.428780\pi$
$263$	30694.9			0.443767			0.221884	+	0.975073i	$0.428780\pi$
$264$		−	1226.13i		−	0.0175925i
$265$	−67017.5	−	54065.8i	−0.954325	−	0.769894i
$266$	133962.			1.89329
$267$	−7423.95			−0.104139
$268$	32081.0			0.446661
$269$	−4391.69			−0.0606914			−0.0303457	−	0.999539i	$-0.509661\pi$
$269$	−4391.69			−0.0606914			−0.0303457	+	0.999539i	$0.509661\pi$
$270$	−7392.30	−	5963.68i	−0.101403	−	0.0818063i
$271$	−115587.			−1.57387			−0.786936	−	0.617034i	$-0.788334\pi$
$271$	−115587.			−1.57387			−0.786936	+	0.617034i	$0.788334\pi$
$272$	5626.71			0.0760531
$273$	15010.2			0.201401
$274$		−	43770.0i		−	0.583009i
$275$	39751.1	−	8602.37i	0.525634	−	0.113750i
$276$	−998.178	+	3379.71i	−0.0131036	+	0.0443671i
$277$			24864.5i			0.324056i	0.986786	+	0.162028i	$0.0518035\pi$
$277$			24864.5i			0.324056i	−0.986786	+	0.162028i	$0.948196\pi$
$278$			44380.7i			0.574254i
$279$	129408.			1.66247
$280$	23746.9	−	29435.5i	0.302894	−	0.375453i
$281$		−	87349.0i		−	1.10623i	−0.833105	−	0.553115i	$-0.813439\pi$
$281$		−	87349.0i		−	1.10623i	0.833105	−	0.553115i	$-0.186561\pi$
$282$		−	5334.36i		−	0.0670786i
$283$	64102.3			0.800388			0.400194	−	0.916430i	$-0.368943\pi$
$283$	64102.3			0.800388			0.400194	+	0.916430i	$0.368943\pi$
$284$	59841.3			0.741932
$285$	11478.1	+	9259.88i	0.141313	+	0.114003i
$286$		−	49624.5i		−	0.606686i
$287$	−58815.8			−0.714053
$288$			14537.0i			0.175263i
$289$	−75791.5			−0.907455
$290$	−3754.78	+	4654.25i	−0.0446466	+	0.0553419i
$291$			4429.09i			0.0523032i
$292$		−	75438.0i		−	0.884758i
$293$	89702.8			1.04489			0.522445	−	0.852673i	$-0.325020\pi$
$293$	89702.8			1.04489			0.522445	+	0.852673i	$0.325020\pi$
$294$	−4872.76			−0.0563742
$295$	93030.9	+	75051.9i	1.06901	+	0.862418i
$296$		−	22981.1i		−	0.262293i
$297$	8740.85			0.0990925
$298$	20645.3			0.232482
$299$	−40398.7	+	136785.i	−0.451882	+	1.53002i
$300$	4069.36	−	880.633i	0.0452151	−	0.00978481i
$301$	−60156.5			−0.663972
$302$			61361.6i			0.672795i
$303$			447.806i			0.00487759i
$304$		−	45338.6i		−	0.490592i
$305$	4961.23	−	6149.72i	0.0533323	−	0.0661082i
$306$			19969.7i			0.213269i
$307$		−	107000.i		−	1.13529i	−0.823272	−	0.567647i	$-0.807854\pi$
$307$		−	107000.i		−	1.13529i	0.823272	−	0.567647i	$-0.192146\pi$
$308$			34805.3i			0.366897i
$309$			1613.40i			0.0168976i
$310$	−71545.0	+	88683.8i	−0.744485	+	0.922829i
$311$	19410.6			0.200686			0.100343	−	0.994953i	$-0.468006\pi$
$311$	19410.6			0.200686			0.100343	+	0.994953i	$0.468006\pi$
$312$		−	5080.11i		−	0.0521872i
$313$	−235.626			−0.00240511			−0.00120255	−	0.999999i	$-0.500383\pi$
$313$	−235.626			−0.00240511			−0.00120255	+	0.999999i	$0.500383\pi$
$314$		−	42540.2i		−	0.431459i
$315$	104469.	+	84279.6i	1.05285	+	0.849378i
$316$		−	52818.0i		−	0.528941i
$317$			156725.i			1.55962i	0.626014	+	0.779812i	$0.284685\pi$
$317$			156725.i			1.55962i	−0.626014	+	0.779812i	$0.715315\pi$
$318$	8112.20			0.0802203
$319$		−	5503.31i		−	0.0540807i
$320$	−9962.27	−	8036.98i	−0.0972878	−	0.0784862i
$321$			3440.10i			0.0333857i
$322$	28334.6	−	95937.5i	0.273278	−	0.925287i
$323$		−	62282.0i		−	0.596977i
$324$	−51143.9			−0.487196
$325$	164697.	−	35641.4i	1.55926	−	0.337433i
$326$	90124.3			0.848021
$327$	37.5311			0.000350991
$328$			19905.9i			0.185026i
$329$			151423.i			1.39894i
$330$	−2405.86	+	2982.19i	−0.0220923	+	0.0273847i
$331$	125665.			1.14698			0.573492	−	0.819211i	$-0.305588\pi$
$331$	125665.			1.14698			0.573492	+	0.819211i	$0.305588\pi$
$332$	60458.0			0.548501
$333$	81561.7			0.735526
$334$	−13565.9			−0.121607
$335$	−78027.2	−	62947.8i	−0.695274	−	0.560907i
$336$			3563.05i			0.0315605i
$337$	−121273.			−1.06784			−0.533918	−	0.845536i	$-0.679281\pi$
$337$	−121273.			−1.06784			−0.533918	+	0.845536i	$0.679281\pi$
$338$		−	124822.i		−	1.09259i
$339$		−	12553.3i		−	0.109234i
$340$	−13685.3	−	11040.5i	−0.118385	−	0.0955059i
$341$		−	104862.i		−	0.901799i
$342$	160910.			1.37573
$343$	−22204.4			−0.188735
$344$			20359.6i			0.172049i
$345$	9059.28	−	6261.54i	0.0761124	−	0.0526069i
$346$	−127185.			−1.06239
$347$			62799.0i			0.521548i	0.965400	+	0.260774i	$0.0839777\pi$
$347$			62799.0i			0.521548i	−0.965400	+	0.260774i	$0.916022\pi$
$348$		−	563.379i		−	0.00465203i
$349$	−182174.			−1.49567			−0.747836	−	0.663884i	$-0.768907\pi$
$349$	−182174.			−1.49567			−0.747836	+	0.663884i	$0.768907\pi$
$350$	−115514.	+	24997.9i	−0.942972	+	0.204065i
$351$	36215.1			0.293952
$352$	11779.6			0.0950708
$353$		−	64031.7i		−	0.513861i	−0.966430	−	0.256931i	$-0.917289\pi$
$353$		−	64031.7i		−	0.513861i	0.966430	−	0.256931i	$-0.0827112\pi$
$354$	−11261.0			−0.0898611
$355$	−145546.	−	117418.i	−1.15490	−	0.931703i
$356$		−	71323.1i		−	0.562769i
$357$			4894.60i			0.0384044i
$358$		−	1484.39i		−	0.0115819i
$359$		−	55056.6i		−	0.427189i	−0.976922	−	0.213595i	$-0.931483\pi$
$359$		−	55056.6i		−	0.427189i	0.976922	−	0.213595i	$-0.0685172\pi$
$360$	28523.9	−	35356.9i	0.220092	−	0.272816i
$361$	−371531.			−2.85089
$362$	−94360.2			−0.720065
$363$			8665.50i			0.0657628i
$364$			144205.i			1.08838i
$365$	−148021.	+	183480.i	−1.11106	+	1.37722i
$366$			744.399i			0.00555704i
$367$	−15904.8			−0.118085			−0.0590427	−	0.998255i	$-0.518805\pi$
$367$	−15904.8			−0.118085			−0.0590427	+	0.998255i	$0.518805\pi$
$368$	−32469.5	−	9589.67i	−0.239762	−	0.0708122i
$369$	−70647.6			−0.518853
$370$	−45092.4	+	55894.4i	−0.329382	+	0.408287i
$371$	−230275.			−1.67301
$372$		−	10734.8i		−	0.0775728i
$373$	−259413.			−1.86455			−0.932275	−	0.361750i	$-0.882179\pi$
$373$	−259413.			−1.86455			−0.932275	+	0.361750i	$0.882179\pi$
$374$	16181.8			0.115687
$375$	−11625.4	−	5842.84i	−0.0826696	−	0.0415490i
$376$	51248.1			0.362495
$377$		−	22801.3i		−	0.160427i
$378$	−25400.3			−0.177769
$379$		−	132152.i		−	0.920013i	−0.887916	−	0.460007i	$-0.847847\pi$
$379$		−	132152.i		−	0.920013i	0.887916	−	0.460007i	$-0.152153\pi$
$380$	−88961.3	+	110272.i	−0.616075	+	0.763658i
$381$	1684.29			0.0116029
$382$	94757.3			0.649360
$383$	151435.			1.03236			0.516178	−	0.856481i	$-0.327354\pi$
$383$	151435.			1.03236			0.516178	+	0.856481i	$0.327354\pi$
$384$	1205.89			0.00817799
$385$	68293.4	−	84653.3i	0.460741	−	0.571114i
$386$	41755.6			0.280246
$387$	−72258.0			−0.482463
$388$	−42551.0			−0.282648
$389$			187786.i			1.24098i	0.784215	+	0.620489i	$0.213066\pi$
$389$			187786.i			1.24098i	−0.784215	+	0.620489i	$0.786934\pi$
$390$	−9967.96	+	12355.8i	−0.0655355	+	0.0812348i
$391$	−44603.6	−	13173.4i	−0.291754	−	0.0861678i
$392$		−	46813.5i		−	0.304648i
$393$		−	17835.3i		−	0.115477i
$394$	−113289.			−0.729783
$395$	−103637.	+	128464.i	−0.664233	+	0.823353i
$396$			41807.0i			0.266599i
$397$		−	278357.i		−	1.76612i	−0.469258	−	0.883061i	$-0.655478\pi$
$397$		−	278357.i		−	1.76612i	0.469258	−	0.883061i	$-0.344522\pi$
$398$	−79235.5			−0.500212
$399$	39439.4			0.247733
$400$	8460.40	+	39095.0i	0.0528775	+	0.244344i
$401$			21583.2i			0.134223i	0.997745	+	0.0671116i	$0.0213784\pi$
$401$			21583.2i			0.134223i	−0.997745	+	0.0671116i	$0.978622\pi$
$402$	9444.88			0.0584446
$403$		−	434465.i		−	2.67513i
$404$	−4302.15			−0.0263586
$405$	124392.	+	100352.i	0.758371	+	0.611810i
$406$			15992.3i			0.0970192i
$407$		−	66091.0i		−	0.398982i
$408$	1656.55			0.00995139
$409$	140985.			0.842801			0.421400	−	0.906875i	$-0.361539\pi$
$409$	140985.			0.842801			0.421400	+	0.906875i	$0.361539\pi$
$410$	39058.4	−	48414.9i	0.232352	−	0.288013i
$411$		−	12886.2i		−	0.0762855i
$412$	−15500.2			−0.0913150
$413$	319659.			1.87407
$414$	34034.5	−	115237.i	0.198572	−	0.672343i
$415$	−147046.	−	118628.i	−0.853800	−	0.688796i
$416$	48805.5			0.282021
$417$			13066.0i			0.0751400i
$418$		−	130389.i		−	0.746256i
$419$		−	147896.i		−	0.842417i	−0.906964	−	0.421208i	$-0.861606\pi$
$419$		−	147896.i		−	0.842417i	0.906964	−	0.421208i	$-0.138394\pi$
$420$	6991.26	−	8666.04i	0.0396330	−	0.0491272i
$421$			236806.i			1.33607i	0.744131	+	0.668033i	$0.232864\pi$
$421$			236806.i			1.33607i	−0.744131	+	0.668033i	$0.767136\pi$
$422$			114694.i			0.644045i
$423$			181884.i			1.01651i
$424$			77935.3i			0.433514i
$425$	11622.1	+	53705.2i	0.0643439	+	0.297330i
$426$	17617.7			0.0970803
$427$		−	21130.7i		−	0.115893i
$428$	−33049.6			−0.180418
$429$		−	14609.8i		−	0.0793836i
$430$	39948.7	−	49518.6i	0.216056	−	0.267813i
$431$		−	200068.i		−	1.07702i	−0.842619	−	0.538510i	$-0.818988\pi$
$431$		−	200068.i		−	1.07702i	0.842619	−	0.538510i	$-0.181012\pi$
$432$			8596.59i			0.0460637i
$433$	167325.			0.892451			0.446225	−	0.894921i	$-0.352768\pi$
$433$	167325.			0.892451			0.446225	+	0.894921i	$0.352768\pi$
$434$			304722.i			1.61780i
$435$	−1105.44	+	1370.25i	−0.00584192	+	0.00724137i
$436$			360.568i			0.00189677i
$437$	−106148.	+	359404.i	−0.555838	+	1.88200i
$438$		−	22209.5i		−	0.115769i
$439$	303714.			1.57593			0.787963	−	0.615722i	$-0.211136\pi$
$439$	303714.			1.57593			0.787963	+	0.615722i	$0.211136\pi$
$440$	−28650.4	−	23113.5i	−0.147988	−	0.119388i
$441$	166145.			0.854299
$442$	67044.5			0.343178
$443$		−	30058.3i		−	0.153164i	−0.997063	−	0.0765819i	$-0.975599\pi$
$443$		−	30058.3i		−	0.153164i	0.997063	−	0.0765819i	$-0.0244007\pi$
$444$		−	6765.80i		−	0.0343205i
$445$	−139947.	+	173472.i	−0.706714	+	0.876010i
$446$	−164405.			−0.826504
$447$	6078.14			0.0304198
$448$	−34230.9			−0.170554
$449$	−139325.			−0.691091			−0.345546	−	0.938402i	$-0.612306\pi$
$449$	−139325.			−0.691091			−0.345546	+	0.938402i	$0.612306\pi$
$450$	−138752.	+	30026.7i	−0.685193	+	0.148280i
$451$			57247.1i			0.281449i
$452$	120602.			0.590305
$453$			18065.3i			0.0880338i
$454$			223109.i			1.08245i
$455$	282953.	−	350736.i	1.36676	−	1.69417i
$456$		−	13348.0i		−	0.0641930i
$457$	−29090.4			−0.139289			−0.0696445	−	0.997572i	$-0.522186\pi$
$457$	−29090.4			−0.139289			−0.0696445	+	0.997572i	$0.522186\pi$
$458$	−92196.6			−0.439525
$459$			11809.2i			0.0560526i
$460$	60155.7	+	87034.1i	0.284290	+	0.411314i
$461$	239855.			1.12862			0.564308	−	0.825564i	$-0.309143\pi$
$461$	239855.			1.12862			0.564308	+	0.825564i	$0.309143\pi$
$462$			10247.0i			0.0480077i
$463$		−	320288.i		−	1.49409i	−0.664771	−	0.747047i	$-0.731471\pi$
$463$		−	320288.i		−	1.49409i	0.664771	−	0.747047i	$-0.268529\pi$
$464$	5412.48			0.0251397
$465$	−21063.4	+	26109.2i	−0.0974143	+	0.120750i
$466$	−170264.			−0.784063
$467$	−296432.			−1.35923			−0.679613	−	0.733571i	$-0.737852\pi$
$467$	−296432.			−1.35923			−0.679613	+	0.733571i	$0.737852\pi$
$468$			173215.i			0.790848i
$469$	−268105.			−1.21888
$470$	−124645.	−	100557.i	−0.564262	−	0.455214i
$471$		−	12524.2i		−	0.0564556i
$472$		−	108187.i		−	0.485612i
$473$			58552.0i			0.261710i
$474$		−	15550.0i		−	0.0692109i
$475$	432742.	−	93648.0i	1.91797	−	0.415061i
$476$	−47023.3			−0.207539
$477$	−276599.			−1.21566
$478$			198059.i			0.866840i
$479$		−	414687.i		−	1.80738i	−0.428188	−	0.903689i	$-0.640848\pi$
$479$		−	414687.i		−	1.80738i	0.428188	−	0.903689i	$-0.359152\pi$
$480$	−2932.97	−	2366.15i	−0.0127299	−	0.0102698i
$481$		−	273829.i		−	1.18356i
$482$	236338.			1.01728
$483$	8341.92	−	28244.7i	0.0357579	−	0.121072i
$484$	−83251.0			−0.355385
$485$	103492.	+	83491.7i	0.439972	+	0.354944i
$486$	−45830.6			−0.194036
$487$		−	103956.i		−	0.438320i	−0.975689	−	0.219160i	$-0.929668\pi$
$487$		−	103956.i		−	0.438320i	0.975689	−	0.219160i	$-0.0703317\pi$
$488$	−7151.57			−0.0300305
$489$	26533.3			0.110962
$490$	−91855.2	+	113860.i	−0.382571	+	0.474217i
$491$	440496.			1.82717			0.913586	−	0.406646i	$-0.133302\pi$
$491$	440496.			1.82717			0.913586	+	0.406646i	$0.133302\pi$
$492$			5860.44i			0.0242103i
$493$	7435.18			0.0305913
$494$		−	540227.i		−	2.21372i
$495$	82031.7	−	101683.i	0.334789	−	0.414989i
$496$	103131.			0.419206
$497$	−500103.			−2.02463
$498$	17799.3			0.0717702
$499$	90560.4			0.363695			0.181847	−	0.983327i	$-0.441792\pi$
$499$	90560.4			0.363695			0.181847	+	0.983327i	$0.441792\pi$
$500$	56133.1	−	111687.i	0.224533	−	0.446750i
$501$	−3993.92			−0.0159120
$502$	177722.			0.705236
$503$	−173466.			−0.685613			−0.342807	−	0.939406i	$-0.611378\pi$
$503$	−173466.			−0.685613			−0.342807	+	0.939406i	$0.611378\pi$
$504$		−	121488.i		−	0.478270i
$505$	10463.7	+	8441.49i	0.0410300	+	0.0331006i
$506$	−93378.7	−	27578.8i	−0.364709	−	0.107715i
$507$		−	36748.5i		−	0.142963i
$508$			16181.2i			0.0627024i
$509$	42103.6			0.162511			0.0812557	−	0.996693i	$-0.474107\pi$
$509$	42103.6			0.162511			0.0812557	+	0.996693i	$0.474107\pi$
$510$	−4029.05	−	3250.40i	−0.0154904	−	0.0124967i
$511$			630446.i			2.41438i
$512$			11585.2i			0.0441942i
$513$	95155.6			0.361576
$514$	−226813.			−0.858505
$515$	37699.4	+	30413.7i	0.142141	+	0.114671i
$516$			5994.03i			0.0225123i
$517$	147384.			0.551403
$518$			192056.i			0.715762i
$519$	−37444.4			−0.139012
$520$	−118705.	−	95763.9i	−0.438996	−	0.354156i
$521$			68393.0i			0.251963i	0.992033	+	0.125981i	$0.0402080\pi$
$521$			68393.0i			0.251963i	−0.992033	+	0.125981i	$0.959792\pi$
$522$			19209.4i			0.0704972i
$523$	−252970.			−0.924839			−0.462419	−	0.886661i	$-0.653019\pi$
$523$	−252970.			−0.924839			−0.462419	+	0.886661i	$0.653019\pi$
$524$	171347.			0.624041
$525$	−34008.2	+	7359.58i	−0.123386	+	0.0267014i
$526$			86818.4i			0.313791i
$527$	141673.			0.510111
$528$	3468.02			0.0124398
$529$	234938.	+	152037.i	0.839540	+	0.543297i
$530$	152921.	−	189554.i	0.544397	−	0.674809i
$531$	383964.			1.36176
$532$			378901.i			1.33876i
$533$			237186.i			0.834902i
$534$		−	20998.1i		−	0.0736372i
$535$	80383.2	+	64848.5i	0.280839	+	0.226565i
$536$			90738.7i			0.315837i
$537$		−	437.015i		−	0.00151547i
$538$		−	12421.6i		−	0.0429153i
$539$		−	134630.i		−	0.463410i
$540$	16867.8	−	20908.6i	0.0578458	−	0.0717030i
$541$	325301.			1.11145			0.555726	−	0.831366i	$-0.312441\pi$
$541$	325301.			1.11145			0.555726	+	0.831366i	$0.312441\pi$
$542$		−	326929.i		−	1.11290i
$543$	−27780.4			−0.0942190
$544$			15914.7i			0.0537777i
$545$	707.490	−	876.971i	0.00238192	−	0.00295252i
$546$			42455.2i			0.142412i
$547$			10744.1i			0.0359083i	0.999839	+	0.0179542i	$0.00571530\pi$
$547$			10744.1i			0.0359083i	−0.999839	+	0.0179542i	$0.994285\pi$
$548$	123800.			0.412250
$549$		−	25381.5i		−	0.0842118i
$550$	24331.2	+	112433.i	0.0804336	+	0.371679i
$551$		−	59910.7i		−	0.197334i
$552$	−9559.27	−	2823.27i	−0.0313723	−	0.00926562i
$553$			441408.i			1.44341i
$554$	−70327.5			−0.229142
$555$	−13275.5	+	16455.8i	−0.0430989	+	0.0534234i
$556$	−125527.			−0.406059
$557$	4177.93			0.0134664			0.00673319	−	0.999977i	$-0.497857\pi$
$557$	4177.93			0.0134664			0.00673319	+	0.999977i	$0.497857\pi$
$558$			366022.i			1.17554i
$559$			242593.i			0.776345i
$560$	83256.2	+	67166.3i	0.265485	+	0.214178i
$561$	4764.05			0.0151374
$562$	247060.			0.782223
$563$	108724.			0.343013			0.171506	−	0.985183i	$-0.445137\pi$
$563$	108724.			0.343013			0.171506	+	0.985183i	$0.445137\pi$
$564$	15087.8			0.0474317
$565$	−293327.	−	236639.i	−0.918872	−	0.741293i
$566$			181309.i			0.565960i
$567$	427417.			1.32949
$568$			169257.i			0.524625i
$569$			155357.i			0.479850i	0.970791	+	0.239925i	$0.0771229\pi$
$569$			155357.i			0.479850i	−0.970791	+	0.239925i	$0.922877\pi$
$570$	−26190.9	+	32465.0i	−0.0806122	+	0.0999231i
$571$			335546.i			1.02915i	0.857444	+	0.514577i	$0.172051\pi$
$571$			335546.i			1.02915i	−0.857444	+	0.514577i	$0.827949\pi$
$572$	140359.			0.428992
$573$	27897.3			0.0849674
$574$		−	166356.i		−	0.504911i
$575$	24463.8	−	329719.i	0.0739925	−	0.997259i
$576$	−41117.0			−0.123930
$577$		−	173415.i		−	0.520878i	−0.965490	−	0.260439i	$-0.916133\pi$
$577$		−	173415.i		−	0.520878i	0.965490	−	0.260439i	$-0.0838673\pi$
$578$		−	214371.i		−	0.641667i
$579$	12293.2			0.0366697
$580$	−13164.2	−	10620.1i	−0.0391326	−	0.0315699i
$581$	−505256.			−1.49679
$582$	−12527.4			−0.0369840
$583$			224133.i			0.659431i
$584$	213371.			0.625618
$585$	339874.	−	421292.i	0.993131	−	1.23104i
$586$			253718.i			0.738849i
$587$			300003.i			0.870661i	0.900271	+	0.435331i	$0.143369\pi$
$587$			300003.i			0.870661i	−0.900271	+	0.435331i	$0.856631\pi$
$588$		−	13782.2i		−	0.0398626i
$589$		−	1.14156e6i		−	3.29055i
$590$	−212279.	+	263131.i	−0.609822	+	0.755907i
$591$	−33353.0			−0.0954906
$592$	65000.3			0.185469
$593$			67393.6i			0.191650i	0.995398	+	0.0958251i	$0.0305489\pi$
$593$			67393.6i			0.191650i	−0.995398	+	0.0958251i	$0.969451\pi$
$594$			24722.9i			0.0700690i
$595$	114370.	+	92266.9i	0.323056	+	0.260623i
$596$			58393.8i			0.164390i
$597$	−23327.6			−0.0654516
$598$	−386887.	−	114265.i	−1.08189	−	0.319529i
$599$	187549.			0.522710			0.261355	−	0.965243i	$-0.415831\pi$
$599$	187549.			0.522710			0.261355	+	0.965243i	$0.415831\pi$
$600$	2490.81	+	11509.9i	0.00691891	+	0.0319719i
$601$	−170946.			−0.473270			−0.236635	−	0.971599i	$-0.576045\pi$
$601$	−170946.			−0.473270			−0.236635	+	0.971599i	$0.576045\pi$
$602$		−	170148.i		−	0.469499i
$603$	−322039.			−0.885674
$604$	−173557.			−0.475738
$605$	202483.	+	163351.i	0.553194	+	0.446285i
$606$	−1266.59			−0.00344897
$607$			165773.i			0.449921i	0.974368	+	0.224960i	$0.0722252\pi$
$607$			165773.i			0.449921i	−0.974368	+	0.224960i	$0.927775\pi$
$608$	128237.			0.346901
$609$			4708.24i			0.0126948i
$610$	17394.0	+	14032.5i	0.0467456	+	0.0377116i
$611$	610642.			1.63570
$612$	−56482.8			−0.150804
$613$	271709.			0.723074			0.361537	−	0.932358i	$-0.382252\pi$
$613$	271709.			0.723074			0.361537	+	0.932358i	$0.382252\pi$
$614$	302643.			0.802775
$615$	11499.1	−	14253.7i	0.0304028	−	0.0376859i
$616$	−98444.3			−0.259435
$617$	374340.			0.983323			0.491662	−	0.870786i	$-0.336390\pi$
$617$	374340.			0.983323			0.491662	+	0.870786i	$0.336390\pi$
$618$	−4563.37			−0.0119484
$619$			445609.i			1.16298i	0.813553	+	0.581490i	$0.197530\pi$
$619$			445609.i			1.16298i	−0.813553	+	0.581490i	$0.802470\pi$
$620$	−250836.	−	202360.i	−0.652539	−	0.526430i
$621$	20126.6	−	68146.2i	0.0521899	−	0.176709i
$622$			54901.4i			0.141907i
$623$			596058.i			1.53572i
$624$	14368.7			0.0369019
$625$	−355675.	+	161504.i	−0.910527	+	0.413449i
$626$		−	666.451i		−	0.00170067i
$627$		−	38387.5i		−	0.0976460i
$628$	120322.			0.305088
$629$	89291.4			0.225688
$630$	−238379.	+	295483.i	−0.600601	+	0.744478i
$631$		−	708324.i		−	1.77899i	−0.456947	−	0.889494i	$-0.651057\pi$
$631$		−	708324.i		−	1.77899i	0.456947	−	0.889494i	$-0.348943\pi$
$632$	149392.			0.374018
$633$			33766.8i			0.0842719i
$634$	−443285.			−1.10282
$635$	31750.1	−	39355.9i	0.0787403	−	0.0976028i
$636$			22944.8i			0.0567243i
$637$		−	557801.i		−	1.37468i
$638$	15565.7			0.0382409
$639$	−600706.			−1.47116
$640$	22732.0	−	28177.6i	0.0554981	−	0.0687929i
$641$			558063.i			1.35821i	0.734040	+	0.679106i	$0.237632\pi$
$641$			558063.i			1.35821i	−0.734040	+	0.679106i	$0.762368\pi$
$642$	−9730.07			−0.0236073
$643$	−670224.			−1.62106			−0.810528	−	0.585700i	$-0.800820\pi$
$643$	−670224.			−1.62106			−0.810528	+	0.585700i	$0.800820\pi$
$644$	271352.	+	80142.3i	0.654277	+	0.193237i
$645$	11761.2	−	14578.7i	0.0282704	−	0.0350427i
$646$	176160.			0.422126
$647$			209010.i			0.499296i	0.968337	+	0.249648i	$0.0803148\pi$
$647$			209010.i			0.499296i	−0.968337	+	0.249648i	$0.919685\pi$
$648$		−	144657.i		−	0.344499i
$649$		−	311133.i		−	0.738681i
$650$	100809.	+	465833.i	0.238601	+	1.10256i
$651$			89712.6i			0.211686i
$652$			254910.i			0.599641i
$653$		−	554990.i		−	1.30154i	−0.759273	−	0.650772i	$-0.774445\pi$
$653$		−	554990.i		−	1.30154i	0.759273	−	0.650772i	$-0.225555\pi$
$654$			106.154i			0.000248188i
$655$	−416749.	−	336209.i	−0.971386	−	0.783658i
$656$	−56302.3			−0.130833
$657$			757271.i			1.75437i
$658$	−428288.			−0.989200
$659$			534636.i			1.23108i	0.788105	+	0.615541i	$0.211062\pi$
$659$			534636.i			1.23108i	−0.788105	+	0.615541i	$0.788938\pi$
$660$	−8434.90	−	6804.79i	−0.0193639	−	0.0156216i
$661$			637749.i			1.45964i	0.683638	+	0.729822i	$0.260397\pi$
$661$			637749.i			1.45964i	−0.683638	+	0.729822i	$0.739603\pi$
$662$			355434.i			0.811041i
$663$	19738.4			0.0449041
$664$			171001.i			0.387849i
$665$	743462.	−	921562.i	1.68119	−	2.08392i
$666$			230691.i			0.520095i
$667$	−42905.4	−	12671.9i	−0.0964407	−	0.0284832i
$668$		−	38370.3i		−	0.0859888i
$669$	−48402.1			−0.108146
$670$	178043.	−	220694.i	0.396621	−	0.491633i
$671$	−20567.1			−0.0456803
$672$	−10077.8			−0.0223166
$673$			107714.i			0.237817i	0.992905	+	0.118909i	$0.0379396\pi$
$673$			107714.i			0.237817i	−0.992905	+	0.118909i	$0.962060\pi$
$674$		−	343012.i		−	0.755074i
$675$	−82051.8	+	17756.5i	−0.180086	+	0.0389717i
$676$	353049.			0.772577
$677$	−685147.			−1.49488			−0.747440	−	0.664329i	$-0.768717\pi$
$677$	−685147.			−1.49488			−0.747440	+	0.664329i	$0.768717\pi$
$678$	35506.1			0.0772402
$679$	355605.			0.771309
$680$	31227.2	−	38707.8i	0.0675328	−	0.0837106i
$681$			65685.2i			0.141636i
$682$	296595.			0.637668
$683$			68155.9i			0.146104i	0.997328	+	0.0730520i	$0.0232739\pi$
$683$			68155.9i			0.146104i	−0.997328	+	0.0730520i	$0.976726\pi$
$684$			455123.i			0.972785i
$685$	−301106.	−	242915.i	−0.641710	−	0.517694i
$686$		−	62803.7i		−	0.133456i
$687$	−27143.4			−0.0575109
$688$	−57585.7			−0.121657
$689$			928631.i			1.95616i
$690$	17710.3	+	25623.5i	0.0371987	+	0.0538196i
$691$	−173246.			−0.362832			−0.181416	−	0.983406i	$-0.558068\pi$
$691$	−173246.			−0.362832			−0.181416	+	0.983406i	$0.558068\pi$
$692$		−	359735.i		−	0.751225i
$693$		−	349387.i		−	0.727512i
$694$	−177622.			−0.368790
$695$	305307.	+	246304.i	0.632074	+	0.509920i
$696$	1593.48			0.00328948
$697$	−77342.9			−0.159204
$698$		−	515267.i		−	1.05760i
$699$	−50127.0			−0.102593
$700$	−70704.8	−	326723.i	−0.144295	−	0.666782i
$701$			413787.i			0.842055i	0.907048	+	0.421028i	$0.138330\pi$
$701$			413787.i			0.842055i	−0.907048	+	0.421028i	$0.861670\pi$
$702$			102432.i			0.207855i
$703$		−	719487.i		−	1.45584i
$704$			33317.9i			0.0672252i
$705$	−36696.6	−	29604.7i	−0.0738325	−	0.0595637i
$706$	181109.			0.363355
$707$	35953.7			0.0719292
$708$		−	31851.0i		−	0.0635414i
$709$		−	852804.i		−	1.69651i	−0.529586	−	0.848256i	$-0.677653\pi$
$709$		−	852804.i		−	1.69651i	0.529586	−	0.848256i	$-0.322347\pi$
$710$	332108.	−	411666.i	0.658813	−	0.816635i
$711$			530204.i			1.04883i
$712$	201732.			0.397938
$713$	−817535.	−	241454.i	−1.60815	−	0.474958i
$714$	−13844.0			−0.0271560
$715$	−341381.	−	275407.i	−0.667771	−	0.538719i
$716$	4198.48			0.00818965
$717$			58310.2i			0.113424i
$718$	155724.			0.302068
$719$	−731970.			−1.41591			−0.707955	−	0.706258i	$-0.750382\pi$
$719$	−731970.			−1.41591			−0.707955	+	0.706258i	$0.750382\pi$
$720$	100005.	+	80677.8i	0.192910	+	0.155629i
$721$	129537.			0.249186
$722$		−	1.05085e6i		−	2.01589i
$723$	69579.7			0.133109
$724$		−	266891.i		−	0.509163i
$725$	11179.6	+	51660.4i	0.0212692	+	0.0982839i
$726$	−24509.7			−0.0465014
$727$	−29001.7			−0.0548725			−0.0274362	−	0.999624i	$-0.508734\pi$
$727$	−29001.7			−0.0548725			−0.0274362	+	0.999624i	$0.508734\pi$
$728$	−407875.			−0.769598
$729$	504339.			0.949002
$730$	−518960.	−	418666.i	−0.973840	−	0.785638i
$731$	−79106.0			−0.148038
$732$	−2105.48			−0.00392942
$733$	1.02433e6			1.90647			0.953235	−	0.302231i	$-0.0977312\pi$
$733$	1.02433e6			1.90647			0.953235	+	0.302231i	$0.0977312\pi$
$734$		−	44985.6i		−	0.0834990i
$735$	−27042.9	+	33521.1i	−0.0500586	+	0.0620503i
$736$	27123.7	−	91837.6i	0.0500718	−	0.169537i
$737$			260954.i			0.480430i
$738$		−	199821.i		−	0.366885i
$739$	−702502.			−1.28635			−0.643174	−	0.765720i	$-0.722383\pi$
$739$	−702502.			−1.28635			−0.643174	+	0.765720i	$0.722383\pi$
$740$	−158093.	−	127541.i	−0.288702	−	0.232908i
$741$		−	159047.i		−	0.289661i
$742$		−	651317.i		−	1.18300i
$743$	68809.7			0.124644			0.0623221	−	0.998056i	$-0.480149\pi$
$743$	68809.7			0.124644			0.0623221	+	0.998056i	$0.480149\pi$
$744$	30362.7			0.0548522
$745$	114578.	−	142025.i	0.206437	−	0.255890i
$746$		−	733731.i		−	1.31844i
$747$	−606897.			−1.08761
$748$			45769.1i			0.0818029i
$749$	276201.			0.492335
$750$	16526.0	−	32881.6i	0.0293796	−	0.0584562i
$751$			240481.i			0.426383i	0.977010	+	0.213192i	$0.0683859\pi$
$751$			240481.i			0.426383i	−0.977010	+	0.213192i	$0.931614\pi$
$752$			144952.i			0.256323i
$753$	52322.8			0.0922786
$754$	64491.9			0.113439
$755$	422124.	+	340545.i	0.740536	+	0.597421i
$756$		−	71843.0i		−	0.125702i
$757$	−428975.			−0.748583			−0.374291	−	0.927311i	$-0.622114\pi$
$757$	−428975.			−0.748583			−0.374291	+	0.927311i	$0.622114\pi$
$758$	373781.			0.650547
$759$	−27491.4	−	8119.42i	−0.0477214	−	0.0140942i
$760$	−311897.	−	251620.i	−0.539988	−	0.435631i
$761$	−698130.			−1.20550			−0.602749	−	0.797930i	$-0.705928\pi$
$761$	−698130.			−1.20550			−0.602749	+	0.797930i	$0.705928\pi$
$762$			4763.88i			0.00820447i
$763$		−	3013.32i		−	0.00517602i
$764$			268014.i			0.459167i
$765$	137377.	+	110828.i	0.234742	+	0.189377i
$766$			428324.i			0.729986i
$767$		−	1.28909e6i		−	2.19125i
$768$			3410.78i			0.00578271i
$769$		−	37692.6i		−	0.0637387i	−0.999492	−	0.0318693i	$-0.989854\pi$
$769$		−	37692.6i		−	0.0637387i	0.999492	−	0.0318693i	$-0.0101460\pi$
$770$	239436.	+	193163.i	0.403838	+	0.325793i
$771$	−66775.7			−0.112334
$772$			118103.i			0.198164i
$773$	−812232.			−1.35932			−0.679659	−	0.733528i	$-0.737872\pi$
$773$	−812232.			−1.35932			−0.679659	+	0.733528i	$0.737872\pi$
$774$		−	204376.i		−	0.341153i
$775$	213021.	+	984357.i	0.354665	+	1.63889i
$776$		−	120353.i		−	0.199863i
$777$			56542.8i			0.0936560i
$778$	−531139.			−0.877504
$779$			623209.i			1.02697i
$780$	−34947.5	−	28193.6i	−0.0574417	−	0.0463406i
$781$			486764.i			0.798025i
$782$	37260.0	−	126158.i	0.0609298	−	0.206301i
$783$			11359.6i			0.0185285i
$784$	132408.			0.215419
$785$	−292646.	−	236090.i	−0.474901	−	0.383123i
$786$	50445.8			0.0816545
$787$	−430599.			−0.695222			−0.347611	−	0.937639i	$-0.613007\pi$
$787$	−430599.			−0.695222			−0.347611	+	0.937639i	$0.613007\pi$
$788$		−	320428.i		−	0.516034i
$789$			25560.0i			0.0410589i
$790$	−363350.	−	293130.i	−0.582198	−	0.469684i
$791$	−1.00789e6			−1.61086
$792$	−118248.			−0.188514
$793$	−85213.9			−0.135508
$794$	787312.			1.24884
$795$	45021.2	−	55806.2i	0.0712332	−	0.0882974i
$796$		−	224112.i		−	0.353703i
$797$	698930.			1.10032			0.550158	−	0.835061i	$-0.314568\pi$
$797$	698930.			1.10032			0.550158	+	0.835061i	$0.314568\pi$
$798$			111551.i			0.175174i
$799$			199121.i			0.311906i
$800$	−110577.	+	23929.6i	−0.172777	+	0.0373900i
$801$			715965.i			1.11590i
$802$	−61046.6			−0.0949102
$803$	613631.			0.951648
$804$			26714.2i			0.0413266i
$805$	−502730.	−	727357.i	−0.775788	−	1.12242i
$806$	1.22885e6			1.89160
$807$		−	3657.01i		−	0.00561537i
$808$		−	12168.3i		−	0.0186384i
$809$	−647568.			−0.989438			−0.494719	−	0.869053i	$-0.664729\pi$
$809$	−647568.			−0.989438			−0.494719	+	0.869053i	$0.664729\pi$
$810$	−283839.	+	351833.i	−0.432615	+	0.536250i
$811$	324338.			0.493124			0.246562	−	0.969127i	$-0.420699\pi$
$811$	324338.			0.493124			0.246562	+	0.969127i	$0.420699\pi$
$812$	−45232.9			−0.0686029
$813$		−	96250.4i		−	0.145620i
$814$	186934.			0.282123
$815$	500173.	−	619991.i	0.753017	−	0.933405i
$816$			4685.42i			0.00703669i
$817$			637415.i			0.954945i
$818$			398764.i			0.595950i
$819$		−	1.44758e6i		−	2.15812i
$820$	136938.	+	110474.i	0.203656	+	0.164298i
$821$	1.02268e6			1.51723			0.758617	−	0.651537i	$-0.225875\pi$
$821$	1.02268e6			1.51723			0.758617	+	0.651537i	$0.225875\pi$
$822$	36447.7			0.0539420
$823$		−	620211.i		−	0.915672i	−0.889037	−	0.457836i	$-0.848625\pi$
$823$		−	620211.i		−	0.915672i	0.889037	−	0.457836i	$-0.151375\pi$
$824$		−	43841.1i		−	0.0645694i
$825$	7163.29	+	33101.2i	0.0105246	+	0.0486335i
$826$			904132.i			1.32517i
$827$	664807.			0.972041			0.486021	−	0.873947i	$-0.338448\pi$
$827$	664807.			0.972041			0.486021	+	0.873947i	$0.338448\pi$
$828$	325939.	+	96264.2i	0.475418	+	0.140412i
$829$	−151083.			−0.219840			−0.109920	−	0.993940i	$-0.535059\pi$
$829$	−151083.			−0.219840			−0.109920	+	0.993940i	$0.535059\pi$
$830$	335530.	−	415908.i	0.487052	−	0.603728i
$831$	−20704.9			−0.0299828
$832$			138043.i			0.199419i
$833$	181891.			0.262132
$834$	−36956.3			−0.0531320
$835$	−75288.4	+	93324.0i	−0.107983	+	0.133851i
$836$	368795.			0.527682
$837$			216450.i			0.308963i
$838$	418312.			0.595679
$839$		−	1.22719e6i		−	1.74337i	−0.490068	−	0.871684i	$-0.663028\pi$
$839$		−	1.22719e6i		−	1.74337i	0.490068	−	0.871684i	$-0.336972\pi$
$840$	24511.3	+	19774.3i	0.0347382	+	0.0280248i
$841$	−700129.			−0.989888
$842$	−669788.			−0.944742
$843$	72736.5			0.102352
$844$	−324404.			−0.455408
$845$	−858685.	−	692737.i	−1.20260	−	0.970186i
$846$	−514445.			−0.718784
$847$	695741.			0.969797
$848$	−220434.			−0.306540
$849$			53378.7i			0.0740547i
$850$	−151901.	+	32872.3i	−0.210244	+	0.0454980i
$851$	−515265.	−	152180.i	−0.711494	−	0.210136i
$852$			49830.5i			0.0686461i
$853$		−	556804.i		−	0.765252i	−0.923903	−	0.382626i	$-0.875020\pi$
$853$		−	556804.i		−	0.765252i	0.923903	−	0.382626i	$-0.124980\pi$
$854$	59766.8			0.0819490
$855$	893022.	−	1.10695e6i	1.22160	−	1.51424i
$856$		−	93478.5i		−	0.127575i
$857$		−	617332.i		−	0.840538i	−0.907400	−	0.420269i	$-0.861936\pi$
$857$		−	617332.i		−	0.840538i	0.907400	−	0.420269i	$-0.138064\pi$
$858$	41322.9			0.0561327
$859$	−558762.			−0.757252			−0.378626	−	0.925550i	$-0.623603\pi$
$859$	−558762.			−0.757252			−0.378626	+	0.925550i	$0.623603\pi$
$860$	140060.	+	112992.i	0.189372	+	0.152774i
$861$		−	48976.6i		−	0.0660666i
$862$	565878.			0.761568
$863$			657675.i			0.883059i	0.897247	+	0.441529i	$0.145564\pi$
$863$			657675.i			0.883059i	−0.897247	+	0.441529i	$0.854436\pi$
$864$	−24314.8			−0.0325720
$865$	−705855.	+	874945.i	−0.943372	+	1.16936i
$866$			473266.i			0.631058i
$867$		−	63112.4i		−	0.0839608i
$868$	−861884.			−1.14396
$869$	429634.			0.568931
$870$	−3875.65	−	3126.65i	−0.00512042	−	0.00413086i
$871$			1.08119e6i			1.42516i
$872$	−1019.84			−0.00134122
$873$	427141.			0.560458
$874$	−1.01655e6	−	300232.i	−1.33078	−	0.393037i
$875$	−469113.	+	933388.i	−0.612719	+	1.21912i
$876$	62818.0			0.0818608
$877$			322590.i			0.419422i	0.977763	+	0.209711i	$0.0672523\pi$
$877$			322590.i			0.419422i	−0.977763	+	0.209711i	$0.932748\pi$
$878$			859034.i			1.11435i
$879$			74696.5i			0.0966769i
$880$	65374.8	−	81035.6i	0.0844200	−	0.104643i
$881$			1.46416e6i			1.88642i	0.332201	+	0.943209i	$0.392209\pi$
$881$			1.46416e6i			1.88642i	−0.332201	+	0.943209i	$0.607791\pi$
$882$			469929.i			0.604081i
$883$			1.02922e6i			1.32004i	0.751248	+	0.660020i	$0.229452\pi$
$883$			1.02922e6i			1.32004i	−0.751248	+	0.660020i	$0.770548\pi$
$884$			189631.i			0.242663i
$885$	−62496.6	+	77467.9i	−0.0797939	+	0.0989088i
$886$	85017.6			0.108303
$887$			898024.i			1.14141i	0.821156	+	0.570704i	$0.193329\pi$
$887$			898024.i			1.14141i	−0.821156	+	0.570704i	$0.806671\pi$
$888$	19136.6			0.0242682
$889$		−	135229.i		−	0.171106i
$890$	−490652.	−	395830.i	−0.619432	−	0.499722i
$891$		−	416017.i		−	0.524029i
$892$		−	465007.i		−	0.584427i
$893$	1.60447e6			2.01200
$894$			17191.6i			0.0215100i
$895$	−10211.5	−	8238.06i	−0.0127481	−	0.0102844i
$896$		−	96819.5i		−	0.120600i
$897$	−113903.	−	33640.4i	−0.141563	−	0.0418097i
$898$		−	394070.i		−	0.488675i
$899$	136279.			0.168620
$900$	−84928.2	−	392449.i	−0.104850	−	0.484504i
$901$	−302813.			−0.373014
$902$	−161919.			−0.199015
$903$		−	50093.0i		−	0.0614329i
$904$			341113.i			0.417409i
$905$	−523681.	+	649131.i	−0.639396	+	0.792565i
$906$	−51096.5			−0.0622493
$907$	−994345.			−1.20871			−0.604355	−	0.796715i	$-0.706569\pi$
$907$	−994345.			−1.20871			−0.604355	+	0.796715i	$0.706569\pi$
$908$	−631049.			−0.765405
$909$	43186.4			0.0522660
$910$	992031.	+	800313.i	1.19796	+	0.966445i
$911$		−	947010.i		−	1.14108i	−0.821268	−	0.570542i	$-0.806733\pi$
$911$		−	947010.i		−	1.14108i	0.821268	−	0.570542i	$-0.193267\pi$
$912$	37753.9			0.0453913
$913$			491780.i			0.589969i
$914$		−	82280.0i		−	0.0984922i
$915$	5120.94	+	4131.27i	0.00611656	+	0.00493448i
$916$		−	260771.i		−	0.310791i
$917$	−1.43197e6			−1.70292
$918$	−33401.5			−0.0396352
$919$			1.07295e6i			1.27042i	0.772340	+	0.635209i	$0.219086\pi$
$919$			1.07295e6i			1.27042i	−0.772340	+	0.635209i	$0.780914\pi$
$920$	−246170.	+	170146.i	−0.290843	+	0.201023i
$921$	89100.4			0.105041
$922$			678411.i			0.798052i
$923$			2.01676e6i			2.36729i
$924$	−28982.8			−0.0339466
$925$	134260.	+	620407.i	0.156914	+	0.725092i
$926$	905910.			1.05648
$927$	155596.			0.181067
$928$			15308.8i			0.0177765i
$929$	−905273.			−1.04893			−0.524467	−	0.851431i	$-0.675735\pi$
$929$	−905273.			−1.04893			−0.524467	+	0.851431i	$0.675735\pi$
$930$	−73848.0	−	59576.3i	−0.0853833	−	0.0688823i
$931$		−	1.46563e6i		−	1.69092i
$932$		−	481579.i		−	0.554416i
$933$			16163.4i			0.0185682i
$934$		−	838437.i		−	0.961118i
$935$	89806.0	−	111319.i	0.102726	−	0.127335i
$936$	−489925.			−0.559214
$937$	1.54572e6			1.76056			0.880279	−	0.474456i	$-0.157355\pi$
$937$	1.54572e6			1.76056			0.880279	+	0.474456i	$0.157355\pi$
$938$		−	758316.i		−	0.861876i
$939$		−	196.208i		−	0.000222529i
$940$	284417.	−	352550.i	0.321885	−	0.398993i
$941$		−	1.67830e6i		−	1.89535i	−0.319230	−	0.947677i	$-0.603424\pi$
$941$		−	1.67830e6i		−	1.89535i	0.319230	−	0.947677i	$-0.396576\pi$
$942$	35423.7			0.0399201
$943$	446315.	+	131816.i	0.501901	+	0.148233i
$944$	305998.			0.343380
$945$	−140967.	+	174736.i	−0.157853	+	0.195668i
$946$	−165610.			−0.185057
$947$		−	1.32630e6i		−	1.47891i	−0.673207	−	0.739454i	$-0.735084\pi$
$947$		−	1.32630e6i		−	1.47891i	0.673207	−	0.739454i	$-0.264916\pi$
$948$	43982.1			0.0489395
$949$	2.54240e6			2.82300
$950$	264877.	+	1.22398e6i	0.293492	+	1.35621i
$951$	−130507.			−0.144302
$952$		−	133002.i		−	0.146752i
$953$	−754162.			−0.830384			−0.415192	−	0.909734i	$-0.636286\pi$
$953$	−754162.			−0.830384			−0.415192	+	0.909734i	$0.636286\pi$
$954$		−	782340.i		−	0.859605i
$955$	525885.	−	651863.i	0.576612	−	0.714742i
$956$	−560196.			−0.612949
$957$	4582.67			0.00500373
$958$	1.17291e6			1.27801
$959$	−1.03462e6			−1.12497
$960$	6692.48	−	8295.69i	0.00726181	−	0.00900140i
$961$	1.67318e6			1.81174
$962$	774504.			0.836900
$963$	331763.			0.357746
$964$			668464.i			0.719323i
$965$	231736.	−	287249.i	0.248850	−	0.308463i
$966$	79888.2	+	23594.5i	0.0856108	+	0.0252846i
$967$			208334.i			0.222796i	0.993776	+	0.111398i	$0.0355328\pi$
$967$			208334.i			0.222796i	−0.993776	+	0.111398i	$0.964467\pi$
$968$		−	235469.i		−	0.251295i
$969$	51862.9			0.0552344
$970$	−236150.	+	292721.i	−0.250983	+	0.311107i
$971$			644353.i			0.683417i	0.939806	+	0.341708i	$0.111006\pi$
$971$			644353.i			0.683417i	−0.939806	+	0.341708i	$0.888994\pi$
$972$		−	129629.i		−	0.137204i
$973$	1.04905e6			1.10808
$974$	294032.			0.309939
$975$	29679.0	+	137145.i	0.0312205	+	0.144268i
$976$		−	20227.7i		−	0.0212347i
$977$	−1.09837e6			−1.15069			−0.575344	−	0.817911i	$-0.695132\pi$
$977$	−1.09837e6			−1.15069			−0.575344	+	0.817911i	$0.695132\pi$
$978$			75047.5i			0.0784618i
$979$	580160.			0.605316
$980$	−322043.	−	259806.i	−0.335322	−	0.270518i
$981$		−	3619.50i		−	0.00376106i
$982$			1.24591e6i			1.29201i
$983$	−377827.			−0.391008			−0.195504	−	0.980703i	$-0.562634\pi$
$983$	−377827.			−0.391008			−0.195504	+	0.980703i	$0.562634\pi$
$984$	−16575.8			−0.0171193
$985$	−628730.	+	779345.i	−0.648025	+	0.803262i
$986$			21029.9i			0.0216313i
$987$	−126091.			−0.129435
$988$	1.52799e6			1.56534
$989$	456489.	+	134821.i	0.466699	+	0.137837i
$990$	287602.	+	232021.i	0.293442	+	0.236732i
$991$	−596613.			−0.607499			−0.303749	−	0.952752i	$-0.598239\pi$
$991$	−596613.			−0.607499			−0.303749	+	0.952752i	$0.598239\pi$
$992$			291700.i			0.296424i
$993$			104642.i			0.106123i
$994$		−	1.41450e6i		−	1.43163i
$995$	−439742.	+	545084.i	−0.444173	+	0.550576i
$996$			50344.0i			0.0507492i
$997$		−	516968.i		−	0.520084i	−0.965597	−	0.260042i	$-0.916264\pi$
$997$		−	516968.i		−	0.520084i	0.965597	−	0.260042i	$-0.0837364\pi$
$998$			256143.i			0.257171i
$999$			136421.i			0.136694i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.c.a.229.8	yes	48
5.4	even	2	inner	230.5.c.a.229.41	yes	48
23.22	odd	2	inner	230.5.c.a.229.42	yes	48
115.114	odd	2	inner	230.5.c.a.229.7	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.c.a.229.7	✓	48	115.114	odd	2	inner
230.5.c.a.229.8	yes	48	1.1	even	1	trivial
230.5.c.a.229.41	yes	48	5.4	even	2	inner
230.5.c.a.229.42	yes	48	23.22	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	230.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.82843i q^{2} +0.832711i q^{3} -8.00000 q^{4} +(19.4576 + 15.6972i) q^{5} -2.35526 q^{6} +66.8572 q^{7} -22.6274i q^{8} +80.3066 q^{9} +O(q^{10})\)	\(q+2.82843i q^{2} +0.832711i q^{3} -8.00000 q^{4} +(19.4576 + 15.6972i) q^{5} -2.35526 q^{6} +66.8572 q^{7} -22.6274i q^{8} +80.3066 q^{9} +(-44.3985 + 55.0343i) q^{10} -65.0740i q^{11} -6.66169i q^{12} -269.615i q^{13} +189.101i q^{14} +(-13.0713 + 16.2025i) q^{15} +64.0000 q^{16} +87.9174 q^{17} +227.141i q^{18} -708.415i q^{19} +(-155.661 - 125.578i) q^{20} +55.6727i q^{21} +184.057 q^{22} +(-507.336 - 149.839i) q^{23} +18.8421 q^{24} +(132.194 + 610.860i) q^{25} +762.586 q^{26} +134.322i q^{27} -534.857 q^{28} +84.5700 q^{29} +(-45.8277 - 36.9711i) q^{30} +1611.43 q^{31} +181.019i q^{32} +54.1878 q^{33} +248.668i q^{34} +(1300.88 + 1049.47i) q^{35} -642.453 q^{36} +1015.63 q^{37} +2003.70 q^{38} +224.511 q^{39} +(355.188 - 440.274i) q^{40} -879.723 q^{41} -157.466 q^{42} -899.776 q^{43} +520.592i q^{44} +(1562.57 + 1260.59i) q^{45} +(423.807 - 1434.96i) q^{46} +2264.87i q^{47} +53.2935i q^{48} +2068.88 q^{49} +(-1727.77 + 373.900i) q^{50} +73.2098i q^{51} +2156.92i q^{52} -3444.29 q^{53} -379.919 q^{54} +(1021.48 - 1266.18i) q^{55} -1512.81i q^{56} +589.905 q^{57} +239.200i q^{58} +4781.22 q^{59} +(104.570 - 129.620i) q^{60} -316.058i q^{61} +4557.81i q^{62} +5369.07 q^{63} -512.000 q^{64} +(4232.21 - 5246.05i) q^{65} +153.266i q^{66} -4010.12 q^{67} -703.339 q^{68} +(124.772 - 422.464i) q^{69} +(-2968.36 + 3679.44i) q^{70} -7480.16 q^{71} -1817.13i q^{72} +9429.75i q^{73} +2872.63i q^{74} +(-508.670 + 110.079i) q^{75} +5667.32i q^{76} -4350.66i q^{77} +635.014i q^{78} +6602.25i q^{79} +(1245.28 + 1004.62i) q^{80} +6392.98 q^{81} -2488.23i q^{82} -7557.25 q^{83} -445.382i q^{84} +(1710.66 + 1380.06i) q^{85} -2544.95i q^{86} +70.4224i q^{87} -1472.46 q^{88} +8915.39i q^{89} +(-3565.49 + 4419.62i) q^{90} -18025.7i q^{91} +(4058.68 + 1198.71i) q^{92} +1341.85i q^{93} -6406.01 q^{94} +(11120.2 - 13784.0i) q^{95} -150.737 q^{96} +5318.88 q^{97} +5851.68i q^{98} -5225.87i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9}+O(q^{10}) \) 48 * q - 384 * q^4 - 64 * q^6 - 1608 * q^9	\( 48 q - 384 q^{4} - 64 q^{6} - 1608 q^{9} + 3072 q^{16} + 512 q^{24} + 1488 q^{25} - 384 q^{26} - 2940 q^{29} + 4732 q^{31} + 2556 q^{35} + 12864 q^{36} + 2736 q^{39} + 828 q^{41} - 64 q^{46} + 32572 q^{49} - 3264 q^{50} + 10112 q^{54} + 12824 q^{55} + 7092 q^{59} - 24576 q^{64} + 14000 q^{69} - 6592 q^{70} - 12708 q^{71} + 24728 q^{75} - 13040 q^{81} - 15700 q^{85} - 9728 q^{94} - 46608 q^{95} - 4096 q^{96}+O(q^{100}) \) 48 * q - 384 * q^4 - 64 * q^6 - 1608 * q^9 + 3072 * q^16 + 512 * q^24 + 1488 * q^25 - 384 * q^26 - 2940 * q^29 + 4732 * q^31 + 2556 * q^35 + 12864 * q^36 + 2736 * q^39 + 828 * q^41 - 64 * q^46 + 32572 * q^49 - 3264 * q^50 + 10112 * q^54 + 12824 * q^55 + 7092 * q^59 - 24576 * q^64 + 14000 * q^69 - 6592 * q^70 - 12708 * q^71 + 24728 * q^75 - 13040 * q^81 - 15700 * q^85 - 9728 * q^94 - 46608 * q^95 - 4096 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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