LMFDB - Embedded newform 380.2.bj.a.23.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(23,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 27, 4]))

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

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

chi := DirichletCharacter("380.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bj (of order $36$, degree $12$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$56$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			23.10
Character	$\chi$	$=$	380.23
Dual form			380.2.bj.a.347.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21069 - 0.730902i) q^{2} +(-2.10842 - 1.47633i) q^{3} +(0.931564 + 1.76980i) q^{4} +(2.23455 + 0.0823462i) q^{5} +(1.47360 + 3.32843i) q^{6} +(-1.24717 + 0.334178i) q^{7} +(0.165710 - 2.82357i) q^{8} +(1.23982 + 3.40636i) q^{9} +O(q^{10})$	\(q+(-1.21069 - 0.730902i) q^{2} +(-2.10842 - 1.47633i) q^{3} +(0.931564 + 1.76980i) q^{4} +(2.23455 + 0.0823462i) q^{5} +(1.47360 + 3.32843i) q^{6} +(-1.24717 + 0.334178i) q^{7} +(0.165710 - 2.82357i) q^{8} +(1.23982 + 3.40636i) q^{9} +(-2.64517 - 1.73293i) q^{10} +(-3.52529 + 2.03532i) q^{11} +(0.648681 - 5.10677i) q^{12} +(-0.628513 + 0.440089i) q^{13} +(1.75419 + 0.506971i) q^{14} +(-4.58980 - 3.47256i) q^{15} +(-2.26438 + 3.29736i) q^{16} +(-7.15010 + 3.33415i) q^{17} +(0.988681 - 5.03025i) q^{18} +(1.09837 + 4.21824i) q^{19} +(1.93589 + 4.03142i) q^{20} +(3.12291 + 1.13665i) q^{21} +(5.75567 + 0.112482i) q^{22} +(6.48724 - 0.567560i) q^{23} +(-4.51791 + 5.70862i) q^{24} +(4.98644 + 0.368014i) q^{25} +(1.08260 - 0.0734326i) q^{26} +(0.416344 - 1.55382i) q^{27} +(-1.75325 - 1.89593i) q^{28} +(-1.82647 - 5.01817i) q^{29} +(3.01875 + 7.55890i) q^{30} +(4.15451 + 2.39861i) q^{31} +(5.15152 - 2.33706i) q^{32} +(10.4376 + 0.913171i) q^{33} +(11.0935 + 1.18939i) q^{34} +(-2.81438 + 0.644038i) q^{35} +(-4.87361 + 5.36747i) q^{36} +(-3.69756 + 3.69756i) q^{37} +(1.75334 - 5.90981i) q^{38} +1.97488 q^{39} +(0.602798 - 6.29576i) q^{40} +(0.850083 + 4.82106i) q^{41} +(-2.95012 - 3.65868i) q^{42} +(-0.479638 + 5.48229i) q^{43} +(-6.88615 - 4.34301i) q^{44} +(2.48993 + 7.71379i) q^{45} +(-8.26889 - 4.05439i) q^{46} +(4.15148 + 1.93587i) q^{47} +(9.64225 - 3.60925i) q^{48} +(-4.61842 + 2.66645i) q^{49} +(-5.76807 - 4.09015i) q^{50} +(19.9977 + 3.52614i) q^{51} +(-1.36437 - 0.702370i) q^{52} +(0.133082 + 1.52113i) q^{53} +(-1.63975 + 1.57689i) q^{54} +(-8.04503 + 4.25774i) q^{55} +(0.736906 + 3.57685i) q^{56} +(3.91171 - 10.5154i) q^{57} +(-1.45650 + 7.41044i) q^{58} +(-6.96070 - 2.53349i) q^{59} +(1.87004 - 11.3579i) q^{60} +(3.51157 + 2.94655i) q^{61} +(-3.27669 - 5.94052i) q^{62} +(-2.68459 - 3.83400i) q^{63} +(-7.94508 - 0.935788i) q^{64} +(-1.44068 + 0.931647i) q^{65} +(-11.9693 - 8.73443i) q^{66} +(-1.94023 - 0.904744i) q^{67} +(-12.5616 - 9.54828i) q^{68} +(-14.5157 - 8.38065i) q^{69} +(3.87809 + 1.27730i) q^{70} +(-5.99460 - 7.14409i) q^{71} +(9.82355 - 2.93623i) q^{72} +(-5.73385 + 8.18878i) q^{73} +(7.17917 - 1.77406i) q^{74} +(-9.97019 - 8.13756i) q^{75} +(-6.44225 + 5.87345i) q^{76} +(3.71647 - 3.71647i) q^{77} +(-2.39098 - 1.44345i) q^{78} +(1.34323 + 7.61786i) q^{79} +(-5.33139 + 7.18166i) q^{80} +(5.15891 - 4.32884i) q^{81} +(2.49453 - 6.45816i) q^{82} +(-2.46040 - 9.18232i) q^{83} +(0.897556 + 6.58579i) q^{84} +(-16.2518 + 6.86154i) q^{85} +(4.58772 - 6.28681i) q^{86} +(-3.55753 + 13.2769i) q^{87} +(5.16270 + 10.2912i) q^{88} +(15.5495 + 2.74179i) q^{89} +(2.62348 - 11.1589i) q^{90} +(0.636794 - 0.758901i) q^{91} +(7.04774 + 10.9524i) q^{92} +(-5.21830 - 11.1907i) q^{93} +(-3.61124 - 5.37807i) q^{94} +(2.10700 + 9.51633i) q^{95} +(-14.3118 - 2.67784i) q^{96} +(3.38484 - 1.57838i) q^{97} +(7.54041 + 0.147361i) q^{98} +(-11.3038 - 9.48498i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.21069	−	0.730902i	−0.856091	−	0.516826i
$2$	−1.21069	−	0.730902i	−0.856091	−	0.516826i
$3$	−2.10842	−	1.47633i	−1.21730	−	0.852360i	−0.224772	−	0.974411i	$-0.572164\pi$
$3$	−2.10842	−	1.47633i	−1.21730	−	0.852360i	−0.992524	+	0.122052i	$0.961053\pi$
$4$	0.931564	+	1.76980i	0.465782	+	0.884900i
$5$	2.23455	+	0.0823462i	0.999322	+	0.0368264i
$5$	2.23455	+	0.0823462i	0.999322	+	0.0368264i
$6$	1.47360	+	3.32843i	0.601594	+	1.35883i
$7$	−1.24717	+	0.334178i	−0.471386	+	0.126307i	−0.486689	−	0.873575i	$-0.661795\pi$
$7$	−1.24717	+	0.334178i	−0.471386	+	0.126307i	0.0153029	+	0.999883i	$0.495129\pi$
$8$	0.165710	−	2.82357i	0.0585874	−	0.998282i
$9$	1.23982	+	3.40636i	0.413272	+	1.13545i
$10$	−2.64517	−	1.73293i	−0.836477	−	0.548002i
$11$	−3.52529	+	2.03532i	−1.06291	+	0.613674i	−0.926237	−	0.376942i	$-0.876976\pi$
$11$	−3.52529	+	2.03532i	−1.06291	+	0.613674i	−0.136677	+	0.990616i	$0.543642\pi$
$12$	0.648681	−	5.10677i	0.187258	−	1.47420i
$13$	−0.628513	+	0.440089i	−0.174318	+	0.122059i	−0.657479	−	0.753473i	$-0.728377\pi$
$13$	−0.628513	+	0.440089i	−0.174318	+	0.122059i	0.483161	+	0.875531i	$0.339488\pi$
$14$	1.75419	+	0.506971i	0.468828	+	0.135494i
$15$	−4.58980	−	3.47256i	−1.18508	−	0.896610i
$16$	−2.26438	+	3.29736i	−0.566094	+	0.824341i
$17$	−7.15010	+	3.33415i	−1.73416	+	0.808650i	−0.744083	+	0.668087i	$0.767114\pi$
$17$	−7.15010	+	3.33415i	−1.73416	+	0.808650i	−0.990072	+	0.140563i	$0.955109\pi$
$18$	0.988681	−	5.03025i	0.233034	−	1.18564i
$19$	1.09837	+	4.21824i	0.251983	+	0.967732i
$19$	1.09837	+	4.21824i	0.251983	+	0.967732i
$20$	1.93589	+	4.03142i	0.432878	+	0.901452i
$21$	3.12291	+	1.13665i	0.681475	+	0.248037i
$22$	5.75567	+	0.112482i	1.22711	+	0.0239812i
$23$	6.48724	−	0.567560i	1.35268	−	0.118344i	0.612351	−	0.790586i	$-0.290224\pi$
$23$	6.48724	−	0.567560i	1.35268	−	0.118344i	0.740332	+	0.672242i	$0.234669\pi$
$24$	−4.51791	+	5.70862i	−0.922214	+	1.16527i
$25$	4.98644	+	0.368014i	0.997288	+	0.0736027i
$26$	1.08260	−	0.0734326i	0.212315	−	0.0144013i
$27$	0.416344	−	1.55382i	0.0801255	−	0.299032i
$28$	−1.75325	−	1.89593i	−0.331332	−	0.358297i
$29$	−1.82647	−	5.01817i	−0.339166	−	0.931851i	−0.985632	−	0.168908i	$-0.945976\pi$
$29$	−1.82647	−	5.01817i	−0.339166	−	0.931851i	0.646466	−	0.762943i	$-0.276246\pi$
$30$	3.01875	+	7.55890i	0.551145	+	1.38006i
$31$	4.15451	+	2.39861i	0.746172	+	0.430802i	0.824309	−	0.566140i	$-0.191564\pi$
$31$	4.15451	+	2.39861i	0.746172	+	0.430802i	−0.0781374	+	0.996943i	$0.524897\pi$
$32$	5.15152	−	2.33706i	0.910668	−	0.413138i
$33$	10.4376	+	0.913171i	1.81695	+	0.158963i
$34$	11.0935	+	1.18939i	1.90253	+	0.203979i
$35$	−2.81438	+	0.644038i	−0.475718	+	0.108862i
$36$	−4.87361	+	5.36747i	−0.812269	+	0.894578i
$37$	−3.69756	+	3.69756i	−0.607875	+	0.607875i	−0.942390	−	0.334515i	$-0.891427\pi$
$37$	−3.69756	+	3.69756i	−0.607875	+	0.607875i	0.334515	+	0.942390i	$0.391427\pi$
$38$	1.75334	−	5.90981i	0.284429	−	0.958697i
$39$	1.97488			0.316235
$40$	0.602798	−	6.29576i	0.0953108	−	0.995448i
$41$	0.850083	+	4.82106i	0.132761	+	0.752923i	0.976393	+	0.216002i	$0.0693017\pi$
$41$	0.850083	+	4.82106i	0.132761	+	0.752923i	−0.843632	+	0.536921i	$0.819587\pi$
$42$	−2.95012	−	3.65868i	−0.455213	−	0.564546i
$43$	−0.479638	+	5.48229i	−0.0731442	+	0.836042i	0.867675	+	0.497132i	$0.165614\pi$
$43$	−0.479638	+	5.48229i	−0.0731442	+	0.836042i	−0.940819	+	0.338910i	$0.889942\pi$
$44$	−6.88615	−	4.34301i	−1.03813	−	0.654734i
$45$	2.48993	+	7.71379i	0.371177	+	1.14990i
$46$	−8.26889	−	4.05439i	−1.21918	−	0.597788i
$47$	4.15148	+	1.93587i	0.605555	+	0.282375i	0.701114	−	0.713049i	$-0.252686\pi$
$47$	4.15148	+	1.93587i	0.605555	+	0.282375i	−0.0955594	+	0.995424i	$0.530464\pi$
$48$	9.64225	−	3.60925i	1.39174	−	0.520950i
$49$	−4.61842	+	2.66645i	−0.659774	+	0.380921i
$50$	−5.76807	−	4.09015i	−0.815729	−	0.578435i
$51$	19.9977	+	3.52614i	2.80024	+	0.493758i
$52$	−1.36437	−	0.702370i	−0.189204	−	0.0974012i
$53$	0.133082	+	1.52113i	0.0182802	+	0.208944i	0.999842	+	0.0177968i	$0.00566520\pi$
$53$	0.133082	+	1.52113i	0.0182802	+	0.208944i	−0.981561	+	0.191147i	$0.938779\pi$
$54$	−1.63975	+	1.57689i	−0.223142	+	0.214588i
$55$	−8.04503	+	4.25774i	−1.08479	+	0.574114i
$56$	0.736906	+	3.57685i	0.0984732	+	0.477976i
$57$	3.91171	−	10.5154i	0.518118	−	1.39280i
$58$	−1.45650	+	7.41044i	−0.191248	+	0.973039i
$59$	−6.96070	−	2.53349i	−0.906206	−	0.329832i	−0.153469	−	0.988153i	$-0.549045\pi$
$59$	−6.96070	−	2.53349i	−0.906206	−	0.329832i	−0.752737	+	0.658321i	$0.771267\pi$
$60$	1.87004	−	11.3579i	0.241421	−	1.46630i
$61$	3.51157	+	2.94655i	0.449610	+	0.377268i	0.839291	−	0.543682i	$-0.182970\pi$
$61$	3.51157	+	2.94655i	0.449610	+	0.377268i	−0.389681	+	0.920950i	$0.627415\pi$
$62$	−3.27669	−	5.94052i	−0.416141	−	0.754447i
$63$	−2.68459	−	3.83400i	−0.338227	−	0.483038i
$64$	−7.94508	−	0.935788i	−0.993135	−	0.116974i
$65$	−1.44068	+	0.931647i	−0.178695	+	0.115557i
$66$	−11.9693	−	8.73443i	−1.47332	−	1.07513i
$67$	−1.94023	−	0.904744i	−0.237037	−	0.110532i	0.300471	−	0.953791i	$-0.402856\pi$
$67$	−1.94023	−	0.904744i	−0.237037	−	0.110532i	−0.537507	+	0.843259i	$0.680634\pi$
$68$	−12.5616	−	9.54828i	−1.52331	−	1.15790i
$69$	−14.5157	−	8.38065i	−1.74749	−	1.00891i
$70$	3.87809	+	1.27730i	0.463520	+	0.152667i
$71$	−5.99460	−	7.14409i	−0.711429	−	0.847848i	0.282340	−	0.959315i	$-0.408890\pi$
$71$	−5.99460	−	7.14409i	−0.711429	−	0.847848i	−0.993768	+	0.111467i	$0.964445\pi$
$72$	9.82355	−	2.93623i	1.15772	−	0.346038i
$73$	−5.73385	+	8.18878i	−0.671096	+	0.958425i	0.328805	+	0.944398i	$0.393354\pi$
$73$	−5.73385	+	8.18878i	−0.671096	+	0.958425i	−0.999902	+	0.0140270i	$0.995535\pi$
$74$	7.17917	−	1.77406i	0.834562	−	0.206231i
$75$	−9.97019	−	8.13756i	−1.15126	−	0.939644i
$76$	−6.44225	+	5.87345i	−0.738976	+	0.673731i
$77$	3.71647	−	3.71647i	0.423531	−	0.423531i
$78$	−2.39098	−	1.44345i	−0.270725	−	0.163438i
$79$	1.34323	+	7.61786i	0.151126	+	0.857076i	0.962243	+	0.272192i	$0.0877487\pi$
$79$	1.34323	+	7.61786i	0.151126	+	0.857076i	−0.811117	+	0.584884i	$0.801140\pi$
$80$	−5.33139	+	7.18166i	−0.596068	+	0.802934i
$81$	5.15891	−	4.32884i	0.573212	−	0.480982i
$82$	2.49453	−	6.45816i	0.275475	−	0.713185i
$83$	−2.46040	−	9.18232i	−0.270064	−	1.00789i	−0.959078	−	0.283143i	$-0.908623\pi$
$83$	−2.46040	−	9.18232i	−0.270064	−	1.00789i	0.689014	−	0.724748i	$-0.258044\pi$
$84$	0.897556	+	6.58579i	0.0979314	+	0.718568i
$85$	−16.2518	+	6.86154i	−1.76276	+	0.744239i
$86$	4.58772	−	6.28681i	0.494706	−	0.677925i
$87$	−3.55753	+	13.2769i	−0.381407	+	1.42343i
$88$	5.16270	+	10.2912i	0.550346	+	1.09704i
$89$	15.5495	+	2.74179i	1.64824	+	0.290629i	0.919186	−	0.393825i	$-0.128848\pi$
$89$	15.5495	+	2.74179i	1.64824	+	0.290629i	0.729056	+	0.684454i	$0.239959\pi$
$90$	2.62348	−	11.1589i	0.276539	−	1.17626i
$91$	0.636794	−	0.758901i	0.0667541	−	0.0795545i
$92$	7.04774	+	10.9524i	0.734778	+	1.14187i
$93$	−5.21830	−	11.1907i	−0.541113	−	1.16042i
$94$	−3.61124	−	5.37807i	−0.372471	−	0.554705i
$95$	2.10700	+	9.51633i	0.216174	+	0.976355i
$96$	−14.3118	−	2.67784i	−1.46069	−	0.273306i
$97$	3.38484	−	1.57838i	0.343679	−	0.160260i	−0.243113	−	0.969998i	$-0.578169\pi$
$97$	3.38484	−	1.57838i	0.343679	−	0.160260i	0.586792	+	0.809738i	$0.300391\pi$
$98$	7.54041	+	0.147361i	0.761696	+	0.0148857i
$99$	−11.3038	−	9.48498i	−1.13607	−	0.953276i
$100$	3.99388	+	9.16782i	0.399388	+	0.916782i
$101$	1.62883	−	9.23754i	0.162074	−	0.919170i	−0.789955	−	0.613164i	$-0.789896\pi$
$101$	1.62883	−	9.23754i	0.162074	−	0.919170i	0.952030	−	0.306005i	$-0.0989926\pi$
$102$	−21.6339	−	18.8854i	−2.14207	−	1.86994i
$103$	−1.23508	−	0.330939i	−0.121696	−	0.0326084i	0.197457	−	0.980312i	$-0.436732\pi$
$103$	−1.23508	−	0.330939i	−0.121696	−	0.0326084i	−0.319153	+	0.947703i	$0.603398\pi$
$104$	1.13847	+	1.84758i	0.111636	+	0.181170i
$105$	6.88471	+	2.79706i	0.671879	+	0.272965i
$106$	0.950679	−	1.93890i	0.0923381	−	0.188323i
$107$	−13.3782	+	3.58469i	−1.29332	+	0.346545i	−0.838922	−	0.544252i	$-0.816814\pi$
$107$	−13.3782	+	3.58469i	−1.29332	+	0.346545i	−0.454401	+	0.890797i	$0.650147\pi$
$108$	3.13780	−	0.710635i	0.301935	−	0.0683809i
$109$	−8.98791	−	10.7114i	−0.860886	−	1.02596i	−0.999366	−	0.0355988i	$-0.988666\pi$
$109$	−8.98791	−	10.7114i	−0.860886	−	1.02596i	0.138480	−	0.990365i	$-0.455778\pi$
$110$	12.8521	+	0.725304i	1.22540	+	0.0691551i
$111$	13.2548	−	2.33718i	1.25809	−	0.221836i
$112$	1.72216	−	4.86908i	0.162728	−	0.460084i
$113$	6.43668	+	6.43668i	0.605512	+	0.605512i	0.941770	−	0.336258i	$-0.109161\pi$
$113$	6.43668	+	6.43668i	0.605512	+	0.605512i	−0.336258	+	0.941770i	$0.609161\pi$
$114$	−12.4216	+	9.87184i	−1.16339	+	0.924582i
$115$	14.5428	−	0.734042i	1.35612	−	0.0684497i
$116$	7.17969	−	7.90722i	0.666617	−	0.734167i
$117$	−2.27834	−	1.59531i	−0.210633	−	0.147487i
$118$	6.57555	+	8.15487i	0.605329	+	0.750717i
$119$	7.80320	−	6.54766i	0.715318	−	0.600223i
$120$	−10.5656	+	12.3842i	−0.964501	+	1.13051i
$121$	2.78509	−	4.82392i	0.253190	−	0.438539i
$122$	−2.09779	−	6.13399i	−0.189925	−	0.555345i
$123$	5.32515	−	11.4198i	0.480152	−	1.02969i
$124$	−0.374861	+	9.58710i	−0.0336635	+	0.860947i
$125$	11.1121	+	1.23296i	0.993901	+	0.110279i
$126$	0.447947	+	6.60397i	0.0399063	+	0.588329i
$127$	−15.3773	+	10.7673i	−1.36451	+	0.955441i	−0.364808	+	0.931083i	$0.618865\pi$
$127$	−15.3773	+	10.7673i	−1.36451	+	0.955441i	−0.999703	+	0.0243579i	$0.992246\pi$
$128$	8.93510	+	6.94003i	0.789759	+	0.613418i
$129$	9.10495	−	10.8509i	0.801646	−	0.955365i
$130$	2.42517	−	0.0749409i	0.212702	−	0.00657275i
$131$	−0.115579	+	0.317552i	−0.0100982	+	0.0277446i	−0.944639	−	0.328111i	$-0.893588\pi$
$131$	−0.115579	+	0.317552i	−0.0100982	+	0.0277446i	0.934541	+	0.355855i	$0.115810\pi$
$132$	8.10715	+	19.3231i	0.705637	+	1.68186i
$133$	−2.77950	−	4.89382i	−0.241013	−	0.424348i
$134$	1.68775	+	2.51349i	0.145799	+	0.217132i
$135$	1.05829	−	3.43780i	0.0910834	−	0.295879i
$136$	8.22935	+	20.7413i	0.705661	+	1.77855i
$137$	−12.5001	+	1.09362i	−1.06795	+	0.0934339i	−0.607555	−	0.794278i	$-0.707849\pi$
$137$	−12.5001	+	1.09362i	−1.06795	+	0.0934339i	−0.460400	+	0.887712i	$0.652294\pi$
$138$	11.4487	+	20.7560i	0.974575	+	1.76687i
$139$	−0.379434	+	2.15188i	−0.0321832	+	0.182520i	−0.996662	−	0.0816410i	$-0.973984\pi$
$139$	−0.379434	+	2.15188i	−0.0321832	+	0.182520i	0.964479	+	0.264161i	$0.0850950\pi$
$140$	−3.76160	−	4.38093i	−0.317913	−	0.370256i
$141$	−5.89507	−	10.2106i	−0.496455	−	0.859885i
$142$	2.03600	+	13.0308i	0.170858	+	1.09352i
$143$	1.31996	−	2.83067i	0.110381	−	0.236712i
$144$	−14.0394	−	3.62517i	−1.16995	−	0.302098i
$145$	−3.66810	−	11.3638i	−0.304619	−	0.943709i
$146$	12.9271	−	5.72324i	1.06986	−	0.473658i
$147$	13.6741	+	1.19633i	1.12782	+	0.0986716i
$148$	−9.98845	−	3.09942i	−0.821046	−	0.254771i
$149$	−16.1588	+	2.84924i	−1.32378	+	0.233419i	−0.790471	−	0.612500i	$-0.790164\pi$
$149$	−16.1588	+	2.84924i	−1.32378	+	0.233419i	−0.533312	+	0.845918i	$0.679053\pi$
$150$	6.12310	+	17.1393i	0.499949	+	1.39942i
$151$			5.76461i			0.469117i	0.972102	+	0.234559i	$0.0753645\pi$
$151$			5.76461i			0.469117i	−0.972102	+	0.234559i	$0.924636\pi$
$152$	12.0925	−	2.40231i	0.980832	−	0.194853i
$153$	−20.2221	−	20.2221i	−1.63486	−	1.63486i
$154$	−7.21588	+	1.78313i	−0.581473	+	0.143689i
$155$	9.08594	+	5.70192i	0.729801	+	0.457989i
$156$	1.83973	+	3.49515i	0.147296	+	0.279836i
$157$	0.222245	−	2.54028i	0.0177371	−	0.202736i	−0.982155	−	0.188071i	$-0.939776\pi$
$157$	0.222245	−	2.54028i	0.0177371	−	0.202736i	0.999892	−	0.0146648i	$-0.00466810\pi$
$158$	3.94166	−	10.2047i	0.313582	−	0.811840i
$159$	1.96510	−	3.40366i	0.155843	−	0.269928i
$160$	11.7038	−	4.79807i	0.925265	−	0.379321i
$161$	−7.90102	+	2.87574i	−0.622687	+	0.226640i
$162$	−9.40982	+	1.47024i	−0.739305	+	0.115513i
$163$	1.01469	+	0.271886i	0.0794769	+	0.0212958i	0.298338	−	0.954460i	$-0.403568\pi$
$163$	1.01469	+	0.271886i	0.0794769	+	0.0212958i	−0.218861	+	0.975756i	$0.570234\pi$
$164$	−7.74040	+	5.99560i	−0.604424	+	0.468178i
$165$	23.2481	+	2.90002i	1.80986	+	0.225766i
$166$	−3.73259	+	12.9153i	−0.289705	+	1.00242i
$167$	−0.832117	−	9.51114i	−0.0643911	−	0.735994i	−0.957929	−	0.287006i	$-0.907340\pi$
$167$	−0.832117	−	9.51114i	−0.0643911	−	0.735994i	0.893538	−	0.448988i	$-0.148215\pi$
$168$	3.72690	−	8.62940i	0.287537	−	0.665773i
$169$	−4.24491	+	11.6628i	−0.326532	+	0.897139i
$170$	24.6911	+	3.57126i	1.89372	+	0.273904i
$171$	−13.0071	+	8.97128i	−0.994678	+	0.686051i
$172$	−10.1494	+	4.25824i	−0.773882	+	0.324688i
$173$	−1.32210	−	2.83525i	−0.100517	−	0.215560i	0.849617	−	0.527399i	$-0.176833\pi$
$173$	−1.32210	−	2.83525i	−0.100517	−	0.215560i	−0.950135	+	0.311839i	$0.899055\pi$
$174$	14.0112	−	13.4740i	1.06218	−	1.02146i
$175$	−6.34192	+	1.20738i	−0.479404	+	0.0912696i
$176$	1.27137	−	16.2329i	0.0958334	−	1.22360i
$177$	10.9358	+	15.6179i	0.821985	+	1.17392i
$178$	−16.8217	−	14.6846i	−1.26084	−	1.10066i
$179$	−6.41883	−	11.1177i	−0.479766	−	0.830979i	0.519964	−	0.854188i	$-0.325945\pi$
$179$	−6.41883	−	11.1177i	−0.479766	−	0.830979i	−0.999731	+	0.0232085i	$0.992612\pi$
$180$	−11.3323	+	11.5926i	−0.844662	+	0.864059i
$181$	−1.44525	+	0.526029i	−0.107425	+	0.0390994i	−0.395173	−	0.918607i	$-0.629315\pi$
$181$	−1.44525	+	0.526029i	−0.107425	+	0.0390994i	0.287749	+	0.957706i	$0.407093\pi$
$182$	−1.32565	+	0.453364i	−0.0982634	+	0.0336056i
$183$	−3.05376	−	11.3968i	−0.225741	−	0.842476i
$184$	−0.527542	−	18.4112i	−0.0388909	−	1.35729i
$185$	−8.56687	+	7.95791i	−0.629849	+	0.585077i
$186$	−1.86153	+	17.3626i	−0.136494	+	1.27309i
$187$	18.4201	−	26.3066i	1.34701	−	1.92373i
$188$	0.441274	+	9.15066i	0.0321832	+	0.667381i
$189$			2.07701i			0.151080i
$190$	4.40457	−	13.0614i	0.319541	−	0.947572i
$191$		−	16.0747i		−	1.16312i	−0.813502	−	0.581562i	$-0.802442\pi$
$191$		−	16.0747i		−	1.16312i	0.813502	−	0.581562i	$-0.197558\pi$
$192$	15.3700	+	13.7026i	1.10924	+	0.988900i
$193$	5.34715	−	7.63652i	0.384896	−	0.549689i	−0.579219	−	0.815172i	$-0.696642\pi$
$193$	5.34715	−	7.63652i	0.384896	−	0.549689i	0.964116	+	0.265483i	$0.0855314\pi$
$194$	−5.25165	−	0.563054i	−0.377046	−	0.0404250i
$195$	4.41298	+	0.162624i	0.316020	+	0.0116458i
$196$	−9.02143	−	5.68971i	−0.644388	−	0.406408i
$197$	5.50664	+	20.5511i	0.392332	+	1.46420i	0.826277	+	0.563264i	$0.190454\pi$
$197$	5.50664	+	20.5511i	0.392332	+	1.46420i	−0.433945	+	0.900939i	$0.642879\pi$
$198$	6.75281	+	19.7454i	0.479901	+	1.40324i
$199$	16.8669	−	6.13906i	1.19566	−	0.435186i	0.333956	−	0.942589i	$-0.391616\pi$
$199$	16.8669	−	6.13906i	1.19566	−	0.435186i	0.861709	+	0.507402i	$0.169394\pi$
$200$	1.86542	−	14.0186i	0.131905	−	0.991262i
$201$	2.75511	+	4.77200i	0.194331	+	0.336591i
$202$	−8.72375	+	9.99333i	−0.613801	+	0.703128i
$203$	3.95488	+	5.64815i	0.277578	+	0.396422i
$204$	12.3886	+	38.6768i	0.867375	+	2.70791i
$205$	1.50256	+	10.8429i	0.104943	+	0.757302i
$206$	1.25342	+	1.30339i	0.0873300	+	0.0908114i
$207$	9.97629	+	21.3942i	0.693400	+	1.48700i
$208$	−0.0279441	−	3.06896i	−0.00193758	−	0.212794i
$209$	−12.4576	−	12.6350i	−0.861707	−	0.873980i
$210$	−6.29091	−	8.41843i	−0.434114	−	0.580927i
$211$	−0.704029	+	1.93430i	−0.0484673	+	0.133163i	−0.961565	−	0.274579i	$-0.911461\pi$
$211$	−0.704029	+	1.93430i	−0.0484673	+	0.133163i	0.913097	+	0.407742i	$0.133684\pi$
$212$	−2.56813	+	1.65256i	−0.176380	+	0.113498i
$213$	2.09209	+	23.9127i	0.143348	+	1.63847i
$214$	18.8170	+	5.43822i	1.28631	+	0.371749i
$215$	−1.52322	+	12.2110i	−0.103883	+	0.832781i
$216$	−4.31832	−	1.43306i	−0.293824	−	0.0975074i
$217$	−5.98294	−	1.60312i	−0.406148	−	0.108827i
$218$	3.05265	+	19.5375i	0.206752	+	1.32325i
$219$	24.1787	−	8.80033i	1.63385	−	0.594671i
$220$	−15.0298	−	10.2717i	−1.01331	−	0.692520i
$221$	3.02661	−	5.24224i	0.203592	−	0.352631i
$222$	−17.7558	−	6.85836i	−1.19169	−	0.460303i
$223$	−1.16600	+	13.3274i	−0.0780809	+	0.892468i	0.851622	+	0.524157i	$0.175620\pi$
$223$	−1.16600	+	13.3274i	−0.0780809	+	0.892468i	−0.929702	+	0.368311i	$0.879936\pi$
$224$	−5.64382	+	4.63624i	−0.377094	+	0.309772i
$225$	4.92867	+	17.4419i	0.328578	+	1.16279i
$226$	−3.08827	−	12.4974i	−0.205429	−	0.831317i
$227$	−9.12081	−	9.12081i	−0.605370	−	0.605370i	0.336363	−	0.941732i	$-0.390803\pi$
$227$	−9.12081	−	9.12081i	−0.605370	−	0.605370i	−0.941732	+	0.336363i	$0.890803\pi$
$228$	22.2541	−	2.87281i	1.47381	−	0.190257i
$229$		−	10.5862i		−	0.699554i	−0.936833	−	0.349777i	$-0.886257\pi$
$229$		−	10.5862i		−	0.699554i	0.936833	−	0.349777i	$-0.113743\pi$
$230$	−18.1434	−	9.74066i	−1.19634	−	0.642280i
$231$	−13.3226	+	2.34913i	−0.876563	+	0.154562i
$232$	−14.4718	+	4.32559i	−0.950121	+	0.283989i
$233$	4.18775	+	0.366381i	0.274349	+	0.0240024i	0.223500	−	0.974704i	$-0.428252\pi$
$233$	4.18775	+	0.366381i	0.274349	+	0.0240024i	0.0508489	+	0.998706i	$0.483807\pi$
$234$	1.59236	+	3.59668i	0.104096	+	0.235123i
$235$	9.11728	+	4.66765i	0.594746	+	0.304484i
$236$	−2.00057	−	14.6792i	−0.130226	−	0.955531i
$237$	8.41438	−	18.0447i	0.546572	−	1.17213i
$238$	−14.2330	+	2.22384i	−0.922587	+	0.144150i
$239$	8.11842	+	14.0615i	0.525137	+	0.909564i	0.999571	+	0.0292732i	$0.00931928\pi$
$239$	8.11842	+	14.0615i	0.525137	+	0.909564i	−0.474434	+	0.880291i	$0.657347\pi$
$240$	21.8433	−	7.27105i	1.40998	−	0.469344i
$241$	−0.361271	+	2.04887i	−0.0232715	+	0.131979i	−0.994230	−	0.107268i	$-0.965790\pi$
$241$	−0.361271	+	2.04887i	−0.0232715	+	0.131979i	0.970959	+	0.239248i	$0.0769008\pi$
$242$	−6.89772	+	3.80467i	−0.443402	+	0.244573i
$243$	−22.0754	+	1.93135i	−1.41614	+	0.123896i
$244$	−1.94356	+	8.95967i	−0.124424	+	0.573584i
$245$	−10.5397	+	5.57800i	−0.673355	+	0.356365i
$246$	−14.7939	+	9.93375i	−0.943224	+	0.633353i
$247$	−2.54674	−	2.16784i	−0.162045	−	0.137936i
$248$	7.46107	−	11.3331i	0.473779	−	0.719650i
$249$	−8.36860	+	22.9925i	−0.530338	+	1.45709i
$250$	−12.5522	−	9.61463i	−0.793874	−	0.608083i
$251$	−10.2406	+	12.2043i	−0.646382	+	0.770328i	−0.985364	−	0.170465i	$-0.945473\pi$
$251$	−10.2406	+	12.2043i	−0.646382	+	0.770328i	0.338982	+	0.940793i	$0.389918\pi$
$252$	4.28453	−	8.32280i	0.269900	−	0.524287i
$253$	−21.7142	+	15.2044i	−1.36516	+	0.955895i
$254$	26.4870	−	1.79661i	1.66194	−	0.112729i
$255$	44.3956	+	9.52607i	2.78016	+	0.596546i
$256$	−5.74519	−	14.9329i	−0.359075	−	0.933309i
$257$	−5.99766	+	12.8620i	−0.374124	+	0.802312i	0.625630	+	0.780120i	$0.284842\pi$
$257$	−5.99766	+	12.8620i	−0.374124	+	0.802312i	−0.999754	+	0.0221914i	$0.992936\pi$
$258$	−18.9542	+	6.48225i	−1.18004	+	0.403567i
$259$	3.37584	−	5.84713i	0.209765	−	0.363323i
$260$	−2.99092	−	1.68183i	−0.185489	−	0.104303i
$261$	14.8292	−	12.4432i	0.917907	−	0.770215i
$262$	0.372031	−	0.299981i	0.0229841	−	0.0185329i
$263$	12.0649	+	8.44792i	0.743952	+	0.520921i	0.883005	−	0.469364i	$-0.155517\pi$
$263$	12.0649	+	8.44792i	0.743952	+	0.520921i	−0.139052	+	0.990285i	$0.544406\pi$
$264$	4.30801	−	29.3199i	0.265140	−	1.80452i
$265$	0.172119	+	3.41001i	0.0105732	+	0.209475i
$266$	−0.211781	+	7.95646i	−0.0129851	+	0.487842i
$267$	−28.7370	−	28.7370i	−1.75868	−	1.75868i
$268$	−0.206233	−	4.27664i	−0.0125977	−	0.261238i
$269$	3.31478	−	0.584486i	0.202106	−	0.0356367i	−0.0716786	−	0.997428i	$-0.522836\pi$
$269$	3.31478	−	0.584486i	0.202106	−	0.0356367i	0.273785	+	0.961791i	$0.411724\pi$
$270$	−3.79397	+	3.38862i	−0.230893	+	0.206225i
$271$	16.7966	+	20.0174i	1.02032	+	1.21597i	0.976184	+	0.216945i	$0.0696092\pi$
$271$	16.7966	+	20.0174i	1.02032	+	1.21597i	0.0441365	+	0.999026i	$0.485946\pi$
$272$	5.19664	−	31.1263i	0.315092	−	1.88731i
$273$	−2.46302	+	0.659963i	−0.149069	+	0.0399428i
$274$	15.9331	+	7.81230i	0.962555	+	0.471959i
$275$	−18.3276	+	8.85167i	−1.10520	+	0.533776i
$276$	1.30975	−	33.4970i	0.0788378	−	2.01628i
$277$	13.2112	+	3.53992i	0.793782	+	0.212693i	0.632852	−	0.774273i	$-0.281884\pi$
$277$	13.2112	+	3.53992i	0.793782	+	0.212693i	0.160930	+	0.986966i	$0.448551\pi$
$278$	2.03219	−	2.32794i	0.121883	−	0.139621i
$279$	−3.01970	+	17.1256i	−0.180785	+	1.02528i
$280$	1.35211	+	8.05333i	0.0808043	+	0.481278i
$281$	−20.2198	−	16.9665i	−1.20621	−	1.01213i	−0.999430	−	0.0337468i	$-0.989256\pi$
$281$	−20.2198	−	16.9665i	−1.20621	−	1.01213i	−0.206783	−	0.978387i	$-0.566300\pi$
$282$	−0.325790	+	16.6706i	−0.0194005	+	0.992720i
$283$	19.6611	−	9.16812i	1.16873	−	0.544988i	0.261328	−	0.965250i	$-0.415840\pi$
$283$	19.6611	−	9.16812i	1.16873	−	0.544988i	0.907403	+	0.420262i	$0.138062\pi$
$284$	7.05925	−	17.2644i	0.418889	−	1.02445i
$285$	9.60681	−	23.1750i	0.569058	−	1.37277i
$286$	−3.66701	+	2.46231i	−0.216835	+	0.145600i
$287$	−2.67129	−	5.72860i	−0.157681	−	0.338149i
$288$	14.3478	+	14.6504i	0.845453	+	0.863285i
$289$	29.0801	−	34.6563i	1.71059	−	2.03860i
$290$	−3.86485	+	16.4391i	−0.226952	+	0.965336i
$291$	−9.46687	−	1.66926i	−0.554957	−	0.0978540i
$292$	−19.8339	−	2.51938i	−1.16069	−	0.147436i
$293$	2.92315	−	10.9093i	0.170772	−	0.637330i	−0.826461	−	0.562994i	$-0.809650\pi$
$293$	2.92315	−	10.9093i	0.170772	−	0.637330i	0.997233	−	0.0743362i	$-0.0236838\pi$
$294$	−15.6808	−	11.4428i	−0.914522	−	0.667359i
$295$	−15.3454	−	6.23440i	−0.893445	−	0.362981i
$296$	9.82759	+	11.0530i	0.571217	+	0.642445i
$297$	1.69479	+	6.32505i	0.0983418	+	0.367016i
$298$	21.6459	+	8.36097i	1.25391	+	0.484338i
$299$	−3.82753	+	3.21168i	−0.221352	+	0.185736i
$300$	5.11397	−	25.2259i	0.295255	−	1.45642i
$301$	−1.23387	−	6.99763i	−0.0711192	−	0.403337i
$302$	4.21337	−	6.97918i	0.242452	−	0.401607i
$303$	−17.0719	+	17.0719i	−0.980756	+	0.980756i
$304$	−16.3962	−	5.92998i	−0.940386	−	0.340108i
$305$	7.60414	+	6.87339i	0.435412	+	0.393569i
$306$	9.70243	+	39.2632i	0.554651	+	2.24453i
$307$	9.45817	−	13.5077i	0.539806	−	0.770923i	−0.452890	−	0.891566i	$-0.649607\pi$
$307$	9.45817	−	13.5077i	0.539806	−	0.770923i	0.992696	+	0.120644i	$0.0384958\pi$
$308$	10.0395	+	3.11527i	0.572055	+	0.177509i
$309$	2.11549	+	2.52114i	0.120346	+	0.143423i
$310$	−6.83276	−	13.5442i	−0.388075	−	0.769260i
$311$	−1.27766	−	0.737657i	−0.0724494	−	0.0418287i	0.463338	−	0.886182i	$-0.346652\pi$
$311$	−1.27766	−	0.737657i	−0.0724494	−	0.0418287i	−0.535787	+	0.844353i	$0.679985\pi$
$312$	0.327259	−	5.57622i	0.0185274	−	0.315691i
$313$	−0.846271	−	0.394622i	−0.0478340	−	0.0223054i	0.398554	−	0.917145i	$-0.369512\pi$
$313$	−0.846271	−	0.394622i	−0.0478340	−	0.0223054i	−0.446388	+	0.894839i	$0.647290\pi$
$314$	−2.12577	+	2.91306i	−0.119964	+	0.164394i
$315$	−5.68314	−	8.78832i	−0.320209	−	0.495166i
$316$	−12.2308	+	9.47378i	−0.688035	+	0.532942i
$317$	9.71802	+	13.8788i	0.545818	+	0.779510i	0.993396	−	0.114736i	$-0.0366021\pi$
$317$	9.71802	+	13.8788i	0.545818	+	0.779510i	−0.447578	+	0.894245i	$0.647713\pi$
$318$	−4.86688	+	2.68450i	−0.272921	+	0.150539i
$319$	16.6524	+	13.9730i	0.932357	+	0.782340i
$320$	−17.6766	−	2.74531i	−0.988154	−	0.153468i
$321$	33.4991	+	12.1927i	1.86974	+	0.680529i
$322$	11.6676	+	2.29323i	0.650210	+	0.127797i
$323$	−21.9177	−	26.4988i	−1.21953	−	1.47443i
$324$	12.4670	+	5.09764i	0.692612	+	0.283202i
$325$	−3.29600	+	1.96318i	−0.182829	+	0.108897i
$326$	−1.02976	−	1.07081i	−0.0570332	−	0.0593068i
$327$	3.13675	+	35.8532i	0.173463	+	1.98269i
$328$	13.7535	−	1.60137i	0.759408	−	0.0884208i
$329$	−5.82452	−	1.02702i	−0.321116	−	0.0566214i
$330$	−26.0268	−	20.5031i	−1.43273	−	1.12866i
$331$	4.65956	−	2.69020i	0.256113	−	0.147867i	−0.366447	−	0.930439i	$-0.619426\pi$
$331$	4.65956	−	2.69020i	0.256113	−	0.147867i	0.622560	+	0.782572i	$0.286093\pi$
$332$	13.9589	−	12.9083i	0.766092	−	0.708437i
$333$	−17.1795	−	8.01094i	−0.941432	−	0.438997i
$334$	−5.94427	+	12.1233i	−0.325256	+	0.663356i
$335$	−4.26104	−	2.18147i	−0.232806	−	0.119186i
$336$	−10.8194	+	7.72357i	−0.590246	+	0.421356i
$337$	2.93908	−	33.5938i	0.160102	−	1.82997i	−0.313909	−	0.949453i	$-0.601639\pi$
$337$	2.93908	−	33.5938i	0.160102	−	1.82997i	0.474011	−	0.880519i	$-0.342806\pi$
$338$	13.6637	−	11.0175i	0.743205	−	0.599272i
$339$	−4.06855	−	23.0739i	−0.220973	−	1.25320i
$340$	−27.2832	−	22.3705i	−1.47964	−	1.21321i
$341$	−19.5278			−1.05749
$342$	22.3048	−	1.35456i	1.20610	−	0.0732463i
$343$	11.2598	−	11.2598i	0.607974	−	0.607974i
$344$	15.4001	+	2.26276i	0.830320	+	0.122000i
$345$	−31.7460	−	19.9223i	−1.70915	−	1.07258i
$346$	−0.471633	+	4.39895i	−0.0253551	+	0.236489i
$347$	−5.24161	−	0.458581i	−0.281384	−	0.0246179i	−0.0544099	−	0.998519i	$-0.517328\pi$
$347$	−5.24161	−	0.458581i	−0.281384	−	0.0246179i	−0.226974	+	0.973901i	$0.572883\pi$
$348$	−26.8115	+	6.07215i	−1.43724	+	0.325501i
$349$	24.9077	+	14.3805i	1.33328	+	0.769768i	0.985801	−	0.167920i	$-0.0537050\pi$
$349$	24.9077	+	14.3805i	1.33328	+	0.769768i	0.347477	+	0.937688i	$0.387038\pi$
$350$	8.56061	+	3.17355i	0.457584	+	0.169633i
$351$	0.422141	+	1.15982i	0.0225322	+	0.0619068i
$352$	−13.4039	+	18.7238i	−0.714430	+	0.997983i
$353$	3.39710	−	12.6782i	0.180810	−	0.674790i	−0.814679	−	0.579912i	$-0.803087\pi$
$353$	3.39710	−	12.6782i	0.180810	−	0.674790i	0.995489	−	0.0948786i	$-0.0302463\pi$
$354$	−1.82473	−	26.9016i	−0.0969833	−	1.42980i
$355$	−12.8070	−	16.4575i	−0.679723	−	0.873472i
$356$	9.63291	+	30.0736i	0.510543	+	1.59390i
$357$	−26.1189	+	2.28511i	−1.38236	+	0.120941i
$358$	−0.354736	+	18.1517i	−0.0187484	+	0.959349i
$359$	−30.8587	−	11.2316i	−1.62866	−	0.592784i	−0.643656	−	0.765315i	$-0.722583\pi$
$359$	−30.8587	−	11.2316i	−1.62866	−	0.592784i	−0.985004	+	0.172531i	$0.944805\pi$
$360$	22.1930	−	5.75223i	1.16967	−	0.303169i
$361$	−16.5872	+	9.26636i	−0.873009	+	0.487703i
$362$	2.13424	+	0.419478i	0.112173	+	0.0220473i
$363$	−12.9938	+	6.05913i	−0.682000	+	0.318022i
$364$	1.93632	+	0.420032i	0.101491	+	0.0220157i
$365$	−13.4869	+	17.8261i	−0.705936	+	0.933061i
$366$	−4.63277	+	16.0301i	−0.242159	+	0.837904i
$367$	18.9608	−	13.2765i	0.989745	−	0.693027i	0.0377966	−	0.999285i	$-0.487966\pi$
$367$	18.9608	−	13.2765i	0.989745	−	0.693027i	0.951948	+	0.306259i	$0.0990772\pi$
$368$	−12.8181	+	22.6759i	−0.668190	+	1.18206i
$369$	−15.3683	+	8.87292i	−0.800044	+	0.461906i
$370$	16.1883	−	3.37305i	0.841590	−	0.175357i
$371$	−0.674306	−	1.85264i	−0.0350082	−	0.0961843i
$372$	14.9441	−	19.6602i	0.774815	−	1.01933i
$373$	−13.8226	+	3.70374i	−0.715705	+	0.191772i	−0.598254	−	0.801306i	$-0.704139\pi$
$373$	−13.8226	+	3.70374i	−0.715705	+	0.191772i	−0.117450	+	0.993079i	$0.537472\pi$
$374$	−41.5287	+	18.3860i	−2.14740	+	0.950717i
$375$	−21.6088	−	19.0048i	−1.11587	−	0.981403i
$376$	6.15399	−	11.4012i	0.317368	−	0.587971i
$377$	3.35640	+	2.35018i	0.172863	+	0.121040i
$378$	1.51809	−	2.51462i	0.0780821	−	0.129338i
$379$	−31.9416			−1.64073			−0.820364	−	0.571841i	$-0.806229\pi$
$379$	−31.9416			−1.64073			−0.820364	+	0.571841i	$0.806229\pi$
$380$	−14.8792	+	12.5940i	−0.763286	+	0.646061i
$381$	48.3177			2.47539
$382$	−11.7490	+	19.4616i	−0.601133	+	0.995740i
$383$	0.146963	+	0.102905i	0.00750948	+	0.00525819i	0.577325	−	0.816514i	$-0.304097\pi$
$383$	0.146963	+	0.102905i	0.00750948	+	0.00525819i	−0.569816	+	0.821773i	$0.692985\pi$
$384$	−8.59314	−	27.8236i	−0.438517	−	1.41987i
$385$	8.61068	−	7.99860i	0.438841	−	0.407647i
$386$	−12.0553	+	5.33725i	−0.613600	+	0.271659i
$387$	−19.2693	+	5.16321i	−0.979516	+	0.262461i
$388$	5.94661	+	4.52013i	0.301893	+	0.229475i
$389$	7.11644	+	19.5523i	0.360818	+	0.991339i	0.978741	+	0.205100i	$0.0657520\pi$
$389$	7.11644	+	19.5523i	0.360818	+	0.991339i	−0.617923	+	0.786238i	$0.712026\pi$
$390$	−5.22391	−	3.42235i	−0.264523	−	0.173297i
$391$	−44.4921	+	25.6875i	−2.25006	+	1.29907i
$392$	6.76357	+	13.4823i	0.341612	+	0.680958i
$393$	0.712501	−	0.498898i	0.0359409	−	0.0251661i
$394$	8.35396	−	28.9059i	0.420866	−	1.45626i
$395$	2.37422	+	17.1331i	0.119460	+	0.862060i
$396$	6.25633	−	28.8413i	0.314393	−	1.44933i
$397$	10.6406	−	4.96180i	0.534037	−	0.249026i	−0.136841	−	0.990593i	$-0.543695\pi$
$397$	10.6406	−	4.96180i	0.534037	−	0.249026i	0.670878	+	0.741567i	$0.265917\pi$
$398$	−24.9078	−	4.89555i	−1.24851	−	0.245392i
$399$	−1.36455	+	14.4217i	−0.0683131	+	0.721986i
$400$	−12.5047	+	15.6088i	−0.625233	+	0.780439i
$401$	28.5442	+	10.3893i	1.42543	+	0.518815i	0.935618	−	0.353013i	$-0.114843\pi$
$401$	28.5442	+	10.3893i	1.42543	+	0.518815i	0.489813	+	0.871828i	$0.337065\pi$
$402$	0.152261	−	7.79115i	0.00759409	−	0.388587i
$403$	−3.66676	+	0.320800i	−0.182654	+	0.0159802i
$404$	17.8660	−	5.72266i	0.888864	−	0.284713i
$405$	11.8843	−	9.24819i	0.590536	−	0.459546i
$406$	−0.659904	−	9.72881i	−0.0327505	−	0.482833i
$407$	5.50922	−	20.5607i	0.273082	−	1.01916i
$408$	13.2701	−	55.8806i	0.656969	−	2.76650i
$409$	5.57168	+	15.3081i	0.275502	+	0.756935i	0.997858	+	0.0654142i	$0.0208369\pi$
$409$	5.57168	+	15.3081i	0.275502	+	0.756935i	−0.722356	+	0.691521i	$0.756941\pi$
$410$	6.10597	−	14.2257i	0.301552	−	0.702556i
$411$	27.9699	+	16.1485i	1.37966	+	0.796544i
$412$	−0.564861	−	2.49413i	−0.0278287	−	0.122877i
$413$	9.52781	+	0.833576i	0.468833	+	0.0410176i
$414$	3.55884	−	33.1936i	0.174907	−	1.63137i
$415$	−4.74175	−	20.7210i	−0.232763	−	1.01715i
$416$	−2.20928	+	3.73600i	−0.108319	+	0.183173i
$417$	3.97689	−	3.97689i	0.194749	−	0.194749i
$418$	5.84736	+	24.4024i	0.286004	+	1.19356i
$419$	11.7243			0.572772			0.286386	−	0.958114i	$-0.407546\pi$
$419$	11.7243			0.572772			0.286386	+	0.958114i	$0.407546\pi$
$420$	1.46332	+	14.7902i	0.0714027	+	0.721687i
$421$	−6.87218	−	38.9741i	−0.334930	−	1.89948i	−0.427925	−	0.903814i	$-0.640755\pi$
$421$	−6.87218	−	38.9741i	−0.334930	−	1.89948i	0.0929948	−	0.995667i	$-0.470356\pi$
$422$	2.26615	−	1.82727i	0.110314	−	0.0889503i
$423$	−1.44720	+	16.5416i	−0.0703652	+	0.804278i
$424$	4.31708	−	0.123699i	0.209656	−	0.00600734i
$425$	−36.8806	+	13.9942i	−1.78897	+	0.678818i
$426$	14.9450	−	30.4802i	0.724087	−	1.47677i
$427$	−5.36419	−	2.50136i	−0.259592	−	0.121050i
$428$	−18.8069	−	20.3374i	−0.909064	−	0.983047i
$429$	−6.96203	+	4.01953i	−0.336130	+	0.194065i
$430$	10.7692	−	13.6704i	0.519336	−	0.659247i
$431$	20.4819	+	3.61151i	0.986578	+	0.173960i	0.643583	−	0.765377i	$-0.277447\pi$
$431$	20.4819	+	3.61151i	0.986578	+	0.173960i	0.342996	+	0.939337i	$0.388558\pi$
$432$	4.18074	+	4.89127i	0.201146	+	0.235331i
$433$	3.05298	+	34.8957i	0.146717	+	1.67698i	0.611260	+	0.791430i	$0.290663\pi$
$433$	3.05298	+	34.8957i	0.146717	+	1.67698i	−0.464543	+	0.885551i	$0.653781\pi$
$434$	6.07179	+	6.31384i	0.291455	+	0.303074i
$435$	−9.04277	+	29.3749i	−0.433568	+	1.40842i
$436$	10.5842	−	25.8851i	0.506890	−	1.23967i
$437$	9.51947	+	26.7414i	0.455378	+	1.27921i
$438$	−35.7052	−	7.01775i	−1.70606	−	0.335321i
$439$	15.9534	+	5.80656i	0.761414	+	0.277132i	0.693401	−	0.720552i	$-0.256112\pi$
$439$	15.9534	+	5.80656i	0.761414	+	0.277132i	0.0680137	+	0.997684i	$0.478334\pi$
$440$	10.6889	+	23.4213i	0.509573	+	1.11656i
$441$	−14.8089	−	12.4261i	−0.705185	−	0.591720i
$442$	−7.49586	+	4.13460i	−0.356542	+	0.196663i
$443$	13.7789	+	19.6783i	0.654654	+	0.934942i	0.999994	−	0.00353532i	$-0.00112533\pi$
$443$	13.7789	+	19.6783i	0.654654	+	0.934942i	−0.345340	+	0.938478i	$0.612236\pi$
$444$	16.4841	+	21.2811i	0.782299	+	1.00996i
$445$	34.5203	+	7.40712i	1.63642	+	0.351131i
$446$	11.1527	−	15.2832i	0.528095	−	0.723680i
$447$	38.2760	+	17.8484i	1.81039	+	0.844200i
$448$	10.2216	−	1.48798i	0.482924	−	0.0703007i
$449$	6.45956	+	3.72943i	0.304846	+	0.176003i	0.644618	−	0.764505i	$-0.277017\pi$
$449$	6.45956	+	3.72943i	0.304846	+	0.176003i	−0.339772	+	0.940508i	$0.610350\pi$
$450$	6.78120	−	24.7192i	0.319669	−	1.16527i
$451$	−12.8092	−	15.2654i	−0.603162	−	0.718821i
$452$	−5.39545	+	17.3878i	−0.253781	+	0.817853i
$453$	8.51047	−	12.1542i	0.399857	−	0.571054i
$454$	4.37610	+	17.7089i	0.205380	+	0.831122i
$455$	1.48544	−	1.64337i	0.0696385	−	0.0770422i
$456$	−29.0427	−	12.7875i	−1.36005	−	0.598828i
$457$	4.94110	−	4.94110i	0.231135	−	0.231135i	−0.582032	−	0.813166i	$-0.697742\pi$
$457$	4.94110	−	4.94110i	0.231135	−	0.231135i	0.813166	+	0.582032i	$0.197742\pi$
$458$	−7.73745	+	12.8166i	−0.361548	+	0.598881i
$459$	2.20375	+	12.4981i	0.102862	+	0.583362i
$460$	14.8467	+	25.0540i	0.692229	+	1.16815i
$461$	4.55868	−	3.82518i	0.212319	−	0.178157i	−0.530426	−	0.847731i	$-0.677968\pi$
$461$	4.55868	−	3.82518i	0.212319	−	0.178157i	0.742745	+	0.669575i	$0.233524\pi$
$462$	17.8466	+	6.89344i	0.830299	+	0.320712i
$463$	1.24334	+	4.64020i	0.0577828	+	0.215648i	0.988780	−	0.149377i	$-0.0477269\pi$
$463$	1.24334	+	4.64020i	0.0577828	+	0.215648i	−0.930997	+	0.365026i	$0.881060\pi$
$464$	20.6825	+	5.34052i	0.960163	+	0.247927i
$465$	−10.7391	−	25.4359i	−0.498012	−	1.17956i
$466$	−4.80230	−	3.50441i	−0.222462	−	0.162339i
$467$	2.63653	−	9.83965i	0.122004	−	0.455325i	−0.877711	−	0.479190i	$-0.840931\pi$
$467$	2.63653	−	9.83965i	0.122004	−	0.455325i	0.999715	+	0.0238652i	$0.00759724\pi$
$468$	0.700961	−	5.51835i	0.0324019	−	0.255086i
$469$	2.72214	+	0.479987i	0.125697	+	0.0221637i
$470$	−7.62664	−	12.3149i	−0.351791	−	0.568046i
$471$	−4.21887	+	5.02786i	−0.194395	+	0.231672i
$472$	−8.30694	+	19.2342i	−0.382358	+	0.885326i
$473$	−9.46738	−	20.3029i	−0.435311	−	0.933527i
$474$	−23.3761	+	15.6965i	−1.07370	+	0.720965i
$475$	3.92457	+	21.4382i	0.180071	+	0.983654i
$476$	18.8572	+	7.71052i	0.864319	+	0.353411i
$477$	−5.01654	+	2.33925i	−0.229692	+	0.107107i
$478$	0.448664	−	22.9580i	0.0205214	−	1.05007i
$479$	3.95089	+	3.31519i	0.180521	+	0.151475i	0.728570	−	0.684971i	$-0.240185\pi$
$479$	3.95089	+	3.31519i	0.180521	+	0.151475i	−0.548050	+	0.836446i	$0.684630\pi$
$480$	−31.7600	−	7.16230i	−1.44964	−	0.326913i
$481$	0.696707	−	3.95122i	0.0317671	−	0.180160i
$482$	1.93491	−	2.21651i	0.0881330	−	0.100959i
$483$	20.9042	+	5.60126i	0.951173	+	0.254866i
$484$	11.1319	+	0.435262i	0.505994	+	0.0197847i
$485$	7.69357	−	3.24824i	0.349347	−	0.147495i
$486$	28.1383	+	13.7967i	1.27638	+	0.625832i
$487$	2.56648	−	0.687686i	0.116298	−	0.0311620i	−0.200200	−	0.979755i	$-0.564159\pi$
$487$	2.56648	−	0.687686i	0.116298	−	0.0311620i	0.316499	+	0.948593i	$0.397493\pi$
$488$	8.90170	−	9.42688i	0.402961	−	0.426735i
$489$	−1.73800	−	2.07127i	−0.0785953	−	0.0936662i
$490$	16.8373	+	0.950210i	0.760632	+	0.0429261i
$491$	15.0012	−	2.64512i	0.676996	−	0.119373i	0.175430	−	0.984492i	$-0.443869\pi$
$491$	15.0012	−	2.64512i	0.676996	−	0.119373i	0.501566	+	0.865119i	$0.332757\pi$
$492$	25.1715	−	1.21385i	1.13482	−	0.0547245i
$493$	29.7907	+	29.7907i	1.34171	+	1.34171i
$494$	1.49885	+	4.48601i	0.0674364	+	0.201835i
$495$	−24.4778	−	22.1255i	−1.10019	−	0.994467i
$496$	−17.3164	+	8.26757i	−0.777531	+	0.371225i
$497$	9.86369	+	6.90663i	0.442447	+	0.309805i
$498$	26.9371	−	21.7203i	1.20708	−	0.973311i
$499$	−18.7353	+	15.7208i	−0.838707	+	0.703759i	−0.957273	−	0.289187i	$-0.906615\pi$
$499$	−18.7353	+	15.7208i	−0.838707	+	0.703759i	0.118565	+	0.992946i	$0.462171\pi$
$500$	8.16958	+	20.8148i	0.365355	+	0.930868i
$501$	−12.2871	+	21.2819i	−0.548948	+	0.950806i
$502$	21.3184	−	7.29078i	0.951487	−	0.325404i
$503$	0.899315	−	1.92859i	0.0400985	−	0.0859914i	−0.885238	−	0.465138i	$-0.846005\pi$
$503$	0.899315	−	1.92859i	0.0400985	−	0.0859914i	0.925337	+	0.379147i	$0.123782\pi$
$504$	−11.2704	+	6.94480i	−0.502024	+	0.309346i
$505$	4.40038	−	20.5076i	0.195814	−	0.912578i
$506$	37.4022	−	2.53699i	1.66273	−	0.112783i
$507$	26.1682	−	18.3232i	1.16217	−	0.813760i
$508$	−33.3808	−	17.1843i	−1.48103	−	0.762428i
$509$	−23.7708	+	28.3289i	−1.05362	+	1.25566i	−0.0878842	+	0.996131i	$0.528011\pi$
$509$	−23.7708	+	28.3289i	−1.05362	+	1.25566i	−0.965736	+	0.259525i	$0.916434\pi$
$510$	−46.7868	−	43.9820i	−2.07176	−	1.94755i
$511$	4.41457	−	12.1289i	0.195289	−	0.536552i
$512$	−3.95884	+	22.2784i	−0.174958	+	0.984576i
$513$	7.01168	+	0.0495797i	0.309573	+	0.00218900i
$514$	16.6622	−	11.1883i	0.734939	−	0.493494i
$515$	−2.73260	−	0.841204i	−0.120413	−	0.0370679i
$516$	27.6857	+	6.00567i	1.21879	+	0.264385i
$517$	−18.5753	+	1.62512i	−0.816939	+	0.0714729i
$518$	−8.36079	+	4.61168i	−0.367352	+	0.202625i
$519$	−1.39823	+	7.92976i	−0.0613755	+	0.348078i
$520$	2.39183	+	4.22225i	0.104889	+	0.185158i
$521$	3.62790	+	6.28370i	0.158941	+	0.275294i	0.934487	−	0.355997i	$-0.115859\pi$
$521$	3.62790	+	6.28370i	0.158941	+	0.275294i	−0.775546	+	0.631291i	$0.782525\pi$
$522$	−27.0485	+	4.22621i	−1.18388	+	0.184976i
$523$	2.13678	−	4.58234i	0.0934349	−	0.200372i	−0.854036	−	0.520214i	$-0.825852\pi$
$523$	2.13678	−	4.58234i	0.0934349	−	0.200372i	0.947471	+	0.319842i	$0.103630\pi$
$524$	−0.669672	+	0.0912675i	−0.0292548	+	0.00398704i
$525$	15.1539	+	6.81710i	0.661371	+	0.297522i
$526$	−8.43229	−	19.0461i	−0.367665	−	0.830450i
$527$	−37.7025	−	3.29854i	−1.64235	−	0.143687i
$528$	−26.6457	+	32.3487i	−1.15960	+	1.40780i
$529$	19.1115	−	3.36988i	0.830936	−	0.146516i
$530$	2.28400	−	4.25429i	0.0992107	−	0.184794i
$531$		−	26.8517i		−	1.16527i
$532$	6.07180	−	9.47805i	0.263246	−	0.410926i
$533$	−2.65599	−	2.65599i	−0.115044	−	0.115044i
$534$	13.7878	+	55.7957i	0.596657	+	2.41452i
$535$	−30.1895	+	6.90852i	−1.30521	+	0.298681i
$536$	−2.87612	+	5.32845i	−0.124230	+	0.230154i
$537$	−2.87988	+	32.9172i	−0.124276	+	1.42048i
$538$	−4.44039	−	1.71515i	−0.191439	−	0.0739453i
$539$	10.8542	−	18.8000i	0.467522	−	0.809772i
$540$	7.07008	−	1.32956i	0.304248	−	0.0572154i
$541$	17.7346	−	6.45485i	0.762468	−	0.277516i	0.0686255	−	0.997642i	$-0.478139\pi$
$541$	17.7346	−	6.45485i	0.762468	−	0.277516i	0.693842	+	0.720127i	$0.255916\pi$
$542$	−5.70479	−	36.5116i	−0.245042	−	1.56831i
$543$	3.82379	+	1.02458i	0.164095	+	0.0439690i
$544$	−29.0418	+	33.8862i	−1.24516	+	1.45286i
$545$	−19.2019	−	24.6752i	−0.822520	−	1.05697i
$546$	3.46433	+	1.00121i	0.148260	+	0.0428478i
$547$	1.96859	+	22.5010i	0.0841707	+	0.962075i	0.914442	+	0.404716i	$0.132630\pi$
$547$	1.96859	+	22.5010i	0.0841707	+	0.962075i	−0.830272	+	0.557359i	$0.811815\pi$
$548$	−13.5801	−	21.1039i	−0.580114	−	0.901512i
$549$	−5.68334	+	15.6149i	−0.242559	+	0.666426i
$550$	28.6589	+	2.67905i	1.22202	+	0.114235i
$551$	19.1617	−	13.2163i	0.816318	−	0.563032i
$552$	−26.0687	+	39.5973i	−1.10956	+	1.68537i
$553$	−4.22096	−	9.05188i	−0.179494	−	0.384925i
$554$	−13.4074	−	13.9418i	−0.569624	−	0.592332i
$555$	29.8110	−	4.13107i	1.26541	−	0.175354i
$556$	−4.16186	+	1.33309i	−0.176502	+	0.0565356i
$557$	26.7464	+	38.1979i	1.13328	+	1.61849i	0.693640	+	0.720322i	$0.256006\pi$
$557$	26.7464	+	38.1979i	1.13328	+	1.61849i	0.439643	+	0.898173i	$0.355105\pi$
$558$	16.1731	−	18.5268i	0.684661	−	0.784300i
$559$	−2.11124	−	3.65677i	−0.0892959	−	0.154665i
$560$	4.24920	−	10.7384i	0.179561	−	0.453780i
$561$	−77.6745	+	28.2712i	−3.27942	+	1.19361i
$562$	12.0792	+	35.3199i	0.509531	+	1.48988i
$563$	2.69432	+	10.0553i	0.113552	+	0.423782i	0.999175	−	0.0406237i	$-0.0129345\pi$
$563$	2.69432	+	10.0553i	0.113552	+	0.423782i	−0.885622	+	0.464406i	$0.846268\pi$
$564$	12.5790	−	19.9449i	0.529672	−	0.839831i
$565$	13.8530	+	14.9131i	0.582802	+	0.627400i
$566$	−30.5046	−	3.27054i	−1.28220	−	0.137471i
$567$	−4.98743	+	7.12279i	−0.209452	+	0.299129i
$568$	−21.1652	+	15.7423i	−0.888072	+	0.660533i
$569$		−	20.0266i		−	0.839560i	−0.907626	−	0.419780i	$-0.862107\pi$
$569$		−	20.0266i		−	0.839560i	0.907626	−	0.419780i	$-0.137893\pi$
$570$	−28.5696	+	21.0363i	−1.19665	+	0.881112i
$571$		−	3.85586i		−	0.161363i	−0.996740	−	0.0806814i	$-0.974290\pi$
$571$		−	3.85586i		−	0.161363i	0.996740	−	0.0806814i	$-0.0257096\pi$
$572$	6.23934	−	0.300881i	0.260880	−	0.0125805i
$573$	−23.7316	+	33.8922i	−0.991401	+	1.41587i
$574$	−0.952930	+	8.88804i	−0.0397745	+	0.370980i
$575$	32.5571	−	0.442709i	1.35772	−	0.0184622i
$576$	−6.66279	−	28.2240i	−0.277616	−	1.17600i
$577$	−5.91284	−	22.0670i	−0.246155	−	0.918661i	−0.972800	−	0.231648i	$-0.925588\pi$
$577$	−5.91284	−	22.0670i	−0.246155	−	0.918661i	0.726645	−	0.687013i	$-0.241079\pi$
$578$	−60.5374	+	20.7035i	−2.51803	+	0.861151i
$579$	−22.5481	+	8.20682i	−0.937065	+	0.341064i
$580$	16.6945	−	17.0779i	0.693202	−	0.709120i
$581$	6.13706	+	10.6297i	0.254608	+	0.440995i
$582$	10.2414	+	8.94032i	0.424520	+	0.370588i
$583$	−3.56516	−	5.09157i	−0.147654	−	0.210871i
$584$	22.1714	+	17.5469i	0.917461	+	0.726095i
$585$	−4.95971	−	3.75242i	−0.205059	−	0.155144i
$586$	−11.5127	+	11.0713i	−0.475585	+	0.457353i
$587$	4.93217	+	10.5771i	0.203572	+	0.436563i	0.981415	−	0.191896i	$-0.0614638\pi$
$587$	4.93217	+	10.5771i	0.203572	+	0.436563i	−0.777843	+	0.628459i	$0.783686\pi$
$588$	10.6211	+	25.3149i	0.438005	+	1.04397i
$589$	−5.55473	+	20.1593i	−0.228879	+	0.830649i
$590$	14.0219	+	18.7640i	0.577272	+	0.772500i
$591$	18.7299	−	51.4599i	0.770443	−	2.11678i
$592$	−3.81952	−	20.5649i	−0.156981	−	0.845211i
$593$	1.41348	+	16.1562i	0.0580447	+	0.663454i	0.968363	+	0.249545i	$0.0802811\pi$
$593$	1.41348	+	16.1562i	0.0580447	+	0.663454i	−0.910318	+	0.413909i	$0.864163\pi$
$594$	2.57112	−	8.89643i	0.105494	−	0.365025i
$595$	17.9758	−	13.9885i	0.736937	−	0.573473i
$596$	−20.0956	−	25.9436i	−0.823146	−	1.06269i
$597$	−44.6258	−	11.9574i	−1.82641	−	0.489386i
$598$	6.98140	−	1.09081i	0.285491	−	0.0446067i
$599$	2.38623	−	0.868517i	0.0974987	−	0.0354866i	−0.292810	−	0.956171i	$-0.594590\pi$
$599$	2.38623	−	0.868517i	0.0974987	−	0.0354866i	0.390309	+	0.920684i	$0.372368\pi$
$600$	−24.6291	+	26.8030i	−1.00548	+	1.09423i
$601$	−2.29764	+	3.97963i	−0.0937227	+	0.162332i	−0.909075	−	0.416633i	$-0.863210\pi$
$601$	−2.29764	+	3.97963i	−0.0937227	+	0.162332i	0.815352	+	0.578965i	$0.196543\pi$
$602$	−3.62074	+	9.37384i	−0.147571	+	0.382049i
$603$	0.676361	−	7.73084i	0.0275436	−	0.314824i
$604$	−10.2022	+	5.37010i	−0.415122	+	0.218506i
$605$	6.62067	−	10.5500i	0.269168	−	0.428917i
$606$	33.1468	−	8.19098i	1.34650	−	0.332736i
$607$	16.3576	+	16.3576i	0.663936	+	0.663936i	0.956305	−	0.292370i	$-0.0944438\pi$
$607$	16.3576	+	16.3576i	0.663936	+	0.663936i	−0.292370	+	0.956305i	$0.594444\pi$
$608$	15.5166	+	19.1634i	0.629279	+	0.777179i
$609$		−	17.7474i		−	0.719159i
$610$	−4.18251	−	13.8795i	−0.169345	−	0.561963i
$611$	−3.46121	+	0.610305i	−0.140026	+	0.0246903i
$612$	16.9509	−	54.6273i	0.685200	−	2.20818i
$613$	−14.4390	−	1.26325i	−0.583185	−	0.0510221i	−0.208254	−	0.978075i	$-0.566778\pi$
$613$	−14.4390	−	1.26325i	−0.583185	−	0.0510221i	−0.374931	+	0.927053i	$0.622334\pi$
$614$	−21.3237	+	9.44066i	−0.860556	+	0.380994i
$615$	12.8397	−	25.0797i	0.517746	−	1.01131i
$616$	−9.87785	−	11.1096i	−0.397990	−	0.447617i
$617$	19.0767	−	40.9100i	0.767998	−	1.64698i	0.00550033	−	0.999985i	$-0.498249\pi$
$617$	19.0767	−	40.9100i	0.767998	−	1.64698i	0.762497	−	0.646991i	$-0.223973\pi$
$618$	−0.718504	−	4.59855i	−0.0289025	−	0.184981i
$619$	−12.6013	−	21.8262i	−0.506491	−	0.877268i	−0.999972	−	0.00751123i	$-0.997609\pi$
$619$	−12.6013	−	21.8262i	−0.506491	−	0.877268i	0.493481	−	0.869757i	$-0.335724\pi$
$620$	−1.62711	+	21.3920i	−0.0653462	+	0.859123i
$621$	1.81904	−	10.3163i	0.0729955	−	0.413978i
$622$	1.00770	+	1.82692i	0.0404051	+	0.0732529i
$623$	−20.3091	+	1.77681i	−0.813666	+	0.0711866i
$624$	−4.47188	+	6.51191i	−0.179019	+	0.260685i
$625$	24.7291	+	3.67016i	0.989165	+	0.146806i
$626$	0.736145	+	1.09631i	0.0294223	+	0.0438173i
$627$	7.61232	+	45.0313i	0.304007	+	1.79838i
$628$	4.70282	−	1.97310i	0.187663	−	0.0787353i
$629$	14.1097	−	38.7662i	0.562592	−	1.54571i
$630$	0.457147	+	14.7938i	0.0182132	+	0.589399i
$631$	4.94571	−	5.89407i	0.196886	−	0.234639i	−0.658565	−	0.752524i	$-0.728836\pi$
$631$	4.94571	−	5.89407i	0.196886	−	0.234639i	0.855450	+	0.517885i	$0.173281\pi$
$632$	21.7321	−	2.53036i	0.864458	−	0.100652i
$633$	4.34006	−	3.03894i	0.172502	−	0.120787i
$634$	−1.62153	−	23.9059i	−0.0643993	−	0.949424i
$635$	−35.2479	+	22.7938i	−1.39877	+	0.904543i
$636$	7.85442	+	0.307112i	0.311448	+	0.0121778i
$637$	1.72926	−	3.70841i	0.0685158	−	0.146933i
$638$	−9.94807	−	29.0884i	−0.393848	−	1.15162i
$639$	16.9032	−	29.2772i	0.668679	−	1.15819i
$640$	19.3944	+	16.2436i	0.766633	+	0.642086i
$641$	−35.2605	+	29.5870i	−1.39270	+	1.16862i	−0.428474	+	0.903554i	$0.640949\pi$
$641$	−35.2605	+	29.5870i	−1.39270	+	1.16862i	−0.964231	+	0.265064i	$0.914607\pi$
$642$	−31.6455	−	39.2462i	−1.24895	−	1.54892i
$643$	35.3937	+	24.7829i	1.39579	+	0.977343i	0.998212	+	0.0597746i	$0.0190382\pi$
$643$	35.3937	+	24.7829i	1.39579	+	0.977343i	0.397578	+	0.917568i	$0.369851\pi$
$644$	−12.4498	−	11.3043i	−0.490590	−	0.445451i
$645$	21.2390	−	23.4970i	0.836285	−	0.925195i
$646$	7.16763	+	48.1016i	0.282007	+	1.89253i
$647$	3.81556	+	3.81556i	0.150005	+	0.150005i	0.778120	−	0.628115i	$-0.216173\pi$
$647$	3.81556	+	3.81556i	0.150005	+	0.150005i	−0.628115	+	0.778120i	$0.716173\pi$
$648$	−11.3679	−	15.2839i	−0.446573	−	0.600407i
$649$	29.6949	−	5.23602i	1.16563	−	0.205532i
$650$	5.42534	+	0.0322444i	0.212799	+	0.00126473i
$651$	10.2478	+	12.2128i	0.401643	+	0.478659i
$652$	0.464068	+	2.04908i	0.0181743	+	0.0802483i
$653$	−7.66460	+	2.05372i	−0.299939	+	0.0803684i	−0.405650	−	0.914028i	$-0.632955\pi$
$653$	−7.66460	+	2.05372i	−0.299939	+	0.0803684i	0.105711	+	0.994397i	$0.466288\pi$
$654$	22.4075	−	45.6999i	0.876204	−	1.78701i
$655$	−0.284417	+	0.700068i	−0.0111131	+	0.0273539i
$656$	−17.8217	−	8.11367i	−0.695820	−	0.316786i
$657$	−35.0029	−	9.37900i	−1.36559	−	0.365910i
$658$	6.30107	+	5.50056i	0.245641	+	0.214434i
$659$	−4.68525	+	26.5714i	−0.182512	+	1.03507i	0.746600	+	0.665274i	$0.231685\pi$
$659$	−4.68525	+	26.5714i	−0.182512	+	1.03507i	−0.929111	+	0.369801i	$0.879426\pi$
$660$	16.5247	+	43.8461i	0.643222	+	1.70671i
$661$	5.46778	+	4.58802i	0.212672	+	0.178453i	0.742901	−	0.669402i	$-0.233449\pi$
$661$	5.46778	+	4.58802i	0.212672	+	0.178453i	−0.530229	+	0.847855i	$0.677894\pi$
$662$	−7.60758	−	0.148674i	−0.295677	−	0.00577836i
$663$	−14.1206	+	6.58456i	−0.548400	+	0.255723i
$664$	−26.3346	+	5.42549i	−1.02198	+	0.210550i
$665$	−5.80794	−	11.1644i	−0.225222	−	0.432936i
$666$	14.9439	+	22.2554i	0.579066	+	0.862378i
$667$	−14.6968	−	31.5174i	−0.569063	−	1.22036i
$668$	16.0576	−	10.3329i	0.621288	−	0.399792i
$669$	22.1340	−	26.3783i	0.855752	−	1.01984i
$670$	3.56438	+	5.75550i	0.137704	+	0.222354i
$671$	−18.3765	−	3.24027i	−0.709416	−	0.125089i
$672$	18.7442	−	1.44298i	0.723071	−	0.0556641i
$673$	1.37854	−	5.14478i	0.0531388	−	0.198317i	−0.934253	−	0.356610i	$-0.883932\pi$
$673$	1.37854	−	5.14478i	0.0531388	−	0.198317i	0.987392	+	0.158293i	$0.0505991\pi$
$674$	−28.1121	+	38.5237i	−1.08284	+	1.48388i
$675$	2.64790	−	7.59479i	0.101918	−	0.292324i
$676$	−24.5952	+	3.35200i	−0.945970	+	0.128923i
$677$	8.53316	+	31.8462i	0.327956	+	1.22395i	0.911307	+	0.411728i	$0.135075\pi$
$677$	8.53316	+	31.8462i	0.327956	+	1.22395i	−0.583351	+	0.812220i	$0.698259\pi$
$678$	−11.9390	+	30.9091i	−0.458513	+	1.18706i
$679$	−3.69401	+	3.09964i	−0.141763	+	0.118953i
$680$	16.6809	+	47.0252i	0.639685	+	1.80333i
$681$	5.76515	+	32.6958i	0.220921	+	1.25291i
$682$	23.6422	+	14.2729i	0.905305	+	0.546537i
$683$	29.4647	−	29.4647i	1.12744	−	1.12744i	0.136843	−	0.990593i	$-0.456304\pi$
$683$	29.4647	−	29.4647i	1.12744	−	1.12744i	0.990593	−	0.136843i	$-0.0436957\pi$
$684$	−27.9943	−	14.6626i	−1.07039	−	0.560640i
$685$	−28.0221	+	1.41441i	−1.07067	+	0.0540417i
$686$	−21.8620	+	5.40238i	−0.834697	+	0.206264i
$687$	−15.6287	+	22.3201i	−0.596271	+	0.851564i
$688$	−16.9910	−	13.9955i	−0.647777	−	0.533574i
$689$	−0.753079	−	0.897484i	−0.0286900	−	0.0341914i
$690$	23.8734	+	47.3230i	0.908846	+	1.80156i
$691$	−2.33917	−	1.35052i	−0.0889862	−	0.0513762i	0.454847	−	0.890570i	$-0.349694\pi$
$691$	−2.33917	−	1.35052i	−0.0889862	−	0.0513762i	−0.543833	+	0.839194i	$0.683027\pi$
$692$	3.78621	−	4.98107i	0.143930	−	0.189352i
$693$	17.2674	+	8.05191i	0.655934	+	0.305867i
$694$	6.01081	+	4.38630i	0.228167	+	0.166502i
$695$	−1.02506	+	4.77724i	−0.0388829	+	0.181211i
$696$	36.8986	+	12.2450i	1.39864	+	0.464147i
$697$	−22.1523	−	31.6368i	−0.839079	−	1.19833i
$698$	−19.6449	−	35.6154i	−0.743570	−	1.34806i
$699$	−8.28864	−	6.95499i	−0.313505	−	0.263062i
$700$	−8.04473	−	10.0992i	−0.304062	−	0.381713i
$701$	−41.1865	−	14.9907i	−1.55559	−	0.566189i	−0.585871	−	0.810404i	$-0.699247\pi$
$701$	−41.1865	−	14.9907i	−1.55559	−	0.566189i	−0.969721	+	0.244215i	$0.921470\pi$
$702$	0.336633	−	1.71274i	0.0127054	−	0.0646430i
$703$	−19.6585	−	11.5359i	−0.741434	−	0.435086i
$704$	29.9133	−	12.8719i	1.12740	−	0.485128i
$705$	−12.3320	−	23.3015i	−0.464451	−	0.877584i
$706$	−13.3793	+	12.8664i	−0.503538	+	0.484235i
$707$	1.05556	+	12.0651i	0.0396984	+	0.453755i
$708$	−17.4532	+	33.9033i	−0.655932	+	1.27416i
$709$	−11.1223	−	1.96116i	−0.417706	−	0.0736528i	−0.0391545	−	0.999233i	$-0.512466\pi$
$709$	−11.1223	−	1.96116i	−0.417706	−	0.0736528i	−0.378551	+	0.925580i	$0.623578\pi$
$710$	3.47652	+	29.2856i	0.130471	+	1.09907i
$711$	−24.2838	+	14.0203i	−0.910715	+	0.525802i
$712$	10.3183	−	43.4507i	0.386696	−	1.62838i
$713$	28.3126	+	13.2024i	1.06032	+	0.494433i
$714$	33.2922	+	16.3238i	1.24593	+	0.610903i
$715$	3.18262	−	6.21658i	0.119023	−	0.232487i
$716$	13.6966	−	21.7169i	0.511867	−	0.811600i
$717$	3.64242	−	41.6330i	0.136029	−	1.55481i
$718$	29.1512	+	36.1528i	1.08791	+	1.34921i
$719$	−4.61615	−	26.1795i	−0.172153	−	0.976330i	−0.941379	−	0.337352i	$-0.890469\pi$
$719$	−4.61615	−	26.1795i	−0.172153	−	0.976330i	0.769225	−	0.638978i	$-0.220642\pi$
$720$	−31.0733	−	9.25673i	−1.15803	−	0.344978i
$721$	1.65095			0.0614845
$722$	26.8548	+	0.904870i	0.999433	+	0.0336758i
$723$	3.78652	−	3.78652i	0.140822	−	0.140822i
$724$	−2.27731	−	2.06778i	−0.0846356	−	0.0768484i
$725$	−7.26080	−	25.6950i	−0.269659	−	0.954287i
$726$	20.1602	+	2.16147i	0.748216	+	0.0802198i
$727$	−11.2789	−	0.986773i	−0.418310	−	0.0365974i	−0.123942	−	0.992289i	$-0.539554\pi$
$727$	−11.2789	−	0.986773i	−0.418310	−	0.0365974i	−0.294368	+	0.955692i	$0.595109\pi$
$728$	−2.03729	−	1.92379i	−0.0755069	−	0.0713004i
$729$	31.8989	+	18.4168i	1.18144	+	0.682105i
$730$	29.3576	−	11.7244i	1.08658	−	0.433938i
$731$	−14.8493	−	40.7982i	−0.549222	−	1.50897i
$732$	17.3253	−	16.0214i	0.640360	−	0.592168i
$733$	6.41762	−	23.9509i	0.237040	−	0.884646i	−0.740178	−	0.672411i	$-0.765259\pi$
$733$	6.41762	−	23.9509i	0.237040	−	0.884646i	0.977219	−	0.212236i	$-0.0680744\pi$
$734$	−32.6595	+	2.21529i	−1.20549	+	0.0817679i
$735$	30.4570	+	3.79927i	1.12342	+	0.140138i
$736$	32.0927	−	18.0849i	1.18295	−	0.666617i
$737$	8.68131	−	0.759516i	0.319780	−	0.0279771i
$738$	25.0916	+	0.490361i	0.923635	+	0.0180504i
$739$	8.07540	+	2.93921i	0.297059	+	0.108120i	0.486250	−	0.873820i	$-0.338364\pi$
$739$	8.07540	+	2.93921i	0.297059	+	0.108120i	−0.189191	+	0.981940i	$0.560587\pi$
$740$	−22.0645	−	7.74833i	−0.811106	−	0.284834i
$741$	2.16915	+	8.33055i	0.0796856	+	0.306030i
$742$	−0.537720	+	2.73583i	−0.0197403	+	0.100436i
$743$	−37.7413	+	17.5991i	−1.38459	+	0.645647i	−0.965045	−	0.262086i	$-0.915590\pi$
$743$	−37.7413	+	17.5991i	−1.38459	+	0.645647i	−0.419549	+	0.907733i	$0.637812\pi$
$744$	−32.4624	+	12.8798i	−1.19013	+	0.472197i
$745$	−36.3424	+	5.03615i	−1.33148	+	0.184510i
$746$	19.4420	+	5.61883i	0.711821	+	0.205720i
$747$	28.2279	−	19.7654i	1.03280	−	0.723178i
$748$	63.7169	+	8.09356i	2.32972	+	0.295930i
$749$	15.4870	−	8.94143i	0.565883	−	0.326713i
$750$	12.2710	+	38.8029i	0.448074	+	1.41688i
$751$	4.81717	+	13.2351i	0.175781	+	0.482954i	0.996026	−	0.0890574i	$-0.0283855\pi$
$751$	4.81717	+	13.2351i	0.175781	+	0.482954i	−0.820246	+	0.572012i	$0.806163\pi$
$752$	−15.7838	+	9.30539i	−0.575574	+	0.339333i
$753$	39.6091	−	10.6132i	1.44343	−	0.386767i
$754$	−2.34583	−	5.29855i	−0.0854300	−	0.192962i
$755$	−0.474694	+	12.8813i	−0.0172759	+	0.468799i
$756$	−3.67589	+	1.93487i	−0.133691	+	0.0703704i
$757$	−9.83362	−	6.88558i	−0.357409	−	0.250261i	0.381056	−	0.924552i	$-0.375560\pi$
$757$	−9.83362	−	6.88558i	−0.357409	−	0.250261i	−0.738466	+	0.674291i	$0.764449\pi$
$758$	38.6715	+	23.3462i	1.40461	+	0.847971i
$759$	68.2294			2.47657
$760$	27.2192	−	4.37231i	0.987343	−	0.158600i
$761$	29.9629			1.08615			0.543077	−	0.839683i	$-0.317259\pi$
$761$	29.9629			1.08615			0.543077	+	0.839683i	$0.317259\pi$
$762$	−58.4980	−	35.3155i	−2.11916	−	1.27935i
$763$	14.7890	+	10.3553i	0.535396	+	0.374889i
$764$	28.4490	−	14.9746i	1.02925	−	0.541763i
$765$	−43.5222	−	46.8526i	−1.57355	−	1.69396i
$766$	−0.102714	−	0.232002i	−0.00371122	−	0.00838258i
$767$	5.48985	−	1.47100i	0.198227	−	0.0531148i
$768$	−9.93268	+	39.9667i	−0.358415	+	1.44217i
$769$	6.59077	+	18.1080i	0.237669	+	0.652991i	0.999983	+	0.00578336i	$0.00184091\pi$
$769$	6.59077	+	18.1080i	0.237669	+	0.652991i	−0.762314	+	0.647207i	$0.775937\pi$
$770$	−16.2711	+	3.39030i	−0.586370	+	0.122178i
$771$	31.6342	−	18.2640i	1.13928	−	0.657762i
$772$	18.4963	+	2.34947i	0.665697	+	0.0845594i
$773$	−30.2085	+	21.1522i	−1.08653	+	0.760793i	−0.972551	−	0.232691i	$-0.925247\pi$
$773$	−30.2085	+	21.1522i	−1.08653	+	0.760793i	−0.113974	+	0.993484i	$0.536358\pi$
$774$	27.1031	+	7.83294i	0.974201	+	0.281549i
$775$	19.8335	+	13.4894i	0.712439	+	0.484554i
$776$	−3.89575	−	9.81888i	−0.139849	−	0.352477i
$777$	−15.7500	+	7.34433i	−0.565027	+	0.263477i
$778$	5.67495	−	28.8732i	0.203457	−	1.03516i
$779$	−19.4027	+	8.88115i	−0.695174	+	0.318200i
$780$	3.82316	+	7.96158i	0.136891	+	0.285070i
$781$	35.6732	+	12.9840i	1.27649	+	0.464604i
$782$	72.6414	+	1.41962i	2.59765	+	0.0507654i
$783$	−8.55776	+	0.748707i	−0.305829	+	0.0267566i
$784$	1.66561	−	21.2664i	0.0594859	−	0.759516i
$785$	0.705801	−	5.65808i	0.0251911	−	0.201946i
$786$	−1.22727	+	0.0832454i	−0.0437752	+	0.00296926i
$787$	−4.61877	+	17.2375i	−0.164641	+	0.614450i	0.833444	+	0.552604i	$0.186366\pi$
$787$	−4.61877	+	17.2375i	−0.164641	+	0.614450i	−0.998086	+	0.0618466i	$0.980301\pi$
$788$	−31.2415	+	28.8903i	−1.11293	+	1.02917i
$789$	−12.9659	−	35.6235i	−0.461598	−	1.26823i
$790$	9.64817	−	22.4783i	0.343266	−	0.799742i
$791$	−10.1786	−	5.87663i	−0.361910	−	0.208949i
$792$	−28.6546	+	30.3452i	−1.01820	+	1.07827i
$793$	−3.50381	−	0.306544i	−0.124424	−	0.0108857i
$794$	−16.5091	−	1.77002i	−0.585887	−	0.0628158i
$795$	4.67141	−	7.44384i	0.165678	−	0.264006i
$796$	26.5775	+	24.1321i	0.942015	+	0.855341i
$797$	20.1994	−	20.1994i	0.715501	−	0.715501i	−0.252179	−	0.967681i	$-0.581147\pi$
$797$	20.1994	−	20.1994i	0.715501	−	0.715501i	0.967681	+	0.252179i	$0.0811473\pi$
$798$	12.1929	−	16.4629i	0.431623	−	0.582780i
$799$	−36.1380			−1.27847
$800$	26.5478	−	9.75778i	0.938606	−	0.344990i
$801$	9.93894	+	56.3665i	0.351175	+	1.99161i
$802$	−26.9648	−	33.4413i	−0.952161	−	1.18085i
$803$	3.54662	−	40.5380i	0.125157	−	1.43056i
$804$	−5.87891	+	9.32142i	−0.207333	+	0.328741i
$805$	−17.8920	+	5.77536i	−0.630611	+	0.203555i
$806$	4.67380	+	2.29165i	0.164628	+	0.0807200i
$807$	−7.85184	−	3.66137i	−0.276398	−	0.128886i
$808$	−25.8129	−	6.12986i	−0.908095	−	0.215648i
$809$	−38.5373	+	22.2495i	−1.35490	+	0.782251i	−0.988931	−	0.148377i	$-0.952595\pi$
$809$	−38.5373	+	22.2495i	−1.35490	+	0.782251i	−0.365968	+	0.930628i	$0.619262\pi$
$810$	−21.1478	+	2.51047i	−0.743057	+	0.0882090i
$811$	−5.34618	−	0.942675i	−0.187730	−	0.0331018i	0.0789928	−	0.996875i	$-0.474830\pi$
$811$	−5.34618	−	0.942675i	−0.187730	−	0.0331018i	−0.266722	+	0.963773i	$0.585941\pi$
$812$	−6.31187	+	12.2609i	−0.221503	+	0.430275i
$813$	−5.86195	−	67.0024i	−0.205587	−	2.34988i
$814$	−21.6978	+	20.8660i	−0.760509	+	0.731354i
$815$	2.24500	+	0.691100i	0.0786388	+	0.0242082i
$816$	−56.9093	+	57.9552i	−1.99222	+	2.02884i
$817$	−23.6525	+	3.99834i	−0.827495	+	0.139884i
$818$	4.44310	−	22.6058i	0.155349	−	0.790392i
$819$	3.37460	+	1.22825i	0.117918	+	0.0429187i
$820$	−17.7900	+	12.7601i	−0.621255	+	0.445602i
$821$	−29.6049	−	24.8415i	−1.03322	−	0.866973i	−0.0419875	−	0.999118i	$-0.513369\pi$
$821$	−29.6049	−	24.8415i	−1.03322	−	0.866973i	−0.991230	+	0.132145i	$0.957813\pi$
$822$	−22.0601	−	39.9941i	−0.769435	−	1.39496i
$823$	−24.6533	−	35.2085i	−0.859359	−	1.22729i	−0.972311	−	0.233691i	$-0.924920\pi$
$823$	−24.6533	−	35.2085i	−0.859359	−	1.22729i	0.112952	−	0.993600i	$-0.463969\pi$
$824$	−1.13909	+	3.43249i	−0.0396822	+	0.119577i
$825$	51.7103	+	8.39464i	1.80032	+	0.292264i
$826$	−10.9260	−	7.97311i	−0.380165	−	0.277420i
$827$	38.4933	+	17.9497i	1.33854	+	0.624172i	0.954242	−	0.299036i	$-0.0966650\pi$
$827$	38.4933	+	17.9497i	1.33854	+	0.624172i	0.384300	+	0.923208i	$0.374443\pi$
$828$	−28.5699	+	37.5861i	−0.992873	+	1.30621i
$829$	−1.16081	−	0.670191i	−0.0403164	−	0.0232767i	0.479706	−	0.877429i	$-0.340743\pi$
$829$	−1.16081	−	0.670191i	−0.0403164	−	0.0232767i	−0.520023	+	0.854152i	$0.674077\pi$
$830$	−9.40419	+	28.5525i	−0.326424	+	0.991073i
$831$	−22.6286	−	26.9677i	−0.784976	−	0.935498i
$832$	5.40541	−	2.90839i	0.187399	−	0.100830i
$833$	24.1319	−	34.4639i	0.836119	−	1.19410i
$834$	−7.72152	+	1.90808i	−0.267374	+	0.0660715i
$835$	−1.07620	−	21.3216i	−0.0372435	−	0.737866i
$836$	10.7564	−	33.8177i	0.372017	−	1.16961i
$837$	5.45670	−	5.45670i	0.188611	−	0.188611i
$838$	−14.1946	−	8.56935i	−0.490344	−	0.296023i
$839$	3.21343	+	18.2243i	0.110940	+	0.629172i	0.988681	+	0.150036i	$0.0479389\pi$
$839$	3.21343	+	18.2243i	0.110940	+	0.629172i	−0.877741	+	0.479136i	$0.840950\pi$
$840$	9.03855	−	18.9759i	0.311860	−	0.654732i
$841$	0.369218	−	0.309811i	0.0127317	−	0.0106831i
$842$	−20.1661	+	52.2086i	−0.694971	+	1.79923i
$843$	17.5838	+	65.6235i	0.605617	+	2.26019i
$844$	−4.07918	+	0.555938i	−0.140411	+	0.0191362i
$845$	−10.4459	+	25.7116i	−0.359349	+	0.884505i
$846$	13.8424	−	18.9690i	0.475911	−	0.652168i
$847$	−1.86143	+	6.94697i	−0.0639597	+	0.238701i
$848$	−5.31708	−	3.00560i	−0.182589	−	0.103213i
$849$	−54.9890	−	9.69604i	−1.88722	−	0.332767i
$850$	54.8795	+	10.0134i	1.88235	+	0.343457i
$851$	−21.8884	+	26.0855i	−0.750323	+	0.894200i
$852$	−40.3718	+	25.9788i	−1.38312	+	0.890020i
$853$	−9.48759	−	20.3462i	−0.324849	−	0.696641i	0.674275	−	0.738480i	$-0.264456\pi$
$853$	−9.48759	−	20.3462i	−0.324849	−	0.696641i	−0.999124	+	0.0418391i	$0.986678\pi$
$854$	4.66615	+	6.94909i	0.159672	+	0.237793i
$855$	−29.8038	+	18.9757i	−1.01927	+	0.648955i
$856$	7.90470	+	38.3684i	0.270177	+	1.31140i
$857$	37.8050	−	17.6288i	1.29139	−	0.602187i	0.349136	−	0.937072i	$-0.386475\pi$
$857$	37.8050	−	17.6288i	1.29139	−	0.602187i	0.942259	+	0.334885i	$0.108697\pi$
$858$	11.3668	+	0.222139i	0.388056	+	0.00758370i
$859$	11.9010	+	9.98614i	0.406057	+	0.340723i	0.822829	−	0.568288i	$-0.192394\pi$
$859$	11.9010	+	9.98614i	0.406057	+	0.340723i	−0.416772	+	0.909011i	$0.636839\pi$
$860$	−23.0299	+	8.67950i	−0.785314	+	0.295968i
$861$	−2.82511	+	16.0220i	−0.0962795	+	0.546028i
$862$	−22.1577	−	19.3427i	−0.754693	−	0.658815i
$863$	29.4768	+	7.89828i	1.00340	+	0.268860i	0.722870	−	0.690984i	$-0.242823\pi$
$863$	29.4768	+	7.89828i	1.00340	+	0.268860i	0.280531	+	0.959845i	$0.409489\pi$
$864$	−1.48656	−	8.97754i	−0.0505739	−	0.305422i
$865$	−2.72083	−	6.44439i	−0.0925110	−	0.219116i
$866$	21.8091	−	44.4795i	0.741104	−	1.51147i
$867$	−112.477	+	30.1381i	−3.81992	+	1.02354i
$868$	−2.73628	−	12.0820i	−0.0928755	−	0.410090i
$869$	−20.2401	−	24.1212i	−0.686598	−	0.818256i
$870$	32.4182	−	28.9546i	1.09908	−	0.981655i
$871$	1.61763	−	0.285231i	0.0548112	−	0.00966469i
$872$	−31.7337	+	23.6030i	−1.07464	+	0.799299i
$873$	9.57310	+	9.57310i	0.324001	+	0.324001i
$874$	8.02014	−	39.3334i	0.271285	−	1.33047i
$875$	−14.2708	+	2.17573i	−0.482440	+	0.0735530i
$876$	38.0988	+	34.5934i	1.28724	+	1.16880i
$877$	−9.21917	−	6.45533i	−0.311309	−	0.217981i	0.407471	−	0.913218i	$-0.366411\pi$
$877$	−9.21917	−	6.45533i	−0.311309	−	0.217981i	−0.718781	+	0.695237i	$0.755299\pi$
$878$	−15.0707	−	18.6904i	−0.508611	−	0.630769i
$879$	−22.2690	+	18.6859i	−0.751114	+	0.630260i
$880$	4.17767	−	36.1685i	0.140829	−	1.21924i
$881$	4.44880	−	7.70554i	0.149884	−	0.259606i	−0.781301	−	0.624155i	$-0.785443\pi$
$881$	4.44880	−	7.70554i	0.149884	−	0.259606i	0.931184	+	0.364549i	$0.118777\pi$
$882$	8.84675	+	25.8681i	0.297886	+	0.871024i
$883$	11.5003	−	24.6625i	0.387016	−	0.829959i	−0.612212	−	0.790693i	$-0.709720\pi$
$883$	11.5003	−	24.6625i	0.387016	−	0.829959i	0.999229	−	0.0392660i	$-0.0125020\pi$
$884$	12.0972	+	0.473007i	0.406873	+	0.0159089i
$885$	23.1505	+	35.7996i	0.778197	+	1.20339i
$886$	−2.29912	−	33.8954i	−0.0772404	−	1.13874i
$887$	46.1601	−	32.3217i	1.54990	−	1.08525i	0.589089	−	0.808068i	$-0.299487\pi$
$887$	46.1601	−	32.3217i	1.54990	−	1.08525i	0.960816	−	0.277187i	$-0.0894020\pi$
$888$	−4.40274	−	37.8132i	−0.147746	−	1.26893i
$889$	15.5799	−	18.5674i	0.522532	−	0.622729i
$890$	−36.3797	−	34.1987i	−1.21945	−	1.14634i
$891$	−9.37603	+	25.7604i	−0.314109	+	0.863007i
$892$	−24.6730	+	10.3517i	−0.826114	+	0.346602i
$893$	−3.60611	+	19.6382i	−0.120674	+	0.657168i
$894$	−33.2951	−	49.5849i	−1.11356	−	1.65837i
$895$	−13.4277	−	25.3717i	−0.448839	−	0.848084i
$896$	−13.4628	−	5.66948i	−0.449760	−	0.189404i
$897$	12.8115	−	1.12086i	0.427765	−	0.0374246i
$898$	−5.09471	−	9.23651i	−0.170013	−	0.308226i
$899$	4.44855	−	25.2290i	0.148368	−	0.841434i
$900$	−26.2773	+	24.9710i	−0.875909	+	0.832367i
$901$	−6.02324	−	10.4326i	−0.200663	−	0.347559i
$902$	4.35052	+	27.8441i	0.144856	+	0.927106i
$903$	−7.72930	+	16.5755i	−0.257215	+	0.551599i
$904$	19.2410	−	17.1078i	0.639947	−	0.568996i
$905$	−3.27281	+	1.05643i	−0.108792	+	0.0351169i
$906$	−19.1871	+	8.49471i	−0.637449	+	0.282218i
$907$	37.9136	+	3.31701i	1.25890	+	0.110139i	0.697003	−	0.717068i	$-0.254516\pi$
$907$	37.9136	+	3.31701i	1.25890	+	0.110139i	0.561896	+	0.827208i	$0.310072\pi$
$908$	7.64538	−	24.6386i	0.253721	−	0.817661i
$909$	33.4859	−	5.90446i	1.11066	−	0.195839i
$910$	−2.99956	+	0.903903i	−0.0994343	+	0.0299641i
$911$			15.0669i			0.499190i	0.968350	+	0.249595i	$0.0802975\pi$
$911$			15.0669i			0.499190i	−0.968350	+	0.249595i	$0.919703\pi$
$912$	25.8154	+	36.7091i	0.854834	+	1.21556i
$913$	27.3626	+	27.3626i	0.905570	+	0.905570i
$914$	−9.59362	+	2.37070i	−0.317329	+	0.0784158i
$915$	−5.88531	−	25.7182i	−0.194562	−	0.850218i
$916$	18.7354	−	9.86169i	0.619035	−	0.325840i
$917$	0.0380283	−	0.434665i	0.00125580	−	0.0143539i
$918$	6.46682	−	16.7421i	0.213437	−	0.552573i
$919$	0.196030	−	0.339534i	0.00646643	−	0.0112002i	−0.862774	−	0.505590i	$-0.831275\pi$
$919$	0.196030	−	0.339534i	0.00646643	−	0.0112002i	0.869241	+	0.494389i	$0.164608\pi$
$920$	0.337274	−	41.1842i	0.0111196	−	1.35780i
$921$	−39.8835	+	14.5164i	−1.31421	+	0.478332i
$922$	−8.31500	+	1.29918i	−0.273840	+	0.0427863i
$923$	6.91172	+	1.85199i	0.227502	+	0.0609590i
$924$	−16.5684	−	21.3900i	−0.545059	−	0.703678i
$925$	−19.7984	+	17.0769i	−0.650968	+	0.561485i
$926$	1.88623	−	6.52663i	0.0619854	−	0.214478i
$927$	−0.403973	−	4.61744i	−0.0132682	−	0.151656i
$928$	−21.1368	−	21.5826i	−0.693851	−	0.708485i
$929$	−3.54830	+	9.74887i	−0.116416	+	0.319850i	−0.984192	−	0.177106i	$-0.943327\pi$
$929$	−3.54830	+	9.74887i	−0.116416	+	0.319850i	0.867776	+	0.496956i	$0.165549\pi$
$930$	−5.58942	+	38.6443i	−0.183284	+	1.26720i
$931$	−16.3204	−	16.5529i	−0.534881	−	0.542499i
$932$	3.25274	+	7.75279i	0.106547	+	0.253951i
$933$	1.60481	+	3.44154i	0.0525393	+	0.112671i
$934$	−10.3838	+	9.98577i	−0.339770	+	0.326744i
$935$	43.3269	−	57.2666i	1.41694	−	1.87282i
$936$	−4.88202	+	6.16870i	−0.159574	+	0.201630i
$937$	−12.7052	−	18.1449i	−0.415061	−	0.592769i	0.556123	−	0.831100i	$-0.312288\pi$
$937$	−12.7052	−	18.1449i	−0.415061	−	0.592769i	−0.971184	+	0.238331i	$0.923400\pi$
$938$	−2.94486	−	2.57074i	−0.0961531	−	0.0839375i
$939$	1.20170	+	2.08140i	0.0392160	+	0.0679240i
$940$	0.232526	+	20.4840i	0.00758416	+	0.668113i
$941$	−2.17179	+	0.790468i	−0.0707984	+	0.0257685i	−0.377177	−	0.926141i	$-0.623105\pi$
$941$	−2.17179	+	0.790468i	−0.0707984	+	0.0257685i	0.306378	+	0.951910i	$0.400883\pi$
$942$	8.78264	−	3.00362i	0.286154	−	0.0978632i
$943$	8.25093	+	30.7929i	0.268687	+	1.00275i
$944$	24.1155	−	17.2152i	0.784892	−	0.560306i
$945$	−0.171034	+	4.64118i	−0.00556373	+	0.150978i
$946$	−3.37730	+	31.5003i	−0.109805	+	1.02416i
$947$	0.186725	−	0.266671i	0.00606775	−	0.00866564i	−0.816107	−	0.577901i	$-0.803872\pi$
$947$	0.186725	−	0.266671i	0.00606775	−	0.00866564i	0.822174	+	0.569236i	$0.192761\pi$
$948$	39.7740	−	1.91803i	1.29180	−	0.0622946i
$949$		−	7.67016i		−	0.248984i
$950$	10.9178	−	28.8236i	0.354220	−	0.935162i
$951$		−	43.6093i		−	1.41413i
$952$	−17.1947	−	23.1179i	−0.557283	−	0.749255i
$953$	33.9900	−	48.5427i	1.10104	−	1.57245i	0.320614	−	0.947210i	$-0.396111\pi$
$953$	33.9900	−	48.5427i	1.10104	−	1.57245i	0.780430	−	0.625243i	$-0.215000\pi$
$954$	7.78327	+	0.834481i	0.251993	+	0.0270173i
$955$	1.32369	−	35.9198i	0.0428336	−	1.16234i
$956$	−17.3232	+	27.4672i	−0.560273	+	0.888352i
$957$	−14.4814	−	54.0455i	−0.468119	−	1.74704i
$958$	−2.36024	−	6.90139i	−0.0762559	−	0.222974i
$959$	15.2243	−	5.54118i	0.491617	−	0.178934i
$960$	33.2167	+	31.8848i	1.07207	+	1.02908i
$961$	−3.99338	−	6.91674i	−0.128819	−	0.223121i
$962$	−3.73145	+	4.27450i	−0.120307	+	0.137815i
$963$	−28.7973	−	41.1268i	−0.927980	−	1.32529i
$964$	−3.96264	+	1.26928i	−0.127628	+	0.0408807i
$965$	12.5773	−	16.6239i	0.404878	−	0.535142i
$966$	−21.2146	−	22.0603i	−0.682569	−	0.709779i
$967$	−14.0214	−	30.0691i	−0.450899	−	0.966957i	−0.992028	−	0.126017i	$-0.959781\pi$
$967$	−14.0214	−	30.0691i	−0.450899	−	0.966957i	0.541129	−	0.840940i	$-0.317997\pi$
$968$	−13.1592	−	8.66328i	−0.422951	−	0.278448i
$969$	7.09072	+	88.2282i	0.227787	+	2.83430i
$970$	−11.6887	−	1.69063i	−0.375302	−	0.0542828i
$971$	−18.3339	+	50.3721i	−0.588364	+	1.61652i	0.185130	+	0.982714i	$0.440729\pi$
$971$	−18.3339	+	50.3721i	−0.588364	+	1.61652i	−0.773494	+	0.633804i	$0.781493\pi$
$972$	−23.9828	−	37.2699i	−0.769248	−	1.19543i
$973$	−0.245892	−	2.81056i	−0.00788293	−	0.0901023i
$974$	−3.60986	−	1.04327i	−0.115667	−	0.0334285i
$975$	9.84764	+	0.726785i	0.315377	+	0.0232757i
$976$	−17.6674	+	4.90680i	−0.565519	+	0.157063i
$977$	−10.7197	−	2.87233i	−0.342953	−	0.0918940i	0.0832314	−	0.996530i	$-0.473476\pi$
$977$	−10.7197	−	2.87233i	−0.342953	−	0.0918940i	−0.426185	+	0.904636i	$0.640143\pi$
$978$	0.590295	+	3.77799i	0.0188755	+	0.120807i
$979$	−60.3968	+	21.9826i	−1.93029	+	0.702568i
$980$	−19.6903	−	13.4568i	−0.628984	−	0.429863i
$981$	25.3435	−	43.8962i	0.809156	−	1.40150i
$982$	−20.0952	−	7.76199i	−0.641264	−	0.247695i
$983$	−2.27046	+	25.9514i	−0.0724164	+	0.827723i	0.869950	+	0.493140i	$0.164151\pi$
$983$	−2.27046	+	25.9514i	−0.0724164	+	0.827723i	−0.942366	+	0.334583i	$0.891405\pi$
$984$	−31.3622	−	16.9283i	−0.999791	−	0.539655i
$985$	10.6126	+	46.3759i	0.338145	+	1.47766i
$986$	−14.2934	−	57.8416i	−0.455194	−	1.84205i
$987$	10.7643	+	10.7643i	0.342631	+	0.342631i
$988$	1.46419	−	6.52670i	0.0465821	−	0.207642i
$989$			35.8371i			1.13956i
$990$	13.4635	+	44.6781i	0.427900	+	1.41996i
$991$	11.3308	−	1.99792i	0.359934	−	0.0634660i	0.00924281	−	0.999957i	$-0.497058\pi$
$991$	11.3308	−	1.99792i	0.359934	−	0.0634660i	0.350691	+	0.936491i	$0.385947\pi$
$992$	27.0077	+	2.64713i	0.857496	+	0.0840463i
$993$	−13.7959	−	1.20699i	−0.437801	−	0.0383026i
$994$	−6.89385	−	15.5712i	−0.218660	−	0.493889i
$995$	38.1955	−	12.3291i	1.21088	−	0.390859i
$996$	−48.4880	+	6.60828i	−1.53640	+	0.209391i
$997$	−8.68743	+	18.6303i	−0.275134	+	0.590026i	−0.994516	−	0.104589i	$-0.966647\pi$
$997$	−8.68743	+	18.6303i	−0.275134	+	0.590026i	0.719382	+	0.694615i	$0.244425\pi$
$998$	34.1731	−	5.33940i	1.08173	−	0.169016i
$999$	4.20588	+	7.28479i	0.133068	+	0.230481i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bj.a.23.10	✓	672
4.3	odd	2	inner	380.2.bj.a.23.28	yes	672
5.2	odd	4	inner	380.2.bj.a.327.39	yes	672
19.5	even	9	inner	380.2.bj.a.43.3	yes	672
20.7	even	4	inner	380.2.bj.a.327.3	yes	672
76.43	odd	18	inner	380.2.bj.a.43.39	yes	672
95.62	odd	36	inner	380.2.bj.a.347.28	yes	672
380.347	even	36	inner	380.2.bj.a.347.10	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bj.a.23.10	✓	672	1.1	even	1	trivial
380.2.bj.a.23.28	yes	672	4.3	odd	2	inner
380.2.bj.a.43.3	yes	672	19.5	even	9	inner
380.2.bj.a.43.39	yes	672	76.43	odd	18	inner
380.2.bj.a.327.3	yes	672	20.7	even	4	inner
380.2.bj.a.327.39	yes	672	5.2	odd	4	inner
380.2.bj.a.347.10	yes	672	380.347	even	36	inner
380.2.bj.a.347.28	yes	672	95.62	odd	36	inner

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bj (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21069 - 0.730902i) q^{2} +(-2.10842 - 1.47633i) q^{3} +(0.931564 + 1.76980i) q^{4} +(2.23455 + 0.0823462i) q^{5} +(1.47360 + 3.32843i) q^{6} +(-1.24717 + 0.334178i) q^{7} +(0.165710 - 2.82357i) q^{8} +(1.23982 + 3.40636i) q^{9} +O(q^{10})\)	\(q+(-1.21069 - 0.730902i) q^{2} +(-2.10842 - 1.47633i) q^{3} +(0.931564 + 1.76980i) q^{4} +(2.23455 + 0.0823462i) q^{5} +(1.47360 + 3.32843i) q^{6} +(-1.24717 + 0.334178i) q^{7} +(0.165710 - 2.82357i) q^{8} +(1.23982 + 3.40636i) q^{9} +(-2.64517 - 1.73293i) q^{10} +(-3.52529 + 2.03532i) q^{11} +(0.648681 - 5.10677i) q^{12} +(-0.628513 + 0.440089i) q^{13} +(1.75419 + 0.506971i) q^{14} +(-4.58980 - 3.47256i) q^{15} +(-2.26438 + 3.29736i) q^{16} +(-7.15010 + 3.33415i) q^{17} +(0.988681 - 5.03025i) q^{18} +(1.09837 + 4.21824i) q^{19} +(1.93589 + 4.03142i) q^{20} +(3.12291 + 1.13665i) q^{21} +(5.75567 + 0.112482i) q^{22} +(6.48724 - 0.567560i) q^{23} +(-4.51791 + 5.70862i) q^{24} +(4.98644 + 0.368014i) q^{25} +(1.08260 - 0.0734326i) q^{26} +(0.416344 - 1.55382i) q^{27} +(-1.75325 - 1.89593i) q^{28} +(-1.82647 - 5.01817i) q^{29} +(3.01875 + 7.55890i) q^{30} +(4.15451 + 2.39861i) q^{31} +(5.15152 - 2.33706i) q^{32} +(10.4376 + 0.913171i) q^{33} +(11.0935 + 1.18939i) q^{34} +(-2.81438 + 0.644038i) q^{35} +(-4.87361 + 5.36747i) q^{36} +(-3.69756 + 3.69756i) q^{37} +(1.75334 - 5.90981i) q^{38} +1.97488 q^{39} +(0.602798 - 6.29576i) q^{40} +(0.850083 + 4.82106i) q^{41} +(-2.95012 - 3.65868i) q^{42} +(-0.479638 + 5.48229i) q^{43} +(-6.88615 - 4.34301i) q^{44} +(2.48993 + 7.71379i) q^{45} +(-8.26889 - 4.05439i) q^{46} +(4.15148 + 1.93587i) q^{47} +(9.64225 - 3.60925i) q^{48} +(-4.61842 + 2.66645i) q^{49} +(-5.76807 - 4.09015i) q^{50} +(19.9977 + 3.52614i) q^{51} +(-1.36437 - 0.702370i) q^{52} +(0.133082 + 1.52113i) q^{53} +(-1.63975 + 1.57689i) q^{54} +(-8.04503 + 4.25774i) q^{55} +(0.736906 + 3.57685i) q^{56} +(3.91171 - 10.5154i) q^{57} +(-1.45650 + 7.41044i) q^{58} +(-6.96070 - 2.53349i) q^{59} +(1.87004 - 11.3579i) q^{60} +(3.51157 + 2.94655i) q^{61} +(-3.27669 - 5.94052i) q^{62} +(-2.68459 - 3.83400i) q^{63} +(-7.94508 - 0.935788i) q^{64} +(-1.44068 + 0.931647i) q^{65} +(-11.9693 - 8.73443i) q^{66} +(-1.94023 - 0.904744i) q^{67} +(-12.5616 - 9.54828i) q^{68} +(-14.5157 - 8.38065i) q^{69} +(3.87809 + 1.27730i) q^{70} +(-5.99460 - 7.14409i) q^{71} +(9.82355 - 2.93623i) q^{72} +(-5.73385 + 8.18878i) q^{73} +(7.17917 - 1.77406i) q^{74} +(-9.97019 - 8.13756i) q^{75} +(-6.44225 + 5.87345i) q^{76} +(3.71647 - 3.71647i) q^{77} +(-2.39098 - 1.44345i) q^{78} +(1.34323 + 7.61786i) q^{79} +(-5.33139 + 7.18166i) q^{80} +(5.15891 - 4.32884i) q^{81} +(2.49453 - 6.45816i) q^{82} +(-2.46040 - 9.18232i) q^{83} +(0.897556 + 6.58579i) q^{84} +(-16.2518 + 6.86154i) q^{85} +(4.58772 - 6.28681i) q^{86} +(-3.55753 + 13.2769i) q^{87} +(5.16270 + 10.2912i) q^{88} +(15.5495 + 2.74179i) q^{89} +(2.62348 - 11.1589i) q^{90} +(0.636794 - 0.758901i) q^{91} +(7.04774 + 10.9524i) q^{92} +(-5.21830 - 11.1907i) q^{93} +(-3.61124 - 5.37807i) q^{94} +(2.10700 + 9.51633i) q^{95} +(-14.3118 - 2.67784i) q^{96} +(3.38484 - 1.57838i) q^{97} +(7.54041 + 0.147361i) q^{98} +(-11.3038 - 9.48498i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

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