LMFDB - Embedded newform 576.2.y.a.335.19

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			335.19
Character	$\chi$	$=$	576.335
Dual form			576.2.y.a.239.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.58764 + 0.692394i) q^{3} +(-2.83365 - 0.759273i) q^{5} +(-1.41719 + 2.45465i) q^{7} +(2.04118 + 2.19854i) q^{9} +O(q^{10})$	\(q+(1.58764 + 0.692394i) q^{3} +(-2.83365 - 0.759273i) q^{5} +(-1.41719 + 2.45465i) q^{7} +(2.04118 + 2.19854i) q^{9} +(-0.794578 + 0.212907i) q^{11} +(3.22468 + 0.864050i) q^{13} +(-3.97308 - 3.16745i) q^{15} +7.28589i q^{17} +(0.951758 + 0.951758i) q^{19} +(-3.94957 + 2.91583i) q^{21} +(-5.13217 + 2.96306i) q^{23} +(3.12293 + 1.80302i) q^{25} +(1.71840 + 4.90379i) q^{27} +(-1.76813 + 0.473770i) q^{29} +(-2.05610 + 1.18709i) q^{31} +(-1.40892 - 0.212143i) q^{33} +(5.87957 - 5.87957i) q^{35} +(6.03704 + 6.03704i) q^{37} +(4.52135 + 3.60455i) q^{39} +(-4.60866 - 7.98243i) q^{41} +(-0.402483 - 1.50209i) q^{43} +(-4.11469 - 7.77970i) q^{45} +(2.85832 - 4.95075i) q^{47} +(-0.516861 - 0.895230i) q^{49} +(-5.04471 + 11.5674i) q^{51} +(4.50856 - 4.50856i) q^{53} +2.41321 q^{55} +(0.852054 + 2.17004i) q^{57} +(2.85508 - 10.6553i) q^{59} +(-2.16531 - 8.08106i) q^{61} +(-8.28938 + 1.89463i) q^{63} +(-8.48155 - 4.89682i) q^{65} +(2.99423 - 11.1746i) q^{67} +(-10.1996 + 1.15078i) q^{69} +2.98978i q^{71} +12.7280i q^{73} +(3.70967 + 5.02484i) q^{75} +(0.603459 - 2.25214i) q^{77} +(8.94529 + 5.16457i) q^{79} +(-0.667162 + 8.97524i) q^{81} +(1.00404 + 3.74713i) q^{83} +(5.53198 - 20.6456i) q^{85} +(-3.13519 - 0.472070i) q^{87} +9.25017 q^{89} +(-6.69092 + 6.69092i) q^{91} +(-4.08627 + 0.461036i) q^{93} +(-1.97430 - 3.41959i) q^{95} +(0.148868 - 0.257847i) q^{97} +(-2.08996 - 1.31233i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

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

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
$3$	1.58764	+	0.692394i	0.916622	+	0.399754i
$3$	1.58764	+	0.692394i	0.916622	+	0.399754i
$4$		0			0
$5$	−2.83365	−	0.759273i	−1.26725	−	0.339557i	−0.438270	−	0.898843i	$-0.644409\pi$
$5$	−2.83365	−	0.759273i	−1.26725	−	0.339557i	−0.828975	+	0.559286i	$0.811075\pi$
$6$		0			0
$7$	−1.41719	+	2.45465i	−0.535648	+	0.927769i	0.463484	+	0.886105i	$0.346599\pi$
$7$	−1.41719	+	2.45465i	−0.535648	+	0.927769i	−0.999132	+	0.0416640i	$0.986734\pi$
$8$		0			0
$9$	2.04118	+	2.19854i	0.680394	+	0.732847i
$10$		0			0
$11$	−0.794578	+	0.212907i	−0.239574	+	0.0641937i	−0.376608	−	0.926373i	$-0.622910\pi$
$11$	−0.794578	+	0.212907i	−0.239574	+	0.0641937i	0.137034	+	0.990566i	$0.456243\pi$
$12$		0			0
$13$	3.22468	+	0.864050i	0.894365	+	0.239644i	0.676595	−	0.736356i	$-0.263455\pi$
$13$	3.22468	+	0.864050i	0.894365	+	0.239644i	0.217770	+	0.976000i	$0.430122\pi$
$14$		0			0
$15$	−3.97308	−	3.16745i	−1.02585	−	0.817832i
$16$		0			0
$17$			7.28589i			1.76709i	0.468348	+	0.883544i	$0.344849\pi$
$17$			7.28589i			1.76709i	−0.468348	+	0.883544i	$0.655151\pi$
$18$		0			0
$19$	0.951758	+	0.951758i	0.218348	+	0.218348i	0.807802	−	0.589454i	$-0.200657\pi$
$19$	0.951758	+	0.951758i	0.218348	+	0.218348i	−0.589454	+	0.807802i	$0.700657\pi$
$20$		0			0
$21$	−3.94957	+	2.91583i	−0.861866	+	0.636287i
$22$		0			0
$23$	−5.13217	+	2.96306i	−1.07013	+	0.617841i	−0.928218	−	0.372038i	$-0.878659\pi$
$23$	−5.13217	+	2.96306i	−1.07013	+	0.617841i	−0.141915	+	0.989879i	$0.545326\pi$
$24$		0			0
$25$	3.12293	+	1.80302i	0.624585	+	0.360605i
$26$		0			0
$27$	1.71840	+	4.90379i	0.330706	+	0.943734i
$28$		0			0
$29$	−1.76813	+	0.473770i	−0.328334	+	0.0879768i	−0.419221	−	0.907884i	$-0.637697\pi$
$29$	−1.76813	+	0.473770i	−0.328334	+	0.0879768i	0.0908866	+	0.995861i	$0.471030\pi$
$30$		0			0
$31$	−2.05610	+	1.18709i	−0.369286	+	0.213207i	−0.673147	−	0.739509i	$-0.735058\pi$
$31$	−2.05610	+	1.18709i	−0.369286	+	0.213207i	0.303860	+	0.952717i	$0.401724\pi$
$32$		0			0
$33$	−1.40892	−	0.212143i	−0.245261	−	0.0369293i
$34$		0			0
$35$	5.87957	−	5.87957i	0.993828	−	0.993828i
$36$		0			0
$37$	6.03704	+	6.03704i	0.992483	+	0.992483i	0.999972	−	0.00748933i	$-0.00238395\pi$
$37$	6.03704	+	6.03704i	0.992483	+	0.992483i	−0.00748933	+	0.999972i	$0.502384\pi$
$38$		0			0
$39$	4.52135	+	3.60455i	0.723996	+	0.577189i
$40$		0			0
$41$	−4.60866	−	7.98243i	−0.719751	−	1.24665i	−0.961098	−	0.276207i	$-0.910923\pi$
$41$	−4.60866	−	7.98243i	−0.719751	−	1.24665i	0.241347	−	0.970439i	$-0.422411\pi$
$42$		0			0
$43$	−0.402483	−	1.50209i	−0.0613780	−	0.229066i	0.928423	−	0.371526i	$-0.121165\pi$
$43$	−0.402483	−	1.50209i	−0.0613780	−	0.229066i	−0.989801	+	0.142460i	$0.954499\pi$
$44$		0			0
$45$	−4.11469	−	7.77970i	−0.613382	−	1.15973i
$46$		0			0
$47$	2.85832	−	4.95075i	0.416928	−	0.722141i	−0.578701	−	0.815540i	$-0.696440\pi$
$47$	2.85832	−	4.95075i	0.416928	−	0.722141i	0.995629	+	0.0933994i	$0.0297733\pi$
$48$		0			0
$49$	−0.516861	−	0.895230i	−0.0738373	−	0.127890i
$50$		0			0
$51$	−5.04471	+	11.5674i	−0.706401	+	1.61975i
$52$		0			0
$53$	4.50856	−	4.50856i	0.619298	−	0.619298i	−0.326053	−	0.945351i	$-0.605719\pi$
$53$	4.50856	−	4.50856i	0.619298	−	0.619298i	0.945351	+	0.326053i	$0.105719\pi$
$54$		0			0
$55$	2.41321			0.325397
$56$		0			0
$57$	0.852054	+	2.17004i	0.112857	+	0.287429i
$58$		0			0
$59$	2.85508	−	10.6553i	0.371700	−	1.38720i	−0.486407	−	0.873732i	$-0.661693\pi$
$59$	2.85508	−	10.6553i	0.371700	−	1.38720i	0.858107	−	0.513471i	$-0.171640\pi$
$60$		0			0
$61$	−2.16531	−	8.08106i	−0.277240	−	1.03467i	−0.954325	−	0.298769i	$-0.903424\pi$
$61$	−2.16531	−	8.08106i	−0.277240	−	1.03467i	0.677086	−	0.735904i	$-0.263243\pi$
$62$		0			0
$63$	−8.28938	+	1.89463i	−1.04436	+	0.238700i
$64$		0			0
$65$	−8.48155	−	4.89682i	−1.05201	−	0.607376i
$66$		0			0
$67$	2.99423	−	11.1746i	0.365804	−	1.36520i	−0.500524	−	0.865723i	$-0.666859\pi$
$67$	2.99423	−	11.1746i	0.365804	−	1.36520i	0.866328	−	0.499476i	$-0.166474\pi$
$68$		0			0
$69$	−10.1996	+	1.15078i	−1.22789	+	0.138538i
$70$		0			0
$71$			2.98978i			0.354821i	0.984137	+	0.177411i	$0.0567721\pi$
$71$			2.98978i			0.354821i	−0.984137	+	0.177411i	$0.943228\pi$
$72$		0			0
$73$			12.7280i			1.48970i	0.667229	+	0.744852i	$0.267480\pi$
$73$			12.7280i			1.48970i	−0.667229	+	0.744852i	$0.732520\pi$
$74$		0			0
$75$	3.70967	+	5.02484i	0.428356	+	0.580219i
$76$		0			0
$77$	0.603459	−	2.25214i	0.0687705	−	0.256655i
$78$		0			0
$79$	8.94529	+	5.16457i	1.00642	+	0.581059i	0.910143	−	0.414295i	$-0.135972\pi$
$79$	8.94529	+	5.16457i	1.00642	+	0.581059i	0.0962815	+	0.995354i	$0.469305\pi$
$80$		0			0
$81$	−0.667162	+	8.97524i	−0.0741291	+	0.997249i
$82$		0			0
$83$	1.00404	+	3.74713i	0.110208	+	0.411301i	0.998884	−	0.0472343i	$-0.0150407\pi$
$83$	1.00404	+	3.74713i	0.110208	+	0.411301i	−0.888676	+	0.458536i	$0.848374\pi$
$84$		0			0
$85$	5.53198	−	20.6456i	0.600028	−	2.23933i
$86$		0			0
$87$	−3.13519	−	0.472070i	−0.336127	−	0.0506113i
$88$		0			0
$89$	9.25017			0.980516			0.490258	−	0.871577i	$-0.336903\pi$
$89$	9.25017			0.980516			0.490258	+	0.871577i	$0.336903\pi$
$90$		0			0
$91$	−6.69092	+	6.69092i	−0.701399	+	0.701399i
$92$		0			0
$93$	−4.08627	+	0.461036i	−0.423727	+	0.0478072i
$94$		0			0
$95$	−1.97430	−	3.41959i	−0.202559	−	0.350843i
$96$		0			0
$97$	0.148868	−	0.257847i	0.0151153	−	0.0261804i	−0.858369	−	0.513033i	$-0.828522\pi$
$97$	0.148868	−	0.257847i	0.0151153	−	0.0261804i	0.873484	+	0.486853i	$0.161855\pi$
$98$		0			0
$99$	−2.08996	−	1.31233i	−0.210049	−	0.131894i
$100$		0			0
$101$	2.11843	+	7.90610i	0.210792	+	0.786687i	0.987606	+	0.156956i	$0.0501681\pi$
$101$	2.11843	+	7.90610i	0.210792	+	0.786687i	−0.776814	+	0.629731i	$0.783165\pi$
$102$		0			0
$103$	5.72414	+	9.91450i	0.564016	+	0.976905i	0.997140	+	0.0755707i	$0.0240779\pi$
$103$	5.72414	+	9.91450i	0.564016	+	0.976905i	−0.433124	+	0.901334i	$0.642589\pi$
$104$		0			0
$105$	13.4056	−	5.26364i	1.30825	−	0.513678i
$106$		0			0
$107$	0.174948	+	0.174948i	0.0169128	+	0.0169128i	0.715513	−	0.698600i	$-0.246193\pi$
$107$	0.174948	+	0.174948i	0.0169128	+	0.0169128i	−0.698600	+	0.715513i	$0.746193\pi$
$108$		0			0
$109$	1.50900	−	1.50900i	0.144536	−	0.144536i	−0.631136	−	0.775672i	$-0.717411\pi$
$109$	1.50900	−	1.50900i	0.144536	−	0.144536i	0.775672	+	0.631136i	$0.217411\pi$
$110$		0			0
$111$	5.40461	+	13.7646i	0.512983	+	1.30648i
$112$		0			0
$113$	−0.513633	+	0.296546i	−0.0483185	+	0.0278967i	−0.523965	−	0.851740i	$-0.675548\pi$
$113$	−0.513633	+	0.296546i	−0.0483185	+	0.0278967i	0.475646	+	0.879637i	$0.342214\pi$
$114$		0			0
$115$	16.7925	−	4.49955i	1.56591	−	0.419585i
$116$		0			0
$117$	4.68250	+	8.85327i	0.432898	+	0.818485i
$118$		0			0
$119$	−17.8843	−	10.3255i	−1.63945	−	0.946537i
$120$		0			0
$121$	−8.94025	+	5.16166i	−0.812750	+	0.469242i
$122$		0			0
$123$	−1.78989	−	15.8642i	−0.161389	−	1.43043i
$124$		0			0
$125$	2.89158	+	2.89158i	0.258631	+	0.258631i
$126$		0			0
$127$		−	14.1816i		−	1.25841i	−0.777240	−	0.629205i	$-0.783381\pi$
$127$		−	14.1816i		−	1.25841i	0.777240	−	0.629205i	$-0.216619\pi$
$128$		0			0
$129$	0.401039	−	2.66344i	0.0353095	−	0.234503i
$130$		0			0
$131$	−3.86197	−	1.03481i	−0.337422	−	0.0904119i	0.0861298	−	0.996284i	$-0.472550\pi$
$131$	−3.86197	−	1.03481i	−0.337422	−	0.0904119i	−0.423551	+	0.905872i	$0.639217\pi$
$132$		0			0
$133$	−3.68505	+	0.987407i	−0.319535	+	0.0856190i
$134$		0			0
$135$	−1.14602	−	15.2003i	−0.0986333	−	1.30824i
$136$		0			0
$137$	3.98207	−	6.89714i	0.340211	−	0.589262i	−0.644261	−	0.764806i	$-0.722835\pi$
$137$	3.98207	−	6.89714i	0.340211	−	0.589262i	0.984472	+	0.175543i	$0.0561682\pi$
$138$		0			0
$139$	−10.3155	−	2.76404i	−0.874952	−	0.234443i	−0.206724	−	0.978399i	$-0.566280\pi$
$139$	−10.3155	−	2.76404i	−0.874952	−	0.234443i	−0.668228	+	0.743957i	$0.732947\pi$
$140$		0			0
$141$	7.96583	−	5.88091i	0.670844	−	0.495262i
$142$		0			0
$143$	−2.74622			−0.229651
$144$		0			0
$145$	5.36998			0.445953
$146$		0			0
$147$	−0.200736	−	1.77917i	−0.0165564	−	0.146744i
$148$		0			0
$149$	4.24117	+	1.13642i	0.347450	+	0.0930990i	0.428324	−	0.903625i	$-0.359104\pi$
$149$	4.24117	+	1.13642i	0.347450	+	0.0930990i	−0.0808734	+	0.996724i	$0.525771\pi$
$150$		0			0
$151$	6.93783	−	12.0167i	0.564592	−	0.977903i	−0.432495	−	0.901636i	$-0.642367\pi$
$151$	6.93783	−	12.0167i	0.564592	−	0.977903i	0.997087	−	0.0762664i	$-0.0242999\pi$
$152$		0			0
$153$	−16.0183	+	14.8718i	−1.29501	+	1.20232i
$154$		0			0
$155$	6.72758	−	1.80265i	0.540372	−	0.144792i
$156$		0			0
$157$	6.01560	+	1.61187i	0.480097	+	0.128642i	0.490748	−	0.871302i	$-0.336724\pi$
$157$	6.01560	+	1.61187i	0.480097	+	0.128642i	−0.0106509	+	0.999943i	$0.503390\pi$
$158$		0			0
$159$	10.2797	−	4.03625i	0.815229	−	0.320096i
$160$		0			0
$161$		−	16.7969i		−	1.32378i
$162$		0			0
$163$	−3.39010	−	3.39010i	−0.265533	−	0.265533i	0.561764	−	0.827297i	$-0.310123\pi$
$163$	−3.39010	−	3.39010i	−0.265533	−	0.265533i	−0.827297	+	0.561764i	$0.810123\pi$
$164$		0			0
$165$	3.83130	+	1.67089i	0.298266	+	0.130079i
$166$		0			0
$167$	−8.58610	+	4.95718i	−0.664412	+	0.383598i	−0.793956	−	0.607975i	$-0.791982\pi$
$167$	−8.58610	+	4.95718i	−0.664412	+	0.383598i	0.129544	+	0.991574i	$0.458649\pi$
$168$		0			0
$169$	−1.60636	−	0.927433i	−0.123566	−	0.0713410i
$170$		0			0
$171$	−0.149769	+	4.03519i	−0.0114531	+	0.308579i
$172$		0			0
$173$	−7.25249	+	1.94330i	−0.551396	+	0.147746i	−0.523751	−	0.851872i	$-0.675468\pi$
$173$	−7.25249	+	1.94330i	−0.551396	+	0.147746i	−0.0276457	+	0.999618i	$0.508801\pi$
$174$		0			0
$175$	−8.85157	+	5.11046i	−0.669116	+	0.386314i
$176$		0			0
$177$	11.9105	−	14.9399i	0.895248	−	1.12295i
$178$		0			0
$179$	0.604756	−	0.604756i	0.0452016	−	0.0452016i	−0.684145	−	0.729346i	$-0.739824\pi$
$179$	0.604756	−	0.604756i	0.0452016	−	0.0452016i	0.729346	+	0.684145i	$0.239824\pi$
$180$		0			0
$181$	−10.1716	−	10.1716i	−0.756048	−	0.756048i	0.219553	−	0.975601i	$-0.429540\pi$
$181$	−10.1716	−	10.1716i	−0.756048	−	0.756048i	−0.975601	+	0.219553i	$0.929540\pi$
$182$		0			0
$183$	2.15755	−	14.3290i	0.159490	−	1.05923i
$184$		0			0
$185$	−12.5231	−	21.6906i	−0.920714	−	1.59472i
$186$		0			0
$187$	−1.55121	−	5.78921i	−0.113436	−	0.423349i
$188$		0			0
$189$	−14.4724	−	2.73154i	−1.05271	−	0.198691i
$190$		0			0
$191$	−5.80282	+	10.0508i	−0.419877	+	0.727249i	−0.995927	−	0.0901660i	$-0.971260\pi$
$191$	−5.80282	+	10.0508i	−0.419877	+	0.727249i	0.576049	+	0.817415i	$0.304594\pi$
$192$		0			0
$193$	5.09572	+	8.82605i	0.366798	+	0.635313i	0.989063	−	0.147494i	$-0.0471206\pi$
$193$	5.09572	+	8.82605i	0.366798	+	0.635313i	−0.622265	+	0.782807i	$0.713787\pi$
$194$		0			0
$195$	−10.0751	−	13.6470i	−0.721492	−	0.977278i
$196$		0			0
$197$	4.32430	−	4.32430i	0.308094	−	0.308094i	−0.536076	−	0.844170i	$-0.680094\pi$
$197$	4.32430	−	4.32430i	0.308094	−	0.308094i	0.844170	+	0.536076i	$0.180094\pi$
$198$		0			0
$199$	27.7260			1.96544			0.982720	−	0.185097i	$-0.0592599\pi$
$199$	27.7260			1.96544			0.982720	+	0.185097i	$0.0592599\pi$
$200$		0			0
$201$	12.4910	−	15.6681i	0.881047	−	1.10514i
$202$		0			0
$203$	1.34284	−	5.01156i	0.0942492	−	0.351743i
$204$		0			0
$205$	6.99846	+	26.1186i	0.488793	+	1.82420i
$206$		0			0
$207$	−16.9901	−	5.23515i	−1.18089	−	0.363868i
$208$		0			0
$209$	−0.958882	−	0.553611i	−0.0663272	−	0.0382940i
$210$		0			0
$211$	−5.10152	+	19.0391i	−0.351203	+	1.31071i	0.533993	+	0.845489i	$0.320691\pi$
$211$	−5.10152	+	19.0391i	−0.351203	+	1.31071i	−0.885196	+	0.465219i	$0.845976\pi$
$212$		0			0
$213$	−2.07010	+	4.74668i	−0.141841	+	0.325237i
$214$		0			0
$215$			4.56197i			0.311124i
$216$		0			0
$217$		−	6.72933i		−	0.456817i
$218$		0			0
$219$	−8.81282	+	20.2075i	−0.595515	+	1.36550i
$220$		0			0
$221$	−6.29538	+	23.4947i	−0.423473	+	1.58042i
$222$		0			0
$223$	10.9074	+	6.29741i	0.730416	+	0.421706i	0.818574	−	0.574401i	$-0.194765\pi$
$223$	10.9074	+	6.29741i	0.730416	+	0.421706i	−0.0881582	+	0.996106i	$0.528098\pi$
$224$		0			0
$225$	2.41044	+	10.5462i	0.160696	+	0.703079i
$226$		0			0
$227$	3.12014	+	11.6445i	0.207091	+	0.772874i	0.988802	+	0.149233i	$0.0476805\pi$
$227$	3.12014	+	11.6445i	0.207091	+	0.772874i	−0.781711	+	0.623641i	$0.785653\pi$
$228$		0			0
$229$	1.46608	−	5.47149i	0.0968814	−	0.361566i	−0.900417	−	0.435029i	$-0.856738\pi$
$229$	1.46608	−	5.47149i	0.0968814	−	0.361566i	0.997298	+	0.0734624i	$0.0234049\pi$
$230$		0			0
$231$	2.51744	−	3.15775i	0.165635	−	0.207764i
$232$		0			0
$233$	−10.1291			−0.663580			−0.331790	−	0.943353i	$-0.607653\pi$
$233$	−10.1291			−0.663580			−0.331790	+	0.943353i	$0.607653\pi$
$234$		0			0
$235$	−11.8584	+	11.8584i	−0.773558	+	0.773558i
$236$		0			0
$237$	10.6260	+	14.3931i	0.690230	+	0.934934i
$238$		0			0
$239$	0.263562	+	0.456503i	0.0170484	+	0.0295287i	0.874424	−	0.485163i	$-0.161240\pi$
$239$	0.263562	+	0.456503i	0.0170484	+	0.0295287i	−0.857375	+	0.514692i	$0.827906\pi$
$240$		0			0
$241$	9.74338	−	16.8760i	0.627626	−	1.08708i	−0.360400	−	0.932798i	$-0.617360\pi$
$241$	9.74338	−	16.8760i	0.627626	−	1.08708i	0.988027	−	0.154283i	$-0.0493068\pi$
$242$		0			0
$243$	−7.27361	+	13.7875i	−0.466603	+	0.884467i
$244$		0			0
$245$	0.784878	+	2.92920i	0.0501440	+	0.187140i
$246$		0			0
$247$	2.24675	+	3.89148i	0.142957	+	0.247609i
$248$		0			0
$249$	−1.00044	+	6.64428i	−0.0634003	+	0.421064i
$250$		0			0
$251$	17.9199	+	17.9199i	1.13110	+	1.13110i	0.989995	+	0.141101i	$0.0450643\pi$
$251$	17.9199	+	17.9199i	1.13110	+	1.13110i	0.141101	+	0.989995i	$0.454936\pi$
$252$		0			0
$253$	3.44706	−	3.44706i	0.216715	−	0.216715i
$254$		0			0
$255$	23.0777	−	28.9475i	1.44518	−	1.81276i
$256$		0			0
$257$	14.6152	−	8.43809i	0.911671	−	0.526353i	0.0307025	−	0.999529i	$-0.490226\pi$
$257$	14.6152	−	8.43809i	0.911671	−	0.526353i	0.880968	+	0.473175i	$0.156892\pi$
$258$		0			0
$259$	−23.3744	+	6.26316i	−1.45242	+	0.389174i
$260$		0			0
$261$	−4.65068	−	2.92026i	−0.287870	−	0.180760i
$262$		0			0
$263$	18.8065	+	10.8579i	1.15966	+	0.669528i	0.951222	−	0.308508i	$-0.0998297\pi$
$263$	18.8065	+	10.8579i	1.15966	+	0.669528i	0.208435	+	0.978036i	$0.433163\pi$
$264$		0			0
$265$	−16.1989	+	9.35243i	−0.995090	+	0.574515i
$266$		0			0
$267$	14.6859	+	6.40476i	0.898763	+	0.391965i
$268$		0			0
$269$	3.50729	+	3.50729i	0.213843	+	0.213843i	0.805898	−	0.592055i	$-0.201683\pi$
$269$	3.50729	+	3.50729i	0.213843	+	0.213843i	−0.592055	+	0.805898i	$0.701683\pi$
$270$		0			0
$271$			2.25749i			0.137133i	0.997647	+	0.0685665i	$0.0218425\pi$
$271$			2.25749i			0.137133i	−0.997647	+	0.0685665i	$0.978157\pi$
$272$		0			0
$273$	−15.2555	+	5.99000i	−0.923306	+	0.362531i
$274$		0			0
$275$	−2.86529	−	0.767751i	−0.172783	−	0.0462971i
$276$		0			0
$277$	−17.7581	+	4.75826i	−1.06698	+	0.285896i	−0.749251	−	0.662286i	$-0.769586\pi$
$277$	−17.7581	+	4.75826i	−1.06698	+	0.285896i	−0.317727	+	0.948182i	$0.602920\pi$
$278$		0			0
$279$	−6.80673	−	2.09735i	−0.407508	−	0.125565i
$280$		0			0
$281$	−4.38270	+	7.59106i	−0.261450	+	0.452845i	−0.966627	−	0.256186i	$-0.917534\pi$
$281$	−4.38270	+	7.59106i	−0.261450	+	0.452845i	0.705177	+	0.709031i	$0.250867\pi$
$282$		0			0
$283$	15.6177	+	4.18474i	0.928375	+	0.248757i	0.691161	−	0.722700i	$-0.257099\pi$
$283$	15.6177	+	4.18474i	0.928375	+	0.248757i	0.237213	+	0.971458i	$0.423766\pi$
$284$		0			0
$285$	−0.766769	−	6.79606i	−0.0454195	−	0.402564i
$286$		0			0
$287$	26.1254			1.54213
$288$		0			0
$289$	−36.0842			−2.12260
$290$		0			0
$291$	0.414880	−	0.306292i	0.0243207	−	0.0179552i
$292$		0			0
$293$	12.1120	+	3.24540i	0.707589	+	0.189598i	0.594628	−	0.804001i	$-0.297300\pi$
$293$	12.1120	+	3.24540i	0.707589	+	0.189598i	0.112962	+	0.993599i	$0.463966\pi$
$294$		0			0
$295$	−16.1806	+	28.0256i	−0.942070	+	1.63171i
$296$		0			0
$297$	−2.40945	−	3.53058i	−0.139810	−	0.204865i
$298$		0			0
$299$	−19.1098	+	5.12047i	−1.10515	+	0.296124i
$300$		0			0
$301$	4.25749	+	1.14079i	0.245397	+	0.0657540i
$302$		0			0
$303$	−2.11084	+	14.0188i	−0.121264	+	0.805360i
$304$		0			0
$305$			24.5429i			1.40532i
$306$		0			0
$307$	−18.9168	−	18.9168i	−1.07964	−	1.07964i	−0.996542	−	0.0830950i	$-0.973519\pi$
$307$	−18.9168	−	18.9168i	−1.07964	−	1.07964i	−0.0830950	−	0.996542i	$-0.526481\pi$
$308$		0			0
$309$	2.22311	+	19.7040i	0.126468	+	1.12092i
$310$		0			0
$311$	5.08666	−	2.93678i	0.288438	−	0.166530i	−0.348799	−	0.937197i	$-0.613411\pi$
$311$	5.08666	−	2.93678i	0.288438	−	0.166530i	0.637237	+	0.770668i	$0.280077\pi$
$312$		0			0
$313$	−14.3490	−	8.28438i	−0.811051	−	0.468261i	0.0362694	−	0.999342i	$-0.488453\pi$
$313$	−14.3490	−	8.28438i	−0.811051	−	0.468261i	−0.847321	+	0.531081i	$0.821786\pi$
$314$		0			0
$315$	24.9277	+	0.925208i	1.40452	+	0.0521296i
$316$		0			0
$317$	−6.73750	+	1.80531i	−0.378416	+	0.101396i	−0.443013	−	0.896515i	$-0.646090\pi$
$317$	−6.73750	+	1.80531i	−0.378416	+	0.101396i	0.0645973	+	0.997911i	$0.479424\pi$
$318$		0			0
$319$	1.30405	−	0.752894i	0.0730128	−	0.0421540i
$320$		0			0
$321$	0.156621	+	0.398886i	0.00874171	+	0.0222636i
$322$		0			0
$323$	−6.93441	+	6.93441i	−0.385841	+	0.385841i
$324$		0			0
$325$	8.51253	+	8.51253i	0.472190	+	0.472190i
$326$		0			0
$327$	3.44058	−	1.35092i	0.190264	−	0.0747063i
$328$		0			0
$329$	8.10156	+	14.0323i	0.446653	+	0.773626i
$330$		0			0
$331$	−5.83736	−	21.7853i	−0.320850	−	1.19743i	−0.918418	−	0.395612i	$-0.870533\pi$
$331$	−5.83736	−	21.7853i	−0.320850	−	1.19743i	0.597567	−	0.801819i	$-0.296134\pi$
$332$		0			0
$333$	−0.949988	+	25.5954i	−0.0520590	+	1.40262i
$334$		0			0
$335$	−16.9692	+	29.3915i	−0.927126	+	1.60583i
$336$		0			0
$337$	5.04210	+	8.73317i	0.274661	+	0.475726i	0.970049	−	0.242908i	$-0.0781012\pi$
$337$	5.04210	+	8.73317i	0.274661	+	0.475726i	−0.695389	+	0.718634i	$0.744768\pi$
$338$		0			0
$339$	−1.02079	+	0.115171i	−0.0554416	+	0.00625523i
$340$		0			0
$341$	1.38099	−	1.38099i	0.0747849	−	0.0747849i
$342$		0			0
$343$	−16.9107			−0.913093
$344$		0			0
$345$	29.7759	+	4.48341i	1.60308	+	0.241379i
$346$		0			0
$347$	7.70540	−	28.7569i	0.413647	−	1.54375i	−0.373882	−	0.927476i	$-0.621974\pi$
$347$	7.70540	−	28.7569i	0.413647	−	1.54375i	0.787530	−	0.616277i	$-0.211360\pi$
$348$		0			0
$349$	−2.31845	−	8.65259i	−0.124104	−	0.463163i	0.875702	−	0.482852i	$-0.160399\pi$
$349$	−2.31845	−	8.65259i	−0.124104	−	0.463163i	−0.999806	+	0.0196892i	$0.993732\pi$
$350$		0			0
$351$	1.30416	+	17.2979i	0.0696110	+	0.923294i
$352$		0			0
$353$	28.1794	+	16.2694i	1.49984	+	0.865933i	1.00000		0.000184008i	$-5.85715e-5\pi$
$353$	28.1794	+	16.2694i	1.49984	+	0.865933i	0.499841	+	0.866117i	$0.333392\pi$
$354$		0			0
$355$	2.27006	−	8.47197i	0.120482	−	0.449645i
$356$		0			0
$357$	−21.2444	−	28.7761i	−1.12438	−	1.52299i
$358$		0			0
$359$			0.581843i			0.0307085i	0.999882	+	0.0153542i	$0.00488760\pi$
$359$			0.581843i			0.0307085i	−0.999882	+	0.0153542i	$0.995112\pi$
$360$		0			0
$361$		−	17.1883i		−	0.904648i
$362$		0			0
$363$	−17.7678	+	2.00466i	−0.932566	+	0.105217i
$364$		0			0
$365$	9.66406	−	36.0668i	0.505840	−	1.88782i
$366$		0			0
$367$	−3.68240	−	2.12603i	−0.192220	−	0.110978i	0.400802	−	0.916165i	$-0.368732\pi$
$367$	−3.68240	−	2.12603i	−0.192220	−	0.110978i	−0.593021	+	0.805187i	$0.702065\pi$
$368$		0			0
$369$	8.14259	−	26.4259i	0.423886	−	1.37568i
$370$		0			0
$371$	4.67743	+	17.4564i	0.242840	+	0.906291i
$372$		0			0
$373$	−1.61385	+	6.02298i	−0.0835621	+	0.311858i	−0.995038	−	0.0994955i	$-0.968277\pi$
$373$	−1.61385	+	6.02298i	−0.0835621	+	0.311858i	0.911476	+	0.411353i	$0.134944\pi$
$374$		0			0
$375$	2.58867	+	6.59289i	0.133678	+	0.340456i
$376$		0			0
$377$	−6.11102			−0.314733
$378$		0			0
$379$	8.99791	−	8.99791i	0.462192	−	0.462192i	−0.437182	−	0.899373i	$-0.644023\pi$
$379$	8.99791	−	8.99791i	0.462192	−	0.462192i	0.899373	+	0.437182i	$0.144023\pi$
$380$		0			0
$381$	9.81923	−	22.5152i	0.503054	−	1.15349i
$382$		0			0
$383$	−4.35960	−	7.55105i	−0.222765	−	0.385840i	0.732882	−	0.680356i	$-0.238175\pi$
$383$	−4.35960	−	7.55105i	−0.222765	−	0.385840i	−0.955647	+	0.294516i	$0.904842\pi$
$384$		0			0
$385$	−3.41998	+	5.92357i	−0.174298	+	0.301893i
$386$		0			0
$387$	2.48086	−	3.95090i	0.126109	−	0.200836i
$388$		0			0
$389$	7.20893	+	26.9041i	0.365507	+	1.36409i	0.866732	+	0.498774i	$0.166216\pi$
$389$	7.20893	+	26.9041i	0.365507	+	1.36409i	−0.501225	+	0.865317i	$0.667117\pi$
$390$		0			0
$391$	−21.5886	−	37.3925i	−1.09178	−	1.89102i
$392$		0			0
$393$	−5.41490	−	4.31691i	−0.273146	−	0.217759i
$394$		0			0
$395$	−21.4265	−	21.4265i	−1.07808	−	1.07808i
$396$		0			0
$397$	3.82319	−	3.82319i	0.191880	−	0.191880i	−0.604628	−	0.796508i	$-0.706678\pi$
$397$	3.82319	−	3.82319i	0.191880	−	0.191880i	0.796508	+	0.604628i	$0.206678\pi$
$398$		0			0
$399$	−6.53420	−	0.983866i	−0.327119	−	0.0492549i
$400$		0			0
$401$	−24.9442	+	14.4015i	−1.24565	+	0.719178i	−0.970239	−	0.242148i	$-0.922148\pi$
$401$	−24.9442	+	14.4015i	−1.24565	+	0.719178i	−0.275414	+	0.961326i	$0.588815\pi$
$402$		0			0
$403$	−7.65596	+	2.05141i	−0.381371	+	0.102188i
$404$		0			0
$405$	8.70516	−	24.9261i	0.432563	−	1.23859i
$406$		0			0
$407$	−6.08222	−	3.51157i	−0.301485	−	0.174062i
$408$		0			0
$409$	9.11179	−	5.26069i	0.450549	−	0.260125i	−0.257513	−	0.966275i	$-0.582903\pi$
$409$	9.11179	−	5.26069i	0.450549	−	0.260125i	0.708062	+	0.706150i	$0.249570\pi$
$410$		0			0
$411$	11.0976	−	8.19299i	0.547405	−	0.404131i
$412$		0			0
$413$	22.1088	+	22.1088i	1.08790	+	1.08790i
$414$		0			0
$415$		−	11.3804i		−	0.558642i
$416$		0			0
$417$	−14.4635	−	11.5307i	−0.708281	−	0.564661i
$418$		0			0
$419$	12.4024	+	3.32320i	0.605895	+	0.162349i	0.548708	−	0.836014i	$-0.315120\pi$
$419$	12.4024	+	3.32320i	0.605895	+	0.162349i	0.0571875	+	0.998363i	$0.481787\pi$
$420$		0			0
$421$	−9.21476	+	2.46909i	−0.449100	+	0.120336i	−0.476278	−	0.879295i	$-0.658015\pi$
$421$	−9.21476	+	2.46909i	−0.449100	+	0.120336i	0.0271782	+	0.999631i	$0.491348\pi$
$422$		0			0
$423$	16.7188	−	3.82125i	0.812894	−	0.185795i
$424$		0			0
$425$	−13.1366	+	22.7533i	−0.637220	+	1.10370i
$426$		0			0
$427$	22.9048	+	6.13732i	1.10844	+	0.297006i
$428$		0			0
$429$	−4.36000	−	1.90147i	−0.210503	−	0.0918037i
$430$		0			0
$431$	16.4451			0.792131			0.396065	−	0.918222i	$-0.370375\pi$
$431$	16.4451			0.792131			0.396065	+	0.918222i	$0.370375\pi$
$432$		0			0
$433$	−3.51715			−0.169023			−0.0845116	−	0.996422i	$-0.526933\pi$
$433$	−3.51715			−0.169023			−0.0845116	+	0.996422i	$0.526933\pi$
$434$		0			0
$435$	8.52558	+	3.71814i	0.408770	+	0.178271i
$436$		0			0
$437$	−7.70471	−	2.06447i	−0.368566	−	0.0987570i
$438$		0			0
$439$	−10.4483	+	18.0969i	−0.498668	+	0.863719i	−0.999999	−	0.00153725i	$-0.999511\pi$
$439$	−10.4483	+	18.0969i	−0.498668	+	0.863719i	0.501331	+	0.865256i	$0.332844\pi$
$440$		0			0
$441$	0.913192	−	2.96367i	0.0434854	−	0.141127i
$442$		0			0
$443$	−10.6793	+	2.86151i	−0.507389	+	0.135954i	−0.503427	−	0.864038i	$-0.667928\pi$
$443$	−10.6793	+	2.86151i	−0.507389	+	0.135954i	−0.00396162	+	0.999992i	$0.501261\pi$
$444$		0			0
$445$	−26.2117	−	7.02341i	−1.24255	−	0.332941i
$446$		0			0
$447$	5.94659	+	4.74078i	0.281264	+	0.224231i
$448$		0			0
$449$		−	17.5860i		−	0.829933i	−0.909837	−	0.414966i	$-0.863793\pi$
$449$		−	17.5860i		−	0.829933i	0.909837	−	0.414966i	$-0.136207\pi$
$450$		0			0
$451$	5.36145	+	5.36145i	0.252461	+	0.252461i
$452$		0			0
$453$	19.3350	−	14.2744i	0.908439	−	0.670670i
$454$		0			0
$455$	24.0399	−	13.8795i	1.12701	−	0.650680i
$456$		0			0
$457$	18.6606	+	10.7737i	0.872905	+	0.503972i	0.868313	−	0.496017i	$-0.165205\pi$
$457$	18.6606	+	10.7737i	0.872905	+	0.503972i	0.00459262	+	0.999989i	$0.498538\pi$
$458$		0			0
$459$	−35.7285	+	12.5201i	−1.66766	+	0.584386i
$460$		0			0
$461$	−16.9925	+	4.55312i	−0.791419	+	0.212060i	−0.631813	−	0.775121i	$-0.717689\pi$
$461$	−16.9925	+	4.55312i	−0.791419	+	0.212060i	−0.159606	+	0.987181i	$0.551022\pi$
$462$		0			0
$463$	−18.4389	+	10.6457i	−0.856930	+	0.494749i	−0.862983	−	0.505233i	$-0.831407\pi$
$463$	−18.4389	+	10.6457i	−0.856930	+	0.494749i	0.00605328	+	0.999982i	$0.498073\pi$
$464$		0			0
$465$	11.9291	+	1.79618i	0.553199	+	0.0832960i
$466$		0			0
$467$	2.62864	−	2.62864i	0.121639	−	0.121639i	−0.643667	−	0.765306i	$-0.722588\pi$
$467$	2.62864	−	2.62864i	0.121639	−	0.121639i	0.765306	+	0.643667i	$0.222588\pi$
$468$		0			0
$469$	23.1864	+	23.1864i	1.07065	+	1.07065i
$470$		0			0
$471$	8.43453	+	6.72423i	0.388643	+	0.309836i
$472$		0			0
$473$	0.639608	+	1.10783i	0.0294092	+	0.0509382i
$474$		0			0
$475$	1.25623	+	4.68831i	0.0576398	+	0.215115i
$476$		0			0
$477$	19.1150	+	0.709466i	0.875217	+	0.0324842i
$478$		0			0
$479$	10.7530	−	18.6247i	0.491317	−	0.850986i	−0.508633	−	0.860983i	$-0.669849\pi$
$479$	10.7530	−	18.6247i	0.491317	−	0.850986i	0.999950	+	0.00999740i	$0.00318233\pi$
$480$		0			0
$481$	14.2512	+	24.6838i	0.649799	+	1.12548i
$482$		0			0
$483$	11.6301	−	26.6674i	0.529187	−	1.21341i
$484$		0			0
$485$	−0.617616	+	0.617616i	−0.0280445	+	0.0280445i
$486$		0			0
$487$	14.6445			0.663607			0.331804	−	0.943348i	$-0.392343\pi$
$487$	14.6445			0.663607			0.331804	+	0.943348i	$0.392343\pi$
$488$		0			0
$489$	−3.03496	−	7.72953i	−0.137246	−	0.349541i
$490$		0			0
$491$	−11.3160	+	42.2317i	−0.510682	+	1.90589i	−0.0975209	+	0.995233i	$0.531091\pi$
$491$	−11.3160	+	42.2317i	−0.510682	+	1.90589i	−0.413161	+	0.910658i	$0.635575\pi$
$492$		0			0
$493$	−3.45183	−	12.8824i	−0.155463	−	0.580195i
$494$		0			0
$495$	4.92579	+	5.30553i	0.221398	+	0.238466i
$496$		0			0
$497$	−7.33885	−	4.23708i	−0.329192	−	0.190059i
$498$		0			0
$499$	2.12060	−	7.91419i	0.0949311	−	0.354288i	−0.902078	−	0.431573i	$-0.857959\pi$
$499$	2.12060	−	7.91419i	0.0949311	−	0.354288i	0.997009	+	0.0772856i	$0.0246253\pi$
$500$		0			0
$501$	−17.0639	+	1.92525i	−0.762360	+	0.0860137i
$502$		0			0
$503$		−	1.90408i		−	0.0848988i	−0.999099	−	0.0424494i	$-0.986484\pi$
$503$		−	1.90408i		−	0.0848988i	0.999099	−	0.0424494i	$-0.0135161\pi$
$504$		0			0
$505$		−	24.0116i		−	1.06850i
$506$		0			0
$507$	−1.90817	−	2.58466i	−0.0847447	−	0.114789i
$508$		0			0
$509$	−1.95009	+	7.27785i	−0.0864364	+	0.322585i	−0.995582	−	0.0938926i	$-0.970069\pi$
$509$	−1.95009	+	7.27785i	−0.0864364	+	0.322585i	0.909146	+	0.416478i	$0.136736\pi$
$510$		0			0
$511$	−31.2428	−	18.0381i	−1.38210	−	0.797957i
$512$		0			0
$513$	−3.03172	+	6.30272i	−0.133854	+	0.278272i
$514$		0			0
$515$	−8.69237	−	32.4404i	−0.383032	−	1.42949i
$516$		0			0
$517$	−1.21711	+	4.54231i	−0.0535284	+	0.199771i
$518$		0			0
$519$	−12.8598	−	1.93633i	−0.564484	−	0.0849954i
$520$		0			0
$521$	29.5974			1.29669			0.648343	−	0.761349i	$-0.275462\pi$
$521$	29.5974			1.29669			0.648343	+	0.761349i	$0.275462\pi$
$522$		0			0
$523$	−29.1710	+	29.1710i	−1.27556	+	1.27556i	−0.332431	+	0.943128i	$0.607869\pi$
$523$	−29.1710	+	29.1710i	−1.27556	+	1.27556i	−0.943128	+	0.332431i	$0.892131\pi$
$524$		0			0
$525$	−17.5915	+	1.98477i	−0.767757	+	0.0866226i
$526$		0			0
$527$	−8.64900	−	14.9805i	−0.376756	−	0.652561i
$528$		0			0
$529$	6.05948	−	10.4953i	0.263456	−	0.456318i
$530$		0			0
$531$	29.2539	−	15.4724i	1.26951	−	0.671445i
$532$		0			0
$533$	−7.96422	−	29.7229i	−0.344969	−	1.28744i
$534$		0			0
$535$	−0.362907	−	0.628573i	−0.0156898	−	0.0271756i
$536$		0			0
$537$	1.37886	−	0.541403i	0.0595023	−	0.0233633i
$538$		0			0
$539$	0.601287	+	0.601287i	0.0258993	+	0.0258993i
$540$		0			0
$541$	7.87135	−	7.87135i	0.338416	−	0.338416i	−0.517355	−	0.855771i	$-0.673083\pi$
$541$	7.87135	−	7.87135i	0.338416	−	0.338416i	0.855771	+	0.517355i	$0.173083\pi$
$542$		0			0
$543$	−9.10603	−	23.1915i	−0.390777	−	0.995243i
$544$		0			0
$545$	−5.42173	+	3.13024i	−0.232241	+	0.134085i
$546$		0			0
$547$	−3.05052	+	0.817385i	−0.130431	+	0.0349488i	−0.323444	−	0.946247i	$-0.604841\pi$
$547$	−3.05052	+	0.817385i	−0.130431	+	0.0349488i	0.193013	+	0.981196i	$0.438174\pi$
$548$		0			0
$549$	13.3467	−	21.2554i	0.569625	−	0.907159i
$550$		0			0
$551$	−2.13375	−	1.23192i	−0.0909007	−	0.0524816i
$552$		0			0
$553$	−25.3544	+	14.6384i	−1.07818	+	0.622486i
$554$		0			0
$555$	−4.86364	−	43.1077i	−0.206450	−	1.82982i
$556$		0			0
$557$	−22.4110	−	22.4110i	−0.949583	−	0.949583i	0.0492055	−	0.998789i	$-0.484331\pi$
$557$	−22.4110	−	22.4110i	−0.949583	−	0.949583i	−0.998789	+	0.0492055i	$0.984331\pi$
$558$		0			0
$559$		−	5.19151i		−	0.219577i
$560$		0			0
$561$	1.54565	−	10.2652i	0.0652574	−	0.433398i
$562$		0			0
$563$	30.2910	+	8.11646i	1.27661	+	0.342068i	0.832561	−	0.553933i	$-0.186873\pi$
$563$	30.2910	+	8.11646i	1.27661	+	0.342068i	0.444053	+	0.896000i	$0.353540\pi$
$564$		0			0
$565$	1.68061	−	0.450319i	0.0707039	−	0.0189450i
$566$		0			0
$567$	−21.0855	−	14.3573i	−0.885510	−	0.602949i
$568$		0			0
$569$	−2.78787	+	4.82873i	−0.116874	+	0.202431i	−0.918527	−	0.395358i	$-0.870621\pi$
$569$	−2.78787	+	4.82873i	−0.116874	+	0.202431i	0.801654	+	0.597789i	$0.203954\pi$
$570$		0			0
$571$	20.1186	+	5.39076i	0.841937	+	0.225596i	0.653915	−	0.756568i	$-0.273126\pi$
$571$	20.1186	+	5.39076i	0.841937	+	0.225596i	0.188023	+	0.982165i	$0.439792\pi$
$572$		0			0
$573$	−16.1719	+	11.9391i	−0.675590	+	0.498765i
$574$		0			0
$575$	−21.3699			−0.891185
$576$		0			0
$577$	20.3551			0.847394			0.423697	−	0.905804i	$-0.360732\pi$
$577$	20.3551			0.847394			0.423697	+	0.905804i	$0.360732\pi$
$578$		0			0
$579$	1.97905	+	17.5408i	0.0822465	+	0.728971i
$580$		0			0
$581$	−10.6208	−	2.84584i	−0.440626	−	0.118065i
$582$		0			0
$583$	−2.62250	+	4.54230i	−0.108613	+	0.188123i
$584$		0			0
$585$	−6.54651	−	28.6423i	−0.270665	−	1.18421i
$586$		0			0
$587$	30.5741	−	8.19230i	1.26193	−	0.338132i	0.434994	−	0.900433i	$-0.356750\pi$
$587$	30.5741	−	8.19230i	1.26193	−	0.338132i	0.826933	+	0.562301i	$0.190084\pi$
$588$		0			0
$589$	−3.08673	−	0.827087i	−0.127186	−	0.0340795i
$590$		0			0
$591$	9.85953	−	3.87130i	0.405567	−	0.159244i
$592$		0			0
$593$		−	18.8148i		−	0.772633i	−0.922366	−	0.386317i	$-0.873747\pi$
$593$		−	18.8148i		−	0.772633i	0.922366	−	0.386317i	$-0.126253\pi$
$594$		0			0
$595$	42.8379	+	42.8379i	1.75618	+	1.75618i
$596$		0			0
$597$	44.0187	+	19.1973i	1.80157	+	0.785693i
$598$		0			0
$599$	−0.618276	+	0.356962i	−0.0252621	+	0.0145851i	−0.512578	−	0.858641i	$-0.671309\pi$
$599$	−0.618276	+	0.356962i	−0.0252621	+	0.0145851i	0.487316	+	0.873226i	$0.337976\pi$
$600$		0			0
$601$	39.9427	+	23.0610i	1.62930	+	0.940676i	0.984302	+	0.176490i	$0.0564742\pi$
$601$	39.9427	+	23.0610i	1.62930	+	0.940676i	0.644996	+	0.764186i	$0.276859\pi$
$602$		0			0
$603$	30.6796	−	16.2265i	1.24937	−	0.660794i
$604$		0			0
$605$	29.2526	−	7.83822i	1.18929	−	0.318669i
$606$		0			0
$607$	25.9512	−	14.9830i	1.05333	−	0.608139i	0.129749	−	0.991547i	$-0.458583\pi$
$607$	25.9512	−	14.9830i	1.05333	−	0.608139i	0.923579	+	0.383408i	$0.125250\pi$
$608$		0			0
$609$	5.60193	−	7.02676i	0.227001	−	0.284739i
$610$		0			0
$611$	13.4948	−	13.4948i	0.545943	−	0.545943i
$612$		0			0
$613$	−4.31839	−	4.31839i	−0.174418	−	0.174418i	0.614499	−	0.788917i	$-0.289358\pi$
$613$	−4.31839	−	4.31839i	−0.174418	−	0.174418i	−0.788917	+	0.614499i	$0.789358\pi$
$614$		0			0
$615$	−6.97336	+	46.3125i	−0.281193	+	1.86750i
$616$		0			0
$617$	14.3245	+	24.8108i	0.576683	+	0.998844i	0.995857	+	0.0909377i	$0.0289864\pi$
$617$	14.3245	+	24.8108i	0.576683	+	0.998844i	−0.419174	+	0.907906i	$0.637680\pi$
$618$		0			0
$619$	−8.44181	−	31.5053i	−0.339305	−	1.26630i	−0.899126	−	0.437690i	$-0.855797\pi$
$619$	−8.44181	−	31.5053i	−0.339305	−	1.26630i	0.559821	−	0.828614i	$-0.310870\pi$
$620$		0			0
$621$	−23.3493	−	20.0754i	−0.936977	−	0.805597i
$622$		0			0
$623$	−13.1093	+	22.7059i	−0.525211	+	0.909693i
$624$		0			0
$625$	−15.0133	−	26.0039i	−0.600533	−	1.04015i
$626$		0			0
$627$	−1.13904	−	1.54286i	−0.0454888	−	0.0616158i
$628$		0			0
$629$	−43.9852	+	43.9852i	−1.75380	+	1.75380i
$630$		0			0
$631$	−19.5062			−0.776529			−0.388265	−	0.921548i	$-0.626925\pi$
$631$	−19.5062			−0.776529			−0.388265	+	0.921548i	$0.626925\pi$
$632$		0			0
$633$	−21.2819	+	26.6950i	−0.845881	+	1.06103i
$634$		0			0
$635$	−10.7677	+	40.1855i	−0.427302	+	1.59471i
$636$		0			0
$637$	−0.893188	−	3.33342i	−0.0353894	−	0.132075i
$638$		0			0
$639$	−6.57315	+	6.10267i	−0.260030	+	0.241418i
$640$		0			0
$641$	0.569361	+	0.328721i	0.0224884	+	0.0129837i	0.511202	−	0.859461i	$-0.329200\pi$
$641$	0.569361	+	0.328721i	0.0224884	+	0.0129837i	−0.488714	+	0.872444i	$0.662534\pi$
$642$		0			0
$643$	6.29265	−	23.4845i	0.248158	−	0.926138i	−0.723612	−	0.690207i	$-0.757519\pi$
$643$	6.29265	−	23.4845i	0.248158	−	0.926138i	0.971770	−	0.235931i	$-0.0758138\pi$
$644$		0			0
$645$	−3.15868	+	7.24276i	−0.124373	+	0.285183i
$646$		0			0
$647$		−	21.5984i		−	0.849122i	−0.905399	−	0.424561i	$-0.860428\pi$
$647$		−	21.5984i		−	0.849122i	0.905399	−	0.424561i	$-0.139572\pi$
$648$		0			0
$649$			9.07434i			0.356199i
$650$		0			0
$651$	4.65935	−	10.6837i	0.182614	−	0.418728i
$652$		0			0
$653$	10.2092	−	38.1014i	0.399519	−	1.49102i	−0.414427	−	0.910082i	$-0.636018\pi$
$653$	10.2092	−	38.1014i	0.399519	−	1.49102i	0.813946	−	0.580941i	$-0.197315\pi$
$654$		0			0
$655$	10.1577	+	5.86458i	0.396896	+	0.229148i
$656$		0			0
$657$	−27.9831	+	25.9802i	−1.09173	+	1.01359i
$658$		0			0
$659$	−3.62321	−	13.5220i	−0.141140	−	0.526742i	−0.999897	−	0.0143586i	$-0.995429\pi$
$659$	−3.62321	−	13.5220i	−0.141140	−	0.526742i	0.858757	−	0.512383i	$-0.171237\pi$
$660$		0			0
$661$	10.7578	−	40.1488i	0.418432	−	1.56161i	−0.359430	−	0.933172i	$-0.617029\pi$
$661$	10.7578	−	40.1488i	0.418432	−	1.56161i	0.777861	−	0.628436i	$-0.216305\pi$
$662$		0			0
$663$	−26.2623	+	32.9421i	−1.01994	+	1.27937i
$664$		0			0
$665$	11.1918			0.434001
$666$		0			0
$667$	7.67055	−	7.67055i	0.297005	−	0.297005i
$668$		0			0
$669$	12.9568	+	17.5503i	0.500937	+	0.678532i
$670$		0			0
$671$	3.44102	+	5.96002i	0.132839	+	0.230084i
$672$		0			0
$673$	2.88063	−	4.98940i	0.111040	−	0.192327i	−0.805150	−	0.593072i	$-0.797915\pi$
$673$	2.88063	−	4.98940i	0.111040	−	0.192327i	0.916190	+	0.400744i	$0.131248\pi$
$674$		0			0
$675$	−3.47521	+	18.4125i	−0.133761	+	0.708696i
$676$		0			0
$677$	−7.27316	−	27.1438i	−0.279530	−	1.04322i	−0.952744	−	0.303773i	$-0.901754\pi$
$677$	−7.27316	−	27.1438i	−0.279530	−	1.04322i	0.673214	−	0.739447i	$-0.264913\pi$
$678$		0			0
$679$	0.421949	+	0.730837i	0.0161929	+	0.0280469i
$680$		0			0
$681$	−3.10895	+	20.6476i	−0.119135	+	0.791219i
$682$		0			0
$683$	4.50875	+	4.50875i	0.172522	+	0.172522i	0.788087	−	0.615564i	$-0.211072\pi$
$683$	4.50875	+	4.50875i	0.172522	+	0.172522i	−0.615564	+	0.788087i	$0.711072\pi$
$684$		0			0
$685$	−16.5206	+	16.5206i	−0.631219	+	0.631219i
$686$		0			0
$687$	6.11603	−	7.67163i	0.233341	−	0.292691i
$688$		0			0
$689$	18.4343	−	10.6430i	0.702290	−	0.405467i
$690$		0			0
$691$	−9.90941	+	2.65522i	−0.376972	+	0.101009i	−0.442329	−	0.896853i	$-0.645848\pi$
$691$	−9.90941	+	2.65522i	−0.376972	+	0.101009i	0.0653578	+	0.997862i	$0.479181\pi$
$692$		0			0
$693$	6.18319	−	3.27029i	0.234880	−	0.124228i
$694$		0			0
$695$	27.1319	+	15.6646i	1.02917	+	0.594193i
$696$		0			0
$697$	58.1591	−	33.5782i	2.20293	−	1.27186i
$698$		0			0
$699$	−16.0813	−	7.01333i	−0.608252	−	0.265269i
$700$		0			0
$701$	−16.5518	−	16.5518i	−0.625154	−	0.625154i	0.321691	−	0.946845i	$-0.395749\pi$
$701$	−16.5518	−	16.5518i	−0.625154	−	0.625154i	−0.946845	+	0.321691i	$0.895749\pi$
$702$		0			0
$703$			11.4916i			0.433414i
$704$		0			0
$705$	−27.0376	+	10.6162i	−1.01829	+	0.399828i
$706$		0			0
$707$	−22.4089	−	6.00445i	−0.842774	−	0.225821i
$708$		0			0
$709$	−40.2743	+	10.7915i	−1.51253	+	0.405282i	−0.917276	−	0.398253i	$-0.869617\pi$
$709$	−40.2743	+	10.7915i	−1.51253	+	0.405282i	−0.595257	+	0.803535i	$0.702950\pi$
$710$		0			0
$711$	6.90445	+	30.2084i	0.258937	+	1.13290i
$712$		0			0
$713$	7.03484	−	12.1847i	0.263457	−	0.456320i
$714$		0			0
$715$	7.78182	+	2.08513i	0.291023	+	0.0779795i
$716$		0			0
$717$	0.102361	+	0.907249i	0.00382274	+	0.0338818i
$718$		0			0
$719$	−26.8494			−1.00131			−0.500656	−	0.865646i	$-0.666908\pi$
$719$	−26.8494			−1.00131			−0.500656	+	0.865646i	$0.666908\pi$
$720$		0			0
$721$	−32.4488			−1.20846
$722$		0			0
$723$	27.1538	−	20.0467i	1.00986	−	0.745547i
$724$		0			0
$725$	−6.37597	−	1.70843i	−0.236797	−	0.0634497i
$726$		0			0
$727$	12.1681	−	21.0758i	0.451290	−	0.781657i	−0.547176	−	0.837017i	$-0.684297\pi$
$727$	12.1681	−	21.0758i	0.451290	−	0.781657i	0.998466	+	0.0553600i	$0.0176306\pi$
$728$		0			0
$729$	−21.0942	+	16.8533i	−0.781268	+	0.624196i
$730$		0			0
$731$	10.9440	−	2.93245i	0.404780	−	0.108460i
$732$		0			0
$733$	−21.8512	−	5.85501i	−0.807093	−	0.216260i	−0.168397	−	0.985719i	$-0.553859\pi$
$733$	−21.8512	−	5.85501i	−0.807093	−	0.216260i	−0.638696	+	0.769459i	$0.720526\pi$
$734$		0			0
$735$	−0.782063	+	5.19396i	−0.0288468	+	0.191582i
$736$		0			0
$737$			9.51661i			0.350549i
$738$		0			0
$739$	12.6742	+	12.6742i	0.466230	+	0.466230i	0.900691	−	0.434461i	$-0.143061\pi$
$739$	12.6742	+	12.6742i	0.466230	+	0.466230i	−0.434461	+	0.900691i	$0.643061\pi$
$740$		0			0
$741$	0.872580	+	7.73389i	0.0320550	+	0.284112i
$742$		0			0
$743$	−25.2864	+	14.5991i	−0.927667	+	0.535589i	−0.886073	−	0.463546i	$-0.846577\pi$
$743$	−25.2864	+	14.5991i	−0.927667	+	0.535589i	−0.0415943	+	0.999135i	$0.513244\pi$
$744$		0			0
$745$	−11.1551	−	6.44042i	−0.408692	−	0.235959i
$746$		0			0
$747$	−6.18880	+	9.85601i	−0.226436	+	0.360612i
$748$		0			0
$749$	−0.677369	+	0.181500i	−0.0247505	+	0.00663188i
$750$		0			0
$751$	−23.9864	+	13.8486i	−0.875277	+	0.505341i	−0.869098	−	0.494639i	$-0.835300\pi$
$751$	−23.9864	+	13.8486i	−0.875277	+	0.505341i	−0.00617885	+	0.999981i	$0.501967\pi$
$752$		0			0
$753$	16.0427	+	40.8580i	0.584628	+	1.48895i
$754$		0			0
$755$	−28.7833	+	28.7833i	−1.04753	+	1.04753i
$756$		0			0
$757$	−6.84906	−	6.84906i	−0.248933	−	0.248933i	0.571599	−	0.820533i	$-0.306323\pi$
$757$	−6.84906	−	6.84906i	−0.248933	−	0.248933i	−0.820533	+	0.571599i	$0.806323\pi$
$758$		0			0
$759$	7.85940	−	3.08595i	0.285278	−	0.112013i
$760$		0			0
$761$	6.92685	+	11.9977i	0.251098	+	0.434915i	0.963828	−	0.266523i	$-0.0858750\pi$
$761$	6.92685	+	11.9977i	0.251098	+	0.434915i	−0.712730	+	0.701438i	$0.752542\pi$
$762$		0			0
$763$	1.56553	+	5.84262i	0.0566758	+	0.211517i
$764$		0			0
$765$	56.6821	−	29.9792i	2.04934	−	1.08390i
$766$		0			0
$767$	18.4134	−	31.8930i	0.664871	−	1.15159i
$768$		0			0
$769$	5.15368	+	8.92644i	0.185846	+	0.321896i	0.943861	−	0.330342i	$-0.107164\pi$
$769$	5.15368	+	8.92644i	0.185846	+	0.321896i	−0.758015	+	0.652237i	$0.773831\pi$
$770$		0			0
$771$	29.0461	−	3.27714i	1.04607	−	0.118023i
$772$		0			0
$773$	29.0684	−	29.0684i	1.04552	−	1.04552i	0.0466043	−	0.998913i	$-0.485160\pi$
$773$	29.0684	−	29.0684i	1.04552	−	1.04552i	0.998913	−	0.0466043i	$-0.0148400\pi$
$774$		0			0
$775$	−8.56139			−0.307534
$776$		0			0
$777$	−41.4467	−	6.24069i	−1.48689	−	0.223884i
$778$		0			0
$779$	3.21101	−	11.9837i	0.115046	−	0.429359i
$780$		0			0
$781$	−0.636543	−	2.37561i	−0.0227773	−	0.0850060i
$782$		0			0
$783$	−5.36162	−	7.85642i	−0.191609	−	0.280765i
$784$		0			0
$785$	−15.8222	−	9.13496i	−0.564719	−	0.326041i
$786$		0			0
$787$	−9.63526	+	35.9593i	−0.343460	+	1.28181i	0.550941	+	0.834544i	$0.314269\pi$
$787$	−9.63526	+	35.9593i	−0.343460	+	1.28181i	−0.894401	+	0.447266i	$0.852398\pi$
$788$		0			0
$789$	22.3399	+	30.2599i	0.795321	+	1.07728i
$790$		0			0
$791$		−	1.68105i		−	0.0597712i
$792$		0			0
$793$		−	27.9297i		−	0.991814i
$794$		0			0
$795$	−32.1935	+	3.63225i	−1.14179	+	0.128823i
$796$		0			0
$797$	2.51421	−	9.38318i	0.0890580	−	0.332369i	−0.906994	−	0.421144i	$-0.861629\pi$
$797$	2.51421	−	9.38318i	0.0890580	−	0.332369i	0.996052	+	0.0887752i	$0.0282953\pi$
$798$		0			0
$799$	36.0706	+	20.8254i	1.27609	+	0.736749i
$800$		0			0
$801$	18.8813	+	20.3369i	0.667137	+	0.718568i
$802$		0			0
$803$	−2.70988	−	10.1134i	−0.0956297	−	0.356895i
$804$		0			0
$805$	−12.7534	+	47.5965i	−0.449500	+	1.67756i
$806$		0			0
$807$	3.13987	+	7.99673i	0.110529	+	0.281498i
$808$		0			0
$809$	−13.1867			−0.463620			−0.231810	−	0.972761i	$-0.574465\pi$
$809$	−13.1867			−0.463620			−0.231810	+	0.972761i	$0.574465\pi$
$810$		0			0
$811$	11.0093	−	11.0093i	0.386587	−	0.386587i	−0.486881	−	0.873468i	$-0.661865\pi$
$811$	11.0093	−	11.0093i	0.386587	−	0.386587i	0.873468	+	0.486881i	$0.161865\pi$
$812$		0			0
$813$	−1.56307	+	3.58408i	−0.0548194	+	0.125699i
$814$		0			0
$815$	7.03233	+	12.1804i	0.246332	+	0.426659i
$816$		0			0
$817$	1.04656	−	1.81269i	0.0366144	−	0.0634179i
$818$		0			0
$819$	−28.3677	−	1.05288i	−0.991246	−	0.0367907i
$820$		0			0
$821$	−1.11987	−	4.17943i	−0.0390839	−	0.145863i	0.943627	−	0.331012i	$-0.107390\pi$
$821$	−1.11987	−	4.17943i	−0.0390839	−	0.145863i	−0.982711	+	0.185149i	$0.940723\pi$
$822$		0			0
$823$	−23.8576	−	41.3225i	−0.831622	−	1.44041i	−0.896751	−	0.442535i	$-0.854079\pi$
$823$	−23.8576	−	41.3225i	−0.831622	−	1.44041i	0.0651287	−	0.997877i	$-0.479254\pi$
$824$		0			0
$825$	−4.01745	−	3.20282i	−0.139870	−	0.111508i
$826$		0			0
$827$	−1.38625	−	1.38625i	−0.0482045	−	0.0482045i	0.682594	−	0.730798i	$-0.260852\pi$
$827$	−1.38625	−	1.38625i	−0.0482045	−	0.0482045i	−0.730798	+	0.682594i	$0.760852\pi$
$828$		0			0
$829$	−21.8345	+	21.8345i	−0.758345	+	0.758345i	−0.976021	−	0.217676i	$-0.930152\pi$
$829$	−21.8345	+	21.8345i	−0.758345	+	0.758345i	0.217676	+	0.976021i	$0.430152\pi$
$830$		0			0
$831$	−31.4879	−	4.74119i	−1.09230	−	0.164470i
$832$		0			0
$833$	6.52255	−	3.76580i	0.225993	−	0.130477i
$834$		0			0
$835$	28.0938	−	7.52771i	0.972227	−	0.260507i
$836$		0			0
$837$	−9.35442	−	8.04278i	−0.323336	−	0.277999i
$838$		0			0
$839$	27.8914	+	16.1031i	0.962916	+	0.555940i	0.897069	−	0.441890i	$-0.145692\pi$
$839$	27.8914	+	16.1031i	0.962916	+	0.555940i	0.0658470	+	0.997830i	$0.479025\pi$
$840$		0			0
$841$	−22.2129	+	12.8246i	−0.765962	+	0.442228i
$842$		0			0
$843$	−12.2141	+	9.01729i	−0.420678	+	0.310572i
$844$		0			0
$845$	3.84768	+	3.84768i	0.132364	+	0.132364i
$846$		0			0
$847$		−	29.2602i		−	1.00539i
$848$		0			0
$849$	21.8977	+	17.4574i	0.751527	+	0.599138i
$850$		0			0
$851$	−48.8712	−	13.0950i	−1.67528	−	0.448891i
$852$		0			0
$853$	44.9166	−	12.0354i	1.53791	−	0.412083i	0.612323	−	0.790608i	$-0.290235\pi$
$853$	44.9166	−	12.0354i	1.53791	−	0.412083i	0.925591	+	0.378525i	$0.123569\pi$
$854$		0			0
$855$	3.48820	−	11.3206i	0.119294	−	0.387156i
$856$		0			0
$857$	10.0139	−	17.3446i	0.342068	−	0.592480i	−0.642748	−	0.766077i	$-0.722206\pi$
$857$	10.0139	−	17.3446i	0.342068	−	0.592480i	0.984817	+	0.173598i	$0.0555392\pi$
$858$		0			0
$859$	−16.6956	−	4.47358i	−0.569648	−	0.152637i	−0.0375129	−	0.999296i	$-0.511944\pi$
$859$	−16.6956	−	4.47358i	−0.569648	−	0.152637i	−0.532135	+	0.846659i	$0.678610\pi$
$860$		0			0
$861$	41.4776	+	18.0891i	1.41355	+	0.616474i
$862$		0			0
$863$	−24.4242			−0.831410			−0.415705	−	0.909499i	$-0.636465\pi$
$863$	−24.4242			−0.831410			−0.415705	+	0.909499i	$0.636465\pi$
$864$		0			0
$865$	22.0265			0.748923
$866$		0			0
$867$	−57.2886	−	24.9845i	−1.94562	−	0.848518i
$868$		0			0
$869$	−8.20731	−	2.19914i	−0.278414	−	0.0746007i
$870$		0			0
$871$	19.3109	−	33.4474i	0.654324	−	1.13332i
$872$		0			0
$873$	0.870754	−	0.199020i	0.0294705	−	0.00673580i
$874$		0			0
$875$	−11.1957	+	2.99989i	−0.378485	+	0.101415i
$876$		0			0
$877$	34.5743	+	9.26415i	1.16749	+	0.312828i	0.789954	−	0.613167i	$-0.210105\pi$
$877$	34.5743	+	9.26415i	1.16749	+	0.312828i	0.377537	+	0.925995i	$0.376771\pi$
$878$		0			0
$879$	16.9823	+	13.5388i	0.572800	+	0.456651i
$880$		0			0
$881$			45.8264i			1.54393i	0.635664	+	0.771966i	$0.280726\pi$
$881$			45.8264i			1.54393i	−0.635664	+	0.771966i	$0.719274\pi$
$882$		0			0
$883$	−7.22790	−	7.22790i	−0.243238	−	0.243238i	0.574950	−	0.818188i	$-0.305021\pi$
$883$	−7.22790	−	7.22790i	−0.243238	−	0.243238i	−0.818188	+	0.574950i	$0.805021\pi$
$884$		0			0
$885$	−45.0936	+	33.2911i	−1.51581	+	1.11907i
$886$		0			0
$887$	36.9502	−	21.3332i	1.24067	−	0.716300i	0.271438	−	0.962456i	$-0.412501\pi$
$887$	36.9502	−	21.3332i	1.24067	−	0.716300i	0.969230	+	0.246156i	$0.0791676\pi$
$888$		0			0
$889$	34.8107	+	20.0980i	1.16751	+	0.674065i
$890$		0			0
$891$	−1.38077	−	7.27357i	−0.0462577	−	0.243674i
$892$		0			0
$893$	7.43234	−	1.99149i	0.248714	−	0.0666426i
$894$		0			0
$895$	−2.17284	+	1.25449i	−0.0726300	+	0.0419330i
$896$		0			0
$897$	−33.8849	−	5.10210i	−1.13138	−	0.170354i
$898$		0			0
$899$	3.07305	−	3.07305i	0.102492	−	0.102492i
$900$		0			0
$901$	32.8489	+	32.8489i	1.09435	+	1.09435i
$902$		0			0
$903$	5.96946	+	4.75902i	0.198651	+	0.158370i
$904$		0			0
$905$	21.0997	+	36.5457i	0.701376	+	1.21482i
$906$		0			0
$907$	10.4458	+	38.9844i	0.346848	+	1.29445i	0.890438	+	0.455104i	$0.150398\pi$
$907$	10.4458	+	38.9844i	0.346848	+	1.29445i	−0.543590	+	0.839351i	$0.682935\pi$
$908$		0			0
$909$	−13.0578	+	20.7953i	−0.433099	+	0.689735i
$910$		0			0
$911$	22.6553	−	39.2402i	0.750605	−	1.30009i	−0.196925	−	0.980419i	$-0.563095\pi$
$911$	22.6553	−	39.2402i	0.750605	−	1.30009i	0.947530	−	0.319667i	$-0.103571\pi$
$912$		0			0
$913$	−1.59558	−	2.76362i	−0.0528060	−	0.0914626i
$914$		0			0
$915$	−16.9934	+	38.9652i	−0.561784	+	1.28815i
$916$		0			0
$917$	8.01324	−	8.01324i	0.264621	−	0.264621i
$918$		0			0
$919$	3.91688			0.129206			0.0646030	−	0.997911i	$-0.479422\pi$
$919$	3.91688			0.129206			0.0646030	+	0.997911i	$0.479422\pi$
$920$		0			0
$921$	−16.9351	−	43.1308i	−0.558030	−	1.42121i
$922$		0			0
$923$	−2.58332	+	9.64107i	−0.0850309	+	0.317340i
$924$		0			0
$925$	7.96831	+	29.7381i	0.261996	+	0.977784i
$926$		0			0
$927$	−10.1134	+	32.8221i	−0.332169	+	1.07802i
$928$		0			0
$929$	−13.7214	−	7.92207i	−0.450185	−	0.259915i	0.257723	−	0.966219i	$-0.417028\pi$
$929$	−13.7214	−	7.92207i	−0.450185	−	0.259915i	−0.707908	+	0.706304i	$0.750361\pi$
$930$		0			0
$931$	0.360116	−	1.34397i	0.0118023	−	0.0440468i
$932$		0			0
$933$	10.1092	−	1.14057i	0.330960	−	0.0373407i
$934$		0			0
$935$			17.5824i			0.575005i
$936$		0			0
$937$		−	38.0380i		−	1.24265i	−0.783554	−	0.621324i	$-0.786595\pi$
$937$		−	38.0380i		−	1.24265i	0.783554	−	0.621324i	$-0.213405\pi$
$938$		0			0
$939$	−17.0449	−	23.0877i	−0.556239	−	0.753439i
$940$		0			0
$941$	−13.2570	+	49.4756i	−0.432164	+	1.61286i	0.315598	+	0.948893i	$0.397795\pi$
$941$	−13.2570	+	49.4756i	−0.432164	+	1.61286i	−0.747762	+	0.663966i	$0.768872\pi$
$942$		0			0
$943$	47.3048	+	27.3115i	1.54046	+	0.889384i
$944$		0			0
$945$	38.9356	+	18.7287i	1.26657	+	0.609245i
$946$		0			0
$947$	−4.24080	−	15.8269i	−0.137808	−	0.514305i	−0.999971	−	0.00767376i	$-0.997557\pi$
$947$	−4.24080	−	15.8269i	−0.137808	−	0.514305i	0.862163	−	0.506631i	$-0.169109\pi$
$948$		0			0
$949$	−10.9977	+	41.0438i	−0.356999	+	1.33234i
$950$		0			0
$951$	−11.9467	−	1.79883i	−0.387398	−	0.0583311i
$952$		0			0
$953$	−19.2107			−0.622295			−0.311147	−	0.950362i	$-0.600713\pi$
$953$	−19.2107			−0.622295			−0.311147	+	0.950362i	$0.600713\pi$
$954$		0			0
$955$	24.0744	−	24.0744i	0.779030	−	0.779030i
$956$		0			0
$957$	2.59166	−	0.292405i	0.0837764	−	0.00945211i
$958$		0			0
$959$	11.2867	+	19.5491i	0.364466	+	0.631274i
$960$		0			0
$961$	−12.6816	+	21.9652i	−0.409085	+	0.708556i
$962$		0			0
$963$	−0.0275297	+	0.741729i	−0.000887134	+	0.0239019i
$964$		0			0
$965$	−7.73809	−	28.8789i	−0.249098	−	0.929646i
$966$		0			0
$967$	17.0779	+	29.5798i	0.549188	+	0.951222i	0.998330	+	0.0577615i	$0.0183963\pi$
$967$	17.0779	+	29.5798i	0.549188	+	0.951222i	−0.449142	+	0.893460i	$0.648270\pi$
$968$		0			0
$969$	−15.8107	+	6.20798i	−0.507912	+	0.199429i
$970$		0			0
$971$	20.2022	+	20.2022i	0.648318	+	0.648318i	0.952586	−	0.304268i	$-0.0984119\pi$
$971$	20.2022	+	20.2022i	0.648318	+	0.648318i	−0.304268	+	0.952586i	$0.598412\pi$
$972$		0			0
$973$	21.4038	−	21.4038i	0.686175	−	0.686175i
$974$		0			0
$975$	7.62078	+	19.4088i	0.244060	+	0.621580i
$976$		0			0
$977$	−7.37615	+	4.25862i	−0.235984	+	0.136245i	−0.613329	−	0.789827i	$-0.710170\pi$
$977$	−7.37615	+	4.25862i	−0.235984	+	0.136245i	0.377346	+	0.926072i	$0.376837\pi$
$978$		0			0
$979$	−7.34998	+	1.96942i	−0.234906	+	0.0629430i
$980$		0			0
$981$	6.39776	+	0.237457i	0.204265	+	0.00758141i
$982$		0			0
$983$	−47.6844	−	27.5306i	−1.52090	−	0.878090i	−0.999696	−	0.0246553i	$-0.992151\pi$
$983$	−47.6844	−	27.5306i	−1.52090	−	0.878090i	−0.521200	−	0.853435i	$-0.674515\pi$
$984$		0			0
$985$	−15.5369	+	8.97021i	−0.495045	+	0.285815i
$986$		0			0
$987$	3.14644	+	27.8877i	0.100152	+	0.887675i
$988$		0			0
$989$	6.51638	+	6.51638i	0.207209	+	0.207209i
$990$		0			0
$991$			61.9180i			1.96689i	0.181210	+	0.983444i	$0.441999\pi$
$991$			61.9180i			1.96689i	−0.181210	+	0.983444i	$0.558001\pi$
$992$		0			0
$993$	5.81643	−	38.6290i	0.184579	−	1.22585i
$994$		0			0
$995$	−78.5655	−	21.0516i	−2.49069	−	0.667380i
$996$		0			0
$997$	17.3680	−	4.65375i	0.550051	−	0.147386i	0.0269194	−	0.999638i	$-0.491430\pi$
$997$	17.3680	−	4.65375i	0.550051	−	0.147386i	0.523132	+	0.852252i	$0.324764\pi$
$998$		0			0
$999$	−19.2303	+	39.9784i	−0.608420	+	1.26486i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.y.a.335.19		88
3.2	odd	2		1728.2.z.a.143.20		88
4.3	odd	2		144.2.u.a.11.18	✓	88
9.4	even	3		1728.2.z.a.719.20		88
9.5	odd	6	inner	576.2.y.a.527.15		88
12.11	even	2		432.2.v.a.251.5		88
16.3	odd	4	inner	576.2.y.a.47.15		88
16.13	even	4		144.2.u.a.83.11	yes	88
36.23	even	6		144.2.u.a.59.11	yes	88
36.31	odd	6		432.2.v.a.395.12		88
48.29	odd	4		432.2.v.a.35.12		88
48.35	even	4		1728.2.z.a.1007.20		88
144.13	even	12		432.2.v.a.179.5		88
144.67	odd	12		1728.2.z.a.1583.20		88
144.77	odd	12		144.2.u.a.131.18	yes	88
144.131	even	12	inner	576.2.y.a.239.19		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.18	✓	88	4.3	odd	2
144.2.u.a.59.11	yes	88	36.23	even	6
144.2.u.a.83.11	yes	88	16.13	even	4
144.2.u.a.131.18	yes	88	144.77	odd	12
432.2.v.a.35.12		88	48.29	odd	4
432.2.v.a.179.5		88	144.13	even	12
432.2.v.a.251.5		88	12.11	even	2
432.2.v.a.395.12		88	36.31	odd	6
576.2.y.a.47.15		88	16.3	odd	4	inner
576.2.y.a.239.19		88	144.131	even	12	inner
576.2.y.a.335.19		88	1.1	even	1	trivial
576.2.y.a.527.15		88	9.5	odd	6	inner
1728.2.z.a.143.20		88	3.2	odd	2
1728.2.z.a.719.20		88	9.4	even	3
1728.2.z.a.1007.20		88	48.35	even	4
1728.2.z.a.1583.20		88	144.67	odd	12

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)

\(f(q)\)	\(=\)	\(q+(1.58764 + 0.692394i) q^{3} +(-2.83365 - 0.759273i) q^{5} +(-1.41719 + 2.45465i) q^{7} +(2.04118 + 2.19854i) q^{9} +O(q^{10})\)	\(q+(1.58764 + 0.692394i) q^{3} +(-2.83365 - 0.759273i) q^{5} +(-1.41719 + 2.45465i) q^{7} +(2.04118 + 2.19854i) q^{9} +(-0.794578 + 0.212907i) q^{11} +(3.22468 + 0.864050i) q^{13} +(-3.97308 - 3.16745i) q^{15} +7.28589i q^{17} +(0.951758 + 0.951758i) q^{19} +(-3.94957 + 2.91583i) q^{21} +(-5.13217 + 2.96306i) q^{23} +(3.12293 + 1.80302i) q^{25} +(1.71840 + 4.90379i) q^{27} +(-1.76813 + 0.473770i) q^{29} +(-2.05610 + 1.18709i) q^{31} +(-1.40892 - 0.212143i) q^{33} +(5.87957 - 5.87957i) q^{35} +(6.03704 + 6.03704i) q^{37} +(4.52135 + 3.60455i) q^{39} +(-4.60866 - 7.98243i) q^{41} +(-0.402483 - 1.50209i) q^{43} +(-4.11469 - 7.77970i) q^{45} +(2.85832 - 4.95075i) q^{47} +(-0.516861 - 0.895230i) q^{49} +(-5.04471 + 11.5674i) q^{51} +(4.50856 - 4.50856i) q^{53} +2.41321 q^{55} +(0.852054 + 2.17004i) q^{57} +(2.85508 - 10.6553i) q^{59} +(-2.16531 - 8.08106i) q^{61} +(-8.28938 + 1.89463i) q^{63} +(-8.48155 - 4.89682i) q^{65} +(2.99423 - 11.1746i) q^{67} +(-10.1996 + 1.15078i) q^{69} +2.98978i q^{71} +12.7280i q^{73} +(3.70967 + 5.02484i) q^{75} +(0.603459 - 2.25214i) q^{77} +(8.94529 + 5.16457i) q^{79} +(-0.667162 + 8.97524i) q^{81} +(1.00404 + 3.74713i) q^{83} +(5.53198 - 20.6456i) q^{85} +(-3.13519 - 0.472070i) q^{87} +9.25017 q^{89} +(-6.69092 + 6.69092i) q^{91} +(-4.08627 + 0.461036i) q^{93} +(-1.97430 - 3.41959i) q^{95} +(0.148868 - 0.257847i) q^{97} +(-2.08996 - 1.31233i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) \) 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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