LMFDB - Embedded newform 1280.2.l.d.321.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1280,2,Mod(321,1280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1280, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1280.321");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1280.l (of order $4$, degree $2$, 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:	$10.2208514587$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			321.4
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1280.321
Dual form			1280.2.l.d.961.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.07313 + 1.07313i) q^{3} +(0.707107 - 0.707107i) q^{5} +0.103425i q^{7} -0.696775i q^{9} +(2.21441 - 2.21441i) q^{11} +(-0.931852 - 0.931852i) q^{13} +1.51764 q^{15} +2.54587 q^{17} +(2.94646 + 2.94646i) q^{19} +(-0.110988 + 0.110988i) q^{21} +1.07812i q^{23} -1.00000i q^{25} +(3.96713 - 3.96713i) q^{27} +(-6.32780 - 6.32780i) q^{29} +0.635674 q^{31} +4.75272 q^{33} +(0.0731322 + 0.0731322i) q^{35} +(3.76733 - 3.76733i) q^{37} -2.00000i q^{39} +5.23143i q^{41} +(5.85872 - 5.85872i) q^{43} +(-0.492694 - 0.492694i) q^{45} +9.86005 q^{47} +6.98930 q^{49} +(2.73205 + 2.73205i) q^{51} +(-6.04284 + 6.04284i) q^{53} -3.13165i q^{55} +6.32389i q^{57} +(-6.78094 + 6.78094i) q^{59} +(-5.58114 - 5.58114i) q^{61} +0.0720636 q^{63} -1.31784 q^{65} +(-0.187769 - 0.187769i) q^{67} +(-1.15696 + 1.15696i) q^{69} +2.42883i q^{71} +14.1662i q^{73} +(1.07313 - 1.07313i) q^{75} +(0.229025 + 0.229025i) q^{77} +10.9647 q^{79} +6.42418 q^{81} +(1.03029 + 1.03029i) q^{83} +(1.80020 - 1.80020i) q^{85} -13.5811i q^{87} -6.75787i q^{89} +(0.0963763 - 0.0963763i) q^{91} +(0.682163 + 0.682163i) q^{93} +4.16693 q^{95} -17.9734 q^{97} +(-1.54295 - 1.54295i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 8 q^{11} + 8 q^{13} + 8 q^{15} - 8 q^{17} + 16 q^{21} + 8 q^{27} + 8 q^{29} + 24 q^{33} - 12 q^{35} + 8 q^{37} + 44 q^{43} - 8 q^{45} + 8 q^{47} + 8 q^{51} - 16 q^{53} - 16 q^{59} - 8 q^{61}+ \cdots - 56 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 + 8 * q^11 + 8 * q^13 + 8 * q^15 - 8 * q^17 + 16 * q^21 + 8 * q^27 + 8 * q^29 + 24 * q^33 - 12 * q^35 + 8 * q^37 + 44 * q^43 - 8 * q^45 + 8 * q^47 + 8 * q^51 - 16 * q^53 - 16 * q^59 - 8 * q^61 - 48 * q^63 - 8 * q^65 - 12 * q^67 - 40 * q^69 - 4 * q^75 - 16 * q^77 + 96 * q^79 - 16 * q^81 + 28 * q^83 + 16 * q^85 - 8 * q^91 + 8 * q^93 + 8 * q^95 - 24 * q^97 - 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	1.07313	+	1.07313i	0.619573	+	0.619573i	0.945422	−	0.325849i	$-0.105650\pi$
$3$	1.07313	+	1.07313i	0.619573	+	0.619573i	−0.325849	+	0.945422i	$0.605650\pi$
$4$		0			0
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$		0			0
$7$			0.103425i			0.0390908i	0.999809	+	0.0195454i	$0.00622189\pi$
$7$			0.103425i			0.0390908i	−0.999809	+	0.0195454i	$0.993778\pi$
$8$		0			0
$9$		−	0.696775i		−	0.232258i
$10$		0			0
$11$	2.21441	−	2.21441i	0.667671	−	0.667671i	−0.289506	−	0.957176i	$-0.593491\pi$
$11$	2.21441	−	2.21441i	0.667671	−	0.667671i	0.957176	+	0.289506i	$0.0934909\pi$
$12$		0			0
$13$	−0.931852	−	0.931852i	−0.258449	−	0.258449i	0.565974	−	0.824423i	$-0.308500\pi$
$13$	−0.931852	−	0.931852i	−0.258449	−	0.258449i	−0.824423	+	0.565974i	$0.808500\pi$
$14$		0			0
$15$	1.51764			0.391852
$16$		0			0
$17$	2.54587			0.617463			0.308732	−	0.951149i	$-0.400096\pi$
$17$	2.54587			0.617463			0.308732	+	0.951149i	$0.400096\pi$
$18$		0			0
$19$	2.94646	+	2.94646i	0.675965	+	0.675965i	0.959085	−	0.283120i	$-0.0913693\pi$
$19$	2.94646	+	2.94646i	0.675965	+	0.675965i	−0.283120	+	0.959085i	$0.591369\pi$
$20$		0			0
$21$	−0.110988	+	0.110988i	−0.0242196	+	0.0242196i
$22$		0			0
$23$			1.07812i			0.224803i	0.993663	+	0.112401i	$0.0358542\pi$
$23$			1.07812i			0.224803i	−0.993663	+	0.112401i	$0.964146\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$		0			0
$27$	3.96713	−	3.96713i	0.763474	−	0.763474i
$28$		0			0
$29$	−6.32780	−	6.32780i	−1.17504	−	1.17504i	−0.980991	−	0.194053i	$-0.937837\pi$
$29$	−6.32780	−	6.32780i	−1.17504	−	1.17504i	−0.194053	−	0.980991i	$-0.562163\pi$
$30$		0			0
$31$	0.635674			0.114171			0.0570853	−	0.998369i	$-0.481819\pi$
$31$	0.635674			0.114171			0.0570853	+	0.998369i	$0.481819\pi$
$32$		0			0
$33$	4.75272			0.827342
$34$		0			0
$35$	0.0731322	+	0.0731322i	0.0123616	+	0.0123616i
$36$		0			0
$37$	3.76733	−	3.76733i	0.619345	−	0.619345i	−0.326019	−	0.945363i	$-0.605707\pi$
$37$	3.76733	−	3.76733i	0.619345	−	0.619345i	0.945363	+	0.326019i	$0.105707\pi$
$38$		0			0
$39$		−	2.00000i		−	0.320256i
$40$		0			0
$41$			5.23143i			0.817012i	0.912756	+	0.408506i	$0.133950\pi$
$41$			5.23143i			0.817012i	−0.912756	+	0.408506i	$0.866050\pi$
$42$		0			0
$43$	5.85872	−	5.85872i	0.893446	−	0.893446i	−0.101399	−	0.994846i	$-0.532332\pi$
$43$	5.85872	−	5.85872i	0.893446	−	0.893446i	0.994846	+	0.101399i	$0.0323320\pi$
$44$		0			0
$45$	−0.492694	−	0.492694i	−0.0734465	−	0.0734465i
$46$		0			0
$47$	9.86005			1.43824			0.719118	−	0.694888i	$-0.244546\pi$
$47$	9.86005			1.43824			0.719118	+	0.694888i	$0.244546\pi$
$48$		0			0
$49$	6.98930			0.998472
$50$		0			0
$51$	2.73205	+	2.73205i	0.382564	+	0.382564i
$52$		0			0
$53$	−6.04284	+	6.04284i	−0.830048	+	0.830048i	−0.987523	−	0.157475i	$-0.949665\pi$
$53$	−6.04284	+	6.04284i	−0.830048	+	0.830048i	0.157475	+	0.987523i	$0.449665\pi$
$54$		0			0
$55$		−	3.13165i		−	0.422272i
$56$		0			0
$57$			6.32389i			0.837620i
$58$		0			0
$59$	−6.78094	+	6.78094i	−0.882804	+	0.882804i	−0.993819	−	0.111015i	$-0.964590\pi$
$59$	−6.78094	+	6.78094i	−0.882804	+	0.882804i	0.111015	+	0.993819i	$0.464590\pi$
$60$		0			0
$61$	−5.58114	−	5.58114i	−0.714592	−	0.714592i	0.252900	−	0.967492i	$-0.418616\pi$
$61$	−5.58114	−	5.58114i	−0.714592	−	0.714592i	−0.967492	+	0.252900i	$0.918616\pi$
$62$		0			0
$63$	0.0720636			0.00907916
$64$		0			0
$65$	−1.31784			−0.163458
$66$		0			0
$67$	−0.187769	−	0.187769i	−0.0229396	−	0.0229396i	0.695544	−	0.718484i	$-0.255163\pi$
$67$	−0.187769	−	0.187769i	−0.0229396	−	0.0229396i	−0.718484	+	0.695544i	$0.755163\pi$
$68$		0			0
$69$	−1.15696	+	1.15696i	−0.139282	+	0.139282i
$70$		0			0
$71$			2.42883i			0.288249i	0.989560	+	0.144124i	$0.0460365\pi$
$71$			2.42883i			0.288249i	−0.989560	+	0.144124i	$0.953963\pi$
$72$		0			0
$73$			14.1662i			1.65803i	0.559228	+	0.829014i	$0.311098\pi$
$73$			14.1662i			1.65803i	−0.559228	+	0.829014i	$0.688902\pi$
$74$		0			0
$75$	1.07313	−	1.07313i	0.123915	−	0.123915i
$76$		0			0
$77$	0.229025	+	0.229025i	0.0260998	+	0.0260998i
$78$		0			0
$79$	10.9647			1.23363			0.616814	−	0.787109i	$-0.288423\pi$
$79$	10.9647			1.23363			0.616814	+	0.787109i	$0.288423\pi$
$80$		0			0
$81$	6.42418			0.713798
$82$		0			0
$83$	1.03029	+	1.03029i	0.113089	+	0.113089i	0.761387	−	0.648298i	$-0.224519\pi$
$83$	1.03029	+	1.03029i	0.113089	+	0.113089i	−0.648298	+	0.761387i	$0.724519\pi$
$84$		0			0
$85$	1.80020	−	1.80020i	0.195259	−	0.195259i
$86$		0			0
$87$		−	13.5811i		−	1.45605i
$88$		0			0
$89$		−	6.75787i		−	0.716333i	−0.933658	−	0.358167i	$-0.883402\pi$
$89$		−	6.75787i		−	0.716333i	0.933658	−	0.358167i	$-0.116598\pi$
$90$		0			0
$91$	0.0963763	−	0.0963763i	0.0101030	−	0.0101030i
$92$		0			0
$93$	0.682163	+	0.682163i	0.0707370	+	0.0707370i
$94$		0			0
$95$	4.16693			0.427518
$96$		0			0
$97$	−17.9734			−1.82493			−0.912464	−	0.409158i	$-0.865822\pi$
$97$	−17.9734			−1.82493			−0.912464	+	0.409158i	$0.865822\pi$
$98$		0			0
$99$	−1.54295	−	1.54295i	−0.155072	−	0.155072i
$100$		0			0
$101$	−6.86370	+	6.86370i	−0.682964	+	0.682964i	−0.960667	−	0.277703i	$-0.910427\pi$
$101$	−6.86370	+	6.86370i	−0.682964	+	0.682964i	0.277703	+	0.960667i	$0.410427\pi$
$102$		0			0
$103$			17.3706i			1.71158i	0.517323	+	0.855790i	$0.326929\pi$
$103$			17.3706i			1.71158i	−0.517323	+	0.855790i	$0.673071\pi$
$104$		0			0
$105$			0.156961i			0.0153178i
$106$		0			0
$107$	12.1184	−	12.1184i	1.17153	−	1.17153i	0.189682	−	0.981846i	$-0.439254\pi$
$107$	12.1184	−	12.1184i	1.17153	−	1.17153i	0.981846	−	0.189682i	$-0.0607457\pi$
$108$		0			0
$109$	−9.08516	−	9.08516i	−0.870201	−	0.870201i	0.122293	−	0.992494i	$-0.460975\pi$
$109$	−9.08516	−	9.08516i	−0.870201	−	0.870201i	−0.992494	+	0.122293i	$0.960975\pi$
$110$		0			0
$111$	8.08568			0.767459
$112$		0			0
$113$	6.39230			0.601337			0.300669	−	0.953729i	$-0.402790\pi$
$113$	6.39230			0.601337			0.300669	+	0.953729i	$0.402790\pi$
$114$		0			0
$115$	0.762343	+	0.762343i	0.0710889	+	0.0710889i
$116$		0			0
$117$	−0.649291	+	0.649291i	−0.0600269	+	0.0600269i
$118$		0			0
$119$			0.263305i			0.0241371i
$120$		0			0
$121$			1.19275i			0.108432i
$122$		0			0
$123$	−5.61401	+	5.61401i	−0.506199	+	0.506199i
$124$		0			0
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$		0			0
$127$	3.19000			0.283066			0.141533	−	0.989934i	$-0.454797\pi$
$127$	3.19000			0.283066			0.141533	+	0.989934i	$0.454797\pi$
$128$		0			0
$129$	12.5744			1.10711
$130$		0			0
$131$	−5.62863	−	5.62863i	−0.491775	−	0.491775i	0.417090	−	0.908865i	$-0.363050\pi$
$131$	−5.62863	−	5.62863i	−0.491775	−	0.491775i	−0.908865	+	0.417090i	$0.863050\pi$
$132$		0			0
$133$	−0.304737	+	0.304737i	−0.0264240	+	0.0264240i
$134$		0			0
$135$		−	5.61037i		−	0.482863i
$136$		0			0
$137$		−	0.277401i		−	0.0237000i	−0.999930	−	0.0118500i	$-0.996228\pi$
$137$		−	0.277401i		−	0.0237000i	0.999930	−	0.0118500i	$-0.00377206\pi$
$138$		0			0
$139$	−12.1586	+	12.1586i	−1.03128	+	1.03128i	−0.0317874	+	0.999495i	$0.510120\pi$
$139$	−12.1586	+	12.1586i	−1.03128	+	1.03128i	−0.999495	+	0.0317874i	$0.989880\pi$
$140$		0			0
$141$	10.5811	+	10.5811i	0.891093	+	0.891093i
$142$		0			0
$143$	−4.12701			−0.345118
$144$		0			0
$145$	−8.94887			−0.743163
$146$		0			0
$147$	7.50045	+	7.50045i	0.618626	+	0.618626i
$148$		0			0
$149$	−5.81722	+	5.81722i	−0.476565	+	0.476565i	−0.904031	−	0.427466i	$-0.859406\pi$
$149$	−5.81722	+	5.81722i	−0.476565	+	0.476565i	0.427466	+	0.904031i	$0.359406\pi$
$150$		0			0
$151$			6.01994i			0.489895i	0.969536	+	0.244948i	$0.0787708\pi$
$151$			6.01994i			0.489895i	−0.969536	+	0.244948i	$0.921229\pi$
$152$		0			0
$153$		−	1.77389i		−	0.143411i
$154$		0			0
$155$	0.449490	−	0.449490i	0.0361039	−	0.0361039i
$156$		0			0
$157$	9.18494	+	9.18494i	0.733038	+	0.733038i	0.971220	−	0.238182i	$-0.0765516\pi$
$157$	9.18494	+	9.18494i	0.733038	+	0.733038i	−0.238182	+	0.971220i	$0.576552\pi$
$158$		0			0
$159$	−12.9695			−1.02855
$160$		0			0
$161$	−0.111504			−0.00878772
$162$		0			0
$163$	−2.74408	−	2.74408i	−0.214933	−	0.214933i	0.591426	−	0.806359i	$-0.298565\pi$
$163$	−2.74408	−	2.74408i	−0.214933	−	0.214933i	−0.806359	+	0.591426i	$0.798565\pi$
$164$		0			0
$165$	3.36068	−	3.36068i	0.261628	−	0.261628i
$166$		0			0
$167$		−	6.66923i		−	0.516080i	−0.966134	−	0.258040i	$-0.916923\pi$
$167$		−	6.66923i		−	0.516080i	0.966134	−	0.258040i	$-0.0830767\pi$
$168$		0			0
$169$		−	11.2633i		−	0.866408i
$170$		0			0
$171$	2.05302	−	2.05302i	0.156998	−	0.156998i
$172$		0			0
$173$	−0.732051	−	0.732051i	−0.0556568	−	0.0556568i	0.678731	−	0.734387i	$-0.262530\pi$
$173$	−0.732051	−	0.732051i	−0.0556568	−	0.0556568i	−0.734387	+	0.678731i	$0.762530\pi$
$174$		0			0
$175$	0.103425			0.00781816
$176$		0			0
$177$	−14.5537			−1.09392
$178$		0			0
$179$	0.619174	+	0.619174i	0.0462792	+	0.0462792i	0.729868	−	0.683588i	$-0.239582\pi$
$179$	0.619174	+	0.619174i	0.0462792	+	0.0462792i	−0.683588	+	0.729868i	$0.739582\pi$
$180$		0			0
$181$	7.55583	−	7.55583i	0.561621	−	0.561621i	−0.368147	−	0.929768i	$-0.620008\pi$
$181$	7.55583	−	7.55583i	0.561621	−	0.561621i	0.929768	+	0.368147i	$0.120008\pi$
$182$		0			0
$183$		−	11.9786i		−	0.885484i
$184$		0			0
$185$		−	5.32780i		−	0.391708i
$186$		0			0
$187$	5.63760	−	5.63760i	0.412262	−	0.412262i
$188$		0			0
$189$	0.410298	+	0.410298i	0.0298448	+	0.0298448i
$190$		0			0
$191$	−24.2268			−1.75299			−0.876494	−	0.481412i	$-0.840124\pi$
$191$	−24.2268			−1.75299			−0.876494	+	0.481412i	$0.840124\pi$
$192$		0			0
$193$	3.78318			0.272319			0.136160	−	0.990687i	$-0.456524\pi$
$193$	3.78318			0.272319			0.136160	+	0.990687i	$0.456524\pi$
$194$		0			0
$195$	−1.41421	−	1.41421i	−0.101274	−	0.101274i
$196$		0			0
$197$	14.5322	−	14.5322i	1.03538	−	1.03538i	0.0360292	−	0.999351i	$-0.488529\pi$
$197$	14.5322	−	14.5322i	1.03538	−	1.03538i	0.999351	−	0.0360292i	$-0.0114709\pi$
$198$		0			0
$199$			24.5851i			1.74279i	0.490583	+	0.871394i	$0.336784\pi$
$199$			24.5851i			1.74279i	−0.490583	+	0.871394i	$0.663216\pi$
$200$		0			0
$201$		−	0.403001i		−	0.0284255i
$202$		0			0
$203$	0.654450	−	0.654450i	0.0459334	−	0.0459334i
$204$		0			0
$205$	3.69918	+	3.69918i	0.258362	+	0.258362i
$206$		0			0
$207$	0.751204			0.0522123
$208$		0			0
$209$	13.0494			0.902644
$210$		0			0
$211$	11.8214	+	11.8214i	0.813817	+	0.813817i	0.985204	−	0.171387i	$-0.0548247\pi$
$211$	11.8214	+	11.8214i	0.813817	+	0.813817i	−0.171387	+	0.985204i	$0.554825\pi$
$212$		0			0
$213$	−2.60645	+	2.60645i	−0.178591	+	0.178591i
$214$		0			0
$215$		−	8.28548i		−	0.565065i
$216$		0			0
$217$			0.0657443i			0.00446302i
$218$		0			0
$219$	−15.2022	+	15.2022i	−1.02727	+	1.02727i
$220$		0			0
$221$	−2.37237	−	2.37237i	−0.159583	−	0.159583i
$222$		0			0
$223$	−20.3129			−1.36026			−0.680128	−	0.733094i	$-0.738076\pi$
$223$	−20.3129			−1.36026			−0.680128	+	0.733094i	$0.738076\pi$
$224$		0			0
$225$	−0.696775			−0.0464516
$226$		0			0
$227$	−19.0831	−	19.0831i	−1.26659	−	1.26659i	−0.947838	−	0.318752i	$-0.896736\pi$
$227$	−19.0831	−	19.0831i	−1.26659	−	1.26659i	−0.318752	−	0.947838i	$-0.603264\pi$
$228$		0			0
$229$	1.26330	−	1.26330i	0.0834815	−	0.0834815i	−0.664133	−	0.747614i	$-0.731199\pi$
$229$	1.26330	−	1.26330i	0.0834815	−	0.0834815i	0.747614	+	0.664133i	$0.231199\pi$
$230$		0			0
$231$			0.491547i			0.0323414i
$232$		0			0
$233$		−	22.7727i		−	1.49189i	−0.666010	−	0.745943i	$-0.731999\pi$
$233$		−	22.7727i		−	1.49189i	0.666010	−	0.745943i	$-0.268001\pi$
$234$		0			0
$235$	6.97211	−	6.97211i	0.454810	−	0.454810i
$236$		0			0
$237$	11.7666	+	11.7666i	0.764323	+	0.764323i
$238$		0			0
$239$	−22.0126			−1.42388			−0.711940	−	0.702241i	$-0.752183\pi$
$239$	−22.0126			−1.42388			−0.711940	+	0.702241i	$0.752183\pi$
$240$		0			0
$241$	−19.5653			−1.26031			−0.630155	−	0.776469i	$-0.717009\pi$
$241$	−19.5653			−1.26031			−0.630155	+	0.776469i	$0.717009\pi$
$242$		0			0
$243$	−5.00739	−	5.00739i	−0.321224	−	0.321224i
$244$		0			0
$245$	4.94218	−	4.94218i	0.315745	−	0.315745i
$246$		0			0
$247$		−	5.49133i		−	0.349405i
$248$		0			0
$249$			2.21128i			0.140134i
$250$		0			0
$251$	−3.92188	+	3.92188i	−0.247547	+	0.247547i	−0.819963	−	0.572416i	$-0.806006\pi$
$251$	−3.92188	+	3.92188i	−0.247547	+	0.247547i	0.572416	+	0.819963i	$0.306006\pi$
$252$		0			0
$253$	2.38739	+	2.38739i	0.150094	+	0.150094i
$254$		0			0
$255$	3.86370			0.241954
$256$		0			0
$257$	−14.4064			−0.898647			−0.449323	−	0.893369i	$-0.648335\pi$
$257$	−14.4064			−0.898647			−0.449323	+	0.893369i	$0.648335\pi$
$258$		0			0
$259$	0.389634	+	0.389634i	0.0242107	+	0.0242107i
$260$		0			0
$261$	−4.40905	+	4.40905i	−0.272914	+	0.272914i
$262$		0			0
$263$			16.0095i			0.987187i	0.869693	+	0.493594i	$0.164317\pi$
$263$			16.0095i			0.987187i	−0.869693	+	0.493594i	$0.835683\pi$
$264$		0			0
$265$			8.54587i			0.524968i
$266$		0			0
$267$	7.25209	−	7.25209i	0.443821	−	0.443821i
$268$		0			0
$269$	−2.24604	−	2.24604i	−0.136944	−	0.136944i	0.635312	−	0.772256i	$-0.280871\pi$
$269$	−2.24604	−	2.24604i	−0.136944	−	0.136944i	−0.772256	+	0.635312i	$0.780871\pi$
$270$		0			0
$271$	2.97202			0.180537			0.0902687	−	0.995917i	$-0.471227\pi$
$271$	2.97202			0.180537			0.0902687	+	0.995917i	$0.471227\pi$
$272$		0			0
$273$	0.206849			0.0125191
$274$		0			0
$275$	−2.21441	−	2.21441i	−0.133534	−	0.133534i
$276$		0			0
$277$	20.1163	−	20.1163i	1.20867	−	1.20867i	0.237215	−	0.971457i	$-0.423765\pi$
$277$	20.1163	−	20.1163i	1.20867	−	1.20867i	0.971457	−	0.237215i	$-0.0762345\pi$
$278$		0			0
$279$		−	0.442922i		−	0.0265170i
$280$		0			0
$281$		−	18.5865i		−	1.10878i	−0.832258	−	0.554388i	$-0.812952\pi$
$281$		−	18.5865i		−	1.10878i	0.832258	−	0.554388i	$-0.187048\pi$
$282$		0			0
$283$	−20.7499	+	20.7499i	−1.23345	+	1.23345i	−0.270827	+	0.962628i	$0.587297\pi$
$283$	−20.7499	+	20.7499i	−1.23345	+	1.23345i	−0.962628	+	0.270827i	$0.912703\pi$
$284$		0			0
$285$	4.47167	+	4.47167i	0.264879	+	0.264879i
$286$		0			0
$287$	−0.541058			−0.0319376
$288$		0			0
$289$	−10.5186			−0.618739
$290$		0			0
$291$	−19.2879	−	19.2879i	−1.13068	−	1.13068i
$292$		0			0
$293$	−6.59059	+	6.59059i	−0.385027	+	0.385027i	−0.872909	−	0.487883i	$-0.837769\pi$
$293$	−6.59059	+	6.59059i	−0.385027	+	0.385027i	0.487883	+	0.872909i	$0.337769\pi$
$294$		0			0
$295$			9.58970i			0.558334i
$296$		0			0
$297$		−	17.5697i		−	1.01950i
$298$		0			0
$299$	1.00464	−	1.00464i	0.0581001	−	0.0581001i
$300$		0			0
$301$	0.605935	+	0.605935i	0.0349255	+	0.0349255i
$302$		0			0
$303$	−14.7313			−0.846292
$304$		0			0
$305$	−7.89293			−0.451948
$306$		0			0
$307$	−0.494394	−	0.494394i	−0.0282166	−	0.0282166i	0.692858	−	0.721074i	$-0.256351\pi$
$307$	−0.494394	−	0.494394i	−0.0282166	−	0.0282166i	−0.721074	+	0.692858i	$0.756351\pi$
$308$		0			0
$309$	−18.6410	+	18.6410i	−1.06045	+	1.06045i
$310$		0			0
$311$		−	10.2409i		−	0.580707i	−0.956919	−	0.290354i	$-0.906227\pi$
$311$		−	10.2409i		−	0.580707i	0.956919	−	0.290354i	$-0.0937729\pi$
$312$		0			0
$313$			10.0058i			0.565563i	0.959184	+	0.282782i	$0.0912572\pi$
$313$			10.0058i			0.565563i	−0.959184	+	0.282782i	$0.908743\pi$
$314$		0			0
$315$	0.0509567	−	0.0509567i	0.00287108	−	0.00287108i
$316$		0			0
$317$	19.3441	+	19.3441i	1.08647	+	1.08647i	0.995889	+	0.0905836i	$0.0288732\pi$
$317$	19.3441	+	19.3441i	1.08647	+	1.08647i	0.0905836	+	0.995889i	$0.471127\pi$
$318$		0			0
$319$	−28.0247			−1.56908
$320$		0			0
$321$	26.0092			1.45169
$322$		0			0
$323$	7.50130	+	7.50130i	0.417384	+	0.417384i
$324$		0			0
$325$	−0.931852	+	0.931852i	−0.0516898	+	0.0516898i
$326$		0			0
$327$		−	19.4992i		−	1.07831i
$328$		0			0
$329$			1.01977i			0.0562218i
$330$		0			0
$331$	−22.2691	+	22.2691i	−1.22402	+	1.22402i	−0.257831	+	0.966190i	$0.583008\pi$
$331$	−22.2691	+	22.2691i	−1.22402	+	1.22402i	−0.966190	+	0.257831i	$0.916992\pi$
$332$		0			0
$333$	−2.62498	−	2.62498i	−0.143848	−	0.143848i
$334$		0			0
$335$	−0.265545			−0.0145083
$336$		0			0
$337$	−17.4689			−0.951592			−0.475796	−	0.879556i	$-0.657840\pi$
$337$	−17.4689			−0.951592			−0.475796	+	0.879556i	$0.657840\pi$
$338$		0			0
$339$	6.85979	+	6.85979i	0.372573	+	0.372573i
$340$		0			0
$341$	1.40765	−	1.40765i	0.0762283	−	0.0762283i
$342$		0			0
$343$			1.44684i			0.0781219i
$344$		0			0
$345$			1.63619i			0.0880895i
$346$		0			0
$347$	7.12078	−	7.12078i	0.382264	−	0.382264i	−0.489654	−	0.871917i	$-0.662877\pi$
$347$	7.12078	−	7.12078i	0.382264	−	0.382264i	0.871917	+	0.489654i	$0.162877\pi$
$348$		0			0
$349$	9.33386	+	9.33386i	0.499630	+	0.499630i	0.911323	−	0.411693i	$-0.135062\pi$
$349$	9.33386	+	9.33386i	0.499630	+	0.499630i	−0.411693	+	0.911323i	$0.635062\pi$
$350$		0			0
$351$	−7.39355			−0.394638
$352$		0			0
$353$	−10.8922			−0.579732			−0.289866	−	0.957067i	$-0.593611\pi$
$353$	−10.8922			−0.579732			−0.289866	+	0.957067i	$0.593611\pi$
$354$		0			0
$355$	1.71744	+	1.71744i	0.0911522	+	0.0911522i
$356$		0			0
$357$	−0.282561	+	0.282561i	−0.0149547	+	0.0149547i
$358$		0			0
$359$			14.9262i			0.787775i	0.919159	+	0.393888i	$0.128870\pi$
$359$			14.9262i			0.787775i	−0.919159	+	0.393888i	$0.871130\pi$
$360$		0			0
$361$		−	1.63671i		−	0.0861424i
$362$		0			0
$363$	−1.27998	+	1.27998i	−0.0671816	+	0.0671816i
$364$		0			0
$365$	10.0170	+	10.0170i	0.524315	+	0.524315i
$366$		0			0
$367$	35.9265			1.87535			0.937673	−	0.347518i	$-0.112975\pi$
$367$	35.9265			1.87535			0.937673	+	0.347518i	$0.112975\pi$
$368$		0			0
$369$	3.64513			0.189758
$370$		0			0
$371$	−0.624978	−	0.624978i	−0.0324472	−	0.0324472i
$372$		0			0
$373$	6.04576	−	6.04576i	0.313038	−	0.313038i	−0.533048	−	0.846085i	$-0.678953\pi$
$373$	6.04576	−	6.04576i	0.313038	−	0.313038i	0.846085	+	0.533048i	$0.178953\pi$
$374$		0			0
$375$		−	1.51764i		−	0.0783705i
$376$		0			0
$377$			11.7932i			0.607378i
$378$		0			0
$379$	−10.9598	+	10.9598i	−0.562969	+	0.562969i	−0.930150	−	0.367181i	$-0.880323\pi$
$379$	−10.9598	+	10.9598i	−0.562969	+	0.562969i	0.367181	+	0.930150i	$0.380323\pi$
$380$		0			0
$381$	3.42329	+	3.42329i	0.175380	+	0.175380i
$382$		0			0
$383$	28.3120			1.44667			0.723337	−	0.690495i	$-0.242607\pi$
$383$	28.3120			1.44667			0.723337	+	0.690495i	$0.242607\pi$
$384$		0			0
$385$	0.323890			0.0165069
$386$		0			0
$387$	−4.08221	−	4.08221i	−0.207510	−	0.207510i
$388$		0			0
$389$	−20.1249	+	20.1249i	−1.02037	+	1.02037i	−0.0205833	+	0.999788i	$0.506552\pi$
$389$	−20.1249	+	20.1249i	−1.02037	+	1.02037i	−0.999788	+	0.0205833i	$0.993448\pi$
$390$		0			0
$391$			2.74474i			0.138807i
$392$		0			0
$393$		−	12.0805i		−	0.609382i
$394$		0			0
$395$	7.75323	−	7.75323i	0.390107	−	0.390107i
$396$		0			0
$397$	−4.43247	−	4.43247i	−0.222459	−	0.222459i	0.587074	−	0.809533i	$-0.300280\pi$
$397$	−4.43247	−	4.43247i	−0.222459	−	0.222459i	−0.809533	+	0.587074i	$0.800280\pi$
$398$		0			0
$399$	−0.654045			−0.0327432
$400$		0			0
$401$	−18.4044			−0.919072			−0.459536	−	0.888159i	$-0.651984\pi$
$401$	−18.4044			−0.919072			−0.459536	+	0.888159i	$0.651984\pi$
$402$		0			0
$403$	−0.592354	−	0.592354i	−0.0295073	−	0.0295073i
$404$		0			0
$405$	4.54258	−	4.54258i	0.225723	−	0.225723i
$406$		0			0
$407$		−	16.6848i		−	0.827036i
$408$		0			0
$409$			26.1503i			1.29305i	0.762892	+	0.646526i	$0.223779\pi$
$409$			26.1503i			1.29305i	−0.762892	+	0.646526i	$0.776221\pi$
$410$		0			0
$411$	0.297688	−	0.297688i	0.0146839	−	0.0146839i
$412$		0			0
$413$	−0.701316	−	0.701316i	−0.0345095	−	0.0345095i
$414$		0			0
$415$	1.45705			0.0715239
$416$		0			0
$417$	−26.0956			−1.27791
$418$		0			0
$419$	−16.3655	−	16.3655i	−0.799506	−	0.799506i	0.183511	−	0.983018i	$-0.441254\pi$
$419$	−16.3655	−	16.3655i	−0.799506	−	0.799506i	−0.983018	+	0.183511i	$0.941254\pi$
$420$		0			0
$421$	−3.77589	+	3.77589i	−0.184025	+	0.184025i	−0.793107	−	0.609082i	$-0.791538\pi$
$421$	−3.77589	+	3.77589i	−0.184025	+	0.184025i	0.609082	+	0.793107i	$0.291538\pi$
$422$		0			0
$423$		−	6.87024i		−	0.334042i
$424$		0			0
$425$		−	2.54587i		−	0.123493i
$426$		0			0
$427$	0.577227	−	0.577227i	0.0279340	−	0.0279340i
$428$		0			0
$429$	−4.42883	−	4.42883i	−0.213826	−	0.213826i
$430$		0			0
$431$	12.9282			0.622730			0.311365	−	0.950290i	$-0.399214\pi$
$431$	12.9282			0.622730			0.311365	+	0.950290i	$0.399214\pi$
$432$		0			0
$433$	−0.716195			−0.0344181			−0.0172091	−	0.999852i	$-0.505478\pi$
$433$	−0.716195			−0.0344181			−0.0172091	+	0.999852i	$0.505478\pi$
$434$		0			0
$435$	−9.60332	−	9.60332i	−0.460444	−	0.460444i
$436$		0			0
$437$	−3.17663	+	3.17663i	−0.151959	+	0.151959i
$438$		0			0
$439$			33.9527i			1.62048i	0.586101	+	0.810238i	$0.300662\pi$
$439$			33.9527i			1.62048i	−0.586101	+	0.810238i	$0.699338\pi$
$440$		0			0
$441$		−	4.86997i		−	0.231903i
$442$		0			0
$443$	−21.3464	+	21.3464i	−1.01420	+	1.01420i	−0.0143006	+	0.999898i	$0.504552\pi$
$443$	−21.3464	+	21.3464i	−1.01420	+	1.01420i	−0.999898	+	0.0143006i	$0.995448\pi$
$444$		0			0
$445$	−4.77854	−	4.77854i	−0.226524	−	0.226524i
$446$		0			0
$447$	−12.4853			−0.590534
$448$		0			0
$449$	30.5066			1.43970			0.719848	−	0.694131i	$-0.244211\pi$
$449$	30.5066			1.43970			0.719848	+	0.694131i	$0.244211\pi$
$450$		0			0
$451$	11.5845	+	11.5845i	0.545495	+	0.545495i
$452$		0			0
$453$	−6.46019	+	6.46019i	−0.303526	+	0.303526i
$454$		0			0
$455$		−	0.136297i		−	0.00638969i
$456$		0			0
$457$			13.8063i			0.645831i	0.946428	+	0.322915i	$0.104663\pi$
$457$			13.8063i			0.645831i	−0.946428	+	0.322915i	$0.895337\pi$
$458$		0			0
$459$	10.0998	−	10.0998i	0.471417	−	0.471417i
$460$		0			0
$461$	−10.8637	−	10.8637i	−0.505973	−	0.505973i	0.407315	−	0.913288i	$-0.366465\pi$
$461$	−10.8637	−	10.8637i	−0.505973	−	0.505973i	−0.913288	+	0.407315i	$0.866465\pi$
$462$		0			0
$463$	−0.401792			−0.0186729			−0.00933643	−	0.999956i	$-0.502972\pi$
$463$	−0.401792			−0.0186729			−0.00933643	+	0.999956i	$0.502972\pi$
$464$		0			0
$465$	0.964724			0.0447380
$466$		0			0
$467$	−0.822963	−	0.822963i	−0.0380822	−	0.0380822i	0.687809	−	0.725891i	$-0.258573\pi$
$467$	−0.822963	−	0.822963i	−0.0380822	−	0.0380822i	−0.725891	+	0.687809i	$0.758573\pi$
$468$		0			0
$469$	0.0194199	−	0.0194199i	0.000896728	−	0.000896728i
$470$		0			0
$471$			19.7133i			0.908341i
$472$		0			0
$473$		−	25.9472i		−	1.19306i
$474$		0			0
$475$	2.94646	−	2.94646i	0.135193	−	0.135193i
$476$		0			0
$477$	4.21050	+	4.21050i	0.192785	+	0.192785i
$478$		0			0
$479$	9.24996			0.422641			0.211321	−	0.977417i	$-0.432224\pi$
$479$	9.24996			0.422641			0.211321	+	0.977417i	$0.432224\pi$
$480$		0			0
$481$	−7.02118			−0.320138
$482$		0			0
$483$	−0.119658	−	0.119658i	−0.00544463	−	0.00544463i
$484$		0			0
$485$	−12.7091	+	12.7091i	−0.577093	+	0.577093i
$486$		0			0
$487$			6.23242i			0.282418i	0.989980	+	0.141209i	$0.0450990\pi$
$487$			6.23242i			0.282418i	−0.989980	+	0.141209i	$0.954901\pi$
$488$		0			0
$489$		−	5.88953i		−	0.266334i
$490$		0			0
$491$	2.91407	−	2.91407i	0.131510	−	0.131510i	−0.638288	−	0.769798i	$-0.720357\pi$
$491$	2.91407	−	2.91407i	0.131510	−	0.131510i	0.769798	+	0.638288i	$0.220357\pi$
$492$		0			0
$493$	−16.1097	−	16.1097i	−0.725546	−	0.725546i
$494$		0			0
$495$	−2.18206			−0.0980761
$496$		0			0
$497$	−0.251200			−0.0112679
$498$		0			0
$499$	2.33145	+	2.33145i	0.104370	+	0.104370i	0.757364	−	0.652993i	$-0.226487\pi$
$499$	2.33145	+	2.33145i	0.104370	+	0.104370i	−0.652993	+	0.757364i	$0.726487\pi$
$500$		0			0
$501$	7.15696	−	7.15696i	0.319749	−	0.319749i
$502$		0			0
$503$		−	30.9063i		−	1.37805i	−0.724740	−	0.689023i	$-0.758040\pi$
$503$		−	30.9063i		−	1.37805i	0.724740	−	0.689023i	$-0.241960\pi$
$504$		0			0
$505$			9.70674i			0.431944i
$506$		0			0
$507$	12.0870	−	12.0870i	0.536803	−	0.536803i
$508$		0			0
$509$	7.41473	+	7.41473i	0.328652	+	0.328652i	0.852074	−	0.523422i	$-0.175345\pi$
$509$	7.41473	+	7.41473i	0.328652	+	0.328652i	−0.523422	+	0.852074i	$0.675345\pi$
$510$		0			0
$511$	−1.46513			−0.0648136
$512$		0			0
$513$	23.3780			1.03216
$514$		0			0
$515$	12.2829	+	12.2829i	0.541249	+	0.541249i
$516$		0			0
$517$	21.8342	−	21.8342i	0.960268	−	0.960268i
$518$		0			0
$519$		−	1.57117i		−	0.0689669i
$520$		0			0
$521$			39.7156i			1.73997i	0.493075	+	0.869987i	$0.335873\pi$
$521$			39.7156i			1.73997i	−0.493075	+	0.869987i	$0.664127\pi$
$522$		0			0
$523$	−0.451554	+	0.451554i	−0.0197451	+	0.0197451i	−0.716910	−	0.697165i	$-0.754444\pi$
$523$	−0.451554	+	0.451554i	−0.0197451	+	0.0197451i	0.697165	+	0.716910i	$0.254444\pi$
$524$		0			0
$525$	0.110988	+	0.110988i	0.00484392	+	0.00484392i
$526$		0			0
$527$	1.61834			0.0704961
$528$		0			0
$529$	21.8377			0.949464
$530$		0			0
$531$	4.72479	+	4.72479i	0.205038	+	0.205038i
$532$		0			0
$533$	4.87492	−	4.87492i	0.211156	−	0.211156i
$534$		0			0
$535$		−	17.1380i		−	0.740939i
$536$		0			0
$537$			1.32891i			0.0573468i
$538$		0			0
$539$	15.4772	−	15.4772i	0.666650	−	0.666650i
$540$		0			0
$541$	−10.4792	−	10.4792i	−0.450537	−	0.450537i	0.444996	−	0.895533i	$-0.353205\pi$
$541$	−10.4792	−	10.4792i	−0.450537	−	0.450537i	−0.895533	+	0.444996i	$0.853205\pi$
$542$		0			0
$543$	16.2168			0.695930
$544$		0			0
$545$	−12.8484			−0.550363
$546$		0			0
$547$	16.6370	+	16.6370i	0.711347	+	0.711347i	0.966817	−	0.255470i	$-0.0822302\pi$
$547$	16.6370	+	16.6370i	0.711347	+	0.711347i	−0.255470	+	0.966817i	$0.582230\pi$
$548$		0			0
$549$	−3.88880	+	3.88880i	−0.165970	+	0.165970i
$550$		0			0
$551$		−	37.2893i		−	1.58858i
$552$		0			0
$553$			1.13402i			0.0482235i
$554$		0			0
$555$	5.71744	−	5.71744i	0.242692	−	0.242692i
$556$		0			0
$557$	−15.2321	−	15.2321i	−0.645405	−	0.645405i	0.306474	−	0.951879i	$-0.400851\pi$
$557$	−15.2321	−	15.2321i	−0.645405	−	0.645405i	−0.951879	+	0.306474i	$0.900851\pi$
$558$		0			0
$559$	−10.9189			−0.461821
$560$		0			0
$561$	12.0998			0.510853
$562$		0			0
$563$	−5.12478	−	5.12478i	−0.215984	−	0.215984i	0.590820	−	0.806804i	$-0.298804\pi$
$563$	−5.12478	−	5.12478i	−0.215984	−	0.215984i	−0.806804	+	0.590820i	$0.798804\pi$
$564$		0			0
$565$	4.52004	−	4.52004i	0.190160	−	0.190160i
$566$		0			0
$567$			0.664418i			0.0279029i
$568$		0			0
$569$			14.3617i			0.602073i	0.953613	+	0.301036i	$0.0973325\pi$
$569$			14.3617i			0.602073i	−0.953613	+	0.301036i	$0.902667\pi$
$570$		0			0
$571$	16.7503	−	16.7503i	0.700979	−	0.700979i	−0.263642	−	0.964621i	$-0.584924\pi$
$571$	16.7503	−	16.7503i	0.700979	−	0.700979i	0.964621	+	0.263642i	$0.0849237\pi$
$572$		0			0
$573$	−25.9985	−	25.9985i	−1.08610	−	1.08610i
$574$		0			0
$575$	1.07812			0.0449605
$576$		0			0
$577$	19.0222			0.791905			0.395952	−	0.918271i	$-0.370414\pi$
$577$	19.0222			0.791905			0.395952	+	0.918271i	$0.370414\pi$
$578$		0			0
$579$	4.05986	+	4.05986i	0.168722	+	0.168722i
$580$		0			0
$581$	−0.106557	+	0.106557i	−0.00442075	+	0.00442075i
$582$		0			0
$583$			26.7627i			1.10840i
$584$		0			0
$585$			0.918236i			0.0379644i
$586$		0			0
$587$	6.13612	−	6.13612i	0.253265	−	0.253265i	−0.569043	−	0.822308i	$-0.692686\pi$
$587$	6.13612	−	6.13612i	0.253265	−	0.253265i	0.822308	+	0.569043i	$0.192686\pi$
$588$		0			0
$589$	1.87299	+	1.87299i	0.0771753	+	0.0771753i
$590$		0			0
$591$	31.1901			1.28299
$592$		0			0
$593$	28.0963			1.15378			0.576889	−	0.816823i	$-0.304267\pi$
$593$	28.0963			1.15378			0.576889	+	0.816823i	$0.304267\pi$
$594$		0			0
$595$	0.186185	+	0.186185i	0.00763283	+	0.00763283i
$596$		0			0
$597$	−26.3830	+	26.3830i	−1.07978	+	1.07978i
$598$		0			0
$599$			2.27156i			0.0928135i	0.998923	+	0.0464068i	$0.0147770\pi$
$599$			2.27156i			0.0928135i	−0.998923	+	0.0464068i	$0.985223\pi$
$600$		0			0
$601$		−	21.4534i		−	0.875103i	−0.899193	−	0.437551i	$-0.855846\pi$
$601$		−	21.4534i		−	0.875103i	0.899193	−	0.437551i	$-0.144154\pi$
$602$		0			0
$603$	−0.130833	+	0.130833i	−0.00532791	+	0.00532791i
$604$		0			0
$605$	0.843403	+	0.843403i	0.0342892	+	0.0342892i
$606$		0			0
$607$	6.63203			0.269186			0.134593	−	0.990901i	$-0.457027\pi$
$607$	6.63203			0.269186			0.134593	+	0.990901i	$0.457027\pi$
$608$		0			0
$609$	1.40462			0.0569182
$610$		0			0
$611$	−9.18811	−	9.18811i	−0.371711	−	0.371711i
$612$		0			0
$613$	24.1766	−	24.1766i	0.976486	−	0.976486i	−0.0232442	−	0.999730i	$-0.507400\pi$
$613$	24.1766	−	24.1766i	0.976486	−	0.976486i	0.999730	+	0.0232442i	$0.00739953\pi$
$614$		0			0
$615$			7.93942i			0.320148i
$616$		0			0
$617$		−	15.0311i		−	0.605131i	−0.953129	−	0.302566i	$-0.902157\pi$
$617$		−	15.0311i		−	0.605131i	0.953129	−	0.302566i	$-0.0978431\pi$
$618$		0			0
$619$	−1.08276	+	1.08276i	−0.0435198	+	0.0435198i	−0.728532	−	0.685012i	$-0.759797\pi$
$619$	−1.08276	+	1.08276i	−0.0435198	+	0.0435198i	0.685012	+	0.728532i	$0.259797\pi$
$620$		0			0
$621$	4.27702	+	4.27702i	0.171631	+	0.171631i
$622$		0			0
$623$	0.698930			0.0280020
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	14.0037	+	14.0037i	0.559254	+	0.559254i
$628$		0			0
$629$	9.59111	−	9.59111i	0.382423	−	0.382423i
$630$		0			0
$631$			16.1104i			0.641346i	0.947190	+	0.320673i	$0.103909\pi$
$631$			16.1104i			0.641346i	−0.947190	+	0.320673i	$0.896091\pi$
$632$		0			0
$633$			25.3718i			1.00844i
$634$		0			0
$635$	2.25567	−	2.25567i	0.0895135	−	0.0895135i
$636$		0			0
$637$	−6.51299	−	6.51299i	−0.258054	−	0.258054i
$638$		0			0
$639$	1.69234			0.0669481
$640$		0			0
$641$	33.5492			1.32511			0.662557	−	0.749012i	$-0.269471\pi$
$641$	33.5492			1.32511			0.662557	+	0.749012i	$0.269471\pi$
$642$		0			0
$643$	25.6497	+	25.6497i	1.01153	+	1.01153i	0.999933	+	0.0115939i	$0.00369055\pi$
$643$	25.6497	+	25.6497i	1.01153	+	1.01153i	0.0115939	+	0.999933i	$0.496309\pi$
$644$		0			0
$645$	8.89142	−	8.89142i	0.350099	−	0.350099i
$646$		0			0
$647$		−	36.6300i		−	1.44008i	−0.693935	−	0.720038i	$-0.744125\pi$
$647$		−	36.6300i		−	1.44008i	0.693935	−	0.720038i	$-0.255875\pi$
$648$		0			0
$649$			30.0316i			1.17884i
$650$		0			0
$651$	−0.0705524	+	0.0705524i	−0.00276517	+	0.00276517i
$652$		0			0
$653$	11.7702	+	11.7702i	0.460605	+	0.460605i	0.898854	−	0.438249i	$-0.144401\pi$
$653$	11.7702	+	11.7702i	0.460605	+	0.460605i	−0.438249	+	0.898854i	$0.644401\pi$
$654$		0			0
$655$	−7.96008			−0.311026
$656$		0			0
$657$	9.87065			0.385091
$658$		0			0
$659$	0.496974	+	0.496974i	0.0193593	+	0.0193593i	0.716720	−	0.697361i	$-0.245642\pi$
$659$	0.496974	+	0.496974i	0.0193593	+	0.0193593i	−0.697361	+	0.716720i	$0.745642\pi$
$660$		0			0
$661$	0.919644	−	0.919644i	0.0357700	−	0.0357700i	−0.688996	−	0.724766i	$-0.741948\pi$
$661$	0.919644	−	0.919644i	0.0357700	−	0.0357700i	0.724766	+	0.688996i	$0.241948\pi$
$662$		0			0
$663$		−	5.09173i		−	0.197746i
$664$		0			0
$665$			0.430963i			0.0167120i
$666$		0			0
$667$	6.82211	−	6.82211i	0.264153	−	0.264153i
$668$		0			0
$669$	−21.7985	−	21.7985i	−0.842778	−	0.842778i
$670$		0			0
$671$	−24.7179			−0.954224
$672$		0			0
$673$	−19.6303			−0.756693			−0.378346	−	0.925664i	$-0.623507\pi$
$673$	−19.6303			−0.756693			−0.378346	+	0.925664i	$0.623507\pi$
$674$		0			0
$675$	−3.96713	−	3.96713i	−0.152695	−	0.152695i
$676$		0			0
$677$	0.644131	−	0.644131i	0.0247560	−	0.0247560i	−0.694620	−	0.719376i	$-0.744428\pi$
$677$	0.644131	−	0.644131i	0.0247560	−	0.0247560i	0.719376	+	0.694620i	$0.244428\pi$
$678$		0			0
$679$		−	1.85890i		−	0.0713379i
$680$		0			0
$681$		−	40.9574i		−	1.56949i
$682$		0			0
$683$	29.6404	−	29.6404i	1.13416	−	1.13416i	0.144682	−	0.989478i	$-0.453784\pi$
$683$	29.6404	−	29.6404i	1.13416	−	1.13416i	0.989478	−	0.144682i	$-0.0462159\pi$
$684$		0			0
$685$	−0.196152	−	0.196152i	−0.00749460	−	0.00749460i
$686$		0			0
$687$	2.71139			0.103446
$688$		0			0
$689$	11.2621			0.429050
$690$		0			0
$691$	25.0761	+	25.0761i	0.953941	+	0.953941i	0.998985	−	0.0450436i	$-0.0143427\pi$
$691$	25.0761	+	25.0761i	0.953941	+	0.953941i	−0.0450436	+	0.998985i	$0.514343\pi$
$692$		0			0
$693$	0.159579	−	0.159579i	0.00606189	−	0.00606189i
$694$		0			0
$695$			17.1949i			0.652240i
$696$		0			0
$697$			13.3185i			0.504475i
$698$		0			0
$699$	24.4381	−	24.4381i	0.924332	−	0.924332i
$700$		0			0
$701$	−15.5904	−	15.5904i	−0.588841	−	0.588841i	0.348477	−	0.937317i	$-0.386699\pi$
$701$	−15.5904	−	15.5904i	−0.588841	−	0.588841i	−0.937317	+	0.348477i	$0.886699\pi$
$702$		0			0
$703$	22.2006			0.837311
$704$		0			0
$705$	14.9640			0.563577
$706$		0			0
$707$	−0.709875	−	0.709875i	−0.0266976	−	0.0266976i
$708$		0			0
$709$	8.59111	−	8.59111i	0.322646	−	0.322646i	−0.527135	−	0.849781i	$-0.676734\pi$
$709$	8.59111	−	8.59111i	0.322646	−	0.322646i	0.849781	+	0.527135i	$0.176734\pi$
$710$		0			0
$711$		−	7.63994i		−	0.286520i
$712$		0			0
$713$			0.685331i			0.0256658i
$714$		0			0
$715$	−2.91824	+	2.91824i	−0.109136	+	0.109136i
$716$		0			0
$717$	−23.6225	−	23.6225i	−0.882197	−	0.882197i
$718$		0			0
$719$	27.1112			1.01108			0.505538	−	0.862804i	$-0.331294\pi$
$719$	27.1112			1.01108			0.505538	+	0.862804i	$0.331294\pi$
$720$		0			0
$721$	−1.79655			−0.0669070
$722$		0			0
$723$	−20.9961	−	20.9961i	−0.780855	−	0.780855i
$724$		0			0
$725$	−6.32780	+	6.32780i	−0.235009	+	0.235009i
$726$		0			0
$727$			40.9979i			1.52053i	0.649614	+	0.760264i	$0.274931\pi$
$727$			40.9979i			1.52053i	−0.649614	+	0.760264i	$0.725069\pi$
$728$		0			0
$729$		−	30.0197i		−	1.11184i
$730$		0			0
$731$	14.9155	−	14.9155i	0.551670	−	0.551670i
$732$		0			0
$733$	−7.49473	−	7.49473i	−0.276824	−	0.276824i	0.555016	−	0.831840i	$-0.312712\pi$
$733$	−7.49473	−	7.49473i	−0.276824	−	0.276824i	−0.831840	+	0.555016i	$0.812712\pi$
$734$		0			0
$735$	10.6072			0.391254
$736$		0			0
$737$	−0.831595			−0.0306322
$738$		0			0
$739$	24.3947	+	24.3947i	0.897374	+	0.897374i	0.995203	−	0.0978293i	$-0.0311899\pi$
$739$	24.3947	+	24.3947i	0.897374	+	0.897374i	−0.0978293	+	0.995203i	$0.531190\pi$
$740$		0			0
$741$	5.89293	−	5.89293i	0.216482	−	0.216482i
$742$		0			0
$743$			13.5703i			0.497848i	0.968523	+	0.248924i	$0.0800769\pi$
$743$			13.5703i			0.497848i	−0.968523	+	0.248924i	$0.919923\pi$
$744$		0			0
$745$			8.22678i			0.301406i
$746$		0			0
$747$	0.717882	−	0.717882i	0.0262659	−	0.0262659i
$748$		0			0
$749$	1.25334	+	1.25334i	0.0457959	+	0.0457959i
$750$		0			0
$751$	22.3407			0.815225			0.407612	−	0.913155i	$-0.366361\pi$
$751$	22.3407			0.815225			0.407612	+	0.913155i	$0.366361\pi$
$752$		0			0
$753$	−8.41740			−0.306747
$754$		0			0
$755$	4.25674	+	4.25674i	0.154919	+	0.154919i
$756$		0			0
$757$	4.33046	−	4.33046i	0.157393	−	0.157393i	−0.624017	−	0.781410i	$-0.714501\pi$
$757$	4.33046	−	4.33046i	0.157393	−	0.157393i	0.781410	+	0.624017i	$0.214501\pi$
$758$		0			0
$759$			5.12398i			0.185989i
$760$		0			0
$761$			16.6770i			0.604541i	0.953222	+	0.302270i	$0.0977446\pi$
$761$			16.6770i			0.604541i	−0.953222	+	0.302270i	$0.902255\pi$
$762$		0			0
$763$	0.939629	−	0.939629i	0.0340168	−	0.0340168i
$764$		0			0
$765$	−1.25433	−	1.25433i	−0.0453505	−	0.0453505i
$766$		0			0
$767$	12.6377			0.456320
$768$		0			0
$769$	−6.38199			−0.230140			−0.115070	−	0.993357i	$-0.536709\pi$
$769$	−6.38199			−0.230140			−0.115070	+	0.993357i	$0.536709\pi$
$770$		0			0
$771$	−15.4600	−	15.4600i	−0.556777	−	0.556777i
$772$		0			0
$773$	−32.7136	+	32.7136i	−1.17663	+	1.17663i	−0.196027	+	0.980598i	$0.562804\pi$
$773$	−32.7136	+	32.7136i	−1.17663	+	1.17663i	−0.980598	+	0.196027i	$0.937196\pi$
$774$		0			0
$775$		−	0.635674i		−	0.0228341i
$776$		0			0
$777$			0.836258i			0.0300006i
$778$		0			0
$779$	−15.4142	+	15.4142i	−0.552272	+	0.552272i
$780$		0			0
$781$	5.37842	+	5.37842i	0.192455	+	0.192455i
$782$		0			0
$783$	−50.2064			−1.79423
$784$		0			0
$785$	12.9895			0.463614
$786$		0			0
$787$	−1.23233	−	1.23233i	−0.0439279	−	0.0439279i	0.684802	−	0.728730i	$-0.259889\pi$
$787$	−1.23233	−	1.23233i	−0.0439279	−	0.0439279i	−0.728730	+	0.684802i	$0.759889\pi$
$788$		0			0
$789$	−17.1803	+	17.1803i	−0.611635	+	0.611635i
$790$		0			0
$791$			0.661121i			0.0235068i
$792$		0			0
$793$			10.4016i			0.369371i
$794$		0			0
$795$	−9.17084	+	9.17084i	−0.325256	+	0.325256i
$796$		0			0
$797$	2.62007	+	2.62007i	0.0928075	+	0.0928075i	0.751986	−	0.659179i	$-0.229096\pi$
$797$	2.62007	+	2.62007i	0.0928075	+	0.0928075i	−0.659179	+	0.751986i	$0.729096\pi$
$798$		0			0
$799$	25.1024			0.888058
$800$		0			0
$801$	−4.70872			−0.166374
$802$		0			0
$803$	31.3698	+	31.3698i	1.10702	+	1.10702i
$804$		0			0
$805$	−0.0788450	+	0.0788450i	−0.00277892	+	0.00277892i
$806$		0			0
$807$		−	4.82060i		−	0.169693i
$808$		0			0
$809$		−	3.63795i		−	0.127904i	−0.997953	−	0.0639518i	$-0.979630\pi$
$809$		−	3.63795i		−	0.127904i	0.997953	−	0.0639518i	$-0.0203704\pi$
$810$		0			0
$811$	−25.1436	+	25.1436i	−0.882913	+	0.882913i	−0.993830	−	0.110917i	$-0.964621\pi$
$811$	−25.1436	+	25.1436i	−0.882913	+	0.882913i	0.110917	+	0.993830i	$0.464621\pi$
$812$		0			0
$813$	3.18937	+	3.18937i	0.111856	+	0.111856i
$814$		0			0
$815$	−3.88072			−0.135936
$816$		0			0
$817$	34.5250			1.20788
$818$		0			0
$819$	−0.0671526	−	0.0671526i	−0.00234650	−	0.00234650i
$820$		0			0
$821$	−8.04790	+	8.04790i	−0.280874	+	0.280874i	−0.833457	−	0.552584i	$-0.813642\pi$
$821$	−8.04790	+	8.04790i	−0.280874	+	0.280874i	0.552584	+	0.833457i	$0.313642\pi$
$822$		0			0
$823$		−	45.1452i		−	1.57366i	−0.617168	−	0.786832i	$-0.711720\pi$
$823$		−	45.1452i		−	1.57366i	0.617168	−	0.786832i	$-0.288280\pi$
$824$		0			0
$825$		−	4.75272i		−	0.165468i
$826$		0			0
$827$	−8.20254	+	8.20254i	−0.285230	+	0.285230i	−0.835191	−	0.549960i	$-0.814643\pi$
$827$	−8.20254	+	8.20254i	−0.285230	+	0.285230i	0.549960	+	0.835191i	$0.314643\pi$
$828$		0			0
$829$	−5.74467	−	5.74467i	−0.199521	−	0.199521i	0.600274	−	0.799795i	$-0.295058\pi$
$829$	−5.74467	−	5.74467i	−0.199521	−	0.199521i	−0.799795	+	0.600274i	$0.795058\pi$
$830$		0			0
$831$	43.1749			1.49772
$832$		0			0
$833$	17.7938			0.616520
$834$		0			0
$835$	−4.71585	−	4.71585i	−0.163199	−	0.163199i
$836$		0			0
$837$	2.52180	−	2.52180i	0.0871662	−	0.0871662i
$838$		0			0
$839$		−	29.7201i		−	1.02605i	−0.858373	−	0.513026i	$-0.828524\pi$
$839$		−	29.7201i		−	1.02605i	0.858373	−	0.513026i	$-0.171476\pi$
$840$		0			0
$841$			51.0822i			1.76146i
$842$		0			0
$843$	19.9457	−	19.9457i	0.686968	−	0.686968i
$844$		0			0
$845$	−7.96436	−	7.96436i	−0.273982	−	0.273982i
$846$		0			0
$847$	−0.123360			−0.00423870
$848$		0			0
$849$	−44.5348			−1.52843
$850$		0			0
$851$	4.06162	+	4.06162i	0.139230	+	0.139230i
$852$		0			0
$853$	−5.09538	+	5.09538i	−0.174463	+	0.174463i	−0.788937	−	0.614474i	$-0.789368\pi$
$853$	−5.09538	+	5.09538i	−0.174463	+	0.174463i	0.614474	+	0.788937i	$0.289368\pi$
$854$		0			0
$855$		−	2.90341i		−	0.0992945i
$856$		0			0
$857$		−	0.735948i		−	0.0251395i	−0.999921	−	0.0125698i	$-0.995999\pi$
$857$		−	0.735948i		−	0.0251395i	0.999921	−	0.0125698i	$-0.00400118\pi$
$858$		0			0
$859$	9.39668	−	9.39668i	0.320611	−	0.320611i	−0.528391	−	0.849001i	$-0.677204\pi$
$859$	9.39668	−	9.39668i	0.320611	−	0.320611i	0.849001	+	0.528391i	$0.177204\pi$
$860$		0			0
$861$	−0.580627	−	0.580627i	−0.0197877	−	0.0197877i
$862$		0			0
$863$	47.0950			1.60313			0.801565	−	0.597907i	$-0.204001\pi$
$863$	47.0950			1.60313			0.801565	+	0.597907i	$0.204001\pi$
$864$		0			0
$865$	−1.03528			−0.0352004
$866$		0			0
$867$	−11.2878	−	11.2878i	−0.383354	−	0.383354i
$868$		0			0
$869$	24.2804	−	24.2804i	0.823657	−	0.823657i
$870$		0			0
$871$			0.349945i			0.0118574i
$872$		0			0
$873$			12.5234i			0.423854i
$874$		0			0
$875$	0.0731322	−	0.0731322i	0.00247232	−	0.00247232i
$876$		0			0
$877$	38.7479	+	38.7479i	1.30842	+	1.30842i	0.922554	+	0.385868i	$0.126098\pi$
$877$	38.7479	+	38.7479i	1.30842	+	1.30842i	0.385868	+	0.922554i	$0.373902\pi$
$878$		0			0
$879$	−14.1452			−0.477104
$880$		0			0
$881$	−1.67684			−0.0564942			−0.0282471	−	0.999601i	$-0.508993\pi$
$881$	−1.67684			−0.0564942			−0.0282471	+	0.999601i	$0.508993\pi$
$882$		0			0
$883$	−31.4734	−	31.4734i	−1.05916	−	1.05916i	−0.998136	−	0.0610287i	$-0.980562\pi$
$883$	−31.4734	−	31.4734i	−1.05916	−	1.05916i	−0.0610287	−	0.998136i	$-0.519438\pi$
$884$		0			0
$885$	−10.2910	+	10.2910i	−0.345929	+	0.345929i
$886$		0			0
$887$			29.4396i			0.988484i	0.869324	+	0.494242i	$0.164554\pi$
$887$			29.4396i			0.988484i	−0.869324	+	0.494242i	$0.835446\pi$
$888$		0			0
$889$			0.329924i			0.0110653i
$890$		0			0
$891$	14.2258	−	14.2258i	0.476582	−	0.476582i
$892$		0			0
$893$	29.0523	+	29.0523i	0.972198	+	0.972198i
$894$		0			0
$895$	0.875644			0.0292696
$896$		0			0
$897$	2.15623			0.0719945
$898$		0			0
$899$	−4.02242	−	4.02242i	−0.134155	−	0.134155i
$900$		0			0
$901$	−15.3843	+	15.3843i	−0.512524	+	0.512524i
$902$		0			0
$903$			1.30050i			0.0432778i
$904$		0			0
$905$		−	10.6856i		−	0.355200i
$906$		0			0
$907$	−35.4520	+	35.4520i	−1.17716	+	1.17716i	−0.196702	+	0.980463i	$0.563023\pi$
$907$	−35.4520	+	35.4520i	−1.17716	+	1.17716i	−0.980463	+	0.196702i	$0.936977\pi$
$908$		0			0
$909$	4.78245	+	4.78245i	0.158624	+	0.158624i
$910$		0			0
$911$	−43.9590			−1.45643			−0.728213	−	0.685351i	$-0.759649\pi$
$911$	−43.9590			−1.45643			−0.728213	+	0.685351i	$0.759649\pi$
$912$		0			0
$913$	4.56298			0.151013
$914$		0			0
$915$	−8.47015	−	8.47015i	−0.280015	−	0.280015i
$916$		0			0
$917$	0.582138	−	0.582138i	0.0192239	−	0.0192239i
$918$		0			0
$919$		−	46.6638i		−	1.53930i	−0.638469	−	0.769648i	$-0.720432\pi$
$919$		−	46.6638i		−	1.53930i	0.638469	−	0.769648i	$-0.279568\pi$
$920$		0			0
$921$		−	1.06110i		−	0.0349644i
$922$		0			0
$923$	2.26330	−	2.26330i	0.0744976	−	0.0744976i
$924$		0			0
$925$	−3.76733	−	3.76733i	−0.123869	−	0.123869i
$926$		0			0
$927$	12.1034			0.397529
$928$		0			0
$929$	−44.3630			−1.45550			−0.727752	−	0.685840i	$-0.759435\pi$
$929$	−44.3630			−1.45550			−0.727752	+	0.685840i	$0.759435\pi$
$930$		0			0
$931$	20.5937	+	20.5937i	0.674932	+	0.674932i
$932$		0			0
$933$	10.9898	−	10.9898i	0.359791	−	0.359791i
$934$		0			0
$935$		−	7.97277i		−	0.260737i
$936$		0			0
$937$		−	1.00338i		−	0.0327790i	−0.999866	−	0.0163895i	$-0.994783\pi$
$937$		−	1.00338i		−	0.0327790i	0.999866	−	0.0163895i	$-0.00521718\pi$
$938$		0			0
$939$	−10.7376	+	10.7376i	−0.350408	+	0.350408i
$940$		0			0
$941$	−10.0597	−	10.0597i	−0.327937	−	0.327937i	0.523865	−	0.851801i	$-0.324490\pi$
$941$	−10.0597	−	10.0597i	−0.327937	−	0.327937i	−0.851801	+	0.523865i	$0.824490\pi$
$942$		0			0
$943$	−5.64009			−0.183667
$944$		0			0
$945$	0.580249			0.0188755
$946$		0			0
$947$	−18.3749	−	18.3749i	−0.597103	−	0.597103i	0.342438	−	0.939541i	$-0.388747\pi$
$947$	−18.3749	−	18.3749i	−0.597103	−	0.597103i	−0.939541	+	0.342438i	$0.888747\pi$
$948$		0			0
$949$	13.2008	−	13.2008i	0.428516	−	0.428516i
$950$		0			0
$951$			41.5175i			1.34630i
$952$		0			0
$953$		−	16.2842i		−	0.527497i	−0.964591	−	0.263749i	$-0.915041\pi$
$953$		−	16.2842i		−	0.527497i	0.964591	−	0.263749i	$-0.0849589\pi$
$954$		0			0
$955$	−17.1309	+	17.1309i	−0.554344	+	0.554344i
$956$		0			0
$957$	−30.0743	−	30.0743i	−0.972163	−	0.972163i
$958$		0			0
$959$	0.0286901			0.000926452
$960$		0			0
$961$	−30.5959			−0.986965
$962$		0			0
$963$	−8.44378	−	8.44378i	−0.272097	−	0.272097i
$964$		0			0
$965$	2.67511	−	2.67511i	0.0861150	−	0.0861150i
$966$		0			0
$967$			29.5190i			0.949269i	0.880183	+	0.474634i	$0.157420\pi$
$967$			29.5190i			0.949269i	−0.880183	+	0.474634i	$0.842580\pi$
$968$		0			0
$969$			16.0998i			0.517199i
$970$		0			0
$971$	−12.0000	+	12.0000i	−0.385099	+	0.385099i	−0.872935	−	0.487836i	$-0.837786\pi$
$971$	−12.0000	+	12.0000i	−0.385099	+	0.385099i	0.487836	+	0.872935i	$0.337786\pi$
$972$		0			0
$973$	−1.25750	−	1.25750i	−0.0403136	−	0.0403136i
$974$		0			0
$975$	−2.00000			−0.0640513
$976$		0			0
$977$	48.0884			1.53848			0.769241	−	0.638958i	$-0.220634\pi$
$977$	48.0884			1.53848			0.769241	+	0.638958i	$0.220634\pi$
$978$		0			0
$979$	−14.9647	−	14.9647i	−0.478275	−	0.478275i
$980$		0			0
$981$	−6.33031	+	6.33031i	−0.202111	+	0.202111i
$982$		0			0
$983$			37.1975i			1.18642i	0.805050	+	0.593208i	$0.202139\pi$
$983$			37.1975i			1.18642i	−0.805050	+	0.593208i	$0.797861\pi$
$984$		0			0
$985$		−	20.5517i		−	0.654832i
$986$		0			0
$987$	−1.09435	+	1.09435i	−0.0348335	+	0.0348335i
$988$		0			0
$989$	6.31638	+	6.31638i	0.200849	+	0.200849i
$990$		0			0
$991$	−42.2588			−1.34240			−0.671198	−	0.741278i	$-0.734220\pi$
$991$	−42.2588			−1.34240			−0.671198	+	0.741278i	$0.734220\pi$
$992$		0			0
$993$	−47.7954			−1.51674
$994$		0			0
$995$	17.3843	+	17.3843i	0.551118	+	0.551118i
$996$		0			0
$997$	−40.6128	+	40.6128i	−1.28622	+	1.28622i	−0.349154	+	0.937065i	$0.613531\pi$
$997$	−40.6128	+	40.6128i	−1.28622	+	1.28622i	−0.937065	+	0.349154i	$0.886469\pi$
$998$		0			0
$999$		−	29.8909i		−	0.945707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.l.d.321.4	yes	8
4.3	odd	2		1280.2.l.g.321.1	yes	8
8.3	odd	2		1280.2.l.a.321.4	✓	8
8.5	even	2		1280.2.l.f.321.1	yes	8
16.3	odd	4		1280.2.l.a.961.4	yes	8
16.5	even	4	inner	1280.2.l.d.961.4	yes	8
16.11	odd	4		1280.2.l.g.961.1	yes	8
16.13	even	4		1280.2.l.f.961.1	yes	8
32.5	even	8		5120.2.a.b.1.2		4
32.11	odd	8		5120.2.a.a.1.2		4
32.21	even	8		5120.2.a.q.1.3		4
32.27	odd	8		5120.2.a.r.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1280.2.l.a.321.4	✓	8	8.3	odd	2
1280.2.l.a.961.4	yes	8	16.3	odd	4
1280.2.l.d.321.4	yes	8	1.1	even	1	trivial
1280.2.l.d.961.4	yes	8	16.5	even	4	inner
1280.2.l.f.321.1	yes	8	8.5	even	2
1280.2.l.f.961.1	yes	8	16.13	even	4
1280.2.l.g.321.1	yes	8	4.3	odd	2
1280.2.l.g.961.1	yes	8	16.11	odd	4
5120.2.a.a.1.2		4	32.11	odd	8
5120.2.a.b.1.2		4	32.5	even	8
5120.2.a.q.1.3		4	32.21	even	8
5120.2.a.r.1.3		4	32.27	odd	8

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:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1280.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.07313 + 1.07313i) q^{3} +(0.707107 - 0.707107i) q^{5} +0.103425i q^{7} -0.696775i q^{9} +(2.21441 - 2.21441i) q^{11} +(-0.931852 - 0.931852i) q^{13} +1.51764 q^{15} +2.54587 q^{17} +(2.94646 + 2.94646i) q^{19} +(-0.110988 + 0.110988i) q^{21} +1.07812i q^{23} -1.00000i q^{25} +(3.96713 - 3.96713i) q^{27} +(-6.32780 - 6.32780i) q^{29} +0.635674 q^{31} +4.75272 q^{33} +(0.0731322 + 0.0731322i) q^{35} +(3.76733 - 3.76733i) q^{37} -2.00000i q^{39} +5.23143i q^{41} +(5.85872 - 5.85872i) q^{43} +(-0.492694 - 0.492694i) q^{45} +9.86005 q^{47} +6.98930 q^{49} +(2.73205 + 2.73205i) q^{51} +(-6.04284 + 6.04284i) q^{53} -3.13165i q^{55} +6.32389i q^{57} +(-6.78094 + 6.78094i) q^{59} +(-5.58114 - 5.58114i) q^{61} +0.0720636 q^{63} -1.31784 q^{65} +(-0.187769 - 0.187769i) q^{67} +(-1.15696 + 1.15696i) q^{69} +2.42883i q^{71} +14.1662i q^{73} +(1.07313 - 1.07313i) q^{75} +(0.229025 + 0.229025i) q^{77} +10.9647 q^{79} +6.42418 q^{81} +(1.03029 + 1.03029i) q^{83} +(1.80020 - 1.80020i) q^{85} -13.5811i q^{87} -6.75787i q^{89} +(0.0963763 - 0.0963763i) q^{91} +(0.682163 + 0.682163i) q^{93} +4.16693 q^{95} -17.9734 q^{97} +(-1.54295 - 1.54295i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 8 q^{11} + 8 q^{13} + 8 q^{15} - 8 q^{17} + 16 q^{21} + 8 q^{27} + 8 q^{29} + 24 q^{33} - 12 q^{35} + 8 q^{37} + 44 q^{43} - 8 q^{45} + 8 q^{47} + 8 q^{51} - 16 q^{53} - 16 q^{59} - 8 q^{61}+ \cdots - 56 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 + 8 * q^11 + 8 * q^13 + 8 * q^15 - 8 * q^17 + 16 * q^21 + 8 * q^27 + 8 * q^29 + 24 * q^33 - 12 * q^35 + 8 * q^37 + 44 * q^43 - 8 * q^45 + 8 * q^47 + 8 * q^51 - 16 * q^53 - 16 * q^59 - 8 * q^61 - 48 * q^63 - 8 * q^65 - 12 * q^67 - 40 * q^69 - 4 * q^75 - 16 * q^77 + 96 * q^79 - 16 * q^81 + 28 * q^83 + 16 * q^85 - 8 * q^91 + 8 * q^93 + 8 * q^95 - 24 * q^97 - 56 * q^99

Introduction

L-functions

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