LMFDB - Embedded newform 189.2.bd.a.59.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(47,189)]

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([7, 15]))

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

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

chi := DirichletCharacter("189.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			59.9
Character	$\chi$	$=$	189.59
Dual form			189.2.bd.a.173.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.170792 + 0.469247i) q^{2} +(-1.53869 - 0.795263i) q^{3} +(1.34107 + 1.12529i) q^{4} +(-0.000430671 - 0.000361376i) q^{5} +(0.635971 - 0.586200i) q^{6} +(1.75023 - 1.98411i) q^{7} +(-1.62200 + 0.936464i) q^{8} +(1.73511 + 2.44732i) q^{9} +(0.000243130 - 0.000140371i) q^{10} +(3.04392 + 3.62761i) q^{11} +(-1.16858 - 2.79797i) q^{12} +(1.77003 - 2.10944i) q^{13} +(0.632115 + 1.16016i) q^{14} +(0.000375278 + 0.000898541i) q^{15} +(0.445582 + 2.52702i) q^{16} +(-0.400086 - 0.692969i) q^{17} +(-1.44474 + 0.396214i) q^{18} +(4.50743 + 2.60237i) q^{19} +(-0.000170906 - 0.000969257i) q^{20} +(-4.27094 + 1.66104i) q^{21} +(-2.22212 + 0.808787i) q^{22} +(0.542669 + 1.49097i) q^{23} +(3.24049 - 0.151005i) q^{24} +(-0.868241 - 4.92404i) q^{25} +(0.687542 + 1.19086i) q^{26} +(-0.723528 - 5.14553i) q^{27} +(4.57987 - 0.691318i) q^{28} +(-5.40692 - 6.44372i) q^{29} +(-0.000485732 + 2.26348e-5i) q^{30} +(-5.19122 + 6.18666i) q^{31} +(-4.95085 - 0.872968i) q^{32} +(-1.79874 - 8.00247i) q^{33} +(0.393506 - 0.0693856i) q^{34} +(-0.00147078 + 0.000222010i) q^{35} +(-0.427042 + 5.23452i) q^{36} +2.05581 q^{37} +(-1.99099 + 1.67064i) q^{38} +(-4.40108 + 1.83813i) q^{39} +(0.00103696 + 0.000182845i) q^{40} +(-5.20305 - 4.36588i) q^{41} +(-0.0499941 - 2.28782i) q^{42} +(-6.39715 - 2.32837i) q^{43} +8.29015i q^{44} +(0.000137141 - 0.00168102i) q^{45} -0.792318 q^{46} +(-5.68085 + 4.76680i) q^{47} +(1.32404 - 4.24265i) q^{48} +(-0.873412 - 6.94530i) q^{49} +(2.45888 + 0.433567i) q^{50} +(0.0645138 + 1.38444i) q^{51} +(4.74745 - 0.837104i) q^{52} +(9.11266 + 5.26120i) q^{53} +(2.53810 + 0.539303i) q^{54} -0.00266231i q^{55} +(-0.980823 + 4.85726i) q^{56} +(-4.86596 - 7.58882i) q^{57} +(3.94716 - 1.43665i) q^{58} +(2.29410 - 13.0105i) q^{59} +(-0.000507844 + 0.00162730i) q^{60} +(-2.33638 - 2.78438i) q^{61} +(-2.01645 - 3.49260i) q^{62} +(7.89260 + 0.840709i) q^{63} +(-1.31080 + 2.27037i) q^{64} +(-0.00152460 + 0.000268828i) q^{65} +(4.06235 + 0.522704i) q^{66} +(-1.99848 + 0.727386i) q^{67} +(0.243248 - 1.37953i) q^{68} +(0.350717 - 2.72570i) q^{69} +(0.000147020 - 0.000728078i) q^{70} +(7.56979 + 4.37042i) q^{71} +(-5.10619 - 2.34469i) q^{72} +7.18246i q^{73} +(-0.351116 + 0.964683i) q^{74} +(-2.57996 + 8.26703i) q^{75} +(3.11635 + 8.56210i) q^{76} +(12.5251 + 0.309645i) q^{77} +(-0.110866 - 2.37913i) q^{78} +(-2.42128 - 0.881273i) q^{79} +(0.000721305 - 0.00124934i) q^{80} +(-2.97877 + 8.49276i) q^{81} +(2.93732 - 1.69586i) q^{82} +(1.47761 - 1.23986i) q^{83} +(-7.59676 - 2.57848i) q^{84} +(-7.81169e-5 + 0.000443023i) q^{85} +(2.18517 - 2.60418i) q^{86} +(3.19510 + 14.2148i) q^{87} +(-8.33438 - 3.03347i) q^{88} +(-1.61790 + 2.80229i) q^{89} +(0.000765391 + 0.000351457i) q^{90} +(-1.08741 - 7.20394i) q^{91} +(-0.950016 + 2.61015i) q^{92} +(12.9077 - 5.39094i) q^{93} +(-1.26656 - 3.47986i) q^{94} +(-0.00100079 - 0.00274964i) q^{95} +(6.92356 + 5.28045i) q^{96} +(0.614218 - 1.68755i) q^{97} +(3.40823 + 0.776355i) q^{98} +(-3.59637 + 13.7438i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20}+ \cdots + 96 q^{99}+O(q^{100}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.170792	+	0.469247i	−0.120768	+	0.331808i	−0.985316	−	0.170744i	$-0.945383\pi$
$2$	−0.170792	+	0.469247i	−0.120768	+	0.331808i	0.864547	+	0.502551i	$0.167605\pi$
$3$	−1.53869	−	0.795263i	−0.888361	−	0.459146i
$3$	−1.53869	−	0.795263i	−0.888361	−	0.459146i
$4$	1.34107	+	1.12529i	0.670533	+	0.562644i
$5$	−0.000430671	0	0.000361376i	−0.000192602	0	0.000161612i	0.642691	−	0.766125i	$-0.277818\pi$
$5$	−0.000430671	0	0.000361376i	−0.000192602	0	0.000161612i	−0.642884	+	0.765964i	$0.722262\pi$
$6$	0.635971	−	0.586200i	0.259634	−	0.239315i
$7$	1.75023	−	1.98411i	0.661524	−	0.749924i
$7$	1.75023	−	1.98411i	0.661524	−	0.749924i
$8$	−1.62200	+	0.936464i	−0.573465	+	0.331090i
$9$	1.73511	+	2.44732i	0.578371	+	0.815774i
$10$	0.000243130	0	0.000140371i	7.68844e−5	0	4.43892e-5i
$11$	3.04392	+	3.62761i	0.917778	+	1.09376i	0.995306	+	0.0967748i	$0.0308526\pi$
$11$	3.04392	+	3.62761i	0.917778	+	1.09376i	−0.0775286	+	0.996990i	$0.524703\pi$
$12$	−1.16858	−	2.79797i	−0.337340	−	0.807703i
$13$	1.77003	−	2.10944i	0.490918	−	0.585053i	−0.462533	−	0.886602i	$-0.653059\pi$
$13$	1.77003	−	2.10944i	0.490918	−	0.585053i	0.953451	+	0.301549i	$0.0975036\pi$
$14$	0.632115	+	1.16016i	0.168940	+	0.310066i
$15$	0.000375278	0	0.000898541i	9.68965e−5	0	0.000232002i
$16$	0.445582	+	2.52702i	0.111395	+	0.631755i
$17$	−0.400086	−	0.692969i	−0.0970351	−	0.168070i	0.813421	−	0.581675i	$-0.197603\pi$
$17$	−0.400086	−	0.692969i	−0.0970351	−	0.168070i	−0.910456	+	0.413606i	$0.864269\pi$
$18$	−1.44474	+	0.396214i	−0.340529	+	0.0933884i
$19$	4.50743	+	2.60237i	1.03408	+	0.597024i	0.918150	−	0.396234i	$-0.129683\pi$
$19$	4.50743	+	2.60237i	1.03408	+	0.597024i	0.115926	+	0.993258i	$0.463016\pi$
$20$	−0.000170906	0	0.000969257i	−3.82158e−5	0	0.000216732i
$21$	−4.27094	+	1.66104i	−0.931996	+	0.362468i
$22$	−2.22212	+	0.808787i	−0.473758	+	0.172434i
$23$	0.542669	+	1.49097i	0.113154	+	0.310889i	0.983324	−	0.181864i	$-0.0582130\pi$
$23$	0.542669	+	1.49097i	0.113154	+	0.310889i	−0.870169	+	0.492753i	$0.835991\pi$
$24$	3.24049	−	0.151005i	0.661462	−	0.0308237i
$25$	−0.868241	−	4.92404i	−0.173648	−	0.984808i
$26$	0.687542	+	1.19086i	0.134838	+	0.233546i
$27$	−0.723528	−	5.14553i	−0.139243	−	0.990258i
$28$	4.57987	−	0.691318i	0.865514	−	0.130647i
$29$	−5.40692	−	6.44372i	−1.00404	−	1.19657i	−0.980434	−	0.196847i	$-0.936930\pi$
$29$	−5.40692	−	6.44372i	−1.00404	−	1.19657i	−0.0236057	−	0.999721i	$-0.507515\pi$
$30$	−0.000485732	0	2.26348e-5i	−8.86822e−5	0	4.13253e-6i
$31$	−5.19122	+	6.18666i	−0.932371	+	1.11116i	0.0612205	+	0.998124i	$0.480501\pi$
$31$	−5.19122	+	6.18666i	−0.932371	+	1.11116i	−0.993591	+	0.113032i	$0.963944\pi$
$32$	−4.95085	−	0.872968i	−0.875194	−	0.154320i
$33$	−1.79874	−	8.00247i	−0.313121	−	1.39305i
$34$	0.393506	−	0.0693856i	0.0674856	−	0.0118995i
$35$	−0.00147078		0.000222010i	−0.000248608		3.75266e-5i
$36$	−0.427042	+	5.23452i	−0.0711737	+	0.872420i
$37$	2.05581			0.337973			0.168986	−	0.985618i	$-0.445951\pi$
$37$	2.05581			0.337973			0.168986	+	0.985618i	$0.445951\pi$
$38$	−1.99099	+	1.67064i	−0.322981	+	0.271013i
$39$	−4.40108	+	1.83813i	−0.704737	+	0.294336i
$40$	0.00103696		0.000182845i	0.000163959		2.89103e-5i
$41$	−5.20305	−	4.36588i	−0.812580	−	0.681836i	0.138642	−	0.990343i	$-0.455726\pi$
$41$	−5.20305	−	4.36588i	−0.812580	−	0.681836i	−0.951222	+	0.308507i	$0.900171\pi$
$42$	−0.0499941	−	2.28782i	−0.00771425	−	0.353018i
$43$	−6.39715	−	2.32837i	−0.975556	−	0.355073i	−0.195445	−	0.980715i	$-0.562615\pi$
$43$	−6.39715	−	2.32837i	−0.975556	−	0.355073i	−0.780111	+	0.625641i	$0.784837\pi$
$44$			8.29015i			1.24979i
$45$	0.000137141	−	0.00168102i	2.04437e−5	−	0.000250591i
$46$	−0.792318			−0.116821
$47$	−5.68085	+	4.76680i	−0.828638	+	0.695310i	−0.954978	−	0.296677i	$-0.904121\pi$
$47$	−5.68085	+	4.76680i	−0.828638	+	0.695310i	0.126340	+	0.991987i	$0.459677\pi$
$48$	1.32404	−	4.24265i	0.191108	−	0.612373i
$49$	−0.873412	−	6.94530i	−0.124773	−	0.992185i
$50$	2.45888	+	0.433567i	0.347738	+	0.0613156i
$51$	0.0645138	+	1.38444i	0.00903374	+	0.193860i
$52$	4.74745	−	0.837104i	0.658353	−	0.116085i
$53$	9.11266	+	5.26120i	1.25172	+	0.722681i	0.971451	−	0.237241i	$-0.0762430\pi$
$53$	9.11266	+	5.26120i	1.25172	+	0.722681i	0.280269	+	0.959921i	$0.409576\pi$
$54$	2.53810	+	0.539303i	0.345392	+	0.0733898i
$55$		−	0.00266231i		−	0.000358985i
$56$	−0.980823	+	4.85726i	−0.131068	+	0.649079i
$57$	−4.86596	−	7.58882i	−0.644512	−	1.00516i
$58$	3.94716	−	1.43665i	0.518287	−	0.188641i
$59$	2.29410	−	13.0105i	0.298666	−	1.69382i	−0.353251	−	0.935529i	$-0.614924\pi$
$59$	2.29410	−	13.0105i	0.298666	−	1.69382i	0.651917	−	0.758291i	$-0.273965\pi$
$60$	−0.000507844		0.00162730i	−6.55623e−5		0.000210083i
$61$	−2.33638	−	2.78438i	−0.299142	−	0.356504i	0.595446	−	0.803395i	$-0.296975\pi$
$61$	−2.33638	−	2.78438i	−0.299142	−	0.356504i	−0.894588	+	0.446892i	$0.852531\pi$
$62$	−2.01645	−	3.49260i	−0.256090	−	0.443560i
$63$	7.89260	+	0.840709i	0.994375	+	0.105919i
$64$	−1.31080	+	2.27037i	−0.163850	+	0.283797i
$65$	−0.00152460		0.000268828i	−0.000189103		3.33440e-5i
$66$	4.06235	+	0.522704i	0.500041	+	0.0643404i
$67$	−1.99848	+	0.727386i	−0.244153	+	0.0888644i	−0.461198	−	0.887297i	$-0.652580\pi$
$67$	−1.99848	+	0.727386i	−0.244153	+	0.0888644i	0.217045	+	0.976162i	$0.430358\pi$
$68$	0.243248	−	1.37953i	0.0294982	−	0.167292i
$69$	0.350717	−	2.72570i	0.0422214	−	0.328136i
$70$	0.000147020	0	0.000728078i	1.75723e−5	0	8.70220e-5i
$71$	7.56979	+	4.37042i	0.898369	+	0.518673i	0.876671	−	0.481091i	$-0.159759\pi$
$71$	7.56979	+	4.37042i	0.898369	+	0.518673i	0.0216981	+	0.999765i	$0.493093\pi$
$72$	−5.10619	−	2.34469i	−0.601770	−	0.276325i
$73$			7.18246i			0.840644i	0.907375	+	0.420322i	$0.138083\pi$
$73$			7.18246i			0.840644i	−0.907375	+	0.420322i	$0.861917\pi$
$74$	−0.351116	+	0.964683i	−0.0408164	+	0.112142i
$75$	−2.57996	+	8.26703i	−0.297908	+	0.954595i
$76$	3.11635	+	8.56210i	0.357470	+	0.982140i
$77$	12.5251	+	0.309645i	1.42737	+	0.0352873i
$78$	−0.110866	−	2.37913i	−0.0125531	−	0.269384i
$79$	−2.42128	−	0.881273i	−0.272415	−	0.0991510i	0.202201	−	0.979344i	$-0.435191\pi$
$79$	−2.42128	−	0.881273i	−0.272415	−	0.0991510i	−0.474616	+	0.880193i	$0.657413\pi$
$80$	0.000721305	−	0.00124934i	8.06443e−5	−	0.000139680i
$81$	−2.97877	+	8.49276i	−0.330975	+	0.943640i
$82$	2.93732	−	1.69586i	0.324373	−	0.187277i
$83$	1.47761	−	1.23986i	0.162188	−	0.136092i	−0.558082	−	0.829786i	$-0.688462\pi$
$83$	1.47761	−	1.23986i	0.162188	−	0.136092i	0.720270	+	0.693694i	$0.244018\pi$
$84$	−7.59676	−	2.57848i	−0.828875	−	0.281335i
$85$	−7.81169e−5	0	0.000443023i	−8.47297e−6	0	4.80526e-5i
$86$	2.18517	−	2.60418i	0.235632	−	0.280816i
$87$	3.19510	+	14.2148i	0.342551	+	1.52399i
$88$	−8.33438	−	3.03347i	−0.888448	−	0.323369i
$89$	−1.61790	+	2.80229i	−0.171498	+	0.297043i	−0.938944	−	0.344071i	$-0.888194\pi$
$89$	−1.61790	+	2.80229i	−0.171498	+	0.297043i	0.767446	+	0.641114i	$0.221527\pi$
$90$	0.000765391	0	0.000351457i	8.06792e−5	0	3.70469e-5i
$91$	−1.08741	−	7.20394i	−0.113992	−	0.755178i
$92$	−0.950016	+	2.61015i	−0.0990461	+	0.272127i
$93$	12.9077	−	5.39094i	1.33846	−	0.559014i
$94$	−1.26656	−	3.47986i	−0.130636	−	0.358920i
$95$	−0.00100079	−	0.00274964i	−0.000102679	−	0.000282107i
$96$	6.92356	+	5.28045i	0.706633	+	0.538934i
$97$	0.614218	−	1.68755i	0.0623644	−	0.171345i	−0.904597	−	0.426268i	$-0.859828\pi$
$97$	0.614218	−	1.68755i	0.0623644	−	0.171345i	0.966961	+	0.254923i	$0.0820502\pi$
$98$	3.40823	+	0.776355i	0.344284	+	0.0784237i
$99$	−3.59637	+	13.7438i	−0.361449	+	1.38130i
$100$	4.37659	−	7.58048i	0.437659	−	0.758048i
$101$	−4.00251	−	1.45679i	−0.398265	−	0.144957i	0.135120	−	0.990829i	$-0.456858\pi$
$101$	−4.00251	−	1.45679i	−0.398265	−	0.144957i	−0.533385	+	0.845873i	$0.679080\pi$
$102$	−0.660661	−	0.206178i	−0.0654152	−	0.0204146i
$103$	−10.3365	+	12.3186i	−1.01849	+	1.21379i	−0.0417981	+	0.999126i	$0.513309\pi$
$103$	−10.3365	+	12.3186i	−1.01849	+	1.21379i	−0.976689	+	0.214660i	$0.931136\pi$
$104$	−0.895580	+	5.07909i	−0.0878189	+	0.498046i
$105$	0.00243963		0.000828055i	0.000238083		8.08099e-5i
$106$	−4.02517	+	3.37752i	−0.390959	+	0.328054i
$107$	−3.48765	+	2.01360i	−0.337164	+	0.194662i	−0.659017	−	0.752128i	$-0.729028\pi$
$107$	−3.48765	+	2.01360i	−0.337164	+	0.194662i	0.321853	+	0.946790i	$0.395694\pi$
$108$	4.81991	−	7.71467i	0.463796	−	0.742345i
$109$	0.587845	−	1.01818i	0.0563054	−	0.0975238i	−0.836499	−	0.547969i	$-0.815401\pi$
$109$	0.587845	−	1.01818i	0.0563054	−	0.0975238i	0.892804	+	0.450445i	$0.148735\pi$
$110$	0.00124928		0.000454701i	0.000119114		4.33540e-5i
$111$	−3.16324	−	1.63491i	−0.300242	−	0.155179i
$112$	5.79376	+	3.53877i	0.547459	+	0.334383i
$113$	−5.04317	−	13.8560i	−0.474422	−	1.30346i	−0.914166	−	0.405340i	$-0.867153\pi$
$113$	−5.04317	−	13.8560i	−0.474422	−	1.30346i	0.439745	−	0.898123i	$-0.355069\pi$
$114$	4.39210	−	0.987227i	0.411358	−	0.0924622i
$115$	0.000305089	0	0.000838225i	2.84497e−5	0	7.81649e-5i
$116$		−	14.7258i		−	1.36726i
$117$	8.23368	+	0.671719i	0.761204	+	0.0621005i
$118$	5.71332	+	3.29858i	0.525953	+	0.303659i
$119$	−2.07517	−	0.419037i	−0.190231	−	0.0384131i
$120$	−0.00145015	−	0.00110600i	−0.000132380	−	0.000100964i
$121$	−1.98393	+	11.2514i	−0.180358	+	1.02286i
$122$	1.70560	−	0.620787i	0.154418	−	0.0562034i
$123$	4.53384	+	10.8555i	0.408803	+	0.978809i
$124$	−13.9235	+	2.45510i	−1.25037	+	0.220474i
$125$	−0.00281100	+	0.00486880i	−0.000251424	+	0.000435479i
$126$	−1.74249	+	3.56000i	−0.155234	+	0.317150i
$127$	−3.46785	−	6.00649i	−0.307722	−	0.532990i	0.670142	−	0.742233i	$-0.266233\pi$
$127$	−3.46785	−	6.00649i	−0.307722	−	0.532990i	−0.977864	+	0.209243i	$0.932900\pi$
$128$	−7.30436	−	8.70500i	−0.645621	−	0.769421i
$129$	7.99154	+	8.67006i	0.703616	+	0.763356i
$130$	0.000134243	0	0.000761329i	1.17739e−5	0	6.67729e-5i
$131$	10.3810	−	3.77837i	0.906990	−	0.330117i	0.153940	−	0.988080i	$-0.450804\pi$
$131$	10.3810	−	3.77837i	0.906990	−	0.330117i	0.753050	+	0.657963i	$0.228582\pi$
$132$	6.59285	−	12.7559i	0.573834	−	1.11026i
$133$	13.0524	−	4.38852i	1.13179	−	0.380533i
$134$		−	1.06201i		−	0.0917438i
$135$	−0.00154787	+	0.00247750i	−0.000133219	+	0.000213229i
$136$	1.29788	+	0.749332i	0.111292	+	0.0642547i
$137$	9.89957	−	1.74556i	0.845777	−	0.149133i	0.266065	−	0.963955i	$-0.414276\pi$
$137$	9.89957	−	1.74556i	0.845777	−	0.149133i	0.579712	+	0.814822i	$0.303165\pi$
$138$	1.21913	+	0.630101i	0.103779	+	0.0536378i
$139$	−0.409252	−	0.0721623i	−0.0347123	−	0.00612072i	0.156265	−	0.987715i	$-0.450055\pi$
$139$	−0.409252	−	0.0721623i	−0.0347123	−	0.00612072i	−0.190977	+	0.981594i	$0.561166\pi$
$140$	−0.00222224	−	0.00135732i	−0.000187814	−	0.000114715i
$141$	12.5319	−	2.81684i	1.05538	−	0.237221i
$142$	−3.34367	+	2.80567i	−0.280594	+	0.235447i
$143$	13.0401			1.09046
$144$	−5.41130	+	5.47515i	−0.450942	+	0.456262i
$145$			0.00472905i			0.000392726i
$146$	−3.37035	−	1.22671i	−0.278932	−	0.101523i
$147$	−4.17943	+	11.3812i	−0.344714	+	0.938708i
$148$	2.75697	+	2.31338i	0.226622	+	0.190158i
$149$	−0.907098	−	0.159946i	−0.0743124	−	0.0131033i	0.136368	−	0.990658i	$-0.456457\pi$
$149$	−0.907098	−	0.159946i	−0.0743124	−	0.0131033i	−0.210681	+	0.977555i	$0.567568\pi$
$150$	−3.43865	−	2.62258i	−0.280764	−	0.214133i
$151$	−0.922118	+	0.773749i	−0.0750409	+	0.0629668i	−0.679537	−	0.733642i	$-0.737819\pi$
$151$	−0.922118	+	0.773749i	−0.0750409	+	0.0629668i	0.604496	+	0.796608i	$0.293375\pi$
$152$	−9.74809			−0.790674
$153$	1.00172	−	2.18152i	0.0809847	−	0.176365i
$154$	−2.28450	+	5.82451i	−0.184090	+	0.469352i
$155$	0.00447142		0.000788431i	0.000359153		6.33283e-5i
$156$	−7.97056	−	2.48744i	−0.638156	−	0.199154i
$157$	−11.3485	−	2.00104i	−0.905706	−	0.159700i	−0.298653	−	0.954362i	$-0.596537\pi$
$157$	−11.3485	−	2.00104i	−0.905706	−	0.159700i	−0.607053	+	0.794661i	$0.707648\pi$
$158$	0.827070	−	0.985664i	0.0657982	−	0.0784152i
$159$	−9.83749	−	15.3423i	−0.780164	−	1.21672i
$160$	0.00181672	+	0.00216508i	0.000143624	+	0.000171164i
$161$	3.90805	+	1.53282i	0.307997	+	0.120803i
$162$	−3.47645	−	2.84828i	−0.273136	−	0.223782i
$163$	−3.42292	−	5.92867i	−0.268104	−	0.464369i	0.700268	−	0.713880i	$-0.253064\pi$
$163$	−3.42292	−	5.92867i	−0.268104	−	0.464369i	−0.968372	+	0.249510i	$0.919730\pi$
$164$	−2.06477	−	11.7099i	−0.161231	−	0.914387i
$165$	−0.00211723	+	0.00409645i	−0.000164826	+	0.000318908i
$166$	0.329437	+	0.905120i	0.0255693	+	0.0702510i
$167$	−4.35768	+	1.58606i	−0.337207	+	0.122733i	−0.505073	−	0.863076i	$-0.668535\pi$
$167$	−4.35768	+	1.58606i	−0.337207	+	0.122733i	0.167866	+	0.985810i	$0.446312\pi$
$168$	5.37198	−	6.69379i	0.414457	−	0.516437i
$169$	0.940696	+	5.33495i	0.0723613	+	0.410381i
$170$	−0.000194546	0	0.000112321i	−1.49210e−5	0	8.61462e-6i
$171$	1.45207	+	15.5465i	0.111042	+	1.18887i
$172$	−5.95891	−	10.3211i	−0.454363	−	0.786979i
$173$	−4.17814	−	23.6954i	−0.317658	−	1.80153i	−0.556914	−	0.830570i	$-0.688015\pi$
$173$	−4.17814	−	23.6954i	−0.317658	−	1.80153i	0.239256	−	0.970956i	$-0.423096\pi$
$174$	−7.21595	−	0.928479i	−0.547040	−	0.0703878i
$175$	−11.2895	−	6.89550i	−0.853404	−	0.521250i
$176$	−7.81072	+	9.30846i	−0.588755	+	0.701651i
$177$	−13.8766	+	18.1946i	−1.04303	+	1.36759i
$178$	−1.03864	−	1.23781i	−0.0778496	−	0.0927776i
$179$	21.3630	−	12.3339i	1.59674	−	0.921880i	0.604634	−	0.796503i	$-0.293319\pi$
$179$	21.3630	−	12.3339i	1.59674	−	0.921880i	0.992109	−	0.125377i	$-0.0400140\pi$
$180$	0.00207554	−	0.00210003i	0.000154702	−	0.000156527i
$181$	−7.78429	+	4.49426i	−0.578601	+	0.334056i	−0.760577	−	0.649247i	$-0.775084\pi$
$181$	−7.78429	+	4.49426i	−0.578601	+	0.334056i	0.181976	+	0.983303i	$0.441751\pi$
$182$	3.56615	+	0.720110i	0.264341	+	0.0533781i
$183$	1.38063	+	6.14233i	0.102059	+	0.454054i
$184$	−2.27645	−	1.91017i	−0.167822	−	0.140820i
$185$	−0.000885377	0	0.000742919i	−6.50942e−5	0	5.46205e-5i
$186$	0.325153	+	6.97763i	0.0238413	+	0.511624i
$187$	1.29599	−	3.56070i	0.0947721	−	0.260384i
$188$	−12.9824			−0.946841
$189$	−11.4757	−	7.57029i	−0.834731	−	0.550657i
$190$	0.00146119			0.000106006
$191$	−7.13465	+	19.6023i	−0.516245	+	1.41837i	0.358382	+	0.933575i	$0.383328\pi$
$191$	−7.13465	+	19.6023i	−0.516245	+	1.41837i	−0.874627	+	0.484796i	$0.838894\pi$
$192$	3.82246	−	2.45096i	0.275862	−	0.176883i
$193$	−14.0017	−	11.7489i	−1.00787	−	0.845701i	−0.0198124	−	0.999804i	$-0.506307\pi$
$193$	−14.0017	−	11.7489i	−1.00787	−	0.845701i	−0.988055	+	0.154103i	$0.950751\pi$
$194$	0.686975	+	0.576440i	0.0493219	+	0.0413860i
$195$	0.00255967		0.000798817i	0.000183302		5.72045e-5i
$196$	6.64415	−	10.2969i	0.474582	−	0.735496i
$197$	−8.92564	+	5.15322i	−0.635925	+	0.367152i	−0.783043	−	0.621967i	$-0.786334\pi$
$197$	−8.92564	+	5.15322i	−0.635925	+	0.367152i	0.147118	+	0.989119i	$0.453000\pi$
$198$	−5.83500	−	4.03492i	−0.414675	−	0.286749i
$199$	−9.67594	+	5.58641i	−0.685909	+	0.396010i	−0.802078	−	0.597220i	$-0.796272\pi$
$199$	−9.67594	+	5.58641i	−0.685909	+	0.396010i	0.116168	+	0.993230i	$0.462939\pi$
$200$	6.01947	+	7.17373i	0.425641	+	0.507259i
$201$	3.65349	+	0.470096i	0.257698	+	0.0331580i
$202$	1.36719	−	1.62936i	0.0961955	−	0.114641i
$203$	−22.2484	−	0.550022i	−1.56153	−	0.0386040i
$204$	−1.47137	+	1.92922i	−0.103017	+	0.135072i
$205$	0.000663080		0.00376051i	4.63115e−5		0.000262646i
$206$	−4.01507	−	6.95430i	−0.279743	−	0.484529i
$207$	−2.70729	+	3.91509i	−0.188170	+	0.272117i
$208$	6.11929	+	3.53297i	0.424297	+	0.244968i
$209$	4.27991	+	24.2726i	0.296048	+	1.67897i
$210$	−0.000805232		0.00100336i	−5.55663e−5		6.92387e-5i
$211$	22.3190	−	8.12346i	1.53651	−	0.559242i	0.571302	−	0.820740i	$-0.306439\pi$
$211$	22.3190	−	8.12346i	1.53651	−	0.559242i	0.965204	+	0.261498i	$0.0842165\pi$
$212$	6.30032	+	17.3100i	0.432707	+	1.18885i
$213$	−8.17190	−	12.7447i	−0.559929	−	0.873251i
$214$	−0.349212	−	1.98048i	−0.0238716	−	0.135383i
$215$	0.00191365	+	0.00331454i	0.000130510	+	0.000226050i
$216$	5.99217	+	7.66851i	0.407716	+	0.521776i
$217$	3.18921	+	21.1280i	0.216498	+	1.43426i
$218$	0.377378	+	0.449742i	0.0255593	+	0.0304603i
$219$	5.71195	−	11.0516i	0.385978	−	0.746795i
$220$	0.00299586	−	0.00357033i	0.000201981	−	0.000240711i
$221$	−2.16994	−	0.382619i	−0.145966	−	0.0257378i
$222$	1.30743	−	1.20511i	0.0877492	−	0.0808820i
$223$	23.8004	−	4.19666i	1.59380	−	0.281029i	0.694871	−	0.719134i	$-0.255461\pi$
$223$	23.8004	−	4.19666i	1.59380	−	0.281029i	0.898924	+	0.438105i	$0.144350\pi$
$224$	−10.3972	+	8.29515i	−0.694690	+	0.554243i
$225$	10.5442	−	10.6686i	0.702948	−	0.711242i
$226$	7.36322			0.489794
$227$	−3.27753	+	2.75018i	−0.217537	+	0.182536i	−0.745044	−	0.667015i	$-0.767572\pi$
$227$	−3.27753	+	2.75018i	−0.217537	+	0.182536i	0.527506	+	0.849551i	$0.323127\pi$
$228$	2.01404	−	15.6527i	0.133383	−	1.03663i
$229$	12.7575	+	2.24949i	0.843037	+	0.148650i	0.578456	−	0.815713i	$-0.303655\pi$
$229$	12.7575	+	2.24949i	0.843037	+	0.148650i	0.264581	+	0.964364i	$0.414766\pi$
$230$	0.000341228	0	0.000286324i	2.24999e−5	0	1.88797e-5i
$231$	−19.0260	−	10.4372i	−1.25182	−	0.686720i
$232$	14.8044	+	5.38834i	0.971953	+	0.353762i
$233$		−	11.2048i		−	0.734052i	−0.930211	−	0.367026i	$-0.880376\pi$
$233$		−	11.2048i		−	0.734052i	0.930211	−	0.367026i	$-0.119624\pi$
$234$	−1.72145	+	3.74891i	−0.112535	+	0.245074i
$235$	0.00416919			0.000271968
$236$	17.7171	−	14.8664i	1.15328	−	0.967719i
$237$	3.02474	+	3.28156i	0.196478	+	0.213160i
$238$	0.551055	−	0.902200i	0.0357196	−	0.0584810i
$239$	12.3508	+	2.17779i	0.798909	+	0.140869i	0.558177	−	0.829722i	$-0.311501\pi$
$239$	12.3508	+	2.17779i	0.798909	+	0.140869i	0.240733	+	0.970591i	$0.422612\pi$
$240$	−0.00210341	+	0.00134871i	−0.000135775	+	8.70588e-5i
$241$	−19.7697	+	3.48594i	−1.27348	+	0.224549i	−0.769209	−	0.638997i	$-0.779350\pi$
$241$	−19.7697	+	3.48594i	−1.27348	+	0.224549i	−0.504271	+	0.863546i	$0.668239\pi$
$242$	−4.94087	−	2.85261i	−0.317611	−	0.183373i
$243$	11.3374	−	10.6988i	0.727293	−	0.686327i
$244$		−	6.36314i		−	0.407358i
$245$	−0.00213371	+	0.00330677i	−0.000136318	+	0.000211262i
$246$	−5.86827	+	0.273457i	−0.374147	+	0.0174350i
$247$	13.4678	−	4.90189i	0.856937	−	0.311900i
$248$	2.62660	−	14.8962i	0.166789	−	0.945908i
$249$	−3.25958	+	0.732667i	−0.206568	+	0.0464309i
$250$	−0.00180458	−	0.00215061i	−0.000114131	−	0.000136016i
$251$	11.2730	+	19.5255i	0.711547	+	1.23244i	0.964276	+	0.264899i	$0.0853386\pi$
$251$	11.2730	+	19.5255i	0.711547	+	1.23244i	−0.252729	+	0.967537i	$0.581328\pi$
$252$	9.63846	+	10.0089i	0.607166	+	0.630501i
$253$	−3.75681	+	6.50699i	−0.236189	+	0.409091i
$254$	3.41081	−	0.601418i	0.214013	−	0.0377363i
$255$	0.000472517	0	0.000619550i	2.95902e−5	0	3.87977e-5i
$256$	0.405328	−	0.147528i	0.0253330	−	0.00922047i
$257$	−5.10311	+	28.9412i	−0.318323	+	1.80530i	0.234627	+	0.972085i	$0.424613\pi$
$257$	−5.10311	+	28.9412i	−0.318323	+	1.80530i	−0.552950	+	0.833214i	$0.686498\pi$
$258$	−5.43329	+	2.26923i	−0.338262	+	0.141276i
$259$	3.59813	−	4.07896i	0.223577	−	0.253454i
$260$	−0.00234710	−	0.00135510i	−0.000145561	−	8.40396e-5i
$261$	6.38824	−	24.4130i	0.395422	−	1.51113i
$262$			5.51656i			0.340814i
$263$	−5.73330	+	15.7521i	−0.353531	+	0.971318i	0.627696	+	0.778459i	$0.283998\pi$
$263$	−5.73330	+	15.7521i	−0.353531	+	0.971318i	−0.981227	+	0.192859i	$0.938224\pi$
$264$	10.4116	+	11.2956i	0.640789	+	0.695195i
$265$	−0.00202329	−	0.00555894i	−0.000124290	−	0.000341483i
$266$	−0.169947	+	6.87434i	−0.0104201	+	0.421493i
$267$	4.71801	−	3.02519i	0.288738	−	0.185139i
$268$	−3.49861	−	1.27339i	−0.213711	−	0.0777846i
$269$	4.71711	−	8.17027i	0.287607	−	0.498150i	−0.685631	−	0.727949i	$-0.740474\pi$
$269$	4.71711	−	8.17027i	0.287607	−	0.498150i	0.973238	+	0.229799i	$0.0738069\pi$
$270$	−0.000898195	−	0.00114947i	−5.46624e−5	−	6.99545e-5i
$271$	−3.40065	+	1.96337i	−0.206575	+	0.119266i	−0.599719	−	0.800211i	$-0.704721\pi$
$271$	−3.40065	+	1.96337i	−0.206575	+	0.119266i	0.393144	+	0.919477i	$0.371388\pi$
$272$	1.57288	−	1.31980i	0.0953696	−	0.0800246i
$273$	−4.05584	+	11.9494i	−0.245471	+	0.723210i
$274$	−0.871668	+	4.94347i	−0.0526594	+	0.298646i
$275$	15.2196	−	18.1380i	0.917778	−	1.09376i
$276$	3.53753	−	3.26069i	0.212934	−	0.196270i
$277$	21.5582	+	7.84655i	1.29531	+	0.471454i	0.895466	−	0.445130i	$-0.146843\pi$
$277$	21.5582	+	7.84655i	1.29531	+	0.471454i	0.399843	+	0.916584i	$0.369065\pi$
$278$	0.103759	−	0.179716i	0.00622305	−	0.0107786i
$279$	−24.1481	−	1.97005i	−1.44571	−	0.117944i
$280$	0.00217771	−	0.00173744i	0.000130143	−	0.000103832i
$281$	0.608889	−	1.67291i	0.0363233	−	0.0997974i	−0.920205	−	0.391436i	$-0.871978\pi$
$281$	0.608889	−	1.67291i	0.0363233	−	0.0997974i	0.956528	+	0.291639i	$0.0942006\pi$
$282$	−0.818558	+	6.36166i	−0.0487444	+	0.378832i
$283$	−1.52431	−	4.18800i	−0.0906106	−	0.248951i	0.886107	−	0.463482i	$-0.153400\pi$
$283$	−1.52431	−	4.18800i	−0.0906106	−	0.248951i	−0.976717	+	0.214531i	$0.931178\pi$
$284$	5.23361	+	14.3792i	0.310557	+	0.853249i
$285$	−0.000646790		0.00502672i	−3.83126e−5		0.000297757i
$286$	−2.22714	+	6.11901i	−0.131693	+	0.361825i
$287$	−17.7689	+	2.68217i	−1.04887	+	0.158323i
$288$	−6.45384	−	13.6310i	−0.380296	−	0.803215i
$289$	8.17986	−	14.1679i	0.481168	−	0.833408i
$290$	−0.00221909		0.000807684i	−0.000130310		4.74289e-5i
$291$	−2.28714	+	2.10815i	−0.134074	+	0.123582i
$292$	−8.08234	+	9.63216i	−0.472983	+	0.563679i
$293$	−1.23196	+	6.98681i	−0.0719721	+	0.408174i	0.927443	+	0.373965i	$0.122002\pi$
$293$	−1.23196	+	6.98681i	−0.0719721	+	0.408174i	−0.999415	+	0.0342085i	$0.989109\pi$
$294$	−4.62680	−	3.90501i	−0.269840	−	0.227745i
$295$	−0.00568967	+	0.00477420i	−0.000331265	+	0.000277965i
$296$	−3.33453	+	1.92519i	−0.193815	+	0.111899i
$297$	16.4636	−	18.2873i	0.955316	−	1.06114i
$298$	0.229979	−	0.398336i	0.0133223	−	0.0230750i
$299$	4.10565	+	1.49434i	0.237436	+	0.0864197i
$300$	−12.7627	+	8.18344i	−0.736854	+	0.472471i
$301$	−15.8162	+	8.61749i	−0.911632	+	0.496704i
$302$	−0.205589	−	0.564852i	−0.0118303	−	0.0325036i
$303$	5.00007	+	5.42460i	0.287247	+	0.311635i
$304$	−4.56780	+	12.5499i	−0.261981	+	0.719788i
$305$			0.00204346i			0.000117008i
$306$	0.852585	+	0.842643i	0.0487391	+	0.0481707i
$307$	6.20672	+	3.58345i	0.354236	+	0.204518i	0.666549	−	0.745461i	$-0.267771\pi$
$307$	6.20672	+	3.58345i	0.354236	+	0.204518i	−0.312313	+	0.949979i	$0.601104\pi$
$308$	16.4486	+	14.5096i	0.937246	+	0.826764i
$309$	25.7012	−	10.7342i	1.46209	−	0.610646i
$310$	−0.000393713		0.00223286i	−2.23614e−5		0.000126818i
$311$	−21.8466	+	7.95150i	−1.23881	+	0.450888i	−0.876605	−	0.481212i	$-0.840197\pi$
$311$	−21.8466	+	7.95150i	−1.23881	+	0.450888i	−0.362201	+	0.932100i	$0.617975\pi$
$312$	5.41723	−	7.10290i	0.306690	−	0.402123i
$313$	23.5238	−	4.14788i	1.32964	−	0.234452i	0.536713	−	0.843765i	$-0.319666\pi$
$313$	23.5238	−	4.14788i	1.32964	−	0.234452i	0.792930	+	0.609313i	$0.208555\pi$
$314$	2.87721	−	4.98347i	0.162370	−	0.281234i
$315$	−0.00309530	−	0.00321426i	−0.000174401	−	0.000181103i
$316$	−2.25541	−	3.90648i	−0.126877	−	0.219757i
$317$	−18.4623	−	22.0025i	−1.03695	−	1.23579i	−0.971279	−	0.237944i	$-0.923526\pi$
$317$	−18.4623	−	22.0025i	−1.03695	−	1.23579i	−0.0656685	−	0.997841i	$-0.520918\pi$
$318$	8.87950	−	1.99587i	0.497937	−	0.111923i
$319$	6.91702	−	39.2284i	0.387279	−	2.19637i
$320$	0.00138498		0.000504092i	7.74228e−5		2.81796e-5i
$321$	6.96774	−	0.324692i	0.388901	−	0.0181225i
$322$	−1.38674	+	1.57205i	−0.0772798	+	0.0876068i
$323$		−	4.16468i		−	0.231729i
$324$	−13.5515	+	8.03737i	−0.752862	+	0.446521i
$325$	−11.9238	−	6.88420i	−0.661412	−	0.381866i
$326$	3.36662	−	0.593626i	0.186460	−	0.0328779i
$327$	−1.71423	+	1.09917i	−0.0947971	+	0.0607840i
$328$	12.5279	+	2.20900i	0.691735	+	0.121972i
$329$	−0.484906	+	19.6144i	−0.0267337	+	1.08138i
$330$	−0.00156064	−	0.00169315i	−8.59106e−5	−	9.32047e-5i
$331$	−19.9199	+	16.7148i	−1.09490	+	0.918726i	−0.997071	−	0.0764775i	$-0.975633\pi$
$331$	−19.9199	+	16.7148i	−1.09490	+	0.918726i	−0.0978240	+	0.995204i	$0.531188\pi$
$332$	3.37676			0.185324
$333$	3.56706	+	5.03123i	0.195474	+	0.275709i
$334$		−	2.31571i		−	0.126710i
$335$	0.00112355		0.000408937i	6.13858e−5		2.23426e-5i
$336$	−6.10053	−	10.0526i	−0.332811	−	0.548416i
$337$	5.30836	+	4.45424i	0.289165	+	0.242638i	0.775817	−	0.630958i	$-0.217338\pi$
$337$	5.30836	+	4.45424i	0.289165	+	0.242638i	−0.486653	+	0.873596i	$0.661782\pi$
$338$	−2.66408	−	0.469749i	−0.144907	−	0.0255510i
$339$	−3.25931	+	25.3307i	−0.177021	+	1.37577i
$340$	−0.000603288	0	0.000506219i	−3.27179e−5	0	2.74536e-5i
$341$	−38.2444			−2.07105
$342$	−7.54317	−	1.97384i	−0.407888	−	0.106733i
$343$	−15.3089	−	10.4229i	−0.826604	−	0.562783i
$344$	12.5566	−	2.21407i	0.677008	−	0.119375i
$345$	−0.00113605	+	0.00104714i	−6.11627e−5	+	5.63761e-5i
$346$	11.8326	+	2.08640i	0.636124	+	0.112166i
$347$	−1.01656	+	1.21149i	−0.0545718	+	0.0650361i	−0.792640	−	0.609690i	$-0.791294\pi$
$347$	−1.01656	+	1.21149i	−0.0545718	+	0.0650361i	0.738068	+	0.674726i	$0.235738\pi$
$348$	−11.7109	+	22.6584i	−0.627769	+	1.21462i
$349$	11.3433	+	13.5184i	0.607194	+	0.723626i	0.978812	−	0.204760i	$-0.0656414\pi$
$349$	11.3433	+	13.5184i	0.607194	+	0.723626i	−0.371618	+	0.928386i	$0.621197\pi$
$350$	5.16384	−	4.11986i	0.276019	−	0.220216i
$351$	−12.1349	−	7.58151i	−0.647711	−	0.404671i
$352$	−11.9032	−	20.6170i	−0.634444	−	1.09889i
$353$	−0.472599	−	2.68024i	−0.0251539	−	0.142655i	0.969644	−	0.244520i	$-0.0786303\pi$
$353$	−0.472599	−	2.68024i	−0.0251539	−	0.142655i	−0.994798	+	0.101865i	$0.967519\pi$
$354$	−6.16776	−	9.61908i	−0.327813	−	0.511248i
$355$	−0.00168072	−	0.00461775i	−8.92035e−5	−	0.000245085i
$356$	−5.32310	+	1.93745i	−0.282124	+	0.102685i
$357$	2.85979	+	2.29507i	0.151356	+	0.121468i
$358$	2.13903	+	12.1311i	0.113051	+	0.641146i
$359$	19.8115	+	11.4382i	1.04561	+	0.603683i	0.921417	−	0.388575i	$-0.127032\pi$
$359$	19.8115	+	11.4382i	1.04561	+	0.603683i	0.124193	+	0.992258i	$0.460366\pi$
$360$	0.00135177	+	0.00285504i	7.12445e−5	+	0.000150474i
$361$	4.04462	+	7.00549i	0.212875	+	0.368710i
$362$	−0.779425	−	4.42034i	−0.0409657	−	0.232328i
$363$	12.0005	−	15.7347i	0.629863	−	0.825857i
$364$	6.64821	−	10.8846i	0.348461	−	0.570509i
$365$	0.00259557	−	0.00309328i	0.000135858	−	0.000161910i
$366$	−3.11807	−	0.401204i	−0.162984	−	0.0209712i
$367$	4.74994	+	5.66075i	0.247945	+	0.295489i	0.875634	−	0.482975i	$-0.160444\pi$
$367$	4.74994	+	5.66075i	0.247945	+	0.295489i	−0.627690	+	0.778464i	$0.715999\pi$
$368$	−3.52591	+	2.03569i	−0.183801	+	0.106117i
$369$	1.65683	−	20.3088i	0.0862513	−	1.05724i
$370$	0.000499828	0	0.000288576i	2.59848e−5	0	1.50023e-5i
$371$	26.3880	−	8.87226i	1.37000	−	0.460625i
$372$	23.3764	+	7.29526i	1.21201	+	0.378242i
$373$	24.8147	+	20.8220i	1.28486	+	1.07812i	0.992555	+	0.121797i	$0.0388658\pi$
$373$	24.8147	+	20.8220i	1.28486	+	1.07812i	0.292302	+	0.956326i	$0.405579\pi$
$374$	1.44950	+	1.21628i	0.0749521	+	0.0628923i
$375$	0.00819723	−	0.00525607i	0.000423303	−	0.000271422i
$376$	4.75042	−	13.0517i	0.244984	−	0.673089i
$377$	−23.1631			−1.19296
$378$	5.51229	−	4.09198i	0.283522	−	0.210469i
$379$	−6.72815			−0.345602			−0.172801	−	0.984957i	$-0.555282\pi$
$379$	−6.72815			−0.345602			−0.172801	+	0.984957i	$0.555282\pi$
$380$	0.00175201	−	0.00481362i	8.98764e−5	−	0.000246933i
$381$	0.559190	+	12.0000i	0.0286482	+	0.614777i
$382$	−7.97978	−	6.69583i	−0.408281	−	0.342588i
$383$	−0.217502	−	0.182506i	−0.0111138	−	0.00932560i	0.637214	−	0.770687i	$-0.280087\pi$
$383$	−0.217502	−	0.182506i	−0.0111138	−	0.00932560i	−0.648328	+	0.761361i	$0.724531\pi$
$384$	4.31636	+	19.2032i	0.220268	+	0.979957i
$385$	−0.00528232	−	0.00465964i	−0.000269212	−	0.000237477i
$386$	7.90450	−	4.56367i	0.402329	−	0.232285i
$387$	−5.40150	−	19.6959i	−0.274574	−	1.00120i
$388$	2.72269	−	1.57194i	0.138223	−	0.0798033i
$389$	0.478715	+	0.570510i	0.0242718	+	0.0289260i	0.778044	−	0.628210i	$-0.216212\pi$
$389$	0.478715	+	0.570510i	0.0242718	+	0.0289260i	−0.753772	+	0.657136i	$0.771768\pi$
$390$	−0.000812014		0.00106469i	−4.11179e−5		5.39126e-5i
$391$	0.816083	−	0.972570i	0.0412711	−	0.0491850i
$392$	7.92070	+	10.4474i	0.400056	+	0.527672i
$393$	−18.9779	−	2.44189i	−0.957307	−	0.123177i
$394$	−0.893706	−	5.06846i	−0.0450243	−	0.255345i
$395$	0.000724303		0.00125453i	3.64437e−5		6.31223e-5i
$396$	−20.2887	+	14.3843i	−1.01954	+	0.722840i
$397$	14.4875	+	8.36439i	0.727109	+	0.419797i	0.817364	−	0.576122i	$-0.195435\pi$
$397$	14.4875	+	8.36439i	0.727109	+	0.419797i	−0.0902545	+	0.995919i	$0.528768\pi$
$398$	−0.968833	−	5.49452i	−0.0485632	−	0.275416i
$399$	−23.5736	−	3.62755i	−1.18016	−	0.181605i
$400$	12.0563	−	4.38812i	0.602814	−	0.219406i
$401$	−6.32052	−	17.3655i	−0.315632	−	0.867191i	−0.991493	−	0.130162i	$-0.958450\pi$
$401$	−6.32052	−	17.3655i	−0.315632	−	0.867191i	0.675861	−	0.737029i	$-0.263772\pi$
$402$	−0.844579	+	1.63410i	−0.0421238	+	0.0815017i
$403$	3.86176	+	21.9011i	0.192368	+	1.09097i
$404$	−3.72832	−	6.45763i	−0.185491	−	0.321279i
$405$	0.00435195	−	0.00258113i	0.000216250	−	0.000128257i
$406$	4.05795	−	10.3461i	0.201393	−	0.513467i
$407$	6.25772	+	7.45767i	0.310184	+	0.369663i
$408$	−1.40112	−	2.18514i	−0.0693656	−	0.108181i
$409$	11.4565	−	13.6534i	0.566489	−	0.675116i	−0.404417	−	0.914575i	$-0.632526\pi$
$409$	11.4565	−	13.6534i	0.566489	−	0.675116i	0.970906	+	0.239459i	$0.0769701\pi$
$410$	−0.00187786		0.000331117i	−9.27409e−5		1.63527e-5i
$411$	−16.6205	−	5.18689i	−0.819830	−	0.255851i
$412$	−27.7239	+	4.88847i	−1.36586	+	0.240838i
$413$	−21.7991	−	27.3230i	−1.07266	−	1.34448i
$414$	−1.37476	−	1.93906i	−0.0675658	−	0.0952994i
$415$	−0.00108442			−5.32319e−5
$416$	−10.6046	+	8.89834i	−0.519934	+	0.436277i
$417$	0.572323	+	0.436499i	0.0280268	+	0.0213754i
$418$	−12.1208	−	2.13723i	−0.592849	−	0.104535i
$419$	−0.812929	−	0.682129i	−0.0397142	−	0.0333242i	0.622715	−	0.782449i	$-0.286030\pi$
$419$	−0.812929	−	0.682129i	−0.0397142	−	0.0333242i	−0.662429	+	0.749125i	$0.730474\pi$
$420$	0.00233990	+	0.00385576i	0.000114176	+	0.000188142i
$421$	−14.4175	−	5.24755i	−0.702667	−	0.255750i	−0.0341181	−	0.999418i	$-0.510862\pi$
$421$	−14.4175	−	5.24755i	−0.702667	−	0.255750i	−0.668549	+	0.743668i	$0.733084\pi$
$422$			11.8606i			0.577364i
$423$	−21.5228	−	5.63194i	−1.04648	−	0.273834i
$424$	−19.7077			−0.957090
$425$	−3.06484	+	2.57170i	−0.148666	+	0.124746i
$426$	7.37610	−	1.65795i	0.357373	−	0.0803280i
$427$	−9.61372	−	0.237669i	−0.465241	−	0.0115016i
$428$	−6.94305	−	1.22425i	−0.335605	−	0.0591762i
$429$	−20.0646	−	10.3703i	−0.968726	−	0.500682i
$430$	−0.00188217		0.000331878i	−9.07665e−5		1.60046e-5i
$431$	3.29736	+	1.90373i	0.158828	+	0.0916996i	0.577308	−	0.816527i	$-0.304103\pi$
$431$	3.29736	+	1.90373i	0.158828	+	0.0916996i	−0.418479	+	0.908226i	$0.637437\pi$
$432$	12.6805	−	4.12113i	0.610090	−	0.198278i
$433$			29.5261i			1.41893i	0.704739	+	0.709467i	$0.251064\pi$
$433$			29.5261i			1.41893i	−0.704739	+	0.709467i	$0.748936\pi$
$434$	−10.4590	−	2.11197i	−0.502046	−	0.101378i
$435$	0.00376084	−	0.00727653i	0.000180319	−	0.000348883i
$436$	1.93408	−	0.703949i	0.0926258	−	0.0337130i
$437$	−1.43401	+	8.13267i	−0.0685980	+	0.389038i
$438$	4.21036	+	4.56784i	0.201179	+	0.218260i
$439$	−10.6109	−	12.6456i	−0.506432	−	0.603543i	0.450885	−	0.892582i	$-0.351109\pi$
$439$	−10.6109	−	12.6456i	−0.506432	−	0.603543i	−0.957317	+	0.289040i	$0.906664\pi$
$440$	0.00249315	+	0.00431827i	0.000118856	+	0.000205865i
$441$	15.4819	−	14.1884i	0.737234	−	0.675638i
$442$	0.550152	−	0.952891i	0.0261681	−	0.0453244i
$443$	−27.5106	+	4.85086i	−1.30707	+	0.230471i	−0.783435	−	0.621474i	$-0.786534\pi$
$443$	−27.5106	+	4.85086i	−1.30707	+	0.230471i	−0.523632	+	0.851945i	$0.675423\pi$
$444$	−2.40238	−	5.75208i	−0.114012	−	0.272982i
$445$	0.00170947		0.000622194i	8.10364e−5		2.94948e-5i
$446$	−2.09565	+	11.8850i	−0.0992321	+	0.562773i
$447$	1.26854	+	0.967489i	0.0599999	+	0.0457606i
$448$	2.21048	+	6.57444i	0.104435	+	0.310613i
$449$	20.1252	+	11.6193i	0.949765	+	0.548347i	0.893008	−	0.450041i	$-0.148591\pi$
$449$	20.1252	+	11.6193i	0.949765	+	0.548347i	0.0567572	+	0.998388i	$0.481924\pi$
$450$	3.20536	+	6.76996i	0.151102	+	0.319139i
$451$		−	32.1640i		−	1.51455i
$452$	8.82876	−	24.2568i	0.415270	−	1.14094i
$453$	2.03418	−	0.457230i	0.0955743	−	0.0214825i
$454$	−0.730736	−	2.00768i	−0.0342952	−	0.0942252i
$455$	−0.00213501	+	0.00349549i	−0.000100091	+	0.000163871i
$456$	14.9993	+	7.75230i	0.702404	+	0.363035i
$457$	−17.0320	−	6.19915i	−0.796724	−	0.289984i	−0.0885960	−	0.996068i	$-0.528238\pi$
$457$	−17.0320	−	6.19915i	−0.796724	−	0.289984i	−0.708128	+	0.706084i	$0.750460\pi$
$458$	−3.23444	+	5.60221i	−0.151135	+	0.261774i
$459$	−3.27622	+	2.56004i	−0.152921	+	0.119492i
$460$	0.00135239		0.000780802i	6.30555e−5		3.64051e-5i
$461$	0.780576	−	0.654981i	0.0363550	−	0.0305055i	−0.624429	−	0.781081i	$-0.714668\pi$
$461$	0.780576	−	0.654981i	0.0363550	−	0.0305055i	0.660784	+	0.750576i	$0.270224\pi$
$462$	8.14714	−	7.14531i	0.379039	−	0.332430i
$463$	5.96496	−	33.8290i	0.277215	−	1.57216i	−0.454621	−	0.890685i	$-0.650225\pi$
$463$	5.96496	−	33.8290i	0.277215	−	1.57216i	0.731837	−	0.681480i	$-0.238663\pi$
$464$	13.8742	−	16.5346i	0.644093	−	0.767600i
$465$	−0.00750712	−	0.00234280i	−0.000348134	−	0.000108645i
$466$	5.25783	+	1.91369i	0.243564	+	0.0886502i
$467$	−0.712541	+	1.23416i	−0.0329724	+	0.0571100i	−0.882041	−	0.471173i	$-0.843831\pi$
$467$	−0.712541	+	1.23416i	−0.0329724	+	0.0571100i	0.849068	+	0.528283i	$0.177164\pi$
$468$	10.2860	+	10.1661i	0.475472	+	0.469927i
$469$	−2.05457	+	5.23830i	−0.0948713	+	0.241882i
$470$	−0.000712064		0.00195638i	−3.28451e−5		9.02410e-5i
$471$	15.8704	+	12.1040i	0.731268	+	0.557722i
$472$	8.46280	+	23.2514i	0.389532	+	1.07023i
$473$	−11.0260	−	30.2937i	−0.506977	−	1.39291i
$474$	−2.05646	+	0.858889i	−0.0944566	+	0.0394501i
$475$	8.90062	−	24.4542i	0.408388	−	1.12204i
$476$	−2.31140	−	2.89712i	−0.105943	−	0.132789i
$477$	2.93564	+	31.4304i	0.134414	+	1.43910i
$478$	−3.13135	+	5.42365i	−0.143224	+	0.248072i
$479$	33.6340	+	12.2418i	1.53678	+	0.559341i	0.965270	−	0.261256i	$-0.0841366\pi$
$479$	33.6340	+	12.2418i	1.53678	+	0.559341i	0.571507	+	0.820597i	$0.306359\pi$
$480$	−0.00107355	−	0.00477614i	−4.90006e−5	−	0.000218000i
$481$	3.63884	−	4.33660i	0.165917	−	0.197732i
$482$	1.74075	−	9.87226i	0.0792888	−	0.449669i
$483$	−4.79427	−	5.46646i	−0.218147	−	0.248732i
$484$	−15.3217	+	12.8564i	−0.696441	+	0.584383i
$485$	−0.000874365	0	0.000504815i	−3.97029e−5	0	2.29225e-5i
$486$	3.08404	+	7.14730i	0.139895	+	0.324208i
$487$	−17.4657	+	30.2515i	−0.791446	+	1.37082i	0.133625	+	0.991032i	$0.457338\pi$
$487$	−17.4657	+	30.2515i	−0.791446	+	1.37082i	−0.925071	+	0.379793i	$0.875995\pi$
$488$	6.39708	+	2.32835i	0.289582	+	0.105399i
$489$	0.551945	+	11.8445i	0.0249598	+	0.535626i
$490$	−0.00118727	−	0.00156601i	−5.36354e−5	−	7.07450e-5i
$491$	−3.72269	−	10.2280i	−0.168003	−	0.461584i	0.826909	−	0.562336i	$-0.190097\pi$
$491$	−3.72269	−	10.2280i	−0.168003	−	0.461584i	−0.994912	+	0.100752i	$0.967875\pi$
$492$	−6.13540	+	19.6598i	−0.276605	+	0.886334i
$493$	−2.30206	+	6.32487i	−0.103680	+	0.284858i
$494$			7.15694i			0.322006i
$495$	0.00651552	−	0.00461940i	0.000292851	−	0.000207626i
$496$	−17.9469	−	10.3617i	−0.805841	−	0.465252i
$497$	21.9203	−	7.37009i	0.983258	−	0.330594i
$498$	0.212909	−	1.65469i	0.00954068	−	0.0741482i
$499$	1.10201	−	6.24980i	0.0493326	−	0.279779i	−0.950155	−	0.311777i	$-0.899076\pi$
$499$	1.10201	−	6.24980i	0.0493326	−	0.279779i	0.999488	+	0.0319977i	$0.0101869\pi$
$500$	−0.00924854	+	0.00336619i	−0.000413607	+	0.000150541i
$501$	7.96643	+	1.02504i	0.355914	+	0.0457956i
$502$	−11.0876	+	1.95505i	−0.494864	+	0.0872579i
$503$	6.72425	−	11.6468i	0.299820	−	0.519303i	−0.676275	−	0.736649i	$-0.736407\pi$
$503$	6.72425	−	11.6468i	0.299820	−	0.519303i	0.976095	+	0.217346i	$0.0697401\pi$
$504$	−13.5891	+	6.02751i	−0.605308	+	0.268486i
$505$	0.00119731	+	0.00207381i	5.32798e−5	+	9.22833e-5i
$506$	−2.41176	−	2.87422i	−0.107216	−	0.127775i
$507$	2.79526	−	8.95692i	0.124142	−	0.397791i
$508$	2.10842	−	11.9574i	0.0935459	−	0.530525i
$509$	16.2407	−	5.91114i	0.719857	−	0.262007i	0.0439919	−	0.999032i	$-0.485992\pi$
$509$	16.2407	−	5.91114i	0.719857	−	0.262007i	0.675865	+	0.737025i	$0.263770\pi$
$510$	0.000210020	0	0.000327542i	9.29984e−6	0	1.45038e-5i
$511$	14.2508	+	12.5709i	0.630419	+	0.556106i
$512$		−	22.5118i		−	0.994888i
$513$	10.1293	−	25.0760i	0.447220	−	1.10713i
$514$	−12.7090	−	7.33754i	−0.560570	−	0.323645i
$515$	0.00890327	−	0.00156989i	0.000392325	−	6.91775e-5i
$516$	0.960873	+	20.6199i	0.0423001	+	0.907740i
$517$	−34.5842	−	6.09812i	−1.52101	−	0.268195i
$518$	1.29951	+	2.38507i	0.0570971	+	0.104794i
$519$	−12.4152	+	39.7825i	−0.544968	+	1.74626i
$520$	0.00222116	−	0.00186377i	9.74043e−5	−	8.17319e-5i
$521$	−28.5570			−1.25111			−0.625553	−	0.780182i	$-0.715126\pi$
$521$	−28.5570			−1.25111			−0.625553	+	0.780182i	$0.715126\pi$
$522$	10.3647	+	7.16722i	0.453651	+	0.313701i
$523$			15.1785i			0.663708i	0.943331	+	0.331854i	$0.107674\pi$
$523$			15.1785i			0.663708i	−0.943331	+	0.331854i	$0.892326\pi$
$524$	18.1733	+	6.61455i	0.793905	+	0.288958i
$525$	11.8872	+	19.5881i	0.518801	+	0.854895i
$526$	−6.41244	−	5.38068i	−0.279596	−	0.234609i
$527$	6.36410	+	1.12216i	0.277224	+	0.0488822i
$528$	19.4209	−	8.11121i	0.845187	−	0.352995i
$529$	15.6905	−	13.1659i	0.682196	−	0.572431i
$530$	0.00295408			0.000128317
$531$	35.8213	−	16.9602i	1.55451	−	0.736011i
$532$	22.4425	+	8.80243i	0.973006	+	0.381634i
$533$	−18.4191	+	3.24779i	−0.797821	+	0.140677i
$534$	0.613764	+	2.73059i	0.0265602	+	0.118164i
$535$	0.00222969		0.000393155i	9.63981e−5		1.69976e-5i
$536$	2.56036	−	3.05132i	0.110591	−	0.131797i
$537$	−42.6796	+	1.98884i	−1.84176	+	0.0858249i
$538$	3.02823	+	3.60891i	0.130556	+	0.155591i
$539$	22.5362	−	24.3094i	0.970703	−	1.04708i
$540$	−0.00486369	+	0.00158069i	−0.000209300	+	6.80220e-5i
$541$	8.84080	+	15.3127i	0.380096	+	0.658345i	0.991076	−	0.133301i	$-0.0425577\pi$
$541$	8.84080	+	15.3127i	0.380096	+	0.658345i	−0.610980	+	0.791646i	$0.709224\pi$
$542$	−0.340501	−	1.93108i	−0.0146258	−	0.0829468i
$543$	15.5517	−	0.724699i	0.667387	−	0.0310998i
$544$	1.37582	+	3.78005i	0.0589880	+	0.162068i
$545$	−0.000621113	0	0.000226067i	−2.66055e−5	0	9.68363e-6i
$546$	−4.91451	−	3.94405i	−0.210322	−	0.168790i
$547$	−1.23750	−	7.01822i	−0.0529117	−	0.300077i	0.946855	−	0.321660i	$-0.104241\pi$
$547$	−1.23750	−	7.01822i	−0.0529117	−	0.300077i	−0.999767	+	0.0215823i	$0.993130\pi$
$548$	15.2402	+	8.79895i	0.651030	+	0.375873i
$549$	2.76041	−	10.5491i	0.117811	−	0.450224i
$550$	5.91184	+	10.2396i	0.252082	+	0.436618i
$551$	−7.60241	−	43.1154i	−0.323873	−	1.83678i
$552$	1.98366	+	4.74953i	0.0844300	+	0.202153i
$553$	−5.98633	+	3.26166i	−0.254565	+	0.138700i
$554$	−7.36395	+	8.77601i	−0.312864	+	0.372857i
$555$	0.000771501		0.00184723i	3.27484e−5		7.84104e-5i
$556$	−0.467631	−	0.557301i	−0.0198320	−	0.0236348i
$557$	−6.62385	+	3.82428i	−0.280662	+	0.162040i	−0.633723	−	0.773560i	$-0.718474\pi$
$557$	−6.62385	+	3.82428i	−0.280662	+	0.162040i	0.353061	+	0.935600i	$0.385141\pi$
$558$	5.04874	−	10.9950i	0.213730	−	0.465454i
$559$	−16.2347	+	9.37312i	−0.686655	+	0.396441i
$560$	−0.00121638	−	0.00361777i	−5.14014e−5	−	0.000152879i
$561$	−4.82582	+	4.44815i	−0.203746	+	0.187801i
$562$	0.681015	+	0.571439i	0.0287269	+	0.0241047i
$563$	27.7146	+	23.2553i	1.16803	+	0.980095i	0.999984	−	0.00568387i	$-0.00180924\pi$
$563$	27.7146	+	23.2553i	1.16803	+	0.980095i	0.168048	+	0.985779i	$0.446254\pi$
$564$	19.9759	+	10.3244i	0.841136	+	0.434738i
$565$	−0.00283527	+	0.00778985i	−0.000119281	+	0.000327722i
$566$	2.22555			0.0935467
$567$	11.6371	+	20.7745i	0.488711	+	0.872446i
$568$	−16.3710			−0.686910
$569$	1.82595	−	5.01676i	0.0765478	−	0.210313i	−0.895516	−	0.445029i	$-0.853194\pi$
$569$	1.82595	−	5.01676i	0.0765478	−	0.210313i	0.972064	+	0.234715i	$0.0754157\pi$
$570$	−0.00224831	−	0.00116203i	−9.41713e−5	−	4.86720e-5i
$571$	28.4696	+	23.8889i	1.19142	+	0.999718i	0.999834	+	0.0182416i	$0.00580681\pi$
$571$	28.4696	+	23.8889i	1.19142	+	0.999718i	0.191584	+	0.981476i	$0.438638\pi$
$572$	17.4876	+	14.6738i	0.731192	+	0.613543i
$573$	26.5670	−	24.4878i	1.10985	−	1.02299i
$574$	1.77619	−	8.79611i	0.0741368	−	0.367143i
$575$	6.87043	−	3.96664i	0.286517	−	0.165421i
$576$	−7.83072	+	0.731401i	−0.326280	+	0.0304750i
$577$	21.9589	−	12.6780i	0.914161	−	0.527791i	0.0323932	−	0.999475i	$-0.489687\pi$
$577$	21.9589	−	12.6780i	0.914161	−	0.527791i	0.881768	+	0.471684i	$0.156354\pi$
$578$	5.25121	+	6.25815i	0.218422	+	0.260305i
$579$	12.2009	+	29.2129i	0.507050	+	1.21405i
$580$	−0.00532154	+	0.00634197i	−0.000220965	+	0.000263336i
$581$	0.126125	−	5.10177i	0.00523256	−	0.211657i
$582$	−0.598617	−	1.43329i	−0.0248135	−	0.0594117i
$583$	8.65269	+	49.0718i	0.358358	+	2.03235i
$584$	−6.72612	−	11.6500i	−0.278329	−	0.482080i
$585$	−0.00330326	−	0.00326474i	−0.000136573	−	0.000134980i
$586$	−3.06813	−	1.77139i	−0.126743	−	0.0731754i
$587$	−2.85469	−	16.1897i	−0.117826	−	0.668222i	−0.985312	−	0.170762i	$-0.945377\pi$
$587$	−2.85469	−	16.1897i	−0.117826	−	0.668222i	0.867487	−	0.497460i	$-0.165734\pi$
$588$	−18.4121	+	10.5599i	−0.759300	+	0.435483i
$589$	−39.4990	+	14.3765i	−1.62753	+	0.592372i
$590$	−0.00126853	−	0.00348526i	−5.22246e−5	−	0.000143486i
$591$	17.8319	−	0.830956i	0.733507	−	0.0341809i
$592$	0.916031	+	5.19507i	0.0376486	+	0.213516i
$593$	15.3209	+	26.5365i	0.629153	+	1.08973i	0.987722	+	0.156222i	$0.0499315\pi$
$593$	15.3209	+	26.5365i	0.629153	+	1.08973i	−0.358569	+	0.933503i	$0.616735\pi$
$594$	5.76941	+	10.8488i	0.236722	+	0.445133i
$595$	0.000742286	0	0.000930384i	3.04307e−5	0	3.81420e-5i
$596$	−1.03649	−	1.23524i	−0.0424564	−	0.0505976i
$597$	19.3309	−	0.900807i	0.791161	−	0.0368676i
$598$	−1.40243	+	1.67135i	−0.0573495	+	0.0683465i
$599$	−19.2428	−	3.39302i	−0.786239	−	0.138635i	−0.233906	−	0.972259i	$-0.575151\pi$
$599$	−19.2428	−	3.39302i	−0.786239	−	0.138635i	−0.552332	+	0.833624i	$0.686262\pi$
$600$	−3.55708	−	15.8252i	−0.145217	−	0.646061i
$601$	20.6262	−	3.63695i	0.841360	−	0.148354i	0.263672	−	0.964612i	$-0.415066\pi$
$601$	20.6262	−	3.63695i	0.841360	−	0.148354i	0.577688	+	0.816258i	$0.303955\pi$
$602$	−1.34245	−	8.89352i	−0.0547142	−	0.362473i
$603$	−5.24773	−	3.62882i	−0.213704	−	0.147777i
$604$	−2.10731			−0.0857453
$605$	0.00492042	−	0.00412872i	0.000200043	−	0.000167856i
$606$	−3.39945	+	1.41979i	−0.138093	+	0.0576751i
$607$	−26.5691	−	4.68485i	−1.07841	−	0.190152i	−0.393896	−	0.919155i	$-0.628873\pi$
$607$	−26.5691	−	4.68485i	−1.07841	−	0.190152i	−0.684511	+	0.729003i	$0.739984\pi$
$608$	−20.0438	−	16.8188i	−0.812884	−	0.682091i
$609$	33.7959	+	18.5397i	1.36948	+	0.751265i
$610$	−0.000958889	0	0.000349007i	−3.88243e−5	0	1.41309e-5i
$611$			20.4208i			0.826138i
$612$	3.79822	−	1.79833i	0.153534	−	0.0726932i
$613$	−26.9051			−1.08669			−0.543343	−	0.839511i	$-0.682842\pi$
$613$	−26.9051			−1.08669			−0.543343	+	0.839511i	$0.682842\pi$
$614$	−2.74158	+	2.30046i	−0.110641	+	0.0928390i
$615$	0.00197033	−	0.00631358i	7.94513e−5	−	0.000254588i
$616$	−20.6058	+	11.2271i	−0.830231	+	0.452353i
$617$	−22.1664	−	3.90853i	−0.892386	−	0.157352i	−0.291390	−	0.956604i	$-0.594118\pi$
$617$	−22.1664	−	3.90853i	−0.892386	−	0.157352i	−0.600995	+	0.799253i	$0.705229\pi$
$618$	0.647429	+	13.8935i	0.0260434	+	0.558879i
$619$	10.5751	−	1.86467i	0.425047	−	0.0749473i	0.0429671	−	0.999076i	$-0.486319\pi$
$619$	10.5751	−	1.86467i	0.425047	−	0.0749473i	0.382080	+	0.924129i	$0.375208\pi$
$620$	0.00688367	+	0.00397429i	0.000276455	+	0.000159611i
$621$	7.27920	−	3.87108i	0.292104	−	0.155341i
$622$		−	11.6095i		−	0.465499i
$623$	2.72837	+	8.11476i	0.109310	+	0.325111i
$624$	−6.60603	−	10.3026i	−0.264453	−	0.412434i
$625$	−23.4923	+	8.55050i	−0.939692	+	0.342020i
$626$	−2.07130	+	11.7469i	−0.0827856	+	0.469500i
$627$	12.7177	−	40.7516i	0.507895	−	1.62746i
$628$	−12.9673	−	15.4538i	−0.517451	−	0.616674i
$629$	−0.822500	−	1.42461i	−0.0327952	−	0.0568030i
$630$	0.00203694		0.000903492i	8.11536e−5		3.59960e-5i
$631$	−0.130873	+	0.226679i	−0.00520998	+	0.00902394i	−0.868619	−	0.495481i	$-0.834992\pi$
$631$	−0.130873	+	0.226679i	−0.00520998	+	0.00902394i	0.863409	+	0.504505i	$0.168325\pi$
$632$	4.75260	−	0.838012i	0.189048	−	0.0333343i
$633$	−40.8023	−	5.25005i	−1.62175	−	0.208671i
$634$	13.4779	−	4.90554i	0.535274	−	0.194824i
$635$	−0.000677099		0.00384002i	−2.68698e−5		0.000152386i
$636$	4.07178	−	31.6450i	0.161457	−	1.25481i
$637$	−16.1967	−	10.4510i	−0.641735	−	0.414083i
$638$	17.2264	+	9.94569i	0.682001	+	0.393754i
$639$	2.43861	+	26.1089i	0.0964698	+	1.03285i
$640$			0.00638861i			0.000252532i
$641$	−17.0992	+	46.9798i	−0.675379	+	1.85559i	−0.188626	+	0.982049i	$0.560404\pi$
$641$	−17.0992	+	46.9798i	−0.675379	+	1.85559i	−0.486753	+	0.873540i	$0.661819\pi$
$642$	−1.03767	+	3.32505i	−0.0409537	+	0.131229i
$643$	−5.42130	−	14.8949i	−0.213795	−	0.587397i	0.785718	−	0.618584i	$-0.212294\pi$
$643$	−5.42130	−	14.8949i	−0.213795	−	0.587397i	−0.999514	+	0.0311869i	$0.990071\pi$
$644$	3.51609	+	6.45329i	0.138553	+	0.254295i
$645$	−0.000308576	−	0.00662189i	−1.21502e−5	−	0.000260737i
$646$	1.95427	+	0.711295i	0.0768896	+	0.0279855i
$647$	−7.51759	+	13.0208i	−0.295547	+	0.511902i	−0.975112	−	0.221713i	$-0.928835\pi$
$647$	−7.51759	+	13.0208i	−0.295547	+	0.511902i	0.679565	+	0.733615i	$0.262169\pi$
$648$	−3.12158	−	16.5648i	−0.122627	−	0.650726i
$649$	54.1799	−	31.2808i	2.12675	−	1.22788i
$650$	5.26688	−	4.41943i	0.206584	−	0.173344i
$651$	11.8951	−	35.0457i	0.466207	−	1.37355i
$652$	2.08110	−	11.8025i	0.0815022	−	0.462222i
$653$	−9.89082	+	11.7874i	−0.387058	+	0.461277i	−0.924029	−	0.382323i	$-0.875124\pi$
$653$	−9.89082	+	11.7874i	−0.387058	+	0.461277i	0.536971	+	0.843601i	$0.319568\pi$
$654$	−0.223003	−	0.992126i	−0.00872012	−	0.0387952i
$655$	−0.00583619	−	0.00212420i	−0.000228039	−	8.29994e-5i
$656$	8.71428	−	15.0936i	0.340236	−	0.589305i
$657$	−17.5778	+	12.4624i	−0.685775	+	0.486204i
$658$	−9.12121	−	3.57753i	−0.355582	−	0.139467i
$659$	−5.58157	+	15.3352i	−0.217427	+	0.597376i	−0.999672	−	0.0255942i	$-0.991852\pi$
$659$	−5.58157	+	15.3352i	−0.217427	+	0.597376i	0.782245	+	0.622971i	$0.214074\pi$
$660$	−0.00744904	+	0.00311112i	−0.000289953	+	0.000121100i
$661$	10.2996	+	28.2979i	0.400608	+	1.10066i	0.961985	+	0.273102i	$0.0880496\pi$
$661$	10.2996	+	28.2979i	0.400608	+	1.10066i	−0.561377	+	0.827560i	$0.689728\pi$
$662$	−4.44120	−	12.2021i	−0.172612	−	0.474248i
$663$	3.03458	+	2.31441i	0.117853	+	0.0898841i
$664$	−1.23560	+	3.39478i	−0.0479505	+	0.131743i
$665$	−0.00720720	−	0.00282682i	−0.000279483	−	0.000109619i
$666$	−2.97011	+	0.814539i	−0.115090	+	0.0315628i
$667$	6.67323	−	11.5584i	0.258388	−	0.447542i
$668$	−7.62871	−	2.77662i	−0.295164	−	0.107431i
$669$	−39.9589	−	12.4703i	−1.54490	−	0.482129i
$670$	−0.000383785	0	0.000457377i	−1.48269e−5	0	1.76700e-5i
$671$	2.98890	−	16.9509i	0.115385	−	0.654383i
$672$	22.5948	−	4.49514i	0.871614	−	0.173404i
$673$	8.51271	−	7.14301i	0.328141	−	0.275343i	−0.463801	−	0.885939i	$-0.653515\pi$
$673$	8.51271	−	7.14301i	0.328141	−	0.275343i	0.791942	+	0.610597i	$0.209070\pi$
$674$	−2.99677	+	1.73018i	−0.115431	+	0.0666442i
$675$	−24.7086	+	8.03024i	−0.951035	+	0.309084i
$676$	−4.74182	+	8.21308i	−0.182378	+	0.315888i
$677$	29.2132	+	10.6327i	1.12276	+	0.408650i	0.835657	−	0.549251i	$-0.185087\pi$
$677$	29.2132	+	10.6327i	1.12276	+	0.408650i	0.287099	+	0.957901i	$0.407309\pi$
$678$	−11.3297	−	5.85570i	−0.435114	−	0.224887i
$679$	−2.27327	−	4.17227i	−0.0872401	−	0.160117i
$680$	−0.000288169	0	0.000791738i	−1.10508e−5	0	3.03618e-5i
$681$	7.23021	−	1.62516i	0.277062	−	0.0622762i
$682$	6.53185	−	17.9461i	0.250117	−	0.687192i
$683$		−	20.0528i		−	0.767298i	−0.923479	−	0.383649i	$-0.874667\pi$
$683$		−	20.0528i		−	0.767298i	0.923479	−	0.383649i	$-0.125333\pi$
$684$	−15.5470	+	22.4829i	−0.594454	+	0.859656i
$685$	−0.00489426	−	0.00282570i	−0.000187000	−	0.000107965i
$686$	7.50556	−	5.40353i	0.286564	−	0.206308i
$687$	−17.8408	−	13.6068i	−0.680669	−	0.519132i
$688$	3.03339	−	17.2032i	0.115647	−	0.655866i
$689$	27.2279	−	9.91013i	1.03730	−	0.377546i
$690$	−0.000297340	0	0.000711930i	−1.13195e−5	0	2.71027e-5i
$691$	−5.23641	+	0.923321i	−0.199203	+	0.0351248i	−0.272359	−	0.962196i	$-0.587804\pi$
$691$	−5.23641	+	0.923321i	−0.199203	+	0.0351248i	0.0731565	+	0.997320i	$0.476693\pi$
$692$	21.0610	−	36.4787i	0.800618	−	1.38671i
$693$	20.9747	+	31.1903i	0.796764	+	1.18482i
$694$	−0.394867	−	0.683930i	−0.0149890	−	0.0259616i
$695$	0.000150175	0	0.000178972i	5.69648e−6	0	6.78880e-6i
$696$	−18.4941	−	20.0643i	−0.701017	−	0.760536i
$697$	−0.943752	+	5.35228i	−0.0357472	+	0.202732i
$698$	−8.28084	+	3.01398i	−0.313435	+	0.114081i
$699$	−8.91078	+	17.2407i	−0.337037	+	0.652103i
$700$	−7.38050	−	21.9512i	−0.278957	−	0.829678i
$701$		−	16.0144i		−	0.604857i	−0.953172	−	0.302428i	$-0.902203\pi$
$701$		−	16.0144i		−	0.604857i	0.953172	−	0.302428i	$-0.0977973\pi$
$702$	5.63014	−	4.39939i	0.212496	−	0.166044i
$703$	9.26641	+	5.34997i	0.349489	+	0.201778i
$704$	−12.2260	+	2.15577i	−0.460785	+	0.0812488i
$705$	−0.00641507	−	0.00331560i	−0.000241605	−	0.000124873i
$706$	1.33841	+	0.235998i	0.0503718	+	0.00888192i
$707$	−9.89575	+	5.39171i	−0.372168	+	0.202776i
$708$	−39.0837	+	8.78497i	−1.46885	+	0.330159i
$709$	0.187155	−	0.157041i	0.00702874	−	0.00589781i	−0.639266	−	0.768985i	$-0.720762\pi$
$709$	0.187155	−	0.157041i	0.00702874	−	0.00589781i	0.646295	+	0.763087i	$0.276317\pi$
$710$	0.00245392			9.20940e−5
$711$	−2.04443	−	7.45476i	−0.0766721	−	0.279575i
$712$		−	6.06044i		−	0.227125i
$713$	−12.0412	−	4.38265i	−0.450948	−	0.164132i
$714$	−1.56539	+	0.949969i	−0.0585832	+	0.0355517i
$715$	−0.00561597	−	0.00471236i	−0.000210025	−	0.000176232i
$716$	42.5283	+	7.49890i	1.58936	+	0.280247i
$717$	−17.2722	−	13.1731i	−0.645040	−	0.491958i
$718$	−8.75097	+	7.34294i	−0.326583	+	0.274036i
$719$	−35.2732			−1.31547			−0.657734	−	0.753250i	$-0.728485\pi$
$719$	−35.2732			−1.31547			−0.657734	+	0.753250i	$0.728485\pi$
$720$	0.00430907		0.000402474i	0.000160590		1.49993e-5i
$721$	6.35021	+	42.0691i	0.236494	+	1.56674i
$722$	−3.97810	+	0.701446i	−0.148049	+	0.0261051i
$723$	33.1916	+	10.3584i	1.23441	+	0.385232i
$724$	−15.4966	−	2.73246i	−0.575926	−	0.101551i
$725$	−27.0346	+	32.2186i	−1.00404	+	1.19657i
$726$	5.33387	+	8.31857i	0.197958	+	0.308731i
$727$	−28.8861	−	34.4251i	−1.07133	−	1.27676i	−0.959098	−	0.283075i	$-0.908645\pi$
$727$	−28.8861	−	34.4251i	−1.07133	−	1.27676i	−0.112229	−	0.993682i	$-0.535799\pi$
$728$	8.51002	+	10.6665i	0.315402	+	0.395326i
$729$	−25.9530	+	7.44587i	−0.961223	+	0.275773i
$730$	0.00100821	+	0.00174627i	3.73155e−5	+	6.46324e-5i
$731$	0.945920	+	5.36458i	0.0349861	+	0.198416i
$732$	−5.06037	+	9.79087i	−0.187037	+	0.361881i
$733$	14.9455	+	41.0625i	0.552025	+	1.51668i	0.830941	+	0.556361i	$0.187803\pi$
$733$	14.9455	+	41.0625i	0.552025	+	1.51668i	−0.278915	+	0.960316i	$0.589975\pi$
$734$	−3.46755	+	1.26208i	−0.127989	+	0.0465843i
$735$	0.00591286	−	0.00339122i	0.000218099	−	0.000125087i
$736$	−1.38510	−	7.85530i	−0.0510555	−	0.289550i
$737$	−8.72188	−	5.03558i	−0.321275	−	0.185488i
$738$	9.24690	+	4.24605i	0.340383	+	0.156299i
$739$	−17.7049	−	30.6658i	−0.651286	−	1.12806i	−0.982811	−	0.184613i	$-0.940897\pi$
$739$	−17.7049	−	30.6658i	−0.651286	−	1.12806i	0.331526	−	0.943446i	$-0.392437\pi$
$740$	−0.000351350	−	0.00199261i	−1.29159e−5	−	7.32497e-5i
$741$	−24.6211	−	3.16800i	−0.904477	−	0.116379i
$742$	−0.343580	+	13.8978i	−0.0126132	+	0.510205i
$743$	14.2073	−	16.9316i	0.521216	−	0.621161i	−0.439652	−	0.898168i	$-0.644898\pi$
$743$	14.2073	−	16.9316i	0.521216	−	0.621161i	0.960868	+	0.277007i	$0.0893426\pi$
$744$	−15.8879	+	20.8317i	−0.582478	+	0.763727i
$745$	0.000332860	0	0.000396687i	1.21951e−5	0	1.45335e-5i
$746$	−14.0088	+	8.08800i	−0.512900	+	0.296123i
$747$	5.59814	+	1.46488i	0.204825	+	0.0535973i
$748$	5.74482	−	3.31677i	0.210051	−	0.121273i
$749$	−2.10898	+	10.4441i	−0.0770603	+	0.381621i
$750$	0.00106637	+	0.00474423i	3.89385e−5	+	0.000173235i
$751$	32.1560	+	26.9821i	1.17339	+	0.984589i	1.00000		0.000264372i	$-8.41522e-5\pi$
$751$	32.1560	+	26.9821i	1.17339	+	0.984589i	0.173388	+	0.984854i	$0.444529\pi$
$752$	−14.5771	−	12.2316i	−0.531572	−	0.446042i
$753$	−1.81777	−	39.0086i	−0.0662434	−	1.42155i
$754$	3.95607	−	10.8692i	0.144071	−	0.395833i
$755$	0.000676743	0		2.46292e−5	0
$756$	−6.87086	−	23.0657i	−0.249891	−	0.838890i
$757$	7.91633			0.287724			0.143862	−	0.989598i	$-0.454048\pi$
$757$	7.91633			0.287724			0.143862	+	0.989598i	$0.454048\pi$
$758$	1.14912	−	3.15717i	0.0417377	−	0.114673i
$759$	10.9553	−	7.02457i	0.397653	−	0.254976i
$760$	0.00419822	+	0.00352272i	0.000152285	+	0.000127783i
$761$	25.3022	+	21.2310i	0.917202	+	0.769624i	0.973476	−	0.228791i	$-0.0734773\pi$
$761$	25.3022	+	21.2310i	0.917202	+	0.769624i	−0.0562731	+	0.998415i	$0.517922\pi$
$762$	−5.72646	−	1.78710i	−0.207448	−	0.0647398i
$763$	−0.991318	−	2.94839i	−0.0358881	−	0.106739i
$764$	−31.6262	+	18.2594i	−1.14420	+	0.660602i
$765$	−0.00121976		0.000577517i	−4.41006e−5		2.08802e-5i
$766$	0.122788	−	0.0708916i	0.00443651	−	0.00256142i
$767$	−23.3842	−	27.8682i	−0.844354	−	1.00626i
$768$	−0.740997	−	0.0953443i	−0.0267384	−	0.00344044i
$769$	19.7511	−	23.5384i	0.712241	−	0.848816i	−0.281611	−	0.959529i	$-0.590869\pi$
$769$	19.7511	−	23.5384i	0.712241	−	0.848816i	0.993852	+	0.110713i	$0.0353133\pi$
$770$	0.00308870	−	0.00168288i	0.000111309	−	6.06469e-5i
$771$	30.8679	−	40.4731i	1.11168	−	1.45760i
$772$	−5.55641	−	31.5120i	−0.199980	−	1.13414i
$773$	15.7630	+	27.3023i	0.566956	+	0.981997i	0.996865	+	0.0791245i	$0.0252125\pi$
$773$	15.7630	+	27.3023i	0.566956	+	0.981997i	−0.429909	+	0.902872i	$0.641454\pi$
$774$	10.1648	+	0.829262i	0.365365	+	0.0298072i
$775$	34.9706	+	20.1903i	1.25618	+	0.725256i
$776$	0.584066	+	3.31240i	0.0209668	+	0.118908i
$777$	−8.78024	+	3.41477i	−0.314989	+	0.122504i
$778$	−0.349471	+	0.127197i	−0.0125291	+	0.00456023i
$779$	−12.0908	−	33.2192i	−0.433197	−	1.19020i
$780$	0.00253379	+	0.00395163i	9.07242e−5	+	0.000141491i
$781$	7.18770	+	40.7635i	0.257196	+	1.45863i
$782$	0.316995	+	0.549052i	0.0113357	+	0.0196341i
$783$	−29.2443	+	32.4837i	−1.04511	+	1.16087i
$784$	17.1617	−	5.30183i	0.612919	−	0.189351i
$785$	0.00416432	+	0.00496285i	0.000148631	+	0.000177132i
$786$	4.38712	−	8.48826i	0.156483	−	0.302766i
$787$	30.6724	−	36.5539i	1.09335	−	1.30301i	0.143726	−	0.989618i	$-0.454092\pi$
$787$	30.6724	−	36.5539i	1.09335	−	1.30301i	0.949625	−	0.313388i	$-0.101464\pi$
$788$	−17.7687	−	3.13310i	−0.632984	−	0.111612i
$789$	21.3488	−	19.6781i	0.760039	−	0.700559i
$790$	−0.000712390	0	0.000125614i	−2.53457e−5	0	4.46913e-6i
$791$	−36.3186	−	14.2449i	−1.29134	−	0.506491i
$792$	−7.03721	−	25.6603i	−0.250056	−	0.911799i
$793$	−10.0089			−0.355428
$794$	−6.39933	+	5.36967i	−0.227104	+	0.190563i
$795$	−0.00130761	+	0.0101625i	−4.63763e−5	+	0.000360427i
$796$	−19.2624	−	3.39648i	−0.682737	−	0.120385i
$797$	29.5128	+	24.7642i	1.04540	+	0.877192i	0.992602	−	0.121413i	$-0.0387426\pi$
$797$	29.5128	+	24.7642i	1.04540	+	0.877192i	0.0527949	+	0.998605i	$0.483187\pi$
$798$	5.72840	−	10.4423i	0.202783	−	0.369653i
$799$	5.57608	+	2.02953i	0.197267	+	0.0717995i
$800$			25.1361i			0.888696i
$801$	−9.66536	+	0.902759i	−0.341509	+	0.0318974i
$802$	9.22821			0.325859
$803$	−26.0552	+	21.8629i	−0.919467	+	0.771524i
$804$	4.37058	+	4.74166i	0.154138	+	0.167225i
$805$	−0.00112916	−	0.00207242i	−3.97976e−5	−	7.30430e-5i
$806$	−10.9366	−	1.92842i	−0.385226	−	0.0679257i
$807$	−13.7557	+	8.82014i	−0.484223	+	0.310484i
$808$	7.85632	−	1.38528i	0.276384	−	0.0487340i
$809$	36.7753	+	21.2322i	1.29295	+	0.746486i	0.979176	−	0.203011i	$-0.0650728\pi$
$809$	36.7753	+	21.2322i	1.29295	+	0.746486i	0.313775	+	0.949497i	$0.398406\pi$
$810$	0.000467909		0.00248298i	1.64406e−5		8.72429e-5i
$811$		−	22.9043i		−	0.804277i	−0.915579	−	0.402139i	$-0.868267\pi$
$811$		−	22.9043i		−	0.804277i	0.915579	−	0.402139i	$-0.131733\pi$
$812$	−29.2176	−	25.7735i	−1.02534	−	0.904472i
$813$	6.79393	−	0.316593i	0.238274	−	0.0111034i
$814$	−4.56826	+	1.66271i	−0.160117	+	0.0582780i
$815$	−0.000668326		0.00379027i	−2.34104e−5		0.000132767i
$816$	−3.46975	+	0.779907i	−0.121466	+	0.0273022i
$817$	−22.7754	−	27.1427i	−0.796812	−	0.949603i
$818$	4.45012	+	7.70784i	0.155595	+	0.269498i
$819$	15.7436	−	15.1609i	0.550125	−	0.529765i
$820$	−0.00334243	+	0.00578925i	−0.000116723	+	0.000202169i
$821$	−2.02629	+	0.357290i	−0.0707180	+	0.0124695i	−0.208895	−	0.977938i	$-0.566987\pi$
$821$	−2.02629	+	0.357290i	−0.0707180	+	0.0124695i	0.138177	+	0.990408i	$0.455876\pi$
$822$	5.27259	−	6.91325i	0.183903	−	0.241127i
$823$	−3.04598	+	1.10865i	−0.106176	+	0.0386450i	−0.394562	−	0.918869i	$-0.629104\pi$
$823$	−3.04598	+	1.10865i	−0.106176	+	0.0386450i	0.288386	+	0.957514i	$0.406881\pi$
$824$	5.22995	−	29.6605i	0.182194	−	1.03327i
$825$	−37.8427	+	15.8051i	−1.31752	+	0.550265i
$826$	16.5444	−	5.56260i	0.575652	−	0.193547i
$827$	47.0423	+	27.1599i	1.63582	+	0.944441i	0.982251	+	0.187574i	$0.0600624\pi$
$827$	47.0423	+	27.1599i	1.63582	+	0.944441i	0.653569	+	0.756867i	$0.273271\pi$
$828$	−8.03626	+	2.20390i	−0.279279	+	0.0765910i
$829$		−	8.47998i		−	0.294522i	−0.989098	−	0.147261i	$-0.952954\pi$
$829$		−	8.47998i		−	0.294522i	0.989098	−	0.147261i	$-0.0470457\pi$
$830$	0.000185210	0	0.000508859i	6.42872e−6	0	1.76628e-5i
$831$	−26.9313	−	29.2179i	−0.934236	−	1.01356i
$832$	2.46906	+	6.78368i	0.0855992	+	0.235182i
$833$	−4.46344	+	3.38396i	−0.154649	+	0.117247i
$834$	−0.302574	+	0.194011i	−0.0104773	+	0.00671804i
$835$	0.00244989		0.000891687i	8.47819e−5		3.08581e-5i
$836$	−21.5740	+	37.3673i	−0.746153	+	1.29237i
$837$	35.5896	+	22.2354i	1.23016	+	0.768567i
$838$	0.458929	−	0.264963i	0.0158534	−	0.00915299i
$839$	11.5622	−	9.70185i	0.399172	−	0.334945i	−0.421002	−	0.907060i	$-0.638321\pi$
$839$	11.5622	−	9.70185i	0.399172	−	0.334945i	0.820173	+	0.572115i	$0.193877\pi$
$840$	−0.00473253		0.000941517i	−0.000163288		3.24854e-5i
$841$	−7.25090	+	41.1219i	−0.250031	+	1.41800i
$842$	4.92480	−	5.86915i	0.169720	−	0.202264i
$843$	−2.26729	+	2.08986i	−0.0780897	+	0.0719784i
$844$	39.0725	+	14.2212i	1.34493	+	0.489515i
$845$	0.00152279	−	0.00263755i	5.23856e−5	−	9.07346e-5i
$846$	6.31870	−	9.13764i	0.217241	−	0.314158i
$847$	18.8518	+	23.6289i	0.647756	+	0.811899i
$848$	−9.23471	+	25.3722i	−0.317121	+	0.871284i
$849$	−0.985132	+	7.65624i	−0.0338096	+	0.262762i
$850$	−0.683315	−	1.87739i	−0.0234375	−	0.0643940i
$851$	1.11562	+	3.06515i	0.0382431	+	0.105072i
$852$	3.38238	−	26.2872i	0.115879	−	0.900584i
$853$	−5.23344	+	14.3788i	−0.179190	+	0.492319i	−0.996473	−	0.0839170i	$-0.973257\pi$
$853$	−5.23344	+	14.3788i	−0.179190	+	0.492319i	0.817283	+	0.576236i	$0.195479\pi$
$854$	1.75347	−	4.47062i	0.0600026	−	0.152982i
$855$	0.00499278	−	0.00722018i	0.000170749	−	0.000246925i
$856$	3.77132	−	6.53212i	0.128901	−	0.223263i
$857$	−16.4933	−	6.00308i	−0.563401	−	0.205061i	0.0445895	−	0.999005i	$-0.485802\pi$
$857$	−16.4933	−	6.00308i	−0.563401	−	0.205061i	−0.607991	+	0.793944i	$0.708024\pi$
$858$	8.29310	−	7.64408i	0.283122	−	0.260965i
$859$	−10.1924	+	12.1469i	−0.347761	+	0.414446i	−0.911365	−	0.411600i	$-0.864970\pi$
$859$	−10.1924	+	12.1469i	−0.347761	+	0.414446i	0.563604	+	0.826045i	$0.309415\pi$
$860$	−0.00116348	+	0.00659842i	−3.96743e−5	+	0.000225004i
$861$	29.4738	+	10.0040i	1.00447	+	0.340934i
$862$	−1.45649	+	1.22214i	−0.0496081	+	0.0416261i
$863$	1.76440	−	1.01868i	0.0600610	−	0.0346762i	−0.469669	−	0.882843i	$-0.655627\pi$
$863$	1.76440	−	1.01868i	0.0600610	−	0.0346762i	0.529730	+	0.848166i	$0.322293\pi$
$864$	−0.909809	+	26.1064i	−0.0309523	+	0.888157i
$865$	−0.00676353	+	0.0117148i	−0.000229967	+	0.000398315i
$866$	−13.8550	−	5.04282i	−0.470813	−	0.171362i
$867$	−23.8535	+	15.2949i	−0.810107	+	0.519441i
$868$	−19.4982	+	31.9229i	−0.661811	+	1.08353i
$869$	−4.17328	−	11.4660i	−0.141569	−	0.388957i
$870$	0.00277217	+	0.00300754i	9.39853e−5	+	0.000101965i
$871$	−2.00299	+	5.50316i	−0.0678686	+	0.186468i
$872$			2.20198i			0.0745686i
$873$	5.19572	−	1.42490i	0.175848	−	0.0482255i
$874$	−3.57132	−	2.06190i	−0.120802	−	0.0697448i
$875$	0.00474036	+	0.0140989i	0.000160253	+	0.000476628i
$876$	20.0963	−	8.39328i	0.678991	−	0.283583i
$877$	−3.15820	+	17.9111i	−0.106645	+	0.604814i	0.883906	+	0.467665i	$0.154905\pi$
$877$	−3.15820	+	17.9111i	−0.106645	+	0.604814i	−0.990551	+	0.137148i	$0.956206\pi$
$878$	7.74619	−	2.81938i	0.261421	−	0.0951495i
$879$	7.45196	−	9.77078i	0.251348	−	0.329560i
$880$	0.00672770	−	0.00118627i	0.000226791	−	3.99893e-5i
$881$	13.3725	−	23.1618i	0.450530	−	0.780341i	−0.547889	−	0.836551i	$-0.684568\pi$
$881$	13.3725	−	23.1618i	0.450530	−	0.780341i	0.998419	+	0.0562101i	$0.0179017\pi$
$882$	4.01368	+	9.68811i	0.135148	+	0.326216i
$883$	10.5208	+	18.2226i	0.354054	+	0.613240i	0.986956	−	0.160992i	$-0.0514694\pi$
$883$	10.5208	+	18.2226i	0.354054	+	0.613240i	−0.632901	+	0.774232i	$0.718136\pi$
$884$	−2.47948	−	2.95493i	−0.0833939	−	0.0993849i
$885$	0.0125514	−	0.00282121i	0.000421909	−	9.48339e-5i
$886$	2.42234	−	13.7378i	0.0813800	−	0.461529i
$887$	−20.9254	+	7.61624i	−0.702608	+	0.255728i	−0.668524	−	0.743691i	$-0.733074\pi$
$887$	−20.9254	+	7.61624i	−0.702608	+	0.255728i	−0.0340838	+	0.999419i	$0.510851\pi$
$888$	6.66183	−	0.310437i	0.223556	−	0.0104176i
$889$	−17.9871	−	3.63212i	−0.603267	−	0.121817i
$890$		0	0.000908428i		0	3.04506e-5i
$891$	−39.8755	+	15.0455i	−1.33588	+	0.504043i
$892$	36.6404	+	21.1543i	1.22681	+	0.708300i
$893$	−38.0110	+	6.70237i	−1.27199	+	0.224286i
$894$	−0.670648	+	0.430020i	−0.0224298	+	0.0143820i
$895$	−0.0136576	−	0.00240820i	−0.000456523	−	8.04973e-5i
$896$	−30.0560	−	0.743041i	−1.00410	−	0.0248233i
$897$	−5.12892	−	5.56439i	−0.171250	−	0.185790i
$898$	−8.88953	+	7.45920i	−0.296647	+	0.248917i
$899$	67.9336			2.26571
$900$	26.1458	−	2.44205i	0.871525	−	0.0814017i
$901$		−	8.41972i		−	0.280502i
$902$	15.0929	+	5.49336i	0.502538	+	0.182909i
$903$	31.1894	−	0.681559i	1.03792	−	0.0226809i
$904$	21.1557	+	17.7517i	0.703627	+	0.590414i
$905$	0.00497658		0.000877506i	0.000165427		2.91693e-5i
$906$	−0.132869	+	1.03263i	−0.00441426	+	0.0343067i
$907$	2.75474	−	2.31150i	0.0914695	−	0.0767520i	−0.595906	−	0.803054i	$-0.703207\pi$
$907$	2.75474	−	2.31150i	0.0914695	−	0.0767520i	0.687376	+	0.726302i	$0.258763\pi$
$908$	−7.49013			−0.248569
$909$	−3.37956	−	12.3231i	−0.112093	−	0.408733i
$910$	−0.00127561	−	0.00159885i	−4.22860e−5	−	5.30014e-5i
$911$	−51.8774	+	9.14738i	−1.71877	+	0.303066i	−0.944189	−	0.329403i	$-0.893152\pi$
$911$	−51.8774	+	9.14738i	−1.71877	+	0.303066i	−0.774585	+	0.632470i	$0.782041\pi$
$912$	17.0089	−	15.6778i	0.563222	−	0.519144i
$913$	8.99544	+	1.58614i	0.297706	+	0.0524935i
$914$	5.81787	−	6.93347i	0.192438	−	0.229339i
$915$	0.00162509	−	0.00314425i	5.37238e−5	−	0.000103946i
$916$	14.5773	+	17.3725i	0.481647	+	0.574005i
$917$	10.6724	−	27.2100i	0.352432	−	0.898555i
$918$	−0.641738	−	1.97459i	−0.0211805	−	0.0651713i
$919$	−27.2723	−	47.2370i	−0.899629	−	1.55820i	−0.827969	−	0.560774i	$-0.810504\pi$
$919$	−27.2723	−	47.2370i	−0.899629	−	1.55820i	−0.0716603	−	0.997429i	$-0.522830\pi$
$920$	0.000290112		0.00164531i	9.56472e−6		5.42442e-5i
$921$	−6.70040	−	10.4498i	−0.220786	−	0.344332i
$922$	0.174032	+	0.478149i	0.00573144	+	0.0157470i
$923$	22.6179	−	8.23224i	0.744477	−	0.270968i
$924$	−13.7702	−	35.4068i	−0.453008	−	1.16480i
$925$	−1.78494	−	10.1229i	−0.0586884	−	0.332838i
$926$	14.8554	+	8.57676i	0.488178	+	0.281850i
$927$	−48.0825	−	3.92267i	−1.57924	−	0.128837i
$928$	21.1437	+	36.6219i	0.694075	+	1.20217i
$929$	7.27715	+	41.2707i	0.238755	+	1.35405i	0.834559	+	0.550919i	$0.185723\pi$
$929$	7.27715	+	41.2707i	0.238755	+	1.35405i	−0.595803	+	0.803130i	$0.703166\pi$
$930$	0.00238151	−	0.00312256i	7.80928e−5	−	0.000102393i
$931$	14.1374	−	33.5784i	0.463333	−	1.10049i
$932$	12.6086	−	15.0264i	0.413010	−	0.492206i
$933$	39.9386	+	5.13891i	1.30753	+	0.168240i
$934$	−0.457428	−	0.545142i	−0.0149675	−	0.0178376i
$935$	−0.00184490	+	0.00106515i	−6.03345e−5	+	3.48342e-5i
$936$	−13.9841	+	6.62101i	−0.457085	+	0.216415i
$937$	24.5420	−	14.1693i	0.801751	−	0.462891i	−0.0423320	−	0.999104i	$-0.513479\pi$
$937$	24.5420	−	14.1693i	0.801751	−	0.462891i	0.844083	+	0.536212i	$0.180145\pi$
$938$	−2.10715	−	1.85876i	−0.0688009	−	0.0606907i
$939$	−39.4944	−	12.3253i	−1.28885	−	0.402222i
$940$	0.00559115	+	0.00469153i	0.000182363	+	0.000153021i
$941$	−12.4382	−	10.4369i	−0.405473	−	0.340232i	0.417132	−	0.908846i	$-0.363035\pi$
$941$	−12.4382	−	10.4369i	−0.405473	−	0.340232i	−0.822604	+	0.568614i	$0.807480\pi$
$942$	−8.39030	+	5.37986i	−0.273371	+	0.175285i
$943$	3.68586	−	10.1268i	0.120028	−	0.329775i
$944$	33.8999			1.10335
$945$	0.00220651	+	0.00740733i	7.17779e−5	+	0.000240960i
$946$	16.0984			0.523405
$947$	−3.35614	+	9.22091i	−0.109060	+	0.299639i	−0.982202	−	0.187825i	$-0.939856\pi$
$947$	−3.35614	+	9.22091i	−0.109060	+	0.299639i	0.873143	+	0.487465i	$0.162078\pi$
$948$	0.363684	+	7.80449i	0.0118119	+	0.253478i
$949$	15.1510	+	12.7132i	0.491822	+	0.412687i
$950$	9.95493	+	8.35318i	0.322981	+	0.271013i
$951$	10.9099	+	48.5374i	0.353778	+	1.57393i
$952$	3.75835	−	1.26364i	0.121809	−	0.0409549i
$953$	−34.8176	+	20.1019i	−1.12785	+	0.651166i	−0.943394	−	0.331675i	$-0.892386\pi$
$953$	−34.8176	+	20.1019i	−1.12785	+	0.651166i	−0.184458	+	0.982840i	$0.559053\pi$
$954$	−15.2500	−	3.99052i	−0.493737	−	0.129198i
$955$	0.0101565	−	0.00586384i	0.000328656	−	0.000189749i
$956$	14.1126	+	16.8188i	0.456436	+	0.543959i
$957$	−41.8400	+	54.8593i	−1.35250	+	1.77335i
$958$	−11.4888	+	13.6919i	−0.371188	+	0.442364i
$959$	13.8631	−	22.6970i	0.447663	−	0.732924i
$960$	−0.00253194		0.000325785i	−8.17179e−5		1.05147e-5i
$961$	−5.94285	−	33.7036i	−0.191705	−	1.08721i
$962$	1.41345	+	2.44818i	0.0455716	+	0.0789323i
$963$	−10.9794	−	5.04159i	−0.353806	−	0.162463i
$964$	−30.4352	−	17.5718i	−0.980251	−	0.565948i
$965$	0.00178439	+	0.0101198i	5.74415e−5	+	0.000325767i
$966$	3.38394	−	1.31607i	0.108877	−	0.0423438i
$967$	−6.39685	+	2.32826i	−0.205709	+	0.0748719i	−0.442820	−	0.896611i	$-0.646022\pi$
$967$	−6.39685	+	2.32826i	−0.205709	+	0.0748719i	0.237111	+	0.971483i	$0.423800\pi$
$968$	−7.31862	−	20.1078i	−0.235229	−	0.646288i
$969$	−3.31202	+	6.40814i	−0.106397	+	0.205859i
$970$	−8.75485e−5	0	0.000496512i	−2.81101e−6	0	1.59420e-5i
$971$	14.6415	+	25.3599i	0.469869	+	0.813836i	0.999406	−	0.0344500i	$-0.0109679\pi$
$971$	14.6415	+	25.3599i	0.469869	+	0.813836i	−0.529538	+	0.848286i	$0.677635\pi$
$972$	27.2434	−	1.58996i	0.873832	−	0.0509980i
$973$	−0.859463	+	0.685703i	−0.0275531	+	0.0219826i
$974$	−11.2124	−	13.3624i	−0.359269	−	0.428160i
$975$	12.8722	+	20.0752i	0.412241	+	0.642920i
$976$	5.99515	−	7.14474i	0.191900	−	0.228698i
$977$	7.70964	+	1.35942i	0.246653	+	0.0434916i	0.295608	−	0.955309i	$-0.404478\pi$
$977$	7.70964	+	1.35942i	0.246653	+	0.0434916i	−0.0489546	+	0.998801i	$0.515589\pi$
$978$	−5.65226	−	1.76395i	−0.180739	−	0.0564048i
$979$	−15.0904	+	2.66085i	−0.482291	+	0.0850410i
$980$	−0.00658251	+	0.00203356i	−0.000210270	+	6.49595e-5i
$981$	3.51179	−	0.328006i	0.112123	−	0.0104724i
$982$	5.43528			0.173447
$983$	4.61869	−	3.87554i	0.147313	−	0.123611i	−0.566153	−	0.824300i	$-0.691569\pi$
$983$	4.61869	−	3.87554i	0.147313	−	0.123611i	0.713466	+	0.700690i	$0.247124\pi$
$984$	−17.5197	−	13.3619i	−0.558508	−	0.425962i
$985$	0.00570626	+	0.00100617i	0.000181817	+	3.20592e-5i
$986$	−2.57475	−	2.16048i	−0.0819969	−	0.0688036i
$987$	16.3448	−	29.7949i	0.520260	−	0.948381i
$988$	23.5773	+	8.58143i	0.750093	+	0.273012i
$989$		−	10.8015i		−	0.343468i
$990$	0.00105484	+	0.00384635i	3.35251e−5	+	0.000122245i
$991$	22.6935			0.720884			0.360442	−	0.932782i	$-0.382626\pi$
$991$	22.6935			0.720884			0.360442	+	0.932782i	$0.382626\pi$
$992$	31.1017	−	26.0974i	0.987480	−	0.828594i
$993$	43.9431	−	9.87723i	1.39449	−	0.313444i
$994$	−0.285409	+	11.5448i	−0.00905261	+	0.366178i
$995$	0.00618594	+	0.00109075i	0.000196107	+	3.45790e-5i
$996$	−5.19578	−	2.68542i	−0.164635	−	0.0850907i
$997$	9.60364	−	1.69338i	0.304150	−	0.0536299i	−0.0194901	−	0.999810i	$-0.506204\pi$
$997$	9.60364	−	1.69338i	0.304150	−	0.0536299i	0.323640	+	0.946180i	$0.395093\pi$
$998$	2.74449	+	1.58453i	0.0868752	+	0.0501574i
$999$	−1.48743	−	10.5782i	−0.0470603	−	0.334680i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.bd.a.59.9	yes	132
3.2	odd	2		567.2.bd.a.206.14		132
7.5	odd	6		189.2.ba.a.5.14	✓	132
21.5	even	6		567.2.ba.a.530.9		132
27.11	odd	18		189.2.ba.a.38.14	yes	132
27.16	even	9		567.2.ba.a.521.9		132
189.124	odd	18		567.2.bd.a.278.14		132
189.173	even	18	inner	189.2.bd.a.173.9	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.5.14	✓	132	7.5	odd	6
189.2.ba.a.38.14	yes	132	27.11	odd	18
189.2.bd.a.59.9	yes	132	1.1	even	1	trivial
189.2.bd.a.173.9	yes	132	189.173	even	18	inner
567.2.ba.a.521.9		132	27.16	even	9
567.2.ba.a.530.9		132	21.5	even	6
567.2.bd.a.206.14		132	3.2	odd	2
567.2.bd.a.278.14		132	189.124	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.bd (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.170792 + 0.469247i) q^{2} +(-1.53869 - 0.795263i) q^{3} +(1.34107 + 1.12529i) q^{4} +(-0.000430671 - 0.000361376i) q^{5} +(0.635971 - 0.586200i) q^{6} +(1.75023 - 1.98411i) q^{7} +(-1.62200 + 0.936464i) q^{8} +(1.73511 + 2.44732i) q^{9} +(0.000243130 - 0.000140371i) q^{10} +(3.04392 + 3.62761i) q^{11} +(-1.16858 - 2.79797i) q^{12} +(1.77003 - 2.10944i) q^{13} +(0.632115 + 1.16016i) q^{14} +(0.000375278 + 0.000898541i) q^{15} +(0.445582 + 2.52702i) q^{16} +(-0.400086 - 0.692969i) q^{17} +(-1.44474 + 0.396214i) q^{18} +(4.50743 + 2.60237i) q^{19} +(-0.000170906 - 0.000969257i) q^{20} +(-4.27094 + 1.66104i) q^{21} +(-2.22212 + 0.808787i) q^{22} +(0.542669 + 1.49097i) q^{23} +(3.24049 - 0.151005i) q^{24} +(-0.868241 - 4.92404i) q^{25} +(0.687542 + 1.19086i) q^{26} +(-0.723528 - 5.14553i) q^{27} +(4.57987 - 0.691318i) q^{28} +(-5.40692 - 6.44372i) q^{29} +(-0.000485732 + 2.26348e-5i) q^{30} +(-5.19122 + 6.18666i) q^{31} +(-4.95085 - 0.872968i) q^{32} +(-1.79874 - 8.00247i) q^{33} +(0.393506 - 0.0693856i) q^{34} +(-0.00147078 + 0.000222010i) q^{35} +(-0.427042 + 5.23452i) q^{36} +2.05581 q^{37} +(-1.99099 + 1.67064i) q^{38} +(-4.40108 + 1.83813i) q^{39} +(0.00103696 + 0.000182845i) q^{40} +(-5.20305 - 4.36588i) q^{41} +(-0.0499941 - 2.28782i) q^{42} +(-6.39715 - 2.32837i) q^{43} +8.29015i q^{44} +(0.000137141 - 0.00168102i) q^{45} -0.792318 q^{46} +(-5.68085 + 4.76680i) q^{47} +(1.32404 - 4.24265i) q^{48} +(-0.873412 - 6.94530i) q^{49} +(2.45888 + 0.433567i) q^{50} +(0.0645138 + 1.38444i) q^{51} +(4.74745 - 0.837104i) q^{52} +(9.11266 + 5.26120i) q^{53} +(2.53810 + 0.539303i) q^{54} -0.00266231i q^{55} +(-0.980823 + 4.85726i) q^{56} +(-4.86596 - 7.58882i) q^{57} +(3.94716 - 1.43665i) q^{58} +(2.29410 - 13.0105i) q^{59} +(-0.000507844 + 0.00162730i) q^{60} +(-2.33638 - 2.78438i) q^{61} +(-2.01645 - 3.49260i) q^{62} +(7.89260 + 0.840709i) q^{63} +(-1.31080 + 2.27037i) q^{64} +(-0.00152460 + 0.000268828i) q^{65} +(4.06235 + 0.522704i) q^{66} +(-1.99848 + 0.727386i) q^{67} +(0.243248 - 1.37953i) q^{68} +(0.350717 - 2.72570i) q^{69} +(0.000147020 - 0.000728078i) q^{70} +(7.56979 + 4.37042i) q^{71} +(-5.10619 - 2.34469i) q^{72} +7.18246i q^{73} +(-0.351116 + 0.964683i) q^{74} +(-2.57996 + 8.26703i) q^{75} +(3.11635 + 8.56210i) q^{76} +(12.5251 + 0.309645i) q^{77} +(-0.110866 - 2.37913i) q^{78} +(-2.42128 - 0.881273i) q^{79} +(0.000721305 - 0.00124934i) q^{80} +(-2.97877 + 8.49276i) q^{81} +(2.93732 - 1.69586i) q^{82} +(1.47761 - 1.23986i) q^{83} +(-7.59676 - 2.57848i) q^{84} +(-7.81169e-5 + 0.000443023i) q^{85} +(2.18517 - 2.60418i) q^{86} +(3.19510 + 14.2148i) q^{87} +(-8.33438 - 3.03347i) q^{88} +(-1.61790 + 2.80229i) q^{89} +(0.000765391 + 0.000351457i) q^{90} +(-1.08741 - 7.20394i) q^{91} +(-0.950016 + 2.61015i) q^{92} +(12.9077 - 5.39094i) q^{93} +(-1.26656 - 3.47986i) q^{94} +(-0.00100079 - 0.00274964i) q^{95} +(6.92356 + 5.28045i) q^{96} +(0.614218 - 1.68755i) q^{97} +(3.40823 + 0.776355i) q^{98} +(-3.59637 + 13.7438i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20}+ \cdots + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Introduction

L-functions

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