LMFDB - Embedded newform 189.2.u.a.4.5

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			4.5
Character	$\chi$	$=$	189.4
Dual form			189.2.u.a.142.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.310937 - 1.76341i) q^{2} +(0.625951 + 1.61499i) q^{3} +(-1.13356 + 0.412582i) q^{4} +(-0.00172074 + 0.000626297i) q^{5} +(2.65326 - 1.60597i) q^{6} +(2.59651 + 0.508047i) q^{7} +(-0.710598 - 1.23079i) q^{8} +(-2.21637 + 2.02181i) q^{9} +O(q^{10})$	\(q+(-0.310937 - 1.76341i) q^{2} +(0.625951 + 1.61499i) q^{3} +(-1.13356 + 0.412582i) q^{4} +(-0.00172074 + 0.000626297i) q^{5} +(2.65326 - 1.60597i) q^{6} +(2.59651 + 0.508047i) q^{7} +(-0.710598 - 1.23079i) q^{8} +(-2.21637 + 2.02181i) q^{9} +(0.00163946 + 0.00283963i) q^{10} +(2.74403 + 0.998747i) q^{11} +(-1.37587 - 1.57243i) q^{12} +(4.96182 - 1.80596i) q^{13} +(0.0885434 - 4.73670i) q^{14} +(-0.00208856 - 0.00238694i) q^{15} +(-3.79762 + 3.18658i) q^{16} +(-2.87705 - 4.98319i) q^{17} +(4.25443 + 3.27972i) q^{18} +(-0.0567992 + 0.0983790i) q^{19} +(0.00169216 - 0.00141989i) q^{20} +(0.804801 + 4.51135i) q^{21} +(0.907981 - 5.14941i) q^{22} +(-0.681306 + 3.86388i) q^{23} +(1.54291 - 1.91802i) q^{24} +(-3.83022 + 3.21394i) q^{25} +(-4.72746 - 8.18821i) q^{26} +(-4.65253 - 2.31386i) q^{27} +(-3.15292 + 0.495374i) q^{28} +(-5.71816 - 2.08124i) q^{29} +(-0.00355975 + 0.00442518i) q^{30} +(-3.79806 + 1.38238i) q^{31} +(4.62268 + 3.87889i) q^{32} +(0.104666 + 5.05675i) q^{33} +(-7.89285 + 6.62288i) q^{34} +(-0.00478610 + 0.000751974i) q^{35} +(1.67823 - 3.20627i) q^{36} -3.24950 q^{37} +(0.191144 + 0.0695707i) q^{38} +(6.02245 + 6.88285i) q^{39} +(0.00199359 + 0.00167282i) q^{40} +(7.51748 - 2.73614i) q^{41} +(7.70514 - 2.82194i) q^{42} +(0.0535565 + 0.303734i) q^{43} -3.52259 q^{44} +(0.00254754 - 0.00486710i) q^{45} +7.02546 q^{46} +(3.61594 + 1.31609i) q^{47} +(-7.52341 - 4.13846i) q^{48} +(6.48378 + 2.63830i) q^{49} +(6.85846 + 5.75493i) q^{50} +(6.24690 - 7.76563i) q^{51} +(-4.87942 + 4.09432i) q^{52} +(-7.14507 + 12.3756i) q^{53} +(-2.63365 + 8.92380i) q^{54} -0.00534727 q^{55} +(-1.21978 - 3.55679i) q^{56} +(-0.194434 - 0.0301495i) q^{57} +(-1.89210 + 10.7306i) q^{58} +(-6.17081 - 5.17793i) q^{59} +(0.00335231 + 0.00184403i) q^{60} +(-7.38012 - 2.68614i) q^{61} +(3.61867 + 6.26772i) q^{62} +(-6.78201 + 4.12363i) q^{63} +(0.445282 - 0.771251i) q^{64} +(-0.00740692 + 0.00621515i) q^{65} +(8.88459 - 1.75690i) q^{66} +(1.62756 - 9.23035i) q^{67} +(5.31728 + 4.46173i) q^{68} +(-6.66658 + 1.31830i) q^{69} +(0.00281422 + 0.00820606i) q^{70} +(-1.75785 + 3.04468i) q^{71} +(4.06337 + 1.29120i) q^{72} -3.09334 q^{73} +(1.01039 + 5.73022i) q^{74} +(-7.58800 - 4.17399i) q^{75} +(0.0237958 - 0.134953i) q^{76} +(6.61751 + 3.98736i) q^{77} +(10.2647 - 12.7602i) q^{78} +(-2.20314 - 12.4946i) q^{79} +(0.00453895 - 0.00786170i) q^{80} +(0.824604 - 8.96214i) q^{81} +(-7.16241 - 12.4057i) q^{82} +(3.21166 + 1.16895i) q^{83} +(-2.77359 - 4.78184i) q^{84} +(0.00807160 + 0.00677287i) q^{85} +(0.518956 - 0.188884i) q^{86} +(-0.218109 - 10.5375i) q^{87} +(-0.720656 - 4.08704i) q^{88} +(-3.32414 + 5.75758i) q^{89} +(-0.00937484 - 0.00297900i) q^{90} +(13.8010 - 2.16835i) q^{91} +(-0.821865 - 4.66103i) q^{92} +(-4.60993 - 5.26852i) q^{93} +(1.19649 - 6.78562i) q^{94} +(3.61219e-5 - 0.000204857i) q^{95} +(-3.37079 + 9.89356i) q^{96} +(1.79903 + 10.2028i) q^{97} +(2.63637 - 12.2539i) q^{98} +(-8.10107 + 3.33431i) 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 $

$2$	−0.310937	−	1.76341i	−0.219866	−	1.24692i	−0.872260	−	0.489042i	$-0.837346\pi$
$2$	−0.310937	−	1.76341i	−0.219866	−	1.24692i	0.652394	−	0.757880i	$-0.273765\pi$
$3$	0.625951	+	1.61499i	0.361393	+	0.932414i
$3$	0.625951	+	1.61499i	0.361393	+	0.932414i
$4$	−1.13356	+	0.412582i	−0.566780	+	0.206291i
$5$	−0.00172074		0.000626297i	−0.000769537		0.000280088i	−0.342405	−	0.939552i	$-0.611241\pi$
$5$	−0.00172074		0.000626297i	−0.000769537		0.000280088i	0.341635	+	0.939833i	$0.389019\pi$
$6$	2.65326	−	1.60597i	1.08319	−	0.655635i
$7$	2.59651	+	0.508047i	0.981390	+	0.192024i
$7$	2.59651	+	0.508047i	0.981390	+	0.192024i
$8$	−0.710598	−	1.23079i	−0.251234	−	0.435151i
$9$	−2.21637	+	2.02181i	−0.738790	+	0.673935i
$10$	0.00163946	+	0.00283963i	0.000518443	+	0.000897970i
$11$	2.74403	+	0.998747i	0.827357	+	0.301133i	0.720774	−	0.693170i	$-0.243787\pi$
$11$	2.74403	+	0.998747i	0.827357	+	0.301133i	0.106584	+	0.994304i	$0.466009\pi$
$12$	−1.37587	−	1.57243i	−0.397179	−	0.453921i
$13$	4.96182	−	1.80596i	1.37616	−	0.500882i	0.455150	−	0.890415i	$-0.349586\pi$
$13$	4.96182	−	1.80596i	1.37616	−	0.500882i	0.921013	+	0.389533i	$0.127364\pi$
$14$	0.0885434	−	4.73670i	0.0236642	−	1.26594i
$15$	−0.00208856	−	0.00238694i	−0.000539263	−	0.000616304i
$16$	−3.79762	+	3.18658i	−0.949404	+	0.796645i
$17$	−2.87705	−	4.98319i	−0.697786	−	1.20860i	−0.969232	−	0.246148i	$-0.920835\pi$
$17$	−2.87705	−	4.98319i	−0.697786	−	1.20860i	0.271446	−	0.962454i	$-0.412498\pi$
$18$	4.25443	+	3.27972i	1.00278	+	0.773038i
$19$	−0.0567992	+	0.0983790i	−0.0130306	+	0.0225697i	−0.872467	−	0.488673i	$-0.837481\pi$
$19$	−0.0567992	+	0.0983790i	−0.0130306	+	0.0225697i	0.859437	+	0.511242i	$0.170815\pi$
$20$	0.00169216	−	0.00141989i	0.000378378	−	0.000317497i
$21$	0.804801	+	4.51135i	0.175622	+	0.984458i
$22$	0.907981	−	5.14941i	0.193582	−	1.09786i
$23$	−0.681306	+	3.86388i	−0.142062	+	0.805674i	0.827617	+	0.561293i	$0.189696\pi$
$23$	−0.681306	+	3.86388i	−0.142062	+	0.805674i	−0.969679	+	0.244381i	$0.921415\pi$
$24$	1.54291	−	1.91802i	0.314946	−	0.391515i
$25$	−3.83022	+	3.21394i	−0.766044	+	0.642787i
$26$	−4.72746	−	8.18821i	−0.927132	−	1.60584i
$27$	−4.65253	−	2.31386i	−0.895380	−	0.445303i
$28$	−3.15292	+	0.495374i	−0.595845	+	0.0936168i
$29$	−5.71816	−	2.08124i	−1.06184	−	0.386477i	−0.248718	−	0.968576i	$-0.580009\pi$
$29$	−5.71816	−	2.08124i	−1.06184	−	0.386477i	−0.813118	+	0.582099i	$0.802232\pi$
$30$	−0.00355975	+	0.00442518i	−0.000649918	+	0.000807923i
$31$	−3.79806	+	1.38238i	−0.682152	+	0.248283i	−0.659771	−	0.751466i	$-0.729347\pi$
$31$	−3.79806	+	1.38238i	−0.682152	+	0.248283i	−0.0223808	+	0.999750i	$0.507125\pi$
$32$	4.62268	+	3.87889i	0.817182	+	0.685697i
$33$	0.104666	+	5.05675i	0.0182201	+	0.880267i
$34$	−7.89285	+	6.62288i	−1.35361	+	1.13582i
$35$	−0.00478610		0.000751974i	−0.000808999		0.000127107i
$36$	1.67823	−	3.20627i	0.279705	−	0.534379i
$37$	−3.24950			−0.534215			−0.267108	−	0.963667i	$-0.586068\pi$
$37$	−3.24950			−0.534215			−0.267108	+	0.963667i	$0.586068\pi$
$38$	0.191144	+	0.0695707i	0.0310076	+	0.0112859i
$39$	6.02245	+	6.88285i	0.964365	+	1.10214i
$40$	0.00199359	+	0.00167282i	0.000315215	+	0.000264497i
$41$	7.51748	−	2.73614i	1.17403	−	0.427313i	0.319943	−	0.947437i	$-0.396336\pi$
$41$	7.51748	−	2.73614i	1.17403	−	0.427313i	0.854091	+	0.520124i	$0.174114\pi$
$42$	7.70514	−	2.82194i	1.18893	−	0.435435i
$43$	0.0535565	+	0.303734i	0.00816729	+	0.0463190i	0.988619	−	0.150441i	$-0.0480692\pi$
$43$	0.0535565	+	0.303734i	0.00816729	+	0.0463190i	−0.980452	+	0.196760i	$0.936958\pi$
$44$	−3.52259			−0.531051
$45$	0.00254754	−	0.00486710i	0.000379765	−	0.000725544i
$46$	7.02546			1.03585
$47$	3.61594	+	1.31609i	0.527439	+	0.191972i	0.591994	−	0.805942i	$-0.298341\pi$
$47$	3.61594	+	1.31609i	0.527439	+	0.191972i	−0.0645555	+	0.997914i	$0.520563\pi$
$48$	−7.52341	−	4.13846i	−1.08591	−	0.597336i
$49$	6.48378	+	2.63830i	0.926254	+	0.376900i
$50$	6.85846	+	5.75493i	0.969932	+	0.813870i
$51$	6.24690	−	7.76563i	0.874742	−	1.08741i
$52$	−4.87942	+	4.09432i	−0.676654	+	0.567780i
$53$	−7.14507	+	12.3756i	−0.981451	+	1.69992i	−0.324699	+	0.945817i	$0.605263\pi$
$53$	−7.14507	+	12.3756i	−0.981451	+	1.69992i	−0.656752	+	0.754106i	$0.728070\pi$
$54$	−2.63365	+	8.92380i	−0.358394	+	1.21438i
$55$	−0.00534727			−0.000721026
$56$	−1.21978	−	3.55679i	−0.163000	−	0.475296i
$57$	−0.194434	−	0.0301495i	−0.0257535	−	0.00399340i
$58$	−1.89210	+	10.7306i	−0.248445	+	1.40900i
$59$	−6.17081	−	5.17793i	−0.803371	−	0.674109i	0.145645	−	0.989337i	$-0.453474\pi$
$59$	−6.17081	−	5.17793i	−0.803371	−	0.674109i	−0.949016	+	0.315228i	$0.897919\pi$
$60$	0.00335231	+	0.00184403i	0.000432782	+	0.000238064i
$61$	−7.38012	−	2.68614i	−0.944928	−	0.343926i	−0.176818	−	0.984244i	$-0.556580\pi$
$61$	−7.38012	−	2.68614i	−0.944928	−	0.343926i	−0.768110	+	0.640318i	$0.778803\pi$
$62$	3.61867	+	6.26772i	0.459572	+	0.796001i
$63$	−6.78201	+	4.12363i	−0.854453	+	0.519528i
$64$	0.445282	−	0.771251i	0.0556603	−	0.0964064i
$65$	−0.00740692	+	0.00621515i	−0.000918716	+	0.000770894i
$66$	8.88459	−	1.75690i	1.09362	−	0.216260i
$67$	1.62756	−	9.23035i	0.198838	−	1.12767i	−0.708008	−	0.706204i	$-0.750406\pi$
$67$	1.62756	−	9.23035i	0.198838	−	1.12767i	0.906846	−	0.421462i	$-0.138483\pi$
$68$	5.31728	+	4.46173i	0.644815	+	0.541064i
$69$	−6.66658	+	1.31830i	−0.802562	+	0.158704i
$70$	0.00281422	+	0.00820606i	0.000336364	+	0.000980812i
$71$	−1.75785	+	3.04468i	−0.208618	+	0.361337i	−0.951279	−	0.308330i	$-0.900230\pi$
$71$	−1.75785	+	3.04468i	−0.208618	+	0.361337i	0.742662	+	0.669667i	$0.233563\pi$
$72$	4.06337	+	1.29120i	0.478873	+	0.152169i
$73$	−3.09334			−0.362049			−0.181024	−	0.983479i	$-0.557941\pi$
$73$	−3.09334			−0.362049			−0.181024	+	0.983479i	$0.557941\pi$
$74$	1.01039	+	5.73022i	0.117456	+	0.666124i
$75$	−7.58800	−	4.17399i	−0.876186	−	0.481971i
$76$	0.0237958	−	0.134953i	0.00272957	−	0.0154801i
$77$	6.61751	+	3.98736i	0.754136	+	0.454402i
$78$	10.2647	−	12.7602i	1.16225	−	1.44481i
$79$	−2.20314	−	12.4946i	−0.247872	−	1.40575i	−0.813727	−	0.581248i	$-0.802565\pi$
$79$	−2.20314	−	12.4946i	−0.247872	−	1.40575i	0.565855	−	0.824505i	$-0.308546\pi$
$80$	0.00453895	−	0.00786170i	0.000507470	−	0.000878964i
$81$	0.824604	−	8.96214i	0.0916226	−	0.995794i
$82$	−7.16241	−	12.4057i	−0.790956	−	1.36998i
$83$	3.21166	+	1.16895i	0.352526	+	0.128309i	0.512212	−	0.858859i	$-0.328826\pi$
$83$	3.21166	+	1.16895i	0.352526	+	0.128309i	−0.159686	+	0.987168i	$0.551048\pi$
$84$	−2.77359	−	4.78184i	−0.302624	−	0.521742i
$85$	0.00807160	+	0.00677287i	0.000875487	+	0.000734621i
$86$	0.518956	−	0.188884i	0.0559604	−	0.0203679i
$87$	−0.218109	−	10.5375i	−0.0233838	−	1.12974i
$88$	−0.720656	−	4.08704i	−0.0768222	−	0.435680i
$89$	−3.32414	+	5.75758i	−0.352358	+	0.610302i	−0.986662	−	0.162781i	$-0.947953\pi$
$89$	−3.32414	+	5.75758i	−0.352358	+	0.610302i	0.634304	+	0.773084i	$0.281287\pi$
$90$	−0.00937484	−	0.00297900i	−0.000988194	−	0.000314014i
$91$	13.8010	−	2.16835i	1.44673	−	0.227305i
$92$	−0.821865	−	4.66103i	−0.0856854	−	0.485946i
$93$	−4.60993	−	5.26852i	−0.478027	−	0.546320i
$94$	1.19649	−	6.78562i	0.123408	−	0.699883i
$95$	3.61219e−5	0	0.000204857i	3.70603e−6	0	2.10179e-5i
$96$	−3.37079	+	9.89356i	−0.344030	+	1.00976i
$97$	1.79903	+	10.2028i	0.182664	+	1.03594i	0.928920	+	0.370280i	$0.120738\pi$
$97$	1.79903	+	10.2028i	0.182664	+	1.03594i	−0.746256	+	0.665659i	$0.768151\pi$
$98$	2.63637	−	12.2539i	0.266314	−	1.23783i
$99$	−8.10107	+	3.33431i	−0.814188	+	0.335111i
$100$	3.01577	−	5.22347i	0.301577	−	0.522347i
$101$	−0.438889	−	2.48906i	−0.0436711	−	0.247671i	0.955155	−	0.296105i	$-0.0956880\pi$
$101$	−0.438889	−	2.48906i	−0.0436711	−	0.247671i	−0.998826	+	0.0484343i	$0.984577\pi$
$102$	−15.6364	−	8.60125i	−1.54824	−	0.851651i
$103$	17.1586	−	6.24521i	1.69069	−	0.615359i	0.695974	−	0.718067i	$-0.254973\pi$
$103$	17.1586	−	6.24521i	1.69069	−	0.615359i	0.994712	+	0.102708i	$0.0327509\pi$
$104$	−5.74862	−	4.82366i	−0.563699	−	0.472999i
$105$	−0.00421029	−	0.00725880i	−0.000410883	−	0.000708387i
$106$	24.0450	+	8.75167i	2.33546	+	0.850038i
$107$	−0.926313	−	1.60442i	−0.0895501	−	0.155105i	0.817771	−	0.575544i	$-0.195210\pi$
$107$	−0.926313	−	1.60442i	−0.0895501	−	0.155105i	−0.907321	+	0.420438i	$0.861876\pi$
$108$	6.22858	+	0.703350i	0.599345	+	0.0676799i
$109$	3.47014	−	6.01046i	0.332379	−	0.575698i	−0.650599	−	0.759422i	$-0.725482\pi$
$109$	3.47014	−	6.01046i	0.332379	−	0.575698i	0.982978	+	0.183724i	$0.0588153\pi$
$110$	0.00166267	+	0.00942945i	0.000158529	+	0.000899063i
$111$	−2.03403	−	5.24791i	−0.193061	−	0.498109i
$112$	−11.4795	+	6.34463i	−1.08471	+	0.599511i
$113$	−0.915044	+	5.18947i	−0.0860801	+	0.488184i	0.911038	+	0.412322i	$0.135282\pi$
$113$	−0.915044	+	5.18947i	−0.0860801	+	0.488184i	−0.997118	+	0.0758624i	$0.975829\pi$
$114$	0.00729085	+	0.352243i	0.000682851	+	0.0329906i
$115$	−0.00124759	−	0.00707541i	−0.000116338	−	0.000659785i
$116$	7.34056			0.681554
$117$	−7.34595	+	14.0345i	−0.679133	+	1.29749i
$118$	−7.21209	+	12.4917i	−0.663927	+	1.14995i
$119$	−4.93860	−	14.4006i	−0.452721	−	1.32010i
$120$	−0.00145370	+	0.00426673i	−0.000132704	+	0.000389498i
$121$	−1.89426	−	1.58947i	−0.172206	−	0.144498i
$122$	−2.44203	+	13.8494i	−0.221091	+	1.25387i
$123$	9.12441	+	10.4280i	0.822720	+	0.940257i
$124$	3.73498	−	3.13402i	0.335412	−	0.281444i
$125$	0.00915584	−	0.0158584i	0.000818923	−	0.00141842i
$126$	9.38044	+	10.6773i	0.835676	+	0.951210i
$127$	−6.51690	−	11.2876i	−0.578281	−	1.00161i	−0.995677	−	0.0928873i	$-0.970390\pi$
$127$	−6.51690	−	11.2876i	−0.578281	−	1.00161i	0.417396	−	0.908725i	$-0.362943\pi$
$128$	9.84262	+	3.58242i	0.869973	+	0.316644i
$129$	−0.457003	+	0.276616i	−0.0402369	+	0.0243546i
$130$	0.0132630	+	0.0111289i	0.00116324	+	0.000976073i
$131$	0.927769	−	5.26164i	0.0810595	−	0.459711i	−0.917078	−	0.398708i	$-0.869459\pi$
$131$	0.927769	−	5.26164i	0.0810595	−	0.459711i	0.998138	−	0.0610036i	$-0.0194301\pi$
$132$	−2.20497	−	5.68894i	−0.191918	−	0.495159i
$133$	−0.197461	+	0.226586i	−0.0171220	+	0.0196475i
$134$	−16.7830			−1.44983
$135$	0.00945494	+	0.00106768i	0.000813752	+	9.18913e-5i
$136$	−4.08885	+	7.08209i	−0.350616	+	0.607285i
$137$	5.66784	−	4.75589i	0.484237	−	0.406323i	−0.367719	−	0.929937i	$-0.619861\pi$
$137$	5.66784	−	4.75589i	0.484237	−	0.406323i	0.851955	+	0.523614i	$0.175417\pi$
$138$	4.39759	+	11.3460i	0.374348	+	0.965838i
$139$	8.27992	+	6.94767i	0.702293	+	0.589294i	0.922425	−	0.386176i	$-0.126204\pi$
$139$	8.27992	+	6.94767i	0.702293	+	0.589294i	−0.220132	+	0.975470i	$0.570649\pi$
$140$	0.00511508	−	0.00282707i	0.000432304	−	0.000238931i
$141$	0.137924	+	6.66351i	0.0116153	+	0.561169i
$142$	5.91560	+	2.15310i	0.496426	+	0.180684i
$143$	15.4191			1.28941
$144$	1.97429	−	14.7407i	0.164524	−	1.22839i
$145$	0.0111429			0.000925369
$146$	0.961836	+	5.45485i	0.0796021	+	0.451446i
$147$	−0.202302	+	12.1227i	−0.0166856	+	0.999861i
$148$	3.68351	−	1.34069i	0.302782	−	0.110204i
$149$	5.37813	+	4.51279i	0.440594	+	0.369702i	0.835932	−	0.548834i	$-0.184928\pi$
$149$	5.37813	+	4.51279i	0.440594	+	0.369702i	−0.395338	+	0.918536i	$0.629372\pi$
$150$	−5.00108	+	14.6786i	−0.408337	+	1.19850i
$151$	−11.0412	−	4.01867i	−0.898521	−	0.327035i	−0.148861	−	0.988858i	$-0.547561\pi$
$151$	−11.0412	−	4.01867i	−0.898521	−	0.327035i	−0.749660	+	0.661823i	$0.769783\pi$
$152$	0.161446			0.0130950
$153$	16.4517	+	5.22777i	1.33004	+	0.422640i
$154$	4.97373	−	12.9092i	0.400795	−	1.04026i
$155$	0.00566968	−	0.00475743i	0.000455400	−	0.000382126i
$156$	−9.66655	−	5.31736i	−0.773943	−	0.425730i
$157$	16.7010	+	14.0138i	1.33289	+	1.11843i	0.983393	+	0.181486i	$0.0580908\pi$
$157$	16.7010	+	14.0138i	1.33289	+	1.11843i	0.349494	+	0.936939i	$0.386354\pi$
$158$	−21.3481	+	7.77008i	−1.69836	+	0.618154i
$159$	−24.4590	−	3.79267i	−1.93972	−	0.300778i
$160$	−0.0103837	−	0.00377937i	−0.000820907	−	0.000298786i
$161$	−3.73205	+	9.68648i	−0.294127	+	0.763401i
$162$	−16.0604	+	1.33255i	−1.26182	+	0.104695i
$163$	7.78249	+	13.4797i	0.609571	+	1.05581i	0.991311	+	0.131539i	$0.0419918\pi$
$163$	7.78249	+	13.4797i	0.609571	+	1.05581i	−0.381740	+	0.924270i	$0.624675\pi$
$164$	−7.39264	+	6.20316i	−0.577268	+	0.484385i
$165$	−0.00334713	−	0.00863578i	−0.000260574	−	0.000672294i
$166$	1.06272	−	6.02696i	0.0824828	−	0.467783i
$167$	−0.487765	+	2.76625i	−0.0377444	+	0.214059i	−0.997847	−	0.0655902i	$-0.979107\pi$
$167$	−0.487765	+	2.76625i	−0.0377444	+	0.214059i	0.960102	+	0.279649i	$0.0902181\pi$
$168$	4.98065	−	4.19630i	0.384265	−	0.323752i
$169$	11.3996	−	9.56543i	0.876895	−	0.735803i
$170$	0.00943361	−	0.0163395i	0.000723525	−	0.00125318i
$171$	−0.0730152	−	0.332881i	−0.00558362	−	0.0254561i
$172$	−0.186025	−	0.322204i	−0.0141842	−	0.0245678i
$173$	3.96049	−	3.32325i	0.301111	−	0.252662i	−0.479696	−	0.877435i	$-0.659253\pi$
$173$	3.96049	−	3.32325i	0.301111	−	0.252662i	0.780806	+	0.624773i	$0.214808\pi$
$174$	−18.5142	+	3.66112i	−1.40356	+	0.277549i
$175$	−11.5781	+	6.39910i	−0.875218	+	0.483727i
$176$	−13.6034	+	4.95122i	−1.02539	+	0.373213i
$177$	4.49966	−	13.2069i	0.338215	−	0.992692i
$178$	11.1866	+	4.07159i	0.838471	+	0.305178i
$179$	8.64845	+	14.9796i	0.646416	+	1.11962i	0.983973	+	0.178320i	$0.0570662\pi$
$179$	8.64845	+	14.9796i	0.646416	+	1.11962i	−0.337557	+	0.941305i	$0.609601\pi$
$180$	−0.000879711		0.00656822i	−6.55698e−5		0.000489566i
$181$	−3.02128	−	5.23301i	−0.224570	−	0.388966i	0.731620	−	0.681712i	$-0.238764\pi$
$181$	−3.02128	−	5.23301i	−0.224570	−	0.388966i	−0.956190	+	0.292746i	$0.905431\pi$
$182$	−8.11493	−	23.6626i	−0.601519	−	1.75399i
$183$	−0.281502	−	13.6002i	−0.0208092	−	1.00536i
$184$	5.23976	−	1.90712i	0.386280	−	0.140595i
$185$	0.00559154	−	0.00203515i	0.000411098	−	0.000149627i
$186$	−7.85718	+	9.76739i	−0.576117	+	0.716180i
$187$	−2.91777	−	16.5475i	−0.213368	−	1.21007i
$188$	−4.64188			−0.338544
$189$	−10.9048	−	8.37168i	−0.793208	−	0.608950i
$190$	−0.000372480	0		−2.70225e−5	0
$191$	0.638035	+	3.61848i	0.0461666	+	0.261824i	0.999151	−	0.0411952i	$-0.0131166\pi$
$191$	0.638035	+	3.61848i	0.0461666	+	0.261824i	−0.952985	+	0.303019i	$0.902005\pi$
$192$	1.52429	+	0.236360i	0.110006	+	0.0170578i
$193$	−0.130197	+	0.0473877i	−0.00937176	+	0.00341104i	−0.346702	−	0.937975i	$-0.612698\pi$
$193$	−0.130197	+	0.0473877i	−0.00937176	+	0.00341104i	0.337330	+	0.941386i	$0.390476\pi$
$194$	17.4324	−	6.34487i	1.25157	−	0.455535i
$195$	−0.0146738	−	0.00807172i	−0.00105081	−	0.000578028i
$196$	−8.43826	−	0.315584i	−0.602733	−	0.0225417i
$197$	11.3397	+	19.6410i	0.807923	+	1.39936i	0.914300	+	0.405038i	$0.132742\pi$
$197$	11.3397	+	19.6410i	0.807923	+	1.39936i	−0.106377	+	0.994326i	$0.533925\pi$
$198$	8.39869	+	13.2488i	0.596869	+	0.941549i
$199$	−13.8174	−	23.9324i	−0.979489	−	1.69652i	−0.664248	−	0.747512i	$-0.731248\pi$
$199$	−13.8174	−	23.9324i	−0.979489	−	1.69652i	−0.315240	−	0.949012i	$-0.602085\pi$
$200$	6.67743	+	2.43039i	0.472166	+	0.171854i
$201$	15.9257	−	3.14925i	1.12331	−	0.222131i
$202$	−4.25278	+	1.54789i	−0.299225	+	0.108909i
$203$	−13.7899	−	8.30907i	−0.967863	−	0.583182i
$204$	−3.87728	+	11.3802i	−0.271464	+	0.796771i
$205$	−0.0112220	+	0.00941635i	−0.000783776	+	0.000657666i
$206$	−16.3481	−	28.3158i	−1.13903	−	1.97286i
$207$	−6.30198	−	9.94125i	−0.438018	−	0.690965i
$208$	−13.0883	+	22.6696i	−0.907509	+	1.57185i
$209$	−0.254115	+	0.213227i	−0.0175775	+	0.0147492i
$210$	−0.0114911	+	0.00968152i	−0.000792963	+	0.000668089i
$211$	−2.79342	+	15.8423i	−0.192307	+	1.09063i	0.723895	+	0.689910i	$0.242350\pi$
$211$	−2.79342	+	15.8423i	−0.192307	+	1.09063i	−0.916202	+	0.400717i	$0.868761\pi$
$212$	2.99341	−	16.9764i	0.205588	−	1.16595i
$213$	−6.01744	−	0.933081i	−0.412308	−	0.0639336i
$214$	−2.54123	+	2.13235i	−0.173715	+	0.145764i
$215$	−0.000282384	0	0.000489104i	−1.92584e−5	0	3.33566e-5i
$216$	0.458197	+	7.37052i	0.0311763	+	0.501501i
$217$	−10.5640	+	1.65978i	−0.717134	+	0.112673i
$218$	−11.6779	−	4.25042i	−0.790929	−	0.287875i
$219$	−1.93628	−	4.99571i	−0.130842	−	0.337579i
$220$	0.00606145	−	0.00220619i	0.000408663	−	0.000148741i
$221$	−23.2748	−	19.5299i	−1.56563	−	1.31372i
$222$	−8.62178	+	5.21860i	−0.578656	+	0.350250i
$223$	11.3720	−	9.54222i	0.761524	−	0.638994i	−0.176999	−	0.984211i	$-0.556639\pi$
$223$	11.3720	−	9.54222i	0.761524	−	0.638994i	0.938523	+	0.345217i	$0.112195\pi$
$224$	10.0322	+	12.4201i	0.670304	+	0.829854i
$225$	1.99124	−	14.8672i	0.132749	−	0.991149i
$226$	9.43570			0.627654
$227$	12.3380	+	4.49065i	0.818899	+	0.298055i	0.717295	−	0.696770i	$-0.245380\pi$
$227$	12.3380	+	4.49065i	0.818899	+	0.298055i	0.101605	+	0.994825i	$0.467602\pi$
$228$	0.232842	−	0.0460438i	0.0154203	−	0.00304933i
$229$	−0.747003	−	0.626810i	−0.0493633	−	0.0414207i	0.617772	−	0.786357i	$-0.288035\pi$
$229$	−0.747003	−	0.626810i	−0.0493633	−	0.0414207i	−0.667136	+	0.744936i	$0.732480\pi$
$230$	−0.0120890	+	0.00440002i	−0.000797122	+	0.000290129i
$231$	−2.29730	+	13.1831i	−0.151151	+	0.867384i
$232$	1.50174	+	8.51679i	0.0985941	+	0.559155i
$233$	−0.741911			−0.0486042			−0.0243021	−	0.999705i	$-0.507736\pi$
$233$	−0.741911			−0.0486042			−0.0243021	+	0.999705i	$0.507736\pi$
$234$	27.0328	+	8.59010i	1.76719	+	0.561552i
$235$	−0.00704634			−0.000459653
$236$	9.13130	+	3.32352i	0.594397	+	0.216343i
$237$	18.7996	−	11.3790i	1.22116	−	0.739148i
$238$	−23.8586	+	13.1865i	−1.54653	+	0.854753i
$239$	16.7661	+	14.0684i	1.08451	+	0.910011i	0.996287	−	0.0860894i	$-0.0274371\pi$
$239$	16.7661	+	14.0684i	1.08451	+	0.910011i	0.0882220	+	0.996101i	$0.471882\pi$
$240$	0.0155377	+	0.00240932i	0.00100295	+	0.000155521i
$241$	−8.17887	+	6.86288i	−0.526847	+	0.442077i	−0.867011	−	0.498289i	$-0.833962\pi$
$241$	−8.17887	+	6.86288i	−0.526847	+	0.442077i	0.340164	+	0.940366i	$0.389517\pi$
$242$	−2.21390	+	3.83459i	−0.142315	+	0.246497i
$243$	14.9899	−	4.27814i	0.961603	−	0.274443i
$244$	9.47406			0.606515
$245$	−0.0128092		0.000479055i	−0.000818352		3.06057e-5i
$246$	15.5517	−	19.3325i	0.991539	−	1.23260i
$247$	−0.104159	+	0.590716i	−0.00662749	+	0.0375864i
$248$	4.40032	+	3.69231i	0.279421	+	0.234462i
$249$	0.122503	+	5.91850i	0.00776333	+	0.375070i
$250$	−0.0308118	−	0.0112146i	−0.00194871	−	0.000709272i
$251$	2.40742	+	4.16977i	0.151955	+	0.263194i	0.931946	−	0.362597i	$-0.118110\pi$
$251$	2.40742	+	4.16977i	0.151955	+	0.263194i	−0.779991	+	0.625790i	$0.784776\pi$
$252$	5.98648	−	7.47251i	0.377113	−	0.470724i
$253$	−5.72856	+	9.92216i	−0.360151	+	0.623801i
$254$	−17.8784	+	15.0017i	−1.12179	+	0.941292i
$255$	−0.00588569	+	0.0172750i	−0.000368576	+	0.00108180i
$256$	3.56614	−	20.2246i	0.222884	−	1.26404i
$257$	13.8604	+	11.6302i	0.864587	+	0.725475i	0.962951	−	0.269676i	$-0.0869165\pi$
$257$	13.8604	+	11.6302i	0.864587	+	0.725475i	−0.0983640	+	0.995151i	$0.531361\pi$
$258$	0.629887	+	0.719875i	0.0392150	+	0.0448175i
$259$	−8.43738	−	1.65090i	−0.524273	−	0.102582i
$260$	0.00583193	−	0.0101012i	0.000361681	−	0.000626450i
$261$	16.8814	−	6.94821i	1.04493	−	0.430083i
$262$	−9.56692			−0.591046
$263$	−1.29613	−	7.35070i	−0.0799226	−	0.453264i	−0.998337	−	0.0576444i	$-0.981641\pi$
$263$	−1.29613	−	7.35070i	−0.0799226	−	0.453264i	0.918415	−	0.395619i	$-0.129470\pi$
$264$	6.14943	−	3.72214i	0.378471	−	0.229082i
$265$	0.00454397	−	0.0257701i	0.000279134	−	0.00158305i
$266$	0.460963	+	0.277751i	0.0282634	+	0.0170300i
$267$	−11.3792	−	1.76448i	−0.696394	−	0.107985i
$268$	1.96334	+	11.1347i	0.119930	+	0.680157i
$269$	6.31420	−	10.9365i	0.384983	−	0.666811i	−0.606784	−	0.794867i	$-0.707541\pi$
$269$	6.31420	−	10.9365i	0.384983	−	0.666811i	0.991767	+	0.128056i	$0.0408739\pi$
$270$	−0.00105713	−	0.0170050i	−6.43350e−5	−	0.00103489i
$271$	−8.60359	−	14.9018i	−0.522631	−	0.905223i	−0.999653	−	0.0263318i	$-0.991617\pi$
$271$	−8.60359	−	14.9018i	−0.522631	−	0.905223i	0.477023	−	0.878891i	$-0.341716\pi$
$272$	26.8053	+	9.75632i	1.62531	+	0.591564i
$273$	12.1406	+	20.9311i	0.734781	+	1.26681i
$274$	−10.1489	−	8.51597i	−0.613120	−	0.514469i
$275$	−13.7202	+	4.99373i	−0.827357	+	0.301133i
$276$	7.01306	−	4.24488i	0.422137	−	0.255512i
$277$	4.75015	+	26.9394i	0.285409	+	1.61863i	0.703822	+	0.710376i	$0.251475\pi$
$277$	4.75015	+	26.9394i	0.285409	+	1.61863i	−0.418414	+	0.908257i	$0.637414\pi$
$278$	9.67709	−	16.7612i	0.580393	−	1.00527i
$279$	5.62301	−	10.7428i	0.336641	−	0.643155i
$280$	0.00432652	+	0.00535635i	0.000258559	+	0.000320103i
$281$	−2.21334	−	12.5525i	−0.132037	−	0.748817i	−0.976878	−	0.213799i	$-0.931416\pi$
$281$	−2.21334	−	12.5525i	−0.132037	−	0.748817i	0.844841	−	0.535017i	$-0.179695\pi$
$282$	11.7076	−	2.31515i	0.697179	−	0.137865i
$283$	−2.70525	+	15.3422i	−0.160811	+	0.912002i	0.792469	+	0.609912i	$0.208795\pi$
$283$	−2.70525	+	15.3422i	−0.160811	+	0.912002i	−0.953280	+	0.302090i	$0.902316\pi$
$284$	0.736443	−	4.17658i	0.0436999	−	0.247834i
$285$	0.000353453	0	6.98943e-5i	2.09367e−5	0	4.14018e-6i
$286$	−4.79438	−	27.1903i	−0.283497	−	1.60779i
$287$	20.9093	−	3.28519i	1.23424	−	0.193919i
$288$	−18.0879	+	0.749102i	−1.06584	+	0.0441412i
$289$	−8.05480	+	13.9513i	−0.473812	+	0.820666i
$290$	−0.00346475	−	0.0196496i	−0.000203457	−	0.00115386i
$291$	−15.3513	+	9.29188i	−0.899910	+	0.544699i
$292$	3.50649	−	1.27626i	0.205202	−	0.0746874i
$293$	−23.0618	−	19.3511i	−1.34728	−	1.13051i	−0.979690	−	0.200520i	$-0.935737\pi$
$293$	−23.0618	−	19.3511i	−1.34728	−	1.13051i	−0.367595	−	0.929986i	$-0.619819\pi$
$294$	21.4402	−	3.41265i	1.25042	−	0.199030i
$295$	0.0138613	+	0.00504508i	0.000807034	+	0.000293736i
$296$	2.30909	+	3.99946i	0.134213	+	0.232464i
$297$	−10.4557	−	10.9960i	−0.606704	−	0.638054i
$298$	6.28565	−	10.8871i	0.364118	−	0.630671i
$299$	3.59747	+	20.4023i	0.208047	+	1.17989i
$300$	10.3236	+	1.60080i	0.596031	+	0.0924222i
$301$	−0.0152509	+	0.815859i	−0.000879047	+	0.0470253i
$302$	−3.65346	+	20.7198i	−0.210233	+	1.19229i
$303$	3.74508	−	2.26683i	0.215149	−	0.130226i
$304$	−0.0977911	−	0.554601i	−0.00560870	−	0.0318085i
$305$	0.0143816			0.000823486
$306$	4.10329	−	30.6366i	0.234570	−	1.75138i
$307$	5.25664	−	9.10477i	0.300012	−	0.519637i	−0.676126	−	0.736786i	$-0.736342\pi$
$307$	5.25664	−	9.10477i	0.300012	−	0.519637i	0.976138	+	0.217149i	$0.0696758\pi$
$308$	−9.14646	−	1.78964i	−0.521168	−	0.101974i
$309$	20.8264	+	23.8017i	1.18477	+	1.35403i
$310$	−0.0101522	−	0.00851873i	−0.000576608	−	0.000483831i
$311$	3.40804	−	19.3279i	0.193252	−	1.09599i	−0.721634	−	0.692275i	$-0.756609\pi$
$311$	3.40804	−	19.3279i	0.193252	−	1.09599i	0.914886	−	0.403712i	$-0.132280\pi$
$312$	4.19181	−	12.3033i	0.237314	−	0.696539i
$313$	1.78384	−	1.49682i	0.100829	−	0.0846054i	−0.590980	−	0.806686i	$-0.701259\pi$
$313$	1.78384	−	1.49682i	0.100829	−	0.0846054i	0.691808	+	0.722081i	$0.256814\pi$
$314$	19.5192	−	33.8082i	1.10153	−	1.90791i
$315$	0.00908744	−	0.0113432i	0.000512019	−	0.000639118i
$316$	7.65243	+	13.2544i	0.430483	+	0.745619i
$317$	−24.4267	−	8.89060i	−1.37194	−	0.499346i	−0.452217	−	0.891908i	$-0.649367\pi$
$317$	−24.4267	−	8.89060i	−1.37194	−	0.499346i	−0.919726	+	0.392562i	$0.871589\pi$
$318$	0.917156	+	44.3105i	0.0514315	+	2.48481i
$319$	−13.6122	−	11.4220i	−0.762137	−	0.639509i
$320$	−0.000283181		0.00160600i	−1.58303e−5		8.97780e-5i
$321$	2.01130	−	2.50027i	0.112260	−	0.139552i
$322$	18.2417	+	3.56926i	1.01657	+	0.198907i
$323$	0.653655			0.0363704
$324$	2.76288	+	10.4993i	0.153493	+	0.583297i
$325$	−13.2006	+	22.8642i	−0.732240	+	1.26828i
$326$	21.3504	−	17.9151i	1.18249	−	0.992224i
$327$	11.8790	+	1.84198i	0.656908	+	0.101862i
$328$	−8.70953	−	7.30816i	−0.480903	−	0.403526i
$329$	8.72020	+	5.25432i	0.480760	+	0.289680i
$330$	−0.0141877	+	0.00858756i	−0.000781007	+	0.000472729i
$331$	−24.5229	−	8.92560i	−1.34790	−	0.490595i	−0.435608	−	0.900137i	$-0.643466\pi$
$331$	−24.5229	−	8.92560i	−1.34790	−	0.490595i	−0.912292	+	0.409541i	$0.865689\pi$
$332$	−4.12290			−0.226274
$333$	7.20211	−	6.56986i	0.394673	−	0.360026i
$334$	5.02971			0.275213
$335$	0.00298034	+	0.0169023i	0.000162833	+	0.000923473i
$336$	−17.4321	−	14.5678i	−0.950999	−	0.794740i
$337$	−20.5364	+	7.47462i	−1.11869	+	0.407169i	−0.834173	−	0.551503i	$-0.814054\pi$
$337$	−20.5364	+	7.47462i	−1.11869	+	0.407169i	−0.284514	+	0.958672i	$0.591832\pi$
$338$	−20.4124	−	17.1280i	−1.11029	−	0.931642i
$339$	−8.95370	+	1.77057i	−0.486298	+	0.0961641i
$340$	−0.0119440	−	0.00434726i	−0.000647754	−	0.000235763i
$341$	−11.8027			−0.639150
$342$	−0.564304	+	0.232261i	−0.0305141	+	0.0125593i
$343$	15.4948	+	10.1445i	0.836643	+	0.547749i
$344$	0.335776	−	0.281750i	0.0181038	−	0.0151909i
$345$	0.0106458	−	0.00644369i	0.000573149	−	0.000346917i
$346$	−7.09173	−	5.95067i	−0.381254	−	0.319910i
$347$	32.0887	−	11.6793i	1.72261	−	0.626980i	0.724551	−	0.689221i	$-0.242047\pi$
$347$	32.0887	−	11.6793i	1.72261	−	0.626980i	0.998061	+	0.0622414i	$0.0198249\pi$
$348$	4.59483	+	11.8549i	0.246309	+	0.635490i
$349$	−14.6096	−	5.31745i	−0.782032	−	0.284636i	−0.0800123	−	0.996794i	$-0.525496\pi$
$349$	−14.6096	−	5.31745i	−0.782032	−	0.284636i	−0.702020	+	0.712157i	$0.747718\pi$
$350$	14.8843	+	18.4272i	0.795600	+	0.984974i
$351$	−27.2638	−	3.07871i	−1.45523	−	0.164329i
$352$	8.81076	+	15.2607i	0.469615	+	0.813397i
$353$	−1.15956	+	0.972982i	−0.0617169	+	0.0517866i	−0.673124	−	0.739529i	$-0.735048\pi$
$353$	−1.15956	+	0.972982i	−0.0617169	+	0.0517866i	0.611407	+	0.791316i	$0.290604\pi$
$354$	−24.6884	−	3.82824i	−1.31217	−	0.203469i
$355$	0.00111792	−	0.00634002i	5.93328e−5	−	0.000336493i
$356$	1.39264	−	7.89804i	0.0738097	−	0.418595i
$357$	20.1655	−	16.9898i	1.06727	−	0.899198i
$358$	23.7260	−	19.9085i	1.25396	−	1.05220i
$359$	−1.62355	+	2.81207i	−0.0856876	+	0.148415i	−0.905684	−	0.423953i	$-0.860642\pi$
$359$	−1.62355	+	2.81207i	−0.0856876	+	0.148415i	0.819996	+	0.572369i	$0.193975\pi$
$360$	−0.00780067		0.000323060i	−0.000411131		1.70268e-5i
$361$	9.49355	+	16.4433i	0.499660	+	0.865437i
$362$	−8.28853	+	6.95490i	−0.435635	+	0.365541i
$363$	1.38127	−	4.05414i	0.0724977	−	0.212787i
$364$	−14.7496	+	8.15198i	−0.773088	+	0.427280i
$365$	0.00532283	−	0.00193735i	0.000278610	−	0.000101406i
$366$	−23.8952	+	4.72521i	−1.24902	+	0.246991i
$367$	−5.97923	−	2.17626i	−0.312113	−	0.113600i	0.181214	−	0.983444i	$-0.441997\pi$
$367$	−5.97923	−	2.17626i	−0.312113	−	0.113600i	−0.493327	+	0.869844i	$0.664220\pi$
$368$	−9.72521	−	16.8446i	−0.506962	−	0.878083i
$369$	−11.1296	+	21.2632i	−0.579383	+	1.10692i
$370$	−0.00532743	−	0.00922739i	−0.000276960	−	0.000479709i
$371$	−24.8397	+	28.5035i	−1.28961	+	1.47983i
$372$	7.39933	+	4.07021i	0.383637	+	0.211031i
$373$	−17.8704	+	6.50428i	−0.925293	+	0.336779i	−0.760342	−	0.649523i	$-0.774969\pi$
$373$	−17.8704	+	6.50428i	−0.925293	+	0.336779i	−0.164951	+	0.986302i	$0.552746\pi$
$374$	−28.2728	+	10.2905i	−1.46195	+	0.532107i
$375$	0.0313422	+	0.00486001i	0.00161850	+	0.000250970i
$376$	−0.949641	−	5.38568i	−0.0489740	−	0.277745i
$377$	−32.1311			−1.65484
$378$	−11.3720	+	21.8328i	−0.584914	+	1.12296i
$379$	21.5974			1.10938			0.554691	−	0.832057i	$-0.312837\pi$
$379$	21.5974			1.10938			0.554691	+	0.832057i	$0.312837\pi$
$380$	4.35742e−5	0	0.000247121i	2.23531e−6	0	1.26771e-5i
$381$	14.1501	−	17.5902i	0.724930	−	0.901173i
$382$	6.18248	−	2.25024i	0.316323	−	0.115132i
$383$	21.1775	−	7.70799i	1.08212	−	0.393860i	0.261425	−	0.965224i	$-0.415808\pi$
$383$	21.1775	−	7.70799i	1.08212	−	0.393860i	0.820697	+	0.571364i	$0.193586\pi$
$384$	0.375429	+	18.1381i	0.0191586	+	0.925607i
$385$	−0.0138843	−	0.00271666i	−0.000707608	−	0.000138454i
$386$	0.124047	+	0.214856i	0.00631384	+	0.0109359i
$387$	−0.732792	−	0.564906i	−0.0372499	−	0.0287158i
$388$	−6.24881	−	10.8233i	−0.317235	−	0.549467i
$389$	−3.17737	−	1.15647i	−0.161099	−	0.0586353i	0.260212	−	0.965552i	$-0.416208\pi$
$389$	−3.17737	−	1.15647i	−0.161099	−	0.0586353i	−0.421311	+	0.906916i	$0.638430\pi$
$390$	−0.00967115	+	0.0283857i	−0.000489718	+	0.00143737i
$391$	21.2146	−	7.72148i	1.07287	−	0.390492i
$392$	−1.36016	−	9.85495i	−0.0686983	−	0.497750i
$393$	9.07822	−	1.79519i	0.457936	−	0.0905554i
$394$	31.1093	−	26.1038i	1.56726	−	1.31509i
$395$	0.0116163	+	0.0201201i	0.000584482	+	0.00101235i
$396$	7.80737	−	7.12200i	0.392335	−	0.357894i
$397$	−12.5390	+	21.7183i	−0.629316	+	1.09001i	0.358373	+	0.933579i	$0.383332\pi$
$397$	−12.5390	+	21.7183i	−0.629316	+	1.09001i	−0.987689	+	0.156429i	$0.950002\pi$
$398$	−37.9064	+	31.8072i	−1.90008	+	1.59435i
$399$	−0.489534	−	0.177065i	−0.0245074	−	0.00886436i
$400$	4.30425	−	24.4106i	0.215212	−	1.22053i
$401$	4.72763	−	26.8117i	0.236087	−	1.33891i	−0.604227	−	0.796812i	$-0.706518\pi$
$401$	4.72763	−	26.8117i	0.236087	−	1.33891i	0.840313	−	0.542101i	$-0.182371\pi$
$402$	−10.5053	−	27.1043i	−0.523958	−	1.35184i
$403$	−16.3488	+	13.7183i	−0.814391	+	0.683356i
$404$	1.52445	+	2.64042i	0.0758442	+	0.131366i
$405$	0.00419404	+	0.0159379i	0.000208403	+	0.000791962i
$406$	−10.3645	+	26.9009i	−0.514382	+	1.33507i
$407$	−8.91675	−	3.24543i	−0.441987	−	0.160870i
$408$	−13.9969	−	2.17040i	−0.692951	−	0.107451i
$409$	28.1524	−	10.2466i	1.39205	−	0.506664i	0.466240	−	0.884658i	$-0.345608\pi$
$409$	28.1524	−	10.2466i	1.39205	−	0.506664i	0.925808	+	0.377994i	$0.123386\pi$
$410$	0.0200943	+	0.0168611i	0.000992384	+	0.000832709i
$411$	11.2285	+	6.17655i	0.553860	+	0.304667i
$412$	−16.8736	+	14.1586i	−0.831303	+	0.697546i
$413$	−13.3920	−	16.5796i	−0.658976	−	0.815830i
$414$	−15.5710	+	14.2041i	−0.765274	+	0.698094i
$415$	−0.00625854			−0.000307219
$416$	29.9420	+	10.8980i	1.46803	+	0.534318i
$417$	−6.03759	+	17.7209i	−0.295662	+	0.867794i
$418$	0.455022	+	0.381809i	0.0222558	+	0.0186749i
$419$	−10.6765	+	3.88594i	−0.521583	+	0.189841i	−0.589376	−	0.807859i	$-0.700626\pi$
$419$	−10.6765	+	3.88594i	−0.521583	+	0.189841i	0.0677934	+	0.997699i	$0.478404\pi$
$420$	0.00776747	+	0.00649119i	0.000379014	+	0.000316738i
$421$	1.69681	+	9.62307i	0.0826973	+	0.469000i	0.997830	+	0.0658463i	$0.0209747\pi$
$421$	1.69681	+	9.62307i	0.0826973	+	0.469000i	−0.915133	+	0.403153i	$0.867914\pi$
$422$	28.8051			1.40221
$423$	−10.6752	+	4.39377i	−0.519044	+	0.213633i
$424$	20.3091			0.986297
$425$	27.0354	+	9.84007i	1.31141	+	0.477314i
$426$	0.225640	+	10.9014i	0.0109323	+	0.528173i
$427$	−17.7979	−	10.7241i	−0.861301	−	0.518974i
$428$	1.71199	+	1.43653i	0.0827520	+	0.0694372i
$429$	9.65160	+	24.9017i	0.465984	+	1.20226i
$430$	−0.000774688	0	0.000650041i	−3.73588e−5	0	3.13477e-5i
$431$	−7.18150	+	12.4387i	−0.345921	+	0.599152i	−0.985521	−	0.169556i	$-0.945767\pi$
$431$	−7.18150	+	12.4387i	−0.345921	+	0.599152i	0.639600	+	0.768708i	$0.279100\pi$
$432$	25.0418	−	6.03850i	1.20483	−	0.290527i
$433$	34.1628			1.64176			0.820880	−	0.571100i	$-0.193483\pi$
$433$	34.1628			1.64176			0.820880	+	0.571100i	$0.193483\pi$
$434$	6.21163	+	18.1127i	0.298168	+	0.869436i
$435$	0.00697492	+	0.0179957i	0.000334422	+	0.000862827i
$436$	−1.45380	+	8.24493i	−0.0696246	+	0.394861i
$437$	−0.341427	−	0.286491i	−0.0163327	−	0.0137047i
$438$	−8.20745	+	4.96782i	−0.392167	+	0.237372i
$439$	25.5052	+	9.28313i	1.21730	+	0.443060i	0.869229	−	0.494410i	$-0.164616\pi$
$439$	25.5052	+	9.28313i	1.21730	+	0.443060i	0.348067	+	0.937470i	$0.386838\pi$
$440$	0.00379976	+	0.00658138i	0.000181146	+	0.000313755i
$441$	−19.7046	+	7.26148i	−0.938314	+	0.345785i
$442$	−27.2023	+	47.1157i	−1.29388	+	2.24107i
$443$	−21.3846	+	17.9438i	−1.01601	+	0.852534i	−0.989121	−	0.147104i	$-0.953005\pi$
$443$	−21.3846	+	17.9438i	−1.01601	+	0.852534i	−0.0268898	+	0.999638i	$0.508560\pi$
$444$	4.47089	+	5.10961i	0.212179	+	0.242492i
$445$	0.00211401	−	0.0119892i	0.000100214	−	0.000568341i
$446$	−20.3629	−	17.0865i	−0.964209	−	0.809067i
$447$	−3.92165	+	11.5104i	−0.185488	+	0.544423i
$448$	1.54801	−	1.77634i	0.0731367	−	0.0839242i
$449$	15.0828	−	26.1241i	0.711801	−	1.23287i	−0.252380	−	0.967628i	$-0.581213\pi$
$449$	15.0828	−	26.1241i	0.711801	−	1.23287i	0.964181	−	0.265247i	$-0.0854534\pi$
$450$	−26.8362	+	1.11141i	−1.26507	+	0.0523923i
$451$	23.3609			1.10002
$452$	−1.10383	−	6.26011i	−0.0519196	−	0.294451i
$453$	−0.421148	−	20.3469i	−0.0197872	−	0.955981i
$454$	4.08254	−	23.1532i	0.191603	−	1.08664i
$455$	−0.0223898	+	0.0123747i	−0.00104965	+	0.000580133i
$456$	0.101057	+	0.260733i	0.00473242	+	0.0122099i
$457$	−4.26288	−	24.1760i	−0.199409	−	1.13091i	−0.905998	−	0.423282i	$-0.860878\pi$
$457$	−4.26288	−	24.1760i	−0.199409	−	1.13091i	0.706589	−	0.707624i	$-0.250233\pi$
$458$	−0.873053	+	1.51217i	−0.0407951	+	0.0706592i
$459$	1.85513	+	29.8415i	0.0865902	+	1.39288i
$460$	0.00433340	+	0.00750567i	0.000202046	+	0.000349954i
$461$	−29.7613	−	10.8322i	−1.38612	−	0.504507i	−0.462094	−	0.886831i	$-0.652902\pi$
$461$	−29.7613	−	10.8322i	−1.38612	−	0.504507i	−0.924028	+	0.382324i	$0.875124\pi$
$462$	23.9616	−	0.0480315i	1.11479	−	0.00223463i
$463$	−14.4821	−	12.1519i	−0.673038	−	0.564746i	0.240925	−	0.970544i	$-0.422549\pi$
$463$	−14.4821	−	12.1519i	−0.673038	−	0.564746i	−0.913963	+	0.405798i	$0.866994\pi$
$464$	28.3474	−	10.3176i	1.31600	−	0.478983i
$465$	0.0112321	+	0.00617855i	0.000520878	+	0.000286523i
$466$	0.230688	+	1.30830i	0.0106864	+	0.0606056i
$467$	5.79658	−	10.0400i	0.268234	−	0.464595i	−0.700172	−	0.713974i	$-0.746893\pi$
$467$	5.79658	−	10.0400i	0.268234	−	0.464595i	0.968406	+	0.249380i	$0.0802267\pi$
$468$	2.53669	−	18.9398i	0.117258	−	0.875491i
$469$	8.91543	−	23.1399i	0.411676	−	1.06850i
$470$	0.00219097	+	0.0124256i	0.000101062	+	0.000573151i
$471$	−12.1781	+	35.7439i	−0.561139	+	1.64699i
$472$	−1.98798	+	11.2744i	−0.0915043	+	0.518947i
$473$	−0.156392	+	0.886946i	−0.00719093	+	0.0407818i
$474$	−25.9115	−	29.6133i	−1.19015	−	1.36018i
$475$	−0.0986306	−	0.559362i	−0.00452548	−	0.0256653i
$476$	11.5396	+	14.2864i	0.528918	+	0.654815i
$477$	−9.18498	−	41.8749i	−0.420552	−	1.91732i
$478$	19.5953	−	33.9400i	0.896266	−	1.55238i
$479$	−1.15008	−	6.52246i	−0.0525487	−	0.298019i	0.947195	−	0.320658i	$-0.103904\pi$
$479$	−1.15008	−	6.52246i	−0.0525487	−	0.298019i	−0.999744	+	0.0226396i	$0.992793\pi$
$480$	−0.000396070	−	0.0191353i	−1.80780e−5	−	0.000873404i
$481$	−16.1235	+	5.86846i	−0.735167	+	0.267579i
$482$	14.6452	+	12.2888i	0.667071	+	0.559739i
$483$	−17.9796	+	0.0360405i	−0.818101	+	0.00163990i
$484$	2.80305	+	1.02023i	0.127411	+	0.0463739i
$485$	−0.00948565	−	0.0164296i	−0.000430721	−	0.000746031i
$486$	−12.2050	−	25.1032i	−0.553632	−	1.13870i
$487$	8.02176	−	13.8941i	0.363501	−	0.629602i	−0.625034	−	0.780598i	$-0.714915\pi$
$487$	8.02176	−	13.8941i	0.363501	−	0.629602i	0.988534	+	0.150996i	$0.0482481\pi$
$488$	1.93822	+	10.9922i	0.0877389	+	0.497592i
$489$	−16.8980	+	21.0062i	−0.764156	+	0.949934i
$490$	0.00313810	+	0.0227369i	0.000141765	+	0.00102715i
$491$	−1.53326	+	8.69553i	−0.0691949	+	0.392424i	0.930466	+	0.366378i	$0.119402\pi$
$491$	−1.53326	+	8.69553i	−0.0691949	+	0.392424i	−0.999661	+	0.0260451i	$0.991709\pi$
$492$	−14.6454	−	8.05614i	−0.660268	−	0.363199i
$493$	6.08020	+	34.4825i	0.273838	+	1.55301i
$494$	1.07406			0.0483244
$495$	0.0118515	−	0.0108111i	0.000532687	−	0.000485925i
$496$	10.0185	−	17.3526i	0.449845	−	0.779154i
$497$	−6.11111	+	7.01248i	−0.274121	+	0.314553i
$498$	10.3987	−	2.05631i	0.465976	−	0.0921454i
$499$	22.8396	+	19.1647i	1.02244	+	0.857931i	0.989933	−	0.141540i	$-0.0452054\pi$
$499$	22.8396	+	19.1647i	1.02244	+	0.857931i	0.0325101	+	0.999471i	$0.489650\pi$
$500$	−0.00383581	+	0.0217540i	−0.000171543	+	0.000972867i
$501$	−4.77278	+	0.943803i	−0.213232	+	0.0421660i
$502$	6.60447	−	5.54181i	0.294772	−	0.247343i
$503$	−18.3458	+	31.7758i	−0.817998	+	1.41681i	0.0891565	+	0.996018i	$0.471583\pi$
$503$	−18.3458	+	31.7758i	−0.817998	+	1.41681i	−0.907155	+	0.420797i	$0.861750\pi$
$504$	9.89461	+	5.41701i	0.440741	+	0.241293i
$505$	0.00231410	+	0.00400815i	0.000102976	+	0.000178360i
$506$	19.2781	+	7.01665i	0.857016	+	0.311928i
$507$	22.5837	+	12.4228i	1.00298	+	0.551715i
$508$	12.0444	+	10.1064i	0.534382	+	0.448399i
$509$	−4.76156	+	27.0042i	−0.211053	+	1.19694i	0.676574	+	0.736375i	$0.263464\pi$
$509$	−4.76156	+	27.0042i	−0.211053	+	1.19694i	−0.887627	+	0.460564i	$0.847647\pi$
$510$	0.0322931	+	0.00500745i	0.00142996	+	0.000221734i
$511$	−8.03191	−	1.57156i	−0.355311	−	0.0695219i
$512$	−15.8246			−0.699353
$513$	0.491895	−	0.326286i	0.0217177	−	0.0144059i
$514$	16.1992	−	28.0579i	0.714517	−	1.23758i
$515$	−0.0256140	+	0.0214927i	−0.00112869	+	0.000947083i
$516$	0.403913	−	0.502111i	0.0177813	−	0.0221042i
$517$	8.60782	+	7.22281i	0.378571	+	0.317659i
$518$	−0.287722	+	15.3919i	−0.0126418	+	0.676282i
$519$	7.84608	+	4.31596i	0.344405	+	0.189450i
$520$	0.0129129	+	0.00469991i	0.000566268	+	0.000206105i
$521$	−14.3142			−0.627117			−0.313559	−	0.949569i	$-0.601521\pi$
$521$	−14.3142			−0.627117			−0.313559	+	0.949569i	$0.601521\pi$
$522$	−17.5016	−	27.6085i	−0.766026	−	1.20839i
$523$	−10.3437			−0.452297			−0.226149	−	0.974093i	$-0.572614\pi$
$523$	−10.3437			−0.452297			−0.226149	+	0.974093i	$0.572614\pi$
$524$	1.11918	+	6.34716i	0.0488914	+	0.277277i
$525$	−17.5818	−	14.6929i	−0.767331	−	0.641250i
$526$	−12.5593	+	4.57122i	−0.547612	+	0.199315i
$527$	17.8159	+	14.9493i	0.776072	+	0.651202i
$528$	−16.5112	−	18.8701i	−0.718558	−	0.821214i
$529$	7.14757	+	2.60150i	0.310764	+	0.113109i
$530$	−0.0468563			−0.00203531
$531$	24.1456	−	0.999976i	1.04783	−	0.0433953i
$532$	0.130349	−	0.338318i	0.00565133	−	0.0146679i
$533$	32.3591	−	27.1525i	1.40163	−	1.17611i
$534$	0.426693	+	20.6148i	0.0184648	+	0.892091i
$535$	0.00259879	+	0.00218064i	0.000112355	+	9.42773e-5i
$536$	−12.5172	+	4.55588i	−0.540660	+	0.196784i
$537$	−18.7783	+	23.3436i	−0.810344	+	1.00735i
$538$	−21.2489	−	7.73397i	−0.916105	−	0.333435i
$539$	15.1567	+	13.7152i	0.652846	+	0.590757i
$540$	−0.0111582	+	0.00269066i	−0.000480175	+	0.000115788i
$541$	−7.72944	−	13.3878i	−0.332315	−	0.575586i	0.650651	−	0.759377i	$-0.274496\pi$
$541$	−7.72944	−	13.3878i	−0.332315	−	0.575586i	−0.982965	+	0.183791i	$0.941163\pi$
$542$	−23.6029	+	19.8052i	−1.01383	+	0.850707i
$543$	6.56007	−	8.15493i	0.281520	−	0.349962i
$544$	6.02958	−	34.1954i	0.258516	−	1.46612i
$545$	−0.00220686	+	0.0125158i	−9.45317e−5	+	0.000536116i
$546$	33.1352	−	27.9171i	1.41806	−	1.19474i
$547$	6.37136	−	5.34621i	0.272420	−	0.228587i	−0.496335	−	0.868131i	$-0.665321\pi$
$547$	6.37136	−	5.34621i	0.272420	−	0.228587i	0.768755	+	0.639544i	$0.220877\pi$
$548$	−4.46265	+	7.72953i	−0.190635	+	0.330189i
$549$	21.7879	−	8.96768i	0.929887	−	0.382731i
$550$	13.0721	+	22.6416i	0.557397	+	0.965440i
$551$	0.529537	−	0.444334i	0.0225590	−	0.0189293i
$552$	6.35981	+	7.26839i	0.270691	+	0.309363i
$553$	0.627371	−	33.5617i	0.0266785	−	1.42719i
$554$	46.0283	−	16.7529i	1.95556	−	0.711764i
$555$	0.00678677	+	0.00775636i	0.000288083	+	0.000329239i
$556$	−12.2523	−	4.45946i	−0.519612	−	0.189123i
$557$	−15.4350	−	26.7341i	−0.654000	−	1.13276i	−0.982143	−	0.188134i	$-0.939756\pi$
$557$	−15.4350	−	26.7341i	−0.654000	−	1.13276i	0.328143	−	0.944628i	$-0.393577\pi$
$558$	−20.6924	−	6.57535i	−0.875980	−	0.278357i
$559$	0.814268	+	1.41035i	0.0344399	+	0.0596516i
$560$	0.0157796	−	0.0181070i	0.000666808	−	0.000765161i
$561$	24.8976	−	15.0701i	1.05118	−	0.636259i
$562$	−21.4470	+	7.80606i	−0.904685	+	0.329279i
$563$	18.7640	−	6.82952i	0.790807	−	0.287830i	0.0851352	−	0.996369i	$-0.472868\pi$
$563$	18.7640	−	6.82952i	0.790807	−	0.287830i	0.705671	+	0.708539i	$0.250646\pi$
$564$	−2.90559	−	7.49658i	−0.122347	−	0.315663i
$565$	−0.00167560	−	0.00950280i	−7.04930e−5	−	0.000399786i
$566$	27.8959			1.17255
$567$	6.69429	−	22.8514i	0.281134	−	0.959669i
$568$	4.99649			0.209648
$569$	−4.66103	−	26.4340i	−0.195400	−	1.10817i	−0.911848	−	0.410529i	$-0.865344\pi$
$569$	−4.66103	−	26.4340i	−0.195400	−	1.10817i	0.716447	−	0.697641i	$-0.245767\pi$
$570$	−0.000233154	0	0.000601551i	−9.76575e−6	0	2.51962e-5i
$571$	28.5000	−	10.3731i	1.19269	−	0.434102i	0.332020	−	0.943272i	$-0.392270\pi$
$571$	28.5000	−	10.3731i	1.19269	−	0.434102i	0.860666	+	0.509170i	$0.170048\pi$
$572$	−17.4785	+	6.36165i	−0.730812	+	0.265994i
$573$	−5.44442	+	3.29541i	−0.227444	+	0.137668i
$574$	−12.2947	−	35.8503i	−0.513169	−	1.49636i
$575$	−9.80870	−	16.9892i	−0.409051	−	0.708497i
$576$	0.572410	+	2.60965i	0.0238504	+	0.108736i
$577$	−6.84381	−	11.8538i	−0.284912	−	0.493482i	0.687676	−	0.726018i	$-0.258631\pi$
$577$	−6.84381	−	11.8538i	−0.284912	−	0.493482i	−0.972588	+	0.232536i	$0.925298\pi$
$578$	27.1065	+	9.86596i	1.12748	+	0.410370i
$579$	−0.158027	−	0.180604i	−0.00656739	−	0.00750563i
$580$	−0.0126312	+	0.00459737i	−0.000524481	+	0.000190895i
$581$	7.74525	+	4.66687i	0.321327	+	0.193615i
$582$	21.1587	+	24.1815i	0.877057	+	1.00236i
$583$	−31.9665	+	26.8230i	−1.32392	+	1.11090i
$584$	2.19812	+	3.80726i	0.0909591	+	0.157546i
$585$	0.00385067	−	0.0287504i	0.000159206	−	0.00118868i
$586$	−26.9533	+	46.6845i	−1.11343	+	1.92852i
$587$	11.7029	−	9.81992i	0.483031	−	0.405312i	−0.368490	−	0.929632i	$-0.620125\pi$
$587$	11.7029	−	9.81992i	0.483031	−	0.405312i	0.851521	+	0.524320i	$0.175681\pi$
$588$	−4.77227	−	13.8252i	−0.196805	−	0.570143i
$589$	0.0797294	−	0.452168i	0.00328519	−	0.0186312i
$590$	0.00458659	−	0.0260118i	0.000188827	−	0.00107089i
$591$	−24.6219	+	30.6078i	−1.01281	+	1.25904i
$592$	12.3404	−	10.3548i	0.507186	−	0.425580i
$593$	−4.67660	−	8.10010i	−0.192045	−	0.332631i	0.753883	−	0.657009i	$-0.228179\pi$
$593$	−4.67660	−	8.10010i	−0.192045	−	0.332631i	−0.945928	+	0.324377i	$0.894845\pi$
$594$	−16.1394	+	21.8569i	−0.662209	+	0.896798i
$595$	0.0175171	+	0.0216866i	0.000718130	+	0.000889064i
$596$	−7.95833	−	2.89660i	−0.325986	−	0.118649i
$597$	30.0016	−	37.2954i	1.22788	−	1.52640i
$598$	34.8591	−	12.6877i	1.42549	−	0.518837i
$599$	−24.3174	−	20.4047i	−0.993582	−	0.833714i	−0.00749930	−	0.999972i	$-0.502387\pi$
$599$	−24.3174	−	20.4047i	−0.993582	−	0.833714i	−0.986082	+	0.166258i	$0.946832\pi$
$600$	0.254699	+	12.3053i	0.0103980	+	0.502361i
$601$	1.79900	−	1.50954i	0.0733827	−	0.0615754i	−0.605359	−	0.795953i	$-0.706970\pi$
$601$	1.79900	−	1.50954i	0.0733827	−	0.0615754i	0.678741	+	0.734378i	$0.262526\pi$
$602$	1.44344	−	0.226787i	0.0588302	−	0.00924316i
$603$	15.0547	+	23.7485i	0.613075	+	0.967113i
$604$	14.1739			0.576728
$605$	0.00425500	+	0.00154870i	0.000172991	+	6.29634e-5i
$606$	−5.16185	−	5.89929i	−0.209686	−	0.239642i
$607$	4.04355	+	3.39294i	0.164123	+	0.137715i	0.721150	−	0.692779i	$-0.243614\pi$
$607$	4.04355	+	3.39294i	0.164123	+	0.137715i	−0.557027	+	0.830494i	$0.688058\pi$
$608$	−0.644165	+	0.234457i	−0.0261244	+	0.00950849i
$609$	4.78723	−	27.4716i	0.193988	−	1.11321i
$610$	−0.00447177	−	0.0253606i	−0.000181056	−	0.00102682i
$611$	20.3185			0.821997
$612$	−20.8058	+	0.861662i	−0.841025	+	0.0348306i
$613$	−36.7281			−1.48343			−0.741716	−	0.670714i	$-0.765988\pi$
$613$	−36.7281			−1.48343			−0.741716	+	0.670714i	$0.765988\pi$
$614$	−17.6900	−	6.43862i	−0.713909	−	0.259842i
$615$	−0.0222317	−	0.0122292i	−0.000896468	−	0.000493128i
$616$	0.205216	−	10.9782i	0.00826839	−	0.442324i
$617$	−1.43466	−	1.20382i	−0.0577572	−	0.0484641i	0.613452	−	0.789732i	$-0.289780\pi$
$617$	−1.43466	−	1.20382i	−0.0577572	−	0.0484641i	−0.671209	+	0.741268i	$0.734225\pi$
$618$	35.4965	−	44.1263i	1.42788	−	1.77502i
$619$	2.32614	−	1.95187i	0.0934956	−	0.0784521i	−0.594842	−	0.803843i	$-0.702785\pi$
$619$	2.32614	−	1.95187i	0.0934956	−	0.0784521i	0.688337	+	0.725391i	$0.258341\pi$
$620$	−0.00446409	+	0.00773204i	−0.000179282	+	0.000310526i
$621$	12.1103	−	16.4004i	0.485968	−	0.658124i
$622$	−35.1428			−1.40910
$623$	−11.5563	+	13.2608i	−0.462993	+	0.531284i
$624$	−44.8037	−	6.94738i	−1.79358	−	0.278118i
$625$	4.34120	−	24.6201i	0.173648	−	0.984806i
$626$	−3.19418	−	2.68024i	−0.127665	−	0.107124i
$627$	−0.503423	−	0.276922i	−0.0201048	−	0.0110592i
$628$	−24.7135	−	8.99497i	−0.986175	−	0.358938i
$629$	9.34897	+	16.1929i	0.372768	+	0.645653i
$630$	−0.0228284	−	0.0124979i	−0.000909506	−	0.000497927i
$631$	−10.2641	+	17.7780i	−0.408609	+	0.707732i	−0.994734	−	0.102489i	$-0.967319\pi$
$631$	−10.2641	+	17.7780i	−0.408609	+	0.707732i	0.586125	+	0.810221i	$0.300653\pi$
$632$	−13.8127	+	11.5902i	−0.549440	+	0.461035i
$633$	−27.3336	+	5.40515i	−1.08641	+	0.214835i
$634$	−8.08263	+	45.8389i	−0.321002	+	1.82049i
$635$	0.0182832	+	0.0153415i	0.000725548	+	0.000608807i
$636$	29.2905	−	5.79211i	1.16144	−	0.229672i
$637$	36.9360	+	1.38138i	1.46346	+	0.0547322i
$638$	−15.9091	+	27.5555i	−0.629849	+	1.09093i
$639$	−2.25971	−	10.3022i	−0.0893927	−	0.407547i
$640$	−0.0191802			−0.000758164
$641$	7.01580	+	39.7886i	0.277107	+	1.57155i	0.732188	+	0.681103i	$0.238499\pi$
$641$	7.01580	+	39.7886i	0.277107	+	1.57155i	−0.455080	+	0.890450i	$0.650389\pi$
$642$	−5.03440	−	2.76932i	−0.198692	−	0.109296i
$643$	−7.46629	+	42.3434i	−0.294442	+	1.66986i	0.375021	+	0.927016i	$0.377635\pi$
$643$	−7.46629	+	42.3434i	−0.294442	+	1.66986i	−0.669463	+	0.742845i	$0.733476\pi$
$644$	0.234037	−	12.5200i	0.00922234	−	0.493356i
$645$	0.000613138	0	0.000762202i	2.41423e−5	0	3.00117e-5i
$646$	−0.203246	−	1.15266i	−0.00799660	−	0.0453510i
$647$	19.9166	−	34.4965i	0.783002	−	1.35620i	−0.147184	−	0.989109i	$-0.547021\pi$
$647$	19.9166	−	34.4965i	0.783002	−	1.35620i	0.930186	−	0.367089i	$-0.119646\pi$
$648$	−11.6165	+	5.35357i	−0.456339	+	0.210308i
$649$	−11.7615	−	20.3715i	−0.461679	−	0.799651i
$650$	44.4236	+	16.1689i	1.74244	+	0.634195i
$651$	−9.29309	−	16.0219i	−0.364225	−	0.627946i
$652$	−14.3834	−	12.0691i	−0.563297	−	0.472662i
$653$	−3.55373	+	1.29345i	−0.139068	+	0.0506167i	−0.410617	−	0.911808i	$-0.634687\pi$
$653$	−3.55373	+	1.29345i	−0.139068	+	0.0506167i	0.271548	+	0.962425i	$0.412464\pi$
$654$	−0.445434	−	21.5203i	−0.0174178	−	0.841509i
$655$	0.00169890	+	0.00963495i	6.63816e−5	+	0.000376469i
$656$	−19.8296	+	34.3459i	−0.774216	+	1.34098i
$657$	6.85600	−	6.25414i	0.267478	−	0.243997i
$658$	6.55411	−	17.0111i	0.255506	−	0.663161i
$659$	0.766060	+	4.34454i	0.0298415	+	0.169239i	0.996086	−	0.0883863i	$-0.0281710\pi$
$659$	0.766060	+	4.34454i	0.0298415	+	0.169239i	−0.966245	+	0.257626i	$0.917060\pi$
$660$	0.00735714	+	0.00840820i	0.000286376	+	0.000327289i
$661$	−0.578375	+	3.28013i	−0.0224962	+	0.127582i	−0.993988	−	0.109492i	$-0.965077\pi$
$661$	−0.578375	+	3.28013i	−0.0224962	+	0.127582i	0.971491	+	0.237075i	$0.0761886\pi$
$662$	−8.11444	+	46.0193i	−0.315377	+	1.78859i
$663$	16.9717	−	49.8133i	0.659124	−	1.93459i
$664$	−0.843468	−	4.78355i	−0.0327329	−	0.185638i
$665$	0.000197868	0	0.000513564i	7.67300e−6	0	1.99151e-5i
$666$	−13.8248	−	10.6575i	−0.535700	−	0.412969i
$667$	11.9375	−	20.6763i	0.462221	−	0.800590i
$668$	−0.588395	−	3.33695i	−0.0227657	−	0.129111i
$669$	22.5289	+	12.3926i	0.871016	+	0.479127i
$670$	0.0288791	−	0.0105111i	0.00111570	−	0.000406080i
$671$	−17.5685	−	14.7417i	−0.678225	−	0.569099i
$672$	−13.7787	+	23.9763i	−0.531525	+	0.924904i
$673$	12.1305	+	4.41516i	0.467598	+	0.170192i	0.565064	−	0.825047i	$-0.308851\pi$
$673$	12.1305	+	4.41516i	0.467598	+	0.170192i	−0.0974659	+	0.995239i	$0.531074\pi$
$674$	19.5664	+	33.8899i	0.753668	+	1.30539i
$675$	25.2568	−	6.09034i	0.972135	−	0.234417i
$676$	−8.97565	+	15.5463i	−0.345217	+	0.597934i
$677$	−5.32513	−	30.2003i	−0.204661	−	1.16069i	−0.897972	−	0.440053i	$-0.854960\pi$
$677$	−5.32513	−	30.2003i	−0.204661	−	1.16069i	0.693310	−	0.720639i	$-0.256152\pi$
$678$	5.90629	+	15.2385i	0.226830	+	0.585233i
$679$	−0.512298	+	27.4058i	−0.0196602	+	1.05174i
$680$	0.00260034	−	0.0147472i	9.97184e−5	−	0.000565531i
$681$	0.470610	+	22.7366i	0.0180338	+	0.871268i
$682$	3.66989	+	20.8130i	0.140527	+	0.796970i
$683$	23.1544			0.885978			0.442989	−	0.896527i	$-0.353918\pi$
$683$	23.1544			0.885978			0.442989	+	0.896527i	$0.353918\pi$
$684$	0.220108	+	0.347216i	0.00841604	+	0.0132761i
$685$	−0.00677427	+	0.0117334i	−0.000258831	+	0.000448309i
$686$	13.0709	−	30.4781i	0.499051	−	1.16366i
$687$	0.544703	−	1.59875i	0.0207817	−	0.0609962i
$688$	−1.17126	−	0.982803i	−0.0446538	−	0.0374690i
$689$	−13.1028	+	74.3094i	−0.499175	+	2.83096i
$690$	−0.0146731	−	0.0167693i	−0.000558594	−	0.000638397i
$691$	−23.4151	+	19.6476i	−0.890751	+	0.747429i	−0.968361	−	0.249555i	$-0.919716\pi$
$691$	−23.4151	+	19.6476i	−0.890751	+	0.747429i	0.0776099	+	0.996984i	$0.475271\pi$
$692$	−3.11834	+	5.40113i	−0.118542	+	0.205320i
$693$	−22.7285	+	4.54186i	−0.863386	+	0.172531i
$694$	−30.5731	−	52.9541i	−1.16054	−	2.01011i
$695$	−0.0185989	−	0.00676943i	−0.000705495	−	0.000256779i
$696$	−12.8145	+	7.75639i	−0.485732	+	0.294005i
$697$	−35.2629	−	29.5891i	−1.33568	−	1.12077i
$698$	−4.83420	+	27.4161i	−0.182977	+	1.03771i
$699$	−0.464400	−	1.19818i	−0.0175652	−	0.0453192i
$700$	10.4843	−	12.0307i	0.396268	−	0.454716i
$701$	−15.5148			−0.585987			−0.292994	−	0.956114i	$-0.594651\pi$
$701$	−15.5148			−0.585987			−0.292994	+	0.956114i	$0.594651\pi$
$702$	3.04829	+	49.0346i	0.115050	+	1.85069i
$703$	0.184569	−	0.319683i	0.00696115	−	0.0120571i
$704$	1.99215	−	1.67162i	0.0750821	−	0.0630014i
$705$	−0.00441066	−	0.0113798i	−0.000166115	−	0.000428586i
$706$	2.07632	+	1.74224i	0.0781433	+	0.0655700i
$707$	0.124979	−	6.68587i	0.00470033	−	0.251448i
$708$	0.348298	+	16.8273i	0.0130898	+	0.632409i
$709$	16.5023	+	6.00633i	0.619756	+	0.225573i	0.632766	−	0.774343i	$-0.281919\pi$
$709$	16.5023	+	6.00633i	0.619756	+	0.225573i	−0.0130108	+	0.999915i	$0.504142\pi$
$710$	−0.0115277			−0.000432626
$711$	30.1446	+	23.2384i	1.13051	+	0.871507i
$712$	9.44851			0.354098
$713$	−2.75371	−	15.6171i	−0.103127	−	0.584864i
$714$	−36.2303	−	30.2773i	−1.35589	−	1.13310i
$715$	−0.0265322	+	0.00965694i	−0.000992248	+	0.000361149i
$716$	−15.9838	−	13.4120i	−0.597344	−	0.501231i
$717$	−12.2256	+	35.8832i	−0.456573	+	1.34008i
$718$	5.46366	+	1.98861i	0.203902	+	0.0742142i
$719$	−35.8972			−1.33874			−0.669370	−	0.742929i	$-0.733436\pi$
$719$	−35.8972			−1.33874			−0.669370	+	0.742929i	$0.733436\pi$
$720$	0.00583482	+	0.0266013i	0.000217451	+	0.000991373i
$721$	47.7254	−	7.49842i	1.77739	−	0.279256i
$722$	26.0445	−	21.8539i	0.969274	−	0.813318i
$723$	−16.2030	−	8.91294i	−0.602598	−	0.331476i
$724$	5.58384	+	4.68540i	0.207522	+	0.174132i
$725$	28.5908	−	10.4062i	1.06184	−	0.386476i
$726$	−7.57861	−	1.17516i	−0.281269	−	0.0436143i
$727$	29.3404	+	10.6790i	1.08818	+	0.396064i	0.822945	−	0.568121i	$-0.192330\pi$
$727$	29.3404	+	10.6790i	1.08818	+	0.396064i	0.265231	+	0.964185i	$0.414552\pi$
$728$	−12.4757	−	15.4453i	−0.462381	−	0.572440i
$729$	16.2921	+	21.5306i	0.603411	+	0.797431i
$730$	−0.00507142	−	0.00878395i	−0.000187702	−	0.000325109i
$731$	1.35948	−	1.14074i	0.0502822	−	0.0421918i
$732$	5.93030	+	15.3005i	0.219190	+	0.565523i
$733$	−0.0680805	+	0.386104i	−0.00251461	+	0.0142611i	−0.986039	−	0.166513i	$-0.946749\pi$
$733$	−0.0680805	+	0.386104i	−0.00251461	+	0.0142611i	0.983525	+	0.180774i	$0.0578603\pi$
$734$	−1.97848	+	11.2205i	−0.0730272	+	0.414158i
$735$	−0.00724428	−	0.0209866i	−0.000267209	−	0.000774103i
$736$	−18.1370	+	15.2187i	−0.668539	+	0.560970i
$737$	13.6849	−	23.7029i	0.504088	−	0.873106i
$738$	40.9564	+	13.0146i	1.50763	+	0.479072i
$739$	9.34861	+	16.1923i	0.343894	+	0.595643i	0.985152	−	0.171683i	$-0.0549205\pi$
$739$	9.34861	+	16.1923i	0.343894	+	0.595643i	−0.641258	+	0.767325i	$0.721587\pi$
$740$	−0.00549867	+	0.00461394i	−0.000202135	+	0.000169612i
$741$	−1.01920	+	0.201543i	−0.0374412	+	0.00740388i
$742$	57.9870	+	34.9399i	2.12877	+	1.28268i
$743$	10.5297	−	3.83249i	0.386296	−	0.140600i	−0.141569	−	0.989928i	$-0.545215\pi$
$743$	10.5297	−	3.83249i	0.386296	−	0.140600i	0.527865	+	0.849328i	$0.322993\pi$
$744$	−3.20865	+	9.41767i	−0.117635	+	0.345268i
$745$	−0.0120807	−	0.00439701i	−0.000442602	−	0.000161094i
$746$	17.0263	+	29.4904i	0.623377	+	1.07972i
$747$	−9.48163	+	3.90253i	−0.346915	+	0.142786i
$748$	10.1347	+	17.5537i	0.370560	+	0.641829i
$749$	−1.59006	−	4.63652i	−0.0580997	−	0.169415i
$750$	−0.00117526	−	0.0567804i	−4.29145e−5	−	0.00207333i
$751$	18.5416	−	6.74860i	0.676594	−	0.246260i	0.0192094	−	0.999815i	$-0.493885\pi$
$751$	18.5416	−	6.74860i	0.676594	−	0.246260i	0.657384	+	0.753556i	$0.271663\pi$
$752$	−17.9258	+	6.52445i	−0.653686	+	0.237922i
$753$	−5.22720	+	6.49802i	−0.190490	+	0.236801i
$754$	9.99077	+	56.6605i	0.363842	+	2.06345i
$755$	0.0215159			0.000783043
$756$	15.8153	+	4.99067i	0.575196	+	0.181509i
$757$	−5.30078			−0.192660			−0.0963300	−	0.995349i	$-0.530710\pi$
$757$	−5.30078			−0.192660			−0.0963300	+	0.995349i	$0.530710\pi$
$758$	−6.71543	−	38.0851i	−0.243915	−	1.38331i
$759$	−19.6100	−	3.04077i	−0.711796	−	0.110373i
$760$	−0.000277805	0	0.000101113i	−1.00771e−5	0	3.66775e-6i
$761$	−18.0471	+	6.56861i	−0.654207	+	0.238112i	−0.647733	−	0.761867i	$-0.724283\pi$
$761$	−18.0471	+	6.56861i	−0.654207	+	0.238112i	−0.00647355	+	0.999979i	$0.502061\pi$
$762$	−35.4186	−	19.4830i	−1.28308	−	0.705794i
$763$	12.0639	−	13.8433i	0.436741	−	0.501159i
$764$	−2.21617	−	3.83852i	−0.0801782	−	0.138873i
$765$	−0.0315831	+	0.00130800i	−0.00114189	+	4.72907e-5i
$766$	−20.1773	−	34.9480i	−0.729034	−	1.26272i
$767$	−39.9696	−	14.5477i	−1.44322	−	0.525288i
$768$	34.8947	−	6.90032i	1.25915	−	0.248994i
$769$	−33.6033	+	12.2306i	−1.21177	+	0.441047i	−0.867316	−	0.497757i	$-0.834157\pi$
$769$	−33.6033	+	12.2306i	−1.21177	+	0.441047i	−0.344451	+	0.938804i	$0.611935\pi$
$770$	−0.000473466		0.0253284i	−1.70625e−5		0.000912773i
$771$	−10.1068	+	29.6643i	−0.363987	+	1.06833i
$772$	0.128034	−	0.107434i	0.00460806	−	0.00386662i
$773$	4.22302	+	7.31448i	0.151891	+	0.263084i	0.931923	−	0.362657i	$-0.118130\pi$
$773$	4.22302	+	7.31448i	0.151891	+	0.263084i	−0.780031	+	0.625740i	$0.784797\pi$
$774$	−0.768311	+	1.46787i	−0.0276164	+	0.0527614i
$775$	10.1045	−	17.5016i	0.362965	−	0.628674i
$776$	11.2792	−	9.46434i	0.404898	−	0.339750i
$777$	−2.61520	−	14.6597i	−0.0938199	−	0.525912i
$778$	−1.05137	+	5.96261i	−0.0376934	+	0.213770i
$779$	−0.157808	+	0.894973i	−0.00565406	+	0.0320657i
$780$	0.0199638	+	0.00309564i	0.000714820	+	0.000110842i
$781$	−7.86445	+	6.59906i	−0.281412	+	0.236133i
$782$	−20.2126	−	35.0092i	−0.722800	−	1.25193i
$783$	21.7882	+	22.9141i	0.778647	+	0.818882i
$784$	−33.0301	+	10.6418i	−1.17964	+	0.380064i
$785$	−0.0375149	−	0.0136543i	−0.00133896	−	0.000487343i
$786$	−5.98842	−	15.4505i	−0.213600	−	0.551100i
$787$	−31.7048	+	11.5396i	−1.13016	+	0.411343i	−0.838349	−	0.545134i	$-0.816479\pi$
$787$	−31.7048	+	11.5396i	−1.13016	+	0.411343i	−0.291807	+	0.956477i	$0.594256\pi$
$788$	−20.9578	−	17.5857i	−0.746591	−	0.626464i
$789$	11.0600	−	6.69441i	0.393746	−	0.238327i
$790$	0.0318681	−	0.0267405i	0.00113382	−	0.000951385i
$791$	−5.01242	+	13.0097i	−0.178221	+	0.462570i
$792$	9.86045	+	7.60138i	0.350376	+	0.270103i
$793$	−41.4699			−1.47264
$794$	42.1971	+	15.3585i	1.49752	+	0.545053i
$795$	0.0444628	−	0.00879238i	0.00157693	−	0.000311834i
$796$	25.5369	+	21.4280i	0.905132	+	0.759496i
$797$	−10.2656	+	3.73638i	−0.363627	+	0.132349i	−0.517371	−	0.855761i	$-0.673089\pi$
$797$	−10.2656	+	3.73638i	−0.363627	+	0.132349i	0.153744	+	0.988111i	$0.450867\pi$
$798$	−0.160025	+	0.918308i	−0.00566483	+	0.0325077i
$799$	−3.84488	−	21.8054i	−0.136022	−	0.771419i
$800$	−30.1724			−1.06675
$801$	−4.27318	−	19.4817i	−0.150985	−	0.688352i
$802$	−48.7501			−1.72143
$803$	−8.48824	−	3.08947i	−0.299544	−	0.109025i
$804$	−16.7534	+	10.1405i	−0.590846	+	0.357628i
$805$	0.000355266	−	0.0190052i	1.25215e−5	−	0.000669847i
$806$	29.2744	+	24.5642i	1.03115	+	0.865236i
$807$	21.6147	+	3.35163i	0.760874	+	0.117983i
$808$	−2.75165	+	2.30891i	−0.0968026	+	0.0812270i
$809$	23.1281	−	40.0590i	0.813140	−	1.40840i	−0.0975153	−	0.995234i	$-0.531089\pi$
$809$	23.1281	−	40.0590i	0.813140	−	1.40840i	0.910656	−	0.413166i	$-0.135577\pi$
$810$	0.0268011	−	0.0123515i	0.000941694	−	0.000433988i
$811$	−6.80553			−0.238974			−0.119487	−	0.992836i	$-0.538125\pi$
$811$	−6.80553			−0.238974			−0.119487	+	0.992836i	$0.538125\pi$
$812$	19.0599	+	3.72935i	0.668870	+	0.130874i
$813$	18.6809	−	23.2225i	0.655167	−	0.814449i
$814$	−2.95049	+	16.7330i	−0.103414	+	0.586493i
$815$	−0.0218339	−	0.0183208i	−0.000764807	−	0.000641749i
$816$	1.02244	+	49.3971i	0.0357925	+	1.72925i
$817$	−0.0329230	−	0.0119830i	−0.00115183	−	0.000419232i
$818$	−26.8227	−	46.4583i	−0.937835	−	1.62438i
$819$	−26.2041	+	32.7087i	−0.915644	+	1.14294i
$820$	0.00883576	−	0.0153040i	0.000308558	−	0.000534438i
$821$	−13.1536	+	11.0372i	−0.459065	+	0.385201i	−0.842787	−	0.538247i	$-0.819087\pi$
$821$	−13.1536	+	11.0372i	−0.459065	+	0.385201i	0.383722	+	0.923449i	$0.374642\pi$
$822$	7.40045	−	21.7210i	0.258120	−	0.757606i
$823$	−2.26051	+	12.8200i	−0.0787963	+	0.446876i	0.919727	+	0.392558i	$0.128410\pi$
$823$	−2.26051	+	12.8200i	−0.0787963	+	0.446876i	−0.998524	+	0.0543183i	$0.982701\pi$
$824$	−19.8794	−	16.6808i	−0.692532	−	0.581103i
$825$	−16.6530	−	19.0321i	−0.579782	−	0.662611i
$826$	−25.0727	+	28.7708i	−0.872390	+	1.00106i
$827$	−19.8828	+	34.4380i	−0.691392	+	1.19753i	0.279990	+	0.960003i	$0.409669\pi$
$827$	−19.8828	+	34.4380i	−0.691392	+	1.19753i	−0.971382	+	0.237523i	$0.923664\pi$
$828$	11.2453	+	8.66892i	0.390800	+	0.301266i
$829$	−10.1286			−0.351781			−0.175891	−	0.984410i	$-0.556280\pi$
$829$	−10.1286			−0.351781			−0.175891	+	0.984410i	$0.556280\pi$
$830$	0.00194601	+	0.0110364i	6.75471e−5	+	0.000383079i
$831$	−40.5335	+	24.5342i	−1.40609	+	0.851081i
$832$	0.816565	−	4.63097i	0.0283093	−	0.160550i
$833$	−5.50696	−	39.9004i	−0.190805	−	1.38247i
$834$	33.1265	+	5.13669i	1.14708	+	0.177869i
$835$	−0.000893179	−	0.00506547i	−3.09097e−5	−	0.000175298i
$836$	0.200080	−	0.346549i	0.00691992	−	0.0119857i
$837$	20.8692	+	2.35662i	0.721347	+	0.0814567i
$838$	10.1722	+	17.6189i	0.351395	+	0.608633i
$839$	6.90812	+	2.51435i	0.238495	+	0.0868050i	0.458503	−	0.888693i	$-0.348386\pi$
$839$	6.90812	+	2.51435i	0.238495	+	0.0868050i	−0.220008	+	0.975498i	$0.570608\pi$
$840$	−0.00594225	+	0.0103401i	−0.000205027	+	0.000356767i
$841$	6.15052	+	5.16090i	0.212087	+	0.177962i
$842$	16.4418	−	5.98434i	0.566623	−	0.206234i
$843$	18.8866	−	11.4317i	0.650490	−	0.393730i
$844$	−3.36973	−	19.1107i	−0.115991	−	0.657817i
$845$	−0.0136250	+	0.0235991i	−0.000468713	+	0.000811835i
$846$	11.0673	+	17.4585i	0.380503	+	0.600236i
$847$	−4.11095	−	5.08946i	−0.141254	−	0.174876i
$848$	−12.3017	−	69.7663i	−0.422441	−	2.39578i
$849$	−26.4709	+	5.23454i	−0.908479	+	0.179649i
$850$	8.94581	−	50.7342i	0.306839	−	1.74017i
$851$	2.21390	−	12.5557i	0.0758917	−	0.430403i
$852$	7.20610	−	1.42499i	0.246877	−	0.0488192i
$853$	1.86666	+	10.5863i	0.0639131	+	0.362469i	0.999944	+	0.0105522i	$0.00335893\pi$
$853$	1.86666	+	10.5863i	0.0639131	+	0.362469i	−0.936031	+	0.351917i	$0.885530\pi$
$854$	−13.3769	+	34.7196i	−0.457749	+	1.18808i
$855$	0.000334122	0	0.000527072i	1.14267e−5	0	1.80255e-5i
$856$	−1.31647	+	2.28020i	−0.0449961	+	0.0779356i
$857$	−7.49810	−	42.5238i	−0.256130	−	1.45259i	−0.793155	−	0.609020i	$-0.791563\pi$
$857$	−7.49810	−	42.5238i	−0.256130	−	1.45259i	0.537025	−	0.843566i	$-0.319548\pi$
$858$	40.9109	−	24.7626i	1.39667	−	0.845382i
$859$	1.10517	−	0.402250i	0.0377080	−	0.0137246i	−0.323097	−	0.946366i	$-0.604724\pi$
$859$	1.10517	−	0.402250i	0.0377080	−	0.0137246i	0.360805	+	0.932641i	$0.382502\pi$
$860$	0.000521895	0	0.000437922i	1.77965e−5	0	1.49330e-5i
$861$	18.3938	+	31.7120i	0.626858	+	1.08074i
$862$	24.1676	+	8.79629i	0.823152	+	0.299603i
$863$	−4.62629	−	8.01298i	−0.157481	−	0.272765i	0.776479	−	0.630143i	$-0.217004\pi$
$863$	−4.62629	−	8.01298i	−0.157481	−	0.272765i	−0.933960	+	0.357379i	$0.883671\pi$
$864$	−12.5319	−	28.7429i	−0.426345	−	0.977853i
$865$	−0.00473363	+	0.00819888i	−0.000160948	+	0.000278770i
$866$	−10.6225	−	60.2432i	−0.360967	−	2.04715i
$867$	−27.5731	−	4.27556i	−0.936433	−	0.145206i
$868$	11.2902	−	6.23999i	0.383213	−	0.211799i
$869$	6.43347	−	36.4860i	0.218240	−	1.23770i
$870$	0.0295651	−	0.0178952i	0.00100235	−	0.000606704i
$871$	−8.59394	−	48.7387i	−0.291195	−	1.65145i
$872$	−9.86350			−0.334020
$873$	−24.6154	−	18.9759i	−0.833106	−	0.642238i
$874$	−0.399040	+	0.691157i	−0.0134977	+	0.0233787i
$875$	0.0318301	−	0.0365249i	0.00107605	−	0.00123477i
$876$	4.25603	+	4.86407i	0.143798	+	0.164342i
$877$	25.2940	+	21.2242i	0.854118	+	0.716690i	0.960692	−	0.277615i	$-0.0895439\pi$
$877$	25.2940	+	21.2242i	0.854118	+	0.716690i	−0.106575	+	0.994305i	$0.533988\pi$
$878$	8.43948	−	47.8627i	0.284819	−	1.61529i
$879$	16.8163	−	49.3574i	0.567200	−	1.66478i
$880$	0.0203069	−	0.0170395i	0.000684545	−	0.000574401i
$881$	−3.34473	+	5.79323i	−0.112687	+	0.195179i	−0.916853	−	0.399226i	$-0.869279\pi$
$881$	−3.34473	+	5.79323i	−0.112687	+	0.195179i	0.804166	+	0.594405i	$0.202612\pi$
$882$	18.9319	+	32.4895i	0.637470	+	1.09398i
$883$	−18.5645	−	32.1546i	−0.624745	−	1.08209i	−0.988590	−	0.150631i	$-0.951870\pi$
$883$	−18.5645	−	32.1546i	−0.624745	−	1.08209i	0.363845	−	0.931459i	$-0.381464\pi$
$884$	34.4411	+	12.5355i	1.15838	+	0.421616i
$885$	0.000528713		0.0255437i	1.77725e−5		0.000858643i
$886$	38.2915	+	32.1304i	1.28643	+	1.07944i
$887$	0.276468	−	1.56793i	0.00928290	−	0.0526459i	−0.979814	−	0.199909i	$-0.935935\pi$
$887$	0.276468	−	1.56793i	0.00928290	−	0.0526459i	0.989097	+	0.147263i	$0.0470464\pi$
$888$	−5.01371	+	6.23262i	−0.168249	+	0.209153i
$889$	−11.1866	−	32.6193i	−0.375186	−	1.09402i
$890$	−0.0217992			−0.000730711
$891$	11.2137	−	23.7689i	0.375672	−	0.796287i
$892$	−8.95387	+	15.5086i	−0.299798	+	0.519265i
$893$	−0.334858	+	0.280980i	−0.0112056	+	0.00940262i
$894$	21.5170	+	3.33648i	0.719636	+	0.111589i
$895$	−0.0242634	−	0.0203594i	−0.000811035	−	0.000680539i
$896$	23.7365	+	14.3023i	0.792980	+	0.477807i
$897$	−30.6976	+	18.5807i	−1.02496	+	0.620391i
$898$	−50.7575	−	18.4742i	−1.69380	−	0.616492i
$899$	24.5950			0.820289
$900$	3.87677	+	17.6744i	0.129226	+	0.589148i
$901$	82.2269			2.73937
$902$	−7.26379	−	41.1950i	−0.241858	−	1.37164i
$903$	−1.32715	+	0.486057i	−0.0441647	+	0.0161750i
$904$	7.03739	−	2.56140i	0.234060	−	0.0851909i
$905$	0.00847624	+	0.00711241i	0.000281760	+	0.000236424i
$906$	−35.7491	+	7.06927i	−1.18768	+	0.234861i
$907$	17.9713	+	6.54101i	0.596727	+	0.217191i	0.622685	−	0.782472i	$-0.286042\pi$
$907$	17.9713	+	6.54101i	0.596727	+	0.217191i	−0.0259587	+	0.999663i	$0.508264\pi$
$908$	−15.8386			−0.525622
$909$	6.00514	+	4.62934i	0.199178	+	0.153546i
$910$	0.0287835	+	0.0356347i	0.000954162	+	0.00118128i
$911$	8.45090	−	7.09114i	0.279991	−	0.234940i	−0.491967	−	0.870614i	$-0.663722\pi$
$911$	8.45090	−	7.09114i	0.279991	−	0.234940i	0.771958	+	0.635674i	$0.219278\pi$
$912$	0.834461	−	0.505084i	0.0276318	−	0.0167250i
$913$	7.64543	+	6.41528i	0.253027	+	0.212315i
$914$	−41.3068	+	15.0345i	−1.36631	+	0.497295i
$915$	0.00900215	+	0.0232260i	0.000297602	+	0.000767829i
$916$	1.10538	+	0.402326i	0.0365229	+	0.0132932i
$917$	5.08212	−	13.1906i	0.167827	−	0.435591i
$918$	52.0461	−	12.5502i	1.71778	−	0.414219i
$919$	4.67488	+	8.09713i	0.154210	+	0.267100i	0.932771	−	0.360469i	$-0.117383\pi$
$919$	4.67488	+	8.09713i	0.154210	+	0.267100i	−0.778561	+	0.627569i	$0.784050\pi$
$920$	−0.00782183	+	0.00656329i	−0.000257878	+	0.000216385i
$921$	17.9945	+	2.79027i	0.592939	+	0.0919427i
$922$	−9.84779	+	55.8496i	−0.324320	+	1.83931i
$923$	−3.22356	+	18.2817i	−0.106105	+	0.601751i
$924$	−2.83498	−	15.8917i	−0.0932641	−	0.522797i
$925$	12.4463	−	10.4437i	0.409232	−	0.343387i
$926$	−16.9258	+	29.3163i	−0.556216	+	0.963395i
$927$	−25.4032	+	48.5330i	−0.834350	+	1.59403i
$928$	−18.3603	−	31.8010i	−0.602707	−	1.04392i
$929$	4.92698	−	4.13423i	0.161649	−	0.135640i	−0.558375	−	0.829588i	$-0.688575\pi$
$929$	4.92698	−	4.13423i	0.161649	−	0.135640i	0.720024	+	0.693949i	$0.244131\pi$
$930$	0.00740285	−	0.0217280i	0.000242749	−	0.000712490i
$931$	−0.627827	+	0.488014i	−0.0205762	+	0.0159940i
$932$	0.841000	−	0.306099i	0.0275479	−	0.0100266i
$933$	33.3477	−	6.59440i	1.09175	−	0.215891i
$934$	−19.5070	−	7.09997i	−0.638289	−	0.232318i
$935$	0.0153843	+	0.0266465i	0.000503122	+	0.000871433i
$936$	22.4936	−	0.931560i	0.735226	−	0.0304490i
$937$	−15.6764	−	27.1522i	−0.512124	−	0.887025i	−0.999901	−	0.0140568i	$-0.995525\pi$
$937$	−15.6764	−	27.1522i	−0.512124	−	0.887025i	0.487777	−	0.872968i	$-0.337808\pi$
$938$	−43.5773	−	8.52655i	−1.42285	−	0.278402i
$939$	3.53395	+	1.94395i	0.115326	+	0.0634383i
$940$	0.00798745	−	0.00290719i	0.000260522	−	9.48222e-5i
$941$	−18.0146	+	6.55678i	−0.587259	+	0.213745i	−0.618523	−	0.785766i	$-0.712269\pi$
$941$	−18.0146	+	6.55678i	−0.587259	+	0.213745i	0.0312644	+	0.999511i	$0.490047\pi$
$942$	66.8179	+	10.3610i	2.17705	+	0.337579i
$943$	5.45040	+	30.9108i	0.177490	+	1.00659i
$944$	39.9342			1.29975
$945$	0.0240075	+	0.00757580i	0.000780963	+	0.000246441i
$946$	1.61268			0.0524328
$947$	6.98810	+	39.6315i	0.227083	+	1.28785i	0.858664	+	0.512540i	$0.171295\pi$
$947$	6.98810	+	39.6315i	0.227083	+	1.28785i	−0.631581	+	0.775310i	$0.717594\pi$
$948$	−16.6157	+	20.6552i	−0.539651	+	0.670850i
$949$	−15.3486	+	5.58644i	−0.498238	+	0.181344i
$950$	−0.955719	+	0.347853i	−0.0310076	+	0.0112858i
$951$	−0.931715	−	45.0140i	−0.0302129	−	1.45968i
$952$	−14.2148	+	16.3114i	−0.460704	+	0.528657i
$953$	2.62555	+	4.54758i	0.0850498	+	0.147311i	0.905412	−	0.424533i	$-0.139562\pi$
$953$	2.62555	+	4.54758i	0.0850498	+	0.147311i	−0.820363	+	0.571844i	$0.806228\pi$
$954$	−70.9869	+	29.2174i	−2.29829	+	0.945949i
$955$	−0.00336413	−	0.00582684i	−0.000108861	−	0.000188552i
$956$	−24.8098	−	9.03002i	−0.802405	−	0.292052i
$957$	9.92581	−	29.1331i	0.320856	−	0.941741i
$958$	−11.1442	+	4.05615i	−0.360052	+	0.131048i
$959$	17.1329	−	9.46920i	0.553249	−	0.305776i
$960$	−0.00277093		0.000547942i	−8.94312e−5		1.76848e-5i
$961$	−11.2331	+	9.42567i	−0.362357	+	0.304054i
$962$	15.3619	+	26.6076i	0.495288	+	0.857864i
$963$	5.29688	+	1.68317i	0.170690	+	0.0542394i
$964$	6.43973	−	11.1539i	0.207410	−	0.359244i
$965$	0.000194355	0	0.000163084i	6.25652e−6	0	5.24985e-6i
$966$	5.65409	+	31.6943i	0.181917	+	1.01975i
$967$	9.05706	−	51.3651i	0.291255	−	1.65179i	−0.390789	−	0.920480i	$-0.627798\pi$
$967$	9.05706	−	51.3651i	0.291255	−	1.65179i	0.682044	−	0.731311i	$-0.261091\pi$
$968$	−0.610253	+	3.46092i	−0.0196143	+	0.111238i
$969$	0.409156	+	1.05565i	0.0131440	+	0.0339122i
$970$	−0.0260228	+	0.0218357i	−0.000835541	+	0.000701102i
$971$	8.20413	+	14.2100i	0.263283	+	0.456020i	0.967112	−	0.254350i	$-0.0818614\pi$
$971$	8.20413	+	14.2100i	0.263283	+	0.456020i	−0.703829	+	0.710369i	$0.748528\pi$
$972$	−15.2269	+	11.0341i	−0.488402	+	0.353919i
$973$	17.9692	+	22.2463i	0.576065	+	0.713184i
$974$	−26.9953	−	9.82549i	−0.864985	−	0.314829i
$975$	−45.1883	−	7.00703i	−1.44719	−	0.224404i
$976$	36.5865	−	13.3164i	1.17110	−	0.426247i
$977$	45.1927	+	37.9212i	1.44584	+	1.21321i	0.935544	+	0.353210i	$0.114910\pi$
$977$	45.1927	+	37.9212i	1.44584	+	1.21321i	0.510300	+	0.859997i	$0.329535\pi$
$978$	42.2969	+	23.2666i	1.35251	+	0.743984i
$979$	−14.8719	+	12.4790i	−0.475309	+	0.398831i
$980$	0.0147177	−	0.00474182i	0.000470139	−	0.000151472i
$981$	4.46086	+	20.3374i	0.142424	+	0.649322i
$982$	15.8106			0.504535
$983$	36.6295	+	13.3321i	1.16830	+	0.425227i	0.852056	−	0.523451i	$-0.175356\pi$
$983$	36.6295	+	13.3321i	1.16830	+	0.425227i	0.316245	+	0.948678i	$0.397578\pi$
$984$	6.35086	−	18.6403i	0.202458	−	0.594232i
$985$	−0.0318138	−	0.0266949i	−0.00101367	−	0.000850572i
$986$	58.9164	−	21.4438i	1.87628	−	0.682910i
$987$	−3.02725	+	17.3720i	−0.0963586	+	0.552956i
$988$	−0.125648	−	0.712586i	−0.00399740	−	0.0226704i
$989$	−1.21008			−0.0384783
$990$	−0.0227496	−	0.0175376i	−0.000723030	−	0.000557381i
$991$	−26.7774			−0.850613			−0.425306	−	0.905049i	$-0.639834\pi$
$991$	−26.7774			−0.850613			−0.425306	+	0.905049i	$0.639834\pi$
$992$	−22.9193	−	8.34195i	−0.727689	−	0.264857i
$993$	−0.935382	−	45.1911i	−0.0296835	−	1.43410i
$994$	14.2661	+	8.59597i	0.452492	+	0.272648i
$995$	0.0387649	+	0.0325276i	0.00122893	+	0.00103119i
$996$	−2.58073	−	6.65844i	−0.0817737	−	0.210981i
$997$	−1.91485	+	1.60675i	−0.0606441	+	0.0508864i	−0.672606	−	0.740001i	$-0.734825\pi$
$997$	−1.91485	+	1.60675i	−0.0606441	+	0.0508864i	0.611962	+	0.790887i	$0.290381\pi$
$998$	26.6936	−	46.2348i	0.844973	−	1.46354i
$999$	15.1184	+	7.51890i	0.478325	+	0.237888i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.u.a.4.5	✓	132
3.2	odd	2		567.2.u.a.550.18		132
7.2	even	3		189.2.w.a.58.5	yes	132
21.2	odd	6		567.2.w.a.226.18		132
27.7	even	9		189.2.w.a.88.5	yes	132
27.20	odd	18		567.2.w.a.424.18		132
189.128	odd	18		567.2.u.a.100.18		132
189.142	even	9	inner	189.2.u.a.142.5	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.4.5	✓	132	1.1	even	1	trivial
189.2.u.a.142.5	yes	132	189.142	even	9	inner
189.2.w.a.58.5	yes	132	7.2	even	3
189.2.w.a.88.5	yes	132	27.7	even	9
567.2.u.a.100.18		132	189.128	odd	18
567.2.u.a.550.18		132	3.2	odd	2
567.2.w.a.226.18		132	21.2	odd	6
567.2.w.a.424.18		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)

\(f(q)\)	\(=\)	\(q+(-0.310937 - 1.76341i) q^{2} +(0.625951 + 1.61499i) q^{3} +(-1.13356 + 0.412582i) q^{4} +(-0.00172074 + 0.000626297i) q^{5} +(2.65326 - 1.60597i) q^{6} +(2.59651 + 0.508047i) q^{7} +(-0.710598 - 1.23079i) q^{8} +(-2.21637 + 2.02181i) q^{9} +O(q^{10})\)	\(q+(-0.310937 - 1.76341i) q^{2} +(0.625951 + 1.61499i) q^{3} +(-1.13356 + 0.412582i) q^{4} +(-0.00172074 + 0.000626297i) q^{5} +(2.65326 - 1.60597i) q^{6} +(2.59651 + 0.508047i) q^{7} +(-0.710598 - 1.23079i) q^{8} +(-2.21637 + 2.02181i) q^{9} +(0.00163946 + 0.00283963i) q^{10} +(2.74403 + 0.998747i) q^{11} +(-1.37587 - 1.57243i) q^{12} +(4.96182 - 1.80596i) q^{13} +(0.0885434 - 4.73670i) q^{14} +(-0.00208856 - 0.00238694i) q^{15} +(-3.79762 + 3.18658i) q^{16} +(-2.87705 - 4.98319i) q^{17} +(4.25443 + 3.27972i) q^{18} +(-0.0567992 + 0.0983790i) q^{19} +(0.00169216 - 0.00141989i) q^{20} +(0.804801 + 4.51135i) q^{21} +(0.907981 - 5.14941i) q^{22} +(-0.681306 + 3.86388i) q^{23} +(1.54291 - 1.91802i) q^{24} +(-3.83022 + 3.21394i) q^{25} +(-4.72746 - 8.18821i) q^{26} +(-4.65253 - 2.31386i) q^{27} +(-3.15292 + 0.495374i) q^{28} +(-5.71816 - 2.08124i) q^{29} +(-0.00355975 + 0.00442518i) q^{30} +(-3.79806 + 1.38238i) q^{31} +(4.62268 + 3.87889i) q^{32} +(0.104666 + 5.05675i) q^{33} +(-7.89285 + 6.62288i) q^{34} +(-0.00478610 + 0.000751974i) q^{35} +(1.67823 - 3.20627i) q^{36} -3.24950 q^{37} +(0.191144 + 0.0695707i) q^{38} +(6.02245 + 6.88285i) q^{39} +(0.00199359 + 0.00167282i) q^{40} +(7.51748 - 2.73614i) q^{41} +(7.70514 - 2.82194i) q^{42} +(0.0535565 + 0.303734i) q^{43} -3.52259 q^{44} +(0.00254754 - 0.00486710i) q^{45} +7.02546 q^{46} +(3.61594 + 1.31609i) q^{47} +(-7.52341 - 4.13846i) q^{48} +(6.48378 + 2.63830i) q^{49} +(6.85846 + 5.75493i) q^{50} +(6.24690 - 7.76563i) q^{51} +(-4.87942 + 4.09432i) q^{52} +(-7.14507 + 12.3756i) q^{53} +(-2.63365 + 8.92380i) q^{54} -0.00534727 q^{55} +(-1.21978 - 3.55679i) q^{56} +(-0.194434 - 0.0301495i) q^{57} +(-1.89210 + 10.7306i) q^{58} +(-6.17081 - 5.17793i) q^{59} +(0.00335231 + 0.00184403i) q^{60} +(-7.38012 - 2.68614i) q^{61} +(3.61867 + 6.26772i) q^{62} +(-6.78201 + 4.12363i) q^{63} +(0.445282 - 0.771251i) q^{64} +(-0.00740692 + 0.00621515i) q^{65} +(8.88459 - 1.75690i) q^{66} +(1.62756 - 9.23035i) q^{67} +(5.31728 + 4.46173i) q^{68} +(-6.66658 + 1.31830i) q^{69} +(0.00281422 + 0.00820606i) q^{70} +(-1.75785 + 3.04468i) q^{71} +(4.06337 + 1.29120i) q^{72} -3.09334 q^{73} +(1.01039 + 5.73022i) q^{74} +(-7.58800 - 4.17399i) q^{75} +(0.0237958 - 0.134953i) q^{76} +(6.61751 + 3.98736i) q^{77} +(10.2647 - 12.7602i) q^{78} +(-2.20314 - 12.4946i) q^{79} +(0.00453895 - 0.00786170i) q^{80} +(0.824604 - 8.96214i) q^{81} +(-7.16241 - 12.4057i) q^{82} +(3.21166 + 1.16895i) q^{83} +(-2.77359 - 4.78184i) q^{84} +(0.00807160 + 0.00677287i) q^{85} +(0.518956 - 0.188884i) q^{86} +(-0.218109 - 10.5375i) q^{87} +(-0.720656 - 4.08704i) q^{88} +(-3.32414 + 5.75758i) q^{89} +(-0.00937484 - 0.00297900i) q^{90} +(13.8010 - 2.16835i) q^{91} +(-0.821865 - 4.66103i) q^{92} +(-4.60993 - 5.26852i) q^{93} +(1.19649 - 6.78562i) q^{94} +(3.61219e-5 - 0.000204857i) q^{95} +(-3.37079 + 9.89356i) q^{96} +(1.79903 + 10.2028i) q^{97} +(2.63637 - 12.2539i) q^{98} +(-8.10107 + 3.33431i) 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

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