LMFDB - Embedded newform 456.2.bg.d.385.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [456,2,Mod(25,456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(456, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 0, 14]))

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

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

chi := DirichletCharacter("456.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bg (of order $9$, degree $6$, 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:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 42 x^{16} + 621 x^{14} + 4302 x^{12} + 15174 x^{10} + 27540 x^{8} + 25929 x^{6} + 12204 x^{4} + \cdots + 192 $ x^18 + 42x^16 + 621x^14 + 4302x^12 + 15174x^10 + 27540x^8 + 25929x^6 + 12204x^4 + 2592x^2 + 192
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			385.1
Root			$-2.26471i$ of defining polynomial
Character	$\chi$	$=$	456.385
Dual form			456.2.bg.d.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.173648 + 0.984808i) q^{3} +(-3.10397 - 2.60454i) q^{5} +(1.83370 + 3.17606i) q^{7} +(-0.939693 - 0.342020i) q^{9} +(-0.455725 + 0.789338i) q^{11} +(0.387516 + 2.19771i) q^{13} +(3.10397 - 2.60454i) q^{15} +(-7.52761 + 2.73983i) q^{17} +(-3.91733 - 1.91168i) q^{19} +(-3.44623 + 1.25433i) q^{21} +(-5.20427 + 4.36690i) q^{23} +(1.98276 + 11.2448i) q^{25} +(0.500000 - 0.866025i) q^{27} +(5.02422 + 1.82867i) q^{29} +(0.410471 + 0.710957i) q^{31} +(-0.698211 - 0.585868i) q^{33} +(2.58043 - 14.6343i) q^{35} -5.54834 q^{37} -2.23162 q^{39} +(0.770364 - 4.36895i) q^{41} +(-5.71862 - 4.79849i) q^{43} +(2.02597 + 3.50909i) q^{45} +(8.17671 + 2.97608i) q^{47} +(-3.22492 + 5.58572i) q^{49} +(-1.39105 - 7.88901i) q^{51} +(-7.86828 + 6.60227i) q^{53} +(3.47042 - 1.26313i) q^{55} +(2.56287 - 3.52586i) q^{57} +(6.79165 - 2.47196i) q^{59} +(6.20047 - 5.20281i) q^{61} +(-0.636838 - 3.61169i) q^{63} +(4.52119 - 7.83094i) q^{65} +(5.89321 + 2.14495i) q^{67} +(-3.39685 - 5.88351i) q^{69} +(10.1698 + 8.53346i) q^{71} +(0.259552 - 1.47199i) q^{73} -11.4182 q^{75} -3.34265 q^{77} +(-1.11277 + 6.31083i) q^{79} +(0.766044 + 0.642788i) q^{81} +(-0.0831851 - 0.144081i) q^{83} +(30.5014 + 11.1016i) q^{85} +(-2.67333 + 4.63035i) q^{87} +(-1.67733 - 9.51263i) q^{89} +(-6.26949 + 5.26073i) q^{91} +(-0.771433 + 0.280779i) q^{93} +(7.18024 + 16.1366i) q^{95} +(-15.9518 + 5.80596i) q^{97} +(0.698211 - 0.585868i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{5} + 6 q^{7} + 9 q^{11} - 18 q^{13} - 3 q^{15} - 3 q^{17} + 3 q^{19} + 3 q^{21} - 24 q^{23} - 3 q^{25} + 9 q^{27} + 15 q^{29} + 9 q^{31} + 6 q^{35} + 30 q^{37} - 18 q^{39} - 3 q^{41} + 30 q^{43}+ \cdots - 9 q^{97}+O(q^{100}) $ 18 * q + 3 * q^5 + 6 * q^7 + 9 * q^11 - 18 * q^13 - 3 * q^15 - 3 * q^17 + 3 * q^19 + 3 * q^21 - 24 * q^23 - 3 * q^25 + 9 * q^27 + 15 * q^29 + 9 * q^31 + 6 * q^35 + 30 * q^37 - 18 * q^39 - 3 * q^41 + 30 * q^43 + 3 * q^45 + 54 * q^47 - 9 * q^49 - 6 * q^51 - 24 * q^53 + 12 * q^55 + 15 * q^57 + 9 * q^59 + 6 * q^61 + 6 * q^63 + 3 * q^65 - 18 * q^67 - 30 * q^69 - 63 * q^71 - 24 * q^73 - 60 * q^75 - 66 * q^77 - 15 * q^79 + 36 * q^83 + 39 * q^85 + 3 * q^87 - 63 * q^89 - 66 * q^91 + 27 * q^93 + 42 * q^95 - 9 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$	$1$	$1$

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
$3$	−0.173648	+	0.984808i	−0.100256	+	0.568579i
$3$	−0.173648	+	0.984808i	−0.100256	+	0.568579i
$4$		0			0
$5$	−3.10397	−	2.60454i	−1.38814	−	1.16478i	−0.966088	−	0.258212i	$-0.916867\pi$
$5$	−3.10397	−	2.60454i	−1.38814	−	1.16478i	−0.422048	−	0.906573i	$-0.638689\pi$
$6$		0			0
$7$	1.83370	+	3.17606i	0.693074	+	1.20044i	0.970826	+	0.239786i	$0.0770774\pi$
$7$	1.83370	+	3.17606i	0.693074	+	1.20044i	−0.277752	+	0.960653i	$0.589589\pi$
$8$		0			0
$9$	−0.939693	−	0.342020i	−0.313231	−	0.114007i
$10$		0			0
$11$	−0.455725	+	0.789338i	−0.137406	+	0.237994i	−0.926514	−	0.376260i	$-0.877210\pi$
$11$	−0.455725	+	0.789338i	−0.137406	+	0.237994i	0.789108	+	0.614255i	$0.210543\pi$
$12$		0			0
$13$	0.387516	+	2.19771i	0.107478	+	0.609536i	0.990202	+	0.139645i	$0.0445960\pi$
$13$	0.387516	+	2.19771i	0.107478	+	0.609536i	−0.882724	+	0.469892i	$0.844293\pi$
$14$		0			0
$15$	3.10397	−	2.60454i	0.801441	−	0.672489i
$16$		0			0
$17$	−7.52761	+	2.73983i	−1.82571	+	0.664505i	−0.831703	+	0.555221i	$0.812634\pi$
$17$	−7.52761	+	2.73983i	−1.82571	+	0.664505i	−0.994011	+	0.109284i	$0.965144\pi$
$18$		0			0
$19$	−3.91733	−	1.91168i	−0.898698	−	0.438569i
$19$	−3.91733	−	1.91168i	−0.898698	−	0.438569i
$20$		0			0
$21$	−3.44623	+	1.25433i	−0.752029	+	0.273716i
$22$		0			0
$23$	−5.20427	+	4.36690i	−1.08517	+	0.910562i	−0.996339	−	0.0854851i	$-0.972756\pi$
$23$	−5.20427	+	4.36690i	−1.08517	+	0.910562i	−0.0888262	+	0.996047i	$0.528312\pi$
$24$		0			0
$25$	1.98276	+	11.2448i	0.396551	+	2.24895i
$26$		0			0
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$		0			0
$29$	5.02422	+	1.82867i	0.932975	+	0.339575i	0.763388	−	0.645940i	$-0.223535\pi$
$29$	5.02422	+	1.82867i	0.932975	+	0.339575i	0.169587	+	0.985515i	$0.445757\pi$
$30$		0			0
$31$	0.410471	+	0.710957i	0.0737228	+	0.127692i	0.900530	−	0.434794i	$-0.143179\pi$
$31$	0.410471	+	0.710957i	0.0737228	+	0.127692i	−0.826807	+	0.562485i	$0.809845\pi$
$32$		0			0
$33$	−0.698211	−	0.585868i	−0.121543	−	0.101987i
$34$		0			0
$35$	2.58043	−	14.6343i	0.436172	−	2.47366i
$36$		0			0
$37$	−5.54834			−0.912142			−0.456071	−	0.889943i	$-0.650744\pi$
$37$	−5.54834			−0.912142			−0.456071	+	0.889943i	$0.650744\pi$
$38$		0			0
$39$	−2.23162			−0.357345
$40$		0			0
$41$	0.770364	−	4.36895i	0.120311	−	0.682316i	−0.863672	−	0.504054i	$-0.831841\pi$
$41$	0.770364	−	4.36895i	0.120311	−	0.682316i	0.983983	−	0.178262i	$-0.0570475\pi$
$42$		0			0
$43$	−5.71862	−	4.79849i	−0.872081	−	0.731763i	0.0924544	−	0.995717i	$-0.470529\pi$
$43$	−5.71862	−	4.79849i	−0.872081	−	0.731763i	−0.964535	+	0.263954i	$0.914973\pi$
$44$		0			0
$45$	2.02597	+	3.50909i	0.302014	+	0.523104i
$46$		0			0
$47$	8.17671	+	2.97608i	1.19270	+	0.434106i	0.860669	−	0.509165i	$-0.170046\pi$
$47$	8.17671	+	2.97608i	1.19270	+	0.434106i	0.332026	+	0.943270i	$0.392268\pi$
$48$		0			0
$49$	−3.22492	+	5.58572i	−0.460703	+	0.797961i
$50$		0			0
$51$	−1.39105	−	7.88901i	−0.194785	−	1.10468i
$52$		0			0
$53$	−7.86828	+	6.60227i	−1.08079	+	0.906892i	−0.995986	−	0.0895057i	$-0.971471\pi$
$53$	−7.86828	+	6.60227i	−1.08079	+	0.906892i	−0.0848053	+	0.996398i	$0.527027\pi$
$54$		0			0
$55$	3.47042	−	1.26313i	0.467951	−	0.170320i
$56$		0			0
$57$	2.56287	−	3.52586i	0.339461	−	0.467012i
$58$		0			0
$59$	6.79165	−	2.47196i	0.884197	−	0.321822i	0.140295	−	0.990110i	$-0.455195\pi$
$59$	6.79165	−	2.47196i	0.884197	−	0.321822i	0.743902	+	0.668288i	$0.232973\pi$
$60$		0			0
$61$	6.20047	−	5.20281i	0.793889	−	0.666152i	−0.152816	−	0.988255i	$-0.548834\pi$
$61$	6.20047	−	5.20281i	0.793889	−	0.666152i	0.946705	+	0.322103i	$0.104390\pi$
$62$		0			0
$63$	−0.636838	−	3.61169i	−0.0802340	−	0.455030i
$64$		0			0
$65$	4.52119	−	7.83094i	0.560785	−	0.971308i
$66$		0			0
$67$	5.89321	+	2.14495i	0.719971	+	0.262048i	0.675913	−	0.736981i	$-0.263749\pi$
$67$	5.89321	+	2.14495i	0.719971	+	0.262048i	0.0440573	+	0.999029i	$0.485972\pi$
$68$		0			0
$69$	−3.39685	−	5.88351i	−0.408932	−	0.708292i
$70$		0			0
$71$	10.1698	+	8.53346i	1.20693	+	1.01274i	0.999404	+	0.0345066i	$0.0109860\pi$
$71$	10.1698	+	8.53346i	1.20693	+	1.01274i	0.207527	+	0.978229i	$0.433458\pi$
$72$		0			0
$73$	0.259552	−	1.47199i	0.0303783	−	0.172284i	−0.965844	−	0.259125i	$-0.916566\pi$
$73$	0.259552	−	1.47199i	0.0303783	−	0.172284i	0.996222	+	0.0868407i	$0.0276771\pi$
$74$		0			0
$75$	−11.4182			−1.31846
$76$		0			0
$77$	−3.34265			−0.380930
$78$		0			0
$79$	−1.11277	+	6.31083i	−0.125196	+	0.710024i	0.855995	+	0.516985i	$0.172946\pi$
$79$	−1.11277	+	6.31083i	−0.125196	+	0.710024i	−0.981191	+	0.193039i	$0.938165\pi$
$80$		0			0
$81$	0.766044	+	0.642788i	0.0851160	+	0.0714208i
$82$		0			0
$83$	−0.0831851	−	0.144081i	−0.00913075	−	0.0158149i	0.861424	−	0.507887i	$-0.169573\pi$
$83$	−0.0831851	−	0.144081i	−0.00913075	−	0.0158149i	−0.870555	+	0.492072i	$0.836240\pi$
$84$		0			0
$85$	30.5014	+	11.1016i	3.30835	+	1.20414i
$86$		0			0
$87$	−2.67333	+	4.63035i	−0.286611	+	0.496425i
$88$		0			0
$89$	−1.67733	−	9.51263i	−0.177797	−	1.00834i	−0.934866	−	0.355002i	$-0.884480\pi$
$89$	−1.67733	−	9.51263i	−0.177797	−	1.00834i	0.757069	−	0.653335i	$-0.226631\pi$
$90$		0			0
$91$	−6.26949	+	5.26073i	−0.657221	+	0.551474i
$92$		0			0
$93$	−0.771433	+	0.280779i	−0.0799939	+	0.0291154i
$94$		0			0
$95$	7.18024	+	16.1366i	0.736677	+	1.65558i
$96$		0			0
$97$	−15.9518	+	5.80596i	−1.61965	+	0.589506i	−0.983316	−	0.181904i	$-0.941774\pi$
$97$	−15.9518	+	5.80596i	−1.61965	+	0.589506i	−0.636339	+	0.771410i	$0.719552\pi$
$98$		0			0
$99$	0.698211	−	0.585868i	0.0701728	−	0.0588820i
$100$		0			0
$101$	−0.0867965	−	0.492247i	−0.00863657	−	0.0489804i	0.980185	−	0.198085i	$-0.0634721\pi$
$101$	−0.0867965	−	0.492247i	−0.00863657	−	0.0489804i	−0.988821	+	0.149104i	$0.952361\pi$
$102$		0			0
$103$	4.06490	−	7.04061i	0.400526	−	0.693731i	−0.593263	−	0.805008i	$-0.702161\pi$
$103$	4.06490	−	7.04061i	0.400526	−	0.693731i	0.993789	+	0.111277i	$0.0354941\pi$
$104$		0			0
$105$	13.9639	+	5.08245i	1.36274	+	0.495997i
$106$		0			0
$107$	−1.81025	−	3.13545i	−0.175004	−	0.303116i	0.765159	−	0.643842i	$-0.222660\pi$
$107$	−1.81025	−	3.13545i	−0.175004	−	0.303116i	−0.940163	+	0.340726i	$0.889327\pi$
$108$		0			0
$109$	−3.64861	−	3.06155i	−0.349473	−	0.293243i	0.451105	−	0.892471i	$-0.351030\pi$
$109$	−3.64861	−	3.06155i	−0.349473	−	0.293243i	−0.800578	+	0.599228i	$0.795474\pi$
$110$		0			0
$111$	0.963459	−	5.46405i	0.0914475	−	0.518625i
$112$		0			0
$113$	−10.3764			−0.976128			−0.488064	−	0.872808i	$-0.662297\pi$
$113$	−10.3764			−0.976128			−0.488064	+	0.872808i	$0.662297\pi$
$114$		0			0
$115$	27.5277			2.56697
$116$		0			0
$117$	0.387516	−	2.19771i	0.0358259	−	0.203179i
$118$		0			0
$119$	−22.5052	−	18.8841i	−2.06305	−	1.73111i
$120$		0			0
$121$	5.08463	+	8.80684i	0.462239	+	0.800622i
$122$		0			0
$123$	4.16881	+	1.51732i	0.375888	+	0.136812i
$124$		0			0
$125$	13.0032	−	22.5221i	1.16304	−	2.01444i
$126$		0			0
$127$	−0.183612	−	1.04131i	−0.0162929	−	0.0924016i	0.975577	−	0.219658i	$-0.0704941\pi$
$127$	−0.183612	−	1.04131i	−0.0162929	−	0.0924016i	−0.991870	+	0.127256i	$0.959383\pi$
$128$		0			0
$129$	5.71862	−	4.79849i	0.503496	−	0.422483i
$130$		0			0
$131$	7.18357	−	2.61461i	0.627632	−	0.228439i	−0.00856848	−	0.999963i	$-0.502727\pi$
$131$	7.18357	−	2.61461i	0.627632	−	0.228439i	0.636200	+	0.771524i	$0.280505\pi$
$132$		0			0
$133$	−1.11161	−	15.9471i	−0.0963887	−	1.38279i
$134$		0			0
$135$	−3.80758	+	1.38585i	−0.327704	+	0.119275i
$136$		0			0
$137$	2.16290	−	1.81489i	0.184789	−	0.155056i	−0.545701	−	0.837980i	$-0.683736\pi$
$137$	2.16290	−	1.81489i	0.184789	−	0.155056i	0.730489	+	0.682924i	$0.239292\pi$
$138$		0			0
$139$	−1.15887	−	6.57229i	−0.0982942	−	0.557454i	−0.993688	−	0.112179i	$-0.964217\pi$
$139$	−1.15887	−	6.57229i	−0.0982942	−	0.557454i	0.895394	−	0.445275i	$-0.146894\pi$
$140$		0			0
$141$	−4.35074	+	7.53569i	−0.366398	+	0.634620i
$142$		0			0
$143$	−1.91134	−	0.695671i	−0.159834	−	0.0581749i
$144$		0			0
$145$	−10.8322	−	18.7619i	−0.899564	−	1.55809i
$146$		0			0
$147$	−4.94086	−	4.14588i	−0.407516	−	0.341946i
$148$		0			0
$149$	−0.934249	+	5.29839i	−0.0765367	+	0.434061i	0.922327	+	0.386409i	$0.126285\pi$
$149$	−0.934249	+	5.29839i	−0.0765367	+	0.434061i	−0.998864	+	0.0476516i	$0.984826\pi$
$150$		0			0
$151$	8.36023			0.680346			0.340173	−	0.940363i	$-0.389514\pi$
$151$	8.36023			0.680346			0.340173	+	0.940363i	$0.389514\pi$
$152$		0			0
$153$	8.01071			0.647628
$154$		0			0
$155$	0.577625	−	3.27588i	0.0463960	−	0.263125i
$156$		0			0
$157$	7.17406	+	6.01975i	0.572552	+	0.480428i	0.882492	−	0.470328i	$-0.155864\pi$
$157$	7.17406	+	6.01975i	0.572552	+	0.480428i	−0.309940	+	0.950756i	$0.600309\pi$
$158$		0			0
$159$	−5.13566	−	8.89522i	−0.407284	−	0.705437i
$160$		0			0
$161$	−23.4126	−	8.52150i	−1.84517	−	0.671589i
$162$		0			0
$163$	−0.251577	+	0.435743i	−0.0197050	+	0.0341301i	−0.875710	−	0.482838i	$-0.839606\pi$
$163$	−0.251577	+	0.435743i	−0.0197050	+	0.0341301i	0.856005	+	0.516968i	$0.172939\pi$
$164$		0			0
$165$	0.641307	+	3.63703i	0.0499257	+	0.283143i
$166$		0			0
$167$	−6.66042	+	5.58876i	−0.515399	+	0.432471i	−0.863024	−	0.505162i	$-0.831433\pi$
$167$	−6.66042	+	5.58876i	−0.515399	+	0.432471i	0.347625	+	0.937634i	$0.386988\pi$
$168$		0			0
$169$	7.53622	−	2.74296i	0.579710	−	0.210997i
$170$		0			0
$171$	3.02726	+	3.13620i	0.231500	+	0.239831i
$172$		0			0
$173$	−2.82249	+	1.02730i	−0.214590	+	0.0781044i	−0.447078	−	0.894495i	$-0.647535\pi$
$173$	−2.82249	+	1.02730i	−0.214590	+	0.0781044i	0.232488	+	0.972599i	$0.425313\pi$
$174$		0			0
$175$	−32.0783	+	26.9169i	−2.42489	+	2.03473i
$176$		0			0
$177$	1.25505	+	7.11772i	0.0943350	+	0.535001i
$178$		0			0
$179$	−8.41525	+	14.5756i	−0.628986	+	1.08943i	0.358770	+	0.933426i	$0.383196\pi$
$179$	−8.41525	+	14.5756i	−0.628986	+	1.08943i	−0.987756	+	0.156009i	$0.950137\pi$
$180$		0			0
$181$	−4.63083	−	1.68548i	−0.344207	−	0.125281i	0.164132	−	0.986438i	$-0.447518\pi$
$181$	−4.63083	−	1.68548i	−0.344207	−	0.125281i	−0.508338	+	0.861157i	$0.669740\pi$
$182$		0			0
$183$	4.04707	+	7.00973i	0.299168	+	0.518174i
$184$		0			0
$185$	17.2219	+	14.4509i	1.26618	+	1.06245i
$186$		0			0
$187$	1.26787	−	7.19044i	0.0927157	−	0.525817i
$188$		0			0
$189$	3.66740			0.266764
$190$		0			0
$191$	4.08333			0.295459			0.147730	−	0.989028i	$-0.452803\pi$
$191$	4.08333			0.295459			0.147730	+	0.989028i	$0.452803\pi$
$192$		0			0
$193$	0.289334	−	1.64090i	0.0208267	−	0.118114i	−0.972622	−	0.232393i	$-0.925345\pi$
$193$	0.289334	−	1.64090i	0.0208267	−	0.118114i	0.993449	+	0.114278i	$0.0364556\pi$
$194$		0			0
$195$	6.92687	+	5.81233i	0.496043	+	0.416230i
$196$		0			0
$197$	9.21770	+	15.9655i	0.656734	+	1.13750i	0.981456	+	0.191687i	$0.0613960\pi$
$197$	9.21770	+	15.9655i	0.656734	+	1.13750i	−0.324722	+	0.945810i	$0.605271\pi$
$198$		0			0
$199$	−0.254572	−	0.0926565i	−0.0180461	−	0.00656825i	0.332981	−	0.942933i	$-0.391945\pi$
$199$	−0.254572	−	0.0926565i	−0.0180461	−	0.00656825i	−0.351027	+	0.936365i	$0.614168\pi$
$200$		0			0
$201$	−3.13571	+	5.43122i	−0.221176	+	0.383088i
$202$		0			0
$203$	3.40496	+	19.3105i	0.238981	+	1.35533i
$204$		0			0
$205$	−13.7703	+	11.5546i	−0.961759	+	0.807011i
$206$		0			0
$207$	6.38398	−	2.32358i	0.443718	−	0.161500i
$208$		0			0
$209$	3.29418	−	2.22090i	0.227863	−	0.153623i
$210$		0			0
$211$	−21.2038	+	7.71757i	−1.45973	+	0.531299i	−0.945292	−	0.326227i	$-0.894223\pi$
$211$	−21.2038	+	7.71757i	−1.45973	+	0.531299i	−0.514441	+	0.857526i	$0.672000\pi$
$212$		0			0
$213$	−10.1698	+	8.53346i	−0.696822	+	0.584703i
$214$		0			0
$215$	5.25255	+	29.7887i	0.358221	+	2.03157i
$216$		0			0
$217$	−1.50536	+	2.60737i	−0.102191	+	0.176999i
$218$		0			0
$219$	1.40456	+	0.511218i	0.0949114	+	0.0345449i
$220$		0			0
$221$	−8.93843	−	15.4818i	−0.601264	−	1.04142i
$222$		0			0
$223$	−2.29734	−	1.92770i	−0.153841	−	0.129088i	0.562618	−	0.826717i	$-0.309794\pi$
$223$	−2.29734	−	1.92770i	−0.153841	−	0.129088i	−0.716460	+	0.697629i	$0.754239\pi$
$224$		0			0
$225$	1.98276	−	11.2448i	0.132184	−	0.749651i
$226$		0			0
$227$	9.03122			0.599423			0.299712	−	0.954030i	$-0.403110\pi$
$227$	9.03122			0.599423			0.299712	+	0.954030i	$0.403110\pi$
$228$		0			0
$229$	−28.4563			−1.88045			−0.940224	−	0.340556i	$-0.889385\pi$
$229$	−28.4563			−1.88045			−0.940224	+	0.340556i	$0.889385\pi$
$230$		0			0
$231$	0.580445	−	3.29187i	0.0381905	−	0.216589i
$232$		0			0
$233$	−10.7597	−	9.02848i	−0.704893	−	0.591475i	0.218268	−	0.975889i	$-0.429959\pi$
$233$	−10.7597	−	9.02848i	−0.704893	−	0.591475i	−0.923161	+	0.384414i	$0.874404\pi$
$234$		0			0
$235$	−17.6289	−	30.5342i	−1.14998	−	1.99183i
$236$		0			0
$237$	−6.02173	−	2.19173i	−0.391153	−	0.142368i
$238$		0			0
$239$	−3.40246	+	5.89324i	−0.220087	+	0.381202i	−0.954834	−	0.297139i	$-0.903967\pi$
$239$	−3.40246	+	5.89324i	−0.220087	+	0.381202i	0.734747	+	0.678341i	$0.237301\pi$
$240$		0			0
$241$	1.09249	+	6.19581i	0.0703734	+	0.399107i	0.999565	+	0.0295078i	$0.00939398\pi$
$241$	1.09249	+	6.19581i	0.0703734	+	0.399107i	−0.929191	+	0.369599i	$0.879495\pi$
$242$		0			0
$243$	−0.766044	+	0.642788i	−0.0491418	+	0.0412348i
$244$		0			0
$245$	24.5583	−	8.93848i	1.56897	−	0.571059i
$246$		0			0
$247$	2.68329	−	9.34998i	0.170734	−	0.594925i
$248$		0			0
$249$	0.156337	−	0.0569020i	0.00990745	−	0.00360602i
$250$		0			0
$251$	−10.8604	+	9.11296i	−0.685503	+	0.575205i	−0.917608	−	0.397486i	$-0.869883\pi$
$251$	−10.8604	+	9.11296i	−0.685503	+	0.575205i	0.232106	+	0.972691i	$0.425438\pi$
$252$		0			0
$253$	−1.07525	−	6.09804i	−0.0676003	−	0.383380i
$254$		0			0
$255$	−16.2295	+	28.1103i	−1.01633	+	1.76033i
$256$		0			0
$257$	20.9048	+	7.60871i	1.30400	+	0.474618i	0.898298	−	0.439386i	$-0.144804\pi$
$257$	20.9048	+	7.60871i	1.30400	+	0.474618i	0.405705	+	0.914004i	$0.367026\pi$
$258$		0			0
$259$	−10.1740	−	17.6219i	−0.632182	−	1.09497i
$260$		0			0
$261$	−4.09578	−	3.43677i	−0.253523	−	0.212731i
$262$		0			0
$263$	−0.382764	+	2.17076i	−0.0236023	+	0.133855i	−0.994332	−	0.106319i	$-0.966093\pi$
$263$	−0.382764	+	2.17076i	−0.0236023	+	0.133855i	0.970730	+	0.240174i	$0.0772046\pi$
$264$		0			0
$265$	41.6188			2.55662
$266$		0			0
$267$	9.65938			0.591145
$268$		0			0
$269$	4.52922	−	25.6865i	0.276152	−	1.56613i	−0.459128	−	0.888370i	$-0.651838\pi$
$269$	4.52922	−	25.6865i	0.276152	−	1.56613i	0.735280	−	0.677764i	$-0.237051\pi$
$270$		0			0
$271$	11.6763	+	9.79756i	0.709283	+	0.595159i	0.924398	−	0.381429i	$-0.124568\pi$
$271$	11.6763	+	9.79756i	0.709283	+	0.595159i	−0.215115	+	0.976589i	$0.569013\pi$
$272$		0			0
$273$	−4.09212	−	7.08776i	−0.247666	−	0.428971i
$274$		0			0
$275$	−9.77952	−	3.55945i	−0.589727	−	0.214643i
$276$		0			0
$277$	−0.222059	+	0.384617i	−0.0133422	+	0.0231094i	−0.872619	−	0.488401i	$-0.837580\pi$
$277$	−0.222059	+	0.384617i	−0.0133422	+	0.0231094i	0.859277	+	0.511510i	$0.170914\pi$
$278$		0			0
$279$	−0.142555	−	0.808470i	−0.00853455	−	0.0484019i
$280$		0			0
$281$	−10.5374	+	8.84193i	−0.628609	+	0.527465i	−0.900496	−	0.434864i	$-0.856797\pi$
$281$	−10.5374	+	8.84193i	−0.628609	+	0.527465i	0.271887	+	0.962329i	$0.412352\pi$
$282$		0			0
$283$	1.95707	−	0.712316i	0.116336	−	0.0423428i	−0.283196	−	0.959062i	$-0.591395\pi$
$283$	1.95707	−	0.712316i	0.116336	−	0.0423428i	0.399532	+	0.916719i	$0.369173\pi$
$284$		0			0
$285$	−17.1383	+	4.26906i	−1.01519	+	0.252877i
$286$		0			0
$287$	15.2887	−	5.56463i	0.902463	−	0.328470i
$288$		0			0
$289$	36.1355	−	30.3213i	2.12562	−	1.78360i
$290$		0			0
$291$	−2.94776	−	16.7176i	−0.172801	−	0.980003i
$292$		0			0
$293$	−15.6339	+	27.0787i	−0.913341	+	1.58195i	−0.104029	+	0.994574i	$0.533173\pi$
$293$	−15.6339	+	27.0787i	−0.913341	+	1.58195i	−0.809312	+	0.587379i	$0.800160\pi$
$294$		0			0
$295$	−27.5194	−	10.0162i	−1.60224	−	0.583168i
$296$		0			0
$297$	0.455725	+	0.789338i	0.0264438	+	0.0458020i
$298$		0			0
$299$	−11.6139	−	9.74526i	−0.671652	−	0.563583i
$300$		0			0
$301$	4.75407	−	26.9617i	0.274020	−	1.55405i
$302$		0			0
$303$	0.499841			0.0287151
$304$		0			0
$305$	−32.7970			−1.87795
$306$		0			0
$307$	−4.55177	+	25.8144i	−0.259783	+	1.47330i	0.523706	+	0.851899i	$0.324549\pi$
$307$	−4.55177	+	25.8144i	−0.259783	+	1.47330i	−0.783489	+	0.621405i	$0.786562\pi$
$308$		0			0
$309$	6.22778	+	5.22573i	0.354286	+	0.297281i
$310$		0			0
$311$	9.44510	+	16.3594i	0.535583	+	0.927656i	0.999135	+	0.0415867i	$0.0132413\pi$
$311$	9.44510	+	16.3594i	0.535583	+	0.927656i	−0.463552	+	0.886070i	$0.653425\pi$
$312$		0			0
$313$	−14.4177	−	5.24761i	−0.814936	−	0.296612i	−0.0992746	−	0.995060i	$-0.531652\pi$
$313$	−14.4177	−	5.24761i	−0.814936	−	0.296612i	−0.715661	+	0.698448i	$0.753874\pi$
$314$		0			0
$315$	−7.43005	+	12.8692i	−0.418636	+	0.725099i
$316$		0			0
$317$	3.47368	+	19.7002i	0.195101	+	1.10647i	0.912274	+	0.409580i	$0.134325\pi$
$317$	3.47368	+	19.7002i	0.195101	+	1.10647i	−0.717173	+	0.696895i	$0.754564\pi$
$318$		0			0
$319$	−3.73310	+	3.13244i	−0.209013	+	0.175383i
$320$		0			0
$321$	3.40216	−	1.23829i	0.189890	−	0.0691144i
$322$		0			0
$323$	34.7258	+	3.65755i	1.93220	+	0.203512i
$324$		0			0
$325$	−23.9444	+	8.71506i	−1.32820	+	0.483425i
$326$		0			0
$327$	3.64861	−	3.06155i	0.201768	−	0.169304i
$328$		0			0
$329$	5.54142	+	31.4270i	0.305509	+	1.73263i
$330$		0			0
$331$	−10.1822	+	17.6362i	−0.559667	+	0.969372i	0.437857	+	0.899045i	$0.355738\pi$
$331$	−10.1822	+	17.6362i	−0.559667	+	0.969372i	−0.997524	+	0.0703270i	$0.977596\pi$
$332$		0			0
$333$	5.21374	+	1.89764i	0.285711	+	0.103990i
$334$		0			0
$335$	−12.7057	−	22.0070i	−0.694188	−	1.20237i
$336$		0			0
$337$	0.946086	+	0.793860i	0.0515366	+	0.0432443i	0.668192	−	0.743989i	$-0.267068\pi$
$337$	0.946086	+	0.793860i	0.0515366	+	0.0432443i	−0.616656	+	0.787233i	$0.711513\pi$
$338$		0			0
$339$	1.80184	−	10.2187i	0.0978625	−	0.555006i
$340$		0			0
$341$	−0.748247			−0.0405199
$342$		0			0
$343$	2.01766			0.108943
$344$		0			0
$345$	−4.78013	+	27.1094i	−0.257353	+	1.45952i
$346$		0			0
$347$	6.57129	+	5.51397i	0.352765	+	0.296005i	0.801899	−	0.597459i	$-0.203823\pi$
$347$	6.57129	+	5.51397i	0.352765	+	0.296005i	−0.449134	+	0.893464i	$0.648267\pi$
$348$		0			0
$349$	−2.00915	−	3.47996i	−0.107548	−	0.186278i	0.807229	−	0.590239i	$-0.200966\pi$
$349$	−2.00915	−	3.47996i	−0.107548	−	0.186278i	−0.914776	+	0.403961i	$0.867633\pi$
$350$		0			0
$351$	2.09703	+	0.763258i	0.111931	+	0.0407397i
$352$		0			0
$353$	7.24610	−	12.5506i	0.385671	−	0.668001i	−0.606191	−	0.795319i	$-0.707303\pi$
$353$	7.24610	−	12.5506i	0.385671	−	0.668001i	0.991862	+	0.127317i	$0.0406367\pi$
$354$		0			0
$355$	−9.34096	−	52.9752i	−0.495766	−	2.81163i
$356$		0			0
$357$	22.5052	−	18.8841i	1.19110	−	0.999455i
$358$		0			0
$359$	14.3741	−	5.23176i	0.758638	−	0.276122i	0.0664023	−	0.997793i	$-0.478848\pi$
$359$	14.3741	−	5.23176i	0.758638	−	0.276122i	0.692236	+	0.721671i	$0.256626\pi$
$360$		0			0
$361$	11.6910	+	14.9773i	0.615315	+	0.788281i
$362$		0			0
$363$	−9.55598	+	3.47809i	−0.501559	+	0.182552i
$364$		0			0
$365$	−4.63951	+	3.89301i	−0.242843	+	0.203769i
$366$		0			0
$367$	6.20757	+	35.2049i	0.324032	+	1.83768i	0.516389	+	0.856354i	$0.327276\pi$
$367$	6.20757	+	35.2049i	0.324032	+	1.83768i	−0.192357	+	0.981325i	$0.561613\pi$
$368$		0			0
$369$	−2.21817	+	3.84199i	−0.115474	+	0.200006i
$370$		0			0
$371$	−35.3973	−	12.8836i	−1.83774	−	0.668882i
$372$		0			0
$373$	−6.44674	−	11.1661i	−0.333800	−	0.578158i	0.649454	−	0.760401i	$-0.274998\pi$
$373$	−6.44674	−	11.1661i	−0.333800	−	0.578158i	−0.983254	+	0.182243i	$0.941664\pi$
$374$		0			0
$375$	19.9220	+	16.7165i	1.02877	+	0.863239i
$376$		0			0
$377$	−2.07192	+	11.7504i	−0.106709	+	0.605179i
$378$		0			0
$379$	24.3960			1.25314			0.626570	−	0.779366i	$-0.284458\pi$
$379$	24.3960			1.25314			0.626570	+	0.779366i	$0.284458\pi$
$380$		0			0
$381$	1.05738			0.0541711
$382$		0			0
$383$	5.28541	−	29.9750i	0.270072	−	1.53165i	−0.484121	−	0.875001i	$-0.660861\pi$
$383$	5.28541	−	29.9750i	0.270072	−	1.53165i	0.754193	−	0.656653i	$-0.228028\pi$
$384$		0			0
$385$	10.3755	+	8.70606i	0.528784	+	0.443702i
$386$		0			0
$387$	3.73256	+	6.46499i	0.189737	+	0.328634i
$388$		0			0
$389$	12.8116	+	4.66305i	0.649576	+	0.236426i	0.645729	−	0.763566i	$-0.276553\pi$
$389$	12.8116	+	4.66305i	0.649576	+	0.236426i	0.00384641	+	0.999993i	$0.498776\pi$
$390$		0			0
$391$	27.2112	−	47.1311i	1.37613	−	2.38352i
$392$		0			0
$393$	1.32747	+	7.52846i	0.0669620	+	0.379761i
$394$		0			0
$395$	19.8908	−	16.6904i	1.00082	−	0.839784i
$396$		0			0
$397$	−3.33245	+	1.21291i	−0.167251	+	0.0608744i	−0.424289	−	0.905527i	$-0.639476\pi$
$397$	−3.33245	+	1.21291i	−0.167251	+	0.0608744i	0.257038	+	0.966401i	$0.417254\pi$
$398$		0			0
$399$	15.8979	+	1.67447i	0.795890	+	0.0838284i
$400$		0			0
$401$	−19.1566	+	6.97243i	−0.956635	+	0.348186i	−0.772714	−	0.634755i	$-0.781101\pi$
$401$	−19.1566	+	6.97243i	−0.956635	+	0.348186i	−0.183921	+	0.982941i	$0.558879\pi$
$402$		0			0
$403$	−1.40342	+	1.17761i	−0.0699091	+	0.0586607i
$404$		0			0
$405$	−0.703612	−	3.99038i	−0.0349628	−	0.198284i
$406$		0			0
$407$	2.52852	−	4.37952i	0.125334	−	0.217085i
$408$		0			0
$409$	−32.4084	−	11.7957i	−1.60249	−	0.583259i	−0.622555	−	0.782576i	$-0.713905\pi$
$409$	−32.4084	−	11.7957i	−1.60249	−	0.583259i	−0.979935	+	0.199317i	$0.936128\pi$
$410$		0			0
$411$	1.41173	+	2.44519i	0.0696356	+	0.120612i
$412$		0			0
$413$	20.3050	+	17.0379i	0.999141	+	0.838379i
$414$		0			0
$415$	−0.117060	+	0.663881i	−0.00574626	+	0.0325887i
$416$		0			0
$417$	6.67368			0.326811
$418$		0			0
$419$	−25.4521			−1.24342			−0.621709	−	0.783248i	$-0.713561\pi$
$419$	−25.4521			−1.24342			−0.621709	+	0.783248i	$0.713561\pi$
$420$		0			0
$421$	3.48515	−	19.7652i	0.169856	−	0.963299i	−0.774060	−	0.633112i	$-0.781777\pi$
$421$	3.48515	−	19.7652i	0.169856	−	0.963299i	0.943916	−	0.330187i	$-0.107112\pi$
$422$		0			0
$423$	−6.66571	−	5.59320i	−0.324098	−	0.271951i
$424$		0			0
$425$	−45.7341	−	79.2138i	−2.21843	−	3.84243i
$426$		0			0
$427$	27.8943	+	10.1527i	1.34990	+	0.491323i
$428$		0			0
$429$	1.01700	−	1.76150i	0.0491014	−	0.0850461i
$430$		0			0
$431$	3.40991	+	19.3385i	0.164249	+	0.931505i	0.949835	+	0.312752i	$0.101251\pi$
$431$	3.40991	+	19.3385i	0.164249	+	0.931505i	−0.785585	+	0.618753i	$0.787638\pi$
$432$		0			0
$433$	−6.34981	+	5.32813i	−0.305153	+	0.256053i	−0.782485	−	0.622669i	$-0.786048\pi$
$433$	−6.34981	+	5.32813i	−0.305153	+	0.256053i	0.477333	+	0.878723i	$0.341604\pi$
$434$		0			0
$435$	20.3579	−	7.40965i	0.976085	−	0.355266i
$436$		0			0
$437$	28.7350	−	7.15772i	1.37458	−	0.342400i
$438$		0			0
$439$	4.20702	−	1.53123i	0.200790	−	0.0730816i	−0.239667	−	0.970855i	$-0.577038\pi$
$439$	4.20702	−	1.53123i	0.200790	−	0.0730816i	0.440458	+	0.897773i	$0.354816\pi$
$440$		0			0
$441$	4.94086	−	4.14588i	0.235279	−	0.197423i
$442$		0			0
$443$	−5.84317	−	33.1383i	−0.277617	−	1.57445i	−0.730523	−	0.682888i	$-0.760724\pi$
$443$	−5.84317	−	33.1383i	−0.277617	−	1.57445i	0.452905	−	0.891559i	$-0.350388\pi$
$444$		0			0
$445$	−19.5696	+	33.8956i	−0.927689	+	1.60681i
$446$		0			0
$447$	−5.05567	−	1.84011i	−0.239125	−	0.0870343i
$448$		0			0
$449$	0.0954662	+	0.165352i	0.00450533	+	0.00780346i	0.868269	−	0.496093i	$-0.165233\pi$
$449$	0.0954662	+	0.165352i	0.00450533	+	0.00780346i	−0.863764	+	0.503897i	$0.831899\pi$
$450$		0			0
$451$	3.09751	+	2.59912i	0.145856	+	0.122388i
$452$		0			0
$453$	−1.45174	+	8.23322i	−0.0682086	+	0.386830i
$454$		0			0
$455$	33.1621			1.55466
$456$		0			0
$457$	41.3845			1.93589			0.967943	−	0.251168i	$-0.0808148\pi$
$457$	41.3845			1.93589			0.967943	+	0.251168i	$0.0808148\pi$
$458$		0			0
$459$	−1.39105	+	7.88901i	−0.0649285	+	0.368228i
$460$		0			0
$461$	6.29047	+	5.27833i	0.292977	+	0.245837i	0.777414	−	0.628989i	$-0.216531\pi$
$461$	6.29047	+	5.27833i	0.292977	+	0.245837i	−0.484437	+	0.874826i	$0.660976\pi$
$462$		0			0
$463$	−5.05869	−	8.76191i	−0.235097	−	0.407201i	0.724204	−	0.689586i	$-0.242208\pi$
$463$	−5.05869	−	8.76191i	−0.235097	−	0.407201i	−0.959301	+	0.282386i	$0.908874\pi$
$464$		0			0
$465$	3.12580	+	1.13770i	0.144956	+	0.0527596i
$466$		0			0
$467$	9.56211	−	16.5621i	0.442482	−	0.766401i	−0.555391	−	0.831589i	$-0.687432\pi$
$467$	9.56211	−	16.5621i	0.442482	−	0.766401i	0.997873	+	0.0651884i	$0.0207649\pi$
$468$		0			0
$469$	3.99388	+	22.6504i	0.184420	+	1.04590i
$470$		0			0
$471$	−7.17406	+	6.01975i	−0.330563	+	0.277375i
$472$		0			0
$473$	6.39374	−	2.32713i	0.293985	−	0.107002i
$474$		0			0
$475$	13.7293	−	47.8399i	0.629941	−	2.19504i
$476$		0			0
$477$	9.65188	−	3.51300i	0.441929	−	0.160849i
$478$		0			0
$479$	2.65387	−	2.22686i	0.121259	−	0.101748i	−0.580142	−	0.814515i	$-0.697003\pi$
$479$	2.65387	−	2.22686i	0.121259	−	0.101748i	0.701401	+	0.712767i	$0.252558\pi$
$480$		0			0
$481$	−2.15007	−	12.1937i	−0.0980349	−	0.555984i
$482$		0			0
$483$	12.4576	−	21.5772i	0.566841	−	0.981797i
$484$		0			0
$485$	64.6356	+	23.5254i	2.93495	+	1.06823i
$486$		0			0
$487$	18.6063	+	32.2270i	0.843130	+	1.46034i	0.887235	+	0.461318i	$0.152623\pi$
$487$	18.6063	+	32.2270i	0.843130	+	1.46034i	−0.0441047	+	0.999027i	$0.514044\pi$
$488$		0			0
$489$	−0.385438	−	0.323421i	−0.0174301	−	0.0146256i
$490$		0			0
$491$	−4.78583	+	27.1418i	−0.215982	+	1.22489i	0.663213	+	0.748430i	$0.269192\pi$
$491$	−4.78583	+	27.1418i	−0.215982	+	1.22489i	−0.879195	+	0.476462i	$0.841919\pi$
$492$		0			0
$493$	−42.8306			−1.92899
$494$		0			0
$495$	−3.69314			−0.165994
$496$		0			0
$497$	−8.45447	+	47.9477i	−0.379235	+	2.15075i
$498$		0			0
$499$	−8.36668	−	7.02047i	−0.374544	−	0.314280i	0.436012	−	0.899941i	$-0.356390\pi$
$499$	−8.36668	−	7.02047i	−0.374544	−	0.314280i	−0.810556	+	0.585661i	$0.800835\pi$
$500$		0			0
$501$	−4.34728	−	7.52971i	−0.194222	−	0.336403i
$502$		0			0
$503$	−6.06410	−	2.20715i	−0.270385	−	0.0984121i	0.203270	−	0.979123i	$-0.434843\pi$
$503$	−6.06410	−	2.20715i	−0.270385	−	0.0984121i	−0.473655	+	0.880711i	$0.657065\pi$
$504$		0			0
$505$	−1.01266	+	1.75398i	−0.0450629	+	0.0780513i
$506$		0			0
$507$	1.39264	+	7.89804i	0.0618492	+	0.350764i
$508$		0			0
$509$	−22.5912	+	18.9562i	−1.00134	+	0.840220i	−0.987169	−	0.159680i	$-0.948954\pi$
$509$	−22.5912	+	18.9562i	−1.00134	+	0.840220i	−0.0141662	+	0.999900i	$0.504509\pi$
$510$		0			0
$511$	5.15109	−	1.87484i	0.227871	−	0.0829382i
$512$		0			0
$513$	−3.61423	+	2.43667i	−0.159572	+	0.107582i
$514$		0			0
$515$	−30.9548	+	11.2666i	−1.36403	+	0.496467i
$516$		0			0
$517$	−6.07546	+	5.09792i	−0.267198	+	0.224206i
$518$		0			0
$519$	−0.521575	−	2.95800i	−0.0228946	−	0.129842i
$520$		0			0
$521$	1.31707	−	2.28123i	0.0577019	−	0.0999426i	−0.835732	−	0.549138i	$-0.814956\pi$
$521$	1.31707	−	2.28123i	0.0577019	−	0.0999426i	0.893433	+	0.449196i	$0.148289\pi$
$522$		0			0
$523$	37.5498	+	13.6670i	1.64194	+	0.597616i	0.987376	−	0.158392i	$-0.0506310\pi$
$523$	37.5498	+	13.6670i	1.64194	+	0.597616i	0.654562	+	0.756009i	$0.272853\pi$
$524$		0			0
$525$	−20.9376	−	36.2650i	−0.913793	−	1.58274i
$526$		0			0
$527$	−5.03776	−	4.22719i	−0.219448	−	0.184139i
$528$		0			0
$529$	4.02070	−	22.8025i	0.174813	−	0.991414i
$530$		0			0
$531$	−7.22752			−0.313648
$532$		0			0
$533$	9.90024			0.428827
$534$		0			0
$535$	−2.54743	+	14.4472i	−0.110135	+	0.624608i
$536$		0			0
$537$	−12.8929	−	10.8184i	−0.556370	−	0.466850i
$538$		0			0
$539$	−2.93935	−	5.09110i	−0.126607	−	0.219289i
$540$		0			0
$541$	−20.6053	−	7.49971i	−0.885890	−	0.322438i	−0.141306	−	0.989966i	$-0.545130\pi$
$541$	−20.6053	−	7.49971i	−0.885890	−	0.322438i	−0.744584	+	0.667528i	$0.767352\pi$
$542$		0			0
$543$	2.46401	−	4.26779i	0.105741	−	0.183149i
$544$		0			0
$545$	3.35125	+	19.0059i	0.143552	+	0.814122i
$546$		0			0
$547$	−1.25868	+	1.05616i	−0.0538173	+	0.0451581i	−0.669300	−	0.742993i	$-0.733406\pi$
$547$	−1.25868	+	1.05616i	−0.0538173	+	0.0451581i	0.615482	+	0.788151i	$0.288961\pi$
$548$		0			0
$549$	−7.60600	+	2.76836i	−0.324616	+	0.118151i
$550$		0			0
$551$	−16.1857	−	16.7682i	−0.689535	−	0.714349i
$552$		0			0
$553$	−22.0841	+	8.03795i	−0.939111	+	0.341809i
$554$		0			0
$555$	−17.2219	+	14.4509i	−0.731028	+	0.613405i
$556$		0			0
$557$	−3.95731	−	22.4430i	−0.167677	−	0.950941i	−0.946262	−	0.323402i	$-0.895173\pi$
$557$	−3.95731	−	22.4430i	−0.167677	−	0.950941i	0.778585	−	0.627539i	$-0.215938\pi$
$558$		0			0
$559$	8.32965	−	14.4274i	0.352307	−	0.610213i
$560$		0			0
$561$	6.86103	+	2.49721i	0.289673	+	0.105432i
$562$		0			0
$563$	18.7833	+	32.5337i	0.791624	+	1.37113i	0.924961	+	0.380062i	$0.124097\pi$
$563$	18.7833	+	32.5337i	0.791624	+	1.37113i	−0.133337	+	0.991071i	$0.542569\pi$
$564$		0			0
$565$	32.2079	+	27.0257i	1.35500	+	1.13698i
$566$		0			0
$567$	−0.636838	+	3.61169i	−0.0267447	+	0.151677i
$568$		0			0
$569$	4.37557			0.183433			0.0917167	−	0.995785i	$-0.470765\pi$
$569$	4.37557			0.183433			0.0917167	+	0.995785i	$0.470765\pi$
$570$		0			0
$571$	10.3397			0.432703			0.216351	−	0.976316i	$-0.430584\pi$
$571$	10.3397			0.432703			0.216351	+	0.976316i	$0.430584\pi$
$572$		0			0
$573$	−0.709062	+	4.02129i	−0.0296215	+	0.167992i
$574$		0			0
$575$	−59.4236	−	49.8623i	−2.47814	−	2.07940i
$576$		0			0
$577$	−18.7355	−	32.4508i	−0.779968	−	1.35094i	−0.931960	−	0.362562i	$-0.881902\pi$
$577$	−18.7355	−	32.4508i	−0.779968	−	1.35094i	0.151992	−	0.988382i	$-0.451431\pi$
$578$		0			0
$579$	1.56573	+	0.569878i	0.0650693	+	0.0236833i
$580$		0			0
$581$	0.305073	−	0.528403i	0.0126566	−	0.0219218i
$582$		0			0
$583$	−1.62566	−	9.21955i	−0.0673278	−	0.381835i
$584$		0			0
$585$	−6.92687	+	5.81233i	−0.286391	+	0.240310i
$586$		0			0
$587$	11.5162	−	4.19155i	0.475325	−	0.173004i	−0.0932383	−	0.995644i	$-0.529722\pi$
$587$	11.5162	−	4.19155i	0.475325	−	0.173004i	0.568563	+	0.822640i	$0.307500\pi$
$588$		0			0
$589$	−0.248832	−	3.56974i	−0.0102529	−	0.147089i
$590$		0			0
$591$	−17.3236	+	6.30528i	−0.712598	+	0.259365i
$592$		0			0
$593$	−8.65810	+	7.26501i	−0.355546	+	0.298338i	−0.803012	−	0.595962i	$-0.796771\pi$
$593$	−8.65810	+	7.26501i	−0.355546	+	0.298338i	0.447467	+	0.894301i	$0.352326\pi$
$594$		0			0
$595$	20.6711	+	117.232i	0.847432	+	4.80602i
$596$		0			0
$597$	0.135455	−	0.234614i	0.00554379	−	0.00960213i
$598$		0			0
$599$	−20.7405	−	7.54894i	−0.847435	−	0.308441i	−0.118441	−	0.992961i	$-0.537790\pi$
$599$	−20.7405	−	7.54894i	−0.847435	−	0.308441i	−0.728994	+	0.684520i	$0.760012\pi$
$600$		0			0
$601$	7.77031	+	13.4586i	0.316958	+	0.548987i	0.979852	−	0.199726i	$-0.0640053\pi$
$601$	7.77031	+	13.4586i	0.316958	+	0.548987i	−0.662894	+	0.748713i	$0.730672\pi$
$602$		0			0
$603$	−4.80419	−	4.03120i	−0.195642	−	0.164163i
$604$		0			0
$605$	7.15522	−	40.5793i	0.290901	−	1.64978i
$606$		0			0
$607$	1.74786			0.0709436			0.0354718	−	0.999371i	$-0.488707\pi$
$607$	1.74786			0.0709436			0.0354718	+	0.999371i	$0.488707\pi$
$608$		0			0
$609$	−19.6084			−0.794571
$610$		0			0
$611$	−3.37196	+	19.1233i	−0.136415	+	0.773648i
$612$		0			0
$613$	7.75780	+	6.50957i	0.313335	+	0.262919i	0.785869	−	0.618394i	$-0.212216\pi$
$613$	7.75780	+	6.50957i	0.313335	+	0.262919i	−0.472534	+	0.881312i	$0.656661\pi$
$614$		0			0
$615$	−8.98792	−	15.5675i	−0.362428	−	0.627743i
$616$		0			0
$617$	25.1687	+	9.16067i	1.01325	+	0.368795i	0.794682	−	0.607026i	$-0.207638\pi$
$617$	25.1687	+	9.16067i	1.01325	+	0.368795i	0.218573	+	0.975821i	$0.429860\pi$
$618$		0			0
$619$	−14.4031	+	24.9469i	−0.578910	+	1.00270i	0.416694	+	0.909047i	$0.363189\pi$
$619$	−14.4031	+	24.9469i	−0.578910	+	1.00270i	−0.995605	+	0.0936554i	$0.970145\pi$
$620$		0			0
$621$	1.17971	+	6.69048i	0.0473402	+	0.268480i
$622$		0			0
$623$	27.1370	−	22.7706i	1.08722	−	0.912287i
$624$		0			0
$625$	−45.3730	+	16.5144i	−1.81492	+	0.660577i
$626$		0			0
$627$	1.61513	+	3.62979i	0.0645022	+	0.144960i
$628$		0			0
$629$	41.7657	−	15.2015i	1.66531	−	0.606123i
$630$		0			0
$631$	31.8615	−	26.7350i	1.26839	−	1.06430i	0.273651	−	0.961829i	$-0.411769\pi$
$631$	31.8615	−	26.7350i	1.26839	−	1.06430i	0.994736	−	0.102474i	$-0.0326757\pi$
$632$		0			0
$633$	−3.91831	−	22.2218i	−0.155739	−	0.883239i
$634$		0			0
$635$	−2.14222	+	3.71043i	−0.0850113	+	0.147244i
$636$		0			0
$637$	−13.5255	−	4.92289i	−0.535901	−	0.195052i
$638$		0			0
$639$	−6.63786	−	11.4971i	−0.262590	−	0.454818i
$640$		0			0
$641$	9.64560	+	8.09362i	0.380978	+	0.319679i	0.813086	−	0.582143i	$-0.197786\pi$
$641$	9.64560	+	8.09362i	0.380978	+	0.319679i	−0.432108	+	0.901822i	$0.642230\pi$
$642$		0			0
$643$	−0.824516	+	4.67606i	−0.0325157	+	0.184406i	−0.996740	−	0.0806825i	$-0.974290\pi$
$643$	−0.824516	+	4.67606i	−0.0325157	+	0.184406i	0.964224	+	0.265088i	$0.0854011\pi$
$644$		0			0
$645$	−30.2482			−1.19102
$646$		0			0
$647$	−7.67738			−0.301829			−0.150914	−	0.988547i	$-0.548222\pi$
$647$	−7.67738			−0.301829			−0.150914	+	0.988547i	$0.548222\pi$
$648$		0			0
$649$	−1.14391	+	6.48744i	−0.0449024	+	0.254654i
$650$		0			0
$651$	−2.30635	−	1.93526i	−0.0903930	−	0.0758487i
$652$		0			0
$653$	7.76920	+	13.4566i	0.304032	+	0.526599i	0.977045	−	0.213031i	$-0.0683336\pi$
$653$	7.76920	+	13.4566i	0.304032	+	0.526599i	−0.673013	+	0.739630i	$0.735000\pi$
$654$		0			0
$655$	−29.1074	−	10.5942i	−1.13732	−	0.413951i
$656$		0			0
$657$	−0.747351	+	1.29445i	−0.0291569	+	0.0505013i
$658$		0			0
$659$	−4.02235	−	22.8119i	−0.156688	−	0.888624i	−0.957226	−	0.289342i	$-0.906564\pi$
$659$	−4.02235	−	22.8119i	−0.156688	−	0.888624i	0.800537	−	0.599283i	$-0.204547\pi$
$660$		0			0
$661$	−0.817662	+	0.686100i	−0.0318034	+	0.0266862i	−0.658551	−	0.752536i	$-0.728830\pi$
$661$	−0.817662	+	0.686100i	−0.0318034	+	0.0266862i	0.626747	+	0.779222i	$0.284386\pi$
$662$		0			0
$663$	16.7987	−	6.11424i	0.652409	−	0.237458i
$664$		0			0
$665$	−38.0845	+	52.3946i	−1.47686	+	2.03178i
$666$		0			0
$667$	−34.1330	+	12.4234i	−1.32164	+	0.481036i
$668$		0			0
$669$	2.29734	−	1.92770i	0.0888204	−	0.0745292i
$670$		0			0
$671$	1.28107	+	7.26532i	0.0494552	+	0.280474i
$672$		0			0
$673$	13.0158	−	22.5440i	0.501723	−	0.869009i	−0.498275	−	0.867019i	$-0.666033\pi$
$673$	13.0158	−	22.5440i	0.501723	−	0.869009i	0.999998	−	0.00199028i	$-0.000633527\pi$
$674$		0			0
$675$	10.7296	+	3.90527i	0.412984	+	0.150314i
$676$		0			0
$677$	−9.78787	−	16.9531i	−0.376178	−	0.651560i	0.614324	−	0.789054i	$-0.289429\pi$
$677$	−9.78787	−	16.9531i	−0.376178	−	0.651560i	−0.990503	+	0.137494i	$0.956095\pi$
$678$		0			0
$679$	−47.6908	−	40.0174i	−1.83021	−	1.53573i
$680$		0			0
$681$	−1.56826	+	8.89402i	−0.0600957	+	0.340819i
$682$		0			0
$683$	−30.0261			−1.14892			−0.574459	−	0.818533i	$-0.694787\pi$
$683$	−30.0261			−1.14892			−0.574459	+	0.818533i	$0.694787\pi$
$684$		0			0
$685$	−11.4405			−0.437119
$686$		0			0
$687$	4.94139	−	28.0240i	0.188526	−	1.06918i
$688$		0			0
$689$	−17.5590	−	14.7337i	−0.668945	−	0.561311i
$690$		0			0
$691$	13.9796	+	24.2133i	0.531808	+	0.921118i	0.999311	+	0.0371267i	$0.0118205\pi$
$691$	13.9796	+	24.2133i	0.531808	+	0.921118i	−0.467503	+	0.883992i	$0.654846\pi$
$692$		0			0
$693$	3.14106	+	1.14325i	0.119319	+	0.0434286i
$694$		0			0
$695$	−13.5207	+	23.4185i	−0.512869	+	0.888314i
$696$		0			0
$697$	6.17117	+	34.9984i	0.233750	+	1.32566i
$698$		0			0
$699$	10.7597	−	9.02848i	0.406970	−	0.341488i
$700$		0			0
$701$	5.85606	−	2.13143i	0.221180	−	0.0805031i	−0.229053	−	0.973414i	$-0.573563\pi$
$701$	5.85606	−	2.13143i	0.221180	−	0.0805031i	0.450234	+	0.892911i	$0.351341\pi$
$702$		0			0
$703$	21.7347	+	10.6066i	0.819740	+	0.400037i
$704$		0			0
$705$	33.1315	−	12.0589i	1.24781	−	0.454164i
$706$		0			0
$707$	1.40425	−	1.17831i	0.0528122	−	0.0443147i
$708$		0			0
$709$	8.01044	+	45.4295i	0.300838	+	1.70614i	0.642475	+	0.766307i	$0.277908\pi$
$709$	8.01044	+	45.4295i	0.300838	+	1.70614i	−0.341636	+	0.939832i	$0.610981\pi$
$710$		0			0
$711$	3.20409	−	5.54965i	0.120163	−	0.208128i
$712$		0			0
$713$	−5.24088	−	1.90753i	−0.196273	−	0.0714374i
$714$		0			0
$715$	4.12084	+	7.13750i	0.154111	+	0.266927i
$716$		0			0
$717$	−5.21287	−	4.37412i	−0.194678	−	0.163355i
$718$		0			0
$719$	6.14153	−	34.8303i	0.229040	−	1.29895i	−0.625768	−	0.780009i	$-0.715214\pi$
$719$	6.14153	−	34.8303i	0.229040	−	1.29895i	0.854809	−	0.518943i	$-0.173674\pi$
$720$		0			0
$721$	29.8152			1.11038
$722$		0			0
$723$	−6.29139			−0.233979
$724$		0			0
$725$	−10.6011	+	60.1220i	−0.393716	+	2.23288i
$726$		0			0
$727$	−4.44311	−	3.72822i	−0.164786	−	0.138272i	0.556666	−	0.830737i	$-0.312080\pi$
$727$	−4.44311	−	3.72822i	−0.164786	−	0.138272i	−0.721452	+	0.692465i	$0.756525\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$		0			0
$731$	56.1945	+	20.4531i	2.07843	+	0.756487i
$732$		0			0
$733$	5.53539	−	9.58757i	0.204454	−	0.354125i	−0.745504	−	0.666501i	$-0.767791\pi$
$733$	5.53539	−	9.58757i	0.204454	−	0.354125i	0.949959	+	0.312376i	$0.101125\pi$
$734$		0			0
$735$	4.53819	+	25.7373i	0.167394	+	0.949336i
$736$		0			0
$737$	−4.37878	+	3.67423i	−0.161294	+	0.135342i
$738$		0			0
$739$	−28.1480	+	10.2450i	−1.03544	+	0.376870i	−0.803151	−	0.595776i	$-0.796845\pi$
$739$	−28.1480	+	10.2450i	−1.03544	+	0.376870i	−0.232292	+	0.972646i	$0.574622\pi$
$740$		0			0
$741$	8.74199	+	4.26613i	0.321145	+	0.156720i
$742$		0			0
$743$	−49.6848	+	18.0838i	−1.82276	+	0.663430i	−0.828057	+	0.560644i	$0.810553\pi$
$743$	−49.6848	+	18.0838i	−1.82276	+	0.663430i	−0.994703	+	0.102786i	$0.967224\pi$
$744$		0			0
$745$	16.6997	−	14.0127i	0.611831	−	0.513387i
$746$		0			0
$747$	0.0288899	+	0.163843i	0.00105703	+	0.00599469i
$748$		0			0
$749$	6.63893	−	11.4990i	0.242581	−	0.420163i
$750$		0			0
$751$	29.0951	+	10.5898i	1.06170	+	0.386426i	0.813065	−	0.582172i	$-0.197797\pi$
$751$	29.0951	+	10.5898i	1.06170	+	0.386426i	0.248631	+	0.968598i	$0.420019\pi$
$752$		0			0
$753$	−7.08862	−	12.2779i	−0.258324	−	0.447430i
$754$		0			0
$755$	−25.9499	−	21.7745i	−0.944413	−	0.792456i
$756$		0			0
$757$	6.93777	−	39.3460i	0.252157	−	1.43006i	−0.551107	−	0.834434i	$-0.685795\pi$
$757$	6.93777	−	39.3460i	0.252157	−	1.43006i	0.803265	−	0.595622i	$-0.203094\pi$
$758$		0			0
$759$	6.19211			0.224759
$760$		0			0
$761$	18.7341			0.679111			0.339555	−	0.940586i	$-0.389723\pi$
$761$	18.7341			0.679111			0.339555	+	0.940586i	$0.389723\pi$
$762$		0			0
$763$	3.03321	−	17.2022i	0.109809	−	0.622760i
$764$		0			0
$765$	−24.8650	−	20.8642i	−0.898996	−	0.754347i
$766$		0			0
$767$	8.06453	+	13.9682i	0.291193	+	0.504362i
$768$		0			0
$769$	23.5914	+	8.58655i	0.850726	+	0.309639i	0.730336	−	0.683088i	$-0.239363\pi$
$769$	23.5914	+	8.58655i	0.850726	+	0.309639i	0.120390	+	0.992727i	$0.461586\pi$
$770$		0			0
$771$	−11.1232	+	19.2659i	−0.400592	+	0.693846i
$772$		0			0
$773$	−4.78337	−	27.1278i	−0.172046	−	0.975721i	−0.941499	−	0.337017i	$-0.890582\pi$
$773$	−4.78337	−	27.1278i	−0.172046	−	0.975721i	0.769453	−	0.638704i	$-0.220529\pi$
$774$		0			0
$775$	−7.18068	+	6.02531i	−0.257938	+	0.216435i
$776$		0			0
$777$	19.1209	−	6.95943i	0.685957	−	0.249668i
$778$		0			0
$779$	−11.3698	+	15.6419i	−0.407365	+	0.560431i
$780$		0			0
$781$	−11.3704	+	4.13849i	−0.406865	+	0.148087i
$782$		0			0
$783$	4.09578	−	3.43677i	0.146371	−	0.122820i
$784$		0			0
$785$	−6.58938	−	37.3702i	−0.235185	−	1.33380i
$786$		0			0
$787$	−21.6567	+	37.5105i	−0.771978	+	1.33711i	0.164499	+	0.986377i	$0.447399\pi$
$787$	−21.6567	+	37.5105i	−0.771978	+	1.33711i	−0.936477	+	0.350728i	$0.885934\pi$
$788$		0			0
$789$	−2.07132	−	0.753898i	−0.0737409	−	0.0268395i
$790$		0			0
$791$	−19.0272	−	32.9560i	−0.676529	−	1.17178i
$792$		0			0
$793$	13.8371	+	11.6107i	0.491369	+	0.412308i
$794$		0			0
$795$	−7.22702	+	40.9865i	−0.256316	+	1.45364i
$796$		0			0
$797$	−28.2922			−1.00216			−0.501081	−	0.865401i	$-0.667064\pi$
$797$	−28.2922			−1.00216			−0.501081	+	0.865401i	$0.667064\pi$
$798$		0			0
$799$	−69.7050			−2.46599
$800$		0			0
$801$	−1.67733	+	9.51263i	−0.0592657	+	0.336112i
$802$		0			0
$803$	1.04362	+	0.875699i	0.0368284	+	0.0309027i
$804$		0			0
$805$	50.4775	+	87.4296i	1.77910	+	3.08149i
$806$		0			0
$807$	24.5098	+	8.92083i	0.862785	+	0.314028i
$808$		0			0
$809$	−24.1854	+	41.8903i	−0.850313	+	1.47278i	0.0306136	+	0.999531i	$0.490254\pi$
$809$	−24.1854	+	41.8903i	−0.850313	+	1.47278i	−0.880926	+	0.473253i	$0.843079\pi$
$810$		0			0
$811$	−5.10284	−	28.9397i	−0.179185	−	1.01621i	−0.933202	−	0.359353i	$-0.882997\pi$
$811$	−5.10284	−	28.9397i	−0.179185	−	1.01621i	0.754016	−	0.656856i	$-0.228114\pi$
$812$		0			0
$813$	−11.6763	+	9.79756i	−0.409505	+	0.343615i
$814$		0			0
$815$	1.91580	−	0.697293i	0.0671074	−	0.0244251i
$816$		0			0
$817$	13.2286	+	29.7294i	0.462809	+	1.04010i
$818$		0			0
$819$	7.69067	−	2.79918i	0.268734	−	0.0978111i
$820$		0			0
$821$	9.46072	−	7.93849i	0.330181	−	0.277055i	−0.462592	−	0.886571i	$-0.653081\pi$
$821$	9.46072	−	7.93849i	0.330181	−	0.277055i	0.792774	+	0.609516i	$0.208636\pi$
$822$		0			0
$823$	0.161621	+	0.916595i	0.00563374	+	0.0319505i	0.987495	−	0.157650i	$-0.0503918\pi$
$823$	0.161621	+	0.916595i	0.00563374	+	0.0319505i	−0.981861	+	0.189601i	$0.939281\pi$
$824$		0			0
$825$	5.20357	−	9.01285i	0.181165	−	0.313787i
$826$		0			0
$827$	−12.5684	−	4.57452i	−0.437045	−	0.159072i	0.114121	−	0.993467i	$-0.463595\pi$
$827$	−12.5684	−	4.57452i	−0.437045	−	0.159072i	−0.551166	+	0.834395i	$0.685817\pi$
$828$		0			0
$829$	−7.57975	−	13.1285i	−0.263256	−	0.455972i	0.703850	−	0.710349i	$-0.251463\pi$
$829$	−7.57975	−	13.1285i	−0.263256	−	0.455972i	−0.967105	+	0.254377i	$0.918130\pi$
$830$		0			0
$831$	−0.340214	−	0.285473i	−0.0118019	−	0.00990295i
$832$		0			0
$833$	8.97202	−	50.8829i	0.310862	−	1.76299i
$834$		0			0
$835$	35.2299			1.21918
$836$		0			0
$837$	0.820942			0.0283759
$838$		0			0
$839$	−1.47532	+	8.36698i	−0.0509338	+	0.288860i	−0.999626	−	0.0273405i	$-0.991296\pi$
$839$	−1.47532	+	8.36698i	−0.0509338	+	0.288860i	0.948692	+	0.316201i	$0.102407\pi$
$840$		0			0
$841$	−0.316509	−	0.265583i	−0.0109141	−	0.00915803i
$842$		0			0
$843$	−6.87780	−	11.9127i	−0.236884	−	0.410295i
$844$		0			0
$845$	−30.5363	−	11.1143i	−1.05048	−	0.382344i
$846$		0			0
$847$	−18.6474	+	32.2982i	−0.640732	+	1.10978i
$848$		0			0
$849$	0.361652	+	2.05103i	0.0124119	+	0.0703912i
$850$		0			0
$851$	28.8751	−	24.2291i	0.989825	−	0.830562i
$852$		0			0
$853$	−24.1916	+	8.80502i	−0.828304	+	0.301478i	−0.721163	−	0.692766i	$-0.756392\pi$
$853$	−24.1916	+	8.80502i	−0.828304	+	0.301478i	−0.107142	+	0.994244i	$0.534170\pi$
$854$		0			0
$855$	−1.22817	−	17.6193i	−0.0420024	−	0.602566i
$856$		0			0
$857$	−13.9063	+	5.06149i	−0.475031	+	0.172897i	−0.568430	−	0.822732i	$-0.692449\pi$
$857$	−13.9063	+	5.06149i	−0.475031	+	0.172897i	0.0933991	+	0.995629i	$0.470227\pi$
$858$		0			0
$859$	−36.1968	+	30.3727i	−1.23502	+	1.03630i	−0.237122	+	0.971480i	$0.576204\pi$
$859$	−36.1968	+	30.3727i	−1.23502	+	1.03630i	−0.997897	+	0.0648237i	$0.979351\pi$
$860$		0			0
$861$	2.82523	+	16.0227i	0.0962837	+	0.546052i
$862$		0			0
$863$	−5.35569	+	9.27632i	−0.182310	+	0.315770i	−0.942667	−	0.333736i	$-0.891691\pi$
$863$	−5.35569	+	9.27632i	−0.182310	+	0.315770i	0.760357	+	0.649505i	$0.225024\pi$
$864$		0			0
$865$	11.4366	+	4.16257i	0.388855	+	0.141532i
$866$		0			0
$867$	23.5858	+	40.8518i	0.801015	+	1.38740i
$868$		0			0
$869$	−4.47427	−	3.75435i	−0.151779	−	0.127358i
$870$		0			0
$871$	−2.43028	+	13.7828i	−0.0823469	+	0.467013i
$872$		0			0
$873$	16.9755			0.574534
$874$		0			0
$875$	95.3757			3.22429
$876$		0			0
$877$	8.81428	−	49.9883i	0.297637	−	1.68798i	−0.358649	−	0.933472i	$-0.616763\pi$
$877$	8.81428	−	49.9883i	0.297637	−	1.68798i	0.656286	−	0.754512i	$-0.272126\pi$
$878$		0			0
$879$	−23.9525	−	20.0985i	−0.807898	−	0.677907i
$880$		0			0
$881$	−25.8312	−	44.7409i	−0.870274	−	1.50736i	−0.861713	−	0.507395i	$-0.830608\pi$
$881$	−25.8312	−	44.7409i	−0.870274	−	1.50736i	−0.00856044	−	0.999963i	$-0.502725\pi$
$882$		0			0
$883$	−8.11623	−	2.95407i	−0.273133	−	0.0994123i	0.201822	−	0.979422i	$-0.435314\pi$
$883$	−8.11623	−	2.95407i	−0.273133	−	0.0994123i	−0.474955	+	0.880010i	$0.657536\pi$
$884$		0			0
$885$	14.6428	−	25.3620i	0.492211	−	0.852534i
$886$		0			0
$887$	−2.06563	−	11.7148i	−0.0693570	−	0.393343i	−0.999648	−	0.0265212i	$-0.991557\pi$
$887$	−2.06563	−	11.7148i	−0.0693570	−	0.393343i	0.930291	−	0.366822i	$-0.119554\pi$
$888$		0			0
$889$	2.97059	−	2.49262i	0.0996304	−	0.0835998i
$890$		0			0
$891$	−0.856482	+	0.311734i	−0.0286932	+	0.0104435i
$892$		0			0
$893$	−26.3416	−	27.2895i	−0.881487	−	0.913209i
$894$		0			0
$895$	64.0835	−	23.3245i	2.14208	−	0.779652i
$896$		0			0
$897$	11.6139	−	9.74526i	0.387778	−	0.325385i
$898$		0			0
$899$	0.762195	+	4.32262i	0.0254206	+	0.144167i
$900$		0			0
$901$	41.1403	−	71.2570i	1.37058	−	2.37392i
$902$		0			0
$903$	25.7265	+	9.36369i	0.856126	+	0.311604i
$904$		0			0
$905$	9.98403	+	17.2928i	0.331880	+	0.574834i
$906$		0			0
$907$	20.6048	+	17.2895i	0.684171	+	0.574087i	0.917222	−	0.398377i	$-0.130426\pi$
$907$	20.6048	+	17.2895i	0.684171	+	0.574087i	−0.233051	+	0.972465i	$0.574871\pi$
$908$		0			0
$909$	−0.0867965	+	0.492247i	−0.00287886	+	0.0163268i
$910$		0			0
$911$	−26.1368			−0.865950			−0.432975	−	0.901406i	$-0.642536\pi$
$911$	−26.1368			−0.865950			−0.432975	+	0.901406i	$0.642536\pi$
$912$		0			0
$913$	0.151638			0.00501849
$914$		0			0
$915$	5.69514	−	32.2987i	0.188275	−	1.06776i
$916$		0			0
$917$	21.4767	+	18.0211i	0.709223	+	0.595108i
$918$		0			0
$919$	26.7362	+	46.3084i	0.881945	+	1.52757i	0.849175	+	0.528111i	$0.177100\pi$
$919$	26.7362	+	46.3084i	0.881945	+	1.52757i	0.0327702	+	0.999463i	$0.489567\pi$
$920$		0			0
$921$	−24.6318	−	8.96524i	−0.811645	−	0.295415i
$922$		0			0
$923$	−14.8132	+	25.6571i	−0.487581	+	0.844515i
$924$		0			0
$925$	−11.0010	−	62.3898i	−0.361711	−	2.05136i
$926$		0			0
$927$	−6.22778	+	5.22573i	−0.204547	+	0.171635i
$928$		0			0
$929$	18.2611	−	6.64648i	0.599126	−	0.218064i	−0.0246126	−	0.999697i	$-0.507835\pi$
$929$	18.2611	−	6.64648i	0.599126	−	0.218064i	0.623739	+	0.781633i	$0.285613\pi$
$930$		0			0
$931$	23.3112	−	15.7161i	0.763993	−	0.515076i
$932$		0			0
$933$	−17.7510	+	6.46083i	−0.581141	+	0.211518i
$934$		0			0
$935$	−22.6632	+	19.0167i	−0.741165	+	0.621912i
$936$		0			0
$937$	2.16285	+	12.2661i	0.0706572	+	0.400717i	0.999540	+	0.0303421i	$0.00965968\pi$
$937$	2.16285	+	12.2661i	0.0706572	+	0.400717i	−0.928882	+	0.370375i	$0.879229\pi$
$938$		0			0
$939$	7.67149	−	13.2874i	0.250350	−	0.433618i
$940$		0			0
$941$	27.4868	+	10.0044i	0.896045	+	0.326134i	0.748667	−	0.662947i	$-0.230694\pi$
$941$	27.4868	+	10.0044i	0.896045	+	0.326134i	0.147378	+	0.989080i	$0.452917\pi$
$942$		0			0
$943$	15.0696	+	26.1013i	0.490734	+	0.849976i
$944$		0			0
$945$	−11.3835	−	9.55189i	−0.370305	−	0.310723i
$946$		0			0
$947$	−2.89823	+	16.4367i	−0.0941797	+	0.534120i	0.900816	+	0.434201i	$0.142969\pi$
$947$	−2.89823	+	16.4367i	−0.0941797	+	0.534120i	−0.994996	+	0.0999184i	$0.968142\pi$
$948$		0			0
$949$	3.33560			0.108278
$950$		0			0
$951$	−20.0041			−0.648678
$952$		0			0
$953$	6.88534	−	39.0487i	0.223038	−	1.26491i	−0.643362	−	0.765562i	$-0.722461\pi$
$953$	6.88534	−	39.0487i	0.223038	−	1.26491i	0.866400	−	0.499350i	$-0.166428\pi$
$954$		0			0
$955$	−12.6745	−	10.6352i	−0.410138	−	0.344146i
$956$		0			0
$957$	−2.43661	−	4.22033i	−0.0787643	−	0.136424i
$958$		0			0
$959$	9.73031	+	3.54154i	0.314208	+	0.114362i
$960$		0			0
$961$	15.1630	−	26.2631i	0.489130	−	0.847198i
$962$		0			0
$963$	0.628695	+	3.56550i	0.0202594	+	0.114897i
$964$		0			0
$965$	−5.17186	+	4.33971i	−0.166488	+	0.139700i
$966$		0			0
$967$	−35.9683	+	13.0914i	−1.15666	+	0.420991i	−0.847904	−	0.530149i	$-0.822136\pi$
$967$	−35.9683	+	13.0914i	−1.15666	+	0.420991i	−0.308759	+	0.951140i	$0.599914\pi$
$968$		0			0
$969$	−9.63206	+	33.5631i	−0.309426	+	1.07820i
$970$		0			0
$971$	−11.8519	+	4.31373i	−0.380345	+	0.138434i	−0.525115	−	0.851031i	$-0.675978\pi$
$971$	−11.8519	+	4.31373i	−0.380345	+	0.138434i	0.144771	+	0.989465i	$0.453756\pi$
$972$		0			0
$973$	18.7490	−	15.7323i	0.601065	−	0.504353i
$974$		0			0
$975$	−4.42475	−	25.0940i	−0.141706	−	0.803652i
$976$		0			0
$977$	18.4011	−	31.8716i	0.588702	−	1.01966i	−0.405701	−	0.914006i	$-0.632972\pi$
$977$	18.4011	−	31.8716i	0.588702	−	1.01966i	0.994403	−	0.105656i	$-0.0336942\pi$
$978$		0			0
$979$	8.27309	+	3.01116i	0.264409	+	0.0962370i
$980$		0			0
$981$	2.38146	+	4.12481i	0.0760341	+	0.131695i
$982$		0			0
$983$	5.84912	+	4.90799i	0.186558	+	0.156541i	0.731283	−	0.682074i	$-0.238922\pi$
$983$	5.84912	+	4.90799i	0.186558	+	0.156541i	−0.544725	+	0.838614i	$0.683366\pi$
$984$		0			0
$985$	12.9714	−	73.5644i	0.413303	−	2.34396i
$986$		0			0
$987$	−31.9118			−1.01576
$988$		0			0
$989$	50.7158			1.61267
$990$		0			0
$991$	8.07919	−	45.8194i	0.256644	−	1.45550i	−0.535174	−	0.844742i	$-0.679754\pi$
$991$	8.07919	−	45.8194i	0.256644	−	1.45550i	0.791818	−	0.610758i	$-0.209135\pi$
$992$		0			0
$993$	−15.6001	−	13.0900i	−0.495054	−	0.415400i
$994$		0			0
$995$	0.548855	+	0.950644i	0.0173999	+	0.0301375i
$996$		0			0
$997$	−4.83733	−	1.76065i	−0.153200	−	0.0557602i	0.264282	−	0.964445i	$-0.414865\pi$
$997$	−4.83733	−	1.76065i	−0.153200	−	0.0557602i	−0.417482	+	0.908685i	$0.637087\pi$
$998$		0			0
$999$	−2.77417	+	4.80500i	−0.0877709	+	0.152024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bg.d.385.1	yes	18
4.3	odd	2		912.2.bo.l.385.1		18
19.2	odd	18		8664.2.a.bp.1.2		9
19.4	even	9	inner	456.2.bg.d.289.1	✓	18
19.17	even	9		8664.2.a.bn.1.2		9
76.23	odd	18		912.2.bo.l.289.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bg.d.289.1	✓	18	19.4	even	9	inner
456.2.bg.d.385.1	yes	18	1.1	even	1	trivial
912.2.bo.l.289.1		18	76.23	odd	18
912.2.bo.l.385.1		18	4.3	odd	2
8664.2.a.bn.1.2		9	19.17	even	9
8664.2.a.bp.1.2		9	19.2	odd	18

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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bg (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{3} +(-3.10397 - 2.60454i) q^{5} +(1.83370 + 3.17606i) q^{7} +(-0.939693 - 0.342020i) q^{9} +(-0.455725 + 0.789338i) q^{11} +(0.387516 + 2.19771i) q^{13} +(3.10397 - 2.60454i) q^{15} +(-7.52761 + 2.73983i) q^{17} +(-3.91733 - 1.91168i) q^{19} +(-3.44623 + 1.25433i) q^{21} +(-5.20427 + 4.36690i) q^{23} +(1.98276 + 11.2448i) q^{25} +(0.500000 - 0.866025i) q^{27} +(5.02422 + 1.82867i) q^{29} +(0.410471 + 0.710957i) q^{31} +(-0.698211 - 0.585868i) q^{33} +(2.58043 - 14.6343i) q^{35} -5.54834 q^{37} -2.23162 q^{39} +(0.770364 - 4.36895i) q^{41} +(-5.71862 - 4.79849i) q^{43} +(2.02597 + 3.50909i) q^{45} +(8.17671 + 2.97608i) q^{47} +(-3.22492 + 5.58572i) q^{49} +(-1.39105 - 7.88901i) q^{51} +(-7.86828 + 6.60227i) q^{53} +(3.47042 - 1.26313i) q^{55} +(2.56287 - 3.52586i) q^{57} +(6.79165 - 2.47196i) q^{59} +(6.20047 - 5.20281i) q^{61} +(-0.636838 - 3.61169i) q^{63} +(4.52119 - 7.83094i) q^{65} +(5.89321 + 2.14495i) q^{67} +(-3.39685 - 5.88351i) q^{69} +(10.1698 + 8.53346i) q^{71} +(0.259552 - 1.47199i) q^{73} -11.4182 q^{75} -3.34265 q^{77} +(-1.11277 + 6.31083i) q^{79} +(0.766044 + 0.642788i) q^{81} +(-0.0831851 - 0.144081i) q^{83} +(30.5014 + 11.1016i) q^{85} +(-2.67333 + 4.63035i) q^{87} +(-1.67733 - 9.51263i) q^{89} +(-6.26949 + 5.26073i) q^{91} +(-0.771433 + 0.280779i) q^{93} +(7.18024 + 16.1366i) q^{95} +(-15.9518 + 5.80596i) q^{97} +(0.698211 - 0.585868i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{5} + 6 q^{7} + 9 q^{11} - 18 q^{13} - 3 q^{15} - 3 q^{17} + 3 q^{19} + 3 q^{21} - 24 q^{23} - 3 q^{25} + 9 q^{27} + 15 q^{29} + 9 q^{31} + 6 q^{35} + 30 q^{37} - 18 q^{39} - 3 q^{41} + 30 q^{43}+ \cdots - 9 q^{97}+O(q^{100}) \) 18 * q + 3 * q^5 + 6 * q^7 + 9 * q^11 - 18 * q^13 - 3 * q^15 - 3 * q^17 + 3 * q^19 + 3 * q^21 - 24 * q^23 - 3 * q^25 + 9 * q^27 + 15 * q^29 + 9 * q^31 + 6 * q^35 + 30 * q^37 - 18 * q^39 - 3 * q^41 + 30 * q^43 + 3 * q^45 + 54 * q^47 - 9 * q^49 - 6 * q^51 - 24 * q^53 + 12 * q^55 + 15 * q^57 + 9 * q^59 + 6 * q^61 + 6 * q^63 + 3 * q^65 - 18 * q^67 - 30 * q^69 - 63 * q^71 - 24 * q^73 - 60 * q^75 - 66 * q^77 - 15 * q^79 + 36 * q^83 + 39 * q^85 + 3 * q^87 - 63 * q^89 - 66 * q^91 + 27 * q^93 + 42 * q^95 - 9 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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