LMFDB - Embedded newform 784.2.x.n.373.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			373.5
Character	$\chi$	$=$	784.373
Dual form			784.2.x.n.557.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0190769 + 1.41408i) q^{2} +(-2.27101 - 0.608516i) q^{3} +(-1.99927 - 0.0539526i) q^{4} +(-1.49452 + 0.400455i) q^{5} +(0.903818 - 3.19980i) q^{6} +(0.114433 - 2.82611i) q^{8} +(2.18914 + 1.26390i) q^{9} +O(q^{10})$	\(q+(-0.0190769 + 1.41408i) q^{2} +(-2.27101 - 0.608516i) q^{3} +(-1.99927 - 0.0539526i) q^{4} +(-1.49452 + 0.400455i) q^{5} +(0.903818 - 3.19980i) q^{6} +(0.114433 - 2.82611i) q^{8} +(2.18914 + 1.26390i) q^{9} +(-0.537766 - 2.12101i) q^{10} +(0.469413 - 1.75187i) q^{11} +(4.50754 + 1.33912i) q^{12} +(-1.49861 + 1.49861i) q^{13} +3.63776 q^{15} +(3.99418 + 0.215732i) q^{16} +(-2.44112 - 4.22814i) q^{17} +(-1.82902 + 3.07152i) q^{18} +(-1.88197 - 7.02361i) q^{19} +(3.00955 - 0.719985i) q^{20} +(2.46834 + 0.697210i) q^{22} +(6.87807 + 3.97105i) q^{23} +(-1.97962 + 6.34851i) q^{24} +(-2.25691 + 1.30303i) q^{25} +(-2.09057 - 2.14774i) q^{26} +(0.785033 + 0.785033i) q^{27} +(-4.18002 + 4.18002i) q^{29} +(-0.0693969 + 5.14409i) q^{30} +(4.73710 + 8.20490i) q^{31} +(-0.381259 + 5.64399i) q^{32} +(-2.13209 + 3.69289i) q^{33} +(6.02552 - 3.37129i) q^{34} +(-4.30849 - 2.64499i) q^{36} +(1.67866 - 0.449796i) q^{37} +(9.96789 - 2.52728i) q^{38} +(4.31528 - 2.49143i) q^{39} +(0.960707 + 4.26950i) q^{40} +10.6111i q^{41} +(2.27704 + 2.27704i) q^{43} +(-1.03300 + 3.47715i) q^{44} +(-3.77784 - 1.01227i) q^{45} +(-5.74662 + 9.65041i) q^{46} +(0.930171 - 1.61110i) q^{47} +(-8.93956 - 2.92045i) q^{48} +(-1.79953 - 3.21632i) q^{50} +(2.97092 + 11.0876i) q^{51} +(3.07697 - 2.91527i) q^{52} +(2.18458 - 8.15297i) q^{53} +(-1.12508 + 1.09513i) q^{54} +2.80619i q^{55} +17.0959i q^{57} +(-5.83116 - 5.99065i) q^{58} +(-1.00211 + 3.73991i) q^{59} +(-7.27286 - 0.196266i) q^{60} +(1.38657 + 5.17474i) q^{61} +(-11.6928 + 6.54214i) q^{62} +(-7.97381 - 0.646803i) q^{64} +(1.63957 - 2.83982i) q^{65} +(-5.18138 - 3.08540i) q^{66} +(-0.647776 - 0.173571i) q^{67} +(4.65234 + 8.58491i) q^{68} +(-13.2037 - 13.2037i) q^{69} -1.50161i q^{71} +(3.82243 - 6.04212i) q^{72} +(8.75126 - 5.05254i) q^{73} +(0.604027 + 2.38235i) q^{74} +(5.91838 - 1.58583i) q^{75} +(3.38363 + 14.1437i) q^{76} +(3.44077 + 6.14970i) q^{78} +(3.90884 - 6.77031i) q^{79} +(-6.05576 + 1.27707i) q^{80} +(-5.09681 - 8.82794i) q^{81} +(-15.0050 - 0.202426i) q^{82} +(8.73286 - 8.73286i) q^{83} +(5.34147 + 5.34147i) q^{85} +(-3.26337 + 3.17649i) q^{86} +(12.0365 - 6.94928i) q^{87} +(-4.89727 - 1.52709i) q^{88} +(3.69289 + 2.13209i) q^{89} +(1.50350 - 5.32288i) q^{90} +(-13.5369 - 8.31031i) q^{92} +(-5.76521 - 21.5160i) q^{93} +(2.26049 + 1.34608i) q^{94} +(5.62528 + 9.74327i) q^{95} +(4.30031 - 12.5856i) q^{96} +12.3413 q^{97} +(3.24180 - 3.24180i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{4}+O(q^{10}) $ 40 * q + 8 * q^4	$ 40 q + 8 q^{4} - 4 q^{11} - 32 q^{15} - 16 q^{18} - 8 q^{29} - 8 q^{30} + 40 q^{32} + 80 q^{36} + 20 q^{37} + 120 q^{43} - 56 q^{44} + 64 q^{46} - 112 q^{50} + 16 q^{51} - 28 q^{53} + 72 q^{58} + 24 q^{60} - 64 q^{64} - 16 q^{65} - 12 q^{67} - 16 q^{72} + 16 q^{74} - 176 q^{78} + 72 q^{79} - 12 q^{81} + 64 q^{85} + 40 q^{86} - 80 q^{88} - 48 q^{92} - 48 q^{93} - 64 q^{95} - 216 q^{99}+O(q^{100}) $ 40 * q + 8 * q^4 - 4 * q^11 - 32 * q^15 - 16 * q^18 - 8 * q^29 - 8 * q^30 + 40 * q^32 + 80 * q^36 + 20 * q^37 + 120 * q^43 - 56 * q^44 + 64 * q^46 - 112 * q^50 + 16 * q^51 - 28 * q^53 + 72 * q^58 + 24 * q^60 - 64 * q^64 - 16 * q^65 - 12 * q^67 - 16 * q^72 + 16 * q^74 - 176 * q^78 + 72 * q^79 - 12 * q^81 + 64 * q^85 + 40 * q^86 - 80 * q^88 - 48 * q^92 - 48 * q^93 - 64 * q^95 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.0190769	+	1.41408i	−0.0134894	+	0.999909i
$2$	−0.0190769	+	1.41408i	−0.0134894	+	0.999909i
$3$	−2.27101	−	0.608516i	−1.31117	−	0.351327i	−0.465508	−	0.885044i	$-0.654128\pi$
$3$	−2.27101	−	0.608516i	−1.31117	−	0.351327i	−0.845663	+	0.533717i	$0.820795\pi$
$4$	−1.99927	−	0.0539526i	−0.999636	−	0.0269763i
$5$	−1.49452	+	0.400455i	−0.668369	+	0.179089i	−0.577020	−	0.816730i	$-0.695784\pi$
$5$	−1.49452	+	0.400455i	−0.668369	+	0.179089i	−0.0913488	+	0.995819i	$0.529118\pi$
$6$	0.903818	−	3.19980i	0.368982	−	1.30631i
$7$		0			0
$7$		0			0
$8$	0.114433	−	2.82611i	0.0404583	−	0.999181i
$9$	2.18914	+	1.26390i	0.729713	+	0.421300i
$10$	−0.537766	−	2.12101i	−0.170057	−	0.670724i
$11$	0.469413	−	1.75187i	0.141533	−	0.528210i	−0.858352	−	0.513062i	$-0.828511\pi$
$11$	0.469413	−	1.75187i	0.141533	−	0.528210i	0.999885	−	0.0151484i	$-0.00482207\pi$
$12$	4.50754	+	1.33912i	1.30122	+	0.386570i
$13$	−1.49861	+	1.49861i	−0.415638	+	0.415638i	−0.883697	−	0.468059i	$-0.844954\pi$
$13$	−1.49861	+	1.49861i	−0.415638	+	0.415638i	0.468059	+	0.883697i	$0.344954\pi$
$14$		0			0
$15$	3.63776			0.939264
$16$	3.99418	+	0.215732i	0.998545	+	0.0539329i
$17$	−2.44112	−	4.22814i	−0.592058	−	1.02547i	−0.993955	−	0.109790i	$-0.964982\pi$
$17$	−2.44112	−	4.22814i	−0.592058	−	1.02547i	0.401897	−	0.915685i	$-0.368351\pi$
$18$	−1.82902	+	3.07152i	−0.431105	+	0.723963i
$19$	−1.88197	−	7.02361i	−0.431754	−	1.61133i	−0.748717	−	0.662890i	$-0.769330\pi$
$19$	−1.88197	−	7.02361i	−0.431754	−	1.61133i	0.316963	−	0.948438i	$-0.397337\pi$
$20$	3.00955	−	0.719985i	0.672957	−	0.160994i
$21$		0			0
$22$	2.46834	+	0.697210i	0.526253	+	0.148646i
$23$	6.87807	+	3.97105i	1.43418	+	0.828022i	0.997436	−	0.0715658i	$-0.0227996\pi$
$23$	6.87807	+	3.97105i	1.43418	+	0.828022i	0.436740	+	0.899588i	$0.356133\pi$
$24$	−1.97962	+	6.34851i	−0.404087	+	1.29588i
$25$	−2.25691	+	1.30303i	−0.451382	+	0.260605i
$26$	−2.09057	−	2.14774i	−0.409994	−	0.421207i
$27$	0.785033	+	0.785033i	0.151080	+	0.151080i
$28$		0			0
$29$	−4.18002	+	4.18002i	−0.776211	+	0.776211i	−0.979184	−	0.202974i	$-0.934939\pi$
$29$	−4.18002	+	4.18002i	−0.776211	+	0.776211i	0.202974	+	0.979184i	$0.434939\pi$
$30$	−0.0693969	+	5.14409i	−0.0126701	+	0.939179i
$31$	4.73710	+	8.20490i	0.850808	+	1.47364i	0.880480	+	0.474083i	$0.157220\pi$
$31$	4.73710	+	8.20490i	0.850808	+	1.47364i	−0.0296718	+	0.999560i	$0.509446\pi$
$32$	−0.381259	+	5.64399i	−0.0673978	+	0.997726i
$33$	−2.13209	+	3.69289i	−0.371149	+	0.642849i
$34$	6.02552	−	3.37129i	1.03337	−	0.578171i
$35$		0			0
$36$	−4.30849	−	2.64499i	−0.718082	−	0.440831i
$37$	1.67866	−	0.449796i	0.275971	−	0.0739461i	−0.118179	−	0.992992i	$-0.537706\pi$
$37$	1.67866	−	0.449796i	0.275971	−	0.0739461i	0.394150	+	0.919046i	$0.371039\pi$
$38$	9.96789	−	2.52728i	1.61700	−	0.409979i
$39$	4.31528	−	2.49143i	0.690998	−	0.398948i
$40$	0.960707	+	4.26950i	0.151901	+	0.675067i
$41$			10.6111i			1.65717i	0.559863	+	0.828585i	$0.310854\pi$
$41$			10.6111i			1.65717i	−0.559863	+	0.828585i	$0.689146\pi$
$42$		0			0
$43$	2.27704	+	2.27704i	0.347245	+	0.347245i	0.859083	−	0.511837i	$-0.171035\pi$
$43$	2.27704	+	2.27704i	0.347245	+	0.347245i	−0.511837	+	0.859083i	$0.671035\pi$
$44$	−1.03300	+	3.47715i	−0.155731	+	0.524200i
$45$	−3.77784	−	1.01227i	−0.563167	−	0.150900i
$46$	−5.74662	+	9.65041i	−0.847293	+	1.42288i
$47$	0.930171	−	1.61110i	0.135679	−	0.235004i	−0.790177	−	0.612878i	$-0.790012\pi$
$47$	0.930171	−	1.61110i	0.135679	−	0.235004i	0.925857	+	0.377875i	$0.123345\pi$
$48$	−8.93956	−	2.92045i	−1.29031	−	0.421531i
$49$		0			0
$50$	−1.79953	−	3.21632i	−0.254493	−	0.454856i
$51$	2.97092	+	11.0876i	0.416012	+	1.55258i
$52$	3.07697	−	2.91527i	0.426700	−	0.404275i
$53$	2.18458	−	8.15297i	0.300075	−	1.11990i	−0.637027	−	0.770842i	$-0.719836\pi$
$53$	2.18458	−	8.15297i	0.300075	−	1.11990i	0.937102	−	0.349055i	$-0.113497\pi$
$54$	−1.12508	+	1.09513i	−0.153104	+	0.149028i
$55$			2.80619i			0.378386i
$56$		0			0
$57$			17.0959i			2.26441i
$58$	−5.83116	−	5.99065i	−0.765669	−	0.786611i
$59$	−1.00211	+	3.73991i	−0.130463	+	0.486895i	−0.999975	−	0.00701626i	$-0.997767\pi$
$59$	−1.00211	+	3.73991i	−0.130463	+	0.486895i	0.869512	+	0.493911i	$0.164433\pi$
$60$	−7.27286	−	0.196266i	−0.938922	−	0.0253379i
$61$	1.38657	+	5.17474i	0.177532	+	0.662558i	0.996107	+	0.0881577i	$0.0280979\pi$
$61$	1.38657	+	5.17474i	0.177532	+	0.662558i	−0.818575	+	0.574400i	$0.805235\pi$
$62$	−11.6928	+	6.54214i	−1.48499	+	0.830852i
$63$		0			0
$64$	−7.97381	−	0.646803i	−0.996726	−	0.0808503i
$65$	1.63957	−	2.83982i	0.203364	−	0.352236i
$66$	−5.18138	−	3.08540i	−0.637784	−	0.379787i
$67$	−0.647776	−	0.173571i	−0.0791384	−	0.0212051i	0.219033	−	0.975718i	$-0.429710\pi$
$67$	−0.647776	−	0.173571i	−0.0791384	−	0.0212051i	−0.298171	+	0.954512i	$0.596377\pi$
$68$	4.65234	+	8.58491i	0.564179	+	1.04107i
$69$	−13.2037	−	13.2037i	−1.58954	−	1.58954i
$70$		0			0
$71$		−	1.50161i		−	0.178208i	−0.996022	−	0.0891041i	$-0.971600\pi$
$71$		−	1.50161i		−	0.178208i	0.996022	−	0.0891041i	$-0.0284004\pi$
$72$	3.82243	−	6.04212i	0.450478	−	0.712070i
$73$	8.75126	−	5.05254i	1.02426	−	0.591355i	0.108923	−	0.994050i	$-0.465260\pi$
$73$	8.75126	−	5.05254i	1.02426	−	0.591355i	0.915334	+	0.402695i	$0.131926\pi$
$74$	0.604027	+	2.38235i	0.0702167	+	0.276943i
$75$	5.91838	−	1.58583i	0.683396	−	0.183115i
$76$	3.38363	+	14.1437i	0.388129	+	1.62239i
$77$		0			0
$78$	3.44077	+	6.14970i	0.389590	+	0.696317i
$79$	3.90884	−	6.77031i	0.439779	−	0.761720i	−0.557893	−	0.829913i	$-0.688390\pi$
$79$	3.90884	−	6.77031i	0.439779	−	0.761720i	0.997672	+	0.0681931i	$0.0217234\pi$
$80$	−6.05576	+	1.27707i	−0.677055	+	0.142781i
$81$	−5.09681	−	8.82794i	−0.566313	−	0.980882i
$82$	−15.0050	−	0.202426i	−1.65702	−	0.0223542i
$83$	8.73286	−	8.73286i	0.958556	−	0.958556i	−0.0406187	−	0.999175i	$-0.512933\pi$
$83$	8.73286	−	8.73286i	0.958556	−	0.958556i	0.999175	+	0.0406187i	$0.0129329\pi$
$84$		0			0
$85$	5.34147	+	5.34147i	0.579364	+	0.579364i
$86$	−3.26337	+	3.17649i	−0.351898	+	0.342530i
$87$	12.0365	−	6.94928i	1.29045	−	0.745041i
$88$	−4.89727	−	1.52709i	−0.522051	−	0.162788i
$89$	3.69289	+	2.13209i	0.391445	+	0.226001i	0.682786	−	0.730618i	$-0.260768\pi$
$89$	3.69289	+	2.13209i	0.391445	+	0.226001i	−0.291341	+	0.956619i	$0.594101\pi$
$90$	1.50350	−	5.32288i	0.158483	−	0.561080i
$91$		0			0
$92$	−13.5369	−	8.31031i	−1.41132	−	0.866409i
$93$	−5.76521	−	21.5160i	−0.597824	−	2.23111i
$94$	2.26049	+	1.34608i	0.233152	+	0.138837i
$95$	5.62528	+	9.74327i	0.577142	+	0.999639i
$96$	4.30031	−	12.5856i	0.438898	−	1.28451i
$97$	12.3413			1.25307			0.626535	−	0.779393i	$-0.284472\pi$
$97$	12.3413			1.25307			0.626535	+	0.779393i	$0.284472\pi$
$98$		0			0
$99$	3.24180	−	3.24180i	0.325813	−	0.325813i
$100$	4.58247	−	2.48334i	0.458247	−	0.248334i
$101$	−3.67256	+	13.7062i	−0.365433	+	1.36382i	0.501399	+	0.865216i	$0.332819\pi$
$101$	−3.67256	+	13.7062i	−0.365433	+	1.36382i	−0.866832	+	0.498600i	$0.833848\pi$
$102$	−15.7355	+	3.98962i	−1.55805	+	0.395031i
$103$	7.37016	+	4.25517i	0.726204	+	0.419274i	0.817032	−	0.576593i	$-0.195618\pi$
$103$	7.37016	+	4.25517i	0.726204	+	0.419274i	−0.0908279	+	0.995867i	$0.528951\pi$
$104$	4.06374	+	4.40672i	0.398482	+	0.432114i
$105$		0			0
$106$	11.4873	+	3.24472i	1.11575	+	0.315155i
$107$	−4.08845	+	1.09550i	−0.395246	+	0.105906i	−0.450967	−	0.892541i	$-0.648921\pi$
$107$	−4.08845	+	1.09550i	−0.395246	+	0.105906i	0.0557213	+	0.998446i	$0.482254\pi$
$108$	−1.52714	−	1.61185i	−0.146949	−	0.155100i
$109$	5.76060	+	1.54355i	0.551765	+	0.147845i	0.523920	−	0.851767i	$-0.324469\pi$
$109$	5.76060	+	1.54355i	0.551765	+	0.147845i	0.0278449	+	0.999612i	$0.491136\pi$
$110$	−3.96819	−	0.0535332i	−0.378352	−	0.00510419i
$111$	−4.08598			−0.387824
$112$		0			0
$113$	−12.4238			−1.16874			−0.584368	−	0.811489i	$-0.698657\pi$
$113$	−12.4238			−1.16874			−0.584368	+	0.811489i	$0.698657\pi$
$114$	−24.1751	−	0.326137i	−2.26421	−	0.0305455i
$115$	−11.8696	−	3.18046i	−1.10685	−	0.296579i
$116$	8.58252	−	8.13148i	0.796867	−	0.754989i
$117$	−5.17474	+	1.38657i	−0.478405	+	0.128188i
$118$	−5.26944	−	1.48841i	−0.485091	−	0.137019i
$119$		0			0
$120$	0.416280	−	10.2807i	0.0380010	−	0.938495i
$121$	6.67757	+	3.85529i	0.607051	+	0.350481i
$122$	−7.34398	+	1.86201i	−0.664892	+	0.168578i
$123$	6.45701	−	24.0979i	0.582209	−	2.17283i
$124$	−9.02808	−	16.6594i	−0.810745	−	1.49606i
$125$	8.32150	−	8.32150i	0.744298	−	0.744298i
$126$		0			0
$127$	18.3696			1.63004			0.815018	−	0.579436i	$-0.196727\pi$
$127$	18.3696			1.63004			0.815018	+	0.579436i	$0.196727\pi$
$128$	1.06675	−	11.2633i	0.0942882	−	0.995545i
$129$	−3.78558	−	6.55681i	−0.333301	−	0.577295i
$130$	3.98446	+	2.37266i	0.349461	+	0.208096i
$131$	−0.312371	−	1.16578i	−0.0272920	−	0.101855i	0.950936	−	0.309387i	$-0.100124\pi$
$131$	−0.312371	−	1.16578i	−0.0272920	−	0.101855i	−0.978228	+	0.207532i	$0.933457\pi$
$132$	4.46187	−	7.26805i	0.388356	−	0.632603i
$133$		0			0
$134$	0.257802	−	0.912699i	0.0222707	−	0.0788452i
$135$	−1.48762	−	0.858876i	−0.128034	−	0.0739202i
$136$	−12.2285	+	6.41503i	−1.04859	+	0.550084i
$137$	−6.76016	+	3.90298i	−0.577560	+	0.333454i	−0.760163	−	0.649733i	$-0.774881\pi$
$137$	−6.76016	+	3.90298i	−0.577560	+	0.333454i	0.182603	+	0.983187i	$0.441548\pi$
$138$	18.9231	−	18.4193i	1.61084	−	1.56796i
$139$	−0.0436953	−	0.0436953i	−0.00370618	−	0.00370618i	0.705251	−	0.708957i	$-0.250834\pi$
$139$	−0.0436953	−	0.0436953i	−0.00370618	−	0.00370618i	−0.708957	+	0.705251i	$0.750834\pi$
$140$		0			0
$141$	−3.09281	+	3.09281i	−0.260462	+	0.260462i
$142$	2.12340	+	0.0286460i	0.178192	+	0.00240392i
$143$	1.92190	+	3.32883i	0.160718	+	0.278371i
$144$	8.47114	+	5.52051i	0.705929	+	0.460042i
$145$	4.57321	−	7.92103i	0.379784	−	0.657805i
$146$	6.97778	+	12.4714i	0.577485	+	1.03214i
$147$		0			0
$148$	−3.38037	+	0.808697i	−0.277865	+	0.0664745i
$149$	−22.0362	+	5.90459i	−1.80528	+	0.483723i	−0.994782	−	0.102020i	$-0.967470\pi$
$149$	−22.0362	+	5.90459i	−1.80528	+	0.483723i	−0.810497	+	0.585743i	$0.800803\pi$
$150$	2.12959	+	8.39935i	0.173880	+	0.685804i
$151$	7.18049	−	4.14566i	0.584340	−	0.337369i	−0.178516	−	0.983937i	$-0.557130\pi$
$151$	7.18049	−	4.14566i	0.584340	−	0.337369i	0.762856	+	0.646568i	$0.223796\pi$
$152$	−20.0649	+	4.51493i	−1.62748	+	0.366209i
$153$		−	12.3413i		−	0.997736i
$154$		0			0
$155$	−10.3654	−	10.3654i	−0.832567	−	0.832567i
$156$	−8.76184	+	4.74822i	−0.701509	+	0.380162i
$157$	−0.367665	−	0.0985155i	−0.0293428	−	0.00786239i	0.244118	−	0.969746i	$-0.421502\pi$
$157$	−0.367665	−	0.0985155i	−0.0293428	−	0.00786239i	−0.273461	+	0.961883i	$0.588168\pi$
$158$	9.49923	+	5.65659i	0.755718	+	0.450014i
$159$	−9.92244	+	17.1862i	−0.786900	+	1.36295i
$160$	−1.69036	−	8.58772i	−0.133635	−	0.678919i
$161$		0			0
$162$	12.5807	−	7.03892i	0.988432	−	0.553030i
$163$	5.18143	+	19.3374i	0.405841	+	1.51462i	0.802500	+	0.596653i	$0.203503\pi$
$163$	5.18143	+	19.3374i	0.405841	+	1.51462i	−0.396659	+	0.917966i	$0.629830\pi$
$164$	0.572495	−	21.2144i	0.0447043	−	1.65657i
$165$	1.70761	−	6.37289i	0.132937	−	0.496129i
$166$	12.1824	+	12.5156i	0.945538	+	0.971399i
$167$		−	0.242171i		−	0.0187397i	−0.999956	−	0.00936987i	$-0.997017\pi$
$167$		−	0.242171i		−	0.0187397i	0.999956	−	0.00936987i	$-0.00298256\pi$
$168$		0			0
$169$			8.50836i			0.654489i
$170$	−7.65520	+	7.45140i	−0.587127	+	0.571496i
$171$	4.75725	−	17.7543i	0.363796	−	1.35770i
$172$	−4.42957	−	4.67528i	−0.337752	−	0.356487i
$173$	−1.99838	−	7.45806i	−0.151934	−	0.567026i	−0.999348	−	0.0360938i	$-0.988508\pi$
$173$	−1.99838	−	7.45806i	−0.151934	−	0.567026i	0.847414	−	0.530932i	$-0.178158\pi$
$174$	9.59725	+	17.1532i	0.727566	+	1.30038i
$175$		0			0
$176$	2.25286	−	6.89603i	0.169815	−	0.519808i
$177$	4.55160	−	7.88360i	0.342119	−	0.592568i
$178$	−3.08540	+	5.18138i	−0.231261	+	0.388361i
$179$	8.85874	+	2.37369i	0.662133	+	0.177418i	0.574208	−	0.818709i	$-0.305310\pi$
$179$	8.85874	+	2.37369i	0.662133	+	0.177418i	0.0879245	+	0.996127i	$0.471977\pi$
$180$	7.49832	+	2.22763i	0.558892	+	0.166037i
$181$	9.82011	+	9.82011i	0.729923	+	0.729923i	0.970604	−	0.240681i	$-0.0773709\pi$
$181$	9.82011	+	9.82011i	0.729923	+	0.729923i	−0.240681	+	0.970604i	$0.577371\pi$
$182$		0			0
$183$		−	12.5957i		−	0.931098i
$184$	12.0097	−	18.9838i	0.885368	−	1.39950i
$185$	−2.32867	+	1.34446i	−0.171207	+	0.0988465i
$186$	30.5355	−	7.74203i	2.23897	−	0.567673i
$187$	−8.55306	+	2.29179i	−0.625462	+	0.167592i
$188$	−1.94659	+	3.17085i	−0.141969	+	0.231258i
$189$		0			0
$190$	−13.8851	+	7.76875i	−1.00733	+	0.563605i
$191$	3.22457	−	5.58512i	0.233322	−	0.404125i	−0.725462	−	0.688262i	$-0.758374\pi$
$191$	3.22457	−	5.58512i	0.233322	−	0.404125i	0.958784	+	0.284137i	$0.0917072\pi$
$192$	17.7150	+	6.32109i	1.27847	+	0.456186i
$193$	3.97562	+	6.88598i	0.286172	+	0.495664i	0.972893	−	0.231257i	$-0.0742839\pi$
$193$	3.97562	+	6.88598i	0.286172	+	0.495664i	−0.686721	+	0.726921i	$0.740951\pi$
$194$	−0.235433	+	17.4517i	−0.0169031	+	1.25296i
$195$	−5.45156	+	5.45156i	−0.390394	+	0.390394i
$196$		0			0
$197$	−9.02399	−	9.02399i	−0.642933	−	0.642933i	0.308343	−	0.951275i	$-0.400226\pi$
$197$	−9.02399	−	9.02399i	−0.642933	−	0.642933i	−0.951275	+	0.308343i	$0.900226\pi$
$198$	4.52234	+	4.64603i	0.321389	+	0.330179i
$199$	−3.84721	+	2.22119i	−0.272722	+	0.157456i	−0.630124	−	0.776495i	$-0.716996\pi$
$199$	−3.84721	+	2.22119i	−0.272722	+	0.157456i	0.357402	+	0.933951i	$0.383663\pi$
$200$	3.42423	+	6.52738i	0.242130	+	0.461556i
$201$	1.36549	+	0.788365i	0.0963141	+	0.0556070i
$202$	−19.3116	−	5.45478i	−1.35876	−	0.383797i
$203$		0			0
$204$	−5.34147	−	22.3275i	−0.373978	−	1.56324i
$205$	−4.24925	−	15.8584i	−0.296781	−	1.10760i
$206$	−6.15777	+	10.3409i	−0.429032	+	0.720482i
$207$	10.0380	+	17.3864i	0.697691	+	1.20844i
$208$	−6.30899	+	5.66240i	−0.437450	+	0.392617i
$209$	−13.1879			−0.912227
$210$		0			0
$211$	18.1613	−	18.1613i	1.25027	−	1.25027i	0.294675	−	0.955598i	$-0.404789\pi$
$211$	18.1613	−	18.1613i	1.25027	−	1.25027i	0.955598	−	0.294675i	$-0.0952113\pi$
$212$	−4.80745	+	16.1821i	−0.330177	+	1.11139i
$213$	−0.913754	+	3.41018i	−0.0626094	+	0.233661i
$214$	−1.47113	−	5.80232i	−0.100565	−	0.396638i
$215$	−4.31493	−	2.49123i	−0.294276	−	0.169900i
$216$	2.30842	−	2.12876i	0.157068	−	0.144844i
$217$		0			0
$218$	−2.29260	+	8.11653i	−0.155275	+	0.549721i
$219$	−22.9488	+	6.14911i	−1.55074	+	0.415518i
$220$	0.151401	−	5.61033i	0.0102075	−	0.378248i
$221$	9.99459	+	2.67804i	0.672309	+	0.180145i
$222$	0.0779476	−	5.77792i	0.00523150	−	0.387788i
$223$	−14.6202			−0.979044			−0.489522	−	0.871991i	$-0.662829\pi$
$223$	−14.6202			−0.979044			−0.489522	+	0.871991i	$0.662829\pi$
$224$		0			0
$225$	−6.58758			−0.439172
$226$	0.237008	−	17.5683i	0.0157655	−	1.16863i
$227$	−5.88466	−	1.57679i	−0.390579	−	0.104655i	0.0581847	−	0.998306i	$-0.481469\pi$
$227$	−5.88466	−	1.57679i	−0.390579	−	0.104655i	−0.448763	+	0.893651i	$0.648135\pi$
$228$	0.922370	−	34.1794i	0.0610854	−	2.26359i
$229$	2.62137	−	0.702394i	0.173225	−	0.0464155i	−0.171164	−	0.985243i	$-0.554753\pi$
$229$	2.62137	−	0.702394i	0.173225	−	0.0464155i	0.344389	+	0.938827i	$0.388086\pi$
$230$	4.72387	−	16.7240i	0.311483	−	1.10275i
$231$		0			0
$232$	11.3349	+	12.2915i	0.744171	+	0.806979i
$233$	−0.544147	−	0.314164i	−0.0356483	−	0.0205815i	0.482070	−	0.876133i	$-0.339885\pi$
$233$	−0.544147	−	0.314164i	−0.0356483	−	0.0205815i	−0.517718	+	0.855551i	$0.673218\pi$
$234$	−1.86201	−	7.34398i	−0.121723	−	0.480091i
$235$	−0.744983	+	2.78031i	−0.0485973	+	0.181368i
$236$	2.20526	−	7.42304i	0.143550	−	0.483199i
$237$	−12.9969	+	12.9969i	−0.844238	+	0.844238i
$238$		0			0
$239$	5.13936			0.332438			0.166219	−	0.986089i	$-0.446844\pi$
$239$	5.13936			0.332438			0.166219	+	0.986089i	$0.446844\pi$
$240$	14.5298	+	0.784779i	0.937897	+	0.0506573i
$241$	11.2792	+	19.5362i	0.726559	+	1.25844i	0.958329	+	0.285667i	$0.0922152\pi$
$241$	11.2792	+	19.5362i	0.726559	+	1.25844i	−0.231769	+	0.972771i	$0.574451\pi$
$242$	−5.57910	+	9.36910i	−0.358638	+	0.602268i
$243$	5.34097	+	19.9328i	0.342623	+	1.27869i
$244$	−2.49294	−	10.4205i	−0.159594	−	0.667106i
$245$		0			0
$246$	33.9533	+	9.59047i	2.16478	+	0.611466i
$247$	13.3460	+	7.70529i	0.849183	+	0.490276i
$248$	23.7300	−	12.4487i	1.50686	−	0.790490i
$249$	−25.1465	+	14.5184i	−1.59360	+	0.920064i
$250$	11.6086	+	11.9261i	0.734190	+	0.754270i
$251$	1.77457	+	1.77457i	0.112010	+	0.112010i	0.760890	−	0.648880i	$-0.224762\pi$
$251$	1.77457	+	1.77457i	0.112010	+	0.112010i	−0.648880	+	0.760890i	$0.724762\pi$
$252$		0			0
$253$	10.1854	−	10.1854i	0.640353	−	0.640353i
$254$	−0.350433	+	25.9761i	−0.0219882	+	1.62989i
$255$	−8.88019	−	15.3809i	−0.556099	−	0.963192i
$256$	15.9069	+	1.72334i	0.994182	+	0.107709i
$257$	10.1818	−	17.6355i	0.635126	−	1.10007i	−0.351363	−	0.936239i	$-0.614282\pi$
$257$	10.1818	−	17.6355i	0.635126	−	1.10007i	0.986488	−	0.163831i	$-0.0523851\pi$
$258$	9.34410	−	5.22804i	0.581738	−	0.325484i
$259$		0			0
$260$	−3.43116	+	5.58911i	−0.212792	+	0.346622i
$261$	−14.4338	+	3.86752i	−0.893428	+	0.239393i
$262$	1.65448	−	0.419479i	0.102214	−	0.0259155i
$263$	−9.97007	+	5.75622i	−0.614781	+	0.354944i	−0.774834	−	0.632164i	$-0.782167\pi$
$263$	−9.97007	+	5.75622i	−0.614781	+	0.354944i	0.160053	+	0.987108i	$0.448833\pi$
$264$	10.1925	+	6.44811i	0.627306	+	0.396854i
$265$			13.0596i			0.802244i
$266$		0			0
$267$	−7.08919	−	7.08919i	−0.433851	−	0.433851i
$268$	1.28572	+	0.381965i	0.0785376	+	0.0233322i
$269$	27.7709	+	7.44120i	1.69322	+	0.453698i	0.971219	−	0.238190i	$-0.0765541\pi$
$269$	27.7709	+	7.44120i	1.69322	+	0.453698i	0.722005	+	0.691888i	$0.243221\pi$
$270$	1.24290	−	2.08723i	0.0756406	−	0.127025i
$271$	8.05308	−	13.9484i	0.489190	−	0.847302i	−0.510733	−	0.859740i	$-0.670626\pi$
$271$	8.05308	−	13.9484i	0.489190	−	0.847302i	0.999923	+	0.0124376i	$0.00395911\pi$
$272$	−8.83812	−	17.4146i	−0.535890	−	1.05591i
$273$		0			0
$274$	−5.39018	−	9.63390i	−0.325633	−	0.582005i
$275$	1.22332	+	4.56548i	0.0737687	+	0.275309i
$276$	25.6855	+	27.1102i	1.54608	+	1.63184i
$277$	1.38050	−	5.15211i	0.0829464	−	0.309560i	−0.911971	−	0.410255i	$-0.865440\pi$
$277$	1.38050	−	5.15211i	0.0829464	−	0.309560i	0.994917	+	0.100694i	$0.0321065\pi$
$278$	0.0626224	−	0.0609552i	0.00375584	−	0.00365585i
$279$			23.9489i			1.43378i
$280$		0			0
$281$			1.98190i			0.118231i	0.998251	+	0.0591153i	$0.0188279\pi$
$281$			1.98190i			0.118231i	−0.998251	+	0.0591153i	$0.981172\pi$
$282$	−4.31450	−	4.43250i	−0.256925	−	0.263952i
$283$	−4.07631	+	15.2130i	−0.242312	+	0.904320i	0.732404	+	0.680870i	$0.238398\pi$
$283$	−4.07631	+	15.2130i	−0.242312	+	0.904320i	−0.974716	+	0.223449i	$0.928268\pi$
$284$	−0.0810157	+	3.00213i	−0.00480740	+	0.178143i
$285$	−6.84615	−	25.5502i	−0.405531	−	1.51346i
$286$	−4.74392	+	2.65423i	−0.280514	+	0.156948i
$287$		0			0
$288$	−7.96807	+	11.8736i	−0.469523	+	0.699659i
$289$	−3.41812	+	5.92036i	−0.201066	+	0.348256i
$290$	11.1138	+	6.61801i	0.652623	+	0.388623i
$291$	−28.0273	−	7.50989i	−1.64299	−	0.440238i
$292$	−17.7687	+	9.62925i	−1.03984	+	0.563509i
$293$	11.6089	+	11.6089i	0.678198	+	0.678198i	0.959592	−	0.281394i	$-0.0907968\pi$
$293$	11.6089	+	11.6089i	0.678198	+	0.678198i	−0.281394	+	0.959592i	$0.590797\pi$
$294$		0			0
$295$		−	5.99066i		−	0.348790i
$296$	−1.07908	−	4.79556i	−0.0627202	−	0.278736i
$297$	1.74378	−	1.00677i	0.101185	−	0.0584190i
$298$	−7.92921	−	31.2738i	−0.459327	−	1.81164i
$299$	−16.2586	+	4.35647i	−0.940256	+	0.251941i
$300$	−11.9180	+	2.85119i	−0.688087	+	0.164613i
$301$		0			0
$302$	5.72533	+	10.2329i	0.329456	+	0.588837i
$303$	16.6809	−	28.8921i	0.958291	−	1.65981i
$304$	−6.00171	−	28.4596i	−0.344222	−	1.63227i
$305$	−4.14450	−	7.17849i	−0.237313	−	0.411039i
$306$	17.4517	+	0.235433i	0.997645	+	0.0134588i
$307$	0.828728	−	0.828728i	0.0472980	−	0.0472980i	−0.683062	−	0.730360i	$-0.739352\pi$
$307$	0.828728	−	0.828728i	0.0472980	−	0.0472980i	0.730360	+	0.683062i	$0.239352\pi$
$308$		0			0
$309$	−14.1484	−	14.1484i	−0.804875	−	0.804875i
$310$	14.8553	−	14.4598i	0.843722	−	0.821260i
$311$	−26.0005	+	15.0114i	−1.47435	+	0.851217i	−0.999582	−	0.0288939i	$-0.990802\pi$
$311$	−26.0005	+	15.0114i	−1.47435	+	0.851217i	−0.474768	+	0.880111i	$0.657468\pi$
$312$	−6.54724	−	12.4806i	−0.370665	−	0.706573i
$313$	−9.71444	−	5.60863i	−0.549093	−	0.317019i	0.199663	−	0.979865i	$-0.436015\pi$
$313$	−9.71444	−	5.60863i	−0.549093	−	0.317019i	−0.748756	+	0.662846i	$0.769348\pi$
$314$	0.146323	−	0.518030i	0.00825749	−	0.0292341i
$315$		0			0
$316$	−8.18011	+	13.3248i	−0.460167	+	0.749579i
$317$	−4.17793	−	15.5922i	−0.234656	−	0.875747i	−0.978304	−	0.207176i	$-0.933573\pi$
$317$	−4.17793	−	15.5922i	−0.234656	−	0.875747i	0.743648	−	0.668571i	$-0.233094\pi$
$318$	−24.1134	−	14.3590i	−1.35221	−	0.805214i
$319$	5.36071	+	9.28503i	0.300142	+	0.519862i
$320$	12.1760	−	2.22649i	0.680660	−	0.124465i
$321$	9.95157			0.555442
$322$		0			0
$323$	−25.1027	+	25.1027i	−1.39675	+	1.39675i
$324$	9.71363	+	17.9244i	0.539646	+	0.995802i
$325$	1.42949	−	5.33494i	0.0792939	−	0.295929i
$326$	−27.4435	+	6.95809i	−1.51996	+	0.385373i
$327$	−12.1431	−	7.01084i	−0.671517	−	0.387700i
$328$	29.9881	+	1.21426i	1.65581	+	0.0670463i
$329$		0			0
$330$	8.97923	+	2.53628i	0.494290	+	0.139618i
$331$	−20.9330	+	5.60899i	−1.15058	+	0.308298i	−0.783199	−	0.621771i	$-0.786413\pi$
$331$	−20.9330	+	5.60899i	−1.15058	+	0.308298i	−0.367385	+	0.930069i	$0.619747\pi$
$332$	−17.9305	+	16.9882i	−0.984065	+	0.932349i
$333$	4.24332	+	1.13699i	0.232533	+	0.0623069i
$334$	0.342450	+	0.00461986i	0.0187380	+	0.000252787i
$335$	1.03762			0.0566912
$336$		0			0
$337$	15.1140			0.823314			0.411657	−	0.911339i	$-0.364950\pi$
$337$	15.1140			0.823314			0.411657	+	0.911339i	$0.364950\pi$
$338$	−12.0315	−	0.162313i	−0.654430	−	0.00882865i
$339$	28.2147	+	7.56010i	1.53241	+	0.410609i
$340$	−10.3909	−	10.9672i	−0.563524	−	0.594783i
$341$	16.5976	−	4.44731i	0.898811	−	0.240836i
$342$	25.0153	+	7.06585i	1.35267	+	0.382077i
$343$		0			0
$344$	6.69574	−	6.17460i	0.361010	−	0.332912i
$345$	25.0207	+	14.4457i	1.34707	+	0.777731i
$346$	10.5845	−	2.68361i	0.569024	−	0.144272i
$347$	−4.81739	+	17.9787i	−0.258611	+	0.965149i	0.707435	+	0.706778i	$0.249852\pi$
$347$	−4.81739	+	17.9787i	−0.258611	+	0.965149i	−0.966046	+	0.258371i	$0.916814\pi$
$348$	−24.4392	+	13.2441i	−1.31008	+	0.709958i
$349$	11.3593	−	11.3593i	0.608051	−	0.608051i	−0.334386	−	0.942436i	$-0.608529\pi$
$349$	11.3593	−	11.3593i	0.608051	−	0.608051i	0.942436	+	0.334386i	$0.108529\pi$
$350$		0			0
$351$	−2.35291			−0.125589
$352$	9.70859	+	3.31728i	0.517470	+	0.176812i
$353$	−6.46116	−	11.1911i	−0.343893	−	0.595640i	0.641259	−	0.767324i	$-0.278412\pi$
$353$	−6.46116	−	11.1911i	−0.343893	−	0.595640i	−0.985152	+	0.171685i	$0.945079\pi$
$354$	11.0612	+	6.58674i	0.587899	+	0.350081i
$355$	0.601327	+	2.24418i	0.0319151	+	0.119109i
$356$	−7.26805	−	4.46187i	−0.385206	−	0.236478i
$357$		0			0
$358$	−3.52560	+	12.4817i	−0.186334	+	0.659679i
$359$	−9.86513	−	5.69564i	−0.520662	−	0.300604i	0.216544	−	0.976273i	$-0.430522\pi$
$359$	−9.86513	−	5.69564i	−0.520662	−	0.300604i	−0.737205	+	0.675669i	$0.763855\pi$
$360$	−3.29310	+	10.5608i	−0.173561	+	0.556601i
$361$	−29.3348	+	16.9365i	−1.54394	+	0.891394i
$362$	−14.0738	+	13.6991i	−0.739703	+	0.720010i
$363$	−12.8188	−	12.8188i	−0.672814	−	0.672814i
$364$		0			0
$365$	−11.0556	+	11.0556i	−0.578676	+	0.578676i
$366$	17.8113	+	0.240286i	0.931013	+	0.0125599i
$367$	−13.4301	−	23.2616i	−0.701044	−	1.21424i	−0.968100	−	0.250564i	$-0.919384\pi$
$367$	−13.4301	−	23.2616i	−0.701044	−	1.21424i	0.267056	−	0.963681i	$-0.413949\pi$
$368$	26.6155	+	17.3449i	1.38743	+	0.904166i
$369$	−13.4113	+	23.2291i	−0.698166	+	1.20926i
$370$	−1.85675	−	3.31858i	−0.0965280	−	0.172525i
$371$		0			0
$372$	10.3654	+	43.3275i	0.537419	+	2.24642i
$373$	12.3529	−	3.30994i	0.639607	−	0.171382i	0.0755816	−	0.997140i	$-0.475919\pi$
$373$	12.3529	−	3.30994i	0.639607	−	0.171382i	0.564025	+	0.825757i	$0.309252\pi$
$374$	−3.07762	−	12.1385i	−0.159140	−	0.627666i
$375$	−23.9620	+	13.8345i	−1.23739	+	0.714409i
$376$	−4.44671	−	2.81313i	−0.229322	−	0.145076i
$377$		−	12.5284i		−	0.645246i
$378$		0			0
$379$	−13.0659	−	13.0659i	−0.671149	−	0.671149i	0.286832	−	0.957981i	$-0.407398\pi$
$379$	−13.0659	−	13.0659i	−0.671149	−	0.671149i	−0.957981	+	0.286832i	$0.907398\pi$
$380$	−10.7208	−	19.7829i	−0.549965	−	1.01484i
$381$	−41.7175	−	11.1782i	−2.13725	−	0.572676i
$382$	7.83631	+	4.66636i	0.400941	+	0.238752i
$383$	7.95002	−	13.7698i	0.406227	−	0.703606i	−0.588236	−	0.808689i	$-0.700178\pi$
$383$	7.95002	−	13.7698i	0.406227	−	0.703606i	0.994463	+	0.105083i	$0.0335109\pi$
$384$	−9.27651	+	24.9300i	−0.473390	+	1.27220i
$385$		0			0
$386$	−9.81321	+	5.49051i	−0.499479	+	0.279459i
$387$	2.10681	+	7.86271i	0.107095	+	0.399684i
$388$	−24.6736	−	0.665846i	−1.25261	−	0.0338032i
$389$	−5.02567	+	18.7561i	−0.254812	+	0.950970i	0.713384	+	0.700774i	$0.247162\pi$
$389$	−5.02567	+	18.7561i	−0.254812	+	0.950970i	−0.968195	+	0.250196i	$0.919505\pi$
$390$	−7.60497	−	7.81297i	−0.385093	−	0.395625i
$391$		−	38.7752i		−	1.96095i
$392$		0			0
$393$			2.83759i			0.143138i
$394$	12.9328	−	12.5885i	0.651547	−	0.634201i
$395$	−3.13063	+	11.6837i	−0.157519	+	0.587869i
$396$	−6.65615	+	6.30634i	−0.334484	+	0.316906i
$397$	9.26535	+	34.5788i	0.465015	+	1.73546i	0.656841	+	0.754029i	$0.271892\pi$
$397$	9.26535	+	34.5788i	0.465015	+	1.73546i	−0.191826	+	0.981429i	$0.561441\pi$
$398$	−3.06756	−	5.48266i	−0.153763	−	0.274821i
$399$		0			0
$400$	−9.29560	+	4.71763i	−0.464780	+	0.235882i
$401$	−13.1203	+	22.7251i	−0.655197	+	1.13483i	0.326647	+	0.945146i	$0.394081\pi$
$401$	−13.1203	+	22.7251i	−0.655197	+	1.13483i	−0.981844	+	0.189689i	$0.939252\pi$
$402$	−1.14086	+	1.91588i	−0.0569011	+	0.0955552i
$403$	−19.3949	−	5.19686i	−0.966131	−	0.258874i
$404$	8.08193	−	27.2042i	0.402091	−	1.35346i
$405$	11.1525	+	11.1525i	0.554171	+	0.554171i
$406$		0			0
$407$		−	3.15195i		−	0.156236i
$408$	31.6749	−	7.12736i	1.56814	−	0.352857i
$409$	−21.9760	+	12.6879i	−1.08664	+	0.627374i	−0.932681	−	0.360703i	$-0.882537\pi$
$409$	−21.9760	+	12.6879i	−1.08664	+	0.627374i	−0.153963	+	0.988077i	$0.549204\pi$
$410$	22.5062	−	5.70628i	1.11150	−	0.281813i
$411$	17.7275	−	4.75006i	0.874431	−	0.234303i
$412$	−14.5054	−	8.90488i	−0.714629	−	0.438712i
$413$		0			0
$414$	−24.7773	+	13.8629i	−1.21774	+	0.681326i
$415$	−9.55430	+	16.5485i	−0.469002	+	0.812336i
$416$	−7.88676	−	9.02948i	−0.386680	−	0.442706i
$417$	0.0726433	+	0.125822i	0.00355736	+	0.00616152i
$418$	0.251584	−	18.6488i	0.0123054	−	0.912144i
$419$	−12.8188	+	12.8188i	−0.626241	+	0.626241i	−0.947120	−	0.320879i	$-0.896022\pi$
$419$	−12.8188	+	12.8188i	−0.626241	+	0.626241i	0.320879	+	0.947120i	$0.396022\pi$
$420$		0			0
$421$	5.55169	+	5.55169i	0.270573	+	0.270573i	0.829331	−	0.558758i	$-0.188722\pi$
$421$	5.55169	+	5.55169i	0.270573	+	0.270573i	−0.558758	+	0.829331i	$0.688722\pi$
$422$	25.3351	+	26.0280i	1.23329	+	1.26702i
$423$	4.07254	−	2.35128i	0.198014	−	0.114323i
$424$	−22.7912	−	7.10684i	−1.10684	−	0.345139i
$425$	11.0188	+	6.36168i	0.534488	+	0.308587i
$426$	−4.80485	−	1.35718i	−0.232796	−	0.0657556i
$427$		0			0
$428$	8.23304	−	1.96962i	0.397959	−	0.0952050i
$429$	−2.33902	−	8.72934i	−0.112929	−	0.421456i
$430$	3.60512	−	6.05415i	0.173854	−	0.291957i
$431$	13.7035	+	23.7352i	0.660076	+	1.14329i	0.980595	+	0.196043i	$0.0628093\pi$
$431$	13.7035	+	23.7352i	0.660076	+	1.14329i	−0.320519	+	0.947242i	$0.603857\pi$
$432$	2.96621	+	3.30492i	0.142712	+	0.159008i
$433$	−32.7756			−1.57510			−0.787548	−	0.616253i	$-0.788650\pi$
$433$	−32.7756			−1.57510			−0.787548	+	0.616253i	$0.788650\pi$
$434$		0			0
$435$	−15.2059	+	15.2059i	−0.729067	+	0.729067i
$436$	−11.4337	−	3.39677i	−0.547576	−	0.162676i
$437$	14.9468	−	55.7823i	0.715003	−	2.66843i
$438$	−8.25757	−	32.5688i	−0.394562	−	1.55620i
$439$	−11.1535	−	6.43948i	−0.532328	−	0.307340i	0.209636	−	0.977779i	$-0.432772\pi$
$439$	−11.1535	−	6.43948i	−0.532328	−	0.307340i	−0.741964	+	0.670440i	$0.766105\pi$
$440$	7.93059	+	0.321121i	0.378076	+	0.0153089i
$441$		0			0
$442$	−3.97764	+	14.0821i	−0.189197	+	0.669818i
$443$	7.30506	−	1.95738i	0.347074	−	0.0929981i	−0.0810709	−	0.996708i	$-0.525834\pi$
$443$	7.30506	−	1.95738i	0.347074	−	0.0929981i	0.428145	+	0.903710i	$0.359167\pi$
$444$	8.16898	+	0.220449i	0.387683	+	0.0104620i
$445$	−6.37289	−	1.70761i	−0.302104	−	0.0809485i
$446$	0.278908	−	20.6743i	0.0132067	−	0.978955i
$447$	53.6377			2.53697
$448$		0			0
$449$	−15.8168			−0.746441			−0.373220	−	0.927743i	$-0.621747\pi$
$449$	−15.8168			−0.746441			−0.373220	+	0.927743i	$0.621747\pi$
$450$	0.125670	−	9.31539i	0.00592415	−	0.439132i
$451$	18.5893	+	4.98098i	0.875334	+	0.234545i
$452$	24.8386	+	0.670298i	1.16831	+	0.0315281i
$453$	−18.8297	+	5.04540i	−0.884696	+	0.237054i
$454$	2.34198	−	8.29133i	0.109914	−	0.389132i
$455$		0			0
$456$	48.3150	+	1.95635i	2.26256	+	0.0916143i
$457$	23.4823	+	13.5575i	1.09845	+	0.634193i	0.935814	−	0.352493i	$-0.114666\pi$
$457$	23.4823	+	13.5575i	1.09845	+	0.634193i	0.162639	+	0.986686i	$0.447999\pi$
$458$	0.943238	+	3.72024i	0.0440746	+	0.173835i
$459$	1.40287	−	5.23559i	0.0654805	−	0.244376i
$460$	23.5590	+	6.99899i	1.09844	+	0.326330i
$461$	−6.31691	+	6.31691i	−0.294208	+	0.294208i	−0.838740	−	0.544532i	$-0.816707\pi$
$461$	−6.31691	+	6.31691i	−0.294208	+	0.294208i	0.544532	+	0.838740i	$0.316707\pi$
$462$		0			0
$463$	2.89508			0.134546			0.0672730	−	0.997735i	$-0.478570\pi$
$463$	2.89508			0.134546			0.0672730	+	0.997735i	$0.478570\pi$
$464$	−17.5975	+	15.7940i	−0.816944	+	0.733217i
$465$	17.2324	+	29.8474i	0.799134	+	1.38414i
$466$	0.454635	−	0.763477i	0.0210605	−	0.0353674i
$467$	0.353162	+	1.31802i	0.0163424	+	0.0609906i	0.973616	−	0.228195i	$-0.0732823\pi$
$467$	0.353162	+	1.31802i	0.0163424	+	0.0609906i	−0.957273	+	0.289185i	$0.906616\pi$
$468$	10.4205	−	2.49294i	0.481689	−	0.115236i
$469$		0			0
$470$	−3.91739	−	1.10651i	−0.180696	−	0.0510394i
$471$	0.775024	+	0.447460i	0.0357112	+	0.0206179i
$472$	10.4547	+	3.26004i	0.481218	+	0.150055i
$473$	5.05796	−	2.92022i	0.232565	−	0.134272i
$474$	−18.1308	−	18.6266i	−0.832773	−	0.855550i
$475$	13.3994	+	13.3994i	0.614806	+	0.614806i
$476$		0			0
$477$	15.0869	−	15.0869i	0.690781	−	0.690781i
$478$	−0.0980429	+	7.26750i	−0.00448438	+	0.332408i
$479$	6.00343	+	10.3983i	0.274304	+	0.475108i	0.969959	−	0.243267i	$-0.0782193\pi$
$479$	6.00343	+	10.3983i	0.274304	+	0.475108i	−0.695655	+	0.718376i	$0.744886\pi$
$480$	−1.38693	+	20.5315i	−0.0633043	+	0.937129i
$481$	−1.84159	+	3.18972i	−0.0839691	+	0.145439i
$482$	−27.8410	+	15.5771i	−1.26812	+	0.709518i
$483$		0			0
$484$	−13.1423	−	8.06805i	−0.597376	−	0.366730i
$485$	−18.4443	+	4.94214i	−0.837513	+	0.224411i
$486$	−28.2885	+	7.17232i	−1.28319	+	0.325343i
$487$	13.8361	−	7.98829i	0.626975	−	0.361984i	−0.152605	−	0.988287i	$-0.548766\pi$
$487$	13.8361	−	7.98829i	0.626975	−	0.361984i	0.779579	+	0.626303i	$0.215433\pi$
$488$	14.7831	−	3.32643i	0.669198	−	0.150581i
$489$		−	47.0684i		−	2.12851i
$490$		0			0
$491$	17.5557	+	17.5557i	0.792277	+	0.792277i	0.981864	−	0.189587i	$-0.0607150\pi$
$491$	17.5557	+	17.5557i	0.792277	+	0.792277i	−0.189587	+	0.981864i	$0.560715\pi$
$492$	−14.2095	+	47.8299i	−0.640612	+	2.15634i
$493$	27.8777	+	7.46979i	1.25555	+	0.336423i
$494$	−11.1505	+	18.7253i	−0.501686	+	0.842492i
$495$	−3.54674	+	6.14313i	−0.159414	+	0.276113i
$496$	17.1508	+	33.7938i	0.770092	+	1.51738i
$497$		0			0
$498$	−20.0505	−	35.8363i	−0.898484	−	1.60586i
$499$	−3.17596	−	11.8528i	−0.142175	−	0.530606i	−0.999865	−	0.0164379i	$-0.994767\pi$
$499$	−3.17596	−	11.8528i	−0.142175	−	0.530606i	0.857689	−	0.514168i	$-0.171899\pi$
$500$	−17.0859	+	16.1880i	−0.764105	+	0.723948i
$501$	−0.147365	+	0.549973i	−0.00658378	+	0.0245710i
$502$	−2.54325	+	2.47554i	−0.113511	+	0.110489i
$503$		−	34.4831i		−	1.53753i	−0.639533	−	0.768764i	$-0.720872\pi$
$503$		−	34.4831i		−	1.53753i	0.639533	−	0.768764i	$-0.279128\pi$
$504$		0			0
$505$		−	21.9548i		−	0.976977i
$506$	14.2088	+	14.5974i	0.631657	+	0.648933i
$507$	5.17748	−	19.3226i	0.229940	−	0.858147i
$508$	−36.7258	−	0.991085i	−1.62944	−	0.0439723i
$509$	4.59211	+	17.1380i	0.203542	+	0.759628i	0.989889	+	0.141843i	$0.0453029\pi$
$509$	4.59211	+	17.1380i	0.203542	+	0.759628i	−0.786347	+	0.617784i	$0.788030\pi$
$510$	21.9194	−	12.2639i	0.970606	−	0.543056i
$511$		0			0
$512$	−2.74041	+	22.4609i	−0.121110	+	0.992639i
$513$	4.03636	−	6.99118i	0.178210	−	0.308668i
$514$	24.7438	+	14.7344i	1.09140	+	0.649907i
$515$	−12.7188	−	3.40800i	−0.560459	−	0.150175i
$516$	7.21464	+	13.3131i	0.317607	+	0.586076i
$517$	−2.38581	−	2.38581i	−0.104928	−	0.104928i
$518$		0			0
$519$			18.1534i			0.796847i
$520$	−7.83802	−	4.95857i	−0.343720	−	0.217448i
$521$	6.31273	−	3.64466i	0.276566	−	0.159675i	−0.355302	−	0.934752i	$-0.615622\pi$
$521$	6.31273	−	3.64466i	0.276566	−	0.159675i	0.631868	+	0.775076i	$0.282289\pi$
$522$	−5.19365	−	20.4844i	−0.227320	−	0.896576i
$523$	27.2020	−	7.28876i	1.18946	−	0.318715i	0.390788	−	0.920481i	$-0.372203\pi$
$523$	27.2020	−	7.28876i	1.18946	−	0.318715i	0.798673	+	0.601766i	$0.205536\pi$
$524$	0.561617	+	2.34757i	0.0245344	+	0.102554i
$525$		0			0
$526$	−7.94959	−	14.2083i	−0.346619	−	0.619513i
$527$	23.1276	−	40.0583i	1.00746	−	1.74496i
$528$	−9.31261	+	14.2901i	−0.405280	+	0.621896i
$529$	20.0385	+	34.7078i	0.871241	+	1.50903i
$530$	−18.4674	−	0.249136i	−0.802171	−	0.0108218i
$531$	−6.92062	+	6.92062i	−0.300330	+	0.300330i
$532$		0			0
$533$	−15.9018	−	15.9018i	−0.688784	−	0.688784i
$534$	10.1599	−	9.88947i	0.439664	−	0.427959i
$535$	5.67157	−	3.27448i	0.245203	−	0.141568i
$536$	−0.564658	+	1.81082i	−0.0243895	+	0.0782157i
$537$	−18.6739	−	10.7814i	−0.805838	−	0.465251i
$538$	−11.0523	+	39.1285i	−0.476497	+	1.68695i
$539$		0			0
$540$	2.92781	+	1.79739i	0.125993	+	0.0773472i
$541$	10.7337	+	40.0586i	0.461476	+	1.72225i	0.668316	+	0.743877i	$0.267015\pi$
$541$	10.7337	+	40.0586i	0.461476	+	1.72225i	−0.206840	+	0.978375i	$0.566318\pi$
$542$	19.5705	+	11.6538i	0.840626	+	0.500575i
$543$	−16.3259	−	28.2773i	−0.700612	−	1.21350i
$544$	24.7943	−	12.1656i	1.06305	−	0.521597i
$545$	−9.22744			−0.395260
$546$		0			0
$547$	8.27618	−	8.27618i	0.353864	−	0.353864i	−0.507681	−	0.861545i	$-0.669497\pi$
$547$	8.27618	−	8.27618i	0.353864	−	0.353864i	0.861545	+	0.507681i	$0.169497\pi$
$548$	13.7260	−	7.43839i	0.586345	−	0.317752i
$549$	−3.50497	+	13.0807i	−0.149588	+	0.558271i
$550$	−6.47931	+	1.64278i	−0.276279	+	0.0700482i
$551$	37.2255	+	21.4922i	1.58586	+	0.915597i
$552$	−38.8262	+	35.8043i	−1.65255	+	1.52393i
$553$		0			0
$554$	7.25919	+	2.05044i	0.308413	+	0.0871147i
$555$	6.10657	−	1.63625i	0.259209	−	0.0694549i
$556$	0.0850012	+	0.0897162i	0.00360485	+	0.00380481i
$557$	16.5931	+	4.44611i	0.703073	+	0.188388i	0.592606	−	0.805492i	$-0.298099\pi$
$557$	16.5931	+	4.44611i	0.703073	+	0.188388i	0.110466	+	0.993880i	$0.464766\pi$
$558$	−33.8657	−	0.456869i	−1.43365	−	0.0193408i
$559$	−6.82477			−0.288657
$560$		0			0
$561$	20.8187			0.878967
$562$	−2.80258	−	0.0378085i	−0.118220	−	0.00159486i
$563$	28.7375	+	7.70019i	1.21114	+	0.324524i	0.807209	−	0.590265i	$-0.200977\pi$
$563$	28.7375	+	7.70019i	1.21114	+	0.324524i	0.403931	+	0.914789i	$0.367644\pi$
$564$	6.35024	−	6.01651i	0.267393	−	0.253341i
$565$	18.5676	−	4.97518i	0.781146	−	0.209308i
$566$	−21.4347	−	6.05447i	−0.900969	−	0.254488i
$567$		0			0
$568$	−4.24371	−	0.171834i	−0.178062	−	0.00721000i
$569$	−0.0913759	−	0.0527559i	−0.00383068	−	0.00221164i	0.498083	−	0.867129i	$-0.334037\pi$
$569$	−0.0913759	−	0.0527559i	−0.00383068	−	0.00221164i	−0.501914	+	0.864917i	$0.667371\pi$
$570$	36.2607	−	9.19362i	1.51880	−	0.385078i
$571$	8.62480	−	32.1882i	0.360937	−	1.34703i	−0.511910	−	0.859039i	$-0.671062\pi$
$571$	8.62480	−	32.1882i	0.360937	−	1.34703i	0.872847	−	0.487995i	$-0.162271\pi$
$572$	−3.66281	−	6.75894i	−0.153150	−	0.282605i
$573$	−10.7217	+	10.7217i	−0.447904	+	0.447904i
$574$		0			0
$575$	−20.6975			−0.863147
$576$	−16.6383	−	11.4940i	−0.693262	−	0.478918i
$577$	−19.0200	−	32.9435i	−0.791811	−	1.37146i	−0.924844	−	0.380346i	$-0.875805\pi$
$577$	−19.0200	−	32.9435i	−0.791811	−	1.37146i	0.133033	−	0.991112i	$-0.457528\pi$
$578$	−8.30668	−	4.94645i	−0.345512	−	0.205745i
$579$	−4.83847	−	18.0574i	−0.201080	−	0.750440i
$580$	−9.57045	+	15.5896i	−0.397391	+	0.647321i
$581$		0			0
$582$	11.1543	−	39.4897i	0.462361	−	1.63690i
$583$	−13.2575	−	7.65423i	−0.549070	−	0.317006i
$584$	−13.2776	−	25.3102i	−0.549431	−	1.04734i
$585$	7.17849	−	4.14450i	0.296794	−	0.171354i
$586$	−16.6374	+	16.1945i	−0.687285	+	0.668988i
$587$	−0.198475	−	0.198475i	−0.00819196	−	0.00819196i	0.702999	−	0.711191i	$-0.251844\pi$
$587$	−0.198475	−	0.198475i	−0.00819196	−	0.00819196i	−0.711191	+	0.702999i	$0.751844\pi$
$588$		0			0
$589$	48.7129	−	48.7129i	2.00718	−	2.00718i
$590$	8.47131	+	0.114283i	0.348758	+	0.00470496i
$591$	15.0024	+	25.9849i	0.617115	+	1.06887i
$592$	6.80192	−	1.43443i	0.279557	−	0.0589546i
$593$	−21.2989	+	36.8908i	−0.874641	+	1.51492i	−0.0174959	+	0.999847i	$0.505569\pi$
$593$	−21.2989	+	36.8908i	−0.874641	+	1.51492i	−0.857145	+	0.515075i	$0.827764\pi$
$594$	1.39040	+	2.48506i	0.0570487	+	0.101963i
$595$		0			0
$596$	44.3750	−	10.6160i	1.81767	−	0.434847i
$597$	10.0887	−	2.70326i	0.412903	−	0.110637i
$598$	−5.85025	−	23.0741i	−0.239235	−	0.943569i
$599$	−28.0505	+	16.1950i	−1.14611	+	0.661708i	−0.947937	−	0.318458i	$-0.896835\pi$
$599$	−28.0505	+	16.1950i	−1.14611	+	0.661708i	−0.198175	+	0.980167i	$0.563502\pi$
$600$	−3.80446	−	16.9075i	−0.155316	−	0.690245i
$601$			0.122467i			0.00499552i	0.999997	+	0.00249776i	$0.000795062\pi$
$601$			0.122467i			0.00499552i	−0.999997	+	0.00249776i	$0.999205\pi$
$602$		0			0
$603$	−1.19869	−	1.19869i	−0.0488146	−	0.0488146i
$604$	−14.5794	+	7.90089i	−0.593228	+	0.321483i
$605$	−11.5236	−	3.08774i	−0.468501	−	0.125535i
$606$	40.5377	+	24.1393i	1.64673	+	0.980594i
$607$	5.95755	−	10.3188i	0.241809	−	0.418826i	−0.719420	−	0.694575i	$-0.755592\pi$
$607$	5.95755	−	10.3188i	0.241809	−	0.418826i	0.961230	+	0.275749i	$0.0889258\pi$
$608$	40.3587	−	7.94401i	1.63676	−	0.322172i
$609$		0			0
$610$	10.2301	−	5.72373i	0.414203	−	0.231747i
$611$	1.02045	+	3.80837i	0.0412829	+	0.154070i
$612$	−0.665846	+	24.6736i	−0.0269152	+	0.997373i
$613$	9.41382	−	35.1329i	0.380221	−	1.41900i	−0.465344	−	0.885130i	$-0.654069\pi$
$613$	9.41382	−	35.1329i	0.380221	−	1.41900i	0.845565	−	0.533873i	$-0.179264\pi$
$614$	1.15608	+	1.18770i	0.0466557	+	0.0479317i
$615$			38.6005i			1.55652i
$616$		0			0
$617$		−	2.53102i		−	0.101895i	−0.998701	−	0.0509475i	$-0.983776\pi$
$617$		−	2.53102i		−	0.101895i	0.998701	−	0.0509475i	$-0.0162241\pi$
$618$	20.2770	−	19.7371i	0.815659	−	0.793945i
$619$	−6.61419	+	24.6845i	−0.265847	+	0.992153i	0.695883	+	0.718155i	$0.255013\pi$
$619$	−6.61419	+	24.6845i	−0.265847	+	0.992153i	−0.961730	+	0.273999i	$0.911654\pi$
$620$	20.1640	+	21.2824i	0.809804	+	0.854723i
$621$	2.28210	+	8.51692i	0.0915776	+	0.341772i
$622$	−20.7313	−	37.0532i	−0.831251	−	1.48570i
$623$		0			0
$624$	17.7735	−	9.02027i	0.711509	−	0.361100i
$625$	−2.58911	+	4.48448i	−0.103565	+	0.179379i
$626$	8.11641	−	13.6300i	0.324397	−	0.544766i
$627$	29.9499	+	8.02506i	1.19609	+	0.320490i
$628$	0.729747	+	0.216796i	0.0291201	+	0.00865109i
$629$	−5.99962	−	5.99962i	−0.239220	−	0.239220i
$630$		0			0
$631$			40.8187i			1.62497i	0.582985	+	0.812483i	$0.301885\pi$
$631$			40.8187i			1.62497i	−0.582985	+	0.812483i	$0.698115\pi$
$632$	−18.6864	−	11.8216i	−0.743303	−	0.470237i
$633$	−52.2959	+	30.1931i	−2.07858	+	1.20007i
$634$	22.1284	−	5.61049i	0.878833	−	0.222821i
$635$	−27.4536	+	7.35618i	−1.08946	+	0.291921i
$636$	20.7649	−	33.8245i	0.823381	−	1.34123i
$637$		0			0
$638$	−13.2321	+	7.40338i	−0.523863	+	0.293102i
$639$	1.89788	−	3.28723i	0.0750791	−	0.130041i
$640$	2.91617	+	17.2604i	0.115272	+	0.682277i
$641$	−16.5926	−	28.7392i	−0.655369	−	1.13513i	−0.981801	−	0.189911i	$-0.939180\pi$
$641$	−16.5926	−	28.7392i	−0.655369	−	1.13513i	0.326433	−	0.945220i	$-0.394153\pi$
$642$	−0.189845	+	14.0724i	−0.00749257	+	0.555392i
$643$	−3.62191	+	3.62191i	−0.142834	+	0.142834i	−0.774908	−	0.632074i	$-0.782204\pi$
$643$	−3.62191	+	3.62191i	−0.142834	+	0.142834i	0.632074	+	0.774908i	$0.282204\pi$
$644$		0			0
$645$	8.28332	+	8.28332i	0.326155	+	0.326155i
$646$	−35.0185	−	35.9763i	−1.37778	−	1.41547i
$647$	12.2945	−	7.09823i	0.483346	−	0.279060i	−0.238464	−	0.971151i	$-0.576644\pi$
$647$	12.2945	−	7.09823i	0.483346	−	0.279060i	0.721810	+	0.692091i	$0.243310\pi$
$648$	−25.5320	+	13.3940i	−1.00299	+	0.526164i
$649$	6.08145	+	3.51113i	0.238718	+	0.137824i
$650$	7.51678	+	2.12320i	0.294832	+	0.0832786i
$651$		0			0
$652$	−9.31579	−	38.9402i	−0.364834	−	1.52502i
$653$	2.27660	+	8.49640i	0.0890904	+	0.332490i	0.996057	−	0.0887120i	$-0.0282751\pi$
$653$	2.27660	+	8.49640i	0.0890904	+	0.332490i	−0.906967	+	0.421202i	$0.861608\pi$
$654$	10.1456	−	17.0377i	0.396723	−	0.666226i
$655$	0.933687	+	1.61719i	0.0364822	+	0.0631890i
$656$	−2.28914	+	42.3825i	−0.0893761	+	1.65476i
$657$	25.5436			0.996552
$658$		0			0
$659$	−4.19659	+	4.19659i	−0.163476	+	0.163476i	−0.784105	−	0.620629i	$-0.786877\pi$
$659$	−4.19659	+	4.19659i	−0.163476	+	0.163476i	0.620629	+	0.784105i	$0.286877\pi$
$660$	−3.75781	+	12.6490i	−0.146273	+	0.492362i
$661$	8.31447	−	31.0300i	0.323395	−	1.20693i	−0.592520	−	0.805556i	$-0.701867\pi$
$661$	8.31447	−	31.0300i	0.323395	−	1.20693i	0.915915	−	0.401372i	$-0.131466\pi$
$662$	−7.53225	−	29.7081i	−0.292749	−	1.15464i
$663$	−21.0682	−	12.1637i	−0.818222	−	0.472401i
$664$	−23.6807	−	25.6794i	−0.918990	−	0.996553i
$665$		0			0
$666$	−1.68876	+	5.97873i	−0.0654380	+	0.231671i
$667$	−45.3496	+	12.1514i	−1.75594	+	0.470503i
$668$	−0.0130657	+	0.484165i	−0.000505528	+	0.0187329i
$669$	33.2028	+	8.89666i	1.28369	+	0.343965i
$670$	−0.0197945	+	1.46728i	−0.000764729	+	0.0566861i
$671$	9.71637			0.375096
$672$		0			0
$673$	13.6167			0.524885			0.262443	−	0.964948i	$-0.415472\pi$
$673$	13.6167			0.524885			0.262443	+	0.964948i	$0.415472\pi$
$674$	−0.288328	+	21.3725i	−0.0111060	+	0.823239i
$675$	−2.79467	−	0.748828i	−0.107567	−	0.0288224i
$676$	0.459048	−	17.0105i	0.0176557	−	0.654251i
$677$	−2.37384	+	0.636069i	−0.0912342	+	0.0244461i	−0.304147	−	0.952625i	$-0.598372\pi$
$677$	−2.37384	+	0.636069i	−0.0912342	+	0.0244461i	0.212913	+	0.977071i	$0.431705\pi$
$678$	−11.2289	+	39.7538i	−0.431242	+	1.52673i
$679$		0			0
$680$	15.7068	−	14.4844i	0.602330	−	0.555450i
$681$	12.4047	+	7.16183i	0.475347	+	0.274442i
$682$	5.97225	+	23.5553i	0.228689	+	0.901978i
$683$	−2.44788	+	9.13560i	−0.0936654	+	0.349564i	−0.996814	−	0.0797647i	$-0.974583\pi$
$683$	−2.44788	+	9.13560i	−0.0936654	+	0.349564i	0.903148	+	0.429329i	$0.141250\pi$
$684$	−10.4689	+	35.2390i	−0.400289	+	1.34740i
$685$	8.54021	−	8.54021i	0.326305	−	0.326305i
$686$		0			0
$687$	−6.38059			−0.243435
$688$	8.60368	+	9.58614i	0.328012	+	0.365468i
$689$	8.94426	+	15.4919i	0.340749	+	0.590195i
$690$	−20.9048	+	35.1058i	−0.795832	+	1.33646i
$691$	−1.11019	−	4.14329i	−0.0422337	−	0.157618i	0.941589	−	0.336765i	$-0.109333\pi$
$691$	−1.11019	−	4.14329i	−0.0422337	−	0.157618i	−0.983822	+	0.179147i	$0.942666\pi$
$692$	3.59293	+	15.0185i	0.136583	+	0.570918i
$693$		0			0
$694$	−25.3316	−	7.15517i	−0.961573	−	0.271607i
$695$	0.0828013	+	0.0478054i	0.00314083	+	0.00181336i
$696$	−18.2621	−	34.8117i	−0.692221	−	1.31953i
$697$	44.8651	−	25.9029i	1.69939	−	0.981141i
$698$	15.8464	+	16.2798i	0.599793	+	0.616198i
$699$	1.04459	+	1.04459i	0.0395101	+	0.0395101i
$700$		0			0
$701$	−4.63375	+	4.63375i	−0.175014	+	0.175014i	−0.789178	−	0.614164i	$-0.789493\pi$
$701$	−4.63375	+	4.63375i	−0.175014	+	0.175014i	0.614164	+	0.789178i	$0.289493\pi$
$702$	0.0448861	−	3.32721i	0.00169412	−	0.125578i
$703$	−6.31839	−	10.9438i	−0.238303	−	0.412752i
$704$	−4.87613	+	13.6655i	−0.183776	+	0.515038i
$705$	3.38373	−	5.86080i	0.127439	−	0.220730i
$706$	15.9484	−	8.92314i	0.600225	−	0.335827i
$707$		0			0
$708$	−9.52522	+	15.5159i	−0.357980	+	0.583123i
$709$	−10.3987	+	2.78632i	−0.390530	+	0.104642i	−0.448741	−	0.893662i	$-0.648127\pi$
$709$	−10.3987	+	2.78632i	−0.390530	+	0.104642i	0.0582103	+	0.998304i	$0.481461\pi$
$710$	−3.18493	+	0.807515i	−0.119528	+	0.0303055i
$711$	17.1140	−	9.88077i	0.641825	−	0.370558i
$712$	6.44811	−	10.1925i	0.241653	−	0.381981i
$713$			75.2451i			2.81795i
$714$		0			0
$715$	−4.20537	−	4.20537i	−0.157272	−	0.157272i
$716$	−17.5830	−	5.22361i	−0.657106	−	0.195215i
$717$	−11.6716	−	3.12739i	−0.435883	−	0.116794i
$718$	8.24231	−	13.8415i	0.307600	−	0.516559i
$719$	12.9391	−	22.4112i	0.482548	−	0.835798i	−0.517251	−	0.855834i	$-0.673045\pi$
$719$	12.9391	−	22.4112i	0.482548	−	0.835798i	0.999799	+	0.0200355i	$0.00637793\pi$
$720$	−14.8710	−	4.85818i	−0.554209	−	0.181054i
$721$		0			0
$722$	−23.3900	−	41.8051i	−0.870486	−	1.55582i
$723$	−13.7272	−	51.2306i	−0.510520	−	1.90529i
$724$	−19.1032	−	20.1629i	−0.709966	−	0.749348i
$725$	3.98724	−	14.8806i	0.148083	−	0.552652i
$726$	18.3715	−	17.8824i	0.681829	−	0.663677i
$727$		−	2.94733i		−	0.109310i	−0.998505	−	0.0546552i	$-0.982594\pi$
$727$		−	2.94733i		−	0.109310i	0.998505	−	0.0546552i	$-0.0174060\pi$
$728$		0			0
$729$		−	17.9368i		−	0.664324i
$730$	−15.4226	−	15.8445i	−0.570818	−	0.586430i
$731$	4.06912	−	15.1862i	0.150502	−	0.561681i
$732$	−0.679569	+	25.1822i	−0.0251176	+	0.930759i
$733$	−9.06642	−	33.8363i	−0.334876	−	1.24977i	−0.904004	−	0.427525i	$-0.859386\pi$
$733$	−9.06642	−	33.8363i	−0.334876	−	1.24977i	0.569128	−	0.822249i	$-0.307281\pi$
$734$	33.1501	−	18.5475i	1.22359	−	0.684601i
$735$		0			0
$736$	−25.0349	+	37.3057i	−0.922799	+	1.37511i
$737$	−0.608149	+	1.05335i	−0.0224015	+	0.0388005i
$738$	−32.5921	−	19.4079i	−1.19973	−	0.714414i
$739$	−3.51934	−	0.943006i	−0.129461	−	0.0346890i	0.193507	−	0.981099i	$-0.438014\pi$
$739$	−3.51934	−	0.943006i	−0.129461	−	0.0346890i	−0.322968	+	0.946410i	$0.604681\pi$
$740$	4.72818	−	2.56230i	0.173811	−	0.0941920i
$741$	−25.6201	−	25.6201i	−0.941177	−	0.941177i
$742$		0			0
$743$			9.54797i			0.350281i	0.984543	+	0.175140i	$0.0560379\pi$
$743$			9.54797i			0.350281i	−0.984543	+	0.175140i	$0.943962\pi$
$744$	−61.4665	+	13.8310i	−2.25347	+	0.507068i
$745$	30.5690	−	17.6490i	1.11996	−	0.646611i
$746$	4.44488	+	17.5311i	0.162739	+	0.641861i
$747$	30.1549	−	8.07998i	1.10331	−	0.295631i
$748$	17.2236	−	4.12045i	0.629755	−	0.150658i
$749$		0			0
$750$	−19.1060	−	34.1482i	−0.697653	−	1.24692i
$751$	−14.9233	+	25.8480i	−0.544560	+	0.943206i	0.454074	+	0.890964i	$0.349970\pi$
$751$	−14.9233	+	25.8480i	−0.544560	+	0.943206i	−0.998634	+	0.0522419i	$0.983363\pi$
$752$	4.06283	−	6.23436i	0.148156	−	0.227344i
$753$	−2.95022	−	5.10994i	−0.107512	−	0.186216i
$754$	17.7162	+	0.239003i	0.645187	+	0.00870396i
$755$	−9.07122	+	9.07122i	−0.330135	+	0.330135i
$756$		0			0
$757$	32.3321	+	32.3321i	1.17513	+	1.17513i	0.980970	+	0.194161i	$0.0621986\pi$
$757$	32.3321	+	32.3321i	1.17513	+	1.17513i	0.194161	+	0.980970i	$0.437801\pi$
$758$	18.7255	−	18.2270i	0.680142	−	0.662035i
$759$	−29.3293	+	16.9333i	−1.06459	+	0.614639i
$760$	28.1793	−	14.7827i	1.02217	−	0.536225i
$761$	−30.3673	−	17.5326i	−1.10081	−	0.635556i	−0.164380	−	0.986397i	$-0.552562\pi$
$761$	−30.3673	−	17.5326i	−1.10081	−	0.635556i	−0.936435	+	0.350842i	$0.885896\pi$
$762$	16.6027	−	58.7789i	0.601454	−	2.12934i
$763$		0			0
$764$	−6.74812	+	10.9922i	−0.244138	+	0.397684i
$765$	4.94214	+	18.4443i	0.178683	+	0.666856i
$766$	19.3201	+	11.5047i	0.698062	+	0.415681i
$767$	−4.10289	−	7.10642i	−0.148147	−	0.256598i
$768$	−35.0762	−	13.5934i	−1.26570	−	0.490508i
$769$	2.64747			0.0954704			0.0477352	−	0.998860i	$-0.484800\pi$
$769$	2.64747			0.0954704			0.0477352	+	0.998860i	$0.484800\pi$
$770$		0			0
$771$	−33.8546	+	33.8546i	−1.21924	+	1.21924i
$772$	−7.57684	−	13.9814i	−0.272696	−	0.503203i
$773$	−10.9533	+	40.8781i	−0.393961	+	1.47028i	0.429581	+	0.903029i	$0.358661\pi$
$773$	−10.9533	+	40.8781i	−0.393961	+	1.47028i	−0.823542	+	0.567255i	$0.808005\pi$
$774$	−11.1587	+	2.82921i	−0.401092	+	0.101694i
$775$	−21.3824	−	12.3451i	−0.768078	−	0.443450i
$776$	1.41226	−	34.8779i	0.0506971	−	1.25204i
$777$		0			0
$778$	−26.4268	−	7.46453i	−0.947446	−	0.267616i
$779$	74.5280	−	19.9697i	2.67024	−	0.715490i
$780$	11.1933	−	10.6050i	0.400784	−	0.379721i
$781$	−2.63063	−	0.704875i	−0.0941313	−	0.0252224i
$782$	54.8315	+	0.739710i	1.96077	+	0.0264520i
$783$	−6.56291			−0.234539
$784$		0			0
$785$	0.588933			0.0210199
$786$	−4.01260	−	0.0541324i	−0.143125	−	0.00193084i
$787$	−29.0159	−	7.77480i	−1.03431	−	0.277142i	−0.298555	−	0.954393i	$-0.596505\pi$
$787$	−29.0159	−	7.77480i	−1.03431	−	0.277142i	−0.735752	+	0.677251i	$0.763171\pi$
$788$	17.5545	+	18.5283i	0.625355	+	0.660043i
$789$	26.1449	−	7.00551i	0.930784	−	0.249403i
$790$	−16.4620	−	4.64986i	−0.585691	−	0.165435i
$791$		0			0
$792$	−8.79073	−	9.53267i	−0.312365	−	0.338729i
$793$	−9.83282	−	5.67698i	−0.349174	−	0.201595i
$794$	−49.0741	+	12.4423i	−1.74157	+	0.441562i
$795$	7.94698	−	29.6585i	0.281850	−	1.05188i
$796$	7.81146	−	4.23319i	0.276870	−	0.150042i
$797$	14.9534	−	14.9534i	0.529676	−	0.529676i	−0.390800	−	0.920476i	$-0.627802\pi$
$797$	14.9534	−	14.9534i	0.529676	−	0.529676i	0.920476	+	0.390800i	$0.127802\pi$
$798$		0			0
$799$	−9.08263			−0.321320
$800$	−6.49380	−	13.2348i	−0.229591	−	0.467919i
$801$	5.38949	+	9.33487i	0.190428	+	0.329832i
$802$	−31.8849	−	18.9868i	−1.12589	−	0.670446i
$803$	−4.74346	−	17.7028i	−0.167393	−	0.624719i
$804$	−2.68745	−	1.64983i	−0.0947790	−	0.0581849i
$805$		0			0
$806$	7.71880	−	27.3270i	0.271883	−	0.962551i
$807$	−58.5401	−	33.7981i	−2.06071	−	1.18975i
$808$	38.3149	+	11.9475i	1.34791	+	0.420312i
$809$	38.5669	−	22.2666i	1.35594	−	0.782853i	0.366867	−	0.930273i	$-0.380430\pi$
$809$	38.5669	−	22.2666i	1.35594	−	0.782853i	0.989074	+	0.147420i	$0.0470970\pi$
$810$	−15.9833	+	15.5578i	−0.561596	+	0.546645i
$811$	−5.06726	−	5.06726i	−0.177935	−	0.177935i	0.612520	−	0.790455i	$-0.290156\pi$
$811$	−5.06726	−	5.06726i	−0.177935	−	0.177935i	−0.790455	+	0.612520i	$0.790156\pi$
$812$		0			0
$813$	−26.7765	+	26.7765i	−0.939092	+	0.939092i
$814$	4.45712	+	0.0601292i	0.156222	+	0.00210753i
$815$	−15.4875	−	26.8251i	−0.542503	−	0.939642i
$816$	9.47444	+	44.9269i	0.331672	+	1.57276i
$817$	11.7077	−	20.2784i	0.409602	−	0.709451i
$818$	−17.5225	−	31.3180i	−0.612659	−	1.09501i
$819$		0			0
$820$	7.63981	+	31.9346i	0.266794	+	1.11520i
$821$	2.47133	−	0.662191i	0.0862500	−	0.0231106i	−0.215436	−	0.976518i	$-0.569117\pi$
$821$	2.47133	−	0.662191i	0.0862500	−	0.0231106i	0.301686	+	0.953407i	$0.402451\pi$
$822$	6.37880	+	25.1587i	0.222486	+	0.877512i
$823$	42.0582	−	24.2823i	1.46606	−	0.846428i	0.466776	−	0.884376i	$-0.345415\pi$
$823$	42.0582	−	24.2823i	1.46606	−	0.846428i	0.999280	+	0.0379480i	$0.0120821\pi$
$824$	12.8690	−	20.3420i	0.448312	−	0.708646i
$825$		−	11.1127i		−	0.386893i
$826$		0			0
$827$	12.3701	+	12.3701i	0.430151	+	0.430151i	0.888680	−	0.458529i	$-0.151623\pi$
$827$	12.3701	+	12.3701i	0.430151	+	0.430151i	−0.458529	+	0.888680i	$0.651623\pi$
$828$	−19.1307	−	35.3017i	−0.664838	−	1.22682i
$829$	−9.59030	−	2.56971i	−0.333085	−	0.0892498i	0.0884006	−	0.996085i	$-0.471824\pi$
$829$	−9.59030	−	2.56971i	−0.333085	−	0.0892498i	−0.421485	+	0.906835i	$0.638491\pi$
$830$	−23.2188	−	13.8263i	−0.805935	−	0.479917i
$831$	−6.27029	+	10.8605i	−0.217514	+	0.376745i
$832$	12.9189	−	10.9803i	0.447882	−	0.380673i
$833$		0			0
$834$	−0.179309	+	0.100323i	−0.00620895	+	0.00347392i
$835$	0.0969784	+	0.361928i	0.00335608	+	0.0125251i
$836$	26.3662	+	0.711522i	0.911895	+	0.0246085i
$837$	−2.72234	+	10.1599i	−0.0940977	+	0.351177i
$838$	−17.8824	−	18.3715i	−0.617737	−	0.634632i
$839$		−	3.24523i		−	0.112038i	−0.998430	−	0.0560190i	$-0.982159\pi$
$839$		−	3.24523i		−	0.112038i	0.998430	−	0.0560190i	$-0.0178407\pi$
$840$		0			0
$841$		−	5.94516i		−	0.205006i
$842$	−7.95648	+	7.74466i	−0.274198	+	0.266899i
$843$	1.20602	−	4.50093i	0.0415376	−	0.155020i
$844$	−37.2891	+	35.3294i	−1.28355	+	1.21609i
$845$	−3.40721	−	12.7159i	−0.117212	−	0.437440i
$846$	3.24722	+	5.80378i	0.111642	+	0.199538i
$847$		0			0
$848$	10.4845	−	32.0931i	0.360038	−	1.10208i
$849$	18.5147	−	32.0685i	0.635424	−	1.10059i
$850$	−9.20616	+	15.4601i	−0.315769	+	0.530277i
$851$	13.3321	+	3.57233i	0.457019	+	0.122458i
$852$	2.01083	−	6.76857i	0.0688899	−	0.231887i
$853$	17.1348	+	17.1348i	0.586685	+	0.586685i	0.936732	−	0.350047i	$-0.113834\pi$
$853$	17.1348	+	17.1348i	0.586685	+	0.586685i	−0.350047	+	0.936732i	$0.613834\pi$
$854$		0			0
$855$			28.4392i			0.972599i
$856$	2.62814	+	11.6798i	0.0898281	+	0.399207i
$857$	6.12761	−	3.53778i	0.209315	−	0.120848i	−0.391678	−	0.920102i	$-0.628105\pi$
$857$	6.12761	−	3.53778i	0.209315	−	0.120848i	0.600993	+	0.799254i	$0.294772\pi$
$858$	12.3886	−	3.14104i	0.422941	−	0.107233i
$859$	−45.2594	+	12.1272i	−1.54423	+	0.413775i	−0.927630	−	0.373500i	$-0.878157\pi$
$859$	−45.2594	+	12.1272i	−1.54423	+	0.413775i	−0.616601	+	0.787276i	$0.711491\pi$
$860$	8.49231	+	5.21344i	0.289585	+	0.177777i
$861$		0			0
$862$	−33.8250	+	18.9252i	−1.15209	+	0.644594i
$863$	7.63479	−	13.2238i	0.259891	−	0.450145i	−0.706321	−	0.707891i	$-0.749647\pi$
$863$	7.63479	−	13.2238i	0.259891	−	0.450145i	0.966213	+	0.257747i	$0.0829799\pi$
$864$	−4.73002	+	4.13142i	−0.160919	+	0.140554i
$865$	5.97324	+	10.3459i	0.203096	+	0.351773i
$866$	0.625256	−	46.3475i	0.0212471	−	1.57495i
$867$	11.3652	−	11.3652i	0.385984	−	0.385984i
$868$		0			0
$869$	−10.0259	−	10.0259i	−0.340104	−	0.340104i
$870$	−21.2123	−	21.7925i	−0.719166	−	0.738835i
$871$	1.23088	−	0.710646i	0.0417066	−	0.0240793i
$872$	5.02144	−	16.1035i	0.170048	−	0.545332i
$873$	27.0168	+	15.5982i	0.914382	+	0.527918i
$874$	78.5958	+	22.2002i	2.65854	+	0.750934i
$875$		0			0
$876$	46.2126	−	11.0556i	1.56138	−	0.373534i
$877$	−1.97634	−	7.37580i	−0.0667362	−	0.249063i	0.924496	−	0.381191i	$-0.124486\pi$
$877$	−1.97634	−	7.37580i	−0.0667362	−	0.249063i	−0.991233	+	0.132128i	$0.957819\pi$
$878$	9.31874	−	15.6492i	0.314492	−	0.528133i
$879$	−19.2997	−	33.4281i	−0.650964	−	1.12750i
$880$	−0.605383	+	11.2084i	−0.0204075	+	0.377835i
$881$	−8.36445			−0.281805			−0.140903	−	0.990023i	$-0.545000\pi$
$881$	−8.36445			−0.281805			−0.140903	+	0.990023i	$0.545000\pi$
$882$		0			0
$883$	1.09301	−	1.09301i	0.0367828	−	0.0367828i	−0.688476	−	0.725259i	$-0.741720\pi$
$883$	1.09301	−	1.09301i	0.0367828	−	0.0367828i	0.725259	+	0.688476i	$0.241720\pi$
$884$	−19.8374	−	5.89337i	−0.667205	−	0.198215i
$885$	−3.64542	+	13.6049i	−0.122539	+	0.457323i
$886$	2.62855	+	10.3673i	0.0883079	+	0.348297i
$887$	33.4773	+	19.3281i	1.12406	+	0.648974i	0.942433	−	0.334394i	$-0.108532\pi$
$887$	33.4773	+	19.3281i	1.12406	+	0.648974i	0.181623	+	0.983368i	$0.441865\pi$
$888$	−0.467572	+	11.5474i	−0.0156907	+	0.387506i
$889$		0			0
$890$	2.53628	−	8.97923i	0.0850163	−	0.300984i
$891$	−17.8580	+	4.78502i	−0.598264	+	0.160304i
$892$	29.2299	+	0.788800i	0.978688	+	0.0264110i
$893$	−13.0663	−	3.50111i	−0.437248	−	0.117160i
$894$	−1.02324	+	75.8482i	−0.0342222	+	2.53674i
$895$	−14.1901			−0.474323
$896$		0			0
$897$	39.5744			1.32135
$898$	0.301735	−	22.3663i	0.0100690	−	0.746373i
$899$	−54.0978	−	14.4955i	−1.80426	−	0.483451i
$900$	13.1704	+	0.355417i	0.439012	+	0.0118472i
$901$	−39.8047	+	10.6656i	−1.32609	+	0.355324i
$902$	−7.39815	+	26.1918i	−0.246331	+	0.872090i
$903$		0			0
$904$	−1.42170	+	35.1111i	−0.0472850	+	1.16778i
$905$	−18.6088	−	10.7438i	−0.618579	−	0.357136i
$906$	−6.77541	−	26.7230i	−0.225098	−	0.887813i
$907$	−12.6328	+	47.1464i	−0.419467	+	1.56547i	0.356250	+	0.934391i	$0.384055\pi$
$907$	−12.6328	+	47.1464i	−0.419467	+	1.56547i	−0.775717	+	0.631081i	$0.782612\pi$
$908$	11.6800	+	3.46993i	0.387613	+	0.115154i
$909$	−25.3630	+	25.3630i	−0.841237	+	0.841237i
$910$		0			0
$911$	14.2220			0.471196			0.235598	−	0.971851i	$-0.424295\pi$
$911$	14.2220			0.471196			0.235598	+	0.971851i	$0.424295\pi$
$912$	−3.68814	+	68.2842i	−0.122126	+	2.26112i
$913$	−11.1996	−	19.3982i	−0.370651	−	0.641986i
$914$	−19.6194	+	32.9473i	−0.648952	+	1.08980i
$915$	5.04399	+	18.8244i	0.166749	+	0.622317i
$916$	−5.27873	+	1.26285i	−0.174414	+	0.0417257i
$917$		0			0
$918$	7.37681	+	2.08366i	0.243471	+	0.0687710i
$919$	18.8177	+	10.8644i	0.620738	+	0.358383i	0.777156	−	0.629308i	$-0.216661\pi$
$919$	18.8177	+	10.8644i	0.620738	+	0.358383i	−0.156418	+	0.987691i	$0.549995\pi$
$920$	−10.3466	+	33.1809i	−0.341117	+	1.09394i
$921$	−2.38635	+	1.37776i	−0.0786329	+	0.0453987i
$922$	−8.81214	−	9.05315i	−0.290212	−	0.298150i
$923$	2.25032	+	2.25032i	0.0740702	+	0.0740702i
$924$		0			0
$925$	−3.20249	+	3.20249i	−0.105297	+	0.105297i
$926$	−0.0552291	+	4.09389i	−0.00181494	+	0.134534i
$927$	10.7562	+	18.6303i	0.353280	+	0.611899i
$928$	−21.9983	−	25.1857i	−0.722131	−	0.826760i
$929$	16.2809	−	28.1994i	0.534160	−	0.925193i	−0.465043	−	0.885288i	$-0.653961\pi$
$929$	16.2809	−	28.1994i	0.534160	−	0.925193i	0.999203	−	0.0399047i	$-0.0127054\pi$
$930$	−42.5355	+	23.7987i	−1.39479	+	0.780390i
$931$		0			0
$932$	1.07095	+	0.657457i	0.0350801	+	0.0215357i
$933$	68.1821	−	18.2693i	2.23218	−	0.598111i
$934$	−1.87053	+	0.474257i	−0.0612055	+	0.0155182i
$935$	11.8650	−	6.85023i	0.388025	−	0.224027i
$936$	3.32643	+	14.7831i	0.108728	+	0.483200i
$937$			25.2755i			0.825714i	0.910796	+	0.412857i	$0.135469\pi$
$937$			25.2755i			0.825714i	−0.910796	+	0.412857i	$0.864531\pi$
$938$		0			0
$939$	18.6487	+	18.6487i	0.608577	+	0.608577i
$940$	1.63943	−	5.51841i	0.0534723	−	0.179991i
$941$	36.8695	+	9.87914i	1.20191	+	0.322051i	0.803583	−	0.595193i	$-0.202924\pi$
$941$	36.8695	+	9.87914i	1.20191	+	0.322051i	0.398327	+	0.917243i	$0.369591\pi$
$942$	−0.647532	+	1.08741i	−0.0210977	+	0.0354298i
$943$	−42.1371	+	72.9836i	−1.37217	+	2.37667i
$944$	−4.80941	+	14.7217i	−0.156533	+	0.479150i
$945$		0			0
$946$	4.03294	+	7.20810i	0.131122	+	0.234355i
$947$	−12.1983	−	45.5247i	−0.396392	−	1.47936i	−0.819396	−	0.573228i	$-0.805691\pi$
$947$	−12.1983	−	45.5247i	−0.396392	−	1.47936i	0.423004	−	0.906128i	$-0.360976\pi$
$948$	26.6855	−	25.2831i	0.866705	−	0.821157i
$949$	−5.54292	+	20.6865i	−0.179931	+	0.671511i
$950$	−19.2035	+	18.6923i	−0.623044	+	0.606457i
$951$			37.9525i			1.23070i
$952$		0			0
$953$		−	0.698407i		−	0.0226236i	−0.999936	−	0.0113118i	$-0.996399\pi$
$953$		−	0.698407i		−	0.0226236i	0.999936	−	0.0113118i	$-0.00360074\pi$
$954$	21.0463	+	21.6220i	0.681400	+	0.700037i
$955$	−2.58259	+	9.63835i	−0.0835706	+	0.311890i
$956$	−10.2750	−	0.277282i	−0.332317	−	0.00896794i
$957$	−6.52417	−	24.3485i	−0.210896	−	0.787076i
$958$	−14.8185	+	8.29100i	−0.478765	+	0.267870i
$959$		0			0
$960$	−29.0068	−	2.35291i	−0.936189	−	0.0759398i
$961$	−29.3802	+	50.8880i	−0.947749	+	1.64155i
$962$	−4.47541	−	2.66501i	−0.144293	−	0.0859234i
$963$	−10.3348	−	2.76920i	−0.333034	−	0.0892362i
$964$	−21.4962	−	39.6667i	−0.692347	−	1.27758i
$965$	−8.69917	−	8.69917i	−0.280036	−	0.280036i
$966$		0			0
$967$		−	21.7169i		−	0.698368i	−0.937054	−	0.349184i	$-0.886459\pi$
$967$		−	21.7169i		−	0.698368i	0.937054	−	0.349184i	$-0.113541\pi$
$968$	11.6596	−	18.4304i	0.374755	−	0.592374i
$969$	72.2840	−	41.7332i	2.32210	−	1.34066i
$970$	−6.63674	−	26.1761i	−0.213093	−	0.840464i
$971$	−42.5750	+	11.4079i	−1.36630	+	0.366098i	−0.866125	−	0.499828i	$-0.833397\pi$
$971$	−42.5750	+	11.4079i	−1.36630	+	0.366098i	−0.500172	+	0.865926i	$0.666730\pi$
$972$	−9.60262	−	40.1392i	−0.308004	−	1.28746i
$973$		0			0
$974$	11.0322	+	19.7178i	0.353493	+	0.631800i
$975$	−6.49279	+	11.2458i	−0.207936	+	0.360155i
$976$	4.42184	+	20.9680i	0.141540	+	0.671168i
$977$	−13.4986	−	23.3803i	−0.431860	−	0.748003i	0.565174	−	0.824972i	$-0.308809\pi$
$977$	−13.4986	−	23.3803i	−0.431860	−	0.748003i	−0.997034	+	0.0769687i	$0.975476\pi$
$978$	66.5587	+	0.897917i	2.12831	+	0.0287122i
$979$	5.46864	−	5.46864i	0.174778	−	0.174778i
$980$		0			0
$981$	10.6599	+	10.6599i	0.340343	+	0.340343i
$982$	−25.1601	+	24.4903i	−0.802892	+	0.781517i
$983$	36.3269	−	20.9734i	1.15865	−	0.668946i	0.207669	−	0.978199i	$-0.433412\pi$
$983$	36.3269	−	20.9734i	1.15865	−	0.668946i	0.950980	+	0.309253i	$0.100079\pi$
$984$	−67.3644	−	21.0058i	−2.14750	−	0.669641i
$985$	17.1002	+	9.87281i	0.544858	+	0.314574i
$986$	−11.0947	+	39.2789i	−0.353329	+	1.25089i
$987$		0			0
$988$	−26.2665	−	16.1250i	−0.835648	−	0.513005i
$989$	6.61939	+	24.7039i	0.210484	+	0.785538i
$990$	−8.61925	−	5.13258i	−0.273938	−	0.163124i
$991$	−22.3707	−	38.7473i	−0.710630	−	1.23085i	−0.964621	−	0.263641i	$-0.915077\pi$
$991$	−22.3707	−	38.7473i	−0.710630	−	1.23085i	0.253991	−	0.967207i	$-0.418257\pi$
$992$	−48.1144	+	23.6080i	−1.52763	+	0.749553i
$993$	50.9524			1.61692
$994$		0			0
$995$	4.86024	−	4.86024i	0.154080	−	0.154080i
$996$	51.0581	−	27.6694i	1.61784	−	0.876740i
$997$	−14.0322	+	52.3690i	−0.444405	+	1.65854i	0.273097	+	0.961986i	$0.411952\pi$
$997$	−14.0322	+	52.3690i	−0.444405	+	1.65854i	−0.717502	+	0.696556i	$0.754715\pi$
$998$	16.8215	−	4.26496i	0.532476	−	0.135005i
$999$	1.67091	+	0.964701i	0.0528653	+	0.0305218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.n.373.5		40
7.2	even	3		784.2.m.i.197.10	yes	20
7.3	odd	6	inner	784.2.x.n.165.1		40
7.4	even	3	inner	784.2.x.n.165.2		40
7.5	odd	6		784.2.m.i.197.9	✓	20
7.6	odd	2	inner	784.2.x.n.373.6		40
16.13	even	4	inner	784.2.x.n.765.2		40
112.13	odd	4	inner	784.2.x.n.765.1		40
112.45	odd	12	inner	784.2.x.n.557.6		40
112.61	odd	12		784.2.m.i.589.9	yes	20
112.93	even	12		784.2.m.i.589.10	yes	20
112.109	even	12	inner	784.2.x.n.557.5		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.m.i.197.9	✓	20	7.5	odd	6
784.2.m.i.197.10	yes	20	7.2	even	3
784.2.m.i.589.9	yes	20	112.61	odd	12
784.2.m.i.589.10	yes	20	112.93	even	12
784.2.x.n.165.1		40	7.3	odd	6	inner
784.2.x.n.165.2		40	7.4	even	3	inner
784.2.x.n.373.5		40	1.1	even	1	trivial
784.2.x.n.373.6		40	7.6	odd	2	inner
784.2.x.n.557.5		40	112.109	even	12	inner
784.2.x.n.557.6		40	112.45	odd	12	inner
784.2.x.n.765.1		40	112.13	odd	4	inner
784.2.x.n.765.2		40	16.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0190769 + 1.41408i) q^{2} +(-2.27101 - 0.608516i) q^{3} +(-1.99927 - 0.0539526i) q^{4} +(-1.49452 + 0.400455i) q^{5} +(0.903818 - 3.19980i) q^{6} +(0.114433 - 2.82611i) q^{8} +(2.18914 + 1.26390i) q^{9} +O(q^{10})\)	\(q+(-0.0190769 + 1.41408i) q^{2} +(-2.27101 - 0.608516i) q^{3} +(-1.99927 - 0.0539526i) q^{4} +(-1.49452 + 0.400455i) q^{5} +(0.903818 - 3.19980i) q^{6} +(0.114433 - 2.82611i) q^{8} +(2.18914 + 1.26390i) q^{9} +(-0.537766 - 2.12101i) q^{10} +(0.469413 - 1.75187i) q^{11} +(4.50754 + 1.33912i) q^{12} +(-1.49861 + 1.49861i) q^{13} +3.63776 q^{15} +(3.99418 + 0.215732i) q^{16} +(-2.44112 - 4.22814i) q^{17} +(-1.82902 + 3.07152i) q^{18} +(-1.88197 - 7.02361i) q^{19} +(3.00955 - 0.719985i) q^{20} +(2.46834 + 0.697210i) q^{22} +(6.87807 + 3.97105i) q^{23} +(-1.97962 + 6.34851i) q^{24} +(-2.25691 + 1.30303i) q^{25} +(-2.09057 - 2.14774i) q^{26} +(0.785033 + 0.785033i) q^{27} +(-4.18002 + 4.18002i) q^{29} +(-0.0693969 + 5.14409i) q^{30} +(4.73710 + 8.20490i) q^{31} +(-0.381259 + 5.64399i) q^{32} +(-2.13209 + 3.69289i) q^{33} +(6.02552 - 3.37129i) q^{34} +(-4.30849 - 2.64499i) q^{36} +(1.67866 - 0.449796i) q^{37} +(9.96789 - 2.52728i) q^{38} +(4.31528 - 2.49143i) q^{39} +(0.960707 + 4.26950i) q^{40} +10.6111i q^{41} +(2.27704 + 2.27704i) q^{43} +(-1.03300 + 3.47715i) q^{44} +(-3.77784 - 1.01227i) q^{45} +(-5.74662 + 9.65041i) q^{46} +(0.930171 - 1.61110i) q^{47} +(-8.93956 - 2.92045i) q^{48} +(-1.79953 - 3.21632i) q^{50} +(2.97092 + 11.0876i) q^{51} +(3.07697 - 2.91527i) q^{52} +(2.18458 - 8.15297i) q^{53} +(-1.12508 + 1.09513i) q^{54} +2.80619i q^{55} +17.0959i q^{57} +(-5.83116 - 5.99065i) q^{58} +(-1.00211 + 3.73991i) q^{59} +(-7.27286 - 0.196266i) q^{60} +(1.38657 + 5.17474i) q^{61} +(-11.6928 + 6.54214i) q^{62} +(-7.97381 - 0.646803i) q^{64} +(1.63957 - 2.83982i) q^{65} +(-5.18138 - 3.08540i) q^{66} +(-0.647776 - 0.173571i) q^{67} +(4.65234 + 8.58491i) q^{68} +(-13.2037 - 13.2037i) q^{69} -1.50161i q^{71} +(3.82243 - 6.04212i) q^{72} +(8.75126 - 5.05254i) q^{73} +(0.604027 + 2.38235i) q^{74} +(5.91838 - 1.58583i) q^{75} +(3.38363 + 14.1437i) q^{76} +(3.44077 + 6.14970i) q^{78} +(3.90884 - 6.77031i) q^{79} +(-6.05576 + 1.27707i) q^{80} +(-5.09681 - 8.82794i) q^{81} +(-15.0050 - 0.202426i) q^{82} +(8.73286 - 8.73286i) q^{83} +(5.34147 + 5.34147i) q^{85} +(-3.26337 + 3.17649i) q^{86} +(12.0365 - 6.94928i) q^{87} +(-4.89727 - 1.52709i) q^{88} +(3.69289 + 2.13209i) q^{89} +(1.50350 - 5.32288i) q^{90} +(-13.5369 - 8.31031i) q^{92} +(-5.76521 - 21.5160i) q^{93} +(2.26049 + 1.34608i) q^{94} +(5.62528 + 9.74327i) q^{95} +(4.30031 - 12.5856i) q^{96} +12.3413 q^{97} +(3.24180 - 3.24180i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{4}+O(q^{10}) \) 40 * q + 8 * q^4	\( 40 q + 8 q^{4} - 4 q^{11} - 32 q^{15} - 16 q^{18} - 8 q^{29} - 8 q^{30} + 40 q^{32} + 80 q^{36} + 20 q^{37} + 120 q^{43} - 56 q^{44} + 64 q^{46} - 112 q^{50} + 16 q^{51} - 28 q^{53} + 72 q^{58} + 24 q^{60} - 64 q^{64} - 16 q^{65} - 12 q^{67} - 16 q^{72} + 16 q^{74} - 176 q^{78} + 72 q^{79} - 12 q^{81} + 64 q^{85} + 40 q^{86} - 80 q^{88} - 48 q^{92} - 48 q^{93} - 64 q^{95} - 216 q^{99}+O(q^{100}) \) 40 * q + 8 * q^4 - 4 * q^11 - 32 * q^15 - 16 * q^18 - 8 * q^29 - 8 * q^30 + 40 * q^32 + 80 * q^36 + 20 * q^37 + 120 * q^43 - 56 * q^44 + 64 * q^46 - 112 * q^50 + 16 * q^51 - 28 * q^53 + 72 * q^58 + 24 * q^60 - 64 * q^64 - 16 * q^65 - 12 * q^67 - 16 * q^72 + 16 * q^74 - 176 * q^78 + 72 * q^79 - 12 * q^81 + 64 * q^85 + 40 * q^86 - 80 * q^88 - 48 * q^92 - 48 * q^93 - 64 * q^95 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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