LMFDB - Embedded newform 841.2.e.j.270.2

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			270.2
Character	$\chi$	$=$	841.270
Dual form			841.2.e.j.651.2

$q$-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	0.784390	−	0.620268i	$-0.212976\pi$
$2$	−0.268155	−	0.556829i	−0.189614	−	0.393738i	−0.974004	+	0.226530i	$0.927262\pi$
$3$	0.483198	−	0.385338i	0.278975	−	0.222475i	−0.473999	−	0.880525i	$-0.657190\pi$
$3$	0.483198	−	0.385338i	0.278975	−	0.222475i	0.752974	+	0.658050i	$0.228619\pi$
$4$	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	−0.420754	−	0.907175i	$-0.638234\pi$
$11$	−1.34732	+	0.307516i	−0.406231	+	0.0927197i	0.0145224	+	0.999895i	$0.495377\pi$
$12$		−	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	$-0.821669\pi$
$17$		−	4.38197i		−	1.06278i	0.847126	−	0.531391i	$-0.178331\pi$
$18$	1.57747	−	0.360046i	0.371812	−	0.0848638i
$19$	−3.79509	−	3.02648i	−0.870653	−	0.694323i	0.0825715	−	0.996585i	$-0.473687\pi$
$19$	−3.79509	−	3.02648i	−0.870653	−	0.694323i	−0.953225	+	0.302262i	$0.902258\pi$
$20$	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	$0.218116\pi$
$31$	4.37796	+	9.09093i	0.786305	+	1.63278i	0.0120317	+	0.999928i	$0.496170\pi$
$32$	−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	0.582490	−	0.812838i	$-0.302079\pi$
$37$	4.59016	+	1.04767i	0.754618	+	0.172237i	0.172128	+	0.985075i	$0.444936\pi$
$38$	−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	$-0.902695\pi$
$41$		−	3.85410i		−	0.601910i	0.953638	−	0.300955i	$-0.0973053\pi$
$42$	0.190056	+	0.832688i	0.0293262	+	0.128487i
$43$	−3.13961	+	6.51947i	−0.478786	+	0.994210i	0.512026	+	0.858970i	$0.328895\pi$
$43$	−3.13961	+	6.51947i	−0.478786	+	0.994210i	−0.990813	+	0.135240i	$0.956819\pi$
$44$	−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	0.306390	−	0.951906i	$-0.400879\pi$
$47$	6.82450	−	1.55765i	0.995455	−	0.227206i	0.689065	+	0.724700i	$0.258022\pi$
$48$	−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	−0.592068	−	0.805888i	$-0.701688\pi$
$61$	0.483198	−	0.385338i	0.0618672	−	0.0493375i	0.653935	+	0.756551i	$0.273117\pi$
$62$	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	$-0.560799\pi$
$73$	5.94777	−	12.3507i	0.696133	−	1.44554i	0.885981	−	0.463722i	$-0.153486\pi$
$74$	−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	0.543064	−	0.839692i	$-0.317264\pi$
$79$	5.93748	+	1.35519i	0.668018	+	0.152471i	0.124955	+	0.992162i	$0.460121\pi$
$80$	−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	0.764199	−	0.644981i	$-0.223135\pi$
$89$	−2.04281	−	4.24195i	−0.216538	−	0.449645i	−0.980736	+	0.195336i	$0.937420\pi$
$90$	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	0.471816	−	0.881697i	$-0.343599\pi$
$97$	−2.78512	−	2.22106i	−0.282786	−	0.225515i	−0.754602	+	0.656183i	$0.772170\pi$
$98$	−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	−0.913884	−	0.405975i	$-0.866932\pi$
$101$	−0.268155	+	0.556829i	−0.0266824	+	0.0554066i	0.887202	+	0.461382i	$0.152646\pi$
$102$	−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	−0.286181	−	0.958175i	$-0.592386\pi$
$113$	6.21108	−	4.95317i	0.584289	−	0.465955i	0.870471	+	0.492220i	$0.163815\pi$
$114$	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	0.532398	−	0.846494i	$-0.321291\pi$
$127$	15.5445	−	3.54793i	1.37935	−	0.314828i	0.846954	+	0.531666i	$0.178434\pi$
$128$			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	$0.358103\pi$
$131$	−6.21592	+	12.9075i	−0.543088	+	1.12773i	−0.974252	+	0.225460i	$0.927612\pi$
$132$	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	−0.0857042	−	0.996321i	$-0.527314\pi$
$137$	−6.96674	−	1.59011i	−0.595208	−	0.135852i	−0.509504	+	0.860468i	$0.670171\pi$
$138$	−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	$-0.802623\pi$
$157$		−	14.5623i		−	1.16220i	0.813833	−	0.581099i	$-0.197377\pi$
$158$	−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	0.0141841	−	0.999899i	$-0.495485\pi$
$163$	5.88315	−	1.34279i	0.460804	−	0.105175i	0.446619	+	0.894724i	$0.352628\pi$
$164$	−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	$0.211363\pi$
$191$			17.0344i			1.23257i	−0.787524	+	0.616284i	$0.788637\pi$
$192$	−0.142240	+	0.0324654i	−0.0102653	+	0.00234299i
$193$	9.75111	+	7.77625i	0.701900	+	0.559747i	0.908095	−	0.418764i	$-0.137537\pi$
$193$	9.75111	+	7.77625i	0.701900	+	0.559747i	−0.206195	+	0.978511i	$0.566108\pi$
$194$	−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	−0.187201	−	0.982322i	$-0.559942\pi$
$211$	−11.3603	−	2.59292i	−0.782077	−	0.178504i	−0.594876	+	0.803818i	$0.702799\pi$
$212$	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	−0.562497	−	0.826799i	$-0.690159\pi$
$229$	1.79180	−	1.42891i	0.118405	−	0.0944251i	0.680902	+	0.732374i	$0.261588\pi$
$230$	−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	0.00416682	−	0.999991i	$-0.498674\pi$
$251$	−15.3649	−	12.2531i	−0.969825	−	0.773410i	−0.973992	+	0.226581i	$0.927245\pi$
$252$	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	$0.0294014\pi$
$263$	7.24942	+	15.0536i	0.447018	+	0.928243i	−0.548719	+	0.836007i	$0.684884\pi$
$264$	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	0.0404396	−	0.999182i	$-0.487124\pi$
$269$	−5.84957	−	1.33513i	−0.356654	−	0.0814040i	−0.397094	+	0.917778i	$0.629981\pi$
$270$	1.84036	−	8.06315i	0.112001	−	0.490708i
$271$	−7.95931	−	6.34734i	−0.483494	−	0.385573i	0.351189	−	0.936305i	$-0.385777\pi$
$271$	−7.95931	−	6.34734i	−0.483494	−	0.385573i	−0.834683	+	0.550731i	$0.814349\pi$
$272$	−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	−0.798591	−	0.601874i	$-0.794421\pi$
$293$	−6.66735	+	5.31704i	−0.389511	+	0.310625i	0.409080	+	0.912498i	$0.365850\pi$
$294$	−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	$-0.815640\pi$
$307$		−	19.1803i		−	1.09468i	0.836910	−	0.547340i	$-0.184360\pi$
$308$	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	0.164354	−	0.986401i	$-0.447446\pi$
$311$	−2.03777	−	0.465107i	−0.115551	−	0.0263738i	−0.279905	+	0.960028i	$0.590303\pi$
$312$	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	$0.140971\pi$
$317$	12.0221	+	24.9642i	0.675231	+	1.40213i	−0.228293	+	0.973592i	$0.573314\pi$
$318$	−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	$-0.802236\pi$
$331$		−	21.1803i		−	1.16418i	0.813126	−	0.582088i	$-0.197764\pi$
$332$	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	0.821712	−	0.569903i	$-0.193019\pi$
$337$	33.2147	−	7.58104i	1.80932	−	0.412966i	0.987609	+	0.156938i	$0.0501622\pi$
$338$	−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	−0.784712	−	0.619860i	$-0.787189\pi$
$359$	−23.1681	+	5.28797i	−1.22277	+	0.279089i	−0.438054	+	0.898949i	$0.644332\pi$
$360$		−	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	0.994429	−	0.105409i	$-0.0336151\pi$
$367$	21.3209	+	17.0029i	1.11294	+	0.887543i	0.118515	+	0.992952i	$0.462187\pi$
$368$	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	$0.0715927\pi$
$379$	10.5398	+	21.8862i	0.541394	+	1.12422i	−0.433419	+	0.901192i	$0.642693\pi$
$380$	−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	$0.161118\pi$
$389$			19.1246i			0.969656i	−0.874609	+	0.484828i	$0.838882\pi$
$390$	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	−0.988350	−	0.152201i	$-0.951364\pi$
$409$	−21.4350	+	17.0939i	−1.05989	+	0.845237i	−0.0715435	+	0.997437i	$0.522792\pi$
$410$	−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	$-0.584166\pi$
$421$	13.4653	−	27.9611i	0.656261	−	1.36274i	0.917605	−	0.397493i	$-0.130120\pi$
$422$	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	0.980722	−	0.195408i	$-0.0626031\pi$
$433$	4.50457	+	9.35383i	0.216476	+	0.449516i	−0.764246	+	0.644924i	$0.776889\pi$
$434$	−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	0.178060	−	0.984020i	$-0.443018\pi$
$443$	−1.86195	−	0.424977i	−0.0884638	−	0.0201913i	−0.266524	+	0.963828i	$0.585875\pi$
$444$	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	$0.354286\pi$
$449$	−11.3350	+	23.5375i	−0.534934	+	1.11080i	−0.976886	+	0.213763i	$0.931428\pi$
$450$	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	$0.647885\pi$
$461$	−30.4748	+	24.3028i	−1.41935	+	1.13190i	−0.971291	+	0.237893i	$0.923543\pi$
$462$	−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	−0.242611	−	0.970124i	$-0.578004\pi$
$467$	14.0294	−	11.1881i	0.649203	−	0.517722i	0.891814	+	0.452401i	$0.149433\pi$
$468$	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	−0.760260	−	0.649618i	$-0.774929\pi$
$479$	4.85097	−	10.0731i	0.221646	−	0.460253i	0.981907	+	0.189365i	$0.0606429\pi$
$480$	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	0.698799	−	0.715318i	$-0.253718\pi$
$491$	−6.56232	−	13.6268i	−0.296153	−	0.614969i	−0.994952	+	0.100349i	$0.968004\pi$
$492$	−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	0.342358	−	0.939569i	$-0.388774\pi$
$503$	−11.1571	−	8.89752i	−0.497472	−	0.396721i	−0.839831	+	0.542849i	$0.817346\pi$
$504$	−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	0.346676	−	0.937985i	$-0.387310\pi$
$541$	−11.4122	−	9.10092i	−0.490649	−	0.391279i	−0.837325	+	0.546706i	$0.815882\pi$
$542$	−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	$-0.795821\pi$
$563$		−	28.3951i		−	1.19671i	0.801230	−	0.598356i	$-0.204179\pi$
$564$	−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	−0.182604	−	0.983187i	$-0.558453\pi$
$569$	1.89552	−	0.432641i	0.0794645	−	0.0181373i	0.262068	+	0.965049i	$0.415595\pi$
$570$	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	−0.667437	−	0.744666i	$-0.732609\pi$
$577$	−2.16093	+	1.72328i	−0.0899607	+	0.0717412i	0.577477	+	0.816407i	$0.304037\pi$
$578$	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	0.809598	−	0.586985i	$-0.199685\pi$
$599$	10.2177	+	8.14832i	0.417482	+	0.332931i	−0.392115	+	0.919916i	$0.628257\pi$
$600$	−3.03030	+	13.2766i	−0.123711	+	0.542015i
$601$	−28.4280	−	6.48850i	−1.15960	−	0.264671i	−0.400907	−	0.916119i	$-0.631305\pi$
$601$	−28.4280	−	6.48850i	−1.15960	−	0.264671i	−0.758694	+	0.651447i	$0.774162\pi$
$602$	−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	0.974993	−	0.222236i	$-0.0713355\pi$
$607$	4.76349	+	9.89148i	0.193344	+	0.401483i	−0.781649	+	0.623718i	$0.785621\pi$
$608$	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	−0.0650196	−	0.997884i	$-0.520711\pi$
$617$	−13.8248	−	3.15542i	−0.556566	−	0.127033i	−0.491546	+	0.870851i	$0.663568\pi$
$618$	−0.780287	+	3.41866i	−0.0313877	+	0.137519i
$619$	−5.51639	−	4.39917i	−0.221722	−	0.176818i	0.506329	−	0.862341i	$-0.331002\pi$
$619$	−5.51639	−	4.39917i	−0.221722	−	0.176818i	−0.728051	+	0.685523i	$0.759574\pi$
$620$	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	−0.779150	−	0.626837i	$-0.784349\pi$
$641$	−8.64372	+	6.89313i	−0.341406	+	0.272262i	0.437744	+	0.899100i	$0.355778\pi$
$642$	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	$0.531520\pi$
$653$	−20.8321	+	43.2584i	−0.815224	+	1.69283i	−0.716362	+	0.697729i	$0.754194\pi$
$654$	−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	0.354390	−	0.935098i	$-0.384688\pi$
$659$	6.87883	+	1.57005i	0.267961	+	0.0611604i	−0.0864291	+	0.996258i	$0.527546\pi$
$660$	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	$0.00145141\pi$
$677$	31.9244	+	25.4588i	1.22695	+	0.978463i	0.226964	+	0.973903i	$0.427120\pi$
$678$	−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	$-0.968690\pi$
$727$	−12.1729	−	25.2773i	−0.451469	−	0.937485i	0.543698	−	0.839281i	$-0.317024\pi$
$728$	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	0.480851	−	0.876802i	$-0.340328\pi$
$733$	14.4481	+	3.29768i	0.533653	+	0.121803i	0.0528016	+	0.998605i	$0.483185\pi$
$734$	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	$0.515407\pi$
$739$	−21.7241	+	45.1105i	−0.799133	+	1.65942i	−0.750749	+	0.660588i	$0.770307\pi$
$740$	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	−0.799932	−	0.600091i	$-0.795131\pi$
$743$	−34.3526	+	7.84076i	−1.26028	+	0.287650i	−0.460344	+	0.887741i	$0.652274\pi$
$744$	−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	−0.851080	−	0.525037i	$-0.824052\pi$
$751$	−14.4857	+	11.5519i	−0.528590	+	0.421536i	0.322490	+	0.946573i	$0.395480\pi$
$752$	−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	−0.623187	−	0.782073i	$-0.714163\pi$
$757$	0.0166422	−	0.0132718i	0.000604873	−	0.000482370i	0.623792	+	0.781590i	$0.285591\pi$
$758$	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	−0.692830	−	0.721101i	$-0.743636\pi$
$769$	8.40028	−	17.4434i	0.302922	−	0.629024i	0.995752	+	0.0920771i	$0.0293506\pi$
$770$	−1.63791	−

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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