LMFDB - Embedded newform 324.2.p.a.239.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(11,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([27, 13]))

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

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

chi := DirichletCharacter("324.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.p (of order $54$, degree $18$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$936$
Relative dimension:	$52$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			239.22
Character	$\chi$	$=$	324.239
Dual form			324.2.p.a.263.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.402236 - 1.35580i) q^{2} +(-1.53000 - 0.811843i) q^{3} +(-1.67641 + 1.09071i) q^{4} +(-0.0601848 - 0.119838i) q^{5} +(-0.485279 + 2.40094i) q^{6} +(-3.38691 - 1.01398i) q^{7} +(2.15310 + 1.83417i) q^{8} +(1.68182 + 2.48425i) q^{9} +O(q^{10})$	\(q+(-0.402236 - 1.35580i) q^{2} +(-1.53000 - 0.811843i) q^{3} +(-1.67641 + 1.09071i) q^{4} +(-0.0601848 - 0.119838i) q^{5} +(-0.485279 + 2.40094i) q^{6} +(-3.38691 - 1.01398i) q^{7} +(2.15310 + 1.83417i) q^{8} +(1.68182 + 2.48425i) q^{9} +(-0.138268 + 0.129802i) q^{10} +(0.107632 + 1.84797i) q^{11} +(3.45040 - 0.307800i) q^{12} +(0.0748364 + 0.100523i) q^{13} +(-0.0124147 + 4.99985i) q^{14} +(-0.00520656 + 0.232213i) q^{15} +(1.62072 - 3.65695i) q^{16} +(-2.20889 + 2.63245i) q^{17} +(2.69166 - 3.27947i) q^{18} +(3.44630 + 4.10715i) q^{19} +(0.231603 + 0.135254i) q^{20} +(4.35880 + 4.30103i) q^{21} +(2.46220 - 0.889249i) q^{22} +(1.49987 + 5.00992i) q^{23} +(-1.80519 - 4.55426i) q^{24} +(2.97505 - 3.99619i) q^{25} +(0.106187 - 0.141897i) q^{26} +(-0.556373 - 5.16628i) q^{27} +(6.78381 - 1.99429i) q^{28} +(-5.98430 + 2.58137i) q^{29} +(0.316930 - 0.0863453i) q^{30} +(-1.69963 - 1.60352i) q^{31} +(-5.61002 - 0.726424i) q^{32} +(1.33559 - 2.91478i) q^{33} +(4.45759 + 1.93596i) q^{34} +(0.0823282 + 0.466906i) q^{35} +(-5.52901 - 2.33025i) q^{36} +(-1.06638 + 6.04776i) q^{37} +(4.18226 - 6.32456i) q^{38} +(-0.0328912 - 0.214555i) q^{39} +(0.0902188 - 0.368412i) q^{40} +(1.04668 + 8.95491i) q^{41} +(4.07809 - 7.63971i) q^{42} +(-3.65095 - 5.55100i) q^{43} +(-2.19603 - 2.98057i) q^{44} +(0.196487 - 0.351060i) q^{45} +(6.18918 - 4.04871i) q^{46} +(3.06377 + 3.24740i) q^{47} +(-5.44858 + 4.27937i) q^{48} +(4.59462 + 3.02193i) q^{49} +(-6.61473 - 2.42618i) q^{50} +(5.51675 - 2.23439i) q^{51} +(-0.235097 - 0.0868930i) q^{52} +(-7.33447 - 4.23456i) q^{53} +(-6.78067 + 2.83240i) q^{54} +(0.214979 - 0.124118i) q^{55} +(-5.43255 - 8.39535i) q^{56} +(-1.93850 - 9.08181i) q^{57} +(5.90694 + 7.07522i) q^{58} +(-0.676398 + 11.6133i) q^{59} +(-0.244548 - 0.394964i) q^{60} +(-14.9993 + 3.55489i) q^{61} +(-1.49040 + 2.94935i) q^{62} +(-3.17722 - 10.1192i) q^{63} +(1.27166 + 7.89828i) q^{64} +(0.00754241 - 0.0150182i) q^{65} +(-4.48910 - 0.638364i) q^{66} +(-8.92825 - 3.85127i) q^{67} +(0.831779 - 6.82233i) q^{68} +(1.77246 - 8.88286i) q^{69} +(0.599918 - 0.299427i) q^{70} +(2.56602 - 0.933954i) q^{71} +(-0.935398 + 8.43357i) q^{72} +(3.31821 + 1.20773i) q^{73} +(8.62851 - 0.986817i) q^{74} +(-7.79612 + 3.69891i) q^{75} +(-10.2571 - 3.12637i) q^{76} +(1.50926 - 6.36806i) q^{77} +(-0.277665 + 0.130896i) q^{78} +(-0.0491922 + 0.420866i) q^{79} +(-0.535784 + 0.0258693i) q^{80} +(-3.34296 + 8.35611i) q^{81} +(11.7201 - 5.02108i) q^{82} +(-0.754832 - 0.0882272i) q^{83} +(-11.9983 - 2.45613i) q^{84} +(0.448409 + 0.106275i) q^{85} +(-6.05753 + 7.18279i) q^{86} +(11.2517 + 0.908801i) q^{87} +(-3.15775 + 4.17628i) q^{88} +(-3.21873 + 8.84339i) q^{89} +(-0.555002 - 0.125189i) q^{90} +(-0.151537 - 0.416344i) q^{91} +(-7.97876 - 6.76278i) q^{92} +(1.29863 + 3.83322i) q^{93} +(3.17049 - 5.46009i) q^{94} +(0.284776 - 0.660186i) q^{95} +(7.99361 + 5.66589i) q^{96} +(1.75329 + 0.880535i) q^{97} +(2.24902 - 7.44493i) q^{98} +(-4.40980 + 3.37534i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{29}{54}\right)$

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 $

$2$	−0.402236	−	1.35580i	−0.284424	−	0.958699i
$2$	−0.402236	−	1.35580i	−0.284424	−	0.958699i
$3$	−1.53000	−	0.811843i	−0.883348	−	0.468718i
$3$	−1.53000	−	0.811843i	−0.883348	−	0.468718i
$4$	−1.67641	+	1.09071i	−0.838206	+	0.545353i
$5$	−0.0601848	−	0.119838i	−0.0269155	−	0.0535931i	0.879773	−	0.475394i	$-0.157694\pi$
$5$	−0.0601848	−	0.119838i	−0.0269155	−	0.0535931i	−0.906689	+	0.421801i	$0.861398\pi$
$6$	−0.485279	+	2.40094i	−0.198114	+	0.980179i
$7$	−3.38691	−	1.01398i	−1.28013	−	0.383247i	−0.426673	−	0.904406i	$-0.640315\pi$
$7$	−3.38691	−	1.01398i	−1.28013	−	0.383247i	−0.853459	+	0.521159i	$0.825500\pi$
$8$	2.15310	+	1.83417i	0.761235	+	0.648476i
$9$	1.68182	+	2.48425i	0.560607	+	0.828082i
$10$	−0.138268	+	0.129802i	−0.0437243	+	0.0410470i
$11$	0.107632	+	1.84797i	0.0324523	+	0.557184i	0.974874	+	0.222757i	$0.0715058\pi$
$11$	0.107632	+	1.84797i	0.0324523	+	0.557184i	−0.942422	+	0.334427i	$0.891457\pi$
$12$	3.45040	−	0.307800i	0.996045	−	0.0888542i
$13$	0.0748364	+	0.100523i	0.0207559	+	0.0278800i	0.812380	−	0.583128i	$-0.198172\pi$
$13$	0.0748364	+	0.100523i	0.0207559	+	0.0278800i	−0.791624	+	0.611008i	$0.790764\pi$
$14$	−0.0124147	+	4.99985i	−0.00331798	+	1.33627i
$15$	−0.00520656	+	0.232213i	−0.00134433	+	0.0599571i
$16$	1.62072	−	3.65695i	0.405180	−	0.914237i
$17$	−2.20889	+	2.63245i	−0.535735	+	0.638464i	−0.964226	−	0.265082i	$-0.914601\pi$
$17$	−2.20889	+	2.63245i	−0.535735	+	0.638464i	0.428491	+	0.903546i	$0.359045\pi$
$18$	2.69166	−	3.27947i	0.634431	−	0.772979i
$19$	3.44630	+	4.10715i	0.790637	+	0.942244i	0.999361	−	0.0357304i	$-0.0113758\pi$
$19$	3.44630	+	4.10715i	0.790637	+	0.942244i	−0.208725	+	0.977974i	$0.566931\pi$
$20$	0.231603	+	0.135254i	0.0517879	+	0.0302437i
$21$	4.35880	+	4.30103i	0.951168	+	0.938561i
$22$	2.46220	−	0.889249i	0.524942	−	0.189588i
$23$	1.49987	+	5.00992i	0.312745	+	1.04464i	0.959445	+	0.281897i	$0.0909636\pi$
$23$	1.49987	+	5.00992i	0.312745	+	1.04464i	−0.646700	+	0.762745i	$0.723851\pi$
$24$	−1.80519	−	4.55426i	−0.368483	−	0.929634i
$25$	2.97505	−	3.99619i	0.595011	−	0.799238i
$26$	0.106187	−	0.141897i	0.0208250	−	0.0278283i
$27$	−0.556373	−	5.16628i	−0.107074	−	0.994251i
$28$	6.78381	−	1.99429i	1.28202	−	0.376885i
$29$	−5.98430	+	2.58137i	−1.11126	+	0.479349i	−0.870962	−	0.491351i	$-0.836503\pi$
$29$	−5.98430	+	2.58137i	−1.11126	+	0.479349i	−0.240294	+	0.970700i	$0.577244\pi$
$30$	0.316930	−	0.0863453i	0.0578632	−	0.0157644i
$31$	−1.69963	−	1.60352i	−0.305262	−	0.288000i	0.518332	−	0.855179i	$-0.326553\pi$
$31$	−1.69963	−	1.60352i	−0.305262	−	0.288000i	−0.823594	+	0.567179i	$0.808035\pi$
$32$	−5.61002	−	0.726424i	−0.991721	−	0.128415i
$33$	1.33559	−	2.91478i	0.232496	−	0.507399i
$34$	4.45759	+	1.93596i	0.764470	+	0.332014i
$35$	0.0823282	+	0.466906i	0.0139160	+	0.0789216i
$36$	−5.52901	−	2.33025i	−0.921501	−	0.388375i
$37$	−1.06638	+	6.04776i	−0.175312	+	0.994245i	0.762471	+	0.647023i	$0.223986\pi$
$37$	−1.06638	+	6.04776i	−0.175312	+	0.994245i	−0.937783	+	0.347222i	$0.887125\pi$
$38$	4.18226	−	6.32456i	0.678452	−	1.02598i
$39$	−0.0328912	−	0.214555i	−0.00526681	−	0.0343564i
$40$	0.0902188	−	0.368412i	0.0142649	−	0.0582510i
$41$	1.04668	+	8.95491i	0.163464	+	1.39852i	0.787109	+	0.616814i	$0.211577\pi$
$41$	1.04668	+	8.95491i	0.163464	+	1.39852i	−0.623645	+	0.781708i	$0.714349\pi$
$42$	4.07809	−	7.63971i	0.629263	−	1.17883i
$43$	−3.65095	−	5.55100i	−0.556765	−	0.846520i	0.441958	−	0.897036i	$-0.354284\pi$
$43$	−3.65095	−	5.55100i	−0.556765	−	0.846520i	−0.998723	+	0.0505155i	$0.983914\pi$
$44$	−2.19603	−	2.98057i	−0.331064	−	0.449338i
$45$	0.196487	−	0.351060i	0.0292905	−	0.0523329i
$46$	6.18918	−	4.04871i	0.912544	−	0.596949i
$47$	3.06377	+	3.24740i	0.446896	+	0.473683i	0.911183	−	0.412003i	$-0.135171\pi$
$47$	3.06377	+	3.24740i	0.446896	+	0.473683i	−0.464286	+	0.885685i	$0.653689\pi$
$48$	−5.44858	+	4.27937i	−0.786434	+	0.617674i
$49$	4.59462	+	3.02193i	0.656374	+	0.431704i
$50$	−6.61473	−	2.42618i	−0.935464	−	0.343114i
$51$	5.51675	−	2.23439i	0.772499	−	0.312877i
$52$	−0.235097	−	0.0868930i	−0.0326021	−	0.0120499i
$53$	−7.33447	−	4.23456i	−1.00747	−	0.581661i	−0.0970177	−	0.995283i	$-0.530930\pi$
$53$	−7.33447	−	4.23456i	−1.00747	−	0.581661i	−0.910449	+	0.413622i	$0.864264\pi$
$54$	−6.78067	+	2.83240i	−0.922733	+	0.385440i
$55$	0.214979	−	0.124118i	0.0289878	−	0.0167361i
$56$	−5.43255	−	8.39535i	−0.725956	−	1.12188i
$57$	−1.93850	−	9.08181i	−0.256760	−	1.20291i
$58$	5.90694	+	7.07522i	0.775619	+	0.929021i
$59$	−0.676398	+	11.6133i	−0.0880596	+	1.51192i	0.607998	+	0.793938i	$0.291973\pi$
$59$	−0.676398	+	11.6133i	−0.0880596	+	1.51192i	−0.696058	+	0.717986i	$0.745064\pi$
$60$	−0.244548	−	0.394964i	−0.0315710	−	0.0509896i
$61$	−14.9993	+	3.55489i	−1.92046	+	0.455157i	−0.922923	+	0.384984i	$0.874207\pi$
$61$	−14.9993	+	3.55489i	−1.92046	+	0.455157i	−0.997535	+	0.0701734i	$0.977645\pi$
$62$	−1.49040	+	2.94935i	−0.189281	+	0.374568i
$63$	−3.17722	−	10.1192i	−0.400292	−	1.27491i
$64$	1.27166	+	7.89828i	0.158958	+	0.987285i
$65$	0.00754241	−	0.0150182i	0.000935521	−	0.00186277i
$66$	−4.48910	−	0.638364i	−0.552570	−	0.0785771i
$67$	−8.92825	−	3.85127i	−1.09076	−	0.470508i	−0.226734	−	0.973957i	$-0.572805\pi$
$67$	−8.92825	−	3.85127i	−1.09076	−	0.470508i	−0.864025	+	0.503449i	$0.832064\pi$
$68$	0.831779	−	6.82233i	0.100868	−	0.827329i
$69$	1.77246	−	8.88286i	0.213379	−	1.06937i
$70$	0.599918	−	0.299427i	0.0717040	−	0.0357884i
$71$	2.56602	−	0.933954i	0.304530	−	0.110840i	−0.185235	−	0.982694i	$-0.559305\pi$
$71$	2.56602	−	0.933954i	0.304530	−	0.110840i	0.489765	+	0.871854i	$0.337082\pi$
$72$	−0.935398	+	8.43357i	−0.110238	+	0.993905i
$73$	3.31821	+	1.20773i	0.388367	+	0.141354i	0.528821	−	0.848733i	$-0.322634\pi$
$73$	3.31821	+	1.20773i	0.388367	+	0.141354i	−0.140454	+	0.990087i	$0.544856\pi$
$74$	8.62851	−	0.986817i	1.00304	−	0.114715i
$75$	−7.79612	+	3.69891i	−0.900219	+	0.427113i
$76$	−10.2571	−	3.12637i	−1.17657	−	0.358619i
$77$	1.50926	−	6.36806i	0.171996	−	0.725707i
$78$	−0.277665	+	0.130896i	−0.0314394	+	0.0148210i
$79$	−0.0491922	+	0.420866i	−0.00553456	+	0.0473512i	−0.995723	−	0.0923843i	$-0.970551\pi$
$79$	−0.0491922	+	0.420866i	−0.00553456	+	0.0473512i	0.990189	+	0.139736i	$0.0446252\pi$
$80$	−0.535784	+	0.0258693i	−0.0599024	+	0.00289227i
$81$	−3.34296	+	8.35611i	−0.371440	+	0.928457i
$82$	11.7201	−	5.02108i	1.29427	−	0.554485i
$83$	−0.754832	−	0.0882272i	−0.0828535	−	0.00968419i	0.0745651	−	0.997216i	$-0.476243\pi$
$83$	−0.754832	−	0.0882272i	−0.0828535	−	0.00968419i	−0.157419	+	0.987532i	$0.550317\pi$
$84$	−11.9983	−	2.45613i	−1.30912	−	0.267986i
$85$	0.448409	+	0.106275i	0.0486368	+	0.0115271i
$86$	−6.05753	+	7.18279i	−0.653201	+	0.774540i
$87$	11.2517	+	0.908801i	1.20631	+	0.0974337i
$88$	−3.15775	+	4.17628i	−0.336617	+	0.445193i
$89$	−3.21873	+	8.84339i	−0.341185	+	0.937397i	0.643867	+	0.765137i	$0.277329\pi$
$89$	−3.21873	+	8.84339i	−0.341185	+	0.937397i	−0.985052	+	0.172260i	$0.944893\pi$
$90$	−0.555002	−	0.125189i	−0.0585024	−	0.0131960i
$91$	−0.151537	−	0.416344i	−0.0158854	−	0.0436447i
$92$	−7.97876	−	6.76278i	−0.831844	−	0.705069i
$93$	1.29863	+	3.83322i	0.134662	+	0.397486i
$94$	3.17049	−	5.46009i	0.327011	−	0.563166i
$95$	0.284776	−	0.660186i	0.0292174	−	0.0677336i
$96$	7.99361	+	5.66589i	0.815844	+	0.578272i
$97$	1.75329	+	0.880535i	0.178019	+	0.0894047i	0.535577	−	0.844486i	$-0.320094\pi$
$97$	1.75329	+	0.880535i	0.178019	+	0.0894047i	−0.357558	+	0.933891i	$0.616390\pi$
$98$	2.24902	−	7.44493i	0.227186	−	0.752052i
$99$	−4.40980	+	3.37534i	−0.443201	+	0.339235i
$100$	−0.628748	+	9.94418i	−0.0628748	+	0.994418i
$101$	−0.156145	−	0.658826i	−0.0155370	−	0.0655557i	0.964724	−	0.263263i	$-0.0847986\pi$
$101$	−0.156145	−	0.658826i	−0.0155370	−	0.0655557i	−0.980261	+	0.197707i	$0.936650\pi$
$102$	−5.24843	−	6.58088i	−0.519672	−	0.651605i
$103$	4.23309	+	0.246549i	0.417098	+	0.0242932i	0.265411	−	0.964135i	$-0.414492\pi$
$103$	4.23309	+	0.246549i	0.417098	+	0.0242932i	0.151687	+	0.988429i	$0.451529\pi$
$104$	−0.0232454	+	0.353698i	−0.00227940	+	0.0346829i
$105$	0.253092	−	0.781206i	0.0246993	−	0.0762379i
$106$	−2.79105	+	11.6474i	−0.271090	+	1.13130i
$107$	−2.07267	−	3.58997i	−0.200372	−	0.347055i	0.748276	−	0.663387i	$-0.230882\pi$
$107$	−2.07267	−	3.58997i	−0.200372	−	0.347055i	−0.948648	+	0.316332i	$0.897549\pi$
$108$	6.56760	+	8.05398i	0.631968	+	0.774994i
$109$	7.92824	−	13.7321i	0.759388	−	1.31530i	−0.183775	−	0.982968i	$-0.558832\pi$
$109$	7.92824	−	13.7321i	0.759388	−	1.31530i	0.943163	−	0.332330i	$-0.107835\pi$
$110$	−0.254752	−	0.241545i	−0.0242897	−	0.0230304i
$111$	6.54140	−	8.38735i	0.620882	−	0.796092i
$112$	−9.19729	+	10.7424i	−0.869062	+	1.01506i
$113$	8.75105	−	13.3053i	0.823229	−	1.25166i	−0.141899	−	0.989881i	$-0.545321\pi$
$113$	8.75105	−	13.3053i	0.823229	−	1.25166i	0.965128	−	0.261778i	$-0.0843088\pi$
$114$	−11.5334	+	6.28125i	−1.08020	+	0.588293i
$115$	0.510109	−	0.481263i	0.0475679	−	0.0448780i
$116$	7.21663	−	10.8546i	0.670047	−	1.00782i
$117$	−0.123862	+	0.354973i	−0.0114510	+	0.0328173i
$118$	16.0175	−	3.75423i	1.47453	−	0.345604i
$119$	10.1506	−	6.67613i	0.930500	−	0.612000i
$120$	−0.437128	+	0.490428i	−0.0399041	+	0.0447697i
$121$	7.52221	−	0.879220i	0.683837	−	0.0799291i
$122$	10.8530	+	18.9062i	0.982582	+	1.71168i
$123$	5.66856	−	14.5508i	0.511117	−	1.31200i
$124$	4.59824	+	0.834360i	0.412934	+	0.0749278i
$125$	−1.31827	−	0.232447i	−0.117910	−	0.0207907i
$126$	−12.4417	+	8.37801i	−1.10840	+	0.746372i
$127$	−19.8904	+	3.50721i	−1.76498	+	0.311214i	−0.959564	−	0.281490i	$-0.909171\pi$
$127$	−19.8904	+	3.50721i	−1.76498	+	0.311214i	−0.805420	+	0.592704i	$0.798060\pi$
$128$	10.1970	−	4.90110i	0.901298	−	0.433200i
$129$	1.07942	+	11.4571i	0.0950380	+	1.00874i
$130$	−0.0233955	−	0.00418519i	−0.00205192	−	0.000367065i
$131$	−7.30449	+	7.74231i	−0.638196	+	0.676448i	−0.963052	−	0.269315i	$-0.913203\pi$
$131$	−7.30449	+	7.74231i	−0.638196	+	0.676448i	0.324856	+	0.945764i	$0.394684\pi$
$132$	0.940179	+	6.34311i	0.0818321	+	0.552097i
$133$	−7.50779	−	17.4050i	−0.651008	−	1.50921i
$134$	−1.63031	+	13.6541i	−0.140837	+	1.17953i
$135$	−0.585631	+	0.377606i	−0.0504031	+	0.0324992i
$136$	−9.58432	+	1.61645i	−0.821848	+	0.138610i
$137$	0.936670	+	0.697325i	0.0800251	+	0.0595765i	0.636428	−	0.771336i	$-0.280411\pi$
$137$	0.936670	+	0.697325i	0.0800251	+	0.0595765i	−0.556403	+	0.830913i	$0.687819\pi$
$138$	−12.7564	+	1.16989i	−1.08589	+	0.0995878i
$139$	6.25057	−	1.87130i	0.530166	−	0.158721i	−0.0105216	−	0.999945i	$-0.503349\pi$
$139$	6.25057	−	1.87130i	0.530166	−	0.158721i	0.540688	+	0.841223i	$0.318164\pi$
$140$	−0.647274	−	0.692932i	−0.0547046	−	0.0585634i
$141$	−2.05119	−	7.45584i	−0.172742	−	0.627895i
$142$	−2.29840	−	3.10335i	−0.192878	−	0.260427i
$143$	−0.177708	+	0.149115i	−0.0148607	+	0.0124696i
$144$	11.8105	−	2.12407i	0.984210	−	0.177005i
$145$	0.669510	+	0.561786i	0.0555998	+	0.0466538i
$146$	0.302743	−	4.98463i	0.0250552	−	0.412531i
$147$	−4.57645	−	8.35367i	−0.377459	−	0.688999i
$148$	−4.80863	−	11.3016i	−0.395267	−	0.928989i
$149$	9.37564	−	6.97991i	0.768083	−	0.571816i	−0.140225	−	0.990120i	$-0.544783\pi$
$149$	9.37564	−	6.97991i	0.768083	−	0.571816i	0.908307	+	0.418303i	$0.137375\pi$
$150$	8.15088	+	9.08219i	0.665516	+	0.741558i
$151$	17.9560	−	1.04582i	1.46124	−	0.0851074i	0.690996	−	0.722859i	$-0.257172\pi$
$151$	17.9560	−	1.04582i	1.46124	−	0.0851074i	0.770242	+	0.637751i	$0.220135\pi$
$152$	−0.112961	+	15.1642i	−0.00916235	+	1.22998i
$153$	−10.2546	−	1.06011i	−0.829037	−	0.0857050i
$154$	−9.24092	+	0.515202i	−0.744654	+	0.0415162i
$155$	−0.0898701	+	0.300187i	−0.00721854	+	0.0241116i
$156$	0.289156	+	0.323809i	0.0231510	+	0.0259255i
$157$	0.907206	−	0.455616i	0.0724030	−	0.0363621i	−0.412229	−	0.911080i	$-0.635250\pi$
$157$	0.907206	−	0.455616i	0.0724030	−	0.0363621i	0.484632	+	0.874718i	$0.338953\pi$
$158$	0.590399	−	0.102592i	0.0469697	−	0.00816182i
$159$	7.78396	+	12.4333i	0.617308	+	0.986027i
$160$	0.250585	+	0.716012i	0.0198105	+	0.0566058i
$161$		−	18.4890i		−	1.45714i
$162$	12.6739	+	1.17127i	0.995757	+	0.0920236i
$163$			10.8729i			0.851632i	0.904810	+	0.425816i	$0.140013\pi$
$163$			10.8729i			0.851632i	−0.904810	+	0.425816i	$0.859987\pi$
$164$	−11.5218	−	13.8705i	−0.899705	−	1.08310i
$165$	−0.429684	+	0.0153720i	−0.0334508	+	0.00119671i
$166$	0.184001	+	1.05889i	0.0142813	+	0.0821860i
$167$	5.41084	−	2.71742i	0.418703	−	0.210281i	−0.226958	−	0.973904i	$-0.572878\pi$
$167$	5.41084	−	2.71742i	0.418703	−	0.210281i	0.645661	+	0.763624i	$0.276582\pi$
$168$	1.49612	+	17.2553i	0.115428	+	1.33128i
$169$	3.72394	−	12.4388i	0.286457	−	0.956832i
$170$	−0.0362782	−	0.650703i	−0.00278241	−	0.0499066i
$171$	−4.40709	+	15.4690i	−0.337019	+	1.18294i
$172$	12.1750	+	5.32366i	0.928336	+	0.405925i
$173$	16.8829	−	0.983315i	1.28358	−	0.0747601i	0.597253	−	0.802053i	$-0.296259\pi$
$173$	16.8829	−	0.983315i	1.28358	−	0.0747601i	0.686327	+	0.727293i	$0.259222\pi$
$174$	−3.29367	−	15.6206i	−0.249692	−	1.18420i
$175$	−14.1283	+	10.5181i	−1.06800	+	0.795095i
$176$	6.93238	+	2.60144i	0.522548	+	0.196091i
$177$	10.4631	−	17.2193i	0.786453	−	1.29428i
$178$	13.2846	+	0.806842i	0.995722	+	0.0604754i
$179$	12.5555	+	10.5353i	0.938442	+	0.787447i	0.977314	−	0.211797i	$-0.0679317\pi$
$179$	12.5555	+	10.5353i	0.938442	+	0.787447i	−0.0388711	+	0.999244i	$0.512376\pi$
$180$	0.0535104	+	0.802830i	0.00398843	+	0.0598394i
$181$	−12.7797	+	10.7235i	−0.949909	+	0.797068i	−0.979282	−	0.202500i	$-0.935093\pi$
$181$	−12.7797	+	10.7235i	−0.949909	+	0.797068i	0.0293732	+	0.999569i	$0.490649\pi$
$182$	−0.503527	+	0.372923i	−0.0373239	+	0.0276429i
$183$	25.8349	+	6.73805i	1.90977	+	0.498091i
$184$	−5.95967	+	13.5379i	−0.439352	+	0.998026i
$185$	0.788930	−	0.236190i	0.0580033	−	0.0173650i
$186$	4.67474	−	3.30255i	0.342768	−	0.242155i
$187$	−5.10245	−	3.79863i	−0.373128	−	0.277783i
$188$	−8.67810	−	2.10232i	−0.632916	−	0.153327i
$189$	−3.35409	+	18.0619i	−0.243974	+	1.31381i
$190$	−1.00963	−	0.120551i	−0.0732463	−	0.00874567i
$191$	1.08326	+	2.51128i	0.0783819	+	0.181710i	0.952901	−	0.303281i	$-0.0980822\pi$
$191$	1.08326	+	2.51128i	0.0783819	+	0.181710i	−0.874519	+	0.484991i	$0.838823\pi$
$192$	4.46652	−	13.1168i	0.322343	−	0.946623i
$193$	−0.380101	+	0.402884i	−0.0273603	+	0.0290002i	−0.740909	−	0.671605i	$-0.765605\pi$
$193$	−0.380101	+	0.402884i	−0.0273603	+	0.0290002i	0.713549	+	0.700605i	$0.247087\pi$
$194$	0.488598	−	2.73130i	0.0350793	−	0.196096i
$195$	−0.0237323	+	0.0168546i	−0.00169951	+	0.00120698i
$196$	−10.9985	−	0.0546195i	−0.785608	−	0.00390139i
$197$	−25.0287	+	4.41324i	−1.78322	+	0.314430i	−0.965348	−	0.260967i	$-0.915959\pi$
$197$	−25.0287	+	4.41324i	−1.78322	+	0.314430i	−0.817874	+	0.575397i	$0.804848\pi$
$198$	6.35008	+	4.62114i	0.451281	+	0.328410i
$199$	0.161401	+	0.0284593i	0.0114414	+	0.00201743i	0.179366	−	0.983782i	$-0.442595\pi$
$199$	0.161401	+	0.0284593i	0.0114414	+	0.00201743i	−0.167925	+	0.985800i	$0.553706\pi$
$200$	13.7353	−	3.14744i	0.971230	−	0.222558i
$201$	10.5336	+	13.1408i	0.742985	+	0.926880i
$202$	−0.830433	+	0.476705i	−0.0584291	+	0.0335409i
$203$	22.8857	−	2.67496i	1.60626	−	0.187745i
$204$	−6.81129	+	9.76291i	−0.476885	+	0.683541i
$205$	1.01014	−	0.664382i	0.0705515	−	0.0464024i
$206$	−1.36843	−	5.83841i	−0.0953428	−	0.406781i
$207$	−9.92337	+	12.1518i	−0.689722	+	0.844612i
$208$	0.488895	−	0.110754i	0.0338988	−	0.00767938i
$209$	−7.21896	+	6.81074i	−0.499346	+	0.471108i
$210$	−1.16097	−	0.0289149i	−0.0801142	−	0.00199532i
$211$	−7.89277	+	12.0004i	−0.543360	+	0.826139i	−0.997912	−	0.0645807i	$-0.979429\pi$
$211$	−7.89277	+	12.0004i	−0.543360	+	0.826139i	0.454552	+	0.890720i	$0.349799\pi$
$212$	16.9143	−	0.900885i	1.16168	−	0.0618730i
$213$	−4.68424	−	0.654251i	−0.320959	−	0.0448286i
$214$	−4.03359	+	4.25414i	−0.275731	+	0.290807i
$215$	−0.445489	+	0.771609i	−0.0303821	+	0.0526233i
$216$	8.27790	−	12.1440i	0.563239	−	0.826294i
$217$	4.13057	+	7.15435i	0.280401	+	0.485669i
$218$	−21.8071	−	5.22560i	−1.47696	−	0.353922i
$219$	−4.09638	−	4.54170i	−0.276808	−	0.306899i
$220$	−0.225017	+	0.442553i	−0.0151707	+	0.0298369i
$221$	−0.429926	−	0.0250404i	−0.0289200	−	0.00168440i
$222$	−14.0028	−	5.49517i	−0.939806	−	0.368811i
$223$	0.223004	+	0.940930i	0.0149335	+	0.0630093i	0.980001	−	0.198990i	$-0.0637662\pi$
$223$	0.223004	+	0.940930i	0.0149335	+	0.0630093i	−0.965068	+	0.262000i	$0.915618\pi$
$224$	18.2641	+	8.14875i	1.22032	+	0.544461i
$225$	14.9310	+	0.669889i	0.995402	+	0.0446593i
$226$	−21.5594	−	6.51283i	−1.43411	−	0.433227i
$227$	−21.0025	−	10.5479i	−1.39399	−	0.700087i	−0.416119	−	0.909310i	$-0.636610\pi$
$227$	−21.0025	−	10.5479i	−1.39399	−	0.700087i	−0.977868	+	0.209223i	$0.932906\pi$
$228$	13.1553	+	13.1105i	0.871232	+	0.868266i
$229$	6.36052	−	14.7453i	0.420315	−	0.974400i	−0.568146	−	0.822928i	$-0.692339\pi$
$229$	6.36052	−	14.7453i	0.420315	−	0.974400i	0.988461	−	0.151473i	$-0.0484015\pi$
$230$	−0.857683	−	0.498027i	−0.0565539	−	0.0328389i
$231$	−7.47903	+	8.51787i	−0.492084	+	0.560434i
$232$	−17.6194	−	5.41825i	−1.15677	−	0.355726i
$233$	7.32302	+	20.1198i	0.479747	+	1.31809i	0.909709	+	0.415247i	$0.136305\pi$
$233$	7.32302	+	20.1198i	0.479747	+	1.31809i	−0.429962	+	0.902847i	$0.641473\pi$
$234$	0.531096	+	0.0251494i	0.0347188	+	0.00164407i
$235$	0.204770	−	0.562600i	0.0133577	−	0.0367000i
$236$	−11.5328	−	20.2065i	−0.750721	−	1.31533i
$237$	0.416942	−	0.603991i	0.0270833	−	0.0392334i
$238$	−13.1344	−	11.0768i	−0.851380	−	0.718002i
$239$	−15.6305	−	3.70450i	−1.01105	−	0.239624i	−0.308477	−	0.951232i	$-0.599819\pi$
$239$	−15.6305	−	3.70450i	−1.01105	−	0.239624i	−0.702577	+	0.711607i	$0.747968\pi$
$240$	0.840753	+	0.395392i	0.0542703	+	0.0255225i
$241$	−10.8266	−	1.26544i	−0.697400	−	0.0815143i	−0.239996	−	0.970774i	$-0.577146\pi$
$241$	−10.8266	−	1.26544i	−0.697400	−	0.0815143i	−0.457403	+	0.889259i	$0.651220\pi$
$242$	−4.21775	−	9.84499i	−0.271127	−	0.632860i
$243$	11.8986	−	10.0709i	0.763295	−	0.646050i
$244$	21.2676	−	22.3192i	1.36152	−	1.42884i
$245$	0.0856150	−	0.732483i	0.00546974	−	0.0467966i
$246$	−22.0081	−	1.83262i	−1.40319	−	0.116843i
$247$	−0.154952	+	0.653796i	−0.00985939	+	0.0416000i
$248$	−0.718348	−	6.56993i	−0.0456152	−	0.417191i
$249$	1.08327	+	0.747793i	0.0686493	+	0.0473894i
$250$	0.215103	+	1.88082i	0.0136043	+	0.118953i
$251$	−20.3407	−	7.40340i	−1.28389	−	0.467299i	−0.392175	−	0.919891i	$-0.628277\pi$
$251$	−20.3407	−	7.40340i	−1.28389	−	0.467299i	−0.891718	+	0.452592i	$0.850499\pi$
$252$	16.3635	+	13.4986i	1.03080	+	0.850334i
$253$	−9.09677	+	3.31095i	−0.571909	+	0.208158i
$254$	12.7557	+	25.5567i	0.800364	+	1.60357i
$255$	−0.599789	−	0.526639i	−0.0375603	−	0.0329794i
$256$	−10.7465	−	11.8538i	−0.671659	−	0.740861i
$257$	18.9613	+	8.17909i	1.18277	+	0.510198i	0.894377	−	0.447314i	$-0.147619\pi$
$257$	18.9613	+	8.17909i	1.18277	+	0.510198i	0.288394	+	0.957512i	$0.406879\pi$
$258$	15.0993	−	6.07193i	0.940044	−	0.378022i
$259$	9.74402	−	19.4019i	0.605464	−	1.20558i
$260$	0.00373622	+	0.0334032i	0.000231711	+	0.00207158i
$261$	−16.4773	−	10.5251i	−1.01992	−	0.651485i
$262$	13.4352	+	6.78923i	0.830028	+	0.419440i
$263$	−2.89689	+	0.686575i	−0.178630	+	0.0423360i	−0.318957	−	0.947769i	$-0.603333\pi$
$263$	−2.89689	+	0.686575i	−0.178630	+	0.0423360i	0.140327	+	0.990105i	$0.455184\pi$
$264$	8.22185	−	3.82613i	0.506020	−	0.235482i
$265$	−0.0660365	+	1.13380i	−0.00405659	+	0.0696490i
$266$	−20.5779	+	17.1800i	−1.26171	+	1.05337i
$267$	12.1041	−	10.9173i	0.740760	−	0.668128i
$268$	19.1680	−	3.28178i	1.17087	−	0.200467i
$269$	−13.9449	+	8.05109i	−0.850235	+	0.490884i	−0.860730	−	0.509061i	$-0.829993\pi$
$269$	−13.9449	+	8.05109i	−0.850235	+	0.490884i	0.0104950	+	0.999945i	$0.496659\pi$
$270$	0.747522	+	0.642114i	0.0454927	+	0.0390778i
$271$	−21.7706	−	12.5693i	−1.32247	−	0.763529i	−0.338348	−	0.941021i	$-0.609868\pi$
$271$	−21.7706	−	12.5693i	−1.32247	−	0.763529i	−0.984122	+	0.177492i	$0.943202\pi$
$272$	6.04675	+	12.3443i	0.366638	+	0.748481i
$273$	−0.106154	+	0.760031i	−0.00642474	+	0.0459992i
$274$	0.568674	−	1.55043i	0.0343549	−	0.0936649i
$275$	7.70506	+	5.06770i	0.464633	+	0.305594i
$276$	6.71722	+	16.8246i	0.404329	+	1.01272i
$277$	−15.5240	−	16.4544i	−0.932744	−	0.988651i	0.0672147	−	0.997739i	$-0.478589\pi$
$277$	−15.5240	−	16.4544i	−0.932744	−	0.988651i	−0.999959	+	0.00908768i	$0.997107\pi$
$278$	−5.05132	−	7.72185i	−0.302958	−	0.463126i
$279$	1.12506	−	6.91912i	0.0673555	−	0.414237i
$280$	−0.679124	+	1.15630i	−0.0405854	+	0.0691021i
$281$	12.6415	+	19.2205i	0.754132	+	1.14660i	0.984821	+	0.173574i	$0.0555315\pi$
$281$	12.6415	+	19.2205i	0.754132	+	1.14660i	−0.230689	+	0.973027i	$0.574098\pi$
$282$	−9.28360	+	5.78002i	−0.552830	+	0.344195i
$283$	3.32873	+	28.4791i	0.197872	+	1.69290i	0.618591	+	0.785713i	$0.287704\pi$
$283$	3.32873	+	28.4791i	0.197872	+	1.69290i	−0.420719	+	0.907191i	$0.638222\pi$
$284$	−3.28303	+	4.36446i	−0.194812	+	0.258983i
$285$	−0.971676	+	0.778893i	−0.0575571	+	0.0461376i
$286$	0.273651	+	0.180958i	0.0161813	+	0.0107003i
$287$	5.53505	−	31.3908i	0.326723	−	1.85294i
$288$	−7.63043	−	15.1584i	−0.449627	−	0.893216i
$289$	0.901407	+	5.11213i	0.0530239	+	0.300714i
$290$	0.492371	−	1.13370i	0.0289130	−	0.0665729i
$291$	−1.96768	−	2.77062i	−0.115348	−	0.162416i
$292$	−6.87997	+	1.59454i	−0.402620	+	0.0933133i
$293$	−2.40015	−	2.26443i	−0.140219	−	0.132289i	0.612937	−	0.790132i	$-0.289988\pi$
$293$	−2.40015	−	2.26443i	−0.140219	−	0.132289i	−0.753156	+	0.657842i	$0.771469\pi$
$294$	−9.48513	+	9.56492i	−0.553184	+	0.557837i
$295$	1.43242	−	0.617887i	0.0833989	−	0.0359748i
$296$	−13.3886	+	11.0655i	−0.778198	+	0.643168i
$297$	9.48726	−	1.58422i	0.550506	−	0.0919257i
$298$	−13.2346	−	9.90397i	−0.766660	−	0.573722i
$299$	−0.391366	+	0.525696i	−0.0226333	+	0.0304018i
$300$	9.03510	−	14.7042i	0.521642	−	0.848946i
$301$	6.73688	+	22.5027i	0.388307	+	1.29704i
$302$	−8.64047	−	23.9242i	−0.497203	−	1.37668i
$303$	−0.295962	+	1.13477i	−0.0170026	+	0.0651909i
$304$	20.6051	−	5.94643i	1.18178	−	0.341051i
$305$	1.32874	+	1.58353i	0.0760833	+	0.0906726i
$306$	2.68747	+	14.3297i	0.153632	+	0.819173i
$307$	16.2252	−	19.3364i	0.926020	−	1.10359i	−0.0683535	−	0.997661i	$-0.521775\pi$
$307$	16.2252	−	19.3364i	0.926020	−	1.10359i	0.994374	−	0.105927i	$-0.0337810\pi$
$308$	4.41554	+	12.3216i	0.251599	+	0.702091i
$309$	−6.27648	−	3.81382i	−0.357056	−	0.216961i
$310$	0.443144	+	0.00110034i	0.0251689	+	6.24950e-5i
$311$	−7.75843	−	10.4214i	−0.439940	−	0.590942i	0.525750	−	0.850639i	$-0.323785\pi$
$311$	−7.75843	−	10.4214i	−0.439940	−	0.590942i	−0.965690	+	0.259697i	$0.916377\pi$
$312$	0.322712	−	0.522287i	0.0182700	−	0.0295687i
$313$	0.422855	+	7.26013i	0.0239012	+	0.410367i	0.988945	+	0.148280i	$0.0473737\pi$
$313$	0.422855	+	7.26013i	0.0239012	+	0.410367i	−0.965044	+	0.262087i	$0.915589\pi$
$314$	−0.982637	−	1.04673i	−0.0554534	−	0.0590704i
$315$	−1.02145	+	0.989776i	−0.0575521	+	0.0557676i
$316$	−0.376575	−	0.759200i	−0.0211840	−	0.0427083i
$317$	2.24602	+	0.672416i	0.126149	+	0.0377666i	0.349256	−	0.937028i	$-0.386435\pi$
$317$	2.24602	+	0.672416i	0.126149	+	0.0377666i	−0.223106	+	0.974794i	$0.571620\pi$
$318$	13.7262	−	15.5547i	0.769725	−	0.872262i
$319$	−5.41441	−	10.7810i	−0.303149	−	0.603619i
$320$	0.869979	−	0.627750i	0.0486333	−	0.0350923i
$321$	0.256699	+	7.17534i	0.0143275	+	0.400488i
$322$	−25.0675	+	7.43694i	−1.39696	+	0.414445i
$323$	−18.4244			−1.02516
$324$	−3.50989	−	17.6545i	−0.194994	−	0.980804i
$325$	0.624350			0.0346327
$326$	14.7415	−	4.37347i	0.816458	−	0.242224i
$327$	−23.2786	+	14.5737i	−1.28731	+	0.805927i
$328$	−14.1712	+	21.2006i	−0.782474	+	1.17061i
$329$	−7.08393	−	14.1053i	−0.390550	−	0.777648i
$330$	0.193675	+	0.576384i	0.0106615	+	0.0317289i
$331$	12.5661	+	3.76206i	0.690698	+	0.206781i	0.612868	−	0.790185i	$-0.290016\pi$
$331$	12.5661	+	3.76206i	0.690698	+	0.206781i	0.0778297	+	0.996967i	$0.475201\pi$
$332$	1.36164	−	0.675394i	0.0747297	−	0.0370671i
$333$	−16.8176	+	7.52208i	−0.921598	+	0.412208i
$334$	−5.86073	−	6.24299i	−0.320685	−	0.341601i
$335$	0.0758172	+	1.30173i	0.00414233	+	0.0711211i
$336$	22.7930	−	8.96914i	1.24346	−	0.489307i
$337$	−13.1010	−	17.5977i	−0.713658	−	0.958608i	−1.00000		0.000481048i	$-0.999847\pi$
$337$	−13.1010	−	17.5977i	−0.713658	−	0.958608i	0.286342	−	0.958127i	$-0.407561\pi$
$338$	−18.3625	−	0.0455946i	−0.998789	−	0.00248002i
$339$	−24.1910	+	13.2527i	−1.31387	+	0.719788i
$340$	−0.867634	+	0.310922i	−0.0470540	+	0.0168621i
$341$	2.78032	−	3.31345i	0.150563	−	0.179434i
$342$	22.7456	−	0.247007i	1.22994	−	0.0133566i
$343$	3.41034	+	4.06429i	0.184141	+	0.219451i
$344$	2.32061	−	18.6483i	0.125119	−	1.00545i
$345$	−1.17118	+	0.322206i	−0.0630542	+	0.0173470i
$346$	−8.12408	−	22.4943i	−0.436753	−	1.20930i
$347$	3.64718	+	12.1824i	0.195791	+	0.653987i	0.998350	+	0.0574148i	$0.0182858\pi$
$347$	3.64718	+	12.1824i	0.195791	+	0.653987i	−0.802560	+	0.596572i	$0.796529\pi$
$348$	−19.8537	+	10.7487i	−1.06427	+	0.576193i
$349$	−10.3254	+	13.8695i	−0.552708	+	0.742416i	−0.987414	−	0.158157i	$-0.949445\pi$
$349$	−10.3254	+	13.8695i	−0.552708	+	0.742416i	0.434706	+	0.900572i	$0.356852\pi$
$350$	19.9434	+	14.9244i	1.06602	+	0.797745i
$351$	0.477691	−	0.442554i	0.0254973	−	0.0236218i
$352$	0.738593	−	10.4453i	0.0393671	−	0.556739i
$353$	5.93410	−	2.55972i	0.315840	−	0.136240i	−0.232258	−	0.972654i	$-0.574611\pi$
$353$	5.93410	−	2.55972i	0.315840	−	0.136240i	0.548098	+	0.836414i	$0.315352\pi$
$354$	−27.5546	−	7.25969i	−1.46451	−	0.385848i
$355$	−0.266358	−	0.251296i	−0.0141368	−	0.0133374i
$356$	−4.24962	−	18.3359i	−0.225229	−	0.971798i
$357$	−20.9504	+	1.97383i	−1.10881	+	0.104466i
$358$	9.23356	−	21.2605i	0.488009	−	1.12365i
$359$	−2.46629	−	13.9870i	−0.130166	−	0.738208i	−0.978105	−	0.208114i	$-0.933268\pi$
$359$	−2.46629	−	13.9870i	−0.130166	−	0.738208i	0.847939	−	0.530094i	$-0.177844\pi$
$360$	1.06696	−	0.395477i	0.0562336	−	0.0208435i
$361$	−1.69232	+	9.59761i	−0.0890693	+	0.505137i
$362$	19.6794	+	13.0134i	1.03432	+	0.683971i
$363$	−12.2228	−	4.76164i	−0.641530	−	0.249921i
$364$	0.708147	+	0.532682i	0.0371170	+	0.0279201i
$365$	−0.0549742	−	0.470334i	−0.00287748	−	0.0246184i
$366$	−1.25625	−	37.7374i	−0.0656651	−	1.97257i
$367$	6.23749	+	9.48364i	0.325594	+	0.495042i	0.960778	−	0.277319i	$-0.0894459\pi$
$367$	6.23749	+	9.48364i	0.325594	+	0.495042i	−0.635184	+	0.772361i	$0.719076\pi$
$368$	20.7519	+	2.63473i	1.08177	+	0.137345i
$369$	−20.4859	+	17.6608i	−1.06645	+	0.919383i
$370$	−0.637564	−	0.974631i	−0.0331454	−	0.0506687i
$371$	20.5475	+	21.7790i	1.06677	+	1.13071i
$372$	−6.35796	−	5.00963i	−0.329645	−	0.259737i
$373$	20.5433	+	13.5116i	1.06369	+	0.699602i	0.955638	−	0.294543i	$-0.0951674\pi$
$373$	20.5433	+	13.5116i	1.06369	+	0.699602i	0.108055	+	0.994145i	$0.465538\pi$
$374$	−3.09781	+	8.44587i	−0.160184	+	0.436725i
$375$	1.82825	+	1.42587i	0.0944104	+	0.0736318i
$376$	0.640310	+	12.6114i	0.0330215	+	0.650385i
$377$	−0.707330	−	0.408377i	−0.0364293	−	0.0210325i
$378$	25.8375	−	2.71764i	1.32894	−	0.139780i
$379$	29.6184	−	17.1002i	1.52140	−	0.878379i	0.521716	−	0.853119i	$-0.325292\pi$
$379$	29.6184	−	17.1002i	1.52140	−	0.878379i	0.999681	−	0.0252600i	$-0.00804137\pi$
$380$	0.242666	+	1.41735i	0.0124485	+	0.0727086i
$381$	33.2796	+	10.7818i	1.70497	+	0.552369i
$382$	2.96908	−	2.47881i	0.151911	−	0.126827i
$383$	0.575760	−	9.88542i	0.0294200	−	0.505121i	−0.951122	−	0.308814i	$-0.900068\pi$
$383$	0.575760	−	9.88542i	0.0294200	−	0.505121i	0.980542	−	0.196307i	$-0.0628950\pi$
$384$	−19.5804	−	0.779690i	−0.999208	−	0.0397884i
$385$	−0.853969	+	0.202394i	−0.0435223	+	0.0103150i
$386$	0.699122	+	0.353289i	0.0355844	+	0.0179819i
$387$	7.64981	−	18.4057i	0.388862	−	0.935612i
$388$	−3.89964	+	0.436183i	−0.197974	+	0.0221439i
$389$	−3.32135	+	6.61336i	−0.168399	+	0.335310i	−0.961964	−	0.273175i	$-0.911926\pi$
$389$	−3.32135	+	6.61336i	−0.168399	+	0.335310i	0.793565	+	0.608485i	$0.208223\pi$
$390$	0.0323975	+	0.0253969i	0.00164051	+	0.00128602i
$391$	−16.5014	−	7.11803i	−0.834514	−	0.359974i
$392$	4.34994	+	14.9338i	0.219705	+	0.754271i
$393$	17.4614	−	5.91565i	0.880813	−	0.298405i
$394$	16.0509	+	32.1589i	0.808634	+	1.62014i
$395$	0.0533964	−	0.0194347i	0.00268666	−	0.000977865i
$396$	3.71114	−	10.4683i	0.186492	−	0.526050i
$397$	−13.3760	−	4.86845i	−0.671320	−	0.244340i	−0.0162037	−	0.999869i	$-0.505158\pi$
$397$	−13.3760	−	4.86845i	−0.671320	−	0.244340i	−0.655116	+	0.755528i	$0.727380\pi$
$398$	−0.0263359	−	0.230275i	−0.00132010	−	0.0115427i
$399$	−2.64320	+	32.7249i	−0.132325	+	1.63829i
$400$	−9.79213	−	17.3563i	−0.489607	−	0.867816i
$401$	6.77095	−	28.5689i	0.338125	−	1.42666i	−0.492734	−	0.870180i	$-0.664003\pi$
$401$	6.77095	−	28.5689i	0.338125	−	1.42666i	0.830859	−	0.556482i	$-0.187849\pi$
$402$	13.5794	−	19.5672i	0.677277	−	0.975925i
$403$	0.0339958	−	0.290852i	0.00169345	−	0.0144884i
$404$	0.980349	+	0.934157i	0.0487742	+	0.0464760i
$405$	1.20257	−	0.102298i	0.0597564	−	0.00508325i
$406$	−12.8322	−	29.9526i	−0.636851	−	1.48652i
$407$	−11.2909	−	1.31971i	−0.559667	−	0.0654157i
$408$	15.9763	+	5.30778i	0.790947	+	0.262774i
$409$	35.5682	+	8.42981i	1.75873	+	0.416827i	0.978095	−	0.208157i	$-0.0667464\pi$
$409$	35.5682	+	8.42981i	1.75873	+	0.416827i	0.780637	+	0.624984i	$0.214895\pi$
$410$	−1.30709	−	1.10232i	−0.0645525	−	0.0544397i
$411$	−0.866989	−	1.82734i	−0.0427654	−	0.0901359i
$412$	−7.36531	+	4.20374i	−0.362863	+	0.207103i
$413$	14.0665	−	38.6474i	0.692168	−	1.90172i
$414$	20.4671	+	8.56624i	1.00590	+	0.421008i
$415$	0.0348565	+	0.0957674i	0.00171104	+	0.00470103i
$416$	−0.346811	−	0.618297i	−0.0170038	−	0.0303145i
$417$	−11.0826	−	2.21139i	−0.542717	−	0.108292i
$418$	12.1377	+	7.04798i	0.593677	+	0.344728i
$419$	12.0182	−	27.8612i	0.587125	−	1.36111i	−0.322851	−	0.946450i	$-0.604641\pi$
$419$	12.0182	−	27.8612i	0.587125	−	1.36111i	0.909976	−	0.414660i	$-0.136099\pi$
$420$	0.427779	+	1.58567i	0.0208735	+	0.0773729i
$421$	24.6551	+	12.3823i	1.20162	+	0.603475i	0.933036	−	0.359782i	$-0.117149\pi$
$421$	24.6551	+	12.3823i	1.20162	+	0.603475i	0.268581	+	0.963257i	$0.413445\pi$
$422$	19.4449	+	5.87407i	0.946563	+	0.285945i
$423$	−2.91464	+	13.0727i	−0.141715	+	0.635617i
$424$	−8.02494	−	22.5701i	−0.389726	−	1.09610i
$425$	3.94822	+	16.6588i	0.191517	+	0.808072i
$426$	0.997132	+	6.61408i	0.0483112	+	0.320453i
$427$	54.4057	+	3.16877i	2.63288	+	0.153348i
$428$	7.39024	+	3.75759i	0.357221	+	0.181630i
$429$	0.392952	−	0.0838751i	0.0189719	−	0.00404953i
$430$	1.22534	+	0.293627i	0.0590912	+	0.0141599i
$431$	−17.9749	−	31.1334i	−0.865820	−	1.49964i	−0.866231	−	0.499644i	$-0.833464\pi$
$431$	−17.9749	−	31.1334i	−0.865820	−	1.49964i	0.000410722	−	1.00000i	$-0.499869\pi$
$432$	−19.7945	−	6.33846i	−0.952365	−	0.304959i
$433$	−19.2321	+	33.3109i	−0.924234	+	1.60082i	−0.131446	+	0.991323i	$0.541962\pi$
$433$	−19.2321	+	33.3109i	−0.924234	+	1.60082i	−0.792788	+	0.609498i	$0.791371\pi$
$434$	8.03844	−	8.47798i	0.385857	−	0.406956i
$435$	−0.568271	−	1.40307i	−0.0272465	−	0.0672721i
$436$	1.68670	+	31.6681i	0.0807784	+	1.51663i
$437$	−15.4075	+	23.4259i	−0.737039	+	1.12061i
$438$	−4.50994	+	7.38073i	−0.215493	+	0.352665i
$439$	−23.9730	+	22.6174i	−1.14417	+	1.07947i	−0.148276	+	0.988946i	$0.547372\pi$
$439$	−23.9730	+	22.6174i	−1.14417	+	1.07947i	−0.995894	+	0.0905228i	$0.971146\pi$
$440$	0.690525	+	0.127069i	0.0329195	+	0.00605777i
$441$	0.220112	+	16.4965i	0.0104815	+	0.785548i
$442$	0.138982	+	0.592968i	0.00661070	+	0.0282046i
$443$	−3.46495	+	2.27893i	−0.164625	+	0.108275i	−0.629148	−	0.777286i	$-0.716596\pi$
$443$	−3.46495	+	2.27893i	−0.164625	+	0.108275i	0.464523	+	0.885561i	$0.346226\pi$
$444$	−1.81795	+	21.1954i	−0.0862760	+	1.00589i
$445$	1.25349	−	0.146512i	0.0594212	−	0.00694534i
$446$	1.18602	−	0.680826i	0.0561595	−	0.0322380i
$447$	−20.0114	+	3.06773i	−0.946505	+	0.145099i
$448$	3.70166	−	28.0402i	0.174887	−	1.32478i
$449$	−27.1144	−	4.78100i	−1.27961	−	0.225629i	−0.507794	−	0.861479i	$-0.669539\pi$
$449$	−27.1144	−	4.78100i	−1.27961	−	0.225629i	−0.771813	+	0.635849i	$0.780650\pi$
$450$	−5.09756	−	20.5130i	−0.240301	−	0.966993i
$451$	−16.4358	+	2.89807i	−0.773930	+	0.136465i
$452$	−0.158170	+	31.8500i	−0.00743968	+	1.49810i
$453$	−28.3218	−	12.9773i	−1.33067	−	0.609729i
$454$	−5.85288	+	32.7181i	−0.274689	+	1.53553i
$455$	−0.0407735	+	0.0432174i	−0.00191149	+	0.00202606i
$456$	12.4838	−	23.1096i	0.584606	−	1.08220i
$457$	−2.49527	−	5.78468i	−0.116724	−	0.270596i	0.849832	−	0.527054i	$-0.176704\pi$
$457$	−2.49527	−	5.78468i	−0.116724	−	0.270596i	−0.966555	+	0.256458i	$0.917444\pi$
$458$	−22.5502	−	2.69252i	−1.05370	−	0.125813i
$459$	14.8290	+	9.94712i	0.692156	+	0.464292i
$460$	−0.330237	+	1.36317i	−0.0153974	+	0.0635584i
$461$	0.846445	+	0.630155i	0.0394229	+	0.0293493i	0.616690	−	0.787206i	$-0.288473\pi$
$461$	0.846445	+	0.630155i	0.0394229	+	0.0293493i	−0.577267	+	0.816556i	$0.695881\pi$
$462$	14.5569	+	6.71392i	0.677248	+	0.312360i
$463$	20.8675	−	6.24731i	0.969794	−	0.290337i	0.237547	−	0.971376i	$-0.423657\pi$
$463$	20.8675	−	6.24731i	0.969794	−	0.290337i	0.732247	+	0.681039i	$0.238471\pi$
$464$	−0.258917	+	26.0679i	−0.0120199	+	1.21017i
$465$	0.381207	−	0.386327i	0.0176780	−	0.0179155i
$466$	24.3330	−	18.0215i	1.12720	−	0.834830i
$467$	−8.67800	+	7.28171i	−0.401570	+	0.336957i	−0.821100	−	0.570784i	$-0.806639\pi$
$467$	−8.67800	+	7.28171i	−0.401570	+	0.336957i	0.419530	+	0.907741i	$0.362195\pi$
$468$	−0.179528	−	0.730178i	−0.00829868	−	0.0337525i
$469$	26.3341	+	22.0969i	1.21600	+	1.02034i
$470$	−0.845141	−	0.0513298i	−0.0389835	−	0.00236767i
$471$	−1.75792	−	0.0394152i	−0.0810006	−	0.00181615i
$472$	−22.7571	+	23.7640i	−1.04748	+	1.09383i
$473$	9.86514	−	7.34432i	0.453600	−	0.337692i
$474$	−0.986602	−	0.322345i	−0.0453161	−	0.0148058i
$475$	26.6659	−	1.55311i	1.22351	−	0.0712616i
$476$	−9.73483	+	22.2632i	−0.446195	+	1.02043i
$477$	−1.81558	−	25.3424i	−0.0831297	−	1.16035i
$478$	1.26457	+	22.6820i	0.0578403	+	1.03745i
$479$	−8.58955	+	28.6911i	−0.392467	+	1.31093i	0.502415	+	0.864627i	$0.332445\pi$
$479$	−8.58955	+	28.6911i	−0.392467	+	1.31093i	−0.894882	+	0.446304i	$0.852740\pi$
$480$	0.197894	−	1.29894i	0.00903258	−	0.0592881i
$481$	−0.687741	+	0.345396i	−0.0313583	+	0.0157487i
$482$	2.63913	+	15.1877i	0.120209	+	0.691781i
$483$	−15.0102	+	28.2883i	−0.682987	+	1.28716i
$484$	−11.6514	+	9.67845i	−0.529607	+	0.439930i
$485$		−	0.263105i		−	0.0119470i
$486$	−18.4402	−	12.0813i	−0.836467	−	0.548018i
$487$			24.9681i			1.13141i	0.824606	+	0.565707i	$0.191397\pi$
$487$			24.9681i			1.13141i	−0.824606	+	0.565707i	$0.808603\pi$
$488$	−38.8151	−	19.8571i	−1.75708	−	0.898890i
$489$	8.82710	−	16.6356i	0.399175	−	0.752287i
$490$	−1.02754	+	0.178554i	−0.0464196	+	0.00806624i
$491$	−16.7520	+	8.41318i	−0.756008	+	0.379682i	−0.784675	−	0.619907i	$-0.787170\pi$
$491$	−16.7520	+	8.41318i	−0.756008	+	0.379682i	0.0286668	+	0.999589i	$0.490874\pi$
$492$	6.36778	+	30.5759i	0.287082	+	1.37847i
$493$	6.42331	−	21.4554i	0.289291	−	0.966300i
$494$	0.948747	−	0.0528948i	0.0426861	−	0.00237985i
$495$	0.669897	+	0.325316i	0.0301096	+	0.0146219i
$496$	−8.61859	+	3.61660i	−0.386986	+	0.162390i
$497$	−9.63788	+	0.561343i	−0.432318	+	0.0251797i
$498$	0.578132	−	1.76949i	0.0259067	−	0.0792927i
$499$	11.8839	−	8.84726i	0.531998	−	0.396058i	−0.297368	−	0.954763i	$-0.596109\pi$
$499$	11.8839	−	8.84726i	0.531998	−	0.396058i	0.829367	+	0.558705i	$0.188702\pi$
$500$	2.46350	−	1.04817i	0.110171	−	0.0468756i
$501$	−10.4847	−	0.235083i	−0.468423	−	0.0105027i
$502$	−1.85582	+	30.5559i	−0.0828292	+	1.36378i
$503$	30.2136	+	25.3523i	1.34716	+	1.13040i	0.979724	+	0.200352i	$0.0642087\pi$
$503$	30.2136	+	25.3523i	1.34716	+	1.13040i	0.367436	+	0.930049i	$0.380236\pi$
$504$	11.7195	−	27.6153i	0.522030	−	1.23008i
$505$	−0.0695548	+	0.0583634i	−0.00309515	+	0.00259714i
$506$	8.14805	+	11.0017i	0.362225	+	0.489083i
$507$	−15.7960	+	16.0082i	−0.701525	+	0.710948i
$508$	29.5191	−	27.5741i	1.30970	−	1.22340i
$509$	−2.68241	+	0.803062i	−0.118896	+	0.0355951i	−0.345698	−	0.938346i	$-0.612358\pi$
$509$	−2.68241	+	0.803062i	−0.118896	+	0.0355951i	0.226803	+	0.973941i	$0.427173\pi$
$510$	−0.472763	+	1.02503i	−0.0209343	+	0.0453891i
$511$	−10.0139	−	7.45505i	−0.442988	−	0.329792i
$512$	−11.7488	+	19.3382i	−0.519227	+	0.854637i
$513$	19.3012	−	20.0897i	0.852170	−	0.886981i
$514$	3.46235	−	28.9977i	0.152718	−	1.27903i
$515$	−0.225222	−	0.522123i	−0.00992445	−	0.0230075i
$516$	−14.3058	−	18.0294i	−0.629780	−	0.793701i
$517$	−5.67135	+	6.01128i	−0.249426	+	0.264376i
$518$	−30.2246	−	5.40683i	−1.32799	−	0.237563i
$519$	−26.6291	−	12.2018i	−1.16889	−	0.535598i
$520$	0.0437854	−	0.0185016i	0.00192012	−	0.000811347i
$521$	36.2003	−	6.38309i	1.58596	−	0.279648i	0.690012	−	0.723798i	$-0.257605\pi$
$521$	36.2003	−	6.38309i	1.58596	−	0.279648i	0.895953	+	0.444150i	$0.146494\pi$
$522$	−7.64217	+	26.5735i	−0.334489	+	1.16309i
$523$	22.9959	+	4.05480i	1.00554	+	0.177304i	0.652084	−	0.758147i	$-0.273895\pi$
$523$	22.9959	+	4.05480i	1.00554	+	0.177304i	0.353457	+	0.935451i	$0.385006\pi$
$524$	3.80076	−	20.9464i	0.166037	−	0.915046i
$525$	30.1554	−	4.62280i	1.31609	−	0.201756i
$526$	2.09609	+	3.65145i	0.0913940	+	0.159211i
$527$	7.97547	−	0.932199i	0.347417	−	0.0406072i
$528$	−8.49460	−	9.60822i	−0.369680	−	0.418144i
$529$	−3.63351	+	2.38980i	−0.157979	+	0.103904i
$530$	1.56378	−	0.366524i	0.0679262	−	0.0159208i
$531$	−29.9879	+	17.8512i	−1.30136	+	0.774675i
$532$	31.5699	+	20.9892i	1.36873	+	0.909997i
$533$	−0.821842	+	0.775368i	−0.0355979	+	0.0335849i
$534$	−19.6704	−	12.0195i	−0.851223	−	0.520134i
$535$	−0.305471	+	0.464446i	−0.0132066	+	0.0200797i
$536$	−12.1595	−	24.6681i	−0.525211	−	1.06550i
$537$	−10.6569	−	26.3122i	−0.459881	−	1.13545i
$538$	16.5248	+	15.6681i	0.712436	+	0.675501i
$539$	−5.08991	+	8.81598i	−0.219238	+	0.379731i
$540$	0.569901	−	1.27178i	0.0245246	−	0.0547285i
$541$	8.02291	+	13.8961i	0.344932	+	0.597439i	0.985341	−	0.170594i	$-0.0545687\pi$
$541$	8.02291	+	13.8961i	0.344932	+	0.597439i	−0.640410	+	0.768034i	$0.721235\pi$
$542$	−8.28456	+	34.5725i	−0.355852	+	1.48502i
$543$	28.2588	−	6.03180i	1.21270	−	0.258849i
$544$	14.3042	−	13.1635i	0.613287	−	0.564381i
$545$	−2.12279	−	0.123638i	−0.0909303	−	0.00529608i
$546$	1.07315	−	0.161787i	0.0459267	−	0.00692387i
$547$	1.15504	+	4.87350i	0.0493860	+	0.208376i	0.992144	−	0.125102i	$-0.0399259\pi$
$547$	1.15504	+	4.87350i	0.0493860	+	0.208376i	−0.942758	+	0.333478i	$0.891778\pi$
$548$	−2.33082	−	0.147373i	−0.0995678	−	0.00629544i
$549$	−34.0573	−	31.2832i	−1.45353	−	1.33513i
$550$	3.77156	−	12.4850i	0.160820	−	0.532361i
$551$	−31.2258	−	15.6822i	−1.33026	−	0.668083i
$552$	20.1089	−	15.8747i	0.855894	−	0.675671i
$553$	0.593358	−	1.37556i	0.0252321	−	0.0584947i
$554$	−16.0647	+	27.6660i	−0.682524	+	1.17542i
$555$	−1.39882	−	0.279116i	−0.0593764	−	0.0118478i
$556$	−8.43750	+	9.95460i	−0.357830	+	0.422169i
$557$	7.50701	+	20.6253i	0.318082	+	0.873923i	0.990959	+	0.134168i	$0.0428363\pi$
$557$	7.50701	+	20.6253i	0.318082	+	0.873923i	−0.672877	+	0.739755i	$0.734941\pi$
$558$	−9.83352	+	1.25776i	−0.416286	+	0.0532451i
$559$	0.284778	−	0.782420i	0.0120448	−	0.0330929i
$560$	1.84088	+	0.455654i	0.0777915	+	0.0192549i
$561$	4.72287	+	9.95430i	0.199400	+	0.420271i
$562$	20.9744	−	24.8707i	0.884752	−	1.04911i
$563$	7.48955	+	1.77506i	0.315647	+	0.0748097i	0.385386	−	0.922756i	$-0.374068\pi$
$563$	7.48955	+	1.77506i	0.315647	+	0.0748097i	−0.0697388	+	0.997565i	$0.522217\pi$
$564$	11.5708	+	10.2618i	0.487218	+	0.432100i
$565$	−2.12116	−	0.247928i	−0.0892379	−	0.0104304i
$566$	37.2731	−	15.9684i	1.56671	−	0.671202i
$567$	19.7952	−	24.9118i	0.831320	−	1.04620i
$568$	7.23791	+	2.69561i	0.303696	+	0.113105i
$569$	0.632163	−	5.40850i	0.0265016	−	0.226736i	−0.973496	−	0.228702i	$-0.926552\pi$
$569$	0.632163	−	5.40850i	0.0265016	−	0.226736i	0.999998	+	0.00196619i	$0.000625858\pi$
$570$	1.44687	+	1.00410i	0.0606027	+	0.0420573i
$571$	2.37631	−	10.0264i	0.0994456	−	0.419594i	−0.900436	−	0.434989i	$-0.856752\pi$
$571$	2.37631	−	10.0264i	0.0994456	−	0.419594i	0.999881	+	0.0153948i	$0.00490052\pi$
$572$	0.135272	−	0.443806i	0.00565600	−	0.0185564i
$573$	0.381373	−	4.72170i	0.0159321	−	0.197252i
$574$	−44.7862	+	5.12206i	−1.86934	+	0.213791i
$575$	24.4828	+	8.91102i	1.02100	+	0.371615i
$576$	−17.4826	+	16.4426i	−0.728441	+	0.685109i
$577$	−5.71655	+	2.08065i	−0.237983	+	0.0866188i	−0.458259	−	0.888819i	$-0.651527\pi$
$577$	−5.71655	+	2.08065i	−0.237983	+	0.0866188i	0.220275	+	0.975438i	$0.429304\pi$
$578$	6.56848	−	3.27841i	0.273213	−	0.136364i
$579$	0.908635	−	0.307831i	0.0377616	−	0.0127930i
$580$	−1.73512	−	0.211546i	−0.0720469	−	0.00878396i
$581$	2.46709	+	1.06420i	0.102352	+	0.0441504i
$582$	−2.96494	+	3.78223i	−0.122901	+	0.156779i
$583$	7.03592	−	14.0097i	0.291398	−	0.580221i
$584$	4.92925	+	8.68651i	0.203974	+	0.359450i
$585$	0.0499938	−	0.00652067i	0.00206699	−	0.000269597i
$586$	−2.10470	+	4.16497i	−0.0869442	+	0.172054i
$587$	−37.2487	+	8.82810i	−1.53742	+	0.364375i	−0.910100	−	0.414388i	$-0.863996\pi$
$587$	−37.2487	+	8.82810i	−1.53742	+	0.364375i	−0.627318	+	0.778763i	$0.715847\pi$
$588$	16.7834	+	9.01264i	0.692136	+	0.371675i
$589$	0.728440	−	12.5068i	0.0300148	−	0.515335i
$590$	−1.41391	−	1.69355i	−0.0582096	−	0.0697224i
$591$	41.8769	+	13.5671i	1.72258	+	0.558077i
$592$	20.3880	+	13.7014i	0.837942	+	0.563125i
$593$	−5.69341	+	3.28709i	−0.233800	+	0.134985i	−0.612324	−	0.790607i	$-0.709765\pi$
$593$	−5.69341	+	3.28709i	−0.233800	+	0.134985i	0.378524	+	0.925592i	$0.376432\pi$
$594$	−5.96401	−	12.2256i	−0.244706	−	0.501624i
$595$	−1.41096	−	0.814620i	−0.0578438	−	0.0333962i
$596$	−8.10442	+	21.9273i	−0.331970	+	0.898176i
$597$	−0.223839	−	0.174575i	−0.00916113	−	0.00714488i
$598$	0.870162	+	0.319162i	0.0355836	+	0.0130515i
$599$	6.12354	+	4.02752i	0.250201	+	0.164560i	0.668415	−	0.743789i	$-0.266973\pi$
$599$	6.12354	+	4.02752i	0.250201	+	0.164560i	−0.418213	+	0.908349i	$0.637344\pi$
$600$	−23.5702	−	6.33528i	−0.962251	−	0.258637i
$601$	33.1119	+	35.0966i	1.35066	+	1.43162i	0.804518	+	0.593928i	$0.202423\pi$
$601$	33.1119	+	35.0966i	1.35066	+	1.43162i	0.546144	+	0.837691i	$0.316095\pi$
$602$	27.7995	−	18.1853i	1.13302	−	0.741177i
$603$	−5.44821	−	28.6571i	−0.221868	−	1.16701i
$604$	−28.9610	+	21.3379i	−1.17841	+	0.868228i
$605$	−0.558087	−	0.848530i	−0.0226894	−	0.0344976i
$606$	1.65758	−	0.0551793i	0.0673344	−	0.00224151i
$607$	0.123763	+	1.05886i	0.00502340	+	0.0429779i	0.995518	−	0.0945768i	$-0.0301498\pi$
$607$	0.123763	+	1.05886i	0.00502340	+	0.0429779i	−0.990494	+	0.137555i	$0.956076\pi$
$608$	−16.3503	−	25.5446i	−0.663092	−	1.03597i
$609$	−37.1869	−	14.4869i	−1.50689	−	0.587040i
$610$	1.61249	−	2.43846i	0.0652878	−	0.0987304i
$611$	−0.0971565	+	0.551002i	−0.00393053	+	0.0222912i
$612$	18.3472	−	9.40759i	0.741643	−	0.380279i
$613$	−7.12245	−	40.3934i	−0.287673	−	1.63148i	−0.695577	−	0.718451i	$-0.744851\pi$
$613$	−7.12245	−	40.3934i	−0.287673	−	1.63148i	0.407904	−	0.913025i	$-0.366260\pi$
$614$	−32.7428	−	14.2204i	−1.32139	−	0.573888i
$615$	−2.08490	+	0.196428i	−0.0840711	+	0.00792075i
$616$	14.9297	−	10.9428i	0.601533	−	0.440899i
$617$	−27.7249	−	26.1571i	−1.11616	−	1.05305i	−0.998197	−	0.0600280i	$-0.980881\pi$
$617$	−27.7249	−	26.1571i	−1.11616	−	1.05305i	−0.117966	−	0.993018i	$-0.537638\pi$
$618$	−2.64618	+	10.0437i	−0.106445	+	0.404018i
$619$	−0.669918	+	0.288975i	−0.0269263	+	0.0116149i	−0.409500	−	0.912310i	$-0.634297\pi$
$619$	−0.669918	+	0.288975i	−0.0269263	+	0.0116149i	0.382574	+	0.923925i	$0.375038\pi$
$620$	−0.176757	−	0.601259i	−0.00709871	−	0.0241472i
$621$	25.0482	−	10.5362i	1.00515	−	0.422801i
$622$	−11.0086	+	14.7108i	−0.441406	+	0.589848i
$623$	19.8685	−	26.6881i	0.796016	−	1.06923i
$624$	−0.837925	−	0.227453i	−0.0335439	−	0.00910539i
$625$	−7.09281	−	23.6916i	−0.283712	−	0.947665i
$626$	9.67324	−	3.49359i	0.386620	−	0.139632i
$627$	16.5743	−	4.55979i	0.661913	−	0.182100i
$628$	−1.02391	+	1.75330i	−0.0408584	+	0.0699642i
$629$	−13.5649	−	16.1660i	−0.540868	−	0.644582i
$630$	1.75281	+	0.986762i	0.0698335	+	0.0393135i
$631$	19.4819	−	23.2176i	0.775561	−	0.924278i	−0.223163	−	0.974781i	$-0.571638\pi$
$631$	19.4819	−	23.2176i	0.775561	−	0.924278i	0.998724	+	0.0505032i	$0.0160825\pi$
$632$	−0.877855	+	0.815940i	−0.0349192	+	0.0324563i
$633$	21.8184	−	11.9529i	0.867203	−	0.475086i
$634$	0.00823282	−	3.31564i	0.000326967	−	0.131681i
$635$	1.61739	+	2.17254i	0.0641844	+	0.0862146i
$636$	−26.6102	−	12.3534i	−1.05516	−	0.489843i
$637$	0.0400722	+	0.688013i	0.00158772	+	0.0272601i
$638$	−12.4390	+	11.6774i	−0.492466	+	0.462312i
$639$	6.63575	+	4.80387i	0.262506	+	0.190038i
$640$	−1.20104	−	0.927018i	−0.0474754	−	0.0366436i
$641$	−19.4943	−	5.83620i	−0.769977	−	0.230516i	−0.122364	−	0.992485i	$-0.539048\pi$
$641$	−19.4943	−	5.83620i	−0.769977	−	0.230516i	−0.647613	+	0.761969i	$0.724233\pi$
$642$	9.62511	−	3.23421i	0.379873	−	0.127644i
$643$	−3.87867	−	7.72306i	−0.152960	−	0.304568i	0.804082	−	0.594519i	$-0.202657\pi$
$643$	−3.87867	−	7.72306i	−0.152960	−	0.304568i	−0.957042	+	0.289951i	$0.906361\pi$
$644$	20.1661	+	30.9952i	0.794655	+	1.22138i
$645$	1.30802	−	0.818897i	0.0515034	−	0.0322440i
$646$	7.41094	+	24.9799i	0.291580	+	0.982819i
$647$	27.6877			1.08852			0.544258	−	0.838918i	$-0.316811\pi$
$647$	27.6877			1.08852			0.544258	+	0.838918i	$0.316811\pi$
$648$	−22.5242	+	11.8600i	−0.884835	+	0.465904i
$649$	−21.5339			−0.845278
$650$	−0.251136	−	0.846497i	−0.00985036	−	0.0332023i
$651$	−0.511569	−	14.2996i	−0.0200500	−	0.560444i
$652$	−11.8592	−	18.2275i	−0.464440	−	0.713843i
$653$	5.98683	+	11.9208i	0.234283	+	0.466496i	0.979797	−	0.199994i	$-0.0640923\pi$
$653$	5.98683	+	11.9208i	0.234283	+	0.466496i	−0.745514	+	0.666490i	$0.767796\pi$
$654$	29.1226	+	25.6991i	1.13878	+	1.00492i
$655$	1.36744	+	0.409385i	0.0534303	+	0.0159960i
$656$	34.4440	+	10.6857i	1.34481	+	0.417208i
$657$	2.58034	+	10.2744i	0.100668	+	0.400844i
$658$	−16.2746	+	15.2781i	−0.634449	+	0.595601i
$659$	−2.02191	−	34.7148i	−0.0787623	−	1.35230i	−0.773849	−	0.633370i	$-0.781671\pi$
$659$	−2.02191	−	34.7148i	−0.0787623	−	1.35230i	0.695087	−	0.718926i	$-0.255366\pi$
$660$	0.703561	−	0.494428i	0.0273861	−	0.0192456i
$661$	−13.7427	−	18.4597i	−0.534531	−	0.717999i	0.450036	−	0.893011i	$-0.351411\pi$
$661$	−13.7427	−	18.4597i	−0.534531	−	0.717999i	−0.984566	+	0.175011i	$0.944004\pi$
$662$	0.0460613	−	18.5505i	0.00179022	−	0.720984i
$663$	0.637460	+	0.387345i	0.0247569	+	0.0150432i
$664$	−1.46340	−	1.57445i	−0.0567911	−	0.0611005i
$665$	−1.63392	+	1.94724i	−0.0633609	+	0.0755106i
$666$	16.9631	+	19.7757i	0.657307	+	0.766293i
$667$	−21.9082	−	26.1091i	−0.848288	−	1.01095i
$668$	−6.10688	+	10.4572i	−0.236282	+	0.404600i
$669$	0.422690	−	1.62067i	0.0163421	−	0.0626587i
$670$	1.73440	−	0.626396i	0.0670056	−	0.0241998i
$671$	−8.18374	−	27.3356i	−0.315930	−	1.05528i
$672$	−21.3286	−	27.2952i	−0.822768	−	1.05293i
$673$	−0.819702	+	1.10105i	−0.0315972	+	0.0424424i	−0.817641	−	0.575728i	$-0.804719\pi$
$673$	−0.819702	+	1.10105i	−0.0315972	+	0.0424424i	0.786044	+	0.618171i	$0.212126\pi$
$674$	−18.5894	+	24.8408i	−0.716036	+	0.956833i
$675$	−22.3007	−	13.1466i	−0.858354	−	0.506012i
$676$	7.32424	+	24.9143i	0.281702	+	0.958243i
$677$	22.3657	−	9.64762i	0.859584	−	0.370788i	0.0797802	−	0.996812i	$-0.474578\pi$
$677$	22.3657	−	9.64762i	0.859584	−	0.370788i	0.779804	+	0.626024i	$0.215319\pi$
$678$	27.6986	+	27.4675i	1.06376	+	1.05488i
$679$	−5.04540	−	4.76008i	−0.193624	−	0.182675i
$680$	0.770543	+	1.05128i	0.0295490	+	0.0403147i
$681$	23.5707	+	33.1890i	0.903232	+	1.27181i
$682$	−5.61074	−	2.43678i	−0.214846	−	0.0933091i
$683$	5.85079	+	33.1815i	0.223874	+	1.26966i	0.864825	+	0.502073i	$0.167429\pi$
$683$	5.85079	+	33.1815i	0.223874	+	1.26966i	−0.640951	+	0.767582i	$0.721460\pi$
$684$	−9.48398	−	30.7392i	−0.362629	−	1.17534i
$685$	0.0271926	−	0.154217i	0.00103898	−	0.00589232i
$686$	4.13862	−	6.25856i	0.158013	−	0.238953i
$687$	−21.7025	+	17.3967i	−0.828003	+	0.663725i
$688$	−26.2169	+	4.35472i	−0.999510	+	0.166022i
$689$	−0.123216	−	1.05418i	−0.00469415	−	0.0401610i
$690$	0.907938	+	1.45829i	0.0345646	+	0.0555161i
$691$	2.73582	+	4.15961i	0.104075	+	0.158239i	0.883771	−	0.467920i	$-0.154996\pi$
$691$	2.73582	+	4.15961i	0.104075	+	0.158239i	−0.779695	+	0.626159i	$0.784626\pi$
$692$	−27.2301	+	20.0627i	−1.03513	+	0.762669i
$693$	18.3581	−	6.96056i	0.697367	−	0.264410i
$694$	15.0500	−	9.84507i	0.571289	−	0.373714i
$695$	−0.600442	−	0.636431i	−0.0227761	−	0.0241412i
$696$	22.5590	+	22.5942i	0.855098	+	0.856430i
$697$	−25.8854	−	17.0251i	−0.980479	−	0.644871i
$698$	22.9576	+	8.42048i	0.868956	+	0.318720i
$699$	5.12991	−	36.7286i	0.194031	−	1.38920i
$700$	12.2127	−	33.0425i	0.461595	−	1.24889i
$701$	17.0370	+	9.83630i	0.643478	+	0.371512i	0.785953	−	0.618286i	$-0.212173\pi$
$701$	17.0370	+	9.83630i	0.643478	+	0.371512i	−0.142475	+	0.989798i	$0.545506\pi$
$702$	−0.792161	−	0.469645i	−0.0298982	−	0.0177256i
$703$	−28.5141	+	16.4626i	−1.07543	+	0.620899i
$704$	−14.4589	+	3.20010i	−0.544942	+	0.120608i
$705$	−0.770041	+	0.694539i	−0.0290014	+	0.0261579i
$706$	−5.85739	−	7.01587i	−0.220446	−	0.264046i
$707$	−0.139185	+	2.38971i	−0.00523459	+	0.0898745i
$708$	1.24073	+	40.2788i	0.0466295	+	1.51377i
$709$	−10.3493	+	2.45284i	−0.388678	+	0.0921183i	−0.420308	−	0.907381i	$-0.638078\pi$
$709$	−10.3493	+	2.45284i	−0.388678	+	0.0921183i	0.0316306	+	0.999500i	$0.489930\pi$
$710$	−0.233570	+	0.462210i	−0.00876571	+	0.0173464i
$711$	−1.12827	+	0.585616i	−0.0423134	+	0.0219623i
$712$	−23.1505	+	13.1370i	−0.867601	+	0.492329i
$713$	5.48427	−	10.9201i	0.205388	−	0.408960i
$714$	11.1031	+	27.6107i	0.415524	+	1.03330i
$715$	0.0285650	+	0.0123217i	0.00106827	+	0.000460806i
$716$	−32.5391	−	3.96718i	−1.21605	−	0.148260i
$717$	20.9073	+	18.3574i	0.780797	+	0.685571i
$718$	−17.9717	+	8.96990i	−0.670697	+	0.334754i
$719$	23.1617	−	8.43017i	0.863786	−	0.314392i	0.128138	−	0.991756i	$-0.459100\pi$
$719$	23.1617	−	8.43017i	0.863786	−	0.314392i	0.735648	+	0.677364i	$0.236878\pi$
$720$	−0.965358	−	1.28751i	−0.0359768	−	0.0479827i
$721$	−14.0871	−	5.12728i	−0.524631	−	0.190950i
$722$	13.6932	−	1.56605i	0.509608	−	0.0582823i
$723$	15.5373	+	10.7256i	0.577839	+	0.398889i
$724$	9.72794	−	31.9159i	0.361536	−	1.18614i
$725$	−7.48794	+	31.5941i	−0.278095	+	1.17338i
$726$	−1.53942	+	18.4870i	−0.0571331	+	0.686118i
$727$	0.0317376	−	0.271532i	0.00117708	−	0.0100706i	−0.992637	−	0.121127i	$-0.961349\pi$
$727$	0.0317376	−	0.271532i	0.00117708	−	0.0100706i	0.993814	+	0.111056i	$0.0354233\pi$
$728$	0.437371	−	1.17437i	0.0162100	−	0.0435251i
$729$	−26.3809	+	5.74876i	−0.977070	+	0.212917i
$730$	−0.615569	+	0.263719i	−0.0227832	+	0.00976069i
$731$	22.6773	+	2.65060i	0.838751	+	0.0980359i
$732$	−50.6592	+	16.8826i	−1.87242	+	0.623997i
$733$	−7.64486	−	1.81187i	−0.282369	−	0.0669228i	0.0869907	−	0.996209i	$-0.472275\pi$
$733$	−7.64486	−	1.81187i	−0.282369	−	0.0669228i	−0.369360	+	0.929286i	$0.620423\pi$
$734$	10.3490	−	12.2715i	0.381990	−	0.452949i
$735$	−0.725653	+	1.05120i	−0.0267661	+	0.0387740i
$736$	−4.77499	−	29.1953i	−0.176008	−	1.07615i
$737$	6.15607	−	16.9137i	0.226762	−	0.623023i
$738$	32.1847	+	20.6711i	1.18474	+	0.760912i
$739$	−5.24470	−	14.4097i	−0.192929	−	0.530069i	0.805078	−	0.593169i	$-0.202123\pi$
$739$	−5.24470	−	14.4097i	−0.192929	−	0.530069i	−0.998007	+	0.0631003i	$0.979901\pi$
$740$	−1.06496	+	1.25644i	−0.0391487	+	0.0461878i
$741$	0.767857	−	0.874512i	0.0282079	−	0.0321260i
$742$	21.2632	−	36.6187i	0.780597	−	1.34431i
$743$	12.2679	−	28.4402i	0.450066	−	1.04337i	−0.530589	−	0.847629i	$-0.678029\pi$
$743$	12.2679	−	28.4402i	0.450066	−	1.04337i	0.980655	−	0.195742i	$-0.0627115\pi$
$744$	−4.23468	+	10.6352i	−0.155251	+	0.389905i
$745$	−1.40073	−	0.703472i	−0.0513187	−	0.0257732i
$746$	10.0558	−	33.2876i	0.368168	−	1.21874i
$747$	−1.05031	−	2.02357i	−0.0384290	−	0.0740385i
$748$	12.6970	+	0.802802i	0.464248	+	0.0293534i
$749$	3.37981	+	14.2605i	0.123496	+	0.521069i
$750$	1.19782	−	3.05229i	0.0437382	−	0.111454i
$751$	32.9708	+	1.92033i	1.20312	+	0.0700737i	0.647963	−	0.761672i	$-0.275621\pi$
$751$	32.9708	+	1.92033i	1.20312	+	0.0700737i	0.555157	+	0.831746i	$0.312658\pi$
$752$	16.8411	−	5.94091i	0.614132	−	0.216643i
$753$	25.1109	+	27.8407i	0.915093	+	1.01457i
$754$	−0.269166	+	1.12326i	−0.00980245	+	0.0409069i
$755$	−1.20601	−	2.08887i	−0.0438911	−	0.0760216i
$756$	−14.0774	−	33.9375i	−0.511989	−	1.23430i
$757$	19.1215	−	33.1194i	0.694983	−	1.20375i	−0.275203	−	0.961386i	$-0.588745\pi$
$757$	19.1215	−	33.1194i	0.694983	−	1.20375i	0.970186	−	0.242360i	$-0.0779215\pi$
$758$	−35.0981	−	33.2785i	−1.27482	−	1.20873i
$759$	16.6061	+	2.31938i	0.602762	+	0.0841882i
$760$	1.82404	−	0.899117i	0.0661650	−	0.0326144i
$761$	5.38059	−	8.18079i	0.195046	−	0.296554i	−0.724702	−	0.689063i	$-0.758022\pi$
$761$	5.38059	−	8.18079i	0.195046	−	0.296554i	0.919748	+	0.392509i	$0.128393\pi$
$762$	1.23178	−	49.4575i	0.0446228	−	1.79166i
$763$	−40.7763	+	38.4705i	−1.47620	+	1.39272i
$764$	−4.55506	−	3.02842i	−0.164796	−	0.109564i
$765$	0.490131	+	1.29269i	0.0177207	+	0.0467375i
$766$	−13.6343	+	3.19565i	−0.492627	+	0.115464i
$767$	−1.21802	+	0.801104i	−0.0439802	+	0.0289262i
$768$	6.81883	+	26.8608i	0.246053	+	0.969256i
$769$	−14.5198	+	1.69712i	−0.523598	+	0.0611999i	−0.373787	−	0.927515i	$-0.621941\pi$
$769$	−14.5198	+	1.69712i	−0.523598	+	0.0611999i	−0.149812	+	0.988715i	$0.547867\pi$
$770$	0.617904	+	1.07640i	0.0222677	+	0.0387909i
$771$	−22.3707	−	27.9076i	−0.805660	−	1.00507i
$772$	0.197779	−	1.08998i	0.00711821	−	0.0392292i
$773$	−28.7715	−	5.07319i	−1.03484	−	0.182470i	−0.369670	−	0.929163i	$-0.620529\pi$
$773$	−28.7715	−	5.07319i	−1.03484	−	0.182470i	−0.665169	+	0.746693i	$0.731641\pi$
$774$	−28.0315	−	2.96824i	−1.00757	−	0.106691i
$775$	−11.4644	+	2.02149i	−0.411815	+	0.0726141i
$776$	2.15995	+	5.11170i	0.0775378	+	0.183499i
$777$	−30.6597	+	21.7744i	−1.09991	+	0.781153i
$778$	10.3024	+	1.84298i	0.369358	+	0.0660739i
$779$	−33.1720	+	35.1602i	−1.18851	+	1.25975i
$780$	0.0214017	−	0.0541402i	0.000766305	−	0.00193853i
$781$	2.00211	+	4.64140i	0.0716410	+	0.166082i
$782$	−3.01319	+	25.2359i	−0.107751	+	0.902433i
$783$	16.6656	+	29.4803i	0.595580	+	1.05354i
$784$	18.4976	−	11.9046i	0.660629	−	0.425164i
$785$	−0.109200	−	0.0812965i	−0.00389752	−	0.00290160i
$786$	−15.0441	−	21.2948i	−0.536605	−	0.759561i
$787$	−4.09388	+	1.22563i	−0.145931	+	0.0436889i	−0.358936	−	0.933362i	$-0.616860\pi$
$787$	−4.09388	+	1.22563i	−0.145931	+	0.0436889i	0.213005	+	0.977051i	$0.431675\pi$
$788$	37.1449	−	34.6974i	1.32323	−	1.23604i
$789$	4.98964	+	1.30136i	0.177636	+	0.0463295i
$790$	−0.0478276	−	0.0645777i	−0.00170163	−	0.00229757i
$791$	−43.1303	+	36.1906i	−1.53354	+	1.28679i
$792$	−15.6857	−	0.820866i	−0.557366	−	0.0291682i
$793$	−1.47984	−	1.24173i	−0.0525505	−	0.0440951i
$794$	−1.22038	+	20.0934i	−0.0433096	+	0.713090i
$795$	1.02151	−	1.68111i	0.0362291	−	0.0596229i
$796$	−0.301615	+	0.128331i	−0.0106905	+	0.00454858i
$797$	−12.4725	+	9.28543i	−0.441799	+	0.328907i	−0.794967	−	0.606653i	$-0.792512\pi$
$797$	−12.4725	+	9.28543i	−0.441799	+	0.328907i	0.353168	+	0.935560i	$0.385104\pi$
$798$	45.4317	−	9.57945i	1.60827	−	0.339109i
$799$	−15.3162	+	0.892065i	−0.541847	+	0.0315590i
$800$	−19.5930	+	20.2576i	−0.692718	+	0.716213i
$801$	−27.3825	+	6.87688i	−0.967512	+	0.242982i
$802$	−41.4573	+	2.31134i	−1.46391	+	0.0816163i
$803$	−1.87470	+	6.26195i	−0.0661569	+	0.220979i
$804$	−31.9915	−	10.5403i	−1.12825	−	0.371728i
$805$	−2.21568	+	1.11276i	−0.0780926	+	0.0392196i
$806$	−0.408013	+	0.0708996i	−0.0143717	+	0.00249733i
$807$	27.8720	−	0.997123i	0.981139	−	0.0351004i
$808$	0.872203	−	1.70491i	0.0306840	−	0.0599786i
$809$		−	14.1486i		−	0.497440i	−0.968575	−	0.248720i	$-0.919990\pi$
$809$		−	14.1486i		−	0.497440i	0.968575	−	0.248720i	$-0.0800098\pi$
$810$	−0.622415	−	1.58931i	−0.0218694	−	0.0558426i
$811$			7.96204i			0.279585i	0.990181	+	0.139793i	$0.0446436\pi$
$811$			7.96204i			0.279585i	−0.990181	+	0.139793i	$0.955356\pi$
$812$	−35.4484	+	29.4460i	−1.24399	+	1.03335i
$813$	23.1048	+	36.9054i	0.810322	+	1.29433i
$814$	2.75232	+	15.8390i	0.0964686	+	0.555158i
$815$	1.30299	−	0.654384i	0.0456416	−	0.0229221i
$816$	0.770058	−	23.7958i	0.0269574	−	0.833019i
$817$	10.2165	−	34.1254i	0.357430	−	1.19390i
$818$	−2.87761	−	51.6143i	−0.100613	−	1.80465i
$819$	0.779443	−	1.07667i	0.0272359	−	0.0376219i
$820$	−0.968772	+	2.21555i	−0.0338310	+	0.0773703i
$821$	11.1936	−	0.651955i	0.390660	−	0.0227534i	0.138309	−	0.990389i	$-0.455833\pi$
$821$	11.1936	−	0.651955i	0.390660	−	0.0227534i	0.252351	+	0.967636i	$0.418796\pi$
$822$	−2.12878	+	1.91049i	−0.0742497	+	0.0666360i
$823$	−32.5864	+	24.2597i	−1.13589	+	0.845639i	−0.989635	−	0.143608i	$-0.954130\pi$
$823$	−32.5864	+	24.2597i	−1.13589	+	0.845639i	−0.146256	+	0.989247i	$0.546722\pi$
$824$	8.66204	+	8.29503i	0.301756	+	0.288971i
$825$	−7.67459	−	14.0089i	−0.267195	−	0.487727i
$826$	−58.0564	−	3.52607i	−2.02004	−	0.122688i
$827$	33.6537	+	28.2388i	1.17025	+	0.981961i	0.999994	−	0.00343850i	$-0.00109451\pi$
$827$	33.6537	+	28.2388i	1.17025	+	0.981961i	0.170261	+	0.985399i	$0.445539\pi$
$828$	3.38156	−	31.1950i	0.117517	−	1.08410i
$829$	16.2280	−	13.6169i	0.563623	−	0.472936i	−0.315900	−	0.948792i	$-0.602306\pi$
$829$	16.2280	−	13.6169i	0.563623	−	0.472936i	0.879523	+	0.475857i	$0.157862\pi$
$830$	0.115821	−	0.0857796i	0.00402022	−	0.00297745i
$831$	10.3933	+	37.7784i	0.360539	+	1.31052i
$832$	−0.698790	+	0.718910i	−0.0242262	+	0.0249237i
$833$	−18.1041	+	5.42001i	−0.627269	+	0.187792i
$834$	1.45960	+	15.9153i	0.0505418	+	0.551103i
$835$	−0.651301	−	0.484875i	−0.0225392	−	0.0167798i
$836$	4.67344	−	19.2914i	0.161634	−	0.667206i
$837$	−7.33859	+	9.67291i	−0.253659	+	0.334345i
$838$	−42.6085	−	5.08750i	−1.47189	−	0.175745i
$839$	−6.11041	−	14.1655i	−0.210955	−	0.489048i	0.779581	−	0.626301i	$-0.215432\pi$
$839$	−6.11041	−	14.1655i	−0.210955	−	0.489048i	−0.990536	+	0.137253i	$0.956173\pi$
$840$	1.97779	−	1.21780i	0.0682404	−	0.0420181i
$841$	9.24731	−	9.80158i	0.318873	−	0.337985i
$842$	6.87077	−	38.4081i	0.236782	−	1.32363i
$843$	−3.73754	−	39.6705i	−0.128728	−	1.36632i
$844$	0.142657	−	28.7263i	0.00491045	−	0.988799i
$845$	−1.71477	+	0.302360i	−0.0589897	+	0.0104015i
$846$	18.8964	−	1.30662i	0.649672	−	0.0449226i
$847$	−26.3686	−	4.64949i	−0.906035	−	0.159758i
$848$	−27.3727	+	19.9587i	−0.939981	+	0.685386i
$849$	18.0276	−	46.2755i	0.618705	−	1.58817i
$850$	20.9980	−	12.0538i	0.720226	−	0.413442i
$851$	−31.8982	+	3.72837i	−1.09346	+	0.127807i
$852$	8.56631	−	4.01233i	0.293477	−	0.137460i
$853$	−36.1376	+	23.7680i	−1.23733	+	0.813802i	−0.987975	−	0.154611i	$-0.950588\pi$
$853$	−36.1376	+	23.7680i	−1.23733	+	0.813802i	−0.249351	+	0.968413i	$0.580217\pi$
$854$	−17.5877	−	75.0382i	−0.601839	−	2.56775i
$855$	2.11901	−	0.402860i	0.0724685	−	0.0137775i
$856$	2.12194	−	11.5312i	0.0725264	−	0.394127i
$857$	−38.1668	+	36.0085i	−1.30375	+	1.23003i	−0.347434	+	0.937704i	$0.612947\pi$
$857$	−38.1668	+	36.0085i	−1.30375	+	1.23003i	−0.956319	+	0.292324i	$0.905571\pi$
$858$	−0.271778	−	0.499029i	−0.00927834	−	0.0170366i
$859$	9.70608	−	14.7574i	0.331167	−	0.503515i	−0.631071	−	0.775725i	$-0.717384\pi$
$859$	9.70608	−	14.7574i	0.331167	−	0.503515i	0.962238	+	0.272210i	$0.0877546\pi$
$860$	−0.0947759	−	1.77943i	−0.00323183	−	0.0606781i
$861$	−33.9531	+	43.5345i	−1.15712	+	1.48365i
$862$	−34.9807	+	36.8934i	−1.19145	+	1.25659i
$863$	−3.30363	+	5.72205i	−0.112457	+	0.194781i	−0.916760	−	0.399438i	$-0.869205\pi$
$863$	−3.30363	+	5.72205i	−0.112457	+	0.194781i	0.804303	+	0.594219i	$0.202539\pi$
$864$	−0.631646	+	29.3871i	−0.0214890	+	0.999769i
$865$	−1.13393	−	1.96403i	−0.0385548	−	0.0667789i
$866$	52.8989	+	12.6761i	1.79758	+	0.430751i
$867$	2.77109	−	8.55338i	0.0941113	−	0.290488i
$868$	−14.7278	−	7.48841i	−0.499895	−	0.254173i
$869$	−0.783044	−	0.0456071i	−0.0265629	−	0.00154712i
$870$	−1.67371	+	1.33483i	−0.0567442	+	0.0452550i
$871$	−0.281018	−	1.18571i	−0.00952192	−	0.0401761i
$872$	42.2573	−	15.0249i	1.43101	−	0.508807i
$873$	0.761253	+	5.83650i	0.0257645	+	0.197536i
$874$	37.9584	+	11.4668i	1.28396	+	0.387870i
$875$	4.22917	+	2.12397i	0.142972	+	0.0718033i
$876$	11.8209	+	3.14580i	0.399391	+	0.106287i
$877$	−6.61906	+	15.3447i	−0.223510	+	0.518154i	−0.992663	−	0.120910i	$-0.961419\pi$
$877$	−6.61906	+	15.3447i	−0.223510	+	0.518154i	0.769154	+	0.639064i	$0.220678\pi$
$878$	40.3076	+	23.4052i	1.36031	+	0.789888i
$879$	1.83388	+	5.41313i	0.0618553	+	0.182580i
$880$	−0.105473	−	0.987329i	−0.00355550	−	0.0332828i
$881$	9.35072	+	25.6909i	0.315034	+	0.865548i	0.991621	+	0.129185i	$0.0412361\pi$
$881$	9.35072	+	25.6909i	0.315034	+	0.865548i	−0.676587	+	0.736363i	$0.736542\pi$
$882$	22.2775	−	6.93391i	0.750122	−	0.233477i
$883$	−13.4022	+	36.8223i	−0.451021	+	1.23917i	0.480985	+	0.876729i	$0.340279\pi$
$883$	−13.4022	+	36.8223i	−0.451021	+	1.23917i	−0.932006	+	0.362442i	$0.881943\pi$
$884$	0.748046	−	0.426946i	0.0251595	−	0.0143597i
$885$	−2.69324	−	0.217534i	−0.0905323	−	0.00731232i
$886$	4.48351	+	3.78113i	0.150627	+	0.127029i
$887$	3.25305	+	0.770986i	0.109227	+	0.0258872i	0.284866	−	0.958567i	$-0.408051\pi$
$887$	3.25305	+	0.770986i	0.109227	+	0.0258872i	−0.175639	+	0.984455i	$0.556199\pi$
$888$	29.4681	−	6.06077i	0.988884	−	0.203386i
$889$	70.9232	+	8.28973i	2.37869	+	0.278029i
$890$	−0.702841	−	1.64056i	−0.0235593	−	0.0549916i
$891$	−15.8017	−	5.27831i	−0.529376	−	0.176830i
$892$	−1.40013	−	1.33415i	−0.0468797	−	0.0446708i
$893$	−2.77889	+	23.7749i	−0.0929919	+	0.795596i
$894$	12.2085	+	25.8975i	0.408314	+	0.866143i
$895$	0.506879	−	2.13869i	0.0169431	−	0.0714886i
$896$	−39.5060	+	6.26006i	−1.31980	+	0.209134i
$897$	1.02557	−	0.486588i	0.0342429	−	0.0162467i
$898$	4.42428	+	38.6849i	0.147640	+	1.29093i
$899$	14.3104	+	5.20854i	0.477277	+	0.173715i
$900$	−25.7612	+	15.1624i	−0.858707	+	0.505412i
$901$	27.3483	−	9.95397i	0.911104	−	0.331615i
$902$	10.5403	+	21.1180i	0.350953	+	0.703152i
$903$	7.96125	−	39.8986i	0.264934	−	1.32774i
$904$	43.2460	−	12.5968i	1.43834	−	0.418962i
$905$	2.05422	+	0.886105i	0.0682846	+	0.0294551i
$906$	−6.20272	+	43.6187i	−0.206072	+	1.44914i
$907$	2.19186	−	4.36435i	0.0727794	−	0.144916i	−0.854301	−	0.519779i	$-0.826014\pi$
$907$	2.19186	−	4.36435i	0.0727794	−	0.144916i	0.927080	+	0.374864i	$0.122310\pi$
$908$	46.7135	−	5.22501i	1.55024	−	0.173398i
$909$	1.37408	−	1.49593i	0.0455753	−	0.0496169i
$910$	0.0749950	+	0.0378974i	0.00248606	+	0.00125629i
$911$	55.3929	−	13.1284i	1.83525	−	0.434962i	0.840907	−	0.541180i	$-0.182022\pi$
$911$	55.3929	−	13.1284i	1.83525	−	0.434962i	0.994343	+	0.106218i	$0.0338741\pi$
$912$	−36.3535	−	7.63007i	−1.20378	−	0.252657i
$913$	0.0817972	−	1.40440i	0.00270709	−	0.0464790i
$914$	−6.83921	+	5.70990i	−0.226221	+	0.188867i
$915$	−0.747397	−	3.50153i	−0.0247082	−	0.115757i
$916$	5.41998	+	31.6568i	0.179081	+	1.04597i
$917$	32.5902	−	18.8159i	1.07622	−	0.621357i
$918$	7.52162	−	24.1063i	0.248250	−	0.795625i
$919$	40.8665	+	23.5943i	1.34806	+	0.778304i	0.987975	−	0.154614i	$-0.0494135\pi$
$919$	40.8665	+	23.5943i	1.34806	+	0.778304i	0.360087	+	0.932919i	$0.382747\pi$
$920$	1.98103	−	0.100581i	0.0653127	−	0.00331607i
$921$	−40.5227	+	16.4125i	−1.33527	+	0.540810i
$922$	0.513897	−	1.40109i	0.0169243	−	0.0461423i
$923$	0.285915	+	0.188049i	0.00941100	+	0.00618971i
$924$	3.24745	−	22.4369i	0.106833	−	0.738119i
$925$	20.9954	+	22.2539i	0.690326	+	0.731703i
$926$	−16.8638	−	25.7793i	−0.554178	−	0.847162i
$927$	6.50680	+	10.9307i	0.213711	+	0.359011i
$928$	35.4472	−	10.1344i	1.16361	−	0.332679i
$929$	−12.3681	−	18.8048i	−0.405784	−	0.616965i	0.573560	−	0.819163i	$-0.305562\pi$
$929$	−12.3681	−	18.8048i	−0.405784	−	0.616965i	−0.979345	+	0.202198i	$0.935191\pi$
$930$	−0.677119	−	0.361447i	−0.0222036	−	0.0118523i
$931$	3.42295	+	29.2852i	0.112183	+	0.959785i
$932$	−34.2212	−	25.7419i	−1.12095	−	0.843203i
$933$	3.40990	+	22.2434i	0.111635	+	0.728215i
$934$	13.3632	+	8.83671i	0.437257	+	0.289146i
$935$	−0.148130	+	0.840086i	−0.00484437	+	0.0274738i
$936$	−0.917766	+	0.537109i	−0.0299981	+	0.0175559i
$937$	0.313169	+	1.77607i	0.0102308	+	0.0580216i	0.989496	−	0.144562i	$-0.0461773\pi$
$937$	0.313169	+	1.77607i	0.0102308	+	0.0580216i	−0.979265	+	0.202584i	$0.935066\pi$
$938$	19.3666	−	44.5921i	0.632342	−	1.45598i
$939$	5.24712	−	11.4513i	0.171233	−	0.373700i
$940$	0.270353	+	1.16649i	0.00881794	+	0.0380468i
$941$	8.39577	+	7.92100i	0.273694	+	0.258217i	0.810834	−	0.585276i	$-0.199014\pi$
$941$	8.39577	+	7.92100i	0.273694	+	0.258217i	−0.537140	+	0.843493i	$0.680495\pi$
$942$	0.653658	+	2.39925i	0.0212973	+	0.0781717i
$943$	−43.2935	+	18.6750i	−1.40983	+	0.608142i
$944$	41.3730	+	21.2955i	1.34658	+	0.693109i
$945$	2.36636	−	0.685105i	0.0769778	−	0.0222865i
$946$	−13.9256	−	10.4211i	−0.452760	−	0.338818i
$947$	−0.967668	+	1.29980i	−0.0314450	+	0.0422379i	−0.817568	−	0.575833i	$-0.804678\pi$
$947$	−0.967668	+	1.29980i	−0.0314450	+	0.0422379i	0.786123	+	0.618071i	$0.212085\pi$
$948$	−0.0401902	+	1.46730i	−0.00130532	+	0.0476556i
$949$	0.126918	+	0.423937i	0.00411995	+	0.0137616i
$950$	−12.8317	−	35.5290i	−0.416315	−	1.15271i
$951$	−2.89053	−	2.85222i	−0.0937318	−	0.0924895i
$952$	34.1003	+	4.24347i	1.10520	+	0.137532i
$953$	18.6086	+	22.1769i	0.602792	+	0.718380i	0.978010	−	0.208557i	$-0.0668766\pi$
$953$	18.6086	+	22.1769i	0.602792	+	0.718380i	−0.375218	+	0.926937i	$0.622432\pi$
$954$	−33.6290	+	12.6552i	−1.08878	+	0.409727i
$955$	0.235750	−	0.280956i	0.00762870	−	0.00909153i
$956$	30.2437	−	10.8380i	0.978152	−	0.350527i
$957$	−0.468398	+	20.8906i	−0.0151412	+	0.675296i
$958$	42.3546	+	0.105167i	1.36841	+	0.00339780i
$959$	−2.46535	−	3.31154i	−0.0796103	−	0.106935i
$960$	−1.84071	+	0.254173i	−0.0594085	+	0.00820341i
$961$	−1.48502	−	25.4968i	−0.0479038	−	0.822477i
$962$	0.744924	+	0.793511i	0.0240173	+	0.0255838i
$963$	5.43250	−	11.1867i	0.175060	−	0.360486i
$964$	19.5300	−	9.68718i	0.629019	−	0.312003i
$965$	0.0711571	+	0.0213030i	0.00229063	+	0.000685769i
$966$	44.3910	+	8.97233i	1.42826	+	0.288680i
$967$	−6.82810	−	13.5959i	−0.219577	−	0.437213i	0.756693	−	0.653770i	$-0.226814\pi$
$967$	−6.82810	−	13.5959i	−0.219577	−	0.437213i	−0.976270	+	0.216557i	$0.930517\pi$
$968$	17.8087	+	11.9039i	0.572393	+	0.382607i
$969$	28.1894	+	14.9577i	0.905573	+	0.480511i
$970$	−0.356719	+	0.105830i	−0.0114536	+	0.00339801i
$971$	17.0759			0.547991			0.273995	−	0.961731i	$-0.411655\pi$
$971$	17.0759			0.547991			0.273995	+	0.961731i	$0.411655\pi$
$972$	−8.96253	+	29.8609i	−0.287473	+	0.957789i
$973$	−23.0676			−0.739513
$974$	33.8519	−	10.0431i	1.08469	−	0.321801i
$975$	−0.955258	−	0.506874i	−0.0305927	−	0.0162330i
$976$	−11.3095	+	60.6130i	−0.362010	+	1.94017i
$977$	2.58414	+	5.14544i	0.0826738	+	0.164617i	0.931171	−	0.364583i	$-0.118788\pi$
$977$	2.58414	+	5.14544i	0.0826738	+	0.164617i	−0.848497	+	0.529200i	$0.822492\pi$
$978$	−26.1052	−	5.27639i	−0.834752	−	0.168720i
$979$	−16.6888	−	4.99629i	−0.533375	−	0.159682i
$980$	0.655398	+	1.32133i	0.0209359	+	0.0422082i
$981$	47.4479	−	3.39926i	1.51489	−	0.108530i
$982$	18.1449	+	19.3284i	0.579027	+	0.616794i
$983$	−0.881403	−	15.1331i	−0.0281124	−	0.482671i	−0.982754	−	0.184915i	$-0.940799\pi$
$983$	−0.881403	−	15.1331i	−0.0281124	−	0.482671i	0.954642	−	0.297756i	$-0.0962381\pi$
$984$	38.8935	−	20.9322i	1.23988	−	0.667293i
$985$	2.03522	+	2.73378i	0.0648476	+	0.0871054i
$986$	−31.6730	−	0.0786447i	−1.00867	−	0.00250456i
$987$	−0.612827	+	27.3321i	−0.0195065	+	0.869991i
$988$	−0.453335	−	1.26504i	−0.0144225	−	0.0402462i
$989$	22.3341	−	26.6168i	0.710185	−	0.846365i
$990$	0.171609	−	1.03910i	0.00545410	−	0.0330249i
$991$	−15.4080	−	18.3626i	−0.489452	−	0.583307i	0.463626	−	0.886031i	$-0.346548\pi$
$991$	−15.4080	−	18.3626i	−0.489452	−	0.583307i	−0.953078	+	0.302725i	$0.902104\pi$
$992$	8.37011	+	10.2304i	0.265751	+	0.324816i
$993$	−16.1720	−	15.9577i	−0.513204	−	0.506402i
$994$	4.63777	+	12.8413i	0.147101	+	0.407301i
$995$	−0.00630338	−	0.0210547i	−0.000199830	−	0.000667480i
$996$	−2.63163	−	0.0720819i	−0.0833863	−	0.00228400i
$997$	−27.6647	+	37.1601i	−0.876148	+	1.17687i	0.107036	+	0.994255i	$0.465864\pi$
$997$	−27.6647	+	37.1601i	−0.876148	+	1.17687i	−0.983184	+	0.182616i	$0.941543\pi$
$998$	−16.7753	−	12.5536i	−0.531013	−	0.397378i
$999$	31.8377	+	2.14442i	1.00730	+	0.0678465i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.p.a.239.22	✓	936
3.2	odd	2		972.2.p.a.179.31		936
4.3	odd	2	inner	324.2.p.a.239.36	yes	936
12.11	even	2		972.2.p.a.179.17		936
81.20	odd	54	inner	324.2.p.a.263.36	yes	936
81.61	even	27		972.2.p.a.467.17		936
324.223	odd	54		972.2.p.a.467.31		936
324.263	even	54	inner	324.2.p.a.263.22	yes	936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.239.22	✓	936	1.1	even	1	trivial
324.2.p.a.239.36	yes	936	4.3	odd	2	inner
324.2.p.a.263.22	yes	936	324.263	even	54	inner
324.2.p.a.263.36	yes	936	81.20	odd	54	inner
972.2.p.a.179.17		936	12.11	even	2
972.2.p.a.179.31		936	3.2	odd	2
972.2.p.a.467.17		936	81.61	even	27
972.2.p.a.467.31		936	324.223	odd	54

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.p (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.402236 - 1.35580i) q^{2} +(-1.53000 - 0.811843i) q^{3} +(-1.67641 + 1.09071i) q^{4} +(-0.0601848 - 0.119838i) q^{5} +(-0.485279 + 2.40094i) q^{6} +(-3.38691 - 1.01398i) q^{7} +(2.15310 + 1.83417i) q^{8} +(1.68182 + 2.48425i) q^{9} +O(q^{10})\)	\(q+(-0.402236 - 1.35580i) q^{2} +(-1.53000 - 0.811843i) q^{3} +(-1.67641 + 1.09071i) q^{4} +(-0.0601848 - 0.119838i) q^{5} +(-0.485279 + 2.40094i) q^{6} +(-3.38691 - 1.01398i) q^{7} +(2.15310 + 1.83417i) q^{8} +(1.68182 + 2.48425i) q^{9} +(-0.138268 + 0.129802i) q^{10} +(0.107632 + 1.84797i) q^{11} +(3.45040 - 0.307800i) q^{12} +(0.0748364 + 0.100523i) q^{13} +(-0.0124147 + 4.99985i) q^{14} +(-0.00520656 + 0.232213i) q^{15} +(1.62072 - 3.65695i) q^{16} +(-2.20889 + 2.63245i) q^{17} +(2.69166 - 3.27947i) q^{18} +(3.44630 + 4.10715i) q^{19} +(0.231603 + 0.135254i) q^{20} +(4.35880 + 4.30103i) q^{21} +(2.46220 - 0.889249i) q^{22} +(1.49987 + 5.00992i) q^{23} +(-1.80519 - 4.55426i) q^{24} +(2.97505 - 3.99619i) q^{25} +(0.106187 - 0.141897i) q^{26} +(-0.556373 - 5.16628i) q^{27} +(6.78381 - 1.99429i) q^{28} +(-5.98430 + 2.58137i) q^{29} +(0.316930 - 0.0863453i) q^{30} +(-1.69963 - 1.60352i) q^{31} +(-5.61002 - 0.726424i) q^{32} +(1.33559 - 2.91478i) q^{33} +(4.45759 + 1.93596i) q^{34} +(0.0823282 + 0.466906i) q^{35} +(-5.52901 - 2.33025i) q^{36} +(-1.06638 + 6.04776i) q^{37} +(4.18226 - 6.32456i) q^{38} +(-0.0328912 - 0.214555i) q^{39} +(0.0902188 - 0.368412i) q^{40} +(1.04668 + 8.95491i) q^{41} +(4.07809 - 7.63971i) q^{42} +(-3.65095 - 5.55100i) q^{43} +(-2.19603 - 2.98057i) q^{44} +(0.196487 - 0.351060i) q^{45} +(6.18918 - 4.04871i) q^{46} +(3.06377 + 3.24740i) q^{47} +(-5.44858 + 4.27937i) q^{48} +(4.59462 + 3.02193i) q^{49} +(-6.61473 - 2.42618i) q^{50} +(5.51675 - 2.23439i) q^{51} +(-0.235097 - 0.0868930i) q^{52} +(-7.33447 - 4.23456i) q^{53} +(-6.78067 + 2.83240i) q^{54} +(0.214979 - 0.124118i) q^{55} +(-5.43255 - 8.39535i) q^{56} +(-1.93850 - 9.08181i) q^{57} +(5.90694 + 7.07522i) q^{58} +(-0.676398 + 11.6133i) q^{59} +(-0.244548 - 0.394964i) q^{60} +(-14.9993 + 3.55489i) q^{61} +(-1.49040 + 2.94935i) q^{62} +(-3.17722 - 10.1192i) q^{63} +(1.27166 + 7.89828i) q^{64} +(0.00754241 - 0.0150182i) q^{65} +(-4.48910 - 0.638364i) q^{66} +(-8.92825 - 3.85127i) q^{67} +(0.831779 - 6.82233i) q^{68} +(1.77246 - 8.88286i) q^{69} +(0.599918 - 0.299427i) q^{70} +(2.56602 - 0.933954i) q^{71} +(-0.935398 + 8.43357i) q^{72} +(3.31821 + 1.20773i) q^{73} +(8.62851 - 0.986817i) q^{74} +(-7.79612 + 3.69891i) q^{75} +(-10.2571 - 3.12637i) q^{76} +(1.50926 - 6.36806i) q^{77} +(-0.277665 + 0.130896i) q^{78} +(-0.0491922 + 0.420866i) q^{79} +(-0.535784 + 0.0258693i) q^{80} +(-3.34296 + 8.35611i) q^{81} +(11.7201 - 5.02108i) q^{82} +(-0.754832 - 0.0882272i) q^{83} +(-11.9983 - 2.45613i) q^{84} +(0.448409 + 0.106275i) q^{85} +(-6.05753 + 7.18279i) q^{86} +(11.2517 + 0.908801i) q^{87} +(-3.15775 + 4.17628i) q^{88} +(-3.21873 + 8.84339i) q^{89} +(-0.555002 - 0.125189i) q^{90} +(-0.151537 - 0.416344i) q^{91} +(-7.97876 - 6.76278i) q^{92} +(1.29863 + 3.83322i) q^{93} +(3.17049 - 5.46009i) q^{94} +(0.284776 - 0.660186i) q^{95} +(7.99361 + 5.66589i) q^{96} +(1.75329 + 0.880535i) q^{97} +(2.24902 - 7.44493i) q^{98} +(-4.40980 + 3.37534i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Introduction

L-functions

Modular forms

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