LMFDB - Embedded newform 841.2.e.j.270.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(63,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("841.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.e (of order $14$, degree $6$, 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:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			270.3
Character	$\chi$	$=$	841.270
Dual form			841.2.e.j.651.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.268155 + 0.556829i) q^{2} +(-0.483198 + 0.385338i) q^{3} +(1.00883 - 1.26503i) q^{4} +(3.47243 - 1.67223i) q^{5} +(-0.344139 - 0.165729i) q^{6} +(-1.39417 - 1.74823i) q^{7} +(2.18001 + 0.497572i) q^{8} +(-0.582567 + 2.55239i) q^{9} +O(q^{10})$	\(q+(0.268155 + 0.556829i) q^{2} +(-0.483198 + 0.385338i) q^{3} +(1.00883 - 1.26503i) q^{4} +(3.47243 - 1.67223i) q^{5} +(-0.344139 - 0.165729i) q^{6} +(-1.39417 - 1.74823i) q^{7} +(2.18001 + 0.497572i) q^{8} +(-0.582567 + 2.55239i) q^{9} +(1.86230 + 1.48513i) q^{10} +(1.34732 - 0.307516i) q^{11} +1.00000i q^{12} +(-0.0525301 - 0.230149i) q^{13} +(0.599613 - 1.24511i) q^{14} +(-1.03350 + 2.14608i) q^{15} +(-0.412577 - 1.80762i) q^{16} +4.38197i q^{17} +(-1.57747 + 0.360046i) q^{18} +(3.79509 + 3.02648i) q^{19} +(1.38766 - 6.07972i) q^{20} +(1.34732 + 0.307516i) q^{21} +(0.532524 + 0.667764i) q^{22} +(1.11366 + 0.536310i) q^{23} +(-1.24511 + 0.599613i) q^{24} +(6.14393 - 7.70425i) q^{25} +(0.114068 - 0.0909659i) q^{26} +(-1.50650 - 3.12829i) q^{27} -3.61803 q^{28} -1.47214 q^{30} +(-4.37796 - 9.09093i) q^{31} +(4.39236 - 3.50279i) q^{32} +(-0.532524 + 0.667764i) q^{33} +(-2.44001 + 1.17505i) q^{34} +(-7.76458 - 3.73922i) q^{35} +(2.64115 + 3.31189i) q^{36} +(-4.59016 - 1.04767i) q^{37} +(-0.667563 + 2.92478i) q^{38} +(0.114068 + 0.0909659i) q^{39} +(8.40196 - 1.91769i) q^{40} +3.85410i q^{41} +(0.190056 + 0.832688i) q^{42} +(3.13961 - 6.51947i) q^{43} +(0.970194 - 2.01463i) q^{44} +(2.24527 + 9.83719i) q^{45} +0.763932i q^{46} +(-6.82450 + 1.55765i) q^{47} +(0.895899 + 0.714456i) q^{48} +(0.445042 - 1.94986i) q^{49} +(5.93748 + 1.35519i) q^{50} +(-1.68854 - 2.11736i) q^{51} +(-0.344139 - 0.165729i) q^{52} +(1.80194 - 0.867767i) q^{53} +(1.33795 - 1.67773i) q^{54} +(4.16422 - 3.32086i) q^{55} +(-2.16942 - 4.50484i) q^{56} -3.00000 q^{57} +6.09017 q^{59} +(1.67223 + 3.47243i) q^{60} +(-0.483198 + 0.385338i) q^{61} +(3.88812 - 4.87555i) q^{62} +(5.27436 - 2.54000i) q^{63} +(-0.212690 - 0.102426i) q^{64} +(-0.567270 - 0.711334i) q^{65} +(-0.514629 - 0.117461i) q^{66} +(-0.339982 + 1.48956i) q^{67} +(5.54332 + 4.42065i) q^{68} +(-0.744779 + 0.169991i) q^{69} -5.32624i q^{70} +(2.33027 + 10.2096i) q^{71} +(-2.54000 + 5.27436i) q^{72} +(-5.94777 + 12.3507i) q^{73} +(-0.647498 - 2.83687i) q^{74} +6.09017i q^{75} +(7.65718 - 1.74770i) q^{76} +(-2.41599 - 1.92669i) q^{77} +(-0.0200647 + 0.0879092i) q^{78} +(-5.93748 - 1.35519i) q^{79} +(-4.45539 - 5.58689i) q^{80} +(-5.14291 - 2.47670i) q^{81} +(-2.14608 + 1.03350i) q^{82} +(-6.20015 + 7.77474i) q^{83} +(1.74823 - 1.39417i) q^{84} +(7.32766 + 15.2161i) q^{85} +4.47214 q^{86} +3.09017 q^{88} +(2.04281 + 4.24195i) q^{89} +(-4.87555 + 3.88812i) q^{90} +(-0.329118 + 0.412701i) q^{91} +(1.80194 - 0.867767i) q^{92} +(5.61850 + 2.70573i) q^{93} +(-2.69737 - 3.38239i) q^{94} +(18.2392 + 4.16297i) q^{95} +(-0.772623 + 3.38508i) q^{96} +(2.78512 + 2.22106i) q^{97} +(1.20508 - 0.275051i) q^{98} +3.61803i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9}+O(q^{10}) $ 24 * q - 2 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^9	$ 24 q - 2 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9} + 8 q^{13} + 6 q^{16} + 16 q^{20} + 10 q^{22} - 4 q^{23} - 10 q^{24} - 26 q^{25} - 60 q^{28} + 72 q^{30} - 10 q^{33} + 16 q^{34} - 30 q^{35} - 8 q^{36} - 12 q^{38} - 10 q^{42} + 18 q^{45} + 8 q^{49} - 16 q^{51} - 6 q^{52} + 8 q^{53} - 22 q^{54} - 72 q^{57} + 12 q^{59} - 16 q^{62} + 10 q^{63} + 8 q^{64} + 26 q^{65} - 24 q^{67} + 24 q^{71} - 34 q^{74} + 22 q^{78} + 42 q^{80} + 4 q^{81} - 14 q^{82} + 4 q^{83} - 60 q^{88} + 20 q^{91} + 8 q^{92} + 16 q^{93} - 14 q^{94} + 4 q^{96}+O(q^{100}) $ 24 * q - 2 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^9 + 8 * q^13 + 6 * q^16 + 16 * q^20 + 10 * q^22 - 4 * q^23 - 10 * q^24 - 26 * q^25 - 60 * q^28 + 72 * q^30 - 10 * q^33 + 16 * q^34 - 30 * q^35 - 8 * q^36 - 12 * q^38 - 10 * q^42 + 18 * q^45 + 8 * q^49 - 16 * q^51 - 6 * q^52 + 8 * q^53 - 22 * q^54 - 72 * q^57 + 12 * q^59 - 16 * q^62 + 10 * q^63 + 8 * q^64 + 26 * q^65 - 24 * q^67 + 24 * q^71 - 34 * q^74 + 22 * q^78 + 42 * q^80 + 4 * q^81 - 14 * q^82 + 4 * q^83 - 60 * q^88 + 20 * q^91 + 8 * q^92 + 16 * q^93 - 14 * q^94 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{14}\right)$

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 $

$2$	0.268155	+	0.556829i	0.189614	+	0.393738i	0.974004	−	0.226530i	$-0.0727382\pi$
$2$	0.268155	+	0.556829i	0.189614	+	0.393738i	−0.784390	+	0.620268i	$0.787024\pi$
$3$	−0.483198	+	0.385338i	−0.278975	+	0.222475i	−0.752974	−	0.658050i	$-0.771381\pi$
$3$	−0.483198	+	0.385338i	−0.278975	+	0.222475i	0.473999	+	0.880525i	$0.342810\pi$
$4$	1.00883	−	1.26503i	0.504414	−	0.632515i
$5$	3.47243	−	1.67223i	1.55292	−	0.747845i	0.556374	−	0.830932i	$-0.312192\pi$
$5$	3.47243	−	1.67223i	1.55292	−	0.747845i	0.996542	+	0.0830872i	$0.0264780\pi$
$6$	−0.344139	−	0.165729i	−0.140494	−	0.0676585i
$7$	−1.39417	−	1.74823i	−0.526945	−	0.660768i	0.445122	−	0.895470i	$-0.353160\pi$
$7$	−1.39417	−	1.74823i	−0.526945	−	0.660768i	−0.972067	+	0.234702i	$0.924589\pi$
$8$	2.18001	+	0.497572i	0.770748	+	0.175918i
$9$	−0.582567	+	2.55239i	−0.194189	+	0.850798i
$10$	1.86230	+	1.48513i	0.588910	+	0.469640i
$11$	1.34732	−	0.307516i	0.406231	−	0.0927197i	−0.0145224	−	0.999895i	$-0.504623\pi$
$11$	1.34732	−	0.307516i	0.406231	−	0.0927197i	0.420754	+	0.907175i	$0.361766\pi$
$12$			1.00000i			0.288675i
$13$	−0.0525301	−	0.230149i	−0.0145692	−	0.0638319i	0.967121	−	0.254318i	$-0.0818509\pi$
$13$	−0.0525301	−	0.230149i	−0.0145692	−	0.0638319i	−0.981690	+	0.190486i	$0.938994\pi$
$14$	0.599613	−	1.24511i	0.160253	−	0.332769i
$15$	−1.03350	+	2.14608i	−0.266848	+	0.554115i
$16$	−0.412577	−	1.80762i	−0.103144	−	0.451904i
$17$			4.38197i			1.06278i	0.847126	+	0.531391i	$0.178331\pi$
$17$			4.38197i			1.06278i	−0.847126	+	0.531391i	$0.821669\pi$
$18$	−1.57747	+	0.360046i	−0.371812	+	0.0848638i
$19$	3.79509	+	3.02648i	0.870653	+	0.694323i	0.953225	−	0.302262i	$-0.0977419\pi$
$19$	3.79509	+	3.02648i	0.870653	+	0.694323i	−0.0825715	+	0.996585i	$0.526313\pi$
$20$	1.38766	−	6.07972i	0.310289	−	1.35947i
$21$	1.34732	+	0.307516i	0.294009	+	0.0671056i
$22$	0.532524	+	0.667764i	0.113534	+	0.142368i
$23$	1.11366	+	0.536310i	0.232214	+	0.111828i	0.546373	−	0.837542i	$-0.316008\pi$
$23$	1.11366	+	0.536310i	0.232214	+	0.111828i	−0.314159	+	0.949370i	$0.601722\pi$
$24$	−1.24511	+	0.599613i	−0.254157	+	0.122395i
$25$	6.14393	−	7.70425i	1.22879	−	1.54085i
$26$	0.114068	−	0.0909659i	0.0223705	−	0.0178399i
$27$	−1.50650	−	3.12829i	−0.289927	−	0.602039i
$28$	−3.61803			−0.683744
$29$		0			0
$29$		0			0
$30$	−1.47214			−0.268774
$31$	−4.37796	−	9.09093i	−0.786305	−	1.63278i	−0.774273	−	0.632851i	$-0.781884\pi$
$31$	−4.37796	−	9.09093i	−0.786305	−	1.63278i	−0.0120317	−	0.999928i	$-0.503830\pi$
$32$	4.39236	−	3.50279i	0.776466	−	0.619211i
$33$	−0.532524	+	0.667764i	−0.0927005	+	0.116243i
$34$	−2.44001	+	1.17505i	−0.418458	+	0.201519i
$35$	−7.76458	−	3.73922i	−1.31245	−	0.632044i
$36$	2.64115	+	3.31189i	0.440191	+	0.551982i
$37$	−4.59016	−	1.04767i	−0.754618	−	0.172237i	−0.172128	−	0.985075i	$-0.555064\pi$
$37$	−4.59016	−	1.04767i	−0.754618	−	0.172237i	−0.582490	+	0.812838i	$0.697921\pi$
$38$	−0.667563	+	2.92478i	−0.108293	+	0.474463i
$39$	0.114068	+	0.0909659i	0.0182654	+	0.0145662i
$40$	8.40196	−	1.91769i	1.32847	−	0.303214i
$41$			3.85410i			0.601910i	0.953638	+	0.300955i	$0.0973053\pi$
$41$			3.85410i			0.601910i	−0.953638	+	0.300955i	$0.902695\pi$
$42$	0.190056	+	0.832688i	0.0293262	+	0.128487i
$43$	3.13961	−	6.51947i	0.478786	−	0.994210i	−0.512026	−	0.858970i	$-0.671105\pi$
$43$	3.13961	−	6.51947i	0.478786	−	0.994210i	0.990813	−	0.135240i	$-0.0431807\pi$
$44$	0.970194	−	2.01463i	0.146262	−	0.303717i
$45$	2.24527	+	9.83719i	0.334706	+	1.46644i
$46$			0.763932i			0.112636i
$47$	−6.82450	+	1.55765i	−0.995455	+	0.227206i	−0.689065	−	0.724700i	$-0.741978\pi$
$47$	−6.82450	+	1.55765i	−0.995455	+	0.227206i	−0.306390	+	0.951906i	$0.599121\pi$
$48$	0.895899	+	0.714456i	0.129312	+	0.103123i
$49$	0.445042	−	1.94986i	0.0635774	−	0.278551i
$50$	5.93748	+	1.35519i	0.839686	+	0.191653i
$51$	−1.68854	−	2.11736i	−0.236443	−	0.296490i
$52$	−0.344139	−	0.165729i	−0.0477236	−	0.0229825i
$53$	1.80194	−	0.867767i	0.247515	−	0.119197i	−0.306013	−	0.952027i	$-0.598995\pi$
$53$	1.80194	−	0.867767i	0.247515	−	0.119197i	0.553529	+	0.832830i	$0.313281\pi$
$54$	1.33795	−	1.67773i	0.182071	−	0.228310i
$55$	4.16422	−	3.32086i	0.561503	−	0.447784i
$56$	−2.16942	−	4.50484i	−0.289901	−	0.601985i
$57$	−3.00000			−0.397360
$58$		0			0
$59$	6.09017			0.792873			0.396436	−	0.918062i	$-0.370247\pi$
$59$	6.09017			0.792873			0.396436	+	0.918062i	$0.370247\pi$
$60$	1.67223	+	3.47243i	0.215884	+	0.448288i
$61$	−0.483198	+	0.385338i	−0.0618672	+	0.0493375i	−0.653935	−	0.756551i	$-0.726883\pi$
$61$	−0.483198	+	0.385338i	−0.0618672	+	0.0493375i	0.592068	+	0.805888i	$0.298312\pi$
$62$	3.88812	−	4.87555i	0.493792	−	0.619196i
$63$	5.27436	−	2.54000i	0.664507	−	0.320010i
$64$	−0.212690	−	0.102426i	−0.0265862	−	0.0128033i
$65$	−0.567270	−	0.711334i	−0.0703612	−	0.0882301i
$66$	−0.514629	−	0.117461i	−0.0633465	−	0.0144584i
$67$	−0.339982	+	1.48956i	−0.0415354	+	0.181978i	−0.991440	−	0.130561i	$-0.958322\pi$
$67$	−0.339982	+	1.48956i	−0.0415354	+	0.181978i	0.949905	+	0.312539i	$0.101179\pi$
$68$	5.54332	+	4.42065i	0.672226	+	0.536082i
$69$	−0.744779	+	0.169991i	−0.0896608	+	0.0204645i
$70$		−	5.32624i		−	0.636607i
$71$	2.33027	+	10.2096i	0.276552	+	1.21165i	0.902120	+	0.431484i	$0.142010\pi$
$71$	2.33027	+	10.2096i	0.276552	+	1.21165i	−0.625568	+	0.780169i	$0.715133\pi$
$72$	−2.54000	+	5.27436i	−0.299342	+	0.621590i
$73$	−5.94777	+	12.3507i	−0.696133	+	1.44554i	0.189847	+	0.981814i	$0.439201\pi$
$73$	−5.94777	+	12.3507i	−0.696133	+	1.44554i	−0.885981	+	0.463722i	$0.846514\pi$
$74$	−0.647498	−	2.83687i	−0.0752701	−	0.329780i
$75$			6.09017i			0.703232i
$76$	7.65718	−	1.74770i	0.878339	−	0.200475i
$77$	−2.41599	−	1.92669i	−0.275328	−	0.219567i
$78$	−0.0200647	+	0.0879092i	−0.00227188	+	0.00995376i
$79$	−5.93748	−	1.35519i	−0.668018	−	0.152471i	−0.124955	−	0.992162i	$-0.539879\pi$
$79$	−5.93748	−	1.35519i	−0.668018	−	0.152471i	−0.543064	+	0.839692i	$0.682736\pi$
$80$	−4.45539	−	5.58689i	−0.498128	−	0.624633i
$81$	−5.14291	−	2.47670i	−0.571435	−	0.275189i
$82$	−2.14608	+	1.03350i	−0.236995	+	0.114131i
$83$	−6.20015	+	7.77474i	−0.680555	+	0.853389i	−0.995405	−	0.0957523i	$-0.969474\pi$
$83$	−6.20015	+	7.77474i	−0.680555	+	0.853389i	0.314850	+	0.949141i	$0.398046\pi$
$84$	1.74823	−	1.39417i	0.190747	−	0.152116i
$85$	7.32766	+	15.2161i	0.794797	+	1.65041i
$86$	4.47214			0.482243
$87$		0			0
$88$	3.09017			0.329413
$89$	2.04281	+	4.24195i	0.216538	+	0.449645i	0.980736	−	0.195336i	$-0.0625796\pi$
$89$	2.04281	+	4.24195i	0.216538	+	0.449645i	−0.764199	+	0.644981i	$0.776865\pi$
$90$	−4.87555	+	3.88812i	−0.513929	+	0.409844i
$91$	−0.329118	+	0.412701i	−0.0345009	+	0.0432628i
$92$	1.80194	−	0.867767i	0.187865	−	0.0904710i
$93$	5.61850	+	2.70573i	0.582612	+	0.280571i
$94$	−2.69737	−	3.38239i	−0.278212	−	0.348867i
$95$	18.2392	+	4.16297i	1.87130	+	0.427111i
$96$	−0.772623	+	3.38508i	−0.0788555	+	0.345489i
$97$	2.78512	+	2.22106i	0.282786	+	0.225515i	0.754602	−	0.656183i	$-0.227830\pi$
$97$	2.78512	+	2.22106i	0.282786	+	0.225515i	−0.471816	+	0.881697i	$0.656401\pi$
$98$	1.20508	−	0.275051i	0.121731	−	0.0277843i
$99$			3.61803i			0.363626i
$100$	−3.54793	−	15.5445i	−0.354793	−	1.55445i
$101$	0.268155	−	0.556829i	0.0266824	−	0.0554066i	−0.887202	−	0.461382i	$-0.847354\pi$
$101$	0.268155	−	0.556829i	0.0266824	−	0.0554066i	0.913884	+	0.405975i	$0.133068\pi$
$102$	0.726218	−	1.50801i	0.0719063	−	0.149315i
$103$	−2.04282	−	8.95017i	−0.201285	−	0.881886i	−0.970156	−	0.242482i	$-0.922038\pi$
$103$	−2.04282	−	8.95017i	−0.201285	−	0.881886i	0.768871	−	0.639404i	$-0.220819\pi$
$104$		−	0.527864i		−	0.0517613i
$105$	5.19270	−	1.18520i	0.506755	−	0.115664i
$106$	0.966397	+	0.770676i	0.0938648	+	0.0748546i
$107$	−1.50512	+	6.59435i	−0.145505	+	0.637500i	0.848596	+	0.529042i	$0.177448\pi$
$107$	−1.50512	+	6.59435i	−0.145505	+	0.637500i	−0.994101	+	0.108458i	$0.965409\pi$
$108$	−5.47718	−	1.25013i	−0.527042	−	0.120294i
$109$	8.96701	+	11.2443i	0.858884	+	1.07701i	0.996253	+	0.0864862i	$0.0275638\pi$
$109$	8.96701	+	11.2443i	0.858884	+	1.07701i	−0.137369	+	0.990520i	$0.543865\pi$
$110$	2.96581	+	1.42826i	0.282778	+	0.136179i
$111$	2.62167	−	1.26253i	0.248838	−	0.119834i
$112$	−2.58493	+	3.24139i	−0.244252	+	0.306283i
$113$	−6.21108	+	4.95317i	−0.584289	+	0.465955i	−0.870471	−	0.492220i	$-0.836185\pi$
$113$	−6.21108	+	4.95317i	−0.584289	+	0.465955i	0.286181	+	0.958175i	$0.407614\pi$
$114$	−0.804465	−	1.67049i	−0.0753450	−	0.156456i
$115$	4.76393			0.444239
$116$		0			0
$117$	0.618034			0.0571373
$118$	1.63311	+	3.39119i	0.150340	+	0.312184i
$119$	7.66068	−	6.10919i	0.702253	−	0.560028i
$120$	−3.32086	+	4.16422i	−0.303151	+	0.380140i
$121$	−8.18996	+	3.94408i	−0.744542	+	0.358552i
$122$	−0.344139	−	0.165729i	−0.0311569	−	0.0150044i
$123$	−1.48513	−	1.86230i	−0.133910	−	0.167918i
$124$	−15.9169	−	3.63293i	−1.42938	−	0.326247i
$125$	4.16297	−	18.2392i	0.372347	−	1.63136i
$126$	2.82869	+	2.25581i	0.252000	+	0.200963i
$127$	−15.5445	+	3.54793i	−1.37935	+	0.314828i	−0.846954	−	0.531666i	$-0.821566\pi$
$127$	−15.5445	+	3.54793i	−1.37935	+	0.314828i	−0.532398	+	0.846494i	$0.678709\pi$
$128$		−	11.3820i		−	1.00603i
$129$	0.995144	+	4.36001i	0.0876175	+	0.383877i
$130$	0.243975	−	0.506620i	0.0213981	−	0.0444335i
$131$	6.21592	−	12.9075i	0.543088	−	1.12773i	−0.431165	−	0.902273i	$-0.641897\pi$
$131$	6.21592	−	12.9075i	0.543088	−	1.12773i	0.974252	−	0.225460i	$-0.0723884\pi$
$132$	0.307516	+	1.34732i	0.0267659	+	0.117269i
$133$		−	10.8541i		−	0.941170i
$134$	−0.920597	+	0.210120i	−0.0795275	+	0.0181516i
$135$	−10.4624	−	8.34352i	−0.900464	−	0.718096i
$136$	−2.18034	+	9.55271i	−0.186963	+	0.819138i
$137$	6.96674	+	1.59011i	0.595208	+	0.135852i	0.509504	−	0.860468i	$-0.329829\pi$
$137$	6.96674	+	1.59011i	0.595208	+	0.135852i	0.0857042	+	0.996321i	$0.472686\pi$
$138$	−0.294372	−	0.369131i	−0.0250586	−	0.0314225i
$139$	−1.16387	−	0.560489i	−0.0987180	−	0.0475401i	0.383873	−	0.923386i	$-0.374590\pi$
$139$	−1.16387	−	0.560489i	−0.0987180	−	0.0475401i	−0.482591	+	0.875846i	$0.660304\pi$
$140$	−12.5634	+	6.05019i	−1.06180	+	0.511335i
$141$	2.69737	−	3.38239i	0.227159	−	0.284849i
$142$	−5.06012	+	4.03531i	−0.424636	+	0.338636i
$143$	−0.141549	−	0.293930i	−0.0118369	−	0.0245797i
$144$	4.85410			0.404508
$145$		0			0
$146$	−8.47214			−0.701159
$147$	0.536310	+	1.11366i	0.0442341	+	0.0918530i
$148$	−5.95602	+	4.74977i	−0.489582	+	0.390428i
$149$	−5.99675	+	7.51968i	−0.491273	+	0.616036i	−0.964236	−	0.265046i	$-0.914613\pi$
$149$	−5.99675	+	7.51968i	−0.491273	+	0.616036i	0.472963	+	0.881082i	$0.343184\pi$
$150$	−3.39119	+	1.63311i	−0.276889	+	0.133343i
$151$	2.40898	+	1.16010i	0.196040	+	0.0944078i	0.529328	−	0.848417i	$-0.322444\pi$
$151$	2.40898	+	1.16010i	0.196040	+	0.0944078i	−0.333288	+	0.942825i	$0.608158\pi$
$152$	6.76742	+	8.48608i	0.548910	+	0.688312i
$153$	−11.1845	−	2.55279i	−0.904214	−	0.206381i
$154$	0.424977	−	1.86195i	0.0342456	−	0.150040i
$155$	−30.4043	−	24.2466i	−2.44213	−	1.94753i
$156$	0.230149	−	0.0525301i	0.0184267	−	0.00420577i
$157$			14.5623i			1.16220i	0.813833	+	0.581099i	$0.197377\pi$
$157$			14.5623i			1.16220i	−0.813833	+	0.581099i	$0.802623\pi$
$158$	−0.837554	−	3.66956i	−0.0666322	−	0.291935i
$159$	−0.536310	+	1.11366i	−0.0425321	+	0.0883189i
$160$	9.39466	−	19.5082i	0.742713	−	1.54226i
$161$	−0.615033	−	2.69463i	−0.0484714	−	0.212367i
$162$		−	3.52786i		−	0.277175i
$163$	−5.88315	+	1.34279i	−0.460804	+	0.105175i	−0.446619	−	0.894724i	$-0.647372\pi$
$163$	−5.88315	+	1.34279i	−0.460804	+	0.105175i	−0.0141841	+	0.999899i	$0.504515\pi$
$164$	4.87555	+	3.88812i	0.380717	+	0.303612i
$165$	−0.732494	+	3.20926i	−0.0570245	+	0.249841i
$166$	−5.99181	−	1.36759i	−0.465054	−	0.106146i
$167$	−6.56402	−	8.23102i	−0.507939	−	0.636935i	0.460061	−	0.887888i	$-0.347828\pi$
$167$	−6.56402	−	8.23102i	−0.507939	−	0.636935i	−0.967999	+	0.250952i	$0.919256\pi$
$168$	2.78415	+	1.34077i	0.214802	+	0.103443i
$169$	11.6624	−	5.61631i	0.897107	−	0.432024i
$170$	−6.50780	+	8.16052i	−0.499125	+	0.625883i
$171$	−9.93567	+	7.92344i	−0.759800	+	0.605920i
$172$	−5.08000	−	10.5487i	−0.387346	−	0.804333i
$173$	−4.09017			−0.310970			−0.155485	−	0.987838i	$-0.549694\pi$
$173$	−4.09017			−0.310970			−0.155485	+	0.987838i	$0.549694\pi$
$174$		0			0
$175$	−22.0344			−1.66565
$176$	−1.11174	−	2.30856i	−0.0838008	−	0.174014i
$177$	−2.94276	+	2.34677i	−0.221191	+	0.176394i
$178$	−1.81425	+	2.27500i	−0.135984	+	0.170518i
$179$	−14.4155	+	6.94214i	−1.07747	+	0.518880i	−0.886506	−	0.462718i	$-0.846874\pi$
$179$	−14.4155	+	6.94214i	−1.07747	+	0.518880i	−0.190960	+	0.981598i	$0.561160\pi$
$180$	14.7094	+	7.08369i	1.09638	+	0.527987i
$181$	3.70619	+	4.64742i	0.275479	+	0.345440i	0.900254	−	0.435365i	$-0.143381\pi$
$181$	3.70619	+	4.64742i	0.275479	+	0.345440i	−0.624775	+	0.780805i	$0.714809\pi$
$182$	−0.318058	−	0.0725948i	−0.0235761	−	0.00538108i
$183$	0.0849954	−	0.372389i	0.00628304	−	0.0275278i
$184$	2.16093	+	1.72328i	0.159306	+	0.127042i
$185$	−17.6909	+	4.03784i	−1.30066	+	0.296868i
$186$			3.85410i			0.282596i
$187$	1.34753	+	5.90390i	0.0985409	+	0.431736i
$188$	−4.91427	+	10.2046i	−0.358410	+	0.744246i
$189$	−3.36864	+	6.99506i	−0.245033	+	0.508816i
$190$	2.57286	+	11.2724i	0.186655	+	0.817787i
$191$		−	17.0344i		−	1.23257i	−0.787524	−	0.616284i	$-0.788637\pi$
$191$		−	17.0344i		−	1.23257i	0.787524	−	0.616284i	$-0.211363\pi$
$192$	0.142240	−	0.0324654i	0.0102653	−	0.00234299i
$193$	−9.75111	−	7.77625i	−0.701900	−	0.559747i	0.206195	−	0.978511i	$-0.433892\pi$
$193$	−9.75111	−	7.77625i	−0.701900	−	0.559747i	−0.908095	+	0.418764i	$0.862463\pi$
$194$	−0.489908	+	2.14643i	−0.0351733	+	0.154104i
$195$	0.548208	+	0.125125i	0.0392580	+	0.00896038i
$196$	−2.01766	−	2.53006i	−0.144118	−	0.180719i
$197$	5.66871	+	2.72991i	0.403879	+	0.194498i	0.624784	−	0.780797i	$-0.285187\pi$
$197$	5.66871	+	2.72991i	0.403879	+	0.194498i	−0.220905	+	0.975295i	$0.570901\pi$
$198$	−2.01463	+	0.970194i	−0.143173	+	0.0689487i
$199$	−3.64997	+	4.57692i	−0.258740	+	0.324449i	−0.894186	−	0.447696i	$-0.852245\pi$
$199$	−3.64997	+	4.57692i	−0.258740	+	0.324449i	0.635446	+	0.772145i	$0.280816\pi$
$200$	17.2272	−	13.7382i	1.21815	−	0.971441i
$201$	−0.409704	−	0.850760i	−0.0288983	−	0.0600080i
$202$	0.381966			0.0268750
$203$		0			0
$204$	−4.38197			−0.306799
$205$	6.44495	+	13.3831i	0.450135	+	0.934715i
$206$	4.43593	−	3.53753i	0.309066	−	0.246472i
$207$	−2.01766	+	2.53006i	−0.140237	+	0.175851i
$208$	−0.394349	+	0.189908i	−0.0273432	+	0.0131678i
$209$	6.04388	+	2.91058i	0.418064	+	0.201329i
$210$	2.05240	+	2.57363i	0.141629	+	0.177597i
$211$	11.3603	+	2.59292i	0.782077	+	0.178504i	0.594876	−	0.803818i	$-0.297201\pi$
$211$	11.3603	+	2.59292i	0.782077	+	0.178504i	0.187201	+	0.982322i	$0.440058\pi$
$212$	0.720093	−	3.15493i	0.0494562	−	0.216682i
$213$	−5.06012	−	4.03531i	−0.346714	−	0.276495i
$214$	−4.07553	+	0.930213i	−0.278597	+	0.0635881i
$215$		−	27.8885i		−	1.90198i
$216$	−1.72764	−	7.56927i	−0.117551	−	0.515024i
$217$	−9.78942	+	20.3279i	−0.664549	+	1.37995i
$218$	−3.85659	+	8.00830i	−0.261202	+	0.542391i
$219$	−1.88523	−	8.25972i	−0.127392	−	0.558140i
$220$		−	8.61803i		−	0.581028i
$221$	1.00851	−	0.230185i	0.0678395	−	0.0154839i
$222$	1.40603	+	1.12127i	0.0943662	+	0.0752546i
$223$	−0.594968	+	2.60673i	−0.0398420	+	0.174559i	−0.990934	−	0.134348i	$-0.957106\pi$
$223$	−0.594968	+	2.60673i	−0.0398420	+	0.174559i	0.951092	+	0.308907i	$0.0999632\pi$
$224$	−12.2473	−	2.79538i	−0.818310	−	0.186774i
$225$	16.0850	+	20.1700i	1.07233	+	1.34467i
$226$	−4.42360	−	2.13030i	−0.294254	−	0.141705i
$227$	18.8199	−	9.06320i	1.24912	−	0.601546i	0.311846	−	0.950133i	$-0.399053\pi$
$227$	18.8199	−	9.06320i	1.24912	−	0.601546i	0.937276	+	0.348587i	$0.113338\pi$
$228$	−3.02648	+	3.79509i	−0.200434	+	0.251336i
$229$	−1.79180	+	1.42891i	−0.118405	+	0.0944251i	−0.680902	−	0.732374i	$-0.738412\pi$
$229$	−1.79180	+	1.42891i	−0.118405	+	0.0944251i	0.562497	+	0.826799i	$0.309841\pi$
$230$	1.27747	+	2.65270i	0.0842340	+	0.174914i
$231$	1.90983			0.125658
$232$		0			0
$233$	15.2361			0.998148			0.499074	−	0.866559i	$-0.333674\pi$
$233$	15.2361			0.998148			0.499074	+	0.866559i	$0.333674\pi$
$234$	0.165729	+	0.344139i	0.0108340	+	0.0224971i
$235$	−21.0928	+	16.8210i	−1.37594	+	1.09728i
$236$	6.14393	−	7.70425i	0.399936	−	0.501504i
$237$	3.39119	−	1.63311i	0.220281	−	0.106082i
$238$	5.45602	+	2.62748i	0.353661	+	0.170314i
$239$	−17.2973	−	21.6901i	−1.11887	−	1.40301i	−0.904612	−	0.426236i	$-0.859839\pi$
$239$	−17.2973	−	21.6901i	−1.11887	−	1.40301i	−0.214255	−	0.976778i	$-0.568732\pi$
$240$	4.30568	+	0.982743i	0.277930	+	0.0634358i
$241$	−1.03527	+	4.53583i	−0.0666878	+	0.292178i	−0.997264	−	0.0739193i	$-0.976449\pi$
$241$	−1.03527	+	4.53583i	−0.0666878	+	0.292178i	0.930576	+	0.366098i	$0.119306\pi$
$242$	−4.39236	−	3.50279i	−0.282351	−	0.225168i
$243$	13.5947	−	3.10289i	0.872098	−	0.199051i
$244$			1.00000i			0.0640184i
$245$	−1.71524	−	7.51494i	−0.109582	−	0.480112i
$246$	0.638736	−	1.32635i	0.0407243	−	0.0845649i
$247$	0.497187	−	1.03242i	0.0316352	−	0.0656912i
$248$	−5.02059	−	21.9966i	−0.318807	−	1.39679i
$249$		−	6.14590i		−	0.389480i
$250$	11.2724	−	2.57286i	0.712930	−	0.162722i
$251$	15.3649	+	12.2531i	0.969825	+	0.773410i	0.973992	−	0.226581i	$-0.0727549\pi$
$251$	15.3649	+	12.2531i	0.969825	+	0.773410i	−0.00416682	+	0.999991i	$0.501326\pi$
$252$	2.10775	−	9.23465i	0.132776	−	0.581728i
$253$	1.66538	+	0.380111i	0.104701	+	0.0238974i
$254$	−6.14393	−	7.70425i	−0.385505	−	0.483407i
$255$	−9.40404	−	4.52875i	−0.588904	−	0.283601i
$256$	5.91243	−	2.84728i	0.369527	−	0.177955i
$257$	−14.4527	+	18.1231i	−0.901535	+	1.13049i	0.0893797	+	0.995998i	$0.471512\pi$
$257$	−14.4527	+	18.1231i	−0.901535	+	1.13049i	−0.990915	+	0.134492i	$0.957060\pi$
$258$	−2.16093	+	1.72328i	−0.134534	+	0.107287i
$259$	4.56787	+	9.48528i	0.283834	+	0.589386i
$260$	−1.47214			−0.0912980
$261$		0			0
$262$	8.85410			0.547008
$263$	−7.24942	−	15.0536i	−0.447018	−	0.928243i	−0.995737	−	0.0922361i	$-0.970599\pi$
$263$	−7.24942	−	15.0536i	−0.447018	−	0.928243i	0.548719	−	0.836007i	$-0.315116\pi$
$264$	−1.49317	+	1.19076i	−0.0918980	+	0.0732862i
$265$	4.80599	−	6.02652i	0.295229	−	0.370206i
$266$	6.04388	−	2.91058i	0.370574	−	0.178459i
$267$	−2.62167	−	1.26253i	−0.160443	−	0.0772655i
$268$	1.54135	+	1.93279i	0.0941530	+	0.118064i
$269$	5.84957	+	1.33513i	0.356654	+	0.0814040i	0.397094	−	0.917778i	$-0.370019\pi$
$269$	5.84957	+	1.33513i	0.356654	+	0.0814040i	−0.0404396	+	0.999182i	$0.512876\pi$
$270$	1.84036	−	8.06315i	0.112001	−	0.490708i
$271$	7.95931	+	6.34734i	0.483494	+	0.385573i	0.834683	−	0.550731i	$-0.185651\pi$
$271$	7.95931	+	6.34734i	0.483494	+	0.385573i	−0.351189	+	0.936305i	$0.614223\pi$
$272$	7.92091	−	1.80790i	0.480276	−	0.109620i
$273$		−	0.326238i		−	0.0197448i
$274$	0.982743	+	4.30568i	0.0593697	+	0.260116i
$275$	5.90864	−	12.2694i	0.356305	−	0.739874i
$276$	−0.536310	+	1.11366i	−0.0322821	+	0.0670344i
$277$	4.75794	+	20.8459i	0.285877	+	1.25251i	0.890127	+	0.455713i	$0.150616\pi$
$277$	4.75794	+	20.8459i	0.285877	+	1.25251i	−0.604250	+	0.796795i	$0.706527\pi$
$278$		−	0.798374i		−	0.0478833i
$279$	25.7541	−	5.87820i	1.54186	−	0.351919i
$280$	−15.0663	−	12.0150i	−0.900383	−	0.718032i
$281$	−5.14571	+	22.5448i	−0.306967	+	1.34491i	0.552411	+	0.833572i	$0.313708\pi$
$281$	−5.14571	+	22.5448i	−0.306967	+	1.34491i	−0.859379	+	0.511340i	$0.829149\pi$
$282$	2.60673	+	0.594968i	0.155228	+	0.0354298i
$283$	3.26463	+	4.09372i	0.194062	+	0.243347i	0.869337	−	0.494220i	$-0.164546\pi$
$283$	3.26463	+	4.09372i	0.194062	+	0.243347i	−0.675274	+	0.737567i	$0.735975\pi$
$284$	15.2663	+	7.35184i	0.905886	+	0.436252i
$285$	−10.4173	+	5.01670i	−0.617066	+	0.297163i
$286$	0.125712	−	0.157638i	0.00743350	−	0.00932131i
$287$	6.73785	−	5.37326i	0.397723	−	0.317173i
$288$	6.38165	+	13.2516i	0.376042	+	0.780860i
$289$	−2.20163			−0.129507
$290$		0			0
$291$	−2.20163			−0.129062
$292$	9.62369	+	19.9838i	0.563184	+	1.16946i
$293$	6.66735	−	5.31704i	0.389511	−	0.310625i	−0.409080	−	0.912498i	$-0.634150\pi$
$293$	6.66735	−	5.31704i	0.389511	−	0.310625i	0.798591	+	0.601874i	$0.205579\pi$
$294$	−0.476304	+	0.597266i	−0.0277786	+	0.0348333i
$295$	21.1477	−	10.1842i	1.23126	−	0.592946i
$296$	−9.48528	−	4.56787i	−0.551321	−	0.265502i
$297$	−2.99174	−	3.75152i	−0.173598	−	0.217685i
$298$	−5.79524	−	1.32272i	−0.335709	−	0.0766234i
$299$	0.0649307	−	0.284480i	0.00375504	−	0.0164519i
$300$	7.70425	+	6.14393i	0.444805	+	0.354720i
$301$	−15.7747	+	3.60046i	−0.909237	+	0.207527i
$302$			1.65248i			0.0950893i
$303$	0.0849954	+	0.372389i	0.00488286	+	0.0213932i
$304$	3.90495	−	8.10872i	0.223964	−	0.465067i
$305$	−1.03350	+	2.14608i	−0.0591778	+	0.122884i
$306$	−1.57771	−	6.91240i	−0.0901917	−	0.395156i
$307$			19.1803i			1.09468i	0.836910	+	0.547340i	$0.184360\pi$
$307$			19.1803i			1.09468i	−0.836910	+	0.547340i	$0.815640\pi$
$308$	−4.87464	+	1.11260i	−0.277758	+	0.0633965i
$309$	4.43593	+	3.53753i	0.252351	+	0.201243i
$310$	5.34817	−	23.4318i	0.303755	−	1.33084i
$311$	2.03777	+	0.465107i	0.115551	+	0.0263738i	0.279905	−	0.960028i	$-0.409697\pi$
$311$	2.03777	+	0.465107i	0.115551	+	0.0263738i	−0.164354	+	0.986401i	$0.552554\pi$
$312$	0.203406	+	0.255063i	0.0115156	+	0.0144401i
$313$	11.6314	+	5.60137i	0.657443	+	0.316608i	0.732695	−	0.680557i	$-0.238262\pi$
$313$	11.6314	+	5.60137i	0.657443	+	0.316608i	−0.0752524	+	0.997165i	$0.523976\pi$
$314$	−8.10872	+	3.90495i	−0.457602	+	0.220369i
$315$	14.0674	−	17.6399i	0.792606	−	0.993897i
$316$	−7.70425	+	6.14393i	−0.433398	+	0.345623i
$317$	−12.0221	−	24.9642i	−0.675231	−	1.40213i	−0.903524	−	0.428538i	$-0.859029\pi$
$317$	−12.0221	−	24.9642i	−0.675231	−	1.40213i	0.228293	−	0.973592i	$-0.426686\pi$
$318$	−0.763932			−0.0428392
$319$		0			0
$320$	−0.909830			−0.0508610
$321$	−1.81378	−	3.76636i	−0.101235	−	0.210217i
$322$	1.33553	−	1.06505i	0.0744260	−	0.0593528i
$323$	−13.2619	+	16.6300i	−0.737914	+	0.925315i
$324$	−8.32141	+	4.00738i	−0.462301	+	0.222632i
$325$	−2.09587	−	1.00932i	−0.116258	−	0.0559868i
$326$	−2.32530	−	2.91583i	−0.128786	−	0.161493i
$327$	−8.66569	−	1.97789i	−0.479214	−	0.109377i
$328$	−1.91769	+	8.40196i	−0.105887	+	0.463921i
$329$	12.2376	+	9.75916i	0.674681	+	0.538040i
$330$	−1.98343	+	0.452706i	−0.109184	+	0.0249206i
$331$			21.1803i			1.16418i	0.813126	+	0.582088i	$0.197764\pi$
$331$			21.1803i			1.16418i	−0.813126	+	0.582088i	$0.802236\pi$
$332$	3.58040	+	15.6868i	0.196500	+	0.860923i
$333$	5.34815	−	11.1056i	0.293077	−	0.608581i
$334$	2.82310	−	5.86222i	0.154473	−	0.320767i
$335$	1.31032	+	5.74091i	0.0715907	+	0.313659i
$336$		−	2.56231i		−	0.139785i
$337$	−33.2147	+	7.58104i	−1.80932	+	0.412966i	−0.987609	−	0.156938i	$-0.949838\pi$
$337$	−33.2147	+	7.58104i	−1.80932	+	0.412966i	−0.821712	+	0.569903i	$0.806981\pi$
$338$	6.25465	+	4.98792i	0.340208	+	0.271307i
$339$	1.09254	−	4.78673i	0.0593386	−	0.259980i
$340$	26.6411	+	6.08066i	1.44482	+	0.329770i
$341$	−8.69411	−	10.9021i	−0.470813	−	0.590380i
$342$	−7.07630	−	3.40777i	−0.382643	−	0.184271i
$343$	−18.1316	+	8.73174i	−0.979017	+	0.471470i
$344$	10.0883	−	12.6503i	0.543923	−	0.682058i
$345$	−2.30192	+	1.83572i	−0.123931	+	0.0988320i
$346$	−1.09680	−	2.27753i	−0.0589643	−	0.122441i
$347$	32.1246			1.72454			0.862270	−	0.506449i	$-0.169042\pi$
$347$	32.1246			1.72454			0.862270	+	0.506449i	$0.169042\pi$
$348$		0			0
$349$	4.52786			0.242371			0.121186	−	0.992630i	$-0.461330\pi$
$349$	4.52786			0.242371			0.121186	+	0.992630i	$0.461330\pi$
$350$	−5.90864	−	12.2694i	−0.315830	−	0.655828i
$351$	−0.640836	+	0.511050i	−0.0342053	+	0.0272778i
$352$	4.84073	−	6.07009i	0.258012	−	0.323537i
$353$	−17.2307	+	8.29786i	−0.917097	+	0.441650i	−0.832034	−	0.554725i	$-0.812823\pi$
$353$	−17.2307	+	8.29786i	−0.917097	+	0.441650i	−0.0850629	+	0.996376i	$0.527109\pi$
$354$	−2.09587	−	1.00932i	−0.111394	−	0.0536446i
$355$	25.1645	+	31.5553i	1.33559	+	1.67478i
$356$	7.42703	+	1.69517i	0.393632	+	0.0898439i
$357$	−1.34753	+	5.90390i	−0.0713187	+	0.312467i
$358$	−7.73117	−	6.16541i	−0.408605	−	0.325852i
$359$	23.1681	−	5.28797i	1.22277	−	0.279089i	0.438054	−	0.898949i	$-0.355668\pi$
$359$	23.1681	−	5.28797i	1.22277	−	0.279089i	0.784712	+	0.619860i	$0.212811\pi$
$360$			22.5623i			1.18914i
$361$	1.01521	+	4.44792i	0.0534320	+	0.234101i
$362$	−1.59399	+	3.30995i	−0.0837780	+	0.173967i
$363$	2.43757	−	5.06167i	0.127939	−	0.265669i
$364$	0.190056	+	0.832688i	0.00996162	+	0.0436447i
$365$			52.8328i			2.76540i
$366$	0.230149	−	0.0525301i	0.0120301	−	0.00274579i
$367$	−21.3209	−	17.0029i	−1.11294	−	0.887543i	−0.118515	−	0.992952i	$-0.537813\pi$
$367$	−21.3209	−	17.0029i	−1.11294	−	0.887543i	−0.994429	+	0.105409i	$0.966385\pi$
$368$	0.509973	−	2.23434i	0.0265842	−	0.116473i
$369$	−9.83719	−	2.24527i	−0.512104	−	0.116884i
$370$	−6.99230	−	8.76807i	−0.363512	−	0.455830i
$371$	−4.02926	−	1.94039i	−0.209189	−	0.100740i
$372$	9.09093	−	4.37796i	0.471343	−	0.226987i
$373$	12.8551	−	16.1198i	0.665614	−	0.834653i	−0.328328	−	0.944564i	$-0.606485\pi$
$373$	12.8551	−	16.1198i	0.665614	−	0.834653i	0.993941	+	0.109911i	$0.0350565\pi$
$374$	−2.92612	+	2.33350i	−0.151306	+	0.120662i
$375$	5.01670	+	10.4173i	0.259061	+	0.537946i
$376$	−15.6525			−0.807215
$377$		0			0
$378$	−4.79837			−0.246802
$379$	−10.5398	−	21.8862i	−0.541394	−	1.12422i	−0.974813	−	0.223024i	$-0.928407\pi$
$379$	−10.5398	−	21.8862i	−0.541394	−	1.12422i	0.433419	−	0.901192i	$-0.357307\pi$
$380$	23.6664	−	18.8734i	1.21406	−	0.968183i
$381$	6.14393	−	7.70425i	0.314763	−	0.394701i
$382$	9.48528	−	4.56787i	0.485309	−	0.233713i
$383$	−25.9966	−	12.5193i	−1.32837	−	0.639708i	−0.371013	−	0.928628i	$-0.620990\pi$
$383$	−25.9966	−	12.5193i	−1.32837	−	0.639708i	−0.957353	+	0.288920i	$0.906704\pi$
$384$	4.38590	+	5.49975i	0.223817	+	0.280658i
$385$	−11.6112	−	2.65019i	−0.591763	−	0.135066i
$386$	1.71524	−	7.51494i	0.0873033	−	0.382501i
$387$	14.8112	+	11.8116i	0.752897	+	0.600415i
$388$	5.61942	−	1.28260i	0.285283	−	0.0651139i
$389$		−	19.1246i		−	0.969656i	−0.874609	−	0.484828i	$-0.838882\pi$
$389$		−	19.1246i		−	0.969656i	0.874609	−	0.484828i	$-0.161118\pi$
$390$	0.0773314	+	0.338811i	0.00391583	+	0.0171564i
$391$	−2.35009	+	4.88001i	−0.118849	+	0.246793i
$392$	1.94039	−	4.02926i	0.0980043	−	0.203508i
$393$	1.97022	+	8.63211i	0.0993846	+	0.435432i
$394$			3.88854i			0.195902i
$395$	−22.8836	+	5.22304i	−1.15140	+	0.262800i
$396$	4.57692	+	3.64997i	0.229999	+	0.183418i
$397$	3.12769	−	13.7033i	0.156974	−	0.687750i	−0.833782	−	0.552094i	$-0.813829\pi$
$397$	3.12769	−	13.7033i	0.156974	−	0.687750i	0.990756	−	0.135656i	$-0.0433141\pi$
$398$	−3.52732	−	0.805088i	−0.176809	−	0.0403554i
$399$	4.18250	+	5.24469i	0.209387	+	0.262563i
$400$	−16.4612	−	7.92728i	−0.823058	−	0.396364i
$401$	−22.5863	+	10.8770i	−1.12791	+	0.543171i	−0.902326	−	0.431054i	$-0.858142\pi$
$401$	−22.5863	+	10.8770i	−1.12791	+	0.543171i	−0.225579	+	0.974225i	$0.572427\pi$
$402$	0.363864	−	0.456271i	0.0181479	−	0.0227567i
$403$	−1.86230	+	1.48513i	−0.0927676	+	0.0739797i
$404$	−0.433884	−	0.900969i	−0.0215865	−	0.0448249i
$405$	−22.0000			−1.09319
$406$		0			0
$407$	−6.50658			−0.322519
$408$	−2.62748	−	5.45602i	−0.130080	−	0.270113i
$409$	21.4350	−	17.0939i	1.05989	−	0.845237i	0.0715435	−	0.997437i	$-0.477208\pi$
$409$	21.4350	−	17.0939i	1.05989	−	0.845237i	0.988350	+	0.152201i	$0.0486361\pi$
$410$	−5.72385	+	7.17748i	−0.282681	+	0.354470i
$411$	−3.97905	+	1.91621i	−0.196272	+	0.0945195i
$412$	−13.3831	−	6.44495i	−0.659337	−	0.317520i
$413$	−8.49071	−	10.6470i	−0.417800	−	0.523905i
$414$	−1.94986	−	0.445042i	−0.0958302	−	0.0218726i
$415$	−8.52839	+	37.3653i	−0.418642	+	1.83419i
$416$	−1.03689	−	0.826896i	−0.0508379	−	0.0405419i
$417$	0.778357	−	0.177655i	0.0381163	−	0.00869980i
$418$			4.14590i			0.202783i
$419$	−3.90798	−	17.1220i	−0.190917	−	0.836464i	−0.976121	−	0.217226i	$-0.930299\pi$
$419$	−3.90798	−	17.1220i	−0.190917	−	0.836464i	0.785204	−	0.619237i	$-0.212558\pi$
$420$	3.73922	−	7.76458i	0.182455	−	0.378873i
$421$	−13.4653	+	27.9611i	−0.656261	+	1.36274i	0.261345	+	0.965246i	$0.415834\pi$
$421$	−13.4653	+	27.9611i	−0.656261	+	1.36274i	−0.917605	+	0.397493i	$0.869880\pi$
$422$	1.60251	+	7.02107i	0.0780091	+	0.341780i
$423$		−	18.3262i		−	0.891052i
$424$	4.36001	−	0.995144i	0.211741	−	0.0483285i
$425$	33.7597	+	26.9225i	1.63759	+	1.30593i
$426$	0.890084	−	3.89971i	0.0431247	−	0.188942i
$427$	1.34732	+	0.307516i	0.0652013	+	0.0148818i
$428$	6.82364	+	8.55658i	0.329833	+	0.413598i
$429$	0.181659	+	0.0874823i	0.00877057	+	0.00422369i
$430$	15.5292	−	7.47845i	0.748883	−	0.360643i
$431$	9.10092	−	11.4122i	0.438376	−	0.549706i	−0.512738	−	0.858545i	$-0.671369\pi$
$431$	9.10092	−	11.4122i	0.438376	−	0.549706i	0.951114	+	0.308839i	$0.0999403\pi$
$432$	−5.03319	+	4.01384i	−0.242160	+	0.193116i
$433$	−4.50457	−	9.35383i	−0.216476	−	0.449516i	0.764246	−	0.644924i	$-0.223111\pi$
$433$	−4.50457	−	9.35383i	−0.216476	−	0.449516i	−0.980722	+	0.195408i	$0.937397\pi$
$434$	−13.9443			−0.669346
$435$		0			0
$436$	23.2705			1.11446
$437$	2.60330	+	5.40581i	0.124533	+	0.258595i
$438$	4.09372	−	3.26463i	0.195606	−	0.155990i
$439$	13.0585	−	16.3749i	0.623250	−	0.781531i	−0.365548	−	0.930793i	$-0.619118\pi$
$439$	13.0585	−	16.3749i	0.623250	−	0.781531i	0.988798	+	0.149262i	$0.0476897\pi$
$440$	10.7304	−	5.16748i	0.511551	−	0.246350i
$441$	4.71753	+	2.27184i	0.224644	+	0.108183i
$442$	0.398610	+	0.499841i	0.0189599	+	0.0237750i
$443$	1.86195	+	0.424977i	0.0884638	+	0.0201913i	0.266524	−	0.963828i	$-0.414125\pi$
$443$	1.86195	+	0.424977i	0.0884638	+	0.0201913i	−0.178060	+	0.984020i	$0.556982\pi$
$444$	1.04767	−	4.59016i	0.0497204	−	0.217839i
$445$	14.1870	+	11.3138i	0.672530	+	0.536325i
$446$	−1.61104	+	0.367710i	−0.0762852	+	0.0174116i
$447$		−	5.94427i		−	0.281154i
$448$	0.117461	+	0.514629i	0.00554950	+	0.0243140i
$449$	11.3350	−	23.5375i	0.534934	−	1.11080i	−0.441952	−	0.897039i	$-0.645714\pi$
$449$	11.3350	−	23.5375i	0.534934	−	1.11080i	0.976886	−	0.213763i	$-0.0685719\pi$
$450$	−6.91796	+	14.3653i	−0.326116	+	0.677186i
$451$	1.18520	+	5.19270i	0.0558089	+	0.244515i
$452$			12.8541i			0.604606i
$453$	−1.61104	+	0.367710i	−0.0756935	+	0.0172765i
$454$	10.0933	+	8.04915i	0.473703	+	0.377765i
$455$	−0.452706	+	1.98343i	−0.0212232	+	0.0929848i
$456$	−6.54002	−	1.49272i	−0.306264	−	0.0699028i
$457$	−11.6644	−	14.6267i	−0.545636	−	0.684206i	0.430194	−	0.902737i	$-0.358445\pi$
$457$	−11.6644	−	14.6267i	−0.545636	−	0.684206i	−0.975830	+	0.218530i	$0.929874\pi$
$458$	−1.27614	−	0.614556i	−0.0596301	−	0.0287163i
$459$	13.7080	−	6.60145i	0.639837	−	0.308129i
$460$	4.80599	−	6.02652i	0.224080	−	0.280988i
$461$	30.4748	−	24.3028i	1.41935	−	1.13190i	0.448061	−	0.894003i	$-0.352115\pi$
$461$	30.4748	−	24.3028i	1.41935	−	1.13190i	0.971291	−	0.237893i	$-0.0764566\pi$
$462$	0.512130	+	1.06345i	0.0238265	+	0.0494761i
$463$	−10.7082			−0.497652			−0.248826	−	0.968548i	$-0.580045\pi$
$463$	−10.7082			−0.497652			−0.248826	+	0.968548i	$0.580045\pi$
$464$		0			0
$465$	24.0344			1.11457
$466$	4.08563	+	8.48389i	0.189263	+	0.393009i
$467$	−14.0294	+	11.1881i	−0.649203	+	0.517722i	−0.891814	−	0.452401i	$-0.850567\pi$
$467$	−14.0294	+	11.1881i	−0.649203	+	0.517722i	0.242611	+	0.970124i	$0.421996\pi$
$468$	0.623490	−	0.781831i	0.0288208	−	0.0361402i
$469$	3.07808	−	1.48232i	0.142132	−	0.0684474i
$470$	−15.0225	−	7.23447i	−0.692938	−	0.333701i
$471$	−5.61141	−	7.03648i	−0.258560	−	0.324224i
$472$	13.2766	+	3.03030i	0.611105	+	0.139481i
$473$	2.22521	−	9.74928i	0.102315	−	0.448272i
$474$	1.81873	+	1.45039i	0.0835369	+	0.0666184i
$475$	46.6335	−	10.6438i	2.13969	−	0.488371i
$476$		−	15.8541i		−	0.726672i
$477$	1.16513	+	5.10479i	0.0533479	+	0.233732i
$478$	7.43933	−	15.4479i	0.340267	−	0.706571i
$479$	−4.85097	+	10.0731i	−0.221646	+	0.460253i	−0.981907	−	0.189365i	$-0.939357\pi$
$479$	−4.85097	+	10.0731i	−0.221646	+	0.460253i	0.760260	+	0.649618i	$0.225071\pi$
$480$	2.97777	+	13.0465i	0.135916	+	0.595486i
$481$			1.11146i			0.0506780i
$482$	−2.80330	+	0.639834i	−0.127687	+	0.0291436i
$483$	1.33553	+	1.06505i	0.0607686	+	0.0484613i
$484$	−3.27288	+	14.3394i	−0.148767	+	0.651793i
$485$	13.3853	+	3.05510i	0.607793	+	0.138725i
$486$	5.37326	+	6.73785i	0.243736	+	0.305635i
$487$	−38.3473	−	18.4671i	−1.73768	−	0.836824i	−0.983674	−	0.179959i	$-0.942403\pi$
$487$	−38.3473	−	18.4671i	−1.73768	−	0.836824i	−0.754009	−	0.656865i	$-0.771882\pi$
$488$	−1.24511	+	0.599613i	−0.0563634	+	0.0271432i
$489$	2.32530	−	2.91583i	0.105154	−	0.131859i
$490$	3.72459	−	2.97026i	0.168260	−	0.134183i
$491$	6.56232	+	13.6268i	0.296153	+	0.614969i	0.994952	−	0.100349i	$-0.0319960\pi$
$491$	6.56232	+	13.6268i	0.296153	+	0.614969i	−0.698799	+	0.715318i	$0.746282\pi$
$492$	−3.85410			−0.173756
$493$		0			0
$494$	0.708204			0.0318636
$495$	6.05019	+	12.5634i	0.271936	+	0.564681i
$496$	−14.6267	+	11.6644i	−0.656757	+	0.523746i
$497$	14.5999	−	18.3077i	0.654895	−	0.821212i
$498$	3.42222	−	1.64805i	0.153353	−	0.0738510i
$499$	22.2421	+	10.7113i	0.995695	+	0.479502i	0.859475	−	0.511177i	$-0.170790\pi$
$499$	22.2421	+	10.7113i	0.995695	+	0.479502i	0.136220	+	0.990679i	$0.456505\pi$
$500$	−18.8734	−	23.6664i	−0.844042	−	1.05840i
$501$	6.34344	+	1.44785i	0.283404	+	0.0646852i
$502$	−2.70272	+	11.8414i	−0.120628	+	0.528506i
$503$	11.1571	+	8.89752i	0.497472	+	0.396721i	0.839831	−	0.542849i	$-0.182654\pi$
$503$	11.1571	+	8.89752i	0.497472	+	0.396721i	−0.342358	+	0.939569i	$0.611226\pi$
$504$	12.7620	−	2.91284i	0.568463	−	0.129748i
$505$		−	2.38197i		−	0.105996i
$506$	0.234922	+	1.02926i	0.0104435	+	0.0457561i
$507$	−3.47107	+	7.20775i	−0.154156	+	0.320107i
$508$	−11.1935	+	23.2435i	−0.496631	+	1.03126i
$509$	−7.02327	−	30.7710i	−0.311301	−	1.36390i	−0.852378	−	0.522926i	$-0.824840\pi$
$509$	−7.02327	−	30.7710i	−0.311301	−	1.36390i	0.541077	−	0.840973i	$-0.318017\pi$
$510$		−	6.45085i		−	0.285648i
$511$	29.8840	−	6.82082i	1.32199	−	0.301735i
$512$	−14.6267	−	11.6644i	−0.646413	−	0.515497i
$513$	3.75039	−	16.4315i	0.165584	−	0.725470i
$514$	−13.9670	−	3.18789i	−0.616060	−	0.140612i
$515$	−22.0603	−	27.6627i	−0.972093	−	1.21897i
$516$	6.51947	+	3.13961i	0.287004	+	0.138214i
$517$	−8.71576	+	4.19729i	−0.383319	+	0.184597i
$518$	−4.05678	+	5.08705i	−0.178245	+	0.223512i
$519$	1.97636	−	1.57610i	0.0867527	−	0.0691830i
$520$	−0.882711	−	1.83297i	−0.0387094	−	0.0803810i
$521$	−4.09017			−0.179194			−0.0895968	−	0.995978i	$-0.528558\pi$
$521$	−4.09017			−0.179194			−0.0895968	+	0.995978i	$0.528558\pi$
$522$		0			0
$523$	−20.3820			−0.891241			−0.445621	−	0.895222i	$-0.647017\pi$
$523$	−20.3820			−0.891241			−0.445621	+	0.895222i	$0.647017\pi$
$524$	−10.0576	−	20.8848i	−0.439367	−	0.912355i
$525$	10.6470	−	8.49071i	0.464674	−	0.370565i
$526$	6.43830	−	8.07338i	0.280723	−	0.352016i
$527$	39.8361	−	19.1841i	1.73529	−	0.835671i
$528$	1.42677	+	0.687095i	0.0620921	+	0.0299020i
$529$	−13.3877	−	16.7876i	−0.582072	−	0.729895i
$530$	4.64449	+	1.06007i	0.201744	+	0.0460467i
$531$	−3.54793	+	15.5445i	−0.153967	+	0.674575i
$532$	−13.7308	−	10.9499i	−0.595304	−	0.474739i
$533$	0.887019	−	0.202456i	0.0384210	−	0.00876935i
$534$		−	1.79837i		−	0.0778232i
$535$	5.80087	+	25.4153i	0.250794	+	1.09880i
$536$	−1.48232	+	3.07808i	−0.0640266	+	0.132953i
$537$	4.29048	−	8.90927i	0.185148	−	0.384463i
$538$	0.825153	+	3.61523i	0.0355749	+	0.155864i
$539$		−	2.76393i		−	0.119051i
$540$	−21.1096	+	4.81813i	−0.908413	+	0.207339i
$541$	11.4122	+	9.10092i	0.490649	+	0.391279i	0.837325	−	0.546706i	$-0.184118\pi$
$541$	11.4122	+	9.10092i	0.490649	+	0.391279i	−0.346676	+	0.937985i	$0.612690\pi$
$542$	−1.40006	+	6.13405i	−0.0601376	+	0.263480i
$543$	−3.58165	−	0.817489i	−0.153703	−	0.0350818i
$544$	15.3491	+	19.2472i	0.658087	+	0.825215i
$545$	49.9403	+	24.0500i	2.13921	+	1.03019i
$546$	0.181659	−	0.0874823i	0.00777428	−	0.00374390i
$547$	4.60258	−	5.77145i	0.196792	−	0.246770i	−0.673638	−	0.739061i	$-0.735269\pi$
$547$	4.60258	−	5.77145i	0.196792	−	0.246770i	0.870430	+	0.492292i	$0.163841\pi$
$548$	9.03977	−	7.20898i	0.386160	−	0.307952i
$549$	−0.702039	−	1.45780i	−0.0299623	−	0.0622173i
$550$	8.41641			0.358877
$551$		0			0
$552$	−1.70820			−0.0727060
$553$	5.90864	+	12.2694i	0.251261	+	0.521749i
$554$	−10.3317	+	8.23928i	−0.438953	+	0.350054i
$555$	6.99230	−	8.76807i	0.296807	−	0.372184i
$556$	−1.88318	+	0.906891i	−0.0798645	+	0.0384607i
$557$	−4.96126	−	2.38921i	−0.210215	−	0.101234i	0.325814	−	0.945434i	$-0.394362\pi$
$557$	−4.96126	−	2.38921i	−0.210215	−	0.101234i	−0.536029	+	0.844200i	$0.680076\pi$
$558$	10.1792	+	12.7644i	0.430922	+	0.540359i
$559$	−1.66538	−	0.380111i	−0.0704379	−	0.0160770i
$560$	−3.55560	+	15.5781i	−0.150251	+	0.658295i
$561$	−2.92612	−	2.33350i	−0.123541	−	0.0985205i
$562$	−13.9335	+	3.18022i	−0.587748	+	0.134150i
$563$			28.3951i			1.19671i	0.801230	+	0.598356i	$0.204179\pi$
$563$			28.3951i			1.19671i	−0.801230	+	0.598356i	$0.795821\pi$
$564$	−1.55765	−	6.82450i	−0.0655888	−	0.287363i
$565$	−13.2847	+	27.5859i	−0.558890	+	1.16055i
$566$	−1.40408	+	2.91560i	−0.0590178	+	0.122552i
$567$	2.84024	+	12.4439i	0.119279	+	0.522595i
$568$			23.4164i			0.982531i
$569$	−1.89552	+	0.432641i	−0.0794645	+	0.0181373i	−0.262068	−	0.965049i	$-0.584405\pi$
$569$	−1.89552	+	0.432641i	−0.0794645	+	0.0181373i	0.182604	+	0.983187i	$0.441547\pi$
$570$	−5.58689	−	4.45539i	−0.234009	−	0.186616i
$571$	7.67844	−	33.6414i	0.321333	−	1.40785i	−0.513851	−	0.857879i	$-0.671782\pi$
$571$	7.67844	−	33.6414i	0.321333	−	1.40785i	0.835184	−	0.549971i	$-0.185361\pi$
$572$	−0.514629	−	0.117461i	−0.0215177	−	0.00491128i
$573$	6.56402	+	8.23102i	0.274216	+	0.343856i
$574$	4.79877	+	2.31097i	0.200297	+	0.0964579i
$575$	10.9741	−	5.28485i	0.457652	−	0.220394i
$576$	0.385338	−	0.483198i	0.0160557	−	0.0201333i
$577$	2.16093	−	1.72328i	0.0899607	−	0.0717412i	−0.577477	−	0.816407i	$-0.695963\pi$
$577$	2.16093	−	1.72328i	0.0899607	−	0.0717412i	0.667437	+	0.744666i	$0.267391\pi$
$578$	−0.590377	−	1.22593i	−0.0245564	−	0.0509920i
$579$	7.70820			0.320342
$580$		0			0
$581$	22.2361			0.922508
$582$	−0.590377	−	1.22593i	−0.0244719	−	0.0508164i
$583$	2.16093	−	1.72328i	0.0894965	−	0.0713711i
$584$	−19.1115	+	23.9651i	−0.790840	+	0.991682i
$585$	2.14608	−	1.03350i	0.0887294	−	0.0427298i
$586$	4.74857	+	2.28679i	0.196161	+	0.0944664i
$587$	29.0659	+	36.4474i	1.19968	+	1.50435i	0.813135	+	0.582075i	$0.197759\pi$
$587$	29.0659	+	36.4474i	1.19968	+	1.50435i	0.386542	+	0.922272i	$0.373669\pi$
$588$	1.94986	+	0.445042i	0.0804107	+	0.0183532i
$589$	10.8988	−	47.7507i	0.449077	−	1.96753i
$590$	11.3417	+	9.04470i	0.466930	+	0.372365i
$591$	−3.79105	+	0.865282i	−0.155943	+	0.0355930i
$592$			8.72949i			0.358780i
$593$	−3.21269	−	14.0757i	−0.131929	−	0.578020i	−0.997070	−	0.0764913i	$-0.975628\pi$
$593$	−3.21269	−	14.0757i	−0.131929	−	0.578020i	0.865141	−	0.501529i	$-0.167229\pi$
$594$	1.28671	−	2.67188i	0.0527942	−	0.109628i
$595$	16.3852	−	34.0241i	0.671726	−	1.39485i
$596$	3.46294	+	15.1721i	0.141848	+	0.621475i
$597$		−	3.61803i		−	0.148076i
$598$	0.175818	−	0.0401294i	0.00718975	−	0.00164101i
$599$	−10.2177	−	8.14832i	−0.417482	−	0.332931i	0.392115	−	0.919916i	$-0.371743\pi$
$599$	−10.2177	−	8.14832i	−0.417482	−	0.332931i	−0.809598	+	0.586985i	$0.800315\pi$
$600$	−3.03030	+	13.2766i	−0.123711	+	0.542015i
$601$	28.4280	+	6.48850i	1.15960	+	0.264671i	0.758694	−	0.651447i	$-0.225838\pi$
$601$	28.4280	+	6.48850i	1.15960	+	0.264671i	0.400907	+	0.916119i	$0.368695\pi$
$602$	−6.23490	−	7.81831i	−0.254115	−	0.318651i
$603$	−3.60388	−	1.73553i	−0.146761	−	0.0706764i
$604$	3.89781	−	1.87708i	0.158599	−	0.0763775i
$605$	−21.8436	+	27.3910i	−0.888069	+	1.11360i
$606$	−0.184565	+	0.147186i	−0.00749746	+	0.00597902i
$607$	−4.76349	−	9.89148i	−0.193344	−	0.401483i	0.781649	−	0.623718i	$-0.214379\pi$
$607$	−4.76349	−	9.89148i	−0.193344	−	0.401483i	−0.974993	+	0.222236i	$0.928665\pi$
$608$	27.2705			1.10597
$609$		0			0
$610$	−1.47214			−0.0596050
$611$	0.716982	+	1.48883i	0.0290060	+	0.0602316i
$612$	−14.5126	+	11.5734i	−0.586637	+	0.467827i
$613$	−17.1715	+	21.5324i	−0.693552	+	0.869687i	−0.996523	−	0.0833128i	$-0.973450\pi$
$613$	−17.1715	+	21.5324i	−0.693552	+	0.869687i	0.302971	+	0.953000i	$0.402021\pi$
$614$	−10.6802	+	5.14330i	−0.431017	+	0.207567i
$615$	−8.27120	−	3.98320i	−0.333527	−	0.160618i
$616$	−4.30821	−	5.40232i	−0.173583	−	0.217666i
$617$	13.8248	+	3.15542i	0.556566	+	0.127033i	0.491546	−	0.870851i	$-0.336432\pi$
$617$	13.8248	+	3.15542i	0.556566	+	0.127033i	0.0650196	+	0.997884i	$0.479289\pi$
$618$	−0.780287	+	3.41866i	−0.0313877	+	0.137519i
$619$	5.51639	+	4.39917i	0.221722	+	0.176818i	0.728051	−	0.685523i	$-0.240426\pi$
$619$	5.51639	+	4.39917i	0.221722	+	0.176818i	−0.506329	+	0.862341i	$0.668998\pi$
$620$	−61.3454	+	14.0017i	−2.46369	+	0.562321i
$621$		−	4.29180i		−	0.172224i
$622$	0.287452	+	1.25941i	0.0115258	+	0.0504977i
$623$	4.56787	−	9.48528i	0.183008	−	0.380020i
$624$	0.117370	−	0.243721i	0.00469855	−	0.00975665i
$625$	−5.08078	−	22.2603i	−0.203231	−	0.890414i
$626$			7.97871i			0.318894i
$627$	−4.04195	+	0.922549i	−0.161420	+	0.0368431i
$628$	18.4218	+	14.6909i	0.735108	+	0.586229i
$629$	4.59087	−	20.1139i	0.183050	−	0.801995i
$630$	13.5947	+	3.10289i	0.541624	+	0.123622i
$631$	17.5916	+	22.0592i	0.700312	+	0.878163i	0.997047	−	0.0767968i	$-0.0244693\pi$
$631$	17.5916	+	22.0592i	0.700312	+	0.878163i	−0.296735	+	0.954960i	$0.595898\pi$
$632$	−12.2694	−	5.90864i	−0.488052	−	0.235033i
$633$	−6.48844	+	3.12467i	−0.257892	+	0.124194i
$634$	10.6770	−	13.3886i	0.424039	−	0.531728i
$635$	−48.0442	+	38.3140i	−1.90658	+	1.52044i
$636$	0.867767	+	1.80194i	0.0344092	+	0.0714515i
$637$	−0.472136			−0.0187067
$638$		0			0
$639$	−27.4164			−1.08458
$640$	−19.0333	−	39.5230i	−0.752357	−	1.56229i
$641$	8.64372	−	6.89313i	0.341406	−	0.272262i	−0.437744	−	0.899100i	$-0.644222\pi$
$641$	8.64372	−	6.89313i	0.341406	−	0.272262i	0.779150	+	0.626837i	$0.215651\pi$
$642$	1.61084	−	2.01993i	0.0635749	−	0.0797204i
$643$	−33.7110	+	16.2344i	−1.32943	+	0.640221i	−0.957606	−	0.288081i	$-0.906983\pi$
$643$	−33.7110	+	16.2344i	−1.32943	+	0.640221i	−0.371827	+	0.928302i	$0.621268\pi$
$644$	−4.02926	−	1.94039i	−0.158775	−	0.0764620i
$645$	10.7465	+	13.4757i	0.423144	+	0.530605i
$646$	−12.8163	−	2.92524i	−0.504251	−	0.115092i
$647$	−6.79309	+	29.7625i	−0.267064	+	1.17008i	0.646347	+	0.763044i	$0.276296\pi$
$647$	−6.79309	+	29.7625i	−0.267064	+	1.17008i	−0.913411	+	0.407039i	$0.866561\pi$
$648$	−9.97924	−	7.95818i	−0.392022	−	0.312627i
$649$	8.20539	−	1.87283i	0.322090	−	0.0735149i
$650$		−	1.43769i		−	0.0563910i
$651$	−3.10289	−	13.5947i	−0.121612	−	0.532817i
$652$	−4.23641	+	8.79700i	−0.165911	+	0.344517i
$653$	20.8321	−	43.2584i	0.815224	−	1.69283i	0.0988626	−	0.995101i	$-0.468480\pi$
$653$	20.8321	−	43.2584i	0.815224	−	1.69283i	0.716362	−	0.697729i	$-0.245806\pi$
$654$	−1.22240	−	5.35569i	−0.0477997	−	0.209424i
$655$		−	55.2148i		−	2.15742i
$656$	6.96674	−	1.59011i	0.272005	−	0.0620834i
$657$	−28.0588	−	22.3761i	−1.09468	−	0.872976i
$658$	−2.15261	+	9.43122i	−0.0839177	+	0.367667i
$659$	−6.87883	−	1.57005i	−0.267961	−	0.0611604i	0.0864291	−	0.996258i	$-0.472454\pi$
$659$	−6.87883	−	1.57005i	−0.267961	−	0.0611604i	−0.354390	+	0.935098i	$0.615312\pi$
$660$	3.32086	+	4.16422i	0.129264	+	0.162092i
$661$	33.7420	+	16.2493i	1.31241	+	0.632025i	0.953513	−	0.301351i	$-0.0974375\pi$
$661$	33.7420	+	16.2493i	1.31241	+	0.632025i	0.358900	+	0.933376i	$0.383152\pi$
$662$	−11.7938	+	5.67961i	−0.458380	+	0.220744i
$663$	−0.398610	+	0.499841i	−0.0154807	+	0.0194122i
$664$	−17.3849	+	13.8640i	−0.674663	+	0.538026i
$665$	−18.1506	−	37.6901i	−0.703849	−	1.46156i
$666$	7.61803			0.295193
$667$		0			0
$668$	−17.0344			−0.659082
$669$	−0.716982	−	1.48883i	−0.0277201	−	0.0575615i
$670$	−2.84534	+	2.26908i	−0.109925	+	0.0876622i
$671$	−0.532524	+	0.667764i	−0.0205579	+	0.0257787i
$672$	6.99506	−	3.36864i	0.269840	−	0.129948i
$673$	−5.83119	−	2.80815i	−0.224776	−	0.108246i	0.318107	−	0.948055i	$-0.396953\pi$
$673$	−5.83119	−	2.80815i	−0.224776	−	0.108246i	−0.542883	+	0.839808i	$0.682667\pi$
$674$	−13.1280	−	16.4620i	−0.505673	−	0.634094i
$675$	−33.3569	−	7.61351i	−1.28391	−	0.293044i
$676$	4.66054	−	20.4192i	0.179251	−	0.785352i
$677$	−31.9244	−	25.4588i	−1.22695	−	0.978463i	−0.999990	−	0.00455972i	$-0.998549\pi$
$677$	−31.9244	−	25.4588i	−1.22695	−	0.978463i	−0.226964	−	0.973903i	$-0.572880\pi$
$678$	2.95836	−	0.675227i	0.113615	−	0.0259319i
$679$		−	7.96556i		−	0.305690i
$680$	8.40327	+	36.8171i	0.322251	+	1.41187i
$681$	−5.60137	+	11.6314i	−0.214645	+	0.445714i
$682$	3.73922	−	7.76458i	0.143182	−	0.297321i
$683$	−4.64047	−	20.3312i	−0.177563	−	0.777954i	−0.982751	−	0.184934i	$-0.940793\pi$
$683$	−4.64047	−	20.3312i	−0.177563	−	0.777954i	0.805188	−	0.593019i	$-0.202064\pi$
$684$			20.5623i			0.786219i
$685$	26.8505	−	6.12845i	1.02591	−	0.234156i
$686$	−9.72418	−	7.75478i	−0.371271	−	0.296079i
$687$	0.315180	−	1.38090i	0.0120249	−	0.0526845i
$688$	−13.0800	−	2.98543i	−0.498671	−	0.113819i
$689$	−0.294372	−	0.369131i	−0.0112147	−	0.0140628i
$690$	−1.63946	−	0.789521i	−0.0624131	−	0.0300565i
$691$	−10.6610	+	5.13407i	−0.405563	+	0.195309i	−0.625533	−	0.780198i	$-0.715118\pi$
$691$	−10.6610	+	5.13407i	−0.405563	+	0.195309i	0.219970	+	0.975507i	$0.429404\pi$
$692$	−4.12628	+	5.17419i	−0.156858	+	0.196693i
$693$	6.32515	−	5.04414i	0.240273	−	0.191611i
$694$	8.61437	+	17.8879i	0.326997	+	0.679016i
$695$	−4.97871			−0.188853
$696$		0			0
$697$	−16.8885			−0.639699
$698$	1.21417	+	2.52125i	0.0459570	+	0.0954306i
$699$	−7.36204	+	5.87103i	−0.278458	+	0.222063i
$700$	−22.2290	+	27.8742i	−0.840176	+	1.05355i
$701$	−18.9706	+	9.13574i	−0.716508	+	0.345052i	−0.756362	−	0.654153i	$-0.773025\pi$
$701$	−18.9706	+	9.13574i	−0.716508	+	0.345052i	0.0398539	+	0.999206i	$0.487311\pi$
$702$	−0.456411	−	0.219796i	−0.0172261	−	0.00829566i
$703$	−14.2493	−	17.8681i	−0.537423	−	0.673907i
$704$	−0.318058	−	0.0725948i	−0.0119873	−	0.00273602i
$705$	3.71026	−	16.2557i	0.139737	−	0.612226i
$706$	−9.24098	−	7.36944i	−0.347789	−	0.277352i
$707$	−1.34732	+	0.307516i	−0.0506711	+	0.0115653i
$708$			6.09017i			0.228883i
$709$	−9.23608	−	40.4659i	−0.346868	−	1.51973i	−0.784245	−	0.620451i	$-0.786949\pi$
$709$	−9.23608	−	40.4659i	−0.346868	−	1.51973i	0.437377	−	0.899278i	$-0.355908\pi$
$710$	−10.8229	+	22.4740i	−0.406177	+	0.843435i
$711$	6.91796	−	14.3653i	0.259444	−	0.538741i
$712$	2.34267	+	10.2639i	0.0877953	+	0.384656i
$713$		−	12.4721i		−	0.467085i
$714$	−3.64881	+	0.832817i	−0.136553	+	0.0311674i
$715$	−0.983039	−	0.783948i	−0.0367636	−	0.0293180i
$716$	−5.76074	+	25.2395i	−0.215289	+	0.943243i
$717$	16.7160	+	3.81532i	0.624271	+	0.142486i
$718$	9.15714	+	11.4827i	0.341742	+	0.428530i
$719$	−7.66416	−	3.69087i	−0.285825	−	0.137646i	0.285478	−	0.958385i	$-0.407848\pi$
$719$	−7.66416	−	3.69087i	−0.285825	−	0.137646i	−0.571303	+	0.820739i	$0.693562\pi$
$720$	16.8555	−	8.11719i	0.628168	−	0.302510i
$721$	−12.7989	+	16.0493i	−0.476656	+	0.597708i
$722$	−2.20450	+	1.75803i	−0.0820430	+	0.0654271i
$723$	−1.24758	−	2.59064i	−0.0463982	−	0.0963468i
$724$	9.61803			0.357451
$725$		0			0
$726$	3.47214			0.128863
$727$	12.1729	+	25.2773i	0.451469	+	0.937485i	0.995166	+	0.0982034i	$0.0313096\pi$
$727$	12.1729	+	25.2773i	0.451469	+	0.937485i	−0.543698	+	0.839281i	$0.682976\pi$
$728$	−0.922827	+	0.735930i	−0.0342022	+	0.0272754i
$729$	5.30376	−	6.65071i	0.196436	−	0.246323i
$730$	−29.4189	+	14.1674i	−1.08884	+	0.524358i
$731$	28.5681	+	13.7577i	1.05663	+	0.508846i
$732$	−0.385338	−	0.483198i	−0.0142425	−	0.0178595i
$733$	−14.4481	−	3.29768i	−0.533653	−	0.121803i	−0.0528016	−	0.998605i	$-0.516815\pi$
$733$	−14.4481	−	3.29768i	−0.533653	−	0.121803i	−0.480851	+	0.876802i	$0.659672\pi$
$734$	3.75039	−	16.4315i	0.138429	−	0.606499i
$735$	3.72459	+	2.97026i	0.137384	+	0.109560i
$736$	6.77016	−	1.54525i	0.249552	−	0.0569585i
$737$			2.11146i			0.0777765i
$738$	−1.38766	−	6.07972i	−0.0510803	−	0.223797i
$739$	21.7241	−	45.1105i	0.799133	−	1.65942i	0.0483844	−	0.998829i	$-0.484593\pi$
$739$	21.7241	−	45.1105i	0.799133	−	1.65942i	0.750749	−	0.660588i	$-0.229693\pi$
$740$	−12.7391	+	26.4531i	−0.468299	+	0.972434i
$741$	0.157590	+	0.690448i	0.00578922	+	0.0253642i
$742$		−	2.76393i		−	0.101467i
$743$	34.3526	−	7.84076i	1.26028	−	0.287650i	0.460344	−	0.887741i	$-0.347726\pi$
$743$	34.3526	−	7.84076i	1.26028	−	0.287650i	0.799932	+	0.600091i	$0.204869\pi$
$744$	10.9021	+	8.69411i	0.399689	+	0.318742i
$745$	−8.24860	+	36.1395i	−0.302205	+	1.32405i
$746$	12.4232	+	2.83551i	0.454844	+	0.103815i
$747$	−16.2322	−	20.3545i	−0.593905	−	0.744734i
$748$	8.82803	+	4.25136i	0.322785	+	0.155445i
$749$	13.6268	−	6.56232i	0.497913	−	0.239782i
$750$	−4.45539	+	5.58689i	−0.162688	+	0.204004i
$751$	14.4857	−	11.5519i	0.528590	−	0.421536i	−0.322490	−	0.946573i	$-0.604520\pi$
$751$	14.4857	−	11.5519i	0.528590	−	0.421536i	0.851080	+	0.525037i	$0.175948\pi$
$752$	5.63125	+	11.6934i	0.205351	+	0.426415i
$753$	−12.1459			−0.442621
$754$		0			0
$755$	10.3050			0.375036
$756$	5.45058	+	11.3182i	0.198236	+	0.411641i
$757$	−0.0166422	+	0.0132718i	−0.000604873	+	0.000482370i	−0.623792	−	0.781590i	$-0.714409\pi$
$757$	−0.0166422	+	0.0132718i	−0.000604873	+	0.000482370i	0.623187	+	0.782073i	$0.285837\pi$
$758$	9.36055	−	11.7378i	0.339990	−	0.426335i
$759$	−0.951178	+	0.458063i	−0.0345256	+	0.0166266i
$760$	37.6901	+	18.1506i	1.36716	+	0.658391i
$761$	15.7130	+	19.7034i	0.569594	+	0.714249i	0.980299	−	0.197520i	$-0.0632887\pi$
$761$	15.7130	+	19.7034i	0.569594	+	0.714249i	−0.410705	+	0.911768i	$0.634717\pi$
$762$	5.93748	+	1.35519i	0.215092	+	0.0490934i
$763$	7.15606	−	31.3528i	0.259067	−	1.13505i
$764$	−21.5491	−	17.1848i	−0.779618	−	0.621725i
$765$	−43.1062	+	9.83871i	−1.55851	+	0.355719i
$766$		−	17.8328i		−	0.644326i
$767$	−0.319917	−	1.40165i	−0.0115515	−	0.0506106i
$768$	−1.75971	+	3.65408i	−0.0634982	+	0.131855i
$769$	−8.40028	+	17.4434i	−0.302922	+	0.629024i	−0.995752	−	0.0920771i	$-0.970649\pi$
$769$	−8.40028	+	17.4434i	−0.302922	+	0.629024i	0.692830	+	0.721101i	$0.256364\pi$
$770$	−1.63791	−	7.17613i

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.e (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.268155 + 0.556829i) q^{2} +(-0.483198 + 0.385338i) q^{3} +(1.00883 - 1.26503i) q^{4} +(3.47243 - 1.67223i) q^{5} +(-0.344139 - 0.165729i) q^{6} +(-1.39417 - 1.74823i) q^{7} +(2.18001 + 0.497572i) q^{8} +(-0.582567 + 2.55239i) q^{9} +O(q^{10})\)	\(q+(0.268155 + 0.556829i) q^{2} +(-0.483198 + 0.385338i) q^{3} +(1.00883 - 1.26503i) q^{4} +(3.47243 - 1.67223i) q^{5} +(-0.344139 - 0.165729i) q^{6} +(-1.39417 - 1.74823i) q^{7} +(2.18001 + 0.497572i) q^{8} +(-0.582567 + 2.55239i) q^{9} +(1.86230 + 1.48513i) q^{10} +(1.34732 - 0.307516i) q^{11} +1.00000i q^{12} +(-0.0525301 - 0.230149i) q^{13} +(0.599613 - 1.24511i) q^{14} +(-1.03350 + 2.14608i) q^{15} +(-0.412577 - 1.80762i) q^{16} +4.38197i q^{17} +(-1.57747 + 0.360046i) q^{18} +(3.79509 + 3.02648i) q^{19} +(1.38766 - 6.07972i) q^{20} +(1.34732 + 0.307516i) q^{21} +(0.532524 + 0.667764i) q^{22} +(1.11366 + 0.536310i) q^{23} +(-1.24511 + 0.599613i) q^{24} +(6.14393 - 7.70425i) q^{25} +(0.114068 - 0.0909659i) q^{26} +(-1.50650 - 3.12829i) q^{27} -3.61803 q^{28} -1.47214 q^{30} +(-4.37796 - 9.09093i) q^{31} +(4.39236 - 3.50279i) q^{32} +(-0.532524 + 0.667764i) q^{33} +(-2.44001 + 1.17505i) q^{34} +(-7.76458 - 3.73922i) q^{35} +(2.64115 + 3.31189i) q^{36} +(-4.59016 - 1.04767i) q^{37} +(-0.667563 + 2.92478i) q^{38} +(0.114068 + 0.0909659i) q^{39} +(8.40196 - 1.91769i) q^{40} +3.85410i q^{41} +(0.190056 + 0.832688i) q^{42} +(3.13961 - 6.51947i) q^{43} +(0.970194 - 2.01463i) q^{44} +(2.24527 + 9.83719i) q^{45} +0.763932i q^{46} +(-6.82450 + 1.55765i) q^{47} +(0.895899 + 0.714456i) q^{48} +(0.445042 - 1.94986i) q^{49} +(5.93748 + 1.35519i) q^{50} +(-1.68854 - 2.11736i) q^{51} +(-0.344139 - 0.165729i) q^{52} +(1.80194 - 0.867767i) q^{53} +(1.33795 - 1.67773i) q^{54} +(4.16422 - 3.32086i) q^{55} +(-2.16942 - 4.50484i) q^{56} -3.00000 q^{57} +6.09017 q^{59} +(1.67223 + 3.47243i) q^{60} +(-0.483198 + 0.385338i) q^{61} +(3.88812 - 4.87555i) q^{62} +(5.27436 - 2.54000i) q^{63} +(-0.212690 - 0.102426i) q^{64} +(-0.567270 - 0.711334i) q^{65} +(-0.514629 - 0.117461i) q^{66} +(-0.339982 + 1.48956i) q^{67} +(5.54332 + 4.42065i) q^{68} +(-0.744779 + 0.169991i) q^{69} -5.32624i q^{70} +(2.33027 + 10.2096i) q^{71} +(-2.54000 + 5.27436i) q^{72} +(-5.94777 + 12.3507i) q^{73} +(-0.647498 - 2.83687i) q^{74} +6.09017i q^{75} +(7.65718 - 1.74770i) q^{76} +(-2.41599 - 1.92669i) q^{77} +(-0.0200647 + 0.0879092i) q^{78} +(-5.93748 - 1.35519i) q^{79} +(-4.45539 - 5.58689i) q^{80} +(-5.14291 - 2.47670i) q^{81} +(-2.14608 + 1.03350i) q^{82} +(-6.20015 + 7.77474i) q^{83} +(1.74823 - 1.39417i) q^{84} +(7.32766 + 15.2161i) q^{85} +4.47214 q^{86} +3.09017 q^{88} +(2.04281 + 4.24195i) q^{89} +(-4.87555 + 3.88812i) q^{90} +(-0.329118 + 0.412701i) q^{91} +(1.80194 - 0.867767i) q^{92} +(5.61850 + 2.70573i) q^{93} +(-2.69737 - 3.38239i) q^{94} +(18.2392 + 4.16297i) q^{95} +(-0.772623 + 3.38508i) q^{96} +(2.78512 + 2.22106i) q^{97} +(1.20508 - 0.275051i) q^{98} +3.61803i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) 24 * q - 2 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^9	\( 24 q - 2 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{9} + 8 q^{13} + 6 q^{16} + 16 q^{20} + 10 q^{22} - 4 q^{23} - 10 q^{24} - 26 q^{25} - 60 q^{28} + 72 q^{30} - 10 q^{33} + 16 q^{34} - 30 q^{35} - 8 q^{36} - 12 q^{38} - 10 q^{42} + 18 q^{45} + 8 q^{49} - 16 q^{51} - 6 q^{52} + 8 q^{53} - 22 q^{54} - 72 q^{57} + 12 q^{59} - 16 q^{62} + 10 q^{63} + 8 q^{64} + 26 q^{65} - 24 q^{67} + 24 q^{71} - 34 q^{74} + 22 q^{78} + 42 q^{80} + 4 q^{81} - 14 q^{82} + 4 q^{83} - 60 q^{88} + 20 q^{91} + 8 q^{92} + 16 q^{93} - 14 q^{94} + 4 q^{96}+O(q^{100}) \) 24 * q - 2 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^9 + 8 * q^13 + 6 * q^16 + 16 * q^20 + 10 * q^22 - 4 * q^23 - 10 * q^24 - 26 * q^25 - 60 * q^28 + 72 * q^30 - 10 * q^33 + 16 * q^34 - 30 * q^35 - 8 * q^36 - 12 * q^38 - 10 * q^42 + 18 * q^45 + 8 * q^49 - 16 * q^51 - 6 * q^52 + 8 * q^53 - 22 * q^54 - 72 * q^57 + 12 * q^59 - 16 * q^62 + 10 * q^63 + 8 * q^64 + 26 * q^65 - 24 * q^67 + 24 * q^71 - 34 * q^74 + 22 * q^78 + 42 * q^80 + 4 * q^81 - 14 * q^82 + 4 * q^83 - 60 * q^88 + 20 * q^91 + 8 * q^92 + 16 * q^93 - 14 * q^94 + 4 * q^96

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