LMFDB - Embedded newform 576.2.y.a.47.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(47,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("576.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.y (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			47.6
Character	$\chi$	$=$	576.47
Dual form			576.2.y.a.527.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06447 - 1.36635i) q^{3} +(0.619079 - 2.31044i) q^{5} +(-2.51270 + 4.35213i) q^{7} +(-0.733803 + 2.90887i) q^{9} +O(q^{10})$	\(q+(-1.06447 - 1.36635i) q^{3} +(0.619079 - 2.31044i) q^{5} +(-2.51270 + 4.35213i) q^{7} +(-0.733803 + 2.90887i) q^{9} +(0.276313 + 1.03121i) q^{11} +(-1.07325 + 4.00543i) q^{13} +(-3.81585 + 1.61352i) q^{15} +2.22468i q^{17} +(0.697254 - 0.697254i) q^{19} +(8.62121 - 1.19949i) q^{21} +(2.20833 - 1.27498i) q^{23} +(-0.624725 - 0.360685i) q^{25} +(4.75564 - 2.09378i) q^{27} +(0.157969 + 0.589549i) q^{29} +(0.190501 - 0.109986i) q^{31} +(1.11487 - 1.47524i) q^{33} +(8.49974 + 8.49974i) q^{35} +(-5.16341 + 5.16341i) q^{37} +(6.61524 - 2.79723i) q^{39} +(-0.828296 - 1.43465i) q^{41} +(4.98067 - 1.33457i) q^{43} +(6.26648 + 3.49623i) q^{45} +(-5.76715 + 9.98900i) q^{47} +(-9.12734 - 15.8090i) q^{49} +(3.03968 - 2.36811i) q^{51} +(7.80379 + 7.80379i) q^{53} +2.55361 q^{55} +(-1.69490 - 0.210484i) q^{57} +(-5.09824 - 1.36607i) q^{59} +(-6.48859 + 1.73861i) q^{61} +(-10.8159 - 10.5027i) q^{63} +(8.58985 + 4.95935i) q^{65} +(-8.22431 - 2.20370i) q^{67} +(-4.09277 - 1.66016i) q^{69} +12.0321i q^{71} +10.3710i q^{73} +(0.172181 + 1.23753i) q^{75} +(-5.18226 - 1.38858i) q^{77} +(7.74084 + 4.46918i) q^{79} +(-7.92307 - 4.26907i) q^{81} +(5.55149 - 1.48752i) q^{83} +(5.13998 + 1.37725i) q^{85} +(0.637375 - 0.843399i) q^{87} -6.56588 q^{89} +(-14.7354 - 14.7354i) q^{91} +(-0.353062 - 0.143214i) q^{93} +(-1.17930 - 2.04262i) q^{95} +(-1.51787 + 2.62902i) q^{97} +(-3.20243 + 0.0470514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.06447	−	1.36635i	−0.614573	−	0.788860i
$3$	−1.06447	−	1.36635i	−0.614573	−	0.788860i
$4$		0			0
$5$	0.619079	−	2.31044i	0.276861	−	1.03326i	−0.677724	−	0.735317i	$-0.737033\pi$
$5$	0.619079	−	2.31044i	0.276861	−	1.03326i	0.954584	−	0.297941i	$-0.0963000\pi$
$6$		0			0
$7$	−2.51270	+	4.35213i	−0.949712	+	1.64495i	−0.203681	+	0.979037i	$0.565291\pi$
$7$	−2.51270	+	4.35213i	−0.949712	+	1.64495i	−0.746030	+	0.665912i	$0.768043\pi$
$8$		0			0
$9$	−0.733803	+	2.90887i	−0.244601	+	0.969624i
$10$		0			0
$11$	0.276313	+	1.03121i	0.0833114	+	0.310922i	0.994989	−	0.0999837i	$-0.0318791\pi$
$11$	0.276313	+	1.03121i	0.0833114	+	0.310922i	−0.911678	+	0.410906i	$0.865212\pi$
$12$		0			0
$13$	−1.07325	+	4.00543i	−0.297666	+	1.11091i	0.641411	+	0.767198i	$0.278350\pi$
$13$	−1.07325	+	4.00543i	−0.297666	+	1.11091i	−0.939077	+	0.343708i	$0.888317\pi$
$14$		0			0
$15$	−3.81585	+	1.61352i	−0.985247	+	0.416608i
$16$		0			0
$17$			2.22468i			0.539564i	0.962921	+	0.269782i	$0.0869517\pi$
$17$			2.22468i			0.539564i	−0.962921	+	0.269782i	$0.913048\pi$
$18$		0			0
$19$	0.697254	−	0.697254i	0.159961	−	0.159961i	−0.622588	−	0.782549i	$-0.713919\pi$
$19$	0.697254	−	0.697254i	0.159961	−	0.159961i	0.782549	+	0.622588i	$0.213919\pi$
$20$		0			0
$21$	8.62121	−	1.19949i	1.88130	−	0.261751i
$22$		0			0
$23$	2.20833	−	1.27498i	0.460469	−	0.265852i	−0.251773	−	0.967786i	$-0.581013\pi$
$23$	2.20833	−	1.27498i	0.460469	−	0.265852i	0.712241	+	0.701935i	$0.247680\pi$
$24$		0			0
$25$	−0.624725	−	0.360685i	−0.124945	−	0.0721370i
$26$		0			0
$27$	4.75564	−	2.09378i	0.915223	−	0.402948i
$28$		0			0
$29$	0.157969	+	0.589549i	0.0293342	+	0.109477i	0.979041	−	0.203665i	$-0.0652853\pi$
$29$	0.157969	+	0.589549i	0.0293342	+	0.109477i	−0.949707	+	0.313141i	$0.898619\pi$
$30$		0			0
$31$	0.190501	−	0.109986i	0.0342150	−	0.0197541i	−0.482795	−	0.875733i	$-0.660378\pi$
$31$	0.190501	−	0.109986i	0.0342150	−	0.0197541i	0.517010	+	0.855979i	$0.327045\pi$
$32$		0			0
$33$	1.11487	−	1.47524i	0.194073	−	0.256806i
$34$		0			0
$35$	8.49974	+	8.49974i	1.43672	+	1.43672i
$36$		0			0
$37$	−5.16341	+	5.16341i	−0.848859	+	0.848859i	−0.989991	−	0.141132i	$-0.954926\pi$
$37$	−5.16341	+	5.16341i	−0.848859	+	0.848859i	0.141132	+	0.989991i	$0.454926\pi$
$38$		0			0
$39$	6.61524	−	2.79723i	1.05929	−	0.447915i
$40$		0			0
$41$	−0.828296	−	1.43465i	−0.129358	−	0.224055i	0.794070	−	0.607826i	$-0.207958\pi$
$41$	−0.828296	−	1.43465i	−0.129358	−	0.224055i	−0.923428	+	0.383772i	$0.874625\pi$
$42$		0			0
$43$	4.98067	−	1.33457i	0.759545	−	0.203519i	0.141797	−	0.989896i	$-0.454712\pi$
$43$	4.98067	−	1.33457i	0.759545	−	0.203519i	0.617748	+	0.786376i	$0.288045\pi$
$44$		0			0
$45$	6.26648	+	3.49623i	0.934151	+	0.521187i
$46$		0			0
$47$	−5.76715	+	9.98900i	−0.841226	+	1.45705i	0.0476333	+	0.998865i	$0.484832\pi$
$47$	−5.76715	+	9.98900i	−0.841226	+	1.45705i	−0.888859	+	0.458181i	$0.848501\pi$
$48$		0			0
$49$	−9.12734	−	15.8090i	−1.30391	−	2.25843i
$50$		0			0
$51$	3.03968	−	2.36811i	0.425641	−	0.331601i
$52$		0			0
$53$	7.80379	+	7.80379i	1.07193	+	1.07193i	0.997204	+	0.0747298i	$0.0238094\pi$
$53$	7.80379	+	7.80379i	1.07193	+	1.07193i	0.0747298	+	0.997204i	$0.476191\pi$
$54$		0			0
$55$	2.55361			0.344329
$56$		0			0
$57$	−1.69490	−	0.210484i	−0.224495	−	0.0278792i
$58$		0			0
$59$	−5.09824	−	1.36607i	−0.663735	−	0.177847i	−0.0888039	−	0.996049i	$-0.528304\pi$
$59$	−5.09824	−	1.36607i	−0.663735	−	0.177847i	−0.574931	+	0.818202i	$0.694971\pi$
$60$		0			0
$61$	−6.48859	+	1.73861i	−0.830779	+	0.222606i	−0.649053	−	0.760743i	$-0.724835\pi$
$61$	−6.48859	+	1.73861i	−0.830779	+	0.222606i	−0.181725	+	0.983349i	$0.558168\pi$
$62$		0			0
$63$	−10.8159	−	10.5027i	−1.36268	−	1.32322i
$64$		0			0
$65$	8.58985	+	4.95935i	1.06544	+	0.615132i
$66$		0			0
$67$	−8.22431	−	2.20370i	−1.00476	−	0.269224i	−0.281321	−	0.959614i	$-0.590773\pi$
$67$	−8.22431	−	2.20370i	−1.00476	−	0.269224i	−0.723438	+	0.690389i	$0.757439\pi$
$68$		0			0
$69$	−4.09277	−	1.66016i	−0.492712	−	0.199860i
$70$		0			0
$71$			12.0321i			1.42795i	0.700171	+	0.713975i	$0.253107\pi$
$71$			12.0321i			1.42795i	−0.700171	+	0.713975i	$0.746893\pi$
$72$		0			0
$73$			10.3710i			1.21383i	0.794766	+	0.606917i	$0.207594\pi$
$73$			10.3710i			1.21383i	−0.794766	+	0.606917i	$0.792406\pi$
$74$		0			0
$75$	0.172181	+	1.23753i	0.0198817	+	0.142898i
$76$		0			0
$77$	−5.18226	−	1.38858i	−0.590574	−	0.158244i
$78$		0			0
$79$	7.74084	+	4.46918i	0.870913	+	0.502822i	0.867651	−	0.497173i	$-0.165629\pi$
$79$	7.74084	+	4.46918i	0.870913	+	0.502822i	0.00326134	+	0.999995i	$0.498962\pi$
$80$		0			0
$81$	−7.92307	−	4.26907i	−0.880341	−	0.474342i
$82$		0			0
$83$	5.55149	−	1.48752i	0.609355	−	0.163276i	0.0590710	−	0.998254i	$-0.481186\pi$
$83$	5.55149	−	1.48752i	0.609355	−	0.163276i	0.550284	+	0.834978i	$0.314520\pi$
$84$		0			0
$85$	5.13998	+	1.37725i	0.557509	+	0.149384i
$86$		0			0
$87$	0.637375	−	0.843399i	0.0683337	−	0.0904219i
$88$		0			0
$89$	−6.56588			−0.695982			−0.347991	−	0.937498i	$-0.613136\pi$
$89$	−6.56588			−0.695982			−0.347991	+	0.937498i	$0.613136\pi$
$90$		0			0
$91$	−14.7354	−	14.7354i	−1.54469	−	1.54469i
$92$		0			0
$93$	−0.353062	−	0.143214i	−0.0366108	−	0.0148506i
$94$		0			0
$95$	−1.17930	−	2.04262i	−0.120994	−	0.209568i
$96$		0			0
$97$	−1.51787	+	2.62902i	−0.154116	+	0.266936i	−0.932737	−	0.360558i	$-0.882586\pi$
$97$	−1.51787	+	2.62902i	−0.154116	+	0.266936i	0.778621	+	0.627495i	$0.215920\pi$
$98$		0			0
$99$	−3.20243	+	0.0470514i	−0.321856	+	0.00472884i
$100$		0			0
$101$	−0.413922	+	0.110910i	−0.0411868	+	0.0110360i	−0.279354	−	0.960188i	$-0.590120\pi$
$101$	−0.413922	+	0.110910i	−0.0411868	+	0.0110360i	0.238167	+	0.971224i	$0.423453\pi$
$102$		0			0
$103$	−4.07491	−	7.05795i	−0.401513	−	0.695440i	0.592396	−	0.805647i	$-0.298182\pi$
$103$	−4.07491	−	7.05795i	−0.401513	−	0.695440i	−0.993909	+	0.110207i	$0.964849\pi$
$104$		0			0
$105$	2.56586	−	20.6613i	0.250402	−	2.01634i
$106$		0			0
$107$	10.5385	−	10.5385i	1.01879	−	1.01879i	0.0189732	−	0.999820i	$-0.493960\pi$
$107$	10.5385	−	10.5385i	1.01879	−	1.01879i	0.999820	−	0.0189732i	$-0.00603973\pi$
$108$		0			0
$109$	−7.21559	−	7.21559i	−0.691128	−	0.691128i	0.271352	−	0.962480i	$-0.412529\pi$
$109$	−7.21559	−	7.21559i	−0.691128	−	0.691128i	−0.962480	+	0.271352i	$0.912529\pi$
$110$		0			0
$111$	12.5513	+	1.55870i	1.19132	+	0.147946i
$112$		0			0
$113$	2.83876	−	1.63896i	0.267048	−	0.154180i	−0.360497	−	0.932760i	$-0.617393\pi$
$113$	2.83876	−	1.63896i	0.267048	−	0.154180i	0.627545	+	0.778580i	$0.284060\pi$
$114$		0			0
$115$	−1.57863	−	5.89152i	−0.147208	−	0.549387i
$116$		0			0
$117$	−10.8637	−	6.06114i	−1.00435	−	0.560353i
$118$		0			0
$119$	−9.68209	−	5.58996i	−0.887555	−	0.512430i
$120$		0			0
$121$	8.53923	−	4.93013i	0.776293	−	0.448193i
$122$		0			0
$123$	−1.07853	+	2.65888i	−0.0972480	+	0.239744i
$124$		0			0
$125$	7.23669	−	7.23669i	0.647269	−	0.647269i
$126$		0			0
$127$			6.21746i			0.551710i	0.961199	+	0.275855i	$0.0889610\pi$
$127$			6.21746i			0.551710i	−0.961199	+	0.275855i	$0.911039\pi$
$128$		0			0
$129$	−7.12526	−	5.38471i	−0.627344	−	0.474097i
$130$		0			0
$131$	3.25160	−	12.1351i	0.284093	−	1.06025i	−0.665406	−	0.746482i	$-0.731742\pi$
$131$	3.25160	−	12.1351i	0.284093	−	1.06025i	0.949499	−	0.313769i	$-0.101592\pi$
$132$		0			0
$133$	1.28255	+	4.78653i	0.111211	+	0.415045i
$134$		0			0
$135$	−1.89343	−	12.2838i	−0.162961	−	1.05722i
$136$		0			0
$137$	−1.22043	+	2.11385i	−0.104269	+	0.180598i	−0.913439	−	0.406975i	$-0.866583\pi$
$137$	−1.22043	+	2.11385i	−0.104269	+	0.180598i	0.809171	+	0.587574i	$0.199917\pi$
$138$		0			0
$139$	−3.77577	+	14.0914i	−0.320257	+	1.19521i	0.598738	+	0.800945i	$0.295669\pi$
$139$	−3.77577	+	14.0914i	−0.320257	+	1.19521i	−0.918995	+	0.394270i	$0.870998\pi$
$140$		0			0
$141$	19.7874	−	2.75308i	1.66640	−	0.231851i
$142$		0			0
$143$	−4.42700			−0.370204
$144$		0			0
$145$	1.45991			0.121239
$146$		0			0
$147$	−11.8848	+	29.2993i	−0.980241	+	2.41657i
$148$		0			0
$149$	−0.0621341	+	0.231888i	−0.00509023	+	0.0189970i	−0.968424	−	0.249308i	$-0.919797\pi$
$149$	−0.0621341	+	0.231888i	−0.00509023	+	0.0189970i	0.963334	+	0.268305i	$0.0864635\pi$
$150$		0			0
$151$	−1.91034	+	3.30881i	−0.155462	+	0.269267i	−0.933227	−	0.359287i	$-0.883020\pi$
$151$	−1.91034	+	3.30881i	−0.155462	+	0.269267i	0.777765	+	0.628555i	$0.216353\pi$
$152$		0			0
$153$	−6.47131	−	1.63248i	−0.523174	−	0.131978i
$154$		0			0
$155$	−0.136180	−	0.508231i	−0.0109382	−	0.0408221i
$156$		0			0
$157$	0.0542841	−	0.202591i	0.00433234	−	0.0161685i	−0.963726	−	0.266894i	$-0.914003\pi$
$157$	0.0542841	−	0.202591i	0.00433234	−	0.0161685i	0.968058	+	0.250726i	$0.0806692\pi$
$158$		0			0
$159$	2.35577	−	18.9696i	0.186825	−	1.50439i
$160$		0			0
$161$			12.8146i			1.00993i
$162$		0			0
$163$	−7.63956	+	7.63956i	−0.598377	+	0.598377i	−0.939880	−	0.341504i	$-0.889064\pi$
$163$	−7.63956	+	7.63956i	−0.598377	+	0.598377i	0.341504	+	0.939880i	$0.389064\pi$
$164$		0			0
$165$	−2.71824	−	3.48912i	−0.211615	−	0.271627i
$166$		0			0
$167$	−3.93638	+	2.27267i	−0.304607	+	0.175865i	−0.644510	−	0.764595i	$-0.722939\pi$
$167$	−3.93638	+	2.27267i	−0.304607	+	0.175865i	0.339904	+	0.940460i	$0.389605\pi$
$168$		0			0
$169$	−3.63324	−	2.09765i	−0.279480	−	0.161358i
$170$		0			0
$171$	1.51658	+	2.53987i	0.115975	+	0.194229i
$172$		0			0
$173$	−4.50521	−	16.8137i	−0.342525	−	1.27832i	−0.895478	−	0.445107i	$-0.853166\pi$
$173$	−4.50521	−	16.8137i	−0.342525	−	1.27832i	0.552953	−	0.833212i	$-0.313501\pi$
$174$		0			0
$175$	3.13949	−	1.81259i	0.237323	−	0.137019i
$176$		0			0
$177$	3.56041	+	8.42011i	0.267617	+	0.632894i
$178$		0			0
$179$	0.113028	+	0.113028i	0.00844808	+	0.00844808i	0.711318	−	0.702870i	$-0.248099\pi$
$179$	0.113028	+	0.113028i	0.00844808	+	0.00844808i	−0.702870	+	0.711318i	$0.748099\pi$
$180$		0			0
$181$	6.17637	−	6.17637i	0.459086	−	0.459086i	−0.439270	−	0.898355i	$-0.644763\pi$
$181$	6.17637	−	6.17637i	0.459086	−	0.459086i	0.898355	+	0.439270i	$0.144763\pi$
$182$		0			0
$183$	9.28246	+	7.01495i	0.686179	+	0.518560i
$184$		0			0
$185$	8.73316	+	15.1263i	0.642075	+	1.11211i
$186$		0			0
$187$	−2.29412	+	0.614707i	−0.167763	+	0.0449519i
$188$		0			0
$189$	−2.83709	+	25.9582i	−0.206368	+	1.88818i
$190$		0			0
$191$	1.91222	−	3.31206i	0.138363	−	0.239653i	−0.788514	−	0.615017i	$-0.789149\pi$
$191$	1.91222	−	3.31206i	0.138363	−	0.239653i	0.926877	+	0.375364i	$0.122482\pi$
$192$		0			0
$193$	4.69587	+	8.13348i	0.338016	+	0.585461i	0.984059	−	0.177840i	$-0.0569109\pi$
$193$	4.69587	+	8.13348i	0.338016	+	0.585461i	−0.646044	+	0.763300i	$0.723578\pi$
$194$		0			0
$195$	−2.36746	−	17.0158i	−0.169537	−	1.21853i
$196$		0			0
$197$	−6.00916	−	6.00916i	−0.428135	−	0.428135i	0.459858	−	0.887993i	$-0.347900\pi$
$197$	−6.00916	−	6.00916i	−0.428135	−	0.428135i	−0.887993	+	0.459858i	$0.847900\pi$
$198$		0			0
$199$	−17.0487			−1.20855			−0.604274	−	0.796776i	$-0.706537\pi$
$199$	−17.0487			−1.20855			−0.604274	+	0.796776i	$0.706537\pi$
$200$		0			0
$201$	5.74353	+	13.5830i	0.405117	+	0.958073i
$202$		0			0
$203$	−2.96272	−	0.793859i	−0.207942	−	0.0557180i
$204$		0			0
$205$	−3.82745	+	1.02556i	−0.267321	+	0.0716284i
$206$		0			0
$207$	2.08828	+	7.35934i	0.145145	+	0.511509i
$208$		0			0
$209$	0.911678	+	0.526357i	0.0630621	+	0.0364089i
$210$		0			0
$211$	0.646700	+	0.173283i	0.0445207	+	0.0119293i	0.281011	−	0.959705i	$-0.409330\pi$
$211$	0.646700	+	0.173283i	0.0445207	+	0.0119293i	−0.236490	+	0.971634i	$0.575997\pi$
$212$		0			0
$213$	16.4400	−	12.8078i	1.12645	−	0.877579i
$214$		0			0
$215$		−	12.3337i		−	0.841152i
$216$		0			0
$217$			1.10545i			0.0750426i
$218$		0			0
$219$	14.1704	−	11.0396i	0.957545	−	0.745989i
$220$		0			0
$221$	−8.91079	−	2.38764i	−0.599405	−	0.160610i
$222$		0			0
$223$	10.6472	+	6.14716i	0.712989	+	0.411644i	0.812167	−	0.583425i	$-0.198288\pi$
$223$	10.6472	+	6.14716i	0.712989	+	0.411644i	−0.0991778	+	0.995070i	$0.531621\pi$
$224$		0			0
$225$	1.50761	−	1.55257i	0.100507	−	0.103505i
$226$		0			0
$227$	18.2009	−	4.87693i	1.20804	−	0.323693i	0.402047	−	0.915619i	$-0.368299\pi$
$227$	18.2009	−	4.87693i	1.20804	−	0.323693i	0.805992	+	0.591926i	$0.201632\pi$
$228$		0			0
$229$	−6.76830	−	1.81356i	−0.447262	−	0.119843i	0.0281561	−	0.999604i	$-0.491036\pi$
$229$	−6.76830	−	1.81356i	−0.447262	−	0.119843i	−0.475418	+	0.879760i	$0.657703\pi$
$230$		0			0
$231$	3.61908	+	8.55887i	0.238118	+	0.563132i
$232$		0			0
$233$	24.5688			1.60956			0.804779	−	0.593575i	$-0.202284\pi$
$233$	24.5688			1.60956			0.804779	+	0.593575i	$0.202284\pi$
$234$		0			0
$235$	19.5086	+	19.5086i	1.27260	+	1.27260i
$236$		0			0
$237$	−2.13346	−	15.3340i	−0.138583	−	0.996049i
$238$		0			0
$239$	1.70661	+	2.95593i	0.110391	+	0.191203i	0.915928	−	0.401343i	$-0.131456\pi$
$239$	1.70661	+	2.95593i	0.110391	+	0.191203i	−0.805537	+	0.592546i	$0.798123\pi$
$240$		0			0
$241$	12.9443	−	22.4201i	0.833813	−	1.44421i	−0.0611802	−	0.998127i	$-0.519486\pi$
$241$	12.9443	−	22.4201i	0.833813	−	1.44421i	0.894993	−	0.446080i	$-0.147180\pi$
$242$		0			0
$243$	2.60084	+	15.3700i	0.166844	+	0.985983i
$244$		0			0
$245$	−42.1762	+	11.3011i	−2.69454	+	0.722000i
$246$		0			0
$247$	2.04447	+	3.54113i	0.130087	+	0.225317i
$248$		0			0
$249$	−7.94186	−	6.00183i	−0.503295	−	0.380351i
$250$		0			0
$251$	−19.0153	+	19.0153i	−1.20024	+	1.20024i	−0.226140	+	0.974095i	$0.572611\pi$
$251$	−19.0153	+	19.0153i	−1.20024	+	1.20024i	−0.974095	+	0.226140i	$0.927389\pi$
$252$		0			0
$253$	1.92497	+	1.92497i	0.121022	+	0.121022i
$254$		0			0
$255$	−3.58955	−	8.48904i	−0.224787	−	0.531604i
$256$		0			0
$257$	−1.47472	+	0.851429i	−0.0919904	+	0.0531107i	−0.545290	−	0.838248i	$-0.683580\pi$
$257$	−1.47472	+	0.851429i	−0.0919904	+	0.0531107i	0.453299	+	0.891358i	$0.350247\pi$
$258$		0			0
$259$	−9.49770	−	35.4459i	−0.590159	−	2.20250i
$260$		0			0
$261$	−1.83084	+	0.0268995i	−0.113326	+	0.00166504i
$262$		0			0
$263$	1.41474	+	0.816800i	0.0872366	+	0.0503661i	0.542984	−	0.839743i	$-0.317295\pi$
$263$	1.41474	+	0.816800i	0.0872366	+	0.0503661i	−0.455747	+	0.890109i	$0.650628\pi$
$264$		0			0
$265$	22.8613	−	13.1990i	1.40436	−	0.810808i
$266$		0			0
$267$	6.98919	+	8.97126i	0.427731	+	0.549032i
$268$		0			0
$269$	1.20285	−	1.20285i	0.0733392	−	0.0733392i	−0.669486	−	0.742825i	$-0.733485\pi$
$269$	1.20285	−	1.20285i	0.0733392	−	0.0733392i	0.742825	+	0.669486i	$0.233485\pi$
$270$		0			0
$271$		−	22.9432i		−	1.39370i	−0.717218	−	0.696849i	$-0.754585\pi$
$271$		−	22.9432i		−	1.39370i	0.717218	−	0.696849i	$-0.245415\pi$
$272$		0			0
$273$	−4.44824	+	35.8190i	−0.269219	+	2.16786i
$274$		0			0
$275$	0.199324	−	0.743886i	0.0120197	−	0.0448580i
$276$		0			0
$277$	1.03947	+	3.87936i	0.0624558	+	0.233088i	0.990097	−	0.140384i	$-0.0448338\pi$
$277$	1.03947	+	3.87936i	0.0624558	+	0.233088i	−0.927641	+	0.373472i	$0.878167\pi$
$278$		0			0
$279$	0.180145	+	0.634852i	0.0107850	+	0.0380076i
$280$		0			0
$281$	−15.2214	+	26.3642i	−0.908031	+	1.57276i	−0.0912360	+	0.995829i	$0.529082\pi$
$281$	−15.2214	+	26.3642i	−0.908031	+	1.57276i	−0.816795	+	0.576927i	$0.804252\pi$
$282$		0			0
$283$	−3.10051	+	11.5713i	−0.184306	+	0.687841i	0.810472	+	0.585778i	$0.199211\pi$
$283$	−3.10051	+	11.5713i	−0.184306	+	0.687841i	−0.994778	+	0.102063i	$0.967456\pi$
$284$		0			0
$285$	−1.53558	+	3.78564i	−0.0909602	+	0.224242i
$286$		0			0
$287$	8.32505			0.491412
$288$		0			0
$289$	12.0508			0.708871
$290$		0			0
$291$	5.20787	−	0.724586i	0.305291	−	0.0424760i
$292$		0			0
$293$	5.00638	−	18.6841i	0.292476	−	1.09153i	−0.650726	−	0.759313i	$-0.725535\pi$
$293$	5.00638	−	18.6841i	0.292476	−	1.09153i	0.943201	−	0.332222i	$-0.107798\pi$
$294$		0			0
$295$	−6.31244	+	10.9335i	−0.367524	+	0.636571i
$296$		0			0
$297$	3.47318	+	4.32554i	0.201534	+	0.250993i
$298$		0			0
$299$	2.73675	+	10.2137i	0.158270	+	0.590672i
$300$		0			0
$301$	−6.70673	+	25.0299i	−0.386570	+	1.44270i
$302$		0			0
$303$	0.592150	+	0.447500i	0.0340181	+	0.0257082i
$304$		0			0
$305$			16.0678i			0.920040i
$306$		0			0
$307$	−2.25289	+	2.25289i	−0.128579	+	0.128579i	−0.768468	−	0.639889i	$-0.778980\pi$
$307$	−2.25289	+	2.25289i	−0.128579	+	0.128579i	0.639889	+	0.768468i	$0.278980\pi$
$308$		0			0
$309$	−5.30598	+	13.0807i	−0.301846	+	0.744136i
$310$		0			0
$311$	24.7389	−	14.2830i	1.40281	−	0.809914i	0.408132	−	0.912923i	$-0.366180\pi$
$311$	24.7389	−	14.2830i	1.40281	−	0.809914i	0.994680	+	0.103009i	$0.0328469\pi$
$312$		0			0
$313$	−18.1750	−	10.4933i	−1.02731	−	0.593119i	−0.111099	−	0.993809i	$-0.535437\pi$
$313$	−18.1750	−	10.4933i	−1.02731	−	0.593119i	−0.916214	+	0.400690i	$0.868770\pi$
$314$		0			0
$315$	−30.9618	+	18.4875i	−1.74450	+	1.04165i
$316$		0			0
$317$	3.07456	+	11.4744i	0.172684	+	0.644466i	0.996934	+	0.0782407i	$0.0249303\pi$
$317$	3.07456	+	11.4744i	0.172684	+	0.644466i	−0.824250	+	0.566226i	$0.808403\pi$
$318$		0			0
$319$	−0.564302	+	0.325800i	−0.0315949	+	0.0182413i
$320$		0			0
$321$	−25.6171	−	3.18130i	−1.42981	−	0.177563i
$322$		0			0
$323$	1.55117	+	1.55117i	0.0863093	+	0.0863093i
$324$		0			0
$325$	2.11518	−	2.11518i	0.117329	−	0.117329i
$326$		0			0
$327$	−2.17821	+	17.5398i	−0.120455	+	0.969952i
$328$		0			0
$329$	−28.9823	−	50.1988i	−1.59784	−	2.76755i
$330$		0			0
$331$	−6.38080	+	1.70973i	−0.350720	+	0.0939753i	−0.429878	−	0.902887i	$-0.641444\pi$
$331$	−6.38080	+	1.70973i	−0.350720	+	0.0939753i	0.0791579	+	0.996862i	$0.474777\pi$
$332$		0			0
$333$	−11.2308	−	18.8086i	−0.615442	−	1.03071i
$334$		0			0
$335$	−10.1830	+	17.6375i	−0.556357	+	0.963638i
$336$		0			0
$337$	13.3790	+	23.1731i	0.728801	+	1.26232i	0.957390	+	0.288798i	$0.0932555\pi$
$337$	13.3790	+	23.1731i	0.728801	+	1.26232i	−0.228589	+	0.973523i	$0.573411\pi$
$338$		0			0
$339$	−5.26117	−	2.13411i	−0.285747	−	0.115909i
$340$		0			0
$341$	0.166057	+	0.166057i	0.00899248	+	0.00899248i
$342$		0			0
$343$	56.5593			3.05391
$344$		0			0
$345$	−6.36945	+	8.42830i	−0.342920	+	0.453765i
$346$		0			0
$347$	2.96361	+	0.794096i	0.159095	+	0.0426293i	0.337487	−	0.941330i	$-0.390423\pi$
$347$	2.96361	+	0.794096i	0.159095	+	0.0426293i	−0.178393	+	0.983959i	$0.557090\pi$
$348$		0			0
$349$	22.6749	−	6.07573i	1.21376	−	0.325226i	0.405524	−	0.914084i	$-0.367089\pi$
$349$	22.6749	−	6.07573i	1.21376	−	0.325226i	0.808236	+	0.588858i	$0.200422\pi$
$350$		0			0
$351$	3.28250	+	21.2955i	0.175207	+	1.13667i
$352$		0			0
$353$	2.70837	+	1.56368i	0.144152	+	0.0832262i	0.570341	−	0.821408i	$-0.306811\pi$
$353$	2.70837	+	1.56368i	0.144152	+	0.0832262i	−0.426189	+	0.904634i	$0.640144\pi$
$354$		0			0
$355$	27.7994	+	7.44884i	1.47544	+	0.395343i
$356$		0			0
$357$	2.66849	+	19.1794i	0.141231	+	1.01508i
$358$		0			0
$359$		−	25.4807i		−	1.34482i	−0.740180	−	0.672409i	$-0.765260\pi$
$359$		−	25.4807i		−	1.34482i	0.740180	−	0.672409i	$-0.234740\pi$
$360$		0			0
$361$			18.0277i			0.948825i
$362$		0			0
$363$	−15.8260	−	6.41956i	−0.830651	−	0.336940i
$364$		0			0
$365$	23.9615	+	6.42047i	1.25420	+	0.336063i
$366$		0			0
$367$	27.1264	+	15.6614i	1.41599	+	0.817520i	0.995943	−	0.0899840i	$-0.0286816\pi$
$367$	27.1264	+	15.6614i	1.41599	+	0.817520i	0.420043	+	0.907504i	$0.362015\pi$
$368$		0			0
$369$	4.78102	−	1.35666i	0.248890	−	0.0706247i
$370$		0			0
$371$	−53.5717	+	14.3545i	−2.78130	+	0.745248i
$372$		0			0
$373$	−11.5188	−	3.08646i	−0.596423	−	0.159811i	−0.0520359	−	0.998645i	$-0.516571\pi$
$373$	−11.5188	−	3.08646i	−0.596423	−	0.159811i	−0.544387	+	0.838834i	$0.683238\pi$
$374$		0			0
$375$	−17.5911	−	2.18457i	−0.908398	−	0.112811i
$376$		0			0
$377$	−2.53094			−0.130350
$378$		0			0
$379$	−3.76992	−	3.76992i	−0.193648	−	0.193648i	0.603623	−	0.797270i	$-0.293723\pi$
$379$	−3.76992	−	3.76992i	−0.193648	−	0.193648i	−0.797270	+	0.603623i	$0.793723\pi$
$380$		0			0
$381$	8.49520	−	6.61830i	0.435222	−	0.339066i
$382$		0			0
$383$	−9.14036	−	15.8316i	−0.467051	−	0.808956i	0.532241	−	0.846593i	$-0.321350\pi$
$383$	−9.14036	−	15.8316i	−0.467051	−	0.808956i	−0.999291	+	0.0376375i	$0.988017\pi$
$384$		0			0
$385$	−6.41646	+	11.1136i	−0.327013	+	0.566403i
$386$		0			0
$387$	0.227254	+	15.4674i	0.0115520	+	0.786254i
$388$		0			0
$389$	24.6006	−	6.59172i	1.24730	−	0.334214i	0.426008	−	0.904719i	$-0.359919\pi$
$389$	24.6006	−	6.59172i	1.24730	−	0.334214i	0.821294	+	0.570506i	$0.193253\pi$
$390$		0			0
$391$	2.83642	+	4.91283i	0.143444	+	0.248452i
$392$		0			0
$393$	−20.0420	+	8.47468i	−1.01099	+	0.427491i
$394$		0			0
$395$	15.1179	−	15.1179i	0.760666	−	0.760666i
$396$		0			0
$397$	−4.35736	−	4.35736i	−0.218689	−	0.218689i	0.589257	−	0.807946i	$-0.299421\pi$
$397$	−4.35736	−	4.35736i	−0.218689	−	0.218689i	−0.807946	+	0.589257i	$0.799421\pi$
$398$		0			0
$399$	5.17482	−	6.84752i	0.259065	−	0.342805i
$400$		0			0
$401$	31.6292	−	18.2611i	1.57948	−	0.911916i	0.584553	−	0.811355i	$-0.301270\pi$
$401$	31.6292	−	18.2611i	1.57948	−	0.911916i	0.994931	−	0.100561i	$-0.0320636\pi$
$402$		0			0
$403$	0.236085	+	0.881081i	0.0117602	+	0.0438898i
$404$		0			0
$405$	−14.7684	+	15.6628i	−0.733849	+	0.778293i
$406$		0			0
$407$	−6.75129	−	3.89786i	−0.334649	−	0.193210i
$408$		0			0
$409$	6.64716	−	3.83774i	0.328681	−	0.189764i	−0.326574	−	0.945172i	$-0.605894\pi$
$409$	6.64716	−	3.83774i	0.328681	−	0.189764i	0.655255	+	0.755407i	$0.272561\pi$
$410$		0			0
$411$	4.18736	−	0.582600i	0.206547	−	0.0287375i
$412$		0			0
$413$	18.7557	−	18.7557i	0.922907	−	0.922907i
$414$		0			0
$415$		−	13.7472i		−	0.674826i
$416$		0			0
$417$	23.2729	−	9.84085i	1.13968	−	0.481908i
$418$		0			0
$419$	1.66712	−	6.22178i	0.0814442	−	0.303954i	−0.913173	−	0.407572i	$-0.866375\pi$
$419$	1.66712	−	6.22178i	0.0814442	−	0.303954i	0.994617	+	0.103618i	$0.0330421\pi$
$420$		0			0
$421$	2.94683	+	10.9977i	0.143620	+	0.535996i	0.999813	+	0.0193401i	$0.00615652\pi$
$421$	2.94683	+	10.9977i	0.143620	+	0.535996i	−0.856193	+	0.516655i	$0.827177\pi$
$422$		0			0
$423$	−24.8248	−	24.1059i	−1.20702	−	1.17207i
$424$		0			0
$425$	0.802409	−	1.38981i	0.0389225	−	0.0674158i
$426$		0			0
$427$	8.73722	−	32.6078i	0.422824	−	1.57800i
$428$		0			0
$429$	4.71242	+	6.04882i	0.227518	+	0.292040i
$430$		0			0
$431$	8.35135			0.402270			0.201135	−	0.979564i	$-0.435537\pi$
$431$	8.35135			0.402270			0.201135	+	0.979564i	$0.435537\pi$
$432$		0			0
$433$	−1.97345			−0.0948380			−0.0474190	−	0.998875i	$-0.515100\pi$
$433$	−1.97345			−0.0948380			−0.0474190	+	0.998875i	$0.515100\pi$
$434$		0			0
$435$	−1.55403	−	1.99474i	−0.0745102	−	0.0956406i
$436$		0			0
$437$	0.650783	−	2.42875i	0.0311312	−	0.116183i
$438$		0			0
$439$	−0.292649	+	0.506883i	−0.0139674	+	0.0241922i	−0.872925	−	0.487855i	$-0.837779\pi$
$439$	−0.292649	+	0.506883i	−0.0139674	+	0.0241922i	0.858957	+	0.512047i	$0.171113\pi$
$440$		0			0
$441$	52.6840	−	14.9496i	2.50876	−	0.711884i
$442$		0			0
$443$	−7.27885	−	27.1650i	−0.345829	−	1.29065i	−0.891641	−	0.452743i	$-0.850446\pi$
$443$	−7.27885	−	27.1650i	−0.345829	−	1.29065i	0.545812	−	0.837907i	$-0.316221\pi$
$444$		0			0
$445$	−4.06480	+	15.1700i	−0.192690	+	0.719129i
$446$		0			0
$447$	0.382979	−	0.161941i	0.0181143	−	0.00765955i
$448$		0			0
$449$		−	31.8656i		−	1.50383i	−0.659258	−	0.751916i	$-0.729130\pi$
$449$		−	31.8656i		−	1.50383i	0.659258	−	0.751916i	$-0.270870\pi$
$450$		0			0
$451$	1.25056	−	1.25056i	0.0588867	−	0.0588867i
$452$		0			0
$453$	6.55449	−	0.911945i	0.307957	−	0.0428469i
$454$		0			0
$455$	−43.1675	+	24.9227i	−2.02372	+	1.16840i
$456$		0			0
$457$	12.6310	+	7.29251i	0.590854	+	0.341129i	0.765435	−	0.643513i	$-0.222524\pi$
$457$	12.6310	+	7.29251i	0.590854	+	0.341129i	−0.174581	+	0.984643i	$0.555857\pi$
$458$		0			0
$459$	4.65799	+	10.5798i	0.217417	+	0.493821i
$460$		0			0
$461$	0.978401	+	3.65144i	0.0455687	+	0.170065i	0.984960	−	0.172782i	$-0.0552756\pi$
$461$	0.978401	+	3.65144i	0.0455687	+	0.170065i	−0.939391	+	0.342847i	$0.888609\pi$
$462$		0			0
$463$	−15.8368	+	9.14339i	−0.735999	+	0.424929i	−0.820613	−	0.571484i	$-0.806368\pi$
$463$	−15.8368	+	9.14339i	−0.735999	+	0.424929i	0.0846136	+	0.996414i	$0.473034\pi$
$464$		0			0
$465$	−0.549459	+	0.727066i	−0.0254806	+	0.0337169i
$466$		0			0
$467$	10.9698	+	10.9698i	0.507621	+	0.507621i	0.913795	−	0.406175i	$-0.133138\pi$
$467$	10.9698	+	10.9698i	0.507621	+	0.507621i	−0.406175	+	0.913795i	$0.633138\pi$
$468$		0			0
$469$	30.2560	−	30.2560i	1.39709	−	1.39709i
$470$		0			0
$471$	−0.334593	+	0.141481i	−0.0154172	+	0.00651912i
$472$		0			0
$473$	2.75244	+	4.76737i	0.126558	+	0.219204i
$474$		0			0
$475$	−0.687081	+	0.184103i	−0.0315254	+	0.00844722i
$476$		0			0
$477$	−28.4267	+	16.9738i	−1.30157	+	0.777177i
$478$		0			0
$479$	−6.26251	+	10.8470i	−0.286142	+	0.495612i	−0.972885	−	0.231288i	$-0.925706\pi$
$479$	−6.26251	+	10.8470i	−0.286142	+	0.495612i	0.686744	+	0.726900i	$0.259039\pi$
$480$		0			0
$481$	−15.1400	−	26.2233i	−0.690326	−	1.19568i
$482$		0			0
$483$	17.5092	−	13.6408i	0.796694	−	0.620676i
$484$		0			0
$485$	5.13450	+	5.13450i	0.233146	+	0.233146i
$486$		0			0
$487$	12.7213			0.576459			0.288230	−	0.957561i	$-0.406933\pi$
$487$	12.7213			0.576459			0.288230	+	0.957561i	$0.406933\pi$
$488$		0			0
$489$	18.5704	+	2.30619i	0.839782	+	0.104290i
$490$		0			0
$491$	10.5795	+	2.83477i	0.477446	+	0.127931i	0.489513	−	0.871996i	$-0.337175\pi$
$491$	10.5795	+	2.83477i	0.477446	+	0.127931i	−0.0120673	+	0.999927i	$0.503841\pi$
$492$		0			0
$493$	−1.31156	+	0.351431i	−0.0590696	+	0.0158277i
$494$		0			0
$495$	−1.87385	+	7.42813i	−0.0842231	+	0.333869i
$496$		0			0
$497$	−52.3653	−	30.2331i	−2.34891	−	1.35614i
$498$		0			0
$499$	23.1524	+	6.20368i	1.03645	+	0.277715i	0.736639	−	0.676286i	$-0.236411\pi$
$499$	23.1524	+	6.20368i	1.03645	+	0.277715i	0.299806	+	0.954000i	$0.403078\pi$
$500$		0			0
$501$	7.29542	+	2.95927i	0.325936	+	0.132210i
$502$		0			0
$503$			27.6712i			1.23380i	0.787042	+	0.616899i	$0.211611\pi$
$503$			27.6712i			1.23380i	−0.787042	+	0.616899i	$0.788389\pi$
$504$		0			0
$505$			1.02500i			0.0456120i
$506$		0			0
$507$	1.00136	+	7.19716i	0.0444720	+	0.319637i
$508$		0			0
$509$	−27.5074	−	7.37058i	−1.21924	−	0.326695i	−0.408861	−	0.912597i	$-0.634074\pi$
$509$	−27.5074	−	7.37058i	−1.21924	−	0.326695i	−0.810383	+	0.585901i	$0.800741\pi$
$510$		0			0
$511$	−45.1359	−	26.0592i	−1.99669	−	1.15279i
$512$		0			0
$513$	1.85599	−	4.77579i	0.0819439	−	0.210856i
$514$		0			0
$515$	−18.8296	+	5.04538i	−0.829732	+	0.222326i
$516$		0			0
$517$	−11.8943	−	3.18708i	−0.523112	−	0.140167i
$518$		0			0
$519$	−18.1776	+	24.0533i	−0.797909	+	1.05582i
$520$		0			0
$521$	−13.7107			−0.600678			−0.300339	−	0.953832i	$-0.597100\pi$
$521$	−13.7107			−0.600678			−0.300339	+	0.953832i	$0.597100\pi$
$522$		0			0
$523$	−4.42816	−	4.42816i	−0.193630	−	0.193630i	0.603633	−	0.797262i	$-0.293719\pi$
$523$	−4.42816	−	4.42816i	−0.193630	−	0.193630i	−0.797262	+	0.603633i	$0.793719\pi$
$524$		0			0
$525$	−5.81852	−	2.36019i	−0.253941	−	0.103007i
$526$		0			0
$527$	0.244683	+	0.423804i	0.0106586	+	0.0184612i
$528$		0			0
$529$	−8.24885	+	14.2874i	−0.358646	+	0.621192i
$530$		0			0
$531$	7.71483	−	13.8277i	0.334795	−	0.600072i
$532$		0			0
$533$	6.63536	−	1.77794i	0.287409	−	0.0770111i
$534$		0			0
$535$	−17.8243	−	30.8726i	−0.770613	−	1.33474i
$536$		0			0
$537$	0.0341202	−	0.274750i	0.00147240	−	0.0118563i
$538$		0			0
$539$	13.7805	−	13.7805i	0.593566	−	0.593566i
$540$		0			0
$541$	−23.9889	−	23.9889i	−1.03136	−	1.03136i	−0.999492	−	0.0318715i	$-0.989853\pi$
$541$	−23.9889	−	23.9889i	−1.03136	−	1.03136i	−0.0318715	−	0.999492i	$-0.510147\pi$
$542$		0			0
$543$	−15.0136	−	1.86449i	−0.644296	−	0.0800129i
$544$		0			0
$545$	−21.1382	+	12.2041i	−0.905460	+	0.522768i
$546$		0			0
$547$	0.642523	+	2.39793i	0.0274723	+	0.102528i	0.978301	−	0.207190i	$-0.0664319\pi$
$547$	0.642523	+	2.39793i	0.0274723	+	0.102528i	−0.950828	+	0.309718i	$0.899765\pi$
$548$		0			0
$549$	−0.296056	−	20.1503i	−0.0126354	−	0.859992i
$550$		0			0
$551$	0.521210	+	0.300921i	0.0222043	+	0.0128197i
$552$		0			0
$553$	−38.9008	+	22.4594i	−1.65423	+	0.955071i
$554$		0			0
$555$	11.3715	−	28.0340i	0.482695	−	1.18998i
$556$		0			0
$557$	−32.9289	+	32.9289i	−1.39524	+	1.39524i	−0.582186	+	0.813056i	$0.697802\pi$
$557$	−32.9289	+	32.9289i	−1.39524	+	1.39524i	−0.813056	+	0.582186i	$0.802198\pi$
$558$		0			0
$559$			21.3820i			0.904363i
$560$		0			0
$561$	3.28193	+	2.48022i	0.138563	+	0.104715i
$562$		0			0
$563$	−1.92423	+	7.18131i	−0.0810964	+	0.302656i	−0.994546	−	0.104295i	$-0.966741\pi$
$563$	−1.92423	+	7.18131i	−0.0810964	+	0.302656i	0.913450	+	0.406951i	$0.133408\pi$
$564$		0			0
$565$	−2.02929	−	7.57342i	−0.0853730	−	0.318616i
$566$		0			0
$567$	38.4879	−	23.7553i	1.61634	−	0.997628i
$568$		0			0
$569$	13.9011	−	24.0775i	0.582766	−	1.00938i	−0.412383	−	0.911010i	$-0.635304\pi$
$569$	13.9011	−	24.0775i	0.582766	−	1.00938i	0.995150	−	0.0983706i	$-0.0313631\pi$
$570$		0			0
$571$	1.02058	−	3.80886i	0.0427100	−	0.159396i	−0.941277	−	0.337635i	$-0.890373\pi$
$571$	1.02058	−	3.80886i	0.0427100	−	0.159396i	0.983987	+	0.178239i	$0.0570399\pi$
$572$		0			0
$573$	−6.56093	+	0.912841i	−0.274087	+	0.0381345i
$574$		0			0
$575$	−1.83947			−0.0767110
$576$		0			0
$577$	−10.6180			−0.442032			−0.221016	−	0.975270i	$-0.570937\pi$
$577$	−10.6180			−0.442032			−0.221016	+	0.975270i	$0.570937\pi$
$578$		0			0
$579$	6.11453	−	15.0740i	0.254111	−	0.626455i
$580$		0			0
$581$	−7.47537	+	27.8985i	−0.310131	+	1.15742i
$582$		0			0
$583$	−5.89109	+	10.2037i	−0.243984	+	0.422593i
$584$		0			0
$585$	−20.7294	+	21.3476i	−0.857054	+	0.882614i
$586$		0			0
$587$	−0.889198	−	3.31853i	−0.0367011	−	0.136970i	0.945144	−	0.326653i	$-0.105921\pi$
$587$	−0.889198	−	3.31853i	−0.0367011	−	0.136970i	−0.981845	+	0.189682i	$0.939254\pi$
$588$		0			0
$589$	0.0561396	−	0.209516i	0.00231319	−	0.00863295i
$590$		0			0
$591$	−1.81401	+	14.6072i	−0.0746186	+	0.600859i
$592$		0			0
$593$		−	27.5541i		−	1.13151i	−0.824573	−	0.565755i	$-0.808585\pi$
$593$		−	27.5541i		−	1.13151i	0.824573	−	0.565755i	$-0.191415\pi$
$594$		0			0
$595$	−18.9092	+	18.9092i	−0.775202	+	0.775202i
$596$		0			0
$597$	18.1478	+	23.2944i	0.742741	+	0.953376i
$598$		0			0
$599$	14.5840	−	8.42008i	0.595886	−	0.344035i	−0.171535	−	0.985178i	$-0.554873\pi$
$599$	14.5840	−	8.42008i	0.595886	−	0.344035i	0.767422	+	0.641143i	$0.221539\pi$
$600$		0			0
$601$	−22.6011	−	13.0487i	−0.921916	−	0.532269i	−0.0376703	−	0.999290i	$-0.511994\pi$
$601$	−22.6011	−	13.0487i	−0.921916	−	0.532269i	−0.884246	+	0.467022i	$0.845327\pi$
$602$		0			0
$603$	12.4453	−	22.3064i	0.506811	−	0.908386i
$604$		0			0
$605$	−6.10428	−	22.7815i	−0.248174	−	0.926198i
$606$		0			0
$607$	14.0103	−	8.08887i	0.568662	−	0.328317i	−0.187953	−	0.982178i	$-0.560185\pi$
$607$	14.0103	−	8.08887i	0.568662	−	0.328317i	0.756615	+	0.653861i	$0.226852\pi$
$608$		0			0
$609$	2.06905	+	4.89314i	0.0838420	+	0.198280i
$610$		0			0
$611$	−33.8206	−	33.8206i	−1.36824	−	1.36824i
$612$		0			0
$613$	−0.969385	+	0.969385i	−0.0391531	+	0.0391531i	−0.726412	−	0.687259i	$-0.758814\pi$
$613$	−0.969385	+	0.969385i	−0.0391531	+	0.0391531i	0.687259	+	0.726412i	$0.258814\pi$
$614$		0			0
$615$	5.47548	+	4.13794i	0.220793	+	0.166858i
$616$		0			0
$617$	12.4805	+	21.6168i	0.502445	+	0.870260i	0.999996	+	0.00282568i	$0.000899442\pi$
$617$	12.4805	+	21.6168i	0.502445	+	0.870260i	−0.497551	+	0.867435i	$0.665767\pi$
$618$		0			0
$619$	9.79499	−	2.62456i	0.393694	−	0.105490i	−0.0565406	−	0.998400i	$-0.518007\pi$
$619$	9.79499	−	2.62456i	0.393694	−	0.105490i	0.450235	+	0.892910i	$0.351340\pi$
$620$		0			0
$621$	7.83249	−	10.6871i	0.314307	−	0.428859i
$622$		0			0
$623$	16.4981	−	28.5755i	0.660982	−	1.14485i
$624$		0			0
$625$	−14.0432	−	24.3236i	−0.561730	−	0.972944i
$626$		0			0
$627$	−0.251268	−	1.80596i	−0.0100347	−	0.0721231i
$628$		0			0
$629$	−11.4869	−	11.4869i	−0.458014	−	0.458014i
$630$		0			0
$631$	−14.5051			−0.577440			−0.288720	−	0.957414i	$-0.593230\pi$
$631$	−14.5051			−0.577440			−0.288720	+	0.957414i	$0.593230\pi$
$632$		0			0
$633$	−0.451630	−	1.06807i	−0.0179507	−	0.0424520i
$634$		0			0
$635$	14.3650	+	3.84910i	0.570059	+	0.152747i
$636$		0			0
$637$	73.1177	−	19.5918i	2.89703	−	0.776257i
$638$		0			0
$639$	−34.9999	−	8.82920i	−1.38457	−	0.349278i
$640$		0			0
$641$	16.9507	+	9.78651i	0.669514	+	0.386544i	0.795892	−	0.605438i	$-0.207002\pi$
$641$	16.9507	+	9.78651i	0.669514	+	0.386544i	−0.126379	+	0.991982i	$0.540335\pi$
$642$		0			0
$643$	37.6479	+	10.0877i	1.48469	+	0.397821i	0.907940	−	0.419101i	$-0.137655\pi$
$643$	37.6479	+	10.0877i	1.48469	+	0.397821i	0.576748	+	0.816922i	$0.304321\pi$
$644$		0			0
$645$	−16.8521	+	13.1289i	−0.663552	+	0.516949i
$646$		0			0
$647$		−	3.37402i		−	0.132647i	−0.997798	−	0.0663233i	$-0.978873\pi$
$647$		−	3.37402i		−	0.132647i	0.997798	−	0.0663233i	$-0.0211269\pi$
$648$		0			0
$649$		−	5.63484i		−	0.221187i
$650$		0			0
$651$	1.51042	−	1.17672i	0.0591982	−	0.0461192i
$652$		0			0
$653$	26.5132	+	7.10419i	1.03754	+	0.278008i	0.737094	−	0.675790i	$-0.236197\pi$
$653$	26.5132	+	7.10419i	1.03754	+	0.278008i	0.300447	+	0.953798i	$0.402864\pi$
$654$		0			0
$655$	−26.0244	−	15.0252i	−1.01686	−	0.587083i
$656$		0			0
$657$	−30.1679	−	7.61026i	−1.17696	−	0.296905i
$658$		0			0
$659$	48.7287	−	13.0568i	1.89820	−	0.508621i	0.901003	−	0.433813i	$-0.142832\pi$
$659$	48.7287	−	13.0568i	1.89820	−	0.508621i	0.997198	−	0.0748080i	$-0.0238344\pi$
$660$		0			0
$661$	4.89081	+	1.31049i	0.190230	+	0.0509721i	0.352676	−	0.935745i	$-0.385272\pi$
$661$	4.89081	+	1.31049i	0.190230	+	0.0509721i	−0.162446	+	0.986717i	$0.551938\pi$
$662$		0			0
$663$	6.22294	+	14.7168i	0.241679	+	0.571553i
$664$		0			0
$665$	11.8530			0.459638
$666$		0			0
$667$	1.10051	+	1.10051i	0.0426120	+	0.0426120i
$668$		0			0
$669$	−2.93448	−	21.0912i	−0.113454	−	0.815434i
$670$		0			0
$671$	−3.58576	−	6.21072i	−0.138427	−	0.239762i
$672$		0			0
$673$	−17.6472	+	30.5658i	−0.680249	+	1.17823i	0.294656	+	0.955603i	$0.404795\pi$
$673$	−17.6472	+	30.5658i	−0.680249	+	1.17823i	−0.974905	+	0.222622i	$0.928538\pi$
$674$		0			0
$675$	−3.72616	−	0.407250i	−0.143420	−	0.0156750i
$676$		0			0
$677$	44.1766	−	11.8371i	1.69785	−	0.454936i	0.725450	−	0.688275i	$-0.241632\pi$
$677$	44.1766	−	11.8371i	1.69785	−	0.454936i	0.972396	+	0.233338i	$0.0749649\pi$
$678$		0			0
$679$	−7.62788	−	13.2119i	−0.292731	−	0.507025i
$680$		0			0
$681$	−26.0380	−	19.6774i	−0.997777	−	0.754041i
$682$		0			0
$683$	−29.7527	+	29.7527i	−1.13845	+	1.13845i	−0.149727	+	0.988727i	$0.547839\pi$
$683$	−29.7527	+	29.7527i	−1.13845	+	1.13845i	−0.988727	+	0.149727i	$0.952161\pi$
$684$		0			0
$685$	4.12837	+	4.12837i	0.157737	+	0.157737i
$686$		0			0
$687$	4.72671	+	11.1783i	0.180335	+	0.426480i
$688$		0			0
$689$	−39.6330	+	22.8821i	−1.50990	+	0.871738i
$690$		0			0
$691$	9.78609	+	36.5222i	0.372280	+	1.38937i	0.857278	+	0.514854i	$0.172154\pi$
$691$	9.78609	+	36.5222i	0.372280	+	1.38937i	−0.484997	+	0.874516i	$0.661179\pi$
$692$		0			0
$693$	7.84197	−	14.0556i	0.297892	−	0.533928i
$694$		0			0
$695$	30.2197	+	17.4474i	1.14630	+	0.661816i
$696$		0			0
$697$	3.19164	−	1.84269i	0.120892	−	0.0697970i
$698$		0			0
$699$	−26.1528	−	33.5695i	−0.989190	−	1.26972i
$700$		0			0
$701$	−19.2180	+	19.2180i	−0.725854	+	0.725854i	−0.969791	−	0.243937i	$-0.921561\pi$
$701$	−19.2180	+	19.2180i	−0.725854	+	0.725854i	0.243937	+	0.969791i	$0.421561\pi$
$702$		0			0
$703$			7.20042i			0.271569i
$704$		0			0
$705$	5.88916	−	47.4219i	0.221799	−	1.78601i
$706$		0			0
$707$	0.557368	−	2.08013i	0.0209620	−	0.0782312i
$708$		0			0
$709$	8.13238	+	30.3504i	0.305418	+	1.13983i	0.932585	+	0.360950i	$0.117548\pi$
$709$	8.13238	+	30.3504i	0.305418	+	1.13983i	−0.627167	+	0.778885i	$0.715786\pi$
$710$		0			0
$711$	−18.6805	+	19.2376i	−0.700574	+	0.721467i
$712$		0			0
$713$	0.280460	−	0.485771i	0.0105033	−	0.0181923i
$714$		0			0
$715$	−2.74066	+	10.2283i	−0.102495	+	0.382517i
$716$		0			0
$717$	2.22219	−	5.47832i	0.0829891	−	0.204591i
$718$		0			0
$719$	19.9203			0.742903			0.371452	−	0.928452i	$-0.378860\pi$
$719$	19.9203			0.742903			0.371452	+	0.928452i	$0.378860\pi$
$720$		0			0
$721$	40.9561			1.52528
$722$		0			0
$723$	−44.4124	+	6.17923i	−1.65172	+	0.229808i
$724$		0			0
$725$	0.113954	−	0.425283i	0.00423216	−	0.0157946i
$726$		0			0
$727$	−11.2366	+	19.4624i	−0.416743	+	0.721819i	−0.995610	−	0.0936026i	$-0.970162\pi$
$727$	−11.2366	+	19.4624i	−0.416743	+	0.721819i	0.578867	+	0.815422i	$0.303495\pi$
$728$		0			0
$729$	18.2322	−	19.9145i	0.675265	−	0.737575i
$730$		0			0
$731$	2.96898	+	11.0804i	0.109812	+	0.409823i
$732$		0			0
$733$	10.8684	−	40.5613i	0.401432	−	1.49817i	−0.409109	−	0.912485i	$-0.634161\pi$
$733$	10.8684	−	40.5613i	0.401432	−	1.49817i	0.810542	−	0.585681i	$-0.199173\pi$
$734$		0			0
$735$	60.3366	+	45.5976i	2.22555	+	1.68189i
$736$		0			0
$737$		−	9.08993i		−	0.334832i
$738$		0			0
$739$	4.75917	−	4.75917i	0.175069	−	0.175069i	−0.614133	−	0.789202i	$-0.710494\pi$
$739$	4.75917	−	4.75917i	0.175069	−	0.175069i	0.789202	+	0.614133i	$0.210494\pi$
$740$		0			0
$741$	2.66213	−	6.56288i	0.0977956	−	0.241094i
$742$		0			0
$743$	26.1387	−	15.0912i	0.958936	−	0.553642i	0.0630904	−	0.998008i	$-0.479904\pi$
$743$	26.1387	−	15.0912i	0.958936	−	0.553642i	0.895845	+	0.444366i	$0.146571\pi$
$744$		0			0
$745$	0.497296	+	0.287114i	0.0182195	+	0.0105190i
$746$		0			0
$747$	0.253299	+	17.2401i	0.00926772	+	0.630782i
$748$		0			0
$749$	19.3847	+	72.3448i	0.708303	+	2.64342i
$750$		0			0
$751$	−30.3572	+	17.5267i	−1.10775	+	0.639559i	−0.938245	−	0.345971i	$-0.887550\pi$
$751$	−30.3572	+	17.5267i	−1.10775	+	0.639559i	−0.169503	+	0.985530i	$0.554216\pi$
$752$		0			0
$753$	46.2227	+	5.74024i	1.68445	+	0.209186i
$754$		0			0
$755$	6.46214	+	6.46214i	0.235182	+	0.235182i
$756$		0			0
$757$	−24.7520	+	24.7520i	−0.899626	+	0.899626i	−0.995403	−	0.0957772i	$-0.969466\pi$
$757$	−24.7520	+	24.7520i	−0.899626	+	0.899626i	0.0957772	+	0.995403i	$0.469466\pi$
$758$		0			0
$759$	0.581099	−	4.67924i	0.0210926	−	0.169846i
$760$		0			0
$761$	24.7912	+	42.9396i	0.898681	+	1.55656i	0.829182	+	0.558978i	$0.188807\pi$
$761$	24.7912	+	42.9396i	0.898681	+	1.55656i	0.0694983	+	0.997582i	$0.477860\pi$
$762$		0			0
$763$	49.5338	−	13.2725i	1.79324	−	0.480498i
$764$		0			0
$765$	−7.77798	+	13.9409i	−0.281214	+	0.504035i
$766$		0			0
$767$	10.9434	−	18.9545i	0.395143	−	0.684408i
$768$		0			0
$769$	23.4383	+	40.5964i	0.845208	+	1.46394i	0.885440	+	0.464754i	$0.153857\pi$
$769$	23.4383	+	40.5964i	0.845208	+	1.46394i	−0.0402316	+	0.999190i	$0.512810\pi$
$770$		0			0
$771$	2.73314	+	1.10865i	0.0984317	+	0.0399272i
$772$		0			0
$773$	−12.8895	−	12.8895i	−0.463605	−	0.463605i	0.436230	−	0.899835i	$-0.356313\pi$
$773$	−12.8895	−	12.8895i	−0.463605	−	0.463605i	−0.899835	+	0.436230i	$0.856313\pi$
$774$		0			0
$775$	−0.158681			−0.00569999
$776$		0			0
$777$	−38.3213	+	50.7083i	−1.37477	+	1.81915i
$778$		0			0
$779$	−1.57785	−	0.422784i	−0.0565323	−	0.0151478i
$780$		0			0
$781$	−12.4077	+	3.32463i	−0.443982	+	0.118965i
$782$		0			0
$783$	1.98563	+	2.47293i	0.0709607	+	0.0883753i
$784$		0			0
$785$	−0.434467	−	0.250840i	−0.0155068	−	0.00895285i
$786$		0			0
$787$	−34.1116	−	9.14019i	−1.21595	−	0.325812i	−0.406855	−	0.913493i	$-0.633375\pi$
$787$	−34.1116	−	9.14019i	−1.21595	−	0.325812i	−0.809093	+	0.587680i	$0.800041\pi$
$788$		0			0
$789$	−0.389918	−	2.80248i	−0.0138814	−	0.0997711i
$790$		0			0
$791$			16.4729i			0.585708i
$792$		0			0
$793$		−	27.8555i		−	0.989179i
$794$		0			0
$795$	−42.3696	−	17.1865i	−1.50270	−	0.609544i
$796$		0			0
$797$	−7.89416	−	2.11523i	−0.279625	−	0.0749254i	0.116281	−	0.993216i	$-0.462903\pi$
$797$	−7.89416	−	2.11523i	−0.279625	−	0.0749254i	−0.395906	+	0.918291i	$0.629569\pi$
$798$		0			0
$799$	−22.2223	−	12.8301i	−0.786170	−	0.453895i
$800$		0			0
$801$	4.81806	−	19.0993i	0.170238	−	0.674841i
$802$		0			0
$803$	−10.6947	+	2.86564i	−0.377408	+	0.101126i
$804$		0			0
$805$	29.6073	+	7.93324i	1.04352	+	0.279610i
$806$		0			0
$807$	−2.92391	−	0.363111i	−0.102927	−	0.0127821i
$808$		0			0
$809$	17.8123			0.626248			0.313124	−	0.949712i	$-0.398625\pi$
$809$	17.8123			0.626248			0.313124	+	0.949712i	$0.398625\pi$
$810$		0			0
$811$	−15.4533	−	15.4533i	−0.542639	−	0.542639i	0.381663	−	0.924302i	$-0.375352\pi$
$811$	−15.4533	−	15.4533i	−0.542639	−	0.542639i	−0.924302	+	0.381663i	$0.875352\pi$
$812$		0			0
$813$	−31.3483	+	24.4223i	−1.09943	+	0.856529i
$814$		0			0
$815$	12.9212	+	22.3802i	0.452611	+	0.783945i
$816$		0			0
$817$	2.54226	−	4.40332i	0.0889424	−	0.154053i
$818$		0			0
$819$	53.6761	−	32.0504i	1.87560	−	1.11993i
$820$		0			0
$821$	−6.17527	+	1.65466i	−0.215518	+	0.0577480i	−0.364963	−	0.931022i	$-0.618918\pi$
$821$	−6.17527	+	1.65466i	−0.215518	+	0.0577480i	0.149444	+	0.988770i	$0.452252\pi$
$822$		0			0
$823$	−16.7762	−	29.0572i	−0.584782	−	1.01287i	−0.994903	−	0.100840i	$-0.967847\pi$
$823$	−16.7762	−	29.0572i	−0.584782	−	1.01287i	0.410121	−	0.912031i	$-0.365486\pi$
$824$		0			0
$825$	−1.22858	+	0.519500i	−0.0427737	+	0.0180867i
$826$		0			0
$827$	−14.6929	+	14.6929i	−0.510921	+	0.510921i	−0.914809	−	0.403888i	$-0.867659\pi$
$827$	−14.6929	+	14.6929i	−0.510921	+	0.510921i	0.403888	+	0.914809i	$0.367659\pi$
$828$		0			0
$829$	18.8540	+	18.8540i	0.654827	+	0.654827i	0.954151	−	0.299324i	$-0.0967612\pi$
$829$	18.8540	+	18.8540i	0.654827	+	0.654827i	−0.299324	+	0.954151i	$0.596761\pi$
$830$		0			0
$831$	4.19406	−	5.54974i	0.145490	−	0.192519i
$832$		0			0
$833$	35.1700	−	20.3054i	1.21857	−	0.703540i
$834$		0			0
$835$	2.81393	+	10.5017i	0.0973800	+	0.363427i
$836$		0			0
$837$	0.675668	−	0.921921i	0.0233545	−	0.0318663i
$838$		0			0
$839$	22.2713	+	12.8583i	0.768891	+	0.443919i	0.832479	−	0.554057i	$-0.186921\pi$
$839$	22.2713	+	12.8583i	0.768891	+	0.443919i	−0.0635881	+	0.997976i	$0.520254\pi$
$840$		0			0
$841$	24.7921	−	14.3137i	0.854901	−	0.493577i
$842$		0			0
$843$	52.2253	−	7.26626i	1.79874	−	0.250263i
$844$		0			0
$845$	−7.09576	+	7.09576i	−0.244101	+	0.244101i
$846$		0			0
$847$			49.5517i			1.70262i
$848$		0			0
$849$	19.1108	−	8.08091i	0.655880	−	0.277336i
$850$		0			0
$851$	−4.81927	+	17.9858i	−0.165202	+	0.616544i
$852$		0			0
$853$	−11.6194	−	43.3641i	−0.397840	−	1.48476i	−0.816889	−	0.576795i	$-0.804303\pi$
$853$	−11.6194	−	43.3641i	−0.397840	−	1.48476i	0.419049	−	0.907963i	$-0.362363\pi$
$854$		0			0
$855$	6.80708	−	1.93157i	0.232797	−	0.0660583i
$856$		0			0
$857$	13.0424	−	22.5901i	0.445520	−	0.771663i	−0.552569	−	0.833467i	$-0.686352\pi$
$857$	13.0424	−	22.5901i	0.445520	−	0.771663i	0.998088	+	0.0618046i	$0.0196856\pi$
$858$		0			0
$859$	−8.14400	+	30.3938i	−0.277870	+	1.03702i	0.676024	+	0.736879i	$0.263701\pi$
$859$	−8.14400	+	30.3938i	−0.277870	+	1.03702i	−0.953894	+	0.300144i	$0.902965\pi$
$860$		0			0
$861$	−8.86177	−	11.3749i	−0.302008	−	0.387655i
$862$		0			0
$863$	−30.7225			−1.04581			−0.522903	−	0.852392i	$-0.675151\pi$
$863$	−30.7225			−1.04581			−0.522903	+	0.852392i	$0.675151\pi$
$864$		0			0
$865$	−41.6360			−1.41566
$866$		0			0
$867$	−12.8277	−	16.4656i	−0.435652	−	0.559200i
$868$		0			0
$869$	−2.46978	+	9.21735i	−0.0837816	+	0.312677i
$870$		0			0
$871$	17.6535	−	30.5767i	0.598166	−	1.03605i
$872$		0			0
$873$	−6.53367	−	6.34446i	−0.221131	−	0.214727i
$874$		0			0
$875$	13.3113	+	49.6786i	0.450005	+	1.67944i
$876$		0			0
$877$	−5.32228	+	19.8630i	−0.179720	+	0.670726i	0.815979	+	0.578082i	$0.196199\pi$
$877$	−5.32228	+	19.8630i	−0.179720	+	0.670726i	−0.995699	+	0.0926441i	$0.970468\pi$
$878$		0			0
$879$	−30.8580	+	13.0482i	−1.04082	+	0.440105i
$880$		0			0
$881$			42.7006i			1.43862i	0.694689	+	0.719310i	$0.255542\pi$
$881$			42.7006i			1.43862i	−0.694689	+	0.719310i	$0.744458\pi$
$882$		0			0
$883$	−20.6871	+	20.6871i	−0.696177	+	0.696177i	−0.963584	−	0.267407i	$-0.913833\pi$
$883$	−20.6871	+	20.6871i	−0.696177	+	0.696177i	0.267407	+	0.963584i	$0.413833\pi$
$884$		0			0
$885$	21.6583	−	3.01338i	0.728035	−	0.101294i
$886$		0			0
$887$	−34.2924	+	19.7987i	−1.15143	+	0.664777i	−0.949235	−	0.314569i	$-0.898140\pi$
$887$	−34.2924	+	19.7987i	−1.15143	+	0.664777i	−0.202192	+	0.979346i	$0.564807\pi$
$888$		0			0
$889$	−27.0592	−	15.6226i	−0.907535	−	0.523966i
$890$		0			0
$891$	2.21308	−	9.34997i	0.0741410	−	0.313236i
$892$		0			0
$893$	2.94370	+	10.9860i	0.0985072	+	0.367634i
$894$		0			0
$895$	0.331116	−	0.191170i	0.0110680	−	0.00639011i
$896$		0			0
$897$	11.0422	−	14.6115i	0.368689	−	0.487864i
$898$		0			0
$899$	0.0949355	+	0.0949355i	0.00316628	+	0.00316628i
$900$		0			0
$901$	−17.3609	+	17.3609i	−0.578377	+	0.578377i
$902$		0			0
$903$	41.3386	−	17.4799i	1.37566	−	0.581693i
$904$		0			0
$905$	−10.4464	−	18.0938i	−0.347251	−	0.601457i
$906$		0			0
$907$	0.845385	−	0.226520i	0.0280705	−	0.00752148i	−0.244756	−	0.969585i	$-0.578708\pi$
$907$	0.845385	−	0.226520i	0.0280705	−	0.00752148i	0.272827	+	0.962063i	$0.412041\pi$
$908$		0			0
$909$	−0.0188861	−	1.28543i	−0.000626412	−	0.0426351i
$910$		0			0
$911$	26.3505	−	45.6405i	0.873032	−	1.51214i	0.0141881	−	0.999899i	$-0.495484\pi$
$911$	26.3505	−	45.6405i	0.873032	−	1.51214i	0.858844	−	0.512237i	$-0.171183\pi$
$912$		0			0
$913$	3.06789	+	5.31375i	0.101532	+	0.175859i
$914$		0			0
$915$	21.9542	−	17.1037i	0.725783	−	0.565431i
$916$		0			0
$917$	44.6433	+	44.6433i	1.47425	+	1.47425i
$918$		0			0
$919$	−17.0903			−0.563758			−0.281879	−	0.959450i	$-0.590958\pi$
$919$	−17.0903			−0.563758			−0.281879	+	0.959450i	$0.590958\pi$
$920$		0			0
$921$	5.47636	+	0.680090i	0.180452	+	0.0224097i
$922$		0			0
$923$	−48.1938	−	12.9135i	−1.58632	−	0.425053i
$924$		0			0
$925$	5.08807	−	1.36335i	0.167295	−	0.0448265i
$926$		0			0
$927$	23.5208	−	6.67424i	0.772526	−	0.219211i
$928$		0			0
$929$	23.0709	+	13.3200i	0.756933	+	0.437015i	0.828193	−	0.560442i	$-0.189369\pi$
$929$	23.0709	+	13.3200i	0.756933	+	0.437015i	−0.0712608	+	0.997458i	$0.522702\pi$
$930$		0			0
$931$	−17.3870	−	4.65882i	−0.569835	−	0.152687i
$932$		0			0
$933$	−45.8493	−	18.5980i	−1.50104	−	0.608872i
$934$		0			0
$935$			5.68097i			0.185787i
$936$		0			0
$937$			26.2397i			0.857214i	0.903491	+	0.428607i	$0.140995\pi$
$937$			26.2397i			0.857214i	−0.903491	+	0.428607i	$0.859005\pi$
$938$		0			0
$939$	5.00923	+	36.0032i	0.163470	+	1.17492i
$940$		0			0
$941$	25.4022	+	6.80651i	0.828089	+	0.221886i	0.647880	−	0.761742i	$-0.275656\pi$
$941$	25.4022	+	6.80651i	0.828089	+	0.221886i	0.180209	+	0.983628i	$0.442322\pi$
$942$		0			0
$943$	−3.65831	−	2.11212i	−0.119131	−	0.0687802i
$944$		0			0
$945$	58.2183	+	22.6251i	1.89384	+	0.735994i
$946$		0			0
$947$	−16.5153	+	4.42526i	−0.536675	+	0.143802i	−0.516969	−	0.856004i	$-0.672940\pi$
$947$	−16.5153	+	4.42526i	−0.536675	+	0.143802i	−0.0197060	+	0.999806i	$0.506273\pi$
$948$		0			0
$949$	−41.5403	−	11.1307i	−1.34845	−	0.361317i
$950$		0			0
$951$	12.4052	−	16.4151i	0.402267	−	0.532295i
$952$		0			0
$953$	−47.3557			−1.53400			−0.767001	−	0.641646i	$-0.778252\pi$
$953$	−47.3557			−1.53400			−0.767001	+	0.641646i	$0.778252\pi$
$954$		0			0
$955$	−6.46849	−	6.46849i	−0.209316	−	0.209316i
$956$		0			0
$957$	1.04584	+	0.424227i	0.0338072	+	0.0137133i
$958$		0			0
$959$	−6.13316	−	10.6229i	−0.198050	−	0.343033i
$960$		0			0
$961$	−15.4758	+	26.8049i	−0.499220	+	0.864674i
$962$		0			0
$963$	22.9219	+	38.3882i	0.738649	+	1.23704i
$964$		0			0
$965$	21.6990	−	5.81423i	0.698515	−	0.187167i
$966$		0			0
$967$	5.54783	+	9.60912i	0.178406	+	0.309009i	0.941335	−	0.337474i	$-0.109573\pi$
$967$	5.54783	+	9.60912i	0.178406	+	0.309009i	−0.762929	+	0.646483i	$0.776239\pi$
$968$		0			0
$969$	0.468258	−	3.77060i	0.0150426	−	0.121129i
$970$		0			0
$971$	11.1100	−	11.1100i	0.356538	−	0.356538i	−0.505997	−	0.862535i	$-0.668875\pi$
$971$	11.1100	−	11.1100i	0.356538	−	0.356538i	0.862535	+	0.505997i	$0.168875\pi$
$972$		0			0
$973$	−51.8401	−	51.8401i	−1.66192	−	1.66192i
$974$		0			0
$975$	−5.14162	−	0.638521i	−0.164664	−	0.0204490i
$976$		0			0
$977$	−37.8418	+	21.8480i	−1.21067	+	0.698979i	−0.962905	−	0.269842i	$-0.913029\pi$
$977$	−37.8418	+	21.8480i	−1.21067	+	0.698979i	−0.247762	+	0.968821i	$0.579695\pi$
$978$		0			0
$979$	−1.81424	−	6.77082i	−0.0579832	−	0.216396i
$980$		0			0
$981$	26.2840	−	15.6944i	0.839185	−	0.501084i
$982$		0			0
$983$	4.32758	+	2.49853i	0.138028	+	0.0796907i	0.567424	−	0.823426i	$-0.307940\pi$
$983$	4.32758	+	2.49853i	0.138028	+	0.0796907i	−0.429396	+	0.903116i	$0.641273\pi$
$984$		0			0
$985$	−17.6039	+	10.1636i	−0.560908	+	0.323840i
$986$		0			0
$987$	−37.7381	+	93.0349i	−1.20122	+	2.96133i
$988$		0			0
$989$	9.29742	−	9.29742i	0.295641	−	0.295641i
$990$		0			0
$991$		−	36.5019i		−	1.15952i	−0.814787	−	0.579760i	$-0.803146\pi$
$991$		−	36.5019i		−	1.15952i	0.814787	−	0.579760i	$-0.196854\pi$
$992$		0			0
$993$	9.12826	+	6.89842i	0.289677	+	0.218915i
$994$		0			0
$995$	−10.5545	+	39.3899i	−0.334600	+	1.24874i
$996$		0			0
$997$	1.74992	+	6.53078i	0.0554204	+	0.206832i	0.988084	−	0.153915i	$-0.0491884\pi$
$997$	1.74992	+	6.53078i	0.0554204	+	0.206832i	−0.932664	+	0.360747i	$0.882522\pi$
$998$		0			0
$999$	−13.7442	+	35.3663i	−0.434849	+	1.11894i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.y.a.47.6		88
3.2	odd	2		1728.2.z.a.1007.4		88
4.3	odd	2		144.2.u.a.83.3	yes	88
9.4	even	3		1728.2.z.a.1583.4		88
9.5	odd	6	inner	576.2.y.a.239.17		88
12.11	even	2		432.2.v.a.35.20		88
16.5	even	4		144.2.u.a.11.11	✓	88
16.11	odd	4	inner	576.2.y.a.335.17		88
36.23	even	6		144.2.u.a.131.11	yes	88
36.31	odd	6		432.2.v.a.179.12		88
48.5	odd	4		432.2.v.a.251.12		88
48.11	even	4		1728.2.z.a.143.4		88
144.5	odd	12		144.2.u.a.59.3	yes	88
144.59	even	12	inner	576.2.y.a.527.6		88
144.85	even	12		432.2.v.a.395.20		88
144.139	odd	12		1728.2.z.a.719.4		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.11	✓	88	16.5	even	4
144.2.u.a.59.3	yes	88	144.5	odd	12
144.2.u.a.83.3	yes	88	4.3	odd	2
144.2.u.a.131.11	yes	88	36.23	even	6
432.2.v.a.35.20		88	12.11	even	2
432.2.v.a.179.12		88	36.31	odd	6
432.2.v.a.251.12		88	48.5	odd	4
432.2.v.a.395.20		88	144.85	even	12
576.2.y.a.47.6		88	1.1	even	1	trivial
576.2.y.a.239.17		88	9.5	odd	6	inner
576.2.y.a.335.17		88	16.11	odd	4	inner
576.2.y.a.527.6		88	144.59	even	12	inner
1728.2.z.a.143.4		88	48.11	even	4
1728.2.z.a.719.4		88	144.139	odd	12
1728.2.z.a.1007.4		88	3.2	odd	2
1728.2.z.a.1583.4		88	9.4	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.06447 - 1.36635i) q^{3} +(0.619079 - 2.31044i) q^{5} +(-2.51270 + 4.35213i) q^{7} +(-0.733803 + 2.90887i) q^{9} +O(q^{10})\)	\(q+(-1.06447 - 1.36635i) q^{3} +(0.619079 - 2.31044i) q^{5} +(-2.51270 + 4.35213i) q^{7} +(-0.733803 + 2.90887i) q^{9} +(0.276313 + 1.03121i) q^{11} +(-1.07325 + 4.00543i) q^{13} +(-3.81585 + 1.61352i) q^{15} +2.22468i q^{17} +(0.697254 - 0.697254i) q^{19} +(8.62121 - 1.19949i) q^{21} +(2.20833 - 1.27498i) q^{23} +(-0.624725 - 0.360685i) q^{25} +(4.75564 - 2.09378i) q^{27} +(0.157969 + 0.589549i) q^{29} +(0.190501 - 0.109986i) q^{31} +(1.11487 - 1.47524i) q^{33} +(8.49974 + 8.49974i) q^{35} +(-5.16341 + 5.16341i) q^{37} +(6.61524 - 2.79723i) q^{39} +(-0.828296 - 1.43465i) q^{41} +(4.98067 - 1.33457i) q^{43} +(6.26648 + 3.49623i) q^{45} +(-5.76715 + 9.98900i) q^{47} +(-9.12734 - 15.8090i) q^{49} +(3.03968 - 2.36811i) q^{51} +(7.80379 + 7.80379i) q^{53} +2.55361 q^{55} +(-1.69490 - 0.210484i) q^{57} +(-5.09824 - 1.36607i) q^{59} +(-6.48859 + 1.73861i) q^{61} +(-10.8159 - 10.5027i) q^{63} +(8.58985 + 4.95935i) q^{65} +(-8.22431 - 2.20370i) q^{67} +(-4.09277 - 1.66016i) q^{69} +12.0321i q^{71} +10.3710i q^{73} +(0.172181 + 1.23753i) q^{75} +(-5.18226 - 1.38858i) q^{77} +(7.74084 + 4.46918i) q^{79} +(-7.92307 - 4.26907i) q^{81} +(5.55149 - 1.48752i) q^{83} +(5.13998 + 1.37725i) q^{85} +(0.637375 - 0.843399i) q^{87} -6.56588 q^{89} +(-14.7354 - 14.7354i) q^{91} +(-0.353062 - 0.143214i) q^{93} +(-1.17930 - 2.04262i) q^{95} +(-1.51787 + 2.62902i) q^{97} +(-3.20243 + 0.0470514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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