LMFDB - Embedded newform 1280.2.l.g.321.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1280,2,Mod(321,1280)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [8,0,4,0,0,0,0,0,0,0,-8,0,8,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(15)] == traces)

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			321.2
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1280.321
Dual form			1280.2.l.g.961.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.341081 + 0.341081i) q^{3} +(-0.707107 + 0.707107i) q^{5} -1.89658i q^{7} -2.76733i q^{9} +(-3.24969 + 3.24969i) q^{11} +(2.93185 + 2.93185i) q^{13} -0.482362 q^{15} -8.00997 q^{17} +(-3.98174 - 3.98174i) q^{19} +(0.646887 - 0.646887i) q^{21} +5.61401i q^{23} -1.00000i q^{25} +(1.96713 - 1.96713i) q^{27} +(1.39960 + 1.39960i) q^{29} -6.29253 q^{31} -2.21682 q^{33} +(1.34108 + 1.34108i) q^{35} +(1.69677 - 1.69677i) q^{37} +2.00000i q^{39} +3.16088i q^{41} +(-3.40923 + 3.40923i) q^{43} +(1.95680 + 1.95680i) q^{45} -5.99635 q^{47} +3.40300 q^{49} +(-2.73205 - 2.73205i) q^{51} +(-1.42126 + 1.42126i) q^{53} -4.59575i q^{55} -2.71619i q^{57} +(-9.70915 + 9.70915i) q^{59} +(7.04524 + 7.04524i) q^{61} -5.24844 q^{63} -4.14626 q^{65} +(-5.84802 - 5.84802i) q^{67} +(-1.91484 + 1.91484i) q^{69} -4.49938i q^{71} -9.77389i q^{73} +(0.341081 - 0.341081i) q^{75} +(6.16328 + 6.16328i) q^{77} -13.0353 q^{79} -6.96008 q^{81} +(-4.23766 - 4.23766i) q^{83} +(5.66390 - 5.66390i) q^{85} +0.954756i q^{87} -5.24213i q^{89} +(5.56048 - 5.56048i) q^{91} +(-2.14626 - 2.14626i) q^{93} +5.63103 q^{95} -5.34706 q^{97} +(8.99295 + 8.99295i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.341081	+	0.341081i	0.196923	+	0.196923i	0.798680	−	0.601756i	$-0.205532\pi$
$3$	0.341081	+	0.341081i	0.196923	+	0.196923i	−0.601756	+	0.798680i	$0.705532\pi$
$4$		0			0
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$		0			0
$7$		−	1.89658i		−	0.716838i	−0.933561	−	0.358419i	$-0.883316\pi$
$7$		−	1.89658i		−	0.716838i	0.933561	−	0.358419i	$-0.116684\pi$
$8$		0			0
$9$		−	2.76733i		−	0.922442i
$10$		0			0
$11$	−3.24969	+	3.24969i	−0.979818	+	0.979818i	−0.999800	−	0.0199823i	$-0.993639\pi$
$11$	−3.24969	+	3.24969i	−0.979818	+	0.979818i	0.0199823	+	0.999800i	$0.493639\pi$
$12$		0			0
$13$	2.93185	+	2.93185i	0.813149	+	0.813149i	0.985105	−	0.171955i	$-0.0550085\pi$
$13$	2.93185	+	2.93185i	0.813149	+	0.813149i	−0.171955	+	0.985105i	$0.555008\pi$
$14$		0			0
$15$	−0.482362			−0.124545
$16$		0			0
$17$	−8.00997			−1.94270			−0.971351	−	0.237648i	$-0.923623\pi$
$17$	−8.00997			−1.94270			−0.971351	+	0.237648i	$0.923623\pi$
$18$		0			0
$19$	−3.98174	−	3.98174i	−0.913474	−	0.913474i	0.0830700	−	0.996544i	$-0.473527\pi$
$19$	−3.98174	−	3.98174i	−0.913474	−	0.913474i	−0.996544	+	0.0830700i	$0.973527\pi$
$20$		0			0
$21$	0.646887	−	0.646887i	0.141162	−	0.141162i
$22$		0			0
$23$			5.61401i			1.17060i	0.810816	+	0.585301i	$0.199024\pi$
$23$			5.61401i			1.17060i	−0.810816	+	0.585301i	$0.800976\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$		0			0
$27$	1.96713	−	1.96713i	0.378574	−	0.378574i
$28$		0			0
$29$	1.39960	+	1.39960i	0.259900	+	0.259900i	0.825013	−	0.565114i	$-0.191168\pi$
$29$	1.39960	+	1.39960i	0.259900	+	0.259900i	−0.565114	+	0.825013i	$0.691168\pi$
$30$		0			0
$31$	−6.29253			−1.13017			−0.565086	−	0.825032i	$-0.691157\pi$
$31$	−6.29253			−1.13017			−0.565086	+	0.825032i	$0.691157\pi$
$32$		0			0
$33$	−2.21682			−0.385898
$34$		0			0
$35$	1.34108	+	1.34108i	0.226684	+	0.226684i
$36$		0			0
$37$	1.69677	−	1.69677i	0.278948	−	0.278948i	−0.553741	−	0.832689i	$-0.686800\pi$
$37$	1.69677	−	1.69677i	0.278948	−	0.278948i	0.832689	+	0.553741i	$0.186800\pi$
$38$		0			0
$39$			2.00000i			0.320256i
$40$		0			0
$41$			3.16088i			0.493646i	0.969061	+	0.246823i	$0.0793866\pi$
$41$			3.16088i			0.493646i	−0.969061	+	0.246823i	$0.920613\pi$
$42$		0			0
$43$	−3.40923	+	3.40923i	−0.519903	+	0.519903i	−0.917542	−	0.397639i	$-0.869830\pi$
$43$	−3.40923	+	3.40923i	−0.519903	+	0.519903i	0.397639	+	0.917542i	$0.369830\pi$
$44$		0			0
$45$	1.95680	+	1.95680i	0.291702	+	0.291702i
$46$		0			0
$47$	−5.99635			−0.874658			−0.437329	−	0.899302i	$-0.644075\pi$
$47$	−5.99635			−0.874658			−0.437329	+	0.899302i	$0.644075\pi$
$48$		0			0
$49$	3.40300			0.486143
$50$		0			0
$51$	−2.73205	−	2.73205i	−0.382564	−	0.382564i
$52$		0			0
$53$	−1.42126	+	1.42126i	−0.195225	+	0.195225i	−0.797950	−	0.602724i	$-0.794082\pi$
$53$	−1.42126	+	1.42126i	−0.195225	+	0.195225i	0.602724	+	0.797950i	$0.294082\pi$
$54$		0			0
$55$		−	4.59575i		−	0.619691i
$56$		0			0
$57$		−	2.71619i		−	0.359769i
$58$		0			0
$59$	−9.70915	+	9.70915i	−1.26402	+	1.26402i	−0.314898	+	0.949126i	$0.601970\pi$
$59$	−9.70915	+	9.70915i	−1.26402	+	1.26402i	−0.949126	+	0.314898i	$0.898030\pi$
$60$		0			0
$61$	7.04524	+	7.04524i	0.902051	+	0.902051i	0.995613	−	0.0935624i	$-0.0298255\pi$
$61$	7.04524	+	7.04524i	0.902051	+	0.902051i	−0.0935624	+	0.995613i	$0.529825\pi$
$62$		0			0
$63$	−5.24844			−0.661242
$64$		0			0
$65$	−4.14626			−0.514281
$66$		0			0
$67$	−5.84802	−	5.84802i	−0.714450	−	0.714450i	0.253013	−	0.967463i	$-0.418578\pi$
$67$	−5.84802	−	5.84802i	−0.714450	−	0.714450i	−0.967463	+	0.253013i	$0.918578\pi$
$68$		0			0
$69$	−1.91484	+	1.91484i	−0.230519	+	0.230519i
$70$		0			0
$71$		−	4.49938i		−	0.533978i	−0.963700	−	0.266989i	$-0.913971\pi$
$71$		−	4.49938i		−	0.533978i	0.963700	−	0.266989i	$-0.0860287\pi$
$72$		0			0
$73$		−	9.77389i		−	1.14395i	−0.820272	−	0.571974i	$-0.806178\pi$
$73$		−	9.77389i		−	1.14395i	0.820272	−	0.571974i	$-0.193822\pi$
$74$		0			0
$75$	0.341081	−	0.341081i	0.0393847	−	0.0393847i
$76$		0			0
$77$	6.16328	+	6.16328i	0.702371	+	0.702371i
$78$		0			0
$79$	−13.0353			−1.46658			−0.733292	−	0.679914i	$-0.762017\pi$
$79$	−13.0353			−1.46658			−0.733292	+	0.679914i	$0.762017\pi$
$80$		0			0
$81$	−6.96008			−0.773342
$82$		0			0
$83$	−4.23766	−	4.23766i	−0.465143	−	0.465143i	0.435194	−	0.900337i	$-0.356680\pi$
$83$	−4.23766	−	4.23766i	−0.465143	−	0.465143i	−0.900337	+	0.435194i	$0.856680\pi$
$84$		0			0
$85$	5.66390	−	5.66390i	0.614336	−	0.614336i
$86$		0			0
$87$			0.954756i			0.102361i
$88$		0			0
$89$		−	5.24213i		−	0.555664i	−0.960630	−	0.277832i	$-0.910384\pi$
$89$		−	5.24213i		−	0.555664i	0.960630	−	0.277832i	$-0.0896159\pi$
$90$		0			0
$91$	5.56048	−	5.56048i	0.582896	−	0.582896i
$92$		0			0
$93$	−2.14626	−	2.14626i	−0.222557	−	0.222557i
$94$		0			0
$95$	5.63103			0.577732
$96$		0			0
$97$	−5.34706			−0.542912			−0.271456	−	0.962451i	$-0.587505\pi$
$97$	−5.34706			−0.542912			−0.271456	+	0.962451i	$0.587505\pi$
$98$		0			0
$99$	8.99295	+	8.99295i	0.903826	+	0.903826i
$100$		0			0
$101$	0.863703	−	0.863703i	0.0859417	−	0.0859417i	−0.662829	−	0.748771i	$-0.730644\pi$
$101$	0.863703	−	0.863703i	0.0859417	−	0.0859417i	0.748771	+	0.662829i	$0.230644\pi$
$102$		0			0
$103$		−	5.02166i		−	0.494799i	−0.968914	−	0.247399i	$-0.920424\pi$
$103$		−	5.02166i		−	0.494799i	0.968914	−	0.247399i	$-0.0795760\pi$
$104$		0			0
$105$			0.914836i			0.0892788i
$106$		0			0
$107$	1.92222	−	1.92222i	0.185828	−	0.185828i	−0.608062	−	0.793890i	$-0.708053\pi$
$107$	1.92222	−	1.92222i	0.185828	−	0.185828i	0.793890	+	0.608062i	$0.208053\pi$
$108$		0			0
$109$	−9.84304	−	9.84304i	−0.942792	−	0.942792i	0.0556578	−	0.998450i	$-0.482274\pi$
$109$	−9.84304	−	9.84304i	−0.942792	−	0.942792i	−0.998450	+	0.0556578i	$0.982274\pi$
$110$		0			0
$111$	1.15748			0.109863
$112$		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
$115$	−3.96971	−	3.96971i	−0.370177	−	0.370177i
$116$		0			0
$117$	8.11339	−	8.11339i	0.750083	−	0.750083i
$118$		0			0
$119$			15.1915i			1.39260i
$120$		0			0
$121$		−	10.1210i		−	0.920087i
$122$		0			0
$123$	−1.07812	+	1.07812i	−0.0972104	+	0.0972104i
$124$		0			0
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$		0			0
$127$	21.5823			1.91512			0.957560	−	0.288235i	$-0.0930683\pi$
$127$	21.5823			1.91512			0.957560	+	0.288235i	$0.0930683\pi$
$128$		0			0
$129$	−2.32565			−0.204762
$130$		0			0
$131$	3.83548	+	3.83548i	0.335107	+	0.335107i	0.854522	−	0.519415i	$-0.173850\pi$
$131$	3.83548	+	3.83548i	0.335107	+	0.335107i	−0.519415	+	0.854522i	$0.673850\pi$
$132$		0			0
$133$	−7.55167	+	7.55167i	−0.654813	+	0.654813i
$134$		0			0
$135$			2.78194i			0.239431i
$136$		0			0
$137$			0.277401i			0.0237000i	0.999930	+	0.0118500i	$0.00377206\pi$
$137$			0.277401i			0.0237000i	−0.999930	+	0.0118500i	$0.996228\pi$
$138$		0			0
$139$	−9.23043	+	9.23043i	−0.782915	+	0.782915i	−0.980322	−	0.197407i	$-0.936748\pi$
$139$	−9.23043	+	9.23043i	−0.782915	+	0.782915i	0.197407	+	0.980322i	$0.436748\pi$
$140$		0			0
$141$	−2.04524	−	2.04524i	−0.172241	−	0.172241i
$142$		0			0
$143$	−19.0552			−1.59348
$144$		0			0
$145$	−1.97934			−0.164375
$146$		0			0
$147$	1.16070	+	1.16070i	0.0957330	+	0.0957330i
$148$		0			0
$149$	−6.57509	+	6.57509i	−0.538652	+	0.538652i	−0.923133	−	0.384481i	$-0.874381\pi$
$149$	−6.57509	+	6.57509i	−0.538652	+	0.538652i	0.384481	+	0.923133i	$0.374381\pi$
$150$		0			0
$151$			15.0917i			1.22815i	0.789249	+	0.614074i	$0.210470\pi$
$151$			15.0917i			1.22815i	−0.789249	+	0.614074i	$0.789530\pi$
$152$		0			0
$153$			22.1662i			1.79203i
$154$		0			0
$155$	4.44949	−	4.44949i	0.357392	−	0.357392i
$156$		0			0
$157$	15.5997	+	15.5997i	1.24499	+	1.24499i	0.957906	+	0.287084i	$0.0926858\pi$
$157$	15.5997	+	15.5997i	1.24499	+	1.24499i	0.287084	+	0.957906i	$0.407314\pi$
$158$		0			0
$159$	−0.969532			−0.0768889
$160$		0			0
$161$	10.6474			0.839133
$162$		0			0
$163$	4.91617	+	4.91617i	0.385064	+	0.385064i	0.872923	−	0.487858i	$-0.162222\pi$
$163$	4.91617	+	4.91617i	0.385064	+	0.385064i	−0.487858	+	0.872923i	$0.662222\pi$
$164$		0			0
$165$	1.56753	−	1.56753i	0.122032	−	0.122032i
$166$		0			0
$167$		−	23.2051i		−	1.79567i	−0.440336	−	0.897833i	$-0.645141\pi$
$167$		−	23.2051i		−	1.79567i	0.440336	−	0.897833i	$-0.354859\pi$
$168$		0			0
$169$			4.19151i			0.322424i
$170$		0			0
$171$	−11.0188	+	11.0188i	−0.842627	+	0.842627i
$172$		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
$175$	−1.89658			−0.143368
$176$		0			0
$177$	−6.62322			−0.497832
$178$		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
$181$	−13.5558	+	13.5558i	−1.00760	+	1.00760i	−0.00762627	+	0.999971i	$0.502428\pi$
$181$	−13.5558	+	13.5558i	−1.00760	+	1.00760i	−0.999971	+	0.00762627i	$0.997572\pi$
$182$		0			0
$183$			4.80600i			0.355270i
$184$		0			0
$185$			2.39960i			0.176422i
$186$		0			0
$187$	26.0299	−	26.0299i	1.90350	−	1.90350i
$188$		0			0
$189$	−3.73081	−	3.73081i	−0.271376	−	0.271376i
$190$		0			0
$191$	6.70142			0.484898			0.242449	−	0.970164i	$-0.422049\pi$
$191$	6.70142			0.484898			0.242449	+	0.970164i	$0.422049\pi$
$192$		0			0
$193$	10.7527			0.773997			0.386999	−	0.922080i	$-0.373512\pi$
$193$	10.7527			0.773997			0.386999	+	0.922080i	$0.373512\pi$
$194$		0			0
$195$	−1.41421	−	1.41421i	−0.101274	−	0.101274i
$196$		0			0
$197$	18.3960	−	18.3960i	1.31066	−	1.31066i	0.389727	−	0.920930i	$-0.372569\pi$
$197$	18.3960	−	18.3960i	1.31066	−	1.31066i	0.920930	−	0.389727i	$-0.127431\pi$
$198$		0			0
$199$		−	13.2713i		−	0.940781i	−0.882458	−	0.470390i	$-0.844113\pi$
$199$		−	13.2713i		−	0.940781i	0.882458	−	0.470390i	$-0.155887\pi$
$200$		0			0
$201$		−	3.98930i		−	0.281384i
$202$		0			0
$203$	2.65445	−	2.65445i	0.186306	−	0.186306i
$204$		0			0
$205$	−2.23508	−	2.23508i	−0.156105	−	0.156105i
$206$		0			0
$207$	15.5358			1.07981
$208$		0			0
$209$	25.8788			1.79008
$210$		0			0
$211$	1.28548	+	1.28548i	0.0884961	+	0.0884961i	0.749969	−	0.661473i	$-0.230068\pi$
$211$	1.28548	+	1.28548i	0.0884961	+	0.0884961i	−0.661473	+	0.749969i	$0.730068\pi$
$212$		0			0
$213$	1.53465	−	1.53465i	0.105153	−	0.105153i
$214$		0			0
$215$		−	4.82138i		−	0.328815i
$216$		0			0
$217$			11.9343i			0.810150i
$218$		0			0
$219$	3.33369	−	3.33369i	0.225270	−	0.225270i
$220$		0			0
$221$	−23.4840	−	23.4840i	−1.57971	−	1.57971i
$222$		0			0
$223$	22.8640			1.53108			0.765542	−	0.643386i	$-0.222471\pi$
$223$	22.8640			1.53108			0.765542	+	0.643386i	$0.222471\pi$
$224$		0			0
$225$	−2.76733			−0.184488
$226$		0			0
$227$	7.11305	+	7.11305i	0.472110	+	0.472110i	0.902597	−	0.430487i	$-0.141658\pi$
$227$	7.11305	+	7.11305i	0.472110	+	0.472110i	−0.430487	+	0.902597i	$0.641658\pi$
$228$		0			0
$229$	−14.1915	+	14.1915i	−0.937801	+	0.937801i	−0.998176	−	0.0603745i	$-0.980770\pi$
$229$	−14.1915	+	14.1915i	−0.937801	+	0.937801i	0.0603745	+	0.998176i	$0.480770\pi$
$230$		0			0
$231$			4.20436i			0.276627i
$232$		0			0
$233$			5.30855i			0.347775i	0.984766	+	0.173887i	$0.0556328\pi$
$233$			5.30855i			0.347775i	−0.984766	+	0.173887i	$0.944367\pi$
$234$		0			0
$235$	4.24006	−	4.24006i	0.276591	−	0.276591i
$236$		0			0
$237$	−4.44609	−	4.44609i	−0.288805	−	0.288805i
$238$		0			0
$239$	8.62838			0.558123			0.279062	−	0.960273i	$-0.409977\pi$
$239$	8.62838			0.558123			0.279062	+	0.960273i	$0.409977\pi$
$240$		0			0
$241$	2.10118			0.135349			0.0676746	−	0.997707i	$-0.478442\pi$
$241$	2.10118			0.135349			0.0676746	+	0.997707i	$0.478442\pi$
$242$		0			0
$243$	−8.27534	−	8.27534i	−0.530863	−	0.530863i
$244$		0			0
$245$	−2.40629	+	2.40629i	−0.153732	+	0.153732i
$246$		0			0
$247$		−	23.3477i		−	1.48558i
$248$		0			0
$249$		−	2.89077i		−	0.183195i
$250$		0			0
$251$	10.6140	−	10.6140i	0.669951	−	0.669951i	−0.287754	−	0.957704i	$-0.592908\pi$
$251$	10.6140	−	10.6140i	0.669951	−	0.669951i	0.957704	+	0.287754i	$0.0929085\pi$
$252$		0			0
$253$	−18.2438	−	18.2438i	−1.14698	−	1.14698i
$254$		0			0
$255$	3.86370			0.241954
$256$		0			0
$257$	−29.3064			−1.82808			−0.914042	−	0.405620i	$-0.867056\pi$
$257$	−29.3064			−1.82808			−0.914042	+	0.405620i	$0.867056\pi$
$258$		0			0
$259$	−3.21806	−	3.21806i	−0.199961	−	0.199961i
$260$		0			0
$261$	3.87316	−	3.87316i	0.239742	−	0.239742i
$262$		0			0
$263$			23.8659i			1.47163i	0.677180	+	0.735817i	$0.263202\pi$
$263$			23.8659i			1.47163i	−0.677180	+	0.735817i	$0.736798\pi$
$264$		0			0
$265$		−	2.00997i		−	0.123471i
$266$		0			0
$267$	1.78799	−	1.78799i	0.109423	−	0.109423i
$268$		0			0
$269$	−5.07447	−	5.07447i	−0.309396	−	0.309396i	0.535279	−	0.844675i	$-0.320206\pi$
$269$	−5.07447	−	5.07447i	−0.309396	−	0.309396i	−0.844675	+	0.535279i	$0.820206\pi$
$270$		0			0
$271$	2.68483			0.163092			0.0815460	−	0.996670i	$-0.474014\pi$
$271$	2.68483			0.163092			0.0815460	+	0.996670i	$0.474014\pi$
$272$		0			0
$273$	3.79315			0.229572
$274$		0			0
$275$	3.24969	+	3.24969i	0.195964	+	0.195964i
$276$		0			0
$277$	−6.65221	+	6.65221i	−0.399693	+	0.399693i	−0.878125	−	0.478432i	$-0.841205\pi$
$277$	−6.65221	+	6.65221i	−0.399693	+	0.399693i	0.478432	+	0.878125i	$0.341205\pi$
$278$		0			0
$279$			17.4135i			1.04252i
$280$		0			0
$281$			20.0506i			1.19612i	0.801453	+	0.598058i	$0.204061\pi$
$281$			20.0506i			1.19612i	−0.801453	+	0.598058i	$0.795939\pi$
$282$		0			0
$283$	−13.0897	+	13.0897i	−0.778100	+	0.778100i	−0.979508	−	0.201408i	$-0.935448\pi$
$283$	−13.0897	+	13.0897i	−0.778100	+	0.778100i	0.201408	+	0.979508i	$0.435448\pi$
$284$		0			0
$285$	1.92064	+	1.92064i	0.113769	+	0.113769i
$286$		0			0
$287$	5.99484			0.353864
$288$		0			0
$289$	47.1596			2.77409
$290$		0			0
$291$	−1.82378	−	1.82378i	−0.106912	−	0.106912i
$292$		0			0
$293$	6.59059	−	6.59059i	0.385027	−	0.385027i	−0.487883	−	0.872909i	$-0.662231\pi$
$293$	6.59059	−	6.59059i	0.385027	−	0.385027i	0.872909	+	0.487883i	$0.162231\pi$
$294$		0			0
$295$		−	13.7308i		−	0.799438i
$296$		0			0
$297$			12.7851i			0.741867i
$298$		0			0
$299$	−16.4595	+	16.4595i	−0.951875	+	0.951875i
$300$		0			0
$301$	6.46586	+	6.46586i	0.372686	+	0.372686i
$302$		0			0
$303$	0.589186			0.0338479
$304$		0			0
$305$	−9.96348			−0.570507
$306$		0			0
$307$	3.70176	+	3.70176i	0.211271	+	0.211271i	0.804807	−	0.593537i	$-0.202269\pi$
$307$	3.70176	+	3.70176i	0.211271	+	0.211271i	−0.593537	+	0.804807i	$0.702269\pi$
$308$		0			0
$309$	1.71279	−	1.71279i	0.0974375	−	0.0974375i
$310$		0			0
$311$			7.61553i			0.431837i	0.976411	+	0.215918i	$0.0692745\pi$
$311$			7.61553i			0.431837i	−0.976411	+	0.215918i	$0.930725\pi$
$312$		0			0
$313$		−	26.0058i		−	1.46994i	−0.678101	−	0.734968i	$-0.737197\pi$
$313$		−	26.0058i		−	1.46994i	0.678101	−	0.734968i	$-0.262803\pi$
$314$		0			0
$315$	3.71121	−	3.71121i	0.209103	−	0.209103i
$316$		0			0
$317$	−5.63128	−	5.63128i	−0.316284	−	0.316284i	0.531054	−	0.847338i	$-0.321796\pi$
$317$	−5.63128	−	5.63128i	−0.316284	−	0.316284i	−0.847338	+	0.531054i	$0.821796\pi$
$318$		0			0
$319$	−9.09654			−0.509308
$320$		0			0
$321$	1.31127			0.0731879
$322$		0			0
$323$	31.8936	+	31.8936i	1.77461	+	1.77461i
$324$		0			0
$325$	2.93185	−	2.93185i	0.162630	−	0.162630i
$326$		0			0
$327$		−	6.71455i		−	0.371316i
$328$		0			0
$329$			11.3725i			0.626988i
$330$		0			0
$331$	10.1232	−	10.1232i	0.556421	−	0.556421i	−0.371865	−	0.928287i	$-0.621282\pi$
$331$	10.1232	−	10.1232i	0.556421	−	0.556421i	0.928287	+	0.371865i	$0.121282\pi$
$332$		0			0
$333$	−4.69553	−	4.69553i	−0.257313	−	0.257313i
$334$		0			0
$335$	8.27035			0.451858
$336$		0			0
$337$	−1.45929			−0.0794928			−0.0397464	−	0.999210i	$-0.512655\pi$
$337$	−1.45929			−0.0794928			−0.0397464	+	0.999210i	$0.512655\pi$
$338$		0			0
$339$	2.18030	+	2.18030i	0.118417	+	0.118417i
$340$		0			0
$341$	20.4488	−	20.4488i	1.10736	−	1.10736i
$342$		0			0
$343$		−	19.7301i		−	1.06532i
$344$		0			0
$345$		−	2.70799i		−	0.145793i
$346$		0			0
$347$	14.9246	−	14.9246i	0.801196	−	0.801196i	−0.182087	−	0.983283i	$-0.558285\pi$
$347$	14.9246	−	14.9246i	0.801196	−	0.801196i	0.983283	+	0.182087i	$0.0582851\pi$
$348$		0			0
$349$	−10.2621	−	10.2621i	−0.549316	−	0.549316i	0.376927	−	0.926243i	$-0.376981\pi$
$349$	−10.2621	−	10.2621i	−0.549316	−	0.549316i	−0.926243	+	0.376927i	$0.876981\pi$
$350$		0			0
$351$	11.5347			0.615674
$352$		0			0
$353$	21.5332			1.14610			0.573048	−	0.819522i	$-0.305761\pi$
$353$	21.5332			1.14610			0.573048	+	0.819522i	$0.305761\pi$
$354$		0			0
$355$	3.18154	+	3.18154i	0.168859	+	0.168859i
$356$		0			0
$357$	−5.18154	+	5.18154i	−0.274236	+	0.274236i
$358$		0			0
$359$			23.7108i			1.25141i	0.780060	+	0.625705i	$0.215188\pi$
$359$			23.7108i			1.25141i	−0.780060	+	0.625705i	$0.784812\pi$
$360$		0			0
$361$			12.7085i			0.668869i
$362$		0			0
$363$	3.45207	−	3.45207i	0.181187	−	0.181187i
$364$		0			0
$365$	6.91119	+	6.91119i	0.361748	+	0.361748i
$366$		0			0
$367$	−2.46583			−0.128715			−0.0643575	−	0.997927i	$-0.520500\pi$
$367$	−2.46583			−0.128715			−0.0643575	+	0.997927i	$0.520500\pi$
$368$		0			0
$369$	8.74718			0.455360
$370$		0			0
$371$	2.69553	+	2.69553i	0.139945	+	0.139945i
$372$		0			0
$373$	−16.5817	+	16.5817i	−0.858566	+	0.858566i	−0.991169	−	0.132603i	$-0.957666\pi$
$373$	−16.5817	+	16.5817i	−0.858566	+	0.858566i	0.132603	+	0.991169i	$0.457666\pi$
$374$		0			0
$375$			0.482362i			0.0249091i
$376$		0			0
$377$			8.20685i			0.422674i
$378$		0			0
$379$	12.7530	−	12.7530i	0.655077	−	0.655077i	−0.299134	−	0.954211i	$-0.596698\pi$
$379$	12.7530	−	12.7530i	0.655077	−	0.655077i	0.954211	+	0.299134i	$0.0966979\pi$
$380$		0			0
$381$	7.36132	+	7.36132i	0.377132	+	0.377132i
$382$		0			0
$383$	27.7761			1.41929			0.709646	−	0.704559i	$-0.248855\pi$
$383$	27.7761			1.41929			0.709646	+	0.704559i	$0.248855\pi$
$384$		0			0
$385$	−8.71619			−0.444218
$386$		0			0
$387$	9.43445	+	9.43445i	0.479580	+	0.479580i
$388$		0			0
$389$	−10.1238	+	10.1238i	−0.513299	+	0.513299i	−0.915536	−	0.402237i	$-0.868233\pi$
$389$	−10.1238	+	10.1238i	−0.513299	+	0.513299i	0.402237	+	0.915536i	$0.368233\pi$
$390$		0			0
$391$		−	44.9681i		−	2.27413i
$392$		0			0
$393$			2.61642i			0.131981i
$394$		0			0
$395$	9.21733	−	9.21733i	0.463774	−	0.463774i
$396$		0			0
$397$	−2.63932	−	2.63932i	−0.132464	−	0.132464i	0.637766	−	0.770230i	$-0.279859\pi$
$397$	−2.63932	−	2.63932i	−0.132464	−	0.132464i	−0.770230	+	0.637766i	$0.779859\pi$
$398$		0			0
$399$	−5.15147			−0.257896
$400$		0			0
$401$	5.33261			0.266298			0.133149	−	0.991096i	$-0.457491\pi$
$401$	5.33261			0.266298			0.133149	+	0.991096i	$0.457491\pi$
$402$		0			0
$403$	−18.4488	−	18.4488i	−0.918998	−	0.918998i
$404$		0			0
$405$	4.92152	−	4.92152i	0.244552	−	0.244552i
$406$		0			0
$407$			11.0280i			0.546637i
$408$		0			0
$409$		−	6.82984i		−	0.337714i	−0.985641	−	0.168857i	$-0.945992\pi$
$409$		−	6.82984i		−	0.337714i	0.985641	−	0.168857i	$-0.0540075\pi$
$410$		0			0
$411$	−0.0946165	+	0.0946165i	−0.00466709	+	0.00466709i
$412$		0			0
$413$	18.4141	+	18.4141i	0.906100	+	0.906100i
$414$		0			0
$415$	5.99295			0.294182
$416$		0			0
$417$	−6.29666			−0.308349
$418$		0			0
$419$	−1.43728	−	1.43728i	−0.0702158	−	0.0702158i	0.671127	−	0.741343i	$-0.265811\pi$
$419$	−1.43728	−	1.43728i	−0.0702158	−	0.0702158i	−0.741343	+	0.671127i	$0.765811\pi$
$420$		0			0
$421$	−18.4728	+	18.4728i	−0.900310	+	0.900310i	−0.995463	−	0.0951523i	$-0.969666\pi$
$421$	−18.4728	+	18.4728i	−0.900310	+	0.900310i	0.0951523	+	0.995463i	$0.469666\pi$
$422$		0			0
$423$			16.5939i			0.806821i
$424$		0			0
$425$			8.00997i			0.388541i
$426$		0			0
$427$	13.3618	−	13.3618i	0.646625	−	0.646625i
$428$		0			0
$429$	−6.49938	−	6.49938i	−0.313793	−	0.313793i
$430$		0			0
$431$	−12.9282			−0.622730			−0.311365	−	0.950290i	$-0.600786\pi$
$431$	−12.9282			−0.622730			−0.311365	+	0.950290i	$0.600786\pi$
$432$		0			0
$433$	8.32389			0.400021			0.200010	−	0.979794i	$-0.435902\pi$
$433$	8.32389			0.400021			0.200010	+	0.979794i	$0.435902\pi$
$434$		0			0
$435$	−0.675115	−	0.675115i	−0.0323693	−	0.0323693i
$436$		0			0
$437$	22.3535	−	22.3535i	1.06932	−	1.06932i
$438$		0			0
$439$			27.3117i			1.30352i	0.758427	+	0.651759i	$0.225968\pi$
$439$			27.3117i			1.30352i	−0.758427	+	0.651759i	$0.774032\pi$
$440$		0			0
$441$		−	9.41722i		−	0.448439i
$442$		0			0
$443$	−6.07846	+	6.07846i	−0.288796	+	0.288796i	−0.836604	−	0.547808i	$-0.815462\pi$
$443$	−6.07846	+	6.07846i	−0.288796	+	0.288796i	0.547808	+	0.836604i	$0.315462\pi$
$444$		0			0
$445$	3.70674	+	3.70674i	0.175716	+	0.175716i
$446$		0			0
$447$	−4.48528			−0.212147
$448$		0			0
$449$	−34.8989			−1.64698			−0.823491	−	0.567329i	$-0.807977\pi$
$449$	−34.8989			−1.64698			−0.823491	+	0.567329i	$0.807977\pi$
$450$		0			0
$451$	−10.2719	−	10.2719i	−0.483683	−	0.483683i
$452$		0			0
$453$	−5.14751	+	5.14751i	−0.241851	+	0.241851i
$454$		0			0
$455$			7.86370i			0.368656i
$456$		0			0
$457$		−	33.5191i		−	1.56796i	−0.620788	−	0.783979i	$-0.713187\pi$
$457$		−	33.5191i		−	1.56796i	0.620788	−	0.783979i	$-0.286813\pi$
$458$		0			0
$459$	−15.7566	+	15.7566i	−0.735457	+	0.735457i
$460$		0			0
$461$	−3.13630	−	3.13630i	−0.146072	−	0.146072i	0.630289	−	0.776361i	$-0.282936\pi$
$461$	−3.13630	−	3.13630i	−0.146072	−	0.146072i	−0.776361	+	0.630289i	$0.782936\pi$
$462$		0			0
$463$	−39.4736			−1.83449			−0.917247	−	0.398320i	$-0.869593\pi$
$463$	−39.4736			−1.83449			−0.917247	+	0.398320i	$0.869593\pi$
$464$		0			0
$465$	3.03528			0.140758
$466$		0			0
$467$	−28.8755	−	28.8755i	−1.33620	−	1.33620i	−0.899708	−	0.436491i	$-0.856221\pi$
$467$	−28.8755	−	28.8755i	−1.33620	−	1.33620i	−0.436491	−	0.899708i	$-0.643779\pi$
$468$		0			0
$469$	−11.0912	+	11.0912i	−0.512145	+	0.512145i
$470$		0			0
$471$			10.6415i			0.490335i
$472$		0			0
$473$		−	22.1579i		−	1.01882i
$474$		0			0
$475$	−3.98174	+	3.98174i	−0.182695	+	0.182695i
$476$		0			0
$477$	3.93310	+	3.93310i	0.180084	+	0.180084i
$478$		0			0
$479$	−13.3911			−0.611853			−0.305927	−	0.952055i	$-0.598966\pi$
$479$	−13.3911			−0.611853			−0.305927	+	0.952055i	$0.598966\pi$
$480$		0			0
$481$	9.94938			0.453653
$482$		0			0
$483$	3.63163	+	3.63163i	0.165245	+	0.165245i
$484$		0			0
$485$	3.78094	−	3.78094i	0.171684	−	0.171684i
$486$		0			0
$487$		−	23.4804i		−	1.06400i	−0.846745	−	0.531999i	$-0.821441\pi$
$487$		−	23.4804i		−	1.06400i	0.846745	−	0.531999i	$-0.178559\pi$
$488$		0			0
$489$			3.35363i			0.151656i
$490$		0			0
$491$	−27.3346	+	27.3346i	−1.23360	+	1.23360i	−0.271022	+	0.962573i	$0.587362\pi$
$491$	−27.3346	+	27.3346i	−1.23360	+	1.23360i	−0.962573	+	0.271022i	$0.912638\pi$
$492$		0			0
$493$	−11.2108	−	11.2108i	−0.504907	−	0.504907i
$494$		0			0
$495$	−12.7180			−0.571630
$496$		0			0
$497$	−8.53341			−0.382776
$498$		0			0
$499$	9.25966	+	9.25966i	0.414519	+	0.414519i	0.883309	−	0.468790i	$-0.155310\pi$
$499$	9.25966	+	9.25966i	0.414519	+	0.414519i	−0.468790	+	0.883309i	$0.655310\pi$
$500$		0			0
$501$	7.91484	−	7.91484i	0.353609	−	0.353609i
$502$		0			0
$503$		−	5.58582i		−	0.249059i	−0.992216	−	0.124530i	$-0.960258\pi$
$503$		−	5.58582i		−	0.249059i	0.992216	−	0.124530i	$-0.0397422\pi$
$504$		0			0
$505$			1.22146i			0.0543543i
$506$		0			0
$507$	−1.42965	+	1.42965i	−0.0634928	+	0.0634928i
$508$		0			0
$509$	−5.41473	−	5.41473i	−0.240004	−	0.240004i	0.576848	−	0.816852i	$-0.304283\pi$
$509$	−5.41473	−	5.41473i	−0.240004	−	0.240004i	−0.816852	+	0.576848i	$0.804283\pi$
$510$		0			0
$511$	−18.5369			−0.820025
$512$		0			0
$513$	−15.6652			−0.691635
$514$		0			0
$515$	3.55085	+	3.55085i	0.156469	+	0.156469i
$516$		0			0
$517$	19.4863	−	19.4863i	0.857005	−	0.857005i
$518$		0			0
$519$		−	0.499378i		−	0.0219203i
$520$		0			0
$521$		−	14.9310i		−	0.654140i	−0.945000	−	0.327070i	$-0.893939\pi$
$521$		−	14.9310i		−	0.654140i	0.945000	−	0.327070i	$-0.106061\pi$
$522$		0			0
$523$	8.28050	−	8.28050i	0.362081	−	0.362081i	−0.502498	−	0.864579i	$-0.667585\pi$
$523$	8.28050	−	8.28050i	0.362081	−	0.362081i	0.864579	+	0.502498i	$0.167585\pi$
$524$		0			0
$525$	−0.646887	−	0.646887i	−0.0282324	−	0.0282324i
$526$		0			0
$527$	50.4030			2.19559
$528$		0			0
$529$	−8.51716			−0.370311
$530$		0			0
$531$	26.8684	+	26.8684i	1.16599	+	1.16599i
$532$		0			0
$533$	−9.26722	+	9.26722i	−0.401408	+	0.401408i
$534$		0			0
$535$			2.71843i			0.117528i
$536$		0			0
$537$			0.422377i			0.0182269i
$538$		0			0
$539$	−11.0587	+	11.0587i	−0.476332	+	0.476332i
$540$		0			0
$541$	−5.37718	−	5.37718i	−0.231183	−	0.231183i	0.582003	−	0.813186i	$-0.302269\pi$
$541$	−5.37718	−	5.37718i	−0.231183	−	0.231183i	−0.813186	+	0.582003i	$0.802269\pi$
$542$		0			0
$543$	−9.24728			−0.396839
$544$		0			0
$545$	13.9202			0.596274
$546$		0			0
$547$	−20.8797	−	20.8797i	−0.892749	−	0.892749i	0.102032	−	0.994781i	$-0.467466\pi$
$547$	−20.8797	−	20.8797i	−0.892749	−	0.892749i	−0.994781	+	0.102032i	$0.967466\pi$
$548$		0			0
$549$	19.4965	−	19.4965i	0.832090	−	0.832090i
$550$		0			0
$551$		−	11.1457i		−	0.474823i
$552$		0			0
$553$			24.7224i			1.05130i
$554$		0			0
$555$	−0.818459	+	0.818459i	−0.0347417	+	0.0347417i
$556$		0			0
$557$	28.3039	+	28.3039i	1.19927	+	1.19927i	0.974384	+	0.224891i	$0.0722026\pi$
$557$	28.3039	+	28.3039i	1.19927	+	1.19927i	0.224891	+	0.974384i	$0.427797\pi$
$558$		0			0
$559$	−19.9907			−0.845517
$560$		0			0
$561$	17.7566			0.749686
$562$		0			0
$563$	0.679067	+	0.679067i	0.0286193	+	0.0286193i	0.721272	−	0.692652i	$-0.243558\pi$
$563$	0.679067	+	0.679067i	0.0286193	+	0.0286193i	−0.692652	+	0.721272i	$0.743558\pi$
$564$		0			0
$565$	−4.52004	+	4.52004i	−0.190160	+	0.190160i
$566$		0			0
$567$			13.2003i			0.554361i
$568$		0			0
$569$			31.8870i			1.33677i	0.743814	+	0.668387i	$0.233015\pi$
$569$			31.8870i			1.33677i	−0.743814	+	0.668387i	$0.766985\pi$
$570$		0			0
$571$	−17.7856	+	17.7856i	−0.744304	+	0.744304i	−0.973403	−	0.229099i	$-0.926422\pi$
$571$	−17.7856	+	17.7856i	−0.744304	+	0.744304i	0.229099	+	0.973403i	$0.426422\pi$
$572$		0			0
$573$	2.28573	+	2.28573i	0.0954877	+	0.0954877i
$574$		0			0
$575$	5.61401			0.234121
$576$		0			0
$577$	−17.9504			−0.747286			−0.373643	−	0.927573i	$-0.621891\pi$
$577$	−17.9504			−0.747286			−0.373643	+	0.927573i	$0.621891\pi$
$578$		0			0
$579$	3.66755	+	3.66755i	0.152418	+	0.152418i
$580$		0			0
$581$	−8.03704	+	8.03704i	−0.333432	+	0.333432i
$582$		0			0
$583$		−	9.23732i		−	0.382571i
$584$		0			0
$585$			11.4741i			0.474394i
$586$		0			0
$587$	−3.13183	+	3.13183i	−0.129264	+	0.129264i	−0.768779	−	0.639515i	$-0.779135\pi$
$587$	−3.13183	+	3.13183i	−0.129264	+	0.129264i	0.639515	+	0.768779i	$0.279135\pi$
$588$		0			0
$589$	25.0552	+	25.0552i	1.03238	+	1.03238i
$590$		0			0
$591$	12.5490			0.516198
$592$		0			0
$593$	−33.1681			−1.36205			−0.681026	−	0.732259i	$-0.738466\pi$
$593$	−33.1681			−1.36205			−0.681026	+	0.732259i	$0.738466\pi$
$594$		0			0
$595$	−10.7420	−	10.7420i	−0.440380	−	0.440380i
$596$		0			0
$597$	4.52661	−	4.52661i	0.185262	−	0.185262i
$598$		0			0
$599$		−	37.7284i		−	1.54154i	−0.637112	−	0.770771i	$-0.719871\pi$
$599$		−	37.7284i		−	1.54154i	0.637112	−	0.770771i	$-0.280129\pi$
$600$		0			0
$601$		−	17.8671i		−	0.728814i	−0.931240	−	0.364407i	$-0.881272\pi$
$601$		−	17.8671i		−	0.728814i	0.931240	−	0.364407i	$-0.118728\pi$
$602$		0			0
$603$	−16.1834	+	16.1834i	−0.659039	+	0.659039i
$604$		0			0
$605$	7.15660	+	7.15660i	0.290957	+	0.290957i
$606$		0			0
$607$	−16.1526			−0.655613			−0.327807	−	0.944745i	$-0.606309\pi$
$607$	−16.1526			−0.655613			−0.327807	+	0.944745i	$0.606309\pi$
$608$		0			0
$609$	1.81077			0.0733760
$610$		0			0
$611$	−17.5804	−	17.5804i	−0.711227	−	0.711227i
$612$		0			0
$613$	19.0003	−	19.0003i	0.767414	−	0.767414i	−0.210237	−	0.977650i	$-0.567424\pi$
$613$	19.0003	−	19.0003i	0.767414	−	0.767414i	0.977650	+	0.210237i	$0.0674235\pi$
$614$		0			0
$615$		−	1.52469i		−	0.0614813i
$616$		0			0
$617$			12.4952i			0.503040i	0.967852	+	0.251520i	$0.0809304\pi$
$617$			12.4952i			0.503040i	−0.967852	+	0.251520i	$0.919070\pi$
$618$		0			0
$619$	9.84544	−	9.84544i	0.395722	−	0.395722i	−0.480999	−	0.876721i	$-0.659726\pi$
$619$	9.84544	−	9.84544i	0.395722	−	0.395722i	0.876721	+	0.480999i	$0.159726\pi$
$620$		0			0
$621$	11.0435	+	11.0435i	0.443160	+	0.443160i
$622$		0			0
$623$	−9.94209			−0.398321
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	8.82679	+	8.82679i	0.352508	+	0.352508i
$628$		0			0
$629$	−13.5911	+	13.5911i	−0.541913	+	0.541913i
$630$		0			0
$631$			30.2540i			1.20439i	0.798348	+	0.602197i	$0.205708\pi$
$631$			30.2540i			1.20439i	−0.798348	+	0.602197i	$0.794292\pi$
$632$		0			0
$633$			0.876907i			0.0348539i
$634$		0			0
$635$	−15.2610	+	15.2610i	−0.605614	+	0.605614i
$636$		0			0
$637$	9.97710	+	9.97710i	0.395307	+	0.395307i
$638$		0			0
$639$	−12.4512			−0.492564
$640$		0			0
$641$	−41.6543			−1.64525			−0.822623	−	0.568587i	$-0.807490\pi$
$641$	−41.6543			−1.64525			−0.822623	+	0.568587i	$0.807490\pi$
$642$		0			0
$643$	−32.7951	−	32.7951i	−1.29331	−	1.29331i	−0.932725	−	0.360589i	$-0.882576\pi$
$643$	−32.7951	−	32.7951i	−1.29331	−	1.29331i	−0.360589	−	0.932725i	$-0.617424\pi$
$644$		0			0
$645$	1.64448	−	1.64448i	0.0647514	−	0.0647514i
$646$		0			0
$647$			7.51356i			0.295388i	0.989033	+	0.147694i	$0.0471852\pi$
$647$			7.51356i			0.295388i	−0.989033	+	0.147694i	$0.952815\pi$
$648$		0			0
$649$		−	63.1034i		−	2.47703i
$650$		0			0
$651$	−4.07055	+	4.07055i	−0.159538	+	0.159538i
$652$		0			0
$653$	−8.30614	−	8.30614i	−0.325045	−	0.325045i	0.525654	−	0.850699i	$-0.323821\pi$
$653$	−8.30614	−	8.30614i	−0.325045	−	0.325045i	−0.850699	+	0.525654i	$0.823821\pi$
$654$		0			0
$655$	−5.42418			−0.211940
$656$		0			0
$657$	−27.0476			−1.05523
$658$		0			0
$659$	−6.43123	−	6.43123i	−0.250525	−	0.250525i	0.570661	−	0.821186i	$-0.306687\pi$
$659$	−6.43123	−	6.43123i	−0.250525	−	0.250525i	−0.821186	+	0.570661i	$0.806687\pi$
$660$		0			0
$661$	−15.8478	+	15.8478i	−0.616410	+	0.616410i	−0.944609	−	0.328199i	$-0.893558\pi$
$661$	−15.8478	+	15.8478i	−0.616410	+	0.616410i	0.328199	+	0.944609i	$0.393558\pi$
$662$		0			0
$663$		−	16.0199i		−	0.622163i
$664$		0			0
$665$		−	10.6797i		−	0.414140i
$666$		0			0
$667$	−7.85738	+	7.85738i	−0.304239	+	0.304239i
$668$		0			0
$669$	7.79847	+	7.79847i	0.301506	+	0.301506i
$670$		0			0
$671$	−45.7897			−1.76769
$672$		0			0
$673$	4.30979			0.166130			0.0830652	−	0.996544i	$-0.473529\pi$
$673$	4.30979			0.166130			0.0830652	+	0.996544i	$0.473529\pi$
$674$		0			0
$675$	−1.96713	−	1.96713i	−0.0757148	−	0.0757148i
$676$		0			0
$677$	−13.5723	+	13.5723i	−0.521627	+	0.521627i	−0.918063	−	0.396435i	$-0.870247\pi$
$677$	−13.5723	+	13.5723i	−0.521627	+	0.521627i	0.396435	+	0.918063i	$0.370247\pi$
$678$		0			0
$679$			10.1411i			0.389180i
$680$		0			0
$681$			4.85226i			0.185939i
$682$		0			0
$683$	−5.87622	+	5.87622i	−0.224847	+	0.224847i	−0.810536	−	0.585689i	$-0.800824\pi$
$683$	−5.87622	+	5.87622i	−0.224847	+	0.224847i	0.585689	+	0.810536i	$0.300824\pi$
$684$		0			0
$685$	−0.196152	−	0.196152i	−0.00749460	−	0.00749460i
$686$		0			0
$687$	−9.68092			−0.369350
$688$		0			0
$689$	−8.33386			−0.317495
$690$		0			0
$691$	−0.100772	−	0.100772i	−0.00383354	−	0.00383354i	0.705187	−	0.709021i	$-0.250863\pi$
$691$	−0.100772	−	0.100772i	−0.00383354	−	0.00383354i	−0.709021	+	0.705187i	$0.750863\pi$
$692$		0			0
$693$	17.0558	−	17.0558i	0.647897	−	0.647897i
$694$		0			0
$695$		−	13.0538i		−	0.495159i
$696$		0			0
$697$		−	25.3185i		−	0.959007i
$698$		0			0
$699$	−1.81065	+	1.81065i	−0.0684850	+	0.0684850i
$700$		0			0
$701$	21.7340	+	21.7340i	0.820881	+	0.820881i	0.986234	−	0.165353i	$-0.0528765\pi$
$701$	21.7340	+	21.7340i	0.820881	+	0.820881i	−0.165353	+	0.986234i	$0.552876\pi$
$702$		0			0
$703$	−13.5122			−0.509623
$704$		0			0
$705$	2.89241			0.108935
$706$		0			0
$707$	−1.63808	−	1.63808i	−0.0616063	−	0.0616063i
$708$		0			0
$709$	−14.5911	+	14.5911i	−0.547981	+	0.547981i	−0.925856	−	0.377876i	$-0.876655\pi$
$709$	−14.5911	+	14.5911i	−0.547981	+	0.547981i	0.377876	+	0.925856i	$0.376655\pi$
$710$		0			0
$711$			36.0729i			1.35284i
$712$		0			0
$713$		−	35.3263i		−	1.32298i
$714$		0			0
$715$	13.4741	−	13.4741i	0.503902	−	0.503902i
$716$		0			0
$717$	2.94298	+	2.94298i	0.109908	+	0.109908i
$718$		0			0
$719$	−15.2427			−0.568455			−0.284228	−	0.958757i	$-0.591737\pi$
$719$	−15.2427			−0.568455			−0.284228	+	0.958757i	$0.591737\pi$
$720$		0			0
$721$	−9.52396			−0.354691
$722$		0			0
$723$	0.716675	+	0.716675i	0.0266534	+	0.0266534i
$724$		0			0
$725$	1.39960	−	1.39960i	0.0519799	−	0.0519799i
$726$		0			0
$727$			13.9261i			0.516491i	0.966079	+	0.258246i	$0.0831444\pi$
$727$			13.9261i			0.516491i	−0.966079	+	0.258246i	$0.916856\pi$
$728$		0			0
$729$			15.2351i			0.564263i
$730$		0			0
$731$	27.3078	−	27.3078i	1.01002	−	1.01002i
$732$		0			0
$733$	10.0306	+	10.0306i	0.370490	+	0.370490i	0.867656	−	0.497166i	$-0.165626\pi$
$733$	10.0306	+	10.0306i	0.370490	+	0.370490i	−0.497166	+	0.867656i	$0.665626\pi$
$734$		0			0
$735$	−1.64148			−0.0605468
$736$		0			0
$737$	38.0085			1.40006
$738$		0			0
$739$	−16.3899	−	16.3899i	−0.602912	−	0.602912i	0.338172	−	0.941084i	$-0.390191\pi$
$739$	−16.3899	−	16.3899i	−0.602912	−	0.602912i	−0.941084	+	0.338172i	$0.890191\pi$
$740$		0			0
$741$	7.96348	−	7.96348i	0.292546	−	0.292546i
$742$		0			0
$743$			39.2832i			1.44116i	0.693372	+	0.720580i	$0.256124\pi$
$743$			39.2832i			1.44116i	−0.693372	+	0.720580i	$0.743876\pi$
$744$		0			0
$745$		−	9.29858i		−	0.340674i
$746$		0			0
$747$	−11.7270	+	11.7270i	−0.429068	+	0.429068i
$748$		0			0
$749$	−3.64564	−	3.64564i	−0.133209	−	0.133209i
$750$		0			0
$751$	53.2689			1.94381			0.971905	−	0.235372i	$-0.0756307\pi$
$751$	53.2689			1.94381			0.971905	+	0.235372i	$0.0756307\pi$
$752$		0			0
$753$	7.24049			0.263858
$754$		0			0
$755$	−10.6715	−	10.6715i	−0.388374	−	0.388374i
$756$		0			0
$757$	−26.5792	+	26.5792i	−0.966036	+	0.966036i	−0.999442	−	0.0334056i	$-0.989365\pi$
$757$	−26.5792	+	26.5792i	−0.966036	+	0.966036i	0.0334056	+	0.999442i	$0.489365\pi$
$758$		0			0
$759$		−	12.4452i		−	0.451734i
$760$		0			0
$761$			8.39479i			0.304311i	0.988357	+	0.152156i	$0.0486215\pi$
$761$			8.39479i			0.304311i	−0.988357	+	0.152156i	$0.951379\pi$
$762$		0			0
$763$	−18.6681	+	18.6681i	−0.675829	+	0.675829i
$764$		0			0
$765$	−15.6739	−	15.6739i	−0.566690	−	0.566690i
$766$		0			0
$767$	−56.9316			−2.05568
$768$		0			0
$769$	4.52558			0.163197			0.0815983	−	0.996665i	$-0.473998\pi$
$769$	4.52558			0.163197			0.0815983	+	0.996665i	$0.473998\pi$
$770$		0			0
$771$	−9.99587	−	9.99587i	−0.359993	−	0.359993i
$772$		0			0
$773$	−7.53513	+	7.53513i	−0.271020	+	0.271020i	−0.829511	−	0.558491i	$-0.811381\pi$
$773$	−7.53513	+	7.53513i	−0.271020	+	0.271020i	0.558491	+	0.829511i	$0.311381\pi$
$774$		0			0
$775$			6.29253i			0.226034i
$776$		0			0
$777$		−	2.19524i		−	0.0787538i
$778$		0			0
$779$	12.5858	−	12.5858i	0.450933	−	0.450933i
$780$		0			0
$781$	14.6216	+	14.6216i	0.523201	+	0.523201i
$782$		0			0
$783$	5.50639			0.196782
$784$		0			0
$785$	−22.0613			−0.787400
$786$		0			0
$787$	24.0356	+	24.0356i	0.856777	+	0.856777i	0.990957	−	0.134180i	$-0.0428400\pi$
$787$	24.0356	+	24.0356i	0.856777	+	0.856777i	−0.134180	+	0.990957i	$0.542840\pi$
$788$		0			0
$789$	−8.14021	+	8.14021i	−0.289799	+	0.289799i
$790$		0			0
$791$		−	12.1235i		−	0.431062i
$792$		0			0
$793$			41.3112i			1.46700i
$794$		0			0
$795$	0.685563	−	0.685563i	0.0243144	−	0.0243144i
$796$		0			0
$797$	−15.9406	−	15.9406i	−0.564644	−	0.564644i	0.365979	−	0.930623i	$-0.380734\pi$
$797$	−15.9406	−	15.9406i	−0.564644	−	0.564644i	−0.930623	+	0.365979i	$0.880734\pi$
$798$		0			0
$799$	48.0306			1.69920
$800$		0			0
$801$	−14.5067			−0.512568
$802$		0			0
$803$	31.7621	+	31.7621i	1.12086	+	1.12086i
$804$		0			0
$805$	−7.52885	+	7.52885i	−0.265357	+	0.265357i
$806$		0			0
$807$		−	3.46161i		−	0.121855i
$808$		0			0
$809$			6.56615i			0.230854i	0.993316	+	0.115427i	$0.0368236\pi$
$809$			6.56615i			0.230854i	−0.993316	+	0.115427i	$0.963176\pi$
$810$		0			0
$811$	6.17686	−	6.17686i	0.216899	−	0.216899i	−0.590291	−	0.807190i	$-0.700987\pi$
$811$	6.17686	−	6.17686i	0.216899	−	0.216899i	0.807190	+	0.590291i	$0.200987\pi$
$812$		0			0
$813$	0.915747	+	0.915747i	0.0321166	+	0.0321166i
$814$		0			0
$815$	−6.95252			−0.243536
$816$		0			0
$817$	27.1493			0.949835
$818$		0			0
$819$	−15.3877	−	15.3877i	−0.537688	−	0.537688i
$820$		0			0
$821$	27.7607	−	27.7607i	0.968855	−	0.968855i	−0.0306740	−	0.999529i	$-0.509765\pi$
$821$	27.7607	−	27.7607i	0.968855	−	0.968855i	0.999529	+	0.0306740i	$0.00976537\pi$
$822$		0			0
$823$		−	32.6093i		−	1.13669i	−0.822791	−	0.568345i	$-0.807584\pi$
$823$		−	32.6093i		−	1.13669i	0.822791	−	0.568345i	$-0.192416\pi$
$824$		0			0
$825$			2.21682i			0.0771797i
$826$		0			0
$827$	−24.3987	+	24.3987i	−0.848426	+	0.848426i	−0.989937	−	0.141511i	$-0.954804\pi$
$827$	−24.3987	+	24.3987i	−0.848426	+	0.848426i	0.141511	+	0.989937i	$0.454804\pi$
$828$		0			0
$829$	27.9934	+	27.9934i	0.972250	+	0.972250i	0.999625	−	0.0273749i	$-0.00871478\pi$
$829$	27.9934	+	27.9934i	0.972250	+	0.972250i	−0.0273749	+	0.999625i	$0.508715\pi$
$830$		0			0
$831$	−4.53789			−0.157418
$832$		0			0
$833$	−27.2579			−0.944431
$834$		0			0
$835$	16.4085	+	16.4085i	0.567840	+	0.567840i
$836$		0			0
$837$	−12.3782	+	12.3782i	−0.427853	+	0.427853i
$838$		0			0
$839$			21.9927i			0.759272i	0.925136	+	0.379636i	$0.123951\pi$
$839$			21.9927i			0.759272i	−0.925136	+	0.379636i	$0.876049\pi$
$840$		0			0
$841$		−	25.0822i		−	0.864904i
$842$		0			0
$843$	−6.83888	+	6.83888i	−0.235543	+	0.235543i
$844$		0			0
$845$	−2.96384	−	2.96384i	−0.101959	−	0.101959i
$846$		0			0
$847$	−19.1952			−0.659553
$848$		0			0
$849$	−8.92928			−0.306452
$850$		0			0
$851$	9.52572	+	9.52572i	0.326537	+	0.326537i
$852$		0			0
$853$	19.8800	−	19.8800i	0.680678	−	0.680678i	−0.279475	−	0.960153i	$-0.590160\pi$
$853$	19.8800	−	19.8800i	0.680678	−	0.680678i	0.960153	+	0.279475i	$0.0901604\pi$
$854$		0			0
$855$		−	15.5829i		−	0.532924i
$856$		0			0
$857$			18.3052i			0.625293i	0.949870	+	0.312646i	$0.101215\pi$
$857$			18.3052i			0.625293i	−0.949870	+	0.312646i	$0.898785\pi$
$858$		0			0
$859$	−19.6751	+	19.6751i	−0.671306	+	0.671306i	−0.958017	−	0.286711i	$-0.907438\pi$
$859$	−19.6751	+	19.6751i	−0.671306	+	0.671306i	0.286711	+	0.958017i	$0.407438\pi$
$860$		0			0
$861$	2.04473	+	2.04473i	0.0696842	+	0.0696842i
$862$		0			0
$863$	26.1668			0.890727			0.445363	−	0.895350i	$-0.353075\pi$
$863$	26.1668			0.890727			0.445363	+	0.895350i	$0.353075\pi$
$864$		0			0
$865$	1.03528			0.0352004
$866$		0			0
$867$	16.0853	+	16.0853i	0.546284	+	0.546284i
$868$		0			0
$869$	42.3606	−	42.3606i	1.43698	−	1.43698i
$870$		0			0
$871$		−	34.2911i		−	1.16191i
$872$		0			0
$873$			14.7971i			0.500805i
$874$		0			0
$875$	1.34108	−	1.34108i	0.0453368	−	0.0453368i
$876$		0			0
$877$	−7.81965	−	7.81965i	−0.264051	−	0.264051i	0.562647	−	0.826698i	$-0.309783\pi$
$877$	−7.81965	−	7.81965i	−0.264051	−	0.264051i	−0.826698	+	0.562647i	$0.809783\pi$
$878$		0			0
$879$	4.49586			0.151642
$880$		0			0
$881$	−24.8591			−0.837523			−0.418761	−	0.908096i	$-0.637536\pi$
$881$	−24.8591			−0.837523			−0.418761	+	0.908096i	$0.637536\pi$
$882$		0			0
$883$	−19.1337	−	19.1337i	−0.643899	−	0.643899i	0.307613	−	0.951512i	$-0.400470\pi$
$883$	−19.1337	−	19.1337i	−0.643899	−	0.643899i	−0.951512	+	0.307613i	$0.900470\pi$
$884$		0			0
$885$	4.68332	−	4.68332i	0.157428	−	0.157428i
$886$		0			0
$887$			4.22417i			0.141834i	0.997482	+	0.0709168i	$0.0225925\pi$
$887$			4.22417i			0.141834i	−0.997482	+	0.0709168i	$0.977408\pi$
$888$		0			0
$889$		−	40.9325i		−	1.37283i
$890$		0			0
$891$	22.6181	−	22.6181i	0.757735	−	0.757735i
$892$		0			0
$893$	23.8759	+	23.8759i	0.798977	+	0.798977i
$894$		0			0
$895$	−0.875644			−0.0292696
$896$		0			0
$897$	−11.2280			−0.374893
$898$		0			0
$899$	−8.80703	−	8.80703i	−0.293731	−	0.293731i
$900$		0			0
$901$	11.3843	−	11.3843i	0.379265	−	0.379265i
$902$		0			0
$903$			4.41077i			0.146781i
$904$		0			0
$905$		−	19.1708i		−	0.637260i
$906$		0			0
$907$	−22.3277	+	22.3277i	−0.741378	+	0.741378i	−0.972843	−	0.231465i	$-0.925648\pi$
$907$	−22.3277	+	22.3277i	−0.741378	+	0.741378i	0.231465	+	0.972843i	$0.425648\pi$
$908$		0			0
$909$	−2.39015	−	2.39015i	−0.0792763	−	0.0792763i
$910$		0			0
$911$	−5.03080			−0.166678			−0.0833389	−	0.996521i	$-0.526558\pi$
$911$	−5.03080			−0.166678			−0.0833389	+	0.996521i	$0.526558\pi$
$912$		0			0
$913$	27.5421			0.911512
$914$		0			0
$915$	−3.39836	−	3.39836i	−0.112346	−	0.112346i
$916$		0			0
$917$	7.27427	−	7.27427i	0.240218	−	0.240218i
$918$		0			0
$919$		−	29.0945i		−	0.959741i	−0.877339	−	0.479870i	$-0.840684\pi$
$919$		−	29.0945i		−	0.959741i	0.877339	−	0.479870i	$-0.159316\pi$
$920$		0			0
$921$			2.52520i			0.0832082i
$922$		0			0
$923$	13.1915	−	13.1915i	0.434204	−	0.434204i
$924$		0			0
$925$	−1.69677	−	1.69677i	−0.0557896	−	0.0557896i
$926$		0			0
$927$	−13.8966			−0.456423
$928$		0			0
$929$	21.0425			0.690383			0.345191	−	0.938532i	$-0.387814\pi$
$929$	21.0425			0.690383			0.345191	+	0.938532i	$0.387814\pi$
$930$		0			0
$931$	−13.5499	−	13.5499i	−0.444079	−	0.444079i
$932$		0			0
$933$	−2.59751	+	2.59751i	−0.0850388	+	0.0850388i
$934$		0			0
$935$			36.8118i			1.20388i
$936$		0			0
$937$			8.03670i			0.262548i	0.991346	+	0.131274i	$0.0419067\pi$
$937$			8.03670i			0.262548i	−0.991346	+	0.131274i	$0.958093\pi$
$938$		0			0
$939$	8.87011	−	8.87011i	0.289465	−	0.289465i
$940$		0			0
$941$	−33.7967	−	33.7967i	−1.10174	−	1.10174i	−0.994201	−	0.107541i	$-0.965702\pi$
$941$	−33.7967	−	33.7967i	−1.10174	−	1.10174i	−0.107541	−	0.994201i	$-0.534298\pi$
$942$		0			0
$943$	−17.7452			−0.577863
$944$		0			0
$945$	5.27616			0.171633
$946$		0			0
$947$	25.9264	+	25.9264i	0.842495	+	0.842495i	0.989183	−	0.146688i	$-0.0468613\pi$
$947$	25.9264	+	25.9264i	0.842495	+	0.842495i	−0.146688	+	0.989183i	$0.546861\pi$
$948$		0			0
$949$	28.6556	−	28.6556i	0.930200	−	0.930200i
$950$		0			0
$951$		−	3.84145i		−	0.124568i
$952$		0			0
$953$		−	38.3568i		−	1.24250i	−0.783613	−	0.621250i	$-0.786625\pi$
$953$		−	38.3568i		−	1.24250i	0.783613	−	0.621250i	$-0.213375\pi$
$954$		0			0
$955$	−4.73862	+	4.73862i	−0.153338	+	0.153338i
$956$		0			0
$957$	−3.10266	−	3.10266i	−0.100295	−	0.100295i
$958$		0			0
$959$	0.526113			0.0169891
$960$		0			0
$961$	8.59592			0.277288
$962$		0			0
$963$	−5.31942	−	5.31942i	−0.171416	−	0.171416i
$964$		0			0
$965$	−7.60332	+	7.60332i	−0.244759	+	0.244759i
$966$		0			0
$967$		−	1.16045i		−	0.0373174i	−0.999826	−	0.0186587i	$-0.994060\pi$
$967$		−	1.16045i		−	0.0373174i	0.999826	−	0.0186587i	$-0.00593960\pi$
$968$		0			0
$969$			21.7566i			0.698924i
$970$		0			0
$971$	−27.3205	+	27.3205i	−0.876758	+	0.876758i	−0.993198	−	0.116440i	$-0.962852\pi$
$971$	−27.3205	+	27.3205i	−0.876758	+	0.876758i	0.116440	+	0.993198i	$0.462852\pi$
$972$		0			0
$973$	17.5062	+	17.5062i	0.561223	+	0.561223i
$974$		0			0
$975$	2.00000			0.0640513
$976$		0			0
$977$	36.0168			1.15228			0.576139	−	0.817352i	$-0.304559\pi$
$977$	36.0168			1.15228			0.576139	+	0.817352i	$0.304559\pi$
$978$		0			0
$979$	17.0353	+	17.0353i	0.544450	+	0.544450i
$980$		0			0
$981$	−27.2389	+	27.2389i	−0.869671	+	0.869671i
$982$		0			0
$983$			6.41287i			0.204539i	0.994757	+	0.102269i	$0.0326104\pi$
$983$			6.41287i			0.204539i	−0.994757	+	0.102269i	$0.967390\pi$
$984$		0			0
$985$			26.0158i			0.828933i
$986$		0			0
$987$	−3.87896	+	3.87896i	−0.123469	+	0.123469i
$988$		0			0
$989$	−19.1395	−	19.1395i	−0.608600	−	0.608600i
$990$		0			0
$991$	−20.1152			−0.638981			−0.319491	−	0.947589i	$-0.603512\pi$
$991$	−20.1152			−0.638981			−0.319491	+	0.947589i	$0.603512\pi$
$992$		0			0
$993$	6.90567			0.219145
$994$		0			0
$995$	9.38426	+	9.38426i	0.297501	+	0.297501i
$996$		0			0
$997$	−29.7795	+	29.7795i	−0.943127	+	0.943127i	−0.998468	−	0.0553402i	$-0.982376\pi$
$997$	−29.7795	+	29.7795i	−0.943127	+	0.943127i	0.0553402	+	0.998468i	$0.482376\pi$
$998$		0			0
$999$		−	6.67555i		−	0.211205i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.l.g.321.2	yes	8
4.3	odd	2		1280.2.l.d.321.3	yes	8
8.3	odd	2		1280.2.l.f.321.2	yes	8
8.5	even	2		1280.2.l.a.321.3	✓	8
16.3	odd	4		1280.2.l.f.961.2	yes	8
16.5	even	4	inner	1280.2.l.g.961.2	yes	8
16.11	odd	4		1280.2.l.d.961.3	yes	8
16.13	even	4		1280.2.l.a.961.3	yes	8
32.5	even	8		5120.2.a.a.1.3		4
32.11	odd	8		5120.2.a.b.1.3		4
32.21	even	8		5120.2.a.r.1.2		4
32.27	odd	8		5120.2.a.q.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1280.2.l.a.321.3	✓	8	8.5	even	2
1280.2.l.a.961.3	yes	8	16.13	even	4
1280.2.l.d.321.3	yes	8	4.3	odd	2
1280.2.l.d.961.3	yes	8	16.11	odd	4
1280.2.l.f.321.2	yes	8	8.3	odd	2
1280.2.l.f.961.2	yes	8	16.3	odd	4
1280.2.l.g.321.2	yes	8	1.1	even	1	trivial
1280.2.l.g.961.2	yes	8	16.5	even	4	inner
5120.2.a.a.1.3		4	32.5	even	8
5120.2.a.b.1.3		4	32.11	odd	8
5120.2.a.q.1.2		4	32.27	odd	8
5120.2.a.r.1.2		4	32.21	even	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.341081 + 0.341081i) q^{3} +(-0.707107 + 0.707107i) q^{5} -1.89658i q^{7} -2.76733i q^{9} +(-3.24969 + 3.24969i) q^{11} +(2.93185 + 2.93185i) q^{13} -0.482362 q^{15} -8.00997 q^{17} +(-3.98174 - 3.98174i) q^{19} +(0.646887 - 0.646887i) q^{21} +5.61401i q^{23} -1.00000i q^{25} +(1.96713 - 1.96713i) q^{27} +(1.39960 + 1.39960i) q^{29} -6.29253 q^{31} -2.21682 q^{33} +(1.34108 + 1.34108i) q^{35} +(1.69677 - 1.69677i) q^{37} +2.00000i q^{39} +3.16088i q^{41} +(-3.40923 + 3.40923i) q^{43} +(1.95680 + 1.95680i) q^{45} -5.99635 q^{47} +3.40300 q^{49} +(-2.73205 - 2.73205i) q^{51} +(-1.42126 + 1.42126i) q^{53} -4.59575i q^{55} -2.71619i q^{57} +(-9.70915 + 9.70915i) q^{59} +(7.04524 + 7.04524i) q^{61} -5.24844 q^{63} -4.14626 q^{65} +(-5.84802 - 5.84802i) q^{67} +(-1.91484 + 1.91484i) q^{69} -4.49938i q^{71} -9.77389i q^{73} +(0.341081 - 0.341081i) q^{75} +(6.16328 + 6.16328i) q^{77} -13.0353 q^{79} -6.96008 q^{81} +(-4.23766 - 4.23766i) q^{83} +(5.66390 - 5.66390i) q^{85} +0.954756i q^{87} -5.24213i q^{89} +(5.56048 - 5.56048i) q^{91} +(-2.14626 - 2.14626i) q^{93} +5.63103 q^{95} -5.34706 q^{97} +(8.99295 + 8.99295i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 8 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{17} + 16 q^{21} - 8 q^{27} + 8 q^{29} + 24 q^{33} + 12 q^{35} + 8 q^{37} - 44 q^{43} - 8 q^{45} - 8 q^{47} - 8 q^{51} - 16 q^{53} + 16 q^{59} - 8 q^{61}+ \cdots + 56 q^{99}+O(q^{100}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more