LMFDB - Embedded newform 1323.2.o.e.440.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(440,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("1323.440");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.o (of order $6$, degree $2$, 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:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			440.16
Character	$\chi$	$=$	1323.440
Dual form			1323.2.o.e.881.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.850109 + 0.490811i) q^{2} +(-0.518210 - 0.897565i) q^{4} +(-0.940599 - 1.62916i) q^{5} -2.98061i q^{8} +O(q^{10})$	\(q+(0.850109 + 0.490811i) q^{2} +(-0.518210 - 0.897565i) q^{4} +(-0.940599 - 1.62916i) q^{5} -2.98061i q^{8} -1.84662i q^{10} +(-3.54040 - 2.04405i) q^{11} +(-3.51415 + 2.02890i) q^{13} +(0.426498 - 0.738716i) q^{16} +1.62145 q^{17} +8.12588i q^{19} +(-0.974855 + 1.68850i) q^{20} +(-2.00648 - 3.47533i) q^{22} +(-3.73318 + 2.15535i) q^{23} +(0.730548 - 1.26535i) q^{25} -3.98322 q^{26} +(0.542317 + 0.313107i) q^{29} +(-3.69833 + 2.13523i) q^{31} +(-4.43744 + 2.56195i) q^{32} +(1.37841 + 0.795827i) q^{34} +7.94153 q^{37} +(-3.98827 + 6.90789i) q^{38} +(-4.85591 + 2.80356i) q^{40} +(0.912023 + 1.57967i) q^{41} +(-3.53614 + 6.12477i) q^{43} +4.23698i q^{44} -4.23148 q^{46} +(-3.96868 + 6.87396i) q^{47} +(1.24209 - 0.717122i) q^{50} +(3.64214 + 2.10279i) q^{52} -8.37133i q^{53} +7.69052i q^{55} +(0.307352 + 0.532350i) q^{58} +(-4.08715 - 7.07915i) q^{59} +(-3.24253 - 1.87208i) q^{61} -4.19198 q^{62} -6.73573 q^{64} +(6.61081 + 3.81676i) q^{65} +(-6.26559 - 10.8523i) q^{67} +(-0.840253 - 1.45536i) q^{68} -14.4969i q^{71} +3.78935i q^{73} +(6.75117 + 3.89779i) q^{74} +(7.29351 - 4.21091i) q^{76} +(-4.18066 + 7.24112i) q^{79} -1.60465 q^{80} +1.79052i q^{82} +(4.38300 - 7.59159i) q^{83} +(-1.52514 - 2.64162i) q^{85} +(-6.01221 + 3.47115i) q^{86} +(-6.09252 + 10.5526i) q^{88} -9.80759 q^{89} +(3.86914 + 2.23385i) q^{92} +(-6.74762 + 3.89574i) q^{94} +(13.2384 - 7.64320i) q^{95} +(-11.4579 - 6.61525i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4}+O(q^{10}) $ 48 * q + 24 * q^4	$ 48 q + 24 q^{4} + 24 q^{11} - 24 q^{16} + 48 q^{23} - 24 q^{25} - 120 q^{32} - 48 q^{50} - 48 q^{64} - 120 q^{65} + 168 q^{74} - 24 q^{79} - 24 q^{85} - 24 q^{86} + 144 q^{92} - 96 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 + 24 * q^11 - 24 * q^16 + 48 * q^23 - 24 * q^25 - 120 * q^32 - 48 * q^50 - 48 * q^64 - 120 * q^65 + 168 * q^74 - 24 * q^79 - 24 * q^85 - 24 * q^86 + 144 * q^92 - 96 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.850109	+	0.490811i	0.601118	+	0.347056i	0.769481	−	0.638669i	$-0.220515\pi$
$2$	0.850109	+	0.490811i	0.601118	+	0.347056i	−0.168363	+	0.985725i	$0.553848\pi$
$3$		0			0
$3$		0			0
$4$	−0.518210	−	0.897565i	−0.259105	−	0.448783i
$5$	−0.940599	−	1.62916i	−0.420648	−	0.728585i	0.575355	−	0.817904i	$-0.304864\pi$
$5$	−0.940599	−	1.62916i	−0.420648	−	0.728585i	−0.996003	+	0.0893196i	$0.971531\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	2.98061i		−	1.05381i
$9$		0			0
$10$		−	1.84662i		−	0.583954i
$11$	−3.54040	−	2.04405i	−1.06747	−	0.616304i	−0.139980	−	0.990154i	$-0.544704\pi$
$11$	−3.54040	−	2.04405i	−1.06747	−	0.616304i	−0.927489	+	0.373850i	$0.878037\pi$
$12$		0			0
$13$	−3.51415	+	2.02890i	−0.974651	+	0.562715i	−0.900651	−	0.434544i	$-0.856910\pi$
$13$	−3.51415	+	2.02890i	−0.974651	+	0.562715i	−0.0739997	+	0.997258i	$0.523576\pi$
$14$		0			0
$15$		0			0
$16$	0.426498	−	0.738716i	0.106625	−	0.184679i
$17$	1.62145			0.393260			0.196630	−	0.980478i	$-0.437000\pi$
$17$	1.62145			0.393260			0.196630	+	0.980478i	$0.437000\pi$
$18$		0			0
$19$			8.12588i			1.86421i	0.362194	+	0.932103i	$0.382028\pi$
$19$			8.12588i			1.86421i	−0.362194	+	0.932103i	$0.617972\pi$
$20$	−0.974855	+	1.68850i	−0.217984	+	0.377560i
$21$		0			0
$22$	−2.00648	−	3.47533i	−0.427783	−	0.740943i
$23$	−3.73318	+	2.15535i	−0.778423	+	0.449423i	−0.835871	−	0.548926i	$-0.815037\pi$
$23$	−3.73318	+	2.15535i	−0.778423	+	0.449423i	0.0574484	+	0.998348i	$0.481704\pi$
$24$		0			0
$25$	0.730548	−	1.26535i	0.146110	−	0.253069i
$26$	−3.98322			−0.781173
$27$		0			0
$28$		0			0
$29$	0.542317	+	0.313107i	0.100706	+	0.0581425i	0.549507	−	0.835489i	$-0.314816\pi$
$29$	0.542317	+	0.313107i	0.100706	+	0.0581425i	−0.448801	+	0.893632i	$0.648149\pi$
$30$		0			0
$31$	−3.69833	+	2.13523i	−0.664240	+	0.383499i	−0.793891	−	0.608060i	$-0.791948\pi$
$31$	−3.69833	+	2.13523i	−0.664240	+	0.383499i	0.129650	+	0.991560i	$0.458615\pi$
$32$	−4.43744	+	2.56195i	−0.784435	+	0.452894i
$33$		0			0
$34$	1.37841	+	0.795827i	0.236396	+	0.136483i
$35$		0			0
$36$		0			0
$37$	7.94153			1.30558			0.652790	−	0.757539i	$-0.273599\pi$
$37$	7.94153			1.30558			0.652790	+	0.757539i	$0.273599\pi$
$38$	−3.98827	+	6.90789i	−0.646983	+	1.12061i
$39$		0			0
$40$	−4.85591	+	2.80356i	−0.767787	+	0.443282i
$41$	0.912023	+	1.57967i	0.142434	+	0.246703i	0.928413	−	0.371551i	$-0.121174\pi$
$41$	0.912023	+	1.57967i	0.142434	+	0.246703i	−0.785979	+	0.618254i	$0.787840\pi$
$42$		0			0
$43$	−3.53614	+	6.12477i	−0.539256	+	0.934019i	0.459688	+	0.888080i	$0.347961\pi$
$43$	−3.53614	+	6.12477i	−0.539256	+	0.934019i	−0.998944	+	0.0459387i	$0.985372\pi$
$44$			4.23698i			0.638749i
$45$		0			0
$46$	−4.23148			−0.623898
$47$	−3.96868	+	6.87396i	−0.578891	+	1.00267i	0.416715	+	0.909037i	$0.363181\pi$
$47$	−3.96868	+	6.87396i	−0.578891	+	1.00267i	−0.995607	+	0.0936324i	$0.970152\pi$
$48$		0			0
$49$		0			0
$50$	1.24209	−	0.717122i	0.175658	−	0.101416i
$51$		0			0
$52$	3.64214	+	2.10279i	0.505073	+	0.291604i
$53$		−	8.37133i		−	1.14989i	−0.818192	−	0.574945i	$-0.805023\pi$
$53$		−	8.37133i		−	1.14989i	0.818192	−	0.574945i	$-0.194977\pi$
$54$		0			0
$55$			7.69052i			1.03699i
$56$		0			0
$57$		0			0
$58$	0.307352	+	0.532350i	0.0403573	+	0.0699009i
$59$	−4.08715	−	7.07915i	−0.532101	−	0.921627i	−0.999298	−	0.0374731i	$-0.988069\pi$
$59$	−4.08715	−	7.07915i	−0.532101	−	0.921627i	0.467196	−	0.884154i	$-0.345264\pi$
$60$		0			0
$61$	−3.24253	−	1.87208i	−0.415164	−	0.239695i	0.277842	−	0.960627i	$-0.410381\pi$
$61$	−3.24253	−	1.87208i	−0.415164	−	0.239695i	−0.693006	+	0.720932i	$0.743714\pi$
$62$	−4.19198			−0.532382
$63$		0			0
$64$	−6.73573			−0.841966
$65$	6.61081	+	3.81676i	0.819971	+	0.473410i
$66$		0			0
$67$	−6.26559	−	10.8523i	−0.765464	−	1.32582i	−0.940001	−	0.341171i	$-0.889176\pi$
$67$	−6.26559	−	10.8523i	−0.765464	−	1.32582i	0.174537	−	0.984651i	$-0.444157\pi$
$68$	−0.840253	−	1.45536i	−0.101896	−	0.176489i
$69$		0			0
$70$		0			0
$71$		−	14.4969i		−	1.72047i	−0.509898	−	0.860235i	$-0.670317\pi$
$71$		−	14.4969i		−	1.72047i	0.509898	−	0.860235i	$-0.329683\pi$
$72$		0			0
$73$			3.78935i			0.443510i	0.975102	+	0.221755i	$0.0711785\pi$
$73$			3.78935i			0.443510i	−0.975102	+	0.221755i	$0.928821\pi$
$74$	6.75117	+	3.89779i	0.784807	+	0.453109i
$75$		0			0
$76$	7.29351	−	4.21091i	0.836623	−	0.483025i
$77$		0			0
$78$		0			0
$79$	−4.18066	+	7.24112i	−0.470361	+	0.814690i	−0.999426	−	0.0338919i	$-0.989210\pi$
$79$	−4.18066	+	7.24112i	−0.470361	+	0.814690i	0.529064	+	0.848582i	$0.322543\pi$
$80$	−1.60465			−0.179406
$81$		0			0
$82$			1.79052i			0.197730i
$83$	4.38300	−	7.59159i	0.481097	−	0.833285i	−0.518668	−	0.854976i	$-0.673572\pi$
$83$	4.38300	−	7.59159i	0.481097	−	0.833285i	0.999765	+	0.0216912i	$0.00690508\pi$
$84$		0			0
$85$	−1.52514	−	2.64162i	−0.165424	−	0.286524i
$86$	−6.01221	+	3.47115i	−0.648313	+	0.374304i
$87$		0			0
$88$	−6.09252	+	10.5526i	−0.649465	+	1.12491i
$89$	−9.80759			−1.03960			−0.519801	−	0.854287i	$-0.673994\pi$
$89$	−9.80759			−1.03960			−0.519801	+	0.854287i	$0.673994\pi$
$90$		0			0
$91$		0			0
$92$	3.86914	+	2.23385i	0.403386	+	0.232895i
$93$		0			0
$94$	−6.74762	+	3.89574i	−0.695964	+	0.401815i
$95$	13.2384	−	7.64320i	1.35823	−	0.784175i
$96$		0			0
$97$	−11.4579	−	6.61525i	−1.16338	−	0.671677i	−0.211267	−	0.977428i	$-0.567759\pi$
$97$	−11.4579	−	6.61525i	−1.16338	−	0.671677i	−0.952111	+	0.305752i	$0.901092\pi$
$98$		0			0
$99$		0			0
$100$	−1.51431			−0.151431
$101$	−0.524900	+	0.909154i	−0.0522295	+	0.0904642i	−0.890958	−	0.454085i	$-0.849966\pi$
$101$	−0.524900	+	0.909154i	−0.0522295	+	0.0904642i	0.838729	+	0.544550i	$0.183299\pi$
$102$		0			0
$103$	1.41937	−	0.819472i	0.139854	−	0.0807449i	−0.428440	−	0.903570i	$-0.640937\pi$
$103$	1.41937	−	0.819472i	0.139854	−	0.0807449i	0.568295	+	0.822825i	$0.307603\pi$
$104$	6.04736	+	10.4743i	0.592992	+	1.02709i
$105$		0			0
$106$	4.10874	−	7.11654i	0.399076	−	0.691220i
$107$		−	3.43549i		−	0.332122i	−0.986116	−	0.166061i	$-0.946895\pi$
$107$		−	3.43549i		−	0.332122i	0.986116	−	0.166061i	$-0.0531048\pi$
$108$		0			0
$109$	3.69058			0.353494			0.176747	−	0.984256i	$-0.443443\pi$
$109$	3.69058			0.353494			0.176747	+	0.984256i	$0.443443\pi$
$110$	−3.77459	+	6.53778i	−0.359893	+	0.623353i
$111$		0			0
$112$		0			0
$113$	−15.0858	+	8.70977i	−1.41915	+	0.819346i	−0.996224	−	0.0868183i	$-0.972330\pi$
$113$	−15.0858	+	8.70977i	−1.41915	+	0.819346i	−0.422925	+	0.906165i	$0.638997\pi$
$114$		0			0
$115$	7.02285	+	4.05465i	0.654885	+	0.378098i
$116$		−	0.649020i		−	0.0602600i
$117$		0			0
$118$		−	8.02407i		−	0.738675i
$119$		0			0
$120$		0			0
$121$	2.85627	+	4.94720i	0.259661	+	0.449746i
$122$	−1.83767	−	3.18294i	−0.166375	−	0.288170i
$123$		0			0
$124$	3.83303	+	2.21300i	0.344216	+	0.198733i
$125$	−12.1546			−1.08714
$126$		0			0
$127$	−10.1288			−0.898783			−0.449391	−	0.893335i	$-0.648359\pi$
$127$	−10.1288			−0.898783			−0.449391	+	0.893335i	$0.648359\pi$
$128$	3.14876	+	1.81794i	0.278314	+	0.160685i
$129$		0			0
$130$	3.74661	+	6.48932i	0.328599	+	0.569151i
$131$	−2.48851	−	4.31022i	−0.217422	−	0.376586i	0.736597	−	0.676332i	$-0.236431\pi$
$131$	−2.48851	−	4.31022i	−0.217422	−	0.376586i	−0.954019	+	0.299746i	$0.903098\pi$
$132$		0			0
$133$		0			0
$134$		−	12.3009i		−	1.06263i
$135$		0			0
$136$		−	4.83293i		−	0.414420i
$137$	−0.728035	−	0.420331i	−0.0622003	−	0.0359113i	0.468577	−	0.883422i	$-0.344767\pi$
$137$	−0.728035	−	0.420331i	−0.0622003	−	0.0359113i	−0.530778	+	0.847511i	$0.678100\pi$
$138$		0			0
$139$	5.74392	−	3.31626i	0.487193	−	0.281281i	−0.236216	−	0.971701i	$-0.575907\pi$
$139$	5.74392	−	3.31626i	0.487193	−	0.281281i	0.723409	+	0.690419i	$0.242574\pi$
$140$		0			0
$141$		0			0
$142$	7.11525	−	12.3240i	0.597098	−	1.03420i
$143$	16.5887			1.38721
$144$		0			0
$145$		−	1.17803i		−	0.0978301i
$146$	−1.85985	+	3.22136i	−0.153923	+	0.266602i
$147$		0			0
$148$	−4.11538	−	7.12804i	−0.338282	−	0.585921i
$149$	14.7023	−	8.48838i	1.20446	−	0.695395i	0.242916	−	0.970047i	$-0.421896\pi$
$149$	14.7023	−	8.48838i	1.20446	−	0.695395i	0.961544	+	0.274652i	$0.0885627\pi$
$150$		0			0
$151$	−0.975709	+	1.68998i	−0.0794021	+	0.137528i	−0.902992	−	0.429657i	$-0.858634\pi$
$151$	−0.975709	+	1.68998i	−0.0794021	+	0.137528i	0.823590	+	0.567186i	$0.191968\pi$
$152$	24.2201			1.96451
$153$		0			0
$154$		0			0
$155$	6.95730	+	4.01680i	0.558823	+	0.322637i
$156$		0			0
$157$	8.24558	−	4.76059i	0.658069	−	0.379936i	−0.133472	−	0.991053i	$-0.542613\pi$
$157$	8.24558	−	4.76059i	0.658069	−	0.379936i	0.791541	+	0.611116i	$0.209279\pi$
$158$	−7.10804	+	4.10383i	−0.565485	+	0.326483i
$159$		0			0
$160$	8.34769	+	4.81954i	0.659943	+	0.381018i
$161$		0			0
$162$		0			0
$163$	1.11021			0.0869585			0.0434793	−	0.999054i	$-0.486156\pi$
$163$	1.11021			0.0869585			0.0434793	+	0.999054i	$0.486156\pi$
$164$	0.945238	−	1.63720i	0.0738107	−	0.127844i
$165$		0			0
$166$	7.45206	−	4.30245i	0.578392	−	0.333935i
$167$	−7.00830	−	12.1387i	−0.542319	−	0.939324i	−0.998770	−	0.0495754i	$-0.984213\pi$
$167$	−7.00830	−	12.1387i	−0.542319	−	0.939324i	0.456452	−	0.889748i	$-0.349120\pi$
$168$		0			0
$169$	1.73285	−	3.00138i	0.133296	−	0.230875i
$170$		−	2.99422i		−	0.229646i
$171$		0			0
$172$	7.32985			0.558896
$173$	3.55884	−	6.16410i	0.270574	−	0.468647i	−0.698435	−	0.715673i	$-0.746120\pi$
$173$	3.55884	−	6.16410i	0.270574	−	0.468647i	0.969009	+	0.247026i	$0.0794533\pi$
$174$		0			0
$175$		0			0
$176$	−3.01994	+	1.74357i	−0.227637	+	0.131426i
$177$		0			0
$178$	−8.33752	−	4.81367i	−0.624924	−	0.360800i
$179$			6.00265i			0.448659i	0.974513	+	0.224330i	$0.0720192\pi$
$179$			6.00265i			0.448659i	−0.974513	+	0.224330i	$0.927981\pi$
$180$		0			0
$181$			1.30283i			0.0968385i	0.998827	+	0.0484192i	$0.0154184\pi$
$181$			1.30283i			0.0968385i	−0.998827	+	0.0484192i	$0.984582\pi$
$182$		0			0
$183$		0			0
$184$	6.42428	+	11.1272i	0.473604	+	0.820307i
$185$	−7.46979	−	12.9381i	−0.549190	−	0.951225i
$186$		0			0
$187$	−5.74059	−	3.31433i	−0.419794	−	0.242368i
$188$	8.22643			0.599974
$189$		0			0
$190$	15.0054			1.08861
$191$	−4.96482	−	2.86644i	−0.359242	−	0.207408i	0.309506	−	0.950897i	$-0.399836\pi$
$191$	−4.96482	−	2.86644i	−0.359242	−	0.207408i	−0.668748	+	0.743489i	$0.733170\pi$
$192$		0			0
$193$	−0.779518	−	1.35016i	−0.0561109	−	0.0971869i	0.836606	−	0.547806i	$-0.184537\pi$
$193$	−0.779518	−	1.35016i	−0.0561109	−	0.0971869i	−0.892716	+	0.450619i	$0.851203\pi$
$194$	−6.49367	−	11.2474i	−0.466218	−	0.807514i
$195$		0			0
$196$		0			0
$197$			19.5504i			1.39291i	0.717602	+	0.696454i	$0.245240\pi$
$197$			19.5504i			1.39291i	−0.717602	+	0.696454i	$0.754760\pi$
$198$		0			0
$199$		−	0.976403i		−	0.0692154i	−0.999401	−	0.0346077i	$-0.988982\pi$
$199$		−	0.976403i		−	0.0692154i	0.999401	−	0.0346077i	$-0.0110182\pi$
$200$	−3.77151	−	2.17748i	−0.266686	−	0.153971i
$201$		0			0
$202$	−0.892445	+	0.515253i	−0.0627922	+	0.0362531i
$203$		0			0
$204$		0			0
$205$	1.71570	−	2.97167i	0.119829	−	0.207551i
$206$	1.60882			0.112092
$207$		0			0
$208$			3.46128i			0.239997i
$209$	16.6097	−	28.7688i	1.14892	−	1.98998i
$210$		0			0
$211$	11.9752	+	20.7417i	0.824408	+	1.42792i	0.902371	+	0.430961i	$0.141825\pi$
$211$	11.9752	+	20.7417i	0.824408	+	1.42792i	−0.0779625	+	0.996956i	$0.524841\pi$
$212$	−7.51382	+	4.33810i	−0.516051	+	0.297942i
$213$		0			0
$214$	1.68618	−	2.92054i	0.115265	−	0.199644i
$215$	13.3044			0.907349
$216$		0			0
$217$		0			0
$218$	3.13740	+	1.81138i	0.212491	+	0.122682i
$219$		0			0
$220$	6.90274	−	3.98530i	0.465383	−	0.268689i
$221$	−5.69804	+	3.28976i	−0.383292	+	0.221293i
$222$		0			0
$223$	2.68394	+	1.54957i	0.179730	+	0.103767i	0.587166	−	0.809467i	$-0.300244\pi$
$223$	2.68394	+	1.54957i	0.179730	+	0.103767i	−0.407436	+	0.913234i	$0.633577\pi$
$224$		0			0
$225$		0			0
$226$	−17.0994			−1.13743
$227$	−10.8991	+	18.8779i	−0.723401	+	1.25297i	0.236228	+	0.971698i	$0.424089\pi$
$227$	−10.8991	+	18.8779i	−0.723401	+	1.25297i	−0.959629	+	0.281269i	$0.909245\pi$
$228$		0			0
$229$	11.1810	−	6.45536i	0.738862	−	0.426582i	−0.0827937	−	0.996567i	$-0.526384\pi$
$229$	11.1810	−	6.45536i	0.738862	−	0.426582i	0.821655	+	0.569985i	$0.193051\pi$
$230$	3.98013	+	6.89378i	0.262442	+	0.454563i
$231$		0			0
$232$	0.933250	−	1.61644i	0.0612709	−	0.106124i
$233$			0.808011i			0.0529345i	0.999650	+	0.0264673i	$0.00842578\pi$
$233$			0.808011i			0.0529345i	−0.999650	+	0.0264673i	$0.991574\pi$
$234$		0			0
$235$	14.9317			0.974039
$236$	−4.23600	+	7.33697i	−0.275740	+	0.477596i
$237$		0			0
$238$		0			0
$239$	−12.2032	+	7.04552i	−0.789360	+	0.455737i	−0.839737	−	0.542993i	$-0.817291\pi$
$239$	−12.2032	+	7.04552i	−0.789360	+	0.455737i	0.0503775	+	0.998730i	$0.483958\pi$
$240$		0			0
$241$	−16.0205	−	9.24943i	−1.03197	−	0.595808i	−0.114422	−	0.993432i	$-0.536502\pi$
$241$	−16.0205	−	9.24943i	−1.03197	−	0.595808i	−0.917549	+	0.397624i	$0.869835\pi$
$242$			5.60755i			0.360467i
$243$		0			0
$244$			3.88051i			0.248424i
$245$		0			0
$246$		0			0
$247$	−16.4866	−	28.5556i	−1.04902	−	1.81695i
$248$	6.36431	+	11.0233i	0.404134	+	0.699981i
$249$		0			0
$250$	−10.3327	−	5.96561i	−0.653499	−	0.377298i
$251$	−22.1733			−1.39957			−0.699783	−	0.714355i	$-0.746720\pi$
$251$	−22.1733			−1.39957			−0.699783	+	0.714355i	$0.746720\pi$
$252$		0			0
$253$	17.6226			1.10792
$254$	−8.61056	−	4.97131i	−0.540274	−	0.311928i
$255$		0			0
$256$	8.52026	+	14.7575i	0.532516	+	0.922345i
$257$	−2.02896	−	3.51427i	−0.126563	−	0.219214i	0.795780	−	0.605586i	$-0.207061\pi$
$257$	−2.02896	−	3.51427i	−0.126563	−	0.219214i	−0.922343	+	0.386372i	$0.873728\pi$
$258$		0			0
$259$		0			0
$260$		−	7.91152i		−	0.490652i
$261$		0			0
$262$		−	4.88554i		−	0.301830i
$263$	8.62617	+	4.98032i	0.531913	+	0.307100i	0.741795	−	0.670627i	$-0.233975\pi$
$263$	8.62617	+	4.98032i	0.531913	+	0.307100i	−0.209882	+	0.977727i	$0.567308\pi$
$264$		0			0
$265$	−13.6383	+	7.87406i	−0.837793	+	0.483700i
$266$		0			0
$267$		0			0
$268$	−6.49378	+	11.2476i	−0.396671	+	0.687054i
$269$	9.96799			0.607759			0.303880	−	0.952710i	$-0.401718\pi$
$269$	9.96799			0.607759			0.303880	+	0.952710i	$0.401718\pi$
$270$		0			0
$271$		−	19.0320i		−	1.15611i	−0.815997	−	0.578057i	$-0.803811\pi$
$271$		−	19.0320i		−	1.15611i	0.815997	−	0.578057i	$-0.196189\pi$
$272$	0.691547	−	1.19780i	0.0419312	−	0.0726270i
$273$		0			0
$274$	−0.412606	−	0.714655i	−0.0249265	−	0.0431739i
$275$	−5.17286	+	2.98655i	−0.311935	+	0.180096i
$276$		0			0
$277$	7.81184	−	13.5305i	0.469368	−	0.812969i	−0.530019	−	0.847986i	$-0.677815\pi$
$277$	7.81184	−	13.5305i	0.469368	−	0.812969i	0.999387	+	0.0350166i	$0.0111484\pi$
$278$	6.51062			0.390481
$279$		0			0
$280$		0			0
$281$	20.8780	+	12.0539i	1.24547	+	0.719075i	0.970203	−	0.242292i	$-0.0778991\pi$
$281$	20.8780	+	12.0539i	1.24547	+	0.719075i	0.275271	+	0.961367i	$0.411232\pi$
$282$		0			0
$283$	2.61349	−	1.50890i	0.155356	−	0.0896946i	−0.420307	−	0.907382i	$-0.638078\pi$
$283$	2.61349	−	1.50890i	0.155356	−	0.0896946i	0.575662	+	0.817687i	$0.304744\pi$
$284$	−13.0119	+	7.51245i	−0.772117	+	0.445782i
$285$		0			0
$286$	14.1022	+	8.14189i	0.833879	+	0.481440i
$287$		0			0
$288$		0			0
$289$	−14.3709			−0.845346
$290$	0.578190	−	1.00145i	0.0339525	−	0.0588074i
$291$		0			0
$292$	3.40119	−	1.96368i	0.199040	−	0.114916i
$293$	14.9237	+	25.8485i	0.871849	+	1.51009i	0.860082	+	0.510156i	$0.170412\pi$
$293$	14.9237	+	25.8485i	0.871849	+	1.51009i	0.0117671	+	0.999931i	$0.496254\pi$
$294$		0			0
$295$	−7.68873	+	13.3173i	−0.447655	+	0.775362i
$296$		−	23.6706i		−	1.37583i
$297$		0			0
$298$	16.6648			0.965363
$299$	8.74598	−	15.1485i	0.505793	−	0.876060i
$300$		0			0
$301$		0			0
$302$	−1.65892	+	0.957777i	−0.0954600	+	0.0551139i
$303$		0			0
$304$	6.00272	+	3.46567i	0.344280	+	0.198770i
$305$			7.04349i			0.403309i
$306$		0			0
$307$		−	2.68853i		−	0.153442i	−0.997053	−	0.0767212i	$-0.975555\pi$
$307$		−	2.68853i		−	0.153442i	0.997053	−	0.0767212i	$-0.0244451\pi$
$308$		0			0
$309$		0			0
$310$	3.94297	+	6.82943i	0.223946	+	0.387886i
$311$	5.53763	+	9.59145i	0.314010	+	0.543881i	0.979227	−	0.202769i	$-0.0649941\pi$
$311$	5.53763	+	9.59145i	0.314010	+	0.543881i	−0.665217	+	0.746650i	$0.731661\pi$
$312$		0			0
$313$	14.4970	+	8.36987i	0.819421	+	0.473093i	0.850217	−	0.526433i	$-0.176471\pi$
$313$	14.4970	+	8.36987i	0.819421	+	0.473093i	−0.0307957	+	0.999526i	$0.509804\pi$
$314$	9.34619			0.527436
$315$		0			0
$316$	8.66584			0.487492
$317$	2.54774	+	1.47094i	0.143095	+	0.0826160i	0.569838	−	0.821757i	$-0.307006\pi$
$317$	2.54774	+	1.47094i	0.143095	+	0.0826160i	−0.426743	+	0.904373i	$0.640339\pi$
$318$		0			0
$319$	−1.28001	−	2.21704i	−0.0716668	−	0.124131i
$320$	6.33562	+	10.9736i	0.354172	+	0.613444i
$321$		0			0
$322$		0			0
$323$			13.1758i			0.733118i
$324$		0			0
$325$			5.92883i			0.328872i
$326$	0.943801	+	0.544904i	0.0522723	+	0.0301794i
$327$		0			0
$328$	4.70839	−	2.71839i	0.259977	−	0.150098i
$329$		0			0
$330$		0			0
$331$	−2.44077	+	4.22753i	−0.134157	+	0.232366i	−0.925275	−	0.379297i	$-0.876166\pi$
$331$	−2.44077	+	4.22753i	−0.134157	+	0.232366i	0.791118	+	0.611663i	$0.209499\pi$
$332$	−9.08526			−0.498618
$333$		0			0
$334$		−	13.7590i		−	0.752859i
$335$	−11.7868	+	20.4154i	−0.643982	+	1.11541i
$336$		0			0
$337$	6.51421	+	11.2830i	0.354852	+	0.614621i	0.987093	−	0.160151i	$-0.0511980\pi$
$337$	6.51421	+	11.2830i	0.354852	+	0.614621i	−0.632241	+	0.774772i	$0.717865\pi$
$338$	2.94622	−	1.70100i	0.160253	−	0.0925221i
$339$		0			0
$340$	−1.58068	+	2.73782i	−0.0857245	+	0.148479i
$341$	17.4581			0.945409
$342$		0			0
$343$		0			0
$344$	18.2556	+	10.5399i	0.984275	+	0.568272i
$345$		0			0
$346$	6.05081	−	3.49344i	0.325293	−	0.187808i
$347$	1.86351	−	1.07590i	0.100039	−	0.0577573i	−0.449146	−	0.893458i	$-0.648272\pi$
$347$	1.86351	−	1.07590i	0.100039	−	0.0577573i	0.549185	+	0.835701i	$0.314938\pi$
$348$		0			0
$349$	−25.2919	−	14.6023i	−1.35384	−	0.781642i	−0.365058	−	0.930985i	$-0.618951\pi$
$349$	−25.2919	−	14.6023i	−1.35384	−	0.781642i	−0.988785	+	0.149343i	$0.952284\pi$
$350$		0			0
$351$		0			0
$352$	20.9470			1.11648
$353$	5.41764	−	9.38362i	0.288352	−	0.499440i	−0.685065	−	0.728482i	$-0.740226\pi$
$353$	5.41764	−	9.38362i	0.288352	−	0.499440i	0.973416	+	0.229042i	$0.0735595\pi$
$354$		0			0
$355$	−23.6179	+	13.6358i	−1.25351	+	0.723713i
$356$	5.08239	+	8.80295i	0.269366	+	0.466556i
$357$		0			0
$358$	−2.94617	+	5.10291i	−0.155710	+	0.269697i
$359$		−	20.9492i		−	1.10566i	−0.833295	−	0.552829i	$-0.813548\pi$
$359$		−	20.9492i		−	1.10566i	0.833295	−	0.552829i	$-0.186452\pi$
$360$		0			0
$361$	−47.0300			−2.47526
$362$	−0.639442	+	1.10755i	−0.0336083	+	0.0582113i
$363$		0			0
$364$		0			0
$365$	6.17348	−	3.56426i	0.323135	−	0.186562i
$366$		0			0
$367$	4.97835	+	2.87425i	0.259868	+	0.150035i	0.624274	−	0.781205i	$-0.285395\pi$
$367$	4.97835	+	2.87425i	0.259868	+	0.150035i	−0.364407	+	0.931240i	$0.618728\pi$
$368$			3.67702i			0.191678i
$369$		0			0
$370$		−	14.6650i		−	0.762398i
$371$		0			0
$372$		0			0
$373$	−14.4467	−	25.0224i	−0.748023	−	1.29561i	−0.948769	−	0.315970i	$-0.897670\pi$
$373$	−14.4467	−	25.0224i	−0.748023	−	1.29561i	0.200747	−	0.979643i	$-0.435663\pi$
$374$	−3.25342	−	5.63509i	−0.168230	−	0.291383i
$375$		0			0
$376$	20.4886	+	11.8291i	1.05662	+	0.610039i
$377$	−2.54104			−0.130870
$378$		0			0
$379$	−0.411434			−0.0211339			−0.0105670	−	0.999944i	$-0.503364\pi$
$379$	−0.411434			−0.0211339			−0.0105670	+	0.999944i	$0.503364\pi$
$380$	−13.7205	−	7.92156i	−0.703849	−	0.406367i
$381$		0			0
$382$	−2.81376	−	4.87358i	−0.143965	−	0.249354i
$383$	12.4007	+	21.4787i	0.633648	+	1.09751i	0.986800	+	0.161944i	$0.0517765\pi$
$383$	12.4007	+	21.4787i	0.633648	+	1.09751i	−0.353152	+	0.935566i	$0.614890\pi$
$384$		0			0
$385$		0			0
$386$		−	1.53038i		−	0.0778944i
$387$		0			0
$388$			13.7123i			0.696139i
$389$	−3.82694	−	2.20948i	−0.194033	−	0.112025i	0.399836	−	0.916587i	$-0.369067\pi$
$389$	−3.82694	−	2.20948i	−0.194033	−	0.112025i	−0.593869	+	0.804561i	$0.702400\pi$
$390$		0			0
$391$	−6.05319	+	3.49481i	−0.306123	+	0.176740i
$392$		0			0
$393$		0			0
$394$	−9.59554	+	16.6200i	−0.483416	+	0.837302i
$395$	15.7293			0.791427
$396$		0			0
$397$		−	22.2603i		−	1.11721i	−0.829434	−	0.558605i	$-0.811337\pi$
$397$		−	22.2603i		−	1.11721i	0.829434	−	0.558605i	$-0.188663\pi$
$398$	0.479229	−	0.830049i	0.0240216	−	0.0416066i
$399$		0			0
$400$	−0.623155	−	1.07934i	−0.0311578	−	0.0539668i
$401$	5.31899	−	3.07092i	0.265617	−	0.153354i	−0.361277	−	0.932459i	$-0.617659\pi$
$401$	5.31899	−	3.07092i	0.265617	−	0.153354i	0.626894	+	0.779104i	$0.284326\pi$
$402$		0			0
$403$	8.66434	−	15.0071i	0.431602	−	0.747556i
$404$	1.08803			0.0541317
$405$		0			0
$406$		0			0
$407$	−28.1162	−	16.2329i	−1.39367	−	0.804633i
$408$		0			0
$409$	−0.765886	+	0.442185i	−0.0378706	+	0.0218646i	−0.518816	−	0.854886i	$-0.673627\pi$
$409$	−0.765886	+	0.442185i	−0.0378706	+	0.0218646i	0.480945	+	0.876751i	$0.340294\pi$
$410$	2.91706	−	1.68416i	0.144063	−	0.0831749i
$411$		0			0
$412$	−1.47106	−	0.849316i	−0.0724739	−	0.0418428i
$413$		0			0
$414$		0			0
$415$	−16.4906			−0.809491
$416$	10.3959	−	18.0062i	0.509700	−	0.882827i
$417$		0			0
$418$	28.2401	−	16.3044i	1.38127	−	0.797476i
$419$	−7.59365	−	13.1526i	−0.370974	−	0.642546i	0.618742	−	0.785595i	$-0.287643\pi$
$419$	−7.59365	−	13.1526i	−0.370974	−	0.642546i	−0.989716	+	0.143049i	$0.954309\pi$
$420$		0			0
$421$	13.3318	−	23.0914i	0.649753	−	1.12541i	−0.333428	−	0.942775i	$-0.608206\pi$
$421$	13.3318	−	23.0914i	0.649753	−	1.12541i	0.983182	−	0.182630i	$-0.0584611\pi$
$422$			23.5103i			1.14446i
$423$		0			0
$424$	−24.9517			−1.21176
$425$	1.18455	−	2.05170i	0.0574592	−	0.0995222i
$426$		0			0
$427$		0			0
$428$	−3.08358	+	1.78031i	−0.149050	+	0.0860543i
$429$		0			0
$430$	11.3102	+	6.52992i	0.545424	+	0.314901i
$431$			4.69715i			0.226254i	0.993581	+	0.113127i	$0.0360866\pi$
$431$			4.69715i			0.226254i	−0.993581	+	0.113127i	$0.963913\pi$
$432$		0			0
$433$			8.97714i			0.431414i	0.976458	+	0.215707i	$0.0692056\pi$
$433$			8.97714i			0.431414i	−0.976458	+	0.215707i	$0.930794\pi$
$434$		0			0
$435$		0			0
$436$	−1.91250	−	3.31254i	−0.0915919	−	0.158642i
$437$	−17.5142	−	30.3354i	−0.837816	−	1.45114i
$438$		0			0
$439$	−14.3012	−	8.25679i	−0.682558	−	0.394075i	0.118260	−	0.992983i	$-0.462268\pi$
$439$	−14.3012	−	8.25679i	−0.682558	−	0.394075i	−0.800818	+	0.598907i	$0.795602\pi$
$440$	22.9225			1.09279
$441$		0			0
$442$	−6.45861			−0.307205
$443$	−0.921171	−	0.531838i	−0.0437661	−	0.0252684i	0.477957	−	0.878383i	$-0.341377\pi$
$443$	−0.921171	−	0.531838i	−0.0437661	−	0.0252684i	−0.521723	+	0.853115i	$0.674711\pi$
$444$		0			0
$445$	9.22500	+	15.9782i	0.437307	+	0.757438i
$446$	1.52110	+	2.63461i	0.0720260	+	0.124753i
$447$		0			0
$448$		0			0
$449$		−	15.9081i		−	0.750749i	−0.926873	−	0.375374i	$-0.877514\pi$
$449$		−	15.9081i		−	0.750749i	0.926873	−	0.375374i	$-0.122486\pi$
$450$		0			0
$451$		−	7.45688i		−	0.351131i
$452$	15.6352	+	9.02697i	0.735417	+	0.424593i
$453$		0			0
$454$	−18.5309	+	10.6988i	−0.869698	+	0.502121i
$455$		0			0
$456$		0			0
$457$	16.3963	−	28.3992i	0.766985	−	1.32846i	−0.172206	−	0.985061i	$-0.555090\pi$
$457$	16.3963	−	28.3992i	0.766985	−	1.32846i	0.939191	−	0.343395i	$-0.111577\pi$
$458$	12.6734			0.592191
$459$		0			0
$460$		−	8.40463i		−	0.391868i
$461$	−9.23690	+	15.9988i	−0.430205	+	0.745138i	−0.996891	−	0.0787967i	$-0.974892\pi$
$461$	−9.23690	+	15.9988i	−0.430205	+	0.745138i	0.566685	+	0.823934i	$0.308226\pi$
$462$		0			0
$463$	−0.201921	−	0.349738i	−0.00938408	−	0.0162537i	0.861295	−	0.508105i	$-0.169654\pi$
$463$	−0.201921	−	0.349738i	−0.00938408	−	0.0162537i	−0.870679	+	0.491851i	$0.836320\pi$
$464$	0.462594	−	0.267079i	0.0214754	−	0.0123988i
$465$		0			0
$466$	−0.396580	+	0.686897i	−0.0183712	+	0.0318199i
$467$	−15.0257			−0.695304			−0.347652	−	0.937624i	$-0.613021\pi$
$467$	−15.0257			−0.695304			−0.347652	+	0.937624i	$0.613021\pi$
$468$		0			0
$469$		0			0
$470$	12.6936	+	7.32866i	0.585512	+	0.338046i
$471$		0			0
$472$	−21.1002	+	12.1822i	−0.971216	+	0.560732i
$473$	25.0387	−	14.4561i	1.15128	−	0.664691i
$474$		0			0
$475$	10.2821	+	5.93635i	0.471773	+	0.272379i
$476$		0			0
$477$		0			0
$478$	−13.8321			−0.632664
$479$	−15.5400	+	26.9161i	−0.710041	+	1.22983i	0.254800	+	0.966994i	$0.417990\pi$
$479$	−15.5400	+	26.9161i	−0.710041	+	1.22983i	−0.964841	+	0.262833i	$0.915343\pi$
$480$		0			0
$481$	−27.9077	+	16.1125i	−1.27248	+	0.734669i
$482$	−9.07944	−	15.7261i	−0.413557	−	0.716302i
$483$		0			0
$484$	2.96029	−	5.12738i	0.134559	−	0.233063i
$485$			24.8892i			1.13016i
$486$		0			0
$487$	13.4956			0.611546			0.305773	−	0.952104i	$-0.401085\pi$
$487$	13.4956			0.611546			0.305773	+	0.952104i	$0.401085\pi$
$488$	−5.57994	+	9.66474i	−0.252592	+	0.437502i
$489$		0			0
$490$		0			0
$491$	7.07098	−	4.08243i	0.319109	−	0.184238i	−0.331886	−	0.943319i	$-0.607685\pi$
$491$	7.07098	−	4.08243i	0.319109	−	0.184238i	0.650995	+	0.759082i	$0.274352\pi$
$492$		0			0
$493$	0.879342	+	0.507688i	0.0396036	+	0.0228651i
$494$		−	32.3672i		−	1.45627i
$495$		0			0
$496$			3.64269i			0.163562i
$497$		0			0
$498$		0			0
$499$	14.0097	+	24.2655i	0.627159	+	1.08627i	0.988119	+	0.153690i	$0.0491158\pi$
$499$	14.0097	+	24.2655i	0.627159	+	1.08627i	−0.360960	+	0.932581i	$0.617551\pi$
$500$	6.29863	+	10.9095i	0.281683	+	0.487890i
$501$		0			0
$502$	−18.8497	−	10.8829i	−0.841305	−	0.485727i
$503$	−5.89656			−0.262915			−0.131457	−	0.991322i	$-0.541966\pi$
$503$	−5.89656			−0.262915			−0.131457	+	0.991322i	$0.541966\pi$
$504$		0			0
$505$	1.97488			0.0878811
$506$	14.9811	+	8.64936i	0.665992	+	0.384511i
$507$		0			0
$508$	5.24883	+	9.09123i	0.232879	+	0.403358i
$509$	−7.01957	−	12.1582i	−0.311137	−	0.538905i	0.667472	−	0.744635i	$-0.267376\pi$
$509$	−7.01957	−	12.1582i	−0.311137	−	0.538905i	−0.978609	+	0.205730i	$0.934043\pi$
$510$		0			0
$511$		0			0
$512$			9.45558i			0.417882i
$513$		0			0
$514$		−	3.98335i		−	0.175698i
$515$	−2.67011	−	1.54159i	−0.117659	−	0.0679305i
$516$		0			0
$517$	28.1014	−	16.2243i	1.23590	−	0.713546i
$518$		0			0
$519$		0			0
$520$	11.3763	−	19.7043i	0.498883	−	0.864090i
$521$	−38.4458			−1.68434			−0.842170	−	0.539213i	$-0.818722\pi$
$521$	−38.4458			−1.68434			−0.842170	+	0.539213i	$0.818722\pi$
$522$		0			0
$523$			10.4932i			0.458834i	0.973328	+	0.229417i	$0.0736819\pi$
$523$			10.4932i			0.458834i	−0.973328	+	0.229417i	$0.926318\pi$
$524$	−2.57914	+	4.46720i	−0.112670	+	0.195150i
$525$		0			0
$526$	4.88879	+	8.46764i	0.213161	+	0.369207i
$527$	−5.99668	+	3.46219i	−0.261220	+	0.150815i
$528$		0			0
$529$	−2.20889	+	3.82591i	−0.0960388	+	0.166344i
$530$	−15.4587			−0.671483
$531$		0			0
$532$		0			0
$533$	−6.40998	−	3.70080i	−0.277647	−	0.160300i
$534$		0			0
$535$	−5.59698	+	3.23142i	−0.241979	+	0.139706i
$536$	−32.3466	+	18.6753i	−1.39716	+	0.806650i
$537$		0			0
$538$	8.47388	+	4.89240i	0.365335	+	0.210926i
$539$		0			0
$540$		0			0
$541$	45.1565			1.94143			0.970715	−	0.240232i	$-0.0772235\pi$
$541$	45.1565			1.94143			0.970715	+	0.240232i	$0.0772235\pi$
$542$	9.34112	−	16.1793i	0.401236	−	0.694960i
$543$		0			0
$544$	−7.19510	+	4.15409i	−0.308487	+	0.178105i
$545$	−3.47136	−	6.01257i	−0.148697	−	0.257550i
$546$		0			0
$547$	−4.05733	+	7.02751i	−0.173479	+	0.300475i	−0.939634	−	0.342181i	$-0.888834\pi$
$547$	−4.05733	+	7.02751i	−0.173479	+	0.300475i	0.766155	+	0.642656i	$0.222168\pi$
$548$			0.871279i			0.0372192i
$549$		0			0
$550$	−5.86333			−0.250013
$551$	−2.54427	+	4.40680i	−0.108389	+	0.187736i
$552$		0			0
$553$		0			0
$554$	13.2818	−	7.66827i	0.564291	−	0.325794i
$555$		0			0
$556$	−5.95311	−	3.43703i	−0.252468	−	0.145763i
$557$			16.2727i			0.689494i	0.938696	+	0.344747i	$0.112035\pi$
$557$			16.2727i			0.689494i	−0.938696	+	0.344747i	$0.887965\pi$
$558$		0			0
$559$		−	28.6978i		−	1.21379i
$560$		0			0
$561$		0			0
$562$	11.8324	+	20.4942i	0.499118	+	0.864498i
$563$	5.13594	+	8.89572i	0.216454	+	0.374910i	0.953721	−	0.300692i	$-0.0972175\pi$
$563$	5.13594	+	8.89572i	0.216454	+	0.374910i	−0.737267	+	0.675601i	$0.763884\pi$
$564$		0			0
$565$	28.3793	+	16.3848i	1.19393	+	0.689314i
$566$	2.96233			0.124516
$567$		0			0
$568$	−43.2098			−1.81304
$569$	17.8537	+	10.3079i	0.748468	+	0.432128i	0.825140	−	0.564928i	$-0.191096\pi$
$569$	17.8537	+	10.3079i	0.748468	+	0.432128i	−0.0766722	+	0.997056i	$0.524429\pi$
$570$		0			0
$571$	−2.12828	−	3.68628i	−0.0890656	−	0.154266i	0.818051	−	0.575146i	$-0.195055\pi$
$571$	−2.12828	−	3.68628i	−0.0890656	−	0.154266i	−0.907116	+	0.420880i	$0.861721\pi$
$572$	−8.59640	−	14.8894i	−0.359434	−	0.622557i
$573$		0			0
$574$		0			0
$575$			6.29836i			0.262660i
$576$		0			0
$577$		−	16.9289i		−	0.704760i	−0.935857	−	0.352380i	$-0.885372\pi$
$577$		−	16.9289i		−	0.704760i	0.935857	−	0.352380i	$-0.114628\pi$
$578$	−12.2168	−	7.05338i	−0.508153	−	0.293382i
$579$		0			0
$580$	−1.05736	+	0.610467i	−0.0439045	+	0.0253483i
$581$		0			0
$582$		0			0
$583$	−17.1114	+	29.6378i	−0.708682	+	1.22747i
$584$	11.2946			0.467374
$585$		0			0
$586$			29.2988i			1.21032i
$587$	12.0558	−	20.8812i	0.497594	−	0.861858i	−0.502402	−	0.864634i	$-0.667550\pi$
$587$	12.0558	−	20.8812i	0.497594	−	0.861858i	0.999996	+	0.00277589i	$0.000883594\pi$
$588$		0			0
$589$	−17.3507	−	30.0522i	−0.714922	−	1.23828i
$590$	−13.0725	+	7.54743i	−0.538187	+	0.310723i
$591$		0			0
$592$	3.38705	−	5.86654i	0.139207	−	0.241113i
$593$	−38.5816			−1.58436			−0.792178	−	0.610290i	$-0.791053\pi$
$593$	−38.5816			−1.58436			−0.792178	+	0.610290i	$0.791053\pi$
$594$		0			0
$595$		0			0
$596$	−15.2378	−	8.79752i	−0.624163	−	0.360360i
$597$		0			0
$598$	14.8701	−	8.58525i	0.608083	−	0.351077i
$599$	29.2921	−	16.9118i	1.19684	−	0.690997i	0.236992	−	0.971511i	$-0.423838\pi$
$599$	29.2921	−	16.9118i	1.19684	−	0.690997i	0.959850	+	0.280514i	$0.0905050\pi$
$600$		0			0
$601$	27.4855	+	15.8688i	1.12116	+	0.647300i	0.941696	−	0.336465i	$-0.109231\pi$
$601$	27.4855	+	15.8688i	1.12116	+	0.647300i	0.179461	+	0.983765i	$0.442565\pi$
$602$		0			0
$603$		0			0
$604$	2.02249			0.0822939
$605$	5.37320	−	9.30666i	0.218452	−	0.378370i
$606$		0			0
$607$	0.169355	−	0.0977772i	0.00687391	−	0.00396865i	−0.496559	−	0.868003i	$-0.665403\pi$
$607$	0.169355	−	0.0977772i	0.00687391	−	0.00396865i	0.503433	+	0.864034i	$0.332070\pi$
$608$	−20.8181	−	36.0581i	−0.844287	−	1.46235i
$609$		0			0
$610$	−3.45702	+	5.98774i	−0.139971	+	0.242436i
$611$		−	32.2082i		−	1.30300i
$612$		0			0
$613$	2.93328			0.118474			0.0592370	−	0.998244i	$-0.481133\pi$
$613$	2.93328			0.118474			0.0592370	+	0.998244i	$0.481133\pi$
$614$	1.31956	−	2.28554i	0.0532530	−	0.0922370i
$615$		0			0
$616$		0			0
$617$	7.86982	−	4.54365i	0.316827	−	0.182920i	−0.333150	−	0.942874i	$-0.608112\pi$
$617$	7.86982	−	4.54365i	0.316827	−	0.182920i	0.649977	+	0.759953i	$0.274778\pi$
$618$		0			0
$619$	−24.8586	−	14.3521i	−0.999152	−	0.576861i	−0.0911550	−	0.995837i	$-0.529056\pi$
$619$	−24.8586	−	14.3521i	−0.999152	−	0.576861i	−0.907997	+	0.418976i	$0.862389\pi$
$620$		−	8.32617i		−	0.334387i
$621$		0			0
$622$			10.8717i			0.435916i
$623$		0			0
$624$		0			0
$625$	7.77986	+	13.4751i	0.311194	+	0.539004i
$626$	8.21604	+	14.2306i	0.328379	+	0.568769i
$627$		0			0
$628$	−8.54588	−	4.93397i	−0.341018	−	0.196887i
$629$	12.8768			0.513433
$630$		0			0
$631$	−20.7691			−0.826805			−0.413403	−	0.910548i	$-0.635660\pi$
$631$	−20.7691			−0.826805			−0.413403	+	0.910548i	$0.635660\pi$
$632$	21.5830	+	12.4609i	0.858525	+	0.495670i
$633$		0			0
$634$	1.44390	+	2.50091i	0.0573447	+	0.0993240i
$635$	9.52711	+	16.5014i	0.378072	+	0.654839i
$636$		0			0
$637$		0			0
$638$		−	2.51297i		−	0.0994895i
$639$		0			0
$640$		−	6.83981i		−	0.270367i
$641$	−39.7733	−	22.9632i	−1.57095	−	0.906990i	−0.996052	−	0.0887664i	$-0.971708\pi$
$641$	−39.7733	−	22.9632i	−1.57095	−	0.906990i	−0.574900	−	0.818224i	$-0.694959\pi$
$642$		0			0
$643$	−9.15428	+	5.28523i	−0.361010	+	0.208429i	−0.669524	−	0.742791i	$-0.733502\pi$
$643$	−9.15428	+	5.28523i	−0.361010	+	0.208429i	0.308514	+	0.951220i	$0.400168\pi$
$644$		0			0
$645$		0			0
$646$	−6.46680	+	11.2008i	−0.254433	+	0.440691i
$647$	−38.5123			−1.51408			−0.757038	−	0.653371i	$-0.773354\pi$
$647$	−38.5123			−1.51408			−0.757038	+	0.653371i	$0.773354\pi$
$648$		0			0
$649$			33.4173i			1.31174i
$650$	−2.90993	+	5.04015i	−0.114137	+	0.197691i
$651$		0			0
$652$	−0.575323	−	0.996488i	−0.0225314	−	0.0390255i
$653$	11.0867	−	6.40089i	0.433855	−	0.250486i	−0.267133	−	0.963660i	$-0.586076\pi$
$653$	11.0867	−	6.40089i	0.433855	−	0.250486i	0.700988	+	0.713173i	$0.252743\pi$
$654$		0			0
$655$	−4.68137	+	8.10837i	−0.182916	+	0.316820i
$656$	1.55590			0.0607479
$657$		0			0
$658$		0			0
$659$	−41.5777	−	24.0049i	−1.61964	−	0.935097i	−0.987014	−	0.160636i	$-0.948645\pi$
$659$	−41.5777	−	24.0049i	−1.61964	−	0.935097i	−0.632622	−	0.774461i	$-0.718021\pi$
$660$		0			0
$661$	9.38011	−	5.41561i	0.364844	−	0.210643i	−0.306360	−	0.951916i	$-0.599111\pi$
$661$	9.38011	−	5.41561i	0.364844	−	0.210643i	0.671204	+	0.741273i	$0.265778\pi$
$662$	−4.14983	+	2.39591i	−0.161288	+	0.0931196i
$663$		0			0
$664$	−22.6276	−	13.0640i	−0.878121	−	0.506983i
$665$		0			0
$666$		0			0
$667$	−2.69942			−0.104522
$668$	−7.26354	+	12.5808i	−0.281035	+	0.486767i
$669$		0			0
$670$	−20.0402	+	11.5702i	−0.774219	+	0.446995i
$671$	7.65323	+	13.2558i	0.295450	+	0.511734i
$672$		0			0
$673$	−6.19553	+	10.7310i	−0.238820	+	0.413649i	−0.960376	−	0.278707i	$-0.910094\pi$
$673$	−6.19553	+	10.7310i	−0.238820	+	0.413649i	0.721556	+	0.692356i	$0.243427\pi$
$674$			12.7890i			0.492613i
$675$		0			0
$676$	−3.59191			−0.138150
$677$	14.4947	−	25.1056i	0.557078	−	0.964888i	−0.440660	−	0.897674i	$-0.645256\pi$
$677$	14.4947	−	25.1056i	0.557078	−	0.964888i	0.997739	−	0.0672139i	$-0.0214110\pi$
$678$		0			0
$679$		0			0
$680$	−7.87364	+	4.54585i	−0.301940	+	0.174325i
$681$		0			0
$682$	14.8413	+	8.56862i	0.568302	+	0.328109i
$683$		−	0.152476i		−	0.00583433i	−0.999996	−	0.00291717i	$-0.999071\pi$
$683$		−	0.152476i		−	0.00583433i	0.999996	−	0.00291717i	$-0.000928564\pi$
$684$		0			0
$685$			1.58145i			0.0604242i
$686$		0			0
$687$		0			0
$688$	3.01631	+	5.22441i	0.114996	+	0.199179i
$689$	16.9846	+	29.4181i	0.647060	+	1.12074i
$690$		0			0
$691$	37.4428	+	21.6176i	1.42439	+	0.822373i	0.996670	−	0.0815369i	$-0.0259828\pi$
$691$	37.4428	+	21.6176i	1.42439	+	0.822373i	0.427722	+	0.903910i	$0.359316\pi$
$692$	−7.37691			−0.280428
$693$		0			0
$694$	2.11225			0.0801799
$695$	−10.8055	−	6.23853i	−0.409874	−	0.236641i
$696$		0			0
$697$	1.47880	+	2.56136i	0.0560137	+	0.0970186i
$698$	−14.3339	−	24.8271i	−0.542546	−	0.939718i
$699$		0			0
$700$		0			0
$701$			11.5821i			0.437451i	0.975786	+	0.218726i	$0.0701900\pi$
$701$			11.5821i			0.437451i	−0.975786	+	0.218726i	$0.929810\pi$
$702$		0			0
$703$			64.5319i			2.43387i
$704$	23.8472	+	13.7682i	0.898774	+	0.518907i
$705$		0			0
$706$	9.21116	−	5.31807i	0.346667	−	0.200148i
$707$		0			0
$708$		0			0
$709$	18.9474	−	32.8178i	0.711584	−	1.23250i	−0.252678	−	0.967550i	$-0.581311\pi$
$709$	18.9474	−	32.8178i	0.711584	−	1.23250i	0.964262	−	0.264949i	$-0.0853552\pi$
$710$	−26.7704			−1.00467
$711$		0			0
$712$			29.2326i			1.09554i
$713$	9.20437	−	15.9424i	0.344707	−	0.597049i
$714$		0			0
$715$	−15.6033	−	27.0256i	−0.583529	−	1.01070i
$716$	5.38777	−	3.11063i	0.201351	−	0.116250i
$717$		0			0
$718$	10.2821	−	17.8091i	0.383724	−	0.664630i
$719$	−46.6317			−1.73907			−0.869534	−	0.493873i	$-0.835581\pi$
$719$	−46.6317			−1.73907			−0.869534	+	0.493873i	$0.835581\pi$
$720$		0			0
$721$		0			0
$722$	−39.9806	−	23.0828i	−1.48792	−	0.859054i
$723$		0			0
$724$	1.16937	−	0.675138i	0.0434594	−	0.0250913i
$725$	0.792377	−	0.457479i	0.0294282	−	0.0169904i
$726$		0			0
$727$	3.72659	+	2.15155i	0.138212	+	0.0797965i	0.567511	−	0.823366i	$-0.307906\pi$
$727$	3.72659	+	2.15155i	0.138212	+	0.0797965i	−0.429300	+	0.903162i	$0.641240\pi$
$728$		0			0
$729$		0			0
$730$	6.99751			0.258989
$731$	−5.73369	+	9.93104i	−0.212068	+	0.367313i
$732$		0			0
$733$	−12.1337	+	7.00539i	−0.448168	+	0.258750i	−0.707056	−	0.707157i	$-0.749977\pi$
$733$	−12.1337	+	7.00539i	−0.448168	+	0.258750i	0.258888	+	0.965907i	$0.416644\pi$
$734$	2.82143	+	4.88685i	0.104141	+	0.180377i
$735$		0			0
$736$	11.0438	−	19.1285i	0.407081	−	0.705086i
$737$			51.2287i			1.88703i
$738$		0			0
$739$	37.8627			1.39280			0.696401	−	0.717653i	$-0.254784\pi$
$739$	37.8627			1.39280			0.696401	+	0.717653i	$0.254784\pi$
$740$	−7.74184	+	13.4093i	−0.284596	+	0.492934i
$741$		0			0
$742$		0			0
$743$	24.0489	−	13.8847i	0.882269	−	0.509378i	0.0108634	−	0.999941i	$-0.496542\pi$
$743$	24.0489	−	13.8847i	0.882269	−	0.509378i	0.871406	+	0.490563i	$0.163209\pi$
$744$		0			0
$745$	−27.6579	−	15.9683i	−1.01331	−	0.585034i
$746$		−	28.3624i		−	1.03842i
$747$		0			0
$748$			6.87007i			0.251195i
$749$		0			0
$750$		0			0
$751$	8.67540	+	15.0262i	0.316570	+	0.548315i	0.979770	−	0.200127i	$-0.0641355\pi$
$751$	8.67540	+	15.0262i	0.316570	+	0.548315i	−0.663200	+	0.748442i	$0.730802\pi$
$752$	3.38527	+	5.86346i	0.123448	+	0.213818i
$753$		0			0
$754$	−2.16017	−	1.24717i	−0.0786686	−	0.0454193i
$755$	3.67100			0.133601
$756$		0			0
$757$	18.8111			0.683701			0.341850	−	0.939754i	$-0.388946\pi$
$757$	18.8111			0.683701			0.341850	+	0.939754i	$0.388946\pi$
$758$	−0.349764	−	0.201936i	−0.0127040	−	0.00733465i
$759$		0			0
$760$	−22.7814	−	39.4586i	−0.826369	−	1.43131i
$761$	4.22520	+	7.31825i	0.153163	+	0.265286i	0.932389	−	0.361457i	$-0.117721\pi$
$761$	4.22520	+	7.31825i	0.153163	+	0.265286i	−0.779225	+	0.626744i	$0.784387\pi$
$762$		0			0
$763$		0			0
$764$			5.94167i			0.214962i
$765$		0			0
$766$			24.3457i			0.879644i
$767$	28.7257	+	16.5848i	1.03723	+	0.598843i
$768$		0			0
$769$	−19.8100	+	11.4373i	−0.714366	+	0.412440i	−0.812676	−	0.582716i	$-0.801990\pi$
$769$	−19.8100	+	11.4373i	−0.714366	+	0.412440i	0.0983092	+	0.995156i	$0.468657\pi$
$770$		0			0
$771$		0			0
$772$	−0.807907	+	1.39934i	−0.0290772	+	0.0503632i
$773$	37.6747			1.35507			0.677533	−	0.735492i	$-0.263049\pi$
$773$	37.6747			1.35507			0.677533	+	0.735492i	$0.263049\pi$
$774$		0			0
$775$			6.23957i			0.224132i
$776$	−19.7175	+	34.1517i	−0.707817	+	1.22598i
$777$		0			0
$778$	−2.16888	−	3.75660i	−0.0777579	−	0.134681i
$779$	−12.8362	+	7.41099i	−0.459905	+	0.265526i
$780$		0			0
$781$	−29.6324	+	51.3249i	−1.06033	+	1.83655i
$782$	−6.86116			−0.245355
$783$		0			0
$784$		0			0
$785$	−15.5116	−	8.95561i	−0.553632	−	0.319639i
$786$		0			0
$787$	20.3222	−	11.7330i	0.724408	−	0.418237i	−0.0919648	−	0.995762i	$-0.529315\pi$
$787$	20.3222	−	11.7330i	0.724408	−	0.418237i	0.816373	+	0.577525i	$0.195981\pi$
$788$	17.5478	−	10.1312i	0.625113	−	0.360909i
$789$		0			0
$790$	13.3716	+	7.72011i	0.475741	+	0.274669i
$791$		0			0
$792$		0			0
$793$	15.1930			0.539519
$794$	10.9256	−	18.9237i	0.387734	−	0.671575i
$795$		0			0
$796$	−0.876386	+	0.505981i	−0.0310627	+	0.0179340i
$797$	−22.8856	−	39.6390i	−0.810648	−	1.40408i	−0.912411	−	0.409275i	$-0.865782\pi$
$797$	−22.8856	−	39.6390i	−0.810648	−	1.40408i	0.101763	−	0.994809i	$-0.467552\pi$
$798$		0			0
$799$	−6.43503	+	11.1458i	−0.227655	+	0.394310i
$800$			7.48653i			0.264689i
$801$		0			0
$802$	6.02896			0.212890
$803$	7.74562	−	13.4158i	0.273337	−	0.473433i
$804$		0			0
$805$		0			0
$806$	14.7313	−	8.50510i	0.518887	−	0.299579i
$807$		0			0
$808$	2.70984	+	1.56453i	0.0953317	+	0.0550398i
$809$			13.2408i			0.465522i	0.972534	+	0.232761i	$0.0747761\pi$
$809$			13.2408i			0.465522i	−0.972534	+	0.232761i	$0.925224\pi$
$810$		0			0
$811$			56.0437i			1.96796i	0.178275	+	0.983981i	$0.442948\pi$
$811$			56.0437i			1.96796i	−0.178275	+	0.983981i	$0.557052\pi$
$812$		0			0
$813$		0			0
$814$	−15.9345	−	27.5994i	−0.558505	−	0.967359i
$815$	−1.04426	−	1.80872i	−0.0365790	−	0.0633566i
$816$		0			0
$817$	−49.7692	−	28.7343i	−1.74120	−	1.00528i
$818$	−0.868116			−0.0303530
$819$		0			0
$820$	−3.55636			−0.124193
$821$	−48.7766	−	28.1612i	−1.70232	−	0.982833i	−0.943407	−	0.331636i	$-0.892399\pi$
$821$	−48.7766	−	28.1612i	−1.70232	−	0.982833i	−0.758909	−	0.651197i	$-0.774267\pi$
$822$		0			0
$823$	−8.52180	−	14.7602i	−0.297051	−	0.514508i	0.678409	−	0.734685i	$-0.262670\pi$
$823$	−8.52180	−	14.7602i	−0.297051	−	0.514508i	−0.975460	+	0.220177i	$0.929337\pi$
$824$	−2.44253	−	4.23058i	−0.0850895	−	0.147379i
$825$		0			0
$826$		0			0
$827$		−	45.7715i		−	1.59163i	−0.605539	−	0.795816i	$-0.707042\pi$
$827$		−	45.7715i		−	1.59163i	0.605539	−	0.795816i	$-0.292958\pi$
$828$		0			0
$829$		−	35.2839i		−	1.22546i	−0.790293	−	0.612730i	$-0.790071\pi$
$829$		−	35.2839i		−	1.22546i	0.790293	−	0.612730i	$-0.209929\pi$
$830$	−14.0188	−	8.09376i	−0.486600	−	0.280938i
$831$		0			0
$832$	23.6704	−	13.6661i	0.820623	−	0.473787i
$833$		0			0
$834$		0			0
$835$	−13.1840	+	22.8354i	−0.456251	+	0.790250i
$836$	−34.4292			−1.19076
$837$		0			0
$838$		−	14.9082i		−	0.514995i
$839$	−22.3195	+	38.6585i	−0.770555	+	1.33464i	0.166704	+	0.986007i	$0.446688\pi$
$839$	−22.3195	+	38.6585i	−0.770555	+	1.33464i	−0.937259	+	0.348634i	$0.886646\pi$
$840$		0			0
$841$	−14.3039	−	24.7751i	−0.493239	−	0.854315i
$842$	22.6670	−	13.0868i	0.781157	−	0.451001i
$843$		0			0
$844$	12.4114	−	21.4971i	0.427216	−	0.739960i
$845$	−6.51965			−0.224283
$846$		0			0
$847$		0			0
$848$	−6.18404	−	3.57036i	−0.212361	−	0.122607i
$849$		0			0
$850$	2.01400	−	1.16278i	0.0690795	−	0.0398831i
$851$	−29.6472	+	17.1168i	−1.01629	+	0.586757i
$852$		0			0
$853$	−47.7652	−	27.5772i	−1.63545	−	0.944227i	−0.982372	−	0.186935i	$-0.940145\pi$
$853$	−47.7652	−	27.5772i	−1.63545	−	0.944227i	−0.653077	−	0.757292i	$-0.726522\pi$
$854$		0			0
$855$		0			0
$856$	−10.2399			−0.349992
$857$	19.0771	−	33.0425i	0.651660	−	1.12871i	−0.331059	−	0.943610i	$-0.607406\pi$
$857$	19.0771	−	33.0425i	0.651660	−	1.12871i	0.982720	−	0.185099i	$-0.0592606\pi$
$858$		0			0
$859$	35.0465	−	20.2341i	1.19577	−	0.690378i	0.236160	−	0.971714i	$-0.424111\pi$
$859$	35.0465	−	20.2341i	1.19577	−	0.690378i	0.959609	+	0.281336i	$0.0907776\pi$
$860$	−6.89444	−	11.9415i	−0.235099	−	0.407203i
$861$		0			0
$862$	−2.30541	+	3.99309i	−0.0785226	+	0.136005i
$863$			36.2021i			1.23233i	0.787616	+	0.616167i	$0.211315\pi$
$863$			36.2021i			1.23233i	−0.787616	+	0.616167i	$0.788685\pi$
$864$		0			0
$865$	−13.3898			−0.455266
$866$	−4.40608	+	7.63155i	−0.149725	+	0.259331i
$867$		0			0
$868$		0			0
$869$	29.6024	−	17.0910i	1.00419	−	0.579771i
$870$		0			0
$871$	44.0365	+	25.4245i	1.49212	+	0.861475i
$872$		−	11.0002i		−	0.372514i
$873$		0			0
$874$		−	34.3846i		−	1.16307i
$875$		0			0
$876$		0			0
$877$	5.53439	+	9.58584i	0.186883	+	0.323691i	0.944209	−	0.329346i	$-0.106828\pi$
$877$	5.53439	+	9.58584i	0.186883	+	0.323691i	−0.757326	+	0.653036i	$0.773495\pi$
$878$	−8.10505	−	14.0384i	−0.273532	−	0.473771i
$879$		0			0
$880$	5.68111	+	3.27999i	0.191510	+	0.110568i
$881$	8.87036			0.298850			0.149425	−	0.988773i	$-0.452258\pi$
$881$	8.87036			0.298850			0.149425	+	0.988773i	$0.452258\pi$
$882$		0			0
$883$	−14.1903			−0.477540			−0.238770	−	0.971076i	$-0.576744\pi$
$883$	−14.1903			−0.477540			−0.238770	+	0.971076i	$0.576744\pi$
$884$	5.90556	+	3.40958i	0.198625	+	0.114676i
$885$		0			0
$886$	−0.522064	−	0.904241i	−0.0175391	−	0.0303786i
$887$	19.5180	+	33.8062i	0.655350	+	1.13510i	0.981806	+	0.189887i	$0.0608123\pi$
$887$	19.5180	+	33.8062i	0.655350	+	1.13510i	−0.326456	+	0.945213i	$0.605854\pi$
$888$		0			0
$889$		0			0
$890$			18.1109i			0.607080i
$891$		0			0
$892$		−	3.21202i		−	0.107546i
$893$	−55.8570	−	32.2490i	−1.86918	−	1.07917i
$894$		0			0
$895$	9.77931	−	5.64609i	0.326886	−	0.188728i
$896$		0			0
$897$		0			0
$898$	7.80786	−	13.5236i	0.260552	−	0.451288i
$899$	−2.67422			−0.0891904
$900$		0			0
$901$		−	13.5737i		−	0.452207i
$902$	3.65992	−	6.33916i	0.121862	−	0.211071i
$903$		0			0
$904$	25.9605	+	44.9648i	0.863432	+	1.49551i
$905$	2.12252	−	1.22544i	0.0705550	−	0.0407350i
$906$		0			0
$907$	−4.93487	+	8.54745i	−0.163860	+	0.283813i	−0.936250	−	0.351335i	$-0.885728\pi$
$907$	−4.93487	+	8.54745i	−0.163860	+	0.283813i	0.772390	+	0.635148i	$0.219061\pi$
$908$	22.5921			0.749747
$909$		0			0
$910$		0			0
$911$	46.6335	+	26.9239i	1.54504	+	0.892028i	0.998509	+	0.0545881i	$0.0173846\pi$
$911$	46.6335	+	26.9239i	1.54504	+	0.892028i	0.546529	+	0.837440i	$0.315949\pi$
$912$		0			0
$913$	−31.0351	+	17.9181i	−1.02711	+	0.593004i
$914$	27.8772	−	16.0949i	0.922096	−	0.532373i
$915$		0			0
$916$	−11.5882	−	6.69046i	−0.382885	−	0.221059i
$917$		0			0
$918$		0			0
$919$	22.1799			0.731647			0.365824	−	0.930684i	$-0.380787\pi$
$919$	22.1799			0.731647			0.365824	+	0.930684i	$0.380787\pi$
$920$	12.0853	−	20.9324i	0.398442	−	0.690122i
$921$		0			0
$922$	−15.7047	+	9.06714i	−0.517208	+	0.298610i
$923$	29.4128	+	50.9444i	0.968133	+	1.67686i
$924$		0			0
$925$	5.80167	−	10.0488i	0.190758	−	0.330402i
$926$		−	0.396421i		−	0.0130272i
$927$		0			0
$928$	−3.20866			−0.105329
$929$	−27.4954	+	47.6234i	−0.902093	+	1.56247i	−0.0773215	+	0.997006i	$0.524637\pi$
$929$	−27.4954	+	47.6234i	−0.902093	+	1.56247i	−0.824772	+	0.565466i	$0.808697\pi$
$930$		0			0
$931$		0			0
$932$	0.725243	−	0.418719i	0.0237561	−	0.0137156i
$933$		0			0
$934$	−12.7734	−	7.37475i	−0.417960	−	0.241309i
$935$			12.4698i			0.407807i
$936$		0			0
$937$		−	29.3132i		−	0.957622i	−0.877918	−	0.478811i	$-0.841068\pi$
$937$		−	29.3132i		−	0.957622i	0.877918	−	0.478811i	$-0.158932\pi$
$938$		0			0
$939$		0			0
$940$	−7.73777	−	13.4022i	−0.252378	−	0.437132i
$941$	−7.58758	−	13.1421i	−0.247348	−	0.428419i	0.715441	−	0.698673i	$-0.246226\pi$
$941$	−7.58758	−	13.1421i	−0.247348	−	0.428419i	−0.962789	+	0.270254i	$0.912892\pi$
$942$		0			0
$943$	−6.80950	−	3.93147i	−0.221748	−	0.128026i
$944$	−6.97265			−0.226940
$945$		0			0
$946$	28.3808			0.922739
$947$	−2.27478	−	1.31335i	−0.0739206	−	0.0426781i	0.462584	−	0.886575i	$-0.346922\pi$
$947$	−2.27478	−	1.31335i	−0.0739206	−	0.0426781i	−0.536505	+	0.843897i	$0.680256\pi$
$948$		0			0
$949$	−7.68820	−	13.3164i	−0.249570	−	0.432267i
$950$	5.82725	+	10.0931i	0.189061	+	0.327463i
$951$		0			0
$952$		0			0
$953$			40.5520i			1.31361i	0.754061	+	0.656805i	$0.228092\pi$
$953$			40.5520i			1.31361i	−0.754061	+	0.656805i	$0.771908\pi$
$954$		0			0
$955$			10.7847i			0.348984i
$956$	12.6476	+	7.30212i	0.409054	+	0.236167i
$957$		0			0
$958$	−26.4214	+	15.2544i	−0.853637	+	0.492847i
$959$		0			0
$960$		0			0
$961$	−6.38155	+	11.0532i	−0.205856	+	0.356554i
$962$	−31.6328			−1.01988
$963$		0			0
$964$			19.1726i			0.617507i
$965$	−1.46643	+	2.53993i	−0.0472059	+	0.0817631i
$966$		0			0
$967$	6.47468	+	11.2145i	0.208212	+	0.360633i	0.951151	−	0.308725i	$-0.0999023\pi$
$967$	6.47468	+	11.2145i	0.208212	+	0.360633i	−0.742939	+	0.669359i	$0.766569\pi$
$968$	14.7457	−	8.51343i	0.473945	−	0.273632i
$969$		0			0
$970$	−12.2159	+	21.1585i	−0.392228	+	0.679359i
$971$	−16.5215			−0.530202			−0.265101	−	0.964221i	$-0.585405\pi$
$971$	−16.5215			−0.530202			−0.265101	+	0.964221i	$0.585405\pi$
$972$		0			0
$973$		0			0
$974$	11.4728	+	6.62381i	0.367611	+	0.212240i
$975$		0			0
$976$	−2.76587	+	1.59687i	−0.0885333	+	0.0511147i
$977$	−5.50730	+	3.17964i	−0.176194	+	0.101726i	−0.585503	−	0.810670i	$-0.699103\pi$
$977$	−5.50730	+	3.17964i	−0.176194	+	0.101726i	0.409309	+	0.912396i	$0.365770\pi$
$978$		0			0
$979$	34.7227	+	20.0472i	1.10974	+	0.640711i
$980$		0			0
$981$		0			0
$982$	8.01481			0.255763
$983$	−1.11487	+	1.93102i	−0.0355590	+	0.0615899i	−0.883257	−	0.468889i	$-0.844654\pi$
$983$	−1.11487	+	1.93102i	−0.0355590	+	0.0615899i	0.847698	+	0.530479i	$0.177988\pi$
$984$		0			0
$985$	31.8508	−	18.3891i	1.01485	−	0.585924i
$986$	0.498358	+	0.863181i	0.0158709	+	0.0274893i
$987$		0			0
$988$	−17.0870	+	29.5956i	−0.543610	+	0.941561i
$989$		−	30.4865i		−	0.969415i
$990$		0			0
$991$	−49.4570			−1.57105			−0.785527	−	0.618828i	$-0.787608\pi$
$991$	−49.4570			−1.57105			−0.785527	+	0.618828i	$0.787608\pi$
$992$	10.9407	−	18.9499i	0.347369	−	0.601661i
$993$		0			0
$994$		0			0
$995$	−1.59072	+	0.918403i	−0.0504293	+	0.0291153i
$996$		0			0
$997$	−7.28219	−	4.20437i	−0.230629	−	0.133154i	0.380233	−	0.924891i	$-0.375844\pi$
$997$	−7.28219	−	4.20437i	−0.230629	−	0.133154i	−0.610862	+	0.791737i	$0.709177\pi$
$998$			27.5044i			0.870636i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.o.e.440.16		48
3.2	odd	2		441.2.o.e.146.9	✓	48
7.2	even	3		1323.2.i.d.521.8		48
7.3	odd	6		1323.2.s.d.656.9		48
7.4	even	3		1323.2.s.d.656.10		48
7.5	odd	6		1323.2.i.d.521.18		48
7.6	odd	2	inner	1323.2.o.e.440.15		48
9.4	even	3		441.2.o.e.293.10	yes	48
9.5	odd	6	inner	1323.2.o.e.881.15		48
21.2	odd	6		441.2.i.d.227.16		48
21.5	even	6		441.2.i.d.227.15		48
21.11	odd	6		441.2.s.d.362.15		48
21.17	even	6		441.2.s.d.362.16		48
21.20	even	2		441.2.o.e.146.10	yes	48
63.4	even	3		441.2.i.d.68.9		48
63.5	even	6		1323.2.s.d.962.10		48
63.13	odd	6		441.2.o.e.293.9	yes	48
63.23	odd	6		1323.2.s.d.962.9		48
63.31	odd	6		441.2.i.d.68.10		48
63.32	odd	6		1323.2.i.d.1097.18		48
63.40	odd	6		441.2.s.d.374.15		48
63.41	even	6	inner	1323.2.o.e.881.16		48
63.58	even	3		441.2.s.d.374.16		48
63.59	even	6		1323.2.i.d.1097.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.9		48	63.4	even	3
441.2.i.d.68.10		48	63.31	odd	6
441.2.i.d.227.15		48	21.5	even	6
441.2.i.d.227.16		48	21.2	odd	6
441.2.o.e.146.9	✓	48	3.2	odd	2
441.2.o.e.146.10	yes	48	21.20	even	2
441.2.o.e.293.9	yes	48	63.13	odd	6
441.2.o.e.293.10	yes	48	9.4	even	3
441.2.s.d.362.15		48	21.11	odd	6
441.2.s.d.362.16		48	21.17	even	6
441.2.s.d.374.15		48	63.40	odd	6
441.2.s.d.374.16		48	63.58	even	3
1323.2.i.d.521.8		48	7.2	even	3
1323.2.i.d.521.18		48	7.5	odd	6
1323.2.i.d.1097.8		48	63.59	even	6
1323.2.i.d.1097.18		48	63.32	odd	6
1323.2.o.e.440.15		48	7.6	odd	2	inner
1323.2.o.e.440.16		48	1.1	even	1	trivial
1323.2.o.e.881.15		48	9.5	odd	6	inner
1323.2.o.e.881.16		48	63.41	even	6	inner
1323.2.s.d.656.9		48	7.3	odd	6
1323.2.s.d.656.10		48	7.4	even	3
1323.2.s.d.962.9		48	63.23	odd	6
1323.2.s.d.962.10		48	63.5	even	6

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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.850109 + 0.490811i) q^{2} +(-0.518210 - 0.897565i) q^{4} +(-0.940599 - 1.62916i) q^{5} -2.98061i q^{8} +O(q^{10})\)	\(q+(0.850109 + 0.490811i) q^{2} +(-0.518210 - 0.897565i) q^{4} +(-0.940599 - 1.62916i) q^{5} -2.98061i q^{8} -1.84662i q^{10} +(-3.54040 - 2.04405i) q^{11} +(-3.51415 + 2.02890i) q^{13} +(0.426498 - 0.738716i) q^{16} +1.62145 q^{17} +8.12588i q^{19} +(-0.974855 + 1.68850i) q^{20} +(-2.00648 - 3.47533i) q^{22} +(-3.73318 + 2.15535i) q^{23} +(0.730548 - 1.26535i) q^{25} -3.98322 q^{26} +(0.542317 + 0.313107i) q^{29} +(-3.69833 + 2.13523i) q^{31} +(-4.43744 + 2.56195i) q^{32} +(1.37841 + 0.795827i) q^{34} +7.94153 q^{37} +(-3.98827 + 6.90789i) q^{38} +(-4.85591 + 2.80356i) q^{40} +(0.912023 + 1.57967i) q^{41} +(-3.53614 + 6.12477i) q^{43} +4.23698i q^{44} -4.23148 q^{46} +(-3.96868 + 6.87396i) q^{47} +(1.24209 - 0.717122i) q^{50} +(3.64214 + 2.10279i) q^{52} -8.37133i q^{53} +7.69052i q^{55} +(0.307352 + 0.532350i) q^{58} +(-4.08715 - 7.07915i) q^{59} +(-3.24253 - 1.87208i) q^{61} -4.19198 q^{62} -6.73573 q^{64} +(6.61081 + 3.81676i) q^{65} +(-6.26559 - 10.8523i) q^{67} +(-0.840253 - 1.45536i) q^{68} -14.4969i q^{71} +3.78935i q^{73} +(6.75117 + 3.89779i) q^{74} +(7.29351 - 4.21091i) q^{76} +(-4.18066 + 7.24112i) q^{79} -1.60465 q^{80} +1.79052i q^{82} +(4.38300 - 7.59159i) q^{83} +(-1.52514 - 2.64162i) q^{85} +(-6.01221 + 3.47115i) q^{86} +(-6.09252 + 10.5526i) q^{88} -9.80759 q^{89} +(3.86914 + 2.23385i) q^{92} +(-6.74762 + 3.89574i) q^{94} +(13.2384 - 7.64320i) q^{95} +(-11.4579 - 6.61525i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4}+O(q^{10}) \) 48 * q + 24 * q^4	\( 48 q + 24 q^{4} + 24 q^{11} - 24 q^{16} + 48 q^{23} - 24 q^{25} - 120 q^{32} - 48 q^{50} - 48 q^{64} - 120 q^{65} + 168 q^{74} - 24 q^{79} - 24 q^{85} - 24 q^{86} + 144 q^{92} - 96 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 + 24 * q^11 - 24 * q^16 + 48 * q^23 - 24 * q^25 - 120 * q^32 - 48 * q^50 - 48 * q^64 - 120 * q^65 + 168 * q^74 - 24 * q^79 - 24 * q^85 - 24 * q^86 + 144 * q^92 - 96 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more