LMFDB - Embedded newform 150.2.l.a.17.9

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			17.9
Character	$\chi$	$=$	150.17
Dual form			150.2.l.a.53.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.891007 + 0.453990i) q^{2} +(0.832356 - 1.51894i) q^{3} +(0.587785 + 0.809017i) q^{4} +(0.0831552 + 2.23452i) q^{5} +(1.43122 - 0.975505i) q^{6} +(0.0556476 + 0.0556476i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-1.61437 - 2.52860i) q^{9} +O(q^{10})$	\(q+(0.891007 + 0.453990i) q^{2} +(0.832356 - 1.51894i) q^{3} +(0.587785 + 0.809017i) q^{4} +(0.0831552 + 2.23452i) q^{5} +(1.43122 - 0.975505i) q^{6} +(0.0556476 + 0.0556476i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-1.61437 - 2.52860i) q^{9} +(-0.940360 + 2.02872i) q^{10} +(1.04749 - 0.340351i) q^{11} +(1.71810 - 0.219422i) q^{12} +(-2.31368 - 4.54086i) q^{13} +(0.0243189 + 0.0748459i) q^{14} +(3.46332 + 1.73361i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-3.10226 + 0.491350i) q^{17} +(-0.290452 - 2.98591i) q^{18} +(-0.824223 + 1.13445i) q^{19} +(-1.75889 + 1.38069i) q^{20} +(0.130844 - 0.0382069i) 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} +(-5.18452 + 0.347436i) q^{27} +(-0.0123110 + 0.0777287i) q^{28} +(-5.66803 + 4.11807i) q^{29} +(2.29880 + 3.11697i) q^{30} +(7.72991 + 5.61611i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.354913 - 1.87437i) q^{33} +(-2.98720 - 0.970601i) q^{34} +(-0.119718 + 0.128973i) q^{35} +(1.09678 - 2.79232i) q^{36} +(9.23065 - 4.70325i) q^{37} +(-1.24942 + 0.636609i) q^{38} +(-8.82310 - 0.265260i) q^{39} +(-2.19400 + 0.431688i) q^{40} +(-3.55210 - 1.15415i) q^{41} +(0.133928 + 0.0253594i) q^{42} +(-1.00563 + 1.00563i) q^{43} +(0.891050 + 0.647386i) q^{44} +(5.51597 - 3.81761i) q^{45} +(-2.02094 + 1.46830i) q^{46} +(1.98797 - 12.5515i) q^{47} +(1.18739 + 1.26100i) 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} +(-4.77718 - 2.04416i) q^{54} +(0.847626 + 2.31234i) q^{55} +(-0.0462573 + 0.0636677i) q^{56} +(1.03711 + 2.19621i) q^{57} +(-6.91981 + 1.09599i) q^{58} +(-2.03647 + 6.26761i) q^{59} +(0.633171 + 3.82088i) q^{60} +(1.23324 + 3.79553i) q^{61} +(4.33774 + 8.51329i) q^{62} +(0.0508748 - 0.230546i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(9.95425 - 5.54757i) q^{65} +(1.16718 - 1.50895i) q^{66} +(-1.04169 - 6.57696i) q^{67} +(-2.22097 - 2.22097i) q^{68} +(2.43683 + 3.57522i) q^{69} +(-0.165222 + 0.0605649i) q^{70} +(7.51096 + 10.3379i) q^{71} +(2.24493 - 1.99005i) q^{72} +(1.18329 + 0.602914i) q^{73} +10.3598 q^{74} +(-3.58579 + 7.88303i) q^{75} -1.40225 q^{76} +(0.0772302 + 0.0393507i) q^{77} +(-7.74102 - 4.24195i) q^{78} +(5.85354 + 8.05671i) q^{79} +(-2.15085 - 0.611420i) q^{80} +(-3.78763 + 8.16418i) q^{81} +(-2.64098 - 2.64098i) q^{82} +(0.137997 + 0.871279i) q^{83} +(0.107818 + 0.0833977i) q^{84} +(-1.35590 - 6.89121i) q^{85} +(-1.35257 + 0.439477i) q^{86} +(1.53728 + 12.0371i) q^{87} +(0.500025 + 0.981353i) q^{88} +(-1.01326 - 3.11850i) q^{89} +(6.64792 - 0.897315i) q^{90} +(0.123937 - 0.381439i) q^{91} +(-2.46727 + 0.390777i) q^{92} +(14.9646 - 7.06668i) q^{93} +(7.46957 - 10.2810i) q^{94} +(-2.60348 - 1.74741i) q^{95} +(0.485490 + 1.66262i) 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 $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{13}{20}\right)$

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
$3$	0.832356	−	1.51894i	0.480561	−	0.876961i
$3$	0.832356	−	1.51894i	0.480561	−	0.876961i
$4$	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
$6$	1.43122	−	0.975505i	0.584293	−	0.398248i
$7$	0.0556476	+	0.0556476i	0.0210328	+	0.0210328i	0.717545	−	0.696512i	$-0.245266\pi$
$7$	0.0556476	+	0.0556476i	0.0210328	+	0.0210328i	−0.696512	+	0.717545i	$0.745266\pi$
$8$	0.156434	+	0.987688i	0.0553079	+	0.349201i
$9$	−1.61437	−	2.52860i	−0.538123	−	0.842867i
$10$	−0.940360	+	2.02872i	−0.297368	+	0.641539i
$11$	1.04749	−	0.340351i	0.315831	−	0.102620i	−0.146812	−	0.989164i	$-0.546901\pi$
$11$	1.04749	−	0.340351i	0.315831	−	0.102620i	0.462643	+	0.886545i	$0.346901\pi$
$12$	1.71810	−	0.219422i	0.495972	−	0.0633416i
$13$	−2.31368	−	4.54086i	−0.641700	−	1.25941i	−0.951220	−	0.308514i	$-0.900168\pi$
$13$	−2.31368	−	4.54086i	−0.641700	−	1.25941i	0.309520	−	0.950893i	$-0.399832\pi$
$14$	0.0243189	+	0.0748459i	0.00649950	+	0.0200034i
$15$	3.46332	+	1.73361i	0.894226	+	0.447616i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−3.10226	+	0.491350i	−0.752408	+	0.119170i	−0.520846	−	0.853650i	$-0.674384\pi$
$17$	−3.10226	+	0.491350i	−0.752408	+	0.119170i	−0.231562	+	0.972820i	$0.574384\pi$
$18$	−0.290452	−	2.98591i	−0.0684602	−	0.703785i
$19$	−0.824223	+	1.13445i	−0.189090	+	0.260260i	−0.893028	−	0.450002i	$-0.851423\pi$
$19$	−0.824223	+	1.13445i	−0.189090	+	0.260260i	0.703938	+	0.710262i	$0.251423\pi$
$20$	−1.75889	+	1.38069i	−0.393299	+	0.308732i
$21$	0.130844	−	0.0382069i	0.0285525	−	0.00833742i
$22$	1.08784	+	0.172297i	0.231928	+	0.0367338i
$23$	−1.13408	+	2.22575i	−0.236472	+	0.464102i	−0.978495	−	0.206273i	$-0.933867\pi$
$23$	−1.13408	+	2.22575i	−0.236472	+	0.464102i	0.742023	+	0.670375i	$0.233867\pi$
$24$	1.63045	+	0.584493i	0.332814	+	0.119309i
$25$	−4.98617	+	0.371624i	−0.997234	+	0.0743249i
$26$		−	5.09632i		−	0.999471i
$27$	−5.18452	+	0.347436i	−0.997762	+	0.0668641i
$28$	−0.0123110	+	0.0777287i	−0.00232656	+	0.0146893i
$29$	−5.66803	+	4.11807i	−1.05253	+	0.764705i	−0.972691	−	0.232103i	$-0.925440\pi$
$29$	−5.66803	+	4.11807i	−1.05253	+	0.764705i	−0.0798355	+	0.996808i	$0.525440\pi$
$30$	2.29880	+	3.11697i	0.419702	+	0.569079i
$31$	7.72991	+	5.61611i	1.38833	+	1.00868i	0.996046	+	0.0888399i	$0.0283160\pi$
$31$	7.72991	+	5.61611i	1.38833	+	1.00868i	0.392287	+	0.919843i	$0.371684\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	0.354913	−	1.87437i	0.0617824	−	0.326286i
$34$	−2.98720	−	0.970601i	−0.512301	−	0.166457i
$35$	−0.119718	+	0.128973i	−0.0202361	+	0.0218004i
$36$	1.09678	−	2.79232i	0.182796	−	0.465387i
$37$	9.23065	−	4.70325i	1.51751	−	0.773210i	0.520755	−	0.853706i	$-0.325650\pi$
$37$	9.23065	−	4.70325i	1.51751	−	0.773210i	0.996755	+	0.0804961i	$0.0256505\pi$
$38$	−1.24942	+	0.636609i	−0.202682	+	0.103272i
$39$	−8.82310	−	0.265260i	−1.41283	−	0.0424756i
$40$	−2.19400	+	0.431688i	−0.346902	+	0.0682558i
$41$	−3.55210	−	1.15415i	−0.554745	−	0.180248i	0.0182101	−	0.999834i	$-0.494203\pi$
$41$	−3.55210	−	1.15415i	−0.554745	−	0.180248i	−0.572956	+	0.819586i	$0.694203\pi$
$42$	0.133928	+	0.0253594i	0.0206656	+	0.00391304i
$43$	−1.00563	+	1.00563i	−0.153357	+	0.153357i	−0.779616	−	0.626258i	$-0.784586\pi$
$43$	−1.00563	+	1.00563i	−0.153357	+	0.153357i	0.626258	+	0.779616i	$0.284586\pi$
$44$	0.891050	+	0.647386i	0.134331	+	0.0975971i
$45$	5.51597	−	3.81761i	0.822272	−	0.569095i
$46$	−2.02094	+	1.46830i	−0.297972	+	0.216489i
$47$	1.98797	−	12.5515i	0.289975	−	1.83083i	−0.225883	−	0.974154i	$-0.572527\pi$
$47$	1.98797	−	12.5515i	0.289975	−	1.83083i	0.515858	−	0.856674i	$-0.327473\pi$
$48$	1.18739	+	1.26100i	0.171385	+	0.182009i
$49$		−	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	$-0.295593\pi$
$53$	6.70559	+	1.06206i	0.921083	+	0.145885i	0.322154	+	0.946687i	$0.395593\pi$
$54$	−4.77718	−	2.04416i	−0.650091	−	0.278175i
$55$	0.847626	+	2.31234i	0.114294	+	0.311796i
$56$	−0.0462573	+	0.0636677i	−0.00618139	+	0.00850795i
$57$	1.03711	+	2.19621i	0.137369	+	0.290895i
$58$	−6.91981	+	1.09599i	−0.908616	+	0.143911i
$59$	−2.03647	+	6.26761i	−0.265126	+	0.815974i	0.726538	+	0.687126i	$0.241128\pi$
$59$	−2.03647	+	6.26761i	−0.265126	+	0.815974i	−0.991664	+	0.128848i	$0.958872\pi$
$60$	0.633171	+	3.82088i	0.0817420	+	0.493273i
$61$	1.23324	+	3.79553i	0.157901	+	0.485968i	0.998443	−	0.0557774i	$-0.0177637\pi$
$61$	1.23324	+	3.79553i	0.157901	+	0.485968i	−0.840543	+	0.541745i	$0.817764\pi$
$62$	4.33774	+	8.51329i	0.550894	+	1.08119i
$63$	0.0508748	−	0.230546i	0.00640962	−	0.0290461i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$	9.95425	−	5.54757i	1.23467	−	0.688091i
$66$	1.16718	−	1.50895i	0.143670	−	0.185739i
$67$	−1.04169	−	6.57696i	−0.127263	−	0.803504i	−0.965919	−	0.258844i	$-0.916659\pi$
$67$	−1.04169	−	6.57696i	−0.127263	−	0.803504i	0.838657	−	0.544660i	$-0.183341\pi$
$68$	−2.22097	−	2.22097i	−0.269332	−	0.269332i
$69$	2.43683	+	3.57522i	0.293360	+	0.430406i
$70$	−0.165222	+	0.0605649i	−0.0197479	+	0.00723889i
$71$	7.51096	+	10.3379i	0.891387	+	1.22689i	0.973135	+	0.230236i	$0.0739497\pi$
$71$	7.51096	+	10.3379i	0.891387	+	1.22689i	−0.0817481	+	0.996653i	$0.526050\pi$
$72$	2.24493	−	1.99005i	0.264567	−	0.234530i
$73$	1.18329	+	0.602914i	0.138493	+	0.0705658i	0.521864	−	0.853029i	$-0.325237\pi$
$73$	1.18329	+	0.602914i	0.138493	+	0.0705658i	−0.383371	+	0.923595i	$0.625237\pi$
$74$	10.3598			1.20430
$75$	−3.58579	+	7.88303i	−0.414052	+	0.910253i
$76$	−1.40225			−0.160849
$77$	0.0772302	+	0.0393507i	0.00880119	+	0.00448443i
$78$	−7.74102	−	4.24195i	−0.876498	−	0.480307i
$79$	5.85354	+	8.05671i	0.658575	+	0.906451i	0.999433	−	0.0336639i	$-0.0107176\pi$
$79$	5.85354	+	8.05671i	0.658575	+	0.906451i	−0.340858	+	0.940115i	$0.610718\pi$
$80$	−2.15085	−	0.611420i	−0.240473	−	0.0683588i
$81$	−3.78763	+	8.16418i	−0.420848	+	0.907131i
$82$	−2.64098	−	2.64098i	−0.291647	−	0.291647i
$83$	0.137997	+	0.871279i	0.0151471	+	0.0956353i	0.994104	−	0.108433i	$-0.0345834\pi$
$83$	0.137997	+	0.871279i	0.0151471	+	0.0956353i	−0.978957	+	0.204069i	$0.934583\pi$
$84$	0.107818	+	0.0833977i	0.0117639	+	0.00909943i
$85$	−1.35590	−	6.89121i	−0.147068	−	0.747456i
$86$	−1.35257	+	0.439477i	−0.145851	+	0.0473900i
$87$	1.53728	+	12.0371i	0.164814	+	1.29051i
$88$	0.500025	+	0.981353i	0.0533028	+	0.104613i
$89$	−1.01326	−	3.11850i	−0.107406	−	0.330560i	0.882882	−	0.469595i	$-0.155600\pi$
$89$	−1.01326	−	3.11850i	−0.107406	−	0.330560i	−0.990288	+	0.139035i	$0.955600\pi$
$90$	6.64792	−	0.897315i	0.700752	−	0.0945853i
$91$	0.123937	−	0.381439i	0.0129921	−	0.0399856i
$92$	−2.46727	+	0.390777i	−0.257230	+	0.0407413i
$93$	14.9646	−	7.06668i	1.55175	−	0.732781i
$94$	7.46957	−	10.2810i	0.770427	−	1.06040i
$95$	−2.60348	−	1.74741i	−0.267112	−	0.179280i
$96$	0.485490	+	1.66262i	0.0495501	+	0.169690i
$97$	−10.2531	−	1.62393i	−1.04104	−	0.164885i	−0.387575	−	0.921838i	$-0.626687\pi$
$97$	−10.2531	−	1.62393i	−1.04104	−	0.164885i	−0.653469	+	0.756953i	$0.726687\pi$
$98$	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	$-0.246104\pi$
$102$	−3.96070	+	3.72950i	−0.392168	+	0.369276i
$103$	−2.06559	+	13.0416i	−0.203529	+	1.28503i	0.648371	+	0.761324i	$0.275451\pi$
$103$	−2.06559	+	13.0416i	−0.203529	+	1.28503i	−0.851900	+	0.523705i	$0.824549\pi$
$104$	4.12301	−	2.99554i	0.404295	−	0.293737i
$105$	0.0962544	+	0.289197i	0.00939347	+	0.0282227i
$106$	5.49256	+	3.99058i	0.533484	+	0.387599i
$107$	13.7619	−	13.7619i	1.33041	−	1.33041i	0.425413	−	0.904999i	$-0.360129\pi$
$107$	13.7619	−	13.7619i	1.33041	−	1.33041i	0.904999	−	0.425413i	$-0.139871\pi$
$108$	−3.32847	−	3.99015i	−0.320282	−	0.383952i
$109$	11.7044	+	3.80299i	1.12108	+	0.364260i	0.810178	−	0.586183i	$-0.199370\pi$
$109$	11.7044	+	3.80299i	1.12108	+	0.364260i	0.310898	+	0.950443i	$0.399370\pi$
$110$	−0.294541	+	2.44513i	−0.0280834	+	0.233134i
$111$	0.539221	−	17.9356i	0.0511805	−	1.70237i
$112$	−0.0701201	+	0.0357280i	−0.00662572	+	0.00337598i
$113$	−6.80204	+	3.46581i	−0.639882	+	0.326036i	−0.743654	−	0.668565i	$-0.766909\pi$
$113$	−6.80204	+	3.46581i	−0.639882	+	0.326036i	0.103771	+	0.994601i	$0.466909\pi$
$114$	−0.0729862	+	2.42768i	−0.00683579	+	0.227373i
$115$	−5.06780	−	2.34904i	−0.472575	−	0.219049i
$116$	−6.66317	−	2.16499i	−0.618660	−	0.201015i
$117$	−7.74688	+	13.1810i	−0.716199	+	1.21858i
$118$	−4.65995	+	4.65995i	−0.428983	+	0.428983i
$119$	−0.199976	−	0.145291i	−0.0183317	−	0.0133188i
$120$	−1.17048	+	3.69188i	−0.106850	+	0.337021i
$121$	−7.91779	+	5.75261i	−0.719799	+	0.522964i
$122$	−0.624308	+	3.94172i	−0.0565222	+	0.356867i
$123$	−4.70970	+	4.43478i	−0.424659	+	0.399870i
$124$			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	−0.946756	−	0.321952i	$-0.895661\pi$
$127$	−1.46280	+	2.87091i	−0.129803	+	0.254752i	0.816954	+	0.576703i	$0.195661\pi$
$128$	−0.987688	−	0.156434i	−0.0873001	−	0.0138270i
$129$	0.690452	+	2.36454i	0.0607909	+	0.208186i
$130$	11.3878	−	0.423786i	0.998780	−	0.0371685i
$131$	−3.12598	+	4.30255i	−0.273118	+	0.375915i	−0.923439	−	0.383744i	$-0.874634\pi$
$131$	−3.12598	+	4.30255i	−0.273118	+	0.375915i	0.650321	+	0.759660i	$0.274634\pi$
$132$	1.72501	−	0.814598i	0.150143	−	0.0709017i
$133$	−0.108995	+	0.0172632i	−0.00945109	+	0.00149690i
$134$	2.05773	−	6.33303i	0.177761	−	0.547091i
$135$	−1.20747	−	11.5560i	−0.103923	−	0.994585i
$136$	−0.970601	−	2.98720i	−0.0832283	−	0.256150i
$137$	5.21451	+	10.2341i	0.445506	+	0.874354i	0.999135	+	0.0415907i	$0.0132426\pi$
$137$	5.21451	+	10.2341i	0.445506	+	0.874354i	−0.553629	+	0.832763i	$0.686757\pi$
$138$	0.548120	+	4.29184i	0.0466591	+	0.365346i
$139$	10.3684	−	3.36891i	0.879440	−	0.285747i	0.165715	−	0.986174i	$-0.447007\pi$
$139$	10.3684	−	3.36891i	0.879440	−	0.285747i	0.713725	+	0.700426i	$0.247007\pi$
$140$	−0.174710	−	0.0210457i	−0.0147657	−	0.00177868i
$141$	−17.4103	−	13.4669i	−1.46622	−	1.13412i
$142$	1.99898	+	12.6211i	0.167751	+	1.05914i
$143$	−3.96905	−	3.96905i	−0.331909	−	0.331909i
$144$	2.90371	−	0.753975i	0.241976	−	0.0628312i
$145$	−9.67323	−	12.3229i	−0.803318	−	1.02336i
$146$	0.780598	+	1.07440i	0.0646028	+	0.0889181i
$147$	−10.6232	−	5.82134i	−0.876186	−	0.480136i
$148$	9.23065	+	4.70325i	0.758755	+	0.386605i
$149$	−14.3679			−1.17707			−0.588534	−	0.808472i	$-0.700295\pi$
$149$	−14.3679			−1.17707			−0.588534	+	0.808472i	$0.700295\pi$
$150$	−6.77378	+	5.39591i	−0.553077	+	0.440574i
$151$	−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
$153$	6.25061	+	7.05115i	0.505332	+	0.570052i
$154$	0.0509477	+	0.0701235i	0.00410548	+	0.00565071i
$155$	−11.9065	+	17.7397i	−0.956356	+	1.42488i
$156$	−4.97149	−	7.29396i	−0.398038	−	0.583984i
$157$	−3.47556	−	3.47556i	−0.277380	−	0.277380i	0.554682	−	0.832062i	$-0.312840\pi$
$157$	−3.47556	−	3.47556i	−0.277380	−	0.277380i	−0.832062	+	0.554682i	$0.812840\pi$
$158$	1.55788	+	9.83604i	0.123938	+	0.782513i
$159$	7.19464	−	9.30139i	0.570572	−	0.737648i
$160$	−1.63884	−	1.52125i	−0.129562	−	0.120265i
$161$	−0.186967	+	0.0607491i	−0.0147350	+	0.00478770i
$162$	−7.08127	+	5.55479i	−0.556357	+	0.436425i
$163$	−0.695961	−	1.36590i	−0.0545119	−	0.106986i	0.862143	−	0.506664i	$-0.169122\pi$
$163$	−0.695961	−	1.36590i	−0.0545119	−	0.106986i	−0.916655	+	0.399679i	$0.869122\pi$
$164$	−1.15415	−	3.55210i	−0.0901239	−	0.277373i
$165$	4.21784	+	0.637197i	0.328358	+	0.0496057i
$166$	−0.272596	+	0.838964i	−0.0211576	+	0.0651163i
$167$	−22.1072	+	3.50144i	−1.71071	+	0.270949i	−0.933573	−	0.358387i	$-0.883327\pi$
$167$	−22.1072	+	3.50144i	−1.71071	+	0.270949i	−0.777133	+	0.629336i	$0.783327\pi$
$168$	0.0582050	+	0.123256i	0.00449061	+	0.00950943i
$169$	−7.62505	+	10.4950i	−0.586542	+	0.807306i
$170$	1.92043	−	6.75568i	0.147290	−	0.518137i
$171$	4.19916	+	0.252718i	0.321118	+	0.0193258i
$172$	−1.40467	−	0.222477i	−0.107105	−	0.0169637i
$173$	6.43491	−	12.6292i	0.489237	−	0.960182i	−0.505985	−	0.862542i	$-0.668871\pi$
$173$	6.43491	−	12.6292i	0.489237	−	0.960182i	0.995222	−	0.0976395i	$-0.0311292\pi$
$174$	−4.09500	+	11.4230i	−0.310441	+	0.865979i
$175$	−0.298148	−	0.256788i	−0.0225379	−	0.0194114i
$176$			1.10140i			0.0830211i
$177$	7.82507	+	8.31016i	0.588168	+	0.624630i
$178$	0.512946	−	3.23861i	0.0384469	−	0.242744i
$179$	12.2896	−	8.92889i	0.918565	−	0.667377i	−0.0246011	−	0.999697i	$-0.507832\pi$
$179$	12.2896	−	8.92889i	0.918565	−	0.667377i	0.943167	+	0.332320i	$0.107832\pi$
$180$	6.33071	+	2.21858i	0.471863	+	0.165363i
$181$	−8.30933	−	6.03708i	−0.617627	−	0.448733i	0.234465	−	0.972125i	$-0.424666\pi$
$181$	−8.30933	−	6.03708i	−0.617627	−	0.448733i	−0.852092	+	0.523392i	$0.824666\pi$
$182$	0.283598	−	0.283598i	0.0210217	−	0.0210217i
$183$	6.79169	+	1.28601i	0.502056	+	0.0950645i
$184$	−2.37576	−	0.771931i	−0.175143	−	0.0569075i
$185$	11.2771	+	20.2350i	0.829109	+	1.48771i
$186$	16.5417	+	0.497315i	1.21290	+	0.0364649i
$187$	−3.08236	+	1.57054i	−0.225405	+	0.114849i
$188$	11.3229	−	5.76930i	0.825807	−	0.420770i
$189$	−0.307840	−	0.269172i	−0.0223921	−	0.0195794i
$190$	−1.52641	−	2.73891i	−0.110738	−	0.198701i
$191$	10.3303	+	3.35652i	0.747475	+	0.242869i	0.657894	−	0.753110i	$-0.271447\pi$
$191$	10.3303	+	3.35652i	0.747475	+	0.242869i	0.0895805	+	0.995980i	$0.471447\pi$
$192$	−0.322239	+	1.70181i	−0.0232556	+	0.122818i
$193$	−13.7241	+	13.7241i	−0.987880	+	0.987880i	−0.999927	−	0.0120476i	$-0.996165\pi$
$193$	−13.7241	+	13.7241i	−0.987880	+	0.987880i	0.0120476	+	0.999927i	$0.496165\pi$
$194$	−8.39833	−	6.10174i	−0.602965	−	0.438080i
$195$	−0.140958	−	19.7375i	−0.0100942	−	1.41343i
$196$	5.65811	−	4.11086i	0.404151	−	0.293633i
$197$	−1.91320	+	12.0795i	−0.136310	+	0.860625i	0.820867	+	0.571120i	$0.193491\pi$
$197$	−1.91320	+	12.0795i	−0.136310	+	0.860625i	−0.957176	+	0.289506i	$0.906509\pi$
$198$	−1.32050	−	3.02886i	−0.0938440	−	0.215252i
$199$		−	15.9356i		−	1.12965i	−0.825212	−	0.564823i	$-0.808944\pi$
$199$		−	15.9356i		−	1.12965i	0.825212	−	0.564823i	$-0.191056\pi$
$200$	−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
$204$	−5.22217	+	1.52489i	−0.365625	+	0.106764i
$205$	2.28359	−	8.03322i	0.159493	−	0.561065i
$206$	−7.76123	+	10.6824i	−0.540750	+	0.744279i
$207$	7.45886	−	0.725556i	0.518427	−	0.0504296i
$208$	5.03358	−	0.797241i	0.349016	−	0.0552787i
$209$	−0.477258	+	1.46885i	−0.0330126	+	0.101602i
$210$	−0.0455293	+	0.301375i	−0.00314182	+	0.0207968i
$211$	−3.41758	−	10.5182i	−0.235276	−	0.724104i	−0.997085	−	0.0763026i	$-0.975689\pi$
$211$	−3.41758	−	10.5182i	−0.235276	−	0.724104i	0.761809	−	0.647802i	$-0.224311\pi$
$212$	3.08222	+	6.04920i	0.211688	+	0.415461i
$213$	21.9545	−	2.80386i	1.50430	−	0.192117i
$214$	18.5097	−	6.01417i	1.26530	−	0.411120i
$215$	−2.33073	−	2.16348i	−0.158954	−	0.147548i
$216$	−1.15420	−	5.06634i	−0.0785331	−	0.344721i
$217$	0.117628	+	0.742674i	0.00798511	+	0.0504160i
$218$	8.70216	+	8.70216i	0.589385	+	0.589385i
$219$	1.90071	−	1.29550i	0.128438	−	0.0875420i
$220$	−1.37250	+	2.04490i	−0.0925341	+	0.137867i
$221$	9.40879	+	12.9501i	0.632904	+	0.871117i
$222$	8.62304	−	15.7359i	0.578741	−	1.05613i
$223$	4.89460	+	2.49393i	0.327767	+	0.167006i	0.610129	−	0.792302i	$-0.291118\pi$
$223$	4.89460	+	2.49393i	0.327767	+	0.167006i	−0.282362	+	0.959308i	$0.591118\pi$
$224$	−0.0786976			−0.00525820
$225$	8.98920	+	12.0081i	0.599280	+	0.800539i
$226$	−7.63411			−0.507814
$227$	−6.02606	−	3.07043i	−0.399964	−	0.203792i	0.242426	−	0.970170i	$-0.422057\pi$
$227$	−6.02606	−	3.07043i	−0.399964	−	0.203792i	−0.642390	+	0.766378i	$0.722057\pi$
$228$	−1.16717	+	2.12994i	−0.0772979	+	0.141059i
$229$	−1.78525	−	2.45719i	−0.117973	−	0.162376i	0.745947	−	0.666006i	$-0.231997\pi$
$229$	−1.78525	−	2.45719i	−0.117973	−	0.162376i	−0.863919	+	0.503630i	$0.831997\pi$
$230$	−3.44900	−	4.39374i	−0.227420	−	0.289715i
$231$	0.124054	−	0.0845543i	0.00816218	−	0.00556326i
$232$	−4.95404	−	4.95404i	−0.325249	−	0.325249i
$233$	0.216297	+	1.36565i	0.0141701	+	0.0894666i	0.993760	−	0.111541i	$-0.0355785\pi$
$233$	0.216297	+	1.36565i	0.0141701	+	0.0894666i	−0.979590	+	0.201007i	$0.935579\pi$
$234$	−12.8866	+	8.22734i	−0.842421	+	0.537838i
$235$	28.2120	+	3.39843i	1.84035	+	0.221689i
$236$	−6.26761	+	2.03647i	−0.407987	+	0.132563i
$237$	17.1099	−	2.18514i	1.11141	−	0.141940i
$238$	−0.112219	−	0.220242i	−0.00727408	−	0.0142762i
$239$	3.51376	+	10.8143i	0.227287	+	0.699516i	0.998051	+	0.0623963i	$0.0198743\pi$
$239$	3.51376	+	10.8143i	0.227287	+	0.699516i	−0.770765	+	0.637120i	$0.780126\pi$
$240$	−2.71899	+	2.75810i	−0.175510	+	0.178035i
$241$	−2.72661	+	8.39163i	−0.175636	+	0.540552i	−0.999662	−	0.0259998i	$-0.991723\pi$
$241$	−2.72661	+	8.39163i	−0.175636	+	0.540552i	0.824026	+	0.566552i	$0.191723\pi$
$242$	−9.66643	+	1.53101i	−0.621382	+	0.0984172i
$243$	9.24826	+	12.5487i	0.593276	+	0.804999i
$244$	−2.34577	+	3.22867i	−0.150172	+	0.206695i
$245$	15.6278	−	0.581572i	0.998424	−	0.0371553i
$246$	−6.20972	+	1.81326i	−0.395917	+	0.115609i
$247$	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	$-0.152545\pi$
$252$	0.216419	−	0.0943531i	0.0136331	−	0.00594369i
$253$	−0.430401	+	2.71745i	−0.0270591	+	0.170844i
$254$	−2.60673	+	1.89390i	−0.163561	+	0.118834i
$255$	−11.5959	−	3.67640i	−0.726165	−	0.230225i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	1.57229	−	1.57229i	0.0980767	−	0.0980767i	−0.656366	−	0.754443i	$-0.727907\pi$
$257$	1.57229	−	1.57229i	0.0980767	−	0.0980767i	0.754443	+	0.656366i	$0.227907\pi$
$258$	−0.458280	+	2.42028i	−0.0285313	+	0.150680i
$259$	0.775389	+	0.251939i	0.0481803	+	0.0156547i
$260$	10.3390	+	4.79238i	0.641200	+	0.297211i
$261$	19.5632	+	7.68411i	1.21093	+	0.475634i
$262$	−4.73859	+	2.41443i	−0.292751	+	0.149164i
$263$	−17.2650	+	8.79695i	−1.06460	+	0.542443i	−0.896371	−	0.443304i	$-0.853806\pi$
$263$	−17.2650	+	8.79695i	−1.06460	+	0.542443i	−0.168233	+	0.985747i	$0.553806\pi$
$264$	1.90682	+	0.0573270i	0.117356	+	0.00352823i
$265$	−1.81559	+	15.0721i	−0.111531	+	0.925872i
$266$	−0.104953	−	0.0341012i	−0.00643507	−	0.00209088i
$267$	−5.58021	−	1.05661i	−0.341503	−	0.0646638i
$268$	4.70859	−	4.70859i	0.287623	−	0.287623i
$269$	−4.44596	−	3.23018i	−0.271075	−	0.196948i	0.443940	−	0.896056i	$-0.353580\pi$
$269$	−4.44596	−	3.23018i	−0.271075	−	0.196948i	−0.715015	+	0.699109i	$0.753580\pi$
$270$	4.17046	−	10.8447i	0.253806	−	0.659987i
$271$	6.02194	−	4.37520i	0.365807	−	0.265774i	−0.389663	−	0.920957i	$-0.627409\pi$
$271$	6.02194	−	4.37520i	0.365807	−	0.265774i	0.755470	+	0.655183i	$0.227409\pi$
$272$	0.491350	−	3.10226i	0.0297924	−	0.188102i
$273$	−0.476224	−	0.505746i	−0.0288224	−	0.0306091i
$274$			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	0.469365	+	0.883004i	$0.344483\pi$
$277$	−8.66928	+	17.0144i	−0.520886	+	1.02230i	−0.990251	+	0.139293i	$0.955517\pi$
$278$	10.7678	+	1.70545i	0.645810	+	0.102286i
$279$	1.72197	−	28.6123i	0.103092	−	1.71297i
$280$	−0.146113	−	0.0980686i	−0.00873194	−	0.00586072i
$281$	−0.827936	+	1.13956i	−0.0493905	+	0.0679802i	−0.832998	−	0.553276i	$-0.813377\pi$
$281$	−0.827936	+	1.13956i	−0.0493905	+	0.0679802i	0.783607	+	0.621256i	$0.213377\pi$
$282$	−9.39887	−	19.9033i	−0.559694	−	1.18522i
$283$	9.41786	−	1.49164i	0.559834	−	0.0886689i	0.129896	−	0.991528i	$-0.458536\pi$
$283$	9.41786	−	1.49164i	0.559834	−	0.0886689i	0.429937	+	0.902859i	$0.358536\pi$
$284$	−3.94874	+	12.1530i	−0.234315	+	0.721147i
$285$	−4.82124	+	2.50007i	−0.285585	+	0.148091i
$286$	−1.73454	−	5.33836i	−0.102565	−	0.315664i
$287$	−0.133440	−	0.261892i	−0.00787674	−	0.0154590i
$288$	2.92952	+	0.646460i	0.172624	+	0.0380930i
$289$	−6.78537	+	2.20470i	−0.399139	+	0.129688i
$290$	−3.02443	−	15.3713i	−0.177601	−	0.902636i
$291$	−11.0009	+	14.2222i	−0.644883	+	0.833718i
$292$	0.207750	+	1.31168i	0.0121577	+	0.0767604i
$293$	−22.0266	−	22.0266i	−1.28681	−	1.28681i	−0.936716	−	0.350091i	$-0.886151\pi$
$293$	−22.0266	−	22.0266i	−1.28681	−	1.28681i	−0.350091	−	0.936716i	$-0.613849\pi$
$294$	−6.82250	−	10.0097i	−0.397896	−	0.583776i
$295$	−14.1745	−	4.02935i	−0.825269	−	0.234598i
$296$	6.08934	+	8.38126i	0.353936	+	0.487151i
$297$	−5.31250	+	2.12849i	−0.308262	+	0.123508i
$298$	−12.8019	−	6.52291i	−0.741596	−	0.377862i
$299$	12.7307			0.736237
$300$	−8.48518	+	1.73256i	−0.489892	+	0.100029i
$301$	−0.111922			−0.00645107
$302$	−0.290856	−	0.148198i	−0.0167369	−	0.00852785i
$303$	−21.3224	−	11.6843i	−1.22494	−	0.671247i
$304$	−0.824223	−	1.13445i	−0.0472724	−	0.0650649i
$305$	−8.37864	+	3.07133i	−0.479760	+	0.175864i
$306$	2.36818	+	9.12034i	0.135380	+	0.521375i
$307$	1.56450	+	1.56450i	0.0892910	+	0.0892910i	0.750341	−	0.661050i	$-0.229889\pi$
$307$	1.56450	+	1.56450i	0.0892910	+	0.0892910i	−0.661050	+	0.750341i	$0.729889\pi$
$308$	0.0135593	+	0.0856103i	0.000772615	+	0.00487810i
$309$	18.0902	+	13.9928i	1.02911	+	0.796022i
$310$	−18.6624	+	10.4007i	−1.05995	+	0.590720i
$311$	−12.9644	+	4.21240i	−0.735145	+	0.238863i	−0.652577	−	0.757722i	$-0.726312\pi$
$311$	−12.9644	+	4.21240i	−0.735145	+	0.238863i	−0.0825681	+	0.996585i	$0.526312\pi$
$312$	−1.11824	−	8.75597i	−0.0633081	−	0.495709i
$313$	−8.67043	−	17.0167i	−0.490082	−	0.961839i	−0.995113	−	0.0987386i	$-0.968519\pi$
$313$	−8.67043	−	17.0167i	−0.490082	−	0.961839i	0.505032	−	0.863101i	$-0.331481\pi$
$314$	−1.51888	−	4.67462i	−0.0857152	−	0.263804i
$315$	0.519391	+	0.0945097i	0.0292644	+	0.00532502i
$316$	−3.07739	+	9.47123i	−0.173117	+	0.532798i
$317$	−8.97408	+	1.42135i	−0.504034	+	0.0798312i	−0.403274	−	0.915079i	$-0.632128\pi$
$317$	−8.97408	+	1.42135i	−0.504034	+	0.0798312i	−0.100761	+	0.994911i	$0.532128\pi$
$318$	10.6332	−	5.02130i	0.596281	−	0.281580i
$319$	−4.53563	+	6.24276i	−0.253947	+	0.349528i
$320$	−0.769590	−	2.09946i	−0.0430214	−	0.117363i
$321$	−9.44872	−	32.3583i	−0.527376	−	1.80606i
$322$	−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
$327$	15.5187	−	14.6128i	0.858187	−	0.808092i
$328$	0.584268	−	3.68892i	0.0322608	−	0.203687i
$329$	0.809088	−	0.587837i	0.0446065	−	0.0324085i
$330$	3.46884	+	2.48261i	0.190953	+	0.136663i
$331$	8.94485	+	6.49882i	0.491654	+	0.357207i	0.805820	−	0.592161i	$-0.201725\pi$
$331$	8.94485	+	6.49882i	0.491654	+	0.357207i	−0.314166	+	0.949368i	$0.601725\pi$
$332$	−0.623767	+	0.623767i	−0.0342336	+	0.0342336i
$333$	−26.7943	−	15.7478i	−1.46832	−	0.862977i
$334$	−21.2873	−	6.91666i	−1.16479	−	0.378463i
$335$	14.6097	−	2.87458i	0.798215	−	0.157055i
$336$	−0.00409615	+	0.136247i	−0.000223464	+	0.00743287i
$337$	15.4169	−	7.85531i	0.839813	−	0.427906i	0.0194923	−	0.999810i	$-0.493795\pi$
$337$	15.4169	−	7.85531i	0.839813	−	0.427906i	0.820321	+	0.571904i	$0.193795\pi$
$338$	−11.5586	+	5.88940i	−0.628705	+	0.320341i
$339$	−0.397350	+	13.2167i	−0.0215811	+	0.717833i
$340$	4.77812	−	5.14750i	0.259130	−	0.279162i
$341$	10.0085	+	3.25195i	0.541989	+	0.176103i
$342$	3.62675	+	2.13155i	0.196112	+	0.115261i
$343$	0.778722	−	0.778722i	0.0420470	−	0.0420470i
$344$	−1.15057	−	0.835934i	−0.0620343	−	0.0450706i
$345$	−7.78627	+	5.74246i	−0.419198	+	0.309163i
$346$	11.4671	−	8.33133i	0.616475	−	0.447895i
$347$	2.33923	−	14.7693i	0.125576	−	0.792857i	−0.841851	−	0.539709i	$-0.818534\pi$
$347$	2.33923	−	14.7693i	0.125576	−	0.792857i	0.967428	−	0.253148i	$-0.0814658\pi$
$348$	−8.83463	+	8.31892i	−0.473586	+	0.445941i
$349$		−	0.345103i		−	0.0184729i	−0.999957	−	0.00923647i	$-0.997060\pi$
$349$		−	0.345103i		−	0.0184729i	0.999957	−	0.00923647i	$-0.00294010\pi$
$350$	−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	$-0.628998\pi$
$353$	−19.7879	−	3.13409i	−1.05320	−	0.166811i	−0.658947	+	0.752190i	$0.728998\pi$
$354$	3.19945	+	10.9569i	0.170049	+	0.582354i
$355$	−22.4758	+	17.6431i	−1.19289	+	0.936396i
$356$	1.92734	−	2.65275i	0.102149	−	0.140596i
$357$	−0.387139	+	0.182818i	−0.0204896	+	0.00967574i
$358$	15.0037	−	2.37636i	0.792971	−	0.125594i
$359$	5.66877	−	17.4467i	0.299186	−	0.920800i	−0.682597	−	0.730795i	$-0.739150\pi$
$359$	5.66877	−	17.4467i	0.299186	−	0.920800i	0.981783	−	0.190005i	$-0.0608505\pi$
$360$	4.63349	+	4.85085i	0.244206	+	0.255662i
$361$	5.26370	+	16.2000i	0.277037	+	0.852632i
$362$	−4.66289	−	9.15143i	−0.245076	−	0.480989i
$363$	2.14746	+	16.8149i	0.112713	+	0.882552i
$364$	0.381439	−	0.123937i	0.0199928	−	0.00649606i
$365$	−1.24883	+	2.69421i	−0.0653667	+	0.141022i
$366$	5.46760	+	4.22920i	0.285796	+	0.221064i
$367$	0.00304877	+	0.0192492i	0.000159144	+	0.00100480i	0.987768	−	0.155932i	$-0.0498381\pi$
$367$	0.00304877	+	0.0192492i	0.000159144	+	0.00100480i	−0.987609	+	0.156937i	$0.949838\pi$
$368$	−1.76637	−	1.76637i	−0.0920783	−	0.0920783i
$369$	2.81602	+	10.8451i	0.146596	+	0.564572i
$370$	0.861472	+	23.1492i	0.0447858	+	1.20347i
$371$	0.314049	+	0.432251i	0.0163046	+	0.0224414i
$372$	14.5130	+	7.95290i	0.752465	+	0.412339i
$373$	−6.23329	−	3.17602i	−0.322748	−	0.164448i	0.285109	−	0.958495i	$-0.407970\pi$
$373$	−6.23329	−	3.17602i	−0.322748	−	0.164448i	−0.607856	+	0.794047i	$0.707970\pi$
$374$	−3.45942			−0.178882
$375$	−17.9130	−	7.35701i	−0.925022	−	0.379915i
$376$	12.7080			0.655364
$377$	31.8136	+	16.2098i	1.63848	+	0.834848i
$378$	−0.152086	−	0.379591i	−0.00782246	−	0.0195241i
$379$	−7.15293	−	9.84516i	−0.367421	−	0.505712i	0.584776	−	0.811194i	$-0.301182\pi$
$379$	−7.15293	−	9.84516i	−0.367421	−	0.505712i	−0.952198	+	0.305483i	$0.901182\pi$
$380$	−0.116605	−	3.13336i	−0.00598169	−	0.160738i
$381$	3.14317	+	4.61152i	0.161030	+	0.236256i
$382$	7.68054	+	7.68054i	0.392971	+	0.392971i
$383$	0.148258	+	0.936062i	0.00757561	+	0.0478305i	0.991187	−	0.132473i	$-0.0422919\pi$
$383$	0.148258	+	0.936062i	0.00757561	+	0.0478305i	−0.983611	+	0.180304i	$0.942292\pi$
$384$	−1.05972	+	1.37003i	−0.0540788	+	0.0699141i
$385$	−0.0815080	+	0.175845i	−0.00415403	+	0.00896187i
$386$	−18.4588	+	5.99764i	−0.939530	+	0.305272i
$387$	4.16630	+	0.919380i	0.211785	+	0.0467347i
$388$	−4.71283	−	9.24945i	−0.239258	−	0.469570i
$389$	6.14102	+	18.9001i	0.311362	+	0.958273i	0.977226	+	0.212200i	$0.0680630\pi$
$389$	6.14102	+	18.9001i	0.311362	+	0.958273i	−0.665864	+	0.746073i	$0.731937\pi$
$390$	8.83503	−	17.6502i	0.447379	−	0.893753i
$391$	2.42458	−	7.46210i	0.122616	−	0.377374i
$392$	6.90770	−	1.09407i	0.348892	−	0.0552590i
$393$	3.93339	+	8.32944i	0.198413	+	0.420164i
$394$	−7.18863	+	9.89430i	−0.362158	+	0.498468i
$395$	−17.5161	+	13.7498i	−0.881333	+	0.691829i
$396$	0.198497	−	3.29823i	0.00997485	−	0.165742i
$397$	26.6394	+	4.21926i	1.33699	+	0.211759i	0.783654	−	0.621198i	$-0.213354\pi$
$397$	26.6394	+	4.21926i	1.33699	+	0.211759i	0.553338	+	0.832957i	$0.313354\pi$
$398$	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	$-0.321849\pi$
$402$	−7.90675	−	8.39690i	−0.394353	−	0.418800i
$403$	7.61739	−	48.0943i	0.379449	−	2.39575i
$404$	11.3567	−	8.25112i	0.565017	−	0.410509i
$405$	−18.5580	−	7.78465i	−0.922154	−	0.386822i
$406$	−0.446060	−	0.324082i	−0.0221376	−	0.0160839i
$407$	8.06828	−	8.06828i	0.399930	−	0.399930i
$408$	−5.34527	−	1.01213i	−0.264630	−	0.0501078i
$409$	−15.1218	−	4.91338i	−0.747726	−	0.242951i	−0.0897236	−	0.995967i	$-0.528598\pi$
$409$	−15.1218	−	4.91338i	−0.747726	−	0.242951i	−0.658002	+	0.753016i	$0.728598\pi$
$410$	5.68170	−	6.12093i	0.280599	−	0.302291i
$411$	19.8853	+	0.597835i	0.980867	+	0.0294890i
$412$	−11.7650	+	5.99458i	−0.579621	+	0.295332i
$413$	−0.462102	+	0.235453i	−0.0227386	+	0.0115859i
$414$	6.97529	+	2.73978i	0.342817	+	0.134653i
$415$	−1.93542	+	0.380809i	−0.0950058	+	0.0186932i
$416$	4.84689	+	1.57485i	0.237638	+	0.0772134i
$417$	3.51305	−	18.5532i	0.172035	−	0.908554i
$418$	−1.09208	+	1.09208i	−0.0534155	+	0.0534155i
$419$	22.2455	+	16.1623i	1.08677	+	0.789582i	0.978850	−	0.204578i	$-0.0655823\pi$
$419$	22.2455	+	16.1623i	1.08677	+	0.789582i	0.107916	+	0.994160i	$0.465582\pi$
$420$	−0.177388	+	0.247857i	−0.00865566	+	0.0120942i
$421$	25.8507	−	18.7816i	1.25988	−	0.915359i	0.261132	−	0.965303i	$-0.415904\pi$
$421$	25.8507	−	18.7816i	1.25988	−	0.915359i	0.998752	+	0.0499438i	$0.0159042\pi$
$422$	1.73009	−	10.9234i	0.0842194	−	0.531741i
$423$	−34.9471	+	15.2360i	−1.69919	+	0.740800i
$424$			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
$429$	−9.33242	+	2.72509i	−0.450573	+	0.131569i
$430$	−1.09449	−	2.98580i	−0.0527812	−	0.143988i
$431$	5.09101	−	7.00718i	0.245225	−	0.337524i	−0.668607	−	0.743616i	$-0.733109\pi$
$431$	5.09101	−	7.00718i	0.245225	−	0.337524i	0.913832	+	0.406093i	$0.133109\pi$
$432$	1.27167	−	5.03814i	0.0611835	−	0.242398i
$433$	10.6490	−	1.68664i	0.511760	−	0.0810548i	0.104786	−	0.994495i	$-0.466584\pi$
$433$	10.6490	−	1.68664i	0.511760	−	0.0810548i	0.406974	+	0.913440i	$0.366584\pi$
$434$	−0.232360	+	0.715129i	−0.0111536	+	0.0343273i
$435$	−26.7693	+	4.43604i	−1.28349	+	0.212692i
$436$	3.80299	+	11.7044i	0.182130	+	0.560538i
$437$	−1.59026	−	3.12107i	−0.0760726	−	0.149301i
$438$	2.28169	−	0.291399i	0.109023	−	0.0139236i
$439$	−32.6251	+	10.6006i	−1.55711	+	0.505937i	−0.956035	−	0.293253i	$-0.905262\pi$
$439$	−32.6251	+	10.6006i	−1.55711	+	0.505937i	−0.601078	+	0.799190i	$0.705262\pi$
$440$	−2.15128	+	1.19892i	−0.102558	+	0.0571563i
$441$	−17.6845	+	11.2906i	−0.842121	+	0.537646i
$442$	2.50408	+	15.8101i	0.119107	+	0.752011i
$443$	4.58214	+	4.58214i	0.217704	+	0.217704i	0.807530	−	0.589826i	$-0.200804\pi$
$443$	4.58214	+	4.58214i	0.217704	+	0.217704i	−0.589826	+	0.807530i	$0.700804\pi$
$444$	14.8272	−	10.1060i	0.703666	−	0.479612i
$445$	6.88409	−	2.52347i	0.326337	−	0.119624i
$446$	3.22891	+	4.44421i	0.152893	+	0.210439i
$447$	−11.9592	+	21.8241i	−0.565653	+	1.03224i
$448$	−0.0701201	−	0.0357280i	−0.00331286	−	0.00168799i
$449$	−22.7460			−1.07345			−0.536726	−	0.843756i	$-0.680339\pi$
$449$	−22.7460			−1.07345			−0.536726	+	0.843756i	$0.680339\pi$
$450$	2.55788	+	14.7803i	0.120580	+	0.696750i
$451$	−4.11362			−0.193703
$452$	−6.80204	−	3.46581i	−0.319941	−	0.163018i
$453$	−0.271710	+	0.495835i	−0.0127660	+	0.0232964i
$454$	−3.97531	−	5.47155i	−0.186571	−	0.256792i
$455$	0.862639	+	0.245221i	0.0404411	+	0.0114961i
$456$	−2.00693	+	1.36790i	−0.0939831	+	0.0640580i
$457$	−6.28077	−	6.28077i	−0.293802	−	0.293802i	0.544778	−	0.838580i	$-0.316614\pi$
$457$	−6.28077	−	6.28077i	−0.293802	−	0.293802i	−0.838580	+	0.544778i	$0.816614\pi$
$458$	−0.475131	−	2.99986i	−0.0222014	−	0.140174i
$459$	15.9130	−	3.62525i	0.742756	−	0.169212i
$460$	−1.07837	−	5.48067i	−0.0502790	−	0.255537i
$461$	21.3397	−	6.93369i	0.993889	−	0.322934i	0.233468	−	0.972364i	$-0.424993\pi$
$461$	21.3397	−	6.93369i	0.993889	−	0.322934i	0.760421	+	0.649430i	$0.224993\pi$
$462$	0.148920	−	0.0190189i	0.00692839	−	0.000884839i
$463$	10.9916	+	21.5722i	0.510823	+	1.00255i	0.992037	+	0.125944i	$0.0401959\pi$
$463$	10.9916	+	21.5722i	0.510823	+	1.00255i	−0.481214	+	0.876603i	$0.659804\pi$
$464$	−2.16499	−	6.66317i	−0.100507	−	0.309330i
$465$	17.0350	+	32.8510i	0.789981	+	1.52343i
$466$	−0.427269	+	1.31500i	−0.0197929	+	0.0609161i
$467$	13.3049	−	2.10730i	0.615679	−	0.0975140i	0.159197	−	0.987247i	$-0.449109\pi$
$467$	13.3049	−	2.10730i	0.615679	−	0.0975140i	0.456482	+	0.889733i	$0.349109\pi$
$468$	−15.2171	+	1.48024i	−0.703413	+	0.0684240i
$469$	0.308025	−	0.423960i	0.0142233	−	0.0195766i
$470$	23.5942	+	15.8360i	1.08832	+	0.730460i
$471$	−8.17208	+	2.38627i	−0.376550	+	0.109954i
$472$	−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
$477$	−8.13976	−	18.6703i	−0.372694	−	0.854855i
$478$	−1.77878	+	11.2308i	−0.0813596	+	0.513684i
$479$	−13.9808	+	10.1576i	−0.638797	+	0.464113i	−0.859437	−	0.511242i	$-0.829186\pi$
$479$	−13.9808	+	10.1576i	−0.638797	+	0.464113i	0.220639	+	0.975355i	$0.429186\pi$
$480$	−3.67479	+	1.22309i	−0.167730	+	0.0558263i
$481$	−42.7136	−	31.0332i	−1.94757	−	1.41499i
$482$	−6.23914	+	6.23914i	−0.284185	+	0.284185i
$483$	−0.0633484	+	0.334556i	−0.00288245	+	0.0152228i
$484$	−9.30791	−	3.02432i	−0.423087	−	0.137469i
$485$	2.77611	−	23.0458i	0.126057	−	1.04646i
$486$	2.54327	+	15.3796i	0.115365	+	0.697632i
$487$	3.22789	−	1.64469i	0.146270	−	0.0745281i	−0.379324	−	0.925264i	$-0.623843\pi$
$487$	3.22789	−	1.64469i	0.146270	−	0.0745281i	0.525593	+	0.850736i	$0.323843\pi$
$488$	−3.55588	+	1.81181i	−0.160967	+	0.0820169i
$489$	−2.65401	−	0.0797909i	−0.120019	−	0.00360827i
$490$	14.1885	+	6.57669i	0.640971	+	0.297105i
$491$	5.48953	+	1.78366i	0.247739	+	0.0804953i	0.430254	−	0.902708i	$-0.358424\pi$
$491$	5.48953	+	1.78366i	0.247739	+	0.0804953i	−0.182515	+	0.983203i	$0.558424\pi$
$492$	−6.35610	−	1.20353i	−0.286555	−	0.0542593i
$493$	15.5603	−	15.5603i	0.700800	−	0.700800i
$494$	5.78150	+	4.20051i	0.260122	+	0.188990i
$495$	4.47861	−	5.87628i	0.201298	−	0.264119i
$496$	−7.72991	+	5.61611i	−0.347083	+	0.252171i
$497$	−0.157315	+	0.993249i	−0.00705655	+	0.0445533i
$498$	1.04744	+	1.11237i	0.0469370	+	0.0498467i
$499$		−	28.5582i		−	1.27844i	−0.769024	−	0.639220i	$-0.779257\pi$
$499$		−	28.5582i		−	1.27844i	0.769024	−	0.639220i	$-0.220743\pi$
$500$	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	$-0.269532\pi$
$503$	23.7938	+	3.76856i	1.06091	+	0.168032i	0.398497	+	0.917170i	$0.369532\pi$
$504$	0.235666	+	0.0141831i	0.0104974	+	0.000631765i
$505$	31.3674	−	1.16730i	1.39583	−	0.0519444i
$506$	−1.61718	+	2.22586i	−0.0718926	+	0.0989517i
$507$	9.59451	+	20.3176i	0.426107	+	0.902335i
$508$	−3.18243	+	0.504047i	−0.141197	+	0.0223635i
$509$	1.35722	−	4.17708i	0.0601576	−	0.185146i	−0.916462	−	0.400123i	$-0.868968\pi$
$509$	1.35722	−	4.17708i	0.0601576	−	0.185146i	0.976619	+	0.214977i	$0.0689675\pi$
$510$	−8.66300	−	8.54014i	−0.383604	−	0.378164i
$511$	0.0322963	+	0.0993978i	0.00142870	+	0.00439710i
$512$	−0.453990	−	0.891007i	−0.0200637	−	0.0393773i
$513$	3.87906	−	6.16793i	0.171265	−	0.272321i
$514$	2.11472	−	0.687116i	0.0932765	−	0.0303074i
$515$	−29.3136	−	3.53113i	−1.29171	−	0.155600i
$516$	−1.50711	+	1.94843i	−0.0663470	+	0.0857747i
$517$	−2.18954	−	13.8242i	−0.0962960	−	0.607989i
$518$	0.576498	+	0.576498i	0.0253299	+	0.0253299i
$519$	−13.8269	−	20.2863i	−0.606934	−	0.890468i
$520$	7.03646	+	8.96386i	0.308569	+	0.393091i
$521$	−3.85216	−	5.30205i	−0.168766	−	0.232287i	0.716254	−	0.697840i	$-0.245855\pi$
$521$	−3.85216	−	5.30205i	−0.168766	−	0.232287i	−0.885020	+	0.465553i	$0.845855\pi$
$522$	13.9424	+	15.7281i	0.610244	+	0.688401i
$523$	7.96973	+	4.06078i	0.348492	+	0.177566i	0.619471	−	0.785020i	$-0.287347\pi$
$523$	7.96973	+	4.06078i	0.348492	+	0.177566i	−0.270979	+	0.962585i	$0.587347\pi$
$524$	−5.31824			−0.232328
$525$	−0.638212	+	0.239131i	−0.0278539	+	0.0104365i
$526$	−19.3769			−0.844875
$527$	−26.7397	−	13.6245i	−1.16480	−	0.593494i
$528$	1.67296	+	0.916756i	0.0728063	+	0.0398967i
$529$	9.85121	+	13.5590i	0.428314	+	0.589523i
$530$	−8.46029	+	12.6051i	−0.367492	+	0.547529i
$531$	19.1359	−	4.96881i	0.830427	−	0.215628i
$532$	−0.0780320	−	0.0780320i	−0.00338312	−	0.00338312i
$533$	2.97762	+	18.7999i	0.128975	+	0.814315i
$534$	−4.49231	−	3.47481i	−0.194401	−	0.150370i
$535$	31.8956	+	29.6069i	1.37897	+	1.28002i
$536$	6.33303	−	2.05773i	0.273545	−	0.0888803i
$537$	−3.33318	−	26.0992i	−0.143837	−	1.12626i
$538$	−2.49491	−	4.89653i	−0.107563	−	0.211105i
$539$	−2.38035	−	7.32596i	−0.102529	−	0.315551i
$540$	8.63930	−	7.76934i	0.371776	−	0.334339i
$541$	4.98127	−	15.3308i	0.214161	−	0.659121i	−0.785051	−	0.619432i	$-0.787363\pi$
$541$	4.98127	−	15.3308i	0.214161	−	0.659121i	0.999212	−	0.0396896i	$-0.0126369\pi$
$542$	7.35189	−	1.16442i	0.315791	−	0.0500163i
$543$	−16.0863	+	7.59639i	−0.690329	+	0.325992i
$544$	1.84619	−	2.54107i	0.0791548	−	0.108947i
$545$	−7.52457	+	26.4699i	−0.322317	+	1.13385i
$546$	−0.194715	−	0.666824i	−0.00833301	−	0.0285374i
$547$	−23.3625	−	3.70025i	−0.998907	−	0.158211i	−0.364494	−	0.931206i	$-0.618758\pi$
$547$	−23.3625	−	3.70025i	−0.998907	−	0.158211i	−0.634413	+	0.772994i	$0.718758\pi$
$548$	−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
$552$	−3.15000	+	2.96612i	−0.134073	+	0.126246i
$553$	−0.122601	+	0.774072i	−0.00521353	+	0.0329169i
$554$	−15.4488	+	11.2242i	−0.656355	+	0.476870i
$555$	40.1223	−	0.286540i	1.70310	−	0.0121629i
$556$	8.81992	+	6.40805i	0.374048	+	0.271762i
$557$	−27.5142	+	27.5142i	−1.16581	+	1.16581i	−0.182634	+	0.983181i	$0.558462\pi$
$557$	−27.5142	+	27.5142i	−1.16581	+	1.16581i	−0.983181	+	0.182634i	$0.941538\pi$
$558$	14.5240	−	24.7120i	0.614850	−	1.04614i
$559$	6.89314	+	2.23972i	0.291549	+	0.0947299i
$560$	−0.0856657	−	0.153714i	−0.00362004	−	0.00649560i
$561$	−0.180060	+	5.98918i	−0.00760215	+	0.252863i
$562$	−1.25504	+	0.639477i	−0.0529408	+	0.0269747i
$563$	22.1789	−	11.3007i	0.934728	−	0.476267i	0.0808412	−	0.996727i	$-0.474239\pi$
$563$	22.1789	−	11.3007i	0.934728	−	0.476267i	0.853886	+	0.520460i	$0.174239\pi$
$564$	0.661442	−	22.0009i	0.0278517	−	0.926406i
$565$	−8.31006	−	14.9111i	−0.349607	−	0.627315i
$566$	9.06857	+	2.94656i	0.381180	+	0.123853i
$567$	−0.665090	+	0.243544i	−0.0279311	+	0.0102279i
$568$	−9.03570	+	9.03570i	−0.379129	+	0.379129i
$569$	−25.9540	−	18.8567i	−1.08805	−	0.790515i	−0.108981	−	0.994044i	$-0.534759\pi$
$569$	−25.9540	−	18.8567i	−1.08805	−	0.790515i	−0.979069	+	0.203529i	$0.934759\pi$
$570$	−5.43076	+	0.0387846i	−0.227470	+	0.00162451i
$571$	−34.1170	+	24.7874i	−1.42775	+	1.03732i	−0.437322	+	0.899305i	$0.644073\pi$
$571$	−34.1170	+	24.7874i	−1.42775	+	1.03732i	−0.990430	+	0.138017i	$0.955927\pi$
$572$	0.878080	−	5.54398i	0.0367144	−	0.231805i
$573$	13.6968	−	12.8973i	0.572194	−	0.538793i
$574$		−	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	0.583052	+	0.812435i	$0.301859\pi$
$577$	−10.0150	+	19.6556i	−0.416931	+	0.818274i	−0.999983	+	0.00583873i	$0.998141\pi$
$578$	−7.04672	−	1.11609i	−0.293105	−	0.0464233i
$579$	9.42275	+	32.2694i	0.391596	+	1.34107i
$580$	4.28365	−	15.0690i	0.177869	−	0.625707i
$581$	−0.0408054	+	0.0561638i	−0.00169289	+	0.00233007i
$582$	−16.2586	+	7.67775i	−0.673940	+	0.318253i
$583$	7.38553	−	1.16975i	0.305877	−	0.0484462i
$584$	−0.410385	+	1.26303i	−0.0169818	+	0.0522647i
$585$	−30.0974	−	16.2145i	−1.24437	−	0.670387i
$586$	−9.62597	−	29.6257i	−0.397645	−	1.22383i
$587$	−5.85750	−	11.4960i	−0.241765	−	0.474490i	0.737958	−	0.674846i	$-0.235790\pi$
$587$	−5.85750	−	11.4960i	−0.241765	−	0.474490i	−0.979723	+	0.200356i	$0.935790\pi$
$588$	−1.53459	−	12.0160i	−0.0632855	−	0.495533i
$589$	−12.7423	+	4.14024i	−0.525039	+	0.170596i
$590$	−10.8002	−	10.0252i	−0.444639	−	0.412733i
$591$	16.7555	+	12.9604i	0.689230	+	0.533121i
$592$	1.62063	+	10.2323i	0.0666075	+	0.420543i
$593$	3.75033	+	3.75033i	0.154007	+	0.154007i	0.779905	−	0.625898i	$-0.215267\pi$
$593$	3.75033	+	3.75033i	0.154007	+	0.154007i	−0.625898	+	0.779905i	$0.715267\pi$
$594$	−5.69979	−	0.515322i	−0.233865	−	0.0211439i
$595$	0.308027	−	0.458932i	0.0126279	−	0.0188144i
$596$	−8.44527	−	11.6239i	−0.345932	−	0.476134i
$597$	−24.2053	−	13.2641i	−0.990656	−	0.542864i
$598$	11.3432	+	5.77963i	0.463856	+	0.236347i
$599$	29.8620			1.22013			0.610065	−	0.792352i	$-0.291143\pi$
$599$	29.8620			1.22013			0.610065	+	0.792352i	$0.291143\pi$
$600$	−8.34691	−	2.30847i	−0.340761	−	0.0942428i
$601$	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
$603$	−14.9488	+	13.2517i	−0.608764	+	0.539649i
$604$	−0.191874	−	0.264091i	−0.00780722	−	0.0107457i
$605$	−13.5127	−	17.2141i	−0.549371	−	0.699853i
$606$	−13.6938	−	20.0910i	−0.556273	−	0.816139i
$607$	29.8007	+	29.8007i	1.20957	+	1.20957i	0.971165	+	0.238406i	$0.0766250\pi$
$607$	29.8007	+	29.8007i	1.20957	+	1.20957i	0.238406	+	0.971165i	$0.423375\pi$
$608$	−0.219361	−	1.38499i	−0.00889625	−	0.0561687i
$609$	−0.584290	+	0.755382i	−0.0236766	+	0.0306096i
$610$	−8.85978	−	1.06725i	−0.358722	−	0.0432118i
$611$	−61.5942	+	20.0132i	−2.49184	+	0.809646i
$612$	−2.03048	+	9.20142i	−0.0820775	+	0.371945i
$613$	0.600877	+	1.17929i	0.0242692	+	0.0476310i	0.902823	−	0.430013i	$-0.141491\pi$
$613$	0.600877	+	1.17929i	0.0242692	+	0.0476310i	−0.878554	+	0.477644i	$0.841491\pi$
$614$	0.683714	+	2.10425i	0.0275924	+	0.0849208i
$615$	−10.3012	−	10.1551i	−0.415386	−	0.409495i
$616$	−0.0267848	+	0.0824351i	−0.00107919	+	0.00332141i
$617$	41.5066	−	6.57400i	1.67099	−	0.264659i	0.752067	−	0.659087i	$-0.229057\pi$
$617$	41.5066	−	6.57400i	1.67099	−	0.264659i	0.918927	+	0.394428i	$0.129057\pi$
$618$	9.76586	+	20.6804i	0.392841	+	0.831889i
$619$	−9.51877	+	13.1015i	−0.382592	+	0.526592i	−0.956269	−	0.292489i	$-0.905516\pi$
$619$	−9.51877	+	13.1015i	−0.382592	+	0.526592i	0.573677	+	0.819082i	$0.305516\pi$
$620$	−21.3502	+	0.794523i	−0.857443	+	0.0319088i
$621$	5.10635	−	11.9335i	0.204911	−	0.478875i
$622$	−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
$627$	1.83385	+	1.94753i	0.0732368	+	0.0777769i
$628$	0.768905	−	4.85468i	0.0306827	−	0.193723i
$629$	−26.3249	+	19.1262i	−1.04964	+	0.762611i
$630$	0.419874	+	0.320007i	0.0167282	+	0.0127494i
$631$	−9.33690	−	6.78365i	−0.371696	−	0.270053i	0.386218	−	0.922408i	$-0.373781\pi$
$631$	−9.33690	−	6.78365i	−0.371696	−	0.270053i	−0.757914	+	0.652355i	$0.773781\pi$
$632$	−7.04182	+	7.04182i	−0.280109	+	0.280109i
$633$	−18.8212	−	3.56380i	−0.748076	−	0.141648i
$634$	−8.64124	−	2.80771i	−0.343188	−	0.111508i
$635$	−6.53674	−	3.02993i	−0.259403	−	0.120239i
$636$	11.7539	+	0.353372i	0.466072	+	0.0140121i
$637$	−31.7579	+	16.1814i	−1.25829	+	0.641132i
$638$	−6.87543	+	3.50321i	−0.272201	+	0.138693i
$639$	14.0151	−	35.6815i	0.554428	−	1.41154i
$640$	0.267425	−	2.22002i	0.0105709	−	0.0877540i
$641$	15.5088	+	5.03912i	0.612561	+	0.199033i	0.598835	−	0.800873i	$-0.295631\pi$
$641$	15.5088	+	5.03912i	0.612561	+	0.199033i	0.0137264	+	0.999906i	$0.495631\pi$
$642$	6.27149	−	33.1211i	0.247516	−	1.30719i
$643$	−12.8296	+	12.8296i	−0.505952	+	0.505952i	−0.913281	−	0.407330i	$-0.866460\pi$
$643$	−12.8296	+	12.8296i	−0.505952	+	0.505952i	0.407330	+	0.913281i	$0.366460\pi$
$644$	−0.159043	−	0.115552i	−0.00626719	−	0.00455338i
$645$	−5.22619	+	1.73945i	−0.205781	+	0.0684909i
$646$	3.56321	−	2.58883i	0.140193	−	0.101856i
$647$	−3.97829	+	25.1179i	−0.156403	+	0.987488i	0.777220	+	0.629229i	$0.216629\pi$
$647$	−3.97829	+	25.1179i	−0.156403	+	0.987488i	−0.933622	+	0.358259i	$0.883371\pi$
$648$	−8.65618	−	2.46384i	−0.340047	−	0.0967889i
$649$			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	$-0.246942\pi$
$653$	30.0615	+	4.76127i	1.17640	+	0.186323i	0.462529	+	0.886604i	$0.346942\pi$
$654$	20.4614	−	5.97478i	0.800103	−	0.233633i
$655$	−9.87407	−	6.62730i	−0.385812	−	0.258950i
$656$	2.19532	−	3.02160i	0.0857129	−	0.117974i
$657$	−0.385730	−	3.96538i	−0.0150488	−	0.154704i
$658$	0.987775	−	0.156448i	0.0385075	−	0.00609899i
$659$	−3.19473	+	9.83236i	−0.124449	+	0.383014i	−0.993800	−	0.111180i	$-0.964537\pi$
$659$	−3.19473	+	9.83236i	−0.124449	+	0.383014i	0.869351	+	0.494195i	$0.164537\pi$
$660$	1.96368	+	3.78684i	0.0764362	+	0.147402i
$661$	3.97825	+	12.2438i	0.154736	+	0.476229i	0.998134	−	0.0610606i	$-0.0194483\pi$
$661$	3.97825	+	12.2438i	0.154736	+	0.476229i	−0.843398	+	0.537289i	$0.819448\pi$
$662$	5.01952	+	9.85137i	0.195089	+	0.382884i
$663$	27.5019	−	3.51232i	1.06809	−	0.136407i
$664$	−0.838964	+	0.272596i	−0.0325581	+	0.0105788i
$665$	−0.0476384	−	0.242117i	−0.00184734	−	0.00938888i
$666$	−16.7245	−	26.1958i	−0.648063	−	1.01507i
$667$	−2.73781	−	17.2859i	−0.106008	−	0.669311i
$668$	−15.8270	−	15.8270i	−0.612365	−	0.612365i
$669$	7.86218	−	5.35879i	0.303969	−	0.207183i
$670$	14.3224	+	4.07141i	0.553323	+	0.157292i
$671$	2.58363	+	3.55605i	0.0997397	+	0.137280i
$672$	−0.0655044	+	0.119537i	−0.00252689	+	0.00461124i
$673$	30.0291	+	15.3006i	1.15754	+	0.589794i	0.923939	−	0.382540i	$-0.124951\pi$
$673$	30.0291	+	15.3006i	1.15754	+	0.589794i	0.233596	+	0.972334i	$0.424951\pi$
$674$	17.3028			0.666479
$675$	25.7218	−	3.65907i	0.990033	−	0.140838i
$676$	−12.9725			−0.498943
$677$	−13.8891	−	7.07682i	−0.533800	−	0.271984i	0.166244	−	0.986085i	$-0.446836\pi$
$677$	−13.8891	−	7.07682i	−0.533800	−	0.271984i	−0.700044	+	0.714100i	$0.746836\pi$
$678$	−6.35430	+	11.5958i	−0.244035	+	0.445333i
$679$	−0.480192	−	0.660928i	−0.0184281	−	0.0253641i
$680$	6.59425	−	2.41723i	0.252878	−	0.0926965i
$681$	−9.67963	+	6.59754i	−0.370924	+	0.252818i
$682$	7.44126	+	7.44126i	0.284940	+	0.284940i
$683$	4.20549	+	26.5524i	0.160919	+	1.01600i	0.927492	+	0.373844i	$0.121960\pi$
$683$	4.20549	+	26.5524i	0.160919	+	1.01600i	−0.766573	+	0.642157i	$0.778040\pi$
$684$	2.26375	+	3.54573i	0.0865567	+	0.135575i
$685$	−22.4346	+	12.5029i	−0.857182	+	0.477713i
$686$	1.04738	−	0.340314i	0.0399891	−	0.0129932i
$687$	−5.21829	+	0.666439i	−0.199090	+	0.0254262i
$688$	−0.645655	−	1.26717i	−0.0246154	−	0.0483104i
$689$	−10.6919	−	32.9064i	−0.407330	−	1.25363i
$690$	−9.54463	+	1.58168i	−0.363358	+	0.0602133i
$691$	7.00128	−	21.5477i	0.266341	−	0.819714i	−0.725040	−	0.688707i	$-0.758179\pi$
$691$	7.00128	−	21.5477i	0.266341	−	0.819714i	0.991381	−	0.131007i	$-0.0418212\pi$
$692$	13.9996	−	2.21732i	0.532185	−	0.0842898i
$693$	−0.0251756	−	0.258811i	−0.000956343	−	0.00983141i
$694$	8.78938	−	12.0975i	0.333640	−	0.459217i
$695$	8.39009	+	22.8884i	0.318254	+	0.868205i
$696$	−11.6484	+	3.40137i	−0.441532	+	0.128929i
$697$	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	$0.746839\pi$
$702$	1.77065	+	26.4220i	0.0668288	+	0.997235i
$703$	−2.27253	+	14.3482i	−0.0857102	+	0.541153i
$704$	−0.891050	+	0.647386i	−0.0335827	+	0.0243993i
$705$	28.6444	−	40.0236i	1.07881	−	1.50738i
$706$	−16.2083	−	11.7760i	−0.610007	−	0.443196i
$707$	0.781162	−	0.781162i	0.0293786	−	0.0293786i
$708$	−2.12360	+	11.2152i	−0.0798099	+	0.421493i
$709$	37.7779	+	12.2748i	1.41878	+	0.460989i	0.915214	−	0.402968i	$-0.132022\pi$
$709$	37.7779	+	12.2748i	1.41878	+	0.460989i	0.503565	+	0.863958i	$0.332022\pi$
$710$	−28.0359	+	5.51628i	−1.05217	+	0.207022i
$711$	10.9224	−	27.8078i	0.409623	−	1.04287i
$712$	2.92160	−	1.48863i	0.109491	−	0.0557887i
$713$	−21.2664	+	10.8358i	−0.796433	+	0.405803i
$714$	−0.427941	−	0.0128657i	−0.0160153	−	0.000481488i
$715$	8.53888	−	9.19897i	0.319336	−	0.344022i
$716$	14.4473	+	4.69420i	0.539919	+	0.175430i
$717$	19.3509	+	3.66410i	0.722673	+	0.136838i
$718$	12.9715	−	12.9715i	0.484093	−	0.484093i
$719$	25.6075	+	18.6049i	0.954998	+	0.693847i	0.951984	−	0.306149i	$-0.0990405\pi$
$719$	25.6075	+	18.6049i	0.954998	+	0.693847i	0.00301445	+	0.999995i	$0.499040\pi$
$720$	1.92623	+	6.42570i	0.0717864	+	0.239472i
$721$	−0.840680	+	0.610790i	−0.0313086	+	0.0227470i
$722$	−2.66466	+	16.8240i	−0.0991682	+	0.626124i
$723$	10.4769	+	11.1264i	0.389640	+	0.413794i
$724$		−	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	−0.174934	+	0.984580i	$0.555971\pi$
$727$	−23.4214	+	45.9671i	−0.868652	+	1.70483i	−0.693719	+	0.720246i	$0.744029\pi$
$728$	0.396131	+	0.0627409i	0.0146816	+	0.00232533i
$729$	26.7586	−	3.60258i	0.991058	−	0.133429i
$730$	−2.33586	+	1.83361i	−0.0864541	+	0.0678648i
$731$	2.62561	−	3.61384i	0.0971117	−	0.133663i
$732$	2.95165	+	6.25049i	0.109096	+	0.231025i
$733$	−20.9008	+	3.31036i	−0.771988	+	0.122271i	−0.529988	−	0.848005i	$-0.677803\pi$
$733$	−20.9008	+	3.31036i	−0.771988	+	0.122271i	−0.242000	+	0.970276i	$0.577803\pi$
$734$	−0.00602247	+	0.0185352i	−0.000222293	+	0.000684148i
$735$	12.1245	−	24.2218i	0.447220	−	0.893435i
$736$	−0.771931	−	2.37576i	−0.0284538	−	0.0875717i
$737$	−3.32964	−	6.53478i	−0.122649	−	0.240712i
$738$	−2.41446	+	10.9415i	−0.0888776	+	0.402761i
$739$	11.8537	−	3.85150i	0.436046	−	0.141680i	−0.0827648	−	0.996569i	$-0.526375\pi$
$739$	11.8537	−	3.85150i	0.436046	−	0.141680i	0.518811	+	0.854889i	$0.326375\pi$
$740$	−9.74194	+	21.0172i	−0.358121	+	0.772607i
$741$	7.57313	−	9.79070i	0.278206	−	0.359670i
$742$	0.0835816	+	0.527714i	0.00306838	+	0.0193730i
$743$	2.30237	+	2.30237i	0.0844658	+	0.0844658i	0.748077	−	0.663612i	$-0.230977\pi$
$743$	2.30237	+	2.30237i	0.0844658	+	0.0844658i	−0.663612	+	0.748077i	$0.730977\pi$
$744$	9.32066	+	13.6749i	0.341712	+	0.501345i
$745$	−1.19477	−	32.1055i	−0.0437730	−	1.17625i
$746$	−4.11202	−	5.65971i	−0.150552	−	0.207217i
$747$	1.98034	−	1.75550i	0.0724567	−	0.0642305i
$748$	−3.08236	−	1.57054i	−0.112702	−	0.0574247i
$749$	1.53163			0.0559646
$750$	−12.6206	−	14.6875i	−0.460838	−	0.536310i
$751$	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
$753$	−22.1923	−	12.1610i	−0.808731	−	0.443172i
$754$	20.9870	+	28.8861i	0.764301	+	1.05197i
$755$	−0.0271448	−	0.729425i	−0.000987899	−	0.0265465i
$756$	0.0368210	−	0.407264i	0.00133917	−	0.0148120i
$757$	−7.02667	−	7.02667i	−0.255389	−	0.255389i	0.567787	−	0.823176i	$-0.307800\pi$
$757$	−7.02667	−	7.02667i	−0.255389	−	0.255389i	−0.823176	+	0.567787i	$0.807800\pi$
$758$	−1.90370	−	12.0195i	−0.0691453	−	0.436567i
$759$	3.76939	+	2.91564i	0.136820	+	0.105831i
$760$	1.31862	−	2.84478i	0.0478314	−	0.103191i
$761$	−48.1462	+	15.6436i	−1.74530	+	0.567081i	−0.995515	−	0.0946038i	$-0.969842\pi$
$761$	−48.1462	+	15.6436i	−1.74530	+	0.567081i	−0.749782	+	0.661685i	$0.769842\pi$
$762$	0.706997	+	5.53587i	0.0256118	+	0.200543i
$763$	0.439694	+	0.862948i	0.0159180	+	0.0312408i
$764$	3.35652	+	10.3303i	0.121435	+	0.373737i
$765$	−15.2362	+	14.5535i	−0.550865	+	0.526182i
$766$	−0.292865	+	0.901344i	−0.0105816	+	0.0325669i
$767$	33.1721	−	5.25394i	1.19777	−	0.189709i
$768$	−1.56620	+	0.739603i	−0.0565154	+	0.0266881i
$769$	21.2813	−	29.2912i	0.767422	−	1.05627i	−0.229138	−	0.973394i	$-0.573591\pi$
$769$	21.2813	−	29.2912i	0.767422	−	1.05627i	0.996560	−	0.0828721i	$-0.0264093\pi$
$770$	−0.152456	+	0.119675i	−0.00549413	+	0.00431278i
$771$	−1.07951	−	3.69692i	−0.0388777	−	0.133141i
$772$	−19.1698	−	3.03620i	−0.689936	−	0.109275i
$773$	10.6768	−	20.9544i	0.384019	−	0.753679i	−0.615384	−	0.788227i	$-0.710999\pi$
$773$	10.6768	−	20.9544i	0.384019	−	0.753679i	0.999403	+	0.0345481i	$0.0109992\pi$
$774$	3.29481	+	2.71063i	0.118429	+	0.0974317i
$775$	−40.6297	−	25.1303i	−1.45946	−	0.902705i
$776$		−	10.3809i		−	0.372653i
$777$	1.02808	−	0.968067i	0.0368822	−	0.0347292i
$778$	−3.10878	+	19.6281i	−0.111455	+	0.703701i
$779$	4.23704	−	3.07839i	0.151808	−	0.110295i
$780$	15.8851	−	11.7154i	0.568778	−	0.419480i
$781$	11.3862	+	8.27256i	0.407430	+	0.296015i
$782$	5.54804	−	5.54804i	0.198397	−	0.198397i
$783$	27.9553	−	23.3195i	0.999040	−	0.833370i
$784$	6.65151	+	2.16121i	0.237554	+	0.0771859i
$785$	7.47721	−	8.05523i	0.266873	−	0.287504i
$786$	−0.276811	+	9.20730i	−0.00987351	+	0.328414i
$787$	−28.0403	+	14.2872i	−0.999529	+	0.509285i	−0.875616	−	0.483008i	$-0.839544\pi$
$787$	−28.0403	+	14.2872i	−0.999529	+	0.509285i	−0.123913	+	0.992293i	$0.539544\pi$
$788$	−10.8970	+	5.55232i	−0.388191	+	0.197793i
$789$	−1.00856	+	33.5467i	−0.0359056	+	1.19429i
$790$	−21.8493	+	4.29902i	−0.777363	+	0.152952i
$791$	−0.571382	−	0.185653i	−0.0203160	−	0.00660107i
$792$	1.67423	−	2.84863i	0.0594910	−	0.101222i
$793$	14.3816	−	14.3816i	0.510707	−	0.510707i
$794$	21.8203	+	15.8534i	0.774375	+	0.562616i
$795$	21.3824	+	15.3031i	0.758356	+	0.542746i
$796$	12.8922	−	9.36672i	0.456952	−	0.331995i
$797$	−0.989635	+	6.24831i	−0.0350547	+	0.221326i	−0.998997	−	0.0447862i	$-0.985739\pi$
$797$	−0.989635	+	6.24831i	−0.0350547	+	0.221326i	0.963942	+	0.266113i	$0.0857393\pi$
$798$	−0.139156	+	0.131033i	−0.00492606	+	0.00463851i
$799$			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
$804$	−3.23285	−	11.0713i	−0.114014	−	0.390454i
$805$	−0.151293	−	0.412729i	−0.00533236	−	0.0145468i
$806$	28.6215	−	39.3941i	1.00815	−	1.38760i
$807$	−8.60707	+	4.06450i	−0.302983	+	0.143077i
$808$	13.8648	−	2.19597i	0.487763	−	0.0772540i
$809$	10.4456	−	32.1483i	0.367249	−	1.13028i	−0.581312	−	0.813681i	$-0.697461\pi$
$809$	10.4456	−	32.1483i	0.367249	−	1.13028i	0.948561	−	0.316595i	$-0.102539\pi$
$810$	−13.0011	−	15.3613i	−0.456813	−	0.539742i
$811$	−11.3720	−	34.9993i	−0.399324	−	1.22899i	−0.925543	−	0.378643i	$-0.876391\pi$
$811$	−11.3720	−	34.9993i	−0.399324	−	1.22899i	0.526219	−	0.850349i	$-0.323609\pi$
$812$	−0.250313	−	0.491266i	−0.00878425	−	0.0172401i
$813$	−1.63327	−	12.7887i	−0.0572813	−	0.448519i
$814$	10.8518	−	3.52597i	0.380356	−	0.123585i
$815$	2.99426	−	1.66872i	0.104884	−	0.0584528i
$816$	−4.30317	−	3.32851i	−0.150641	−	0.116521i
$817$	−0.311969	−	1.96970i	−0.0109144	−	0.0689110i
$818$	−11.2430	−	11.2430i	−0.393103	−	0.393103i
$819$	−1.16459	+	0.302395i	−0.0406939	+	0.0105666i
$820$	7.84128	−	2.87435i	0.273829	−	0.100376i
$821$	1.94467	+	2.67661i	0.0678695	+	0.0934144i	0.841602	−	0.540098i	$-0.181613\pi$
$821$	1.94467	+	2.67661i	0.0678695	+	0.0934144i	−0.773733	+	0.633512i	$0.781613\pi$
$822$	17.4465	+	9.56039i	0.608516	+	0.333457i
$823$	−31.6727	−	16.1380i	−1.10404	−	0.562537i	−0.195656	−	0.980673i	$-0.562684\pi$
$823$	−31.6727	−	16.1380i	−1.10404	−	0.562537i	−0.908385	+	0.418136i	$0.862684\pi$
$824$	−13.2042			−0.459990
$825$	−1.07309	+	9.47784i	−0.0373604	+	0.329976i
$826$	−0.518630			−0.0180454
$827$	7.96567	+	4.05871i	0.276993	+	0.141135i	0.586969	−	0.809609i	$-0.300321\pi$
$827$	7.96567	+	4.05871i	0.276993	+	0.141135i	−0.309976	+	0.950744i	$0.600321\pi$
$828$	4.97120	+	5.60787i	0.172761	+	0.194887i
$829$	−6.82593	−	9.39508i	−0.237074	−	0.326305i	0.673858	−	0.738861i	$-0.264636\pi$
$829$	−6.82593	−	9.39508i	−0.237074	−	0.326305i	−0.910932	+	0.412556i	$0.864636\pi$
$830$	−1.89735	−	0.539357i	−0.0658580	−	0.0187214i
$831$	18.6280	+	27.3302i	0.646198	+	0.948073i
$832$	3.60364	+	3.60364i	0.124934	+	0.124934i
$833$	3.43640	+	21.6966i	0.119064	+	0.751743i
$834$	11.5531	−	14.9361i	0.400052	−	0.517195i
$835$	−9.66236	−	49.1078i	−0.334380	−	1.69945i
$836$	−1.46885	+	0.477258i	−0.0508012	+	0.0165063i
$837$	−42.0271	−	26.4312i	−1.45267	−	0.913596i
$838$	12.4834	+	24.5000i	0.431231	+	0.846339i
$839$	1.99464	+	6.13888i	0.0688628	+	0.211938i	0.979566	−	0.201124i	$-0.0644594\pi$
$839$	1.99464	+	6.13888i	0.0688628	+	0.211938i	−0.910703	+	0.413062i	$0.864459\pi$
$840$	−0.270579	+	0.140310i	−0.00933585	+	0.00484115i
$841$	6.20662	−	19.1020i	0.214021	−	0.658690i
$842$	31.5598	−	4.99858i	1.08762	−	0.172262i
$843$	1.04178	+	2.20610i	0.0358809	+	0.0759822i
$844$	6.50062	−	8.94734i	0.223761	−	0.307980i
$845$	−24.0853	−	16.1656i	−0.828560	−	0.556115i
$846$	−38.0551	−	2.29027i	−1.30836	−	0.0787410i
$847$	−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
$852$	15.1729	+	16.1135i	0.519816	+	0.552040i
$853$	−4.13209	+	26.0890i	−0.141480	+	0.893271i	0.810194	+	0.586162i	$0.199362\pi$
$853$	−4.13209	+	26.0890i	−0.141480	+	0.893271i	−0.951674	+	0.307109i	$0.900638\pi$
$854$	−0.254089	+	0.184606i	−0.00869474	+	0.00631710i
$855$	−0.215521	+	9.40412i	−0.00737065	+	0.321614i
$856$	15.7453	+	11.4396i	0.538163	+	0.390998i
$857$	−21.7170	+	21.7170i	−0.741840	+	0.741840i	−0.972932	−	0.231092i	$-0.925770\pi$
$857$	−21.7170	+	21.7170i	−0.741840	+	0.741840i	0.231092	+	0.972932i	$0.425770\pi$
$858$	−9.55241	−	1.80875i	−0.326114	−	0.0617498i
$859$	−2.16755	−	0.704281i	−0.0739560	−	0.0240298i	0.271805	−	0.962352i	$-0.412379\pi$
$859$	−2.16755	−	0.704281i	−0.0739560	−	0.0240298i	−0.345761	+	0.938322i	$0.612379\pi$
$860$	0.380325	−	3.15726i	0.0129690	−	0.107662i
$861$	−0.508868	−	0.0152987i	−0.0173422	−	0.000521380i
$862$	7.71732	−	3.93217i	0.262853	−	0.133930i
$863$	−1.81350	+	0.924026i	−0.0617324	+	0.0314542i	−0.484584	−	0.874745i	$-0.661029\pi$
$863$	−1.81350	+	0.924026i	−0.0617324	+	0.0314542i	0.422852	+	0.906199i	$0.361029\pi$
$864$	3.42034	−	3.91169i	0.116362	−	0.133078i
$865$	28.7554	+	13.3288i	0.977712	+	0.453191i
$866$	10.2541	+	3.33175i	0.348448	+	0.113218i
$867$	−2.29903	+	12.1417i	−0.0780792	+	0.412353i
$868$	−0.531696	+	0.531696i	−0.0180469	+	0.0180469i
$869$	8.87365	+	6.44709i	0.301018	+	0.218702i
$870$	−25.8656	−	8.20048i	−0.876925	−	0.278022i
$871$	−27.4549	+	19.9472i	−0.930274	+	0.675884i
$872$	−1.92520	+	12.1552i	−0.0651953	+	0.411627i
$873$	12.4460	+	28.5476i	0.421233	+	0.966190i
$874$		−	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	−0.934617	−	0.355657i	$-0.884257\pi$
$877$	−2.88829	+	5.66858i	−0.0975305	+	0.191414i	0.837086	+	0.547071i	$0.184257\pi$
$878$	−33.8818	−	5.36634i	−1.14345	−	0.181105i
$879$	−51.7911	+	15.1231i	−1.74687	+	0.510091i
$880$	−2.46110	+	0.0915871i	−0.0829636	+	0.00308740i
$881$	3.61099	−	4.97010i	0.121657	−	0.167447i	−0.743844	−	0.668353i	$-0.767000\pi$
$881$	3.61099	−	4.97010i	0.121657	−	0.167447i	0.865502	+	0.500906i	$0.167000\pi$
$882$	−20.8829	+	2.03137i	−0.703162	+	0.0683996i
$883$	−39.1067	+	6.19390i	−1.31605	+	0.208441i	−0.774684	−	0.632348i	$-0.782091\pi$
$883$	−39.1067	+	6.19390i	−1.31605	+	0.208441i	−0.541362	+	0.840789i	$0.682091\pi$
$884$	−4.94649	+	15.2237i	−0.166369	+	0.512030i
$885$	−17.9185	+	18.1763i	−0.602325	+	0.610990i
$886$	2.00247	+	6.16296i	0.0672742	+	0.207049i
$887$	−21.9363	−	43.0525i	−0.736550	−	1.44556i	−0.889313	−	0.457299i	$-0.848817\pi$
$887$	−21.9363	−	43.0525i	−0.736550	−	1.44556i	0.152763	−	0.988263i	$-0.451183\pi$
$888$	17.7991	−	2.27316i	0.597300	−	0.0762824i
$889$	−0.241160	+	0.0783578i	−0.00808826	+	0.00262804i
$890$	7.27940	+	0.876881i	0.244006	+	0.0293931i
$891$	−1.18883	+	9.84104i	−0.0398273	+	0.329687i
$892$	0.859348	+	5.42571i	0.0287731	+	0.181666i
$893$	12.6005	+	12.6005i	0.421660	+	0.421660i
$894$	−20.5637	+	14.0160i	−0.687753	+	0.468766i
$895$	20.9737	+	26.7188i	0.701075	+	0.893112i
$896$	−0.0462573	−	0.0636677i	−0.00154535	−	0.00212699i
$897$	10.5965	−	19.3372i	0.353807	−	0.645652i
$898$	−20.2669	−	10.3265i	−0.676314	−	0.344599i
$899$	−66.9409			−2.23260
$900$	−4.43103	+	14.3306i	−0.147701	+	0.477687i
$901$	−21.3243			−0.710416
$902$	−3.66526	−	1.86754i	−0.122040	−	0.0621824i
$903$	−0.0931588	+	0.170003i	−0.00310013	+	0.00565734i
$904$	−4.48722	−	6.17613i	−0.149243	−	0.205415i
$905$	12.7990	−	19.0694i	0.425454	−	0.633888i
$906$	−0.467200	+	0.318439i	−0.0155217	+	0.0105794i
$907$	−24.7561	−	24.7561i	−0.822014	−	0.822014i	0.164383	−	0.986397i	$-0.447437\pi$
$907$	−24.7561	−	24.7561i	−0.822014	−	0.822014i	−0.986397	+	0.164383i	$0.947437\pi$
$908$	−1.05800	−	6.67994i	−0.0351109	−	0.221682i
$909$	−35.4956	+	22.6619i	−1.17731	+	0.751649i
$910$	0.657289	+	0.610124i	0.0217889	+	0.0202254i
$911$	−48.5335	+	15.7695i	−1.60799	+	0.522466i	−0.969065	−	0.246806i	$-0.920619\pi$
$911$	−48.5335	+	15.7695i	−1.60799	+	0.522466i	−0.638921	+	0.769272i	$0.720619\pi$
$912$	−2.40920	+	0.307684i	−0.0797767	+	0.0101884i
$913$	0.441091	+	0.865690i	0.0145980	+	0.0286502i
$914$	−2.74480	−	8.44762i	−0.0907898	−	0.279422i
$915$	−2.30885	+	15.2831i	−0.0763282	+	0.505244i
$916$	0.938563	−	2.88860i	0.0310110	−	0.0954420i
$917$	−0.413380	+	0.0654729i	−0.0136510	+	0.00216211i
$918$	15.8244	+	3.99424i	0.522284	+	0.131830i
$919$	6.34757	−	8.73668i	0.209387	−	0.288196i	−0.691387	−	0.722485i	$-0.743000\pi$
$919$	6.34757	−	8.73668i	0.209387	−	0.288196i	0.900774	+	0.434288i	$0.143000\pi$
$920$	1.52734	−	5.37288i	0.0503549	−	0.177139i
$921$	3.67862	−	1.07417i	0.121215	−	0.0353950i
$922$	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
$927$	36.3117	−	15.8309i	1.19263	−	0.519956i
$928$	1.09599	−	6.91981i	0.0359777	−	0.227154i
$929$	38.0194	−	27.6227i	1.24738	−	0.906272i	0.249310	−	0.968424i	$-0.419796\pi$
$929$	38.0194	−	27.6227i	1.24738	−	0.906272i	0.998067	+	0.0621513i	$0.0197961\pi$
$930$	0.264271	+	37.0042i	0.00866580	+	1.21342i
$931$	7.93409	+	5.76446i	0.260029	+	0.188922i
$932$	−0.977696	+	0.977696i	−0.0320255	+	0.0320255i
$933$	−4.39263	+	23.1984i	−0.143808	+	0.759482i
$934$	12.8115	+	4.16270i	0.419204	+	0.136208i
$935$	−3.76572	−	6.75700i	−0.123152	−	0.220978i
$936$	−14.2306	−	5.58954i	−0.465141	−	0.182700i
$937$	40.7667	−	20.7717i	1.33179	−	0.678581i	0.364250	−	0.931301i	$-0.381325\pi$
$937$	40.7667	−	20.7717i	1.33179	−	0.678581i	0.967539	+	0.252721i	$0.0813253\pi$
$938$	0.466926	−	0.237911i	0.0152457	−	0.00776806i
$939$	−33.0642	−	0.994051i	−1.07901	−	0.0324396i
$940$	13.8332	+	24.8215i	0.451189	+	0.809588i
$941$	29.1364	+	9.46699i	0.949820	+	0.308615i	0.742642	−	0.669688i	$-0.233572\pi$
$941$	29.1364	+	9.46699i	0.949820	+	0.308615i	0.207177	+	0.978303i	$0.433572\pi$
$942$	−8.36473	−	1.58386i	−0.272537	−	0.0516051i
$943$	6.59721	−	6.59721i	0.214835	−	0.214835i
$944$	−5.33155	−	3.87360i	−0.173527	−	0.126075i
$945$	0.575873	−	0.710259i	0.0187331	−	0.0231047i
$946$	−1.26723	+	0.920697i	−0.0412012	+	0.0299344i
$947$	−2.25687	+	14.2493i	−0.0733384	+	0.463040i	0.923501	+	0.383596i	$0.125315\pi$
$947$	−2.25687	+	14.2493i	−0.0733384	+	0.463040i	−0.996839	+	0.0794442i	$0.974685\pi$
$948$	11.8248	+	12.5578i	0.384051	+	0.407859i
$949$		−	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	$-0.470334\pi$
$953$	−3.89283	−	0.616563i	−0.126101	−	0.0199724i	−0.219166	+	0.975688i	$0.570334\pi$
$954$	1.22356	−	20.3307i	0.0396143	−	0.658232i
$955$	−6.64120	+	23.3624i	−0.214904	+	0.755990i
$956$	−6.68358	+	9.19915i	−0.216162	+	0.297522i
$957$	5.70713	+	12.0856i	0.184485	+	0.390671i
$958$	−17.0684	+	2.70337i	−0.551455	+	0.0873420i
$959$	−0.279326	+	0.859676i	−0.00901989	+	0.0277604i
$960$	−3.82953	−	0.578534i	−0.123598	−	0.0186721i
$961$	18.6313	+	57.3413i	0.601010	+	1.84972i
$962$	−23.9693	−	47.0424i	−0.772801	−	1.51671i
$963$	−57.0151	−	12.5816i	−1.83729	−	0.405435i
$964$	−8.39163	+	2.72661i	−0.270276	+	0.0878181i
$965$	−31.8079	−	29.5255i	−1.02393	−	0.950459i
$966$	−0.208329	+	0.269332i	−0.00670288	+	0.00866563i
$967$	−8.16627	−	51.5598i	−0.262610	−	1.65805i	−0.668189	−	0.743992i	$-0.732930\pi$
$967$	−8.16627	−	51.5598i	−0.262610	−	1.65805i	0.405579	−	0.914060i	$-0.367070\pi$
$968$	−6.92040	−	6.92040i	−0.222430	−	0.222430i
$969$	−4.29649	−	6.30363i	−0.138023	−	0.202502i
$970$	12.9361	−	19.2736i	0.415353	−	0.618839i
$971$	−2.69176	−	3.70489i	−0.0863828	−	0.118896i	0.763638	−	0.645644i	$-0.223411\pi$
$971$	−2.69176	−	3.70489i	−0.0863828	−	0.118896i	−0.850021	+	0.526748i	$0.823411\pi$
$972$	−4.71612	+	14.8579i	−0.151270	+	0.476568i
$973$	0.764451	+	0.389507i	0.0245072	+	0.0124870i
$974$	3.62274			0.116080
$975$	44.0921	−	1.95625i	1.41208	−	0.0626501i
$976$	−3.99086			−0.127744
$977$	−3.68285	−	1.87651i	−0.117825	−	0.0600348i	0.394085	−	0.919074i	$-0.371062\pi$
$977$	−3.68285	−	1.87651i	−0.117825	−	0.0600348i	−0.511910	+	0.859039i	$0.671062\pi$
$978$	−2.32852	−	1.27599i	−0.0744578	−	0.0408017i
$979$	−2.12277	−	2.92174i	−0.0678439	−	0.0933792i
$980$	9.65630	+	12.3013i	0.308459	+	0.392951i
$981$	−9.27896	−	35.7351i	−0.296254	−	1.14093i
$982$	4.08144	+	4.08144i	0.130244	+	0.130244i
$983$	−4.05781	−	25.6200i	−0.129424	−	0.817151i	−0.963931	−	0.266153i	$-0.914247\pi$
$983$	−4.05781	−	25.6200i	−0.129424	−	0.817151i	0.834507	−	0.550998i	$-0.185753\pi$
$984$	−5.11694	−	3.95796i	−0.163122	−	0.126175i
$985$	−27.1509	−	3.27061i	−0.865099	−	0.104210i
$986$	20.9285	−	6.80010i	0.666501	−	0.216559i
$987$	−0.219441	−	1.71825i	−0.00698488	−	0.0546924i
$988$	3.24437	+	6.36743i	0.103217	+	0.202575i
$989$	−1.09782	−	3.37875i	−0.0349087	−	0.107438i
$990$	6.65824	−	3.20256i	0.211613	−	0.101784i
$991$	−7.36863	+	22.6783i	−0.234072	+	0.720400i	0.763171	+	0.646197i	$0.223641\pi$
$991$	−7.36863	+	22.6783i	−0.234072	+	0.720400i	−0.997243	+	0.0742035i	$0.976359\pi$
$992$	−9.43706	+	1.49468i	−0.299627	+	0.0474562i
$993$	17.3166	−	8.17738i	0.549526	−	0.259501i
$994$	−0.591094	+	0.813572i	−0.0187484	+	0.0258049i
$995$	35.6085	−	1.32513i	1.12887	−	0.0420095i
$996$	0.428269	+	1.46666i	0.0135702	+	0.0464729i
$997$	15.5032	+	2.45546i	0.490990	+	0.0777652i	0.397020	−	0.917810i	$-0.370044\pi$
$997$	15.5032	+	2.45546i	0.490990	+	0.0777652i	0.0939699	+	0.995575i	$0.470044\pi$
$998$	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.17.9	yes	80
3.2	odd	2	inner	150.2.l.a.17.3	✓	80
5.2	odd	4		750.2.l.a.143.1		80
5.3	odd	4		750.2.l.c.143.10		80
5.4	even	2		750.2.l.b.107.2		80
15.2	even	4		750.2.l.a.143.6		80
15.8	even	4		750.2.l.c.143.5		80
15.14	odd	2		750.2.l.b.107.8		80
25.3	odd	20	inner	150.2.l.a.53.3	yes	80
25.4	even	10		750.2.l.a.257.6		80
25.21	even	5		750.2.l.c.257.5		80
25.22	odd	20		750.2.l.b.743.8		80
75.29	odd	10		750.2.l.a.257.1		80
75.47	even	20		750.2.l.b.743.2		80
75.53	even	20	inner	150.2.l.a.53.9	yes	80
75.71	odd	10		750.2.l.c.257.10		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.17.3	✓	80	3.2	odd	2	inner
150.2.l.a.17.9	yes	80	1.1	even	1	trivial
150.2.l.a.53.3	yes	80	25.3	odd	20	inner
150.2.l.a.53.9	yes	80	75.53	even	20	inner
750.2.l.a.143.1		80	5.2	odd	4
750.2.l.a.143.6		80	15.2	even	4
750.2.l.a.257.1		80	75.29	odd	10
750.2.l.a.257.6		80	25.4	even	10
750.2.l.b.107.2		80	5.4	even	2
750.2.l.b.107.8		80	15.14	odd	2
750.2.l.b.743.2		80	75.47	even	20
750.2.l.b.743.8		80	25.22	odd	20
750.2.l.c.143.5		80	15.8	even	4
750.2.l.c.143.10		80	5.3	odd	4
750.2.l.c.257.5		80	25.21	even	5
750.2.l.c.257.10		80	75.71	odd	10

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)

\(f(q)\)	\(=\)	\(q+(0.891007 + 0.453990i) q^{2} +(0.832356 - 1.51894i) q^{3} +(0.587785 + 0.809017i) q^{4} +(0.0831552 + 2.23452i) q^{5} +(1.43122 - 0.975505i) q^{6} +(0.0556476 + 0.0556476i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-1.61437 - 2.52860i) q^{9} +O(q^{10})\)	\(q+(0.891007 + 0.453990i) q^{2} +(0.832356 - 1.51894i) q^{3} +(0.587785 + 0.809017i) q^{4} +(0.0831552 + 2.23452i) q^{5} +(1.43122 - 0.975505i) q^{6} +(0.0556476 + 0.0556476i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-1.61437 - 2.52860i) q^{9} +(-0.940360 + 2.02872i) q^{10} +(1.04749 - 0.340351i) q^{11} +(1.71810 - 0.219422i) q^{12} +(-2.31368 - 4.54086i) q^{13} +(0.0243189 + 0.0748459i) q^{14} +(3.46332 + 1.73361i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-3.10226 + 0.491350i) q^{17} +(-0.290452 - 2.98591i) q^{18} +(-0.824223 + 1.13445i) q^{19} +(-1.75889 + 1.38069i) q^{20} +(0.130844 - 0.0382069i) 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} +(-5.18452 + 0.347436i) q^{27} +(-0.0123110 + 0.0777287i) q^{28} +(-5.66803 + 4.11807i) q^{29} +(2.29880 + 3.11697i) q^{30} +(7.72991 + 5.61611i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.354913 - 1.87437i) q^{33} +(-2.98720 - 0.970601i) q^{34} +(-0.119718 + 0.128973i) q^{35} +(1.09678 - 2.79232i) q^{36} +(9.23065 - 4.70325i) q^{37} +(-1.24942 + 0.636609i) q^{38} +(-8.82310 - 0.265260i) q^{39} +(-2.19400 + 0.431688i) q^{40} +(-3.55210 - 1.15415i) q^{41} +(0.133928 + 0.0253594i) q^{42} +(-1.00563 + 1.00563i) q^{43} +(0.891050 + 0.647386i) q^{44} +(5.51597 - 3.81761i) q^{45} +(-2.02094 + 1.46830i) q^{46} +(1.98797 - 12.5515i) q^{47} +(1.18739 + 1.26100i) 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} +(-4.77718 - 2.04416i) q^{54} +(0.847626 + 2.31234i) q^{55} +(-0.0462573 + 0.0636677i) q^{56} +(1.03711 + 2.19621i) q^{57} +(-6.91981 + 1.09599i) q^{58} +(-2.03647 + 6.26761i) q^{59} +(0.633171 + 3.82088i) q^{60} +(1.23324 + 3.79553i) q^{61} +(4.33774 + 8.51329i) q^{62} +(0.0508748 - 0.230546i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(9.95425 - 5.54757i) q^{65} +(1.16718 - 1.50895i) q^{66} +(-1.04169 - 6.57696i) q^{67} +(-2.22097 - 2.22097i) q^{68} +(2.43683 + 3.57522i) q^{69} +(-0.165222 + 0.0605649i) q^{70} +(7.51096 + 10.3379i) q^{71} +(2.24493 - 1.99005i) q^{72} +(1.18329 + 0.602914i) q^{73} +10.3598 q^{74} +(-3.58579 + 7.88303i) q^{75} -1.40225 q^{76} +(0.0772302 + 0.0393507i) q^{77} +(-7.74102 - 4.24195i) q^{78} +(5.85354 + 8.05671i) q^{79} +(-2.15085 - 0.611420i) q^{80} +(-3.78763 + 8.16418i) q^{81} +(-2.64098 - 2.64098i) q^{82} +(0.137997 + 0.871279i) q^{83} +(0.107818 + 0.0833977i) q^{84} +(-1.35590 - 6.89121i) q^{85} +(-1.35257 + 0.439477i) q^{86} +(1.53728 + 12.0371i) q^{87} +(0.500025 + 0.981353i) q^{88} +(-1.01326 - 3.11850i) q^{89} +(6.64792 - 0.897315i) q^{90} +(0.123937 - 0.381439i) q^{91} +(-2.46727 + 0.390777i) q^{92} +(14.9646 - 7.06668i) q^{93} +(7.46957 - 10.2810i) q^{94} +(-2.60348 - 1.74741i) q^{95} +(0.485490 + 1.66262i) 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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