LMFDB - Embedded newform 126.5.n.a.19.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,5,Mod(19,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.19"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	126.n (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,-16,-54] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$13.0246153486$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	126.19
Dual form			126.5.n.a.73.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41421 + 2.44949i) q^{2} +(-4.00000 - 6.92820i) q^{4} +(-5.01472 - 2.89525i) q^{5} +(-7.00000 + 48.4974i) q^{7} +22.6274 q^{8} +(14.1838 - 8.18900i) q^{10} +(5.01472 + 8.68575i) q^{11} -190.220i q^{13} +(-108.894 - 85.7321i) q^{14} +(-32.0000 + 55.4256i) q^{16} +(-365.265 + 210.886i) q^{17} +(-374.338 - 216.124i) q^{19} +46.3240i q^{20} -28.3675 q^{22} +(460.911 - 798.322i) q^{23} +(-295.735 - 512.228i) q^{25} +(465.941 + 269.011i) q^{26} +(364.000 - 145.492i) q^{28} -877.882 q^{29} +(627.175 - 362.100i) q^{31} +(-90.5097 - 156.767i) q^{32} -1192.95i q^{34} +(175.515 - 222.934i) q^{35} +(270.338 - 468.239i) q^{37} +(1058.79 - 611.291i) q^{38} +(-113.470 - 65.5120i) q^{40} -894.280i q^{41} -1246.82 q^{43} +(40.1177 - 69.4860i) q^{44} +(1303.65 + 2257.99i) q^{46} +(-1516.17 - 875.364i) q^{47} +(-2303.00 - 678.964i) q^{49} +1672.93 q^{50} +(-1317.88 + 760.879i) q^{52} +(406.101 + 703.388i) q^{53} -58.0754i q^{55} +(-158.392 + 1097.37i) q^{56} +(1241.51 - 2150.36i) q^{58} +(-2472.07 + 1427.25i) q^{59} +(5052.57 + 2917.10i) q^{61} +2048.35i q^{62} +512.000 q^{64} +(-550.733 + 953.898i) q^{65} +(1101.89 + 1908.54i) q^{67} +(2922.12 + 1687.08i) q^{68} +(297.859 + 745.199i) q^{70} -3408.24 q^{71} +(-8136.88 + 4697.83i) q^{73} +(764.630 + 1324.38i) q^{74} +3457.98i q^{76} +(-456.339 + 182.401i) q^{77} +(-1176.12 + 2037.09i) q^{79} +(320.942 - 185.296i) q^{80} +(2190.53 + 1264.70i) q^{82} +3750.16i q^{83} +2442.26 q^{85} +(1763.27 - 3054.07i) q^{86} +(113.470 + 196.536i) q^{88} +(5511.35 + 3181.98i) q^{89} +(9225.16 + 1331.54i) q^{91} -7374.58 q^{92} +(4288.39 - 2475.90i) q^{94} +(1251.47 + 2167.60i) q^{95} -6370.47i q^{97} +(4920.05 - 4680.97i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{4} - 54 q^{5} - 28 q^{7} - 96 q^{10} + 54 q^{11} - 128 q^{16} - 918 q^{17} + 30 q^{19} + 192 q^{22} + 486 q^{23} - 572 q^{25} + 1728 q^{26} + 1456 q^{28} - 3240 q^{29} - 546 q^{31} + 1890 q^{35}+ \cdots - 8910 q^{95}+O(q^{100}) $ 4 * q - 16 * q^4 - 54 * q^5 - 28 * q^7 - 96 * q^10 + 54 * q^11 - 128 * q^16 - 918 * q^17 + 30 * q^19 + 192 * q^22 + 486 * q^23 - 572 * q^25 + 1728 * q^26 + 1456 * q^28 - 3240 * q^29 - 546 * q^31 + 1890 * q^35 - 446 * q^37 + 4320 * q^38 + 768 * q^40 + 2344 * q^43 + 432 * q^44 + 3840 * q^46 - 702 * q^47 - 9212 * q^49 + 3456 * q^50 - 384 * q^52 - 2754 * q^53 + 384 * q^58 - 12366 * q^59 + 7686 * q^61 + 2048 * q^64 + 3024 * q^65 - 5062 * q^67 + 7344 * q^68 - 2016 * q^70 - 18792 * q^71 - 17274 * q^73 + 4320 * q^74 - 4914 * q^77 + 794 * q^79 + 3456 * q^80 + 9984 * q^82 + 10380 * q^85 + 10368 * q^86 - 768 * q^88 + 12474 * q^89 + 2688 * q^91 - 7776 * q^92 + 15168 * q^94 - 8910 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.41421	+	2.44949i	−0.353553	+	0.612372i
$2$	−1.41421	+	2.44949i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−4.00000	−	6.92820i	−0.250000	−	0.433013i
$5$	−5.01472	−	2.89525i	−0.200589	−	0.115810i	0.396341	−	0.918103i	$-0.370280\pi$
$5$	−5.01472	−	2.89525i	−0.200589	−	0.115810i	−0.596930	+	0.802293i	$0.703613\pi$
$6$		0			0
$7$	−7.00000	+	48.4974i	−0.142857	+	0.989743i
$7$	−7.00000	+	48.4974i	−0.142857	+	0.989743i
$8$	22.6274			0.353553
$9$		0			0
$10$	14.1838	−	8.18900i	0.141838	−	0.0818900i
$11$	5.01472	+	8.68575i	0.0414440	+	0.0717830i	0.886003	−	0.463679i	$-0.153471\pi$
$11$	5.01472	+	8.68575i	0.0414440	+	0.0717830i	−0.844559	+	0.535462i	$0.820138\pi$
$12$		0			0
$13$		−	190.220i		−	1.12556i	−0.826607	−	0.562780i	$-0.809732\pi$
$13$		−	190.220i		−	1.12556i	0.826607	−	0.562780i	$-0.190268\pi$
$14$	−108.894	−	85.7321i	−0.555584	−	0.437409i
$15$		0			0
$16$	−32.0000	+	55.4256i	−0.125000	+	0.216506i
$17$	−365.265	+	210.886i	−1.26389	+	0.729708i	−0.973825	−	0.227299i	$-0.927011\pi$
$17$	−365.265	+	210.886i	−1.26389	+	0.729708i	−0.290066	+	0.957007i	$0.593677\pi$
$18$		0			0
$19$	−374.338	−	216.124i	−1.03695	−	0.598681i	−0.117980	−	0.993016i	$-0.537642\pi$
$19$	−374.338	−	216.124i	−1.03695	−	0.598681i	−0.918967	+	0.394335i	$0.870975\pi$
$20$			46.3240i			0.115810i
$21$		0			0
$22$	−28.3675			−0.0586106
$23$	460.911	−	798.322i	0.871288	−	1.50911i	0.0106225	−	0.999944i	$-0.496619\pi$
$23$	460.911	−	798.322i	0.871288	−	1.50911i	0.860665	−	0.509171i	$-0.170048\pi$
$24$		0			0
$25$	−295.735	−	512.228i	−0.473176	−	0.819565i
$26$	465.941	+	269.011i	0.689262	+	0.397946i
$27$		0			0
$28$	364.000	−	145.492i	0.464286	−	0.185577i
$29$	−877.882			−1.04386			−0.521928	−	0.852990i	$-0.674787\pi$
$29$	−877.882			−1.04386			−0.521928	+	0.852990i	$0.674787\pi$
$30$		0			0
$31$	627.175	−	362.100i	0.652628	−	0.376795i	−0.136834	−	0.990594i	$-0.543693\pi$
$31$	627.175	−	362.100i	0.652628	−	0.376795i	0.789462	+	0.613799i	$0.210360\pi$
$32$	−90.5097	−	156.767i	−0.0883883	−	0.153093i
$33$		0			0
$34$		−	1192.95i		−	1.03196i
$35$	175.515	−	222.934i	0.143278	−	0.181987i
$36$		0			0
$37$	270.338	−	468.239i	0.197471	−	0.342030i	−0.750237	−	0.661169i	$-0.770061\pi$
$37$	270.338	−	468.239i	0.197471	−	0.342030i	0.947708	+	0.319140i	$0.103394\pi$
$38$	1058.79	−	611.291i	0.733232	−	0.423332i
$39$		0			0
$40$	−113.470	−	65.5120i	−0.0709188	−	0.0409450i
$41$		−	894.280i		−	0.531993i	−0.963974	−	0.265996i	$-0.914299\pi$
$41$		−	894.280i		−	0.531993i	0.963974	−	0.265996i	$-0.0857009\pi$
$42$		0			0
$43$	−1246.82			−0.674322			−0.337161	−	0.941447i	$-0.609467\pi$
$43$	−1246.82			−0.674322			−0.337161	+	0.941447i	$0.609467\pi$
$44$	40.1177	−	69.4860i	0.0207220	−	0.0358915i
$45$		0			0
$46$	1303.65	+	2257.99i	0.616094	+	1.06711i
$47$	−1516.17	−	875.364i	−0.686362	−	0.396271i	0.115886	−	0.993263i	$-0.463029\pi$
$47$	−1516.17	−	875.364i	−0.686362	−	0.396271i	−0.802248	+	0.596991i	$0.796363\pi$
$48$		0			0
$49$	−2303.00	−	678.964i	−0.959184	−	0.282784i
$50$	1672.93			0.669172
$51$		0			0
$52$	−1317.88	+	760.879i	−0.487382	+	0.281390i
$53$	406.101	+	703.388i	0.144571	+	0.250405i	0.929213	−	0.369545i	$-0.120486\pi$
$53$	406.101	+	703.388i	0.144571	+	0.250405i	−0.784642	+	0.619950i	$0.787153\pi$
$54$		0			0
$55$		−	58.0754i		−	0.0191985i
$56$	−158.392	+	1097.37i	−0.0505076	+	0.349927i
$57$		0			0
$58$	1241.51	−	2150.36i	0.369059	−	0.639228i
$59$	−2472.07	+	1427.25i	−0.710162	+	0.410012i	−0.811121	−	0.584878i	$-0.801142\pi$
$59$	−2472.07	+	1427.25i	−0.710162	+	0.410012i	0.100959	+	0.994891i	$0.467809\pi$
$60$		0			0
$61$	5052.57	+	2917.10i	1.35785	+	0.783956i	0.989334	−	0.145664i	$-0.0465319\pi$
$61$	5052.57	+	2917.10i	1.35785	+	0.783956i	0.368518	+	0.929620i	$0.379865\pi$
$62$			2048.35i			0.532868i
$63$		0			0
$64$	512.000			0.125000
$65$	−550.733	+	953.898i	−0.130351	+	0.225775i
$66$		0			0
$67$	1101.89	+	1908.54i	0.245465	+	0.425158i	0.962262	−	0.272124i	$-0.0877259\pi$
$67$	1101.89	+	1908.54i	0.245465	+	0.425158i	−0.716797	+	0.697282i	$0.754393\pi$
$68$	2922.12	+	1687.08i	0.631946	+	0.364854i
$69$		0			0
$70$	297.859	+	745.199i	0.0607876	+	0.152081i
$71$	−3408.24			−0.676103			−0.338052	−	0.941128i	$-0.609768\pi$
$71$	−3408.24			−0.676103			−0.338052	+	0.941128i	$0.609768\pi$
$72$		0			0
$73$	−8136.88	+	4697.83i	−1.52690	+	0.881559i	−0.527416	+	0.849607i	$0.676839\pi$
$73$	−8136.88	+	4697.83i	−1.52690	+	0.881559i	−0.999489	+	0.0319515i	$0.989828\pi$
$74$	764.630	+	1324.38i	0.139633	+	0.241851i
$75$		0			0
$76$			3457.98i			0.598681i
$77$	−456.339	+	182.401i	−0.0769673	+	0.0307642i
$78$		0			0
$79$	−1176.12	+	2037.09i	−0.188450	+	0.326405i	−0.944734	−	0.327839i	$-0.893680\pi$
$79$	−1176.12	+	2037.09i	−0.188450	+	0.326405i	0.756284	+	0.654244i	$0.227013\pi$
$80$	320.942	−	185.296i	0.0501472	−	0.0289525i
$81$		0			0
$82$	2190.53	+	1264.70i	0.325778	+	0.188088i
$83$			3750.16i			0.544370i	0.962245	+	0.272185i	$0.0877462\pi$
$83$			3750.16i			0.544370i	−0.962245	+	0.272185i	$0.912254\pi$
$84$		0			0
$85$	2442.26			0.338030
$86$	1763.27	−	3054.07i	0.238409	−	0.412936i
$87$		0			0
$88$	113.470	+	196.536i	0.0146527	+	0.0253791i
$89$	5511.35	+	3181.98i	0.695790	+	0.401714i	0.805777	−	0.592219i	$-0.201748\pi$
$89$	5511.35	+	3181.98i	0.695790	+	0.401714i	−0.109988	+	0.993933i	$0.535081\pi$
$90$		0			0
$91$	9225.16	+	1331.54i	1.11402	+	0.160794i
$92$	−7374.58			−0.871288
$93$		0			0
$94$	4288.39	−	2475.90i	0.485331	−	0.280206i
$95$	1251.47	+	2167.60i	0.138667	+	0.240177i
$96$		0			0
$97$		−	6370.47i		−	0.677062i	−0.940955	−	0.338531i	$-0.890070\pi$
$97$		−	6370.47i		−	0.677062i	0.940955	−	0.338531i	$-0.109930\pi$
$98$	4920.05	−	4680.97i	0.512292	−	0.487398i
$99$		0			0
$100$	−2365.88	+	4097.83i	−0.236588	+	0.409783i
$101$	−7890.21	+	4555.42i	−0.773474	+	0.446566i	−0.834113	−	0.551594i	$-0.814020\pi$
$101$	−7890.21	+	4555.42i	−0.773474	+	0.446566i	0.0606384	+	0.998160i	$0.480686\pi$
$102$		0			0
$103$	−13953.3	−	8055.91i	−1.31523	−	0.759347i	−0.332271	−	0.943184i	$-0.607815\pi$
$103$	−13953.3	−	8055.91i	−1.31523	−	0.759347i	−0.982957	+	0.183837i	$0.941148\pi$
$104$		−	4304.18i		−	0.397946i
$105$		0			0
$106$	−2297.26			−0.204455
$107$	10275.7	−	17798.0i	0.897518	−	1.55455i	0.0668618	−	0.997762i	$-0.478701\pi$
$107$	10275.7	−	17798.0i	0.897518	−	1.55455i	0.830657	−	0.556785i	$-0.187965\pi$
$108$		0			0
$109$	7128.87	+	12347.6i	0.600023	+	1.03927i	0.992817	+	0.119643i	$0.0381751\pi$
$109$	7128.87	+	12347.6i	0.600023	+	1.03927i	−0.392794	+	0.919626i	$0.628492\pi$
$110$	142.255	+	82.1311i	0.0117566	+	0.00678769i
$111$		0			0
$112$	−2464.00	−	1939.90i	−0.196429	−	0.154647i
$113$	10304.7			0.807010			0.403505	−	0.914978i	$-0.367792\pi$
$113$	10304.7			0.807010			0.403505	+	0.914978i	$0.367792\pi$
$114$		0			0
$115$	−4622.68	+	2668.91i	−0.349541	+	0.201808i
$116$	3511.53	+	6082.15i	0.260964	+	0.452003i
$117$		0			0
$118$		−	8073.76i		−	0.579845i
$119$	−7670.55	−	19190.6i	−0.541668	−	1.35517i
$120$		0			0
$121$	7270.21	−	12592.4i	0.496565	−	0.860075i
$122$	−14290.8	+	8250.81i	−0.960147	+	0.554341i
$123$		0			0
$124$	−5017.40	−	2896.80i	−0.326314	−	0.188397i
$125$			7043.97i			0.450814i
$126$		0			0
$127$	−2116.70			−0.131236			−0.0656179	−	0.997845i	$-0.520902\pi$
$127$	−2116.70			−0.131236			−0.0656179	+	0.997845i	$0.520902\pi$
$128$	−724.077	+	1254.14i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−1557.71	−	2698.03i	−0.0921721	−	0.159647i
$131$	5245.64	+	3028.57i	0.305672	+	0.176480i	0.644988	−	0.764192i	$-0.276862\pi$
$131$	5245.64	+	3028.57i	0.305672	+	0.176480i	−0.339316	+	0.940672i	$0.610196\pi$
$132$		0			0
$133$	13101.8	−	16641.5i	0.740676	−	0.940785i
$134$	−6233.25			−0.347140
$135$		0			0
$136$	−8264.99	+	4771.80i	−0.446853	+	0.257991i
$137$	1430.13	+	2477.05i	0.0761962	+	0.131976i	0.901606	−	0.432559i	$-0.142389\pi$
$137$	1430.13	+	2477.05i	0.0761962	+	0.131976i	−0.825410	+	0.564534i	$0.809056\pi$
$138$		0			0
$139$		−	16966.2i		−	0.878124i	−0.898457	−	0.439062i	$-0.855311\pi$
$139$		−	16966.2i		−	0.878124i	0.898457	−	0.439062i	$-0.144689\pi$
$140$	−2246.59	−	324.268i	−0.114622	−	0.0165443i
$141$		0			0
$142$	4819.98	−	8348.44i	0.239039	−	0.414027i
$143$	1652.20	−	953.898i	0.0807961	−	0.0466477i
$144$		0			0
$145$	4402.33	+	2541.69i	0.209386	+	0.120889i
$146$		−	26574.9i		−	1.24671i
$147$		0			0
$148$	−4325.40			−0.197471
$149$	−7455.05	+	12912.5i	−0.335798	+	0.581619i	−0.983638	−	0.180157i	$-0.942339\pi$
$149$	−7455.05	+	12912.5i	−0.335798	+	0.581619i	0.647840	+	0.761777i	$0.275673\pi$
$150$		0			0
$151$	1080.72	+	1871.87i	0.0473981	+	0.0820959i	0.888751	−	0.458390i	$-0.151574\pi$
$151$	1080.72	+	1871.87i	0.0473981	+	0.0820959i	−0.841353	+	0.540486i	$0.818240\pi$
$152$	−8470.29	−	4890.33i	−0.366616	−	0.211666i
$153$		0			0
$154$	198.573	−	1375.75i	0.00837294	−	0.0580095i
$155$	−4193.48			−0.174546
$156$		0			0
$157$	−35986.6	+	20776.9i	−1.45996	+	0.842909i	−0.999009	−	0.0445152i	$-0.985826\pi$
$157$	−35986.6	+	20776.9i	−1.45996	+	0.842909i	−0.460953	+	0.887425i	$0.652492\pi$
$158$	−3326.56	−	5761.77i	−0.133254	−	0.230803i
$159$		0			0
$160$			1048.19i			0.0409450i
$161$	35490.2	+	27941.3i	1.36917	+	1.07794i
$162$		0			0
$163$	5882.56	−	10188.9i	0.221407	−	0.383488i	−0.733828	−	0.679335i	$-0.762268\pi$
$163$	5882.56	−	10188.9i	0.221407	−	0.383488i	0.955235	+	0.295847i	$0.0956018\pi$
$164$	−6195.75	+	3577.12i	−0.230360	+	0.132998i
$165$		0			0
$166$	−9185.98	−	5303.53i	−0.333357	−	0.192464i
$167$		−	13600.3i		−	0.487660i	−0.969818	−	0.243830i	$-0.921596\pi$
$167$		−	13600.3i		−	0.487660i	0.969818	−	0.243830i	$-0.0784038\pi$
$168$		0			0
$169$	−7622.52			−0.266886
$170$	−3453.88	+	5982.30i	−0.119512	+	0.207000i
$171$		0			0
$172$	4987.28	+	8638.23i	0.168580	+	0.291990i
$173$	−39103.8	−	22576.6i	−1.30655	−	0.754337i	−0.325032	−	0.945703i	$-0.605375\pi$
$173$	−39103.8	−	22576.6i	−1.30655	−	0.754337i	−0.981519	+	0.191366i	$0.938708\pi$
$174$		0			0
$175$	26911.9	−	10756.8i	0.878756	−	0.351242i
$176$	−641.884			−0.0207220
$177$		0			0
$178$	−15588.4	+	9000.00i	−0.491998	+	0.284055i
$179$	9926.19	+	17192.7i	0.309797	+	0.536583i	0.978318	−	0.207110i	$-0.0664057\pi$
$179$	9926.19	+	17192.7i	0.309797	+	0.536583i	−0.668521	+	0.743693i	$0.733072\pi$
$180$		0			0
$181$			21398.5i			0.653170i	0.945168	+	0.326585i	$0.105898\pi$
$181$			21398.5i			0.653170i	−0.945168	+	0.326585i	$0.894102\pi$
$182$	−16307.9	+	20713.9i	−0.492330	+	0.625343i
$183$		0			0
$184$	10429.2	−	18064.0i	0.308047	−	0.533553i
$185$	−2711.33	+	1565.39i	−0.0792209	+	0.0457382i
$186$		0			0
$187$	−3663.40	−	2115.06i	−0.104761	−	0.0604840i
$188$			14005.8i			0.396271i
$189$		0			0
$190$	−7079.36			−0.196104
$191$	5812.94	−	10068.3i	0.159341	−	0.275988i	−0.775290	−	0.631606i	$-0.782396\pi$
$191$	5812.94	−	10068.3i	0.159341	−	0.275988i	0.934631	+	0.355618i	$0.115730\pi$
$192$		0			0
$193$	26273.5	+	45507.0i	0.705347	+	1.22170i	0.966566	+	0.256417i	$0.0825420\pi$
$193$	26273.5	+	45507.0i	0.705347	+	1.22170i	−0.261220	+	0.965279i	$0.584125\pi$
$194$	15604.4	+	9009.21i	0.414614	+	0.239377i
$195$		0			0
$196$	4508.00	+	18671.5i	0.117347	+	0.486035i
$197$	54811.7			1.41235			0.706173	−	0.708039i	$-0.250420\pi$
$197$	54811.7			1.41235			0.706173	+	0.708039i	$0.250420\pi$
$198$		0			0
$199$	5172.66	−	2986.44i	0.130619	−	0.0754131i	−0.433266	−	0.901266i	$-0.642639\pi$
$199$	5172.66	−	2986.44i	0.130619	−	0.0754131i	0.563886	+	0.825853i	$0.309306\pi$
$200$	−6691.72	−	11590.4i	−0.167293	−	0.289760i
$201$		0			0
$202$		−	25769.3i		−	0.631539i
$203$	6145.18	−	42575.0i	0.149122	−	1.03315i
$204$		0			0
$205$	−2589.16	+	4484.56i	−0.0616101	+	0.106712i
$206$	39465.8	−	22785.6i	0.930007	−	0.536940i
$207$		0			0
$208$	10543.0	+	6087.03i	0.243691	+	0.140695i
$209$		−	4335.20i		−	0.0992469i
$210$		0			0
$211$	3042.82			0.0683457			0.0341729	−	0.999416i	$-0.489120\pi$
$211$	3042.82			0.0683457			0.0341729	+	0.999416i	$0.489120\pi$
$212$	3248.81	−	5627.10i	0.0722857	−	0.125203i
$213$		0			0
$214$	29064.0	+	50340.4i	0.634641	+	1.09923i
$215$	6252.46	+	3609.86i	0.135261	+	0.0780932i
$216$		0			0
$217$	13170.7	+	32951.1i	0.279698	+	0.699762i
$218$	−40327.0			−0.848560
$219$		0			0
$220$	−402.358	+	232.302i	−0.00831319	+	0.00479962i
$221$	40114.6	+	69480.5i	0.821330	+	1.42259i
$222$		0			0
$223$		−	42104.7i		−	0.846683i	−0.905970	−	0.423341i	$-0.860857\pi$
$223$		−	42104.7i		−	0.846683i	0.905970	−	0.423341i	$-0.139143\pi$
$224$	8236.38	−	3292.11i	0.164150	−	0.0656113i
$225$		0			0
$226$	−14573.1	+	25241.3i	−0.285321	+	0.494190i
$227$	−79838.4	+	46094.7i	−1.54939	+	0.894540i	−0.551200	+	0.834373i	$0.685830\pi$
$227$	−79838.4	+	46094.7i	−1.54939	+	0.894540i	−0.998188	+	0.0601663i	$0.980837\pi$
$228$		0			0
$229$	−20752.6	−	11981.5i	−0.395733	−	0.228477i	0.288908	−	0.957357i	$-0.406708\pi$
$229$	−20752.6	−	11981.5i	−0.395733	−	0.228477i	−0.684641	+	0.728880i	$0.740041\pi$
$230$		−	15097.6i		−	0.285399i
$231$		0			0
$232$	−19864.2			−0.369059
$233$	−17674.1	+	30612.4i	−0.325555	+	0.563878i	−0.981625	−	0.190822i	$-0.938885\pi$
$233$	−17674.1	+	30612.4i	−0.325555	+	0.563878i	0.656069	+	0.754701i	$0.272218\pi$
$234$		0			0
$235$	5068.79	+	8779.41i	0.0917844	+	0.158975i
$236$	19776.6	+	11418.0i	0.355081	+	0.205006i
$237$		0			0
$238$	57854.9	+	8350.64i	1.02138	+	0.147423i
$239$	−14393.5			−0.251983			−0.125992	−	0.992031i	$-0.540211\pi$
$239$	−14393.5			−0.251983			−0.125992	+	0.992031i	$0.540211\pi$
$240$		0			0
$241$	6495.14	−	3749.97i	0.111829	−	0.0645645i	−0.443042	−	0.896501i	$-0.646101\pi$
$241$	6495.14	−	3749.97i	0.111829	−	0.0645645i	0.554871	+	0.831936i	$0.312768\pi$
$242$	20563.2	+	35616.6i	0.351124	+	0.608165i
$243$		0			0
$244$		−	46673.6i		−	0.783956i
$245$	9583.13	+	10072.6i	0.159652	+	0.167806i
$246$		0			0
$247$	−41111.0	+	71206.4i	−0.673852	+	1.16715i
$248$	14191.4	−	8193.38i	0.230739	−	0.133217i
$249$		0			0
$250$	−17254.1	−	9961.68i	−0.276066	−	0.159387i
$251$		−	45414.9i		−	0.720860i	−0.932786	−	0.360430i	$-0.882630\pi$
$251$		−	45414.9i		−	0.720860i	0.932786	−	0.360430i	$-0.117370\pi$
$252$		0			0
$253$	9245.36			0.144438
$254$	2993.47	−	5184.84i	0.0463988	−	0.0803652i
$255$		0			0
$256$	−2048.00	−	3547.24i	−0.0312500	−	0.0541266i
$257$	−44797.7	−	25864.0i	−0.678250	−	0.391588i	0.120946	−	0.992659i	$-0.461407\pi$
$257$	−44797.7	−	25864.0i	−0.678250	−	0.391588i	−0.799195	+	0.601072i	$0.794741\pi$
$258$		0			0
$259$	20816.0	+	16388.3i	0.310311	+	0.244307i
$260$	8811.73			0.130351
$261$		0			0
$262$	−14836.9	+	8566.10i	−0.216143	+	0.124790i
$263$	−44917.0	−	77798.4i	−0.649380	−	1.12476i	−0.983271	−	0.182147i	$-0.941695\pi$
$263$	−44917.0	−	77798.4i	−0.649380	−	1.12476i	0.333891	−	0.942612i	$-0.391638\pi$
$264$		0			0
$265$		−	4703.06i		−	0.0669713i
$266$	22234.5	+	55627.5i	0.314242	+	0.786187i
$267$		0			0
$268$	8815.15	−	15268.3i	0.122733	−	0.212579i
$269$	20580.0	−	11881.9i	0.284408	−	0.164203i	−0.351009	−	0.936372i	$-0.614162\pi$
$269$	20580.0	−	11881.9i	0.284408	−	0.164203i	0.635417	+	0.772169i	$0.280828\pi$
$270$		0			0
$271$	−95971.7	−	55409.3i	−1.30679	−	0.754473i	−0.325228	−	0.945636i	$-0.605441\pi$
$271$	−95971.7	−	55409.3i	−1.30679	−	0.754473i	−0.981558	+	0.191162i	$0.938774\pi$
$272$		−	26993.4i		−	0.364854i
$273$		0			0
$274$	−8090.01			−0.107758
$275$	2966.06	−	5137.36i	0.0392206	−	0.0679320i
$276$		0			0
$277$	3561.19	+	6168.17i	0.0464126	+	0.0803890i	0.888298	−	0.459267i	$-0.151888\pi$
$277$	3561.19	+	6168.17i	0.0464126	+	0.0803890i	−0.841886	+	0.539656i	$0.818554\pi$
$278$	41558.6	+	23993.9i	0.537739	+	0.310464i
$279$		0			0
$280$	3971.45	−	5044.42i	0.0506563	−	0.0643422i
$281$	−90209.2			−1.14245			−0.571226	−	0.820792i	$-0.693532\pi$
$281$	−90209.2			−1.14245			−0.571226	+	0.820792i	$0.693532\pi$
$282$		0			0
$283$	−62743.0	+	36224.7i	−0.783415	+	0.452305i	−0.837639	−	0.546224i	$-0.816065\pi$
$283$	−62743.0	+	36224.7i	−0.783415	+	0.452305i	0.0542240	+	0.998529i	$0.482732\pi$
$284$	13632.9	+	23613.0i	0.169026	+	0.292761i
$285$		0			0
$286$			5396.06i			0.0659698i
$287$	43370.3	+	6259.96i	0.526536	+	0.0759990i
$288$		0			0
$289$	47184.9	−	81726.7i	0.564947	−	0.978517i
$290$	−12451.7	+	7188.98i	−0.148058	+	0.0854813i
$291$		0			0
$292$	65095.0	+	37582.6i	0.763452	+	0.440779i
$293$			89167.8i			1.03866i	0.854574	+	0.519329i	$0.173818\pi$
$293$			89167.8i			1.03866i	−0.854574	+	0.519329i	$0.826182\pi$
$294$		0			0
$295$	16529.0			0.189934
$296$	6117.04	−	10595.0i	0.0698165	−	0.120926i
$297$		0			0
$298$	−21086.1	−	36522.2i	−0.237445	−	0.411267i
$299$	−151856.	−	87674.4i	−1.69860	−	0.980687i
$300$		0			0
$301$	8727.75	−	60467.6i	0.0963317	−	0.667405i
$302$	−6113.49			−0.0670310
$303$		0			0
$304$	23957.6	−	13831.9i	0.259237	−	0.149670i
$305$	−16891.5	−	29256.9i	−0.181580	−	0.314506i
$306$		0			0
$307$		−	113110.i		−	1.20012i	−0.799954	−	0.600061i	$-0.795143\pi$
$307$		−	113110.i		−	1.20012i	0.799954	−	0.600061i	$-0.204857\pi$
$308$	3089.07	+	2432.01i	0.0325631	+	0.0256368i
$309$		0			0
$310$	5930.47	−	10271.9i	0.0617115	−	0.106887i
$311$	56589.7	−	32672.1i	0.585082	−	0.337797i	−0.178068	−	0.984018i	$-0.556985\pi$
$311$	56589.7	−	32672.1i	0.585082	−	0.337797i	0.763151	+	0.646221i	$0.223651\pi$
$312$		0			0
$313$	1696.42	+	979.430i	0.0173159	+	0.00999734i	0.508633	−	0.860983i	$-0.330151\pi$
$313$	1696.42	+	979.430i	0.0173159	+	0.00999734i	−0.491317	+	0.870981i	$0.663484\pi$
$314$		−	117532.i		−	1.19205i
$315$		0			0
$316$	18817.8			0.188450
$317$	−43075.6	+	74609.1i	−0.428660	+	0.742461i	−0.996754	−	0.0805027i	$-0.974347\pi$
$317$	−43075.6	+	74609.1i	−0.428660	+	0.742461i	0.568095	+	0.822963i	$0.307681\pi$
$318$		0			0
$319$	−4402.33	−	7625.06i	−0.0432615	−	0.0749311i
$320$	−2567.54	−	1482.37i	−0.0250736	−	0.0144762i
$321$		0			0
$322$	−118633.	+	47417.9i	−1.14417	+	0.457331i
$323$	182310.			1.74745
$324$		0			0
$325$	−97435.9	+	56254.6i	−0.922470	+	0.532588i
$326$	16638.4	+	28818.5i	0.156558	+	0.271167i
$327$		0			0
$328$		−	20235.2i		−	0.188088i
$329$	53066.1	−	67403.0i	0.490259	−	0.622712i
$330$		0			0
$331$	45311.1	−	78481.2i	0.413570	−	0.716324i	−0.581707	−	0.813398i	$-0.697615\pi$
$331$	45311.1	−	78481.2i	0.413570	−	0.716324i	0.995277	+	0.0970742i	$0.0309484\pi$
$332$	25981.9	−	15000.6i	0.235719	−	0.136092i
$333$		0			0
$334$	33313.9	+	19233.8i	0.298629	+	0.172414i
$335$		−	12761.0i		−	0.113709i
$336$		0			0
$337$	−26197.5			−0.230675			−0.115338	−	0.993326i	$-0.536795\pi$
$337$	−26197.5			−0.230675			−0.115338	+	0.993326i	$0.536795\pi$
$338$	10779.9	−	18671.3i	0.0943583	−	0.163433i
$339$		0			0
$340$	−9769.06	−	16920.5i	−0.0845074	−	0.146371i
$341$	6290.22	+	3631.66i	0.0540950	+	0.0312317i
$342$		0			0
$343$	49049.0	−	106937.i	0.416910	−	0.908948i
$344$	−28212.3			−0.238409
$345$		0			0
$346$	110602.	−	63856.2i	0.923871	−	0.533397i
$347$	−80330.4	−	139136.i	−0.667146	−	1.15553i	−0.978699	−	0.205302i	$-0.934182\pi$
$347$	−80330.4	−	139136.i	−0.667146	−	1.15553i	0.311553	−	0.950229i	$-0.399151\pi$
$348$		0			0
$349$			18120.2i			0.148769i	0.997230	+	0.0743845i	$0.0236992\pi$
$349$			18120.2i			0.148769i	−0.997230	+	0.0743845i	$0.976301\pi$
$350$	−11710.5	+	81132.8i	−0.0955960	+	0.662309i
$351$		0			0
$352$	907.761	−	1572.29i	0.00732633	−	0.0126896i
$353$	11457.1	−	6614.74i	0.0919441	−	0.0530839i	−0.453323	−	0.891346i	$-0.649762\pi$
$353$	11457.1	−	6614.74i	0.0919441	−	0.0530839i	0.545267	+	0.838262i	$0.316428\pi$
$354$		0			0
$355$	17091.4	+	9867.70i	0.135619	+	0.0782995i
$356$		−	50911.7i		−	0.401714i
$357$		0			0
$358$	−56151.0			−0.438119
$359$	−53867.4	+	93301.1i	−0.417962	+	0.723932i	−0.995734	−	0.0922663i	$-0.970589\pi$
$359$	−53867.4	+	93301.1i	−0.417962	+	0.723932i	0.577772	+	0.816198i	$0.303922\pi$
$360$		0			0
$361$	28258.6	+	48945.4i	0.216839	+	0.375575i
$362$	−52415.4	−	30262.0i	−0.399983	−	0.230930i
$363$		0			0
$364$	−27675.5	−	69240.0i	−0.208878	−	0.522582i
$365$	54405.5			0.408373
$366$		0			0
$367$	60991.7	−	35213.6i	0.452834	−	0.261444i	−0.256192	−	0.966626i	$-0.582468\pi$
$367$	60991.7	−	35213.6i	0.452834	−	0.261444i	0.709026	+	0.705182i	$0.249135\pi$
$368$	29498.3	+	51092.6i	0.217822	+	0.377279i
$369$		0			0
$370$		−	8855.18i		−	0.0646836i
$371$	−36955.2	+	14771.1i	−0.268490	+	0.107316i
$372$		0			0
$373$	−95526.7	+	165457.i	−0.686605	+	1.18924i	0.286324	+	0.958133i	$0.407567\pi$
$373$	−95526.7	+	165457.i	−0.686605	+	1.18924i	−0.972929	+	0.231102i	$0.925767\pi$
$374$	10361.7	−	5982.30i	0.0740774	−	0.0427686i
$375$		0			0
$376$	−34307.1	−	19807.2i	−0.242666	−	0.140103i
$377$			166990.i			1.17492i
$378$		0			0
$379$	74979.5			0.521992			0.260996	−	0.965340i	$-0.415949\pi$
$379$	74979.5			0.521992			0.260996	+	0.965340i	$0.415949\pi$
$380$	10011.7	−	17340.8i	0.0693333	−	0.120089i
$381$		0			0
$382$	16441.5	+	28477.5i	0.112671	+	0.195153i
$383$	111403.	+	64318.4i	0.759449	+	0.438468i	0.829098	−	0.559104i	$-0.188855\pi$
$383$	111403.	+	64318.4i	0.759449	+	0.438468i	−0.0696492	+	0.997572i	$0.522188\pi$
$384$		0			0
$385$	2816.51	+	406.528i	0.0190016	+	0.00274264i
$386$	−148625.			−0.997511
$387$		0			0
$388$	−44135.9	+	25481.9i	−0.293176	+	0.169265i
$389$	13154.0	+	22783.4i	0.0869278	+	0.150563i	0.906211	−	0.422826i	$-0.138962\pi$
$389$	13154.0	+	22783.4i	0.0869278	+	0.150563i	−0.819283	+	0.573389i	$0.805628\pi$
$390$		0			0
$391$			388798.i			2.54314i
$392$	−52110.9	−	15363.2i	−0.339123	−	0.0999792i
$393$		0			0
$394$	−77515.5	+	134261.i	−0.499340	+	0.864882i
$395$	11795.8	−	6810.30i	0.0756018	−	0.0436487i
$396$		0			0
$397$	−76233.0	−	44013.1i	−0.483684	−	0.279255i	0.238266	−	0.971200i	$-0.423421\pi$
$397$	−76233.0	−	44013.1i	−0.483684	−	0.279255i	−0.721951	+	0.691945i	$0.756754\pi$
$398$			16893.8i			0.106650i
$399$		0			0
$400$	37854.1			0.236588
$401$	132300.	−	229150.i	0.822755	−	1.42505i	−0.0808687	−	0.996725i	$-0.525769\pi$
$401$	132300.	−	229150.i	0.822755	−	1.42505i	0.903623	−	0.428328i	$-0.140897\pi$
$402$		0			0
$403$	−68878.5	−	119301.i	−0.424105	−	0.734572i
$404$	63121.7	+	36443.3i	0.386737	+	0.223283i
$405$		0			0
$406$	95596.5	+	75262.7i	0.579949	+	0.456592i
$407$	5422.67			0.0327359
$408$		0			0
$409$	121392.	−	70085.4i	0.725674	−	0.418968i	−0.0911633	−	0.995836i	$-0.529059\pi$
$409$	121392.	−	70085.4i	0.725674	−	0.418968i	0.816838	+	0.576868i	$0.195725\pi$
$410$	−7323.26	−	12684.3i	−0.0435649	−	0.0754566i
$411$		0			0
$412$			128895.i			0.759347i
$413$	−51913.6	−	129880.i	−0.304355	−	0.761451i
$414$		0			0
$415$	10857.7	−	18806.0i	0.0630434	−	0.109194i
$416$	−29820.2	+	17216.7i	−0.172316	+	0.0994864i
$417$		0			0
$418$	10619.0	+	6130.90i	0.0607761	+	0.0350891i
$419$			319409.i			1.81936i	0.415306	+	0.909682i	$0.363675\pi$
$419$			319409.i			1.81936i	−0.415306	+	0.909682i	$0.636325\pi$
$420$		0			0
$421$	315726.			1.78134			0.890670	−	0.454651i	$-0.150236\pi$
$421$	315726.			1.78134			0.890670	+	0.454651i	$0.150236\pi$
$422$	−4303.20	+	7453.36i	−0.0241639	+	0.0418530i
$423$		0			0
$424$	9189.02	+	15915.9i	0.0511137	+	0.0885316i
$425$	216043.	+	124733.i	1.19609	+	0.690561i
$426$		0			0
$427$	−176840.	+	224617.i	−0.969895	+	1.23193i
$428$	−164411.			−0.897518
$429$		0			0
$430$	−17684.6	+	10210.2i	−0.0956442	+	0.0552202i
$431$	84265.4	+	145952.i	0.453623	+	0.785698i	0.998608	−	0.0527481i	$-0.0167980\pi$
$431$	84265.4	+	145952.i	0.453623	+	0.785698i	−0.544985	+	0.838446i	$0.683465\pi$
$432$		0			0
$433$		−	17104.3i		−	0.0912284i	−0.998959	−	0.0456142i	$-0.985476\pi$
$433$		−	17104.3i		−	0.0912284i	0.998959	−	0.0456142i	$-0.0145245\pi$
$434$	−99339.5	−	14338.4i	−0.527403	−	0.0761241i
$435$		0			0
$436$	57030.9	−	98780.5i	0.300011	−	0.519635i
$437$	−345073.	+	199228.i	−1.80696	+	1.04325i
$438$		0			0
$439$	192241.	+	110991.i	0.997511	+	0.575913i	0.907511	−	0.420029i	$-0.137980\pi$
$439$	192241.	+	110991.i	0.997511	+	0.575913i	0.0899998	+	0.995942i	$0.471313\pi$
$440$		−	1314.10i		−	0.00678769i
$441$		0			0
$442$	−226922.			−1.16154
$443$	17115.4	−	29644.7i	0.0872124	−	0.151056i	−0.819119	−	0.573623i	$-0.805537\pi$
$443$	17115.4	−	29644.7i	0.0872124	−	0.151056i	0.906332	+	0.422567i	$0.138871\pi$
$444$		0			0
$445$	−18425.2	−	31913.5i	−0.0930450	−	0.161159i
$446$	103135.	+	59545.0i	0.518485	+	0.299348i
$447$		0			0
$448$	−3584.00	+	24830.7i	−0.0178571	+	0.123718i
$449$	187206.			0.928598			0.464299	−	0.885679i	$-0.346306\pi$
$449$	187206.			0.928598			0.464299	+	0.885679i	$0.346306\pi$
$450$		0			0
$451$	7767.49	−	4484.56i	0.0381881	−	0.0220479i
$452$	−41218.8	−	71393.1i	−0.201752	−	0.349445i
$453$		0			0
$454$		−	260751.i		−	1.26507i
$455$	−42406.5	−	33386.4i	−0.204837	−	0.161268i
$456$		0			0
$457$	−73922.5	+	128038.i	−0.353952	+	0.613063i	−0.986938	−	0.161100i	$-0.948496\pi$
$457$	−73922.5	+	128038.i	−0.353952	+	0.613063i	0.632986	+	0.774163i	$0.281829\pi$
$458$	58697.3	−	33888.9i	0.279826	−	0.161557i
$459$		0			0
$460$	36981.4	+	21351.2i	0.174771	+	0.100904i
$461$		−	73979.5i		−	0.348105i	−0.984736	−	0.174052i	$-0.944314\pi$
$461$		−	73979.5i		−	0.348105i	0.984736	−	0.174052i	$-0.0556862\pi$
$462$		0			0
$463$	−66987.3			−0.312486			−0.156243	−	0.987719i	$-0.549938\pi$
$463$	−66987.3			−0.312486			−0.156243	+	0.987719i	$0.549938\pi$
$464$	28092.2	−	48657.2i	0.130482	−	0.226001i
$465$		0			0
$466$	−49989.8	−	86584.9i	−0.230202	−	0.398722i
$467$	−200947.	−	116017.i	−0.921399	−	0.531970i	−0.0373181	−	0.999303i	$-0.511881\pi$
$467$	−200947.	−	116017.i	−0.921399	−	0.531970i	−0.884081	+	0.467333i	$0.845215\pi$
$468$		0			0
$469$	−100272.	+	40079.2i	−0.455864	+	0.182211i
$470$	−28673.4			−0.129803
$471$		0			0
$472$	−55936.7	+	32295.0i	−0.251080	+	0.144961i
$473$	−6252.46	−	10829.6i	−0.0279466	−	0.0484049i
$474$		0			0
$475$			255662.i			1.13313i
$476$	−102274.	+	129906.i	−0.451390	+	0.573342i
$477$		0			0
$478$	20355.5	−	35256.8i	0.0890895	−	0.154308i
$479$	190568.	−	110024.i	0.830575	−	0.479532i	−0.0234748	−	0.999724i	$-0.507473\pi$
$479$	190568.	−	110024.i	0.830575	−	0.479532i	0.854049	+	0.520192i	$0.174140\pi$
$480$		0			0
$481$	−89068.2	−	51423.5i	−0.384975	−	0.222265i
$482$			21213.0i			0.0913079i
$483$		0			0
$484$	−116323.			−0.496565
$485$	−18444.1	+	31946.1i	−0.0784105	+	0.135811i
$486$		0			0
$487$	−69828.1	−	120946.i	−0.294423	−	0.509956i	0.680427	−	0.732816i	$-0.261794\pi$
$487$	−69828.1	−	120946.i	−0.294423	−	0.509956i	−0.974851	+	0.222859i	$0.928461\pi$
$488$	114327.	+	66006.5i	0.480073	+	0.277170i
$489$		0			0
$490$	−38225.2	+	9229.00i	−0.159206	+	0.0384382i
$491$	284872.			1.18164			0.590821	−	0.806802i	$-0.298804\pi$
$491$	284872.			1.18164			0.590821	+	0.806802i	$0.298804\pi$
$492$		0			0
$493$	320659.	−	185133.i	1.31932	−	0.761709i
$494$	−116280.	−	201402.i	−0.476485	−	0.825297i
$495$		0			0
$496$			46348.8i			0.188397i
$497$	23857.7	−	165291.i	0.0965862	−	0.669169i
$498$		0			0
$499$	156787.	−	271562.i	0.629663	−	1.09061i	−0.357957	−	0.933738i	$-0.616526\pi$
$499$	156787.	−	271562.i	0.629663	−	1.09061i	0.987619	−	0.156869i	$-0.0501402\pi$
$500$	48802.0	−	28175.9i	0.195208	−	0.112703i
$501$		0			0
$502$	111243.	+	64226.4i	0.441435	+	0.254862i
$503$		−	192865.i		−	0.762285i	−0.924516	−	0.381143i	$-0.875531\pi$
$503$		−	192865.i		−	0.762285i	0.924516	−	0.381143i	$-0.124469\pi$
$504$		0			0
$505$	52756.2			0.206867
$506$	−13074.9	+	22646.4i	−0.0510667	+	0.0884501i
$507$		0			0
$508$	8466.81	+	14664.9i	0.0328089	+	0.0568267i
$509$	−150044.	−	86628.1i	−0.579141	−	0.334367i	0.181651	−	0.983363i	$-0.441856\pi$
$509$	−150044.	−	86628.1i	−0.579141	−	0.334367i	−0.760792	+	0.648996i	$0.775189\pi$
$510$		0			0
$511$	−170874.	−	427502.i	−0.654388	−	1.63718i
$512$	11585.2			0.0441942
$513$		0			0
$514$	126707.	−	73154.4i	0.479595	−	0.276894i
$515$	46647.8	+	80796.3i	0.175880	+	0.304633i
$516$		0			0
$517$		−	17558.8i		−	0.0656922i
$518$	−69581.4	+	27812.0i	−0.259318	+	0.103651i
$519$		0			0
$520$	−12461.7	+	21584.3i	−0.0460861	+	0.0798234i
$521$	145761.	−	84155.4i	0.536991	−	0.310032i	−0.206868	−	0.978369i	$-0.566327\pi$
$521$	145761.	−	84155.4i	0.536991	−	0.310032i	0.743859	+	0.668337i	$0.232994\pi$
$522$		0			0
$523$	392069.	+	226361.i	1.43337	+	0.827558i	0.997376	−	0.0723902i	$-0.0230627\pi$
$523$	392069.	+	226361.i	1.43337	+	0.827558i	0.435996	+	0.899948i	$0.356396\pi$
$524$		−	48457.2i		−	0.176480i
$525$		0			0
$526$	254089.			0.918362
$527$	−152723.	+	264524.i	−0.549900	+	0.952455i
$528$		0			0
$529$	−284958.	−	493562.i	−1.01828	−	1.76372i
$530$	11520.1	+	6651.13i	0.0410114	+	0.0236779i
$531$		0			0
$532$	−167703.	−	24205.9i	−0.592541	−	0.0855259i
$533$	−170110.			−0.598790
$534$		0			0
$535$	−103059.	+	59501.4i	−0.360064	+	0.207883i
$536$	24933.0	+	43185.2i	0.0867851	+	0.150316i
$537$		0			0
$538$			67214.1i			0.232218i
$539$	−5651.59	−	23408.1i	−0.0194533	−	0.0805728i
$540$		0			0
$541$	7236.20	−	12533.5i	0.0247238	−	0.0428230i	−0.853399	−	0.521259i	$-0.825463\pi$
$541$	7236.20	−	12533.5i	0.0247238	−	0.0428230i	0.878123	+	0.478436i	$0.158796\pi$
$542$	271449.	−	156721.i	0.924038	−	0.533493i
$543$		0			0
$544$	66119.9	+	38174.4i	0.223426	+	0.128995i
$545$		−	82559.4i		−	0.277954i
$546$		0			0
$547$	−370524.			−1.23835			−0.619173	−	0.785255i	$-0.712532\pi$
$547$	−370524.			−1.23835			−0.619173	+	0.785255i	$0.712532\pi$
$548$	11441.0	−	19816.4i	0.0380981	−	0.0659878i
$549$		0			0
$550$	8389.27	+	14530.6i	0.0277331	+	0.0480352i
$551$	328624.	+	189731.i	1.08242	+	0.624937i
$552$		0			0
$553$	−90560.9	−	71298.2i	−0.296135	−	0.233146i
$554$	−20145.1			−0.0656373
$555$		0			0
$556$	−117545.	+	67864.9i	−0.380239	+	0.219531i
$557$	−218641.	−	378697.i	−0.704727	−	1.22062i	−0.966790	−	0.255572i	$-0.917736\pi$
$557$	−218641.	−	378697.i	−0.704727	−	1.22062i	0.262064	−	0.965051i	$-0.415597\pi$
$558$		0			0
$559$			237170.i			0.758990i
$560$	6739.78	+	16861.9i	0.0214917	+	0.0537689i
$561$		0			0
$562$	127575.	−	220967.i	0.403918	−	0.699607i
$563$	3518.41	−	2031.36i	0.0111002	−	0.00640869i	−0.494440	−	0.869212i	$-0.664627\pi$
$563$	3518.41	−	2031.36i	0.0111002	−	0.00640869i	0.505540	+	0.862803i	$0.331293\pi$
$564$		0			0
$565$	−51675.2	−	29834.7i	−0.161877	−	0.0934597i
$566$		−	204918.i		−	0.639656i
$567$		0			0
$568$	−77119.6			−0.239039
$569$	216682.	−	375304.i	0.669266	−	1.15920i	−0.308844	−	0.951113i	$-0.599942\pi$
$569$	216682.	−	375304.i	0.669266	−	1.15920i	0.978110	−	0.208089i	$-0.0667245\pi$
$570$		0			0
$571$	−23818.3	−	41254.5i	−0.0730530	−	0.126532i	0.827185	−	0.561930i	$-0.189941\pi$
$571$	−23818.3	−	41254.5i	−0.0730530	−	0.126532i	−0.900238	+	0.435398i	$0.856608\pi$
$572$	−13217.6	−	7631.18i	−0.0403981	−	0.0233238i
$573$		0			0
$574$	−76668.5	+	97382.1i	−0.232698	+	0.295567i
$575$	−545230.			−1.64909
$576$		0			0
$577$	20898.1	−	12065.5i	0.0627703	−	0.0362404i	−0.468286	−	0.883577i	$-0.655128\pi$
$577$	20898.1	−	12065.5i	0.0627703	−	0.0362404i	0.531057	+	0.847336i	$0.321795\pi$
$578$	133459.	+	231158.i	0.399478	+	0.691916i
$579$		0			0
$580$		−	40667.0i		−	0.120889i
$581$	−181873.	−	26251.1i	−0.538786	−	0.0777671i
$582$		0			0
$583$	−4072.97	+	7054.59i	−0.0119832	+	0.0207556i
$584$	−184117.	+	106300.i	−0.539842	+	0.311678i
$585$		0			0
$586$	−218416.	−	126102.i	−0.636046	−	0.367221i
$587$			680260.i			1.97423i	0.160003	+	0.987117i	$0.448850\pi$
$587$			680260.i			1.97423i	−0.160003	+	0.987117i	$0.551150\pi$
$588$		0			0
$589$	−313034.			−0.902320
$590$	−23375.6	+	40487.6i	−0.0671518	+	0.116310i
$591$		0			0
$592$	17301.6	+	29967.3i	0.0493677	+	0.0855074i
$593$	−305380.	−	176311.i	−0.868422	−	0.501383i	−0.00159823	−	0.999999i	$-0.500509\pi$
$593$	−305380.	−	176311.i	−0.868422	−	0.501383i	−0.866823	+	0.498615i	$0.833842\pi$
$594$		0			0
$595$	−17095.9	+	118444.i	−0.0482900	+	0.334563i
$596$	119281.			0.335798
$597$		0			0
$598$	429515.	−	247981.i	1.20109	−	0.693450i
$599$	−191298.	−	331338.i	−0.533159	−	0.923458i	−0.999250	−	0.0387216i	$-0.987671\pi$
$599$	−191298.	−	331338.i	−0.533159	−	0.923458i	0.466091	−	0.884737i	$-0.345662\pi$
$600$		0			0
$601$		−	8474.87i		−	0.0234630i	−0.999931	−	0.0117315i	$-0.996266\pi$
$601$		−	8474.87i		−	0.0234630i	0.999931	−	0.0117315i	$-0.00373434\pi$
$602$	135772.	+	106893.i	0.374642	+	0.294954i
$603$		0			0
$604$	8645.79	−	14974.9i	0.0236990	−	0.0410479i
$605$	−72916.1	+	42098.1i	−0.199211	+	0.115014i
$606$		0			0
$607$	−192303.	−	111026.i	−0.521926	−	0.301334i	0.215796	−	0.976438i	$-0.430765\pi$
$607$	−192303.	−	111026.i	−0.521926	−	0.301334i	−0.737722	+	0.675104i	$0.764099\pi$
$608$			78245.2i			0.211666i
$609$		0			0
$610$	95552.6			0.256793
$611$	−166511.	+	288406.i	−0.446027	+	0.772542i
$612$		0			0
$613$	−6570.21	−	11379.9i	−0.0174847	−	0.0302844i	0.857151	−	0.515066i	$-0.172233\pi$
$613$	−6570.21	−	11379.9i	−0.0174847	−	0.0302844i	−0.874635	+	0.484781i	$0.838899\pi$
$614$	277063.	+	159962.i	0.734922	+	0.424307i
$615$		0			0
$616$	−10325.8	+	4127.26i	−0.0272121	+	0.0108768i
$617$	235797.			0.619394			0.309697	−	0.950835i	$-0.399772\pi$
$617$	235797.			0.619394			0.309697	+	0.950835i	$0.399772\pi$
$618$		0			0
$619$	535169.	−	308980.i	1.39672	−	0.806397i	0.402673	−	0.915344i	$-0.368081\pi$
$619$	535169.	−	308980.i	1.39672	−	0.806397i	0.994048	+	0.108947i	$0.0347478\pi$
$620$	16773.9	+	29053.3i	0.0436366	+	0.0755808i
$621$		0			0
$622$			184821.i			0.477718i
$623$	−192897.	+	245012.i	−0.496993	+	0.631265i
$624$		0			0
$625$	−164440.	+	284819.i	−0.420967	+	0.729137i
$626$	−4798.21	+	2770.25i	−0.0122442	+	0.00706919i
$627$		0			0
$628$	287893.	+	166215.i	0.729981	+	0.421455i
$629$			228041.i			0.576384i
$630$		0			0
$631$	453628.			1.13931			0.569653	−	0.821885i	$-0.307077\pi$
$631$	453628.			1.13931			0.569653	+	0.821885i	$0.307077\pi$
$632$	−26612.5	+	46094.1i	−0.0666271	+	0.115402i
$633$		0			0
$634$	−121836.	−	211026.i	−0.303108	−	0.524999i
$635$	10614.7	+	6128.38i	0.0263244	+	0.0151984i
$636$		0			0
$637$	−129152.	+	438076.i	−0.318290	+	1.07962i
$638$	24903.4			0.0611810
$639$		0			0
$640$	7262.09	−	4192.77i	0.0177297	−	0.0102363i
$641$	−72469.1	−	125520.i	−0.176375	−	0.305490i	0.764261	−	0.644907i	$-0.223104\pi$
$641$	−72469.1	−	125520.i	−0.176375	−	0.305490i	−0.940636	+	0.339416i	$0.889770\pi$
$642$		0			0
$643$		−	238775.i		−	0.577520i	−0.957401	−	0.288760i	$-0.906757\pi$
$643$		−	238775.i		−	0.577520i	0.957401	−	0.288760i	$-0.0932430\pi$
$644$	51622.1	−	357648.i	0.124470	−	0.862351i
$645$		0			0
$646$	−257825.	+	446566.i	−0.617817	+	1.07009i
$647$	−28818.4	+	16638.3i	−0.0688432	+	0.0397466i	−0.534026	−	0.845468i	$-0.679322\pi$
$647$	−28818.4	+	16638.3i	−0.0688432	+	0.0397466i	0.465183	+	0.885214i	$0.345988\pi$
$648$		0			0
$649$	−24793.5	−	14314.5i	−0.0588639	−	0.0339851i
$650$		−	318224.i		−	0.753193i
$651$		0			0
$652$	−94121.0			−0.221407
$653$	38782.2	−	67172.7i	0.0909507	−	0.157531i	−0.816961	−	0.576693i	$-0.804343\pi$
$653$	38782.2	−	67172.7i	0.0909507	−	0.157531i	0.907911	+	0.419162i	$0.137676\pi$
$654$		0			0
$655$	−17536.9	−	30374.9i	−0.0408763	−	0.0707998i
$656$	49566.0	+	28617.0i	0.115180	+	0.0664991i
$657$		0			0
$658$	90056.2	+	225307.i	0.207999	+	0.520383i
$659$	762599.			1.75600			0.878001	−	0.478658i	$-0.158877\pi$
$659$	762599.			1.75600			0.878001	+	0.478658i	$0.158877\pi$
$660$		0			0
$661$	−432725.	+	249834.i	−0.990396	+	0.571805i	−0.905393	−	0.424575i	$-0.860423\pi$
$661$	−432725.	+	249834.i	−0.990396	+	0.571805i	−0.0850035	+	0.996381i	$0.527090\pi$
$662$	128159.	+	221978.i	0.292438	+	0.506518i
$663$		0			0
$664$			84856.5i			0.192464i
$665$	−113883.	+	45519.6i	−0.257524	+	0.102933i
$666$		0			0
$667$	−404626.	+	700832.i	−0.909498	+	1.57530i
$668$	−94225.9	+	54401.3i	−0.211163	+	0.121915i
$669$		0			0
$670$	31258.0	+	18046.8i	0.0696324	+	0.0402023i
$671$			58513.8i			0.129961i
$672$		0			0
$673$	601790.			1.32866			0.664332	−	0.747438i	$-0.268716\pi$
$673$	601790.			1.32866			0.664332	+	0.747438i	$0.268716\pi$
$674$	37048.9	−	64170.6i	0.0815559	−	0.141259i
$675$		0			0
$676$	30490.1	+	52810.4i	0.0667214	+	0.115565i
$677$	140213.	+	80951.9i	0.305922	+	0.176624i	0.645100	−	0.764098i	$-0.276816\pi$
$677$	140213.	+	80951.9i	0.305922	+	0.176624i	−0.339178	+	0.940722i	$0.610149\pi$
$678$		0			0
$679$	308952.	+	44593.3i	0.670117	+	0.0967231i
$680$	55262.1			0.119512
$681$		0			0
$682$	−17791.4	+	10271.9i	−0.0382509	+	0.0220842i
$683$	−6717.15	−	11634.4i	−0.0143994	−	0.0249404i	0.858736	−	0.512418i	$-0.171250\pi$
$683$	−6717.15	−	11634.4i	−0.0143994	−	0.0249404i	−0.873135	+	0.487478i	$0.837917\pi$
$684$		0			0
$685$		−	16562.3i		−	0.0352971i
$686$	192575.	+	271377.i	0.409215	+	0.576666i
$687$		0			0
$688$	39898.3	−	69105.8i	0.0842902	−	0.145995i
$689$	133798.	−	77248.5i	0.281846	−	0.162724i
$690$		0			0
$691$	−213194.	−	123088.i	−0.446497	−	0.257785i	0.259853	−	0.965648i	$-0.416326\pi$
$691$	−213194.	−	123088.i	−0.446497	−	0.257785i	−0.706350	+	0.707863i	$0.749659\pi$
$692$			361225.i			0.754337i
$693$		0			0
$694$	454417.			0.943487
$695$	−49121.4	+	85080.8i	−0.101695	+	0.176142i
$696$		0			0
$697$	188591.	+	326649.i	0.388199	+	0.672381i
$698$	−44385.3	−	25625.8i	−0.0911020	−	0.0525978i
$699$		0			0
$700$	−182173.	−	143424.i	−0.371781	−	0.292702i
$701$	−750473.			−1.52721			−0.763605	−	0.645683i	$-0.776573\pi$
$701$	−750473.			−1.52721			−0.763605	+	0.645683i	$0.776573\pi$
$702$		0			0
$703$	−202395.	+	116853.i	−0.409533	+	0.236444i
$704$	2567.54	+	4447.10i	0.00518049	+	0.00897288i
$705$		0			0
$706$			37418.6i			0.0750720i
$707$	−165694.	−	414543.i	−0.331489	−	0.829336i
$708$		0			0
$709$	297668.	−	515576.i	0.592161	−	1.02565i	−0.401780	−	0.915736i	$-0.631608\pi$
$709$	297668.	−	515576.i	0.592161	−	1.02565i	0.993941	−	0.109916i	$-0.0350583\pi$
$710$	−48341.6	+	27910.1i	−0.0958969	+	0.0553661i
$711$		0			0
$712$	124708.	+	72000.0i	0.245999	+	0.142027i
$713$		−	667584.i		−	1.31319i
$714$		0			0
$715$	−11047.1			−0.0216091
$716$	79409.5	−	137541.i	0.154898	−	0.268292i
$717$		0			0
$718$	−152360.	−	263895.i	−0.295544	−	0.511897i
$719$	23147.3	+	13364.1i	0.0447757	+	0.0258513i	0.522221	−	0.852810i	$-0.325104\pi$
$719$	23147.3	+	13364.1i	0.0447757	+	0.0258513i	−0.477445	+	0.878662i	$0.658437\pi$
$720$		0			0
$721$	488364.	−	620305.i	0.939449	−	1.19326i
$722$	−159855.			−0.306656
$723$		0			0
$724$	148253.	−	85594.0i	0.282831	−	0.163292i
$725$	259621.	+	449676.i	0.493927	+	0.855507i
$726$		0			0
$727$			514869.i			0.974154i	0.873359	+	0.487077i	$0.161937\pi$
$727$			514869.i			0.974154i	−0.873359	+	0.487077i	$0.838063\pi$
$728$	208742.	+	30129.3i	0.393864	+	0.0568494i
$729$		0			0
$730$	−76941.0	+	133266.i	−0.144382	+	0.250077i
$731$	455419.	−	262936.i	0.852269	−	0.492058i
$732$		0			0
$733$	209395.	+	120894.i	0.389725	+	0.225008i	0.682041	−	0.731314i	$-0.261092\pi$
$733$	209395.	+	120894.i	0.389725	+	0.225008i	−0.292316	+	0.956322i	$0.594426\pi$
$734$			199198.i			0.369737i
$735$		0			0
$736$	−166868.			−0.308047
$737$	−11051.4	+	19141.5i	−0.0203461	+	0.0352405i
$738$		0			0
$739$	335761.	+	581555.i	0.614811	+	1.06488i	0.990418	+	0.138105i	$0.0441010\pi$
$739$	335761.	+	581555.i	0.614811	+	1.06488i	−0.375607	+	0.926779i	$0.622566\pi$
$740$	21690.7	+	12523.1i	0.0396104	+	0.0228691i
$741$		0			0
$742$	16080.8	−	111411.i	0.0292079	−	0.202358i
$743$	134542.			0.243714			0.121857	−	0.992548i	$-0.461115\pi$
$743$	134542.			0.243714			0.121857	+	0.992548i	$0.461115\pi$
$744$		0			0
$745$	74770.0	−	43168.5i	0.134715	−	0.0777775i
$746$	−270190.	−	467983.i	−0.485503	−	0.840916i
$747$		0			0
$748$			33841.0i			0.0604840i
$749$	791228.	+	622930.i	1.41039	+	1.11039i
$750$		0			0
$751$	−223281.	+	386733.i	−0.395887	+	0.685696i	−0.993214	−	0.116302i	$-0.962896\pi$
$751$	−223281.	+	386733.i	−0.395887	+	0.685696i	0.597327	+	0.801998i	$0.296229\pi$
$752$	97035.2	−	56023.3i	0.171591	−	0.0990679i
$753$		0			0
$754$	−409041.	−	236160.i	−0.719490	−	0.415398i
$755$		−	12515.9i		−	0.0219567i
$756$		0			0
$757$	−939360.			−1.63923			−0.819616	−	0.572913i	$-0.805813\pi$
$757$	−939360.			−1.63923			−0.819616	+	0.572913i	$0.805813\pi$
$758$	−106037.	+	183662.i	−0.184552	+	0.319654i
$759$		0			0
$760$	28317.4	+	49047.2i	0.0490260	+	0.0849156i
$761$	−858619.	−	495724.i	−1.48262	−	0.855994i	−0.482819	−	0.875720i	$-0.660387\pi$
$761$	−858619.	−	495724.i	−1.48262	−	0.855994i	−0.999805	+	0.0197266i	$0.993720\pi$
$762$		0			0
$763$	−648727.	+	259299.i	−1.11433	+	0.445401i
$764$	−93007.0			−0.159341
$765$		0			0
$766$	−315095.	+	181920.i	−0.537011	+	0.310044i
$767$	271492.	+	470237.i	0.461494	+	0.799330i
$768$		0			0
$769$		−	180922.i		−	0.305942i	−0.988231	−	0.152971i	$-0.951116\pi$
$769$		−	180922.i		−	0.305942i	0.988231	−	0.152971i	$-0.0488841\pi$
$770$	−4978.93	+	6324.09i	−0.00839759	+	0.0106664i
$771$		0			0
$772$	210188.	−	364056.i	0.352673	−	0.610848i
$773$	16688.7	−	9635.20i	0.0279295	−	0.0161251i	−0.485970	−	0.873975i	$-0.661534\pi$
$773$	16688.7	−	9635.20i	0.0279295	−	0.0161251i	0.513900	+	0.857850i	$0.328200\pi$
$774$		0			0
$775$	−370955.	−	214171.i	−0.617616	−	0.356581i
$776$		−	144147.i		−	0.239377i
$777$		0			0
$778$	−74410.3			−0.122935
$779$	−193275.	+	334763.i	−0.318494	+	0.551648i
$780$		0			0
$781$	−17091.4	−	29603.1i	−0.0280204	−	0.0485328i
$782$	−952357.	−	549844.i	−1.55735	−	0.899137i
$783$		0			0
$784$	111328.	−	105918.i	0.181122	−	0.172321i
$785$	240617.			0.390469
$786$		0			0
$787$	240896.	−	139081.i	0.388938	−	0.224553i	−0.292762	−	0.956185i	$-0.594574\pi$
$787$	240896.	−	139081.i	0.388938	−	0.224553i	0.681700	+	0.731632i	$0.261241\pi$
$788$	−219247.	−	379747.i	−0.353086	−	0.611564i
$789$		0			0
$790$			38524.8i			0.0617286i
$791$	−72132.9	+	499752.i	−0.115287	+	0.798732i
$792$		0			0
$793$	554890.	−	961098.i	0.882390	−	1.52834i
$794$	215619.	−	124488.i	0.342016	−	0.197463i
$795$		0			0
$796$	−41381.3	−	23891.5i	−0.0653097	−	0.0377066i
$797$			60214.6i			0.0947950i	0.998876	+	0.0473975i	$0.0150927\pi$
$797$			60214.6i			0.0947950i	−0.998876	+	0.0473975i	$0.984907\pi$
$798$		0			0
$799$	738406.			1.15665
$800$	−53533.8	+	92723.2i	−0.0836465	+	0.144880i
$801$		0			0
$802$	374200.	+	648134.i	0.581775	+	1.00766i
$803$	−81608.3	−	47116.6i	−0.126562	−	0.0730706i
$804$		0			0
$805$	−97076.3	−	242870.i	−0.149803	−	0.374786i
$806$	389636.			0.599775
$807$		0			0
$808$	−178535.	+	103077.i	−0.273464	+	0.157885i
$809$	35236.9	+	61032.2i	0.0538395	+	0.0932528i	0.891689	−	0.452648i	$-0.149521\pi$
$809$	35236.9	+	61032.2i	0.0538395	+	0.0932528i	−0.837850	+	0.545901i	$0.816187\pi$
$810$		0			0
$811$		−	1.08434e6i		−	1.64863i	−0.566133	−	0.824314i	$-0.691561\pi$
$811$		−	1.08434e6i		−	1.64863i	0.566133	−	0.824314i	$-0.308439\pi$
$812$	−319549.	+	127725.i	−0.484647	+	0.193715i
$813$		0			0
$814$	−7668.81	+	13282.8i	−0.0115739	+	0.0200466i
$815$	−58998.8	+	34063.0i	−0.0888235	+	0.0512823i
$816$		0			0
$817$	466732.	+	269468.i	0.699235	+	0.403704i
$818$			396463.i			0.592511i
$819$		0			0
$820$	41426.6			0.0616101
$821$	−323845.	+	560916.i	−0.480453	+	0.832169i	−0.999749	−	0.0224257i	$-0.992861\pi$
$821$	−323845.	+	560916.i	−0.480453	+	0.832169i	0.519295	+	0.854595i	$0.326194\pi$
$822$		0			0
$823$	−539512.	−	934463.i	−0.796529	−	1.37963i	−0.921863	−	0.387515i	$-0.873334\pi$
$823$	−539512.	−	934463.i	−0.796529	−	1.37963i	0.125334	−	0.992115i	$-0.460000\pi$
$824$	−315726.	−	182285.i	−0.465003	−	0.268470i
$825$		0			0
$826$	391557.	+	56516.3i	0.573898	+	0.0828350i
$827$	−9026.16			−0.0131975			−0.00659875	−	0.999978i	$-0.502100\pi$
$827$	−9026.16			−0.0131975			−0.00659875	+	0.999978i	$0.502100\pi$
$828$		0			0
$829$	−654736.	+	378012.i	−0.952702	+	0.550043i	−0.893919	−	0.448228i	$-0.852055\pi$
$829$	−654736.	+	378012.i	−0.952702	+	0.550043i	−0.0587830	+	0.998271i	$0.518722\pi$
$830$	30710.1	+	53191.4i	0.0445784	+	0.0772121i
$831$		0			0
$832$		−	97392.5i		−	0.140695i
$833$	984388.	−	237668.i	1.41865	−	0.342516i
$834$		0			0
$835$	−39376.4	+	68201.9i	−0.0564758	+	0.0978190i
$836$	−30035.2	+	17340.8i	−0.0429752	+	0.0248117i
$837$		0			0
$838$	−782390.	−	451713.i	−1.11413	−	0.643242i
$839$		−	654438.i		−	0.929704i	−0.885388	−	0.464852i	$-0.846107\pi$
$839$		−	654438.i		−	0.929704i	0.885388	−	0.464852i	$-0.153893\pi$
$840$		0			0
$841$	63396.2			0.0896337
$842$	−446504.	+	773368.i	−0.629798	+	1.09084i
$843$		0			0
$844$	−12171.3	−	21081.3i	−0.0170864	−	0.0295946i
$845$	38224.8	+	22069.1i	0.0535343	+	0.0309080i
$846$		0			0
$847$	559806.	+	440733.i	0.780316	+	0.614340i
$848$	−51981.0			−0.0722857
$849$		0			0
$850$	−611062.	+	352797.i	−0.845761	+	0.488300i
$851$	−249203.	−	431633.i	−0.344108	−	0.596013i
$852$		0			0
$853$		−	123790.i		−	0.170133i	−0.996375	−	0.0850664i	$-0.972890\pi$
$853$		−	123790.i		−	0.170133i	0.996375	−	0.0850664i	$-0.0271102\pi$
$854$	−300107.	−	750824.i	−0.411491	−	1.02949i
$855$		0			0
$856$	232512.	−	402723.i	0.317321	−	0.549615i
$857$	150023.	−	86615.8i	0.204266	−	0.117933i	−0.394378	−	0.918948i	$-0.629040\pi$
$857$	150023.	−	86615.8i	0.204266	−	0.117933i	0.598644	+	0.801015i	$0.295707\pi$
$858$		0			0
$859$	231499.	+	133656.i	0.313735	+	0.181135i	0.648597	−	0.761132i	$-0.275356\pi$
$859$	231499.	+	133656.i	0.313735	+	0.181135i	−0.334862	+	0.942267i	$0.608690\pi$
$860$		−	57757.7i		−	0.0780932i
$861$		0			0
$862$	−476677.			−0.641519
$863$	619521.	−	1.07304e6i	0.831830	−	1.44077i	−0.0647550	−	0.997901i	$-0.520627\pi$
$863$	619521.	−	1.07304e6i	0.831830	−	1.44077i	0.896585	−	0.442871i	$-0.146040\pi$
$864$		0			0
$865$	130730.	+	226430.i	0.174720	+	0.302623i
$866$	41896.9	+	24189.2i	0.0558658	+	0.0322541i
$867$		0			0
$868$	175609.	−	223054.i	0.233081	−	0.296053i
$869$	−23591.6			−0.0312404
$870$		0			0
$871$	363041.	−	209602.i	0.478541	−	0.276286i
$872$	161308.	+	279393.i	0.212140	+	0.367437i
$873$		0			0
$874$		−	1.12700e6i		−	1.47537i
$875$	−341614.	−	49307.8i	−0.446190	−	0.0644020i
$876$		0			0
$877$	−348961.	+	604419.i	−0.453710	+	0.785848i	−0.998613	−	0.0526507i	$-0.983233\pi$
$877$	−348961.	+	604419.i	−0.453710	+	0.785848i	0.544903	+	0.838499i	$0.316566\pi$
$878$	−543740.	+	313929.i	−0.705347	+	0.407232i
$879$		0			0
$880$	3218.87	+	1858.41i	0.00415660	+	0.00239981i
$881$		−	1.44660e6i		−	1.86378i	−0.362735	−	0.931892i	$-0.618157\pi$
$881$		−	1.44660e6i		−	1.86378i	0.362735	−	0.931892i	$-0.381843\pi$
$882$		0			0
$883$	−539049.			−0.691364			−0.345682	−	0.938352i	$-0.612352\pi$
$883$	−539049.			−0.691364			−0.345682	+	0.938352i	$0.612352\pi$
$884$	320917.	−	555844.i	0.410665	−	0.711293i
$885$		0			0
$886$	48409.5	+	83847.8i	0.0616685	+	0.106813i
$887$	851540.	+	491637.i	1.08233	+	0.624881i	0.931523	−	0.363683i	$-0.118481\pi$
$887$	851540.	+	491637.i	1.08233	+	0.624881i	0.150803	+	0.988564i	$0.451814\pi$
$888$		0			0
$889$	14816.9	−	102655.i	0.0187480	−	0.129890i
$890$	104229.			0.131586
$891$		0			0
$892$	−291710.	+	168419.i	−0.366624	+	0.211671i
$893$	378374.	+	655363.i	0.474481	+	0.821825i
$894$		0			0
$895$		−	114955.i		−	0.143510i
$896$	−55754.0	−	43894.9i	−0.0694480	−	0.0546761i
$897$		0			0
$898$	−264750.	+	458560.i	−0.328309	+	0.568648i
$899$	−550586.	+	317881.i	−0.681249	+	0.393319i
$900$		0			0
$901$	−296669.	−	171282.i	−0.365445	−	0.210990i
$902$			25368.5i			0.0311804i
$903$		0			0
$904$	233169.			0.285321
$905$	61954.0	−	107307.i	0.0756436	−	0.131018i
$906$		0			0
$907$	−146541.	−	253816.i	−0.178133	−	0.308535i	0.763108	−	0.646271i	$-0.223672\pi$
$907$	−146541.	−	253816.i	−0.178133	−	0.308535i	−0.941241	+	0.337736i	$0.890339\pi$
$908$	638707.	+	368758.i	0.774694	+	0.447270i
$909$		0			0
$910$	141752.	−	56658.7i	0.171177	−	0.0684201i
$911$	−1.39546e6			−1.68143			−0.840716	−	0.541477i	$-0.817865\pi$
$911$	−1.39546e6			−1.68143			−0.840716	+	0.541477i	$0.817865\pi$
$912$		0			0
$913$	−32573.0	+	18806.0i	−0.0390765	+	0.0225608i
$914$	−209084.	−	362145.i	−0.250282	−	0.433501i
$915$		0			0
$916$			191705.i			0.228477i
$917$	−183597.	+	233200.i	−0.218337	+	0.277326i
$918$		0			0
$919$	430159.	−	745057.i	0.509328	−	0.882182i	−0.490613	−	0.871377i	$-0.663227\pi$
$919$	430159.	−	745057.i	0.509328	−	0.882182i	0.999942	−	0.0108051i	$-0.00343942\pi$
$920$	−104599.	+	60390.4i	−0.123581	+	0.0713498i
$921$		0			0
$922$	181212.	+	104623.i	0.213170	+	0.123074i
$923$			648314.i			0.760995i
$924$		0			0
$925$	−319793.			−0.373754
$926$	94734.3	−	164085.i	0.110480	−	0.191358i
$927$		0			0
$928$	79456.8	+	137623.i	0.0922646	+	0.159807i
$929$	935631.	+	540187.i	1.08411	+	0.625911i	0.932002	−	0.362453i	$-0.118061\pi$
$929$	935631.	+	540187.i	1.08411	+	0.625911i	0.152108	+	0.988364i	$0.451394\pi$
$930$		0			0
$931$	715359.	+	751895.i	0.825325	+	0.867477i
$932$	282785.			0.325555
$933$		0			0
$934$	568364.	−	328145.i	0.651528	−	0.376160i
$935$	12247.3	+	21212.9i	0.0140093	+	0.0242648i
$936$		0			0
$937$		−	659462.i		−	0.751122i	−0.926798	−	0.375561i	$-0.877450\pi$
$937$		−	659462.i		−	0.751122i	0.926798	−	0.375561i	$-0.122550\pi$
$938$	43632.8	−	302297.i	0.0495915	−	0.343580i
$939$		0			0
$940$	40550.3	−	70235.2i	0.0458922	−	0.0794876i
$941$	−771364.	+	445347.i	−0.871124	+	0.502944i	−0.867722	−	0.497051i	$-0.834416\pi$
$941$	−771364.	+	445347.i	−0.871124	+	0.502944i	−0.00340238	+	0.999994i	$0.501083\pi$
$942$		0			0
$943$	−713923.	−	412184.i	−0.802838	−	0.463519i
$944$		−	182688.i		−	0.205006i
$945$		0			0
$946$	35369.2			0.0395224
$947$	761268.	−	1.31855e6i	0.848863	−	1.47027i	−0.0333612	−	0.999443i	$-0.510621\pi$
$947$	761268.	−	1.31855e6i	0.848863	−	1.47027i	0.882224	−	0.470830i	$-0.156046\pi$
$948$		0			0
$949$	893619.	+	1.54779e6i	0.992248	+	1.71862i
$950$	−626241.	−	361560.i	−0.693896	−	0.400621i
$951$		0			0
$952$	−173565.	−	434233.i	−0.191508	−	0.479126i
$953$	464150.			0.511061			0.255530	−	0.966801i	$-0.417750\pi$
$953$	464150.			0.511061			0.255530	+	0.966801i	$0.417750\pi$
$954$		0			0
$955$	−58300.5	+	33659.8i	−0.0639242	+	0.0369067i
$956$	57574.1	+	99721.3i	0.0629958	+	0.109112i
$957$		0			0
$958$			622392.i			0.678161i
$959$	−130141.	+	52018.1i	−0.141507	+	0.0565610i
$960$		0			0
$961$	−199528.	+	345592.i	−0.216051	+	0.374212i
$962$	251923.	−	145448.i	0.272218	−	0.157165i
$963$		0			0
$964$	−51961.1	−	29999.8i	−0.0559145	−	0.0322822i
$965$		−	304273.i		−	0.326745i
$966$		0			0
$967$	61596.4			0.0658723			0.0329361	−	0.999457i	$-0.489514\pi$
$967$	61596.4			0.0658723			0.0329361	+	0.999457i	$0.489514\pi$
$968$	164506.	−	284933.i	0.175562	−	0.304083i
$969$		0			0
$970$	−52167.8	−	90357.3i	−0.0554446	−	0.0960329i
$971$	668830.	+	386149.i	0.709377	+	0.409559i	0.810830	−	0.585281i	$-0.199016\pi$
$971$	668830.	+	386149.i	0.709377	+	0.409559i	−0.101453	+	0.994840i	$0.532349\pi$
$972$		0			0
$973$	822818.	+	118764.i	0.869117	+	0.125446i
$974$	395007.			0.416378
$975$		0			0
$976$	−323364.	+	186695.i	−0.339463	+	0.195989i
$977$	501672.	+	868921.i	0.525570	+	0.910314i	0.999556	+	0.0297817i	$0.00948120\pi$
$977$	501672.	+	868921.i	0.525570	+	0.910314i	−0.473987	+	0.880532i	$0.657185\pi$
$978$		0			0
$979$			63826.9i			0.0665945i
$980$	31452.3	−	106684.i	0.0327492	−	0.111083i
$981$		0			0
$982$	−402869.	+	697790.i	−0.417774	+	0.723606i
$983$	453001.	−	261540.i	0.468805	−	0.270665i	−0.246934	−	0.969032i	$-0.579423\pi$
$983$	453001.	−	261540.i	0.468805	−	0.270665i	0.715739	+	0.698367i	$0.246090\pi$
$984$		0			0
$985$	−274865.	−	158694.i	−0.283301	−	0.163564i
$986$			1.04727e6i			1.07722i
$987$		0			0
$988$	657776.			0.673852
$989$	−574674.	+	995364.i	−0.587528	+	1.01763i
$990$		0			0
$991$	837744.	+	1.45102e6i	0.853029	+	1.47749i	0.878461	+	0.477814i	$0.158571\pi$
$991$	837744.	+	1.45102e6i	0.853029	+	1.47749i	−0.0254316	+	0.999677i	$0.508096\pi$
$992$	−113531.	−	65547.1i	−0.115369	−	0.0666085i
$993$		0			0
$994$	371138.	+	292195.i	0.375632	+	0.295734i
$995$	−34585.9			−0.0349344
$996$		0			0
$997$	−568548.	+	328251.i	−0.571975	+	0.330230i	−0.757938	−	0.652327i	$-0.773793\pi$
$997$	−568548.	+	328251.i	−0.571975	+	0.330230i	0.185963	+	0.982557i	$0.440460\pi$
$998$	443460.	+	768094.i	0.445239	+	0.771176i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.5.n.a.19.1		4
3.2	odd	2		14.5.d.a.5.2	yes	4
7.2	even	3		882.5.c.b.685.4		4
7.3	odd	6	inner	126.5.n.a.73.1		4
7.5	odd	6		882.5.c.b.685.3		4
12.11	even	2		112.5.s.b.33.1		4
15.2	even	4		350.5.i.a.299.4		8
15.8	even	4		350.5.i.a.299.1		8
15.14	odd	2		350.5.k.a.201.1		4
21.2	odd	6		98.5.b.b.97.2		4
21.5	even	6		98.5.b.b.97.1		4
21.11	odd	6		98.5.d.a.31.2		4
21.17	even	6		14.5.d.a.3.2	✓	4
21.20	even	2		98.5.d.a.19.2		4
84.23	even	6		784.5.c.b.97.2		4
84.47	odd	6		784.5.c.b.97.3		4
84.59	odd	6		112.5.s.b.17.1		4
105.17	odd	12		350.5.i.a.199.1		8
105.38	odd	12		350.5.i.a.199.4		8
105.59	even	6		350.5.k.a.101.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.5.d.a.3.2	✓	4	21.17	even	6
14.5.d.a.5.2	yes	4	3.2	odd	2
98.5.b.b.97.1		4	21.5	even	6
98.5.b.b.97.2		4	21.2	odd	6
98.5.d.a.19.2		4	21.20	even	2
98.5.d.a.31.2		4	21.11	odd	6
112.5.s.b.17.1		4	84.59	odd	6
112.5.s.b.33.1		4	12.11	even	2
126.5.n.a.19.1		4	1.1	even	1	trivial
126.5.n.a.73.1		4	7.3	odd	6	inner
350.5.i.a.199.1		8	105.17	odd	12
350.5.i.a.199.4		8	105.38	odd	12
350.5.i.a.299.1		8	15.8	even	4
350.5.i.a.299.4		8	15.2	even	4
350.5.k.a.101.1		4	105.59	even	6
350.5.k.a.201.1		4	15.14	odd	2
784.5.c.b.97.2		4	84.23	even	6
784.5.c.b.97.3		4	84.47	odd	6
882.5.c.b.685.3		4	7.5	odd	6
882.5.c.b.685.4		4	7.2	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	126.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 + 2.44949i) q^{2} +(-4.00000 - 6.92820i) q^{4} +(-5.01472 - 2.89525i) q^{5} +(-7.00000 + 48.4974i) q^{7} +22.6274 q^{8} +(14.1838 - 8.18900i) q^{10} +(5.01472 + 8.68575i) q^{11} -190.220i q^{13} +(-108.894 - 85.7321i) q^{14} +(-32.0000 + 55.4256i) q^{16} +(-365.265 + 210.886i) q^{17} +(-374.338 - 216.124i) q^{19} +46.3240i q^{20} -28.3675 q^{22} +(460.911 - 798.322i) q^{23} +(-295.735 - 512.228i) q^{25} +(465.941 + 269.011i) q^{26} +(364.000 - 145.492i) q^{28} -877.882 q^{29} +(627.175 - 362.100i) q^{31} +(-90.5097 - 156.767i) q^{32} -1192.95i q^{34} +(175.515 - 222.934i) q^{35} +(270.338 - 468.239i) q^{37} +(1058.79 - 611.291i) q^{38} +(-113.470 - 65.5120i) q^{40} -894.280i q^{41} -1246.82 q^{43} +(40.1177 - 69.4860i) q^{44} +(1303.65 + 2257.99i) q^{46} +(-1516.17 - 875.364i) q^{47} +(-2303.00 - 678.964i) q^{49} +1672.93 q^{50} +(-1317.88 + 760.879i) q^{52} +(406.101 + 703.388i) q^{53} -58.0754i q^{55} +(-158.392 + 1097.37i) q^{56} +(1241.51 - 2150.36i) q^{58} +(-2472.07 + 1427.25i) q^{59} +(5052.57 + 2917.10i) q^{61} +2048.35i q^{62} +512.000 q^{64} +(-550.733 + 953.898i) q^{65} +(1101.89 + 1908.54i) q^{67} +(2922.12 + 1687.08i) q^{68} +(297.859 + 745.199i) q^{70} -3408.24 q^{71} +(-8136.88 + 4697.83i) q^{73} +(764.630 + 1324.38i) q^{74} +3457.98i q^{76} +(-456.339 + 182.401i) q^{77} +(-1176.12 + 2037.09i) q^{79} +(320.942 - 185.296i) q^{80} +(2190.53 + 1264.70i) q^{82} +3750.16i q^{83} +2442.26 q^{85} +(1763.27 - 3054.07i) q^{86} +(113.470 + 196.536i) q^{88} +(5511.35 + 3181.98i) q^{89} +(9225.16 + 1331.54i) q^{91} -7374.58 q^{92} +(4288.39 - 2475.90i) q^{94} +(1251.47 + 2167.60i) q^{95} -6370.47i q^{97} +(4920.05 - 4680.97i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{4} - 54 q^{5} - 28 q^{7} - 96 q^{10} + 54 q^{11} - 128 q^{16} - 918 q^{17} + 30 q^{19} + 192 q^{22} + 486 q^{23} - 572 q^{25} + 1728 q^{26} + 1456 q^{28} - 3240 q^{29} - 546 q^{31} + 1890 q^{35}+ \cdots - 8910 q^{95}+O(q^{100}) \) 4 * q - 16 * q^4 - 54 * q^5 - 28 * q^7 - 96 * q^10 + 54 * q^11 - 128 * q^16 - 918 * q^17 + 30 * q^19 + 192 * q^22 + 486 * q^23 - 572 * q^25 + 1728 * q^26 + 1456 * q^28 - 3240 * q^29 - 546 * q^31 + 1890 * q^35 - 446 * q^37 + 4320 * q^38 + 768 * q^40 + 2344 * q^43 + 432 * q^44 + 3840 * q^46 - 702 * q^47 - 9212 * q^49 + 3456 * q^50 - 384 * q^52 - 2754 * q^53 + 384 * q^58 - 12366 * q^59 + 7686 * q^61 + 2048 * q^64 + 3024 * q^65 - 5062 * q^67 + 7344 * q^68 - 2016 * q^70 - 18792 * q^71 - 17274 * q^73 + 4320 * q^74 - 4914 * q^77 + 794 * q^79 + 3456 * q^80 + 9984 * q^82 + 10380 * q^85 + 10368 * q^86 - 768 * q^88 + 12474 * q^89 + 2688 * q^91 - 7776 * q^92 + 15168 * q^94 - 8910 * q^95

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