LMFDB - Embedded newform 882.2.l.a.227.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(227,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("882.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.l (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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			227.7
Root			$-1.40917 + 1.00709i$ of defining polynomial
Character	$\chi$	$=$	882.227
Dual form			882.2.l.a.509.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.167584 + 1.72392i) q^{3} -1.00000 q^{4} +(1.17468 - 2.03460i) q^{5} +(-1.72392 + 0.167584i) q^{6} -1.00000i q^{8} +(-2.94383 + 0.577806i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.167584 + 1.72392i) q^{3} -1.00000 q^{4} +(1.17468 - 2.03460i) q^{5} +(-1.72392 + 0.167584i) q^{6} -1.00000i q^{8} +(-2.94383 + 0.577806i) q^{9} +(2.03460 + 1.17468i) q^{10} +(4.91614 - 2.83834i) q^{11} +(-0.167584 - 1.72392i) q^{12} +(1.48943 - 0.859925i) q^{13} +(3.70436 + 1.68409i) q^{15} +1.00000 q^{16} +(0.884414 - 1.53185i) q^{17} +(-0.577806 - 2.94383i) q^{18} +(-0.986680 + 0.569660i) q^{19} +(-1.17468 + 2.03460i) q^{20} +(2.83834 + 4.91614i) q^{22} +(3.18272 + 1.83755i) q^{23} +(1.72392 - 0.167584i) q^{24} +(-0.259741 - 0.449885i) q^{25} +(0.859925 + 1.48943i) q^{26} +(-1.48943 - 4.97811i) q^{27} +(3.59886 + 2.07781i) q^{29} +(-1.68409 + 3.70436i) q^{30} -8.37019i q^{31} +1.00000i q^{32} +(5.71694 + 7.99939i) q^{33} +(1.53185 + 0.884414i) q^{34} +(2.94383 - 0.577806i) q^{36} +(4.59886 + 7.96547i) q^{37} +(-0.569660 - 0.986680i) q^{38} +(1.73205 + 2.42356i) q^{39} +(-2.03460 - 1.17468i) q^{40} +(3.99709 + 6.92317i) q^{41} +(1.76053 - 3.04933i) q^{43} +(-4.91614 + 2.83834i) q^{44} +(-2.28245 + 6.66826i) q^{45} +(-1.83755 + 3.18272i) q^{46} -11.8099 q^{47} +(0.167584 + 1.72392i) q^{48} +(0.449885 - 0.259741i) q^{50} +(2.78901 + 1.26795i) q^{51} +(-1.48943 + 0.859925i) q^{52} +(4.97811 - 1.48943i) q^{54} -13.3365i q^{55} +(-1.14740 - 1.60550i) q^{57} +(-2.07781 + 3.59886i) q^{58} -2.22966 q^{59} +(-3.70436 - 1.68409i) q^{60} -8.99970i q^{61} +8.37019 q^{62} -1.00000 q^{64} -4.04054i q^{65} +(-7.99939 + 5.71694i) q^{66} +10.8712 q^{67} +(-0.884414 + 1.53185i) q^{68} +(-2.63442 + 5.79472i) q^{69} +4.52106i q^{71} +(0.577806 + 2.94383i) q^{72} +(-4.62660 - 2.67117i) q^{73} +(-7.96547 + 4.59886i) q^{74} +(0.732039 - 0.523168i) q^{75} +(0.986680 - 0.569660i) q^{76} +(-2.42356 + 1.73205i) q^{78} -13.0284 q^{79} +(1.17468 - 2.03460i) q^{80} +(8.33228 - 3.40192i) q^{81} +(-6.92317 + 3.99709i) q^{82} +(-6.27298 + 10.8651i) q^{83} +(-2.07781 - 3.59886i) q^{85} +(3.04933 + 1.76053i) q^{86} +(-2.97887 + 6.55238i) q^{87} +(-2.83834 - 4.91614i) q^{88} +(0.580529 + 1.00551i) q^{89} +(-6.66826 - 2.28245i) q^{90} +(-3.18272 - 1.83755i) q^{92} +(14.4296 - 1.40271i) q^{93} -11.8099i q^{94} +2.67667i q^{95} +(-1.72392 + 0.167584i) q^{96} +(-3.97536 - 2.29517i) q^{97} +(-12.8323 + 11.1962i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 12 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 - 12 * q^9	$ 16 q - 16 q^{4} - 12 q^{9} + 12 q^{11} + 16 q^{16} + 12 q^{18} + 48 q^{23} - 8 q^{25} - 12 q^{29} + 12 q^{30} + 12 q^{36} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} + 60 q^{50} + 24 q^{51} + 48 q^{57} - 12 q^{58} - 16 q^{64} + 56 q^{67} - 12 q^{72} - 36 q^{74} - 24 q^{78} + 8 q^{79} - 12 q^{85} + 24 q^{86} - 48 q^{92} + 84 q^{93} - 72 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 - 12 * q^9 + 12 * q^11 + 16 * q^16 + 12 * q^18 + 48 * q^23 - 8 * q^25 - 12 * q^29 + 12 * q^30 + 12 * q^36 + 4 * q^37 + 4 * q^43 - 12 * q^44 - 12 * q^46 + 60 * q^50 + 24 * q^51 + 48 * q^57 - 12 * q^58 - 16 * q^64 + 56 * q^67 - 12 * q^72 - 36 * q^74 - 24 * q^78 + 8 * q^79 - 12 * q^85 + 24 * q^86 - 48 * q^92 + 84 * q^93 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.167584	+	1.72392i	0.0967549	+	0.995308i
$3$	0.167584	+	1.72392i	0.0967549	+	0.995308i
$4$	−1.00000			−0.500000
$5$	1.17468	−	2.03460i	0.525332	−	0.909902i	−0.474232	−	0.880400i	$-0.657274\pi$
$5$	1.17468	−	2.03460i	0.525332	−	0.909902i	0.999565	−	0.0295026i	$-0.00939234\pi$
$6$	−1.72392	+	0.167584i	−0.703789	+	0.0684160i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−2.94383	+	0.577806i	−0.981277	+	0.192602i
$10$	2.03460	+	1.17468i	0.643398	+	0.371466i
$11$	4.91614	−	2.83834i	1.48227	−	0.855790i	0.482475	−	0.875910i	$-0.339738\pi$
$11$	4.91614	−	2.83834i	1.48227	−	0.855790i	0.999798	+	0.0201197i	$0.00640473\pi$
$12$	−0.167584	−	1.72392i	−0.0483774	−	0.497654i
$13$	1.48943	−	0.859925i	0.413094	−	0.238500i	−0.279024	−	0.960284i	$-0.590011\pi$
$13$	1.48943	−	0.859925i	0.413094	−	0.238500i	0.692118	+	0.721784i	$0.256678\pi$
$14$		0			0
$15$	3.70436	+	1.68409i	0.956462	+	0.434830i
$16$	1.00000			0.250000
$17$	0.884414	−	1.53185i	0.214502	−	0.371528i	−0.738616	−	0.674126i	$-0.764520\pi$
$17$	0.884414	−	1.53185i	0.214502	−	0.371528i	0.953118	+	0.302598i	$0.0978538\pi$
$18$	−0.577806	−	2.94383i	−0.136190	−	0.693868i
$19$	−0.986680	+	0.569660i	−0.226360	+	0.130689i	−0.608892	−	0.793253i	$-0.708386\pi$
$19$	−0.986680	+	0.569660i	−0.226360	+	0.130689i	0.382532	+	0.923942i	$0.375052\pi$
$20$	−1.17468	+	2.03460i	−0.262666	+	0.454951i
$21$		0			0
$22$	2.83834	+	4.91614i	0.605135	+	1.04812i
$23$	3.18272	+	1.83755i	0.663644	+	0.383155i	0.793664	−	0.608356i	$-0.208171\pi$
$23$	3.18272	+	1.83755i	0.663644	+	0.383155i	−0.130020	+	0.991511i	$0.541504\pi$
$24$	1.72392	−	0.167584i	0.351895	−	0.0342080i
$25$	−0.259741	−	0.449885i	−0.0519482	−	0.0899769i
$26$	0.859925	+	1.48943i	0.168645	+	0.292102i
$27$	−1.48943	−	4.97811i	−0.286642	−	0.958038i
$28$		0			0
$29$	3.59886	+	2.07781i	0.668292	+	0.385839i	0.795429	−	0.606046i	$-0.207245\pi$
$29$	3.59886	+	2.07781i	0.668292	+	0.385839i	−0.127137	+	0.991885i	$0.540579\pi$
$30$	−1.68409	+	3.70436i	−0.307471	+	0.676321i
$31$		−	8.37019i		−	1.50333i	−0.659545	−	0.751665i	$-0.729251\pi$
$31$		−	8.37019i		−	1.50333i	0.659545	−	0.751665i	$-0.270749\pi$
$32$			1.00000i			0.176777i
$33$	5.71694	+	7.99939i	0.995192	+	1.39252i
$34$	1.53185	+	0.884414i	0.262710	+	0.151676i
$35$		0			0
$36$	2.94383	−	0.577806i	0.490638	−	0.0963009i
$37$	4.59886	+	7.96547i	0.756049	+	1.30951i	0.944851	+	0.327500i	$0.106206\pi$
$37$	4.59886	+	7.96547i	0.756049	+	1.30951i	−0.188803	+	0.982015i	$0.560461\pi$
$38$	−0.569660	−	0.986680i	−0.0924111	−	0.160061i
$39$	1.73205	+	2.42356i	0.277350	+	0.388080i
$40$	−2.03460	−	1.17468i	−0.321699	−	0.185733i
$41$	3.99709	+	6.92317i	0.624241	+	1.08122i	0.988687	+	0.149993i	$0.0479251\pi$
$41$	3.99709	+	6.92317i	0.624241	+	1.08122i	−0.364446	+	0.931225i	$0.618742\pi$
$42$		0			0
$43$	1.76053	−	3.04933i	0.268478	−	0.465018i	−0.699991	−	0.714152i	$-0.746813\pi$
$43$	1.76053	−	3.04933i	0.268478	−	0.465018i	0.968469	+	0.249134i	$0.0801459\pi$
$44$	−4.91614	+	2.83834i	−0.741136	+	0.427895i
$45$	−2.28245	+	6.66826i	−0.340248	+	0.994046i
$46$	−1.83755	+	3.18272i	−0.270931	+	0.469267i
$47$	−11.8099			−1.72265			−0.861324	−	0.508055i	$-0.830365\pi$
$47$	−11.8099			−1.72265			−0.861324	+	0.508055i	$0.830365\pi$
$48$	0.167584	+	1.72392i	0.0241887	+	0.248827i
$49$		0			0
$50$	0.449885	−	0.259741i	0.0636233	−	0.0367329i
$51$	2.78901	+	1.26795i	0.390539	+	0.177548i
$52$	−1.48943	+	0.859925i	−0.206547	+	0.119250i
$53$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$53$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$54$	4.97811	−	1.48943i	0.677435	−	0.202686i
$55$		−	13.3365i		−	1.79830i
$56$		0			0
$57$	−1.14740	−	1.60550i	−0.151977	−	0.212653i
$58$	−2.07781	+	3.59886i	−0.272829	+	0.472554i
$59$	−2.22966			−0.290277			−0.145139	−	0.989411i	$-0.546363\pi$
$59$	−2.22966			−0.290277			−0.145139	+	0.989411i	$0.546363\pi$
$60$	−3.70436	−	1.68409i	−0.478231	−	0.217415i
$61$		−	8.99970i		−	1.15229i	−0.817346	−	0.576146i	$-0.804556\pi$
$61$		−	8.99970i		−	1.15229i	0.817346	−	0.576146i	$-0.195444\pi$
$62$	8.37019			1.06301
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	4.04054i		−	0.501167i
$66$	−7.99939	+	5.71694i	−0.984657	+	0.703707i
$67$	10.8712			1.32813			0.664067	−	0.747673i	$-0.268829\pi$
$67$	10.8712			1.32813			0.664067	+	0.747673i	$0.268829\pi$
$68$	−0.884414	+	1.53185i	−0.107251	+	0.185764i
$69$	−2.63442	+	5.79472i	−0.317147	+	0.697602i
$70$		0			0
$71$			4.52106i			0.536551i	0.963342	+	0.268276i	$0.0864538\pi$
$71$			4.52106i			0.536551i	−0.963342	+	0.268276i	$0.913546\pi$
$72$	0.577806	+	2.94383i	0.0680950	+	0.346934i
$73$	−4.62660	−	2.67117i	−0.541503	−	0.312637i	0.204185	−	0.978932i	$-0.434546\pi$
$73$	−4.62660	−	2.67117i	−0.541503	−	0.312637i	−0.745688	+	0.666295i	$0.767879\pi$
$74$	−7.96547	+	4.59886i	−0.925967	+	0.534607i
$75$	0.732039	−	0.523168i	0.0845285	−	0.0604102i
$76$	0.986680	−	0.569660i	0.113180	−	0.0653445i
$77$		0			0
$78$	−2.42356	+	1.73205i	−0.274414	+	0.196116i
$79$	−13.0284			−1.46581			−0.732907	−	0.680329i	$-0.761837\pi$
$79$	−13.0284			−1.46581			−0.732907	+	0.680329i	$0.761837\pi$
$80$	1.17468	−	2.03460i	0.131333	−	0.227476i
$81$	8.33228	−	3.40192i	0.925809	−	0.377992i
$82$	−6.92317	+	3.99709i	−0.764536	+	0.441405i
$83$	−6.27298	+	10.8651i	−0.688549	+	1.19260i	0.283758	+	0.958896i	$0.408419\pi$
$83$	−6.27298	+	10.8651i	−0.688549	+	1.19260i	−0.972307	+	0.233707i	$0.924915\pi$
$84$		0			0
$85$	−2.07781	−	3.59886i	−0.225370	−	0.390352i
$86$	3.04933	+	1.76053i	0.328817	+	0.189843i
$87$	−2.97887	+	6.55238i	−0.319368	+	0.702489i
$88$	−2.83834	−	4.91614i	−0.302568	−	0.524062i
$89$	0.580529	+	1.00551i	0.0615360	+	0.106583i	0.895152	−	0.445761i	$-0.147067\pi$
$89$	0.580529	+	1.00551i	0.0615360	+	0.106583i	−0.833616	+	0.552344i	$0.813733\pi$
$90$	−6.66826	−	2.28245i	−0.702897	−	0.240591i
$91$		0			0
$92$	−3.18272	−	1.83755i	−0.331822	−	0.191577i
$93$	14.4296	−	1.40271i	1.49628	−	0.145454i
$94$		−	11.8099i		−	1.21810i
$95$			2.67667i			0.274621i
$96$	−1.72392	+	0.167584i	−0.175947	+	0.0171040i
$97$	−3.97536	−	2.29517i	−0.403636	−	0.233039i	0.284416	−	0.958701i	$-0.408200\pi$
$97$	−3.97536	−	2.29517i	−0.403636	−	0.233039i	−0.688052	+	0.725662i	$0.741534\pi$
$98$		0			0
$99$	−12.8323	+	11.1962i	−1.28969	+	1.12526i
$100$	0.259741	+	0.449885i	0.0259741	+	0.0449885i
$101$	3.31155	+	5.73577i	0.329511	+	0.570730i	0.982415	−	0.186711i	$-0.0597827\pi$
$101$	3.31155	+	5.73577i	0.329511	+	0.570730i	−0.652904	+	0.757441i	$0.726449\pi$
$102$	−1.26795	+	2.78901i	−0.125546	+	0.276153i
$103$	5.07471	+	2.92989i	0.500026	+	0.288690i	0.728724	−	0.684807i	$-0.240114\pi$
$103$	5.07471	+	2.92989i	0.500026	+	0.288690i	−0.228698	+	0.973497i	$0.573447\pi$
$104$	−0.859925	−	1.48943i	−0.0843225	−	0.146051i
$105$		0			0
$106$		0			0
$107$	−4.08386	+	2.35782i	−0.394802	+	0.227939i	−0.684239	−	0.729258i	$-0.739865\pi$
$107$	−4.08386	+	2.35782i	−0.394802	+	0.227939i	0.289437	+	0.957197i	$0.406532\pi$
$108$	1.48943	+	4.97811i	0.143321	+	0.479019i
$109$	−2.11835	+	3.66908i	−0.202901	+	0.351435i	−0.949462	−	0.313882i	$-0.898370\pi$
$109$	−2.11835	+	3.66908i	−0.202901	+	0.351435i	0.746561	+	0.665317i	$0.231704\pi$
$110$	13.3365			1.27159
$111$	−12.9612	+	9.26298i	−1.23022	+	0.879203i
$112$		0			0
$113$	5.91693	−	3.41614i	0.556618	−	0.321363i	−0.195169	−	0.980770i	$-0.562526\pi$
$113$	5.91693	−	3.41614i	0.556618	−	0.321363i	0.751787	+	0.659406i	$0.229192\pi$
$114$	1.60550	−	1.14740i	0.150368	−	0.107464i
$115$	7.47736	−	4.31705i	0.697267	−	0.402567i
$116$	−3.59886	−	2.07781i	−0.334146	−	0.192919i
$117$	−3.88777	+	3.39208i	−0.359424	+	0.313597i
$118$		−	2.22966i		−	0.205257i
$119$		0			0
$120$	1.68409	−	3.70436i	0.153736	−	0.338160i
$121$	10.6123	−	18.3810i	0.964754	−	1.67100i
$122$	8.99970			0.814794
$123$	−11.2652	+	8.05090i	−1.01575	+	0.725926i
$124$			8.37019i			0.751665i
$125$	10.5263			0.941504
$126$		0			0
$127$	−6.67667			−0.592459			−0.296229	−	0.955117i	$-0.595729\pi$
$127$	−6.67667			−0.592459			−0.296229	+	0.955117i	$0.595729\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	5.55185	+	2.52400i	0.488813	+	0.222226i
$130$	4.04054			0.354379
$131$	3.73653	−	6.47185i	0.326462	−	0.565448i	−0.655345	−	0.755329i	$-0.727477\pi$
$131$	3.73653	−	6.47185i	0.326462	−	0.565448i	0.981807	+	0.189881i	$0.0608102\pi$
$132$	−5.71694	−	7.99939i	−0.497596	−	0.696258i
$133$		0			0
$134$			10.8712i			0.939133i
$135$	−11.8781	−	2.81728i	−1.02230	−	0.242473i
$136$	−1.53185	−	0.884414i	−0.131355	−	0.0758379i
$137$	−6.91772	+	3.99395i	−0.591021	+	0.341226i	−0.765501	−	0.643435i	$-0.777509\pi$
$137$	−6.91772	+	3.99395i	−0.591021	+	0.341226i	0.174480	+	0.984661i	$0.444175\pi$
$138$	−5.79472	−	2.63442i	−0.493279	−	0.224256i
$139$	17.9792	−	10.3803i	1.52498	−	0.880446i	0.525415	−	0.850846i	$-0.323910\pi$
$139$	17.9792	−	10.3803i	1.52498	−	0.880446i	0.999562	−	0.0295993i	$-0.00942312\pi$
$140$		0			0
$141$	−1.97915	−	20.3593i	−0.166675	−	1.71457i
$142$	−4.52106			−0.379399
$143$	4.88151	−	8.45502i	0.408212	−	0.707044i
$144$	−2.94383	+	0.577806i	−0.245319	+	0.0481505i
$145$	8.45502	−	4.88151i	0.702151	−	0.405387i
$146$	2.67117	−	4.62660i	0.221068	−	0.382900i
$147$		0			0
$148$	−4.59886	−	7.96547i	−0.378024	−	0.654757i
$149$	1.03726	+	0.598865i	0.0849760	+	0.0490609i	0.541886	−	0.840452i	$-0.317710\pi$
$149$	1.03726	+	0.598865i	0.0849760	+	0.0490609i	−0.456910	+	0.889513i	$0.651044\pi$
$150$	0.523168	+	0.732039i	0.0427165	+	0.0597707i
$151$	−7.61229	−	13.1849i	−0.619480	−	1.07297i	−0.989581	−	0.143979i	$-0.954010\pi$
$151$	−7.61229	−	13.1849i	−0.619480	−	1.07297i	0.370101	−	0.928991i	$-0.379323\pi$
$152$	0.569660	+	0.986680i	0.0462055	+	0.0800303i
$153$	−1.71845	+	5.02053i	−0.138929	+	0.405886i
$154$		0			0
$155$	−17.0300	−	9.83228i	−1.36788	−	0.789748i
$156$	−1.73205	−	2.42356i	−0.138675	−	0.194040i
$157$			10.0269i			0.800237i	0.916463	+	0.400118i	$0.131031\pi$
$157$			10.0269i			0.800237i	−0.916463	+	0.400118i	$0.868969\pi$
$158$		−	13.0284i		−	1.03649i
$159$		0			0
$160$	2.03460	+	1.17468i	0.160850	+	0.0928665i
$161$		0			0
$162$	3.40192	+	8.33228i	0.267280	+	0.654646i
$163$	−6.00158	−	10.3950i	−0.470080	−	0.814202i	0.529335	−	0.848413i	$-0.322442\pi$
$163$	−6.00158	−	10.3950i	−0.470080	−	0.814202i	−0.999415	+	0.0342109i	$0.989108\pi$
$164$	−3.99709	−	6.92317i	−0.312121	−	0.540609i
$165$	22.9912	−	2.23499i	1.78986	−	0.173994i
$166$	−10.8651	−	6.27298i	−0.843297	−	0.486878i
$167$	8.57472	+	14.8518i	0.663532	+	1.14927i	0.979681	+	0.200561i	$0.0642765\pi$
$167$	8.57472	+	14.8518i	0.663532	+	1.14927i	−0.316150	+	0.948709i	$0.602390\pi$
$168$		0			0
$169$	−5.02106	+	8.69673i	−0.386235	+	0.668979i
$170$	3.59886	−	2.07781i	0.276020	−	0.159360i
$171$	2.57547	−	2.24709i	0.196951	−	0.171839i
$172$	−1.76053	+	3.04933i	−0.134239	+	0.232509i
$173$	−1.98748			−0.151105			−0.0755525	−	0.997142i	$-0.524072\pi$
$173$	−1.98748			−0.151105			−0.0755525	+	0.997142i	$0.524072\pi$
$174$	−6.55238	−	2.97887i	−0.496735	−	0.225827i
$175$		0			0
$176$	4.91614	−	2.83834i	0.370568	−	0.213948i
$177$	−0.373656	−	3.84377i	−0.0280857	−	0.288915i
$178$	−1.00551	+	0.580529i	−0.0753659	+	0.0435125i
$179$	7.19773	+	4.15561i	0.537984	+	0.310605i	0.744261	−	0.667889i	$-0.232802\pi$
$179$	7.19773	+	4.15561i	0.537984	+	0.310605i	−0.206278	+	0.978493i	$0.566135\pi$
$180$	2.28245	−	6.66826i	0.170124	−	0.497023i
$181$		−	15.4541i		−	1.14870i	−0.818611	−	0.574348i	$-0.805256\pi$
$181$		−	15.4541i		−	1.14870i	0.818611	−	0.574348i	$-0.194744\pi$
$182$		0			0
$183$	15.5148	−	1.50821i	1.14689	−	0.111490i
$184$	1.83755	−	3.18272i	0.135466	−	0.234634i
$185$	21.6088			1.58871
$186$	1.40271	+	14.4296i	0.102852	+	1.05803i
$187$		−	10.0411i		−	0.734275i
$188$	11.8099			0.861324
$189$		0			0
$190$	−2.67667			−0.194186
$191$		−	12.3381i		−	0.892752i	−0.894845	−	0.446376i	$-0.852714\pi$
$191$		−	12.3381i		−	0.892752i	0.894845	−	0.446376i	$-0.147286\pi$
$192$	−0.167584	−	1.72392i	−0.0120944	−	0.124414i
$193$	4.39388			0.316279			0.158139	−	0.987417i	$-0.449451\pi$
$193$	4.39388			0.316279			0.158139	+	0.987417i	$0.449451\pi$
$194$	2.29517	−	3.97536i	0.164784	−	0.285414i
$195$	6.96559	−	0.677132i	0.498816	−	0.0484904i
$196$		0			0
$197$		−	10.8865i		−	0.775632i	−0.921737	−	0.387816i	$-0.873230\pi$
$197$		−	10.8865i		−	0.775632i	0.921737	−	0.387816i	$-0.126770\pi$
$198$	−11.1962	−	12.8323i	−0.795676	−	0.911951i
$199$	−23.8733	−	13.7832i	−1.69233	−	0.977068i	−0.952629	−	0.304135i	$-0.901633\pi$
$199$	−23.8733	−	13.7832i	−1.69233	−	0.977068i	−0.739703	−	0.672933i	$-0.765034\pi$
$200$	−0.449885	+	0.259741i	−0.0318116	+	0.0183665i
$201$	1.82185	+	18.7412i	0.128503	+	1.32190i
$202$	−5.73577	+	3.31155i	−0.403567	+	0.233000i
$203$		0			0
$204$	−2.78901	−	1.26795i	−0.195270	−	0.0887742i
$205$	18.7812			1.31174
$206$	−2.92989	+	5.07471i	−0.204135	+	0.353572i
$207$	−10.4311	−	3.57043i	−0.725015	−	0.248162i
$208$	1.48943	−	0.859925i	0.103274	−	0.0596250i
$209$	−3.23377	+	5.60106i	−0.223685	+	0.387433i
$210$		0			0
$211$	5.15561	+	8.92978i	0.354927	+	0.614751i	0.987105	−	0.160071i	$-0.0511724\pi$
$211$	5.15561	+	8.92978i	0.354927	+	0.614751i	−0.632179	+	0.774823i	$0.717839\pi$
$212$		0			0
$213$	−7.79396	+	0.757659i	−0.534034	+	0.0519139i
$214$	−2.35782	−	4.08386i	−0.161177	−	0.279167i
$215$	−4.13611	−	7.16396i	−0.282081	−	0.488578i
$216$	−4.97811	+	1.48943i	−0.338718	+	0.101343i
$217$		0			0
$218$	−3.66908	−	2.11835i	−0.248502	−	0.143473i
$219$	3.82955	−	8.42356i	0.258777	−	0.569211i
$220$			13.3365i			0.899149i
$221$		−	3.04212i		−	0.204635i
$222$	−9.26298	−	12.9612i	−0.621691	−	0.869897i
$223$	−6.24329	−	3.60456i	−0.418081	−	0.241379i	0.276175	−	0.961107i	$-0.410933\pi$
$223$	−6.24329	−	3.60456i	−0.418081	−	0.241379i	−0.694256	+	0.719728i	$0.744267\pi$
$224$		0			0
$225$	1.02458	+	1.17430i	0.0683053	+	0.0782870i
$226$	3.41614	+	5.91693i	0.227238	+	0.393588i
$227$	6.37800	+	11.0470i	0.423323	+	0.733217i	0.996262	−	0.0863812i	$-0.0275303\pi$
$227$	6.37800	+	11.0470i	0.423323	+	0.733217i	−0.572939	+	0.819598i	$0.694197\pi$
$228$	1.14740	+	1.60550i	0.0759886	+	0.106327i
$229$	−3.89208	−	2.24709i	−0.257196	−	0.148492i	0.365859	−	0.930670i	$-0.380775\pi$
$229$	−3.89208	−	2.24709i	−0.257196	−	0.148492i	−0.623055	+	0.782178i	$0.714109\pi$
$230$	4.31705	+	7.47736i	0.284658	+	0.493042i
$231$		0			0
$232$	2.07781	−	3.59886i	0.136415	−	0.236277i
$233$	−1.86545	+	1.07702i	−0.122210	+	0.0705577i	−0.559859	−	0.828588i	$-0.689145\pi$
$233$	−1.86545	+	1.07702i	−0.122210	+	0.0705577i	0.437649	+	0.899146i	$0.355811\pi$
$234$	−3.39208	−	3.88777i	−0.221747	−	0.254151i
$235$	−13.8728	+	24.0284i	−0.904963	+	1.56744i
$236$	2.22966			0.145139
$237$	−2.18336	−	22.4600i	−0.141825	−	1.45894i
$238$		0			0
$239$	−8.78317	+	5.07096i	−0.568136	+	0.328013i	−0.756404	−	0.654104i	$-0.773046\pi$
$239$	−8.78317	+	5.07096i	−0.568136	+	0.328013i	0.188269	+	0.982118i	$0.439712\pi$
$240$	3.70436	+	1.68409i	0.239115	+	0.108708i
$241$	−9.13490	+	5.27404i	−0.588431	+	0.339731i	−0.764477	−	0.644651i	$-0.777003\pi$
$241$	−9.13490	+	5.27404i	−0.588431	+	0.339731i	0.176046	+	0.984382i	$0.443669\pi$
$242$	18.3810	+	10.6123i	1.18158	+	0.682184i
$243$	7.26102	+	13.7941i	0.465795	+	0.884893i
$244$			8.99970i			0.576146i
$245$		0			0
$246$	−8.05090	−	11.2652i	−0.513307	−	0.718241i
$247$	−0.979729	+	1.69694i	−0.0623387	+	0.107974i
$248$	−8.37019			−0.531507
$249$	−19.7819	−	8.99332i	−1.25363	−	0.569929i
$250$			10.5263i			0.665744i
$251$	−29.3005			−1.84943			−0.924714	−	0.380662i	$-0.875696\pi$
$251$	−29.3005			−1.84943			−0.924714	+	0.380662i	$0.875696\pi$
$252$		0			0
$253$	20.8623			1.31160
$254$		−	6.67667i		−	0.418932i
$255$	5.85596	−	4.18509i	0.366715	−	0.262081i
$256$	1.00000			0.0625000
$257$	−3.81430	+	6.60656i	−0.237930	+	0.412106i	−0.960120	−	0.279588i	$-0.909802\pi$
$257$	−3.81430	+	6.60656i	−0.237930	+	0.412106i	0.722190	+	0.691694i	$0.243135\pi$
$258$	−2.52400	+	5.55185i	−0.157137	+	0.345643i
$259$		0			0
$260$			4.04054i			0.250584i
$261$	−11.7950	−	4.03726i	−0.730093	−	0.249900i
$262$	6.47185	+	3.73653i	0.399832	+	0.230843i
$263$	10.5531	−	6.09281i	0.650729	−	0.375699i	−0.138006	−	0.990431i	$-0.544069\pi$
$263$	10.5531	−	6.09281i	0.650729	−	0.375699i	0.788736	+	0.614733i	$0.210736\pi$
$264$	7.99939	−	5.71694i	0.492329	−	0.351854i
$265$		0			0
$266$		0			0
$267$	−1.63613	+	1.16930i	−0.100129	+	0.0715597i
$268$	−10.8712			−0.664067
$269$	−1.38717	+	2.40264i	−0.0845771	+	0.146492i	−0.905211	−	0.424963i	$-0.860287\pi$
$269$	−1.38717	+	2.40264i	−0.0845771	+	0.146492i	0.820634	+	0.571454i	$0.193621\pi$
$270$	2.81728	−	11.8781i	0.171454	−	0.722877i
$271$	−2.77815	+	1.60396i	−0.168760	+	0.0974338i	−0.582001	−	0.813188i	$-0.697730\pi$
$271$	−2.77815	+	1.60396i	−0.168760	+	0.0974338i	0.413241	+	0.910622i	$0.364397\pi$
$272$	0.884414	−	1.53185i	0.0536255	−	0.0928821i
$273$		0			0
$274$	−3.99395	−	6.91772i	−0.241283	−	0.417915i
$275$	−2.55385	−	1.47446i	−0.154003	−	0.0889135i
$276$	2.63442	−	5.79472i	0.158573	−	0.348801i
$277$	−5.04054	−	8.73047i	−0.302857	−	0.524563i	0.673925	−	0.738800i	$-0.264607\pi$
$277$	−5.04054	−	8.73047i	−0.302857	−	0.524563i	−0.976782	+	0.214236i	$0.931274\pi$
$278$	10.3803	+	17.9792i	0.622569	+	1.07832i
$279$	4.83634	+	24.6404i	0.289544	+	1.47518i
$280$		0			0
$281$	4.21999	+	2.43641i	0.251743	+	0.145344i	0.620562	−	0.784157i	$-0.286904\pi$
$281$	4.21999	+	2.43641i	0.251743	+	0.145344i	−0.368819	+	0.929501i	$0.620238\pi$
$282$	20.3593	−	1.97915i	1.21238	−	0.117857i
$283$		−	2.81781i		−	0.167502i	−0.996487	−	0.0837508i	$-0.973310\pi$
$283$		−	2.81781i		−	0.167502i	0.996487	−	0.0837508i	$-0.0266900\pi$
$284$		−	4.52106i		−	0.268276i
$285$	−4.61438	+	0.448568i	−0.273332	+	0.0265709i
$286$	8.45502	+	4.88151i	0.499956	+	0.288650i
$287$		0			0
$288$	−0.577806	−	2.94383i	−0.0340475	−	0.173467i
$289$	6.93562	+	12.0129i	0.407978	+	0.706638i
$290$	4.88151	+	8.45502i	0.286652	+	0.496496i
$291$	3.29050	−	7.23785i	0.192892	−	0.424290i
$292$	4.62660	+	2.67117i	0.270751	+	0.156318i
$293$	−4.05694	−	7.02683i	−0.237009	−	0.410512i	0.722846	−	0.691010i	$-0.242834\pi$
$293$	−4.05694	−	7.02683i	−0.237009	−	0.410512i	−0.959855	+	0.280498i	$0.909500\pi$
$294$		0			0
$295$	−2.61914	+	4.53648i	−0.152492	+	0.264124i
$296$	7.96547	−	4.59886i	0.462983	−	0.267304i
$297$	−21.4518	−	20.2456i	−1.24476	−	1.17477i
$298$	−0.598865	+	1.03726i	−0.0346913	+	0.0600871i
$299$	6.32061			0.365530
$300$	−0.732039	+	0.523168i	−0.0422643	+	0.0302051i
$301$		0			0
$302$	13.1849	−	7.61229i	0.758705	−	0.438038i
$303$	−9.33307	+	6.67008i	−0.536171	+	0.383186i
$304$	−0.986680	+	0.569660i	−0.0565900	+	0.0326722i
$305$	−18.3108	−	10.5718i	−1.04847	−	0.605337i
$306$	−5.02053	−	1.71845i	−0.287004	−	0.0982375i
$307$			10.8996i			0.622074i	0.950398	+	0.311037i	$0.100676\pi$
$307$			10.8996i			0.622074i	−0.950398	+	0.311037i	$0.899324\pi$
$308$		0			0
$309$	−4.20046	+	9.23943i	−0.238956	+	0.525613i
$310$	9.83228	−	17.0300i	0.558436	−	0.967240i
$311$	−8.23637			−0.467042			−0.233521	−	0.972352i	$-0.575025\pi$
$311$	−8.23637			−0.467042			−0.233521	+	0.972352i	$0.575025\pi$
$312$	2.42356	−	1.73205i	0.137207	−	0.0980581i
$313$			33.8023i			1.91062i	0.295611	+	0.955308i	$0.404477\pi$
$313$			33.8023i			1.91062i	−0.295611	+	0.955308i	$0.595523\pi$
$314$	−10.0269			−0.565853
$315$		0			0
$316$	13.0284			0.732907
$317$		−	6.73090i		−	0.378045i	−0.981973	−	0.189022i	$-0.939468\pi$
$317$		−	6.73090i		−	0.378045i	0.981973	−	0.189022i	$-0.0605319\pi$
$318$		0			0
$319$	23.5900			1.32079
$320$	−1.17468	+	2.03460i	−0.0656665	+	0.113738i
$321$	−4.74909	−	6.64513i	−0.265068	−	0.370895i
$322$		0			0
$323$			2.01526i			0.112132i
$324$	−8.33228	+	3.40192i	−0.462905	+	0.188996i
$325$	−0.773734	−	0.446715i	−0.0429190	−	0.0247793i
$326$	10.3950	−	6.00158i	0.575728	−	0.332397i
$327$	−6.68023	−	3.03699i	−0.369417	−	0.167946i
$328$	6.92317	−	3.99709i	0.382268	−	0.220703i
$329$		0			0
$330$	2.23499	+	22.9912i	0.123032	+	1.26562i
$331$	−32.0569			−1.76200			−0.881002	−	0.473112i	$-0.843131\pi$
$331$	−32.0569			−1.76200			−0.881002	+	0.473112i	$0.843131\pi$
$332$	6.27298	−	10.8651i	0.344275	−	0.596301i
$333$	−18.1408	−	20.7917i	−0.994108	−	1.13938i
$334$	−14.8518	+	8.57472i	−0.812657	+	0.469188i
$335$	12.7702	−	22.1187i	0.697712	−	1.20847i
$336$		0			0
$337$	−12.1123	−	20.9791i	−0.659799	−	1.14280i	−0.980668	−	0.195681i	$-0.937308\pi$
$337$	−12.1123	−	20.9791i	−0.659799	−	1.14280i	0.320869	−	0.947124i	$-0.396025\pi$
$338$	−8.69673	−	5.02106i	−0.473040	−	0.273110i
$339$	6.88075	+	9.62785i	0.373711	+	0.522913i
$340$	2.07781	+	3.59886i	0.112685	+	0.195176i
$341$	−23.7574	−	41.1490i	−1.28654	−	2.22834i
$342$	2.24709	+	2.57547i	0.121509	+	0.139265i
$343$		0			0
$344$	−3.04933	−	1.76053i	−0.164409	−	0.0949214i
$345$	8.69536	+	12.1669i	0.468143	+	0.655045i
$346$		−	1.98748i		−	0.106847i
$347$			22.7999i			1.22396i	0.790873	+	0.611981i	$0.209627\pi$
$347$			22.7999i			1.22396i	−0.790873	+	0.611981i	$0.790373\pi$
$348$	2.97887	−	6.55238i	0.159684	−	0.351244i
$349$	−2.46389	−	1.42253i	−0.131889	−	0.0761461i	0.432604	−	0.901584i	$-0.357595\pi$
$349$	−2.46389	−	1.42253i	−0.131889	−	0.0761461i	−0.564493	+	0.825438i	$0.690928\pi$
$350$		0			0
$351$	−6.49921	−	6.13376i	−0.346902	−	0.327396i
$352$	2.83834	+	4.91614i	0.151284	+	0.262031i
$353$	−3.57212	−	6.18709i	−0.190125	−	0.329306i	0.755167	−	0.655533i	$-0.227556\pi$
$353$	−3.57212	−	6.18709i	−0.190125	−	0.329306i	−0.945291	+	0.326227i	$0.894223\pi$
$354$	3.84377	−	0.373656i	0.204294	−	0.0198596i
$355$	9.19856	+	5.31079i	0.488209	+	0.281868i
$356$	−0.580529	−	1.00551i	−0.0307680	−	0.0532917i
$357$		0			0
$358$	−4.15561	+	7.19773i	−0.219631	+	0.380412i
$359$	−10.0491	+	5.80186i	−0.530372	+	0.306210i	−0.741168	−	0.671320i	$-0.765728\pi$
$359$	−10.0491	+	5.80186i	−0.530372	+	0.306210i	0.210796	+	0.977530i	$0.432394\pi$
$360$	6.66826	+	2.28245i	0.351448	+	0.120296i
$361$	−8.85097	+	15.3303i	−0.465841	+	0.806860i
$362$	15.4541			0.812250
$363$	33.4660	+	15.2144i	1.75651	+	0.798550i
$364$		0			0
$365$	−10.8695	+	6.27554i	−0.568938	+	0.328477i
$366$	1.50821	+	15.5148i	0.0788353	+	0.810971i
$367$	−6.78525	+	3.91747i	−0.354187	+	0.204490i	−0.666528	−	0.745480i	$-0.732220\pi$
$367$	−6.78525	+	3.91747i	−0.354187	+	0.204490i	0.312341	+	0.949970i	$0.398887\pi$
$368$	3.18272	+	1.83755i	0.165911	+	0.0957887i
$369$	−15.7670	−	18.0711i	−0.820798	−	0.940744i
$370$			21.6088i			1.12339i
$371$		0			0
$372$	−14.4296	+	1.40271i	−0.748138	+	0.0727272i
$373$	−12.8339	+	22.2289i	−0.664512	+	1.15097i	0.314905	+	0.949123i	$0.398027\pi$
$373$	−12.8339	+	22.2289i	−0.664512	+	1.15097i	−0.979417	+	0.201845i	$0.935306\pi$
$374$	10.0411			0.519211
$375$	1.76405	+	18.1466i	0.0910951	+	0.937087i
$376$			11.8099i			0.609048i
$377$	7.14702			0.368091
$378$		0			0
$379$	−15.1045			−0.775868			−0.387934	−	0.921687i	$-0.626811\pi$
$379$	−15.1045			−0.775868			−0.387934	+	0.921687i	$0.626811\pi$
$380$		−	2.67667i		−	0.137310i
$381$	−1.11891	−	11.5101i	−0.0573233	−	0.589679i
$382$	12.3381			0.631271
$383$	0.763322	−	1.32211i	0.0390040	−	0.0675568i	−0.845864	−	0.533398i	$-0.820915\pi$
$383$	0.763322	−	1.32211i	0.0390040	−	0.0675568i	0.884868	+	0.465841i	$0.154248\pi$
$384$	1.72392	−	0.167584i	0.0879737	−	0.00855200i
$385$		0			0
$386$			4.39388i			0.223643i
$387$	−3.42078	+	9.99395i	−0.173888	+	0.508021i
$388$	3.97536	+	2.29517i	0.201818	+	0.116520i
$389$	−12.8948	+	7.44483i	−0.653794	+	0.377468i	−0.789908	−	0.613225i	$-0.789872\pi$
$389$	−12.8948	+	7.44483i	−0.653794	+	0.377468i	0.136115	+	0.990693i	$0.456538\pi$
$390$	0.677132	+	6.96559i	0.0342879	+	0.352716i
$391$	5.62969	−	3.25030i	0.284706	−	0.164375i
$392$		0			0
$393$	11.7832	+	5.35691i	0.594382	+	0.270220i
$394$	10.8865			0.548454
$395$	−15.3042	+	26.5077i	−0.770039	+	1.33375i
$396$	12.8323	−	11.1962i	0.644846	−	0.562628i
$397$	24.9302	−	14.3935i	1.25121	−	0.722388i	0.279862	−	0.960040i	$-0.409711\pi$
$397$	24.9302	−	14.3935i	1.25121	−	0.722388i	0.971350	+	0.237653i	$0.0763780\pi$
$398$	13.7832	−	23.8733i	0.690892	−	1.19666i
$399$		0			0
$400$	−0.259741	−	0.449885i	−0.0129871	−	0.0224942i
$401$	33.0592	+	19.0868i	1.65090	+	0.953147i	0.976703	+	0.214595i	$0.0688431\pi$
$401$	33.0592	+	19.0868i	1.65090	+	0.953147i	0.674196	+	0.738552i	$0.264490\pi$
$402$	−18.7412	+	1.82185i	−0.934726	+	0.0908657i
$403$	−7.19773	−	12.4668i	−0.358544	−	0.621017i
$404$	−3.31155	−	5.73577i	−0.164756	−	0.285365i
$405$	2.86619	−	20.9491i	0.142422	−	1.04097i
$406$		0			0
$407$	45.2173	+	26.1062i	2.24134	+	1.29404i
$408$	1.26795	−	2.78901i	0.0627728	−	0.138076i
$409$			6.96694i			0.344493i	0.985054	+	0.172247i	$0.0551026\pi$
$409$			6.96694i			0.344493i	−0.985054	+	0.172247i	$0.944897\pi$
$410$			18.7812i			0.927538i
$411$	−8.04456	−	11.2563i	−0.396809	−	0.555232i
$412$	−5.07471	−	2.92989i	−0.250013	−	0.144345i
$413$		0			0
$414$	3.57043	−	10.4311i	0.175477	−	0.512663i
$415$	14.7375	+	25.5261i	0.723435	+	1.25303i
$416$	0.859925	+	1.48943i	0.0421613	+	0.0730255i
$417$	20.9079	+	29.2552i	1.02386	+	1.43263i
$418$	−5.60106	−	3.23377i	−0.273957	−	0.158169i
$419$	−17.4232	−	30.1778i	−0.851177	−	1.47428i	−0.880146	−	0.474702i	$-0.842556\pi$
$419$	−17.4232	−	30.1778i	−0.851177	−	1.47428i	0.0289690	−	0.999580i	$-0.490778\pi$
$420$		0			0
$421$	2.84597	−	4.92936i	0.138704	−	0.240242i	−0.788302	−	0.615288i	$-0.789040\pi$
$421$	2.84597	−	4.92936i	0.138704	−	0.240242i	0.927006	+	0.375046i	$0.122373\pi$
$422$	−8.92978	+	5.15561i	−0.434695	+	0.250971i
$423$	34.7663	−	6.82382i	1.69040	−	0.331785i
$424$		0			0
$425$	−0.918875			−0.0445720
$426$	−0.757659	−	7.79396i	−0.0367087	−	0.377619i
$427$		0			0
$428$	4.08386	−	2.35782i	0.197401	−	0.113969i
$429$	15.3939	+	6.99842i	0.743224	+	0.337887i
$430$	7.16396	−	4.13611i	0.345477	−	0.199461i
$431$	−26.2350	−	15.1468i	−1.26370	−	0.729595i	−0.289908	−	0.957055i	$-0.593625\pi$
$431$	−26.2350	−	15.1468i	−1.26370	−	0.729595i	−0.973787	+	0.227460i	$0.926958\pi$
$432$	−1.48943	−	4.97811i	−0.0716604	−	0.239509i
$433$			23.6094i			1.13459i	0.823513	+	0.567297i	$0.192011\pi$
$433$			23.6094i			1.13459i	−0.823513	+	0.567297i	$0.807989\pi$
$434$		0			0
$435$	9.83228	+	13.7578i	0.471422	+	0.659634i
$436$	2.11835	−	3.66908i	0.101450	−	0.175717i
$437$	−4.18711			−0.200297
$438$	8.42356	+	3.82955i	0.402493	+	0.182983i
$439$		−	25.0202i		−	1.19415i	−0.802185	−	0.597075i	$-0.796329\pi$
$439$		−	25.0202i		−	1.19415i	0.802185	−	0.597075i	$-0.203671\pi$
$440$	−13.3365			−0.635794
$441$		0			0
$442$	3.04212			0.144699
$443$			23.0300i			1.09419i	0.837071	+	0.547094i	$0.184266\pi$
$443$			23.0300i			1.09419i	−0.837071	+	0.547094i	$0.815734\pi$
$444$	12.9612	−	9.26298i	0.615110	−	0.439602i
$445$	2.72774			0.129307
$446$	3.60456	−	6.24329i	0.170681	−	0.295628i
$447$	−0.858568	+	1.88853i	−0.0406089	+	0.0893242i
$448$		0			0
$449$		−	15.9028i		−	0.750501i	−0.926923	−	0.375251i	$-0.877557\pi$
$449$		−	15.9028i		−	0.750501i	0.926923	−	0.375251i	$-0.122443\pi$
$450$	−1.17430	+	1.02458i	−0.0553572	+	0.0482991i
$451$	39.3006	+	22.6902i	1.85059	+	1.06844i
$452$	−5.91693	+	3.41614i	−0.278309	+	0.160682i
$453$	21.4540	−	15.3326i	1.00800	−	0.720388i
$454$	−11.0470	+	6.37800i	−0.518462	+	0.299334i
$455$		0			0
$456$	−1.60550	+	1.14740i	−0.0751842	+	0.0537321i
$457$	−5.66614			−0.265051			−0.132525	−	0.991180i	$-0.542309\pi$
$457$	−5.66614			−0.265051			−0.132525	+	0.991180i	$0.542309\pi$
$458$	2.24709	−	3.89208i	0.105000	−	0.181865i
$459$	−8.94300	−	2.12112i	−0.417423	−	0.0990056i
$460$	−7.47736	+	4.31705i	−0.348634	+	0.201284i
$461$	−15.7292	+	27.2438i	−0.732582	+	1.26887i	0.223194	+	0.974774i	$0.428352\pi$
$461$	−15.7292	+	27.2438i	−0.732582	+	1.26887i	−0.955776	+	0.294095i	$0.904982\pi$
$462$		0			0
$463$	4.55148	+	7.88340i	0.211525	+	0.366373i	0.952192	−	0.305500i	$-0.0988236\pi$
$463$	4.55148	+	7.88340i	0.211525	+	0.366373i	−0.740667	+	0.671873i	$0.765490\pi$
$464$	3.59886	+	2.07781i	0.167073	+	0.0964597i
$465$	14.0961	−	31.0062i	0.653693	−	1.43788i
$466$	−1.07702	−	1.86545i	−0.0498918	−	0.0864152i
$467$	15.1516	+	26.2433i	0.701132	+	1.21440i	0.968069	+	0.250682i	$0.0806549\pi$
$467$	15.1516	+	26.2433i	0.701132	+	1.21440i	−0.266938	+	0.963714i	$0.586012\pi$
$468$	3.88777	−	3.39208i	0.179712	−	0.156799i
$469$		0			0
$470$	−24.0284	−	13.8728i	−1.10835	−	0.639906i
$471$	−17.2857	+	1.68036i	−0.796482	+	0.0774268i
$472$			2.22966i			0.102628i
$473$		−	19.9879i		−	0.919044i
$474$	22.4600	−	2.18336i	1.03162	−	0.100285i
$475$	0.512563	+	0.295928i	0.0235180	+	0.0135781i
$476$		0			0
$477$		0			0
$478$	−5.07096	−	8.78317i	−0.231940	−	0.401733i
$479$	−2.33143	−	4.03816i	−0.106526	−	0.184508i	0.807835	−	0.589409i	$-0.200639\pi$
$479$	−2.33143	−	4.03816i	−0.106526	−	0.184508i	−0.914361	+	0.404901i	$0.867306\pi$
$480$	−1.68409	+	3.70436i	−0.0768678	+	0.169080i
$481$	13.6994	+	7.90935i	0.624639	+	0.360636i
$482$	−5.27404	−	9.13490i	−0.240226	−	0.416083i
$483$		0			0
$484$	−10.6123	+	18.3810i	−0.482377	+	0.835501i
$485$	−9.33953	+	5.39218i	−0.424086	+	0.244846i
$486$	−13.7941	+	7.26102i	−0.625714	+	0.329367i
$487$	9.74105	−	16.8720i	0.441409	−	0.764543i	−0.556385	−	0.830924i	$-0.687812\pi$
$487$	9.74105	−	16.8720i	0.441409	−	0.764543i	0.997794	+	0.0663816i	$0.0211455\pi$
$488$	−8.99970			−0.407397
$489$	16.9145	−	12.0883i	0.764900	−	0.546652i
$490$		0			0
$491$	−17.7437	+	10.2443i	−0.800762	+	0.462320i	−0.843737	−	0.536756i	$-0.819649\pi$
$491$	−17.7437	+	10.2443i	−0.800762	+	0.462320i	0.0429758	+	0.999076i	$0.486316\pi$
$492$	11.2652	−	8.05090i	0.507873	−	0.362963i
$493$	6.36577	−	3.67528i	0.286700	−	0.165526i
$494$	−1.69694	−	0.979729i	−0.0763490	−	0.0440801i
$495$	7.70592	+	39.2605i	0.346355	+	1.76463i
$496$		−	8.37019i		−	0.375832i
$497$		0			0
$498$	8.99332	−	19.7819i	0.403000	−	0.886449i
$499$	5.12598	−	8.87845i	0.229470	−	0.397454i	−0.728181	−	0.685385i	$-0.759634\pi$
$499$	5.12598	−	8.87845i	0.229470	−	0.397454i	0.957651	+	0.287931i	$0.0929673\pi$
$500$	−10.5263			−0.470752
$501$	−24.1665	+	17.2711i	−1.07968	+	0.771616i
$502$		−	29.3005i		−	1.30774i
$503$	−14.5521			−0.648845			−0.324422	−	0.945912i	$-0.605170\pi$
$503$	−14.5521			−0.648845			−0.324422	+	0.945912i	$0.605170\pi$
$504$		0			0
$505$	15.5600			0.692412
$506$			20.8623i			0.927442i
$507$	−15.8340	−	7.19849i	−0.703211	−	0.319696i
$508$	6.67667			0.296229
$509$	−16.6617	+	28.8589i	−0.738517	+	1.27915i	0.214646	+	0.976692i	$0.431140\pi$
$509$	−16.6617	+	28.8589i	−0.738517	+	1.27915i	−0.953163	+	0.302457i	$0.902193\pi$
$510$	4.18509	+	5.85596i	0.185319	+	0.259306i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	4.30542	+	4.06333i	0.190089	+	0.179401i
$514$	−6.60656	−	3.81430i	−0.291403	−	0.168242i
$515$	11.9223	−	6.88335i	0.525360	−	0.303317i
$516$	−5.55185	−	2.52400i	−0.244406	−	0.111113i
$517$	−58.0591	+	33.5204i	−2.55343	+	1.47423i
$518$		0			0
$519$	−0.333070	−	3.42626i	−0.0146202	−	0.150396i
$520$	−4.04054			−0.177189
$521$	3.26963	−	5.66316i	0.143245	−	0.248108i	−0.785472	−	0.618897i	$-0.787580\pi$
$521$	3.26963	−	5.66316i	0.143245	−	0.248108i	0.928717	+	0.370790i	$0.120913\pi$
$522$	4.03726	−	11.7950i	0.176706	−	0.516254i
$523$	−0.681439	+	0.393429i	−0.0297972	+	0.0172034i	−0.514825	−	0.857296i	$-0.672143\pi$
$523$	−0.681439	+	0.393429i	−0.0297972	+	0.0172034i	0.485027	+	0.874499i	$0.338810\pi$
$524$	−3.73653	+	6.47185i	−0.163231	+	0.282724i
$525$		0			0
$526$	6.09281	+	10.5531i	0.265659	+	0.460135i
$527$	−12.8219	−	7.40271i	−0.558530	−	0.322467i
$528$	5.71694	+	7.99939i	0.248798	+	0.348129i
$529$	−4.74685	−	8.22178i	−0.206385	−	0.357469i
$530$		0			0
$531$	6.56374	−	1.28831i	0.284842	−	0.0559079i
$532$		0			0
$533$	11.9068	+	6.87440i	0.515741	+	0.297763i
$534$	−1.16930	−	1.63613i	−0.0506004	−	0.0708022i
$535$			11.0787i			0.478975i
$536$		−	10.8712i		−	0.469566i
$537$	−5.95773	+	13.1048i	−0.257095	+	0.565512i
$538$	−2.40264	−	1.38717i	−0.103585	−	0.0598050i
$539$		0			0
$540$	11.8781	+	2.81728i	0.511152	+	0.121236i
$541$	−2.80227	−	4.85367i	−0.120479	−	0.208676i	0.799478	−	0.600696i	$-0.205110\pi$
$541$	−2.80227	−	4.85367i	−0.120479	−	0.208676i	−0.919957	+	0.392020i	$0.871776\pi$
$542$	−1.60396	−	2.77815i	−0.0688961	−	0.119332i
$543$	26.6417	−	2.58987i	1.14331	−	0.111142i
$544$	1.53185	+	0.884414i	0.0656775	+	0.0379189i
$545$	4.97675	+	8.61999i	0.213181	+	0.369240i
$546$		0			0
$547$	−6.91456	+	11.9764i	−0.295645	+	0.512073i	−0.975135	−	0.221612i	$-0.928868\pi$
$547$	−6.91456	+	11.9764i	−0.295645	+	0.512073i	0.679489	+	0.733685i	$0.262201\pi$
$548$	6.91772	−	3.99395i	0.295510	−	0.170613i
$549$	5.20007	+	26.4936i	0.221934	+	1.13072i
$550$	1.47446	−	2.55385i	0.0628714	−	0.108896i
$551$	−4.73457			−0.201700
$552$	5.79472	+	2.63442i	0.246640	+	0.112128i
$553$		0			0
$554$	8.73047	−	5.04054i	0.370922	−	0.214152i
$555$	3.62129	+	37.2519i	0.153715	+	1.58125i
$556$	−17.9792	+	10.3803i	−0.762488	+	0.440223i
$557$	24.0957	+	13.9117i	1.02097	+	0.589456i	0.914384	−	0.404848i	$-0.132675\pi$
$557$	24.0957	+	13.9117i	1.02097	+	0.589456i	0.106584	+	0.994304i	$0.466009\pi$
$558$	−24.6404	+	4.83634i	−1.04311	+	0.204739i
$559$		−	6.05569i		−	0.256128i
$560$		0			0
$561$	17.3100	−	1.68272i	0.730830	−	0.0710447i
$562$	−2.43641	+	4.21999i	−0.102774	+	0.178009i
$563$	−24.5300			−1.03382			−0.516909	−	0.856040i	$-0.672917\pi$
$563$	−24.5300			−1.03382			−0.516909	+	0.856040i	$0.672917\pi$
$564$	1.97915	+	20.3593i	0.0833373	+	0.857283i
$565$		−	16.0515i		−	0.675291i
$566$	2.81781			0.118441
$567$		0			0
$568$	4.52106			0.189699
$569$			27.1079i			1.13642i	0.822882	+	0.568212i	$0.192365\pi$
$569$			27.1079i			1.13642i	−0.822882	+	0.568212i	$0.807635\pi$
$570$	−0.448568	−	4.61438i	−0.0187885	−	0.193275i
$571$	−29.8354			−1.24857			−0.624287	−	0.781195i	$-0.714610\pi$
$571$	−29.8354			−1.24857			−0.624287	+	0.781195i	$0.714610\pi$
$572$	−4.88151	+	8.45502i	−0.204106	+	0.353522i
$573$	21.2699	−	2.06767i	0.888563	−	0.0863781i
$574$		0			0
$575$		−	1.90915i		−	0.0796169i
$576$	2.94383	−	0.577806i	0.122660	−	0.0240752i
$577$	24.3930	+	14.0833i	1.01549	+	0.586296i	0.912796	−	0.408416i	$-0.133919\pi$
$577$	24.3930	+	14.0833i	1.01549	+	0.586296i	0.102699	+	0.994712i	$0.467252\pi$
$578$	−12.0129	+	6.93562i	−0.499669	+	0.288484i
$579$	0.736346	+	7.57472i	0.0306015	+	0.314795i
$580$	−8.45502	+	4.88151i	−0.351076	+	0.202694i
$581$		0			0
$582$	7.23785	+	3.29050i	0.300018	+	0.136395i
$583$		0			0
$584$	−2.67117	+	4.62660i	−0.110534	+	0.191450i
$585$	2.33465	+	11.8947i	0.0965258	+	0.491784i
$586$	7.02683	−	4.05694i	0.290276	−	0.167591i
$587$	4.95928	−	8.58973i	0.204692	−	0.354536i	−0.745343	−	0.666681i	$-0.767714\pi$
$587$	4.95928	−	8.58973i	0.204692	−	0.354536i	0.950034	+	0.312145i	$0.101048\pi$
$588$		0			0
$589$	4.76816	+	8.25870i	0.196469	+	0.340294i
$590$	−4.53648	−	2.61914i	−0.186764	−	0.107828i
$591$	18.7675	−	1.82441i	0.771992	−	0.0750461i
$592$	4.59886	+	7.96547i	0.189012	+	0.327379i
$593$	2.34936	+	4.06921i	0.0964766	+	0.167102i	0.910224	−	0.414116i	$-0.135909\pi$
$593$	2.34936	+	4.06921i	0.0964766	+	0.167102i	−0.813747	+	0.581219i	$0.802576\pi$
$594$	20.2456	−	21.4518i	0.830686	−	0.880178i
$595$		0			0
$596$	−1.03726	−	0.598865i	−0.0424880	−	0.0245305i
$597$	19.7605	−	43.4656i	0.808743	−	1.77893i
$598$			6.32061i			0.258469i
$599$			14.7004i			0.600641i	0.953838	+	0.300320i	$0.0970936\pi$
$599$			14.7004i			0.600641i	−0.953838	+	0.300320i	$0.902906\pi$
$600$	−0.523168	−	0.732039i	−0.0213582	−	0.0298854i
$601$	16.2923	+	9.40634i	0.664575	+	0.383693i	0.794018	−	0.607894i	$-0.207986\pi$
$601$	16.2923	+	9.40634i	0.664575	+	0.383693i	−0.129443	+	0.991587i	$0.541319\pi$
$602$		0			0
$603$	−32.0031	+	6.28147i	−1.30327	+	0.255801i
$604$	7.61229	+	13.1849i	0.309740	+	0.536485i
$605$	−24.9321	−	43.1836i	−1.01363	−	1.75566i
$606$	−6.67008	−	9.33307i	−0.270954	−	0.379130i
$607$	−10.9051	−	6.29608i	−0.442625	−	0.255550i	0.262085	−	0.965045i	$-0.415590\pi$
$607$	−10.9051	−	6.29608i	−0.442625	−	0.255550i	−0.704711	+	0.709495i	$0.748923\pi$
$608$	−0.569660	−	0.986680i	−0.0231028	−	0.0400152i
$609$		0			0
$610$	10.5718	−	18.3108i	0.428038	−	0.741383i
$611$	−17.5900	+	10.1556i	−0.711617	+	0.410852i
$612$	1.71845	−	5.02053i	0.0694644	−	0.202943i
$613$	4.91009	−	8.50452i	0.198317	−	0.343494i	−0.749666	−	0.661816i	$-0.769786\pi$
$613$	4.91009	−	8.50452i	0.198317	−	0.343494i	0.947983	+	0.318322i	$0.103119\pi$
$614$	−10.8996			−0.439873
$615$	3.14744	+	32.3774i	0.126917	+	1.30558i
$616$		0			0
$617$	−3.25158	+	1.87730i	−0.130904	+	0.0755772i	−0.564022	−	0.825760i	$-0.690747\pi$
$617$	−3.25158	+	1.87730i	−0.130904	+	0.0755772i	0.433118	+	0.901337i	$0.357413\pi$
$618$	−9.23943	−	4.20046i	−0.371664	−	0.168967i
$619$	−9.56902	+	5.52468i	−0.384611	+	0.222055i	−0.679823	−	0.733376i	$-0.737943\pi$
$619$	−9.56902	+	5.52468i	−0.384611	+	0.222055i	0.295211	+	0.955432i	$0.404610\pi$
$620$	17.0300	+	9.83228i	0.683942	+	0.394874i
$621$	4.40706	−	18.5809i	0.176849	−	0.745624i
$622$		−	8.23637i		−	0.330248i
$623$		0			0
$624$	1.73205	+	2.42356i	0.0693375	+	0.0970201i
$625$	13.6638	−	23.6664i	0.546551	−	0.946654i
$626$	−33.8023			−1.35101
$627$	−10.1977	−	4.63613i	−0.407258	−	0.185149i
$628$		−	10.0269i		−	0.400118i
$629$	16.2692			0.648696
$630$		0			0
$631$	19.4921			0.775969			0.387984	−	0.921666i	$-0.373171\pi$
$631$	19.4921			0.775969			0.387984	+	0.921666i	$0.373171\pi$
$632$			13.0284i			0.518243i
$633$	−14.5303	+	10.3844i	−0.577526	+	0.412742i
$634$	6.73090			0.267318
$635$	−7.84294	+	13.5844i	−0.311238	+	0.539080i
$636$		0			0
$637$		0			0
$638$			23.5900i			0.933938i
$639$	−2.61229	−	13.3092i	−0.103341	−	0.526505i
$640$	−2.03460	−	1.17468i	−0.0804248	−	0.0464333i
$641$	22.6669	−	13.0868i	0.895290	−	0.516896i	0.0196208	−	0.999807i	$-0.493754\pi$
$641$	22.6669	−	13.0868i	0.895290	−	0.516896i	0.875669	+	0.482912i	$0.160421\pi$
$642$	6.64513	−	4.74909i	0.262262	−	0.187432i
$643$	9.50955	−	5.49034i	0.375020	−	0.216518i	−0.300629	−	0.953741i	$-0.597197\pi$
$643$	9.50955	−	5.49034i	0.375020	−	0.216518i	0.675649	+	0.737223i	$0.263863\pi$
$644$		0			0
$645$	11.6570	−	8.33092i	0.458993	−	0.328029i
$646$	−2.01526			−0.0792894
$647$	−16.0063	+	27.7237i	−0.629273	+	1.08993i	0.358425	+	0.933558i	$0.383314\pi$
$647$	−16.0063	+	27.7237i	−0.629273	+	1.08993i	−0.987698	+	0.156374i	$0.950019\pi$
$648$	−3.40192	−	8.33228i	−0.133640	−	0.327323i
$649$	−10.9613	+	6.32852i	−0.430270	+	0.248416i
$650$	0.446715	−	0.773734i	0.0175216	−	0.0303483i
$651$		0			0
$652$	6.00158	+	10.3950i	0.235040	+	0.407101i
$653$	−19.3686	−	11.1825i	−0.757952	−	0.437604i	0.0706080	−	0.997504i	$-0.477506\pi$
$653$	−19.3686	−	11.1825i	−0.757952	−	0.437604i	−0.828560	+	0.559900i	$0.810839\pi$
$654$	3.03699	−	6.68023i	0.118756	−	0.261218i
$655$	−8.77843	−	15.2047i	−0.343002	−	0.594097i
$656$	3.99709	+	6.92317i	0.156060	+	0.270304i
$657$	15.1634	+	5.19020i	0.591579	+	0.202489i
$658$		0			0
$659$	−19.2546	−	11.1166i	−0.750053	−	0.433043i	0.0756603	−	0.997134i	$-0.475894\pi$
$659$	−19.2546	−	11.1166i	−0.750053	−	0.433043i	−0.825713	+	0.564091i	$0.809227\pi$
$660$	−22.9912	+	2.23499i	−0.894930	+	0.0869970i
$661$		−	10.5499i		−	0.410343i	−0.978726	−	0.205171i	$-0.934225\pi$
$661$		−	10.5499i		−	0.410343i	0.978726	−	0.205171i	$-0.0657751\pi$
$662$		−	32.0569i		−	1.24593i
$663$	5.24438	−	0.509811i	0.203675	−	0.0197994i
$664$	10.8651	+	6.27298i	0.421649	+	0.243439i
$665$		0			0
$666$	20.7917	−	18.1408i	0.805664	−	0.702941i
$667$	7.63613	+	13.2262i	0.295672	+	0.512119i
$668$	−8.57472	−	14.8518i	−0.331766	−	0.574635i
$669$	5.16772	−	11.3670i	0.199796	−	0.439475i
$670$	22.1187	+	12.7702i	0.854519	+	0.493357i
$671$	−25.5442	−	44.2438i	−0.986121	−	1.70801i
$672$		0			0
$673$	9.93562	−	17.2090i	0.382990	−	0.663358i	−0.608498	−	0.793555i	$-0.708228\pi$
$673$	9.93562	−	17.2090i	0.382990	−	0.663358i	0.991488	+	0.130197i	$0.0415610\pi$
$674$	20.9791	−	12.1123i	0.808085	−	0.466548i
$675$	−1.85271	+	1.96309i	−0.0713108	+	0.0755595i
$676$	5.02106	−	8.69673i	0.193118	−	0.334490i
$677$	15.9290			0.612201			0.306100	−	0.951999i	$-0.400976\pi$
$677$	15.9290			0.612201			0.306100	+	0.951999i	$0.400976\pi$
$678$	−9.62785	+	6.88075i	−0.369755	+	0.264254i
$679$		0			0
$680$	−3.59886	+	2.07781i	−0.138010	+	0.0796802i
$681$	−17.9754	+	12.8465i	−0.688818	+	0.492279i
$682$	41.1490	−	23.7574i	1.57568	−	0.909718i
$683$	−16.4777	−	9.51343i	−0.630503	−	0.364021i	0.150444	−	0.988619i	$-0.451930\pi$
$683$	−16.4777	−	9.51343i	−0.630503	−	0.364021i	−0.780947	+	0.624597i	$0.785263\pi$
$684$	−2.57547	+	2.24709i	−0.0984754	+	0.0859197i
$685$			18.7664i			0.717028i
$686$		0			0
$687$	3.22157	−	7.08623i	0.122910	−	0.270356i
$688$	1.76053	−	3.04933i	0.0671196	−	0.116254i
$689$		0			0
$690$	−12.1669	+	8.69536i	−0.463187	+	0.331027i
$691$		−	0.161055i		−	0.00612681i	−0.999995	−	0.00306340i	$-0.999025\pi$
$691$		−	0.161055i		−	0.00612681i	0.999995	−	0.00306340i	$-0.000975113\pi$
$692$	1.98748			0.0755525
$693$		0			0
$694$	−22.7999			−0.865471
$695$		−	48.7741i		−	1.85011i
$696$	6.55238	+	2.97887i	0.248367	+	0.112914i
$697$	14.1403			0.535604
$698$	1.42253	−	2.46389i	0.0538434	−	0.0932595i
$699$	−2.16932	−	3.03540i	−0.0820511	−	0.114809i
$700$		0			0
$701$		−	9.98234i		−	0.377028i	−0.982071	−	0.188514i	$-0.939633\pi$
$701$		−	9.98234i		−	0.377028i	0.982071	−	0.188514i	$-0.0603670\pi$
$702$	6.13376	−	6.49921i	0.231504	−	0.245297i
$703$	−9.07522	−	5.23958i	−0.342278	−	0.197614i
$704$	−4.91614	+	2.83834i	−0.185284	+	0.106974i
$705$	−43.7481	−	19.8889i	−1.64765	−	0.749060i
$706$	6.18709	−	3.57212i	0.232854	−	0.134438i
$707$		0			0
$708$	0.373656	+	3.84377i	0.0140429	+	0.144458i
$709$	−24.3923			−0.916072			−0.458036	−	0.888934i	$-0.651447\pi$
$709$	−24.3923			−0.916072			−0.458036	+	0.888934i	$0.651447\pi$
$710$	−5.31079	+	9.19856i	−0.199311	+	0.345216i
$711$	38.3535	−	7.52790i	1.43837	−	0.282318i
$712$	1.00551	−	0.580529i	0.0376829	−	0.0217563i
$713$	15.3806	−	26.6400i	0.576008	−	0.997676i
$714$		0			0
$715$	−11.4684	−	19.8639i	−0.428894	−	0.742867i
$716$	−7.19773	−	4.15561i	−0.268992	−	0.155302i
$717$	−10.2139	−	14.2917i	−0.381444	−	0.533733i
$718$	−5.80186	−	10.0491i	−0.216523	−	0.375030i
$719$	8.13460	+	14.0895i	0.303370	+	0.525451i	0.976897	−	0.213711i	$-0.0685550\pi$
$719$	8.13460	+	14.0895i	0.303370	+	0.525451i	−0.673527	+	0.739162i	$0.735222\pi$
$720$	−2.28245	+	6.66826i	−0.0850619	+	0.248512i
$721$		0			0
$722$	−15.3303	−	8.85097i	−0.570536	−	0.329399i
$723$	−10.6229	−	14.8640i	−0.395070	−	0.552799i
$724$			15.4541i			0.574348i
$725$		−	2.15877i		−	0.0801745i
$726$	−15.2144	+	33.4660i	−0.564660	+	1.24204i
$727$	20.6626	+	11.9296i	0.766335	+	0.442444i	0.831566	−	0.555427i	$-0.187445\pi$
$727$	20.6626	+	11.9296i	0.766335	+	0.442444i	−0.0652306	+	0.997870i	$0.520778\pi$
$728$		0			0
$729$	−22.5632	+	14.8291i	−0.835673	+	0.549227i
$730$	−6.27554	−	10.8695i	−0.232268	−	0.402300i
$731$	−3.11408	−	5.39374i	−0.115178	−	0.199495i
$732$	−15.5148	+	1.50821i	−0.573443	+	0.0557450i
$733$	−10.6259	−	6.13486i	−0.392476	−	0.226596i	0.290756	−	0.956797i	$-0.406093\pi$
$733$	−10.6259	−	6.13486i	−0.392476	−	0.226596i	−0.683233	+	0.730201i	$0.739426\pi$
$734$	−3.91747	−	6.78525i	−0.144596	−	0.250448i
$735$		0			0
$736$	−1.83755	+	3.18272i	−0.0677329	+	0.117317i
$737$	53.4446	−	30.8562i	1.96866	−	1.13660i
$738$	18.0711	−	15.7670i	0.665206	−	0.580392i
$739$	−20.9446	+	36.2771i	−0.770459	+	1.33447i	0.166853	+	0.985982i	$0.446639\pi$
$739$	−20.9446	+	36.2771i	−0.770459	+	1.33447i	−0.937312	+	0.348492i	$0.886694\pi$
$740$	−21.6088			−0.794354
$741$	−3.08959	−	1.40460i	−0.113499	−	0.0515992i
$742$		0			0
$743$	43.9160	−	25.3549i	1.61112	−	0.930182i	0.622011	−	0.783008i	$-0.286316\pi$
$743$	43.9160	−	25.3549i	1.61112	−	0.930182i	0.989111	−	0.147173i	$-0.0470176\pi$
$744$	−1.40271	−	14.4296i	−0.0514259	−	0.529014i
$745$	2.43690	−	1.40695i	0.0892813	−	0.0515466i
$746$	−22.2289	−	12.8339i	−0.813858	−	0.469881i
$747$	12.1887	−	35.6097i	0.445960	−	1.30289i
$748$			10.0411i			0.367137i
$749$		0			0
$750$	−18.1466	+	1.76405i	−0.662621	+	0.0644140i
$751$	16.3683	−	28.3508i	0.597289	−	1.03454i	−0.395930	−	0.918281i	$-0.629578\pi$
$751$	16.3683	−	28.3508i	0.597289	−	1.03454i	0.993219	−	0.116255i	$-0.0370890\pi$
$752$	−11.8099			−0.430662
$753$	−4.91030	−	50.5118i	−0.178941	−	1.84075i
$754$			7.14702i			0.260279i
$755$	−35.7680			−1.30173
$756$		0			0
$757$	−17.9255			−0.651512			−0.325756	−	0.945454i	$-0.605619\pi$
$757$	−17.9255			−0.651512			−0.325756	+	0.945454i	$0.605619\pi$
$758$		−	15.1045i		−	0.548622i
$759$	3.49619	+	35.9650i	0.126904	+	1.30545i
$760$	2.67667			0.0970930
$761$	21.8509	−	37.8469i	0.792096	−	1.37195i	−0.132571	−	0.991174i	$-0.542323\pi$
$761$	21.8509	−	37.8469i	0.792096	−	1.37195i	0.924667	−	0.380777i	$-0.124343\pi$
$762$	11.5101	−	1.11891i	0.416966	−	0.0405337i
$763$		0			0
$764$			12.3381i			0.446376i
$765$	8.19615	+	9.39388i	0.296333	+	0.339637i
$766$	1.32211	+	0.763322i	0.0477699	+	0.0275800i
$767$	−3.32093	+	1.91734i	−0.119912	+	0.0692311i
$768$	0.167584	+	1.72392i	0.00604718	+	0.0622068i
$769$	−37.0864	+	21.4118i	−1.33737	+	0.772131i	−0.986417	−	0.164262i	$-0.947476\pi$
$769$	−37.0864	+	21.4118i	−1.33737	+	0.772131i	−0.350953	+	0.936393i	$0.614142\pi$
$770$		0			0
$771$	−12.0284	−	5.46841i	−0.433193	−	0.196940i
$772$	−4.39388			−0.158139
$773$	10.8025	−	18.7105i	0.388540	−	0.672971i	−0.603714	−	0.797201i	$-0.706313\pi$
$773$	10.8025	−	18.7105i	0.388540	−	0.672971i	0.992253	+	0.124231i	$0.0396462\pi$
$774$	−9.99395	−	3.42078i	−0.359225	−	0.122958i
$775$	−3.76562	+	2.17408i	−0.135265	+	0.0780953i
$776$	−2.29517	+	3.97536i	−0.0823919	+	0.142707i
$777$		0			0
$778$	−7.44483	−	12.8948i	−0.266910	−	0.462302i
$779$	−7.88771	−	4.55397i	−0.282606	−	0.163163i
$780$	−6.96559	+	0.677132i	−0.249408	+	0.0242452i
$781$	12.8323	+	22.2262i	0.459175	+	0.795315i
$782$	3.25030	+	5.62969i	0.116231	+	0.201317i
$783$	4.98328	−	21.0103i	0.178088	−	0.750847i
$784$		0			0
$785$	20.4008	+	11.7784i	0.728137	+	0.420390i
$786$	−5.35691	+	11.7832i	−0.191075	+	0.420292i
$787$		−	51.3042i		−	1.82880i	−0.404817	−	0.914398i	$-0.632665\pi$
$787$		−	51.3042i		−	1.82880i	0.404817	−	0.914398i	$-0.367335\pi$
$788$			10.8865i			0.387816i
$789$	12.2721	+	17.1716i	0.436897	+	0.611326i
$790$	−26.5077	−	15.3042i	−0.943102	−	0.544500i
$791$		0			0
$792$	11.1962	+	12.8323i	0.397838	+	0.455975i
$793$	−7.73906	−	13.4044i	−0.274822	−	0.476006i
$794$	14.3935	+	24.9302i	0.510805	+	0.884740i
$795$		0			0
$796$	23.8733	+	13.7832i	0.846166	+	0.488534i
$797$	−0.899094	−	1.55728i	−0.0318476	−	0.0551616i	0.849662	−	0.527327i	$-0.176806\pi$
$797$	−0.899094	−	1.55728i	−0.0318476	−	0.0551616i	−0.881510	+	0.472166i	$0.843472\pi$
$798$		0			0
$799$	−10.4448	+	18.0910i	−0.369512	+	0.640013i
$800$	0.449885	−	0.259741i	0.0159058	−	0.00918323i
$801$	−2.28997	−	2.62461i	−0.0809120	−	0.0927359i
$802$	−19.0868	+	33.0592i	−0.673977	+	1.16736i
$803$	−30.3267			−1.07021
$804$	−1.82185	−	18.7412i	−0.0642517	−	0.660951i
$805$		0			0
$806$	12.4668	−	7.19773i	0.439125	−	0.253529i
$807$	−4.37444	−	1.98873i	−0.153988	−	0.0700065i
$808$	5.73577	−	3.31155i	0.201784	−	0.116500i
$809$	35.2371	+	20.3441i	1.23887	+	0.715262i	0.968863	−	0.247597i	$-0.0796409\pi$
$809$	35.2371	+	20.3441i	1.23887	+	0.715262i	0.270006	+	0.962859i	$0.412974\pi$
$810$	20.9491	+	2.86619i	0.736075	+	0.100708i
$811$		−	0.378710i		−	0.0132983i	−0.999978	−	0.00664916i	$-0.997883\pi$
$811$		−	0.378710i		−	0.0132983i	0.999978	−	0.00664916i	$-0.00211651\pi$
$812$		0			0
$813$	−3.23068	−	4.52051i	−0.113305	−	0.158541i
$814$	−26.1062	+	45.2173i	−0.915023	+	1.58487i
$815$	−28.1997			−0.987793
$816$	2.78901	+	1.26795i	0.0976348	+	0.0443871i
$817$			4.01161i			0.140349i
$818$	−6.96694			−0.243593
$819$		0			0
$820$	−18.7812			−0.655868
$821$		−	13.2754i		−	0.463315i	−0.972797	−	0.231658i	$-0.925585\pi$
$821$		−	13.2754i		−	0.463315i	0.972797	−	0.231658i	$-0.0744149\pi$
$822$	11.2563	−	8.04456i	0.392609	−	0.280586i
$823$	27.7422			0.967034			0.483517	−	0.875335i	$-0.339359\pi$
$823$	27.7422			0.967034			0.483517	+	0.875335i	$0.339359\pi$
$824$	2.92989	−	5.07471i	0.102067	−	0.176786i
$825$	2.11388	−	4.64974i	0.0735959	−	0.161883i
$826$		0			0
$827$		−	27.7183i		−	0.963859i	−0.876210	−	0.481929i	$-0.839936\pi$
$827$		−	27.7183i		−	0.963859i	0.876210	−	0.481929i	$-0.160064\pi$
$828$	10.4311	+	3.57043i	0.362507	+	0.124081i
$829$	37.0105	+	21.3680i	1.28543	+	0.742143i	0.977835	−	0.209375i	$-0.0671431\pi$
$829$	37.0105	+	21.3680i	1.28543	+	0.742143i	0.307593	+	0.951518i	$0.400476\pi$
$830$	−25.5261	+	14.7375i	−0.886023	+	0.511545i
$831$	14.2060	−	10.1526i	0.492799	−	0.352190i
$832$	−1.48943	+	0.859925i	−0.0516368	+	0.0298125i
$833$		0			0
$834$	−29.2552	+	20.9079i	−1.01303	+	0.723981i
$835$	40.2902			1.39430
$836$	3.23377	−	5.60106i	0.111842	−	0.193717i
$837$	−41.6677	+	12.4668i	−1.44025	+	0.430917i
$838$	30.1778	−	17.4232i	1.04248	−	0.601873i
$839$	−1.92438	+	3.33313i	−0.0664370	+	0.115072i	−0.897331	−	0.441359i	$-0.854496\pi$
$839$	−1.92438	+	3.33313i	−0.0664370	+	0.115072i	0.830894	+	0.556431i	$0.187830\pi$
$840$		0			0
$841$	−5.86545	−	10.1593i	−0.202257	−	0.350319i
$842$	4.92936	+	2.84597i	0.169877	+	0.0980785i
$843$	−3.49299	+	7.68325i	−0.120305	+	0.264625i
$844$	−5.15561	−	8.92978i	−0.177463	−	0.307376i
$845$	11.7963	+	20.4317i	0.405804	+	0.702873i
$846$	6.82382	+	34.7663i	0.234608	+	1.19529i
$847$		0			0
$848$		0			0
$849$	4.85769	−	0.472221i	0.166716	−	0.0162066i
$850$		−	0.918875i		−	0.0315171i
$851$			33.8025i			1.15874i
$852$	7.79396	−	0.757659i	0.267017	−	0.0259570i
$853$	−26.3470	−	15.2114i	−0.902103	−	0.520830i	−0.0242213	−	0.999707i	$-0.507711\pi$
$853$	−26.3470	−	15.2114i	−0.902103	−	0.520830i	−0.877882	+	0.478877i	$0.841044\pi$
$854$		0			0
$855$	−1.54660	−	7.87967i	−0.0528924	−	0.269479i
$856$	2.35782	+	4.08386i	0.0805885	+	0.139583i
$857$	19.4657	+	33.7156i	0.664937	+	1.15170i	0.979303	+	0.202402i	$0.0648748\pi$
$857$	19.4657	+	33.7156i	0.664937	+	1.15170i	−0.314366	+	0.949302i	$0.601792\pi$
$858$	−6.99842	+	15.3939i	−0.238922	+	0.525538i
$859$	−11.5922	−	6.69275i	−0.395520	−	0.228354i	0.289029	−	0.957320i	$-0.406668\pi$
$859$	−11.5922	−	6.69275i	−0.395520	−	0.228354i	−0.684549	+	0.728967i	$0.740001\pi$
$860$	4.13611	+	7.16396i	0.141040	+	0.244289i
$861$		0			0
$862$	15.1468	−	26.2350i	0.515901	−	0.893567i
$863$	18.8118	−	10.8610i	0.640360	−	0.369712i	−0.144393	−	0.989520i	$-0.546123\pi$
$863$	18.8118	−	10.8610i	0.640360	−	0.369712i	0.784753	+	0.619809i	$0.212790\pi$
$864$	4.97811	−	1.48943i	0.169359	−	0.0506715i
$865$	−2.33465	+	4.04373i	−0.0793804	+	0.137491i
$866$	−23.6094			−0.802279
$867$	−19.5469	+	13.9697i	−0.663849	+	0.474434i
$868$		0			0
$869$	−64.0496	+	36.9791i	−2.17273	+	1.25443i
$870$	−13.7578	+	9.83228i	−0.466432	+	0.333346i
$871$	16.1920	−	9.34845i	0.548645	−	0.316760i
$872$	3.66908	+	2.11835i	0.124251	+	0.0717363i
$873$	13.0289	+	4.45962i	0.440963	+	0.150935i
$874$		−	4.18711i		−	0.141631i
$875$		0			0
$876$	−3.82955	+	8.42356i	−0.129388	+	0.284606i
$877$	−0.196152	+	0.339746i	−0.00662360	+	0.0114724i	−0.869318	−	0.494253i	$-0.835442\pi$
$877$	−0.196152	+	0.339746i	−0.00662360	+	0.0114724i	0.862695	+	0.505725i	$0.168775\pi$
$878$	25.0202			0.844392
$879$	11.4338	−	8.17145i	0.385654	−	0.275616i
$880$		−	13.3365i		−	0.449574i
$881$	43.3363			1.46004			0.730018	−	0.683427i	$-0.239511\pi$
$881$	43.3363			1.46004			0.730018	+	0.683427i	$0.239511\pi$
$882$		0			0
$883$	2.17403			0.0731618			0.0365809	−	0.999331i	$-0.488353\pi$
$883$	2.17403			0.0731618			0.0365809	+	0.999331i	$0.488353\pi$
$884$			3.04212i			0.102318i
$885$	−8.25947	−	3.75495i	−0.277639	−	0.126221i
$886$	−23.0300			−0.773708
$887$	−5.72215	+	9.91105i	−0.192131	+	0.332781i	−0.945956	−	0.324294i	$-0.894873\pi$
$887$	−5.72215	+	9.91105i	−0.192131	+	0.332781i	0.753825	+	0.657075i	$0.228207\pi$
$888$	9.26298	+	12.9612i	0.310845	+	0.434948i
$889$		0			0
$890$			2.72774i			0.0914341i
$891$	31.3069	−	40.3741i	1.04882	−	1.35258i
$892$	6.24329	+	3.60456i	0.209041	+	0.120690i
$893$	11.6526	−	6.72762i	0.389939	−	0.225131i
$894$	−1.88853	−	0.858568i	−0.0631617	−	0.0287148i
$895$	16.9100	−	9.76302i	0.565240	−	0.326342i
$896$		0			0
$897$	1.05923	+	10.8962i	0.0353668	+	0.363815i
$898$	15.9028			0.530684
$899$	17.3916	−	30.1232i	0.580043	−	1.00466i
$900$	−1.02458	−	1.17430i	−0.0341527	−	0.0391435i
$901$		0			0
$902$	−22.6902	+	39.3006i	−0.755501	+	1.30857i
$903$		0			0
$904$	−3.41614	−	5.91693i	−0.113619	−	0.196794i
$905$	−31.4430	−	18.1536i	−1.04520	−	0.603447i
$906$	15.3326	+	21.4540i	0.509391	+	0.712763i
$907$	26.9446	+	46.6694i	0.894680	+	1.54963i	0.834200	+	0.551462i	$0.185930\pi$
$907$	26.9446	+	46.6694i	0.894680	+	1.54963i	0.0604797	+	0.998169i	$0.480737\pi$
$908$	−6.37800	−	11.0470i	−0.211661	−	0.366608i
$909$	−13.0628	−	14.9717i	−0.433266	−	0.496580i
$910$		0			0
$911$	−7.00460	−	4.04411i	−0.232073	−	0.133987i	0.379455	−	0.925210i	$-0.376111\pi$
$911$	−7.00460	−	4.04411i	−0.232073	−	0.133987i	−0.611528	+	0.791223i	$0.709445\pi$
$912$	−1.14740	−	1.60550i	−0.0379943	−	0.0531633i
$913$			71.2193i			2.35702i
$914$		−	5.66614i		−	0.187419i
$915$	15.1563	−	33.3381i	0.501052	−	1.10212i
$916$	3.89208	+	2.24709i	0.128598	+	0.0742460i
$917$		0			0
$918$	2.12112	−	8.94300i	0.0700075	−	0.295163i
$919$	−12.8375	−	22.2353i	−0.423472	−	0.733474i	0.572805	−	0.819692i	$-0.305855\pi$
$919$	−12.8375	−	22.2353i	−0.423472	−	0.733474i	−0.996276	+	0.0862175i	$0.972522\pi$
$920$	−4.31705	−	7.47736i	−0.142329	−	0.246521i
$921$	−18.7901	+	1.82661i	−0.619156	+	0.0601887i
$922$	−27.2438	−	15.7292i	−0.897226	−	0.518014i
$923$	3.88777	+	6.73382i	0.127968	+	0.221646i
$924$		0			0
$925$	2.38903	−	4.13792i	0.0785507	−	0.136054i
$926$	−7.88340	+	4.55148i	−0.259064	+	0.149571i
$927$	−16.6320	−	5.69289i	−0.546267	−	0.186979i
$928$	−2.07781	+	3.59886i	−0.0682073	+	0.118139i
$929$	−10.8524			−0.356055			−0.178027	−	0.984026i	$-0.556972\pi$
$929$	−10.8524			−0.356055			−0.178027	+	0.984026i	$0.556972\pi$
$930$	31.0062	+	14.0961i	1.01673	+	0.462231i
$931$		0			0
$932$	1.86545	−	1.07702i	0.0611048	−	0.0352789i
$933$	−1.38029	−	14.1989i	−0.0451886	−	0.464851i
$934$	−26.2433	+	15.1516i	−0.858708	+	0.495775i
$935$	−20.4296	−	11.7950i	−0.668118	−	0.385738i
$936$	3.39208	+	3.88777i	0.110873	+	0.127076i
$937$		−	0.458120i		−	0.0149661i	−0.999972	−	0.00748306i	$-0.997618\pi$
$937$		−	0.458120i		−	0.0149661i	0.999972	−	0.00748306i	$-0.00238195\pi$
$938$		0			0
$939$	−58.2725	+	5.66473i	−1.90165	+	0.184861i
$940$	13.8728	−	24.0284i	0.452482	−	0.783721i
$941$	7.37780			0.240510			0.120255	−	0.992743i	$-0.461629\pi$
$941$	7.37780			0.240510			0.120255	+	0.992743i	$0.461629\pi$
$942$	−1.68036	−	17.2857i	−0.0547490	−	0.563198i
$943$			29.3794i			0.956725i
$944$	−2.22966			−0.0725693
$945$		0			0
$946$	19.9879			0.649862
$947$			11.9910i			0.389657i	0.980837	+	0.194828i	$0.0624150\pi$
$947$			11.9910i			0.389657i	−0.980837	+	0.194828i	$0.937585\pi$
$948$	2.18336	+	22.4600i	0.0709123	+	0.729468i
$949$	−9.18802			−0.298256
$950$	−0.295928	+	0.512563i	−0.00960118	+	0.0166297i
$951$	11.6036	−	1.12799i	0.376271	−	0.0365777i
$952$		0			0
$953$		−	58.6883i		−	1.90110i	−0.310572	−	0.950550i	$-0.600521\pi$
$953$		−	58.6883i		−	1.90110i	0.310572	−	0.950550i	$-0.399479\pi$
$954$		0			0
$955$	−25.1031	−	14.4933i	−0.812317	−	0.468992i
$956$	8.78317	−	5.07096i	0.284068	−	0.164007i
$957$	3.95332	+	40.6674i	0.127793	+	1.31459i
$958$	4.03816	−	2.33143i	0.130467	−	0.0753251i
$959$		0			0
$960$	−3.70436	−	1.68409i	−0.119558	−	0.0543538i
$961$	−39.0600			−1.26000
$962$	−7.90935	+	13.6994i	−0.255008	+	0.441686i
$963$	10.6598	−	9.30069i	0.343508	−	0.299711i
$964$	9.13490	−	5.27404i	0.294215	−	0.169865i
$965$	5.16140	−	8.93981i	0.166151	−	0.287783i
$966$		0			0
$967$	−3.37560	−	5.84671i	−0.108552	−	0.188018i	0.806632	−	0.591054i	$-0.201288\pi$
$967$	−3.37560	−	5.84671i	−0.108552	−	0.188018i	−0.915184	+	0.403037i	$0.867955\pi$
$968$	−18.3810	−	10.6123i	−0.590789	−	0.341092i
$969$	−3.47416	+	0.337726i	−0.111606	+	0.0108493i
$970$	−5.39218	−	9.33953i	−0.173133	−	0.299874i
$971$	3.20362	+	5.54883i	0.102809	+	0.178070i	0.912841	−	0.408315i	$-0.133884\pi$
$971$	3.20362	+	5.54883i	0.102809	+	0.178070i	−0.810032	+	0.586386i	$0.800550\pi$
$972$	−7.26102	−	13.7941i	−0.232897	−	0.442446i
$973$		0			0
$974$	16.8720	+	9.74105i	0.540613	+	0.312123i
$975$	0.640438	−	1.40872i	0.0205104	−	0.0451152i
$976$		−	8.99970i		−	0.288073i
$977$			13.5987i			0.435062i	0.976053	+	0.217531i	$0.0698004\pi$
$977$			13.5987i			0.435062i	−0.976053	+	0.217531i	$0.930200\pi$
$978$	12.0883	+	16.9145i	0.386542	+	0.540866i
$979$	5.70793	+	3.29547i	0.182426	+	0.105324i
$980$		0			0
$981$	4.11604	−	12.0252i	0.131415	−	0.383934i
$982$	−10.2443	−	17.7437i	−0.326910	−	0.566224i
$983$	11.3849	+	19.7192i	0.363122	+	0.628946i	0.988473	−	0.151398i	$-0.0483774\pi$
$983$	11.3849	+	19.7192i	0.363122	+	0.628946i	−0.625351	+	0.780344i	$0.715044\pi$
$984$	8.05090	+	11.2652i	0.256653	+	0.359121i
$985$	−22.1497	−	12.7882i	−0.705749	−	0.407464i
$986$	3.67528	+	6.36577i	0.117045	+	0.202728i
$987$		0			0
$988$	0.979729	−	1.69694i	0.0311693	−	0.0539869i
$989$	11.2066	−	6.47011i	0.356348	−	0.205738i
$990$	−39.2605	+	7.70592i	−1.24778	+	0.244910i
$991$	13.4953	−	23.3745i	0.428691	−	0.742515i	−0.568066	−	0.822983i	$-0.692308\pi$
$991$	13.4953	−	23.3745i	0.428691	−	0.742515i	0.996757	+	0.0804680i	$0.0256415\pi$
$992$	8.37019			0.265754
$993$	−5.37223	−	55.2636i	−0.170483	−	1.75374i
$994$		0			0
$995$	−56.0869	+	32.3818i	−1.77807	+	1.02657i
$996$	19.7819	+	8.99332i	0.626814	+	0.284964i
$997$	16.7263	−	9.65694i	0.529728	−	0.305838i	−0.211178	−	0.977448i	$-0.567730\pi$
$997$	16.7263	−	9.65694i	0.529728	−	0.305838i	0.740906	+	0.671609i	$0.234397\pi$
$998$	8.87845	+	5.12598i	0.281043	+	0.162260i
$999$	32.8033	−	34.7577i	1.03785	−	1.09968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.l.a.227.7		16
3.2	odd	2		2646.2.l.b.521.2		16
7.2	even	3		882.2.t.b.803.5		16
7.3	odd	6		126.2.m.a.83.2	yes	16
7.4	even	3		126.2.m.a.83.3	yes	16
7.5	odd	6		882.2.t.b.803.8		16
7.6	odd	2	inner	882.2.l.a.227.6		16
9.4	even	3		2646.2.t.a.2285.2		16
9.5	odd	6		882.2.t.b.815.8		16
21.2	odd	6		2646.2.t.a.1979.3		16
21.5	even	6		2646.2.t.a.1979.2		16
21.11	odd	6		378.2.m.a.251.6		16
21.17	even	6		378.2.m.a.251.7		16
21.20	even	2		2646.2.l.b.521.3		16
28.3	even	6		1008.2.cc.b.209.6		16
28.11	odd	6		1008.2.cc.b.209.3		16
63.4	even	3		378.2.m.a.125.7		16
63.5	even	6	inner	882.2.l.a.509.3		16
63.11	odd	6		1134.2.d.a.1133.7		16
63.13	odd	6		2646.2.t.a.2285.3		16
63.23	odd	6	inner	882.2.l.a.509.2		16
63.25	even	3		1134.2.d.a.1133.10		16
63.31	odd	6		378.2.m.a.125.6		16
63.32	odd	6		126.2.m.a.41.2	✓	16
63.38	even	6		1134.2.d.a.1133.2		16
63.40	odd	6		2646.2.l.b.1097.6		16
63.41	even	6		882.2.t.b.815.5		16
63.52	odd	6		1134.2.d.a.1133.15		16
63.58	even	3		2646.2.l.b.1097.7		16
63.59	even	6		126.2.m.a.41.3	yes	16
84.11	even	6		3024.2.cc.b.2897.2		16
84.59	odd	6		3024.2.cc.b.2897.7		16
252.31	even	6		3024.2.cc.b.881.2		16
252.59	odd	6		1008.2.cc.b.545.3		16
252.67	odd	6		3024.2.cc.b.881.7		16
252.95	even	6		1008.2.cc.b.545.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.2	✓	16	63.32	odd	6
126.2.m.a.41.3	yes	16	63.59	even	6
126.2.m.a.83.2	yes	16	7.3	odd	6
126.2.m.a.83.3	yes	16	7.4	even	3
378.2.m.a.125.6		16	63.31	odd	6
378.2.m.a.125.7		16	63.4	even	3
378.2.m.a.251.6		16	21.11	odd	6
378.2.m.a.251.7		16	21.17	even	6
882.2.l.a.227.6		16	7.6	odd	2	inner
882.2.l.a.227.7		16	1.1	even	1	trivial
882.2.l.a.509.2		16	63.23	odd	6	inner
882.2.l.a.509.3		16	63.5	even	6	inner
882.2.t.b.803.5		16	7.2	even	3
882.2.t.b.803.8		16	7.5	odd	6
882.2.t.b.815.5		16	63.41	even	6
882.2.t.b.815.8		16	9.5	odd	6
1008.2.cc.b.209.3		16	28.11	odd	6
1008.2.cc.b.209.6		16	28.3	even	6
1008.2.cc.b.545.3		16	252.59	odd	6
1008.2.cc.b.545.6		16	252.95	even	6
1134.2.d.a.1133.2		16	63.38	even	6
1134.2.d.a.1133.7		16	63.11	odd	6
1134.2.d.a.1133.10		16	63.25	even	3
1134.2.d.a.1133.15		16	63.52	odd	6
2646.2.l.b.521.2		16	3.2	odd	2
2646.2.l.b.521.3		16	21.20	even	2
2646.2.l.b.1097.6		16	63.40	odd	6
2646.2.l.b.1097.7		16	63.58	even	3
2646.2.t.a.1979.2		16	21.5	even	6
2646.2.t.a.1979.3		16	21.2	odd	6
2646.2.t.a.2285.2		16	9.4	even	3
2646.2.t.a.2285.3		16	63.13	odd	6
3024.2.cc.b.881.2		16	252.31	even	6
3024.2.cc.b.881.7		16	252.67	odd	6
3024.2.cc.b.2897.2		16	84.11	even	6
3024.2.cc.b.2897.7		16	84.59	odd	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.167584 + 1.72392i) q^{3} -1.00000 q^{4} +(1.17468 - 2.03460i) q^{5} +(-1.72392 + 0.167584i) q^{6} -1.00000i q^{8} +(-2.94383 + 0.577806i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.167584 + 1.72392i) q^{3} -1.00000 q^{4} +(1.17468 - 2.03460i) q^{5} +(-1.72392 + 0.167584i) q^{6} -1.00000i q^{8} +(-2.94383 + 0.577806i) q^{9} +(2.03460 + 1.17468i) q^{10} +(4.91614 - 2.83834i) q^{11} +(-0.167584 - 1.72392i) q^{12} +(1.48943 - 0.859925i) q^{13} +(3.70436 + 1.68409i) q^{15} +1.00000 q^{16} +(0.884414 - 1.53185i) q^{17} +(-0.577806 - 2.94383i) q^{18} +(-0.986680 + 0.569660i) q^{19} +(-1.17468 + 2.03460i) q^{20} +(2.83834 + 4.91614i) q^{22} +(3.18272 + 1.83755i) q^{23} +(1.72392 - 0.167584i) q^{24} +(-0.259741 - 0.449885i) q^{25} +(0.859925 + 1.48943i) q^{26} +(-1.48943 - 4.97811i) q^{27} +(3.59886 + 2.07781i) q^{29} +(-1.68409 + 3.70436i) q^{30} -8.37019i q^{31} +1.00000i q^{32} +(5.71694 + 7.99939i) q^{33} +(1.53185 + 0.884414i) q^{34} +(2.94383 - 0.577806i) q^{36} +(4.59886 + 7.96547i) q^{37} +(-0.569660 - 0.986680i) q^{38} +(1.73205 + 2.42356i) q^{39} +(-2.03460 - 1.17468i) q^{40} +(3.99709 + 6.92317i) q^{41} +(1.76053 - 3.04933i) q^{43} +(-4.91614 + 2.83834i) q^{44} +(-2.28245 + 6.66826i) q^{45} +(-1.83755 + 3.18272i) q^{46} -11.8099 q^{47} +(0.167584 + 1.72392i) q^{48} +(0.449885 - 0.259741i) q^{50} +(2.78901 + 1.26795i) q^{51} +(-1.48943 + 0.859925i) q^{52} +(4.97811 - 1.48943i) q^{54} -13.3365i q^{55} +(-1.14740 - 1.60550i) q^{57} +(-2.07781 + 3.59886i) q^{58} -2.22966 q^{59} +(-3.70436 - 1.68409i) q^{60} -8.99970i q^{61} +8.37019 q^{62} -1.00000 q^{64} -4.04054i q^{65} +(-7.99939 + 5.71694i) q^{66} +10.8712 q^{67} +(-0.884414 + 1.53185i) q^{68} +(-2.63442 + 5.79472i) q^{69} +4.52106i q^{71} +(0.577806 + 2.94383i) q^{72} +(-4.62660 - 2.67117i) q^{73} +(-7.96547 + 4.59886i) q^{74} +(0.732039 - 0.523168i) q^{75} +(0.986680 - 0.569660i) q^{76} +(-2.42356 + 1.73205i) q^{78} -13.0284 q^{79} +(1.17468 - 2.03460i) q^{80} +(8.33228 - 3.40192i) q^{81} +(-6.92317 + 3.99709i) q^{82} +(-6.27298 + 10.8651i) q^{83} +(-2.07781 - 3.59886i) q^{85} +(3.04933 + 1.76053i) q^{86} +(-2.97887 + 6.55238i) q^{87} +(-2.83834 - 4.91614i) q^{88} +(0.580529 + 1.00551i) q^{89} +(-6.66826 - 2.28245i) q^{90} +(-3.18272 - 1.83755i) q^{92} +(14.4296 - 1.40271i) q^{93} -11.8099i q^{94} +2.67667i q^{95} +(-1.72392 + 0.167584i) q^{96} +(-3.97536 - 2.29517i) q^{97} +(-12.8323 + 11.1962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 12 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 - 12 * q^9	\( 16 q - 16 q^{4} - 12 q^{9} + 12 q^{11} + 16 q^{16} + 12 q^{18} + 48 q^{23} - 8 q^{25} - 12 q^{29} + 12 q^{30} + 12 q^{36} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} + 60 q^{50} + 24 q^{51} + 48 q^{57} - 12 q^{58} - 16 q^{64} + 56 q^{67} - 12 q^{72} - 36 q^{74} - 24 q^{78} + 8 q^{79} - 12 q^{85} + 24 q^{86} - 48 q^{92} + 84 q^{93} - 72 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 - 12 * q^9 + 12 * q^11 + 16 * q^16 + 12 * q^18 + 48 * q^23 - 8 * q^25 - 12 * q^29 + 12 * q^30 + 12 * q^36 + 4 * q^37 + 4 * q^43 - 12 * q^44 - 12 * q^46 + 60 * q^50 + 24 * q^51 + 48 * q^57 - 12 * q^58 - 16 * q^64 + 56 * q^67 - 12 * q^72 - 36 * q^74 - 24 * q^78 + 8 * q^79 - 12 * q^85 + 24 * q^86 - 48 * q^92 + 84 * q^93 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more