LMFDB - Embedded newform 588.2.n.h.263.1

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)

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")

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);

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			263.1
Character	$\chi$	$=$	588.263
Dual form			588.2.n.h.275.1

$q$-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} +(-0.299892 - 1.70589i) q^{3} +(1.83875 - 0.786769i) q^{4} +(0.695526 - 0.401562i) q^{5} +(0.899858 + 2.27821i) q^{6} +(-2.32403 + 1.61211i) q^{8} +(-2.82013 + 1.02317i) q^{9} +(-0.849569 + 0.753822i) q^{10} +(1.17273 - 2.03122i) q^{11} +(-1.89357 - 2.90076i) q^{12} +5.26858 q^{13} +(-0.893604 - 1.06607i) q^{15} +(2.76199 - 2.89334i) q^{16} +(-1.02661 - 0.592715i) q^{17} +(3.61652 - 2.21828i) 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} +(3.44704 + 3.48108i) q^{24} +(-2.17750 + 3.77153i) q^{25} +(-7.29917 + 1.49600i) q^{26} +(2.59115 + 4.50399i) q^{27} +4.23132i q^{29} +(1.54072 + 1.22321i) q^{30} +(-4.24264 - 2.44949i) q^{31} +(-3.00494 + 4.79274i) q^{32} +(-3.81673 - 1.39140i) q^{33} +(1.59058 + 0.529652i) q^{34} +(-4.38051 + 4.10014i) q^{36} +(-0.523976 - 0.907554i) q^{37} +(-7.53630 + 6.68696i) q^{38} +(-1.58001 - 8.98762i) q^{39} +(-0.969059 + 2.05450i) q^{40} -7.16942i q^{41} -7.94315i q^{43} +(0.558245 - 4.65757i) q^{44} +(-1.55061 + 1.84410i) q^{45} +(7.40294 + 8.34323i) q^{46} +(3.04954 + 5.28195i) q^{47} +(-5.76402 - 3.84396i) q^{48} +(1.94582 - 5.84343i) q^{50} +(-0.703234 + 1.92904i) q^{51} +(9.68759 - 4.14516i) q^{52} +(-7.55175 - 4.36001i) q^{53} +(-4.86871 - 5.50415i) q^{54} -1.88369i q^{55} +(-7.92692 - 9.45679i) q^{57} +(-1.20147 - 5.86214i) q^{58} +(0.331087 - 0.573459i) q^{59} +(-2.48186 - 1.25717i) 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} +(5.68284 + 0.843910i) q^{66} +(-7.29738 - 4.21314i) q^{67} +(-2.35401 - 0.282146i) q^{68} +(-10.4693 + 8.77567i) q^{69} +9.67432 q^{71} +(4.90460 - 6.92422i) q^{72} +(0.707107 - 1.22474i) q^{73} +(0.983622 + 1.10856i) q^{74} +(7.08684 + 2.58352i) q^{75} +(8.54216 - 11.4041i) q^{76} +(4.74097 + 12.0029i) q^{78} +(-6.00000 + 3.46410i) q^{79} +(0.759178 - 3.12150i) q^{80} +(6.90626 - 5.77092i) q^{81} +(2.03574 + 9.93263i) q^{82} -5.18229 q^{83} -0.952047 q^{85} +(2.25543 + 11.0046i) q^{86} +(7.21818 - 1.26894i) q^{87} +(0.549103 + 6.61118i) q^{88} +(14.1733 - 8.18296i) q^{89} +(1.62461 - 2.99513i) q^{90} +(-12.6252 - 9.45679i) q^{92} +(-2.90623 + 7.97207i) q^{93} +(-5.72467 - 6.45179i) q^{94} +(2.86085 - 4.95513i) q^{95} +(9.07704 + 3.68880i) 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 $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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
$3$	−0.299892	−	1.70589i	−0.173143	−	0.984897i
$3$	−0.299892	−	1.70589i	−0.173143	−	0.984897i
$4$	1.83875	−	0.786769i	0.919374	−	0.393385i
$5$	0.695526	−	0.401562i	0.311049	−	0.179584i	−0.336347	−	0.941738i	$-0.609192\pi$
$5$	0.695526	−	0.401562i	0.311049	−	0.179584i	0.647396	+	0.762154i	$0.275858\pi$
$6$	0.899858	+	2.27821i	0.367365	+	0.930077i
$7$		0			0
$7$		0			0
$8$	−2.32403	+	1.61211i	−0.821668	+	0.569967i
$9$	−2.82013	+	1.02317i	−0.940043	+	0.341056i
$10$	−0.849569	+	0.753822i	−0.268657	+	0.238380i
$11$	1.17273	−	2.03122i	0.353590	−	0.612436i	−0.633285	−	0.773918i	$-0.718294\pi$
$11$	1.17273	−	2.03122i	0.353590	−	0.612436i	0.986876	+	0.161482i	$0.0516274\pi$
$12$	−1.89357	−	2.90076i	−0.546626	−	0.837377i
$13$	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	$-0.379251\pi$
$17$	−1.02661	−	0.592715i	−0.248990	−	0.143754i	−0.619302	+	0.785153i	$0.712584\pi$
$18$	3.61652	−	2.21828i	0.852423	−	0.522853i
$19$	6.16982	−	3.56215i	1.41545	−	0.817213i	0.419560	−	0.907728i	$-0.362185\pi$
$19$	6.16982	−	3.56215i	1.41545	−	0.817213i	0.995895	+	0.0905147i	$0.0288512\pi$
$20$	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	−0.903974	−	0.427587i	$-0.859364\pi$
$23$	−3.94356	−	6.83044i	−0.822288	−	1.42425i	0.0816860	−	0.996658i	$-0.473970\pi$
$24$	3.44704	+	3.48108i	0.703624	+	0.710572i
$25$	−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	$0.871483\pi$
$30$	1.54072	+	1.22321i	0.281295	+	0.223326i
$31$	−4.24264	−	2.44949i	−0.762001	−	0.439941i	0.0680129	−	0.997684i	$-0.478334\pi$
$31$	−4.24264	−	2.44949i	−0.762001	−	0.439941i	−0.830014	+	0.557743i	$0.811667\pi$
$32$	−3.00494	+	4.79274i	−0.531204	+	0.847244i
$33$	−3.81673	−	1.39140i	−0.664408	−	0.242211i
$34$	1.59058	+	0.529652i	0.272783	+	0.0908346i
$35$		0			0
$36$	−4.38051	+	4.10014i	−0.730085	+	0.683356i
$37$	−0.523976	−	0.907554i	−0.0861412	−	0.149201i	0.819736	−	0.572742i	$-0.194120\pi$
$37$	−0.523976	−	0.907554i	−0.0861412	−	0.149201i	−0.905877	+	0.423541i	$0.860787\pi$
$38$	−7.53630	+	6.68696i	−1.22255	+	1.08477i
$39$	−1.58001	−	8.98762i	−0.253003	−	1.43917i
$40$	−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	$-0.792909\pi$
$43$		−	7.94315i		−	1.21132i	0.795724	−	0.605659i	$-0.207091\pi$
$44$	0.558245	−	4.65757i	0.0841587	−	0.702155i
$45$	−1.55061	+	1.84410i	−0.231151	+	0.274902i
$46$	7.40294	+	8.34323i	1.09150	+	1.23014i
$47$	3.04954	+	5.28195i	0.444821	+	0.770452i	0.998040	−	0.0625838i	$-0.0199341\pi$
$47$	3.04954	+	5.28195i	0.444821	+	0.770452i	−0.553219	+	0.833036i	$0.686601\pi$
$48$	−5.76402	−	3.84396i	−0.831965	−	0.554828i
$49$		0			0
$50$	1.94582	−	5.84343i	0.275180	−	0.826386i
$51$	−0.703234	+	1.92904i	−0.0984725	+	0.270120i
$52$	9.68759	−	4.14516i	1.34343	−	0.574830i
$53$	−7.55175	−	4.36001i	−1.03731	−	0.598893i	−0.118242	−	0.992985i	$-0.537726\pi$
$53$	−7.55175	−	4.36001i	−1.03731	−	0.598893i	−0.919071	+	0.394092i	$0.871059\pi$
$54$	−4.86871	−	5.50415i	−0.662547	−	0.749020i
$55$		−	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	$-0.819609\pi$
$59$	0.331087	−	0.573459i	0.0431038	−	0.0746580i	0.886772	+	0.462206i	$0.152942\pi$
$60$	−2.48186	−	1.25717i	−0.320407	−	0.162300i
$61$	−0.479062	−	0.829760i	−0.0613376	−	0.106240i	0.833726	−	0.552178i	$-0.186203\pi$
$61$	−0.479062	−	0.829760i	−0.0613376	−	0.106240i	−0.895064	+	0.445939i	$0.852870\pi$
$62$	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
$66$	5.68284	+	0.843910i	0.699510	+	0.103878i
$67$	−7.29738	−	4.21314i	−0.891517	−	0.514717i	−0.0170783	−	0.999854i	$-0.505436\pi$
$67$	−7.29738	−	4.21314i	−0.891517	−	0.514717i	−0.874438	+	0.485137i	$0.838770\pi$
$68$	−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	$-0.305366\pi$
$71$	9.67432			1.14813			0.574065	+	0.818810i	$0.305366\pi$
$72$	4.90460	−	6.92422i	0.578013	−	0.816028i
$73$	0.707107	−	1.22474i	0.0827606	−	0.143346i	−0.821674	−	0.569958i	$-0.806960\pi$
$73$	0.707107	−	1.22474i	0.0827606	−	0.143346i	0.904435	+	0.426612i	$0.140293\pi$
$74$	0.983622	+	1.10856i	0.114344	+	0.128867i
$75$	7.08684	+	2.58352i	0.818318	+	0.298319i
$76$	8.54216	−	11.4041i	0.979853	−	1.30814i
$77$		0			0
$78$	4.74097	+	12.0029i	0.536810	+	1.35907i
$79$	−6.00000	+	3.46410i	−0.675053	+	0.389742i	−0.797988	−	0.602673i	$-0.794102\pi$
$79$	−6.00000	+	3.46410i	−0.675053	+	0.389742i	0.122936	+	0.992415i	$0.460769\pi$
$80$	0.759178	−	3.12150i	0.0848787	−	0.348995i
$81$	6.90626	−	5.77092i	0.767362	−	0.641214i
$82$	2.03574	+	9.93263i	0.224810	+	1.09688i
$83$	−5.18229			−0.568830			−0.284415	−	0.958701i	$-0.591799\pi$
$83$	−5.18229			−0.568830			−0.284415	+	0.958701i	$0.591799\pi$
$84$		0			0
$85$	−0.952047			−0.103264
$86$	2.25543	+	11.0046i	0.243210	+	1.18665i
$87$	7.21818	−	1.26894i	0.773870	−	0.136045i
$88$	0.549103	+	6.61118i	0.0585345	+	0.704754i
$89$	14.1733	−	8.18296i	1.50237	−	0.867392i	0.502370	−	0.864653i	$-0.332461\pi$
$89$	14.1733	−	8.18296i	1.50237	−	0.867392i	0.999996	−	0.00273917i	$-0.000871906\pi$
$90$	1.62461	−	2.99513i	0.171249	−	0.315714i
$91$		0			0
$92$	−12.6252	−	9.45679i	−1.31627	−	0.985938i
$93$	−2.90623	+	7.97207i	−0.301362	+	0.826665i
$94$	−5.72467	−	6.45179i	−0.590455	−	0.665451i
$95$	2.86085	−	4.95513i	0.293517	−	0.508386i
$96$	9.07704	+	3.68880i	0.926422	+	0.376487i
$97$	−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	$-0.196210\pi$
$101$	7.26887	+	4.19668i	0.723279	+	0.417586i	−0.0926791	+	0.995696i	$0.529543\pi$
$102$	0.426526	−	2.87220i	0.0422323	−	0.284390i
$103$	−2.22304	+	1.28347i	−0.219043	+	0.126465i	−0.605507	−	0.795840i	$-0.707030\pi$
$103$	−2.22304	+	1.28347i	−0.219043	+	0.126465i	0.386464	+	0.922304i	$0.373696\pi$
$104$	−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	$-0.0713970\pi$
$107$	3.04995	+	5.28267i	0.294850	+	0.510695i	−0.680100	+	0.733119i	$0.738064\pi$
$108$	8.30807	+	6.24308i	0.799444	+	0.600740i
$109$	−2.72545	+	4.72062i	−0.261051	+	0.452153i	−0.966521	−	0.256586i	$-0.917402\pi$
$109$	−2.72545	+	4.72062i	−0.261051	+	0.452153i	0.705471	+	0.708739i	$0.250736\pi$
$110$	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	$0.891648\pi$
$114$	13.6673	+	10.8507i	1.28006	+	1.01627i
$115$	−5.48569	−	3.16716i	−0.511543	−	0.295340i
$116$	3.32907	+	7.78034i	0.309097	+	0.722386i
$117$	−14.8581	+	5.39064i	−1.37363	+	0.498364i
$118$	−0.295860	+	0.888490i	−0.0272361	+	0.0817921i
$119$		0			0
$120$	3.79537	+	1.03698i	0.346469	+	0.0946629i
$121$	2.74943	+	4.76214i	0.249948	+	0.432922i
$122$	0.899307	+	1.01353i	0.0814195	+	0.0917610i
$123$	−12.2303	+	2.15005i	−1.10277	+	0.193864i
$124$	−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	$0.0591184\pi$
$127$			4.16202i			0.369320i	−0.982802	+	0.184660i	$0.940882\pi$
$128$	−1.75456	+	11.1768i	−0.155082	+	0.987902i
$129$	−13.5501	+	2.38209i	−1.19302	+	0.209731i
$130$	−4.47602	+	3.97157i	−0.392573	+	0.348330i
$131$	−5.24594	−	9.08624i	−0.458340	−	0.793869i	0.540533	−	0.841323i	$-0.318223\pi$
$131$	−5.24594	−	9.08624i	−0.458340	−	0.793869i	−0.998873	+	0.0474541i	$0.984889\pi$
$132$	−8.11272	+	0.444463i	−0.706122	+	0.0386855i
$133$		0			0
$134$	11.3062	+	3.76488i	0.976707	+	0.325236i
$135$	3.61084	+	2.09214i	0.310772	+	0.180063i
$136$	3.34140	−	0.277525i	0.286522	−	0.0237976i
$137$	11.6844	+	6.74600i	0.998267	+	0.576350i	0.907735	−	0.419544i	$-0.137810\pi$
$137$	11.6844	+	6.74600i	0.998267	+	0.576350i	0.0905318	+	0.995894i	$0.471143\pi$
$138$	12.0126	−	15.1307i	1.02258	−	1.28801i
$139$		−	7.57264i		−	0.642303i	−0.947028	−	0.321151i	$-0.895930\pi$
$139$		−	7.57264i		−	0.642303i	0.947028	−	0.321151i	$-0.104070\pi$
$140$		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
$144$	−4.82879	+	10.9856i	−0.402400	+	0.915464i
$145$	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	$-0.437419\pi$
$149$	13.9442	−	8.05067i	1.14235	−	0.659536i	0.947012	+	0.321199i	$0.104086\pi$
$150$	−10.5518	−	1.56696i	−0.861550	−	0.127941i
$151$	15.0553	+	8.69219i	1.22518	+	0.707360i	0.966019	−	0.258473i	$-0.0832192\pi$
$151$	15.0553	+	8.69219i	1.22518	+	0.707360i	0.259166	+	0.965833i	$0.416552\pi$
$152$	−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
$156$	−9.97642	−	15.2829i	−0.798753	−	1.22361i
$157$	1.96109	−	3.39671i	0.156512	−	0.271087i	−0.777096	−	0.629381i	$-0.783308\pi$
$157$	1.96109	−	3.39671i	0.156512	−	0.271087i	0.933609	+	0.358295i	$0.116642\pi$
$158$	7.32887	−	6.50290i	0.583053	−	0.517343i
$159$	−5.17299	+	14.1900i	−0.410244	+	1.12534i
$160$	−0.165435	+	4.54014i	−0.0130788	+	0.358930i
$161$		0			0
$162$	−7.92940	+	9.95614i	−0.622992	+	0.782228i
$163$	−6.32987	+	3.65455i	−0.495793	+	0.286246i	−0.726975	−	0.686664i	$-0.759074\pi$
$163$	−6.32987	+	3.65455i	−0.495793	+	0.286246i	0.231181	+	0.972911i	$0.425741\pi$
$164$	−5.64068	−	13.1828i	−0.440463	−	1.02940i
$165$	−3.21337	+	0.564904i	−0.250160	+	0.0439777i
$166$	7.17962	−	1.47150i	0.557247	−	0.114210i
$167$	−8.37196			−0.647842			−0.323921	−	0.946084i	$-0.605001\pi$
$167$	−8.37196			−0.647842			−0.323921	+	0.946084i	$0.605001\pi$
$168$		0			0
$169$	14.7579			1.13523
$170$	1.31898	−	0.270331i	0.101161	−	0.0207335i
$171$	−13.7550	+	16.3585i	−1.05187	+	1.25096i
$172$	−6.24943	−	14.6054i	−0.476514	−	1.11365i
$173$	11.0601	−	6.38556i	0.840884	−	0.485485i	−0.0166803	−	0.999861i	$-0.505310\pi$
$173$	11.0601	−	6.38556i	0.840884	−	0.485485i	0.857565	+	0.514376i	$0.171976\pi$
$174$	−9.63986	+	3.80759i	−0.730796	+	0.288653i
$175$		0			0
$176$	−2.63796	−	9.00331i	−0.198844	−	0.678650i
$177$	−1.07755	−	0.392822i	−0.0809935	−	0.0295263i
$178$	−17.3124	+	15.3613i	−1.29762	+	1.15137i
$179$	−10.5589	+	18.2885i	−0.789206	+	1.36694i	0.137248	+	0.990537i	$0.456174\pi$
$179$	−10.5589	+	18.2885i	−0.789206	+	1.36694i	−0.926454	+	0.376408i	$0.877159\pi$
$180$	−1.40030	+	4.61080i	−0.104372	+	0.343669i
$181$	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
$186$	1.76269	−	11.8698i	0.129246	−	0.870338i
$187$	−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	$-0.0958368\pi$
$191$	3.04995	+	5.28267i	0.220687	+	0.382241i	−0.734330	+	0.678793i	$0.762503\pi$
$192$	−13.6229	−	2.53312i	−0.983148	−	0.182812i
$193$	−0.322504	+	0.558593i	−0.0232144	+	0.0402084i	−0.877399	−	0.479761i	$-0.840723\pi$
$193$	−0.322504	+	0.558593i	−0.0232144	+	0.0402084i	0.854185	+	0.519969i	$0.174057\pi$
$194$	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	$0.821747\pi$
$198$	−0.264622	−	9.94740i	−0.0188059	−	0.706931i
$199$	16.1940	+	9.34962i	1.14796	+	0.662777i	0.948390	−	0.317106i	$-0.102711\pi$
$199$	16.1940	+	9.34962i	1.14796	+	0.662777i	0.199573	+	0.979883i	$0.436044\pi$
$200$	−1.01956	−	12.2755i	−0.0720940	−	0.868010i
$201$	−4.99874	+	13.7120i	−0.352584	+	0.967171i
$202$	−11.2620	−	3.75017i	−0.792394	−	0.263861i
$203$		0			0
$204$	0.224639	+	4.10030i	0.0157278	+	0.287078i
$205$	−2.87897	−	4.98652i	−0.201076	−	0.348274i
$206$	2.71540	−	2.40937i	0.189191	−	0.167869i
$207$	18.1100	+	15.2278i	1.25873	+	1.05841i
$208$	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	$0.132229\pi$
$211$			11.7243i			0.807132i	−0.914950	+	0.403566i	$0.867771\pi$
$212$	−17.3161	−	2.07547i	−1.18927	−	0.142544i
$213$	−2.90125	−	16.5033i	−0.198791	−	1.13079i
$214$	−5.72545	−	6.45267i	−0.391384	−	0.441095i
$215$	−3.18967	−	5.52466i	−0.217533	−	0.376779i
$216$	−13.2828	−	6.29020i	−0.903782	−	0.427994i
$217$		0			0
$218$	2.43547	−	7.31389i	0.164951	−	0.495359i
$219$	−2.30134	−	0.838956i	−0.155510	−	0.0566914i
$220$	−1.48203	−	3.46363i	−0.0999184	−	0.233518i
$221$	−5.40879	−	3.12277i	−0.363835	−	0.210060i
$222$	1.59610	−	2.01040i	0.107123	−	0.134929i
$223$		−	0.683260i		−	0.0457545i	−0.999738	−	0.0228772i	$-0.992717\pi$
$223$		−	0.683260i		−	0.0457545i	0.999738	−	0.0228772i	$-0.00728269\pi$
$224$		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	$-0.927157\pi$
$227$	−4.37694	+	7.58108i	−0.290507	+	0.503174i	0.683422	+	0.730023i	$0.260491\pi$
$228$	−22.0159	−	11.1520i	−1.45804	−	0.738559i
$229$	9.24927	+	16.0202i	0.611209	+	1.05864i	0.991037	+	0.133588i	$0.0426498\pi$
$229$	9.24927	+	16.0202i	0.611209	+	1.05864i	−0.379828	+	0.925057i	$0.624017\pi$
$230$	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	$-0.774430\pi$
$233$	−8.78072	+	5.06955i	−0.575244	+	0.332117i	0.183997	+	0.982927i	$0.441096\pi$
$234$	19.0539	−	11.6872i	1.24560	−	0.764015i
$235$	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	$-0.515394\pi$
$239$	−1.49470			−0.0966841			−0.0483421	+	0.998831i	$0.515394\pi$
$240$	−5.55262	−	0.358961i	−0.358420	−	0.0231709i
$241$	5.16686	−	8.94926i	0.332827	−	0.576472i	−0.650238	−	0.759730i	$-0.725331\pi$
$241$	5.16686	−	8.94926i	0.332827	−	0.576472i	0.983065	+	0.183258i	$0.0586643\pi$
$242$	−5.16129	−	5.81685i	−0.331780	−	0.373921i
$243$	−11.9157	−	10.0507i	−0.764393	−	0.644751i
$244$	−1.53370	−	1.14881i	−0.0981853	−	0.0735449i
$245$		0			0
$246$	16.3335	−	6.45146i	1.04138	−	0.411330i
$247$	32.5062	−	18.7675i	2.06832	−	1.19415i
$248$	13.8089	−	1.14692i	0.876863	−	0.0728294i
$249$	1.55413	+	8.84042i	0.0984889	+	0.560239i
$250$	−2.13336	−	10.4089i	−0.134925	−	0.658318i
$251$	26.9555			1.70142			0.850709	−	0.525636i	$-0.176173\pi$
$251$	26.9555			1.70142			0.850709	+	0.525636i	$0.176173\pi$
$252$		0			0
$253$	−18.4989			−1.16301
$254$	−1.18179	−	5.76613i	−0.0741524	−	0.361799i
$255$	0.285511	+	1.62409i	0.0178794	+	0.101704i
$256$	−0.742842	−	15.9827i	−0.0464276	−	0.998922i
$257$	−2.41766	+	1.39584i	−0.150810	+	0.0870700i	−0.573506	−	0.819201i	$-0.694417\pi$
$257$	−2.41766	+	1.39584i	−0.150810	+	0.0870700i	0.422696	+	0.906271i	$0.361084\pi$
$258$	18.0962	−	7.14771i	1.12662	−	0.444997i
$259$		0			0
$260$	5.07343	−	6.77323i	0.314641	−	0.420058i
$261$	−4.32935	−	11.9329i	−0.267980	−	0.738627i
$262$	9.84782	+	11.0986i	0.608400	+	0.685676i
$263$	7.65516	−	13.2591i	0.472037	−	0.817592i	−0.527451	−	0.849586i	$-0.676852\pi$
$263$	7.65516	−	13.2591i	0.472037	−	0.817592i	0.999488	+	0.0319931i	$0.0101855\pi$
$264$	11.1133	−	2.91935i	0.683975	−	0.179674i
$265$	−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	0.986834	+	0.161739i	$0.0517102\pi$
$269$	26.5752	+	15.3432i	1.62032	+	0.935492i	0.633487	+	0.773754i	$0.281623\pi$
$270$	−5.59657	−	1.87319i	−0.340596	−	0.113999i
$271$	−17.0488	+	9.84312i	−1.03564	+	0.597927i	−0.918595	−	0.395199i	$-0.870675\pi$
$271$	−17.0488	+	9.84312i	−1.03564	+	0.597927i	−0.117045	+	0.993127i	$0.537342\pi$
$272$	−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
$276$	−12.3461	+	24.3732i	−0.743145	+	1.46709i
$277$	6.55646	−	11.3561i	0.393940	−	0.682324i	−0.599025	−	0.800730i	$-0.704445\pi$
$277$	6.55646	−	11.3561i	0.393940	−	0.682324i	0.992965	+	0.118406i	$0.0377785\pi$
$278$	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	$0.972749\pi$
$282$	−9.28927	+	11.7005i	−0.553168	+	0.696755i
$283$	1.72374	+	0.995200i	0.102466	+	0.0591585i	0.550357	−	0.834929i	$-0.314492\pi$
$283$	1.72374	+	0.995200i	0.102466	+	0.0591585i	−0.447892	+	0.894088i	$0.647825\pi$
$284$	17.7886	−	7.61146i	1.05556	−	0.451657i
$285$	−9.31086	−	3.39429i	−0.551528	−	0.201060i
$286$	−5.52122	+	16.5806i	−0.326477	+	0.980433i
$287$		0			0
$288$	3.57056	−	16.5907i	0.210397	−	0.977616i
$289$	−7.79738	−	13.5055i	−0.458669	−	0.794439i
$290$	−3.18967	−	3.59480i	−0.187304	−	0.211094i
$291$	1.31301	+	7.46886i	0.0769700	+	0.437832i
$292$	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
$297$	12.1873	+	0.0187619i	0.707180	+	0.00108867i
$298$	−17.0325	+	15.1129i	−0.986666	+	0.875468i
$299$	−20.7769	−	35.9867i	−1.20156	−	2.08117i
$300$	15.0635	−	0.825270i	0.869694	−	0.0476470i
$301$		0			0
$302$	−23.3260	−	7.76737i	−1.34226	−	0.446962i
$303$	4.97921	−	13.6585i	0.286048	−	0.784657i
$304$	6.73447	−	27.6900i	0.386248	−	1.58813i
$305$	−0.666400	−	0.384746i	−0.0381579	−	0.0220305i
$306$	−5.02757	+	0.133744i	−0.287407	+	0.00764565i
$307$			15.4869i			0.883885i	0.897043	+	0.441942i	$0.145710\pi$
$307$			15.4869i			0.883885i	−0.897043	+	0.441942i	$0.854290\pi$
$308$		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	$-0.933336\pi$
$311$	−5.44973	+	9.43920i	−0.309026	+	0.535248i	0.669124	+	0.743151i	$0.266670\pi$
$312$	18.1610	+	18.3403i	1.02816	+	1.03832i
$313$	−16.9011	−	29.2736i	−0.955308	−	1.65464i	−0.733662	−	0.679514i	$-0.762190\pi$
$313$	−16.9011	−	29.2736i	−0.955308	−	1.65464i	−0.221646	−	0.975127i	$-0.571143\pi$
$314$	−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	$-0.750651\pi$
$317$	−8.04243	+	4.64330i	−0.451708	+	0.260794i	0.256843	+	0.966453i	$0.417318\pi$
$318$	3.13752	−	21.1279i	0.175943	−	1.18479i
$319$	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
$324$	8.15849	−	16.0449i	0.453249	−	0.891384i
$325$	−11.4723	+	19.8706i	−0.636369	+	1.10222i
$326$	7.73179	−	6.86041i	0.428224	−	0.379963i
$327$	8.87020	+	3.23364i	0.490523	+	0.178821i
$328$	11.5579	+	16.6619i	0.638178	+	0.920002i
$329$		0			0
$330$	4.29145	−	1.69505i	0.236236	−	0.0933096i
$331$	0.878968	−	0.507473i	0.0483125	−	0.0278932i	−0.475649	−	0.879635i	$-0.657787\pi$
$331$	0.878968	−	0.507473i	0.0483125	−	0.0278932i	0.523962	+	0.851742i	$0.324453\pi$
$332$	−9.52893	+	4.07727i	−0.522968	+	0.223769i
$333$	2.40626	+	2.02330i	0.131862	+	0.110876i
$334$	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
$339$	12.1085	−	2.12864i	0.657641	−	0.115612i
$340$	−1.75057	+	0.749041i	−0.0949383	+	0.0406225i
$341$	−9.95091	+	5.74516i	−0.538872	+	0.311118i
$342$	14.4115	−	26.5690i	0.779283	−	1.43669i
$343$		0			0
$344$	12.8052	+	18.4601i	0.690411	+	0.995302i
$345$	−3.75772	+	10.3078i	−0.202309	+	0.554953i
$346$	−13.5097	+	11.9871i	−0.726285	+	0.644432i
$347$	−12.8143	+	22.1950i	−0.687907	+	1.19149i	0.284607	+	0.958644i	$0.408137\pi$
$347$	−12.8143	+	22.1950i	−0.687907	+	1.19149i	−0.972514	+	0.232846i	$0.925196\pi$
$348$	12.2740	−	8.01230i	0.657958	−	0.429504i
$349$	−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	$-0.421759\pi$
$353$	−8.92430	−	5.15245i	−0.474993	−	0.274237i	−0.718327	+	0.695705i	$0.755092\pi$
$354$	1.60439	+	0.238254i	0.0852725	+	0.0126631i
$355$	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	−0.965500	−	0.260402i	$-0.916145\pi$
$359$	−13.4197	−	23.2436i	−0.708265	−	1.22675i	0.257235	−	0.966349i	$-0.417188\pi$
$360$	0.630772	−	6.78548i	0.0332446	−	0.357626i
$361$	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
$366$	1.45928	−	1.83807i	0.0762779	−	0.0960775i
$367$	11.5631	+	6.67596i	0.603589	+	0.348482i	0.770452	−	0.637498i	$-0.220031\pi$
$367$	11.5631	+	6.67596i	0.603589	+	0.348482i	−0.166863	+	0.985980i	$0.553364\pi$
$368$	−30.6548	−	7.45554i	−1.59799	−	0.388647i
$369$	7.33552	+	20.2187i	0.381872	+	1.05254i
$370$	1.12929	+	0.376045i	0.0587089	+	0.0195496i
$371$		0			0
$372$	0.928355	+	16.9452i	0.0481330	+	0.878565i
$373$	11.4029	+	19.7505i	0.590422	+	1.02264i	0.994176	+	0.107773i	$0.0343720\pi$
$373$	11.4029	+	19.7505i	0.590422	+	1.02264i	−0.403753	+	0.914868i	$0.632295\pi$
$374$	2.94116	−	2.60969i	0.152084	−	0.134944i
$375$	12.8167	−	2.25315i	0.661853	−	0.116352i
$376$	−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	$-0.983796\pi$
$379$		−	1.98122i		−	0.101768i	0.998705	−	0.0508842i	$-0.0162040\pi$
$380$	1.36183	−	11.3621i	0.0698605	−	0.582862i
$381$	7.09996	−	1.24816i	0.363742	−	0.0639451i
$382$	−5.72545	−	6.45267i	−0.292939	−	0.330147i
$383$	14.4104	+	24.9596i	0.736339	+	1.27538i	0.954134	+	0.299381i	$0.0967803\pi$
$383$	14.4104	+	24.9596i	0.736339	+	1.27538i	−0.217795	+	0.975995i	$0.569886\pi$
$384$	19.5926	−	0.358762i	0.999832	−	0.0183080i
$385$		0			0
$386$	0.288191	−	0.865458i	0.0146685	−	0.0440506i
$387$	8.12716	+	22.4007i	0.413127	+	1.13869i
$388$	−8.05054	+	3.44469i	−0.408704	+	0.174878i
$389$	1.69719	+	0.979873i	0.0860509	+	0.0496815i	0.542408	−	0.840115i	$-0.317513\pi$
$389$	1.69719	+	0.979873i	0.0860509	+	0.0496815i	−0.456357	+	0.889797i	$0.650846\pi$
$390$	8.11740	+	6.44457i	0.411040	+	0.326333i
$391$			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
$396$	3.19115	+	13.7061i	0.160361	+	0.688759i
$397$	2.28155	+	3.95176i	0.114508	+	0.198333i	0.917583	−	0.397545i	$-0.130138\pi$
$397$	2.28155	+	3.95176i	0.114508	+	0.198333i	−0.803075	+	0.595878i	$0.796804\pi$
$398$	−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	$-0.433521\pi$
$401$	23.1931	−	13.3905i	1.15821	−	0.668692i	0.950874	+	0.309578i	$0.100188\pi$
$402$	3.03183	−	20.4162i	0.151214	−	1.01827i
$403$	−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
$408$	−1.47549	−	5.61683i	−0.0730475	−	0.278075i
$409$	−9.02122	+	15.6252i	−0.446071	+	0.772617i	−0.998126	−	0.0611902i	$-0.980510\pi$
$409$	−9.02122	+	15.6252i	−0.446071	+	0.772617i	0.552055	+	0.833807i	$0.313844\pi$
$410$	5.40447	+	6.09092i	0.266908	+	0.300809i
$411$	8.00388	−	21.9554i	0.394802	−	1.08298i
$412$	−3.07782	+	4.10901i	−0.151633	+	0.202436i
$413$		0			0
$414$	−29.4138	−	15.9545i	−1.44561	−	0.784123i
$415$	−3.60442	+	2.08101i	−0.176934	+	0.102153i
$416$	−15.8318	+	25.2509i	−0.776217	+	1.23803i
$417$	−12.9181	+	2.27097i	−0.632602	+	0.111210i
$418$	4.74468	+	23.1499i	0.232070	+	1.13230i
$419$	−17.5395			−0.856861			−0.428430	−	0.903575i	$-0.640933\pi$
$419$	−17.5395			−0.856861			−0.428430	+	0.903575i	$0.640933\pi$
$420$		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
$423$	−14.0044	−	11.7756i	−0.680918	−	0.572550i
$424$	24.5793	−	2.04147i	1.19368	−	0.0991428i
$425$	4.47089	−	2.58127i	0.216870	−	0.125210i
$426$	8.70551	+	22.0402i	0.421784	+	1.06785i
$427$		0			0
$428$	9.76434	+	7.31389i	0.471977	+	0.353530i
$429$	−20.1088	−	7.33068i	−0.970861	−	0.353929i
$430$	5.98772	+	6.74825i	0.288754	+	0.325430i
$431$	4.50180	−	7.79735i	0.216844	−	0.375585i	−0.736997	−	0.675896i	$-0.763757\pi$
$431$	4.50180	−	7.79735i	0.216844	−	0.375585i	0.953841	+	0.300311i	$0.0970903\pi$
$432$	20.1883	+	4.94291i	0.971310	+	0.237816i
$433$	−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
$438$	3.42653	+	0.508844i	0.163726	+	0.0243135i
$439$	−25.3306	+	14.6246i	−1.20896	+	0.697996i	−0.962533	−	0.271164i	$-0.912591\pi$
$439$	−25.3306	+	14.6246i	−1.20896	+	0.697996i	−0.246432	+	0.969160i	$0.579258\pi$
$440$	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	$-0.221506\pi$
$443$	−3.60820	−	6.24958i	−0.171431	−	0.296927i	−0.938920	+	0.344135i	$0.888172\pi$
$444$	−1.64041	+	3.23844i	−0.0778503	+	0.153690i
$445$	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	$0.966634\pi$
$450$	0.491345	+	18.4701i	0.0231622	+	0.870690i
$451$	−14.5627	−	8.40777i	−0.685730	−	0.395907i
$452$	5.58451	+	13.0515i	0.262673	+	0.613890i
$453$	10.3130	−	28.2894i	0.484545	−	1.32915i
$454$	3.91125	−	11.7458i	0.183564	−	0.551256i
$455$		0			0
$456$	33.6678	+	9.19877i	1.57664	+	0.430772i
$457$	−6.83102	−	11.8317i	−0.319541	−	0.553462i	0.660851	−	0.750517i	$-0.270196\pi$
$457$	−6.83102	−	11.8317i	−0.319541	−	0.553462i	−0.980392	+	0.197055i	$0.936862\pi$
$458$	−17.3630	−	19.5683i	−0.811318	−	0.914368i
$459$	0.00948255	−	6.15967i	0.000442608	−	0.287509i
$460$	−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	$0.120351\pi$
$463$			15.8863i			0.738299i	−0.929370	+	0.369149i	$0.879649\pi$
$464$	12.2427	+	11.6869i	0.568351	+	0.542549i
$465$	1.17992	+	6.71181i	0.0547176	+	0.311253i
$466$	10.7254	−	9.51669i	0.496847	−	0.440852i
$467$	13.5384	+	23.4491i	0.626481	+	1.08510i	0.988252	+	0.152830i	$0.0488388\pi$
$467$	13.5384	+	23.4491i	0.626481	+	1.08510i	−0.361771	+	0.932267i	$0.617828\pi$
$468$	−23.0791	+	21.6019i	−1.06683	+	0.998548i
$469$		0			0
$470$	−6.57245	−	2.18858i	−0.303164	−	0.100951i
$471$	−6.38253	−	2.32676i	−0.294092	−	0.107212i
$472$	0.155024	+	1.86648i	0.00713555	+	0.0859118i
$473$	−16.1343	−	9.31514i	−0.741856	−	0.428311i
$474$	−13.2911	−	10.5521i	−0.610481	−	0.484673i
$475$			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	$-0.719979\pi$
$479$	7.63026	−	13.2160i	0.348635	−	0.603854i	0.986007	+	0.166702i	$0.0533119\pi$
$480$	7.79460	−	1.07934i	0.355773	−	0.0492649i
$481$	−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
$486$	19.3621	+	10.5409i	0.878280	+	0.478146i
$487$	−5.25172	−	3.03208i	−0.237978	−	0.137397i	0.376269	−	0.926511i	$-0.377207\pi$
$487$	−5.25172	−	3.03208i	−0.237978	−	0.137397i	−0.614247	+	0.789114i	$0.710540\pi$
$488$	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	$-0.470954\pi$
$491$	4.03833			0.182247			0.0911235	+	0.995840i	$0.470954\pi$
$492$	−20.7968	+	13.5758i	−0.937591	+	0.612044i
$493$	2.50797	−	4.34393i	0.112953	−	0.195641i
$494$	−39.7056	+	35.2308i	−1.78644	+	1.58511i
$495$	1.92733	+	5.31225i	0.0866270	+	0.238768i
$496$	−18.8053	+	5.50994i	−0.844384	+	0.247404i
$497$		0			0
$498$	−4.66333	−	11.8064i	−0.208969	−	0.529056i
$499$	−33.3430	+	19.2506i	−1.49264	+	0.861776i	−0.999964	−	0.00843800i	$-0.997314\pi$
$499$	−33.3430	+	19.2506i	−1.49264	+	0.861776i	−0.492675	+	0.870214i	$0.663981\pi$
$500$	5.91117	+	13.8149i	0.264356	+	0.617822i
$501$	2.51068	+	14.2816i	0.112169	+	0.638057i
$502$	−37.3446	+	7.65395i	−1.66677	+	0.341613i
$503$	14.3498			0.639827			0.319914	−	0.947447i	$-0.396346\pi$
$503$	14.3498			0.639827			0.319914	+	0.947447i	$0.396346\pi$
$504$		0			0
$505$	6.74091			0.299967
$506$	25.6286	−	5.25270i	1.13933	−	0.233511i
$507$	−4.42579	−	25.1754i	−0.196556	−	1.11808i
$508$	3.27455	+	7.65291i	0.145285	+	0.339543i
$509$	−10.4646	+	6.04176i	−0.463837	+	0.267796i	−0.713656	−	0.700496i	$-0.752962\pi$
$509$	−10.4646	+	6.04176i	−0.463837	+	0.267796i	0.249819	+	0.968292i	$0.419629\pi$
$510$	−0.856707	−	2.16897i	−0.0379356	−	0.0960435i
$511$		0			0
$512$	5.56740	+	21.9318i	0.246047	+	0.969258i
$513$	32.0308	+	18.5588i	1.41419	+	0.819391i
$514$	2.95312	−	2.62030i	0.130257	−	0.115577i
$515$	−1.03079	+	1.78538i	−0.0454220	+	0.0786732i
$516$	−23.0412	+	15.0409i	−1.01433	+	0.662139i
$517$	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	$-0.0873512\pi$
$521$	27.6002	+	15.9350i	1.20919	+	0.698125i	0.246606	+	0.969116i	$0.420684\pi$
$522$	9.38625	+	15.3027i	0.410825	+	0.669780i
$523$	31.7039	−	18.3043i	1.38631	−	0.800389i	0.393417	−	0.919360i	$-0.371293\pi$
$523$	31.7039	−	18.3043i	1.38631	−	0.800389i	0.992898	+	0.118971i	$0.0379596\pi$
$524$	−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
$528$	−14.5676	+	7.20009i	−0.633972	+	0.313344i
$529$	−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
$534$	31.3965	+	24.9263i	1.35866	+	1.07867i
$535$	4.24264	+	2.44949i	0.183425	+	0.105901i
$536$	23.7514	−	1.97271i	1.02590	−	0.0852080i
$537$	34.3647	+	12.5277i	1.48294	+	0.540610i
$538$	−41.1744	−	13.7108i	−1.77515	−	0.591113i
$539$		0			0
$540$	8.28546	+	1.00602i	0.356549	+	0.0432921i
$541$	18.1033	+	31.3558i	0.778320	+	1.34809i	0.932909	+	0.360111i	$0.117261\pi$
$541$	18.1033	+	31.3558i	0.778320	+	1.34809i	−0.154589	+	0.987979i	$0.549405\pi$
$542$	20.8247	−	18.4778i	0.894498	−	0.793688i
$543$	−3.72090	−	21.1658i	−0.159679	−	0.908311i
$544$	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	$-0.765820\pi$
$547$		−	31.3917i		−	1.34221i	0.741361	−	0.671106i	$-0.234180\pi$
$548$	26.7922	+	3.21126i	1.14451	+	0.137178i
$549$	2.20000	+	1.84987i	0.0938937	+	0.0789505i
$550$	−9.58739	−	10.8051i	−0.408808	−	0.460733i
$551$	15.0726	+	26.1065i	0.642115	+	1.11218i
$552$	10.1837	−	37.2726i	0.433447	−	1.58643i
$553$		0			0
$554$	−5.85888	+	17.5946i	−0.248920	+	0.747525i
$555$	−0.499285	+	1.36959i	−0.0211935	+	0.0581357i
$556$	−5.95792	−	13.9242i	−0.252672	−	0.590517i
$557$	30.5691	+	17.6491i	1.29526	+	0.747816i	0.979581	−	0.201051i	$-0.0644356\pi$
$557$	30.5691	+	17.6491i	1.29526	+	0.747816i	0.315675	+	0.948867i	$0.397769\pi$
$558$	−20.7773	+	0.552719i	−0.879572	+	0.0233985i
$559$		−	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	0.440432	+	0.897786i	$0.354825\pi$
$563$	−13.2232	+	22.9032i	−0.557290	+	0.965254i	−0.997721	+	0.0674681i	$0.978508\pi$
$564$	9.54716	−	18.8477i	0.402008	−	0.793632i
$565$	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	$-0.861444\pi$
$569$	−23.7332	+	13.7024i	−0.994948	+	0.574434i	−0.0881985	+	0.996103i	$0.528111\pi$
$570$	13.8632	+	2.05870i	0.580666	+	0.0862296i
$571$	−24.3299	−	14.0469i	−1.01817	−	0.587843i	−0.104599	−	0.994514i	$-0.533356\pi$
$571$	−24.3299	−	14.0469i	−1.01817	−	0.587843i	−0.913574	+	0.406672i	$0.866689\pi$
$572$	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
$576$	−0.235827	+	23.9988i	−0.00982612	+	0.999952i
$577$	11.4154	−	19.7721i	0.475231	−	0.823124i	−0.524367	−	0.851492i	$-0.675698\pi$
$577$	11.4154	−	19.7721i	0.475231	−	0.823124i	0.999598	+	0.0283688i	$0.00903129\pi$
$578$	14.6374	+	16.4966i	0.608837	+	0.686169i
$579$	1.04962	+	0.382639i	0.0436206	+	0.0159019i
$580$	5.43974	+	4.07459i	0.225873	+	0.169188i
$581$		0			0
$582$	−3.93982	−	9.97464i	−0.163311	−	0.413462i
$583$	−17.7123	+	10.2262i	−0.733568	+	0.423526i
$584$	0.331087	+	3.98627i	0.0137005	+	0.164953i
$585$	−8.16950	+	9.71577i	−0.337767	+	0.401697i
$586$	4.75561	+	23.2032i	0.196452	+	0.958517i
$587$	−28.4011			−1.17224			−0.586119	−	0.810225i	$-0.699345\pi$
$587$	−28.4011			−1.17224			−0.586119	+	0.810225i	$0.699345\pi$
$588$		0			0
$589$	−34.9018			−1.43810
$590$	0.151005	+	0.736774i	0.00621679	+	0.0303325i
$591$	25.4367	−	4.47172i	1.04633	−	0.183942i
$592$	−4.07308	−	0.990610i	−0.167403	−	0.0407138i
$593$	−20.6799	+	11.9396i	−0.849223	+	0.490299i	−0.860389	−	0.509638i	$-0.829779\pi$
$593$	−20.6799	+	11.9396i	−0.849223	+	0.490299i	0.0111655	+	0.999938i	$0.496446\pi$
$594$	−16.8898	+	3.43456i	−0.692998	+	0.140922i
$595$		0			0
$596$	19.3058	−	25.7740i	0.790796	−	1.05574i
$597$	11.0930	−	30.4291i	0.454005	−	1.24538i
$598$	39.0030	+	43.9570i	1.59495	+	1.79753i
$599$	19.5625	−	33.8832i	0.799300	−	1.38443i	−0.120772	−	0.992680i	$-0.538537\pi$
$599$	19.5625	−	33.8832i	0.799300	−	1.38443i	0.920072	−	0.391749i	$-0.128130\pi$
$600$	−20.6349	+	5.42059i	−0.842417	+	0.221295i
$601$	−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
$606$	−3.01999	+	20.3365i	−0.122679	+	0.826112i
$607$	27.4754	−	15.8630i	1.11519	−	0.643857i	0.175024	−	0.984564i	$-0.444000\pi$
$607$	27.4754	−	15.8630i	1.11519	−	0.643857i	0.940170	+	0.340707i	$0.110666\pi$
$608$	−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
$612$	6.92730	−	1.61286i	0.280019	−	0.0651959i
$613$	−16.4834	+	28.5501i	−0.665758	+	1.15313i	0.313322	+	0.949647i	$0.398558\pi$
$613$	−16.4834	+	28.5501i	−0.665758	+	1.15313i	−0.979079	+	0.203479i	$0.934775\pi$
$614$	−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	$-0.0936021\pi$
$618$	−4.92445	−	3.90962i	−0.198091	−	0.157268i
$619$	−21.3838	−	12.3460i	−0.859489	−	0.496226i	0.00435197	−	0.999991i	$-0.498615\pi$
$619$	−21.3838	−	12.3460i	−0.859489	−	0.496226i	−0.863841	+	0.503764i	$0.831948\pi$
$620$	−7.23453	+	3.09553i	−0.290546	+	0.124320i
$621$	20.5459	−	35.4604i	0.824480	−	1.42298i
$622$	4.86990	−	14.6246i	0.195265	−	0.586395i
$623$		0			0
$624$	−30.3682	−	20.2522i	−1.21570	−	0.810738i
$625$	−7.87046	−	13.6320i	−0.314818	−	0.545281i
$626$	31.7272	+	35.7571i	1.26807	+	1.42914i
$627$	−28.5049	+	5.01111i	−1.13838	+	0.200124i
$628$	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	$0.102411\pi$
$631$			15.8863i			0.632423i	−0.948689	+	0.316212i	$0.897589\pi$
$632$	8.35966	−	17.7233i	0.332529	−	0.704996i
$633$	20.0003	−	3.51602i	0.794942	−	0.139749i
$634$	9.82365	−	8.71652i	0.390147	−	0.346177i
$635$	1.67131	+	2.89479i	0.0663239	+	0.114876i
$636$	1.65244	+	30.1618i	0.0655235	+	1.19599i
$637$		0			0
$638$	−13.3163	−	4.43423i	−0.527197	−	0.175553i
$639$	−27.2828	+	9.89844i	−1.07929	+	0.391576i
$640$	3.26785	+	8.47834i	0.129173	+	0.335136i
$641$	−16.8007	−	9.69989i	−0.663588	−	0.383122i	0.130055	−	0.991507i	$-0.458485\pi$
$641$	−16.8007	−	9.69989i	−0.663588	−	0.383122i	−0.793643	+	0.608384i	$0.791818\pi$
$642$	−9.29053	+	11.7021i	−0.366668	+	0.461845i
$643$		−	37.0568i		−	1.46138i	−0.682710	−	0.730690i	$-0.739199\pi$
$643$		−	37.0568i		−	1.46138i	0.682710	−	0.730690i	$-0.260801\pi$
$644$		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	0.0557235	−	0.998446i	$-0.482253\pi$
$647$	22.7029	−	39.3225i	0.892542	−	1.54593i	0.836818	−	0.547481i	$-0.184413\pi$
$648$	−6.74698	+	24.5454i	−0.265046	+	0.964236i
$649$	−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	$-0.660517\pi$
$653$	0.855070	−	0.493675i	0.0334615	−	0.0193190i	0.516637	+	0.856204i	$0.327184\pi$
$654$	−13.2071	−	1.96127i	−0.516438	−	0.0766917i
$655$	−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	$-0.541509\pi$
$659$	−6.67629			−0.260071			−0.130036	+	0.991509i	$0.541509\pi$
$660$	−5.46413	+	3.56690i	−0.212691	+	0.138841i
$661$	−1.35571	+	2.34815i	−0.0527309	+	0.0913326i	−0.891186	−	0.453638i	$-0.850126\pi$
$661$	−1.35571	+	2.34815i	−0.0527309	+	0.0913326i	0.838455	+	0.544971i	$0.183459\pi$
$662$	−1.07364	+	0.952641i	−0.0417282	+	0.0370254i
$663$	−3.70505	+	10.1633i	−0.143892	+	0.394710i
$664$	12.0438	−	8.35442i	0.467390	−	0.324214i
$665$		0			0
$666$	−3.90818	−	2.11986i	−0.151439	−	0.0821431i
$667$	28.9018	−	16.6865i	1.11908	−	0.646102i
$668$	−15.3939	+	6.58680i	−0.595609	+	0.254851i
$669$	−1.16557	+	0.204904i	−0.0450634	+	0.00792206i
$670$	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
$675$	−22.6292	−	0.0348367i	−0.870997	−	0.00134086i
$676$	27.1361	−	11.6111i	1.04370	−	0.446580i
$677$	9.63730	−	5.56410i	0.370392	−	0.213846i	−0.303238	−	0.952915i	$-0.598068\pi$
$677$	9.63730	−	5.56410i	0.370392	−	0.213846i	0.673630	+	0.739069i	$0.264734\pi$
$678$	−16.1708	+	6.38722i	−0.621037	+	0.245300i
$679$		0			0
$680$	2.21258	−	1.53480i	0.0848487	−	0.0588570i
$681$	14.2451	+	5.19307i	0.545873	+	0.198999i
$682$	12.1548	−	10.7850i	0.465432	−	0.412978i
$683$	4.83716	−	8.37821i	0.185089	−	0.320583i	−0.758518	−	0.651652i	$-0.774076\pi$
$683$	4.83716	−	8.37821i	0.185089	−	0.320583i	0.943606	+	0.331069i	$0.107409\pi$
$684$	−12.4217	+	40.9012i	−0.474955	+	1.56389i
$685$	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
$690$	2.27913	−	15.3476i	0.0867652	−	0.584272i
$691$	−7.20943	+	4.16236i	−0.274260	+	0.158344i	−0.630822	−	0.775928i	$-0.717282\pi$
$691$	−7.20943	+	4.16236i	−0.274260	+	0.158344i	0.356562	+	0.934272i	$0.383949\pi$
$692$	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
$696$	−14.7296	+	14.5855i	−0.558323	+	0.552863i
$697$	−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	$-0.222348\pi$
$702$	−25.6512	−	28.9991i	−0.968141	−	1.09450i
$703$	−6.46568	−	3.73296i	−0.243858	−	0.140791i
$704$	−11.9341	−	14.4793i	−0.449782	−	0.545711i
$705$	2.90583	−	7.97098i	0.109440	−	0.300205i
$706$	13.8269	+	4.60425i	0.520382	+	0.173283i
$707$		0			0
$708$	−2.29040	+	0.125482i	−0.0860785	+	0.00471589i
$709$	−4.82135	−	8.35083i	−0.181070	−	0.313622i	0.761175	−	0.648546i	$-0.224623\pi$
$709$	−4.82135	−	8.35083i	−0.181070	−	0.313622i	−0.942245	+	0.334924i	$0.891289\pi$
$710$	−8.21900	+	7.29272i	−0.308454	+	0.273691i
$711$	13.3764	−	15.9082i	0.501655	−	0.596605i
$712$	−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
$717$	0.448249	+	2.54980i	0.0167402	+	0.0952239i
$718$	25.1918	+	28.3915i	0.940150	+	1.05956i
$719$	4.04585	+	7.00762i	0.150885	+	0.261340i	0.931553	−	0.363606i	$-0.118454\pi$
$719$	4.04585	+	7.00762i	0.150885	+	0.261340i	−0.780668	+	0.624946i	$0.785121\pi$
$720$	1.05284	+	9.57981i	0.0392369	+	0.357018i
$721$		0			0
$722$	−14.1885	+	42.6090i	−0.528040	+	1.58574i
$723$	−16.8160	−	6.13028i	−0.625392	−	0.227988i
$724$	22.8142	−	9.76181i	0.847883	−	0.362795i
$725$	−15.9586	−	9.21369i	−0.592687	−	0.342188i
$726$	−8.37509	+	10.5490i	−0.310829	+	0.391511i
$727$			36.9501i			1.37040i	0.728353	+	0.685202i	$0.240286\pi$
$727$			36.9501i			1.37040i	−0.728353	+	0.685202i	$0.759714\pi$
$728$		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
$732$	−1.49980	+	2.96085i	−0.0554340	+	0.109436i
$733$	18.9776	+	32.8702i	0.700954	+	1.21409i	0.968132	+	0.250440i	$0.0805753\pi$
$733$	18.9776	+	32.8702i	0.700954	+	1.21409i	−0.267178	+	0.963647i	$0.586091\pi$
$734$	−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
$738$	−15.9038	−	25.9284i	−0.585426	−	0.954437i
$739$	−19.1667	−	11.0659i	−0.705058	−	0.407065i	0.104171	−	0.994559i	$-0.466781\pi$
$739$	−19.1667	−	11.0659i	−0.705058	−	0.407065i	−0.809228	+	0.587494i	$0.800115\pi$
$740$	−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	$-0.630875\pi$
$743$	−21.7884			−0.799340			−0.399670	+	0.916659i	$0.630875\pi$
$744$	−6.09769	−	23.2125i	−0.223552	−	0.851010i
$745$	6.46568	−	11.1989i	0.236884	−	0.410296i
$746$	−21.4059	−	24.1248i	−0.783726	−	0.883271i
$747$	14.6147	−	5.30235i	0.534725	−	0.194003i
$748$	−3.33371	+	4.45064i	−0.121893	+	0.162731i
$749$		0			0
$750$	−17.1167	+	6.76083i	−0.625014	+	0.246871i
$751$	−4.44124	+	2.56415i	−0.162063	+	0.0935671i	−0.578838	−	0.815443i	$-0.696494\pi$
$751$	−4.44124	+	2.56415i	−0.162063	+	0.0935671i	0.416775	+	0.909010i	$0.363160\pi$
$752$	23.7053	+	5.76534i	0.864443	+	0.210240i
$753$	−8.08376	−	45.9832i	−0.294588	−	1.67572i
$754$	−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
$759$	5.54766	+	31.5570i	0.201367	+	1.14545i
$760$	1.33953	+	16.1279i	0.0485897	+	0.585019i
$761$	−37.0224	+	21.3749i	−1.34206	+	0.774839i	−0.987110	−	0.160046i	$-0.948836\pi$
$761$	−37.0224	+	21.3749i	−1.34206	+	0.774839i	−0.354951	+	0.934885i	$0.615502\pi$
$762$	−9.48197	+	3.74523i	−0.343496	+	0.135675i
$763$		0			0
$764$	9.76434	+	7.31389i	0.353261	+	0.264607i
$765$	2.68490	−	0.974103i	0.0970726	−	0.0352188i
$766$	−27.0516	−	30.4876i	−0.977415	−	1.10156i
$767$	1.74436	−	3.02131i	0.0629851	−	0.109093i
$768$	−27.0421	+	6.06031i	−0.975796	+	0.218683i
$769$	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	$-0.326442\pi$
$773$	1.04249	+	0.601881i	0.0374957	+	0.0216482i	−0.481135	+	0.876647i	$0.659775\pi$
$774$	−17.6201	−	28.7266i	−0.633342	−	1.03256i
$775$	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
$780$	−13.0759	−	6.62348i	−0.468192	−	0.237159i
$781$	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
$786$	15.9798	−	20.1277i	0.569980	−	0.717931i
$787$	19.4895	+	11.2522i	0.694724	+	0.401099i	0.805380	−	0.592760i	$-0.201962\pi$
$787$	19.4895	+	11.2522i	0.694724	+	0.401099i	−0.110655	+	0.993859i	$0.535295\pi$
$788$	11.7316	+	27.4177i	0.417920	+	0.976716i
$789$	−24.9143	−	9.08256i	−0.886974	−	0.323348i
$790$	2.48610	−	7.46593i	0.0884514	−	0.265626i
$791$		0			0
$792$	−8.31288	−	18.0826i	−0.295385	−	0.642536i
$793$	−2.52398	−	4.37166i	−0.0896290	−	0.155242i
$794$	−4.28298	−	4.82699i	−0.151997	−	0.171303i
$795$	2.10022	+	11.9468i	0.0744871	+	0.423709i
$796$	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
$801$	−31.5980	+	37.5786i	−1.11646	+	1.32778i
$802$	−28.3299	+	25.1371i	−1.00036	+	0.887621i
$803$	−1.65849	−	2.87258i	−0.0585267	−	0.101371i
$804$	1.59678	+	29.1458i	0.0563140	+	1.02789i
$805$		0			0
$806$	34.6322	+	11.5323i	1.21987	+	0.406206i
$807$	18.2042	−	49.9358i	0.640817	−	1.75782i
$808$	−23.6586	+	1.96500i	−0.832305	+	0.0691285i
$809$	11.5087	+	6.64455i	0.404624	+	0.233610i	0.688477	−	0.725258i	$-0.258279\pi$
$809$	11.5087	+	6.64455i	0.404624	+	0.233610i	−0.283853	+	0.958868i	$0.591613\pi$
$810$	−1.51709	+	10.1089i	−0.0533052	+	0.355190i
$811$			6.46254i			0.226930i	0.993542	+	0.113465i	$0.0361950\pi$
$811$			6.46254i			0.226930i	−0.993542	+	0.113465i	$0.963805\pi$
$812$		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
$816$	3.63904	+	7.36268i	0.127392	+	0.257745i
$817$	−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	$-0.828631\pi$
$821$	−24.1767	+	13.9584i	−0.843774	+	0.487153i	0.0147715	+	0.999891i	$0.495298\pi$
$822$	−4.85451	+	32.6900i	−0.169321	+	1.14020i
$823$	38.9668	+	22.4975i	1.35830	+	0.784213i	0.989394	−	0.145256i	$-0.0464004\pi$
$823$	38.9668	+	22.4975i	1.35830	+	0.784213i	0.368902	+	0.929468i	$0.379734\pi$
$824$	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	$-0.703381\pi$
$827$	−34.2989			−1.19269			−0.596344	+	0.802729i	$0.703381\pi$
$828$	45.2805	+	13.7517i	1.57361	+	0.477904i
$829$	−11.5078	+	19.9322i	−0.399684	+	0.692273i	−0.993687	−	0.112190i	$-0.964213\pi$
$829$	−11.5078	+	19.9322i	−0.399684	+	0.692273i	0.594003	+	0.804463i	$0.297547\pi$
$830$	4.40272	−	3.90653i	0.152820	−	0.135598i
$831$	−21.3386	−	7.77900i	−0.740226	−	0.269851i
$832$	14.7637	−	39.4784i	0.511838	−	1.36867i
$833$		0			0
$834$	17.2521	−	6.81430i	0.597391	−	0.235960i
$835$	−5.82291	+	3.36186i	−0.201510	+	0.116342i
$836$	−13.1467	−	30.7249i	−0.454688	−	1.06264i
$837$	0.0391882	−	25.4558i	0.00135454	−	0.879882i
$838$	24.2995	−	4.98029i	0.839412	−	0.172041i
$839$	46.9847			1.62209			0.811046	−	0.584983i	$-0.198899\pi$
$839$	46.9847			1.62209			0.811046	+	0.584983i	$0.198899\pi$
$840$		0			0
$841$	11.0959			0.382617
$842$	−21.3363	+	4.37297i	−0.735297	+	0.150703i
$843$	4.89029	−	0.859702i	0.168430	−	0.0296097i
$844$	9.22430	+	21.5580i	0.317513	+	0.742056i
$845$	10.2645	−	5.92623i	0.353110	−	0.203868i
$846$	22.7456	+	12.3376i	0.782009	+	0.424175i
$847$		0			0
$848$	−33.4728	+	9.80751i	−1.14946	+	0.336791i
$849$	1.18077	−	3.23896i	0.0405238	−	0.111161i
$850$	−5.46109	+	4.84562i	−0.187314	+	0.166204i
$851$	−4.13266	+	7.15798i	−0.141666	+	0.245372i
$852$	−18.3190	−	28.0629i	−0.627598	−	0.961418i
$853$	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	$-0.160654\pi$
$857$	26.1774	+	15.1136i	0.894204	+	0.516269i	0.0188889	+	0.999822i	$0.493987\pi$
$858$	29.9405	+	4.44621i	1.02215	+	0.151791i
$859$	15.8982	−	9.17880i	0.542438	−	0.313177i	−0.203628	−	0.979048i	$-0.565273\pi$
$859$	15.8982	−	9.17880i	0.542438	−	0.313177i	0.746066	+	0.665872i	$0.231940\pi$
$860$	−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	$-0.0183669\pi$
$863$	13.1968	+	22.8576i	0.449225	+	0.778080i	−0.549111	+	0.835749i	$0.685034\pi$
$864$	−29.3727	−	1.11557i	−0.999280	−	0.0379525i
$865$	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
$870$	−5.17578	+	6.51928i	−0.175476	+	0.221024i
$871$	−38.4468	−	22.1973i	−1.30272	−	0.752126i
$872$	−1.27613	−	15.3646i	−0.0432152	−	0.520310i
$873$	12.3473	−	4.47970i	0.417893	−	0.151615i
$874$	75.3947	+	25.1059i	2.55026	+	0.849218i
$875$		0			0
$876$	−4.89164	+	0.267993i	−0.165273	+	0.00905464i
$877$	0.468662	+	0.811746i	0.0158256	+	0.0274107i	0.873830	−	0.486232i	$-0.161629\pi$
$877$	0.468662	+	0.811746i	0.0158256	+	0.0274107i	−0.858004	+	0.513643i	$0.828296\pi$
$878$	30.9408	−	27.4538i	1.04420	−	0.926519i
$879$	−28.5706	+	5.02266i	−0.963664	+	0.169410i
$880$	−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	$0.0309116\pi$
$883$			5.76235i			0.193918i	−0.995288	+	0.0969592i	$0.969088\pi$
$884$	−12.4023	−	1.48651i	−0.417134	−	0.0499968i
$885$	−0.907205	+	0.159485i	−0.0304954	+	0.00536102i
$886$	6.77340	+	7.63372i	0.227557	+	0.256460i
$887$	−13.0672	−	22.6330i	−0.438752	−	0.759941i	0.558841	−	0.829275i	$-0.311246\pi$
$887$	−13.0672	−	22.6330i	−0.438752	−	0.759941i	−0.997594	+	0.0693335i	$0.977913\pi$
$888$	1.35310	−	4.95238i	0.0454070	−	0.166191i
$889$		0			0
$890$	−5.87270	+	17.6361i	−0.196853	+	0.591165i
$891$	−3.62287	−	20.7959i	−0.121371	−	0.696688i
$892$	−0.537568	−	1.25634i	−0.0179991	−	0.0420655i
$893$	37.6302	+	21.7258i	1.25925	+	0.727027i
$894$	30.8889	+	24.5233i	1.03308	+	0.820183i
$895$			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
$900$	−5.92526	−	25.4493i	−0.197509	−	0.848309i
$901$	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
$906$	−6.25502	+	42.1210i	−0.207809	+	1.39937i
$907$	35.3624	+	20.4165i	1.17419	+	0.677918i	0.954663	−	0.297689i	$-0.0962160\pi$
$907$	35.3624	+	20.4165i	1.17419	+	0.677918i	0.219525	+	0.975607i	$0.429549\pi$
$908$	−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	$-0.522760\pi$
$911$	−4.31270			−0.142886			−0.0714430	+	0.997445i	$0.522760\pi$
$912$	−49.2558	−	3.18425i	−1.63102	−	0.105441i
$913$	−6.07741	+	10.5264i	−0.201133	+	0.348372i
$914$	12.8234	+	14.4521i	0.424159	+	0.478034i
$915$	−0.456487	+	1.25219i	−0.0150910	+	0.0413961i
$916$	29.6113	+	22.1801i	0.978384	+	0.732850i
$917$		0			0
$918$	1.73588	+	8.53639i	0.0572927	+	0.281743i
$919$	14.9668	−	8.64107i	0.493708	−	0.285043i	−0.232403	−	0.972620i	$-0.574659\pi$
$919$	14.9668	−	8.64107i	0.493708	−	0.285043i	0.726112	+	0.687577i	$0.241326\pi$
$920$	17.8547	−	1.48295i	0.588652	−	0.0488915i
$921$	26.4190	−	4.64440i	0.870535	−	0.153038i
$922$	−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
$927$	4.95606	−	5.89411i	0.162778	−	0.193588i
$928$	−20.2796	−	12.7149i	−0.665711	−	0.417387i
$929$	−20.0527	+	11.5774i	−0.657908	+	0.379843i	−0.791479	−	0.611196i	$-0.790689\pi$
$929$	−20.0527	+	11.5774i	−0.657908	+	0.379843i	0.133571	+	0.991039i	$0.457355\pi$
$930$	−3.54048	−	8.96360i	−0.116097	−	0.293928i
$931$		0			0
$932$	−12.1570	+	16.2300i	−0.398214	+	0.531632i
$933$	17.7366	+	6.46590i	0.580670	+	0.211684i
$934$	−25.4146	−	28.6426i	−0.831590	−	0.937215i
$935$	−1.11649	+	1.93382i	−0.0365132	+	0.0632426i
$936$	25.8403	−	36.4808i	0.844616	−	1.19241i
$937$	−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	$-0.459304\pi$
$941$	−20.4823	−	11.8254i	−0.667703	−	0.385498i	−0.795206	+	0.606340i	$0.792637\pi$
$942$	9.50313	+	1.41123i	0.309629	+	0.0459803i
$943$	−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	0.774897	+	0.632087i	$0.217802\pi$
$947$	28.7686	+	49.8286i	0.934852	+	1.61921i	0.159955	+	0.987124i	$0.448865\pi$
$948$	21.4099	+	10.8450i	0.695362	+	0.352230i
$949$	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	$-0.0738490\pi$
$954$	−36.9828	+	0.983821i	−1.19736	+	0.0318524i
$955$	4.24264	+	2.44949i	0.137289	+	0.0792636i
$956$	−2.74838	+	1.17598i	−0.0888889	+	0.0380340i
$957$	5.88745	−	16.1498i	0.190314	−	0.522050i
$958$	−6.81842	+	20.4762i	−0.220293	+	0.661557i
$959$		0			0
$960$	−10.4923	+	3.70859i	−0.338637	+	0.119694i
$961$	−3.50000	−	6.06218i	−0.112903	−	0.195554i
$962$	5.18229	+	5.84052i	0.167084	+	0.188306i
$963$	−14.0063	−	11.7772i	−0.451347	−	0.379515i
$964$	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	$-0.830511\pi$
$967$		−	31.5730i		−	1.01532i	0.861558	−	0.507660i	$-0.169489\pi$
$968$	−14.0668	−	6.63498i	−0.452125	−	0.213256i
$969$	2.53270	+	14.4069i	0.0813619	+	0.462815i
$970$	3.71964	−	3.30044i	0.119431	−	0.105971i
$971$	−14.6620	−	25.3953i	−0.470526	−	0.814974i	0.528906	−	0.848680i	$-0.322602\pi$
$971$	−14.6620	−	25.3953i	−0.470526	−	0.814974i	−0.999432	+	0.0337060i	$0.989269\pi$
$972$	−29.8175	−	9.10575i	−0.956398	−	0.292067i
$973$		0			0
$974$	8.13677	+	2.70948i	0.260719	+	0.0868174i
$975$	37.3376	+	13.6115i	1.19576	+	0.435916i
$976$	−3.72394	−	0.905697i	−0.119200	−	0.0289907i
$977$	−10.3022	−	5.94797i	−0.329596	−	0.190292i	0.326066	−	0.945347i	$-0.394277\pi$
$977$	−10.3022	−	5.94797i	−0.329596	−	0.190292i	−0.655662	+	0.755055i	$0.727610\pi$
$978$	−14.0218	−	11.1322i	−0.448368	−	0.355969i
$979$		−	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	$-0.910119\pi$
$983$	−7.49013	+	12.9733i	−0.238898	+	0.413783i	0.721500	+	0.692414i	$0.243453\pi$
$984$	24.9573	−	24.7133i	0.795611	−	0.787831i
$985$	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
$990$	−4.17855	−	6.81241i	−0.132803	−	0.216513i
$991$	18.0000	+	10.3923i	0.571789	+	0.330122i	0.757863	−	0.652413i	$-0.226243\pi$
$991$	18.0000	+	10.3923i	0.571789	+	0.330122i	−0.186075	+	0.982536i	$0.559577\pi$
$992$	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
$996$	9.81302	+	15.0326i	0.310938	+	0.476325i
$997$	9.81912	−	17.0072i	0.310975	−	0.538624i	−0.667599	−	0.744521i	$-0.732678\pi$
$997$	9.81912	−	17.0072i	0.310975	−	0.538624i	0.978574	+	0.205897i	$0.0660113\pi$
$998$	40.7278	−	36.1377i	1.28922	−	1.14392i
$999$	2.72992	−	4.71159i	0.0863708	−	0.149068i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.e.f.491.9	✓	24	28.3	even	6
588.2.e.f.491.10	yes	24	28.11	odd	6
588.2.e.f.491.11	yes	24	21.17	even	6
588.2.e.f.491.12	yes	24	21.11	odd	6
588.2.e.f.491.13	yes	24	7.4	even	3
588.2.e.f.491.14	yes	24	7.3	odd	6
588.2.e.f.491.15	yes	24	84.11	even	6
588.2.e.f.491.16	yes	24	84.59	odd	6
588.2.n.d.263.3		24	28.27	even	2
588.2.n.d.263.4		24	4.3	odd	2
588.2.n.d.263.9		24	84.83	odd	2
588.2.n.d.263.10		24	12.11	even	2
588.2.n.d.275.3		24	21.5	even	6
588.2.n.d.275.4		24	21.2	odd	6
588.2.n.d.275.9		24	7.5	odd	6
588.2.n.d.275.10		24	7.2	even	3
588.2.n.h.263.1		24	1.1	even	1	trivial
588.2.n.h.263.2		24	7.6	odd	2	inner
588.2.n.h.263.11		24	3.2	odd	2	inner
588.2.n.h.263.12		24	21.20	even	2	inner
588.2.n.h.275.1		24	84.23	even	6	inner
588.2.n.h.275.2		24	84.47	odd	6	inner
588.2.n.h.275.11		24	28.23	odd	6	inner
588.2.n.h.275.12		24	28.19	even	6	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} +(-0.299892 - 1.70589i) q^{3} +(1.83875 - 0.786769i) q^{4} +(0.695526 - 0.401562i) q^{5} +(0.899858 + 2.27821i) q^{6} +(-2.32403 + 1.61211i) q^{8} +(-2.82013 + 1.02317i) q^{9} +(-0.849569 + 0.753822i) q^{10} +(1.17273 - 2.03122i) q^{11} +(-1.89357 - 2.90076i) q^{12} +5.26858 q^{13} +(-0.893604 - 1.06607i) q^{15} +(2.76199 - 2.89334i) q^{16} +(-1.02661 - 0.592715i) q^{17} +(3.61652 - 2.21828i) 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} +(3.44704 + 3.48108i) q^{24} +(-2.17750 + 3.77153i) q^{25} +(-7.29917 + 1.49600i) q^{26} +(2.59115 + 4.50399i) q^{27} +4.23132i q^{29} +(1.54072 + 1.22321i) q^{30} +(-4.24264 - 2.44949i) q^{31} +(-3.00494 + 4.79274i) q^{32} +(-3.81673 - 1.39140i) q^{33} +(1.59058 + 0.529652i) q^{34} +(-4.38051 + 4.10014i) q^{36} +(-0.523976 - 0.907554i) q^{37} +(-7.53630 + 6.68696i) q^{38} +(-1.58001 - 8.98762i) q^{39} +(-0.969059 + 2.05450i) q^{40} -7.16942i q^{41} -7.94315i q^{43} +(0.558245 - 4.65757i) q^{44} +(-1.55061 + 1.84410i) q^{45} +(7.40294 + 8.34323i) q^{46} +(3.04954 + 5.28195i) q^{47} +(-5.76402 - 3.84396i) q^{48} +(1.94582 - 5.84343i) q^{50} +(-0.703234 + 1.92904i) q^{51} +(9.68759 - 4.14516i) q^{52} +(-7.55175 - 4.36001i) q^{53} +(-4.86871 - 5.50415i) q^{54} -1.88369i q^{55} +(-7.92692 - 9.45679i) q^{57} +(-1.20147 - 5.86214i) q^{58} +(0.331087 - 0.573459i) q^{59} +(-2.48186 - 1.25717i) 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} +(5.68284 + 0.843910i) q^{66} +(-7.29738 - 4.21314i) q^{67} +(-2.35401 - 0.282146i) q^{68} +(-10.4693 + 8.77567i) q^{69} +9.67432 q^{71} +(4.90460 - 6.92422i) q^{72} +(0.707107 - 1.22474i) q^{73} +(0.983622 + 1.10856i) q^{74} +(7.08684 + 2.58352i) q^{75} +(8.54216 - 11.4041i) q^{76} +(4.74097 + 12.0029i) q^{78} +(-6.00000 + 3.46410i) q^{79} +(0.759178 - 3.12150i) q^{80} +(6.90626 - 5.77092i) q^{81} +(2.03574 + 9.93263i) q^{82} -5.18229 q^{83} -0.952047 q^{85} +(2.25543 + 11.0046i) q^{86} +(7.21818 - 1.26894i) q^{87} +(0.549103 + 6.61118i) q^{88} +(14.1733 - 8.18296i) q^{89} +(1.62461 - 2.99513i) q^{90} +(-12.6252 - 9.45679i) q^{92} +(-2.90623 + 7.97207i) q^{93} +(-5.72467 - 6.45179i) q^{94} +(2.86085 - 4.95513i) q^{95} +(9.07704 + 3.68880i) 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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