LMFDB - Embedded newform 144.5.q.a.65.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,5,Mod(65,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("144.65");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	144.q (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:	$14.8852746841$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.39400128.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 11x^{4} + 14x^{3} + 98x^{2} + 20x + 4 $ x^6 - x^5 + 11x^4 + 14x^3 + 98x^2 + 20x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.1
Root			$-0.102534 - 0.177594i$ of defining polynomial
Character	$\chi$	$=$	144.65
Dual form			144.5.q.a.113.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.32172 - 3.42768i) q^{3} +(-30.0804 + 17.3669i) q^{5} +(-15.6054 + 27.0294i) q^{7} +(57.5020 + 57.0484i) q^{9} +(-49.9968 - 28.8657i) q^{11} +(36.6478 + 63.4758i) q^{13} +(309.848 - 41.4165i) q^{15} -386.985i q^{17} -115.791 q^{19} +(222.512 - 171.441i) q^{21} +(474.852 - 274.156i) q^{23} +(290.719 - 503.539i) q^{25} +(-282.971 - 671.839i) q^{27} +(-680.082 - 392.645i) q^{29} +(272.367 + 471.753i) q^{31} +(317.117 + 411.585i) q^{33} -1084.07i q^{35} +898.827 q^{37} +(-87.3975 - 653.845i) q^{39} +(2242.01 - 1294.43i) q^{41} +(1000.05 - 1732.14i) q^{43} +(-2720.43 - 717.406i) q^{45} +(702.646 + 405.673i) q^{47} +(713.441 + 1235.72i) q^{49} +(-1326.46 + 3220.38i) q^{51} +2221.00i q^{53} +2005.23 q^{55} +(963.579 + 396.895i) q^{57} +(-1309.65 + 756.128i) q^{59} +(951.281 - 1647.67i) q^{61} +(-2439.33 + 663.979i) q^{63} +(-2204.76 - 1272.92i) q^{65} +(2253.55 + 3903.26i) q^{67} +(-4891.30 + 653.806i) q^{69} -3993.54i q^{71} -3436.70 q^{73} +(-4145.25 + 3193.82i) q^{75} +(1560.44 - 900.923i) q^{77} +(601.388 - 1041.63i) q^{79} +(51.9555 + 6560.79i) q^{81} +(-8016.22 - 4628.17i) q^{83} +(6720.72 + 11640.6i) q^{85} +(4313.58 + 5598.59i) q^{87} -8929.99i q^{89} -2287.62 q^{91} +(-649.539 - 4859.38i) q^{93} +(3483.03 - 2010.93i) q^{95} +(-3335.14 + 5776.64i) q^{97} +(-1228.18 - 4512.07i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 12 q^{5} - 12 q^{7} + 99 q^{9} - 483 q^{11} - 6 q^{13} + 1026 q^{15} + 258 q^{19} + 480 q^{21} + 282 q^{23} - 273 q^{25} - 54 q^{27} - 1056 q^{29} - 1290 q^{31} + 279 q^{33} + 12 q^{37}+ \cdots + 9126 q^{99}+O(q^{100}) $ 6 * q + 3 * q^3 - 12 * q^5 - 12 * q^7 + 99 * q^9 - 483 * q^11 - 6 * q^13 + 1026 * q^15 + 258 * q^19 + 480 * q^21 + 282 * q^23 - 273 * q^25 - 54 * q^27 - 1056 * q^29 - 1290 * q^31 + 279 * q^33 + 12 * q^37 - 1974 * q^39 + 7629 * q^41 + 285 * q^43 - 4212 * q^45 + 9642 * q^47 - 1863 * q^49 - 2457 * q^51 - 2016 * q^55 + 5367 * q^57 - 6225 * q^59 + 3630 * q^61 + 7578 * q^63 - 7158 * q^65 + 5055 * q^67 - 13878 * q^69 - 14622 * q^73 - 21021 * q^75 + 2580 * q^77 - 4764 * q^79 + 18387 * q^81 + 1866 * q^83 + 12366 * q^85 + 21564 * q^87 - 34836 * q^91 + 19254 * q^93 + 13362 * q^95 - 28959 * q^97 + 9126 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	−8.32172	−	3.42768i	−0.924635	−	0.380854i
$3$	−8.32172	−	3.42768i	−0.924635	−	0.380854i
$4$		0			0
$5$	−30.0804	+	17.3669i	−1.20321	+	0.694676i	−0.961268	−	0.275614i	$-0.911119\pi$
$5$	−30.0804	+	17.3669i	−1.20321	+	0.694676i	−0.241946	+	0.970290i	$0.577786\pi$
$6$		0			0
$7$	−15.6054	+	27.0294i	−0.318478	+	0.551620i	−0.980171	−	0.198155i	$-0.936505\pi$
$7$	−15.6054	+	27.0294i	−0.318478	+	0.551620i	0.661693	+	0.749775i	$0.269838\pi$
$8$		0			0
$9$	57.5020	+	57.0484i	0.709901	+	0.704301i
$10$		0			0
$11$	−49.9968	−	28.8657i	−0.413197	−	0.238559i	0.278965	−	0.960301i	$-0.410009\pi$
$11$	−49.9968	−	28.8657i	−0.413197	−	0.238559i	−0.692162	+	0.721742i	$0.743342\pi$
$12$		0			0
$13$	36.6478	+	63.4758i	0.216851	+	0.375597i	0.953844	−	0.300304i	$-0.0970882\pi$
$13$	36.6478	+	63.4758i	0.216851	+	0.375597i	−0.736993	+	0.675901i	$0.763755\pi$
$14$		0			0
$15$	309.848	−	41.4165i	1.37710	−	0.184074i
$16$		0			0
$17$		−	386.985i		−	1.33905i	−0.742791	−	0.669524i	$-0.766498\pi$
$17$		−	386.985i		−	1.33905i	0.742791	−	0.669524i	$-0.233502\pi$
$18$		0			0
$19$	−115.791			−0.320750			−0.160375	−	0.987056i	$-0.551270\pi$
$19$	−115.791			−0.320750			−0.160375	+	0.987056i	$0.551270\pi$
$20$		0			0
$21$	222.512	−	171.441i	0.504563	−	0.388754i
$22$		0			0
$23$	474.852	−	274.156i	0.897641	−	0.518253i	0.0212066	−	0.999775i	$-0.493249\pi$
$23$	474.852	−	274.156i	0.897641	−	0.518253i	0.876434	+	0.481522i	$0.159916\pi$
$24$		0			0
$25$	290.719	−	503.539i	0.465150	−	0.805663i
$26$		0			0
$27$	−282.971	−	671.839i	−0.388164	−	0.921590i
$28$		0			0
$29$	−680.082	−	392.645i	−0.808658	−	0.466879i	0.0378313	−	0.999284i	$-0.487955\pi$
$29$	−680.082	−	392.645i	−0.808658	−	0.466879i	−0.846490	+	0.532405i	$0.821288\pi$
$30$		0			0
$31$	272.367	+	471.753i	0.283420	+	0.490898i	0.972225	−	0.234049i	$-0.0751976\pi$
$31$	272.367	+	471.753i	0.283420	+	0.490898i	−0.688805	+	0.724947i	$0.741864\pi$
$32$		0			0
$33$	317.117	+	411.585i	0.291200	+	0.377948i
$34$		0			0
$35$		−	1084.07i		−	0.884957i
$36$		0			0
$37$	898.827			0.656557			0.328279	−	0.944581i	$-0.393532\pi$
$37$	898.827			0.656557			0.328279	+	0.944581i	$0.393532\pi$
$38$		0			0
$39$	−87.3975	−	653.845i	−0.0574606	−	0.429878i
$40$		0			0
$41$	2242.01	−	1294.43i	1.33374	−	0.770034i	0.347867	−	0.937544i	$-0.386906\pi$
$41$	2242.01	−	1294.43i	1.33374	−	0.770034i	0.985870	+	0.167510i	$0.0535727\pi$
$42$		0			0
$43$	1000.05	−	1732.14i	0.540862	−	0.936801i	−0.457993	−	0.888956i	$-0.651431\pi$
$43$	1000.05	−	1732.14i	0.540862	−	0.936801i	0.998855	−	0.0478447i	$-0.0152352\pi$
$44$		0			0
$45$	−2720.43	−	717.406i	−1.34342	−	0.354274i
$46$		0			0
$47$	702.646	+	405.673i	0.318083	+	0.183645i	0.650538	−	0.759474i	$-0.274544\pi$
$47$	702.646	+	405.673i	0.318083	+	0.183645i	−0.332455	+	0.943119i	$0.607877\pi$
$48$		0			0
$49$	713.441	+	1235.72i	0.297143	+	0.514667i
$50$		0			0
$51$	−1326.46	+	3220.38i	−0.509981	+	1.23813i
$52$		0			0
$53$			2221.00i			0.790672i	0.918537	+	0.395336i	$0.129372\pi$
$53$			2221.00i			0.790672i	−0.918537	+	0.395336i	$0.870628\pi$
$54$		0			0
$55$	2005.23			0.662886
$56$		0			0
$57$	963.579	+	396.895i	0.296577	+	0.122159i
$58$		0			0
$59$	−1309.65	+	756.128i	−0.376229	+	0.217216i	−0.676176	−	0.736740i	$-0.736364\pi$
$59$	−1309.65	+	756.128i	−0.376229	+	0.217216i	0.299947	+	0.953956i	$0.403031\pi$
$60$		0			0
$61$	951.281	−	1647.67i	0.255652	−	0.442802i	−0.709420	−	0.704786i	$-0.751043\pi$
$61$	951.281	−	1647.67i	0.255652	−	0.442802i	0.965072	+	0.261983i	$0.0843765\pi$
$62$		0			0
$63$	−2439.33	+	663.979i	−0.614595	+	0.167291i
$64$		0			0
$65$	−2204.76	−	1272.92i	−0.521836	−	0.301282i
$66$		0			0
$67$	2253.55	+	3903.26i	0.502015	+	0.869516i	0.999997	+	0.00232883i	$0.000741290\pi$
$67$	2253.55	+	3903.26i	0.502015	+	0.869516i	−0.497982	+	0.867187i	$0.665925\pi$
$68$		0			0
$69$	−4891.30	+	653.806i	−1.02737	+	0.137325i
$70$		0			0
$71$		−	3993.54i		−	0.792213i	−0.918205	−	0.396106i	$-0.870361\pi$
$71$		−	3993.54i		−	0.792213i	0.918205	−	0.396106i	$-0.129639\pi$
$72$		0			0
$73$	−3436.70			−0.644905			−0.322452	−	0.946586i	$-0.604507\pi$
$73$	−3436.70			−0.644905			−0.322452	+	0.946586i	$0.604507\pi$
$74$		0			0
$75$	−4145.25	+	3193.82i	−0.736934	+	0.567790i
$76$		0			0
$77$	1560.44	−	900.923i	0.263188	−	0.151952i
$78$		0			0
$79$	601.388	−	1041.63i	0.0963608	−	0.166902i	−0.813815	−	0.581124i	$-0.802613\pi$
$79$	601.388	−	1041.63i	0.0963608	−	0.166902i	0.910176	+	0.414222i	$0.135946\pi$
$80$		0			0
$81$	51.9555	+	6560.79i	0.00791883	+	0.999969i
$82$		0			0
$83$	−8016.22	−	4628.17i	−1.16363	−	0.671820i	−0.211456	−	0.977387i	$-0.567821\pi$
$83$	−8016.22	−	4628.17i	−1.16363	−	0.671820i	−0.952170	+	0.305567i	$0.901154\pi$
$84$		0			0
$85$	6720.72	+	11640.6i	0.930204	+	1.61116i
$86$		0			0
$87$	4313.58	+	5598.59i	0.569902	+	0.739673i
$88$		0			0
$89$		−	8929.99i		−	1.12738i	−0.825986	−	0.563691i	$-0.809381\pi$
$89$		−	8929.99i		−	1.12738i	0.825986	−	0.563691i	$-0.190619\pi$
$90$		0			0
$91$	−2287.62			−0.276249
$92$		0			0
$93$	−649.539	−	4859.38i	−0.0751000	−	0.561843i
$94$		0			0
$95$	3483.03	−	2010.93i	0.385932	−	0.222818i
$96$		0			0
$97$	−3335.14	+	5776.64i	−0.354463	+	0.613948i	−0.987026	−	0.160561i	$-0.948670\pi$
$97$	−3335.14	+	5776.64i	−0.354463	+	0.613948i	0.632563	+	0.774509i	$0.282003\pi$
$98$		0			0
$99$	−1228.18	−	4512.07i	−0.125311	−	0.460369i
$100$		0			0
$101$	−7924.19	−	4575.03i	−0.776805	−	0.448489i	0.0584918	−	0.998288i	$-0.481371\pi$
$101$	−7924.19	−	4575.03i	−0.776805	−	0.448489i	−0.835297	+	0.549799i	$0.814704\pi$
$102$		0			0
$103$	7656.20	+	13260.9i	0.721670	+	1.24997i	0.960330	+	0.278866i	$0.0899586\pi$
$103$	7656.20	+	13260.9i	0.721670	+	1.24997i	−0.238660	+	0.971103i	$0.576708\pi$
$104$		0			0
$105$	−3715.85	+	9021.34i	−0.337039	+	0.818262i
$106$		0			0
$107$		−	6099.28i		−	0.532735i	−0.963872	−	0.266367i	$-0.914177\pi$
$107$		−	6099.28i		−	0.532735i	0.963872	−	0.266367i	$-0.0858234\pi$
$108$		0			0
$109$	15169.5			1.27679			0.638393	−	0.769710i	$-0.279599\pi$
$109$	15169.5			1.27679			0.638393	+	0.769710i	$0.279599\pi$
$110$		0			0
$111$	−7479.78	−	3080.89i	−0.607076	−	0.250052i
$112$		0			0
$113$	−1189.11	+	686.532i	−0.0931246	+	0.0537655i	−0.545839	−	0.837890i	$-0.683789\pi$
$113$	−1189.11	+	686.532i	−0.0931246	+	0.0537655i	0.452714	+	0.891656i	$0.350456\pi$
$114$		0			0
$115$	−9522.48	+	16493.4i	−0.720036	+	1.24714i
$116$		0			0
$117$	−1513.88	+	5740.68i	−0.110591	+	0.419365i
$118$		0			0
$119$	10460.0	+	6039.06i	0.738646	+	0.426457i
$120$		0			0
$121$	−5654.04	−	9793.09i	−0.386179	−	0.668881i
$122$		0			0
$123$	−23094.3	+	3086.94i	−1.52649	+	0.204042i
$124$		0			0
$125$		−	1513.10i		−	0.0968386i
$126$		0			0
$127$	19152.4			1.18745			0.593726	−	0.804667i	$-0.297656\pi$
$127$	19152.4			1.18745			0.593726	+	0.804667i	$0.297656\pi$
$128$		0			0
$129$	−14259.4	+	10986.5i	−0.856884	+	0.660210i
$130$		0			0
$131$	2615.39	−	1510.00i	0.152403	−	0.0879902i	−0.421859	−	0.906661i	$-0.638622\pi$
$131$	2615.39	−	1510.00i	0.152403	−	0.0879902i	0.574262	+	0.818671i	$0.305289\pi$
$132$		0			0
$133$	1806.97	−	3129.76i	0.102152	−	0.176932i
$134$		0			0
$135$	20179.6	+	15294.8i	1.10725	+	0.839223i
$136$		0			0
$137$	−8788.30	−	5073.93i	−0.468235	−	0.270336i	0.247266	−	0.968948i	$-0.420468\pi$
$137$	−8788.30	−	5073.93i	−0.468235	−	0.270336i	−0.715501	+	0.698612i	$0.753801\pi$
$138$		0			0
$139$	−17563.2	−	30420.3i	−0.909021	−	1.57447i	−0.815427	−	0.578860i	$-0.803498\pi$
$139$	−17563.2	−	30420.3i	−0.909021	−	1.57447i	−0.0935938	−	0.995610i	$-0.529835\pi$
$140$		0			0
$141$	−4456.70	−	5784.34i	−0.224169	−	0.290948i
$142$		0			0
$143$		−	4231.45i		−	0.206927i
$144$		0			0
$145$	27276.1			1.29732
$146$		0			0
$147$	−1701.41	−	12728.7i	−0.0787363	−	0.589048i
$148$		0			0
$149$	32373.7	−	18691.0i	1.45821	−	0.841899i	0.459288	−	0.888288i	$-0.348105\pi$
$149$	32373.7	−	18691.0i	1.45821	−	0.841899i	0.998923	+	0.0463890i	$0.0147714\pi$
$150$		0			0
$151$	16635.0	−	28812.7i	0.729573	−	1.26366i	−0.227490	−	0.973780i	$-0.573052\pi$
$151$	16635.0	−	28812.7i	0.729573	−	1.26366i	0.957064	−	0.289878i	$-0.0936146\pi$
$152$		0			0
$153$	22076.9	−	22252.4i	0.943093	−	0.950591i
$154$		0			0
$155$	−16385.8	−	9460.33i	−0.682030	−	0.393770i
$156$		0			0
$157$	−4040.16	−	6997.77i	−0.163908	−	0.283897i	0.772359	−	0.635186i	$-0.219077\pi$
$157$	−4040.16	−	6997.77i	−0.163908	−	0.283897i	−0.936267	+	0.351289i	$0.885743\pi$
$158$		0			0
$159$	7612.87	−	18482.5i	0.301130	−	0.731083i
$160$		0			0
$161$			17113.3i			0.660209i
$162$		0			0
$163$	25427.1			0.957022			0.478511	−	0.878081i	$-0.341177\pi$
$163$	25427.1			0.957022			0.478511	+	0.878081i	$0.341177\pi$
$164$		0			0
$165$	−16687.0	−	6873.29i	−0.612928	−	0.252463i
$166$		0			0
$167$	30356.6	−	17526.4i	1.08848	−	0.628434i	0.155309	−	0.987866i	$-0.450363\pi$
$167$	30356.6	−	17526.4i	1.08848	−	0.628434i	0.933171	+	0.359432i	$0.117029\pi$
$168$		0			0
$169$	11594.4	−	20082.1i	0.405951	−	0.703129i
$170$		0			0
$171$	−6658.21	−	6605.69i	−0.227701	−	0.225905i
$172$		0			0
$173$	12731.0	+	7350.23i	0.425372	+	0.245589i	0.697373	−	0.716708i	$-0.254352\pi$
$173$	12731.0	+	7350.23i	0.425372	+	0.245589i	−0.272001	+	0.962297i	$0.587685\pi$
$174$		0			0
$175$	9073.58	+	15715.9i	0.296280	+	0.513172i
$176$		0			0
$177$	13490.3	−	1803.21i	0.430602	−	0.0575573i
$178$		0			0
$179$			37052.5i			1.15641i	0.815892	+	0.578205i	$0.196247\pi$
$179$			37052.5i			1.15641i	−0.815892	+	0.578205i	$0.803753\pi$
$180$		0			0
$181$	−39664.7			−1.21073			−0.605365	−	0.795948i	$-0.706973\pi$
$181$	−39664.7			−1.21073			−0.605365	+	0.795948i	$0.706973\pi$
$182$		0			0
$183$	−13564.0	+	10450.7i	−0.405028	+	0.312065i
$184$		0			0
$185$	−27037.0	+	15609.8i	−0.789979	+	0.456094i
$186$		0			0
$187$	−11170.6	+	19348.0i	−0.319442	+	0.553290i
$188$		0			0
$189$	22575.3	+	2835.80i	0.631990	+	0.0793874i
$190$		0			0
$191$	−49915.1	−	28818.5i	−1.36825	−	0.789959i	−0.377545	−	0.925991i	$-0.623232\pi$
$191$	−49915.1	−	28818.5i	−1.36825	−	0.789959i	−0.990704	+	0.136032i	$0.956565\pi$
$192$		0			0
$193$	−2089.81	−	3619.67i	−0.0561039	−	0.0971748i	0.836609	−	0.547800i	$-0.184534\pi$
$193$	−2089.81	−	3619.67i	−0.0561039	−	0.0971748i	−0.892713	+	0.450625i	$0.851201\pi$
$194$		0			0
$195$	13984.2	+	18150.1i	0.367763	+	0.477319i
$196$		0			0
$197$		−	22191.5i		−	0.571812i	−0.958258	−	0.285906i	$-0.907705\pi$
$197$		−	22191.5i		−	0.571812i	0.958258	−	0.285906i	$-0.0922945\pi$
$198$		0			0
$199$	−50608.7			−1.27797			−0.638983	−	0.769221i	$-0.720645\pi$
$199$	−50608.7			−1.27797			−0.638983	+	0.769221i	$0.720645\pi$
$200$		0			0
$201$	−5374.25	−	40206.3i	−0.133023	−	0.995180i
$202$		0			0
$203$	21225.9	−	12254.8i	0.515080	−	0.297382i
$204$		0			0
$205$	−44960.4	+	77873.6i	−1.06985	+	1.85303i
$206$		0			0
$207$	42945.1	+	11325.0i	1.00224	+	0.264301i
$208$		0			0
$209$	5789.18	+	3342.38i	0.132533	+	0.0765180i
$210$		0			0
$211$	−4459.02	−	7723.26i	−0.100156	−	0.173474i	0.811593	−	0.584223i	$-0.198601\pi$
$211$	−4459.02	−	7723.26i	−0.100156	−	0.173474i	−0.911749	+	0.410749i	$0.865267\pi$
$212$		0			0
$213$	−13688.6	+	33233.1i	−0.301717	+	0.732508i
$214$		0			0
$215$			69471.4i			1.50290i
$216$		0			0
$217$	−17001.6			−0.361052
$218$		0			0
$219$	28599.2	+	11779.9i	0.596302	+	0.245614i
$220$		0			0
$221$	24564.2	−	14182.1i	0.502941	−	0.290373i
$222$		0			0
$223$	−4248.76	+	7359.07i	−0.0854384	+	0.147984i	−0.905578	−	0.424180i	$-0.860562\pi$
$223$	−4248.76	+	7359.07i	−0.0854384	+	0.147984i	0.820140	+	0.572164i	$0.193896\pi$
$224$		0			0
$225$	45443.0	−	12369.5i	0.897640	−	0.244335i
$226$		0			0
$227$	−16543.5	−	9551.40i	−0.321052	−	0.185360i	0.330809	−	0.943698i	$-0.392678\pi$
$227$	−16543.5	−	9551.40i	−0.321052	−	0.185360i	−0.651862	+	0.758338i	$0.726012\pi$
$228$		0			0
$229$	5361.51	+	9286.40i	0.102239	+	0.177083i	0.912607	−	0.408839i	$-0.134066\pi$
$229$	5361.51	+	9286.40i	0.102239	+	0.177083i	−0.810368	+	0.585921i	$0.800733\pi$
$230$		0			0
$231$	−16073.7	+	2148.52i	−0.301225	+	0.0402638i
$232$		0			0
$233$			102200.i			1.88251i	0.337694	+	0.941256i	$0.390353\pi$
$233$			102200.i			1.88251i	−0.337694	+	0.941256i	$0.609647\pi$
$234$		0			0
$235$	−28181.1			−0.510296
$236$		0			0
$237$	−8574.97	+	6606.82i	−0.152664	+	0.117624i
$238$		0			0
$239$	−13440.9	+	7760.09i	−0.235305	+	0.135854i	−0.613017	−	0.790070i	$-0.710044\pi$
$239$	−13440.9	+	7760.09i	−0.235305	+	0.135854i	0.377712	+	0.925923i	$0.376711\pi$
$240$		0			0
$241$	35978.9	−	62317.3i	0.619461	−	1.07294i	−0.370123	−	0.928983i	$-0.620685\pi$
$241$	35978.9	−	62317.3i	0.619461	−	1.07294i	0.989584	−	0.143955i	$-0.0459820\pi$
$242$		0			0
$243$	22056.0	−	54775.2i	0.373520	−	0.927622i
$244$		0			0
$245$	−42921.1	−	24780.5i	−0.715054	−	0.412837i
$246$		0			0
$247$	−4243.48	−	7349.92i	−0.0695550	−	0.120473i
$248$		0			0
$249$	50844.9	+	65991.4i	0.820065	+	1.06436i
$250$		0			0
$251$			41487.8i			0.658526i	0.944238	+	0.329263i	$0.106800\pi$
$251$			41487.8i			0.658526i	−0.944238	+	0.329263i	$0.893200\pi$
$252$		0			0
$253$	−31654.8			−0.494537
$254$		0			0
$255$	−16027.6	−	119907.i	−0.246483	−	1.84401i
$256$		0			0
$257$	−62812.2	+	36264.6i	−0.950994	+	0.549057i	−0.893390	−	0.449283i	$-0.851680\pi$
$257$	−62812.2	+	36264.6i	−0.950994	+	0.549057i	−0.0576045	+	0.998339i	$0.518346\pi$
$258$		0			0
$259$	−14026.6	+	24294.7i	−0.209099	+	0.362170i
$260$		0			0
$261$	−16706.2	−	61375.5i	−0.245244	−	0.900977i
$262$		0			0
$263$	74383.1	+	42945.1i	1.07538	+	0.620872i	0.929647	−	0.368451i	$-0.120112\pi$
$263$	74383.1	+	42945.1i	1.07538	+	0.620872i	0.145735	+	0.989324i	$0.453445\pi$
$264$		0			0
$265$	−38571.8	−	66808.4i	−0.549261	−	0.951347i
$266$		0			0
$267$	−30609.2	+	74312.8i	−0.429367	+	1.04242i
$268$		0			0
$269$			88967.6i			1.22950i	0.788724	+	0.614748i	$0.210742\pi$
$269$			88967.6i			1.22950i	−0.788724	+	0.614748i	$0.789258\pi$
$270$		0			0
$271$	−96541.6			−1.31455			−0.657273	−	0.753652i	$-0.728290\pi$
$271$	−96541.6			−1.31455			−0.657273	+	0.753652i	$0.728290\pi$
$272$		0			0
$273$	19036.9	+	7841.23i	0.255429	+	0.105210i
$274$		0			0
$275$	−29070.0	+	16783.6i	−0.384397	+	0.221932i
$276$		0			0
$277$	11770.8	−	20387.6i	0.153407	−	0.265710i	−0.779071	−	0.626936i	$-0.784309\pi$
$277$	11770.8	−	20387.6i	0.153407	−	0.265710i	0.932478	+	0.361227i	$0.117642\pi$
$278$		0			0
$279$	−11251.1	+	42664.8i	−0.144540	+	0.548102i
$280$		0			0
$281$	−50584.4	−	29204.9i	−0.640626	−	0.369865i	0.144230	−	0.989544i	$-0.453930\pi$
$281$	−50584.4	−	29204.9i	−0.640626	−	0.369865i	−0.784855	+	0.619679i	$0.787263\pi$
$282$		0			0
$283$	−38058.6	−	65919.5i	−0.475204	−	0.823078i	0.524393	−	0.851477i	$-0.324292\pi$
$283$	−38058.6	−	65919.5i	−0.475204	−	0.823078i	−0.999597	+	0.0283989i	$0.990959\pi$
$284$		0			0
$285$	−35877.6	+	4795.66i	−0.441707	+	0.0590417i
$286$		0			0
$287$			80800.3i			0.980956i
$288$		0			0
$289$	−66236.1			−0.793047
$290$		0			0
$291$	47554.6	−	36639.7i	0.561573	−	0.432680i
$292$		0			0
$293$	121166.	−	69955.5i	1.41139	−	0.814866i	0.415871	−	0.909424i	$-0.363477\pi$
$293$	121166.	−	69955.5i	1.41139	−	0.814866i	0.995519	+	0.0945573i	$0.0301436\pi$
$294$		0			0
$295$	26263.2	−	45489.2i	0.301789	−	0.522714i
$296$		0			0
$297$	−5245.43	+	41758.0i	−0.0594660	+	0.473399i
$298$		0			0
$299$	34804.5	+	20094.4i	0.389308	+	0.224767i
$300$		0			0
$301$	31212.5	+	54061.7i	0.344505	+	0.596701i
$302$		0			0
$303$	50261.1	+	65233.7i	0.547453	+	0.710537i
$304$		0			0
$305$			66083.2i			0.710381i
$306$		0			0
$307$	81796.8			0.867880			0.433940	−	0.900942i	$-0.357123\pi$
$307$	81796.8			0.867880			0.433940	+	0.900942i	$0.357123\pi$
$308$		0			0
$309$	−18258.5	−	136597.i	−0.191226	−	1.43062i
$310$		0			0
$311$	1474.59	−	851.354i	0.0152458	−	0.00880216i	−0.492358	−	0.870393i	$-0.663865\pi$
$311$	1474.59	−	851.354i	0.0152458	−	0.00880216i	0.507604	+	0.861591i	$0.330531\pi$
$312$		0			0
$313$	34980.1	−	60587.3i	0.357052	−	0.618433i	−0.630415	−	0.776259i	$-0.717115\pi$
$313$	34980.1	−	60587.3i	0.357052	−	0.618433i	0.987467	+	0.157826i	$0.0504484\pi$
$314$		0			0
$315$	61844.6	−	62336.3i	0.623276	−	0.628232i
$316$		0			0
$317$	101004.	+	58314.7i	1.00512	+	0.580309i	0.909760	−	0.415134i	$-0.136265\pi$
$317$	101004.	+	58314.7i	1.00512	+	0.580309i	0.0953639	+	0.995442i	$0.469599\pi$
$318$		0			0
$319$	22668.0	+	39262.1i	0.222757	+	0.385826i
$320$		0			0
$321$	−20906.4	+	50756.5i	−0.202894	+	0.492585i
$322$		0			0
$323$			44809.3i			0.429500i
$324$		0			0
$325$	42616.8			0.403472
$326$		0			0
$327$	−126236.	−	51996.2i	−1.18056	−	0.486269i
$328$		0			0
$329$	−21930.2	+	12661.4i	−0.202605	+	0.116974i
$330$		0			0
$331$	50418.1	−	87326.8i	0.460183	−	0.797061i	−0.538787	−	0.842442i	$-0.681117\pi$
$331$	50418.1	−	87326.8i	0.460183	−	0.797061i	0.998970	+	0.0453817i	$0.0144504\pi$
$332$		0			0
$333$	51684.3	+	51276.6i	0.466090	+	0.462414i
$334$		0			0
$335$	−135575.	−	78274.3i	−1.20806	−	0.697476i
$336$		0			0
$337$	−20047.2	−	34722.8i	−0.176520	−	0.305742i	0.764166	−	0.645020i	$-0.223151\pi$
$337$	−20047.2	−	34722.8i	−0.176520	−	0.305742i	−0.940686	+	0.339277i	$0.889817\pi$
$338$		0			0
$339$	12248.6	−	1637.24i	0.106583	−	0.0142466i
$340$		0			0
$341$		−	31448.2i		−	0.270450i
$342$		0			0
$343$	−119471.			−1.01549
$344$		0			0
$345$	135778.	−	104613.i	1.14075	−	0.878920i
$346$		0			0
$347$	196035.	−	113181.i	1.62808	−	0.939971i	0.643412	−	0.765520i	$-0.277518\pi$
$347$	196035.	−	113181.i	1.62808	−	0.939971i	0.984666	−	0.174451i	$-0.0558150\pi$
$348$		0			0
$349$	−39799.1	+	68934.1i	−0.326755	+	0.565957i	−0.981866	−	0.189576i	$-0.939289\pi$
$349$	−39799.1	+	68934.1i	−0.326755	+	0.565957i	0.655111	+	0.755533i	$0.272622\pi$
$350$		0			0
$351$	32275.3	−	42583.3i	0.261973	−	0.345641i
$352$		0			0
$353$	−121173.	−	69959.4i	−0.972427	−	0.561431i	−0.0724520	−	0.997372i	$-0.523082\pi$
$353$	−121173.	−	69959.4i	−0.972427	−	0.561431i	−0.899975	+	0.435941i	$0.856416\pi$
$354$		0			0
$355$	69355.5	+	120127.i	0.550331	+	0.953202i
$356$		0			0
$357$	−66344.9	−	86108.8i	−0.520560	−	0.675633i
$358$		0			0
$359$		−	211616.i		−	1.64195i	−0.570963	−	0.820976i	$-0.693430\pi$
$359$		−	211616.i		−	1.64195i	0.570963	−	0.820976i	$-0.306570\pi$
$360$		0			0
$361$	−116913.			−0.897119
$362$		0			0
$363$	13483.7	+	100876.i	0.102329	+	0.765549i
$364$		0			0
$365$	103377.	−	59684.8i	0.775959	−	0.448000i
$366$		0			0
$367$	−15996.8	+	27707.3i	−0.118769	+	0.205713i	−0.919280	−	0.393604i	$-0.871228\pi$
$367$	−15996.8	+	27707.3i	−0.118769	+	0.205713i	0.800511	+	0.599318i	$0.204561\pi$
$368$		0			0
$369$	202765.	+	53471.2i	1.48916	+	0.392706i
$370$		0			0
$371$	−60032.2	−	34659.6i	−0.436151	−	0.251812i
$372$		0			0
$373$	61573.9	+	106649.i	0.442567	+	0.766548i	0.997879	−	0.0650938i	$-0.0207347\pi$
$373$	61573.9	+	106649.i	0.442567	+	0.766548i	−0.555312	+	0.831642i	$0.687401\pi$
$374$		0			0
$375$	−5186.44	+	12591.6i	−0.0368813	+	0.0895404i
$376$		0			0
$377$		−	57558.3i		−	0.404972i
$378$		0			0
$379$	116524.			0.811218			0.405609	−	0.914047i	$-0.367059\pi$
$379$	116524.			0.811218			0.405609	+	0.914047i	$0.367059\pi$
$380$		0			0
$381$	−159381.	−	65648.4i	−1.09796	−	0.452246i
$382$		0			0
$383$	−156848.	+	90556.2i	−1.06925	+	0.617334i	−0.927978	−	0.372636i	$-0.878454\pi$
$383$	−156848.	+	90556.2i	−1.06925	+	0.617334i	−0.141277	+	0.989970i	$0.545121\pi$
$384$		0			0
$385$	−31292.5	+	54200.2i	−0.211115	+	0.365661i
$386$		0			0
$387$	156321.	−	42550.2i	1.04375	−	0.284106i
$388$		0			0
$389$	−44017.9	−	25413.7i	−0.290891	−	0.167946i	0.347453	−	0.937697i	$-0.387047\pi$
$389$	−44017.9	−	25413.7i	−0.290891	−	0.167946i	−0.638343	+	0.769752i	$0.720380\pi$
$390$		0			0
$391$	−106094.	−	183760.i	−0.693965	−	1.20198i
$392$		0			0
$393$	−26940.4	+	3601.04i	−0.174429	+	0.0233154i
$394$		0			0
$395$			41777.0i			0.267758i
$396$		0			0
$397$	228710.			1.45112			0.725561	−	0.688158i	$-0.241580\pi$
$397$	228710.			1.45112			0.725561	+	0.688158i	$0.241580\pi$
$398$		0			0
$399$	−25764.9	+	19851.3i	−0.161839	+	0.124693i
$400$		0			0
$401$	163618.	−	94464.9i	1.01752	−	0.587465i	0.104134	−	0.994563i	$-0.466793\pi$
$401$	163618.	−	94464.9i	1.01752	−	0.587465i	0.913384	+	0.407099i	$0.133459\pi$
$402$		0			0
$403$	−19963.3	+	34577.4i	−0.122920	+	0.212903i
$404$		0			0
$405$	−115504.	−	196449.i	−0.704182	−	1.19768i
$406$		0			0
$407$	−44938.5	−	25945.2i	−0.271287	−	0.156628i
$408$		0			0
$409$	−138713.	−	240258.i	−0.829223	−	1.43626i	−0.898649	−	0.438669i	$-0.855450\pi$
$409$	−138713.	−	240258.i	−0.829223	−	1.43626i	0.0694256	−	0.997587i	$-0.477883\pi$
$410$		0			0
$411$	55741.9	+	72347.3i	0.329988	+	0.428291i
$412$		0			0
$413$		−	47198.8i		−	0.276714i
$414$		0			0
$415$	321508.			1.86679
$416$		0			0
$417$	41884.6	+	313351.i	0.240870	+	1.80201i
$418$		0			0
$419$	88699.9	−	51210.9i	0.505237	−	0.291699i	−0.225637	−	0.974212i	$-0.572446\pi$
$419$	88699.9	−	51210.9i	0.505237	−	0.291699i	0.730874	+	0.682513i	$0.239113\pi$
$420$		0			0
$421$	−23567.9	+	40820.8i	−0.132971	+	0.230312i	−0.924821	−	0.380404i	$-0.875785\pi$
$421$	−23567.9	+	40820.8i	−0.132971	+	0.230312i	0.791850	+	0.610716i	$0.209118\pi$
$422$		0			0
$423$	17260.5	+	63411.8i	0.0964658	+	0.354397i
$424$		0			0
$425$	−194862.	−	112504.i	−1.07882	−	0.622857i
$426$		0			0
$427$	29690.3	+	51425.1i	0.162839	+	0.282046i
$428$		0			0
$429$	−14504.1	+	35213.0i	−0.0788090	+	0.191332i
$430$		0			0
$431$		−	45556.1i		−	0.245240i	−0.992454	−	0.122620i	$-0.960870\pi$
$431$		−	45556.1i		−	0.245240i	0.992454	−	0.122620i	$-0.0391297\pi$
$432$		0			0
$433$	209599.			1.11793			0.558965	−	0.829192i	$-0.311199\pi$
$433$	209599.			1.11793			0.558965	+	0.829192i	$0.311199\pi$
$434$		0			0
$435$	−226984.	−	93493.9i	−1.19955	−	0.494089i
$436$		0			0
$437$	−54983.5	+	31744.8i	−0.287919	+	0.166230i
$438$		0			0
$439$	−91842.1	+	159075.i	−0.476555	+	0.825417i	−0.999639	−	0.0268637i	$-0.991448\pi$
$439$	−91842.1	+	159075.i	−0.476555	+	0.825417i	0.523084	+	0.852281i	$0.324781\pi$
$440$		0			0
$441$	−29471.4	+	111757.i	−0.151539	+	0.574641i
$442$		0			0
$443$	100410.	+	57971.5i	0.511644	+	0.295398i	0.733509	−	0.679680i	$-0.237881\pi$
$443$	100410.	+	57971.5i	0.511644	+	0.295398i	−0.221865	+	0.975077i	$0.571215\pi$
$444$		0			0
$445$	155086.	+	268617.i	0.783165	+	1.35648i
$446$		0			0
$447$	−333472.	+	44574.2i	−1.66895	+	0.223084i
$448$		0			0
$449$			328940.i			1.63164i	0.578305	+	0.815820i	$0.303714\pi$
$449$			328940.i			1.63164i	−0.578305	+	0.815820i	$0.696286\pi$
$450$		0			0
$451$	−149458.			−0.734795
$452$		0			0
$453$	−237192.	+	182751.i	−1.15586	+	0.890562i
$454$		0			0
$455$	68812.3	−	39728.8i	0.332387	−	0.191904i
$456$		0			0
$457$	106369.	−	184236.i	0.509308	−	0.882148i	−0.490634	−	0.871366i	$-0.663235\pi$
$457$	106369.	−	184236.i	0.509308	−	0.882148i	0.999942	−	0.0107819i	$-0.00343204\pi$
$458$		0			0
$459$	−259992.	+	109506.i	−1.23405	+	0.519770i
$460$		0			0
$461$	−41957.2	−	24224.0i	−0.197426	−	0.113984i	0.398028	−	0.917373i	$-0.369695\pi$
$461$	−41957.2	−	24224.0i	−0.197426	−	0.113984i	−0.595454	+	0.803389i	$0.703028\pi$
$462$		0			0
$463$	84550.6	+	146446.i	0.394416	+	0.683149i	0.993026	−	0.117892i	$-0.0376135\pi$
$463$	84550.6	+	146446.i	0.394416	+	0.683149i	−0.598610	+	0.801040i	$0.704280\pi$
$464$		0			0
$465$	103931.	+	134891.i	0.480660	+	0.623848i
$466$		0			0
$467$			54646.4i			0.250569i	0.992121	+	0.125285i	$0.0399844\pi$
$467$			54646.4i			0.250569i	−0.992121	+	0.125285i	$0.960016\pi$
$468$		0			0
$469$	−140670.			−0.639524
$470$		0			0
$471$	9634.97	+	72081.9i	0.0434319	+	0.324926i
$472$		0			0
$473$	−99999.1	+	57734.5i	−0.446965	+	0.258055i
$474$		0			0
$475$	−33662.6	+	58305.3i	−0.149197	+	0.258417i
$476$		0			0
$477$	−126704.	+	127712.i	−0.556871	+	0.561299i
$478$		0			0
$479$	120011.	+	69288.6i	0.523060	+	0.301989i	0.738186	−	0.674597i	$-0.235683\pi$
$479$	120011.	+	69288.6i	0.523060	+	0.301989i	−0.215126	+	0.976586i	$0.569016\pi$
$480$		0			0
$481$	32940.0	+	57053.7i	0.142375	+	0.246601i
$482$		0			0
$483$	58658.9	−	142412.i	0.251443	−	0.610453i
$484$		0			0
$485$		−	231684.i		−	0.984948i
$486$		0			0
$487$	−23464.1			−0.0989340			−0.0494670	−	0.998776i	$-0.515752\pi$
$487$	−23464.1			−0.0989340			−0.0494670	+	0.998776i	$0.515752\pi$
$488$		0			0
$489$	−211597.	−	87156.1i	−0.884897	−	0.364485i
$490$		0			0
$491$	−64368.8	+	37163.4i	−0.267001	+	0.154153i	−0.627524	−	0.778597i	$-0.715932\pi$
$491$	−64368.8	+	37163.4i	−0.267001	+	0.154153i	0.360523	+	0.932750i	$0.382598\pi$
$492$		0			0
$493$	−151948.	+	263181.i	−0.625173	+	1.08283i
$494$		0			0
$495$	115305.	+	114395.i	0.470583	+	0.466872i
$496$		0			0
$497$	107943.	+	62321.0i	0.437001	+	0.252302i
$498$		0			0
$499$	−9486.01	−	16430.2i	−0.0380963	−	0.0659847i	0.846349	−	0.532629i	$-0.178796\pi$
$499$	−9486.01	−	16430.2i	−0.0380963	−	0.0659847i	−0.884445	+	0.466645i	$0.845463\pi$
$500$		0			0
$501$	−312694.	+	41796.9i	−1.24579	+	0.166521i
$502$		0			0
$503$			117856.i			0.465818i	0.972498	+	0.232909i	$0.0748245\pi$
$503$			117856.i			0.465818i	−0.972498	+	0.232909i	$0.925175\pi$
$504$		0			0
$505$	317816.			1.24622
$506$		0			0
$507$	−165320.	+	127375.i	−0.643146	+	0.495529i
$508$		0			0
$509$	158881.	−	91730.2i	0.613250	−	0.354060i	−0.160986	−	0.986957i	$-0.551468\pi$
$509$	158881.	−	91730.2i	0.613250	−	0.354060i	0.774236	+	0.632897i	$0.218134\pi$
$510$		0			0
$511$	53631.2	−	92891.9i	0.205388	−	0.355743i
$512$		0			0
$513$	32765.5	+	77792.9i	0.124504	+	0.295601i
$514$		0			0
$515$	−460602.	−	265929.i	−1.73665	−	1.00265i
$516$		0			0
$517$	−23420.0	−	40564.7i	−0.0876207	−	0.151763i
$518$		0			0
$519$	−80749.2	−	104804.i	−0.299781	−	0.389085i
$520$		0			0
$521$		−	409498.i		−	1.50861i	−0.656526	−	0.754303i	$-0.727975\pi$
$521$		−	409498.i		−	1.50861i	0.656526	−	0.754303i	$-0.272025\pi$
$522$		0			0
$523$	211852.			0.774513			0.387256	−	0.921972i	$-0.373423\pi$
$523$	211852.			0.774513			0.387256	+	0.921972i	$0.373423\pi$
$524$		0			0
$525$	−21638.6	−	161885.i	−0.0785075	−	0.587336i
$526$		0			0
$527$	182561.	−	105402.i	0.657336	−	0.379513i
$528$		0			0
$529$	10402.4	−	18017.4i	0.0371724	−	0.0643845i
$530$		0			0
$531$	−118444.	−	31234.7i	−0.420071	−	0.110777i
$532$		0			0
$533$	164330.	+	94875.7i	0.578444	+	0.333965i
$534$		0			0
$535$	105926.	+	183468.i	0.370078	+	0.640994i
$536$		0			0
$537$	127004.	−	308341.i	0.440423	−	1.06926i
$538$		0			0
$539$		−	82375.9i		−	0.283545i
$540$		0			0
$541$	44016.5			0.150391			0.0751954	−	0.997169i	$-0.476042\pi$
$541$	44016.5			0.150391			0.0751954	+	0.997169i	$0.476042\pi$
$542$		0			0
$543$	330078.	+	135958.i	1.11948	+	0.461111i
$544$		0			0
$545$	−456304.	+	263447.i	−1.53625	+	0.886953i
$546$		0			0
$547$	−21429.6	+	37117.1i	−0.0716207	+	0.124051i	−0.899612	−	0.436691i	$-0.856150\pi$
$547$	−21429.6	+	37117.1i	−0.0716207	+	0.124051i	0.827991	+	0.560741i	$0.189484\pi$
$548$		0			0
$549$	148697.	−	40475.0i	0.493354	−	0.134290i
$550$		0			0
$551$	78747.3	+	45464.8i	0.259378	+	0.149752i
$552$		0			0
$553$	18769.8	+	32510.3i	0.0613776	+	0.106309i
$554$		0			0
$555$	278500.	−	37226.3i	0.904148	−	0.120855i
$556$		0			0
$557$		−	311007.i		−	1.00244i	−0.865319	−	0.501222i	$-0.832884\pi$
$557$		−	311007.i		−	1.00244i	0.865319	−	0.501222i	$-0.167116\pi$
$558$		0			0
$559$	146599.			0.469145
$560$		0			0
$561$	159277.	−	122719.i	0.506090	−	0.389931i
$562$		0			0
$563$	247482.	−	142884.i	0.780777	−	0.450782i	−0.0559288	−	0.998435i	$-0.517812\pi$
$563$	247482.	−	142884.i	0.780777	−	0.450782i	0.836705	+	0.547653i	$0.184479\pi$
$564$		0			0
$565$	23845.9	−	41302.2i	0.0746992	−	0.129383i
$566$		0			0
$567$	−178145.	−	100980.i	−0.554125	−	0.314100i
$568$		0			0
$569$	−118371.	−	68341.3i	−0.365611	−	0.211086i	0.305928	−	0.952055i	$-0.401033\pi$
$569$	−118371.	−	68341.3i	−0.365611	−	0.211086i	−0.671539	+	0.740969i	$0.734367\pi$
$570$		0			0
$571$	−14255.0	−	24690.4i	−0.0437215	−	0.0757279i	0.843337	−	0.537386i	$-0.180588\pi$
$571$	−14255.0	−	24690.4i	−0.0437215	−	0.0757279i	−0.887058	+	0.461658i	$0.847255\pi$
$572$		0			0
$573$	316599.	+	410912.i	0.964273	+	1.25153i
$574$		0			0
$575$		−	318809.i		−	0.964261i
$576$		0			0
$577$	−293742.			−0.882297			−0.441149	−	0.897434i	$-0.645429\pi$
$577$	−293742.			−0.882297			−0.441149	+	0.897434i	$0.645429\pi$
$578$		0			0
$579$	4983.78	+	37285.1i	0.0148663	+	0.111219i
$580$		0			0
$581$	250193.	−	144449.i	0.741179	−	0.427920i
$582$		0			0
$583$	64110.6	−	111043.i	0.188622	−	0.326703i
$584$		0			0
$585$	−54160.0	−	198973.i	−0.158258	−	0.581410i
$586$		0			0
$587$	−334334.	−	193028.i	−0.970295	−	0.560200i	−0.0709687	−	0.997479i	$-0.522609\pi$
$587$	−334334.	−	193028.i	−0.970295	−	0.560200i	−0.899326	+	0.437279i	$0.855942\pi$
$588$		0			0
$589$	−31537.6	−	54624.7i	−0.0909072	−	0.157456i
$590$		0			0
$591$	−76065.3	+	184671.i	−0.217777	+	0.528718i
$592$		0			0
$593$			305581.i			0.868995i	0.900673	+	0.434497i	$0.143074\pi$
$593$			305581.i			0.868995i	−0.900673	+	0.434497i	$0.856926\pi$
$594$		0			0
$595$	−419519.			−1.18500
$596$		0			0
$597$	421152.	+	173471.i	1.18165	+	0.486718i
$598$		0			0
$599$	−229270.	+	132369.i	−0.638988	+	0.368920i	−0.784225	−	0.620477i	$-0.786939\pi$
$599$	−229270.	+	132369.i	−0.638988	+	0.368920i	0.145236	+	0.989397i	$0.453606\pi$
$600$		0			0
$601$	66101.5	−	114491.i	0.183005	−	0.316973i	−0.759898	−	0.650043i	$-0.774751\pi$
$601$	66101.5	−	114491.i	0.183005	−	0.316973i	0.942902	+	0.333069i	$0.108084\pi$
$602$		0			0
$603$	−93091.3	+	353006.i	−0.256020	+	0.970841i
$604$		0			0
$605$	340151.	+	196386.i	0.929312	+	0.536538i
$606$		0			0
$607$	−127073.	−	220097.i	−0.344886	−	0.597360i	0.640447	−	0.768002i	$-0.278749\pi$
$607$	−127073.	−	220097.i	−0.344886	−	0.597360i	−0.985333	+	0.170642i	$0.945416\pi$
$608$		0			0
$609$	−218642.	+	29225.2i	−0.589520	+	0.0787994i
$610$		0			0
$611$			59468.0i			0.159295i
$612$		0			0
$613$	−492878.			−1.31165			−0.655826	−	0.754912i	$-0.727680\pi$
$613$	−492878.			−1.31165			−0.655826	+	0.754912i	$0.727680\pi$
$614$		0			0
$615$	641074.	−	493933.i	1.69495	−	1.30592i
$616$		0			0
$617$	−105029.	+	60638.8i	−0.275893	+	0.159287i	−0.631563	−	0.775325i	$-0.717586\pi$
$617$	−105029.	+	60638.8i	−0.275893	+	0.159287i	0.355670	+	0.934612i	$0.384253\pi$
$618$		0			0
$619$	153682.	−	266185.i	0.401090	−	0.694709i	−0.592768	−	0.805374i	$-0.701965\pi$
$619$	153682.	−	266185.i	0.401090	−	0.694709i	0.993858	+	0.110665i	$0.0352981\pi$
$620$		0			0
$621$	−318558.	−	241446.i	−0.826049	−	0.626090i
$622$		0			0
$623$	241372.	+	139356.i	0.621886	+	0.359046i
$624$		0			0
$625$	207977.	+	360227.i	0.532421	+	0.922181i
$626$		0			0
$627$	−36719.3	−	47657.9i	−0.0934026	−	0.121227i
$628$		0			0
$629$		−	347832.i		−	0.879161i
$630$		0			0
$631$	254196.			0.638425			0.319212	−	0.947683i	$-0.396582\pi$
$631$	254196.			0.638425			0.319212	+	0.947683i	$0.396582\pi$
$632$		0			0
$633$	10633.9	+	79554.9i	0.0265390	+	0.198545i
$634$		0			0
$635$	−576112.	+	332618.i	−1.42876	+	0.824895i
$636$		0			0
$637$	−52292.1	+	90572.5i	−0.128872	+	0.223212i
$638$		0			0
$639$	227825.	−	229637.i	0.557957	−	0.562393i
$640$		0			0
$641$	316954.	+	182993.i	0.771400	+	0.445368i	0.833374	−	0.552710i	$-0.186406\pi$
$641$	316954.	+	182993.i	0.771400	+	0.445368i	−0.0619737	+	0.998078i	$0.519739\pi$
$642$		0			0
$643$	115391.	+	199864.i	0.279094	+	0.483406i	0.971160	−	0.238429i	$-0.0766324\pi$
$643$	115391.	+	199864.i	0.279094	+	0.483406i	−0.692066	+	0.721835i	$0.743299\pi$
$644$		0			0
$645$	238126.	−	578121.i	0.572383	−	1.38963i
$646$		0			0
$647$		−	278596.i		−	0.665529i	−0.943010	−	0.332764i	$-0.892019\pi$
$647$		−	278596.i		−	0.665529i	0.943010	−	0.332764i	$-0.107981\pi$
$648$		0			0
$649$	87304.7			0.207276
$650$		0			0
$651$	141483.	+	58276.1i	0.333842	+	0.137508i
$652$		0			0
$653$	−67988.8	+	39253.4i	−0.159445	+	0.0920557i	−0.577600	−	0.816320i	$-0.696010\pi$
$653$	−67988.8	+	39253.4i	−0.159445	+	0.0920557i	0.418154	+	0.908376i	$0.362677\pi$
$654$		0			0
$655$	−52448.0	+	90842.6i	−0.122249	+	0.211742i
$656$		0			0
$657$	−197617.	−	196058.i	−0.457819	−	0.454208i
$658$		0			0
$659$	742420.	+	428637.i	1.70954	+	0.987003i	0.935121	+	0.354328i	$0.115290\pi$
$659$	742420.	+	428637.i	1.70954	+	0.987003i	0.774418	+	0.632675i	$0.218043\pi$
$660$		0			0
$661$	−11172.0	−	19350.4i	−0.0255698	−	0.0442882i	0.852957	−	0.521981i	$-0.174807\pi$
$661$	−11172.0	−	19350.4i	−0.0255698	−	0.0442882i	−0.878527	+	0.477692i	$0.841473\pi$
$662$		0			0
$663$	−253028.	+	33821.5i	−0.575627	+	0.0769424i
$664$		0			0
$665$			125526.i			0.283850i
$666$		0			0
$667$	−430584.			−0.967846
$668$		0			0
$669$	60581.6	−	46676.7i	0.135359	−	0.104291i
$670$		0			0
$671$	−95122.1	+	54918.8i	−0.211269	+	0.121976i
$672$		0			0
$673$	331739.	−	574588.i	0.732430	−	1.26861i	−0.223412	−	0.974724i	$-0.571719\pi$
$673$	331739.	−	574588.i	0.732430	−	1.26861i	0.955842	−	0.293882i	$-0.0949472\pi$
$674$		0			0
$675$	−420563.	−	52829.0i	−0.923046	−	0.115948i
$676$		0			0
$677$	−197558.	−	114060.i	−0.431040	−	0.248861i	0.268749	−	0.963210i	$-0.413390\pi$
$677$	−197558.	−	114060.i	−0.431040	−	0.248861i	−0.699790	+	0.714349i	$0.746723\pi$
$678$		0			0
$679$	−104093.	−	180294.i	−0.225777	−	0.391058i
$680$		0			0
$681$	104931.	+	136190.i	0.226261	+	0.293664i
$682$		0			0
$683$		−	53606.6i		−	0.114915i	−0.998348	−	0.0574575i	$-0.981701\pi$
$683$		−	53606.6i		−	0.114915i	0.998348	−	0.0574575i	$-0.0182994\pi$
$684$		0			0
$685$	352474.			0.751182
$686$		0			0
$687$	−12786.1	−	95656.4i	−0.0270910	−	0.202675i
$688$		0			0
$689$	−140980.	+	81394.6i	−0.296974	+	0.171458i
$690$		0			0
$691$	378663.	−	655863.i	0.793043	−	1.37359i	−0.131031	−	0.991378i	$-0.541829\pi$
$691$	378663.	−	655863.i	0.793043	−	1.37359i	0.924074	−	0.382213i	$-0.124838\pi$
$692$		0			0
$693$	141125.	+	37216.0i	0.293858	+	0.0774932i
$694$		0			0
$695$	1.05661e6	+	610036.i	2.18749	+	1.26295i
$696$		0			0
$697$	−500923.	−	867624.i	−1.03111	−	1.78594i
$698$		0			0
$699$	350308.	−	850477.i	0.716962	−	1.74064i
$700$		0			0
$701$			506359.i			1.03044i	0.857058	+	0.515220i	$0.172290\pi$
$701$			506359.i			1.03044i	−0.857058	+	0.515220i	$0.827710\pi$
$702$		0			0
$703$	−104076.			−0.210591
$704$		0			0
$705$	234515.	+	96595.9i	0.471838	+	0.194348i
$706$		0			0
$707$	247321.	−	142791.i	0.494791	−	0.285668i
$708$		0			0
$709$	325622.	−	563993.i	0.647770	−	1.12197i	−0.335885	−	0.941903i	$-0.609035\pi$
$709$	325622.	−	563993.i	0.647770	−	1.12197i	0.983654	−	0.180067i	$-0.0576314\pi$
$710$		0			0
$711$	94004.6	−	25587.8i	0.185956	−	0.0506167i
$712$		0			0
$713$	258668.	+	149342.i	0.508819	+	0.293767i
$714$		0			0
$715$	73487.2	+	127284.i	0.143747	+	0.248978i
$716$		0			0
$717$	138450.	−	18506.3i	0.269312	−	0.0359981i
$718$		0			0
$719$			69724.6i			0.134874i	0.997724	+	0.0674370i	$0.0214822\pi$
$719$			69724.6i			0.134874i	−0.997724	+	0.0674370i	$0.978518\pi$
$720$		0			0
$721$	−477913.			−0.919345
$722$		0			0
$723$	−513010.	+	395263.i	−0.981407	+	0.756152i
$724$		0			0
$725$	−395425.	+	228299.i	−0.752294	+	0.434337i
$726$		0			0
$727$	−373864.	+	647552.i	−0.707367	+	1.22520i	0.258463	+	0.966021i	$0.416784\pi$
$727$	−373864.	+	647552.i	−0.707367	+	1.22520i	−0.965830	+	0.259175i	$0.916549\pi$
$728$		0			0
$729$	−371295.	+	380223.i	−0.698658	+	0.715456i
$730$		0			0
$731$	−670313.	−	387006.i	−1.25442	−	0.724240i
$732$		0			0
$733$	−32869.3	−	56931.2i	−0.0611761	−	0.105960i	0.833815	−	0.552044i	$-0.186152\pi$
$733$	−32869.3	−	56931.2i	−0.0611761	−	0.105960i	−0.894991	+	0.446083i	$0.852818\pi$
$734$		0			0
$735$	272238.	+	353337.i	0.503934	+	0.654054i
$736$		0			0
$737$		−	260201.i		−	0.479042i
$738$		0			0
$739$	−977921.			−1.79067			−0.895334	−	0.445395i	$-0.853063\pi$
$739$	−977921.			−1.79067			−0.895334	+	0.445395i	$0.853063\pi$
$740$		0			0
$741$	10119.8	+	75709.3i	0.0184305	+	0.137884i
$742$		0			0
$743$	−437233.	+	252437.i	−0.792019	+	0.457272i	−0.840673	−	0.541543i	$-0.817840\pi$
$743$	−437233.	+	252437.i	−0.792019	+	0.457272i	0.0486539	+	0.998816i	$0.484507\pi$
$744$		0			0
$745$	−649209.	+	1.12446e6i	−1.16969	+	2.02597i
$746$		0			0
$747$	−196919.	−	723442.i	−0.352896	−	1.29647i
$748$		0			0
$749$	164860.	+	95181.9i	0.293867	+	0.169664i
$750$		0			0
$751$	−266395.	−	461411.i	−0.472332	−	0.818102i	0.527167	−	0.849762i	$-0.323254\pi$
$751$	−266395.	−	461411.i	−0.472332	−	0.818102i	−0.999499	+	0.0316593i	$0.989921\pi$
$752$		0			0
$753$	142207.	−	345250.i	0.250802	−	0.608896i
$754$		0			0
$755$			1.15559e6i			2.02727i
$756$		0			0
$757$	−293571.			−0.512297			−0.256148	−	0.966637i	$-0.582454\pi$
$757$	−293571.			−0.512297			−0.256148	+	0.966637i	$0.582454\pi$
$758$		0			0
$759$	263422.	+	108503.i	0.457266	+	0.188346i
$760$		0			0
$761$	−22249.2	+	12845.6i	−0.0384190	+	0.0221812i	−0.519086	−	0.854722i	$-0.673728\pi$
$761$	−22249.2	+	12845.6i	−0.0384190	+	0.0221812i	0.480667	+	0.876903i	$0.340394\pi$
$762$		0			0
$763$	−236727.	+	410022.i	−0.406629	+	0.704301i
$764$		0			0
$765$	−277625.	+	1.05277e6i	−0.474390	+	1.79891i
$766$		0			0
$767$	−95991.7	−	55420.9i	−0.163171	−	0.0942069i
$768$		0			0
$769$	323572.	+	560443.i	0.547165	+	0.947717i	0.998467	+	0.0553463i	$0.0176263\pi$
$769$	323572.	+	560443.i	0.547165	+	0.947717i	−0.451302	+	0.892371i	$0.649040\pi$
$770$		0			0
$771$	647009.	−	86483.8i	1.08843	−	0.145488i
$772$		0			0
$773$			610238.i			1.02127i	0.859798	+	0.510634i	$0.170589\pi$
$773$			610238.i			1.02127i	−0.859798	+	0.510634i	$0.829411\pi$
$774$		0			0
$775$	316728.			0.527331
$776$		0			0
$777$	200000.	−	154095.i	0.331274	−	0.255239i
$778$		0			0
$779$	−259605.	+	149883.i	−0.427797	+	0.246989i
$780$		0			0
$781$	−115276.	+	199665.i	−0.188990	+	0.327340i
$782$		0			0
$783$	−71351.0	+	568013.i	−0.116379	+	0.926477i
$784$		0			0
$785$	243059.	+	140330.i	0.394432	+	0.227726i
$786$		0			0
$787$	−290160.	−	502572.i	−0.468477	−	0.811427i	0.530874	−	0.847451i	$-0.321864\pi$
$787$	−290160.	−	502572.i	−0.468477	−	0.811427i	−0.999351	+	0.0360244i	$0.988531\pi$
$788$		0			0
$789$	−471793.	−	612339.i	−0.757875	−	0.983644i
$790$		0			0
$791$		−	42854.5i		−	0.0684926i
$792$		0			0
$793$	139449.			0.221753
$794$		0			0
$795$	91986.0	+	688172.i	0.145542	+	1.08884i
$796$		0			0
$797$	−915508.	+	528569.i	−1.44127	+	0.832118i	−0.997935	−	0.0642373i	$-0.979539\pi$
$797$	−915508.	+	528569.i	−1.44127	+	0.832118i	−0.443336	+	0.896355i	$0.646205\pi$
$798$		0			0
$799$	156989.	−	271913.i	0.245910	−	0.425928i
$800$		0			0
$801$	509442.	−	513492.i	0.794016	−	0.800329i
$802$		0			0
$803$	171824.	+	99202.7i	0.266473	+	0.153848i
$804$		0			0
$805$	−297205.	−	514774.i	−0.458631	−	0.794373i
$806$		0			0
$807$	304953.	−	740363.i	0.468258	−	1.13684i
$808$		0			0
$809$		−	355969.i		−	0.543895i	−0.962312	−	0.271947i	$-0.912332\pi$
$809$		−	355969.i		−	0.543895i	0.962312	−	0.271947i	$-0.0876677\pi$
$810$		0			0
$811$	136417.			0.207409			0.103704	−	0.994608i	$-0.466930\pi$
$811$	136417.			0.207409			0.103704	+	0.994608i	$0.466930\pi$
$812$		0			0
$813$	803392.	+	330914.i	1.21548	+	0.500650i
$814$		0			0
$815$	−764857.	+	441590.i	−1.15150	+	0.664820i
$816$		0			0
$817$	−115797.	+	200567.i	−0.173482	+	0.300479i
$818$		0			0
$819$	−131543.	−	130505.i	−0.196109	−	0.194563i
$820$		0			0
$821$	−394889.	−	227989.i	−0.585854	−	0.338243i	0.177603	−	0.984102i	$-0.443166\pi$
$821$	−394889.	−	227989.i	−0.585854	−	0.338243i	−0.763456	+	0.645860i	$0.776499\pi$
$822$		0			0
$823$	251795.	+	436122.i	0.371747	+	0.643885i	0.989834	−	0.142225i	$-0.0454255\pi$
$823$	251795.	+	436122.i	0.371747	+	0.643885i	−0.618087	+	0.786109i	$0.712092\pi$
$824$		0			0
$825$	299441.	−	40025.4i	0.439951	−	0.0588069i
$826$		0			0
$827$		−	551861.i		−	0.806898i	−0.915002	−	0.403449i	$-0.867811\pi$
$827$		−	551861.i		−	0.806898i	0.915002	−	0.403449i	$-0.132189\pi$
$828$		0			0
$829$	−182308.			−0.265275			−0.132638	−	0.991165i	$-0.542345\pi$
$829$	−182308.			−0.265275			−0.132638	+	0.991165i	$0.542345\pi$
$830$		0			0
$831$	−167836.	+	129314.i	−0.243042	+	0.187259i
$832$		0			0
$833$	478203.	−	276091.i	0.689164	−	0.397889i
$834$		0			0
$835$	−608759.	+	1.05440e6i	−0.873117	+	1.51228i
$836$		0			0
$837$	239870.	−	316479.i	0.342394	−	0.451746i
$838$		0			0
$839$	359993.	+	207842.i	0.511410	+	0.295263i	0.733413	−	0.679783i	$-0.237926\pi$
$839$	359993.	+	207842.i	0.511410	+	0.295263i	−0.222003	+	0.975046i	$0.571259\pi$
$840$		0			0
$841$	−45299.7	−	78461.4i	−0.0640477	−	0.110934i
$842$		0			0
$843$	320844.	+	416423.i	0.451480	+	0.585975i
$844$		0			0
$845$			805434.i			1.12802i
$846$		0			0
$847$	352935.			0.491958
$848$		0			0
$849$	90762.1	+	679016.i	0.125918	+	0.942030i
$850$		0			0
$851$	426809.	−	246419.i	0.589352	−	0.340263i
$852$		0			0
$853$	−75135.3	+	130138.i	−0.103263	+	0.178857i	−0.913027	−	0.407898i	$-0.866262\pi$
$853$	−75135.3	+	130138.i	−0.103263	+	0.178857i	0.809764	+	0.586756i	$0.199595\pi$
$854$		0			0
$855$	315002.	+	83069.1i	0.430904	+	0.113634i
$856$		0			0
$857$	125373.	+	72383.9i	0.170703	+	0.0985554i	0.582917	−	0.812532i	$-0.301911\pi$
$857$	125373.	+	72383.9i	0.170703	+	0.0985554i	−0.412214	+	0.911087i	$0.635245\pi$
$858$		0			0
$859$	166948.	+	289163.i	0.226254	+	0.391883i	0.956695	−	0.291093i	$-0.0940188\pi$
$859$	166948.	+	289163.i	0.226254	+	0.391883i	−0.730441	+	0.682976i	$0.760685\pi$
$860$		0			0
$861$	276958.	−	672398.i	0.373601	−	0.907026i
$862$		0			0
$863$		−	1.13280e6i		−	1.52101i	−0.649330	−	0.760507i	$-0.724951\pi$
$863$		−	1.13280e6i		−	1.52101i	0.649330	−	0.760507i	$-0.275049\pi$
$864$		0			0
$865$	−510603.			−0.682418
$866$		0			0
$867$	551198.	+	227036.i	0.733279	+	0.302035i
$868$		0			0
$869$	−60135.0	+	34718.9i	−0.0796320	+	0.0459755i
$870$		0			0
$871$	−165175.	+	286092.i	−0.217725	+	0.377111i
$872$		0			0
$873$	−521325.	+	141903.i	−0.684038	+	0.186193i
$874$		0			0
$875$	40898.3	+	23612.6i	0.0534181	+	0.0308410i
$876$		0			0
$877$	−248271.	−	430017.i	−0.322795	−	0.559097i	0.658269	−	0.752783i	$-0.271289\pi$
$877$	−248271.	−	430017.i	−0.322795	−	0.559097i	−0.981064	+	0.193686i	$0.937956\pi$
$878$		0			0
$879$	−1.24810e6	+	166830.i	−1.61537	+	0.215921i
$880$		0			0
$881$		−	1.21533e6i		−	1.56583i	−0.622131	−	0.782913i	$-0.713733\pi$
$881$		−	1.21533e6i		−	1.56583i	0.622131	−	0.782913i	$-0.286267\pi$
$882$		0			0
$883$	999070.			1.28137			0.640685	−	0.767804i	$-0.278651\pi$
$883$	999070.			1.28137			0.640685	+	0.767804i	$0.278651\pi$
$884$		0			0
$885$	−374478.	+	288527.i	−0.478123	+	0.368383i
$886$		0			0
$887$	−938048.	+	541582.i	−1.19228	+	0.688362i	−0.958823	−	0.284005i	$-0.908337\pi$
$887$	−938048.	+	541582.i	−1.19228	+	0.688362i	−0.233456	+	0.972367i	$0.575003\pi$
$888$		0			0
$889$	−298882.	+	517678.i	−0.378178	+	0.655023i
$890$		0			0
$891$	186784.	−	329519.i	0.235280	−	0.415073i
$892$		0			0
$893$	−81360.0	−	46973.2i	−0.102025	−	0.0589044i
$894$		0			0
$895$	−643488.	−	1.11455e6i	−0.803330	−	1.39141i
$896$		0			0
$897$	−220756.	−	286519.i	−0.274365	−	0.356097i
$898$		0			0
$899$		−	427774.i		−	0.529292i
$900$		0			0
$901$	859491.			1.05875
$902$		0			0
$903$	−74435.6	−	556873.i	−0.0912862	−	0.682937i
$904$		0			0
$905$	1.19313e6	−	688853.i	1.45677	−	0.841065i
$906$		0			0
$907$	638426.	−	1.10579e6i	0.776061	−	1.34418i	−0.158135	−	0.987417i	$-0.550548\pi$
$907$	638426.	−	1.10579e6i	0.776061	−	1.34418i	0.934196	−	0.356760i	$-0.116118\pi$
$908$		0			0
$909$	−194658.	−	715136.i	−0.235583	−	0.865487i
$910$		0			0
$911$	−236846.	−	136743.i	−0.285383	−	0.164766i	0.350475	−	0.936572i	$-0.386020\pi$
$911$	−236846.	−	136743.i	−0.285383	−	0.164766i	−0.635858	+	0.771806i	$0.719354\pi$
$912$		0			0
$913$	267191.	+	462788.i	0.320538	+	0.555188i
$914$		0			0
$915$	226512.	−	549926.i	0.270551	−	0.656844i
$916$		0			0
$917$			94256.7i			0.112092i
$918$		0			0
$919$	−1.15882e6			−1.37210			−0.686051	−	0.727553i	$-0.740657\pi$
$919$	−1.15882e6			−1.37210			−0.686051	+	0.727553i	$0.740657\pi$
$920$		0			0
$921$	−680690.	−	280373.i	−0.802472	−	0.330535i
$922$		0			0
$923$	253493.	−	146355.i	0.297552	−	0.171792i
$924$		0			0
$925$	261306.	−	452595.i	0.305397	−	0.528964i
$926$		0			0
$927$	−316268.	+	1.19930e6i	−0.368041	+	1.39563i
$928$		0			0
$929$	738465.	+	426353.i	0.855655	+	0.494012i	0.862555	−	0.505964i	$-0.168863\pi$
$929$	738465.	+	426353.i	0.855655	+	0.494012i	−0.00690018	+	0.999976i	$0.502196\pi$
$930$		0			0
$931$	−82610.0	−	143085.i	−0.0953089	−	0.165080i
$932$		0			0
$933$	−15189.3	+	2030.31i	−0.0174491	+	0.00233237i
$934$		0			0
$935$		−	775993.i		−	0.887636i
$936$		0			0
$937$	629989.			0.717552			0.358776	−	0.933424i	$-0.383194\pi$
$937$	629989.			0.717552			0.358776	+	0.933424i	$0.383194\pi$
$938$		0			0
$939$	−498768.	+	384290.i	−0.565676	+	0.435840i
$940$		0			0
$941$	−366547.	+	211626.i	−0.413953	+	0.238996i	−0.692487	−	0.721431i	$-0.743485\pi$
$941$	−366547.	+	211626.i	−0.413953	+	0.238996i	0.278534	+	0.960426i	$0.410152\pi$
$942$		0			0
$943$	709749.	−	1.22932e6i	0.798145	−	1.38243i
$944$		0			0
$945$	−728322.	+	306761.i	−0.815568	+	0.343508i
$946$		0			0
$947$	1.20762e6	+	697219.i	1.34657	+	0.777444i	0.987762	−	0.155967i	$-0.0498493\pi$
$947$	1.20762e6	+	697219.i	1.34657	+	0.777444i	0.358810	+	0.933411i	$0.383183\pi$
$948$		0			0
$949$	−125947.	−	218147.i	−0.139848	−	0.242224i
$950$		0			0
$951$	−640642.	−	831488.i	−0.708361	−	0.919379i
$952$		0			0
$953$			24001.0i			0.0264267i	0.999913	+	0.0132134i	$0.00420607\pi$
$953$			24001.0i			0.0264267i	−0.999913	+	0.0132134i	$0.995794\pi$
$954$		0			0
$955$	2.00195e6			2.19506
$956$		0			0
$957$	−54058.5	−	404426.i	−0.0590255	−	0.441586i
$958$		0			0
$959$	274290.	−	158362.i	0.298245	−	0.172192i
$960$		0			0
$961$	313393.	−	542813.i	0.339346	−	0.587765i
$962$		0			0
$963$	347954.	−	350721.i	0.375206	−	0.378189i
$964$		0			0
$965$	125725.	+	72587.2i	0.135010	+	0.0779481i
$966$		0			0
$967$	522031.	+	904183.i	0.558268	+	0.966949i	0.997641	+	0.0686443i	$0.0218673\pi$
$967$	522031.	+	904183.i	0.558268	+	0.966949i	−0.439373	+	0.898305i	$0.644799\pi$
$968$		0			0
$969$	153592.	−	372890.i	0.163577	−	0.397131i
$970$		0			0
$971$			605213.i			0.641904i	0.947096	+	0.320952i	$0.104003\pi$
$971$			605213.i			0.641904i	−0.947096	+	0.320952i	$0.895997\pi$
$972$		0			0
$973$	1.09632e6			1.15801
$974$		0			0
$975$	−354645.	−	146077.i	−0.373065	−	0.153664i
$976$		0			0
$977$	41660.2	−	24052.5i	0.0436448	−	0.0251983i	−0.478019	−	0.878350i	$-0.658645\pi$
$977$	41660.2	−	24052.5i	0.0436448	−	0.0251983i	0.521664	+	0.853151i	$0.325312\pi$
$978$		0			0
$979$	−257770.	+	446471.i	−0.268947	+	0.465831i
$980$		0			0
$981$	872276.	+	865396.i	0.906392	+	0.899243i
$982$		0			0
$983$	107286.	+	61941.5i	0.111029	+	0.0641024i	0.554486	−	0.832193i	$-0.312915\pi$
$983$	107286.	+	61941.5i	0.111029	+	0.0641024i	−0.443457	+	0.896295i	$0.646248\pi$
$984$		0			0
$985$	385397.	+	667527.i	0.397224	+	0.688012i
$986$		0			0
$987$	225896.	−	30194.9i	0.231886	−	0.0309955i
$988$		0			0
$989$		−	1.09668e6i		−	1.12121i
$990$		0			0
$991$	−851418.			−0.866953			−0.433477	−	0.901165i	$-0.642713\pi$
$991$	−851418.			−0.866953			−0.433477	+	0.901165i	$0.642713\pi$
$992$		0			0
$993$	−718894.	+	553891.i	−0.729065	+	0.561728i
$994$		0			0
$995$	1.52233e6	−	878917.i	1.53767	−	0.887773i
$996$		0			0
$997$	801524.	−	1.38828e6i	0.806355	−	1.39665i	−0.109018	−	0.994040i	$-0.534771\pi$
$997$	801524.	−	1.38828e6i	0.806355	−	1.39665i	0.915373	−	0.402607i	$-0.131896\pi$
$998$		0			0
$999$	−254342.	−	603867.i	−0.254852	−	0.605077i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.5.q.a.65.1		6
3.2	odd	2		432.5.q.a.305.3		6
4.3	odd	2		9.5.d.a.2.2	✓	6
9.2	odd	6		1296.5.e.c.161.6		6
9.4	even	3		432.5.q.a.17.3		6
9.5	odd	6	inner	144.5.q.a.113.1		6
9.7	even	3		1296.5.e.c.161.1		6
12.11	even	2		27.5.d.a.8.2		6
36.7	odd	6		81.5.b.a.80.3		6
36.11	even	6		81.5.b.a.80.4		6
36.23	even	6		9.5.d.a.5.2	yes	6
36.31	odd	6		27.5.d.a.17.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.5.d.a.2.2	✓	6	4.3	odd	2
9.5.d.a.5.2	yes	6	36.23	even	6
27.5.d.a.8.2		6	12.11	even	2
27.5.d.a.17.2		6	36.31	odd	6
81.5.b.a.80.3		6	36.7	odd	6
81.5.b.a.80.4		6	36.11	even	6
144.5.q.a.65.1		6	1.1	even	1	trivial
144.5.q.a.113.1		6	9.5	odd	6	inner
432.5.q.a.17.3		6	9.4	even	3
432.5.q.a.305.3		6	3.2	odd	2
1296.5.e.c.161.1		6	9.7	even	3
1296.5.e.c.161.6		6	9.2	odd	6

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	144.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-8.32172 - 3.42768i) q^{3} +(-30.0804 + 17.3669i) q^{5} +(-15.6054 + 27.0294i) q^{7} +(57.5020 + 57.0484i) q^{9} +(-49.9968 - 28.8657i) q^{11} +(36.6478 + 63.4758i) q^{13} +(309.848 - 41.4165i) q^{15} -386.985i q^{17} -115.791 q^{19} +(222.512 - 171.441i) q^{21} +(474.852 - 274.156i) q^{23} +(290.719 - 503.539i) q^{25} +(-282.971 - 671.839i) q^{27} +(-680.082 - 392.645i) q^{29} +(272.367 + 471.753i) q^{31} +(317.117 + 411.585i) q^{33} -1084.07i q^{35} +898.827 q^{37} +(-87.3975 - 653.845i) q^{39} +(2242.01 - 1294.43i) q^{41} +(1000.05 - 1732.14i) q^{43} +(-2720.43 - 717.406i) q^{45} +(702.646 + 405.673i) q^{47} +(713.441 + 1235.72i) q^{49} +(-1326.46 + 3220.38i) q^{51} +2221.00i q^{53} +2005.23 q^{55} +(963.579 + 396.895i) q^{57} +(-1309.65 + 756.128i) q^{59} +(951.281 - 1647.67i) q^{61} +(-2439.33 + 663.979i) q^{63} +(-2204.76 - 1272.92i) q^{65} +(2253.55 + 3903.26i) q^{67} +(-4891.30 + 653.806i) q^{69} -3993.54i q^{71} -3436.70 q^{73} +(-4145.25 + 3193.82i) q^{75} +(1560.44 - 900.923i) q^{77} +(601.388 - 1041.63i) q^{79} +(51.9555 + 6560.79i) q^{81} +(-8016.22 - 4628.17i) q^{83} +(6720.72 + 11640.6i) q^{85} +(4313.58 + 5598.59i) q^{87} -8929.99i q^{89} -2287.62 q^{91} +(-649.539 - 4859.38i) q^{93} +(3483.03 - 2010.93i) q^{95} +(-3335.14 + 5776.64i) q^{97} +(-1228.18 - 4512.07i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 12 q^{5} - 12 q^{7} + 99 q^{9} - 483 q^{11} - 6 q^{13} + 1026 q^{15} + 258 q^{19} + 480 q^{21} + 282 q^{23} - 273 q^{25} - 54 q^{27} - 1056 q^{29} - 1290 q^{31} + 279 q^{33} + 12 q^{37}+ \cdots + 9126 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 - 12 * q^5 - 12 * q^7 + 99 * q^9 - 483 * q^11 - 6 * q^13 + 1026 * q^15 + 258 * q^19 + 480 * q^21 + 282 * q^23 - 273 * q^25 - 54 * q^27 - 1056 * q^29 - 1290 * q^31 + 279 * q^33 + 12 * q^37 - 1974 * q^39 + 7629 * q^41 + 285 * q^43 - 4212 * q^45 + 9642 * q^47 - 1863 * q^49 - 2457 * q^51 - 2016 * q^55 + 5367 * q^57 - 6225 * q^59 + 3630 * q^61 + 7578 * q^63 - 7158 * q^65 + 5055 * q^67 - 13878 * q^69 - 14622 * q^73 - 21021 * q^75 + 2580 * q^77 - 4764 * q^79 + 18387 * q^81 + 1866 * q^83 + 12366 * q^85 + 21564 * q^87 - 34836 * q^91 + 19254 * q^93 + 13362 * q^95 - 28959 * q^97 + 9126 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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