LMFDB - Embedded newform 882.2.t.a.815.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [882,2,Mod(803,882)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(882, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("882.803"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,8,0,0,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			815.3
Root			$1.71298 + 0.256290i$ of defining polynomial
Character	$\chi$	$=$	882.815
Dual form			882.2.t.a.803.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.128499 + 1.72728i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.61932 q^{5} +(0.752355 - 1.56012i) q^{6} -1.00000i q^{8} +(-2.96698 + 0.443907i) q^{9} +(-3.13442 - 1.80966i) q^{10} +2.00379i q^{11} +(-1.43162 + 0.974922i) q^{12} +(2.95206 + 1.70437i) q^{13} +(0.465079 + 6.25156i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.08709 + 5.34700i) q^{17} +(2.79143 + 1.09905i) q^{18} +(-0.877353 + 0.506540i) q^{19} +(1.80966 + 3.13442i) q^{20} +(1.00190 - 1.73534i) q^{22} -3.02799i q^{23} +(1.72728 - 0.128499i) q^{24} +8.09945 q^{25} +(-1.70437 - 2.95206i) q^{26} +(-1.14800 - 5.06775i) q^{27} +(5.04560 - 2.91308i) q^{29} +(2.72301 - 5.64655i) q^{30} +(-0.787812 + 0.454844i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-3.46111 + 0.257486i) q^{33} +(5.34700 - 3.08709i) q^{34} +(-1.86792 - 2.34752i) q^{36} +(3.66825 + 6.35359i) q^{37} +1.01308 q^{38} +(-2.56459 + 5.31804i) q^{39} -3.61932i q^{40} +(-2.85045 + 4.93712i) q^{41} +(-2.39949 - 4.15605i) q^{43} +(-1.73534 + 1.00190i) q^{44} +(-10.7384 + 1.60664i) q^{45} +(-1.51400 + 2.62232i) q^{46} +(1.11511 - 1.93143i) q^{47} +(-1.56012 - 0.752355i) q^{48} +(-7.01433 - 4.04972i) q^{50} +(-9.63244 - 4.64518i) q^{51} +3.40874i q^{52} +(-7.58088 - 4.37683i) q^{53} +(-1.53967 + 4.96280i) q^{54} +7.25237i q^{55} +(-0.987674 - 1.45034i) q^{57} -5.82616 q^{58} +(-4.49313 - 7.78233i) q^{59} +(-5.18147 + 3.52855i) q^{60} +(12.7410 + 7.35603i) q^{61} +0.909687 q^{62} -1.00000 q^{64} +(10.6844 + 6.16866i) q^{65} +(3.12615 + 1.50757i) q^{66} +(4.15821 + 7.20222i) q^{67} -6.17418 q^{68} +(5.23019 - 0.389094i) q^{69} +0.466287i q^{71} +(0.443907 + 2.96698i) q^{72} +(3.65022 + 2.10746i) q^{73} -7.33650i q^{74} +(1.04077 + 13.9900i) q^{75} +(-0.877353 - 0.506540i) q^{76} +(4.88001 - 3.32326i) q^{78} +(-1.91267 + 3.31284i) q^{79} +(-1.80966 + 3.13442i) q^{80} +(8.60589 - 2.63412i) q^{81} +(4.93712 - 2.85045i) q^{82} +(-4.00481 - 6.93654i) q^{83} +(-11.1732 + 19.3525i) q^{85} +4.79899i q^{86} +(5.68005 + 8.34083i) q^{87} +2.00379 q^{88} +(-2.39324 - 4.14521i) q^{89} +(10.1031 + 3.97782i) q^{90} +(2.62232 - 1.51400i) q^{92} +(-0.886874 - 1.30232i) q^{93} +(-1.93143 + 1.11511i) q^{94} +(-3.17542 + 1.83333i) q^{95} +(0.974922 + 1.43162i) q^{96} +(-10.1835 + 5.87944i) q^{97} +(-0.889499 - 5.94521i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 6 q^{9} + 6 q^{13} - 18 q^{15} - 8 q^{16} - 18 q^{17} + 12 q^{18} + 6 q^{24} + 16 q^{25} + 12 q^{26} + 36 q^{27} + 6 q^{29} - 18 q^{30} - 6 q^{31} - 18 q^{33} - 2 q^{37} - 30 q^{39} - 6 q^{41}+ \cdots + 18 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 - 6 * q^9 + 6 * q^13 - 18 * q^15 - 8 * q^16 - 18 * q^17 + 12 * q^18 + 6 * q^24 + 16 * q^25 + 12 * q^26 + 36 * q^27 + 6 * q^29 - 18 * q^30 - 6 * q^31 - 18 * q^33 - 2 * q^37 - 30 * q^39 - 6 * q^41 - 2 * q^43 + 12 * q^44 - 12 * q^45 + 6 * q^46 + 18 * q^47 - 12 * q^50 + 36 * q^53 - 18 * q^54 + 6 * q^57 - 12 * q^58 - 30 * q^59 - 6 * q^60 + 60 * q^61 + 36 * q^62 - 16 * q^64 + 42 * q^65 - 48 * q^66 + 14 * q^67 - 36 * q^68 - 42 * q^69 - 30 * q^75 - 16 * q^79 + 54 * q^81 - 12 * q^85 + 48 * q^87 - 24 * q^89 + 18 * q^90 + 6 * q^92 + 30 * q^93 - 66 * q^95 + 6 * q^96 + 6 * q^97 + 18 * q^99

Character values

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

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.128499	+	1.72728i	0.0741890	+	0.997244i
$3$	0.128499	+	1.72728i	0.0741890	+	0.997244i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	3.61932			1.61861			0.809304	−	0.587391i	$-0.199845\pi$
$5$	3.61932			1.61861			0.809304	+	0.587391i	$0.199845\pi$
$6$	0.752355	−	1.56012i	0.307148	−	0.636915i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−2.96698	+	0.443907i	−0.988992	+	0.147969i
$10$	−3.13442	−	1.80966i	−0.991190	−	0.572264i
$11$			2.00379i			0.604167i	0.953281	+	0.302083i	$0.0976821\pi$
$11$			2.00379i			0.604167i	−0.953281	+	0.302083i	$0.902318\pi$
$12$	−1.43162	+	0.974922i	−0.413272	+	0.281436i
$13$	2.95206	+	1.70437i	0.818754	+	0.472708i	0.849987	−	0.526804i	$-0.176610\pi$
$13$	2.95206	+	1.70437i	0.818754	+	0.472708i	−0.0312328	+	0.999512i	$0.509943\pi$
$14$		0			0
$15$	0.465079	+	6.25156i	0.120083	+	1.61415i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.08709	+	5.34700i	−0.748730	+	1.29684i	0.199702	+	0.979857i	$0.436002\pi$
$17$	−3.08709	+	5.34700i	−0.748730	+	1.29684i	−0.948432	+	0.316981i	$0.897331\pi$
$18$	2.79143	+	1.09905i	0.657946	+	0.259049i
$19$	−0.877353	+	0.506540i	−0.201279	+	0.116208i	−0.597252	−	0.802054i	$-0.703741\pi$
$19$	−0.877353	+	0.506540i	−0.201279	+	0.116208i	0.395973	+	0.918262i	$0.370407\pi$
$20$	1.80966	+	3.13442i	0.404652	+	0.700877i
$21$		0			0
$22$	1.00190	−	1.73534i	0.213605	−	0.369975i
$23$		−	3.02799i		−	0.631380i	−0.948862	−	0.315690i	$-0.897764\pi$
$23$		−	3.02799i		−	0.631380i	0.948862	−	0.315690i	$-0.102236\pi$
$24$	1.72728	−	0.128499i	0.352579	−	0.0262298i
$25$	8.09945			1.61989
$26$	−1.70437	−	2.95206i	−0.334255	−	0.578946i
$27$	−1.14800	−	5.06775i	−0.220934	−	0.975289i
$28$		0			0
$29$	5.04560	−	2.91308i	0.936945	−	0.540945i	0.0479434	−	0.998850i	$-0.484733\pi$
$29$	5.04560	−	2.91308i	0.936945	−	0.540945i	0.889001	+	0.457905i	$0.151400\pi$
$30$	2.72301	−	5.64655i	0.497152	−	1.03091i
$31$	−0.787812	+	0.454844i	−0.141495	+	0.0816923i	−0.569076	−	0.822285i	$-0.692699\pi$
$31$	−0.787812	+	0.454844i	−0.141495	+	0.0816923i	0.427581	+	0.903977i	$0.359366\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−3.46111	+	0.257486i	−0.602502	+	0.0448225i
$34$	5.34700	−	3.08709i	0.917003	−	0.529432i
$35$		0			0
$36$	−1.86792	−	2.34752i	−0.311320	−	0.391254i
$37$	3.66825	+	6.35359i	0.603056	+	1.04452i	0.992355	+	0.123413i	$0.0393839\pi$
$37$	3.66825	+	6.35359i	0.603056	+	1.04452i	−0.389299	+	0.921111i	$0.627283\pi$
$38$	1.01308			0.164343
$39$	−2.56459	+	5.31804i	−0.410663	+	0.851567i
$40$		−	3.61932i		−	0.572264i
$41$	−2.85045	+	4.93712i	−0.445165	+	0.771048i	−0.998064	−	0.0622002i	$-0.980188\pi$
$41$	−2.85045	+	4.93712i	−0.445165	+	0.771048i	0.552899	+	0.833248i	$0.313522\pi$
$42$		0			0
$43$	−2.39949	−	4.15605i	−0.365919	−	0.633791i	0.623004	−	0.782219i	$-0.285912\pi$
$43$	−2.39949	−	4.15605i	−0.365919	−	0.633791i	−0.988923	+	0.148428i	$0.952579\pi$
$44$	−1.73534	+	1.00190i	−0.261612	+	0.151042i
$45$	−10.7384	+	1.60664i	−1.60079	+	0.239504i
$46$	−1.51400	+	2.62232i	−0.223227	+	0.386640i
$47$	1.11511	−	1.93143i	0.162655	−	0.281727i	−0.773165	−	0.634205i	$-0.781327\pi$
$47$	1.11511	−	1.93143i	0.162655	−	0.281727i	0.935820	+	0.352478i	$0.114661\pi$
$48$	−1.56012	−	0.752355i	−0.225183	−	0.108593i
$49$		0			0
$50$	−7.01433	−	4.04972i	−0.991975	−	0.572717i
$51$	−9.63244	−	4.64518i	−1.34881	−	0.650455i
$52$			3.40874i			0.472708i
$53$	−7.58088	−	4.37683i	−1.04131	−	0.601203i	−0.121109	−	0.992639i	$-0.538645\pi$
$53$	−7.58088	−	4.37683i	−1.04131	−	0.601203i	−0.920205	+	0.391436i	$0.871978\pi$
$54$	−1.53967	+	4.96280i	−0.209523	+	0.675352i
$55$			7.25237i			0.977909i
$56$		0			0
$57$	−0.987674	−	1.45034i	−0.130821	−	0.192103i
$58$	−5.82616			−0.765012
$59$	−4.49313	−	7.78233i	−0.584956	−	1.01317i	−0.994881	−	0.101054i	$-0.967778\pi$
$59$	−4.49313	−	7.78233i	−0.584956	−	1.01317i	0.409925	−	0.912119i	$-0.365555\pi$
$60$	−5.18147	+	3.52855i	−0.668925	+	0.455534i
$61$	12.7410	+	7.35603i	1.63132	+	0.941843i	0.983686	+	0.179892i	$0.0575747\pi$
$61$	12.7410	+	7.35603i	1.63132	+	0.941843i	0.647634	+	0.761952i	$0.275759\pi$
$62$	0.909687			0.115530
$63$		0			0
$64$	−1.00000			−0.125000
$65$	10.6844	+	6.16866i	1.32524	+	0.765128i
$66$	3.12615	+	1.50757i	0.384803	+	0.185569i
$67$	4.15821	+	7.20222i	0.508006	+	0.879892i	0.999957	+	0.00926908i	$0.00295048\pi$
$67$	4.15821	+	7.20222i	0.508006	+	0.879892i	−0.491951	+	0.870623i	$0.663716\pi$
$68$	−6.17418			−0.748730
$69$	5.23019	−	0.389094i	0.629640	−	0.0468415i
$70$		0			0
$71$			0.466287i			0.0553381i	0.999617	+	0.0276691i	$0.00880846\pi$
$71$			0.466287i			0.0553381i	−0.999617	+	0.0276691i	$0.991192\pi$
$72$	0.443907	+	2.96698i	0.0523149	+	0.349661i
$73$	3.65022	+	2.10746i	0.427226	+	0.246659i	0.698164	−	0.715938i	$-0.254000\pi$
$73$	3.65022	+	2.10746i	0.427226	+	0.246659i	−0.270938	+	0.962597i	$0.587334\pi$
$74$		−	7.33650i		−	0.852850i
$75$	1.04077	+	13.9900i	0.120178	+	1.61543i
$76$	−0.877353	−	0.506540i	−0.100639	−	0.0581041i
$77$		0			0
$78$	4.88001	−	3.32326i	0.552553	−	0.376285i
$79$	−1.91267	+	3.31284i	−0.215192	+	0.372723i	−0.953332	−	0.301924i	$-0.902371\pi$
$79$	−1.91267	+	3.31284i	−0.215192	+	0.372723i	0.738140	+	0.674648i	$0.235704\pi$
$80$	−1.80966	+	3.13442i	−0.202326	+	0.350439i
$81$	8.60589	−	2.63412i	0.956210	−	0.292680i
$82$	4.93712	−	2.85045i	0.545213	−	0.314779i
$83$	−4.00481	−	6.93654i	−0.439585	−	0.761384i	0.558072	−	0.829792i	$-0.311541\pi$
$83$	−4.00481	−	6.93654i	−0.439585	−	0.761384i	−0.997657	+	0.0684084i	$0.978208\pi$
$84$		0			0
$85$	−11.1732	+	19.3525i	−1.21190	+	2.09907i
$86$			4.79899i			0.517488i
$87$	5.68005	+	8.34083i	0.608965	+	0.894230i
$88$	2.00379			0.213605
$89$	−2.39324	−	4.14521i	−0.253683	−	0.439391i	0.710854	−	0.703339i	$-0.248309\pi$
$89$	−2.39324	−	4.14521i	−0.253683	−	0.439391i	−0.964537	+	0.263948i	$0.914975\pi$
$90$	10.1031	+	3.97782i	1.06496	+	0.419299i
$91$		0			0
$92$	2.62232	−	1.51400i	0.273396	−	0.157845i
$93$	−0.886874	−	1.30232i	−0.0919646	−	0.135045i
$94$	−1.93143	+	1.11511i	−0.199211	+	0.115015i
$95$	−3.17542	+	1.83333i	−0.325791	+	0.188096i
$96$	0.974922	+	1.43162i	0.0995026	+	0.146114i
$97$	−10.1835	+	5.87944i	−1.03398	+	0.596967i	−0.918121	−	0.396299i	$-0.870294\pi$
$97$	−10.1835	+	5.87944i	−1.03398	+	0.596967i	−0.115856	+	0.993266i	$0.536961\pi$
$98$		0			0
$99$	−0.889499	−	5.94521i	−0.0893980	−	0.597516i
$100$	4.04972	+	7.01433i	0.404972	+	0.701433i
$101$	12.8922			1.28282			0.641411	−	0.767197i	$-0.278349\pi$
$101$	12.8922			1.28282			0.641411	+	0.767197i	$0.278349\pi$
$102$	6.01935	+	8.83906i	0.596004	+	0.875198i
$103$			10.7588i			1.06010i	0.847968	+	0.530048i	$0.177826\pi$
$103$			10.7588i			1.06010i	−0.847968	+	0.530048i	$0.822174\pi$
$104$	1.70437	−	2.95206i	0.167127	−	0.289473i
$105$		0			0
$106$	4.37683	+	7.58088i	0.425115	+	0.736321i
$107$	2.28602	−	1.31983i	0.220998	−	0.127593i	−0.385414	−	0.922744i	$-0.625942\pi$
$107$	2.28602	−	1.31983i	0.220998	−	0.127593i	0.606412	+	0.795151i	$0.292608\pi$
$108$	3.81480	−	3.52808i	0.367079	−	0.339489i
$109$	4.51768	−	7.82484i	0.432715	−	0.749484i	−0.564391	−	0.825507i	$-0.690889\pi$
$109$	4.51768	−	7.82484i	0.432715	−	0.749484i	0.997106	+	0.0760233i	$0.0242224\pi$
$110$	3.62618	−	6.28073i	0.345743	−	0.598844i
$111$	−10.5031	+	7.15251i	−0.996905	+	0.678886i
$112$		0			0
$113$	−1.46411	−	0.845306i	−0.137732	−	0.0795197i	0.429551	−	0.903043i	$-0.358672\pi$
$113$	−1.46411	−	0.845306i	−0.137732	−	0.0795197i	−0.567283	+	0.823523i	$0.692005\pi$
$114$	0.130180	+	1.74987i	0.0121925	+	0.163890i
$115$		−	10.9593i		−	1.02196i
$116$	5.04560	+	2.91308i	0.468472	+	0.270473i
$117$	−9.51527	−	3.74639i	−0.879687	−	0.346354i
$118$			8.98627i			0.827253i
$119$		0			0
$120$	6.25156	−	0.465079i	0.570687	−	0.0424557i
$121$	6.98481			0.634982
$122$	−7.35603	−	12.7410i	−0.665984	−	1.15352i
$123$	−8.89405	−	4.28910i	−0.801950	−	0.386735i
$124$	−0.787812	−	0.454844i	−0.0707476	−	0.0408462i
$125$	11.2179			1.00336
$126$		0			0
$127$	17.9292			1.59096			0.795478	−	0.605983i	$-0.207220\pi$
$127$	17.9292			1.59096			0.795478	+	0.605983i	$0.207220\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	6.87031	−	4.67864i	0.604897	−	0.411931i
$130$	−6.16866	−	10.6844i	−0.541027	−	0.937087i
$131$	−17.3313			−1.51425			−0.757123	−	0.653272i	$-0.773396\pi$
$131$	−17.3313			−1.51425			−0.757123	+	0.653272i	$0.773396\pi$
$132$	−1.95354	−	2.86867i	−0.170034	−	0.249685i
$133$		0			0
$134$		−	8.31641i		−	0.718429i
$135$	−4.15499	−	18.3418i	−0.357605	−	1.57861i
$136$	5.34700	+	3.08709i	0.458501	+	0.264716i
$137$		0	0.000645123i		0	5.51166e-5i	−1.00000		2.75583e-5i	$-0.999991\pi$
$137$		0	0.000645123i		0	5.51166e-5i	1.00000		2.75583e-5i	$-8.77208e-6\pi$
$138$	−4.72402	−	2.27813i	−0.402135	−	0.193927i
$139$	−8.73273	−	5.04185i	−0.740701	−	0.427644i	0.0816233	−	0.996663i	$-0.473990\pi$
$139$	−8.73273	−	5.04185i	−0.740701	−	0.427644i	−0.822324	+	0.569019i	$0.807323\pi$
$140$		0			0
$141$	3.47940	+	1.67792i	0.293018	+	0.141306i
$142$	0.233144	−	0.403817i	0.0195650	−	0.0338875i
$143$	−3.41521	+	5.91532i	−0.285594	+	0.494664i
$144$	1.09905	−	2.79143i	0.0915878	−	0.232619i
$145$	18.2616	−	10.5434i	1.51655	−	0.875578i
$146$	−2.10746	−	3.65022i	−0.174414	−	0.302095i
$147$		0			0
$148$	−3.66825	+	6.35359i	−0.301528	+	0.522262i
$149$		−	11.2475i		−	0.921433i	−0.887547	−	0.460716i	$-0.847593\pi$
$149$		−	11.2475i		−	0.921433i	0.887547	−	0.460716i	$-0.152407\pi$
$150$	6.09366	−	12.6361i	0.497545	−	1.03173i
$151$	−4.72379			−0.384417			−0.192208	−	0.981354i	$-0.561565\pi$
$151$	−4.72379			−0.384417			−0.192208	+	0.981354i	$0.561565\pi$
$152$	0.506540	+	0.877353i	0.0410858	+	0.0711627i
$153$	6.78575	−	17.2348i	0.548596	−	1.39335i
$154$		0			0
$155$	−2.85134	+	1.64622i	−0.229025	+	0.132228i
$156$	−5.88785	+	0.438020i	−0.471405	+	0.0350697i
$157$	−2.65845	+	1.53486i	−0.212168	+	0.122495i	−0.602318	−	0.798256i	$-0.705756\pi$
$157$	−2.65845	+	1.53486i	−0.212168	+	0.122495i	0.390151	+	0.920751i	$0.372423\pi$
$158$	3.31284	−	1.91267i	0.263555	−	0.152164i
$159$	6.58586	−	13.6567i	0.522292	−	1.08305i
$160$	3.13442	−	1.80966i	0.247798	−	0.143066i
$161$		0			0
$162$	−8.76998	−	2.02173i	−0.689035	−	0.158842i
$163$	−1.43687	−	2.48873i	−0.112544	−	0.194932i	0.804251	−	0.594289i	$-0.202567\pi$
$163$	−1.43687	−	2.48873i	−0.112544	−	0.194932i	−0.916795	+	0.399357i	$0.869233\pi$
$164$	−5.70089			−0.445165
$165$	−12.5268	+	0.931922i	−0.975214	+	0.0725500i
$166$			8.00963i			0.621668i
$167$	0.730517	−	1.26529i	0.0565291	−	0.0979113i	−0.836376	−	0.548156i	$-0.815330\pi$
$167$	0.730517	−	1.26529i	0.0565291	−	0.0979113i	0.892905	+	0.450245i	$0.148663\pi$
$168$		0			0
$169$	−0.690233	−	1.19552i	−0.0530948	−	0.0919630i
$170$	19.3525	−	11.1732i	1.48427	−	0.856942i
$171$	2.37823	−	1.89236i	0.181868	−	0.144712i
$172$	2.39949	−	4.15605i	0.182960	−	0.316896i
$173$	1.53541	−	2.65940i	0.116735	−	0.202191i	−0.801737	−	0.597677i	$-0.796091\pi$
$173$	1.53541	−	2.65940i	0.116735	−	0.202191i	0.918472	+	0.395486i	$0.129424\pi$
$174$	−0.748656	−	10.0634i	−0.0567554	−	0.762904i
$175$		0			0
$176$	−1.73534	−	1.00190i	−0.130806	−	0.0755209i
$177$	12.8649	−	8.76091i	0.966984	−	0.658510i
$178$			4.78647i			0.358761i
$179$	−16.7310	−	9.65966i	−1.25054	−	0.721997i	−0.279320	−	0.960198i	$-0.590109\pi$
$179$	−16.7310	−	9.65966i	−1.25054	−	0.721997i	−0.971216	+	0.238201i	$0.923442\pi$
$180$	−6.76060	−	8.49643i	−0.503906	−	0.633286i
$181$		−	7.89318i		−	0.586695i	−0.956006	−	0.293348i	$-0.905231\pi$
$181$		−	7.89318i		−	0.586695i	0.956006	−	0.293348i	$-0.0947693\pi$
$182$		0			0
$183$	−11.0687	+	22.9525i	−0.818222	+	1.69670i
$184$	−3.02799			−0.223227
$185$	13.2765	+	22.9957i	0.976111	+	1.69067i
$186$	0.116894	+	1.57128i	0.00857108	+	0.115212i
$187$	−10.7143	−	6.18590i	−0.783506	−	0.452358i
$188$	2.23022			0.162655
$189$		0			0
$190$	3.66666			0.266007
$191$	11.5218	+	6.65211i	0.833688	+	0.481330i	0.855114	−	0.518441i	$-0.173487\pi$
$191$	11.5218	+	6.65211i	0.833688	+	0.481330i	−0.0214259	+	0.999770i	$0.506821\pi$
$192$	−0.128499	−	1.72728i	−0.00927362	−	0.124656i
$193$	−3.26786	−	5.66011i	−0.235226	−	0.407423i	0.724112	−	0.689682i	$-0.242250\pi$
$193$	−3.26786	−	5.66011i	−0.235226	−	0.407423i	−0.959338	+	0.282259i	$0.908916\pi$
$194$	11.7589			0.844239
$195$	−9.28205	+	19.2476i	−0.664701	+	1.37835i
$196$		0			0
$197$		−	4.44250i		−	0.316515i	−0.987398	−	0.158258i	$-0.949412\pi$
$197$		−	4.44250i		−	0.316515i	0.987398	−	0.158258i	$-0.0505876\pi$
$198$	−2.20228	+	5.59345i	−0.156509	+	0.397509i
$199$	−9.96868	−	5.75542i	−0.706661	−	0.407991i	0.103163	−	0.994665i	$-0.467104\pi$
$199$	−9.96868	−	5.75542i	−0.706661	−	0.407991i	−0.809823	+	0.586674i	$0.800437\pi$
$200$		−	8.09945i		−	0.572717i
$201$	−11.9059	+	8.10786i	−0.839779	+	0.571884i
$202$	−11.1650	−	6.44610i	−0.785565	−	0.453546i
$203$		0			0
$204$	−0.793376	−	10.6645i	−0.0555475	−	0.746666i
$205$	−10.3167	+	17.8690i	−0.720547	+	1.24802i
$206$	5.37940	−	9.31740i	0.374801	−	0.649174i
$207$	1.34415	+	8.98399i	0.0934247	+	0.624430i
$208$	−2.95206	+	1.70437i	−0.204688	+	0.118177i
$209$	−1.01500	−	1.75804i	−0.0702092	−	0.121606i
$210$		0			0
$211$	11.3005	−	19.5731i	0.777961	−	1.34747i	−0.155155	−	0.987890i	$-0.549588\pi$
$211$	11.3005	−	19.5731i	0.777961	−	1.34747i	0.933115	−	0.359577i	$-0.117079\pi$
$212$		−	8.75365i		−	0.601203i
$213$	−0.805408	+	0.0599175i	−0.0551856	+	0.00410548i
$214$	−2.63967			−0.180444
$215$	−8.68453	−	15.0420i	−0.592280	−	1.02586i
$216$	−5.06775	+	1.14800i	−0.344817	+	0.0781118i
$217$		0			0
$218$	−7.82484	+	4.51768i	−0.529965	+	0.305976i
$219$	−3.17111	+	6.57576i	−0.214284	+	0.444348i
$220$	−6.28073	+	3.62618i	−0.423447	+	0.244477i
$221$	−18.2265	+	10.5231i	−1.22605	+	0.707860i
$222$	12.6722	−	0.942733i	0.850500	−	0.0632721i
$223$	16.2994	−	9.41045i	1.09149	−	0.630170i	0.157515	−	0.987517i	$-0.449652\pi$
$223$	16.2994	−	9.41045i	1.09149	−	0.630170i	0.933972	+	0.357346i	$0.116318\pi$
$224$		0			0
$225$	−24.0309	+	3.59540i	−1.60206	+	0.239693i
$226$	0.845306	+	1.46411i	0.0562289	+	0.0973914i
$227$	14.6133			0.969919			0.484960	−	0.874537i	$-0.338834\pi$
$227$	14.6133			0.969919			0.484960	+	0.874537i	$0.338834\pi$
$228$	0.762196	−	1.58052i	0.0504777	−	0.104673i
$229$			2.37919i			0.157221i	0.996905	+	0.0786106i	$0.0250484\pi$
$229$			2.37919i			0.157221i	−0.996905	+	0.0786106i	$0.974952\pi$
$230$	−5.47963	+	9.49100i	−0.361316	+	0.625818i
$231$		0			0
$232$	−2.91308	−	5.04560i	−0.191253	−	0.331260i
$233$	−9.03470	+	5.21619i	−0.591883	+	0.341724i	−0.765842	−	0.643029i	$-0.777677\pi$
$233$	−9.03470	+	5.21619i	−0.591883	+	0.341724i	0.173959	+	0.984753i	$0.444344\pi$
$234$	6.36727	+	8.00210i	0.416241	+	0.523114i
$235$	4.03593	−	6.99044i	0.263275	−	0.456006i
$236$	4.49313	−	7.78233i	0.292478	−	0.506587i
$237$	−5.96796	−	2.87801i	−0.387661	−	0.186947i
$238$		0			0
$239$	20.5971	+	11.8917i	1.33232	+	0.769213i	0.985654	−	0.168777i	$-0.0539818\pi$
$239$	20.5971	+	11.8917i	1.33232	+	0.769213i	0.346662	+	0.937990i	$0.387315\pi$
$240$	−5.64655	−	2.72301i	−0.364483	−	0.175770i
$241$		−	28.6487i		−	1.84542i	−0.385489	−	0.922712i	$-0.625967\pi$
$241$		−	28.6487i		−	1.84542i	0.385489	−	0.922712i	$-0.374033\pi$
$242$	−6.04902	−	3.49240i	−0.388846	−	0.224500i
$243$	5.65571	+	14.5263i	0.362814	+	0.931862i
$244$			14.7121i			0.941843i
$245$		0			0
$246$	5.55793	+	8.16149i	0.354360	+	0.520358i
$247$	−3.45333			−0.219730
$248$	0.454844	+	0.787812i	0.0288826	+	0.0500261i
$249$	11.4667	−	7.80876i	0.726673	−	0.494860i
$250$	−9.71496	−	5.60894i	−0.614428	−	0.354740i
$251$	−11.0301			−0.696216			−0.348108	−	0.937454i	$-0.613176\pi$
$251$	−11.0301			−0.696216			−0.348108	+	0.937454i	$0.613176\pi$
$252$		0			0
$253$	6.06748			0.381459
$254$	−15.5271	−	8.96458i	−0.974257	−	0.562488i
$255$	−34.8628	−	16.8124i	−2.18320	−	1.05283i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	15.0978			0.941775			0.470888	−	0.882193i	$-0.343934\pi$
$257$	15.0978			0.941775			0.470888	+	0.882193i	$0.343934\pi$
$258$	−8.28919	+	0.616665i	−0.516062	+	0.0383919i
$259$		0			0
$260$			12.3373i			0.765128i
$261$	−13.6770	+	10.8828i	−0.846588	+	0.673629i
$262$	15.0094	+	8.66567i	0.927283	+	0.535367i
$263$		−	19.6385i		−	1.21096i	−0.795859	−	0.605482i	$-0.792980\pi$
$263$		−	19.6385i		−	1.21096i	0.795859	−	0.605482i	$-0.207020\pi$
$264$	0.257486	+	3.46111i	0.0158472	+	0.213017i
$265$	−27.4376	−	15.8411i	−1.68548	−	0.973112i
$266$		0			0
$267$	6.85240	−	4.66644i	0.419360	−	0.285581i
$268$	−4.15821	+	7.20222i	−0.254003	+	0.439946i
$269$	0.245503	−	0.425223i	0.0149686	−	0.0259263i	−0.858444	−	0.512907i	$-0.828569\pi$
$269$	0.245503	−	0.425223i	0.0149686	−	0.0259263i	0.873413	+	0.486981i	$0.161902\pi$
$270$	−5.57257	+	17.9619i	−0.339136	+	1.09313i
$271$	12.1927	−	7.03945i	0.740653	−	0.427616i	−0.0816537	−	0.996661i	$-0.526020\pi$
$271$	12.1927	−	7.03945i	0.740653	−	0.427616i	0.822307	+	0.569045i	$0.192687\pi$
$272$	−3.08709	−	5.34700i	−0.187182	−	0.324209i
$273$		0			0
$274$	−0.000322562	0	0.000558693i	−1.94867e−5	0	3.37519e-5i
$275$			16.2296i			0.978683i
$276$	2.95206	+	4.33493i	0.177693	+	0.260932i
$277$	30.7200			1.84579			0.922894	−	0.385054i	$-0.125817\pi$
$277$	30.7200			1.84579			0.922894	+	0.385054i	$0.125817\pi$
$278$	5.04185	+	8.73273i	0.302390	+	0.523755i
$279$	2.13551	−	1.69923i	0.127850	−	0.101730i
$280$		0			0
$281$	6.86286	−	3.96227i	0.409404	−	0.236369i	−0.281130	−	0.959670i	$-0.590709\pi$
$281$	6.86286	−	3.96227i	0.409404	−	0.236369i	0.690534	+	0.723300i	$0.257376\pi$
$282$	−2.17429	−	3.19282i	−0.129477	−	0.190130i
$283$	9.97303	−	5.75793i	0.592835	−	0.342273i	−0.173383	−	0.984855i	$-0.555470\pi$
$283$	9.97303	−	5.75793i	0.592835	−	0.342273i	0.766218	+	0.642581i	$0.222136\pi$
$284$	−0.403817	+	0.233144i	−0.0239621	+	0.0138345i
$285$	−3.57471	−	5.24925i	−0.211747	−	0.310939i
$286$	5.91532	−	3.41521i	0.349780	−	0.201946i
$287$		0			0
$288$	−2.34752	+	1.86792i	−0.138329	+	0.110068i
$289$	−10.5603	−	18.2909i	−0.621192	−	1.07594i
$290$	−21.0867			−1.23825
$291$	−11.4640	−	16.8342i	−0.672031	−	0.986839i
$292$			4.21492i			0.246659i
$293$	−2.50937	+	4.34636i	−0.146599	+	0.253917i	−0.929968	−	0.367639i	$-0.880166\pi$
$293$	−2.50937	+	4.34636i	−0.146599	+	0.253917i	0.783369	+	0.621557i	$0.213499\pi$
$294$		0			0
$295$	−16.2621	−	28.1667i	−0.946814	−	1.63993i
$296$	6.35359	−	3.66825i	0.369295	−	0.213213i
$297$	10.1547	−	2.30037i	0.589237	−	0.133481i
$298$	−5.62376	+	9.74064i	−0.325776	+	0.564260i
$299$	5.16083	−	8.93882i	0.298458	−	0.516945i
$300$	−11.5953	+	7.89633i	−0.669455	+	0.455895i
$301$		0			0
$302$	4.09092	+	2.36189i	0.235406	+	0.135912i
$303$	1.65664	+	22.2684i	0.0951712	+	1.27929i
$304$		−	1.01308i		−	0.0581041i
$305$	46.1138	+	26.6238i	2.64047	+	1.52447i
$306$	−14.4940	+	11.5329i	−0.828569	+	0.659292i
$307$			17.5309i			1.00054i	0.865869	+	0.500271i	$0.166766\pi$
$307$			17.5309i			1.00054i	−0.865869	+	0.500271i	$0.833234\pi$
$308$		0			0
$309$	−18.5834	+	1.38250i	−1.05717	+	0.0786474i
$310$	3.29245			0.186998
$311$	−8.64759	−	14.9781i	−0.490360	−	0.849328i	0.509579	−	0.860424i	$-0.329801\pi$
$311$	−8.64759	−	14.9781i	−0.490360	−	0.849328i	−0.999938	+	0.0110959i	$0.996468\pi$
$312$	5.31804	+	2.56459i	0.301074	+	0.145191i
$313$	−7.78988	−	4.49749i	−0.440310	−	0.254213i	0.263419	−	0.964681i	$-0.415150\pi$
$313$	−7.78988	−	4.49749i	−0.440310	−	0.254213i	−0.703729	+	0.710468i	$0.748483\pi$
$314$	3.06972			0.173234
$315$		0			0
$316$	−3.82533			−0.215192
$317$	−5.82002	−	3.36019i	−0.326885	−	0.188727i	0.327572	−	0.944826i	$-0.393770\pi$
$317$	−5.82002	−	3.36019i	−0.326885	−	0.188727i	−0.654457	+	0.756099i	$0.727103\pi$
$318$	−12.5319	+	8.53413i	−0.702753	+	0.478570i
$319$	5.83721	+	10.1103i	0.326821	+	0.566071i
$320$	−3.61932			−0.202326
$321$	2.57347	+	3.77899i	0.143637	+	0.210923i
$322$		0			0
$323$		−	6.25494i		−	0.348034i
$324$	6.58416	+	6.13586i	0.365787	+	0.340881i
$325$	23.9100	+	13.8045i	1.32629	+	0.765734i
$326$			2.87373i			0.159161i
$327$	14.0962	+	6.79780i	0.779521	+	0.375919i
$328$	4.93712	+	2.85045i	0.272607	+	0.157390i
$329$		0			0
$330$	11.3145	+	5.45636i	0.622844	+	0.300363i
$331$	9.38725	−	16.2592i	0.515970	−	0.893686i	−0.483858	−	0.875146i	$-0.660765\pi$
$331$	9.38725	−	16.2592i	0.515970	−	0.893686i	0.999828	−	0.0185396i	$-0.00590167\pi$
$332$	4.00481	−	6.93654i	0.219793	−	0.380692i
$333$	−13.7040	−	17.2226i	−0.750975	−	0.943792i
$334$	−1.26529	+	0.730517i	−0.0692338	+	0.0399721i
$335$	15.0499	+	26.0671i	0.822262	+	1.42420i
$336$		0			0
$337$	2.42287	−	4.19654i	0.131982	−	0.228600i	−0.792458	−	0.609926i	$-0.791199\pi$
$337$	2.42287	−	4.19654i	0.131982	−	0.228600i	0.924441	+	0.381326i	$0.124532\pi$
$338$			1.38047i			0.0750874i
$339$	1.27194	−	2.63755i	0.0690824	−	0.143252i
$340$	−22.3463			−1.21190
$341$	−0.911413	−	1.57861i	−0.0493558	−	0.0854868i
$342$	−3.00578	+	0.449713i	−0.162534	+	0.0243177i
$343$		0			0
$344$	−4.15605	+	2.39949i	−0.224079	+	0.129372i
$345$	18.9297	−	1.40826i	1.01914	−	0.0758179i
$346$	−2.65940	+	1.53541i	−0.142970	+	0.0825440i
$347$	−15.1305	+	8.73559i	−0.812247	+	0.468951i	−0.847736	−	0.530419i	$-0.822035\pi$
$347$	−15.1305	+	8.73559i	−0.812247	+	0.468951i	0.0354887	+	0.999370i	$0.488701\pi$
$348$	−4.38334	+	9.08948i	−0.234972	+	0.487247i
$349$	20.6338	−	11.9129i	1.10450	−	0.637683i	0.167101	−	0.985940i	$-0.446560\pi$
$349$	20.6338	−	11.9129i	1.10450	−	0.637683i	0.937399	+	0.348257i	$0.113226\pi$
$350$		0			0
$351$	5.24835	−	16.9169i	0.280136	−	0.902958i
$352$	1.00190	+	1.73534i	0.0534013	+	0.0924938i
$353$	−10.0412			−0.534441			−0.267220	−	0.963635i	$-0.586105\pi$
$353$	−10.0412			−0.534441			−0.267220	+	0.963635i	$0.586105\pi$
$354$	−15.5218	+	1.15473i	−0.824973	+	0.0613730i
$355$			1.68764i			0.0895707i
$356$	2.39324	−	4.14521i	0.126841	−	0.219696i
$357$		0			0
$358$	9.65966	+	16.7310i	0.510529	+	0.884262i
$359$	10.5353	−	6.08254i	0.556030	−	0.321024i	−0.195521	−	0.980700i	$-0.562640\pi$
$359$	10.5353	−	6.08254i	0.556030	−	0.321024i	0.751550	+	0.659676i	$0.229306\pi$
$360$	1.60664	+	10.7384i	0.0846774	+	0.565965i
$361$	−8.98683	+	15.5657i	−0.472991	+	0.819245i
$362$	−3.94659	+	6.83569i	−0.207428	+	0.359276i
$363$	0.897541	+	12.0647i	0.0471087	+	0.633233i
$364$		0			0
$365$	13.2113	+	7.62756i	0.691512	+	0.399245i
$366$	21.0620	−	14.3431i	1.10093	−	0.749727i
$367$		−	3.63061i		−	0.189516i	−0.995500	−	0.0947582i	$-0.969792\pi$
$367$		−	3.63061i		−	0.189516i	0.995500	−	0.0947582i	$-0.0302078\pi$
$368$	2.62232	+	1.51400i	0.136698	+	0.0789225i
$369$	6.26558	−	15.9136i	0.326173	−	0.828431i
$370$		−	26.5531i		−	1.38043i
$371$		0			0
$372$	0.684408	−	1.41922i	0.0354849	−	0.0735830i
$373$	5.49231			0.284381			0.142191	−	0.989839i	$-0.454585\pi$
$373$	5.49231			0.284381			0.142191	+	0.989839i	$0.454585\pi$
$374$	6.18590	+	10.7143i	0.319865	+	0.554023i
$375$	1.44149	+	19.3764i	0.0744380	+	1.00059i
$376$	−1.93143	−	1.11511i	−0.0996057	−	0.0575074i
$377$	19.8599			1.02284
$378$		0			0
$379$	−15.5960			−0.801112			−0.400556	−	0.916272i	$-0.631183\pi$
$379$	−15.5960			−0.801112			−0.400556	+	0.916272i	$0.631183\pi$
$380$	−3.17542	−	1.83333i	−0.162896	−	0.0940478i
$381$	2.30388	+	30.9686i	0.118031	+	1.58657i
$382$	−6.65211	−	11.5218i	−0.340352	−	0.589506i
$383$	−9.43067			−0.481885			−0.240942	−	0.970539i	$-0.577456\pi$
$383$	−9.43067			−0.481885			−0.240942	+	0.970539i	$0.577456\pi$
$384$	−0.752355	+	1.56012i	−0.0383935	+	0.0796143i
$385$		0			0
$386$			6.53573i			0.332660i
$387$	8.96414	+	11.2657i	0.455673	+	0.572670i
$388$	−10.1835	−	5.87944i	−0.516989	−	0.298483i
$389$		−	6.42177i		−	0.325597i	−0.986659	−	0.162798i	$-0.947948\pi$
$389$		−	6.42177i		−	0.325597i	0.986659	−	0.162798i	$-0.0520520\pi$
$390$	17.6623	−	12.0279i	0.894366	−	0.609058i
$391$	16.1907	+	9.34769i	0.818798	+	0.472733i
$392$		0			0
$393$	−2.22706	−	29.9360i	−0.112340	−	1.51007i
$394$	−2.22125	+	3.84732i	−0.111905	+	0.193825i
$395$	−6.92255	+	11.9902i	−0.348311	+	0.603293i
$396$	4.70395	−	3.74293i	0.236383	−	0.188090i
$397$	−5.99750	+	3.46266i	−0.301006	+	0.173786i	−0.642895	−	0.765955i	$-0.722267\pi$
$397$	−5.99750	+	3.46266i	−0.301006	+	0.173786i	0.341889	+	0.939740i	$0.388933\pi$
$398$	5.75542	+	9.96868i	0.288493	+	0.499685i
$399$		0			0
$400$	−4.04972	+	7.01433i	−0.202486	+	0.350716i
$401$		−	10.5869i		−	0.528682i	−0.964429	−	0.264341i	$-0.914846\pi$
$401$		−	10.5869i		−	0.528682i	0.964429	−	0.264341i	$-0.0851545\pi$
$402$	14.3648	−	1.06865i	0.716449	−	0.0532995i
$403$	−3.10089			−0.154466
$404$	6.44610	+	11.1650i	0.320705	+	0.555478i
$405$	31.1474	−	9.53372i	1.54773	−	0.473735i
$406$		0			0
$407$	−12.7313	+	7.35042i	−0.631067	+	0.364347i
$408$	−4.64518	+	9.63244i	−0.229971	+	0.476877i
$409$	−7.72792	+	4.46172i	−0.382121	+	0.220618i	−0.678741	−	0.734378i	$-0.737474\pi$
$409$	−7.72792	+	4.46172i	−0.382121	+	0.220618i	0.296620	+	0.954996i	$0.404141\pi$
$410$	17.8690	−	10.3167i	0.882486	−	0.509504i
$411$	0.00111431		8.28977e-5i	5.49647e−5		4.08904e-6i
$412$	−9.31740	+	5.37940i	−0.459035	+	0.265024i
$413$		0			0
$414$	3.32793	−	8.45243i	0.163559	−	0.415414i
$415$	−14.4947	−	25.1055i	−0.711516	−	1.23238i
$416$	3.40874			0.167127
$417$	7.58652	−	15.7317i	0.371513	−	0.770386i
$418$			2.03000i			0.0992908i
$419$	17.1924	−	29.7781i	0.839903	−	1.45475i	−0.0500724	−	0.998746i	$-0.515945\pi$
$419$	17.1924	−	29.7781i	0.839903	−	1.45475i	0.889975	−	0.456009i	$-0.150721\pi$
$420$		0			0
$421$	−17.7840	−	30.8028i	−0.866739	−	1.50124i	−0.865310	−	0.501237i	$-0.832879\pi$
$421$	−17.7840	−	30.8028i	−0.866739	−	1.50124i	−0.00142877	−	0.999999i	$-0.500455\pi$
$422$	−19.5731	+	11.3005i	−0.952803	+	0.550101i
$423$	−2.45113	+	6.22550i	−0.119178	+	0.302694i
$424$	−4.37683	+	7.58088i	−0.212557	+	0.368160i
$425$	−25.0037	+	43.3077i	−1.21286	+	2.10073i
$426$	0.727462	+	0.350814i	0.0352457	+	0.0169970i
$427$		0			0
$428$	2.28602	+	1.31983i	0.110499	+	0.0637965i
$429$	−10.6563	−	5.13891i	−0.514489	−	0.248109i
$430$			17.3691i			0.837610i
$431$	26.7338	+	15.4348i	1.28772	+	0.743466i	0.978247	−	0.207442i	$-0.0665138\pi$
$431$	26.7338	+	15.4348i	1.28772	+	0.743466i	0.309474	+	0.950908i	$0.399847\pi$
$432$	4.96280	+	1.53967i	0.238773	+	0.0740776i
$433$			23.2463i			1.11715i	0.829455	+	0.558574i	$0.188651\pi$
$433$			23.2463i			1.11715i	−0.829455	+	0.558574i	$0.811349\pi$
$434$		0			0
$435$	20.5579	+	30.1881i	0.985676	+	1.44741i
$436$	9.03535			0.432715
$437$	1.53380	+	2.65662i	0.0733716	+	0.127083i
$438$	6.03414	−	4.10922i	0.288323	−	0.196346i
$439$	−19.2887	−	11.1364i	−0.920601	−	0.531509i	−0.0367744	−	0.999324i	$-0.511708\pi$
$439$	−19.2887	−	11.1364i	−0.920601	−	0.531509i	−0.883827	+	0.467814i	$0.845042\pi$
$440$	7.25237			0.345743
$441$		0			0
$442$	21.0462			1.00107
$443$	15.5756	+	8.99259i	0.740020	+	0.427251i	0.822077	−	0.569377i	$-0.192815\pi$
$443$	15.5756	+	8.99259i	0.740020	+	0.427251i	−0.0820566	+	0.996628i	$0.526149\pi$
$444$	−11.4458	−	5.51965i	−0.543193	−	0.261951i
$445$	−8.66188	−	15.0028i	−0.410612	−	0.711202i
$446$	−18.8209			−0.891195
$447$	19.4276	−	1.44530i	0.918894	−	0.0683601i
$448$		0			0
$449$			9.44363i			0.445673i	0.974856	+	0.222836i	$0.0715315\pi$
$449$			9.44363i			0.445673i	−0.974856	+	0.222836i	$0.928468\pi$
$450$	22.6090	+	8.90172i	1.06580	+	0.419631i
$451$	−9.89297	−	5.71171i	−0.465842	−	0.268954i
$452$		−	1.69061i		−	0.0795197i
$453$	−0.607002	−	8.15930i	−0.0285195	−	0.383357i
$454$	−12.6555	−	7.30665i	−0.593952	−	0.342918i
$455$		0			0
$456$	−1.45034	+	0.987674i	−0.0679185	+	0.0462521i
$457$	0.922251	−	1.59739i	0.0431411	−	0.0747225i	−0.843649	−	0.536896i	$-0.819597\pi$
$457$	0.922251	−	1.59739i	0.0431411	−	0.0747225i	0.886790	+	0.462173i	$0.152930\pi$
$458$	1.18959	−	2.06044i	0.0555861	−	0.0962779i
$459$	30.6412	+	9.50623i	1.43021	+	0.443713i
$460$	9.49100	−	5.47963i	0.442520	−	0.255489i
$461$	−18.1869	−	31.5007i	−0.847050	−	1.46713i	−0.883829	−	0.467810i	$-0.845043\pi$
$461$	−18.1869	−	31.5007i	−0.847050	−	1.46713i	0.0367790	−	0.999323i	$-0.488290\pi$
$462$		0			0
$463$	−15.9830	+	27.6834i	−0.742794	+	1.28656i	0.208425	+	0.978038i	$0.433166\pi$
$463$	−15.9830	+	27.6834i	−0.742794	+	1.28656i	−0.951219	+	0.308518i	$0.900167\pi$
$464$			5.82616i			0.270473i
$465$	−3.20988	−	4.71352i	−0.148855	−	0.218584i
$466$	10.4324			0.483271
$467$	12.2206	+	21.1666i	0.565500	+	0.979475i	0.997003	+	0.0773632i	$0.0246501\pi$
$467$	12.2206	+	21.1666i	0.565500	+	0.979475i	−0.431503	+	0.902112i	$0.642017\pi$
$468$	−1.51317	−	10.1137i	−0.0699461	−	0.467504i
$469$		0			0
$470$	−6.99044	+	4.03593i	−0.322445	+	0.186164i
$471$	−2.99273	−	4.39466i	−0.137898	−	0.202495i
$472$	−7.78233	+	4.49313i	−0.358211	+	0.206813i
$473$	8.32786	−	4.80809i	0.382916	−	0.221076i
$474$	3.72940	+	5.47641i	0.171297	+	0.251540i
$475$	−7.10607	+	4.10269i	−0.326049	+	0.188245i
$476$		0			0
$477$	24.4352	+	9.62073i	1.11881	+	0.440503i
$478$	−11.8917	−	20.5971i	−0.543916	−	0.942090i
$479$	−10.9606			−0.500805			−0.250402	−	0.968142i	$-0.580563\pi$
$479$	−10.9606			−0.500805			−0.250402	+	0.968142i	$0.580563\pi$
$480$	3.52855	+	5.18147i	0.161056	+	0.236501i
$481$			25.0082i			1.14028i
$482$	−14.3243	+	24.8105i	−0.652456	+	1.13009i
$483$		0			0
$484$	3.49240	+	6.04902i	0.158746	+	0.274955i
$485$	−36.8573	+	21.2796i	−1.67360	+	0.966255i
$486$	2.36515	−	15.4080i	0.107286	−	0.698920i
$487$	−16.8087	+	29.1136i	−0.761677	+	1.31926i	0.180309	+	0.983610i	$0.442290\pi$
$487$	−16.8087	+	29.1136i	−0.761677	+	1.31926i	−0.941986	+	0.335653i	$0.891043\pi$
$488$	7.35603	−	12.7410i	0.332992	−	0.576759i
$489$	4.11408	−	2.80167i	0.186045	−	0.126696i
$490$		0			0
$491$	−19.6893	−	11.3676i	−0.888568	−	0.513015i	−0.0150939	−	0.999886i	$-0.504805\pi$
$491$	−19.6893	−	11.3676i	−0.888568	−	0.513015i	−0.873474	+	0.486871i	$0.838138\pi$
$492$	−0.732559	−	9.84702i	−0.0330263	−	0.443938i
$493$			35.9718i			1.62009i
$494$	2.99067	+	1.72667i	0.134557	+	0.0776863i
$495$	−3.21938	−	21.5176i	−0.144700	−	0.967144i
$496$		−	0.909687i		−	0.0408462i
$497$		0			0
$498$	−13.8348	+	1.02923i	−0.619954	+	0.0461209i
$499$	19.5235			0.873992			0.436996	−	0.899463i	$-0.356042\pi$
$499$	19.5235			0.873992			0.436996	+	0.899463i	$0.356042\pi$
$500$	5.60894	+	9.71496i	0.250839	+	0.434466i
$501$	2.27938	+	1.09922i	0.101835	+	0.0491094i
$502$	9.55238	+	5.51507i	0.426343	+	0.246149i
$503$	−13.6867			−0.610262			−0.305131	−	0.952310i	$-0.598700\pi$
$503$	−13.6867			−0.610262			−0.305131	+	0.952310i	$0.598700\pi$
$504$		0			0
$505$	46.6609			2.07638
$506$	−5.25459	−	3.03374i	−0.233595	−	0.134866i
$507$	1.97630	−	1.34585i	0.0877705	−	0.0597712i
$508$	8.96458	+	15.5271i	0.397739	+	0.688904i
$509$	2.29166			0.101576			0.0507881	−	0.998709i	$-0.483827\pi$
$509$	2.29166			0.101576			0.0507881	+	0.998709i	$0.483827\pi$
$510$	21.7859	+	31.9914i	0.964697	+	1.41660i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	3.57422	+	3.86470i	0.157806	+	0.170630i
$514$	−13.0751	−	7.54890i	−0.576717	−	0.332968i
$515$			38.9395i			1.71588i
$516$	7.48698	+	3.61054i	0.329596	+	0.158945i
$517$	3.87018	+	2.23445i	0.170210	+	0.0982710i
$518$		0			0
$519$	4.79082	+	2.31034i	0.210294	+	0.101413i
$520$	6.16866	−	10.6844i	0.270514	−	0.468543i
$521$	8.54102	−	14.7935i	0.374189	−	0.648114i	−0.616017	−	0.787733i	$-0.711255\pi$
$521$	8.54102	−	14.7935i	0.374189	−	0.648114i	0.990205	+	0.139619i	$0.0445879\pi$
$522$	17.2861	−	2.58627i	0.756591	−	0.113198i
$523$	−35.7462	+	20.6381i	−1.56307	+	0.902440i	−0.566128	+	0.824317i	$0.691559\pi$
$523$	−35.7462	+	20.6381i	−1.56307	+	0.902440i	−0.996944	+	0.0781229i	$0.975107\pi$
$524$	−8.66567	−	15.0094i	−0.378562	−	0.655688i
$525$		0			0
$526$	−9.81926	+	17.0075i	−0.428140	+	0.741561i
$527$		−	5.61657i		−	0.244662i
$528$	1.50757	−	3.12615i	0.0656084	−	0.136048i
$529$	13.8313			0.601359
$530$	15.8411	+	27.4376i	0.688094	+	1.19181i
$531$	16.7857	+	21.0955i	0.728435	+	0.915465i
$532$		0			0
$533$	−16.8294	+	9.71644i	−0.728961	+	0.420866i
$534$	−8.26757	+	0.615057i	−0.357773	+	0.0266161i
$535$	8.27382	−	4.77689i	0.357708	−	0.206523i
$536$	7.20222	−	4.15821i	0.311089	−	0.179607i
$537$	14.5350	−	30.1404i	0.627231	−	1.30065i
$538$	−0.425223	+	0.245503i	−0.0183327	+	0.0105844i
$539$		0			0
$540$	13.8070	−	12.7692i	0.594157	−	0.549500i
$541$	22.7197	+	39.3516i	0.976795	+	1.69186i	0.673880	+	0.738841i	$0.264627\pi$
$541$	22.7197	+	39.3516i	0.976795	+	1.69186i	0.302915	+	0.953018i	$0.402040\pi$
$542$	−14.0789			−0.604741
$543$	13.6337	−	1.01427i	0.585078	−	0.0435263i
$544$			6.17418i			0.264716i
$545$	16.3509	−	28.3206i	0.700395	−	1.21312i
$546$		0			0
$547$	15.1095	+	26.1705i	0.646037	+	1.11897i	0.984061	+	0.177832i	$0.0569082\pi$
$547$	15.1095	+	26.1705i	0.646037	+	1.11897i	−0.338024	+	0.941138i	$0.609758\pi$
$548$	0.000558693	0	0.000322562i	2.38662e−5	0	1.37791e-5i
$549$	−41.0677	−	16.1693i	−1.75273	−	0.690091i
$550$	8.11481	−	14.0553i	0.346017	−	0.599319i
$551$	−2.95118	+	5.11160i	−0.125725	+	0.217761i
$552$	−0.389094	−	5.23019i	−0.0165610	−	0.222612i
$553$		0			0
$554$	−26.6043	−	15.3600i	−1.13031	−	0.652585i
$555$	−38.0139	+	25.8872i	−1.61360	+	1.09885i
$556$		−	10.0837i		−	0.427644i
$557$	−22.0154	−	12.7106i	−0.932822	−	0.538565i	−0.0451189	−	0.998982i	$-0.514367\pi$
$557$	−22.0154	−	12.7106i	−0.932822	−	0.538565i	−0.887703	+	0.460417i	$0.847700\pi$
$558$	−2.69902	+	0.403817i	−0.114259	+	0.0170949i
$559$		−	16.3585i		−	0.691892i
$560$		0			0
$561$	9.30799	−	19.3014i	0.392983	−	0.814907i
$562$	−7.92455			−0.334277
$563$	−1.44346	−	2.50015i	−0.0608346	−	0.105369i	0.834004	−	0.551758i	$-0.186043\pi$
$563$	−1.44346	−	2.50015i	−0.0608346	−	0.105369i	−0.894839	+	0.446390i	$0.852710\pi$
$564$	0.286581	+	3.85221i	0.0120672	+	0.162207i
$565$	−5.29909	−	3.05943i	−0.222934	−	0.128711i
$566$	−11.5159			−0.484048
$567$		0			0
$568$	0.466287			0.0195650
$569$	−38.5945	−	22.2826i	−1.61797	−	0.934134i	−0.987445	−	0.157963i	$-0.949507\pi$
$569$	−38.5945	−	22.2826i	−1.61797	−	0.934134i	−0.630523	−	0.776171i	$-0.717159\pi$
$570$	0.471162	+	6.33333i	0.0197348	+	0.265274i
$571$	3.26470	+	5.65462i	0.136623	+	0.236638i	0.926216	−	0.376992i	$-0.123042\pi$
$571$	3.26470	+	5.65462i	0.136623	+	0.236638i	−0.789593	+	0.613631i	$0.789708\pi$
$572$	−6.83042			−0.285594
$573$	−10.0095	+	20.7561i	−0.418153	+	0.867100i
$574$		0			0
$575$		−	24.5251i		−	1.02277i
$576$	2.96698	−	0.443907i	0.123624	−	0.0184961i
$577$	−1.17720	−	0.679658i	−0.0490076	−	0.0282945i	0.475296	−	0.879826i	$-0.342341\pi$
$577$	−1.17720	−	0.679658i	−0.0490076	−	0.0282945i	−0.524304	+	0.851531i	$0.675674\pi$
$578$			21.1205i			0.878498i
$579$	9.35666	−	6.37183i	0.388850	−	0.264804i
$580$	18.2616	+	10.5434i	0.758273	+	0.437789i
$581$		0			0
$582$	1.51101	+	20.3109i	0.0626332	+	0.841912i
$583$	8.77026	−	15.1905i	0.363227	−	0.629128i
$584$	2.10746	−	3.65022i	0.0872072	−	0.151047i
$585$	−34.4388	−	13.5594i	−1.42387	−	0.560611i
$586$	4.34636	−	2.50937i	0.179547	−	0.103661i
$587$	22.2025	+	38.4559i	0.916397	+	1.58725i	0.804843	+	0.593488i	$0.202250\pi$
$587$	22.2025	+	38.4559i	0.916397	+	1.58725i	0.111555	+	0.993758i	$0.464417\pi$
$588$		0			0
$589$	0.460793	−	0.798117i	0.0189866	−	0.0328858i
$590$			32.5241i			1.33900i
$591$	7.67343	−	0.570857i	0.315643	−	0.0234819i
$592$	−7.33650			−0.301528
$593$	7.17564	+	12.4286i	0.294668	+	0.510380i	0.974908	−	0.222610i	$-0.0714576\pi$
$593$	7.17564	+	12.4286i	0.294668	+	0.510380i	−0.680240	+	0.732990i	$0.738124\pi$
$594$	−9.94444	−	3.08519i	−0.408025	−	0.126587i
$595$		0			0
$596$	9.74064	−	5.62376i	0.398992	−	0.230358i
$597$	8.66024	−	17.9582i	0.354440	−	0.734982i
$598$	−8.93882	+	5.16083i	−0.365535	+	0.211042i
$599$	−3.03349	+	1.75139i	−0.123945	+	0.0715597i	−0.560691	−	0.828025i	$-0.689464\pi$
$599$	−3.03349	+	1.75139i	−0.123945	+	0.0715597i	0.436746	+	0.899585i	$0.356131\pi$
$600$	13.9900	−	1.04077i	0.571139	−	0.0424893i
$601$	15.1846	−	8.76685i	0.619394	−	0.357607i	−0.157239	−	0.987561i	$-0.550259\pi$
$601$	15.1846	−	8.76685i	0.619394	−	0.357607i	0.776633	+	0.629953i	$0.216926\pi$
$602$		0			0
$603$	−15.5344	−	19.5230i	−0.632610	−	0.795037i
$604$	−2.36189	−	4.09092i	−0.0961041	−	0.166457i
$605$	25.2802			1.02779
$606$	9.69952	−	20.1133i	0.394016	−	0.817048i
$607$			0.0872864i			0.00354285i	0.999998	+	0.00177142i	$0.000563862\pi$
$607$			0.0872864i			0.00354285i	−0.999998	+	0.00177142i	$0.999436\pi$
$608$	−0.506540	+	0.877353i	−0.0205429	+	0.0355814i
$609$		0			0
$610$	−26.6238	−	46.1138i	−1.07797	−	1.86709i
$611$	6.58373	−	3.80112i	0.266349	−	0.153777i
$612$	18.3186	−	2.74076i	0.740488	−	0.110789i
$613$	12.5352	−	21.7116i	0.506292	−	0.876924i	−0.493681	−	0.869643i	$-0.664349\pi$
$613$	12.5352	−	21.7116i	0.506292	−	0.876924i	0.999973	−	0.00728071i	$-0.00231754\pi$
$614$	8.76545	−	15.1822i	0.353745	−	0.612704i
$615$	−32.1904	−	15.5236i	−1.29804	−	0.625972i
$616$		0			0
$617$	−10.6365	−	6.14101i	−0.428211	−	0.247228i	0.270373	−	0.962756i	$-0.412853\pi$
$617$	−10.6365	−	6.14101i	−0.428211	−	0.247228i	−0.698584	+	0.715528i	$0.746186\pi$
$618$	16.7850	+	8.09444i	0.675191	+	0.325606i
$619$			20.3076i			0.816229i	0.912931	+	0.408115i	$0.133814\pi$
$619$			20.3076i			0.816229i	−0.912931	+	0.408115i	$0.866186\pi$
$620$	−2.85134	−	1.64622i	−0.114513	−	0.0661139i
$621$	−15.3451	+	3.47615i	−0.615778	+	0.139493i
$622$			17.2952i			0.693474i
$623$		0			0
$624$	−3.32326	−	4.88001i	−0.133037	−	0.195357i
$625$	0.103794			0.00415176
$626$	4.49749	+	7.78988i	0.179756	+	0.311346i
$627$	2.90619	−	1.97910i	0.116062	−	0.0790375i
$628$	−2.65845	−	1.53486i	−0.106084	−	0.0612475i
$629$	−45.2969			−1.80610
$630$		0			0
$631$	−45.9665			−1.82990			−0.914950	−	0.403568i	$-0.867770\pi$
$631$	−45.9665			−1.82990			−0.914950	+	0.403568i	$0.867770\pi$
$632$	3.31284	+	1.91267i	0.131778	+	0.0760818i
$633$	35.2603	+	17.0040i	1.40147	+	0.675850i
$634$	3.36019	+	5.82002i	0.133450	+	0.231143i
$635$	64.8913			2.57513
$636$	15.1200	−	1.12484i	0.599546	−	0.0446026i
$637$		0			0
$638$		−	11.6744i		−	0.462195i
$639$	−0.206988	−	1.38346i	−0.00818833	−	0.0547290i
$640$	3.13442	+	1.80966i	0.123899	+	0.0715330i
$641$			31.6509i			1.25013i	0.780571	+	0.625067i	$0.214928\pi$
$641$			31.6509i			1.25013i	−0.780571	+	0.625067i	$0.785072\pi$
$642$	−0.339195	−	4.55944i	−0.0133869	−	0.179947i
$643$	−10.0106	−	5.77960i	−0.394778	−	0.227925i	0.289450	−	0.957193i	$-0.406528\pi$
$643$	−10.0106	−	5.77960i	−0.394778	−	0.227925i	−0.684228	+	0.729268i	$0.739861\pi$
$644$		0			0
$645$	24.8658	−	16.9335i	0.979091	−	0.666755i
$646$	−3.12747	+	5.41694i	−0.123049	+	0.213127i
$647$	−13.0365	+	22.5799i	−0.512519	+	0.887708i	0.487376	+	0.873192i	$0.337954\pi$
$647$	−13.0365	+	22.5799i	−0.512519	+	0.887708i	−0.999895	+	0.0145160i	$0.995379\pi$
$648$	−2.63412	−	8.60589i	−0.103478	−	0.338071i
$649$	15.5942	−	9.00332i	0.612126	−	0.353411i
$650$	−13.8045	−	23.9100i	−0.541456	−	0.937829i
$651$		0			0
$652$	1.43687	−	2.48873i	0.0562720	−	0.0974660i
$653$			18.9315i			0.740847i	0.928863	+	0.370424i	$0.120788\pi$
$653$			18.9315i			0.740847i	−0.928863	+	0.370424i	$0.879212\pi$
$654$	−8.80877	−	12.9352i	−0.344450	−	0.505805i
$655$	−62.7276			−2.45097
$656$	−2.85045	−	4.93712i	−0.111291	−	0.192762i
$657$	−11.7656	−	4.63242i	−0.459021	−	0.180728i
$658$		0			0
$659$	23.3508	−	13.4816i	0.909618	−	0.525168i	0.0293098	−	0.999570i	$-0.490669\pi$
$659$	23.3508	−	13.4816i	0.909618	−	0.525168i	0.880308	+	0.474402i	$0.157336\pi$
$660$	−7.07049	−	10.3826i	−0.275219	−	0.404142i
$661$	−22.3201	+	12.8865i	−0.868151	+	0.501227i	−0.866733	−	0.498772i	$-0.833785\pi$
$661$	−22.3201	+	12.8865i	−0.868151	+	0.501227i	−0.00141768	+	0.999999i	$0.500451\pi$
$662$	−16.2592	+	9.38725i	−0.631931	+	0.364846i
$663$	−20.5184	−	30.1301i	−0.796869	−	1.17016i
$664$	−6.93654	+	4.00481i	−0.269190	+	0.155417i
$665$		0			0
$666$	3.25672	+	21.7672i	0.126195	+	0.843462i
$667$	−8.82079	−	15.2780i	−0.341542	−	0.591568i
$668$	1.46103			0.0565291
$669$	18.3489	+	26.9443i	0.709410	+	1.04173i
$670$		−	30.0997i		−	1.16285i
$671$	−14.7400	+	25.5304i	−0.569030	+	0.985590i
$672$		0			0
$673$	−12.9608	−	22.4487i	−0.499601	−	0.865335i	0.500398	−	0.865795i	$-0.333187\pi$
$673$	−12.9608	−	22.4487i	−0.499601	−	0.865335i	−1.00000		0.000460130i	$0.999854\pi$
$674$	−4.19654	+	2.42287i	−0.161645	+	0.0933256i
$675$	−9.29820	−	41.0460i	−0.357888	−	1.57986i
$676$	0.690233	−	1.19552i	0.0265474	−	0.0459815i
$677$	−6.55382	+	11.3515i	−0.251884	+	0.436275i	−0.964044	−	0.265741i	$-0.914383\pi$
$677$	−6.55382	+	11.3515i	−0.251884	+	0.436275i	0.712161	+	0.702016i	$0.247717\pi$
$678$	−2.42031	+	1.64822i	−0.0929514	+	0.0632993i
$679$		0			0
$680$	19.3525	+	11.1732i	0.742134	+	0.428471i
$681$	1.87780	+	25.2412i	0.0719573	+	0.967246i
$682$			1.82283i			0.0697996i
$683$	−25.6910	−	14.8327i	−0.983038	−	0.567557i	−0.0798523	−	0.996807i	$-0.525445\pi$
$683$	−25.6910	−	14.8327i	−0.983038	−	0.567557i	−0.903186	+	0.429249i	$0.858778\pi$
$684$	2.82794	+	1.11343i	0.108129	+	0.0425730i
$685$		−	0.00233490i		−	8.92121e-5i
$686$		0			0
$687$	−4.10952	+	0.305723i	−0.156788	+	0.0116641i
$688$	4.79899			0.182960
$689$	−14.9195	−	25.8413i	−0.568387	−	0.984475i
$690$	−17.0977	−	8.24526i	−0.650899	−	0.313892i
$691$	−40.9767	−	23.6579i	−1.55883	−	0.899990i	−0.997369	−	0.0724857i	$-0.976907\pi$
$691$	−40.9767	−	23.6579i	−1.55883	−	0.899990i	−0.561459	−	0.827504i	$-0.689760\pi$
$692$	3.07081			0.116735
$693$		0			0
$694$	17.4712			0.663197
$695$	−31.6065	−	18.2480i	−1.19890	−	0.692187i
$696$	8.34083	−	5.68005i	0.316158	−	0.215302i
$697$	−17.5992	−	30.4827i	−0.666616	−	1.15461i
$698$	−23.8258			−0.901820
$699$	−10.1708	−	14.9352i	−0.384693	−	0.564900i
$700$		0			0
$701$			13.7742i			0.520244i	0.965576	+	0.260122i	$0.0837627\pi$
$701$			13.7742i			0.520244i	−0.965576	+	0.260122i	$0.916237\pi$
$702$	−13.0037	+	12.0263i	−0.490792	+	0.453904i
$703$	−6.43670	−	3.71623i	−0.242765	−	0.140160i
$704$		−	2.00379i		−	0.0755209i
$705$	12.5930	+	6.07291i	0.474281	+	0.228719i
$706$	8.69596	+	5.02061i	0.327277	+	0.188953i
$707$		0			0
$708$	14.0196	+	6.76087i	0.526889	+	0.254089i
$709$	21.9691	−	38.0517i	0.825069	−	1.42906i	−0.0767981	−	0.997047i	$-0.524470\pi$
$709$	21.9691	−	38.0517i	0.825069	−	1.42906i	0.901867	−	0.432014i	$-0.142197\pi$
$710$	0.843820	−	1.46154i	0.0316680	−	0.0548506i
$711$	4.20425	−	10.6782i	0.157672	−	0.400462i
$712$	−4.14521	+	2.39324i	−0.155348	+	0.0896903i
$713$	1.37726	+	2.38549i	0.0515789	+	0.0893373i
$714$		0			0
$715$	−12.3607	+	21.4094i	−0.462265	+	0.800667i
$716$		−	19.3193i		−	0.721997i
$717$	−17.8936	+	37.1050i	−0.668250	+	1.38571i
$718$	−12.1651			−0.453997
$719$	−14.7930	−	25.6223i	−0.551687	−	0.955549i	−0.998153	−	0.0607489i	$-0.980651\pi$
$719$	−14.7930	−	25.6223i	−0.551687	−	0.955549i	0.446466	−	0.894800i	$-0.352682\pi$
$720$	3.97782	−	10.1031i	0.148245	−	0.376519i
$721$		0			0
$722$	15.5657	−	8.98683i	0.579294	−	0.334455i
$723$	49.4843	−	3.68133i	1.84034	−	0.136910i
$724$	6.83569	−	3.94659i	0.254046	−	0.146674i
$725$	40.8666	−	23.5943i	1.51775	−	0.876271i
$726$	5.25506	−	10.8971i	0.195033	−	0.404430i
$727$	10.1244	−	5.84534i	0.375494	−	0.216792i	−0.300362	−	0.953825i	$-0.597107\pi$
$727$	10.1244	−	5.84534i	0.375494	−	0.216792i	0.675856	+	0.737034i	$0.263774\pi$
$728$		0			0
$729$	−24.3642	+	11.6356i	−0.902377	+	0.430948i
$730$	−7.62756	−	13.2113i	−0.282308	−	0.488973i
$731$	29.6298			1.09590
$732$	−25.4118	+	1.89049i	−0.939248	+	0.0698744i
$733$		−	33.0733i		−	1.22159i	−0.791789	−	0.610795i	$-0.790850\pi$
$733$		−	33.0733i		−	1.22159i	0.791789	−	0.610795i	$-0.209150\pi$
$734$	−1.81531	+	3.14420i	−0.0670042	+	0.116055i
$735$		0			0
$736$	−1.51400	−	2.62232i	−0.0558067	−	0.0966600i
$737$	−14.4318	+	8.33219i	−0.531601	+	0.306920i
$738$	−13.3830	+	10.6488i	−0.492634	+	0.391989i
$739$	−21.7528	+	37.6770i	−0.800190	+	1.38597i	0.119301	+	0.992858i	$0.461935\pi$
$739$	−21.7528	+	37.6770i	−0.800190	+	1.38597i	−0.919491	+	0.393111i	$0.871399\pi$
$740$	−13.2765	+	22.9957i	−0.488056	+	0.845337i
$741$	−0.443750	−	5.96486i	−0.0163016	−	0.219125i
$742$		0			0
$743$	18.0206	+	10.4042i	0.661112	+	0.381693i	0.792701	−	0.609611i	$-0.208674\pi$
$743$	18.0206	+	10.4042i	0.661112	+	0.381693i	−0.131589	+	0.991304i	$0.542008\pi$
$744$	−1.30232	+	0.886874i	−0.0477455	+	0.0325144i
$745$		−	40.7083i		−	1.49144i
$746$	−4.75648	−	2.74616i	−0.174147	−	0.100544i
$747$	14.9614	+	18.8028i	0.547408	+	0.687958i
$748$		−	12.3718i		−	0.452358i
$749$		0			0
$750$	8.43983	−	17.5012i	0.308179	−	0.639053i
$751$	−39.8984			−1.45591			−0.727957	−	0.685623i	$-0.759530\pi$
$751$	−39.8984			−1.45591			−0.727957	+	0.685623i	$0.759530\pi$
$752$	1.11511	+	1.93143i	0.0406638	+	0.0704318i
$753$	−1.41736	−	19.0521i	−0.0516515	−	0.694297i
$754$	−17.1992	−	9.92994i	−0.626357	−	0.361627i
$755$	−17.0969			−0.622219
$756$		0			0
$757$	7.45545			0.270973			0.135486	−	0.990779i	$-0.456740\pi$
$757$	7.45545			0.270973			0.135486	+	0.990779i	$0.456740\pi$
$758$	13.5065	+	7.79800i	0.490579	+	0.283236i
$759$	0.779665	+	10.4802i	0.0283001	+	0.380408i
$760$	1.83333	+	3.17542i	0.0665018	+	0.115185i
$761$	8.64924			0.313535			0.156767	−	0.987636i	$-0.449893\pi$
$761$	8.64924			0.313535			0.156767	+	0.987636i	$0.449893\pi$
$762$	13.4891	−	27.9716i	0.488658	−	1.01330i
$763$		0			0
$764$			13.3042i			0.481330i
$765$	24.5598	−	62.3782i	0.887961	−	2.25529i
$766$	8.16720	+	4.71534i	0.295093	+	0.170372i
$767$		−	30.6319i		−	1.10605i
$768$	1.43162	−	0.974922i	0.0516590	−	0.0351795i
$769$	20.4818	+	11.8252i	0.738592	+	0.426426i	0.821557	−	0.570126i	$-0.193106\pi$
$769$	20.4818	+	11.8252i	0.738592	+	0.426426i	−0.0829652	+	0.996552i	$0.526439\pi$
$770$		0			0
$771$	1.94005	+	26.0781i	0.0698693	+	0.939180i
$772$	3.26786	−	5.66011i	0.117613	−	0.203712i
$773$	23.2849	−	40.3307i	0.837501	−	1.45059i	−0.0544774	−	0.998515i	$-0.517349\pi$
$773$	23.2849	−	40.3307i	0.837501	−	1.45059i	0.891978	−	0.452079i	$-0.149317\pi$
$774$	−2.13030	−	14.2385i	−0.0765722	−	0.511792i
$775$	−6.38084	+	3.68398i	−0.229207	+	0.132333i
$776$	5.87944	+	10.1835i	0.211060	+	0.365566i
$777$		0			0
$778$	−3.21089	+	5.56142i	−0.115116	+	0.199387i
$779$		−	5.77546i		−	0.206927i
$780$	−21.3100	+	1.58533i	−0.763020	+	0.0567641i
$781$	−0.934344			−0.0334335
$782$	−9.34769	−	16.1907i	−0.334273	−	0.578977i
$783$	−20.5551	−	22.2256i	−0.734580	−	0.794279i
$784$		0			0
$785$	−9.62178	+	5.55513i	−0.343416	+	0.198271i
$786$	−13.0393	+	27.0389i	−0.465098	+	0.964446i
$787$	21.1657	−	12.2200i	0.754474	−	0.435596i	−0.0728341	−	0.997344i	$-0.523204\pi$
$787$	21.1657	−	12.2200i	0.754474	−	0.435596i	0.827308	+	0.561748i	$0.189871\pi$
$788$	3.84732	−	2.22125i	0.137055	−	0.0791288i
$789$	33.9212	−	2.52353i	1.20763	−	0.0898401i
$790$	11.9902	−	6.92255i	0.426592	−	0.246293i
$791$		0			0
$792$	−5.94521	+	0.889499i	−0.211254	+	0.0316070i
$793$	25.0748	+	43.4309i	0.890433	+	1.54228i
$794$	6.92531			0.245770
$795$	23.8363	−	49.4279i	0.845386	−	1.75303i
$796$		−	11.5108i		−	0.407991i
$797$	−24.9202	+	43.1631i	−0.882719	+	1.52891i	−0.0344128	+	0.999408i	$0.510956\pi$
$797$	−24.9202	+	43.1631i	−0.882719	+	1.52891i	−0.848306	+	0.529506i	$0.822377\pi$
$798$		0			0
$799$	6.88489	+	11.9250i	0.243570	+	0.421875i
$800$	7.01433	−	4.04972i	0.247994	−	0.143179i
$801$	8.94076	+	11.2364i	0.315906	+	0.397017i
$802$	−5.29343	+	9.16848i	−0.186917	+	0.323750i
$803$	−4.22291	+	7.31430i	−0.149023	+	0.258116i
$804$	−12.9746	−	6.25690i	−0.457578	−	0.220664i
$805$		0			0
$806$	2.68545	+	1.55045i	0.0945910	+	0.0546121i
$807$	0.766025	+	0.369410i	0.0269654	+	0.0130039i
$808$		−	12.8922i		−	0.453546i
$809$	10.6735	+	6.16237i	0.375262	+	0.216657i	0.675755	−	0.737127i	$-0.263818\pi$
$809$	10.6735	+	6.16237i	0.375262	+	0.216657i	−0.300493	+	0.953784i	$0.597151\pi$
$810$	−31.7413	−	7.31728i	−1.11528	−	0.257103i
$811$			24.8017i			0.870906i	0.900212	+	0.435453i	$0.143412\pi$
$811$			24.8017i			0.870906i	−0.900212	+	0.435453i	$0.856588\pi$
$812$		0			0
$813$	13.7258	+	20.1556i	0.481386	+	0.706888i
$814$	14.7008			0.515264
$815$	−5.20047	−	9.00748i	−0.182165	−	0.315518i
$816$	8.83906	−	6.01935i	0.309429	−	0.210719i
$817$	4.21041	+	2.43088i	0.147304	+	0.0850457i
$818$	8.92343			0.312000
$819$		0			0
$820$	−20.6333			−0.720547
$821$	31.3573	+	18.1041i	1.09438	+	0.631839i	0.934738	−	0.355336i	$-0.115634\pi$
$821$	31.3573	+	18.1041i	1.09438	+	0.631839i	0.159639	+	0.987175i	$0.448967\pi$
$822$	−0.00100647		0.000485362i	−3.51046e−5		1.69289e-5i
$823$	9.54093	+	16.5254i	0.332576	+	0.576038i	0.983016	−	0.183519i	$-0.0587489\pi$
$823$	9.54093	+	16.5254i	0.332576	+	0.576038i	−0.650440	+	0.759557i	$0.725416\pi$
$824$	10.7588			0.374801
$825$	−28.0331	+	2.08549i	−0.975986	+	0.0726075i
$826$		0			0
$827$			31.9013i			1.10932i	0.832079	+	0.554658i	$0.187151\pi$
$827$			31.9013i			1.10932i	−0.832079	+	0.554658i	$0.812849\pi$
$828$	−7.10829	+	5.65606i	−0.247030	+	0.196562i
$829$	−13.0645	−	7.54278i	−0.453748	−	0.261971i	0.255664	−	0.966766i	$-0.417706\pi$
$829$	−13.0645	−	7.54278i	−0.453748	−	0.261971i	−0.709412	+	0.704794i	$0.751039\pi$
$830$			28.9894i			1.00624i
$831$	3.94750	+	53.0620i	0.136937	+	1.84070i
$832$	−2.95206	−	1.70437i	−0.102344	−	0.0590885i
$833$		0			0
$834$	−14.4360	+	9.83082i	−0.499877	+	0.340413i
$835$	2.64397	−	4.57950i	0.0914985	−	0.158480i
$836$	1.01500	−	1.75804i	0.0351046	−	0.0608029i
$837$	3.20945	+	3.47027i	0.110935	+	0.119950i
$838$	−29.7781	+	17.1924i	−1.02867	+	0.593901i
$839$	−8.19860	−	14.2004i	−0.283047	−	0.490252i	0.689087	−	0.724679i	$-0.258012\pi$
$839$	−8.19860	−	14.2004i	−0.283047	−	0.490252i	−0.972134	+	0.234427i	$0.924679\pi$
$840$		0			0
$841$	2.47206	−	4.28173i	0.0852434	−	0.147646i
$842$			35.5680i			1.22575i
$843$	7.72582	+	11.3449i	0.266091	+	0.390740i
$844$	22.6011			0.777961
$845$	−2.49817	−	4.32696i	−0.0859397	−	0.148852i
$846$	5.23549	−	4.16587i	0.180000	−	0.143226i
$847$		0			0
$848$	7.58088	−	4.37683i	0.260329	−	0.150301i
$849$	11.2271	+	16.4863i	0.385312	+	0.565808i
$850$	43.3077	−	25.0037i	1.48544	−	0.857621i
$851$	19.2386	−	11.1074i	0.659492	−	0.380758i
$852$	−0.454594	−	0.667545i	−0.0155741	−	0.0228697i
$853$	16.5936	−	9.58030i	0.568153	−	0.328023i	−0.188258	−	0.982120i	$-0.560284\pi$
$853$	16.5936	−	9.58030i	0.568153	−	0.328023i	0.756411	+	0.654096i	$0.226951\pi$
$854$		0			0
$855$	8.60756	−	6.84903i	0.294372	−	0.234232i
$856$	−1.31983	−	2.28602i	−0.0451110	−	0.0781345i
$857$	−16.1145			−0.550460			−0.275230	−	0.961378i	$-0.588754\pi$
$857$	−16.1145			−0.550460			−0.275230	+	0.961378i	$0.588754\pi$
$858$	6.65913	+	9.77855i	0.227339	+	0.333834i
$859$			12.1048i			0.413009i	0.978446	+	0.206505i	$0.0662089\pi$
$859$			12.1048i			0.413009i	−0.978446	+	0.206505i	$0.933791\pi$
$860$	8.68453	−	15.0420i	0.296140	−	0.512929i
$861$		0			0
$862$	−15.4348	−	26.7338i	−0.525710	−	0.910556i
$863$	−32.2728	+	18.6327i	−1.09858	+	0.634265i	−0.935848	−	0.352405i	$-0.885364\pi$
$863$	−32.2728	+	18.6327i	−1.09858	+	0.634265i	−0.162732	+	0.986670i	$0.552031\pi$
$864$	−3.52808	−	3.81480i	−0.120028	−	0.129782i
$865$	5.55712	−	9.62522i	0.188948	−	0.327267i
$866$	11.6232	−	20.1319i	0.394971	−	0.684110i
$867$	30.2365	−	20.5909i	1.02689	−	0.699303i
$868$		0			0
$869$	−6.63824	−	3.83259i	−0.225187	−	0.130012i
$870$	−2.70962	−	36.4226i	−0.0918648	−	1.23484i
$871$			28.3485i			0.960553i
$872$	−7.82484	−	4.51768i	−0.264983	−	0.152988i
$873$	27.6043	−	21.9647i	0.934262	−	0.743392i
$874$		−	3.06760i		−	0.103763i
$875$		0			0
$876$	−7.28033	+	0.541613i	−0.245980	+	0.0182994i
$877$	−9.70948			−0.327866			−0.163933	−	0.986471i	$-0.552418\pi$
$877$	−9.70948			−0.327866			−0.163933	+	0.986471i	$0.552418\pi$
$878$	11.1364	+	19.2887i	0.375834	+	0.650963i
$879$	−7.82983	−	3.77588i	−0.264094	−	0.127357i
$880$	−6.28073	−	3.62618i	−0.211723	−	0.122239i
$881$	−2.63241			−0.0886881			−0.0443440	−	0.999016i	$-0.514120\pi$
$881$	−2.63241			−0.0886881			−0.0443440	+	0.999016i	$0.514120\pi$
$882$		0			0
$883$	−36.3181			−1.22220			−0.611101	−	0.791553i	$-0.709273\pi$
$883$	−36.3181			−1.22220			−0.611101	+	0.791553i	$0.709273\pi$
$884$	−18.2265	−	10.5231i	−0.613025	−	0.353930i
$885$	46.5621	−	31.7085i	1.56517	−	1.06587i
$886$	−8.99259	−	15.5756i	−0.302112	−	0.523273i
$887$	16.3642			0.549455			0.274728	−	0.961522i	$-0.411412\pi$
$887$	16.3642			0.549455			0.274728	+	0.961522i	$0.411412\pi$
$888$	7.15251	+	10.5031i	0.240023	+	0.352459i
$889$		0			0
$890$			17.3238i			0.580694i
$891$	5.27824	+	17.2444i	0.176828	+	0.577711i
$892$	16.2994	+	9.41045i	0.545744	+	0.315085i
$893$			2.25939i			0.0756076i
$894$	−17.5474	−	8.46213i	−0.586874	−	0.283016i
$895$	−60.5549	−	34.9614i	−2.02413	−	1.16863i
$896$		0			0
$897$	16.1030	+	7.76555i	0.537663	+	0.259284i
$898$	4.72182	−	8.17843i	0.157569	−	0.272918i
$899$	−2.64999	+	4.58992i	−0.0883822	+	0.153082i
$900$	−15.1291	−	19.0136i	−0.504305	−	0.633788i
$901$	46.8058	−	27.0233i	1.55933	−	0.900277i
$902$	5.71171	+	9.89297i	0.190179	+	0.329400i
$903$		0			0
$904$	−0.845306	+	1.46411i	−0.0281145	+	0.0486957i
$905$		−	28.5679i		−	0.949629i
$906$	−3.55397	+	7.36966i	−0.118073	+	0.244840i
$907$	10.8333			0.359714			0.179857	−	0.983693i	$-0.442436\pi$
$907$	10.8333			0.359714			0.179857	+	0.983693i	$0.442436\pi$
$908$	7.30665	+	12.6555i	0.242480	+	0.419987i
$909$	−38.2509	+	5.72294i	−1.26870	+	0.189818i
$910$		0			0
$911$	36.8512	−	21.2760i	1.22093	−	0.704907i	0.255817	−	0.966725i	$-0.417655\pi$
$911$	36.8512	−	21.2760i	1.22093	−	0.704907i	0.965117	+	0.261818i	$0.0843221\pi$
$912$	1.74987	−	0.130180i	0.0579440	−	0.00431069i
$913$	13.8994	−	8.02482i	0.460003	−	0.265583i
$914$	−1.59739	+	0.922251i	−0.0528368	+	0.0305053i
$915$	−40.0611	+	83.0724i	−1.32438	+	2.74629i
$916$	−2.06044	+	1.18959i	−0.0680788	+	0.0393053i
$917$		0			0
$918$	−21.7830	−	23.5533i	−0.718946	−	0.777373i
$919$	−12.9697	−	22.4641i	−0.427829	−	0.741022i	0.568851	−	0.822441i	$-0.307388\pi$
$919$	−12.9697	−	22.4641i	−0.427829	−	0.741022i	−0.996680	+	0.0814187i	$0.974055\pi$
$920$	−10.9593			−0.361316
$921$	−30.2807	+	2.25271i	−0.997785	+	0.0742292i
$922$			36.3739i			1.19791i
$923$	−0.794727	+	1.37651i	−0.0261588	+	0.0453083i
$924$		0			0
$925$	29.7108	+	51.4606i	0.976884	+	1.69201i
$926$	27.6834	−	15.9830i	0.909733	−	0.525234i
$927$	−4.77591	−	31.9211i	−0.156861	−	1.04843i
$928$	2.91308	−	5.04560i	0.0956265	−	0.165630i
$929$	−23.4456	+	40.6089i	−0.769224	+	1.33234i	0.168760	+	0.985657i	$0.446024\pi$
$929$	−23.4456	+	40.6089i	−0.769224	+	1.33234i	−0.937984	+	0.346678i	$0.887310\pi$
$930$	0.423076	+	5.68697i	0.0138732	+	0.186483i
$931$		0			0
$932$	−9.03470	−	5.21619i	−0.295942	−	0.170862i
$933$	24.7601	−	16.8615i	0.810608	−	0.552019i
$934$		−	24.4411i		−	0.799738i
$935$	−38.7784	−	22.3887i	−1.26819	−	0.732189i
$936$	−3.74639	+	9.51527i	−0.122455	+	0.311016i
$937$			0.209357i			0.00683939i	0.999994	+	0.00341969i	$0.00108852\pi$
$937$			0.209357i			0.00683939i	−0.999994	+	0.00341969i	$0.998911\pi$
$938$		0			0
$939$	6.76742	−	14.0332i	0.220846	−	0.457956i
$940$	8.07186			0.263275
$941$	0.388565	+	0.673014i	0.0126669	+	0.0219396i	0.872289	−	0.488990i	$-0.162635\pi$
$941$	0.388565	+	0.673014i	0.0126669	+	0.0219396i	−0.859622	+	0.510930i	$0.829301\pi$
$942$	0.394456	+	5.30225i	0.0128521	+	0.172757i
$943$	14.9496	+	8.63113i	0.486825	+	0.281068i
$944$	8.98627			0.292478
$945$		0			0
$946$	−9.61619			−0.312649
$947$	43.1233	+	24.8972i	1.40132	+	0.809052i	0.994528	−	0.104470i	$-0.0333145\pi$
$947$	43.1233	+	24.8972i	1.40132	+	0.809052i	0.406791	+	0.913521i	$0.366648\pi$
$948$	−0.491552	−	6.60741i	−0.0159649	−	0.214599i
$949$	7.18378	+	12.4427i	0.233196	+	0.403906i
$950$	8.20539			0.266218
$951$	5.05612	−	10.4846i	0.163956	−	0.339986i
$952$		0			0
$953$			41.4104i			1.34141i	0.741722	+	0.670707i	$0.234009\pi$
$953$			41.4104i			1.34141i	−0.741722	+	0.670707i	$0.765991\pi$
$954$	−16.3511	−	20.5494i	−0.529388	−	0.665311i
$955$	41.7010	+	24.0761i	1.34941	+	0.779084i
$956$			23.7835i			0.769213i
$957$	−16.7133	+	11.3817i	−0.540264	+	0.367917i
$958$	9.49220	+	5.48032i	0.306679	+	0.177061i
$959$		0			0
$960$	−0.465079	−	6.25156i	−0.0150103	−	0.201768i
$961$	−15.0862	+	26.1301i	−0.486653	+	0.842907i
$962$	12.5041	−	21.6578i	0.403149	−	0.698274i
$963$	−6.19668	+	4.93069i	−0.199685	+	0.158889i
$964$	24.8105	−	14.3243i	0.799092	−	0.461356i
$965$	−11.8274	−	20.4857i	−0.380739	−	0.659459i
$966$		0			0
$967$	22.8028	−	39.4956i	0.733289	−	1.27009i	−0.222181	−	0.975005i	$-0.571318\pi$
$967$	22.8028	−	39.4956i	0.733289	−	1.27009i	0.955470	−	0.295088i	$-0.0953491\pi$
$968$		−	6.98481i		−	0.224500i
$969$	10.8040	−	0.803754i	0.347075	−	0.0258203i
$970$	42.5591			1.36649
$971$	−4.36733	−	7.56444i	−0.140154	−	0.242754i	0.787400	−	0.616442i	$-0.211427\pi$
$971$	−4.36733	−	7.56444i	−0.140154	−	0.242754i	−0.927555	+	0.373688i	$0.878093\pi$
$972$	−9.75228	+	12.1611i	−0.312804	+	0.390068i
$973$		0			0
$974$	29.1136	−	16.8087i	0.932860	−	0.538587i
$975$	−20.7717	+	43.0731i	−0.665228	+	1.37944i
$976$	−12.7410	+	7.35603i	−0.407830	+	0.235461i
$977$	−12.9058	+	7.45114i	−0.412892	+	0.238383i	−0.692031	−	0.721867i	$-0.743284\pi$
$977$	−12.9058	+	7.45114i	−0.412892	+	0.238383i	0.279140	+	0.960250i	$0.409951\pi$
$978$	−4.96373	+	0.369272i	−0.158723	+	0.0118080i
$979$	8.30615	−	4.79556i	0.265466	−	0.153267i
$980$		0			0
$981$	−9.93033	+	25.2216i	−0.317051	+	0.805262i
$982$	11.3676	+	19.6893i	0.362756	+	0.628312i
$983$	3.06917			0.0978912			0.0489456	−	0.998801i	$-0.484414\pi$
$983$	3.06917			0.0978912			0.0489456	+	0.998801i	$0.484414\pi$
$984$	−4.28910	+	8.89405i	−0.136731	+	0.283532i
$985$		−	16.0788i		−	0.512314i
$986$	17.9859	−	31.1525i	0.572787	−	0.992096i
$987$		0			0
$988$	−1.72667	−	2.99067i	−0.0549325	−	0.0951460i
$989$	−12.5845	+	7.26565i	−0.400163	+	0.231034i
$990$	−7.97074	+	20.2445i	−0.253327	+	0.643412i
$991$	27.9075	−	48.3372i	0.886510	−	1.53548i	0.0425375	−	0.999095i	$-0.486456\pi$
$991$	27.9075	−	48.3372i	0.886510	−	1.53548i	0.843973	−	0.536386i	$-0.180211\pi$
$992$	−0.454844	+	0.787812i	−0.0144413	+	0.0250131i
$993$	29.2904	+	14.1251i	0.929502	+	0.448246i
$994$		0			0
$995$	−36.0798	−	20.8307i	−1.14381	−	0.660377i
$996$	12.4959	+	6.02608i	0.395949	+	0.190944i
$997$		−	6.12692i		−	0.194042i	−0.995282	−	0.0970208i	$-0.969069\pi$
$997$		−	6.12692i		−	0.194042i	0.995282	−	0.0970208i	$-0.0309313\pi$
$998$	−16.9079	−	9.76175i	−0.535209	−	0.309003i
$999$	27.9872	−	25.8837i	0.885477	−	0.818924i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.t.a.815.3		16
3.2	odd	2		2646.2.t.b.2285.5		16
7.2	even	3		126.2.l.a.5.5	✓	16
7.3	odd	6		882.2.m.a.293.6		16
7.4	even	3		882.2.m.b.293.7		16
7.5	odd	6		882.2.l.b.509.8		16
7.6	odd	2		126.2.t.a.59.2	yes	16
9.2	odd	6		882.2.l.b.227.4		16
9.7	even	3		2646.2.l.a.521.5		16
21.2	odd	6		378.2.l.a.341.4		16
21.5	even	6		2646.2.l.a.1097.1		16
21.11	odd	6		2646.2.m.b.881.4		16
21.17	even	6		2646.2.m.a.881.1		16
21.20	even	2		378.2.t.a.17.8		16
28.23	odd	6		1008.2.ca.c.257.8		16
28.27	even	2		1008.2.df.c.689.5		16
63.2	odd	6		126.2.t.a.47.2	yes	16
63.11	odd	6		882.2.m.a.587.6		16
63.13	odd	6		1134.2.k.b.647.8		16
63.16	even	3		378.2.t.a.89.8		16
63.20	even	6		126.2.l.a.101.1	yes	16
63.23	odd	6		1134.2.k.b.971.8		16
63.25	even	3		2646.2.m.a.1763.1		16
63.34	odd	6		378.2.l.a.143.8		16
63.38	even	6		882.2.m.b.587.7		16
63.41	even	6		1134.2.k.a.647.1		16
63.47	even	6	inner	882.2.t.a.803.3		16
63.52	odd	6		2646.2.m.b.1763.4		16
63.58	even	3		1134.2.k.a.971.1		16
63.61	odd	6		2646.2.t.b.1979.5		16
84.23	even	6		3024.2.ca.c.2609.7		16
84.83	odd	2		3024.2.df.c.17.7		16
252.79	odd	6		3024.2.df.c.1601.7		16
252.83	odd	6		1008.2.ca.c.353.8		16
252.191	even	6		1008.2.df.c.929.5		16
252.223	even	6		3024.2.ca.c.2033.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.5	✓	16	7.2	even	3
126.2.l.a.101.1	yes	16	63.20	even	6
126.2.t.a.47.2	yes	16	63.2	odd	6
126.2.t.a.59.2	yes	16	7.6	odd	2
378.2.l.a.143.8		16	63.34	odd	6
378.2.l.a.341.4		16	21.2	odd	6
378.2.t.a.17.8		16	21.20	even	2
378.2.t.a.89.8		16	63.16	even	3
882.2.l.b.227.4		16	9.2	odd	6
882.2.l.b.509.8		16	7.5	odd	6
882.2.m.a.293.6		16	7.3	odd	6
882.2.m.a.587.6		16	63.11	odd	6
882.2.m.b.293.7		16	7.4	even	3
882.2.m.b.587.7		16	63.38	even	6
882.2.t.a.803.3		16	63.47	even	6	inner
882.2.t.a.815.3		16	1.1	even	1	trivial
1008.2.ca.c.257.8		16	28.23	odd	6
1008.2.ca.c.353.8		16	252.83	odd	6
1008.2.df.c.689.5		16	28.27	even	2
1008.2.df.c.929.5		16	252.191	even	6
1134.2.k.a.647.1		16	63.41	even	6
1134.2.k.a.971.1		16	63.58	even	3
1134.2.k.b.647.8		16	63.13	odd	6
1134.2.k.b.971.8		16	63.23	odd	6
2646.2.l.a.521.5		16	9.7	even	3
2646.2.l.a.1097.1		16	21.5	even	6
2646.2.m.a.881.1		16	21.17	even	6
2646.2.m.a.1763.1		16	63.25	even	3
2646.2.m.b.881.4		16	21.11	odd	6
2646.2.m.b.1763.4		16	63.52	odd	6
2646.2.t.b.1979.5		16	63.61	odd	6
2646.2.t.b.2285.5		16	3.2	odd	2
3024.2.ca.c.2033.7		16	252.223	even	6
3024.2.ca.c.2609.7		16	84.23	even	6
3024.2.df.c.17.7		16	84.83	odd	2
3024.2.df.c.1601.7		16	252.79	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.128499 + 1.72728i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.61932 q^{5} +(0.752355 - 1.56012i) q^{6} -1.00000i q^{8} +(-2.96698 + 0.443907i) q^{9} +(-3.13442 - 1.80966i) q^{10} +2.00379i q^{11} +(-1.43162 + 0.974922i) q^{12} +(2.95206 + 1.70437i) q^{13} +(0.465079 + 6.25156i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.08709 + 5.34700i) q^{17} +(2.79143 + 1.09905i) q^{18} +(-0.877353 + 0.506540i) q^{19} +(1.80966 + 3.13442i) q^{20} +(1.00190 - 1.73534i) q^{22} -3.02799i q^{23} +(1.72728 - 0.128499i) q^{24} +8.09945 q^{25} +(-1.70437 - 2.95206i) q^{26} +(-1.14800 - 5.06775i) q^{27} +(5.04560 - 2.91308i) q^{29} +(2.72301 - 5.64655i) q^{30} +(-0.787812 + 0.454844i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-3.46111 + 0.257486i) q^{33} +(5.34700 - 3.08709i) q^{34} +(-1.86792 - 2.34752i) q^{36} +(3.66825 + 6.35359i) q^{37} +1.01308 q^{38} +(-2.56459 + 5.31804i) q^{39} -3.61932i q^{40} +(-2.85045 + 4.93712i) q^{41} +(-2.39949 - 4.15605i) q^{43} +(-1.73534 + 1.00190i) q^{44} +(-10.7384 + 1.60664i) q^{45} +(-1.51400 + 2.62232i) q^{46} +(1.11511 - 1.93143i) q^{47} +(-1.56012 - 0.752355i) q^{48} +(-7.01433 - 4.04972i) q^{50} +(-9.63244 - 4.64518i) q^{51} +3.40874i q^{52} +(-7.58088 - 4.37683i) q^{53} +(-1.53967 + 4.96280i) q^{54} +7.25237i q^{55} +(-0.987674 - 1.45034i) q^{57} -5.82616 q^{58} +(-4.49313 - 7.78233i) q^{59} +(-5.18147 + 3.52855i) q^{60} +(12.7410 + 7.35603i) q^{61} +0.909687 q^{62} -1.00000 q^{64} +(10.6844 + 6.16866i) q^{65} +(3.12615 + 1.50757i) q^{66} +(4.15821 + 7.20222i) q^{67} -6.17418 q^{68} +(5.23019 - 0.389094i) q^{69} +0.466287i q^{71} +(0.443907 + 2.96698i) q^{72} +(3.65022 + 2.10746i) q^{73} -7.33650i q^{74} +(1.04077 + 13.9900i) q^{75} +(-0.877353 - 0.506540i) q^{76} +(4.88001 - 3.32326i) q^{78} +(-1.91267 + 3.31284i) q^{79} +(-1.80966 + 3.13442i) q^{80} +(8.60589 - 2.63412i) q^{81} +(4.93712 - 2.85045i) q^{82} +(-4.00481 - 6.93654i) q^{83} +(-11.1732 + 19.3525i) q^{85} +4.79899i q^{86} +(5.68005 + 8.34083i) q^{87} +2.00379 q^{88} +(-2.39324 - 4.14521i) q^{89} +(10.1031 + 3.97782i) q^{90} +(2.62232 - 1.51400i) q^{92} +(-0.886874 - 1.30232i) q^{93} +(-1.93143 + 1.11511i) q^{94} +(-3.17542 + 1.83333i) q^{95} +(0.974922 + 1.43162i) q^{96} +(-10.1835 + 5.87944i) q^{97} +(-0.889499 - 5.94521i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 6 q^{9} + 6 q^{13} - 18 q^{15} - 8 q^{16} - 18 q^{17} + 12 q^{18} + 6 q^{24} + 16 q^{25} + 12 q^{26} + 36 q^{27} + 6 q^{29} - 18 q^{30} - 6 q^{31} - 18 q^{33} - 2 q^{37} - 30 q^{39} - 6 q^{41}+ \cdots + 18 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 - 6 * q^9 + 6 * q^13 - 18 * q^15 - 8 * q^16 - 18 * q^17 + 12 * q^18 + 6 * q^24 + 16 * q^25 + 12 * q^26 + 36 * q^27 + 6 * q^29 - 18 * q^30 - 6 * q^31 - 18 * q^33 - 2 * q^37 - 30 * q^39 - 6 * q^41 - 2 * q^43 + 12 * q^44 - 12 * q^45 + 6 * q^46 + 18 * q^47 - 12 * q^50 + 36 * q^53 - 18 * q^54 + 6 * q^57 - 12 * q^58 - 30 * q^59 - 6 * q^60 + 60 * q^61 + 36 * q^62 - 16 * q^64 + 42 * q^65 - 48 * q^66 + 14 * q^67 - 36 * q^68 - 42 * q^69 - 30 * q^75 - 16 * q^79 + 54 * q^81 - 12 * q^85 + 48 * q^87 - 24 * q^89 + 18 * q^90 + 6 * q^92 + 30 * q^93 - 66 * q^95 + 6 * q^96 + 6 * q^97 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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