LMFDB - Embedded newform 576.2.y.a.47.15

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			47.15
Character	$\chi$	$=$	576.47
Dual form			576.2.y.a.527.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.692394 - 1.58764i) q^{3} +(-0.759273 + 2.83365i) q^{5} +(-1.41719 + 2.45465i) q^{7} +(-2.04118 - 2.19854i) q^{9} +O(q^{10})$	\(q+(0.692394 - 1.58764i) q^{3} +(-0.759273 + 2.83365i) q^{5} +(-1.41719 + 2.45465i) q^{7} +(-2.04118 - 2.19854i) q^{9} +(-0.212907 - 0.794578i) q^{11} +(-0.864050 + 3.22468i) q^{13} +(3.97308 + 3.16745i) q^{15} +7.28589i q^{17} +(0.951758 - 0.951758i) q^{19} +(2.91583 + 3.94957i) q^{21} +(-5.13217 + 2.96306i) q^{23} +(-3.12293 - 1.80302i) q^{25} +(-4.90379 + 1.71840i) q^{27} +(-0.473770 - 1.76813i) q^{29} +(2.05610 - 1.18709i) q^{31} +(-1.40892 - 0.212143i) q^{33} +(-5.87957 - 5.87957i) q^{35} +(6.03704 - 6.03704i) q^{37} +(4.52135 + 3.60455i) q^{39} +(4.60866 + 7.98243i) q^{41} +(1.50209 - 0.402483i) q^{43} +(7.77970 - 4.11469i) q^{45} +(-2.85832 + 4.95075i) q^{47} +(-0.516861 - 0.895230i) q^{49} +(11.5674 + 5.04471i) q^{51} +(-4.50856 - 4.50856i) q^{53} +2.41321 q^{55} +(-0.852054 - 2.17004i) q^{57} +(10.6553 + 2.85508i) q^{59} +(8.08106 - 2.16531i) q^{61} +(8.28938 - 1.89463i) q^{63} +(-8.48155 - 4.89682i) q^{65} +(-11.1746 - 2.99423i) q^{67} +(1.15078 + 10.1996i) q^{69} +2.98978i q^{71} -12.7280i q^{73} +(-5.02484 + 3.70967i) q^{75} +(2.25214 + 0.603459i) q^{77} +(-8.94529 - 5.16457i) q^{79} +(-0.667162 + 8.97524i) q^{81} +(3.74713 - 1.00404i) q^{83} +(-20.6456 - 5.53198i) q^{85} +(-3.13519 - 0.472070i) q^{87} -9.25017 q^{89} +(-6.69092 - 6.69092i) q^{91} +(-0.461036 - 4.08627i) q^{93} +(1.97430 + 3.41959i) q^{95} +(0.148868 - 0.257847i) q^{97} +(-1.31233 + 2.08996i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.692394	−	1.58764i	0.399754	−	0.916622i
$3$	0.692394	−	1.58764i	0.399754	−	0.916622i
$4$		0			0
$5$	−0.759273	+	2.83365i	−0.339557	+	1.26725i	0.559286	+	0.828975i	$0.311075\pi$
$5$	−0.759273	+	2.83365i	−0.339557	+	1.26725i	−0.898843	+	0.438270i	$0.855591\pi$
$6$		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
$11$	−0.212907	−	0.794578i	−0.0641937	−	0.239574i	0.926373	−	0.376608i	$-0.122910\pi$
$11$	−0.212907	−	0.794578i	−0.0641937	−	0.239574i	−0.990566	+	0.137034i	$0.956243\pi$
$12$		0			0
$13$	−0.864050	+	3.22468i	−0.239644	+	0.894365i	0.736356	+	0.676595i	$0.236545\pi$
$13$	−0.864050	+	3.22468i	−0.239644	+	0.894365i	−0.976000	+	0.217770i	$0.930122\pi$
$14$		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	−0.589454	−	0.807802i	$-0.700657\pi$
$19$	0.951758	−	0.951758i	0.218348	−	0.218348i	0.807802	+	0.589454i	$0.200657\pi$
$20$		0			0
$21$	2.91583	+	3.94957i	0.636287	+	0.861866i
$22$		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
$27$	−4.90379	+	1.71840i	−0.943734	+	0.330706i
$28$		0			0
$29$	−0.473770	−	1.76813i	−0.0879768	−	0.328334i	0.907884	−	0.419221i	$-0.137697\pi$
$29$	−0.473770	−	1.76813i	−0.0879768	−	0.328334i	−0.995861	+	0.0908866i	$0.971030\pi$
$30$		0			0
$31$	2.05610	−	1.18709i	0.369286	−	0.213207i	−0.303860	−	0.952717i	$-0.598276\pi$
$31$	2.05610	−	1.18709i	0.369286	−	0.213207i	0.673147	+	0.739509i	$0.264942\pi$
$32$		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	−0.00748933	−	0.999972i	$-0.502384\pi$
$37$	6.03704	−	6.03704i	0.992483	−	0.992483i	0.999972	+	0.00748933i	$0.00238395\pi$
$38$		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	$0.0890774\pi$
$41$	4.60866	+	7.98243i	0.719751	+	1.24665i	−0.241347	+	0.970439i	$0.577589\pi$
$42$		0			0
$43$	1.50209	−	0.402483i	0.229066	−	0.0613780i	−0.142460	−	0.989801i	$-0.545501\pi$
$43$	1.50209	−	0.402483i	0.229066	−	0.0613780i	0.371526	+	0.928423i	$0.378835\pi$
$44$		0			0
$45$	7.77970	−	4.11469i	1.15973	−	0.613382i
$46$		0			0
$47$	−2.85832	+	4.95075i	−0.416928	+	0.722141i	−0.995629	−	0.0933994i	$-0.970227\pi$
$47$	−2.85832	+	4.95075i	−0.416928	+	0.722141i	0.578701	+	0.815540i	$0.303560\pi$
$48$		0			0
$49$	−0.516861	−	0.895230i	−0.0738373	−	0.127890i
$50$		0			0
$51$	11.5674	+	5.04471i	1.61975	+	0.706401i
$52$		0			0
$53$	−4.50856	−	4.50856i	−0.619298	−	0.619298i	0.326053	−	0.945351i	$-0.394281\pi$
$53$	−4.50856	−	4.50856i	−0.619298	−	0.619298i	−0.945351	+	0.326053i	$0.894281\pi$
$54$		0			0
$55$	2.41321			0.325397
$56$		0			0
$57$	−0.852054	−	2.17004i	−0.112857	−	0.287429i
$58$		0			0
$59$	10.6553	+	2.85508i	1.38720	+	0.371700i	0.873732	−	0.486407i	$-0.161693\pi$
$59$	10.6553	+	2.85508i	1.38720	+	0.371700i	0.513471	+	0.858107i	$0.328360\pi$
$60$		0			0
$61$	8.08106	−	2.16531i	1.03467	−	0.277240i	0.298769	−	0.954325i	$-0.403424\pi$
$61$	8.08106	−	2.16531i	1.03467	−	0.277240i	0.735904	+	0.677086i	$0.236757\pi$
$62$		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
$67$	−11.1746	−	2.99423i	−1.36520	−	0.365804i	−0.499476	−	0.866328i	$-0.666474\pi$
$67$	−11.1746	−	2.99423i	−1.36520	−	0.365804i	−0.865723	+	0.500524i	$0.833141\pi$
$68$		0			0
$69$	1.15078	+	10.1996i	0.138538	+	1.22789i
$70$		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	$-0.732520\pi$
$73$		−	12.7280i		−	1.48970i	0.667229	−	0.744852i	$-0.267480\pi$
$74$		0			0
$75$	−5.02484	+	3.70967i	−0.580219	+	0.428356i
$76$		0			0
$77$	2.25214	+	0.603459i	0.256655	+	0.0687705i
$78$		0			0
$79$	−8.94529	−	5.16457i	−1.00642	−	0.581059i	−0.0962815	−	0.995354i	$-0.530695\pi$
$79$	−8.94529	−	5.16457i	−1.00642	−	0.581059i	−0.910143	+	0.414295i	$0.864028\pi$
$80$		0			0
$81$	−0.667162	+	8.97524i	−0.0741291	+	0.997249i
$82$		0			0
$83$	3.74713	−	1.00404i	0.411301	−	0.110208i	−0.0472343	−	0.998884i	$-0.515041\pi$
$83$	3.74713	−	1.00404i	0.411301	−	0.110208i	0.458536	+	0.888676i	$0.348374\pi$
$84$		0			0
$85$	−20.6456	−	5.53198i	−2.23933	−	0.600028i
$86$		0			0
$87$	−3.13519	−	0.472070i	−0.336127	−	0.0506113i
$88$		0			0
$89$	−9.25017			−0.980516			−0.490258	−	0.871577i	$-0.663097\pi$
$89$	−9.25017			−0.980516			−0.490258	+	0.871577i	$0.663097\pi$
$90$		0			0
$91$	−6.69092	−	6.69092i	−0.701399	−	0.701399i
$92$		0			0
$93$	−0.461036	−	4.08627i	−0.0478072	−	0.423727i
$94$		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
$99$	−1.31233	+	2.08996i	−0.131894	+	0.210049i
$100$		0			0
$101$	7.90610	−	2.11843i	0.786687	−	0.210792i	0.156956	−	0.987606i	$-0.449832\pi$
$101$	7.90610	−	2.11843i	0.786687	−	0.210792i	0.629731	+	0.776814i	$0.283165\pi$
$102$		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	$-0.753807\pi$
$107$	−0.174948	+	0.174948i	−0.0169128	+	0.0169128i	0.698600	+	0.715513i	$0.253807\pi$
$108$		0			0
$109$	1.50900	+	1.50900i	0.144536	+	0.144536i	0.775672	−	0.631136i	$-0.217411\pi$
$109$	1.50900	+	1.50900i	0.144536	+	0.144536i	−0.631136	+	0.775672i	$0.717411\pi$
$110$		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
$115$	−4.49955	−	16.7925i	−0.419585	−	1.56591i
$116$		0			0
$117$	8.85327	−	4.68250i	0.818485	−	0.432898i
$118$		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
$123$	15.8642	−	1.78989i	1.43043	−	0.161389i
$124$		0			0
$125$	−2.89158	+	2.89158i	−0.258631	+	0.258631i
$126$		0			0
$127$			14.1816i			1.25841i	0.777240	+	0.629205i	$0.216619\pi$
$127$			14.1816i			1.25841i	−0.777240	+	0.629205i	$0.783381\pi$
$128$		0			0
$129$	0.401039	−	2.66344i	0.0353095	−	0.234503i
$130$		0			0
$131$	−1.03481	+	3.86197i	−0.0904119	+	0.337422i	−0.996284	−	0.0861298i	$-0.972550\pi$
$131$	−1.03481	+	3.86197i	−0.0904119	+	0.337422i	0.905872	+	0.423551i	$0.139217\pi$
$132$		0			0
$133$	0.987407	+	3.68505i	0.0856190	+	0.319535i
$134$		0			0
$135$	−1.14602	−	15.2003i	−0.0986333	−	1.30824i
$136$		0			0
$137$	−3.98207	+	6.89714i	−0.340211	+	0.589262i	−0.984472	−	0.175543i	$-0.943832\pi$
$137$	−3.98207	+	6.89714i	−0.340211	+	0.589262i	0.644261	+	0.764806i	$0.277165\pi$
$138$		0			0
$139$	2.76404	−	10.3155i	0.234443	−	0.874952i	−0.743957	−	0.668228i	$-0.767053\pi$
$139$	2.76404	−	10.3155i	0.234443	−	0.874952i	0.978399	−	0.206724i	$-0.0662803\pi$
$140$		0			0
$141$	5.88091	+	7.96583i	0.495262	+	0.670844i
$142$		0			0
$143$	2.74622			0.229651
$144$		0			0
$145$	5.36998			0.445953
$146$		0			0
$147$	−1.77917	+	0.200736i	−0.146744	+	0.0165564i
$148$		0			0
$149$	1.13642	−	4.24117i	0.0930990	−	0.347450i	−0.903625	−	0.428324i	$-0.859104\pi$
$149$	1.13642	−	4.24117i	0.0930990	−	0.347450i	0.996724	+	0.0808734i	$0.0257710\pi$
$150$		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
$155$	1.80265	+	6.72758i	0.144792	+	0.540372i
$156$		0			0
$157$	−1.61187	+	6.01560i	−0.128642	+	0.480097i	−0.999943	−	0.0106509i	$-0.996610\pi$
$157$	−1.61187	+	6.01560i	−0.128642	+	0.480097i	0.871302	+	0.490748i	$0.163276\pi$
$158$		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	−0.827297	−	0.561764i	$-0.810123\pi$
$163$	−3.39010	+	3.39010i	−0.265533	+	0.265533i	0.561764	+	0.827297i	$0.310123\pi$
$164$		0			0
$165$	1.67089	−	3.83130i	0.130079	−	0.298266i
$166$		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
$171$	−4.03519	−	0.149769i	−0.308579	−	0.0114531i
$172$		0			0
$173$	−1.94330	−	7.25249i	−0.147746	−	0.551396i	−0.999618	−	0.0276457i	$-0.991199\pi$
$173$	−1.94330	−	7.25249i	−0.147746	−	0.551396i	0.851872	−	0.523751i	$-0.175468\pi$
$174$		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	$-0.260176\pi$
$179$	−0.604756	−	0.604756i	−0.0452016	−	0.0452016i	−0.729346	+	0.684145i	$0.760176\pi$
$180$		0			0
$181$	−10.1716	+	10.1716i	−0.756048	+	0.756048i	−0.975601	−	0.219553i	$-0.929540\pi$
$181$	−10.1716	+	10.1716i	−0.756048	+	0.756048i	0.219553	+	0.975601i	$0.429540\pi$
$182$		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
$187$	5.78921	−	1.55121i	0.423349	−	0.113436i
$188$		0			0
$189$	2.73154	−	14.4724i	0.198691	−	1.05271i
$190$		0			0
$191$	5.80282	−	10.0508i	0.419877	−	0.727249i	−0.576049	−	0.817415i	$-0.695406\pi$
$191$	5.80282	−	10.0508i	0.419877	−	0.727249i	0.995927	+	0.0901660i	$0.0287398\pi$
$192$		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
$195$	−13.6470	+	10.0751i	−0.977278	+	0.721492i
$196$		0			0
$197$	−4.32430	−	4.32430i	−0.308094	−	0.308094i	0.536076	−	0.844170i	$-0.319906\pi$
$197$	−4.32430	−	4.32430i	−0.308094	−	0.308094i	−0.844170	+	0.536076i	$0.819906\pi$
$198$		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
$203$	5.01156	+	1.34284i	0.351743	+	0.0942492i
$204$		0			0
$205$	−26.1186	+	6.99846i	−1.82420	+	0.488793i
$206$		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
$211$	19.0391	+	5.10152i	1.31071	+	0.351203i	0.845489	−	0.533993i	$-0.179309\pi$
$211$	19.0391	+	5.10152i	1.31071	+	0.351203i	0.465219	+	0.885196i	$0.345976\pi$
$212$		0			0
$213$	4.74668	+	2.07010i	0.325237	+	0.141841i
$214$		0			0
$215$			4.56197i			0.311124i
$216$		0			0
$217$			6.72933i			0.456817i
$218$		0			0
$219$	−20.2075	−	8.81282i	−1.36550	−	0.595515i
$220$		0			0
$221$	−23.4947	−	6.29538i	−1.58042	−	0.423473i
$222$		0			0
$223$	−10.9074	−	6.29741i	−0.730416	−	0.421706i	0.0881582	−	0.996106i	$-0.471902\pi$
$223$	−10.9074	−	6.29741i	−0.730416	−	0.421706i	−0.818574	+	0.574401i	$0.805235\pi$
$224$		0			0
$225$	2.41044	+	10.5462i	0.160696	+	0.703079i
$226$		0			0
$227$	11.6445	−	3.12014i	0.772874	−	0.207091i	0.149233	−	0.988802i	$-0.452320\pi$
$227$	11.6445	−	3.12014i	0.772874	−	0.207091i	0.623641	+	0.781711i	$0.285653\pi$
$228$		0			0
$229$	−5.47149	−	1.46608i	−0.361566	−	0.0968814i	0.0734624	−	0.997298i	$-0.476595\pi$
$229$	−5.47149	−	1.46608i	−0.361566	−	0.0968814i	−0.435029	+	0.900417i	$0.643262\pi$
$230$		0			0
$231$	2.51744	−	3.15775i	0.165635	−	0.207764i
$232$		0			0
$233$	10.1291			0.663580			0.331790	−	0.943353i	$-0.392347\pi$
$233$	10.1291			0.663580			0.331790	+	0.943353i	$0.392347\pi$
$234$		0			0
$235$	−11.8584	−	11.8584i	−0.773558	−	0.773558i
$236$		0			0
$237$	−14.3931	+	10.6260i	−0.934934	+	0.690230i
$238$		0			0
$239$	−0.263562	−	0.456503i	−0.0170484	−	0.0295287i	0.857375	−	0.514692i	$-0.172094\pi$
$239$	−0.263562	−	0.456503i	−0.0170484	−	0.0295287i	−0.874424	+	0.485163i	$0.838760\pi$
$240$		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
$243$	13.7875	+	7.27361i	0.884467	+	0.466603i
$244$		0			0
$245$	2.92920	−	0.784878i	0.187140	−	0.0501440i
$246$		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	−0.141101	+	0.989995i	$0.545064\pi$
$251$	−17.9199	+	17.9199i	−1.13110	+	1.13110i	−0.989995	+	0.141101i	$0.954936\pi$
$252$		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
$259$	6.26316	+	23.3744i	0.389174	+	1.45242i
$260$		0			0
$261$	−2.92026	+	4.65068i	−0.180760	+	0.287870i
$262$		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
$267$	−6.40476	+	14.6859i	−0.391965	+	0.898763i
$268$		0			0
$269$	−3.50729	+	3.50729i	−0.213843	+	0.213843i	−0.805898	−	0.592055i	$-0.798317\pi$
$269$	−3.50729	+	3.50729i	−0.213843	+	0.213843i	0.592055	+	0.805898i	$0.298317\pi$
$270$		0			0
$271$		−	2.25749i		−	0.137133i	−0.997647	−	0.0685665i	$-0.978157\pi$
$271$		−	2.25749i		−	0.137133i	0.997647	−	0.0685665i	$-0.0218425\pi$
$272$		0			0
$273$	−15.2555	+	5.99000i	−0.923306	+	0.362531i
$274$		0			0
$275$	−0.767751	+	2.86529i	−0.0462971	+	0.172783i
$276$		0			0
$277$	4.75826	+	17.7581i	0.285896	+	1.06698i	0.948182	+	0.317727i	$0.102920\pi$
$277$	4.75826	+	17.7581i	0.285896	+	1.06698i	−0.662286	+	0.749251i	$0.730414\pi$
$278$		0			0
$279$	−6.80673	−	2.09735i	−0.407508	−	0.125565i
$280$		0			0
$281$	4.38270	−	7.59106i	0.261450	−	0.452845i	−0.705177	−	0.709031i	$-0.749133\pi$
$281$	4.38270	−	7.59106i	0.261450	−	0.452845i	0.966627	+	0.256186i	$0.0824660\pi$
$282$		0			0
$283$	−4.18474	+	15.6177i	−0.248757	+	0.928375i	0.722700	+	0.691161i	$0.242901\pi$
$283$	−4.18474	+	15.6177i	−0.248757	+	0.928375i	−0.971458	+	0.237213i	$0.923766\pi$
$284$		0			0
$285$	6.79606	−	0.766769i	0.402564	−	0.0454195i
$286$		0			0
$287$	−26.1254			−1.54213
$288$		0			0
$289$	−36.0842			−2.12260
$290$		0			0
$291$	−0.306292	−	0.414880i	−0.0179552	−	0.0243207i
$292$		0			0
$293$	3.24540	−	12.1120i	0.189598	−	0.707589i	−0.804001	−	0.594628i	$-0.797300\pi$
$293$	3.24540	−	12.1120i	0.189598	−	0.707589i	0.993599	−	0.112962i	$-0.0360338\pi$
$294$		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
$299$	−5.12047	−	19.1098i	−0.296124	−	1.10515i
$300$		0			0
$301$	−1.14079	+	4.25749i	−0.0657540	+	0.245397i
$302$		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	−0.0830950	+	0.996542i	$0.526481\pi$
$307$	−18.9168	+	18.9168i	−1.07964	+	1.07964i	−0.996542	+	0.0830950i	$0.973519\pi$
$308$		0			0
$309$	19.7040	−	2.22311i	1.12092	−	0.126468i
$310$		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	0.847321	−	0.531081i	$-0.178214\pi$
$313$	14.3490	+	8.28438i	0.811051	+	0.468261i	−0.0362694	+	0.999342i	$0.511547\pi$
$314$		0			0
$315$	−0.925208	+	24.9277i	−0.0521296	+	1.40452i
$316$		0			0
$317$	−1.80531	−	6.73750i	−0.101396	−	0.378416i	0.896515	−	0.443013i	$-0.146090\pi$
$317$	−1.80531	−	6.73750i	−0.101396	−	0.378416i	−0.997911	+	0.0645973i	$0.979424\pi$
$318$		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
$331$	21.7853	−	5.83736i	1.19743	−	0.320850i	0.395612	−	0.918418i	$-0.370533\pi$
$331$	21.7853	−	5.83736i	1.19743	−	0.320850i	0.801819	+	0.597567i	$0.203866\pi$
$332$		0			0
$333$	−25.5954	−	0.949988i	−1.40262	−	0.0520590i
$334$		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
$339$	0.115171	+	1.02079i	0.00625523	+	0.0554416i
$340$		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
$347$	28.7569	+	7.70540i	1.54375	+	0.413647i	0.927476	−	0.373882i	$-0.121974\pi$
$347$	28.7569	+	7.70540i	1.54375	+	0.413647i	0.616277	+	0.787530i	$0.288640\pi$
$348$		0			0
$349$	8.65259	−	2.31845i	0.463163	−	0.124104i	−0.0196892	−	0.999806i	$-0.506268\pi$
$349$	8.65259	−	2.31845i	0.463163	−	0.124104i	0.482852	+	0.875702i	$0.339601\pi$
$350$		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
$355$	−8.47197	−	2.27006i	−0.449645	−	0.120482i
$356$		0			0
$357$	−28.7761	+	21.2444i	−1.52299	+	1.12438i
$358$		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
$363$	−2.00466	−	17.7678i	−0.105217	−	0.932566i
$364$		0			0
$365$	36.0668	+	9.66406i	1.88782	+	0.505840i
$366$		0			0
$367$	3.68240	+	2.12603i	0.192220	+	0.110978i	0.593021	−	0.805187i	$-0.297935\pi$
$367$	3.68240	+	2.12603i	0.192220	+	0.110978i	−0.400802	+	0.916165i	$0.631268\pi$
$368$		0			0
$369$	8.14259	−	26.4259i	0.423886	−	1.37568i
$370$		0			0
$371$	17.4564	−	4.67743i	0.906291	−	0.242840i
$372$		0			0
$373$	6.02298	+	1.61385i	0.311858	+	0.0835621i	0.411353	−	0.911476i	$-0.365056\pi$
$373$	6.02298	+	1.61385i	0.311858	+	0.0835621i	−0.0994955	+	0.995038i	$0.531723\pi$
$374$		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	0.899373	−	0.437182i	$-0.144023\pi$
$379$	8.99791	+	8.99791i	0.462192	+	0.462192i	−0.437182	+	0.899373i	$0.644023\pi$
$380$		0			0
$381$	22.5152	+	9.81923i	1.15349	+	0.503054i
$382$		0			0
$383$	4.35960	+	7.55105i	0.222765	+	0.385840i	0.955647	−	0.294516i	$-0.0951584\pi$
$383$	4.35960	+	7.55105i	0.222765	+	0.385840i	−0.732882	+	0.680356i	$0.761825\pi$
$384$		0			0
$385$	−3.41998	+	5.92357i	−0.174298	+	0.301893i
$386$		0			0
$387$	−3.95090	−	2.48086i	−0.200836	−	0.126109i
$388$		0			0
$389$	26.9041	−	7.20893i	1.36409	−	0.365507i	0.498774	−	0.866732i	$-0.333784\pi$
$389$	26.9041	−	7.20893i	1.36409	−	0.365507i	0.865317	+	0.501225i	$0.167117\pi$
$390$		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	0.796508	−	0.604628i	$-0.206678\pi$
$397$	3.82319	+	3.82319i	0.191880	+	0.191880i	−0.604628	+	0.796508i	$0.706678\pi$
$398$		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
$403$	2.05141	+	7.65596i	0.102188	+	0.381371i
$404$		0			0
$405$	−24.9261	−	8.70516i	−1.23859	−	0.432563i
$406$		0			0
$407$	−6.08222	−	3.51157i	−0.301485	−	0.174062i
$408$		0			0
$409$	−9.11179	+	5.26069i	−0.450549	+	0.260125i	−0.708062	−	0.706150i	$-0.750430\pi$
$409$	−9.11179	+	5.26069i	−0.450549	+	0.260125i	0.257513	+	0.966275i	$0.417097\pi$
$410$		0			0
$411$	8.19299	+	11.0976i	0.404131	+	0.547405i
$412$		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
$419$	3.32320	−	12.4024i	0.162349	−	0.605895i	−0.836014	−	0.548708i	$-0.815120\pi$
$419$	3.32320	−	12.4024i	0.162349	−	0.605895i	0.998363	−	0.0571875i	$-0.0182133\pi$
$420$		0			0
$421$	2.46909	+	9.21476i	0.120336	+	0.449100i	0.999631	−	0.0271782i	$-0.00865216\pi$
$421$	2.46909	+	9.21476i	0.120336	+	0.449100i	−0.879295	+	0.476278i	$0.841985\pi$
$422$		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
$427$	−6.13732	+	22.9048i	−0.297006	+	1.10844i
$428$		0			0
$429$	1.90147	−	4.36000i	0.0918037	−	0.210503i
$430$		0			0
$431$	−16.4451			−0.792131			−0.396065	−	0.918222i	$-0.629625\pi$
$431$	−16.4451			−0.792131			−0.396065	+	0.918222i	$0.629625\pi$
$432$		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
$435$	3.71814	−	8.52558i	0.178271	−	0.408770i
$436$		0			0
$437$	−2.06447	+	7.70471i	−0.0987570	+	0.368566i
$438$		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
$443$	−2.86151	−	10.6793i	−0.135954	−	0.507389i	−0.999992	−	0.00396162i	$-0.998739\pi$
$443$	−2.86151	−	10.6793i	−0.135954	−	0.507389i	0.864038	−	0.503427i	$-0.167928\pi$
$444$		0			0
$445$	7.02341	−	26.2117i	0.332941	−	1.24255i
$446$		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
$453$	−14.2744	−	19.3350i	−0.670670	−	0.908439i
$454$		0			0
$455$	24.0399	−	13.8795i	1.12701	−	0.650680i
$456$		0			0
$457$	−18.6606	−	10.7737i	−0.872905	−	0.503972i	−0.00459262	−	0.999989i	$-0.501462\pi$
$457$	−18.6606	−	10.7737i	−0.872905	−	0.503972i	−0.868313	+	0.496017i	$0.834795\pi$
$458$		0			0
$459$	−12.5201	−	35.7285i	−0.584386	−	1.66766i
$460$		0			0
$461$	−4.55312	−	16.9925i	−0.212060	−	0.791419i	−0.987181	−	0.159606i	$-0.948978\pi$
$461$	−4.55312	−	16.9925i	−0.212060	−	0.791419i	0.775121	−	0.631813i	$-0.217689\pi$
$462$		0			0
$463$	18.4389	−	10.6457i	0.856930	−	0.494749i	−0.00605328	−	0.999982i	$-0.501927\pi$
$463$	18.4389	−	10.6457i	0.856930	−	0.494749i	0.862983	+	0.505233i	$0.168593\pi$
$464$		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	$-0.277412\pi$
$467$	−2.62864	−	2.62864i	−0.121639	−	0.121639i	−0.765306	+	0.643667i	$0.777412\pi$
$468$		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
$475$	−4.68831	+	1.25623i	−0.215115	+	0.0576398i
$476$		0			0
$477$	−0.709466	+	19.1150i	−0.0324842	+	0.875217i
$478$		0			0
$479$	−10.7530	+	18.6247i	−0.491317	+	0.850986i	−0.999950	−	0.00999740i	$-0.996818\pi$
$479$	−10.7530	+	18.6247i	−0.491317	+	0.850986i	0.508633	+	0.860983i	$0.330151\pi$
$480$		0			0
$481$	14.2512	+	24.6838i	0.649799	+	1.12548i
$482$		0			0
$483$	−26.6674	−	11.6301i	−1.21341	−	0.529187i
$484$		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
$491$	−42.2317	−	11.3160i	−1.90589	−	0.510682i	−0.995233	−	0.0975209i	$-0.968909\pi$
$491$	−42.2317	−	11.3160i	−1.90589	−	0.510682i	−0.910658	−	0.413161i	$-0.864425\pi$
$492$		0			0
$493$	12.8824	−	3.45183i	0.580195	−	0.155463i
$494$		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
$499$	−7.91419	−	2.12060i	−0.354288	−	0.0949311i	0.0772856	−	0.997009i	$-0.475375\pi$
$499$	−7.91419	−	2.12060i	−0.354288	−	0.0949311i	−0.431573	+	0.902078i	$0.642041\pi$
$500$		0			0
$501$	1.92525	+	17.0639i	0.0860137	+	0.762360i
$502$		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
$507$	2.58466	−	1.90817i	0.114789	−	0.0847447i
$508$		0			0
$509$	−7.27785	−	1.95009i	−0.322585	−	0.0864364i	0.0938926	−	0.995582i	$-0.470069\pi$
$509$	−7.27785	−	1.95009i	−0.322585	−	0.0864364i	−0.416478	+	0.909146i	$0.636736\pi$
$510$		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
$515$	−32.4404	+	8.69237i	−1.42949	+	0.383032i
$516$		0			0
$517$	4.54231	+	1.21711i	0.199771	+	0.0535284i
$518$		0			0
$519$	−12.8598	−	1.93633i	−0.564484	−	0.0849954i
$520$		0			0
$521$	−29.5974			−1.29669			−0.648343	−	0.761349i	$-0.724538\pi$
$521$	−29.5974			−1.29669			−0.648343	+	0.761349i	$0.724538\pi$
$522$		0			0
$523$	−29.1710	−	29.1710i	−1.27556	−	1.27556i	−0.943128	−	0.332431i	$-0.892131\pi$
$523$	−29.1710	−	29.1710i	−1.27556	−	1.27556i	−0.332431	−	0.943128i	$-0.607869\pi$
$524$		0			0
$525$	−1.98477	−	17.5915i	−0.0866226	−	0.767757i
$526$		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
$531$	−15.4724	−	29.2539i	−0.671445	−	1.26951i
$532$		0			0
$533$	−29.7229	+	7.96422i	−1.28744	+	0.344969i
$534$		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	0.855771	−	0.517355i	$-0.173083\pi$
$541$	7.87135	+	7.87135i	0.338416	+	0.338416i	−0.517355	+	0.855771i	$0.673083\pi$
$542$		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
$547$	0.817385	+	3.05052i	0.0349488	+	0.130431i	0.981196	−	0.193013i	$-0.0618260\pi$
$547$	0.817385	+	3.05052i	0.0349488	+	0.130431i	−0.946247	+	0.323444i	$0.895159\pi$
$548$		0			0
$549$	−21.2554	−	13.3467i	−0.907159	−	0.569625i
$550$		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
$555$	43.1077	−	4.86364i	1.82982	−	0.206450i
$556$		0			0
$557$	22.4110	−	22.4110i	0.949583	−	0.949583i	−0.0492055	−	0.998789i	$-0.515669\pi$
$557$	22.4110	−	22.4110i	0.949583	−	0.949583i	0.998789	+	0.0492055i	$0.0156689\pi$
$558$		0			0
$559$			5.19151i			0.219577i
$560$		0			0
$561$	1.54565	−	10.2652i	0.0652574	−	0.433398i
$562$		0			0
$563$	8.11646	−	30.2910i	0.342068	−	1.27661i	−0.553933	−	0.832561i	$-0.686873\pi$
$563$	8.11646	−	30.2910i	0.342068	−	1.27661i	0.896000	−	0.444053i	$-0.146460\pi$
$564$		0			0
$565$	−0.450319	−	1.68061i	−0.0189450	−	0.0707039i
$566$		0			0
$567$	−21.0855	−	14.3573i	−0.885510	−	0.602949i
$568$		0			0
$569$	2.78787	−	4.82873i	0.116874	−	0.202431i	−0.801654	−	0.597789i	$-0.796046\pi$
$569$	2.78787	−	4.82873i	0.116874	−	0.202431i	0.918527	+	0.395358i	$0.129379\pi$
$570$		0			0
$571$	−5.39076	+	20.1186i	−0.225596	+	0.841937i	0.756568	+	0.653915i	$0.226874\pi$
$571$	−5.39076	+	20.1186i	−0.225596	+	0.841937i	−0.982165	+	0.188023i	$0.939792\pi$
$572$		0			0
$573$	−11.9391	−	16.1719i	−0.498765	−	0.675590i
$574$		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
$579$	17.5408	−	1.97905i	0.728971	−	0.0822465i
$580$		0			0
$581$	−2.84584	+	10.6208i	−0.118065	+	0.440626i
$582$		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
$587$	8.19230	+	30.5741i	0.338132	+	1.26193i	0.900433	+	0.434994i	$0.143250\pi$
$587$	8.19230	+	30.5741i	0.338132	+	1.26193i	−0.562301	+	0.826933i	$0.690084\pi$
$588$		0			0
$589$	0.827087	−	3.08673i	0.0340795	−	0.127186i
$590$		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
$597$	19.1973	−	44.0187i	0.785693	−	1.80157i
$598$		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	$-0.943526\pi$
$601$	−39.9427	−	23.0610i	−1.62930	−	0.940676i	−0.644996	−	0.764186i	$-0.723141\pi$
$602$		0			0
$603$	16.2265	+	30.6796i	0.660794	+	1.24937i
$604$		0			0
$605$	7.83822	+	29.2526i	0.318669	+	1.18929i
$606$		0			0
$607$	−25.9512	+	14.9830i	−1.05333	+	0.608139i	−0.923579	−	0.383408i	$-0.874750\pi$
$607$	−25.9512	+	14.9830i	−1.05333	+	0.608139i	−0.129749	+	0.991547i	$0.541417\pi$
$608$		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	−0.788917	−	0.614499i	$-0.789358\pi$
$613$	−4.31839	+	4.31839i	−0.174418	+	0.174418i	0.614499	+	0.788917i	$0.289358\pi$
$614$		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	$-0.971014\pi$
$617$	−14.3245	−	24.8108i	−0.576683	−	0.998844i	0.419174	−	0.907906i	$-0.362320\pi$
$618$		0			0
$619$	31.5053	−	8.44181i	1.26630	−	0.339305i	0.437690	−	0.899126i	$-0.355797\pi$
$619$	31.5053	−	8.44181i	1.26630	−	0.339305i	0.828614	+	0.559821i	$0.189130\pi$
$620$		0			0
$621$	20.0754	−	23.3493i	0.805597	−	0.936977i
$622$		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
$627$	−1.54286	+	1.13904i	−0.0616158	+	0.0454888i
$628$		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
$635$	−40.1855	−	10.7677i	−1.59471	−	0.427302i
$636$		0			0
$637$	3.33342	−	0.893188i	0.132075	−	0.0353894i
$638$		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
$643$	−23.4845	−	6.29265i	−0.926138	−	0.248158i	−0.235931	−	0.971770i	$-0.575814\pi$
$643$	−23.4845	−	6.29265i	−0.926138	−	0.248158i	−0.690207	+	0.723612i	$0.742481\pi$
$644$		0			0
$645$	7.24276	+	3.15868i	0.285183	+	0.124373i
$646$		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
$651$	10.6837	+	4.65935i	0.418728	+	0.182614i
$652$		0			0
$653$	38.1014	+	10.2092i	1.49102	+	0.399519i	0.910082	−	0.414427i	$-0.136018\pi$
$653$	38.1014	+	10.2092i	1.49102	+	0.399519i	0.580941	+	0.813946i	$0.302685\pi$
$654$		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
$659$	−13.5220	+	3.62321i	−0.526742	+	0.141140i	−0.512383	−	0.858757i	$-0.671237\pi$
$659$	−13.5220	+	3.62321i	−0.526742	+	0.141140i	−0.0143586	+	0.999897i	$0.504571\pi$
$660$		0			0
$661$	−40.1488	−	10.7578i	−1.56161	−	0.418432i	−0.628436	−	0.777861i	$-0.716305\pi$
$661$	−40.1488	−	10.7578i	−1.56161	−	0.418432i	−0.933172	+	0.359430i	$0.882971\pi$
$662$		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
$669$	−17.5503	+	12.9568i	−0.678532	+	0.500937i
$670$		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
$675$	18.4125	+	3.47521i	0.708696	+	0.133761i
$676$		0			0
$677$	−27.1438	+	7.27316i	−1.04322	+	0.279530i	−0.739447	−	0.673214i	$-0.764913\pi$
$677$	−27.1438	+	7.27316i	−1.04322	+	0.279530i	−0.303773	+	0.952744i	$0.598246\pi$
$678$		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	$-0.788928\pi$
$683$	−4.50875	+	4.50875i	−0.172522	+	0.172522i	0.615564	+	0.788087i	$0.288928\pi$
$684$		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
$691$	2.65522	+	9.90941i	0.101009	+	0.376972i	0.997862	−	0.0653578i	$-0.0208189\pi$
$691$	2.65522	+	9.90941i	0.101009	+	0.376972i	−0.896853	+	0.442329i	$0.854152\pi$
$692$		0			0
$693$	−3.27029	−	6.18319i	−0.124228	−	0.234880i
$694$		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
$699$	7.01333	−	16.0813i	0.265269	−	0.608252i
$700$		0			0
$701$	16.5518	−	16.5518i	0.625154	−	0.625154i	−0.321691	−	0.946845i	$-0.604251\pi$
$701$	16.5518	−	16.5518i	0.625154	−	0.625154i	0.946845	+	0.321691i	$0.104251\pi$
$702$		0			0
$703$		−	11.4916i		−	0.433414i
$704$		0			0
$705$	−27.0376	+	10.6162i	−1.01829	+	0.399828i
$706$		0			0
$707$	−6.00445	+	22.4089i	−0.225821	+	0.842774i
$708$		0			0
$709$	10.7915	+	40.2743i	0.405282	+	1.51253i	0.803535	+	0.595257i	$0.202950\pi$
$709$	10.7915	+	40.2743i	0.405282	+	1.51253i	−0.398253	+	0.917276i	$0.630383\pi$
$710$		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
$715$	−2.08513	+	7.78182i	−0.0779795	+	0.291023i
$716$		0			0
$717$	−0.907249	+	0.102361i	−0.0338818	+	0.00382274i
$718$		0			0
$719$	26.8494			1.00131			0.500656	−	0.865646i	$-0.333092\pi$
$719$	26.8494			1.00131			0.500656	+	0.865646i	$0.333092\pi$
$720$		0			0
$721$	−32.4488			−1.20846
$722$		0			0
$723$	−20.0467	−	27.1538i	−0.745547	−	1.00986i
$724$		0			0
$725$	−1.70843	+	6.37597i	−0.0634497	+	0.236797i
$726$		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
$731$	2.93245	+	10.9440i	0.108460	+	0.404780i
$732$		0			0
$733$	5.85501	−	21.8512i	0.216260	−	0.807093i	−0.769459	−	0.638696i	$-0.779474\pi$
$733$	5.85501	−	21.8512i	0.216260	−	0.807093i	0.985719	−	0.168397i	$-0.0538591\pi$
$734$		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	−0.434461	−	0.900691i	$-0.643061\pi$
$739$	12.6742	−	12.6742i	0.466230	−	0.466230i	0.900691	+	0.434461i	$0.143061\pi$
$740$		0			0
$741$	7.73389	−	0.872580i	0.284112	−	0.0320550i
$742$		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
$747$	−9.85601	−	6.18880i	−0.360612	−	0.226436i
$748$		0			0
$749$	−0.181500	−	0.677369i	−0.00663188	−	0.0247505i
$750$		0			0
$751$	23.9864	−	13.8486i	0.875277	−	0.505341i	0.00617885	−	0.999981i	$-0.498033\pi$
$751$	23.9864	−	13.8486i	0.875277	−	0.505341i	0.869098	+	0.494639i	$0.164700\pi$
$752$		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	−0.820533	−	0.571599i	$-0.806323\pi$
$757$	−6.84906	+	6.84906i	−0.248933	+	0.248933i	0.571599	+	0.820533i	$0.306323\pi$
$758$		0			0
$759$	7.85940	−	3.08595i	0.285278	−	0.112013i
$760$		0			0
$761$	−6.92685	−	11.9977i	−0.251098	−	0.434915i	0.712730	−	0.701438i	$-0.247458\pi$
$761$	−6.92685	−	11.9977i	−0.251098	−	0.434915i	−0.963828	+	0.266523i	$0.914125\pi$
$762$		0			0
$763$	−5.84262	+	1.56553i	−0.211517	+	0.0566758i
$764$		0			0
$765$	29.9792	+	56.6821i	1.08390	+	2.04934i
$766$		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
$771$	−3.27714	−	29.0461i	−0.118023	−	1.04607i
$772$		0			0
$773$	−29.0684	−	29.0684i	−1.04552	−	1.04552i	−0.998913	−	0.0466043i	$-0.985160\pi$
$773$	−29.0684	−	29.0684i	−1.04552	−	1.04552i	−0.0466043	−	0.998913i	$-0.514840\pi$
$774$		0			0
$775$	−8.56139			−0.307534
$776$		0			0
$777$	41.4467	+	6.24069i	1.48689	+	0.223884i
$778$		0			0
$779$	11.9837	+	3.21101i	0.429359	+	0.115046i
$780$		0			0
$781$	2.37561	−	0.636543i	0.0850060	−	0.0227773i
$782$		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
$787$	35.9593	+	9.63526i	1.28181	+	0.343460i	0.834544	−	0.550941i	$-0.185731\pi$
$787$	35.9593	+	9.63526i	1.28181	+	0.343460i	0.447266	+	0.894401i	$0.352398\pi$
$788$		0			0
$789$	30.2599	−	22.3399i	1.07728	−	0.795321i
$790$		0			0
$791$		−	1.68105i		−	0.0597712i
$792$		0			0
$793$			27.9297i			0.991814i
$794$		0			0
$795$	−3.63225	−	32.1935i	−0.128823	−	1.14179i
$796$		0			0
$797$	9.38318	+	2.51421i	0.332369	+	0.0890580i	0.421144	−	0.906994i	$-0.361629\pi$
$797$	9.38318	+	2.51421i	0.332369	+	0.0890580i	−0.0887752	+	0.996052i	$0.528295\pi$
$798$		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
$803$	−10.1134	+	2.70988i	−0.356895	+	0.0956297i
$804$		0			0
$805$	47.5965	+	12.7534i	1.67756	+	0.449500i
$806$		0			0
$807$	3.13987	+	7.99673i	0.110529	+	0.281498i
$808$		0			0
$809$	13.1867			0.463620			0.231810	−	0.972761i	$-0.425535\pi$
$809$	13.1867			0.463620			0.231810	+	0.972761i	$0.425535\pi$
$810$		0			0
$811$	11.0093	+	11.0093i	0.386587	+	0.386587i	0.873468	−	0.486881i	$-0.161865\pi$
$811$	11.0093	+	11.0093i	0.386587	+	0.386587i	−0.486881	+	0.873468i	$0.661865\pi$
$812$		0			0
$813$	−3.58408	−	1.56307i	−0.125699	−	0.0548194i
$814$		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
$819$	−1.05288	+	28.3677i	−0.0367907	+	0.991246i
$820$		0			0
$821$	−4.17943	+	1.11987i	−0.145863	+	0.0390839i	−0.331012	−	0.943627i	$-0.607390\pi$
$821$	−4.17943	+	1.11987i	−0.145863	+	0.0390839i	0.185149	+	0.982711i	$0.440723\pi$
$822$		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	$-0.739148\pi$
$827$	1.38625	−	1.38625i	0.0482045	−	0.0482045i	0.730798	+	0.682594i	$0.239148\pi$
$828$		0			0
$829$	−21.8345	−	21.8345i	−0.758345	−	0.758345i	0.217676	−	0.976021i	$-0.430152\pi$
$829$	−21.8345	−	21.8345i	−0.758345	−	0.758345i	−0.976021	+	0.217676i	$0.930152\pi$
$830$		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
$835$	−7.52771	−	28.0938i	−0.260507	−	0.972227i
$836$		0			0
$837$	−8.04278	+	9.35442i	−0.277999	+	0.323336i
$838$		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
$843$	−9.01729	−	12.2141i	−0.310572	−	0.420678i
$844$		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
$851$	−13.0950	+	48.8712i	−0.448891	+	1.67528i
$852$		0			0
$853$	−12.0354	−	44.9166i	−0.412083	−	1.53791i	−0.790608	−	0.612323i	$-0.790235\pi$
$853$	−12.0354	−	44.9166i	−0.412083	−	1.53791i	0.378525	−	0.925591i	$-0.376431\pi$
$854$		0			0
$855$	3.48820	−	11.3206i	0.119294	−	0.387156i
$856$		0			0
$857$	−10.0139	+	17.3446i	−0.342068	+	0.592480i	−0.984817	−	0.173598i	$-0.944461\pi$
$857$	−10.0139	+	17.3446i	−0.342068	+	0.592480i	0.642748	+	0.766077i	$0.277794\pi$
$858$		0			0
$859$	4.47358	−	16.6956i	0.152637	−	0.569648i	−0.846659	−	0.532135i	$-0.821390\pi$
$859$	4.47358	−	16.6956i	0.152637	−	0.569648i	0.999296	−	0.0375129i	$-0.0119435\pi$
$860$		0			0
$861$	−18.0891	+	41.4776i	−0.616474	+	1.41355i
$862$		0			0
$863$	24.4242			0.831410			0.415705	−	0.909499i	$-0.363535\pi$
$863$	24.4242			0.831410			0.415705	+	0.909499i	$0.363535\pi$
$864$		0			0
$865$	22.0265			0.748923
$866$		0			0
$867$	−24.9845	+	57.2886i	−0.848518	+	1.94562i
$868$		0			0
$869$	−2.19914	+	8.20731i	−0.0746007	+	0.278414i
$870$		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
$875$	−2.99989	−	11.1957i	−0.101415	−	0.378485i
$876$		0			0
$877$	−9.26415	+	34.5743i	−0.312828	+	1.16749i	0.613167	+	0.789954i	$0.289895\pi$
$877$	−9.26415	+	34.5743i	−0.312828	+	1.16749i	−0.925995	+	0.377537i	$0.876771\pi$
$878$		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	−0.818188	−	0.574950i	$-0.805021\pi$
$883$	−7.22790	+	7.22790i	−0.243238	+	0.243238i	0.574950	+	0.818188i	$0.305021\pi$
$884$		0			0
$885$	33.2911	+	45.0936i	1.11907	+	1.51581i
$886$		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
$891$	7.27357	−	1.38077i	0.243674	−	0.0462577i
$892$		0			0
$893$	1.99149	+	7.43234i	0.0666426	+	0.248714i
$894$		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
$907$	−38.9844	+	10.4458i	−1.29445	+	0.346848i	−0.839351	−	0.543590i	$-0.817065\pi$
$907$	−38.9844	+	10.4458i	−1.29445	+	0.346848i	−0.455104	+	0.890438i	$0.650398\pi$
$908$		0			0
$909$	−20.7953	−	13.0578i	−0.689735	−	0.433099i
$910$		0			0
$911$	−22.6553	+	39.2402i	−0.750605	+	1.30009i	0.196925	+	0.980419i	$0.436905\pi$
$911$	−22.6553	+	39.2402i	−0.750605	+	1.30009i	−0.947530	+	0.319667i	$0.896429\pi$
$912$		0			0
$913$	−1.59558	−	2.76362i	−0.0528060	−	0.0914626i
$914$		0			0
$915$	38.9652	+	16.9934i	1.28815	+	0.561784i
$916$		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
$923$	−9.64107	−	2.58332i	−0.317340	−	0.0850309i
$924$		0			0
$925$	−29.7381	+	7.96831i	−0.977784	+	0.261996i
$926$		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
$931$	−1.34397	−	0.360116i	−0.0440468	−	0.0118023i
$932$		0			0
$933$	−1.14057	−	10.1092i	−0.0373407	−	0.330960i
$934$		0			0
$935$			17.5824i			0.575005i
$936$		0			0
$937$			38.0380i			1.24265i	0.783554	+	0.621324i	$0.213405\pi$
$937$			38.0380i			1.24265i	−0.783554	+	0.621324i	$0.786595\pi$
$938$		0			0
$939$	23.0877	−	17.0449i	0.753439	−	0.556239i
$940$		0			0
$941$	−49.4756	−	13.2570i	−1.61286	−	0.432164i	−0.663966	−	0.747762i	$-0.731128\pi$
$941$	−49.4756	−	13.2570i	−1.61286	−	0.432164i	−0.948893	+	0.315598i	$0.897795\pi$
$942$		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
$947$	−15.8269	+	4.24080i	−0.514305	+	0.137808i	−0.506631	−	0.862163i	$-0.669109\pi$
$947$	−15.8269	+	4.24080i	−0.514305	+	0.137808i	−0.00767376	+	0.999971i	$0.502443\pi$
$948$		0			0
$949$	41.0438	+	10.9977i	1.33234	+	0.356999i
$950$		0			0
$951$	−11.9467	−	1.79883i	−0.387398	−	0.0583311i
$952$		0			0
$953$	19.2107			0.622295			0.311147	−	0.950362i	$-0.399287\pi$
$953$	19.2107			0.622295			0.311147	+	0.950362i	$0.399287\pi$
$954$		0			0
$955$	24.0744	+	24.0744i	0.779030	+	0.779030i
$956$		0			0
$957$	0.292405	+	2.59166i	0.00945211	+	0.0837764i
$958$		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
$963$	0.741729	+	0.0275297i	0.0239019	+	0.000887134i
$964$		0			0
$965$	−28.8789	+	7.73809i	−0.929646	+	0.249098i
$966$		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	$-0.901588\pi$
$971$	−20.2022	+	20.2022i	−0.648318	+	0.648318i	0.304268	+	0.952586i	$0.401588\pi$
$972$		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
$979$	1.96942	+	7.34998i	0.0629430	+	0.234906i
$980$		0			0
$981$	0.237457	−	6.39776i	0.00758141	−	0.204265i
$982$		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
$987$	−27.8877	+	3.14644i	−0.887675	+	0.100152i
$988$		0			0
$989$	−6.51638	+	6.51638i	−0.207209	+	0.207209i
$990$		0			0
$991$		−	61.9180i		−	1.96689i	−0.181210	−	0.983444i	$-0.558001\pi$
$991$		−	61.9180i		−	1.96689i	0.181210	−	0.983444i	$-0.441999\pi$
$992$		0			0
$993$	5.81643	−	38.6290i	0.184579	−	1.22585i
$994$		0			0
$995$	−21.0516	+	78.5655i	−0.667380	+	2.49069i
$996$		0			0
$997$	−4.65375	−	17.3680i	−0.147386	−	0.550051i	−0.999638	−	0.0269194i	$-0.991430\pi$
$997$	−4.65375	−	17.3680i	−0.147386	−	0.550051i	0.852252	−	0.523132i	$-0.175236\pi$
$998$		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.47.15		88
3.2	odd	2		1728.2.z.a.1007.20		88
4.3	odd	2		144.2.u.a.83.11	yes	88
9.4	even	3		1728.2.z.a.1583.20		88
9.5	odd	6	inner	576.2.y.a.239.19		88
12.11	even	2		432.2.v.a.35.12		88
16.5	even	4		144.2.u.a.11.18	✓	88
16.11	odd	4	inner	576.2.y.a.335.19		88
36.23	even	6		144.2.u.a.131.18	yes	88
36.31	odd	6		432.2.v.a.179.5		88
48.5	odd	4		432.2.v.a.251.5		88
48.11	even	4		1728.2.z.a.143.20		88
144.5	odd	12		144.2.u.a.59.11	yes	88
144.59	even	12	inner	576.2.y.a.527.15		88
144.85	even	12		432.2.v.a.395.12		88
144.139	odd	12		1728.2.z.a.719.20		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.18	✓	88	16.5	even	4
144.2.u.a.59.11	yes	88	144.5	odd	12
144.2.u.a.83.11	yes	88	4.3	odd	2
144.2.u.a.131.18	yes	88	36.23	even	6
432.2.v.a.35.12		88	12.11	even	2
432.2.v.a.179.5		88	36.31	odd	6
432.2.v.a.251.5		88	48.5	odd	4
432.2.v.a.395.12		88	144.85	even	12
576.2.y.a.47.15		88	1.1	even	1	trivial
576.2.y.a.239.19		88	9.5	odd	6	inner
576.2.y.a.335.19		88	16.11	odd	4	inner
576.2.y.a.527.15		88	144.59	even	12	inner
1728.2.z.a.143.20		88	48.11	even	4
1728.2.z.a.719.20		88	144.139	odd	12
1728.2.z.a.1007.20		88	3.2	odd	2
1728.2.z.a.1583.20		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)

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