LMFDB - Embedded newform 363.2.e.n.124.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(124,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("363.124");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.e (of order $5$, degree $4$, not 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:	$2.89856959337$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	16.0.22502537891856000000000000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 7x^{14} + 45x^{12} + 287x^{10} + 1829x^{8} + 1148x^{6} + 720x^{4} + 448x^{2} + 256 $ x^16 + 7x^14 + 45x^12 + 287x^10 + 1829x^8 + 1148x^6 + 720x^4 + 448*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			124.4
Root			$2.04223 + 1.48377i$ of defining polynomial
Character	$\chi$	$=$	363.124
Dual form			363.2.e.n.202.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.04223 - 1.48377i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.35111 - 4.15829i) q^{4} +(1.91922 + 1.39439i) q^{5} +(2.04223 + 1.48377i) q^{6} +(-0.244830 + 0.753510i) q^{7} +(-1.85053 - 5.69534i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(2.04223 - 1.48377i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.35111 - 4.15829i) q^{4} +(1.91922 + 1.39439i) q^{5} +(2.04223 + 1.48377i) q^{6} +(-0.244830 + 0.753510i) q^{7} +(-1.85053 - 5.69534i) q^{8} +(-0.809017 + 0.587785i) q^{9} +5.98844 q^{10} +4.37228 q^{12} +(-3.32418 + 2.41516i) q^{13} +(0.618034 + 1.90211i) q^{14} +(-0.733075 + 2.25617i) q^{15} +(-5.15528 - 3.74553i) q^{16} +(-4.84475 - 3.51992i) q^{17} +(-0.780063 + 2.40079i) q^{18} +(-1.31530 - 4.04807i) q^{19} +(8.39135 - 6.09667i) q^{20} -0.792287 q^{21} +2.00000 q^{23} +(4.84475 - 3.51992i) q^{24} +(0.193976 + 0.596996i) q^{25} +(-3.20521 + 9.86463i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(2.80252 + 2.03615i) q^{28} +(0.780063 - 2.40079i) q^{29} +(1.85053 + 5.69534i) q^{30} +(-5.96430 + 4.33332i) q^{31} -4.10891 q^{32} -15.1168 q^{34} +(-1.52057 + 1.10476i) q^{35} +(1.35111 + 4.15829i) q^{36} +(1.54508 - 4.75528i) q^{37} +(-8.69253 - 6.31550i) q^{38} +(-3.32418 - 2.41516i) q^{39} +(4.38998 - 13.5110i) q^{40} +(1.75938 + 5.41483i) q^{41} +(-1.61803 + 1.17557i) q^{42} +6.63325 q^{43} -2.37228 q^{45} +(4.08446 - 2.96754i) q^{46} +(-0.387951 - 1.19399i) q^{47} +(1.96914 - 6.06040i) q^{48} +(5.15528 + 3.74553i) q^{49} +(1.28195 + 0.931389i) q^{50} +(1.85053 - 5.69534i) q^{51} +(5.55159 + 17.0860i) q^{52} +(-10.6117 + 7.70989i) q^{53} -2.52434 q^{54} +4.74456 q^{56} +(3.44349 - 2.50184i) q^{57} +(-1.96914 - 6.06040i) q^{58} +(-1.85410 + 5.70634i) q^{59} +(8.39135 + 6.09667i) q^{60} +(-2.16154 - 1.57045i) q^{61} +(-5.75085 + 17.6993i) q^{62} +(-0.244830 - 0.753510i) q^{63} +(1.91922 - 1.39439i) q^{64} -9.74749 q^{65} +16.1168 q^{67} +(-21.1826 + 15.3901i) q^{68} +(0.618034 + 1.90211i) q^{69} +(-1.46615 + 4.51235i) q^{70} +(-0.602364 - 0.437643i) q^{71} +(4.84475 + 3.51992i) q^{72} +(-2.29462 + 7.06210i) q^{73} +(-3.90032 - 12.0039i) q^{74} +(-0.507835 + 0.368964i) q^{75} -18.6101 q^{76} -10.3723 q^{78} +(4.72544 - 3.43323i) q^{79} +(-4.67136 - 14.3770i) q^{80} +(0.309017 - 0.951057i) q^{81} +(11.6274 + 8.44782i) q^{82} +(6.88698 + 5.00368i) q^{83} +(-1.07047 + 3.29456i) q^{84} +(-4.38998 - 13.5110i) q^{85} +(13.5466 - 9.84221i) q^{86} +2.52434 q^{87} -6.37228 q^{89} +(-4.84475 + 3.51992i) q^{90} +(-1.00599 - 3.09610i) q^{91} +(2.70222 - 8.31657i) q^{92} +(-5.96430 - 4.33332i) q^{93} +(-2.56389 - 1.86278i) q^{94} +(3.12025 - 9.60315i) q^{95} +(-1.26972 - 3.90781i) q^{96} +(10.1039 - 7.34092i) q^{97} +16.0858 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{3} - 6 q^{4} - 2 q^{5} - 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^3 - 6 * q^4 - 2 * q^5 - 4 * q^9	$ 16 q - 4 q^{3} - 6 q^{4} - 2 q^{5} - 4 q^{9} + 24 q^{12} - 8 q^{14} - 2 q^{15} - 14 q^{16} + 30 q^{20} + 32 q^{23} - 14 q^{25} + 30 q^{26} - 4 q^{27} - 18 q^{31} - 104 q^{34} - 6 q^{36} - 20 q^{37} - 20 q^{38} - 8 q^{42} + 8 q^{45} + 28 q^{47} - 14 q^{48} + 14 q^{49} - 18 q^{53} - 16 q^{56} + 14 q^{58} + 24 q^{59} + 30 q^{60} - 2 q^{64} + 120 q^{67} - 8 q^{69} - 4 q^{70} + 20 q^{71} - 14 q^{75} - 120 q^{78} + 26 q^{80} - 4 q^{81} + 46 q^{82} + 44 q^{86} - 56 q^{89} + 36 q^{91} - 12 q^{92} - 18 q^{93} + 4 q^{97}+O(q^{100}) $ 16 * q - 4 * q^3 - 6 * q^4 - 2 * q^5 - 4 * q^9 + 24 * q^12 - 8 * q^14 - 2 * q^15 - 14 * q^16 + 30 * q^20 + 32 * q^23 - 14 * q^25 + 30 * q^26 - 4 * q^27 - 18 * q^31 - 104 * q^34 - 6 * q^36 - 20 * q^37 - 20 * q^38 - 8 * q^42 + 8 * q^45 + 28 * q^47 - 14 * q^48 + 14 * q^49 - 18 * q^53 - 16 * q^56 + 14 * q^58 + 24 * q^59 + 30 * q^60 - 2 * q^64 + 120 * q^67 - 8 * q^69 - 4 * q^70 + 20 * q^71 - 14 * q^75 - 120 * q^78 + 26 * q^80 - 4 * q^81 + 46 * q^82 + 44 * q^86 - 56 * q^89 + 36 * q^91 - 12 * q^92 - 18 * q^93 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	2.04223	−	1.48377i	1.44408	−	1.04918i	0.456905	−	0.889515i	$-0.348958\pi$
$2$	2.04223	−	1.48377i	1.44408	−	1.04918i	0.987171	−	0.159667i	$-0.0510422\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	1.35111	−	4.15829i	0.675555	−	2.07914i
$5$	1.91922	+	1.39439i	0.858299	+	0.623591i	0.927422	−	0.374017i	$-0.122020\pi$
$5$	1.91922	+	1.39439i	0.858299	+	0.623591i	−0.0691223	+	0.997608i	$0.522020\pi$
$6$	2.04223	+	1.48377i	0.833738	+	0.605746i
$7$	−0.244830	+	0.753510i	−0.0925371	+	0.284800i	−0.986604	−	0.163134i	$-0.947840\pi$
$7$	−0.244830	+	0.753510i	−0.0925371	+	0.284800i	0.894067	+	0.447933i	$0.147840\pi$
$8$	−1.85053	−	5.69534i	−0.654261	−	2.01361i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	5.98844			1.89371
$11$		0			0
$11$		0			0
$12$	4.37228			1.26217
$13$	−3.32418	+	2.41516i	−0.921961	+	0.669844i	−0.944011	−	0.329913i	$-0.892981\pi$
$13$	−3.32418	+	2.41516i	−0.921961	+	0.669844i	0.0220500	+	0.999757i	$0.492981\pi$
$14$	0.618034	+	1.90211i	0.165177	+	0.508361i
$15$	−0.733075	+	2.25617i	−0.189279	+	0.582542i
$16$	−5.15528	−	3.74553i	−1.28882	−	0.936383i
$17$	−4.84475	−	3.51992i	−1.17502	−	0.853705i	−0.183423	−	0.983034i	$-0.558718\pi$
$17$	−4.84475	−	3.51992i	−1.17502	−	0.853705i	−0.991602	+	0.129329i	$0.958718\pi$
$18$	−0.780063	+	2.40079i	−0.183863	+	0.565871i
$19$	−1.31530	−	4.04807i	−0.301750	−	0.928690i	−0.980870	−	0.194663i	$-0.937639\pi$
$19$	−1.31530	−	4.04807i	−0.301750	−	0.928690i	0.679120	−	0.734027i	$-0.262361\pi$
$20$	8.39135	−	6.09667i	1.87636	−	1.36326i
$21$	−0.792287			−0.172891
$22$		0			0
$23$	2.00000			0.417029			0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000			0.417029			0.208514	+	0.978019i	$0.433137\pi$
$24$	4.84475	−	3.51992i	0.988930	−	0.718500i
$25$	0.193976	+	0.596996i	0.0387951	+	0.119399i
$26$	−3.20521	+	9.86463i	−0.628594	+	1.93461i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	2.80252	+	2.03615i	0.529626	+	0.384796i
$29$	0.780063	−	2.40079i	0.144854	−	0.445815i	−0.852138	−	0.523317i	$-0.824694\pi$
$29$	0.780063	−	2.40079i	0.144854	−	0.445815i	0.996992	+	0.0775019i	$0.0246944\pi$
$30$	1.85053	+	5.69534i	0.337859	+	1.03982i
$31$	−5.96430	+	4.33332i	−1.07122	+	0.778287i	−0.976131	−	0.217182i	$-0.930314\pi$
$31$	−5.96430	+	4.33332i	−1.07122	+	0.778287i	−0.0950889	+	0.995469i	$0.530314\pi$
$32$	−4.10891			−0.726360
$33$		0			0
$34$	−15.1168			−2.59252
$35$	−1.52057	+	1.10476i	−0.257023	+	0.186738i
$36$	1.35111	+	4.15829i	0.225185	+	0.693048i
$37$	1.54508	−	4.75528i	0.254010	−	0.781764i	−0.740013	−	0.672593i	$-0.765181\pi$
$37$	1.54508	−	4.75528i	0.254010	−	0.781764i	0.994023	−	0.109171i	$-0.0348195\pi$
$38$	−8.69253	−	6.31550i	−1.41012	−	1.02451i
$39$	−3.32418	−	2.41516i	−0.532295	−	0.386735i
$40$	4.38998	−	13.5110i	0.694116	−	2.13627i
$41$	1.75938	+	5.41483i	0.274770	+	0.845654i	0.989280	+	0.146029i	$0.0466494\pi$
$41$	1.75938	+	5.41483i	0.274770	+	0.845654i	−0.714511	+	0.699625i	$0.753351\pi$
$42$	−1.61803	+	1.17557i	−0.249668	+	0.181394i
$43$	6.63325			1.01156			0.505781	−	0.862662i	$-0.331205\pi$
$43$	6.63325			1.01156			0.505781	+	0.862662i	$0.331205\pi$
$44$		0			0
$45$	−2.37228			−0.353639
$46$	4.08446	−	2.96754i	0.602221	−	0.437539i
$47$	−0.387951	−	1.19399i	−0.0565885	−	0.174162i	0.918767	−	0.394800i	$-0.129186\pi$
$47$	−0.387951	−	1.19399i	−0.0565885	−	0.174162i	−0.975356	+	0.220638i	$0.929186\pi$
$48$	1.96914	−	6.06040i	0.284221	−	0.874743i
$49$	5.15528	+	3.74553i	0.736469	+	0.535076i
$50$	1.28195	+	0.931389i	0.181295	+	0.131718i
$51$	1.85053	−	5.69534i	0.259126	−	0.797508i
$52$	5.55159	+	17.0860i	0.769867	+	2.36941i
$53$	−10.6117	+	7.70989i	−1.45764	+	1.05903i	−0.473665	+	0.880705i	$0.657069\pi$
$53$	−10.6117	+	7.70989i	−1.45764	+	1.05903i	−0.983971	+	0.178329i	$0.942931\pi$
$54$	−2.52434			−0.343519
$55$		0			0
$56$	4.74456			0.634019
$57$	3.44349	−	2.50184i	0.456101	−	0.331377i
$58$	−1.96914	−	6.06040i	−0.258561	−	0.795769i
$59$	−1.85410	+	5.70634i	−0.241384	+	0.742902i	0.754827	+	0.655924i	$0.227721\pi$
$59$	−1.85410	+	5.70634i	−0.241384	+	0.742902i	−0.996210	+	0.0869778i	$0.972279\pi$
$60$	8.39135	+	6.09667i	1.08332	+	0.787077i
$61$	−2.16154	−	1.57045i	−0.276757	−	0.201076i	0.440745	−	0.897633i	$-0.354714\pi$
$61$	−2.16154	−	1.57045i	−0.276757	−	0.201076i	−0.717502	+	0.696557i	$0.754714\pi$
$62$	−5.75085	+	17.6993i	−0.730358	+	2.24781i
$63$	−0.244830	−	0.753510i	−0.0308457	−	0.0949333i
$64$	1.91922	−	1.39439i	0.239902	−	0.174299i
$65$	−9.74749			−1.20903
$66$		0			0
$67$	16.1168			1.96899			0.984493	−	0.175424i	$-0.0561297\pi$
$67$	16.1168			1.96899			0.984493	+	0.175424i	$0.0561297\pi$
$68$	−21.1826	+	15.3901i	−2.56877	+	1.86632i
$69$	0.618034	+	1.90211i	0.0744025	+	0.228988i
$70$	−1.46615	+	4.51235i	−0.175239	+	0.539329i
$71$	−0.602364	−	0.437643i	−0.0714874	−	0.0519387i	0.551468	−	0.834196i	$-0.314068\pi$
$71$	−0.602364	−	0.437643i	−0.0714874	−	0.0519387i	−0.622955	+	0.782258i	$0.714068\pi$
$72$	4.84475	+	3.51992i	0.570959	+	0.414826i
$73$	−2.29462	+	7.06210i	−0.268565	+	0.826557i	0.722286	+	0.691594i	$0.243091\pi$
$73$	−2.29462	+	7.06210i	−0.268565	+	0.826557i	−0.990851	+	0.134962i	$0.956909\pi$
$74$	−3.90032	−	12.0039i	−0.453403	−	1.39543i
$75$	−0.507835	+	0.368964i	−0.0586397	+	0.0426043i
$76$	−18.6101			−2.13473
$77$		0			0
$78$	−10.3723			−1.17443
$79$	4.72544	−	3.43323i	0.531653	−	0.386269i	−0.289323	−	0.957232i	$-0.593430\pi$
$79$	4.72544	−	3.43323i	0.531653	−	0.386269i	0.820976	+	0.570963i	$0.193430\pi$
$80$	−4.67136	−	14.3770i	−0.522274	−	1.60739i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	11.6274	+	8.44782i	1.28403	+	0.932905i
$83$	6.88698	+	5.00368i	0.755944	+	0.549226i	0.897664	−	0.440681i	$-0.145263\pi$
$83$	6.88698	+	5.00368i	0.755944	+	0.549226i	−0.141719	+	0.989907i	$0.545263\pi$
$84$	−1.07047	+	3.29456i	−0.116797	+	0.359466i
$85$	−4.38998	−	13.5110i	−0.476160	−	1.46547i
$86$	13.5466	−	9.84221i	1.46077	−	1.06131i
$87$	2.52434			0.270637
$88$		0			0
$89$	−6.37228			−0.675460			−0.337730	−	0.941243i	$-0.609659\pi$
$89$	−6.37228			−0.675460			−0.337730	+	0.941243i	$0.609659\pi$
$90$	−4.84475	+	3.51992i	−0.510681	+	0.371032i
$91$	−1.00599	−	3.09610i	−0.105456	−	0.324560i
$92$	2.70222	−	8.31657i	0.281726	−	0.867063i
$93$	−5.96430	−	4.33332i	−0.618469	−	0.449344i
$94$	−2.56389	−	1.86278i	−0.264446	−	0.192131i
$95$	3.12025	−	9.60315i	0.320131	−	0.985263i
$96$	−1.26972	−	3.90781i	−0.129591	−	0.398839i
$97$	10.1039	−	7.34092i	1.02590	−	0.745358i	0.0584137	−	0.998292i	$-0.481396\pi$
$97$	10.1039	−	7.34092i	1.02590	−	0.745358i	0.967483	+	0.252935i	$0.0813957\pi$
$98$	16.0858			1.62491
$99$		0			0
$100$	2.74456			0.274456
$101$	−4.32309	+	3.14091i	−0.430163	+	0.312532i	−0.781714	−	0.623637i	$-0.785654\pi$
$101$	−4.32309	+	3.14091i	−0.430163	+	0.312532i	0.351551	+	0.936169i	$0.385654\pi$
$102$	−4.67136	−	14.3770i	−0.462534	−	1.42353i
$103$	2.50824	−	7.71958i	0.247144	−	0.760633i	−0.748132	−	0.663550i	$-0.769049\pi$
$103$	2.50824	−	7.71958i	0.247144	−	0.760633i	0.995276	−	0.0970824i	$-0.0309511\pi$
$104$	19.9066	+	14.4630i	1.95201	+	1.41822i
$105$	−1.52057	−	1.10476i	−0.148392	−	0.107813i
$106$	−10.2320	+	31.4908i	−0.993817	+	3.05865i
$107$	0.0911457	+	0.280518i	0.00881139	+	0.0271187i	0.955366	−	0.295426i	$-0.0954617\pi$
$107$	0.0911457	+	0.280518i	0.00881139	+	0.0271187i	−0.946554	+	0.322545i	$0.895462\pi$
$108$	−3.53725	+	2.56996i	−0.340372	+	0.247295i
$109$	−9.94987			−0.953025			−0.476513	−	0.879168i	$-0.658099\pi$
$109$	−9.94987			−0.953025			−0.476513	+	0.879168i	$0.658099\pi$
$110$		0			0
$111$	5.00000			0.474579
$112$	4.08446	−	2.96754i	0.385946	−	0.280406i
$113$	−1.35111	−	4.15829i	−0.127102	−	0.391179i	0.867176	−	0.498001i	$-0.165932\pi$
$113$	−1.35111	−	4.15829i	−0.127102	−	0.391179i	−0.994278	+	0.106822i	$0.965932\pi$
$114$	3.32025	−	10.2187i	0.310970	−	0.957068i
$115$	3.83843	+	2.78878i	0.357936	+	0.260055i
$116$	−8.92921	−	6.48745i	−0.829057	−	0.602345i
$117$	1.26972	−	3.90781i	0.117386	−	0.361277i
$118$	4.68038	+	14.4047i	0.430864	+	1.32606i
$119$	3.83843	−	2.78878i	0.351868	−	0.255647i
$120$	14.2063			1.29685
$121$		0			0
$122$	−6.74456			−0.610624
$123$	−4.60613	+	3.34655i	−0.415320	+	0.301748i
$124$	9.96076	+	30.6561i	0.894502	+	2.75300i
$125$	3.20521	−	9.86463i	0.286683	−	0.882319i
$126$	−1.61803	−	1.17557i	−0.144146	−	0.104728i
$127$	15.9355	+	11.5778i	1.41405	+	1.02737i	0.992718	+	0.120458i	$0.0384363\pi$
$127$	15.9355	+	11.5778i	1.41405	+	1.02737i	0.421329	+	0.906908i	$0.361564\pi$
$128$	4.38998	−	13.5110i	0.388023	−	1.19421i
$129$	2.04979	+	6.30860i	0.180474	+	0.555441i
$130$	−19.9066	+	14.4630i	−1.74593	+	1.26849i
$131$	−6.63325			−0.579550			−0.289775	−	0.957095i	$-0.593580\pi$
$131$	−6.63325			−0.579550			−0.289775	+	0.957095i	$0.593580\pi$
$132$		0			0
$133$	3.37228			0.292414
$134$	32.9143	−	23.9137i	2.84337	−	2.06583i
$135$	−0.733075	−	2.25617i	−0.0630931	−	0.194181i
$136$	−11.0818	+	34.1062i	−0.950255	+	2.92458i
$137$	−0.602364	−	0.437643i	−0.0514634	−	0.0373904i	0.561756	−	0.827303i	$-0.310126\pi$
$137$	−0.602364	−	0.437643i	−0.0514634	−	0.0373904i	−0.613220	+	0.789912i	$0.710126\pi$
$138$	4.08446	+	2.96754i	0.347693	+	0.252614i
$139$	3.21140	−	9.88367i	0.272387	−	0.838322i	−0.717512	−	0.696547i	$-0.754719\pi$
$139$	3.21140	−	9.88367i	0.272387	−	0.838322i	0.989899	−	0.141775i	$-0.0452810\pi$
$140$	2.53945	+	7.81561i	0.214622	+	0.660540i
$141$	1.01567	−	0.737928i	0.0855349	−	0.0621447i
$142$	−1.87953			−0.157726
$143$		0			0
$144$	6.37228			0.531023
$145$	4.84475	−	3.51992i	0.402335	−	0.292313i
$146$	5.79239	+	17.8271i	0.479381	+	1.47538i
$147$	−1.96914	+	6.06040i	−0.162412	+	0.499853i
$148$	−17.6862	−	12.8498i	−1.45380	−	1.05625i
$149$	−4.84475	−	3.51992i	−0.396897	−	0.288363i	0.371379	−	0.928481i	$-0.378885\pi$
$149$	−4.84475	−	3.51992i	−0.396897	−	0.288363i	−0.768276	+	0.640119i	$0.778885\pi$
$150$	−0.489660	+	1.50702i	−0.0399806	+	0.123048i
$151$	−0.671952	−	2.06805i	−0.0546827	−	0.168296i	0.919985	−	0.391953i	$-0.128200\pi$
$151$	−0.671952	−	2.06805i	−0.0546827	−	0.168296i	−0.974668	+	0.223657i	$0.928200\pi$
$152$	−20.6211	+	14.9821i	−1.67259	+	1.21521i
$153$	5.98844			0.484137
$154$		0			0
$155$	−17.4891			−1.40476
$156$	−14.5342	+	10.5597i	−1.16367	+	0.845457i
$157$	2.04808	+	6.30334i	0.163454	+	0.503061i	0.998919	−	0.0464833i	$-0.0148014\pi$
$157$	2.04808	+	6.30334i	0.163454	+	0.503061i	−0.835465	+	0.549544i	$0.814801\pi$
$158$	4.55632	−	14.0229i	0.362481	−	1.11560i
$159$	−10.6117	−	7.70989i	−0.841566	−	0.611434i
$160$	−7.88589	−	5.72943i	−0.623434	−	0.452951i
$161$	−0.489660	+	1.50702i	−0.0385906	+	0.118770i
$162$	−0.780063	−	2.40079i	−0.0612876	−	0.188624i
$163$	7.58233	−	5.50889i	0.593894	−	0.431489i	−0.249812	−	0.968294i	$-0.580369\pi$
$163$	7.58233	−	5.50889i	0.593894	−	0.431489i	0.843706	+	0.536805i	$0.180369\pi$
$164$	24.8935			1.94386
$165$		0			0
$166$	21.4891			1.66788
$167$	−2.32527	+	1.68941i	−0.179935	+	0.130730i	−0.674107	−	0.738634i	$-0.735471\pi$
$167$	−2.32527	+	1.68941i	−0.179935	+	0.130730i	0.494172	+	0.869364i	$0.335471\pi$
$168$	1.46615	+	4.51235i	0.113116	+	0.348135i
$169$	1.19996	−	3.69310i	0.0923047	−	0.284085i
$170$	−29.0125	−	21.0788i	−2.22516	−	1.61667i
$171$	3.44349	+	2.50184i	0.263330	+	0.191321i
$172$	8.96224	−	27.5830i	0.683365	−	2.10318i
$173$	2.14093	+	6.58911i	0.162772	+	0.500961i	0.998865	−	0.0476266i	$-0.0151657\pi$
$173$	2.14093	+	6.58911i	0.162772	+	0.500961i	−0.836093	+	0.548588i	$0.815166\pi$
$174$	5.15528	−	3.74553i	0.390821	−	0.283948i
$175$	−0.497333			−0.0375949
$176$		0			0
$177$	−6.00000			−0.450988
$178$	−13.0137	+	9.45499i	−0.975416	+	0.708681i
$179$	−7.48862	−	23.0476i	−0.559726	−	1.72266i	−0.683125	−	0.730302i	$-0.739379\pi$
$179$	−7.48862	−	23.0476i	−0.559726	−	1.72266i	0.123399	−	0.992357i	$-0.460621\pi$
$180$	−3.20521	+	9.86463i	−0.238902	+	0.735266i
$181$	−13.7533	−	9.99235i	−1.02227	−	0.742725i	−0.0555261	−	0.998457i	$-0.517684\pi$
$181$	−13.7533	−	9.99235i	−1.02227	−	0.742725i	−0.966748	+	0.255732i	$0.917684\pi$
$182$	−6.64836	−	4.83032i	−0.492809	−	0.358047i
$183$	0.825636	−	2.54105i	0.0610328	−	0.187840i
$184$	−3.70106	−	11.3907i	−0.272846	−	0.839733i
$185$	9.59608	−	6.97196i	0.705518	−	0.512589i
$186$	−18.6101			−1.36456
$187$		0			0
$188$	−5.48913			−0.400336
$189$	0.640974	−	0.465695i	0.0466240	−	0.0338743i
$190$	−7.87657	−	24.2416i	−0.571427	−	1.75867i
$191$	−5.40444	+	16.6331i	−0.391051	+	1.20353i	0.540943	+	0.841059i	$0.318067\pi$
$191$	−5.40444	+	16.6331i	−0.391051	+	1.20353i	−0.931994	+	0.362473i	$0.881933\pi$
$192$	1.91922	+	1.39439i	0.138507	+	0.100632i
$193$	−13.8933	−	10.0941i	−1.00006	−	0.726586i	−0.0379588	−	0.999279i	$-0.512086\pi$
$193$	−13.8933	−	10.0941i	−1.00006	−	0.726586i	−0.962101	+	0.272693i	$0.912086\pi$
$194$	9.74231	−	29.9837i	0.699457	−	2.15271i
$195$	−3.01214	−	9.27042i	−0.215704	−	0.663868i
$196$	22.5404	−	16.3765i	1.61003	−	1.16975i
$197$	−21.1345			−1.50577			−0.752884	−	0.658153i	$-0.771338\pi$
$197$	−21.1345			−1.50577			−0.752884	+	0.658153i	$0.771338\pi$
$198$		0			0
$199$	−6.86141			−0.486392			−0.243196	−	0.969977i	$-0.578196\pi$
$199$	−6.86141			−0.486392			−0.243196	+	0.969977i	$0.578196\pi$
$200$	3.04114	−	2.20952i	0.215041	−	0.156236i
$201$	4.98038	+	15.3280i	0.351289	+	1.08116i
$202$	−4.16837	+	12.8289i	−0.293285	+	0.902640i
$203$	1.61803	+	1.17557i	0.113564	+	0.0825089i
$204$	−21.1826	−	15.3901i	−1.48308	−	1.07752i
$205$	−4.17375	+	12.8455i	−0.291508	+	0.897168i
$206$	−6.33165	−	19.4868i	−0.441147	−	1.35771i
$207$	−1.61803	+	1.17557i	−0.112461	+	0.0817078i
$208$	26.1831			1.81547
$209$		0			0
$210$	−4.74456			−0.327406
$211$	10.0918	−	7.33216i	0.694752	−	0.504767i	−0.183467	−	0.983026i	$-0.558732\pi$
$211$	10.0918	−	7.33216i	0.694752	−	0.504767i	0.878219	+	0.478259i	$0.158732\pi$
$212$	17.7223	+	54.5436i	1.21717	+	3.74607i
$213$	0.230083	−	0.708121i	0.0157650	−	0.0485197i
$214$	0.602364	+	0.437643i	0.0411767	+	0.0299167i
$215$	12.7306	+	9.24935i	0.868222	+	0.630800i
$216$	−1.85053	+	5.69534i	−0.125913	+	0.387519i
$217$	−1.80496	−	5.55509i	−0.122528	−	0.377104i
$218$	−20.3200	+	14.7633i	−1.37624	+	0.999898i
$219$	−7.42554			−0.501771
$220$		0			0
$221$	24.6060			1.65518
$222$	10.2112	−	7.41884i	0.685328	−	0.497920i
$223$	−1.50226	−	4.62347i	−0.100599	−	0.309611i	0.888074	−	0.459701i	$-0.152043\pi$
$223$	−1.50226	−	4.62347i	−0.100599	−	0.309611i	−0.988672	+	0.150091i	$0.952043\pi$
$224$	1.00599	−	3.09610i	0.0672152	−	0.206867i
$225$	−0.507835	−	0.368964i	−0.0338557	−	0.0245976i
$226$	−8.92921	−	6.48745i	−0.593962	−	0.431539i
$227$	−7.80063	+	24.0079i	−0.517746	+	1.59346i	0.260483	+	0.965478i	$0.416118\pi$
$227$	−7.80063	+	24.0079i	−0.517746	+	1.59346i	−0.778229	+	0.627980i	$0.783882\pi$
$228$	−5.75085	−	17.6993i	−0.380859	−	1.17216i
$229$	2.93489	−	2.13232i	0.193943	−	0.140908i	−0.486576	−	0.873638i	$-0.661754\pi$
$229$	2.93489	−	2.13232i	0.193943	−	0.140908i	0.680519	+	0.732730i	$0.261754\pi$
$230$	11.9769			0.789732
$231$		0			0
$232$	−15.1168			−0.992469
$233$	2.04223	−	1.48377i	0.133791	−	0.0972049i	−0.518877	−	0.854849i	$-0.673650\pi$
$233$	2.04223	−	1.48377i	0.133791	−	0.0972049i	0.652668	+	0.757644i	$0.273650\pi$
$234$	−3.20521	−	9.86463i	−0.209531	−	0.644871i
$235$	0.920330	−	2.83248i	0.0600357	−	0.184771i
$236$	21.2235	+	15.4198i	1.38153	+	1.00374i
$237$	4.72544	+	3.43323i	0.306950	+	0.223012i
$238$	3.70106	−	11.3907i	0.239904	−	0.738349i
$239$	9.05339	+	27.8635i	0.585615	+	1.80234i	0.596786	+	0.802400i	$0.296444\pi$
$239$	9.05339	+	27.8635i	0.585615	+	1.80234i	−0.0111708	+	0.999938i	$0.503556\pi$
$240$	12.2298	−	8.88546i	0.789429	−	0.573554i
$241$	13.2665			0.854570			0.427285	−	0.904117i	$-0.359470\pi$
$241$	13.2665			0.854570			0.427285	+	0.904117i	$0.359470\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$	−9.45088	+	6.86646i	−0.605030	+	0.439580i
$245$	4.67136	+	14.3770i	0.298442	+	0.918511i
$246$	−4.44128	+	13.6689i	−0.283166	+	0.871494i
$247$	14.1490	+	10.2798i	0.900279	+	0.654091i
$248$	35.7169	+	25.9498i	2.26802	+	1.64781i
$249$	−2.63059	+	8.09613i	−0.166707	+	0.513072i
$250$	−8.09104	−	24.9016i	−0.511722	−	1.57492i
$251$	0.413306	−	0.300285i	0.0260877	−	0.0189538i	−0.574665	−	0.818389i	$-0.694868\pi$
$251$	0.413306	−	0.300285i	0.0260877	−	0.0189538i	0.600753	+	0.799435i	$0.294868\pi$
$252$	−3.46410			−0.218218
$253$		0			0
$254$	49.7228			3.11989
$255$	11.4931	−	8.35023i	0.719726	−	0.522912i
$256$	−9.61563	−	29.5939i	−0.600977	−	1.84962i
$257$	7.53145	−	23.1794i	0.469799	−	1.44589i	−0.383047	−	0.923729i	$-0.625125\pi$
$257$	7.53145	−	23.1794i	0.469799	−	1.44589i	0.852846	−	0.522163i	$-0.174875\pi$
$258$	13.5466	+	9.84221i	0.843377	+	0.612749i
$259$	3.20487	+	2.32847i	0.199141	+	0.144684i
$260$	−13.1699	+	40.5329i	−0.816764	+	2.51374i
$261$	0.780063	+	2.40079i	0.0482847	+	0.148605i
$262$	−13.5466	+	9.84221i	−0.836914	+	0.608054i
$263$	22.3692			1.37934			0.689671	−	0.724122i	$-0.257755\pi$
$263$	22.3692			1.37934			0.689671	+	0.724122i	$0.257755\pi$
$264$		0			0
$265$	−31.1168			−1.91149
$266$	6.88698	−	5.00368i	0.422268	−	0.306796i
$267$	−1.96914	−	6.06040i	−0.120510	−	0.370890i
$268$	21.7756	−	67.0185i	1.33016	−	4.09380i
$269$	−7.37568	−	5.35875i	−0.449703	−	0.326729i	0.339775	−	0.940507i	$-0.389649\pi$
$269$	−7.37568	−	5.35875i	−0.449703	−	0.326729i	−0.789479	+	0.613778i	$0.789649\pi$
$270$	−4.84475	−	3.51992i	−0.294842	−	0.214215i
$271$	3.21140	−	9.88367i	0.195079	−	0.600390i	−0.804897	−	0.593414i	$-0.797780\pi$
$271$	3.21140	−	9.88367i	0.195079	−	0.600390i	0.999976	−	0.00697572i	$-0.00222046\pi$
$272$	11.7921	+	36.2923i	0.715001	+	2.20055i
$273$	2.63370	−	1.91350i	0.159399	−	0.115810i
$274$	−1.87953			−0.113546
$275$		0			0
$276$	8.74456			0.526361
$277$	−7.00629	+	5.09037i	−0.420967	+	0.305851i	−0.778027	−	0.628231i	$-0.783779\pi$
$277$	−7.00629	+	5.09037i	−0.420967	+	0.305851i	0.357060	+	0.934082i	$0.383779\pi$
$278$	−8.10666	−	24.9497i	−0.486205	−	1.49638i
$279$	2.27816	−	7.01146i	0.136390	−	0.419765i
$280$	9.10584	+	6.61578i	0.544178	+	0.395368i
$281$	−0.477245	−	0.346739i	−0.0284701	−	0.0206847i	0.573459	−	0.819234i	$-0.305601\pi$
$281$	−0.477245	−	0.346739i	−0.0284701	−	0.0206847i	−0.601929	+	0.798549i	$0.705601\pi$
$282$	0.979321	−	3.01404i	0.0583177	−	0.179483i
$283$	0.734490	+	2.26053i	0.0436609	+	0.134375i	0.970511	−	0.241058i	$-0.0774943\pi$
$283$	0.734490	+	2.26053i	0.0436609	+	0.134375i	−0.926850	+	0.375432i	$0.877494\pi$
$284$	−2.63370	+	1.91350i	−0.156282	+	0.113545i
$285$	10.0974			0.598115
$286$		0			0
$287$	−4.51087			−0.266269
$288$	3.32418	−	2.41516i	0.195879	−	0.142315i
$289$	5.82850	+	17.9383i	0.342853	+	1.05519i
$290$	4.67136	−	14.3770i	0.274312	−	0.844245i
$291$	10.1039	+	7.34092i	0.592302	+	0.430333i
$292$	26.2660	+	19.0834i	1.53710	+	1.11677i
$293$	−2.03282	+	6.25638i	−0.118759	+	0.365502i	−0.992712	−	0.120508i	$-0.961548\pi$
$293$	−2.03282	+	6.25638i	−0.118759	+	0.365502i	0.873954	+	0.486009i	$0.161548\pi$
$294$	4.97078	+	15.2985i	0.289902	+	0.892226i
$295$	−11.5153	+	8.36635i	−0.670446	+	0.487108i
$296$	−29.9422			−1.74035
$297$		0			0
$298$	−15.1168			−0.875695
$299$	−6.64836	+	4.83032i	−0.384485	+	0.279344i
$300$	0.848116	+	2.61023i	0.0489660	+	0.150702i
$301$	−1.62402	+	4.99822i	−0.0936069	+	0.288092i
$302$	−4.44080	−	3.22643i	−0.255539	−	0.185660i
$303$	−4.32309	−	3.14091i	−0.248355	−	0.180440i
$304$	−8.38144	+	25.7954i	−0.480708	+	1.47947i
$305$	−1.95864	−	6.02808i	−0.112151	−	0.345167i
$306$	12.2298	−	8.88546i	0.699130	−	0.507948i
$307$	17.8178			1.01692			0.508459	−	0.861086i	$-0.330215\pi$
$307$	17.8178			1.01692			0.508459	+	0.861086i	$0.330215\pi$
$308$		0			0
$309$	8.11684			0.461751
$310$	−35.7169	+	25.9498i	−2.02858	+	1.47385i
$311$	−2.01197	−	6.19221i	−0.114088	−	0.351128i	0.877667	−	0.479270i	$-0.159099\pi$
$311$	−2.01197	−	6.19221i	−0.114088	−	0.351128i	−0.991756	+	0.128142i	$0.959099\pi$
$312$	−7.60366	+	23.4017i	−0.430473	+	1.32486i
$313$	−7.37568	−	5.35875i	−0.416898	−	0.302894i	0.359490	−	0.933149i	$-0.382951\pi$
$313$	−7.37568	−	5.35875i	−0.416898	−	0.302894i	−0.776389	+	0.630255i	$0.782951\pi$
$314$	13.5353	+	9.83400i	0.763843	+	0.554965i
$315$	0.580806	−	1.78754i	0.0327247	−	0.100716i
$316$	−7.89178	−	24.2884i	−0.443947	−	1.36633i
$317$	−12.3419	+	8.96692i	−0.693191	+	0.503632i	−0.877707	−	0.479197i	$-0.840928\pi$
$317$	−12.3419	+	8.96692i	−0.693191	+	0.503632i	0.184517	+	0.982829i	$0.440928\pi$
$318$	−33.1113			−1.85679
$319$		0			0
$320$	5.62772			0.314599
$321$	−0.238623	+	0.173369i	−0.0133186	+	0.00967654i
$322$	1.23607	+	3.80423i	0.0688834	+	0.212001i
$323$	−7.87657	+	24.2416i	−0.438264	+	1.34884i
$324$	−3.53725	−	2.56996i	−0.196514	−	0.142776i
$325$	−2.08665	−	1.51604i	−0.115746	−	0.0840947i
$326$	7.31097	−	22.5009i	0.404917	−	1.24621i
$327$	−3.07468	−	9.46289i	−0.170030	−	0.523299i
$328$	27.5835	−	20.0406i	1.52304	−	1.10656i
$329$	0.994667			0.0548377
$330$		0			0
$331$	−0.627719			−0.0345025			−0.0172513	−	0.999851i	$-0.505492\pi$
$331$	−0.627719			−0.0345025			−0.0172513	+	0.999851i	$0.505492\pi$
$332$	30.1118	−	21.8775i	1.65260	−	1.20068i
$333$	1.54508	+	4.75528i	0.0846701	+	0.260588i
$334$	−2.24205	+	6.90033i	−0.122680	+	0.377569i
$335$	30.9317	+	22.4732i	1.68998	+	1.22784i
$336$	4.08446	+	2.96754i	0.222826	+	0.161892i
$337$	−4.72595	+	14.5450i	−0.257439	+	0.792316i	0.735900	+	0.677090i	$0.236759\pi$
$337$	−4.72595	+	14.5450i	−0.257439	+	0.792316i	−0.993339	+	0.115226i	$0.963241\pi$
$338$	−3.02911	−	9.32263i	−0.164762	−	0.507084i
$339$	3.53725	−	2.56996i	0.192117	−	0.139581i
$340$	−62.1138			−3.36859
$341$		0			0
$342$	10.7446			0.580999
$343$	−8.57128	+	6.22740i	−0.462806	+	0.336248i
$344$	−12.2750	−	37.7786i	−0.661825	−	2.03689i
$345$	−1.46615	+	4.51235i	−0.0789349	+	0.242937i
$346$	14.1490	+	10.2798i	0.760655	+	0.552648i
$347$	−14.5787	−	10.5920i	−0.782624	−	0.568609i	0.123142	−	0.992389i	$-0.460703\pi$
$347$	−14.5787	−	10.5920i	−0.782624	−	0.568609i	−0.905765	+	0.423780i	$0.860703\pi$
$348$	3.41066	−	10.4969i	0.182830	−	0.562694i
$349$	8.02850	+	24.7092i	0.429756	+	1.32265i	0.898366	+	0.439247i	$0.144755\pi$
$349$	8.02850	+	24.7092i	0.429756	+	1.32265i	−0.468611	+	0.883405i	$0.655245\pi$
$350$	−1.01567	+	0.737928i	−0.0542899	+	0.0394439i
$351$	4.10891			0.219317
$352$		0			0
$353$	−29.3505			−1.56217			−0.781086	−	0.624424i	$-0.785334\pi$
$353$	−29.3505			−1.56217			−0.781086	+	0.624424i	$0.785334\pi$
$354$	−12.2534	+	8.90261i	−0.651260	+	0.473168i
$355$	−0.545820	−	1.67986i	−0.0289691	−	0.0891578i
$356$	−8.60965	+	26.4978i	−0.456310	+	1.40438i
$357$	3.83843	+	2.78878i	0.203151	+	0.147598i
$358$	−49.4908	−	35.9572i	−2.61567	−	1.90040i
$359$	0.398515	−	1.22650i	0.0210328	−	0.0647323i	−0.939989	−	0.341204i	$-0.889165\pi$
$359$	0.398515	−	1.22650i	0.0210328	−	0.0647323i	0.961022	+	0.276472i	$0.0891653\pi$
$360$	4.38998	+	13.5110i	0.231372	+	0.712090i
$361$	0.714488	−	0.519106i	0.0376046	−	0.0273214i
$362$	−42.9137			−2.25550
$363$		0			0
$364$	−14.2337			−0.746048
$365$	−14.2512	+	10.3541i	−0.745942	+	0.541959i
$366$	−2.08418	−	6.41446i	−0.108942	−	0.335289i
$367$	−7.33075	+	22.5617i	−0.382662	+	1.17771i	0.555500	+	0.831517i	$0.312527\pi$
$367$	−7.33075	+	22.5617i	−0.382662	+	1.17771i	−0.938162	+	0.346196i	$0.887473\pi$
$368$	−10.3106	−	7.49107i	−0.537475	−	0.390499i
$369$	−4.60613	−	3.34655i	−0.239785	−	0.174214i
$370$	9.25265	−	28.4767i	0.481022	−	1.48043i
$371$	−3.21140	−	9.88367i	−0.166728	−	0.513135i
$372$	−26.0776	+	18.9465i	−1.35206	+	0.982330i
$373$	24.4511			1.26603			0.633015	−	0.774140i	$-0.281817\pi$
$373$	24.4511			1.26603			0.633015	+	0.774140i	$0.281817\pi$
$374$		0			0
$375$	10.3723			0.535622
$376$	−6.08228	+	4.41903i	−0.313670	+	0.227894i
$377$	3.20521	+	9.86463i	0.165077	+	0.508054i
$378$	0.618034	−	1.90211i	0.0317882	−	0.0978341i
$379$	−19.1922	−	13.9439i	−0.985835	−	0.716251i	−0.0268299	−	0.999640i	$-0.508541\pi$
$379$	−19.1922	−	13.9439i	−0.985835	−	0.716251i	−0.959005	+	0.283389i	$0.908541\pi$
$380$	−35.7169	−	25.9498i	−1.83224	−	1.33120i
$381$	−6.08682	+	18.7333i	−0.311837	+	0.959737i
$382$	13.6426	+	41.9877i	0.698017	+	2.14828i
$383$	19.0031	−	13.8066i	0.971013	−	0.705482i	0.0153309	−	0.999882i	$-0.495120\pi$
$383$	19.0031	−	13.8066i	0.971013	−	0.705482i	0.955682	+	0.294400i	$0.0951198\pi$
$384$	14.2063			0.724960
$385$		0			0
$386$	−43.3505			−2.20648
$387$	−5.36641	+	3.89893i	−0.272790	+	0.198194i
$388$	−16.8742	−	51.9334i	−0.856656	−	2.63652i
$389$	−2.81726	+	8.67063i	−0.142841	+	0.439619i	−0.996727	−	0.0808411i	$-0.974239\pi$
$389$	−2.81726	+	8.67063i	−0.142841	+	0.439619i	0.853886	+	0.520460i	$0.174239\pi$
$390$	−19.9066	−	14.4630i	−1.00801	−	0.732364i
$391$	−9.68950	−	7.03983i	−0.490019	−	0.356020i
$392$	11.7921	−	36.2923i	0.595591	−	1.83304i
$393$	−2.04979	−	6.30860i	−0.103398	−	0.318227i
$394$	−43.1615	+	31.3587i	−2.17444	+	1.57983i
$395$	13.8564			0.697191
$396$		0			0
$397$	24.4891			1.22907			0.614537	−	0.788888i	$-0.289343\pi$
$397$	24.4891			1.22907			0.614537	+	0.788888i	$0.289343\pi$
$398$	−14.0126	+	10.1807i	−0.702387	+	0.510314i
$399$	1.04209	+	3.20723i	0.0521699	+	0.160562i
$400$	1.23607	−	3.80423i	0.0618034	−	0.190211i
$401$	15.4659	+	11.2366i	0.772328	+	0.561129i	0.902667	−	0.430341i	$-0.141607\pi$
$401$	15.4659	+	11.2366i	0.772328	+	0.561129i	−0.130339	+	0.991470i	$0.541607\pi$
$402$	32.9143	+	23.9137i	1.64162	+	1.19271i
$403$	9.36076	−	28.8095i	0.466293	−	1.43510i
$404$	7.21983	+	22.2203i	0.359200	+	1.10550i
$405$	1.91922	−	1.39439i	0.0953666	−	0.0692879i
$406$	5.04868			0.250562
$407$		0			0
$408$	−35.8614			−1.77540
$409$	0.357934	−	0.260054i	0.0176987	−	0.0128588i	−0.578901	−	0.815398i	$-0.696518\pi$
$409$	0.357934	−	0.260054i	0.0176987	−	0.0128588i	0.596599	+	0.802539i	$0.296518\pi$
$410$	10.5360	+	32.4264i	0.520334	+	1.60142i
$411$	0.230083	−	0.708121i	0.0113491	−	0.0349290i
$412$	−28.7113	−	20.8600i	−1.41450	−	1.02770i
$413$	−3.84584	−	2.79417i	−0.189242	−	0.137492i
$414$	−1.56013	+	4.80158i	−0.0766760	+	0.235985i
$415$	6.24051	+	19.2063i	0.306334	+	0.942800i
$416$	13.6588	−	9.92367i	0.669676	−	0.486548i
$417$	10.3923			0.508913
$418$		0			0
$419$	−8.51087			−0.415783			−0.207892	−	0.978152i	$-0.566660\pi$
$419$	−8.51087			−0.415783			−0.207892	+	0.978152i	$0.566660\pi$
$420$	−6.64836	+	4.83032i	−0.324407	+	0.235695i
$421$	1.89693	+	5.83815i	0.0924507	+	0.284534i	0.986581	−	0.163273i	$-0.0522052\pi$
$421$	1.89693	+	5.83815i	0.0924507	+	0.284534i	−0.894130	+	0.447807i	$0.852205\pi$
$422$	9.73067	−	29.9479i	0.473682	−	1.45784i
$423$	1.01567	+	0.737928i	0.0493836	+	0.0358793i
$424$	63.5478	+	46.1702i	3.08615	+	2.24222i
$425$	1.16161	−	3.57507i	0.0563465	−	0.173417i
$426$	−0.580806	−	1.78754i	−0.0281401	−	0.0866065i
$427$	1.71256	−	1.24425i	0.0828767	−	0.0602135i
$428$	1.28962			0.0623362
$429$		0			0
$430$	39.7228			1.91560
$431$	19.1404	−	13.9063i	0.921959	−	0.669843i	−0.0220516	−	0.999757i	$-0.507020\pi$
$431$	19.1404	−	13.9063i	0.921959	−	0.669843i	0.944011	+	0.329914i	$0.107020\pi$
$432$	1.96914	+	6.06040i	0.0947404	+	0.291581i
$433$	−7.17960	+	22.0966i	−0.345030	+	1.06189i	0.616538	+	0.787325i	$0.288535\pi$
$433$	−7.17960	+	22.0966i	−0.345030	+	1.06189i	−0.961568	+	0.274567i	$0.911465\pi$
$434$	−11.9286	−	8.66664i	−0.572591	−	0.416012i
$435$	4.84475	+	3.51992i	0.232288	+	0.168767i
$436$	−13.4434	+	41.3744i	−0.643821	+	1.98148i
$437$	−2.63059	−	8.09613i	−0.125838	−	0.387291i
$438$	−15.1647	+	11.0178i	−0.724596	+	0.526450i
$439$	−24.4511			−1.16699			−0.583493	−	0.812118i	$-0.698315\pi$
$439$	−24.4511			−1.16699			−0.583493	+	0.812118i	$0.698315\pi$
$440$		0			0
$441$	−6.37228			−0.303442
$442$	50.2511	−	36.5096i	2.39020	−	1.73658i
$443$	6.41042	+	19.7293i	0.304568	+	0.937365i	0.979838	+	0.199794i	$0.0640273\pi$
$443$	6.41042	+	19.7293i	0.304568	+	0.937365i	−0.675270	+	0.737571i	$0.735973\pi$
$444$	6.75555	−	20.7914i	0.320604	−	0.986718i
$445$	−12.2298	−	8.88546i	−0.579747	−	0.421211i
$446$	−9.92812	−	7.21320i	−0.470110	−	0.341555i
$447$	1.85053	−	5.69534i	0.0875270	−	0.269381i
$448$	0.580806	+	1.78754i	0.0274405	+	0.0844532i
$449$	−19.9066	+	14.4630i	−0.939453	+	0.682552i	−0.948289	−	0.317409i	$-0.897187\pi$
$449$	−19.9066	+	14.4630i	−0.939453	+	0.682552i	0.00883611	+	0.999961i	$0.497187\pi$
$450$	−1.58457			−0.0746975
$451$		0			0
$452$	−19.1168			−0.899181
$453$	1.75919	−	1.27813i	0.0826541	−	0.0600517i
$454$	19.6914	+	60.6040i	0.924165	+	2.84429i
$455$	2.38648	−	7.34483i	0.111880	−	0.344331i
$456$	−20.6211	−	14.9821i	−0.965673	−	0.701603i
$457$	−6.84256	−	4.97141i	−0.320082	−	0.232553i	0.416129	−	0.909306i	$-0.363387\pi$
$457$	−6.84256	−	4.97141i	−0.320082	−	0.232553i	−0.736210	+	0.676753i	$0.763387\pi$
$458$	2.82985	−	8.70938i	0.132230	−	0.406963i
$459$	1.85053	+	5.69534i	0.0863753	+	0.265836i
$460$	16.7827	−	12.1933i	0.782498	−	0.568518i
$461$	−14.5012			−0.675389			−0.337694	−	0.941256i	$-0.609647\pi$
$461$	−14.5012			−0.675389			−0.337694	+	0.941256i	$0.609647\pi$
$462$		0			0
$463$	−3.25544			−0.151293			−0.0756465	−	0.997135i	$-0.524102\pi$
$463$	−3.25544			−0.151293			−0.0756465	+	0.997135i	$0.524102\pi$
$464$	−13.0137	+	9.45499i	−0.604145	+	0.438937i
$465$	−5.40444	−	16.6331i	−0.250625	−	0.771344i
$466$	1.96914	−	6.06040i	0.0912188	−	0.280743i
$467$	17.9874	+	13.0686i	0.832359	+	0.604744i	0.920226	−	0.391388i	$-0.128005\pi$
$467$	17.9874	+	13.0686i	0.832359	+	0.604744i	−0.0878667	+	0.996132i	$0.528005\pi$
$468$	−14.5342	−	10.5597i	−0.671846	−	0.488125i
$469$	−3.94589	+	12.1442i	−0.182204	+	0.560767i
$470$	−2.32322	−	7.15015i	−0.107162	−	0.329812i
$471$	−5.36194	+	3.89568i	−0.247065	+	0.179503i
$472$	35.9306			1.65384
$473$		0			0
$474$	14.7446			0.677240
$475$	2.16154	−	1.57045i	0.0991784	−	0.0720573i
$476$	−6.41042	−	19.7293i	−0.293821	−	0.904289i
$477$	4.05333	−	12.4749i	0.185589	−	0.571185i
$478$	59.8321	+	43.4705i	2.73666	+	1.98830i
$479$	30.3504	+	22.0509i	1.38675	+	1.00753i	0.996213	+	0.0869422i	$0.0277095\pi$
$479$	30.3504	+	22.0509i	1.38675	+	1.00753i	0.390534	+	0.920589i	$0.372290\pi$
$480$	3.01214	−	9.27042i	0.137485	−	0.423135i
$481$	6.34862	+	19.5390i	0.289472	+	0.890903i
$482$	27.0933	−	19.6844i	1.23406	−	0.896600i
$483$	−1.58457			−0.0721006
$484$		0			0
$485$	29.6277			1.34533
$486$	2.04223	−	1.48377i	0.0926375	−	0.0673051i
$487$	−3.93829	−	12.1208i	−0.178461	−	0.549246i	0.821314	−	0.570477i	$-0.193242\pi$
$487$	−3.93829	−	12.1208i	−0.178461	−	0.549246i	−0.999775	+	0.0212308i	$0.993242\pi$
$488$	−4.94427	+	15.2169i	−0.223817	+	0.688837i
$489$	7.58233	+	5.50889i	0.342885	+	0.249121i
$490$	30.8721	+	22.4299i	1.39466	+	1.01328i
$491$	−5.75085	+	17.6993i	−0.259532	+	0.798758i	0.733371	+	0.679829i	$0.237946\pi$
$491$	−5.75085	+	17.6993i	−0.259532	+	0.798758i	−0.992903	+	0.118929i	$0.962054\pi$
$492$	7.69252	+	23.6751i	0.346806	+	1.06736i
$493$	−12.2298	+	8.88546i	−0.550802	+	0.400181i
$494$	44.1485			1.98633
$495$		0			0
$496$	46.9783			2.10939
$497$	0.477245	−	0.346739i	0.0214074	−	0.0155534i
$498$	6.64050	+	20.4374i	0.297568	+	0.915821i
$499$	−11.6931	+	35.9877i	−0.523455	+	1.61103i	0.243896	+	0.969801i	$0.421574\pi$
$499$	−11.6931	+	35.9877i	−0.523455	+	1.61103i	−0.767351	+	0.641227i	$0.778426\pi$
$500$	−36.6894	−	26.6564i	−1.64080	−	1.19211i
$501$	−2.32527	−	1.68941i	−0.103885	−	0.0754772i
$502$	0.398515	−	1.22650i	0.0177866	−	0.0547415i
$503$	−6.82131	−	20.9938i	−0.304147	−	0.936069i	−0.979994	−	0.199027i	$-0.936222\pi$
$503$	−6.82131	−	20.9938i	−0.304147	−	0.936069i	0.675847	−	0.737042i	$-0.263778\pi$
$504$	−3.83843	+	2.78878i	−0.170977	+	0.124222i
$505$	−12.6766			−0.564101
$506$		0			0
$507$	3.88316			0.172457
$508$	69.6745	−	50.6215i	3.09131	−	2.24597i
$509$	−12.6630	−	38.9726i	−0.561277	−	1.72743i	−0.678763	−	0.734357i	$-0.737484\pi$
$509$	−12.6630	−	38.9726i	−0.561277	−	1.72743i	0.117487	−	0.993074i	$-0.462516\pi$
$510$	11.0818	−	34.1062i	0.490710	−	1.51025i
$511$	−4.75957	−	3.45803i	−0.210551	−	0.152974i
$512$	−40.5616	−	29.4697i	−1.79259	−	1.30239i
$513$	−1.31530	+	4.04807i	−0.0580718	+	0.178726i
$514$	−19.0119	−	58.5127i	−0.838580	−	2.58088i
$515$	15.5780	−	11.3181i	0.686448	−	0.498733i
$516$	29.0024			1.27676
$517$		0			0
$518$	10.0000			0.439375
$519$	−5.60503	+	4.07230i	−0.246034	+	0.178754i
$520$	18.0380	+	55.5153i	0.791020	+	2.43451i
$521$	5.24657	−	16.1473i	0.229856	−	0.707425i	−0.767906	−	0.640563i	$-0.778701\pi$
$521$	5.24657	−	16.1473i	0.229856	−	0.707425i	0.997762	−	0.0668623i	$-0.0212988\pi$
$522$	5.15528	+	3.74553i	0.225641	+	0.163938i
$523$	−5.53014	−	4.01788i	−0.241816	−	0.175690i	0.460276	−	0.887776i	$-0.347750\pi$
$523$	−5.53014	−	4.01788i	−0.241816	−	0.175690i	−0.702092	+	0.712086i	$0.747750\pi$
$524$	−8.96224	+	27.5830i	−0.391517	+	1.20497i
$525$	−0.153684	−	0.472992i	−0.00670734	−	0.0206431i
$526$	45.6831	−	33.1907i	1.99188	−	1.44718i
$527$	44.1485			1.92314
$528$		0			0
$529$	−19.0000			−0.826087
$530$	−63.5478	+	46.1702i	−2.76034	+	2.00551i
$531$	−1.85410	−	5.70634i	−0.0804612	−	0.247634i
$532$	4.55632	−	14.0229i	0.197542	−	0.607970i
$533$	−18.9262	−	13.7507i	−0.819783	−	0.595607i
$534$	−13.0137	−	9.45499i	−0.563157	−	0.409157i
$535$	−0.216223	+	0.665467i	−0.00934814	+	0.0287706i
$536$	−29.8247	−	91.7910i	−1.28823	−	3.96477i
$537$	19.6055	−	14.2442i	0.846038	−	0.614683i
$538$	−23.0140			−0.992204
$539$		0			0
$540$	−10.3723			−0.446352
$541$	−22.4201	+	16.2892i	−0.963917	+	0.700327i	−0.954057	−	0.299625i	$-0.903139\pi$
$541$	−22.4201	+	16.2892i	−0.963917	+	0.700327i	−0.00985982	+	0.999951i	$0.503139\pi$
$542$	−8.10666	−	24.9497i	−0.348211	−	1.07168i
$543$	5.25329	−	16.1680i	0.225440	−	0.693834i
$544$	19.9066	+	14.4630i	0.853490	+	0.620097i
$545$	−19.0960	−	13.8740i	−0.817981	−	0.594298i
$546$	2.53945	−	7.81561i	0.108678	−	0.334477i
$547$	−12.9707	−	39.9196i	−0.554586	−	1.70684i	−0.697034	−	0.717038i	$-0.745498\pi$
$547$	−12.9707	−	39.9196i	−0.554586	−	1.70684i	0.142448	−	0.989802i	$-0.454502\pi$
$548$	−2.63370	+	1.91350i	−0.112506	+	0.0817406i
$549$	2.67181			0.114030
$550$		0			0
$551$	−10.7446			−0.457734
$552$	9.68950	−	7.03983i	0.412412	−	0.299635i
$553$	1.43004	+	4.40122i	0.0608116	+	0.187159i
$554$	−6.75555	+	20.7914i	−0.287016	+	0.883343i
$555$	9.59608	+	6.97196i	0.407331	+	0.295943i
$556$	−36.7602	−	26.7078i	−1.55898	−	1.13266i
$557$	−2.93796	+	9.04212i	−0.124485	+	0.383127i	−0.993807	−	0.111120i	$-0.964556\pi$
$557$	−2.93796	+	9.04212i	−0.124485	+	0.383127i	0.869322	+	0.494247i	$0.164556\pi$
$558$	−5.75085	−	17.6993i	−0.243453	−	0.749270i
$559$	−22.0501	+	16.0203i	−0.932620	+	0.677588i
$560$	11.9769			0.506116
$561$		0			0
$562$	−1.48913			−0.0628150
$563$	11.7761	−	8.55587i	0.496305	−	0.360587i	−0.311299	−	0.950312i	$-0.600764\pi$
$563$	11.7761	−	8.55587i	0.496305	−	0.360587i	0.807604	+	0.589725i	$0.200764\pi$
$564$	−1.69623	−	5.22047i	−0.0714243	−	0.219821i
$565$	3.20521	−	9.86463i	0.134844	−	0.415008i
$566$	4.85410	+	3.52671i	0.204033	+	0.148239i
$567$	0.640974	+	0.465695i	0.0269184	+	0.0195573i
$568$	−1.37784	+	4.24054i	−0.0578127	+	0.177929i
$569$	−7.58441	−	23.3424i	−0.317955	−	0.978565i	−0.974521	−	0.224296i	$-0.927992\pi$
$569$	−7.58441	−	23.3424i	−0.317955	−	0.978565i	0.656566	−	0.754269i	$-0.272008\pi$
$570$	20.6211	−	14.9821i	0.863724	−	0.627532i
$571$	−4.55134			−0.190468			−0.0952339	−	0.995455i	$-0.530360\pi$
$571$	−4.55134			−0.190468			−0.0952339	+	0.995455i	$0.530360\pi$
$572$		0			0
$573$	−17.4891			−0.730619
$574$	−9.21225	+	6.69309i	−0.384512	+	0.279364i
$575$	0.387951	+	1.19399i	0.0161787	+	0.0497929i
$576$	−0.733075	+	2.25617i	−0.0305448	+	0.0940072i
$577$	13.3400	+	9.69206i	0.555351	+	0.403486i	0.829754	−	0.558129i	$-0.188480\pi$
$577$	13.3400	+	9.69206i	0.555351	+	0.403486i	−0.274404	+	0.961615i	$0.588480\pi$
$578$	38.5194	+	27.9860i	1.60219	+	1.16406i
$579$	5.30676	−	16.3325i	0.220541	−	0.678757i
$580$	−8.09104	−	24.9016i	−0.335962	−	1.03398i
$581$	−5.45647	+	3.96435i	−0.226372	+	0.164469i
$582$	31.5268			1.30683
$583$		0			0
$584$	44.4674			1.84007
$585$	7.88589	−	5.72943i	0.326041	−	0.236883i
$586$	5.13153	+	15.7932i	0.211981	+	0.652412i
$587$	12.0449	−	37.0705i	0.497148	−	1.53006i	−0.316434	−	0.948614i	$-0.602486\pi$
$587$	12.0449	−	37.0705i	0.497148	−	1.53006i	0.813582	−	0.581450i	$-0.197514\pi$
$588$	22.5404	+	16.3765i	0.929548	+	0.675356i
$589$	25.3864	+	18.4443i	1.04603	+	0.759984i
$590$	−11.1032	+	34.1721i	−0.457111	+	1.40684i
$591$	−6.53091	−	20.1001i	−0.268646	−	0.826806i
$592$	−25.7764	+	18.7277i	−1.05940	+	0.769702i
$593$	−27.7677			−1.14028			−0.570142	−	0.821546i	$-0.693112\pi$
$593$	−27.7677			−1.14028			−0.570142	+	0.821546i	$0.693112\pi$
$594$		0			0
$595$	11.2554			0.461428
$596$	−21.1826	+	15.3901i	−0.867673	+	0.630402i
$597$	−2.12029	−	6.52559i	−0.0867777	−	0.267074i
$598$	−6.41042	+	19.7293i	−0.262142	+	0.806789i
$599$	−32.7388	−	23.7861i	−1.33767	−	0.971875i	−0.999526	−	0.0307807i	$-0.990201\pi$
$599$	−32.7388	−	23.7861i	−1.33767	−	0.971875i	−0.338145	−	0.941094i	$-0.609799\pi$
$600$	3.04114	+	2.20952i	0.124154	+	0.0902032i
$601$	12.4354	−	38.2723i	0.507252	−	1.56116i	−0.289699	−	0.957118i	$-0.593555\pi$
$601$	12.4354	−	38.2723i	0.507252	−	1.56116i	0.796951	−	0.604044i	$-0.206445\pi$
$602$	4.09957	+	12.6172i	0.167086	+	0.514238i
$603$	−13.0388	+	9.47324i	−0.530981	+	0.385780i
$604$	−9.50744			−0.386852
$605$		0			0
$606$	−13.4891			−0.547958
$607$	21.1382	−	15.3578i	0.857973	−	0.623354i	−0.0693600	−	0.997592i	$-0.522096\pi$
$607$	21.1382	−	15.3578i	0.857973	−	0.623354i	0.927333	+	0.374238i	$0.122096\pi$
$608$	5.40444	+	16.6331i	0.219179	+	0.674563i
$609$	−0.618034	+	1.90211i	−0.0250440	+	0.0770775i
$610$	−12.9443	−	9.40456i	−0.524098	−	0.380780i
$611$	4.17330	+	3.03208i	0.168834	+	0.122665i
$612$	8.09104	−	24.9016i	0.327061	−	1.00659i
$613$	13.4148	+	41.2864i	0.541817	+	1.66754i	0.728440	+	0.685110i	$0.240246\pi$
$613$	13.4148	+	41.2864i	0.541817	+	1.66754i	−0.186623	+	0.982432i	$0.559754\pi$
$614$	36.3882	−	26.4376i	1.46851	−	1.06693i
$615$	−13.5065			−0.544637
$616$		0			0
$617$	43.8614			1.76579			0.882897	−	0.469567i	$-0.155590\pi$
$617$	43.8614			1.76579			0.882897	+	0.469567i	$0.155590\pi$
$618$	16.5765	−	12.0435i	0.666804	−	0.484461i
$619$	3.16238	+	9.73282i	0.127107	+	0.391195i	0.994279	−	0.106814i	$-0.0340648\pi$
$619$	3.16238	+	9.73282i	0.127107	+	0.391195i	−0.867172	+	0.498009i	$0.834065\pi$
$620$	−23.6297	+	72.7248i	−0.948992	+	2.92070i
$621$	−1.61803	−	1.17557i	−0.0649295	−	0.0471740i
$622$	−13.2967	−	9.66063i	−0.533150	−	0.387356i
$623$	1.56013	−	4.80158i	0.0625052	−	0.192371i
$624$	8.09104	+	24.9016i	0.323901	+	0.996864i
$625$	22.4458	−	16.3078i	0.897833	−	0.652314i
$626$	−23.0140			−0.919824
$627$		0			0
$628$	28.9783			1.15636
$629$	−24.2237	+	17.5996i	−0.965864	+	0.701741i
$630$	−1.46615	−	4.51235i	−0.0584128	−	0.179776i
$631$	6.87059	−	21.1455i	0.273514	−	0.841789i	−0.716095	−	0.698003i	$-0.754072\pi$
$631$	6.87059	−	21.1455i	0.273514	−	0.841789i	0.989609	−	0.143786i	$-0.0459277\pi$
$632$	−28.2980	−	20.5597i	−1.12563	−	0.817821i
$633$	10.0918	+	7.33216i	0.401115	+	0.291427i
$634$	−11.9002	+	36.6251i	−0.472618	+	1.45457i
$635$	14.4397	+	44.4407i	0.573020	+	1.76357i
$636$	−46.3976	+	33.7098i	−1.83978	+	1.33668i
$637$	−26.1831			−1.03741
$638$		0			0
$639$	0.744563			0.0294544
$640$	27.2649	−	19.8091i	1.07774	−	0.783023i
$641$	2.19923	+	6.76852i	0.0868642	+	0.267340i	0.985048	−	0.172279i	$-0.0551132\pi$
$641$	2.19923	+	6.76852i	0.0868642	+	0.267340i	−0.898184	+	0.439620i	$0.855113\pi$
$642$	−0.230083	+	0.708121i	−0.00908063	+	0.0279473i
$643$	−17.0663	−	12.3994i	−0.673029	−	0.488984i	0.198009	−	0.980200i	$-0.436553\pi$
$643$	−17.0663	−	12.3994i	−0.673029	−	0.488984i	−0.871038	+	0.491216i	$0.836553\pi$
$644$	5.60503	+	4.07230i	0.220869	+	0.160471i
$645$	−4.86267	+	14.9658i	−0.191467	+	0.589276i
$646$	19.8831	+	61.1940i	0.782291	+	2.40765i
$647$	9.70820	−	7.05342i	0.381669	−	0.277299i	−0.380364	−	0.924837i	$-0.624201\pi$
$647$	9.70820	−	7.05342i	0.381669	−	0.277299i	0.762033	+	0.647538i	$0.224201\pi$
$648$	−5.98844			−0.235248
$649$		0			0
$650$	−6.51087			−0.255378
$651$	4.72544	−	3.43323i	0.185205	−	0.134559i
$652$	−12.6630	−	38.9726i	−0.495920	−	1.52629i
$653$	1.39394	−	4.29010i	0.0545490	−	0.167884i	−0.920070	−	0.391753i	$-0.871869\pi$
$653$	1.39394	−	4.29010i	0.0545490	−	0.167884i	0.974619	+	0.223869i	$0.0718687\pi$
$654$	−20.3200	−	14.7633i	−0.794573	−	0.577291i
$655$	−12.7306	−	9.24935i	−0.497427	−	0.361402i
$656$	11.2113	−	34.5048i	0.437727	−	1.34719i
$657$	−2.29462	−	7.06210i	−0.0895215	−	0.275519i
$658$	2.03134	−	1.47586i	0.0791899	−	0.0575348i
$659$	−22.3692			−0.871380			−0.435690	−	0.900097i	$-0.643496\pi$
$659$	−22.3692			−0.871380			−0.435690	+	0.900097i	$0.643496\pi$
$660$		0			0
$661$	−26.7228			−1.03940			−0.519698	−	0.854350i	$-0.673956\pi$
$661$	−26.7228			−1.03940			−0.519698	+	0.854350i	$0.673956\pi$
$662$	−1.28195	+	0.931389i	−0.0498243	+	0.0361995i
$663$	7.60366	+	23.4017i	0.295302	+	0.908845i
$664$	15.7531	−	48.4832i	0.611341	−	1.88151i
$665$	6.47214	+	4.70228i	0.250979	+	0.182347i
$666$	10.2112	+	7.41884i	0.395674	+	0.287474i
$667$	1.56013	−	4.80158i	0.0604083	−	0.185918i
$668$	3.88335	+	11.9517i	0.150251	+	0.462426i
$669$	3.93296	−	2.85746i	0.152057	−	0.110476i
$670$	96.5147			3.72869
$671$		0			0
$672$	3.25544			0.125581
$673$	33.5553	−	24.3794i	1.29346	−	0.939755i	0.293593	−	0.955931i	$-0.405149\pi$
$673$	33.5553	−	24.3794i	1.29346	−	0.939755i	0.999869	+	0.0161752i	$0.00514896\pi$
$674$	11.9299	+	36.7165i	0.459523	+	1.41427i
$675$	0.193976	−	0.596996i	0.00746613	−	0.0229784i
$676$	−13.7357	−	9.97957i	−0.528296	−	0.383829i
$677$	29.3515	+	21.3251i	1.12807	+	0.819592i	0.985413	−	0.170180i	$-0.0544350\pi$
$677$	29.3515	+	21.3251i	1.12807	+	0.819592i	0.142658	+	0.989772i	$0.454435\pi$
$678$	3.41066	−	10.4969i	0.130985	−	0.403132i
$679$	3.05771	+	9.41068i	0.117344	+	0.361149i
$680$	−68.8258	+	50.0049i	−2.63935	+	1.91760i
$681$	−25.2434			−0.967328
$682$		0			0
$683$	2.00000			0.0765279			0.0382639	−	0.999268i	$-0.487817\pi$
$683$	2.00000			0.0765279			0.0382639	+	0.999268i	$0.487817\pi$
$684$	15.0559	−	10.9388i	0.575677	−	0.418254i
$685$	−0.545820	−	1.67986i	−0.0208547	−	0.0641843i
$686$	−8.26452	+	25.4356i	−0.315541	+	0.971135i
$687$	2.93489	+	2.13232i	0.111973	+	0.0813531i
$688$	−34.1963	−	24.8451i	−1.30372	−	0.947209i
$689$	16.6548	−	51.2581i	0.634496	−	1.95278i
$690$	3.70106	+	11.3907i	0.140897	+	0.433636i
$691$	3.33060	−	2.41982i	0.126702	−	0.0920543i	−0.522629	−	0.852560i	$-0.675049\pi$
$691$	3.33060	−	2.41982i	0.126702	−	0.0920543i	0.649331	+	0.760506i	$0.275049\pi$
$692$	30.2921			1.15153
$693$		0			0
$694$	−45.4891			−1.72674
$695$	19.9451	−	14.4909i	0.756560	−	0.549673i
$696$	−4.67136	−	14.3770i	−0.177068	−	0.544958i
$697$	10.5360	−	32.4264i	0.399078	−	1.22824i
$698$	53.0587	+	38.5494i	2.00830	+	1.45912i
$699$	2.04223	+	1.48377i	0.0772443	+	0.0561213i
$700$	−0.671952	+	2.06805i	−0.0253974	+	0.0781651i
$701$	−3.10329	−	9.55094i	−0.117210	−	0.360734i	0.875192	−	0.483776i	$-0.160735\pi$
$701$	−3.10329	−	9.55094i	−0.117210	−	0.360734i	−0.992401	+	0.123042i	$0.960735\pi$
$702$	8.39135	−	6.09667i	0.316711	−	0.230104i
$703$	−21.2819			−0.802664
$704$		0			0
$705$	2.97825			0.112167
$706$	−59.9406	+	43.5494i	−2.25589	+	1.63900i
$707$	−1.30828	−	4.02648i	−0.0492030	−	0.151431i
$708$	−8.10666	+	24.9497i	−0.304667	+	0.937668i
$709$	−4.85410	−	3.52671i	−0.182300	−	0.132448i	0.492893	−	0.870090i	$-0.335939\pi$
$709$	−4.85410	−	3.52671i	−0.182300	−	0.132448i	−0.675192	+	0.737642i	$0.735939\pi$
$710$	−3.60722	−	2.62080i	−0.135377	−	0.0983568i
$711$	−1.80496	+	5.55509i	−0.0676912	+	0.208332i
$712$	11.7921	+	36.2923i	0.441927	+	1.36011i
$713$	−11.9286	+	8.66664i	−0.446730	+	0.324568i
$714$	11.9769			0.448223
$715$		0			0
$716$	−105.957			−3.95978
$717$	−23.7021	+	17.2206i	−0.885171	+	0.643114i
$718$	−1.00599	−	3.09610i	−0.0375430	−	0.115546i
$719$	−1.85410	+	5.70634i	−0.0691463	+	0.212811i	−0.979659	−	0.200672i	$-0.935688\pi$
$719$	−1.85410	+	5.70634i	−0.0691463	+	0.212811i	0.910512	+	0.413482i	$0.135688\pi$
$720$	12.2298	+	8.88546i	0.455777	+	0.331141i
$721$	5.20268	+	3.77997i	0.193758	+	0.140773i
$722$	0.688918	−	2.12027i	0.0256389	−	0.0789083i
$723$	4.09957	+	12.6172i	0.152465	+	0.469238i
$724$	−60.1332	+	43.6894i	−2.23483	+	1.62370i
$725$	1.58457			0.0588496
$726$		0			0
$727$	7.25544			0.269089			0.134545	−	0.990908i	$-0.457043\pi$
$727$	7.25544			0.269089			0.134545	+	0.990908i	$0.457043\pi$
$728$	−15.7718	+	11.4589i	−0.584541	+	0.424694i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−13.7412	+	42.2910i	−0.508584	+	1.56526i
$731$	−32.1364	−	23.3485i	−1.18861	−	0.863575i
$732$	−9.45088	−	6.86646i	−0.349314	−	0.253792i
$733$	2.82985	−	8.70938i	0.104523	−	0.321688i	−0.885095	−	0.465410i	$-0.845907\pi$
$733$	2.82985	−	8.70938i	0.104523	−	0.321688i	0.989618	+	0.143721i	$0.0459069\pi$
$734$	18.5053	+	56.9534i	0.683043	+	2.10219i
$735$	−12.2298	+	8.88546i	−0.451102	+	0.327745i
$736$	−8.21782			−0.302913
$737$		0			0
$738$	−14.3723			−0.529051
$739$	−31.4687	+	22.8633i	−1.15759	+	0.841041i	−0.989472	−	0.144725i	$-0.953770\pi$
$739$	−31.4687	+	22.8633i	−1.15759	+	0.841041i	−0.168122	+	0.985766i	$0.553770\pi$
$740$	−16.0261	−	49.3231i	−0.589130	−	1.81315i
$741$	−5.40444	+	16.6331i	−0.198537	+	0.611034i
$742$	−21.2235	−	15.4198i	−0.779139	−	0.566078i
$743$	−19.9451	−	14.4909i	−0.731714	−	0.531621i	0.158391	−	0.987376i	$-0.449369\pi$
$743$	−19.9451	−	14.4909i	−0.731714	−	0.531621i	−0.890105	+	0.455755i	$0.849369\pi$
$744$	−13.6426	+	41.9877i	−0.500163	+	1.53934i
$745$	−4.38998	−	13.5110i	−0.160836	−	0.495003i
$746$	49.9348	−	36.2798i	1.82824	−	1.32830i
$747$	−8.51278			−0.311466
$748$		0			0
$749$	−0.233688			−0.00853877
$750$	21.1826	−	15.3901i	0.773479	−	0.561966i
$751$	−5.05259	−	15.5503i	−0.184372	−	0.567438i	0.815565	−	0.578665i	$-0.196426\pi$
$751$	−5.05259	−	15.5503i	−0.184372	−	0.567438i	−0.999937	+	0.0112273i	$0.996426\pi$
$752$	−2.47214	+	7.60845i	−0.0901495	+	0.277452i
$753$	0.413306	+	0.300285i	0.0150617	+	0.0109430i
$754$	21.1826	+	15.3901i	0.771425	+	0.560473i
$755$	1.59406	−	4.90601i	0.0580137	−	0.178548i
$756$	−1.07047	−	3.29456i	−0.0389325	−	0.119822i
$757$	−7.69446	+	5.59035i	−0.279660	+	0.203185i	−0.718769	−	0.695249i	$-0.755294\pi$
$757$	−7.69446	+	5.59035i	−0.279660	+	0.203185i	0.439109	+	0.898434i	$0.355294\pi$
$758$	−59.8844			−2.17510
$759$		0			0
$760$	−60.4674			−2.19338
$761$	32.8699	−	23.8814i	1.19153	−	0.865700i	0.198108	−	0.980180i	$-0.436520\pi$
$761$	32.8699	−	23.8814i	1.19153	−	0.865700i	0.993426	+	0.114480i	$0.0365203\pi$
$762$	15.3652	+	47.2892i	0.556622	+	1.71311i
$763$	2.43603	−	7.49733i	0.0881902	−	0.271421i
$764$	61.8634	+	44.9464i	2.23814	+	1.62610i
$765$	11.4931	+	8.35023i	0.415534	+	0.301903i
$766$	18.3230	−	56.3924i	0.662037	−	2.03754i
$767$	−7.61834	−	23.4468i	−0.275082	−	0.846616i
$768$	25.1741	−	18.2900i	0.908390	−	0.659984i
$769$	−34.7885			−1.25451			−0.627253	−	0.778816i	$-0.715821\pi$
$769$	−34.7885			−1.25451			−0.627253	+	0.778816i	$0.715821\pi$
$770$		0			0
$771$	24.3723			0.877746
$772$	−60.7453	+	44.1340i	−2.18627	+	1.58842i

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.04223 - 1.48377i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.35111 - 4.15829i) q^{4} +(1.91922 + 1.39439i) q^{5} +(2.04223 + 1.48377i) q^{6} +(-0.244830 + 0.753510i) q^{7} +(-1.85053 - 5.69534i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(2.04223 - 1.48377i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.35111 - 4.15829i) q^{4} +(1.91922 + 1.39439i) q^{5} +(2.04223 + 1.48377i) q^{6} +(-0.244830 + 0.753510i) q^{7} +(-1.85053 - 5.69534i) q^{8} +(-0.809017 + 0.587785i) q^{9} +5.98844 q^{10} +4.37228 q^{12} +(-3.32418 + 2.41516i) q^{13} +(0.618034 + 1.90211i) q^{14} +(-0.733075 + 2.25617i) q^{15} +(-5.15528 - 3.74553i) q^{16} +(-4.84475 - 3.51992i) q^{17} +(-0.780063 + 2.40079i) q^{18} +(-1.31530 - 4.04807i) q^{19} +(8.39135 - 6.09667i) q^{20} -0.792287 q^{21} +2.00000 q^{23} +(4.84475 - 3.51992i) q^{24} +(0.193976 + 0.596996i) q^{25} +(-3.20521 + 9.86463i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(2.80252 + 2.03615i) q^{28} +(0.780063 - 2.40079i) q^{29} +(1.85053 + 5.69534i) q^{30} +(-5.96430 + 4.33332i) q^{31} -4.10891 q^{32} -15.1168 q^{34} +(-1.52057 + 1.10476i) q^{35} +(1.35111 + 4.15829i) q^{36} +(1.54508 - 4.75528i) q^{37} +(-8.69253 - 6.31550i) q^{38} +(-3.32418 - 2.41516i) q^{39} +(4.38998 - 13.5110i) q^{40} +(1.75938 + 5.41483i) q^{41} +(-1.61803 + 1.17557i) q^{42} +6.63325 q^{43} -2.37228 q^{45} +(4.08446 - 2.96754i) q^{46} +(-0.387951 - 1.19399i) q^{47} +(1.96914 - 6.06040i) q^{48} +(5.15528 + 3.74553i) q^{49} +(1.28195 + 0.931389i) q^{50} +(1.85053 - 5.69534i) q^{51} +(5.55159 + 17.0860i) q^{52} +(-10.6117 + 7.70989i) q^{53} -2.52434 q^{54} +4.74456 q^{56} +(3.44349 - 2.50184i) q^{57} +(-1.96914 - 6.06040i) q^{58} +(-1.85410 + 5.70634i) q^{59} +(8.39135 + 6.09667i) q^{60} +(-2.16154 - 1.57045i) q^{61} +(-5.75085 + 17.6993i) q^{62} +(-0.244830 - 0.753510i) q^{63} +(1.91922 - 1.39439i) q^{64} -9.74749 q^{65} +16.1168 q^{67} +(-21.1826 + 15.3901i) q^{68} +(0.618034 + 1.90211i) q^{69} +(-1.46615 + 4.51235i) q^{70} +(-0.602364 - 0.437643i) q^{71} +(4.84475 + 3.51992i) q^{72} +(-2.29462 + 7.06210i) q^{73} +(-3.90032 - 12.0039i) q^{74} +(-0.507835 + 0.368964i) q^{75} -18.6101 q^{76} -10.3723 q^{78} +(4.72544 - 3.43323i) q^{79} +(-4.67136 - 14.3770i) q^{80} +(0.309017 - 0.951057i) q^{81} +(11.6274 + 8.44782i) q^{82} +(6.88698 + 5.00368i) q^{83} +(-1.07047 + 3.29456i) q^{84} +(-4.38998 - 13.5110i) q^{85} +(13.5466 - 9.84221i) q^{86} +2.52434 q^{87} -6.37228 q^{89} +(-4.84475 + 3.51992i) q^{90} +(-1.00599 - 3.09610i) q^{91} +(2.70222 - 8.31657i) q^{92} +(-5.96430 - 4.33332i) q^{93} +(-2.56389 - 1.86278i) q^{94} +(3.12025 - 9.60315i) q^{95} +(-1.26972 - 3.90781i) q^{96} +(10.1039 - 7.34092i) q^{97} +16.0858 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{3} - 6 q^{4} - 2 q^{5} - 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^3 - 6 * q^4 - 2 * q^5 - 4 * q^9	\( 16 q - 4 q^{3} - 6 q^{4} - 2 q^{5} - 4 q^{9} + 24 q^{12} - 8 q^{14} - 2 q^{15} - 14 q^{16} + 30 q^{20} + 32 q^{23} - 14 q^{25} + 30 q^{26} - 4 q^{27} - 18 q^{31} - 104 q^{34} - 6 q^{36} - 20 q^{37} - 20 q^{38} - 8 q^{42} + 8 q^{45} + 28 q^{47} - 14 q^{48} + 14 q^{49} - 18 q^{53} - 16 q^{56} + 14 q^{58} + 24 q^{59} + 30 q^{60} - 2 q^{64} + 120 q^{67} - 8 q^{69} - 4 q^{70} + 20 q^{71} - 14 q^{75} - 120 q^{78} + 26 q^{80} - 4 q^{81} + 46 q^{82} + 44 q^{86} - 56 q^{89} + 36 q^{91} - 12 q^{92} - 18 q^{93} + 4 q^{97}+O(q^{100}) \) 16 * q - 4 * q^3 - 6 * q^4 - 2 * q^5 - 4 * q^9 + 24 * q^12 - 8 * q^14 - 2 * q^15 - 14 * q^16 + 30 * q^20 + 32 * q^23 - 14 * q^25 + 30 * q^26 - 4 * q^27 - 18 * q^31 - 104 * q^34 - 6 * q^36 - 20 * q^37 - 20 * q^38 - 8 * q^42 + 8 * q^45 + 28 * q^47 - 14 * q^48 + 14 * q^49 - 18 * q^53 - 16 * q^56 + 14 * q^58 + 24 * q^59 + 30 * q^60 - 2 * q^64 + 120 * q^67 - 8 * q^69 - 4 * q^70 + 20 * q^71 - 14 * q^75 - 120 * q^78 + 26 * q^80 - 4 * q^81 + 46 * q^82 + 44 * q^86 - 56 * q^89 + 36 * q^91 - 12 * q^92 - 18 * q^93 + 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more