LMFDB - Embedded newform 666.2.k.a.175.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(175,666)] 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("666.175"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.k (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			175.15
Character	$\chi$	$=$	666.175
Dual form			666.2.k.a.529.34

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +(1.36456 + 1.06676i) q^{3} -1.00000 q^{4} +3.20544i q^{5} +(1.06676 - 1.36456i) q^{6} +(-1.70419 + 2.95174i) q^{7} +1.00000i q^{8} +(0.724027 + 2.91132i) q^{9} +3.20544 q^{10} +(-1.60579 - 2.78131i) q^{11} +(-1.36456 - 1.06676i) q^{12} -3.57233i q^{13} +(2.95174 + 1.70419i) q^{14} +(-3.41945 + 4.37400i) q^{15} +1.00000 q^{16} +(-2.61351 - 1.50891i) q^{17} +(2.91132 - 0.724027i) q^{18} +(-3.74370 + 2.16143i) q^{19} -3.20544i q^{20} +(-5.47428 + 2.20985i) q^{21} +(-2.78131 + 1.60579i) q^{22} +(2.61622 + 1.51048i) q^{23} +(-1.06676 + 1.36456i) q^{24} -5.27484 q^{25} -3.57233 q^{26} +(-2.11772 + 4.74503i) q^{27} +(1.70419 - 2.95174i) q^{28} +(-7.81905 + 4.51433i) q^{29} +(4.37400 + 3.41945i) q^{30} +(7.54507 + 4.35615i) q^{31} -1.00000i q^{32} +(0.775813 - 5.50826i) q^{33} +(-1.50891 + 2.61351i) q^{34} +(-9.46164 - 5.46268i) q^{35} +(-0.724027 - 2.91132i) q^{36} +(-2.80409 + 5.39787i) q^{37} +(2.16143 + 3.74370i) q^{38} +(3.81083 - 4.87464i) q^{39} -3.20544 q^{40} +9.32045 q^{41} +(2.20985 + 5.47428i) q^{42} +(9.99006 - 5.76777i) q^{43} +(1.60579 + 2.78131i) q^{44} +(-9.33206 + 2.32082i) q^{45} +(1.51048 - 2.61622i) q^{46} +(1.54662 + 2.67882i) q^{47} +(1.36456 + 1.06676i) q^{48} +(-2.30853 - 3.99849i) q^{49} +5.27484i q^{50} +(-1.95663 - 4.84699i) q^{51} +3.57233i q^{52} +(1.90438 - 3.29849i) q^{53} +(4.74503 + 2.11772i) q^{54} +(8.91533 - 5.14727i) q^{55} +(-2.95174 - 1.70419i) q^{56} +(-7.41422 - 1.04426i) q^{57} +(4.51433 + 7.81905i) q^{58} +(-4.50165 + 2.59903i) q^{59} +(3.41945 - 4.37400i) q^{60} +(2.85899 + 1.65064i) q^{61} +(4.35615 - 7.54507i) q^{62} +(-9.82735 - 2.82430i) q^{63} -1.00000 q^{64} +11.4509 q^{65} +(-5.50826 - 0.775813i) q^{66} +10.0655 q^{67} +(2.61351 + 1.50891i) q^{68} +(1.95866 + 4.85203i) q^{69} +(-5.46268 + 9.46164i) q^{70} +(-2.62144 - 4.54046i) q^{71} +(-2.91132 + 0.724027i) q^{72} +3.96039 q^{73} +(5.39787 + 2.80409i) q^{74} +(-7.19782 - 5.62702i) q^{75} +(3.74370 - 2.16143i) q^{76} +10.9463 q^{77} +(-4.87464 - 3.81083i) q^{78} +(9.93076 + 5.73353i) q^{79} +3.20544i q^{80} +(-7.95157 + 4.21575i) q^{81} -9.32045i q^{82} -14.6809 q^{83} +(5.47428 - 2.20985i) q^{84} +(4.83671 - 8.37744i) q^{85} +(-5.76777 - 9.99006i) q^{86} +(-15.4853 - 2.18103i) q^{87} +(2.78131 - 1.60579i) q^{88} +(-4.80960 - 2.77683i) q^{89} +(2.32082 + 9.33206i) q^{90} +(10.5446 + 6.08793i) q^{91} +(-2.61622 - 1.51048i) q^{92} +(5.64869 + 13.9930i) q^{93} +(2.67882 - 1.54662i) q^{94} +(-6.92832 - 12.0002i) q^{95} +(1.06676 - 1.36456i) q^{96} +(-7.86397 + 4.54026i) q^{97} +(-3.99849 + 2.30853i) q^{98} +(6.93466 - 6.68872i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) $ 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.36456	+	1.06676i	0.787827	+	0.615897i
$3$	1.36456	+	1.06676i	0.787827	+	0.615897i
$4$	−1.00000			−0.500000
$5$			3.20544i			1.43352i	0.697322	+	0.716758i	$0.254375\pi$
$5$			3.20544i			1.43352i	−0.697322	+	0.716758i	$0.745625\pi$
$6$	1.06676	−	1.36456i	0.435505	−	0.557078i
$7$	−1.70419	+	2.95174i	−0.644123	+	1.11565i	0.340380	+	0.940288i	$0.389444\pi$
$7$	−1.70419	+	2.95174i	−0.644123	+	1.11565i	−0.984503	+	0.175366i	$0.943889\pi$
$8$			1.00000i			0.353553i
$9$	0.724027	+	2.91132i	0.241342	+	0.970440i
$10$	3.20544			1.01365
$11$	−1.60579	−	2.78131i	−0.484165	−	0.838598i	0.515670	−	0.856787i	$-0.327543\pi$
$11$	−1.60579	−	2.78131i	−0.484165	−	0.838598i	−0.999835	+	0.0181896i	$0.994210\pi$
$12$	−1.36456	−	1.06676i	−0.393913	−	0.307948i
$13$		−	3.57233i		−	0.990786i	−0.868669	−	0.495393i	$-0.835024\pi$
$13$		−	3.57233i		−	0.990786i	0.868669	−	0.495393i	$-0.164976\pi$
$14$	2.95174	+	1.70419i	0.788887	+	0.455464i
$15$	−3.41945	+	4.37400i	−0.882898	+	1.12936i
$16$	1.00000			0.250000
$17$	−2.61351	−	1.50891i	−0.633868	−	0.365964i	0.148380	−	0.988930i	$-0.452594\pi$
$17$	−2.61351	−	1.50891i	−0.633868	−	0.365964i	−0.782249	+	0.622966i	$0.785927\pi$
$18$	2.91132	−	0.724027i	0.686205	−	0.170655i
$19$	−3.74370	+	2.16143i	−0.858864	+	0.495865i	−0.863632	−	0.504124i	$-0.831816\pi$
$19$	−3.74370	+	2.16143i	−0.858864	+	0.495865i	0.00476802	+	0.999989i	$0.498482\pi$
$20$		−	3.20544i		−	0.716758i
$21$	−5.47428	+	2.20985i	−1.19459	+	0.482229i
$22$	−2.78131	+	1.60579i	−0.592978	+	0.342356i
$23$	2.61622	+	1.51048i	0.545520	+	0.314956i	0.747313	−	0.664472i	$-0.231343\pi$
$23$	2.61622	+	1.51048i	0.545520	+	0.314956i	−0.201793	+	0.979428i	$0.564677\pi$
$24$	−1.06676	+	1.36456i	−0.217752	+	0.278539i
$25$	−5.27484			−1.05497
$26$	−3.57233			−0.700591
$27$	−2.11772	+	4.74503i	−0.407555	+	0.913181i
$28$	1.70419	−	2.95174i	0.322062	−	0.557827i
$29$	−7.81905	+	4.51433i	−1.45196	+	0.838291i	−0.998593	−	0.0530324i	$-0.983111\pi$
$29$	−7.81905	+	4.51433i	−1.45196	+	0.838291i	−0.453369	+	0.891323i	$0.649778\pi$
$30$	4.37400	+	3.41945i	0.798580	+	0.624303i
$31$	7.54507	+	4.35615i	1.35513	+	0.782387i	0.988963	−	0.148160i	$-0.0473351\pi$
$31$	7.54507	+	4.35615i	1.35513	+	0.782387i	0.366171	+	0.930547i	$0.380668\pi$
$32$		−	1.00000i		−	0.176777i
$33$	0.775813	−	5.50826i	0.135052	−	0.958865i
$34$	−1.50891	+	2.61351i	−0.258776	+	0.448213i
$35$	−9.46164	−	5.46268i	−1.59931	−	0.923361i
$36$	−0.724027	−	2.91132i	−0.120671	−	0.485220i
$37$	−2.80409	+	5.39787i	−0.460990	+	0.887405i
$37$	−2.80409	+	5.39787i	−0.460990	+	0.887405i
$38$	2.16143	+	3.74370i	0.350630	+	0.607308i
$39$	3.81083	−	4.87464i	0.610222	−	0.780567i
$40$	−3.20544			−0.506825
$41$	9.32045			1.45561			0.727805	−	0.685784i	$-0.240541\pi$
$41$	9.32045			1.45561			0.727805	+	0.685784i	$0.240541\pi$
$42$	2.20985	+	5.47428i	0.340987	+	0.844700i
$43$	9.99006	−	5.76777i	1.52347	−	0.879576i	0.523856	−	0.851807i	$-0.324493\pi$
$43$	9.99006	−	5.76777i	1.52347	−	0.879576i	0.999614	−	0.0277695i	$-0.00884043\pi$
$44$	1.60579	+	2.78131i	0.242082	+	0.419299i
$45$	−9.33206	+	2.32082i	−1.39114	+	0.345968i
$46$	1.51048	−	2.61622i	0.222708	−	0.385741i
$47$	1.54662	+	2.67882i	0.225598	+	0.390746i	0.956499	−	0.291737i	$-0.0942332\pi$
$47$	1.54662	+	2.67882i	0.225598	+	0.390746i	−0.730901	+	0.682484i	$0.760900\pi$
$48$	1.36456	+	1.06676i	0.196957	+	0.153974i
$49$	−2.30853	−	3.99849i	−0.329790	−	0.571213i
$50$			5.27484i			0.745976i
$51$	−1.95663	−	4.84699i	−0.273982	−	0.678714i
$52$			3.57233i			0.495393i
$53$	1.90438	−	3.29849i	0.261587	−	0.453082i	−0.705077	−	0.709131i	$-0.749087\pi$
$53$	1.90438	−	3.29849i	0.261587	−	0.453082i	0.966664	+	0.256049i	$0.0824208\pi$
$54$	4.74503	+	2.11772i	0.645716	+	0.288185i
$55$	8.91533	−	5.14727i	1.20214	−	0.694058i
$56$	−2.95174	−	1.70419i	−0.394443	−	0.227732i
$57$	−7.41422	−	1.04426i	−0.982037	−	0.138315i
$58$	4.51433	+	7.81905i	0.592761	+	1.02669i
$59$	−4.50165	+	2.59903i	−0.586065	+	0.338365i	−0.763540	−	0.645760i	$-0.776540\pi$
$59$	−4.50165	+	2.59903i	−0.586065	+	0.338365i	0.177475	+	0.984125i	$0.443207\pi$
$60$	3.41945	−	4.37400i	0.441449	−	0.564681i
$61$	2.85899	+	1.65064i	0.366056	+	0.211343i	0.671734	−	0.740792i	$-0.265550\pi$
$61$	2.85899	+	1.65064i	0.366056	+	0.211343i	−0.305678	+	0.952135i	$0.598883\pi$
$62$	4.35615	−	7.54507i	0.553231	−	0.958225i
$63$	−9.82735	−	2.82430i	−1.23813	−	0.355828i
$64$	−1.00000			−0.125000
$65$	11.4509			1.42031
$66$	−5.50826	−	0.775813i	−0.678020	−	0.0954960i
$67$	10.0655			1.22969			0.614846	−	0.788648i	$-0.289218\pi$
$67$	10.0655			1.22969			0.614846	+	0.788648i	$0.289218\pi$
$68$	2.61351	+	1.50891i	0.316934	+	0.182982i
$69$	1.95866	+	4.85203i	0.235795	+	0.584115i
$70$	−5.46268	+	9.46164i	−0.652915	+	1.13088i
$71$	−2.62144	−	4.54046i	−0.311107	−	0.538853i	0.667495	−	0.744614i	$-0.267366\pi$
$71$	−2.62144	−	4.54046i	−0.311107	−	0.538853i	−0.978602	+	0.205761i	$0.934033\pi$
$72$	−2.91132	+	0.724027i	−0.343102	+	0.0853274i
$73$	3.96039			0.463528			0.231764	−	0.972772i	$-0.425550\pi$
$73$	3.96039			0.463528			0.231764	+	0.972772i	$0.425550\pi$
$74$	5.39787	+	2.80409i	0.627490	+	0.325969i
$75$	−7.19782	−	5.62702i	−0.831133	−	0.649752i
$76$	3.74370	−	2.16143i	0.429432	−	0.247933i
$77$	10.9463			1.24745
$78$	−4.87464	−	3.81083i	−0.551945	−	0.431492i
$79$	9.93076	+	5.73353i	1.11730	+	0.645072i	0.940710	−	0.339213i	$-0.110161\pi$
$79$	9.93076	+	5.73353i	1.11730	+	0.645072i	0.176588	+	0.984285i	$0.443494\pi$
$80$			3.20544i			0.358379i
$81$	−7.95157	+	4.21575i	−0.883508	+	0.468417i
$82$		−	9.32045i		−	1.02927i
$83$	−14.6809			−1.61144			−0.805722	−	0.592294i	$-0.798222\pi$
$83$	−14.6809			−1.61144			−0.805722	+	0.592294i	$0.798222\pi$
$84$	5.47428	−	2.20985i	0.597293	−	0.241115i
$85$	4.83671	−	8.37744i	0.524615	−	0.908660i
$86$	−5.76777	−	9.99006i	−0.621954	−	1.07726i
$87$	−15.4853	−	2.18103i	−1.66019	−	0.233831i
$88$	2.78131	−	1.60579i	0.296489	−	0.171178i
$89$	−4.80960	−	2.77683i	−0.509817	−	0.294343i	0.222941	−	0.974832i	$-0.428434\pi$
$89$	−4.80960	−	2.77683i	−0.509817	−	0.294343i	−0.732758	+	0.680489i	$0.761767\pi$
$90$	2.32082	+	9.33206i	0.244636	+	0.983686i
$91$	10.5446	+	6.08793i	1.10537	+	0.638188i
$92$	−2.61622	−	1.51048i	−0.272760	−	0.157478i
$93$	5.64869	+	13.9930i	0.585742	+	1.45101i
$94$	2.67882	−	1.54662i	0.276299	−	0.159522i
$95$	−6.92832	−	12.0002i	−0.710831	−	1.23119i
$96$	1.06676	−	1.36456i	0.108876	−	0.139269i
$97$	−7.86397	+	4.54026i	−0.798465	+	0.460994i	−0.842934	−	0.538017i	$-0.819174\pi$
$97$	−7.86397	+	4.54026i	−0.798465	+	0.460994i	0.0444691	+	0.999011i	$0.485840\pi$
$98$	−3.99849	+	2.30853i	−0.403908	+	0.233197i
$99$	6.93466	−	6.68872i	0.696959	−	0.672242i
$100$	5.27484			0.527484
$101$	−4.70686	−	8.15253i	−0.468350	−	0.811207i	0.530995	−	0.847375i	$-0.321818\pi$
$101$	−4.70686	−	8.15253i	−0.468350	−	0.811207i	−0.999346	+	0.0361681i	$0.988485\pi$
$102$	−4.84699	+	1.95663i	−0.479923	+	0.193735i
$103$	14.1659	+	8.17871i	1.39581	+	0.805872i	0.993950	−	0.109829i	$-0.0350304\pi$
$103$	14.1659	+	8.17871i	1.39581	+	0.805872i	0.401860	+	0.915701i	$0.368364\pi$
$104$	3.57233			0.350296
$105$	−7.08354	−	17.5475i	−0.691283	−	1.71246i
$106$	−3.29849	−	1.90438i	−0.320377	−	0.184970i
$107$	8.09077	+	14.0136i	0.782164	+	1.35475i	0.930679	+	0.365837i	$0.119217\pi$
$107$	8.09077	+	14.0136i	0.782164	+	1.35475i	−0.148515	+	0.988910i	$0.547449\pi$
$108$	2.11772	−	4.74503i	0.203777	−	0.456590i
$109$	14.9563	+	8.63504i	1.43256	+	0.827087i	0.997315	−	0.0732277i	$-0.0233300\pi$
$109$	14.9563	+	8.63504i	1.43256	+	0.827087i	0.435241	+	0.900314i	$0.356663\pi$
$110$	−5.14727	−	8.91533i	−0.490773	−	0.850044i
$111$	−9.58461	+	4.37439i	−0.909731	+	0.415199i
$112$	−1.70419	+	2.95174i	−0.161031	+	0.278914i
$113$	−9.69019	+	5.59464i	−0.911577	+	0.526299i	−0.880938	−	0.473231i	$-0.843087\pi$
$113$	−9.69019	+	5.59464i	−0.911577	+	0.526299i	−0.0306387	+	0.999531i	$0.509754\pi$
$114$	−1.04426	+	7.41422i	−0.0978038	+	0.694405i
$115$	−4.84174	+	8.38615i	−0.451495	+	0.782012i
$116$	7.81905	−	4.51433i	0.725981	−	0.419145i
$117$	10.4002	−	2.58646i	0.961498	−	0.239118i
$118$	2.59903	+	4.50165i	0.239260	+	0.414411i
$119$	8.90782	−	5.14293i	0.816579	−	0.471452i
$120$	−4.37400	−	3.41945i	−0.399290	−	0.312152i
$121$	0.342862	−	0.593855i	0.0311693	−	0.0539868i
$122$	1.65064	−	2.85899i	0.149442	−	0.258841i
$123$	12.7183	+	9.94273i	1.14677	+	0.896505i
$124$	−7.54507	−	4.35615i	−0.677567	−	0.391194i
$125$		−	0.880996i		−	0.0787987i
$126$	−2.82430	+	9.82735i	−0.251609	+	0.875490i
$127$	−0.118556	+	0.205345i	−0.0105201	+	0.0182214i	−0.871238	−	0.490862i	$-0.836682\pi$
$127$	−0.118556	+	0.205345i	−0.0105201	+	0.0182214i	0.860717	+	0.509083i	$0.170015\pi$
$128$			1.00000i			0.0883883i
$129$	19.7849	+	2.78661i	1.74196	+	0.245347i
$130$		−	11.4509i		−	1.00431i
$131$	6.93146	−	4.00188i	0.605604	−	0.349646i	−0.165639	−	0.986186i	$-0.552969\pi$
$131$	6.93146	−	4.00188i	0.605604	−	0.349646i	0.771243	+	0.636541i	$0.219635\pi$
$132$	−0.775813	+	5.50826i	−0.0675259	+	0.479433i
$133$		−	14.7339i		−	1.27759i
$134$		−	10.0655i		−	0.869523i
$135$	−15.2099	−	6.78822i	−1.30906	−	0.584237i
$136$	1.50891	−	2.61351i	0.129388	−	0.224106i
$137$	0.481722	+	0.834367i	0.0411563	+	0.0712848i	0.885870	−	0.463934i	$-0.153563\pi$
$137$	0.481722	+	0.834367i	0.0411563	+	0.0712848i	−0.844713	+	0.535219i	$0.820229\pi$
$138$	4.85203	−	1.95866i	0.413032	−	0.166732i
$139$	−5.64045	−	9.76955i	−0.478417	−	0.828642i	0.521277	−	0.853388i	$-0.325456\pi$
$139$	−5.64045	−	9.76955i	−0.478417	−	0.828642i	−0.999694	+	0.0247454i	$0.992122\pi$
$140$	9.46164	+	5.46268i	0.799654	+	0.461681i
$141$	−0.747224	+	5.30528i	−0.0629277	+	0.446785i
$142$	−4.54046	+	2.62144i	−0.381027	+	0.219986i
$143$	−9.93577	+	5.73642i	−0.830870	+	0.479703i
$144$	0.724027	+	2.91132i	0.0603356	+	0.242610i
$145$	−14.4704	−	25.0635i	−1.20170	−	2.08141i
$146$		−	3.96039i		−	0.327764i
$147$	1.11533	−	7.91882i	0.0919908	−	0.653133i
$148$	2.80409	−	5.39787i	0.230495	−	0.443703i
$149$	2.05732	−	3.56338i	0.168542	−	0.291923i	−0.769365	−	0.638809i	$-0.779427\pi$
$149$	2.05732	−	3.56338i	0.168542	−	0.291923i	0.937907	+	0.346885i	$0.112761\pi$
$150$	−5.62702	+	7.19782i	−0.459444	+	0.587700i
$151$	−4.88996	+	8.46967i	−0.397940	+	0.689252i	−0.993472	−	0.114080i	$-0.963608\pi$
$151$	−4.88996	+	8.46967i	−0.397940	+	0.689252i	0.595532	+	0.803332i	$0.296941\pi$
$152$	−2.16143	−	3.74370i	−0.175315	−	0.303654i
$153$	2.50067	−	8.70124i	0.202167	−	0.703454i
$154$		−	10.9463i		−	0.882078i
$155$	−13.9634	+	24.1853i	−1.12156	+	1.94261i
$156$	−3.81083	+	4.87464i	−0.305111	+	0.390284i
$157$	0.850473	+	1.47306i	0.0678752	+	0.117563i	0.897966	−	0.440065i	$-0.145045\pi$
$157$	0.850473	+	1.47306i	0.0678752	+	0.117563i	−0.830091	+	0.557629i	$0.811711\pi$
$158$	5.73353	−	9.93076i	0.456135	−	0.790049i
$159$	6.11734	−	2.46944i	0.485137	−	0.195840i
$160$	3.20544			0.253412
$161$	−8.91709	+	5.14828i	−0.702765	+	0.405741i
$162$	4.21575	+	7.95157i	0.331221	+	0.624734i
$163$	−4.69770	−	2.71222i	−0.367953	−	0.212438i	0.304611	−	0.952477i	$-0.401474\pi$
$163$	−4.69770	−	2.71222i	−0.367953	−	0.212438i	−0.672564	+	0.740039i	$0.734807\pi$
$164$	−9.32045			−0.727805
$165$	17.6564	+	2.48682i	1.37455	+	0.193599i
$166$			14.6809i			1.13946i
$167$		−	5.05408i		−	0.391096i	−0.980694	−	0.195548i	$-0.937351\pi$
$167$		−	5.05408i		−	0.391096i	0.980694	−	0.195548i	$-0.0626486\pi$
$168$	−2.20985	−	5.47428i	−0.170494	−	0.422350i
$169$	0.238472			0.0183440
$170$	−8.37744	−	4.83671i	−0.642520	−	0.370959i
$171$	−9.00314	−	9.33418i	−0.688487	−	0.713802i
$172$	−9.99006	+	5.76777i	−0.761735	+	0.439788i
$173$	−17.7902			−1.35256			−0.676281	−	0.736644i	$-0.736409\pi$
$173$	−17.7902			−1.35256			−0.676281	+	0.736644i	$0.736409\pi$
$174$	−2.18103	+	15.4853i	−0.165343	+	1.17394i
$175$	8.98934	−	15.5700i	0.679530	−	1.17698i
$176$	−1.60579	−	2.78131i	−0.121041	−	0.209649i
$177$	−8.91531	−	1.25568i	−0.670116	−	0.0943827i
$178$	−2.77683	+	4.80960i	−0.208132	+	0.360495i
$179$		−	3.03460i		−	0.226817i	−0.993548	−	0.113408i	$-0.963823\pi$
$179$		−	3.03460i		−	0.226817i	0.993548	−	0.113408i	$-0.0361768\pi$
$180$	9.33206	−	2.32082i	0.695571	−	0.172984i
$181$	−5.46278	−	9.46181i	−0.406045	−	0.703291i	0.588397	−	0.808572i	$-0.299759\pi$
$181$	−5.46278	−	9.46181i	−0.406045	−	0.703291i	−0.994443	+	0.105281i	$0.966426\pi$
$182$	6.08793	−	10.5446i	0.451267	−	0.781618i
$183$	2.14041	+	5.30226i	0.158224	+	0.391954i
$184$	−1.51048	+	2.61622i	−0.111354	+	0.192871i
$185$	−17.3026	−	8.98836i	−1.27211	−	0.660837i
$186$	13.9930	−	5.64869i	1.02602	−	0.414182i
$187$			9.69197i			0.708747i
$188$	−1.54662	−	2.67882i	−0.112799	−	0.195373i
$189$	−10.3971	−	14.3374i	−0.756278	−	1.04289i
$190$	−12.0002	+	6.92832i	−0.870586	+	0.502633i
$191$	14.4155	−	8.32278i	1.04307	−	0.602215i	0.122367	−	0.992485i	$-0.460952\pi$
$191$	14.4155	−	8.32278i	1.04307	−	0.602215i	0.920701	+	0.390270i	$0.127618\pi$
$192$	−1.36456	−	1.06676i	−0.0984784	−	0.0769871i
$193$	−22.3559	−	12.9072i	−1.60922	−	0.929081i	−0.989546	−	0.144218i	$-0.953933\pi$
$193$	−22.3559	−	12.9072i	−1.60922	−	0.929081i	−0.619670	−	0.784863i	$-0.712733\pi$
$194$	4.54026	+	7.86397i	0.325972	+	0.564600i
$195$	15.6254	+	12.2154i	1.11896	+	0.874763i
$196$	2.30853	+	3.99849i	0.164895	+	0.285606i
$197$	8.41516	−	14.5755i	0.599555	−	1.03846i	−0.393331	−	0.919397i	$-0.628677\pi$
$197$	8.41516	−	14.5755i	0.599555	−	1.03846i	0.992887	−	0.119064i	$-0.0379893\pi$
$198$	−6.68872	−	6.93466i	−0.475347	−	0.492825i
$199$		−	5.47143i		−	0.387859i	−0.981015	−	0.193930i	$-0.937877\pi$
$199$		−	5.47143i		−	0.387859i	0.981015	−	0.193930i	$-0.0621234\pi$
$200$		−	5.27484i		−	0.372988i
$201$	13.7349	+	10.7375i	0.968784	+	0.757363i
$202$	−8.15253	+	4.70686i	−0.573610	+	0.331174i
$203$		−	30.7731i		−	2.15985i
$204$	1.95663	+	4.84699i	0.136991	+	0.339357i
$205$			29.8761i			2.08664i
$206$	8.17871	−	14.1659i	0.569837	−	0.986987i
$207$	−2.50327	+	8.71029i	−0.173989	+	0.605407i
$208$		−	3.57233i		−	0.247696i
$209$	12.0232	+	6.94160i	0.831663	+	0.480161i
$210$	−17.5475	+	7.08354i	−1.21089	+	0.488811i
$211$	7.09886	−	12.2956i	0.488706	−	0.846463i	−0.511210	−	0.859456i	$-0.670803\pi$
$211$	7.09886	−	12.2956i	0.488706	−	0.846463i	0.999916	+	0.0129930i	$0.00413591\pi$
$212$	−1.90438	+	3.29849i	−0.130794	+	0.226541i
$213$	1.26651	−	8.99217i	0.0867795	−	0.616133i
$214$	14.0136	−	8.09077i	0.957951	−	0.553073i
$215$	18.4882	+	32.0226i	1.26089	+	2.18392i
$216$	−4.74503	−	2.11772i	−0.322858	−	0.144092i
$217$	−25.7165	+	14.8474i	−1.74575	+	1.00791i
$218$	8.63504	−	14.9563i	0.584838	−	1.01297i
$219$	5.40417	+	4.22480i	0.365180	+	0.285485i
$220$	−8.91533	+	5.14727i	−0.601072	+	0.347029i
$221$	−5.39032	+	9.33630i	−0.362592	+	0.628028i
$222$	4.37439	+	9.58461i	0.293590	+	0.643277i
$223$	5.97172	+	10.3433i	0.399896	+	0.692640i	0.993713	−	0.111960i	$-0.0357130\pi$
$223$	5.97172	+	10.3433i	0.399896	+	0.692640i	−0.593817	+	0.804600i	$0.702380\pi$
$224$	2.95174	+	1.70419i	0.197222	+	0.113866i
$225$	−3.81913	−	15.3568i	−0.254609	−	1.02378i
$226$	5.59464	+	9.69019i	0.372150	+	0.644582i
$227$	7.24441	+	4.18256i	0.480829	+	0.277607i	0.720762	−	0.693183i	$-0.243792\pi$
$227$	7.24441	+	4.18256i	0.480829	+	0.277607i	−0.239933	+	0.970789i	$0.577126\pi$
$228$	7.41422	+	1.04426i	0.491019	+	0.0691577i
$229$	2.68705			0.177565			0.0887826	−	0.996051i	$-0.471702\pi$
$229$	2.68705			0.177565			0.0887826	+	0.996051i	$0.471702\pi$
$230$	8.38615	+	4.84174i	0.552966	+	0.319255i
$231$	14.9368	+	11.6771i	0.982772	+	0.768299i
$232$	−4.51433	−	7.81905i	−0.296380	−	0.513346i
$233$	8.55045			0.560159			0.280079	−	0.959977i	$-0.409639\pi$
$233$	8.55045			0.560159			0.280079	+	0.959977i	$0.409639\pi$
$234$	−2.58646	−	10.4002i	−0.169082	−	0.679882i
$235$	−8.58681	+	4.95759i	−0.560141	+	0.323398i
$236$	4.50165	−	2.59903i	0.293033	−	0.169182i
$237$	7.43476	+	18.4175i	0.482939	+	1.19635i
$238$	−5.14293	−	8.90782i	−0.333367	−	0.577408i
$239$	19.1510	−	11.0569i	1.23878	−	0.715209i	0.269934	−	0.962879i	$-0.412998\pi$
$239$	19.1510	−	11.0569i	1.23878	−	0.715209i	0.968844	+	0.247670i	$0.0796649\pi$
$240$	−3.41945	+	4.37400i	−0.220725	+	0.282341i
$241$	−3.77224	−	2.17790i	−0.242991	−	0.140291i	0.373560	−	0.927606i	$-0.378137\pi$
$241$	−3.77224	−	2.17790i	−0.242991	−	0.140291i	−0.616551	+	0.787315i	$0.711470\pi$
$242$	−0.593855	−	0.342862i	−0.0381744	−	0.0220400i
$243$	−15.3476	−	2.72983i	−0.984547	−	0.175118i
$244$	−2.85899	−	1.65064i	−0.183028	−	0.105671i
$245$	12.8169	−	7.39985i	0.818843	−	0.472759i
$246$	9.94273	−	12.7183i	0.633925	−	0.810888i
$247$	7.72132	+	13.3737i	0.491296	+	0.850950i
$248$	−4.35615	+	7.54507i	−0.276616	+	0.479112i
$249$	−20.0330	−	15.6611i	−1.26954	−	0.992483i
$250$	−0.880996			−0.0557191
$251$		−	10.3801i		−	0.655189i	−0.944818	−	0.327595i	$-0.893762\pi$
$251$		−	10.3801i		−	0.655189i	0.944818	−	0.327595i	$-0.106238\pi$
$252$	9.82735	+	2.82430i	0.619065	+	0.177914i
$253$		−	9.70205i		−	0.609963i
$254$	0.205345	+	0.118556i	0.0128845	+	0.00743886i
$255$	15.5367	−	6.27185i	0.972947	−	0.392758i
$256$	1.00000			0.0625000
$257$	−3.96174	+	2.28731i	−0.247127	+	0.142679i	−0.618448	−	0.785826i	$-0.712238\pi$
$257$	−3.96174	+	2.28731i	−0.247127	+	0.142679i	0.371321	+	0.928504i	$0.378905\pi$
$258$	2.78661	−	19.7849i	0.173486	−	1.23175i
$259$	−11.1544	−	17.4760i	−0.693103	−	1.08590i
$260$	−11.4509			−0.710154
$261$	−18.8039	−	19.4953i	−1.16393	−	1.20673i
$262$	−4.00188	−	6.93146i	−0.247237	−	0.428227i
$263$	8.63923	−	14.9636i	0.532718	−	0.922695i	−0.466552	−	0.884494i	$-0.654504\pi$
$263$	8.63923	−	14.9636i	0.532718	−	0.922695i	0.999270	−	0.0382009i	$-0.0121627\pi$
$264$	5.50826	+	0.775813i	0.339010	+	0.0477480i
$265$	10.5731	+	6.10438i	0.649500	+	0.374989i
$266$	−14.7339			−0.903395
$267$	−3.60076	−	8.91985i	−0.220363	−	0.545886i
$268$	−10.0655			−0.614846
$269$	−1.27599			−0.0777987			−0.0388994	−	0.999243i	$-0.512385\pi$
$269$	−1.27599			−0.0777987			−0.0388994	+	0.999243i	$0.512385\pi$
$270$	−6.78822	+	15.2099i	−0.413118	+	0.925645i
$271$	3.77368	−	6.53621i	0.229235	−	0.397046i	−0.728347	−	0.685209i	$-0.759711\pi$
$271$	3.77368	−	6.53621i	0.229235	−	0.397046i	0.957582	+	0.288162i	$0.0930443\pi$
$272$	−2.61351	−	1.50891i	−0.158467	−	0.0914910i
$273$	7.89431	+	19.5559i	0.477786	+	1.18358i
$274$	0.834367	−	0.481722i	0.0504059	−	0.0291019i
$275$	8.47030	+	14.6710i	0.510779	+	0.884694i
$276$	−1.95866	−	4.85203i	−0.117898	−	0.292058i
$277$	−12.2422	−	7.06806i	−0.735565	−	0.424679i	0.0848897	−	0.996390i	$-0.472946\pi$
$277$	−12.2422	−	7.06806i	−0.735565	−	0.424679i	−0.820455	+	0.571712i	$0.806280\pi$
$278$	−9.76955	+	5.64045i	−0.585938	+	0.338292i
$279$	−7.21931	+	25.1201i	−0.432209	+	1.50390i
$280$	5.46268	−	9.46164i	0.326458	−	0.565441i
$281$			21.9473i			1.30927i	0.755946	+	0.654634i	$0.227177\pi$
$281$			21.9473i			1.30927i	−0.755946	+	0.654634i	$0.772823\pi$
$282$	5.30528	+	0.747224i	0.315925	+	0.0444966i
$283$			22.9686i			1.36534i	0.730726	+	0.682671i	$0.239182\pi$
$283$			22.9686i			1.36534i	−0.730726	+	0.682671i	$0.760818\pi$
$284$	2.62144	+	4.54046i	0.155554	+	0.269427i
$285$	3.34731	−	23.7658i	0.198277	−	1.40777i
$286$	5.73642	+	9.93577i	0.339201	+	0.587514i
$287$	−15.8838	+	27.5116i	−0.937592	+	1.62396i
$288$	2.91132	−	0.724027i	0.171551	−	0.0426637i
$289$	−3.94639	−	6.83535i	−0.232141	−	0.402079i
$290$	−25.0635	+	14.4704i	−1.47178	+	0.849732i
$291$	−15.5742	−	2.19356i	−0.912977	−	0.128589i
$292$	−3.96039			−0.231764
$293$	0.243840			0.0142453			0.00712263	−	0.999975i	$-0.497733\pi$
$293$	0.243840			0.0142453			0.00712263	+	0.999975i	$0.497733\pi$
$294$	−7.91882	−	1.11533i	−0.461835	−	0.0650473i
$295$	−8.33103	−	14.4298i	−0.485052	−	0.840134i
$296$	−5.39787	−	2.80409i	−0.313745	−	0.162985i
$297$	16.5980	−	1.72949i	0.963115	−	0.100355i
$298$	−3.56338	−	2.05732i	−0.206421	−	0.119177i
$299$	5.39592	−	9.34601i	0.312054	−	0.540494i
$300$	7.19782	+	5.62702i	0.415566	+	0.324876i
$301$			39.3175i			2.26622i
$302$	8.46967	+	4.88996i	0.487375	+	0.281386i
$303$	2.27405	−	16.1457i	0.130641	−	0.927546i
$304$	−3.74370	+	2.16143i	−0.214716	+	0.123966i
$305$	−5.29102	+	9.16432i	−0.302963	+	0.524748i
$306$	−8.70124	−	2.50067i	−0.497417	−	0.142954i
$307$	22.8567			1.30450			0.652251	−	0.758003i	$-0.273825\pi$
$307$	22.8567			1.30450			0.652251	+	0.758003i	$0.273825\pi$
$308$	−10.9463			−0.623723
$309$	10.6055	+	26.2720i	0.603323	+	1.49456i
$310$	24.1853	+	13.9634i	1.37363	+	0.793066i
$311$	−13.0554	+	7.53751i	−0.740301	+	0.427413i	−0.822179	−	0.569229i	$-0.807242\pi$
$311$	−13.0554	+	7.53751i	−0.740301	+	0.427413i	0.0818775	+	0.996642i	$0.473908\pi$
$312$	4.87464	+	3.81083i	0.275972	+	0.215746i
$313$		−	32.8309i		−	1.85571i	−0.372936	−	0.927857i	$-0.621649\pi$
$313$		−	32.8309i		−	1.85571i	0.372936	−	0.927857i	$-0.378351\pi$
$314$	1.47306	−	0.850473i	0.0831298	−	0.0479950i
$315$	9.05313	−	31.5010i	0.510086	−	1.77488i
$316$	−9.93076	−	5.73353i	−0.558649	−	0.322536i
$317$	21.3433			1.19876			0.599380	−	0.800465i	$-0.295414\pi$
$317$	21.3433			1.19876			0.599380	+	0.800465i	$0.295414\pi$
$318$	−2.46944	−	6.11734i	−0.138479	−	0.343044i
$319$	25.1116	+	14.4982i	1.40598	+	0.811741i
$320$		−	3.20544i		−	0.179190i
$321$	−3.90893	+	27.7533i	−0.218175	+	1.54904i
$322$	5.14828	+	8.91709i	0.286903	+	0.496930i
$323$	13.0456			0.725875
$324$	7.95157	−	4.21575i	0.441754	−	0.234208i
$325$			18.8435i			1.04525i
$326$	−2.71222	+	4.69770i	−0.150216	+	0.260182i
$327$	11.1972	+	27.7379i	0.619206	+	1.53391i
$328$			9.32045i			0.514636i
$329$	−10.5429			−0.581251
$330$	2.48682	−	17.6564i	0.136895	−	0.971953i
$331$			1.93316i			0.106256i	0.998588	+	0.0531280i	$0.0169191\pi$
$331$			1.93316i			0.106256i	−0.998588	+	0.0531280i	$0.983081\pi$
$332$	14.6809			0.805722
$333$	−17.7452	−	4.25541i	−0.972430	−	0.233195i
$334$	−5.05408			−0.276547
$335$			32.2642i			1.76278i
$336$	−5.47428	+	2.20985i	−0.298646	+	0.120557i
$337$	22.3662			1.21836			0.609181	−	0.793031i	$-0.291498\pi$
$337$	22.3662			1.21836			0.609181	+	0.793031i	$0.291498\pi$
$338$		−	0.238472i		−	0.0129712i
$339$	−19.1910	−	2.70296i	−1.04231	−	0.146805i
$340$	−4.83671	+	8.37744i	−0.262308	+	0.454330i
$341$		−	27.9803i		−	1.51522i
$342$	−9.33418	+	9.00314i	−0.504734	+	0.486834i
$343$	−8.12197			−0.438545
$344$	5.76777	+	9.99006i	0.310977	+	0.538628i
$345$	−15.5529	+	6.27837i	−0.837339	+	0.338016i
$346$			17.7902i			0.956405i
$347$	−20.3381	−	11.7422i	−1.09181	−	0.630355i	−0.157750	−	0.987479i	$-0.550424\pi$
$347$	−20.3381	−	11.7422i	−1.09181	−	0.630355i	−0.934057	+	0.357124i	$0.883757\pi$
$348$	15.4853	+	2.18103i	0.830097	+	0.116915i
$349$	−17.2371			−0.922679			−0.461339	−	0.887224i	$-0.652631\pi$
$349$	−17.2371			−0.922679			−0.461339	+	0.887224i	$0.652631\pi$
$350$	−15.5700	−	8.98934i	−0.832251	−	0.480500i
$351$	16.9508	+	7.56518i	0.904766	+	0.403800i
$352$	−2.78131	+	1.60579i	−0.148245	+	0.0855890i
$353$			18.5070i			0.985030i	0.870304	+	0.492515i	$0.163922\pi$
$353$			18.5070i			0.985030i	−0.870304	+	0.492515i	$0.836078\pi$
$354$	−1.25568	+	8.91531i	−0.0667386	+	0.473843i
$355$	14.5542	−	8.40285i	0.772455	−	0.445977i
$356$	4.80960	+	2.77683i	0.254909	+	0.147172i
$357$	17.6415	+	2.48473i	0.933688	+	0.131506i
$358$	−3.03460			−0.160384
$359$	19.0158			1.00361			0.501807	−	0.864980i	$-0.332669\pi$
$359$	19.0158			1.00361			0.501807	+	0.864980i	$0.332669\pi$
$360$	−2.32082	−	9.33206i	−0.122318	−	0.491843i
$361$	−0.156477	+	0.271026i	−0.00823563	+	0.0142645i
$362$	−9.46181	+	5.46278i	−0.497302	+	0.287117i
$363$	1.10136	−	0.444595i	0.0578063	−	0.0233352i
$364$	−10.5446	−	6.08793i	−0.552687	−	0.319094i
$365$			12.6948i			0.664475i
$366$	5.30226	−	2.14041i	0.277154	−	0.111881i
$367$	0.542070	−	0.938892i	0.0282958	−	0.0490098i	−0.851531	−	0.524305i	$-0.824325\pi$
$367$	0.542070	−	0.938892i	0.0282958	−	0.0490098i	0.879827	+	0.475295i	$0.157659\pi$
$368$	2.61622	+	1.51048i	0.136380	+	0.0787391i
$369$	6.74826	+	27.1348i	0.351300	+	1.41258i
$370$	−8.98836	+	17.3026i	−0.467282	+	0.899517i
$371$	6.49086	+	11.2425i	0.336989	+	0.583681i
$372$	−5.64869	−	13.9930i	−0.292871	−	0.725504i
$373$	7.43066			0.384745			0.192373	−	0.981322i	$-0.438382\pi$
$373$	7.43066			0.384745			0.192373	+	0.981322i	$0.438382\pi$
$374$	9.69197			0.501160
$375$	0.939816	−	1.20217i	0.0485319	−	0.0620797i
$376$	−2.67882	+	1.54662i	−0.138150	+	0.0797608i
$377$	16.1267	+	27.9322i	0.830566	+	1.43858i
$378$	−14.3374	+	10.3971i	−0.737436	+	0.534770i
$379$	6.95638	−	12.0488i	0.357325	−	0.618905i	−0.630188	−	0.776443i	$-0.717022\pi$
$379$	6.95638	−	12.0488i	0.357325	−	0.618905i	0.987513	+	0.157537i	$0.0503554\pi$
$380$	6.92832	+	12.0002i	0.355415	+	0.615597i
$381$	−0.380831	+	0.153733i	−0.0195106	+	0.00787600i
$382$	−8.32278	−	14.4155i	−0.425831	−	0.737560i
$383$			29.8204i			1.52375i	0.647724	+	0.761875i	$0.275721\pi$
$383$			29.8204i			1.52375i	−0.647724	+	0.761875i	$0.724279\pi$
$384$	−1.06676	+	1.36456i	−0.0544381	+	0.0696347i
$385$			35.0877i			1.78824i
$386$	−12.9072	+	22.3559i	−0.656959	+	1.13789i
$387$	24.0249	+	24.9083i	1.22125	+	1.26616i
$388$	7.86397	−	4.54026i	0.399232	−	0.230497i
$389$	−22.1037	−	12.7615i	−1.12070	−	0.647036i	−0.179120	−	0.983827i	$-0.557325\pi$
$389$	−22.1037	−	12.7615i	−1.12070	−	0.647036i	−0.941579	+	0.336791i	$0.890658\pi$
$390$	12.2154	−	15.6254i	0.618551	−	0.791221i
$391$	−4.55834	−	7.89528i	−0.230525	−	0.399282i
$392$	3.99849	−	2.30853i	0.201954	−	0.116598i
$393$	13.7274	+	1.93344i	0.692457	+	0.0975294i
$394$	−14.5755	−	8.41516i	−0.734302	−	0.423950i
$395$	−18.3785	+	31.8325i	−0.924722	+	1.60166i
$396$	−6.93466	+	6.68872i	−0.348480	+	0.336121i
$397$	18.8098			0.944036			0.472018	−	0.881589i	$-0.343526\pi$
$397$	18.8098			0.944036			0.472018	+	0.881589i	$0.343526\pi$
$398$	−5.47143			−0.274258
$399$	15.7176	−	20.1053i	0.786866	−	1.00652i
$400$	−5.27484			−0.263742
$401$	−7.16059	−	4.13417i	−0.357583	−	0.206450i	0.310437	−	0.950594i	$-0.399525\pi$
$401$	−7.16059	−	4.13417i	−0.357583	−	0.206450i	−0.668020	+	0.744143i	$0.732858\pi$
$402$	10.7375	−	13.7349i	0.535536	−	0.685034i
$403$	15.5616	−	26.9535i	0.775178	−	1.34265i
$404$	4.70686	+	8.15253i	0.234175	+	0.405603i
$405$	−13.5133	−	25.4883i	−0.671483	−	1.26652i
$406$	−30.7731			−1.52724
$407$	19.5160	−	0.868799i	0.967371	−	0.0430647i
$408$	4.84699	−	1.95663i	0.239962	−	0.0968674i
$409$	−25.9886	+	15.0045i	−1.28505	+	0.741927i	−0.977768	−	0.209690i	$-0.932755\pi$
$409$	−25.9886	+	15.0045i	−1.28505	+	0.741927i	−0.307287	+	0.951617i	$0.599421\pi$
$410$	29.8761			1.47548
$411$	−0.232736	+	1.65242i	−0.0114800	+	0.0815081i
$412$	−14.1659	−	8.17871i	−0.697905	−	0.402936i
$413$		−	17.7170i		−	0.871795i
$414$	8.71029	+	2.50327i	0.428087	+	0.123029i
$415$		−	47.0589i		−	2.31003i
$416$	−3.57233			−0.175148
$417$	2.72509	−	19.3481i	0.133448	−	0.947482i
$418$	6.94160	−	12.0232i	0.339525	−	0.588074i
$419$	−1.33888	−	2.31901i	−0.0654086	−	0.113291i	0.831467	−	0.555575i	$-0.187502\pi$
$419$	−1.33888	−	2.31901i	−0.0654086	−	0.113291i	−0.896875	+	0.442284i	$0.854168\pi$
$420$	7.08354	+	17.5475i	0.345642	+	0.856229i
$421$	−25.4525	+	14.6950i	−1.24048	+	0.716190i	−0.969191	−	0.246309i	$-0.920782\pi$
$421$	−25.4525	+	14.6950i	−1.24048	+	0.716190i	−0.271286	+	0.962499i	$0.587449\pi$
$422$	−12.2956	−	7.09886i	−0.598540	−	0.345567i
$423$	−6.67912	+	6.44224i	−0.324750	+	0.313233i
$424$	3.29849	+	1.90438i	0.160189	+	0.0924850i
$425$	13.7858	+	7.95926i	0.668711	+	0.386081i
$426$	−8.99217	−	1.26651i	−0.435672	−	0.0613624i
$427$	−9.74453	+	5.62601i	−0.471571	+	0.272262i
$428$	−8.09077	−	14.0136i	−0.391082	−	0.677374i
$429$	−19.6773	−	2.77146i	−0.950030	−	0.133807i
$430$	32.0226	−	18.4882i	1.54426	−	0.891582i
$431$	4.53824	−	2.62016i	0.218599	−	0.126208i	−0.386702	−	0.922205i	$-0.626386\pi$
$431$	4.53824	−	2.62016i	0.218599	−	0.126208i	0.605302	+	0.795996i	$0.293053\pi$
$432$	−2.11772	+	4.74503i	−0.101889	+	0.228295i
$433$	−3.66469			−0.176114			−0.0880568	−	0.996115i	$-0.528066\pi$
$433$	−3.66469			−0.176114			−0.0880568	+	0.996115i	$0.528066\pi$
$434$	14.8474	+	25.7165i	0.712699	+	1.23443i
$435$	6.99115	−	49.6371i	0.335200	−	2.37992i
$436$	−14.9563	−	8.63504i	−0.716278	−	0.413543i
$437$	−13.0591			−0.624703
$438$	4.22480	−	5.40417i	0.201869	−	0.258221i
$439$	21.6941	+	12.5251i	1.03540	+	0.597791i	0.918528	−	0.395355i	$-0.129379\pi$
$439$	21.6941	+	12.5251i	1.03540	+	0.597791i	0.116876	+	0.993146i	$0.462712\pi$
$440$	5.14727	+	8.91533i	0.245386	+	0.425022i
$441$	9.96945	−	9.61588i	0.474735	−	0.457899i
$442$	9.33630	+	5.39032i	0.444083	+	0.256391i
$443$	0.323124	+	0.559668i	0.0153521	+	0.0265906i	0.873599	−	0.486646i	$-0.161780\pi$
$443$	0.323124	+	0.559668i	0.0153521	+	0.0265906i	−0.858247	+	0.513236i	$0.828446\pi$
$444$	9.58461	−	4.37439i	0.454865	−	0.207600i
$445$	8.90095	−	15.4169i	0.421945	−	0.730831i
$446$	10.3433	−	5.97172i	0.489770	−	0.282769i
$447$	6.60861	−	2.66776i	0.312577	−	0.126181i
$448$	1.70419	−	2.95174i	0.0805154	−	0.139457i
$449$	15.5354	−	8.96939i	0.733162	−	0.423291i	−0.0864156	−	0.996259i	$-0.527541\pi$
$449$	15.5354	−	8.96939i	0.733162	−	0.423291i	0.819578	+	0.572968i	$0.194208\pi$
$450$	−15.3568	+	3.81913i	−0.723925	+	0.180035i
$451$	−14.9667	−	25.9231i	−0.704755	−	1.22067i
$452$	9.69019	−	5.59464i	0.455788	−	0.263150i
$453$	−15.7078	+	6.34090i	−0.738015	+	0.297921i
$454$	4.18256	−	7.24441i	0.196297	−	0.339997i
$455$	−19.5145	+	33.8001i	−0.914853	+	1.58457i
$456$	1.04426	−	7.41422i	0.0489019	−	0.347203i
$457$	−29.3484	−	16.9443i	−1.37286	−	0.792622i	−0.381574	−	0.924338i	$-0.624618\pi$
$457$	−29.3484	−	16.9443i	−1.37286	−	0.792622i	−0.991287	+	0.131716i	$0.957951\pi$
$458$		−	2.68705i		−	0.125558i
$459$	12.6945	−	9.20571i	0.592527	−	0.429686i
$460$	4.84174	−	8.38615i	0.225748	−	0.391006i
$461$		−	22.0094i		−	1.02508i	−0.858664	−	0.512539i	$-0.828705\pi$
$461$		−	22.0094i		−	1.02508i	0.858664	−	0.512539i	$-0.171295\pi$
$462$	11.6771	−	14.9368i	0.543269	−	0.694925i
$463$		−	6.73630i		−	0.313062i	−0.987673	−	0.156531i	$-0.949969\pi$
$463$		−	6.73630i		−	0.313062i	0.987673	−	0.156531i	$-0.0500312\pi$
$464$	−7.81905	+	4.51433i	−0.362990	+	0.209573i
$465$	−44.8538	+	18.1065i	−2.08004	+	0.839670i
$466$		−	8.55045i		−	0.396092i
$467$			22.7699i			1.05367i	0.849969	+	0.526833i	$0.176621\pi$
$467$			22.7699i			1.05367i	−0.849969	+	0.526833i	$0.823379\pi$
$468$	−10.4002	+	2.58646i	−0.480749	+	0.119559i
$469$	−17.1535	+	29.7107i	−0.792073	+	1.37191i
$470$	4.95759	+	8.58681i	0.228677	+	0.396080i
$471$	−0.410893	+	2.91733i	−0.0189329	+	0.134424i
$472$	−2.59903	−	4.50165i	−0.119630	−	0.207205i
$473$	−32.0839	−	18.5237i	−1.47522	−	0.851719i
$474$	18.4175	−	7.43476i	0.845944	−	0.341490i
$475$	19.7474	−	11.4012i	0.906074	−	0.523122i
$476$	−8.90782	+	5.14293i	−0.408289	+	0.235726i
$477$	10.9818	+	3.15607i	0.502821	+	0.144507i
$478$	−11.0569	−	19.1510i	−0.505729	−	0.875948i
$479$		−	9.39864i		−	0.429435i	−0.976676	−	0.214717i	$-0.931117\pi$
$479$		−	9.39864i		−	0.429435i	0.976676	−	0.214717i	$-0.0688831\pi$
$480$	4.37400	+	3.41945i	0.199645	+	0.156076i
$481$	19.2830	+	10.0171i	0.879228	+	0.456743i
$482$	−2.17790	+	3.77224i	−0.0992007	+	0.171821i
$483$	−17.6599	−	2.48731i	−0.803552	−	0.113177i
$484$	−0.342862	+	0.593855i	−0.0155847	+	0.0269934i
$485$	−14.5535	−	25.2075i	−0.660842	−	1.14461i
$486$	−2.72983	+	15.3476i	−0.123827	+	0.696180i
$487$			29.6909i			1.34542i	0.739904	+	0.672712i	$0.234871\pi$
$487$			29.6909i			1.34542i	−0.739904	+	0.672712i	$0.765129\pi$
$488$	−1.65064	+	2.85899i	−0.0747209	+	0.129420i
$489$	−3.51698	−	8.71232i	−0.159043	−	0.393985i
$490$	−7.39985	−	12.8169i	−0.334291	−	0.579009i
$491$	5.52334	−	9.56671i	0.249265	−	0.431740i	−0.714057	−	0.700088i	$-0.753144\pi$
$491$	5.52334	−	9.56671i	0.249265	−	0.431740i	0.963322	+	0.268348i	$0.0864776\pi$
$492$	−12.7183	−	9.94273i	−0.573384	−	0.448253i
$493$	27.2469			1.22714
$494$	13.3737	−	7.72132i	0.601712	−	0.347399i
$495$	21.4403	+	22.2286i	0.963670	+	0.999103i
$496$	7.54507	+	4.35615i	0.338784	+	0.195597i
$497$	17.8697			0.801566
$498$	−15.6611	+	20.0330i	−0.701791	+	0.897699i
$499$			18.4487i			0.825878i	0.910759	+	0.412939i	$0.135498\pi$
$499$			18.4487i			0.825878i	−0.910759	+	0.412939i	$0.864502\pi$
$500$			0.880996i			0.0393994i
$501$	5.39151	−	6.89657i	0.240875	−	0.308116i
$502$	−10.3801			−0.463289
$503$	19.3002	+	11.1430i	0.860554	+	0.496841i	0.864198	−	0.503152i	$-0.167827\pi$
$503$	19.3002	+	11.1430i	0.860554	+	0.496841i	−0.00364372	+	0.999993i	$0.501160\pi$
$504$	2.82430	−	9.82735i	0.125804	−	0.437745i
$505$	26.1324	−	15.0876i	1.16288	−	0.671388i
$506$	−9.70205			−0.431309
$507$	0.325408	+	0.254393i	0.0144519	+	0.0112980i
$508$	0.118556	−	0.205345i	0.00526007	−	0.00911071i
$509$	0.411769	+	0.713205i	0.0182514	+	0.0316123i	0.875007	−	0.484111i	$-0.160857\pi$
$509$	0.411769	+	0.713205i	0.0182514	+	0.0316123i	−0.856755	+	0.515723i	$0.827523\pi$
$510$	−6.27185	−	15.5367i	−0.277722	−	0.687978i
$511$	−6.74925	+	11.6900i	−0.298569	+	0.517137i
$512$		−	1.00000i		−	0.0441942i
$513$	−2.32792	−	22.3412i	−0.102780	−	0.986390i
$514$	2.28731	+	3.96174i	0.100889	+	0.174745i
$515$	−26.2163	+	45.4080i	−1.15523	+	2.00092i
$516$	−19.7849	−	2.78661i	−0.870980	−	0.122673i
$517$	4.96710	−	8.60327i	0.218453	−	0.378371i
$518$	−17.4760	+	11.1544i	−0.767850	+	0.490098i
$519$	−24.2757	−	18.9779i	−1.06558	−	0.833038i
$520$			11.4509i			0.502154i
$521$	−13.8199	−	23.9368i	−0.605463	−	1.04869i	−0.991978	−	0.126409i	$-0.959655\pi$
$521$	−13.8199	−	23.9368i	−0.605463	−	1.04869i	0.386516	−	0.922283i	$-0.373679\pi$
$522$	−19.4953	+	18.8039i	−0.853285	+	0.823023i
$523$	−18.1997	+	10.5076i	−0.795816	+	0.459465i	−0.842006	−	0.539468i	$-0.818625\pi$
$523$	−18.1997	+	10.5076i	−0.795816	+	0.459465i	0.0461898	+	0.998933i	$0.485292\pi$
$524$	−6.93146	+	4.00188i	−0.302802	+	0.174823i
$525$	28.8760	−	11.6566i	1.26025	−	0.508737i
$526$	−14.9636	−	8.63923i	−0.652444	−	0.376688i
$527$	−13.1461	−	22.7696i	−0.572651	−	0.991861i
$528$	0.775813	−	5.50826i	0.0337629	−	0.239716i
$529$	−6.93692	−	12.0151i	−0.301605	−	0.522395i
$530$	6.10438	−	10.5731i	0.265157	−	0.459266i
$531$	−10.8259	−	11.2240i	−0.469805	−	0.487079i
$532$			14.7339i			0.638797i
$533$		−	33.2957i		−	1.44220i
$534$	−8.91985	+	3.60076i	−0.386000	+	0.155820i
$535$	−44.9198	+	25.9345i	−1.94205	+	1.12124i
$536$			10.0655i			0.434761i
$537$	3.23720	−	4.14088i	0.139696	−	0.178692i
$538$			1.27599i			0.0550120i
$539$	−7.41404	+	12.8415i	−0.319345	+	0.553122i
$540$	15.2099	+	6.78822i	0.654530	+	0.292118i
$541$		−	20.9976i		−	0.902757i	−0.892333	−	0.451378i	$-0.850932\pi$
$541$		−	20.9976i		−	0.902757i	0.892333	−	0.451378i	$-0.149068\pi$
$542$	−6.53621	−	3.77368i	−0.280754	−	0.162093i
$543$	2.63926	−	18.7387i	0.113261	−	0.804154i
$544$	−1.50891	+	2.61351i	−0.0646939	+	0.112053i
$545$	−27.6791	+	47.9416i	−1.18564	+	2.05359i
$546$	19.5559	−	7.89431i	0.836916	−	0.337845i
$547$	−0.859453	+	0.496206i	−0.0367476	+	0.0212162i	−0.518261	−	0.855222i	$-0.673421\pi$
$547$	−0.859453	+	0.496206i	−0.0367476	+	0.0212162i	0.481514	+	0.876439i	$0.340087\pi$
$548$	−0.481722	−	0.834367i	−0.0205781	−	0.0356424i
$549$	−2.73555	+	9.51855i	−0.116751	+	0.406242i
$550$	14.6710	−	8.47030i	0.625573	−	0.361175i
$551$	19.5148	−	33.8006i	0.831358	−	1.43995i
$552$	−4.85203	+	1.95866i	−0.206516	+	0.0833661i
$553$	−33.8478	+	19.5420i	−1.43936	+	0.831012i
$554$	−7.06806	+	12.2422i	−0.300293	+	0.520123i
$555$	−14.0219	−	30.7229i	−0.595195	−	1.30411i
$556$	5.64045	+	9.76955i	0.239208	+	0.414321i
$557$	12.5131	+	7.22445i	0.530198	+	0.306110i	0.741097	−	0.671398i	$-0.234306\pi$
$557$	12.5131	+	7.22445i	0.530198	+	0.306110i	−0.210899	+	0.977508i	$0.567639\pi$
$558$	25.1201	+	7.21931i	1.06342	+	0.305618i
$559$	−20.6044	−	35.6878i	−0.871471	−	1.50943i
$560$	−9.46164	−	5.46268i	−0.399827	−	0.230840i
$561$	−10.3391	+	13.2252i	−0.436515	+	0.558370i
$562$	21.9473			0.925793
$563$	14.0473	+	8.11021i	0.592023	+	0.341805i	0.765897	−	0.642963i	$-0.222295\pi$
$563$	14.0473	+	8.11021i	0.592023	+	0.341805i	−0.173874	+	0.984768i	$0.555629\pi$
$564$	0.747224	−	5.30528i	0.0314638	−	0.223393i
$565$	−17.9333	−	31.0613i	−0.754458	−	1.30676i
$566$	22.9686			0.965443
$567$	1.10718	−	30.6554i	0.0464970	−	1.28741i
$568$	4.54046	−	2.62144i	0.190513	−	0.109993i
$569$	−32.5379	+	18.7858i	−1.36406	+	0.787540i	−0.990161	−	0.139930i	$-0.955312\pi$
$569$	−32.5379	+	18.7858i	−1.36406	+	0.787540i	−0.373898	+	0.927470i	$0.621979\pi$
$570$	−23.7658	−	3.34731i	−0.995441	−	0.140203i
$571$	−15.7462	−	27.2732i	−0.658957	−	1.14135i	−0.980886	−	0.194584i	$-0.937664\pi$
$571$	−15.7462	−	27.2732i	−0.658957	−	1.14135i	0.321929	−	0.946764i	$-0.395669\pi$
$572$	9.93577	−	5.73642i	0.415435	−	0.239852i
$573$	28.5492	+	4.02102i	1.19266	+	0.167981i
$574$	27.5116	+	15.8838i	1.14831	+	0.662978i
$575$	−13.8002	−	7.96753i	−0.575507	−	0.332269i
$576$	−0.724027	−	2.91132i	−0.0301678	−	0.121305i
$577$	37.4987	+	21.6499i	1.56109	+	0.901296i	0.997147	+	0.0754822i	$0.0240496\pi$
$577$	37.4987	+	21.6499i	1.56109	+	0.901296i	0.563943	+	0.825814i	$0.309284\pi$
$578$	−6.83535	+	3.94639i	−0.284313	+	0.164148i
$579$	−16.7370	−	41.4611i	−0.695565	−	1.72307i
$580$	14.4704	+	25.0635i	0.600852	+	1.04071i
$581$	25.0191	−	43.3344i	1.03797	−	1.79781i
$582$	−2.19356	+	15.5742i	−0.0909259	+	0.645572i
$583$	−12.2322			−0.506605
$584$			3.96039i			0.163882i
$585$	8.29075	+	33.3372i	0.342780	+	1.37832i
$586$		−	0.243840i		−	0.0100729i
$587$	−28.5474	−	16.4818i	−1.17828	−	0.680278i	−0.222661	−	0.974896i	$-0.571474\pi$
$587$	−28.5474	−	16.4818i	−1.17828	−	0.680278i	−0.955615	+	0.294618i	$0.904808\pi$
$588$	−1.11533	+	7.91882i	−0.0459954	+	0.326567i
$589$	−37.6620			−1.55183
$590$	−14.4298	+	8.33103i	−0.594064	+	0.342983i
$591$	27.0316	−	10.9121i	1.11193	−	0.448863i
$592$	−2.80409	+	5.39787i	−0.115248	+	0.221851i
$593$	−38.1630			−1.56717			−0.783583	−	0.621287i	$-0.786610\pi$
$593$	−38.1630			−1.56717			−0.783583	+	0.621287i	$0.786610\pi$
$594$	−1.72949	−	16.5980i	−0.0709618	−	0.681025i
$595$	16.4854	+	28.5535i	0.675834	+	1.17058i
$596$	−2.05732	+	3.56338i	−0.0842711	+	0.145962i
$597$	5.83673	−	7.46607i	0.238881	−	0.305566i
$598$	−9.34601	−	5.39592i	−0.382187	−	0.220656i
$599$	25.6763			1.04910			0.524552	−	0.851379i	$-0.324233\pi$
$599$	25.6763			1.04910			0.524552	+	0.851379i	$0.324233\pi$
$600$	5.62702	−	7.19782i	0.229722	−	0.293850i
$601$	22.7828			0.929330			0.464665	−	0.885487i	$-0.346175\pi$
$601$	22.7828			0.929330			0.464665	+	0.885487i	$0.346175\pi$
$602$	39.3175			1.60246
$603$	7.28766	+	29.3038i	0.296777	+	1.19334i
$604$	4.88996	−	8.46967i	0.198970	−	0.344626i
$605$	1.90357	+	1.09902i	0.0773910	+	0.0446817i
$606$	−16.1457	−	2.27405i	−0.655874	−	0.0923768i
$607$	27.6934	−	15.9888i	1.12404	−	0.648965i	0.181611	−	0.983370i	$-0.441869\pi$
$607$	27.6934	−	15.9888i	1.12404	−	0.648965i	0.942429	+	0.334406i	$0.108536\pi$
$608$	2.16143	+	3.74370i	0.0876574	+	0.151827i
$609$	32.8277	−	41.9917i	1.33024	−	1.70159i
$610$	9.16432	+	5.29102i	0.371053	+	0.214227i
$611$	9.56963	−	5.52503i	0.387146	−	0.223519i
$612$	−2.50067	+	8.70124i	−0.101083	+	0.351727i
$613$	14.2435	−	24.6705i	0.575291	−	0.996434i	−0.420718	−	0.907191i	$-0.638222\pi$
$613$	14.2435	−	24.6705i	0.575291	−	0.996434i	0.996010	−	0.0892427i	$-0.0284447\pi$
$614$		−	22.8567i		−	0.922423i
$615$	−31.8708	+	40.7677i	−1.28516	+	1.64391i
$616$			10.9463i			0.441039i
$617$	0.468598	+	0.811636i	0.0188650	+	0.0326752i	0.875304	−	0.483573i	$-0.160661\pi$
$617$	0.468598	+	0.811636i	0.0188650	+	0.0326752i	−0.856439	+	0.516249i	$0.827328\pi$
$618$	26.2720	−	10.6055i	1.05682	−	0.426614i
$619$	6.90536	+	11.9604i	0.277550	+	0.480731i	0.970775	−	0.239990i	$-0.0771442\pi$
$619$	6.90536	+	11.9604i	0.277550	+	0.480731i	−0.693225	+	0.720721i	$0.743811\pi$
$620$	13.9634	−	24.1853i	0.560782	−	0.971304i
$621$	−12.7077	+	9.21529i	−0.509942	+	0.369797i
$622$	7.53751	+	13.0554i	0.302227	+	0.523472i
$623$	16.3930	−	9.46448i	0.656770	−	0.379186i
$624$	3.81083	−	4.87464i	0.152555	−	0.195142i
$625$	−23.5502			−0.942010
$626$	−32.8309			−1.31219
$627$	9.00129	+	22.2981i	0.359477	+	0.890502i
$628$	−0.850473	−	1.47306i	−0.0339376	−	0.0587816i
$629$	15.4734	−	9.87626i	0.616965	−	0.393792i
$630$	−31.5010	−	9.05313i	−1.25503	−	0.360685i
$631$	−11.3856	−	6.57349i	−0.453255	−	0.261687i	0.255949	−	0.966690i	$-0.417612\pi$
$631$	−11.3856	−	6.57349i	−0.453255	−	0.261687i	−0.709204	+	0.705004i	$0.750945\pi$
$632$	−5.73353	+	9.93076i	−0.228067	+	0.395024i
$633$	22.8033	−	9.20520i	0.906349	−	0.365874i
$634$		−	21.3433i		−	0.847652i
$635$	−0.658221	−	0.380024i	−0.0261207	−	0.0150808i
$636$	−6.11734	+	2.46944i	−0.242568	+	0.0979198i
$637$	−14.2839	+	8.24682i	−0.565949	+	0.326751i
$638$	14.4982	−	25.1116i	0.573988	−	0.994176i
$639$	11.3207	−	10.9193i	0.447842	−	0.431959i
$640$	−3.20544			−0.126706
$641$	26.4323			1.04401			0.522007	−	0.852941i	$-0.325183\pi$
$641$	26.4323			1.04401			0.522007	+	0.852941i	$0.325183\pi$
$642$	27.7533	+	3.90893i	1.09534	+	0.154273i
$643$	40.8167	+	23.5656i	1.60966	+	0.929335i	0.989447	+	0.144898i	$0.0462854\pi$
$643$	40.8167	+	23.5656i	1.60966	+	0.929335i	0.620209	+	0.784437i	$0.287048\pi$
$644$	8.91709	−	5.14828i	0.351382	−	0.202871i
$645$	−8.93229	+	63.4192i	−0.351709	+	2.49713i
$646$		−	13.0456i		−	0.513271i
$647$	−41.8960	+	24.1887i	−1.64710	+	0.950954i	−0.668885	+	0.743366i	$0.733228\pi$
$647$	−41.8960	+	24.1887i	−1.64710	+	0.950954i	−0.978216	+	0.207588i	$0.933439\pi$
$648$	−4.21575	−	7.95157i	−0.165610	−	0.312367i
$649$	14.4574	+	8.34700i	0.567504	+	0.327649i
$650$	18.8435			0.739102
$651$	−50.9303	−	7.17329i	−1.99611	−	0.281143i
$652$	4.69770	+	2.71222i	0.183976	+	0.106219i
$653$			28.9016i			1.13101i	0.824746	+	0.565504i	$0.191318\pi$
$653$			28.9016i			1.13101i	−0.824746	+	0.565504i	$0.808682\pi$
$654$	27.7379	−	11.1972i	1.08464	−	0.437845i
$655$	12.8278	+	22.2184i	0.501223	+	0.868144i
$656$	9.32045			0.363902
$657$	2.86743	+	11.5299i	0.111869	+	0.449826i
$658$			10.5429i			0.411006i
$659$	18.7562	−	32.4866i	0.730636	−	1.26550i	−0.225975	−	0.974133i	$-0.572557\pi$
$659$	18.7562	−	32.4866i	0.730636	−	1.26550i	0.956612	−	0.291366i	$-0.0941097\pi$
$660$	−17.6564	−	2.48682i	−0.687274	−	0.0967994i
$661$			6.22654i			0.242184i	0.992641	+	0.121092i	$0.0386397\pi$
$661$			6.22654i			0.242184i	−0.992641	+	0.121092i	$0.961360\pi$
$662$	1.93316			0.0751343
$663$	−17.3150	+	6.98971i	−0.672460	+	0.271458i
$664$		−	14.6809i		−	0.569731i
$665$	47.2287			1.83145
$666$	−4.25541	+	17.7452i	−0.164894	+	0.687612i
$667$	−27.2752			−1.05610
$668$			5.05408i			0.195548i
$669$	−2.88514	+	20.4845i	−0.111546	+	0.791975i
$670$	32.2642			1.24648
$671$		−	10.6023i		−	0.409299i
$672$	2.20985	+	5.47428i	0.0852469	+	0.211175i
$673$	0.666494	−	1.15440i	0.0256914	−	0.0444989i	−0.852894	−	0.522084i	$-0.825155\pi$
$673$	0.666494	−	1.15440i	0.0256914	−	0.0444989i	0.878585	+	0.477586i	$0.158488\pi$
$674$		−	22.3662i		−	0.861512i
$675$	11.1706	−	25.0293i	0.429958	−	0.963377i
$676$	−0.238472			−0.00917199
$677$	−9.81811	−	17.0055i	−0.377341	−	0.653573i	0.613334	−	0.789824i	$-0.289828\pi$
$677$	−9.81811	−	17.0055i	−0.377341	−	0.653573i	−0.990674	+	0.136251i	$0.956495\pi$
$678$	−2.70296	+	19.1910i	−0.103807	+	0.737025i
$679$		−	30.9499i		−	1.18775i
$680$	8.37744	+	4.83671i	0.321260	+	0.185480i
$681$	5.42360	+	13.4354i	0.207833	+	0.514847i
$682$	−27.9803			−1.07142
$683$	25.0564	+	14.4663i	0.958755	+	0.553537i	0.895790	−	0.444478i	$-0.146611\pi$
$683$	25.0564	+	14.4663i	0.958755	+	0.553537i	0.0629652	+	0.998016i	$0.479944\pi$
$684$	9.00314	+	9.33418i	0.344244	+	0.356901i
$685$	−2.67451	+	1.54413i	−0.102188	+	0.0589982i
$686$			8.12197i			0.310098i
$687$	3.66663	+	2.86645i	0.139891	+	0.109362i
$688$	9.99006	−	5.76777i	0.380868	−	0.219894i
$689$	−11.7833	−	6.80308i	−0.448907	−	0.259177i
$690$	6.27837	+	15.5529i	0.239013	+	0.592088i
$691$	20.3628			0.774637			0.387318	−	0.921946i	$-0.373401\pi$
$691$	20.3628			0.774637			0.387318	+	0.921946i	$0.373401\pi$
$692$	17.7902			0.676281
$693$	7.92542	+	31.8682i	0.301062	+	1.21057i
$694$	−11.7422	+	20.3381i	−0.445728	+	0.772024i
$695$	31.3157	−	18.0801i	1.18787	−	0.685818i
$696$	2.18103	−	15.4853i	0.0826717	−	0.586968i
$697$	−24.3591	−	14.0637i	−0.922665	−	0.532701i
$698$			17.2371i			0.652433i
$699$	11.6676	+	9.12132i	0.441308	+	0.345000i
$700$	−8.98934	+	15.5700i	−0.339765	+	0.588490i
$701$	16.2689	+	9.39286i	0.614468	+	0.354763i	0.774712	−	0.632314i	$-0.217895\pi$
$701$	16.2689	+	9.39286i	0.614468	+	0.354763i	−0.160244	+	0.987077i	$0.551228\pi$
$702$	7.56518	−	16.9508i	0.285529	−	0.639766i
$703$	−1.16942	−	26.2689i	−0.0441055	−	0.990749i
$704$	1.60579	+	2.78131i	0.0605206	+	0.104825i
$705$	−17.0058	−	2.39518i	−0.640474	−	0.0902078i
$706$	18.5070			0.696521
$707$	32.0856			1.20670
$708$	8.91531	+	1.25568i	0.335058	+	0.0471913i
$709$	−2.32020	+	1.33957i	−0.0871369	+	0.0503085i	−0.542935	−	0.839775i	$-0.682687\pi$
$709$	−2.32020	+	1.33957i	−0.0871369	+	0.0503085i	0.455798	+	0.890083i	$0.349354\pi$
$710$	−8.40285	−	14.5542i	−0.315353	−	0.546208i
$711$	−9.50200	+	33.0629i	−0.356353	+	1.23995i
$712$	2.77683	−	4.80960i	0.104066	−	0.180248i
$713$	13.1597	+	22.7933i	0.492836	+	0.853616i
$714$	2.48473	−	17.6415i	0.0929886	−	0.660217i
$715$	−18.3877	−	31.8485i	−0.687662	−	1.19107i
$716$			3.03460i			0.113408i
$717$	37.9277	+	5.34195i	1.41644	+	0.199499i
$718$		−	19.0158i		−	0.709662i
$719$	−3.59282	+	6.22294i	−0.133990	+	0.232077i	−0.925211	−	0.379453i	$-0.876112\pi$
$719$	−3.59282	+	6.22294i	−0.133990	+	0.232077i	0.791221	+	0.611530i	$0.209446\pi$
$720$	−9.33206	+	2.32082i	−0.347785	+	0.0864920i
$721$	−48.2829	+	27.8761i	−1.79815	+	1.03816i
$722$	0.271026	+	0.156477i	0.0100865	+	0.00582347i
$723$	−2.82412	−	6.99596i	−0.105030	−	0.260182i
$724$	5.46278	+	9.46181i	0.203023	+	0.351646i
$725$	41.2443	−	23.8124i	1.53177	−	0.884370i
$726$	−0.444595	−	1.10136i	−0.0165005	−	0.0408752i
$727$	−8.47540	−	4.89328i	−0.314335	−	0.181482i	0.334530	−	0.942385i	$-0.391423\pi$
$727$	−8.47540	−	4.89328i	−0.314335	−	0.181482i	−0.648865	+	0.760904i	$0.724756\pi$
$728$	−6.08793	+	10.5446i	−0.225634	+	0.390809i
$729$	−18.0305	−	20.0972i	−0.667798	−	0.744343i
$730$	12.6948			0.469855
$731$	−34.8121			−1.28757
$732$	−2.14041	−	5.30226i	−0.0791118	−	0.195977i
$733$	−8.72877			−0.322404			−0.161202	−	0.986921i	$-0.551537\pi$
$733$	−8.72877			−0.322404			−0.161202	+	0.986921i	$0.551537\pi$
$734$	−0.938892	−	0.542070i	−0.0346551	−	0.0200082i
$735$	25.3833	+	3.57512i	0.936277	+	0.131870i
$736$	1.51048	−	2.61622i	0.0556769	−	0.0964353i
$737$	−16.1630	−	27.9952i	−0.595373	−	1.03122i
$738$	27.1348	−	6.74826i	0.998846	−	0.248407i
$739$	−49.5703			−1.82347			−0.911736	−	0.410776i	$-0.865258\pi$
$739$	−49.5703			−1.82347			−0.911736	+	0.410776i	$0.865258\pi$
$740$	17.3026	+	8.98836i	0.636055	+	0.330419i
$741$	−3.73043	+	26.4860i	−0.137041	+	0.972989i
$742$	11.2425	−	6.49086i	0.412725	−	0.238287i
$743$	25.4385			0.933248			0.466624	−	0.884456i	$-0.345470\pi$
$743$	25.4385			0.933248			0.466624	+	0.884456i	$0.345470\pi$
$744$	−13.9930	+	5.64869i	−0.513009	+	0.207091i
$745$	11.4222	+	6.59461i	0.418477	+	0.241608i
$746$		−	7.43066i		−	0.272056i
$747$	−10.6294	−	42.7409i	−0.388910	−	1.56381i
$748$		−	9.69197i		−	0.354374i
$749$	−55.1528			−2.01524
$750$	−1.20217	−	0.939816i	−0.0438970	−	0.0343172i
$751$	5.77594	−	10.0042i	0.210767	−	0.365059i	−0.741188	−	0.671298i	$-0.765737\pi$
$751$	5.77594	−	10.0042i	0.210767	−	0.365059i	0.951955	+	0.306239i	$0.0990705\pi$
$752$	1.54662	+	2.67882i	0.0563994	+	0.0976866i
$753$	11.0732	−	14.1643i	0.403529	−	0.516176i
$754$	27.9322	−	16.1267i	1.01723	−	0.587299i
$755$	−27.1490	−	15.6745i	−0.988054	−	0.570453i
$756$	10.3971	+	14.3374i	0.378139	+	0.521446i
$757$	10.4054	+	6.00757i	0.378191	+	0.218349i	0.677031	−	0.735954i	$-0.263266\pi$
$757$	10.4054	+	6.00757i	0.378191	+	0.218349i	−0.298840	+	0.954303i	$0.596600\pi$
$758$	−12.0488	−	6.95638i	−0.437632	−	0.252667i
$759$	10.3498	−	13.2390i	0.375674	−	0.480545i
$760$	12.0002	−	6.92832i	0.435293	−	0.251317i
$761$	−0.738577	−	1.27925i	−0.0267734	−	0.0463729i	0.852328	−	0.523007i	$-0.175190\pi$
$761$	−0.738577	−	1.27925i	−0.0267734	−	0.0463729i	−0.879102	+	0.476634i	$0.841857\pi$
$762$	0.153733	+	0.380831i	0.00556917	+	0.0137960i
$763$	−50.9768	+	29.4315i	−1.84549	+	1.06549i
$764$	−14.4155	+	8.32278i	−0.521534	+	0.301108i
$765$	27.8913	+	8.01574i	1.00841	+	0.289810i
$766$	29.8204			1.07745
$767$	9.28459	+	16.0814i	0.335247	+	0.580665i
$768$	1.36456	+	1.06676i	0.0492392	+	0.0384935i
$769$	9.89141	+	5.71081i	0.356693	+	0.205937i	0.667629	−	0.744494i	$-0.267309\pi$
$769$	9.89141	+	5.71081i	0.356693	+	0.205937i	−0.310936	+	0.950431i	$0.600642\pi$
$770$	35.0877			1.26447
$771$	−7.84604	−	1.10508i	−0.282568	−	0.0397984i
$772$	22.3559	+	12.9072i	0.804608	+	0.464540i
$773$	23.5459	+	40.7827i	0.846886	+	1.46685i	0.883973	+	0.467538i	$0.154859\pi$
$773$	23.5459	+	40.7827i	0.846886	+	1.46685i	−0.0370864	+	0.999312i	$0.511808\pi$
$774$	24.9083	−	24.0249i	0.895309	−	0.863557i
$775$	−39.7991	−	22.9780i	−1.42962	−	0.825394i
$776$	−4.54026	−	7.86397i	−0.162986	−	0.282300i
$777$	3.42190	−	35.7461i	0.122760	−	1.28238i
$778$	−12.7615	+	22.1037i	−0.457524	+	0.792454i
$779$	−34.8930	+	20.1455i	−1.25017	+	0.721786i
$780$	−15.6254	−	12.2154i	−0.559478	−	0.437381i
$781$	−8.41896	+	14.5821i	−0.301254	+	0.521787i
$782$	−7.89528	+	4.55834i	−0.282335	+	0.163006i
$783$	−4.86208	−	46.6617i	−0.173757	−	1.66755i
$784$	−2.30853	−	3.99849i	−0.0824475	−	0.142803i
$785$	−4.72181	+	2.72614i	−0.168529	+	0.0973001i
$786$	1.93344	−	13.7274i	0.0689637	−	0.489641i
$787$	0.814850	−	1.41136i	0.0290463	−	0.0503096i	−0.851137	−	0.524944i	$-0.824086\pi$
$787$	0.814850	−	1.41136i	0.0290463	−	0.0503096i	0.880183	+	0.474634i	$0.157420\pi$
$788$	−8.41516	+	14.5755i	−0.299778	+	0.519230i
$789$	27.7513	−	11.2026i	0.987974	−	0.398824i
$790$	31.8325	+	18.3785i	1.13255	+	0.653877i
$791$		−	38.1373i		−	1.35601i
$792$	6.68872	+	6.93466i	0.237673	+	0.246412i
$793$	5.89662	−	10.2133i	0.209395	−	0.362683i
$794$		−	18.8098i		−	0.667534i
$795$	7.91565	+	19.6088i	0.280739	+	0.695452i
$796$			5.47143i			0.193930i
$797$	−31.9381	+	18.4395i	−1.13131	+	0.653160i	−0.944263	−	0.329192i	$-0.893224\pi$
$797$	−31.9381	+	18.4395i	−1.13131	+	0.653160i	−0.187043	+	0.982352i	$0.559890\pi$
$798$	−20.1053	−	15.7176i	−0.711719	−	0.556398i
$799$		−	9.33483i		−	0.330242i
$800$			5.27484i			0.186494i
$801$	4.60195	−	16.0128i	0.162602	−	0.565784i
$802$	−4.13417	+	7.16059i	−0.145983	+	0.252849i
$803$	−6.35956	−	11.0151i	−0.224424	−	0.388714i
$804$	−13.7349	−	10.7375i	−0.484392	−	0.378681i
$805$	−16.5025	−	28.5832i	−0.581637	−	1.00742i
$806$	−26.9535	−	15.5616i	−0.949395	−	0.548134i
$807$	−1.74117	−	1.36119i	−0.0612919	−	0.0479160i
$808$	8.15253	−	4.70686i	0.286805	−	0.165587i
$809$	25.0114	−	14.4404i	0.879355	−	0.507696i	0.00890958	−	0.999960i	$-0.497164\pi$
$809$	25.0114	−	14.4404i	0.879355	−	0.507696i	0.870446	+	0.492264i	$0.163831\pi$
$810$	−25.4883	+	13.5133i	−0.895567	+	0.474810i
$811$	19.6144	+	33.9732i	0.688755	+	1.19296i	0.972241	+	0.233982i	$0.0751758\pi$
$811$	19.6144	+	33.9732i	0.688755	+	1.19296i	−0.283486	+	0.958976i	$0.591491\pi$
$812$			30.7731i			1.07993i
$813$	12.1220	−	4.89339i	0.425137	−	0.171619i
$814$	−0.868799	−	19.5160i	−0.0304514	−	0.684035i
$815$	8.69386	−	15.0582i	0.304533	−	0.527466i
$816$	−1.95663	−	4.84699i	−0.0684956	−	0.169678i
$817$	−24.9332	+	43.1856i	−0.872302	+	1.51087i
$818$	15.0045	+	25.9886i	0.524621	+	0.908671i
$819$	−10.0893	+	35.1065i	−0.352550	+	1.22672i
$820$		−	29.8761i		−	1.04332i
$821$	5.01890	−	8.69299i	0.175161	−	0.303388i	−0.765056	−	0.643964i	$-0.777289\pi$
$821$	5.01890	−	8.69299i	0.175161	−	0.303388i	0.940217	+	0.340576i	$0.110622\pi$
$822$	1.65242	+	0.232736i	0.0576349	+	0.00811761i
$823$	15.0325	+	26.0371i	0.524002	+	0.907598i	0.999610	+	0.0279402i	$0.00889479\pi$
$823$	15.0325	+	26.0371i	0.524002	+	0.907598i	−0.475608	+	0.879657i	$0.657772\pi$
$824$	−8.17871	+	14.1659i	−0.284919	+	0.493494i
$825$	−4.09229	+	29.0552i	−0.142475	+	1.01157i
$826$	−17.7170			−0.616452
$827$	−46.8493	+	27.0485i	−1.62911	+	0.940568i	−0.644753	+	0.764391i	$0.723040\pi$
$827$	−46.8493	+	27.0485i	−1.62911	+	0.940568i	−0.984359	+	0.176177i	$0.943627\pi$
$828$	2.50327	−	8.71029i	0.0869945	−	0.302704i
$829$	26.3189	+	15.1952i	0.914093	+	0.527752i	0.881746	−	0.471725i	$-0.156369\pi$
$829$	26.3189	+	15.1952i	0.914093	+	0.527752i	0.0323469	+	0.999477i	$0.489702\pi$
$830$	−47.0589			−1.63344
$831$	−9.16527	−	22.7043i	−0.317940	−	0.787605i
$832$			3.57233i			0.123848i
$833$			13.9334i			0.482765i
$834$	−19.3481	−	2.72509i	−0.669971	−	0.0943623i
$835$	16.2005			0.560643
$836$	−12.0232	−	6.94160i	−0.415831	−	0.240080i
$837$	−36.6484	+	26.5765i	−1.26675	+	0.918617i
$838$	−2.31901	+	1.33888i	−0.0801089	+	0.0462509i
$839$	22.2151			0.766950			0.383475	−	0.923551i	$-0.374727\pi$
$839$	22.2151			0.766950			0.383475	+	0.923551i	$0.374727\pi$
$840$	17.5475	−	7.08354i	0.605445	−	0.244405i
$841$	26.2584	−	45.4809i	0.905462	−	1.56831i
$842$	14.6950	+	25.4525i	0.506423	+	0.877150i
$843$	−23.4126	+	29.9484i	−0.806374	+	1.03148i
$844$	−7.09886	+	12.2956i	−0.244353	+	0.423231i
$845$			0.764407i			0.0262964i
$846$	6.44224	+	6.67912i	0.221489	+	0.229633i
$847$	1.16861	+	2.02408i	0.0401537	+	0.0695483i
$848$	1.90438	−	3.29849i	0.0653968	−	0.113270i
$849$	−24.5021	+	31.3420i	−0.840910	+	1.07565i
$850$	7.95926	−	13.7858i	0.273000	−	0.472850i
$851$	−15.4895	+	9.88653i	−0.530973	+	0.338906i
$852$	−1.26651	+	8.99217i	−0.0433897	+	0.308067i
$853$		−	24.6685i		−	0.844633i	−0.906448	−	0.422317i	$-0.861217\pi$
$853$		−	24.6685i		−	0.844633i	0.906448	−	0.422317i	$-0.138783\pi$
$854$	5.62601	+	9.74453i	0.192518	+	0.333451i
$855$	29.9201	−	28.8590i	1.02325	−	0.986958i
$856$	−14.0136	+	8.09077i	−0.478976	+	0.276537i
$857$	12.3219	−	7.11406i	0.420909	−	0.243012i	−0.274557	−	0.961571i	$-0.588531\pi$
$857$	12.3219	−	7.11406i	0.420909	−	0.243012i	0.695466	+	0.718559i	$0.255198\pi$
$858$	−2.77146	+	19.6773i	−0.0946160	+	0.671772i
$859$	−28.7627	−	16.6062i	−0.981371	−	0.566595i	−0.0786869	−	0.996899i	$-0.525073\pi$
$859$	−28.7627	−	16.6062i	−0.981371	−	0.566595i	−0.902684	+	0.430305i	$0.858406\pi$
$860$	−18.4882	−	32.0226i	−0.630443	−	1.09196i
$861$	−51.0228	+	20.5968i	−1.73885	+	0.701937i
$862$	−2.62016	−	4.53824i	−0.0892428	−	0.154573i
$863$	2.64334	−	4.57840i	0.0899803	−	0.155850i	−0.817522	−	0.575897i	$-0.804653\pi$
$863$	2.64334	−	4.57840i	0.0899803	−	0.155850i	0.907503	+	0.420047i	$0.137986\pi$
$864$	4.74503	+	2.11772i	0.161429	+	0.0720462i
$865$		−	57.0253i		−	1.93892i
$866$			3.66469i			0.124531i
$867$	1.90664	−	13.5371i	0.0647528	−	0.459744i
$868$	25.7165	−	14.8474i	0.872874	−	0.503954i
$869$		−	36.8274i		−	1.24928i
$870$	−49.6371	−	6.99115i	−1.68286	−	0.237022i
$871$		−	35.9571i		−	1.21836i
$872$	−8.63504	+	14.9563i	−0.292419	+	0.506485i
$873$	−18.9119	−	19.6073i	−0.640070	−	0.663605i
$874$			13.0591i			0.441732i
$875$	2.60048	+	1.50139i	0.0879121	+	0.0507561i
$876$	−5.40417	−	4.22480i	−0.182590	−	0.142743i
$877$	−18.4857	+	32.0182i	−0.624218	+	1.08118i	0.364474	+	0.931214i	$0.381249\pi$
$877$	−18.4857	+	32.0182i	−0.624218	+	1.08118i	−0.988692	+	0.149964i	$0.952084\pi$
$878$	12.5251	−	21.6941i	0.422702	−	0.732141i
$879$	0.332733	+	0.260119i	0.0112228	+	0.00877361i
$880$	8.91533	−	5.14727i	0.300536	−	0.173514i
$881$	9.18265	+	15.9048i	0.309371	+	0.535847i	0.978225	−	0.207547i	$-0.0665480\pi$
$881$	9.18265	+	15.9048i	0.309371	+	0.535847i	−0.668854	+	0.743394i	$0.733215\pi$
$882$	−9.61588	−	9.96945i	−0.323784	−	0.335689i
$883$	−5.97606	+	3.45028i	−0.201110	+	0.116111i	−0.597173	−	0.802112i	$-0.703710\pi$
$883$	−5.97606	+	3.45028i	−0.201110	+	0.116111i	0.396063	+	0.918223i	$0.370376\pi$
$884$	5.39032	−	9.33630i	0.181296	−	0.314014i
$885$	4.02501	−	28.5775i	0.135299	−	0.960622i
$886$	0.559668	−	0.323124i	0.0188024	−	0.0108556i
$887$	11.9649	−	20.7239i	0.401743	−	0.695840i	−0.592193	−	0.805796i	$-0.701738\pi$
$887$	11.9649	−	20.7239i	0.401743	−	0.695840i	0.993936	+	0.109956i	$0.0350711\pi$
$888$	−4.37439	−	9.58461i	−0.146795	−	0.321638i
$889$	−0.404084	−	0.699894i	−0.0135525	−	0.0234737i
$890$	−15.4169	−	8.90095i	−0.516776	−	0.298361i
$891$	24.4939	+	15.3462i	0.820576	+	0.514117i
$892$	−5.97172	−	10.3433i	−0.199948	−	0.346320i
$893$	−11.5802	−	6.68580i	−0.387515	−	0.223732i
$894$	−2.66776	−	6.60861i	−0.0892232	−	0.221025i
$895$	9.72722			0.325145
$896$	−2.95174	−	1.70419i	−0.0986109	−	0.0569330i
$897$	17.3330	−	6.99698i	0.578733	−	0.233622i
$898$	−8.96939	−	15.5354i	−0.299312	−	0.518424i
$899$	−78.6604			−2.62347
$900$	3.81913	+	15.3568i	0.127304	+	0.511892i
$901$	−9.95423	+	5.74708i	−0.331623	+	0.191463i
$902$	−25.9231	+	14.9667i	−0.863145	+	0.498337i
$903$	−41.9425	+	53.6509i	−1.39576	+	1.78539i
$904$	−5.59464	−	9.69019i	−0.186075	−	0.322291i
$905$	30.3293	−	17.5106i	1.00818	−	0.582072i
$906$	6.34090	+	15.7078i	0.210662	+	0.521856i
$907$	−28.2879	−	16.3320i	−0.939285	−	0.542296i	−0.0495487	−	0.998772i	$-0.515778\pi$
$907$	−28.2879	−	16.3320i	−0.939285	−	0.542296i	−0.889736	+	0.456475i	$0.849112\pi$
$908$	−7.24441	−	4.18256i	−0.240414	−	0.138803i
$909$	20.3267	−	19.6058i	0.674195	−	0.650284i
$910$	33.8001	+	19.5145i	1.12046	+	0.646899i
$911$	−38.1893	+	22.0486i	−1.26527	+	0.730504i	−0.974089	−	0.226165i	$-0.927381\pi$
$911$	−38.1893	+	22.0486i	−1.26527	+	0.730504i	−0.291180	+	0.956668i	$0.594048\pi$
$912$	−7.41422	−	1.04426i	−0.245509	−	0.0345789i
$913$	23.5746	+	40.8323i	0.780204	+	1.35135i
$914$	−16.9443	+	29.3484i	−0.560468	+	0.970760i
$915$	−16.9961	+	6.86096i	−0.561873	+	0.226816i
$916$	−2.68705			−0.0887826
$917$			27.2799i			0.900860i
$918$	−9.20571	−	12.6945i	−0.303834	−	0.418980i
$919$			55.8008i			1.84070i	0.391096	+	0.920350i	$0.372096\pi$
$919$			55.8008i			1.84070i	−0.391096	+	0.920350i	$0.627904\pi$
$920$	−8.38615	−	4.84174i	−0.276483	−	0.159628i
$921$	31.1893	+	24.3828i	1.02772	+	0.803439i
$922$	−22.0094			−0.724839
$923$	−16.2200	+	9.36463i	−0.533888	+	0.308240i
$924$	−14.9368	−	11.6771i	−0.491386	−	0.384149i
$925$	14.7912	−	28.4729i	0.486330	−	0.936185i
$926$	−6.73630			−0.221369
$927$	−13.5543	+	47.1632i	−0.445182	+	1.54904i
$928$	4.51433	+	7.81905i	0.148190	+	0.256673i
$929$	7.59614	−	13.1569i	0.249221	−	0.431664i	−0.714089	−	0.700055i	$-0.753159\pi$
$929$	7.59614	−	13.1569i	0.249221	−	0.431664i	0.963310	+	0.268391i	$0.0864921\pi$
$930$	18.1065	+	44.8538i	0.593736	+	1.47081i
$931$	17.2849	+	9.97943i	0.566489	+	0.327063i
$932$	−8.55045			−0.280079
$933$	−25.8555	−	3.64163i	−0.846472	−	0.119222i
$934$	22.7699			0.745054
$935$	−31.0670			−1.01600
$936$	2.58646	+	10.4002i	0.0845412	+	0.339941i
$937$	−4.78817	+	8.29335i	−0.156423	+	0.270932i	−0.933576	−	0.358379i	$-0.883330\pi$
$937$	−4.78817	+	8.29335i	−0.156423	+	0.270932i	0.777154	+	0.629311i	$0.216663\pi$
$938$	29.7107	+	17.1535i	0.970087	+	0.560080i
$939$	35.0229	−	44.7997i	1.14293	−	1.46198i
$940$	8.58681	−	4.95759i	0.280071	−	0.161699i
$941$	−8.40281	−	14.5541i	−0.273924	−	0.474450i	0.695939	−	0.718101i	$-0.254988\pi$
$941$	−8.40281	−	14.5541i	−0.273924	−	0.474450i	−0.969863	+	0.243651i	$0.921655\pi$
$942$	2.91733	+	0.410893i	0.0950518	+	0.0133876i
$943$	24.3844	+	14.0783i	0.794065	+	0.458454i
$944$	−4.50165	+	2.59903i	−0.146516	+	0.0845912i
$945$	45.9576	−	33.3273i	1.49500	−	1.08414i
$946$	−18.5237	+	32.0839i	−0.602256	+	1.04314i
$947$			28.2764i			0.918858i	0.888214	+	0.459429i	$0.151946\pi$
$947$			28.2764i			0.918858i	−0.888214	+	0.459429i	$0.848054\pi$
$948$	−7.43476	−	18.4175i	−0.241470	−	0.598173i
$949$		−	14.1478i		−	0.459257i
$950$	−11.4012	−	19.7474i	−0.369903	−	0.640691i
$951$	29.1242	+	22.7683i	0.944416	+	0.738313i
$952$	5.14293	+	8.90782i	0.166683	+	0.288704i
$953$	2.12364	−	3.67824i	0.0687913	−	0.119150i	−0.829578	−	0.558391i	$-0.811419\pi$
$953$	2.12364	−	3.67824i	0.0687913	−	0.119150i	0.898369	+	0.439241i	$0.144752\pi$
$954$	3.15607	−	10.9818i	0.102182	−	0.355548i
$955$	26.6782	+	46.2080i	0.863286	+	1.49525i
$956$	−19.1510	+	11.0569i	−0.619389	+	0.357604i
$957$	18.8000	+	46.5717i	0.607718	+	1.50545i
$958$	−9.39864			−0.303656
$959$	−3.28378			−0.106039
$960$	3.41945	−	4.37400i	0.110362	−	0.141170i
$961$	22.4521	+	38.8881i	0.724260	+	1.25445i
$962$	10.0171	−	19.2830i	0.322966	−	0.621708i
$963$	−34.9402	+	33.7010i	−1.12593	+	1.08600i
$964$	3.77224	+	2.17790i	0.121496	+	0.0701455i
$965$	41.3733	−	71.6606i	1.33185	−	2.30684i
$966$	−2.48731	+	17.6599i	−0.0800279	+	0.568197i
$967$		−	5.41674i		−	0.174191i	−0.996200	−	0.0870954i	$-0.972242\pi$
$967$		−	5.41674i		−	0.174191i	0.996200	−	0.0870954i	$-0.0277585\pi$
$968$	0.593855	+	0.342862i	0.0190872	+	0.0110200i
$969$	17.8014	+	13.9166i	0.571864	+	0.447064i
$970$	−25.2075	+	14.5535i	−0.809363	+	0.467286i
$971$	28.8732	−	50.0098i	0.926584	−	1.60489i	0.137591	−	0.990489i	$-0.456064\pi$
$971$	28.8732	−	50.0098i	0.926584	−	1.60489i	0.788993	−	0.614402i	$-0.210603\pi$
$972$	15.3476	+	2.72983i	0.492274	+	0.0875592i
$973$	38.4496			1.23264
$974$	29.6909			0.951358
$975$	−20.1015	+	25.7130i	−0.643765	+	0.823474i
$976$	2.85899	+	1.65064i	0.0915141	+	0.0528357i
$977$	25.1093	−	14.4969i	0.803319	−	0.463797i	−0.0413112	−	0.999146i	$-0.513154\pi$
$977$	25.1093	−	14.4969i	0.803319	−	0.463797i	0.844630	+	0.535350i	$0.179820\pi$
$978$	−8.71232	+	3.51698i	−0.278589	+	0.112461i
$979$			17.8360i			0.570042i
$980$	−12.8169	+	7.39985i	−0.409421	+	0.236380i
$981$	−14.3106	+	49.7946i	−0.456902	+	1.58982i
$982$	−9.56671	−	5.52334i	−0.305286	−	0.176257i
$983$	−20.9434			−0.667990			−0.333995	−	0.942575i	$-0.608397\pi$
$983$	−20.9434			−0.667990			−0.333995	+	0.942575i	$0.608397\pi$
$984$	−9.94273	+	12.7183i	−0.316963	+	0.405444i
$985$	46.7208	+	26.9743i	1.48865	+	0.859473i
$986$		−	27.2469i		−	0.867717i
$987$	−14.3864	−	11.2468i	−0.457925	−	0.357990i
$988$	−7.72132	−	13.3737i	−0.245648	−	0.425475i
$989$	34.8483			1.10811
$990$	22.2286	−	21.4403i	0.706472	−	0.681417i
$991$		−	32.2433i		−	1.02424i	−0.858914	−	0.512121i	$-0.828860\pi$
$991$		−	32.2433i		−	1.02424i	0.858914	−	0.512121i	$-0.171140\pi$
$992$	4.35615	−	7.54507i	0.138308	−	0.239556i
$993$	−2.06222	+	2.63790i	−0.0654427	+	0.0837113i
$994$		−	17.8697i		−	0.566792i
$995$	17.5383			0.556003
$996$	20.0330	+	15.6611i	0.634769	+	0.496241i
$997$		−	25.4306i		−	0.805394i	−0.915333	−	0.402697i	$-0.868073\pi$
$997$		−	25.4306i		−	0.805394i	0.915333	−	0.402697i	$-0.131927\pi$
$998$	18.4487			0.583984
$999$	−19.6748	−	24.7367i	−0.622482	−	0.782634i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.k.a.175.15	✓	76
3.2	odd	2		1998.2.k.a.1063.23		76
9.2	odd	6		1998.2.t.a.397.36		76
9.7	even	3		666.2.t.a.619.11	yes	76
37.11	even	6		666.2.t.a.85.11	yes	76
111.11	odd	6		1998.2.t.a.307.36		76
333.11	odd	6		1998.2.k.a.1639.16		76
333.196	even	6	inner	666.2.k.a.529.34	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.15	✓	76	1.1	even	1	trivial
666.2.k.a.529.34	yes	76	333.196	even	6	inner
666.2.t.a.85.11	yes	76	37.11	even	6
666.2.t.a.619.11	yes	76	9.7	even	3
1998.2.k.a.1063.23		76	3.2	odd	2
1998.2.k.a.1639.16		76	333.11	odd	6
1998.2.t.a.307.36		76	111.11	odd	6
1998.2.t.a.397.36		76	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.36456 + 1.06676i) q^{3} -1.00000 q^{4} +3.20544i q^{5} +(1.06676 - 1.36456i) q^{6} +(-1.70419 + 2.95174i) q^{7} +1.00000i q^{8} +(0.724027 + 2.91132i) q^{9} +3.20544 q^{10} +(-1.60579 - 2.78131i) q^{11} +(-1.36456 - 1.06676i) q^{12} -3.57233i q^{13} +(2.95174 + 1.70419i) q^{14} +(-3.41945 + 4.37400i) q^{15} +1.00000 q^{16} +(-2.61351 - 1.50891i) q^{17} +(2.91132 - 0.724027i) q^{18} +(-3.74370 + 2.16143i) q^{19} -3.20544i q^{20} +(-5.47428 + 2.20985i) q^{21} +(-2.78131 + 1.60579i) q^{22} +(2.61622 + 1.51048i) q^{23} +(-1.06676 + 1.36456i) q^{24} -5.27484 q^{25} -3.57233 q^{26} +(-2.11772 + 4.74503i) q^{27} +(1.70419 - 2.95174i) q^{28} +(-7.81905 + 4.51433i) q^{29} +(4.37400 + 3.41945i) q^{30} +(7.54507 + 4.35615i) q^{31} -1.00000i q^{32} +(0.775813 - 5.50826i) q^{33} +(-1.50891 + 2.61351i) q^{34} +(-9.46164 - 5.46268i) q^{35} +(-0.724027 - 2.91132i) q^{36} +(-2.80409 + 5.39787i) q^{37} +(2.16143 + 3.74370i) q^{38} +(3.81083 - 4.87464i) q^{39} -3.20544 q^{40} +9.32045 q^{41} +(2.20985 + 5.47428i) q^{42} +(9.99006 - 5.76777i) q^{43} +(1.60579 + 2.78131i) q^{44} +(-9.33206 + 2.32082i) q^{45} +(1.51048 - 2.61622i) q^{46} +(1.54662 + 2.67882i) q^{47} +(1.36456 + 1.06676i) q^{48} +(-2.30853 - 3.99849i) q^{49} +5.27484i q^{50} +(-1.95663 - 4.84699i) q^{51} +3.57233i q^{52} +(1.90438 - 3.29849i) q^{53} +(4.74503 + 2.11772i) q^{54} +(8.91533 - 5.14727i) q^{55} +(-2.95174 - 1.70419i) q^{56} +(-7.41422 - 1.04426i) q^{57} +(4.51433 + 7.81905i) q^{58} +(-4.50165 + 2.59903i) q^{59} +(3.41945 - 4.37400i) q^{60} +(2.85899 + 1.65064i) q^{61} +(4.35615 - 7.54507i) q^{62} +(-9.82735 - 2.82430i) q^{63} -1.00000 q^{64} +11.4509 q^{65} +(-5.50826 - 0.775813i) q^{66} +10.0655 q^{67} +(2.61351 + 1.50891i) q^{68} +(1.95866 + 4.85203i) q^{69} +(-5.46268 + 9.46164i) q^{70} +(-2.62144 - 4.54046i) q^{71} +(-2.91132 + 0.724027i) q^{72} +3.96039 q^{73} +(5.39787 + 2.80409i) q^{74} +(-7.19782 - 5.62702i) q^{75} +(3.74370 - 2.16143i) q^{76} +10.9463 q^{77} +(-4.87464 - 3.81083i) q^{78} +(9.93076 + 5.73353i) q^{79} +3.20544i q^{80} +(-7.95157 + 4.21575i) q^{81} -9.32045i q^{82} -14.6809 q^{83} +(5.47428 - 2.20985i) q^{84} +(4.83671 - 8.37744i) q^{85} +(-5.76777 - 9.99006i) q^{86} +(-15.4853 - 2.18103i) q^{87} +(2.78131 - 1.60579i) q^{88} +(-4.80960 - 2.77683i) q^{89} +(2.32082 + 9.33206i) q^{90} +(10.5446 + 6.08793i) q^{91} +(-2.61622 - 1.51048i) q^{92} +(5.64869 + 13.9930i) q^{93} +(2.67882 - 1.54662i) q^{94} +(-6.92832 - 12.0002i) q^{95} +(1.06676 - 1.36456i) q^{96} +(-7.86397 + 4.54026i) q^{97} +(-3.99849 + 2.30853i) q^{98} +(6.93466 - 6.68872i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) \) 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Introduction

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