LMFDB - Embedded newform 57.2.i.a.28.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [57,2,Mod(4,57)] 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("57.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(57, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	57.i (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.455147291521$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			28.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	57.28
Dual form			57.2.i.a.55.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.326352 + 1.85083i) q^{2} +(-0.766044 + 0.642788i) q^{3} +(-1.43969 + 0.524005i) q^{4} +(-0.826352 - 0.300767i) q^{5} +(-1.43969 - 1.20805i) q^{6} +(1.43969 - 2.49362i) q^{7} +(0.439693 + 0.761570i) q^{8} +(0.173648 - 0.984808i) q^{9} +(0.286989 - 1.62760i) q^{10} +(0.918748 + 1.59132i) q^{11} +(0.766044 - 1.32683i) q^{12} +(-2.11334 - 1.77330i) q^{13} +(5.08512 + 1.85083i) q^{14} +(0.826352 - 0.300767i) q^{15} +(-3.61334 + 3.03195i) q^{16} +(-1.23396 - 6.99811i) q^{17} +1.87939 q^{18} +(3.93969 + 1.86516i) q^{19} +1.34730 q^{20} +(0.500000 + 2.83564i) q^{21} +(-2.64543 + 2.21978i) q^{22} +(-6.19846 + 2.25606i) q^{23} +(-0.826352 - 0.300767i) q^{24} +(-3.23783 - 2.71686i) q^{25} +(2.59240 - 4.49016i) q^{26} +(0.500000 + 0.866025i) q^{27} +(-0.766044 + 4.34445i) q^{28} +(-0.543233 + 3.08083i) q^{29} +(0.826352 + 1.43128i) q^{30} +(-3.82635 + 6.62744i) q^{31} +(-5.44356 - 4.56769i) q^{32} +(-1.72668 - 0.628461i) q^{33} +(12.5496 - 4.56769i) q^{34} +(-1.93969 + 1.62760i) q^{35} +(0.266044 + 1.50881i) q^{36} +2.83750 q^{37} +(-2.16637 + 7.90041i) q^{38} +2.75877 q^{39} +(-0.134285 - 0.761570i) q^{40} +(3.05303 - 2.56180i) q^{41} +(-5.08512 + 1.85083i) q^{42} +(10.7626 + 3.91728i) q^{43} +(-2.15657 - 1.80958i) q^{44} +(-0.439693 + 0.761570i) q^{45} +(-6.19846 - 10.7361i) q^{46} +(0.383256 - 2.17355i) q^{47} +(0.819078 - 4.64522i) q^{48} +(-0.645430 - 1.11792i) q^{49} +(3.97178 - 6.87933i) q^{50} +(5.44356 + 4.56769i) q^{51} +(3.97178 + 1.44561i) q^{52} +(-2.53936 + 0.924252i) q^{53} +(-1.43969 + 1.20805i) q^{54} +(-0.280592 - 1.59132i) q^{55} +2.53209 q^{56} +(-4.21688 + 1.10359i) q^{57} -5.87939 q^{58} +(-1.46064 - 8.28368i) q^{59} +(-1.03209 + 0.866025i) q^{60} +(-0.578726 + 0.210639i) q^{61} +(-13.5150 - 4.91906i) q^{62} +(-2.20574 - 1.85083i) q^{63} +(1.96064 - 3.39592i) q^{64} +(1.21301 + 2.10100i) q^{65} +(0.599670 - 3.40090i) q^{66} +(-0.638156 + 3.61916i) q^{67} +(5.44356 + 9.42853i) q^{68} +(3.29813 - 5.71253i) q^{69} +(-3.64543 - 3.05888i) q^{70} +(7.00387 + 2.54920i) q^{71} +(0.826352 - 0.300767i) q^{72} +(-7.66637 + 6.43285i) q^{73} +(0.926022 + 5.25173i) q^{74} +4.22668 q^{75} +(-6.64930 - 0.620838i) q^{76} +5.29086 q^{77} +(0.900330 + 5.10602i) q^{78} +(1.23396 - 1.03541i) q^{79} +(3.89780 - 1.41868i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(5.73783 + 4.81461i) q^{82} +(-0.492726 + 0.853427i) q^{83} +(-2.20574 - 3.82045i) q^{84} +(-1.08512 + 6.15403i) q^{85} +(-3.73783 + 21.1983i) q^{86} +(-1.56418 - 2.70924i) q^{87} +(-0.807934 + 1.39938i) q^{88} +(13.0667 + 10.9643i) q^{89} +(-1.55303 - 0.565258i) q^{90} +(-7.46451 + 2.71686i) q^{91} +(7.74170 - 6.49605i) q^{92} +(-1.32888 - 7.53644i) q^{93} +4.14796 q^{94} +(-2.69459 - 2.72621i) q^{95} +7.10607 q^{96} +(-1.02481 - 5.81201i) q^{97} +(1.85844 - 1.55942i) q^{98} +(1.72668 - 0.628461i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} - 6 q^{10} + 3 q^{11} - 6 q^{13} + 9 q^{14} + 6 q^{15} - 15 q^{16} - 12 q^{17} + 18 q^{19} + 6 q^{20} + 3 q^{21} - 9 q^{23} - 6 q^{24} + 12 q^{26}+ \cdots - 3 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 - 6 * q^10 + 3 * q^11 - 6 * q^13 + 9 * q^14 + 6 * q^15 - 15 * q^16 - 12 * q^17 + 18 * q^19 + 6 * q^20 + 3 * q^21 - 9 * q^23 - 6 * q^24 + 12 * q^26 + 3 * q^27 + 12 * q^29 + 6 * q^30 - 24 * q^31 - 3 * q^32 + 3 * q^33 + 21 * q^34 - 6 * q^35 - 3 * q^36 + 12 * q^37 + 6 * q^38 - 6 * q^39 + 9 * q^40 + 6 * q^41 - 9 * q^42 + 18 * q^43 + 9 * q^44 + 3 * q^45 - 9 * q^46 - 33 * q^47 - 12 * q^48 + 12 * q^49 + 9 * q^50 + 3 * q^51 + 9 * q^52 - 24 * q^53 - 3 * q^54 - 33 * q^55 + 6 * q^56 - 9 * q^57 - 24 * q^58 + 3 * q^60 - 21 * q^61 - 51 * q^62 - 3 * q^63 + 3 * q^64 + 15 * q^65 + 18 * q^66 + 30 * q^67 + 3 * q^68 + 6 * q^69 - 6 * q^70 + 18 * q^71 + 6 * q^72 - 27 * q^73 + 21 * q^74 + 12 * q^75 - 9 * q^78 + 12 * q^79 + 24 * q^80 + 15 * q^82 + 15 * q^83 - 3 * q^84 + 15 * q^85 - 3 * q^86 + 9 * q^87 + 6 * q^88 + 45 * q^89 + 3 * q^90 - 12 * q^91 + 3 * q^92 + 6 * q^93 - 6 * q^94 - 12 * q^95 + 18 * q^96 + 21 * q^97 + 3 * q^98 - 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.326352	+	1.85083i	0.230766	+	1.30874i	0.851350	+	0.524597i	$0.175784\pi$
$2$	0.326352	+	1.85083i	0.230766	+	1.30874i	−0.620585	+	0.784139i	$0.713105\pi$
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$4$	−1.43969	+	0.524005i	−0.719846	+	0.262003i
$5$	−0.826352	−	0.300767i	−0.369556	−	0.134507i	0.150565	−	0.988600i	$-0.451891\pi$
$5$	−0.826352	−	0.300767i	−0.369556	−	0.134507i	−0.520121	+	0.854093i	$0.674113\pi$
$6$	−1.43969	−	1.20805i	−0.587752	−	0.493183i
$7$	1.43969	−	2.49362i	0.544153	−	0.942500i	−0.454507	−	0.890743i	$-0.650185\pi$
$7$	1.43969	−	2.49362i	0.544153	−	0.942500i	0.998660	−	0.0517569i	$-0.0164821\pi$
$8$	0.439693	+	0.761570i	0.155455	+	0.269256i
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$	0.286989	−	1.62760i	0.0907539	−	0.514691i
$11$	0.918748	+	1.59132i	0.277013	+	0.479801i	0.970641	−	0.240533i	$-0.0773222\pi$
$11$	0.918748	+	1.59132i	0.277013	+	0.479801i	−0.693628	+	0.720333i	$0.743989\pi$
$12$	0.766044	−	1.32683i	0.221138	−	0.383022i
$13$	−2.11334	−	1.77330i	−0.586135	−	0.491826i	0.300820	−	0.953681i	$-0.402740\pi$
$13$	−2.11334	−	1.77330i	−0.586135	−	0.491826i	−0.886955	+	0.461855i	$0.847184\pi$
$14$	5.08512	+	1.85083i	1.35906	+	0.494656i
$15$	0.826352	−	0.300767i	0.213363	−	0.0776578i
$16$	−3.61334	+	3.03195i	−0.903335	+	0.757988i
$17$	−1.23396	−	6.99811i	−0.299278	−	1.69729i	−0.649286	−	0.760544i	$-0.724932\pi$
$17$	−1.23396	−	6.99811i	−0.299278	−	1.69729i	0.350008	−	0.936747i	$-0.386179\pi$
$18$	1.87939			0.442975
$19$	3.93969	+	1.86516i	0.903827	+	0.427897i
$19$	3.93969	+	1.86516i	0.903827	+	0.427897i
$20$	1.34730			0.301265
$21$	0.500000	+	2.83564i	0.109109	+	0.618788i
$22$	−2.64543	+	2.21978i	−0.564008	+	0.473258i
$23$	−6.19846	+	2.25606i	−1.29247	+	0.470420i	−0.894537	−	0.446995i	$-0.852494\pi$
$23$	−6.19846	+	2.25606i	−1.29247	+	0.470420i	−0.397932	+	0.917415i	$0.630272\pi$
$24$	−0.826352	−	0.300767i	−0.168678	−	0.0613939i
$25$	−3.23783	−	2.71686i	−0.647565	−	0.543372i
$26$	2.59240	−	4.49016i	0.508411	−	0.880593i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	−0.766044	+	4.34445i	−0.144769	+	0.821025i
$29$	−0.543233	+	3.08083i	−0.100876	+	0.572096i	0.891912	+	0.452209i	$0.149364\pi$
$29$	−0.543233	+	3.08083i	−0.100876	+	0.572096i	−0.992788	+	0.119886i	$0.961747\pi$
$30$	0.826352	+	1.43128i	0.150871	+	0.261315i
$31$	−3.82635	+	6.62744i	−0.687233	+	1.19032i	0.285496	+	0.958380i	$0.407842\pi$
$31$	−3.82635	+	6.62744i	−0.687233	+	1.19032i	−0.972729	+	0.231943i	$0.925492\pi$
$32$	−5.44356	−	4.56769i	−0.962295	−	0.807461i
$33$	−1.72668	−	0.628461i	−0.300577	−	0.109401i
$34$	12.5496	−	4.56769i	2.15224	−	0.783353i
$35$	−1.93969	+	1.62760i	−0.327868	+	0.275114i
$36$	0.266044	+	1.50881i	0.0443407	+	0.251469i
$37$	2.83750			0.466481			0.233241	−	0.972419i	$-0.425067\pi$
$37$	2.83750			0.466481			0.233241	+	0.972419i	$0.425067\pi$
$38$	−2.16637	+	7.90041i	−0.351432	+	1.28162i
$39$	2.75877			0.441757
$40$	−0.134285	−	0.761570i	−0.0212324	−	0.120415i
$41$	3.05303	−	2.56180i	0.476804	−	0.400086i	−0.372465	−	0.928046i	$-0.621487\pi$
$41$	3.05303	−	2.56180i	0.476804	−	0.400086i	0.849269	+	0.527960i	$0.177043\pi$
$42$	−5.08512	+	1.85083i	−0.784651	+	0.285590i
$43$	10.7626	+	3.91728i	1.64129	+	0.597380i	0.987263	−	0.159094i	$-0.0508573\pi$
$43$	10.7626	+	3.91728i	1.64129	+	0.597380i	0.654024	+	0.756474i	$0.273080\pi$
$44$	−2.15657	−	1.80958i	−0.325116	−	0.272805i
$45$	−0.439693	+	0.761570i	−0.0655455	+	0.113528i
$46$	−6.19846	−	10.7361i	−0.913914	−	1.58294i
$47$	0.383256	−	2.17355i	0.0559036	−	0.317045i	−0.944014	−	0.329906i	$-0.892983\pi$
$47$	0.383256	−	2.17355i	0.0559036	−	0.317045i	0.999917	+	0.0128613i	$0.00409398\pi$
$48$	0.819078	−	4.64522i	0.118224	−	0.670480i
$49$	−0.645430	−	1.11792i	−0.0922042	−	0.159702i
$50$	3.97178	−	6.87933i	0.561695	−	0.972884i
$51$	5.44356	+	4.56769i	0.762251	+	0.639605i
$52$	3.97178	+	1.44561i	0.550787	+	0.200470i
$53$	−2.53936	+	0.924252i	−0.348808	+	0.126956i	−0.510482	−	0.859888i	$-0.670533\pi$
$53$	−2.53936	+	0.924252i	−0.348808	+	0.126956i	0.161674	+	0.986844i	$0.448311\pi$
$54$	−1.43969	+	1.20805i	−0.195917	+	0.164394i
$55$	−0.280592	−	1.59132i	−0.0378351	−	0.214573i
$56$	2.53209			0.338365
$57$	−4.21688	+	1.10359i	−0.558540	+	0.146174i
$58$	−5.87939			−0.772001
$59$	−1.46064	−	8.28368i	−0.190159	−	1.07844i	−0.919146	−	0.393917i	$-0.871120\pi$
$59$	−1.46064	−	8.28368i	−0.190159	−	1.07844i	0.728987	−	0.684527i	$-0.239991\pi$
$60$	−1.03209	+	0.866025i	−0.133242	+	0.111803i
$61$	−0.578726	+	0.210639i	−0.0740982	+	0.0269696i	−0.378803	−	0.925477i	$-0.623664\pi$
$61$	−0.578726	+	0.210639i	−0.0740982	+	0.0269696i	0.304705	+	0.952447i	$0.401442\pi$
$62$	−13.5150	−	4.91906i	−1.71641	−	0.624722i
$63$	−2.20574	−	1.85083i	−0.277897	−	0.233183i
$64$	1.96064	−	3.39592i	0.245080	−	0.424490i
$65$	1.21301	+	2.10100i	0.150456	+	0.260597i
$66$	0.599670	−	3.40090i	0.0738143	−	0.418622i
$67$	−0.638156	+	3.61916i	−0.0779631	+	0.442151i	0.920691	+	0.390292i	$0.127626\pi$
$67$	−0.638156	+	3.61916i	−0.0779631	+	0.442151i	−0.998654	+	0.0518592i	$0.983485\pi$
$68$	5.44356	+	9.42853i	0.660129	+	1.14338i
$69$	3.29813	−	5.71253i	0.397049	−	0.687708i
$70$	−3.64543	−	3.05888i	−0.435712	−	0.365606i
$71$	7.00387	+	2.54920i	0.831206	+	0.302534i	0.722354	−	0.691523i	$-0.243060\pi$
$71$	7.00387	+	2.54920i	0.831206	+	0.302534i	0.108853	+	0.994058i	$0.465282\pi$
$72$	0.826352	−	0.300767i	0.0973865	−	0.0354458i
$73$	−7.66637	+	6.43285i	−0.897281	+	0.752908i	−0.969657	−	0.244469i	$-0.921386\pi$
$73$	−7.66637	+	6.43285i	−0.897281	+	0.752908i	0.0723759	+	0.997377i	$0.476942\pi$
$74$	0.926022	+	5.25173i	0.107648	+	0.610501i
$75$	4.22668			0.488055
$76$	−6.64930	−	0.620838i	−0.762727	−	0.0712149i
$77$	5.29086			0.602949
$78$	0.900330	+	5.10602i	0.101942	+	0.578143i
$79$	1.23396	−	1.03541i	0.138831	−	0.116493i	−0.570728	−	0.821139i	$-0.693339\pi$
$79$	1.23396	−	1.03541i	0.138831	−	0.116493i	0.709559	+	0.704646i	$0.248894\pi$
$80$	3.89780	−	1.41868i	0.435788	−	0.158614i
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$	5.73783	+	4.81461i	0.633637	+	0.531684i
$83$	−0.492726	+	0.853427i	−0.0540837	+	0.0936757i	−0.891800	−	0.452430i	$-0.850557\pi$
$83$	−0.492726	+	0.853427i	−0.0540837	+	0.0936757i	0.837716	+	0.546106i	$0.183890\pi$
$84$	−2.20574	−	3.82045i	−0.240666	−	0.416845i
$85$	−1.08512	+	6.15403i	−0.117698	+	0.667499i
$86$	−3.73783	+	21.1983i	−0.403060	+	2.28587i
$87$	−1.56418	−	2.70924i	−0.167697	−	0.290461i
$88$	−0.807934	+	1.39938i	−0.0861260	+	0.149175i
$89$	13.0667	+	10.9643i	1.38507	+	1.16221i	0.967294	+	0.253659i	$0.0816341\pi$
$89$	13.0667	+	10.9643i	1.38507	+	1.16221i	0.417774	+	0.908551i	$0.362810\pi$
$90$	−1.55303	−	0.565258i	−0.163704	−	0.0595834i
$91$	−7.46451	+	2.71686i	−0.782493	+	0.284804i
$92$	7.74170	−	6.49605i	0.807128	−	0.677261i
$93$	−1.32888	−	7.53644i	−0.137798	−	0.781493i
$94$	4.14796			0.427829
$95$	−2.69459	−	2.72621i	−0.276459	−	0.279703i
$96$	7.10607			0.725260
$97$	−1.02481	−	5.81201i	−0.104054	−	0.590121i	−0.991594	−	0.129389i	$-0.958698\pi$
$97$	−1.02481	−	5.81201i	−0.104054	−	0.590121i	0.887540	−	0.460731i	$-0.152413\pi$
$98$	1.85844	−	1.55942i	0.187731	−	0.157525i
$99$	1.72668	−	0.628461i	0.173538	−	0.0631627i
$100$	6.08512	+	2.21480i	0.608512	+	0.221480i
$101$	−3.29813	−	2.76746i	−0.328177	−	0.275373i	0.463780	−	0.885950i	$-0.346493\pi$
$101$	−3.29813	−	2.76746i	−0.328177	−	0.275373i	−0.791956	+	0.610578i	$0.790937\pi$
$102$	−6.67752	+	11.5658i	−0.661173	+	1.14518i
$103$	−8.90420	−	15.4225i	−0.877357	−	1.51963i	−0.854231	−	0.519894i	$-0.825971\pi$
$103$	−8.90420	−	15.4225i	−0.877357	−	1.51963i	−0.0231262	−	0.999733i	$-0.507362\pi$
$104$	0.421274	−	2.38917i	0.0413093	−	0.234277i
$105$	0.439693	−	2.49362i	0.0429096	−	0.243352i
$106$	−2.53936	−	4.39831i	−0.246645	−	0.427201i
$107$	−2.94356	+	5.09840i	−0.284565	+	0.492881i	−0.972504	−	0.232888i	$-0.925182\pi$
$107$	−2.94356	+	5.09840i	−0.284565	+	0.492881i	0.687939	+	0.725769i	$0.258516\pi$
$108$	−1.17365	−	0.984808i	−0.112934	−	0.0947632i
$109$	−14.2023	−	5.16923i	−1.36034	−	0.495122i	−0.444178	−	0.895938i	$-0.646504\pi$
$109$	−14.2023	−	5.16923i	−1.36034	−	0.495122i	−0.916158	+	0.400816i	$0.868727\pi$
$110$	2.85369	−	1.03866i	0.272089	−	0.0990323i
$111$	−2.17365	+	1.82391i	−0.206314	+	0.173118i
$112$	2.35844	+	13.3754i	0.222852	+	1.26385i
$113$	−6.08378			−0.572314			−0.286157	−	0.958183i	$-0.592378\pi$
$113$	−6.08378			−0.572314			−0.286157	+	0.958183i	$0.592378\pi$
$114$	−3.41875	−	7.44459i	−0.320195	−	0.697249i
$115$	5.80066			0.540914
$116$	−0.832282	−	4.72010i	−0.0772754	−	0.438251i
$117$	−2.11334	+	1.77330i	−0.195378	+	0.163942i
$118$	14.8550	−	5.40679i	1.36752	−	0.497735i
$119$	−19.2271	−	6.99811i	−1.76255	−	0.641516i
$120$	0.592396	+	0.497079i	0.0540781	+	0.0453769i
$121$	3.81180	−	6.60224i	0.346528	−	0.600203i
$122$	−0.578726	−	1.00238i	−0.0523954	−	0.0907514i
$123$	−0.692066	+	3.92490i	−0.0624015	+	0.353897i
$124$	2.03596	−	11.5465i	0.182835	−	1.03691i
$125$	4.05690	+	7.02676i	0.362861	+	0.628493i
$126$	2.70574	−	4.68647i	0.241046	−	0.417504i
$127$	9.13223	+	7.66285i	0.810354	+	0.679968i	0.950692	−	0.310136i	$-0.100375\pi$
$127$	9.13223	+	7.66285i	0.810354	+	0.679968i	−0.140338	+	0.990104i	$0.544819\pi$
$128$	−6.42989	−	2.34029i	−0.568328	−	0.206854i
$129$	−10.7626	+	3.91728i	−0.947598	+	0.344897i
$130$	−3.49273	+	2.93075i	−0.306332	+	0.257043i
$131$	−0.415345	−	2.35554i	−0.0362888	−	0.205804i	0.961272	−	0.275600i	$-0.0888764\pi$
$131$	−0.415345	−	2.35554i	−0.0362888	−	0.205804i	−0.997561	+	0.0697956i	$0.977765\pi$
$132$	2.81521			0.245032
$133$	10.3229	−	7.13884i	0.895113	−	0.619016i
$134$	−6.90673			−0.596650
$135$	−0.152704	−	0.866025i	−0.0131426	−	0.0745356i
$136$	4.78699	−	4.01676i	0.410481	−	0.344434i
$137$	20.5069	−	7.46389i	1.75202	−	0.637683i	0.752244	−	0.658884i	$-0.228971\pi$
$137$	20.5069	−	7.46389i	1.75202	−	0.637683i	0.999775	+	0.0212013i	$0.00674907\pi$
$138$	11.6493	+	4.24000i	0.991654	+	0.360933i
$139$	6.33409	+	5.31493i	0.537251	+	0.450807i	0.870596	−	0.491998i	$-0.163733\pi$
$139$	6.33409	+	5.31493i	0.537251	+	0.450807i	−0.333346	+	0.942805i	$0.608178\pi$
$140$	1.93969	−	3.35965i	0.163934	−	0.283942i
$141$	1.10354	+	1.91139i	0.0929349	+	0.160968i
$142$	−2.43242	+	13.7949i	−0.204124	+	1.15764i
$143$	0.880263	−	4.99222i	0.0736113	−	0.417470i
$144$	2.35844	+	4.08494i	0.196537	+	0.340412i
$145$	1.37551	−	2.38246i	0.114230	−	0.197853i
$146$	−14.4081	−	12.0898i	−1.19242	−	1.00056i
$147$	1.21301	+	0.441500i	0.100047	+	0.0364143i
$148$	−4.08512	+	1.48686i	−0.335795	+	0.122219i
$149$	5.88532	−	4.93837i	0.482144	−	0.404567i	−0.369057	−	0.929407i	$-0.620319\pi$
$149$	5.88532	−	4.93837i	0.482144	−	0.404567i	0.851201	+	0.524840i	$0.175875\pi$
$150$	1.37939	+	7.82288i	0.112626	+	0.638736i
$151$	−5.94356			−0.483680			−0.241840	−	0.970316i	$-0.577751\pi$
$151$	−5.94356			−0.483680			−0.241840	+	0.970316i	$0.577751\pi$
$152$	0.311804	+	3.82045i	0.0252906	+	0.309879i
$153$	−7.10607			−0.574491
$154$	1.72668	+	9.79250i	0.139140	+	0.789102i
$155$	5.15523	−	4.32575i	0.414078	−	0.347453i
$156$	−3.97178	+	1.44561i	−0.317997	+	0.115741i
$157$	9.76991	+	3.55596i	0.779724	+	0.283796i	0.701058	−	0.713105i	$-0.252712\pi$
$157$	9.76991	+	3.55596i	0.779724	+	0.283796i	0.0786665	+	0.996901i	$0.474934\pi$
$158$	2.31908	+	1.94594i	0.184496	+	0.154810i
$159$	1.35117	−	2.34029i	0.107154	−	0.185597i
$160$	3.12449	+	5.41177i	0.247012	+	0.427838i
$161$	−3.29813	+	18.7046i	−0.259929	+	1.47413i
$162$	0.326352	−	1.85083i	0.0256406	−	0.145415i
$163$	−5.03596	−	8.72254i	−0.394447	−	0.683202i	0.598584	−	0.801060i	$-0.295730\pi$
$163$	−5.03596	−	8.72254i	−0.394447	−	0.683202i	−0.993030	+	0.117858i	$0.962397\pi$
$164$	−3.05303	+	5.28801i	−0.238402	+	0.412924i
$165$	1.23783	+	1.03866i	0.0963646	+	0.0808595i
$166$	−1.74035	−	0.633436i	−0.135078	−	0.0491642i
$167$	−7.63816	+	2.78006i	−0.591058	+	0.215128i	−0.620195	−	0.784448i	$-0.712946\pi$
$167$	−7.63816	+	2.78006i	−0.591058	+	0.215128i	0.0291366	+	0.999575i	$0.490724\pi$
$168$	−1.93969	+	1.62760i	−0.149651	+	0.125572i
$169$	−0.935822	−	5.30731i	−0.0719863	−	0.408255i
$170$	−11.7442			−0.900741
$171$	2.52094	−	3.55596i	0.192781	−	0.271931i
$172$	−17.5476			−1.33799
$173$	−0.922618	−	5.23243i	−0.0701454	−	0.397814i	−0.999584	−	0.0288377i	$-0.990819\pi$
$173$	−0.922618	−	5.23243i	−0.0701454	−	0.397814i	0.929439	−	0.368977i	$-0.120292\pi$
$174$	4.50387	−	3.77920i	0.341438	−	0.286500i
$175$	−11.4363	+	4.16247i	−0.864502	+	0.314653i
$176$	−8.14455	−	2.96437i	−0.613919	−	0.223448i
$177$	6.44356	+	5.40679i	0.484328	+	0.406399i
$178$	−16.0287	+	27.7625i	−1.20140	+	2.08089i
$179$	8.51367	+	14.7461i	0.636342	+	1.10218i	0.986229	+	0.165384i	$0.0528864\pi$
$179$	8.51367	+	14.7461i	0.636342	+	1.10218i	−0.349888	+	0.936792i	$0.613780\pi$
$180$	0.233956	−	1.32683i	0.0174380	−	0.0988959i
$181$	−2.96404	+	16.8099i	−0.220315	+	1.24947i	0.651125	+	0.758970i	$0.274297\pi$
$181$	−2.96404	+	16.8099i	−0.220315	+	1.24947i	−0.871441	+	0.490501i	$0.836814\pi$
$182$	−7.46451	−	12.9289i	−0.553306	−	0.958354i
$183$	0.307934	−	0.533356i	0.0227631	−	0.0394268i
$184$	−4.44356	−	3.72859i	−0.327584	−	0.274875i
$185$	−2.34477	−	0.853427i	−0.172391	−	0.0627452i
$186$	13.5150	−	4.91906i	0.990969	−	0.360683i
$187$	10.0025	−	8.39312i	0.731457	−	0.613765i
$188$	0.587182	+	3.33007i	0.0428246	+	0.242871i
$189$	2.87939			0.209444
$190$	4.16637	−	5.87695i	0.302261	−	0.426358i
$191$	3.62361			0.262195			0.131098	−	0.991369i	$-0.458150\pi$
$191$	3.62361			0.262195			0.131098	+	0.991369i	$0.458150\pi$
$192$	0.680922	+	3.86170i	0.0491413	+	0.278694i
$193$	−3.92468	+	3.29320i	−0.282504	+	0.237049i	−0.773018	−	0.634384i	$-0.781254\pi$
$193$	−3.92468	+	3.29320i	−0.282504	+	0.237049i	0.490513	+	0.871434i	$0.336809\pi$
$194$	10.4226	−	3.79352i	0.748300	−	0.272359i
$195$	−2.27972	−	0.829748i	−0.163254	−	0.0594195i
$196$	1.51501	+	1.27125i	0.108215	+	0.0908035i
$197$	4.56418	−	7.90539i	0.325184	−	0.563236i	−0.656365	−	0.754443i	$-0.727907\pi$
$197$	4.56418	−	7.90539i	0.325184	−	0.563236i	0.981550	+	0.191208i	$0.0612404\pi$
$198$	1.72668	+	2.99070i	0.122710	+	0.212540i
$199$	3.83497	−	21.7492i	0.271854	−	1.54176i	−0.476928	−	0.878943i	$-0.658250\pi$
$199$	3.83497	−	21.7492i	0.271854	−	1.54176i	0.748781	−	0.662817i	$-0.230639\pi$
$200$	0.645430	−	3.66041i	0.0456388	−	0.258830i
$201$	−1.83750	−	3.18264i	−0.129607	−	0.224486i
$202$	4.04576	−	7.00746i	0.284659	−	0.493043i
$203$	6.90033	+	5.79006i	0.484308	+	0.406383i
$204$	−10.2306	−	3.72362i	−0.716282	−	0.260705i
$205$	−3.29339	+	1.19869i	−0.230020	+	0.0837204i
$206$	25.6386	−	21.5134i	1.78633	−	1.49891i
$207$	1.14543	+	6.49605i	0.0796129	+	0.451507i
$208$	13.0128			0.902275
$209$	0.651522	+	7.98292i	0.0450667	+	0.552190i
$210$	4.75877			0.328386
$211$	1.16756	+	6.62154i	0.0803779	+	0.455846i	0.998259	+	0.0589893i	$0.0187878\pi$
$211$	1.16756	+	6.62154i	0.0803779	+	0.455846i	−0.917881	+	0.396856i	$0.870101\pi$
$212$	3.17159	−	2.66128i	0.217826	−	0.182777i
$213$	−7.00387	+	2.54920i	−0.479897	+	0.174668i
$214$	−10.3969	−	3.78417i	−0.710719	−	0.258681i
$215$	−7.71554	−	6.47410i	−0.526195	−	0.441530i
$216$	−0.439693	+	0.761570i	−0.0299173	+	0.0518183i
$217$	11.0175	+	19.0829i	0.747919	+	1.29543i
$218$	4.93242	−	27.9731i	0.334066	−	1.89458i
$219$	1.73783	−	9.85570i	0.117431	−	0.665987i
$220$	1.23783	+	2.14398i	0.0834542	+	0.144547i
$221$	−9.80200	+	16.9776i	−0.659354	+	1.14203i
$222$	−4.08512	−	3.42782i	−0.274175	−	0.230061i
$223$	4.30066	+	1.56531i	0.287993	+	0.104821i	0.481977	−	0.876184i	$-0.339919\pi$
$223$	4.30066	+	1.56531i	0.287993	+	0.104821i	−0.193984	+	0.981005i	$0.562141\pi$
$224$	−19.2271	+	6.99811i	−1.28467	+	0.467581i
$225$	−3.23783	+	2.71686i	−0.215855	+	0.181124i
$226$	−1.98545	−	11.2601i	−0.132070	−	0.749008i
$227$	−15.8425			−1.05151			−0.525753	−	0.850637i	$-0.676217\pi$
$227$	−15.8425			−1.05151			−0.525753	+	0.850637i	$0.676217\pi$
$228$	5.49273	−	3.79850i	0.363765	−	0.251562i
$229$	3.86753			0.255573			0.127787	−	0.991802i	$-0.459213\pi$
$229$	3.86753			0.255573			0.127787	+	0.991802i	$0.459213\pi$
$230$	1.89306	+	10.7361i	0.124824	+	0.707914i
$231$	−4.05303	+	3.40090i	−0.266670	+	0.223763i
$232$	−2.58512	+	0.940908i	−0.169722	+	0.0617736i
$233$	22.2939	+	8.11430i	1.46052	+	0.531585i	0.945508	−	0.325598i	$-0.105566\pi$
$233$	22.2939	+	8.11430i	1.46052	+	0.531585i	0.515011	+	0.857184i	$0.327788\pi$
$234$	−3.97178	−	3.33272i	−0.259643	−	0.217867i
$235$	−0.970437	+	1.68085i	−0.0633044	+	0.109646i
$236$	6.44356	+	11.1606i	0.419440	+	0.726492i
$237$	−0.279715	+	1.58634i	−0.0181694	+	0.103044i
$238$	6.67752	−	37.8701i	0.432839	−	2.45475i
$239$	−2.27332	−	3.93750i	−0.147049	−	0.254696i	0.783087	−	0.621913i	$-0.213644\pi$
$239$	−2.27332	−	3.93750i	−0.147049	−	0.254696i	−0.930135	+	0.367217i	$0.880311\pi$
$240$	−2.07398	+	3.59224i	−0.133875	+	0.231878i
$241$	−0.837496	−	0.702743i	−0.0539479	−	0.0452676i	0.615415	−	0.788203i	$-0.288988\pi$
$241$	−0.837496	−	0.702743i	−0.0539479	−	0.0452676i	−0.669363	+	0.742936i	$0.733433\pi$
$242$	13.4636	+	4.90036i	0.865475	+	0.315007i
$243$	0.939693	−	0.342020i	0.0602813	−	0.0219406i
$244$	0.722811	−	0.606511i	0.0462732	−	0.0388279i
$245$	0.197119	+	1.11792i	0.0125935	+	0.0714211i
$246$	−7.49020			−0.477558
$247$	−5.01842	−	10.9280i	−0.319314	−	0.695331i
$248$	−6.72967			−0.427335
$249$	−0.171122	−	0.970481i	−0.0108444	−	0.0615017i
$250$	−11.6814	+	9.80185i	−0.738796	+	0.619923i
$251$	−12.9427	+	4.71075i	−0.816935	+	0.297340i	−0.716485	−	0.697602i	$-0.754250\pi$
$251$	−12.9427	+	4.71075i	−0.816935	+	0.297340i	−0.100450	+	0.994942i	$0.532028\pi$
$252$	4.14543	+	1.50881i	0.261138	+	0.0950463i
$253$	−9.28493	−	7.79098i	−0.583739	−	0.489815i
$254$	−11.2023	+	19.4030i	−0.702897	+	1.21745i
$255$	−3.12449	−	5.41177i	−0.195663	−	0.338898i
$256$	3.59492	−	20.3878i	0.224683	−	1.27424i
$257$	2.23442	−	12.6720i	0.139379	−	0.790460i	−0.832330	−	0.554280i	$-0.812994\pi$
$257$	2.23442	−	12.6720i	0.139379	−	0.790460i	0.971709	−	0.236180i	$-0.0758954\pi$
$258$	−10.7626	−	18.6414i	−0.670053	−	1.16057i
$259$	4.08512	−	7.07564i	0.253837	−	0.439659i
$260$	−2.84730	−	2.38917i	−0.176582	−	0.148170i
$261$	2.93969	+	1.06996i	0.181962	+	0.0662289i
$262$	4.22416	−	1.53747i	0.260969	−	0.0949850i
$263$	−10.6040	+	8.89782i	−0.653871	+	0.548663i	−0.908243	−	0.418444i	$-0.862576\pi$
$263$	−10.6040	+	8.89782i	−0.653871	+	0.548663i	0.254372	+	0.967107i	$0.418131\pi$
$264$	−0.280592	−	1.59132i	−0.0172693	−	0.0979389i
$265$	2.37639			0.145981
$266$	16.5817	+	16.7763i	1.01669	+	1.02862i
$267$	−17.0574			−1.04389
$268$	−0.977711	−	5.54488i	−0.0597232	−	0.338707i
$269$	−10.6382	+	8.92647i	−0.648620	+	0.544257i	−0.906652	−	0.421880i	$-0.861370\pi$
$269$	−10.6382	+	8.92647i	−0.648620	+	0.544257i	0.258032	+	0.966136i	$0.416926\pi$
$270$	1.55303	−	0.565258i	0.0945146	−	0.0344005i
$271$	−5.53849	−	2.01584i	−0.336439	−	0.122454i	0.168276	−	0.985740i	$-0.446180\pi$
$271$	−5.53849	−	2.01584i	−0.336439	−	0.122454i	−0.504715	+	0.863286i	$0.668402\pi$
$272$	25.6766	+	21.5453i	1.55688	+	1.30637i
$273$	3.97178	−	6.87933i	0.240383	−	0.416356i
$274$	20.5069	+	35.5189i	1.23886	+	2.14578i
$275$	1.34864	−	7.64852i	0.0813261	−	0.461223i
$276$	−1.75490	+	9.95253i	−0.105633	+	0.599072i
$277$	2.26945	+	3.93080i	0.136358	+	0.236179i	0.926115	−	0.377240i	$-0.123127\pi$
$277$	2.26945	+	3.93080i	0.136358	+	0.236179i	−0.789757	+	0.613419i	$0.789794\pi$
$278$	−7.76991	+	13.4579i	−0.466009	+	0.807150i
$279$	5.86231	+	4.91906i	0.350967	+	0.294497i
$280$	−2.09240	−	0.761570i	−0.125045	−	0.0455125i
$281$	16.0052	−	5.82542i	0.954791	−	0.347516i	0.182801	−	0.983150i	$-0.441484\pi$
$281$	16.0052	−	5.82542i	0.954791	−	0.347516i	0.771990	+	0.635634i	$0.219261\pi$
$282$	−3.17752	+	2.66625i	−0.189218	+	0.158773i
$283$	3.95290	+	22.4180i	0.234975	+	1.33261i	0.842666	+	0.538437i	$0.180985\pi$
$283$	3.95290	+	22.4180i	0.234975	+	1.33261i	−0.607690	+	0.794174i	$0.707904\pi$
$284$	−11.4192			−0.677606
$285$	3.81655	+	0.356347i	0.226073	+	0.0211082i
$286$	9.52704			0.563345
$287$	−1.99273	−	11.3013i	−0.117627	−	0.667095i
$288$	−5.44356	+	4.56769i	−0.320765	+	0.269154i
$289$	−31.4761	+	11.4564i	−1.85154	+	0.673904i
$290$	4.85844	+	1.76833i	0.285297	+	0.103840i
$291$	4.52094	+	3.79352i	0.265022	+	0.222380i
$292$	7.66637	−	13.2785i	0.448641	−	0.777068i
$293$	2.77972	+	4.81461i	0.162393	+	0.281272i	0.935726	−	0.352727i	$-0.114746\pi$
$293$	2.77972	+	4.81461i	0.162393	+	0.281272i	−0.773334	+	0.633999i	$0.781412\pi$
$294$	−0.421274	+	2.38917i	−0.0245692	+	0.139339i
$295$	−1.28446	+	7.28455i	−0.0747843	+	0.424123i
$296$	1.24763	+	2.16095i	0.0725168	+	0.125603i
$297$	−0.918748	+	1.59132i	−0.0533112	+	0.0923377i
$298$	11.0608	+	9.28109i	0.640733	+	0.537639i
$299$	17.1001	+	6.22394i	0.988926	+	0.359940i
$300$	−6.08512	+	2.21480i	−0.351325	+	0.127872i
$301$	25.2631	−	21.1983i	1.45614	−	1.22185i
$302$	−1.93969	−	11.0005i	−0.111617	−	0.633010i
$303$	4.30541			0.247339
$304$	−19.8905	+	5.20550i	−1.14080	+	0.298556i
$305$	0.541584			0.0310110
$306$	−2.31908	−	13.1521i	−0.132573	−	0.751858i
$307$	−9.06283	+	7.60462i	−0.517243	+	0.434019i	−0.863669	−	0.504059i	$-0.831840\pi$
$307$	−9.06283	+	7.60462i	−0.517243	+	0.434019i	0.346426	+	0.938077i	$0.387395\pi$
$308$	−7.61721	+	2.77244i	−0.434031	+	0.157974i
$309$	16.7344	+	6.09083i	0.951988	+	0.346495i
$310$	9.68866	+	8.12975i	0.550279	+	0.461739i
$311$	9.02141	−	15.6255i	0.511557	−	0.886043i	−0.488353	−	0.872646i	$-0.662402\pi$
$311$	9.02141	−	15.6255i	0.511557	−	0.886043i	0.999910	−	0.0133970i	$-0.00426454\pi$
$312$	1.21301	+	2.10100i	0.0686732	+	0.118946i
$313$	1.19712	−	6.78920i	0.0676652	−	0.383748i	−0.932103	−	0.362195i	$-0.882028\pi$
$313$	1.19712	−	6.78920i	0.0676652	−	0.383748i	0.999768	−	0.0215537i	$-0.00686128\pi$
$314$	−3.39306	+	19.2430i	−0.191481	+	1.08594i
$315$	1.26604	+	2.19285i	0.0713335	+	0.123553i
$316$	−1.23396	+	2.13727i	−0.0694154	+	0.120231i
$317$	−25.5292	−	21.4215i	−1.43386	−	1.20315i	−0.943387	−	0.331695i	$-0.892379\pi$
$317$	−25.5292	−	21.4215i	−1.43386	−	1.20315i	−0.490473	−	0.871456i	$-0.663176\pi$
$318$	4.77244	+	1.73703i	0.267625	+	0.0974076i
$319$	−5.40167	+	1.96605i	−0.302436	+	0.110078i
$320$	−2.64156	+	2.21653i	−0.147668	+	0.123908i
$321$	−1.02229	−	5.79769i	−0.0570586	−	0.323595i
$322$	−35.6955			−1.98923
$323$	8.19119	−	29.8719i	0.455770	−	1.66212i
$324$	1.53209			0.0851160
$325$	2.02481	+	11.4833i	0.112317	+	0.636979i
$326$	14.5005	−	12.1673i	0.803107	−	0.673886i
$327$	14.2023	−	5.16923i	0.785391	−	0.285859i
$328$	3.29339	+	1.19869i	0.181847	+	0.0661868i
$329$	−4.86824	−	4.08494i	−0.268395	−	0.225210i
$330$	−1.51842	+	2.62998i	−0.0835862	+	0.144776i
$331$	−2.47178	−	4.28125i	−0.135861	−	0.235319i	0.790065	−	0.613023i	$-0.210047\pi$
$331$	−2.47178	−	4.28125i	−0.135861	−	0.235319i	−0.925926	+	0.377705i	$0.876714\pi$
$332$	0.262174	−	1.48686i	0.0143887	−	0.0816022i
$333$	0.492726	−	2.79439i	0.0270012	−	0.153132i
$334$	−7.63816	−	13.2297i	−0.417941	−	0.723896i
$335$	1.61587	−	2.79876i	0.0882842	−	0.152913i
$336$	−10.4042	−	8.73016i	−0.567596	−	0.476269i
$337$	−8.85117	−	3.22156i	−0.482154	−	0.175490i	0.0894963	−	0.995987i	$-0.471474\pi$
$337$	−8.85117	−	3.22156i	−0.482154	−	0.175490i	−0.571650	+	0.820498i	$0.693697\pi$
$338$	9.51754	−	3.46410i	0.517686	−	0.188422i
$339$	4.66044	−	3.91058i	0.253121	−	0.212393i
$340$	−1.66250	−	9.42853i	−0.0901619	−	0.511334i
$341$	−14.0618			−0.761490
$342$	7.40420	+	3.50535i	0.400373	+	0.189548i
$343$	16.4388			0.887613
$344$	1.74897	+	9.91890i	0.0942982	+	0.534791i
$345$	−4.44356	+	3.72859i	−0.239233	+	0.200741i
$346$	9.38326	−	3.41523i	0.504447	−	0.183604i
$347$	11.1493	+	4.05801i	0.598526	+	0.217846i	0.623475	−	0.781843i	$-0.285720\pi$
$347$	11.1493	+	4.05801i	0.598526	+	0.217846i	−0.0249494	+	0.999689i	$0.507942\pi$
$348$	3.67159	+	3.08083i	0.196818	+	0.165150i
$349$	−10.9709	+	19.0022i	−0.587259	+	1.01716i	0.407331	+	0.913281i	$0.366460\pi$
$349$	−10.9709	+	19.0022i	−0.587259	+	1.01716i	−0.994590	+	0.103882i	$0.966874\pi$
$350$	−11.4363	−	19.8082i	−0.611295	−	1.05879i
$351$	0.479055	−	2.71686i	0.0255701	−	0.145015i
$352$	2.26739	−	12.8590i	0.120852	−	0.685387i
$353$	−1.94697	−	3.37225i	−0.103627	−	0.179486i	0.809550	−	0.587051i	$-0.199711\pi$
$353$	−1.94697	−	3.37225i	−0.103627	−	0.179486i	−0.913176	+	0.407565i	$0.866378\pi$
$354$	−7.90420	+	13.6905i	−0.420103	+	0.727641i
$355$	−5.02094	−	4.21307i	−0.266484	−	0.223607i
$356$	−24.5574	−	8.93815i	−1.30154	−	0.473721i
$357$	19.2271	−	6.99811i	1.01761	−	0.370379i
$358$	−24.5141	+	20.5698i	−1.29561	+	1.08715i
$359$	−2.08466	−	11.8227i	−0.110024	−	0.623977i	−0.989094	−	0.147284i	$-0.952947\pi$
$359$	−2.08466	−	11.8227i	−0.110024	−	0.623977i	0.879070	−	0.476692i	$-0.158164\pi$
$360$	−0.773318			−0.0407575
$361$	12.0424	+	14.6963i	0.633808	+	0.773490i
$362$	−32.0797			−1.68607
$363$	1.32383	+	7.50779i	0.0694828	+	0.394057i
$364$	9.32295	−	7.82288i	0.488655	−	0.410030i
$365$	8.26991	−	3.01000i	0.432867	−	0.157551i
$366$	1.08765	+	0.395872i	0.0568523	+	0.0206925i
$367$	−20.5326	−	17.2289i	−1.07179	−	0.899339i	−0.0765772	−	0.997064i	$-0.524399\pi$
$367$	−20.5326	−	17.2289i	−1.07179	−	0.899339i	−0.995214	+	0.0977245i	$0.968844\pi$
$368$	15.5569	−	26.9453i	0.810960	−	1.40462i
$369$	−1.99273	−	3.45150i	−0.103737	−	0.179678i
$370$	0.814330	−	4.61830i	0.0423350	−	0.240094i
$371$	−1.35117	+	7.66285i	−0.0701491	+	0.397835i
$372$	5.86231	+	10.1538i	0.303947	+	0.526451i
$373$	14.2909	−	24.7525i	0.739953	−	1.28164i	−0.212563	−	0.977147i	$-0.568181\pi$
$373$	14.2909	−	24.7525i	0.739953	−	1.28164i	0.952516	−	0.304488i	$-0.0984855\pi$
$374$	18.7986	+	15.7739i	0.972052	+	0.815649i
$375$	−7.62449	−	2.77509i	−0.393727	−	0.143305i
$376$	1.82383	−	0.663818i	0.0940566	−	0.0342338i
$377$	6.61128	−	5.54752i	0.340498	−	0.285712i
$378$	0.939693	+	5.32926i	0.0483326	+	0.274108i
$379$	−3.09833			−0.159150			−0.0795752	−	0.996829i	$-0.525356\pi$
$379$	−3.09833			−0.159150			−0.0795752	+	0.996829i	$0.525356\pi$
$380$	5.30793	+	2.51292i	0.272291	+	0.128910i
$381$	−11.9213			−0.610745
$382$	1.18257	+	6.70669i	0.0605056	+	0.343144i
$383$	−21.9270	+	18.3989i	−1.12042	+	0.940140i	−0.998625	−	0.0524160i	$-0.983308\pi$
$383$	−21.9270	+	18.3989i	−1.12042	+	0.940140i	−0.121790	+	0.992556i	$0.538863\pi$
$384$	6.42989	−	2.34029i	0.328124	−	0.119427i
$385$	−4.37211	−	1.59132i	−0.222823	−	0.0811011i
$386$	−7.37598	−	6.18918i	−0.375428	−	0.315021i
$387$	5.72668	−	9.91890i	0.291104	−	0.504206i
$388$	4.52094	+	7.83051i	0.229516	+	0.397534i
$389$	−3.89218	+	22.0736i	−0.197341	+	1.11918i	0.711704	+	0.702480i	$0.247924\pi$
$389$	−3.89218	+	22.0736i	−0.197341	+	1.11918i	−0.909045	+	0.416698i	$0.863187\pi$
$390$	0.791737	−	4.49016i	0.0400911	−	0.227368i
$391$	23.4368	+	40.5937i	1.18525	+	2.05291i
$392$	0.567581	−	0.983080i	0.0286672	−	0.0496530i
$393$	1.83228	+	1.53747i	0.0924264	+	0.0775549i
$394$	16.1211	+	5.86759i	0.812168	+	0.295605i
$395$	−1.33110	+	0.484481i	−0.0669749	+	0.0243769i
$396$	−2.15657	+	1.80958i	−0.108372	+	0.0909348i
$397$	−2.38444	−	13.5228i	−0.119671	−	0.678691i	−0.984331	−	0.176332i	$-0.943577\pi$
$397$	−2.38444	−	13.5228i	−0.119671	−	0.678691i	0.864659	−	0.502359i	$-0.167534\pi$
$398$	41.5057			2.08049
$399$	−3.31908	+	12.1041i	−0.166162	+	0.605965i
$400$	19.9368			0.996838
$401$	−5.08559	−	28.8418i	−0.253962	−	1.44029i	−0.798723	−	0.601699i	$-0.794491\pi$
$401$	−5.08559	−	28.8418i	−0.253962	−	1.44029i	0.544760	−	0.838592i	$-0.316621\pi$
$402$	5.29086	−	4.43956i	0.263884	−	0.221425i
$403$	19.8388	−	7.22075i	0.988243	−	0.359691i
$404$	6.19846	+	2.25606i	0.308385	+	0.112243i
$405$	0.673648	+	0.565258i	0.0334738	+	0.0280879i
$406$	−8.46451	+	14.6610i	−0.420086	+	0.727611i
$407$	2.60694	+	4.51536i	0.129221	+	0.223818i
$408$	−1.08512	+	6.15403i	−0.0537216	+	0.304670i
$409$	−0.405544	+	2.29996i	−0.0200529	+	0.113726i	−0.993191	−	0.116496i	$-0.962834\pi$
$409$	−0.405544	+	2.29996i	−0.0200529	+	0.113726i	0.973138	+	0.230221i	$0.0739450\pi$
$410$	−3.29339	−	5.70431i	−0.162649	−	0.281716i
$411$	−10.9115	+	18.8992i	−0.538223	+	0.932230i
$412$	20.9008	+	17.5379i	1.02971	+	0.864028i
$413$	−22.7592	−	8.28368i	−1.11991	−	0.407613i
$414$	−11.6493	+	4.24000i	−0.572532	+	0.208385i
$415$	0.663848	−	0.557035i	0.0325870	−	0.0273438i
$416$	3.40420	+	19.3062i	0.166905	+	0.946563i
$417$	−8.26857			−0.404914
$418$	−14.5624	+	3.81110i	−0.712271	+	0.186407i
$419$	2.27362			0.111074			0.0555369	−	0.998457i	$-0.482313\pi$
$419$	2.27362			0.111074			0.0555369	+	0.998457i	$0.482313\pi$
$420$	0.673648	+	3.82045i	0.0328707	+	0.186419i
$421$	14.5688	−	12.2246i	0.710038	−	0.595793i	−0.214572	−	0.976708i	$-0.568836\pi$
$421$	14.5688	−	12.2246i	0.710038	−	0.595793i	0.924610	+	0.380916i	$0.124391\pi$
$422$	−11.8743	+	4.32190i	−0.578033	+	0.210387i
$423$	−2.07398	−	0.754866i	−0.100840	−	0.0367029i
$424$	−1.82042	−	1.52752i	−0.0884075	−	0.0741827i
$425$	−15.0175	+	26.0111i	−0.728458	+	1.26173i
$426$	−7.00387	−	12.1311i	−0.339339	−	0.587752i
$427$	−0.307934	+	1.74638i	−0.0149019	+	0.0845131i
$428$	1.56624	−	8.88257i	0.0757069	−	0.429355i
$429$	2.53462	+	4.39008i	0.122372	+	0.211955i
$430$	9.46451	−	16.3930i	0.456419	−	0.790541i
$431$	−9.80066	−	8.22373i	−0.472081	−	0.396123i	0.375472	−	0.926834i	$-0.377481\pi$
$431$	−9.80066	−	8.22373i	−0.472081	−	0.396123i	−0.847553	+	0.530711i	$0.821925\pi$
$432$	−4.43242	−	1.61327i	−0.213255	−	0.0776184i
$433$	−13.6959	+	4.98491i	−0.658185	+	0.239560i	−0.649452	−	0.760402i	$-0.725002\pi$
$433$	−13.6959	+	4.98491i	−0.658185	+	0.239560i	−0.00873229	+	0.999962i	$0.502780\pi$
$434$	−31.7237	+	26.6194i	−1.52279	+	1.27777i
$435$	0.477711	+	2.70924i	0.0229045	+	0.129898i
$436$	23.1557			1.10896
$437$	−28.6279	−	2.67296i	−1.36946	−	0.127865i
$438$	18.8084			0.898700
$439$	4.27513	+	24.2455i	0.204041	+	1.15717i	0.898942	+	0.438068i	$0.144337\pi$
$439$	4.27513	+	24.2455i	0.204041	+	1.15717i	−0.694901	+	0.719105i	$0.744552\pi$
$440$	1.08853	−	0.913382i	0.0518934	−	0.0435438i
$441$	−1.21301	+	0.441500i	−0.0577624	+	0.0210238i
$442$	−34.6215	−	12.6012i	−1.64678	−	0.599379i
$443$	29.5198	+	24.7701i	1.40253	+	1.17686i	0.959963	+	0.280125i	$0.0903760\pi$
$443$	29.5198	+	24.7701i	1.40253	+	1.17686i	0.442565	+	0.896736i	$0.354068\pi$
$444$	2.17365	−	3.76487i	0.103157	−	0.178673i
$445$	−7.50000	−	12.9904i	−0.355534	−	0.615803i
$446$	−1.49360	+	8.47065i	−0.0707242	+	0.401097i
$447$	−1.33409	+	7.56602i	−0.0631004	+	0.357860i
$448$	−5.64543	−	9.77817i	−0.266721	−	0.461975i
$449$	17.5903	−	30.4674i	0.830139	−	1.43784i	−0.0677880	−	0.997700i	$-0.521594\pi$
$449$	17.5903	−	30.4674i	0.830139	−	1.43784i	0.897927	−	0.440144i	$-0.145073\pi$
$450$	−6.08512	−	5.10602i	−0.286855	−	0.240700i
$451$	6.88161	+	2.50470i	0.324042	+	0.117942i
$452$	8.75877	−	3.18793i	0.411978	−	0.149948i
$453$	4.55303	−	3.82045i	0.213920	−	0.179500i
$454$	−5.17024	−	29.3219i	−0.242652	−	1.37615i
$455$	6.98545			0.327483
$456$	−2.69459	−	2.72621i	−0.126186	−	0.127666i
$457$	−13.7983			−0.645457			−0.322729	−	0.946492i	$-0.604600\pi$
$457$	−13.7983			−0.645457			−0.322729	+	0.946492i	$0.604600\pi$
$458$	1.26217	+	7.15814i	0.0589775	+	0.334478i
$459$	5.44356	−	4.56769i	0.254084	−	0.213202i
$460$	−8.35117	+	3.03958i	−0.389375	+	0.141721i
$461$	−22.8084	−	8.30158i	−1.06229	−	0.386643i	−0.249004	−	0.968503i	$-0.580103\pi$
$461$	−22.8084	−	8.30158i	−1.06229	−	0.386643i	−0.813289	+	0.581859i	$0.802325\pi$
$462$	−7.61721	−	6.39160i	−0.354385	−	0.297364i
$463$	5.64543	−	9.77817i	0.262365	−	0.454430i	−0.704505	−	0.709699i	$-0.748831\pi$
$463$	5.64543	−	9.77817i	0.262365	−	0.454430i	0.966870	+	0.255269i	$0.0821641\pi$
$464$	−7.37804	−	12.7791i	−0.342517	−	0.593257i
$465$	−1.16860	+	6.62744i	−0.0541923	+	0.307340i
$466$	−7.74257	+	43.9103i	−0.358668	+	2.03411i
$467$	2.39393	+	4.14641i	0.110778	+	0.191873i	0.916084	−	0.400986i	$-0.131332\pi$
$467$	2.39393	+	4.14641i	0.110778	+	0.191873i	−0.805306	+	0.592859i	$0.797999\pi$
$468$	2.11334	−	3.66041i	0.0976892	−	0.169203i
$469$	8.10607	+	6.80180i	0.374303	+	0.314078i
$470$	−3.42767	−	1.24757i	−0.158107	−	0.0575461i
$471$	−9.76991	+	3.55596i	−0.450174	+	0.163850i
$472$	5.66637	−	4.75465i	0.260816	−	0.218851i
$473$	3.65451	+	20.7258i	0.168035	+	0.952972i
$474$	−3.02734			−0.139050
$475$	−7.68866	−	16.7427i	−0.352780	−	0.768206i
$476$	31.3482			1.43684
$477$	0.469255	+	2.66128i	0.0214857	+	0.121852i
$478$	6.54576	−	5.49254i	0.299396	−	0.251223i
$479$	15.8897	−	5.78336i	0.726017	−	0.264248i	0.0475389	−	0.998869i	$-0.484862\pi$
$479$	15.8897	−	5.78336i	0.726017	−	0.264248i	0.678478	+	0.734621i	$0.262640\pi$
$480$	−5.87211	−	2.13727i	−0.268024	−	0.0975528i
$481$	−5.99660	−	5.03174i	−0.273421	−	0.229428i
$482$	1.02734	−	1.77941i	0.0467941	−	0.0810498i
$483$	−9.49660	−	16.4486i	−0.432110	−	0.748437i
$484$	−2.02822	+	11.5026i	−0.0921917	+	0.522845i
$485$	−0.901207	+	5.11100i	−0.0409217	+	0.232079i
$486$	0.939693	+	1.62760i	0.0426253	+	0.0738292i
$487$	−3.88191	+	6.72367i	−0.175906	+	0.304678i	−0.940475	−	0.339864i	$-0.889619\pi$
$487$	−3.88191	+	6.72367i	−0.175906	+	0.304678i	0.764568	+	0.644543i	$0.222952\pi$
$488$	−0.414878	−	0.348124i	−0.0187806	−	0.0157588i
$489$	9.46451	+	3.44480i	0.428000	+	0.155779i
$490$	−2.00475	+	0.729669i	−0.0905653	+	0.0329631i
$491$	−11.1270	+	9.33667i	−0.502155	+	0.421358i	−0.858359	−	0.513050i	$-0.828515\pi$
$491$	−11.1270	+	9.33667i	−0.502155	+	0.421358i	0.356204	+	0.934408i	$0.384071\pi$
$492$	−1.06031	−	6.01330i	−0.0478023	−	0.271101i
$493$	22.2303			1.00120
$494$	18.5881	−	12.8546i	0.836319	−	0.578357i
$495$	−1.61587			−0.0726278
$496$	−6.26816	−	35.5485i	−0.281449	−	1.59617i
$497$	16.4402	−	13.7949i	0.737442	−	0.618787i
$498$	1.74035	−	0.633436i	0.0779870	−	0.0283850i
$499$	−26.5646	−	9.66874i	−1.18920	−	0.432832i	−0.329755	−	0.944066i	$-0.606966\pi$
$499$	−26.5646	−	9.66874i	−1.18920	−	0.432832i	−0.859441	+	0.511234i	$0.829188\pi$
$500$	−9.52276	−	7.99054i	−0.425871	−	0.357348i
$501$	4.06418	−	7.03936i	0.181574	−	0.314496i
$502$	−12.9427	−	22.4174i	−0.577660	−	1.00054i
$503$	−6.60947	+	37.4842i	−0.294702	+	1.67134i	0.373710	+	0.927545i	$0.378085\pi$
$503$	−6.60947	+	37.4842i	−0.294702	+	1.67134i	−0.668412	+	0.743791i	$0.733026\pi$
$504$	0.439693	−	2.49362i	0.0195855	−	0.111075i
$505$	1.89306	+	3.27887i	0.0842399	+	0.145908i
$506$	11.3897	−	19.7275i	0.506332	−	0.876992i
$507$	4.12836	+	3.46410i	0.183347	+	0.153846i
$508$	−17.1630	−	6.24681i	−0.761484	−	0.277157i
$509$	12.9226	−	4.70345i	0.572785	−	0.208477i	−0.0393561	−	0.999225i	$-0.512531\pi$
$509$	12.9226	−	4.70345i	0.572785	−	0.208477i	0.612141	+	0.790749i	$0.290308\pi$
$510$	8.99660	−	7.54904i	0.398376	−	0.334277i
$511$	5.00387	+	28.3784i	0.221358	+	1.25538i
$512$	25.2226			1.11469
$513$	0.354570	+	4.34445i	0.0156547	+	0.191812i
$514$	24.1830			1.06667
$515$	2.71941	+	15.4225i	0.119831	+	0.679598i
$516$	13.4422	−	11.2794i	0.591761	−	0.496546i
$517$	3.81093	−	1.38706i	0.167604	−	0.0610030i
$518$	14.4290	+	5.25173i	0.633975	+	0.230748i
$519$	4.07011	+	3.41523i	0.178658	+	0.149912i
$520$	−1.06670	+	1.84759i	−0.0467781	+	0.0810220i
$521$	−7.69712	−	13.3318i	−0.337217	−	0.584077i	0.646691	−	0.762752i	$-0.276152\pi$
$521$	−7.69712	−	13.3318i	−0.337217	−	0.584077i	−0.983908	+	0.178675i	$0.942819\pi$
$522$	−1.02094	+	5.79006i	−0.0446855	+	0.253424i
$523$	0.0452926	−	0.256867i	0.00198051	−	0.0112320i	−0.983801	−	0.179261i	$-0.942629\pi$
$523$	0.0452926	−	0.256867i	0.00198051	−	0.0112320i	0.985782	+	0.168029i	$0.0537403\pi$
$524$	1.83228	+	3.17360i	0.0800436	+	0.138640i
$525$	6.08512	−	10.5397i	0.265577	−	0.459992i
$526$	−19.9290	−	16.7224i	−0.868946	−	0.729133i
$527$	51.1011	+	18.5993i	2.22600	+	0.810197i
$528$	8.14455	−	2.96437i	0.354446	−	0.129008i
$529$	15.7121	−	13.1840i	0.683136	−	0.573219i
$530$	0.775540	+	4.39831i	0.0336873	+	0.191050i
$531$	−8.41147			−0.365027
$532$	−11.1211	+	15.6870i	−0.482160	+	0.680118i
$533$	−10.9949			−0.476244
$534$	−5.56670	−	31.5703i	−0.240895	−	1.36618i
$535$	3.96585	−	3.32774i	0.171459	−	0.143871i
$536$	−3.03684	+	1.10532i	−0.131171	+	0.0477425i
$537$	−16.0005	−	5.82369i	−0.690471	−	0.251311i
$538$	−19.9932	−	16.7763i	−0.861968	−	0.723277i
$539$	1.18597	−	2.05417i	0.0510835	−	0.0884793i
$540$	0.673648	+	1.16679i	0.0289892	+	0.0502108i
$541$	0.202333	−	1.14749i	0.00869900	−	0.0493345i	−0.980149	−	0.198261i	$-0.936471\pi$
$541$	0.202333	−	1.14749i	0.00869900	−	0.0493345i	0.988848	+	0.148926i	$0.0475818\pi$
$542$	1.92350	−	10.9087i	0.0826212	−	0.468568i
$543$	−8.53462	−	14.7824i	−0.366255	−	0.634373i
$544$	−25.2481	+	43.7310i	−1.08250	+	1.87495i
$545$	10.1814	+	8.54320i	0.436123	+	0.365950i
$546$	14.0287	+	5.10602i	0.600372	+	0.218518i
$547$	−5.18954	+	1.88884i	−0.221889	+	0.0807609i	−0.450572	−	0.892740i	$-0.648780\pi$
$547$	−5.18954	+	1.88884i	−0.221889	+	0.0807609i	0.228684	+	0.973501i	$0.426558\pi$
$548$	−25.6125	+	21.4914i	−1.09411	+	0.918067i
$549$	0.106944	+	0.606511i	0.00456427	+	0.0258852i
$550$	14.5963			0.622387
$551$	−7.88641	+	11.1243i	−0.335972	+	0.473911i
$552$	5.80066			0.246892
$553$	−0.805407	−	4.56769i	−0.0342494	−	0.194238i
$554$	−6.53462	+	5.48319i	−0.277629	+	0.232959i
$555$	2.34477	−	0.853427i	0.0995299	−	0.0362259i
$556$	−11.9042	−	4.33277i	−0.504851	−	0.183751i
$557$	−22.7178	−	19.0625i	−0.962585	−	0.807704i	0.0187869	−	0.999824i	$-0.494020\pi$
$557$	−22.7178	−	19.0625i	−0.962585	−	0.807704i	−0.981372	+	0.192119i	$0.938464\pi$
$558$	−7.19119	+	12.4555i	−0.304427	+	0.527284i
$559$	−15.7986	−	27.3640i	−0.668210	−	1.15737i
$560$	2.07398	−	11.7621i	0.0876416	−	0.497040i
$561$	−2.26739	+	12.8590i	−0.0957292	+	0.542907i
$562$	16.0052	+	27.7218i	0.675139	+	1.16938i
$563$	−6.15389	+	10.6588i	−0.259355	+	0.449217i	−0.966069	−	0.258283i	$-0.916843\pi$
$563$	−6.15389	+	10.6588i	−0.259355	+	0.449217i	0.706714	+	0.707499i	$0.250177\pi$
$564$	−2.59034	−	2.17355i	−0.109073	−	0.0915230i
$565$	5.02734	+	1.82980i	0.211502	+	0.0769804i
$566$	−40.2019	+	14.6323i	−1.68981	+	0.615042i
$567$	−2.20574	+	1.85083i	−0.0926322	+	0.0777277i
$568$	1.13816	+	6.45480i	0.0477560	+	0.270837i
$569$	24.3054			1.01894			0.509468	−	0.860490i	$-0.329842\pi$
$569$	24.3054			1.01894			0.509468	+	0.860490i	$0.329842\pi$
$570$	0.586000	+	7.18009i	0.0245448	+	0.300741i
$571$	−7.99731			−0.334677			−0.167339	−	0.985899i	$-0.553517\pi$
$571$	−7.99731			−0.334677			−0.167339	+	0.985899i	$0.553517\pi$
$572$	1.34864	+	7.64852i	0.0563895	+	0.319801i
$573$	−2.77584	+	2.32921i	−0.115963	+	0.0973042i
$574$	20.2665	−	7.37641i	0.845908	−	0.307885i
$575$	26.1989	+	9.53563i	1.09257	+	0.397663i
$576$	−3.00387	−	2.52055i	−0.125161	−	0.105023i
$577$	5.84848	−	10.1299i	0.243475	−	0.421712i	−0.718227	−	0.695809i	$-0.755046\pi$
$577$	5.84848	−	10.1299i	0.243475	−	0.421712i	0.961702	+	0.274098i	$0.0883792\pi$
$578$	−31.4761	−	54.5182i	−1.30923	−	2.26766i
$579$	0.889652	−	5.04547i	0.0369727	−	0.209683i
$580$	−0.731896	+	4.15079i	−0.0303903	+	0.172352i
$581$	1.41875	+	2.45734i	0.0588596	+	0.101948i
$582$	−5.54576	+	9.60554i	−0.229879	+	0.398162i
$583$	−3.80381	−	3.19178i	−0.157538	−	0.132190i
$584$	−8.26991	−	3.01000i	−0.342212	−	0.124555i
$585$	2.27972	−	0.829748i	0.0942546	−	0.0343059i
$586$	−8.00387	+	6.71604i	−0.330637	+	0.277437i
$587$	1.12748	+	6.39425i	0.0465360	+	0.263919i	0.999195	−	0.0401228i	$-0.0127749\pi$
$587$	1.12748	+	6.39425i	0.0465360	+	0.263919i	−0.952659	+	0.304042i	$0.901664\pi$
$588$	−1.97771			−0.0815594
$589$	−27.4359	+	18.9733i	−1.13048	+	0.781781i
$590$	−13.9017			−0.572323
$591$	1.58512	+	8.98968i	0.0652032	+	0.369786i
$592$	−10.2528	+	8.60315i	−0.421389	+	0.353587i
$593$	−21.5021	+	7.82613i	−0.882986	+	0.321381i	−0.743414	−	0.668831i	$-0.766795\pi$
$593$	−21.5021	+	7.82613i	−0.882986	+	0.321381i	−0.139572	+	0.990212i	$0.544573\pi$
$594$	−3.24510	−	1.18112i	−0.133148	−	0.0484619i
$595$	13.7836	+	11.5658i	0.565072	+	0.474152i
$596$	−5.88532	+	10.1937i	−0.241072	+	0.417549i
$597$	11.0424	+	19.1259i	0.451934	+	0.782772i
$598$	−5.93882	+	33.6807i	−0.242856	+	1.37731i
$599$	4.79339	−	27.1846i	0.195852	−	1.11073i	−0.715347	−	0.698769i	$-0.753731\pi$
$599$	4.79339	−	27.1846i	0.195852	−	1.11073i	0.911200	−	0.411965i	$-0.135157\pi$
$600$	1.85844	+	3.21891i	0.0758705	+	0.131412i
$601$	7.06552	−	12.2378i	0.288209	−	0.499192i	−0.685174	−	0.728380i	$-0.740274\pi$
$601$	7.06552	−	12.2378i	0.288209	−	0.499192i	0.973382	+	0.229188i	$0.0736070\pi$
$602$	47.4791	+	39.8397i	1.93510	+	1.62375i
$603$	3.45336	+	1.25692i	0.140632	+	0.0511858i
$604$	8.55690	−	3.11446i	0.348175	−	0.126726i
$605$	−5.13563	+	4.30930i	−0.208793	+	0.175198i
$606$	1.40508	+	7.96859i	0.0570774	+	0.323702i
$607$	9.50980			0.385991			0.192995	−	0.981200i	$-0.438180\pi$
$607$	9.50980			0.385991			0.192995	+	0.981200i	$0.438180\pi$
$608$	−12.9265	−	28.1484i	−0.524238	−	1.14157i
$609$	−9.00774			−0.365012
$610$	0.176747	+	1.00238i	0.00715628	+	0.0405853i
$611$	−4.66431	+	3.91382i	−0.188698	+	0.158336i
$612$	10.2306	−	3.72362i	0.413546	−	0.150518i
$613$	39.5766	+	14.4047i	1.59848	+	0.581800i	0.979116	−	0.203302i	$-0.0651674\pi$
$613$	39.5766	+	14.4047i	1.59848	+	0.581800i	0.619366	+	0.785102i	$0.287390\pi$
$614$	−17.0326	−	14.2920i	−0.687378	−	0.576779i
$615$	1.75237	−	3.03520i	0.0706625	−	0.122391i
$616$	2.32635	+	4.02936i	0.0937314	+	0.162348i
$617$	−5.02915	+	28.5217i	−0.202466	+	1.14824i	0.698912	+	0.715208i	$0.253668\pi$
$617$	−5.02915	+	28.5217i	−0.202466	+	1.14824i	−0.901378	+	0.433034i	$0.857443\pi$
$618$	−5.81180	+	32.9604i	−0.233785	+	1.32586i
$619$	−15.4598	−	26.7771i	−0.621380	−	1.07626i	−0.989229	−	0.146376i	$-0.953239\pi$
$619$	−15.4598	−	26.7771i	−0.621380	−	1.07626i	0.367849	−	0.929886i	$-0.380094\pi$
$620$	−5.15523	+	8.92912i	−0.207039	+	0.358602i
$621$	−5.05303	−	4.24000i	−0.202771	−	0.170145i
$622$	31.8644	+	11.5977i	1.27765	+	0.465026i
$623$	46.1528	−	16.7982i	1.84907	−	0.673007i
$624$	−9.96838	+	8.36446i	−0.399054	+	0.334846i
$625$	2.43077	+	13.7856i	0.0972308	+	0.551423i
$626$	12.9564			0.517840
$627$	−5.63041	−	5.69648i	−0.224857	−	0.227495i
$628$	−15.9290			−0.635637
$629$	−3.50134	−	19.8571i	−0.139608	−	0.791755i
$630$	−3.64543	+	3.05888i	−0.145237	+	0.121869i
$631$	8.05778	−	2.93279i	0.320775	−	0.116753i	−0.176614	−	0.984280i	$-0.556514\pi$
$631$	8.05778	−	2.93279i	0.320775	−	0.116753i	0.497389	+	0.867528i	$0.334292\pi$
$632$	1.33110	+	0.484481i	0.0529483	+	0.0192716i
$633$	−5.15064	−	4.32190i	−0.204720	−	0.171780i
$634$	31.3161	−	54.2411i	1.24372	−	2.15419i
$635$	−5.24170	−	9.07888i	−0.208010	−	0.360285i
$636$	−0.718941	+	4.07732i	−0.0285079	+	0.161676i
$637$	−0.618393	+	3.50708i	−0.0245016	+	0.138956i
$638$	−5.40167	−	9.35597i	−0.213854	−	0.370407i
$639$	3.72668	−	6.45480i	0.147425	−	0.255348i
$640$	4.60947	+	3.86780i	0.182205	+	0.152888i
$641$	−24.9234	−	9.07137i	−0.984415	−	0.358298i	−0.200860	−	0.979620i	$-0.564374\pi$
$641$	−24.9234	−	9.07137i	−0.984415	−	0.358298i	−0.783555	+	0.621322i	$0.786596\pi$
$642$	10.3969	−	3.78417i	0.410334	−	0.149349i
$643$	−16.0974	+	13.5074i	−0.634821	+	0.532678i	−0.902423	−	0.430851i	$-0.858213\pi$
$643$	−16.0974	+	13.5074i	−0.634821	+	0.532678i	0.267602	+	0.963530i	$0.413769\pi$
$644$	−5.05303	−	28.6572i	−0.199117	−	1.12925i
$645$	10.0719			0.396581
$646$	57.9612	+	5.41177i	2.28045	+	0.212923i
$647$	38.0273			1.49501			0.747505	−	0.664257i	$-0.231252\pi$
$647$	38.0273			1.49501			0.747505	+	0.664257i	$0.231252\pi$
$648$	−0.152704	−	0.866025i	−0.00599877	−	0.0340207i
$649$	11.8400	−	9.93496i	0.464762	−	0.389981i
$650$	−20.5929	+	7.49519i	−0.807719	+	0.293986i
$651$	−20.7062	−	7.53644i	−0.811540	−	0.295376i
$652$	11.8209	+	9.91890i	0.462942	+	0.388454i
$653$	−16.5959	+	28.7449i	−0.649446	+	1.12487i	0.333809	+	0.942641i	$0.391666\pi$
$653$	−16.5959	+	28.7449i	−0.649446	+	1.12487i	−0.983255	+	0.182233i	$0.941668\pi$
$654$	14.2023	+	24.5992i	0.555355	+	0.961903i
$655$	−0.365248	+	2.07142i	−0.0142714	+	0.0809372i
$656$	−3.26440	+	18.5133i	−0.127453	+	0.722823i
$657$	5.00387	+	8.66696i	0.195220	+	0.338130i
$658$	5.97178	−	10.3434i	0.232804	−	0.403229i
$659$	−30.1976	−	25.3388i	−1.17633	−	0.987059i	−0.999996	−	0.00272857i	$-0.999131\pi$
$659$	−30.1976	−	25.3388i	−1.17633	−	0.987059i	−0.176335	−	0.984330i	$-0.556424\pi$
$660$	−2.32635	−	0.846723i	−0.0905531	−	0.0329586i
$661$	1.81180	−	0.659443i	0.0704710	−	0.0256493i	−0.306544	−	0.951856i	$-0.599173\pi$
$661$	1.81180	−	0.659443i	0.0704710	−	0.0256493i	0.377015	+	0.926207i	$0.376950\pi$
$662$	7.11721	−	5.97205i	0.276618	−	0.232110i
$663$	−3.40420	−	19.3062i	−0.132208	−	0.749790i
$664$	−0.866592			−0.0336303
$665$	−10.6775	+	2.79439i	−0.414056	+	0.108362i
$666$	5.33275			0.206640
$667$	−3.58331	−	20.3220i	−0.138746	−	0.786870i
$668$	9.53983	−	8.00487i	0.369107	−	0.309718i
$669$	−4.30066	+	1.56531i	−0.166273	+	0.0605185i
$670$	5.70739	+	2.07732i	0.220496	+	0.0802538i
$671$	−0.866897	−	0.727413i	−0.0334662	−	0.0280815i
$672$	10.2306	−	17.7198i	0.394652	−	0.683558i
$673$	−6.69325	−	11.5930i	−0.258006	−	0.446879i	0.707702	−	0.706511i	$-0.249732\pi$
$673$	−6.69325	−	11.5930i	−0.258006	−	0.446879i	−0.965708	+	0.259632i	$0.916399\pi$
$674$	3.07398	−	17.4334i	0.118405	−	0.671509i
$675$	0.733956	−	4.16247i	0.0282500	−	0.160213i
$676$	4.12836	+	7.15052i	0.158783	+	0.275020i
$677$	−5.52094	+	9.56256i	−0.212187	+	0.367519i	−0.952399	−	0.304855i	$-0.901392\pi$
$677$	−5.52094	+	9.56256i	−0.212187	+	0.367519i	0.740212	+	0.672374i	$0.234725\pi$
$678$	8.75877	+	7.34948i	0.336379	+	0.282255i
$679$	−15.9684	−	5.81201i	−0.612810	−	0.223045i
$680$	−5.16385	+	1.87949i	−0.198025	+	0.0720750i
$681$	12.1361	−	10.1834i	0.465056	−	0.390229i
$682$	−4.58910	−	26.0261i	−0.175726	−	0.996590i
$683$	−9.16014			−0.350503			−0.175252	−	0.984524i	$-0.556074\pi$
$683$	−9.16014			−0.350503			−0.175252	+	0.984524i	$0.556074\pi$
$684$	−1.76604	+	6.44047i	−0.0675264	+	0.246258i
$685$	−19.1908			−0.733242
$686$	5.36484	+	30.4255i	0.204830	+	1.16165i
$687$	−2.96270	+	2.48600i	−0.113034	+	0.0948467i
$688$	−50.7661	+	18.4773i	−1.93544	+	0.704442i
$689$	7.00552	+	2.54980i	0.266889	+	0.0971397i
$690$	−8.35117	−	7.00746i	−0.317923	−	0.266769i
$691$	4.89693	−	8.48172i	0.186288	−	0.322660i	−0.757722	−	0.652578i	$-0.773688\pi$
$691$	4.89693	−	8.48172i	0.186288	−	0.322660i	0.944010	+	0.329918i	$0.107021\pi$
$692$	4.07011	+	7.04963i	0.154722	+	0.267987i
$693$	0.918748	−	5.21048i	0.0349004	−	0.197930i
$694$	−3.87211	+	21.9598i	−0.146983	+	0.833584i
$695$	−3.63563	−	6.29710i	−0.137907	−	0.238862i
$696$	1.37551	−	2.38246i	0.0521388	−	0.0903070i
$697$	−21.6951	−	18.2043i	−0.821759	−	0.689538i
$698$	−38.7502	−	14.1039i	−1.46672	−	0.533841i
$699$	−22.2939	+	8.11430i	−0.843231	+	0.306911i
$700$	14.2836	−	11.9854i	0.539869	−	0.453004i
$701$	−3.16163	−	17.9305i	−0.119413	−	0.677225i	−0.984470	−	0.175552i	$-0.943829\pi$
$701$	−3.16163	−	17.9305i	−0.119413	−	0.677225i	0.865057	−	0.501673i	$-0.167282\pi$
$702$	5.18479			0.195687
$703$	11.1789	+	5.29238i	0.421619	+	0.199606i
$704$	7.20533			0.271561
$705$	−0.337029	−	1.91139i	−0.0126933	−	0.0719871i
$706$	5.60607	−	4.70405i	0.210987	−	0.177039i
$707$	−11.6493	+	4.24000i	−0.438117	+	0.159462i
$708$	−12.1099	−	4.40766i	−0.455119	−	0.165650i
$709$	32.3109	+	27.1121i	1.21346	+	1.01822i	0.999140	+	0.0414527i	$0.0131986\pi$
$709$	32.3109	+	27.1121i	1.21346	+	1.01822i	0.214322	+	0.976763i	$0.431246\pi$
$710$	6.15910	−	10.6679i	0.231147	−	0.400358i
$711$	−0.805407	−	1.39501i	−0.0302051	−	0.0523168i
$712$	−2.60472	+	14.7721i	−0.0976161	+	0.553608i
$713$	8.76563	−	49.7124i	0.328276	−	1.86174i
$714$	19.2271	+	33.3024i	0.719558	+	1.24631i
$715$	−2.22890	+	3.86057i	−0.0833563	+	0.144377i
$716$	−19.9841	−	16.7687i	−0.746841	−	0.626674i
$717$	4.27244	+	1.55504i	0.159557	+	0.0580741i
$718$	21.2015	−	7.71670i	0.791231	−	0.287985i
$719$	−3.46451	+	2.90707i	−0.129204	+	0.108415i	−0.705100	−	0.709108i	$-0.749098\pi$
$719$	−3.46451	+	2.90707i	−0.129204	+	0.108415i	0.575896	+	0.817523i	$0.304653\pi$
$720$	−0.720285	−	4.08494i	−0.0268434	−	0.152237i
$721$	−51.2772			−1.90966
$722$	−23.2704	+	27.0846i	−0.866034	+	1.00798i
$723$	1.09327			0.0406593
$724$	−4.54117	−	25.7543i	−0.168771	−	0.957150i
$725$	10.1291	−	8.49930i	0.376184	−	0.315656i
$726$	−13.4636	+	4.90036i	−0.499682	+	0.181869i
$727$	−25.0834	−	9.12960i	−0.930291	−	0.338598i	−0.167966	−	0.985793i	$-0.553720\pi$
$727$	−25.0834	−	9.12960i	−0.930291	−	0.338598i	−0.762325	+	0.647195i	$0.775942\pi$
$728$	−5.35117	−	4.49016i	−0.198327	−	0.166416i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	8.26991	+	14.3239i	0.306083	+	0.530152i
$731$	14.1329	−	80.1519i	0.522726	−	2.96452i
$732$	−0.163848	+	0.929228i	−0.00605600	+	0.0343453i
$733$	2.52481	+	4.37311i	0.0932562	+	0.161524i	0.908879	−	0.417059i	$-0.136939\pi$
$733$	2.52481	+	4.37311i	0.0932562	+	0.161524i	−0.815623	+	0.578583i	$0.803606\pi$
$734$	25.1869	−	43.6250i	0.929666	−	1.61023i
$735$	−0.869585	−	0.729669i	−0.0320751	−	0.0269142i
$736$	44.0467	+	16.0317i	1.62358	+	0.590936i
$737$	−6.34554	+	2.30959i	−0.233741	+	0.0850748i
$738$	5.73783	−	4.81461i	0.211212	−	0.177228i
$739$	−1.46286	−	8.29628i	−0.0538121	−	0.305184i	0.946008	−	0.324143i	$-0.105076\pi$
$739$	−1.46286	−	8.29628i	−0.0538121	−	0.305184i	−0.999820	+	0.0189592i	$0.993965\pi$
$740$	3.82295			0.140534
$741$	10.8687	+	5.14555i	0.399272	+	0.189026i
$742$	−14.6236			−0.536850
$743$	9.20068	+	52.1797i	0.337540	+	1.91429i	0.400552	+	0.916274i	$0.368818\pi$
$743$	9.20068	+	52.1797i	0.337540	+	1.91429i	−0.0630120	+	0.998013i	$0.520071\pi$
$744$	5.15523	−	4.32575i	0.189000	−	0.158590i
$745$	−6.34864	+	2.31072i	−0.232596	+	0.0846581i
$746$	50.4766	+	18.3720i	1.84808	+	0.672646i
$747$	0.754900	+	0.633436i	0.0276203	+	0.0231762i
$748$	−10.0025	+	17.3249i	−0.365729	+	0.633460i
$749$	8.47565	+	14.6803i	0.309694	+	0.536405i
$750$	2.64796	−	15.0173i	0.0966897	−	0.548354i
$751$	−2.06939	+	11.7361i	−0.0755132	+	0.428257i	0.923490	+	0.383622i	$0.125323\pi$
$751$	−2.06939	+	11.7361i	−0.0755132	+	0.428257i	−0.999003	+	0.0446346i	$0.985788\pi$
$752$	5.20527	+	9.01579i	0.189817	+	0.328772i
$753$	6.88666	−	11.9280i	0.250964	−	0.434682i
$754$	12.4251	+	10.4259i	0.452497	+	0.379690i
$755$	4.91147	+	1.78763i	0.178747	+	0.0650585i
$756$	−4.14543	+	1.50881i	−0.150768	+	0.0548750i
$757$	−23.6138	+	19.8143i	−0.858258	+	0.720164i	−0.961592	−	0.274482i	$-0.911493\pi$
$757$	−23.6138	+	19.8143i	−0.858258	+	0.720164i	0.103334	+	0.994647i	$0.467049\pi$
$758$	−1.01114	−	5.73448i	−0.0367264	−	0.208286i
$759$	12.1206			0.439950
$760$	0.891407	−	3.25082i	0.0323347	−	0.117919i
$761$	43.9053			1.59157			0.795783	−	0.605582i	$-0.207060\pi$
$761$	43.9053			1.59157			0.795783	+	0.605582i	$0.207060\pi$
$762$	−3.89053	−	22.0643i	−0.140939	−	0.799305i
$763$	−33.3371	+	27.9731i	−1.20688	+	1.01270i
$764$	−5.21688	+	1.89879i	−0.188740	+	0.0686958i
$765$	5.87211	+	2.13727i	0.212307	+	0.0772733i
$766$	−41.2092	−	34.5786i	−1.48895	−	1.24938i
$767$	−11.6027	+	20.0964i	−0.418948	+	0.725639i
$768$	10.3512	+	17.9287i	0.373516	+	0.646948i
$769$	−1.53895	+	8.72783i	−0.0554960	+	0.314734i	−0.999901	−	0.0140500i	$-0.995528\pi$
$769$	−1.53895	+	8.72783i	−0.0554960	+	0.314734i	0.944405	+	0.328784i	$0.106639\pi$
$770$	1.51842	−	8.61138i	0.0547200	−	0.310333i
$771$	6.43376	+	11.1436i	0.231706	+	0.401327i
$772$	3.92468	−	6.79774i	0.141252	−	0.244656i
$773$	34.1987	+	28.6961i	1.23004	+	1.03213i	0.998236	+	0.0593647i	$0.0189075\pi$
$773$	34.1987	+	28.6961i	1.23004	+	1.03213i	0.231805	+	0.972762i	$0.425537\pi$
$774$	20.2271	+	7.36208i	0.727050	+	0.264624i
$775$	30.3949	−	11.0628i	1.09182	−	0.397388i
$776$	3.97565	−	3.33597i	0.142718	−	0.119754i
$777$	1.41875	+	8.04612i	0.0508973	+	0.288653i
$778$	−42.1248			−1.51025
$779$	16.8062	−	4.39831i	0.602144	−	0.157586i
$780$	3.71688			0.133086
$781$	2.37820	+	13.4875i	0.0850988	+	0.482619i
$782$	−67.4834	+	56.6253i	−2.41320	+	2.02492i
$783$	−2.93969	+	1.06996i	−0.105056	+	0.0382373i
$784$	5.72163	+	2.08250i	0.204344	+	0.0743751i
$785$	−7.00387	−	5.87695i	−0.249979	−	0.209757i
$786$	−2.24763	+	3.89300i	−0.0801702	+	0.138859i
$787$	9.25268	+	16.0261i	0.329822	+	0.571269i	0.982476	−	0.186387i	$-0.0596778\pi$
$787$	9.25268	+	16.0261i	0.329822	+	0.571269i	−0.652654	+	0.757656i	$0.726344\pi$
$788$	−2.42855	+	13.7730i	−0.0865134	+	0.490642i
$789$	2.40373	−	13.6322i	0.0855752	−	0.485321i
$790$	−1.33110	−	2.30553i	−0.0473584	−	0.0820271i
$791$	−8.75877	+	15.1706i	−0.311426	+	0.539406i
$792$	1.23783	+	1.03866i	0.0439842	+	0.0369072i
$793$	1.59657	+	0.581104i	0.0566959	+	0.0206356i
$794$	24.2503	−	8.82639i	0.860611	−	0.313237i
$795$	−1.82042	+	1.52752i	−0.0645637	+	0.0541754i
$796$	5.87551	+	33.3217i	0.208252	+	1.18106i
$797$	−15.3209			−0.542694			−0.271347	−	0.962482i	$-0.587469\pi$
$797$	−15.3209			−0.542694			−0.271347	+	0.962482i	$0.587469\pi$
$798$	−23.4859	−	2.19285i	−0.831393	−	0.0776262i
$799$	−15.6837			−0.554848
$800$	5.21554	+	29.5788i	0.184397	+	1.04577i
$801$	13.0667	−	10.9643i	0.461689	−	0.387403i
$802$	51.7217	−	18.8252i	1.82636	−	0.664739i
$803$	−17.2802	−	6.28947i	−0.609804	−	0.221951i
$804$	4.31315	+	3.61916i	0.152113	+	0.127638i
$805$	8.35117	−	14.4646i	0.294340	−	0.509812i
$806$	19.8388	+	34.3619i	0.698793	+	1.21035i
$807$	2.41147	−	13.6761i	0.0848879	−	0.481423i
$808$	0.657451	−	3.72859i	0.0231291	−	0.131171i
$809$	7.04798	+	12.2075i	0.247794	+	0.429191i	0.962913	−	0.269811i	$-0.0869611\pi$
$809$	7.04798	+	12.2075i	0.247794	+	0.429191i	−0.715120	+	0.699002i	$0.753628\pi$
$810$	−0.826352	+	1.43128i	−0.0290350	+	0.0502902i
$811$	−33.4996	−	28.1095i	−1.17633	−	0.987058i	−0.999996	−	0.00272731i	$-0.999132\pi$
$811$	−33.4996	−	28.1095i	−1.17633	−	0.987058i	−0.176333	−	0.984330i	$-0.556424\pi$
$812$	−12.9684	−	4.72010i	−0.455101	−	0.165643i
$813$	5.53849	−	2.01584i	0.194243	−	0.0706987i
$814$	−7.50640	+	6.29861i	−0.263099	+	0.220766i
$815$	1.53802	+	8.72254i	0.0538744	+	0.305537i
$816$	−33.5185			−1.17338
$817$	35.0951	+	35.5069i	1.22782	+	1.24223i
$818$	−4.38919			−0.153464
$819$	1.37939	+	7.82288i	0.0481996	+	0.273354i
$820$	4.11334	−	3.45150i	0.143644	−	0.120532i
$821$	12.1189	−	4.41090i	0.422951	−	0.153942i	−0.121771	−	0.992558i	$-0.538857\pi$
$821$	12.1189	−	4.41090i	0.422951	−	0.153942i	0.544722	+	0.838617i	$0.316635\pi$
$822$	−38.5403	−	14.0275i	−1.34425	−	0.489266i
$823$	23.7802	+	19.9539i	0.828925	+	0.695551i	0.955044	−	0.296464i	$-0.0958076\pi$
$823$	23.7802	+	19.9539i	0.828925	+	0.695551i	−0.126119	+	0.992015i	$0.540252\pi$
$824$	7.83022	−	13.5623i	0.272779	−	0.472467i
$825$	3.88326	+	6.72600i	0.135198	+	0.234169i
$826$	7.90420	−	44.8269i	0.275022	−	1.55973i
$827$	4.61990	−	26.2008i	0.160650	−	0.911089i	−0.792788	−	0.609498i	$-0.791371\pi$
$827$	4.61990	−	26.2008i	0.160650	−	0.911089i	0.953437	−	0.301591i	$-0.0975179\pi$
$828$	−5.05303	−	8.75211i	−0.175605	−	0.304157i
$829$	−24.1832	+	41.8865i	−0.839917	+	1.45478i	0.0500459	+	0.998747i	$0.484063\pi$
$829$	−24.1832	+	41.8865i	−0.839917	+	1.45478i	−0.889963	+	0.456032i	$0.849270\pi$
$830$	1.24763	+	1.04688i	0.0433057	+	0.0363378i
$831$	−4.26517	−	1.55239i	−0.147957	−	0.0538519i
$832$	−10.1655	+	3.69994i	−0.352425	+	0.128272i
$833$	−7.02687	+	5.89625i	−0.243467	+	0.204293i
$834$	−2.69846	−	15.3037i	−0.0934401	−	0.529925i
$835$	7.14796			0.247365
$836$	−5.12108	−	11.1515i	−0.177116	−	0.385684i
$837$	−7.65270			−0.264516
$838$	0.742001	+	4.20810i	0.0256320	+	0.145366i
$839$	−13.4003	+	11.2442i	−0.462631	+	0.388193i	−0.844098	−	0.536189i	$-0.819863\pi$
$839$	−13.4003	+	11.2442i	−0.462631	+	0.388193i	0.381467	+	0.924382i	$0.375419\pi$
$840$	2.09240	−	0.761570i	0.0721945	−	0.0262767i
$841$	18.0547	+	6.57137i	0.622575	+	0.226599i
$842$	27.3803	+	22.9748i	0.943588	+	0.791764i
$843$	−8.51620	+	14.7505i	−0.293313	+	0.508034i
$844$	−5.15064	−	8.92118i	−0.177292	−	0.307080i
$845$	−0.822948	+	4.66717i	−0.0283103	+	0.160556i
$846$	0.720285	−	4.08494i	0.0247639	−	0.140443i
$847$	−10.9757	−	19.0104i	−0.377128	−	0.653205i
$848$	6.37329	−	11.0389i	0.218860	−	0.379076i
$849$	−17.4381	−	14.6323i	−0.598474	−	0.502179i
$850$	−53.0433	−	19.3062i	−1.81937	−	0.662196i
$851$	−17.5881	+	6.40155i	−0.602913	+	0.219442i
$852$	8.74763	−	7.34013i	0.299689	−	0.251469i
$853$	−9.83884	−	55.7988i	−0.336875	−	1.91052i	−0.407872	−	0.913039i	$-0.633729\pi$
$853$	−9.83884	−	55.7988i	−0.336875	−	1.91052i	0.0709964	−	0.997477i	$-0.477382\pi$
$854$	−3.33275			−0.114044
$855$	−3.15270	+	2.18025i	−0.107820	+	0.0745631i
$856$	−5.17705			−0.176948
$857$	5.05927	+	28.6925i	0.172821	+	0.980118i	0.940629	+	0.339437i	$0.110237\pi$
$857$	5.05927	+	28.6925i	0.172821	+	0.980118i	−0.767807	+	0.640681i	$0.778652\pi$
$858$	−7.29813	+	6.12386i	−0.249154	+	0.209065i
$859$	16.8332	−	6.12679i	0.574342	−	0.209043i	−0.0384868	−	0.999259i	$-0.512254\pi$
$859$	16.8332	−	6.12679i	0.574342	−	0.209043i	0.612829	+	0.790216i	$0.290032\pi$
$860$	14.5005	+	5.27774i	0.494462	+	0.179969i
$861$	8.79086	+	7.37641i	0.299592	+	0.251387i
$862$	12.0223	−	20.8232i	0.409481	−	0.709242i
$863$	11.6373	+	20.1564i	0.396138	+	0.686130i	0.993246	−	0.116030i	$-0.0370170\pi$
$863$	11.6373	+	20.1564i	0.396138	+	0.686130i	−0.597108	+	0.802161i	$0.703684\pi$
$864$	1.23396	−	6.99811i	0.0419800	−	0.238081i
$865$	−0.811337	+	4.60132i	−0.0275863	+	0.156450i
$866$	−13.6959	−	23.7221i	−0.465407	−	0.806108i
$867$	16.7481	−	29.0085i	0.568795	−	0.985182i
$868$	−25.8614	−	21.7003i	−0.877794	−	0.736557i
$869$	2.78136	+	1.01233i	0.0943513	+	0.0343411i
$870$	−4.85844	+	1.76833i	−0.164717	+	0.0599519i
$871$	7.76651	−	6.51688i	0.263158	−	0.220816i
$872$	−2.30793	−	13.0889i	−0.0781565	−	0.443247i
$873$	−5.90167			−0.199741
$874$	−4.39558	−	53.8579i	−0.148683	−	1.82177i
$875$	23.3628			0.789806
$876$	2.66250	+	15.0998i	0.0899577	+	0.510175i
$877$	21.1713	−	17.7649i	0.714905	−	0.599877i	−0.211065	−	0.977472i	$-0.567693\pi$
$877$	21.1713	−	17.7649i	0.714905	−	0.599877i	0.925971	+	0.377595i	$0.123249\pi$
$878$	−43.4791	+	15.8251i	−1.46735	+	0.534071i
$879$	−5.22416	−	1.90144i	−0.176206	−	0.0641339i
$880$	5.83868	+	4.89923i	0.196822	+	0.165153i
$881$	−7.70187	+	13.3400i	−0.259482	+	0.449437i	−0.966103	−	0.258155i	$-0.916885\pi$
$881$	−7.70187	+	13.3400i	−0.259482	+	0.449437i	0.706621	+	0.707592i	$0.250219\pi$
$882$	−1.21301	−	2.10100i	−0.0408442	−	0.0707442i
$883$	3.94727	−	22.3861i	0.132836	−	0.753352i	−0.843506	−	0.537120i	$-0.819512\pi$
$883$	3.94727	−	22.3861i	0.132836	−	0.753352i	0.976342	−	0.216232i	$-0.0693767\pi$
$884$	5.21554	−	29.5788i	0.175418	−	0.994842i
$885$	−3.69846	−	6.40593i	−0.124322	−	0.215333i
$886$	−36.2114	+	62.7200i	−1.21655	+	2.10712i
$887$	−9.23577	−	7.74973i	−0.310107	−	0.260210i	0.474429	−	0.880294i	$-0.342654\pi$
$887$	−9.23577	−	7.74973i	−0.310107	−	0.260210i	−0.784536	+	0.620083i	$0.787099\pi$
$888$	−2.34477	−	0.853427i	−0.0786853	−	0.0286391i
$889$	32.2558	−	11.7402i	1.08183	−	0.393752i
$890$	21.5954	−	18.1207i	0.723879	−	0.607407i
$891$	−0.319078	−	1.80958i	−0.0106895	−	0.0606232i
$892$	−7.01186			−0.234774
$893$	5.56393	−	7.84829i	0.186190	−	0.262633i
$894$	−14.4388			−0.482906
$895$	−2.60014	−	14.7461i	−0.0869130	−	0.492908i
$896$	−15.0929	+	12.6644i	−0.504217	+	0.423088i
$897$	−17.1001	+	6.22394i	−0.570957	+	0.207811i
$898$	62.1306	+	22.6137i	2.07333	+	0.754629i
$899$	−18.3394	−	15.3886i	−0.611653	−	0.513238i
$900$	3.23783	−	5.60808i	0.107928	−	0.186936i
$901$	9.60148	+	16.6303i	0.319872	+	0.554034i
$902$	−2.38996	+	13.5541i	−0.0795769	+	0.451303i
$903$	−5.72668	+	32.4776i	−0.190572	+	1.08079i
$904$	−2.67499	−	4.63322i	−0.0889689	−	0.154099i
$905$	7.50521	−	12.9994i	0.249482	−	0.432115i
$906$	8.55690	+	7.18009i	0.284284	+	0.238543i
$907$	33.4320	+	12.1683i	1.11009	+	0.404040i	0.831027	−	0.556232i	$-0.187753\pi$
$907$	33.4320	+	12.1683i	1.11009	+	0.404040i	0.279065	+	0.960272i	$0.409976\pi$
$908$	22.8084	−	8.30158i	0.756923	−	0.275498i
$909$	−3.29813	+	2.76746i	−0.109392	+	0.0917909i
$910$	2.27972	+	12.9289i	0.0755718	+	0.428589i
$911$	7.00505			0.232088			0.116044	−	0.993244i	$-0.462979\pi$
$911$	7.00505			0.232088			0.116044	+	0.993244i	$0.462979\pi$
$912$	11.8910	−	16.7730i	0.393750	−	0.555411i
$913$	−1.81076			−0.0599276
$914$	−4.50310	−	25.5383i	−0.148949	−	0.844733i
$915$	−0.414878	+	0.348124i	−0.0137154	+	0.0115086i
$916$	−5.56805	+	2.02660i	−0.183973	+	0.0669609i
$917$	−6.47178	−	2.35554i	−0.213717	−	0.0777866i
$918$	10.2306	+	8.58445i	0.337659	+	0.283329i
$919$	4.18227	−	7.24390i	0.137960	−	0.238954i	−0.788764	−	0.614696i	$-0.789279\pi$
$919$	4.18227	−	7.24390i	0.137960	−	0.238954i	0.926724	+	0.375742i	$0.122612\pi$
$920$	2.55051	+	4.41761i	0.0840877	+	0.145644i
$921$	2.05438	−	11.6510i	0.0676940	−	0.383912i
$922$	7.92127	−	44.9238i	0.260873	−	1.47949i
$923$	−10.2811	−	17.8073i	−0.338405	−	0.586135i
$924$	4.05303	−	7.02006i	0.133335	−	0.230943i
$925$	−9.18732	−	7.70908i	−0.302077	−	0.253473i
$926$	19.9402	+	7.25762i	0.655274	+	0.238500i
$927$	−16.7344	+	6.09083i	−0.549631	+	0.200049i
$928$	17.0294	−	14.2894i	0.559017	−	0.469071i
$929$	8.83322	+	50.0957i	0.289808	+	1.64359i	0.687586	+	0.726103i	$0.258671\pi$
$929$	8.83322	+	50.0957i	0.289808	+	1.64359i	−0.397777	+	0.917482i	$0.630218\pi$
$930$	−12.6477			−0.414733
$931$	−0.457700	−	5.60808i	−0.0150005	−	0.183797i
$932$	−36.3482			−1.19063
$933$	3.13310	+	17.7687i	0.102573	+	0.581722i
$934$	−6.89306	+	5.78396i	−0.225548	+	0.189257i
$935$	−10.7900	+	3.92723i	−0.352870	+	0.128434i
$936$	−2.27972	−	0.829748i	−0.0745148	−	0.0271212i
$937$	18.0646	+	15.1580i	0.590146	+	0.495191i	0.888261	−	0.459338i	$-0.151913\pi$
$937$	18.0646	+	15.1580i	0.590146	+	0.495191i	−0.298115	+	0.954530i	$0.596358\pi$
$938$	−9.94356	+	17.2228i	−0.324669	+	0.562343i
$939$	3.44697	+	5.97032i	0.112488	+	0.194834i
$940$	0.516359	−	2.92842i	0.0168418	−	0.0955144i
$941$	−7.76036	+	44.0112i	−0.252981	+	1.43472i	0.548223	+	0.836332i	$0.315305\pi$
$941$	−7.76036	+	44.0112i	−0.252981	+	1.43472i	−0.801203	+	0.598392i	$0.795807\pi$
$942$	−9.76991	−	16.9220i	−0.318321	−	0.551348i
$943$	−13.1446	+	22.7670i	−0.428046	+	0.741397i
$944$	30.3935	+	25.5032i	0.989225	+	0.830058i
$945$	−2.37939	−	0.866025i	−0.0774014	−	0.0281718i
$946$	−37.1673	+	13.5278i	−1.20841	+	0.439827i
$947$	−32.3107	+	27.1119i	−1.04996	+	0.881018i	−0.993089	−	0.117364i	$-0.962556\pi$
$947$	−32.3107	+	27.1119i	−1.04996	+	0.881018i	−0.0568670	+	0.998382i	$0.518111\pi$
$948$	−0.428548	−	2.43042i	−0.0139186	−	0.0789363i
$949$	27.6091			0.896228
$950$	28.4786	−	19.6944i	0.923969	−	0.638972i
$951$	33.3259			1.08067
$952$	−3.12449	−	17.7198i	−0.101265	−	0.574303i
$953$	39.6430	−	33.2644i	1.28416	−	1.07754i	0.291505	−	0.956569i	$-0.405844\pi$
$953$	39.6430	−	33.2644i	1.28416	−	1.07754i	0.992656	−	0.120970i	$-0.0386005\pi$
$954$	−4.77244	+	1.73703i	−0.154513	+	0.0562383i
$955$	−2.99437	−	1.08986i	−0.0968957	−	0.0352671i
$956$	5.33615	+	4.47756i	0.172583	+	0.144815i
$957$	2.87417	−	4.97821i	0.0929087	−	0.160923i
$958$	15.8897	+	27.5217i	0.513371	+	0.889185i
$959$	10.9115	−	61.8820i	0.352350	−	1.99828i
$960$	0.598793	−	3.39592i	0.0193260	−	0.109603i
$961$	−13.7819	−	23.8710i	−0.444579	−	0.770033i
$962$	7.35591	−	12.7408i	0.237164	−	0.410780i
$963$	4.50980	+	3.78417i	0.145326	+	0.121943i
$964$	1.57398	+	0.572881i	0.0506944	+	0.0184513i
$965$	4.23365	−	1.54092i	0.136286	−	0.0496041i
$966$	27.3444	−	22.9446i	0.879790	−	0.738232i
$967$	3.10039	+	17.5832i	0.0997017	+	0.565436i	0.993205	+	0.116379i	$0.0371288\pi$
$967$	3.10039	+	17.5832i	0.0997017	+	0.565436i	−0.893503	+	0.449057i	$0.851760\pi$
$968$	6.70409			0.215478
$969$	12.9265	+	28.1484i	0.415259	+	0.904257i
$970$	−9.75372			−0.313173
$971$	−7.21419	−	40.9137i	−0.231514	−	1.31298i	−0.849831	−	0.527055i	$-0.823296\pi$
$971$	−7.21419	−	40.9137i	−0.231514	−	1.31298i	0.618317	−	0.785929i	$-0.287815\pi$
$972$	−1.17365	+	0.984808i	−0.0376448	+	0.0315877i
$973$	22.3726	−	8.14295i	0.717232	−	0.261051i
$974$	−13.7113	−	4.99049i	−0.439337	−	0.159906i
$975$	−8.93242	−	7.49519i	−0.286066	−	0.240038i
$976$	1.45249	−	2.51578i	0.0464929	−	0.0805281i
$977$	−6.17634	−	10.6977i	−0.197599	−	0.342251i	0.750151	−	0.661267i	$-0.229981\pi$
$977$	−6.17634	−	10.6977i	−0.197599	−	0.342251i	−0.947749	+	0.319016i	$0.896648\pi$
$978$	−3.28699	+	18.6414i	−0.105106	+	0.596088i
$979$	−5.44263	+	30.8667i	−0.173947	+	0.986504i
$980$	−0.869585	−	1.50617i	−0.0277779	−	0.0481127i
$981$	−7.55690	+	13.0889i	−0.241273	+	0.417898i
$982$	−20.9119	−	17.5472i	−0.667327	−	0.559954i
$983$	−15.2875	−	5.56418i	−0.487594	−	0.177470i	0.0865117	−	0.996251i	$-0.472428\pi$
$983$	−15.2875	−	5.56418i	−0.487594	−	0.177470i	−0.574106	+	0.818781i	$0.694650\pi$
$984$	−3.29339	+	1.19869i	−0.104989	+	0.0382130i
$985$	−6.14930	+	5.15988i	−0.195933	+	0.164407i
$986$	7.25490	+	41.1446i	0.231043	+	1.31031i
$987$	6.35504			0.202283
$988$	12.9513	+	13.1033i	0.412036	+	0.416870i
$989$	−75.5494			−2.40233
$990$	−0.527341	−	2.99070i	−0.0167600	−	0.0950507i
$991$	8.50253	−	7.13447i	0.270092	−	0.226634i	−0.497675	−	0.867364i	$-0.665813\pi$
$991$	8.50253	−	7.13447i	0.270092	−	0.226634i	0.767766	+	0.640730i	$0.221368\pi$
$992$	51.1011	−	18.5993i	1.62246	−	0.590527i
$993$	4.64543	+	1.69080i	0.147418	+	0.0536559i
$994$	30.8974	+	25.9260i	0.980006	+	0.822323i
$995$	−9.71048	+	16.8191i	−0.307843	+	0.533200i
$996$	0.754900	+	1.30753i	0.0239199	+	0.0414305i
$997$	−2.71688	+	15.4082i	−0.0860445	+	0.487983i	0.911082	+	0.412226i	$0.135248\pi$
$997$	−2.71688	+	15.4082i	−0.0860445	+	0.487983i	−0.997126	+	0.0757570i	$0.975863\pi$
$998$	9.22580	−	52.3221i	0.292038	−	1.65623i
$999$	1.41875	+	2.45734i	0.0448872	+	0.0777469i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.2.i.a.28.1	✓	6
3.2	odd	2		171.2.u.a.28.1		6
4.3	odd	2		912.2.bo.b.769.1		6
19.6	even	9		1083.2.a.m.1.3		3
19.13	odd	18		1083.2.a.n.1.1		3
19.17	even	9	inner	57.2.i.a.55.1	yes	6
57.17	odd	18		171.2.u.a.55.1		6
57.32	even	18		3249.2.a.x.1.3		3
57.44	odd	18		3249.2.a.w.1.1		3
76.55	odd	18		912.2.bo.b.625.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.i.a.28.1	✓	6	1.1	even	1	trivial
57.2.i.a.55.1	yes	6	19.17	even	9	inner
171.2.u.a.28.1		6	3.2	odd	2
171.2.u.a.55.1		6	57.17	odd	18
912.2.bo.b.625.1		6	76.55	odd	18
912.2.bo.b.769.1		6	4.3	odd	2
1083.2.a.m.1.3		3	19.6	even	9
1083.2.a.n.1.1		3	19.13	odd	18
3249.2.a.w.1.1		3	57.44	odd	18
3249.2.a.x.1.3		3	57.32	even	18

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:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	57.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.326352 + 1.85083i) q^{2} +(-0.766044 + 0.642788i) q^{3} +(-1.43969 + 0.524005i) q^{4} +(-0.826352 - 0.300767i) q^{5} +(-1.43969 - 1.20805i) q^{6} +(1.43969 - 2.49362i) q^{7} +(0.439693 + 0.761570i) q^{8} +(0.173648 - 0.984808i) q^{9} +(0.286989 - 1.62760i) q^{10} +(0.918748 + 1.59132i) q^{11} +(0.766044 - 1.32683i) q^{12} +(-2.11334 - 1.77330i) q^{13} +(5.08512 + 1.85083i) q^{14} +(0.826352 - 0.300767i) q^{15} +(-3.61334 + 3.03195i) q^{16} +(-1.23396 - 6.99811i) q^{17} +1.87939 q^{18} +(3.93969 + 1.86516i) q^{19} +1.34730 q^{20} +(0.500000 + 2.83564i) q^{21} +(-2.64543 + 2.21978i) q^{22} +(-6.19846 + 2.25606i) q^{23} +(-0.826352 - 0.300767i) q^{24} +(-3.23783 - 2.71686i) q^{25} +(2.59240 - 4.49016i) q^{26} +(0.500000 + 0.866025i) q^{27} +(-0.766044 + 4.34445i) q^{28} +(-0.543233 + 3.08083i) q^{29} +(0.826352 + 1.43128i) q^{30} +(-3.82635 + 6.62744i) q^{31} +(-5.44356 - 4.56769i) q^{32} +(-1.72668 - 0.628461i) q^{33} +(12.5496 - 4.56769i) q^{34} +(-1.93969 + 1.62760i) q^{35} +(0.266044 + 1.50881i) q^{36} +2.83750 q^{37} +(-2.16637 + 7.90041i) q^{38} +2.75877 q^{39} +(-0.134285 - 0.761570i) q^{40} +(3.05303 - 2.56180i) q^{41} +(-5.08512 + 1.85083i) q^{42} +(10.7626 + 3.91728i) q^{43} +(-2.15657 - 1.80958i) q^{44} +(-0.439693 + 0.761570i) q^{45} +(-6.19846 - 10.7361i) q^{46} +(0.383256 - 2.17355i) q^{47} +(0.819078 - 4.64522i) q^{48} +(-0.645430 - 1.11792i) q^{49} +(3.97178 - 6.87933i) q^{50} +(5.44356 + 4.56769i) q^{51} +(3.97178 + 1.44561i) q^{52} +(-2.53936 + 0.924252i) q^{53} +(-1.43969 + 1.20805i) q^{54} +(-0.280592 - 1.59132i) q^{55} +2.53209 q^{56} +(-4.21688 + 1.10359i) q^{57} -5.87939 q^{58} +(-1.46064 - 8.28368i) q^{59} +(-1.03209 + 0.866025i) q^{60} +(-0.578726 + 0.210639i) q^{61} +(-13.5150 - 4.91906i) q^{62} +(-2.20574 - 1.85083i) q^{63} +(1.96064 - 3.39592i) q^{64} +(1.21301 + 2.10100i) q^{65} +(0.599670 - 3.40090i) q^{66} +(-0.638156 + 3.61916i) q^{67} +(5.44356 + 9.42853i) q^{68} +(3.29813 - 5.71253i) q^{69} +(-3.64543 - 3.05888i) q^{70} +(7.00387 + 2.54920i) q^{71} +(0.826352 - 0.300767i) q^{72} +(-7.66637 + 6.43285i) q^{73} +(0.926022 + 5.25173i) q^{74} +4.22668 q^{75} +(-6.64930 - 0.620838i) q^{76} +5.29086 q^{77} +(0.900330 + 5.10602i) q^{78} +(1.23396 - 1.03541i) q^{79} +(3.89780 - 1.41868i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(5.73783 + 4.81461i) q^{82} +(-0.492726 + 0.853427i) q^{83} +(-2.20574 - 3.82045i) q^{84} +(-1.08512 + 6.15403i) q^{85} +(-3.73783 + 21.1983i) q^{86} +(-1.56418 - 2.70924i) q^{87} +(-0.807934 + 1.39938i) q^{88} +(13.0667 + 10.9643i) q^{89} +(-1.55303 - 0.565258i) q^{90} +(-7.46451 + 2.71686i) q^{91} +(7.74170 - 6.49605i) q^{92} +(-1.32888 - 7.53644i) q^{93} +4.14796 q^{94} +(-2.69459 - 2.72621i) q^{95} +7.10607 q^{96} +(-1.02481 - 5.81201i) q^{97} +(1.85844 - 1.55942i) q^{98} +(1.72668 - 0.628461i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} - 6 q^{10} + 3 q^{11} - 6 q^{13} + 9 q^{14} + 6 q^{15} - 15 q^{16} - 12 q^{17} + 18 q^{19} + 6 q^{20} + 3 q^{21} - 9 q^{23} - 6 q^{24} + 12 q^{26}+ \cdots - 3 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 - 6 * q^10 + 3 * q^11 - 6 * q^13 + 9 * q^14 + 6 * q^15 - 15 * q^16 - 12 * q^17 + 18 * q^19 + 6 * q^20 + 3 * q^21 - 9 * q^23 - 6 * q^24 + 12 * q^26 + 3 * q^27 + 12 * q^29 + 6 * q^30 - 24 * q^31 - 3 * q^32 + 3 * q^33 + 21 * q^34 - 6 * q^35 - 3 * q^36 + 12 * q^37 + 6 * q^38 - 6 * q^39 + 9 * q^40 + 6 * q^41 - 9 * q^42 + 18 * q^43 + 9 * q^44 + 3 * q^45 - 9 * q^46 - 33 * q^47 - 12 * q^48 + 12 * q^49 + 9 * q^50 + 3 * q^51 + 9 * q^52 - 24 * q^53 - 3 * q^54 - 33 * q^55 + 6 * q^56 - 9 * q^57 - 24 * q^58 + 3 * q^60 - 21 * q^61 - 51 * q^62 - 3 * q^63 + 3 * q^64 + 15 * q^65 + 18 * q^66 + 30 * q^67 + 3 * q^68 + 6 * q^69 - 6 * q^70 + 18 * q^71 + 6 * q^72 - 27 * q^73 + 21 * q^74 + 12 * q^75 - 9 * q^78 + 12 * q^79 + 24 * q^80 + 15 * q^82 + 15 * q^83 - 3 * q^84 + 15 * q^85 - 3 * q^86 + 9 * q^87 + 6 * q^88 + 45 * q^89 + 3 * q^90 - 12 * q^91 + 3 * q^92 + 6 * q^93 - 6 * q^94 - 12 * q^95 + 18 * q^96 + 21 * q^97 + 3 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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