LMFDB - Embedded newform 483.2.bc.a.11.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [483,2,Mod(11,483)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("483.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(483, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([33, 44, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.bc (of order $66$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$1200$
Relative dimension:	$60$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			11.19
Character	$\chi$	$=$	483.11
Dual form			483.2.bc.a.44.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.528482 + 1.02511i) q^{2} +(-1.73132 - 0.0502508i) q^{3} +(0.388554 + 0.545647i) q^{4} +(-0.207815 - 0.198151i) q^{5} +(0.966484 - 1.74824i) q^{6} +(2.41072 + 1.09014i) q^{7} +(-3.04785 + 0.438215i) q^{8} +(2.99495 + 0.174001i) q^{9} +(0.312954 - 0.108314i) q^{10} +(-3.93951 + 2.03096i) q^{11} +(-0.645292 - 0.964216i) q^{12} +(0.275755 - 0.318239i) q^{13} +(-2.39154 + 1.89514i) q^{14} +(0.349838 + 0.353506i) q^{15} +(0.723339 - 2.08995i) q^{16} +(4.65656 + 0.444647i) q^{17} +(-1.76115 + 2.97820i) q^{18} +(0.576168 + 6.03390i) q^{19} +(0.0273734 - 0.190386i) q^{20} +(-4.11896 - 2.00853i) q^{21} -5.11176i q^{22} +(-2.66522 + 3.98705i) q^{23} +(5.29883 - 0.605534i) q^{24} +(-0.233986 - 4.91198i) q^{25} +(0.180498 + 0.450863i) q^{26} +(-5.17648 - 0.451749i) q^{27} +(0.341861 + 1.73898i) q^{28} +(-4.08752 + 1.86671i) q^{29} +(-0.547266 + 0.171801i) q^{30} +(-6.03274 - 2.41514i) q^{31} +(-2.48961 - 2.61103i) q^{32} +(6.92261 - 3.31828i) q^{33} +(-2.91672 + 4.53850i) q^{34} +(-0.284971 - 0.704236i) q^{35} +(1.06876 + 1.70179i) q^{36} +(-10.2958 + 2.49774i) q^{37} +(-6.48992 - 2.59817i) q^{38} +(-0.493413 + 0.537117i) q^{39} +(0.720223 + 0.512868i) q^{40} +(0.411214 + 1.40047i) q^{41} +(4.23576 - 3.16092i) q^{42} +(-8.01887 - 1.15294i) q^{43} +(-2.63890 - 1.36045i) q^{44} +(-0.587917 - 0.629613i) q^{45} +(-2.67865 - 4.83923i) q^{46} +(5.95056 - 3.43556i) q^{47} +(-1.35735 + 3.58203i) q^{48} +(4.62317 + 5.25607i) q^{49} +(5.15898 + 2.35603i) q^{50} +(-8.03965 - 1.00382i) q^{51} +(0.280792 + 0.0268124i) q^{52} +(0.505182 - 0.0973658i) q^{53} +(3.19877 - 5.06772i) q^{54} +(1.22113 + 0.358555i) q^{55} +(-7.82525 - 2.26618i) q^{56} +(-0.694324 - 10.4756i) q^{57} +(0.246596 - 5.17669i) q^{58} +(-2.17773 + 0.753720i) q^{59} +(-0.0569592 + 0.328244i) q^{60} +(4.17019 + 5.30282i) q^{61} +(5.66398 - 4.90787i) q^{62} +(7.03031 + 3.68439i) q^{63} +(8.23632 - 2.41840i) q^{64} +(-0.120366 + 0.0114935i) q^{65} +(-0.256870 + 8.85010i) q^{66} +(13.3572 - 0.636282i) q^{67} +(1.56670 + 2.71361i) q^{68} +(4.81471 - 6.76894i) q^{69} +(0.872522 + 0.0800487i) q^{70} +(1.29888 + 2.02110i) q^{71} +(-9.20442 + 0.782104i) q^{72} +(1.75016 + 2.45776i) q^{73} +(2.88070 - 11.8744i) q^{74} +(0.158275 + 8.51597i) q^{75} +(-3.06851 + 2.65888i) q^{76} +(-11.7111 + 0.601445i) q^{77} +(-0.289845 - 0.789659i) q^{78} +(-3.09556 + 16.0613i) q^{79} +(-0.564447 + 0.290993i) q^{80} +(8.93945 + 1.04225i) q^{81} +(-1.65295 - 0.318581i) q^{82} +(14.6256 + 4.29447i) q^{83} +(-0.504486 - 3.02792i) q^{84} +(-0.879595 - 1.01511i) q^{85} +(5.41971 - 7.61092i) q^{86} +(7.17062 - 3.02647i) q^{87} +(11.1170 - 7.91641i) q^{88} +(-8.71958 + 3.49080i) q^{89} +(0.956127 - 0.269942i) q^{90} +(1.01170 - 0.466572i) q^{91} +(-3.21111 + 0.0949141i) q^{92} +(10.3232 + 4.48454i) q^{93} +(0.377067 + 7.91561i) q^{94} +(1.07589 - 1.36810i) q^{95} +(4.17912 + 4.64564i) q^{96} +(-1.66982 - 5.68689i) q^{97} +(-7.83132 + 1.96153i) q^{98} +(-12.1520 + 5.39714i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1200 q - 9 q^{3} - 74 q^{4} - 20 q^{6} - 44 q^{7} - 13 q^{9} - 22 q^{10} - 25 q^{12} - 72 q^{13} - 44 q^{15} + 38 q^{16} - 45 q^{18} - 22 q^{19} + 44 q^{21} + 2 q^{24} + 18 q^{25} - 90 q^{27} - 44 q^{28}+ \cdots - 308 q^{99}+O(q^{100}) $ 1200 * q - 9 * q^3 - 74 * q^4 - 20 * q^6 - 44 * q^7 - 13 * q^9 - 22 * q^10 - 25 * q^12 - 72 * q^13 - 44 * q^15 + 38 * q^16 - 45 * q^18 - 22 * q^19 + 44 * q^21 + 2 * q^24 + 18 * q^25 - 90 * q^27 - 44 * q^28 - 55 * q^30 - 18 * q^31 - 11 * q^33 - 88 * q^34 - 108 * q^36 - 66 * q^37 + q^39 - 22 * q^40 - 22 * q^42 - 2 * q^46 - 228 * q^48 - 128 * q^49 - 11 * q^51 - 166 * q^52 + 35 * q^54 - 160 * q^55 - 44 * q^57 - 126 * q^58 - 11 * q^60 + 66 * q^61 + 33 * q^63 + 40 * q^64 + 22 * q^66 - 22 * q^67 - 24 * q^69 + 68 * q^70 - 149 * q^72 - 42 * q^73 + 123 * q^75 - 88 * q^76 - 108 * q^78 - 66 * q^79 - 81 * q^81 - 14 * q^82 + 44 * q^84 - 200 * q^85 + 75 * q^87 + 66 * q^88 + 16 * q^93 - 146 * q^94 + 5 * q^96 - 88 * q^97 - 308 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−0.528482	+	1.02511i	−0.373693	+	0.724863i	−0.998432	−	0.0559701i	$-0.982175\pi$
$2$	−0.528482	+	1.02511i	−0.373693	+	0.724863i	0.624740	+	0.780833i	$0.285205\pi$
$3$	−1.73132	−	0.0502508i	−0.999579	−	0.0290123i
$3$	−1.73132	−	0.0502508i	−0.999579	−	0.0290123i
$4$	0.388554	+	0.545647i	0.194277	+	0.272824i
$5$	−0.207815	−	0.198151i	−0.0929377	−	0.0886159i	0.642186	−	0.766549i	$-0.278028\pi$
$5$	−0.207815	−	0.198151i	−0.0929377	−	0.0886159i	−0.735124	+	0.677933i	$0.762876\pi$
$6$	0.966484	−	1.74824i	0.394566	−	0.713716i
$7$	2.41072	+	1.09014i	0.911168	+	0.412036i
$7$	2.41072	+	1.09014i	0.911168	+	0.412036i
$8$	−3.04785	+	0.438215i	−1.07758	+	0.154932i
$9$	2.99495	+	0.174001i	0.998317	+	0.0580002i
$10$	0.312954	−	0.108314i	0.0989646	−	0.0342520i
$11$	−3.93951	+	2.03096i	−1.18781	+	0.612357i	−0.934823	−	0.355114i	$-0.884442\pi$
$11$	−3.93951	+	2.03096i	−1.18781	+	0.612357i	−0.252984	+	0.967471i	$0.581412\pi$
$12$	−0.645292	−	0.964216i	−0.186280	−	0.278345i
$13$	0.275755	−	0.318239i	0.0764808	−	0.0882635i	−0.716220	−	0.697875i	$-0.754129\pi$
$13$	0.275755	−	0.318239i	0.0764808	−	0.0882635i	0.792700	+	0.609612i	$0.208675\pi$
$14$	−2.39154	+	1.89514i	−0.639166	+	0.506497i
$15$	0.349838	+	0.353506i	0.0903277	+	0.0912750i
$16$	0.723339	−	2.08995i	0.180835	−	0.522488i
$17$	4.65656	+	0.444647i	1.12938	+	0.107843i	0.642973	−	0.765889i	$-0.277701\pi$
$17$	4.65656	+	0.444647i	1.12938	+	0.107843i	0.486408	+	0.873732i	$0.338307\pi$
$18$	−1.76115	+	2.97820i	−0.415106	+	0.701969i
$19$	0.576168	+	6.03390i	0.132182	+	1.38427i	0.781571	+	0.623816i	$0.214419\pi$
$19$	0.576168	+	6.03390i	0.132182	+	1.38427i	−0.649389	+	0.760456i	$0.724975\pi$
$20$	0.0273734	−	0.190386i	0.00612088	−	0.0425716i
$21$	−4.11896	−	2.00853i	−0.898830	−	0.438297i
$22$		−	5.11176i		−	1.08983i
$23$	−2.66522	+	3.98705i	−0.555737	+	0.831358i
$23$	−2.66522	+	3.98705i	−0.555737	+	0.831358i
$24$	5.29883	−	0.605534i	1.08162	−	0.123604i
$25$	−0.233986	−	4.91198i	−0.0467973	−	0.982396i
$26$	0.180498	+	0.450863i	0.0353986	+	0.0884215i
$27$	−5.17648	−	0.451749i	−0.996214	−	0.0869392i
$28$	0.341861	+	1.73898i	0.0646057	+	0.328637i
$29$	−4.08752	+	1.86671i	−0.759034	+	0.346639i	−0.757048	−	0.653359i	$-0.773359\pi$
$29$	−4.08752	+	1.86671i	−0.759034	+	0.346639i	−0.00198556	+	0.999998i	$0.500632\pi$
$30$	−0.547266	+	0.171801i	−0.0999167	+	0.0313664i
$31$	−6.03274	−	2.41514i	−1.08351	−	0.433772i	−0.239939	−	0.970788i	$-0.577127\pi$
$31$	−6.03274	−	2.41514i	−1.08351	−	0.433772i	−0.843572	+	0.537015i	$0.819552\pi$
$32$	−2.48961	−	2.61103i	−0.440106	−	0.461570i
$33$	6.92261	−	3.31828i	1.20507	−	0.577638i
$34$	−2.91672	+	4.53850i	−0.500213	+	0.778346i
$35$	−0.284971	−	0.704236i	−0.0481689	−	0.119038i
$36$	1.06876	+	1.70179i	0.178126	+	0.283632i
$37$	−10.2958	+	2.49774i	−1.69263	+	0.410627i	−0.962195	−	0.272360i	$-0.912196\pi$
$37$	−10.2958	+	2.49774i	−1.69263	+	0.410627i	−0.730431	+	0.682987i	$0.760681\pi$
$38$	−6.48992	−	2.59817i	−1.05280	−	0.421479i
$39$	−0.493413	+	0.537117i	−0.0790093	+	0.0860075i
$40$	0.720223	+	0.512868i	0.113877	+	0.0810916i
$41$	0.411214	+	1.40047i	0.0642209	+	0.218716i	0.985351	−	0.170539i	$-0.0545507\pi$
$41$	0.411214	+	1.40047i	0.0642209	+	0.218716i	−0.921130	+	0.389255i	$0.872733\pi$
$42$	4.23576	−	3.16092i	0.653592	−	0.487740i
$43$	−8.01887	−	1.15294i	−1.22287	−	0.175822i	−0.499517	−	0.866304i	$-0.666489\pi$
$43$	−8.01887	−	1.15294i	−1.22287	−	0.175822i	−0.723349	+	0.690483i	$0.757398\pi$
$44$	−2.63890	−	1.36045i	−0.397829	−	0.205095i
$45$	−0.587917	−	0.629613i	−0.0876415	−	0.0938572i
$46$	−2.67865	−	4.83923i	−0.394946	−	0.713506i
$47$	5.95056	−	3.43556i	0.867978	−	0.501127i	0.00130232	−	0.999999i	$-0.499585\pi$
$47$	5.95056	−	3.43556i	0.867978	−	0.501127i	0.866676	+	0.498872i	$0.166252\pi$
$48$	−1.35735	+	3.58203i	−0.195917	+	0.517021i
$49$	4.62317	+	5.25607i	0.660453	+	0.750867i
$50$	5.15898	+	2.35603i	0.729590	+	0.333193i
$51$	−8.03965	−	1.00382i	−1.12578	−	0.140563i
$52$	0.280792	+	0.0268124i	0.0389388	+	0.00371821i
$53$	0.505182	−	0.0973658i	0.0693920	−	0.0133742i	−0.154437	−	0.988003i	$-0.549356\pi$
$53$	0.505182	−	0.0973658i	0.0693920	−	0.0133742i	0.223829	+	0.974628i	$0.428144\pi$
$54$	3.19877	−	5.06772i	0.435297	−	0.689630i
$55$	1.22113	+	0.358555i	0.164657	+	0.0483476i
$56$	−7.82525	−	2.26618i	−1.04569	−	0.302832i
$57$	−0.694324	−	10.4756i	−0.0919654	−	1.38752i
$58$	0.246596	−	5.17669i	0.0323796	−	0.679732i
$59$	−2.17773	+	0.753720i	−0.283517	+	0.0981260i	−0.465125	−	0.885245i	$-0.653991\pi$
$59$	−2.17773	+	0.753720i	−0.283517	+	0.0981260i	0.181609	+	0.983371i	$0.441870\pi$
$60$	−0.0569592	+	0.328244i	−0.00735340	+	0.0423761i
$61$	4.17019	+	5.30282i	0.533938	+	0.678957i	0.975936	−	0.218059i	$-0.0699725\pi$
$61$	4.17019	+	5.30282i	0.533938	+	0.678957i	−0.441998	+	0.897016i	$0.645730\pi$
$62$	5.66398	−	4.90787i	0.719326	−	0.623300i
$63$	7.03031	+	3.68439i	0.885736	+	0.464190i
$64$	8.23632	−	2.41840i	1.02954	−	0.302300i
$65$	−0.120366	+	0.0114935i	−0.0149295	+	0.00142559i
$66$	−0.256870	+	8.85010i	−0.0316185	+	1.08937i
$67$	13.3572	−	0.636282i	1.63184	−	0.0777342i	0.788473	−	0.615069i	$-0.210872\pi$
$67$	13.3572	−	0.636282i	1.63184	−	0.0777342i	0.843369	+	0.537335i	$0.180569\pi$
$68$	1.56670	+	2.71361i	0.189990	+	0.329073i
$69$	4.81471	−	6.76894i	0.579623	−	0.814885i
$70$	0.872522	+	0.0800487i	0.104286	+	0.00956765i
$71$	1.29888	+	2.02110i	0.154149	+	0.239861i	0.909735	−	0.415188i	$-0.136284\pi$
$71$	1.29888	+	2.02110i	0.154149	+	0.239861i	−0.755586	+	0.655049i	$0.772648\pi$
$72$	−9.20442	+	0.782104i	−1.08475	+	0.0921719i
$73$	1.75016	+	2.45776i	0.204841	+	0.287659i	0.904198	−	0.427114i	$-0.140470\pi$
$73$	1.75016	+	2.45776i	0.204841	+	0.287659i	−0.699357	+	0.714773i	$0.746530\pi$
$74$	2.88070	−	11.8744i	0.334874	−	1.38037i
$75$	0.158275	+	8.51597i	0.0182760	+	0.983340i
$76$	−3.06851	+	2.65888i	−0.351982	+	0.304994i
$77$	−11.7111	+	0.601445i	−1.33460	+	0.0685411i
$78$	−0.289845	−	0.789659i	−0.0328184	−	0.0894113i
$79$	−3.09556	+	16.0613i	−0.348278	+	1.80704i	0.210356	+	0.977625i	$0.432538\pi$
$79$	−3.09556	+	16.0613i	−0.348278	+	1.80704i	−0.558634	+	0.829414i	$0.688674\pi$
$80$	−0.564447	+	0.290993i	−0.0631071	+	0.0325340i
$81$	8.93945	+	1.04225i	0.993272	+	0.115805i
$82$	−1.65295	−	0.318581i	−0.182538	−	0.0351814i
$83$	14.6256	+	4.29447i	1.60537	+	0.471379i	0.957034	−	0.289976i	$-0.0936473\pi$
$83$	14.6256	+	4.29447i	1.60537	+	0.471379i	0.648335	+	0.761355i	$0.275465\pi$
$84$	−0.504486	−	3.02792i	−0.0550440	−	0.330373i
$85$	−0.879595	−	1.01511i	−0.0954055	−	0.110104i
$86$	5.41971	−	7.61092i	0.584423	−	0.820707i
$87$	7.17062	−	3.02647i	0.768771	−	0.324472i
$88$	11.1170	−	7.91641i	1.18508	−	0.843893i
$89$	−8.71958	+	3.49080i	−0.924274	+	0.370024i	−0.784478	−	0.620157i	$-0.787069\pi$
$89$	−8.71958	+	3.49080i	−0.924274	+	0.370024i	−0.139796	+	0.990180i	$0.544645\pi$
$90$	0.956127	−	0.269942i	0.100785	−	0.0284544i
$91$	1.01170	−	0.466572i	0.106055	−	0.0489101i
$92$	−3.21111	+	0.0949141i	−0.334781	+	0.00989548i
$93$	10.3232	+	4.48454i	1.07047	+	0.465025i
$94$	0.377067	+	7.91561i	0.0388915	+	0.816433i
$95$	1.07589	−	1.36810i	0.110384	−	0.140365i
$96$	4.17912	+	4.64564i	0.426529	+	0.474144i
$97$	−1.66982	−	5.68689i	−0.169545	−	0.577416i	−0.999799	−	0.0200318i	$-0.993623\pi$
$97$	−1.66982	−	5.68689i	−0.169545	−	0.577416i	0.830255	−	0.557384i	$-0.188195\pi$
$98$	−7.83132	+	1.96153i	−0.791083	+	0.198144i
$99$	−12.1520	+	5.39714i	−1.22132	+	0.542433i
$100$	2.58929	−	2.03624i	0.258929	−	0.203624i
$101$	−7.16166	−	7.51094i	−0.712612	−	0.747366i	0.263494	−	0.964661i	$-0.415125\pi$
$101$	−7.16166	−	7.51094i	−0.712612	−	0.747366i	−0.976106	+	0.217295i	$0.930277\pi$
$102$	5.27784	−	7.71104i	0.522584	−	0.763506i
$103$	7.91932	+	0.377244i	0.780314	+	0.0371709i	0.433959	−	0.900933i	$-0.357116\pi$
$103$	7.91932	+	0.377244i	0.780314	+	0.0371709i	0.346355	+	0.938104i	$0.387419\pi$
$104$	−0.701005	+	1.09078i	−0.0687392	+	0.106960i
$105$	0.457988	+	1.23358i	0.0446951	+	0.120385i
$106$	−0.167168	+	0.569323i	−0.0162368	+	0.0552976i
$107$	−5.49301	+	4.31975i	−0.531029	+	0.417606i	−0.847341	−	0.531049i	$-0.821798\pi$
$107$	−5.49301	+	4.31975i	−0.531029	+	0.417606i	0.316312	+	0.948655i	$0.397555\pi$
$108$	−1.76484	−	3.00006i	−0.169822	−	0.288681i
$109$	−0.596851	+	6.25050i	−0.0571679	+	0.598689i	0.920814	+	0.390001i	$0.127525\pi$
$109$	−0.596851	+	6.25050i	−0.0571679	+	0.598689i	−0.977982	+	0.208688i	$0.933081\pi$
$110$	−1.01290	+	1.06230i	−0.0965764	+	0.101286i
$111$	17.9509	−	3.80703i	1.70383	−	0.361347i
$112$	4.02212	−	4.24975i	0.380054	−	0.401564i
$113$	11.8467	−	7.61341i	1.11444	−	0.716210i	0.152187	−	0.988352i	$-0.451368\pi$
$113$	11.8467	−	7.61341i	1.11444	−	0.716210i	0.962257	+	0.272142i	$0.0877320\pi$
$114$	11.1056	+	4.82439i	1.04013	+	0.451846i
$115$	1.34391	−	0.300453i	0.125321	−	0.0280174i
$116$	−2.60679	−	1.50503i	−0.242034	−	0.139738i
$117$	0.881247	−	0.905127i	0.0814713	−	0.0836790i
$118$	0.378244	−	2.63074i	0.0348202	−	0.242180i
$119$	10.7409	+	6.14824i	0.984620	+	0.563608i
$120$	−1.22117	−	0.924132i	−0.111477	−	0.0843613i
$121$	5.01431	−	7.04162i	0.455847	−	0.640147i
$122$	−7.63985	+	1.47246i	−0.691680	+	0.133310i
$123$	−0.641570	−	2.44532i	−0.0578484	−	0.220487i
$124$	−1.02623	−	4.23016i	−0.0921577	−	0.379879i
$125$	−1.86488	+	2.15219i	−0.166800	+	0.192498i
$126$	−7.49230	+	5.25971i	−0.667467	+	0.468573i
$127$	−5.53279	−	3.55571i	−0.490955	−	0.315518i	0.271634	−	0.962401i	$-0.412436\pi$
$127$	−5.53279	−	3.55571i	−0.490955	−	0.315518i	−0.762589	+	0.646883i	$0.776072\pi$
$128$	−0.508079	+	2.63617i	−0.0449083	+	0.233006i
$129$	13.8253	+	2.39906i	1.21725	+	0.211226i
$130$	0.0518288	−	0.129462i	0.00454569	−	0.0113546i
$131$	16.9729	+	5.87439i	1.48293	+	0.513248i	0.944241	−	0.329254i	$-0.106797\pi$
$131$	16.9729	+	5.87439i	1.48293	+	0.513248i	0.538692	+	0.842503i	$0.318919\pi$
$132$	4.50042	+	2.48798i	0.391711	+	0.216551i
$133$	−5.18884	+	15.1742i	−0.449930	+	1.31577i
$134$	−6.40678	+	14.0289i	−0.553461	+	1.21191i
$135$	0.986235	+	1.11961i	0.0848816	+	0.0963603i
$136$	−14.3874	+	0.685354i	−1.23371	+	0.0587686i
$137$	5.61743	−	9.72967i	0.479929	−	0.831261i	−0.519806	−	0.854284i	$-0.673996\pi$
$137$	5.61743	−	9.72967i	0.479929	−	0.831261i	0.999735	+	0.0230229i	$0.00732907\pi$
$138$	4.39444	+	8.51287i	0.374079	+	0.724664i
$139$	−13.1963			−1.11930			−0.559648	−	0.828730i	$-0.689064\pi$
$139$	−13.1963			−1.11930			−0.559648	+	0.828730i	$0.689064\pi$
$140$	0.273538	−	0.429127i	0.0231182	−	0.0362679i
$141$	−10.4750	+	5.64903i	−0.882152	+	0.475734i
$142$	−2.75829	+	0.263385i	−0.231470	+	0.0221027i
$143$	−0.440011	+	1.81375i	−0.0367956	+	0.151674i
$144$	2.53002	−	6.13344i	0.210835	−	0.511120i
$145$	1.21934	+	0.422018i	0.101261	+	0.0350467i
$146$	−3.44440	+	0.495231i	−0.285061	+	0.0409856i
$147$	−7.74008	−	9.33227i	−0.638391	−	0.769712i
$148$	−5.36337	−	4.64739i	−0.440867	−	0.382013i
$149$	0.352109	−	7.39167i	0.0288459	−	0.605549i	−0.937451	−	0.348118i	$-0.886821\pi$
$149$	0.352109	−	7.39167i	0.0288459	−	0.605549i	0.966297	−	0.257431i	$-0.0828761\pi$
$150$	−8.81347	−	4.33829i	−0.719616	−	0.354220i
$151$	4.20535	+	12.1506i	0.342227	+	0.988800i	0.976468	+	0.215664i	$0.0691916\pi$
$151$	4.20535	+	12.1506i	0.342227	+	0.988800i	−0.634241	+	0.773136i	$0.718687\pi$
$152$	−4.40022	−	18.1380i	−0.356905	−	1.47118i
$153$	13.8688	+	2.14194i	1.12122	+	0.173166i
$154$	5.57255	−	12.3230i	0.449049	−	0.993018i
$155$	0.775130	+	1.69730i	0.0622599	+	0.136330i
$156$	−0.484793	−	0.0605308i	−0.0388145	−	0.00484634i
$157$	13.0577	−	9.29835i	1.04212	−	0.742089i	0.0751985	−	0.997169i	$-0.476041\pi$
$157$	13.0577	−	9.29835i	1.04212	−	0.742089i	0.966920	+	0.255079i	$0.0821016\pi$
$158$	−14.8287	−	11.6614i	−1.17971	−	0.927732i
$159$	−0.879524	+	0.143186i	−0.0697508	+	0.0113554i
$160$			1.03593i			0.0818976i
$161$	−10.7716	+	6.70621i	−0.848919	+	0.528523i
$162$	−5.79275	+	8.61312i	−0.455121	+	0.676711i
$163$	−7.84349	−	4.04360i	−0.614349	−	0.316719i	0.122818	−	0.992429i	$-0.460807\pi$
$163$	−7.84349	−	4.04360i	−0.614349	−	0.316719i	−0.737167	+	0.675710i	$0.763837\pi$
$164$	−0.604382	+	0.768535i	−0.0471943	+	0.0600125i
$165$	−2.09614	−	0.682137i	−0.163185	−	0.0531043i
$166$	−12.1317	+	12.7233i	−0.941600	+	0.987522i
$167$	−3.55709	+	1.62447i	−0.275256	+	0.125705i	−0.548261	−	0.836308i	$-0.684710\pi$
$167$	−3.55709	+	1.62447i	−0.275256	+	0.125705i	0.273005	+	0.962013i	$0.411983\pi$
$168$	13.4341	+	4.31672i	1.03647	+	0.333042i
$169$	1.82486	+	12.6922i	0.140374	+	0.976321i
$170$	1.50545	−	0.365218i	0.115463	−	0.0280109i
$171$	0.675692	+	18.1715i	0.0516714	+	1.38961i
$172$	−2.48666	−	4.82345i	−0.189606	−	0.367785i
$173$	24.5868	+	1.17121i	1.86930	+	0.0890457i	0.951435	−	0.307850i	$-0.0996095\pi$
$173$	24.5868	+	1.17121i	1.86930	+	0.0890457i	0.917864	+	0.396896i	$0.129913\pi$
$174$	−0.687069	+	8.95012i	−0.0520866	+	0.678507i
$175$	4.79069	−	12.0965i	0.362142	−	0.914409i
$176$	1.39500	+	9.70245i	0.105152	+	0.731350i
$177$	3.80823	−	1.19550i	0.286244	−	0.0898593i
$178$	1.02969	−	10.7834i	0.0771783	−	0.808247i
$179$	15.9730	+	3.87501i	1.19388	+	0.289631i	0.782978	−	0.622049i	$-0.213700\pi$
$179$	15.9730	+	3.87501i	1.19388	+	0.289631i	0.410899	+	0.911681i	$0.365215\pi$
$180$	0.115109	−	0.565434i	0.00857973	−	0.0421450i
$181$	3.63240	+	0.522261i	0.269994	+	0.0388193i	0.275982	−	0.961163i	$-0.410997\pi$
$181$	3.63240	+	0.522261i	0.269994	+	0.0388193i	−0.00598785	+	0.999982i	$0.501906\pi$
$182$	−0.0563741	+	1.28368i	−0.00417873	+	0.0951523i
$183$	−6.95346	−	9.39045i	−0.514015	−	0.694162i
$184$	6.37601	−	13.3199i	0.470046	−	0.981956i
$185$	2.63456	+	1.52107i	0.193697	+	0.111831i
$186$	−10.0528	+	8.21248i	−0.737107	+	0.602168i
$187$	−19.2476	+	7.70558i	−1.40752	+	0.563488i
$188$	4.18671	+	1.91201i	0.305347	+	0.139447i
$189$	−11.9866	−	6.73215i	−0.871896	−	0.489692i
$190$	0.833872	+	1.82592i	0.0604954	+	0.132466i
$191$	−1.09444	+	3.16217i	−0.0791907	+	0.228807i	−0.977646	−	0.210259i	$-0.932569\pi$
$191$	−1.09444	+	3.16217i	−0.0791907	+	0.228807i	0.898455	+	0.439066i	$0.144690\pi$
$192$	−14.3812	+	3.77315i	−1.03788	+	0.272304i
$193$	−0.568560	+	0.542120i	−0.0409258	+	0.0390227i	−0.710266	−	0.703933i	$-0.751425\pi$
$193$	−0.568560	+	0.542120i	−0.0409258	+	0.0390227i	0.669340	+	0.742956i	$0.266577\pi$
$194$	6.71216	+	1.29366i	0.481905	+	0.0928796i
$195$	0.208969	−	0.0138505i	0.0149646	−	0.000991855i
$196$	−1.07161	+	4.56489i	−0.0765436	+	0.326063i
$197$	10.5458	+	9.13801i	0.751359	+	0.651057i	0.943900	−	0.330233i	$-0.107127\pi$
$197$	10.5458	+	9.13801i	0.751359	+	0.651057i	−0.192540	+	0.981289i	$0.561673\pi$
$198$	0.889449	−	15.3095i	0.0632104	−	1.08800i
$199$	1.77614	−	4.43659i	0.125907	−	0.314502i	−0.851999	−	0.523543i	$-0.824610\pi$
$199$	1.77614	−	4.43659i	0.125907	−	0.314502i	0.977907	+	0.209041i	$0.0670343\pi$
$200$	2.86566	+	14.8685i	0.202633	+	1.05136i
$201$	−23.1576	+	0.430399i	−1.63341	+	0.0303580i
$202$	11.4844	−	3.37211i	0.808036	−	0.237261i
$203$	−11.8889	+	0.0441304i	−0.834435	+	0.00309734i
$204$	−2.57610	−	4.77685i	−0.180363	−	0.334447i
$205$	0.192048	−	0.372521i	0.0134132	−	0.0260180i
$206$	−4.57193	+	7.91882i	−0.318542	+	0.551730i
$207$	−8.67595	+	11.4773i	−0.603020	+	0.797726i
$208$	−0.465639	−	0.806510i	−0.0322862	−	0.0559214i
$209$	−14.5244	−	22.6004i	−1.00468	−	1.56331i
$210$	−1.50659	−	0.182435i	−0.103965	−	0.0125892i
$211$	−2.89832	+	6.34645i	−0.199529	+	0.436907i	−0.982775	−	0.184804i	$-0.940835\pi$
$211$	−2.89832	+	6.34645i	−0.199529	+	0.436907i	0.783247	+	0.621711i	$0.213562\pi$
$212$	0.249417	+	0.237819i	0.0171301	+	0.0163335i
$213$	−2.14722	−	3.56445i	−0.147125	−	0.244232i
$214$	−1.52527	−	7.91385i	−0.104265	−	0.540980i
$215$	1.43799	+	1.82855i	0.0980698	+	0.124706i
$216$	15.9751	−	0.891545i	1.08697	−	0.0606620i
$217$	−11.9104	−	12.3988i	−0.808531	−	0.841685i
$218$	−6.09203	−	3.91511i	−0.412605	−	0.265165i
$219$	−2.90659	−	4.34312i	−0.196409	−	0.293481i
$220$	0.278828	+	0.805622i	0.0187986	+	0.0543150i
$221$	1.42557	−	1.35928i	0.0958945	−	0.0914352i
$222$	−5.58411	+	20.4136i	−0.374781	+	1.37007i
$223$	−12.6397	−	14.5869i	−0.846414	−	0.976814i	0.153521	−	0.988145i	$-0.450939\pi$
$223$	−12.6397	−	14.5869i	−0.846414	−	0.976814i	−0.999936	+	0.0113310i	$0.996393\pi$
$224$	−3.15537	−	9.00851i	−0.210827	−	0.601907i
$225$	0.153909	−	14.7518i	0.0102606	−	0.983456i
$226$	1.54383	+	16.1677i	0.102694	+	1.07546i
$227$	−6.39044	−	5.02550i	−0.424148	−	0.333554i	0.383162	−	0.923681i	$-0.374835\pi$
$227$	−6.39044	−	5.02550i	−0.424148	−	0.333554i	−0.807310	+	0.590127i	$0.799078\pi$
$228$	5.44619	−	4.44918i	0.360683	−	0.294654i
$229$	7.60424	−	4.39031i	0.502503	−	0.290120i	−0.227244	−	0.973838i	$-0.572971\pi$
$229$	7.60424	−	4.39031i	0.502503	−	0.290120i	0.729746	+	0.683718i	$0.239638\pi$
$230$	−0.402235	+	1.53644i	−0.0265226	+	0.101310i
$231$	20.3059	−	0.452804i	1.33603	−	0.0297923i
$232$	11.6401	−	7.48067i	0.764213	−	0.491130i
$233$	2.45385	+	6.12943i	0.160757	+	0.401552i	0.986776	−	0.162091i	$-0.0518237\pi$
$233$	2.45385	+	6.12943i	0.160757	+	0.401552i	−0.826019	+	0.563643i	$0.809399\pi$
$234$	0.462133	+	1.38172i	0.0302106	+	0.0903258i
$235$	−1.91738	−	0.465150i	−0.125076	−	0.0303431i
$236$	−1.25743	−	0.895413i	−0.0818518	−	0.0582864i
$237$	6.16651	−	27.6517i	0.400558	−	1.79617i
$238$	−11.9790	+	7.76143i	−0.776484	+	0.503099i
$239$	−0.953470	+	3.24722i	−0.0616749	+	0.210045i	−0.984565	−	0.175017i	$-0.944002\pi$
$239$	−0.953470	+	3.24722i	−0.0616749	+	0.210045i	0.922891	+	0.385062i	$0.125820\pi$
$240$	0.991862	−	0.475438i	0.0640244	−	0.0306894i
$241$	−1.75650	−	3.40713i	−0.113146	−	0.219472i	0.825462	−	0.564457i	$-0.190914\pi$
$241$	−1.75650	−	3.40713i	−0.113146	−	0.219472i	−0.938608	+	0.344985i	$0.887884\pi$
$242$	4.56847	+	8.86160i	0.293672	+	0.569645i
$243$	−15.4247	−	2.25368i	−0.989494	−	0.144573i
$244$	−1.27313	+	4.33588i	−0.0815038	+	0.277576i
$245$	0.0807323	−	2.00838i	0.00515780	−	0.128311i
$246$	2.84579	+	0.634628i	0.181441	+	0.0404624i
$247$	2.07910	+	1.48052i	0.132290	+	0.0942034i
$248$	19.4452	+	4.71737i	1.23477	+	0.299553i
$249$	−25.1058	−	8.17005i	−1.59102	−	0.517756i
$250$	−1.22068	−	3.04910i	−0.0772024	−	0.192842i
$251$	−0.651145	+	0.418466i	−0.0410999	+	0.0264133i	−0.561029	−	0.827796i	$-0.689595\pi$
$251$	−0.651145	+	0.418466i	−0.0410999	+	0.0264133i	0.519930	+	0.854209i	$0.325958\pi$
$252$	0.721273	+	5.26765i	0.0454359	+	0.331831i
$253$	2.40212	−	21.1200i	0.151020	−	1.32780i
$254$	6.56897	−	3.79260i	0.412174	−	0.237969i
$255$	1.47185	+	1.80168i	0.0921710	+	0.112825i
$256$	11.0612	+	8.69859i	0.691322	+	0.543662i
$257$	−2.14597	−	22.4737i	−0.133862	−	1.40187i	−0.773794	−	0.633437i	$-0.781644\pi$
$257$	−2.14597	−	22.4737i	−0.133862	−	1.40187i	0.639932	−	0.768431i	$-0.278962\pi$
$258$	−9.76572	+	12.9046i	−0.607987	+	0.803406i
$259$	−27.5433	−	5.20258i	−1.71146	−	0.323273i
$260$	−0.0530399	−	0.0612113i	−0.00328939	−	0.00379616i
$261$	−12.5667	+	4.87947i	−0.777861	+	0.302032i
$262$	−14.9918	+	14.2947i	−0.926196	+	0.883126i
$263$	−5.24099	−	15.1429i	−0.323174	−	0.933749i	−0.983204	−	0.182510i	$-0.941578\pi$
$263$	−5.24099	−	15.1429i	−0.323174	−	0.933749i	0.660030	−	0.751239i	$-0.270543\pi$
$264$	−19.6450	+	13.1472i	−1.20907	+	0.809155i
$265$	−0.124277	−	0.0798683i	−0.00763431	−	0.00490627i
$266$	−12.8130	−	13.3384i	−0.785616	−	0.817830i
$267$	15.2718	−	5.60552i	0.934620	−	0.343052i
$268$	5.53718	+	7.04109i	0.338237	+	0.430103i
$269$	5.11846	+	26.5571i	0.312078	+	1.61921i	0.711665	+	0.702519i	$0.247941\pi$
$269$	5.11846	+	26.5571i	0.312078	+	1.61921i	−0.399587	+	0.916695i	$0.630846\pi$
$270$	−1.66893	+	0.419310i	−0.101568	+	0.0255184i
$271$	9.97799	+	9.51399i	0.606119	+	0.577934i	0.929723	−	0.368259i	$-0.120046\pi$
$271$	9.97799	+	9.51399i	0.606119	+	0.577934i	−0.323604	+	0.946193i	$0.604894\pi$
$272$	4.29756	−	9.41035i	0.260578	−	0.570586i
$273$	−1.77502	+	0.756948i	−0.107429	+	0.0458126i
$274$	7.00528	+	10.9004i	0.423205	+	0.658519i
$275$	10.8978	+	18.8756i	0.657163	+	1.13824i
$276$	5.56423	−	0.00296635i	0.334927	−	0.000178553i
$277$	6.72138	−	11.6418i	0.403849	−	0.699486i	−0.590338	−	0.807156i	$-0.701006\pi$
$277$	6.72138	−	11.6418i	0.403849	−	0.699486i	0.994187	+	0.107670i	$0.0343389\pi$
$278$	6.97400	−	13.5277i	0.418273	−	0.811336i
$279$	−17.6475	−	8.28293i	−1.05653	−	0.495886i
$280$	1.17716	+	2.02153i	0.0703486	+	0.120810i
$281$	−22.5613	+	6.62460i	−1.34590	+	0.395191i	−0.873770	−	0.486340i	$-0.838332\pi$
$281$	−22.5613	+	6.62460i	−1.34590	+	0.395191i	−0.472127	+	0.881531i	$0.656513\pi$
$282$	−0.255059	−	13.7234i	−0.0151885	−	0.817218i
$283$	−2.66025	−	13.8027i	−0.158136	−	0.820486i	−0.971192	−	0.238300i	$-0.923410\pi$
$283$	−2.66025	−	13.8027i	−0.158136	−	0.820486i	0.813056	−	0.582186i	$-0.197802\pi$
$284$	−0.598122	+	1.49404i	−0.0354920	+	0.0886548i
$285$	−1.93146	+	2.31456i	−0.114410	+	0.137103i
$286$	−1.62676	−	1.40959i	−0.0961923	−	0.0833511i
$287$	−0.535387	+	3.82442i	−0.0316029	+	0.225749i
$288$	−7.00195	−	8.25311i	−0.412594	−	0.486319i
$289$	4.79302	+	0.923779i	0.281942	+	0.0543399i
$290$	−1.07701	+	1.02693i	−0.0632444	+	0.0603034i
$291$	2.60523	+	9.92974i	0.152721	+	0.582092i
$292$	−0.661037	+	1.90994i	−0.0386843	+	0.111771i
$293$	0.890807	+	1.95059i	0.0520415	+	0.113955i	0.933867	−	0.357622i	$-0.116412\pi$
$293$	0.890807	+	1.95059i	0.0520415	+	0.113955i	−0.881825	+	0.471577i	$0.843685\pi$
$294$	13.6571	−	3.00251i	0.796498	−	0.175110i
$295$	0.601916	+	0.274886i	0.0350449	+	0.0160045i
$296$	30.2857	−	12.1246i	1.76032	−	0.704725i
$297$	21.3103	−	8.73354i	1.23655	−	0.506771i
$298$	7.39120	+	4.26731i	0.428161	+	0.247199i
$299$	0.533886	+	1.94763i	0.0308754	+	0.112634i
$300$	−4.58522	+	3.39527i	−0.264728	+	0.196026i
$301$	−18.0744	−	11.5211i	−1.04179	−	0.664067i
$302$	−14.6781	−	2.11040i	−0.844632	−	0.121440i
$303$	12.0217	+	13.3637i	0.690629	+	0.767726i
$304$	13.0273	+	3.16040i	0.747168	+	0.181261i
$305$	0.184134	−	1.92833i	0.0105435	−	0.110416i
$306$	−9.52512	+	13.0851i	−0.544515	+	0.748024i
$307$	4.10423	+	28.5455i	0.234241	+	1.62918i	0.679429	+	0.733741i	$0.262228\pi$
$307$	4.10423	+	28.5455i	0.234241	+	1.62918i	−0.445188	+	0.895437i	$0.646863\pi$
$308$	−4.87857	−	6.15644i	−0.277982	−	0.350796i
$309$	−13.6919	−	1.05108i	−0.778907	−	0.0597940i
$310$	−2.14956	−	0.102396i	−0.122087	−	0.00581571i
$311$	−3.54136	−	6.86929i	−0.200812	−	0.389522i	0.766829	−	0.641852i	$-0.221833\pi$
$311$	−3.54136	−	6.86929i	−0.200812	−	0.389522i	−0.967641	+	0.252330i	$0.918803\pi$
$312$	1.26848	−	1.85327i	0.0718134	−	0.104921i
$313$	16.0058	−	3.88296i	0.904701	−	0.219478i	0.243689	−	0.969853i	$-0.421642\pi$
$313$	16.0058	−	3.88296i	0.904701	−	0.219478i	0.661012	+	0.750375i	$0.270127\pi$
$314$	2.63109	+	18.2996i	0.148481	+	1.03271i
$315$	−0.730937	−	2.15874i	−0.0411836	−	0.121631i
$316$	−9.96660	+	4.55160i	−0.560665	+	0.256047i
$317$	−20.8547	+	21.8717i	−1.17131	+	1.22844i	−0.202872	+	0.979205i	$0.565027\pi$
$317$	−20.8547	+	21.8717i	−1.17131	+	1.22844i	−0.968443	+	0.249234i	$0.919821\pi$
$318$	0.318031	−	0.977281i	0.0178343	−	0.0548032i
$319$	12.3116	−	15.6555i	0.689319	−	0.876540i
$320$	−2.19084	−	1.12946i	−0.122472	−	0.0631385i
$321$	9.72723	−	7.20285i	0.542921	−	0.402024i
$322$	−1.18203	−	14.5862i	−0.0658721	−	0.812855i
$323$			28.3534i			1.57763i
$324$	2.90476	+	5.28275i	0.161375	+	0.293486i
$325$	−1.62770	−	1.28004i	−0.0902888	−	0.0710039i
$326$	8.29027	−	5.90348i	0.459156	−	0.326963i
$327$	1.34743	−	10.7916i	0.0745132	−	0.596779i
$328$	−1.86703	−	4.08822i	−0.103089	−	0.225734i
$329$	18.0904	−	1.79521i	0.997356	−	0.0989731i
$330$	1.80704	−	1.78828i	0.0994743	−	0.0984418i
$331$	−2.89771	−	11.9445i	−0.159273	−	0.656530i	−0.994327	−	0.106363i	$-0.966079\pi$
$331$	−2.89771	−	11.9445i	−0.159273	−	0.656530i	0.835055	−	0.550167i	$-0.185436\pi$
$332$	3.33957	+	9.64905i	0.183283	+	0.529561i
$333$	−31.2701	+	5.68914i	−1.71359	+	0.311763i
$334$	0.214596	−	4.50492i	0.0117422	−	0.246498i
$335$	−2.90191	−	2.51452i	−0.158548	−	0.137383i
$336$	−7.17713	+	7.15557i	−0.391545	+	0.390368i
$337$	20.2322	−	2.90896i	1.10212	−	0.158461i	0.432840	−	0.901471i	$-0.357512\pi$
$337$	20.2322	−	2.90896i	1.10212	−	0.158461i	0.669281	+	0.743010i	$0.266602\pi$
$338$	−13.9753	−	4.83689i	−0.760155	−	0.263092i
$339$	−20.8930	+	12.5860i	−1.13475	+	0.683576i
$340$	0.212120	−	0.874372i	0.0115038	−	0.0474195i
$341$	28.6711	−	2.73776i	1.55263	−	0.148258i
$342$	−18.9849	−	8.91064i	−1.02659	−	0.481832i
$343$	5.41531	+	17.7109i	0.292399	+	0.956296i
$344$	24.9456			1.34497
$345$	−2.34184	+	0.452648i	−0.126081	+	0.0243698i
$346$	−14.1943	+	24.5852i	−0.763090	+	1.32171i
$347$	−2.35346	+	0.112109i	−0.126340	+	0.00601832i	−0.110657	−	0.993859i	$-0.535295\pi$
$347$	−2.35346	+	0.112109i	−0.126340	+	0.00601832i	−0.0156834	+	0.999877i	$0.504992\pi$
$348$	4.43756	+	2.73668i	0.237878	+	0.146702i
$349$	6.61194	−	14.4781i	0.353929	−	0.774996i	−0.646003	−	0.763335i	$-0.723561\pi$
$349$	6.61194	−	14.4781i	0.353929	−	0.774996i	0.999932	−	0.0116614i	$-0.00371202\pi$
$350$	9.86847	+	11.3038i	0.527492	+	0.604212i
$351$	−1.57121	+	1.52278i	−0.0838647	+	0.0812801i
$352$	15.1108	+	5.22988i	0.805406	+	0.278754i
$353$	−7.33257	+	18.3159i	−0.390273	+	0.974855i	0.594978	+	0.803742i	$0.297161\pi$
$353$	−7.33257	+	18.3159i	−0.390273	+	0.974855i	−0.985251	+	0.171113i	$0.945264\pi$
$354$	−0.787059	+	4.53566i	−0.0418317	+	0.241068i
$355$	0.130556	−	0.677390i	0.00692921	−	0.0359522i
$356$	−5.29277	−	3.40146i	−0.280516	−	0.180277i
$357$	−18.2871	−	11.1843i	−0.967854	−	0.591937i
$358$	−12.4137	+	14.3262i	−0.656087	+	0.757164i
$359$	0.421172	+	1.73610i	0.0222286	+	0.0916277i	0.981845	−	0.189683i	$-0.0607460\pi$
$359$	0.421172	+	1.73610i	0.0222286	+	0.0916277i	−0.959617	+	0.281311i	$0.909231\pi$
$360$	2.06779	+	1.66133i	0.108982	+	0.0875600i
$361$	−17.4194	+	3.35731i	−0.916809	+	0.176700i
$362$	−2.45503	+	3.44761i	−0.129034	+	0.181202i
$363$	−9.03524	+	11.9393i	−0.474227	+	0.626653i
$364$	0.647682	+	0.370741i	0.0339478	+	0.0194321i
$365$	0.123298	−	0.857556i	0.00645371	−	0.0448865i
$366$	13.3010	−	2.16539i	0.695256	−	0.113187i
$367$	22.4521	+	12.9627i	1.17199	+	0.676649i	0.954148	−	0.299335i	$-0.0967648\pi$
$367$	22.4521	+	12.9627i	1.17199	+	0.676649i	0.217842	+	0.975984i	$0.430098\pi$
$368$	6.40489	+	8.45417i	0.333878	+	0.440704i
$369$	0.987884	+	4.26588i	0.0514272	+	0.222073i
$370$	−2.95158	+	1.89686i	−0.153445	+	0.0986133i
$371$	1.32400	+	0.315999i	0.0687384	+	0.0164058i
$372$	1.56416	+	7.37533i	0.0810978	+	0.382393i
$373$	6.15322	−	6.45331i	0.318601	−	0.334140i	−0.544886	−	0.838510i	$-0.683427\pi$
$373$	6.15322	−	6.45331i	0.318601	−	0.334140i	0.863487	+	0.504371i	$0.168275\pi$
$374$	2.27293	−	23.8032i	0.117530	−	1.23083i
$375$	3.33686	−	3.63242i	0.172315	−	0.187577i
$376$	−16.6309	+	13.0787i	−0.857674	+	0.674482i
$377$	−0.533097	+	1.81556i	−0.0274559	+	0.0935062i
$378$	13.2359	−	8.72976i	0.680781	−	0.449011i
$379$	−16.1419	+	25.1172i	−0.829152	+	1.29019i	0.125389	+	0.992108i	$0.459982\pi$
$379$	−16.1419	+	25.1172i	−0.829152	+	1.29019i	−0.954541	+	0.298078i	$0.903654\pi$
$380$	1.16454	+	0.0554740i	0.0597398	+	0.00284576i
$381$	9.40036	+	6.43410i	0.481595	+	0.329629i
$382$	−2.66319	−	2.79307i	−0.136260	−	0.142906i
$383$	−22.5037	+	17.6971i	−1.14988	+	0.904279i	−0.996476	−	0.0838836i	$-0.973268\pi$
$383$	−22.5037	+	17.6971i	−1.14988	+	0.904279i	−0.153409	+	0.988163i	$0.549025\pi$
$384$	1.01212	−	4.53852i	0.0516495	−	0.231605i
$385$	2.55292	+	2.19558i	0.130109	+	0.111897i
$386$	−0.255261	−	0.869337i	−0.0129924	−	0.0442481i
$387$	−23.8155	−	4.84828i	−1.21061	−	0.246452i
$388$	2.45422	−	3.12079i	0.124594	−	0.158434i
$389$	−0.659710	−	13.8490i	−0.0334486	−	0.702173i	−0.951858	−	0.306541i	$-0.900828\pi$
$389$	−0.659710	−	13.8490i	−0.0334486	−	0.702173i	0.918409	−	0.395633i	$-0.129475\pi$
$390$	−0.0962379	+	0.221536i	−0.00487320	+	0.0112179i
$391$	−14.1836	+	17.3809i	−0.717295	+	0.878988i
$392$	−16.3940	−	13.9938i	−0.828024	−	0.706793i
$393$	−29.0904	−	11.0234i	−1.46742	−	0.556056i
$394$	−14.9408	+	5.98138i	−0.752705	+	0.301337i
$395$	3.82587	−	2.72439i	0.192501	−	0.137079i
$396$	−7.66665	−	4.53364i	−0.385263	−	0.227824i
$397$	−3.61604	+	5.07802i	−0.181484	+	0.254859i	−0.895289	−	0.445486i	$-0.853031\pi$
$397$	−3.61604	+	5.07802i	−0.181484	+	0.254859i	0.713805	+	0.700345i	$0.246970\pi$
$398$	3.60934	+	4.16540i	0.180920	+	0.208793i
$399$	9.74607	−	26.0106i	0.487914	−	1.30216i
$400$	−10.4350	−	3.06401i	−0.521752	−	0.153200i
$401$	6.33962	+	1.22186i	0.316585	+	0.0610168i	0.345069	−	0.938577i	$-0.387856\pi$
$401$	6.33962	+	1.22186i	0.316585	+	0.0610168i	−0.0284833	+	0.999594i	$0.509068\pi$
$402$	11.7972	−	23.9666i	0.588389	−	1.19534i
$403$	−2.43215	+	1.25386i	−0.121154	+	0.0624593i
$404$	1.31563	−	6.82614i	0.0654551	−	0.339613i
$405$	−1.65123	−	1.98796i	−0.0820503	−	0.0987824i
$406$	6.23781	−	12.2107i	0.309577	−	0.606008i
$407$	35.4878	−	30.7503i	1.75906	−	1.52424i
$408$	24.9436	−	0.463593i	1.23489	−	0.0229513i
$409$	3.10457	−	12.7972i	0.153511	−	0.632781i	−0.842111	−	0.539305i	$-0.818687\pi$
$409$	3.10457	−	12.7972i	0.153511	−	0.632781i	0.995622	−	0.0934759i	$-0.0297978\pi$
$410$	0.280382	+	0.393741i	0.0138471	+	0.0194455i
$411$	−10.2145	+	16.5629i	−0.503844	+	0.816988i
$412$	2.87124	+	4.46774i	0.141456	+	0.220110i
$413$	−6.07157	−	0.557030i	−0.298763	−	0.0274097i
$414$	−7.18040	−	14.9593i	−0.352898	−	0.735212i
$415$	−2.18847	−	3.79054i	−0.107428	−	0.186070i
$416$	−1.51746	+	0.0722853i	−0.0743994	+	0.00354408i
$417$	22.8470	+	0.663125i	1.11882	+	0.0324733i
$418$	30.8439	−	2.94523i	1.50862	−	0.144056i
$419$	10.2543	−	3.01092i	0.500953	−	0.147093i	−0.0214870	−	0.999769i	$-0.506840\pi$
$419$	10.2543	−	3.01092i	0.500953	−	0.147093i	0.522440	+	0.852676i	$0.325022\pi$
$420$	−0.495146	+	0.729212i	−0.0241607	+	0.0355819i
$421$	15.0142	−	13.0099i	0.731749	−	0.634064i	−0.207129	−	0.978314i	$-0.566412\pi$
$421$	15.0142	−	13.0099i	0.731749	−	0.634064i	0.938878	+	0.344250i	$0.111867\pi$
$422$	−4.97410	−	6.32508i	−0.242135	−	0.307900i
$423$	18.4194	−	9.25392i	0.895582	−	0.449941i
$424$	−1.49705	+	0.518135i	−0.0727033	+	0.0251628i
$425$	1.09453	−	22.9769i	0.0530924	−	1.11455i
$426$	4.78872	−	0.317397i	0.232014	−	0.0153780i
$427$	4.27232	+	17.3297i	0.206752	+	0.838645i
$428$	−4.49139	−	1.31879i	−0.217099	−	0.0637461i
$429$	0.852944	−	3.11808i	0.0411805	−	0.150542i
$430$	−2.63441	+	0.507741i	−0.127043	+	0.0244855i
$431$	37.6081	+	3.59114i	1.81152	+	0.172979i	0.945196	−	0.326503i	$-0.105870\pi$
$431$	37.6081	+	3.59114i	1.81152	+	0.172979i	0.866324	+	0.499482i	$0.166476\pi$
$432$	−4.68848	+	10.4918i	−0.225575	+	0.504788i
$433$	20.8391	+	9.51690i	1.00146	+	0.457353i	0.847541	−	0.530730i	$-0.178082\pi$
$433$	20.8391	+	9.51690i	1.00146	+	0.457353i	0.153922	+	0.988083i	$0.450809\pi$
$434$	19.0046	−	5.65695i	0.912248	−	0.271542i
$435$	−2.08986	−	0.791921i	−0.100201	−	0.0379697i
$436$	−3.64248	+	2.10299i	−0.174443	+	0.100715i
$437$	−25.5931	−	13.7845i	−1.22428	−	0.659401i
$438$	5.98826	−	0.684319i	0.286130	−	0.0326980i
$439$	−4.26350	−	2.19799i	−0.203486	−	0.104904i	0.353472	−	0.935445i	$-0.385001\pi$
$439$	−4.26350	−	2.19799i	−0.203486	−	0.104904i	−0.556958	+	0.830541i	$0.688031\pi$
$440$	−3.87894	−	0.557707i	−0.184921	−	0.0265876i
$441$	12.9316	+	16.5461i	0.615791	+	0.787910i
$442$	0.640026	+	2.17973i	0.0304429	+	0.103679i
$443$	4.45662	+	3.17355i	0.211740	+	0.150780i	0.681007	−	0.732277i	$-0.261542\pi$
$443$	4.45662	+	3.17355i	0.211740	+	0.150780i	−0.469267	+	0.883057i	$0.655482\pi$
$444$	9.05219	+	8.31564i	0.429598	+	0.394643i
$445$	2.50377	+	1.00236i	0.118690	+	0.0475163i
$446$	21.6331	−	5.24813i	1.02436	−	0.248506i
$447$	−0.981051	+	12.7797i	−0.0464021	+	0.604458i
$448$	22.4919	+	3.14868i	1.06264	+	0.148761i
$449$	3.24535	−	5.04987i	0.153158	−	0.238318i	−0.756193	−	0.654349i	$-0.772943\pi$
$449$	3.24535	−	5.04987i	0.153158	−	0.238318i	0.909351	+	0.416031i	$0.136579\pi$
$450$	15.0409	+	7.95385i	0.709037	+	0.374948i
$451$	−4.46427	−	4.68199i	−0.210214	−	0.220467i
$452$	8.75732	+	3.50590i	0.411910	+	0.164904i
$453$	−6.67025	−	21.2479i	−0.313395	−	0.998312i
$454$	8.52892	−	3.89503i	0.400282	−	0.182803i
$455$	−0.302697	−	0.103508i	−0.0141907	−	0.00485253i
$456$	6.70675	+	31.6238i	0.314073	+	1.48092i
$457$	2.00972	+	5.02005i	0.0940109	+	0.234828i	0.967919	−	0.251264i	$-0.0808462\pi$
$457$	2.00972	+	5.02005i	0.0940109	+	0.234828i	−0.873908	+	0.486092i	$0.838422\pi$
$458$	0.481856	+	10.1154i	0.0225156	+	0.472661i
$459$	−23.9037	−	4.40530i	−1.11573	−	0.205622i
$460$	0.686124	+	0.616560i	0.0319907	+	0.0287473i
$461$			8.49024i			0.395430i	0.980260	+	0.197715i	$0.0633520\pi$
$461$			8.49024i			0.395430i	−0.980260	+	0.197715i	$0.936648\pi$
$462$	−10.2671	+	21.0551i	−0.477670	+	0.979572i
$463$	−0.781934	+	5.43847i	−0.0363396	+	0.252747i	−0.999891	−	0.0147766i	$-0.995296\pi$
$463$	−0.781934	+	5.43847i	−0.0363396	+	0.252747i	0.963551	+	0.267524i	$0.0862054\pi$
$464$	0.944666	+	9.89299i	0.0438550	+	0.459270i
$465$	−1.25671	−	2.97752i	−0.0582785	−	0.138079i
$466$	−7.58016	−	0.723818i	−0.351144	−	0.0335302i
$467$	2.83643	−	8.19532i	0.131254	−	0.379234i	−0.860155	−	0.510033i	$-0.829633\pi$
$467$	2.83643	−	8.19532i	0.131254	−	0.379234i	0.991409	+	0.130799i	$0.0417543\pi$
$468$	0.836292	+	0.129160i	0.0386576	+	0.00597040i
$469$	32.8942	+	13.0274i	1.51891	+	0.601548i
$470$	1.49013	−	1.71970i	0.0687345	−	0.0793238i
$471$	−23.0743	+	15.4423i	−1.06321	+	0.711543i
$472$	6.30711	−	3.25154i	0.290308	−	0.149664i
$473$	33.9320	−	11.7440i	1.56019	−	0.539988i
$474$	25.0872	+	20.9348i	1.15229	+	0.961567i
$475$	29.5036	−	4.24198i	1.35372	−	0.194635i
$476$	0.818661	+	8.24968i	0.0375233	+	0.378124i
$477$	1.52993	−	0.203704i	0.0700509	−	0.00932695i
$478$	−2.82487	−	2.69351i	−0.129207	−	0.123198i
$479$	−14.4239	−	20.2555i	−0.659043	−	0.925497i	0.340850	−	0.940118i	$-0.389285\pi$
$479$	−14.4239	−	20.2555i	−0.659043	−	0.925497i	−0.999893	+	0.0146208i	$0.995346\pi$
$480$	0.0520564	−	1.79353i	0.00237604	−	0.0818632i
$481$	−2.04425	+	3.96530i	−0.0932100	+	0.180802i
$482$	4.42096			0.201369
$483$	18.9860	−	11.0693i	0.863895	−	0.503672i
$484$	5.79057			0.263208
$485$	−0.779850	+	1.51270i	−0.0354112	+	0.0686881i
$486$	10.4619	−	14.6210i	0.474563	−	0.663222i
$487$	−3.13201	−	4.39829i	−0.141925	−	0.199306i	0.737495	−	0.675353i	$-0.236009\pi$
$487$	−3.13201	−	4.39829i	−0.141925	−	0.199306i	−0.879420	+	0.476047i	$0.842069\pi$
$488$	−15.0339	−	14.3348i	−0.680552	−	0.648905i
$489$	13.3764	+	7.39491i	0.604902	+	0.334409i
$490$	2.01615	+	1.14415i	0.0910802	+	0.0516874i
$491$	17.6516	−	2.53792i	0.796608	−	0.114535i	0.268020	−	0.963413i	$-0.413631\pi$
$491$	17.6516	−	2.53792i	0.796608	−	0.114535i	0.528588	+	0.848879i	$0.322722\pi$
$492$	1.08500	−	1.30021i	0.0489156	−	0.0586180i
$493$	−19.8638	+	6.87493i	−0.894621	+	0.309631i
$494$	−2.61647	+	1.34888i	−0.117720	+	0.0606891i
$495$	3.59482	+	1.28633i	0.161575	+	0.0578163i
$496$	−9.41124	+	10.8612i	−0.422577	+	0.487680i
$497$	0.927955	+	6.28828i	0.0416245	+	0.282068i
$498$	21.6432	−	21.4186i	0.969854	−	0.959788i
$499$	13.8779	−	40.0975i	0.621259	−	1.79501i	0.0148078	−	0.999890i	$-0.495286\pi$
$499$	13.8779	−	40.0975i	0.621259	−	1.79501i	0.606451	−	0.795121i	$-0.292592\pi$
$500$	−1.89894	−	0.181327i	−0.0849233	−	0.00810919i
$501$	6.24010	−	2.63373i	0.278787	−	0.117666i
$502$	−0.0848556	−	0.888648i	−0.00378729	−	0.0396623i
$503$	−1.41693	+	9.85493i	−0.0631776	+	0.439410i	0.933541	+	0.358470i	$0.116701\pi$
$503$	−1.41693	+	9.85493i	−0.0631776	+	0.439410i	−0.996719	+	0.0809401i	$0.974208\pi$
$504$	−23.0419	−	8.14870i	−1.02637	−	0.362972i
$505$			2.97998i			0.132607i
$506$	20.3809	+	13.6240i	0.906040	+	0.605659i
$507$	−2.52163	−	22.0659i	−0.111989	−	0.979982i
$508$	−0.209623	−	4.40053i	−0.00930052	−	0.195242i
$509$	−11.0093	−	27.4999i	−0.487979	−	1.21891i	−0.944297	−	0.329095i	$-0.893256\pi$
$509$	−11.0093	−	27.4999i	−0.487979	−	1.21891i	0.456318	−	0.889817i	$-0.349168\pi$
$510$	−2.62477	+	0.556659i	−0.116227	+	0.0246493i
$511$	1.53985	+	7.83290i	0.0681187	+	0.346507i
$512$	−19.6468	+	8.97239i	−0.868273	+	0.396527i
$513$	−0.256708	−	31.4946i	−0.0113339	−	1.39052i
$514$	24.1721	+	9.67705i	1.06619	+	0.426837i
$515$	−1.57100	−	1.64762i	−0.0692267	−	0.0726028i
$516$	4.06283	+	8.47590i	0.178856	+	0.373131i
$517$	−16.4648	+	25.6197i	−0.724121	+	1.12675i
$518$	19.8894	−	25.4855i	0.873889	−	1.11977i
$519$	−42.5088	−	3.26325i	−1.86593	−	0.143241i
$520$	0.361820	−	0.0877765i	0.0158668	−	0.00384926i
$521$	8.23208	+	3.29563i	0.360654	+	0.144384i	0.544911	−	0.838494i	$-0.316564\pi$
$521$	8.23208	+	3.29563i	0.360654	+	0.144384i	−0.184257	+	0.982878i	$0.558988\pi$
$522$	1.63929	−	15.4610i	0.0717497	−	0.676710i
$523$	−6.99363	−	4.98014i	−0.305810	−	0.217766i	0.416841	−	0.908979i	$-0.363137\pi$
$523$	−6.99363	−	4.98014i	−0.305810	−	0.217766i	−0.722651	+	0.691213i	$0.757077\pi$
$524$	3.38955	+	11.5438i	0.148073	+	0.504291i
$525$	−8.90208	+	20.7022i	−0.388519	+	0.903518i
$526$	18.2929	+	2.63012i	0.797608	+	0.114679i
$527$	−27.0179	−	13.9287i	−1.17692	−	0.606743i
$528$	−1.92764	−	16.8682i	−0.0838898	−	0.734093i
$529$	−8.79320	−	21.2528i	−0.382313	−	0.924033i
$530$	0.147552	−	0.0851893i	0.00640926	−	0.00370039i
$531$	−6.65334	+	1.87843i	−0.288731	+	0.0815168i
$532$	−10.2959	+	3.06470i	−0.446383	+	0.132872i
$533$	0.559077	+	0.255322i	0.0242163	+	0.0110592i
$534$	−2.32459	+	18.6177i	−0.100595	+	0.805668i
$535$	1.99749	+	0.190738i	0.0863592	+	0.00824630i
$536$	−40.4320	+	7.79262i	−1.74640	+	0.336590i
$537$	−27.4597	−	7.51154i	−1.18497	−	0.324147i
$538$	−29.9290	−	8.78794i	−1.29033	−	0.378875i
$539$	−28.8879	−	11.3169i	−1.24429	−	0.487452i
$540$	−0.227705	+	0.973164i	−0.00979884	+	0.0418783i
$541$	0.0621051	−	1.30375i	0.00267011	−	0.0560524i	−0.997139	−	0.0755894i	$-0.975916\pi$
$541$	0.0621051	−	1.30375i	0.00267011	−	0.0560524i	0.999809	+	0.0195370i	$0.00621920\pi$
$542$	−15.0261	+	5.20058i	−0.645425	+	0.223384i
$543$	−6.26261	−	1.08673i	−0.268754	−	0.0466361i
$544$	−10.4320	−	13.2654i	−0.447270	−	0.568750i
$545$	1.36258	−	1.18068i	0.0583665	−	0.0505749i
$546$	0.162107	−	2.21962i	0.00693756	−	0.0949911i
$547$	−3.28124	+	0.963459i	−0.140296	+	0.0411945i	−0.351126	−	0.936328i	$-0.614201\pi$
$547$	−3.28124	+	0.963459i	−0.140296	+	0.0411945i	0.210831	+	0.977523i	$0.432383\pi$
$548$	7.49164	−	0.715364i	0.320027	−	0.0305589i
$549$	11.5668	+	16.6073i	0.493659	+	0.708783i
$550$	−25.1089	+	1.19608i	−1.07064	+	0.0510011i
$551$	−13.6186	−	23.5882i	−0.580174	−	1.00489i
$552$	−11.7083	+	22.7406i	−0.498337	+	0.967905i
$553$	−24.9717	+	35.3448i	−1.06190	+	1.50301i
$554$	8.38199	+	13.0426i	0.356117	+	0.554128i
$555$	−4.48484	−	2.76584i	−0.190371	−	0.117403i
$556$	−5.12747	−	7.20053i	−0.217453	−	0.305370i
$557$	−7.51518	+	30.9780i	−0.318428	+	1.31258i	0.557515	+	0.830167i	$0.311755\pi$
$557$	−7.51518	+	30.9780i	−0.318428	+	1.31258i	−0.875944	+	0.482413i	$0.839760\pi$
$558$	17.8173	−	13.7133i	0.754267	−	0.580529i
$559$	−2.57816	+	2.23398i	−0.109044	+	0.0944875i
$560$	−1.67795	+	0.0861742i	−0.0709063	+	0.00364153i
$561$	33.7110	−	12.3736i	1.42328	−	0.522415i
$562$	5.13229	−	26.6289i	0.216493	−	1.12327i
$563$	14.5155	−	7.48324i	0.611753	−	0.315381i	−0.124362	−	0.992237i	$-0.539688\pi$
$563$	14.5155	−	7.48324i	0.611753	−	0.315381i	0.736115	+	0.676856i	$0.236658\pi$
$564$	−7.15247	−	3.52069i	−0.301173	−	0.148248i
$565$	−3.97053	−	0.765257i	−0.167042	−	0.0321946i
$566$	15.5552	+	4.56742i	0.653834	+	0.191983i
$567$	20.4143	+	12.2579i	0.857322	+	0.514781i
$568$	−4.84448	−	5.59083i	−0.203270	−	0.234586i
$569$	−4.61097	+	6.47520i	−0.193302	+	0.271455i	−0.899840	−	0.436221i	$-0.856317\pi$
$569$	−4.61097	+	6.47520i	−0.193302	+	0.271455i	0.706538	+	0.707675i	$0.250256\pi$
$570$	−1.35195	−	3.20316i	−0.0566268	−	0.134166i
$571$	0.345268	−	0.245865i	0.0144490	−	0.0102891i	−0.572810	−	0.819688i	$-0.694147\pi$
$571$	0.345268	−	0.245865i	0.0144490	−	0.0102891i	0.587259	+	0.809399i	$0.300207\pi$
$572$	−1.16064	+	0.464649i	−0.0485286	+	0.0194279i
$573$	2.05372	−	5.41974i	0.0857956	−	0.226413i
$574$	−3.63752	−	2.56997i	−0.151827	−	0.107268i
$575$	20.2080	+	12.1586i	0.842730	+	0.507048i
$576$	25.0882	−	5.80987i	1.04534	−	0.242078i
$577$	0.185821	+	3.90085i	0.00773581	+	0.162395i	0.999430	+	0.0337729i	$0.0107523\pi$
$577$	0.185821	+	3.90085i	0.00773581	+	0.162395i	−0.991694	+	0.128622i	$0.958945\pi$
$578$	−3.48000	+	4.42518i	−0.144749	+	0.184063i
$579$	1.01160	−	0.910014i	0.0420407	−	0.0378189i
$580$	0.243506	+	0.829306i	0.0101110	+	0.0344350i
$581$	30.5767	+	26.2968i	1.26854	+	1.09097i
$582$	−11.5559	−	2.57704i	−0.479008	−	0.106822i
$583$	−1.79242	+	1.40958i	−0.0742345	+	0.0583787i
$584$	−6.41126	−	6.72394i	−0.265300	−	0.278239i
$585$	−0.362489	+	0.0134788i	−0.0149871	+	0.000557281i
$586$	−2.47035	−	0.117677i	−0.102049	−	0.00486121i
$587$	−6.86837	+	10.6874i	−0.283488	+	0.441116i	−0.953570	−	0.301171i	$-0.902623\pi$
$587$	−6.86837	+	10.6874i	−0.283488	+	0.441116i	0.670082	+	0.742287i	$0.266259\pi$
$588$	2.08469	−	7.84944i	0.0859712	−	0.323705i
$589$	11.0969	−	37.7925i	0.457239	−	1.55721i
$590$	−0.599890	+	0.471759i	−0.0246971	+	0.0194220i
$591$	−17.7990	−	16.3508i	−0.732154	−	0.672581i
$592$	−2.22722	+	23.3245i	−0.0915383	+	0.958632i
$593$	−26.4087	+	27.6966i	−1.08447	+	1.13736i	−0.0945846	+	0.995517i	$0.530152\pi$
$593$	−26.4087	+	27.6966i	−1.08447	+	1.13736i	−0.989889	+	0.141846i	$0.954696\pi$
$594$	−2.30923	+	26.4609i	−0.0947490	+	1.08570i
$595$	−1.01385	−	3.40603i	−0.0415637	−	0.139634i
$596$	4.17006	−	2.67993i	0.170812	−	0.109774i
$597$	−3.29802	+	7.59191i	−0.134979	+	0.310716i
$598$	−2.27868	−	0.481993i	−0.0931823	−	0.0197102i
$599$	−11.0218	−	6.36343i	−0.450338	−	0.260003i	0.257635	−	0.966242i	$-0.417057\pi$
$599$	−11.0218	−	6.36343i	−0.450338	−	0.260003i	−0.707973	+	0.706240i	$0.750390\pi$
$600$	−4.21423	−	25.8861i	−0.172045	−	1.05679i
$601$	−1.26235	+	8.77984i	−0.0514924	+	0.358137i	0.947743	+	0.319035i	$0.103359\pi$
$601$	−1.26235	+	8.77984i	−0.0514924	+	0.358137i	−0.999235	+	0.0391020i	$0.987550\pi$
$602$	21.3624	−	12.4396i	0.870668	−	0.506999i
$603$	40.1149	+	0.418528i	1.63360	+	0.0170438i
$604$	−4.99592	+	7.01579i	−0.203281	+	0.285468i
$605$	−2.43736	+	0.469762i	−0.0990926	+	0.0190985i
$606$	−20.0526	+	5.26111i	−0.814580	+	0.213718i
$607$	−5.78541	−	23.8478i	−0.234822	−	0.967951i	−0.960136	−	0.279533i	$-0.909820\pi$
$607$	−5.78541	−	23.8478i	−0.234822	−	0.967951i	0.725314	−	0.688418i	$-0.241695\pi$
$608$	14.3203	−	16.5265i	0.580764	−	0.670237i
$609$	20.5857	+	0.521021i	0.834174	+	0.0211128i
$610$	1.87945	+	1.20785i	0.0760966	+	0.0489043i
$611$	0.547571	−	2.84107i	0.0221524	−	0.114937i
$612$	4.22002	+	8.39972i	0.170584	+	0.339539i
$613$	−14.0306	+	35.0467i	−0.566689	+	1.41552i	0.317440	+	0.948278i	$0.397177\pi$
$613$	−14.0306	+	35.0467i	−0.566689	+	1.41552i	−0.884129	+	0.467243i	$0.845247\pi$
$614$	−31.4313	−	10.8785i	−1.26847	−	0.439020i
$615$	−0.351216	+	0.635303i	−0.0141624	+	0.0256179i
$616$	35.4302	−	6.96510i	1.42752	−	0.280632i
$617$	−9.55855	+	20.9303i	−0.384813	+	0.842623i	0.613774	+	0.789482i	$0.289651\pi$
$617$	−9.55855	+	20.9303i	−0.384813	+	0.842623i	−0.998587	+	0.0531411i	$0.983077\pi$
$618$	8.31341	−	13.4803i	0.334415	−	0.542256i
$619$	40.3105	−	1.92022i	1.62021	−	0.0771803i	0.782271	−	0.622938i	$-0.214061\pi$
$619$	40.3105	−	1.92022i	1.62021	−	0.0771803i	0.837943	+	0.545758i	$0.183758\pi$
$620$	−0.624946	+	1.08244i	−0.0250984	+	0.0434718i
$621$	15.5976	−	19.4349i	0.625910	−	0.779895i
$622$	8.91333			0.357392
$623$	−24.8260	−	1.09026i	−0.994632	−	0.0436804i
$624$	0.765642	+	1.41973i	0.0306502	+	0.0568345i
$625$	−23.6624	+	2.25949i	−0.946496	+	0.0903794i
$626$	−4.47830	+	18.4598i	−0.178989	+	0.737802i
$627$	24.0108	+	39.8585i	0.958897	+	1.59180i
$628$	10.1472	+	3.51199i	0.404919	+	0.140144i
$629$	−49.0538	+	7.05287i	−1.95590	+	0.281216i
$630$	2.59923	+	0.391561i	0.103556	+	0.0156002i
$631$	−13.7675	−	11.9296i	−0.548076	−	0.474910i	0.336255	−	0.941771i	$-0.390840\pi$
$631$	−13.7675	−	11.9296i	−0.548076	−	0.474910i	−0.884331	+	0.466861i	$0.845385\pi$
$632$	2.39652	−	50.3090i	0.0953283	−	2.00119i
$633$	5.33685	−	10.8421i	0.212121	−	0.430935i
$634$	−11.3997	−	32.9372i	−0.452739	−	1.30810i
$635$	0.445229	+	1.83526i	0.0176684	+	0.0728300i
$636$	−0.419871	−	0.424275i	−0.0166490	−	0.0168236i
$637$	2.94755	−	0.0218824i	0.116786	−	0.000867010i
$638$	9.54217	+	20.8944i	0.377778	+	0.827218i
$639$	3.53842	+	6.27910i	0.139978	+	0.248397i
$640$	0.627946	−	0.447159i	0.0248218	−	0.0176755i
$641$	4.68830	+	3.68692i	0.185177	+	0.145625i	0.706444	−	0.707769i	$-0.250298\pi$
$641$	4.68830	+	3.68692i	0.185177	+	0.145625i	−0.521267	+	0.853393i	$0.674541\pi$
$642$	2.24306	+	13.7781i	0.0885263	+	0.543777i
$643$		−	22.9687i		−	0.905798i	−0.891562	−	0.452899i	$-0.850390\pi$
$643$		−	22.9687i		−	0.905798i	0.891562	−	0.452899i	$-0.149610\pi$
$644$	−7.84456	−	3.27176i	−0.309119	−	0.128925i
$645$	−2.39773	−	3.23806i	−0.0944105	−	0.127499i
$646$	−29.0654	−	14.9842i	−1.14356	−	0.589547i
$647$	−19.2752	+	24.5104i	−0.757785	+	0.963602i	−0.999978	−	0.00662618i	$-0.997891\pi$
$647$	−19.2752	+	24.5104i	−0.757785	+	0.963602i	0.242193	+	0.970228i	$0.422133\pi$
$648$	−27.7029	+	0.740790i	−1.08827	+	0.0291010i
$649$	7.04842	−	7.39217i	0.276675	−	0.290168i
$650$	2.17240	−	0.992100i	0.0852084	−	0.0389134i
$651$	19.9977	+	22.0648i	0.783771	+	0.864788i
$652$	−0.841237	−	5.85093i	−0.0329454	−	0.229140i
$653$	−32.9290	+	7.98848i	−1.28861	+	0.312614i	−0.820800	−	0.571215i	$-0.806472\pi$
$653$	−32.9290	+	7.98848i	−1.28861	+	0.312614i	−0.467810	+	0.883829i	$0.654957\pi$
$654$	10.3505	+	7.08445i	0.404738	+	0.277024i
$655$	−2.36322	−	4.58400i	−0.0923385	−	0.179112i
$656$	3.22436	+	0.153595i	0.125890	+	0.00599688i
$657$	4.81400	+	7.66539i	0.187812	+	0.299055i
$658$	−7.72015	+	19.4934i	−0.300963	+	0.759932i
$659$	−1.37540	−	9.56608i	−0.0535778	−	0.372642i	−0.998916	−	0.0465501i	$-0.985177\pi$
$659$	−1.37540	−	9.56608i	−0.0535778	−	0.372642i	0.945338	−	0.326092i	$-0.105732\pi$
$660$	−0.442259	−	1.40880i	−0.0172149	−	0.0548376i
$661$	−0.891227	+	9.33336i	−0.0346647	+	0.363025i	0.961451	+	0.274975i	$0.0886697\pi$
$661$	−0.891227	+	9.33336i	−0.0346647	+	0.363025i	−0.996116	+	0.0880502i	$0.971936\pi$
$662$	13.7758	+	3.34198i	0.535414	+	0.129890i
$663$	−2.53643	+	2.28172i	−0.0985069	+	0.0886146i
$664$	−46.4586	−	6.67974i	−1.80294	−	0.259224i
$665$	4.08510	−	2.12525i	0.158413	−	0.0824135i
$666$	10.6937	−	35.0620i	0.414372	−	1.35862i
$667$	3.45148	−	21.2724i	0.133642	−	0.823669i
$668$	−2.26851	−	1.30972i	−0.0877712	−	0.0506747i
$669$	21.1503	+	25.8899i	0.817719	+	1.00096i
$670$	4.11127	−	1.64590i	0.158832	−	0.0635868i
$671$	−27.1983	−	12.4210i	−1.04998	−	0.479509i
$672$	5.01028	+	15.7552i	0.193276	+	0.607770i
$673$	7.61121	+	16.6662i	0.293390	+	0.642436i	0.997724	−	0.0674339i	$-0.0214812\pi$
$673$	7.61121	+	16.6662i	0.293390	+	0.642436i	−0.704333	+	0.709869i	$0.748754\pi$
$674$	−7.71036	+	22.2776i	−0.296992	+	0.858102i
$675$	−1.00776	+	25.5325i	−0.0387886	+	0.982745i
$676$	−6.21639	+	5.92732i	−0.239092	+	0.227974i
$677$	12.3279	+	2.37601i	0.473801	+	0.0913176i	0.420561	−	0.907264i	$-0.361833\pi$
$677$	12.3279	+	2.37601i	0.473801	+	0.0913176i	0.0532395	+	0.998582i	$0.483045\pi$
$678$	−1.86043	−	28.0691i	−0.0714493	−	1.07799i
$679$	2.17405	−	15.5299i	0.0834324	−	0.595981i
$680$	3.12571	+	2.70845i	0.119866	+	0.103864i
$681$	10.8114	+	9.02188i	0.414293	+	0.345719i
$682$	−12.3456	+	30.8379i	−0.472739	+	1.18084i
$683$	−0.0108668	−	0.0563822i	−0.000415806	−	0.00215741i	0.981720	−	0.190330i	$-0.0609557\pi$
$683$	−0.0108668	−	0.0563822i	−0.000415806	−	0.00215741i	−0.982136	+	0.188172i	$0.939744\pi$
$684$	−9.65268	+	7.42929i	−0.369079	+	0.284066i
$685$	−3.09533	+	0.908871i	−0.118267	+	0.0347262i
$686$	−21.0175	−	3.80856i	−0.802451	−	0.145412i
$687$	−13.3860	+	7.21892i	−0.510708	+	0.275419i
$688$	−8.20995	+	15.9251i	−0.313001	+	0.607138i
$689$	0.108321	−	0.187617i	0.00412670	−	0.00714765i
$690$	0.773606	−	2.63987i	0.0294507	−	0.100498i
$691$	8.11783	+	14.0605i	0.308817	+	0.534886i	0.978104	−	0.208118i	$-0.0667337\pi$
$691$	8.11783	+	14.0605i	0.308817	+	0.534886i	−0.669287	+	0.743004i	$0.733400\pi$
$692$	8.91421	+	13.8708i	0.338868	+	0.527288i
$693$	−35.1788	−	0.236439i	−1.33633	−	0.00898158i
$694$	1.12883	−	2.47180i	0.0428499	−	0.0938283i
$695$	2.74239	+	2.61486i	0.104025	+	0.0991875i
$696$	−20.5288	+	12.3665i	−0.778140	+	0.468752i
$697$	1.29213	+	6.70420i	0.0489429	+	0.253940i
$698$	11.3474	+	14.4294i	0.429505	+	0.546161i
$699$	−3.94040	−	10.7353i	−0.149040	−	0.406047i
$700$	8.46186	−	2.08611i	0.319828	−	0.0788477i
$701$	−29.7859	−	19.1422i	−1.12500	−	0.722992i	−0.160487	−	0.987038i	$-0.551307\pi$
$701$	−29.7859	−	19.1422i	−1.12500	−	0.722992i	−0.964510	+	0.264046i	$0.914943\pi$
$702$	−0.730669	−	2.41542i	−0.0275773	−	0.0911643i
$703$	−21.0033	−	60.6850i	−0.792154	−	2.28878i
$704$	−27.5354	+	26.2549i	−1.03778	+	0.989520i
$705$	3.29622	+	0.901674i	0.124143	+	0.0339590i
$706$	−14.9007	−	17.1963i	−0.560794	−	0.647191i
$707$	−9.07679	−	25.9140i	−0.341368	−	0.974598i
$708$	2.13202	+	1.61343i	0.0801263	+	0.0606366i
$709$	2.51781	+	26.3677i	0.0945582	+	0.990258i	0.910883	+	0.412665i	$0.135402\pi$
$709$	2.51781	+	26.3677i	0.0945582	+	0.990258i	−0.816325	+	0.577593i	$0.803992\pi$
$710$	0.625404	+	0.491823i	0.0234710	+	0.0184578i
$711$	−12.0657	+	47.5642i	−0.452500	+	1.78380i
$712$	25.0463	−	14.4605i	0.938650	−	0.541930i
$713$	25.7079	−	17.6160i	0.962768	−	0.659723i
$714$	21.1295	−	12.8356i	0.790753	−	0.480359i
$715$	0.450838	−	0.289736i	0.0168604	−	0.0108355i
$716$	4.09198	+	10.2213i	0.152924	+	0.381987i
$717$	1.81394	−	5.57407i	0.0677428	−	0.208168i
$718$	−2.00227	−	0.485746i	−0.0747242	−	0.0181279i
$719$	34.3772	+	24.4799i	1.28205	+	0.912945i	0.998935	−	0.0461401i	$-0.0146921\pi$
$719$	34.3772	+	24.4799i	1.28205	+	0.912945i	0.283117	+	0.959085i	$0.408631\pi$
$720$	−1.74112	+	0.773295i	−0.0648879	+	0.0288190i
$721$	18.6800	+	9.54263i	0.695681	+	0.355386i
$722$	5.76420	−	19.6311i	0.214521	−	0.730593i
$723$	2.86985	+	5.98710i	0.106731	+	0.222663i
$724$	1.12641	+	2.18494i	0.0418628	+	0.0812025i
$725$	10.1257	+	19.6410i	0.376058	+	0.729450i
$726$	−7.46419	−	15.5718i	−0.277022	−	0.577925i
$727$	2.39096	−	8.14286i	0.0886758	−	0.302002i	−0.903199	−	0.429223i	$-0.858788\pi$
$727$	2.39096	−	8.14286i	0.0886758	−	0.302002i	0.991874	+	0.127221i	$0.0406057\pi$
$728$	−2.87904	+	1.86538i	−0.106704	+	0.0691357i
$729$	26.5918	+	4.67694i	0.984883	+	0.173220i
$730$	0.813930	+	0.579597i	0.0301249	+	0.0214518i
$731$	−36.8277	−	8.93429i	−1.36212	−	0.330447i
$732$	2.42208	−	7.44283i	0.0895226	−	0.275095i
$733$	−7.67351	−	19.1675i	−0.283427	−	0.707967i	−0.999946	−	0.0103994i	$-0.996690\pi$
$733$	−7.67351	−	19.1675i	−0.283427	−	0.707967i	0.716519	−	0.697568i	$-0.245735\pi$
$734$	−25.1538	+	16.1653i	−0.928442	+	0.596674i
$735$	−0.240696	+	3.47309i	−0.00887821	+	0.128107i
$736$	17.0457	−	2.96725i	0.628313	−	0.109374i
$737$	−51.3286	+	29.6346i	−1.89071	+	1.09160i
$738$	−4.89508	−	1.24175i	−0.180190	−	0.0457094i
$739$	−0.266234	−	0.209369i	−0.00979359	−	0.00770177i	0.613250	−	0.789889i	$-0.289862\pi$
$739$	−0.266234	−	0.209369i	−0.00979359	−	0.00770177i	−0.623044	+	0.782187i	$0.714104\pi$
$740$	0.193704	+	2.02856i	0.00712069	+	0.0745713i
$741$	−3.52520	−	2.66774i	−0.129501	−	0.0980017i
$742$	−1.02364	+	1.19024i	−0.0375790	+	0.0436952i
$743$	21.6070	+	24.9358i	0.792684	+	0.914807i	0.997956	−	0.0638984i	$-0.0203534\pi$
$743$	21.6070	+	24.9358i	0.792684	+	0.914807i	−0.205272	+	0.978705i	$0.565808\pi$
$744$	−33.4289	−	9.14442i	−1.22556	−	0.335251i
$745$	−1.53784	+	1.46633i	−0.0563422	+	0.0537222i
$746$	3.36350	+	9.71818i	0.123146	+	0.355808i
$747$	43.0557	+	15.4066i	1.57533	+	0.563697i
$748$	−11.6833	−	7.50837i	−0.427182	−	0.274533i
$749$	−17.9513	+	4.42555i	−0.655925	+	0.161706i
$750$	1.96016	+	5.34032i	0.0715751	+	0.195001i
$751$	20.1315	+	25.5993i	0.734608	+	0.934130i	0.999546	−	0.0301355i	$-0.00959389\pi$
$751$	20.1315	+	25.5993i	0.734608	+	0.934130i	−0.264938	+	0.964265i	$0.585351\pi$
$752$	−2.87587	−	14.9214i	−0.104872	−	0.544129i
$753$	1.14837	−	0.691778i	0.0418489	−	0.0252098i
$754$	−1.57942	−	1.50598i	−0.0575191	−	0.0548444i
$755$	1.53372	−	3.35837i	0.0558176	−	0.122224i
$756$	−0.984052	−	9.15625i	−0.0357896	−	0.333009i
$757$	−25.1349	−	39.1107i	−0.913543	−	1.42150i	−0.906818	−	0.421523i	$-0.861496\pi$
$757$	−25.1349	−	39.1107i	−0.913543	−	1.42150i	−0.00672556	−	0.999977i	$-0.502141\pi$
$758$	−17.2173	−	29.8212i	−0.625360	−	1.08315i
$759$	−5.22014	+	36.4448i	−0.189479	+	1.32286i
$760$	−2.67963	+	4.64125i	−0.0972003	+	0.168356i
$761$	0.204442	−	0.396562i	0.00741101	−	0.0143753i	−0.885101	−	0.465399i	$-0.845911\pi$
$761$	0.204442	−	0.396562i	0.00741101	−	0.0143753i	0.892512	+	0.451024i	$0.148941\pi$
$762$	−11.5636	+	6.23611i	−0.418904	+	0.225910i
$763$	−8.25279	+	14.4176i	−0.298771	+	0.521951i
$764$	−2.15068	+	0.631496i	−0.0778088	+	0.0228467i
$765$	−2.45771	−	3.19324i	−0.0888589	−	0.115452i
$766$	−6.24871	−	32.4214i	−0.225775	−	1.17143i
$767$	−0.360658	+	0.900881i	−0.0130226	+	0.0325289i
$768$	−18.7133	−	15.6159i	−0.675258	−	0.563490i
$769$	18.0063	+	15.6025i	0.649322	+	0.562641i	0.916017	−	0.401140i	$-0.131386\pi$
$769$	18.0063	+	15.6025i	0.649322	+	0.562641i	−0.266694	+	0.963781i	$0.585931\pi$
$770$	−3.59989	+	1.45670i	−0.129731	+	0.0524960i
$771$	2.58605	+	39.0170i	0.0931344	+	1.40516i
$772$	−0.516722	−	0.0995901i	−0.0185972	−	0.00358433i
$773$	12.9600	−	12.3573i	0.466137	−	0.444461i	−0.420248	−	0.907409i	$-0.638057\pi$
$773$	12.9600	−	12.3573i	0.466137	−	0.444461i	0.886385	+	0.462948i	$0.153208\pi$
$774$	17.5561	−	21.8513i	0.631040	−	0.785429i
$775$	−10.4516	+	30.1978i	−0.375431	+	1.08474i
$776$	7.58145	+	16.6011i	0.272158	+	0.595943i
$777$	47.4249	+	10.3914i	1.70136	+	0.372790i
$778$	14.5454	+	6.64268i	0.521479	+	0.238152i
$779$	−8.21336	+	3.28813i	−0.294274	+	0.117810i
$780$	0.0887531	+	0.108642i	0.00317787	+	0.00389000i
$781$	−9.22173	−	5.32417i	−0.329979	−	0.190514i
$782$	−10.3216	−	23.7252i	−0.369098	−	0.848412i
$783$	22.0023	−	7.81644i	0.786296	−	0.279337i
$784$	14.3291	−	5.86028i	0.511752	−	0.209296i
$785$	−4.55607	−	0.655064i	−0.162613	−	0.0233802i
$786$	26.6739	−	23.9953i	0.951428	−	0.855884i
$787$	−24.0131	−	5.82552i	−0.855976	−	0.207657i	−0.216323	−	0.976322i	$-0.569407\pi$
$787$	−24.0131	−	5.82552i	−0.855976	−	0.207657i	−0.639652	+	0.768664i	$0.720922\pi$
$788$	−0.888511	+	9.30491i	−0.0316519	+	0.331474i
$789$	8.31291	+	26.4805i	0.295947	+	0.942732i
$790$	0.770902	+	5.36174i	0.0274274	+	0.190762i
$791$	36.8588	−	5.43922i	1.31055	−	0.193396i
$792$	34.6725	−	21.7749i	1.23203	−	0.773737i
$793$	2.83751	+	0.135167i	0.100763	+	0.00479994i
$794$	−3.29453	−	6.39049i	−0.116918	−	0.226790i
$795$	0.211151	+	0.144523i	0.00748875	+	0.00512569i
$796$	3.11094	−	0.754706i	0.110264	−	0.0267498i
$797$	−0.942859	−	6.55773i	−0.0333978	−	0.232287i	0.966285	−	0.257475i	$-0.0828905\pi$
$797$	−0.942859	−	6.55773i	−0.0333978	−	0.232287i	−0.999683	+	0.0251884i	$0.991981\pi$
$798$	21.5132	+	23.7369i	0.761558	+	0.840279i
$799$	29.2367	−	13.3520i	1.03432	−	0.472359i
$800$	−12.2428	+	12.8399i	−0.432848	+	0.453958i
$801$	−26.7221	+	8.93754i	−0.944180	+	0.315793i
$802$	−4.60291	+	5.85308i	−0.162535	+	0.206680i
$803$	−11.8864	−	6.12786i	−0.419461	−	0.216247i
$804$	−9.23281	−	12.4686i	−0.325616	−	0.439735i
$805$	3.56734	+	0.740749i	0.125732	+	0.0261080i
$806$		−	3.15587i		−	0.111161i
$807$	−7.52718	−	46.2361i	−0.264969	−	1.62759i
$808$	25.1191	+	19.7539i	0.883687	+	0.694939i
$809$	−40.9179	+	29.1375i	−1.43860	+	1.02442i	−0.447073	+	0.894498i	$0.647534\pi$
$809$	−40.9179	+	29.1375i	−1.43860	+	1.02442i	−0.991524	+	0.129923i	$0.958527\pi$
$810$	2.91052	−	0.642095i	0.102265	−	0.0225609i
$811$	−20.7846	−	45.5119i	−0.729846	−	1.59814i	−0.799570	−	0.600573i	$-0.794939\pi$
$811$	−20.7846	−	45.5119i	−0.729846	−	1.59814i	0.0697240	−	0.997566i	$-0.477788\pi$
$812$	−4.64354	−	6.46998i	−0.162956	−	0.227052i
$813$	−16.7970	−	16.9732i	−0.589097	−	0.595275i
$814$	12.7679	+	52.6299i	0.447514	+	1.84468i
$815$	0.828750	+	2.39452i	0.0290299	+	0.0838763i
$816$	−7.91334	+	16.0764i	−0.277022	+	0.562786i
$817$	2.33651	−	49.0493i	0.0817441	−	1.71602i
$818$	11.4778	+	9.94561i	0.401313	+	0.347740i
$819$	3.11116	−	1.22132i	0.108713	−	0.0426765i
$820$	0.277886	−	0.0399540i	0.00970420	−	0.00139525i
$821$	26.0441	+	9.01396i	0.908946	+	0.314589i	0.741234	−	0.671247i	$-0.234241\pi$
$821$	26.0441	+	9.01396i	0.908946	+	0.314589i	0.167712	+	0.985836i	$0.446362\pi$
$822$	−11.5806	−	19.2242i	−0.403921	−	0.670520i
$823$	−5.71159	+	23.5435i	−0.199094	+	0.820675i	0.781385	+	0.624049i	$0.214514\pi$
$823$	−5.71159	+	23.5435i	−0.199094	+	0.820675i	−0.980479	+	0.196626i	$0.937002\pi$
$824$	−24.3022	+	2.32058i	−0.846609	+	0.0808413i
$825$	−17.9191	−	33.2273i	−0.623863	−	1.15683i
$826$	3.77973	−	5.92966i	0.131514	−	0.206319i
$827$	39.7940			1.38377			0.691886	−	0.722006i	$-0.256780\pi$
$827$	39.7940			1.38377			0.691886	+	0.722006i	$0.256780\pi$
$828$	−9.63362	−	0.274471i	−0.334791	−	0.00953853i
$829$	8.19746	−	14.1984i	0.284710	−	0.493131i	−0.687829	−	0.725873i	$-0.741436\pi$
$829$	8.19746	−	14.1984i	0.284710	−	0.493131i	0.972539	+	0.232741i	$0.0747695\pi$
$830$	5.04229	−	0.240194i	0.175020	−	0.00833725i
$831$	−12.2219	+	19.8179i	−0.423972	+	0.687475i
$832$	1.50158	−	3.28800i	0.0520579	−	0.113991i
$833$	19.1910	+	26.5309i	0.664928	+	0.919240i
$834$	−12.7540	+	23.0703i	−0.441636	+	0.798860i
$835$	1.06111	+	0.367253i	0.0367212	+	0.0127093i
$836$	6.68835	−	16.7067i	0.231321	−	0.577813i
$837$	30.1373	+	15.2272i	1.04170	+	0.526330i
$838$	−2.33265	+	12.1030i	−0.0805802	+	0.418090i
$839$	10.0737	+	6.47396i	0.347782	+	0.223506i	0.702856	−	0.711332i	$-0.251908\pi$
$839$	10.0737	+	6.47396i	0.347782	+	0.223506i	−0.355074	+	0.934838i	$0.615544\pi$
$840$	−1.93645	−	3.55907i	−0.0668140	−	0.122800i
$841$	−5.76772	+	6.65631i	−0.198887	+	0.229528i
$842$	5.40185	+	22.2667i	0.186160	+	0.767363i
$843$	39.3938	−	10.3356i	1.35680	−	0.355977i
$844$	−4.58907	+	0.884472i	−0.157962	+	0.0304448i
$845$	2.13574	−	2.99922i	0.0734716	−	0.103176i
$846$	−0.248024	+	23.7725i	−0.00852723	+	0.817314i
$847$	19.7645	−	11.5091i	0.679116	−	0.395456i
$848$	0.161928	−	1.12623i	0.00556063	−	0.0386750i
$849$	3.91216	+	24.0306i	0.134265	+	0.824728i
$850$	22.9755	+	13.2649i	0.788053	+	0.454983i
$851$	17.4821	−	47.7071i	0.599277	−	1.63538i
$852$	1.11062	−	2.55660i	0.0380492	−	0.0875878i
$853$	20.1805	−	12.9692i	0.690966	−	0.444057i	−0.147463	−	0.989068i	$-0.547111\pi$
$853$	20.1805	−	12.9692i	0.690966	−	0.444057i	0.838429	+	0.545010i	$0.183474\pi$
$854$	−20.0228	−	4.77884i	−0.685165	−	0.163529i
$855$	3.46028	−	3.91020i	0.118339	−	0.133726i
$856$	14.8489	−	15.5731i	0.507525	−	0.532277i
$857$	4.89652	−	51.2787i	0.167262	−	1.75165i	−0.389549	−	0.921006i	$-0.627369\pi$
$857$	4.89652	−	51.2787i	0.167262	−	1.75165i	0.556810	−	0.830640i	$-0.312025\pi$
$858$	2.74561	+	2.52221i	0.0937336	+	0.0861068i
$859$	0.934124	−	0.734603i	0.0318719	−	0.0250643i	−0.602096	−	0.798424i	$-0.705668\pi$
$859$	0.934124	−	0.734603i	0.0318719	−	0.0250643i	0.633968	+	0.773359i	$0.281425\pi$
$860$	−0.439007	+	1.49512i	−0.0149700	+	0.0509832i
$861$	1.11911	−	6.59440i	0.0381391	−	0.224737i
$862$	−23.5565	+	36.6547i	−0.802339	+	1.24846i
$863$	−23.6139	−	1.12487i	−0.803826	−	0.0382909i	−0.358353	−	0.933586i	$-0.616661\pi$
$863$	−23.6139	−	1.12487i	−0.803826	−	0.0382909i	−0.445473	+	0.895295i	$0.646964\pi$
$864$	11.7079	+	14.6406i	0.398311	+	0.498084i
$865$	−4.87743	−	5.11530i	−0.165838	−	0.173925i
$866$	−20.7690	+	16.3329i	−0.705758	+	0.555014i
$867$	−8.25184	−	1.84021i	−0.280247	−	0.0624969i
$868$	2.13754	−	11.3165i	0.0725527	−	0.384106i
$869$	−20.4248	−	69.5606i	−0.692866	−	2.35968i
$870$	1.91626	−	1.72383i	0.0649673	−	0.0584432i
$871$	3.48083	−	4.42624i	0.117943	−	0.149977i
$872$	−0.919952	−	19.3122i	−0.0311535	−	0.653992i
$873$	−4.01151	−	17.3225i	−0.135769	−	0.586278i
$874$	27.6561	−	18.9509i	0.935482	−	0.641025i
$875$	−6.84191	+	3.15534i	−0.231299	+	0.106670i
$876$	1.24044	−	3.27351i	0.0419107	−	0.110602i
$877$	4.95782	−	1.98481i	0.167414	−	0.0670224i	−0.286442	−	0.958098i	$-0.592472\pi$
$877$	4.95782	−	1.98481i	0.167414	−	0.0670224i	0.453856	+	0.891075i	$0.350048\pi$
$878$	4.50637	−	3.20897i	0.152083	−	0.108297i
$879$	−1.44425	−	3.42187i	−0.0487135	−	0.115417i
$880$	1.63265	−	2.29274i	0.0550367	−	0.0772882i
$881$	−8.35655	−	9.64397i	−0.281539	−	0.324914i	0.597312	−	0.802009i	$-0.296235\pi$
$881$	−8.35655	−	9.64397i	−0.281539	−	0.324914i	−0.878852	+	0.477095i	$0.841690\pi$
$882$	−23.7957	+	4.51203i	−0.801243	+	0.151928i
$883$	−29.0280	−	8.52340i	−0.976871	−	0.286835i	−0.245939	−	0.969285i	$-0.579096\pi$
$883$	−29.0280	−	8.52340i	−0.976871	−	0.286835i	−0.730932	+	0.682450i	$0.760914\pi$
$884$	1.29560	+	0.249707i	0.0435758	+	0.00839854i
$885$	−1.02830	−	0.506163i	−0.0345658	−	0.0170145i
$886$	−5.60848	+	2.89137i	−0.188421	+	0.0971375i
$887$	10.3376	−	53.6363i	0.347101	−	1.80093i	−0.218043	−	0.975939i	$-0.569967\pi$
$887$	10.3376	−	53.6363i	0.347101	−	1.80093i	0.565144	−	0.824992i	$-0.308820\pi$
$888$	−53.0435	+	19.4696i	−1.78002	+	0.653358i
$889$	−9.46178	−	14.6034i	−0.317338	−	0.489781i
$890$	−2.35072	+	2.03691i	−0.0787964	+	0.0682774i
$891$	−37.3338	+	14.0497i	−1.25073	+	0.470683i
$892$	3.04814	−	12.5646i	0.102059	−	0.420694i
$893$	24.1583	+	33.9256i	0.808428	+	1.13528i
$894$	−12.5821	−	7.75950i	−0.420809	−	0.259517i
$895$	−2.55159	−	3.97035i	−0.0852903	−	0.132714i
$896$	−4.09864	+	5.80119i	−0.136926	+	0.193804i
$897$	−0.826458	−	3.39880i	−0.0275946	−	0.113483i
$898$	3.46157	+	5.99561i	0.115514	+	0.200076i
$899$	29.1673	−	1.38941i	0.972784	−	0.0463394i
$900$	8.10910	−	5.64790i	0.270303	−	0.188263i
$901$	2.39570	−	0.228762i	0.0798123	−	0.00762115i
$902$	7.15885	−	2.10203i	0.238364	−	0.0699899i
$903$	30.7137	+	20.8550i	1.02209	+	0.694012i
$904$	−32.7707	+	28.3960i	−1.08994	+	0.944436i
$905$	−0.651381	−	0.828299i	−0.0216527	−	0.0275336i
$906$	25.3065	+	4.39137i	0.840753	+	0.145893i
$907$	−9.55555	+	3.30721i	−0.317287	+	0.109814i	−0.481070	−	0.876682i	$-0.659752\pi$
$907$	−9.55555	+	3.30721i	−0.317287	+	0.109814i	0.163783	+	0.986496i	$0.447630\pi$
$908$	0.259120	−	5.43960i	0.00859920	−	0.180519i
$909$	−20.1419	−	23.7410i	−0.668065	−	0.787440i
$910$	0.266077	−	0.255596i	0.00882038	−	0.00847294i
$911$	11.3657	+	3.33728i	0.376563	+	0.110569i	0.464537	−	0.885554i	$-0.346221\pi$
$911$	11.3657	+	3.33728i	0.376563	+	0.110569i	−0.0879735	+	0.996123i	$0.528039\pi$
$912$	−22.3957	−	6.12629i	−0.741595	−	0.202862i
$913$	−66.3396	+	12.7859i	−2.19552	+	0.423152i
$914$	−6.20821	−	0.592812i	−0.205349	−	0.0196085i
$915$	−0.415695	+	3.32932i	−0.0137424	+	0.110064i
$916$	5.35022	+	2.44336i	0.176776	+	0.0807310i
$917$	34.5131	+	32.6645i	1.13972	+	1.07868i
$918$	17.1486	−	22.1758i	0.565988	−	0.731911i
$919$	−9.91174	+	5.72254i	−0.326958	+	0.188769i	−0.654490	−	0.756071i	$-0.727117\pi$
$919$	−9.91174	+	5.72254i	−0.326958	+	0.188769i	0.327532	+	0.944840i	$0.393783\pi$
$920$	−3.96439	+	1.50466i	−0.130702	+	0.0496072i
$921$	−5.67130	−	49.6277i	−0.186876	−	1.63529i
$922$	−8.70344	−	4.48693i	−0.286632	−	0.147769i
$923$	1.00137	+	0.143975i	0.0329604	+	0.00473899i
$924$	8.13701	+	10.9039i	0.267688	+	0.358713i
$925$	14.6780	+	49.9885i	0.482608	+	1.64361i
$926$	−5.16180	−	3.67570i	−0.169627	−	0.120791i
$927$	23.6523	+	2.50779i	0.776845	+	0.0823667i
$928$	15.0504	+	6.02527i	0.494053	+	0.197789i
$929$	−18.4880	+	4.48515i	−0.606572	+	0.147153i	−0.527270	−	0.849698i	$-0.676784\pi$
$929$	−18.4880	+	4.48515i	−0.606572	+	0.147153i	−0.0793023	+	0.996851i	$0.525269\pi$
$930$	3.71644	+	0.285298i	0.121867	+	0.00935528i
$931$	−29.0509	+	30.9241i	−0.952105	+	1.01350i
$932$	−2.39105	+	3.72055i	−0.0783215	+	0.121871i
$933$	5.78605	+	12.0709i	0.189427	+	0.395184i
$934$	6.90212	+	7.23873i	0.225844	+	0.236859i
$935$	5.52681	+	2.21260i	0.180746	+	0.0723598i
$936$	−2.28927	+	3.14487i	−0.0748272	+	0.102793i
$937$	20.4493	−	9.33889i	0.668050	−	0.305088i	−0.0523683	−	0.998628i	$-0.516677\pi$
$937$	20.4493	−	9.33889i	0.668050	−	0.305088i	0.720419	+	0.693539i	$0.243950\pi$
$938$	−30.7385	+	26.8354i	−1.00365	+	0.876208i
$939$	−27.9063	+	5.91836i	−0.910688	+	0.193138i
$940$	−0.491195	−	1.22695i	−0.0160210	−	0.0400186i
$941$	1.57688	+	33.1028i	0.0514048	+	1.07912i	0.866304	+	0.499517i	$0.166489\pi$
$941$	1.57688	+	33.1028i	0.0514048	+	1.07912i	−0.814899	+	0.579602i	$0.803208\pi$
$942$	−3.63569	−	31.8147i	−0.118457	−	1.03658i
$943$	−6.67972	−	2.09302i	−0.217521	−	0.0681581i
$944$			5.09655i			0.165879i
$945$	1.15701	+	3.77420i	0.0376375	+	0.122775i
$946$	−5.89355	+	40.9905i	−0.191616	+	1.33272i
$947$	−4.10113	−	42.9490i	−0.133269	−	1.39565i	−0.776565	−	0.630037i	$-0.783040\pi$
$947$	−4.10113	−	42.9490i	−0.133269	−	1.39565i	0.643296	−	0.765617i	$-0.277566\pi$
$948$	17.4841	−	7.37945i	0.567858	−	0.239673i
$949$	1.26477	+	0.120771i	0.0410562	+	0.00392039i
$950$	−11.2436	+	32.4863i	−0.364791	+	1.05399i
$951$	37.2052	−	36.8191i	1.20646	−	1.19394i
$952$	−35.4311	−	14.0321i	−1.14833	−	0.454783i
$953$	−10.8893	+	12.5669i	−0.352739	+	0.407083i	−0.904194	−	0.427122i	$-0.859527\pi$
$953$	−10.8893	+	12.5669i	−0.352739	+	0.407083i	0.551455	+	0.834205i	$0.314073\pi$
$954$	−0.599723	+	1.67601i	−0.0194168	+	0.0542627i
$955$	0.854029	−	0.440282i	0.0276357	−	0.0142472i
$956$	−2.14231	+	0.741461i	−0.0692873	+	0.0239806i
$957$	−22.1021	+	26.4860i	−0.714459	+	0.856172i
$958$	28.3869	−	4.08142i	0.917138	−	0.131865i
$959$	24.1488	−	17.3317i	0.779805	−	0.559671i
$960$	3.73629	+	2.06554i	0.120588	+	0.0666652i
$961$	8.12523	+	7.74739i	0.262104	+	0.249916i
$962$	−2.98452	−	4.19118i	−0.0962249	−	0.135129i
$963$	−17.2029	+	11.9816i	−0.554356	+	0.386103i
$964$	1.17660	−	2.28228i	0.0378956	−	0.0735073i
$965$	0.225577			0.00726158
$966$	1.31351	+	25.3127i	0.0422616	+	0.814424i
$967$	−4.73146			−0.152154			−0.0760768	−	0.997102i	$-0.524239\pi$
$967$	−4.73146			−0.152154			−0.0760768	+	0.997102i	$0.524239\pi$
$968$	−12.1971	+	23.6592i	−0.392031	+	0.760434i
$969$	1.42478	−	49.0889i	0.0457705	−	1.57696i
$970$	−1.13855	−	1.59887i	−0.0365566	−	0.0513365i
$971$	−28.9470	−	27.6010i	−0.928955	−	0.885757i	0.0647368	−	0.997902i	$-0.479379\pi$
$971$	−28.9470	−	27.6010i	−0.928955	−	0.885757i	−0.993692	+	0.112146i	$0.964228\pi$
$972$	−4.76361	−	9.29211i	−0.152793	−	0.298045i
$973$	−31.8126	−	14.3859i	−1.01987	−	0.461190i
$974$	6.16394	−	0.886241i	0.197506	−	0.0283970i
$975$	2.75376	+	2.29796i	0.0881908	+	0.0735935i
$976$	14.0991	−	4.87975i	0.451301	−	0.156197i
$977$	30.5218	−	15.7351i	0.976477	−	0.503409i	0.105334	−	0.994437i	$-0.466409\pi$
$977$	30.5218	−	15.7351i	0.976477	−	0.503409i	0.871144	+	0.491028i	$0.163379\pi$
$978$	−14.6498	+	9.80423i	−0.468449	+	0.313505i
$979$	27.2612	−	31.4611i	0.871272	−	1.00550i
$980$	1.12723	−	0.736311i	0.0360082	−	0.0235206i
$981$	−2.87513	+	18.6161i	−0.0917958	+	0.594366i
$982$	−6.72692	+	19.4361i	−0.214664	+	0.620232i
$983$	−53.5338	−	5.11186i	−1.70746	−	0.163043i	−0.804844	−	0.593486i	$-0.797751\pi$
$983$	−53.5338	−	5.11186i	−1.70746	−	0.163043i	−0.902618	+	0.430443i	$0.858357\pi$
$984$	3.02699	+	7.17184i	0.0964969	+	0.228630i
$985$	−0.380873	−	3.98869i	−0.0121356	−	0.127090i
$986$	3.45009	−	23.9959i	0.109873	−	0.764185i
$987$	−31.4105	+	2.19903i	−0.999808	+	0.0699959i
$988$			1.70972i			0.0543934i
$989$	25.9689	−	28.8988i	0.825762	−	0.918929i
$990$	−3.21843	+	3.00529i	−0.102288	+	0.0955144i
$991$	0.473511	+	9.94023i	0.0150416	+	0.315762i	0.993832	+	0.110897i	$0.0353724\pi$
$991$	0.473511	+	9.94023i	0.0150416	+	0.315762i	−0.978790	+	0.204865i	$0.934325\pi$
$992$	8.71317	+	21.7644i	0.276643	+	0.691022i
$993$	4.41665	+	20.8254i	0.140158	+	0.660875i
$994$	−6.93660	−	2.37198i	−0.220016	−	0.0752348i
$995$	−1.24823	+	0.570045i	−0.0395714	+	0.0180717i
$996$	−5.29700	−	16.8734i	−0.167842	−	0.534655i
$997$	16.1567	+	6.46818i	0.511689	+	0.204849i	0.613115	−	0.789994i	$-0.289916\pi$
$997$	16.1567	+	6.46818i	0.511689	+	0.204849i	−0.101426	+	0.994843i	$0.532340\pi$
$998$	33.7702	+	35.4172i	1.06898	+	1.12111i
$999$	54.4246	−	8.27838i	1.72192	−	0.261916i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.bc.a.11.19	✓	1200
3.2	odd	2	inner	483.2.bc.a.11.42	yes	1200
7.2	even	3	inner	483.2.bc.a.149.42	yes	1200
21.2	odd	6	inner	483.2.bc.a.149.19	yes	1200
23.21	odd	22	inner	483.2.bc.a.389.19	yes	1200
69.44	even	22	inner	483.2.bc.a.389.42	yes	1200
161.44	odd	66	inner	483.2.bc.a.44.42	yes	1200
483.44	even	66	inner	483.2.bc.a.44.19	yes	1200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.bc.a.11.19	✓	1200	1.1	even	1	trivial
483.2.bc.a.11.42	yes	1200	3.2	odd	2	inner
483.2.bc.a.44.19	yes	1200	483.44	even	66	inner
483.2.bc.a.44.42	yes	1200	161.44	odd	66	inner
483.2.bc.a.149.19	yes	1200	21.2	odd	6	inner
483.2.bc.a.149.42	yes	1200	7.2	even	3	inner
483.2.bc.a.389.19	yes	1200	23.21	odd	22	inner
483.2.bc.a.389.42	yes	1200	69.44	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.bc (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.528482 + 1.02511i) q^{2} +(-1.73132 - 0.0502508i) q^{3} +(0.388554 + 0.545647i) q^{4} +(-0.207815 - 0.198151i) q^{5} +(0.966484 - 1.74824i) q^{6} +(2.41072 + 1.09014i) q^{7} +(-3.04785 + 0.438215i) q^{8} +(2.99495 + 0.174001i) q^{9} +(0.312954 - 0.108314i) q^{10} +(-3.93951 + 2.03096i) q^{11} +(-0.645292 - 0.964216i) q^{12} +(0.275755 - 0.318239i) q^{13} +(-2.39154 + 1.89514i) q^{14} +(0.349838 + 0.353506i) q^{15} +(0.723339 - 2.08995i) q^{16} +(4.65656 + 0.444647i) q^{17} +(-1.76115 + 2.97820i) q^{18} +(0.576168 + 6.03390i) q^{19} +(0.0273734 - 0.190386i) q^{20} +(-4.11896 - 2.00853i) q^{21} -5.11176i q^{22} +(-2.66522 + 3.98705i) q^{23} +(5.29883 - 0.605534i) q^{24} +(-0.233986 - 4.91198i) q^{25} +(0.180498 + 0.450863i) q^{26} +(-5.17648 - 0.451749i) q^{27} +(0.341861 + 1.73898i) q^{28} +(-4.08752 + 1.86671i) q^{29} +(-0.547266 + 0.171801i) q^{30} +(-6.03274 - 2.41514i) q^{31} +(-2.48961 - 2.61103i) q^{32} +(6.92261 - 3.31828i) q^{33} +(-2.91672 + 4.53850i) q^{34} +(-0.284971 - 0.704236i) q^{35} +(1.06876 + 1.70179i) q^{36} +(-10.2958 + 2.49774i) q^{37} +(-6.48992 - 2.59817i) q^{38} +(-0.493413 + 0.537117i) q^{39} +(0.720223 + 0.512868i) q^{40} +(0.411214 + 1.40047i) q^{41} +(4.23576 - 3.16092i) q^{42} +(-8.01887 - 1.15294i) q^{43} +(-2.63890 - 1.36045i) q^{44} +(-0.587917 - 0.629613i) q^{45} +(-2.67865 - 4.83923i) q^{46} +(5.95056 - 3.43556i) q^{47} +(-1.35735 + 3.58203i) q^{48} +(4.62317 + 5.25607i) q^{49} +(5.15898 + 2.35603i) q^{50} +(-8.03965 - 1.00382i) q^{51} +(0.280792 + 0.0268124i) q^{52} +(0.505182 - 0.0973658i) q^{53} +(3.19877 - 5.06772i) q^{54} +(1.22113 + 0.358555i) q^{55} +(-7.82525 - 2.26618i) q^{56} +(-0.694324 - 10.4756i) q^{57} +(0.246596 - 5.17669i) q^{58} +(-2.17773 + 0.753720i) q^{59} +(-0.0569592 + 0.328244i) q^{60} +(4.17019 + 5.30282i) q^{61} +(5.66398 - 4.90787i) q^{62} +(7.03031 + 3.68439i) q^{63} +(8.23632 - 2.41840i) q^{64} +(-0.120366 + 0.0114935i) q^{65} +(-0.256870 + 8.85010i) q^{66} +(13.3572 - 0.636282i) q^{67} +(1.56670 + 2.71361i) q^{68} +(4.81471 - 6.76894i) q^{69} +(0.872522 + 0.0800487i) q^{70} +(1.29888 + 2.02110i) q^{71} +(-9.20442 + 0.782104i) q^{72} +(1.75016 + 2.45776i) q^{73} +(2.88070 - 11.8744i) q^{74} +(0.158275 + 8.51597i) q^{75} +(-3.06851 + 2.65888i) q^{76} +(-11.7111 + 0.601445i) q^{77} +(-0.289845 - 0.789659i) q^{78} +(-3.09556 + 16.0613i) q^{79} +(-0.564447 + 0.290993i) q^{80} +(8.93945 + 1.04225i) q^{81} +(-1.65295 - 0.318581i) q^{82} +(14.6256 + 4.29447i) q^{83} +(-0.504486 - 3.02792i) q^{84} +(-0.879595 - 1.01511i) q^{85} +(5.41971 - 7.61092i) q^{86} +(7.17062 - 3.02647i) q^{87} +(11.1170 - 7.91641i) q^{88} +(-8.71958 + 3.49080i) q^{89} +(0.956127 - 0.269942i) q^{90} +(1.01170 - 0.466572i) q^{91} +(-3.21111 + 0.0949141i) q^{92} +(10.3232 + 4.48454i) q^{93} +(0.377067 + 7.91561i) q^{94} +(1.07589 - 1.36810i) q^{95} +(4.17912 + 4.64564i) q^{96} +(-1.66982 - 5.68689i) q^{97} +(-7.83132 + 1.96153i) q^{98} +(-12.1520 + 5.39714i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1200 q - 9 q^{3} - 74 q^{4} - 20 q^{6} - 44 q^{7} - 13 q^{9} - 22 q^{10} - 25 q^{12} - 72 q^{13} - 44 q^{15} + 38 q^{16} - 45 q^{18} - 22 q^{19} + 44 q^{21} + 2 q^{24} + 18 q^{25} - 90 q^{27} - 44 q^{28}+ \cdots - 308 q^{99}+O(q^{100}) \) 1200 * q - 9 * q^3 - 74 * q^4 - 20 * q^6 - 44 * q^7 - 13 * q^9 - 22 * q^10 - 25 * q^12 - 72 * q^13 - 44 * q^15 + 38 * q^16 - 45 * q^18 - 22 * q^19 + 44 * q^21 + 2 * q^24 + 18 * q^25 - 90 * q^27 - 44 * q^28 - 55 * q^30 - 18 * q^31 - 11 * q^33 - 88 * q^34 - 108 * q^36 - 66 * q^37 + q^39 - 22 * q^40 - 22 * q^42 - 2 * q^46 - 228 * q^48 - 128 * q^49 - 11 * q^51 - 166 * q^52 + 35 * q^54 - 160 * q^55 - 44 * q^57 - 126 * q^58 - 11 * q^60 + 66 * q^61 + 33 * q^63 + 40 * q^64 + 22 * q^66 - 22 * q^67 - 24 * q^69 + 68 * q^70 - 149 * q^72 - 42 * q^73 + 123 * q^75 - 88 * q^76 - 108 * q^78 - 66 * q^79 - 81 * q^81 - 14 * q^82 + 44 * q^84 - 200 * q^85 + 75 * q^87 + 66 * q^88 + 16 * q^93 - 146 * q^94 + 5 * q^96 - 88 * q^97 - 308 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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