LMFDB - Embedded newform 189.2.ba.a.101.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(5,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

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

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

chi := DirichletCharacter("189.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (of order $18$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.20
Character	$\chi$	$=$	189.101
Dual form			189.2.ba.a.131.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.47978 - 1.76353i) q^{2} +(1.66401 - 0.480715i) q^{3} +(-0.573000 - 3.24965i) q^{4} +(-1.41208 + 1.18487i) q^{5} +(1.61460 - 3.64587i) q^{6} +(-2.40040 + 1.11270i) q^{7} +(-2.59137 - 1.49613i) q^{8} +(2.53783 - 1.59982i) q^{9} +O(q^{10})$	\(q+(1.47978 - 1.76353i) q^{2} +(1.66401 - 0.480715i) q^{3} +(-0.573000 - 3.24965i) q^{4} +(-1.41208 + 1.18487i) q^{5} +(1.61460 - 3.64587i) q^{6} +(-2.40040 + 1.11270i) q^{7} +(-2.59137 - 1.49613i) q^{8} +(2.53783 - 1.59982i) q^{9} +4.24358i q^{10} +(-0.0789393 + 0.0940762i) q^{11} +(-2.51563 - 5.13198i) q^{12} +(0.0159063 - 0.0437022i) q^{13} +(-1.58977 + 5.87972i) q^{14} +(-1.78012 + 2.65044i) q^{15} +(-0.271551 + 0.0988366i) q^{16} +0.157246 q^{17} +(0.934081 - 6.84292i) q^{18} +7.59626i q^{19} +(4.65954 + 3.90982i) q^{20} +(-3.45938 + 3.00544i) q^{21} +(0.0490936 + 0.278423i) q^{22} +(0.332628 - 0.913889i) q^{23} +(-5.03126 - 1.24385i) q^{24} +(-0.278205 + 1.57778i) q^{25} +(-0.0535324 - 0.0927208i) q^{26} +(3.45390 - 3.88209i) q^{27} +(4.99131 + 7.16286i) q^{28} +(-3.33678 - 9.16772i) q^{29} +(2.03995 + 7.06135i) q^{30} +(-4.49600 + 0.792766i) q^{31} +(1.81929 - 4.99845i) q^{32} +(-0.0861316 + 0.194490i) q^{33} +(0.232689 - 0.277308i) q^{34} +(2.07113 - 4.41538i) q^{35} +(-6.65304 - 7.33034i) q^{36} +(-4.68718 + 8.11843i) q^{37} +(13.3962 + 11.2408i) q^{38} +(0.00545988 - 0.0803671i) q^{39} +(5.43192 - 0.957794i) q^{40} +(-5.76925 - 2.09983i) q^{41} +(0.181079 + 10.5481i) q^{42} +(1.67890 - 9.52153i) q^{43} +(0.350947 + 0.202619i) q^{44} +(-1.68802 + 5.26607i) q^{45} +(-1.11945 - 1.93895i) q^{46} +(0.723937 - 4.10565i) q^{47} +(-0.404351 + 0.295003i) q^{48} +(4.52380 - 5.34184i) q^{49} +(2.37078 + 2.82539i) q^{50} +(0.261658 - 0.0755904i) q^{51} +(-0.151131 - 0.0266485i) q^{52} +(0.141686 + 0.0818025i) q^{53} +(-1.73517 - 11.8357i) q^{54} -0.226376i q^{55} +(7.88504 + 0.707881i) q^{56} +(3.65163 + 12.6402i) q^{57} +(-21.1052 - 7.68168i) q^{58} +(11.1248 + 4.04911i) q^{59} +(9.63300 + 4.26604i) q^{60} +(2.98946 + 0.527123i) q^{61} +(-5.25501 + 9.10194i) q^{62} +(-4.31166 + 6.66405i) q^{63} +(-6.41175 - 11.1055i) q^{64} +(0.0293206 + 0.0805578i) q^{65} +(0.215534 + 0.439698i) q^{66} +(-7.53281 + 6.32078i) q^{67} +(-0.0901020 - 0.510994i) q^{68} +(0.114175 - 1.68062i) q^{69} +(-4.72184 - 10.1863i) q^{70} +(-0.863276 + 0.498413i) q^{71} +(-8.96997 + 0.348821i) q^{72} +(7.95454 - 4.59256i) q^{73} +(7.38112 + 20.2795i) q^{74} +(0.295527 + 2.75917i) q^{75} +(24.6852 - 4.35266i) q^{76} +(0.0848069 - 0.313656i) q^{77} +(-0.133650 - 0.128554i) q^{78} +(1.99133 + 1.67093i) q^{79} +(0.266342 - 0.461318i) q^{80} +(3.88113 - 8.12015i) q^{81} +(-12.2403 + 7.06695i) q^{82} +(6.02764 - 2.19388i) q^{83} +(11.7489 + 9.51964i) q^{84} +(-0.222043 + 0.186316i) q^{85} +(-14.3071 - 17.0505i) q^{86} +(-9.95947 - 13.6511i) q^{87} +(0.345310 - 0.125683i) q^{88} -10.6041 q^{89} +(6.78899 + 10.7695i) q^{90} +(0.0104460 + 0.122602i) q^{91} +(-3.16041 - 0.557266i) q^{92} +(-7.10027 + 3.48046i) q^{93} +(-6.16918 - 7.35214i) q^{94} +(-9.00059 - 10.7265i) q^{95} +(0.624474 - 9.19200i) q^{96} +(-13.2580 - 2.33775i) q^{97} +(-2.72628 - 15.8826i) q^{98} +(-0.0498289 + 0.365038i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.47978	−	1.76353i	1.04636	−	1.24700i	0.0781303	−	0.996943i	$-0.475105\pi$
$2$	1.47978	−	1.76353i	1.04636	−	1.24700i	0.968230	−	0.250061i	$-0.0804506\pi$
$3$	1.66401	−	0.480715i	0.960714	−	0.277541i
$3$	1.66401	−	0.480715i	0.960714	−	0.277541i
$4$	−0.573000	−	3.24965i	−0.286500	−	1.62482i
$5$	−1.41208	+	1.18487i	−0.631499	+	0.529891i	−0.901394	−	0.432999i	$-0.857455\pi$
$5$	−1.41208	+	1.18487i	−0.631499	+	0.529891i	0.269895	+	0.962890i	$0.413011\pi$
$6$	1.61460	−	3.64587i	0.659159	−	1.48842i
$7$	−2.40040	+	1.11270i	−0.907264	+	0.420561i
$7$	−2.40040	+	1.11270i	−0.907264	+	0.420561i
$8$	−2.59137	−	1.49613i	−0.916186	−	0.528960i
$9$	2.53783	−	1.59982i	0.845942	−	0.533275i
$10$			4.24358i			1.34194i
$11$	−0.0789393	+	0.0940762i	−0.0238011	+	0.0283650i	−0.777814	−	0.628495i	$-0.783671\pi$
$11$	−0.0789393	+	0.0940762i	−0.0238011	+	0.0283650i	0.754013	+	0.656860i	$0.228116\pi$
$12$	−2.51563	−	5.13198i	−0.726200	−	1.48147i
$13$	0.0159063	−	0.0437022i	0.00441162	−	0.0121208i	−0.937467	−	0.348073i	$-0.886836\pi$
$13$	0.0159063	−	0.0437022i	0.00441162	−	0.0121208i	0.941879	+	0.335953i	$0.109058\pi$
$14$	−1.58977	+	5.87972i	−0.424884	+	1.57142i
$15$	−1.78012	+	2.65044i	−0.459624	+	0.684340i
$16$	−0.271551	+	0.0988366i	−0.0678878	+	0.0247091i
$17$	0.157246			0.0381377			0.0190689	−	0.999818i	$-0.493930\pi$
$17$	0.157246			0.0381377			0.0190689	+	0.999818i	$0.493930\pi$
$18$	0.934081	−	6.84292i	0.220165	−	1.61289i
$19$			7.59626i			1.74270i	0.490661	+	0.871350i	$0.336755\pi$
$19$			7.59626i			1.74270i	−0.490661	+	0.871350i	$0.663245\pi$
$20$	4.65954	+	3.90982i	1.04190	+	0.874261i
$21$	−3.45938	+	3.00544i	−0.754898	+	0.655842i
$22$	0.0490936	+	0.278423i	0.0104668	+	0.0593601i
$23$	0.332628	−	0.913889i	0.0693578	−	0.190559i	−0.900171	−	0.435537i	$-0.856559\pi$
$23$	0.332628	−	0.913889i	0.0693578	−	0.190559i	0.969529	+	0.244978i	$0.0787807\pi$
$24$	−5.03126	−	1.24385i	−1.02700	−	0.253900i
$25$	−0.278205	+	1.57778i	−0.0556411	+	0.315556i
$26$	−0.0535324	−	0.0927208i	−0.0104986	−	0.0181840i
$27$	3.45390	−	3.88209i	0.664703	−	0.747108i
$28$	4.99131	+	7.16286i	0.943269	+	1.35365i
$29$	−3.33678	−	9.16772i	−0.619624	−	1.70240i	−0.707906	−	0.706307i	$-0.750360\pi$
$29$	−3.33678	−	9.16772i	−0.619624	−	1.70240i	0.0882816	−	0.996096i	$-0.471862\pi$
$30$	2.03995	+	7.06135i	0.372443	+	1.28922i
$31$	−4.49600	+	0.792766i	−0.807505	+	0.142385i	−0.562136	−	0.827045i	$-0.690020\pi$
$31$	−4.49600	+	0.792766i	−0.807505	+	0.142385i	−0.245369	+	0.969430i	$0.578909\pi$
$32$	1.81929	−	4.99845i	0.321607	−	0.883609i
$33$	−0.0861316	+	0.194490i	−0.0149936	+	0.0338564i
$34$	0.232689	−	0.277308i	0.0399058	−	0.0475579i
$35$	2.07113	−	4.41538i	0.350085	−	0.746335i
$36$	−6.65304	−	7.33034i	−1.10884	−	1.22172i
$37$	−4.68718	+	8.11843i	−0.770567	+	1.33466i	0.166685	+	0.986010i	$0.446694\pi$
$37$	−4.68718	+	8.11843i	−0.770567	+	1.33466i	−0.937252	+	0.348652i	$0.886640\pi$
$38$	13.3962	+	11.2408i	2.17315	+	1.82349i
$39$	0.00545988	−	0.0803671i	0.000874280	−	0.0128690i
$40$	5.43192	−	0.957794i	0.858862	−	0.151441i
$41$	−5.76925	−	2.09983i	−0.901005	−	0.327939i	−0.150350	−	0.988633i	$-0.548040\pi$
$41$	−5.76925	−	2.09983i	−0.901005	−	0.327939i	−0.750656	+	0.660694i	$0.770262\pi$
$42$	0.181079	+	10.5481i	0.0279411	+	1.62761i
$43$	1.67890	−	9.52153i	0.256030	−	1.45202i	−0.537384	−	0.843338i	$-0.680587\pi$
$43$	1.67890	−	9.52153i	0.256030	−	1.45202i	0.793414	−	0.608682i	$-0.208301\pi$
$44$	0.350947	+	0.202619i	0.0529072	+	0.0305460i
$45$	−1.68802	+	5.26607i	−0.251635	+	0.785020i
$46$	−1.11945	−	1.93895i	−0.165055	−	0.285883i
$47$	0.723937	−	4.10565i	0.105597	−	0.598871i	−0.885383	−	0.464862i	$-0.846104\pi$
$47$	0.723937	−	4.10565i	0.105597	−	0.598871i	0.990980	−	0.134009i	$-0.0427851\pi$
$48$	−0.404351	+	0.295003i	−0.0583630	+	0.0425801i
$49$	4.52380	−	5.34184i	0.646257	−	0.763120i
$50$	2.37078	+	2.82539i	0.335279	+	0.399570i
$51$	0.261658	−	0.0755904i	0.0366395	−	0.0105848i
$52$	−0.151131	−	0.0266485i	−0.0209581	−	0.00369548i
$53$	0.141686	+	0.0818025i	0.0194621	+	0.0112364i	0.509699	−	0.860353i	$-0.329757\pi$
$53$	0.141686	+	0.0818025i	0.0194621	+	0.0112364i	−0.490237	+	0.871589i	$0.663090\pi$
$54$	−1.73517	−	11.8357i	−0.236127	−	1.61063i
$55$		−	0.226376i		−	0.0305245i
$56$	7.88504	+	0.707881i	1.05368	+	0.0945946i
$57$	3.65163	+	12.6402i	0.483671	+	1.67424i
$58$	−21.1052	−	7.68168i	−2.77125	−	1.00865i
$59$	11.1248	+	4.04911i	1.44833	+	0.527150i	0.942125	−	0.335262i	$-0.108825\pi$
$59$	11.1248	+	4.04911i	1.44833	+	0.527150i	0.506207	+	0.862412i	$0.331047\pi$
$60$	9.63300	+	4.26604i	1.24361	+	0.550744i
$61$	2.98946	+	0.527123i	0.382762	+	0.0674912i	0.361718	−	0.932287i	$-0.382190\pi$
$61$	2.98946	+	0.527123i	0.382762	+	0.0674912i	0.0210431	+	0.999779i	$0.493301\pi$
$62$	−5.25501	+	9.10194i	−0.667387	+	1.15595i
$63$	−4.31166	+	6.66405i	−0.543219	+	0.839591i
$64$	−6.41175	−	11.1055i	−0.801469	−	1.38818i
$65$	0.0293206	+	0.0805578i	0.00363678	+	0.00999196i
$66$	0.215534	+	0.439698i	0.0265304	+	0.0541231i
$67$	−7.53281	+	6.32078i	−0.920279	+	0.772206i	−0.974047	−	0.226348i	$-0.927321\pi$
$67$	−7.53281	+	6.32078i	−0.920279	+	0.772206i	0.0537674	+	0.998553i	$0.482877\pi$
$68$	−0.0901020	−	0.510994i	−0.0109265	−	0.0619671i
$69$	0.114175	−	1.68062i	0.0137451	−	0.202322i
$70$	−4.72184	−	10.1863i	−0.564367	−	1.21749i
$71$	−0.863276	+	0.498413i	−0.102452	+	0.0591507i	−0.550351	−	0.834934i	$-0.685506\pi$
$71$	−0.863276	+	0.498413i	−0.102452	+	0.0591507i	0.447899	+	0.894084i	$0.352173\pi$
$72$	−8.96997	+	0.348821i	−1.05712	+	0.0411089i
$73$	7.95454	−	4.59256i	0.931009	−	0.537518i	0.0438782	−	0.999037i	$-0.486029\pi$
$73$	7.95454	−	4.59256i	0.931009	−	0.537518i	0.887130	+	0.461519i	$0.152695\pi$
$74$	7.38112	+	20.2795i	0.858037	+	2.35744i
$75$	0.295527	+	2.75917i	0.0341246	+	0.318602i
$76$	24.6852	−	4.35266i	2.83158	−	0.499284i
$77$	0.0848069	−	0.313656i	0.00966465	−	0.0357444i
$78$	−0.133650	−	0.128554i	−0.0151329	−	0.0145559i
$79$	1.99133	+	1.67093i	0.224043	+	0.187994i	0.747899	−	0.663812i	$-0.231063\pi$
$79$	1.99133	+	1.67093i	0.224043	+	0.187994i	−0.523856	+	0.851807i	$0.675507\pi$
$80$	0.266342	−	0.461318i	0.0297780	−	0.0515769i
$81$	3.88113	−	8.12015i	0.431236	−	0.902239i
$82$	−12.2403	+	7.06695i	−1.35172	+	0.780414i
$83$	6.02764	−	2.19388i	0.661619	−	0.240810i	0.0106840	−	0.999943i	$-0.496599\pi$
$83$	6.02764	−	2.19388i	0.661619	−	0.240810i	0.650935	+	0.759133i	$0.274377\pi$
$84$	11.7489	+	9.51964i	1.28191	+	1.03868i
$85$	−0.222043	+	0.186316i	−0.0240840	+	0.0202088i
$86$	−14.3071	−	17.0505i	−1.54277	−	1.83861i
$87$	−9.95947	−	13.6511i	−1.06777	−	1.46355i
$88$	0.345310	−	0.125683i	0.0368102	−	0.0133978i
$89$	−10.6041			−1.12403			−0.562014	−	0.827128i	$-0.689973\pi$
$89$	−10.6041			−1.12403			−0.562014	+	0.827128i	$0.689973\pi$
$90$	6.78899	+	10.7695i	0.715622	+	1.13520i
$91$	0.0104460	+	0.122602i	0.00109504	+	0.0128521i
$92$	−3.16041	−	0.557266i	−0.329496	−	0.0580990i
$93$	−7.10027	+	3.48046i	−0.736264	+	0.360907i
$94$	−6.16918	−	7.35214i	−0.636302	−	0.758315i
$95$	−9.00059	−	10.7265i	−0.923441	−	1.10051i
$96$	0.624474	−	9.19200i	0.0637351	−	0.938155i
$97$	−13.2580	−	2.33775i	−1.34615	−	0.237363i	−0.546313	−	0.837581i	$-0.683969\pi$
$97$	−13.2580	−	2.33775i	−1.34615	−	0.237363i	−0.799836	+	0.600218i	$0.795080\pi$
$98$	−2.72628	−	15.8826i	−0.275396	−	1.60438i
$99$	−0.0498289	+	0.365038i	−0.00500799	+	0.0366877i
$100$	5.28664			0.528664
$101$	−13.0579	+	4.75270i	−1.29931	+	0.472911i	−0.896773	−	0.442492i	$-0.854095\pi$
$101$	−13.0579	+	4.75270i	−1.29931	+	0.472911i	−0.402540	+	0.915403i	$0.631872\pi$
$102$	0.253890	−	0.573299i	0.0251388	−	0.0567650i
$103$	5.01435	+	5.97587i	0.494079	+	0.588820i	0.954250	−	0.299010i	$-0.0966564\pi$
$103$	5.01435	+	5.97587i	0.494079	+	0.588820i	−0.460171	+	0.887830i	$0.652212\pi$
$104$	−0.106603	+	0.0894506i	−0.0104533	+	0.00877135i
$105$	1.32384	−	8.34284i	0.129193	−	0.814177i
$106$	0.353925	−	0.128818i	0.0343762	−	0.0125119i
$107$	6.46785	−	3.73421i	0.625271	−	0.361000i	−0.153648	−	0.988126i	$-0.549102\pi$
$107$	6.46785	−	3.73421i	0.625271	−	0.361000i	0.778918	+	0.627126i	$0.215769\pi$
$108$	−14.5945	−	8.99951i	−1.40436	−	0.865978i
$109$	4.37239	−	7.57320i	0.418799	−	0.725381i	−0.577020	−	0.816730i	$-0.695784\pi$
$109$	4.37239	−	7.57320i	0.418799	−	0.725381i	0.995819	+	0.0913488i	$0.0291178\pi$
$110$	−0.399220	−	0.334985i	−0.0380641	−	0.0319396i
$111$	−3.89684	+	15.7623i	−0.369872	+	1.49609i
$112$	0.541855	−	0.539402i	0.0512005	−	0.0509687i
$113$	16.2059	−	2.85754i	1.52453	−	0.268815i	0.652317	−	0.757947i	$-0.273797\pi$
$113$	16.2059	−	2.85754i	1.52453	−	0.268815i	0.872210	+	0.489131i	$0.162686\pi$
$114$	27.6950	+	12.2649i	2.59387	+	1.14872i
$115$	0.613145	+	1.68460i	0.0571761	+	0.157090i
$116$	−27.8799	+	16.0965i	−2.58858	+	1.49452i
$117$	−0.0295484	−	0.136356i	−0.00273175	−	0.0126061i
$118$	23.6030	−	13.6272i	2.17283	−	1.25449i
$119$	−0.377452	+	0.174968i	−0.0346010	+	0.0160392i
$120$	8.57832	−	4.20498i	0.783090	−	0.383860i
$121$	1.90751	+	10.8180i	0.173410	+	0.983458i
$122$	5.35334	−	4.49198i	0.484668	−	0.406685i
$123$	−10.6095	−	0.720773i	−0.956625	−	0.0649899i
$124$	5.15242	+	14.1562i	0.462701	+	1.27126i
$125$	−6.08496	−	10.5395i	−0.544255	−	0.942677i
$126$	5.37195	+	17.4651i	0.478571	+	1.55591i
$127$	−2.14737	+	3.71936i	−0.190549	+	0.330040i	−0.945432	−	0.325819i	$-0.894360\pi$
$127$	−2.14737	+	3.71936i	−0.190549	+	0.330040i	0.754884	+	0.655859i	$0.227693\pi$
$128$	−18.5960	−	3.27897i	−1.64367	−	0.289823i
$129$	−1.78344	−	16.6509i	−0.157023	−	1.46603i
$130$	0.185454	+	0.0674998i	0.0162654	+	0.00592012i
$131$	4.06526	+	1.47963i	0.355184	+	0.129276i	0.513448	−	0.858120i	$-0.328368\pi$
$131$	4.06526	+	1.47963i	0.355184	+	0.129276i	−0.158265	+	0.987397i	$0.550590\pi$
$132$	0.681379	+	0.168454i	0.0593064	+	0.0146620i
$133$	−8.45235	−	18.2340i	−0.732912	−	1.58109i
$134$			22.6377i			1.95560i
$135$	−0.277390	+	9.57423i	−0.0238739	+	0.824018i
$136$	−0.407482	−	0.235260i	−0.0349413	−	0.0201733i
$137$	−1.72630	−	0.304394i	−0.147488	−	0.0260061i	0.0994166	−	0.995046i	$-0.468302\pi$
$137$	−1.72630	−	0.304394i	−0.147488	−	0.0260061i	−0.246905	+	0.969040i	$0.579413\pi$
$138$	−2.79486	−	2.68829i	−0.237914	−	0.228842i
$139$	8.74606	+	10.4232i	0.741831	+	0.884080i	0.996555	−	0.0829338i	$-0.0264290\pi$
$139$	8.74606	+	10.4232i	0.741831	+	0.884080i	−0.254724	+	0.967014i	$0.581985\pi$
$140$	−15.5352	−	4.20044i	−1.31296	−	0.355002i
$141$	−0.769013	−	7.17984i	−0.0647625	−	0.604651i
$142$	−0.398491	+	2.25995i	−0.0334406	+	0.189651i
$143$	0.00285570	+	0.00494623i	0.000238806	+	0.000413624i
$144$	−0.531029	+	0.685264i	−0.0442524	+	0.0571054i
$145$	15.5744	+	8.99186i	1.29338	+	0.746733i
$146$	3.67184	−	20.8240i	0.303884	−	1.72341i
$147$	4.95972	−	11.0635i	0.409071	−	0.912503i
$148$	29.0678	+	10.5798i	2.38936	+	0.869655i
$149$	9.13243	−	1.61029i	0.748158	−	0.131920i	0.213446	−	0.976955i	$-0.431531\pi$
$149$	9.13243	−	1.61029i	0.748158	−	0.131920i	0.534712	+	0.845034i	$0.320420\pi$
$150$	5.30320	+	3.56179i	0.433004	+	0.290819i
$151$	7.47831	+	6.27505i	0.608576	+	0.510656i	0.894189	−	0.447689i	$-0.147753\pi$
$151$	7.47831	+	6.27505i	0.608576	+	0.510656i	−0.285613	+	0.958345i	$0.592197\pi$
$152$	11.3650	−	19.6847i	0.921820	−	1.59664i
$153$	0.399063	−	0.251566i	0.0322623	−	0.0203379i
$154$	−0.427646	−	0.613700i	−0.0344607	−	0.0494534i
$155$	5.40936	−	6.44663i	0.434490	−	0.517806i
$156$	−0.264293	+	0.0283077i	−0.0211604	+	0.00226643i
$157$	5.53496	−	15.2072i	0.441738	−	1.21366i	−0.496611	−	0.867973i	$-0.665422\pi$
$157$	5.53496	−	15.2072i	0.441738	−	1.21366i	0.938348	−	0.345691i	$-0.112356\pi$
$158$	5.89346	−	1.03918i	0.468859	−	0.0826725i
$159$	0.275090	+	0.0680092i	0.0218161	+	0.00539348i
$160$	3.35355	+	9.21381i	0.265122	+	0.728415i
$161$	0.218444	+	2.56381i	0.0172158	+	0.202057i
$162$	−8.57692	−	18.8605i	−0.673867	−	1.48182i
$163$	5.65656	+	9.79745i	0.443056	+	0.767396i	0.997915	−	0.0645491i	$-0.0205609\pi$
$163$	5.65656	+	9.79745i	0.443056	+	0.767396i	−0.554858	+	0.831945i	$0.687228\pi$
$164$	−3.51794	+	19.9512i	−0.274705	+	1.55793i
$165$	−0.108822	−	0.376690i	−0.00847179	−	0.0293253i
$166$	5.05059	−	13.8764i	0.392002	−	1.07702i
$167$	0.331914	+	1.88238i	0.0256843	+	0.145663i	0.994953	−	0.100341i	$-0.0319935\pi$
$167$	0.331914	+	1.88238i	0.0256843	+	0.145663i	−0.969269	+	0.246004i	$0.920882\pi$
$168$	13.4610	−	2.61254i	1.03854	−	0.201562i
$169$	9.95692	+	8.35485i	0.765917	+	0.642681i
$170$			0.667286i			0.0511785i
$171$	12.1527	+	19.2780i	0.929338	+	1.47422i
$172$	−31.9036			−2.43263
$173$	−22.9967	+	8.37010i	−1.74840	+	0.636367i	−0.999649	−	0.0264796i	$-0.991570\pi$
$173$	−22.9967	+	8.37010i	−1.74840	+	0.636367i	−0.748755	+	0.662847i	$0.769348\pi$
$174$	−38.8119	−	2.63675i	−2.94232	−	0.199892i
$175$	−1.08779	−	4.09686i	−0.0822295	−	0.309693i
$176$	0.0121379	−	0.0333486i	0.000914928	−	0.00251374i
$177$	20.4583	+	1.38987i	1.53774	+	0.104469i
$178$	−15.6916	+	18.7006i	−1.17614	+	1.40167i
$179$			18.4669i			1.38028i	0.723676	+	0.690140i	$0.242451\pi$
$179$			18.4669i			1.38028i	−0.723676	+	0.690140i	$0.757549\pi$
$180$	18.0801	+	2.46800i	1.34761	+	0.183954i
$181$	−5.58272	−	3.22319i	−0.414960	−	0.239577i	0.277958	−	0.960593i	$-0.410342\pi$
$181$	−5.58272	−	3.22319i	−0.414960	−	0.239577i	−0.692919	+	0.721016i	$0.743676\pi$
$182$	0.231669	+	0.163001i	0.0171725	+	0.0120824i
$183$	5.22788	−	0.559944i	0.386456	−	0.0413922i
$184$	−2.22925	+	1.87057i	−0.164343	+	0.137900i
$185$	−3.00065	−	17.0175i	−0.220612	−	1.25116i
$186$	−4.36892	+	17.6718i	−0.320345	+	1.29576i
$187$	−0.0124129	+	0.0147931i	−0.000907720	+	0.00108178i
$188$	−13.7567			−1.00331
$189$	−3.97112	+	13.1617i	−0.288857	+	0.957372i
$190$	−32.2354			−2.33860
$191$	−6.44902	+	7.68564i	−0.466635	+	0.556113i	−0.947116	−	0.320891i	$-0.896018\pi$
$191$	−6.44902	+	7.68564i	−0.466635	+	0.556113i	0.480481	+	0.877005i	$0.340462\pi$
$192$	−16.0078	−	15.3974i	−1.15526	−	1.11121i
$193$	−4.27327	−	24.2349i	−0.307597	−	1.74447i	−0.611022	−	0.791614i	$-0.709241\pi$
$193$	−4.27327	−	24.2349i	−0.307597	−	1.74447i	0.303424	−	0.952855i	$-0.401870\pi$
$194$	−23.7416	+	19.9216i	−1.70455	+	1.43029i
$195$	0.0875150	+	0.119954i	0.00626708	+	0.00859006i
$196$	−19.9512	−	11.6399i	−1.42509	−	0.831419i
$197$	12.0988	+	6.98527i	0.862007	+	0.497680i	0.864684	−	0.502316i	$-0.167519\pi$
$197$	12.0988	+	6.98527i	0.862007	+	0.497680i	−0.00267677	+	0.999996i	$0.500852\pi$
$198$	0.570019	+	0.628049i	0.0405095	+	0.0446335i
$199$			12.8790i			0.912968i	0.889732	+	0.456484i	$0.150892\pi$
$199$			12.8790i			0.912968i	−0.889732	+	0.456484i	$0.849108\pi$
$200$	3.08149	−	3.67238i	0.217894	−	0.259676i
$201$	−9.49614	+	14.1389i	−0.669806	+	0.997284i
$202$	−10.9413	+	30.0610i	−0.769827	+	2.11508i
$203$	18.2105	+	18.2933i	1.27813	+	1.28394i
$204$	−0.395572	−	0.806983i	−0.0276956	−	0.0565001i
$205$	10.6347	−	3.87070i	0.742756	−	0.270341i
$206$	17.9587			1.25125
$207$	−0.617908	−	2.85144i	−0.0429476	−	0.198189i
$208$			0.0134395i			0.000931863i
$209$	−0.714627	−	0.599643i	−0.0494318	−	0.0414782i
$210$	−12.7539	−	14.6802i	−0.880100	−	1.01303i
$211$	−0.918282	−	5.20784i	−0.0632171	−	0.358522i	−0.999964	−	0.00851397i	$-0.997290\pi$
$211$	−0.918282	−	5.20784i	−0.0632171	−	0.358522i	0.936747	−	0.350008i	$-0.113821\pi$
$212$	0.184643	−	0.507302i	0.0126813	−	0.0348417i
$213$	−1.19690	+	1.24435i	−0.0820104	+	0.0852615i
$214$	2.98558	−	16.9320i	0.204090	−	1.15745i
$215$	8.91106	+	15.4344i	0.607729	+	1.05262i
$216$	−14.7584	+	4.89244i	−1.00418	+	0.332888i
$217$	9.91006	−	6.90565i	0.672739	−	0.468786i
$218$	−6.88541	−	18.9175i	−0.466339	−	1.28125i
$219$	11.0287	−	11.4659i	0.745250	−	0.774794i
$220$	−0.735641	+	0.129713i	−0.0495969	+	0.00874527i
$221$	0.00250120	−	0.00687200i	0.000168249	−	0.000462260i
$222$	22.0308	+	30.1969i	1.47861	+	2.02668i
$223$	−5.38046	+	6.41218i	−0.360302	+	0.429392i	−0.915495	−	0.402330i	$-0.868200\pi$
$223$	−5.38046	+	6.41218i	−0.360302	+	0.429392i	0.555192	+	0.831722i	$0.312645\pi$
$224$	1.19477	+	14.0226i	0.0798286	+	0.936922i
$225$	1.81813	+	4.44921i	0.121209	+	0.296614i
$226$	18.9418	−	32.8082i	1.25999	−	2.18237i
$227$	−15.4623	−	12.9744i	−1.02627	−	0.861143i	−0.0358677	−	0.999357i	$-0.511419\pi$
$227$	−15.4623	−	12.9744i	−1.02627	−	0.861143i	−0.990402	+	0.138214i	$0.955864\pi$
$228$	38.9838	−	19.1094i	2.58177	−	1.26555i
$229$	5.72074	−	1.00872i	0.378037	−	0.0666582i	0.0185989	−	0.999827i	$-0.494079\pi$
$229$	5.72074	−	1.00872i	0.378037	−	0.0666582i	0.359438	+	0.933169i	$0.382968\pi$
$230$	3.87817	+	1.41154i	0.255719	+	0.0930740i
$231$	−0.00965973	−	0.562693i	−0.000635564	−	0.0370225i
$232$	−5.06925	+	28.7491i	−0.332813	+	1.88747i
$233$	5.33662	+	3.08110i	0.349614	+	0.201850i	0.664515	−	0.747275i	$-0.268638\pi$
$233$	5.33662	+	3.08110i	0.349614	+	0.201850i	−0.314901	+	0.949124i	$0.601971\pi$
$234$	−0.284193	−	0.149667i	−0.0185783	−	0.00978403i
$235$	3.84242	+	6.65527i	0.250652	+	0.434142i
$236$	6.78365	−	38.4720i	0.441578	−	2.50431i
$237$	4.11683	+	1.82317i	0.267417	+	0.118428i
$238$	−0.249985	+	0.924562i	−0.0162041	+	0.0599304i
$239$	11.9974	+	14.2979i	0.776046	+	0.924856i	0.998748	−	0.0500310i	$-0.0159320\pi$
$239$	11.9974	+	14.2979i	0.776046	+	0.924856i	−0.222702	+	0.974887i	$0.571488\pi$
$240$	0.221432	−	0.895671i	0.0142934	−	0.0578153i
$241$	−12.0008	−	2.11606i	−0.773039	−	0.136308i	−0.226805	−	0.973940i	$-0.572828\pi$
$241$	−12.0008	−	2.11606i	−0.773039	−	0.136308i	−0.546234	+	0.837633i	$0.683939\pi$
$242$	21.9006	+	12.6443i	1.40782	+	0.812808i
$243$	2.55474	−	15.3777i	0.163887	−	0.986479i
$244$		−	10.0167i		−	0.641256i
$245$	−0.0585478	+	12.9032i	−0.00374048	+	0.824355i
$246$	−16.9708	+	17.6436i	−1.08202	+	1.12491i
$247$	0.331973	+	0.120828i	0.0211230	+	0.00768813i
$248$	12.8368	+	4.67223i	0.815141	+	0.296687i
$249$	8.97539	−	6.54820i	0.568792	−	0.414976i
$250$	−27.5910	−	4.86504i	−1.74501	−	0.307692i
$251$	1.90241	−	3.29506i	0.120079	−	0.207983i	−0.799720	−	0.600373i	$-0.795019\pi$
$251$	1.90241	−	3.29506i	0.120079	−	0.207983i	0.919799	+	0.392391i	$0.128352\pi$
$252$	24.1264	+	10.1929i	1.51982	+	0.642091i
$253$	0.0597177	+	0.103434i	0.00375442	+	0.00650285i
$254$	3.38157	+	9.29078i	0.212178	+	0.582956i
$255$	−0.279916	+	0.416771i	−0.0175290	+	0.0260992i
$256$	−13.6537	+	11.4568i	−0.853355	+	0.716050i
$257$	−3.82957	−	21.7186i	−0.238882	−	1.35477i	−0.834282	−	0.551339i	$-0.814117\pi$
$257$	−3.82957	−	21.7186i	−0.238882	−	1.35477i	0.595399	−	0.803430i	$-0.296994\pi$
$258$	−32.0035	−	21.4946i	−1.99245	−	1.33819i
$259$	2.21771	−	24.7029i	0.137802	−	1.53496i
$260$	0.244984	−	0.141441i	0.0151932	−	0.00877182i
$261$	−23.1349	−	17.9278i	−1.43201	−	1.10970i
$262$	8.62506	−	4.97968i	0.532858	−	0.307646i
$263$	0.651083	+	1.78884i	0.0401475	+	0.110304i	0.958146	−	0.286278i	$-0.0924182\pi$
$263$	0.651083	+	1.78884i	0.0401475	+	0.110304i	−0.917999	+	0.396583i	$0.870196\pi$
$264$	0.514180	−	0.375132i	0.0316456	−	0.0230878i
$265$	−0.296997	+	0.0523686i	−0.0182444	+	0.00321698i
$266$	−44.6638	−	12.0763i	−2.73852	−	0.740446i
$267$	−17.6452	+	5.09752i	−1.07987	+	0.311963i
$268$	24.8566	+	20.8572i	1.51836	+	1.27405i
$269$	6.11936	−	10.5990i	0.373104	−	0.646235i	−0.616937	−	0.787012i	$-0.711627\pi$
$269$	6.11936	−	10.5990i	0.373104	−	0.646235i	0.990041	+	0.140777i	$0.0449601\pi$
$270$	16.4740	+	14.6569i	1.00257	+	0.891991i
$271$	10.1008	−	5.83167i	0.613577	−	0.354249i	−0.160787	−	0.986989i	$-0.551403\pi$
$271$	10.1008	−	5.83167i	0.613577	−	0.354249i	0.774364	+	0.632740i	$0.218070\pi$
$272$	−0.0427003	+	0.0155416i	−0.00258909	+	0.000942351i
$273$	0.0763186	+	0.198988i	0.00461901	+	0.0120433i
$274$	−3.09135	+	2.59395i	−0.186755	+	0.156706i
$275$	−0.126470	−	0.150721i	−0.00762644	−	0.00908884i
$276$	−5.52683	+	0.591964i	−0.332676	+	0.0356320i
$277$	17.8050	−	6.48049i	1.06980	−	0.389375i	0.253698	−	0.967284i	$-0.418353\pi$
$277$	17.8050	−	6.48049i	1.06980	−	0.389375i	0.816102	+	0.577908i	$0.196131\pi$
$278$	31.3238			1.87867
$279$	−10.1418	+	9.20471i	−0.607172	+	0.551071i
$280$	−11.9730	+	8.34318i	−0.715525	+	0.498601i
$281$	0.401346	+	0.0707682i	0.0239423	+	0.00422168i	0.185607	−	0.982624i	$-0.440575\pi$
$281$	0.401346	+	0.0707682i	0.0239423	+	0.00422168i	−0.161664	+	0.986846i	$0.551686\pi$
$282$	−13.7998	−	9.26838i	−0.821767	−	0.551924i
$283$	2.99151	+	3.56515i	0.177827	+	0.211926i	0.847594	−	0.530645i	$-0.178050\pi$
$283$	2.99151	+	3.56515i	0.177827	+	0.211926i	−0.669767	+	0.742571i	$0.733606\pi$
$284$	2.11432	+	2.51975i	0.125462	+	0.149520i
$285$	−20.1334	−	13.5222i	−1.19260	−	0.800987i
$286$	0.0129486	+	0.00228319i	0.000765668	+	0.000135008i
$287$	16.1850	−	1.37901i	0.955368	−	0.0814003i
$288$	−3.37960	−	15.5957i	−0.199145	−	0.918987i
$289$	−16.9753			−0.998546
$290$	38.9040	−	14.1599i	2.28452	−	0.831498i
$291$	−23.1852	+	2.48331i	−1.35914	+	0.145574i
$292$	−19.4821	−	23.2179i	−1.14011	−	1.35873i
$293$	6.35829	−	5.33524i	0.371455	−	0.311688i	−0.437882	−	0.899033i	$-0.644271\pi$
$293$	6.35829	−	5.33524i	0.371455	−	0.311688i	0.809337	+	0.587345i	$0.199827\pi$
$294$	−12.1715	−	25.1181i	−0.709859	−	1.46492i
$295$	−20.5068	+	7.46387i	−1.19395	+	0.434563i
$296$	24.2924	−	14.0252i	1.41197	−	0.815199i
$297$	0.0925635	+	0.631378i	0.00537108	+	0.0366363i
$298$	10.6742	−	18.4882i	0.618338	−	1.07099i
$299$	−0.0346481	−	0.0290732i	−0.00200375	−	0.00168135i
$300$	8.79700	−	2.54137i	0.507895	−	0.146726i
$301$	6.56457	+	24.7236i	0.378376	+	1.42504i
$302$	22.1325	−	3.90255i	1.27358	−	0.224567i
$303$	−19.4438	+	14.1857i	−1.11702	+	0.814944i
$304$	−0.750788	−	2.06277i	−0.0430606	−	0.118308i
$305$	−4.84592	+	2.79779i	−0.277477	+	0.160201i
$306$	0.146880	−	1.07602i	0.00839660	−	0.0615120i
$307$	5.10853	−	2.94941i	0.291559	−	0.168332i	−0.347086	−	0.937833i	$-0.612829\pi$
$307$	5.10853	−	2.94941i	0.291559	−	0.168332i	0.638645	+	0.769502i	$0.279495\pi$
$308$	−1.06786	−	0.0958678i	−0.0608472	−	0.00546257i
$309$	11.2166	+	7.53341i	0.638090	+	0.428561i
$310$	−3.36417	−	19.0791i	−0.191072	−	1.08362i
$311$	−10.3978	+	8.72479i	−0.589605	+	0.494737i	−0.888085	−	0.459678i	$-0.847965\pi$
$311$	−10.3978	+	8.72479i	−0.589605	+	0.494737i	0.298481	+	0.954416i	$0.403520\pi$
$312$	−0.134388	+	0.200092i	−0.00760821	+	0.0113280i
$313$	−1.95490	−	5.37104i	−0.110497	−	0.303589i	0.872103	−	0.489323i	$-0.162756\pi$
$313$	−1.95490	−	5.37104i	−0.110497	−	0.303589i	−0.982600	+	0.185734i	$0.940534\pi$
$314$	−18.6278	−	32.2643i	−1.05123	−	1.82078i
$315$	−1.80765	−	14.5189i	−0.101850	−	0.818048i
$316$	4.28889	−	7.42858i	0.241269	−	0.417890i
$317$	−2.37171	−	0.418197i	−0.133209	−	0.0234883i	0.106646	−	0.994297i	$-0.465989\pi$
$317$	−2.37171	−	0.418197i	−0.133209	−	0.0234883i	−0.239855	+	0.970809i	$0.577100\pi$
$318$	0.527008	−	0.384491i	0.0295531	−	0.0215612i
$319$	1.12587	+	0.409782i	0.0630364	+	0.0229434i
$320$	22.2125	+	8.08467i	1.24171	+	0.451947i
$321$	8.96744	−	9.32294i	0.500514	−	0.520356i
$322$	4.84461	+	3.40864i	0.269979	+	0.189956i
$323$			1.19448i			0.0664627i
$324$	−28.6115	−	7.95945i	−1.58953	−	0.442191i
$325$	0.0645273	+	0.0372549i	0.00357933	+	0.00206653i
$326$	25.6485	+	4.52253i	1.42054	+	0.250480i
$327$	3.63513	−	14.7037i	0.201023	−	0.813118i
$328$	11.8086	+	14.0730i	0.652022	+	0.777049i
$329$	2.83062	+	10.6607i	0.156057	+	0.587744i
$330$	−0.825337	−	0.365506i	−0.0454333	−	0.0201205i
$331$	1.83986	−	10.4344i	0.101128	−	0.573525i	−0.891568	−	0.452886i	$-0.850394\pi$
$331$	1.83986	−	10.4344i	0.101128	−	0.573525i	0.992696	−	0.120639i	$-0.0384944\pi$
$332$	−10.5832	−	18.3306i	−0.580827	−	1.00602i
$333$	1.09281	+	28.1018i	0.0598858	+	1.53997i
$334$	3.81079	+	2.20016i	0.208517	+	0.120387i
$335$	3.14758	−	17.8508i	0.171971	−	0.975295i
$336$	0.642351	−	1.15805i	0.0350431	−	0.0631766i
$337$	−21.6242	−	7.87058i	−1.17795	−	0.428738i	−0.322471	−	0.946579i	$-0.604514\pi$
$337$	−21.6242	−	7.87058i	−1.17795	−	0.428738i	−0.855477	+	0.517841i	$0.826736\pi$
$338$	29.4680	−	5.19601i	1.60285	−	0.282626i
$339$	25.5931	−	12.5454i	1.39003	−	0.681373i
$340$	0.732693	+	0.614802i	0.0397359	+	0.0333423i
$341$	0.280330	−	0.485547i	0.0151807	−	0.0262938i
$342$	51.9805	+	7.09552i	2.81079	+	0.383682i
$343$	−4.91504	+	17.8562i	−0.265387	+	0.964142i
$344$	−18.5961	+	22.1619i	−1.00263	+	1.19489i
$345$	1.83009	+	2.50844i	0.0985287	+	0.135050i
$346$	−19.2690	+	52.9412i	−1.03591	+	2.84614i
$347$	−3.79271	+	0.668756i	−0.203603	+	0.0359007i	−0.274519	−	0.961582i	$-0.588519\pi$
$347$	−3.79271	+	0.668756i	−0.203603	+	0.0359007i	0.0709164	+	0.997482i	$0.477408\pi$
$348$	−38.6545	+	40.1869i	−2.07210	+	2.15424i
$349$	−0.721690	−	1.98283i	−0.0386312	−	0.106138i	0.918877	−	0.394543i	$-0.129097\pi$
$349$	−0.721690	−	1.98283i	−0.0386312	−	0.106138i	−0.957508	+	0.288405i	$0.906875\pi$
$350$	−8.83462	−	4.14408i	−0.472230	−	0.221510i
$351$	−0.114717	−	0.212693i	−0.00612314	−	0.0113527i
$352$	0.326622	+	0.565725i	0.0174090	+	0.0301533i
$353$	−2.13381	+	12.1014i	−0.113571	+	0.644094i	0.873877	+	0.486148i	$0.161598\pi$
$353$	−2.13381	+	12.1014i	−0.113571	+	0.644094i	−0.987448	+	0.157946i	$0.949513\pi$
$354$	32.7248	−	34.0221i	1.73930	−	1.80825i
$355$	0.628456	−	1.72667i	0.0333550	−	0.0916421i
$356$	6.07613	+	34.4594i	0.322034	+	1.82635i
$357$	−0.543973	+	0.472594i	−0.0287901	+	0.0250123i
$358$	32.5669	+	27.3269i	1.72122	+	1.44427i
$359$		−	30.5874i		−	1.61434i	−0.590319	−	0.807170i	$-0.700998\pi$
$359$		−	30.5874i		−	1.61434i	0.590319	−	0.807170i	$-0.299002\pi$
$360$	12.2530	−	11.1208i	0.645788	−	0.586119i
$361$	−38.7031			−2.03701
$362$	−13.9454	+	5.07570i	−0.732952	+	0.266773i
$363$	8.37450	+	17.0843i	0.439547	+	0.896693i
$364$	0.392426	−	0.104197i	0.0205687	−	0.00546139i
$365$	−5.79082	+	15.9102i	−0.303105	+	0.832775i
$366$	6.74862	−	10.0481i	0.352756	−	0.525223i
$367$	8.80842	−	10.4975i	0.459796	−	0.547964i	−0.485475	−	0.874251i	$-0.661353\pi$
$367$	8.80842	−	10.4975i	0.459796	−	0.547964i	0.945271	+	0.326287i	$0.105798\pi$
$368$			0.281044i			0.0146504i
$369$	−18.0007	+	3.90076i	−0.937080	+	0.203066i
$370$	−34.4513	−	19.8904i	−1.79104	−	1.03405i
$371$	−0.431124	−	0.0387043i	−0.0223829	−	0.00200942i
$372$	15.3787	+	21.0791i	0.797349	+	1.09290i
$373$	−8.95196	+	7.51159i	−0.463515	+	0.388935i	−0.844422	−	0.535678i	$-0.820056\pi$
$373$	−8.95196	+	7.51159i	−0.463515	+	0.388935i	0.380907	+	0.924613i	$0.375612\pi$
$374$	0.00771976	+	0.0437810i	0.000399180	+	0.00226386i
$375$	−15.1919	−	14.6126i	−0.784505	−	0.754590i
$376$	−8.01856	+	9.55615i	−0.413526	+	0.492821i
$377$	−0.453725			−0.0233681
$378$	17.3347	+	26.4796i	0.891599	+	1.36196i
$379$	−12.7028			−0.652500			−0.326250	−	0.945283i	$-0.605785\pi$
$379$	−12.7028			−0.652500			−0.326250	+	0.945283i	$0.605785\pi$
$380$	−29.7000	+	35.3950i	−1.52358	+	1.81573i
$381$	−1.78529	+	7.22131i	−0.0914632	+	0.369959i
$382$	4.01075	+	22.7461i	0.205208	+	1.16379i
$383$	−6.13567	+	5.14843i	−0.313518	+	0.263073i	−0.785944	−	0.618297i	$-0.787823\pi$
$383$	−6.13567	+	5.14843i	−0.313518	+	0.263073i	0.472426	+	0.881370i	$0.343378\pi$
$384$	−32.5200	+	3.48313i	−1.65953	+	0.177748i
$385$	0.251888	+	0.543391i	0.0128374	+	0.0276938i
$386$	−49.0625	−	28.3263i	−2.49722	−	1.44177i
$387$	−10.9720	−	26.8499i	−0.557738	−	1.36486i
$388$			44.4235i			2.25526i
$389$	−8.23656	+	9.81595i	−0.417610	+	0.497689i	−0.933305	−	0.359084i	$-0.883089\pi$
$389$	−8.23656	+	9.81595i	−0.417610	+	0.497689i	0.515695	+	0.856772i	$0.327534\pi$
$390$	0.341045	+	0.0231694i	0.0172695	+	0.00117323i
$391$	0.0523045	−	0.143705i	0.00264515	−	0.00726749i
$392$	−19.7149	+	7.07449i	−0.995752	+	0.357316i
$393$	7.47590	+	0.507888i	0.377109	+	0.0256195i
$394$	30.2223	−	11.0000i	1.52258	−	0.554174i
$395$	−4.79175			−0.241099
$396$	1.21480	−	0.0472405i	0.0610458	−	0.00237392i
$397$		−	9.99710i		−	0.501740i	−0.968021	−	0.250870i	$-0.919283\pi$
$397$		−	9.99710i		−	0.501740i	0.968021	−	0.250870i	$-0.0807167\pi$
$398$	22.7125	+	19.0581i	1.13848	+	0.955294i
$399$	−22.8301	−	26.2783i	−1.14294	−	1.31556i
$400$	−0.0803954	−	0.455945i	−0.00401977	−	0.0227973i
$401$	−12.6777	+	34.8316i	−0.633092	+	1.73941i	0.0393162	+	0.999227i	$0.487482\pi$
$401$	−12.6777	+	34.8316i	−0.633092	+	1.73941i	−0.672409	+	0.740180i	$0.734740\pi$
$402$	10.8823	+	37.6692i	0.542758	+	1.87877i
$403$	−0.0368691	+	0.209095i	−0.00183658	+	0.0104158i
$404$	22.9268	+	39.7104i	1.14065	+	1.97566i
$405$	4.14089	+	16.0649i	0.205763	+	0.798272i
$406$	59.2083	−	5.04473i	2.93846	−	0.250366i
$407$	−0.393748	−	1.08181i	−0.0195174	−	0.0536236i
$408$	−0.791144	−	0.195591i	−0.0391675	−	0.00968319i
$409$	−2.30593	+	0.406597i	−0.114021	+	0.0201050i	−0.230367	−	0.973104i	$-0.573993\pi$
$409$	−2.30593	+	0.406597i	−0.114021	+	0.0201050i	0.116347	+	0.993209i	$0.462882\pi$
$410$	8.91083	−	24.4823i	0.440074	−	1.20909i
$411$	−3.01890	+	0.323346i	−0.148912	+	0.0159495i
$412$	16.5462	−	19.7190i	0.815175	−	0.971488i
$413$	−31.2095	+	2.65914i	−1.53572	+	0.130848i
$414$	−5.94296	−	3.12979i	−0.292081	−	0.153821i
$415$	−5.91201	+	10.2399i	−0.290209	+	0.502657i
$416$	−0.189505	−	0.159014i	−0.00929125	−	0.00779629i
$417$	19.5641	+	13.1398i	0.958056	+	0.643460i
$418$	−2.11498	+	0.372927i	−0.103447	+	0.0182405i
$419$	−28.6465	−	10.4265i	−1.39947	−	0.509366i	−0.471451	−	0.881892i	$-0.656270\pi$
$419$	−28.6465	−	10.4265i	−1.39947	−	0.509366i	−0.928022	+	0.372526i	$0.878492\pi$
$420$	−27.8698	+	0.478441i	−1.35991	+	0.0233455i
$421$	0.369085	−	2.09318i	0.0179881	−	0.102015i	−0.974492	−	0.224423i	$-0.927950\pi$
$421$	0.369085	−	2.09318i	0.0179881	−	0.102015i	0.992480	+	0.122407i	$0.0390614\pi$
$422$	−10.5430	−	6.08702i	−0.513227	−	0.296311i
$423$	−4.73109	−	11.5776i	−0.230034	−	0.562923i
$424$	−0.244774	−	0.423960i	−0.0118873	−	0.0205893i
$425$	−0.0437466	+	0.248100i	−0.00212202	+	0.0120346i
$426$	0.423302	+	3.95213i	0.0205091	+	0.191482i
$427$	−7.76242	+	2.06107i	−0.375650	+	0.0997423i
$428$	−15.8410	−	18.8785i	−0.765702	−	0.912528i
$429$	0.00712963	+	0.00685777i	0.000344222	+	0.000331096i
$430$	40.4054	+	7.12457i	1.94852	+	0.343577i
$431$	1.02928	+	0.594254i	0.0495786	+	0.0286242i	0.524584	−	0.851358i	$-0.324221\pi$
$431$	1.02928	+	0.594254i	0.0495786	+	0.0286242i	−0.475006	+	0.879983i	$0.657554\pi$
$432$	−0.554218	+	1.39556i	−0.0266648	+	0.0671438i
$433$			11.1104i			0.533930i	0.963706	+	0.266965i	$0.0860208\pi$
$433$			11.1104i			0.533930i	−0.963706	+	0.266965i	$0.913979\pi$
$434$	2.48637	−	27.6955i	0.119350	−	1.32943i
$435$	30.2383	+	7.47568i	1.44982	+	0.358431i
$436$	−27.1156	−	9.86928i	−1.29860	−	0.472653i
$437$	6.94214	+	2.52673i	0.332087	+	0.120870i
$438$	−3.90046	−	36.4164i	−0.186371	−	1.74004i
$439$	5.47998	+	0.966269i	0.261545	+	0.0461175i	0.302883	−	0.953028i	$-0.402051\pi$
$439$	5.47998	+	0.966269i	0.261545	+	0.0461175i	−0.0413377	+	0.999145i	$0.513162\pi$
$440$	−0.338686	+	0.586622i	−0.0161462	+	0.0279661i
$441$	2.93461	−	20.7939i	0.139743	−	0.990188i
$442$	−0.00841775	−	0.0145800i	−0.000400391	−	0.000693498i
$443$	9.30703	+	25.5708i	0.442190	+	1.21491i	0.938048	+	0.346504i	$0.112631\pi$
$443$	9.30703	+	25.5708i	0.442190	+	1.21491i	−0.495858	+	0.868403i	$0.665146\pi$
$444$	53.4548	+	3.63154i	2.53685	+	0.172345i
$445$	14.9737	−	12.5644i	0.709823	−	0.595612i
$446$	3.34619	+	18.9772i	0.158447	+	0.898597i
$447$	14.4223	−	7.06963i	0.682152	−	0.334382i
$448$	27.7478	+	19.5232i	1.31096	+	0.922384i
$449$	−21.3299	+	12.3148i	−1.00662	+	0.581171i	−0.910200	−	0.414170i	$-0.864072\pi$
$449$	−21.3299	+	12.3148i	−1.00662	+	0.581171i	−0.0964182	+	0.995341i	$0.530739\pi$
$450$	10.5368	+	3.37751i	0.496707	+	0.159217i
$451$	0.652965	−	0.376989i	0.0307469	−	0.0177517i
$452$	−18.5720	−	51.0262i	−0.873554	−	2.40007i
$453$	15.4605	+	6.84678i	0.726395	+	0.321690i
$454$	−45.7616	+	8.06900i	−2.14770	+	0.378697i
$455$	−0.160018	−	0.160745i	−0.00750175	−	0.00753586i
$456$	9.44863	−	38.2187i	0.442473	−	1.78976i
$457$	−5.39560	−	4.52745i	−0.252396	−	0.211785i	0.507808	−	0.861471i	$-0.330456\pi$
$457$	−5.39560	−	4.52745i	−0.252396	−	0.211785i	−0.760203	+	0.649686i	$0.774901\pi$
$458$	6.68651	−	11.5814i	0.312440	−	0.541162i
$459$	0.543111	−	0.610442i	0.0253503	−	0.0284930i
$460$	5.12303	−	2.95778i	0.238863	−	0.137907i
$461$	6.82236	−	2.48314i	0.317749	−	0.115651i	−0.178222	−	0.983990i	$-0.557034\pi$
$461$	6.82236	−	2.48314i	0.317749	−	0.115651i	0.495971	+	0.868339i	$0.334812\pi$
$462$	−1.00662	−	0.815625i	−0.0468322	−	0.0379463i
$463$	6.25076	−	5.24501i	0.290498	−	0.243756i	−0.485878	−	0.874026i	$-0.661500\pi$
$463$	6.25076	−	5.24501i	0.290498	−	0.243756i	0.776376	+	0.630270i	$0.217056\pi$
$464$	1.81221	+	2.15971i	0.0841298	+	0.100262i
$465$	5.90222	−	13.3276i	0.273709	−	0.618052i
$466$	13.3306	−	4.85195i	0.617529	−	0.224762i
$467$	12.7628			0.590592			0.295296	−	0.955406i	$-0.404582\pi$
$467$	12.7628			0.590592			0.295296	+	0.955406i	$0.404582\pi$
$468$	−0.426177	+	0.174154i	−0.0197001	+	0.00805027i
$469$	11.0486	−	23.5541i	0.510177	−	1.08763i
$470$	17.4227	+	3.07209i	0.803649	+	0.141705i
$471$	1.89989	−	27.9656i	0.0875422	−	1.28858i
$472$	−22.7706	−	27.1369i	−1.04810	−	1.24908i
$473$	0.763218	+	0.909567i	0.0350928	+	0.0418219i
$474$	9.30721	−	4.56227i	0.427494	−	0.209552i
$475$	−11.9852	−	2.11332i	−0.549920	−	0.0969657i
$476$	0.784863	+	1.12633i	0.0359741	+	0.0516253i
$477$	0.490444	−	0.0190722i	0.0224559	−	0.000873256i
$478$	42.9683			1.96532
$479$	−18.7249	+	6.81531i	−0.855564	+	0.311400i	−0.732307	−	0.680975i	$-0.761556\pi$
$479$	−18.7249	+	6.81531i	−0.855564	+	0.311400i	−0.123257	+	0.992375i	$0.539334\pi$
$480$	10.0095	+	13.7197i	0.456871	+	0.626217i
$481$	0.280238	+	0.333974i	0.0127777	+	0.0152279i
$482$	−21.4902	+	18.0325i	−0.978854	+	0.821356i
$483$	1.59595	+	4.16118i	0.0726184	+	0.189340i
$484$	34.0618	−	12.3975i	1.54826	−	0.563522i
$485$	21.4913	−	12.4080i	0.975869	−	0.563418i
$486$	−23.3386	−	27.2609i	−1.05866	−	1.23658i
$487$	−16.5334	+	28.6367i	−0.749200	+	1.29765i	0.199007	+	0.979998i	$0.436228\pi$
$487$	−16.5334	+	28.6367i	−0.749200	+	1.29765i	−0.948207	+	0.317654i	$0.897105\pi$
$488$	−6.95815	−	5.83858i	−0.314981	−	0.264300i
$489$	14.1223	+	13.5838i	0.638634	+	0.614282i
$490$	22.6685	+	19.1971i	1.02406	+	0.867237i
$491$	1.71158	−	0.301798i	0.0772427	−	0.0136200i	−0.134893	−	0.990860i	$-0.543069\pi$
$491$	1.71158	−	0.301798i	0.0772427	−	0.0136200i	0.212136	+	0.977240i	$0.431958\pi$
$492$	3.73698	+	34.8901i	0.168476	+	1.57297i
$493$	−0.524695	−	1.44159i	−0.0236311	−	0.0649258i
$494$	0.704331	−	0.406646i	0.0316894	−	0.0182959i
$495$	−0.362161	−	0.574502i	−0.0162779	−	0.0258219i
$496$	1.14254	−	0.659646i	0.0513015	−	0.0296190i
$497$	1.51762	−	2.15696i	0.0680746	−	0.0967527i
$498$	1.73363	−	25.5183i	0.0776856	−	1.14350i
$499$	−5.96043	−	33.8033i	−0.266825	−	1.51324i	−0.763786	−	0.645469i	$-0.776662\pi$
$499$	−5.96043	−	33.8033i	−0.266825	−	1.51324i	0.496961	−	0.867773i	$-0.334449\pi$
$500$	−30.7628	+	25.8131i	−1.37576	+	1.15440i
$501$	1.45719	+	2.97273i	0.0651026	+	0.132812i
$502$	−2.99581	−	8.23091i	−0.133709	−	0.367364i
$503$	−6.14413	−	10.6419i	−0.273953	−	0.474501i	0.695917	−	0.718122i	$-0.254998\pi$
$503$	−6.14413	−	10.6419i	−0.273953	−	0.474501i	−0.969870	+	0.243621i	$0.921665\pi$
$504$	21.1434	−	10.8182i	0.941800	−	0.481881i
$505$	12.8074	−	22.1831i	0.569924	−	0.987137i
$506$	0.270778	+	0.0477455i	0.0120376	+	0.00212255i
$507$	20.5847	+	9.11607i	0.914197	+	0.404859i
$508$	13.3171	+	4.84701i	0.590849	+	0.215051i
$509$	24.5995	+	8.95349i	1.09035	+	0.396856i	0.823752	−	0.566950i	$-0.191877\pi$
$509$	24.5995	+	8.95349i	1.09035	+	0.396856i	0.266602	+	0.963807i	$0.414099\pi$
$510$	0.320774	+	1.11037i	0.0142041	+	0.0491679i
$511$	−13.9839	+	19.8750i	−0.618612	+	0.879217i
$512$			3.26654i			0.144362i
$513$	29.4893	+	26.2367i	1.30199	+	1.15838i
$514$	−43.9683	−	25.3851i	−1.93936	−	1.11969i
$515$	−14.1613	−	2.49702i	−0.624021	−	0.110032i
$516$	−53.0878	+	15.3365i	−2.33706	+	0.675154i
$517$	0.329097	+	0.392203i	0.0144737	+	0.0172490i
$518$	−40.2825	−	40.4657i	−1.76991	−	1.77796i
$519$	−34.2429	+	24.9827i	−1.50310	+	1.09662i
$520$	0.0445441	−	0.252622i	0.00195339	−	0.0110782i
$521$	7.13299	+	12.3547i	0.312502	+	0.541269i	0.978903	−	0.204324i	$-0.0654996\pi$
$521$	7.13299	+	12.3547i	0.312502	+	0.541269i	−0.666401	+	0.745593i	$0.732166\pi$
$522$	−65.8507	+	14.2699i	−2.88221	+	0.624576i
$523$	17.4049	+	10.0487i	0.761062	+	0.439399i	0.829677	−	0.558244i	$-0.188525\pi$
$523$	17.4049	+	10.0487i	0.761062	+	0.439399i	−0.0686150	+	0.997643i	$0.521858\pi$
$524$	2.47889	−	14.0585i	0.108291	−	0.614148i
$525$	−3.77951	−	6.29427i	−0.164951	−	0.274705i
$526$	4.11812	+	1.49887i	0.179559	+	0.0653540i
$527$	−0.706977	+	0.124659i	−0.0307964	+	0.00543024i
$528$	0.00416636	−	0.0613271i	0.000181317	−	0.00266892i
$529$	16.8945	+	14.1761i	0.734542	+	0.616354i
$530$	−0.347136	+	0.601257i	−0.0150786	+	0.0261169i
$531$	34.7108	−	7.52185i	1.50632	−	0.326420i
$532$	−54.4109	+	37.9153i	−2.35901	+	1.64384i
$533$	−0.183535	+	0.218728i	−0.00794978	+	0.00947418i
$534$	−17.1213	+	38.6610i	−0.740912	+	1.67303i
$535$	−4.70852	+	12.9366i	−0.203567	+	0.559297i
$536$	28.9769	−	5.10942i	1.25161	−	0.220693i
$537$	8.87731	+	30.7290i	0.383084	+	1.32605i
$538$	−9.63644	−	26.4759i	−0.415457	−	1.14146i
$539$	0.145434	+	0.847262i	0.00626430	+	0.0364942i
$540$	31.2718	−	4.58462i	1.34572	−	0.197291i
$541$	3.47620	+	6.02095i	0.149453	+	0.258861i	0.931026	−	0.364954i	$-0.118915\pi$
$541$	3.47620	+	6.02095i	0.149453	+	0.258861i	−0.781572	+	0.623815i	$0.785582\pi$
$542$	4.66254	−	26.4426i	0.200273	−	1.13581i
$543$	−10.8391	−	2.67970i	−0.465151	−	0.114997i
$544$	0.286075	−	0.785986i	0.0122654	−	0.0336989i
$545$	2.79913	+	15.8747i	0.119902	+	0.679996i
$546$	0.463856	+	0.159868i	0.0198512	+	0.00684171i
$547$	−10.1175	−	8.48957i	−0.432592	−	0.362988i	0.400337	−	0.916368i	$-0.368893\pi$
$547$	−10.1175	−	8.48957i	−0.432592	−	0.362988i	−0.832929	+	0.553380i	$0.813338\pi$
$548$			5.78429i			0.247093i
$549$	8.43004	−	3.44487i	0.359786	−	0.147023i
$550$	−0.452949			−0.0193138
$551$	69.6404	−	25.3470i	2.96678	−	1.07982i
$552$	−2.81028	+	4.18427i	−0.119614	+	0.178094i
$553$	−6.63923	−	1.79513i	−0.282329	−	0.0763367i
$554$	14.9189	−	40.9894i	0.633844	−	1.74147i
$555$	−13.1737	−	26.8748i	−0.559192	−	1.14077i
$556$	28.8601	−	34.3941i	1.22394	−	1.45863i
$557$		−	42.4357i		−	1.79806i	−0.437890	−	0.899028i	$-0.644274\pi$
$557$		−	42.4357i		−	1.79806i	0.437890	−	0.899028i	$-0.355726\pi$
$558$	1.22520	+	31.5062i	0.0518669	+	1.33377i
$559$	−0.389407	−	0.224824i	−0.0164702	−	0.00950905i
$560$	−0.126018	+	1.40371i	−0.00532523	+	0.0593174i
$561$	−0.0135438	+	0.0305828i	−0.000571821	+	0.00129121i
$562$	0.718705	−	0.603065i	0.0303167	−	0.0254388i
$563$	−5.38665	−	30.5492i	−0.227020	−	1.28750i	−0.858785	−	0.512336i	$-0.828780\pi$
$563$	−5.38665	−	30.5492i	−0.227020	−	1.28750i	0.631764	−	0.775160i	$-0.282331\pi$
$564$	−22.8913	+	6.61307i	−0.963897	+	0.278460i
$565$	−19.4982	+	23.2370i	−0.820295	+	0.977589i
$566$	10.7140			0.450344
$567$	−0.280952	+	23.8101i	−0.0117989	+	0.999930i
$568$	2.98275			0.125154
$569$	−7.35768	+	8.76854i	−0.308450	+	0.367596i	−0.897893	−	0.440213i	$-0.854903\pi$
$569$	−7.35768	+	8.76854i	−0.308450	+	0.367596i	0.589443	+	0.807810i	$0.299347\pi$
$570$	−53.6398	+	15.4960i	−2.24672	+	0.649057i
$571$	2.64153	+	14.9809i	0.110545	+	0.626931i	0.988860	+	0.148849i	$0.0475567\pi$
$571$	2.64153	+	14.9809i	0.110545	+	0.626931i	−0.878315	+	0.478082i	$0.841332\pi$
$572$	0.0144372	−	0.0121142i	0.000603648	−	0.000506521i
$573$	−7.03660	+	15.8891i	−0.293958	+	0.663776i
$574$	21.5182	−	30.5833i	0.898153	−	1.27652i
$575$	1.34938	+	0.779063i	0.0562729	+	0.0324892i
$576$	−34.0387	−	17.9261i	−1.41828	−	0.746921i
$577$		−	16.7644i		−	0.697913i	−0.937139	−	0.348956i	$-0.886536\pi$
$577$		−	16.7644i		−	0.697913i	0.937139	−	0.348956i	$-0.113464\pi$
$578$	−25.1196	+	29.9364i	−1.04484	+	1.24519i
$579$	−18.7608	−	38.2728i	−0.779674	−	1.59057i
$580$	20.2963	−	55.7635i	0.842756	−	2.31545i
$581$	−12.0276	+	11.9731i	−0.498988	+	0.496729i
$582$	−29.9296	+	44.5626i	−1.24062	+	1.84718i
$583$	−0.0188803	+	0.00687185i	−0.000781940	+	0.000284603i
$584$	−27.4842			−1.13730
$585$	0.203289	+	0.157534i	0.00840496	+	0.00651322i
$586$		−	19.1080i		−	0.789344i
$587$	1.10643	+	0.928404i	0.0456672	+	0.0383193i	0.665336	−	0.746544i	$-0.268288\pi$
$587$	1.10643	+	0.928404i	0.0456672	+	0.0383193i	−0.619668	+	0.784864i	$0.712733\pi$
$588$	−38.7944	−	9.77795i	−1.59985	−	0.403236i
$589$	−6.02205	−	34.1528i	−0.248134	−	1.40724i
$590$	−17.1828	+	47.2092i	−0.707403	+	1.94357i
$591$	23.4905	+	5.80744i	0.966269	+	0.238886i
$592$	0.470411	−	2.66784i	0.0193338	−	0.109647i
$593$	−17.6222	−	30.5226i	−0.723657	−	1.25341i	−0.959524	−	0.281626i	$-0.909126\pi$
$593$	−17.6222	−	30.5226i	−0.723657	−	1.25341i	0.235867	−	0.971785i	$-0.424207\pi$
$594$	1.25043	+	0.771061i	0.0513057	+	0.0316370i
$595$	0.325677	−	0.694300i	0.0133515	−	0.0284635i
$596$	−10.4658	−	28.7545i	−0.428695	−	1.17783i
$597$	6.19113	+	21.4307i	0.253386	+	0.877101i
$598$	−0.102543	+	0.0180811i	−0.00419329	+	0.000739390i
$599$	−14.8549	+	40.8135i	−0.606955	+	1.66759i	0.129887	+	0.991529i	$0.458538\pi$
$599$	−14.8549	+	40.8135i	−0.606955	+	1.66759i	−0.736842	+	0.676065i	$0.763684\pi$
$600$	3.36225	−	7.59217i	0.137263	−	0.309949i
$601$	−12.1502	+	14.4801i	−0.495618	+	0.590655i	−0.954637	−	0.297772i	$-0.903757\pi$
$601$	−12.1502	+	14.4801i	−0.495618	+	0.590655i	0.459019	+	0.888427i	$0.348201\pi$
$602$	53.3148	+	25.0085i	2.17295	+	1.01927i
$603$	−9.00483	+	28.0922i	−0.366705	+	1.14400i
$604$	16.1066	−	27.8975i	0.655369	−	1.13513i
$605$	−15.5115	−	13.0157i	−0.630634	−	0.529164i
$606$	−3.75563	+	55.2813i	−0.152562	+	2.24565i
$607$	−2.09328	+	0.369101i	−0.0849635	+	0.0149814i	−0.215968	−	0.976400i	$-0.569291\pi$
$607$	−2.09328	+	0.369101i	−0.0849635	+	0.0149814i	0.131005	+	0.991382i	$0.458180\pi$
$608$	37.9695	+	13.8198i	1.53987	+	0.560465i
$609$	39.0962	+	21.6861i	1.58426	+	0.878766i
$610$	−2.23689	+	12.6860i	−0.0905691	+	0.513643i
$611$	−0.167911	−	0.0969435i	−0.00679295	−	0.00392191i
$612$	−1.04616	−	1.15267i	−0.0422886	−	0.0465938i
$613$	9.12735	+	15.8090i	0.368650	+	0.638521i	0.989355	−	0.145523i	$-0.0464866\pi$
$613$	9.12735	+	15.8090i	0.368650	+	0.638521i	−0.620704	+	0.784045i	$0.713153\pi$
$614$	2.35811	−	13.3735i	0.0951657	−	0.539711i
$615$	15.8354	−	11.5531i	0.638545	−	0.465866i
$616$	−0.689034	+	0.685915i	−0.0277620	+	0.0276363i
$617$	−5.58064	−	6.65075i	−0.224668	−	0.267749i	0.641922	−	0.766770i	$-0.278137\pi$
$617$	−5.58064	−	6.65075i	−0.224668	−	0.267749i	−0.866590	+	0.499021i	$0.833693\pi$
$618$	29.8835	−	8.63304i	1.20209	−	0.347272i
$619$	−38.7265	−	6.82853i	−1.55655	−	0.274462i	−0.671874	−	0.740666i	$-0.734510\pi$
$619$	−38.7265	−	6.82853i	−1.55655	−	0.274462i	−0.884677	+	0.466204i	$0.845621\pi$
$620$	−24.0488	−	13.8846i	−0.965824	−	0.557619i
$621$	−2.39893	−	4.44777i	−0.0962658	−	0.178483i
$622$			31.2476i			1.25291i
$623$	25.4539	−	11.7991i	1.01979	−	0.472722i
$624$	0.00646057	+	0.0223634i	0.000258630	+	0.000895254i
$625$	13.5528	+	4.93282i	0.542113	+	0.197313i
$626$	−12.3648	−	4.50042i	−0.494197	−	0.179873i
$627$	−1.47740	−	0.654277i	−0.0590017	−	0.0261293i
$628$	−52.5895	−	9.27294i	−2.09855	−	0.370031i
$629$	−0.737040	+	1.27659i	−0.0293877	+	0.0509010i
$630$	−28.2795	−	18.2969i	−1.12668	−	0.728966i
$631$	5.26401	+	9.11753i	0.209557	+	0.362963i	0.951575	−	0.307417i	$-0.0994645\pi$
$631$	5.26401	+	9.11753i	0.209557	+	0.362963i	−0.742018	+	0.670380i	$0.766131\pi$
$632$	−2.66036	−	7.30927i	−0.105823	−	0.290747i
$633$	−4.03151	−	8.22443i	−0.160238	−	0.326892i
$634$	−4.24711	+	3.56375i	−0.168674	+	0.141535i
$635$	−1.37471	−	7.79638i	−0.0545538	−	0.309390i
$636$	0.0633791	−	0.932915i	0.00251315	−	0.0369925i
$637$	−0.161493	−	0.282669i	−0.00639860	−	0.0111998i
$638$	2.38869	−	1.37911i	0.0945693	−	0.0545996i
$639$	−1.39347	+	2.64598i	−0.0551249	+	0.104673i
$640$	30.1441	−	17.4037i	1.19155	−	0.687941i
$641$	4.22019	+	11.5949i	0.166688	+	0.457970i	0.994710	−	0.102725i	$-0.0327562\pi$
$641$	4.22019	+	11.5949i	0.166688	+	0.457970i	−0.828022	+	0.560695i	$0.810534\pi$
$642$	−3.17147	−	29.6102i	−0.125168	−	1.16862i
$643$	22.7208	−	4.00630i	0.896023	−	0.157993i	0.293372	−	0.955998i	$-0.405222\pi$
$643$	22.7208	−	4.00630i	0.896023	−	0.157993i	0.602650	+	0.798005i	$0.294111\pi$
$644$	8.20631	−	2.17893i	0.323374	−	0.0858620i
$645$	22.2476	+	21.3993i	0.875998	+	0.842595i
$646$	2.10650	+	1.76757i	0.0828792	+	0.0695439i
$647$	−19.2253	+	33.2993i	−0.755826	+	1.30913i	0.189137	+	0.981951i	$0.439431\pi$
$647$	−19.2253	+	33.2993i	−0.755826	+	1.30913i	−0.944963	+	0.327178i	$0.893902\pi$
$648$	−22.2062	+	15.2356i	−0.872341	+	0.598512i
$649$	−1.25911	+	0.726949i	−0.0494245	+	0.0285352i
$650$	0.161186	−	0.0586669i	0.00632224	−	0.00230111i
$651$	13.1707	−	16.2549i	0.516202	−	0.637082i
$652$	28.5970	−	23.9958i	1.11995	−	0.939747i
$653$	9.10813	+	10.8547i	0.356429	+	0.424775i	0.914228	−	0.405201i	$-0.132798\pi$
$653$	9.10813	+	10.8547i	0.356429	+	0.424775i	−0.557799	+	0.829976i	$0.688354\pi$
$654$	−20.5513	−	28.1689i	−0.803618	−	1.10149i
$655$	−7.49363	+	2.72746i	−0.292801	+	0.106571i
$656$	1.77419			0.0692704
$657$	12.8400	−	24.3810i	0.500935	−	0.951192i
$658$	22.9892	+	10.7836i	0.896212	+	0.420388i
$659$	39.3185	+	6.93292i	1.53163	+	0.270068i	0.874993	−	0.484136i	$-0.160866\pi$
$659$	39.3185	+	6.93292i	1.53163	+	0.270068i	0.656640	+	0.754204i	$0.271977\pi$
$660$	−1.16175	+	0.569477i	−0.0452212	+	0.0221669i
$661$	15.7489	+	18.7688i	0.612562	+	0.730023i	0.979772	−	0.200115i	$-0.0641315\pi$
$661$	15.7489	+	18.7688i	0.612562	+	0.730023i	−0.367210	+	0.930138i	$0.619687\pi$
$662$	−15.6787	−	18.6852i	−0.609372	−	0.726221i
$663$	0.000858543	−	0.0126374i	3.33431e−5	−	0.000490796i
$664$	−18.9021	−	3.33296i	−0.733545	−	0.129344i
$665$	33.5403	+	15.7329i	1.30064	+	0.610094i
$666$	51.1755	+	39.6572i	1.98301	+	1.53669i
$667$	−9.48818			−0.367384
$668$	5.92687	−	2.15721i	0.229318	−	0.0834648i
$669$	−5.87068	+	13.2564i	−0.226974	+	0.512521i
$670$	−26.8228	−	31.9661i	−1.03625	−	1.23496i
$671$	−0.285576	+	0.239627i	−0.0110245	+	0.00925068i
$672$	8.72895	+	22.7593i	0.336727	+	0.877959i
$673$	−12.2850	+	4.47136i	−0.473551	+	0.172358i	−0.567760	−	0.823194i	$-0.692190\pi$
$673$	−12.2850	+	4.47136i	−0.473551	+	0.172358i	0.0942095	+	0.995552i	$0.469968\pi$
$674$	−45.8791	+	26.4883i	−1.76720	+	1.02029i
$675$	5.16419	+	6.52951i	0.198770	+	0.251321i
$676$	21.4450	−	37.1438i	0.824807	−	1.42861i
$677$	−20.8680	−	17.5103i	−0.802021	−	0.672976i	0.146668	−	0.989186i	$-0.453145\pi$
$677$	−20.8680	−	17.5103i	−0.802021	−	0.672976i	−0.948689	+	0.316210i	$0.897590\pi$
$678$	15.7479	−	63.6986i	0.604794	−	2.44633i
$679$	34.4257	−	9.14069i	1.32114	−	0.350788i
$680$	0.854147	−	0.150609i	0.0327551	−	0.00577560i
$681$	−31.9664	−	14.1565i	−1.22495	−	0.542480i
$682$	−0.441449	−	1.21287i	−0.0169040	−	0.0464433i
$683$	40.3439	−	23.2926i	1.54372	−	0.891265i	0.545117	−	0.838360i	$-0.316485\pi$
$683$	40.3439	−	23.2926i	1.54372	−	0.891265i	0.998600	−	0.0529057i	$-0.0168483\pi$
$684$	55.6832	−	50.5382i	2.12910	−	1.93238i
$685$	2.79834	−	1.61562i	0.106919	−	0.0617297i
$686$	24.2167	+	35.0910i	0.924598	+	1.33978i
$687$	9.03444	−	4.42856i	0.344685	−	0.168960i
$688$	0.485167	+	2.75152i	0.0184968	+	0.104901i
$689$	0.00582865	−	0.00489082i	0.000222054	−	0.000186325i
$690$	7.13183	+	0.484513i	0.271504	+	0.0184451i
$691$	−3.08293	−	8.47029i	−0.117280	−	0.322225i	0.867138	−	0.498068i	$-0.165957\pi$
$691$	−3.08293	−	8.47029i	−0.117280	−	0.322225i	−0.984418	+	0.175843i	$0.943735\pi$
$692$	40.3770	+	69.9350i	1.53490	+	2.65853i
$693$	−0.286569	−	0.931680i	−0.0108858	−	0.0353916i
$694$	−4.43299	+	7.67816i	−0.168274	+	0.291459i
$695$	−24.7002	−	4.35531i	−0.936932	−	0.165206i
$696$	5.38488	+	50.2756i	0.204113	+	1.90569i
$697$	−0.907191	−	0.330190i	−0.0343623	−	0.0125069i
$698$	−4.56471	−	1.66142i	−0.172777	−	0.0628857i
$699$	10.3613	+	2.56157i	0.391900	+	0.0968876i
$700$	−12.6900	+	5.88245i	−0.479638	+	0.222336i
$701$		−	28.1670i		−	1.06385i	−0.846790	−	0.531927i	$-0.821468\pi$
$701$		−	28.1670i		−	1.06385i	0.846790	−	0.531927i	$-0.178532\pi$
$702$	−0.544845	−	0.112431i	−0.0205639	−	0.00424343i
$703$	−61.6697	−	35.6050i	−2.32592	−	1.34287i
$704$	1.55090	+	0.273465i	0.0584517	+	0.0103066i
$705$	9.59309	+	9.22729i	0.361297	+	0.347520i
$706$	18.1837	+	21.6704i	0.684351	+	0.815578i
$707$	26.0559	−	25.9379i	0.979932	−	0.975495i
$708$	−7.20602	−	67.2786i	−0.270819	−	2.52848i
$709$	−6.18586	+	35.0818i	−0.232315	+	1.31752i	0.615880	+	0.787840i	$0.288800\pi$
$709$	−6.18586	+	35.0818i	−0.232315	+	1.31752i	−0.848195	+	0.529684i	$0.822311\pi$
$710$	−2.11506	−	3.66339i	−0.0793767	−	0.137484i
$711$	7.72685	+	1.05474i	0.289780	+	0.0395559i
$712$	27.4790	+	15.8650i	1.02982	+	0.594566i
$713$	−0.770997	+	4.37254i	−0.0288741	+	0.163753i
$714$	0.0284740	+	1.65865i	0.00106561	+	0.0620733i
$715$	−0.00989312	−	0.00360080i	−0.000369982	−	0.000134662i
$716$	60.0109	−	10.5815i	2.24271	−	0.395451i
$717$	26.8369	+	18.0245i	1.00224	+	0.673137i
$718$	−53.9418	−	45.2625i	−2.01309	−	1.68918i
$719$	4.56902	−	7.91377i	0.170396	−	0.295134i	−0.768163	−	0.640255i	$-0.778829\pi$
$719$	4.56902	−	7.91377i	0.170396	−	0.295134i	0.938558	+	0.345121i	$0.112162\pi$
$720$	−0.0620975	−	1.59685i	−0.00231424	−	0.0595109i
$721$	−18.6858	−	8.76499i	−0.695895	−	0.326425i
$722$	−57.2720	+	68.2541i	−2.13144	+	2.54016i
$723$	−20.9866	+	2.24782i	−0.780500	+	0.0835972i
$724$	−7.27531	+	19.9888i	−0.270385	+	0.742876i
$725$	15.3930	−	2.71419i	0.571680	−	0.100803i
$726$	42.5211	+	10.5123i	1.57810	+	0.390147i
$727$	−3.56316	−	9.78970i	−0.132150	−	0.363080i	0.855915	−	0.517117i	$-0.172995\pi$
$727$	−3.56316	−	9.78970i	−0.132150	−	0.363080i	−0.988065	+	0.154037i	$0.950772\pi$
$728$	0.156358	−	0.333334i	0.00579501	−	0.0123542i
$729$	−3.14118	−	26.8167i	−0.116340	−	0.993209i
$730$	19.4889	+	33.7558i	0.721317	+	1.24936i
$731$	0.264001	−	1.49722i	0.00976442	−	0.0553768i
$732$	−4.81520	−	16.6679i	−0.177975	−	0.616064i
$733$	9.50030	−	26.1019i	0.350902	−	0.964094i	−0.631180	−	0.775637i	$-0.717429\pi$
$733$	9.50030	−	26.1019i	0.350902	−	0.964094i	0.982081	−	0.188458i	$-0.0603488\pi$
$734$	−5.47810	−	31.0678i	−0.202200	−	1.14673i
$735$	6.10534	+	21.4991i	0.225199	+	0.793008i
$736$	−3.96288	−	3.32525i	−0.146074	−	0.122570i
$737$		−	1.20762i		−	0.0444831i
$738$	−19.7579	+	37.5171i	−0.727300	+	1.38102i
$739$	−35.6793			−1.31248			−0.656242	−	0.754551i	$-0.727855\pi$
$739$	−35.6793			−1.31248			−0.656242	+	0.754551i	$0.727855\pi$
$740$	−53.5816	+	19.5021i	−1.96970	+	0.716912i
$741$	0.610489	+	0.0414746i	0.0224269	+	0.00152361i
$742$	−0.706224	+	0.703027i	−0.0259263	+	0.0258089i
$743$	2.30236	−	6.32568i	0.0844653	−	0.232067i	−0.890269	−	0.455436i	$-0.849483\pi$
$743$	2.30236	−	6.32568i	0.0844653	−	0.232067i	0.974734	+	0.223369i	$0.0717056\pi$
$744$	23.6066	+	1.60375i	0.865460	+	0.0587965i
$745$	−10.9877	+	13.0946i	−0.402558	+	0.479750i
$746$			26.9025i			0.984972i
$747$	11.7873	−	15.2108i	0.431274	−	0.556536i
$748$	0.0551849	+	0.0318610i	0.00201776	+	0.00116495i
$749$	−11.3703	+	16.1604i	−0.415463	+	0.590487i
$750$	−48.2503	+	5.16796i	−1.76185	+	0.188707i
$751$	−36.6592	+	30.7607i	−1.33771	+	1.12247i	−0.355504	+	0.934675i	$0.615691\pi$
$751$	−36.6592	+	30.7607i	−1.33771	+	1.12247i	−0.982208	+	0.187799i	$0.939865\pi$
$752$	0.209203	+	1.18645i	0.00762883	+	0.0432653i
$753$	1.58163	−	6.39752i	0.0576377	−	0.233139i
$754$	−0.671413	+	0.800158i	−0.0244514	+	0.0291401i
$755$	−17.9951			−0.654907
$756$	45.0463	+	5.36310i	1.63832	+	0.195054i
$757$	35.1225			1.27655			0.638274	−	0.769809i	$-0.279649\pi$
$757$	35.1225			1.27655			0.638274	+	0.769809i	$0.279649\pi$
$758$	−18.7974	+	22.4018i	−0.682751	+	0.813671i
$759$	0.149093	+	0.143408i	0.00541173	+	0.00520537i
$760$	7.27565	+	41.2623i	0.263916	+	1.49674i
$761$	−26.2041	+	21.9878i	−0.949897	+	0.797059i	−0.979280	−	0.202510i	$-0.935090\pi$
$761$	−26.2041	+	21.9878i	−0.949897	+	0.797059i	0.0293828	+	0.999568i	$0.490646\pi$
$762$	10.0932	+	13.8343i	0.365637	+	0.501165i
$763$	−2.06877	+	23.0438i	−0.0748943	+	0.834243i
$764$	28.6709	+	16.5532i	1.03728	+	0.598872i
$765$	−0.265434	+	0.828068i	−0.00959678	+	0.0299389i
$766$			18.4390i			0.666227i
$767$	0.353910	−	0.421774i	0.0127790	−	0.0152294i
$768$	−17.2124	+	25.6277i	−0.621097	+	0.924760i
$769$	−3.20130	+	8.79549i	−0.115442	+	0.317174i	−0.983935	−	0.178528i	$-0.942867\pi$
$769$	−3.20130	+	8.79549i	−0.115442	+	0.317174i	0.868493	+	0.495701i	$0.165089\pi$
$770$	1.33102	+	0.359885i	0.0479668	+	0.0129694i
$771$	−16.8129	−	34.2989i	−0.605501	−	1.23525i
$772$	−76.3064	+	27.7733i	−2.74633	+	0.999582i
$773$	20.1128			0.723406			0.361703	−	0.932293i	$-0.382195\pi$
$773$	20.1128			0.723406			0.361703	+	0.932293i	$0.382195\pi$
$774$	−63.5868	−	20.3825i	−2.28558	−	0.732633i
$775$		−	7.31425i		−	0.262736i
$776$	30.8589	+	25.8936i	1.10777	+	0.929528i
$777$	−8.18476	−	42.1718i	−0.293627	−	1.51290i
$778$	5.12245	+	29.0509i	0.183649	+	1.04152i
$779$	15.9509	−	43.8247i	0.571500	−	1.57018i
$780$	0.339661	−	0.353126i	0.0121618	−	0.0126440i
$781$	0.0212576	−	0.120558i	0.000760658	−	0.00431391i
$782$	−0.176030	−	0.304892i	−0.00629481	−	0.0109029i
$783$	−47.1148	−	18.7107i	−1.68374	−	0.668666i
$784$	−0.700474	+	1.89770i	−0.0250169	+	0.0677750i
$785$	10.2028	+	28.0319i	0.364153	+	1.00050i
$786$	11.9583	−	12.4324i	0.426540	−	0.443449i
$787$	47.3837	−	8.35503i	1.68905	−	0.297825i	0.755200	−	0.655495i	$-0.227540\pi$
$787$	47.3837	−	8.35503i	1.68905	−	0.297825i	0.933848	+	0.357670i	$0.116429\pi$
$788$	15.7670	−	43.3195i	0.561677	−	1.54319i
$789$	1.94333	+	2.66365i	0.0691842	+	0.0948283i
$790$	−7.09073	+	8.45040i	−0.252277	+	0.300652i
$791$	−35.7211	+	24.8916i	−1.27010	+	0.885043i
$792$	0.675267	−	0.871396i	0.0239946	−	0.0309637i
$793$	0.0705878	−	0.122262i	0.00250665	−	0.00434164i
$794$	−17.6302	−	14.7935i	−0.625672	−	0.525001i
$795$	−0.469030	+	0.229912i	−0.0166348	+	0.00815415i
$796$	41.8522	−	7.37968i	1.48341	−	0.261566i
$797$	−30.7365	−	11.1872i	−1.08874	−	0.396270i	−0.265588	−	0.964087i	$-0.585566\pi$
$797$	−30.7365	−	11.1872i	−1.08874	−	0.396270i	−0.823155	+	0.567817i	$0.807788\pi$
$798$	−80.1261	+	1.37552i	−2.83643	+	0.0486930i
$799$	0.113836	−	0.645597i	0.00402724	−	0.0228396i
$800$	7.38032	+	4.26103i	0.260934	+	0.150650i
$801$	−26.9112	+	16.9646i	−0.950862	+	0.599415i
$802$	42.6664	+	73.9004i	1.50660	+	2.60952i
$803$	−0.195876	+	1.11087i	−0.00691230	+	0.0392016i
$804$	51.3879	+	22.7575i	1.81231	+	0.802595i
$805$	−3.34625	−	3.36147i	−0.117940	−	0.118476i
$806$	0.314187	+	0.374434i	0.0110668	+	0.0131889i
$807$	5.08753	−	20.5785i	0.179090	−	0.724399i
$808$	40.9485	+	7.22032i	1.44056	+	0.254010i
$809$	−2.72104	−	1.57099i	−0.0956666	−	0.0552332i	0.451403	−	0.892320i	$-0.350924\pi$
$809$	−2.72104	−	1.57099i	−0.0956666	−	0.0552332i	−0.547070	+	0.837087i	$0.684257\pi$
$810$	34.4585	+	16.4699i	1.21075	+	0.578693i
$811$			36.4973i			1.28159i	0.767711	+	0.640797i	$0.221396\pi$
$811$			36.4973i			1.28159i	−0.767711	+	0.640797i	$0.778604\pi$
$812$	49.0122	−	69.6598i	1.71999	−	2.44458i
$813$	14.0043	−	14.5595i	0.491154	−	0.510625i
$814$	−2.49047	−	0.906458i	−0.0872910	−	0.0317713i
$815$	−19.5962	−	7.13244i	−0.686426	−	0.249839i
$816$	−0.0635825	+	0.0463881i	−0.00222583	+	0.00162391i
$817$	72.3280	+	12.7534i	2.53044	+	0.446184i
$818$	−2.69521	+	4.66825i	−0.0942360	+	0.163221i
$819$	0.222651	+	0.294430i	0.00778006	+	0.0102882i
$820$	−18.6721	−	32.3409i	−0.652056	−	1.12939i
$821$	−15.7386	−	43.2415i	−0.549282	−	1.50914i	−0.834683	−	0.550731i	$-0.814349\pi$
$821$	−15.7386	−	43.2415i	−0.549282	−	1.50914i	0.285401	−	0.958408i	$-0.407873\pi$
$822$	−3.89707	+	5.80241i	−0.135926	+	0.202382i
$823$	32.5272	−	27.2935i	1.13383	−	0.951393i	0.134607	−	0.990899i	$-0.457023\pi$
$823$	32.5272	−	27.2935i	1.13383	−	0.951393i	0.999219	+	0.0395062i	$0.0125785\pi$
$824$	−4.05336	−	22.9878i	−0.141206	−	0.800817i
$825$	−0.282901	−	0.190005i	−0.00984935	−	0.00661512i
$826$	−41.4936	+	58.9738i	−1.44375	+	2.05196i
$827$	−9.94149	+	5.73972i	−0.345699	+	0.199590i	−0.662789	−	0.748806i	$-0.730628\pi$
$827$	−9.94149	+	5.73972i	−0.345699	+	0.199590i	0.317090	+	0.948395i	$0.397294\pi$
$828$	−8.91211	+	3.64186i	−0.309717	+	0.126563i
$829$	32.3724	−	18.6902i	1.12434	−	0.649137i	0.181834	−	0.983329i	$-0.441797\pi$
$829$	32.3724	−	18.6902i	1.12434	−	0.649137i	0.942505	+	0.334192i	$0.108463\pi$
$830$	9.30992	+	25.5788i	0.323152	+	0.887853i
$831$	26.5124	−	19.3427i	0.919704	−	0.670991i
$832$	−0.587321	+	0.103561i	−0.0203617	+	0.00359032i
$833$	0.711349	−	0.839983i	0.0246468	−	0.0291037i
$834$	52.1229	−	15.0578i	1.80487	−	0.521409i
$835$	−2.69906	−	2.26478i	−0.0934050	−	0.0783761i
$836$	−1.53915	+	2.66588i	−0.0532325	+	0.0922014i
$837$	−12.4511	+	20.1920i	−0.430374	+	0.697937i
$838$	−60.7778	+	35.0901i	−2.09954	+	1.21217i
$839$	−14.8437	+	5.40267i	−0.512462	+	0.186521i	−0.585291	−	0.810824i	$-0.699020\pi$
$839$	−14.8437	+	5.40267i	−0.512462	+	0.186521i	0.0728286	+	0.997344i	$0.476797\pi$
$840$	−15.9125	+	19.6387i	−0.549033	+	0.677600i
$841$	−50.6977	+	42.5404i	−1.74820	+	1.46691i
$842$	−3.14523	−	3.74833i	−0.108392	−	0.129176i
$843$	0.701862	−	0.0751745i	0.0241734	−	0.00258915i
$844$	−16.3975	+	5.96818i	−0.564424	+	0.205433i
$845$	−23.9594			−0.824227
$846$	−27.4184	−	8.78886i	−0.942665	−	0.302167i
$847$	−16.6160	−	23.8451i	−0.570933	−	0.819326i
$848$	−0.0465601	−	0.00820980i	−0.00159888	−	0.000281926i
$849$	6.69171	+	4.49436i	0.229659	+	0.154246i
$850$	0.372796	+	0.444281i	0.0127868	+	0.0152387i
$851$	5.86026	+	6.98398i	0.200887	+	0.239408i
$852$	4.72953	+	3.17649i	0.162031	+	0.108825i
$853$	30.8230	+	5.43493i	1.05536	+	0.186089i	0.674297	−	0.738460i	$-0.264447\pi$
$853$	30.8230	+	5.43493i	1.05536	+	0.186089i	0.381064	+	0.924549i	$0.375558\pi$
$854$	−7.85190	+	16.7392i	−0.268686	+	0.572803i
$855$	−40.0024	−	12.8226i	−1.36805	−	0.438524i
$856$	−22.3474			−0.763819
$857$	−25.0495	+	9.11726i	−0.855673	+	0.311440i	−0.732351	−	0.680927i	$-0.761577\pi$
$857$	−25.0495	+	9.11726i	−0.855673	+	0.311440i	−0.123322	+	0.992367i	$0.539355\pi$
$858$	0.0226441	−	0.00242535i	0.000773058	−	8.28001e-5i
$859$	18.2968	+	21.8052i	0.624278	+	0.743985i	0.981800	−	0.189920i	$-0.0608228\pi$
$859$	18.2968	+	21.8052i	0.624278	+	0.743985i	−0.357522	+	0.933905i	$0.616378\pi$
$860$	45.0503	−	37.8017i	1.53620	−	1.28903i
$861$	26.2690	−	10.0750i	0.895244	−	0.343356i
$862$	2.57109	−	0.935799i	0.0875716	−	0.0318734i
$863$	−2.69995	+	1.55882i	−0.0919074	+	0.0530628i	−0.545249	−	0.838274i	$-0.683565\pi$
$863$	−2.69995	+	1.55882i	−0.0919074	+	0.0530628i	0.453342	+	0.891337i	$0.350232\pi$
$864$	−13.1208	−	24.3268i	−0.446378	−	0.827613i
$865$	22.5555	−	39.0673i	0.766911	−	1.32833i
$866$	19.5935	+	16.4409i	0.665813	+	0.558683i
$867$	−28.2469	+	8.16026i	−0.959317	+	0.277137i
$868$	−28.1194	−	28.2473i	−0.954434	−	0.958775i
$869$	−0.314389	+	0.0554353i	−0.0106649	+	0.00188051i
$870$	57.9296	−	42.2639i	1.96400	−	1.43288i
$871$	0.156413	+	0.429741i	0.00529985	+	0.0145612i
$872$	−22.6609	+	13.0833i	−0.767396	+	0.443056i
$873$	−37.3866	+	15.2777i	−1.26534	+	0.517072i
$874$	14.7288	−	8.50367i	0.498208	−	0.287641i
$875$	26.3335	+	18.5281i	0.890236	+	0.626365i
$876$	−43.5796	−	29.2694i	−1.47242	−	0.988920i
$877$	1.13187	+	6.41916i	0.0382206	+	0.216760i	0.997936	−	0.0642135i	$-0.0204539\pi$
$877$	1.13187	+	6.41916i	0.0382206	+	0.216760i	−0.959716	+	0.280973i	$0.909343\pi$
$878$	9.81320	−	8.23425i	0.331179	−	0.277892i
$879$	8.01550	−	11.9344i	0.270356	−	0.402537i
$880$	0.0223742	+	0.0614726i	0.000754234	+	0.00207224i
$881$	−0.192986	−	0.334261i	−0.00650186	−	0.0112615i	0.862756	−	0.505620i	$-0.168736\pi$
$881$	−0.192986	−	0.334261i	−0.00650186	−	0.0112615i	−0.869258	+	0.494359i	$0.835403\pi$
$882$	−32.3282	−	35.9457i	−1.08855	−	1.21035i
$883$	6.61385	−	11.4555i	0.222574	−	0.385509i	−0.733015	−	0.680212i	$-0.761888\pi$
$883$	6.61385	−	11.4555i	0.222574	−	0.385509i	0.955589	+	0.294704i	$0.0952209\pi$
$884$	−0.0237648	−	0.00419037i	−0.000799295	−	0.000140937i
$885$	−30.5354	+	22.2778i	−1.02644	+	0.748861i
$886$	58.8673	+	21.4259i	1.97768	+	0.719818i
$887$	−22.2545	−	8.09998i	−0.747233	−	0.271971i	−0.0597923	−	0.998211i	$-0.519044\pi$
$887$	−22.2545	−	8.09998i	−0.747233	−	0.271971i	−0.687441	+	0.726240i	$0.741266\pi$
$888$	33.6805	−	35.0157i	1.13024	−	1.17505i
$889$	1.01601	−	11.3173i	0.0340760	−	0.379571i
$890$		−	44.9992i		−	1.50838i
$891$	0.457539	+	1.00612i	0.0153281	+	0.0337063i
$892$	23.9203	+	13.8104i	0.800912	+	0.462407i
$893$	31.1876	+	5.49922i	1.04365	+	0.184024i
$894$	8.87431	−	35.8957i	0.296801	−	1.20053i
$895$	−21.8809	−	26.0767i	−0.731398	−	0.871647i
$896$	48.2862	−	12.8209i	1.61313	−	0.428316i
$897$	−0.0716305	−	0.0317221i	−0.00239167	−	0.00105917i
$898$	−9.84592	+	55.8390i	−0.328563	+	1.86337i
$899$	22.2700	+	38.5728i	0.742746	+	1.28647i
$900$	13.4166	−	8.45770i	0.447219	−	0.281923i
$901$	0.0222796	+	0.0128631i	0.000742240	+	0.000428532i
$902$	0.301410	−	1.70938i	0.0100359	−	0.0569162i
$903$	22.8085	+	37.9844i	0.759018	+	1.26404i
$904$	−46.2708	−	16.8412i	−1.53894	−	0.560129i
$905$	11.7023	−	2.06343i	0.388997	−	0.0685907i
$906$	34.9525	−	17.1333i	1.16122	−	0.569215i
$907$	9.64234	+	8.09089i	0.320169	+	0.268653i	0.788680	−	0.614804i	$-0.210765\pi$
$907$	9.64234	+	8.09089i	0.320169	+	0.268653i	−0.468511	+	0.883458i	$0.655209\pi$
$908$	−33.3024	+	57.6814i	−1.10518	+	1.91423i
$909$	−25.5353	+	32.9519i	−0.846952	+	1.09295i
$910$	−0.520270	+	0.0443286i	−0.0172468	+	0.00146948i
$911$	12.9220	−	15.3999i	0.428125	−	0.510220i	−0.508255	−	0.861207i	$-0.669709\pi$
$911$	12.9220	−	15.3999i	0.428125	−	0.510220i	0.936380	+	0.350987i	$0.114154\pi$
$912$	−2.24092	−	3.07155i	−0.0742043	−	0.101709i
$913$	−0.269425	+	0.740240i	−0.00891668	+	0.0244984i
$914$	−15.9686	+	2.81569i	−0.528193	+	0.0931347i
$915$	−6.71870	+	6.98505i	−0.222113	+	0.230919i
$916$	−6.55597	−	18.0124i	−0.216615	−	0.595146i
$917$	−11.4046	+	0.971709i	−0.376614	+	0.0320886i
$918$	−0.272849	−	1.86111i	−0.00900536	−	0.0614258i
$919$	−4.76251	−	8.24891i	−0.157101	−	0.272106i	0.776721	−	0.629845i	$-0.216881\pi$
$919$	−4.76251	−	8.24891i	−0.157101	−	0.272106i	−0.933822	+	0.357738i	$0.883548\pi$
$920$	0.931494	−	5.28276i	0.0307104	−	0.174168i
$921$	7.08280	−	7.36358i	0.233386	−	0.242638i
$922$	5.71649	−	15.7059i	0.188263	−	0.517247i
$923$	0.00805021	+	0.0456550i	0.000264976	+	0.00150275i
$924$	−1.82302	+	0.353814i	−0.0599729	+	0.0116396i
$925$	−11.5051	−	9.65393i	−0.378286	−	0.317419i
$926$		−	18.7849i		−	0.617309i
$927$	22.2859	+	7.14365i	0.731965	+	0.234628i
$928$	−51.8949			−1.70353
$929$	−45.8614	+	16.6922i	−1.50467	+	0.547653i	−0.957264	−	0.289217i	$-0.906605\pi$
$929$	−45.8614	+	16.6922i	−1.50467	+	0.547653i	−0.547402	+	0.836870i	$0.684383\pi$
$930$	−14.7696	−	30.1306i	−0.484315	−	0.988021i
$931$	40.5780	+	34.3639i	1.32989	+	1.12623i
$932$	6.95460	−	19.1076i	0.227805	−	0.625890i
$933$	−13.1079	+	19.5165i	−0.429132	+	0.638940i
$934$	18.8861	−	22.5076i	0.617972	−	0.736471i
$935$		−	0.0355966i		−	0.00116413i
$936$	−0.127435	+	0.397556i	−0.00416534	+	0.0129945i
$937$	−14.6214	−	8.44169i	−0.477661	−	0.275778i	0.241780	−	0.970331i	$-0.422269\pi$
$937$	−14.6214	−	8.44169i	−0.477661	−	0.275778i	−0.719441	+	0.694553i	$0.755602\pi$
$938$	−25.1889	−	54.3394i	−0.822448	−	1.77424i
$939$	−5.83490	−	7.99770i	−0.190415	−	0.260995i
$940$	19.4256	−	16.3000i	0.633592	−	0.531647i
$941$	1.58531	+	8.99075i	0.0516797	+	0.293090i	0.999683	−	0.0251698i	$-0.00801265\pi$
$941$	1.58531	+	8.99075i	0.0516797	+	0.293090i	−0.948004	+	0.318260i	$0.896902\pi$
$942$	−46.5067	−	44.7333i	−1.51527	−	1.45749i
$943$	−3.83803	+	4.57399i	−0.124984	+	0.148950i
$944$	−3.42117			−0.111349
$945$	−9.98740	−	23.2906i	−0.324890	−	0.757643i
$946$	2.73344			0.0888718
$947$	25.8747	−	30.8363i	0.840815	−	1.00204i	−0.159076	−	0.987266i	$-0.550852\pi$
$947$	25.8747	−	30.8363i	0.840815	−	1.00204i	0.999891	−	0.0147774i	$-0.00470398\pi$
$948$	3.56571	−	14.4229i	0.115809	−	0.468435i
$949$	−0.0741775	−	0.420682i	−0.00240790	−	0.0136559i
$950$	−21.4624	+	18.0091i	−0.696331	+	0.584291i
$951$	−4.14758	+	0.444236i	−0.134494	+	0.0144053i
$952$	1.23989	+	0.111311i	0.0401851	+	0.00360762i
$953$	−15.4047	−	8.89392i	−0.499008	−	0.288102i	0.229296	−	0.973357i	$-0.426358\pi$
$953$	−15.4047	−	8.89392i	−0.499008	−	0.288102i	−0.728304	+	0.685254i	$0.759691\pi$
$954$	0.692114	−	0.893135i	0.0224080	−	0.0289163i
$955$		−	18.4940i		−	0.598451i
$956$	39.5887	−	47.1800i	1.28039	−	1.52591i
$957$	2.07044	+	0.140659i	0.0669277	+	0.00454684i
$958$	−15.6897	+	43.1071i	−0.506911	+	1.39273i
$959$	4.48251	−	1.19019i	0.144748	−	0.0384333i
$960$	40.8481	+	2.77508i	1.31837	+	0.0895654i
$961$	−9.54495	+	3.47408i	−0.307902	+	0.112067i
$962$	1.00366			0.0323594
$963$	10.4402	−	19.8242i	0.336431	−	0.638826i
$964$			40.2108i			1.29510i
$965$	34.7495	+	29.1583i	1.11863	+	0.938639i
$966$	9.70003	+	3.34311i	0.312093	+	0.107563i
$967$	−2.19010	−	12.4206i	−0.0704287	−	0.399421i	−0.999560	−	0.0296704i	$-0.990554\pi$
$967$	−2.19010	−	12.4206i	−0.0704287	−	0.399421i	0.929131	−	0.369751i	$-0.120557\pi$
$968$	11.2421	−	30.8874i	0.361334	−	0.992757i
$969$	0.574204	+	1.98762i	0.0184461	+	0.0638516i
$970$	9.92044	−	56.2616i	0.318526	−	1.80645i
$971$	−9.58786	−	16.6067i	−0.307689	−	0.532933i	0.670167	−	0.742210i	$-0.266222\pi$
$971$	−9.58786	−	16.6067i	−0.307689	−	0.532933i	−0.977856	+	0.209277i	$0.932889\pi$
$972$	−51.4359	+	0.509416i	−1.64981	+	0.0163395i
$973$	−32.5918	−	15.2879i	−1.04485	−	0.490109i
$974$	26.0359	+	71.5330i	0.834244	+	2.29207i
$975$	0.125283	+	0.0309730i	0.00401226	+	0.000991931i
$976$	−0.863892	+	0.152327i	−0.0276525	+	0.00487588i
$977$	8.45265	−	23.2235i	0.270424	−	0.742985i	−0.727931	−	0.685651i	$-0.759518\pi$
$977$	8.45265	−	23.2235i	0.270424	−	0.742985i	0.998355	−	0.0573341i	$-0.0182600\pi$
$978$	44.8534	−	4.80412i	1.43425	−	0.153619i
$979$	0.837076	−	0.997588i	0.0267531	−	0.0318831i
$980$	41.9644	−	7.20328i	1.34050	−	0.230100i
$981$	−1.01942	−	26.2145i	−0.0325476	−	0.836966i
$982$	2.00053	−	3.46502i	0.0638395	−	0.110573i
$983$	13.0228	+	10.9274i	0.415363	+	0.348531i	0.826396	−	0.563090i	$-0.190387\pi$
$983$	13.0228	+	10.9274i	0.415363	+	0.348531i	−0.411033	+	0.911620i	$0.634832\pi$
$984$	26.4147	+	17.7409i	0.842069	+	0.565559i
$985$	−25.3611	+	4.47185i	−0.808073	+	0.142485i
$986$	−3.31871	−	1.20791i	−0.105689	−	0.0384678i
$987$	9.83494	+	16.3788i	0.313049	+	0.521342i
$988$	0.202429	−	1.14803i	0.00644012	−	0.0365237i
$989$	−8.14317	−	4.70146i	−0.258938	−	0.149498i
$990$	−1.54907	−	0.211453i	−0.0492326	−	0.00672042i
$991$	1.42204	+	2.46304i	0.0451725	+	0.0782411i	0.887728	−	0.460369i	$-0.152283\pi$
$991$	1.42204	+	2.46304i	0.0451725	+	0.0782411i	−0.842555	+	0.538610i	$0.818950\pi$
$992$	−4.21691	+	23.9153i	−0.133887	+	0.759311i
$993$	−1.95442	−	18.2473i	−0.0620216	−	0.579061i
$994$	−1.55811	−	5.86818i	−0.0494204	−	0.186127i
$995$	−15.2600	−	18.1861i	−0.483774	−	0.576539i
$996$	−26.4223	−	25.4147i	−0.837221	−	0.805297i
$997$	34.6537	+	6.11039i	1.09750	+	0.193518i	0.692940	−	0.720995i	$-0.256315\pi$
$997$	34.6537	+	6.11039i	1.09750	+	0.193518i	0.404555	+	0.914513i	$0.367426\pi$
$998$	−68.4332	−	39.5099i	−2.16621	−	1.25066i
$999$	15.3274	+	46.2363i	0.484938	+	1.46285i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.101.20	✓	132
3.2	odd	2		567.2.ba.a.143.3		132
7.5	odd	6		189.2.bd.a.47.3	yes	132
21.5	even	6		567.2.bd.a.467.20		132
27.4	even	9		567.2.bd.a.17.20		132
27.23	odd	18		189.2.bd.a.185.3	yes	132
189.131	even	18	inner	189.2.ba.a.131.20	yes	132
189.166	odd	18		567.2.ba.a.341.3		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.20	✓	132	1.1	even	1	trivial
189.2.ba.a.131.20	yes	132	189.131	even	18	inner
189.2.bd.a.47.3	yes	132	7.5	odd	6
189.2.bd.a.185.3	yes	132	27.23	odd	18
567.2.ba.a.143.3		132	3.2	odd	2
567.2.ba.a.341.3		132	189.166	odd	18
567.2.bd.a.17.20		132	27.4	even	9
567.2.bd.a.467.20		132	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.47978 - 1.76353i) q^{2} +(1.66401 - 0.480715i) q^{3} +(-0.573000 - 3.24965i) q^{4} +(-1.41208 + 1.18487i) q^{5} +(1.61460 - 3.64587i) q^{6} +(-2.40040 + 1.11270i) q^{7} +(-2.59137 - 1.49613i) q^{8} +(2.53783 - 1.59982i) q^{9} +O(q^{10})\)	\(q+(1.47978 - 1.76353i) q^{2} +(1.66401 - 0.480715i) q^{3} +(-0.573000 - 3.24965i) q^{4} +(-1.41208 + 1.18487i) q^{5} +(1.61460 - 3.64587i) q^{6} +(-2.40040 + 1.11270i) q^{7} +(-2.59137 - 1.49613i) q^{8} +(2.53783 - 1.59982i) q^{9} +4.24358i q^{10} +(-0.0789393 + 0.0940762i) q^{11} +(-2.51563 - 5.13198i) q^{12} +(0.0159063 - 0.0437022i) q^{13} +(-1.58977 + 5.87972i) q^{14} +(-1.78012 + 2.65044i) q^{15} +(-0.271551 + 0.0988366i) q^{16} +0.157246 q^{17} +(0.934081 - 6.84292i) q^{18} +7.59626i q^{19} +(4.65954 + 3.90982i) q^{20} +(-3.45938 + 3.00544i) q^{21} +(0.0490936 + 0.278423i) q^{22} +(0.332628 - 0.913889i) q^{23} +(-5.03126 - 1.24385i) q^{24} +(-0.278205 + 1.57778i) q^{25} +(-0.0535324 - 0.0927208i) q^{26} +(3.45390 - 3.88209i) q^{27} +(4.99131 + 7.16286i) q^{28} +(-3.33678 - 9.16772i) q^{29} +(2.03995 + 7.06135i) q^{30} +(-4.49600 + 0.792766i) q^{31} +(1.81929 - 4.99845i) q^{32} +(-0.0861316 + 0.194490i) q^{33} +(0.232689 - 0.277308i) q^{34} +(2.07113 - 4.41538i) q^{35} +(-6.65304 - 7.33034i) q^{36} +(-4.68718 + 8.11843i) q^{37} +(13.3962 + 11.2408i) q^{38} +(0.00545988 - 0.0803671i) q^{39} +(5.43192 - 0.957794i) q^{40} +(-5.76925 - 2.09983i) q^{41} +(0.181079 + 10.5481i) q^{42} +(1.67890 - 9.52153i) q^{43} +(0.350947 + 0.202619i) q^{44} +(-1.68802 + 5.26607i) q^{45} +(-1.11945 - 1.93895i) q^{46} +(0.723937 - 4.10565i) q^{47} +(-0.404351 + 0.295003i) q^{48} +(4.52380 - 5.34184i) q^{49} +(2.37078 + 2.82539i) q^{50} +(0.261658 - 0.0755904i) q^{51} +(-0.151131 - 0.0266485i) q^{52} +(0.141686 + 0.0818025i) q^{53} +(-1.73517 - 11.8357i) q^{54} -0.226376i q^{55} +(7.88504 + 0.707881i) q^{56} +(3.65163 + 12.6402i) q^{57} +(-21.1052 - 7.68168i) q^{58} +(11.1248 + 4.04911i) q^{59} +(9.63300 + 4.26604i) q^{60} +(2.98946 + 0.527123i) q^{61} +(-5.25501 + 9.10194i) q^{62} +(-4.31166 + 6.66405i) q^{63} +(-6.41175 - 11.1055i) q^{64} +(0.0293206 + 0.0805578i) q^{65} +(0.215534 + 0.439698i) q^{66} +(-7.53281 + 6.32078i) q^{67} +(-0.0901020 - 0.510994i) q^{68} +(0.114175 - 1.68062i) q^{69} +(-4.72184 - 10.1863i) q^{70} +(-0.863276 + 0.498413i) q^{71} +(-8.96997 + 0.348821i) q^{72} +(7.95454 - 4.59256i) q^{73} +(7.38112 + 20.2795i) q^{74} +(0.295527 + 2.75917i) q^{75} +(24.6852 - 4.35266i) q^{76} +(0.0848069 - 0.313656i) q^{77} +(-0.133650 - 0.128554i) q^{78} +(1.99133 + 1.67093i) q^{79} +(0.266342 - 0.461318i) q^{80} +(3.88113 - 8.12015i) q^{81} +(-12.2403 + 7.06695i) q^{82} +(6.02764 - 2.19388i) q^{83} +(11.7489 + 9.51964i) q^{84} +(-0.222043 + 0.186316i) q^{85} +(-14.3071 - 17.0505i) q^{86} +(-9.95947 - 13.6511i) q^{87} +(0.345310 - 0.125683i) q^{88} -10.6041 q^{89} +(6.78899 + 10.7695i) q^{90} +(0.0104460 + 0.122602i) q^{91} +(-3.16041 - 0.557266i) q^{92} +(-7.10027 + 3.48046i) q^{93} +(-6.16918 - 7.35214i) q^{94} +(-9.00059 - 10.7265i) q^{95} +(0.624474 - 9.19200i) q^{96} +(-13.2580 - 2.33775i) q^{97} +(-2.72628 - 15.8826i) q^{98} +(-0.0498289 + 0.365038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more