LMFDB - Embedded newform 150.2.l.a.53.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(17,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("150.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.l (of order $20$, 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:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			53.3
Character	$\chi$	$=$	150.53
Dual form			150.2.l.a.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.891007 + 0.453990i) q^{2} +(-0.322239 + 1.70181i) q^{3} +(0.587785 - 0.809017i) q^{4} +(-0.0831552 + 2.23452i) q^{5} +(-0.485490 - 1.66262i) q^{6} +(0.0556476 - 0.0556476i) q^{7} +(-0.156434 + 0.987688i) q^{8} +(-2.79232 - 1.09678i) q^{9} +O(q^{10})$	\(q+(-0.891007 + 0.453990i) q^{2} +(-0.322239 + 1.70181i) q^{3} +(0.587785 - 0.809017i) q^{4} +(-0.0831552 + 2.23452i) q^{5} +(-0.485490 - 1.66262i) q^{6} +(0.0556476 - 0.0556476i) q^{7} +(-0.156434 + 0.987688i) q^{8} +(-2.79232 - 1.09678i) q^{9} +(-0.940360 - 2.02872i) q^{10} +(-1.04749 - 0.340351i) q^{11} +(1.18739 + 1.26100i) q^{12} +(-2.31368 + 4.54086i) q^{13} +(-0.0243189 + 0.0748459i) q^{14} +(-3.77594 - 0.861563i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(3.10226 + 0.491350i) q^{17} +(2.98591 - 0.290452i) q^{18} +(-0.824223 - 1.13445i) q^{19} +(1.75889 + 1.38069i) q^{20} +(0.0767699 + 0.112634i) q^{21} +(1.08784 - 0.172297i) q^{22} +(1.13408 + 2.22575i) q^{23} +(-1.63045 - 0.584493i) q^{24} +(-4.98617 - 0.371624i) q^{25} -5.09632i q^{26} +(2.76630 - 4.39859i) q^{27} +(-0.0123110 - 0.0777287i) q^{28} +(5.66803 + 4.11807i) q^{29} +(3.75553 - 0.946581i) q^{30} +(7.72991 - 5.61611i) q^{31} +(0.707107 + 0.707107i) q^{32} +(0.916756 - 1.67296i) q^{33} +(-2.98720 + 0.970601i) q^{34} +(0.119718 + 0.128973i) q^{35} +(-2.52860 + 1.61437i) q^{36} +(9.23065 + 4.70325i) q^{37} +(1.24942 + 0.636609i) q^{38} +(-6.98213 - 5.40069i) q^{39} +(-2.19400 - 0.431688i) q^{40} +(3.55210 - 1.15415i) q^{41} +(-0.119537 - 0.0655044i) q^{42} +(-1.00563 - 1.00563i) q^{43} +(-0.891050 + 0.647386i) q^{44} +(2.68297 - 6.14831i) q^{45} +(-2.02094 - 1.46830i) q^{46} +(-1.98797 - 12.5515i) q^{47} +(1.71810 - 0.219422i) q^{48} +6.99381i q^{49} +(4.61142 - 1.93255i) q^{50} +(-1.83585 + 5.12113i) q^{51} +(2.31368 + 4.54086i) q^{52} +(-6.70559 + 1.06206i) q^{53} +(-0.467880 + 5.17504i) q^{54} +(0.847626 - 2.31234i) q^{55} +(0.0462573 + 0.0636677i) q^{56} +(2.19621 - 1.03711i) q^{57} +(-6.91981 - 1.09599i) q^{58} +(2.03647 + 6.26761i) q^{59} +(-2.91646 + 2.54838i) q^{60} +(1.23324 - 3.79553i) q^{61} +(-4.33774 + 8.51329i) q^{62} +(-0.216419 + 0.0943531i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(-9.95425 - 5.54757i) q^{65} +(-0.0573270 + 1.90682i) q^{66} +(-1.04169 + 6.57696i) q^{67} +(2.22097 - 2.22097i) q^{68} +(-4.15326 + 1.21276i) q^{69} +(-0.165222 - 0.0605649i) q^{70} +(-7.51096 + 10.3379i) q^{71} +(1.52009 - 2.58637i) q^{72} +(1.18329 - 0.602914i) q^{73} -10.3598 q^{74} +(2.23917 - 8.36577i) q^{75} -1.40225 q^{76} +(-0.0772302 + 0.0393507i) q^{77} +(8.67298 + 1.64223i) q^{78} +(5.85354 - 8.05671i) q^{79} +(2.15085 - 0.611420i) q^{80} +(6.59415 + 6.12512i) q^{81} +(-2.64098 + 2.64098i) q^{82} +(-0.137997 + 0.871279i) q^{83} +(0.136247 + 0.00409615i) q^{84} +(-1.35590 + 6.89121i) q^{85} +(1.35257 + 0.439477i) q^{86} +(-8.83463 + 8.31892i) q^{87} +(0.500025 - 0.981353i) q^{88} +(1.01326 - 3.11850i) q^{89} +(0.400727 + 6.69622i) q^{90} +(0.123937 + 0.381439i) q^{91} +(2.46727 + 0.390777i) q^{92} +(7.06668 + 14.9646i) q^{93} +(7.46957 + 10.2810i) q^{94} +(2.60348 - 1.74741i) q^{95} +(-1.43122 + 0.975505i) q^{96} +(-10.2531 + 1.62393i) q^{97} +(-3.17512 - 6.23153i) q^{98} +(2.55165 + 2.09924i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q + 4 * q^3 + 4 * q^7	$ 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{7}{20}\right)$

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 $

$2$	−0.891007	+	0.453990i	−0.630037	+	0.321020i
$2$	−0.891007	+	0.453990i	−0.630037	+	0.321020i
$3$	−0.322239	+	1.70181i	−0.186045	+	0.982541i
$3$	−0.322239	+	1.70181i	−0.186045	+	0.982541i
$4$	0.587785	−	0.809017i	0.293893	−	0.404508i
$5$	−0.0831552	+	2.23452i	−0.0371882	+	0.999308i
$5$	−0.0831552	+	2.23452i	−0.0371882	+	0.999308i
$6$	−0.485490	−	1.66262i	−0.198200	−	0.678761i
$7$	0.0556476	−	0.0556476i	0.0210328	−	0.0210328i	−0.696512	−	0.717545i	$-0.745266\pi$
$7$	0.0556476	−	0.0556476i	0.0210328	−	0.0210328i	0.717545	+	0.696512i	$0.245266\pi$
$8$	−0.156434	+	0.987688i	−0.0553079	+	0.349201i
$9$	−2.79232	−	1.09678i	−0.930775	−	0.365593i
$10$	−0.940360	−	2.02872i	−0.297368	−	0.641539i
$11$	−1.04749	−	0.340351i	−0.315831	−	0.102620i	0.146812	−	0.989164i	$-0.453099\pi$
$11$	−1.04749	−	0.340351i	−0.315831	−	0.102620i	−0.462643	+	0.886545i	$0.653099\pi$
$12$	1.18739	+	1.26100i	0.342769	+	0.364018i
$13$	−2.31368	+	4.54086i	−0.641700	+	1.25941i	0.309520	+	0.950893i	$0.399832\pi$
$13$	−2.31368	+	4.54086i	−0.641700	+	1.25941i	−0.951220	+	0.308514i	$0.900168\pi$
$14$	−0.0243189	+	0.0748459i	−0.00649950	+	0.0200034i
$15$	−3.77594	−	0.861563i	−0.974943	−	0.222455i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	3.10226	+	0.491350i	0.752408	+	0.119170i	0.520846	−	0.853650i	$-0.325616\pi$
$17$	3.10226	+	0.491350i	0.752408	+	0.119170i	0.231562	+	0.972820i	$0.425616\pi$
$18$	2.98591	−	0.290452i	0.703785	−	0.0684602i
$19$	−0.824223	−	1.13445i	−0.189090	−	0.260260i	0.703938	−	0.710262i	$-0.251423\pi$
$19$	−0.824223	−	1.13445i	−0.189090	−	0.260260i	−0.893028	+	0.450002i	$0.851423\pi$
$20$	1.75889	+	1.38069i	0.393299	+	0.308732i
$21$	0.0767699	+	0.112634i	0.0167526	+	0.0245787i
$22$	1.08784	−	0.172297i	0.231928	−	0.0367338i
$23$	1.13408	+	2.22575i	0.236472	+	0.464102i	0.978495	−	0.206273i	$-0.0661334\pi$
$23$	1.13408	+	2.22575i	0.236472	+	0.464102i	−0.742023	+	0.670375i	$0.766133\pi$
$24$	−1.63045	−	0.584493i	−0.332814	−	0.119309i
$25$	−4.98617	−	0.371624i	−0.997234	−	0.0743249i
$26$		−	5.09632i		−	0.999471i
$27$	2.76630	−	4.39859i	0.532376	−	0.846508i
$28$	−0.0123110	−	0.0777287i	−0.00232656	−	0.0146893i
$29$	5.66803	+	4.11807i	1.05253	+	0.764705i	0.972691	−	0.232103i	$-0.0745605\pi$
$29$	5.66803	+	4.11807i	1.05253	+	0.764705i	0.0798355	+	0.996808i	$0.474560\pi$
$30$	3.75553	−	0.946581i	0.685662	−	0.172821i
$31$	7.72991	−	5.61611i	1.38833	−	1.00868i	0.392287	−	0.919843i	$-0.371684\pi$
$31$	7.72991	−	5.61611i	1.38833	−	1.00868i	0.996046	−	0.0888399i	$-0.0283160\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	0.916756	−	1.67296i	0.159587	−	0.291225i
$34$	−2.98720	+	0.970601i	−0.512301	+	0.166457i
$35$	0.119718	+	0.128973i	0.0202361	+	0.0218004i
$36$	−2.52860	+	1.61437i	−0.421433	+	0.269061i
$37$	9.23065	+	4.70325i	1.51751	+	0.773210i	0.996755	−	0.0804961i	$-0.0256505\pi$
$37$	9.23065	+	4.70325i	1.51751	+	0.773210i	0.520755	+	0.853706i	$0.325650\pi$
$38$	1.24942	+	0.636609i	0.202682	+	0.103272i
$39$	−6.98213	−	5.40069i	−1.11803	−	0.864803i
$40$	−2.19400	−	0.431688i	−0.346902	−	0.0682558i
$41$	3.55210	−	1.15415i	0.554745	−	0.180248i	−0.0182101	−	0.999834i	$-0.505797\pi$
$41$	3.55210	−	1.15415i	0.554745	−	0.180248i	0.572956	+	0.819586i	$0.305797\pi$
$42$	−0.119537	−	0.0655044i	−0.0184450	−	0.0101075i
$43$	−1.00563	−	1.00563i	−0.153357	−	0.153357i	0.626258	−	0.779616i	$-0.284586\pi$
$43$	−1.00563	−	1.00563i	−0.153357	−	0.153357i	−0.779616	+	0.626258i	$0.784586\pi$
$44$	−0.891050	+	0.647386i	−0.134331	+	0.0975971i
$45$	2.68297	−	6.14831i	0.399954	−	0.916535i
$46$	−2.02094	−	1.46830i	−0.297972	−	0.216489i
$47$	−1.98797	−	12.5515i	−0.289975	−	1.83083i	−0.515858	−	0.856674i	$-0.672527\pi$
$47$	−1.98797	−	12.5515i	−0.289975	−	1.83083i	0.225883	−	0.974154i	$-0.427473\pi$
$48$	1.71810	−	0.219422i	0.247986	−	0.0316708i
$49$			6.99381i			0.999115i
$50$	4.61142	−	1.93255i	0.652154	−	0.273304i
$51$	−1.83585	+	5.12113i	−0.257071	+	0.717101i
$52$	2.31368	+	4.54086i	0.320850	+	0.629704i
$53$	−6.70559	+	1.06206i	−0.921083	+	0.145885i	−0.598929	−	0.800802i	$-0.704407\pi$
$53$	−6.70559	+	1.06206i	−0.921083	+	0.145885i	−0.322154	+	0.946687i	$0.604407\pi$
$54$	−0.467880	+	5.17504i	−0.0636704	+	0.704234i
$55$	0.847626	−	2.31234i	0.114294	−	0.311796i
$56$	0.0462573	+	0.0636677i	0.00618139	+	0.00850795i
$57$	2.19621	−	1.03711i	0.290895	−	0.137369i
$58$	−6.91981	−	1.09599i	−0.908616	−	0.143911i
$59$	2.03647	+	6.26761i	0.265126	+	0.815974i	0.991664	+	0.128848i	$0.0411279\pi$
$59$	2.03647	+	6.26761i	0.265126	+	0.815974i	−0.726538	+	0.687126i	$0.758872\pi$
$60$	−2.91646	+	2.54838i	−0.376513	+	0.328995i
$61$	1.23324	−	3.79553i	0.157901	−	0.485968i	−0.840543	−	0.541745i	$-0.817764\pi$
$61$	1.23324	−	3.79553i	0.157901	−	0.485968i	0.998443	+	0.0557774i	$0.0177637\pi$
$62$	−4.33774	+	8.51329i	−0.550894	+	1.08119i
$63$	−0.216419	+	0.0943531i	−0.0272663	+	0.0118874i
$64$	−0.951057	−	0.309017i	−0.118882	−	0.0386271i
$65$	−9.95425	−	5.54757i	−1.23467	−	0.688091i
$66$	−0.0573270	+	1.90682i	−0.00705647	+	0.234713i
$67$	−1.04169	+	6.57696i	−0.127263	+	0.803504i	0.838657	+	0.544660i	$0.183341\pi$
$67$	−1.04169	+	6.57696i	−0.127263	+	0.803504i	−0.965919	+	0.258844i	$0.916659\pi$
$68$	2.22097	−	2.22097i	0.269332	−	0.269332i
$69$	−4.15326	+	1.21276i	−0.499993	+	0.146000i
$70$	−0.165222	−	0.0605649i	−0.0197479	−	0.00723889i
$71$	−7.51096	+	10.3379i	−0.891387	+	1.22689i	0.0817481	+	0.996653i	$0.473950\pi$
$71$	−7.51096	+	10.3379i	−0.891387	+	1.22689i	−0.973135	+	0.230236i	$0.926050\pi$
$72$	1.52009	−	2.58637i	0.179144	−	0.304807i
$73$	1.18329	−	0.602914i	0.138493	−	0.0705658i	−0.383371	−	0.923595i	$-0.625237\pi$
$73$	1.18329	−	0.602914i	0.138493	−	0.0705658i	0.521864	+	0.853029i	$0.325237\pi$
$74$	−10.3598			−1.20430
$75$	2.23917	−	8.36577i	0.258557	−	0.965996i
$76$	−1.40225			−0.160849
$77$	−0.0772302	+	0.0393507i	−0.00880119	+	0.00448443i
$78$	8.67298	+	1.64223i	0.982022	+	0.185946i
$79$	5.85354	−	8.05671i	0.658575	−	0.906451i	−0.340858	−	0.940115i	$-0.610718\pi$
$79$	5.85354	−	8.05671i	0.658575	−	0.906451i	0.999433	+	0.0336639i	$0.0107176\pi$
$80$	2.15085	−	0.611420i	0.240473	−	0.0683588i
$81$	6.59415	+	6.12512i	0.732684	+	0.680569i
$82$	−2.64098	+	2.64098i	−0.291647	+	0.291647i
$83$	−0.137997	+	0.871279i	−0.0151471	+	0.0956353i	−0.994104	−	0.108433i	$-0.965417\pi$
$83$	−0.137997	+	0.871279i	−0.0151471	+	0.0956353i	0.978957	+	0.204069i	$0.0654166\pi$
$84$	0.136247	+	0.00409615i	0.0148657	+	0.000446927i
$85$	−1.35590	+	6.89121i	−0.147068	+	0.747456i
$86$	1.35257	+	0.439477i	0.145851	+	0.0473900i
$87$	−8.83463	+	8.31892i	−0.947172	+	0.891882i
$88$	0.500025	−	0.981353i	0.0533028	−	0.104613i
$89$	1.01326	−	3.11850i	0.107406	−	0.330560i	−0.882882	−	0.469595i	$-0.844400\pi$
$89$	1.01326	−	3.11850i	0.107406	−	0.330560i	0.990288	+	0.139035i	$0.0444000\pi$
$90$	0.400727	+	6.69622i	0.0422404	+	0.705844i
$91$	0.123937	+	0.381439i	0.0129921	+	0.0399856i
$92$	2.46727	+	0.390777i	0.257230	+	0.0407413i
$93$	7.06668	+	14.9646i	0.732781	+	1.55175i
$94$	7.46957	+	10.2810i	0.770427	+	1.06040i
$95$	2.60348	−	1.74741i	0.267112	−	0.179280i
$96$	−1.43122	+	0.975505i	−0.146073	+	0.0995621i
$97$	−10.2531	+	1.62393i	−1.04104	+	0.164885i	−0.653469	−	0.756953i	$-0.726687\pi$
$97$	−10.2531	+	1.62393i	−1.04104	+	0.164885i	−0.387575	+	0.921838i	$0.626687\pi$
$98$	−3.17512	−	6.23153i	−0.320736	−	0.629479i
$99$	2.55165	+	2.09924i	0.256450	+	0.210981i
$100$	−3.23145	+	3.81546i	−0.323145	+	0.381546i
$101$		−	14.0377i		−	1.39680i	−0.715708	−	0.698399i	$-0.753896\pi$
$101$		−	14.0377i		−	1.39680i	0.715708	−	0.698399i	$-0.246104\pi$
$102$	−0.689188	−	5.39642i	−0.0682398	−	0.534325i
$103$	−2.06559	−	13.0416i	−0.203529	−	1.28503i	−0.851900	−	0.523705i	$-0.824549\pi$
$103$	−2.06559	−	13.0416i	−0.203529	−	1.28503i	0.648371	−	0.761324i	$-0.275451\pi$
$104$	−4.12301	−	2.99554i	−0.404295	−	0.293737i
$105$	−0.258066	+	0.162178i	−0.0251846	+	0.0158269i
$106$	5.49256	−	3.99058i	0.533484	−	0.387599i
$107$	−13.7619	−	13.7619i	−1.33041	−	1.33041i	−0.904999	−	0.425413i	$-0.860129\pi$
$107$	−13.7619	−	13.7619i	−1.33041	−	1.33041i	−0.425413	−	0.904999i	$-0.639871\pi$
$108$	−1.93254	−	4.82341i	−0.185958	−	0.464133i
$109$	11.7044	−	3.80299i	1.12108	−	0.364260i	0.310898	−	0.950443i	$-0.399370\pi$
$109$	11.7044	−	3.80299i	1.12108	−	0.364260i	0.810178	+	0.586183i	$0.199370\pi$
$110$	0.294541	+	2.44513i	0.0280834	+	0.233134i
$111$	−10.9785	+	14.1933i	−1.04204	+	1.34716i
$112$	−0.0701201	−	0.0357280i	−0.00662572	−	0.00337598i
$113$	6.80204	+	3.46581i	0.639882	+	0.326036i	0.743654	−	0.668565i	$-0.233091\pi$
$113$	6.80204	+	3.46581i	0.639882	+	0.326036i	−0.103771	+	0.994601i	$0.533091\pi$
$114$	−1.48600	+	1.92113i	−0.139177	+	0.179930i
$115$	−5.06780	+	2.34904i	−0.472575	+	0.219049i
$116$	6.66317	−	2.16499i	0.618660	−	0.201015i
$117$	11.4409	−	10.1420i	1.05771	−	0.937624i
$118$	−4.65995	−	4.65995i	−0.428983	−	0.428983i
$119$	0.199976	−	0.145291i	0.0183317	−	0.0133188i
$120$	1.44164	−	3.59467i	0.131603	−	0.328147i
$121$	−7.91779	−	5.75261i	−0.719799	−	0.522964i
$122$	0.624308	+	3.94172i	0.0565222	+	0.356867i
$123$	0.819518	+	6.41692i	0.0738935	+	0.578594i
$124$		−	9.55469i		−	0.858037i
$125$	1.24503	−	11.1108i	0.111359	−	0.993780i
$126$	0.149996	−	0.182322i	0.0133627	−	0.0162425i
$127$	−1.46280	−	2.87091i	−0.129803	−	0.254752i	0.816954	−	0.576703i	$-0.195661\pi$
$127$	−1.46280	−	2.87091i	−0.129803	−	0.254752i	−0.946756	+	0.321952i	$0.895661\pi$
$128$	0.987688	−	0.156434i	0.0873001	−	0.0138270i
$129$	2.03545	−	1.38734i	0.179211	−	0.122149i
$130$	11.3878	+	0.423786i	0.998780	+	0.0371685i
$131$	3.12598	+	4.30255i	0.273118	+	0.375915i	0.923439	−	0.383744i	$-0.125366\pi$
$131$	3.12598	+	4.30255i	0.273118	+	0.375915i	−0.650321	+	0.759660i	$0.725366\pi$
$132$	−0.814598	−	1.72501i	−0.0709017	−	0.150143i
$133$	−0.108995	−	0.0172632i	−0.00945109	−	0.00149690i
$134$	−2.05773	−	6.33303i	−0.177761	−	0.547091i
$135$	9.59870	+	6.54713i	0.826125	+	0.563487i
$136$	−0.970601	+	2.98720i	−0.0832283	+	0.256150i
$137$	−5.21451	+	10.2341i	−0.445506	+	0.874354i	0.553629	+	0.832763i	$0.313243\pi$
$137$	−5.21451	+	10.2341i	−0.445506	+	0.874354i	−0.999135	+	0.0415907i	$0.986757\pi$
$138$	3.15000	−	2.96612i	0.268146	−	0.252493i
$139$	10.3684	+	3.36891i	0.879440	+	0.285747i	0.713725	−	0.700426i	$-0.247007\pi$
$139$	10.3684	+	3.36891i	0.879440	+	0.285747i	0.165715	+	0.986174i	$0.447007\pi$
$140$	0.174710	−	0.0210457i	0.0147657	−	0.00177868i
$141$	22.0009	+	0.661442i	1.85281	+	0.0557034i
$142$	1.99898	−	12.6211i	0.167751	−	1.05914i
$143$	3.96905	−	3.96905i	0.331909	−	0.331909i
$144$	−0.180223	+	2.99458i	−0.0150186	+	0.249548i
$145$	−9.67323	+	12.3229i	−0.803318	+	1.02336i
$146$	−0.780598	+	1.07440i	−0.0646028	+	0.0889181i
$147$	−11.9021	−	2.25367i	−0.981672	−	0.185880i
$148$	9.23065	−	4.70325i	0.758755	−	0.386605i
$149$	14.3679			1.17707			0.588534	−	0.808472i	$-0.299705\pi$
$149$	14.3679			1.17707			0.588534	+	0.808472i	$0.299705\pi$
$150$	1.80286	+	8.47052i	0.147203	+	0.691615i
$151$	−0.326435			−0.0265649			−0.0132824	−	0.999912i	$-0.504228\pi$
$151$	−0.326435			−0.0265649			−0.0132824	+	0.999912i	$0.504228\pi$
$152$	1.24942	−	0.636609i	0.101341	−	0.0516358i
$153$	−8.12361	−	4.77450i	−0.656755	−	0.385995i
$154$	0.0509477	−	0.0701235i	0.00410548	−	0.00565071i
$155$	11.9065	+	17.7397i	0.956356	+	1.42488i
$156$	−8.47324	+	2.47421i	−0.678402	+	0.198096i
$157$	−3.47556	+	3.47556i	−0.277380	+	0.277380i	−0.832062	−	0.554682i	$-0.812840\pi$
$157$	−3.47556	+	3.47556i	−0.277380	+	0.277380i	0.554682	+	0.832062i	$0.312840\pi$
$158$	−1.55788	+	9.83604i	−0.123938	+	0.782513i
$159$	0.353372	−	11.7539i	0.0280242	−	0.932144i
$160$	−1.63884	+	1.52125i	−0.129562	+	0.120265i
$161$	0.186967	+	0.0607491i	0.0147350	+	0.00478770i
$162$	−8.65618	−	2.46384i	−0.680094	−	0.193578i
$163$	−0.695961	+	1.36590i	−0.0545119	+	0.106986i	−0.916655	−	0.399679i	$-0.869122\pi$
$163$	−0.695961	+	1.36590i	−0.0545119	+	0.106986i	0.862143	+	0.506664i	$0.169122\pi$
$164$	1.15415	−	3.55210i	0.0901239	−	0.277373i
$165$	3.66203	+	2.18763i	0.285089	+	0.170306i
$166$	−0.272596	−	0.838964i	−0.0211576	−	0.0651163i
$167$	22.1072	+	3.50144i	1.71071	+	0.270949i	0.933573	−	0.358387i	$-0.116673\pi$
$167$	22.1072	+	3.50144i	1.71071	+	0.270949i	0.777133	+	0.629336i	$0.216673\pi$
$168$	−0.123256	+	0.0582050i	−0.00950943	+	0.00449061i
$169$	−7.62505	−	10.4950i	−0.586542	−	0.807306i
$170$	−1.92043	−	6.75568i	−0.147290	−	0.518137i
$171$	1.05726	+	4.07173i	0.0808509	+	0.311373i
$172$	−1.40467	+	0.222477i	−0.107105	+	0.0169637i
$173$	−6.43491	−	12.6292i	−0.489237	−	0.960182i	−0.995222	−	0.0976395i	$-0.968871\pi$
$173$	−6.43491	−	12.6292i	−0.489237	−	0.960182i	0.505985	−	0.862542i	$-0.331129\pi$
$174$	4.09500	−	11.4230i	0.310441	−	0.865979i
$175$	−0.298148	+	0.256788i	−0.0225379	+	0.0194114i
$176$			1.10140i			0.0830211i
$177$	−11.3225	+	1.44602i	−0.851053	+	0.108690i
$178$	0.512946	+	3.23861i	0.0384469	+	0.242744i
$179$	−12.2896	−	8.92889i	−0.918565	−	0.667377i	0.0246011	−	0.999697i	$-0.492168\pi$
$179$	−12.2896	−	8.92889i	−0.918565	−	0.667377i	−0.943167	+	0.332320i	$0.892168\pi$
$180$	−3.39707	−	5.78445i	−0.253203	−	0.431148i
$181$	−8.30933	+	6.03708i	−0.617627	+	0.448733i	−0.852092	−	0.523392i	$-0.824666\pi$
$181$	−8.30933	+	6.03708i	−0.617627	+	0.448733i	0.234465	+	0.972125i	$0.424666\pi$
$182$	−0.283598	−	0.283598i	−0.0210217	−	0.0210217i
$183$	6.06188	+	3.32181i	0.448107	+	0.245556i
$184$	−2.37576	+	0.771931i	−0.175143	+	0.0569075i
$185$	−11.2771	+	20.2350i	−0.829109	+	1.48771i
$186$	−13.0902	−	10.1253i	−0.959823	−	0.742425i
$187$	−3.08236	−	1.57054i	−0.225405	−	0.114849i
$188$	−11.3229	−	5.76930i	−0.825807	−	0.420770i
$189$	−0.0908325	−	0.398709i	−0.00660709	−	0.0290018i
$190$	−1.52641	+	2.73891i	−0.110738	+	0.198701i
$191$	−10.3303	+	3.35652i	−0.747475	+	0.242869i	−0.657894	−	0.753110i	$-0.728553\pi$
$191$	−10.3303	+	3.35652i	−0.747475	+	0.242869i	−0.0895805	+	0.995980i	$0.528553\pi$
$192$	0.832356	−	1.51894i	0.0600701	−	0.109620i
$193$	−13.7241	−	13.7241i	−0.987880	−	0.987880i	0.0120476	−	0.999927i	$-0.496165\pi$
$193$	−13.7241	−	13.7241i	−0.987880	−	0.987880i	−0.999927	+	0.0120476i	$0.996165\pi$
$194$	8.39833	−	6.10174i	0.602965	−	0.438080i
$195$	12.6486	−	15.1526i	0.905782	−	1.08510i
$196$	5.65811	+	4.11086i	0.404151	+	0.293633i
$197$	1.91320	+	12.0795i	0.136310	+	0.860625i	0.957176	+	0.289506i	$0.0934909\pi$
$197$	1.91320	+	12.0795i	0.136310	+	0.860625i	−0.820867	+	0.571120i	$0.806509\pi$
$198$	−3.22657	−	0.712010i	−0.229302	−	0.0506003i
$199$			15.9356i			1.12965i	0.825212	+	0.564823i	$0.191056\pi$
$199$			15.9356i			1.12965i	−0.825212	+	0.564823i	$0.808944\pi$
$200$	1.14706	−	4.86665i	0.0811092	−	0.344124i
$201$	−10.8571	−	3.89211i	−0.765799	−	0.274528i
$202$	6.37296	+	12.5076i	0.448400	+	0.880034i
$203$	0.544573	−	0.0862519i	0.0382215	−	0.00605369i
$204$	3.06399	+	4.49536i	0.214522	+	0.314738i
$205$	2.28359	+	8.03322i	0.159493	+	0.561065i
$206$	7.76123	+	10.6824i	0.540750	+	0.744279i
$207$	−0.725556	−	7.45886i	−0.0504296	−	0.518427i
$208$	5.03358	+	0.797241i	0.349016	+	0.0552787i
$209$	0.477258	+	1.46885i	0.0330126	+	0.101602i
$210$	0.156311	−	0.261661i	0.0107865	−	0.0180563i
$211$	−3.41758	+	10.5182i	−0.235276	+	0.724104i	0.761809	+	0.647802i	$0.224311\pi$
$211$	−3.41758	+	10.5182i	−0.235276	+	0.724104i	−0.997085	+	0.0763026i	$0.975689\pi$
$212$	−3.08222	+	6.04920i	−0.211688	+	0.415461i
$213$	−15.1729	−	16.1135i	−1.03963	−	1.10408i
$214$	18.5097	+	6.01417i	1.26530	+	0.411120i
$215$	2.33073	−	2.16348i	0.158954	−	0.147548i
$216$	3.91169	+	3.42034i	0.266157	+	0.232724i
$217$	0.117628	−	0.742674i	0.00798511	−	0.0504160i
$218$	−8.70216	+	8.70216i	−0.589385	+	0.589385i
$219$	0.644746	+	2.20801i	0.0435679	+	0.149204i
$220$	−1.37250	−	2.04490i	−0.0925341	−	0.137867i
$221$	−9.40879	+	12.9501i	−0.632904	+	0.871117i
$222$	3.33833	−	17.6304i	0.224054	−	1.18328i
$223$	4.89460	−	2.49393i	0.327767	−	0.167006i	−0.282362	−	0.959308i	$-0.591118\pi$
$223$	4.89460	−	2.49393i	0.327767	−	0.167006i	0.610129	+	0.792302i	$0.291118\pi$
$224$	0.0786976			0.00525820
$225$	13.5154	+	6.50642i	0.901028	+	0.433761i
$226$	−7.63411			−0.507814
$227$	6.02606	−	3.07043i	0.399964	−	0.203792i	−0.242426	−	0.970170i	$-0.577943\pi$
$227$	6.02606	−	3.07043i	0.399964	−	0.203792i	0.642390	+	0.766378i	$0.277943\pi$
$228$	0.451860	−	2.38637i	0.0299251	−	0.158041i
$229$	−1.78525	+	2.45719i	−0.117973	+	0.162376i	−0.863919	−	0.503630i	$-0.831997\pi$
$229$	−1.78525	+	2.45719i	−0.117973	+	0.162376i	0.745947	+	0.666006i	$0.231997\pi$
$230$	3.44900	−	4.39374i	0.227420	−	0.289715i
$231$	−0.0420810	−	0.144111i	−0.00276873	−	0.00948184i
$232$	−4.95404	+	4.95404i	−0.325249	+	0.325249i
$233$	−0.216297	+	1.36565i	−0.0141701	+	0.0894666i	−0.993760	−	0.111541i	$-0.964421\pi$
$233$	−0.216297	+	1.36565i	−0.0141701	+	0.0894666i	0.979590	+	0.201007i	$0.0644215\pi$
$234$	−5.58954	+	14.2306i	−0.365400	+	0.930283i
$235$	28.2120	−	3.39843i	1.84035	−	0.221689i
$236$	6.26761	+	2.03647i	0.407987	+	0.132563i
$237$	11.8248	+	12.5578i	0.768101	+	0.815717i
$238$	−0.112219	+	0.220242i	−0.00727408	+	0.0142762i
$239$	−3.51376	+	10.8143i	−0.227287	+	0.699516i	0.770765	+	0.637120i	$0.219874\pi$
$239$	−3.51376	+	10.8143i	−0.227287	+	0.699516i	−0.998051	+	0.0623963i	$0.980126\pi$
$240$	0.347433	+	3.85737i	0.0224267	+	0.248992i
$241$	−2.72661	−	8.39163i	−0.175636	−	0.540552i	0.824026	−	0.566552i	$-0.191723\pi$
$241$	−2.72661	−	8.39163i	−0.175636	−	0.540552i	−0.999662	+	0.0259998i	$0.991723\pi$
$242$	9.66643	+	1.53101i	0.621382	+	0.0984172i
$243$	−12.5487	+	9.24826i	−0.804999	+	0.593276i
$244$	−2.34577	−	3.22867i	−0.150172	−	0.206695i
$245$	−15.6278	−	0.581572i	−0.998424	−	0.0371553i
$246$	−3.64342	−	5.34547i	−0.232296	−	0.340814i
$247$	7.05835	−	1.11793i	0.449112	−	0.0711323i
$248$	4.33774	+	8.51329i	0.275447	+	0.540595i
$249$	−1.43828	−	0.515604i	−0.0911475	−	0.0326751i
$250$	3.93487	+	10.4650i	0.248863	+	0.661866i
$251$		−	14.6104i		−	0.922197i	−0.887349	−	0.461099i	$-0.847455\pi$
$251$		−	14.6104i		−	0.922197i	0.887349	−	0.461099i	$-0.152545\pi$
$252$	−0.0508748	+	0.230546i	−0.00320481	+	0.0145230i
$253$	−0.430401	−	2.71745i	−0.0270591	−	0.170844i
$254$	2.60673	+	1.89390i	0.163561	+	0.118834i
$255$	−11.2906	−	4.52810i	−0.707045	−	0.283561i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−1.57229	−	1.57229i	−0.0980767	−	0.0980767i	0.656366	−	0.754443i	$-0.272093\pi$
$257$	−1.57229	−	1.57229i	−0.0980767	−	0.0980767i	−0.754443	+	0.656366i	$0.772093\pi$
$258$	−1.18376	+	2.16020i	−0.0736975	+	0.134488i
$259$	0.775389	−	0.251939i	0.0481803	−	0.0156547i
$260$	−10.3390	+	4.79238i	−0.641200	+	0.297211i
$261$	−11.3104	−	17.7155i	−0.700095	−	1.09656i
$262$	−4.73859	−	2.41443i	−0.292751	−	0.149164i
$263$	17.2650	+	8.79695i	1.06460	+	0.542443i	0.896371	−	0.443304i	$-0.146194\pi$
$263$	17.2650	+	8.79695i	1.06460	+	0.542443i	0.168233	+	0.985747i	$0.446194\pi$
$264$	1.50895	+	1.16718i	0.0928695	+	0.0718348i
$265$	−1.81559	−	15.0721i	−0.111531	−	0.925872i
$266$	0.104953	−	0.0341012i	0.00643507	−	0.00209088i
$267$	4.98058	+	2.72928i	0.304807	+	0.167029i
$268$	4.70859	+	4.70859i	0.287623	+	0.287623i
$269$	4.44596	−	3.23018i	0.271075	−	0.196948i	−0.443940	−	0.896056i	$-0.646420\pi$
$269$	4.44596	−	3.23018i	0.271075	−	0.196948i	0.715015	+	0.699109i	$0.246420\pi$
$270$	−11.5248	−	1.47582i	−0.701379	−	0.0898155i
$271$	6.02194	+	4.37520i	0.365807	+	0.265774i	0.755470	−	0.655183i	$-0.227409\pi$
$271$	6.02194	+	4.37520i	0.365807	+	0.265774i	−0.389663	+	0.920957i	$0.627409\pi$
$272$	−0.491350	−	3.10226i	−0.0297924	−	0.188102i
$273$	−0.689074	+	0.0880031i	−0.0417047	+	0.00532619i
$274$		−	11.4859i		−	0.693891i
$275$	5.09649	+	2.08632i	0.307330	+	0.125810i
$276$	−1.46008	+	4.07290i	−0.0878863	+	0.245160i
$277$	−8.66928	−	17.0144i	−0.520886	−	1.02230i	−0.990251	−	0.139293i	$-0.955517\pi$
$277$	−8.66928	−	17.0144i	−0.520886	−	1.02230i	0.469365	−	0.883004i	$-0.344483\pi$
$278$	−10.7678	+	1.70545i	−0.645810	+	0.102286i
$279$	−27.7440	+	7.20400i	−1.66099	+	0.431292i
$280$	−0.146113	+	0.0980686i	−0.00873194	+	0.00586072i
$281$	0.827936	+	1.13956i	0.0493905	+	0.0679802i	0.832998	−	0.553276i	$-0.186623\pi$
$281$	0.827936	+	1.13956i	0.0493905	+	0.0679802i	−0.783607	+	0.621256i	$0.786623\pi$
$282$	−19.9033	+	9.39887i	−1.18522	+	0.559694i
$283$	9.41786	+	1.49164i	0.559834	+	0.0886689i	0.429937	−	0.902859i	$-0.358536\pi$
$283$	9.41786	+	1.49164i	0.559834	+	0.0886689i	0.129896	+	0.991528i	$0.458536\pi$
$284$	3.94874	+	12.1530i	0.234315	+	0.721147i
$285$	2.13482	+	4.99372i	0.126456	+	0.295802i
$286$	−1.73454	+	5.33836i	−0.102565	+	0.315664i
$287$	0.133440	−	0.261892i	0.00787674	−	0.0154590i
$288$	−1.19893	−	2.75001i	−0.0706478	−	0.162046i
$289$	−6.78537	−	2.20470i	−0.399139	−	0.129688i
$290$	3.02443	−	15.3713i	0.177601	−	0.902636i
$291$	0.540319	−	17.9721i	0.0316740	−	1.05355i
$292$	0.207750	−	1.31168i	0.0121577	−	0.0767604i
$293$	22.0266	−	22.0266i	1.28681	−	1.28681i	0.350091	−	0.936716i	$-0.386151\pi$
$293$	22.0266	−	22.0266i	1.28681	−	1.28681i	0.936716	−	0.350091i	$-0.113849\pi$
$294$	11.6280	−	3.39542i	0.678161	−	0.198025i
$295$	−14.1745	+	4.02935i	−0.825269	+	0.234598i
$296$	−6.08934	+	8.38126i	−0.353936	+	0.487151i
$297$	−4.39475	+	3.66597i	−0.255009	+	0.212721i
$298$	−12.8019	+	6.52291i	−0.741596	+	0.377862i
$299$	−12.7307			−0.736237
$300$	−5.45190	−	6.72880i	−0.314766	−	0.388488i
$301$	−0.111922			−0.00645107
$302$	0.290856	−	0.148198i	0.0167369	−	0.00852785i
$303$	23.8894	+	4.52347i	1.37241	+	0.259867i
$304$	−0.824223	+	1.13445i	−0.0472724	+	0.0650649i
$305$	8.37864	+	3.07133i	0.479760	+	0.175864i
$306$	9.40577	+	0.566067i	0.537692	+	0.0323599i
$307$	1.56450	−	1.56450i	0.0892910	−	0.0892910i	−0.661050	−	0.750341i	$-0.729889\pi$
$307$	1.56450	−	1.56450i	0.0892910	−	0.0892910i	0.750341	+	0.661050i	$0.229889\pi$
$308$	−0.0135593	+	0.0856103i	−0.000772615	+	0.00487810i
$309$	22.8600	+	0.687269i	1.30046	+	0.0390974i
$310$	−18.6624	−	10.4007i	−1.05995	−	0.590720i
$311$	12.9644	+	4.21240i	0.735145	+	0.238863i	0.652577	−	0.757722i	$-0.273688\pi$
$311$	12.9644	+	4.21240i	0.735145	+	0.238863i	0.0825681	+	0.996585i	$0.473688\pi$
$312$	6.42644	−	6.05131i	0.363826	−	0.342588i
$313$	−8.67043	+	17.0167i	−0.490082	+	0.961839i	0.505032	+	0.863101i	$0.331481\pi$
$313$	−8.67043	+	17.0167i	−0.490082	+	0.961839i	−0.995113	+	0.0987386i	$0.968519\pi$
$314$	1.51888	−	4.67462i	0.0857152	−	0.263804i
$315$	−0.192838	−	0.491439i	−0.0108652	−	0.0276895i
$316$	−3.07739	−	9.47123i	−0.173117	−	0.532798i
$317$	8.97408	+	1.42135i	0.504034	+	0.0798312i	0.403274	−	0.915079i	$-0.367872\pi$
$317$	8.97408	+	1.42135i	0.504034	+	0.0798312i	0.100761	+	0.994911i	$0.467872\pi$
$318$	5.02130	+	10.6332i	0.281580	+	0.596281i
$319$	−4.53563	−	6.24276i	−0.253947	−	0.349528i
$320$	0.769590	−	2.09946i	0.0430214	−	0.117363i
$321$	27.8548	−	18.9855i	1.55470	−	1.05967i
$322$	−0.194168	+	0.0307532i	−0.0108206	+	0.00171381i
$323$	−1.99954	−	3.92433i	−0.111258	−	0.218355i
$324$	8.83128	−	1.73453i	0.490626	−	0.0963625i
$325$	13.2239	−	21.7817i	0.733530	−	1.20823i
$326$		−	1.53299i		−	0.0849043i
$327$	2.70036	+	21.1441i	0.149330	+	1.16927i
$328$	0.584268	+	3.68892i	0.0322608	+	0.203687i
$329$	−0.809088	−	0.587837i	−0.0446065	−	0.0324085i
$330$	−4.25606	−	0.286660i	−0.234288	−	0.0157801i
$331$	8.94485	−	6.49882i	0.491654	−	0.357207i	−0.314166	−	0.949368i	$-0.601725\pi$
$331$	8.94485	−	6.49882i	0.491654	−	0.357207i	0.805820	+	0.592161i	$0.201725\pi$
$332$	0.623767	+	0.623767i	0.0342336	+	0.0342336i
$333$	−20.6166	−	23.2570i	−1.12978	−	1.27448i
$334$	−21.2873	+	6.91666i	−1.16479	+	0.378463i
$335$	−14.6097	−	2.87458i	−0.798215	−	0.157055i
$336$	0.0833977	−	0.107818i	0.00454971	−	0.00588197i
$337$	15.4169	+	7.85531i	0.839813	+	0.427906i	0.820321	−	0.571904i	$-0.193795\pi$
$337$	15.4169	+	7.85531i	0.839813	+	0.427906i	0.0194923	+	0.999810i	$0.493795\pi$
$338$	11.5586	+	5.88940i	0.628705	+	0.320341i
$339$	−8.09004	+	10.4590i	−0.439391	+	0.568054i
$340$	4.77812	+	5.14750i	0.259130	+	0.279162i
$341$	−10.0085	+	3.25195i	−0.541989	+	0.176103i
$342$	−2.79056	−	3.14795i	−0.150896	−	0.170222i
$343$	0.778722	+	0.778722i	0.0420470	+	0.0420470i
$344$	1.15057	−	0.835934i	0.0620343	−	0.0450706i
$345$	−2.36458	−	9.38139i	−0.127305	−	0.505077i
$346$	11.4671	+	8.33133i	0.616475	+	0.447895i
$347$	−2.33923	−	14.7693i	−0.125576	−	0.792857i	−0.967428	−	0.253148i	$-0.918534\pi$
$347$	−2.33923	−	14.7693i	−0.125576	−	0.792857i	0.841851	−	0.539709i	$-0.181466\pi$
$348$	1.53728	+	12.0371i	0.0824070	+	0.645256i
$349$			0.345103i			0.0184729i	0.999957	+	0.00923647i	$0.00294010\pi$
$349$			0.345103i			0.0184729i	−0.999957	+	0.00923647i	$0.997060\pi$
$350$	0.149073	−	0.364157i	0.00796827	−	0.0194650i
$351$	13.5730	+	22.7383i	0.724473	+	1.21368i
$352$	−0.500025	−	0.981353i	−0.0266514	−	0.0523063i
$353$	19.7879	−	3.13409i	1.05320	−	0.166811i	0.394256	−	0.919001i	$-0.371002\pi$
$353$	19.7879	−	3.13409i	1.05320	−	0.166811i	0.658947	+	0.752190i	$0.271002\pi$
$354$	9.43196	−	6.42874i	0.501303	−	0.341683i
$355$	−22.4758	−	17.6431i	−1.19289	−	0.936396i
$356$	−1.92734	−	2.65275i	−0.102149	−	0.140596i
$357$	0.182818	+	0.387139i	0.00967574	+	0.0204896i
$358$	15.0037	+	2.37636i	0.792971	+	0.125594i
$359$	−5.66877	−	17.4467i	−0.299186	−	0.920800i	−0.981783	−	0.190005i	$-0.939150\pi$
$359$	−5.66877	−	17.4467i	−0.299186	−	0.920800i	0.682597	−	0.730795i	$-0.260850\pi$
$360$	5.65290	+	3.61175i	0.297934	+	0.190356i
$361$	5.26370	−	16.2000i	0.277037	−	0.852632i
$362$	4.66289	−	9.15143i	0.245076	−	0.480989i
$363$	12.3413	−	11.6209i	0.647749	−	0.609937i
$364$	0.381439	+	0.123937i	0.0199928	+	0.00649606i
$365$	1.24883	+	2.69421i	0.0653667	+	0.141022i
$366$	−6.90925	−	0.207721i	−0.361152	−	0.0108578i
$367$	0.00304877	−	0.0192492i	0.000159144	−	0.00100480i	−0.987609	−	0.156937i	$-0.949838\pi$
$367$	0.00304877	−	0.0192492i	0.000159144	−	0.00100480i	0.987768	+	0.155932i	$0.0498381\pi$
$368$	1.76637	−	1.76637i	0.0920783	−	0.0920783i
$369$	−11.1845	−	0.673114i	−0.582240	−	0.0350409i
$370$	0.861472	−	23.1492i	0.0447858	−	1.20347i
$371$	−0.314049	+	0.432251i	−0.0163046	+	0.0224414i
$372$	16.2603	+	3.07889i	0.843057	+	0.159633i
$373$	−6.23329	+	3.17602i	−0.322748	+	0.164448i	−0.607856	−	0.794047i	$-0.707970\pi$
$373$	−6.23329	+	3.17602i	−0.322748	+	0.164448i	0.285109	+	0.958495i	$0.407970\pi$
$374$	3.45942			0.178882
$375$	18.5073	+	5.69913i	0.955712	+	0.294302i
$376$	12.7080			0.655364
$377$	−31.8136	+	16.2098i	−1.63848	+	0.834848i
$378$	0.261942	+	0.314015i	0.0134729	+	0.0161512i
$379$	−7.15293	+	9.84516i	−0.367421	+	0.505712i	−0.952198	−	0.305483i	$-0.901182\pi$
$379$	−7.15293	+	9.84516i	−0.367421	+	0.505712i	0.584776	+	0.811194i	$0.301182\pi$
$380$	0.116605	−	3.13336i	0.00598169	−	0.160738i
$381$	5.35711	−	1.56429i	0.274453	−	0.0801412i
$382$	7.68054	−	7.68054i	0.392971	−	0.392971i
$383$	−0.148258	+	0.936062i	−0.00757561	+	0.0478305i	−0.991187	−	0.132473i	$-0.957708\pi$
$383$	−0.148258	+	0.936062i	−0.00757561	+	0.0478305i	0.983611	+	0.180304i	$0.0577081\pi$
$384$	−0.0520493	+	1.73127i	−0.00265613	+	0.0883484i
$385$	−0.0815080	−	0.175845i	−0.00415403	−	0.00896187i
$386$	18.4588	+	5.99764i	0.939530	+	0.305272i
$387$	1.70509	+	3.91100i	0.0866748	+	0.198807i
$388$	−4.71283	+	9.24945i	−0.239258	+	0.469570i
$389$	−6.14102	+	18.9001i	−0.311362	+	0.958273i	0.665864	+	0.746073i	$0.268063\pi$
$389$	−6.14102	+	18.9001i	−0.311362	+	0.958273i	−0.977226	+	0.212200i	$0.931937\pi$
$390$	−4.39081	+	19.2434i	−0.222337	+	0.974428i
$391$	2.42458	+	7.46210i	0.122616	+	0.377374i
$392$	−6.90770	−	1.09407i	−0.348892	−	0.0552590i
$393$	−8.32944	+	3.93339i	−0.420164	+	0.198413i
$394$	−7.18863	−	9.89430i	−0.362158	−	0.498468i
$395$	17.5161	+	13.7498i	0.881333	+	0.691829i
$396$	3.19814	−	0.830427i	0.160713	−	0.0417305i
$397$	26.6394	−	4.21926i	1.33699	−	0.211759i	0.553338	−	0.832957i	$-0.313354\pi$
$397$	26.6394	−	4.21926i	1.33699	−	0.211759i	0.783654	+	0.621198i	$0.213354\pi$
$398$	−7.23462	−	14.1987i	−0.362639	−	0.711719i
$399$	0.0645011	−	0.179927i	0.00322909	−	0.00900759i
$400$	1.18738	+	4.85697i	0.0593688	+	0.242848i
$401$		−	33.9394i		−	1.69485i	−0.530912	−	0.847427i	$-0.678151\pi$
$401$		−	33.9394i		−	1.69485i	0.530912	−	0.847427i	$-0.321849\pi$
$402$	11.4407	−	1.46112i	0.570611	−	0.0728739i
$403$	7.61739	+	48.0943i	0.379449	+	2.39575i
$404$	−11.3567	−	8.25112i	−0.565017	−	0.410509i
$405$	−14.2351	+	14.2254i	−0.707346	+	0.706868i
$406$	−0.446060	+	0.324082i	−0.0221376	+	0.0160839i
$407$	−8.06828	−	8.06828i	−0.399930	−	0.399930i
$408$	−4.77089	−	2.61437i	−0.236194	−	0.129431i
$409$	−15.1218	+	4.91338i	−0.747726	+	0.242951i	−0.658002	−	0.753016i	$-0.728598\pi$
$409$	−15.1218	+	4.91338i	−0.747726	+	0.242951i	−0.0897236	+	0.995967i	$0.528598\pi$
$410$	−5.68170	−	6.12093i	−0.280599	−	0.302291i
$411$	−15.7361	−	12.1719i	−0.776205	−	0.600396i
$412$	−11.7650	−	5.99458i	−0.579621	−	0.295332i
$413$	0.462102	+	0.235453i	0.0227386	+	0.0115859i
$414$	4.03273	+	6.31650i	0.198198	+	0.310439i
$415$	−1.93542	−	0.380809i	−0.0950058	−	0.0186932i
$416$	−4.84689	+	1.57485i	−0.237638	+	0.0772134i
$417$	−9.07436	+	16.5595i	−0.444373	+	0.810924i
$418$	−1.09208	−	1.09208i	−0.0534155	−	0.0534155i
$419$	−22.2455	+	16.1623i	−1.08677	+	0.789582i	−0.978850	−	0.204578i	$-0.934418\pi$
$419$	−22.2455	+	16.1623i	−1.08677	+	0.789582i	−0.107916	+	0.994160i	$0.534418\pi$
$420$	−0.0204826	+	0.304105i	−0.000999447	+	0.0148388i
$421$	25.8507	+	18.7816i	1.25988	+	0.915359i	0.998752	−	0.0499438i	$-0.0159042\pi$
$421$	25.8507	+	18.7816i	1.25988	+	0.915359i	0.261132	+	0.965303i	$0.415904\pi$
$422$	−1.73009	−	10.9234i	−0.0842194	−	0.531741i
$423$	−8.21520	+	37.2283i	−0.399437	+	1.81010i
$424$		−	6.78917i		−	0.329711i
$425$	−15.2858	−	3.60283i	−0.741470	−	0.174763i
$426$	20.8346	+	7.46889i	1.00944	+	0.361869i
$427$	−0.142585	−	0.279839i	−0.00690018	−	0.0135424i
$428$	−19.2226	+	3.04457i	−0.929162	+	0.147165i
$429$	5.47559	+	8.03356i	0.264364	+	0.387864i
$430$	−1.09449	+	2.98580i	−0.0527812	+	0.143988i
$431$	−5.09101	−	7.00718i	−0.245225	−	0.337524i	0.668607	−	0.743616i	$-0.266891\pi$
$431$	−5.09101	−	7.00718i	−0.245225	−	0.337524i	−0.913832	+	0.406093i	$0.866891\pi$
$432$	−5.03814	−	1.27167i	−0.242398	−	0.0611835i
$433$	10.6490	+	1.68664i	0.511760	+	0.0810548i	0.406974	−	0.913440i	$-0.366584\pi$
$433$	10.6490	+	1.68664i	0.511760	+	0.0810548i	0.104786	+	0.994495i	$0.466584\pi$
$434$	0.232360	+	0.715129i	0.0111536	+	0.0343273i
$435$	−17.8542	−	20.4329i	−0.856041	−	0.979684i
$436$	3.80299	−	11.7044i	0.182130	−	0.560538i
$437$	1.59026	−	3.12107i	0.0760726	−	0.149301i
$438$	−1.57689	−	1.67464i	−0.0753467	−	0.0800176i
$439$	−32.6251	−	10.6006i	−1.55711	−	0.505937i	−0.601078	−	0.799190i	$-0.705262\pi$
$439$	−32.6251	−	10.6006i	−1.55711	−	0.505937i	−0.956035	+	0.293253i	$0.905262\pi$
$440$	2.15128	+	1.19892i	0.102558	+	0.0571563i
$441$	7.67066	−	19.5290i	0.365269	−	0.929951i
$442$	2.50408	−	15.8101i	0.119107	−	0.752011i
$443$	−4.58214	+	4.58214i	−0.217704	+	0.217704i	−0.807530	−	0.589826i	$-0.799196\pi$
$443$	−4.58214	+	4.58214i	−0.217704	+	0.217704i	0.589826	+	0.807530i	$0.299196\pi$
$444$	5.02958	+	17.2244i	0.238693	+	0.817434i
$445$	6.88409	+	2.52347i	0.326337	+	0.119624i
$446$	−3.22891	+	4.44421i	−0.152893	+	0.210439i
$447$	−4.62991	+	24.4515i	−0.218987	+	1.15652i
$448$	−0.0701201	+	0.0357280i	−0.00331286	+	0.00168799i
$449$	22.7460			1.07345			0.536726	−	0.843756i	$-0.319661\pi$
$449$	22.7460			1.07345			0.536726	+	0.843756i	$0.319661\pi$
$450$	−14.9962	+	0.338608i	−0.706927	+	0.0159621i
$451$	−4.11362			−0.193703
$452$	6.80204	−	3.46581i	0.319941	−	0.163018i
$453$	0.105190	−	0.555530i	0.00494225	−	0.0261011i
$454$	−3.97531	+	5.47155i	−0.186571	+	0.256792i
$455$	−0.862639	+	0.245221i	−0.0404411	+	0.0114961i
$456$	0.680779	+	2.33141i	0.0318804	+	0.109178i
$457$	−6.28077	+	6.28077i	−0.293802	+	0.293802i	−0.838580	−	0.544778i	$-0.816614\pi$
$457$	−6.28077	+	6.28077i	−0.293802	+	0.293802i	0.544778	+	0.838580i	$0.316614\pi$
$458$	0.475131	−	2.99986i	0.0222014	−	0.140174i
$459$	10.7430	−	12.2863i	0.501442	−	0.573477i
$460$	−1.07837	+	5.48067i	−0.0502790	+	0.255537i
$461$	−21.3397	−	6.93369i	−0.993889	−	0.322934i	−0.233468	−	0.972364i	$-0.575007\pi$
$461$	−21.3397	−	6.93369i	−0.993889	−	0.322934i	−0.760421	+	0.649430i	$0.775007\pi$
$462$	0.102920	+	0.109300i	0.00478826	+	0.00508509i
$463$	10.9916	−	21.5722i	0.510823	−	1.00255i	−0.481214	−	0.876603i	$-0.659804\pi$
$463$	10.9916	−	21.5722i	0.510823	−	1.00255i	0.992037	−	0.125944i	$-0.0401959\pi$
$464$	2.16499	−	6.66317i	0.100507	−	0.309330i
$465$	−34.0263	+	14.5463i	−1.57793	+	0.674567i
$466$	−0.427269	−	1.31500i	−0.0197929	−	0.0609161i
$467$	−13.3049	−	2.10730i	−0.615679	−	0.0975140i	−0.159197	−	0.987247i	$-0.550891\pi$
$467$	−13.3049	−	2.10730i	−0.615679	−	0.0975140i	−0.456482	+	0.889733i	$0.650891\pi$
$468$	−1.48024	−	15.2171i	−0.0684240	−	0.703413i
$469$	0.308025	+	0.423960i	0.0142233	+	0.0195766i
$470$	−23.5942	+	15.8360i	−1.08832	+	0.730460i
$471$	−4.79479	−	7.03472i	−0.220932	−	0.324143i
$472$	−6.50902	+	1.03093i	−0.299602	+	0.0474523i
$473$	0.711123	+	1.39566i	0.0326975	+	0.0641724i
$474$	−16.2371	−	5.82076i	−0.745793	−	0.267356i
$475$	3.68813	+	5.96284i	0.169223	+	0.273594i
$476$		−	0.247184i		−	0.0113296i
$477$	19.8890	+	4.38893i	0.910656	+	0.200955i
$478$	−1.77878	−	11.2308i	−0.0813596	−	0.513684i
$479$	13.9808	+	10.1576i	0.638797	+	0.464113i	0.859437	−	0.511242i	$-0.170814\pi$
$479$	13.9808	+	10.1576i	0.638797	+	0.464113i	−0.220639	+	0.975355i	$0.570814\pi$
$480$	−2.06077	−	3.27921i	−0.0940610	−	0.149675i
$481$	−42.7136	+	31.0332i	−1.94757	+	1.41499i
$482$	6.23914	+	6.23914i	0.284185	+	0.284185i
$483$	−0.163631	+	0.298606i	−0.00744549	+	0.0135871i
$484$	−9.30791	+	3.02432i	−0.423087	+	0.137469i
$485$	−2.77611	−	23.0458i	−0.126057	−	1.04646i
$486$	6.98235	−	13.9372i	0.316726	−	0.632206i
$487$	3.22789	+	1.64469i	0.146270	+	0.0745281i	0.525593	−	0.850736i	$-0.323843\pi$
$487$	3.22789	+	1.64469i	0.146270	+	0.0745281i	−0.379324	+	0.925264i	$0.623843\pi$
$488$	3.55588	+	1.81181i	0.160967	+	0.0820169i
$489$	−2.10024	−	1.62454i	−0.0949761	−	0.0734643i
$490$	14.1885	−	6.57669i	0.640971	−	0.297105i
$491$	−5.48953	+	1.78366i	−0.247739	+	0.0804953i	−0.430254	−	0.902708i	$-0.641576\pi$
$491$	−5.48953	+	1.78366i	−0.247739	+	0.0804953i	0.182515	+	0.983203i	$0.441576\pi$
$492$	5.67310	+	3.10877i	0.255763	+	0.140154i
$493$	15.5603	+	15.5603i	0.700800	+	0.700800i
$494$	−5.78150	+	4.20051i	−0.260122	+	0.188990i
$495$	−4.90297	+	5.52715i	−0.220372	+	0.248427i
$496$	−7.72991	−	5.61611i	−0.347083	−	0.252171i
$497$	0.157315	+	0.993249i	0.00705655	+	0.0445533i
$498$	1.51560	−	0.193560i	0.0679157	−	0.00867365i
$499$			28.5582i			1.27844i	0.769024	+	0.639220i	$0.220743\pi$
$499$			28.5582i			1.27844i	−0.769024	+	0.639220i	$0.779257\pi$
$500$	−8.25702	−	7.53801i	−0.369265	−	0.337110i
$501$	−13.0826	+	36.4940i	−0.584486	+	1.63043i
$502$	6.63296	+	13.0179i	0.296044	+	0.581018i
$503$	−23.7938	+	3.76856i	−1.06091	+	0.168032i	−0.662414	−	0.749138i	$-0.730468\pi$
$503$	−23.7938	+	3.76856i	−1.06091	+	0.168032i	−0.398497	+	0.917170i	$0.630468\pi$
$504$	−0.0593360	−	0.228515i	−0.00264304	−	0.0101789i
$505$	31.3674	+	1.16730i	1.39583	+	0.0519444i
$506$	1.61718	+	2.22586i	0.0718926	+	0.0989517i
$507$	20.3176	−	9.59451i	0.902335	−	0.426107i
$508$	−3.18243	−	0.504047i	−0.141197	−	0.0223635i
$509$	−1.35722	−	4.17708i	−0.0601576	−	0.185146i	0.916462	−	0.400123i	$-0.131032\pi$
$509$	−1.35722	−	4.17708i	−0.0601576	−	0.185146i	−0.976619	+	0.214977i	$0.931032\pi$
$510$	12.1157	−	1.09126i	0.536493	−	0.0483220i
$511$	0.0322963	−	0.0993978i	0.00142870	−	0.00439710i
$512$	0.453990	−	0.891007i	0.0200637	−	0.0393773i
$513$	−7.27001	+	0.487193i	−0.320979	+	0.0215101i
$514$	2.11472	+	0.687116i	0.0932765	+	0.0303074i
$515$	29.3136	−	3.53113i	1.29171	−	0.155600i
$516$	0.0740233	−	2.46217i	0.00325869	−	0.108391i
$517$	−2.18954	+	13.8242i	−0.0962960	+	0.607989i
$518$	−0.576498	+	0.576498i	−0.0253299	+	0.0253299i
$519$	23.5661	−	6.88138i	1.03444	−	0.302059i
$520$	7.03646	−	8.96386i	0.308569	−	0.393091i
$521$	3.85216	−	5.30205i	0.168766	−	0.232287i	−0.716254	−	0.697840i	$-0.754145\pi$
$521$	3.85216	−	5.30205i	0.168766	−	0.232287i	0.885020	+	0.465553i	$0.154145\pi$
$522$	18.1203	+	10.6499i	0.793104	+	0.466132i
$523$	7.96973	−	4.06078i	0.348492	−	0.177566i	−0.270979	−	0.962585i	$-0.587347\pi$
$523$	7.96973	−	4.06078i	0.348492	−	0.177566i	0.619471	+	0.785020i	$0.287347\pi$
$524$	5.31824			0.232328
$525$	−0.340931	−	0.590140i	−0.0148794	−	0.0257558i
$526$	−19.3769			−0.844875
$527$	26.7397	−	13.6245i	1.16480	−	0.593494i
$528$	−1.87437	−	0.354913i	−0.0815716	−	0.0154456i
$529$	9.85121	−	13.5590i	0.428314	−	0.589523i
$530$	8.46029	+	12.6051i	0.367492	+	0.547529i
$531$	1.18770	−	19.7348i	0.0515416	−	0.856416i
$532$	−0.0780320	+	0.0780320i	−0.00338312	+	0.00338312i
$533$	−2.97762	+	18.7999i	−0.128975	+	0.814315i
$534$	−5.67680	−	0.170669i	−0.245659	−	0.00738556i
$535$	31.8956	−	29.6069i	1.37897	−	1.28002i
$536$	−6.33303	−	2.05773i	−0.273545	−	0.0888803i
$537$	19.1555	−	18.0373i	0.826619	−	0.778367i
$538$	−2.49491	+	4.89653i	−0.107563	+	0.211105i
$539$	2.38035	−	7.32596i	0.102529	−	0.315551i
$540$	10.9387	−	3.91720i	0.470727	−	0.168570i
$541$	4.98127	+	15.3308i	0.214161	+	0.659121i	0.999212	+	0.0396896i	$0.0126369\pi$
$541$	4.98127	+	15.3308i	0.214161	+	0.659121i	−0.785051	+	0.619432i	$0.787363\pi$
$542$	−7.35189	−	1.16442i	−0.315791	−	0.0500163i
$543$	−7.59639	−	16.0863i	−0.325992	−	0.690329i
$544$	1.84619	+	2.54107i	0.0791548	+	0.108947i
$545$	7.52457	+	26.4699i	0.322317	+	1.13385i
$546$	0.574017	−	0.391244i	0.0245657	−	0.0167437i
$547$	−23.3625	+	3.70025i	−0.998907	+	0.158211i	−0.634413	−	0.772994i	$-0.718758\pi$
$547$	−23.3625	+	3.70025i	−0.998907	+	0.158211i	−0.364494	+	0.931206i	$0.618758\pi$
$548$	5.21451	+	10.2341i	0.222753	+	0.437177i
$549$	−7.60647	+	9.24576i	−0.324636	+	0.394599i
$550$	−5.48818	+	0.454833i	−0.234017	+	0.0193942i
$551$		−	9.82428i		−	0.418528i
$552$	−0.548120	−	4.29184i	−0.0233295	−	0.182673i
$553$	−0.122601	−	0.774072i	−0.00521353	−	0.0329169i
$554$	15.4488	+	11.2242i	0.656355	+	0.476870i
$555$	−30.8022	−	25.7120i	−1.30748	−	1.09141i
$556$	8.81992	−	6.40805i	0.374048	−	0.271762i
$557$	27.5142	+	27.5142i	1.16581	+	1.16581i	0.983181	+	0.182634i	$0.0584623\pi$
$557$	27.5142	+	27.5142i	1.16581	+	1.16581i	0.182634	+	0.983181i	$0.441538\pi$
$558$	21.4496	−	19.0143i	0.908033	−	0.804941i
$559$	6.89314	−	2.23972i	0.291549	−	0.0947299i
$560$	0.0856657	−	0.153714i	0.00362004	−	0.00649560i
$561$	3.66602	−	4.73951i	0.154780	−	0.200102i
$562$	−1.25504	−	0.639477i	−0.0529408	−	0.0269747i
$563$	−22.1789	−	11.3007i	−0.934728	−	0.476267i	−0.0808412	−	0.996727i	$-0.525761\pi$
$563$	−22.1789	−	11.3007i	−0.934728	−	0.476267i	−0.853886	+	0.520460i	$0.825761\pi$
$564$	13.4669	−	17.4103i	0.567061	−	0.733108i
$565$	−8.31006	+	14.9111i	−0.349607	+	0.627315i
$566$	−9.06857	+	2.94656i	−0.381180	+	0.123853i
$567$	0.707797	−	0.0261004i	0.0297247	−	0.00109611i
$568$	−9.03570	−	9.03570i	−0.379129	−	0.379129i
$569$	25.9540	−	18.8567i	1.08805	−	0.790515i	0.108981	−	0.994044i	$-0.465241\pi$
$569$	25.9540	−	18.8567i	1.08805	−	0.790515i	0.979069	+	0.203529i	$0.0652412\pi$
$570$	−4.16924	−	3.48025i	−0.174630	−	0.145772i
$571$	−34.1170	−	24.7874i	−1.42775	−	1.03732i	−0.990430	−	0.138017i	$-0.955927\pi$
$571$	−34.1170	−	24.7874i	−1.42775	−	1.03732i	−0.437322	−	0.899305i	$-0.644073\pi$
$572$	−0.878080	−	5.54398i	−0.0367144	−	0.231805i
$573$	−2.38334	−	18.6618i	−0.0995655	−	0.779609i
$574$			0.293928i			0.0122683i
$575$	−4.82756	−	11.5194i	−0.201323	−	0.480394i
$576$	2.31674	+	1.90597i	0.0965306	+	0.0794156i
$577$	−10.0150	−	19.6556i	−0.416931	−	0.818274i	−0.999983	−	0.00583873i	$-0.998141\pi$
$577$	−10.0150	−	19.6556i	−0.416931	−	0.818274i	0.583052	−	0.812435i	$-0.301859\pi$
$578$	7.04672	−	1.11609i	0.293105	−	0.0464233i
$579$	27.7782	−	18.9333i	1.15442	−	0.786843i
$580$	4.28365	+	15.0690i	0.177869	+	0.625707i
$581$	0.0408054	+	0.0561638i	0.00169289	+	0.00233007i
$582$	7.67775	+	16.2586i	0.318253	+	0.673940i
$583$	7.38553	+	1.16975i	0.305877	+	0.0484462i
$584$	0.410385	+	1.26303i	0.0169818	+	0.0522647i
$585$	21.7110	+	26.4082i	0.897641	+	1.09185i
$586$	−9.62597	+	29.6257i	−0.397645	+	1.22383i
$587$	5.85750	−	11.4960i	0.241765	−	0.474490i	−0.737958	−	0.674846i	$-0.764210\pi$
$587$	5.85750	−	11.4960i	0.241765	−	0.474490i	0.979723	+	0.200356i	$0.0642099\pi$
$588$	−8.81916	+	8.30436i	−0.363696	+	0.342466i
$589$	−12.7423	−	4.14024i	−0.525039	−	0.170596i
$590$	10.8002	−	10.0252i	0.444639	−	0.412733i
$591$	−21.1735	−	0.636564i	−0.870960	−	0.0261848i
$592$	1.62063	−	10.2323i	0.0666075	−	0.420543i
$593$	−3.75033	+	3.75033i	−0.154007	+	0.154007i	−0.779905	−	0.625898i	$-0.784733\pi$
$593$	−3.75033	+	3.75033i	−0.154007	+	0.154007i	0.625898	+	0.779905i	$0.284733\pi$
$594$	2.25143	−	5.26158i	0.0923774	−	0.215885i
$595$	0.308027	+	0.458932i	0.0126279	+	0.0188144i
$596$	8.44527	−	11.6239i	0.345932	−	0.476134i
$597$	−27.1194	−	5.13507i	−1.10992	−	0.210165i
$598$	11.3432	−	5.77963i	0.463856	−	0.236347i
$599$	−29.8620			−1.22013			−0.610065	−	0.792352i	$-0.708857\pi$
$599$	−29.8620			−1.22013			−0.610065	+	0.792352i	$0.708857\pi$
$600$	7.91249	+	3.52030i	0.323026	+	0.143716i
$601$	19.0008			0.775058			0.387529	−	0.921858i	$-0.373329\pi$
$601$	19.0008			0.775058			0.387529	+	0.921858i	$0.373329\pi$
$602$	0.0997231	−	0.0508115i	0.00406441	−	0.00207092i
$603$	10.1222	−	17.2225i	0.412208	−	0.701355i
$604$	−0.191874	+	0.264091i	−0.00780722	+	0.0107457i
$605$	13.5127	−	17.2141i	0.549371	−	0.699853i
$606$	−23.3393	+	6.81513i	−0.948092	+	0.276846i
$607$	29.8007	−	29.8007i	1.20957	−	1.20957i	0.238406	−	0.971165i	$-0.423375\pi$
$607$	29.8007	−	29.8007i	1.20957	−	1.20957i	0.971165	−	0.238406i	$-0.0766250\pi$
$608$	0.219361	−	1.38499i	0.00889625	−	0.0561687i
$609$	−0.0286980	+	0.954554i	−0.00116290	+	0.0386805i
$610$	−8.85978	+	1.06725i	−0.358722	+	0.0432118i
$611$	61.5942	+	20.0132i	2.49184	+	0.809646i
$612$	−8.63759	+	3.76576i	−0.349154	+	0.152222i
$613$	0.600877	−	1.17929i	0.0242692	−	0.0476310i	−0.878554	−	0.477644i	$-0.841491\pi$
$613$	0.600877	−	1.17929i	0.0242692	−	0.0476310i	0.902823	+	0.430013i	$0.141491\pi$
$614$	−0.683714	+	2.10425i	−0.0275924	+	0.0849208i
$615$	−14.4069	+	1.29763i	−0.580942	+	0.0523255i
$616$	−0.0267848	−	0.0824351i	−0.00107919	−	0.00332141i
$617$	−41.5066	−	6.57400i	−1.67099	−	0.264659i	−0.752067	−	0.659087i	$-0.770943\pi$
$617$	−41.5066	−	6.57400i	−1.67099	−	0.264659i	−0.918927	+	0.394428i	$0.870943\pi$
$618$	−20.6804	+	9.76586i	−0.831889	+	0.392841i
$619$	−9.51877	−	13.1015i	−0.382592	−	0.526592i	0.573677	−	0.819082i	$-0.305516\pi$
$619$	−9.51877	−	13.1015i	−0.382592	−	0.526592i	−0.956269	+	0.292489i	$0.905516\pi$
$620$	21.3502	+	0.794523i	0.857443	+	0.0319088i
$621$	12.9274	+	1.16877i	0.518758	+	0.0469013i
$622$	−13.4638	+	2.13245i	−0.539848	+	0.0855036i
$623$	−0.117151	−	0.229923i	−0.00469357	−	0.00921165i
$624$	−2.97877	+	8.30930i	−0.119246	+	0.332638i
$625$	24.7238	+	3.70596i	0.988952	+	0.148239i
$626$		−	19.0983i		−	0.763320i
$627$	−2.65349	+	0.338883i	−0.105970	+	0.0135337i
$628$	0.768905	+	4.85468i	0.0306827	+	0.193723i
$629$	26.3249	+	19.1262i	1.04964	+	0.762611i
$630$	0.394928	+	0.350329i	0.0157343	+	0.0139575i
$631$	−9.33690	+	6.78365i	−0.371696	+	0.270053i	−0.757914	−	0.652355i	$-0.773781\pi$
$631$	−9.33690	+	6.78365i	−0.371696	+	0.270053i	0.386218	+	0.922408i	$0.373781\pi$
$632$	7.04182	+	7.04182i	0.280109	+	0.280109i
$633$	−16.7988	−	9.20545i	−0.667691	−	0.365884i
$634$	−8.64124	+	2.80771i	−0.343188	+	0.111508i
$635$	6.53674	−	3.02993i	0.259403	−	0.120239i
$636$	−9.30139	−	7.19464i	−0.368824	−	0.285286i
$637$	−31.7579	−	16.1814i	−1.25829	−	0.641132i
$638$	6.87543	+	3.50321i	0.272201	+	0.138693i
$639$	32.3115	−	20.6290i	1.27822	−	0.816073i
$640$	0.267425	+	2.22002i	0.0105709	+	0.0877540i
$641$	−15.5088	+	5.03912i	−0.612561	+	0.199033i	−0.598835	−	0.800873i	$-0.704369\pi$
$641$	−15.5088	+	5.03912i	−0.612561	+	0.199033i	−0.0137264	+	0.999906i	$0.504369\pi$
$642$	−16.1995	+	29.5620i	−0.639344	+	1.16672i
$643$	−12.8296	−	12.8296i	−0.505952	−	0.505952i	0.407330	−	0.913281i	$-0.366460\pi$
$643$	−12.8296	−	12.8296i	−0.505952	−	0.505952i	−0.913281	+	0.407330i	$0.866460\pi$
$644$	0.159043	−	0.115552i	0.00626719	−	0.00455338i
$645$	2.93078	+	4.66361i	0.115400	+	0.183630i
$646$	3.56321	+	2.58883i	0.140193	+	0.101856i
$647$	3.97829	+	25.1179i	0.156403	+	0.987488i	0.933622	+	0.358259i	$0.116629\pi$
$647$	3.97829	+	25.1179i	0.156403	+	0.987488i	−0.777220	+	0.629229i	$0.783371\pi$
$648$	−7.08127	+	5.55479i	−0.278178	+	0.218213i
$649$		−	7.25839i		−	0.284917i
$650$	−1.89392	+	25.4111i	−0.0742856	+	0.996707i
$651$	1.22599	+	0.439499i	0.0480502	+	0.0172253i
$652$	0.695961	+	1.36590i	0.0272559	+	0.0534928i
$653$	−30.0615	+	4.76127i	−1.17640	+	0.186323i	−0.713867	−	0.700281i	$-0.753058\pi$
$653$	−30.0615	+	4.76127i	−1.17640	+	0.186323i	−0.462529	+	0.886604i	$0.653058\pi$
$654$	−12.0053	−	17.6136i	−0.469443	−	0.688747i
$655$	−9.87407	+	6.62730i	−0.385812	+	0.258950i
$656$	−2.19532	−	3.02160i	−0.0857129	−	0.117974i
$657$	−3.96538	+	0.385730i	−0.154704	+	0.0150488i
$658$	0.987775	+	0.156448i	0.0385075	+	0.00609899i
$659$	3.19473	+	9.83236i	0.124449	+	0.383014i	0.993800	−	0.111180i	$-0.0354631\pi$
$659$	3.19473	+	9.83236i	0.124449	+	0.383014i	−0.869351	+	0.494195i	$0.835463\pi$
$660$	3.92231	−	1.67679i	0.152676	−	0.0652691i
$661$	3.97825	−	12.2438i	0.154736	−	0.476229i	−0.843398	−	0.537289i	$-0.819448\pi$
$661$	3.97825	−	12.2438i	0.154736	−	0.476229i	0.998134	+	0.0610606i	$0.0194483\pi$
$662$	−5.01952	+	9.85137i	−0.195089	+	0.382884i
$663$	−19.0067	−	20.1850i	−0.738161	−	0.783921i
$664$	−0.838964	−	0.272596i	−0.0325581	−	0.0105788i
$665$	0.0476384	−	0.242117i	0.00184734	−	0.00938888i
$666$	28.9279	+	11.3624i	1.12093	+	0.440284i
$667$	−2.73781	+	17.2859i	−0.106008	+	0.669311i
$668$	15.8270	−	15.8270i	0.612365	−	0.612365i
$669$	2.66696	+	9.13333i	0.103111	+	0.353115i
$670$	14.3224	−	4.07141i	0.553323	−	0.157292i
$671$	−2.58363	+	3.55605i	−0.0997397	+	0.137280i
$672$	−0.0253594	+	0.133928i	−0.000978260	+	0.00516640i
$673$	30.0291	−	15.3006i	1.15754	−	0.589794i	0.233596	−	0.972334i	$-0.424951\pi$
$673$	30.0291	−	15.3006i	1.15754	−	0.589794i	0.923939	+	0.382540i	$0.124951\pi$
$674$	−17.3028			−0.666479
$675$	−15.4279	+	20.9041i	−0.593820	+	0.804598i
$676$	−12.9725			−0.498943
$677$	13.8891	−	7.07682i	0.533800	−	0.271984i	−0.166244	−	0.986085i	$-0.553164\pi$
$677$	13.8891	−	7.07682i	0.533800	−	0.271984i	0.700044	+	0.714100i	$0.253164\pi$
$678$	2.46001	−	12.9918i	0.0944759	−	0.498948i
$679$	−0.480192	+	0.660928i	−0.0184281	+	0.0253641i
$680$	−6.59425	−	2.41723i	−0.252878	−	0.0926965i
$681$	3.28346	+	11.2446i	0.125823	+	0.430895i
$682$	7.44126	−	7.44126i	0.284940	−	0.284940i
$683$	−4.20549	+	26.5524i	−0.160919	+	1.01600i	0.766573	+	0.642157i	$0.221960\pi$
$683$	−4.20549	+	26.5524i	−0.160919	+	1.01600i	−0.927492	+	0.373844i	$0.878040\pi$
$684$	3.91554	+	1.53796i	0.149715	+	0.0588054i
$685$	−22.4346	−	12.5029i	−0.857182	−	0.477713i
$686$	−1.04738	−	0.340314i	−0.0399891	−	0.0129932i
$687$	−3.60640	−	3.82996i	−0.137593	−	0.146122i
$688$	−0.645655	+	1.26717i	−0.0246154	+	0.0483104i
$689$	10.6919	−	32.9064i	0.407330	−	1.25363i
$690$	6.36592	+	7.28538i	0.242346	+	0.277350i
$691$	7.00128	+	21.5477i	0.266341	+	0.819714i	0.991381	+	0.131007i	$0.0418212\pi$
$691$	7.00128	+	21.5477i	0.266341	+	0.819714i	−0.725040	+	0.688707i	$0.758179\pi$
$692$	−13.9996	−	2.21732i	−0.532185	−	0.0842898i
$693$	0.258811	−	0.0251756i	0.00983141	−	0.000956343i
$694$	8.78938	+	12.0975i	0.333640	+	0.459217i
$695$	−8.39009	+	22.8884i	−0.318254	+	0.868205i
$696$	−6.83446	−	10.0272i	−0.259060	−	0.380081i
$697$	11.5866	−	1.83514i	0.438875	−	0.0695110i
$698$	−0.156673	−	0.307489i	−0.00593018	−	0.0116386i
$699$	−2.25438	−	0.808162i	−0.0852684	−	0.0305675i
$700$	0.0324990	+	0.392144i	0.00122834	+	0.0148216i
$701$			37.8133i			1.42819i	0.700049	+	0.714095i	$0.253161\pi$
$701$			37.8133i			1.42819i	−0.700049	+	0.714095i	$0.746839\pi$
$702$	−22.4166	−	14.0980i	−0.846061	−	0.532094i
$703$	−2.27253	−	14.3482i	−0.0857102	−	0.541153i
$704$	0.891050	+	0.647386i	0.0335827	+	0.0243993i
$705$	−3.30750	+	49.1066i	−0.124568	+	1.84946i
$706$	−16.2083	+	11.7760i	−0.610007	+	0.443196i
$707$	−0.781162	−	0.781162i	−0.0293786	−	0.0293786i
$708$	−5.48536	+	10.0101i	−0.206152	+	0.376201i
$709$	37.7779	−	12.2748i	1.41878	−	0.460989i	0.503565	−	0.863958i	$-0.332022\pi$
$709$	37.7779	−	12.2748i	1.41878	−	0.460989i	0.915214	+	0.402968i	$0.132022\pi$
$710$	28.0359	+	5.51628i	1.05217	+	0.207022i
$711$	−25.1814	+	16.0769i	−0.944377	+	0.602931i
$712$	2.92160	+	1.48863i	0.109491	+	0.0557887i
$713$	21.2664	+	10.8358i	0.796433	+	0.405803i
$714$	−0.338649	−	0.261946i	−0.0126736	−	0.00980309i
$715$	8.53888	+	9.19897i	0.319336	+	0.344022i
$716$	−14.4473	+	4.69420i	−0.539919	+	0.175430i
$717$	−17.2716	−	9.46453i	−0.645018	−	0.353459i
$718$	12.9715	+	12.9715i	0.484093	+	0.484093i
$719$	−25.6075	+	18.6049i	−0.954998	+	0.693847i	−0.951984	−	0.306149i	$-0.900960\pi$
$719$	−25.6075	+	18.6049i	−0.954998	+	0.693847i	−0.00301445	+	0.999995i	$0.500960\pi$
$720$	−6.67647	−	0.651726i	−0.248817	−	0.0242884i
$721$	−0.840680	−	0.610790i	−0.0313086	−	0.0227470i
$722$	2.66466	+	16.8240i	0.0991682	+	0.626124i
$723$	15.1596	−	1.93606i	0.563791	−	0.0720029i
$724$			10.2709i			0.381715i
$725$	−26.7314	−	22.6398i	−0.992779	−	0.840819i
$726$	−5.72039	+	15.9571i	−0.212304	+	0.592223i
$727$	−23.4214	−	45.9671i	−0.868652	−	1.70483i	−0.693719	−	0.720246i	$-0.744029\pi$
$727$	−23.4214	−	45.9671i	−0.868652	−	1.70483i	−0.174934	−	0.984580i	$-0.555971\pi$
$728$	−0.396131	+	0.0627409i	−0.0146816	+	0.00232533i
$729$	−11.6951	−	24.3357i	−0.433152	−	0.901321i
$730$	−2.33586	−	1.83361i	−0.0864541	−	0.0678648i
$731$	−2.62561	−	3.61384i	−0.0971117	−	0.133663i
$732$	6.25049	−	2.95165i	0.231025	−	0.109096i
$733$	−20.9008	−	3.31036i	−0.771988	−	0.122271i	−0.242000	−	0.970276i	$-0.577803\pi$
$733$	−20.9008	−	3.31036i	−0.771988	−	0.122271i	−0.529988	+	0.848005i	$0.677803\pi$
$734$	0.00602247	+	0.0185352i	0.000222293	+	0.000684148i
$735$	6.02561	−	26.4082i	0.222258	−	0.974080i
$736$	−0.771931	+	2.37576i	−0.0284538	+	0.0875717i
$737$	3.32964	−	6.53478i	0.122649	−	0.240712i
$738$	10.2710	−	4.47789i	0.378082	−	0.164834i
$739$	11.8537	+	3.85150i	0.436046	+	0.141680i	0.518811	−	0.854889i	$-0.326375\pi$
$739$	11.8537	+	3.85150i	0.436046	+	0.141680i	−0.0827648	+	0.996569i	$0.526375\pi$
$740$	9.74194	+	21.0172i	0.358121	+	0.772607i
$741$	−0.371961	+	12.3722i	−0.0136643	+	0.454505i
$742$	0.0835816	−	0.527714i	0.00306838	−	0.0193730i
$743$	−2.30237	+	2.30237i	−0.0844658	+	0.0844658i	−0.748077	−	0.663612i	$-0.769023\pi$
$743$	−2.30237	+	2.30237i	−0.0844658	+	0.0844658i	0.663612	+	0.748077i	$0.269023\pi$
$744$	−15.8858	+	4.63870i	−0.582402	+	0.170063i
$745$	−1.19477	+	32.1055i	−0.0437730	+	1.17625i
$746$	4.11202	−	5.65971i	0.150552	−	0.207217i
$747$	1.34093	−	2.28154i	0.0490621	−	0.0834772i
$748$	−3.08236	+	1.57054i	−0.112702	+	0.0574247i
$749$	−1.53163			−0.0559646
$750$	−19.0775	+	3.32417i	−0.696611	+	0.121382i
$751$	18.7652			0.684751			0.342375	−	0.939563i	$-0.388769\pi$
$751$	18.7652			0.684751			0.342375	+	0.939563i	$0.388769\pi$
$752$	−11.3229	+	5.76930i	−0.412904	+	0.210385i
$753$	24.8641	+	4.70802i	0.906097	+	0.171570i
$754$	20.9870	−	28.8861i	0.764301	−	1.05197i
$755$	0.0271448	−	0.729425i	0.000987899	−	0.0265465i
$756$	−0.375952	−	0.160870i	−0.0136733	−	0.00585079i
$757$	−7.02667	+	7.02667i	−0.255389	+	0.255389i	−0.823176	−	0.567787i	$-0.807800\pi$
$757$	−7.02667	+	7.02667i	−0.255389	+	0.255389i	0.567787	+	0.823176i	$0.307800\pi$
$758$	1.90370	−	12.0195i	0.0691453	−	0.436567i
$759$	4.76327	+	0.143204i	0.172896	+	0.00519798i
$760$	1.31862	+	2.84478i	0.0478314	+	0.103191i
$761$	48.1462	+	15.6436i	1.74530	+	0.567081i	0.995515	−	0.0946038i	$-0.0301584\pi$
$761$	48.1462	+	15.6436i	1.74530	+	0.567081i	0.749782	+	0.661685i	$0.230158\pi$
$762$	−4.06305	+	3.82587i	−0.147189	+	0.138597i
$763$	0.439694	−	0.862948i	0.0159180	−	0.0312408i
$764$	−3.35652	+	10.3303i	−0.121435	+	0.373737i
$765$	11.3442	−	17.7554i	0.410152	−	0.641947i
$766$	−0.292865	−	0.901344i	−0.0105816	−	0.0325669i
$767$	−33.1721	−	5.25394i	−1.19777	−	0.189709i
$768$	−0.739603	−	1.56620i	−0.0266881	−	0.0565154i
$769$	21.2813	+	29.2912i	0.767422	+	1.05627i	0.996560	+	0.0828721i	$0.0264093\pi$
$769$	21.2813	+	29.2912i	0.767422	+	1.05627i	−0.229138	+	0.973394i	$0.573591\pi$
$770$	0.152456	+	0.119675i	0.00549413	+	0.00431278i
$771$	3.18239	−	2.16909i	0.114611	−	0.0781178i
$772$	−19.1698	+	3.03620i	−0.689936	+	0.109275i
$773$	−10.6768	−	20.9544i	−0.384019	−	0.753679i	0.615384	−	0.788227i	$-0.289001\pi$
$773$	−10.6768	−	20.9544i	−0.384019	−	0.753679i	−0.999403	+	0.0345481i	$0.989001\pi$
$774$	−3.29481	−	2.71063i	−0.118429	−	0.0974317i
$775$	−40.6297	+	25.1303i	−1.45946	+	0.902705i
$776$		−	10.3809i		−	0.372653i
$777$	0.178893	+	1.40075i	0.00641774	+	0.0502516i
$778$	−3.10878	−	19.6281i	−0.111455	−	0.703701i
$779$	−4.23704	−	3.07839i	−0.151808	−	0.110295i
$780$	−4.82408	−	19.1394i	−0.172730	−	0.685300i
$781$	11.3862	−	8.27256i	0.407430	−	0.296015i
$782$	−5.54804	−	5.54804i	−0.198397	−	0.198397i
$783$	33.7932	−	13.5395i	1.20767	−	0.483862i
$784$	6.65151	−	2.16121i	0.237554	−	0.0771859i
$785$	−7.47721	−	8.05523i	−0.266873	−	0.287504i
$786$	5.63586	−	7.28616i	0.201025	−	0.259889i
$787$	−28.0403	−	14.2872i	−0.999529	−	0.509285i	−0.123913	−	0.992293i	$-0.539544\pi$
$787$	−28.0403	−	14.2872i	−0.999529	−	0.509285i	−0.875616	+	0.483008i	$0.839544\pi$
$788$	10.8970	+	5.55232i	0.388191	+	0.197793i
$789$	−20.5342	+	26.5470i	−0.731036	+	0.945099i
$790$	−21.8493	−	4.29902i	−0.777363	−	0.152952i
$791$	0.571382	−	0.185653i	0.0203160	−	0.00660107i
$792$	−2.47256	+	2.19184i	−0.0878585	+	0.0778837i
$793$	14.3816	+	14.3816i	0.510707	+	0.510707i
$794$	−21.8203	+	15.8534i	−0.774375	+	0.562616i
$795$	26.2349	+	1.76701i	0.930457	+	0.0626695i
$796$	12.8922	+	9.36672i	0.456952	+	0.331995i
$797$	0.989635	+	6.24831i	0.0350547	+	0.221326i	0.998997	−	0.0447862i	$-0.0142607\pi$
$797$	0.989635	+	6.24831i	0.0350547	+	0.221326i	−0.963942	+	0.266113i	$0.914261\pi$
$798$	0.0242140	+	0.189599i	0.000857167	+	0.00671172i
$799$		−	39.9149i		−	1.41209i
$800$	−3.26298	−	3.78853i	−0.115364	−	0.133945i
$801$	−6.24966	+	7.59654i	−0.220821	+	0.268410i
$802$	15.4082	+	30.2402i	0.544081	+	1.06782i
$803$	−1.44469	+	0.228816i	−0.0509818	+	0.00807473i
$804$	−9.53041	+	6.49584i	−0.336112	+	0.229091i
$805$	−0.151293	+	0.412729i	−0.00533236	+	0.0145468i
$806$	−28.6215	−	39.3941i	−1.00815	−	1.38760i
$807$	4.06450	+	8.60707i	0.143077	+	0.302983i
$808$	13.8648	+	2.19597i	0.487763	+	0.0772540i
$809$	−10.4456	−	32.1483i	−0.367249	−	1.13028i	−0.948561	−	0.316595i	$-0.897461\pi$
$809$	−10.4456	−	32.1483i	−0.367249	−	1.13028i	0.581312	−	0.813681i	$-0.302539\pi$
$810$	6.22531	−	19.1375i	0.218735	−	0.672425i
$811$	−11.3720	+	34.9993i	−0.399324	+	1.22899i	0.526219	+	0.850349i	$0.323609\pi$
$811$	−11.3720	+	34.9993i	−0.399324	+	1.22899i	−0.925543	+	0.378643i	$0.876391\pi$
$812$	0.250313	−	0.491266i	0.00878425	−	0.0172401i
$813$	−9.38626	+	8.83835i	−0.329191	+	0.309975i
$814$	10.8518	+	3.52597i	0.380356	+	0.123585i
$815$	−2.99426	−	1.66872i	−0.104884	−	0.0584528i
$816$	5.43779	+	0.163483i	0.190361	+	0.00572306i
$817$	−0.311969	+	1.96970i	−0.0109144	+	0.0689110i
$818$	11.2430	−	11.2430i	0.393103	−	0.393103i
$819$	0.0722816	−	1.20103i	0.00252572	−	0.0419675i
$820$	7.84128	+	2.87435i	0.273829	+	0.100376i
$821$	−1.94467	+	2.67661i	−0.0678695	+	0.0934144i	−0.841602	−	0.540098i	$-0.818387\pi$
$821$	−1.94467	+	2.67661i	−0.0678695	+	0.0934144i	0.773733	+	0.633512i	$0.218387\pi$
$822$	19.5469	+	3.70121i	0.681777	+	0.129095i
$823$	−31.6727	+	16.1380i	−1.10404	+	0.562537i	−0.908385	−	0.418136i	$-0.862684\pi$
$823$	−31.6727	+	16.1380i	−1.10404	+	0.562537i	−0.195656	+	0.980673i	$0.562684\pi$
$824$	13.2042			0.459990
$825$	−5.19281	+	8.00098i	−0.180791	+	0.278558i
$826$	−0.518630			−0.0180454
$827$	−7.96567	+	4.05871i	−0.276993	+	0.141135i	−0.586969	−	0.809609i	$-0.699679\pi$
$827$	−7.96567	+	4.05871i	−0.276993	+	0.141135i	0.309976	+	0.950744i	$0.399679\pi$
$828$	−6.46082	−	3.79722i	−0.224529	−	0.131963i
$829$	−6.82593	+	9.39508i	−0.237074	+	0.326305i	−0.910932	−	0.412556i	$-0.864636\pi$
$829$	−6.82593	+	9.39508i	−0.237074	+	0.326305i	0.673858	+	0.738861i	$0.264636\pi$
$830$	1.89735	−	0.539357i	0.0658580	−	0.0187214i
$831$	31.7489	−	9.27078i	1.10136	−	0.321600i
$832$	3.60364	−	3.60364i	0.124934	−	0.124934i
$833$	−3.43640	+	21.6966i	−0.119064	+	0.751743i
$834$	0.567443	−	18.8743i	0.0196489	−	0.653565i
$835$	−9.66236	+	49.1078i	−0.334380	+	1.69945i
$836$	1.46885	+	0.477258i	0.0508012	+	0.0165063i
$837$	−3.31965	−	49.5365i	−0.114744	−	1.71223i
$838$	12.4834	−	24.5000i	0.431231	−	0.846339i
$839$	−1.99464	+	6.13888i	−0.0688628	+	0.211938i	−0.979566	−	0.201124i	$-0.935541\pi$
$839$	−1.99464	+	6.13888i	−0.0688628	+	0.211938i	0.910703	+	0.413062i	$0.135541\pi$
$840$	−0.119811	−	0.280259i	−0.00413387	−	0.00966985i
$841$	6.20662	+	19.1020i	0.214021	+	0.658690i
$842$	−31.5598	−	4.99858i	−1.08762	−	0.172262i
$843$	−2.20610	+	1.04178i	−0.0759822	+	0.0358809i
$844$	6.50062	+	8.94734i	0.223761	+	0.307980i
$845$	24.0853	−	16.1656i	0.828560	−	0.556115i
$846$	−9.58150	−	36.9003i	−0.329419	−	1.26866i
$847$	−0.760725	+	0.120487i	−0.0261388	+	0.00413998i
$848$	3.08222	+	6.04920i	0.105844	+	0.207730i
$849$	−5.57329	+	15.5468i	−0.191275	+	0.533563i
$850$	15.2554	−	3.72946i	0.523256	−	0.127920i
$851$			25.8790i			0.887121i
$852$	−21.9545	+	2.80386i	−0.752150	+	0.0960586i
$853$	−4.13209	−	26.0890i	−0.141480	−	0.893271i	−0.951674	−	0.307109i	$-0.900638\pi$
$853$	−4.13209	−	26.0890i	−0.141480	−	0.893271i	0.810194	−	0.586162i	$-0.199362\pi$
$854$	0.254089	+	0.184606i	0.00869474	+	0.00631710i
$855$	−9.18629	+	2.02389i	−0.314164	+	0.0692156i
$856$	15.7453	−	11.4396i	0.538163	−	0.390998i
$857$	21.7170	+	21.7170i	0.741840	+	0.741840i	0.972932	−	0.231092i	$-0.0742298\pi$
$857$	21.7170	+	21.7170i	0.741840	+	0.741840i	−0.231092	+	0.972932i	$0.574230\pi$
$858$	−8.52595	−	4.67208i	−0.291071	−	0.159502i
$859$	−2.16755	+	0.704281i	−0.0739560	+	0.0240298i	−0.345761	−	0.938322i	$-0.612379\pi$
$859$	−2.16755	+	0.704281i	−0.0739560	+	0.0240298i	0.271805	+	0.962352i	$0.412379\pi$
$860$	−0.380325	−	3.15726i	−0.0129690	−	0.107662i
$861$	0.402691	+	0.311482i	0.0137237	+	0.0106153i
$862$	7.71732	+	3.93217i	0.262853	+	0.133930i
$863$	1.81350	+	0.924026i	0.0617324	+	0.0314542i	0.484584	−	0.874745i	$-0.338971\pi$
$863$	1.81350	+	0.924026i	0.0617324	+	0.0314542i	−0.422852	+	0.906199i	$0.638971\pi$
$864$	5.06634	−	1.15420i	0.172360	−	0.0392666i
$865$	28.7554	−	13.3288i	0.977712	−	0.453191i
$866$	−10.2541	+	3.33175i	−0.348448	+	0.113218i
$867$	5.93849	−	10.8370i	0.201682	−	0.368043i
$868$	−0.531696	−	0.531696i	−0.0180469	−	0.0180469i
$869$	−8.87365	+	6.44709i	−0.301018	+	0.218702i
$870$	25.1845	+	10.1003i	0.853835	+	0.342431i
$871$	−27.4549	−	19.9472i	−0.930274	−	0.675884i
$872$	1.92520	+	12.1552i	0.0651953	+	0.411627i
$873$	30.4111	+	6.71083i	1.02926	+	0.227127i
$874$			3.50286i			0.118486i
$875$	−0.549007	−	0.687572i	−0.0185598	−	0.0232442i
$876$	2.16529	+	0.776226i	0.0731584	+	0.0262263i
$877$	−2.88829	−	5.66858i	−0.0975305	−	0.191414i	0.837086	−	0.547071i	$-0.184257\pi$
$877$	−2.88829	−	5.66858i	−0.0975305	−	0.191414i	−0.934617	+	0.355657i	$0.884257\pi$
$878$	33.8818	−	5.36634i	1.14345	−	0.181105i
$879$	30.3873	+	44.5829i	1.02494	+	1.50374i
$880$	−2.46110	−	0.0915871i	−0.0829636	−	0.00308740i
$881$	−3.61099	−	4.97010i	−0.121657	−	0.167447i	0.743844	−	0.668353i	$-0.233000\pi$
$881$	−3.61099	−	4.97010i	−0.121657	−	0.167447i	−0.865502	+	0.500906i	$0.833000\pi$
$882$	2.03137	+	20.8829i	0.0683996	+	0.703162i
$883$	−39.1067	−	6.19390i	−1.31605	−	0.208441i	−0.541362	−	0.840789i	$-0.682091\pi$
$883$	−39.1067	−	6.19390i	−1.31605	−	0.208441i	−0.774684	+	0.632348i	$0.782091\pi$
$884$	4.94649	+	15.2237i	0.166369	+	0.512030i
$885$	−2.28964	−	25.4207i	−0.0769655	−	0.854506i
$886$	2.00247	−	6.16296i	0.0672742	−	0.207049i
$887$	21.9363	−	43.0525i	0.736550	−	1.44556i	−0.152763	−	0.988263i	$-0.548817\pi$
$887$	21.9363	−	43.0525i	0.736550	−	1.44556i	0.889313	−	0.457299i	$-0.151183\pi$
$888$	−12.3011	−	13.0637i	−0.412798	−	0.438388i
$889$	−0.241160	−	0.0783578i	−0.00808826	−	0.00262804i
$890$	−7.27940	+	0.876881i	−0.244006	+	0.0293931i
$891$	−4.82263	−	8.66035i	−0.161564	−	0.290133i
$892$	0.859348	−	5.42571i	0.0287731	−	0.181666i
$893$	−12.6005	+	12.6005i	−0.421660	+	0.421660i
$894$	−6.97549	−	23.8884i	−0.233295	−	0.798948i
$895$	20.9737	−	26.7188i	0.701075	−	0.893112i
$896$	0.0462573	−	0.0636677i	0.00154535	−	0.00212699i
$897$	4.10233	−	21.6653i	0.136973	−	0.723383i
$898$	−20.2669	+	10.3265i	−0.676314	+	0.344599i
$899$	66.9409			2.23260
$900$	13.2080	−	7.10982i	0.440266	−	0.236994i
$901$	−21.3243			−0.710416
$902$	3.66526	−	1.86754i	0.122040	−	0.0621824i
$903$	0.0360655	−	0.190470i	0.00120019	−	0.00633844i
$904$	−4.48722	+	6.17613i	−0.149243	+	0.205415i
$905$	−12.7990	−	19.0694i	−0.425454	−	0.633888i
$906$	0.158481	+	0.542736i	0.00526517	+	0.0180312i
$907$	−24.7561	+	24.7561i	−0.822014	+	0.822014i	−0.986397	−	0.164383i	$-0.947437\pi$
$907$	−24.7561	+	24.7561i	−0.822014	+	0.822014i	0.164383	+	0.986397i	$0.447437\pi$
$908$	1.05800	−	6.67994i	0.0351109	−	0.221682i
$909$	−15.3962	+	39.1977i	−0.510660	+	1.30010i
$910$	0.657289	−	0.610124i	0.0217889	−	0.0202254i
$911$	48.5335	+	15.7695i	1.60799	+	0.522466i	0.969065	−	0.246806i	$-0.0793810\pi$
$911$	48.5335	+	15.7695i	1.60799	+	0.522466i	0.638921	+	0.769272i	$0.279381\pi$
$912$	−1.66502	−	1.76823i	−0.0551342	−	0.0585521i
$913$	0.441091	−	0.865690i	0.0145980	−	0.0286502i
$914$	2.74480	−	8.44762i	0.0907898	−	0.279422i
$915$	−7.92674	+	13.2692i	−0.262050	+	0.438665i
$916$	0.938563	+	2.88860i	0.0310110	+	0.0954420i
$917$	0.413380	+	0.0654729i	0.0136510	+	0.00216211i
$918$	−3.99424	+	15.8244i	−0.131830	+	0.522284i
$919$	6.34757	+	8.73668i	0.209387	+	0.288196i	0.900774	−	0.434288i	$-0.143000\pi$
$919$	6.34757	+	8.73668i	0.209387	+	0.288196i	−0.691387	+	0.722485i	$0.743000\pi$
$920$	−1.52734	−	5.37288i	−0.0503549	−	0.177139i
$921$	2.15835	+	3.16664i	0.0711200	+	0.104344i
$922$	22.1617	−	3.51006i	0.729855	−	0.115598i
$923$	−29.5652	−	58.0249i	−0.973150	−	1.90991i
$924$	−0.141323	−	0.0506624i	−0.00464919	−	0.00166667i
$925$	−44.2778	−	26.8816i	−1.45584	−	0.883860i
$926$			24.2111i			0.795626i
$927$	−8.53597	+	38.6819i	−0.280358	+	1.27048i
$928$	1.09599	+	6.91981i	0.0359777	+	0.227154i
$929$	−38.0194	−	27.6227i	−1.24738	−	0.906272i	−0.249310	−	0.968424i	$-0.580204\pi$
$929$	−38.0194	−	27.6227i	−1.24738	−	0.906272i	−0.998067	+	0.0621513i	$0.980204\pi$
$930$	23.7138	−	28.4084i	0.777606	−	0.931549i
$931$	7.93409	−	5.76446i	0.260029	−	0.188922i
$932$	0.977696	+	0.977696i	0.0320255	+	0.0320255i
$933$	−11.3463	+	20.7056i	−0.371463	+	0.677871i
$934$	12.8115	−	4.16270i	0.419204	−	0.136208i
$935$	3.76572	−	6.75700i	0.123152	−	0.220978i
$936$	8.22734	+	12.8866i	0.268919	+	0.421210i
$937$	40.7667	+	20.7717i	1.33179	+	0.678581i	0.967539	−	0.252721i	$-0.0813253\pi$
$937$	40.7667	+	20.7717i	1.33179	+	0.678581i	0.364250	+	0.931301i	$0.381325\pi$
$938$	−0.466926	−	0.237911i	−0.0152457	−	0.00776806i
$939$	−26.1652	−	20.2389i	−0.853870	−	0.660470i
$940$	13.8332	−	24.8215i	0.451189	−	0.809588i
$941$	−29.1364	+	9.46699i	−0.949820	+	0.308615i	−0.742642	−	0.669688i	$-0.766428\pi$
$941$	−29.1364	+	9.46699i	−0.949820	+	0.308615i	−0.207177	+	0.978303i	$0.566428\pi$
$942$	7.46589	+	4.09119i	0.243252	+	0.133298i
$943$	6.59721	+	6.59721i	0.214835	+	0.214835i
$944$	5.33155	−	3.87360i	0.173527	−	0.126075i
$945$	0.898477	−	0.169812i	0.0292275	−	0.00552400i
$946$	−1.26723	−	0.920697i	−0.0412012	−	0.0299344i
$947$	2.25687	+	14.2493i	0.0733384	+	0.463040i	0.996839	+	0.0794442i	$0.0253146\pi$
$947$	2.25687	+	14.2493i	0.0733384	+	0.463040i	−0.923501	+	0.383596i	$0.874685\pi$
$948$	17.1099	−	2.18514i	0.555704	−	0.0709701i
$949$			6.76809i			0.219701i
$950$	−5.99322	−	3.63856i	−0.194446	−	0.118050i
$951$	−5.31067	+	14.8142i	−0.172210	+	0.480382i
$952$	0.112219	+	0.220242i	0.00363704	+	0.00713809i
$953$	3.89283	−	0.616563i	0.126101	−	0.0199724i	−0.0930649	−	0.995660i	$-0.529666\pi$
$953$	3.89283	−	0.616563i	0.126101	−	0.0199724i	0.219166	+	0.975688i	$0.429666\pi$
$954$	−19.7138	+	5.11887i	−0.638257	+	0.165729i
$955$	−6.64120	−	23.3624i	−0.214904	−	0.755990i
$956$	6.68358	+	9.19915i	0.216162	+	0.297522i
$957$	12.0856	−	5.70713i	0.390671	−	0.184485i
$958$	−17.0684	−	2.70337i	−0.551455	−	0.0873420i
$959$	0.279326	+	0.859676i	0.00901989	+	0.0277604i
$960$	3.32489	+	1.98622i	0.107310	+	0.0641051i
$961$	18.6313	−	57.3413i	0.601010	−	1.84972i
$962$	23.9693	−	47.0424i	0.772801	−	1.51671i
$963$	23.3339	+	53.5214i	0.751925	+	1.72470i
$964$	−8.39163	−	2.72661i	−0.270276	−	0.0878181i
$965$	31.8079	−	29.5255i	1.02393	−	0.950459i
$966$	0.0102323	−	0.340347i	0.000329218	−	0.0109505i
$967$	−8.16627	+	51.5598i	−0.262610	+	1.65805i	0.405579	+	0.914060i	$0.367070\pi$
$967$	−8.16627	+	51.5598i	−0.262610	+	1.65805i	−0.668189	+	0.743992i	$0.732930\pi$
$968$	6.92040	−	6.92040i	0.222430	−	0.222430i
$969$	7.32280	−	2.13828i	0.235242	−	0.0686914i
$970$	12.9361	+	19.2736i	0.415353	+	0.618839i
$971$	2.69176	−	3.70489i	0.0863828	−	0.118896i	−0.763638	−	0.645644i	$-0.776589\pi$
$971$	2.69176	−	3.70489i	0.0863828	−	0.118896i	0.850021	+	0.526748i	$0.176589\pi$
$972$	0.106057	+	15.5881i	0.00340179	+	0.499988i
$973$	0.764451	−	0.389507i	0.0245072	−	0.0124870i
$974$	−3.62274			−0.116080
$975$	32.8070	+	29.5235i	1.05067	+	0.945508i
$976$	−3.99086			−0.127744
$977$	3.68285	−	1.87651i	0.117825	−	0.0600348i	−0.394085	−	0.919074i	$-0.628938\pi$
$977$	3.68285	−	1.87651i	0.117825	−	0.0600348i	0.511910	+	0.859039i	$0.328938\pi$
$978$	2.60885	+	0.493987i	0.0834219	+	0.0157960i
$979$	−2.12277	+	2.92174i	−0.0678439	+	0.0933792i
$980$	−9.65630	+	12.3013i	−0.308459	+	0.392951i
$981$	−36.8535	−	2.21795i	−1.17664	−	0.0708137i
$982$	4.08144	−	4.08144i	0.130244	−	0.130244i
$983$	4.05781	−	25.6200i	0.129424	−	0.817151i	−0.834507	−	0.550998i	$-0.814247\pi$
$983$	4.05781	−	25.6200i	0.129424	−	0.817151i	0.963931	−	0.266153i	$-0.0857527\pi$
$984$	−6.46612	−	0.194399i	−0.206132	−	0.00619722i
$985$	−27.1509	+	3.27061i	−0.865099	+	0.104210i
$986$	−20.9285	−	6.80010i	−0.666501	−	0.216559i
$987$	1.26111	−	1.18749i	0.0401415	−	0.0377983i
$988$	3.24437	−	6.36743i	0.103217	−	0.202575i
$989$	1.09782	−	3.37875i	0.0349087	−	0.107438i
$990$	1.85931	−	7.15063i	0.0590927	−	0.227262i
$991$	−7.36863	−	22.6783i	−0.234072	−	0.720400i	−0.997243	−	0.0742035i	$-0.976359\pi$
$991$	−7.36863	−	22.6783i	−0.234072	−	0.720400i	0.763171	−	0.646197i	$-0.223641\pi$
$992$	9.43706	+	1.49468i	0.299627	+	0.0474562i
$993$	8.17738	+	17.3166i	0.259501	+	0.549526i
$994$	−0.591094	−	0.813572i	−0.0187484	−	0.0258049i
$995$	−35.6085	−	1.32513i	−1.12887	−	0.0420095i
$996$	−1.26253	+	0.860532i	−0.0400049	+	0.0272670i
$997$	15.5032	−	2.45546i	0.490990	−	0.0777652i	0.0939699	−	0.995575i	$-0.470044\pi$
$997$	15.5032	−	2.45546i	0.490990	−	0.0777652i	0.397020	+	0.917810i	$0.370044\pi$
$998$	−12.9651	−	25.4455i	−0.410404	−	0.805464i
$999$	46.2225	−	27.5912i	1.46241	−	0.872947i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.l.a.53.3	yes	80
3.2	odd	2	inner	150.2.l.a.53.9	yes	80
5.2	odd	4		750.2.l.c.257.5		80
5.3	odd	4		750.2.l.a.257.6		80
5.4	even	2		750.2.l.b.743.8		80
15.2	even	4		750.2.l.c.257.10		80
15.8	even	4		750.2.l.a.257.1		80
15.14	odd	2		750.2.l.b.743.2		80
25.6	even	5		750.2.l.c.143.10		80
25.8	odd	20		750.2.l.b.107.2		80
25.17	odd	20	inner	150.2.l.a.17.9	yes	80
25.19	even	10		750.2.l.a.143.1		80
75.8	even	20		750.2.l.b.107.8		80
75.17	even	20	inner	150.2.l.a.17.3	✓	80
75.44	odd	10		750.2.l.a.143.6		80
75.56	odd	10		750.2.l.c.143.5		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.17.3	✓	80	75.17	even	20	inner
150.2.l.a.17.9	yes	80	25.17	odd	20	inner
150.2.l.a.53.3	yes	80	1.1	even	1	trivial
150.2.l.a.53.9	yes	80	3.2	odd	2	inner
750.2.l.a.143.1		80	25.19	even	10
750.2.l.a.143.6		80	75.44	odd	10
750.2.l.a.257.1		80	15.8	even	4
750.2.l.a.257.6		80	5.3	odd	4
750.2.l.b.107.2		80	25.8	odd	20
750.2.l.b.107.8		80	75.8	even	20
750.2.l.b.743.2		80	15.14	odd	2
750.2.l.b.743.8		80	5.4	even	2
750.2.l.c.143.5		80	75.56	odd	10
750.2.l.c.143.10		80	25.6	even	5
750.2.l.c.257.5		80	5.2	odd	4
750.2.l.c.257.10		80	15.2	even	4

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.891007 + 0.453990i) q^{2} +(-0.322239 + 1.70181i) q^{3} +(0.587785 - 0.809017i) q^{4} +(-0.0831552 + 2.23452i) q^{5} +(-0.485490 - 1.66262i) q^{6} +(0.0556476 - 0.0556476i) q^{7} +(-0.156434 + 0.987688i) q^{8} +(-2.79232 - 1.09678i) q^{9} +O(q^{10})\)	\(q+(-0.891007 + 0.453990i) q^{2} +(-0.322239 + 1.70181i) q^{3} +(0.587785 - 0.809017i) q^{4} +(-0.0831552 + 2.23452i) q^{5} +(-0.485490 - 1.66262i) q^{6} +(0.0556476 - 0.0556476i) q^{7} +(-0.156434 + 0.987688i) q^{8} +(-2.79232 - 1.09678i) q^{9} +(-0.940360 - 2.02872i) q^{10} +(-1.04749 - 0.340351i) q^{11} +(1.18739 + 1.26100i) q^{12} +(-2.31368 + 4.54086i) q^{13} +(-0.0243189 + 0.0748459i) q^{14} +(-3.77594 - 0.861563i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(3.10226 + 0.491350i) q^{17} +(2.98591 - 0.290452i) q^{18} +(-0.824223 - 1.13445i) q^{19} +(1.75889 + 1.38069i) q^{20} +(0.0767699 + 0.112634i) q^{21} +(1.08784 - 0.172297i) q^{22} +(1.13408 + 2.22575i) q^{23} +(-1.63045 - 0.584493i) q^{24} +(-4.98617 - 0.371624i) q^{25} -5.09632i q^{26} +(2.76630 - 4.39859i) q^{27} +(-0.0123110 - 0.0777287i) q^{28} +(5.66803 + 4.11807i) q^{29} +(3.75553 - 0.946581i) q^{30} +(7.72991 - 5.61611i) q^{31} +(0.707107 + 0.707107i) q^{32} +(0.916756 - 1.67296i) q^{33} +(-2.98720 + 0.970601i) q^{34} +(0.119718 + 0.128973i) q^{35} +(-2.52860 + 1.61437i) q^{36} +(9.23065 + 4.70325i) q^{37} +(1.24942 + 0.636609i) q^{38} +(-6.98213 - 5.40069i) q^{39} +(-2.19400 - 0.431688i) q^{40} +(3.55210 - 1.15415i) q^{41} +(-0.119537 - 0.0655044i) q^{42} +(-1.00563 - 1.00563i) q^{43} +(-0.891050 + 0.647386i) q^{44} +(2.68297 - 6.14831i) q^{45} +(-2.02094 - 1.46830i) q^{46} +(-1.98797 - 12.5515i) q^{47} +(1.71810 - 0.219422i) q^{48} +6.99381i q^{49} +(4.61142 - 1.93255i) q^{50} +(-1.83585 + 5.12113i) q^{51} +(2.31368 + 4.54086i) q^{52} +(-6.70559 + 1.06206i) q^{53} +(-0.467880 + 5.17504i) q^{54} +(0.847626 - 2.31234i) q^{55} +(0.0462573 + 0.0636677i) q^{56} +(2.19621 - 1.03711i) q^{57} +(-6.91981 - 1.09599i) q^{58} +(2.03647 + 6.26761i) q^{59} +(-2.91646 + 2.54838i) q^{60} +(1.23324 - 3.79553i) q^{61} +(-4.33774 + 8.51329i) q^{62} +(-0.216419 + 0.0943531i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(-9.95425 - 5.54757i) q^{65} +(-0.0573270 + 1.90682i) q^{66} +(-1.04169 + 6.57696i) q^{67} +(2.22097 - 2.22097i) q^{68} +(-4.15326 + 1.21276i) q^{69} +(-0.165222 - 0.0605649i) q^{70} +(-7.51096 + 10.3379i) q^{71} +(1.52009 - 2.58637i) q^{72} +(1.18329 - 0.602914i) q^{73} -10.3598 q^{74} +(2.23917 - 8.36577i) q^{75} -1.40225 q^{76} +(-0.0772302 + 0.0393507i) q^{77} +(8.67298 + 1.64223i) q^{78} +(5.85354 - 8.05671i) q^{79} +(2.15085 - 0.611420i) q^{80} +(6.59415 + 6.12512i) q^{81} +(-2.64098 + 2.64098i) q^{82} +(-0.137997 + 0.871279i) q^{83} +(0.136247 + 0.00409615i) q^{84} +(-1.35590 + 6.89121i) q^{85} +(1.35257 + 0.439477i) q^{86} +(-8.83463 + 8.31892i) q^{87} +(0.500025 - 0.981353i) q^{88} +(1.01326 - 3.11850i) q^{89} +(0.400727 + 6.69622i) q^{90} +(0.123937 + 0.381439i) q^{91} +(2.46727 + 0.390777i) q^{92} +(7.06668 + 14.9646i) q^{93} +(7.46957 + 10.2810i) q^{94} +(2.60348 - 1.74741i) q^{95} +(-1.43122 + 0.975505i) q^{96} +(-10.2531 + 1.62393i) q^{97} +(-3.17512 - 6.23153i) q^{98} +(2.55165 + 2.09924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q + 4 * q^3 + 4 * q^7	\( 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Introduction

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