LMFDB - Embedded newform 336.4.bj.e.95.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,4,Mod(95,336)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("336.95"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 3, 4])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,0,0,0,0,0,-38] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			95.13
Character	$\chi$	$=$	336.95
Dual form			336.4.bj.e.191.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.04533 - 1.24284i) q^{3} +(11.5701 - 6.68000i) q^{5} +(16.4792 - 8.45200i) q^{7} +(23.9107 - 12.5411i) q^{9} +(11.6130 - 20.1143i) q^{11} -10.0140 q^{13} +(50.0727 - 48.0826i) q^{15} +(-11.8337 - 6.83218i) q^{17} +(-86.0386 + 49.6744i) q^{19} +(72.6384 - 63.1242i) q^{21} +(19.9988 + 34.6389i) q^{23} +(26.7447 - 46.3232i) q^{25} +(105.051 - 92.9913i) q^{27} +107.245i q^{29} +(-190.094 - 109.751i) q^{31} +(33.5924 - 115.916i) q^{33} +(134.206 - 207.871i) q^{35} +(36.4793 + 63.1841i) q^{37} +(-50.5238 + 12.4458i) q^{39} +469.609i q^{41} -223.017i q^{43} +(192.874 - 304.825i) q^{45} +(-29.2317 - 50.6307i) q^{47} +(200.127 - 278.564i) q^{49} +(-68.1962 - 19.7632i) q^{51} +(152.639 + 88.1261i) q^{53} -310.299i q^{55} +(-372.356 + 357.556i) q^{57} +(302.084 - 523.224i) q^{59} +(452.924 + 784.488i) q^{61} +(288.031 - 408.760i) q^{63} +(-115.863 + 66.8933i) q^{65} +(-536.945 - 310.005i) q^{67} +(143.951 + 149.909i) q^{69} -415.880 q^{71} +(-80.5578 + 139.530i) q^{73} +(77.3634 - 266.955i) q^{75} +(21.3667 - 429.620i) q^{77} +(25.4816 - 14.7118i) q^{79} +(414.441 - 599.733i) q^{81} +1419.98 q^{83} -182.556 q^{85} +(133.289 + 541.088i) q^{87} +(1167.51 - 674.063i) q^{89} +(-165.022 + 84.6381i) q^{91} +(-1095.49 - 317.472i) q^{93} +(-663.650 + 1149.48i) q^{95} +229.880 q^{97} +(25.4190 - 626.586i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 38 q^{7} - 70 q^{9} + 124 q^{13} + 462 q^{19} + 500 q^{21} + 566 q^{25} - 1266 q^{31} + 64 q^{33} + 338 q^{37} - 1254 q^{39} - 488 q^{45} - 206 q^{49} - 522 q^{51} + 2324 q^{57} - 340 q^{61} + 840 q^{63}+ \cdots - 3344 q^{97}+O(q^{100}) $ 28 * q - 38 * q^7 - 70 * q^9 + 124 * q^13 + 462 * q^19 + 500 * q^21 + 566 * q^25 - 1266 * q^31 + 64 * q^33 + 338 * q^37 - 1254 * q^39 - 488 * q^45 - 206 * q^49 - 522 * q^51 + 2324 * q^57 - 340 * q^61 + 840 * q^63 - 2934 * q^67 - 776 * q^69 + 2050 * q^73 + 1458 * q^75 - 2070 * q^79 + 910 * q^81 + 2400 * q^85 - 3132 * q^87 + 5170 * q^91 + 714 * q^93 - 3344 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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
$3$	5.04533	−	1.24284i	0.970974	−	0.239185i
$3$	5.04533	−	1.24284i	0.970974	−	0.239185i
$4$		0			0
$5$	11.5701	−	6.68000i	1.03486	−	0.597477i	0.116487	−	0.993192i	$-0.462837\pi$
$5$	11.5701	−	6.68000i	1.03486	−	0.597477i	0.918373	+	0.395715i	$0.129503\pi$
$6$		0			0
$7$	16.4792	−	8.45200i	0.889793	−	0.456365i
$7$	16.4792	−	8.45200i	0.889793	−	0.456365i
$8$		0			0
$9$	23.9107	−	12.5411i	0.885581	−	0.464486i
$10$		0			0
$11$	11.6130	−	20.1143i	0.318314	−	0.551335i	−0.661823	−	0.749660i	$-0.730217\pi$
$11$	11.6130	−	20.1143i	0.318314	−	0.551335i	0.980136	+	0.198325i	$0.0635502\pi$
$12$		0			0
$13$	−10.0140			−0.213644			−0.106822	−	0.994278i	$-0.534068\pi$
$13$	−10.0140			−0.213644			−0.106822	+	0.994278i	$0.534068\pi$
$14$		0			0
$15$	50.0727	−	48.0826i	0.861915	−	0.827658i
$16$		0			0
$17$	−11.8337	−	6.83218i	−0.168829	−	0.0974734i	0.413205	−	0.910638i	$-0.364409\pi$
$17$	−11.8337	−	6.83218i	−0.168829	−	0.0974734i	−0.582034	+	0.813165i	$0.697743\pi$
$18$		0			0
$19$	−86.0386	+	49.6744i	−1.03887	+	0.599794i	−0.919514	−	0.393057i	$-0.871418\pi$
$19$	−86.0386	+	49.6744i	−1.03887	+	0.599794i	−0.119360	+	0.992851i	$0.538084\pi$
$20$		0			0
$21$	72.6384	−	63.1242i	0.754809	−	0.655944i
$22$		0			0
$23$	19.9988	+	34.6389i	0.181306	+	0.314031i	0.942326	−	0.334698i	$-0.108634\pi$
$23$	19.9988	+	34.6389i	0.181306	+	0.314031i	−0.761020	+	0.648729i	$0.775301\pi$
$24$		0			0
$25$	26.7447	−	46.3232i	0.213958	−	0.370586i
$26$		0			0
$27$	105.051	−	92.9913i	0.748778	−	0.662821i
$28$		0			0
$29$			107.245i			0.686723i	0.939203	+	0.343362i	$0.111566\pi$
$29$			107.245i			0.686723i	−0.939203	+	0.343362i	$0.888434\pi$
$30$		0			0
$31$	−190.094	−	109.751i	−1.10135	−	0.635865i	−0.164775	−	0.986331i	$-0.552690\pi$
$31$	−190.094	−	109.751i	−1.10135	−	0.635865i	−0.936575	+	0.350466i	$0.886023\pi$
$32$		0			0
$33$	33.5924	−	115.916i	0.177203	−	0.611468i
$34$		0			0
$35$	134.206	−	207.871i	0.648144	−	1.00391i
$36$		0			0
$37$	36.4793	+	63.1841i	0.162086	+	0.280740i	0.935616	−	0.353018i	$-0.114845\pi$
$37$	36.4793	+	63.1841i	0.162086	+	0.280740i	−0.773531	+	0.633759i	$0.781511\pi$
$38$		0			0
$39$	−50.5238	+	12.4458i	−0.207443	+	0.0511006i
$40$		0			0
$41$			469.609i			1.78880i	0.447272	+	0.894398i	$0.352396\pi$
$41$			469.609i			1.78880i	−0.447272	+	0.894398i	$0.647604\pi$
$42$		0			0
$43$		−	223.017i		−	0.790926i	−0.918482	−	0.395463i	$-0.870584\pi$
$43$		−	223.017i		−	0.790926i	0.918482	−	0.395463i	$-0.129416\pi$
$44$		0			0
$45$	192.874	−	304.825i	0.638933	−	1.00979i
$46$		0			0
$47$	−29.2317	−	50.6307i	−0.0907208	−	0.157133i	0.817094	−	0.576505i	$-0.195584\pi$
$47$	−29.2317	−	50.6307i	−0.0907208	−	0.157133i	−0.907815	+	0.419372i	$0.862250\pi$
$48$		0			0
$49$	200.127	−	278.564i	0.583462	−	0.812141i
$50$		0			0
$51$	−68.1962	−	19.7632i	−0.187243	−	0.0542627i
$52$		0			0
$53$	152.639	+	88.1261i	0.395596	+	0.228397i	0.684582	−	0.728936i	$-0.259985\pi$
$53$	152.639	+	88.1261i	0.395596	+	0.228397i	−0.288986	+	0.957333i	$0.593318\pi$
$54$		0			0
$55$		−	310.299i		−	0.760740i
$56$		0			0
$57$	−372.356	+	357.556i	−0.865258	+	0.830868i
$58$		0			0
$59$	302.084	−	523.224i	0.666575	−	1.15454i	−0.312281	−	0.949990i	$-0.601093\pi$
$59$	302.084	−	523.224i	0.666575	−	1.15454i	0.978856	−	0.204552i	$-0.0655737\pi$
$60$		0			0
$61$	452.924	+	784.488i	0.950672	+	1.64661i	0.743975	+	0.668208i	$0.232938\pi$
$61$	452.924	+	784.488i	0.950672	+	1.64661i	0.206697	+	0.978405i	$0.433728\pi$
$62$		0			0
$63$	288.031	−	408.760i	0.576008	−	0.817444i
$64$		0			0
$65$	−115.863	+	66.8933i	−0.221092	+	0.127648i
$66$		0			0
$67$	−536.945	−	310.005i	−0.979078	−	0.565271i	−0.0770864	−	0.997024i	$-0.524562\pi$
$67$	−536.945	−	310.005i	−0.979078	−	0.565271i	−0.901992	+	0.431753i	$0.857895\pi$
$68$		0			0
$69$	143.951	+	149.909i	0.251155	+	0.261550i
$70$		0			0
$71$	−415.880			−0.695153			−0.347576	−	0.937652i	$-0.612995\pi$
$71$	−415.880			−0.695153			−0.347576	+	0.937652i	$0.612995\pi$
$72$		0			0
$73$	−80.5578	+	139.530i	−0.129159	+	0.223709i	−0.923351	−	0.383957i	$-0.874561\pi$
$73$	−80.5578	+	139.530i	−0.129159	+	0.223709i	0.794192	+	0.607667i	$0.207894\pi$
$74$		0			0
$75$	77.3634	−	266.955i	0.119109	−	0.411005i
$76$		0			0
$77$	21.3667	−	429.620i	0.0316228	−	0.635841i
$78$		0			0
$79$	25.4816	−	14.7118i	0.0362900	−	0.0209520i	−0.481745	−	0.876311i	$-0.659997\pi$
$79$	25.4816	−	14.7118i	0.0362900	−	0.0209520i	0.518035	+	0.855359i	$0.326664\pi$
$80$		0			0
$81$	414.441	−	599.733i	0.568506	−	0.822679i
$82$		0			0
$83$	1419.98			1.87787			0.938935	−	0.344095i	$-0.111814\pi$
$83$	1419.98			1.87787			0.938935	+	0.344095i	$0.111814\pi$
$84$		0			0
$85$	−182.556			−0.232953
$86$		0			0
$87$	133.289	+	541.088i	0.164254	+	0.666790i
$88$		0			0
$89$	1167.51	−	674.063i	1.39052	−	0.802815i	0.397144	−	0.917756i	$-0.370001\pi$
$89$	1167.51	−	674.063i	1.39052	−	0.802815i	0.993372	+	0.114941i	$0.0366679\pi$
$90$		0			0
$91$	−165.022	+	84.6381i	−0.190099	+	0.0974999i
$92$		0			0
$93$	−1095.49	−	317.472i	−1.22147	−	0.353981i
$94$		0			0
$95$	−663.650	+	1149.48i	−0.716727	+	1.24141i
$96$		0			0
$97$	229.880			0.240627			0.120313	−	0.992736i	$-0.461610\pi$
$97$	229.880			0.240627			0.120313	+	0.992736i	$0.461610\pi$
$98$		0			0
$99$	25.4190	−	626.586i	0.0258051	−	0.636104i
$100$		0			0
$101$	−856.215	−	494.336i	−0.843530	−	0.487012i	0.0149325	−	0.999889i	$-0.495247\pi$
$101$	−856.215	−	494.336i	−0.843530	−	0.487012i	−0.858463	+	0.512876i	$0.828580\pi$
$102$		0			0
$103$	−1249.44	+	721.366i	−1.19525	+	0.690081i	−0.959494	−	0.281731i	$-0.909092\pi$
$103$	−1249.44	+	721.366i	−1.19525	+	0.690081i	−0.235761	+	0.971811i	$0.575758\pi$
$104$		0			0
$105$	418.764	−	1215.58i	0.389211	−	1.12979i
$106$		0			0
$107$	669.798	+	1160.12i	0.605157	+	1.04816i	0.992027	+	0.126029i	$0.0402231\pi$
$107$	669.798	+	1160.12i	0.605157	+	1.04816i	−0.386869	+	0.922135i	$0.626444\pi$
$108$		0			0
$109$	−621.761	+	1076.92i	−0.546366	+	0.946333i	0.452154	+	0.891940i	$0.350656\pi$
$109$	−621.761	+	1076.92i	−0.546366	+	0.946333i	−0.998520	+	0.0543932i	$0.982678\pi$
$110$		0			0
$111$	262.578	+	273.446i	0.224530	+	0.233823i
$112$		0			0
$113$		−	1678.88i		−	1.39766i	−0.715285	−	0.698832i	$-0.753703\pi$
$113$		−	1678.88i		−	1.39766i	0.715285	−	0.698832i	$-0.246297\pi$
$114$		0			0
$115$	462.776	+	267.184i	0.375253	+	0.216652i
$116$		0			0
$117$	−239.441	+	125.586i	−0.189199	+	0.0992347i
$118$		0			0
$119$	−252.755	−	12.5705i	−0.194706	−	0.00968349i
$120$		0			0
$121$	395.777	+	685.505i	0.297353	+	0.515030i
$122$		0			0
$123$	583.651	+	2369.33i	0.427854	+	1.73687i
$124$		0			0
$125$			955.380i			0.683615i
$126$		0			0
$127$			51.9979i			0.0363312i	0.999835	+	0.0181656i	$0.00578261\pi$
$127$			51.9979i			0.0363312i	−0.999835	+	0.0181656i	$0.994217\pi$
$128$		0			0
$129$	−277.176	−	1125.20i	−0.189178	−	0.767968i
$130$		0			0
$131$	−1266.66	−	2193.92i	−0.844799	−	1.46323i	−0.885796	−	0.464075i	$-0.846387\pi$
$131$	−1266.66	−	2193.92i	−0.844799	−	1.46323i	0.0409970	−	0.999159i	$-0.486947\pi$
$132$		0			0
$133$	−997.998	+	1545.79i	−0.650657	+	1.00780i
$134$		0			0
$135$	594.264	−	1777.66i	0.378860	−	1.13331i
$136$		0			0
$137$	672.176	+	388.081i	0.419182	+	0.242015i	0.694727	−	0.719273i	$-0.255525\pi$
$137$	672.176	+	388.081i	0.419182	+	0.242015i	−0.275546	+	0.961288i	$0.588858\pi$
$138$		0			0
$139$			2238.46i			1.36592i	0.730454	+	0.682962i	$0.239309\pi$
$139$			2238.46i			1.36592i	−0.730454	+	0.682962i	$0.760691\pi$
$140$		0			0
$141$	−210.409	−	219.118i	−0.125671	−	0.130873i
$142$		0			0
$143$	−116.292	+	201.424i	−0.0680059	+	0.117790i
$144$		0			0
$145$	716.399	+	1240.84i	0.410301	+	0.710663i
$146$		0			0
$147$	663.496	−	1654.18i	0.372274	−	0.928123i
$148$		0			0
$149$	−2026.78	+	1170.16i	−1.11436	+	0.643377i	−0.939956	−	0.341297i	$-0.889134\pi$
$149$	−2026.78	+	1170.16i	−1.11436	+	0.643377i	−0.174406	+	0.984674i	$0.555801\pi$
$150$		0			0
$151$	1937.87	+	1118.83i	1.04438	+	0.602973i	0.921071	−	0.389396i	$-0.127316\pi$
$151$	1937.87	+	1118.83i	1.04438	+	0.602973i	0.123309	+	0.992368i	$0.460649\pi$
$152$		0			0
$153$	−368.635	−	14.9545i	−0.194787	−	0.00790198i
$154$		0			0
$155$	−2932.54			−1.51966
$156$		0			0
$157$	−1587.02	+	2748.81i	−0.806741	+	1.39732i	0.108369	+	0.994111i	$0.465437\pi$
$157$	−1587.02	+	2748.81i	−0.806741	+	1.39732i	−0.915110	+	0.403205i	$0.867896\pi$
$158$		0			0
$159$	879.640	+	254.919i	0.438742	+	0.127147i
$160$		0			0
$161$	622.332	+	401.792i	0.304638	+	0.196681i
$162$		0			0
$163$	−1826.31	+	1054.42i	−0.877591	+	0.506678i	−0.869863	−	0.493293i	$-0.835793\pi$
$163$	−1826.31	+	1054.42i	−0.877591	+	0.506678i	−0.00772789	+	0.999970i	$0.502460\pi$
$164$		0			0
$165$	−385.653	−	1565.56i	−0.181958	−	0.738659i
$166$		0			0
$167$	−996.345			−0.461673			−0.230837	−	0.972993i	$-0.574146\pi$
$167$	−996.345			−0.461673			−0.230837	+	0.972993i	$0.574146\pi$
$168$		0			0
$169$	−2096.72			−0.954356
$170$		0			0
$171$	−1434.27	+	2266.77i	−0.641411	+	1.01371i
$172$		0			0
$173$	−3624.74	+	2092.74i	−1.59297	+	0.919702i	−0.600177	+	0.799867i	$0.704903\pi$
$173$	−3624.74	+	2092.74i	−1.59297	+	0.919702i	−0.992794	+	0.119835i	$0.961764\pi$
$174$		0			0
$175$	49.2075	−	989.416i	0.0212556	−	0.427387i
$176$		0			0
$177$	873.825	−	3015.28i	0.371077	−	1.28046i
$178$		0			0
$179$	−1752.48	+	3035.39i	−0.731769	+	1.26746i	0.224358	+	0.974507i	$0.427972\pi$
$179$	−1752.48	+	3035.39i	−0.731769	+	1.26746i	−0.956127	+	0.292954i	$0.905362\pi$
$180$		0			0
$181$	1770.87			0.727225			0.363612	−	0.931550i	$-0.381543\pi$
$181$	1770.87			0.727225			0.363612	+	0.931550i	$0.381543\pi$
$182$		0			0
$183$	3260.15	+	3395.08i	1.31692	+	1.37143i
$184$		0			0
$185$	844.139	+	487.364i	0.335472	+	0.193685i
$186$		0			0
$187$	−274.849	+	158.684i	−0.107481	+	0.0620542i
$188$		0			0
$189$	945.186	−	2420.31i	0.363768	−	0.931490i
$190$		0			0
$191$	715.639	+	1239.52i	0.271109	+	0.469574i	0.969146	−	0.246487i	$-0.0792763\pi$
$191$	715.639	+	1239.52i	0.271109	+	0.469574i	−0.698037	+	0.716062i	$0.745943\pi$
$192$		0			0
$193$	2049.20	−	3549.32i	0.764274	−	1.32376i	−0.176356	−	0.984327i	$-0.556431\pi$
$193$	2049.20	−	3549.32i	0.764274	−	1.32376i	0.940630	−	0.339435i	$-0.110236\pi$
$194$		0			0
$195$	−501.427	+	481.498i	−0.184143	+	0.176825i
$196$		0			0
$197$		−	3993.72i		−	1.44437i	−0.691700	−	0.722185i	$-0.743138\pi$
$197$		−	3993.72i		−	1.44437i	0.691700	−	0.722185i	$-0.256862\pi$
$198$		0			0
$199$	−1629.07	−	940.544i	−0.580310	−	0.335042i	0.180947	−	0.983493i	$-0.442084\pi$
$199$	−1629.07	−	940.544i	−0.580310	−	0.335042i	−0.761257	+	0.648451i	$0.775417\pi$
$200$		0			0
$201$	−3094.35	−	896.739i	−1.08586	−	0.314682i
$202$		0			0
$203$	906.438	+	1767.32i	0.313397	+	0.611041i
$204$		0			0
$205$	3136.99	+	5433.42i	1.06876	+	1.85115i
$206$		0			0
$207$	912.596	+	577.433i	0.306424	+	0.193886i
$208$		0			0
$209$			2307.48i			0.763691i
$210$		0			0
$211$		−	579.780i		−	0.189164i	−0.995517	−	0.0945822i	$-0.969848\pi$
$211$		−	579.780i		−	0.189164i	0.995517	−	0.0945822i	$-0.0301515\pi$
$212$		0			0
$213$	−2098.25	+	516.874i	−0.674975	+	0.166270i
$214$		0			0
$215$	−1489.75	−	2580.33i	−0.472560	−	0.818498i
$216$		0			0
$217$	−4060.21	−	201.930i	−1.27016	−	0.0631700i
$218$		0			0
$219$	−233.026	+	804.096i	−0.0719016	+	0.248109i
$220$		0			0
$221$	118.502	+	68.4173i	0.0360694	+	0.0208247i
$222$		0			0
$223$		−	2261.10i		−	0.678990i	−0.940608	−	0.339495i	$-0.889744\pi$
$223$		−	2261.10i		−	0.678990i	0.940608	−	0.339495i	$-0.110256\pi$
$224$		0			0
$225$	58.5399	−	1443.03i	0.0173452	−	0.427564i
$226$		0			0
$227$	1311.07	−	2270.83i	0.383341	−	0.663967i	−0.608196	−	0.793787i	$-0.708107\pi$
$227$	1311.07	−	2270.83i	0.383341	−	0.663967i	0.991538	+	0.129820i	$0.0414399\pi$
$228$		0			0
$229$	1128.44	+	1954.51i	0.325629	+	0.564007i	0.981640	−	0.190745i	$-0.0610905\pi$
$229$	1128.44	+	1954.51i	0.325629	+	0.564007i	−0.656010	+	0.754752i	$0.727757\pi$
$230$		0			0
$231$	−426.149	−	2194.13i	−0.121379	−	0.624949i
$232$		0			0
$233$	3251.45	−	1877.23i	0.914205	−	0.527817i	0.0324233	−	0.999474i	$-0.489678\pi$
$233$	3251.45	−	1877.23i	0.914205	−	0.527817i	0.881782	+	0.471658i	$0.156344\pi$
$234$		0			0
$235$	−676.426	−	390.535i	−0.187767	−	0.108407i
$236$		0			0
$237$	110.279	−	105.896i	0.0302252	−	0.0290239i
$238$		0			0
$239$	3346.72			0.905780			0.452890	−	0.891566i	$-0.350393\pi$
$239$	3346.72			0.905780			0.452890	+	0.891566i	$0.350393\pi$
$240$		0			0
$241$	−1180.68	+	2045.00i	−0.315579	+	0.546599i	−0.979560	−	0.201150i	$-0.935532\pi$
$241$	−1180.68	+	2045.00i	−0.315579	+	0.546599i	0.663981	+	0.747749i	$0.268865\pi$
$242$		0			0
$243$	1345.62	−	3540.94i	0.355232	−	0.934778i
$244$		0			0
$245$	454.684	−	4559.87i	0.118566	−	1.18906i
$246$		0			0
$247$	861.589	−	497.439i	0.221950	−	0.128143i
$248$		0			0
$249$	7164.27	−	1764.82i	1.82336	−	0.449159i
$250$		0			0
$251$	2672.34			0.672018			0.336009	−	0.941859i	$-0.390923\pi$
$251$	2672.34			0.672018			0.336009	+	0.941859i	$0.390923\pi$
$252$		0			0
$253$	928.984			0.230849
$254$		0			0
$255$	−921.055	+	226.888i	−0.226191	+	0.0557189i
$256$		0			0
$257$	−2224.11	+	1284.09i	−0.539829	+	0.311670i	−0.745010	−	0.667054i	$-0.767555\pi$
$257$	−2224.11	+	1284.09i	−0.539829	+	0.311670i	0.205181	+	0.978724i	$0.434222\pi$
$258$		0			0
$259$	1135.18	+	732.899i	0.272343	+	0.175831i
$260$		0			0
$261$	1344.98	+	2564.31i	0.318973	+	0.608149i
$262$		0			0
$263$	3535.00	−	6122.81i	0.828812	−	1.43555i	−0.0701582	−	0.997536i	$-0.522350\pi$
$263$	3535.00	−	6122.81i	0.828812	−	1.43555i	0.898970	−	0.438009i	$-0.144316\pi$
$264$		0			0
$265$	2354.73			0.545848
$266$		0			0
$267$	5052.72	−	4851.90i	1.15813	−	1.11210i
$268$		0			0
$269$	5423.90	+	3131.49i	1.22937	+	0.709779i	0.966899	−	0.255161i	$-0.0821283\pi$
$269$	5423.90	+	3131.49i	1.22937	+	0.709779i	0.262474	+	0.964939i	$0.415462\pi$
$270$		0			0
$271$	−4335.37	+	2503.03i	−0.971790	+	0.561063i	−0.899782	−	0.436341i	$-0.856274\pi$
$271$	−4335.37	+	2503.03i	−0.971790	+	0.561063i	−0.0720087	+	0.997404i	$0.522941\pi$
$272$		0			0
$273$	−727.399	+	632.124i	−0.161261	+	0.140139i
$274$		0			0
$275$	−621.173	−	1075.90i	−0.136211	−	0.235925i
$276$		0			0
$277$	3255.53	−	5638.74i	0.706157	−	1.22310i	−0.260115	−	0.965578i	$-0.583760\pi$
$277$	3255.53	−	5638.74i	0.706157	−	1.22310i	0.966272	−	0.257523i	$-0.0829063\pi$
$278$		0			0
$279$	−5921.67	−	240.227i	−1.27069	−	0.0515484i
$280$		0			0
$281$		−	3819.59i		−	0.810882i	−0.914121	−	0.405441i	$-0.867118\pi$
$281$		−	3819.59i		−	0.810882i	0.914121	−	0.405441i	$-0.132882\pi$
$282$		0			0
$283$	−3017.67	−	1742.25i	−0.633859	−	0.365958i	0.148386	−	0.988929i	$-0.452592\pi$
$283$	−3017.67	−	1742.25i	−0.633859	−	0.365958i	−0.782245	+	0.622971i	$0.785925\pi$
$284$		0			0
$285$	−1919.71	+	6624.30i	−0.398997	+	1.37680i
$286$		0			0
$287$	3969.14	+	7738.78i	0.816344	+	1.59166i
$288$		0			0
$289$	−2363.14	−	4093.08i	−0.480998	−	0.833113i
$290$		0			0
$291$	1159.82	−	285.705i	0.233642	−	0.0575544i
$292$		0			0
$293$		−	485.271i		−	0.0967571i	−0.998829	−	0.0483785i	$-0.984595\pi$
$293$		−	485.271i		−	0.0967571i	0.998829	−	0.0483785i	$-0.0154054\pi$
$294$		0			0
$295$		−	8071.67i		−	1.59305i
$296$		0			0
$297$	−650.502	−	3192.93i	−0.127091	−	0.623813i
$298$		0			0
$299$	−200.268	−	346.874i	−0.0387350	−	0.0670910i
$300$		0			0
$301$	−1884.94	−	3675.14i	−0.360951	−	0.703760i
$302$		0			0
$303$	−4934.27	−	1429.95i	−0.935532	−	0.271116i
$304$		0			0
$305$	10480.8	+	6051.07i	1.96763	+	1.13601i
$306$		0			0
$307$			1611.66i			0.299617i	0.988715	+	0.149808i	$0.0478656\pi$
$307$			1611.66i			0.299617i	−0.988715	+	0.149808i	$0.952134\pi$
$308$		0			0
$309$	−5407.30	+	5192.39i	−0.995504	+	0.955938i
$310$		0			0
$311$	3502.15	−	6065.90i	0.638549	−	1.10600i	−0.347202	−	0.937790i	$-0.612868\pi$
$311$	3502.15	−	6065.90i	0.638549	−	1.10600i	0.985751	−	0.168209i	$-0.0537984\pi$
$312$		0			0
$313$	72.0217	+	124.745i	0.0130061	+	0.0225272i	0.872455	−	0.488694i	$-0.162527\pi$
$313$	72.0217	+	124.745i	0.0130061	+	0.0225272i	−0.859449	+	0.511221i	$0.829193\pi$
$314$		0			0
$315$	602.029	−	6653.44i	0.107684	−	1.19009i
$316$		0			0
$317$	−7703.34	+	4447.53i	−1.36487	+	0.788006i	−0.990267	−	0.139180i	$-0.955553\pi$
$317$	−7703.34	+	4447.53i	−1.36487	+	0.788006i	−0.374600	+	0.927186i	$0.622220\pi$
$318$		0			0
$319$	2157.17	+	1245.44i	0.378615	+	0.218593i
$320$		0			0
$321$	4821.21	+	5020.75i	0.838297	+	0.872994i
$322$		0			0
$323$	1357.54			0.233856
$324$		0			0
$325$	−267.821	+	463.880i	−0.0457109	+	0.0791736i
$326$		0			0
$327$	−1798.54	+	6206.17i	−0.304158	+	1.04955i
$328$		0			0
$329$	−909.645	−	587.287i	−0.152433	−	0.0984140i
$330$		0			0
$331$	−2898.68	+	1673.55i	−0.481346	+	0.277905i	−0.720977	−	0.692959i	$-0.756307\pi$
$331$	−2898.68	+	1673.55i	−0.481346	+	0.277905i	0.239631	+	0.970864i	$0.422974\pi$
$332$		0			0
$333$	1664.64	+	1053.28i	0.273940	+	0.173332i
$334$		0			0
$335$	−8283.33			−1.35095
$336$		0			0
$337$	3073.13			0.496748			0.248374	−	0.968664i	$-0.420104\pi$
$337$	3073.13			0.496748			0.248374	+	0.968664i	$0.420104\pi$
$338$		0			0
$339$	−2086.59	−	8470.52i	−0.334301	−	1.35710i
$340$		0			0
$341$	−4415.12	+	2549.07i	−0.701150	+	0.404809i
$342$		0			0
$343$	943.511	−	6281.99i	0.148527	−	0.988908i
$344$		0			0
$345$	2666.93	+	772.872i	0.416181	+	0.120609i
$346$		0			0
$347$	−844.772	+	1463.19i	−0.130691	+	0.226363i	−0.923943	−	0.382530i	$-0.875053\pi$
$347$	−844.772	+	1463.19i	−0.130691	+	0.226363i	0.793252	+	0.608893i	$0.208386\pi$
$348$		0			0
$349$	1586.49			0.243333			0.121666	−	0.992571i	$-0.461176\pi$
$349$	1586.49			0.243333			0.121666	+	0.992571i	$0.461176\pi$
$350$		0			0
$351$	−1051.97	+	931.212i	−0.159972	+	0.141608i
$352$		0			0
$353$	−8288.27	−	4785.23i	−1.24969	−	0.721508i	−0.278641	−	0.960395i	$-0.589884\pi$
$353$	−8288.27	−	4785.23i	−1.24969	−	0.721508i	−0.971047	+	0.238887i	$0.923217\pi$
$354$		0			0
$355$	−4811.77	+	2778.08i	−0.719386	+	0.415338i
$356$		0			0
$357$	−1290.86	+	250.713i	−0.191371	+	0.0371685i
$358$		0			0
$359$	−1449.67	−	2510.91i	−0.213122	−	0.369138i	0.739568	−	0.673082i	$-0.235030\pi$
$359$	−1449.67	−	2510.91i	−0.213122	−	0.369138i	−0.952690	+	0.303944i	$0.901697\pi$
$360$		0			0
$361$	1505.60	−	2607.77i	0.219507	−	0.380197i
$362$		0			0
$363$	2848.80	+	2966.71i	0.411910	+	0.428959i
$364$		0			0
$365$			2152.50i			0.308677i
$366$		0			0
$367$	5074.96	+	2930.03i	0.721828	+	0.416748i	0.815425	−	0.578863i	$-0.196503\pi$
$367$	5074.96	+	2930.03i	0.721828	+	0.416748i	−0.0935971	+	0.995610i	$0.529837\pi$
$368$		0			0
$369$	5889.42	+	11228.7i	0.830870	+	1.58412i
$370$		0			0
$371$	3260.21	+	162.143i	0.456231	+	0.0226901i
$372$		0			0
$373$	−3571.94	−	6186.79i	−0.495840	−	0.858820i	0.504149	−	0.863617i	$-0.331806\pi$
$373$	−3571.94	−	6186.79i	−0.495840	−	0.858820i	−0.999988	+	0.00479716i	$0.998473\pi$
$374$		0			0
$375$	1187.39	+	4820.21i	0.163511	+	0.663772i
$376$		0			0
$377$		−	1073.95i		−	0.146715i
$378$		0			0
$379$		−	2290.29i		−	0.310408i	−0.987882	−	0.155204i	$-0.950397\pi$
$379$		−	2290.29i		−	0.310408i	0.987882	−	0.155204i	$-0.0496034\pi$
$380$		0			0
$381$	64.6253	+	262.346i	0.00868990	+	0.0352767i
$382$		0			0
$383$	1469.76	+	2545.70i	0.196087	+	0.339632i	0.947256	−	0.320477i	$-0.103843\pi$
$383$	1469.76	+	2545.70i	0.196087	+	0.339632i	−0.751170	+	0.660109i	$0.770510\pi$
$384$		0			0
$385$	−2622.65	−	5113.48i	−0.347175	−	0.676901i
$386$		0			0
$387$	−2796.88	−	5332.49i	−0.367374	−	0.700429i
$388$		0			0
$389$	12685.1	+	7323.74i	1.65337	+	0.954571i	0.975674	+	0.219226i	$0.0703531\pi$
$389$	12685.1	+	7323.74i	1.65337	+	0.954571i	0.677692	+	0.735346i	$0.262980\pi$
$390$		0			0
$391$		−	546.542i		−	0.0706901i
$392$		0			0
$393$	−9117.42	−	9494.79i	−1.17026	−	1.21870i
$394$		0			0
$395$	196.550	−	340.435i	0.0250367	−	0.0433649i
$396$		0			0
$397$	3630.54	+	6288.28i	0.458971	+	0.794961i	0.998907	−	0.0467449i	$-0.0148848\pi$
$397$	3630.54	+	6288.28i	0.458971	+	0.794961i	−0.539936	+	0.841706i	$0.681551\pi$
$398$		0			0
$399$	−3114.05	+	9039.39i	−0.390721	+	1.13417i
$400$		0			0
$401$	422.755	−	244.078i	0.0526469	−	0.0303957i	−0.473446	−	0.880823i	$-0.656990\pi$
$401$	422.755	−	244.078i	0.0526469	−	0.0303957i	0.526092	+	0.850427i	$0.323657\pi$
$402$		0			0
$403$	1903.60	+	1099.04i	0.235297	+	0.135849i
$404$		0			0
$405$	788.908	−	9707.43i	0.0967930	−	1.19103i
$406$		0			0
$407$	1694.54			0.206376
$408$		0			0
$409$	1873.82	−	3245.56i	0.226539	−	0.392377i	−0.730241	−	0.683190i	$-0.760592\pi$
$409$	1873.82	−	3245.56i	0.226539	−	0.392377i	0.956780	+	0.290812i	$0.0939255\pi$
$410$		0			0
$411$	3873.67	+	1122.59i	0.464901	+	0.134728i
$412$		0			0
$413$	555.801	−	11175.5i	0.0662208	−	1.33150i
$414$		0			0
$415$	16429.3	−	9485.47i	1.94333	−	1.12198i
$416$		0			0
$417$	2782.05	+	11293.8i	0.326709	+	1.32628i
$418$		0			0
$419$	−8857.57			−1.03275			−0.516373	−	0.856364i	$-0.672718\pi$
$419$	−8857.57			−1.03275			−0.516373	+	0.856364i	$0.672718\pi$
$420$		0			0
$421$	−16445.8			−1.90385			−0.951926	−	0.306329i	$-0.900899\pi$
$421$	−16445.8			−1.90385			−0.951926	+	0.306329i	$0.900899\pi$
$422$		0			0
$423$	−1333.91	−	844.018i	−0.153327	−	0.0970155i
$424$		0			0
$425$	−632.978	+	365.450i	−0.0722446	+	0.0417104i
$426$		0			0
$427$	14094.3	+	9099.61i	1.59736	+	1.03129i
$428$		0			0
$429$	−336.394	+	1160.78i	−0.0378584	+	0.130637i
$430$		0			0
$431$	−1918.68	+	3323.25i	−0.214430	+	0.371404i	−0.953096	−	0.302668i	$-0.902123\pi$
$431$	−1918.68	+	3323.25i	−0.214430	+	0.371404i	0.738666	+	0.674072i	$0.235456\pi$
$432$		0			0
$433$	4469.43			0.496044			0.248022	−	0.968754i	$-0.420219\pi$
$433$	4469.43			0.496044			0.248022	+	0.968754i	$0.420219\pi$
$434$		0			0
$435$	5156.64	+	5370.07i	0.568372	+	0.591897i
$436$		0			0
$437$	−3441.34	−	1986.86i	−0.376708	−	0.217493i
$438$		0			0
$439$	−4013.35	+	2317.11i	−0.436325	+	0.251912i	−0.702037	−	0.712140i	$-0.747726\pi$
$439$	−4013.35	+	2317.11i	−0.436325	+	0.251912i	0.265713	+	0.964052i	$0.414393\pi$
$440$		0			0
$441$	1291.68	−	9170.48i	0.139475	−	0.990226i
$442$		0			0
$443$	−4541.62	−	7866.31i	−0.487085	−	0.843656i	0.512804	−	0.858505i	$-0.328607\pi$
$443$	−4541.62	−	7866.31i	−0.487085	−	0.843656i	−0.999890	+	0.0148490i	$0.995273\pi$
$444$		0			0
$445$	9005.48	−	15597.9i	0.959327	−	1.66160i
$446$		0			0
$447$	−8771.42	+	8422.81i	−0.928130	+	0.891242i
$448$		0			0
$449$			2239.89i			0.235427i	0.993048	+	0.117713i	$0.0375564\pi$
$449$			2239.89i			0.235427i	−0.993048	+	0.117713i	$0.962444\pi$
$450$		0			0
$451$	9445.86	+	5453.57i	0.986226	+	0.569398i
$452$		0			0
$453$	11167.7	+	3236.39i	1.15829	+	0.335671i
$454$		0			0
$455$	−1343.94	+	2081.62i	−0.138472	+	0.214479i
$456$		0			0
$457$	2777.88	+	4811.43i	0.284341	+	0.492492i	0.972449	−	0.233115i	$-0.0748920\pi$
$457$	2777.88	+	4811.43i	0.284341	+	0.492492i	−0.688108	+	0.725608i	$0.741559\pi$
$458$		0			0
$459$	−1878.47	+	382.705i	−0.191023	+	0.0389175i
$460$		0			0
$461$		−	2893.36i		−	0.292315i	−0.989261	−	0.146157i	$-0.953309\pi$
$461$		−	2893.36i		−	0.292315i	0.989261	−	0.146157i	$-0.0466906\pi$
$462$		0			0
$463$		−	7368.39i		−	0.739607i	−0.929110	−	0.369804i	$-0.879425\pi$
$463$		−	7368.39i		−	0.739607i	0.929110	−	0.369804i	$-0.120575\pi$
$464$		0			0
$465$	−14795.6	+	3644.69i	−1.47555	+	0.363480i
$466$		0			0
$467$	3290.33	+	5699.02i	0.326035	+	0.564709i	0.981721	−	0.190324i	$-0.0609540\pi$
$467$	3290.33	+	5699.02i	0.326035	+	0.564709i	−0.655686	+	0.755033i	$0.727621\pi$
$468$		0			0
$469$	−11468.6	−	570.376i	−1.12915	−	0.0561568i
$470$		0			0
$471$	−4590.72	+	15841.0i	−0.449107	+	1.54972i
$472$		0			0
$473$	−4485.83	−	2589.90i	−0.436065	−	0.251762i
$474$		0			0
$475$			5314.12i			0.513323i
$476$		0			0
$477$	4754.90	+	192.894i	0.456419	+	0.0185157i
$478$		0			0
$479$	−5132.23	+	8889.28i	−0.489556	+	0.847936i	−0.999928	−	0.0120177i	$-0.996175\pi$
$479$	−5132.23	+	8889.28i	−0.489556	+	0.847936i	0.510372	+	0.859954i	$0.329508\pi$
$480$		0			0
$481$	−365.303	−	632.724i	−0.0346287	−	0.0599786i
$482$		0			0
$483$	3639.24	+	1253.71i	0.342838	+	0.118107i
$484$		0			0
$485$	2659.73	−	1535.60i	0.249015	−	0.143769i
$486$		0			0
$487$	2124.30	+	1226.47i	0.197662	+	0.114120i	0.595564	−	0.803308i	$-0.296928\pi$
$487$	2124.30	+	1226.47i	0.197662	+	0.114120i	−0.397902	+	0.917428i	$0.630262\pi$
$488$		0			0
$489$	−7903.84	+	7589.70i	−0.730928	+	0.701878i
$490$		0			0
$491$	3723.61			0.342249			0.171125	−	0.985249i	$-0.445260\pi$
$491$	3723.61			0.342249			0.171125	+	0.985249i	$0.445260\pi$
$492$		0			0
$493$	732.720	−	1269.11i	0.0669373	−	0.115939i
$494$		0			0
$495$	−3891.50	−	7419.46i	−0.353353	−	0.673697i
$496$		0			0
$497$	−6853.36	+	3515.02i	−0.618542	+	0.317243i
$498$		0			0
$499$	−7233.48	+	4176.25i	−0.648928	+	0.374659i	−0.788045	−	0.615617i	$-0.788907\pi$
$499$	−7233.48	+	4176.25i	−0.648928	+	0.374659i	0.139117	+	0.990276i	$0.455573\pi$
$500$		0			0
$501$	−5026.89	+	1238.30i	−0.448273	+	0.110426i
$502$		0			0
$503$	−5873.38			−0.520638			−0.260319	−	0.965523i	$-0.583828\pi$
$503$	−5873.38			−0.520638			−0.260319	+	0.965523i	$0.583828\pi$
$504$		0			0
$505$	−13208.6			−1.16391
$506$		0			0
$507$	−10578.6	+	2605.90i	−0.926655	+	0.228268i
$508$		0			0
$509$	−7741.87	+	4469.77i	−0.674170	+	0.389232i	−0.797655	−	0.603114i	$-0.793926\pi$
$509$	−7741.87	+	4469.77i	−0.674170	+	0.389232i	0.123485	+	0.992346i	$0.460593\pi$
$510$		0			0
$511$	−148.218	+	2980.22i	−0.0128312	+	0.257998i
$512$		0			0
$513$	−4419.12	+	13219.2i	−0.380329	+	1.13770i
$514$		0			0
$515$	−9637.44	+	16692.5i	−0.824615	+	1.42827i
$516$		0			0
$517$	−1357.87			−0.115511
$518$		0			0
$519$	−15687.1	+	15063.6i	−1.32675	+	1.27402i
$520$		0			0
$521$	−12183.1	−	7033.94i	−1.02448	−	0.591483i	−0.109081	−	0.994033i	$-0.534791\pi$
$521$	−12183.1	−	7033.94i	−1.02448	−	0.591483i	−0.915398	+	0.402550i	$0.868124\pi$
$522$		0			0
$523$	−13073.1	+	7547.76i	−1.09302	+	0.631053i	−0.934378	−	0.356284i	$-0.884044\pi$
$523$	−13073.1	+	7547.76i	−1.09302	+	0.631053i	−0.158638	+	0.987337i	$0.550710\pi$
$524$		0			0
$525$	−981.422	−	5053.09i	−0.0815862	−	0.420066i
$526$		0			0
$527$	1499.68	+	2597.51i	0.123960	+	0.214705i
$528$		0			0
$529$	5283.60	−	9151.46i	0.434256	−	0.752154i
$530$		0			0
$531$	661.212	−	16299.1i	0.0540380	−	1.33205i
$532$		0			0
$533$		−	4702.66i		−	0.382166i
$534$		0			0
$535$	15499.3	+	8948.50i	1.25251	+	0.723135i
$536$		0			0
$537$	−5069.33	+	17492.6i	−0.407370	+	1.40570i
$538$		0			0
$539$	−3279.05	−	7260.39i	−0.262038	−	0.580198i
$540$		0			0
$541$	−1937.02	−	3355.01i	−0.153935	−	0.266623i	0.778736	−	0.627352i	$-0.215861\pi$
$541$	−1937.02	−	3355.01i	−0.153935	−	0.266623i	−0.932671	+	0.360729i	$0.882528\pi$
$542$		0			0
$543$	8934.62	−	2200.91i	0.706116	−	0.173942i
$544$		0			0
$545$			16613.4i			1.30576i
$546$		0			0
$547$		−	3872.55i		−	0.302703i	−0.988480	−	0.151351i	$-0.951638\pi$
$547$		−	3872.55i		−	0.302703i	0.988480	−	0.151351i	$-0.0483625\pi$
$548$		0			0
$549$	20668.1	+	13077.5i	1.60672	+	1.01663i
$550$		0			0
$551$	−5327.35	−	9227.25i	−0.411893	−	0.713419i
$552$		0			0
$553$	295.572	−	457.810i	0.0227288	−	0.0352044i
$554$		0			0
$555$	4864.68	+	1409.78i	0.372061	+	0.107823i
$556$		0			0
$557$	−641.603	−	370.430i	−0.0488072	−	0.0281788i	0.475398	−	0.879771i	$-0.342304\pi$
$557$	−641.603	−	370.430i	−0.0488072	−	0.0281788i	−0.524205	+	0.851592i	$0.675637\pi$
$558$		0			0
$559$			2233.29i			0.168977i
$560$		0			0
$561$	−1189.48	+	1142.21i	−0.0895189	+	0.0859609i
$562$		0			0
$563$	−537.329	+	930.681i	−0.0402233	+	0.0696688i	−0.885436	−	0.464761i	$-0.846140\pi$
$563$	−537.329	+	930.681i	−0.0402233	+	0.0696688i	0.845213	+	0.534430i	$0.179474\pi$
$564$		0			0
$565$	−11214.9	−	19424.8i	−0.835073	−	1.44639i
$566$		0			0
$567$	1760.71	−	13386.0i	0.130411	−	0.991460i
$568$		0			0
$569$	11504.1	−	6641.88i	0.847585	−	0.489353i	−0.0122506	−	0.999925i	$-0.503900\pi$
$569$	11504.1	−	6641.88i	0.847585	−	0.489353i	0.859835	+	0.510572i	$0.170566\pi$
$570$		0			0
$571$	20824.1	+	12022.8i	1.52620	+	0.881153i	0.999517	+	0.0310917i	$0.00989839\pi$
$571$	20824.1	+	12022.8i	1.52620	+	0.881153i	0.526684	+	0.850061i	$0.323435\pi$
$572$		0			0
$573$	5151.17	+	5364.37i	0.375555	+	0.391099i
$574$		0			0
$575$	2139.45			0.155167
$576$		0			0
$577$	−7539.75	+	13059.2i	−0.543993	+	0.942223i	0.454677	+	0.890657i	$0.349755\pi$
$577$	−7539.75	+	13059.2i	−0.543993	+	0.942223i	−0.998670	+	0.0515666i	$0.983579\pi$
$578$		0			0
$579$	5927.65	−	20454.3i	0.425466	−	1.46814i
$580$		0			0
$581$	23400.1	−	12001.7i	1.67091	−	0.856994i
$582$		0			0
$583$	3545.19	−	2046.82i	0.251847	−	0.145404i
$584$		0			0
$585$	−1931.44	+	3052.51i	−0.136505	+	0.215736i
$586$		0			0
$587$	4997.70			0.351409			0.175705	−	0.984443i	$-0.443780\pi$
$587$	4997.70			0.351409			0.175705	+	0.984443i	$0.443780\pi$
$588$		0			0
$589$	21807.2			1.52555
$590$		0			0
$591$	−4963.57	−	20149.6i	−0.345472	−	1.40244i
$592$		0			0
$593$	−3718.80	+	2147.05i	−0.257526	+	0.148683i	−0.623205	−	0.782058i	$-0.714170\pi$
$593$	−3718.80	+	2147.05i	−0.257526	+	0.148683i	0.365680	+	0.930741i	$0.380837\pi$
$594$		0			0
$595$	−3008.37	+	1542.96i	−0.207279	+	0.106311i
$596$		0			0
$597$	−9388.14	−	2720.67i	−0.643603	−	0.186515i
$598$		0			0
$599$	164.026	−	284.101i	0.0111885	−	0.0193790i	−0.860377	−	0.509658i	$-0.829772\pi$
$599$	164.026	−	284.101i	0.0111885	−	0.0193790i	0.871565	+	0.490279i	$0.163105\pi$
$600$		0			0
$601$	−6205.79			−0.421197			−0.210599	−	0.977573i	$-0.567541\pi$
$601$	−6205.79			−0.421197			−0.210599	+	0.977573i	$0.567541\pi$
$602$		0			0
$603$	−16726.5	−	678.551i	−1.12961	−	0.0458254i
$604$		0			0
$605$	9158.35	+	5287.58i	0.615438	+	0.355323i
$606$		0			0
$607$	8076.57	−	4663.01i	0.540063	−	0.311805i	−0.205042	−	0.978753i	$-0.565733\pi$
$607$	8076.57	−	4663.01i	0.540063	−	0.311805i	0.745104	+	0.666948i	$0.232400\pi$
$608$		0			0
$609$	6769.78	+	7790.13i	0.450452	+	0.518345i
$610$		0			0
$611$	292.725	+	507.015i	0.0193820	+	0.0335706i
$612$		0			0
$613$	−2329.07	+	4034.07i	−0.153459	+	0.265798i	−0.932497	−	0.361178i	$-0.882375\pi$
$613$	−2329.07	+	4034.07i	−0.153459	+	0.265798i	0.779038	+	0.626977i	$0.215708\pi$
$614$		0			0
$615$	22580.0	+	23514.6i	1.48051	+	1.54179i
$616$		0			0
$617$		−	13705.7i		−	0.894280i	−0.894464	−	0.447140i	$-0.852443\pi$
$617$		−	13705.7i		−	0.894280i	0.894464	−	0.447140i	$-0.147557\pi$
$618$		0			0
$619$	−13377.8	−	7723.69i	−0.868659	−	0.501520i	−0.00175654	−	0.999998i	$-0.500559\pi$
$619$	−13377.8	−	7723.69i	−0.868659	−	0.501520i	−0.866902	+	0.498478i	$0.833892\pi$
$620$		0			0
$621$	5322.00	+	1779.13i	0.343905	+	0.114966i
$622$		0			0
$623$	13542.5	−	20975.8i	0.870895	−	1.34892i
$624$		0			0
$625$	9725.03	+	16844.2i	0.622402	+	1.07803i
$626$		0			0
$627$	2867.83	+	11642.0i	0.182664	+	0.741524i
$628$		0			0
$629$		−	996.934i		−	0.0631961i
$630$		0			0
$631$		−	23178.5i		−	1.46232i	−0.682207	−	0.731159i	$-0.738980\pi$
$631$		−	23178.5i		−	1.46232i	0.682207	−	0.731159i	$-0.261020\pi$
$632$		0			0
$633$	−720.575	−	2925.18i	−0.0452453	−	0.183674i
$634$		0			0
$635$	347.346	+	601.621i	0.0217071	+	0.0375978i
$636$		0			0
$637$	−2004.07	+	2789.54i	−0.124653	+	0.173509i
$638$		0			0
$639$	−9943.97	+	5215.59i	−0.615614	+	0.322888i
$640$		0			0
$641$	−12963.0	−	7484.22i	−0.798767	−	0.461168i	0.0442730	−	0.999019i	$-0.485903\pi$
$641$	−12963.0	−	7484.22i	−0.798767	−	0.461168i	−0.843040	+	0.537851i	$0.819236\pi$
$642$		0			0
$643$		−	4802.69i		−	0.294556i	−0.989095	−	0.147278i	$-0.952949\pi$
$643$		−	4802.69i		−	0.294556i	0.989095	−	0.147278i	$-0.0470513\pi$
$644$		0			0
$645$	−10723.2	−	11167.1i	−0.654616	−	0.681711i
$646$		0			0
$647$	−3086.70	+	5346.31i	−0.187559	+	0.324861i	−0.944436	−	0.328696i	$-0.893391\pi$
$647$	−3086.70	+	5346.31i	−0.187559	+	0.324861i	0.756877	+	0.653557i	$0.226724\pi$
$648$		0			0
$649$	−7016.19	−	12152.4i	−0.424360	−	0.735013i
$650$		0			0
$651$	−20736.0	+	4027.40i	−1.24840	+	0.242467i
$652$		0			0
$653$	2287.04	−	1320.42i	0.137058	−	0.0791304i	−0.429903	−	0.902875i	$-0.641452\pi$
$653$	2287.04	−	1320.42i	0.137058	−	0.0791304i	0.566961	+	0.823745i	$0.308119\pi$
$654$		0			0
$655$	−29310.8	−	16922.6i	−1.74850	−	1.00950i
$656$		0			0
$657$	−176.328	+	4346.55i	−0.0104706	+	0.258105i
$658$		0			0
$659$	26277.5			1.55330			0.776650	−	0.629932i	$-0.216917\pi$
$659$	26277.5			1.55330			0.776650	+	0.629932i	$0.216917\pi$
$660$		0			0
$661$	7099.71	−	12297.1i	0.417771	−	0.723601i	−0.577944	−	0.816077i	$-0.696145\pi$
$661$	7099.71	−	12297.1i	0.417771	−	0.723601i	0.995715	+	0.0924758i	$0.0294781\pi$
$662$		0			0
$663$	682.915	+	197.908i	0.0400034	+	0.0115929i
$664$		0			0
$665$	−1221.05	+	24551.6i	−0.0712032	+	1.43168i
$666$		0			0
$667$	−3714.87	+	2144.78i	−0.215653	+	0.124507i
$668$		0			0
$669$	−2810.20	−	11408.0i	−0.162404	−	0.659281i
$670$		0			0
$671$	21039.2			1.21045
$672$		0			0
$673$	27705.8			1.58689			0.793446	−	0.608641i	$-0.208285\pi$
$673$	27705.8			1.58689			0.793446	+	0.608641i	$0.208285\pi$
$674$		0			0
$675$	−1498.11	−	7353.31i	−0.0854254	−	0.419302i
$676$		0			0
$677$	7290.15	−	4208.97i	0.413860	−	0.238942i	−0.278587	−	0.960411i	$-0.589866\pi$
$677$	7290.15	−	4208.97i	0.413860	−	0.238942i	0.692447	+	0.721469i	$0.256533\pi$
$678$		0			0
$679$	3788.24	−	1942.95i	0.214108	−	0.109814i
$680$		0			0
$681$	3792.47	−	13086.5i	0.213403	−	0.736384i
$682$		0			0
$683$	5075.16	−	8790.44i	0.284328	−	0.492470i	−0.688118	−	0.725599i	$-0.741563\pi$
$683$	5075.16	−	8790.44i	0.284328	−	0.492470i	0.972446	+	0.233129i	$0.0748963\pi$
$684$		0			0
$685$	10369.5			0.578393
$686$		0			0
$687$	8122.48	+	8458.67i	0.451080	+	0.469750i
$688$		0			0
$689$	−1528.52	−	882.493i	−0.0845168	−	0.0487958i
$690$		0			0
$691$	−15978.4	+	9225.13i	−0.879662	+	0.507873i	−0.870547	−	0.492085i	$-0.836235\pi$
$691$	−15978.4	+	9225.13i	−0.879662	+	0.507873i	−0.00911511	+	0.999958i	$0.502901\pi$
$692$		0			0
$693$	−4877.02	−	10540.5i	−0.267335	−	0.577777i
$694$		0			0
$695$	14952.9	+	25899.2i	0.816109	+	1.41354i
$696$		0			0
$697$	3208.46	−	5557.21i	0.174360	−	0.302001i
$698$		0			0
$699$	14071.5	−	13512.3i	0.761423	−	0.731161i
$700$		0			0
$701$			3673.68i			0.197936i	0.995091	+	0.0989678i	$0.0315541\pi$
$701$			3673.68i			0.197936i	−0.995091	+	0.0989678i	$0.968446\pi$
$702$		0			0
$703$	−6277.26	−	3624.18i	−0.336773	−	0.194436i
$704$		0			0
$705$	−3898.17	−	1129.68i	−0.208246	−	0.0603495i
$706$		0			0
$707$	−18287.8	−	909.525i	−0.972822	−	0.0483822i
$708$		0			0
$709$	−3464.86	−	6001.31i	−0.183534	−	0.317890i	0.759548	−	0.650452i	$-0.225420\pi$
$709$	−3464.86	−	6001.31i	−0.183534	−	0.317890i	−0.943081	+	0.332562i	$0.892087\pi$
$710$		0			0
$711$	424.781	−	671.338i	0.0224058	−	0.0354109i
$712$		0			0
$713$		−	8779.54i		−	0.461145i
$714$		0			0
$715$			3107.33i			0.162528i
$716$		0			0
$717$	16885.3	−	4159.45i	0.879489	−	0.216649i
$718$		0			0
$719$	−11904.0	−	20618.3i	−0.617445	−	1.06945i	−0.989950	−	0.141416i	$-0.954834\pi$
$719$	−11904.0	−	20618.3i	−0.617445	−	1.06945i	0.372505	−	0.928030i	$-0.378499\pi$
$720$		0			0
$721$	−14492.8	+	22447.8i	−0.748600	+	1.15950i
$722$		0			0
$723$	−3415.32	+	11785.1i	−0.175680	+	0.606215i
$724$		0			0
$725$	4967.95	+	2868.25i	0.254490	+	0.146930i
$726$		0			0
$727$		−	24707.5i		−	1.26045i	−0.776411	−	0.630227i	$-0.782962\pi$
$727$		−	24707.5i		−	1.26045i	0.776411	−	0.630227i	$-0.217038\pi$
$728$		0			0
$729$	2388.25	−	19537.6i	0.121336	−	0.992612i
$730$		0			0
$731$	−1523.69	+	2639.12i	−0.0770942	+	0.133531i
$732$		0			0
$733$	−7155.22	−	12393.2i	−0.360551	−	0.624493i	0.627500	−	0.778616i	$-0.284078\pi$
$733$	−7155.22	−	12393.2i	−0.360551	−	0.624493i	−0.988052	+	0.154123i	$0.950745\pi$
$734$		0			0
$735$	−3373.17	−	23571.1i	−0.169281	−	1.18290i
$736$		0			0
$737$	−12471.1	+	7200.18i	−0.623308	+	0.359867i
$738$		0			0
$739$	−26994.8	−	15585.5i	−1.34373	−	0.775806i	−0.356381	−	0.934341i	$-0.615990\pi$
$739$	−26994.8	−	15585.5i	−1.34373	−	0.775806i	−0.987353	+	0.158535i	$0.949323\pi$
$740$		0			0
$741$	3728.76	−	3580.56i	0.184858	−	0.177510i
$742$		0			0
$743$	5859.01			0.289295			0.144648	−	0.989483i	$-0.453795\pi$
$743$	5859.01			0.289295			0.144648	+	0.989483i	$0.453795\pi$
$744$		0			0
$745$	−15633.3	+	27077.7i	−0.768806	+	1.33161i
$746$		0			0
$747$	33952.7	−	17808.1i	1.66301	−	0.872243i
$748$		0			0
$749$	20843.1	+	13456.8i	1.01681	+	0.656475i
$750$		0			0
$751$	22074.4	−	12744.7i	1.07258	−	0.619255i	0.143695	−	0.989622i	$-0.454102\pi$
$751$	22074.4	−	12744.7i	1.07258	−	0.619255i	0.928885	+	0.370367i	$0.120768\pi$
$752$		0			0
$753$	13482.8	−	3321.30i	0.652512	−	0.160737i
$754$		0			0
$755$	29895.1			1.44105
$756$		0			0
$757$	18677.8			0.896771			0.448386	−	0.893840i	$-0.351999\pi$
$757$	18677.8			0.896771			0.448386	+	0.893840i	$0.351999\pi$
$758$		0			0
$759$	4687.03	−	1154.58i	0.224148	−	0.0552156i
$760$		0			0
$761$	12760.1	−	7367.04i	0.607823	−	0.350927i	−0.164290	−	0.986412i	$-0.552533\pi$
$761$	12760.1	−	7367.04i	0.607823	−	0.350927i	0.772113	+	0.635485i	$0.219200\pi$
$762$		0			0
$763$	−1143.97	+	23001.9i	−0.0542786	+	1.09138i
$764$		0			0
$765$	−4365.04	+	2289.45i	−0.206298	+	0.108203i
$766$		0			0
$767$	−3025.06	+	5239.55i	−0.142410	+	0.246661i
$768$		0			0
$769$	31479.3			1.47617			0.738084	−	0.674709i	$-0.235731\pi$
$769$	31479.3			1.47617			0.738084	+	0.674709i	$0.235731\pi$
$770$		0			0
$771$	−9625.43	+	9242.87i	−0.449613	+	0.431743i
$772$		0			0
$773$	−1236.84	−	714.087i	−0.0575497	−	0.0332263i	0.470949	−	0.882160i	$-0.343912\pi$
$773$	−1236.84	−	714.087i	−0.0575497	−	0.0332263i	−0.528499	+	0.848934i	$0.677245\pi$
$774$		0			0
$775$	−10168.0	+	5870.51i	−0.471285	+	0.272097i
$776$		0			0
$777$	6638.24	+	2286.86i	0.306494	+	0.105586i
$778$		0			0
$779$	−23327.6	−	40404.5i	−1.07291	−	1.85833i
$780$		0			0
$781$	−4829.61	+	8365.13i	−0.221277	+	0.383262i
$782$		0			0
$783$	9972.88	+	11266.2i	0.455175	+	0.514203i
$784$		0			0
$785$			42405.3i			1.92804i
$786$		0			0
$787$	19331.3	+	11160.9i	0.875585	+	0.505519i	0.869200	−	0.494461i	$-0.164634\pi$
$787$	19331.3	+	11160.9i	0.875585	+	0.505519i	0.00638468	+	0.999980i	$0.497968\pi$
$788$		0			0
$789$	10225.6	−	35285.0i	0.461394	−	1.59212i
$790$		0			0
$791$	−14189.9	−	27666.7i	−0.637846	−	1.24363i
$792$		0			0
$793$	−4535.57	−	7855.84i	−0.203106	−	0.351790i
$794$		0			0
$795$	11880.4	−	2926.56i	0.530005	−	0.130559i
$796$		0			0
$797$			22722.5i			1.00988i	0.863155	+	0.504940i	$0.168485\pi$
$797$			22722.5i			1.00988i	−0.863155	+	0.504940i	$0.831515\pi$
$798$		0			0
$799$			798.865i			0.0353715i
$800$		0			0
$801$	19462.5	−	30759.2i	0.858519	−	1.35683i
$802$		0			0
$803$	1871.03	+	3240.73i	0.0822259	+	0.142419i
$804$		0			0
$805$	9884.41	+	491.590i	0.432770	+	0.0215233i
$806$		0			0
$807$	31257.3	+	9058.34i	1.36346	+	0.395129i
$808$		0			0
$809$	−27700.9	−	15993.1i	−1.20385	−	0.695042i	−0.242439	−	0.970167i	$-0.577947\pi$
$809$	−27700.9	−	15993.1i	−1.20385	−	0.695042i	−0.961408	+	0.275125i	$0.911281\pi$
$810$		0			0
$811$		−	18662.5i		−	0.808052i	−0.914747	−	0.404026i	$-0.867610\pi$
$811$		−	18662.5i		−	0.808052i	0.914747	−	0.404026i	$-0.132390\pi$
$812$		0			0
$813$	−18762.5	+	18016.8i	−0.809385	+	0.777216i
$814$		0			0
$815$	−14087.0	+	24399.5i	−0.605457	+	1.04868i
$816$		0			0
$817$	11078.3	+	19188.1i	0.474393	+	0.821672i
$818$		0			0
$819$	−2884.34	+	4093.32i	−0.123061	+	0.174642i
$820$		0			0
$821$	−9947.69	+	5743.30i	−0.422871	+	0.244145i	−0.696305	−	0.717746i	$-0.745174\pi$
$821$	−9947.69	+	5743.30i	−0.422871	+	0.244145i	0.273434	+	0.961891i	$0.411840\pi$
$822$		0			0
$823$	−25767.3	−	14876.7i	−1.09136	−	0.630098i	−0.157423	−	0.987531i	$-0.550319\pi$
$823$	−25767.3	−	14876.7i	−1.09136	−	0.630098i	−0.933939	+	0.357433i	$0.883652\pi$
$824$		0			0
$825$	−4471.20	−	4656.26i	−0.188688	−	0.196497i
$826$		0			0
$827$	−11379.7			−0.478490			−0.239245	−	0.970959i	$-0.576900\pi$
$827$	−11379.7			−0.478490			−0.239245	+	0.970959i	$0.576900\pi$
$828$		0			0
$829$	−12294.6	+	21294.8i	−0.515088	+	0.892159i	0.484758	+	0.874648i	$0.338908\pi$
$829$	−12294.6	+	21294.8i	−0.515088	+	0.892159i	−0.999847	+	0.0175109i	$0.994426\pi$
$830$		0			0
$831$	9417.13	−	32495.4i	0.393113	−	1.35650i
$832$		0			0
$833$	−4271.45	+	1929.14i	−0.177667	+	0.0802408i
$834$		0			0
$835$	−11527.8	+	6655.58i	−0.477768	+	0.275839i
$836$		0			0
$837$	−30175.3	+	6147.69i	−1.24613	+	0.253877i
$838$		0			0
$839$	−20586.7			−0.847119			−0.423560	−	0.905868i	$-0.639220\pi$
$839$	−20586.7			−0.847119			−0.423560	+	0.905868i	$0.639220\pi$
$840$		0			0
$841$	12887.4			0.528411
$842$		0			0
$843$	−4747.16	−	19271.1i	−0.193951	−	0.787345i
$844$		0			0
$845$	−24259.3	+	14006.1i	−0.987626	+	0.570206i
$846$		0			0
$847$	12316.0	+	7951.47i	0.499624	+	0.322569i
$848$		0			0
$849$	−17390.5	−	5039.75i	−0.702992	−	0.203726i
$850$		0			0
$851$	−1459.09	+	2527.21i	−0.0587742	+	0.101800i
$852$		0			0
$853$	−35278.5			−1.41608			−0.708039	−	0.706173i	$-0.750420\pi$
$853$	−35278.5			−1.41608			−0.708039	+	0.706173i	$0.750420\pi$
$854$		0			0
$855$	−1452.62	+	35807.6i	−0.0581037	+	1.43228i
$856$		0			0
$857$	10111.6	+	5837.95i	0.403041	+	0.232696i	0.687795	−	0.725905i	$-0.258579\pi$
$857$	10111.6	+	5837.95i	0.403041	+	0.232696i	−0.284754	+	0.958601i	$0.591912\pi$
$858$		0			0
$859$	−37200.2	+	21477.6i	−1.47760	+	0.853091i	−0.999680	−	0.0253141i	$-0.991941\pi$
$859$	−37200.2	+	21477.6i	−1.47760	+	0.853091i	−0.477917	+	0.878405i	$0.658608\pi$
$860$		0			0
$861$	29643.7	+	34111.7i	1.17335	+	1.35020i
$862$		0			0
$863$	−5736.03	−	9935.10i	−0.226254	−	0.391883i	0.730441	−	0.682976i	$-0.239314\pi$
$863$	−5736.03	−	9935.10i	−0.226254	−	0.391883i	−0.956695	+	0.291093i	$0.905981\pi$
$864$		0			0
$865$	−27959.1	+	48426.5i	−1.09900	+	1.90353i
$866$		0			0
$867$	−17009.9	−	17713.9i	−0.666305	−	0.693883i
$868$		0			0
$869$		−	683.394i		−	0.0266773i
$870$		0			0
$871$	5376.95	+	3104.38i	0.209175	+	0.120767i
$872$		0			0
$873$	5496.59	−	2882.95i	0.213094	−	0.111768i
$874$		0			0
$875$	8074.88	+	15743.9i	0.311978	+	0.608275i
$876$		0			0
$877$	12866.6	+	22285.6i	0.495409	+	0.858074i	0.999986	−	0.00529264i	$-0.00168471\pi$
$877$	12866.6	+	22285.6i	0.495409	+	0.858074i	−0.504577	+	0.863367i	$0.668351\pi$
$878$		0			0
$879$	−603.116	−	2448.35i	−0.0231429	−	0.0939486i
$880$		0			0
$881$		−	19839.4i		−	0.758692i	−0.925255	−	0.379346i	$-0.876149\pi$
$881$		−	19839.4i		−	0.758692i	0.925255	−	0.379346i	$-0.123851\pi$
$882$		0			0
$883$		−	13843.4i		−	0.527595i	−0.964578	−	0.263798i	$-0.915025\pi$
$883$		−	13843.4i		−	0.527595i	0.964578	−	0.263798i	$-0.0849751\pi$
$884$		0			0
$885$	−10031.8	−	40724.2i	−0.381035	−	1.54681i
$886$		0			0
$887$	21827.5	+	37806.4i	0.826265	+	1.43113i	0.900949	+	0.433925i	$0.142872\pi$
$887$	21827.5	+	37806.4i	0.826265	+	1.43113i	−0.0746845	+	0.997207i	$0.523795\pi$
$888$		0			0
$889$	439.486	+	856.883i	0.0165803	+	0.0323273i
$890$		0			0
$891$	−7250.30	−	15300.9i	−0.272609	−	0.575307i
$892$		0			0
$893$	5030.10	+	2904.13i	0.188495	+	0.108828i
$894$		0			0
$895$			46826.3i			1.74886i
$896$		0			0
$897$	−1441.53	−	1501.19i	−0.0536579	−	0.0558788i
$898$		0			0
$899$	11770.3	−	20386.7i	0.436663	−	0.756323i
$900$		0			0
$901$	−1204.19	−	2085.71i	−0.0445253	−	0.0771201i
$902$		0			0
$903$	−14077.8	−	16199.6i	−0.518803	−	0.596998i
$904$		0			0
$905$	20489.1	−	11829.4i	0.752576	−	0.434500i
$906$		0			0
$907$	25970.7	+	14994.2i	0.950765	+	0.548924i	0.893318	−	0.449424i	$-0.148371\pi$
$907$	25970.7	+	14994.2i	0.950765	+	0.548924i	0.0574465	+	0.998349i	$0.481704\pi$
$908$		0			0
$909$	−26672.2	−	1082.02i	−0.973224	−	0.0394812i
$910$		0			0
$911$	−38084.0			−1.38505			−0.692525	−	0.721394i	$-0.743502\pi$
$911$	−38084.0			−1.38505			−0.692525	+	0.721394i	$0.743502\pi$
$912$		0			0
$913$	16490.2	−	28561.9i	0.597752	−	1.03534i
$914$		0			0
$915$	60399.4	+	17503.7i	2.18223	+	0.632408i
$916$		0			0
$917$	−39416.6	−	25448.2i	−1.41946	−	0.916438i
$918$		0			0
$919$	−3703.12	+	2138.00i	−0.132921	+	0.0767421i	−0.564986	−	0.825100i	$-0.691118\pi$
$919$	−3703.12	+	2138.00i	−0.132921	+	0.0767421i	0.432065	+	0.901843i	$0.357785\pi$
$920$		0			0
$921$	2003.04	+	8131.35i	0.0716639	+	0.290920i
$922$		0			0
$923$	4164.61			0.148515
$924$		0			0
$925$	3902.52			0.138718
$926$		0			0
$927$	−20828.3	+	32917.7i	−0.737962	+	1.16630i
$928$		0			0
$929$	42898.6	−	24767.5i	1.51502	−	0.874700i	0.515179	−	0.857082i	$-0.327725\pi$
$929$	42898.6	−	24767.5i	1.51502	−	0.874700i	0.999845	−	0.0176172i	$-0.00560802\pi$
$930$		0			0
$931$	−3381.16	+	33908.5i	−0.119026	+	1.19367i
$932$		0			0
$933$	10130.5	−	34957.1i	0.355476	−	1.22663i
$934$		0			0
$935$	−2120.02	+	3671.98i	−0.0741520	+	0.128435i
$936$		0			0
$937$	−36318.1			−1.26623			−0.633116	−	0.774057i	$-0.718224\pi$
$937$	−36318.1			−1.26623			−0.633116	+	0.774057i	$0.718224\pi$
$938$		0			0
$939$	518.412	+	539.869i	0.0180167	+	0.0187625i
$940$		0			0
$941$	1766.52	+	1019.90i	0.0611974	+	0.0353323i	0.530287	−	0.847819i	$-0.322084\pi$
$941$	1766.52	+	1019.90i	0.0611974	+	0.0353323i	−0.469089	+	0.883151i	$0.655418\pi$
$942$		0			0
$943$	−16266.8	+	9391.62i	−0.561738	+	0.324320i
$944$		0			0
$945$	−5231.76	−	34317.0i	−0.180094	−	1.18131i
$946$		0			0
$947$	17814.9	+	30856.3i	0.611305	+	1.05881i	0.991021	+	0.133708i	$0.0426884\pi$
$947$	17814.9	+	30856.3i	0.611305	+	1.05881i	−0.379716	+	0.925103i	$0.623978\pi$
$948$		0			0
$949$	806.704	−	1397.25i	0.0275940	−	0.0477942i
$950$		0			0
$951$	−33338.3	+	32013.3i	−1.13677	+	1.09159i
$952$		0			0
$953$			7559.30i			0.256946i	0.991713	+	0.128473i	$0.0410076\pi$
$953$			7559.30i			0.256946i	−0.991713	+	0.128473i	$0.958992\pi$
$954$		0			0
$955$	16560.0	+	9560.93i	0.561120	+	0.323963i
$956$		0			0
$957$	12431.5	+	3602.63i	0.419909	+	0.121689i
$958$		0			0
$959$	14357.0	+	714.028i	0.483432	+	0.0240429i
$960$		0			0
$961$	9194.96	+	15926.1i	0.308649	+	0.534596i
$962$		0			0
$963$	30564.6	+	19339.4i	1.02277	+	0.647146i
$964$		0			0
$965$		−	54754.7i		−	1.82654i
$966$		0			0
$967$			379.123i			0.0126078i	0.999980	+	0.00630392i	$0.00200661\pi$
$967$			379.123i			0.0126078i	−0.999980	+	0.00630392i	$0.997993\pi$
$968$		0			0
$969$	6849.23	−	1687.21i	0.227068	−	0.0559350i
$970$		0			0
$971$	17749.5	+	30743.1i	0.586622	+	1.01606i	0.994671	+	0.103099i	$0.0328758\pi$
$971$	17749.5	+	30743.1i	0.586622	+	1.01606i	−0.408049	+	0.912960i	$0.633791\pi$
$972$		0			0
$973$	18919.5	+	36888.0i	0.623361	+	1.21539i
$974$		0			0
$975$	−774.715	+	2673.29i	−0.0254469	+	0.0878089i
$976$		0			0
$977$	−40699.3	−	23497.8i	−1.33274	−	0.769458i	−0.347022	−	0.937857i	$-0.612807\pi$
$977$	−40699.3	−	23497.8i	−1.33274	−	0.769458i	−0.985719	+	0.168399i	$0.946140\pi$
$978$		0			0
$979$		−	31311.6i		−	1.02219i
$980$		0			0
$981$	−1360.93	+	33547.5i	−0.0442928	+	1.09183i
$982$		0			0
$983$	−9799.29	+	16972.9i	−0.317954	+	0.550712i	−0.980061	−	0.198697i	$-0.936329\pi$
$983$	−9799.29	+	16972.9i	−0.317954	+	0.550712i	0.662107	+	0.749409i	$0.269662\pi$
$984$		0			0
$985$	−26678.0	−	46207.7i	−0.862978	−	1.49472i
$986$		0			0
$987$	−5319.37	−	1832.51i	−0.171547	−	0.0590977i
$988$		0			0
$989$	7725.08	−	4460.08i	0.248375	−	0.143400i
$990$		0			0
$991$	−29849.0	−	17233.3i	−0.956796	−	0.552406i	−0.0616102	−	0.998100i	$-0.519624\pi$
$991$	−29849.0	−	17233.3i	−0.956796	−	0.552406i	−0.895185	+	0.445694i	$0.852957\pi$
$992$		0			0
$993$	−12544.8	+	12046.2i	−0.400904	+	0.384970i
$994$		0			0
$995$	−25131.3			−0.800720
$996$		0			0
$997$	−20728.6	+	35903.0i	−0.658456	+	1.14048i	0.322559	+	0.946549i	$0.395457\pi$
$997$	−20728.6	+	35903.0i	−0.658456	+	1.14048i	−0.981015	+	0.193930i	$0.937876\pi$
$998$		0			0
$999$	9707.74	+	3245.26i	0.307447	+	0.102778i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bj.e.95.13	yes	28
3.2	odd	2	inner	336.4.bj.e.95.9	✓	28
4.3	odd	2		336.4.bj.f.95.2	yes	28
7.2	even	3		336.4.bj.f.191.6	yes	28
12.11	even	2		336.4.bj.f.95.6	yes	28
21.2	odd	6		336.4.bj.f.191.2	yes	28
28.23	odd	6	inner	336.4.bj.e.191.9	yes	28
84.23	even	6	inner	336.4.bj.e.191.13	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.4.bj.e.95.9	✓	28	3.2	odd	2	inner
336.4.bj.e.95.13	yes	28	1.1	even	1	trivial
336.4.bj.e.191.9	yes	28	28.23	odd	6	inner
336.4.bj.e.191.13	yes	28	84.23	even	6	inner
336.4.bj.f.95.2	yes	28	4.3	odd	2
336.4.bj.f.95.6	yes	28	12.11	even	2
336.4.bj.f.191.2	yes	28	21.2	odd	6
336.4.bj.f.191.6	yes	28	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.04533 - 1.24284i) q^{3} +(11.5701 - 6.68000i) q^{5} +(16.4792 - 8.45200i) q^{7} +(23.9107 - 12.5411i) q^{9} +(11.6130 - 20.1143i) q^{11} -10.0140 q^{13} +(50.0727 - 48.0826i) q^{15} +(-11.8337 - 6.83218i) q^{17} +(-86.0386 + 49.6744i) q^{19} +(72.6384 - 63.1242i) q^{21} +(19.9988 + 34.6389i) q^{23} +(26.7447 - 46.3232i) q^{25} +(105.051 - 92.9913i) q^{27} +107.245i q^{29} +(-190.094 - 109.751i) q^{31} +(33.5924 - 115.916i) q^{33} +(134.206 - 207.871i) q^{35} +(36.4793 + 63.1841i) q^{37} +(-50.5238 + 12.4458i) q^{39} +469.609i q^{41} -223.017i q^{43} +(192.874 - 304.825i) q^{45} +(-29.2317 - 50.6307i) q^{47} +(200.127 - 278.564i) q^{49} +(-68.1962 - 19.7632i) q^{51} +(152.639 + 88.1261i) q^{53} -310.299i q^{55} +(-372.356 + 357.556i) q^{57} +(302.084 - 523.224i) q^{59} +(452.924 + 784.488i) q^{61} +(288.031 - 408.760i) q^{63} +(-115.863 + 66.8933i) q^{65} +(-536.945 - 310.005i) q^{67} +(143.951 + 149.909i) q^{69} -415.880 q^{71} +(-80.5578 + 139.530i) q^{73} +(77.3634 - 266.955i) q^{75} +(21.3667 - 429.620i) q^{77} +(25.4816 - 14.7118i) q^{79} +(414.441 - 599.733i) q^{81} +1419.98 q^{83} -182.556 q^{85} +(133.289 + 541.088i) q^{87} +(1167.51 - 674.063i) q^{89} +(-165.022 + 84.6381i) q^{91} +(-1095.49 - 317.472i) q^{93} +(-663.650 + 1149.48i) q^{95} +229.880 q^{97} +(25.4190 - 626.586i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 38 q^{7} - 70 q^{9} + 124 q^{13} + 462 q^{19} + 500 q^{21} + 566 q^{25} - 1266 q^{31} + 64 q^{33} + 338 q^{37} - 1254 q^{39} - 488 q^{45} - 206 q^{49} - 522 q^{51} + 2324 q^{57} - 340 q^{61} + 840 q^{63}+ \cdots - 3344 q^{97}+O(q^{100}) \) 28 * q - 38 * q^7 - 70 * q^9 + 124 * q^13 + 462 * q^19 + 500 * q^21 + 566 * q^25 - 1266 * q^31 + 64 * q^33 + 338 * q^37 - 1254 * q^39 - 488 * q^45 - 206 * q^49 - 522 * q^51 + 2324 * q^57 - 340 * q^61 + 840 * q^63 - 2934 * q^67 - 776 * q^69 + 2050 * q^73 + 1458 * q^75 - 2070 * q^79 + 910 * q^81 + 2400 * q^85 - 3132 * q^87 + 5170 * q^91 + 714 * q^93 - 3344 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

Properties

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