LMFDB - Embedded newform 588.2.n.h.275.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(263,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.263"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			275.11
Character	$\chi$	$=$	588.275
Dual form			588.2.n.h.263.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.38541 + 0.283947i) q^{2} +(-1.62729 - 0.593231i) q^{3} +(1.83875 + 0.786769i) q^{4} +(-0.695526 - 0.401562i) q^{5} +(-2.08603 - 1.28394i) q^{6} +(2.32403 + 1.61211i) q^{8} +(2.29615 + 1.93072i) q^{9} +(-0.849569 - 0.753822i) q^{10} +(-1.17273 - 2.03122i) q^{11} +(-2.52544 - 2.37111i) q^{12} +5.26858 q^{13} +(0.893604 + 1.06607i) q^{15} +(2.76199 + 2.89334i) q^{16} +(1.02661 - 0.592715i) q^{17} +(2.63290 + 3.32683i) q^{18} +(6.16982 + 3.56215i) q^{19} +(-0.962960 - 1.28559i) q^{20} +(-1.04795 - 3.14708i) q^{22} +(3.94356 - 6.83044i) q^{23} +(-2.82552 - 4.00206i) q^{24} +(-2.17750 - 3.77153i) q^{25} +(7.29917 + 1.49600i) q^{26} +(-2.59115 - 4.50399i) q^{27} +4.23132i q^{29} +(0.935305 + 1.73068i) q^{30} +(-4.24264 + 2.44949i) q^{31} +(3.00494 + 4.79274i) q^{32} +(0.703383 + 4.00109i) q^{33} +(1.59058 - 0.529652i) q^{34} +(2.70302 + 5.35665i) q^{36} +(-0.523976 + 0.907554i) q^{37} +(7.53630 + 6.68696i) q^{38} +(-8.57351 - 3.12549i) q^{39} +(-0.969059 - 2.05450i) q^{40} -7.16942i q^{41} +7.94315i q^{43} +(-0.558245 - 4.65757i) q^{44} +(-0.821730 - 2.26491i) q^{45} +(7.40294 - 8.34323i) q^{46} +(-3.04954 + 5.28195i) q^{47} +(-2.77814 - 6.34681i) q^{48} +(-1.94582 - 5.84343i) q^{50} +(-2.02221 + 0.355501i) q^{51} +(9.68759 + 4.14516i) q^{52} +(7.55175 - 4.36001i) q^{53} +(-2.31091 - 6.97565i) q^{54} +1.88369i q^{55} +(-7.92692 - 9.45679i) q^{57} +(-1.20147 + 5.86214i) q^{58} +(-0.331087 - 0.573459i) q^{59} +(0.804364 + 2.66329i) q^{60} +(-0.479062 + 0.829760i) q^{61} +(-6.57334 + 2.18887i) q^{62} +(2.80221 + 7.49317i) q^{64} +(-3.66443 - 2.11566i) q^{65} +(-0.161621 + 5.74289i) q^{66} +(-7.29738 + 4.21314i) q^{67} +(2.35401 - 0.282146i) q^{68} +(-10.4693 + 8.77567i) q^{69} -9.67432 q^{71} +(2.22379 + 8.18870i) q^{72} +(0.707107 + 1.22474i) q^{73} +(-0.983622 + 1.10856i) q^{74} +(1.30603 + 7.42914i) q^{75} +(8.54216 + 11.4041i) q^{76} +(-10.9904 - 6.76452i) q^{78} +(-6.00000 - 3.46410i) q^{79} +(-0.759178 - 3.12150i) q^{80} +(1.54464 + 8.86646i) q^{81} +(2.03574 - 9.93263i) q^{82} +5.18229 q^{83} -0.952047 q^{85} +(-2.25543 + 11.0046i) q^{86} +(2.51015 - 6.88559i) q^{87} +(0.549103 - 6.61118i) q^{88} +(-14.1733 - 8.18296i) q^{89} +(-0.495321 - 3.37117i) q^{90} +(12.6252 - 9.45679i) q^{92} +(8.35713 - 1.46917i) q^{93} +(-5.72467 + 6.45179i) q^{94} +(-2.86085 - 4.95513i) q^{95} +(-2.04672 - 9.58180i) q^{96} -4.37827 q^{97} +(1.22896 - 6.92820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4} + 60 q^{16} + 24 q^{18} + 12 q^{25} + 36 q^{30} + 12 q^{36} - 96 q^{39} + 24 q^{46} + 12 q^{51} - 24 q^{57} + 48 q^{58} + 12 q^{60} - 48 q^{64} - 48 q^{67} - 36 q^{72} - 24 q^{78} - 144 q^{79}+ \cdots - 24 q^{93}+O(q^{100}) $ 24 * q + 12 * q^4 + 60 * q^16 + 24 * q^18 + 12 * q^25 + 36 * q^30 + 12 * q^36 - 96 * q^39 + 24 * q^46 + 12 * q^51 - 24 * q^57 + 48 * q^58 + 12 * q^60 - 48 * q^64 - 48 * q^67 - 36 * q^72 - 24 * q^78 - 144 * q^79 + 12 * q^81 - 48 * q^85 + 192 * q^88 - 24 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.38541	+	0.283947i	0.979636	+	0.200781i
$2$	1.38541	+	0.283947i	0.979636	+	0.200781i
$3$	−1.62729	−	0.593231i	−0.939517	−	0.342502i
$3$	−1.62729	−	0.593231i	−0.939517	−	0.342502i
$4$	1.83875	+	0.786769i	0.919374	+	0.393385i
$5$	−0.695526	−	0.401562i	−0.311049	−	0.179584i	0.336347	−	0.941738i	$-0.390808\pi$
$5$	−0.695526	−	0.401562i	−0.311049	−	0.179584i	−0.647396	+	0.762154i	$0.724142\pi$
$6$	−2.08603	−	1.28394i	−0.851617	−	0.524165i
$7$		0			0
$7$		0			0
$8$	2.32403	+	1.61211i	0.821668	+	0.569967i
$9$	2.29615	+	1.93072i	0.765384	+	0.643573i
$10$	−0.849569	−	0.753822i	−0.268657	−	0.238380i
$11$	−1.17273	−	2.03122i	−0.353590	−	0.612436i	0.633285	−	0.773918i	$-0.281706\pi$
$11$	−1.17273	−	2.03122i	−0.353590	−	0.612436i	−0.986876	+	0.161482i	$0.948373\pi$
$12$	−2.52544	−	2.37111i	−0.729032	−	0.684479i
$13$	5.26858			1.46124			0.730621	−	0.682784i	$-0.239231\pi$
$13$	5.26858			1.46124			0.730621	+	0.682784i	$0.239231\pi$
$14$		0			0
$15$	0.893604	+	1.06607i	0.230727	+	0.275257i
$16$	2.76199	+	2.89334i	0.690497	+	0.723335i
$17$	1.02661	−	0.592715i	0.248990	−	0.143754i	−0.370312	−	0.928908i	$-0.620749\pi$
$17$	1.02661	−	0.592715i	0.248990	−	0.143754i	0.619302	+	0.785153i	$0.287416\pi$
$18$	2.63290	+	3.32683i	0.620581	+	0.784142i
$19$	6.16982	+	3.56215i	1.41545	+	0.817213i	0.995895	−	0.0905147i	$-0.0288512\pi$
$19$	6.16982	+	3.56215i	1.41545	+	0.817213i	0.419560	+	0.907728i	$0.362185\pi$
$20$	−0.962960	−	1.28559i	−0.215324	−	0.287467i
$21$		0			0
$22$	−1.04795	−	3.14708i	−0.223424	−	0.670959i
$23$	3.94356	−	6.83044i	0.822288	−	1.42425i	−0.0816860	−	0.996658i	$-0.526030\pi$
$23$	3.94356	−	6.83044i	0.822288	−	1.42425i	0.903974	−	0.427587i	$-0.140636\pi$
$24$	−2.82552	−	4.00206i	−0.576756	−	0.816916i
$25$	−2.17750	−	3.77153i	−0.435499	−	0.754307i
$26$	7.29917	+	1.49600i	1.43148	+	0.293389i
$27$	−2.59115	−	4.50399i	−0.498666	−	0.866794i
$28$		0			0
$29$			4.23132i			0.785737i	0.919595	+	0.392868i	$0.128517\pi$
$29$			4.23132i			0.785737i	−0.919595	+	0.392868i	$0.871483\pi$
$30$	0.935305	+	1.73068i	0.170763	+	0.315977i
$31$	−4.24264	+	2.44949i	−0.762001	+	0.439941i	−0.830014	−	0.557743i	$-0.811667\pi$
$31$	−4.24264	+	2.44949i	−0.762001	+	0.439941i	0.0680129	+	0.997684i	$0.478334\pi$
$32$	3.00494	+	4.79274i	0.531204	+	0.847244i
$33$	0.703383	+	4.00109i	0.122443	+	0.696500i
$34$	1.59058	−	0.529652i	0.272783	−	0.0908346i
$35$		0			0
$36$	2.70302	+	5.35665i	0.450503	+	0.892775i
$37$	−0.523976	+	0.907554i	−0.0861412	+	0.149201i	−0.905877	−	0.423541i	$-0.860787\pi$
$37$	−0.523976	+	0.907554i	−0.0861412	+	0.149201i	0.819736	+	0.572742i	$0.194120\pi$
$38$	7.53630	+	6.68696i	1.22255	+	1.08477i
$39$	−8.57351	−	3.12549i	−1.37286	−	0.500478i
$40$	−0.969059	−	2.05450i	−0.153222	−	0.324846i
$41$		−	7.16942i		−	1.11968i	−0.828602	−	0.559838i	$-0.810863\pi$
$41$		−	7.16942i		−	1.11968i	0.828602	−	0.559838i	$-0.189137\pi$
$42$		0			0
$43$			7.94315i			1.21132i	0.795724	+	0.605659i	$0.207091\pi$
$43$			7.94315i			1.21132i	−0.795724	+	0.605659i	$0.792909\pi$
$44$	−0.558245	−	4.65757i	−0.0841587	−	0.702155i
$45$	−0.821730	−	2.26491i	−0.122496	−	0.337633i
$46$	7.40294	−	8.34323i	1.09150	−	1.23014i
$47$	−3.04954	+	5.28195i	−0.444821	+	0.770452i	−0.998040	−	0.0625838i	$-0.980066\pi$
$47$	−3.04954	+	5.28195i	−0.444821	+	0.770452i	0.553219	+	0.833036i	$0.313399\pi$
$48$	−2.77814	−	6.34681i	−0.400990	−	0.916083i
$49$		0			0
$50$	−1.94582	−	5.84343i	−0.275180	−	0.826386i
$51$	−2.02221	+	0.355501i	−0.283167	+	0.0497801i
$52$	9.68759	+	4.14516i	1.34343	+	0.574830i
$53$	7.55175	−	4.36001i	1.03731	−	0.598893i	0.118242	−	0.992985i	$-0.462274\pi$
$53$	7.55175	−	4.36001i	1.03731	−	0.598893i	0.919071	+	0.394092i	$0.128941\pi$
$54$	−2.31091	−	6.97565i	−0.314476	−	0.949266i
$55$			1.88369i			0.253997i
$56$		0			0
$57$	−7.92692	−	9.45679i	−1.04995	−	1.25258i
$58$	−1.20147	+	5.86214i	−0.157761	+	0.769736i
$59$	−0.331087	−	0.573459i	−0.0431038	−	0.0746580i	0.843669	−	0.536864i	$-0.180391\pi$
$59$	−0.331087	−	0.573459i	−0.0431038	−	0.0746580i	−0.886772	+	0.462206i	$0.847058\pi$
$60$	0.804364	+	2.66329i	0.103843	+	0.343829i
$61$	−0.479062	+	0.829760i	−0.0613376	+	0.106240i	−0.895064	−	0.445939i	$-0.852870\pi$
$61$	−0.479062	+	0.829760i	−0.0613376	+	0.106240i	0.833726	+	0.552178i	$0.186203\pi$
$62$	−6.57334	+	2.18887i	−0.834815	+	0.277987i
$63$		0			0
$64$	2.80221	+	7.49317i	0.350276	+	0.936647i
$65$	−3.66443	−	2.11566i	−0.454517	−	0.262416i
$66$	−0.161621	+	5.74289i	−0.0198941	+	0.706901i
$67$	−7.29738	+	4.21314i	−0.891517	+	0.514717i	−0.874438	−	0.485137i	$-0.838770\pi$
$67$	−7.29738	+	4.21314i	−0.891517	+	0.514717i	−0.0170783	+	0.999854i	$0.505436\pi$
$68$	2.35401	−	0.282146i	0.285466	−	0.0342153i
$69$	−10.4693	+	8.77567i	−1.26036	+	1.05647i
$70$		0			0
$71$	−9.67432			−1.14813			−0.574065	−	0.818810i	$-0.694634\pi$
$71$	−9.67432			−1.14813			−0.574065	+	0.818810i	$0.694634\pi$
$72$	2.22379	+	8.18870i	0.262076	+	0.965047i
$73$	0.707107	+	1.22474i	0.0827606	+	0.143346i	0.904435	−	0.426612i	$-0.140293\pi$
$73$	0.707107	+	1.22474i	0.0827606	+	0.143346i	−0.821674	+	0.569958i	$0.806960\pi$
$74$	−0.983622	+	1.10856i	−0.114344	+	0.128867i
$75$	1.30603	+	7.42914i	0.150807	+	0.857843i
$76$	8.54216	+	11.4041i	0.979853	+	1.30814i
$77$		0			0
$78$	−10.9904	−	6.76452i	−1.24442	−	0.765931i
$79$	−6.00000	−	3.46410i	−0.675053	−	0.389742i	0.122936	−	0.992415i	$-0.460769\pi$
$79$	−6.00000	−	3.46410i	−0.675053	−	0.389742i	−0.797988	+	0.602673i	$0.794102\pi$
$80$	−0.759178	−	3.12150i	−0.0848787	−	0.348995i
$81$	1.54464	+	8.86646i	0.171626	+	0.985162i
$82$	2.03574	−	9.93263i	0.224810	−	1.09688i
$83$	5.18229			0.568830			0.284415	−	0.958701i	$-0.408201\pi$
$83$	5.18229			0.568830			0.284415	+	0.958701i	$0.408201\pi$
$84$		0			0
$85$	−0.952047			−0.103264
$86$	−2.25543	+	11.0046i	−0.243210	+	1.18665i
$87$	2.51015	−	6.88559i	0.269117	−	0.738213i
$88$	0.549103	−	6.61118i	0.0585345	−	0.704754i
$89$	−14.1733	−	8.18296i	−1.50237	−	0.867392i	−0.999996	−	0.00273917i	$-0.999128\pi$
$89$	−14.1733	−	8.18296i	−1.50237	−	0.867392i	−0.502370	−	0.864653i	$-0.667539\pi$
$90$	−0.495321	−	3.37117i	−0.0522114	−	0.355353i
$91$		0			0
$92$	12.6252	−	9.45679i	1.31627	−	0.985938i
$93$	8.35713	−	1.46917i	0.866594	−	0.152345i
$94$	−5.72467	+	6.45179i	−0.590455	+	0.665451i
$95$	−2.86085	−	4.95513i	−0.293517	−	0.508386i
$96$	−2.04672	−	9.58180i	−0.208892	−	0.977939i
$97$	−4.37827			−0.444546			−0.222273	−	0.974984i	$-0.571348\pi$
$97$	−4.37827			−0.444546			−0.222273	+	0.974984i	$0.571348\pi$
$98$		0			0
$99$	1.22896	−	6.92820i	0.123515	−	0.696311i
$100$	−1.03654	−	8.64809i	−0.103654	−	0.864809i
$101$	−7.26887	+	4.19668i	−0.723279	+	0.417586i	−0.815959	−	0.578110i	$-0.803790\pi$
$101$	−7.26887	+	4.19668i	−0.723279	+	0.417586i	0.0926791	+	0.995696i	$0.470457\pi$
$102$	−2.90255	−	0.0816857i	−0.287395	−	0.00808809i
$103$	−2.22304	−	1.28347i	−0.219043	−	0.126465i	0.386464	−	0.922304i	$-0.373696\pi$
$103$	−2.22304	−	1.28347i	−0.219043	−	0.126465i	−0.605507	+	0.795840i	$0.707030\pi$
$104$	12.2443	+	8.49353i	1.20065	+	0.832859i
$105$		0			0
$106$	11.7003	−	3.89612i	1.13644	−	0.378424i
$107$	−3.04995	+	5.28267i	−0.294850	+	0.510695i	−0.974950	−	0.222424i	$-0.928603\pi$
$107$	−3.04995	+	5.28267i	−0.294850	+	0.510695i	0.680100	+	0.733119i	$0.261936\pi$
$108$	−1.22086	−	10.3203i	−0.117477	−	0.993076i
$109$	−2.72545	−	4.72062i	−0.261051	−	0.452153i	0.705471	−	0.708739i	$-0.250736\pi$
$109$	−2.72545	−	4.72062i	−0.261051	−	0.452153i	−0.966521	+	0.256586i	$0.917402\pi$
$110$	−0.534868	+	2.60969i	−0.0509977	+	0.248824i
$111$	1.39105	−	1.16601i	0.132033	−	0.110673i
$112$		0			0
$113$			7.09803i			0.667726i	0.942622	+	0.333863i	$0.108352\pi$
$113$			7.09803i			0.667726i	−0.942622	+	0.333863i	$0.891648\pi$
$114$	−8.29684	−	15.3524i	−0.777071	−	1.43788i
$115$	−5.48569	+	3.16716i	−0.511543	+	0.295340i
$116$	−3.32907	+	7.78034i	−0.309097	+	0.722386i
$117$	12.0975	+	10.1722i	1.11841	+	0.940416i
$118$	−0.295860	−	0.888490i	−0.0272361	−	0.0817921i
$119$		0			0
$120$	0.358145	+	3.91815i	0.0326940	+	0.357677i
$121$	2.74943	−	4.76214i	0.249948	−	0.432922i
$122$	−0.899307	+	1.01353i	−0.0814195	+	0.0917610i
$123$	−4.25313	+	11.6667i	−0.383492	+	1.05195i
$124$	−9.72833	+	1.16601i	−0.873630	+	0.104711i
$125$			7.51322i			0.672003i
$126$		0			0
$127$		−	4.16202i		−	0.369320i	−0.982802	−	0.184660i	$-0.940882\pi$
$127$		−	4.16202i		−	0.369320i	0.982802	−	0.184660i	$-0.0591184\pi$
$128$	1.75456	+	11.1768i	0.155082	+	0.987902i
$129$	4.71212	−	12.9258i	0.414879	−	1.13805i
$130$	−4.47602	−	3.97157i	−0.392573	−	0.348330i
$131$	5.24594	−	9.08624i	0.458340	−	0.793869i	−0.540533	−	0.841323i	$-0.681777\pi$
$131$	5.24594	−	9.08624i	0.458340	−	0.793869i	0.998873	+	0.0474541i	$0.0151108\pi$
$132$	−1.85459	+	7.91039i	−0.161421	+	0.688511i
$133$		0			0
$134$	−11.3062	+	3.76488i	−0.976707	+	0.325236i
$135$	−0.00642439	+	4.17315i	−0.000552924	+	0.359168i
$136$	3.34140	+	0.277525i	0.286522	+	0.0237976i
$137$	−11.6844	+	6.74600i	−0.998267	+	0.576350i	−0.907735	−	0.419544i	$-0.862190\pi$
$137$	−11.6844	+	6.74600i	−0.998267	+	0.576350i	−0.0905318	+	0.995894i	$0.528857\pi$
$138$	−16.9962	+	9.18520i	−1.44681	+	0.781897i
$139$			7.57264i			0.642303i	0.947028	+	0.321151i	$0.104070\pi$
$139$			7.57264i			0.642303i	−0.947028	+	0.321151i	$0.895930\pi$
$140$		0			0
$141$	8.09591	−	6.78619i	0.681798	−	0.571501i
$142$	−13.4029	−	2.74700i	−1.12475	−	0.230523i
$143$	−6.17860	−	10.7017i	−0.516681	−	0.894917i
$144$	0.755715	+	11.9762i	0.0629763	+	0.998015i
$145$	1.69914	−	2.94299i	0.141106	−	0.244402i
$146$	0.631873	+	1.89756i	0.0522942	+	0.157043i
$147$		0			0
$148$	−1.67750	+	1.25651i	−0.137889	+	0.103285i
$149$	−13.9442	−	8.05067i	−1.14235	−	0.659536i	−0.195339	−	0.980736i	$-0.562581\pi$
$149$	−13.9442	−	8.05067i	−1.14235	−	0.659536i	−0.947012	+	0.321199i	$0.895914\pi$
$150$	−0.300094	+	10.6633i	−0.0245026	+	0.870654i
$151$	15.0553	−	8.69219i	1.22518	−	0.707360i	0.259166	−	0.965833i	$-0.416552\pi$
$151$	15.0553	−	8.69219i	1.22518	−	0.707360i	0.966019	+	0.258473i	$0.0832192\pi$
$152$	8.59627	+	18.2250i	0.697249	+	1.47824i
$153$	3.50163	+	0.621137i	0.283090	+	0.0502160i
$154$		0			0
$155$	3.93449			0.316026
$156$	−13.3055	−	12.4924i	−1.06529	−	1.00019i
$157$	1.96109	+	3.39671i	0.156512	+	0.271087i	0.933609	−	0.358295i	$-0.116642\pi$
$157$	1.96109	+	3.39671i	0.156512	+	0.271087i	−0.777096	+	0.629381i	$0.783308\pi$
$158$	−7.32887	−	6.50290i	−0.583053	−	0.517343i
$159$	−14.8754	+	2.61506i	−1.17970	+	0.207388i
$160$	−0.165435	−	4.54014i	−0.0130788	−	0.358930i
$161$		0			0
$162$	−0.377643	+	12.7223i	−0.0296704	+	0.999560i
$163$	−6.32987	−	3.65455i	−0.495793	−	0.286246i	0.231181	−	0.972911i	$-0.425741\pi$
$163$	−6.32987	−	3.65455i	−0.495793	−	0.286246i	−0.726975	+	0.686664i	$0.759074\pi$
$164$	5.64068	−	13.1828i	0.440463	−	1.02940i
$165$	1.11746	−	3.06531i	0.0869944	−	0.238634i
$166$	7.17962	+	1.47150i	0.557247	+	0.114210i
$167$	8.37196			0.647842			0.323921	−	0.946084i	$-0.394999\pi$
$167$	8.37196			0.647842			0.323921	+	0.946084i	$0.394999\pi$
$168$		0			0
$169$	14.7579			1.13523
$170$	−1.31898	−	0.270331i	−0.101161	−	0.0207335i
$171$	7.28935	+	20.0914i	0.557430	+	1.53643i
$172$	−6.24943	+	14.6054i	−0.476514	+	1.11365i
$173$	−11.0601	−	6.38556i	−0.840884	−	0.485485i	0.0166803	−	0.999861i	$-0.494690\pi$
$173$	−11.0601	−	6.38556i	−0.840884	−	0.485485i	−0.857565	+	0.514376i	$0.828024\pi$
$174$	5.43275	−	8.82665i	0.411856	−	0.669147i
$175$		0			0
$176$	2.63796	−	9.00331i	0.198844	−	0.678650i
$177$	0.198581	+	1.12960i	0.0149262	+	0.0849056i
$178$	−17.3124	−	15.3613i	−1.29762	−	1.15137i
$179$	10.5589	+	18.2885i	0.789206	+	1.36694i	0.926454	+	0.376408i	$0.122841\pi$
$179$	10.5589	+	18.2885i	0.789206	+	1.36694i	−0.137248	+	0.990537i	$0.543826\pi$
$180$	0.271011	−	4.81112i	0.0201999	−	0.358599i
$181$	12.4075			0.922239			0.461120	−	0.887338i	$-0.347448\pi$
$181$	12.4075			0.922239			0.461120	+	0.887338i	$0.347448\pi$
$182$		0			0
$183$	1.27181	−	1.06607i	0.0940151	−	0.0788059i
$184$	20.1763	−	9.51669i	1.48742	−	0.701579i
$185$	0.728878	−	0.420818i	0.0535882	−	0.0309392i
$186$	11.9953	+	0.337579i	0.879534	+	0.0247525i
$187$	−2.40787	−	1.39019i	−0.176081	−	0.101660i
$188$	−9.76301	+	7.31290i	−0.712041	+	0.533348i
$189$		0			0
$190$	−2.55646	−	7.67724i	−0.185465	−	0.556966i
$191$	−3.04995	+	5.28267i	−0.220687	+	0.382241i	−0.955017	−	0.296552i	$-0.904163\pi$
$191$	−3.04995	+	5.28267i	−0.220687	+	0.382241i	0.734330	+	0.678793i	$0.237497\pi$
$192$	−0.114824	−	13.8559i	−0.00828673	−	0.999966i
$193$	−0.322504	−	0.558593i	−0.0232144	−	0.0402084i	0.854185	−	0.519969i	$-0.174057\pi$
$193$	−0.322504	−	0.558593i	−0.0232144	−	0.0402084i	−0.877399	+	0.479761i	$0.840723\pi$
$194$	−6.06572	−	1.24320i	−0.435493	−	0.0892564i
$195$	4.70802	+	5.61665i	0.337149	+	0.402217i
$196$		0			0
$197$			14.9111i			1.06237i	0.847256	+	0.531185i	$0.178253\pi$
$197$			14.9111i			1.06237i	−0.847256	+	0.531185i	$0.821747\pi$
$198$	3.66987	−	9.24947i	0.260806	−	0.657332i
$199$	16.1940	−	9.34962i	1.14796	−	0.662777i	0.199573	−	0.979883i	$-0.436044\pi$
$199$	16.1940	−	9.34962i	1.14796	−	0.662777i	0.948390	+	0.317106i	$0.102711\pi$
$200$	1.01956	−	12.2755i	0.0720940	−	0.868010i
$201$	14.3743	−	2.52698i	1.01389	−	0.178239i
$202$	−11.2620	+	3.75017i	−0.792394	+	0.263861i
$203$		0			0
$204$	−3.99804	−	0.937339i	−0.279919	−	0.0656269i
$205$	−2.87897	+	4.98652i	−0.201076	+	0.348274i
$206$	−2.71540	−	2.40937i	−0.189191	−	0.167869i
$207$	22.2427	−	8.06983i	1.54597	−	0.560892i
$208$	14.5518	+	15.2438i	1.00898	+	1.05697i
$209$		−	16.7097i		−	1.15583i
$210$		0			0
$211$		−	11.7243i		−	0.807132i	−0.914950	−	0.403566i	$-0.867771\pi$
$211$		−	11.7243i		−	0.807132i	0.914950	−	0.403566i	$-0.132229\pi$
$212$	17.3161	−	2.07547i	1.18927	−	0.142544i
$213$	15.7429	+	5.73911i	1.07869	+	0.393237i
$214$	−5.72545	+	6.45267i	−0.391384	+	0.441095i
$215$	3.18967	−	5.52466i	0.217533	−	0.376779i
$216$	1.23904	−	14.6446i	0.0843057	−	0.996440i
$217$		0			0
$218$	−2.43547	−	7.31389i	−0.164951	−	0.495359i
$219$	−0.424112	−	2.41249i	−0.0286588	−	0.163021i
$220$	−1.48203	+	3.46363i	−0.0999184	+	0.233518i
$221$	5.40879	−	3.12277i	0.363835	−	0.210060i
$222$	2.25827	−	1.22043i	0.151565	−	0.0819098i
$223$			0.683260i			0.0457545i	0.999738	+	0.0228772i	$0.00728269\pi$
$223$			0.683260i			0.0457545i	−0.999738	+	0.0228772i	$0.992717\pi$
$224$		0			0
$225$	2.28191	−	12.8642i	0.152128	−	0.857610i
$226$	−2.01546	+	9.83371i	−0.134067	+	0.654129i
$227$	4.37694	+	7.58108i	0.290507	+	0.503174i	0.973930	−	0.226850i	$-0.0728426\pi$
$227$	4.37694	+	7.58108i	0.290507	+	0.503174i	−0.683422	+	0.730023i	$0.739509\pi$
$228$	−7.13530	−	23.6253i	−0.472547	−	1.56462i
$229$	9.24927	−	16.0202i	0.611209	−	1.05864i	−0.379828	−	0.925057i	$-0.624017\pi$
$229$	9.24927	−	16.0202i	0.611209	−	1.05864i	0.991037	−	0.133588i	$-0.0426498\pi$
$230$	−8.49926	+	2.83019i	−0.560425	+	0.186617i
$231$		0			0
$232$	−6.82135	+	9.83371i	−0.447844	+	0.645615i
$233$	8.78072	+	5.06955i	0.575244	+	0.332117i	0.759241	−	0.650810i	$-0.225570\pi$
$233$	8.78072	+	5.06955i	0.575244	+	0.332117i	−0.183997	+	0.982927i	$0.558904\pi$
$234$	13.8717	+	17.5277i	0.906818	+	1.14582i
$235$	4.24206	−	2.44916i	0.276722	−	0.159765i
$236$	−0.157605	−	1.31494i	−0.0102592	−	0.0855950i
$237$	7.70873	+	9.19649i	0.500736	+	0.597376i
$238$		0			0
$239$	1.49470			0.0966841			0.0483421	−	0.998831i	$-0.484606\pi$
$239$	1.49470			0.0966841			0.0483421	+	0.998831i	$0.484606\pi$
$240$	−0.616369	+	5.52996i	−0.0397865	+	0.356958i
$241$	5.16686	+	8.94926i	0.332827	+	0.576472i	0.983065	−	0.183258i	$-0.0586643\pi$
$241$	5.16686	+	8.94926i	0.332827	+	0.576472i	−0.650238	+	0.759730i	$0.725331\pi$
$242$	5.16129	−	5.81685i	0.331780	−	0.373921i
$243$	2.74629	−	15.3446i	0.176174	−	0.984359i
$244$	−1.53370	+	1.14881i	−0.0981853	+	0.0735449i
$245$		0			0
$246$	−9.20508	+	14.9556i	−0.586895	+	0.953535i
$247$	32.5062	+	18.7675i	2.06832	+	1.19415i
$248$	−13.8089	−	1.14692i	−0.876863	−	0.0728294i
$249$	−8.43310	−	3.07430i	−0.534426	−	0.194826i
$250$	−2.13336	+	10.4089i	−0.134925	+	0.658318i
$251$	−26.9555			−1.70142			−0.850709	−	0.525636i	$-0.823827\pi$
$251$	−26.9555			−1.70142			−0.850709	+	0.525636i	$0.823827\pi$
$252$		0			0
$253$	−18.4989			−1.16301
$254$	1.18179	−	5.76613i	0.0741524	−	0.361799i
$255$	1.54926	+	0.564784i	0.0970183	+	0.0353682i
$256$	−0.742842	+	15.9827i	−0.0464276	+	0.998922i
$257$	2.41766	+	1.39584i	0.150810	+	0.0870700i	0.573506	−	0.819201i	$-0.305583\pi$
$257$	2.41766	+	1.39584i	0.150810	+	0.0870700i	−0.422696	+	0.906271i	$0.638916\pi$
$258$	10.1985	−	16.5696i	0.634931	−	1.03158i
$259$		0			0
$260$	−5.07343	−	6.77323i	−0.314641	−	0.420058i
$261$	−8.16950	+	9.71577i	−0.505679	+	0.601391i
$262$	9.84782	−	11.0986i	0.608400	−	0.685676i
$263$	−7.65516	−	13.2591i	−0.472037	−	0.817592i	0.527451	−	0.849586i	$-0.323148\pi$
$263$	−7.65516	−	13.2591i	−0.472037	−	0.817592i	−0.999488	+	0.0319931i	$0.989815\pi$
$264$	−4.81551	+	10.4326i	−0.296374	+	0.642080i
$265$	−7.00325			−0.430206
$266$		0			0
$267$	18.2097	+	21.7241i	1.11442	+	1.32949i
$268$	−16.7328	+	2.00556i	−1.02212	+	0.122509i
$269$	−26.5752	+	15.3432i	−1.62032	+	0.935492i	−0.633487	+	0.773754i	$0.718377\pi$
$269$	−26.5752	+	15.3432i	−1.62032	+	0.935492i	−0.986834	+	0.161739i	$0.948290\pi$
$270$	−1.19385	+	5.77972i	−0.0726557	+	0.351742i
$271$	−17.0488	−	9.84312i	−1.03564	−	0.597927i	−0.117045	−	0.993127i	$-0.537342\pi$
$271$	−17.0488	−	9.84312i	−1.03564	−	0.597927i	−0.918595	+	0.395199i	$0.870675\pi$
$272$	4.55042	+	1.33327i	0.275910	+	0.0808412i
$273$		0			0
$274$	−18.1033	+	6.02825i	−1.09366	+	0.364180i
$275$	−5.10721	+	8.84595i	−0.307977	+	0.533431i
$276$	−26.1549	+	7.89929i	−1.57434	+	0.475481i
$277$	6.55646	+	11.3561i	0.393940	+	0.682324i	0.992965	−	0.118406i	$-0.0377785\pi$
$277$	6.55646	+	11.3561i	0.393940	+	0.682324i	−0.599025	+	0.800730i	$0.704445\pi$
$278$	−2.15023	+	10.4912i	−0.128962	+	0.629223i
$279$	−14.4710	−	2.56695i	−0.866358	−	0.153679i
$280$		0			0
$281$			2.86670i			0.171013i	0.996338	+	0.0855066i	$0.0272509\pi$
$281$			2.86670i			0.171013i	−0.996338	+	0.0855066i	$0.972749\pi$
$282$	13.1431	−	7.10288i	0.782661	−	0.422971i
$283$	1.72374	−	0.995200i	0.102466	−	0.0591585i	−0.447892	−	0.894088i	$-0.647825\pi$
$283$	1.72374	−	0.995200i	0.102466	−	0.0591585i	0.550357	+	0.834929i	$0.314492\pi$
$284$	−17.7886	−	7.61146i	−1.05556	−	0.451657i
$285$	1.71589	+	9.76059i	0.101641	+	0.578167i
$286$	−5.52122	−	16.5806i	−0.326477	−	0.980433i
$287$		0			0
$288$	−2.35362	+	16.8066i	−0.138689	+	0.990336i
$289$	−7.79738	+	13.5055i	−0.458669	+	0.794439i
$290$	3.18967	−	3.59480i	0.187304	−	0.211094i
$291$	7.12472	+	2.59733i	0.417659	+	0.152258i
$292$	0.336600	+	2.80833i	0.0196980	+	0.164345i
$293$		−	16.7482i		−	0.978441i	−0.872160	−	0.489221i	$-0.837281\pi$
$293$		−	16.7482i		−	0.978441i	0.872160	−	0.489221i	$-0.162719\pi$
$294$		0			0
$295$			0.531807i			0.0309630i
$296$	−2.68081	+	1.26447i	−0.155819	+	0.0734960i
$297$	−6.10991	+	10.5451i	−0.354533	+	0.611891i
$298$	−17.0325	−	15.1129i	−0.986666	−	0.875468i
$299$	20.7769	−	35.9867i	1.20156	−	2.08117i
$300$	−3.44356	+	14.6879i	−0.198814	+	0.848004i
$301$		0			0
$302$	23.3260	−	7.76737i	1.34226	−	0.446962i
$303$	14.3182	−	2.51710i	0.822557	−	0.144604i
$304$	6.73447	+	27.6900i	0.386248	+	1.58813i
$305$	0.666400	−	0.384746i	0.0381579	−	0.0220305i
$306$	4.67483	+	1.85481i	0.267242	+	0.106032i
$307$		−	15.4869i		−	0.883885i	−0.897043	−	0.441942i	$-0.854290\pi$
$307$		−	15.4869i		−	0.883885i	0.897043	−	0.441942i	$-0.145710\pi$
$308$		0			0
$309$	2.85614	+	3.40737i	0.162480	+	0.193838i
$310$	5.45090	+	1.11719i	0.309590	+	0.0634519i
$311$	5.44973	+	9.43920i	0.309026	+	0.535248i	0.978149	−	0.207903i	$-0.0666638\pi$
$311$	5.44973	+	9.43920i	0.309026	+	0.535248i	−0.669124	+	0.743151i	$0.733330\pi$
$312$	−14.8865	−	21.0852i	−0.842780	−	1.19371i
$313$	−16.9011	+	29.2736i	−0.955308	+	1.65464i	−0.221646	+	0.975127i	$0.571143\pi$
$313$	−16.9011	+	29.2736i	−0.955308	+	1.65464i	−0.733662	+	0.679514i	$0.762190\pi$
$314$	1.75244	+	5.26270i	0.0988958	+	0.296991i
$315$		0			0
$316$	−8.30704	−	11.0902i	−0.467307	−	0.623874i
$317$	8.04243	+	4.64330i	0.451708	+	0.260794i	0.708551	−	0.705659i	$-0.249349\pi$
$317$	8.04243	+	4.64330i	0.451708	+	0.260794i	−0.256843	+	0.966453i	$0.582682\pi$
$318$	−21.3511	−	0.600879i	−1.19731	−	0.0336956i
$319$	8.59476	−	4.96218i	0.481214	−	0.277829i
$320$	1.05996	−	6.33695i	0.0592538	−	0.354247i
$321$	8.09701	−	6.78712i	0.451931	−	0.378820i
$322$		0			0
$323$	8.44536			0.469912
$324$	−4.13566	+	17.5185i	−0.229759	+	0.973248i
$325$	−11.4723	−	19.8706i	−0.636369	−	1.10222i
$326$	−7.73179	−	6.86041i	−0.428224	−	0.379963i
$327$	1.63468	+	9.29864i	0.0903981	+	0.514216i
$328$	11.5579	−	16.6619i	0.638178	−	0.920002i
$329$		0			0
$330$	2.41854	−	3.92943i	0.133136	−	0.216308i
$331$	0.878968	+	0.507473i	0.0483125	+	0.0278932i	0.523962	−	0.851742i	$-0.324453\pi$
$331$	0.878968	+	0.507473i	0.0483125	+	0.0278932i	−0.475649	+	0.879635i	$0.657787\pi$
$332$	9.52893	+	4.07727i	0.522968	+	0.223769i
$333$	−2.95536	+	1.07223i	−0.161953	+	0.0587579i
$334$	11.5986	+	2.37719i	0.634649	+	0.130074i
$335$	6.76735			0.369740
$336$		0			0
$337$	−12.6597			−0.689620			−0.344810	−	0.938673i	$-0.612057\pi$
$337$	−12.6597			−0.689620			−0.344810	+	0.938673i	$0.612057\pi$
$338$	20.4459	+	4.19047i	1.11211	+	0.227932i
$339$	4.21077	−	11.5506i	0.228698	−	0.627340i
$340$	−1.75057	−	0.749041i	−0.0949383	−	0.0406225i
$341$	9.95091	+	5.74516i	0.538872	+	0.311118i
$342$	4.39386	+	29.9048i	0.237593	+	1.61706i
$343$		0			0
$344$	−12.8052	+	18.4601i	−0.690411	+	0.995302i
$345$	10.8057	−	1.89962i	0.581758	−	0.102272i
$346$	−13.5097	−	11.9871i	−0.726285	−	0.644432i
$347$	12.8143	+	22.1950i	0.687907	+	1.19149i	0.972514	+	0.232846i	$0.0748037\pi$
$347$	12.8143	+	22.1950i	0.687907	+	1.19149i	−0.284607	+	0.958644i	$0.591863\pi$
$348$	10.0329	−	10.6860i	0.537821	−	0.572828i
$349$	−28.1235			−1.50542			−0.752709	−	0.658354i	$-0.771253\pi$
$349$	−28.1235			−1.50542			−0.752709	+	0.658354i	$0.771253\pi$
$350$		0			0
$351$	−13.6517	−	23.7297i	−0.728672	−	1.26660i
$352$	6.21113	−	11.7243i	0.331055	−	0.624906i
$353$	8.92430	−	5.15245i	0.474993	−	0.274237i	−0.243335	−	0.969942i	$-0.578241\pi$
$353$	8.92430	−	5.15245i	0.474993	−	0.274237i	0.718327	+	0.695705i	$0.244908\pi$
$354$	−0.0456291	+	1.62134i	−0.00242516	+	0.0861735i
$355$	6.72874	+	3.88484i	0.357124	+	0.206186i
$356$	−19.6230	−	26.1975i	−1.04002	−	1.38847i
$357$		0			0
$358$	9.43543	+	28.3353i	0.498678	+	1.49757i
$359$	13.4197	−	23.2436i	0.708265	−	1.22675i	−0.257235	−	0.966349i	$-0.582812\pi$
$359$	13.4197	−	23.2436i	0.708265	−	1.22675i	0.965500	−	0.260402i	$-0.0838551\pi$
$360$	1.74157	−	6.58844i	0.0917886	−	0.347241i
$361$	15.8778	+	27.5012i	0.835675	+	1.44743i
$362$	17.1895	+	3.52306i	0.903459	+	0.185168i
$363$	−7.29917	+	6.11835i	−0.383107	+	0.321130i
$364$		0			0
$365$		−	1.13579i		−	0.0594499i
$366$	2.06469	−	1.11582i	0.107923	−	0.0583246i
$367$	11.5631	−	6.67596i	0.603589	−	0.348482i	−0.166863	−	0.985980i	$-0.553364\pi$
$367$	11.5631	−	6.67596i	0.603589	−	0.348482i	0.770452	+	0.637498i	$0.220031\pi$
$368$	30.6548	−	7.45554i	1.59799	−	0.388647i
$369$	13.8422	−	16.4621i	0.720594	−	0.856982i
$370$	1.12929	−	0.376045i	0.0587089	−	0.0195496i
$371$		0			0
$372$	16.5225	+	3.87371i	0.856654	+	0.200842i
$373$	11.4029	−	19.7505i	0.590422	−	1.02264i	−0.403753	−	0.914868i	$-0.632295\pi$
$373$	11.4029	−	19.7505i	0.590422	−	1.02264i	0.994176	−	0.107773i	$-0.0343720\pi$
$374$	−2.94116	−	2.60969i	−0.152084	−	0.134944i
$375$	4.45708	−	12.2262i	0.230162	−	0.631358i
$376$	−15.6023	+	7.35922i	−0.804627	+	0.379523i
$377$			22.2931i			1.14815i
$378$		0			0
$379$			1.98122i			0.101768i	0.998705	+	0.0508842i	$0.0162040\pi$
$379$			1.98122i			0.101768i	−0.998705	+	0.0508842i	$0.983796\pi$
$380$	−1.36183	−	11.3621i	−0.0698605	−	0.582862i
$381$	−2.46904	+	6.77282i	−0.126493	+	0.346982i
$382$	−5.72545	+	6.45267i	−0.292939	+	0.330147i
$383$	−14.4104	+	24.9596i	−0.736339	+	1.27538i	0.217795	+	0.975995i	$0.430114\pi$
$383$	−14.4104	+	24.9596i	−0.736339	+	1.27538i	−0.954134	+	0.299381i	$0.903220\pi$
$384$	3.77527	−	19.2288i	0.192656	−	0.981266i
$385$		0			0
$386$	−0.288191	−	0.865458i	−0.0146685	−	0.0440506i
$387$	−15.3360	+	18.2387i	−0.779573	+	0.927124i
$388$	−8.05054	−	3.44469i	−0.408704	−	0.174878i
$389$	−1.69719	+	0.979873i	−0.0860509	+	0.0496815i	−0.542408	−	0.840115i	$-0.682487\pi$
$389$	−1.69719	+	0.979873i	−0.0860509	+	0.0496815i	0.456357	+	0.889797i	$0.349154\pi$
$390$	4.92773	+	9.11823i	0.249525	+	0.461719i
$391$		−	9.34962i		−	0.472831i
$392$		0			0
$393$	−13.9269	+	11.6739i	−0.702520	+	0.588870i
$394$	−4.23396	+	20.6580i	−0.213304	+	1.04074i
$395$	2.78210	+	4.81874i	0.139983	+	0.242457i
$396$	7.71065	−	11.7723i	0.387475	−	0.591581i
$397$	2.28155	−	3.95176i	0.114508	−	0.198333i	−0.803075	−	0.595878i	$-0.796804\pi$
$397$	2.28155	−	3.95176i	0.114508	−	0.198333i	0.917583	+	0.397545i	$0.130138\pi$
$398$	25.0902	−	8.35485i	1.25766	−	0.418791i
$399$		0			0
$400$	4.89811	−	16.7172i	0.244906	−	0.835858i
$401$	−23.1931	−	13.3905i	−1.15821	−	0.668692i	−0.207335	−	0.978270i	$-0.566479\pi$
$401$	−23.1931	−	13.3905i	−1.15821	−	0.668692i	−0.950874	+	0.309578i	$0.899812\pi$
$402$	20.6319	+	0.580639i	1.02903	+	0.0289596i
$403$	−22.3527	+	12.9053i	−1.11347	+	0.642860i
$404$	−16.6674	+	1.99772i	−0.829236	+	0.0993903i
$405$	2.48610	−	6.78712i	0.123535	−	0.337255i
$406$		0			0
$407$	2.45792			0.121835
$408$	−5.27279	−	2.43384i	−0.261042	−	0.120493i
$409$	−9.02122	−	15.6252i	−0.446071	−	0.772617i	0.552055	−	0.833807i	$-0.313844\pi$
$409$	−9.02122	−	15.6252i	−0.446071	−	0.772617i	−0.998126	+	0.0611902i	$0.980510\pi$
$410$	−5.40447	+	6.09092i	−0.266908	+	0.300809i
$411$	23.0159	−	4.04614i	1.13529	−	0.199582i
$412$	−3.07782	−	4.10901i	−0.151633	−	0.202436i
$413$		0			0
$414$	33.1067	−	4.86432i	1.62711	−	0.239068i
$415$	−3.60442	−	2.08101i	−0.176934	−	0.102153i
$416$	15.8318	+	25.2509i	0.776217	+	1.23803i
$417$	4.49233	−	12.3229i	0.219990	−	0.603454i
$418$	4.74468	−	23.1499i	0.232070	−	1.13230i
$419$	17.5395			0.856861			0.428430	−	0.903575i	$-0.359067\pi$
$419$	17.5395			0.856861			0.428430	+	0.903575i	$0.359067\pi$
$420$		0			0
$421$	15.4006			0.750582			0.375291	−	0.926907i	$-0.377543\pi$
$421$	15.4006			0.750582			0.375291	+	0.926907i	$0.377543\pi$
$422$	3.32907	−	16.2430i	0.162057	−	0.790696i
$423$	−17.2002	+	6.24037i	−0.836301	+	0.303417i
$424$	24.5793	+	2.04147i	1.19368	+	0.0991428i
$425$	−4.47089	−	2.58127i	−0.216870	−	0.125210i
$426$	20.1809	+	12.4212i	0.977767	+	0.601810i
$427$		0			0
$428$	−9.76434	+	7.31389i	−0.471977	+	0.353530i
$429$	3.70583	+	21.0801i	0.178919	+	1.01775i
$430$	5.98772	−	6.74825i	0.288754	−	0.325430i
$431$	−4.50180	−	7.79735i	−0.216844	−	0.375585i	0.736997	−	0.675896i	$-0.236243\pi$
$431$	−4.50180	−	7.79735i	−0.216844	−	0.375585i	−0.953841	+	0.300311i	$0.902910\pi$
$432$	5.87488	−	19.9370i	0.282655	−	0.959222i
$433$	−6.15889			−0.295977			−0.147989	−	0.988989i	$-0.547280\pi$
$433$	−6.15889			−0.295977			−0.147989	+	0.988989i	$0.547280\pi$
$434$		0			0
$435$	−4.51087	+	3.78113i	−0.216280	+	0.181291i
$436$	−1.29738	−	10.8243i	−0.0621331	−	0.518391i
$437$	48.6621	−	28.0951i	2.32782	−	1.34397i
$438$	0.0974507	−	3.46273i	0.00465638	−	0.165456i
$439$	−25.3306	−	14.6246i	−1.20896	−	0.697996i	−0.246432	−	0.969160i	$-0.579258\pi$
$439$	−25.3306	−	14.6246i	−1.20896	−	0.697996i	−0.962533	+	0.271164i	$0.912591\pi$
$440$	−3.03671	+	4.37775i	−0.144770	+	0.208701i
$441$		0			0
$442$	8.38012	−	2.79052i	0.398602	−	0.132731i
$443$	3.60820	−	6.24958i	0.171431	−	0.296927i	−0.767490	−	0.641061i	$-0.778494\pi$
$443$	3.60820	−	6.24958i	0.171431	−	0.296927i	0.938920	+	0.344135i	$0.111828\pi$
$444$	3.47518	−	1.04957i	0.164925	−	0.0498104i
$445$	6.57193	+	11.3829i	0.311539	+	0.539602i
$446$	−0.194010	+	0.946599i	−0.00918663	+	0.0448227i
$447$	17.9153	+	21.3729i	0.847365	+	1.01090i
$448$		0			0
$449$			4.43423i			0.209264i	0.994511	+	0.104632i	$0.0333665\pi$
$449$			4.43423i			0.209264i	−0.994511	+	0.104632i	$0.966634\pi$
$450$	6.81414	−	17.1742i	0.321221	−	0.809602i
$451$	−14.5627	+	8.40777i	−0.685730	+	0.395907i
$452$	−5.58451	+	13.0515i	−0.262673	+	0.613890i
$453$	−29.6559	+	5.21344i	−1.39335	+	0.244949i
$454$	3.91125	+	11.7458i	0.183564	+	0.551256i
$455$		0			0
$456$	−3.17701	−	34.7569i	−0.148777	−	1.62764i
$457$	−6.83102	+	11.8317i	−0.319541	+	0.553462i	−0.980392	−	0.197055i	$-0.936862\pi$
$457$	−6.83102	+	11.8317i	−0.319541	+	0.553462i	0.660851	+	0.750517i	$0.270196\pi$
$458$	17.3630	−	19.5683i	0.811318	−	0.914368i
$459$	−5.32969	−	3.08805i	−0.248768	−	0.144138i
$460$	−12.5786	+	1.50764i	−0.586482	+	0.0702943i
$461$			5.25789i			0.244885i	0.992476	+	0.122442i	$0.0390726\pi$
$461$			5.25789i			0.244885i	−0.992476	+	0.122442i	$0.960927\pi$
$462$		0			0
$463$		−	15.8863i		−	0.738299i	−0.929370	−	0.369149i	$-0.879649\pi$
$463$		−	15.8863i		−	0.738299i	0.929370	−	0.369149i	$-0.120351\pi$
$464$	−12.2427	+	11.6869i	−0.568351	+	0.542549i
$465$	−6.40256	−	2.33406i	−0.296911	−	0.108240i
$466$	10.7254	+	9.51669i	0.496847	+	0.440852i
$467$	−13.5384	+	23.4491i	−0.626481	+	1.08510i	0.361771	+	0.932267i	$0.382172\pi$
$467$	−13.5384	+	23.4491i	−0.626481	+	1.08510i	−0.988252	+	0.152830i	$0.951161\pi$
$468$	14.2411	+	28.2219i	0.658293	+	1.30456i
$469$		0			0
$470$	6.57245	−	2.18858i	0.303164	−	0.100951i
$471$	−1.17623	−	6.69082i	−0.0541979	−	0.308297i
$472$	0.155024	−	1.86648i	0.00713555	−	0.0859118i
$473$	16.1343	−	9.31514i	0.741856	−	0.428311i
$474$	8.06847	+	14.9298i	0.370597	+	0.685750i
$475$		−	31.0263i		−	1.42358i
$476$		0			0
$477$	25.7579	+	4.56908i	1.17937	+	0.209204i
$478$	2.07078	+	0.424416i	0.0947152	+	0.0194123i
$479$	−7.63026	−	13.2160i	−0.348635	−	0.603854i	0.637372	−	0.770556i	$-0.280021\pi$
$479$	−7.63026	−	13.2160i	−0.348635	−	0.603854i	−0.986007	+	0.166702i	$0.946688\pi$
$480$	−2.42414	+	7.48627i	−0.110647	+	0.341700i
$481$	−2.76061	+	4.78152i	−0.125873	+	0.218019i
$482$	4.61712	+	13.8655i	0.210304	+	0.631558i
$483$		0			0
$484$	8.80221	−	6.59322i	0.400100	−	0.299692i
$485$	3.04520	+	1.75815i	0.138275	+	0.0798334i
$486$	8.16181	−	20.4789i	0.370227	−	0.928941i
$487$	−5.25172	+	3.03208i	−0.237978	+	0.137397i	−0.614247	−	0.789114i	$-0.710540\pi$
$487$	−5.25172	+	3.03208i	−0.237978	+	0.137397i	0.376269	+	0.926511i	$0.377207\pi$
$488$	−2.45102	+	1.15608i	−0.110952	+	0.0523335i
$489$	8.13254	+	9.70209i	0.367766	+	0.438744i
$490$		0			0
$491$	−4.03833			−0.182247			−0.0911235	−	0.995840i	$-0.529046\pi$
$491$	−4.03833			−0.182247			−0.0911235	+	0.995840i	$0.529046\pi$
$492$	−16.9995	+	18.1060i	−0.766395	+	0.816280i
$493$	2.50797	+	4.34393i	0.112953	+	0.195641i
$494$	39.7056	+	35.2308i	1.78644	+	1.58511i
$495$	−3.63688	+	4.32524i	−0.163466	+	0.194405i
$496$	−18.8053	−	5.50994i	−0.844384	−	0.247404i
$497$		0			0
$498$	−10.8104	−	6.65373i	−0.484426	−	0.298161i
$499$	−33.3430	−	19.2506i	−1.49264	−	0.861776i	−0.492675	−	0.870214i	$-0.663981\pi$
$499$	−33.3430	−	19.2506i	−1.49264	−	0.861776i	−0.999964	+	0.00843800i	$0.997314\pi$
$500$	−5.91117	+	13.8149i	−0.264356	+	0.617822i
$501$	−13.6236	−	4.96651i	−0.608658	−	0.221887i
$502$	−37.3446	−	7.65395i	−1.66677	−	0.341613i
$503$	−14.3498			−0.639827			−0.319914	−	0.947447i	$-0.603654\pi$
$503$	−14.3498			−0.639827			−0.319914	+	0.947447i	$0.603654\pi$
$504$		0			0
$505$	6.74091			0.299967
$506$	−25.6286	−	5.25270i	−1.13933	−	0.233511i
$507$	−24.0155	−	8.75487i	−1.06656	−	0.388817i
$508$	3.27455	−	7.65291i	0.145285	−	0.339543i
$509$	10.4646	+	6.04176i	0.463837	+	0.267796i	0.713656	−	0.700496i	$-0.247038\pi$
$509$	10.4646	+	6.04176i	0.463837	+	0.267796i	−0.249819	+	0.968292i	$0.580371\pi$
$510$	1.98600	+	1.22237i	0.0879414	+	0.0541274i
$511$		0			0
$512$	−5.56740	+	21.9318i	−0.246047	+	0.969258i
$513$	0.0569891	−	37.0189i	0.00251613	−	1.63442i
$514$	2.95312	+	2.62030i	0.130257	+	0.115577i
$515$	1.03079	+	1.78538i	0.0454220	+	0.0786732i
$516$	18.8340	−	20.0600i	0.829123	−	0.883091i
$517$	14.3051			0.629137
$518$		0			0
$519$	14.2099	+	16.9524i	0.623746	+	0.744126i
$520$	−5.10557	−	10.8243i	−0.223894	−	0.474678i
$521$	−27.6002	+	15.9350i	−1.20919	+	0.698125i	−0.962582	−	0.270990i	$-0.912649\pi$
$521$	−27.6002	+	15.9350i	−1.20919	+	0.698125i	−0.246606	+	0.969116i	$0.579316\pi$
$522$	−14.0769	+	11.1407i	−0.616130	+	0.487613i
$523$	31.7039	+	18.3043i	1.38631	+	0.800389i	0.992898	−	0.118971i	$-0.0379596\pi$
$523$	31.7039	+	18.3043i	1.38631	+	0.800389i	0.393417	+	0.919360i	$0.371293\pi$
$524$	16.7947	−	12.5800i	0.733682	−	0.549558i
$525$		0			0
$526$	−6.84068	−	20.5430i	−0.298268	−	0.895719i
$527$	−2.90370	+	5.02935i	−0.126487	+	0.219082i
$528$	−9.63377	+	13.0861i	−0.419256	+	0.569499i
$529$	−19.6033	−	33.9539i	−0.852316	−	1.47625i
$530$	−9.70241	−	1.98855i	−0.421446	−	0.0863773i
$531$	0.346963	−	1.95599i	0.0150569	−	0.0848825i
$532$		0			0
$533$		−	37.7727i		−	1.63612i
$534$	19.0595	+	35.2675i	0.824784	+	1.52617i
$535$	4.24264	−	2.44949i	0.183425	−	0.105901i
$536$	−23.7514	−	1.97271i	−1.02590	−	0.0852080i
$537$	−6.33303	−	36.0245i	−0.273291	−	1.55457i
$538$	−41.1744	+	13.7108i	−1.77515	+	0.591113i
$539$		0			0
$540$	−3.29512	+	7.66832i	−0.141799	+	0.329992i
$541$	18.1033	−	31.3558i	0.778320	−	1.34809i	−0.154589	−	0.987979i	$-0.549405\pi$
$541$	18.1033	−	31.3558i	0.778320	−	1.34809i	0.932909	−	0.360111i	$-0.117261\pi$
$542$	−20.8247	−	18.4778i	−0.894498	−	0.793688i
$543$	−20.1906	−	7.36050i	−0.866460	−	0.315869i
$544$	5.92564	+	3.13921i	0.254060	+	0.134592i
$545$			4.37775i			0.187522i
$546$		0			0
$547$			31.3917i			1.34221i	0.741361	+	0.671106i	$0.234180\pi$
$547$			31.3917i			1.34221i	−0.741361	+	0.671106i	$0.765820\pi$
$548$	−26.7922	+	3.21126i	−1.14451	+	0.137178i
$549$	−2.70203	+	0.980320i	−0.115320	+	0.0418391i
$550$	−9.58739	+	10.8051i	−0.408808	+	0.460733i
$551$	−15.0726	+	26.1065i	−0.642115	+	1.11218i
$552$	−38.4784	+	3.51718i	−1.63775	+	0.149701i
$553$		0			0
$554$	5.85888	+	17.5946i	0.248920	+	0.747525i
$555$	−1.43574	+	0.252400i	−0.0609437	+	0.0107138i
$556$	−5.95792	+	13.9242i	−0.252672	+	0.590517i
$557$	−30.5691	+	17.6491i	−1.29526	+	0.747816i	−0.979581	−	0.201051i	$-0.935564\pi$
$557$	−30.5691	+	17.6491i	−1.29526	+	0.747816i	−0.315675	+	0.948867i	$0.602231\pi$
$558$	−19.3195	−	7.66530i	−0.817860	−	0.324498i
$559$			41.8491i			1.77003i
$560$		0			0
$561$	3.09361	+	3.69066i	0.130612	+	0.155820i
$562$	−0.813993	+	3.97157i	−0.0343362	+	0.167531i
$563$	13.2232	+	22.9032i	0.557290	+	0.965254i	0.997721	+	0.0674681i	$0.0214921\pi$
$563$	13.2232	+	22.9032i	0.557290	+	0.965254i	−0.440432	+	0.897786i	$0.645175\pi$
$564$	20.2255	−	6.10849i	0.851647	−	0.257214i
$565$	2.85030	−	4.93686i	0.119913	−	0.207695i
$566$	2.67067	−	0.889314i	0.112257	−	0.0373807i
$567$		0			0
$568$	−22.4834	−	15.5961i	−0.943382	−	0.654396i
$569$	23.7332	+	13.7024i	0.994948	+	0.574434i	0.906750	−	0.421669i	$-0.138556\pi$
$569$	23.7332	+	13.7024i	0.994948	+	0.574434i	0.0881985	+	0.996103i	$0.471889\pi$
$570$	−0.394271	+	14.0097i	−0.0165142	+	0.586801i
$571$	−24.3299	+	14.0469i	−1.01817	+	0.587843i	−0.913574	−	0.406672i	$-0.866689\pi$
$571$	−24.3299	+	14.0469i	−1.01817	+	0.587843i	−0.104599	+	0.994514i	$0.533356\pi$
$572$	−2.94116	−	24.5388i	−0.122976	−	1.02602i
$573$	8.09701	−	6.78712i	0.338257	−	0.283536i
$574$		0			0
$575$	−34.3483			−1.43242
$576$	−8.03292	+	22.6158i	−0.334705	+	0.942323i
$577$	11.4154	+	19.7721i	0.475231	+	0.823124i	0.999598	−	0.0283688i	$-0.00903129\pi$
$577$	11.4154	+	19.7721i	0.475231	+	0.823124i	−0.524367	+	0.851492i	$0.675698\pi$
$578$	−14.6374	+	16.4966i	−0.608837	+	0.686169i
$579$	0.193433	+	1.10031i	0.00803880	+	0.0457275i
$580$	5.43974	−	4.07459i	0.225873	−	0.169188i
$581$		0			0
$582$	9.13319	+	5.62142i	0.378583	+	0.233015i
$583$	−17.7123	−	10.2262i	−0.733568	−	0.423526i
$584$	−0.331087	+	3.98627i	−0.0137005	+	0.164953i
$585$	−4.32935	−	11.9329i	−0.178997	−	0.493364i
$586$	4.75561	−	23.2032i	0.196452	−	0.958517i
$587$	28.4011			1.17224			0.586119	−	0.810225i	$-0.300655\pi$
$587$	28.4011			1.17224			0.586119	+	0.810225i	$0.300655\pi$
$588$		0			0
$589$	−34.9018			−1.43810
$590$	−0.151005	+	0.736774i	−0.00621679	+	0.0303325i
$591$	8.84572	−	24.2647i	0.363864	−	0.998115i
$592$	−4.07308	+	0.990610i	−0.167403	+	0.0407138i
$593$	20.6799	+	11.9396i	0.849223	+	0.490299i	0.860389	−	0.509638i	$-0.170221\pi$
$593$	20.6799	+	11.9396i	0.849223	+	0.490299i	−0.0111655	+	0.999938i	$0.503554\pi$
$594$	−11.4590	+	12.8745i	−0.470169	+	0.528247i
$595$		0			0
$596$	−19.3058	−	25.7740i	−0.790796	−	1.05574i
$597$	−31.8989	+	5.60775i	−1.30553	+	0.229510i
$598$	39.0030	−	43.9570i	1.59495	−	1.79753i
$599$	−19.5625	−	33.8832i	−0.799300	−	1.38443i	−0.920072	−	0.391749i	$-0.871870\pi$
$599$	−19.5625	−	33.8832i	−0.799300	−	1.38443i	0.120772	−	0.992680i	$-0.461463\pi$
$600$	−8.94134	+	19.3710i	−0.365029	+	0.790817i
$601$	−4.88356			−0.199204			−0.0996022	−	0.995027i	$-0.531757\pi$
$601$	−4.88356			−0.199204			−0.0996022	+	0.995027i	$0.531757\pi$
$602$		0			0
$603$	−24.8903	−	4.41518i	−1.01361	−	0.179800i
$604$	34.5217	−	4.13769i	1.40467	−	0.168360i
$605$	−3.82459	+	2.20813i	−0.155492	+	0.0897732i
$606$	20.5513	+	0.578371i	0.834841	+	0.0234947i
$607$	27.4754	+	15.8630i	1.11519	+	0.643857i	0.940170	−	0.340707i	$-0.110666\pi$
$607$	27.4754	+	15.8630i	1.11519	+	0.643857i	0.175024	+	0.984564i	$0.444000\pi$
$608$	1.46753	+	40.2744i	0.0595161	+	1.63334i
$609$		0			0
$610$	1.03249	−	0.343811i	0.0418042	−	0.0139205i
$611$	−16.0667	+	27.8284i	−0.649990	+	1.12582i
$612$	5.94992	+	3.89709i	0.240511	+	0.157530i
$613$	−16.4834	−	28.5501i	−0.665758	−	1.15313i	−0.979079	−	0.203479i	$-0.934775\pi$
$613$	−16.4834	−	28.5501i	−0.665758	−	1.15313i	0.313322	−	0.949647i	$-0.398558\pi$
$614$	4.39746	−	21.4558i	0.177467	−	0.865885i
$615$	7.64308	−	6.40662i	0.308199	−	0.258340i
$616$		0			0
$617$		−	14.3990i		−	0.579680i	−0.957075	−	0.289840i	$-0.906398\pi$
$617$		−	14.3990i		−	0.579680i	0.957075	−	0.289840i	$-0.0936021\pi$
$618$	2.98943	+	5.53161i	0.120252	+	0.222514i
$619$	−21.3838	+	12.3460i	−0.859489	+	0.496226i	−0.863841	−	0.503764i	$-0.831948\pi$
$619$	−21.3838	+	12.3460i	−0.859489	+	0.496226i	0.00435197	+	0.999991i	$0.498615\pi$
$620$	7.23453	+	3.09553i	0.290546	+	0.124320i
$621$	−40.9826	−	0.0630910i	−1.64457	−	0.00253175i
$622$	4.86990	+	14.6246i	0.195265	+	0.586395i
$623$		0			0
$624$	−14.6368	−	33.4387i	−0.585943	−	1.33862i
$625$	−7.87046	+	13.6320i	−0.314818	+	0.545281i
$626$	−31.7272	+	35.7571i	−1.26807	+	1.42914i
$627$	−9.91272	+	27.1916i	−0.395876	+	1.08593i
$628$	0.933526	+	7.78862i	0.0372517	+	0.310800i
$629$			1.24227i			0.0495327i
$630$		0			0
$631$		−	15.8863i		−	0.632423i	−0.948689	−	0.316212i	$-0.897589\pi$
$631$		−	15.8863i		−	0.632423i	0.948689	−	0.316212i	$-0.102411\pi$
$632$	−8.35966	−	17.7233i	−0.332529	−	0.704996i
$633$	−6.95521	+	19.0788i	−0.276445	+	0.758315i
$634$	9.82365	+	8.71652i	0.390147	+	0.346177i
$635$	−1.67131	+	2.89479i	−0.0663239	+	0.114876i
$636$	−29.4096	−	6.89506i	−1.16616	−	0.273407i
$637$		0			0
$638$	13.3163	−	4.43423i	0.527197	−	0.175553i
$639$	−22.2137	−	18.6784i	−0.878761	−	0.738906i
$640$	3.26785	−	8.47834i	0.129173	−	0.335136i
$641$	16.8007	−	9.69989i	0.663588	−	0.383122i	−0.130055	−	0.991507i	$-0.541515\pi$
$641$	16.8007	−	9.69989i	0.663588	−	0.383122i	0.793643	+	0.608384i	$0.208182\pi$
$642$	13.1449	−	7.10385i	0.518788	−	0.280367i
$643$			37.0568i			1.46138i	0.682710	+	0.730690i	$0.260801\pi$
$643$			37.0568i			1.46138i	−0.682710	+	0.730690i	$0.739199\pi$
$644$		0			0
$645$	−8.46792	+	7.09803i	−0.333424	+	0.279485i
$646$	11.7003	+	2.39804i	0.460343	+	0.0943494i
$647$	−22.7029	−	39.3225i	−0.892542	−	1.54593i	−0.836818	−	0.547481i	$-0.815587\pi$
$647$	−22.7029	−	39.3225i	−0.892542	−	1.54593i	−0.0557235	−	0.998446i	$-0.517747\pi$
$648$	−10.7039	+	23.0960i	−0.420490	+	0.907297i
$649$	−0.776548	+	1.34502i	−0.0304822	+	0.0527967i
$650$	−10.2517	−	30.7866i	−0.402105	−	1.20755i
$651$		0			0
$652$	−8.76374	−	11.6999i	−0.343215	−	0.458205i
$653$	−0.855070	−	0.493675i	−0.0334615	−	0.0193190i	0.483176	−	0.875523i	$-0.339483\pi$
$653$	−0.855070	−	0.493675i	−0.0334615	−	0.0193190i	−0.516637	+	0.856204i	$0.672816\pi$
$654$	−0.375611	+	13.3466i	−0.0146875	+	0.521895i
$655$	−7.29738	+	4.21314i	−0.285132	+	0.164621i
$656$	20.7436	−	19.8019i	0.809901	−	0.773133i
$657$	−0.741015	+	4.17743i	−0.0289097	+	0.162977i
$658$		0			0
$659$	6.67629			0.260071			0.130036	−	0.991509i	$-0.458491\pi$
$659$	6.67629			0.260071			0.130036	+	0.991509i	$0.458491\pi$
$660$	4.46643	−	4.75715i	0.173855	−	0.185172i
$661$	−1.35571	−	2.34815i	−0.0527309	−	0.0913326i	0.838455	−	0.544971i	$-0.183459\pi$
$661$	−1.35571	−	2.34815i	−0.0527309	−	0.0913326i	−0.891186	+	0.453638i	$0.850126\pi$
$662$	1.07364	+	0.952641i	0.0417282	+	0.0370254i
$663$	−10.6542	+	1.87299i	−0.413775	+	0.0727408i
$664$	12.0438	+	8.35442i	0.467390	+	0.324214i
$665$		0			0
$666$	−4.39886	+	0.646317i	−0.170452	+	0.0250443i
$667$	28.9018	+	16.6865i	1.11908	+	0.646102i
$668$	15.3939	+	6.58680i	0.595609	+	0.254851i
$669$	0.405331	−	1.11186i	0.0156710	−	0.0429871i
$670$	9.37559	+	1.92157i	0.362211	+	0.0742368i
$671$	2.24723			0.0867535
$672$		0			0
$673$	37.2088			1.43430			0.717148	−	0.696921i	$-0.245447\pi$
$673$	37.2088			1.43430			0.717148	+	0.696921i	$0.245447\pi$
$674$	−17.5390	−	3.59470i	−0.675576	−	0.138462i
$675$	−11.3448	+	19.5800i	−0.436660	+	0.753635i
$676$	27.1361	+	11.6111i	1.04370	+	0.446580i
$677$	−9.63730	−	5.56410i	−0.370392	−	0.213846i	0.303238	−	0.952915i	$-0.401932\pi$
$677$	−9.63730	−	5.56410i	−0.370392	−	0.213846i	−0.673630	+	0.739069i	$0.735266\pi$
$678$	9.11341	−	14.8067i	0.349999	−	0.568647i
$679$		0			0
$680$	−2.21258	−	1.53480i	−0.0848487	−	0.0588570i
$681$	−2.62522	−	14.9332i	−0.100599	−	0.572240i
$682$	12.1548	+	10.7850i	0.465432	+	0.412978i
$683$	−4.83716	−	8.37821i	−0.185089	−	0.320583i	0.758518	−	0.651652i	$-0.225924\pi$
$683$	−4.83716	−	8.37821i	−0.185089	−	0.320583i	−0.943606	+	0.331069i	$0.892591\pi$
$684$	−2.40406	+	42.6781i	−0.0919217	+	1.63184i
$685$	10.8357			0.414013
$686$		0			0
$687$	−24.5549	+	20.5826i	−0.936829	+	0.785274i
$688$	−22.9822	+	21.9389i	−0.876190	+	0.836412i
$689$	39.7870	−	22.9710i	1.51576	−	0.875127i
$690$	15.5097	+	0.436486i	0.590445	+	0.0166168i
$691$	−7.20943	−	4.16236i	−0.274260	−	0.158344i	0.356562	−	0.934272i	$-0.383949\pi$
$691$	−7.20943	−	4.16236i	−0.274260	−	0.158344i	−0.630822	+	0.775928i	$0.717282\pi$
$692$	−15.3128	−	20.4432i	−0.582105	−	0.777133i
$693$		0			0
$694$	11.4509	+	34.3879i	0.434670	+	1.30535i
$695$	3.04088	−	5.26697i	0.115347	−	0.199787i
$696$	16.9340	−	11.9557i	0.641881	−	0.453179i
$697$	−4.24943	−	7.36022i	−0.160958	−	0.278788i
$698$	−38.9627	−	7.98559i	−1.47476	−	0.302259i
$699$	−11.2814	−	13.4586i	−0.426700	−	0.509052i
$700$		0			0
$701$		−	34.0535i		−	1.28618i	−0.765790	−	0.643091i	$-0.777652\pi$
$701$		−	34.0535i		−	1.28618i	0.765790	−	0.643091i	$-0.222348\pi$
$702$	−12.1752	−	36.7518i	−0.459525	−	1.38711i
$703$	−6.46568	+	3.73296i	−0.243858	+	0.140791i
$704$	11.9341	−	14.4793i	0.449782	−	0.545711i
$705$	−8.35599	+	1.46897i	−0.314705	+	0.0553244i
$706$	13.8269	−	4.60425i	0.520382	−	0.173283i
$707$		0			0
$708$	−0.523592	+	2.23328i	−0.0196778	+	0.0839318i
$709$	−4.82135	+	8.35083i	−0.181070	+	0.313622i	−0.942245	−	0.334924i	$-0.891289\pi$
$709$	−4.82135	+	8.35083i	−0.181070	+	0.313622i	0.761175	+	0.648546i	$0.224623\pi$
$710$	8.21900	+	7.29272i	0.308454	+	0.273691i
$711$	−7.08871	−	19.5384i	−0.265847	−	0.732748i
$712$	−19.7473	−	41.8663i	−0.740062	−	1.56901i
$713$			38.6388i			1.44703i
$714$		0			0
$715$			9.92437i			0.371150i
$716$	5.02626	+	41.9353i	0.187840	+	1.56719i
$717$	−2.43231	−	0.886703i	−0.0908364	−	0.0331145i
$718$	25.1918	−	28.3915i	0.940150	−	1.05956i
$719$	−4.04585	+	7.00762i	−0.150885	+	0.261340i	−0.931553	−	0.363606i	$-0.881546\pi$
$719$	−4.04585	+	7.00762i	−0.150885	+	0.261340i	0.780668	+	0.624946i	$0.214879\pi$
$720$	4.28356	−	8.63321i	0.159639	−	0.321741i
$721$		0			0
$722$	14.1885	+	42.6090i	0.528040	+	1.58574i
$723$	−3.09900	−	17.6282i	−0.115253	−	0.655599i
$724$	22.8142	+	9.76181i	0.847883	+	0.362795i
$725$	15.9586	−	9.21369i	0.592687	−	0.342188i
$726$	−11.8497	+	6.40387i	−0.439782	+	0.237670i
$727$		−	36.9501i		−	1.37040i	−0.728353	−	0.685202i	$-0.759714\pi$
$727$		−	36.9501i		−	1.37040i	0.728353	−	0.685202i	$-0.240286\pi$
$728$		0			0
$729$	−13.5719	+	23.3410i	−0.502664	+	0.864482i
$730$	0.322504	−	1.57354i	0.0119364	−	0.0582393i
$731$	4.70802	+	8.15453i	0.174133	+	0.301606i
$732$	3.17729	−	0.959603i	0.117436	−	0.0354680i
$733$	18.9776	−	32.8702i	0.700954	−	1.21409i	−0.267178	−	0.963647i	$-0.586091\pi$
$733$	18.9776	−	32.8702i	0.700954	−	1.21409i	0.968132	−	0.250440i	$-0.0805753\pi$
$734$	17.9153	−	5.96566i	0.661266	−	0.220197i
$735$		0			0
$736$	44.5867	−	1.62466i	1.64349	−	0.0598857i
$737$	17.1157	+	9.88173i	0.630463	+	0.363998i
$738$	23.8515	−	18.8764i	0.877985	−	0.694849i
$739$	−19.1667	+	11.0659i	−0.705058	+	0.407065i	−0.809228	−	0.587494i	$-0.800115\pi$
$739$	−19.1667	+	11.0659i	−0.705058	+	0.407065i	0.104171	+	0.994559i	$0.466781\pi$
$740$	1.67131	−	0.200319i	0.0614386	−	0.00736388i
$741$	−41.7636	−	49.8238i	−1.53422	−	1.83032i
$742$		0			0
$743$	21.7884			0.799340			0.399670	−	0.916659i	$-0.369125\pi$
$743$	21.7884			0.799340			0.399670	+	0.916659i	$0.369125\pi$
$744$	21.7906	+	10.0582i	0.798884	+	0.368752i
$745$	6.46568	+	11.1989i	0.236884	+	0.410296i
$746$	21.4059	−	24.1248i	0.783726	−	0.883271i
$747$	11.8993	+	10.0056i	0.435374	+	0.366084i
$748$	−3.33371	−	4.45064i	−0.121893	−	0.162731i
$749$		0			0
$750$	9.64649	−	15.6728i	0.352240	−	0.572289i
$751$	−4.44124	−	2.56415i	−0.162063	−	0.0935671i	0.416775	−	0.909010i	$-0.363160\pi$
$751$	−4.44124	−	2.56415i	−0.162063	−	0.0935671i	−0.578838	+	0.815443i	$0.696494\pi$
$752$	−23.7053	+	5.76534i	−0.864443	+	0.210240i
$753$	43.8645	+	15.9909i	1.59851	+	0.582740i
$754$	−6.33005	+	30.8851i	−0.230527	+	1.12477i
$755$	−13.9618			−0.508122
$756$		0			0
$757$	−30.4486			−1.10667			−0.553337	−	0.832958i	$-0.686646\pi$
$757$	−30.4486			−1.10667			−0.553337	+	0.832958i	$0.686646\pi$
$758$	−0.562562	+	2.74481i	−0.0204332	+	0.0996961i
$759$	30.1030	+	10.9741i	1.09267	+	0.398335i
$760$	1.33953	−	16.1279i	0.0485897	−	0.585019i
$761$	37.0224	+	21.3749i	1.34206	+	0.774839i	0.987110	−	0.160046i	$-0.0511642\pi$
$761$	37.0224	+	21.3749i	1.34206	+	0.774839i	0.354951	+	0.934885i	$0.384498\pi$
$762$	−5.34377	+	8.68209i	−0.193584	+	0.314519i
$763$		0			0
$764$	−9.76434	+	7.31389i	−0.353261	+	0.264607i
$765$	−2.18605	−	1.83814i	−0.0790367	−	0.0664580i
$766$	−27.0516	+	30.4876i	−0.977415	+	1.10156i
$767$	−1.74436	−	3.02131i	−0.0629851	−	0.109093i
$768$	10.6903	−	25.5679i	0.385753	−	0.922602i
$769$	7.77655			0.280430			0.140215	−	0.990121i	$-0.455221\pi$
$769$	7.77655			0.280430			0.140215	+	0.990121i	$0.455221\pi$
$770$		0			0
$771$	−3.10619	−	3.70567i	−0.111867	−	0.133456i
$772$	−0.153520	−	1.28085i	−0.00552529	−	0.0460988i
$773$	−1.04249	+	0.601881i	−0.0374957	+	0.0216482i	−0.518631	−	0.854998i	$-0.673558\pi$
$773$	−1.04249	+	0.601881i	−0.0374957	+	0.0216482i	0.481135	+	0.876647i	$0.340225\pi$
$774$	−26.4255	+	20.9135i	−0.949846	+	0.751721i
$775$	18.4767	+	10.6675i	0.663701	+	0.383188i
$776$	−10.1752	−	7.05825i	−0.365269	−	0.253376i
$777$		0			0
$778$	−2.62954	+	0.875618i	−0.0942737	+	0.0313924i
$779$	25.5386	−	44.2341i	0.915014	−	1.58485i
$780$	4.23786	+	14.0317i	0.151740	+	0.502417i
$781$	11.3453	+	19.6507i	0.405968	+	0.703157i
$782$	2.65480	−	12.9531i	0.0949354	−	0.463202i
$783$	19.0579	−	10.9640i	0.681072	−	0.391820i
$784$		0			0
$785$		−	3.15000i		−	0.112428i
$786$	−22.6093	+	12.2187i	−0.806448	+	0.435826i
$787$	19.4895	−	11.2522i	0.694724	−	0.401099i	−0.110655	−	0.993859i	$-0.535295\pi$
$787$	19.4895	−	11.2522i	0.694724	−	0.401099i	0.805380	+	0.592760i	$0.201962\pi$
$788$	−11.7316	+	27.4177i	−0.417920	+	0.976716i
$789$	4.59144	+	26.1177i	0.163460	+	0.929816i
$790$	2.48610	+	7.46593i	0.0884514	+	0.265626i
$791$		0			0
$792$	14.0252	−	14.1201i	0.498362	−	0.501736i
$793$	−2.52398	+	4.37166i	−0.0896290	+	0.155242i
$794$	4.28298	−	4.82699i	0.151997	−	0.171303i
$795$	11.3963	+	4.15455i	0.404186	+	0.147347i
$796$	37.1327	−	4.45064i	1.31613	−	0.157749i
$797$		−	18.3911i		−	0.651447i	−0.945465	−	0.325724i	$-0.894392\pi$
$797$		−	18.3911i		−	0.651447i	0.945465	−	0.325724i	$-0.105608\pi$
$798$		0			0
$799$			7.23003i			0.255780i
$800$	11.5327	−	21.7694i	0.407743	−	0.769665i
$801$	−16.7451	−	46.1540i	−0.591658	−	1.63077i
$802$	−28.3299	−	25.1371i	−1.00036	−	0.887621i
$803$	1.65849	−	2.87258i	0.0585267	−	0.101371i
$804$	28.4189	+	6.66281i	1.00226	+	0.234979i
$805$		0			0
$806$	−34.6322	+	11.5323i	−1.21987	+	0.406206i
$807$	52.3477	−	9.20262i	1.84273	−	0.323948i
$808$	−23.6586	−	1.96500i	−0.832305	−	0.0691285i
$809$	−11.5087	+	6.64455i	−0.404624	+	0.233610i	−0.688477	−	0.725258i	$-0.741721\pi$
$809$	−11.5087	+	6.64455i	−0.404624	+	0.233610i	0.283853	+	0.958868i	$0.408387\pi$
$810$	5.37146	−	8.69705i	0.188734	−	0.305583i
$811$		−	6.46254i		−	0.226930i	−0.993542	−	0.113465i	$-0.963805\pi$
$811$		−	6.46254i		−	0.226930i	0.993542	−	0.113465i	$-0.0361950\pi$
$812$		0			0
$813$	21.9041	+	26.1315i	0.768210	+	0.916472i
$814$	3.40524	+	0.697921i	0.119354	+	0.0244621i
$815$	2.93506	+	5.08367i	0.102811	+	0.178073i
$816$	−6.61392	−	4.86907i	−0.231533	−	0.170451i
$817$	−28.2947	+	49.0078i	−0.989906	+	1.71457i
$818$	−8.06140	−	24.2090i	−0.281860	−	0.846446i
$819$		0			0
$820$	−9.21694	+	6.90387i	−0.321869	+	0.241094i
$821$	24.1767	+	13.9584i	0.843774	+	0.487153i	0.858545	−	0.512738i	$-0.171369\pi$
$821$	24.1767	+	13.9584i	0.843774	+	0.487153i	−0.0147715	+	0.999891i	$0.504702\pi$
$822$	33.0354	+	0.929708i	1.15224	+	0.0324273i
$823$	38.9668	−	22.4975i	1.35830	−	0.784213i	0.368902	−	0.929468i	$-0.379734\pi$
$823$	38.9668	−	22.4975i	1.35830	−	0.784213i	0.989394	+	0.145256i	$0.0464004\pi$
$824$	−3.09731	−	6.56662i	−0.107900	−	0.228759i
$825$	13.5586	−	11.3652i	0.472051	−	0.395685i
$826$		0			0
$827$	34.2989			1.19269			0.596344	−	0.802729i	$-0.296619\pi$
$827$	34.2989			1.19269			0.596344	+	0.802729i	$0.296619\pi$
$828$	47.2478	+	2.66147i	1.64197	+	0.0924925i
$829$	−11.5078	−	19.9322i	−0.399684	−	0.692273i	0.594003	−	0.804463i	$-0.297547\pi$
$829$	−11.5078	−	19.9322i	−0.399684	−	0.692273i	−0.993687	+	0.112190i	$0.964213\pi$
$830$	−4.40272	−	3.90653i	−0.152820	−	0.135598i
$831$	−3.93246	−	22.3692i	−0.136416	−	0.775980i
$832$	14.7637	+	39.4784i	0.511838	+	1.36867i
$833$		0			0
$834$	9.72279	−	15.7967i	0.336673	−	0.546996i
$835$	−5.82291	−	3.36186i	−0.201510	−	0.116342i
$836$	13.1467	−	30.7249i	0.454688	−	1.06264i
$837$	22.0258	+	12.7618i	0.761323	+	0.441114i
$838$	24.2995	+	4.98029i	0.839412	+	0.172041i
$839$	−46.9847			−1.62209			−0.811046	−	0.584983i	$-0.801101\pi$
$839$	−46.9847			−1.62209			−0.811046	+	0.584983i	$0.801101\pi$
$840$		0			0
$841$	11.0959			0.382617
$842$	21.3363	+	4.37297i	0.735297	+	0.150703i
$843$	1.70062	−	4.66496i	0.0585724	−	0.160670i
$844$	9.22430	−	21.5580i	0.317513	−	0.742056i
$845$	−10.2645	−	5.92623i	−0.353110	−	0.203868i
$846$	−25.6013	+	3.76156i	−0.880191	+	0.129325i
$847$		0			0
$848$	33.4728	+	9.80751i	1.14946	+	0.336791i
$849$	−3.39541	+	0.596905i	−0.116530	+	0.0204857i
$850$	−5.46109	−	4.84562i	−0.187314	−	0.166204i
$851$	4.13266	+	7.15798i	0.141666	+	0.245372i
$852$	24.4319	+	22.9388i	0.837024	+	0.785872i
$853$	12.7498			0.436545			0.218272	−	0.975888i	$-0.429958\pi$
$853$	12.7498			0.436545			0.218272	+	0.975888i	$0.429958\pi$
$854$		0			0
$855$	2.99803	−	16.9012i	0.102531	−	0.578010i
$856$	−15.6044	+	7.36022i	−0.533348	+	0.251567i
$857$	−26.1774	+	15.1136i	−0.894204	+	0.516269i	−0.875315	−	0.483553i	$-0.839346\pi$
$857$	−26.1774	+	15.1136i	−0.894204	+	0.516269i	−0.0188889	+	0.999822i	$0.506013\pi$
$858$	−0.851511	+	30.2569i	−0.0290701	+	1.03295i
$859$	15.8982	+	9.17880i	0.542438	+	0.313177i	0.746066	−	0.665872i	$-0.231940\pi$
$859$	15.8982	+	9.17880i	0.542438	+	0.313177i	−0.203628	+	0.979048i	$0.565273\pi$
$860$	10.2116	−	7.64893i	0.348214	−	0.260826i
$861$		0			0
$862$	−4.02283	−	12.0808i	−0.137018	−	0.411475i
$863$	−13.1968	+	22.8576i	−0.449225	+	0.778080i	−0.998336	−	0.0576693i	$-0.981633\pi$
$863$	−13.1968	+	22.8576i	−0.449225	+	0.778080i	0.549111	+	0.835749i	$0.314966\pi$
$864$	13.8002	−	25.9529i	0.469493	−	0.882936i
$865$	5.12839	+	8.88264i	0.174371	+	0.302019i
$866$	−8.53261	−	1.74880i	−0.289950	−	0.0594266i
$867$	20.7005	−	17.3517i	0.703025	−	0.589293i
$868$		0			0
$869$			16.2498i			0.551236i
$870$	−7.32307	+	3.95758i	−0.248275	+	0.134174i
$871$	−38.4468	+	22.1973i	−1.30272	+	0.752126i
$872$	1.27613	−	15.3646i	0.0432152	−	0.520310i
$873$	−10.0532	−	8.45322i	−0.340249	−	0.286098i
$874$	75.3947	−	25.1059i	2.55026	−	0.849218i
$875$		0			0
$876$	1.11824	−	4.76965i	0.0377819	−	0.161151i
$877$	0.468662	−	0.811746i	0.0158256	−	0.0274107i	−0.858004	−	0.513643i	$-0.828296\pi$
$877$	0.468662	−	0.811746i	0.0158256	−	0.0274107i	0.873830	+	0.486232i	$0.161629\pi$
$878$	−30.9408	−	27.4538i	−1.04420	−	0.926519i
$879$	−9.93557	+	27.2542i	−0.335118	+	0.919262i
$880$	−5.45016	+	5.20273i	−0.183725	+	0.175384i
$881$			37.1298i			1.25093i	0.780251	+	0.625467i	$0.215091\pi$
$881$			37.1298i			1.25093i	−0.780251	+	0.625467i	$0.784909\pi$
$882$		0			0
$883$		−	5.76235i		−	0.193918i	−0.995288	−	0.0969592i	$-0.969088\pi$
$883$		−	5.76235i		−	0.193918i	0.995288	−	0.0969592i	$-0.0309116\pi$
$884$	12.4023	−	1.48651i	0.417134	−	0.0499968i
$885$	0.315485	−	0.865405i	0.0106049	−	0.0290903i
$886$	6.77340	−	7.63372i	0.227557	−	0.256460i
$887$	13.0672	−	22.6330i	0.438752	−	0.759941i	−0.558841	−	0.829275i	$-0.688754\pi$
$887$	13.0672	−	22.6330i	0.438752	−	0.759941i	0.997594	+	0.0693335i	$0.0220873\pi$
$888$	5.11259	−	0.467324i	0.171567	−	0.0156824i
$889$		0			0
$890$	5.87270	+	17.6361i	0.196853	+	0.591165i
$891$	16.1983	−	13.5354i	0.542664	−	0.453454i
$892$	−0.537568	+	1.25634i	−0.0179991	+	0.0420655i
$893$	−37.6302	+	21.7258i	−1.25925	+	0.727027i
$894$	18.7514	+	34.6973i	0.627139	+	1.16045i
$895$		−	16.9601i		−	0.566915i
$896$		0			0
$897$	−55.1586	+	46.2353i	−1.84169	+	1.54375i
$898$	−1.25909	+	6.14324i	−0.0420163	+	0.205003i
$899$	−10.3646	−	17.9520i	−0.345678	−	0.598732i
$900$	14.3170	−	21.8586i	0.477233	−	0.728620i
$901$	5.16848	−	8.95207i	0.172187	−	0.298237i
$902$	−22.5627	+	7.51322i	−0.751257	+	0.250163i
$903$		0			0
$904$	−11.4428	+	16.4960i	−0.380582	+	0.548649i
$905$	−8.62971	−	4.98237i	−0.286861	−	0.165619i
$906$	−42.5660	−	1.19792i	−1.41416	−	0.0397984i
$907$	35.3624	−	20.4165i	1.17419	−	0.677918i	0.219525	−	0.975607i	$-0.429549\pi$
$907$	35.3624	−	20.4165i	1.17419	−	0.677918i	0.954663	+	0.297689i	$0.0962160\pi$
$908$	2.08352	+	17.3833i	0.0691442	+	0.576886i
$909$	−24.7931	−	4.39793i	−0.822334	−	0.145870i
$910$		0			0
$911$	4.31270			0.142886			0.0714430	−	0.997445i	$-0.477240\pi$
$911$	4.31270			0.142886			0.0714430	+	0.997445i	$0.477240\pi$
$912$	5.46765	−	49.0548i	0.181052	−	1.62437i
$913$	−6.07741	−	10.5264i	−0.201133	−	0.348372i
$914$	−12.8234	+	14.4521i	−0.424159	+	0.478034i
$915$	−1.31267	+	0.230765i	−0.0433955	+	0.00762885i
$916$	29.6113	−	22.1801i	0.978384	−	0.732850i
$917$		0			0
$918$	−6.50699	−	5.79157i	−0.214763	−	0.191150i
$919$	14.9668	+	8.64107i	0.493708	+	0.285043i	0.726112	−	0.687577i	$-0.241326\pi$
$919$	14.9668	+	8.64107i	0.493708	+	0.285043i	−0.232403	+	0.972620i	$0.574659\pi$
$920$	−17.8547	−	1.48295i	−0.588652	−	0.0488915i
$921$	−9.18732	+	25.2017i	−0.302733	+	0.830425i
$922$	−1.49296	+	7.28436i	−0.0491682	+	0.239898i
$923$	−50.9699			−1.67770
$924$		0			0
$925$	4.56383			0.150058
$926$	4.51087	−	22.0091i	0.148236	−	0.723264i
$927$	−2.62642	−	7.23913i	−0.0862629	−	0.237764i
$928$	−20.2796	+	12.7149i	−0.665711	+	0.417387i
$929$	20.0527	+	11.5774i	0.657908	+	0.379843i	0.791479	−	0.611196i	$-0.209311\pi$
$929$	20.0527	+	11.5774i	0.657908	+	0.379843i	−0.133571	+	0.991039i	$0.542645\pi$
$930$	−8.20745	−	5.05163i	−0.269133	−	0.165650i
$931$		0			0
$932$	12.1570	+	16.2300i	0.398214	+	0.531632i
$933$	−3.26866	−	18.5933i	−0.107011	−	0.608717i
$934$	−25.4146	+	28.6426i	−0.831590	+	0.937215i
$935$	1.11649	+	1.93382i	0.0365132	+	0.0632426i
$936$	11.7162	+	43.1428i	0.382957	+	1.41017i
$937$	−3.10294			−0.101369			−0.0506843	−	0.998715i	$-0.516140\pi$
$937$	−3.10294			−0.101369			−0.0506843	+	0.998715i	$0.516140\pi$
$938$		0			0
$939$	44.8691	−	37.6104i	1.46425	−	1.22737i
$940$	9.72701	−	1.16586i	0.317260	−	0.0380260i
$941$	20.4823	−	11.8254i	0.667703	−	0.385498i	−0.127503	−	0.991838i	$-0.540696\pi$
$941$	20.4823	−	11.8254i	0.667703	−	0.385498i	0.795206	+	0.606340i	$0.207363\pi$
$942$	0.270270	−	9.60354i	0.00880587	−	0.312900i
$943$	−48.9703	−	28.2730i	−1.59469	−	0.920696i
$944$	0.744755	−	2.54183i	0.0242397	−	0.0827296i
$945$		0			0
$946$	24.9977	−	8.32404i	0.812745	−	0.270638i
$947$	−28.7686	+	49.8286i	−0.934852	+	1.61921i	−0.159955	+	0.987124i	$0.551135\pi$
$947$	−28.7686	+	49.8286i	−0.934852	+	1.61921i	−0.774897	+	0.632087i	$0.782198\pi$
$948$	6.93890	+	22.9750i	0.225365	+	0.746194i
$949$	3.72545	+	6.45267i	0.120933	+	0.209462i
$950$	8.80982	−	42.9842i	0.285828	−	1.39459i
$951$	−10.3328	−	12.3270i	−0.335065	−	0.399731i
$952$		0			0
$953$		−	14.1961i		−	0.459855i	−0.973208	−	0.229928i	$-0.926151\pi$
$953$		−	14.1961i		−	0.459855i	0.973208	−	0.229928i	$-0.0738490\pi$
$954$	34.3880	+	13.6440i	1.11335	+	0.441740i
$955$	4.24264	−	2.44949i	0.137289	−	0.0792636i
$956$	2.74838	+	1.17598i	0.0888889	+	0.0380340i
$957$	−16.9299	+	2.97624i	−0.547266	+	0.0962082i
$958$	−6.81842	−	20.4762i	−0.220293	−	0.661557i
$959$		0			0
$960$	−5.48415	+	9.68327i	−0.177000	+	0.312526i
$961$	−3.50000	+	6.06218i	−0.112903	+	0.195554i
$962$	−5.18229	+	5.84052i	−0.167084	+	0.188306i
$963$	−17.2025	+	6.24122i	−0.554343	+	0.201120i
$964$	2.45955	+	20.5206i	0.0792166	+	0.660923i
$965$			0.518021i			0.0166757i
$966$		0			0
$967$			31.5730i			1.01532i	0.861558	+	0.507660i	$0.169489\pi$
$967$			31.5730i			1.01532i	−0.861558	+	0.507660i	$0.830511\pi$
$968$	14.0668	−	6.63498i	0.452125	−	0.213256i
$969$	−13.7431	−	5.01005i	−0.441491	−	0.160946i
$970$	3.71964	+	3.30044i	0.119431	+	0.105971i
$971$	14.6620	−	25.3953i	0.470526	−	0.814974i	−0.528906	−	0.848680i	$-0.677398\pi$
$971$	14.6620	−	25.3953i	0.470526	−	0.814974i	0.999432	+	0.0337060i	$0.0107310\pi$
$972$	17.1224	−	26.0542i	0.549202	−	0.835690i
$973$		0			0
$974$	−8.13677	+	2.70948i	−0.260719	+	0.0868174i
$975$	6.88091	+	39.1410i	0.220366	+	1.25352i
$976$	−3.72394	+	0.905697i	−0.119200	+	0.0289907i
$977$	10.3022	−	5.94797i	0.329596	−	0.190292i	−0.326066	−	0.945347i	$-0.605723\pi$
$977$	10.3022	−	5.94797i	0.329596	−	0.190292i	0.655662	+	0.755055i	$0.272390\pi$
$978$	8.51206	+	15.7506i	0.272186	+	0.503650i
$979$			38.3855i			1.22681i
$980$		0			0
$981$	2.85614	−	16.1013i	0.0911896	−	0.514076i
$982$	−5.59476	−	1.14667i	−0.178536	−	0.0365918i
$983$	7.49013	+	12.9733i	0.238898	+	0.413783i	0.960398	−	0.278631i	$-0.0898805\pi$
$983$	7.49013	+	12.9733i	0.238898	+	0.413783i	−0.721500	+	0.692414i	$0.756547\pi$
$984$	−28.6924	+	20.2573i	−0.914682	+	0.645780i
$985$	5.98772	−	10.3710i	0.190785	−	0.330449i
$986$	2.24113	+	6.73027i	0.0713721	+	0.214336i
$987$		0			0
$988$	45.0051	+	60.0835i	1.43180	+	1.91151i
$989$	54.2552	+	31.3243i	1.72521	+	0.996053i
$990$	−6.26672	+	4.95957i	−0.199170	+	0.157625i
$991$	18.0000	−	10.3923i	0.571789	−	0.330122i	−0.186075	−	0.982536i	$-0.559577\pi$
$991$	18.0000	−	10.3923i	0.571789	−	0.330122i	0.757863	+	0.652413i	$0.226243\pi$
$992$	−24.4887	−	12.9733i	−0.777515	−	0.411902i
$993$	−1.12929	−	1.34724i	−0.0358369	−	0.0427533i
$994$		0			0
$995$	−15.0178			−0.476096
$996$	−13.0876	−	12.2878i	−0.414696	−	0.389353i
$997$	9.81912	+	17.0072i	0.310975	+	0.538624i	0.978574	−	0.205897i	$-0.0660113\pi$
$997$	9.81912	+	17.0072i	0.310975	+	0.538624i	−0.667599	+	0.744521i	$0.732678\pi$
$998$	−40.7278	−	36.1377i	−1.28922	−	1.14392i
$999$	5.44532	+	0.00838284i	0.172282	+	0.000265221i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.n.h.275.11		24
3.2	odd	2	inner	588.2.n.h.275.1		24
4.3	odd	2		588.2.n.d.275.10		24
7.2	even	3		588.2.e.f.491.10	yes	24
7.3	odd	6		588.2.n.d.263.3		24
7.4	even	3		588.2.n.d.263.4		24
7.5	odd	6		588.2.e.f.491.9	✓	24
7.6	odd	2	inner	588.2.n.h.275.12		24
12.11	even	2		588.2.n.d.275.4		24
21.2	odd	6		588.2.e.f.491.15	yes	24
21.5	even	6		588.2.e.f.491.16	yes	24
21.11	odd	6		588.2.n.d.263.10		24
21.17	even	6		588.2.n.d.263.9		24
21.20	even	2	inner	588.2.n.h.275.2		24
28.3	even	6	inner	588.2.n.h.263.2		24
28.11	odd	6	inner	588.2.n.h.263.1		24
28.19	even	6		588.2.e.f.491.14	yes	24
28.23	odd	6		588.2.e.f.491.13	yes	24
28.27	even	2		588.2.n.d.275.9		24
84.11	even	6	inner	588.2.n.h.263.11		24
84.23	even	6		588.2.e.f.491.12	yes	24
84.47	odd	6		588.2.e.f.491.11	yes	24
84.59	odd	6	inner	588.2.n.h.263.12		24
84.83	odd	2		588.2.n.d.275.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.e.f.491.9	✓	24	7.5	odd	6
588.2.e.f.491.10	yes	24	7.2	even	3
588.2.e.f.491.11	yes	24	84.47	odd	6
588.2.e.f.491.12	yes	24	84.23	even	6
588.2.e.f.491.13	yes	24	28.23	odd	6
588.2.e.f.491.14	yes	24	28.19	even	6
588.2.e.f.491.15	yes	24	21.2	odd	6
588.2.e.f.491.16	yes	24	21.5	even	6
588.2.n.d.263.3		24	7.3	odd	6
588.2.n.d.263.4		24	7.4	even	3
588.2.n.d.263.9		24	21.17	even	6
588.2.n.d.263.10		24	21.11	odd	6
588.2.n.d.275.3		24	84.83	odd	2
588.2.n.d.275.4		24	12.11	even	2
588.2.n.d.275.9		24	28.27	even	2
588.2.n.d.275.10		24	4.3	odd	2
588.2.n.h.263.1		24	28.11	odd	6	inner
588.2.n.h.263.2		24	28.3	even	6	inner
588.2.n.h.263.11		24	84.11	even	6	inner
588.2.n.h.263.12		24	84.59	odd	6	inner
588.2.n.h.275.1		24	3.2	odd	2	inner
588.2.n.h.275.2		24	21.20	even	2	inner
588.2.n.h.275.11		24	1.1	even	1	trivial
588.2.n.h.275.12		24	7.6	odd	2	inner

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.38541 + 0.283947i) q^{2} +(-1.62729 - 0.593231i) q^{3} +(1.83875 + 0.786769i) q^{4} +(-0.695526 - 0.401562i) q^{5} +(-2.08603 - 1.28394i) q^{6} +(2.32403 + 1.61211i) q^{8} +(2.29615 + 1.93072i) q^{9} +(-0.849569 - 0.753822i) q^{10} +(-1.17273 - 2.03122i) q^{11} +(-2.52544 - 2.37111i) q^{12} +5.26858 q^{13} +(0.893604 + 1.06607i) q^{15} +(2.76199 + 2.89334i) q^{16} +(1.02661 - 0.592715i) q^{17} +(2.63290 + 3.32683i) q^{18} +(6.16982 + 3.56215i) q^{19} +(-0.962960 - 1.28559i) q^{20} +(-1.04795 - 3.14708i) q^{22} +(3.94356 - 6.83044i) q^{23} +(-2.82552 - 4.00206i) q^{24} +(-2.17750 - 3.77153i) q^{25} +(7.29917 + 1.49600i) q^{26} +(-2.59115 - 4.50399i) q^{27} +4.23132i q^{29} +(0.935305 + 1.73068i) q^{30} +(-4.24264 + 2.44949i) q^{31} +(3.00494 + 4.79274i) q^{32} +(0.703383 + 4.00109i) q^{33} +(1.59058 - 0.529652i) q^{34} +(2.70302 + 5.35665i) q^{36} +(-0.523976 + 0.907554i) q^{37} +(7.53630 + 6.68696i) q^{38} +(-8.57351 - 3.12549i) q^{39} +(-0.969059 - 2.05450i) q^{40} -7.16942i q^{41} +7.94315i q^{43} +(-0.558245 - 4.65757i) q^{44} +(-0.821730 - 2.26491i) q^{45} +(7.40294 - 8.34323i) q^{46} +(-3.04954 + 5.28195i) q^{47} +(-2.77814 - 6.34681i) q^{48} +(-1.94582 - 5.84343i) q^{50} +(-2.02221 + 0.355501i) q^{51} +(9.68759 + 4.14516i) q^{52} +(7.55175 - 4.36001i) q^{53} +(-2.31091 - 6.97565i) q^{54} +1.88369i q^{55} +(-7.92692 - 9.45679i) q^{57} +(-1.20147 + 5.86214i) q^{58} +(-0.331087 - 0.573459i) q^{59} +(0.804364 + 2.66329i) q^{60} +(-0.479062 + 0.829760i) q^{61} +(-6.57334 + 2.18887i) q^{62} +(2.80221 + 7.49317i) q^{64} +(-3.66443 - 2.11566i) q^{65} +(-0.161621 + 5.74289i) q^{66} +(-7.29738 + 4.21314i) q^{67} +(2.35401 - 0.282146i) q^{68} +(-10.4693 + 8.77567i) q^{69} -9.67432 q^{71} +(2.22379 + 8.18870i) q^{72} +(0.707107 + 1.22474i) q^{73} +(-0.983622 + 1.10856i) q^{74} +(1.30603 + 7.42914i) q^{75} +(8.54216 + 11.4041i) q^{76} +(-10.9904 - 6.76452i) q^{78} +(-6.00000 - 3.46410i) q^{79} +(-0.759178 - 3.12150i) q^{80} +(1.54464 + 8.86646i) q^{81} +(2.03574 - 9.93263i) q^{82} +5.18229 q^{83} -0.952047 q^{85} +(-2.25543 + 11.0046i) q^{86} +(2.51015 - 6.88559i) q^{87} +(0.549103 - 6.61118i) q^{88} +(-14.1733 - 8.18296i) q^{89} +(-0.495321 - 3.37117i) q^{90} +(12.6252 - 9.45679i) q^{92} +(8.35713 - 1.46917i) q^{93} +(-5.72467 + 6.45179i) q^{94} +(-2.86085 - 4.95513i) q^{95} +(-2.04672 - 9.58180i) q^{96} -4.37827 q^{97} +(1.22896 - 6.92820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4} + 60 q^{16} + 24 q^{18} + 12 q^{25} + 36 q^{30} + 12 q^{36} - 96 q^{39} + 24 q^{46} + 12 q^{51} - 24 q^{57} + 48 q^{58} + 12 q^{60} - 48 q^{64} - 48 q^{67} - 36 q^{72} - 24 q^{78} - 144 q^{79}+ \cdots - 24 q^{93}+O(q^{100}) \) 24 * q + 12 * q^4 + 60 * q^16 + 24 * q^18 + 12 * q^25 + 36 * q^30 + 12 * q^36 - 96 * q^39 + 24 * q^46 + 12 * q^51 - 24 * q^57 + 48 * q^58 + 12 * q^60 - 48 * q^64 - 48 * q^67 - 36 * q^72 - 24 * q^78 - 144 * q^79 + 12 * q^81 - 48 * q^85 + 192 * q^88 - 24 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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