LMFDB - Embedded newform 672.4.bb.a.271.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [672,4,Mod(271,672)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(672, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 0, 5])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("672.271"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	672.bb (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$39.6492835239$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.20
Character	$\chi$	$=$	672.271
Dual form			672.4.bb.a.367.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.59808 + 1.50000i) q^{3} +(7.30307 - 12.6493i) q^{5} +(-0.782311 + 18.5037i) q^{7} +(4.50000 - 7.79423i) q^{9} +(29.8704 + 51.7370i) q^{11} +3.68912 q^{13} +43.8184i q^{15} +(-29.8369 + 17.2263i) q^{17} +(-1.17719 - 0.679649i) q^{19} +(-25.7231 - 49.2476i) q^{21} +(-152.250 - 87.9014i) q^{23} +(-44.1698 - 76.5043i) q^{25} +27.0000i q^{27} -2.05927i q^{29} +(-53.5006 - 92.6658i) q^{31} +(-155.211 - 89.6112i) q^{33} +(228.346 + 145.030i) q^{35} +(237.518 + 137.131i) q^{37} +(-9.58462 + 5.53369i) q^{39} +316.949i q^{41} +187.107 q^{43} +(-65.7277 - 113.844i) q^{45} +(-174.173 + 301.677i) q^{47} +(-341.776 - 28.9513i) q^{49} +(51.6790 - 89.5107i) q^{51} +(260.246 - 150.253i) q^{53} +872.583 q^{55} +4.07790 q^{57} +(-711.540 + 410.808i) q^{59} +(-67.3551 + 116.662i) q^{61} +(140.702 + 89.3643i) q^{63} +(26.9419 - 46.6648i) q^{65} +(-53.6072 - 92.8504i) q^{67} +527.409 q^{69} +451.011i q^{71} +(-394.990 + 228.048i) q^{73} +(229.513 + 132.509i) q^{75} +(-980.696 + 512.239i) q^{77} +(1038.98 + 599.857i) q^{79} +(-40.5000 - 70.1481i) q^{81} -543.746i q^{83} +503.221i q^{85} +(3.08891 + 5.35015i) q^{87} +(-1088.45 - 628.419i) q^{89} +(-2.88604 + 68.2625i) q^{91} +(277.997 + 160.502i) q^{93} +(-17.1942 + 9.92706i) q^{95} +1031.36i q^{97} +537.667 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 432 q^{9} - 40 q^{11} - 1200 q^{25} - 456 q^{35} + 1616 q^{43} - 360 q^{49} - 336 q^{57} - 4128 q^{59} + 1440 q^{67} - 648 q^{73} - 3888 q^{81} + 104 q^{91} - 720 q^{99}+O(q^{100}) $ 96 * q + 432 * q^9 - 40 * q^11 - 1200 * q^25 - 456 * q^35 + 1616 * q^43 - 360 * q^49 - 336 * q^57 - 4128 * q^59 + 1440 * q^67 - 648 * q^73 - 3888 * q^81 + 104 * q^91 - 720 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−2.59808	+	1.50000i	−0.500000	+	0.288675i
$3$	−2.59808	+	1.50000i	−0.500000	+	0.288675i
$4$		0			0
$5$	7.30307	−	12.6493i	0.653207	−	1.13139i	−0.329133	−	0.944283i	$-0.606757\pi$
$5$	7.30307	−	12.6493i	0.653207	−	1.13139i	0.982340	−	0.187104i	$-0.0599101\pi$
$6$		0			0
$7$	−0.782311	+	18.5037i	−0.0422408	+	0.999107i
$7$	−0.782311	+	18.5037i	−0.0422408	+	0.999107i
$8$		0			0
$9$	4.50000	−	7.79423i	0.166667	−	0.288675i
$10$		0			0
$11$	29.8704	+	51.7370i	0.818751	+	1.41812i	0.906603	+	0.421985i	$0.138667\pi$
$11$	29.8704	+	51.7370i	0.818751	+	1.41812i	−0.0878515	+	0.996134i	$0.528000\pi$
$12$		0			0
$13$	3.68912			0.0787061			0.0393530	−	0.999225i	$-0.487470\pi$
$13$	3.68912			0.0787061			0.0393530	+	0.999225i	$0.487470\pi$
$14$		0			0
$15$			43.8184i			0.754258i
$16$		0			0
$17$	−29.8369	+	17.2263i	−0.425677	+	0.245765i	−0.697503	−	0.716582i	$-0.745706\pi$
$17$	−29.8369	+	17.2263i	−0.425677	+	0.245765i	0.271826	+	0.962346i	$0.412372\pi$
$18$		0			0
$19$	−1.17719	−	0.679649i	−0.0142140	−	0.00820643i	0.492876	−	0.870099i	$-0.335946\pi$
$19$	−1.17719	−	0.679649i	−0.0142140	−	0.00820643i	−0.507090	+	0.861893i	$0.669279\pi$
$20$		0			0
$21$	−25.7231	−	49.2476i	−0.267297	−	0.511748i
$22$		0			0
$23$	−152.250	−	87.9014i	−1.38027	−	0.796901i	−0.388081	−	0.921625i	$-0.626862\pi$
$23$	−152.250	−	87.9014i	−1.38027	−	0.796901i	−0.992191	+	0.124725i	$0.960195\pi$
$24$		0			0
$25$	−44.1698	−	76.5043i	−0.353358	−	0.612034i
$26$		0			0
$27$			27.0000i			0.192450i
$28$		0			0
$29$		−	2.05927i		−	0.0131861i	−0.999978	−	0.00659306i	$-0.997901\pi$
$29$		−	2.05927i		−	0.0131861i	0.999978	−	0.00659306i	$-0.00209865\pi$
$30$		0			0
$31$	−53.5006	−	92.6658i	−0.309968	−	0.536880i	0.668387	−	0.743813i	$-0.266985\pi$
$31$	−53.5006	−	92.6658i	−0.309968	−	0.536880i	−0.978355	+	0.206934i	$0.933652\pi$
$32$		0			0
$33$	−155.211	−	89.6112i	−0.818751	−	0.472706i
$34$		0			0
$35$	228.346	+	145.030i	1.10279	+	0.700414i
$36$		0			0
$37$	237.518	+	137.131i	1.05534	+	0.609303i	0.924141	−	0.382052i	$-0.124782\pi$
$37$	237.518	+	137.131i	1.05534	+	0.609303i	0.131204	+	0.991355i	$0.458116\pi$
$38$		0			0
$39$	−9.58462	+	5.53369i	−0.0393530	+	0.0227205i
$40$		0			0
$41$			316.949i			1.20729i	0.797252	+	0.603647i	$0.206286\pi$
$41$			316.949i			1.20729i	−0.797252	+	0.603647i	$0.793714\pi$
$42$		0			0
$43$	187.107			0.663572			0.331786	−	0.943355i	$-0.392349\pi$
$43$	187.107			0.663572			0.331786	+	0.943355i	$0.392349\pi$
$44$		0			0
$45$	−65.7277	−	113.844i	−0.217736	−	0.377129i
$46$		0			0
$47$	−174.173	+	301.677i	−0.540549	+	0.936258i	0.458324	+	0.888785i	$0.348450\pi$
$47$	−174.173	+	301.677i	−0.540549	+	0.936258i	−0.998873	+	0.0474729i	$0.984883\pi$
$48$		0			0
$49$	−341.776	−	28.9513i	−0.996431	−	0.0844062i
$50$		0			0
$51$	51.6790	−	89.5107i	0.141892	−	0.245765i
$52$		0			0
$53$	260.246	−	150.253i	0.674482	−	0.389412i	−0.123291	−	0.992371i	$-0.539345\pi$
$53$	260.246	−	150.253i	0.674482	−	0.389412i	0.797773	+	0.602958i	$0.206011\pi$
$54$		0			0
$55$	872.583			2.13926
$56$		0			0
$57$	4.07790			0.00947597
$58$		0			0
$59$	−711.540	+	410.808i	−1.57008	+	0.906485i	−0.573921	+	0.818911i	$0.694578\pi$
$59$	−711.540	+	410.808i	−1.57008	+	0.906485i	−0.996158	+	0.0875743i	$0.972088\pi$
$60$		0			0
$61$	−67.3551	+	116.662i	−0.141376	+	0.244870i	−0.928015	−	0.372543i	$-0.878486\pi$
$61$	−67.3551	+	116.662i	−0.141376	+	0.244870i	0.786639	+	0.617413i	$0.211819\pi$
$62$		0			0
$63$	140.702	+	89.3643i	0.281377	+	0.178712i
$64$		0			0
$65$	26.9419	−	46.6648i	0.0514113	−	0.0890470i
$66$		0			0
$67$	−53.6072	−	92.8504i	−0.0977487	−	0.169306i	0.813004	−	0.582258i	$-0.197831\pi$
$67$	−53.6072	−	92.8504i	−0.0977487	−	0.169306i	−0.910752	+	0.412953i	$0.864497\pi$
$68$		0			0
$69$	527.409			0.920182
$70$		0			0
$71$			451.011i			0.753875i	0.926239	+	0.376938i	$0.123023\pi$
$71$			451.011i			0.753875i	−0.926239	+	0.376938i	$0.876977\pi$
$72$		0			0
$73$	−394.990	+	228.048i	−0.633289	+	0.365629i	−0.782025	−	0.623248i	$-0.785813\pi$
$73$	−394.990	+	228.048i	−0.633289	+	0.365629i	0.148736	+	0.988877i	$0.452480\pi$
$74$		0			0
$75$	229.513	+	132.509i	0.353358	+	0.204011i
$76$		0			0
$77$	−980.696	+	512.239i	−1.45144	+	0.758118i
$78$		0			0
$79$	1038.98	+	599.857i	1.47968	+	0.854294i	0.999735	−	0.0230042i	$-0.00732311\pi$
$79$	1038.98	+	599.857i	1.47968	+	0.854294i	0.479945	+	0.877298i	$0.340656\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	543.746i		−	0.719082i	−0.933129	−	0.359541i	$-0.882933\pi$
$83$		−	543.746i		−	0.719082i	0.933129	−	0.359541i	$-0.117067\pi$
$84$		0			0
$85$			503.221i			0.642141i
$86$		0			0
$87$	3.08891	+	5.35015i	0.00380651	+	0.00659306i
$88$		0			0
$89$	−1088.45	−	628.419i	−1.29636	−	0.748453i	−0.316586	−	0.948564i	$-0.602536\pi$
$89$	−1088.45	−	628.419i	−1.29636	−	0.748453i	−0.979773	+	0.200111i	$0.935870\pi$
$90$		0			0
$91$	−2.88604	+	68.2625i	−0.00332461	+	0.0786358i
$92$		0			0
$93$	277.997	+	160.502i	0.309968	+	0.178960i
$94$		0			0
$95$	−17.1942	+	9.92706i	−0.0185693	+	0.0107210i
$96$		0			0
$97$			1031.36i			1.07958i	0.841800	+	0.539790i	$0.181496\pi$
$97$			1031.36i			1.07958i	−0.841800	+	0.539790i	$0.818504\pi$
$98$		0			0
$99$	537.667			0.545834
$100$		0			0
$101$	524.728	+	908.856i	0.516954	+	0.895391i	0.999806	+	0.0196891i	$0.00626764\pi$
$101$	524.728	+	908.856i	0.516954	+	0.895391i	−0.482852	+	0.875702i	$0.660399\pi$
$102$		0			0
$103$	−247.505	+	428.691i	−0.236771	+	0.410099i	−0.959786	−	0.280733i	$-0.909422\pi$
$103$	−247.505	+	428.691i	−0.236771	+	0.410099i	0.723015	+	0.690832i	$0.242756\pi$
$104$		0			0
$105$	−810.805	−	34.2796i	−0.753585	−	0.0318605i
$106$		0			0
$107$	−975.400	+	1689.44i	−0.881266	+	1.52640i	−0.0313312	+	0.999509i	$0.509975\pi$
$107$	−975.400	+	1689.44i	−0.881266	+	1.52640i	−0.849935	+	0.526888i	$0.823359\pi$
$108$		0			0
$109$	113.918	−	65.7708i	0.100105	−	0.0577954i	−0.449112	−	0.893476i	$-0.648260\pi$
$109$	113.918	−	65.7708i	0.100105	−	0.0577954i	0.549217	+	0.835680i	$0.314926\pi$
$110$		0			0
$111$	−822.787			−0.703563
$112$		0			0
$113$	1197.97			0.997303			0.498652	−	0.866803i	$-0.333829\pi$
$113$	1197.97			0.997303			0.498652	+	0.866803i	$0.333829\pi$
$114$		0			0
$115$	−2223.78	+	1283.90i	−1.80321	+	1.04108i
$116$		0			0
$117$	16.6011	−	28.7539i	0.0131177	−	0.0227205i
$118$		0			0
$119$	−295.410	−	565.570i	−0.227565	−	0.435679i
$120$		0			0
$121$	−1118.98	+	1938.13i	−0.840707	+	1.45615i
$122$		0			0
$123$	−475.423	−	823.457i	−0.348516	−	0.603647i
$124$		0			0
$125$	535.468			0.383150
$126$		0			0
$127$		−	1079.60i		−	0.754322i	−0.926148	−	0.377161i	$-0.876900\pi$
$127$		−	1079.60i		−	0.754322i	0.926148	−	0.377161i	$-0.123100\pi$
$128$		0			0
$129$	−486.119	+	280.661i	−0.331786	+	0.191557i
$130$		0			0
$131$	−1600.22	−	923.885i	−1.06726	−	0.616185i	−0.139831	−	0.990175i	$-0.544656\pi$
$131$	−1600.22	−	923.885i	−1.06726	−	0.616185i	−0.927432	+	0.373991i	$0.877989\pi$
$132$		0			0
$133$	13.4970	−	21.2507i	0.00879952	−	0.0138546i
$134$		0			0
$135$	341.531	+	197.183i	0.217736	+	0.125710i
$136$		0			0
$137$	1295.60	+	2244.04i	0.807959	+	1.39943i	0.914275	+	0.405094i	$0.132761\pi$
$137$	1295.60	+	2244.04i	0.807959	+	1.39943i	−0.106316	+	0.994332i	$0.533905\pi$
$138$		0			0
$139$			3020.36i			1.84305i	0.388319	+	0.921525i	$0.373056\pi$
$139$			3020.36i			1.84305i	−0.388319	+	0.921525i	$0.626944\pi$
$140$		0			0
$141$		−	1045.04i		−	0.624172i
$142$		0			0
$143$	110.196	+	190.864i	0.0644407	+	0.111615i
$144$		0			0
$145$	−26.0484	−	15.0390i	−0.0149186	−	0.00861327i
$146$		0			0
$147$	931.387	−	437.446i	0.522582	−	0.245442i
$148$		0			0
$149$	592.829	+	342.270i	0.325949	+	0.188187i	0.654041	−	0.756459i	$-0.273072\pi$
$149$	592.829	+	342.270i	0.325949	+	0.188187i	−0.328092	+	0.944646i	$0.606406\pi$
$150$		0			0
$151$	−2681.30	+	1548.05i	−1.44504	+	0.834294i	−0.998180	−	0.0603091i	$-0.980791\pi$
$151$	−2681.30	+	1548.05i	−1.44504	+	0.834294i	−0.446861	+	0.894604i	$0.647458\pi$
$152$		0			0
$153$			310.074i			0.163843i
$154$		0			0
$155$	−1562.88			−0.809892
$156$		0			0
$157$	487.393	+	844.190i	0.247759	+	0.429132i	0.962904	−	0.269845i	$-0.0869725\pi$
$157$	487.393	+	844.190i	0.247759	+	0.429132i	−0.715145	+	0.698977i	$0.753639\pi$
$158$		0			0
$159$	−450.760	+	780.738i	−0.224827	+	0.389412i
$160$		0			0
$161$	1745.61	−	2748.42i	0.854493	−	1.34538i
$162$		0			0
$163$	1169.12	−	2024.97i	0.561795	−	0.973057i	−0.435545	−	0.900167i	$-0.643444\pi$
$163$	1169.12	−	2024.97i	0.561795	−	0.973057i	0.997340	−	0.0728901i	$-0.0232222\pi$
$164$		0			0
$165$	−2267.04	+	1308.87i	−1.06963	+	0.617550i
$166$		0			0
$167$	4248.42			1.96858			0.984290	−	0.176558i	$-0.0564964\pi$
$167$	4248.42			1.96858			0.984290	+	0.176558i	$0.0564964\pi$
$168$		0			0
$169$	−2183.39			−0.993805
$170$		0			0
$171$	−10.5947	+	6.11684i	−0.00473799	+	0.00273548i
$172$		0			0
$173$	1110.85	−	1924.04i	0.488185	−	0.845562i	−0.511722	−	0.859151i	$-0.670992\pi$
$173$	1110.85	−	1924.04i	0.488185	−	0.845562i	0.999908	+	0.0135890i	$0.00432563\pi$
$174$		0			0
$175$	1450.17	−	757.455i	0.626414	−	0.327190i
$176$		0			0
$177$	1232.42	−	2134.62i	0.523360	−	0.906485i
$178$		0			0
$179$	−1419.31	−	2458.31i	−0.592647	−	1.02650i	−0.993874	−	0.110517i	$-0.964749\pi$
$179$	−1419.31	−	2458.31i	−0.592647	−	1.02650i	0.401227	−	0.915979i	$-0.368584\pi$
$180$		0			0
$181$	646.757			0.265597			0.132798	−	0.991143i	$-0.457604\pi$
$181$	646.757			0.265597			0.132798	+	0.991143i	$0.457604\pi$
$182$		0			0
$183$		−	404.131i		−	0.163247i
$184$		0			0
$185$	3469.23	−	2002.96i	1.37872	−	0.796002i
$186$		0			0
$187$	−1782.48	−	1029.12i	−0.697048	−	0.402441i
$188$		0			0
$189$	−499.601	−	21.1224i	−0.192278	−	0.00812925i
$190$		0			0
$191$	−2565.46	−	1481.17i	−0.971887	−	0.561119i	−0.0720758	−	0.997399i	$-0.522962\pi$
$191$	−2565.46	−	1481.17i	−0.971887	−	0.561119i	−0.899811	+	0.436280i	$0.856296\pi$
$192$		0			0
$193$	1557.81	+	2698.21i	0.581004	+	1.00633i	0.995361	+	0.0962141i	$0.0306734\pi$
$193$	1557.81	+	2698.21i	0.581004	+	1.00633i	−0.414356	+	0.910115i	$0.635993\pi$
$194$		0			0
$195$			161.652i			0.0593647i
$196$		0			0
$197$			215.710i			0.0780137i	0.999239	+	0.0390068i	$0.0124194\pi$
$197$			215.710i			0.0780137i	−0.999239	+	0.0390068i	$0.987581\pi$
$198$		0			0
$199$	1208.29	+	2092.81i	0.430418	+	0.745506i	0.996909	−	0.0785620i	$-0.0250329\pi$
$199$	1208.29	+	2092.81i	0.430418	+	0.745506i	−0.566491	+	0.824068i	$0.691700\pi$
$200$		0			0
$201$	278.551	+	160.822i	0.0977487	+	0.0564353i
$202$		0			0
$203$	38.1042	+	1.61099i	0.0131744	+	0.000556992i
$204$		0			0
$205$	4009.18	+	2314.70i	1.36592	+	0.788613i
$206$		0			0
$207$	−1370.25	+	791.113i	−0.460091	+	0.265634i
$208$		0			0
$209$		−	81.2056i		−	0.0268761i
$210$		0			0
$211$	4710.50			1.53689			0.768445	−	0.639915i	$-0.221031\pi$
$211$	4710.50			1.53689			0.768445	+	0.639915i	$0.221031\pi$
$212$		0			0
$213$	−676.516	−	1171.76i	−0.217625	−	0.376938i
$214$		0			0
$215$	1366.46	−	2366.77i	0.433450	−	0.750757i
$216$		0			0
$217$	1756.52	−	917.468i	0.549494	−	0.287013i
$218$		0			0
$219$	684.143	−	1184.97i	0.211096	−	0.365629i
$220$		0			0
$221$	−110.072	+	63.5501i	−0.0335034	+	0.0193432i
$222$		0			0
$223$	1574.47			0.472799			0.236399	−	0.971656i	$-0.424033\pi$
$223$	1574.47			0.472799			0.236399	+	0.971656i	$0.424033\pi$
$224$		0			0
$225$	−795.056			−0.235572
$226$		0			0
$227$	4128.15	−	2383.39i	1.20703	−	0.696877i	0.244918	−	0.969544i	$-0.421239\pi$
$227$	4128.15	−	2383.39i	1.20703	−	0.696877i	0.962108	+	0.272667i	$0.0879057\pi$
$228$		0			0
$229$	−222.868	+	386.019i	−0.0643124	+	0.111392i	−0.896389	−	0.443269i	$-0.853819\pi$
$229$	−222.868	+	386.019i	−0.0643124	+	0.111392i	0.832076	+	0.554661i	$0.187152\pi$
$230$		0			0
$231$	1779.56	−	2801.88i	0.506869	−	0.798053i
$232$		0			0
$233$	323.623	−	560.532i	0.0909926	−	0.157604i	−0.816936	−	0.576728i	$-0.804329\pi$
$233$	323.623	−	560.532i	0.0909926	−	0.157604i	0.907929	+	0.419124i	$0.137663\pi$
$234$		0			0
$235$	2544.00	+	4406.34i	0.706181	+	1.22314i
$236$		0			0
$237$	−3599.14			−0.986454
$238$		0			0
$239$		−	1481.31i		−	0.400912i	−0.979703	−	0.200456i	$-0.935758\pi$
$239$		−	1481.31i		−	0.400912i	0.979703	−	0.200456i	$-0.0642424\pi$
$240$		0			0
$241$	−2967.07	+	1713.04i	−0.793052	+	0.457869i	−0.841036	−	0.540979i	$-0.818054\pi$
$241$	−2967.07	+	1713.04i	−0.793052	+	0.457869i	0.0479838	+	0.998848i	$0.484720\pi$
$242$		0			0
$243$	210.444	+	121.500i	0.0555556	+	0.0320750i
$244$		0			0
$245$	−2862.23	+	4111.79i	−0.746372	+	1.07222i
$246$		0			0
$247$	−4.34279	−	2.50731i	−0.00111872	−	0.000645896i
$248$		0			0
$249$	815.618	+	1412.69i	0.207581	+	0.359541i
$250$		0			0
$251$		−	984.409i		−	0.247551i	−0.992310	−	0.123776i	$-0.960500\pi$
$251$		−	984.409i		−	0.247551i	0.992310	−	0.123776i	$-0.0395003\pi$
$252$		0			0
$253$		−	10502.6i		−	2.60985i
$254$		0			0
$255$	−754.832	−	1307.41i	−0.185370	−	0.321071i
$256$		0			0
$257$	−4647.53	−	2683.25i	−1.12803	−	0.651271i	−0.184595	−	0.982815i	$-0.559097\pi$
$257$	−4647.53	−	2683.25i	−1.12803	−	0.651271i	−0.943440	+	0.331544i	$0.892431\pi$
$258$		0			0
$259$	−2723.25	+	4287.69i	−0.653338	+	1.02867i
$260$		0			0
$261$	−16.0505	−	9.26673i	−0.00380651	−	0.00219769i
$262$		0			0
$263$	−5562.21	+	3211.34i	−1.30411	+	0.752927i	−0.981106	−	0.193471i	$-0.938025\pi$
$263$	−5562.21	+	3211.34i	−1.30411	+	0.752927i	−0.323002	+	0.946398i	$0.604692\pi$
$264$		0			0
$265$		−	4389.24i		−	1.01747i
$266$		0			0
$267$	3770.52			0.864239
$268$		0			0
$269$	−2724.40	−	4718.80i	−0.617509	−	1.06956i	−0.989939	−	0.141496i	$-0.954809\pi$
$269$	−2724.40	−	4718.80i	−0.617509	−	1.06956i	0.372430	−	0.928060i	$-0.378525\pi$
$270$		0			0
$271$	2644.96	−	4581.21i	0.592878	−	1.02689i	−0.400965	−	0.916093i	$-0.631325\pi$
$271$	2644.96	−	4581.21i	0.592878	−	1.02689i	0.993843	−	0.110801i	$-0.0353416\pi$
$272$		0			0
$273$	−94.8957	−	181.680i	−0.0210379	−	0.0402776i
$274$		0			0
$275$	2638.74	−	4570.43i	0.578625	−	1.00221i
$276$		0			0
$277$	734.901	−	424.295i	0.159408	−	0.0920341i	−0.418174	−	0.908367i	$-0.637330\pi$
$277$	734.901	−	424.295i	0.159408	−	0.0920341i	0.577582	+	0.816333i	$0.303996\pi$
$278$		0			0
$279$	−963.012			−0.206645
$280$		0			0
$281$	2590.85			0.550026			0.275013	−	0.961441i	$-0.411318\pi$
$281$	2590.85			0.550026			0.275013	+	0.961441i	$0.411318\pi$
$282$		0			0
$283$	−1757.27	+	1014.56i	−0.369113	+	0.213108i	−0.673071	−	0.739578i	$-0.735025\pi$
$283$	−1757.27	+	1014.56i	−0.369113	+	0.213108i	0.303958	+	0.952686i	$0.401692\pi$
$284$		0			0
$285$	29.7812	−	51.5825i	0.00618977	−	0.0107210i
$286$		0			0
$287$	−5864.73	−	247.952i	−1.20622	−	0.0509971i
$288$		0			0
$289$	−1863.01	+	3226.82i	−0.379199	+	0.656792i
$290$		0			0
$291$	−1547.05	−	2679.56i	−0.311648	−	0.539790i
$292$		0			0
$293$	−9290.50			−1.85241			−0.926206	−	0.377017i	$-0.876950\pi$
$293$	−9290.50			−1.85241			−0.926206	+	0.377017i	$0.876950\pi$
$294$		0			0
$295$			12000.6i			2.36849i
$296$		0			0
$297$	−1396.90	+	806.501i	−0.272917	+	0.157569i
$298$		0			0
$299$	−561.668	−	324.279i	−0.108636	−	0.0627209i
$300$		0			0
$301$	−146.376	+	3462.18i	−0.0280298	+	0.662979i
$302$		0			0
$303$	−2726.57	−	1574.18i	−0.516954	−	0.298464i
$304$		0			0
$305$	983.799	+	1703.99i	0.184696	+	0.319902i
$306$		0			0
$307$			2214.01i			0.411598i	0.978594	+	0.205799i	$0.0659793\pi$
$307$			2214.01i			0.411598i	−0.978594	+	0.205799i	$0.934021\pi$
$308$		0			0
$309$		−	1485.03i		−	0.273399i
$310$		0			0
$311$	−4427.78	−	7669.15i	−0.807320	−	1.39832i	−0.914713	−	0.404103i	$-0.867584\pi$
$311$	−4427.78	−	7669.15i	−0.807320	−	1.39832i	0.107393	−	0.994217i	$-0.465750\pi$
$312$		0			0
$313$	164.785	+	95.1386i	0.0297578	+	0.0171807i	0.514805	−	0.857307i	$-0.327864\pi$
$313$	164.785	+	95.1386i	0.0297578	+	0.0171807i	−0.485047	+	0.874488i	$0.661198\pi$
$314$		0			0
$315$	2157.95	−	1127.15i	0.385990	−	0.201611i
$316$		0			0
$317$	−378.138	−	218.318i	−0.0669980	−	0.0386813i	0.466127	−	0.884718i	$-0.345649\pi$
$317$	−378.138	−	218.318i	−0.0669980	−	0.0386813i	−0.533125	+	0.846037i	$0.678982\pi$
$318$		0			0
$319$	106.541	−	61.5113i	0.0186995	−	0.0107962i
$320$		0			0
$321$		−	5852.40i		−	1.01760i
$322$		0			0
$323$	46.8315			0.00806741
$324$		0			0
$325$	−162.948	−	282.234i	−0.0278114	−	0.0481708i
$326$		0			0
$327$	−197.312	+	341.755i	−0.0333682	+	0.0577954i
$328$		0			0
$329$	−5445.90	−	3458.86i	−0.912589	−	0.579615i
$330$		0			0
$331$	4927.37	−	8534.46i	0.818226	−	1.41721i	−0.0887622	−	0.996053i	$-0.528291\pi$
$331$	4927.37	−	8534.46i	0.818226	−	1.41721i	0.906988	−	0.421156i	$-0.138376\pi$
$332$		0			0
$333$	2137.66	−	1234.18i	0.351781	−	0.203101i
$334$		0			0
$335$	−1565.99			−0.255401
$336$		0			0
$337$	2518.25			0.407057			0.203528	−	0.979069i	$-0.434759\pi$
$337$	2518.25			0.407057			0.203528	+	0.979069i	$0.434759\pi$
$338$		0			0
$339$	−3112.41	+	1796.95i	−0.498652	+	0.287897i
$340$		0			0
$341$	3196.17	−	5535.93i	0.507573	−	0.879142i
$342$		0			0
$343$	803.082	−	6301.48i	0.126421	−	0.991977i
$344$		0			0
$345$	3851.70	−	6671.35i	0.601069	−	1.04108i
$346$		0			0
$347$	5797.56	+	10041.7i	0.896914	+	1.55350i	0.831417	+	0.555648i	$0.187530\pi$
$347$	5797.56	+	10041.7i	0.896914	+	1.55350i	0.0654969	+	0.997853i	$0.479137\pi$
$348$		0			0
$349$	1813.09			0.278088			0.139044	−	0.990286i	$-0.455597\pi$
$349$	1813.09			0.278088			0.139044	+	0.990286i	$0.455597\pi$
$350$		0			0
$351$			99.6063i			0.0151470i
$352$		0			0
$353$	2083.52	−	1202.92i	0.314149	−	0.181374i	−0.334633	−	0.942349i	$-0.608612\pi$
$353$	2083.52	−	1202.92i	0.314149	−	0.181374i	0.648782	+	0.760975i	$0.275279\pi$
$354$		0			0
$355$	5704.97	+	3293.76i	0.852925	+	0.492436i
$356$		0			0
$357$	1615.85	+	1026.28i	0.239552	+	0.152147i
$358$		0			0
$359$	6925.06	+	3998.18i	1.01808	+	0.587789i	0.913547	−	0.406733i	$-0.133332\pi$
$359$	6925.06	+	3998.18i	1.01808	+	0.587789i	0.104533	+	0.994521i	$0.466665\pi$
$360$		0			0
$361$	−3428.58	−	5938.47i	−0.499865	−	0.865792i
$362$		0			0
$363$		−	6713.89i		−	0.970765i
$364$		0			0
$365$			6661.79i			0.955326i
$366$		0			0
$367$	−617.136	−	1068.91i	−0.0877773	−	0.152035i	0.818794	−	0.574087i	$-0.194643\pi$
$367$	−617.136	−	1068.91i	−0.0877773	−	0.152035i	−0.906571	+	0.422053i	$0.861310\pi$
$368$		0			0
$369$	2470.37	+	1426.27i	0.348516	+	0.201216i
$370$		0			0
$371$	2576.65	+	4933.07i	0.360574	+	0.690329i
$372$		0			0
$373$	11025.6	+	6365.63i	1.53052	+	0.883646i	0.999338	+	0.0363881i	$0.0115853\pi$
$373$	11025.6	+	6365.63i	1.53052	+	0.883646i	0.531182	+	0.847258i	$0.321748\pi$
$374$		0			0
$375$	−1391.19	+	803.202i	−0.191575	+	0.110606i
$376$		0			0
$377$		−	7.59692i		−	0.00103783i
$378$		0			0
$379$	−11102.4			−1.50472			−0.752362	−	0.658750i	$-0.771086\pi$
$379$	−11102.4			−1.50472			−0.752362	+	0.658750i	$0.771086\pi$
$380$		0			0
$381$	1619.40	+	2804.88i	0.217754	+	0.377161i
$382$		0			0
$383$	1130.11	−	1957.40i	0.150772	−	0.261145i	−0.780739	−	0.624857i	$-0.785157\pi$
$383$	1130.11	−	1957.40i	0.150772	−	0.261145i	0.931512	+	0.363712i	$0.118491\pi$
$384$		0			0
$385$	−682.631	+	16146.0i	−0.0903639	+	2.13735i
$386$		0			0
$387$	841.983	−	1458.36i	0.110595	−	0.191557i
$388$		0			0
$389$	6521.27	−	3765.06i	0.849978	−	0.490735i	−0.0106655	−	0.999943i	$-0.503395\pi$
$389$	6521.27	−	3765.06i	0.849978	−	0.490735i	0.860643	+	0.509208i	$0.170062\pi$
$390$		0			0
$391$	6056.88			0.783401
$392$		0			0
$393$	5543.31			0.711509
$394$		0			0
$395$	15175.5	−	8761.61i	1.93308	−	1.11606i
$396$		0			0
$397$	2213.94	−	3834.66i	0.279885	−	0.484775i	−0.691471	−	0.722404i	$-0.743037\pi$
$397$	2213.94	−	3834.66i	0.279885	−	0.484775i	0.971356	+	0.237629i	$0.0763703\pi$
$398$		0			0
$399$	−3.19018	+	75.4563i	−0.000400273	+	0.00946752i
$400$		0			0
$401$	3501.96	−	6065.57i	0.436108	−	0.755361i	−0.561277	−	0.827628i	$-0.689690\pi$
$401$	3501.96	−	6065.57i	0.436108	−	0.755361i	0.997385	+	0.0722664i	$0.0230232\pi$
$402$		0			0
$403$	−197.370	−	341.856i	−0.0243963	−	0.0422557i
$404$		0			0
$405$	−1183.10			−0.145157
$406$		0			0
$407$			16384.7i			1.99547i
$408$		0			0
$409$	7550.94	−	4359.54i	0.912885	−	0.527055i	0.0315269	−	0.999503i	$-0.489963\pi$
$409$	7550.94	−	4359.54i	0.912885	−	0.527055i	0.881358	+	0.472448i	$0.156630\pi$
$410$		0			0
$411$	−6732.13	−	3886.79i	−0.807959	−	0.466476i
$412$		0			0
$413$	−7044.83	−	13487.5i	−0.839355	−	1.60697i
$414$		0			0
$415$	−6878.00	−	3971.01i	−0.813561	−	0.469709i
$416$		0			0
$417$	−4530.55	−	7847.14i	−0.532043	−	0.921525i
$418$		0			0
$419$		−	7052.74i		−	0.822312i	−0.911565	−	0.411156i	$-0.865125\pi$
$419$		−	7052.74i		−	0.822312i	0.911565	−	0.411156i	$-0.134875\pi$
$420$		0			0
$421$			6931.64i			0.802440i	0.915982	+	0.401220i	$0.131414\pi$
$421$			6931.64i			0.802440i	−0.915982	+	0.401220i	$0.868586\pi$
$422$		0			0
$423$	1567.56	+	2715.09i	0.180183	+	0.312086i
$424$		0			0
$425$	2635.78	+	1521.77i	0.300833	+	0.173686i
$426$		0			0
$427$	−2106.00	−	1337.59i	−0.238680	−	0.151593i
$428$		0			0
$429$	−572.593	−	330.587i	−0.0644407	−	0.0372048i
$430$		0			0
$431$	−2301.26	+	1328.63i	−0.257187	+	0.148487i	−0.623051	−	0.782181i	$-0.714107\pi$
$431$	−2301.26	+	1328.63i	−0.257187	+	0.148487i	0.365863	+	0.930669i	$0.380774\pi$
$432$		0			0
$433$			2301.97i			0.255487i	0.991807	+	0.127743i	$0.0407734\pi$
$433$			2301.97i			0.255487i	−0.991807	+	0.127743i	$0.959227\pi$
$434$		0			0
$435$	90.2342			0.00994574
$436$		0			0
$437$	119.484	+	206.953i	0.0130794	+	0.0226542i
$438$		0			0
$439$	5316.12	−	9207.78i	0.577960	−	1.00106i	−0.417753	−	0.908561i	$-0.637182\pi$
$439$	5316.12	−	9207.78i	0.577960	−	1.00106i	0.995713	−	0.0924954i	$-0.0294843\pi$
$440$		0			0
$441$	−1763.65	+	2533.60i	−0.190438	+	0.273577i
$442$		0			0
$443$	821.461	−	1422.81i	0.0881011	−	0.152596i	−0.818607	−	0.574354i	$-0.805253\pi$
$443$	821.461	−	1422.81i	0.0881011	−	0.152596i	0.906708	+	0.421758i	$0.138587\pi$
$444$		0			0
$445$	−15898.1	+	9178.79i	−1.69358	+	0.977789i
$446$		0			0
$447$	−2053.62			−0.217299
$448$		0			0
$449$	−6402.50			−0.672945			−0.336473	−	0.941693i	$-0.609234\pi$
$449$	−6402.50			−0.672945			−0.336473	+	0.941693i	$0.609234\pi$
$450$		0			0
$451$	−16398.0	+	9467.38i	−1.71209	+	0.988474i
$452$		0			0
$453$	4644.15	−	8043.90i	0.481680	−	0.834294i
$454$		0			0
$455$	842.396	+	535.033i	0.0867959	+	0.0551269i
$456$		0			0
$457$	−782.070	+	1354.59i	−0.0800519	+	0.138654i	−0.903272	−	0.429068i	$-0.858842\pi$
$457$	−782.070	+	1354.59i	−0.0800519	+	0.138654i	0.823220	+	0.567722i	$0.192175\pi$
$458$		0			0
$459$	−465.111	−	805.597i	−0.0472975	−	0.0819216i
$460$		0			0
$461$	−12965.9			−1.30994			−0.654970	−	0.755655i	$-0.727319\pi$
$461$	−12965.9			−1.30994			−0.654970	+	0.755655i	$0.727319\pi$
$462$		0			0
$463$		−	1919.05i		−	0.192626i	−0.995351	−	0.0963130i	$-0.969295\pi$
$463$		−	1919.05i		−	0.192626i	0.995351	−	0.0963130i	$-0.0307050\pi$
$464$		0			0
$465$	4060.47	−	2344.31i	0.404946	−	0.233796i
$466$		0			0
$467$	−3383.20	−	1953.29i	−0.335237	−	0.193549i	0.322927	−	0.946424i	$-0.395333\pi$
$467$	−3383.20	−	1953.29i	−0.335237	−	0.193549i	−0.658164	+	0.752875i	$0.728667\pi$
$468$		0			0
$469$	1760.02	−	919.296i	0.173284	−	0.0905099i
$470$		0			0
$471$	−2532.57	−	1462.18i	−0.247759	−	0.143044i
$472$		0			0
$473$	5588.97	+	9680.38i	0.543300	+	0.941024i
$474$		0			0
$475$			120.080i			0.0115992i
$476$		0			0
$477$		−	2704.56i		−	0.259608i
$478$		0			0
$479$	−9988.48	−	17300.6i	−0.952788	−	1.65028i	−0.739352	−	0.673320i	$-0.764868\pi$
$479$	−9988.48	−	17300.6i	−0.952788	−	1.65028i	−0.213436	−	0.976957i	$-0.568466\pi$
$480$		0			0
$481$	876.234	+	505.894i	0.0830620	+	0.0479559i
$482$		0			0
$483$	−412.597	+	9759.03i	−0.0388692	+	0.919360i
$484$		0			0
$485$	13046.0	+	7532.13i	1.22142	+	0.705189i
$486$		0			0
$487$	6372.05	−	3678.91i	0.592906	−	0.342314i	−0.173340	−	0.984862i	$-0.555456\pi$
$487$	6372.05	−	3678.91i	0.592906	−	0.342314i	0.766246	+	0.642548i	$0.222123\pi$
$488$		0			0
$489$			7014.72i			0.648705i
$490$		0			0
$491$	−11334.2			−1.04176			−0.520882	−	0.853629i	$-0.674397\pi$
$491$	−11334.2			−1.04176			−0.520882	+	0.853629i	$0.674397\pi$
$492$		0			0
$493$	35.4738	+	61.4424i	0.00324069	+	0.00561303i
$494$		0			0
$495$	3926.62	−	6801.11i	0.356543	−	0.617550i
$496$		0			0
$497$	−8345.38	−	352.830i	−0.753202	−	0.0318443i
$498$		0			0
$499$	−3535.75	+	6124.10i	−0.317198	+	0.549404i	−0.979902	−	0.199478i	$-0.936075\pi$
$499$	−3535.75	+	6124.10i	−0.317198	+	0.549404i	0.662704	+	0.748881i	$0.269409\pi$
$500$		0			0
$501$	−11037.7	+	6372.64i	−0.984290	+	0.568280i
$502$		0			0
$503$	9193.47			0.814944			0.407472	−	0.913218i	$-0.366410\pi$
$503$	9193.47			0.814944			0.407472	+	0.913218i	$0.366410\pi$
$504$		0			0
$505$	15328.5			1.35071
$506$		0			0
$507$	5672.61	−	3275.09i	0.496903	−	0.286887i
$508$		0			0
$509$	−1268.09	+	2196.40i	−0.110427	+	0.191265i	−0.915942	−	0.401310i	$-0.868555\pi$
$509$	−1268.09	+	2196.40i	−0.110427	+	0.191265i	0.805516	+	0.592574i	$0.201888\pi$
$510$		0			0
$511$	−3910.72	−	7487.19i	−0.338552	−	0.648168i
$512$		0			0
$513$	18.3505	−	31.7841i	0.00157933	−	0.00273548i
$514$		0			0
$515$	3615.09	+	6261.52i	0.309320	+	0.535759i
$516$		0			0
$517$	−20810.5			−1.77030
$518$		0			0
$519$			6665.08i			0.563708i
$520$		0			0
$521$	−16234.3	+	9372.88i	−1.36514	+	0.788164i	−0.990303	−	0.138927i	$-0.955635\pi$
$521$	−16234.3	+	9372.88i	−1.36514	+	0.788164i	−0.374837	+	0.927091i	$0.622301\pi$
$522$		0			0
$523$	−1445.82	−	834.745i	−0.120882	−	0.0697913i	0.438340	−	0.898809i	$-0.355567\pi$
$523$	−1445.82	−	834.745i	−0.120882	−	0.0697913i	−0.559222	+	0.829018i	$0.688900\pi$
$524$		0			0
$525$	−2631.47	+	4143.18i	−0.218755	+	0.344425i
$526$		0			0
$527$	3192.59	+	1843.24i	0.263892	+	0.152358i
$528$		0			0
$529$	9369.82	+	16229.0i	0.770101	+	1.33385i
$530$		0			0
$531$			7394.54i			0.604324i
$532$		0			0
$533$			1169.26i			0.0950214i
$534$		0			0
$535$	14246.8	+	24676.2i	1.15130	+	1.99411i
$536$		0			0
$537$	7374.93	+	4257.92i	0.592647	+	0.342165i
$538$		0			0
$539$	−8711.13	−	18547.3i	−0.696131	−	1.48217i
$540$		0			0
$541$	11917.6	+	6880.64i	0.947096	+	0.546806i	0.892177	−	0.451685i	$-0.149177\pi$
$541$	11917.6	+	6880.64i	0.947096	+	0.546806i	0.0549180	+	0.998491i	$0.482510\pi$
$542$		0			0
$543$	−1680.32	+	970.135i	−0.132798	+	0.0766712i
$544$		0			0
$545$		−	1921.32i		−	0.151009i
$546$		0			0
$547$	−10496.8			−0.820494			−0.410247	−	0.911974i	$-0.634558\pi$
$547$	−10496.8			−0.820494			−0.410247	+	0.911974i	$0.634558\pi$
$548$		0			0
$549$	606.196	+	1049.96i	0.0471253	+	0.0816235i
$550$		0			0
$551$	−1.39958	+	2.42415i	−0.000108211	+	0.000187427i
$552$		0			0
$553$	−11912.4	+	18755.8i	−0.916035	+	1.44227i
$554$		0			0
$555$	−6008.87	+	10407.7i	−0.459572	+	0.796002i
$556$		0			0
$557$	8319.18	−	4803.08i	0.632846	−	0.365374i	−0.149008	−	0.988836i	$-0.547608\pi$
$557$	8319.18	−	4803.08i	0.632846	−	0.365374i	0.781853	+	0.623462i	$0.214275\pi$
$558$		0			0
$559$	690.262			0.0522271
$560$		0			0
$561$	6174.69			0.464698
$562$		0			0
$563$	3141.56	−	1813.78i	0.235171	−	0.135776i	−0.377784	−	0.925894i	$-0.623314\pi$
$563$	3141.56	−	1813.78i	0.235171	−	0.135776i	0.612955	+	0.790118i	$0.289981\pi$
$564$		0			0
$565$	8748.84	−	15153.4i	0.651445	−	1.12834i
$566$		0			0
$567$	1329.68	−	694.523i	0.0984859	−	0.0514413i
$568$		0			0
$569$	2995.10	−	5187.66i	0.220670	−	0.382211i	−0.734342	−	0.678780i	$-0.762509\pi$
$569$	2995.10	−	5187.66i	0.220670	−	0.382211i	0.955012	+	0.296569i	$0.0958424\pi$
$570$		0			0
$571$	3174.42	+	5498.26i	0.232654	+	0.402969i	0.958588	−	0.284795i	$-0.0919256\pi$
$571$	3174.42	+	5498.26i	0.232654	+	0.402969i	−0.725934	+	0.687764i	$0.758592\pi$
$572$		0			0
$573$	8887.02			0.647924
$574$		0			0
$575$			15530.3i			1.12637i
$576$		0			0
$577$	−628.970	+	363.136i	−0.0453802	+	0.0262003i	−0.522518	−	0.852628i	$-0.675007\pi$
$577$	−628.970	+	363.136i	−0.0453802	+	0.0262003i	0.477138	+	0.878828i	$0.341674\pi$
$578$		0			0
$579$	−8094.63	−	4673.44i	−0.581004	−	0.335443i
$580$		0			0
$581$	10061.3	+	425.378i	0.718440	+	0.0303746i
$582$		0			0
$583$	15547.3	+	8976.24i	1.10447	+	0.637664i
$584$		0			0
$585$	−242.477	−	419.983i	−0.0171371	−	0.0296823i
$586$		0			0
$587$			16660.1i			1.17144i	0.810512	+	0.585722i	$0.199189\pi$
$587$			16660.1i			1.17144i	−0.810512	+	0.585722i	$0.800811\pi$
$588$		0			0
$589$			145.447i			0.0101749i
$590$		0			0
$591$	−323.565	−	560.431i	−0.0225206	−	0.0390068i
$592$		0			0
$593$	−10634.9	−	6140.07i	−0.736465	−	0.425198i	0.0843179	−	0.996439i	$-0.473129\pi$
$593$	−10634.9	−	6140.07i	−0.736465	−	0.425198i	−0.820782	+	0.571241i	$0.806462\pi$
$594$		0			0
$595$	−9311.47	−	393.675i	−0.641568	−	0.0271246i
$596$		0			0
$597$	−6278.44	−	3624.86i	−0.430418	−	0.248502i
$598$		0			0
$599$	−8795.74	+	5078.22i	−0.599974	+	0.346395i	−0.769031	−	0.639211i	$-0.779261\pi$
$599$	−8795.74	+	5078.22i	−0.599974	+	0.346395i	0.169058	+	0.985606i	$0.445928\pi$
$600$		0			0
$601$		−	11938.9i		−	0.810316i	−0.914247	−	0.405158i	$-0.867217\pi$
$601$		−	11938.9i		−	0.810316i	0.914247	−	0.405158i	$-0.132783\pi$
$602$		0			0
$603$	−964.930			−0.0651658
$604$		0			0
$605$	16344.0	+	28308.6i	1.09831	+	1.90233i
$606$		0			0
$607$	−5904.55	+	10227.0i	−0.394824	+	0.683856i	−0.993079	−	0.117450i	$-0.962528\pi$
$607$	−5904.55	+	10227.0i	−0.394824	+	0.683856i	0.598254	+	0.801306i	$0.295861\pi$
$608$		0			0
$609$	−101.414	+	52.9709i	−0.00674797	+	0.00352461i
$610$		0			0
$611$	−642.547	+	1112.92i	−0.0425445	+	0.0736892i
$612$		0			0
$613$	−917.232	+	529.564i	−0.0604350	+	0.0348922i	−0.529913	−	0.848052i	$-0.677775\pi$
$613$	−917.232	+	529.564i	−0.0604350	+	0.0348922i	0.469478	+	0.882944i	$0.344442\pi$
$614$		0			0
$615$	−13888.2			−0.910612
$616$		0			0
$617$	−17095.6			−1.11546			−0.557732	−	0.830021i	$-0.688328\pi$
$617$	−17095.6			−1.11546			−0.557732	+	0.830021i	$0.688328\pi$
$618$		0			0
$619$	20388.9	−	11771.5i	1.32391	−	0.764358i	0.339557	−	0.940585i	$-0.389723\pi$
$619$	20388.9	−	11771.5i	1.32391	−	0.764358i	0.984349	+	0.176228i	$0.0563895\pi$
$620$		0			0
$621$	2373.34	−	4110.74i	0.153364	−	0.265634i
$622$		0			0
$623$	12479.6	−	19648.8i	0.802544	−	1.26359i
$624$		0			0
$625$	9431.78	−	16336.3i	0.603634	−	1.04553i
$626$		0			0
$627$	121.808	+	210.978i	0.00775847	+	0.0134381i
$628$		0			0
$629$	−9449.08			−0.598982
$630$		0			0
$631$		−	4861.23i		−	0.306692i	−0.988173	−	0.153346i	$-0.950995\pi$
$631$		−	4861.23i		−	0.306692i	0.988173	−	0.153346i	$-0.0490049\pi$
$632$		0			0
$633$	−12238.2	+	7065.75i	−0.768445	+	0.443662i
$634$		0			0
$635$	−13656.2	−	7884.39i	−0.853430	−	0.492728i
$636$		0			0
$637$	−1260.85	−	106.805i	−0.0784252	−	0.00664328i
$638$		0			0
$639$	3515.28	+	2029.55i	0.217625	+	0.125646i
$640$		0			0
$641$	2933.33	+	5080.68i	0.180748	+	0.313066i	0.942136	−	0.335232i	$-0.108815\pi$
$641$	2933.33	+	5080.68i	0.180748	+	0.313066i	−0.761387	+	0.648297i	$0.775481\pi$
$642$		0			0
$643$			7634.50i			0.468235i	0.972208	+	0.234118i	$0.0752200\pi$
$643$			7634.50i			0.468235i	−0.972208	+	0.234118i	$0.924780\pi$
$644$		0			0
$645$			8198.75i			0.500504i
$646$		0			0
$647$	6255.81	+	10835.4i	0.380126	+	0.658397i	0.991080	−	0.133269i	$-0.0425474\pi$
$647$	6255.81	+	10835.4i	0.380126	+	0.658397i	−0.610954	+	0.791666i	$0.709214\pi$
$648$		0			0
$649$	−42508.0	−	24542.0i	−2.57101	−	1.48437i
$650$		0			0
$651$	−3187.36	+	5018.43i	−0.191893	+	0.302132i
$652$		0			0
$653$	15946.7	+	9206.83i	0.955655	+	0.551748i	0.894833	−	0.446401i	$-0.147294\pi$
$653$	15946.7	+	9206.83i	0.955655	+	0.551748i	0.0608221	+	0.998149i	$0.480628\pi$
$654$		0			0
$655$	−23373.0	+	13494.4i	−1.39429	+	0.804992i
$656$		0			0
$657$			4104.86i			0.243753i
$658$		0			0
$659$	17590.5			1.03980			0.519900	−	0.854227i	$-0.325969\pi$
$659$	17590.5			1.03980			0.519900	+	0.854227i	$0.325969\pi$
$660$		0			0
$661$	11474.0	+	19873.5i	0.675167	+	1.16942i	0.976420	+	0.215880i	$0.0692619\pi$
$661$	11474.0	+	19873.5i	0.675167	+	1.16942i	−0.301253	+	0.953544i	$0.597405\pi$
$662$		0			0
$663$	190.650	−	330.216i	0.0111678	−	0.0193432i
$664$		0			0
$665$	−170.236	−	325.922i	−0.00992705	−	0.0190056i
$666$		0			0
$667$	−181.013	+	313.524i	−0.0105080	+	0.0182004i
$668$		0			0
$669$	−4090.59	+	2361.70i	−0.236399	+	0.136485i
$670$		0			0
$671$	−8047.70			−0.463007
$672$		0			0
$673$	−7222.11			−0.413658			−0.206829	−	0.978377i	$-0.566314\pi$
$673$	−7222.11			−0.413658			−0.206829	+	0.978377i	$0.566314\pi$
$674$		0			0
$675$	2065.62	−	1192.58i	0.117786	−	0.0680038i
$676$		0			0
$677$	3598.04	−	6231.99i	0.204260	−	0.353789i	−0.745637	−	0.666353i	$-0.767855\pi$
$677$	3598.04	−	6231.99i	0.204260	−	0.353789i	0.949897	+	0.312564i	$0.101188\pi$
$678$		0			0
$679$	−19084.1	−	806.847i	−1.07862	−	0.0456023i
$680$		0			0
$681$	−7150.17	+	12384.5i	−0.402342	+	0.696877i
$682$		0			0
$683$	10062.8	+	17429.2i	0.563751	+	0.976445i	0.997165	+	0.0752497i	$0.0239754\pi$
$683$	10062.8	+	17429.2i	0.563751	+	0.976445i	−0.433414	+	0.901195i	$0.642691\pi$
$684$		0			0
$685$	37847.4			2.11106
$686$		0			0
$687$		−	1337.21i		−	0.0742616i
$688$		0			0
$689$	960.080	−	554.303i	0.0530858	−	0.0306491i
$690$		0			0
$691$	11399.1	+	6581.29i	0.627559	+	0.362322i	0.779806	−	0.626021i	$-0.215318\pi$
$691$	11399.1	+	6581.29i	0.627559	+	0.362322i	−0.152247	+	0.988342i	$0.548651\pi$
$692$		0			0
$693$	−420.623	+	9948.85i	−0.0230565	+	0.545347i
$694$		0			0
$695$	38205.5	+	22057.9i	2.08520	+	1.20389i
$696$		0			0
$697$	−5459.87	−	9456.77i	−0.296711	−	0.513918i
$698$		0			0
$699$			1941.74i			0.105069i
$700$		0			0
$701$		−	18196.2i		−	0.980402i	−0.871609	−	0.490201i	$-0.836923\pi$
$701$		−	18196.2i		−	0.980402i	0.871609	−	0.490201i	$-0.163077\pi$
$702$		0			0
$703$	−186.402	−	322.858i	−0.0100004	−	0.0173212i
$704$		0			0
$705$	−13219.0	−	7632.01i	−0.706181	−	0.407714i
$706$		0			0
$707$	−17227.7	+	8998.42i	−0.916429	+	0.478671i
$708$		0			0
$709$	−16885.4	−	9748.77i	−0.894419	−	0.516393i	−0.0190336	−	0.999819i	$-0.506059\pi$
$709$	−16885.4	−	9748.77i	−0.894419	−	0.516393i	−0.875385	+	0.483426i	$0.839392\pi$
$710$		0			0
$711$	9350.85	−	5398.72i	0.493227	−	0.284765i
$712$		0			0
$713$			18811.1i			0.988054i
$714$		0			0
$715$	3219.07			0.168372
$716$		0			0
$717$	2221.97	+	3848.56i	0.115733	+	0.200456i
$718$		0			0
$719$	7262.67	−	12579.3i	0.376707	−	0.652475i	−0.613874	−	0.789404i	$-0.710390\pi$
$719$	7262.67	−	12579.3i	0.376707	−	0.652475i	0.990581	+	0.136929i	$0.0437232\pi$
$720$		0			0
$721$	−7738.75	−	4915.13i	−0.399731	−	0.253882i
$722$		0			0
$723$	5139.11	−	8901.20i	0.264351	−	0.457869i
$724$		0			0
$725$	−157.543	+	90.9577i	−0.00807036	+	0.00465942i
$726$		0			0
$727$	1.46093			7.45292e−5			3.72646e−5	−	1.00000i	$-0.499988\pi$
$727$	1.46093			7.45292e−5			3.72646e−5		1.00000i	$0.499988\pi$
$728$		0			0
$729$	−729.000			−0.0370370
$730$		0			0
$731$	−5582.70	+	3223.17i	−0.282467	+	0.163083i
$732$		0			0
$733$	2012.81	−	3486.29i	0.101426	−	0.175674i	−0.810847	−	0.585259i	$-0.800993\pi$
$733$	2012.81	−	3486.29i	0.101426	−	0.175674i	0.912272	+	0.409584i	$0.134326\pi$
$734$		0			0
$735$	1268.60	−	14976.1i	0.0636641	−	0.751567i
$736$		0			0
$737$	3202.54	−	5546.96i	0.160064	−	0.277239i
$738$		0			0
$739$	−4955.72	−	8583.56i	−0.246684	−	0.427269i	0.715920	−	0.698182i	$-0.246008\pi$
$739$	−4955.72	−	8583.56i	−0.246684	−	0.427269i	−0.962604	+	0.270914i	$0.912674\pi$
$740$		0			0
$741$	15.0439			0.000745817
$742$		0			0
$743$		−	5753.42i		−	0.284081i	−0.989861	−	0.142041i	$-0.954634\pi$
$743$		−	5753.42i		−	0.284081i	0.989861	−	0.142041i	$-0.0453664\pi$
$744$		0			0
$745$	8658.94	−	4999.24i	0.425824	−	0.245850i
$746$		0			0
$747$	−4238.08	−	2446.86i	−0.207581	−	0.119847i
$748$		0			0
$749$	−30497.9	−	19370.2i	−1.48781	−	0.944956i
$750$		0			0
$751$	−18819.5	−	10865.4i	−0.914426	−	0.527944i	−0.0325731	−	0.999469i	$-0.510370\pi$
$751$	−18819.5	−	10865.4i	−0.914426	−	0.527944i	−0.881852	+	0.471526i	$0.843704\pi$
$752$		0			0
$753$	1476.61	+	2557.57i	0.0714619	+	0.123776i
$754$		0			0
$755$			45222.1i			2.17987i
$756$		0			0
$757$		−	6876.55i		−	0.330162i	−0.986280	−	0.165081i	$-0.947212\pi$
$757$		−	6876.55i		−	0.330162i	0.986280	−	0.165081i	$-0.0527885\pi$
$758$		0			0
$759$	15753.9	+	27286.6i	0.753400	+	1.30493i
$760$		0			0
$761$	17277.0	+	9974.87i	0.822983	+	0.475150i	0.851444	−	0.524445i	$-0.175727\pi$
$761$	17277.0	+	9974.87i	0.822983	+	0.475150i	−0.0284609	+	0.999595i	$0.509061\pi$
$762$		0			0
$763$	1127.89	+	2159.37i	0.0535153	+	0.102457i
$764$		0			0
$765$	3922.22	+	2264.50i	0.185370	+	0.107024i
$766$		0			0
$767$	−2624.96	+	1515.52i	−0.123575	+	0.0713459i
$768$		0			0
$769$			22540.2i			1.05698i	0.848938	+	0.528492i	$0.177242\pi$
$769$			22540.2i			1.05698i	−0.848938	+	0.528492i	$0.822758\pi$
$770$		0			0
$771$	16099.5			0.752023
$772$		0			0
$773$	−4451.60	−	7710.40i	−0.207132	−	0.358763i	0.743678	−	0.668538i	$-0.233080\pi$
$773$	−4451.60	−	7710.40i	−0.207132	−	0.358763i	−0.950810	+	0.309775i	$0.899746\pi$
$774$		0			0
$775$	−4726.22	+	8186.06i	−0.219059	+	0.379422i
$776$		0			0
$777$	643.675	−	15224.6i	0.0297191	−	0.702935i
$778$		0			0
$779$	215.414	−	373.108i	0.00990758	−	0.0171604i
$780$		0			0
$781$	−23334.0	+	13471.9i	−1.06908	+	0.617236i
$782$		0			0
$783$	55.6004			0.00253767
$784$		0			0
$785$	14237.9			0.647352
$786$		0			0
$787$	16667.3	−	9622.88i	0.754925	−	0.435856i	−0.0725459	−	0.997365i	$-0.523112\pi$
$787$	16667.3	−	9622.88i	0.754925	−	0.435856i	0.827471	+	0.561509i	$0.189779\pi$
$788$		0			0
$789$	9634.03	−	16686.6i	0.434703	−	0.752927i
$790$		0			0
$791$	−937.182	+	22166.9i	−0.0421269	+	0.996413i
$792$		0			0
$793$	−248.481	+	430.382i	−0.0111272	+	0.0192728i
$794$		0			0
$795$	6583.86	+	11403.6i	0.293718	+	0.508734i
$796$		0			0
$797$	−8439.84			−0.375100			−0.187550	−	0.982255i	$-0.560055\pi$
$797$	−8439.84			−0.375100			−0.187550	+	0.982255i	$0.560055\pi$
$798$		0			0
$799$		−	12001.5i		−	0.531392i
$800$		0			0
$801$	−9796.09	+	5655.77i	−0.432120	+	0.249484i
$802$		0			0
$803$	−23597.0	−	13623.7i	−1.03701	−	0.598719i
$804$		0			0
$805$	−22017.3	−	42152.7i	−0.963984	−	1.84557i
$806$		0			0
$807$	14156.4	+	8173.21i	0.617509	+	0.356519i
$808$		0			0
$809$	303.899	+	526.369i	0.0132071	+	0.0228754i	0.872553	−	0.488519i	$-0.162463\pi$
$809$	303.899	+	526.369i	0.0132071	+	0.0228754i	−0.859346	+	0.511394i	$0.829129\pi$
$810$		0			0
$811$		−	11135.6i		−	0.482151i	−0.970506	−	0.241076i	$-0.922500\pi$
$811$		−	11135.6i		−	0.482151i	0.970506	−	0.241076i	$-0.0775002\pi$
$812$		0			0
$813$			15869.8i			0.684596i
$814$		0			0
$815$	−17076.3	−	29577.1i	−0.733936	−	1.27121i
$816$		0			0
$817$	−220.260	−	127.167i	−0.00943198	−	0.00544556i
$818$		0			0
$819$	519.067	+	329.676i	0.0221461	+	0.0140657i
$820$		0			0
$821$	−15564.9	−	8986.41i	−0.661656	−	0.382007i	0.131252	−	0.991349i	$-0.458100\pi$
$821$	−15564.9	−	8986.41i	−0.661656	−	0.382007i	−0.792908	+	0.609342i	$0.791434\pi$
$822$		0			0
$823$	13440.2	−	7759.71i	0.569255	−	0.328659i	−0.187597	−	0.982246i	$-0.560070\pi$
$823$	13440.2	−	7759.71i	0.569255	−	0.328659i	0.756852	+	0.653587i	$0.226737\pi$
$824$		0			0
$825$			15832.4i			0.668138i
$826$		0			0
$827$	21438.2			0.901426			0.450713	−	0.892669i	$-0.351170\pi$
$827$	21438.2			0.901426			0.450713	+	0.892669i	$0.351170\pi$
$828$		0			0
$829$	−7490.88	−	12974.6i	−0.313835	−	0.543578i	0.665354	−	0.746528i	$-0.268280\pi$
$829$	−7490.88	−	12974.6i	−0.313835	−	0.543578i	−0.979189	+	0.202950i	$0.934947\pi$
$830$		0			0
$831$	−1272.89	+	2204.70i	−0.0531359	+	0.0920341i
$832$		0			0
$833$	10696.3	−	5023.73i	0.444902	−	0.208958i
$834$		0			0
$835$	31026.6	−	53739.6i	1.28589	−	2.22723i
$836$		0			0
$837$	2501.98	−	1444.52i	0.103323	−	0.0596533i
$838$		0			0
$839$	−12563.7			−0.516980			−0.258490	−	0.966014i	$-0.583225\pi$
$839$	−12563.7			−0.516980			−0.258490	+	0.966014i	$0.583225\pi$
$840$		0			0
$841$	24384.8			0.999826
$842$		0			0
$843$	−6731.23	+	3886.28i	−0.275013	+	0.158779i
$844$		0			0
$845$	−15945.5	+	27618.3i	−0.649160	+	1.12438i
$846$		0			0
$847$	−34987.3	−	22221.5i	−1.41934	−	0.901466i
$848$		0			0
$849$	3043.69	−	5271.82i	0.123038	−	0.213108i
$850$		0			0
$851$	−24108.1	−	41756.4i	−0.971109	−	1.68201i
$852$		0			0
$853$	−19238.5			−0.772231			−0.386116	−	0.922450i	$-0.626183\pi$
$853$	−19238.5			−0.772231			−0.386116	+	0.922450i	$0.626183\pi$
$854$		0			0
$855$			178.687i			0.00714733i
$856$		0			0
$857$	6425.02	−	3709.48i	0.256096	−	0.147857i	−0.366456	−	0.930435i	$-0.619429\pi$
$857$	6425.02	−	3709.48i	0.256096	−	0.147857i	0.622552	+	0.782578i	$0.286096\pi$
$858$		0			0
$859$	−6056.93	−	3496.97i	−0.240582	−	0.138900i	0.374862	−	0.927080i	$-0.377690\pi$
$859$	−6056.93	−	3496.97i	−0.240582	−	0.138900i	−0.615444	+	0.788181i	$0.711023\pi$
$860$		0			0
$861$	15609.0	−	8152.90i	0.617830	−	0.322706i
$862$		0			0
$863$	2819.97	+	1628.11i	0.111232	+	0.0642196i	0.554584	−	0.832128i	$-0.312878\pi$
$863$	2819.97	+	1628.11i	0.111232	+	0.0642196i	−0.443352	+	0.896348i	$0.646211\pi$
$864$		0			0
$865$	−16225.2	−	28102.8i	−0.637772	−	1.10465i
$866$		0			0
$867$		−	11178.0i		−	0.437862i
$868$		0			0
$869$			71671.9i			2.79782i
$870$		0			0
$871$	−197.764	−	342.537i	−0.00769342	−	0.0133254i
$872$		0			0
$873$	8038.69	+	4641.14i	0.311648	+	0.179930i
$874$		0			0
$875$	−418.902	+	9908.16i	−0.0161846	+	0.382808i
$876$		0			0
$877$	18211.8	+	10514.6i	0.701218	+	0.404848i	0.807801	−	0.589455i	$-0.200658\pi$
$877$	18211.8	+	10514.6i	0.701218	+	0.404848i	−0.106583	+	0.994304i	$0.533991\pi$
$878$		0			0
$879$	24137.4	−	13935.8i	0.926206	−	0.534745i
$880$		0			0
$881$			12959.5i			0.495593i	0.968812	+	0.247796i	$0.0797064\pi$
$881$			12959.5i			0.495593i	−0.968812	+	0.247796i	$0.920294\pi$
$882$		0			0
$883$	31770.3			1.21082			0.605411	−	0.795913i	$-0.293009\pi$
$883$	31770.3			1.21082			0.605411	+	0.795913i	$0.293009\pi$
$884$		0			0
$885$	−18001.0	−	31178.6i	−0.683724	−	1.18424i
$886$		0			0
$887$	10095.1	−	17485.3i	0.382143	−	0.661891i	−0.609225	−	0.792997i	$-0.708520\pi$
$887$	10095.1	−	17485.3i	0.382143	−	0.661891i	0.991368	+	0.131106i	$0.0418528\pi$
$888$		0			0
$889$	19976.6	+	844.581i	0.753648	+	0.0318632i
$890$		0			0
$891$	2419.50	−	4190.70i	0.0909724	−	0.157569i
$892$		0			0
$893$	410.069	−	236.754i	0.0153667	−	0.00887196i
$894$		0			0
$895$	−41461.2			−1.54849
$896$		0			0
$897$	1945.68			0.0724239
$898$		0			0
$899$	−190.824	+	110.172i	−0.00707936	+	0.00408727i
$900$		0			0
$901$	−5176.63	+	8966.18i	−0.191408	+	0.331528i
$902$		0			0
$903$	−4812.98	−	9214.58i	−0.177371	−	0.339581i
$904$		0			0
$905$	4723.31	−	8181.02i	0.173490	−	0.300493i
$906$		0			0
$907$	11196.6	+	19393.1i	0.409897	+	0.709962i	0.994878	−	0.101085i	$-0.0322313\pi$
$907$	11196.6	+	19393.1i	0.409897	+	0.709962i	−0.584981	+	0.811047i	$0.698898\pi$
$908$		0			0
$909$	9445.10			0.344636
$910$		0			0
$911$		−	37754.2i		−	1.37306i	−0.727104	−	0.686528i	$-0.759134\pi$
$911$		−	37754.2i		−	1.37306i	0.727104	−	0.686528i	$-0.240866\pi$
$912$		0			0
$913$	28131.8	−	16241.9i	1.01974	−	0.588750i
$914$		0			0
$915$	−5111.97	−	2951.40i	−0.184696	−	0.106634i
$916$		0			0
$917$	18347.2	−	28887.2i	0.660717	−	1.04028i
$918$		0			0
$919$	37420.7	+	21604.8i	1.34319	+	0.775493i	0.987275	−	0.159024i	$-0.0508348\pi$
$919$	37420.7	+	21604.8i	1.34319	+	0.775493i	0.355918	+	0.934517i	$0.384168\pi$
$920$		0			0
$921$	−3321.02	−	5752.18i	−0.118818	−	0.205799i
$922$		0			0
$923$			1663.83i			0.0593345i
$924$		0			0
$925$		−	24228.2i		−	0.861209i
$926$		0			0
$927$	2227.54	+	3858.22i	0.0789235	+	0.136700i
$928$		0			0
$929$	10561.3	+	6097.59i	0.372988	+	0.215345i	0.674763	−	0.738034i	$-0.264246\pi$
$929$	10561.3	+	6097.59i	0.372988	+	0.215345i	−0.301775	+	0.953379i	$0.597579\pi$
$930$		0			0
$931$	382.658	+	266.369i	0.0134706	+	0.00937690i
$932$		0			0
$933$	23007.4	+	13283.4i	0.807320	+	0.466107i
$934$		0			0
$935$	−26035.2	+	15031.4i	−0.910632	+	0.525754i
$936$		0			0
$937$		−	30925.8i		−	1.07823i	−0.842232	−	0.539116i	$-0.818758\pi$
$937$		−	30925.8i		−	1.07823i	0.842232	−	0.539116i	$-0.181242\pi$
$938$		0			0
$939$	−570.831			−0.0198385
$940$		0			0
$941$	10353.7	+	17933.2i	0.358684	+	0.621259i	0.987741	−	0.156100i	$-0.0498922\pi$
$941$	10353.7	+	17933.2i	0.358684	+	0.621259i	−0.629057	+	0.777359i	$0.716559\pi$
$942$		0			0
$943$	27860.2	−	48255.4i	0.962094	−	1.66640i
$944$		0			0
$945$	−3915.80	+	6165.34i	−0.134795	+	0.212231i
$946$		0			0
$947$	−11086.5	+	19202.4i	−0.380425	+	0.658916i	−0.991123	−	0.132948i	$-0.957556\pi$
$947$	−11086.5	+	19202.4i	−0.380425	+	0.658916i	0.610698	+	0.791864i	$0.290889\pi$
$948$		0			0
$949$	−1457.17	+	841.295i	−0.0498437	+	0.0287772i
$950$		0			0
$951$	1309.91			0.0446653
$952$		0			0
$953$	44804.6			1.52294			0.761471	−	0.648199i	$-0.224477\pi$
$953$	44804.6			1.52294			0.761471	+	0.648199i	$0.224477\pi$
$954$		0			0
$955$	−37471.5	+	21634.2i	−1.26969	+	0.733053i
$956$		0			0
$957$	−184.534	+	319.622i	−0.00623316	+	0.0107962i
$958$		0			0
$959$	−42536.7	+	22217.9i	−1.43231	+	0.748125i
$960$		0			0
$961$	9170.86	−	15884.4i	0.307840	−	0.533195i
$962$		0			0
$963$	8778.60	+	15205.0i	0.293755	+	0.508799i
$964$		0			0
$965$	45507.3			1.51806
$966$		0			0
$967$		−	9889.71i		−	0.328885i	−0.986387	−	0.164442i	$-0.947418\pi$
$967$		−	9889.71i		−	0.328885i	0.986387	−	0.164442i	$-0.0525825\pi$
$968$		0			0
$969$	−121.672	+	70.2473i	−0.00403371	+	0.00232886i
$970$		0			0
$971$	−17583.8	−	10152.0i	−0.581144	−	0.335524i	0.180444	−	0.983585i	$-0.442247\pi$
$971$	−17583.8	−	10152.0i	−0.581144	−	0.335524i	−0.761588	+	0.648062i	$0.775580\pi$
$972$		0			0
$973$	−55888.0	−	2362.86i	−1.84140	−	0.0778519i
$974$		0			0
$975$	846.701	+	488.843i	0.0278114	+	0.0160569i
$976$		0			0
$977$	6912.50	+	11972.8i	0.226357	+	0.392061i	0.956726	−	0.290992i	$-0.0939852\pi$
$977$	6912.50	+	11972.8i	0.226357	+	0.392061i	−0.730369	+	0.683053i	$0.760652\pi$
$978$		0			0
$979$		−	75084.6i		−	2.45119i
$980$		0			0
$981$		−	1183.87i		−	0.0385303i
$982$		0			0
$983$	3749.52	+	6494.36i	0.121659	+	0.210720i	0.920422	−	0.390926i	$-0.127845\pi$
$983$	3749.52	+	6494.36i	0.121659	+	0.210720i	−0.798763	+	0.601646i	$0.794512\pi$
$984$		0			0
$985$	2728.58	+	1575.35i	0.0882637	+	0.0509591i
$986$		0			0
$987$	19337.1	+	817.546i	0.623615	+	0.0263655i
$988$		0			0
$989$	−28487.0	−	16447.0i	−0.915910	−	0.528801i
$990$		0			0
$991$	−9141.90	+	5278.08i	−0.293039	+	0.169186i	−0.639312	−	0.768948i	$-0.720781\pi$
$991$	−9141.90	+	5278.08i	−0.293039	+	0.169186i	0.346272	+	0.938134i	$0.387447\pi$
$992$		0			0
$993$			29564.2i			0.944806i
$994$		0			0
$995$	35296.8			1.12461
$996$		0			0
$997$	−29838.4	−	51681.7i	−0.947836	−	1.64170i	−0.749971	−	0.661471i	$-0.769932\pi$
$997$	−29838.4	−	51681.7i	−0.947836	−	1.64170i	−0.197866	−	0.980229i	$-0.563401\pi$
$998$		0			0
$999$	−3702.54	+	6412.99i	−0.117260	+	0.203101i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.4.bb.a.271.20		96
4.3	odd	2		168.4.t.a.19.29	yes	96
7.3	odd	6	inner	672.4.bb.a.367.19		96
8.3	odd	2	inner	672.4.bb.a.271.19		96
8.5	even	2		168.4.t.a.19.3	✓	96
28.3	even	6		168.4.t.a.115.3	yes	96
56.3	even	6	inner	672.4.bb.a.367.20		96
56.45	odd	6		168.4.t.a.115.29	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.t.a.19.3	✓	96	8.5	even	2
168.4.t.a.19.29	yes	96	4.3	odd	2
168.4.t.a.115.3	yes	96	28.3	even	6
168.4.t.a.115.29	yes	96	56.45	odd	6
672.4.bb.a.271.19		96	8.3	odd	2	inner
672.4.bb.a.271.20		96	1.1	even	1	trivial
672.4.bb.a.367.19		96	7.3	odd	6	inner
672.4.bb.a.367.20		96	56.3	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	672.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.59808 + 1.50000i) q^{3} +(7.30307 - 12.6493i) q^{5} +(-0.782311 + 18.5037i) q^{7} +(4.50000 - 7.79423i) q^{9} +(29.8704 + 51.7370i) q^{11} +3.68912 q^{13} +43.8184i q^{15} +(-29.8369 + 17.2263i) q^{17} +(-1.17719 - 0.679649i) q^{19} +(-25.7231 - 49.2476i) q^{21} +(-152.250 - 87.9014i) q^{23} +(-44.1698 - 76.5043i) q^{25} +27.0000i q^{27} -2.05927i q^{29} +(-53.5006 - 92.6658i) q^{31} +(-155.211 - 89.6112i) q^{33} +(228.346 + 145.030i) q^{35} +(237.518 + 137.131i) q^{37} +(-9.58462 + 5.53369i) q^{39} +316.949i q^{41} +187.107 q^{43} +(-65.7277 - 113.844i) q^{45} +(-174.173 + 301.677i) q^{47} +(-341.776 - 28.9513i) q^{49} +(51.6790 - 89.5107i) q^{51} +(260.246 - 150.253i) q^{53} +872.583 q^{55} +4.07790 q^{57} +(-711.540 + 410.808i) q^{59} +(-67.3551 + 116.662i) q^{61} +(140.702 + 89.3643i) q^{63} +(26.9419 - 46.6648i) q^{65} +(-53.6072 - 92.8504i) q^{67} +527.409 q^{69} +451.011i q^{71} +(-394.990 + 228.048i) q^{73} +(229.513 + 132.509i) q^{75} +(-980.696 + 512.239i) q^{77} +(1038.98 + 599.857i) q^{79} +(-40.5000 - 70.1481i) q^{81} -543.746i q^{83} +503.221i q^{85} +(3.08891 + 5.35015i) q^{87} +(-1088.45 - 628.419i) q^{89} +(-2.88604 + 68.2625i) q^{91} +(277.997 + 160.502i) q^{93} +(-17.1942 + 9.92706i) q^{95} +1031.36i q^{97} +537.667 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 432 q^{9} - 40 q^{11} - 1200 q^{25} - 456 q^{35} + 1616 q^{43} - 360 q^{49} - 336 q^{57} - 4128 q^{59} + 1440 q^{67} - 648 q^{73} - 3888 q^{81} + 104 q^{91} - 720 q^{99}+O(q^{100}) \) 96 * q + 432 * q^9 - 40 * q^11 - 1200 * q^25 - 456 * q^35 + 1616 * q^43 - 360 * q^49 - 336 * q^57 - 4128 * q^59 + 1440 * q^67 - 648 * q^73 - 3888 * q^81 + 104 * q^91 - 720 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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