LMFDB - Embedded newform 144.4.k.b.37.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [144,4,Mod(37,144)] 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("144.37"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(144, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	144.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$8.49627504083$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.7
Character	$\chi$	$=$	144.37
Dual form			144.4.k.b.109.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.716137 - 2.73627i) q^{2} +(-6.97430 - 3.91908i) q^{4} +(11.7719 + 11.7719i) q^{5} +14.7089i q^{7} +(-15.7182 + 16.2769i) q^{8} +(40.6415 - 23.7808i) q^{10} +(24.9380 + 24.9380i) q^{11} +(-58.1345 + 58.1345i) q^{13} +(40.2475 + 10.5336i) q^{14} +(33.2816 + 54.6657i) q^{16} +75.8798 q^{17} +(51.8464 - 51.8464i) q^{19} +(-35.9658 - 128.236i) q^{20} +(86.0960 - 50.3779i) q^{22} -149.444i q^{23} +152.157i q^{25} +(117.439 + 200.704i) q^{26} +(57.6455 - 102.584i) q^{28} +(-48.5419 + 48.5419i) q^{29} +29.6074 q^{31} +(173.414 - 51.9192i) q^{32} +(54.3403 - 207.627i) q^{34} +(-173.153 + 173.153i) q^{35} +(-147.751 - 147.751i) q^{37} +(-104.736 - 178.994i) q^{38} +(-376.645 + 6.57727i) q^{40} +225.232i q^{41} +(81.7640 + 81.7640i) q^{43} +(-76.1909 - 271.659i) q^{44} +(-408.917 - 107.022i) q^{46} -46.5418 q^{47} +126.648 q^{49} +(416.342 + 108.965i) q^{50} +(633.281 - 177.613i) q^{52} +(156.105 + 156.105i) q^{53} +587.137i q^{55} +(-239.416 - 231.198i) q^{56} +(98.0609 + 167.586i) q^{58} +(238.199 + 238.199i) q^{59} +(-594.013 + 594.013i) q^{61} +(21.2029 - 81.0137i) q^{62} +(-17.8765 - 511.688i) q^{64} -1368.71 q^{65} +(299.623 - 299.623i) q^{67} +(-529.208 - 297.379i) q^{68} +(349.790 + 597.792i) q^{70} -693.932i q^{71} -462.446i q^{73} +(-510.096 + 298.476i) q^{74} +(-564.782 + 158.402i) q^{76} +(-366.811 + 366.811i) q^{77} -878.797 q^{79} +(-251.732 + 1035.31i) q^{80} +(616.293 + 161.297i) q^{82} +(926.380 - 926.380i) q^{83} +(893.252 + 893.252i) q^{85} +(282.282 - 165.174i) q^{86} +(-797.894 + 13.9335i) q^{88} -350.770i q^{89} +(-855.096 - 855.096i) q^{91} +(-585.682 + 1042.26i) q^{92} +(-33.3303 + 127.351i) q^{94} +1220.66 q^{95} -766.194 q^{97} +(90.6971 - 346.542i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{4} - 84 q^{8} + 72 q^{10} + 40 q^{11} + 348 q^{14} - 192 q^{16} + 24 q^{19} - 80 q^{20} + 704 q^{22} + 20 q^{26} - 344 q^{28} - 400 q^{29} - 744 q^{31} + 960 q^{32} - 704 q^{34} + 456 q^{35}+ \cdots - 6760 q^{98}+O(q^{100}) $ 24 * q - 20 * q^4 - 84 * q^8 + 72 * q^10 + 40 * q^11 + 348 * q^14 - 192 * q^16 + 24 * q^19 - 80 * q^20 + 704 * q^22 + 20 * q^26 - 344 * q^28 - 400 * q^29 - 744 * q^31 + 960 * q^32 - 704 * q^34 + 456 * q^35 + 16 * q^37 - 1256 * q^38 + 1744 * q^40 + 1240 * q^43 + 200 * q^44 - 1432 * q^46 - 1176 * q^49 - 708 * q^50 + 1008 * q^52 - 752 * q^53 - 1344 * q^56 + 1936 * q^58 + 1376 * q^59 - 912 * q^61 + 996 * q^62 - 56 * q^64 - 976 * q^65 - 2256 * q^67 + 1568 * q^68 - 1760 * q^70 + 2740 * q^74 - 1880 * q^76 - 1904 * q^77 + 5992 * q^79 - 712 * q^80 - 40 * q^82 - 2680 * q^83 - 240 * q^85 + 1712 * q^86 - 3936 * q^88 - 3496 * q^91 - 5296 * q^92 + 5272 * q^94 + 7728 * q^95 - 6760 * q^98

Character values

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

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.716137	−	2.73627i	0.253193	−	0.967416i
$2$	0.716137	−	2.73627i	0.253193	−	0.967416i
$3$		0			0
$3$		0			0
$4$	−6.97430	−	3.91908i	−0.871787	−	0.489885i
$5$	11.7719	+	11.7719i	1.05291	+	1.05291i	0.998520	+	0.0543947i	$0.0173229\pi$
$5$	11.7719	+	11.7719i	1.05291	+	1.05291i	0.0543947	+	0.998520i	$0.482677\pi$
$6$		0			0
$7$			14.7089i			0.794207i	0.917774	+	0.397104i	$0.129985\pi$
$7$			14.7089i			0.794207i	−0.917774	+	0.397104i	$0.870015\pi$
$8$	−15.7182	+	16.2769i	−0.694653	+	0.719345i
$9$		0			0
$10$	40.6415	−	23.7808i	1.28520	−	0.752016i
$11$	24.9380	+	24.9380i	0.683553	+	0.683553i	0.960799	−	0.277246i	$-0.0894216\pi$
$11$	24.9380	+	24.9380i	0.683553	+	0.683553i	−0.277246	+	0.960799i	$0.589422\pi$
$12$		0			0
$13$	−58.1345	+	58.1345i	−1.24028	+	1.24028i	−0.280393	+	0.959885i	$0.590465\pi$
$13$	−58.1345	+	58.1345i	−1.24028	+	1.24028i	−0.959885	+	0.280393i	$0.909535\pi$
$14$	40.2475	+	10.5336i	0.768329	+	0.201087i
$15$		0			0
$16$	33.2816	+	54.6657i	0.520025	+	0.854151i
$17$	75.8798			1.08256			0.541281	−	0.840842i	$-0.317940\pi$
$17$	75.8798			1.08256			0.541281	+	0.840842i	$0.317940\pi$
$18$		0			0
$19$	51.8464	−	51.8464i	0.626020	−	0.626020i	−0.321045	−	0.947064i	$-0.604034\pi$
$19$	51.8464	−	51.8464i	0.626020	−	0.626020i	0.947064	+	0.321045i	$0.104034\pi$
$20$	−35.9658	−	128.236i	−0.402110	−	1.43372i
$21$		0			0
$22$	86.0960	−	50.3779i	0.834351	−	0.488210i
$23$		−	149.444i		−	1.35483i	−0.735600	−	0.677416i	$-0.763100\pi$
$23$		−	149.444i		−	1.35483i	0.735600	−	0.677416i	$-0.236900\pi$
$24$		0			0
$25$			152.157i			1.21726i
$26$	117.439	+	200.704i	0.885836	+	1.51389i
$27$		0			0
$28$	57.6455	−	102.584i	0.389070	−	0.692379i
$29$	−48.5419	+	48.5419i	−0.310828	+	0.310828i	−0.845230	−	0.534402i	$-0.820537\pi$
$29$	−48.5419	+	48.5419i	−0.310828	+	0.310828i	0.534402	+	0.845230i	$0.320537\pi$
$30$		0			0
$31$	29.6074			0.171537			0.0857685	−	0.996315i	$-0.472665\pi$
$31$	29.6074			0.171537			0.0857685	+	0.996315i	$0.472665\pi$
$32$	173.414	−	51.9192i	0.957986	−	0.286816i
$33$		0			0
$34$	54.3403	−	207.627i	0.274097	−	1.04729i
$35$	−173.153	+	173.153i	−0.836232	+	0.836232i
$36$		0			0
$37$	−147.751	−	147.751i	−0.656489	−	0.656489i	0.298058	−	0.954548i	$-0.403661\pi$
$37$	−147.751	−	147.751i	−0.656489	−	0.656489i	−0.954548	+	0.298058i	$0.903661\pi$
$38$	−104.736	−	178.994i	−0.447118	−	0.764125i
$39$		0			0
$40$	−376.645	+	6.57727i	−1.48882	+	0.0259990i
$41$			225.232i			0.857933i	0.903320	+	0.428967i	$0.141122\pi$
$41$			225.232i			0.857933i	−0.903320	+	0.428967i	$0.858878\pi$
$42$		0			0
$43$	81.7640	+	81.7640i	0.289974	+	0.289974i	0.837070	−	0.547096i	$-0.184267\pi$
$43$	81.7640	+	81.7640i	0.289974	+	0.289974i	−0.547096	+	0.837070i	$0.684267\pi$
$44$	−76.1909	−	271.659i	−0.261050	−	0.930776i
$45$		0			0
$46$	−408.917	−	107.022i	−1.31069	−	0.343034i
$47$	−46.5418			−0.144443			−0.0722215	−	0.997389i	$-0.523009\pi$
$47$	−46.5418			−0.144443			−0.0722215	+	0.997389i	$0.523009\pi$
$48$		0			0
$49$	126.648			0.369235
$50$	416.342	+	108.965i	1.17759	+	0.308200i
$51$		0			0
$52$	633.281	−	177.613i	1.68885	−	0.473664i
$53$	156.105	+	156.105i	0.404578	+	0.404578i	0.879843	−	0.475265i	$-0.157648\pi$
$53$	156.105	+	156.105i	0.404578	+	0.404578i	−0.475265	+	0.879843i	$0.657648\pi$
$54$		0			0
$55$			587.137i			1.43945i
$56$	−239.416	−	231.198i	−0.571309	−	0.551698i
$57$		0			0
$58$	98.0609	+	167.586i	0.222000	+	0.379399i
$59$	238.199	+	238.199i	0.525608	+	0.525608i	0.919260	−	0.393652i	$-0.128788\pi$
$59$	238.199	+	238.199i	0.525608	+	0.525608i	−0.393652	+	0.919260i	$0.628788\pi$
$60$		0			0
$61$	−594.013	+	594.013i	−1.24681	+	1.24681i	−0.289692	+	0.957120i	$0.593553\pi$
$61$	−594.013	+	594.013i	−1.24681	+	1.24681i	−0.957120	+	0.289692i	$0.906447\pi$
$62$	21.2029	−	81.0137i	0.0434319	−	0.165948i
$63$		0			0
$64$	−17.8765	−	511.688i	−0.0349150	−	0.999390i
$65$	−1368.71			−2.61181
$66$		0			0
$67$	299.623	−	299.623i	0.546339	−	0.546339i	−0.379041	−	0.925380i	$-0.623746\pi$
$67$	299.623	−	299.623i	0.546339	−	0.546339i	0.925380	+	0.379041i	$0.123746\pi$
$68$	−529.208	−	297.379i	−0.943763	−	0.530331i
$69$		0			0
$70$	349.790	+	597.792i	0.597256	+	1.02071i
$71$		−	693.932i		−	1.15992i	−0.814644	−	0.579962i	$-0.803067\pi$
$71$		−	693.932i		−	1.15992i	0.814644	−	0.579962i	$-0.196933\pi$
$72$		0			0
$73$		−	462.446i		−	0.741441i	−0.928745	−	0.370720i	$-0.879111\pi$
$73$		−	462.446i		−	0.741441i	0.928745	−	0.370720i	$-0.120889\pi$
$74$	−510.096	+	298.476i	−0.801316	+	0.468880i
$75$		0			0
$76$	−564.782	+	158.402i	−0.852433	+	0.239078i
$77$	−366.811	+	366.811i	−0.542883	+	0.542883i
$78$		0			0
$79$	−878.797			−1.25155			−0.625775	−	0.780004i	$-0.715217\pi$
$79$	−878.797			−1.25155			−0.625775	+	0.780004i	$0.715217\pi$
$80$	−251.732	+	1035.31i	−0.351806	+	1.44689i
$81$		0			0
$82$	616.293	+	161.297i	0.829978	+	0.217222i
$83$	926.380	−	926.380i	1.22510	−	1.22510i	0.259306	−	0.965795i	$-0.416506\pi$
$83$	926.380	−	926.380i	1.22510	−	1.22510i	0.965795	−	0.259306i	$-0.0834938\pi$
$84$		0			0
$85$	893.252	+	893.252i	1.13984	+	1.13984i
$86$	282.282	−	165.174i	0.353945	−	0.207106i
$87$		0			0
$88$	−797.894	+	13.9335i	−0.966543	+	0.0168786i
$89$		−	350.770i		−	0.417770i	−0.977940	−	0.208885i	$-0.933017\pi$
$89$		−	350.770i		−	0.417770i	0.977940	−	0.208885i	$-0.0669834\pi$
$90$		0			0
$91$	−855.096	−	855.096i	−0.985038	−	0.985038i
$92$	−585.682	+	1042.26i	−0.663713	+	1.18113i
$93$		0			0
$94$	−33.3303	+	127.351i	−0.0365719	+	0.139737i
$95$	1220.66			1.31829
$96$		0			0
$97$	−766.194			−0.802013			−0.401006	−	0.916075i	$-0.631339\pi$
$97$	−766.194			−0.802013			−0.401006	+	0.916075i	$0.631339\pi$
$98$	90.6971	−	346.542i	0.0934876	−	0.357204i
$99$		0			0
$100$	596.316	−	1061.19i	0.596316	−	1.06119i
$101$	983.994	+	983.994i	0.969417	+	0.969417i	0.999546	−	0.0301291i	$-0.00959184\pi$
$101$	983.994	+	983.994i	0.969417	+	0.969417i	−0.0301291	+	0.999546i	$0.509592\pi$
$102$		0			0
$103$		−	512.291i		−	0.490074i	−0.969514	−	0.245037i	$-0.921200\pi$
$103$		−	512.291i		−	0.490074i	0.969514	−	0.245037i	$-0.0788000\pi$
$104$	−32.4812	−	1860.02i	−0.0306254	−	1.75375i
$105$		0			0
$106$	538.937	−	315.352i	0.493832	−	0.288959i
$107$	−633.097	−	633.097i	−0.571998	−	0.571998i	0.360688	−	0.932686i	$-0.382542\pi$
$107$	−633.097	−	633.097i	−0.571998	−	0.571998i	−0.932686	+	0.360688i	$0.882542\pi$
$108$		0			0
$109$	983.894	−	983.894i	0.864587	−	0.864587i	−0.127280	−	0.991867i	$-0.540625\pi$
$109$	983.894	−	983.894i	0.864587	−	0.864587i	0.991867	+	0.127280i	$0.0406246\pi$
$110$	1606.56	+	420.471i	1.39254	+	0.364457i
$111$		0			0
$112$	−804.073	+	489.536i	−0.678373	+	0.413007i
$113$	−332.042			−0.276424			−0.138212	−	0.990403i	$-0.544136\pi$
$113$	−332.042			−0.276424			−0.138212	+	0.990403i	$0.544136\pi$
$114$		0			0
$115$	1759.24	−	1759.24i	1.42652	−	1.42652i
$116$	528.785	−	148.306i	0.423245	−	0.118706i
$117$		0			0
$118$	822.359	−	481.193i	0.641562	−	0.375401i
$119$			1116.11i			0.859778i
$120$		0			0
$121$		−	87.1933i		−	0.0655096i
$122$	1199.98	+	2050.77i	0.890502	+	1.52187i
$123$		0			0
$124$	−206.491	−	116.034i	−0.149544	−	0.0840334i
$125$	−319.692	+	319.692i	−0.228753	+	0.228753i
$126$		0			0
$127$	712.949			0.498141			0.249071	−	0.968485i	$-0.419875\pi$
$127$	712.949			0.498141			0.249071	+	0.968485i	$0.419875\pi$
$128$	−1412.92	−	317.524i	−0.975666	−	0.219261i
$129$		0			0
$130$	−980.186	+	3745.16i	−0.661292	+	2.52671i
$131$	2039.63	−	2039.63i	1.36033	−	1.36033i	0.486843	−	0.873489i	$-0.338148\pi$
$131$	2039.63	−	2039.63i	1.36033	−	1.36033i	0.873489	−	0.486843i	$-0.161852\pi$
$132$		0			0
$133$	762.604	+	762.604i	0.497189	+	0.497189i
$134$	−605.276	−	1034.42i	−0.390208	−	0.666866i
$135$		0			0
$136$	−1192.69	+	1235.09i	−0.752004	+	0.778735i
$137$			761.248i			0.474728i	0.971421	+	0.237364i	$0.0762835\pi$
$137$			761.248i			0.474728i	−0.971421	+	0.237364i	$0.923717\pi$
$138$		0			0
$139$	1277.92	+	1277.92i	0.779798	+	0.779798i	0.979796	−	0.199998i	$-0.0640937\pi$
$139$	1277.92	+	1277.92i	0.779798	+	0.779798i	−0.199998	+	0.979796i	$0.564094\pi$
$140$	1886.22	−	529.018i	1.13867	−	0.319358i
$141$		0			0
$142$	−1898.78	−	496.950i	−1.12213	−	0.293684i
$143$	−2899.52			−1.69559
$144$		0			0
$145$	−1142.86			−0.654550
$146$	−1265.37	−	331.175i	−0.717282	−	0.187727i
$147$		0			0
$148$	451.411	+	1609.51i	0.250714	+	0.893923i
$149$	−746.651	−	746.651i	−0.410524	−	0.410524i	0.471397	−	0.881921i	$-0.343750\pi$
$149$	−746.651	−	746.651i	−0.410524	−	0.410524i	−0.881921	+	0.471397i	$0.843750\pi$
$150$		0			0
$151$			1186.11i			0.639234i	0.947547	+	0.319617i	$0.103554\pi$
$151$			1186.11i			0.639234i	−0.947547	+	0.319617i	$0.896446\pi$
$152$	28.9678	+	1658.83i	0.0154579	+	0.885190i
$153$		0			0
$154$	741.005	+	1266.38i	0.387740	+	0.662648i
$155$	348.536	+	348.536i	0.180614	+	0.180614i
$156$		0			0
$157$	219.416	−	219.416i	0.111537	−	0.111537i	−0.649136	−	0.760673i	$-0.724869\pi$
$157$	219.416	−	219.416i	0.111537	−	0.111537i	0.760673	+	0.649136i	$0.224869\pi$
$158$	−629.339	+	2404.62i	−0.316883	+	1.21077i
$159$		0			0
$160$	2652.61	+	1430.23i	1.31067	+	0.706685i
$161$	2198.15			1.07602
$162$		0			0
$163$	1321.49	−	1321.49i	0.635011	−	0.635011i	−0.314309	−	0.949321i	$-0.601773\pi$
$163$	1321.49	−	1321.49i	0.635011	−	0.635011i	0.949321	+	0.314309i	$0.101773\pi$
$164$	882.701	−	1570.83i	0.420289	−	0.747935i
$165$		0			0
$166$	−1871.41	−	3198.24i	−0.874996	−	1.49537i
$167$			1180.83i			0.547160i	0.961849	+	0.273580i	$0.0882078\pi$
$167$			1180.83i			0.547160i	−0.961849	+	0.273580i	$0.911792\pi$
$168$		0			0
$169$		−	4562.25i		−	2.07658i
$170$	3083.86	−	1804.48i	1.39130	−	0.814103i
$171$		0			0
$172$	−249.807	−	890.687i	−0.110742	−	0.394850i
$173$	1559.35	−	1559.35i	0.685289	−	0.685289i	−0.275898	−	0.961187i	$-0.588975\pi$
$173$	1559.35	−	1559.35i	0.685289	−	0.685289i	0.961187	+	0.275898i	$0.0889753\pi$
$174$		0			0
$175$	−2238.07			−0.966754
$176$	−533.276	+	2193.23i	−0.228393	+	0.939323i
$177$		0			0
$178$	−959.799	−	251.199i	−0.404157	−	0.105776i
$179$	−1718.83	+	1718.83i	−0.717717	+	0.717717i	−0.968137	−	0.250420i	$-0.919431\pi$
$179$	−1718.83	+	1718.83i	−0.717717	+	0.717717i	0.250420	+	0.968137i	$0.419431\pi$
$180$		0			0
$181$	703.803	+	703.803i	0.289023	+	0.289023i	0.836694	−	0.547671i	$-0.184485\pi$
$181$	703.803	+	703.803i	0.289023	+	0.289023i	−0.547671	+	0.836694i	$0.684485\pi$
$182$	−2952.14	+	1727.40i	−1.20235	+	0.703537i
$183$		0			0
$184$	2432.48	+	2348.99i	0.974593	+	0.941138i
$185$		−	3478.63i		−	1.38245i
$186$		0			0
$187$	1892.29	+	1892.29i	0.739989	+	0.739989i
$188$	324.597	+	182.401i	0.125924	+	0.0707605i
$189$		0			0
$190$	874.163	−	3340.06i	0.333781	−	1.27533i
$191$	−290.013			−0.109867			−0.0549335	−	0.998490i	$-0.517495\pi$
$191$	−290.013			−0.109867			−0.0549335	+	0.998490i	$0.517495\pi$
$192$		0			0
$193$	−4295.94			−1.60222			−0.801111	−	0.598516i	$-0.795757\pi$
$193$	−4295.94			−1.60222			−0.801111	+	0.598516i	$0.795757\pi$
$194$	−548.700	+	2096.51i	−0.203064	+	0.775880i
$195$		0			0
$196$	−883.278	−	496.342i	−0.321894	−	0.180883i
$197$	−936.690	−	936.690i	−0.338764	−	0.338764i	0.517138	−	0.855902i	$-0.326997\pi$
$197$	−936.690	−	936.690i	−0.338764	−	0.338764i	−0.855902	+	0.517138i	$0.826997\pi$
$198$		0			0
$199$		−	3333.18i		−	1.18735i	−0.804705	−	0.593675i	$-0.797676\pi$
$199$		−	3333.18i		−	1.18735i	0.804705	−	0.593675i	$-0.202324\pi$
$200$	−2476.65	−	2391.64i	−0.875628	−	0.845571i
$201$		0			0
$202$	3397.14	−	1987.80i	1.18328	−	0.692380i
$203$	−713.999	−	713.999i	−0.246862	−	0.246862i
$204$		0			0
$205$	−2651.41	+	2651.41i	−0.903330	+	0.903330i
$206$	−1401.77	−	366.871i	−0.474105	−	0.124083i
$207$		0			0
$208$	−5112.77	−	1243.15i	−1.70436	−	0.414409i
$209$	2585.89			0.855836
$210$		0			0
$211$	−3810.99	+	3810.99i	−1.24341	+	1.24341i	−0.284831	+	0.958578i	$0.591937\pi$
$211$	−3810.99	+	3810.99i	−1.24341	+	1.24341i	−0.958578	+	0.284831i	$0.908063\pi$
$212$	−476.934	−	1700.51i	−0.154509	−	0.550903i
$213$		0			0
$214$	−2185.71	+	1278.94i	−0.698186	+	0.408534i
$215$			1925.04i			0.610636i
$216$		0			0
$217$			435.493i			0.136236i
$218$	−1987.59	−	3396.80i	−0.617508	−	1.05532i
$219$		0			0
$220$	2301.04	−	4094.87i	0.705163	−	1.25489i
$221$	−4411.23	+	4411.23i	−1.34268	+	1.34268i
$222$		0			0
$223$	−3093.27			−0.928882			−0.464441	−	0.885604i	$-0.653745\pi$
$223$	−3093.27			−0.928882			−0.464441	+	0.885604i	$0.653745\pi$
$224$	763.675	+	2550.73i	0.227791	+	0.760839i
$225$		0			0
$226$	−237.788	+	908.555i	−0.0699885	+	0.267417i
$227$	−97.5310	+	97.5310i	−0.0285170	+	0.0285170i	−0.721222	−	0.692705i	$-0.756419\pi$
$227$	−97.5310	+	97.5310i	−0.0285170	+	0.0285170i	0.692705	+	0.721222i	$0.256419\pi$
$228$		0			0
$229$	2867.04	+	2867.04i	0.827334	+	0.827334i	0.987147	−	0.159813i	$-0.0510892\pi$
$229$	2867.04	+	2867.04i	0.827334	+	0.827334i	−0.159813	+	0.987147i	$0.551089\pi$
$230$	−3553.89	−	6073.61i	−1.01886	−	1.74123i
$231$		0			0
$232$	−27.1216	−	1553.10i	−0.00767508	−	0.439510i
$233$			260.384i			0.0732116i	0.999330	+	0.0366058i	$0.0116546\pi$
$233$			260.384i			0.0732116i	−0.999330	+	0.0366058i	$0.988345\pi$
$234$		0			0
$235$	−547.888	−	547.888i	−0.152086	−	0.152086i
$236$	−727.749	−	2594.79i	−0.200731	−	0.715706i
$237$		0			0
$238$	3053.97	+	799.287i	0.831763	+	0.217689i
$239$	−1133.63			−0.306814			−0.153407	−	0.988163i	$-0.549025\pi$
$239$	−1133.63			−0.306814			−0.153407	+	0.988163i	$0.549025\pi$
$240$		0			0
$241$	2717.65			0.726386			0.363193	−	0.931714i	$-0.381686\pi$
$241$	2717.65			0.726386			0.363193	+	0.931714i	$0.381686\pi$
$242$	−238.584	−	62.4423i	−0.0633750	−	0.0165866i
$243$		0			0
$244$	6470.80	−	1814.84i	1.69775	−	0.476160i
$245$	1490.89	+	1490.89i	0.388773	+	0.388773i
$246$		0			0
$247$			6028.13i			1.55288i
$248$	−465.375	+	481.917i	−0.119159	+	0.123394i
$249$		0			0
$250$	645.818	+	1103.70i	0.163381	+	0.279218i
$251$	−902.500	−	902.500i	−0.226953	−	0.226953i	0.584465	−	0.811419i	$-0.301304\pi$
$251$	−902.500	−	902.500i	−0.226953	−	0.226953i	−0.811419	+	0.584465i	$0.801304\pi$
$252$		0			0
$253$	3726.82	−	3726.82i	0.926101	−	0.926101i
$254$	510.569	−	1950.82i	0.126126	−	0.481910i
$255$		0			0
$256$	−1880.67	+	3638.72i	−0.459148	+	0.888360i
$257$	49.0728			0.0119108			0.00595541	−	0.999982i	$-0.498104\pi$
$257$	49.0728			0.0119108			0.00595541	+	0.999982i	$0.498104\pi$
$258$		0			0
$259$	2173.26	−	2173.26i	0.521388	−	0.521388i
$260$	9545.81	+	5364.10i	2.27695	+	1.27949i
$261$		0			0
$262$	−4120.32	−	7041.63i	−0.971581	−	1.66043i
$263$		−	448.347i		−	0.105119i	−0.998618	−	0.0525594i	$-0.983262\pi$
$263$		−	448.347i		−	0.105119i	0.998618	−	0.0525594i	$-0.0167379\pi$
$264$		0			0
$265$			3675.31i			0.851973i
$266$	2632.82	−	1540.56i	0.606873	−	0.355104i
$267$		0			0
$268$	−3263.90	+	915.411i	−0.743935	+	0.208648i
$269$	4691.01	−	4691.01i	1.06326	−	1.06326i	0.0653970	−	0.997859i	$-0.479169\pi$
$269$	4691.01	−	4691.01i	1.06326	−	1.06326i	0.997859	−	0.0653970i	$-0.0208314\pi$
$270$		0			0
$271$	310.218			0.0695365			0.0347683	−	0.999395i	$-0.488931\pi$
$271$	310.218			0.0695365			0.0347683	+	0.999395i	$0.488931\pi$
$272$	2525.40	+	4148.02i	0.562959	+	0.924671i
$273$		0			0
$274$	2082.98	+	545.158i	0.459260	+	0.120198i
$275$	−3794.49	+	3794.49i	−0.832060	+	0.832060i
$276$		0			0
$277$	3523.42	+	3523.42i	0.764267	+	0.764267i	0.977091	−	0.212823i	$-0.0682659\pi$
$277$	3523.42	+	3523.42i	0.764267	+	0.764267i	−0.212823	+	0.977091i	$0.568266\pi$
$278$	4411.90	−	2581.57i	0.951828	−	0.556950i
$279$		0			0
$280$	−96.7446	−	5540.04i	−0.0206486	−	1.18243i
$281$		−	1369.74i		−	0.290789i	−0.989374	−	0.145395i	$-0.953555\pi$
$281$		−	1369.74i		−	0.290789i	0.989374	−	0.145395i	$-0.0464452\pi$
$282$		0			0
$283$	−5575.17	−	5575.17i	−1.17106	−	1.17106i	−0.981958	−	0.189100i	$-0.939443\pi$
$283$	−5575.17	−	5575.17i	−1.17106	−	1.17106i	−0.189100	−	0.981958i	$-0.560557\pi$
$284$	−2719.58	+	4839.69i	−0.568229	+	1.01121i
$285$		0			0
$286$	−2076.45	+	7933.85i	−0.429312	+	1.64034i
$287$	−3312.91			−0.681377
$288$		0			0
$289$	844.738			0.171939
$290$	−818.448	+	3127.18i	−0.165727	+	0.633222i
$291$		0			0
$292$	−1812.36	+	3225.23i	−0.363221	+	0.646378i
$293$	1651.17	+	1651.17i	0.329222	+	0.329222i	0.852291	−	0.523068i	$-0.175213\pi$
$293$	1651.17	+	1651.17i	0.329222	+	0.329222i	−0.523068	+	0.852291i	$0.675213\pi$
$294$		0			0
$295$			5608.13i			1.10684i
$296$	4727.31	−	82.5521i	0.928274	−	0.0162103i
$297$		0			0
$298$	−2577.74	+	1508.33i	−0.501089	+	0.293206i
$299$	8687.84	+	8687.84i	1.68037	+	1.68037i
$300$		0			0
$301$	−1202.66	+	1202.66i	−0.230300	+	0.230300i
$302$	3245.51	+	849.418i	0.618405	+	0.161849i
$303$		0			0
$304$	4559.75	+	1108.69i	0.860261	+	0.209169i
$305$	−13985.4			−2.62557
$306$		0			0
$307$	−1930.51	+	1930.51i	−0.358892	+	0.358892i	−0.863404	−	0.504512i	$-0.831672\pi$
$307$	−1930.51	+	1930.51i	−0.358892	+	0.358892i	0.504512	+	0.863404i	$0.331672\pi$
$308$	3995.81	−	1120.69i	0.739229	−	0.207328i
$309$		0			0
$310$	1203.29	−	704.088i	0.220459	−	0.128998i
$311$			3967.14i			0.723331i	0.932308	+	0.361665i	$0.117792\pi$
$311$			3967.14i			0.723331i	−0.932308	+	0.361665i	$0.882208\pi$
$312$		0			0
$313$		−	7329.46i		−	1.32360i	−0.749682	−	0.661798i	$-0.769794\pi$
$313$		−	7329.46i		−	1.32360i	0.749682	−	0.661798i	$-0.230206\pi$
$314$	−443.247	−	757.511i	−0.0796621	−	0.136143i
$315$		0			0
$316$	6128.99	+	3444.08i	1.09108	+	0.613115i
$317$	3264.85	−	3264.85i	0.578461	−	0.578461i	−0.356018	−	0.934479i	$-0.615866\pi$
$317$	3264.85	−	3264.85i	0.578461	−	0.578461i	0.934479	+	0.356018i	$0.115866\pi$
$318$		0			0
$319$	−2421.07			−0.424935
$320$	5813.12	−	6234.00i	1.01551	−	1.08903i
$321$		0			0
$322$	1574.18	−	6014.74i	0.272440	−	1.04096i
$323$	3934.09	−	3934.09i	0.677705	−	0.677705i
$324$		0			0
$325$	−8845.58	−	8845.58i	−1.50974	−	1.50974i
$326$	−2669.57	−	4562.30i	−0.453540	−	0.775100i
$327$		0			0
$328$	−3666.08	−	3540.23i	−0.617150	−	0.595966i
$329$		−	684.580i		−	0.114718i
$330$		0			0
$331$	7640.33	+	7640.33i	1.26873	+	1.26873i	0.946743	+	0.321991i	$0.104352\pi$
$331$	7640.33	+	7640.33i	1.26873	+	1.26873i	0.321991	+	0.946743i	$0.395648\pi$
$332$	−10091.4	+	2830.29i	−1.66819	+	0.467868i
$333$		0			0
$334$	3231.08	+	845.639i	0.529331	+	0.138537i
$335$	7054.28			1.15050
$336$		0			0
$337$	10375.8			1.67716			0.838582	−	0.544775i	$-0.183385\pi$
$337$	10375.8			1.67716			0.838582	+	0.544775i	$0.183385\pi$
$338$	−12483.5	−	3267.20i	−2.00892	−	0.525775i
$339$		0			0
$340$	−2729.08	−	9730.53i	−0.435309	−	1.55209i
$341$	738.349	+	738.349i	0.117255	+	0.117255i
$342$		0			0
$343$			6908.01i			1.08746i
$344$	−2616.05	+	45.6836i	−0.410023	+	0.00716016i
$345$		0			0
$346$	−3150.08	−	5383.49i	−0.489449	−	0.836469i
$347$	−3827.22	−	3827.22i	−0.592092	−	0.592092i	0.346104	−	0.938196i	$-0.387504\pi$
$347$	−3827.22	−	3827.22i	−0.592092	−	0.592092i	−0.938196	+	0.346104i	$0.887504\pi$
$348$		0			0
$349$	783.575	−	783.575i	0.120183	−	0.120183i	−0.644457	−	0.764640i	$-0.722917\pi$
$349$	783.575	−	783.575i	0.120183	−	0.120183i	0.764640	+	0.644457i	$0.222917\pi$
$350$	−1602.76	+	6123.94i	−0.244775	+	0.935253i
$351$		0			0
$352$	5619.36	+	3029.84i	0.850888	+	0.458781i
$353$	9151.32			1.37982			0.689909	−	0.723896i	$-0.257651\pi$
$353$	9151.32			1.37982			0.689909	+	0.723896i	$0.257651\pi$
$354$		0			0
$355$	8168.92	−	8168.92i	1.22130	−	1.22130i
$356$	−1374.70	+	2446.37i	−0.204659	+	0.364206i
$357$		0			0
$358$	3472.26	+	5934.09i	0.512610	+	0.876052i
$359$		−	290.943i		−	0.0427727i	−0.999771	−	0.0213863i	$-0.993192\pi$
$359$		−	290.943i		−	0.0427727i	0.999771	−	0.0213863i	$-0.00680800\pi$
$360$		0			0
$361$			1482.91i			0.216199i
$362$	2429.81	−	1421.77i	0.352784	−	0.206427i
$363$		0			0
$364$	2612.50	+	9314.89i	0.376188	+	1.34130i
$365$	5443.88	−	5443.88i	0.780674	−	0.780674i
$366$		0			0
$367$	−5526.68			−0.786077			−0.393039	−	0.919522i	$-0.628576\pi$
$367$	−5526.68			−0.786077			−0.393039	+	0.919522i	$0.628576\pi$
$368$	8169.44	−	4973.72i	1.15723	−	0.704547i
$369$		0			0
$370$	−9518.45	−	2491.18i	−1.33741	−	0.350027i
$371$	−2296.13	+	2296.13i	−0.321319	+	0.321319i
$372$		0			0
$373$	−978.030	−	978.030i	−0.135765	−	0.135765i	0.635958	−	0.771724i	$-0.280605\pi$
$373$	−978.030	−	978.030i	−0.135765	−	0.135765i	−0.771724	+	0.635958i	$0.780605\pi$
$374$	6532.94	−	3822.67i	0.903236	−	0.528517i
$375$		0			0
$376$	731.554	−	757.558i	0.100338	−	0.103904i
$377$		−	5643.92i		−	0.771026i
$378$		0			0
$379$	−4408.79	−	4408.79i	−0.597531	−	0.597531i	0.342124	−	0.939655i	$-0.388854\pi$
$379$	−4408.79	−	4408.79i	−0.597531	−	0.597531i	−0.939655	+	0.342124i	$0.888854\pi$
$380$	−8513.27	−	4783.88i	−1.14927	−	0.645811i
$381$		0			0
$382$	−207.689	+	793.553i	−0.0278175	+	0.106287i
$383$	−6799.13			−0.907101			−0.453550	−	0.891231i	$-0.649843\pi$
$383$	−6799.13			−0.907101			−0.453550	+	0.891231i	$0.649843\pi$
$384$		0			0
$385$	−8636.15			−1.14322
$386$	−3076.48	+	11754.8i	−0.405671	+	1.55001i
$387$		0			0
$388$	5343.66	+	3002.78i	0.699184	+	0.392894i
$389$	5520.37	+	5520.37i	0.719521	+	0.719521i	0.968507	−	0.248986i	$-0.0800972\pi$
$389$	5520.37	+	5520.37i	0.719521	+	0.719521i	−0.248986	+	0.968507i	$0.580097\pi$
$390$		0			0
$391$		−	11339.7i		−	1.46669i
$392$	−1990.67	+	2061.43i	−0.256490	+	0.265607i
$393$		0			0
$394$	−3233.83	+	1892.23i	−0.413498	+	0.241953i
$395$	−10345.1	−	10345.1i	−1.31777	−	1.31777i
$396$		0			0
$397$	−4743.70	+	4743.70i	−0.599696	+	0.599696i	−0.940232	−	0.340536i	$-0.889392\pi$
$397$	−4743.70	+	4743.70i	−0.599696	+	0.599696i	0.340536	+	0.940232i	$0.389392\pi$
$398$	−9120.46	−	2387.01i	−1.14866	−	0.300628i
$399$		0			0
$400$	−8317.77	+	5064.03i	−1.03972	+	0.633004i
$401$	1674.92			0.208582			0.104291	−	0.994547i	$-0.466743\pi$
$401$	1674.92			0.208582			0.104291	+	0.994547i	$0.466743\pi$
$402$		0			0
$403$	−1721.21	+	1721.21i	−0.212754	+	0.212754i
$404$	−3006.31	−	10719.0i	−0.370222	−	1.32003i
$405$		0			0
$406$	−2465.01	+	1442.37i	−0.301321	+	0.176314i
$407$		−	7369.22i		−	0.897491i
$408$		0			0
$409$			11918.0i			1.44084i	0.693536	+	0.720422i	$0.256052\pi$
$409$			11918.0i			1.44084i	−0.693536	+	0.720422i	$0.743948\pi$
$410$	5356.19	+	9153.74i	0.645179	+	1.10261i
$411$		0			0
$412$	−2007.71	+	3572.87i	−0.240080	+	0.427240i
$413$	−3503.65	+	3503.65i	−0.417442	+	0.417442i
$414$		0			0
$415$	21810.6			2.57985
$416$	−7063.04	+	13099.6i	−0.832438	+	1.54390i
$417$		0			0
$418$	1851.85	−	7075.68i	0.216691	−	0.827949i
$419$	−4342.25	+	4342.25i	−0.506284	+	0.506284i	−0.913384	−	0.407100i	$-0.866540\pi$
$419$	−4342.25	+	4342.25i	−0.506284	+	0.506284i	0.407100	+	0.913384i	$0.366540\pi$
$420$		0			0
$421$	−8933.14	−	8933.14i	−1.03414	−	1.03414i	−0.999396	−	0.0347474i	$-0.988937\pi$
$421$	−8933.14	−	8933.14i	−1.03414	−	1.03414i	−0.0347474	−	0.999396i	$-0.511063\pi$
$422$	7698.69	+	13157.1i	0.888071	+	1.51772i
$423$		0			0
$424$	−4994.59	+	87.2197i	−0.572073	+	0.00999000i
$425$			11545.6i			1.31776i
$426$		0			0
$427$	−8737.28	−	8737.28i	−0.990227	−	0.990227i
$428$	1934.25	+	6896.57i	0.218447	+	0.778874i
$429$		0			0
$430$	5267.43	+	1378.59i	0.590739	+	0.154609i
$431$	6175.68			0.690191			0.345095	−	0.938568i	$-0.387847\pi$
$431$	6175.68			0.690191			0.345095	+	0.938568i	$0.387847\pi$
$432$		0			0
$433$	7.68815			0.000853276			0.000426638	−	1.00000i	$-0.499864\pi$
$433$	7.68815			0.000853276			0.000426638		1.00000i	$0.499864\pi$
$434$	1191.62	+	311.872i	0.131797	+	0.0344939i
$435$		0			0
$436$	−10717.9	+	3006.01i	−1.17728	+	0.330187i
$437$	−7748.11	−	7748.11i	−0.848152	−	0.848152i
$438$		0			0
$439$		−	15185.1i		−	1.65090i	−0.564477	−	0.825449i	$-0.690922\pi$
$439$		−	15185.1i		−	1.65090i	0.564477	−	0.825449i	$-0.309078\pi$
$440$	−9556.78	−	9228.74i	−1.03546	−	0.999915i
$441$		0			0
$442$	8911.26	+	15229.4i	0.958971	+	1.63888i
$443$	3404.98	+	3404.98i	0.365182	+	0.365182i	0.865716	−	0.500535i	$-0.166863\pi$
$443$	3404.98	+	3404.98i	0.365182	+	0.365182i	−0.500535	+	0.865716i	$0.666863\pi$
$444$		0			0
$445$	4129.24	−	4129.24i	0.439876	−	0.439876i
$446$	−2215.21	+	8464.01i	−0.235186	+	0.898615i
$447$		0			0
$448$	7526.38	−	262.944i	0.793723	−	0.0277297i
$449$	−6766.99			−0.711257			−0.355628	−	0.934627i	$-0.615733\pi$
$449$	−6766.99			−0.711257			−0.355628	+	0.934627i	$0.615733\pi$
$450$		0			0
$451$	−5616.82	+	5616.82i	−0.586443	+	0.586443i
$452$	2315.76	+	1301.30i	0.240983	+	0.135416i
$453$		0			0
$454$	197.025	+	336.716i	0.0203675	+	0.0348081i
$455$		−	20132.3i		−	2.07432i
$456$		0			0
$457$		−	7528.20i		−	0.770578i	−0.922796	−	0.385289i	$-0.874102\pi$
$457$		−	7528.20i		−	0.770578i	0.922796	−	0.385289i	$-0.125898\pi$
$458$	9898.18	−	5791.79i	1.00985	−	0.590901i
$459$		0			0
$460$	−19164.1	+	5374.86i	−1.94246	+	0.544792i
$461$	−9029.85	+	9029.85i	−0.912282	+	0.912282i	−0.996451	−	0.0841690i	$-0.973176\pi$
$461$	−9029.85	+	9029.85i	−0.912282	+	0.912282i	0.0841690	+	0.996451i	$0.473176\pi$
$462$		0			0
$463$	8555.19			0.858733			0.429367	−	0.903130i	$-0.358737\pi$
$463$	8555.19			0.858733			0.429367	+	0.903130i	$0.358737\pi$
$464$	−4269.13	−	1038.02i	−0.427132	−	0.103856i
$465$		0			0
$466$	712.479	+	186.470i	0.0708261	+	0.0185366i
$467$	−1326.73	+	1326.73i	−0.131464	+	0.131464i	−0.769777	−	0.638313i	$-0.779632\pi$
$467$	−1326.73	+	1326.73i	−0.131464	+	0.131464i	0.638313	+	0.769777i	$0.279632\pi$
$468$		0			0
$469$	4407.13	+	4407.13i	0.433907	+	0.433907i
$470$	−1891.53	+	1106.80i	−0.185638	+	0.108623i
$471$		0			0
$472$	−7621.21	+	133.088i	−0.743209	+	0.0129785i
$473$			4078.06i			0.396426i
$474$		0			0
$475$	7888.79	+	7888.79i	0.762027	+	0.762027i
$476$	4374.12	−	7784.08i	0.421193	−	0.749543i
$477$		0			0
$478$	−811.835	+	3101.91i	−0.0776830	+	0.296816i
$479$	6121.90			0.583960			0.291980	−	0.956424i	$-0.405686\pi$
$479$	6121.90			0.583960			0.291980	+	0.956424i	$0.405686\pi$
$480$		0			0
$481$	17178.9			1.62846
$482$	1946.21	−	7436.21i	0.183916	−	0.702718i
$483$		0			0
$484$	−341.718	+	608.112i	−0.0320922	+	0.0571104i
$485$	−9019.59	−	9019.59i	−0.844450	−	0.844450i
$486$		0			0
$487$		−	6508.23i		−	0.605577i	−0.953058	−	0.302789i	$-0.902082\pi$
$487$		−	6508.23i		−	0.605577i	0.953058	−	0.302789i	$-0.0979177\pi$
$488$	−331.890	−	19005.5i	−0.0307867	−	1.76299i
$489$		0			0
$490$	5147.15	−	3011.79i	0.474540	−	0.277671i
$491$	8093.67	+	8093.67i	0.743915	+	0.743915i	0.973329	−	0.229414i	$-0.0736811\pi$
$491$	8093.67	+	8093.67i	0.743915	+	0.743915i	−0.229414	+	0.973329i	$0.573681\pi$
$492$		0			0
$493$	−3683.35	+	3683.35i	−0.336490	+	0.336490i
$494$	16494.6	+	4316.97i	1.50228	+	0.393177i
$495$		0			0
$496$	985.381	+	1618.51i	0.0892035	+	0.146518i
$497$	10207.0			0.921219
$498$		0			0
$499$	−6772.14	+	6772.14i	−0.607540	+	0.607540i	−0.942303	−	0.334762i	$-0.891344\pi$
$499$	−6772.14	+	6772.14i	−0.607540	+	0.607540i	0.334762	+	0.942303i	$0.391344\pi$
$500$	3482.52	−	976.727i	0.311486	−	0.0873611i
$501$		0			0
$502$	−3115.79	+	1823.17i	−0.277021	+	0.162095i
$503$			3296.12i			0.292180i	0.989271	+	0.146090i	$0.0466689\pi$
$503$			3296.12i			0.292180i	−0.989271	+	0.146090i	$0.953331\pi$
$504$		0			0
$505$			23167.0i			2.04143i
$506$	−7528.66	−	12866.5i	−0.661443	−	1.13041i
$507$		0			0
$508$	−4972.31	−	2794.10i	−0.434273	−	0.244032i
$509$	−6445.02	+	6445.02i	−0.561239	+	0.561239i	−0.929659	−	0.368421i	$-0.879899\pi$
$509$	−6445.02	+	6445.02i	−0.561239	+	0.561239i	0.368421	+	0.929659i	$0.379899\pi$
$510$		0			0
$511$	6802.08			0.588858
$512$	8609.69	+	7751.84i	0.743160	+	0.669113i
$513$		0			0
$514$	35.1429	−	134.276i	0.00301573	−	0.0115227i
$515$	6030.66	−	6030.66i	0.516005	−	0.516005i
$516$		0			0
$517$	−1160.66	−	1160.66i	−0.0987346	−	0.0987346i
$518$	−4390.26	−	7502.96i	−0.372388	−	0.636411i
$519$		0			0
$520$	21513.7	−	22278.4i	1.81430	−	1.87880i
$521$			15572.4i			1.30948i	0.755854	+	0.654740i	$0.227222\pi$
$521$			15572.4i			1.30948i	−0.755854	+	0.654740i	$0.772778\pi$
$522$		0			0
$523$	2333.98	+	2333.98i	0.195139	+	0.195139i	0.797913	−	0.602773i	$-0.205938\pi$
$523$	2333.98	+	2333.98i	0.195139	+	0.195139i	−0.602773	+	0.797913i	$0.705938\pi$
$524$	−22218.5	+	6231.52i	−1.85233	+	0.519513i
$525$		0			0
$526$	−1226.80	−	321.078i	−0.101694	−	0.0266153i
$527$	2246.60			0.185699
$528$		0			0
$529$	−10166.4			−0.835572
$530$	10056.6	+	2632.03i	0.824212	+	0.215713i
$531$		0			0
$532$	−2329.92	−	8307.33i	−0.189877	−	0.677009i
$533$	−13093.7	−	13093.7i	−1.06408	−	1.06408i
$534$		0			0
$535$		−	14905.6i		−	1.20453i
$536$	167.407	+	9586.46i	0.0134904	+	0.772523i
$537$		0			0
$538$	−9476.44	−	16195.3i	−0.759402	−	1.29782i
$539$	3158.34	+	3158.34i	0.252392	+	0.252392i
$540$		0			0
$541$	8320.06	−	8320.06i	0.661196	−	0.661196i	−0.294466	−	0.955662i	$-0.595142\pi$
$541$	8320.06	−	8320.06i	0.661196	−	0.661196i	0.955662	+	0.294466i	$0.0951417\pi$
$542$	222.159	−	848.839i	0.0176061	−	0.0672707i
$543$		0			0
$544$	13158.6	−	3939.61i	1.03708	−	0.310496i
$545$	23164.7			1.82067
$546$		0			0
$547$	−10206.5	+	10206.5i	−0.797801	+	0.797801i	−0.982748	−	0.184947i	$-0.940789\pi$
$547$	−10206.5	+	10206.5i	−0.797801	+	0.797801i	0.184947	+	0.982748i	$0.440789\pi$
$548$	2983.39	−	5309.17i	0.232562	−	0.413862i
$549$		0			0
$550$	7665.36	+	13100.1i	0.594277	+	1.01562i
$551$			5033.44i			0.389168i
$552$		0			0
$553$		−	12926.2i		−	0.993989i
$554$	12164.3	−	7117.77i	0.932871	−	0.545858i
$555$		0			0
$556$	−3904.32	−	13920.9i	−0.297806	−	1.06183i
$557$	−9984.48	+	9984.48i	−0.759526	+	0.759526i	−0.976236	−	0.216710i	$-0.930467\pi$
$557$	−9984.48	+	9984.48i	−0.759526	+	0.759526i	0.216710	+	0.976236i	$0.430467\pi$
$558$		0			0
$559$	−9506.63			−0.719298
$560$	−15228.3	−	3702.71i	−1.14913	−	0.279407i
$561$		0			0
$562$	−3747.97	−	980.921i	−0.281314	−	0.0736257i
$563$	12193.3	−	12193.3i	0.912761	−	0.912761i	−0.0837279	−	0.996489i	$-0.526683\pi$
$563$	12193.3	−	12193.3i	0.912761	−	0.912761i	0.996489	+	0.0837279i	$0.0266827\pi$
$564$		0			0
$565$	−3908.78	−	3908.78i	−0.291051	−	0.291051i
$566$	−19247.7	+	11262.6i	−1.42940	+	0.836397i
$567$		0			0
$568$	11295.1	+	10907.4i	0.834385	+	0.805744i
$569$		−	4990.14i		−	0.367659i	−0.982958	−	0.183829i	$-0.941151\pi$
$569$		−	4990.14i		−	0.367659i	0.982958	−	0.183829i	$-0.0588494\pi$
$570$		0			0
$571$	6896.58	+	6896.58i	0.505451	+	0.505451i	0.913127	−	0.407676i	$-0.133661\pi$
$571$	6896.58	+	6896.58i	0.505451	+	0.505451i	−0.407676	+	0.913127i	$0.633661\pi$
$572$	20222.1	+	11363.4i	1.47820	+	0.830646i
$573$		0			0
$574$	−2372.50	+	9065.01i	−0.172520	+	0.659174i
$575$	22738.9			1.64918
$576$		0			0
$577$	−12824.7			−0.925299			−0.462649	−	0.886541i	$-0.653101\pi$
$577$	−12824.7			−0.925299			−0.462649	+	0.886541i	$0.653101\pi$
$578$	604.948	−	2311.43i	0.0435338	−	0.166337i
$579$		0			0
$580$	7970.67	+	4478.98i	0.570628	+	0.320654i
$581$	13626.0	+	13626.0i	0.972984	+	0.972984i
$582$		0			0
$583$			7785.88i			0.553102i
$584$	7527.19	+	7268.81i	0.533352	+	0.515044i
$585$		0			0
$586$	5700.49	−	3335.57i	0.401852	−	0.235138i
$587$	−15610.1	−	15610.1i	−1.09761	−	1.09761i	−0.994690	−	0.102920i	$-0.967181\pi$
$587$	−15610.1	−	15610.1i	−1.09761	−	1.09761i	−0.102920	−	0.994690i	$-0.532819\pi$
$588$		0			0
$589$	1535.04	−	1535.04i	0.107385	−	0.107385i
$590$	15345.3	+	4016.19i	1.07077	+	0.280244i
$591$		0			0
$592$	3159.52	−	12994.3i	0.219350	−	0.902132i
$593$	−16469.9			−1.14054			−0.570268	−	0.821458i	$-0.693161\pi$
$593$	−16469.9			−1.14054			−0.570268	+	0.821458i	$0.693161\pi$
$594$		0			0
$595$	−13138.8	+	13138.8i	−0.905272	+	0.905272i
$596$	2281.18	+	8133.55i	0.156780	+	0.558999i
$597$		0			0
$598$	29993.9	−	17550.5i	2.05107	−	1.20016i
$599$			10220.6i			0.697164i	0.937278	+	0.348582i	$0.113337\pi$
$599$			10220.6i			0.697164i	−0.937278	+	0.348582i	$0.886663\pi$
$600$		0			0
$601$			16286.3i			1.10538i	0.833387	+	0.552690i	$0.186399\pi$
$601$			16286.3i			1.10538i	−0.833387	+	0.552690i	$0.813601\pi$
$602$	2429.53	+	4152.07i	0.164485	+	0.281106i
$603$		0			0
$604$	4648.47	−	8272.29i	0.313151	−	0.557276i
$605$	1026.43	−	1026.43i	0.0689760	−	0.0689760i
$606$		0			0
$607$	−21362.6			−1.42847			−0.714235	−	0.699906i	$-0.753225\pi$
$607$	−21362.6			−1.42847			−0.714235	+	0.699906i	$0.753225\pi$
$608$	6299.06	−	11682.7i	0.420166	−	0.779270i
$609$		0			0
$610$	−10015.4	+	38267.7i	−0.664776	+	2.54002i
$611$	2705.69	−	2705.69i	0.179150	−	0.179150i
$612$		0			0
$613$	1189.98	+	1189.98i	0.0784057	+	0.0784057i	0.745222	−	0.666816i	$-0.232343\pi$
$613$	1189.98	+	1189.98i	0.0784057	+	0.0784057i	−0.666816	+	0.745222i	$0.732343\pi$
$614$	3899.87	+	6664.89i	0.256329	+	0.438067i
$615$		0			0
$616$	−204.946	−	11736.2i	−0.0134051	−	0.767635i
$617$			1361.21i			0.0888173i	0.999013	+	0.0444087i	$0.0141404\pi$
$617$			1361.21i			0.0888173i	−0.999013	+	0.0444087i	$0.985860\pi$
$618$		0			0
$619$	−5468.68	−	5468.68i	−0.355097	−	0.355097i	0.506905	−	0.862002i	$-0.330789\pi$
$619$	−5468.68	−	5468.68i	−0.355097	−	0.355097i	−0.862002	+	0.506905i	$0.830789\pi$
$620$	−1064.85	−	3796.74i	−0.0689767	−	0.245937i
$621$		0			0
$622$	10855.1	+	2841.02i	0.699762	+	0.183142i
$623$	5159.44			0.331796
$624$		0			0
$625$	11492.9			0.735543
$626$	−20055.4	−	5248.90i	−1.28047	−	0.335125i
$627$		0			0
$628$	−2390.18	+	670.361i	−0.151876	+	0.0425961i
$629$	−11211.3	−	11211.3i	−0.710690	−	0.710690i
$630$		0			0
$631$			11369.6i			0.717303i	0.933472	+	0.358651i	$0.116763\pi$
$631$			11369.6i			0.717303i	−0.933472	+	0.358651i	$0.883237\pi$
$632$	13813.1	−	14304.1i	0.869392	−	0.900296i
$633$		0			0
$634$	−6595.42	−	11271.6i	−0.413151	−	0.706075i
$635$	8392.79	+	8392.79i	0.524500	+	0.524500i
$636$		0			0
$637$	−7362.60	+	7362.60i	−0.457954	+	0.457954i
$638$	−1733.82	+	6624.70i	−0.107590	+	0.411089i
$639$		0			0
$640$	−12894.9	−	20370.6i	−0.796430	−	1.25816i
$641$	−9280.18			−0.571833			−0.285917	−	0.958255i	$-0.592298\pi$
$641$	−9280.18			−0.571833			−0.285917	+	0.958255i	$0.592298\pi$
$642$		0			0
$643$	−9377.81	+	9377.81i	−0.575155	+	0.575155i	−0.933565	−	0.358409i	$-0.883319\pi$
$643$	−9377.81	+	9377.81i	−0.575155	+	0.575155i	0.358409	+	0.933565i	$0.383319\pi$
$644$	−15330.6	−	8614.75i	−0.938058	−	0.527125i
$645$		0			0
$646$	−7947.37	−	13582.1i	−0.484032	−	0.827212i
$647$			1950.32i			0.118508i	0.998243	+	0.0592542i	$0.0188723\pi$
$647$			1950.32i			0.118508i	−0.998243	+	0.0592542i	$0.981128\pi$
$648$		0			0
$649$			11880.4i			0.718562i
$650$	−30538.5	+	17869.2i	−1.84280	+	1.07829i
$651$		0			0
$652$	−14395.5	+	4037.42i	−0.864677	+	0.242512i
$653$	8699.36	−	8699.36i	0.521336	−	0.521336i	−0.396639	−	0.917975i	$-0.629823\pi$
$653$	8699.36	−	8699.36i	0.521336	−	0.521336i	0.917975	+	0.396639i	$0.129823\pi$
$654$		0			0
$655$	48020.9			2.86463
$656$	−12312.4	+	7496.06i	−0.732804	+	0.446147i
$657$		0			0
$658$	−1873.19	−	490.253i	−0.110980	−	0.0290457i
$659$	−7958.47	+	7958.47i	−0.470437	+	0.470437i	−0.902056	−	0.431619i	$-0.857942\pi$
$659$	−7958.47	+	7958.47i	−0.470437	+	0.470437i	0.431619	+	0.902056i	$0.357942\pi$
$660$		0			0
$661$	7483.62	+	7483.62i	0.440362	+	0.440362i	0.892134	−	0.451772i	$-0.149208\pi$
$661$	7483.62	+	7483.62i	0.440362	+	0.440362i	−0.451772	+	0.892134i	$0.649208\pi$
$662$	26377.5	−	15434.5i	1.54863	−	0.906159i
$663$		0			0
$664$	517.591	+	29639.6i	0.0302507	+	1.73229i
$665$			17954.7i			1.04700i
$666$		0			0
$667$	7254.28	+	7254.28i	0.421120	+	0.421120i
$668$	4627.79	−	8235.49i	0.268046	−	0.477007i
$669$		0			0
$670$	5051.83	−	19302.4i	0.291297	−	1.11301i
$671$	−29627.0			−1.70452
$672$		0			0
$673$	3592.82			0.205785			0.102892	−	0.994692i	$-0.467190\pi$
$673$	3592.82			0.205785			0.102892	+	0.994692i	$0.467190\pi$
$674$	7430.48	−	28390.9i	0.424646	−	1.62252i
$675$		0			0
$676$	−17879.8	+	31818.5i	−1.01729	+	1.81034i
$677$	16494.8	+	16494.8i	0.936408	+	0.936408i	0.998096	−	0.0616872i	$-0.0196481\pi$
$677$	16494.8	+	16494.8i	0.936408	+	0.936408i	−0.0616872	+	0.998096i	$0.519648\pi$
$678$		0			0
$679$		−	11269.9i		−	0.636964i
$680$	−28579.7	+	499.082i	−1.61174	+	0.0281455i
$681$		0			0
$682$	2549.08	−	1491.56i	0.143122	−	0.0837460i
$683$	−20875.1	−	20875.1i	−1.16949	−	1.16949i	−0.982328	−	0.187166i	$-0.940070\pi$
$683$	−20875.1	−	20875.1i	−1.16949	−	1.16949i	−0.187166	−	0.982328i	$-0.559930\pi$
$684$		0			0
$685$	−8961.36	+	8961.36i	−0.499848	+	0.499848i
$686$	18902.1	+	4947.08i	1.05202	+	0.275336i
$687$		0			0
$688$	−1748.45	+	7190.92i	−0.0968880	+	0.398476i
$689$	−18150.2			−1.00358
$690$		0			0
$691$	22267.3	−	22267.3i	1.22589	−	1.22589i	0.260382	−	0.965506i	$-0.416151\pi$
$691$	22267.3	−	22267.3i	1.22589	−	1.22589i	0.965506	−	0.260382i	$-0.0838487\pi$
$692$	−16986.6	+	4764.14i	−0.933138	+	0.261713i
$693$		0			0
$694$	−13213.1	+	7731.47i	−0.722712	+	0.422886i
$695$			30087.2i			1.64212i
$696$		0			0
$697$			17090.5i			0.928765i
$698$	−1582.92	−	2705.21i	−0.0858373	−	0.146696i
$699$		0			0
$700$	15608.9	+	8771.17i	0.842803	+	0.473598i
$701$	12419.0	−	12419.0i	0.669129	−	0.669129i	−0.288385	−	0.957515i	$-0.593118\pi$
$701$	12419.0	−	12419.0i	0.669129	−	0.669129i	0.957515	+	0.288385i	$0.0931183\pi$
$702$		0			0
$703$	−15320.7			−0.821950
$704$	12314.7	−	13206.3i	0.659270	−	0.707003i
$705$		0			0
$706$	6553.60	−	25040.4i	0.349360	−	1.33486i
$707$	−14473.5	+	14473.5i	−0.769918	+	0.769918i
$708$		0			0
$709$	−17027.9	−	17027.9i	−0.901970	−	0.901970i	0.0936362	−	0.995606i	$-0.470151\pi$
$709$	−17027.9	−	17027.9i	−0.901970	−	0.901970i	−0.995606	+	0.0936362i	$0.970151\pi$
$710$	−16502.3	−	28202.4i	−0.872281	−	1.49073i
$711$		0			0
$712$	5709.45	+	5513.47i	0.300521	+	0.290205i
$713$		−	4424.64i		−	0.232404i
$714$		0			0
$715$	−34132.9	−	34132.9i	−1.78531	−	1.78531i
$716$	18723.9	−	5251.39i	0.977296	−	0.274097i
$717$		0			0
$718$	−796.097	−	208.355i	−0.0413790	−	0.0108297i
$719$	−9987.52			−0.518041			−0.259021	−	0.965872i	$-0.583400\pi$
$719$	−9987.52			−0.518041			−0.259021	+	0.965872i	$0.583400\pi$
$720$		0			0
$721$	7535.25			0.389220
$722$	4057.63	+	1061.97i	0.209154	+	0.0547400i
$723$		0			0
$724$	−2150.27	−	7666.79i	−0.110379	−	0.393555i
$725$	−7385.99	−	7385.99i	−0.378357	−	0.378357i
$726$		0			0
$727$			18495.4i			0.943545i	0.881720	+	0.471772i	$0.156386\pi$
$727$			18495.4i			0.943545i	−0.881720	+	0.471772i	$0.843614\pi$
$728$	27358.9	−	477.763i	1.39284	−	0.0243229i
$729$		0			0
$730$	−10997.3	−	18794.5i	−0.557575	−	0.952897i
$731$	6204.24	+	6204.24i	0.313915	+	0.313915i
$732$		0			0
$733$	3852.08	−	3852.08i	0.194106	−	0.194106i	−0.603362	−	0.797468i	$-0.706172\pi$
$733$	3852.08	−	3852.08i	0.194106	−	0.194106i	0.797468	+	0.603362i	$0.206172\pi$
$734$	−3957.86	+	15122.5i	−0.199029	+	0.760464i
$735$		0			0
$736$	−7758.99	−	25915.6i	−0.388587	−	1.29791i
$737$	14944.0			0.746904
$738$		0			0
$739$	16168.9	−	16168.9i	0.804846	−	0.804846i	−0.179003	−	0.983849i	$-0.557287\pi$
$739$	16168.9	−	16168.9i	0.804846	−	0.804846i	0.983849	+	0.179003i	$0.0572871\pi$
$740$	−13633.0	+	24261.0i	−0.677244	+	1.20521i
$741$		0			0
$742$	4638.49	+	7927.18i	0.229493	+	0.392205i
$743$		−	36990.3i		−	1.82644i	−0.407471	−	0.913218i	$-0.633589\pi$
$743$		−	36990.3i		−	1.82644i	0.407471	−	0.913218i	$-0.366411\pi$
$744$		0			0
$745$		−	17579.1i		−	0.864492i
$746$	−3376.55	+	1975.75i	−0.165716	+	0.0969667i
$747$		0			0
$748$	−5781.35	−	20613.4i	−0.282603	−	1.00762i
$749$	9312.18	−	9312.18i	0.454285	−	0.454285i
$750$		0			0
$751$	−10125.3			−0.491981			−0.245990	−	0.969272i	$-0.579113\pi$
$751$	−10125.3			−0.491981			−0.245990	+	0.969272i	$0.579113\pi$
$752$	−1548.99	−	2544.24i	−0.0751140	−	0.123376i
$753$		0			0
$754$	−15443.3	−	4041.82i	−0.745903	−	0.195218i
$755$	−13962.8	+	13962.8i	−0.673059	+	0.673059i
$756$		0			0
$757$	−8998.60	−	8998.60i	−0.432047	−	0.432047i	0.457277	−	0.889324i	$-0.348825\pi$
$757$	−8998.60	−	8998.60i	−0.432047	−	0.432047i	−0.889324	+	0.457277i	$0.848825\pi$
$758$	−15220.9	+	8906.32i	−0.729351	+	0.426770i
$759$		0			0
$760$	−19186.6	+	19868.7i	−0.915754	+	0.948305i
$761$		−	25265.9i		−	1.20353i	−0.798672	−	0.601766i	$-0.794464\pi$
$761$		−	25265.9i		−	1.20353i	0.798672	−	0.601766i	$-0.205536\pi$
$762$		0			0
$763$	14472.0	+	14472.0i	0.686661	+	0.686661i
$764$	2022.64	+	1136.58i	0.0957807	+	0.0538222i
$765$		0			0
$766$	−4869.11	+	18604.2i	−0.229671	+	0.877544i
$767$	−27695.2			−1.30380
$768$		0			0
$769$	−28077.3			−1.31664			−0.658318	−	0.752740i	$-0.728732\pi$
$769$	−28077.3			−1.31664			−0.658318	+	0.752740i	$0.728732\pi$
$770$	−6184.67	+	23630.8i	−0.289455	+	1.10597i
$771$		0			0
$772$	29961.2	+	16836.2i	1.39680	+	0.784905i
$773$	8413.75	+	8413.75i	0.391490	+	0.391490i	0.875218	−	0.483728i	$-0.160718\pi$
$773$	8413.75	+	8413.75i	0.391490	+	0.391490i	−0.483728	+	0.875218i	$0.660718\pi$
$774$		0			0
$775$			4504.97i			0.208804i
$776$	12043.2	−	12471.3i	0.557120	−	0.576924i
$777$		0			0
$778$	19058.5	−	11151.9i	0.878254	−	0.513899i
$779$	11677.4	+	11677.4i	0.537083	+	0.537083i
$780$		0			0
$781$	17305.3	−	17305.3i	0.792870	−	0.792870i
$782$	−31028.6	−	8120.81i	−1.41890	−	0.371355i
$783$		0			0
$784$	4215.04	+	6923.28i	0.192011	+	0.315383i
$785$	5165.89			0.234877
$786$		0			0
$787$	8677.71	−	8677.71i	0.393046	−	0.393046i	−0.482726	−	0.875772i	$-0.660353\pi$
$787$	8677.71	−	8677.71i	0.393046	−	0.393046i	0.875772	+	0.482726i	$0.160353\pi$
$788$	2861.79	+	10203.7i	0.129374	+	0.461285i
$789$		0			0
$790$	−35715.6	+	20898.5i	−1.60849	+	0.941185i
$791$		−	4883.98i		−	0.219538i
$792$		0			0
$793$		−	69065.3i		−	3.09279i
$794$	9582.88	+	16377.1i	0.428317	+	0.731994i
$795$		0			0
$796$	−13063.0	+	23246.6i	−0.581665	+	1.03512i
$797$	−16951.1	+	16951.1i	−0.753374	+	0.753374i	−0.975107	−	0.221733i	$-0.928829\pi$
$797$	−16951.1	+	16951.1i	−0.753374	+	0.753374i	0.221733	+	0.975107i	$0.428829\pi$
$798$		0			0
$799$	−3531.58			−0.156369
$800$	7899.87	+	26386.2i	0.349128	+	1.16611i
$801$		0			0
$802$	1199.47	−	4583.01i	0.0528114	−	0.201785i
$803$	11532.5	−	11532.5i	0.506814	−	0.506814i
$804$		0			0
$805$	25876.5	+	25876.5i	1.13295	+	1.13295i
$806$	3477.07	+	5942.32i	0.151954	+	0.259689i
$807$		0			0
$808$	−31483.0	+	549.782i	−1.37075	+	0.0239372i
$809$		−	39305.4i		−	1.70816i	−0.520138	−	0.854082i	$-0.674120\pi$
$809$		−	39305.4i		−	1.70816i	0.520138	−	0.854082i	$-0.325880\pi$
$810$		0			0
$811$	25524.4	+	25524.4i	1.10516	+	1.10516i	0.993778	+	0.111378i	$0.0355263\pi$
$811$	25524.4	+	25524.4i	1.10516	+	1.10516i	0.111378	+	0.993778i	$0.464474\pi$
$812$	2181.42	+	7777.86i	0.0942769	+	0.336145i
$813$		0			0
$814$	−20164.1	−	5277.37i	−0.868247	−	0.227238i
$815$	31112.9			1.33722
$816$		0			0
$817$	8478.34			0.363059
$818$	32610.7	+	8534.89i	1.39389	+	0.364811i
$819$		0			0
$820$	28882.8	−	8100.63i	1.23004	−	0.344983i
$821$	20817.5	+	20817.5i	0.884939	+	0.884939i	0.994032	−	0.109093i	$-0.0347945\pi$
$821$	20817.5	+	20817.5i	0.884939	+	0.884939i	−0.109093	+	0.994032i	$0.534794\pi$
$822$		0			0
$823$		−	8625.74i		−	0.365339i	−0.983174	−	0.182670i	$-0.941526\pi$
$823$		−	8625.74i		−	0.365339i	0.983174	−	0.182670i	$-0.0584739\pi$
$824$	8338.53	+	8052.30i	0.352532	+	0.340431i
$825$		0			0
$826$	7077.82	+	12096.0i	0.298147	+	0.509533i
$827$	16592.0	+	16592.0i	0.697654	+	0.697654i	0.963904	−	0.266250i	$-0.0857848\pi$
$827$	16592.0	+	16592.0i	0.697654	+	0.697654i	−0.266250	+	0.963904i	$0.585785\pi$
$828$		0			0
$829$	−11523.3	+	11523.3i	−0.482777	+	0.482777i	−0.906018	−	0.423240i	$-0.860893\pi$
$829$	−11523.3	+	11523.3i	−0.482777	+	0.482777i	0.423240	+	0.906018i	$0.360893\pi$
$830$	15619.4	−	59679.5i	0.653200	−	2.49579i
$831$		0			0
$832$	30786.0	+	28707.5i	1.28283	+	1.19622i
$833$	9609.99			0.399720
$834$		0			0
$835$	−13900.7	+	13900.7i	−0.576112	+	0.576112i
$836$	−18034.7	−	10134.3i	−0.746106	−	0.419261i
$837$		0			0
$838$	8771.91	+	14991.2i	0.361600	+	0.617975i
$839$		−	1709.60i		−	0.0703482i	−0.999381	−	0.0351741i	$-0.988801\pi$
$839$		−	1709.60i		−	0.0703482i	0.999381	−	0.0351741i	$-0.0111986\pi$
$840$		0			0
$841$			19676.4i			0.806772i
$842$	−30840.8	+	18046.1i	−1.26228	+	0.738609i
$843$		0			0
$844$	41514.5	−	11643.4i	1.69312	−	0.474860i
$845$	53706.5	−	53706.5i	2.18646	−	2.18646i
$846$		0			0
$847$	1282.52			0.0520282
$848$	−3338.16	+	13729.0i	−0.135180	+	0.555962i
$849$		0			0
$850$	31591.9	+	8268.26i	1.27482	+	0.333646i
$851$	−22080.4	+	22080.4i	−0.889433	+	0.889433i
$852$		0			0
$853$	−27950.1	−	27950.1i	−1.12191	−	1.12191i	−0.991453	−	0.130462i	$-0.958354\pi$
$853$	−27950.1	−	27950.1i	−1.12191	−	1.12191i	−0.130462	−	0.991453i	$-0.541646\pi$
$854$	−30164.6	+	17650.4i	−1.20868	+	0.707243i
$855$		0			0
$856$	20256.0	−	353.727i	0.808805	−	0.0141240i
$857$		−	20208.0i		−	0.805477i	−0.915315	−	0.402739i	$-0.868058\pi$
$857$		−	20208.0i		−	0.805477i	0.915315	−	0.402739i	$-0.131942\pi$
$858$		0			0
$859$	−6906.75	−	6906.75i	−0.274337	−	0.274337i	0.556507	−	0.830843i	$-0.312141\pi$
$859$	−6906.75	−	6906.75i	−0.274337	−	0.274337i	−0.830843	+	0.556507i	$0.812141\pi$
$860$	7544.40	−	13425.8i	0.299142	−	0.532345i
$861$		0			0
$862$	4422.64	−	16898.3i	0.174751	−	0.667702i
$863$	−16342.0			−0.644599			−0.322300	−	0.946638i	$-0.604456\pi$
$863$	−16342.0			−0.644599			−0.322300	+	0.946638i	$0.604456\pi$
$864$		0			0
$865$	36713.1			1.44310
$866$	5.50577	−	21.0368i	0.000216043	−	0.000825473i
$867$		0			0
$868$	1706.73	−	3037.26i	0.0667399	−	0.118769i
$869$	−21915.4	−	21915.4i	−0.855501	−	0.855501i
$870$		0			0
$871$			34836.9i			1.35523i
$872$	549.726	+	31479.8i	0.0213487	+	1.22252i
$873$		0			0
$874$	−26749.6	+	15652.2i	−1.03526	+	0.605770i
$875$	−4702.32	−	4702.32i	−0.181677	−	0.181677i
$876$		0			0
$877$	517.041	−	517.041i	0.0199079	−	0.0199079i	−0.697083	−	0.716991i	$-0.745519\pi$
$877$	517.041	−	517.041i	0.0199079	−	0.0199079i	0.716991	+	0.697083i	$0.245519\pi$
$878$	−41550.4	−	10874.6i	−1.59710	−	0.417995i
$879$		0			0
$880$	−32096.2	+	19540.9i	−1.22950	+	0.748548i
$881$	22171.2			0.847861			0.423931	−	0.905695i	$-0.360650\pi$
$881$	22171.2			0.847861			0.423931	+	0.905695i	$0.360650\pi$
$882$		0			0
$883$	589.293	−	589.293i	0.0224590	−	0.0224590i	−0.695788	−	0.718247i	$-0.744945\pi$
$883$	589.293	−	589.293i	0.0224590	−	0.0224590i	0.718247	+	0.695788i	$0.244945\pi$
$884$	48053.2	−	13477.3i	1.82829	−	0.512771i
$885$		0			0
$886$	11755.4	−	6878.50i	0.445744	−	0.260821i
$887$		−	13685.0i		−	0.518034i	−0.965873	−	0.259017i	$-0.916601\pi$
$887$		−	13685.0i		−	0.518034i	0.965873	−	0.259017i	$-0.0833985\pi$
$888$		0			0
$889$			10486.7i			0.395627i
$890$	−8341.60	−	14255.8i	−0.314170	−	0.536916i
$891$		0			0
$892$	21573.4	+	12122.8i	0.809787	+	0.455046i
$893$	−2413.03	+	2413.03i	−0.0904242	+	0.0904242i
$894$		0			0
$895$	−40467.9			−1.51139
$896$	4670.43	−	20782.5i	0.174139	−	0.774881i
$897$		0			0
$898$	−4846.10	+	18516.3i	−0.180085	+	0.688081i
$899$	−1437.20	+	1437.20i	−0.0533184	+	0.0533184i
$900$		0			0
$901$	11845.2	+	11845.2i	0.437981	+	0.437981i
$902$	11346.7	+	19391.5i	0.418851	+	0.715817i
$903$		0			0
$904$	5219.10	−	5404.62i	0.192019	−	0.198844i
$905$			16570.2i			0.608634i
$906$		0			0
$907$	−32330.9	−	32330.9i	−1.18361	−	1.18361i	−0.978803	−	0.204804i	$-0.934344\pi$
$907$	−32330.9	−	32330.9i	−1.18361	−	1.18361i	−0.204804	−	0.978803i	$-0.565656\pi$
$908$	1062.44	−	297.978i	0.0388308	−	0.0108907i
$909$		0			0
$910$	−55087.3	−	14417.5i	−2.00673	−	0.525203i
$911$	36436.3			1.32513			0.662563	−	0.749006i	$-0.269469\pi$
$911$	36436.3			1.32513			0.662563	+	0.749006i	$0.269469\pi$
$912$		0			0
$913$	46204.1			1.67484
$914$	−20599.1	−	5391.22i	−0.745469	−	0.195105i
$915$		0			0
$916$	−8759.43	−	31231.8i	−0.315960	−	1.12656i
$917$	30000.8	+	30000.8i	1.08039	+	1.08039i
$918$		0			0
$919$			18351.8i			0.658726i	0.944203	+	0.329363i	$0.106834\pi$
$919$			18351.8i			0.658726i	−0.944203	+	0.329363i	$0.893166\pi$
$920$	982.932	+	56287.2i	0.0352242	+	2.01710i
$921$		0			0
$922$	18241.5	+	31174.7i	0.651573	+	1.11354i
$923$	40341.4	+	40341.4i	1.43863	+	1.43863i
$924$		0			0
$925$	22481.4	−	22481.4i	0.799116	−	0.799116i
$926$	6126.69	−	23409.3i	0.217425	−	0.830752i
$927$		0			0
$928$	−5897.59	+	10938.1i	−0.208618	+	0.386919i
$929$	−25908.3			−0.914989			−0.457495	−	0.889212i	$-0.651253\pi$
$929$	−25908.3			−0.914989			−0.457495	+	0.889212i	$0.651253\pi$
$930$		0			0
$931$	6566.22	−	6566.22i	0.231148	−	0.231148i
$932$	1020.47	−	1815.99i	0.0358653	−	0.0638249i
$933$		0			0
$934$	2680.16	+	4580.39i	0.0938944	+	0.160466i
$935$			44551.8i			1.55829i
$936$		0			0
$937$		−	41822.4i		−	1.45814i	−0.684438	−	0.729071i	$-0.739953\pi$
$937$		−	41822.4i		−	1.45814i	0.684438	−	0.729071i	$-0.260047\pi$
$938$	15215.2	−	8902.96i	0.529630	−	0.309906i
$939$		0			0
$940$	1673.91	+	5968.35i	0.0580820	+	0.207092i
$941$	−35805.6	+	35805.6i	−1.24041	+	1.24041i	−0.280585	+	0.959829i	$0.590529\pi$
$941$	−35805.6	+	35805.6i	−1.24041	+	1.24041i	−0.959829	+	0.280585i	$0.909471\pi$
$942$		0			0
$943$	33659.4			1.16236
$944$	−5093.67	+	20949.0i	−0.175619	+	0.722278i
$945$		0			0
$946$	11158.7	+	2920.45i	0.383509	+	0.100372i
$947$	−4833.07	+	4833.07i	−0.165844	+	0.165844i	−0.785150	−	0.619306i	$-0.787414\pi$
$947$	−4833.07	+	4833.07i	−0.165844	+	0.165844i	0.619306	+	0.785150i	$0.287414\pi$
$948$		0			0
$949$	26884.1	+	26884.1i	0.919593	+	0.919593i
$950$	27235.3	−	15936.4i	0.930136	−	0.544257i
$951$		0			0
$952$	−18166.8	−	17543.2i	−0.618477	−	0.597247i
$953$			54695.5i			1.85914i	0.368645	+	0.929570i	$0.379822\pi$
$953$			54695.5i			1.85914i	−0.368645	+	0.929570i	$0.620178\pi$
$954$		0			0
$955$	−3414.02	−	3414.02i	−0.115681	−	0.115681i
$956$	7906.28	+	4442.79i	0.267476	+	0.150304i
$957$		0			0
$958$	4384.12	−	16751.2i	0.147854	−	0.564932i
$959$	−11197.1			−0.377033
$960$		0			0
$961$	−28914.4			−0.970575
$962$	12302.4	−	47005.9i	0.412314	−	1.57540i
$963$		0			0
$964$	−18953.7	−	10650.7i	−0.633254	−	0.355846i
$965$	−50571.6	−	50571.6i	−1.68700	−	1.68700i
$966$		0			0
$967$		−	11587.6i		−	0.385350i	−0.981263	−	0.192675i	$-0.938284\pi$
$967$		−	11587.6i		−	0.385350i	0.981263	−	0.192675i	$-0.0617163\pi$
$968$	1419.24	+	1370.52i	0.0471240	+	0.0455064i
$969$		0			0
$970$	−31139.3	+	18220.7i	−1.03074	+	0.603126i
$971$	−36545.7	−	36545.7i	−1.20784	−	1.20784i	−0.971727	−	0.236109i	$-0.924128\pi$
$971$	−36545.7	−	36545.7i	−1.20784	−	1.20784i	−0.236109	−	0.971727i	$-0.575872\pi$
$972$		0			0
$973$	−18796.8	+	18796.8i	−0.619321	+	0.619321i
$974$	−17808.3	−	4660.79i	−0.585845	−	0.153328i
$975$		0			0
$976$	−52241.8	−	12702.4i	−1.71334	−	0.416592i
$977$	−11161.4			−0.365490			−0.182745	−	0.983160i	$-0.558498\pi$
$977$	−11161.4			−0.365490			−0.182745	+	0.983160i	$0.558498\pi$
$978$		0			0
$979$	8747.49	−	8747.49i	0.285568	−	0.285568i
$980$	−4554.98	−	16240.8i	−0.148473	−	0.529381i
$981$		0			0
$982$	27942.6	−	16350.2i	0.908028	−	0.531321i
$983$		−	52855.9i		−	1.71500i	−0.514486	−	0.857499i	$-0.672017\pi$
$983$		−	52855.9i		−	1.71500i	0.514486	−	0.857499i	$-0.327983\pi$
$984$		0			0
$985$		−	22053.3i		−	0.713378i
$986$	7440.83	+	12716.4i	0.240329	+	0.410723i
$987$		0			0
$988$	23624.7	−	42041.9i	0.760732	−	1.35378i
$989$	12219.1	−	12219.1i	0.392867	−	0.392867i
$990$		0			0
$991$	−50245.9			−1.61061			−0.805305	−	0.592861i	$-0.797998\pi$
$991$	−50245.9			−1.61061			−0.805305	+	0.592861i	$0.797998\pi$
$992$	5134.33	−	1537.19i	0.164330	−	0.0491995i
$993$		0			0
$994$	7309.60	−	27929.0i	0.233246	−	0.891202i
$995$	39238.0	−	39238.0i	1.25018	−	1.25018i
$996$		0			0
$997$	−3886.25	−	3886.25i	−0.123449	−	0.123449i	0.642683	−	0.766132i	$-0.277821\pi$
$997$	−3886.25	−	3886.25i	−0.123449	−	0.123449i	−0.766132	+	0.642683i	$0.777821\pi$
$998$	13680.6	+	23380.2i	0.433919	+	0.741569i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.4.k.b.37.7		24
3.2	odd	2		48.4.j.a.37.6	yes	24
4.3	odd	2		576.4.k.b.433.11		24
12.11	even	2		192.4.j.a.49.7		24
16.3	odd	4		576.4.k.b.145.11		24
16.13	even	4	inner	144.4.k.b.109.7		24
24.5	odd	2		384.4.j.b.97.12		24
24.11	even	2		384.4.j.a.97.1		24
48.5	odd	4		384.4.j.b.289.12		24
48.11	even	4		384.4.j.a.289.1		24
48.29	odd	4		48.4.j.a.13.6	✓	24
48.35	even	4		192.4.j.a.145.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.6	✓	24	48.29	odd	4
48.4.j.a.37.6	yes	24	3.2	odd	2
144.4.k.b.37.7		24	1.1	even	1	trivial
144.4.k.b.109.7		24	16.13	even	4	inner
192.4.j.a.49.7		24	12.11	even	2
192.4.j.a.145.7		24	48.35	even	4
384.4.j.a.97.1		24	24.11	even	2
384.4.j.a.289.1		24	48.11	even	4
384.4.j.b.97.12		24	24.5	odd	2
384.4.j.b.289.12		24	48.5	odd	4
576.4.k.b.145.11		24	16.3	odd	4
576.4.k.b.433.11		24	4.3	odd	2

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	144.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.716137 - 2.73627i) q^{2} +(-6.97430 - 3.91908i) q^{4} +(11.7719 + 11.7719i) q^{5} +14.7089i q^{7} +(-15.7182 + 16.2769i) q^{8} +(40.6415 - 23.7808i) q^{10} +(24.9380 + 24.9380i) q^{11} +(-58.1345 + 58.1345i) q^{13} +(40.2475 + 10.5336i) q^{14} +(33.2816 + 54.6657i) q^{16} +75.8798 q^{17} +(51.8464 - 51.8464i) q^{19} +(-35.9658 - 128.236i) q^{20} +(86.0960 - 50.3779i) q^{22} -149.444i q^{23} +152.157i q^{25} +(117.439 + 200.704i) q^{26} +(57.6455 - 102.584i) q^{28} +(-48.5419 + 48.5419i) q^{29} +29.6074 q^{31} +(173.414 - 51.9192i) q^{32} +(54.3403 - 207.627i) q^{34} +(-173.153 + 173.153i) q^{35} +(-147.751 - 147.751i) q^{37} +(-104.736 - 178.994i) q^{38} +(-376.645 + 6.57727i) q^{40} +225.232i q^{41} +(81.7640 + 81.7640i) q^{43} +(-76.1909 - 271.659i) q^{44} +(-408.917 - 107.022i) q^{46} -46.5418 q^{47} +126.648 q^{49} +(416.342 + 108.965i) q^{50} +(633.281 - 177.613i) q^{52} +(156.105 + 156.105i) q^{53} +587.137i q^{55} +(-239.416 - 231.198i) q^{56} +(98.0609 + 167.586i) q^{58} +(238.199 + 238.199i) q^{59} +(-594.013 + 594.013i) q^{61} +(21.2029 - 81.0137i) q^{62} +(-17.8765 - 511.688i) q^{64} -1368.71 q^{65} +(299.623 - 299.623i) q^{67} +(-529.208 - 297.379i) q^{68} +(349.790 + 597.792i) q^{70} -693.932i q^{71} -462.446i q^{73} +(-510.096 + 298.476i) q^{74} +(-564.782 + 158.402i) q^{76} +(-366.811 + 366.811i) q^{77} -878.797 q^{79} +(-251.732 + 1035.31i) q^{80} +(616.293 + 161.297i) q^{82} +(926.380 - 926.380i) q^{83} +(893.252 + 893.252i) q^{85} +(282.282 - 165.174i) q^{86} +(-797.894 + 13.9335i) q^{88} -350.770i q^{89} +(-855.096 - 855.096i) q^{91} +(-585.682 + 1042.26i) q^{92} +(-33.3303 + 127.351i) q^{94} +1220.66 q^{95} -766.194 q^{97} +(90.6971 - 346.542i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{4} - 84 q^{8} + 72 q^{10} + 40 q^{11} + 348 q^{14} - 192 q^{16} + 24 q^{19} - 80 q^{20} + 704 q^{22} + 20 q^{26} - 344 q^{28} - 400 q^{29} - 744 q^{31} + 960 q^{32} - 704 q^{34} + 456 q^{35}+ \cdots - 6760 q^{98}+O(q^{100}) \) 24 * q - 20 * q^4 - 84 * q^8 + 72 * q^10 + 40 * q^11 + 348 * q^14 - 192 * q^16 + 24 * q^19 - 80 * q^20 + 704 * q^22 + 20 * q^26 - 344 * q^28 - 400 * q^29 - 744 * q^31 + 960 * q^32 - 704 * q^34 + 456 * q^35 + 16 * q^37 - 1256 * q^38 + 1744 * q^40 + 1240 * q^43 + 200 * q^44 - 1432 * q^46 - 1176 * q^49 - 708 * q^50 + 1008 * q^52 - 752 * q^53 - 1344 * q^56 + 1936 * q^58 + 1376 * q^59 - 912 * q^61 + 996 * q^62 - 56 * q^64 - 976 * q^65 - 2256 * q^67 + 1568 * q^68 - 1760 * q^70 + 2740 * q^74 - 1880 * q^76 - 1904 * q^77 + 5992 * q^79 - 712 * q^80 - 40 * q^82 - 2680 * q^83 - 240 * q^85 + 1712 * q^86 - 3936 * q^88 - 3496 * q^91 - 5296 * q^92 + 5272 * q^94 + 7728 * q^95 - 6760 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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