LMFDB - Embedded newform 420.2.bv.c.233.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(53,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 9, 8]))

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

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

chi := DirichletCharacter("420.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.bv (of order $12$, degree $4$, 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:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			233.3
Character	$\chi$	$=$	420.233
Dual form			420.2.bv.c.137.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53846 - 0.795708i) q^{3} +(2.19857 - 0.407811i) q^{5} +(1.10146 + 2.40557i) q^{7} +(1.73370 + 2.44833i) q^{9} +O(q^{10})$	\(q+(-1.53846 - 0.795708i) q^{3} +(2.19857 - 0.407811i) q^{5} +(1.10146 + 2.40557i) q^{7} +(1.73370 + 2.44833i) q^{9} +(-2.63993 + 1.52416i) q^{11} +(0.512041 + 0.512041i) q^{13} +(-3.70690 - 1.12202i) q^{15} +(1.04198 - 3.88873i) q^{17} +(5.78739 + 3.34135i) q^{19} +(0.219587 - 4.57731i) q^{21} +(0.614611 + 2.29376i) q^{23} +(4.66738 - 1.79320i) q^{25} +(-0.719065 - 5.14616i) q^{27} +8.51556 q^{29} +(0.921008 + 1.59523i) q^{31} +(5.27420 - 0.244246i) q^{33} +(3.40265 + 4.83962i) q^{35} +(-0.747413 - 2.78938i) q^{37} +(-0.380318 - 1.19519i) q^{39} +8.91355i q^{41} +(-7.54399 - 7.54399i) q^{43} +(4.81010 + 4.67578i) q^{45} +(7.28063 - 1.95084i) q^{47} +(-4.57357 + 5.29929i) q^{49} +(-4.69734 + 5.15352i) q^{51} +(-10.5024 - 2.81412i) q^{53} +(-5.18248 + 4.42756i) q^{55} +(-6.24491 - 9.74561i) q^{57} +(1.06765 + 1.84923i) q^{59} +(7.12318 - 12.3377i) q^{61} +(-3.98003 + 6.86727i) q^{63} +(1.33457 + 0.916940i) q^{65} +(-3.86614 - 1.03593i) q^{67} +(0.879611 - 4.01790i) q^{69} +3.41895i q^{71} +(-2.95269 + 11.0196i) q^{73} +(-8.60742 - 0.955118i) q^{75} +(-6.57426 - 4.67173i) q^{77} +(-12.1569 - 7.01879i) q^{79} +(-2.98859 + 8.48931i) q^{81} +(-0.995323 + 0.995323i) q^{83} +(0.705000 - 8.97455i) q^{85} +(-13.1008 - 6.77590i) q^{87} +(-0.706248 + 1.22326i) q^{89} +(-0.667760 + 1.79575i) q^{91} +(-0.147591 - 3.18705i) q^{93} +(14.0866 + 4.98602i) q^{95} +(-0.556234 + 0.556234i) q^{97} +(-8.30847 - 3.82096i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{3} - 8 q^{7}+O(q^{10}) $ 48 * q - 2 * q^3 - 8 * q^7	$ 48 q - 2 q^{3} - 8 q^{7} + 32 q^{13} - 16 q^{21} + 16 q^{25} - 32 q^{27} - 64 q^{31} + 34 q^{33} - 40 q^{37} - 24 q^{43} + 30 q^{45} + 36 q^{51} + 92 q^{57} - 18 q^{63} + 28 q^{67} - 8 q^{73} - 38 q^{75} + 20 q^{81} - 56 q^{85} - 24 q^{87} - 24 q^{91} + 6 q^{93} + 56 q^{97}+O(q^{100}) $ 48 * q - 2 * q^3 - 8 * q^7 + 32 * q^13 - 16 * q^21 + 16 * q^25 - 32 * q^27 - 64 * q^31 + 34 * q^33 - 40 * q^37 - 24 * q^43 + 30 * q^45 + 36 * q^51 + 92 * q^57 - 18 * q^63 + 28 * q^67 - 8 * q^73 - 38 * q^75 + 20 * q^81 - 56 * q^85 - 24 * q^87 - 24 * q^91 + 6 * q^93 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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			0
$2$		0			0
$3$	−1.53846	−	0.795708i	−0.888228	−	0.459402i
$3$	−1.53846	−	0.795708i	−0.888228	−	0.459402i
$4$		0			0
$5$	2.19857	−	0.407811i	0.983228	−	0.182378i
$5$	2.19857	−	0.407811i	0.983228	−	0.182378i
$6$		0			0
$7$	1.10146	+	2.40557i	0.416313	+	0.909221i
$7$	1.10146	+	2.40557i	0.416313	+	0.909221i
$8$		0			0
$9$	1.73370	+	2.44833i	0.577899	+	0.816108i
$10$		0			0
$11$	−2.63993	+	1.52416i	−0.795968	+	0.459552i	−0.842059	−	0.539385i	$-0.818657\pi$
$11$	−2.63993	+	1.52416i	−0.795968	+	0.459552i	0.0460916	+	0.998937i	$0.485323\pi$
$12$		0			0
$13$	0.512041	+	0.512041i	0.142015	+	0.142015i	0.774540	−	0.632525i	$-0.217982\pi$
$13$	0.512041	+	0.512041i	0.142015	+	0.142015i	−0.632525	+	0.774540i	$0.717982\pi$
$14$		0			0
$15$	−3.70690	−	1.12202i	−0.957116	−	0.289704i
$16$		0			0
$17$	1.04198	−	3.88873i	0.252718	−	0.943155i	−0.716628	−	0.697455i	$-0.754316\pi$
$17$	1.04198	−	3.88873i	0.252718	−	0.943155i	0.969346	−	0.245700i	$-0.0790177\pi$
$18$		0			0
$19$	5.78739	+	3.34135i	1.32772	+	0.766559i	0.984947	−	0.172859i	$-0.0553005\pi$
$19$	5.78739	+	3.34135i	1.32772	+	0.766559i	0.342773	+	0.939418i	$0.388634\pi$
$20$		0			0
$21$	0.219587	−	4.57731i	0.0479178	−	0.998851i
$22$		0			0
$23$	0.614611	+	2.29376i	0.128155	+	0.478282i	0.999932	−	0.0116206i	$-0.00369905\pi$
$23$	0.614611	+	2.29376i	0.128155	+	0.478282i	−0.871777	+	0.489902i	$0.837032\pi$
$24$		0			0
$25$	4.66738	−	1.79320i	0.933476	−	0.358639i
$26$		0			0
$27$	−0.719065	−	5.14616i	−0.138384	−	0.990379i
$28$		0			0
$29$	8.51556			1.58130			0.790650	−	0.612269i	$-0.209743\pi$
$29$	8.51556			1.58130			0.790650	+	0.612269i	$0.209743\pi$
$30$		0			0
$31$	0.921008	+	1.59523i	0.165418	+	0.286512i	0.936804	−	0.349856i	$-0.113769\pi$
$31$	0.921008	+	1.59523i	0.165418	+	0.286512i	−0.771386	+	0.636368i	$0.780436\pi$
$32$		0			0
$33$	5.27420	−	0.244246i	0.918120	−	0.0425178i
$34$		0			0
$35$	3.40265	+	4.83962i	0.575153	+	0.818046i
$36$		0			0
$37$	−0.747413	−	2.78938i	−0.122874	−	0.458572i	0.876881	−	0.480707i	$-0.159620\pi$
$37$	−0.747413	−	2.78938i	−0.122874	−	0.458572i	−0.999755	+	0.0221357i	$0.992953\pi$
$38$		0			0
$39$	−0.380318	−	1.19519i	−0.0608996	−	0.191383i
$40$		0			0
$41$			8.91355i			1.39206i	0.718012	+	0.696031i	$0.245052\pi$
$41$			8.91355i			1.39206i	−0.718012	+	0.696031i	$0.754948\pi$
$42$		0			0
$43$	−7.54399	−	7.54399i	−1.15045	−	1.15045i	−0.986463	−	0.163984i	$-0.947565\pi$
$43$	−7.54399	−	7.54399i	−1.15045	−	1.15045i	−0.163984	−	0.986463i	$-0.552435\pi$
$44$		0			0
$45$	4.81010	+	4.67578i	0.717047	+	0.697025i
$46$		0			0
$47$	7.28063	−	1.95084i	1.06199	−	0.284559i	0.314791	−	0.949161i	$-0.398066\pi$
$47$	7.28063	−	1.95084i	1.06199	−	0.284559i	0.747198	+	0.664602i	$0.231399\pi$
$48$		0			0
$49$	−4.57357	+	5.29929i	−0.653367	+	0.757041i
$50$		0			0
$51$	−4.69734	+	5.15352i	−0.657759	+	0.721638i
$52$		0			0
$53$	−10.5024	−	2.81412i	−1.44262	−	0.386549i	−0.549171	−	0.835710i	$-0.685056\pi$
$53$	−10.5024	−	2.81412i	−1.44262	−	0.386549i	−0.893451	+	0.449161i	$0.851723\pi$
$54$		0			0
$55$	−5.18248	+	4.42756i	−0.698806	+	0.597012i
$56$		0			0
$57$	−6.24491	−	9.74561i	−0.827159	−	1.29084i
$58$		0			0
$59$	1.06765	+	1.84923i	0.138996	+	0.240749i	0.927117	−	0.374772i	$-0.122279\pi$
$59$	1.06765	+	1.84923i	0.138996	+	0.240749i	−0.788121	+	0.615521i	$0.788946\pi$
$60$		0			0
$61$	7.12318	−	12.3377i	0.912029	−	1.57968i	0.100836	−	0.994903i	$-0.467848\pi$
$61$	7.12318	−	12.3377i	0.912029	−	1.57968i	0.811193	−	0.584778i	$-0.198818\pi$
$62$		0			0
$63$	−3.98003	+	6.86727i	−0.501437	+	0.865194i
$64$		0			0
$65$	1.33457	+	0.916940i	0.165533	+	0.113732i
$66$		0			0
$67$	−3.86614	−	1.03593i	−0.472325	−	0.126559i	0.0148018	−	0.999890i	$-0.495288\pi$
$67$	−3.86614	−	1.03593i	−0.472325	−	0.126559i	−0.487126	+	0.873331i	$0.661955\pi$
$68$		0			0
$69$	0.879611	−	4.01790i	0.105893	−	0.483698i
$70$		0			0
$71$			3.41895i			0.405755i	0.979204	+	0.202878i	$0.0650293\pi$
$71$			3.41895i			0.405755i	−0.979204	+	0.202878i	$0.934971\pi$
$72$		0			0
$73$	−2.95269	+	11.0196i	−0.345586	+	1.28975i	0.546340	+	0.837564i	$0.316021\pi$
$73$	−2.95269	+	11.0196i	−0.345586	+	1.28975i	−0.891926	+	0.452182i	$0.850646\pi$
$74$		0			0
$75$	−8.60742	−	0.955118i	−0.993900	−	0.110288i
$76$		0			0
$77$	−6.57426	−	4.67173i	−0.749206	−	0.532393i
$78$		0			0
$79$	−12.1569	−	7.01879i	−1.36776	−	0.789675i	−0.377117	−	0.926166i	$-0.623084\pi$
$79$	−12.1569	−	7.01879i	−1.36776	−	0.789675i	−0.990641	+	0.136490i	$0.956418\pi$
$80$		0			0
$81$	−2.98859	+	8.48931i	−0.332066	+	0.943256i
$82$		0			0
$83$	−0.995323	+	0.995323i	−0.109251	+	0.109251i	−0.759619	−	0.650368i	$-0.774615\pi$
$83$	−0.995323	+	0.995323i	−0.109251	+	0.109251i	0.650368	+	0.759619i	$0.274615\pi$
$84$		0			0
$85$	0.705000	−	8.97455i	0.0764680	−	0.973427i
$86$		0			0
$87$	−13.1008	−	6.77590i	−1.40456	−	0.726453i
$88$		0			0
$89$	−0.706248	+	1.22326i	−0.0748622	+	0.129665i	−0.901026	−	0.433764i	$-0.857185\pi$
$89$	−0.706248	+	1.22326i	−0.0748622	+	0.129665i	0.826164	+	0.563429i	$0.190518\pi$
$90$		0			0
$91$	−0.667760	+	1.79575i	−0.0700003	+	0.188245i
$92$		0			0
$93$	−0.147591	−	3.18705i	−0.0153045	−	0.330482i
$94$		0			0
$95$	14.0866	+	4.98602i	1.44526	+	0.511555i
$96$		0			0
$97$	−0.556234	+	0.556234i	−0.0564770	+	0.0564770i	−0.734781	−	0.678304i	$-0.762715\pi$
$97$	−0.556234	+	0.556234i	−0.0564770	+	0.0564770i	0.678304	+	0.734781i	$0.262715\pi$
$98$		0			0
$99$	−8.30847	−	3.82096i	−0.835033	−	0.384021i
$100$		0			0
$101$	−2.90475	+	1.67706i	−0.289034	+	0.166874i	−0.637506	−	0.770445i	$-0.720034\pi$
$101$	−2.90475	+	1.67706i	−0.289034	+	0.166874i	0.348472	+	0.937319i	$0.386701\pi$
$102$		0			0
$103$	−1.67206	+	0.448028i	−0.164753	+	0.0441456i	−0.340253	−	0.940334i	$-0.610513\pi$
$103$	−1.67206	+	0.448028i	−0.164753	+	0.0441456i	0.175499	+	0.984480i	$0.443846\pi$
$104$		0			0
$105$	−1.38390	−	10.1531i	−0.135055	−	0.990838i
$106$		0			0
$107$	7.69158	−	2.06095i	0.743573	−	0.199240i	0.132908	−	0.991128i	$-0.457569\pi$
$107$	7.69158	−	2.06095i	0.743573	−	0.199240i	0.610666	+	0.791889i	$0.290902\pi$
$108$		0			0
$109$	−2.12083	+	1.22446i	−0.203138	+	0.117282i	−0.598119	−	0.801408i	$-0.704085\pi$
$109$	−2.12083	+	1.22446i	−0.203138	+	0.117282i	0.394980	+	0.918690i	$0.370751\pi$
$110$		0			0
$111$	−1.06967	+	4.88607i	−0.101529	+	0.463765i
$112$		0			0
$113$	−5.01803	+	5.01803i	−0.472056	+	0.472056i	−0.902580	−	0.430523i	$-0.858329\pi$
$113$	−5.01803	+	5.01803i	−0.472056	+	0.472056i	0.430523	+	0.902580i	$0.358329\pi$
$114$		0			0
$115$	2.28668	+	4.79233i	0.213234	+	0.446888i
$116$		0			0
$117$	−0.365919	+	2.14137i	−0.0338292	+	0.197969i
$118$		0			0
$119$	10.5023	−	1.77671i	0.962746	−	0.162871i
$120$		0			0
$121$	−0.853861	+	1.47893i	−0.0776237	+	0.134448i
$122$		0			0
$123$	7.09258	−	13.7131i	0.639517	−	1.23647i
$124$		0			0
$125$	9.53026	−	5.84587i	0.852412	−	0.522870i
$126$		0			0
$127$	−5.74490	+	5.74490i	−0.509777	+	0.509777i	−0.914458	−	0.404681i	$-0.867383\pi$
$127$	−5.74490	+	5.74490i	−0.509777	+	0.509777i	0.404681	+	0.914458i	$0.367383\pi$
$128$		0			0
$129$	5.60328	+	17.6089i	0.493342	+	1.55038i
$130$		0			0
$131$	1.12384	+	0.648847i	0.0981900	+	0.0566900i	0.548291	−	0.836288i	$-0.315279\pi$
$131$	1.12384	+	0.648847i	0.0981900	+	0.0566900i	−0.450101	+	0.892978i	$0.648612\pi$
$132$		0			0
$133$	−1.66329	+	17.6024i	−0.144226	+	1.52632i
$134$		0			0
$135$	−3.67957	−	11.0209i	−0.316687	−	0.948530i
$136$		0			0
$137$	0.136116	−	0.507990i	0.0116291	−	0.0434006i	−0.959867	−	0.280454i	$-0.909515\pi$
$137$	0.136116	−	0.507990i	0.0116291	−	0.0434006i	0.971497	+	0.237053i	$0.0761817\pi$
$138$		0			0
$139$		−	17.6744i		−	1.49912i	−0.661936	−	0.749561i	$-0.730265\pi$
$139$		−	17.6744i		−	1.49912i	0.661936	−	0.749561i	$-0.269735\pi$
$140$		0			0
$141$	−12.7532	−	2.79198i	−1.07402	−	0.235127i
$142$		0			0
$143$	−2.13218	−	0.571317i	−0.178302	−	0.0477759i
$144$		0			0
$145$	18.7220	−	3.47274i	1.55478	−	0.288395i
$146$		0			0
$147$	11.2529	−	4.51349i	0.928126	−	0.372267i
$148$		0			0
$149$	−10.3981	+	18.0100i	−0.851842	+	1.47543i	0.0277017	+	0.999616i	$0.491181\pi$
$149$	−10.3981	+	18.0100i	−0.851842	+	1.47543i	−0.879544	+	0.475818i	$0.842152\pi$
$150$		0			0
$151$	−5.44655	−	9.43371i	−0.443234	−	0.767704i	0.554693	−	0.832055i	$-0.312836\pi$
$151$	−5.44655	−	9.43371i	−0.443234	−	0.767704i	−0.997927	+	0.0643508i	$0.979502\pi$
$152$		0			0
$153$	11.3273	−	4.19077i	0.915762	−	0.338803i
$154$		0			0
$155$	2.67545	+	3.13163i	0.214897	+	0.251538i
$156$		0			0
$157$	9.64763	+	2.58508i	0.769965	+	0.206312i	0.622356	−	0.782734i	$-0.286176\pi$
$157$	9.64763	+	2.58508i	0.769965	+	0.206312i	0.147609	+	0.989046i	$0.452842\pi$
$158$		0			0
$159$	13.9183	+	12.6863i	1.10380	+	1.00609i
$160$		0			0
$161$	−4.84084	+	4.00498i	−0.381511	+	0.315636i
$162$		0			0
$163$	3.29581	−	0.883109i	0.258148	−	0.0691705i	−0.127424	−	0.991848i	$-0.540671\pi$
$163$	3.29581	−	0.883109i	0.258148	−	0.0691705i	0.385572	+	0.922678i	$0.374004\pi$
$164$		0			0
$165$	11.4961	−	2.68787i	0.894968	−	0.209250i
$166$		0			0
$167$	−10.6613	−	10.6613i	−0.824994	−	0.824994i	0.161825	−	0.986819i	$-0.448262\pi$
$167$	−10.6613	−	10.6613i	−0.824994	−	0.824994i	−0.986819	+	0.161825i	$0.948262\pi$
$168$		0			0
$169$		−	12.4756i		−	0.959664i
$170$		0			0
$171$	1.85287	+	19.9623i	0.141692	+	1.52656i
$172$		0			0
$173$	−4.49399	−	16.7718i	−0.341672	−	1.27514i	−0.896453	−	0.443140i	$-0.853865\pi$
$173$	−4.49399	−	16.7718i	−0.341672	−	1.27514i	0.554781	−	0.831996i	$-0.312802\pi$
$174$		0			0
$175$	9.45460	+	9.25260i	0.714701	+	0.699430i
$176$		0			0
$177$	−0.171091	−	3.69450i	−0.0128600	−	0.277695i
$178$		0			0
$179$	−7.14090	−	12.3684i	−0.533736	−	0.924458i	−0.999223	−	0.0394031i	$-0.987454\pi$
$179$	−7.14090	−	12.3684i	−0.533736	−	0.924458i	0.465488	−	0.885054i	$-0.345879\pi$
$180$		0			0
$181$	−5.90010			−0.438551			−0.219275	−	0.975663i	$-0.570369\pi$
$181$	−5.90010			−0.438551			−0.219275	+	0.975663i	$0.570369\pi$
$182$		0			0
$183$	−20.7759	+	13.3130i	−1.53580	+	0.984129i
$184$		0			0
$185$	−2.78078	−	5.82784i	−0.204447	−	0.428471i
$186$		0			0
$187$	3.17630	+	11.8541i	0.232274	+	0.866858i
$188$		0			0
$189$	11.5874	−	7.39805i	0.842863	−	0.538129i
$190$		0			0
$191$	−9.55692	−	5.51769i	−0.691514	−	0.399246i	0.112665	−	0.993633i	$-0.464061\pi$
$191$	−9.55692	−	5.51769i	−0.691514	−	0.399246i	−0.804179	+	0.594387i	$0.797395\pi$
$192$		0			0
$193$	3.64505	−	13.6035i	0.262377	−	0.979203i	−0.701460	−	0.712709i	$-0.747468\pi$
$193$	3.64505	−	13.6035i	0.262377	−	0.979203i	0.963837	−	0.266494i	$-0.0858652\pi$
$194$		0			0
$195$	−1.32356	−	2.47260i	−0.0947824	−	0.177067i
$196$		0			0
$197$	1.63139	+	1.63139i	0.116232	+	0.116232i	0.762830	−	0.646599i	$-0.223809\pi$
$197$	1.63139	+	1.63139i	0.116232	+	0.116232i	−0.646599	+	0.762830i	$0.723809\pi$
$198$		0			0
$199$	−9.65354	+	5.57347i	−0.684321	+	0.395093i	−0.801481	−	0.598020i	$-0.795954\pi$
$199$	−9.65354	+	5.57347i	−0.684321	+	0.395093i	0.117160	+	0.993113i	$0.462621\pi$
$200$		0			0
$201$	5.12360	+	4.67006i	0.361391	+	0.329400i
$202$		0			0
$203$	9.37955	+	20.4848i	0.658315	+	1.43775i
$204$		0			0
$205$	3.63504	+	19.5970i	0.253882	+	1.36872i
$206$		0			0
$207$	−4.55032	+	5.48145i	−0.316269	+	0.380987i
$208$		0			0
$209$	−20.3711			−1.40910
$210$		0			0
$211$	2.72171			0.187370			0.0936852	−	0.995602i	$-0.470135\pi$
$211$	2.72171			0.187370			0.0936852	+	0.995602i	$0.470135\pi$
$212$		0			0
$213$	2.72049	−	5.25991i	0.186405	−	0.360403i
$214$		0			0
$215$	−19.6625	−	13.5094i	−1.34097	−	0.921336i
$216$		0			0
$217$	−2.82300	+	3.97264i	−0.191638	+	0.269680i
$218$		0			0
$219$	13.3110	−	14.6037i	0.899472	−	0.986825i
$220$		0			0
$221$	2.52473	−	1.45765i	0.169831	−	0.0980522i
$222$		0			0
$223$	13.0957	+	13.0957i	0.876950	+	0.876950i	0.993218	−	0.116268i	$-0.0370931\pi$
$223$	13.0957	+	13.0957i	0.876950	+	0.876950i	−0.116268	+	0.993218i	$0.537093\pi$
$224$		0			0
$225$	12.4822	+	8.31841i	0.832143	+	0.554560i
$226$		0			0
$227$	3.54662	−	13.2362i	0.235397	−	0.878515i	−0.742572	−	0.669766i	$-0.766394\pi$
$227$	3.54662	−	13.2362i	0.235397	−	0.878515i	0.977969	−	0.208748i	$-0.0669390\pi$
$228$		0			0
$229$	10.3326	+	5.96554i	0.682799	+	0.394214i	0.800909	−	0.598787i	$-0.204350\pi$
$229$	10.3326	+	5.96554i	0.682799	+	0.394214i	−0.118110	+	0.993001i	$0.537684\pi$
$230$		0			0
$231$	6.39687	+	12.4184i	0.420883	+	0.817074i
$232$		0			0
$233$	−2.61577	−	9.76217i	−0.171365	−	0.639541i	−0.997142	−	0.0755455i	$-0.975930\pi$
$233$	−2.61577	−	9.76217i	−0.171365	−	0.639541i	0.825778	−	0.563996i	$-0.190736\pi$
$234$		0			0
$235$	15.2114	−	7.25816i	0.992280	−	0.473470i
$236$		0			0
$237$	13.1180	+	20.4714i	0.852103	+	1.32976i
$238$		0			0
$239$	21.4204			1.38557			0.692784	−	0.721145i	$-0.256384\pi$
$239$	21.4204			1.38557			0.692784	+	0.721145i	$0.256384\pi$
$240$		0			0
$241$	−5.02811	−	8.70894i	−0.323889	−	0.560992i	0.657398	−	0.753544i	$-0.271657\pi$
$241$	−5.02811	−	8.70894i	−0.323889	−	0.560992i	−0.981287	+	0.192552i	$0.938324\pi$
$242$		0			0
$243$	11.3528	−	10.6824i	0.728284	−	0.685275i
$244$		0			0
$245$	−7.89419	+	13.5160i	−0.504341	+	0.863504i
$246$		0			0
$247$	1.25247	+	4.67429i	0.0796930	+	0.297418i
$248$		0			0
$249$	2.32325	−	0.739275i	0.147230	−	0.0468496i
$250$		0			0
$251$		−	5.13237i		−	0.323952i	−0.986795	−	0.161976i	$-0.948213\pi$
$251$		−	5.13237i		−	0.323952i	0.986795	−	0.161976i	$-0.0517867\pi$
$252$		0			0
$253$	−5.11859	−	5.11859i	−0.321803	−	0.321803i
$254$		0			0
$255$	−8.22574	+	13.2460i	−0.515116	+	0.829496i
$256$		0			0
$257$	10.8330	−	2.90270i	0.675745	−	0.181065i	0.0954037	−	0.995439i	$-0.469586\pi$
$257$	10.8330	−	2.90270i	0.675745	−	0.181065i	0.580341	+	0.814373i	$0.302919\pi$
$258$		0			0
$259$	5.88682	−	4.87035i	0.365789	−	0.302629i
$260$		0			0
$261$	14.7634	+	20.8489i	0.913831	+	1.29051i
$262$		0			0
$263$	13.7673	+	3.68895i	0.848931	+	0.227470i	0.656955	−	0.753930i	$-0.271844\pi$
$263$	13.7673	+	3.68895i	0.848931	+	0.227470i	0.191975	+	0.981400i	$0.438511\pi$
$264$		0			0
$265$	−24.2379	−	1.90402i	−1.48893	−	0.116963i
$266$		0			0
$267$	2.05989	−	1.31996i	0.126063	−	0.0807803i
$268$		0			0
$269$	−7.17746	−	12.4317i	−0.437618	−	0.757976i	0.559888	−	0.828568i	$-0.310844\pi$
$269$	−7.17746	−	12.4317i	−0.437618	−	0.757976i	−0.997505	+	0.0705927i	$0.977511\pi$
$270$		0			0
$271$	0.840888	−	1.45646i	0.0510803	−	0.0884737i	−0.839355	−	0.543584i	$-0.817067\pi$
$271$	0.840888	−	1.45646i	0.0510803	−	0.0884737i	0.890435	+	0.455110i	$0.150400\pi$
$272$		0			0
$273$	2.45621	−	2.23133i	0.148657	−	0.135046i
$274$		0			0
$275$	−9.58842	+	11.8478i	−0.578203	+	0.714446i
$276$		0			0
$277$	7.58569	+	2.03258i	0.455780	+	0.122126i	0.479403	−	0.877595i	$-0.340853\pi$
$277$	7.58569	+	2.03258i	0.455780	+	0.122126i	−0.0236225	+	0.999721i	$0.507520\pi$
$278$		0			0
$279$	−2.30890	+	5.02058i	−0.138230	+	0.300574i
$280$		0			0
$281$		−	8.01304i		−	0.478018i	−0.971017	−	0.239009i	$-0.923177\pi$
$281$		−	8.01304i		−	0.478018i	0.971017	−	0.239009i	$-0.0768225\pi$
$282$		0			0
$283$	−0.363933	+	1.35822i	−0.0216336	+	0.0807376i	−0.975899	−	0.218224i	$-0.929974\pi$
$283$	−0.363933	+	1.35822i	−0.0216336	+	0.0807376i	0.954265	+	0.298962i	$0.0966403\pi$
$284$		0			0
$285$	−17.7042	−	18.8796i	−1.04871	−	1.11833i
$286$		0			0
$287$	−21.4422	+	9.81791i	−1.26569	+	0.579533i
$288$		0			0
$289$	0.685955	+	0.396036i	0.0403503	+	0.0232963i
$290$		0			0
$291$	1.29834	−	0.413142i	0.0761102	−	0.0242188i
$292$		0			0
$293$	3.47074	−	3.47074i	0.202763	−	0.202763i	−0.598420	−	0.801183i	$-0.704205\pi$
$293$	3.47074	−	3.47074i	0.202763	−	0.202763i	0.801183	+	0.598420i	$0.204205\pi$
$294$		0			0
$295$	3.10144	+	3.63025i	0.180573	+	0.211361i
$296$		0			0
$297$	9.74186	+	12.4895i	0.565280	+	0.724715i
$298$		0			0
$299$	−0.859793	+	1.48920i	−0.0497231	+	0.0861229i
$300$		0			0
$301$	9.83822	−	26.4570i	0.567066	−	1.52496i
$302$		0			0
$303$	5.80329	−	0.268748i	0.333390	−	0.0154392i
$304$		0			0
$305$	10.6293	−	30.0302i	0.608633	−	1.71952i
$306$		0			0
$307$	19.7303	−	19.7303i	1.12607	−	1.12607i	0.135254	−	0.990811i	$-0.456815\pi$
$307$	19.7303	−	19.7303i	1.12607	−	1.12607i	0.990811	−	0.135254i	$-0.0431852\pi$
$308$		0			0
$309$	2.92890	+	0.641204i	0.166619	+	0.0364768i
$310$		0			0
$311$	23.7702	−	13.7238i	1.34789	−	0.778203i	0.359937	−	0.932977i	$-0.382798\pi$
$311$	23.7702	−	13.7238i	1.34789	−	0.778203i	0.987950	+	0.154774i	$0.0494649\pi$
$312$		0			0
$313$	−22.7817	+	6.10435i	−1.28770	+	0.345038i	−0.836786	−	0.547530i	$-0.815568\pi$
$313$	−22.7817	+	6.10435i	−1.28770	+	0.345038i	−0.450913	+	0.892568i	$0.648902\pi$
$314$		0			0
$315$	−5.94981	+	16.7212i	−0.335234	+	0.942135i
$316$		0			0
$317$	−31.0135	+	8.31005i	−1.74189	+	0.466739i	−0.982866	−	0.184320i	$-0.940992\pi$
$317$	−31.0135	+	8.31005i	−1.74189	+	0.466739i	−0.759027	+	0.651059i	$0.774325\pi$
$318$		0			0
$319$	−22.4804	+	12.9791i	−1.25866	+	0.726690i
$320$		0			0
$321$	−13.4731	−	2.94957i	−0.751994	−	0.164629i
$322$		0			0
$323$	19.0240	−	19.0240i	1.05852	−	1.05852i
$324$		0			0
$325$	3.30808	+	1.47170i	0.183499	+	0.0816352i
$326$		0			0
$327$	4.23711	−	0.196219i	0.234313	−	0.0108509i
$328$		0			0
$329$	12.7122	+	15.3653i	0.700847	+	0.847117i
$330$		0			0
$331$	13.9114	−	24.0952i	0.764637	−	1.32439i	−0.175801	−	0.984426i	$-0.556252\pi$
$331$	13.9114	−	24.0952i	0.764637	−	1.32439i	0.940438	−	0.339965i	$-0.110415\pi$
$332$		0			0
$333$	5.53353	−	6.66585i	0.303236	−	0.365287i
$334$		0			0
$335$	−8.92243	−	0.700906i	−0.487485	−	0.0382946i
$336$		0			0
$337$	−5.16934	+	5.16934i	−0.281592	+	0.281592i	−0.833744	−	0.552152i	$-0.813807\pi$
$337$	−5.16934	+	5.16934i	−0.281592	+	0.281592i	0.552152	+	0.833744i	$0.313807\pi$
$338$		0			0
$339$	11.7129	−	3.72713i	0.636158	−	0.202430i
$340$		0			0
$341$	−4.86279	−	2.80753i	−0.263335	−	0.152036i
$342$		0			0
$343$	−17.7854	−	5.16511i	−0.960323	−	0.278890i
$344$		0			0
$345$	0.295340	−	9.19233i	0.0159006	−	0.494898i
$346$		0			0
$347$	−6.66941	+	24.8906i	−0.358033	+	1.33620i	0.518592	+	0.855022i	$0.326457\pi$
$347$	−6.66941	+	24.8906i	−0.358033	+	1.33620i	−0.876625	+	0.481175i	$0.840210\pi$
$348$		0			0
$349$			18.4866i			0.989563i	0.869017	+	0.494782i	$0.164752\pi$
$349$			18.4866i			0.989563i	−0.869017	+	0.494782i	$0.835248\pi$
$350$		0			0
$351$	2.26685	−	3.00323i	0.120996	−	0.160301i
$352$		0			0
$353$	−25.4066	−	6.80767i	−1.35226	−	0.362336i	−0.491289	−	0.870997i	$-0.663474\pi$
$353$	−25.4066	−	6.80767i	−1.35226	−	0.362336i	−0.860967	+	0.508661i	$0.830141\pi$
$354$		0			0
$355$	1.39429	+	7.51679i	0.0740010	+	0.398950i
$356$		0			0
$357$	−17.5711	−	5.62339i	−0.929962	−	0.297621i
$358$		0			0
$359$	−4.69610	+	8.13389i	−0.247851	+	0.429290i	−0.962929	−	0.269754i	$-0.913058\pi$
$359$	−4.69610	+	8.13389i	−0.247851	+	0.429290i	0.715078	+	0.699044i	$0.246391\pi$
$360$		0			0
$361$	12.8293	+	22.2210i	0.675226	+	1.16953i
$362$		0			0
$363$	2.49043	−	1.59585i	0.130713	−	0.0837602i
$364$		0			0
$365$	−1.99778	+	25.4314i	−0.104568	+	1.33114i
$366$		0			0
$367$	−13.2291	−	3.54474i	−0.690555	−	0.185034i	−0.103559	−	0.994623i	$-0.533023\pi$
$367$	−13.2291	−	3.54474i	−0.690555	−	0.185034i	−0.586996	+	0.809590i	$0.699690\pi$
$368$		0			0
$369$	−21.8233	+	15.4534i	−1.13607	+	0.804471i
$370$		0			0
$371$	−4.79845	−	28.3641i	−0.249123	−	1.47259i
$372$		0			0
$373$	−28.3844	+	7.60558i	−1.46969	+	0.393802i	−0.902825	−	0.430008i	$-0.858511\pi$
$373$	−28.3844	+	7.60558i	−1.46969	+	0.393802i	−0.566865	+	0.823811i	$0.691844\pi$
$374$		0			0
$375$	−19.3135	+	1.41031i	−0.997345	+	0.0728281i
$376$		0			0
$377$	4.36032	+	4.36032i	0.224568	+	0.224568i
$378$		0			0
$379$			0.342505i			0.0175933i	0.999961	+	0.00879664i	$0.00280009\pi$
$379$			0.342505i			0.0175933i	−0.999961	+	0.00879664i	$0.997200\pi$
$380$		0			0
$381$	13.4095	−	4.26701i	0.686991	−	0.218606i
$382$		0			0
$383$	6.70768	+	25.0334i	0.342746	+	1.27915i	0.895223	+	0.445618i	$0.147016\pi$
$383$	6.70768	+	25.0334i	0.342746	+	1.27915i	−0.552477	+	0.833528i	$0.686317\pi$
$384$		0			0
$385$	−16.3591	−	7.59006i	−0.833738	−	0.386825i
$386$		0			0
$387$	5.39115	−	31.5491i	0.274047	−	1.60373i
$388$		0			0
$389$	−14.6458	−	25.3673i	−0.742572	−	1.28617i	−0.951321	−	0.308203i	$-0.900272\pi$
$389$	−14.6458	−	25.3673i	−0.742572	−	1.28617i	0.208749	−	0.977969i	$-0.433061\pi$
$390$		0			0
$391$	9.56022			0.483481
$392$		0			0
$393$	−1.21268	−	1.89247i	−0.0611716	−	0.0954624i
$394$		0			0
$395$	−29.5901	−	10.4736i	−1.48884	−	0.526982i
$396$		0			0
$397$	−7.37078	−	27.5081i	−0.369929	−	1.38059i	−0.860615	−	0.509257i	$-0.829920\pi$
$397$	−7.37078	−	27.5081i	−0.369929	−	1.38059i	0.490686	−	0.871337i	$-0.336746\pi$
$398$		0			0
$399$	16.5653	−	25.7570i	0.829300	−	1.28946i
$400$		0			0
$401$	22.3395	+	12.8977i	1.11558	+	0.644081i	0.940269	−	0.340432i	$-0.110573\pi$
$401$	22.3395	+	12.8977i	1.11558	+	0.644081i	0.175311	+	0.984513i	$0.443907\pi$
$402$		0			0
$403$	−0.345231	+	1.28842i	−0.0171972	+	0.0641807i
$404$		0			0
$405$	−3.10858	+	19.8831i	−0.154467	+	0.987998i
$406$		0			0
$407$	6.22459	+	6.22459i	0.308541	+	0.308541i
$408$		0			0
$409$	−25.1282	+	14.5078i	−1.24251	+	0.717364i	−0.969605	−	0.244677i	$-0.921318\pi$
$409$	−25.1282	+	14.5078i	−1.24251	+	0.717364i	−0.272905	+	0.962041i	$0.587985\pi$
$410$		0			0
$411$	−0.613620	+	0.673213i	−0.0302677	+	0.0332071i
$412$		0			0
$413$	−3.27248	+	4.60517i	−0.161028	+	0.226605i
$414$		0			0
$415$	−1.78238	+	2.59419i	−0.0874936	+	0.127344i
$416$		0			0
$417$	−14.0636	+	27.1913i	−0.688700	+	1.33156i
$418$		0			0
$419$	−20.0060			−0.977359			−0.488679	−	0.872463i	$-0.662521\pi$
$419$	−20.0060			−0.977359			−0.488679	+	0.872463i	$0.662521\pi$
$420$		0			0
$421$	−0.405902			−0.0197825			−0.00989124	−	0.999951i	$-0.503149\pi$
$421$	−0.405902			−0.0197825			−0.00989124	+	0.999951i	$0.503149\pi$
$422$		0			0
$423$	17.3987	+	14.4432i	0.845953	+	0.702252i
$424$		0			0
$425$	−2.10993	−	20.0187i	−0.102347	−	0.971047i
$426$		0			0
$427$	37.5251	+	3.54584i	1.81597	+	0.171595i
$428$		0			0
$429$	2.82567	+	2.57554i	0.136425	+	0.124348i
$430$		0			0
$431$	−34.8654	+	20.1295i	−1.67940	+	0.969605i	−0.717364	+	0.696698i	$0.754652\pi$
$431$	−34.8654	+	20.1295i	−1.67940	+	0.969605i	−0.962041	+	0.272907i	$0.912015\pi$
$432$		0			0
$433$	−9.70713	−	9.70713i	−0.466495	−	0.466495i	0.434282	−	0.900777i	$-0.357002\pi$
$433$	−9.70713	−	9.70713i	−0.466495	−	0.466495i	−0.900777	+	0.434282i	$0.857002\pi$
$434$		0			0
$435$	−31.5663	−	9.55461i	−1.51349	−	0.458108i
$436$		0			0
$437$	−4.10727	+	15.3285i	−0.196477	+	0.733263i
$438$		0			0
$439$	−10.6016	−	6.12083i	−0.505987	−	0.292131i	0.225196	−	0.974314i	$-0.427698\pi$
$439$	−10.6016	−	6.12083i	−0.505987	−	0.292131i	−0.731182	+	0.682182i	$0.761031\pi$
$440$		0			0
$441$	−20.9036	−	2.01023i	−0.995408	−	0.0957255i
$442$		0			0
$443$	2.83043	+	10.5633i	0.134478	+	0.501879i	0.999999	+	0.00100695i	$0.000320522\pi$
$443$	2.83043	+	10.5633i	0.134478	+	0.501879i	−0.865521	+	0.500872i	$0.833013\pi$
$444$		0			0
$445$	−1.05388	+	2.97743i	−0.0499585	+	0.141144i
$446$		0			0
$447$	30.3276	−	19.4337i	1.43445	−	0.919184i
$448$		0			0
$449$	22.4970			1.06170			0.530849	−	0.847467i	$-0.321873\pi$
$449$	22.4970			1.06170			0.530849	+	0.847467i	$0.321873\pi$
$450$		0			0
$451$	−13.5857	−	23.5311i	−0.639725	−	1.10804i
$452$		0			0
$453$	0.872807	+	18.8472i	0.0410080	+	0.885520i
$454$		0			0
$455$	−0.735790	+	4.22038i	−0.0344944	+	0.197855i
$456$		0			0
$457$	4.82030	+	17.9896i	0.225484	+	0.841517i	0.982210	+	0.187785i	$0.0601309\pi$
$457$	4.82030	+	17.9896i	0.225484	+	0.841517i	−0.756726	+	0.653732i	$0.773202\pi$
$458$		0			0
$459$	−20.7613	−	2.56596i	−0.969053	−	0.119769i
$460$		0			0
$461$		−	5.92233i		−	0.275830i	−0.990444	−	0.137915i	$-0.955960\pi$
$461$		−	5.92233i		−	0.275830i	0.990444	−	0.137915i	$-0.0440402\pi$
$462$		0			0
$463$	26.3657	+	26.3657i	1.22532	+	1.22532i	0.965715	+	0.259605i	$0.0835922\pi$
$463$	26.3657	+	26.3657i	1.22532	+	1.22532i	0.259605	+	0.965715i	$0.416408\pi$
$464$		0			0
$465$	−1.62420	−	6.94675i	−0.0753205	−	0.322148i
$466$		0			0
$467$	39.0245	−	10.4566i	1.80584	−	0.483873i	0.810973	−	0.585083i	$-0.198938\pi$
$467$	39.0245	−	10.4566i	1.80584	−	0.483873i	0.994865	+	0.101210i	$0.0322714\pi$
$468$		0			0
$469$	−1.76640	−	10.4413i	−0.0815646	−	0.482136i
$470$		0			0
$471$	−12.7855	−	11.6537i	−0.589125	−	0.536975i
$472$		0			0
$473$	31.4138	+	8.41731i	1.44441	+	0.387028i
$474$		0			0
$475$	33.0037	+	5.21743i	1.51431	+	0.239392i
$476$		0			0
$477$	−11.3182	−	30.5922i	−0.518224	−	1.40072i
$478$		0			0
$479$	−0.363532	−	0.629656i	−0.0166102	−	0.0287697i	0.857601	−	0.514316i	$-0.171954\pi$
$479$	−0.363532	−	0.629656i	−0.0166102	−	0.0287697i	−0.874211	+	0.485546i	$0.838621\pi$
$480$		0			0
$481$	1.04557	−	1.81098i	0.0476740	−	0.0825738i
$482$		0			0
$483$	10.6342	−	2.30959i	0.483873	−	0.105090i
$484$		0			0
$485$	−0.996079	+	1.44976i	−0.0452296	+	0.0658300i
$486$		0			0
$487$	−17.6503	−	4.72938i	−0.799812	−	0.214309i	−0.164310	−	0.986409i	$-0.552540\pi$
$487$	−17.6503	−	4.72938i	−0.799812	−	0.214309i	−0.635501	+	0.772100i	$0.719207\pi$
$488$		0			0
$489$	−5.77316	−	1.26388i	−0.261071	−	0.0571545i
$490$		0			0
$491$		−	37.6269i		−	1.69808i	−0.528330	−	0.849039i	$-0.677182\pi$
$491$		−	37.6269i		−	1.69808i	0.528330	−	0.849039i	$-0.322818\pi$
$492$		0			0
$493$	8.87305	−	33.1147i	0.399622	−	1.49141i
$494$		0			0
$495$	−19.8250	−	5.01235i	−0.891065	−	0.225288i
$496$		0			0
$497$	−8.22455	+	3.76584i	−0.368921	+	0.168921i
$498$		0			0
$499$	−3.10886	−	1.79490i	−0.139172	−	0.0803509i	0.428797	−	0.903401i	$-0.358937\pi$
$499$	−3.10886	−	1.79490i	−0.139172	−	0.0803509i	−0.567969	+	0.823050i	$0.692271\pi$
$500$		0			0
$501$	7.91864	+	24.8852i	0.353779	+	1.11179i
$502$		0			0
$503$	11.0730	−	11.0730i	0.493722	−	0.493722i	−0.415754	−	0.909477i	$-0.636482\pi$
$503$	11.0730	−	11.0730i	0.493722	−	0.493722i	0.909477	+	0.415754i	$0.136482\pi$
$504$		0			0
$505$	−5.70237	+	4.87172i	−0.253752	+	0.216789i
$506$		0			0
$507$	−9.92696	+	19.1932i	−0.440872	+	0.852400i
$508$		0			0
$509$	−17.1754	+	29.7487i	−0.761287	+	1.31859i	0.180900	+	0.983502i	$0.442099\pi$
$509$	−17.1754	+	29.7487i	−0.761287	+	1.31859i	−0.942187	+	0.335087i	$0.891234\pi$
$510$		0			0
$511$	−29.7607	+	5.03472i	−1.31654	+	0.222723i
$512$		0			0
$513$	13.0336	−	32.1855i	0.575449	−	1.42102i
$514$		0			0
$515$	−3.49343	+	1.66691i	−0.153939	+	0.0734526i
$516$		0			0
$517$	−16.2469	+	16.2469i	−0.714539	+	0.714539i
$518$		0			0
$519$	−6.43165	+	29.3786i	−0.282318	+	1.28958i
$520$		0			0
$521$	23.1158	−	13.3459i	1.01272	−	0.584696i	0.100736	−	0.994913i	$-0.467880\pi$
$521$	23.1158	−	13.3459i	1.01272	−	0.584696i	0.911988	+	0.410217i	$0.134547\pi$
$522$		0			0
$523$	−25.7231	+	6.89247i	−1.12479	+	0.301387i	−0.772821	−	0.634625i	$-0.781155\pi$
$523$	−25.7231	+	6.89247i	−1.12479	+	0.301387i	−0.351970	+	0.936011i	$0.614488\pi$
$524$		0			0
$525$	−7.18313	−	21.7578i	−0.313497	−	0.949589i
$526$		0			0
$527$	7.16310	−	1.91935i	0.312029	−	0.0836080i
$528$		0			0
$529$	15.0350	−	8.68046i	0.653696	−	0.377411i
$530$		0			0
$531$	−2.67653	+	5.81996i	−0.116151	+	0.252565i
$532$		0			0
$533$	−4.56410	+	4.56410i	−0.197693	+	0.197693i
$534$		0			0
$535$	16.0700	−	7.66785i	0.694765	−	0.331510i
$536$		0			0
$537$	1.14432	+	24.7103i	0.0493812	+	1.06633i
$538$		0			0
$539$	3.99692	−	20.9606i	0.172160	−	0.902836i
$540$		0			0
$541$	4.10742	−	7.11425i	0.176592	−	0.305866i	−0.764119	−	0.645075i	$-0.776826\pi$
$541$	4.10742	−	7.11425i	0.176592	−	0.305866i	0.940711	+	0.339209i	$0.110159\pi$
$542$		0			0
$543$	9.07704	+	4.69475i	0.389533	+	0.201471i
$544$		0			0
$545$	−4.16343	+	3.55695i	−0.178342	+	0.152363i
$546$		0			0
$547$	−22.4125	+	22.4125i	−0.958288	+	0.958288i	−0.999164	−	0.0408761i	$-0.986985\pi$
$547$	−22.4125	+	22.4125i	−0.958288	+	0.958288i	0.0408761	+	0.999164i	$0.486985\pi$
$548$		0			0
$549$	42.5561	−	3.94998i	1.81625	−	0.168581i
$550$		0			0
$551$	49.2829	+	28.4535i	2.09952	+	1.21216i
$552$		0			0
$553$	3.49388	−	36.9752i	0.148575	−	1.57235i
$554$		0			0
$555$	−0.359156	+	11.1786i	−0.0152453	+	0.474504i
$556$		0			0
$557$	−9.63625	+	35.9630i	−0.408301	+	1.52380i	0.389585	+	0.920991i	$0.372618\pi$
$557$	−9.63625	+	35.9630i	−0.408301	+	1.52380i	−0.797886	+	0.602809i	$0.794048\pi$
$558$		0			0
$559$		−	7.72566i		−	0.326761i
$560$		0			0
$561$	4.54581	−	20.7644i	0.191924	−	0.876675i
$562$		0			0
$563$	21.1995	+	5.68038i	0.893450	+	0.239399i	0.676201	−	0.736717i	$-0.263625\pi$
$563$	21.1995	+	5.68038i	0.893450	+	0.239399i	0.217249	+	0.976116i	$0.430292\pi$
$564$		0			0
$565$	−8.98606	+	13.0789i	−0.378046	+	0.550232i
$566$		0			0
$567$	−23.7135	+	2.16135i	−0.995872	+	0.0907683i
$568$		0			0
$569$	13.0396	−	22.5852i	0.546648	−	0.946821i	−0.451854	−	0.892092i	$-0.649237\pi$
$569$	13.0396	−	22.5852i	0.546648	−	0.946821i	0.998501	−	0.0547292i	$-0.0174296\pi$
$570$		0			0
$571$	0.341798	+	0.592011i	0.0143038	+	0.0247749i	0.873089	−	0.487561i	$-0.162113\pi$
$571$	0.341798	+	0.592011i	0.0143038	+	0.0247749i	−0.858785	+	0.512336i	$0.828780\pi$
$572$		0			0
$573$	10.3124	+	16.0932i	0.430808	+	0.672305i
$574$		0			0
$575$	6.98178	+	9.60373i	0.291161	+	0.400503i
$576$		0			0
$577$	27.9391	+	7.48627i	1.16312	+	0.311657i	0.788212	−	0.615404i	$-0.211007\pi$
$577$	27.9391	+	7.48627i	1.16312	+	0.311657i	0.374910	+	0.927061i	$0.377674\pi$
$578$		0			0
$579$	−16.4322	+	18.0280i	−0.682898	+	0.749219i
$580$		0			0
$581$	−3.49063	−	1.29801i	−0.144816	−	0.0538507i
$582$		0			0
$583$	32.0149	−	8.57836i	1.32592	−	0.355279i
$584$		0			0
$585$	0.0687753	+	4.85716i	0.00284351	+	0.200819i
$586$		0			0
$587$	32.5547	+	32.5547i	1.34367	+	1.34367i	0.892370	+	0.451304i	$0.149041\pi$
$587$	32.5547	+	32.5547i	1.34367	+	1.34367i	0.451304	+	0.892370i	$0.350959\pi$
$588$		0			0
$589$			12.3097i			0.507211i
$590$		0			0
$591$	−1.21171	−	3.80793i	−0.0498431	−	0.156637i
$592$		0			0
$593$	−9.47201	−	35.3500i	−0.388969	−	1.45165i	−0.831815	−	0.555053i	$-0.812698\pi$
$593$	−9.47201	−	35.3500i	−0.388969	−	1.45165i	0.442846	−	0.896598i	$-0.353969\pi$
$594$		0			0
$595$	22.3655	−	8.18918i	0.916895	−	0.335724i
$596$		0			0
$597$	19.2864	−	0.893145i	0.789340	−	0.0365540i
$598$		0			0
$599$	−16.8528	−	29.1898i	−0.688585	−	1.19266i	−0.972296	−	0.233754i	$-0.924899\pi$
$599$	−16.8528	−	29.1898i	−0.688585	−	1.19266i	0.283711	−	0.958910i	$-0.408434\pi$
$600$		0			0
$601$	7.76968			0.316932			0.158466	−	0.987364i	$-0.449345\pi$
$601$	7.76968			0.316932			0.158466	+	0.987364i	$0.449345\pi$
$602$		0			0
$603$	−4.16643	−	11.2616i	−0.169670	−	0.458606i
$604$		0			0
$605$	−1.27415	+	3.59974i	−0.0518014	+	0.146350i
$606$		0			0
$607$	−0.00235838	−	0.00880159i	−9.57237e−5	−	0.000357246i	0.965878	−	0.258998i	$-0.0833922\pi$
$607$	−0.00235838	−	0.00880159i	−9.57237e−5	−	0.000357246i	−0.965974	+	0.258640i	$0.916726\pi$
$608$		0			0
$609$	1.86990	−	38.9784i	0.0757724	−	1.57948i
$610$		0			0
$611$	4.72689	+	2.72907i	0.191229	+	0.110406i
$612$		0			0
$613$	−9.89035	+	36.9113i	−0.399467	+	1.49083i	0.414568	+	0.910018i	$0.363933\pi$
$613$	−9.89035	+	36.9113i	−0.399467	+	1.49083i	−0.814036	+	0.580815i	$0.802734\pi$
$614$		0			0
$615$	10.0012	−	33.0416i	0.403286	−	1.33237i
$616$		0			0
$617$	13.3739	+	13.3739i	0.538413	+	0.538413i	0.923063	−	0.384650i	$-0.125678\pi$
$617$	13.3739	+	13.3739i	0.538413	+	0.538413i	−0.384650	+	0.923063i	$0.625678\pi$
$618$		0			0
$619$	35.2461	−	20.3493i	1.41666	−	0.817908i	0.420655	−	0.907221i	$-0.361800\pi$
$619$	35.2461	−	20.3493i	1.41666	−	0.817908i	0.996004	+	0.0893126i	$0.0284670\pi$
$620$		0			0
$621$	11.3621	−	4.81225i	0.455945	−	0.193109i
$622$		0			0
$623$	−3.72054	−	0.351563i	−0.149060	−	0.0140851i
$624$		0			0
$625$	18.5689	−	16.7391i	0.742756	−	0.669563i
$626$		0			0
$627$	31.3400	+	16.2094i	1.25160	+	0.647342i
$628$		0			0
$629$	−11.6259			−0.463557
$630$		0			0
$631$	12.9314			0.514789			0.257395	−	0.966306i	$-0.417136\pi$
$631$	12.9314			0.514789			0.257395	+	0.966306i	$0.417136\pi$
$632$		0			0
$633$	−4.18724	−	2.16569i	−0.166428	−	0.0860784i
$634$		0			0
$635$	−10.2877	+	14.9734i	−0.408255	+	0.594200i
$636$		0			0
$637$	−5.05531	+	0.371596i	−0.200299	+	0.0147232i
$638$		0			0
$639$	−8.37071	+	5.92743i	−0.331140	+	0.234485i
$640$		0			0
$641$	−1.71838	+	0.992107i	−0.0678719	+	0.0391859i	−0.533552	−	0.845767i	$-0.679143\pi$
$641$	−1.71838	+	0.992107i	−0.0678719	+	0.0391859i	0.465680	+	0.884953i	$0.345810\pi$
$642$		0			0
$643$	−3.02169	−	3.02169i	−0.119164	−	0.119164i	0.645010	−	0.764174i	$-0.276853\pi$
$643$	−3.02169	−	3.02169i	−0.119164	−	0.119164i	−0.764174	+	0.645010i	$0.776853\pi$
$644$		0			0
$645$	19.5003	+	36.4293i	0.767823	+	1.43440i
$646$		0			0
$647$	5.46518	−	20.3963i	0.214858	−	0.801862i	−0.771358	−	0.636401i	$-0.780422\pi$
$647$	5.46518	−	20.3963i	0.214858	−	0.801862i	0.986216	−	0.165461i	$-0.0529112\pi$
$648$		0			0
$649$	−5.63704	−	3.25455i	−0.221273	−	0.127752i
$650$		0			0
$651$	7.50412	−	3.86545i	0.294110	−	0.151499i
$652$		0			0
$653$	0.394244	+	1.47134i	0.0154279	+	0.0575779i	0.973211	−	0.229915i	$-0.0738449\pi$
$653$	0.394244	+	1.47134i	0.0154279	+	0.0575779i	−0.957783	+	0.287493i	$0.907178\pi$
$654$		0			0
$655$	2.73543	+	0.968220i	0.106882	+	0.0378315i
$656$		0			0
$657$	−32.0986	+	11.8755i	−1.25229	+	0.463307i
$658$		0			0
$659$	28.8543			1.12400			0.562002	−	0.827136i	$-0.310031\pi$
$659$	28.8543			1.12400			0.562002	+	0.827136i	$0.310031\pi$
$660$		0			0
$661$	−5.34839	−	9.26369i	−0.208028	−	0.360316i	0.743065	−	0.669219i	$-0.233371\pi$
$661$	−5.34839	−	9.26369i	−0.208028	−	0.360316i	−0.951093	+	0.308903i	$0.900038\pi$
$662$		0			0
$663$	−5.04405	+	0.233588i	−0.195894	+	0.00907179i
$664$		0			0
$665$	3.52158	+	39.3783i	0.136561	+	1.52702i
$666$		0			0
$667$	5.23376	+	19.5326i	0.202652	+	0.756307i
$668$		0			0
$669$	−9.72678	−	30.5674i	−0.376059	−	1.18180i
$670$		0			0
$671$			43.4275i			1.67650i
$672$		0			0
$673$	25.9024	+	25.9024i	0.998464	+	0.998464i	0.999999	−	0.00153521i	$-0.000488674\pi$
$673$	25.9024	+	25.9024i	0.998464	+	0.998464i	−0.00153521	+	0.999999i	$0.500489\pi$
$674$		0			0
$675$	−12.5842	−	22.7297i	−0.484367	−	0.874865i
$676$		0			0
$677$	−11.2558	+	3.01599i	−0.432597	+	0.115914i	−0.468545	−	0.883440i	$-0.655222\pi$
$677$	−11.2558	+	3.01599i	−0.432597	+	0.115914i	0.0359478	+	0.999354i	$0.488555\pi$
$678$		0			0
$679$	−1.95073	−	0.725393i	−0.0748622	−	0.0278380i
$680$		0			0
$681$	−15.9884	+	17.5412i	−0.612678	+	0.672179i
$682$		0			0
$683$	−18.4392	−	4.94076i	−0.705556	−	0.189053i	−0.111838	−	0.993726i	$-0.535674\pi$
$683$	−18.4392	−	4.94076i	−0.705556	−	0.189053i	−0.593718	+	0.804673i	$0.702340\pi$
$684$		0			0
$685$	0.0920952	−	1.17236i	0.00351878	−	0.0447936i
$686$		0			0
$687$	−11.1495	−	17.3995i	−0.425378	−	0.663831i
$688$		0			0
$689$	−3.93674	−	6.81863i	−0.149978	−	0.259769i
$690$		0			0
$691$	−21.0814	+	36.5141i	−0.801976	+	1.38906i	0.116338	+	0.993210i	$0.462885\pi$
$691$	−21.0814	+	36.5141i	−0.801976	+	1.38906i	−0.918314	+	0.395854i	$0.870449\pi$
$692$		0			0
$693$	0.0401546	−	24.1953i	0.00152535	−	0.919103i
$694$		0			0
$695$	−7.20780	−	38.8583i	−0.273407	−	1.47398i
$696$		0			0
$697$	34.6624	+	9.28775i	1.31293	+	0.351799i
$698$		0			0
$699$	−3.74360	+	17.1001i	−0.141596	+	0.646784i
$700$		0			0
$701$			0.0274102i			0.00103527i	1.00000		0.000517635i	$0.000164768\pi$
$701$			0.0274102i			0.00103527i	−1.00000		0.000517635i	$0.999835\pi$
$702$		0			0
$703$	4.99474	−	18.6406i	0.188380	−	0.703045i
$704$		0			0
$705$	−29.1774	−	0.937440i	−1.09888	−	0.0353060i
$706$		0			0
$707$	−7.23376	−	5.14039i	−0.272054	−	0.193324i
$708$		0			0
$709$	24.5893	+	14.1966i	0.923471	+	0.533166i	0.884741	−	0.466084i	$-0.154335\pi$
$709$	24.5893	+	14.1966i	0.923471	+	0.533166i	0.0387299	+	0.999250i	$0.487669\pi$
$710$		0			0
$711$	−3.89210	−	41.9325i	−0.145965	−	1.57259i
$712$		0			0
$713$	−3.09302	+	3.09302i	−0.115834	+	0.115834i
$714$		0			0
$715$	−4.92074	−	0.386550i	−0.184025	−	0.0144562i
$716$		0			0
$717$	−32.9543	−	17.0444i	−1.23070	−	0.636533i
$718$		0			0
$719$	6.78490	−	11.7518i	0.253034	−	0.438268i	−0.711326	−	0.702863i	$-0.751905\pi$
$719$	6.78490	−	11.7518i	0.253034	−	0.438268i	0.964360	+	0.264595i	$0.0852382\pi$
$720$		0			0
$721$	−2.91948	−	3.52879i	−0.108727	−	0.131419i
$722$		0			0
$723$	0.805751	+	17.3992i	0.0299662	+	0.647084i
$724$		0			0
$725$	39.7454	−	15.2701i	1.47611	−	0.567116i
$726$		0			0
$727$	−11.5270	+	11.5270i	−0.427515	+	0.427515i	−0.887781	−	0.460266i	$-0.847754\pi$
$727$	−11.5270	+	11.5270i	−0.427515	+	0.427515i	0.460266	+	0.887781i	$0.347754\pi$
$728$		0			0
$729$	−25.9659	+	7.40084i	−0.961700	+	0.274105i
$730$		0			0
$731$	−37.1972	+	21.4758i	−1.37579	+	0.794312i
$732$		0			0
$733$	−12.8796	+	3.45107i	−0.475718	+	0.127468i	−0.488708	−	0.872447i	$-0.662532\pi$
$733$	−12.8796	+	3.45107i	−0.475718	+	0.127468i	0.0129901	+	0.999916i	$0.495865\pi$
$734$		0			0
$735$	22.8996	−	14.5123i	0.844666	−	0.535293i
$736$		0			0
$737$	11.7853	−	3.15785i	0.434116	−	0.116321i
$738$		0			0
$739$	−25.3089	+	14.6121i	−0.931003	+	0.537515i	−0.887129	−	0.461522i	$-0.847303\pi$
$739$	−25.3089	+	14.6121i	−0.931003	+	0.537515i	−0.0438740	+	0.999037i	$0.513970\pi$
$740$		0			0
$741$	1.79250	−	8.18780i	0.0658491	−	0.300786i
$742$		0			0
$743$	−12.8645	+	12.8645i	−0.471952	+	0.471952i	−0.902546	−	0.430594i	$-0.858304\pi$
$743$	−12.8645	+	12.8645i	−0.471952	+	0.471952i	0.430594	+	0.902546i	$0.358304\pi$
$744$		0			0
$745$	−15.5162	+	43.8365i	−0.568468	+	1.60605i
$746$		0			0
$747$	−4.16246	−	0.711286i	−0.152297	−	0.0260246i
$748$		0			0
$749$	13.4297	+	16.2326i	0.490712	+	0.593127i
$750$		0			0
$751$	−10.6527	+	18.4510i	−0.388721	+	0.673285i	−0.992278	−	0.124035i	$-0.960416\pi$
$751$	−10.6527	+	18.4510i	−0.388721	+	0.673285i	0.603556	+	0.797320i	$0.293750\pi$
$752$		0			0
$753$	−4.08387	+	7.89592i	−0.148824	+	0.287743i
$754$		0			0
$755$	−15.8218	−	18.5195i	−0.575813	−	0.673992i
$756$		0			0
$757$	18.4939	−	18.4939i	0.672174	−	0.672174i	−0.286043	−	0.958217i	$-0.592340\pi$
$757$	18.4939	−	18.4939i	0.672174	−	0.672174i	0.958217	+	0.286043i	$0.0923401\pi$
$758$		0			0
$759$	3.80182	+	11.9476i	0.137997	+	0.433671i
$760$		0			0
$761$	29.7628	+	17.1835i	1.07890	+	0.622903i	0.930599	−	0.366039i	$-0.119286\pi$
$761$	29.7628	+	17.1835i	1.07890	+	0.622903i	0.148300	+	0.988942i	$0.452620\pi$
$762$		0			0
$763$	−5.28153	−	3.75311i	−0.191204	−	0.135872i
$764$		0			0
$765$	23.1949	−	13.8331i	0.838613	−	0.500136i
$766$		0			0
$767$	−0.400199	+	1.49356i	−0.0144503	+	0.0539294i
$768$		0			0
$769$			8.44100i			0.304390i	0.988350	+	0.152195i	$0.0486342\pi$
$769$			8.44100i			0.304390i	−0.988350	+	0.152195i	$0.951366\pi$
$770$		0			0
$771$	−18.9758	−	4.15425i	−0.683398	−	0.149612i
$772$		0			0
$773$	−23.4549	−	6.28472i	−0.843614	−	0.226046i	−0.188970	−	0.981983i	$-0.560515\pi$
$773$	−23.4549	−	6.28472i	−0.843614	−	0.226046i	−0.654644	+	0.755937i	$0.727182\pi$
$774$		0			0
$775$	7.15926	+	5.79401i	0.257168	+	0.208127i
$776$		0			0
$777$	−12.9320	+	2.80863i	−0.463933	+	0.100759i
$778$		0			0
$779$	−29.7833	+	51.5862i	−1.06710	+	1.84827i
$780$		0			0
$781$	−5.21104	−	9.02578i	−0.186466	−	0.322968i
$782$		0			0
$783$	−6.12324	−	43.8224i	−0.218827	−	1.56609i
$784$		0			0
$785$	22.2652	+	1.74905i	0.794678	+	0.0624263i
$786$		0			0
$787$	−1.95091	−	0.522746i	−0.0695426	−	0.0186339i	0.223880	−	0.974617i	$-0.428128\pi$
$787$	−1.95091	−	0.522746i	−0.0695426	−	0.0186339i	−0.293423	+	0.955983i	$0.594794\pi$
$788$		0			0
$789$	−18.2451	−	16.6301i	−0.649544	−	0.592046i
$790$		0			0
$791$	−17.5984	−	6.54408i	−0.625727	−	0.232681i
$792$		0			0
$793$	9.96477	−	2.67005i	0.353859	−	0.0948163i
$794$		0			0
$795$	35.7740	+	22.2156i	1.26877	+	0.787906i
$796$		0			0
$797$	10.5999	+	10.5999i	0.375468	+	0.375468i	0.869464	−	0.493996i	$-0.164464\pi$
$797$	10.5999	+	10.5999i	0.375468	+	0.375468i	−0.493996	+	0.869464i	$0.664464\pi$
$798$		0			0
$799$		−	30.3451i		−	1.07353i
$800$		0			0
$801$	−4.21935	+	0.391633i	−0.149084	+	0.0138377i
$802$		0			0
$803$	−9.00076	−	33.5913i	−0.317630	−	1.18541i
$804$		0			0
$805$	−9.00963	+	10.7793i	−0.317548	+	0.379922i
$806$		0			0
$807$	1.15018	+	24.8368i	0.0404884	+	0.874298i
$808$		0			0
$809$	2.50317	+	4.33563i	0.0880069	+	0.152432i	0.906669	−	0.421844i	$-0.138617\pi$
$809$	2.50317	+	4.33563i	0.0880069	+	0.152432i	−0.818662	+	0.574276i	$0.805284\pi$
$810$		0			0
$811$	6.45712			0.226740			0.113370	−	0.993553i	$-0.463835\pi$
$811$	6.45712			0.226740			0.113370	+	0.993553i	$0.463835\pi$
$812$		0			0
$813$	−2.45259	+	1.57160i	−0.0860160	+	0.0551184i
$814$		0			0
$815$	6.88591	−	3.28564i	0.241203	−	0.115091i
$816$		0			0
$817$	−18.4529	−	68.8672i	−0.645585	−	2.40936i
$818$		0			0
$819$	−5.55426	+	1.47838i	−0.194082	+	0.0516589i
$820$		0			0
$821$	−7.96631	−	4.59935i	−0.278026	−	0.160518i	0.354503	−	0.935055i	$-0.384650\pi$
$821$	−7.96631	−	4.59935i	−0.278026	−	0.160518i	−0.632530	+	0.774536i	$0.717983\pi$
$822$		0			0
$823$	−3.37717	+	12.6038i	−0.117721	+	0.439340i	−0.999476	−	0.0323671i	$-0.989695\pi$
$823$	−3.37717	+	12.6038i	−0.117721	+	0.439340i	0.881755	+	0.471707i	$0.156362\pi$
$824$		0			0
$825$	24.1787	−	10.5977i	0.841795	−	0.368963i
$826$		0			0
$827$	−8.73603	−	8.73603i	−0.303782	−	0.303782i	0.538710	−	0.842491i	$-0.318912\pi$
$827$	−8.73603	−	8.73603i	−0.303782	−	0.303782i	−0.842491	+	0.538710i	$0.818912\pi$
$828$		0			0
$829$	23.6216	−	13.6379i	0.820411	−	0.473665i	−0.0301471	−	0.999545i	$-0.509598\pi$
$829$	23.6216	−	13.6379i	0.820411	−	0.473665i	0.850558	+	0.525881i	$0.176264\pi$
$830$		0			0
$831$	−10.0529	−	9.16304i	−0.348732	−	0.317862i
$832$		0			0
$833$	15.8419	+	23.3071i	0.548889	+	0.807544i
$834$		0			0
$835$	−27.7873	−	19.0917i	−0.961619	−	0.660696i
$836$		0			0
$837$	7.54706	−	5.88673i	0.260864	−	0.203475i
$838$		0			0
$839$	22.7675			0.786022			0.393011	−	0.919534i	$-0.371433\pi$
$839$	22.7675			0.786022			0.393011	+	0.919534i	$0.371433\pi$
$840$		0			0
$841$	43.5147			1.50051
$842$		0			0
$843$	−6.37604	+	12.3277i	−0.219602	+	0.424589i
$844$		0			0
$845$	−5.08769	−	27.4285i	−0.175022	−	0.943569i
$846$		0			0
$847$	−4.49817	−	0.425043i	−0.154559	−	0.0146046i
$848$		0			0
$849$	1.64064	−	1.79997i	0.0563066	−	0.0617749i
$850$		0			0
$851$	5.93881	−	3.42877i	0.203580	−	0.117537i
$852$		0			0
$853$	7.75252	+	7.75252i	0.265441	+	0.265441i	0.827260	−	0.561819i	$-0.189898\pi$
$853$	7.75252	+	7.75252i	0.265441	+	0.265441i	−0.561819	+	0.827260i	$0.689898\pi$
$854$		0			0
$855$	12.2145	+	43.1328i	0.417727	+	1.47511i
$856$		0			0
$857$	14.4896	−	54.0758i	0.494954	−	1.84719i	−0.0353310	−	0.999376i	$-0.511249\pi$
$857$	14.4896	−	54.0758i	0.494954	−	1.84719i	0.530285	−	0.847819i	$-0.322085\pi$
$858$		0			0
$859$	−14.4633	−	8.35040i	−0.493482	−	0.284912i	0.232536	−	0.972588i	$-0.425298\pi$
$859$	−14.4633	−	8.35040i	−0.493482	−	0.284912i	−0.726018	+	0.687676i	$0.758631\pi$
$860$		0			0
$861$	40.8001	+	1.95730i	1.39046	+	0.0667045i
$862$		0			0
$863$	9.38019	+	35.0073i	0.319305	+	1.19166i	0.919914	+	0.392121i	$0.128258\pi$
$863$	9.38019	+	35.0073i	0.319305	+	1.19166i	−0.600609	+	0.799543i	$0.705075\pi$
$864$		0			0
$865$	−16.7200	−	35.0412i	−0.568499	−	1.19144i
$866$		0			0
$867$	−0.740183	−	1.15511i	−0.0251379	−	0.0392294i
$868$		0			0
$869$	42.7911			1.45159
$870$		0			0
$871$	−1.44919	−	2.51006i	−0.0491038	−	0.0850502i
$872$		0			0
$873$	−2.32618	−	0.397501i	−0.0787294	−	0.0134534i
$874$		0			0
$875$	24.5599	+	16.4868i	0.830275	+	0.557354i
$876$		0			0
$877$	−9.71119	−	36.2427i	−0.327924	−	1.22383i	−0.911340	−	0.411654i	$-0.864951\pi$
$877$	−9.71119	−	36.2427i	−0.327924	−	1.22383i	0.583416	−	0.812173i	$-0.301716\pi$
$878$		0			0
$879$	−8.10128	+	2.57788i	−0.273249	+	0.0869499i
$880$		0			0
$881$		−	38.3229i		−	1.29113i	−0.763704	−	0.645566i	$-0.776621\pi$
$881$		−	38.3229i		−	1.29113i	0.763704	−	0.645566i	$-0.223379\pi$
$882$		0			0
$883$	14.7904	+	14.7904i	0.497735	+	0.497735i	0.910732	−	0.412997i	$-0.135518\pi$
$883$	14.7904	+	14.7904i	0.497735	+	0.497735i	−0.412997	+	0.910732i	$0.635518\pi$
$884$		0			0
$885$	−1.88281	−	8.05282i	−0.0632899	−	0.270693i
$886$		0			0
$887$	−0.826754	+	0.221528i	−0.0277597	+	0.00743818i	−0.272672	−	0.962107i	$-0.587907\pi$
$887$	−0.826754	+	0.221528i	−0.0277597	+	0.00743818i	0.244912	+	0.969545i	$0.421241\pi$
$888$		0			0
$889$	−20.1475	−	7.49200i	−0.675727	−	0.251274i
$890$		0			0
$891$	−5.04942	−	26.9662i	−0.169162	−	0.903403i
$892$		0			0
$893$	48.6543	+	13.0369i	1.62815	+	0.436263i
$894$		0			0
$895$	−20.7437	−	24.2806i	−0.693385	−	0.811611i
$896$		0			0
$897$	2.50773	−	1.60693i	0.0837305	−	0.0536539i
$898$		0			0
$899$	7.84290	+	13.5843i	0.261575	+	0.453062i
$900$		0			0
$901$	−21.8867	+	37.9089i	−0.729152	+	1.26293i
$902$		0			0
$903$	−36.1877	+	32.8746i	−1.20425	+	1.09400i
$904$		0			0
$905$	−12.9717	+	2.40612i	−0.431195	+	0.0799822i
$906$		0			0
$907$	−45.6627	−	12.2353i	−1.51621	−	0.406266i	−0.597715	−	0.801709i	$-0.703925\pi$
$907$	−45.6627	−	12.2353i	−1.51621	−	0.406266i	−0.918491	+	0.395443i	$0.870591\pi$
$908$		0			0
$909$	−9.14195	−	4.20427i	−0.303219	−	0.139447i
$910$		0			0
$911$			32.5777i			1.07935i	0.841875	+	0.539673i	$0.181452\pi$
$911$			32.5777i			1.07935i	−0.841875	+	0.539673i	$0.818548\pi$
$912$		0			0
$913$	1.11055	−	4.14461i	0.0367537	−	0.137167i
$914$		0			0
$915$	−40.2480	+	37.7422i	−1.33056	+	1.24772i
$916$		0			0
$917$	−0.322989	+	3.41815i	−0.0106660	+	0.112877i
$918$		0			0
$919$	−17.0821	−	9.86237i	−0.563487	−	0.325329i	0.191057	−	0.981579i	$-0.438809\pi$
$919$	−17.0821	−	9.86237i	−0.563487	−	0.325329i	−0.754544	+	0.656250i	$0.772142\pi$
$920$		0			0
$921$	−46.0537	+	14.6546i	−1.51752	+	0.482886i
$922$		0			0
$923$	−1.75064	+	1.75064i	−0.0576232	+	0.0576232i
$924$		0			0
$925$	−8.49037	−	11.6789i	−0.279162	−	0.383998i
$926$		0			0
$927$	−3.99577	−	3.31701i	−0.131238	−	0.108945i
$928$		0			0
$929$	−22.4160	+	38.8256i	−0.735444	+	1.27383i	0.219085	+	0.975706i	$0.429693\pi$
$929$	−22.4160	+	38.8256i	−0.735444	+	1.27383i	−0.954528	+	0.298120i	$0.903641\pi$
$930$		0			0
$931$	−44.1759	+	15.3871i	−1.44781	+	0.504293i
$932$		0			0
$933$	−47.4896	+	2.19922i	−1.55474	+	0.0719993i
$934$		0			0
$935$	11.8175	+	24.7667i	0.386474	+	0.809957i
$936$		0			0
$937$	−20.1180	+	20.1180i	−0.657228	+	0.657228i	−0.954723	−	0.297495i	$-0.903849\pi$
$937$	−20.1180	+	20.1180i	−0.657228	+	0.657228i	0.297495	+	0.954723i	$0.403849\pi$
$938$		0			0
$939$	39.9060	+	8.73634i	1.30228	+	0.285100i
$940$		0			0
$941$	−30.7949	+	17.7794i	−1.00389	+	0.579593i	−0.909395	−	0.415933i	$-0.863455\pi$
$941$	−30.7949	+	17.7794i	−1.00389	+	0.579593i	−0.0944896	+	0.995526i	$0.530122\pi$
$942$		0			0
$943$	−20.4455	+	5.47836i	−0.665798	+	0.178400i
$944$		0			0
$945$	22.4588	−	20.9906i	0.730583	−	0.682824i
$946$		0			0
$947$	7.54155	−	2.02075i	0.245068	−	0.0656657i	−0.134194	−	0.990955i	$-0.542845\pi$
$947$	7.54155	−	2.02075i	0.245068	−	0.0656657i	0.379262	+	0.925289i	$0.376178\pi$
$948$		0			0
$949$	−7.15438	+	4.13058i	−0.232241	+	0.134084i
$950$		0			0
$951$	54.3253	+	11.8931i	1.76162	+	0.385659i
$952$		0			0
$953$	−9.66000	+	9.66000i	−0.312918	+	0.312918i	−0.846039	−	0.533121i	$-0.821019\pi$
$953$	−9.66000	+	9.66000i	−0.312918	+	0.312918i	0.533121	+	0.846039i	$0.321019\pi$
$954$		0			0
$955$	−23.2617	−	8.23359i	−0.752730	−	0.266433i
$956$		0			0
$957$	44.9128	−	2.07989i	1.45182	−	0.0672333i
$958$		0			0
$959$	1.37193	−	0.232095i	0.0443021	−	0.00749474i
$960$		0			0
$961$	13.8035	−	23.9083i	0.445274	−	0.771237i
$962$		0			0
$963$	18.3807	+	15.2584i	0.592311	+	0.491696i
$964$		0			0
$965$	2.46623	−	31.3947i	0.0793906	−	1.01063i
$966$		0			0
$967$	−11.2478	+	11.2478i	−0.361704	+	0.361704i	−0.864440	−	0.502736i	$-0.832327\pi$
$967$	−11.2478	+	11.2478i	−0.361704	+	0.361704i	0.502736	+	0.864440i	$0.332327\pi$
$968$		0			0
$969$	−44.4051	+	14.1300i	−1.42650	+	0.453922i
$970$		0			0
$971$	−23.4447	−	13.5358i	−0.752375	−	0.434384i	0.0741766	−	0.997245i	$-0.476367\pi$
$971$	−23.4447	−	13.5358i	−0.752375	−	0.434384i	−0.826551	+	0.562861i	$0.809700\pi$
$972$		0			0
$973$	42.5170	−	19.4676i	1.36303	−	0.624103i
$974$		0			0
$975$	−3.91829	−	4.89641i	−0.125486	−	0.156811i
$976$		0			0
$977$	8.26594	−	30.8489i	0.264451	−	0.986944i	−0.698135	−	0.715966i	$-0.745986\pi$
$977$	8.26594	−	30.8489i	0.264451	−	0.986944i	0.962586	−	0.270978i	$-0.0873470\pi$
$978$		0			0
$979$		−	4.30575i		−	0.137612i
$980$		0			0
$981$	−6.67475	−	3.06963i	−0.213108	−	0.0980058i
$982$		0			0
$983$	−27.6268	−	7.40257i	−0.881157	−	0.236105i	−0.210251	−	0.977648i	$-0.567428\pi$
$983$	−27.6268	−	7.40257i	−0.881157	−	0.236105i	−0.670906	+	0.741542i	$0.734095\pi$
$984$		0			0
$985$	4.25201	+	2.92142i	0.135480	+	0.0930841i
$986$		0			0
$987$	−7.33087	−	33.7541i	−0.233344	−	1.07440i
$988$		0			0
$989$	12.6675	−	21.9407i	0.402802	−	0.697674i
$990$		0			0
$991$	9.37664	+	16.2408i	0.297859	+	0.515907i	0.975646	−	0.219352i	$-0.0703942\pi$
$991$	9.37664	+	16.2408i	0.297859	+	0.515907i	−0.677787	+	0.735258i	$0.737061\pi$
$992$		0			0
$993$	−40.5747	+	26.0000i	−1.28760	+	0.825085i
$994$		0			0
$995$	−18.9510	+	16.1905i	−0.600787	+	0.513272i
$996$		0			0
$997$	27.1101	+	7.26414i	0.858587	+	0.230058i	0.661146	−	0.750257i	$-0.270070\pi$
$997$	27.1101	+	7.26414i	0.858587	+	0.230058i	0.197441	+	0.980315i	$0.436737\pi$
$998$		0			0
$999$	−13.8172	+	5.85205i	−0.437156	+	0.185151i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.bv.c.233.3	yes	48
3.2	odd	2	inner	420.2.bv.c.233.12	yes	48
5.2	odd	4	inner	420.2.bv.c.317.5	yes	48
7.4	even	3	inner	420.2.bv.c.53.7	yes	48
15.2	even	4	inner	420.2.bv.c.317.7	yes	48
21.11	odd	6	inner	420.2.bv.c.53.5	✓	48
35.32	odd	12	inner	420.2.bv.c.137.12	yes	48
105.32	even	12	inner	420.2.bv.c.137.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bv.c.53.5	✓	48	21.11	odd	6	inner
420.2.bv.c.53.7	yes	48	7.4	even	3	inner
420.2.bv.c.137.3	yes	48	105.32	even	12	inner
420.2.bv.c.137.12	yes	48	35.32	odd	12	inner
420.2.bv.c.233.3	yes	48	1.1	even	1	trivial
420.2.bv.c.233.12	yes	48	3.2	odd	2	inner
420.2.bv.c.317.5	yes	48	5.2	odd	4	inner
420.2.bv.c.317.7	yes	48	15.2	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:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.53846 - 0.795708i) q^{3} +(2.19857 - 0.407811i) q^{5} +(1.10146 + 2.40557i) q^{7} +(1.73370 + 2.44833i) q^{9} +O(q^{10})\)	\(q+(-1.53846 - 0.795708i) q^{3} +(2.19857 - 0.407811i) q^{5} +(1.10146 + 2.40557i) q^{7} +(1.73370 + 2.44833i) q^{9} +(-2.63993 + 1.52416i) q^{11} +(0.512041 + 0.512041i) q^{13} +(-3.70690 - 1.12202i) q^{15} +(1.04198 - 3.88873i) q^{17} +(5.78739 + 3.34135i) q^{19} +(0.219587 - 4.57731i) q^{21} +(0.614611 + 2.29376i) q^{23} +(4.66738 - 1.79320i) q^{25} +(-0.719065 - 5.14616i) q^{27} +8.51556 q^{29} +(0.921008 + 1.59523i) q^{31} +(5.27420 - 0.244246i) q^{33} +(3.40265 + 4.83962i) q^{35} +(-0.747413 - 2.78938i) q^{37} +(-0.380318 - 1.19519i) q^{39} +8.91355i q^{41} +(-7.54399 - 7.54399i) q^{43} +(4.81010 + 4.67578i) q^{45} +(7.28063 - 1.95084i) q^{47} +(-4.57357 + 5.29929i) q^{49} +(-4.69734 + 5.15352i) q^{51} +(-10.5024 - 2.81412i) q^{53} +(-5.18248 + 4.42756i) q^{55} +(-6.24491 - 9.74561i) q^{57} +(1.06765 + 1.84923i) q^{59} +(7.12318 - 12.3377i) q^{61} +(-3.98003 + 6.86727i) q^{63} +(1.33457 + 0.916940i) q^{65} +(-3.86614 - 1.03593i) q^{67} +(0.879611 - 4.01790i) q^{69} +3.41895i q^{71} +(-2.95269 + 11.0196i) q^{73} +(-8.60742 - 0.955118i) q^{75} +(-6.57426 - 4.67173i) q^{77} +(-12.1569 - 7.01879i) q^{79} +(-2.98859 + 8.48931i) q^{81} +(-0.995323 + 0.995323i) q^{83} +(0.705000 - 8.97455i) q^{85} +(-13.1008 - 6.77590i) q^{87} +(-0.706248 + 1.22326i) q^{89} +(-0.667760 + 1.79575i) q^{91} +(-0.147591 - 3.18705i) q^{93} +(14.0866 + 4.98602i) q^{95} +(-0.556234 + 0.556234i) q^{97} +(-8.30847 - 3.82096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{3} - 8 q^{7}+O(q^{10}) \) 48 * q - 2 * q^3 - 8 * q^7	\( 48 q - 2 q^{3} - 8 q^{7} + 32 q^{13} - 16 q^{21} + 16 q^{25} - 32 q^{27} - 64 q^{31} + 34 q^{33} - 40 q^{37} - 24 q^{43} + 30 q^{45} + 36 q^{51} + 92 q^{57} - 18 q^{63} + 28 q^{67} - 8 q^{73} - 38 q^{75} + 20 q^{81} - 56 q^{85} - 24 q^{87} - 24 q^{91} + 6 q^{93} + 56 q^{97}+O(q^{100}) \) 48 * q - 2 * q^3 - 8 * q^7 + 32 * q^13 - 16 * q^21 + 16 * q^25 - 32 * q^27 - 64 * q^31 + 34 * q^33 - 40 * q^37 - 24 * q^43 + 30 * q^45 + 36 * q^51 + 92 * q^57 - 18 * q^63 + 28 * q^67 - 8 * q^73 - 38 * q^75 + 20 * q^81 - 56 * q^85 - 24 * q^87 - 24 * q^91 + 6 * q^93 + 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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