LMFDB - Embedded newform 231.2.ba.a.19.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(19,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 25, 9]))

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

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

chi := DirichletCharacter("231.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.ba (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.11
Character	$\chi$	$=$	231.19
Dual form			231.2.ba.a.73.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.788039 - 0.0828262i) q^{2} +(0.743145 + 0.669131i) q^{3} +(-1.34215 + 0.285283i) q^{4} +(0.490588 + 1.10188i) q^{5} +(0.641048 + 0.465749i) q^{6} +(2.62289 + 0.347026i) q^{7} +(-2.54123 + 0.825697i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(0.788039 - 0.0828262i) q^{2} +(0.743145 + 0.669131i) q^{3} +(-1.34215 + 0.285283i) q^{4} +(0.490588 + 1.10188i) q^{5} +(0.641048 + 0.465749i) q^{6} +(2.62289 + 0.347026i) q^{7} +(-2.54123 + 0.825697i) q^{8} +(0.104528 + 0.994522i) q^{9} +(0.477866 + 0.827689i) q^{10} +(2.93854 + 1.53784i) q^{11} +(-1.18830 - 0.686067i) q^{12} +(-0.306792 + 0.222897i) q^{13} +(2.09568 + 0.0562252i) q^{14} +(-0.372723 + 1.14712i) q^{15} +(0.572815 - 0.255034i) q^{16} +(0.112336 - 1.06881i) q^{17} +(0.164745 + 0.775064i) q^{18} +(-4.52576 - 0.961979i) q^{19} +(-0.972789 - 1.33893i) q^{20} +(1.71698 + 2.01295i) q^{21} +(2.44306 + 0.968491i) q^{22} +(0.580792 - 1.00596i) q^{23} +(-2.44100 - 1.08680i) q^{24} +(2.37219 - 2.63459i) q^{25} +(-0.223302 + 0.201062i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(-3.61932 + 0.282506i) q^{28} +(-6.27112 - 2.03761i) q^{29} +(-0.198708 + 0.934848i) q^{30} +(2.33612 - 5.24702i) q^{31} +(5.05833 - 2.92043i) q^{32} +(1.15475 + 3.10911i) q^{33} -0.851564i q^{34} +(0.904379 + 3.06036i) q^{35} +(-0.424013 - 1.30498i) q^{36} +(-7.07143 - 7.85362i) q^{37} +(-3.64615 - 0.383226i) q^{38} +(-0.377138 - 0.0396388i) q^{39} +(-2.15651 - 2.39505i) q^{40} +(1.56301 + 4.81045i) q^{41} +(1.51978 + 1.44407i) q^{42} -10.6749i q^{43} +(-4.38269 - 1.22570i) q^{44} +(-1.04456 + 0.603078i) q^{45} +(0.374366 - 0.840841i) q^{46} +(-2.40399 + 11.3099i) q^{47} +(0.596336 + 0.193761i) q^{48} +(6.75915 + 1.82042i) q^{49} +(1.65117 - 2.27264i) q^{50} +(0.798652 - 0.719110i) q^{51} +(0.348172 - 0.386684i) q^{52} +(8.57905 + 3.81964i) q^{53} +(-0.396190 + 0.686221i) q^{54} +(-0.252901 + 3.99236i) q^{55} +(-6.95192 + 1.28384i) q^{56} +(-2.71960 - 3.74321i) q^{57} +(-5.11065 - 1.08630i) q^{58} +(0.238191 + 1.12060i) q^{59} +(0.172995 - 1.64594i) q^{60} +(-0.0370143 + 0.0164798i) q^{61} +(1.40637 - 4.32835i) q^{62} +(-0.0709575 + 2.64480i) q^{63} +(2.72973 - 1.98326i) q^{64} +(-0.396113 - 0.228696i) q^{65} +(1.16750 + 2.35445i) q^{66} +(-1.03631 - 1.79495i) q^{67} +(0.154140 + 1.46654i) q^{68} +(1.10473 - 0.358949i) q^{69} +(0.966164 + 2.33677i) q^{70} +(-1.06724 - 0.775393i) q^{71} +(-1.08680 - 2.44100i) q^{72} +(-6.23982 + 1.32632i) q^{73} +(-6.22304 - 5.60325i) q^{74} +(3.52577 - 0.370573i) q^{75} +6.34868 q^{76} +(7.17382 + 5.05335i) q^{77} -0.300482 q^{78} +(-1.47598 + 0.155132i) q^{79} +(0.562032 + 0.506056i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(1.63014 + 3.66136i) q^{82} +(-11.5042 - 8.35828i) q^{83} +(-2.87871 - 2.21185i) q^{84} +(1.23280 - 0.400562i) q^{85} +(-0.884158 - 8.41220i) q^{86} +(-3.29692 - 5.71044i) q^{87} +(-8.73732 - 1.48167i) q^{88} +(-4.61647 - 2.66532i) q^{89} +(-0.773204 + 0.561766i) q^{90} +(-0.882033 + 0.478171i) q^{91} +(-0.492526 + 1.51584i) q^{92} +(5.24702 - 2.33612i) q^{93} +(-0.957683 + 9.11174i) q^{94} +(-1.16030 - 5.45877i) q^{95} +(5.71322 + 1.21438i) q^{96} +(9.91056 + 13.6407i) q^{97} +(5.47725 + 0.874729i) q^{98} +(-1.22226 + 3.08319i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9}+O(q^{10}) $ 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9	$ 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9} - 2 q^{11} + 12 q^{14} + 12 q^{15} + 40 q^{16} - 60 q^{17} - 10 q^{18} + 52 q^{22} - 24 q^{23} - 90 q^{24} - 20 q^{25} + 24 q^{26} + 30 q^{28} + 40 q^{29} - 18 q^{31} + 18 q^{33} - 80 q^{35} - 24 q^{36} - 8 q^{37} - 24 q^{38} - 90 q^{40} + 14 q^{42} - 82 q^{44} + 12 q^{45} + 70 q^{46} - 24 q^{47} - 94 q^{49} - 20 q^{51} + 4 q^{53} - 104 q^{56} - 32 q^{58} + 48 q^{59} + 30 q^{61} - 10 q^{63} - 48 q^{64} + 36 q^{66} - 40 q^{67} + 180 q^{68} + 146 q^{70} - 32 q^{71} + 10 q^{72} + 90 q^{73} + 40 q^{74} - 24 q^{75} - 72 q^{78} + 50 q^{79} + 228 q^{80} + 16 q^{81} + 168 q^{82} - 60 q^{84} - 20 q^{85} + 146 q^{86} + 16 q^{88} + 48 q^{91} - 204 q^{92} + 44 q^{93} + 10 q^{95} - 44 q^{99}+O(q^{100}) $ 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9 - 2 * q^11 + 12 * q^14 + 12 * q^15 + 40 * q^16 - 60 * q^17 - 10 * q^18 + 52 * q^22 - 24 * q^23 - 90 * q^24 - 20 * q^25 + 24 * q^26 + 30 * q^28 + 40 * q^29 - 18 * q^31 + 18 * q^33 - 80 * q^35 - 24 * q^36 - 8 * q^37 - 24 * q^38 - 90 * q^40 + 14 * q^42 - 82 * q^44 + 12 * q^45 + 70 * q^46 - 24 * q^47 - 94 * q^49 - 20 * q^51 + 4 * q^53 - 104 * q^56 - 32 * q^58 + 48 * q^59 + 30 * q^61 - 10 * q^63 - 48 * q^64 + 36 * q^66 - 40 * q^67 + 180 * q^68 + 146 * q^70 - 32 * q^71 + 10 * q^72 + 90 * q^73 + 40 * q^74 - 24 * q^75 - 72 * q^78 + 50 * q^79 + 228 * q^80 + 16 * q^81 + 168 * q^82 - 60 * q^84 - 20 * q^85 + 146 * q^86 + 16 * q^88 + 48 * q^91 - 204 * q^92 + 44 * q^93 + 10 * q^95 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.788039	−	0.0828262i	0.557227	−	0.0585670i	0.178271	−	0.983981i	$-0.442950\pi$
$2$	0.788039	−	0.0828262i	0.557227	−	0.0585670i	0.378957	+	0.925414i	$0.376283\pi$
$3$	0.743145	+	0.669131i	0.429055	+	0.386323i
$3$	0.743145	+	0.669131i	0.429055	+	0.386323i
$4$	−1.34215	+	0.285283i	−0.671075	+	0.142641i
$5$	0.490588	+	1.10188i	0.219397	+	0.492775i	0.989391	−	0.145277i	$-0.0464073\pi$
$5$	0.490588	+	1.10188i	0.219397	+	0.492775i	−0.769994	+	0.638052i	$0.779741\pi$
$6$	0.641048	+	0.465749i	0.261707	+	0.190141i
$7$	2.62289	+	0.347026i	0.991361	+	0.131163i
$7$	2.62289	+	0.347026i	0.991361	+	0.131163i
$8$	−2.54123	+	0.825697i	−0.898461	+	0.291928i
$9$	0.104528	+	0.994522i	0.0348428	+	0.331507i
$10$	0.477866	+	0.827689i	0.151115	+	0.261738i
$11$	2.93854	+	1.53784i	0.886004	+	0.463677i
$11$	2.93854	+	1.53784i	0.886004	+	0.463677i
$12$	−1.18830	−	0.686067i	−0.343034	−	0.198051i
$13$	−0.306792	+	0.222897i	−0.0850887	+	0.0618205i	−0.629516	−	0.776987i	$-0.716747\pi$
$13$	−0.306792	+	0.222897i	−0.0850887	+	0.0618205i	0.544428	+	0.838808i	$0.316747\pi$
$14$	2.09568	+	0.0562252i	0.560095	+	0.0150268i
$15$	−0.372723	+	1.14712i	−0.0962365	+	0.296186i
$16$	0.572815	−	0.255034i	0.143204	−	0.0637584i
$17$	0.112336	−	1.06881i	0.0272455	−	0.259223i	−0.972417	−	0.233249i	$-0.925064\pi$
$17$	0.112336	−	1.06881i	0.0272455	−	0.259223i	0.999663	−	0.0259747i	$-0.00826893\pi$
$18$	0.164745	+	0.775064i	0.0388308	+	0.182684i
$19$	−4.52576	−	0.961979i	−1.03828	−	0.220693i	−0.342927	−	0.939362i	$-0.611418\pi$
$19$	−4.52576	−	0.961979i	−1.03828	−	0.220693i	−0.695353	+	0.718669i	$0.744752\pi$
$20$	−0.972789	−	1.33893i	−0.217522	−	0.299394i
$21$	1.71698	+	2.01295i	0.374677	+	0.439261i
$22$	2.44306	+	0.968491i	0.520862	+	0.206483i
$23$	0.580792	−	1.00596i	0.121103	−	0.209757i	−0.799100	−	0.601199i	$-0.794690\pi$
$23$	0.580792	−	1.00596i	0.121103	−	0.209757i	0.920203	+	0.391441i	$0.128023\pi$
$24$	−2.44100	−	1.08680i	−0.498268	−	0.221843i
$25$	2.37219	−	2.63459i	0.474439	−	0.526918i
$26$	−0.223302	+	0.201062i	−0.0437931	+	0.0394315i
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$	−3.61932	+	0.282506i	−0.683987	+	0.0533887i
$29$	−6.27112	−	2.03761i	−1.16452	−	0.378375i	−0.337923	−	0.941174i	$-0.609724\pi$
$29$	−6.27112	−	2.03761i	−1.16452	−	0.378375i	−0.826594	+	0.562799i	$0.809724\pi$
$30$	−0.198708	+	0.934848i	−0.0362789	+	0.170679i
$31$	2.33612	−	5.24702i	0.419580	−	0.942393i	−0.572859	−	0.819654i	$-0.694166\pi$
$31$	2.33612	−	5.24702i	0.419580	−	0.942393i	0.992439	−	0.122739i	$-0.0391677\pi$
$32$	5.05833	−	2.92043i	0.894196	−	0.516264i
$33$	1.15475	+	3.10911i	0.201016	+	0.541226i
$34$		−	0.851564i		−	0.146042i
$35$	0.904379	+	3.06036i	0.152868	+	0.517294i
$36$	−0.424013	−	1.30498i	−0.0706688	−	0.217496i
$37$	−7.07143	−	7.85362i	−1.16254	−	1.29113i	−0.949388	−	0.314107i	$-0.898295\pi$
$37$	−7.07143	−	7.85362i	−1.16254	−	1.29113i	−0.213148	−	0.977020i	$-0.568372\pi$
$38$	−3.64615	−	0.383226i	−0.591483	−	0.0621674i
$39$	−0.377138	−	0.0396388i	−0.0603904	−	0.00634729i
$40$	−2.15651	−	2.39505i	−0.340975	−	0.378691i
$41$	1.56301	+	4.81045i	0.244101	+	0.751266i	0.995783	+	0.0917399i	$0.0292428\pi$
$41$	1.56301	+	4.81045i	0.244101	+	0.751266i	−0.751682	+	0.659526i	$0.770757\pi$
$42$	1.51978	+	1.44407i	0.234506	+	0.222825i
$43$		−	10.6749i		−	1.62790i	−0.580934	−	0.813950i	$-0.697313\pi$
$43$		−	10.6749i		−	1.62790i	0.580934	−	0.813950i	$-0.302687\pi$
$44$	−4.38269	−	1.22570i	−0.660715	−	0.184781i
$45$	−1.04456	+	0.603078i	−0.155714	+	0.0899015i
$46$	0.374366	−	0.840841i	0.0551973	−	0.123975i
$47$	−2.40399	+	11.3099i	−0.350658	+	1.64972i	0.350391	+	0.936604i	$0.386049\pi$
$47$	−2.40399	+	11.3099i	−0.350658	+	1.64972i	−0.701049	+	0.713113i	$0.747285\pi$
$48$	0.596336	+	0.193761i	0.0860736	+	0.0279670i
$49$	6.75915	+	1.82042i	0.965592	+	0.260060i
$50$	1.65117	−	2.27264i	0.233510	−	0.321400i
$51$	0.798652	−	0.719110i	0.111834	−	0.100695i
$52$	0.348172	−	0.386684i	0.0482827	−	0.0536234i
$53$	8.57905	+	3.81964i	1.17842	+	0.524668i	0.900042	−	0.435803i	$-0.143535\pi$
$53$	8.57905	+	3.81964i	1.17842	+	0.524668i	0.278381	+	0.960471i	$0.410202\pi$
$54$	−0.396190	+	0.686221i	−0.0539146	+	0.0933828i
$55$	−0.252901	+	3.99236i	−0.0341012	+	0.538330i
$56$	−6.95192	+	1.28384i	−0.928990	+	0.171561i
$57$	−2.71960	−	3.74321i	−0.360220	−	0.495801i
$58$	−5.11065	−	1.08630i	−0.671061	−	0.142638i
$59$	0.238191	+	1.12060i	0.0310099	+	0.145890i	0.990929	−	0.134388i	$-0.0429068\pi$
$59$	0.238191	+	1.12060i	0.0310099	+	0.145890i	−0.959919	+	0.280278i	$0.909573\pi$
$60$	0.172995	−	1.64594i	0.0223336	−	0.212490i
$61$	−0.0370143	+	0.0164798i	−0.00473919	+	0.00211002i	−0.409105	−	0.912487i	$-0.634159\pi$
$61$	−0.0370143	+	0.0164798i	−0.00473919	+	0.00211002i	0.404366	+	0.914597i	$0.367492\pi$
$62$	1.40637	−	4.32835i	0.178609	−	0.549701i
$63$	−0.0709575	+	2.64480i	−0.00893980	+	0.333213i
$64$	2.72973	−	1.98326i	0.341216	−	0.247908i
$65$	−0.396113	−	0.228696i	−0.0491318	−	0.0283663i
$66$	1.16750	+	2.35445i	0.143709	+	0.289813i
$67$	−1.03631	−	1.79495i	−0.126606	−	0.219288i	0.795754	−	0.605620i	$-0.207075\pi$
$67$	−1.03631	−	1.79495i	−0.126606	−	0.219288i	−0.922359	+	0.386333i	$0.873742\pi$
$68$	0.154140	+	1.46654i	0.0186922	+	0.177845i
$69$	1.10473	−	0.358949i	0.132994	−	0.0432124i
$70$	0.966164	+	2.33677i	0.115479	+	0.279298i
$71$	−1.06724	−	0.775393i	−0.126658	−	0.0920222i	0.522653	−	0.852546i	$-0.324942\pi$
$71$	−1.06724	−	0.775393i	−0.126658	−	0.0920222i	−0.649310	+	0.760523i	$0.724942\pi$
$72$	−1.08680	−	2.44100i	−0.128081	−	0.287675i
$73$	−6.23982	+	1.32632i	−0.730316	+	0.155233i	−0.558039	−	0.829815i	$-0.688446\pi$
$73$	−6.23982	+	1.32632i	−0.730316	+	0.155233i	−0.172277	+	0.985048i	$0.555113\pi$
$74$	−6.22304	−	5.60325i	−0.723414	−	0.651365i
$75$	3.52577	−	0.370573i	0.407121	−	0.0427901i
$76$	6.34868			0.728244
$77$	7.17382	+	5.05335i	0.817533	+	0.575882i
$78$	−0.300482			−0.0340229
$79$	−1.47598	+	0.155132i	−0.166061	+	0.0174537i	−0.187194	−	0.982323i	$-0.559939\pi$
$79$	−1.47598	+	0.155132i	−0.166061	+	0.0174537i	0.0211329	+	0.999777i	$0.493273\pi$
$80$	0.562032	+	0.506056i	0.0628371	+	0.0565788i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	1.63014	+	3.66136i	0.180019	+	0.404330i
$83$	−11.5042	−	8.35828i	−1.26275	−	0.917440i	−0.263859	−	0.964561i	$-0.584995\pi$
$83$	−11.5042	−	8.35828i	−1.26275	−	0.917440i	−0.998889	+	0.0471213i	$0.984995\pi$
$84$	−2.87871	−	2.21185i	−0.314093	−	0.241333i
$85$	1.23280	−	0.400562i	0.133716	−	0.0434471i
$86$	−0.884158	−	8.41220i	−0.0953412	−	0.907111i
$87$	−3.29692	−	5.71044i	−0.353467	−	0.612223i
$88$	−8.73732	−	1.48167i	−0.931401	−	0.157947i
$89$	−4.61647	−	2.66532i	−0.489345	−	0.282524i	0.234958	−	0.972006i	$-0.424505\pi$
$89$	−4.61647	−	2.66532i	−0.489345	−	0.282524i	−0.724303	+	0.689482i	$0.757838\pi$
$90$	−0.773204	+	0.561766i	−0.0815028	+	0.0592153i
$91$	−0.882033	+	0.478171i	−0.0924622	+	0.0501259i
$92$	−0.492526	+	1.51584i	−0.0513494	+	0.158037i
$93$	5.24702	−	2.33612i	0.544091	−	0.242245i
$94$	−0.957683	+	9.11174i	−0.0987774	+	0.939804i
$95$	−1.16030	−	5.45877i	−0.119044	−	0.560058i
$96$	5.71322	+	1.21438i	0.583104	+	0.123942i
$97$	9.91056	+	13.6407i	1.00626	+	1.38500i	0.921401	+	0.388612i	$0.127045\pi$
$97$	9.91056	+	13.6407i	1.00626	+	1.38500i	0.0848633	+	0.996393i	$0.472955\pi$
$98$	5.47725	+	0.874729i	0.553286	+	0.0883610i
$99$	−1.22226	+	3.08319i	−0.122841	+	0.309873i
$100$	−2.43224	+	4.21276i	−0.243224	+	0.421276i
$101$	12.2788	+	5.46688i	1.22179	+	0.543975i	0.913313	−	0.407258i	$-0.133515\pi$
$101$	12.2788	+	5.46688i	1.22179	+	0.543975i	0.308475	+	0.951233i	$0.400182\pi$
$102$	0.569808	−	0.632835i	0.0564194	−	0.0626600i
$103$	−9.28967	+	8.36445i	−0.915338	+	0.824174i	−0.984850	−	0.173407i	$-0.944522\pi$
$103$	−9.28967	+	8.36445i	−0.915338	+	0.824174i	0.0695121	+	0.997581i	$0.477856\pi$
$104$	0.595583	−	0.819750i	0.0584018	−	0.0803831i
$105$	−1.37569	+	2.87943i	−0.134254	+	0.281004i
$106$	7.07699	+	2.29945i	0.687378	+	0.223343i
$107$	−0.343687	+	1.61692i	−0.0332255	+	0.156314i	−0.991633	−	0.129090i	$-0.958794\pi$
$107$	−0.343687	+	1.61692i	−0.0332255	+	0.156314i	0.958407	+	0.285404i	$0.0921277\pi$
$108$	0.558098	−	1.25351i	0.0537030	−	0.120619i
$109$	11.1675	−	6.44757i	1.06965	−	0.617566i	0.141568	−	0.989929i	$-0.454786\pi$
$109$	11.1675	−	6.44757i	1.06965	−	0.617566i	0.928087	+	0.372363i	$0.121452\pi$
$110$	0.131376	+	3.16708i	0.0125262	+	0.301969i
$111$		−	10.5681i		−	1.00308i
$112$	1.59094	−	0.470145i	0.150329	−	0.0444245i
$113$	3.02558	+	9.31178i	0.284623	+	0.875979i	0.986511	+	0.163692i	$0.0523403\pi$
$113$	3.02558	+	9.31178i	0.284623	+	0.875979i	−0.701889	+	0.712287i	$0.747660\pi$
$114$	−2.45319	−	2.72454i	−0.229762	−	0.255177i
$115$	1.39337	+	0.146450i	0.129933	+	0.0136565i
$116$	8.99808	+	0.945736i	0.835451	+	0.0878094i
$117$	−0.253745	−	0.281812i	−0.0234587	−	0.0260535i
$118$	0.280519	+	0.863350i	0.0258239	+	0.0794778i
$119$	0.665548	−	2.76438i	0.0610107	−	0.253410i
$120$		−	3.22286i		−	0.294205i
$121$	6.27008	+	9.03804i	0.570007	+	0.821640i
$122$	−0.0278037	+	0.0160525i	−0.00251723	+	0.00145332i
$123$	−2.05728	+	4.62072i	−0.185498	+	0.416636i
$124$	−1.63854	+	7.70875i	−0.147146	+	0.692266i
$125$	9.80237	+	3.18498i	0.876751	+	0.284874i
$126$	0.163141	+	2.09008i	0.0145338	+	0.186199i
$127$	3.87165	−	5.32886i	0.343553	−	0.472860i	−0.601922	−	0.798555i	$-0.705598\pi$
$127$	3.87165	−	5.32886i	0.343553	−	0.472860i	0.945475	+	0.325695i	$0.105598\pi$
$128$	−6.69435	+	6.02762i	−0.591702	+	0.532771i
$129$	7.14287	−	7.93297i	0.628895	−	0.698459i
$130$	−0.331095	−	0.147413i	−0.0290389	−	0.0129290i
$131$	−0.317831	+	0.550499i	−0.0277690	+	0.0480973i	−0.879576	−	0.475759i	$-0.842174\pi$
$131$	−0.317831	+	0.550499i	−0.0277690	+	0.0480973i	0.851807	+	0.523856i	$0.175507\pi$
$132$	−2.43682	−	3.84346i	−0.212098	−	0.334531i
$133$	−11.5367	−	4.09372i	−1.00036	−	0.354971i
$134$	−0.965323	−	1.32865i	−0.0833912	−	0.114778i
$135$	−1.17980	−	0.250774i	−0.101541	−	0.0215832i
$136$	0.597037	+	2.80884i	0.0511955	+	0.240856i
$137$	0.179551	−	1.70831i	0.0153401	−	0.145951i	−0.984171	−	0.177222i	$-0.943289\pi$
$137$	0.179551	−	1.70831i	0.0153401	−	0.145951i	0.999511	+	0.0312712i	$0.00995554\pi$
$138$	0.840841	−	0.374366i	0.0715771	−	0.0318682i
$139$	0.214074	−	0.658851i	0.0181575	−	0.0558830i	−0.941567	−	0.336825i	$-0.890647\pi$
$139$	0.214074	−	0.658851i	0.0181575	−	0.0558830i	0.959725	+	0.280942i	$0.0906469\pi$
$140$	−2.08688	−	3.84945i	−0.176374	−	0.325338i
$141$	−9.35431	+	6.79630i	−0.787775	+	0.572352i
$142$	−0.905247	−	0.522644i	−0.0759666	−	0.0438593i
$143$	−1.24430	+	0.183196i	−0.104054	+	0.0153196i
$144$	0.313512	+	0.543019i	0.0261260	+	0.0452516i
$145$	−0.831336	−	7.90963i	−0.0690387	−	0.656859i
$146$	−4.80737	+	1.56201i	−0.397861	+	0.129273i
$147$	3.80492	+	5.87559i	0.313825	+	0.484610i
$148$	11.7314	+	8.52338i	0.964317	+	0.700617i
$149$	−0.166545	−	0.374067i	−0.0136439	−	0.0306448i	0.906595	−	0.422002i	$-0.138672\pi$
$149$	−0.166545	−	0.374067i	−0.0136439	−	0.0306448i	−0.920239	+	0.391357i	$0.872006\pi$
$150$	2.74775	−	0.584052i	0.224353	−	0.0476876i
$151$	−8.98602	−	8.09105i	−0.731272	−	0.658440i	0.216901	−	0.976194i	$-0.430405\pi$
$151$	−8.98602	−	8.09105i	−0.731272	−	0.658440i	−0.948173	+	0.317753i	$0.897072\pi$
$152$	12.2953	−	1.29229i	0.997281	−	0.104818i
$153$	1.07469			0.0868837
$154$	6.07180	+	3.38805i	0.489279	+	0.273017i
$155$	6.92765			0.556442
$156$	0.517484	−	0.0543898i	0.0414319	−	0.00435467i
$157$	−1.93347	−	1.74091i	−0.154308	−	0.138940i	0.588361	−	0.808599i	$-0.299774\pi$
$157$	−1.93347	−	1.74091i	−0.154308	−	0.138940i	−0.742669	+	0.669659i	$0.766440\pi$
$158$	−1.15028	+	0.244500i	−0.0915117	+	0.0194514i
$159$	3.81964	+	8.57905i	0.302917	+	0.680363i
$160$	5.69951	+	4.14094i	0.450586	+	0.327370i
$161$	1.87245	−	2.43698i	0.147570	−	0.192061i
$162$	−0.753598	+	0.244859i	−0.0592082	+	0.0192379i
$163$	0.523448	+	4.98028i	0.0409996	+	0.390085i	0.995709	+	0.0925441i	$0.0294999\pi$
$163$	0.523448	+	4.98028i	0.0409996	+	0.390085i	−0.954709	+	0.297541i	$0.903833\pi$
$164$	−3.47013	−	6.01044i	−0.270972	−	0.469337i
$165$	−2.85935	+	2.79768i	−0.222600	+	0.217799i
$166$	−9.75802	−	5.63380i	−0.757369	−	0.437267i
$167$	−5.11356	+	3.71522i	−0.395699	+	0.287492i	−0.767787	−	0.640705i	$-0.778642\pi$
$167$	−5.11356	+	3.71522i	−0.395699	+	0.287492i	0.372088	+	0.928198i	$0.378642\pi$
$168$	−6.02534	−	3.69766i	−0.464865	−	0.285281i
$169$	−3.97278	+	12.2270i	−0.305599	+	0.940536i
$170$	0.938319	−	0.417767i	0.0719658	−	0.0320412i
$171$	0.483639	−	4.60152i	0.0369848	−	0.351887i
$172$	3.04535	+	14.3273i	0.232206	+	1.09244i
$173$	−18.9718	−	4.03259i	−1.44240	−	0.306592i	−0.580746	−	0.814085i	$-0.697239\pi$
$173$	−18.9718	−	4.03259i	−1.44240	−	0.306592i	−0.861656	+	0.507493i	$0.830572\pi$
$174$	−3.07107	−	4.22697i	−0.232818	−	0.320446i
$175$	7.13629	−	6.08704i	0.539452	−	0.460137i
$176$	2.07544	+	0.131472i	0.156443	+	0.00991004i
$177$	−0.572819	+	0.992151i	−0.0430557	+	0.0745747i
$178$	−3.85872	−	1.71801i	−0.289223	−	0.128770i
$179$	3.61918	−	4.01950i	0.270510	−	0.300432i	−0.592550	−	0.805534i	$-0.701879\pi$
$179$	3.61918	−	4.01950i	0.270510	−	0.300432i	0.863060	+	0.505102i	$0.168545\pi$
$180$	1.22991	−	1.10742i	0.0916721	−	0.0825419i
$181$	−9.73127	+	13.3939i	−0.723320	+	0.995564i	0.276087	+	0.961133i	$0.410962\pi$
$181$	−9.73127	+	13.3939i	−0.723320	+	0.995564i	−0.999407	+	0.0344317i	$0.989038\pi$
$182$	−0.655471	+	0.449873i	−0.0485867	+	0.0333468i
$183$	−0.0385341	−	0.0125205i	−0.00284852	−	0.000925541i
$184$	−0.645308	+	3.03594i	−0.0475728	+	0.223812i
$185$	5.18457	−	11.6447i	0.381177	−	0.856138i
$186$	3.94136	−	2.27555i	0.288995	−	0.166851i
$187$	1.97376	−	2.96798i	0.144335	−	0.217040i
$188$		−	15.8654i		−	1.15710i
$189$	−1.82245	+	1.91799i	−0.132564	+	0.139513i
$190$	−1.36649	−	4.20562i	−0.0991354	−	0.305107i
$191$	−11.0267	−	12.2464i	−0.797862	−	0.886116i	0.197696	−	0.980263i	$-0.436654\pi$
$191$	−11.0267	−	12.2464i	−0.797862	−	0.886116i	−0.995558	+	0.0941476i	$0.969987\pi$
$192$	3.35565	+	0.352693i	0.242173	+	0.0254534i
$193$	15.1556	+	1.59292i	1.09092	+	0.114661i	0.632866	−	0.774261i	$-0.281878\pi$
$193$	15.1556	+	1.59292i	1.09092	+	0.114661i	0.458059	+	0.888922i	$0.348545\pi$
$194$	8.93971	+	9.92856i	0.641834	+	0.712829i
$195$	−0.141342	−	0.435006i	−0.0101217	−	0.0311514i
$196$	−9.59113	−	0.515012i	−0.685081	−	0.0367866i
$197$		−	12.8617i		−	0.916358i	−0.888860	−	0.458179i	$-0.848502\pi$
$197$		−	12.8617i		−	0.916358i	0.888860	−	0.458179i	$-0.151498\pi$
$198$	−0.707816	+	2.53091i	−0.0503023	+	0.179864i
$199$	−13.9041	+	8.02753i	−0.985634	+	0.569056i	−0.903966	−	0.427603i	$-0.859358\pi$
$199$	−13.9041	+	8.02753i	−0.985634	+	0.569056i	−0.0816679	+	0.996660i	$0.526025\pi$
$200$	−3.85293	+	8.65382i	−0.272443	+	0.611917i
$201$	0.430923	−	2.02733i	0.0303950	−	0.142997i
$202$	10.1290	+	3.29111i	0.712673	+	0.231561i
$203$	−15.7414	−	7.52067i	−1.10483	−	0.527848i
$204$	−0.866762	+	1.19300i	−0.0606855	+	0.0835264i
$205$	−4.53373	+	4.08219i	−0.316650	+	0.285113i
$206$	−6.62782	+	7.36094i	−0.461782	+	0.512861i
$207$	1.06116	+	0.472458i	0.0737557	+	0.0328381i
$208$	−0.118889	+	0.205921i	−0.00824344	+	0.0142781i
$209$	−11.8198	−	9.78672i	−0.817590	−	0.676962i
$210$	−0.845606	+	2.38305i	−0.0583524	+	0.164446i
$211$	−9.08915	−	12.5101i	−0.625723	−	0.861233i	0.372031	−	0.928220i	$-0.378661\pi$
$211$	−9.08915	−	12.5101i	−0.625723	−	0.861233i	−0.997754	+	0.0669869i	$0.978661\pi$
$212$	−12.6041	−	2.67907i	−0.865650	−	0.184000i
$213$	−0.274272	−	1.29035i	−0.0187928	−	0.0884133i
$214$	−0.136915	+	1.30266i	−0.00935935	+	0.0890483i
$215$	11.7624	−	5.23695i	0.802188	−	0.357157i
$216$	0.825697	−	2.54123i	0.0561815	−	0.172909i
$217$	7.94826	−	12.9517i	0.539563	−	0.879218i
$218$	8.26641	−	6.00590i	0.559872	−	0.406771i
$219$	−5.52457	−	3.18961i	−0.373316	−	0.215534i
$220$	−0.799521	−	5.43050i	−0.0539037	−	0.366124i
$221$	0.203770	+	0.352940i	0.0137070	+	0.0237413i
$222$	−0.875314	−	8.32806i	−0.0587472	−	0.558943i
$223$	6.04220	−	1.96323i	0.404615	−	0.131468i	−0.0996370	−	0.995024i	$-0.531768\pi$
$223$	6.04220	−	1.96323i	0.404615	−	0.131468i	0.504252	+	0.863556i	$0.331768\pi$
$224$	14.2809	−	5.90461i	0.954185	−	0.394518i
$225$	2.86812	+	2.08381i	0.191208	+	0.138921i
$226$	3.15553	+	7.08745i	0.209903	+	0.471450i
$227$	2.55217	−	0.542480i	0.169393	−	0.0360057i	−0.122434	−	0.992477i	$-0.539070\pi$
$227$	2.55217	−	0.542480i	0.169393	−	0.0360057i	0.291828	+	0.956471i	$0.405737\pi$
$228$	4.71799	+	4.24810i	0.312457	+	0.281337i
$229$	−10.8667	+	1.14214i	−0.718092	+	0.0754745i	−0.456525	−	0.889711i	$-0.650906\pi$
$229$	−10.8667	+	1.14214i	−0.718092	+	0.0754745i	−0.261567	+	0.965185i	$0.584239\pi$
$230$	1.11016			0.0732020
$231$	1.94984	+	8.55559i	0.128290	+	0.562917i
$232$	17.6188			1.15673
$233$	14.1066	−	1.48266i	0.924155	−	0.0971326i	0.369517	−	0.929224i	$-0.379523\pi$
$233$	14.1066	−	1.48266i	0.924155	−	0.0971326i	0.554638	+	0.832092i	$0.312857\pi$
$234$	−0.223302	−	0.201062i	−0.0145977	−	0.0131438i
$235$	−13.6415	+	2.89959i	−0.889872	+	0.189148i
$236$	−0.639378	−	1.43607i	−0.0416199	−	0.0934799i
$237$	−1.20067	−	0.872341i	−0.0779921	−	0.0566646i
$238$	0.295515	−	2.23356i	0.0191554	−	0.144780i
$239$	−26.8225	+	8.71515i	−1.73500	+	0.563736i	−0.994157	−	0.107940i	$-0.965574\pi$
$239$	−26.8225	+	8.71515i	−1.73500	+	0.563736i	−0.740844	+	0.671677i	$0.765574\pi$
$240$	0.0790537	+	0.752146i	0.00510289	+	0.0485508i
$241$	−0.0638441	−	0.110581i	−0.00411256	−	0.00712316i	0.863962	−	0.503557i	$-0.167976\pi$
$241$	−0.0638441	−	0.110581i	−0.00411256	−	0.00712316i	−0.868074	+	0.496434i	$0.834642\pi$
$242$	5.68965	+	6.60299i	0.365745	+	0.424457i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	0.0449773	−	0.0326779i	0.00287938	−	0.00209199i
$245$	1.31007	+	8.34083i	0.0836973	+	0.532876i
$246$	−1.23850	+	3.81170i	−0.0789636	+	0.243025i
$247$	1.60289	−	0.713651i	0.101989	−	0.0454085i
$248$	−1.60419	+	15.2628i	−0.101866	+	0.969191i
$249$	−2.95649	−	13.9092i	−0.187360	−	0.881460i
$250$	7.98845	+	1.69800i	0.505234	+	0.107391i
$251$	4.86452	+	6.69544i	0.307046	+	0.422613i	0.934457	−	0.356076i	$-0.115885\pi$
$251$	4.86452	+	6.69544i	0.307046	+	0.422613i	−0.627411	+	0.778688i	$0.715885\pi$
$252$	−0.659281	−	3.56996i	−0.0415308	−	0.224886i
$253$	3.25369	−	2.06289i	0.204558	−	0.129693i
$254$	2.60964	−	4.52002i	0.163743	−	0.283611i
$255$	1.18418	+	0.527231i	0.0741562	+	0.0330165i
$256$	−9.29163	+	10.3194i	−0.580727	+	0.644962i
$257$	20.4978	−	18.4563i	1.27862	−	1.15127i	0.298163	−	0.954515i	$-0.403626\pi$
$257$	20.4978	−	18.4563i	1.27862	−	1.15127i	0.980453	−	0.196756i	$-0.0630406\pi$
$258$	4.97180	−	6.84310i	0.309531	−	0.426033i
$259$	−15.8222	−	23.0532i	−0.983144	−	1.43245i
$260$	0.596887	+	0.193940i	0.0370174	+	0.0120277i
$261$	1.37094	−	6.44975i	0.0848589	−	0.399230i
$262$	−0.204867	+	0.460139i	−0.0126567	+	0.0284275i
$263$	−20.6969	+	11.9493i	−1.27622	+	0.736828i	−0.976152	−	0.217089i	$-0.930344\pi$
$263$	−20.6969	+	11.9493i	−1.27622	+	0.736828i	−0.300071	+	0.953917i	$0.597010\pi$
$264$	−5.50166	−	6.94750i	−0.338604	−	0.427589i
$265$			11.3269i			0.695808i
$266$	−9.43047	−	2.27047i	−0.578219	−	0.139211i
$267$	−1.64726	−	5.06975i	−0.100811	−	0.310263i
$268$	1.90295	+	2.11345i	0.116241	+	0.129099i
$269$	−18.3914	−	1.93301i	−1.12134	−	0.117858i	−0.474338	−	0.880343i	$-0.657312\pi$
$269$	−18.3914	−	1.93301i	−1.12134	−	0.117858i	−0.647006	+	0.762485i	$0.723979\pi$
$270$	−0.950497	−	0.0999013i	−0.0578454	−	0.00607980i
$271$	−17.1492	−	19.0461i	−1.04174	−	1.15697i	−0.987367	−	0.158450i	$-0.949350\pi$
$271$	−17.1492	−	19.0461i	−1.04174	−	1.15697i	−0.0543744	−	0.998521i	$-0.517316\pi$
$272$	−0.208234	−	0.640877i	−0.0126260	−	0.0388589i
$273$	−0.975437	−	0.234845i	−0.0590361	−	0.0142135i
$274$		−	1.36109i		−	0.0822263i
$275$	11.0224	−	4.09379i	0.664675	−	0.246865i
$276$	−1.38031	+	0.796924i	−0.0830851	+	0.0479692i
$277$	−2.39215	+	5.37285i	−0.143730	+	0.322823i	−0.971038	−	0.238926i	$-0.923205\pi$
$277$	−2.39215	+	5.37285i	−0.143730	+	0.322823i	0.827308	+	0.561749i	$0.189871\pi$
$278$	0.114128	−	0.536931i	0.00684496	−	0.0322030i
$279$	5.46247	+	1.77486i	0.327029	+	0.106258i
$280$	−4.82516	−	7.03033i	−0.288359	−	0.420143i
$281$	−16.7454	+	23.0480i	−0.998944	+	1.37493i	−0.0729737	+	0.997334i	$0.523249\pi$
$281$	−16.7454	+	23.0480i	−0.998944	+	1.37493i	−0.925971	+	0.377595i	$0.876751\pi$
$282$	−6.80864	+	6.13053i	−0.405449	+	0.365068i
$283$	10.9476	−	12.1585i	0.650766	−	0.722748i	−0.323981	−	0.946064i	$-0.605021\pi$
$283$	10.9476	−	12.1585i	0.650766	−	0.722748i	0.974746	+	0.223315i	$0.0716880\pi$
$284$	1.65360	+	0.736230i	0.0981230	+	0.0436872i
$285$	2.79036	−	4.83304i	0.165287	−	0.286285i
$286$	−0.965384	+	0.247426i	−0.0570843	+	0.0146306i
$287$	2.43026	+	13.1597i	0.143454	+	0.776792i
$288$	3.43317	+	4.72536i	0.202302	+	0.278444i
$289$	15.4988	+	3.29437i	0.911693	+	0.193786i
$290$	−1.31025	−	6.16424i	−0.0769405	−	0.361976i
$291$	−1.76244	+	16.7685i	−0.103316	+	0.982986i
$292$	7.99641	−	3.56023i	0.467954	−	0.208347i
$293$	7.57791	−	23.3224i	0.442706	−	1.36251i	−0.442273	−	0.896880i	$-0.645828\pi$
$293$	7.57791	−	23.3224i	0.442706	−	1.36251i	0.884980	−	0.465630i	$-0.154172\pi$
$294$	3.48508	+	4.31504i	0.203254	+	0.251658i
$295$	−1.11791	+	0.812212i	−0.0650874	+	0.0472888i
$296$	24.4549	+	14.1190i	1.42141	+	0.820651i
$297$	−2.97137	+	1.47341i	−0.172417	+	0.0854960i
$298$	−0.162227	−	0.280985i	−0.00939755	−	0.0162770i
$299$	0.0460437	+	0.438077i	0.00266278	+	0.0253346i
$300$	−4.62639	+	1.50321i	−0.267105	+	0.0867877i
$301$	3.70445	−	27.9990i	0.213521	−	1.61384i
$302$	−7.75148	−	5.63178i	−0.446048	−	0.324073i
$303$	5.46688	+	12.2788i	0.314064	+	0.705400i
$304$	−2.83776	+	0.603184i	−0.162757	+	0.0345950i
$305$	−0.0363175	−	0.0327004i	−0.00207953	−	0.00187242i
$306$	0.846899	−	0.0890127i	0.0484140	−	0.00508852i
$307$	−26.1242			−1.49099			−0.745494	−	0.666512i	$-0.767786\pi$
$307$	−26.1242			−1.49099			−0.745494	+	0.666512i	$0.767786\pi$
$308$	−11.0700	−	4.73579i	−0.630771	−	0.269846i
$309$	−12.5005			−0.711128
$310$	5.45925	−	0.573791i	0.310065	−	0.0325891i
$311$	15.0079	+	13.5132i	0.851019	+	0.766261i	0.974096	−	0.226136i	$-0.0726095\pi$
$311$	15.0079	+	13.5132i	0.851019	+	0.766261i	−0.123077	+	0.992397i	$0.539276\pi$
$312$	0.991125	−	0.210670i	0.0561114	−	0.0119268i
$313$	5.95005	+	13.3640i	0.336317	+	0.755380i	0.999973	+	0.00734220i	$0.00233712\pi$
$313$	5.95005	+	13.3640i	0.336317	+	0.755380i	−0.663656	+	0.748038i	$0.730996\pi$
$314$	−1.66784	−	1.21176i	−0.0941219	−	0.0683836i
$315$	−2.94906	+	1.21932i	−0.166161	+	0.0687009i
$316$	1.93674	−	0.629284i	0.108950	−	0.0354000i
$317$	1.82201	+	17.3353i	0.102334	+	0.973646i	0.918391	+	0.395674i	$0.129489\pi$
$317$	1.82201	+	17.3353i	0.102334	+	0.973646i	−0.816057	+	0.577972i	$0.803844\pi$
$318$	3.72059	+	6.44426i	0.208641	+	0.361376i
$319$	−15.2944	−	15.6316i	−0.856324	−	0.875201i
$320$	3.52448	+	2.03486i	0.197025	+	0.113752i
$321$	−1.33734	+	0.971636i	−0.0746431	+	0.0542314i
$322$	1.27372	−	2.07552i	0.0709814	−	0.115664i
$323$	−1.53657	+	4.72909i	−0.0854972	+	0.263133i
$324$	1.25351	−	0.558098i	0.0696393	−	0.0310054i
$325$	−0.140527	+	1.33703i	−0.00779503	+	0.0741648i
$326$	0.824995	+	3.88130i	0.0456922	+	0.214965i
$327$	12.6134	+	2.68105i	0.697520	+	0.148263i
$328$	−7.94394	−	10.9339i	−0.438631	−	0.603723i
$329$	−10.2302	+	28.8304i	−0.564011	+	1.58947i
$330$	−2.02156	+	2.44151i	−0.111283	+	0.134401i
$331$	10.7196	−	18.5669i	0.589203	−	1.02053i	−0.405135	−	0.914257i	$-0.632775\pi$
$331$	10.7196	−	18.5669i	0.589203	−	1.02053i	0.994337	−	0.106272i	$-0.0338914\pi$
$332$	17.8248	+	7.93612i	0.978264	+	0.435551i
$333$	7.07143	−	7.85362i	0.387512	−	0.430376i
$334$	−3.72197	+	3.35128i	−0.203657	+	0.183374i
$335$	1.46941	−	2.02247i	0.0802824	−	0.110499i
$336$	1.49688	+	0.715159i	0.0816618	+	0.0390151i
$337$	28.5884	+	9.28892i	1.55731	+	0.506000i	0.956087	−	0.293083i	$-0.0946813\pi$
$337$	28.5884	+	9.28892i	1.55731	+	0.506000i	0.601221	+	0.799083i	$0.294681\pi$
$338$	−2.11799	+	9.96437i	−0.115204	+	0.541990i
$339$	−3.98235	+	8.94451i	−0.216292	+	0.485799i
$340$	−1.54033	+	0.889312i	−0.0835363	+	0.0482297i
$341$	14.9339	−	11.8260i	0.808716	−	0.640414i
$342$		−	3.66623i		−	0.198247i
$343$	17.0968	+	7.12037i	0.923140	+	0.384464i
$344$	8.81419	+	27.1273i	0.475229	+	1.46261i
$345$	0.937485	+	1.04118i	0.0504725	+	0.0560554i
$346$	−15.2845	−	1.60647i	−0.821702	−	0.0863644i
$347$	−0.846383	−	0.0889584i	−0.0454362	−	0.00477554i	0.0817831	−	0.996650i	$-0.473939\pi$
$347$	−0.846383	−	0.0889584i	−0.0454362	−	0.00477554i	−0.127219	+	0.991875i	$0.540605\pi$
$348$	6.05405	+	6.72371i	0.324531	+	0.360429i
$349$	8.71538	+	26.8232i	0.466524	+	1.43581i	0.857056	+	0.515223i	$0.172291\pi$
$349$	8.71538	+	26.8232i	0.466524	+	1.43581i	−0.390533	+	0.920589i	$0.627709\pi$
$350$	5.11950	−	5.38789i	0.273649	−	0.287995i
$351$		−	0.379215i		−	0.0202410i
$352$	19.3553	−	0.802893i	1.03164	−	0.0427943i
$353$	12.0480	−	6.95591i	0.641250	−	0.370226i	−0.143846	−	0.989600i	$-0.545947\pi$
$353$	12.0480	−	6.95591i	0.641250	−	0.370226i	0.785096	+	0.619374i	$0.212614\pi$
$354$	−0.369227	+	0.829298i	−0.0196242	+	0.0440767i
$355$	0.330815	−	1.55636i	0.0175578	−	0.0826032i
$356$	6.95637	+	2.26026i	0.368687	+	0.119794i
$357$	2.34433	−	1.60900i	0.124075	−	0.0851571i
$358$	2.51913	−	3.46729i	0.133140	−	0.183252i
$359$	−2.00914	+	1.80904i	−0.106038	+	0.0954773i	−0.720445	−	0.693512i	$-0.756062\pi$
$359$	−2.00914	+	1.80904i	−0.106038	+	0.0954773i	0.614406	+	0.788990i	$0.289396\pi$
$360$	2.15651	−	2.39505i	0.113658	−	0.126230i
$361$	2.19971	+	0.979374i	0.115774	+	0.0515460i
$362$	−6.55925	+	11.3610i	−0.344746	+	0.597118i
$363$	−1.38805	+	10.9121i	−0.0728536	+	0.572735i
$364$	1.04741	−	0.893406i	0.0548990	−	0.0468272i
$365$	−4.52262	−	6.22485i	−0.236725	−	0.325823i
$366$	−0.0314034	−	0.00667499i	−0.00164148	−	0.000348908i
$367$	6.42747	+	30.2389i	0.335511	+	1.57846i	0.745589	+	0.666406i	$0.232168\pi$
$367$	6.42747	+	30.2389i	0.335511	+	1.57846i	−0.410078	+	0.912050i	$0.634499\pi$
$368$	0.0761324	−	0.724351i	0.00396867	−	0.0377594i
$369$	−4.62072	+	2.05728i	−0.240545	+	0.107097i
$370$	3.12115	−	9.60592i	0.162261	−	0.499388i
$371$	21.1764	+	12.9957i	1.09943	+	0.674701i
$372$	−6.37584	+	4.63232i	−0.330572	+	0.240174i
$373$	10.9674	+	6.33202i	0.567870	+	0.327860i	0.756298	−	0.654227i	$-0.227006\pi$
$373$	10.9674	+	6.33202i	0.567870	+	0.327860i	−0.188428	+	0.982087i	$0.560339\pi$
$374$	1.30957	−	2.50236i	0.0677163	−	0.129394i
$375$	5.15341	+	8.92597i	0.266121	+	0.460935i
$376$	−3.22944	−	30.7260i	−0.166545	−	1.58457i
$377$	2.37810	−	0.772692i	0.122479	−	0.0397957i
$378$	−1.27730	+	1.66240i	−0.0656972	+	0.0855044i
$379$	7.23647	+	5.25760i	0.371713	+	0.270065i	0.757921	−	0.652347i	$-0.226215\pi$
$379$	7.23647	+	5.25760i	0.371713	+	0.270065i	−0.386208	+	0.922412i	$0.626215\pi$
$380$	3.11459	+	6.99547i	0.159775	+	0.358860i
$381$	6.44290	−	1.36948i	0.330080	−	0.0701606i
$382$	−9.70377	−	8.73731i	−0.496488	−	0.447040i
$383$	6.77685	−	0.712275i	0.346281	−	0.0363956i	0.0702081	−	0.997532i	$-0.477634\pi$
$383$	6.77685	−	0.712275i	0.346281	−	0.0363956i	0.276073	+	0.961137i	$0.410967\pi$
$384$	−9.00813			−0.459694
$385$	−2.04878	+	10.3838i	−0.104416	+	0.529206i
$386$	12.0751			0.614609
$387$	10.6164	−	1.11583i	0.539661	−	0.0567207i
$388$	−17.1929	−	15.4806i	−0.872838	−	0.785907i
$389$	−20.1788	+	4.28913i	−1.02310	+	0.217468i	−0.688765	−	0.724985i	$-0.741847\pi$
$389$	−20.1788	+	4.28913i	−1.02310	+	0.217468i	−0.334340	+	0.942453i	$0.608513\pi$
$390$	−0.147413	−	0.331095i	−0.00746454	−	0.0167656i
$391$	−1.00993	−	0.733759i	−0.0510745	−	0.0371078i
$392$	−18.6797	+	0.954886i	−0.943466	+	0.0482290i
$393$	−0.604550	+	0.196430i	−0.0304955	+	0.00990859i
$394$	−1.06529	−	10.1355i	−0.0536683	−	0.510620i
$395$	−0.895036	−	1.55025i	−0.0450342	−	0.0780015i
$396$	0.760869	−	4.48680i	0.0382351	−	0.225470i
$397$	17.0455	+	9.84124i	0.855490	+	0.493918i	0.862500	−	0.506058i	$-0.168898\pi$
$397$	17.0455	+	9.84124i	0.855490	+	0.493918i	−0.00700915	+	0.999975i	$0.502231\pi$
$398$	−10.2921	+	7.47762i	−0.515895	+	0.374819i
$399$	−5.83424	−	10.7618i	−0.292077	−	0.538765i
$400$	0.686920	−	2.11412i	0.0343460	−	0.105706i
$401$	5.61952	−	2.50197i	0.280626	−	0.124943i	−0.261598	−	0.965177i	$-0.584249\pi$
$401$	5.61952	−	2.50197i	0.280626	−	0.124943i	0.542223	+	0.840234i	$0.317583\pi$
$402$	0.171668	−	1.63331i	0.00856200	−	0.0814620i
$403$	0.452843	+	2.13046i	0.0225577	+	0.106126i
$404$	−18.0396	−	3.83444i	−0.897505	−	0.190771i
$405$	−0.708960	−	0.975800i	−0.0352285	−	0.0484879i
$406$	−13.0277	−	4.62278i	−0.646555	−	0.229425i
$407$	−8.70208	−	33.9529i	−0.431346	−	1.68299i
$408$	−1.43579	+	2.48687i	−0.0710824	+	0.123118i
$409$	15.2518	+	6.79054i	0.754153	+	0.335771i	0.747548	−	0.664207i	$-0.231231\pi$
$409$	15.2518	+	6.79054i	0.754153	+	0.335771i	0.00660514	+	0.999978i	$0.497898\pi$
$410$	−3.23464	+	3.59244i	−0.159748	+	0.177418i
$411$	1.27652	−	1.14938i	0.0629659	−	0.0566948i
$412$	10.0819	−	13.8765i	0.496699	−	0.683648i
$413$	0.235873	+	3.02188i	0.0116066	+	0.148697i
$414$	0.875366	+	0.284424i	0.0430219	+	0.0139787i
$415$	3.56599	−	16.7767i	0.175048	−	0.823534i
$416$	−0.900899	+	2.02345i	−0.0441702	+	0.0992079i
$417$	0.599945	−	0.346379i	0.0293794	−	0.0169622i
$418$	−10.1250	−	6.73333i	−0.495231	−	0.329338i
$419$			30.3688i			1.48361i	0.670615	+	0.741806i	$0.266030\pi$
$419$			30.3688i			1.48361i	−0.670615	+	0.741806i	$0.733970\pi$
$420$	1.02493	−	4.25710i	0.0500116	−	0.207725i
$421$	−8.54671	−	26.3041i	−0.416541	−	1.28198i	−0.910865	−	0.412705i	$-0.864584\pi$
$421$	−8.54671	−	26.3041i	−0.416541	−	1.28198i	0.494324	−	0.869278i	$-0.335416\pi$
$422$	−8.19877	−	9.10565i	−0.399110	−	0.443256i
$423$	−11.4992	−	1.20862i	−0.559111	−	0.0587649i
$424$	−24.9552	−	2.62290i	−1.21193	−	0.127379i
$425$	−2.54938	−	2.83137i	−0.123663	−	0.137342i
$426$	−0.323012	−	0.994129i	−0.0156500	−	0.0481657i
$427$	−0.102803	+	0.0303799i	−0.00497500	+	0.00147019i
$428$		−	2.26820i		−	0.109638i
$429$	−1.04728	−	0.696459i	−0.0505631	−	0.0336254i
$430$	8.83546	−	5.10116i	0.426084	−	0.246000i
$431$	−5.11478	+	11.4880i	−0.246370	+	0.553357i	−0.993825	−	0.110956i	$-0.964609\pi$
$431$	−5.11478	+	11.4880i	−0.246370	+	0.553357i	0.747455	+	0.664312i	$0.231276\pi$
$432$	−0.130366	+	0.613322i	−0.00627222	+	0.0295085i
$433$	−12.1688	−	3.95390i	−0.584797	−	0.190012i	0.00165129	−	0.999999i	$-0.499474\pi$
$433$	−12.1688	−	3.95390i	−0.584797	−	0.190012i	−0.586449	+	0.809986i	$0.699474\pi$
$434$	5.19079	−	10.8648i	0.249166	−	0.521525i
$435$	4.67477	−	6.43427i	0.224138	−	0.308500i
$436$	−13.1491	+	11.8395i	−0.629729	+	0.567010i
$437$	−3.59623	+	3.99402i	−0.172031	+	0.191060i
$438$	−4.61776	−	2.05596i	−0.220645	−	0.0982375i
$439$	−2.70288	+	4.68152i	−0.129001	+	0.223437i	−0.923290	−	0.384104i	$-0.874510\pi$
$439$	−2.70288	+	4.68152i	−0.129001	+	0.223437i	0.794289	+	0.607541i	$0.207844\pi$
$440$	−2.65380	−	10.3543i	−0.126515	−	0.493624i
$441$	−1.10393	+	6.91241i	−0.0525680	+	0.329162i
$442$	0.189811	+	0.261253i	0.00902840	+	0.0124265i
$443$	24.4861	+	5.20468i	1.16337	+	0.247282i	0.748838	−	0.662753i	$-0.230612\pi$
$443$	24.4861	+	5.20468i	1.16337	+	0.247282i	0.414531	+	0.910035i	$0.363946\pi$
$444$	3.01489	+	14.1840i	0.143081	+	0.673141i
$445$	0.672075	−	6.39436i	0.0318594	−	0.303122i
$446$	4.59888	−	2.04755i	0.217763	−	0.0969544i
$447$	0.126532	−	0.389427i	0.00598478	−	0.0184193i
$448$	7.84803	−	4.25460i	0.370785	−	0.201011i
$449$	−13.1899	+	9.58302i	−0.622470	+	0.452251i	−0.853783	−	0.520629i	$-0.825698\pi$
$449$	−13.1899	+	9.58302i	−0.622470	+	0.452251i	0.231314	+	0.972879i	$0.425698\pi$
$450$	2.43278	+	1.40457i	0.114682	+	0.0662119i
$451$	−2.80474	+	16.5394i	−0.132070	+	0.778809i
$452$	−6.71728	−	11.6347i	−0.315954	−	0.547249i
$453$	−1.26395	−	12.0256i	−0.0593854	−	0.565014i
$454$	1.96628	−	0.638882i	0.0922819	−	0.0299842i
$455$	−0.959600	−	0.737308i	−0.0449868	−	0.0345655i
$456$	10.0019	+	7.26681i	0.468382	+	0.340299i
$457$	−3.99730	−	8.97807i	−0.186986	−	0.419976i	0.795591	−	0.605834i	$-0.207160\pi$
$457$	−3.99730	−	8.97807i	−0.186986	−	0.419976i	−0.982577	+	0.185857i	$0.940494\pi$
$458$	−8.46879	+	1.80010i	−0.395720	+	0.0841130i
$459$	0.798652	+	0.719110i	0.0372779	+	0.0335652i
$460$	−1.91190	+	0.200949i	−0.0891427	+	0.00936928i
$461$	−17.1955			−0.800875			−0.400438	−	0.916324i	$-0.631142\pi$
$461$	−17.1955			−0.800875			−0.400438	+	0.916324i	$0.631142\pi$
$462$	2.24517	+	6.58064i	0.104455	+	0.306159i
$463$	7.06449			0.328315			0.164157	−	0.986434i	$-0.447510\pi$
$463$	7.06449			0.328315			0.164157	+	0.986434i	$0.447510\pi$
$464$	−4.11185	+	0.432173i	−0.190888	+	0.0200631i
$465$	5.14825	+	4.63550i	0.238744	+	0.214966i
$466$	10.9938	−	2.33679i	0.509276	−	0.108250i
$467$	−7.82301	−	17.5708i	−0.362006	−	0.813078i	−0.999105	−	0.0422964i	$-0.986533\pi$
$467$	−7.82301	−	17.5708i	−0.362006	−	0.813078i	0.637099	−	0.770782i	$-0.280134\pi$
$468$	0.420959	+	0.305845i	0.0194589	+	0.0141377i
$469$	−2.09525	−	5.06758i	−0.0967495	−	0.233999i
$470$	−10.5099	+	3.41486i	−0.484783	+	0.157516i
$471$	−0.271956	−	2.58749i	−0.0125311	−	0.119225i
$472$	−1.53058	−	2.65104i	−0.0704506	−	0.122024i
$473$	16.4163	−	31.3685i	0.754820	−	1.44233i
$474$	−1.01843	−	0.587991i	−0.0467780	−	0.0270073i
$475$	−13.2704	+	9.64151i	−0.608888	+	0.442383i
$476$	−0.104636	+	3.90008i	−0.00479596	+	0.178760i
$477$	−2.90196	+	8.93132i	−0.132872	+	0.408937i
$478$	−20.4153	+	9.08948i	−0.933774	+	0.415743i
$479$	3.69769	−	35.1812i	0.168952	−	1.60747i	−0.501257	−	0.865298i	$-0.667129\pi$
$479$	3.69769	−	35.1812i	0.168952	−	1.60747i	0.670209	−	0.742172i	$-0.266204\pi$
$480$	1.46473	+	6.89104i	0.0668557	+	0.314531i
$481$	3.92000	+	0.833222i	0.178737	+	0.0379917i
$482$	−0.0594706	−	0.0818543i	−0.00270881	−	0.00372836i
$483$	3.02216	−	0.558115i	0.137513	−	0.0253951i
$484$	−10.9938	−	10.3417i	−0.499718	−	0.470075i
$485$	−10.1684	+	17.6122i	−0.461723	+	0.799728i
$486$	−0.723875	−	0.322290i	−0.0328356	−	0.0146194i
$487$	19.1352	−	21.2518i	0.867100	−	0.963012i	−0.132504	−	0.991183i	$-0.542302\pi$
$487$	19.1352	−	21.2518i	0.867100	−	0.963012i	0.999603	+	0.0281709i	$0.00896825\pi$
$488$	0.0804545	−	0.0724416i	0.00364200	−	0.00327928i
$489$	−2.94346	+	4.05132i	−0.133108	+	0.183207i
$490$	1.72322	+	6.46439i	0.0778474	+	0.292031i
$491$	24.0555	+	7.81611i	1.08561	+	0.352736i	0.796549	−	0.604574i	$-0.206657\pi$
$491$	24.0555	+	7.81611i	1.08561	+	0.352736i	0.289062	+	0.957310i	$0.406657\pi$
$492$	1.44296	−	6.78860i	0.0650537	−	0.306054i
$493$	−2.88228	+	6.47370i	−0.129811	+	0.291561i
$494$	1.20403	−	0.695146i	0.0541718	−	0.0312761i
$495$	−3.99693	+	0.165800i	−0.179649	+	0.00745215i
$496$		−	3.60136i		−	0.161706i
$497$	−2.53017	−	2.40413i	−0.113494	−	0.107840i
$498$	−3.48188	−	10.7161i	−0.156027	−	0.480201i
$499$	−10.2019	−	11.3303i	−0.456699	−	0.507215i	0.470183	−	0.882569i	$-0.344188\pi$
$499$	−10.2019	−	11.3303i	−0.456699	−	0.507215i	−0.926882	+	0.375354i	$0.877521\pi$
$500$	−14.0649	−	1.47828i	−0.629001	−	0.0661106i
$501$	−6.28609	−	0.660694i	−0.280842	−	0.0295176i
$502$	4.38799	+	4.87336i	0.195846	+	0.217509i
$503$	4.26343	+	13.1215i	0.190097	+	0.585058i	0.999999	−	0.00150720i	$-0.000479756\pi$
$503$	4.26343	+	13.1215i	0.190097	+	0.585058i	−0.809902	+	0.586565i	$0.800480\pi$
$504$	−2.00348	−	6.77964i	−0.0892422	−	0.301989i
$505$			16.2117i			0.721413i
$506$	2.39317	−	1.89513i	0.106389	−	0.0842488i
$507$	−11.1338	+	6.42810i	−0.494469	+	0.285482i
$508$	−3.67610	+	8.25665i	−0.163100	+	0.366330i
$509$	8.84190	−	41.5978i	0.391910	−	1.84379i	−0.130971	−	0.991386i	$-0.541809\pi$
$509$	8.84190	−	41.5978i	0.391910	−	1.84379i	0.522881	−	0.852406i	$-0.324857\pi$
$510$	0.976848	+	0.317397i	0.0432555	+	0.0140546i
$511$	−16.8267	+	1.31341i	−0.744368	+	0.0581017i
$512$	4.12225	−	5.67379i	0.182179	−	0.250749i
$513$	3.43843	−	3.09598i	0.151810	−	0.136691i
$514$	14.6244	−	16.2420i	0.645053	−	0.716404i
$515$	−13.7740	−	6.13258i	−0.606955	−	0.270234i
$516$	−7.32367	+	12.6850i	−0.322407	+	0.558425i
$517$	−24.4571	+	29.5376i	−1.07562	+	1.29906i
$518$	−14.3779	−	16.8563i	−0.631729	−	0.740623i
$519$	−11.4005	−	15.6914i	−0.500426	−	0.688778i
$520$	1.19545	+	0.254101i	0.0524240	+	0.0111431i
$521$	−7.79855	−	36.6893i	−0.341661	−	1.60739i	−0.728369	−	0.685185i	$-0.759721\pi$
$521$	−7.79855	−	36.6893i	−0.341661	−	1.60739i	0.386708	−	0.922202i	$-0.373612\pi$
$522$	0.546143	−	5.19620i	0.0239040	−	0.227432i
$523$	12.7460	−	5.67488i	0.557344	−	0.248145i	−0.108679	−	0.994077i	$-0.534662\pi$
$523$	12.7460	−	5.67488i	0.557344	−	0.248145i	0.666023	+	0.745932i	$0.267995\pi$
$524$	0.269529	−	0.829524i	0.0117744	−	0.0362379i
$525$	9.37632	+	0.251558i	0.409216	+	0.0109789i
$526$	−15.3202	+	11.1308i	−0.667993	+	0.485325i
$527$	−5.34561	−	3.08629i	−0.232858	−	0.134441i
$528$	1.45438	+	1.48645i	0.0632939	+	0.0646892i
$529$	10.8254	+	18.7501i	0.470668	+	0.815221i
$530$	0.938167	+	8.92606i	0.0407514	+	0.387723i
$531$	−1.08957	+	0.354022i	−0.0472831	+	0.0153632i
$532$	16.6519	+	2.20316i	0.721952	+	0.0955189i
$533$	−1.55175	−	1.12741i	−0.0672139	−	0.0488337i
$534$	−1.71801	−	3.85872i	−0.0743457	−	0.166983i
$535$	−1.95026	+	0.414540i	−0.0843171	+	0.0179221i
$536$	4.11559	+	3.70570i	0.177767	+	0.160062i
$537$	5.37915	−	0.565371i	0.232127	−	0.0243976i
$538$	−14.6532			−0.631746
$539$	17.0625	+	15.7439i	0.734935	+	0.678138i
$540$	1.65501			0.0712202
$541$	−12.2433	+	1.28682i	−0.526381	+	0.0553248i	−0.363992	−	0.931402i	$-0.618586\pi$
$541$	−12.2433	+	1.28682i	−0.526381	+	0.0553248i	−0.162389	+	0.986727i	$0.551920\pi$
$542$	−15.0918	−	13.5887i	−0.648247	−	0.583684i
$543$	−16.1940	+	3.44215i	−0.694953	+	0.147717i
$544$	−2.55314	−	5.73444i	−0.109465	−	0.245862i
$545$	12.5831	+	9.14215i	0.539000	+	0.391607i
$546$	−0.788133	−	0.104275i	−0.0337290	−	0.00446256i
$547$	−14.4580	+	4.69769i	−0.618179	+	0.200859i	−0.601332	−	0.798999i	$-0.705363\pi$
$547$	−14.4580	+	4.69769i	−0.618179	+	0.200859i	−0.0168475	+	0.999858i	$0.505363\pi$
$548$	0.246368	+	2.34404i	0.0105243	+	0.100132i
$549$	−0.0202586	−	0.0350889i	−0.000864615	−	0.00149756i
$550$	8.34699	−	4.13901i	0.355917	−	0.176488i
$551$	26.4214	+	15.2544i	1.12559	+	0.649860i
$552$	−2.51100	+	1.82435i	−0.106875	+	0.0776493i
$553$	−3.92519	−	0.105309i	−0.166916	−	0.00447819i
$554$	−1.44009	+	4.43215i	−0.0611836	+	0.188304i
$555$	11.6447	−	5.18457i	0.494292	−	0.220073i
$556$	−0.0993602	+	0.945349i	−0.00421381	+	0.0400917i
$557$	4.15319	+	19.5392i	0.175977	+	0.827904i	0.974225	+	0.225577i	$0.0724266\pi$
$557$	4.15319	+	19.5392i	0.175977	+	0.827904i	−0.798249	+	0.602328i	$0.794240\pi$
$558$	4.45164	+	0.946226i	0.188453	+	0.0400569i
$559$	2.37940	+	3.27496i	0.100638	+	0.138516i
$560$	1.29854	+	1.52237i	0.0548732	+	0.0643319i
$561$	3.45275	−	0.884934i	0.145775	−	0.0373619i
$562$	−11.2870	+	19.5497i	−0.476114	+	0.824653i
$563$	15.4593	+	6.88291i	0.651530	+	0.290080i	0.705763	−	0.708448i	$-0.250604\pi$
$563$	15.4593	+	6.88291i	0.651530	+	0.290080i	−0.0542323	+	0.998528i	$0.517271\pi$
$564$	10.6160	−	11.7903i	0.447015	−	0.496460i
$565$	−8.77613	+	7.90206i	−0.369215	+	0.332442i
$566$	7.62007	−	10.4881i	0.320295	−	0.440849i
$567$	−2.63773	+	0.205888i	−0.110774	+	0.00864649i
$568$	3.35234	+	1.08924i	0.140661	+	0.0457035i
$569$	2.73339	−	12.8596i	0.114590	−	0.539101i	−0.882979	−	0.469412i	$-0.844466\pi$
$569$	2.73339	−	12.8596i	0.114590	−	0.539101i	0.997569	−	0.0696893i	$-0.0222008\pi$
$570$	1.79861	−	4.03974i	0.0753354	−	0.169206i
$571$	−3.84826	+	2.22180i	−0.161045	+	0.0929793i	−0.578356	−	0.815784i	$-0.696306\pi$
$571$	−3.84826	+	2.22180i	−0.161045	+	0.0929793i	0.417312	+	0.908763i	$0.362972\pi$
$572$	1.61778	−	0.600854i	0.0676426	−	0.0251230i
$573$		−	16.4791i		−	0.688425i
$574$	3.00511	+	10.1691i	0.125431	+	0.424448i
$575$	−1.27254	−	3.91648i	−0.0530687	−	0.163329i
$576$	2.25773	+	2.50747i	0.0940722	+	0.104478i
$577$	38.6361	+	4.06082i	1.60844	+	0.169054i	0.865714	−	0.500538i	$-0.166864\pi$
$577$	38.6361	+	4.06082i	1.60844	+	0.169054i	0.742729	+	0.669592i	$0.233531\pi$
$578$	12.4865	+	1.31238i	0.519370	+	0.0545880i
$579$	10.1969	+	11.3249i	0.423771	+	0.470645i
$580$	3.37226	+	10.3787i	0.140025	+	0.430954i
$581$	−27.2737	−	25.9151i	−1.13150	−	1.07514i
$582$			13.3602i			0.553798i
$583$	19.3359	+	24.4174i	0.800812	+	1.01127i
$584$	14.7617	−	8.52267i	0.610844	−	0.352671i
$585$	0.186038	−	0.417849i	0.00769174	−	0.0172759i
$586$	4.03998	−	19.0066i	0.166890	−	0.785156i
$587$	31.4703	+	10.2253i	1.29892	+	0.422044i	0.875205	−	0.483753i	$-0.160727\pi$
$587$	31.4703	+	10.2253i	1.29892	+	0.422044i	0.423713	+	0.905797i	$0.360727\pi$
$588$	−6.78299	−	6.80045i	−0.279726	−	0.280446i
$589$	−15.6203	+	21.4994i	−0.643621	+	0.885869i
$590$	−0.813687	+	0.732647i	−0.0334989	+	0.0301626i
$591$	8.60616	−	9.55811i	0.354010	−	0.393168i
$592$	−6.05356	−	2.69522i	−0.248800	−	0.110773i
$593$	−9.41234	+	16.3027i	−0.386519	+	0.669470i	−0.991979	−	0.126406i	$-0.959656\pi$
$593$	−9.41234	+	16.3027i	−0.386519	+	0.669470i	0.605460	+	0.795876i	$0.292989\pi$
$594$	−2.21952	+	1.40721i	−0.0910680	+	0.0577386i
$595$	3.37252	−	0.622818i	0.138260	−	0.0255330i
$596$	0.330244	+	0.454542i	0.0135273	+	0.0186188i
$597$	−15.7042	−	3.33803i	−0.642731	−	0.136617i
$598$	0.0725685	+	0.341408i	0.00296755	+	0.0139612i
$599$	0.0683104	−	0.649930i	0.00279109	−	0.0265554i	−0.993038	−	0.117797i	$-0.962417\pi$
$599$	0.0683104	−	0.649930i	0.00279109	−	0.0265554i	0.995829	+	0.0912414i	$0.0290835\pi$
$600$	−8.65382	+	3.85293i	−0.353291	+	0.157295i
$601$	8.79714	−	27.0748i	0.358843	−	1.10440i	−0.594905	−	0.803796i	$-0.702810\pi$
$601$	8.79714	−	27.0748i	0.358843	−	1.10440i	0.953748	−	0.300608i	$-0.0971896\pi$
$602$	0.600196	−	22.3711i	0.0244622	−	0.911780i
$603$	1.67679	−	1.21826i	0.0682841	−	0.0496113i
$604$	14.3688	+	8.29585i	0.584660	+	0.337553i
$605$	−6.88279	+	11.3428i	−0.279825	+	0.461151i
$606$	5.32512	+	9.22338i	0.216318	+	0.374674i
$607$	1.36806	+	13.0162i	0.0555278	+	0.528311i	0.986563	+	0.163382i	$0.0522403\pi$
$607$	1.36806	+	13.0162i	0.0555278	+	0.528311i	−0.931035	+	0.364930i	$0.881093\pi$
$608$	−25.7022	+	8.35115i	−1.04236	+	0.338684i
$609$	−6.66581	−	16.1220i	−0.270112	−	0.653296i
$610$	−0.0313280	−	0.0227611i	−0.00126843	−	0.000921571i
$611$	−1.78342	−	4.00562i	−0.0721493	−	0.162050i
$612$	−1.44240	+	0.306591i	−0.0583055	+	0.0123932i
$613$	26.1148	+	23.5138i	1.05477	+	0.949715i	0.998813	−	0.0487183i	$-0.0155137\pi$
$613$	26.1148	+	23.5138i	1.05477	+	0.949715i	0.0559529	+	0.998433i	$0.482180\pi$
$614$	−20.5869	+	2.16377i	−0.830819	+	0.0873226i
$615$	−6.10074			−0.246005
$616$	−22.4029	−	6.91833i	−0.902638	−	0.278748i
$617$	42.0432			1.69260			0.846298	−	0.532709i	$-0.178826\pi$
$617$	42.0432			1.69260			0.846298	+	0.532709i	$0.178826\pi$
$618$	−9.85086	+	1.03537i	−0.396260	+	0.0416486i
$619$	5.68918	+	5.12256i	0.228667	+	0.205893i	0.775498	−	0.631350i	$-0.217499\pi$
$619$	5.68918	+	5.12256i	0.228667	+	0.205893i	−0.546830	+	0.837243i	$0.684166\pi$
$620$	−9.29795	+	1.97634i	−0.373415	+	0.0793717i
$621$	0.472458	+	1.06116i	0.0189591	+	0.0425828i
$622$	12.9460	+	9.40584i	0.519089	+	0.377140i
$623$	−11.1836	−	8.59289i	−0.448061	−	0.344267i
$624$	−0.226140	+	0.0734772i	−0.00905283	+	0.00294144i
$625$	−0.553406	−	5.26531i	−0.0221363	−	0.210612i
$626$	5.79576	+	10.0386i	0.231645	+	0.401221i
$627$	−2.23520	−	15.1819i	−0.0892654	−	0.606307i
$628$	3.09166	+	1.78497i	0.123371	+	0.0712282i
$629$	−9.18836	+	6.67574i	−0.366364	+	0.266179i
$630$	−2.22298	+	1.20513i	−0.0885656	+	0.0480135i
$631$	−3.16160	+	9.73041i	−0.125861	+	0.387362i	−0.994057	−	0.108861i	$-0.965280\pi$
$631$	−3.16160	+	9.73041i	−0.125861	+	0.387362i	0.868196	+	0.496222i	$0.165280\pi$
$632$	3.62273	−	1.61294i	0.144104	−	0.0641594i
$633$	1.61636	−	15.3787i	0.0642447	−	0.611247i
$634$	2.87163	+	13.5100i	0.114047	+	0.536549i
$635$	7.77114	+	1.65181i	0.308388	+	0.0655499i
$636$	−7.57399	−	10.4247i	−0.300328	−	0.413366i
$637$	−2.47942	+	0.948104i	−0.0982380	+	0.0375652i
$638$	−13.3473	−	11.0515i	−0.528425	−	0.437534i
$639$	0.659589	−	1.14244i	0.0260929	−	0.0451943i
$640$	−9.92586	−	4.41928i	−0.392354	−	0.174687i
$641$	−12.9307	+	14.3610i	−0.510732	+	0.567225i	−0.942263	−	0.334873i	$-0.891307\pi$
$641$	−12.9307	+	14.3610i	−0.510732	+	0.567225i	0.431532	+	0.902098i	$0.357973\pi$
$642$	−0.973400	+	0.876453i	−0.0384170	+	0.0345909i
$643$	29.0184	−	39.9405i	1.14438	−	1.57510i	0.387053	−	0.922058i	$-0.373493\pi$
$643$	29.0184	−	39.9405i	1.14438	−	1.57510i	0.757323	−	0.653040i	$-0.226507\pi$
$644$	−1.81788	+	3.80497i	−0.0716345	+	0.149937i
$645$	12.2454	+	3.97876i	0.482161	+	0.156664i
$646$	−0.819187	+	3.85397i	−0.0322305	+	0.151632i
$647$	−8.90307	+	19.9966i	−0.350016	+	0.786148i	0.649648	+	0.760235i	$0.274916\pi$
$647$	−8.90307	+	19.9966i	−0.350016	+	0.786148i	−0.999664	+	0.0259135i	$0.991751\pi$
$648$	2.31403	−	1.33601i	0.0909036	−	0.0524832i
$649$	−1.02337	+	3.65924i	−0.0401710	+	0.143638i
$650$			1.06527i			0.0417832i
$651$	14.5731	−	4.30656i	0.571164	−	0.168787i
$652$	−2.12333	−	6.53495i	−0.0831562	−	0.255928i
$653$	−18.8611	−	20.9473i	−0.738090	−	0.819732i	0.250853	−	0.968025i	$-0.419289\pi$
$653$	−18.8611	−	20.9473i	−0.738090	−	0.819732i	−0.988943	+	0.148293i	$0.952622\pi$
$654$	10.1619	+	1.06806i	0.397361	+	0.0417643i
$655$	−0.762506	−	0.0801426i	−0.0297936	−	0.00313143i
$656$	2.12214	+	2.35688i	0.0828557	+	0.0920206i
$657$	−1.97129	−	6.06700i	−0.0769073	−	0.236696i
$658$	−5.67391	+	23.5668i	−0.221192	+	0.918729i
$659$		−	4.61974i		−	0.179960i	−0.995944	−	0.0899798i	$-0.971320\pi$
$659$		−	4.61974i		−	0.179960i	0.995944	−	0.0899798i	$-0.0286802\pi$
$660$	3.03955	−	4.57063i	0.118314	−	0.177912i
$661$	−36.7567	+	21.2215i	−1.42967	+	0.825421i	−0.997094	−	0.0761754i	$-0.975729\pi$
$661$	−36.7567	+	21.2215i	−1.42967	+	0.825421i	−0.432577	+	0.901597i	$0.642396\pi$
$662$	6.90963	−	15.5193i	0.268551	−	0.603174i
$663$	−0.0847323	+	0.398634i	−0.00329073	+	0.0154817i
$664$	36.1362	+	11.7414i	1.40236	+	0.455653i
$665$	−1.14900	−	14.7204i	−0.0445564	−	0.570833i
$666$	4.92207	−	6.77465i	0.190726	−	0.262513i
$667$	−5.69197	+	5.12507i	−0.220394	+	0.198443i
$668$	5.80328	−	6.44520i	0.224536	−	0.249372i
$669$	5.80388	+	2.58406i	0.224391	+	0.0999054i
$670$	0.990438	−	1.71549i	0.0382639	−	0.0662751i
$671$	−0.134111	−	0.00849545i	−0.00517731	−	0.000327963i
$672$	14.5638	+	5.16783i	0.561809	+	0.199354i
$673$	−8.25702	−	11.3648i	−0.318285	−	0.438081i	0.619658	−	0.784872i	$-0.287271\pi$
$673$	−8.25702	−	11.3648i	−0.318285	−	0.438081i	−0.937943	+	0.346791i	$0.887271\pi$
$674$	23.2981	+	4.95217i	0.897409	+	0.190750i
$675$	0.737086	+	3.46772i	0.0283705	+	0.133473i
$676$	1.84393	−	17.5438i	0.0709203	−	0.674762i
$677$	−38.2593	+	17.0341i	−1.47042	+	0.654675i	−0.976635	−	0.214906i	$-0.931056\pi$
$677$	−38.2593	+	17.0341i	−1.47042	+	0.654675i	−0.493790	+	0.869581i	$0.664389\pi$
$678$	−2.39741	+	7.37846i	−0.0920719	+	0.283368i
$679$	21.2607	+	39.2174i	0.815910	+	1.50502i
$680$	−2.80210	+	2.03584i	−0.107456	+	0.0780710i
$681$	2.25962	+	1.30459i	0.0865889	+	0.0499921i
$682$	10.7890	−	10.5563i	0.413131	−	0.404220i
$683$	−8.82101	−	15.2784i	−0.337526	−	0.584613i	0.646440	−	0.762965i	$-0.276257\pi$
$683$	−8.82101	−	15.2784i	−0.337526	−	0.584613i	−0.983967	+	0.178352i	$0.942924\pi$
$684$	0.663618	+	6.31390i	0.0253741	+	0.241418i
$685$	1.97044	−	0.640234i	0.0752866	−	0.0244621i
$686$	14.0627	+	4.19507i	0.536916	+	0.160168i
$687$	−8.83978	−	6.42247i	−0.337259	−	0.245033i
$688$	−2.72245	−	6.11472i	−0.103792	−	0.233122i
$689$	−3.48337	+	0.740413i	−0.132706	+	0.0282075i
$690$	0.825012	+	0.742844i	0.0314077	+	0.0282796i
$691$	−31.1970	+	3.27893i	−1.18679	+	0.124736i	−0.677277	−	0.735728i	$-0.736840\pi$
$691$	−31.1970	+	3.27893i	−1.18679	+	0.124736i	−0.509511	+	0.860464i	$0.670174\pi$
$692$	26.6135			1.01169
$693$	−4.27580	+	7.66274i	−0.162424	+	0.291083i
$694$	−0.674350			−0.0255980
$695$	0.830995	−	0.0873411i	0.0315215	−	0.00331304i
$696$	13.0933	+	11.7893i	0.496301	+	0.446872i
$697$	5.31701	−	1.13017i	0.201396	−	0.0428081i
$698$	9.08972	+	20.4158i	0.344051	+	0.772751i
$699$	11.4754	+	8.33733i	0.434038	+	0.315347i
$700$	−7.84144	+	10.2056i	−0.296379	+	0.385735i
$701$	−2.16439	+	0.703254i	−0.0817480	+	0.0265615i	−0.349605	−	0.936897i	$-0.613684\pi$
$701$	−2.16439	+	0.703254i	−0.0817480	+	0.0265615i	0.267857	+	0.963459i	$0.413684\pi$
$702$	−0.0314090	−	0.298836i	−0.00118545	−	0.0112788i
$703$	24.4486	+	42.3461i	0.922095	+	1.59711i
$704$	11.0714	−	1.63002i	0.417268	−	0.0614335i
$705$	−12.0778	−	6.97312i	−0.454876	−	0.262623i
$706$	8.91815	−	6.47941i	0.335639	−	0.243856i
$707$	30.3089	+	18.6001i	1.13988	+	0.699529i
$708$	0.485765	−	1.49503i	0.0182562	−	0.0561867i
$709$	−12.1230	+	5.39753i	−0.455290	+	0.202708i	−0.621551	−	0.783373i	$-0.713497\pi$
$709$	−12.1230	+	5.39753i	−0.455290	+	0.202708i	0.166261	+	0.986082i	$0.446831\pi$
$710$	0.131787	−	1.25387i	0.00494590	−	0.0470571i
$711$	−0.308565	−	1.45168i	−0.0115721	−	0.0544424i
$712$	13.9323	+	2.96140i	0.522134	+	0.110983i
$713$	−3.92149	−	5.39747i	−0.146861	−	0.202137i
$714$	1.71415	−	1.46212i	0.0641506	−	0.0547186i
$715$	−0.812298	−	1.28119i	−0.0303782	−	0.0479139i
$716$	−3.71079	+	6.42727i	−0.138679	+	0.240198i
$717$	−25.7646	−	11.4711i	−0.962195	−	0.428397i
$718$	−1.43344	+	1.59200i	−0.0534957	+	0.0594129i
$719$	−7.92284	+	7.13376i	−0.295472	+	0.266044i	−0.803511	−	0.595290i	$-0.797037\pi$
$719$	−7.92284	+	7.13376i	−0.295472	+	0.266044i	0.508039	+	0.861334i	$0.330371\pi$
$720$	−0.444535	+	0.611850i	−0.0165669	+	0.0228023i
$721$	−27.2685	+	18.7153i	−1.01553	+	0.696995i
$722$	1.81457	+	0.589591i	0.0675314	+	0.0219423i
$723$	0.0265479	−	0.124898i	0.000987325	−	0.00464500i
$724$	9.23977	−	20.7529i	0.343393	−	0.771274i
$725$	−20.2446	+	11.6882i	−0.751865	+	0.434089i
$726$	−0.190029	+	8.71410i	−0.00705265	+	0.323411i
$727$		−	53.7153i		−	1.99219i	−0.0882861	−	0.996095i	$-0.528139\pi$
$727$		−	53.7153i		−	1.99219i	0.0882861	−	0.996095i	$-0.471861\pi$
$728$	1.84663	−	1.94344i	0.0684405	−	0.0720285i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	−4.07958	−	4.53083i	−0.150992	−	0.167694i
$731$	−11.4093	−	1.19917i	−0.421990	−	0.0443529i
$732$	0.0552904	+	0.00581126i	0.00204359	+	0.000214790i
$733$	13.7295	+	15.2482i	0.507111	+	0.563204i	0.941280	−	0.337628i	$-0.109624\pi$
$733$	13.7295	+	15.2482i	0.507111	+	0.563204i	−0.434169	+	0.900832i	$0.642958\pi$
$734$	7.56967	+	23.2970i	0.279401	+	0.859909i
$735$	−4.60753	+	7.07505i	−0.169951	+	0.260967i
$736$		−	6.78465i		−	0.250085i
$737$	−0.284906	−	6.86821i	−0.0104946	−	0.252994i
$738$	−3.47091	+	2.00393i	−0.127766	+	0.0737656i
$739$	12.2155	−	27.4366i	0.449356	−	1.00927i	−0.536839	−	0.843684i	$-0.680382\pi$
$739$	12.2155	−	27.4366i	0.449356	−	1.00927i	0.986195	−	0.165586i	$-0.0529514\pi$
$740$	−3.63643	+	17.1081i	−0.133678	+	0.628905i
$741$	1.66870	+	0.542194i	0.0613013	+	0.0199180i
$742$	17.7642	+	8.48712i	0.652145	+	0.311572i
$743$	7.92631	−	10.9096i	0.290788	−	0.400236i	−0.638482	−	0.769637i	$-0.720437\pi$
$743$	7.92631	−	10.9096i	0.290788	−	0.400236i	0.929270	+	0.369401i	$0.120437\pi$
$744$	−11.4050	+	10.2691i	−0.418126	+	0.376483i
$745$	0.330471	−	0.367025i	0.0121075	−	0.0134468i
$746$	9.16718	+	4.08149i	0.335634	+	0.149434i
$747$	7.10997	−	12.3148i	0.260140	−	0.450576i
$748$	−1.80237	+	4.54655i	−0.0659011	+	0.166238i
$749$	−1.46257	+	4.12175i	−0.0534411	+	0.150605i
$750$	4.80039	+	6.60717i	0.175286	+	0.241260i
$751$	−31.5381	−	6.70363i	−1.15084	−	0.244619i	−0.407291	−	0.913299i	$-0.633526\pi$
$751$	−31.5381	−	6.70363i	−1.15084	−	0.244619i	−0.743551	+	0.668680i	$0.766860\pi$
$752$	1.50736	+	7.09157i	0.0549678	+	0.258603i
$753$	−0.865080	+	8.23068i	−0.0315253	+	0.299943i
$754$	1.81004	−	0.805881i	0.0659177	−	0.0293484i
$755$	4.50692	−	13.8709i	0.164024	−	0.504813i
$756$	1.89883	−	3.09414i	0.0690598	−	0.112533i
$757$	−4.15237	+	3.01687i	−0.150920	+	0.109650i	−0.660683	−	0.750665i	$-0.729733\pi$
$757$	−4.15237	+	3.01687i	−0.150920	+	0.109650i	0.509763	+	0.860315i	$0.329733\pi$
$758$	6.13809	+	3.54383i	0.222945	+	0.128718i
$759$	3.79831	+	0.644115i	0.137870	+	0.0233799i
$760$	7.45587	+	12.9139i	0.270453	+	0.468438i
$761$	3.85094	+	36.6392i	0.139596	+	1.32817i	0.810112	+	0.586275i	$0.199406\pi$
$761$	3.85094	+	36.6392i	0.139596	+	1.32817i	−0.670516	+	0.741895i	$0.733927\pi$
$762$	4.96382	−	1.61284i	0.179820	−	0.0584272i
$763$	31.5287	−	13.0359i	1.14142	−	0.471931i
$764$	18.2931	+	13.2907i	0.661822	+	0.480842i
$765$	0.527231	+	1.18418i	0.0190621	+	0.0428141i
$766$	5.28142	−	1.12260i	0.190826	−	0.0405612i
$767$	−0.322854	−	0.290699i	−0.0116576	−	0.0104965i
$768$	−13.8100	+	1.45149i	−0.498327	+	0.0523763i
$769$	−24.8757			−0.897040			−0.448520	−	0.893773i	$-0.648049\pi$
$769$	−24.8757			−0.897040			−0.448520	+	0.893773i	$0.648049\pi$
$770$	−0.754473	+	8.35251i	−0.0271893	+	0.301004i
$771$	27.5825			0.993358
$772$	−20.7955	+	2.18570i	−0.748448	+	0.0786651i
$773$	−31.3140	−	28.1952i	−1.12628	−	1.01411i	−0.999755	−	0.0221485i	$-0.992949\pi$
$773$	−31.3140	−	28.1952i	−1.12628	−	1.01411i	−0.126530	−	0.991963i	$-0.540384\pi$
$774$	8.27370	−	1.75863i	0.297392	−	0.0632126i
$775$	−8.28200	−	18.6017i	−0.297498	−	0.668192i
$776$	−36.4481	−	26.4811i	−1.30841	−	0.950617i
$777$	3.66740	−	27.7190i	0.131567	−	0.994412i
$778$	−15.5464	+	5.05133i	−0.557366	+	0.181099i
$779$	−2.44625	−	23.2745i	−0.0876459	−	0.833895i
$780$	0.313802	+	0.543521i	0.0112359	+	0.0194612i
$781$	−1.94369	−	3.91977i	−0.0695507	−	0.140260i
$782$	−0.856640	−	0.494581i	−0.0306334	−	0.0176862i
$783$	5.33453	−	3.87576i	0.190641	−	0.138508i
$784$	4.33601	−	0.681045i	0.154858	−	0.0243230i
$785$	0.969729	−	2.98452i	0.0346111	−	0.106522i
$786$	−0.460139	+	0.204867i	−0.0164126	+	0.00730737i
$787$	−2.69515	+	25.6427i	−0.0960718	+	0.914062i	0.835251	+	0.549868i	$0.185322\pi$
$787$	−2.69515	+	25.6427i	−0.0960718	+	0.914062i	−0.931323	+	0.364194i	$0.881345\pi$
$788$	3.66922	+	17.2623i	0.130711	+	0.614945i
$789$	−23.3764	−	4.96881i	−0.832223	−	0.176894i
$790$	−0.833724	−	1.14752i	−0.0296626	−	0.0408270i
$791$	4.70435	+	25.4738i	0.167267	+	0.905743i
$792$	0.560255	−	8.84433i	0.0199078	−	0.314270i
$793$	0.00768236	−	0.0133062i	0.000272809	−	0.000472518i
$794$	14.2476	+	6.34346i	0.505630	+	0.225121i
$795$	−7.57920	+	8.41755i	−0.268806	+	0.298540i
$796$	16.3713	−	14.7407i	0.580264	−	0.522472i
$797$	19.4251	−	26.7364i	0.688074	−	0.947052i	−0.311922	−	0.950108i	$-0.600973\pi$
$797$	19.4251	−	26.7364i	0.688074	−	0.947052i	0.999995	+	0.00305568i	$0.000972656\pi$
$798$	−5.48897	−	7.99750i	−0.194307	−	0.283109i
$799$	11.8180	+	3.83990i	0.418091	+	0.135846i
$800$	4.30522	−	20.2545i	0.152212	−	0.716103i
$801$	2.16817	−	4.86979i	0.0766085	−	0.172065i
$802$	4.22117	−	2.43709i	0.149055	−	0.0860568i
$803$	−20.3757	−	5.69843i	−0.719041	−	0.201093i
$804$			2.84392i			0.100297i
$805$	3.60385	+	0.867658i	0.127019	+	0.0305809i
$806$	0.533315	+	1.64138i	0.0187852	+	0.0578150i
$807$	−12.3740	−	13.7428i	−0.435587	−	0.483768i
$808$	−35.7173	−	3.75404i	−1.25653	−	0.132067i
$809$	30.5579	+	3.21176i	1.07436	+	0.112919i	0.625147	−	0.780507i	$-0.285039\pi$
$809$	30.5579	+	3.21176i	1.07436	+	0.112919i	0.449210	+	0.893426i	$0.351706\pi$
$810$	−0.639510	−	0.710248i	−0.0224701	−	0.0249556i
$811$	−0.119626	−	0.368171i	−0.00420064	−	0.0129282i	0.948934	−	0.315474i	$-0.102163\pi$
$811$	−0.119626	−	0.368171i	−0.00420064	−	0.0129282i	−0.953135	+	0.302546i	$0.902163\pi$
$812$	23.2728	+	5.60313i	0.816716	+	0.196631i
$813$		−	25.6291i		−	0.898852i
$814$	−9.66977	−	26.0355i	−0.338925	−	0.912543i
$815$	−5.23086	+	3.02004i	−0.183229	+	0.105787i
$816$	0.274083	−	0.615600i	0.00959482	−	0.0215503i
$817$	−10.2690	+	48.3118i	−0.359267	+	1.69022i
$818$	12.5814	+	4.08796i	0.439900	+	0.142932i
$819$	−0.567749	−	0.827218i	−0.0198388	−	0.0289054i
$820$	4.92037	−	6.77231i	0.171827	−	0.236499i
$821$	−26.5895	+	23.9413i	−0.927979	+	0.835556i	−0.986672	−	0.162720i	$-0.947973\pi$
$821$	−26.5895	+	23.9413i	−0.927979	+	0.835556i	0.0586932	+	0.998276i	$0.481307\pi$
$822$	0.910746	−	1.01149i	0.0317659	−	0.0352796i
$823$	23.8383	+	10.6135i	0.830951	+	0.369963i	0.777714	−	0.628619i	$-0.216379\pi$
$823$	23.8383	+	10.6135i	0.830951	+	0.369963i	0.0532372	+	0.998582i	$0.483046\pi$
$824$	16.7007	−	28.9265i	0.581797	−	1.00770i
$825$	10.9305	+	4.33313i	0.380551	+	0.150860i
$826$	0.436168	+	2.36182i	0.0151762	+	0.0821783i
$827$	−19.9761	−	27.4948i	−0.694638	−	0.956087i	−0.999993	−	0.00384841i	$-0.998775\pi$
$827$	−19.9761	−	27.4948i	−0.694638	−	0.956087i	0.305355	−	0.952239i	$-0.401225\pi$
$828$	−1.55902	−	0.331380i	−0.0541797	−	0.0115162i
$829$	−9.57460	−	45.0449i	−0.332540	−	1.56448i	−0.753532	−	0.657411i	$-0.771651\pi$
$829$	−9.57460	−	45.0449i	−0.332540	−	1.56448i	0.420992	−	0.907064i	$-0.361682\pi$
$830$	1.42059	−	13.5160i	0.0493094	−	0.469148i
$831$	−5.37285	+	2.39215i	−0.186382	+	0.0829827i
$832$	−0.395394	+	1.21690i	−0.0137078	+	0.0421883i
$833$	2.70497	−	7.01971i	0.0937217	−	0.243219i
$834$	0.444091	−	0.322651i	0.0153776	−	0.0111725i
$835$	−6.60237	−	3.81188i	−0.228484	−	0.131916i
$836$	18.6559	+	9.76327i	0.645227	+	0.337670i
$837$	2.87179	+	4.97409i	0.0992636	+	0.171930i
$838$	2.51533	+	23.9318i	0.0868906	+	0.826709i
$839$	40.3881	−	13.1229i	1.39435	−	0.453052i	0.486991	−	0.873407i	$-0.338094\pi$
$839$	40.3881	−	13.1229i	1.39435	−	0.453052i	0.907360	+	0.420355i	$0.138094\pi$
$840$	1.11841	−	8.45322i	0.0385890	−	0.291664i
$841$	11.7136	+	8.51040i	0.403916	+	0.293462i
$842$	−8.91381	−	20.0207i	−0.307190	−	0.689960i
$843$	−27.8664	+	5.92318i	−0.959768	+	0.204005i
$844$	15.7679	+	14.1975i	0.542755	+	0.488698i
$845$	−15.4216	+	1.62088i	−0.530520	+	0.0557599i
$846$	−9.16193			−0.314994
$847$	13.3093	+	25.8817i	0.457314	+	0.889305i
$848$	5.88835			0.202207
$849$	16.2713	−	1.71018i	0.558428	−	0.0586932i
$850$	−2.24352	−	2.02008i	−0.0769521	−	0.0692880i
$851$	−12.0075	+	2.55226i	−0.411610	+	0.0874905i
$852$	0.736230	+	1.65360i	0.0252228	+	0.0566514i
$853$	−19.3198	−	14.0367i	−0.661498	−	0.480606i	0.205671	−	0.978621i	$-0.434062\pi$
$853$	−19.3198	−	14.0367i	−0.661498	−	0.480606i	−0.867168	+	0.498015i	$0.834062\pi$
$854$	−0.0784968	+	0.0324553i	−0.00268610	+	0.00111060i
$855$	5.30758	−	1.72454i	0.181515	−	0.0589779i
$856$	−0.461697	−	4.39276i	−0.0157805	−	0.150141i
$857$	−8.68578	−	15.0442i	−0.296700	−	0.513900i	0.678679	−	0.734435i	$-0.262553\pi$
$857$	−8.68578	−	15.0442i	−0.296700	−	0.513900i	−0.975379	+	0.220535i	$0.929220\pi$
$858$	−0.882980	−	0.462094i	−0.0301445	−	0.0157756i
$859$	13.4299	+	7.75377i	0.458223	+	0.264555i	0.711297	−	0.702892i	$-0.248108\pi$
$859$	13.4299	+	7.75377i	0.458223	+	0.264555i	−0.253074	+	0.967447i	$0.581441\pi$
$860$	−14.2929	+	10.3844i	−0.487383	+	0.354105i
$861$	−6.99952	+	11.4057i	−0.238543	+	0.388706i
$862$	−3.07914	+	9.47661i	−0.104876	+	0.322775i
$863$	−34.6615	+	15.4323i	−1.17989	+	0.525322i	−0.900500	−	0.434855i	$-0.856800\pi$
$863$	−34.6615	+	15.4323i	−1.17989	+	0.525322i	−0.279392	+	0.960177i	$0.590133\pi$
$864$	−0.610536	+	5.80886i	−0.0207709	+	0.197622i
$865$	−4.86393	−	22.8830i	−0.165379	−	0.778045i
$866$	−9.91700	−	2.10792i	−0.336994	−	0.0716302i
$867$	9.31348	+	12.8189i	0.316302	+	0.435353i
$868$	−6.97286	+	19.6506i	−0.236674	+	0.666985i
$869$	−4.57581	−	1.81397i	−0.155224	−	0.0615347i
$870$	3.15098	−	5.45765i	0.106828	−	0.185032i
$871$	0.718020	+	0.319683i	0.0243292	+	0.0108321i
$872$	−23.0555	+	25.6058i	−0.780759	+	0.867121i
$873$	−12.5301	+	11.2821i	−0.424078	+	0.381842i
$874$	−2.50316	+	3.44531i	−0.0846707	+	0.116539i
$875$	24.6053	+	11.7556i	0.831812	+	0.397410i
$876$	8.32475	+	2.70487i	0.281267	+	0.0913892i
$877$	6.43652	−	30.2814i	0.217346	−	1.02253i	−0.725222	−	0.688516i	$-0.758263\pi$
$877$	6.43652	−	30.2814i	0.217346	−	1.02253i	0.942567	−	0.334016i	$-0.108404\pi$
$878$	−1.74222	+	3.91309i	−0.0587971	+	0.132060i
$879$	21.2372	−	12.2613i	0.716314	−	0.413564i
$880$	0.873322	+	2.35138i	0.0294397	+	0.0792651i
$881$		−	4.42680i		−	0.149143i	−0.997216	−	0.0745714i	$-0.976241\pi$
$881$		−	4.42680i		−	0.149143i	0.997216	−	0.0745714i	$-0.0237589\pi$
$882$	−0.297409	+	5.53868i	−0.0100143	+	0.186497i
$883$	9.24944	+	28.4669i	0.311269	+	0.957986i	0.977263	+	0.212030i	$0.0680073\pi$
$883$	9.24944	+	28.4669i	0.311269	+	0.957986i	−0.665995	+	0.745956i	$0.731993\pi$
$884$	−0.374177	−	0.415566i	−0.0125850	−	0.0139770i
$885$	−1.37425	−	0.144439i	−0.0461948	−	0.00485527i
$886$	19.7271	+	2.07340i	0.662744	+	0.0696572i
$887$	6.85419	+	7.61235i	0.230141	+	0.255598i	0.847144	−	0.531363i	$-0.178320\pi$
$887$	6.85419	+	7.61235i	0.230141	+	0.255598i	−0.617003	+	0.786961i	$0.711653\pi$
$888$	8.72603	+	26.8560i	0.292826	+	0.901227i
$889$	12.0042	−	12.6335i	0.402607	−	0.423713i
$890$		−	5.09467i		−	0.170774i
$891$	−3.19407	−	0.893279i	−0.107005	−	0.0299260i
$892$	−7.54946	+	4.35868i	−0.252775	+	0.145940i
$893$	21.7598	−	48.8732i	0.728163	−	1.63548i
$894$	0.0674577	−	0.317363i	0.00225612	−	0.0106142i
$895$	6.20453	+	2.01597i	0.207394	+	0.0673865i
$896$	−19.6503	+	13.4867i	−0.656470	+	0.450559i
$897$	−0.258914	+	0.356364i	−0.00864487	+	0.0118986i
$898$	−9.60042	+	8.64426i	−0.320370	+	0.288463i
$899$	−25.3415	+	28.1446i	−0.845186	+	0.938674i
$900$	−4.44392	−	1.97856i	−0.148131	−	0.0659521i
$901$	5.04619	−	8.74025i	0.168113	−	0.291180i
$902$	−0.840349	+	13.2660i	−0.0279806	+	0.441708i
$903$	21.4879	−	18.3286i	0.715074	−	0.609937i
$904$	−15.3774	−	21.1652i	−0.511445	−	0.703944i
$905$	−19.5325	−	4.15177i	−0.649283	−	0.138009i
$906$	−1.99208	−	9.37199i	−0.0661823	−	0.311363i
$907$	−1.33279	+	12.6807i	−0.0442547	+	0.421055i	0.949856	+	0.312687i	$0.101229\pi$
$907$	−1.33279	+	12.6807i	−0.0442547	+	0.421055i	−0.994111	+	0.108368i	$0.965438\pi$
$908$	−3.27064	+	1.45618i	−0.108540	+	0.0483251i
$909$	−4.15345	+	12.7830i	−0.137761	+	0.423985i
$910$	−0.817270	−	0.501547i	−0.0270923	−	0.0166261i
$911$	30.1979	−	21.9400i	1.00050	−	0.726906i	0.0383045	−	0.999266i	$-0.487804\pi$
$911$	30.1979	−	21.9400i	1.00050	−	0.726906i	0.962195	+	0.272360i	$0.0878043\pi$
$912$	−2.51248	−	1.45058i	−0.0831964	−	0.0480335i
$913$	−20.9518	−	42.2528i	−0.693404	−	1.39836i
$914$	−3.89364	−	6.74399i	−0.128790	−	0.223071i
$915$	−0.00510830	−	0.0486023i	−0.000168875	−	0.00160674i
$916$	14.2589	−	4.63301i	0.471128	−	0.153079i
$917$	−1.02467	+	1.33360i	−0.0338377	+	0.0440395i
$918$	0.688930	+	0.500537i	0.0227381	+	0.0165202i
$919$	−4.41385	−	9.91368i	−0.145600	−	0.327022i	0.825994	−	0.563680i	$-0.190615\pi$
$919$	−4.41385	−	9.91368i	−0.145600	−	0.327022i	−0.971593	+	0.236658i	$0.923948\pi$
$920$	−3.66181	+	0.778342i	−0.120726	+	0.0256612i
$921$	−19.4141	−	17.4805i	−0.639716	−	0.576002i
$922$	−13.5507	+	1.42424i	−0.446270	+	0.0469048i
$923$	0.500252			0.0164660
$924$	−5.05774	−	10.9266i	−0.166387	−	0.359460i
$925$	−37.4659			−1.23187
$926$	5.56709	−	0.585125i	0.182946	−	0.0192284i
$927$	−9.28967	−	8.36445i	−0.305113	−	0.274725i
$928$	−37.6721	+	8.00745i	−1.23665	+	0.262858i
$929$	1.35226	+	3.03723i	0.0443663	+	0.0996484i	0.934369	−	0.356307i	$-0.115964\pi$
$929$	1.35226	+	3.03723i	0.0443663	+	0.0996484i	−0.890003	+	0.455955i	$0.849298\pi$
$930$	4.44096	+	3.22654i	0.145625	+	0.105803i
$931$	−28.8390	−	14.7410i	−0.945162	−	0.483115i
$932$	−18.5102	+	6.01433i	−0.606322	+	0.197006i
$933$	2.11096	+	20.0845i	0.0691098	+	0.657536i
$934$	−7.62015	−	13.1985i	−0.249339	−	0.431868i
$935$	4.23865	+	0.718788i	0.138619	+	0.0235069i
$936$	0.877515	+	0.506633i	0.0286825	+	0.0165598i
$937$	−15.5011	+	11.2622i	−0.506398	+	0.367920i	−0.811455	−	0.584414i	$-0.801324\pi$
$937$	−15.5011	+	11.2622i	−0.506398	+	0.367920i	0.305058	+	0.952334i	$0.401324\pi$
$938$	−2.07086	−	3.81991i	−0.0676161	−	0.124724i
$939$	−4.52053	+	13.9128i	−0.147522	+	0.454026i
$940$	17.4817	−	7.78336i	0.570191	−	0.253865i
$941$	−1.47898	+	14.0715i	−0.0482132	+	0.458718i	0.943606	+	0.331070i	$0.107410\pi$
$941$	−1.47898	+	14.0715i	−0.0482132	+	0.458718i	−0.991819	+	0.127648i	$0.959257\pi$
$942$	−0.428624	−	2.01652i	−0.0139653	−	0.0657017i
$943$	5.74690	+	1.22154i	0.187145	+	0.0397789i
$944$	0.422231	+	0.581151i	0.0137425	+	0.0189149i
$945$	−3.00746	−	1.06717i	−0.0978327	−	0.0347151i
$946$	10.3385	−	26.0793i	0.336134	−	0.847912i
$947$	−29.4803	+	51.0614i	−0.957982	+	1.65927i	−0.230591	+	0.973051i	$0.574066\pi$
$947$	−29.4803	+	51.0614i	−0.957982	+	1.65927i	−0.727391	+	0.686223i	$0.759267\pi$
$948$	1.86035	+	0.828281i	0.0604213	+	0.0269013i
$949$	1.61869	−	1.79774i	0.0525450	−	0.0583571i
$950$	−9.65902	+	8.69702i	−0.313380	+	0.282168i
$951$	−10.2455	+	14.1018i	−0.332235	+	0.457282i
$952$	0.591226	+	7.57447i	0.0191617	+	0.245490i
$953$	32.7290	+	10.6343i	1.06020	+	0.344478i	0.786662	−	0.617384i	$-0.211808\pi$
$953$	32.7290	+	10.6343i	1.06020	+	0.344478i	0.273534	+	0.961862i	$0.411808\pi$
$954$	−1.54711	+	7.27858i	−0.0500895	+	0.235653i
$955$	8.08445	−	18.1580i	0.261607	−	0.587578i
$956$	33.5135	−	19.3490i	1.08390	−	0.625793i
$957$	−0.906399	−	21.8505i	−0.0292997	−	0.706327i
$958$		−	28.0304i		−	0.905622i
$959$	1.06377	−	4.41842i	0.0343510	−	0.142678i
$960$	1.25761	+	3.87054i	0.0405893	+	0.124921i
$961$	−1.33070	−	1.47789i	−0.0429258	−	0.0476739i
$962$	3.15813	+	0.331933i	0.101822	+	0.0107019i
$963$	−1.64399	−	0.172790i	−0.0529768	−	0.00556809i
$964$	0.117235	+	0.130203i	0.00377589	+	0.00419355i
$965$	5.67995	+	17.4811i	0.182844	+	0.562737i
$966$	2.33535	−	0.690130i	0.0751387	−	0.0222046i
$967$		−	18.5798i		−	0.597485i	−0.954334	−	0.298742i	$-0.903433\pi$
$967$		−	18.5798i		−	0.597485i	0.954334	−	0.298742i	$-0.0965671\pi$
$968$	−23.3964	−	17.7906i	−0.751989	−	0.571810i
$969$	−4.30627	+	2.48623i	−0.138337	+	0.0798692i
$970$	−6.55434	+	14.7213i	−0.210447	+	0.472672i
$971$	5.37729	−	25.2981i	0.172565	−	0.811856i	−0.803658	−	0.595091i	$-0.797116\pi$
$971$	5.37729	−	25.2981i	0.172565	−	0.811856i	0.976224	−	0.216765i	$-0.0695506\pi$
$972$	1.30498	+	0.424013i	0.0418572	+	0.0136002i
$973$	0.790131	−	1.65381i	0.0253304	−	0.0530186i
$974$	13.3191	−	18.3321i	0.426771	−	0.587400i
$975$	−0.999076	+	0.899572i	−0.0319960	+	0.0288094i
$976$	−0.0169994	+	0.0188798i	−0.000544138	+	0.000604327i
$977$	−11.2930	−	5.02797i	−0.361295	−	0.160859i	0.218058	−	0.975936i	$-0.430028\pi$
$977$	−11.2930	−	5.02797i	−0.361295	−	0.160859i	−0.579353	+	0.815077i	$0.696695\pi$
$978$	−1.98400	+	3.43639i	−0.0634414	+	0.109884i
$979$	−9.46687	−	14.9316i	−0.302562	−	0.477215i
$980$	−4.13781	−	10.8209i	−0.132177	−	0.345661i
$981$	7.57958	+	10.4324i	0.241997	+	0.333081i
$982$	19.6041	+	4.16697i	0.625591	+	0.132973i
$983$	3.39766	+	15.9847i	0.108369	+	0.509834i	0.998531	+	0.0541900i	$0.0172577\pi$
$983$	3.39766	+	15.9847i	0.108369	+	0.509834i	−0.890162	+	0.455644i	$0.849409\pi$
$984$	1.41271	−	13.4410i	0.0450354	−	0.428483i
$985$	14.1720	−	6.30979i	0.451558	−	0.201047i
$986$	−1.73515	+	5.34026i	−0.0552586	+	0.170068i
$987$	−26.8938	+	14.5798i	−0.856040	+	0.464080i
$988$	−1.94772	+	1.41510i	−0.0619653	+	0.0450204i
$989$	−10.7385	−	6.19987i	−0.341464	−	0.197144i
$990$	−3.13600	+	0.461707i	−0.0996686	+	0.0146740i
$991$	1.00540	+	1.74141i	0.0319376	+	0.0553176i	0.881552	−	0.472086i	$-0.156499\pi$
$991$	1.00540	+	1.74141i	0.0319376	+	0.0553176i	−0.849615	+	0.527404i	$0.823166\pi$
$992$	−3.50666	−	33.3637i	−0.111337	−	1.05930i
$993$	20.3899	−	6.62508i	0.647054	−	0.210241i
$994$	−2.19300	−	1.68498i	−0.0695576	−	0.0534445i
$995$	−15.6665	−	11.3824i	−0.496662	−	0.360846i
$996$	7.93612	+	17.8248i	0.251466	+	0.564801i
$997$	25.5302	−	5.42660i	0.808549	−	0.171862i	0.214951	−	0.976625i	$-0.431041\pi$
$997$	25.5302	−	5.42660i	0.808549	−	0.171862i	0.593597	+	0.804762i	$0.297707\pi$
$998$	−8.97792	−	8.08375i	−0.284191	−	0.255887i
$999$	10.5102	−	1.10467i	0.332528	−	0.0349501i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.ba.a.19.11	✓	128
3.2	odd	2		693.2.cg.c.19.6		128
7.3	odd	6	inner	231.2.ba.a.52.6	yes	128
11.7	odd	10	inner	231.2.ba.a.40.6	yes	128
21.17	even	6		693.2.cg.c.514.11		128
33.29	even	10		693.2.cg.c.271.11		128
77.73	even	30	inner	231.2.ba.a.73.11	yes	128
231.227	odd	30		693.2.cg.c.73.6		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.ba.a.19.11	✓	128	1.1	even	1	trivial
231.2.ba.a.40.6	yes	128	11.7	odd	10	inner
231.2.ba.a.52.6	yes	128	7.3	odd	6	inner
231.2.ba.a.73.11	yes	128	77.73	even	30	inner
693.2.cg.c.19.6		128	3.2	odd	2
693.2.cg.c.73.6		128	231.227	odd	30
693.2.cg.c.271.11		128	33.29	even	10
693.2.cg.c.514.11		128	21.17	even	6

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.ba (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.788039 - 0.0828262i) q^{2} +(0.743145 + 0.669131i) q^{3} +(-1.34215 + 0.285283i) q^{4} +(0.490588 + 1.10188i) q^{5} +(0.641048 + 0.465749i) q^{6} +(2.62289 + 0.347026i) q^{7} +(-2.54123 + 0.825697i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(0.788039 - 0.0828262i) q^{2} +(0.743145 + 0.669131i) q^{3} +(-1.34215 + 0.285283i) q^{4} +(0.490588 + 1.10188i) q^{5} +(0.641048 + 0.465749i) q^{6} +(2.62289 + 0.347026i) q^{7} +(-2.54123 + 0.825697i) q^{8} +(0.104528 + 0.994522i) q^{9} +(0.477866 + 0.827689i) q^{10} +(2.93854 + 1.53784i) q^{11} +(-1.18830 - 0.686067i) q^{12} +(-0.306792 + 0.222897i) q^{13} +(2.09568 + 0.0562252i) q^{14} +(-0.372723 + 1.14712i) q^{15} +(0.572815 - 0.255034i) q^{16} +(0.112336 - 1.06881i) q^{17} +(0.164745 + 0.775064i) q^{18} +(-4.52576 - 0.961979i) q^{19} +(-0.972789 - 1.33893i) q^{20} +(1.71698 + 2.01295i) q^{21} +(2.44306 + 0.968491i) q^{22} +(0.580792 - 1.00596i) q^{23} +(-2.44100 - 1.08680i) q^{24} +(2.37219 - 2.63459i) q^{25} +(-0.223302 + 0.201062i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(-3.61932 + 0.282506i) q^{28} +(-6.27112 - 2.03761i) q^{29} +(-0.198708 + 0.934848i) q^{30} +(2.33612 - 5.24702i) q^{31} +(5.05833 - 2.92043i) q^{32} +(1.15475 + 3.10911i) q^{33} -0.851564i q^{34} +(0.904379 + 3.06036i) q^{35} +(-0.424013 - 1.30498i) q^{36} +(-7.07143 - 7.85362i) q^{37} +(-3.64615 - 0.383226i) q^{38} +(-0.377138 - 0.0396388i) q^{39} +(-2.15651 - 2.39505i) q^{40} +(1.56301 + 4.81045i) q^{41} +(1.51978 + 1.44407i) q^{42} -10.6749i q^{43} +(-4.38269 - 1.22570i) q^{44} +(-1.04456 + 0.603078i) q^{45} +(0.374366 - 0.840841i) q^{46} +(-2.40399 + 11.3099i) q^{47} +(0.596336 + 0.193761i) q^{48} +(6.75915 + 1.82042i) q^{49} +(1.65117 - 2.27264i) q^{50} +(0.798652 - 0.719110i) q^{51} +(0.348172 - 0.386684i) q^{52} +(8.57905 + 3.81964i) q^{53} +(-0.396190 + 0.686221i) q^{54} +(-0.252901 + 3.99236i) q^{55} +(-6.95192 + 1.28384i) q^{56} +(-2.71960 - 3.74321i) q^{57} +(-5.11065 - 1.08630i) q^{58} +(0.238191 + 1.12060i) q^{59} +(0.172995 - 1.64594i) q^{60} +(-0.0370143 + 0.0164798i) q^{61} +(1.40637 - 4.32835i) q^{62} +(-0.0709575 + 2.64480i) q^{63} +(2.72973 - 1.98326i) q^{64} +(-0.396113 - 0.228696i) q^{65} +(1.16750 + 2.35445i) q^{66} +(-1.03631 - 1.79495i) q^{67} +(0.154140 + 1.46654i) q^{68} +(1.10473 - 0.358949i) q^{69} +(0.966164 + 2.33677i) q^{70} +(-1.06724 - 0.775393i) q^{71} +(-1.08680 - 2.44100i) q^{72} +(-6.23982 + 1.32632i) q^{73} +(-6.22304 - 5.60325i) q^{74} +(3.52577 - 0.370573i) q^{75} +6.34868 q^{76} +(7.17382 + 5.05335i) q^{77} -0.300482 q^{78} +(-1.47598 + 0.155132i) q^{79} +(0.562032 + 0.506056i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(1.63014 + 3.66136i) q^{82} +(-11.5042 - 8.35828i) q^{83} +(-2.87871 - 2.21185i) q^{84} +(1.23280 - 0.400562i) q^{85} +(-0.884158 - 8.41220i) q^{86} +(-3.29692 - 5.71044i) q^{87} +(-8.73732 - 1.48167i) q^{88} +(-4.61647 - 2.66532i) q^{89} +(-0.773204 + 0.561766i) q^{90} +(-0.882033 + 0.478171i) q^{91} +(-0.492526 + 1.51584i) q^{92} +(5.24702 - 2.33612i) q^{93} +(-0.957683 + 9.11174i) q^{94} +(-1.16030 - 5.45877i) q^{95} +(5.71322 + 1.21438i) q^{96} +(9.91056 + 13.6407i) q^{97} +(5.47725 + 0.874729i) q^{98} +(-1.22226 + 3.08319i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9}+O(q^{10}) \) 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9	\( 128 q - 12 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 16 q^{9} - 2 q^{11} + 12 q^{14} + 12 q^{15} + 40 q^{16} - 60 q^{17} - 10 q^{18} + 52 q^{22} - 24 q^{23} - 90 q^{24} - 20 q^{25} + 24 q^{26} + 30 q^{28} + 40 q^{29} - 18 q^{31} + 18 q^{33} - 80 q^{35} - 24 q^{36} - 8 q^{37} - 24 q^{38} - 90 q^{40} + 14 q^{42} - 82 q^{44} + 12 q^{45} + 70 q^{46} - 24 q^{47} - 94 q^{49} - 20 q^{51} + 4 q^{53} - 104 q^{56} - 32 q^{58} + 48 q^{59} + 30 q^{61} - 10 q^{63} - 48 q^{64} + 36 q^{66} - 40 q^{67} + 180 q^{68} + 146 q^{70} - 32 q^{71} + 10 q^{72} + 90 q^{73} + 40 q^{74} - 24 q^{75} - 72 q^{78} + 50 q^{79} + 228 q^{80} + 16 q^{81} + 168 q^{82} - 60 q^{84} - 20 q^{85} + 146 q^{86} + 16 q^{88} + 48 q^{91} - 204 q^{92} + 44 q^{93} + 10 q^{95} - 44 q^{99}+O(q^{100}) \) 128 * q - 12 * q^4 + 12 * q^5 - 10 * q^7 - 40 * q^8 - 16 * q^9 - 2 * q^11 + 12 * q^14 + 12 * q^15 + 40 * q^16 - 60 * q^17 - 10 * q^18 + 52 * q^22 - 24 * q^23 - 90 * q^24 - 20 * q^25 + 24 * q^26 + 30 * q^28 + 40 * q^29 - 18 * q^31 + 18 * q^33 - 80 * q^35 - 24 * q^36 - 8 * q^37 - 24 * q^38 - 90 * q^40 + 14 * q^42 - 82 * q^44 + 12 * q^45 + 70 * q^46 - 24 * q^47 - 94 * q^49 - 20 * q^51 + 4 * q^53 - 104 * q^56 - 32 * q^58 + 48 * q^59 + 30 * q^61 - 10 * q^63 - 48 * q^64 + 36 * q^66 - 40 * q^67 + 180 * q^68 + 146 * q^70 - 32 * q^71 + 10 * q^72 + 90 * q^73 + 40 * q^74 - 24 * q^75 - 72 * q^78 + 50 * q^79 + 228 * q^80 + 16 * q^81 + 168 * q^82 - 60 * q^84 - 20 * q^85 + 146 * q^86 + 16 * q^88 + 48 * q^91 - 204 * q^92 + 44 * q^93 + 10 * q^95 - 44 * q^99

Introduction

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