LMFDB - Embedded newform 189.2.u.a.4.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(4,189)]

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([2, 12]))

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

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

chi := DirichletCharacter("189.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.u (of order $9$, 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 $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			4.17
Character	$\chi$	$=$	189.4
Dual form			189.2.u.a.142.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.246187 + 1.39619i) q^{2} +(-1.04527 + 1.38109i) q^{3} +(-0.00936568 + 0.00340883i) q^{4} +(3.04103 - 1.10685i) q^{5} +(-2.18560 - 1.11939i) q^{6} +(1.78778 + 1.95034i) q^{7} +(1.41067 + 2.44335i) q^{8} +(-0.814825 - 2.88722i) q^{9} +O(q^{10})$	\(q+(0.246187 + 1.39619i) q^{2} +(-1.04527 + 1.38109i) q^{3} +(-0.00936568 + 0.00340883i) q^{4} +(3.04103 - 1.10685i) q^{5} +(-2.18560 - 1.11939i) q^{6} +(1.78778 + 1.95034i) q^{7} +(1.41067 + 2.44335i) q^{8} +(-0.814825 - 2.88722i) q^{9} +(2.29403 + 3.97338i) q^{10} +(-5.43045 - 1.97652i) q^{11} +(0.00508176 - 0.0164980i) q^{12} +(0.00633019 - 0.00230400i) q^{13} +(-2.28293 + 2.97624i) q^{14} +(-1.65004 + 5.35690i) q^{15} +(-3.07937 + 2.58390i) q^{16} +(-2.21375 - 3.83432i) q^{17} +(3.83053 - 1.84845i) q^{18} +(0.999072 - 1.73044i) q^{19} +(-0.0247083 + 0.0207327i) q^{20} +(-4.56231 + 0.430461i) q^{21} +(1.42270 - 8.06856i) q^{22} +(-0.981664 + 5.56729i) q^{23} +(-4.84901 - 0.605696i) q^{24} +(4.19256 - 3.51797i) q^{25} +(0.00477525 + 0.00827097i) q^{26} +(4.83923 + 1.89258i) q^{27} +(-0.0233922 - 0.0121720i) q^{28} +(-7.63544 - 2.77907i) q^{29} +(-7.88549 - 0.984985i) q^{30} +(5.59460 - 2.03627i) q^{31} +(-0.0431895 - 0.0362403i) q^{32} +(8.40604 - 5.43395i) q^{33} +(4.80846 - 4.03478i) q^{34} +(7.59544 + 3.95225i) q^{35} +(0.0174734 + 0.0242632i) q^{36} +0.125602 q^{37} +(2.66199 + 0.968887i) q^{38} +(-0.00343472 + 0.0111509i) q^{39} +(6.99430 + 5.86891i) q^{40} +(7.54818 - 2.74731i) q^{41} +(-1.72419 - 6.26390i) q^{42} +(-0.536306 - 3.04154i) q^{43} +0.0575975 q^{44} +(-5.67362 - 7.87826i) q^{45} -8.01469 q^{46} +(-4.87676 - 1.77500i) q^{47} +(-0.349829 - 6.95376i) q^{48} +(-0.607659 + 6.97358i) q^{49} +(5.94393 + 4.98755i) q^{50} +(7.60950 + 0.950512i) q^{51} +(-5.14326e-5 + 4.31571e-5i) q^{52} +(1.70019 - 2.94481i) q^{53} +(-1.45105 + 7.22243i) q^{54} -18.7019 q^{55} +(-2.24339 + 7.11946i) q^{56} +(1.34560 + 3.18859i) q^{57} +(2.00038 - 11.3447i) q^{58} +(-4.10949 - 3.44827i) q^{59} +(-0.00280696 - 0.0557957i) q^{60} +(2.98856 + 1.08775i) q^{61} +(4.22034 + 7.30985i) q^{62} +(4.17434 - 6.75092i) q^{63} +(-3.97987 + 6.89333i) q^{64} +(0.0167002 - 0.0140131i) q^{65} +(9.65631 + 10.3987i) q^{66} +(0.603468 - 3.42244i) q^{67} +(0.0338038 + 0.0283647i) q^{68} +(-6.66283 - 7.17509i) q^{69} +(-3.64822 + 11.5777i) q^{70} +(-3.49843 + 6.05945i) q^{71} +(5.90505 - 6.06382i) q^{72} -0.991568 q^{73} +(0.0309215 + 0.175365i) q^{74} +(0.476291 + 9.46753i) q^{75} +(-0.00345821 + 0.0196125i) q^{76} +(-5.85358 - 14.1248i) q^{77} +(-0.0164144 - 0.00205034i) q^{78} +(-0.354954 - 2.01305i) q^{79} +(-6.50449 + 11.2661i) q^{80} +(-7.67212 + 4.70516i) q^{81} +(5.69404 + 9.86237i) q^{82} +(4.23105 + 1.53998i) q^{83} +(0.0412618 - 0.0195837i) q^{84} +(-10.9761 - 9.21002i) q^{85} +(4.11455 - 1.49757i) q^{86} +(11.8192 - 7.64036i) q^{87} +(-2.83123 - 16.0567i) q^{88} +(5.63968 - 9.76821i) q^{89} +(9.60281 - 9.86100i) q^{90} +(0.0158106 + 0.00822698i) q^{91} +(-0.00978400 - 0.0554878i) q^{92} +(-3.03559 + 9.85510i) q^{93} +(1.27765 - 7.24589i) q^{94} +(1.12288 - 6.36816i) q^{95} +(0.0951959 - 0.0217678i) q^{96} +(1.10493 + 6.26639i) q^{97} +(-9.88606 + 0.868391i) q^{98} +(-1.28180 + 17.2895i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.246187	+	1.39619i	0.174080	+	0.987259i	0.939200	+	0.343370i	$0.111569\pi$
$2$	0.246187	+	1.39619i	0.174080	+	0.987259i	−0.765120	+	0.643888i	$0.777320\pi$
$3$	−1.04527	+	1.38109i	−0.603486	+	0.797373i
$3$	−1.04527	+	1.38109i	−0.603486	+	0.797373i
$4$	−0.00936568	+	0.00340883i	−0.00468284	+	0.00170442i
$5$	3.04103	−	1.10685i	1.35999	−	0.494996i	0.443940	−	0.896057i	$-0.353580\pi$
$5$	3.04103	−	1.10685i	1.35999	−	0.494996i	0.916052	+	0.401060i	$0.131358\pi$
$6$	−2.18560	−	1.11939i	−0.892269	−	0.456990i
$7$	1.78778	+	1.95034i	0.675719	+	0.737160i
$7$	1.78778	+	1.95034i	0.675719	+	0.737160i
$8$	1.41067	+	2.44335i	0.498746	+	0.863854i
$9$	−0.814825	−	2.88722i	−0.271608	−	0.962408i
$10$	2.29403	+	3.97338i	0.725437	+	1.25649i
$11$	−5.43045	−	1.97652i	−1.63734	−	0.595944i	−0.650771	−	0.759274i	$-0.725554\pi$
$11$	−5.43045	−	1.97652i	−1.63734	−	0.595944i	−0.986572	+	0.163330i	$0.947777\pi$
$12$	0.00508176	−	0.0164980i	0.00146698	−	0.00476256i
$13$	0.00633019	−	0.00230400i	0.00175568	−	0.000639015i	−0.341142	−	0.940012i	$-0.610814\pi$
$13$	0.00633019	−	0.00230400i	0.00175568	−	0.000639015i	0.342898	+	0.939373i	$0.388592\pi$
$14$	−2.28293	+	2.97624i	−0.610138	+	0.795434i
$15$	−1.65004	+	5.35690i	−0.426039	+	1.38314i
$16$	−3.07937	+	2.58390i	−0.769843	+	0.645975i
$17$	−2.21375	−	3.83432i	−0.536912	−	0.929959i	−0.999068	−	0.0431605i	$-0.986257\pi$
$17$	−2.21375	−	3.83432i	−0.536912	−	0.929959i	0.462156	−	0.886799i	$-0.347076\pi$
$18$	3.83053	−	1.84845i	0.902864	−	0.435684i
$19$	0.999072	−	1.73044i	0.229203	−	0.396991i	−0.728369	−	0.685185i	$-0.759721\pi$
$19$	0.999072	−	1.73044i	0.229203	−	0.396991i	0.957572	+	0.288194i	$0.0930547\pi$
$20$	−0.0247083	+	0.0207327i	−0.00552495	+	0.00463598i
$21$	−4.56231	+	0.430461i	−0.995578	+	0.0939343i
$22$	1.42270	−	8.06856i	0.303322	−	1.72022i
$23$	−0.981664	+	5.56729i	−0.204691	+	1.16086i	0.693234	+	0.720712i	$0.256185\pi$
$23$	−0.981664	+	5.56729i	−0.204691	+	1.16086i	−0.897925	+	0.440148i	$0.854926\pi$
$24$	−4.84901	−	0.605696i	−0.989801	−	0.123637i
$25$	4.19256	−	3.51797i	0.838511	−	0.703595i
$26$	0.00477525	+	0.00827097i	0.000936503	+	0.00162207i
$27$	4.83923	+	1.89258i	0.931310	+	0.364227i
$28$	−0.0233922	−	0.0121720i	−0.00442071	−	0.00230030i
$29$	−7.63544	−	2.77907i	−1.41787	−	0.516061i	−0.484438	−	0.874826i	$-0.660976\pi$
$29$	−7.63544	−	2.77907i	−1.41787	−	0.516061i	−0.933428	+	0.358765i	$0.883198\pi$
$30$	−7.88549	−	0.984985i	−1.43969	−	0.179833i
$31$	5.59460	−	2.03627i	1.00482	−	0.365725i	0.213379	−	0.976970i	$-0.431553\pi$
$31$	5.59460	−	2.03627i	1.00482	−	0.365725i	0.791441	+	0.611245i	$0.209331\pi$
$32$	−0.0431895	−	0.0362403i	−0.00763490	−	0.00640645i
$33$	8.40604	−	5.43395i	1.46330	−	0.945929i
$34$	4.80846	−	4.03478i	0.824644	−	0.691959i
$35$	7.59544	+	3.95225i	1.28386	+	0.668053i
$36$	0.0174734	+	0.0242632i	0.00291224	+	0.00404387i
$37$	0.125602			0.0206488			0.0103244	−	0.999947i	$-0.496714\pi$
$37$	0.125602			0.0206488			0.0103244	+	0.999947i	$0.496714\pi$
$38$	2.66199	+	0.968887i	0.431832	+	0.157174i
$39$	−0.00343472	+	0.0111509i	−0.000549995	+	0.00178557i
$40$	6.99430	+	5.86891i	1.10590	+	0.927957i
$41$	7.54818	−	2.74731i	1.17883	−	0.429058i	0.323040	−	0.946385i	$-0.395295\pi$
$41$	7.54818	−	2.74731i	1.17883	−	0.429058i	0.855788	+	0.517327i	$0.173073\pi$
$42$	−1.72419	−	6.26390i	−0.266048	−	0.966541i
$43$	−0.536306	−	3.04154i	−0.0817858	−	0.463831i	−0.998004	−	0.0631508i	$-0.979885\pi$
$43$	−0.536306	−	3.04154i	−0.0817858	−	0.463831i	0.916218	−	0.400680i	$-0.131226\pi$
$44$	0.0575975			0.00868315
$45$	−5.67362	−	7.87826i	−0.845774	−	1.17442i
$46$	−8.01469			−1.18170
$47$	−4.87676	−	1.77500i	−0.711349	−	0.258910i	−0.0391004	−	0.999235i	$-0.512449\pi$
$47$	−4.87676	−	1.77500i	−0.711349	−	0.258910i	−0.672249	+	0.740325i	$0.734671\pi$
$48$	−0.349829	−	6.95376i	−0.0504934	−	1.00369i
$49$	−0.607659	+	6.97358i	−0.0868085	+	0.996225i
$50$	5.94393	+	4.98755i	0.840598	+	0.705346i
$51$	7.60950	+	0.950512i	1.06554	+	0.133098i
$52$	−5.14326e−5	0	4.31571e-5i	−7.13243e−6	0	5.98482e-6i
$53$	1.70019	−	2.94481i	0.233539	−	0.404501i	−0.725308	−	0.688424i	$-0.758303\pi$
$53$	1.70019	−	2.94481i	0.233539	−	0.404501i	0.958847	+	0.283923i	$0.0916361\pi$
$54$	−1.45105	+	7.22243i	−0.197463	+	0.982849i
$55$	−18.7019			−2.52176
$56$	−2.24339	+	7.11946i	−0.299786	+	0.951378i
$57$	1.34560	+	3.18859i	0.178229	+	0.422339i
$58$	2.00038	−	11.3447i	0.262663	−	1.48964i
$59$	−4.10949	−	3.44827i	−0.535011	−	0.448927i	0.334817	−	0.942283i	$-0.391326\pi$
$59$	−4.10949	−	3.44827i	−0.535011	−	0.448927i	−0.869827	+	0.493356i	$0.835770\pi$
$60$	−0.00280696	−	0.0557957i	−0.000362377	−	0.00720320i
$61$	2.98856	+	1.08775i	0.382646	+	0.139272i	0.526179	−	0.850374i	$-0.323624\pi$
$61$	2.98856	+	1.08775i	0.382646	+	0.139272i	−0.143533	+	0.989646i	$0.545846\pi$
$62$	4.22034	+	7.30985i	0.535984	+	0.928352i
$63$	4.17434	−	6.75092i	0.525917	−	0.850536i
$64$	−3.97987	+	6.89333i	−0.497484	+	0.861667i
$65$	0.0167002	−	0.0140131i	0.00207140	−	0.00173811i
$66$	9.65631	+	10.3987i	1.18861	+	1.27999i
$67$	0.603468	−	3.42244i	0.0737254	−	0.418117i	−0.925499	−	0.378749i	$-0.876354\pi$
$67$	0.603468	−	3.42244i	0.0737254	−	0.418117i	0.999225	−	0.0393683i	$-0.0125346\pi$
$68$	0.0338038	+	0.0283647i	0.00409931	+	0.00343973i
$69$	−6.66283	−	7.17509i	−0.802111	−	0.863779i
$70$	−3.64822	+	11.5777i	−0.436045	+	1.38380i
$71$	−3.49843	+	6.05945i	−0.415187	+	0.719125i	−0.995448	−	0.0953058i	$-0.969617\pi$
$71$	−3.49843	+	6.05945i	−0.415187	+	0.719125i	0.580261	+	0.814430i	$0.302950\pi$
$72$	5.90505	−	6.06382i	0.695916	−	0.714627i
$73$	−0.991568			−0.116054			−0.0580271	−	0.998315i	$-0.518481\pi$
$73$	−0.991568			−0.116054			−0.0580271	+	0.998315i	$0.518481\pi$
$74$	0.0309215	+	0.175365i	0.00359455	+	0.0203857i
$75$	0.476291	+	9.46753i	0.0549973	+	1.09322i
$76$	−0.00345821	+	0.0196125i	−0.000396683	+	0.00224970i
$77$	−5.85358	−	14.1248i	−0.667077	−	1.60967i
$78$	−0.0164144	−	0.00205034i	−0.00185856	−	0.000232155i
$79$	−0.354954	−	2.01305i	−0.0399355	−	0.226485i	0.958307	−	0.285739i	$-0.0922390\pi$
$79$	−0.354954	−	2.01305i	−0.0399355	−	0.226485i	−0.998243	+	0.0592537i	$0.981128\pi$
$80$	−6.50449	+	11.2661i	−0.727225	+	1.25959i
$81$	−7.67212	+	4.70516i	−0.852458	+	0.522796i
$82$	5.69404	+	9.86237i	0.628802	+	1.08912i
$83$	4.23105	+	1.53998i	0.464418	+	0.169034i	0.563622	−	0.826033i	$-0.309407\pi$
$83$	4.23105	+	1.53998i	0.464418	+	0.169034i	−0.0992039	+	0.995067i	$0.531630\pi$
$84$	0.0412618	−	0.0195837i	0.00450203	−	0.00213676i
$85$	−10.9761	−	9.21002i	−1.19052	−	0.998967i
$86$	4.11455	−	1.49757i	0.443683	−	0.161488i
$87$	11.8192	−	7.64036i	1.26716	−	0.819132i
$88$	−2.83123	−	16.0567i	−0.301810	−	1.71165i
$89$	5.63968	−	9.76821i	0.597805	−	1.03543i	−0.395339	−	0.918535i	$-0.629373\pi$
$89$	5.63968	−	9.76821i	0.597805	−	1.03543i	0.993144	−	0.116894i	$-0.0372936\pi$
$90$	9.60281	−	9.86100i	1.01223	−	1.03944i
$91$	0.0158106	+	0.00822698i	0.00165740	+	0.000862422i
$92$	−0.00978400	−	0.0554878i	−0.00102005	−	0.00578501i
$93$	−3.03559	+	9.85510i	−0.314776	+	1.02193i
$94$	1.27765	−	7.24589i	0.131779	−	0.747357i
$95$	1.12288	−	6.36816i	0.115205	−	0.653359i
$96$	0.0951959	−	0.0217678i	0.00971589	−	0.00222167i
$97$	1.10493	+	6.26639i	0.112189	+	0.636256i	0.988104	+	0.153790i	$0.0491478\pi$
$97$	1.10493	+	6.26639i	0.112189	+	0.636256i	−0.875915	+	0.482466i	$0.839741\pi$
$98$	−9.88606	+	0.868391i	−0.998643	+	0.0877207i
$99$	−1.28180	+	17.2895i	−0.128825	+	1.73766i
$100$	−0.0272740	+	0.0472399i	−0.00272740	+	0.00472399i
$101$	2.69141	+	15.2637i	0.267805	+	1.51880i	0.760927	+	0.648837i	$0.224745\pi$
$101$	2.69141	+	15.2637i	0.267805	+	1.51880i	−0.493122	+	0.869960i	$0.664144\pi$
$102$	0.546260	+	10.8584i	0.0540878	+	1.07514i
$103$	−12.1372	+	4.41757i	−1.19591	+	0.435276i	−0.861796	−	0.507255i	$-0.830660\pi$
$103$	−12.1372	+	4.41757i	−1.19591	+	0.435276i	−0.334116	+	0.942532i	$0.608438\pi$
$104$	0.0145593	+	0.0122167i	0.00142766	+	0.00119794i
$105$	−13.3977	+	6.35882i	−1.30748	+	0.620558i
$106$	4.53010	+	1.64882i	0.440002	+	0.160148i
$107$	4.13929	+	7.16946i	0.400160	+	0.693098i	0.993745	−	0.111673i	$-0.0356210\pi$
$107$	4.13929	+	7.16946i	0.400160	+	0.693098i	−0.593584	+	0.804772i	$0.702288\pi$
$108$	−0.0517742	−	0.00122917i	−0.00498197	−	0.000118277i
$109$	−1.80341	+	3.12360i	−0.172735	+	0.299186i	−0.939375	−	0.342891i	$-0.888594\pi$
$109$	−1.80341	+	3.12360i	−0.172735	+	0.299186i	0.766640	+	0.642077i	$0.221927\pi$
$110$	−4.60416	−	26.1115i	−0.438989	−	2.48963i
$111$	−0.131288	+	0.173467i	−0.0124613	+	0.0164648i
$112$	−10.5447	−	1.38637i	−0.996384	−	0.131000i
$113$	1.68033	−	9.52963i	0.158072	−	0.896472i	−0.797851	−	0.602855i	$-0.794030\pi$
$113$	1.68033	−	9.52963i	0.158072	−	0.896472i	0.955923	−	0.293617i	$-0.0948591\pi$
$114$	−4.12062	+	2.66371i	−0.385931	+	0.249479i
$115$	3.17686	+	18.0169i	0.296244	+	1.68008i
$116$	0.0809845			0.00751922
$117$	−0.0118102	−	0.0163993i	−0.00109185	−	0.00151612i
$118$	3.80276	−	6.58657i	0.350072	−	0.606343i
$119$	3.52053	−	11.1725i	0.322727	−	1.02418i
$120$	−15.4164	+	3.52517i	−1.40732	+	0.321802i
$121$	17.1567	+	14.3962i	1.55970	+	1.30874i
$122$	−0.782963	+	4.44040i	−0.0708861	+	0.402015i
$123$	−4.09559	+	13.2964i	−0.369287	+	1.19890i
$124$	−0.0454560	+	0.0381421i	−0.00408207	+	0.00342526i
$125$	0.765353	−	1.32563i	0.0684552	−	0.118568i
$126$	10.4533	+	4.16620i	0.931250	+	0.371155i
$127$	7.49523	+	12.9821i	0.665094	+	1.15198i	0.979260	+	0.202609i	$0.0649420\pi$
$127$	7.49523	+	12.9821i	0.665094	+	1.15198i	−0.314165	+	0.949368i	$0.601725\pi$
$128$	−10.7102	−	3.89819i	−0.946656	−	0.344554i
$129$	4.76123	+	2.43854i	0.419203	+	0.214702i
$130$	0.0236764	+	0.0198668i	0.00207655	+	0.00174244i
$131$	0.424017	−	2.40472i	0.0370465	−	0.210101i	−0.960666	−	0.277708i	$-0.910425\pi$
$131$	0.424017	−	2.40472i	0.0370465	−	0.210101i	0.997712	+	0.0676067i	$0.0215363\pi$
$132$	−0.0602049	+	0.0795474i	−0.00524017	+	0.00692372i
$133$	5.16108	−	1.14513i	0.447522	−	0.0992952i
$134$	4.92695			0.425624
$135$	16.8111	+	0.399112i	1.44687	+	0.0343501i
$136$	6.24572	−	10.8179i	0.535566	−	0.927628i
$137$	−2.83510	+	2.37893i	−0.242219	+	0.203246i	−0.755813	−	0.654788i	$-0.772758\pi$
$137$	−2.83510	+	2.37893i	−0.242219	+	0.203246i	0.513594	+	0.858033i	$0.328314\pi$
$138$	8.37751	−	11.0690i	0.713141	−	0.942258i
$139$	4.54359	+	3.81253i	0.385382	+	0.323374i	0.814811	−	0.579727i	$-0.196841\pi$
$139$	4.54359	+	3.81253i	0.385382	+	0.323374i	−0.429429	+	0.903101i	$0.641285\pi$
$140$	−0.0846090	−	0.0111240i	−0.00715077	−	0.000940149i
$141$	7.54896	−	4.87991i	0.635737	−	0.410962i
$142$	−9.32144	−	3.39273i	−0.782238	−	0.284711i
$143$	−0.0389297			−0.00325547
$144$	9.96945	+	6.78541i	0.830787	+	0.565451i
$145$	−26.2956			−2.18373
$146$	−0.244111	−	1.38442i	−0.0202028	−	0.114576i
$147$	−8.99597	−	8.12850i	−0.741975	−	0.670427i
$148$	−0.00117635		0.000428155i	−9.66951e−5		3.51941e-5i
$149$	5.08481	+	4.26666i	0.416564	+	0.349538i	0.826854	−	0.562416i	$-0.190128\pi$
$149$	5.08481	+	4.26666i	0.416564	+	0.349538i	−0.410290	+	0.911955i	$0.634573\pi$
$150$	−13.1013	+	2.99578i	−1.06971	+	0.244604i
$151$	−3.73656	−	1.36000i	−0.304077	−	0.110675i	0.185475	−	0.982649i	$-0.440618\pi$
$151$	−3.73656	−	1.36000i	−0.304077	−	0.110675i	−0.489552	+	0.871974i	$0.662840\pi$
$152$	5.63744			0.457256
$153$	−9.26672	+	9.51588i	−0.749170	+	0.769313i
$154$	18.2799	−	11.6501i	1.47304	−	0.938790i
$155$	14.7595	−	12.3847i	1.18551	−	0.994765i
$156$	−5.84295e−6	0	0.000116144i	−4.67810e−7	0	9.29896e-6i
$157$	−15.5531	−	13.0506i	−1.24128	−	1.04155i	−0.997423	−	0.0717415i	$-0.977144\pi$
$157$	−15.5531	−	13.0506i	−1.24128	−	1.04155i	−0.243852	−	0.969812i	$-0.578411\pi$
$158$	2.72322	−	0.991170i	0.216648	−	0.0788533i
$159$	2.28990	+	5.42624i	0.181601	+	0.430329i
$160$	−0.171453	−	0.0624039i	−0.0135546	−	0.00493346i
$161$	−12.6131	+	8.03853i	−0.994053	+	0.633525i
$162$	−8.45810	−	9.55342i	−0.664531	−	0.750588i
$163$	−9.67387	−	16.7556i	−0.757716	−	1.31240i	−0.944013	−	0.329909i	$-0.892982\pi$
$163$	−9.67387	−	16.7556i	−0.757716	−	1.31240i	0.186297	−	0.982493i	$-0.440351\pi$
$164$	−0.0613287	+	0.0514609i	−0.00478897	+	0.00401842i
$165$	19.5485	−	25.8290i	1.52185	−	2.01079i
$166$	−1.10848	+	6.28649i	−0.0860346	+	0.487927i
$167$	−0.997535	+	5.65730i	−0.0771915	+	0.437775i	0.921578	+	0.388192i	$0.126900\pi$
$167$	−0.997535	+	5.65730i	−0.0771915	+	0.437775i	−0.998770	+	0.0495829i	$0.984211\pi$
$168$	−7.48767	−	10.5401i	−0.577687	−	0.813185i
$169$	−9.95854	+	8.35621i	−0.766042	+	0.642785i
$170$	10.1568	−	17.5921i	0.778992	−	1.34925i
$171$	−5.81025	−	1.47454i	−0.444321	−	0.112761i
$172$	0.0153910	+	0.0266579i	0.00117355	+	0.00203265i
$173$	−0.373753	+	0.313616i	−0.0284159	+	0.0238438i	−0.656885	−	0.753991i	$-0.728126\pi$
$173$	−0.373753	+	0.313616i	−0.0284159	+	0.0238438i	0.628469	+	0.777835i	$0.283682\pi$
$174$	13.5772	+	14.6210i	1.02928	+	1.10842i
$175$	14.3566	+	1.88754i	1.08526	+	0.142685i
$176$	21.8295	−	7.94529i	1.64546	−	0.598899i
$177$	9.05791	−	2.07121i	0.680834	−	0.155682i
$178$	15.0267	+	5.46929i	1.12630	+	0.409940i
$179$	−13.2713	−	22.9866i	−0.991945	−	1.71810i	−0.605669	−	0.795717i	$-0.707094\pi$
$179$	−13.2713	−	22.9866i	−0.991945	−	1.71810i	−0.386277	−	0.922383i	$-0.626239\pi$
$180$	0.0799930	+	0.0544449i	0.00596233	+	0.00405808i
$181$	−1.63338	−	2.82910i	−0.121408	−	0.210285i	0.798915	−	0.601444i	$-0.205408\pi$
$181$	−1.63338	−	2.82910i	−0.121408	−	0.210285i	−0.920323	+	0.391159i	$0.872074\pi$
$182$	−0.00759410	+	0.0241001i	−0.000562912	+	0.00178641i
$183$	−4.62613	+	2.99049i	−0.341973	+	0.221063i
$184$	−14.9876	+	5.45505i	−1.10490	+	0.402152i
$185$	0.381959	−	0.139022i	0.0280822	−	0.0102211i
$186$	−14.5070	−	1.81208i	−1.06370	−	0.132868i
$187$	4.44302	+	25.1976i	0.324906	+	1.84263i
$188$	0.0517249			0.00377243
$189$	4.96032	+	12.8217i	0.360811	+	0.932639i
$190$	9.16762			0.665089
$191$	1.47689	+	8.37585i	0.106864	+	0.606055i	0.990459	+	0.137804i	$0.0440045\pi$
$191$	1.47689	+	8.37585i	0.106864	+	0.606055i	−0.883596	+	0.468251i	$0.844884\pi$
$192$	−5.36029	−	12.7019i	−0.386846	−	0.916684i
$193$	6.80533	−	2.47694i	0.489858	−	0.178294i	−0.0852688	−	0.996358i	$-0.527175\pi$
$193$	6.80533	−	2.47694i	0.489858	−	0.178294i	0.575127	+	0.818064i	$0.304953\pi$
$194$	−8.47708	+	3.08541i	−0.608619	+	0.221519i
$195$	0.00189720	+	0.0377119i	0.000135862	+	0.00270061i
$196$	−0.0180806	−	0.0673837i	−0.00129147	−	0.00481312i
$197$	10.8209	+	18.7424i	0.770959	+	1.33534i	0.937038	+	0.349228i	$0.113556\pi$
$197$	10.8209	+	18.7424i	0.770959	+	1.33534i	−0.166078	+	0.986113i	$0.553111\pi$
$198$	−24.4550	+	2.46680i	−1.73794	+	0.175308i
$199$	0.652269	+	1.12976i	0.0462381	+	0.0800868i	0.888218	−	0.459422i	$-0.151943\pi$
$199$	0.652269	+	1.12976i	0.0462381	+	0.0800868i	−0.841980	+	0.539509i	$0.818610\pi$
$200$	14.5099	+	5.28119i	1.02601	+	0.373436i
$201$	4.09591	+	4.41081i	0.288903	+	0.311115i
$202$	−20.6485	+	7.51545i	−1.45283	+	0.528786i
$203$	−8.23037	−	19.8601i	−0.577659	−	1.39391i
$204$	−0.0745083	+	0.0170373i	−0.00521663	+	0.00119285i
$205$	19.9134	−	16.7093i	1.39081	−	1.16703i
$206$	−9.15581	−	15.8583i	−0.637915	−	1.10490i
$207$	16.8739	−	1.70209i	1.17282	−	0.118303i
$208$	−0.0135397	+	0.0234515i	−0.000938810	+	0.00162607i
$209$	−8.84568	+	7.42240i	−0.611868	+	0.513418i
$210$	−12.1765	−	17.1403i	−0.840258	−	1.18280i
$211$	0.922352	−	5.23092i	0.0634973	−	0.360111i	−0.936459	−	0.350777i	$-0.885918\pi$
$211$	0.922352	−	5.23092i	0.0634973	−	0.360111i	0.999956	−	0.00933440i	$-0.00297128\pi$
$212$	−0.00588506	+	0.0333758i	−0.000404188	+	0.00229226i
$213$	−4.71186	−	11.1654i	−0.322851	−	0.765041i
$214$	−8.99093	+	7.54428i	−0.614607	+	0.515717i
$215$	−4.99744	−	8.65582i	−0.340823	−	0.590322i
$216$	2.20232	+	14.4937i	0.149849	+	0.986173i
$217$	13.9734	+	7.27097i	0.948573	+	0.493586i
$218$	−4.80512	−	1.74892i	−0.325444	−	0.118452i
$219$	1.03646	−	1.36945i	0.0700372	−	0.0925385i
$220$	0.175156	−	0.0637516i	0.0118090	−	0.00429813i
$221$	−0.0228477	−	0.0191715i	−0.00153690	−	0.00128962i
$222$	−0.274516	−	0.140598i	−0.0184243	−	0.00943630i
$223$	−2.10279	+	1.76445i	−0.140813	+	0.118156i	−0.710474	−	0.703724i	$-0.751519\pi$
$223$	−2.10279	+	1.76445i	−0.140813	+	0.118156i	0.569660	+	0.821880i	$0.307075\pi$
$224$	−0.00653256	−	0.149024i	−0.000436475	−	0.00995710i
$225$	−13.5734	−	9.23832i	−0.904892	−	0.615888i
$226$	13.7189			0.912567
$227$	3.14495	+	1.14467i	0.208738	+	0.0759744i	0.444273	−	0.895891i	$-0.353462\pi$
$227$	3.14495	+	1.14467i	0.208738	+	0.0759744i	−0.235535	+	0.971866i	$0.575684\pi$
$228$	−0.0234718	−	0.0252764i	−0.00155446	−	0.00167397i
$229$	−21.7522	−	18.2523i	−1.43743	−	1.20614i	−0.941154	−	0.337978i	$-0.890257\pi$
$229$	−21.7522	−	18.2523i	−1.43743	−	1.20614i	−0.496273	−	0.868167i	$-0.665298\pi$
$230$	−24.3730	+	8.87103i	−1.60711	+	0.584938i
$231$	25.6262	+	6.67992i	1.68608	+	0.439506i
$232$	−3.98083	−	22.5764i	−0.261354	−	1.48221i
$233$	7.98422			0.523064			0.261532	−	0.965195i	$-0.415772\pi$
$233$	7.98422			0.523064			0.261532	+	0.965195i	$0.415772\pi$
$234$	0.0199891	−	0.0205266i	0.00130673	−	0.00134187i
$235$	−16.7951			−1.09559
$236$	0.0502428	+	0.0182869i	0.00327053	+	0.00119037i
$237$	3.15122	+	1.61395i	0.204694	+	0.104837i
$238$	16.4657	+	2.16483i	1.06731	+	0.140325i
$239$	−9.14520	−	7.67373i	−0.591554	−	0.496372i	0.297165	−	0.954826i	$-0.403959\pi$
$239$	−9.14520	−	7.67373i	−0.591554	−	0.496372i	−0.888718	+	0.458454i	$0.848403\pi$
$240$	−8.76058	−	20.7594i	−0.565493	−	1.34001i
$241$	2.55800	−	2.14642i	0.164775	−	0.138263i	−0.556672	−	0.830733i	$-0.687922\pi$
$241$	2.55800	−	2.14642i	0.164775	−	0.138263i	0.721447	+	0.692470i	$0.243477\pi$
$242$	−15.8761	+	27.4982i	−1.02055	+	1.76765i
$243$	1.52117	−	15.5141i	0.0975831	−	0.995227i
$244$	−0.0316979			−0.00202925
$245$	5.87076	+	21.8795i	0.375069	+	1.39783i
$246$	−19.5726	−	2.44484i	−1.24791	−	0.155877i
$247$	0.00233737	−	0.0132559i	0.000148724	−	0.000843453i
$248$	12.8674	+	10.7971i	0.817083	+	0.685614i
$249$	−6.54944	+	4.23378i	−0.415054	+	0.268305i
$250$	2.03926	+	0.742229i	0.128974	+	0.0469427i
$251$	0.120361	+	0.208472i	0.00759714	+	0.0131586i	0.869799	−	0.493406i	$-0.164248\pi$
$251$	0.120361	+	0.208472i	0.00759714	+	0.0131586i	−0.862202	+	0.506565i	$0.830915\pi$
$252$	−0.0160828	+	0.0774566i	−0.00101312	+	0.00487931i
$253$	16.3348	−	28.2926i	1.02696	−	1.77874i
$254$	−16.2803	+	13.6608i	−1.02152	+	0.857157i
$255$	24.1928	−	5.53201i	1.51501	−	0.346428i
$256$	0.0415360	−	0.235562i	0.00259600	−	0.0147226i
$257$	5.72588	+	4.80458i	0.357171	+	0.299702i	0.803662	−	0.595086i	$-0.202882\pi$
$257$	5.72588	+	4.80458i	0.357171	+	0.299702i	−0.446491	+	0.894788i	$0.647327\pi$
$258$	−2.23253	+	7.24794i	−0.138991	+	0.451237i
$259$	0.224549	+	0.244966i	0.0139528	+	0.0152215i
$260$	−0.000108640	0	0.000188170i	−6.73758e−6	0	1.16698e-5i
$261$	−1.80226	+	24.3097i	−0.111557	+	1.50473i
$262$	3.46184			0.213873
$263$	4.79058	+	27.1687i	0.295400	+	1.67529i	0.665574	+	0.746332i	$0.268187\pi$
$263$	4.79058	+	27.1687i	0.295400	+	1.67529i	−0.370175	+	0.928962i	$0.620702\pi$
$264$	25.1352	+	12.8734i	1.54696	+	0.792302i
$265$	1.91088	−	10.8371i	0.117384	−	0.665719i
$266$	2.86941	+	6.92396i	0.175935	+	0.424535i
$267$	7.59581	+	17.9993i	0.464856	+	1.10154i
$268$	0.00601462	+	0.0341106i	0.000367401	+	0.00208364i
$269$	−9.01536	+	15.6151i	−0.549676	+	0.952067i	0.448620	+	0.893723i	$0.351916\pi$
$269$	−9.01536	+	15.6151i	−0.549676	+	0.952067i	−0.998296	+	0.0583449i	$0.981418\pi$
$270$	3.58142	+	23.5698i	0.217958	+	1.43441i
$271$	0.526488	+	0.911904i	0.0319819	+	0.0553942i	0.881573	−	0.472047i	$-0.156485\pi$
$271$	0.526488	+	0.911904i	0.0319819	+	0.0553942i	−0.849591	+	0.527441i	$0.823151\pi$
$272$	16.7244	+	6.08720i	1.01407	+	0.369091i
$273$	−0.0278885	+	0.0132365i	−0.00168789	+	0.000801108i
$274$	−4.01941	−	3.37268i	−0.242821	−	0.203751i
$275$	−29.7208	+	10.8175i	−1.79223	+	0.652320i
$276$	0.0868606	+	0.0444871i	0.00522840	+	0.00267781i
$277$	1.08250	+	6.13916i	0.0650411	+	0.368866i	0.999904	+	0.0138574i	$0.00441110\pi$
$277$	1.08250	+	6.13916i	0.0650411	+	0.368866i	−0.934863	+	0.355009i	$0.884478\pi$
$278$	−4.20446	+	7.28233i	−0.252166	+	0.436765i
$279$	−10.4378	−	14.4937i	−0.624894	−	0.867713i
$280$	1.05791	+	24.1336i	0.0632223	+	1.44226i
$281$	3.27981	+	18.6007i	0.195657	+	1.10962i	0.911480	+	0.411344i	$0.134940\pi$
$281$	3.27981	+	18.6007i	0.195657	+	1.10962i	−0.715823	+	0.698281i	$0.753948\pi$
$282$	8.67175	+	9.33845i	0.516395	+	0.556097i
$283$	−2.04526	+	11.5992i	−0.121578	+	0.689503i	0.861704	+	0.507412i	$0.169398\pi$
$283$	−2.04526	+	11.5992i	−0.121578	+	0.689503i	−0.983282	+	0.182091i	$0.941713\pi$
$284$	0.0121095	−	0.0686764i	0.000718567	−	0.00407520i
$285$	7.62129	+	8.20723i	0.451447	+	0.486155i
$286$	−0.00958398	−	0.0543535i	−0.000566713	−	0.00321399i
$287$	18.8527	+	9.80992i	1.11284	+	0.579061i
$288$	−0.0694420	+	0.154227i	−0.00409191	+	0.00908794i
$289$	−1.30134	+	2.25398i	−0.0765493	+	0.132587i
$290$	−6.47364	−	36.7138i	−0.380145	−	2.15591i
$291$	−9.80941	−	5.02405i	−0.575038	−	0.294515i
$292$	0.00928671	−	0.00338009i	0.000543464	−	0.000197805i
$293$	5.29229	+	4.44076i	0.309179	+	0.259432i	0.784153	−	0.620568i	$-0.213098\pi$
$293$	5.29229	+	4.44076i	0.309179	+	0.259432i	−0.474974	+	0.880000i	$0.657542\pi$
$294$	9.13427	−	14.5613i	0.532721	−	0.849230i
$295$	−16.3138	−	5.93774i	−0.949827	−	0.345709i
$296$	0.177182	+	0.306889i	0.0102985	+	0.0178376i
$297$	−22.5385	−	19.8424i	−1.30782	−	1.15137i
$298$	−4.70528	+	8.14978i	−0.272569	+	0.472104i
$299$	0.00661293	+	0.0375038i	0.000382436	+	0.00216890i
$300$	−0.0367340	−	0.0870463i	−0.00212084	−	0.00502562i
$301$	4.97324	−	6.48360i	0.286653	−	0.373708i
$302$	0.978928	−	5.55177i	0.0563310	−	0.319469i
$303$	−23.8938	−	12.2376i	−1.37267	−	0.703033i
$304$	1.39478	+	7.91018i	0.0799960	+	0.453680i
$305$	10.2923			0.589335
$306$	−15.5674	−	10.5955i	−0.889927	−	0.605702i
$307$	10.5306	−	18.2395i	0.601013	−	1.04098i	−0.391656	−	0.920112i	$-0.628098\pi$
$307$	10.5306	−	18.2395i	0.601013	−	1.04098i	0.992668	−	0.120872i	$-0.0385692\pi$
$308$	0.102972	+	0.112335i	0.00586737	+	0.00640087i
$309$	6.58555	−	21.3801i	0.374639	−	1.21627i
$310$	20.9251	+	17.5582i	1.18846	+	0.997240i
$311$	−4.86537	+	27.5929i	−0.275890	+	1.56465i	0.460232	+	0.887799i	$0.347766\pi$
$311$	−4.86537	+	27.5929i	−0.275890	+	1.56465i	−0.736122	+	0.676849i	$0.763345\pi$
$312$	−0.0320907	+	0.00733797i	−0.00181678	+	0.000415431i
$313$	9.65313	−	8.09994i	0.545627	−	0.457836i	−0.327830	−	0.944737i	$-0.606317\pi$
$313$	9.65313	−	8.09994i	0.545627	−	0.457836i	0.873457	+	0.486901i	$0.161873\pi$
$314$	14.3922	−	24.9281i	0.812201	−	1.40677i
$315$	5.22208	−	25.1501i	0.294231	−	1.41705i
$316$	0.0101865	+	0.0176436i	0.000573037	+	0.000992528i
$317$	15.9492	+	5.80504i	0.895797	+	0.326043i	0.748567	−	0.663059i	$-0.230742\pi$
$317$	15.9492	+	5.80504i	0.895797	+	0.326043i	0.147230	+	0.989102i	$0.452964\pi$
$318$	−7.01234	+	4.53301i	−0.393232	+	0.254199i
$319$	35.9710	+	30.1832i	2.01399	+	1.68994i
$320$	−4.47306	+	25.3680i	−0.250051	+	1.41811i
$321$	−14.2284	−	1.77728i	−0.794149	−	0.0991981i
$322$	−14.3285	−	15.6314i	−0.798498	−	0.871103i
$323$	−8.84677			−0.492247
$324$	0.0558155	−	0.0702200i	0.00310086	−	0.00390111i
$325$	0.0184343	−	0.0319291i	0.00102255	−	0.00177111i
$326$	21.0125	−	17.6316i	1.16378	−	0.976525i
$327$	−2.42892	−	5.75567i	−0.134320	−	0.318289i
$328$	17.3606	+	14.5673i	0.958580	+	0.804344i
$329$	−5.25675	−	12.6847i	−0.289814	−	0.699328i
$330$	40.8749	+	20.9348i	2.25009	+	1.15242i
$331$	−14.2427	−	5.18393i	−0.782852	−	0.284935i	−0.0804906	−	0.996755i	$-0.525649\pi$
$331$	−14.2427	−	5.18393i	−0.782852	−	0.284935i	−0.702361	+	0.711821i	$0.747871\pi$
$332$	−0.0448762			−0.00246290
$333$	−0.102343	−	0.362640i	−0.00560839	−	0.0198726i
$334$	−8.14427			−0.445635
$335$	−1.95294	−	11.0757i	−0.106701	−	0.605130i
$336$	12.9368	−	13.1141i	0.705760	−	0.715433i
$337$	−24.3574	+	8.86536i	−1.32683	+	0.482927i	−0.905641	−	0.424045i	$-0.860610\pi$
$337$	−24.3574	+	8.86536i	−1.32683	+	0.482927i	−0.421190	+	0.906972i	$0.638388\pi$
$338$	−14.1186	−	11.8469i	−0.767948	−	0.644385i
$339$	11.4049	+	12.2817i	0.619429	+	0.667051i
$340$	0.134194	+	0.0488426i	0.00727768	+	0.00264886i
$341$	−34.4059			−1.86319
$342$	0.628333	−	8.47525i	0.0339763	−	0.458289i
$343$	−14.6872	+	11.2821i	−0.793035	+	0.609176i
$344$	6.67499	−	5.60099i	0.359892	−	0.301985i
$345$	−28.2036	−	14.4449i	−1.51843	−	0.777690i
$346$	−0.529882	−	0.444624i	−0.0284866	−	0.0239031i
$347$	26.4514	−	9.62753i	1.41999	−	0.516833i	0.485943	−	0.873991i	$-0.338476\pi$
$347$	26.4514	−	9.62753i	1.41999	−	0.516833i	0.934044	+	0.357158i	$0.116254\pi$
$348$	−0.0846506	+	0.111847i	−0.00453775	+	0.00599563i
$349$	−4.71905	−	1.71759i	−0.252605	−	0.0919407i	0.212614	−	0.977136i	$-0.431802\pi$
$349$	−4.71905	−	1.71759i	−0.252605	−	0.0919407i	−0.465219	+	0.885196i	$0.654024\pi$
$350$	0.899038	+	20.5093i	0.0480556	+	1.09627i
$351$	0.0349938		0.000830789i	0.00186783		4.43442e-5i
$352$	0.162909	+	0.282167i	0.00868307	+	0.0150395i
$353$	10.0552	−	8.43735i	0.535186	−	0.449075i	−0.334702	−	0.942324i	$-0.608636\pi$
$353$	10.0552	−	8.43735i	0.535186	−	0.449075i	0.869888	+	0.493250i	$0.164191\pi$
$354$	5.12175	+	12.1367i	0.272218	+	0.645058i
$355$	−3.93195	+	22.2992i	−0.208686	+	1.18352i
$356$	−0.0195213	+	0.110711i	−0.00103463	+	0.00586766i
$357$	11.7503	+	16.5404i	0.621893	+	0.875413i
$358$	28.8266	−	24.1883i	1.52353	−	1.27839i
$359$	1.35194	−	2.34164i	0.0713529	−	0.123587i	−0.828142	−	0.560519i	$-0.810602\pi$
$359$	1.35194	−	2.34164i	0.0713529	−	0.123587i	0.899494	+	0.436932i	$0.143935\pi$
$360$	11.2457	−	24.9762i	0.592702	−	1.31636i
$361$	7.50371	+	12.9968i	0.394932	+	0.684042i
$362$	3.54785	−	2.97700i	0.186471	−	0.156468i
$363$	−37.8158	+	8.64707i	−1.98481	+	0.453854i
$364$	−0.000176122	0	2.31556e-5i	−9.23128e−6	0	1.21368e-6i
$365$	−3.01539	+	1.09751i	−0.157833	+	0.0574464i
$366$	−5.31419	−	5.72276i	−0.277777	−	0.299133i
$367$	−10.1865	−	3.70757i	−0.531729	−	0.193533i	0.0621813	−	0.998065i	$-0.480194\pi$
$367$	−10.1865	−	3.70757i	−0.531729	−	0.193533i	−0.593910	+	0.804531i	$0.702417\pi$
$368$	−11.3624	−	19.6803i	−0.592307	−	1.02591i
$369$	−14.0826	−	19.5547i	−0.733108	−	1.01798i
$370$	0.288135	+	0.499064i	0.0149794	+	0.0259451i
$371$	8.78296	−	1.94874i	0.455988	−	0.101174i
$372$	−0.00516398	−	0.102648i	−0.000267740	−	0.00532203i
$373$	−5.00163	+	1.82045i	−0.258975	+	0.0942591i	−0.468245	−	0.883599i	$-0.655113\pi$
$373$	−5.00163	+	1.82045i	−0.258975	+	0.0942591i	0.209270	+	0.977858i	$0.432891\pi$
$374$	−34.0869	+	12.4066i	−1.76259	+	0.641532i
$375$	1.03082	+	2.44266i	0.0532311	+	0.126139i
$376$	−2.54256	−	14.4196i	−0.131122	−	0.743632i
$377$	−0.0547368			−0.00281909
$378$	−16.6804	+	10.0821i	−0.857946	+	0.518567i
$379$	1.33171			0.0684055			0.0342028	−	0.999415i	$-0.489111\pi$
$379$	1.33171			0.0684055			0.0342028	+	0.999415i	$0.489111\pi$
$380$	0.0111914	+	0.0634698i	0.000574109	+	0.00325593i
$381$	−25.7640	−	3.21821i	−1.31993	−	0.164874i
$382$	−11.3307	+	4.12405i	−0.579730	+	0.211005i
$383$	0.780305	−	0.284008i	0.0398717	−	0.0145121i	−0.322007	−	0.946737i	$-0.604358\pi$
$383$	0.780305	−	0.284008i	0.0398717	−	0.0145121i	0.361879	+	0.932225i	$0.382135\pi$
$384$	16.5788	−	10.7171i	0.846032	−	0.546904i
$385$	−33.4349	−	36.4751i	−1.70400	−	1.85894i
$386$	5.13367	+	8.89177i	0.261297	+	0.452579i
$387$	−8.34461	+	4.02676i	−0.424180	+	0.204692i
$388$	−0.0317095	−	0.0549225i	−0.00160981	−	0.00278827i
$389$	−6.61352	−	2.40712i	−0.335319	−	0.122046i	0.168873	−	0.985638i	$-0.445987\pi$
$389$	−6.61352	−	2.40712i	−0.335319	−	0.122046i	−0.504192	+	0.863592i	$0.668209\pi$
$390$	−0.0521861	+	0.0119330i	−0.00264254	+	0.000604253i
$391$	23.5199	−	8.56055i	1.18945	−	0.432926i
$392$	−17.8961	+	8.35267i	−0.903889	+	0.421874i
$393$	2.87793	+	3.09919i	0.145172	+	0.156333i
$394$	−23.5041	+	19.7223i	−1.18412	+	0.993593i
$395$	−3.30756	−	5.72886i	−0.166421	−	0.288250i
$396$	−0.0469319	−	0.166297i	−0.00235842	−	0.00835674i
$397$	13.1429	−	22.7642i	0.659623	−	1.14250i	−0.321090	−	0.947049i	$-0.604049\pi$
$397$	13.1429	−	22.7642i	0.659623	−	1.14250i	0.980713	−	0.195452i	$-0.0626174\pi$
$398$	−1.41679	+	1.18883i	−0.0710172	+	0.0595905i
$399$	−3.81319	+	8.32489i	−0.190898	+	0.416766i
$400$	−3.82035	+	21.6663i	−0.191018	+	1.08331i
$401$	2.35377	−	13.3489i	0.117542	−	0.666611i	−0.867919	−	0.496706i	$-0.834543\pi$
$401$	2.35377	−	13.3489i	0.117542	−	0.666611i	0.985460	−	0.169905i	$-0.0543462\pi$
$402$	−5.14999	+	6.80457i	−0.256858	+	0.339381i
$403$	0.0307233	−	0.0257799i	0.00153044	−	0.00128419i
$404$	−0.0772383	−	0.133781i	−0.00384275	−	0.00665584i
$405$	−18.1233	+	22.8004i	−0.900553	+	1.13296i
$406$	25.7023	−	16.3805i	1.27559	−	0.812950i
$407$	−0.682074	−	0.248255i	−0.0338092	−	0.0123055i
$408$	8.41205	+	19.9335i	0.416459	+	0.986857i
$409$	36.2955	−	13.2105i	1.79469	−	0.653215i	0.795833	−	0.605516i	$-0.207033\pi$
$409$	36.2955	−	13.2105i	1.79469	−	0.653215i	0.998862	−	0.0476990i	$-0.0151888\pi$
$410$	28.2319	+	23.6894i	1.39427	+	1.16994i
$411$	−0.322078	−	6.40215i	−0.0158869	−	0.315795i
$412$	0.0986143	−	0.0827472i	0.00485838	−	0.00407666i
$413$	−0.621574	−	14.1797i	−0.0305857	−	0.697737i
$414$	6.53057	+	23.1402i	0.320960	+	1.13728i
$415$	14.5713			0.715277
$416$	−0.000356896	0	0.000129900i	−1.74983e−5	0	6.36885e-6i
$417$	−10.0147	+	2.29000i	−0.490423	+	0.112142i
$418$	−12.5408	−	10.5230i	−0.613391	−	0.514696i
$419$	6.04738	−	2.20107i	0.295434	−	0.107529i	−0.190051	−	0.981774i	$-0.560865\pi$
$419$	6.04738	−	2.20107i	0.295434	−	0.107529i	0.485485	+	0.874245i	$0.338643\pi$
$420$	0.103802	−	0.105225i	0.00506504	−	0.00513446i
$421$	−1.23460	−	7.00177i	−0.0601708	−	0.341246i	0.939829	−	0.341645i	$-0.110984\pi$
$421$	−1.23460	−	7.00177i	−0.0601708	−	0.341246i	−1.00000		0.000399310i	$0.999873\pi$
$422$	7.53045			0.366576
$423$	−1.15110	+	15.5266i	−0.0559686	+	0.754930i
$424$	9.59361			0.465907
$425$	−22.7703	−	8.28771i	−1.10452	−	0.402013i
$426$	14.4291	−	9.32744i	0.699091	−	0.451916i
$427$	3.22142	+	7.77337i	0.155896	+	0.376180i
$428$	−0.0632068	−	0.0530368i	−0.00305522	−	0.00256363i
$429$	0.0406920	−	0.0537655i	0.00196463	−	0.00259582i
$430$	10.8549	−	9.10835i	0.523470	−	0.439243i
$431$	16.1115	−	27.9059i	0.776062	−	1.34418i	−0.158134	−	0.987418i	$-0.550548\pi$
$431$	16.1115	−	27.9059i	0.776062	−	1.34418i	0.934196	−	0.356761i	$-0.116119\pi$
$432$	−19.7920	+	6.67613i	−0.952244	+	0.321206i
$433$	28.9030			1.38899			0.694496	−	0.719497i	$-0.255627\pi$
$433$	28.9030			1.38899			0.694496	+	0.719497i	$0.255627\pi$
$434$	−6.71164	+	21.2995i	−0.322169	+	1.02241i
$435$	27.4860	−	36.3167i	1.31785	−	1.74125i
$436$	0.00624235	−	0.0354021i	0.000298954	−	0.00169545i
$437$	8.65313	+	7.26084i	0.413935	+	0.347333i
$438$	2.16717	+	1.10995i	0.103552	+	0.0530356i
$439$	26.3927	+	9.60616i	1.25966	+	0.458477i	0.883653	−	0.468142i	$-0.155076\pi$
$439$	26.3927	+	9.60616i	1.25966	+	0.458477i	0.376002	+	0.926619i	$0.377299\pi$
$440$	−26.3822	−	45.6952i	−1.25772	−	2.17844i
$441$	20.6294	−	3.92780i	0.982353	−	0.187038i
$442$	0.0211424	−	0.0366196i	0.00100564	−	0.00174182i
$443$	−6.59456	+	5.53350i	−0.313317	+	0.262904i	−0.785861	−	0.618403i	$-0.787780\pi$
$443$	−6.59456	+	5.53350i	−0.313317	+	0.262904i	0.472544	+	0.881307i	$0.343336\pi$
$444$	0.000638277	−	0.00207218i	3.02913e−5	−	9.83413e-5i
$445$	6.33855	−	35.9477i	0.300476	−	1.70409i
$446$	−2.98120	−	2.50152i	−0.141164	−	0.118450i
$447$	−11.2076	+	2.56277i	−0.530103	+	0.121215i
$448$	−20.5595	+	4.56169i	−0.971345	+	0.215520i
$449$	−1.00338	+	1.73790i	−0.0473523	+	0.0820166i	−0.888730	−	0.458431i	$-0.848412\pi$
$449$	−1.00338	+	1.73790i	−0.0473523	+	0.0820166i	0.841378	+	0.540447i	$0.181745\pi$
$450$	9.55690	−	21.2254i	0.450517	−	1.00058i
$451$	−46.4201			−2.18584
$452$	0.0167474	+	0.0949795i	0.000787734	+	0.00446746i
$453$	5.78399	−	3.73897i	0.271755	−	0.175672i
$454$	−0.823935	+	4.67277i	−0.0386692	+	0.219304i
$455$	0.0571866	+	0.00751862i	0.00268095	+	0.000352478i
$456$	−5.89264	+	7.78581i	−0.275948	+	0.364604i
$457$	3.84265	+	21.7927i	0.179751	+	1.01942i	0.932515	+	0.361130i	$0.117609\pi$
$457$	3.84265	+	21.7927i	0.179751	+	1.01942i	−0.752764	+	0.658291i	$0.771280\pi$
$458$	20.1286	−	34.8638i	0.940549	−	1.62908i
$459$	−3.45608	−	22.7448i	−0.161316	−	1.06164i
$460$	−0.0911699	−	0.157911i	−0.00425082	−	0.00736264i
$461$	−4.59624	−	1.67289i	−0.214068	−	0.0779145i	0.232760	−	0.972534i	$-0.425224\pi$
$461$	−4.59624	−	1.67289i	−0.214068	−	0.0779145i	−0.446828	+	0.894620i	$0.647447\pi$
$462$	−3.01763	+	37.4237i	−0.140393	+	1.74111i
$463$	−7.11816	−	5.97285i	−0.330809	−	0.277582i	0.462220	−	0.886765i	$-0.347053\pi$
$463$	−7.11816	−	5.97285i	−0.330809	−	0.277582i	−0.793029	+	0.609183i	$0.791497\pi$
$464$	30.6932	−	11.1714i	1.42490	−	0.518620i
$465$	1.67674	+	33.3296i	0.0777570	+	1.54562i
$466$	1.96561	+	11.1475i	0.0910551	+	0.516399i
$467$	16.7554	−	29.0212i	0.775347	−	1.34294i	−0.159252	−	0.987238i	$-0.550908\pi$
$467$	16.7554	−	29.0212i	0.775347	−	1.34294i	0.934599	−	0.355703i	$-0.115758\pi$
$468$	0.000166513	0	0.000113332i	7.69706e−6	0	5.23878e-6i
$469$	7.75379	−	4.94161i	0.358037	−	0.228182i
$470$	−4.13472	−	23.4492i	−0.190720	−	1.08163i
$471$	34.2813	−	7.83888i	1.57960	−	0.361196i
$472$	2.62821	−	14.9053i	0.120973	−	0.686072i
$473$	−3.09929	+	17.5770i	−0.142506	+	0.808190i
$474$	−1.47760	+	4.79705i	−0.0678684	+	0.220336i
$475$	−1.89899	−	10.7697i	−0.0871315	−	0.494147i
$476$	0.00511293	+	0.116639i	0.000234351	+	0.00534614i
$477$	−9.88769	−	2.50932i	−0.452726	−	0.114894i
$478$	8.46259	−	14.6576i	0.387070	−	0.670425i
$479$	−5.53869	−	31.4114i	−0.253069	−	1.43523i	−0.800981	−	0.598690i	$-0.795688\pi$
$479$	−5.53869	−	31.4114i	−0.253069	−	1.43523i	0.547912	−	0.836536i	$-0.315423\pi$
$480$	0.265400	−	0.171564i	0.0121138	−	0.00783078i
$481$	0.000795084	0	0.000289387i	3.62527e−5	0	1.31949e-5i
$482$	3.62656	+	3.04305i	0.165185	+	0.138607i
$483$	2.08216	−	25.8223i	0.0947414	−	1.17496i
$484$	−0.209758	−	0.0763457i	−0.00953446	−	0.00347026i
$485$	10.2961	+	17.8333i	0.467521	+	0.809769i
$486$	22.0351	−	1.69551i	0.999534	−	0.0769098i
$487$	−18.6767	+	32.3490i	−0.846322	+	1.46587i	0.0381466	+	0.999272i	$0.487855\pi$
$487$	−18.6767	+	32.3490i	−0.846322	+	1.46587i	−0.884468	+	0.466600i	$0.845479\pi$
$488$	1.55812	+	8.83655i	0.0705329	+	0.400012i
$489$	33.2528	+	4.15365i	1.50375	+	0.187835i
$490$	−29.1027	+	13.5832i	−1.31473	+	0.613624i
$491$	−2.23151	+	12.6555i	−0.100706	+	0.571135i	0.892142	+	0.451755i	$0.149202\pi$
$491$	−2.23151	+	12.6555i	−0.100706	+	0.571135i	−0.992849	+	0.119380i	$0.961909\pi$
$492$	−0.00696718	−	0.138491i	−0.000314105	−	0.00624366i
$493$	6.24707	+	35.4289i	0.281354	+	1.59564i
$494$	0.0190833			0.000858596
$495$	15.2388	+	53.9966i	0.684932	+	2.42696i
$496$	−11.9663	+	20.7263i	−0.537305	+	0.930639i
$497$	−18.0724	+	4.00986i	−0.810659	+	0.179867i
$498$	−7.52356	−	8.10199i	−0.337139	−	0.363059i
$499$	−22.2368	−	18.6589i	−0.995458	−	0.835288i	−0.00910927	−	0.999959i	$-0.502900\pi$
$499$	−22.2368	−	18.6589i	−0.995458	−	0.835288i	−0.986349	+	0.164670i	$0.947344\pi$
$500$	−0.00264920	+	0.0150244i	−0.000118476	+	0.000671911i
$501$	−6.77055	−	7.29109i	−0.302486	−	0.325742i
$502$	−0.261436	+	0.219371i	−0.0116685	+	0.00979100i
$503$	3.40133	−	5.89128i	0.151658	−	0.262679i	−0.780179	−	0.625556i	$-0.784872\pi$
$503$	3.40133	−	5.89128i	0.151658	−	0.262679i	0.931837	+	0.362877i	$0.118205\pi$
$504$	22.3835	+	0.676063i	0.997038	+	0.0301142i
$505$	25.0793	+	43.4385i	1.11601	+	1.93299i
$506$	43.5234	+	15.8412i	1.93485	+	0.704228i
$507$	−1.13133	−	22.4881i	−0.0502441	−	0.998733i
$508$	−0.114452	−	0.0960365i	−0.00507798	−	0.00426093i
$509$	2.13572	−	12.1122i	0.0946639	−	0.536866i	−0.900186	−	0.435506i	$-0.856570\pi$
$509$	2.13572	−	12.1122i	0.0946639	−	0.536866i	0.994850	−	0.101360i	$-0.0323194\pi$
$510$	13.6797	+	32.4160i	0.605748	+	1.43540i
$511$	−1.77271	−	1.93390i	−0.0784200	−	0.0855505i
$512$	−22.4560			−0.992423
$513$	8.10974	−	6.48319i	0.358054	−	0.286240i
$514$	−5.29850	+	9.17727i	−0.233707	+	0.404792i
$515$	−32.0200	+	26.8680i	−1.41097	+	1.18394i
$516$	−0.0529047	−	0.00660839i	−0.00232900	−	0.000290918i
$517$	22.9747	+	19.2781i	1.01043	+	0.847849i
$518$	−0.286740	+	0.373821i	−0.0125986	+	0.0164248i
$519$	−0.0424598	−	0.844000i	−0.00186378	−	0.0370475i
$520$	0.0577973	+	0.0210365i	0.00253458	+	0.000922511i
$521$	18.9909			0.832005			0.416003	−	0.909363i	$-0.363431\pi$
$521$	18.9909			0.832005			0.416003	+	0.909363i	$0.363431\pi$
$522$	−34.3847	+	3.46842i	−1.50498	+	0.151809i
$523$	−18.2926			−0.799880			−0.399940	−	0.916541i	$-0.630969\pi$
$523$	−18.2926			−0.799880			−0.399940	+	0.916541i	$0.630969\pi$
$524$	0.00422607	+	0.0239673i	0.000184617	+	0.00104701i
$525$	−17.6134	+	17.8548i	−0.768712	+	0.779249i
$526$	−36.7534	+	13.3771i	−1.60252	+	0.583271i
$527$	−20.1927	−	16.9437i	−0.879609	−	0.738080i
$528$	−11.8445	+	38.4535i	−0.515468	+	1.67347i
$529$	−8.41814	−	3.06395i	−0.366006	−	0.133215i
$530$	15.6012			0.677671
$531$	−6.60742	+	14.6748i	−0.286738	+	0.636831i
$532$	−0.0444335	+	0.0283181i	−0.00192644	+	0.00122775i
$533$	0.0414516	−	0.0347820i	0.00179547	−	0.00150658i
$534$	−23.2606	+	15.0364i	−1.00658	+	0.650690i
$535$	20.5232	+	17.2210i	0.887296	+	0.744530i
$536$	9.21350	−	3.35344i	0.397963	−	0.144847i
$537$	45.6187	+	5.69828i	1.96859	+	0.245899i
$538$	−24.0211	−	8.74298i	−1.03562	−	0.376937i
$539$	17.0833	−	36.6686i	0.735830	−	1.57943i
$540$	−0.158808	+	0.0535681i	−0.00683399	+	0.00230520i
$541$	1.87261	+	3.24346i	0.0805099	+	0.139447i	0.903469	−	0.428653i	$-0.141012\pi$
$541$	1.87261	+	3.24346i	0.0805099	+	0.139447i	−0.822959	+	0.568101i	$0.807678\pi$
$542$	−1.14358	+	0.959578i	−0.0491210	+	0.0412174i
$543$	5.61456	+	0.701321i	0.240944	+	0.0300966i
$544$	−0.0433464	+	0.245829i	−0.00185846	+	0.0105398i
$545$	−2.02689	+	11.4951i	−0.0868224	+	0.492394i
$546$	−0.0253465	−	0.0356792i	−0.00108473	−	0.00152693i
$547$	10.8661	−	9.11778i	0.464603	−	0.389848i	−0.380218	−	0.924897i	$-0.624151\pi$
$547$	10.8661	−	9.11778i	0.464603	−	0.389848i	0.844821	+	0.535049i	$0.179707\pi$
$548$	0.0184433	−	0.0319447i	0.000787857	−	0.00136461i
$549$	0.705415	−	9.51497i	0.0301064	−	0.406089i
$550$	−22.4202	−	38.8329i	−0.956001	−	1.65584i
$551$	−12.4374	+	10.4362i	−0.529850	+	0.444597i
$552$	8.13219	−	26.4013i	0.346129	−	1.12371i
$553$	3.29154	−	4.29117i	0.139971	−	0.182479i
$554$	−8.30497	+	3.02276i	−0.352844	+	0.128425i
$555$	−0.207248	+	0.672836i	−0.00879721	+	0.0285603i
$556$	−0.0555501	−	0.0202186i	−0.00235585	−	0.000857459i
$557$	7.98181	+	13.8249i	0.338200	+	0.585780i	0.984094	−	0.177647i	$-0.0568485\pi$
$557$	7.98181	+	13.8249i	0.338200	+	0.585780i	−0.645894	+	0.763427i	$0.723515\pi$
$558$	17.6663	−	18.1413i	0.747875	−	0.767983i
$559$	−0.0104026	−	0.0180179i	−0.000439985	−	0.000762076i
$560$	−33.6014	+	7.45539i	−1.41992	+	0.315048i
$561$	−39.4443	−	20.2021i	−1.66534	−	0.852932i
$562$	−25.1628	+	9.15849i	−1.06143	+	0.386328i
$563$	−10.0115	+	3.64389i	−0.421934	+	0.153572i	−0.544256	−	0.838919i	$-0.683188\pi$
$563$	−10.0115	+	3.64389i	−0.421934	+	0.153572i	0.122322	+	0.992490i	$0.460966\pi$
$564$	−0.0540664	+	0.0714368i	−0.00227661	+	0.00300803i
$565$	−5.43789	−	30.8398i	−0.228774	−	1.29744i
$566$	−16.6983			−0.701882
$567$	−22.8928	−	6.55143i	−0.961406	−	0.275134i
$568$	−19.7405			−0.828292
$569$	−5.19377	−	29.4553i	−0.217734	−	1.23483i	−0.876099	−	0.482132i	$-0.839863\pi$
$569$	−5.19377	−	29.4553i	−0.217734	−	1.23483i	0.658365	−	0.752699i	$-0.271248\pi$
$570$	−9.58263	+	12.6613i	−0.401372	+	0.530324i
$571$	−18.2661	+	6.64832i	−0.764413	+	0.278224i	−0.694658	−	0.719340i	$-0.744444\pi$
$571$	−18.2661	+	6.64832i	−0.764413	+	0.278224i	−0.0697556	+	0.997564i	$0.522222\pi$
$572$	0.000364604	0	0.000132705i	1.52448e−5	0	5.54867e-6i
$573$	−13.1116	−	6.71530i	−0.547743	−	0.280536i
$574$	−9.05527	+	28.7371i	−0.377960	+	1.19946i
$575$	15.4699	+	26.7947i	0.645139	+	1.11741i
$576$	23.1455	+	5.87391i	0.964396	+	0.244746i
$577$	−3.76412	−	6.51965i	−0.156702	−	0.271417i	0.776975	−	0.629531i	$-0.216753\pi$
$577$	−3.76412	−	6.51965i	−0.156702	−	0.271417i	−0.933678	+	0.358115i	$0.883420\pi$
$578$	−3.46737	−	1.26202i	−0.144224	−	0.0524931i
$579$	−3.69252	+	11.9878i	−0.153456	+	0.498198i
$580$	0.246277	−	0.0896374i	0.0102261	−	0.00372199i
$581$	4.56073	+	11.0051i	0.189211	+	0.456570i
$582$	4.59961	−	14.9327i	0.190660	−	0.618980i
$583$	−15.0533	+	12.6312i	−0.623443	+	0.523131i
$584$	−1.39877	−	2.42275i	−0.0578816	−	0.100254i
$585$	−0.0540667	−	0.0367989i	−0.00223538	−	0.00152145i
$586$	−4.89727	+	8.48233i	−0.202305	+	0.350402i
$587$	−18.8178	+	15.7900i	−0.776695	+	0.651724i	−0.942414	−	0.334449i	$-0.891450\pi$
$587$	−18.8178	+	15.7900i	−0.776695	+	0.651724i	0.165719	+	0.986173i	$0.447006\pi$
$588$	0.111962	+	0.0454632i	0.00461724	+	0.00187487i
$589$	2.06576	−	11.7155i	0.0851183	−	0.482730i
$590$	4.27400	−	24.2391i	0.175958	−	0.997906i
$591$	−37.1957	−	4.64616i	−1.53003	−	0.191118i
$592$	−0.386775	+	0.324542i	−0.0158963	+	0.0133386i
$593$	19.7803	+	34.2605i	0.812280	+	1.40691i	0.911264	+	0.411822i	$0.135107\pi$
$593$	19.7803	+	34.2605i	0.812280	+	1.40691i	−0.0989842	+	0.995089i	$0.531559\pi$
$594$	22.1552	−	36.3530i	0.909038	−	1.49158i
$595$	−1.66017	−	37.8726i	−0.0680602	−	1.55263i
$596$	−0.0621670	−	0.0226269i	−0.00254646	−	0.000926836i
$597$	−2.24210	−	0.280064i	−0.0917632	−	0.0114622i
$598$	−0.0507346	+	0.0184659i	−0.00207469	+	0.000755126i
$599$	−26.4174	−	22.1669i	−1.07939	−	0.905714i	−0.0835178	−	0.996506i	$-0.526616\pi$
$599$	−26.4174	−	22.1669i	−1.07939	−	0.905714i	−0.995870	+	0.0907925i	$0.971060\pi$
$600$	−22.4606	+	14.5193i	−0.916950	+	0.592747i
$601$	−7.46053	+	6.26013i	−0.304322	+	0.255356i	−0.782140	−	0.623102i	$-0.785872\pi$
$601$	−7.46053	+	6.26013i	−0.304322	+	0.255356i	0.477819	+	0.878458i	$0.341428\pi$
$602$	10.2767	+	5.34744i	0.418847	+	0.217945i
$603$	−10.3731	+	1.04634i	−0.422424	+	0.0426103i
$604$	0.0396314			0.00161258
$605$	68.1084	+	24.7894i	2.76900	+	1.00783i
$606$	11.2038	−	36.3732i	0.455121	−	1.47756i
$607$	−11.3370	−	9.51291i	−0.460157	−	0.386117i	0.383032	−	0.923735i	$-0.374880\pi$
$607$	−11.3370	−	9.51291i	−0.460157	−	0.386117i	−0.843189	+	0.537618i	$0.819324\pi$
$608$	−0.105861	+	0.0385304i	−0.00429324	+	0.00156261i
$609$	36.0316	+	9.39224i	1.46007	+	0.380593i
$610$	2.53383	+	14.3700i	0.102592	+	0.581826i
$611$	−0.0349605			−0.00141435
$612$	0.0543512	−	0.120711i	0.00219702	−	0.00487947i
$613$	36.8492			1.48832			0.744162	−	0.667999i	$-0.232849\pi$
$613$	36.8492			1.48832			0.744162	+	0.667999i	$0.232849\pi$
$614$	28.0584	+	10.2124i	1.13235	+	0.412140i
$615$	2.26224	+	44.9680i	0.0912224	+	1.81328i
$616$	26.2544	−	34.2278i	1.05782	−	1.37908i
$617$	16.0437	+	13.4622i	0.645894	+	0.541969i	0.905822	−	0.423659i	$-0.139254\pi$
$617$	16.0437	+	13.4622i	0.645894	+	0.541969i	−0.259928	+	0.965628i	$0.583699\pi$
$618$	31.4721	+	3.93121i	1.26599	+	0.158136i
$619$	−0.423157	+	0.355071i	−0.0170081	+	0.0142715i	−0.651252	−	0.758861i	$-0.725756\pi$
$619$	−0.423157	+	0.355071i	−0.0170081	+	0.0142715i	0.634244	+	0.773133i	$0.281311\pi$
$620$	−0.0960158	+	0.166304i	−0.00385609	+	0.00667894i
$621$	−15.2870	+	25.0835i	−0.613447	+	1.00657i
$622$	−39.7228			−1.59274
$623$	29.1339	−	6.46415i	1.16722	−	0.258981i
$624$	−0.0182360	−	0.0432127i	−0.000730023	−	0.00172989i
$625$	−3.89168	+	22.0708i	−0.155667	+	0.882833i
$626$	13.6856	+	11.4836i	0.546985	+	0.458975i
$627$	−1.00490	−	19.9751i	−0.0401320	−	0.797728i
$628$	0.190153	+	0.0692101i	0.00758794	+	0.00276178i
$629$	−0.278050	−	0.481597i	−0.0110866	−	0.0192025i
$630$	36.4001	+	1.09942i	1.45021	+	0.0438018i
$631$	−11.2617	+	19.5059i	−0.448322	+	0.776516i	−0.998277	−	0.0586779i	$-0.981311\pi$
$631$	−11.2617	+	19.5059i	−0.448322	+	0.776516i	0.549955	+	0.835194i	$0.314645\pi$
$632$	4.41785	−	3.70702i	0.175733	−	0.147457i
$633$	6.26027	+	6.74157i	0.248823	+	0.267953i
$634$	−4.17848	+	23.6973i	−0.165949	+	0.941141i
$635$	37.1625	+	31.1830i	1.47475	+	1.23746i
$636$	−0.0399436	−	0.0430145i	−0.00158387	−	0.00170564i
$637$	0.0122205	+	0.0455441i	0.000484195	+	0.00180452i
$638$	−33.2861	+	57.6532i	−1.31781	+	2.28251i
$639$	20.3456	+	5.16334i	0.804859	+	0.204259i
$640$	−36.8847			−1.45800
$641$	−5.05246	−	28.6539i	−0.199560	−	1.13176i	−0.905773	−	0.423763i	$-0.860709\pi$
$641$	−5.05246	−	28.6539i	−0.199560	−	1.13176i	0.706213	−	0.708000i	$-0.250402\pi$
$642$	−1.02140	−	20.3031i	−0.0403116	−	0.801299i
$643$	7.97294	−	45.2168i	0.314422	−	1.78318i	−0.261020	−	0.965333i	$-0.584059\pi$
$643$	7.97294	−	45.2168i	0.314422	−	1.78318i	0.575442	−	0.817842i	$-0.304830\pi$
$644$	0.0907285	−	0.118282i	0.00357520	−	0.00466098i
$645$	17.1781	+	2.14574i	0.676389	+	0.0844885i
$646$	−2.17796	−	12.3518i	−0.0856905	−	0.485975i
$647$	−4.49895	+	7.79241i	−0.176872	+	0.306351i	−0.940808	−	0.338941i	$-0.889931\pi$
$647$	−4.49895	+	7.79241i	−0.176872	+	0.306351i	0.763936	+	0.645293i	$0.223265\pi$
$648$	−22.3192	−	12.1082i	−0.876780	−	0.475657i
$649$	15.5008	+	26.8482i	0.608460	+	1.05388i
$650$	0.0491175	+	0.0178773i	0.00192655	+	0.000701206i
$651$	−24.6478	+	11.6984i	−0.966023	+	0.458495i
$652$	0.147719	+	0.123951i	0.00578514	+	0.00485431i
$653$	−38.1922	+	13.9008i	−1.49457	+	0.543981i	−0.954649	−	0.297732i	$-0.903770\pi$
$653$	−38.1922	+	13.9008i	−1.49457	+	0.543981i	−0.539925	+	0.841713i	$0.681547\pi$
$654$	7.43807	−	4.80822i	0.290851	−	0.188016i
$655$	−1.37220	−	7.78216i	−0.0536165	−	0.304074i
$656$	−16.1449	+	27.9637i	−0.630351	+	1.09180i
$657$	0.807954	+	2.86288i	0.0315213	+	0.111692i
$658$	16.4161	−	10.4622i	0.639967	−	0.407861i
$659$	−8.33564	−	47.2738i	−0.324711	−	1.84153i	−0.511701	−	0.859163i	$-0.670985\pi$
$659$	−8.33564	−	47.2738i	−0.324711	−	1.84153i	0.186991	−	0.982362i	$-0.440127\pi$
$660$	−0.0950385	+	0.308544i	−0.00369937	+	0.0120101i
$661$	−0.283344	+	1.60693i	−0.0110208	+	0.0625022i	−0.989822	−	0.142310i	$-0.954547\pi$
$661$	−0.283344	+	1.60693i	−0.0110208	+	0.0625022i	0.978801	+	0.204812i	$0.0656582\pi$
$662$	3.73141	−	21.1619i	0.145025	−	0.822479i
$663$	0.0503596	−	0.0115154i	0.00195581	−	0.000447221i
$664$	2.20591	+	12.5103i	0.0856059	+	0.485495i
$665$	14.4275	−	9.19489i	0.559476	−	0.356563i
$666$	0.481121	−	0.232169i	0.0186431	−	0.00899635i
$667$	22.9673	−	39.7806i	0.889299	−	1.54031i
$668$	−0.00994218	−	0.0563849i	−0.000384674	−	0.00218160i
$669$	−0.238885	−	4.74847i	−0.00923584	−	0.183587i
$670$	14.9830	−	5.45338i	0.578845	−	0.210682i
$671$	−14.0793	−	11.8139i	−0.543525	−	0.456072i
$672$	0.212644	+	0.146748i	0.00820293	+	0.00566094i
$673$	6.52093	+	2.37342i	0.251363	+	0.0914887i	0.464629	−	0.885506i	$-0.346188\pi$
$673$	6.52093	+	2.37342i	0.251363	+	0.0914887i	−0.213266	+	0.976994i	$0.568410\pi$
$674$	−18.3742	−	31.8251i	−0.707749	−	1.22586i
$675$	26.9468	−	9.08954i	1.03718	−	0.349857i
$676$	0.0647837	−	0.112209i	0.00249168	−	0.00431572i
$677$	−3.60943	−	20.4701i	−0.138722	−	0.786730i	−0.972195	−	0.234171i	$-0.924762\pi$
$677$	−3.60943	−	20.4701i	−0.138722	−	0.786730i	0.833474	−	0.552559i	$-0.186349\pi$
$678$	−14.3399	+	18.9470i	−0.550722	+	0.727657i
$679$	−10.2462	+	13.3580i	−0.393214	+	0.512631i
$680$	7.01969	−	39.8107i	0.269193	−	1.52667i
$681$	−4.86822	+	3.14698i	−0.186550	+	0.120593i
$682$	−8.47029	−	48.0374i	−0.324344	−	1.83945i
$683$	−41.4893			−1.58754			−0.793772	−	0.608216i	$-0.791886\pi$
$683$	−41.4893			−1.58754			−0.793772	+	0.608216i	$0.791886\pi$
$684$	0.0594434	−	0.00599611i	0.00227287	−	0.000229267i
$685$	−5.98852	+	10.3724i	−0.228809	+	0.396310i
$686$	−19.3678	−	17.7287i	−0.739466	−	0.676885i
$687$	47.9450	−	10.9633i	1.82921	−	0.418274i
$688$	9.51052	+	7.98027i	0.362585	+	0.304245i
$689$	0.00397767	−	0.0225585i	0.000151537	−	0.000859410i
$690$	13.2246	−	42.9339i	0.503452	−	1.63447i
$691$	−6.71271	+	5.63263i	−0.255364	+	0.214276i	−0.761478	−	0.648191i	$-0.775526\pi$
$691$	−6.71271	+	5.63263i	−0.255364	+	0.214276i	0.506114	+	0.862466i	$0.331081\pi$
$692$	0.00243139	−	0.00421129i	9.24275e−5	−	0.000160089i
$693$	−36.0119	+	28.4099i	−1.36798	+	1.07920i
$694$	19.9539	+	34.5612i	0.757440	+	1.31192i
$695$	18.0371	+	6.56497i	0.684186	+	0.249023i
$696$	35.3411	+	18.1005i	1.33960	+	0.686098i
$697$	−27.2438	−	22.8603i	−1.03193	−	0.865895i
$698$	1.23633	−	7.01156i	0.0467957	−	0.265392i
$699$	−8.34566	+	11.0269i	−0.315662	+	0.417077i
$700$	−0.140894	+	0.0312612i	−0.00532529	+	0.00118156i
$701$	−9.63663			−0.363970			−0.181985	−	0.983301i	$-0.558252\pi$
$701$	−9.63663			−0.363970			−0.181985	+	0.983301i	$0.558252\pi$
$702$	0.00745506	+	0.0490626i	0.000281373	+	0.00185175i
$703$	0.125485	−	0.217347i	0.00473277	−	0.00819739i
$704$	35.2373	−	29.5676i	1.32806	−	1.11437i
$705$	17.5553	−	23.1955i	0.661173	−	0.873593i
$706$	14.2556	+	11.9619i	0.536518	+	0.450192i
$707$	−24.9578	+	32.5374i	−0.938635	+	1.22370i
$708$	−0.0777731	+	0.0502752i	−0.00292289	+	0.00188946i
$709$	33.5168	+	12.1991i	1.25875	+	0.458148i	0.883349	−	0.468715i	$-0.155283\pi$
$709$	33.5168	+	12.1991i	1.25875	+	0.458148i	0.375401	+	0.926863i	$0.377505\pi$
$710$	−32.1020			−1.20477
$711$	−5.52289	+	2.66511i	−0.207124	+	0.0999495i
$712$	31.8229			1.19261
$713$	5.84448	+	33.1457i	0.218878	+	1.24132i
$714$	−20.2009	+	20.4778i	−0.755999	+	0.766361i
$715$	−0.118387	+	0.0430892i	−0.00442741	+	0.00161145i
$716$	0.202652	+	0.170046i	0.00757348	+	0.00635490i
$717$	20.1573	−	4.60924i	0.752789	−	0.172135i
$718$	3.60221	+	1.31110i	0.134433	+	0.0489297i
$719$	12.2923			0.458426			0.229213	−	0.973376i	$-0.426385\pi$
$719$	12.2923			0.458426			0.229213	+	0.973376i	$0.426385\pi$
$720$	37.8278	+	9.60002i	1.40976	+	0.357772i
$721$	−30.3144	−	15.7740i	−1.12897	−	0.587454i
$722$	−16.2988	+	13.6763i	−0.606577	+	0.508978i
$723$	0.290599	+	5.77642i	0.0108075	+	0.214827i
$724$	0.0249416	+	0.0209285i	0.000926948	+	0.000777802i
$725$	−41.7887	+	15.2099i	−1.55199	+	0.564880i
$726$	−21.3827	−	50.6694i	−0.793588	−	1.88052i
$727$	49.4183	+	17.9868i	1.83282	+	0.667094i	0.992072	+	0.125674i	$0.0401095\pi$
$727$	49.4183	+	17.9868i	1.83282	+	0.667094i	0.840753	+	0.541419i	$0.182113\pi$
$728$	0.00220214	+	0.0502364i	8.16167e−5	+	0.00186188i
$729$	19.8363	+	18.3172i	0.734678	+	0.678416i
$730$	−2.27469	−	3.93988i	−0.0841901	−	0.145821i
$731$	−10.4750	+	8.78956i	−0.387432	+	0.325094i
$732$	0.0331328	−	0.0437777i	0.00122462	−	0.00161807i
$733$	4.72845	−	26.8164i	0.174649	−	0.990486i	−0.763898	−	0.645336i	$-0.776717\pi$
$733$	4.72845	−	26.8164i	0.174649	−	0.990486i	0.938548	−	0.345149i	$-0.112172\pi$
$734$	2.66871	−	15.1350i	0.0985040	−	0.558644i
$735$	−36.3541	−	14.7619i	−1.34094	−	0.544500i
$736$	0.244158	−	0.204873i	0.00899979	−	0.00755172i
$737$	−10.0416	+	17.3926i	−0.369888	+	0.640665i
$738$	23.8352	−	24.4761i	0.877387	−	0.900977i
$739$	−14.1632	−	24.5314i	−0.521002	−	0.902401i	−0.999702	−	0.0244229i	$-0.992225\pi$
$739$	−14.1632	−	24.5314i	−0.521002	−	0.902401i	0.478700	−	0.877979i	$-0.341108\pi$
$740$	−0.00310341	+	0.00260407i	−0.000114084	+	9.57275e-5i
$741$	0.0158644	+	0.0170841i	0.000582794	+	0.000627601i
$742$	4.88307	+	11.7830i	0.179263	+	0.432566i
$743$	31.7652	−	11.5616i	1.16535	−	0.424154i	0.314346	−	0.949308i	$-0.398215\pi$
$743$	31.7652	−	11.5616i	1.16535	−	0.424154i	0.851007	+	0.525155i	$0.175993\pi$
$744$	−28.3617	+	6.48527i	−1.03979	+	0.237761i
$745$	20.1856	+	7.34696i	0.739544	+	0.269172i
$746$	−3.77303	−	6.53508i	−0.138141	−	0.239266i
$747$	0.998691	−	13.4708i	0.0365402	−	0.492871i
$748$	−0.127506	−	0.220847i	−0.00466209	−	0.00807498i
$749$	−6.58274	+	20.8905i	−0.240528	+	0.763322i
$750$	−3.15666	+	2.04057i	−0.115265	+	0.0745111i
$751$	51.4079	−	18.7109i	1.87590	−	0.682772i	0.917135	−	0.398578i	$-0.130496\pi$
$751$	51.4079	−	18.7109i	1.87590	−	0.682772i	0.958767	−	0.284195i	$-0.0917262\pi$
$752$	19.6038	−	7.13519i	0.714876	−	0.260194i
$753$	−0.413729	−	0.0516793i	−0.0150771	−	0.00188330i
$754$	−0.0134755	−	0.0764232i	−0.000490748	−	0.00278317i
$755$	−12.8683			−0.468326
$756$	−0.0901637	−	0.103175i	−0.00327922	−	0.00375243i
$757$	−8.90458			−0.323642			−0.161821	−	0.986820i	$-0.551737\pi$
$757$	−8.90458			−0.323642			−0.161821	+	0.986820i	$0.551737\pi$
$758$	0.327850	+	1.85933i	0.0119081	+	0.0675339i
$759$	22.0005	+	52.1332i	0.798567	+	1.89232i
$760$	17.1436	−	6.23977i	0.621865	−	0.226340i
$761$	25.2244	−	9.18092i	0.914383	−	0.332808i	0.158381	−	0.987378i	$-0.449372\pi$
$761$	25.2244	−	9.18092i	0.914383	−	0.332808i	0.756002	+	0.654570i	$0.227150\pi$
$762$	−1.84951	−	36.7639i	−0.0670007	−	1.33181i
$763$	−9.31618	+	2.06705i	−0.337268	+	0.0748323i
$764$	−0.0423839	−	0.0734111i	−0.00153340	−	0.00265592i
$765$	−17.6478	+	39.1949i	−0.638058	+	1.41710i
$766$	0.588631	+	1.01954i	0.0212681	+	0.0368374i
$767$	−0.0339587	−	0.0123600i	−0.00122618	−	0.000446293i
$768$	0.281917	+	0.303591i	0.0101728	+	0.0109549i
$769$	−29.5221	+	10.7452i	−1.06460	+	0.387481i	−0.814153	−	0.580650i	$-0.802798\pi$
$769$	−29.5221	+	10.7452i	−1.06460	+	0.387481i	−0.250443	+	0.968131i	$0.580576\pi$
$770$	42.6951	−	55.6614i	1.53862	−	2.00590i
$771$	−12.6207	+	2.88588i	−0.454522	+	0.103932i
$772$	−0.0552931	+	0.0463964i	−0.00199004	+	0.00166984i
$773$	14.4407	+	25.0121i	0.519397	+	0.899622i	0.999746	+	0.0225442i	$0.00717664\pi$
$773$	14.4407	+	25.0121i	0.519397	+	0.899622i	−0.480349	+	0.877077i	$0.659490\pi$
$774$	−7.67647	−	10.6594i	−0.275925	−	0.383143i
$775$	16.2921	−	28.2188i	0.585231	−	1.01365i
$776$	−13.7523	+	11.5395i	−0.493678	+	0.414245i
$777$	−0.573035	+	0.0540667i	−0.0205575	+	0.00193963i
$778$	1.73265	−	9.82636i	0.0621186	−	0.352292i
$779$	2.78711	−	15.8065i	0.0998584	−	0.566325i
$780$	−0.000146322	0	0.000346731i	−5.23917e−6	0	1.24149e-5i
$781$	30.9747	−	25.9908i	1.10836	−	0.930025i
$782$	17.7425	+	30.7309i	0.634470	+	1.09893i
$783$	−31.6900	−	27.8992i	−1.13251	−	0.997037i
$784$	−16.1478	−	23.0444i	−0.576707	−	0.823013i
$785$	−61.7427	−	22.4725i	−2.20369	−	0.802078i
$786$	−3.61856	+	4.78112i	−0.129070	+	0.170537i
$787$	−35.8552	+	13.0502i	−1.27810	+	0.465190i	−0.889803	−	0.456345i	$-0.849158\pi$
$787$	−35.8552	+	13.0502i	−1.27810	+	0.465190i	−0.388295	+	0.921535i	$0.626936\pi$
$788$	−0.165235	−	0.138649i	−0.00588626	−	0.00493915i
$789$	−42.5299	−	21.7824i	−1.51410	−	0.775473i
$790$	7.18433	−	6.02836i	0.255607	−	0.214480i
$791$	21.5901	−	13.7597i	0.767655	−	0.489239i
$792$	−44.0523	+	21.2578i	−1.56533	+	0.755363i
$793$	0.0214244			0.000760801
$794$	35.0188	+	12.7458i	1.24277	+	0.452332i
$795$	12.9697	+	13.9668i	0.459987	+	0.495352i
$796$	−0.00996012	−	0.00835753i	−0.000353027	−	0.000296225i
$797$	44.8444	−	16.3220i	1.58847	−	0.578156i	0.611446	−	0.791286i	$-0.290588\pi$
$797$	44.8444	−	16.3220i	1.58847	−	0.578156i	0.977024	+	0.213131i	$0.0683660\pi$
$798$	−12.5619	−	3.27448i	−0.444687	−	0.115915i
$799$	3.99001	+	22.6285i	0.141156	+	0.800537i
$800$	−0.308567			−0.0109095
$801$	−32.7984	−	8.32363i	−1.15887	−	0.294101i
$802$	19.2171			0.678579
$803$	5.38466	+	1.95986i	0.190021	+	0.0691618i
$804$	−0.0533967	−	0.0273480i	−0.00188316	−	0.000964490i
$805$	−29.4595	+	38.4062i	−1.03831	+	1.35364i
$806$	0.0435575	+	0.0365491i	0.00153425	+	0.00128739i
$807$	−12.1423	−	28.7730i	−0.427431	−	1.01286i
$808$	−33.4979	+	28.1081i	−1.17845	+	0.988839i
$809$	−14.1518	+	24.5116i	−0.497549	+	0.861781i	−0.999996	−	0.00282733i	$-0.999100\pi$
$809$	−14.1518	+	24.5116i	−0.497549	+	0.861781i	0.502447	+	0.864608i	$0.332433\pi$
$810$	−36.2955	−	19.6905i	−1.27529	−	0.691853i
$811$	41.9313			1.47241			0.736204	−	0.676759i	$-0.236616\pi$
$811$	41.9313			1.47241			0.736204	+	0.676759i	$0.236616\pi$
$812$	0.144783	+	0.157947i	0.00508088	+	0.00554287i
$813$	−1.80974	−	0.226057i	−0.0634705	−	0.00792817i
$814$	0.178694	−	1.01343i	0.00626323	−	0.0355205i
$815$	−47.9644	−	40.2469i	−1.68012	−	1.40979i
$816$	−25.8885	+	16.7352i	−0.906279	+	0.585850i
$817$	−5.79902	−	2.11067i	−0.202882	−	0.0738431i
$818$	27.3798	+	47.4233i	0.957313	+	1.65812i
$819$	0.0108702	−	0.0523523i	0.000379837	−	0.00182934i
$820$	−0.129543	+	0.224376i	−0.00452385	+	0.00783554i
$821$	−38.8205	+	32.5743i	−1.35485	+	1.13685i	−0.377309	+	0.926087i	$0.623150\pi$
$821$	−38.8205	+	32.5743i	−1.35485	+	1.13685i	−0.977537	+	0.210763i	$0.932405\pi$
$822$	8.85935	−	2.02581i	0.309005	−	0.0706581i
$823$	2.17471	−	12.3334i	0.0758057	−	0.429915i	−0.923159	−	0.384419i	$-0.874402\pi$
$823$	2.17471	−	12.3334i	0.0758057	−	0.429915i	0.998964	−	0.0454966i	$-0.0144870\pi$
$824$	−27.9152	−	23.4236i	−0.972472	−	0.816001i
$825$	16.1263	−	52.3544i	0.561446	−	1.82275i
$826$	19.6446	−	4.35869i	0.683522	−	0.151658i
$827$	16.5188	−	28.6115i	0.574416	−	0.994918i	−0.421689	−	0.906741i	$-0.638562\pi$
$827$	16.5188	−	28.6115i	0.574416	−	0.994918i	0.996105	−	0.0881773i	$-0.0281042\pi$
$828$	−0.152234	+	0.0734615i	−0.00529048	+	0.00255296i
$829$	−36.7431			−1.27614			−0.638071	−	0.769978i	$-0.720267\pi$
$829$	−36.7431			−1.27614			−0.638071	+	0.769978i	$0.720267\pi$
$830$	3.58726	+	20.3444i	0.124516	+	0.706163i
$831$	−9.61024	−	4.92204i	−0.333376	−	0.170744i
$832$	−0.00931108	+	0.0528058i	−0.000322804	+	0.00183071i
$833$	28.0841	−	13.1078i	0.973057	−	0.454157i
$834$	−5.66277	−	13.4187i	−0.196086	−	0.464653i
$835$	3.22822	+	18.3082i	0.111717	+	0.633580i
$836$	0.0575441	−	0.0996693i	0.00199020	−	0.00344713i
$837$	30.9274	+	0.734248i	1.06901	+	0.0253793i
$838$	4.56190	+	7.90145i	0.157588	+	0.272951i
$839$	36.7965	+	13.3928i	1.27036	+	0.462372i	0.887231	−	0.461325i	$-0.152626\pi$
$839$	36.7965	+	13.3928i	1.27036	+	0.462372i	0.383124	+	0.923697i	$0.374848\pi$
$840$	−34.4365	−	23.7651i	−1.18817	−	0.819972i
$841$	28.3614	+	23.7980i	0.977980	+	0.820622i
$842$	9.47189	−	3.44749i	0.326423	−	0.118808i
$843$	−29.1175	−	14.9130i	−1.00286	−	0.513632i
$844$	0.00919285	+	0.0521352i	0.000316431	+	0.00179457i
$845$	−21.0352	+	36.4341i	−0.723634	+	1.25337i
$846$	−21.9616	+	2.21528i	−0.755054	+	0.0761630i
$847$	2.59500	+	59.1986i	0.0891654	+	2.03409i
$848$	2.37359	+	13.4613i	0.0815094	+	0.462263i
$849$	−13.8818	−	14.9490i	−0.476421	−	0.513049i
$850$	5.96551	−	33.8321i	0.204615	−	1.16043i
$851$	−0.123299	+	0.699262i	−0.00422663	+	0.0239704i
$852$	0.0821907	+	0.0885097i	0.00281581	+	0.00303229i
$853$	−1.52501	−	8.64877i	−0.0522154	−	0.296128i	0.947506	−	0.319738i	$-0.103595\pi$
$853$	−1.52501	−	8.64877i	−0.0522154	−	0.296128i	−0.999721	+	0.0236102i	$0.992484\pi$
$854$	−10.0601	+	6.41144i	−0.344248	+	0.219395i
$855$	−19.3012	+	1.94693i	−0.660089	+	0.0665837i
$856$	−11.6783	+	20.2275i	−0.399157	+	0.691361i
$857$	−9.65282	−	54.7439i	−0.329734	−	1.87002i	−0.474071	−	0.880487i	$-0.657216\pi$
$857$	−9.65282	−	54.7439i	−0.329734	−	1.87002i	0.144337	−	0.989529i	$-0.453895\pi$
$858$	0.0850849	+	0.0435777i	0.00290475	+	0.00148772i
$859$	28.6669	−	10.4339i	0.978102	−	0.356000i	0.197000	−	0.980403i	$-0.436880\pi$
$859$	28.6669	−	10.4339i	0.978102	−	0.356000i	0.781102	+	0.624403i	$0.214658\pi$
$860$	0.0763107	+	0.0640323i	0.00260217	+	0.00218348i
$861$	−33.2545	+	15.7833i	−1.13331	+	0.537893i
$862$	42.9285	+	15.6247i	1.46215	+	0.532179i
$863$	−5.65975	−	9.80298i	−0.192660	−	0.333697i	0.753471	−	0.657481i	$-0.228378\pi$
$863$	−5.65975	−	9.80298i	−0.192660	−	0.333697i	−0.946131	+	0.323784i	$0.895045\pi$
$864$	−0.140416	−	0.257115i	−0.00477707	−	0.00874723i
$865$	−0.789471	+	1.36740i	−0.0268428	+	0.0464931i
$866$	7.11555	+	40.3543i	0.241796	+	1.37129i
$867$	−1.75271	−	4.15329i	−0.0595251	−	0.141053i
$868$	−0.155656	−	0.0204648i	−0.00528329	−	0.000694622i
$869$	−2.05127	+	11.6333i	−0.0695845	+	0.394633i
$870$	57.4718	+	29.4351i	1.94848	+	0.997945i
$871$	−0.00406523	−	0.0230551i	−0.000137745	−	0.000781192i
$872$	−10.1760			−0.344604
$873$	17.1921	−	8.29621i	0.581866	−	0.280784i
$874$	−8.00726	+	13.8690i	−0.270850	+	0.469125i
$875$	3.95372	−	0.877241i	0.133660	−	0.0296561i
$876$	−0.00503890	+	0.0163589i	−0.000170249	+	0.000552716i
$877$	4.83210	+	4.05461i	0.163168	+	0.136914i	0.720716	−	0.693230i	$-0.243813\pi$
$877$	4.83210	+	4.05461i	0.163168	+	0.136914i	−0.557548	+	0.830145i	$0.688258\pi$
$878$	−6.91453	+	39.2143i	−0.233354	+	1.32342i
$879$	−11.6650	+	2.66735i	−0.393450	+	0.0899674i
$880$	57.5901	−	48.3238i	1.94136	−	1.62900i
$881$	−8.18550	+	14.1777i	−0.275777	+	0.477659i	−0.970331	−	0.241781i	$-0.922268\pi$
$881$	−8.18550	+	14.1777i	−0.275777	+	0.477659i	0.694554	+	0.719440i	$0.255602\pi$
$882$	10.5627	+	27.8357i	0.355663	+	0.937276i
$883$	12.2658	+	21.2450i	0.412778	+	0.714953i	0.995192	−	0.0979394i	$-0.0312251\pi$
$883$	12.2658	+	21.2450i	0.412778	+	0.714953i	−0.582414	+	0.812892i	$0.697892\pi$
$884$	0.000279337	0	0.000101670i	9.39512e−6	0	3.41954e-6i
$885$	25.2529	−	16.3243i	0.848867	−	0.548736i
$886$	−9.34933	−	7.84502i	−0.314097	−	0.263559i
$887$	−8.10196	+	45.9485i	−0.272037	+	1.54280i	0.476181	+	0.879347i	$0.342021\pi$
$887$	−8.10196	+	45.9485i	−0.272037	+	1.54280i	−0.748219	+	0.663452i	$0.769091\pi$
$888$	−0.609045	−	0.0760765i	−0.0204382	−	0.00255296i
$889$	−11.9197	+	37.8275i	−0.399774	+	1.26869i
$890$	51.7505			1.73468
$891$	50.9629	−	10.3870i	1.70732	−	0.347979i
$892$	0.0136794	−	0.0236934i	0.000458019	−	0.000793312i
$893$	−7.94377	+	6.66561i	−0.265828	+	0.223056i
$894$	−6.33730	−	15.0171i	−0.211951	−	0.502248i
$895$	−65.8012	−	55.2137i	−2.19949	−	1.84559i
$896$	−11.5447	−	27.8576i	−0.385681	−	0.930658i
$897$	−0.0587084	−	0.0300685i	−0.00196022	−	0.00100396i
$898$	−2.67347	−	0.973062i	−0.0892147	−	0.0324715i
$899$	−48.3762			−1.61344
$900$	0.158616	+	0.0402538i	0.00528719	+	0.00134179i
$901$	−15.0551			−0.501559
$902$	−11.4280	−	64.8116i	−0.380512	−	2.15799i
$903$	3.75606	+	13.6456i	0.124994	+	0.454097i
$904$	25.6546	−	9.33751i	0.853259	−	0.310561i
$905$	−8.09853	−	6.79548i	−0.269204	−	0.225889i
$906$	6.64426	+	7.15509i	0.220741	+	0.237712i
$907$	38.2999	+	13.9400i	1.27173	+	0.462871i	0.887688	−	0.460446i	$-0.152311\pi$
$907$	38.2999	+	13.9400i	1.27173	+	0.462871i	0.384039	+	0.923317i	$0.374533\pi$
$908$	−0.0333566			−0.00110698
$909$	41.8768	−	20.2080i	1.38896	−	0.670256i
$910$	0.00358113	+	0.0816946i	0.000118713	+	0.00270815i
$911$	−27.4029	+	22.9938i	−0.907899	+	0.761818i	−0.971718	−	0.236144i	$-0.924116\pi$
$911$	−27.4029	+	22.9938i	−0.907899	+	0.761818i	0.0638192	+	0.997961i	$0.479672\pi$
$912$	−12.3826	−	6.34195i	−0.410029	−	0.210003i
$913$	−19.9327	−	16.7255i	−0.659677	−	0.553535i
$914$	−29.4809	+	10.7302i	−0.975141	+	0.354922i
$915$	−10.7582	+	14.2146i	−0.355656	+	0.469920i
$916$	0.265943	+	0.0967954i	0.00878701	+	0.00319821i
$917$	5.44808	−	3.47214i	0.179911	−	0.114660i
$918$	30.9054	−	10.4248i	1.02003	−	0.344071i
$919$	−18.3669	−	31.8124i	−0.605867	−	1.04939i	−0.991914	−	0.126914i	$-0.959493\pi$
$919$	−18.3669	−	31.8124i	−0.605867	−	1.04939i	0.386046	−	0.922479i	$-0.373841\pi$
$920$	−39.5400	+	33.1780i	−1.30360	+	1.09385i
$921$	14.1831	+	33.6089i	0.467350	+	1.10745i
$922$	1.20415	−	6.82909i	0.0396566	−	0.224904i
$923$	−0.00818473	+	0.0464179i	−0.000269404	+	0.00152786i
$924$	−0.262778	+	0.0247935i	−0.00864476	+	0.000815646i
$925$	0.526593	−	0.441864i	0.0173143	−	0.0145284i
$926$	6.58686	−	11.4088i	0.216458	−	0.374915i
$927$	22.6442	+	31.4432i	0.743733	+	1.03273i
$928$	0.229057	+	0.396738i	0.00751915	+	0.0130236i
$929$	39.8408	−	33.4304i	1.30713	−	1.09682i	0.318270	−	0.948000i	$-0.396898\pi$
$929$	39.8408	−	33.4304i	1.30713	−	1.09682i	0.988865	−	0.148816i	$-0.0475462\pi$
$930$	−46.1219	+	10.5464i	−1.51240	+	0.345829i
$931$	11.4603	+	8.01862i	0.375596	+	0.262800i
$932$	−0.0747777	+	0.0272168i	−0.00244942	+	0.000891517i
$933$	−33.0226	−	35.5615i	−1.08111	−	1.16423i
$934$	44.6442	+	16.2492i	1.46080	+	0.531689i
$935$	41.4012	+	71.7090i	1.35397	+	2.34514i
$936$	0.0234090	−	0.0519904i	0.000765148	−	0.00169936i
$937$	−24.7191	−	42.8147i	−0.807537	−	1.39869i	−0.914565	−	0.404439i	$-0.867467\pi$
$937$	−24.7191	−	42.8147i	−0.807537	−	1.39869i	0.107028	−	0.994256i	$-0.465866\pi$
$938$	8.80833	+	9.60924i	0.287602	+	0.313753i
$939$	1.09663	+	21.7985i	0.0357873	+	0.711366i
$940$	0.157297	−	0.0572515i	0.00513047	−	0.00186734i
$941$	31.8322	−	11.5860i	1.03770	−	0.377692i	0.233692	−	0.972311i	$-0.424919\pi$
$941$	31.8322	−	11.5860i	1.03770	−	0.377692i	0.804008	+	0.594619i	$0.202697\pi$
$942$	19.3842	+	45.9336i	0.631572	+	1.49660i
$943$	7.88532	+	44.7198i	0.256781	+	1.45628i
$944$	21.5647			0.701870
$945$	29.2761	+	33.5008i	0.952352	+	1.08978i
$946$	−25.3039			−0.822699
$947$	−3.53441	−	20.0446i	−0.114853	−	0.651363i	−0.986823	−	0.161804i	$-0.948269\pi$
$947$	−3.53441	−	20.0446i	−0.114853	−	0.651363i	0.871970	−	0.489559i	$-0.162842\pi$
$948$	−0.0350150	−	0.00437377i	−0.00113724	−	0.000142053i
$949$	−0.00627682	+	0.00228457i	−0.000203754	+	7.41604e-5i
$950$	14.5691	−	5.30271i	0.472683	−	0.172043i
$951$	−24.6885	+	15.9595i	−0.800580	+	0.517522i
$952$	32.2646	−	7.15879i	1.04570	−	0.232018i
$953$	−19.3556	−	33.5249i	−0.626989	−	1.08598i	−0.988153	−	0.153475i	$-0.950954\pi$
$953$	−19.3556	−	33.5249i	−0.626989	−	1.08598i	0.361163	−	0.932503i	$-0.382380\pi$
$954$	1.06928	−	14.4229i	0.0346191	−	0.466959i
$955$	13.7620	+	23.8366i	0.445329	+	0.771333i
$956$	0.111809	+	0.0406953i	0.00361618	+	0.00131618i
$957$	−79.2852	+	18.1296i	−2.56293	+	0.586047i
$958$	42.4929	−	15.4662i	1.37288	−	0.499689i
$959$	−9.70826	−	1.27640i	−0.313496	−	0.0412170i
$960$	−30.3599	−	32.6940i	−0.979862	−	1.05520i
$961$	3.40580	−	2.85780i	0.109864	−	0.0921872i
$962$	0.000599779		0.00103885i	1.93377e−5		3.34938e-5i
$963$	17.3270	−	17.7929i	0.558356	−	0.573369i
$964$	−0.0166407	+	0.0288225i	−0.000535960	+	0.000928309i
$965$	17.9536	−	15.0649i	0.577948	−	0.484956i
$966$	36.5655	−	3.45001i	1.17648	−	0.111002i
$967$	−3.33492	+	18.9133i	−0.107244	+	0.608210i	0.883057	+	0.469267i	$0.155482\pi$
$967$	−3.33492	+	18.9133i	−0.107244	+	0.608210i	−0.990300	+	0.138943i	$0.955629\pi$
$968$	−10.9725	+	62.2280i	−0.352668	+	2.00008i
$969$	9.24725	−	12.2182i	0.297064	−	0.392505i
$970$	−22.3640	+	18.7656i	−0.718066	+	0.602529i
$971$	−26.6443	−	46.1494i	−0.855058	−	1.48100i	−0.876591	−	0.481235i	$-0.840188\pi$
$971$	−26.6443	−	46.1494i	−0.855058	−	1.48100i	0.0215336	−	0.999768i	$-0.493145\pi$
$972$	0.0386380	+	0.150485i	0.00123931	+	0.00482681i
$973$	0.687233	+	15.6775i	0.0220317	+	0.502598i
$974$	−49.7634	−	18.1124i	−1.59452	−	0.580359i
$975$	0.0248282	+	0.0588339i	0.000795140	+	0.00188419i
$976$	−12.0135	+	4.37257i	−0.384544	+	0.139962i
$977$	2.61506	+	2.19430i	0.0836632	+	0.0702017i	0.683660	−	0.729801i	$-0.260387\pi$
$977$	2.61506	+	2.19430i	0.0836632	+	0.0702017i	−0.599997	+	0.800002i	$0.704832\pi$
$978$	2.38711	+	47.4500i	0.0763312	+	1.51728i
$979$	−49.9331	+	41.8989i	−1.59587	+	1.33909i
$980$	−0.129567	−	0.184904i	−0.00413887	−	0.00590653i
$981$	10.4880	+	2.66166i	0.334856	+	0.0849803i
$982$	−18.2189			−0.581389
$983$	23.0548	+	8.39126i	0.735333	+	0.267640i	0.682421	−	0.730960i	$-0.260927\pi$
$983$	23.0548	+	8.39126i	0.735333	+	0.267640i	0.0529128	+	0.998599i	$0.483149\pi$
$984$	−38.2653	+	8.74986i	−1.21985	+	0.278935i
$985$	53.6518	+	45.0192i	1.70949	+	1.43443i
$986$	−47.9277	+	17.4442i	−1.52633	+	0.555538i
$987$	23.0134	+	5.99884i	0.732524	+	0.190945i
$988$	2.32960e−5	0	0.000132118i	7.41146e−7	0	4.20325e-6i
$989$	17.4596			0.555183
$990$	−71.6381	+	34.5695i	−2.27681	+	1.09869i
$991$	20.5940			0.654191			0.327095	−	0.944991i	$-0.393930\pi$
$991$	20.5940			0.654191			0.327095	+	0.944991i	$0.393930\pi$
$992$	−0.315423	−	0.114805i	−0.0100147	−	0.00364505i
$993$	22.0470	−	14.2519i	0.699640	−	0.452271i
$994$	−10.0477	−	24.2454i	−0.318695	−	0.769019i
$995$	3.23405	+	2.71369i	0.102526	+	0.0860297i
$996$	0.0469077	−	0.0619782i	0.00148633	−	0.00196385i
$997$	19.7008	−	16.5310i	0.623932	−	0.523541i	−0.275105	−	0.961414i	$-0.588713\pi$
$997$	19.7008	−	16.5310i	0.623932	−	0.523541i	0.899037	+	0.437873i	$0.144268\pi$
$998$	20.5771	−	35.6405i	0.651356	−	1.12818i
$999$	0.607816	+	0.237711i	0.0192304	+	0.00752085i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.u.a.4.17	✓	132
3.2	odd	2		567.2.u.a.550.6		132
7.2	even	3		189.2.w.a.58.17	yes	132
21.2	odd	6		567.2.w.a.226.6		132
27.7	even	9		189.2.w.a.88.17	yes	132
27.20	odd	18		567.2.w.a.424.6		132
189.128	odd	18		567.2.u.a.100.6		132
189.142	even	9	inner	189.2.u.a.142.17	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.4.17	✓	132	1.1	even	1	trivial
189.2.u.a.142.17	yes	132	189.142	even	9	inner
189.2.w.a.58.17	yes	132	7.2	even	3
189.2.w.a.88.17	yes	132	27.7	even	9
567.2.u.a.100.6		132	189.128	odd	18
567.2.u.a.550.6		132	3.2	odd	2
567.2.w.a.226.6		132	21.2	odd	6
567.2.w.a.424.6		132	27.20	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.246187 + 1.39619i) q^{2} +(-1.04527 + 1.38109i) q^{3} +(-0.00936568 + 0.00340883i) q^{4} +(3.04103 - 1.10685i) q^{5} +(-2.18560 - 1.11939i) q^{6} +(1.78778 + 1.95034i) q^{7} +(1.41067 + 2.44335i) q^{8} +(-0.814825 - 2.88722i) q^{9} +O(q^{10})\)	\(q+(0.246187 + 1.39619i) q^{2} +(-1.04527 + 1.38109i) q^{3} +(-0.00936568 + 0.00340883i) q^{4} +(3.04103 - 1.10685i) q^{5} +(-2.18560 - 1.11939i) q^{6} +(1.78778 + 1.95034i) q^{7} +(1.41067 + 2.44335i) q^{8} +(-0.814825 - 2.88722i) q^{9} +(2.29403 + 3.97338i) q^{10} +(-5.43045 - 1.97652i) q^{11} +(0.00508176 - 0.0164980i) q^{12} +(0.00633019 - 0.00230400i) q^{13} +(-2.28293 + 2.97624i) q^{14} +(-1.65004 + 5.35690i) q^{15} +(-3.07937 + 2.58390i) q^{16} +(-2.21375 - 3.83432i) q^{17} +(3.83053 - 1.84845i) q^{18} +(0.999072 - 1.73044i) q^{19} +(-0.0247083 + 0.0207327i) q^{20} +(-4.56231 + 0.430461i) q^{21} +(1.42270 - 8.06856i) q^{22} +(-0.981664 + 5.56729i) q^{23} +(-4.84901 - 0.605696i) q^{24} +(4.19256 - 3.51797i) q^{25} +(0.00477525 + 0.00827097i) q^{26} +(4.83923 + 1.89258i) q^{27} +(-0.0233922 - 0.0121720i) q^{28} +(-7.63544 - 2.77907i) q^{29} +(-7.88549 - 0.984985i) q^{30} +(5.59460 - 2.03627i) q^{31} +(-0.0431895 - 0.0362403i) q^{32} +(8.40604 - 5.43395i) q^{33} +(4.80846 - 4.03478i) q^{34} +(7.59544 + 3.95225i) q^{35} +(0.0174734 + 0.0242632i) q^{36} +0.125602 q^{37} +(2.66199 + 0.968887i) q^{38} +(-0.00343472 + 0.0111509i) q^{39} +(6.99430 + 5.86891i) q^{40} +(7.54818 - 2.74731i) q^{41} +(-1.72419 - 6.26390i) q^{42} +(-0.536306 - 3.04154i) q^{43} +0.0575975 q^{44} +(-5.67362 - 7.87826i) q^{45} -8.01469 q^{46} +(-4.87676 - 1.77500i) q^{47} +(-0.349829 - 6.95376i) q^{48} +(-0.607659 + 6.97358i) q^{49} +(5.94393 + 4.98755i) q^{50} +(7.60950 + 0.950512i) q^{51} +(-5.14326e-5 + 4.31571e-5i) q^{52} +(1.70019 - 2.94481i) q^{53} +(-1.45105 + 7.22243i) q^{54} -18.7019 q^{55} +(-2.24339 + 7.11946i) q^{56} +(1.34560 + 3.18859i) q^{57} +(2.00038 - 11.3447i) q^{58} +(-4.10949 - 3.44827i) q^{59} +(-0.00280696 - 0.0557957i) q^{60} +(2.98856 + 1.08775i) q^{61} +(4.22034 + 7.30985i) q^{62} +(4.17434 - 6.75092i) q^{63} +(-3.97987 + 6.89333i) q^{64} +(0.0167002 - 0.0140131i) q^{65} +(9.65631 + 10.3987i) q^{66} +(0.603468 - 3.42244i) q^{67} +(0.0338038 + 0.0283647i) q^{68} +(-6.66283 - 7.17509i) q^{69} +(-3.64822 + 11.5777i) q^{70} +(-3.49843 + 6.05945i) q^{71} +(5.90505 - 6.06382i) q^{72} -0.991568 q^{73} +(0.0309215 + 0.175365i) q^{74} +(0.476291 + 9.46753i) q^{75} +(-0.00345821 + 0.0196125i) q^{76} +(-5.85358 - 14.1248i) q^{77} +(-0.0164144 - 0.00205034i) q^{78} +(-0.354954 - 2.01305i) q^{79} +(-6.50449 + 11.2661i) q^{80} +(-7.67212 + 4.70516i) q^{81} +(5.69404 + 9.86237i) q^{82} +(4.23105 + 1.53998i) q^{83} +(0.0412618 - 0.0195837i) q^{84} +(-10.9761 - 9.21002i) q^{85} +(4.11455 - 1.49757i) q^{86} +(11.8192 - 7.64036i) q^{87} +(-2.83123 - 16.0567i) q^{88} +(5.63968 - 9.76821i) q^{89} +(9.60281 - 9.86100i) q^{90} +(0.0158106 + 0.00822698i) q^{91} +(-0.00978400 - 0.0554878i) q^{92} +(-3.03559 + 9.85510i) q^{93} +(1.27765 - 7.24589i) q^{94} +(1.12288 - 6.36816i) q^{95} +(0.0951959 - 0.0217678i) q^{96} +(1.10493 + 6.26639i) q^{97} +(-9.88606 + 0.868391i) q^{98} +(-1.28180 + 17.2895i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more