LMFDB - Embedded newform 224.4.t.a.81.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,4,Mod(81,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("224.81");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	224.t (of order $6$, 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:	$13.2164278413$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			81.17
Character	$\chi$	$=$	224.81
Dual form			224.4.t.a.177.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.43871 + 2.56269i) q^{3} +(-13.1631 + 7.59971i) q^{5} +(-1.45519 - 18.4630i) q^{7} +(-0.365251 - 0.632633i) q^{9} +(-35.5292 - 20.5128i) q^{11} -15.1225i q^{13} -77.9028 q^{15} +(27.3391 - 47.3526i) q^{17} +(37.1763 - 21.4637i) q^{19} +(40.8558 - 85.6811i) q^{21} +(-69.1294 - 119.736i) q^{23} +(53.0113 - 91.8183i) q^{25} -142.129i q^{27} +271.056i q^{29} +(-9.18381 + 15.9068i) q^{31} +(-105.136 - 182.100i) q^{33} +(159.468 + 231.971i) q^{35} +(202.736 - 117.050i) q^{37} +(38.7541 - 67.1242i) q^{39} -347.517 q^{41} +314.997i q^{43} +(9.61566 + 5.55160i) q^{45} +(-196.536 - 340.410i) q^{47} +(-338.765 + 53.7343i) q^{49} +(242.700 - 140.123i) q^{51} +(-439.900 - 253.976i) q^{53} +623.565 q^{55} +220.020 q^{57} +(-640.900 - 370.024i) q^{59} +(198.404 - 114.549i) q^{61} +(-11.1488 + 7.66422i) q^{63} +(114.926 + 199.058i) q^{65} +(-262.711 - 151.676i) q^{67} -708.629i q^{69} -82.4824 q^{71} +(135.675 - 234.997i) q^{73} +(470.603 - 271.703i) q^{75} +(-327.026 + 685.825i) q^{77} +(304.852 + 528.019i) q^{79} +(354.371 - 613.789i) q^{81} +587.294i q^{83} +831.076i q^{85} +(-694.633 + 1203.14i) q^{87} +(804.220 + 1392.95i) q^{89} +(-279.206 + 22.0060i) q^{91} +(-81.5285 + 47.0705i) q^{93} +(-326.237 + 565.058i) q^{95} -339.739 q^{97} +29.9692i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{7} + 160 q^{9} + 116 q^{15} - 2 q^{17} - 162 q^{23} + 348 q^{25} + 374 q^{31} - 110 q^{33} - 52 q^{39} - 8 q^{41} + 738 q^{47} + 356 q^{49} + 2268 q^{55} - 452 q^{57} - 668 q^{63} + 248 q^{65}+ \cdots + 1672 q^{97}+O(q^{100}) $ 44 * q + 4 * q^7 + 160 * q^9 + 116 * q^15 - 2 * q^17 - 162 * q^23 + 348 * q^25 + 374 * q^31 - 110 * q^33 - 52 * q^39 - 8 * q^41 + 738 * q^47 + 356 * q^49 + 2268 * q^55 - 452 * q^57 - 668 * q^63 + 248 * q^65 - 1248 * q^71 - 218 * q^73 - 298 * q^79 - 1050 * q^81 - 2140 * q^87 + 422 * q^89 + 2434 * q^95 + 1672 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	4.43871	+	2.56269i	0.854230	+	0.493190i	0.862076	−	0.506780i	$-0.169164\pi$
$3$	4.43871	+	2.56269i	0.854230	+	0.493190i	−0.00784607	+	0.999969i	$0.502498\pi$
$4$		0			0
$5$	−13.1631	+	7.59971i	−1.17734	+	0.679739i	−0.955398	−	0.295320i	$-0.904574\pi$
$5$	−13.1631	+	7.59971i	−1.17734	+	0.679739i	−0.221944	+	0.975059i	$0.571240\pi$
$6$		0			0
$7$	−1.45519	−	18.4630i	−0.0785728	−	0.996908i
$7$	−1.45519	−	18.4630i	−0.0785728	−	0.996908i
$8$		0			0
$9$	−0.365251	−	0.632633i	−0.0135278	−	0.0234308i
$10$		0			0
$11$	−35.5292	−	20.5128i	−0.973859	−	0.562258i	−0.0734485	−	0.997299i	$-0.523400\pi$
$11$	−35.5292	−	20.5128i	−0.973859	−	0.562258i	−0.900411	+	0.435041i	$0.856734\pi$
$12$		0			0
$13$		−	15.1225i		−	0.322632i	−0.986903	−	0.161316i	$-0.948426\pi$
$13$		−	15.1225i		−	0.322632i	0.986903	−	0.161316i	$-0.0515738\pi$
$14$		0			0
$15$	−77.9028			−1.34096
$16$		0			0
$17$	27.3391	−	47.3526i	0.390041	−	0.675571i	−0.602414	−	0.798184i	$-0.705794\pi$
$17$	27.3391	−	47.3526i	0.390041	−	0.675571i	0.992455	+	0.122613i	$0.0391275\pi$
$18$		0			0
$19$	37.1763	−	21.4637i	0.448886	−	0.259164i	−0.258474	−	0.966018i	$-0.583220\pi$
$19$	37.1763	−	21.4637i	0.448886	−	0.259164i	0.707359	+	0.706854i	$0.249886\pi$
$20$		0			0
$21$	40.8558	−	85.6811i	0.424546	−	0.890340i
$22$		0			0
$23$	−69.1294	−	119.736i	−0.626717	−	1.08550i	−0.988206	−	0.153129i	$-0.951065\pi$
$23$	−69.1294	−	119.736i	−0.626717	−	1.08550i	0.361490	−	0.932376i	$-0.382268\pi$
$24$		0			0
$25$	53.0113	−	91.8183i	0.424090	−	0.734546i
$26$		0			0
$27$		−	142.129i		−	1.01307i
$28$		0			0
$29$			271.056i			1.73565i	0.496869	+	0.867826i	$0.334483\pi$
$29$			271.056i			1.73565i	−0.496869	+	0.867826i	$0.665517\pi$
$30$		0			0
$31$	−9.18381	+	15.9068i	−0.0532084	+	0.0921597i	−0.891403	−	0.453212i	$-0.850278\pi$
$31$	−9.18381	+	15.9068i	−0.0532084	+	0.0921597i	0.838194	+	0.545372i	$0.183611\pi$
$32$		0			0
$33$	−105.136	−	182.100i	−0.554599	−	0.960594i
$34$		0			0
$35$	159.468	+	231.971i	0.770145	+	1.12029i
$36$		0			0
$37$	202.736	−	117.050i	0.900801	−	0.520078i	0.0233409	−	0.999728i	$-0.492570\pi$
$37$	202.736	−	117.050i	0.900801	−	0.520078i	0.877460	+	0.479650i	$0.159236\pi$
$38$		0			0
$39$	38.7541	−	67.1242i	0.159119	−	0.275602i
$40$		0			0
$41$	−347.517			−1.32373			−0.661866	−	0.749622i	$-0.730235\pi$
$41$	−347.517			−1.32373			−0.661866	+	0.749622i	$0.730235\pi$
$42$		0			0
$43$			314.997i			1.11713i	0.829460	+	0.558566i	$0.188648\pi$
$43$			314.997i			1.11713i	−0.829460	+	0.558566i	$0.811352\pi$
$44$		0			0
$45$	9.61566	+	5.55160i	0.0318537	+	0.0183908i
$46$		0			0
$47$	−196.536	−	340.410i	−0.609951	−	1.05647i	−0.991248	−	0.132013i	$-0.957856\pi$
$47$	−196.536	−	340.410i	−0.609951	−	1.05647i	0.381297	−	0.924452i	$-0.375477\pi$
$48$		0			0
$49$	−338.765	+	53.7343i	−0.987653	+	0.156660i
$50$		0			0
$51$	242.700	−	140.123i	0.666369	−	0.384728i
$52$		0			0
$53$	−439.900	−	253.976i	−1.14009	−	0.658233i	−0.193639	−	0.981073i	$-0.562029\pi$
$53$	−439.900	−	253.976i	−1.14009	−	0.658233i	−0.946454	+	0.322840i	$0.895363\pi$
$54$		0			0
$55$	623.565			1.52875
$56$		0			0
$57$	220.020			0.511269
$58$		0			0
$59$	−640.900	−	370.024i	−1.41420	−	0.816491i	−0.418423	−	0.908252i	$-0.637417\pi$
$59$	−640.900	−	370.024i	−1.41420	−	0.816491i	−0.995781	+	0.0917608i	$0.970750\pi$
$60$		0			0
$61$	198.404	−	114.549i	0.416443	−	0.240433i	−0.277111	−	0.960838i	$-0.589377\pi$
$61$	198.404	−	114.549i	0.416443	−	0.240433i	0.693554	+	0.720404i	$0.256044\pi$
$62$		0			0
$63$	−11.1488	+	7.66422i	−0.0222955	+	0.0153270i
$64$		0			0
$65$	114.926	+	199.058i	0.219305	+	0.379848i
$66$		0			0
$67$	−262.711	−	151.676i	−0.479034	−	0.276570i	0.240980	−	0.970530i	$-0.422531\pi$
$67$	−262.711	−	151.676i	−0.479034	−	0.276570i	−0.720014	+	0.693960i	$0.755865\pi$
$68$		0			0
$69$		−	708.629i		−	1.23636i
$70$		0			0
$71$	−82.4824			−0.137871			−0.0689356	−	0.997621i	$-0.521960\pi$
$71$	−82.4824			−0.137871			−0.0689356	+	0.997621i	$0.521960\pi$
$72$		0			0
$73$	135.675	−	234.997i	0.217529	−	0.376771i	−0.736523	−	0.676412i	$-0.763534\pi$
$73$	135.675	−	234.997i	0.217529	−	0.376771i	0.954052	+	0.299641i	$0.0968670\pi$
$74$		0			0
$75$	470.603	−	271.703i	0.724541	−	0.418314i
$76$		0			0
$77$	−327.026	+	685.825i	−0.484001	+	1.01503i
$78$		0			0
$79$	304.852	+	528.019i	0.434159	+	0.751985i	0.997227	−	0.0744258i	$-0.0237124\pi$
$79$	304.852	+	528.019i	0.434159	+	0.751985i	−0.563068	+	0.826411i	$0.690379\pi$
$80$		0			0
$81$	354.371	−	613.789i	0.486106	−	0.841961i
$82$		0			0
$83$			587.294i			0.776674i	0.921518	+	0.388337i	$0.126950\pi$
$83$			587.294i			0.776674i	−0.921518	+	0.388337i	$0.873050\pi$
$84$		0			0
$85$			831.076i			1.06050i
$86$		0			0
$87$	−694.633	+	1203.14i	−0.856005	+	1.48264i
$88$		0			0
$89$	804.220	+	1392.95i	0.957833	+	1.65902i	0.727748	+	0.685845i	$0.240567\pi$
$89$	804.220	+	1392.95i	0.957833	+	1.65902i	0.230085	+	0.973170i	$0.426100\pi$
$90$		0			0
$91$	−279.206	+	22.0060i	−0.321634	+	0.0253501i
$92$		0			0
$93$	−81.5285	+	47.0705i	−0.0909045	+	0.0524837i
$94$		0			0
$95$	−326.237	+	565.058i	−0.352328	+	0.610250i
$96$		0			0
$97$	−339.739			−0.355622			−0.177811	−	0.984065i	$-0.556901\pi$
$97$	−339.739			−0.355622			−0.177811	+	0.984065i	$0.556901\pi$
$98$		0			0
$99$			29.9692i			0.0304245i
$100$		0			0
$101$	691.541	+	399.261i	0.681296	+	0.393347i	0.800343	−	0.599542i	$-0.204651\pi$
$101$	691.541	+	399.261i	0.681296	+	0.393347i	−0.119047	+	0.992889i	$0.537984\pi$
$102$		0			0
$103$	−441.683	−	765.018i	−0.422527	−	0.731839i	0.573658	−	0.819095i	$-0.305524\pi$
$103$	−441.683	−	765.018i	−0.422527	−	0.731839i	−0.996186	+	0.0872555i	$0.972190\pi$
$104$		0			0
$105$	113.363	+	1438.32i	0.105363	+	1.33682i
$106$		0			0
$107$	−301.588	+	174.122i	−0.272482	+	0.157318i	−0.630015	−	0.776583i	$-0.716951\pi$
$107$	−301.588	+	174.122i	−0.272482	+	0.157318i	0.357533	+	0.933901i	$0.383618\pi$
$108$		0			0
$109$	182.882	+	105.587i	0.160706	+	0.0927836i	0.578196	−	0.815898i	$-0.303757\pi$
$109$	182.882	+	105.587i	0.160706	+	0.0927836i	−0.417490	+	0.908681i	$0.637090\pi$
$110$		0			0
$111$	1199.85			1.02599
$112$		0			0
$113$	1594.12			1.32710			0.663552	−	0.748131i	$-0.269048\pi$
$113$	1594.12			1.32710			0.663552	+	0.748131i	$0.269048\pi$
$114$		0			0
$115$	1819.91	+	1050.73i	1.47572	+	0.852007i
$116$		0			0
$117$	−9.56696	+	5.52349i	−0.00755954	+	0.00436450i
$118$		0			0
$119$	−914.055	−	435.854i	−0.704129	−	0.335754i
$120$		0			0
$121$	176.048	+	304.924i	0.132268	+	0.229094i
$122$		0			0
$123$	−1542.53	−	890.578i	−1.13077	−	0.652851i
$124$		0			0
$125$		−	288.446i		−	0.206395i
$126$		0			0
$127$	1607.77			1.12336			0.561679	−	0.827355i	$-0.310156\pi$
$127$	1607.77			1.12336			0.561679	+	0.827355i	$0.310156\pi$
$128$		0			0
$129$	−807.240	+	1398.18i	−0.550958	+	0.954287i
$130$		0			0
$131$	1370.67	−	791.358i	0.914169	−	0.527796i	0.0323987	−	0.999475i	$-0.489685\pi$
$131$	1370.67	−	791.358i	0.914169	−	0.527796i	0.881770	+	0.471679i	$0.156352\pi$
$132$		0			0
$133$	−450.384	−	655.152i	−0.293633	−	0.427135i
$134$		0			0
$135$	1080.14	+	1870.86i	0.688621	+	1.19273i
$136$		0			0
$137$	337.449	−	584.478i	0.210439	−	0.364492i	−0.741413	−	0.671049i	$-0.765844\pi$
$137$	337.449	−	584.478i	0.210439	−	0.364492i	0.951852	+	0.306558i	$0.0991772\pi$
$138$		0			0
$139$			158.324i			0.0966103i	0.998833	+	0.0483051i	$0.0153820\pi$
$139$			158.324i			0.0966103i	−0.998833	+	0.0483051i	$0.984618\pi$
$140$		0			0
$141$		−	2014.64i		−	1.20329i
$142$		0			0
$143$	−310.204	+	537.288i	−0.181402	+	0.314198i
$144$		0			0
$145$	−2059.95	−	3567.94i	−1.17979	−	2.04346i
$146$		0			0
$147$	−1641.38	−	629.638i	−0.920945	−	0.353277i
$148$		0			0
$149$	−2116.50	+	1221.96i	−1.16369	+	0.671859i	−0.952186	−	0.305518i	$-0.901171\pi$
$149$	−2116.50	+	1221.96i	−1.16369	+	0.671859i	−0.211507	+	0.977376i	$0.567837\pi$
$150$		0			0
$151$	304.069	−	526.663i	0.163873	−	0.283836i	−0.772382	−	0.635159i	$-0.780935\pi$
$151$	304.069	−	526.663i	0.163873	−	0.283836i	0.936254	+	0.351323i	$0.114268\pi$
$152$		0			0
$153$	−39.9424			−0.0211056
$154$		0			0
$155$		−	279.177i		−	0.144671i
$156$		0			0
$157$	−1132.37	−	653.776i	−0.575626	−	0.332338i	0.183767	−	0.982970i	$-0.441171\pi$
$157$	−1132.37	−	653.776i	−0.575626	−	0.332338i	−0.759393	+	0.650632i	$0.774504\pi$
$158$		0			0
$159$	−1301.73	−	2254.65i	−0.649268	−	1.12456i
$160$		0			0
$161$	−2110.08	+	1450.57i	−1.03291	+	0.710070i
$162$		0			0
$163$	−1615.48	+	932.699i	−0.776284	+	0.448188i	−0.835112	−	0.550080i	$-0.814597\pi$
$163$	−1615.48	+	932.699i	−0.776284	+	0.448188i	0.0588277	+	0.998268i	$0.481264\pi$
$164$		0			0
$165$	2767.82	+	1598.00i	1.30591	+	0.753966i
$166$		0			0
$167$	417.840			0.193613			0.0968067	−	0.995303i	$-0.469137\pi$
$167$	417.840			0.193613			0.0968067	+	0.995303i	$0.469137\pi$
$168$		0			0
$169$	1968.31			0.895909
$170$		0			0
$171$	−27.1573	−	15.6793i	−0.0121449	−	0.00701185i
$172$		0			0
$173$	1789.20	−	1032.99i	0.786301	−	0.453971i	−0.0523575	−	0.998628i	$-0.516674\pi$
$173$	1789.20	−	1032.99i	0.786301	−	0.453971i	0.838659	+	0.544657i	$0.183340\pi$
$174$		0			0
$175$	−1772.38	−	845.135i	−0.765597	−	0.365064i
$176$		0			0
$177$	−1896.51	−	3284.85i	−0.805370	−	1.39494i
$178$		0			0
$179$	1788.56	+	1032.63i	0.746835	+	0.431185i	0.824549	−	0.565790i	$-0.191429\pi$
$179$	1788.56	+	1032.63i	0.746835	+	0.431185i	−0.0777142	+	0.996976i	$0.524762\pi$
$180$		0			0
$181$			1483.01i			0.609012i	0.952510	+	0.304506i	$0.0984913\pi$
$181$			1483.01i			0.609012i	−0.952510	+	0.304506i	$0.901509\pi$
$182$		0			0
$183$	1174.21			0.474317
$184$		0			0
$185$	−1779.09	+	3081.47i	−0.707034	+	1.22462i
$186$		0			0
$187$	−1942.67	+	1121.60i	−0.759690	+	0.438607i
$188$		0			0
$189$	−2624.13	+	206.825i	−1.00993	+	0.0795995i
$190$		0			0
$191$	−312.673	−	541.565i	−0.118451	−	0.205164i	0.800703	−	0.599062i	$-0.204460\pi$
$191$	−312.673	−	541.565i	−0.118451	−	0.205164i	−0.919154	+	0.393898i	$0.871126\pi$
$192$		0			0
$193$	2661.55	−	4609.95i	0.992657	−	1.71933i	0.391575	−	0.920146i	$-0.371930\pi$
$193$	2661.55	−	4609.95i	0.992657	−	1.71933i	0.601083	−	0.799187i	$-0.294736\pi$
$194$		0			0
$195$			1178.08i			0.432637i
$196$		0			0
$197$		−	574.940i		−	0.207933i	−0.994581	−	0.103966i	$-0.966847\pi$
$197$		−	574.940i		−	0.207933i	0.994581	−	0.103966i	$-0.0331535\pi$
$198$		0			0
$199$	1177.89	−	2040.17i	0.419590	−	0.726751i	−0.576308	−	0.817232i	$-0.695507\pi$
$199$	1177.89	−	2040.17i	0.419590	−	0.726751i	0.995898	+	0.0904813i	$0.0288405\pi$
$200$		0			0
$201$	−777.399	−	1346.49i	−0.272803	−	0.472509i
$202$		0			0
$203$	5004.51	−	394.438i	1.73029	−	0.136375i
$204$		0			0
$205$	4574.40	−	2641.03i	1.55849	−	0.899793i
$206$		0			0
$207$	−50.4991	+	87.4671i	−0.0169562	+	0.0293690i
$208$		0			0
$209$	−1761.12			−0.582869
$210$		0			0
$211$		−	3735.73i		−	1.21885i	−0.792842	−	0.609427i	$-0.791400\pi$
$211$		−	3735.73i		−	1.21885i	0.792842	−	0.609427i	$-0.208600\pi$
$212$		0			0
$213$	−366.115	−	211.377i	−0.117774	−	0.0679967i
$214$		0			0
$215$	−2393.89	−	4146.34i	−0.759358	−	1.31525i
$216$		0			0
$217$	307.052	+	146.413i	0.0960555	+	0.0458027i
$218$		0			0
$219$	1204.45	−	695.388i	0.371639	−	0.214566i
$220$		0			0
$221$	−716.088	−	413.434i	−0.217961	−	0.125840i
$222$		0			0
$223$	−1942.28			−0.583249			−0.291624	−	0.956533i	$-0.594196\pi$
$223$	−1942.28			−0.583249			−0.291624	+	0.956533i	$0.594196\pi$
$224$		0			0
$225$	−77.4497			−0.0229480
$226$		0			0
$227$	−3495.47	−	2018.11i	−1.02204	−	0.590073i	−0.107344	−	0.994222i	$-0.534235\pi$
$227$	−3495.47	−	2018.11i	−1.02204	−	0.590073i	−0.914693	+	0.404149i	$0.867568\pi$
$228$		0			0
$229$	−2941.05	+	1698.02i	−0.848690	+	0.489992i	−0.860209	−	0.509942i	$-0.829667\pi$
$229$	−2941.05	+	1698.02i	−0.848690	+	0.489992i	0.0115185	+	0.999934i	$0.496333\pi$
$230$		0			0
$231$	−3209.13	+	2206.11i	−0.914048	+	0.628361i
$232$		0			0
$233$	2806.20	+	4860.49i	0.789015	+	1.36661i	0.926571	+	0.376120i	$0.122742\pi$
$233$	2806.20	+	4860.49i	0.789015	+	1.36661i	−0.137556	+	0.990494i	$0.543925\pi$
$234$		0			0
$235$	5174.03	+	2987.23i	1.43624	+	0.829214i
$236$		0			0
$237$			3124.96i			0.856490i
$238$		0			0
$239$	1154.25			0.312394			0.156197	−	0.987726i	$-0.450077\pi$
$239$	1154.25			0.312394			0.156197	+	0.987726i	$0.450077\pi$
$240$		0			0
$241$	1134.86	−	1965.63i	0.303330	−	0.525383i	−0.673558	−	0.739134i	$-0.735235\pi$
$241$	1134.86	−	1965.63i	0.303330	−	0.525383i	0.976888	+	0.213751i	$0.0685682\pi$
$242$		0			0
$243$	−177.463	+	102.458i	−0.0468487	+	0.0270481i
$244$		0			0
$245$	4050.83	−	3281.83i	1.05632	−	0.855788i
$246$		0			0
$247$	−324.585	−	562.197i	−0.0836147	−	0.144825i
$248$		0			0
$249$	−1505.05	+	2606.83i	−0.383047	+	0.663458i
$250$		0			0
$251$		−	2730.85i		−	0.686733i	−0.939202	−	0.343366i	$-0.888433\pi$
$251$		−	2730.85i		−	0.686733i	0.939202	−	0.343366i	$-0.111567\pi$
$252$		0			0
$253$			5672.15i			1.40950i
$254$		0			0
$255$	−2129.79	+	3688.90i	−0.523030	+	0.905914i
$256$		0			0
$257$	−3236.06	−	5605.01i	−0.785446	−	1.36043i	−0.928732	−	0.370751i	$-0.879100\pi$
$257$	−3236.06	−	5605.01i	−0.785446	−	1.36043i	0.143286	−	0.989681i	$-0.454233\pi$
$258$		0			0
$259$	−2456.11	−	3572.79i	−0.589248	−	0.857152i
$260$		0			0
$261$	171.479	−	99.0035i	0.0406678	−	0.0234795i
$262$		0			0
$263$	622.289	−	1077.84i	0.145901	−	0.252708i	−0.783808	−	0.621004i	$-0.786725\pi$
$263$	622.289	−	1077.84i	0.145901	−	0.252708i	0.929709	+	0.368296i	$0.120059\pi$
$264$		0			0
$265$	7720.59			1.78971
$266$		0			0
$267$			8243.86i			1.88957i
$268$		0			0
$269$	−2732.98	−	1577.89i	−0.619453	−	0.357641i	0.157203	−	0.987566i	$-0.449752\pi$
$269$	−2732.98	−	1577.89i	−0.619453	−	0.357641i	−0.776656	+	0.629925i	$0.783086\pi$
$270$		0			0
$271$	−997.435	−	1727.61i	−0.223579	−	0.387250i	0.732313	−	0.680968i	$-0.238441\pi$
$271$	−997.435	−	1727.61i	−0.223579	−	0.387250i	−0.955892	+	0.293718i	$0.905107\pi$
$272$		0			0
$273$	−1295.71	−	617.840i	−0.287252	−	0.136972i
$274$		0			0
$275$	−3766.89	+	2174.82i	−0.826008	+	0.476896i
$276$		0			0
$277$	−1046.97	−	604.470i	−0.227099	−	0.131116i	0.382134	−	0.924107i	$-0.375189\pi$
$277$	−1046.97	−	604.470i	−0.227099	−	0.131116i	−0.609233	+	0.792991i	$0.708523\pi$
$278$		0			0
$279$	13.4176			0.00287917
$280$		0			0
$281$	4944.71			1.04974			0.524869	−	0.851183i	$-0.324114\pi$
$281$	4944.71			1.04974			0.524869	+	0.851183i	$0.324114\pi$
$282$		0			0
$283$	−4177.28	−	2411.76i	−0.877434	−	0.506587i	−0.00762240	−	0.999971i	$-0.502426\pi$
$283$	−4177.28	−	2411.76i	−0.877434	−	0.506587i	−0.869811	+	0.493384i	$0.835760\pi$
$284$		0			0
$285$	−2896.14	+	1672.09i	−0.601938	+	0.347529i
$286$		0			0
$287$	505.703	+	6416.21i	0.104009	+	1.31964i
$288$		0			0
$289$	961.651	+	1665.63i	0.195736	+	0.339025i
$290$		0			0
$291$	−1508.00	−	870.646i	−0.303782	−	0.175389i
$292$		0			0
$293$		−	3239.94i		−	0.646004i	−0.946398	−	0.323002i	$-0.895308\pi$
$293$		−	3239.94i		−	0.646004i	0.946398	−	0.323002i	$-0.104692\pi$
$294$		0			0
$295$	11248.3			2.22000
$296$		0			0
$297$	−2915.47	+	5049.74i	−0.569605	+	0.986584i
$298$		0			0
$299$	−1810.70	+	1045.41i	−0.350218	+	0.202199i
$300$		0			0
$301$	5815.80	−	458.380i	1.11368	−	0.0877761i
$302$		0			0
$303$	2046.37	+	3544.41i	0.387989	+	0.672017i
$304$		0			0
$305$	−1741.07	+	3015.63i	−0.326864	+	0.566145i
$306$		0			0
$307$			232.720i			0.0432640i	0.999766	+	0.0216320i	$0.00688622\pi$
$307$			232.720i			0.0432640i	−0.999766	+	0.0216320i	$0.993114\pi$
$308$		0			0
$309$		−	4527.59i		−	0.833545i
$310$		0			0
$311$	−4470.58	+	7743.27i	−0.815123	+	1.41183i	0.0941169	+	0.995561i	$0.469997\pi$
$311$	−4470.58	+	7743.27i	−0.815123	+	1.41183i	−0.909240	+	0.416273i	$0.863336\pi$
$312$		0			0
$313$	−728.675	−	1262.10i	−0.131588	−	0.227918i	0.792701	−	0.609611i	$-0.208674\pi$
$313$	−728.675	−	1262.10i	−0.131588	−	0.227918i	−0.924289	+	0.381693i	$0.875341\pi$
$314$		0			0
$315$	88.5066	−	185.613i	0.0158311	−	0.0332003i
$316$		0			0
$317$	−6186.03	+	3571.51i	−1.09603	+	0.632794i	−0.935176	−	0.354184i	$-0.884759\pi$
$317$	−6186.03	+	3571.51i	−1.09603	+	0.632794i	−0.160856	+	0.986978i	$0.551425\pi$
$318$		0			0
$319$	5560.12	−	9630.41i	0.975883	−	1.69028i
$320$		0			0
$321$	−1784.88			−0.310350
$322$		0			0
$323$		−	2347.19i		−	0.404339i
$324$		0			0
$325$	−1388.52	−	801.661i	−0.236988	−	0.136825i
$326$		0			0
$327$	541.174	+	937.341i	0.0915199	+	0.158517i
$328$		0			0
$329$	−5998.99	+	4124.00i	−1.00527	+	0.691074i
$330$		0			0
$331$	8679.66	−	5011.20i	1.44132	−	0.832147i	0.443383	−	0.896332i	$-0.353778\pi$
$331$	8679.66	−	5011.20i	1.44132	−	0.832147i	0.997938	+	0.0641853i	$0.0204449\pi$
$332$		0			0
$333$	−148.099	−	85.5051i	−0.0243717	−	0.0140710i
$334$		0			0
$335$	4610.79			0.751983
$336$		0			0
$337$	−1689.89			−0.273158			−0.136579	−	0.990629i	$-0.543611\pi$
$337$	−1689.89			−0.273158			−0.136579	+	0.990629i	$0.543611\pi$
$338$		0			0
$339$	7075.85	+	4085.25i	1.13365	+	0.654514i
$340$		0			0
$341$	652.587	−	376.771i	0.103635	−	0.0598337i
$342$		0			0
$343$	1485.06	+	6176.42i	0.233778	+	0.972290i
$344$		0			0
$345$	5385.38	+	9327.74i	0.840403	+	1.45562i
$346$		0			0
$347$	−2192.29	−	1265.72i	−0.339160	−	0.195814i	0.320740	−	0.947167i	$-0.396068\pi$
$347$	−2192.29	−	1265.72i	−0.339160	−	0.195814i	−0.659901	+	0.751353i	$0.729402\pi$
$348$		0			0
$349$		−	2583.30i		−	0.396221i	−0.980180	−	0.198110i	$-0.936520\pi$
$349$		−	2583.30i		−	0.396221i	0.980180	−	0.198110i	$-0.0634804\pi$
$350$		0			0
$351$	−2149.34			−0.326848
$352$		0			0
$353$	725.039	−	1255.80i	0.109320	−	0.189348i	−0.806175	−	0.591677i	$-0.798466\pi$
$353$	725.039	−	1255.80i	0.109320	−	0.189348i	0.915495	+	0.402329i	$0.131799\pi$
$354$		0			0
$355$	1085.72	−	626.843i	0.162322	−	0.0937165i
$356$		0			0
$357$	−2940.27	−	4277.07i	−0.435897	−	0.634080i
$358$		0			0
$359$	−247.731	−	429.083i	−0.0364199	−	0.0630811i	0.847241	−	0.531209i	$-0.178262\pi$
$359$	−247.731	−	429.083i	−0.0364199	−	0.0630811i	−0.883661	+	0.468128i	$0.844929\pi$
$360$		0			0
$361$	−2508.12	+	4344.18i	−0.365668	+	0.633355i
$362$		0			0
$363$			1804.63i			0.260932i
$364$		0			0
$365$			4124.38i			0.591451i
$366$		0			0
$367$	1665.41	−	2884.57i	0.236876	−	0.410281i	−0.722940	−	0.690911i	$-0.757210\pi$
$367$	1665.41	−	2884.57i	0.236876	−	0.410281i	0.959816	+	0.280629i	$0.0905431\pi$
$368$		0			0
$369$	126.931	+	219.851i	0.0179072	+	0.0310162i
$370$		0			0
$371$	−4049.03	+	8491.46i	−0.566618	+	1.18829i
$372$		0			0
$373$	−1973.29	+	1139.28i	−0.273923	+	0.158149i	−0.630669	−	0.776052i	$-0.717219\pi$
$373$	−1973.29	+	1139.28i	−0.273923	+	0.158149i	0.356746	+	0.934201i	$0.383886\pi$
$374$		0			0
$375$	739.197	−	1280.33i	0.101792	−	0.176309i
$376$		0			0
$377$	4099.04			0.559976
$378$		0			0
$379$			9424.88i			1.27737i	0.769468	+	0.638685i	$0.220521\pi$
$379$			9424.88i			1.27737i	−0.769468	+	0.638685i	$0.779479\pi$
$380$		0			0
$381$	7136.42	+	4120.21i	0.959606	+	0.554029i
$382$		0			0
$383$	4945.41	+	8565.70i	0.659788	+	1.14279i	0.980670	+	0.195667i	$0.0626871\pi$
$383$	4945.41	+	8565.70i	0.659788	+	1.14279i	−0.320883	+	0.947119i	$0.603980\pi$
$384$		0			0
$385$	−907.404	−	11512.9i	−0.120118	−	1.52403i
$386$		0			0
$387$	199.278	−	115.053i	0.0261753	−	0.0151123i
$388$		0			0
$389$	7363.48	+	4251.31i	0.959751	+	0.554113i	0.896096	−	0.443859i	$-0.146391\pi$
$389$	7363.48	+	4251.31i	0.959751	+	0.554113i	0.0636548	+	0.997972i	$0.479724\pi$
$390$		0			0
$391$	−7559.73			−0.977780
$392$		0			0
$393$	8112.01			1.04121
$394$		0			0
$395$	−8025.59	−	4633.58i	−1.02231	−	0.590229i
$396$		0			0
$397$	12788.4	−	7383.40i	1.61671	−	0.933406i	0.628943	−	0.777452i	$-0.283488\pi$
$397$	12788.4	−	7383.40i	1.61671	−	0.933406i	0.987764	−	0.155954i	$-0.0498453\pi$
$398$		0			0
$399$	−320.170	−	4062.22i	−0.0401718	−	0.509688i
$400$		0			0
$401$	−2506.57	−	4341.51i	−0.312150	−	0.540660i	0.666677	−	0.745346i	$-0.267716\pi$
$401$	−2506.57	−	4341.51i	−0.312150	−	0.540660i	−0.978828	+	0.204686i	$0.934383\pi$
$402$		0			0
$403$	240.550	+	138.882i	0.0297337	+	0.0171667i
$404$		0			0
$405$			10772.5i			1.32170i
$406$		0			0
$407$	−9604.07			−1.16967
$408$		0			0
$409$	699.767	−	1212.03i	0.0845997	−	0.146531i	−0.820621	−	0.571473i	$-0.806372\pi$
$409$	699.767	−	1212.03i	0.0845997	−	0.146531i	0.905221	+	0.424942i	$0.139706\pi$
$410$		0			0
$411$	2995.67	−	1729.55i	0.359527	−	0.207573i
$412$		0			0
$413$	−5899.12	+	12371.4i	−0.702849	+	1.47399i
$414$		0			0
$415$	−4463.27	−	7730.61i	−0.527935	−	0.914411i
$416$		0			0
$417$	−405.734	+	702.752i	−0.0476472	+	0.0825273i
$418$		0			0
$419$			306.232i			0.0357050i	0.999841	+	0.0178525i	$0.00568293\pi$
$419$			306.232i			0.0357050i	−0.999841	+	0.0178525i	$0.994317\pi$
$420$		0			0
$421$		−	5155.25i		−	0.596797i	−0.954441	−	0.298398i	$-0.903548\pi$
$421$		−	5155.25i		−	0.596797i	0.954441	−	0.298398i	$-0.0964524\pi$
$422$		0			0
$423$	−143.570	+	248.670i	−0.0165026	+	0.0285833i
$424$		0			0
$425$	−2898.56	−	5020.45i	−0.330825	−	0.573006i
$426$		0			0
$427$	−2403.63	−	3496.44i	−0.272411	−	0.396264i
$428$		0			0
$429$	−2753.81	+	1589.91i	−0.309918	+	0.178931i
$430$		0			0
$431$	−3748.15	+	6491.98i	−0.418891	+	0.725540i	−0.995828	−	0.0912485i	$-0.970914\pi$
$431$	−3748.15	+	6491.98i	−0.418891	+	0.725540i	0.576938	+	0.816788i	$0.304248\pi$
$432$		0			0
$433$	9121.97			1.01241			0.506205	−	0.862413i	$-0.331048\pi$
$433$	9121.97			1.01241			0.506205	+	0.862413i	$0.331048\pi$
$434$		0			0
$435$		−	21116.0i		−	2.32744i
$436$		0			0
$437$	−5139.95	−	2967.55i	−0.562648	−	0.324845i
$438$		0			0
$439$	−4597.08	−	7962.38i	−0.499788	−	0.865658i	0.500212	−	0.865903i	$-0.333255\pi$
$439$	−4597.08	−	7962.38i	−0.499788	−	0.865658i	−1.00000		0.000245077i	$0.999922\pi$
$440$		0			0
$441$	157.728	+	194.687i	0.0170314	+	0.0210223i
$442$		0			0
$443$	1378.95	−	796.139i	0.147892	−	0.0853853i	−0.424228	−	0.905555i	$-0.639455\pi$
$443$	1378.95	−	796.139i	0.147892	−	0.0853853i	0.572120	+	0.820170i	$0.306121\pi$
$444$		0			0
$445$	−21172.0	−	12223.7i	−2.25540	−	1.30215i
$446$		0			0
$447$	−12526.0			−1.32542
$448$		0			0
$449$	−6521.40			−0.685443			−0.342721	−	0.939437i	$-0.611349\pi$
$449$	−6521.40			−0.685443			−0.342721	+	0.939437i	$0.611349\pi$
$450$		0			0
$451$	12347.0	+	7128.54i	1.28913	+	0.744279i
$452$		0			0
$453$	2699.34	−	1558.47i	0.279970	−	0.161641i
$454$		0			0
$455$	3507.97	−	2411.55i	0.361442	−	0.248473i
$456$		0			0
$457$	−1766.24	−	3059.22i	−0.180791	−	0.313138i	0.761359	−	0.648330i	$-0.224532\pi$
$457$	−1766.24	−	3059.22i	−0.180791	−	0.313138i	−0.942150	+	0.335192i	$0.891199\pi$
$458$		0			0
$459$	−6730.20	−	3885.68i	−0.684398	−	0.395137i
$460$		0			0
$461$		−	16783.8i		−	1.69566i	−0.530270	−	0.847829i	$-0.677910\pi$
$461$		−	16783.8i		−	1.69566i	0.530270	−	0.847829i	$-0.322090\pi$
$462$		0			0
$463$	2743.41			0.275372			0.137686	−	0.990476i	$-0.456033\pi$
$463$	2743.41			0.275372			0.137686	+	0.990476i	$0.456033\pi$
$464$		0			0
$465$	715.445	−	1239.19i	0.0713505	−	0.123583i
$466$		0			0
$467$	2302.88	−	1329.57i	0.228189	−	0.131745i	−0.381547	−	0.924349i	$-0.624609\pi$
$467$	2302.88	−	1329.57i	0.228189	−	0.131745i	0.609736	+	0.792604i	$0.291275\pi$
$468$		0			0
$469$	−2418.11	+	5071.15i	−0.238076	+	0.499284i
$470$		0			0
$471$	−3350.85	−	5803.84i	−0.327811	−	0.567785i
$472$		0			0
$473$	6461.47	−	11191.6i	0.628116	−	1.08793i
$474$		0			0
$475$		−	4551.28i		−	0.439636i
$476$		0			0
$477$			371.060i			0.0356178i
$478$		0			0
$479$	4415.98	−	7648.70i	0.421234	−	0.729599i	−0.574826	−	0.818276i	$-0.694930\pi$
$479$	4415.98	−	7648.70i	0.421234	−	0.729599i	0.996061	+	0.0886762i	$0.0282636\pi$
$480$		0			0
$481$	−1770.08	−	3065.87i	−0.167794	−	0.290627i
$482$		0			0
$483$	−13083.4	+	1031.19i	−1.23254	+	0.0971443i
$484$		0			0
$485$	4472.02	−	2581.92i	0.418688	−	0.241730i
$486$		0			0
$487$	6615.85	−	11459.0i	0.615591	−	1.06623i	−0.374690	−	0.927150i	$-0.622251\pi$
$487$	6615.85	−	11459.0i	0.615591	−	1.06623i	0.990281	−	0.139084i	$-0.0444158\pi$
$488$		0			0
$489$	−9560.87			−0.884166
$490$		0			0
$491$		−	834.685i		−	0.0767186i	−0.999264	−	0.0383593i	$-0.987787\pi$
$491$		−	834.685i		−	0.0767186i	0.999264	−	0.0383593i	$-0.0122131\pi$
$492$		0			0
$493$	12835.2	+	7410.42i	1.17256	+	0.676975i
$494$		0			0
$495$	−227.758	−	394.488i	−0.0206807	−	0.0358200i
$496$		0			0
$497$	120.027	+	1522.87i	0.0108329	+	0.137445i
$498$		0			0
$499$	−5413.50	+	3125.49i	−0.485655	+	0.280393i	−0.722770	−	0.691089i	$-0.757131\pi$
$499$	−5413.50	+	3125.49i	−0.485655	+	0.280393i	0.237115	+	0.971482i	$0.423798\pi$
$500$		0			0
$501$	1854.67	+	1070.79i	0.165390	+	0.0954882i
$502$		0			0
$503$	3208.62			0.284424			0.142212	−	0.989836i	$-0.454579\pi$
$503$	3208.62			0.284424			0.142212	+	0.989836i	$0.454579\pi$
$504$		0			0
$505$	−12137.1			−1.06949
$506$		0			0
$507$	8736.76	+	5044.17i	0.765312	+	0.441853i
$508$		0			0
$509$	10253.9	−	5920.12i	0.892923	−	0.515530i	0.0180259	−	0.999838i	$-0.494262\pi$
$509$	10253.9	−	5920.12i	0.892923	−	0.515530i	0.874898	+	0.484308i	$0.160929\pi$
$510$		0			0
$511$	−4536.18	−	2163.01i	−0.392698	−	0.187252i
$512$		0			0
$513$	−3050.63	−	5283.84i	−0.262551	−	0.454751i
$514$		0			0
$515$	11627.8	+	6713.33i	0.994919	+	0.574417i
$516$		0			0
$517$			16126.0i			1.37180i
$518$		0			0
$519$	10589.0			0.895576
$520$		0			0
$521$	−2562.84	+	4438.96i	−0.215508	+	0.373272i	−0.953430	−	0.301615i	$-0.902474\pi$
$521$	−2562.84	+	4438.96i	−0.215508	+	0.373272i	0.737921	+	0.674887i	$0.235808\pi$
$522$		0			0
$523$	−2362.76	+	1364.14i	−0.197545	+	0.114053i	−0.595510	−	0.803348i	$-0.703050\pi$
$523$	−2362.76	+	1364.14i	−0.197545	+	0.114053i	0.397965	+	0.917401i	$0.369717\pi$
$524$		0			0
$525$	−5701.27	−	8293.37i	−0.473950	−	0.689433i
$526$		0			0
$527$	502.154	+	869.756i	0.0415069	+	0.0718921i
$528$		0			0
$529$	−3474.25	+	6017.58i	−0.285547	+	0.494582i
$530$		0			0
$531$			540.606i			0.0441813i
$532$		0			0
$533$			5255.31i			0.427078i
$534$		0			0
$535$	2646.55	−	4583.96i	0.213870	−	0.370433i
$536$		0			0
$537$	5292.61	+	9167.06i	0.425312	+	0.736663i
$538$		0			0
$539$	13138.3	+	5039.87i	1.04992	+	0.402751i
$540$		0			0
$541$	7335.89	−	4235.38i	0.582985	−	0.336586i	−0.179334	−	0.983788i	$-0.557394\pi$
$541$	7335.89	−	4235.38i	0.582985	−	0.336586i	0.762319	+	0.647202i	$0.224061\pi$
$542$		0			0
$543$	−3800.49	+	6582.64i	−0.300358	+	0.520236i
$544$		0			0
$545$	−3209.73			−0.252275
$546$		0			0
$547$			22768.8i			1.77975i	0.456205	+	0.889875i	$0.349208\pi$
$547$			22768.8i			1.77975i	−0.456205	+	0.889875i	$0.650792\pi$
$548$		0			0
$549$	−144.934	−	83.6779i	−0.0112671	−	0.00650507i
$550$		0			0
$551$	5817.88	+	10076.9i	0.449819	+	0.779109i
$552$		0			0
$553$	9305.20	−	6396.85i	0.715547	−	0.491902i
$554$		0			0
$555$	−15793.7	+	9118.51i	−1.20794	+	0.697404i
$556$		0			0
$557$	499.794	+	288.556i	0.0380196	+	0.0219507i	0.518889	−	0.854841i	$-0.326346\pi$
$557$	499.794	+	288.556i	0.0380196	+	0.0219507i	−0.480870	+	0.876792i	$0.659679\pi$
$558$		0			0
$559$	4763.53			0.360422
$560$		0			0
$561$	−11497.2			−0.865266
$562$		0			0
$563$	3255.62	+	1879.63i	0.243709	+	0.140705i	0.616880	−	0.787057i	$-0.288396\pi$
$563$	3255.62	+	1879.63i	0.243709	+	0.140705i	−0.373171	+	0.927762i	$0.621730\pi$
$564$		0			0
$565$	−20983.6	+	12114.9i	−1.56245	+	0.902084i
$566$		0			0
$567$	−11848.1	−	5649.58i	−0.877552	−	0.418448i
$568$		0			0
$569$	−9117.06	−	15791.2i	−0.671717	−	1.16345i	−0.977417	−	0.211320i	$-0.932224\pi$
$569$	−9117.06	−	15791.2i	−0.671717	−	1.16345i	0.305700	−	0.952128i	$-0.401109\pi$
$570$		0			0
$571$	−14512.2	−	8378.64i	−1.06360	−	0.614072i	−0.137177	−	0.990547i	$-0.543803\pi$
$571$	−14512.2	−	8378.64i	−1.06360	−	0.614072i	−0.926427	+	0.376474i	$0.877136\pi$
$572$		0			0
$573$		−	3205.13i		−	0.233676i
$574$		0			0
$575$	−14658.6			−1.06314
$576$		0			0
$577$	619.415	−	1072.86i	0.0446908	−	0.0774067i	−0.842815	−	0.538204i	$-0.819103\pi$
$577$	619.415	−	1072.86i	0.0446908	−	0.0774067i	0.887506	+	0.460797i	$0.152436\pi$
$578$		0			0
$579$	23627.7	−	13641.5i	1.69591	−	0.979137i
$580$		0			0
$581$	10843.2	−	854.624i	0.774272	−	0.0610254i
$582$		0			0
$583$	10419.5	+	18047.1i	0.740193	+	1.28205i
$584$		0			0
$585$	83.9538	−	145.412i	0.00593344	−	0.0102770i
$586$		0			0
$587$		−	18938.9i		−	1.33167i	−0.746097	−	0.665837i	$-0.768075\pi$
$587$		−	18938.9i		−	1.33167i	0.746097	−	0.665837i	$-0.231925\pi$
$588$		0			0
$589$			788.476i			0.0551589i
$590$		0			0
$591$	1473.39	−	2551.99i	0.102550	−	0.177622i
$592$		0			0
$593$	9678.40	+	16763.5i	0.670226	+	1.16087i	0.977840	+	0.209355i	$0.0671363\pi$
$593$	9678.40	+	16763.5i	0.670226	+	1.16087i	−0.307613	+	0.951511i	$0.599530\pi$
$594$		0			0
$595$	15344.2	−	1209.37i	1.05723	−	0.0833268i
$596$		0			0
$597$	10456.6	−	6037.13i	0.716852	−	0.413875i
$598$		0			0
$599$	−10946.0	+	18959.0i	−0.746644	+	1.29323i	0.202779	+	0.979225i	$0.435003\pi$
$599$	−10946.0	+	18959.0i	−0.746644	+	1.29323i	−0.949423	+	0.314001i	$0.898331\pi$
$600$		0			0
$601$	−11257.4			−0.764059			−0.382029	−	0.924150i	$-0.624775\pi$
$601$	−11257.4			−0.764059			−0.382029	+	0.924150i	$0.624775\pi$
$602$		0			0
$603$			221.600i			0.0149656i
$604$		0			0
$605$	−4634.67	−	2675.83i	−0.311448	−	0.179815i
$606$		0			0
$607$	9229.65	+	15986.2i	0.617166	+	1.06896i	0.990000	+	0.141065i	$0.0450528\pi$
$607$	9229.65	+	15986.2i	0.617166	+	1.06896i	−0.372834	+	0.927898i	$0.621614\pi$
$608$		0			0
$609$	23224.4	+	11074.2i	1.54532	+	0.736863i
$610$		0			0
$611$	−5147.83	+	2972.10i	−0.340849	+	0.196789i
$612$		0			0
$613$	13231.8	+	7639.39i	0.871823	+	0.503347i	0.867954	−	0.496645i	$-0.165435\pi$
$613$	13231.8	+	7639.39i	0.871823	+	0.503347i	0.00386941	+	0.999993i	$0.498768\pi$
$614$		0			0
$615$	27072.6			1.77507
$616$		0			0
$617$	−7018.11			−0.457923			−0.228961	−	0.973436i	$-0.573533\pi$
$617$	−7018.11			−0.457923			−0.228961	+	0.973436i	$0.573533\pi$
$618$		0			0
$619$	−22065.9	−	12739.8i	−1.43280	−	0.827228i	−0.435468	−	0.900204i	$-0.643417\pi$
$619$	−22065.9	−	12739.8i	−1.43280	−	0.827228i	−0.997334	+	0.0729760i	$0.976750\pi$
$620$		0			0
$621$	−17017.9	+	9825.32i	−1.09969	+	0.634906i
$622$		0			0
$623$	24547.7	−	16875.3i	1.57863	−	1.08523i
$624$		0			0
$625$	8818.52	+	15274.1i	0.564385	+	0.977544i
$626$		0			0
$627$	−7817.12	−	4513.21i	−0.497904	−	0.287465i
$628$		0			0
$629$		−	12800.1i		−	0.811406i
$630$		0			0
$631$	−18127.4			−1.14365			−0.571824	−	0.820377i	$-0.693764\pi$
$631$	−18127.4			−1.14365			−0.571824	+	0.820377i	$0.693764\pi$
$632$		0			0
$633$	9573.51	−	16581.8i	0.601126	−	1.04118i
$634$		0			0
$635$	−21163.2	+	12218.6i	−1.32258	+	0.763590i
$636$		0			0
$637$	812.594	+	5122.96i	0.0505434	+	0.318648i
$638$		0			0
$639$	30.1268	+	52.1811i	0.00186510	+	0.00323044i
$640$		0			0
$641$	1097.34	−	1900.65i	0.0676166	−	0.117115i	−0.830235	−	0.557413i	$-0.811794\pi$
$641$	1097.34	−	1900.65i	0.0676166	−	0.117115i	0.897852	+	0.440298i	$0.145127\pi$
$642$		0			0
$643$			5435.55i			0.333370i	0.986010	+	0.166685i	$0.0533064\pi$
$643$			5435.55i			0.333370i	−0.986010	+	0.166685i	$0.946694\pi$
$644$		0			0
$645$		−	24539.2i		−	1.49803i
$646$		0			0
$647$	6711.08	−	11623.9i	0.407790	−	0.706313i	−0.586852	−	0.809694i	$-0.699633\pi$
$647$	6711.08	−	11623.9i	0.407790	−	0.706313i	0.994642	+	0.103382i	$0.0329663\pi$
$648$		0			0
$649$	15180.4	+	26293.3i	0.918157	+	1.59029i
$650$		0			0
$651$	987.702	+	1436.76i	0.0594641	+	0.0864996i
$652$		0			0
$653$	1330.30	−	768.048i	0.0797222	−	0.0460276i	−0.459609	−	0.888121i	$-0.652010\pi$
$653$	1330.30	−	768.048i	0.0797222	−	0.0460276i	0.539331	+	0.842094i	$0.318677\pi$
$654$		0			0
$655$	−12028.2	+	20833.4i	−0.717527	+	1.24279i
$656$		0			0
$657$	−198.222			−0.0117708
$658$		0			0
$659$			1960.03i			0.115860i	0.998321	+	0.0579301i	$0.0184501\pi$
$659$			1960.03i			0.115860i	−0.998321	+	0.0579301i	$0.981550\pi$
$660$		0			0
$661$	−20878.2	−	12054.1i	−1.22855	−	0.709302i	−0.261821	−	0.965116i	$-0.584323\pi$
$661$	−20878.2	−	12054.1i	−1.22855	−	0.709302i	−0.966726	+	0.255815i	$0.917656\pi$
$662$		0			0
$663$	−2119.00	−	3670.22i	−0.124126	−	0.214992i
$664$		0			0
$665$	10907.4	+	5201.04i	0.636047	+	0.303290i
$666$		0			0
$667$	32455.1	−	18738.0i	1.88406	−	1.08776i
$668$		0			0
$669$	−8621.20	−	4977.45i	−0.498228	−	0.287652i
$670$		0			0
$671$	−9398.84			−0.540742
$672$		0			0
$673$	21235.3			1.21629			0.608143	−	0.793827i	$-0.291915\pi$
$673$	21235.3			1.21629			0.608143	+	0.793827i	$0.291915\pi$
$674$		0			0
$675$	−13050.1	−	7534.46i	−0.744144	−	0.429632i
$676$		0			0
$677$	−12582.6	+	7264.57i	−0.714312	+	0.412408i	−0.812655	−	0.582745i	$-0.801979\pi$
$677$	−12582.6	+	7264.57i	−0.714312	+	0.412408i	0.0983439	+	0.995152i	$0.468645\pi$
$678$		0			0
$679$	494.385	+	6272.61i	0.0279422	+	0.354522i
$680$		0			0
$681$	−10343.6	−	17915.6i	−0.582036	−	1.00812i
$682$		0			0
$683$	6086.87	+	3514.25i	0.341006	+	0.196880i	0.660717	−	0.750635i	$-0.270252\pi$
$683$	6086.87	+	3514.25i	0.341006	+	0.196880i	−0.319711	+	0.947515i	$0.603586\pi$
$684$		0			0
$685$			10258.1i			0.572175i
$686$		0			0
$687$	−17405.9			−0.966635
$688$		0			0
$689$	−3840.75	+	6652.37i	−0.212367	+	0.367830i
$690$		0			0
$691$	−28337.1	+	16360.4i	−1.56005	+	0.900695i	−0.562798	+	0.826594i	$0.690275\pi$
$691$	−28337.1	+	16360.4i	−1.56005	+	0.900695i	−0.997251	+	0.0741006i	$0.976391\pi$
$692$		0			0
$693$	553.322	−	43.6109i	0.0303304	−	0.00239053i
$694$		0			0
$695$	−1203.21	−	2084.03i	−0.0656698	−	0.113743i
$696$		0			0
$697$	−9500.79	+	16455.8i	−0.516310	+	0.894275i
$698$		0			0
$699$			28765.7i			1.55654i
$700$		0			0
$701$			33247.8i			1.79137i	0.444685	+	0.895687i	$0.353316\pi$
$701$			33247.8i			1.79137i	−0.444685	+	0.895687i	$0.646684\pi$
$702$		0			0
$703$	5024.66	−	8702.96i	0.269571	−	0.466911i
$704$		0			0
$705$	15310.7	+	26518.9i	0.817920	+	1.41668i
$706$		0			0
$707$	6365.24	−	13348.9i	0.338599	−	0.710096i
$708$		0			0
$709$	−12015.8	+	6937.33i	−0.636478	+	0.367471i	−0.783257	−	0.621698i	$-0.786443\pi$
$709$	−12015.8	+	6937.33i	−0.636478	+	0.367471i	0.146778	+	0.989169i	$0.453110\pi$
$710$		0			0
$711$	222.695	−	385.719i	0.0117464	−	0.0203454i
$712$		0			0
$713$	2539.49			0.133386
$714$		0			0
$715$		−	9429.83i		−	0.493225i
$716$		0			0
$717$	5123.38	+	2957.98i	0.266856	+	0.154070i
$718$		0			0
$719$	7233.72	+	12529.2i	0.375205	+	0.649873i	0.990358	−	0.138534i	$-0.0442391\pi$
$719$	7233.72	+	12529.2i	0.375205	+	0.649873i	−0.615153	+	0.788408i	$0.710906\pi$
$720$		0			0
$721$	−13481.8	+	9268.04i	−0.696377	+	0.478724i
$722$		0			0
$723$	10074.6	−	5816.57i	0.518227	−	0.299199i
$724$		0			0
$725$	24887.9	+	14369.0i	1.27492	+	0.736073i
$726$		0			0
$727$	−28059.8			−1.43147			−0.715736	−	0.698371i	$-0.753909\pi$
$727$	−28059.8			−1.43147			−0.715736	+	0.698371i	$0.753909\pi$
$728$		0			0
$729$	−20186.3			−1.02557
$730$		0			0
$731$	14916.0	+	8611.73i	0.754701	+	0.435727i
$732$		0			0
$733$	19847.4	−	11458.9i	1.00011	−	0.577413i	0.0918288	−	0.995775i	$-0.470729\pi$
$733$	19847.4	−	11458.9i	1.00011	−	0.577413i	0.908281	+	0.418361i	$0.137395\pi$
$734$		0			0
$735$	26390.7	−	4186.05i	1.32440	−	0.210075i
$736$		0			0
$737$	6222.61	+	10777.9i	0.311008	+	0.538681i
$738$		0			0
$739$	3194.68	+	1844.45i	0.159023	+	0.0918121i	0.577400	−	0.816462i	$-0.304067\pi$
$739$	3194.68	+	1844.45i	0.159023	+	0.0918121i	−0.418377	+	0.908274i	$0.637401\pi$
$740$		0			0
$741$		−	3327.24i		−	0.164952i
$742$		0			0
$743$	3171.06			0.156575			0.0782873	−	0.996931i	$-0.475055\pi$
$743$	3171.06			0.156575			0.0782873	+	0.996931i	$0.475055\pi$
$744$		0			0
$745$	18573.1	−	32169.6i	0.913377	−	1.58202i
$746$		0			0
$747$	371.542	−	214.510i	0.0181981	−	0.0105067i
$748$		0			0
$749$	3653.68	+	5314.83i	0.178241	+	0.259279i
$750$		0			0
$751$	886.894	+	1536.14i	0.0430935	+	0.0746401i	0.886768	−	0.462215i	$-0.152945\pi$
$751$	886.894	+	1536.14i	0.0430935	+	0.0746401i	−0.843674	+	0.536856i	$0.819612\pi$
$752$		0			0
$753$	6998.33	−	12121.5i	0.338690	−	0.586627i
$754$		0			0
$755$			9243.34i			0.445563i
$756$		0			0
$757$			370.903i			0.0178081i	0.999960	+	0.00890403i	$0.00283428\pi$
$757$			370.903i			0.0178081i	−0.999960	+	0.00890403i	$0.997166\pi$
$758$		0			0
$759$	−14535.9	+	25177.0i	−0.695153	+	1.20404i
$760$		0			0
$761$	−14664.5	−	25399.6i	−0.698538	−	1.20990i	−0.968973	−	0.247165i	$-0.920501\pi$
$761$	−14664.5	−	25399.6i	−0.698538	−	1.20990i	0.270435	−	0.962738i	$-0.412832\pi$
$762$		0			0
$763$	1683.33	−	3530.21i	0.0798697	−	0.167499i
$764$		0			0
$765$	525.766	−	303.551i	0.0248485	−	0.0143463i
$766$		0			0
$767$	−5595.67	+	9691.98i	−0.263426	+	0.456267i
$768$		0			0
$769$	−26755.7			−1.25466			−0.627331	−	0.778753i	$-0.715853\pi$
$769$	−26755.7			−1.25466			−0.627331	+	0.778753i	$0.715853\pi$
$770$		0			0
$771$		−	33172.0i		−	1.54950i
$772$		0			0
$773$	−12808.3	−	7394.87i	−0.595967	−	0.344082i	0.171486	−	0.985186i	$-0.445143\pi$
$773$	−12808.3	−	7394.87i	−0.595967	−	0.344082i	−0.767453	+	0.641105i	$0.778476\pi$
$774$		0			0
$775$	973.692	+	1686.48i	0.0451304	+	0.0781681i
$776$		0			0
$777$	−1746.01	−	22152.8i	−0.0806147	−	1.02282i
$778$		0			0
$779$	−12919.4	+	7459.02i	−0.594205	+	0.343064i
$780$		0			0
$781$	2930.53	+	1691.94i	0.134267	+	0.0775192i
$782$		0			0
$783$	38525.0			1.75833
$784$		0			0
$785$	19874.0			0.903611
$786$		0			0
$787$	−9694.95	−	5597.38i	−0.439120	−	0.253526i	0.264104	−	0.964494i	$-0.414924\pi$
$787$	−9694.95	−	5597.38i	−0.439120	−	0.253526i	−0.703224	+	0.710968i	$0.748257\pi$
$788$		0			0
$789$	5524.32	−	3189.46i	0.249266	−	0.143914i
$790$		0			0
$791$	−2319.75	−	29432.3i	−0.104274	−	1.32300i
$792$		0			0
$793$	−1732.26	−	3000.35i	−0.0775715	−	0.134358i
$794$		0			0
$795$	34269.5	+	19785.5i	1.52882	+	0.882665i
$796$		0			0
$797$		−	11568.6i		−	0.514153i	−0.966391	−	0.257076i	$-0.917241\pi$
$797$		−	11568.6i		−	0.514153i	0.966391	−	0.257076i	$-0.0827592\pi$
$798$		0			0
$799$	−21492.4			−0.951623
$800$		0			0
$801$	587.484	−	1017.55i	0.0259148	−	0.0448857i
$802$		0			0
$803$	−9640.87	+	5566.16i	−0.423685	+	0.244615i
$804$		0			0
$805$	16751.3	−	35130.1i	0.733422	−	1.53810i
$806$		0			0
$807$	−8087.27	−	14007.6i	−0.352770	−	0.611016i
$808$		0			0
$809$	8617.10	−	14925.2i	0.374488	−	0.648633i	−0.615762	−	0.787932i	$-0.711152\pi$
$809$	8617.10	−	14925.2i	0.374488	−	0.648633i	0.990250	+	0.139300i	$0.0444851\pi$
$810$		0			0
$811$			6011.49i			0.260286i	0.991495	+	0.130143i	$0.0415437\pi$
$811$			6011.49i			0.260286i	−0.991495	+	0.130143i	$0.958456\pi$
$812$		0			0
$813$		−	10224.5i		−	0.441067i
$814$		0			0
$815$	14176.5	−	24554.4i	0.609302	−	1.05534i
$816$		0			0
$817$	6761.02	+	11710.4i	0.289520	+	0.501464i
$818$		0			0
$819$	115.902	+	168.597i	0.00494498	+	0.00719323i
$820$		0			0
$821$	−146.755	+	84.7289i	−0.00623846	+	0.00360178i	−0.503116	−	0.864219i	$-0.667813\pi$
$821$	−146.755	+	84.7289i	−0.00623846	+	0.00360178i	0.496878	+	0.867821i	$0.334480\pi$
$822$		0			0
$823$	−3086.68	+	5346.28i	−0.130735	+	0.226439i	−0.923960	−	0.382489i	$-0.875067\pi$
$823$	−3086.68	+	5346.28i	−0.130735	+	0.226439i	0.793225	+	0.608928i	$0.208400\pi$
$824$		0			0
$825$	−22293.5			−0.940801
$826$		0			0
$827$		−	12247.9i		−	0.514995i	−0.966279	−	0.257497i	$-0.917102\pi$
$827$		−	12247.9i		−	0.514995i	0.966279	−	0.257497i	$-0.0828978\pi$
$828$		0			0
$829$	19887.0	+	11481.8i	0.833176	+	0.481035i	0.854939	−	0.518729i	$-0.173594\pi$
$829$	19887.0	+	11481.8i	0.833176	+	0.481035i	−0.0217626	+	0.999763i	$0.506928\pi$
$830$		0			0
$831$	−3098.14	−	5366.13i	−0.129330	−	0.224006i
$832$		0			0
$833$	−6717.05	+	17510.5i	−0.279390	+	0.728333i
$834$		0			0
$835$	−5500.07	+	3175.47i	−0.227949	+	0.131607i
$836$		0			0
$837$	2260.83	+	1305.29i	0.0933639	+	0.0539037i
$838$		0			0
$839$	27390.4			1.12708			0.563541	−	0.826088i	$-0.309439\pi$
$839$	27390.4			1.12708			0.563541	+	0.826088i	$0.309439\pi$
$840$		0			0
$841$	−49082.5			−2.01249
$842$		0			0
$843$	21948.1	+	12671.7i	0.896718	+	0.517720i
$844$		0			0
$845$	−25909.1	+	14958.6i	−1.05479	+	0.608984i
$846$		0			0
$847$	5373.63	−	3694.10i	0.217993	−	0.149859i
$848$		0			0
$849$	−12361.2	−	21410.2i	−0.499687	−	0.865483i
$850$		0			0
$851$	−28030.1	−	16183.2i	−1.12909	−	0.651882i
$852$		0			0
$853$		−	27281.2i		−	1.09506i	−0.836785	−	0.547532i	$-0.815568\pi$
$853$		−	27281.2i		−	1.09506i	0.836785	−	0.547532i	$-0.184432\pi$
$854$		0			0
$855$	476.633			0.0190649
$856$		0			0
$857$	2898.81	−	5020.89i	0.115544	−	0.200129i	−0.802453	−	0.596716i	$-0.796472\pi$
$857$	2898.81	−	5020.89i	0.115544	−	0.200129i	0.917997	+	0.396587i	$0.129805\pi$
$858$		0			0
$859$	23919.8	−	13810.1i	0.950095	−	0.548537i	0.0569844	−	0.998375i	$-0.481851\pi$
$859$	23919.8	−	13810.1i	0.950095	−	0.548537i	0.893110	+	0.449838i	$0.148518\pi$
$860$		0			0
$861$	−14198.1	+	29775.6i	−0.561985	+	1.17857i
$862$		0			0
$863$	−23042.4	−	39910.5i	−0.908889	−	1.57424i	−0.815610	−	0.578601i	$-0.803599\pi$
$863$	−23042.4	−	39910.5i	−0.908889	−	1.57424i	−0.0932784	−	0.995640i	$-0.529735\pi$
$864$		0			0
$865$	−15700.9	+	27194.8i	−0.617164	+	1.06896i
$866$		0			0
$867$			9857.65i			0.386140i
$868$		0			0
$869$		−	25013.4i		−	0.976436i
$870$		0			0
$871$	−2293.72	+	3972.84i	−0.0892304	+	0.154552i
$872$		0			0
$873$	124.090	+	214.930i	0.00481078	+	0.00833251i
$874$		0			0
$875$	−5325.58	+	419.743i	−0.205757	+	0.0162170i
$876$		0			0
$877$	−11574.9	+	6682.75i	−0.445673	+	0.257309i	−0.706001	−	0.708211i	$-0.749503\pi$
$877$	−11574.9	+	6682.75i	−0.445673	+	0.257309i	0.260328	+	0.965520i	$0.416169\pi$
$878$		0			0
$879$	8302.96	−	14381.1i	0.318603	−	0.551836i
$880$		0			0
$881$	5901.17			0.225670			0.112835	−	0.993614i	$-0.464007\pi$
$881$	5901.17			0.225670			0.112835	+	0.993614i	$0.464007\pi$
$882$		0			0
$883$			4207.25i			0.160346i	0.996781	+	0.0801729i	$0.0255472\pi$
$883$			4207.25i			0.160346i	−0.996781	+	0.0801729i	$0.974453\pi$
$884$		0			0
$885$	49927.9	+	28825.9i	1.89639	+	1.09488i
$886$		0			0
$887$	−10064.4	−	17432.1i	−0.380982	−	0.659880i	0.610221	−	0.792231i	$-0.291081\pi$
$887$	−10064.4	−	17432.1i	−0.380982	−	0.659880i	−0.991203	+	0.132351i	$0.957747\pi$
$888$		0			0
$889$	−2339.61	−	29684.3i	−0.0882654	−	1.11989i
$890$		0			0
$891$	−25181.0	+	14538.3i	−0.946798	+	0.546634i
$892$		0			0
$893$	−14612.9	−	8436.79i	−0.547596	−	0.316155i
$894$		0			0
$895$	−31390.7			−1.17237
$896$		0			0
$897$	−10716.2			−0.398889
$898$		0			0
$899$	−4311.65	−	2489.33i	−0.159957	−	0.0923513i
$900$		0			0
$901$	−24052.9	+	13887.0i	−0.889366	+	0.513476i
$902$		0			0
$903$	26989.3	+	12869.5i	0.994627	+	0.474273i
$904$		0			0
$905$	−11270.4	−	19521.0i	−0.413969	−	0.717015i
$906$		0			0
$907$	6350.05	+	3666.20i	0.232469	+	0.134216i	0.611711	−	0.791081i	$-0.290482\pi$
$907$	6350.05	+	3666.20i	0.232469	+	0.134216i	−0.379241	+	0.925298i	$0.623815\pi$
$908$		0			0
$909$		−	583.322i		−	0.0212845i
$910$		0			0
$911$	−38942.4			−1.41627			−0.708133	−	0.706079i	$-0.750462\pi$
$911$	−38942.4			−1.41627			−0.708133	+	0.706079i	$0.750462\pi$
$912$		0			0
$913$	12047.0	−	20866.1i	0.436691	−	0.756371i
$914$		0			0
$915$	−15456.2	+	8923.65i	−0.558434	+	0.322412i
$916$		0			0
$917$	−16605.4	−	24155.1i	−0.597993	−	0.869872i
$918$		0			0
$919$	5166.34	+	8948.36i	0.185443	+	0.321196i	0.943726	−	0.330729i	$-0.107295\pi$
$919$	5166.34	+	8948.36i	0.185443	+	0.321196i	−0.758283	+	0.651926i	$0.773961\pi$
$920$		0			0
$921$	−596.390	+	1032.98i	−0.0213374	+	0.0369574i
$922$		0			0
$923$			1247.34i			0.0444817i
$924$		0			0
$925$		−	24819.9i		−	0.882240i
$926$		0			0
$927$	−322.650	+	558.846i	−0.0114317	+	0.0198004i
$928$		0			0
$929$	6917.69	+	11981.8i	0.244308	+	0.423154i	0.961937	−	0.273272i	$-0.0881059\pi$
$929$	6917.69	+	11981.8i	0.244308	+	0.423154i	−0.717629	+	0.696426i	$0.754773\pi$
$930$		0			0
$931$	−11440.7	+	9268.81i	−0.402743	+	0.326287i
$932$		0			0
$933$	−39687.2	+	22913.4i	−1.39260	+	0.804020i
$934$		0			0
$935$	17047.7	−	29527.4i	0.596277	−	1.03278i
$936$		0			0
$937$	−25168.3			−0.877495			−0.438747	−	0.898610i	$-0.644578\pi$
$937$	−25168.3			−0.877495			−0.438747	+	0.898610i	$0.644578\pi$
$938$		0			0
$939$		−	7469.46i		−	0.259592i
$940$		0			0
$941$	−27803.9	−	16052.6i	−0.963210	−	0.556110i	−0.0660507	−	0.997816i	$-0.521040\pi$
$941$	−27803.9	−	16052.6i	−0.963210	−	0.556110i	−0.897160	+	0.441707i	$0.854373\pi$
$942$		0			0
$943$	24023.6	+	41610.2i	0.829605	+	1.43692i
$944$		0			0
$945$	32969.9	−	22665.1i	1.13493	−	0.780208i
$946$		0			0
$947$	35980.9	−	20773.6i	1.23466	−	0.712830i	0.266661	−	0.963791i	$-0.414080\pi$
$947$	35980.9	−	20773.6i	1.23466	−	0.712830i	0.967997	+	0.250960i	$0.0807464\pi$
$948$		0			0
$949$	−3553.73	−	2051.75i	−0.121558	−	0.0701817i
$950$		0			0
$951$	−36610.6			−1.24835
$952$		0			0
$953$	42752.7			1.45320			0.726599	−	0.687062i	$-0.241100\pi$
$953$	42752.7			1.45320			0.726599	+	0.687062i	$0.241100\pi$
$954$		0			0
$955$	8231.48	+	4752.45i	0.278916	+	0.161032i
$956$		0			0
$957$	49359.5	−	28497.7i	1.66726	−	0.962591i
$958$		0			0
$959$	−11282.3	−	5379.79i	−0.379900	−	0.181150i
$960$		0			0
$961$	14726.8	+	25507.6i	0.494338	+	0.856218i
$962$		0			0
$963$	220.310	+	127.196i	0.00737217	+	0.00425632i
$964$		0			0
$965$			80908.2i			2.69899i
$966$		0			0
$967$	46475.7			1.54556			0.772780	−	0.634674i	$-0.218866\pi$
$967$	46475.7			1.54556			0.772780	+	0.634674i	$0.218866\pi$
$968$		0			0
$969$	6015.13	−	10418.5i	0.199416	−	0.345398i
$970$		0			0
$971$	52110.5	−	30086.0i	1.72225	−	0.994343i	0.808015	−	0.589161i	$-0.200542\pi$
$971$	52110.5	−	30086.0i	1.72225	−	0.994343i	0.914236	−	0.405181i	$-0.132792\pi$
$972$		0			0
$973$	2923.13	−	230.391i	0.0963116	−	0.00759094i
$974$		0			0
$975$	−4108.81	−	7116.68i	−0.134961	−	0.233760i
$976$		0			0
$977$	−4830.84	+	8367.26i	−0.158191	+	0.273994i	−0.934216	−	0.356707i	$-0.883899\pi$
$977$	−4830.84	+	8367.26i	−0.158191	+	0.273994i	0.776026	+	0.630701i	$0.217233\pi$
$978$		0			0
$979$		−	65987.1i		−	2.15420i
$980$		0			0
$981$		−	154.263i		−	0.00502063i
$982$		0			0
$983$	−147.336	+	255.194i	−0.00478057	+	0.00828019i	−0.868406	−	0.495854i	$-0.834855\pi$
$983$	−147.336	+	255.194i	−0.00478057	+	0.00828019i	0.863625	+	0.504134i	$0.168188\pi$
$984$		0			0
$985$	4369.38	+	7567.99i	0.141340	+	0.244808i
$986$		0			0
$987$	−37196.3	+	2931.68i	−1.19957	+	0.0945455i
$988$		0			0
$989$	37716.4	−	21775.6i	1.21265	−	0.700125i
$990$		0			0
$991$	−17842.6	+	30904.3i	−0.571937	+	0.990624i	0.424430	+	0.905461i	$0.360474\pi$
$991$	−17842.6	+	30904.3i	−0.571937	+	0.990624i	−0.996367	+	0.0851632i	$0.972859\pi$
$992$		0			0
$993$	51368.6			1.64163
$994$		0			0
$995$			35806.5i			1.14085i
$996$		0			0
$997$	22310.1	+	12880.7i	0.708693	+	0.409164i	0.810577	−	0.585632i	$-0.199154\pi$
$997$	22310.1	+	12880.7i	0.708693	+	0.409164i	−0.101884	+	0.994796i	$0.532487\pi$
$998$		0			0
$999$	−16636.2	−	28814.8i	−0.526873	−	0.912571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.4.t.a.81.17		44
4.3	odd	2		56.4.p.a.53.16	yes	44
7.2	even	3	inner	224.4.t.a.177.6		44
8.3	odd	2		56.4.p.a.53.14	yes	44
8.5	even	2	inner	224.4.t.a.81.6		44
28.23	odd	6		56.4.p.a.37.14	✓	44
56.37	even	6	inner	224.4.t.a.177.17		44
56.51	odd	6		56.4.p.a.37.16	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.4.p.a.37.14	✓	44	28.23	odd	6
56.4.p.a.37.16	yes	44	56.51	odd	6
56.4.p.a.53.14	yes	44	8.3	odd	2
56.4.p.a.53.16	yes	44	4.3	odd	2
224.4.t.a.81.6		44	8.5	even	2	inner
224.4.t.a.81.17		44	1.1	even	1	trivial
224.4.t.a.177.6		44	7.2	even	3	inner
224.4.t.a.177.17		44	56.37	even	6	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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	224.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.43871 + 2.56269i) q^{3} +(-13.1631 + 7.59971i) q^{5} +(-1.45519 - 18.4630i) q^{7} +(-0.365251 - 0.632633i) q^{9} +(-35.5292 - 20.5128i) q^{11} -15.1225i q^{13} -77.9028 q^{15} +(27.3391 - 47.3526i) q^{17} +(37.1763 - 21.4637i) q^{19} +(40.8558 - 85.6811i) q^{21} +(-69.1294 - 119.736i) q^{23} +(53.0113 - 91.8183i) q^{25} -142.129i q^{27} +271.056i q^{29} +(-9.18381 + 15.9068i) q^{31} +(-105.136 - 182.100i) q^{33} +(159.468 + 231.971i) q^{35} +(202.736 - 117.050i) q^{37} +(38.7541 - 67.1242i) q^{39} -347.517 q^{41} +314.997i q^{43} +(9.61566 + 5.55160i) q^{45} +(-196.536 - 340.410i) q^{47} +(-338.765 + 53.7343i) q^{49} +(242.700 - 140.123i) q^{51} +(-439.900 - 253.976i) q^{53} +623.565 q^{55} +220.020 q^{57} +(-640.900 - 370.024i) q^{59} +(198.404 - 114.549i) q^{61} +(-11.1488 + 7.66422i) q^{63} +(114.926 + 199.058i) q^{65} +(-262.711 - 151.676i) q^{67} -708.629i q^{69} -82.4824 q^{71} +(135.675 - 234.997i) q^{73} +(470.603 - 271.703i) q^{75} +(-327.026 + 685.825i) q^{77} +(304.852 + 528.019i) q^{79} +(354.371 - 613.789i) q^{81} +587.294i q^{83} +831.076i q^{85} +(-694.633 + 1203.14i) q^{87} +(804.220 + 1392.95i) q^{89} +(-279.206 + 22.0060i) q^{91} +(-81.5285 + 47.0705i) q^{93} +(-326.237 + 565.058i) q^{95} -339.739 q^{97} +29.9692i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{7} + 160 q^{9} + 116 q^{15} - 2 q^{17} - 162 q^{23} + 348 q^{25} + 374 q^{31} - 110 q^{33} - 52 q^{39} - 8 q^{41} + 738 q^{47} + 356 q^{49} + 2268 q^{55} - 452 q^{57} - 668 q^{63} + 248 q^{65}+ \cdots + 1672 q^{97}+O(q^{100}) \) 44 * q + 4 * q^7 + 160 * q^9 + 116 * q^15 - 2 * q^17 - 162 * q^23 + 348 * q^25 + 374 * q^31 - 110 * q^33 - 52 * q^39 - 8 * q^41 + 738 * q^47 + 356 * q^49 + 2268 * q^55 - 452 * q^57 - 668 * q^63 + 248 * q^65 - 1248 * q^71 - 218 * q^73 - 298 * q^79 - 1050 * q^81 - 2140 * q^87 + 422 * q^89 + 2434 * q^95 + 1672 * q^97

Introduction

L-functions

Modular forms

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Database

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