LMFDB - Embedded newform 686.2.g.h.471.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [686,2,Mod(67,686)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(686, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("686.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 686 = 2 \cdot 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	686.g (of order $21$, degree $12$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.47773757866$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	no (minimal twist has level 98)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			471.1
Character	$\chi$	$=$	686.471
Dual form			686.2.g.h.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.955573 - 0.294755i) q^{2} +(-1.12318 + 2.86182i) q^{3} +(0.826239 + 0.563320i) q^{4} +(2.99159 - 0.450910i) q^{5} +(1.91682 - 2.40361i) q^{6} +(-0.623490 - 0.781831i) q^{8} +(-4.72932 - 4.38817i) q^{9} +O(q^{10})$	\(q+(-0.955573 - 0.294755i) q^{2} +(-1.12318 + 2.86182i) q^{3} +(0.826239 + 0.563320i) q^{4} +(2.99159 - 0.450910i) q^{5} +(1.91682 - 2.40361i) q^{6} +(-0.623490 - 0.781831i) q^{8} +(-4.72932 - 4.38817i) q^{9} +(-2.99159 - 0.450910i) q^{10} +(-2.21776 + 2.05778i) q^{11} +(-2.54014 + 1.73184i) q^{12} +(0.532118 + 2.33136i) q^{13} +(-2.06968 + 9.06784i) q^{15} +(0.365341 + 0.930874i) q^{16} +(-0.0480527 - 0.641218i) q^{17} +(3.22577 + 5.58720i) q^{18} +(-0.314647 + 0.544985i) q^{19} +(2.72577 + 1.31266i) q^{20} +(2.72577 - 1.31266i) q^{22} +(-0.702234 + 9.37066i) q^{23} +(2.93775 - 0.906177i) q^{24} +(3.96842 - 1.22410i) q^{25} +(0.178703 - 2.38463i) q^{26} +(9.56038 - 4.60404i) q^{27} +(-3.84228 - 1.85034i) q^{29} +(4.65052 - 8.05494i) q^{30} +(1.25538 + 2.17437i) q^{31} +(-0.0747301 - 0.997204i) q^{32} +(-3.39805 - 8.65809i) q^{33} +(-0.143085 + 0.626894i) q^{34} +(-1.43560 - 6.28979i) q^{36} +(-5.30769 + 3.61872i) q^{37} +(0.461306 - 0.428029i) q^{38} +(-7.26960 - 1.09572i) q^{39} +(-2.21776 - 2.05778i) q^{40} +(1.29087 + 1.61870i) q^{41} +(0.845798 - 1.06060i) q^{43} +(-2.99159 + 0.450910i) q^{44} +(-16.1268 - 10.9951i) q^{45} +(3.43309 - 8.74736i) q^{46} +(1.01315 + 0.312515i) q^{47} -3.07434 q^{48} -4.15293 q^{50} +(1.88902 + 0.582686i) q^{51} +(-0.873646 + 2.22601i) q^{52} +(3.87195 + 2.63985i) q^{53} +(-10.4927 + 1.58152i) q^{54} +(-5.70676 + 7.15605i) q^{55} +(-1.20624 - 1.51258i) q^{57} +(3.12618 + 2.90067i) q^{58} +(-3.10939 - 0.468666i) q^{59} +(-6.81814 + 6.32631i) q^{60} +(-4.45904 + 3.04012i) q^{61} +(-0.558695 - 2.44780i) q^{62} +(-0.222521 + 0.974928i) q^{64} +(2.64311 + 6.73454i) q^{65} +(0.695067 + 9.27503i) q^{66} +(-3.16144 - 5.47577i) q^{67} +(0.321508 - 0.556868i) q^{68} +(-26.0284 - 12.5346i) q^{69} +(-12.7586 + 6.14419i) q^{71} +(-0.482125 + 6.43351i) q^{72} +(3.97419 - 1.22587i) q^{73} +(6.13853 - 1.89348i) q^{74} +(-0.954116 + 12.7318i) q^{75} +(-0.566975 + 0.273041i) q^{76} +(6.62367 + 3.18979i) q^{78} +(5.61055 - 9.71776i) q^{79} +(1.51269 + 2.62006i) q^{80} +(0.991505 + 13.2307i) q^{81} +(-0.756398 - 1.92727i) q^{82} +(-1.69664 + 7.43348i) q^{83} +(-0.432885 - 1.89659i) q^{85} +(-1.12084 + 0.764175i) q^{86} +(9.61093 - 8.91764i) q^{87} +(2.99159 + 0.450910i) q^{88} +(-0.873285 - 0.810290i) q^{89} +(12.1695 + 15.2601i) q^{90} +(-5.85889 + 7.34682i) q^{92} +(-7.63268 + 1.15044i) q^{93} +(-0.876021 - 0.597261i) q^{94} +(-0.695557 + 1.77225i) q^{95} +(2.93775 + 0.906177i) q^{96} +16.3992 q^{97} +19.5184 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} + 5 q^{3} + 3 q^{4} + 10 q^{6} + 6 q^{8} + 10 q^{9}+O(q^{10}) $ 36 * q - 3 * q^2 + 5 * q^3 + 3 * q^4 + 10 * q^6 + 6 * q^8 + 10 * q^9	$ 36 q - 3 q^{2} + 5 q^{3} + 3 q^{4} + 10 q^{6} + 6 q^{8} + 10 q^{9} - 7 q^{11} - 2 q^{12} - 20 q^{13} + 14 q^{15} + 3 q^{16} - q^{17} + 32 q^{18} + 44 q^{19} + 14 q^{20} + 14 q^{22} - 21 q^{23} + 2 q^{24} - q^{25} - 3 q^{26} + 20 q^{27} + 22 q^{29} + 24 q^{31} - 3 q^{32} + 14 q^{33} - 2 q^{34} - 20 q^{36} + 13 q^{37} + 19 q^{38} + 3 q^{39} - 7 q^{40} + 16 q^{41} - 48 q^{43} - 98 q^{45} - 21 q^{46} - 40 q^{47} + 4 q^{48} - 100 q^{50} - 36 q^{51} - 18 q^{52} - 10 q^{53} - 4 q^{54} + 98 q^{55} + 38 q^{57} - 24 q^{58} - 13 q^{59} - 7 q^{60} - 27 q^{61} - 22 q^{62} - 6 q^{64} + 21 q^{66} + 86 q^{67} + 34 q^{68} - 182 q^{69} - 3 q^{72} - 5 q^{73} - 13 q^{74} + 3 q^{75} - 4 q^{76} + 76 q^{78} + 66 q^{79} + 2 q^{81} + 8 q^{82} + 110 q^{83} - 98 q^{85} + 18 q^{86} + 110 q^{87} - 62 q^{89} + 42 q^{90} - 42 q^{92} - 46 q^{93} - 23 q^{94} + 7 q^{95} + 2 q^{96} - 64 q^{97} + 28 q^{99}+O(q^{100}) $ 36 * q - 3 * q^2 + 5 * q^3 + 3 * q^4 + 10 * q^6 + 6 * q^8 + 10 * q^9 - 7 * q^11 - 2 * q^12 - 20 * q^13 + 14 * q^15 + 3 * q^16 - q^17 + 32 * q^18 + 44 * q^19 + 14 * q^20 + 14 * q^22 - 21 * q^23 + 2 * q^24 - q^25 - 3 * q^26 + 20 * q^27 + 22 * q^29 + 24 * q^31 - 3 * q^32 + 14 * q^33 - 2 * q^34 - 20 * q^36 + 13 * q^37 + 19 * q^38 + 3 * q^39 - 7 * q^40 + 16 * q^41 - 48 * q^43 - 98 * q^45 - 21 * q^46 - 40 * q^47 + 4 * q^48 - 100 * q^50 - 36 * q^51 - 18 * q^52 - 10 * q^53 - 4 * q^54 + 98 * q^55 + 38 * q^57 - 24 * q^58 - 13 * q^59 - 7 * q^60 - 27 * q^61 - 22 * q^62 - 6 * q^64 + 21 * q^66 + 86 * q^67 + 34 * q^68 - 182 * q^69 - 3 * q^72 - 5 * q^73 - 13 * q^74 + 3 * q^75 - 4 * q^76 + 76 * q^78 + 66 * q^79 + 2 * q^81 + 8 * q^82 + 110 * q^83 - 98 * q^85 + 18 * q^86 + 110 * q^87 - 62 * q^89 + 42 * q^90 - 42 * q^92 - 46 * q^93 - 23 * q^94 + 7 * q^95 + 2 * q^96 - 64 * q^97 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/686\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{13}{21}\right)$

Coefficient data

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

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

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

$2$	−0.955573	−	0.294755i	−0.675692	−	0.208423i
$2$	−0.955573	−	0.294755i	−0.675692	−	0.208423i
$3$	−1.12318	+	2.86182i	−0.648469	+	1.65227i	0.104747	+	0.994499i	$0.466597\pi$
$3$	−1.12318	+	2.86182i	−0.648469	+	1.65227i	−0.753216	+	0.657773i	$0.771498\pi$
$4$	0.826239	+	0.563320i	0.413119	+	0.281660i
$5$	2.99159	−	0.450910i	1.33788	−	0.201653i	0.559178	−	0.829048i	$-0.311117\pi$
$5$	2.99159	−	0.450910i	1.33788	−	0.201653i	0.778701	+	0.627395i	$0.215879\pi$
$6$	1.91682	−	2.40361i	0.782538	−	0.981271i
$7$		0			0
$7$		0			0
$8$	−0.623490	−	0.781831i	−0.220437	−	0.276419i
$9$	−4.72932	−	4.38817i	−1.57644	−	1.46272i
$10$	−2.99159	−	0.450910i	−0.946024	−	0.142590i
$11$	−2.21776	+	2.05778i	−0.668680	+	0.620444i	−0.939647	−	0.342144i	$-0.888847\pi$
$11$	−2.21776	+	2.05778i	−0.668680	+	0.620444i	0.270967	+	0.962589i	$0.412656\pi$
$12$	−2.54014	+	1.73184i	−0.733274	+	0.499938i
$13$	0.532118	+	2.33136i	0.147583	+	0.646603i	0.993553	+	0.113372i	$0.0361653\pi$
$13$	0.532118	+	2.33136i	0.147583	+	0.646603i	−0.845970	+	0.533231i	$0.820978\pi$
$14$		0			0
$15$	−2.06968	+	9.06784i	−0.534388	+	2.34131i
$16$	0.365341	+	0.930874i	0.0913353	+	0.232718i
$17$	−0.0480527	−	0.641218i	−0.0116545	−	0.155518i	−0.999995	−	0.00325658i	$-0.998963\pi$
$17$	−0.0480527	−	0.641218i	−0.0116545	−	0.155518i	0.988340	−	0.152262i	$-0.0486557\pi$
$18$	3.22577	+	5.58720i	0.760322	+	1.31692i
$19$	−0.314647	+	0.544985i	−0.0721851	+	0.125028i	−0.899859	−	0.436182i	$-0.856331\pi$
$19$	−0.314647	+	0.544985i	−0.0721851	+	0.125028i	0.827674	+	0.561210i	$0.189664\pi$
$20$	2.72577	+	1.31266i	0.609501	+	0.293520i
$21$		0			0
$22$	2.72577	−	1.31266i	0.581137	−	0.279861i
$23$	−0.702234	+	9.37066i	−0.146426	+	1.95392i	0.126704	+	0.991941i	$0.459560\pi$
$23$	−0.702234	+	9.37066i	−0.146426	+	1.95392i	−0.273130	+	0.961977i	$0.588059\pi$
$24$	2.93775	−	0.906177i	0.599666	−	0.184973i
$25$	3.96842	−	1.22410i	0.793685	−	0.244819i
$26$	0.178703	−	2.38463i	0.0350466	−	0.467665i
$27$	9.56038	−	4.60404i	1.83990	−	0.886047i
$28$		0			0
$29$	−3.84228	−	1.85034i	−0.713493	−	0.343600i	0.0416749	−	0.999131i	$-0.486731\pi$
$29$	−3.84228	−	1.85034i	−0.713493	−	0.343600i	−0.755168	+	0.655531i	$0.772445\pi$
$30$	4.65052	−	8.05494i	0.849065	−	1.47062i
$31$	1.25538	+	2.17437i	0.225472	+	0.390529i	0.956461	−	0.291860i	$-0.0942742\pi$
$31$	1.25538	+	2.17437i	0.225472	+	0.390529i	−0.730989	+	0.682389i	$0.760941\pi$
$32$	−0.0747301	−	0.997204i	−0.0132105	−	0.176282i
$33$	−3.39805	−	8.65809i	−0.591525	−	1.50718i
$34$	−0.143085	+	0.626894i	−0.0245388	+	0.107512i
$35$		0			0
$36$	−1.43560	−	6.28979i	−0.239267	−	1.04830i
$37$	−5.30769	+	3.61872i	−0.872580	+	0.594915i	−0.914671	−	0.404199i	$-0.867550\pi$
$37$	−5.30769	+	3.61872i	−0.872580	+	0.594915i	0.0420915	+	0.999114i	$0.486598\pi$
$38$	0.461306	−	0.428029i	0.0748337	−	0.0694355i
$39$	−7.26960	−	1.09572i	−1.16407	−	0.175455i
$40$	−2.21776	−	2.05778i	−0.350659	−	0.325364i
$41$	1.29087	+	1.61870i	0.201600	+	0.252798i	0.872346	−	0.488889i	$-0.162598\pi$
$41$	1.29087	+	1.61870i	0.201600	+	0.252798i	−0.670747	+	0.741687i	$0.734026\pi$
$42$		0			0
$43$	0.845798	−	1.06060i	0.128983	−	0.161740i	−0.713146	−	0.701015i	$-0.752730\pi$
$43$	0.845798	−	1.06060i	0.128983	−	0.161740i	0.842129	+	0.539276i	$0.181302\pi$
$44$	−2.99159	+	0.450910i	−0.450999	+	0.0679772i
$45$	−16.1268	−	10.9951i	−2.40405	−	1.63905i
$46$	3.43309	−	8.74736i	0.506181	−	1.28973i
$47$	1.01315	+	0.312515i	0.147783	+	0.0455850i	0.367764	−	0.929919i	$-0.380123\pi$
$47$	1.01315	+	0.312515i	0.147783	+	0.0455850i	−0.219981	+	0.975504i	$0.570600\pi$
$48$	−3.07434			−0.443742
$49$		0			0
$50$	−4.15293			−0.587313
$51$	1.88902	+	0.582686i	0.264516	+	0.0815924i
$52$	−0.873646	+	2.22601i	−0.121153	+	0.308693i
$53$	3.87195	+	2.63985i	0.531853	+	0.362611i	0.799272	−	0.600969i	$-0.205219\pi$
$53$	3.87195	+	2.63985i	0.531853	+	0.362611i	−0.267419	+	0.963580i	$0.586171\pi$
$54$	−10.4927	+	1.58152i	−1.42788	+	0.215218i
$55$	−5.70676	+	7.15605i	−0.769499	+	0.964921i
$56$		0			0
$57$	−1.20624	−	1.51258i	−0.159771	−	0.200346i
$58$	3.12618	+	2.90067i	0.410487	+	0.380877i
$59$	−3.10939	−	0.468666i	−0.404809	−	0.0610151i	−0.0565178	−	0.998402i	$-0.518000\pi$
$59$	−3.10939	−	0.468666i	−0.404809	−	0.0610151i	−0.348291	+	0.937387i	$0.613238\pi$
$60$	−6.81814	+	6.32631i	−0.880219	+	0.816723i
$61$	−4.45904	+	3.04012i	−0.570921	+	0.389247i	−0.814092	−	0.580736i	$-0.802765\pi$
$61$	−4.45904	+	3.04012i	−0.570921	+	0.389247i	0.243171	+	0.969984i	$0.421812\pi$
$62$	−0.558695	−	2.44780i	−0.0709543	−	0.310871i
$63$		0			0
$64$	−0.222521	+	0.974928i	−0.0278151	+	0.121866i
$65$	2.64311	+	6.73454i	0.327838	+	0.835317i
$66$	0.695067	+	9.27503i	0.0855569	+	1.14168i
$67$	−3.16144	−	5.47577i	−0.386231	−	0.668972i	0.605708	−	0.795687i	$-0.292890\pi$
$67$	−3.16144	−	5.47577i	−0.386231	−	0.668972i	−0.991939	+	0.126715i	$0.959557\pi$
$68$	0.321508	−	0.556868i	0.0389886	−	0.0675302i
$69$	−26.0284	−	12.5346i	−3.13345	−	1.50899i
$70$		0			0
$71$	−12.7586	+	6.14419i	−1.51416	+	0.729182i	−0.992301	−	0.123849i	$-0.960476\pi$
$71$	−12.7586	+	6.14419i	−1.51416	+	0.729182i	−0.521860	+	0.853031i	$0.674762\pi$
$72$	−0.482125	+	6.43351i	−0.0568189	+	0.758196i
$73$	3.97419	−	1.22587i	0.465143	−	0.143478i	−0.0533201	−	0.998577i	$-0.516980\pi$
$73$	3.97419	−	1.22587i	0.465143	−	0.143478i	0.518464	+	0.855100i	$0.326504\pi$
$74$	6.13853	−	1.89348i	0.713589	−	0.220113i
$75$	−0.954116	+	12.7318i	−0.110172	+	1.47014i
$76$	−0.566975	+	0.273041i	−0.0650365	+	0.0313199i
$77$		0			0
$78$	6.62367	+	3.18979i	0.749982	+	0.361173i
$79$	5.61055	−	9.71776i	0.631236	−	1.09333i	−0.356063	−	0.934462i	$-0.615881\pi$
$79$	5.61055	−	9.71776i	0.631236	−	1.09333i	0.987299	−	0.158872i	$-0.0507856\pi$
$80$	1.51269	+	2.62006i	0.169124	+	0.292931i
$81$	0.991505	+	13.2307i	0.110167	+	1.47008i
$82$	−0.756398	−	1.92727i	−0.0835302	−	0.212832i
$83$	−1.69664	+	7.43348i	−0.186231	+	0.815930i	0.792350	+	0.610067i	$0.208857\pi$
$83$	−1.69664	+	7.43348i	−0.186231	+	0.815930i	−0.978581	+	0.205864i	$0.934000\pi$
$84$		0			0
$85$	−0.432885	−	1.89659i	−0.0469530	−	0.205715i
$86$	−1.12084	+	0.764175i	−0.120863	+	0.0824031i
$87$	9.61093	−	8.91764i	1.03040	−	0.956071i
$88$	2.99159	+	0.450910i	0.318905	+	0.0480671i
$89$	−0.873285	−	0.810290i	−0.0925680	−	0.0858905i	0.632532	−	0.774535i	$-0.282016\pi$
$89$	−0.873285	−	0.810290i	−0.0925680	−	0.0858905i	−0.725100	+	0.688644i	$0.758206\pi$
$90$	12.1695	+	15.2601i	1.28278	+	1.60855i
$91$		0			0
$92$	−5.85889	+	7.34682i	−0.610832	+	0.765959i
$93$	−7.63268	+	1.15044i	−0.791472	+	0.119295i
$94$	−0.876021	−	0.597261i	−0.0903547	−	0.0616028i
$95$	−0.695557	+	1.77225i	−0.0713626	+	0.181829i
$96$	2.93775	+	0.906177i	0.299833	+	0.0924863i
$97$	16.3992			1.66509			0.832543	−	0.553961i	$-0.186884\pi$
$97$	16.3992			1.66509			0.832543	+	0.553961i	$0.186884\pi$
$98$		0			0
$99$	19.5184			1.96167
$100$	3.96842	+	1.22410i	0.396842	+	0.122410i
$101$	5.24985	−	13.3764i	0.522380	−	1.33100i	−0.389682	−	0.920950i	$-0.627415\pi$
$101$	5.24985	−	13.3764i	0.522380	−	1.33100i	0.912062	−	0.410053i	$-0.134490\pi$
$102$	−1.63335	−	1.11360i	−0.161726	−	0.110263i
$103$	16.1498	−	2.43420i	1.59129	−	0.239849i	0.707148	−	0.707065i	$-0.249981\pi$
$103$	16.1498	−	2.43420i	1.59129	−	0.239849i	0.884143	+	0.467217i	$0.154743\pi$
$104$	1.49096	−	1.86961i	0.146201	−	0.183330i
$105$		0			0
$106$	−2.92182	−	3.66385i	−0.283792	−	0.355864i
$107$	−12.2301	−	11.3478i	−1.18233	−	1.09704i	−0.993359	−	0.115054i	$-0.963296\pi$
$107$	−12.2301	−	11.3478i	−1.18233	−	1.09704i	−0.188967	−	0.981984i	$-0.560514\pi$
$108$	10.4927	+	1.58152i	1.00966	+	0.152182i
$109$	−1.22063	+	1.13258i	−0.116916	+	0.108482i	−0.736464	−	0.676476i	$-0.763506\pi$
$109$	−1.22063	+	1.13258i	−0.116916	+	0.108482i	0.619549	+	0.784958i	$0.287316\pi$
$110$	7.56250	−	5.15603i	0.721056	−	0.491608i
$111$	−4.39463	−	19.2541i	−0.417120	−	1.82752i
$112$		0			0
$113$	2.05961	−	9.02372i	0.193751	−	0.848880i	−0.780812	−	0.624767i	$-0.785194\pi$
$113$	2.05961	−	9.02372i	0.193751	−	0.848880i	0.974563	−	0.224114i	$-0.0719487\pi$
$114$	0.706812	+	1.80093i	0.0661990	+	0.168672i
$115$	2.12452	+	28.3498i	0.198113	+	2.64363i
$116$	−2.13230	−	3.69326i	−0.197979	−	0.342911i
$117$	7.71385	−	13.3608i	0.713145	−	1.23520i
$118$	2.83311	+	1.36435i	0.260809	+	0.125599i
$119$		0			0
$120$	8.37995	−	4.03557i	0.764981	−	0.368395i
$121$	−0.138032	+	1.84191i	−0.0125484	+	0.167446i
$122$	5.15703	−	1.59073i	0.466895	−	0.144018i
$123$	−6.08229	+	1.87614i	−0.548422	+	0.169166i
$124$	−0.187629	+	2.50373i	−0.0168496	+	0.224842i
$125$	−2.30893	+	1.11192i	−0.206517	+	0.0994533i
$126$		0			0
$127$	12.0689	+	5.81208i	1.07094	+	0.515739i	0.884410	−	0.466710i	$-0.154561\pi$
$127$	12.0689	+	5.81208i	1.07094	+	0.515739i	0.186532	+	0.982449i	$0.440275\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	2.08525	+	3.61177i	0.183596	+	0.317998i
$130$	−0.540646	−	7.21441i	−0.0474178	−	0.632746i
$131$	7.10144	+	18.0942i	0.620456	+	1.58090i	0.801876	+	0.597490i	$0.203835\pi$
$131$	7.10144	+	18.0942i	0.620456	+	1.58090i	−0.181420	+	0.983406i	$0.558069\pi$
$132$	2.06968	−	9.06784i	0.180142	−	0.789254i
$133$		0			0
$134$	1.40697	+	6.16435i	0.121544	+	0.532518i
$135$	26.5247	−	18.0842i	2.28288	−	1.55644i
$136$	−0.471364	+	0.437362i	−0.0404192	+	0.0375035i
$137$	−7.79804	−	1.17537i	−0.666232	−	0.100418i	−0.192785	−	0.981241i	$-0.561752\pi$
$137$	−7.79804	−	1.17537i	−0.666232	−	0.100418i	−0.473446	+	0.880823i	$0.656990\pi$
$138$	21.1774	+	19.6497i	1.80274	+	1.67270i
$139$	−0.182803	−	0.229228i	−0.0155052	−	0.0194428i	0.774018	−	0.633163i	$-0.218244\pi$
$139$	−0.182803	−	0.229228i	−0.0155052	−	0.0194428i	−0.789524	+	0.613720i	$0.789672\pi$
$140$		0			0
$141$	−2.03231	+	2.54844i	−0.171151	+	0.214617i
$142$	14.0028	−	2.11058i	1.17509	−	0.177116i
$143$	−5.97754	−	4.07542i	−0.499867	−	0.340804i
$144$	2.35701	−	6.00558i	0.196418	−	0.500465i
$145$	−12.3289	−	3.80295i	−1.02386	−	0.315818i
$146$	−4.15896			−0.344198
$147$		0			0
$148$	−6.42392			−0.528043
$149$	−6.77821	−	2.09080i	−0.555293	−	0.171285i	0.00439247	−	0.999990i	$-0.498602\pi$
$149$	−6.77821	−	2.09080i	−0.555293	−	0.171285i	−0.559685	+	0.828705i	$0.689078\pi$
$150$	4.66449	−	11.8849i	0.380854	−	0.970400i
$151$	9.74713	+	6.64548i	0.793210	+	0.540802i	0.890784	−	0.454427i	$-0.150156\pi$
$151$	9.74713	+	6.64548i	0.793210	+	0.540802i	−0.0975740	+	0.995228i	$0.531108\pi$
$152$	0.622266	−	0.0937916i	0.0504725	−	0.00760750i
$153$	−2.58652	+	3.24339i	−0.209107	+	0.262212i
$154$		0			0
$155$	4.73601	+	5.93877i	0.380406	+	0.477014i
$156$	−5.38919	−	5.00044i	−0.431480	−	0.400355i
$157$	13.0101	+	1.96096i	1.03832	+	0.156502i	0.646008	−	0.763330i	$-0.276437\pi$
$157$	13.0101	+	1.96096i	1.03832	+	0.156502i	0.392312	+	0.919832i	$0.371675\pi$
$158$	−8.22565	+	7.63229i	−0.654398	+	0.607192i
$159$	−11.9037	+	8.11579i	−0.944023	+	0.643624i
$160$	−0.673210	−	2.94953i	−0.0532220	−	0.233181i
$161$		0			0
$162$	2.95237	−	12.9352i	0.231960	−	1.01628i
$163$	4.89948	+	12.4837i	0.383757	+	0.977797i	0.984030	+	0.178002i	$0.0569632\pi$
$163$	4.89948	+	12.4837i	0.383757	+	0.977797i	−0.600273	+	0.799795i	$0.704942\pi$
$164$	0.154720	+	2.06460i	0.0120816	+	0.161218i
$165$	−14.0696	−	24.3692i	−1.09532	−	1.89714i
$166$	3.81232	−	6.60314i	0.295894	−	0.512503i
$167$	8.54332	+	4.11425i	0.661102	+	0.318370i	0.734179	−	0.678956i	$-0.237567\pi$
$167$	8.54332	+	4.11425i	0.661102	+	0.318370i	−0.0730766	+	0.997326i	$0.523282\pi$
$168$		0			0
$169$	6.56050	−	3.15937i	0.504654	−	0.243028i
$170$	−0.145378	+	1.93993i	−0.0111500	+	0.148786i
$171$	3.87956	−	1.19668i	0.296677	−	0.0915127i
$172$	1.29629	−	0.399852i	0.0988410	−	0.0304884i
$173$	−0.0786526	+	1.04955i	−0.00597984	+	0.0797955i	−0.999395	−	0.0347725i	$-0.988929\pi$
$173$	−0.0786526	+	1.04955i	−0.00597984	+	0.0797955i	0.993415	+	0.114568i	$0.0365484\pi$
$174$	−11.8125	+	5.68858i	−0.895500	+	0.431250i
$175$		0			0
$176$	−2.72577	−	1.31266i	−0.205463	−	0.0989457i
$177$	4.83365	−	8.37213i	0.363319	−	0.629288i
$178$	0.595650	+	1.03170i	0.0446459	+	0.0773289i
$179$	−0.761651	−	10.1635i	−0.0569284	−	0.759657i	−0.950498	−	0.310732i	$-0.899426\pi$
$179$	−0.761651	−	10.1635i	−0.0569284	−	0.759657i	0.893569	−	0.448925i	$-0.148193\pi$
$180$	−7.13087	−	18.1692i	−0.531503	−	1.35425i
$181$	−3.08835	+	13.5309i	−0.229555	+	1.00575i	0.720449	+	0.693508i	$0.243936\pi$
$181$	−3.08835	+	13.5309i	−0.229555	+	1.00575i	−0.950004	+	0.312238i	$0.898921\pi$
$182$		0			0
$183$	−3.69197	−	16.1756i	−0.272918	−	1.19573i
$184$	7.76411	−	5.29348i	0.572378	−	0.390241i
$185$	−14.2467	+	13.2190i	−1.04744	+	0.971882i
$186$	7.63268	+	1.15044i	0.559655	+	0.0843545i
$187$	1.42606	+	1.32319i	0.104284	+	0.0967610i
$188$	0.661056	+	0.828938i	0.0482125	+	0.0604565i
$189$		0			0
$190$	1.18704	−	1.48850i	0.0861166	−	0.107987i
$191$	−6.64691	+	1.00186i	−0.480954	+	0.0724921i	−0.385044	−	0.922898i	$-0.625814\pi$
$191$	−6.64691	+	1.00186i	−0.480954	+	0.0724921i	−0.0959091	+	0.995390i	$0.530576\pi$
$192$	−2.54014	−	1.73184i	−0.183319	−	0.124984i
$193$	−0.847805	+	2.16017i	−0.0610263	+	0.155493i	−0.958135	−	0.286318i	$-0.907569\pi$
$193$	−0.847805	+	2.16017i	−0.0610263	+	0.155493i	0.897108	+	0.441811i	$0.145664\pi$
$194$	−15.6706	−	4.83375i	−1.12508	−	0.347043i
$195$	−22.2417			−1.59276
$196$		0			0
$197$	8.72306			0.621492			0.310746	−	0.950493i	$-0.399421\pi$
$197$	8.72306			0.621492			0.310746	+	0.950493i	$0.399421\pi$
$198$	−18.6512	−	5.75314i	−1.32549	−	0.408858i
$199$	−3.90149	+	9.94084i	−0.276569	+	0.704687i	0.723330	+	0.690503i	$0.242611\pi$
$199$	−3.90149	+	9.94084i	−0.276569	+	0.704687i	−0.999899	+	0.0141849i	$0.995485\pi$
$200$	−3.43131	−	2.33943i	−0.242630	−	0.165422i
$201$	19.2215	−	2.89718i	1.35578	−	0.204351i
$202$	−8.95938	+	11.2347i	−0.630380	+	0.790472i
$203$		0			0
$204$	1.23254	+	1.54556i	0.0862954	+	0.108211i
$205$	4.59163	+	4.26041i	0.320693	+	0.297560i
$206$	−16.1498	−	2.43420i	−1.12521	−	0.169599i
$207$	44.4411	−	41.2353i	3.08887	−	2.86605i
$208$	−1.97580	+	1.34708i	−0.136997	+	0.0934030i
$209$	−0.423648	−	1.85612i	−0.0293043	−	0.128391i
$210$		0			0
$211$	3.16480	−	13.8659i	0.217874	−	0.954566i	−0.741172	−	0.671315i	$-0.765730\pi$
$211$	3.16480	−	13.8659i	0.217874	−	0.954566i	0.959046	−	0.283251i	$-0.0914131\pi$
$212$	1.71207	+	4.36229i	0.117586	+	0.299603i
$213$	−3.25341	−	43.4137i	−0.222920	−	2.97466i
$214$	8.34189	+	14.4486i	0.570240	+	0.987684i
$215$	2.05205	−	3.55425i	0.139948	−	0.242398i
$216$	−9.56038	−	4.60404i	−0.650501	−	0.313265i
$217$		0			0
$218$	1.50024	−	0.722477i	0.101609	−	0.0489323i
$219$	−0.955502	+	12.7503i	−0.0645668	+	0.861584i
$220$	−8.74629	+	2.69787i	−0.589675	+	0.181891i
$221$	1.46934	−	0.453232i	0.0988386	−	0.0304877i
$222$	−1.47587	+	19.6941i	−0.0990537	+	1.32178i
$223$	8.73560	−	4.20684i	0.584979	−	0.281711i	−0.117894	−	0.993026i	$-0.537614\pi$
$223$	8.73560	−	4.20684i	0.584979	−	0.281711i	0.702873	+	0.711315i	$0.251900\pi$
$224$		0			0
$225$	−24.1395	−	11.6250i	−1.60930	−	0.774997i
$226$	−4.62789	+	8.01574i	−0.307843	+	0.533199i
$227$	3.09799	+	5.36588i	0.205621	+	0.356146i	0.950330	−	0.311243i	$-0.100745\pi$
$227$	3.09799	+	5.36588i	0.205621	+	0.356146i	−0.744709	+	0.667389i	$0.767412\pi$
$228$	−0.144578	−	1.92926i	−0.00957489	−	0.127768i
$229$	0.199958	+	0.509485i	0.0132136	+	0.0336677i	0.937328	−	0.348447i	$-0.113291\pi$
$229$	0.199958	+	0.509485i	0.0132136	+	0.0336677i	−0.924115	+	0.382115i	$0.875196\pi$
$230$	6.32612	−	27.7165i	0.417132	−	1.82757i
$231$		0			0
$232$	0.948965	+	4.15769i	0.0623026	+	0.272965i
$233$	5.60005	−	3.81805i	0.366871	−	0.250129i	−0.365826	−	0.930683i	$-0.619213\pi$
$233$	5.60005	−	3.81805i	0.366871	−	0.250129i	0.732697	+	0.680555i	$0.238261\pi$
$234$	−11.3093	+	10.4935i	−0.739312	+	0.685981i
$235$	3.17184	+	0.478078i	0.206908	+	0.0311863i
$236$	−2.30509	−	2.13881i	−0.150049	−	0.139225i
$237$	21.5088	+	26.9712i	1.39715	+	1.75197i
$238$		0			0
$239$	−4.24070	+	5.31767i	−0.274308	+	0.343971i	−0.899834	−	0.436232i	$-0.856313\pi$
$239$	−4.24070	+	5.31767i	−0.274308	+	0.343971i	0.625526	+	0.780203i	$0.284884\pi$
$240$	−9.19715	+	1.38625i	−0.593674	+	0.0894819i
$241$	21.5354	+	14.6826i	1.38722	+	0.945789i	0.999714	+	0.0239202i	$0.00761477\pi$
$241$	21.5354	+	14.6826i	1.38722	+	0.945789i	0.387503	+	0.921868i	$0.373338\pi$
$242$	0.674812	−	1.71939i	0.0433785	−	0.110527i
$243$	−8.55820	−	2.63985i	−0.549008	−	0.169347i
$244$	−5.39679			−0.345494
$245$		0			0
$246$	6.36508			0.405822
$247$	−1.43799	−	0.443561i	−0.0914970	−	0.0282231i
$248$	0.917280	−	2.33719i	0.0582474	−	0.148412i
$249$	−19.3676	−	13.2046i	−1.22737	−	0.836810i
$250$	2.53410	−	0.381953i	0.160270	−	0.0241569i
$251$	−16.3304	+	20.4777i	−1.03077	+	1.29254i	−0.0753889	+	0.997154i	$0.524020\pi$
$251$	−16.3304	+	20.4777i	−1.03077	+	1.29254i	−0.955378	+	0.295386i	$0.904552\pi$
$252$		0			0
$253$	−17.7254	−	22.2269i	−1.11439	−	1.39739i
$254$	−9.81958	−	9.11124i	−0.616135	−	0.571690i
$255$	5.91392	+	0.891380i	0.370344	+	0.0558204i
$256$	−0.733052	+	0.680173i	−0.0458157	+	0.0425108i
$257$	11.0777	−	7.55262i	0.691005	−	0.471119i	−0.166201	−	0.986092i	$-0.553150\pi$
$257$	11.0777	−	7.55262i	0.691005	−	0.471119i	0.857207	+	0.514972i	$0.172198\pi$
$258$	−0.928025	−	4.06594i	−0.0577763	−	0.253135i
$259$		0			0
$260$	−1.60986	+	7.05326i	−0.0998393	+	0.437424i
$261$	10.0517	+	25.6114i	0.622187	+	1.58531i
$262$	−1.45259	−	19.3835i	−0.0897414	−	1.19752i
$263$	5.28132	+	9.14751i	0.325660	+	0.564060i	0.981646	−	0.190714i	$-0.0610802\pi$
$263$	5.28132	+	9.14751i	0.325660	+	0.564060i	−0.655986	+	0.754773i	$0.727747\pi$
$264$	−4.65052	+	8.05494i	−0.286220	+	0.495747i
$265$	12.7736	+	6.15145i	0.784677	+	0.377880i
$266$		0			0
$267$	3.29976	−	1.58908i	0.201942	−	0.0972502i
$268$	0.472509	−	6.30519i	0.0288631	−	0.385151i
$269$	−11.3902	+	3.51341i	−0.694473	+	0.214217i	−0.621842	−	0.783142i	$-0.713616\pi$
$269$	−11.3902	+	3.51341i	−0.694473	+	0.214217i	−0.0726305	+	0.997359i	$0.523139\pi$
$270$	−30.6767	+	9.46252i	−1.86693	+	0.575870i
$271$	1.85854	−	24.8005i	0.112898	−	1.50652i	−0.597013	−	0.802232i	$-0.703646\pi$
$271$	1.85854	−	24.8005i	0.112898	−	1.50652i	0.709911	−	0.704291i	$-0.248735\pi$
$272$	0.579338	−	0.278994i	0.0351275	−	0.0169165i
$273$		0			0
$274$	7.10515	+	3.42166i	0.429238	+	0.206710i
$275$	−6.28209	+	10.8809i	−0.378824	+	0.656143i
$276$	−14.4447	−	25.0189i	−0.869467	−	1.50596i
$277$	2.07597	+	27.7019i	0.124733	+	1.66445i	0.611747	+	0.791053i	$0.290467\pi$
$277$	2.07597	+	27.7019i	0.124733	+	1.66445i	−0.487014	+	0.873394i	$0.661914\pi$
$278$	0.107116	+	0.272926i	0.00642436	+	0.0163690i
$279$	3.60445	−	15.7921i	0.215793	−	0.945449i
$280$		0			0
$281$	6.94033	+	30.4076i	0.414025	+	1.81396i	0.564600	+	0.825365i	$0.309031\pi$
$281$	6.94033	+	30.4076i	0.414025	+	1.81396i	−0.150574	+	0.988599i	$0.548112\pi$
$282$	2.69318	−	1.83618i	0.160377	−	0.109343i
$283$	13.9154	−	12.9116i	0.827186	−	0.767516i	−0.147981	−	0.988990i	$-0.547277\pi$
$283$	13.9154	−	12.9116i	0.827186	−	0.767516i	0.975166	+	0.221474i	$0.0710868\pi$
$284$	−14.0028	−	2.11058i	−0.830911	−	0.125240i
$285$	−4.29062	−	3.98112i	−0.254155	−	0.235821i
$286$	4.51073	+	5.65627i	0.266725	+	0.334462i
$287$		0			0
$288$	−4.02247	+	5.04402i	−0.237027	+	0.297222i
$289$	16.4013	−	2.47209i	0.964781	−	0.145417i
$290$	10.6602	+	7.26799i	0.625988	+	0.426791i
$291$	−18.4193	+	46.9315i	−1.07976	+	2.75117i
$292$	3.97419	+	1.22587i	0.232572	+	0.0717389i
$293$	19.6220			1.14633			0.573163	−	0.819441i	$-0.305716\pi$
$293$	19.6220			1.14633			0.573163	+	0.819441i	$0.305716\pi$
$294$		0			0
$295$	−9.51336			−0.553889
$296$	6.13853	+	1.89348i	0.356795	+	0.110057i
$297$	−11.7285	+	29.8838i	−0.680559	+	1.73403i
$298$	5.86080	+	3.99583i	0.339507	+	0.231472i
$299$	−22.2201	+	3.34914i	−1.28502	+	0.193686i
$300$	−7.96040	+	9.98203i	−0.459594	+	0.576313i
$301$		0			0
$302$	−7.35530	−	9.22326i	−0.423250	−	0.530739i
$303$	32.3843	+	30.0483i	1.86043	+	1.72623i
$304$	−0.622266	−	0.0937916i	−0.0356894	−	0.00537931i
$305$	−11.9688	+	11.1054i	−0.685331	+	0.635894i
$306$	3.42761	−	2.33690i	0.195943	−	0.133592i
$307$	−4.68518	−	20.5271i	−0.267397	−	1.17154i	−0.913029	−	0.407895i	$-0.866263\pi$
$307$	−4.68518	−	20.5271i	−0.267397	−	1.17154i	0.645632	−	0.763649i	$-0.276594\pi$
$308$		0			0
$309$	−11.1730	+	48.9520i	−0.635608	+	2.78478i
$310$	−2.77512	−	7.07090i	−0.157616	−	0.401600i
$311$	−0.879985	−	11.7426i	−0.0498994	−	0.665861i	−0.964935	−	0.262488i	$-0.915457\pi$
$311$	−0.879985	−	11.7426i	−0.0498994	−	0.665861i	0.915036	−	0.403373i	$-0.132162\pi$
$312$	3.67586	+	6.36677i	0.208104	+	0.360447i
$313$	−10.7261	+	18.5781i	−0.606275	+	1.05010i	0.385574	+	0.922677i	$0.374004\pi$
$313$	−10.7261	+	18.5781i	−0.606275	+	1.05010i	−0.991849	+	0.127422i	$0.959330\pi$
$314$	−11.8541	−	5.70864i	−0.668966	−	0.322157i
$315$		0			0
$316$	10.1099	−	4.86865i	0.568724	−	0.273883i
$317$	2.21824	−	29.6003i	0.124589	−	1.66252i	−0.488543	−	0.872540i	$-0.662471\pi$
$317$	2.21824	−	29.6003i	0.124589	−	1.66252i	0.613131	−	0.789981i	$-0.289910\pi$
$318$	13.7670	−	4.24656i	0.772015	−	0.238135i
$319$	12.3289	−	3.80295i	0.690284	−	0.212924i
$320$	−0.226087	+	3.01692i	−0.0126386	+	0.168651i
$321$	46.2121	−	22.2546i	2.57931	−	1.24213i
$322$		0			0
$323$	0.364574	+	0.175570i	0.0202855	+	0.00976896i
$324$	−6.63391	+	11.4903i	−0.368551	+	0.638348i
$325$	4.96548	+	8.60047i	0.275435	+	0.477068i
$326$	−1.00218	−	13.3732i	−0.0555058	−	0.740673i
$327$	−1.87025	−	4.76533i	−0.103425	−	0.263523i
$328$	0.460705	−	2.01848i	0.0254382	−	0.111452i
$329$		0			0
$330$	6.26156	+	27.4337i	0.344687	+	1.51017i
$331$	−0.678290	+	0.462450i	−0.0372822	+	0.0254186i	−0.581818	−	0.813319i	$-0.697658\pi$
$331$	−0.678290	+	0.462450i	−0.0372822	+	0.0254186i	0.544536	+	0.838738i	$0.316706\pi$
$332$	−5.58926	+	5.18608i	−0.306751	+	0.284623i
$333$	40.9813	+	6.17694i	2.24576	+	0.338494i
$334$	−6.95107	−	6.44965i	−0.380346	−	0.352909i
$335$	−11.9268	−	14.9557i	−0.651631	−	0.817119i
$336$		0			0
$337$	2.24830	−	2.81928i	0.122473	−	0.153576i	−0.716815	−	0.697263i	$-0.754401\pi$
$337$	2.24830	−	2.81928i	0.122473	−	0.153576i	0.839288	+	0.543687i	$0.182972\pi$
$338$	−7.20027	+	1.08527i	−0.391643	+	0.0590307i
$339$	23.5110	+	16.0295i	1.27694	+	0.870603i
$340$	0.710723	−	1.81089i	0.0385444	−	0.0982094i
$341$	−7.25851	−	2.23895i	−0.393070	−	0.121246i
$342$	−4.05993			−0.219536
$343$		0			0
$344$	−1.35656			−0.0731406
$345$	−83.5183	−	25.7620i	−4.49647	−	1.38698i
$346$	0.384517	−	0.979734i	0.0206718	−	0.0526708i
$347$	−13.6683	−	9.31891i	−0.733755	−	0.500265i	0.137863	−	0.990451i	$-0.455977\pi$
$347$	−13.6683	−	9.31891i	−0.733755	−	0.500265i	−0.871618	+	0.490186i	$0.836929\pi$
$348$	12.9644	−	1.95407i	0.694965	−	0.104749i
$349$	1.47185	−	1.84565i	0.0787865	−	0.0987951i	−0.740876	−	0.671642i	$-0.765589\pi$
$349$	1.47185	−	1.84565i	0.0787865	−	0.0987951i	0.819663	+	0.572847i	$0.194161\pi$
$350$		0			0
$351$	15.8209	+	19.8388i	0.844458	+	1.05892i
$352$	2.21776	+	2.05778i	0.118207	+	0.109680i
$353$	3.75456	+	0.565909i	0.199835	+	0.0301203i	0.248197	−	0.968710i	$-0.420162\pi$
$353$	3.75456	+	0.565909i	0.199835	+	0.0301203i	−0.0483618	+	0.998830i	$0.515400\pi$
$354$	−7.08663	+	6.57543i	−0.376650	+	0.349480i
$355$	−35.3979	+	24.1339i	−1.87872	+	1.28089i
$356$	−0.265089	−	1.16143i	−0.0140497	−	0.0615558i
$357$		0			0
$358$	−2.26794	+	9.93649i	−0.119864	+	0.525160i
$359$	−10.2064	−	26.0055i	−0.538674	−	1.37252i	−0.898284	−	0.439416i	$-0.855185\pi$
$359$	−10.2064	−	26.0055i	−0.538674	−	1.37252i	0.359610	−	0.933103i	$-0.382910\pi$
$360$	1.45861	+	19.4638i	0.0768755	+	1.02583i
$361$	9.30199	+	16.1115i	0.489579	+	0.847975i
$362$	6.93946	−	12.0195i	0.364730	−	0.631730i
$363$	−5.11617	−	2.46382i	−0.268530	−	0.129317i
$364$		0			0
$365$	11.3364	−	5.45931i	0.593373	−	0.285753i
$366$	−1.23989	+	16.5452i	−0.0648100	+	0.864829i
$367$	−29.8002	+	9.19215i	−1.55556	+	0.479826i	−0.949017	−	0.315225i	$-0.897920\pi$
$367$	−29.8002	+	9.19215i	−1.55556	+	0.479826i	−0.606542	+	0.795051i	$0.707444\pi$
$368$	−8.97946	+	2.76980i	−0.468087	+	0.144386i
$369$	0.998186	−	13.3199i	0.0519635	−	0.693405i
$370$	17.5102	−	8.43245i	0.910310	−	0.438382i
$371$		0			0
$372$	−6.95448	−	3.34910i	−0.360573	−	0.173643i
$373$	8.12270	−	14.0689i	0.420578	−	0.728462i	−0.575418	−	0.817859i	$-0.695161\pi$
$373$	8.12270	−	14.0689i	0.420578	−	0.728462i	0.995996	+	0.0893974i	$0.0284941\pi$
$374$	−0.972684	−	1.68474i	−0.0502963	−	0.0871158i
$375$	−0.588773	−	7.85663i	−0.0304041	−	0.405715i
$376$	−0.387353	−	0.986961i	−0.0199762	−	0.0508986i
$377$	2.26928	−	9.94235i	0.116874	−	0.512057i
$378$		0			0
$379$	−6.55969	−	28.7399i	−0.336949	−	1.47627i	−0.805375	−	0.592766i	$-0.798036\pi$
$379$	−6.55969	−	28.7399i	−0.336949	−	1.47627i	0.468426	−	0.883503i	$-0.344821\pi$
$380$	−1.57304	+	1.07248i	−0.0806953	+	0.0550171i
$381$	−30.1887	+	28.0110i	−1.54661	+	1.43505i
$382$	6.64691	+	1.00186i	0.340086	+	0.0512596i
$383$	12.3133	+	11.4251i	0.629181	+	0.583795i	0.928945	−	0.370219i	$-0.120717\pi$
$383$	12.3133	+	11.4251i	0.629181	+	0.583795i	−0.299764	+	0.954014i	$0.596908\pi$
$384$	1.91682	+	2.40361i	0.0978172	+	0.122659i
$385$		0			0
$386$	1.44686	−	1.81431i	0.0736433	−	0.0923458i
$387$	−8.65413	+	1.30440i	−0.439914	+	0.0663064i
$388$	13.5496	+	9.23799i	0.687879	+	0.468988i
$389$	−4.23586	+	10.7928i	−0.214767	+	0.547217i	−0.997139	−	0.0755946i	$-0.975915\pi$
$389$	−4.23586	+	10.7928i	−0.214767	+	0.547217i	0.782372	+	0.622812i	$0.214010\pi$
$390$	21.2536	+	6.55587i	1.07622	+	0.331969i
$391$	6.04238			0.305576
$392$		0			0
$393$	−59.7585			−3.01442
$394$	−8.33551	−	2.57117i	−0.419937	−	0.129533i
$395$	12.4026	−	31.6014i	0.624044	−	1.59004i
$396$	16.1268	+	10.9951i	0.810405	+	0.552524i
$397$	−13.5010	+	2.03496i	−0.677598	+	0.102131i	−0.478820	−	0.877913i	$-0.658935\pi$
$397$	−13.5010	+	2.03496i	−0.677598	+	0.102131i	−0.198778	+	0.980045i	$0.563697\pi$
$398$	6.65827	−	8.34921i	0.333749	−	0.418508i
$399$		0			0
$400$	2.58931	+	3.24689i	0.129465	+	0.162344i
$401$	−8.85686	−	8.21796i	−0.442290	−	0.410386i	0.427338	−	0.904092i	$-0.359451\pi$
$401$	−8.85686	−	8.21796i	−0.442290	−	0.410386i	−0.869629	+	0.493706i	$0.835642\pi$
$402$	−19.2215	−	2.89718i	−0.958683	−	0.144498i
$403$	−4.40125	+	4.08376i	−0.219242	+	0.203427i
$404$	11.8728	−	8.09476i	0.590695	−	0.402729i
$405$	8.93203	+	39.1338i	0.443836	+	1.94457i
$406$		0			0
$407$	4.32465	−	18.9475i	0.214365	−	0.939195i
$408$	−0.722224	−	1.84020i	−0.0357554	−	0.0911033i
$409$	−1.88072	−	25.0964i	−0.0929955	−	1.24094i	−0.827160	−	0.561967i	$-0.810045\pi$
$409$	−1.88072	−	25.0964i	−0.0929955	−	1.24094i	0.734165	−	0.678972i	$-0.237574\pi$
$410$	−3.13186	−	5.42454i	−0.154671	−	0.267899i
$411$	12.1223	−	20.9964i	0.597949	−	1.03568i
$412$	14.7149	+	7.08630i	0.724949	+	0.349117i
$413$		0			0
$414$	−54.6210	+	26.3041i	−2.68448	+	1.29278i
$415$	−1.72383	+	23.0030i	−0.0846196	+	1.12917i
$416$	2.28508	−	0.704853i	0.112035	−	0.0345583i
$417$	0.861329	−	0.265685i	0.0421795	−	0.0130106i
$418$	−0.142275	+	1.89853i	−0.00695892	+	0.0928603i
$419$	−19.3992	+	9.34214i	−0.947711	+	0.456393i	−0.842883	−	0.538097i	$-0.819143\pi$
$419$	−19.3992	+	9.34214i	−0.947711	+	0.456393i	−0.104828	+	0.994490i	$0.533429\pi$
$420$		0			0
$421$	25.2231	+	12.1468i	1.22930	+	0.591998i	0.931886	−	0.362751i	$-0.118163\pi$
$421$	25.2231	+	12.1468i	1.22930	+	0.591998i	0.297411	+	0.954750i	$0.403877\pi$
$422$	−7.11123	+	12.3170i	−0.346169	+	0.599583i
$423$	−3.42013	−	5.92384i	−0.166293	−	0.288027i
$424$	−0.350203	−	4.67313i	−0.0170073	−	0.226947i
$425$	−0.975606	−	2.48580i	−0.0473239	−	0.120579i
$426$	−9.68755	+	42.4439i	−0.469363	+	2.05642i
$427$		0			0
$428$	−3.71249	−	16.2655i	−0.179450	−	0.786222i
$429$	18.3770	−	12.5292i	0.887249	−	0.604916i
$430$	−3.00851	+	2.79149i	−0.145083	+	0.134618i
$431$	17.4819	+	2.63498i	0.842076	+	0.126923i	0.555894	−	0.831253i	$-0.312376\pi$
$431$	17.4819	+	2.63498i	0.842076	+	0.126923i	0.286181	+	0.958175i	$0.407614\pi$
$432$	7.77857	+	7.21746i	0.374247	+	0.347250i
$433$	−0.735843	−	0.922718i	−0.0353624	−	0.0443430i	0.763836	−	0.645411i	$-0.223314\pi$
$433$	−0.735843	−	0.922718i	−0.0353624	−	0.0443430i	−0.799198	+	0.601068i	$0.794742\pi$
$434$		0			0
$435$	24.7309	−	31.0116i	1.18576	−	1.48689i
$436$	−1.64654	+	0.248176i	−0.0788551	+	0.0118855i
$437$	−4.88592	−	3.33116i	−0.233725	−	0.159351i
$438$	4.67126	−	11.9022i	0.223202	−	0.568708i
$439$	−20.4013	−	6.29297i	−0.973702	−	0.300347i	−0.233220	−	0.972424i	$-0.574926\pi$
$439$	−20.4013	−	6.29297i	−0.973702	−	0.300347i	−0.740482	+	0.672077i	$0.765403\pi$
$440$	9.15293			0.436349
$441$		0			0
$442$	−1.53766			−0.0731388
$443$	8.23971	+	2.54161i	0.391481	+	0.120756i	0.484245	−	0.874932i	$-0.339094\pi$
$443$	8.23971	+	2.54161i	0.391481	+	0.120756i	−0.0927647	+	0.995688i	$0.529570\pi$
$444$	7.21523	−	18.3841i	0.342420	−	0.872471i
$445$	−2.97788	−	2.03028i	−0.141165	−	0.0962446i
$446$	−9.58749	+	1.44508i	−0.453981	+	0.0684266i
$447$	13.5967	−	17.0497i	0.643100	−	0.806422i
$448$		0			0
$449$	10.4421	+	13.0940i	0.492794	+	0.617944i	0.964587	−	0.263765i	$-0.0849644\pi$
$449$	10.4421	+	13.0940i	0.492794	+	0.617944i	−0.471793	+	0.881710i	$0.656393\pi$
$450$	19.6405	+	18.2237i	0.925863	+	0.859075i
$451$	−6.19376	−	0.933559i	−0.291653	−	0.0439596i
$452$	6.78497	−	6.29553i	0.319138	−	0.296117i
$453$	−29.9660	+	20.4304i	−1.40792	+	0.959906i
$454$	−1.37874	−	6.04064i	−0.0647073	−	0.283501i
$455$		0			0
$456$	−0.430503	+	1.88616i	−0.0201602	+	0.0883275i
$457$	2.92849	+	7.46166i	0.136989	+	0.349042i	0.982862	−	0.184342i	$-0.0590154\pi$
$457$	2.92849	+	7.46166i	0.136989	+	0.349042i	−0.845873	+	0.533384i	$0.820920\pi$
$458$	−0.0409012	−	0.545789i	−0.00191119	−	0.0255031i
$459$	−3.41159	−	5.90905i	−0.159240	−	0.275811i
$460$	−14.2147	+	24.6205i	−0.662762	+	1.14794i
$461$	−16.3204	−	7.85951i	−0.760118	−	0.366054i	0.0133316	−	0.999911i	$-0.495756\pi$
$461$	−16.3204	−	7.85951i	−0.760118	−	0.366054i	−0.773450	+	0.633857i	$0.781471\pi$
$462$		0			0
$463$	−4.79374	+	2.30855i	−0.222784	+	0.107287i	−0.541947	−	0.840413i	$-0.682313\pi$
$463$	−4.79374	+	2.30855i	−0.222784	+	0.107287i	0.319163	+	0.947700i	$0.396598\pi$
$464$	0.318695	−	4.25268i	0.0147950	−	0.197426i
$465$	−22.3151	+	6.88330i	−1.03484	+	0.319205i
$466$	−6.47664	+	1.99778i	−0.300025	+	0.0925454i
$467$	−2.50762	+	33.4619i	−0.116039	+	1.54843i	0.570474	+	0.821316i	$0.306760\pi$
$467$	−2.50762	+	33.4619i	−0.116039	+	1.54843i	−0.686513	+	0.727118i	$0.740859\pi$
$468$	13.8999	−	6.69383i	0.642522	−	0.309422i
$469$		0			0
$470$	−2.89001	−	1.39175i	−0.133306	−	0.0641968i
$471$	−20.2246	+	35.0301i	−0.931902	+	1.61410i
$472$	1.57226	+	2.72323i	0.0723690	+	0.125347i
$473$	0.306699	+	4.09262i	0.0141021	+	0.188179i
$474$	−12.6033	−	32.1128i	−0.578890	−	1.47499i
$475$	−0.581540	+	2.54789i	−0.0266829	+	0.116905i
$476$		0			0
$477$	−6.72758	−	29.4754i	−0.308035	−	1.34959i
$478$	5.61971	−	3.83145i	0.257039	−	0.175247i
$479$	12.2731	−	11.3878i	0.560773	−	0.520321i	−0.348065	−	0.937470i	$-0.613161\pi$
$479$	12.2731	−	11.3878i	0.560773	−	0.520321i	0.908838	+	0.417149i	$0.136971\pi$
$480$	9.19715	+	1.38625i	0.419791	+	0.0632733i
$481$	−11.2609	−	10.4486i	−0.513452	−	0.476414i
$482$	−16.2509	−	20.3780i	−0.740207	−	0.928190i
$483$		0			0
$484$	−1.15163	+	1.44410i	−0.0523469	+	0.0656409i
$485$	49.0596	−	7.39455i	2.22768	−	0.335769i
$486$	7.39987	+	5.04514i	0.335665	+	0.228852i
$487$	9.73577	−	24.8063i	0.441170	−	1.12408i	−0.521463	−	0.853274i	$-0.674614\pi$
$487$	9.73577	−	24.8063i	0.441170	−	1.12408i	0.962633	−	0.270809i	$-0.0872911\pi$
$488$	5.15703	+	1.59073i	0.233448	+	0.0720090i
$489$	−41.2290			−1.86444
$490$		0			0
$491$	7.56655			0.341474			0.170737	−	0.985317i	$-0.445385\pi$
$491$	7.56655			0.341474			0.170737	+	0.985317i	$0.445385\pi$
$492$	−6.08229	−	1.87614i	−0.274211	−	0.0845829i
$493$	−1.00184	+	2.55265i	−0.0451207	+	0.114966i
$494$	1.24336	+	0.847709i	0.0559414	+	0.0381402i
$495$	58.3910	−	8.80103i	2.62448	−	0.395577i
$496$	−1.56543	+	1.96298i	−0.0702898	+	0.0881406i
$497$		0			0
$498$	14.6151	+	18.3267i	0.654916	+	0.821239i
$499$	7.68768	+	7.13313i	0.344148	+	0.319323i	0.833242	−	0.552908i	$-0.186482\pi$
$499$	7.68768	+	7.13313i	0.344148	+	0.319323i	−0.489094	+	0.872231i	$0.662673\pi$
$500$	−2.53410	−	0.381953i	−0.113328	−	0.0170815i
$501$	−21.3699	+	19.8284i	−0.954738	+	0.885868i
$502$	21.6408	−	14.7545i	0.965877	−	0.658523i
$503$	0.109148	+	0.478210i	0.00486668	+	0.0213223i	0.977303	−	0.211846i	$-0.0679477\pi$
$503$	0.109148	+	0.478210i	0.00486668	+	0.0213223i	−0.972436	+	0.233169i	$0.925091\pi$
$504$		0			0
$505$	9.67386	−	42.3839i	0.430481	−	1.88606i
$506$	10.3864	+	26.4641i	0.461731	+	1.17647i
$507$	1.67292	+	22.3235i	0.0742968	+	0.991422i
$508$	6.69774	+	11.6008i	0.297164	+	0.514703i
$509$	7.97197	−	13.8079i	0.353351	−	0.612022i	−0.633483	−	0.773757i	$-0.718375\pi$
$509$	7.97197	−	13.8079i	0.353351	−	0.612022i	0.986834	+	0.161734i	$0.0517087\pi$
$510$	−5.38844	−	2.59494i	−0.238604	−	0.114906i
$511$		0			0
$512$	0.900969	−	0.433884i	0.0398176	−	0.0191751i
$513$	−0.499017	+	6.65891i	−0.0220321	+	0.293998i
$514$	−12.8117	+	3.95188i	−0.565099	+	0.174310i
$515$	47.2161	−	14.5642i	2.08059	−	0.641777i
$516$	−0.311662	+	4.15885i	−0.0137202	+	0.183083i
$517$	−2.89001	+	1.39175i	−0.127102	+	0.0612093i
$518$		0			0
$519$	−2.91527	−	1.40392i	−0.127966	−	0.0616252i
$520$	3.61732	−	6.26539i	0.158630	−	0.274755i
$521$	−15.9248	−	27.5825i	−0.697677	−	1.20841i	−0.969270	−	0.246000i	$-0.920884\pi$
$521$	−15.9248	−	27.5825i	−0.697677	−	1.20841i	0.271593	−	0.962412i	$-0.412450\pi$
$522$	−2.05607	−	27.4364i	−0.0899919	−	1.20086i
$523$	−15.5021	−	39.4986i	−0.677858	−	1.72715i	−0.686435	−	0.727191i	$-0.740825\pi$
$523$	−15.5021	−	39.4986i	−0.677858	−	1.72715i	0.00857657	−	0.999963i	$-0.497270\pi$
$524$	−4.32533	+	18.9505i	−0.188953	+	0.827856i
$525$		0			0
$526$	−2.35041	−	10.2978i	−0.102483	−	0.449006i
$527$	1.33392	−	0.909454i	0.0581067	−	0.0396165i
$528$	6.81814	−	6.32631i	0.296722	−	0.275317i
$529$	−64.5730	−	9.73282i	−2.80752	−	0.423166i
$530$	−10.3929	−	9.64324i	−0.451441	−	0.418876i
$531$	12.6487	+	15.8610i	0.548908	+	0.688309i
$532$		0			0
$533$	−3.08687	+	3.87082i	−0.133707	+	0.167664i
$534$	−3.62155	+	0.545861i	−0.156720	+	0.0236217i
$535$	−41.7042	−	28.4334i	−1.80303	−	1.22929i
$536$	−2.31001	+	5.88580i	−0.0997770	+	0.254228i
$537$	29.9416	+	9.23577i	1.29208	+	0.398553i
$538$	11.9198			0.513898
$539$		0			0
$540$	32.1030			1.38149
$541$	6.25089	+	1.92814i	0.268747	+	0.0828974i	0.426200	−	0.904629i	$-0.359852\pi$
$541$	6.25089	+	1.92814i	0.268747	+	0.0828974i	−0.157453	+	0.987526i	$0.550328\pi$
$542$	−9.08604	+	23.1509i	−0.390279	+	0.994415i
$543$	−35.2543	−	24.0360i	−1.51291	−	1.03148i
$544$	−0.635834	+	0.0958366i	−0.0272612	+	0.00410896i
$545$	−3.14094	+	3.93862i	−0.134543	+	0.168712i
$546$		0			0
$547$	11.3933	+	14.2867i	0.487141	+	0.610856i	0.963275	−	0.268517i	$-0.0865336\pi$
$547$	11.3933	+	14.2867i	0.487141	+	0.610856i	−0.476134	+	0.879373i	$0.657962\pi$
$548$	−5.78094	−	5.36393i	−0.246949	−	0.229136i
$549$	34.4288	+	5.18930i	1.46938	+	0.221474i
$550$	9.21020	−	8.54581i	0.392724	−	0.364395i
$551$	2.21737	−	1.51178i	0.0944633	−	0.0644040i
$552$	6.42848	+	28.1650i	0.273614	+	1.19878i
$553$		0			0
$554$	6.18154	−	27.0831i	0.262629	−	1.15065i
$555$	−21.8288	−	55.6189i	−0.926582	−	2.36089i
$556$	−0.0219104	−	0.292373i	−0.000929206	−	0.0123994i
$557$	18.2235	+	31.5640i	0.772153	+	1.33741i	0.936381	+	0.350986i	$0.114154\pi$
$557$	18.2235	+	31.5640i	0.772153	+	1.33741i	−0.164227	+	0.986423i	$0.552513\pi$
$558$	−8.09912	+	14.0281i	−0.342863	+	0.593856i
$559$	2.92270	+	1.40750i	0.123617	+	0.0595309i
$560$		0			0
$561$	−5.38844	+	2.59494i	−0.227500	+	0.109558i
$562$	2.33080	−	31.1023i	0.0983188	−	1.31197i
$563$	5.88173	−	1.81427i	0.247885	−	0.0764625i	−0.168323	−	0.985732i	$-0.553835\pi$
$563$	5.88173	−	1.81427i	0.247885	−	0.0764625i	0.416208	+	0.909269i	$0.363359\pi$
$564$	−3.11476	+	0.960775i	−0.131155	+	0.0404559i
$565$	2.09261	−	27.9240i	0.0880368	−	1.17477i
$566$	−17.1030	+	8.23635i	−0.718891	+	0.346200i
$567$		0			0
$568$	12.7586	+	6.14419i	0.535337	+	0.257805i
$569$	−4.20966	+	7.29134i	−0.176478	+	0.305669i	−0.940672	−	0.339318i	$-0.889804\pi$
$569$	−4.20966	+	7.29134i	−0.176478	+	0.305669i	0.764194	+	0.644987i	$0.223137\pi$
$570$	2.92655	+	5.06893i	0.122580	+	0.212314i
$571$	−2.61820	−	34.9375i	−0.109568	−	1.46209i	−0.733010	−	0.680218i	$-0.761885\pi$
$571$	−2.61820	−	34.9375i	−0.109568	−	1.46209i	0.623442	−	0.781870i	$-0.285734\pi$
$572$	−2.64311	−	6.73454i	−0.110514	−	0.281585i
$573$	4.59854	−	20.1475i	0.192107	−	0.841675i
$574$		0			0
$575$	8.68383	+	38.0464i	0.362141	+	1.58664i
$576$	5.33052	−	3.63429i	0.222105	−	0.151429i
$577$	25.5143	−	23.6738i	1.06218	−	0.985555i	0.0622534	−	0.998060i	$-0.480171\pi$
$577$	25.5143	−	23.6738i	1.06218	−	0.985555i	0.999922	+	0.0125059i	$0.00398084\pi$
$578$	−16.4013	−	2.47209i	−0.682203	−	0.102826i
$579$	−5.22978	−	4.85253i	−0.217342	−	0.201664i
$580$	−8.04430	−	10.0872i	−0.334022	−	0.418850i
$581$		0			0
$582$	31.4343	−	39.4173i	1.30299	−	1.63390i
$583$	−14.0193	+	2.11307i	−0.580620	+	0.0875143i
$584$	−3.43629	−	2.34282i	−0.142195	−	0.0969468i
$585$	17.0522	−	43.4482i	0.705020	−	1.79636i
$586$	−18.7502	−	5.78367i	−0.774564	−	0.238921i
$587$	19.8051			0.817443			0.408722	−	0.912659i	$-0.365975\pi$
$587$	19.8051			0.817443			0.408722	+	0.912659i	$0.365975\pi$
$588$		0			0
$589$	−1.58000			−0.0651029
$590$	9.09071	+	2.80411i	0.374258	+	0.115443i
$591$	−9.79757	+	24.9638i	−0.403018	+	1.02687i
$592$	−5.30769	−	3.61872i	−0.218145	−	0.148729i
$593$	−10.4198	+	1.57054i	−0.427891	+	0.0644942i	−0.359457	−	0.933161i	$-0.617038\pi$
$593$	−10.4198	+	1.57054i	−0.427891	+	0.0644942i	−0.0684336	+	0.997656i	$0.521800\pi$
$594$	20.0159	−	25.0991i	0.821261	−	1.02983i
$595$		0			0
$596$	−4.42263	−	5.54581i	−0.181158	−	0.227165i
$597$	−24.0668	−	22.3307i	−0.984989	−	0.913936i
$598$	22.2201	+	3.34914i	0.908646	+	0.136956i
$599$	2.72801	−	2.53123i	0.111464	−	0.103423i	−0.622472	−	0.782642i	$-0.713872\pi$
$599$	2.72801	−	2.53123i	0.111464	−	0.103423i	0.733936	+	0.679219i	$0.237681\pi$
$600$	10.5490	−	7.19219i	0.430661	−	0.293620i
$601$	−0.0432317	−	0.189411i	−0.00176346	−	0.00772622i	0.974039	−	0.226382i	$-0.0726899\pi$
$601$	−0.0432317	−	0.189411i	−0.00176346	−	0.00772622i	−0.975802	+	0.218656i	$0.929833\pi$
$602$		0			0
$603$	−9.07715	+	39.7696i	−0.369650	+	1.61954i
$604$	4.30992	+	10.9815i	0.175368	+	0.446831i
$605$	0.417599	+	5.57247i	0.0169778	+	0.226553i
$606$	−22.0887	−	38.2588i	−0.897292	−	1.55416i
$607$	10.1464	−	17.5741i	0.411829	−	0.713309i	−0.583261	−	0.812285i	$-0.698223\pi$
$607$	10.1464	−	17.5741i	0.411829	−	0.713309i	0.995090	+	0.0989761i	$0.0315567\pi$
$608$	0.566975	+	0.273041i	0.0229939	+	0.0110733i
$609$		0			0
$610$	14.7104	−	7.08417i	0.595608	−	0.286830i
$611$	−0.189471	+	2.52831i	−0.00766516	+	0.102284i
$612$	−3.96415	+	1.22278i	−0.160241	+	0.0494278i
$613$	13.9582	−	4.30553i	0.563766	−	0.173899i	0.000244110	−	1.00000i	$-0.499922\pi$
$613$	13.9582	−	4.30553i	0.563766	−	0.173899i	0.563522	+	0.826101i	$0.309446\pi$
$614$	−1.57344	+	20.9961i	−0.0634989	+	0.847334i
$615$	−17.3498	+	8.35520i	−0.699610	+	0.336914i
$616$		0			0
$617$	−10.5371	−	5.07442i	−0.424209	−	0.204288i	0.209584	−	0.977791i	$-0.432789\pi$
$617$	−10.5371	−	5.07442i	−0.424209	−	0.204288i	−0.633794	+	0.773502i	$0.718503\pi$
$618$	25.1054	−	43.4839i	1.00989	−	1.74918i
$619$	18.7316	+	32.4440i	0.752885	+	1.30404i	0.946419	+	0.322942i	$0.104672\pi$
$619$	18.7316	+	32.4440i	0.752885	+	1.30404i	−0.193534	+	0.981094i	$0.561995\pi$
$620$	0.567648	+	7.57474i	0.0227973	+	0.304209i
$621$	36.4292	+	92.8202i	1.46185	+	3.72474i
$622$	−2.62030	+	11.4803i	−0.105064	+	0.460317i
$623$		0			0
$624$	−1.63591	−	7.16739i	−0.0654888	−	0.286925i
$625$	−23.5625	+	16.0647i	−0.942502	+	0.642587i
$626$	15.7256	−	14.5912i	0.628520	−	0.583182i
$627$	5.78772	+	0.872359i	0.231139	+	0.0348387i
$628$	9.64482	+	8.94908i	0.384870	+	0.357107i
$629$	2.57544	+	3.22950i	0.102690	+	0.128769i
$630$		0			0
$631$	−8.17143	+	10.2467i	−0.325300	+	0.407913i	−0.917410	−	0.397944i	$-0.869724\pi$
$631$	−8.17143	+	10.2467i	−0.325300	+	0.407913i	0.592110	+	0.805857i	$0.298295\pi$
$632$	−11.0958	+	1.67242i	−0.441366	+	0.0665253i
$633$	36.1270	+	24.6310i	1.43592	+	0.978993i
$634$	−10.8445	+	27.6314i	−0.430692	+	1.09738i
$635$	38.7259	+	11.9454i	1.53679	+	0.474038i
$636$	−14.4071			−0.571277
$637$		0			0
$638$	−12.9021			−0.510798
$639$	87.3010	+	26.9288i	3.45357	+	1.06529i
$640$	1.10530	−	2.81625i	0.0436906	−	0.111322i
$641$	−9.52494	−	6.49399i	−0.376212	−	0.256497i	0.360421	−	0.932790i	$-0.382633\pi$
$641$	−9.52494	−	6.49399i	−0.376212	−	0.256497i	−0.736633	+	0.676293i	$0.763586\pi$
$642$	−50.7187	+	7.64461i	−2.00171	+	0.301709i
$643$	−14.3138	+	17.9489i	−0.564481	+	0.707836i	−0.979379	−	0.202031i	$-0.935246\pi$
$643$	−14.3138	+	17.9489i	−0.564481	+	0.707836i	0.414898	+	0.909868i	$0.363817\pi$
$644$		0			0
$645$	7.86680	+	9.86466i	0.309755	+	0.388421i
$646$	−0.296627	−	0.275230i	−0.0116706	−	0.0108288i
$647$	−2.57249	−	0.387740i	−0.101135	−	0.0152436i	0.0982798	−	0.995159i	$-0.468666\pi$
$647$	−2.57249	−	0.387740i	−0.101135	−	0.0152436i	−0.199415	+	0.979915i	$0.563904\pi$
$648$	9.72600	−	9.02441i	0.382073	−	0.354512i
$649$	7.86030	−	5.35906i	0.308544	−	0.210362i
$650$	−2.20985	−	9.68197i	−0.0866773	−	0.379758i
$651$		0			0
$652$	−2.98416	+	13.0745i	−0.116869	+	0.512036i
$653$	12.9347	+	32.9571i	0.506174	+	1.28971i	0.924420	+	0.381376i	$0.124550\pi$
$653$	12.9347	+	32.9571i	0.506174	+	1.28971i	−0.418246	+	0.908334i	$0.637355\pi$
$654$	0.382559	+	5.10489i	0.0149592	+	0.199617i
$655$	29.4034	+	50.9282i	1.14889	+	1.98993i
$656$	−1.03519	+	1.79301i	−0.0404176	+	0.0700053i
$657$	−24.1745	−	11.6418i	−0.943139	−	0.454192i
$658$		0			0
$659$	24.6402	−	11.8661i	0.959847	−	0.462238i	0.112719	−	0.993627i	$-0.464044\pi$
$659$	24.6402	−	11.8661i	0.959847	−	0.462238i	0.847128	+	0.531389i	$0.178330\pi$
$660$	2.10284	−	28.0605i	0.0818531	−	1.09225i
$661$	3.30279	−	1.01877i	0.128464	−	0.0396257i	−0.229857	−	0.973224i	$-0.573826\pi$
$661$	3.30279	−	1.01877i	0.128464	−	0.0396257i	0.358320	+	0.933599i	$0.383350\pi$
$662$	0.784465	−	0.241975i	0.0304891	−	0.00940464i
$663$	−0.353269	+	4.71405i	−0.0137198	+	0.183079i
$664$	6.86957	−	3.30821i	0.266591	−	0.128383i
$665$		0			0
$666$	−37.3400	−	17.9820i	−1.44689	−	0.696788i
$667$	20.0371	−	34.7053i	0.775841	−	1.34380i
$668$	4.74119	+	8.21197i	0.183442	+	0.317731i
$669$	2.22756	+	29.7247i	0.0861225	+	1.14923i
$670$	6.98865	+	17.8068i	0.269995	+	0.687936i
$671$	3.63318	−	15.9180i	0.140257	−	0.614507i
$672$		0			0
$673$	4.76589	+	20.8807i	0.183712	+	0.804893i	0.979843	+	0.199769i	$0.0640192\pi$
$673$	4.76589	+	20.8807i	0.183712	+	0.804893i	−0.796131	+	0.605124i	$0.793124\pi$
$674$	−2.97941	+	2.03133i	−0.114763	+	0.0782438i
$675$	32.3038	−	29.9736i	1.24338	−	1.15368i
$676$	7.20027	+	1.08527i	0.276934	+	0.0417410i
$677$	13.6515	+	12.6668i	0.524670	+	0.486823i	0.897462	−	0.441092i	$-0.145409\pi$
$677$	13.6515	+	12.6668i	0.524670	+	0.486823i	−0.372791	+	0.927915i	$0.621599\pi$
$678$	−17.7416	−	22.2473i	−0.681364	−	0.854403i
$679$		0			0
$680$	−1.21292	+	1.52095i	−0.0465133	+	0.0583258i
$681$	−18.8358	+	2.83904i	−0.721789	+	0.108792i
$682$	6.27609	+	4.27897i	0.240324	+	0.163850i
$683$	−2.27605	+	5.79928i	−0.0870907	+	0.221903i	−0.967783	−	0.251785i	$-0.918982\pi$
$683$	−2.27605	+	5.79928i	−0.0870907	+	0.221903i	0.880693	+	0.473688i	$0.157078\pi$
$684$	3.87956	+	1.19668i	0.148338	+	0.0457564i
$685$	−23.8585			−0.911587
$686$		0			0
$687$	−1.68264			−0.0641969
$688$	1.29629	+	0.399852i	0.0494205	+	0.0152442i
$689$	−4.09411	+	10.4316i	−0.155973	+	0.397413i
$690$	72.2143	+	49.2349i	2.74915	+	1.87434i
$691$	22.2269	−	3.35016i	0.845549	−	0.127446i	0.288042	−	0.957618i	$-0.406996\pi$
$691$	22.2269	−	3.35016i	0.845549	−	0.127446i	0.557508	+	0.830172i	$0.311758\pi$
$692$	−0.656216	+	0.822869i	−0.0249456	+	0.0312808i
$693$		0			0
$694$	10.3143	+	12.9337i	0.391525	+	0.490957i
$695$	−0.650233	−	0.603328i	−0.0246647	−	0.0228855i
$696$	−12.9644	−	1.95407i	−0.491415	−	0.0740688i
$697$	0.975908	−	0.905510i	0.0369651	−	0.0342986i
$698$	−1.95048	+	1.32981i	−0.0738266	+	0.0503341i
$699$	4.63669	+	20.3147i	0.175376	+	0.768372i
$700$		0			0
$701$	5.47281	−	23.9779i	0.206705	−	0.905634i	−0.760037	−	0.649880i	$-0.774819\pi$
$701$	5.47281	−	23.9779i	0.206705	−	0.905634i	0.966742	−	0.255754i	$-0.0823237\pi$
$702$	−9.27045	−	23.6207i	−0.349891	−	0.891507i
$703$	−0.302100	−	4.03124i	−0.0113939	−	0.152041i
$704$	−1.51269	−	2.62006i	−0.0570117	−	0.0987471i
$705$	−4.93072	+	8.54026i	−0.185702	+	0.321645i
$706$	−3.42095	−	1.64744i	−0.128749	−	0.0620024i
$707$		0			0
$708$	8.70994	−	4.19448i	0.327340	−	0.157638i
$709$	0.313937	−	4.18920i	0.0117902	−	0.157329i	−0.988201	−	0.153162i	$-0.951054\pi$
$709$	0.313937	−	4.18920i	0.0117902	−	0.157329i	0.999991	−	0.00416716i	$-0.00132645\pi$
$710$	40.9388	−	12.6280i	1.53641	−	0.473919i
$711$	−69.1772	+	21.3384i	−2.59435	+	0.800251i
$712$	−0.0890260	+	1.18797i	−0.00333639	+	0.0445210i
$713$	−21.2569	+	10.2368i	−0.796077	+	0.383370i
$714$		0			0
$715$	−19.7200	−	9.49665i	−0.737486	−	0.355155i
$716$	5.09601	−	8.82655i	0.190447	−	0.329864i
$717$	−10.4551	−	18.1088i	−0.390454	−	0.676286i
$718$	2.08771	+	27.8586i	0.0779126	+	1.03967i
$719$	16.8922	+	43.0407i	0.629973	+	1.60515i	0.786583	+	0.617485i	$0.211848\pi$
$719$	16.8922	+	43.0407i	0.629973	+	1.60515i	−0.156609	+	0.987661i	$0.550056\pi$
$720$	4.34325	−	19.0290i	0.161863	−	0.709170i
$721$		0			0
$722$	−4.13978	−	18.1375i	−0.154067	−	0.675010i
$723$	−66.2071	+	45.1392i	−2.46227	+	1.67875i
$724$	−10.1740	+	9.44006i	−0.378112	+	0.350837i
$725$	−17.5128	−	2.63963i	−0.650409	−	0.0980334i
$726$	4.16265	+	3.86238i	0.154491	+	0.143346i
$727$	0.337641	+	0.423389i	0.0125224	+	0.0157026i	0.788053	−	0.615607i	$-0.211089\pi$
$727$	0.337641	+	0.423389i	0.0125224	+	0.0157026i	−0.775531	+	0.631310i	$0.782518\pi$
$728$		0			0
$729$	−7.64986	+	9.59262i	−0.283328	+	0.355282i
$730$	−12.4419	+	1.87531i	−0.460495	+	0.0694085i
$731$	−0.720717	−	0.491377i	−0.0266567	−	0.0181742i
$732$	6.06157	−	15.4446i	0.224042	−	0.570850i
$733$	16.0855	+	4.96173i	0.594133	+	0.183266i	0.577217	−	0.816591i	$-0.304139\pi$
$733$	16.0855	+	4.96173i	0.594133	+	0.183266i	0.0169165	+	0.999857i	$0.494615\pi$
$734$	31.1857			1.15109
$735$		0			0
$736$	9.39694			0.346376
$737$	18.2792	+	5.63840i	0.673325	+	0.207693i
$738$	−4.87994	+	12.4339i	−0.179633	+	0.457698i
$739$	−11.0285	−	7.51909i	−0.405689	−	0.276594i	0.343235	−	0.939249i	$-0.388477\pi$
$739$	−11.0285	−	7.51909i	−0.405689	−	0.276594i	−0.748925	+	0.662655i	$0.769430\pi$
$740$	−19.2177	+	2.89661i	−0.706458	+	0.106481i
$741$	2.88451	−	3.61706i	0.105965	−	0.132876i
$742$		0			0
$743$	−25.2863	−	31.7080i	−0.927663	−	1.16325i	−0.986298	−	0.164973i	$-0.947246\pi$
$743$	−25.2863	−	31.7080i	−0.927663	−	1.16325i	0.0586353	−	0.998279i	$-0.481325\pi$
$744$	5.65835	+	5.25018i	0.207445	+	0.192481i
$745$	−21.2204	−	3.19846i	−0.777455	−	0.117183i
$746$	−11.9087	+	11.0497i	−0.436009	+	0.404558i
$747$	40.6433	−	27.7101i	1.48706	−	1.01386i
$748$	0.432885	+	1.89659i	0.0158279	+	0.0693464i
$749$		0			0
$750$	−1.75317	+	7.68113i	−0.0640166	+	0.280475i
$751$	−8.10010	−	20.6387i	−0.295577	−	0.753118i	−0.999099	−	0.0424442i	$-0.986486\pi$
$751$	−8.10010	−	20.6387i	−0.295577	−	0.753118i	0.703522	−	0.710674i	$-0.251610\pi$
$752$	0.0792327	+	1.05729i	0.00288932	+	0.0385553i
$753$	−40.2614	−	69.7349i	−1.46721	−	2.54128i
$754$	−5.09902	+	8.83175i	−0.185695	+	0.321634i
$755$	32.1559	+	15.4855i	1.17027	+	0.563574i
$756$		0			0
$757$	−16.4965	+	7.94430i	−0.599576	+	0.288740i	−0.708948	−	0.705260i	$-0.750830\pi$
$757$	−16.4965	+	7.94430i	−0.599576	+	0.288740i	0.109373	+	0.994001i	$0.465116\pi$
$758$	−2.20297	+	29.3966i	−0.0800154	+	1.06773i
$759$	83.5183	−	25.7620i	3.03152	−	0.935100i
$760$	1.81927	−	0.561172i	0.0659920	−	0.0203558i
$761$	1.97901	−	26.4080i	0.0717390	−	0.957291i	−0.838953	−	0.544204i	$-0.816832\pi$
$761$	1.97901	−	26.4080i	0.0717390	−	0.957291i	0.910692	−	0.413087i	$-0.135549\pi$
$762$	37.1039	−	17.8683i	1.34413	−	0.647300i
$763$		0			0
$764$	−6.05630	−	2.91656i	−0.219109	−	0.105518i
$765$	−6.27532	+	10.8692i	−0.226885	+	0.392976i
$766$	−8.39867	−	14.5469i	−0.303456	−	0.525601i
$767$	−0.561936	−	7.49851i	−0.0202903	−	0.270755i
$768$	−1.12318	−	2.86182i	−0.0405293	−	0.103267i
$769$	11.1387	−	48.8018i	0.401671	−	1.75984i	−0.218960	−	0.975734i	$-0.570266\pi$
$769$	11.1387	−	48.8018i	0.401671	−	1.75984i	0.620631	−	0.784103i	$-0.286877\pi$
$770$		0			0
$771$	9.17201	+	40.1852i	0.330322	+	1.44724i
$772$	−1.91736	+	1.30723i	−0.0690072	+	0.0470483i
$773$	6.94924	−	6.44795i	0.249947	−	0.231917i	−0.545242	−	0.838279i	$-0.683562\pi$
$773$	6.94924	−	6.44795i	0.249947	−	0.231917i	0.795189	+	0.606362i	$0.207372\pi$
$774$	8.65413	+	1.30440i	0.311066	+	0.0468857i
$775$	7.64351	+	7.09214i	0.274563	+	0.254757i
$776$	−10.2247	−	12.8214i	−0.367046	−	0.460261i
$777$		0			0
$778$	7.22891	−	9.06477i	0.259169	−	0.324988i
$779$	−1.28833	+	0.194185i	−0.0461594	+	0.00695740i
$780$	−18.3770	−	12.5292i	−0.658001	−	0.448618i
$781$	15.6520	−	39.8807i	0.560073	−	1.42704i
$782$	−5.77394	−	1.78102i	−0.206476	−	0.0636893i
$783$	−45.2527			−1.61720
$784$		0			0
$785$	39.8052			1.42071
$786$	57.1036	+	17.6141i	2.03682	+	0.628275i
$787$	−15.9380	+	40.6093i	−0.568128	+	1.44757i	0.301311	+	0.953526i	$0.402576\pi$
$787$	−15.9380	+	40.6093i	−0.568128	+	1.44757i	−0.869439	+	0.494040i	$0.835520\pi$
$788$	7.20733	+	4.91387i	0.256750	+	0.175049i
$789$	−32.1104	+	4.83986i	−1.14316	+	0.172304i
$790$	−21.1663	+	26.5417i	−0.753063	+	0.944311i
$791$		0			0
$792$	−12.1695	−	15.2601i	−0.432425	−	0.542244i
$793$	−9.46035	−	8.77793i	−0.335947	−	0.311713i
$794$	13.5010	+	2.03496i	0.479134	+	0.0722179i
$795$	−31.9514	+	29.6466i	−1.13320	+	1.05146i
$796$	−8.82344	+	6.01572i	−0.312738	+	0.213221i
$797$	1.46387	+	6.41362i	0.0518528	+	0.227182i	0.994214	−	0.107414i	$-0.0342572\pi$
$797$	1.46387	+	6.41362i	0.0518528	+	0.227182i	−0.942362	+	0.334596i	$0.891400\pi$
$798$		0			0
$799$	0.151706	−	0.664666i	0.00536696	−	0.0235142i
$800$	−1.51723	−	3.86585i	−0.0536423	−	0.136678i
$801$	0.574355	+	7.66424i	0.0202938	+	0.270803i
$802$	6.04109	+	10.4635i	0.213318	+	0.369478i
$803$	−6.29121	+	10.8967i	−0.222012	+	0.384536i
$804$	17.5136	+	8.43411i	0.617658	+	0.297448i
$805$		0			0
$806$	5.40942	−	2.60504i	0.190539	−	0.0917586i
$807$	2.73851	−	36.5429i	0.0964002	−	1.28637i
$808$	−13.7313	+	4.23555i	−0.483066	+	0.149006i
$809$	34.2505	−	10.5649i	1.20418	−	0.371441i	0.373206	−	0.927749i	$-0.378259\pi$
$809$	34.2505	−	10.5649i	1.20418	−	0.371441i	0.830977	+	0.556307i	$0.187782\pi$
$810$	2.99968	−	40.0280i	0.105398	−	1.40644i
$811$	−23.6835	+	11.4054i	−0.831642	+	0.400498i	−0.800731	−	0.599025i	$-0.795555\pi$
$811$	−23.6835	+	11.4054i	−0.831642	+	0.400498i	−0.0309111	+	0.999522i	$0.509841\pi$
$812$		0			0
$813$	68.8871	+	33.1743i	2.41597	+	1.16347i
$814$	−9.71741	+	16.8310i	−0.340595	+	0.589928i
$815$	20.2862	+	35.1368i	0.710596	+	1.23079i
$816$	0.147730	+	1.97132i	0.00517159	+	0.0690100i
$817$	0.311882	+	0.794662i	0.0109114	+	0.0278017i
$818$	−5.60014	+	24.5358i	−0.195804	+	0.857874i
$819$		0			0
$820$	1.39381	+	6.10667i	0.0486739	+	0.213254i
$821$	28.9211	−	19.7181i	1.00935	−	0.688166i	0.0586537	−	0.998278i	$-0.481319\pi$
$821$	28.9211	−	19.7181i	1.00935	−	0.688166i	0.950700	+	0.310113i	$0.100367\pi$
$822$	−17.7726	+	16.4905i	−0.619889	+	0.575173i
$823$	−26.7540	−	4.03252i	−0.932587	−	0.140565i	−0.334863	−	0.942267i	$-0.608690\pi$
$823$	−26.7540	−	4.03252i	−0.932587	−	0.140565i	−0.597724	+	0.801702i	$0.703928\pi$
$824$	−11.9724	−	11.1088i	−0.417078	−	0.386992i
$825$	−24.0832	−	30.1994i	−0.838471	−	1.05141i
$826$		0			0
$827$	−19.5888	+	24.5635i	−0.681168	+	0.854157i	−0.995461	−	0.0951686i	$-0.969661\pi$
$827$	−19.5888	+	24.5635i	−0.681168	+	0.854157i	0.314293	+	0.949326i	$0.398232\pi$
$828$	59.9476	−	9.03565i	2.08332	−	0.314011i
$829$	−15.7930	−	10.7675i	−0.548513	−	0.373970i	0.257125	−	0.966378i	$-0.417225\pi$
$829$	−15.7930	−	10.7675i	−0.548513	−	0.373970i	−0.805638	+	0.592408i	$0.798177\pi$
$830$	8.42749	−	21.4729i	0.292522	−	0.745335i
$831$	−81.6096	−	25.1732i	−2.83101	−	0.873250i
$832$	−2.39132			−0.0829040
$833$		0			0
$834$	−0.901375			−0.0312121
$835$	27.4133	+	8.45587i	0.948675	+	0.292628i
$836$	0.695557	−	1.77225i	0.0240563	−	0.0612946i
$837$	22.0128	+	15.0080i	0.760872	+	0.518754i
$838$	21.2910	−	3.20909i	0.735484	−	0.110856i
$839$	6.82417	−	8.55724i	0.235597	−	0.295429i	−0.649952	−	0.759975i	$-0.725211\pi$
$839$	6.82417	−	8.55724i	0.235597	−	0.295429i	0.885549	+	0.464546i	$0.153783\pi$
$840$		0			0
$841$	−6.74187	−	8.45403i	−0.232478	−	0.291518i
$842$	−20.5221	−	19.0418i	−0.707240	−	0.656223i
$843$	−94.8162	−	14.2912i	−3.26564	−	0.492217i
$844$	10.4258	−	9.67373i	0.358871	−	0.332984i
$845$	18.2017	−	12.4097i	0.626158	−	0.426908i
$846$	1.52210	+	6.66876i	0.0523309	+	0.229277i
$847$		0			0
$848$	−1.04279	+	4.56874i	−0.0358094	+	0.156891i
$849$	21.3212	+	54.3255i	0.731741	+	1.86445i
$850$	0.199559	+	2.66293i	0.00684482	+	0.0913378i
$851$	−30.1826	−	52.2778i	−1.03465	−	1.79206i
$852$	21.7677	−	37.7028i	0.745750	−	1.29168i
$853$	44.1593	+	21.2660i	1.51199	+	0.728134i	0.992023	−	0.126056i	$-0.0402318\pi$
$853$	44.1593	+	21.2660i	1.51199	+	0.728134i	0.519962	+	0.854189i	$0.325946\pi$
$854$		0			0
$855$	11.0664	−	5.32932i	0.378464	−	0.182259i
$856$	−1.24678	+	16.6371i	−0.0426141	+	0.568645i
$857$	−10.5765	+	3.26243i	−0.361287	+	0.111442i	−0.470084	−	0.882622i	$-0.655776\pi$
$857$	−10.5765	+	3.26243i	−0.361287	+	0.111442i	0.108797	+	0.994064i	$0.465300\pi$
$858$	−21.2536	+	6.55587i	−0.725586	+	0.223814i
$859$	−1.10439	+	14.7371i	−0.0376813	+	0.502823i	0.946150	+	0.323727i	$0.104936\pi$
$859$	−1.10439	+	14.7371i	−0.0376813	+	0.502823i	−0.983832	+	0.179095i	$0.942683\pi$
$860$	3.69766	−	1.78070i	0.126089	−	0.0607214i
$861$		0			0
$862$	−15.9286	−	7.67081i	−0.542530	−	0.261269i
$863$	3.53496	−	6.12273i	0.120331	−	0.208420i	−0.799567	−	0.600577i	$-0.794938\pi$
$863$	3.53496	−	6.12273i	0.120331	−	0.208420i	0.919898	+	0.392157i	$0.128271\pi$
$864$	−5.30561	−	9.18958i	−0.180500	−	0.312636i
$865$	0.237954	+	3.17527i	0.00809068	+	0.107963i
$866$	0.431176	+	1.09862i	0.0146519	+	0.0373326i
$867$	−11.3469	+	49.7141i	−0.385361	+	1.68838i
$868$		0			0
$869$	7.55417	+	33.0970i	0.256258	+	1.12274i
$870$	−32.7730	+	22.3443i	−1.11111	+	0.757541i
$871$	11.0837	−	10.2842i	0.375558	−	0.348467i
$872$	1.64654	+	0.248176i	0.0557590	+	0.00840431i
$873$	−77.5570	−	71.9624i	−2.62491	−	2.43556i
$874$	3.68697	+	4.62332i	0.124714	+	0.156386i
$875$		0			0
$876$	−7.97196	+	9.99653i	−0.269348	+	0.337751i
$877$	−47.6558	+	7.18295i	−1.60922	+	0.242551i	−0.891247	−	0.453518i	$-0.850169\pi$
$877$	−47.6558	+	7.18295i	−1.60922	+	0.242551i	−0.717974	+	0.696069i	$0.754931\pi$
$878$	17.6401	+	12.0268i	0.595323	+	0.405885i
$879$	−22.0390	+	56.1545i	−0.743357	+	1.89404i
$880$	−8.74629	−	2.69787i	−0.294837	−	0.0909453i
$881$	5.91801			0.199383			0.0996915	−	0.995018i	$-0.468214\pi$
$881$	5.91801			0.199383			0.0996915	+	0.995018i	$0.468214\pi$
$882$		0			0
$883$	−29.4616			−0.991461			−0.495730	−	0.868477i	$-0.665100\pi$
$883$	−29.4616			−0.991461			−0.495730	+	0.868477i	$0.665100\pi$
$884$	1.46934	+	0.453232i	0.0494193	+	0.0152438i
$885$	10.6852	−	27.2255i	0.359180	−	0.915176i
$886$	−7.12449	−	4.85740i	−0.239352	−	0.163187i
$887$	−22.9909	+	3.46532i	−0.771960	+	0.116354i	−0.523199	−	0.852211i	$-0.675261\pi$
$887$	−22.9909	+	3.46532i	−0.771960	+	0.116354i	−0.248761	+	0.968565i	$0.580023\pi$
$888$	−12.3135	+	15.4406i	−0.413214	+	0.518154i
$889$		0			0
$890$	2.24714	+	2.81783i	0.0753244	+	0.0944538i
$891$	−29.4248	−	27.3023i	−0.985770	−	0.914660i
$892$	9.58749	+	1.44508i	0.321013	+	0.0483849i
$893$	−0.489100	+	0.453819i	−0.0163671	+	0.0151865i
$894$	−18.0181	+	12.2845i	−0.602615	+	0.410856i
$895$	−6.86137	−	30.0616i	−0.229350	−	1.00485i
$896$		0			0
$897$	15.3725	−	67.3515i	0.513274	−	2.24880i
$898$	−6.11868	−	15.5901i	−0.204183	−	0.520250i
$899$	−0.800163	−	10.6774i	−0.0266869	−	0.356112i
$900$	−13.3964	−	23.2032i	−0.446547	−	0.773442i
$901$	1.50666	−	2.60962i	0.0501942	−	0.0869389i
$902$	5.64341	+	2.71773i	0.187905	+	0.0904903i
$903$		0			0
$904$	−8.33917	+	4.01593i	−0.277357	+	0.133568i
$905$	−3.13784	+	41.8716i	−0.104305	+	1.39186i
$906$	34.6566	−	10.6902i	1.15139	−	0.355157i
$907$	16.1483	−	4.98110i	0.536196	−	0.165395i	−0.0148183	−	0.999890i	$-0.504717\pi$
$907$	16.1483	−	4.98110i	0.536196	−	0.165395i	0.551015	+	0.834496i	$0.314241\pi$
$908$	−0.463027	+	6.17866i	−0.0153661	+	0.205046i
$909$	−83.5261	+	40.2241i	−2.77039	+	1.33415i
$910$		0			0
$911$	−43.4454	−	20.9222i	−1.43941	−	0.693183i	−0.458688	−	0.888597i	$-0.651680\pi$
$911$	−43.4454	−	20.9222i	−1.43941	−	0.693183i	−0.980721	+	0.195415i	$0.937395\pi$
$912$	0.967332	−	1.67547i	0.0320316	−	0.0554803i
$913$	−11.5337	−	19.9770i	−0.381711	−	0.661142i
$914$	−0.599019	−	7.99335i	−0.0198138	−	0.264397i
$915$	−18.3386	−	46.7259i	−0.606254	−	1.54471i
$916$	−0.121790	+	0.533597i	−0.00402406	+	0.0176305i
$917$		0			0
$918$	1.51830	+	6.65211i	0.0501114	+	0.219552i
$919$	−8.67910	+	5.91731i	−0.286297	+	0.195194i	−0.697950	−	0.716147i	$-0.745904\pi$
$919$	−8.67910	+	5.91731i	−0.286297	+	0.195194i	0.411653	+	0.911341i	$0.364952\pi$
$920$	20.8402	−	19.3368i	0.687080	−	0.637517i
$921$	64.0072	+	9.64753i	2.10911	+	0.317897i
$922$	13.2787	+	12.3209i	0.437312	+	0.405766i
$923$	−21.1134	−	26.4754i	−0.694956	−	0.871447i
$924$		0			0
$925$	−16.6335	+	20.8578i	−0.546906	+	0.685799i
$926$	5.26123	−	0.793002i	0.172895	−	0.0260597i
$927$	−87.0594	−	59.3561i	−2.85941	−	1.94951i
$928$	−1.55804	+	3.96981i	−0.0511451	+	0.130315i
$929$	33.6044	+	10.3656i	1.10252	+	0.340083i	0.792024	−	0.610490i	$-0.209028\pi$
$929$	33.6044	+	10.3656i	1.10252	+	0.340083i	0.310500	+	0.950574i	$0.399504\pi$
$930$	23.3526			0.765762
$931$		0			0
$932$	6.77776			0.222013
$933$	34.5936	+	10.6707i	1.13254	+	0.349343i
$934$	12.2593	−	31.2362i	0.401136	−	1.02208i
$935$	4.86281	+	3.31541i	0.159031	+	0.108425i
$936$	−15.2554	+	2.29938i	−0.498638	+	0.0751575i
$937$	16.0560	−	20.1336i	0.524527	−	0.657736i	−0.447036	−	0.894516i	$-0.647520\pi$
$937$	16.0560	−	20.1336i	0.524527	−	0.657736i	0.971563	+	0.236779i	$0.0760919\pi$
$938$		0			0
$939$	−41.1200	−	51.5628i	−1.34190	−	1.68269i
$940$	2.35138	+	2.18177i	0.0766937	+	0.0711614i
$941$	1.02742	+	0.154858i	0.0334928	+	0.00504822i	0.165767	−	0.986165i	$-0.446990\pi$
$941$	1.02742	+	0.154858i	0.0334928	+	0.00504822i	−0.132274	+	0.991213i	$0.542228\pi$
$942$	29.6514	−	27.5125i	0.966095	−	0.896406i
$943$	−16.0747	+	10.9596i	−0.523466	+	0.356893i
$944$	−0.699721	−	3.06568i	−0.0227740	−	0.0997793i
$945$		0			0
$946$	0.913247	−	4.00120i	0.0296922	−	0.130090i
$947$	−12.4948	−	31.8362i	−0.406026	−	1.03454i	−0.976938	−	0.213525i	$-0.931505\pi$
$947$	−12.4948	−	31.8362i	−0.406026	−	1.03454i	0.570912	−	0.821011i	$-0.306590\pi$
$948$	2.57800	+	34.4010i	0.0837295	+	1.11729i
$949$	4.97269	+	8.61296i	0.161420	+	0.279588i
$950$	1.30671	−	2.26328i	0.0423952	−	0.0734306i
$951$	82.2194	+	39.5948i	2.66615	+	1.28395i
$952$		0			0
$953$	19.4727	−	9.37756i	0.630783	−	0.303769i	−0.0910396	−	0.995847i	$-0.529019\pi$
$953$	19.4727	−	9.37756i	0.630783	−	0.303769i	0.721822	+	0.692078i	$0.243305\pi$
$954$	−2.25935	+	30.1489i	−0.0731491	+	0.976107i
$955$	−19.4331	+	5.99431i	−0.628840	+	0.193971i
$956$	−6.49938	+	2.00479i	−0.210205	+	0.0648396i
$957$	−2.96419	+	39.5544i	−0.0958187	+	1.27861i
$958$	−15.0845	+	7.26429i	−0.487357	+	0.234699i
$959$		0			0
$960$	−8.37995	−	4.03557i	−0.270462	−	0.130247i
$961$	12.3481	−	21.3875i	0.398325	−	0.689919i
$962$	7.68082	+	13.3036i	0.247640	+	0.428924i
$963$	8.04366	+	107.335i	0.259203	+	3.45883i
$964$	9.52239	+	24.2626i	0.306695	+	0.781447i
$965$	−1.56224	+	6.84463i	−0.0502904	+	0.220336i
$966$		0			0
$967$	6.95133	+	30.4558i	0.223540	+	0.979392i	0.954790	+	0.297282i	$0.0960802\pi$
$967$	6.95133	+	30.4558i	0.223540	+	0.979392i	−0.731250	+	0.682110i	$0.761063\pi$
$968$	1.52612	−	1.04049i	0.0490515	−	0.0334427i
$969$	−0.911932	+	0.846149i	−0.0292955	+	0.0271822i
$970$	−49.0596	−	7.39455i	−1.57521	−	0.237425i
$971$	−6.22959	−	5.78022i	−0.199917	−	0.185496i	0.573861	−	0.818953i	$-0.305445\pi$
$971$	−6.22959	−	5.78022i	−0.199917	−	0.185496i	−0.773778	+	0.633457i	$0.781635\pi$
$972$	−5.58403	−	7.00215i	−0.179108	−	0.224594i
$973$		0			0
$974$	−16.6150	+	20.8346i	−0.532380	+	0.667583i
$975$	−30.1901	+	4.55043i	−0.966858	+	0.145730i
$976$	−4.45904	−	3.04012i	−0.142730	−	0.0973119i
$977$	0.795066	−	2.02580i	0.0254364	−	0.0648110i	−0.917591	−	0.397525i	$-0.869869\pi$
$977$	0.795066	−	2.02580i	0.0254364	−	0.0648110i	0.943028	+	0.332714i	$0.107964\pi$
$978$	39.3973	+	12.1525i	1.25979	+	0.388593i
$979$	3.60414			0.115189
$980$		0			0
$981$	10.7427			0.342989
$982$	−7.23039	−	2.23028i	−0.230731	−	0.0711711i
$983$	−10.0445	+	25.5929i	−0.320369	+	0.816287i	0.676442	+	0.736496i	$0.263521\pi$
$983$	−10.0445	+	25.5929i	−0.320369	+	0.816287i	−0.996812	+	0.0797918i	$0.974574\pi$
$984$	5.25907	+	3.58558i	0.167653	+	0.114304i
$985$	26.0958	−	3.93331i	0.831481	−	0.125326i
$986$	1.70974	−	2.14395i	0.0544493	−	0.0682772i
$987$		0			0
$988$	−0.938255	−	1.17653i	−0.0298499	−	0.0374305i
$989$	9.34455	+	8.67048i	0.297139	+	0.275705i
$990$	−58.3910	−	8.80103i	−1.85579	−	0.279715i
$991$	0.462608	−	0.429238i	0.0146952	−	0.0136352i	−0.672791	−	0.739833i	$-0.734905\pi$
$991$	0.462608	−	0.429238i	0.0146952	−	0.0136352i	0.687486	+	0.726197i	$0.258714\pi$
$992$	2.07448	−	1.41436i	0.0658648	−	0.0449059i
$993$	−0.561607	−	2.46056i	−0.0178220	−	0.0780835i
$994$		0			0
$995$	−7.18924	+	31.4981i	−0.227914	+	0.998558i
$996$	−8.56386	−	21.8204i	−0.271356	−	0.691405i
$997$	1.53156	+	20.4372i	0.0485049	+	0.647252i	0.967482	+	0.252941i	$0.0813978\pi$
$997$	1.53156	+	20.4372i	0.0485049	+	0.647252i	−0.918977	+	0.394311i	$0.870983\pi$
$998$	−5.24361	−	9.08221i	−0.165984	−	0.287492i
$999$	−34.0828	+	59.0332i	−1.07833	+	1.86773i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	686.2.g.h.471.1		36
7.2	even	3		98.2.e.b.85.1	yes	18
7.3	odd	6		686.2.g.g.655.1		36
7.4	even	3	inner	686.2.g.h.655.3		36
7.5	odd	6		686.2.e.b.589.3		18
7.6	odd	2		686.2.g.g.471.3		36
21.2	odd	6		882.2.u.g.379.3		18
28.23	odd	6		784.2.u.d.673.3		18
49.5	odd	42		4802.2.a.c.1.9		9
49.9	even	21		98.2.e.b.15.1	✓	18
49.15	even	7	inner	686.2.g.h.177.3		36
49.24	odd	42		686.2.g.g.67.3		36
49.25	even	21	inner	686.2.g.h.67.1		36
49.34	odd	14		686.2.g.g.177.1		36
49.40	odd	42		686.2.e.b.99.3		18
49.44	even	21		4802.2.a.d.1.1		9
147.107	odd	42		882.2.u.g.505.3		18
196.107	odd	42		784.2.u.d.113.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.e.b.15.1	✓	18	49.9	even	21
98.2.e.b.85.1	yes	18	7.2	even	3
686.2.e.b.99.3		18	49.40	odd	42
686.2.e.b.589.3		18	7.5	odd	6
686.2.g.g.67.3		36	49.24	odd	42
686.2.g.g.177.1		36	49.34	odd	14
686.2.g.g.471.3		36	7.6	odd	2
686.2.g.g.655.1		36	7.3	odd	6
686.2.g.h.67.1		36	49.25	even	21	inner
686.2.g.h.177.3		36	49.15	even	7	inner
686.2.g.h.471.1		36	1.1	even	1	trivial
686.2.g.h.655.3		36	7.4	even	3	inner
784.2.u.d.113.3		18	196.107	odd	42
784.2.u.d.673.3		18	28.23	odd	6
882.2.u.g.379.3		18	21.2	odd	6
882.2.u.g.505.3		18	147.107	odd	42
4802.2.a.c.1.9		9	49.5	odd	42
4802.2.a.d.1.1		9	49.44	even	21

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 686 = 2 \cdot 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	686.g (of order \(21\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.955573 - 0.294755i) q^{2} +(-1.12318 + 2.86182i) q^{3} +(0.826239 + 0.563320i) q^{4} +(2.99159 - 0.450910i) q^{5} +(1.91682 - 2.40361i) q^{6} +(-0.623490 - 0.781831i) q^{8} +(-4.72932 - 4.38817i) q^{9} +O(q^{10})\)	\(q+(-0.955573 - 0.294755i) q^{2} +(-1.12318 + 2.86182i) q^{3} +(0.826239 + 0.563320i) q^{4} +(2.99159 - 0.450910i) q^{5} +(1.91682 - 2.40361i) q^{6} +(-0.623490 - 0.781831i) q^{8} +(-4.72932 - 4.38817i) q^{9} +(-2.99159 - 0.450910i) q^{10} +(-2.21776 + 2.05778i) q^{11} +(-2.54014 + 1.73184i) q^{12} +(0.532118 + 2.33136i) q^{13} +(-2.06968 + 9.06784i) q^{15} +(0.365341 + 0.930874i) q^{16} +(-0.0480527 - 0.641218i) q^{17} +(3.22577 + 5.58720i) q^{18} +(-0.314647 + 0.544985i) q^{19} +(2.72577 + 1.31266i) q^{20} +(2.72577 - 1.31266i) q^{22} +(-0.702234 + 9.37066i) q^{23} +(2.93775 - 0.906177i) q^{24} +(3.96842 - 1.22410i) q^{25} +(0.178703 - 2.38463i) q^{26} +(9.56038 - 4.60404i) q^{27} +(-3.84228 - 1.85034i) q^{29} +(4.65052 - 8.05494i) q^{30} +(1.25538 + 2.17437i) q^{31} +(-0.0747301 - 0.997204i) q^{32} +(-3.39805 - 8.65809i) q^{33} +(-0.143085 + 0.626894i) q^{34} +(-1.43560 - 6.28979i) q^{36} +(-5.30769 + 3.61872i) q^{37} +(0.461306 - 0.428029i) q^{38} +(-7.26960 - 1.09572i) q^{39} +(-2.21776 - 2.05778i) q^{40} +(1.29087 + 1.61870i) q^{41} +(0.845798 - 1.06060i) q^{43} +(-2.99159 + 0.450910i) q^{44} +(-16.1268 - 10.9951i) q^{45} +(3.43309 - 8.74736i) q^{46} +(1.01315 + 0.312515i) q^{47} -3.07434 q^{48} -4.15293 q^{50} +(1.88902 + 0.582686i) q^{51} +(-0.873646 + 2.22601i) q^{52} +(3.87195 + 2.63985i) q^{53} +(-10.4927 + 1.58152i) q^{54} +(-5.70676 + 7.15605i) q^{55} +(-1.20624 - 1.51258i) q^{57} +(3.12618 + 2.90067i) q^{58} +(-3.10939 - 0.468666i) q^{59} +(-6.81814 + 6.32631i) q^{60} +(-4.45904 + 3.04012i) q^{61} +(-0.558695 - 2.44780i) q^{62} +(-0.222521 + 0.974928i) q^{64} +(2.64311 + 6.73454i) q^{65} +(0.695067 + 9.27503i) q^{66} +(-3.16144 - 5.47577i) q^{67} +(0.321508 - 0.556868i) q^{68} +(-26.0284 - 12.5346i) q^{69} +(-12.7586 + 6.14419i) q^{71} +(-0.482125 + 6.43351i) q^{72} +(3.97419 - 1.22587i) q^{73} +(6.13853 - 1.89348i) q^{74} +(-0.954116 + 12.7318i) q^{75} +(-0.566975 + 0.273041i) q^{76} +(6.62367 + 3.18979i) q^{78} +(5.61055 - 9.71776i) q^{79} +(1.51269 + 2.62006i) q^{80} +(0.991505 + 13.2307i) q^{81} +(-0.756398 - 1.92727i) q^{82} +(-1.69664 + 7.43348i) q^{83} +(-0.432885 - 1.89659i) q^{85} +(-1.12084 + 0.764175i) q^{86} +(9.61093 - 8.91764i) q^{87} +(2.99159 + 0.450910i) q^{88} +(-0.873285 - 0.810290i) q^{89} +(12.1695 + 15.2601i) q^{90} +(-5.85889 + 7.34682i) q^{92} +(-7.63268 + 1.15044i) q^{93} +(-0.876021 - 0.597261i) q^{94} +(-0.695557 + 1.77225i) q^{95} +(2.93775 + 0.906177i) q^{96} +16.3992 q^{97} +19.5184 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} + 5 q^{3} + 3 q^{4} + 10 q^{6} + 6 q^{8} + 10 q^{9}+O(q^{10}) \) 36 * q - 3 * q^2 + 5 * q^3 + 3 * q^4 + 10 * q^6 + 6 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} + 5 q^{3} + 3 q^{4} + 10 q^{6} + 6 q^{8} + 10 q^{9} - 7 q^{11} - 2 q^{12} - 20 q^{13} + 14 q^{15} + 3 q^{16} - q^{17} + 32 q^{18} + 44 q^{19} + 14 q^{20} + 14 q^{22} - 21 q^{23} + 2 q^{24} - q^{25} - 3 q^{26} + 20 q^{27} + 22 q^{29} + 24 q^{31} - 3 q^{32} + 14 q^{33} - 2 q^{34} - 20 q^{36} + 13 q^{37} + 19 q^{38} + 3 q^{39} - 7 q^{40} + 16 q^{41} - 48 q^{43} - 98 q^{45} - 21 q^{46} - 40 q^{47} + 4 q^{48} - 100 q^{50} - 36 q^{51} - 18 q^{52} - 10 q^{53} - 4 q^{54} + 98 q^{55} + 38 q^{57} - 24 q^{58} - 13 q^{59} - 7 q^{60} - 27 q^{61} - 22 q^{62} - 6 q^{64} + 21 q^{66} + 86 q^{67} + 34 q^{68} - 182 q^{69} - 3 q^{72} - 5 q^{73} - 13 q^{74} + 3 q^{75} - 4 q^{76} + 76 q^{78} + 66 q^{79} + 2 q^{81} + 8 q^{82} + 110 q^{83} - 98 q^{85} + 18 q^{86} + 110 q^{87} - 62 q^{89} + 42 q^{90} - 42 q^{92} - 46 q^{93} - 23 q^{94} + 7 q^{95} + 2 q^{96} - 64 q^{97} + 28 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 + 5 * q^3 + 3 * q^4 + 10 * q^6 + 6 * q^8 + 10 * q^9 - 7 * q^11 - 2 * q^12 - 20 * q^13 + 14 * q^15 + 3 * q^16 - q^17 + 32 * q^18 + 44 * q^19 + 14 * q^20 + 14 * q^22 - 21 * q^23 + 2 * q^24 - q^25 - 3 * q^26 + 20 * q^27 + 22 * q^29 + 24 * q^31 - 3 * q^32 + 14 * q^33 - 2 * q^34 - 20 * q^36 + 13 * q^37 + 19 * q^38 + 3 * q^39 - 7 * q^40 + 16 * q^41 - 48 * q^43 - 98 * q^45 - 21 * q^46 - 40 * q^47 + 4 * q^48 - 100 * q^50 - 36 * q^51 - 18 * q^52 - 10 * q^53 - 4 * q^54 + 98 * q^55 + 38 * q^57 - 24 * q^58 - 13 * q^59 - 7 * q^60 - 27 * q^61 - 22 * q^62 - 6 * q^64 + 21 * q^66 + 86 * q^67 + 34 * q^68 - 182 * q^69 - 3 * q^72 - 5 * q^73 - 13 * q^74 + 3 * q^75 - 4 * q^76 + 76 * q^78 + 66 * q^79 + 2 * q^81 + 8 * q^82 + 110 * q^83 - 98 * q^85 + 18 * q^86 + 110 * q^87 - 62 * q^89 + 42 * q^90 - 42 * q^92 - 46 * q^93 - 23 * q^94 + 7 * q^95 + 2 * q^96 - 64 * q^97 + 28 * q^99

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