LMFDB - Embedded newform 1536.2.j.e.385.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1536,2,Mod(385,1536)] 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("1536.385"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1536, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1536 = 2^{9} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1536.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,-8,0,0,0,0,0,0,0,8,0,0,0,0,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)

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

Self dual:	no
Analytic conductor:	$12.2650217505$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			385.1
Root			$-0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	1536.385
Dual form			1536.2.j.e.1153.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{3} +(-2.84776 - 2.84776i) q^{5} +4.61313i q^{7} -1.00000i q^{9} +(1.08239 + 1.08239i) q^{11} +(3.94495 - 3.94495i) q^{13} +4.02734 q^{15} +1.29769 q^{17} +(-3.08239 + 3.08239i) q^{19} +(-3.26197 - 3.26197i) q^{21} -4.00000i q^{23} +11.2195i q^{25} +(0.707107 + 0.707107i) q^{27} +(-1.31703 + 1.31703i) q^{29} -2.77791 q^{31} -1.53073 q^{33} +(13.1371 - 13.1371i) q^{35} +(-2.81204 - 2.81204i) q^{37} +5.57900i q^{39} +3.03188i q^{41} +(2.14386 + 2.14386i) q^{43} +(-2.84776 + 2.84776i) q^{45} -9.65685 q^{47} -14.2809 q^{49} +(-0.917608 + 0.917608i) q^{51} +(-6.07401 - 6.07401i) q^{53} -6.16478i q^{55} -4.35916i q^{57} +(-4.05468 - 4.05468i) q^{59} +(-5.40743 + 5.40743i) q^{61} +4.61313 q^{63} -22.4685 q^{65} +(-6.21946 + 6.21946i) q^{67} +(2.82843 + 2.82843i) q^{69} -6.88311i q^{71} +3.50114i q^{73} +(-7.93336 - 7.93336i) q^{75} +(-4.99321 + 4.99321i) q^{77} -8.18252 q^{79} -1.00000 q^{81} +(-2.91761 + 2.91761i) q^{83} +(-3.69552 - 3.69552i) q^{85} -1.86256i q^{87} +7.98642i q^{89} +(18.1985 + 18.1985i) q^{91} +(1.96428 - 1.96428i) q^{93} +17.5558 q^{95} -1.40461 q^{97} +(1.08239 - 1.08239i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{5} + 8 q^{13} - 16 q^{19} - 8 q^{29} + 16 q^{31} + 32 q^{35} + 8 q^{37} - 16 q^{43} - 8 q^{45} - 32 q^{47} - 8 q^{49} - 16 q^{51} + 8 q^{53} + 32 q^{59} + 8 q^{61} + 16 q^{63} - 16 q^{65} + 32 q^{67}+ \cdots - 32 q^{97}+O(q^{100}) $ 8 * q - 8 * q^5 + 8 * q^13 - 16 * q^19 - 8 * q^29 + 16 * q^31 + 32 * q^35 + 8 * q^37 - 16 * q^43 - 8 * q^45 - 32 * q^47 - 8 * q^49 - 16 * q^51 + 8 * q^53 + 32 * q^59 + 8 * q^61 + 16 * q^63 - 16 * q^65 + 32 * q^67 - 16 * q^75 - 48 * q^79 - 8 * q^81 - 32 * q^83 + 48 * q^91 + 64 * q^95 - 32 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1536\mathbb{Z}\right)^\times$.

$n$	$511$	$517$	$1025$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	−2.84776	−	2.84776i	−1.27356	−	1.27356i	−0.944209	−	0.329348i	$-0.893171\pi$
$5$	−2.84776	−	2.84776i	−1.27356	−	1.27356i	−0.329348	−	0.944209i	$-0.606829\pi$
$6$		0			0
$7$			4.61313i			1.74360i	0.489864	+	0.871799i	$0.337046\pi$
$7$			4.61313i			1.74360i	−0.489864	+	0.871799i	$0.662954\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	1.08239	+	1.08239i	0.326354	+	0.326354i	0.851198	−	0.524845i	$-0.175877\pi$
$11$	1.08239	+	1.08239i	0.326354	+	0.326354i	−0.524845	+	0.851198i	$0.675877\pi$
$12$		0			0
$13$	3.94495	−	3.94495i	1.09413	−	1.09413i	0.0990490	−	0.995083i	$-0.468420\pi$
$13$	3.94495	−	3.94495i	1.09413	−	1.09413i	0.995083	−	0.0990490i	$-0.0315800\pi$
$14$		0			0
$15$	4.02734			1.03985
$16$		0			0
$17$	1.29769			0.314737			0.157368	−	0.987540i	$-0.449699\pi$
$17$	1.29769			0.314737			0.157368	+	0.987540i	$0.449699\pi$
$18$		0			0
$19$	−3.08239	+	3.08239i	−0.707149	+	0.707149i	−0.965935	−	0.258786i	$-0.916678\pi$
$19$	−3.08239	+	3.08239i	−0.707149	+	0.707149i	0.258786	+	0.965935i	$0.416678\pi$
$20$		0			0
$21$	−3.26197	−	3.26197i	−0.711821	−	0.711821i
$22$		0			0
$23$		−	4.00000i		−	0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$		−	4.00000i		−	0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$		0			0
$25$			11.2195i			2.24389i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$	−1.31703	+	1.31703i	−0.244565	+	0.244565i	−0.818736	−	0.574170i	$-0.805325\pi$
$29$	−1.31703	+	1.31703i	−0.244565	+	0.244565i	0.574170	+	0.818736i	$0.305325\pi$
$30$		0			0
$31$	−2.77791			−0.498927			−0.249464	−	0.968384i	$-0.580254\pi$
$31$	−2.77791			−0.498927			−0.249464	+	0.968384i	$0.580254\pi$
$32$		0			0
$33$	−1.53073			−0.266467
$34$		0			0
$35$	13.1371	−	13.1371i	2.22057	−	2.22057i
$36$		0			0
$37$	−2.81204	−	2.81204i	−0.462296	−	0.462296i	0.437111	−	0.899407i	$-0.356002\pi$
$37$	−2.81204	−	2.81204i	−0.462296	−	0.462296i	−0.899407	+	0.437111i	$0.856002\pi$
$38$		0			0
$39$			5.57900i			0.893355i
$40$		0			0
$41$			3.03188i			0.473499i	0.971571	+	0.236750i	$0.0760821\pi$
$41$			3.03188i			0.473499i	−0.971571	+	0.236750i	$0.923918\pi$
$42$		0			0
$43$	2.14386	+	2.14386i	0.326936	+	0.326936i	0.851420	−	0.524484i	$-0.175742\pi$
$43$	2.14386	+	2.14386i	0.326936	+	0.326936i	−0.524484	+	0.851420i	$0.675742\pi$
$44$		0			0
$45$	−2.84776	+	2.84776i	−0.424519	+	0.424519i
$46$		0			0
$47$	−9.65685			−1.40860			−0.704298	−	0.709904i	$-0.748738\pi$
$47$	−9.65685			−1.40860			−0.704298	+	0.709904i	$0.748738\pi$
$48$		0			0
$49$	−14.2809			−2.04013
$50$		0			0
$51$	−0.917608	+	0.917608i	−0.128491	+	0.128491i
$52$		0			0
$53$	−6.07401	−	6.07401i	−0.834330	−	0.834330i	0.153776	−	0.988106i	$-0.450857\pi$
$53$	−6.07401	−	6.07401i	−0.834330	−	0.834330i	−0.988106	+	0.153776i	$0.950857\pi$
$54$		0			0
$55$		−	6.16478i		−	0.831259i
$56$		0			0
$57$		−	4.35916i		−	0.577385i
$58$		0			0
$59$	−4.05468	−	4.05468i	−0.527874	−	0.527874i	0.392064	−	0.919938i	$-0.371761\pi$
$59$	−4.05468	−	4.05468i	−0.527874	−	0.527874i	−0.919938	+	0.392064i	$0.871761\pi$
$60$		0			0
$61$	−5.40743	+	5.40743i	−0.692350	+	0.692350i	−0.962748	−	0.270399i	$-0.912845\pi$
$61$	−5.40743	+	5.40743i	−0.692350	+	0.692350i	0.270399	+	0.962748i	$0.412845\pi$
$62$		0			0
$63$	4.61313			0.581199
$64$		0			0
$65$	−22.4685			−2.78688
$66$		0			0
$67$	−6.21946	+	6.21946i	−0.759828	+	0.759828i	−0.976291	−	0.216463i	$-0.930548\pi$
$67$	−6.21946	+	6.21946i	−0.759828	+	0.759828i	0.216463	+	0.976291i	$0.430548\pi$
$68$		0			0
$69$	2.82843	+	2.82843i	0.340503	+	0.340503i
$70$		0			0
$71$		−	6.88311i		−	0.816874i	−0.912786	−	0.408437i	$-0.866074\pi$
$71$		−	6.88311i		−	0.816874i	0.912786	−	0.408437i	$-0.133926\pi$
$72$		0			0
$73$			3.50114i			0.409778i	0.978785	+	0.204889i	$0.0656833\pi$
$73$			3.50114i			0.409778i	−0.978785	+	0.204889i	$0.934317\pi$
$74$		0			0
$75$	−7.93336	−	7.93336i	−0.916065	−	0.916065i
$76$		0			0
$77$	−4.99321	+	4.99321i	−0.569029	+	0.569029i
$78$		0			0
$79$	−8.18252			−0.920606			−0.460303	−	0.887762i	$-0.652259\pi$
$79$	−8.18252			−0.920606			−0.460303	+	0.887762i	$0.652259\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−2.91761	+	2.91761i	−0.320249	+	0.320249i	−0.848863	−	0.528614i	$-0.822712\pi$
$83$	−2.91761	+	2.91761i	−0.320249	+	0.320249i	0.528614	+	0.848863i	$0.322712\pi$
$84$		0			0
$85$	−3.69552	−	3.69552i	−0.400835	−	0.400835i
$86$		0			0
$87$		−	1.86256i		−	0.199687i
$88$		0			0
$89$			7.98642i			0.846559i	0.905999	+	0.423280i	$0.139121\pi$
$89$			7.98642i			0.846559i	−0.905999	+	0.423280i	$0.860879\pi$
$90$		0			0
$91$	18.1985	+	18.1985i	1.90773	+	1.90773i
$92$		0			0
$93$	1.96428	−	1.96428i	0.203686	−	0.203686i
$94$		0			0
$95$	17.5558			1.80119
$96$		0			0
$97$	−1.40461			−0.142617			−0.0713084	−	0.997454i	$-0.522717\pi$
$97$	−1.40461			−0.142617			−0.0713084	+	0.997454i	$0.522717\pi$
$98$		0			0
$99$	1.08239	−	1.08239i	0.108785	−	0.108785i
$100$		0			0
$101$	0.323814	+	0.323814i	0.0322207	+	0.0322207i	0.723034	−	0.690813i	$-0.242747\pi$
$101$	0.323814	+	0.323814i	0.0322207	+	0.0322207i	−0.690813	+	0.723034i	$0.742747\pi$
$102$		0			0
$103$			7.77563i			0.766155i	0.923716	+	0.383078i	$0.125136\pi$
$103$			7.77563i			0.766155i	−0.923716	+	0.383078i	$0.874864\pi$
$104$		0			0
$105$			18.5786i			1.81309i
$106$		0			0
$107$	−10.3978	−	10.3978i	−1.00520	−	1.00520i	−0.999986	−	0.00520923i	$-0.998342\pi$
$107$	−10.3978	−	10.3978i	−1.00520	−	1.00520i	−0.00520923	−	0.999986i	$-0.501658\pi$
$108$		0			0
$109$	0.773374	−	0.773374i	0.0740758	−	0.0740758i	−0.669098	−	0.743174i	$-0.733319\pi$
$109$	0.773374	−	0.773374i	0.0740758	−	0.0740758i	0.743174	+	0.669098i	$0.233319\pi$
$110$		0			0
$111$	3.97682			0.377463
$112$		0			0
$113$	7.65685			0.720296			0.360148	−	0.932895i	$-0.382726\pi$
$113$	7.65685			0.720296			0.360148	+	0.932895i	$0.382726\pi$
$114$		0			0
$115$	−11.3910	+	11.3910i	−1.06222	+	1.06222i
$116$		0			0
$117$	−3.94495	−	3.94495i	−0.364711	−	0.364711i
$118$		0			0
$119$			5.98642i			0.548775i
$120$		0			0
$121$		−	8.65685i		−	0.786987i
$122$		0			0
$123$	−2.14386	−	2.14386i	−0.193305	−	0.193305i
$124$		0			0
$125$	17.7115	−	17.7115i	1.58417	−	1.58417i
$126$		0			0
$127$	−0.900845			−0.0799371			−0.0399685	−	0.999201i	$-0.512726\pi$
$127$	−0.900845			−0.0799371			−0.0399685	+	0.999201i	$0.512726\pi$
$128$		0			0
$129$	−3.03188			−0.266942
$130$		0			0
$131$	−11.1161	+	11.1161i	−0.971222	+	0.971222i	−0.999597	−	0.0283751i	$-0.990967\pi$
$131$	−11.1161	+	11.1161i	−0.971222	+	0.971222i	0.0283751	+	0.999597i	$0.490967\pi$
$132$		0			0
$133$	−14.2195	−	14.2195i	−1.23298	−	1.23298i
$134$		0			0
$135$		−	4.02734i		−	0.346618i
$136$		0			0
$137$			1.76377i			0.150689i	0.997158	+	0.0753447i	$0.0240057\pi$
$137$			1.76377i			0.150689i	−0.997158	+	0.0753447i	$0.975994\pi$
$138$		0			0
$139$	−12.9932	−	12.9932i	−1.10207	−	1.10207i	−0.994161	−	0.107909i	$-0.965584\pi$
$139$	−12.9932	−	12.9932i	−1.10207	−	1.10207i	−0.107909	−	0.994161i	$-0.534416\pi$
$140$		0			0
$141$	6.82843	−	6.82843i	0.575057	−	0.575057i
$142$		0			0
$143$	8.53996			0.714147
$144$		0			0
$145$	7.50114			0.622936
$146$		0			0
$147$	10.0981	−	10.0981i	0.832881	−	0.832881i
$148$		0			0
$149$	−1.19090	−	1.19090i	−0.0975627	−	0.0975627i	0.656641	−	0.754203i	$-0.271977\pi$
$149$	−1.19090	−	1.19090i	−0.0975627	−	0.0975627i	−0.754203	+	0.656641i	$0.771977\pi$
$150$		0			0
$151$		−	10.3118i		−	0.839165i	−0.907717	−	0.419582i	$-0.862177\pi$
$151$		−	10.3118i		−	0.839165i	0.907717	−	0.419582i	$-0.137823\pi$
$152$		0			0
$153$		−	1.29769i		−	0.104912i
$154$		0			0
$155$	7.91082	+	7.91082i	0.635412	+	0.635412i
$156$		0			0
$157$	−9.64047	+	9.64047i	−0.769393	+	0.769393i	−0.978000	−	0.208607i	$-0.933107\pi$
$157$	−9.64047	+	9.64047i	−0.769393	+	0.769393i	0.208607	+	0.978000i	$0.433107\pi$
$158$		0			0
$159$	8.58995			0.681227
$160$		0			0
$161$	18.4525			1.45426
$162$		0			0
$163$	2.24489	−	2.24489i	0.175834	−	0.175834i	−0.613703	−	0.789537i	$-0.710321\pi$
$163$	2.24489	−	2.24489i	0.175834	−	0.175834i	0.789537	+	0.613703i	$0.210321\pi$
$164$		0			0
$165$	4.35916	+	4.35916i	0.339360	+	0.339360i
$166$		0			0
$167$			18.4170i			1.42515i	0.701595	+	0.712576i	$0.252472\pi$
$167$			18.4170i			1.42515i	−0.701595	+	0.712576i	$0.747528\pi$
$168$		0			0
$169$		−	18.1252i		−	1.39425i
$170$		0			0
$171$	3.08239	+	3.08239i	0.235716	+	0.235716i
$172$		0			0
$173$	−7.80231	+	7.80231i	−0.593198	+	0.593198i	−0.938494	−	0.345296i	$-0.887779\pi$
$173$	−7.80231	+	7.80231i	−0.593198	+	0.593198i	0.345296	+	0.938494i	$0.387779\pi$
$174$		0			0
$175$	−51.7568			−3.91245
$176$		0			0
$177$	5.73418			0.431008
$178$		0			0
$179$	0.562609	−	0.562609i	0.0420514	−	0.0420514i	−0.685768	−	0.727820i	$-0.740534\pi$
$179$	0.562609	−	0.562609i	0.0420514	−	0.0420514i	0.727820	+	0.685768i	$0.240534\pi$
$180$		0			0
$181$	−3.71191	−	3.71191i	−0.275904	−	0.275904i	0.555568	−	0.831471i	$-0.312501\pi$
$181$	−3.71191	−	3.71191i	−0.275904	−	0.275904i	−0.831471	+	0.555568i	$0.812501\pi$
$182$		0			0
$183$		−	7.64725i		−	0.565301i
$184$		0			0
$185$			16.0160i			1.17752i
$186$		0			0
$187$	1.40461	+	1.40461i	0.102715	+	0.102715i
$188$		0			0
$189$	−3.26197	+	3.26197i	−0.237274	+	0.237274i
$190$		0			0
$191$	25.0060			1.80937			0.904687	−	0.426077i	$-0.140105\pi$
$191$	25.0060			1.80937			0.904687	+	0.426077i	$0.140105\pi$
$192$		0			0
$193$	22.9378			1.65110			0.825549	−	0.564331i	$-0.190866\pi$
$193$	22.9378			1.65110			0.825549	+	0.564331i	$0.190866\pi$
$194$		0			0
$195$	15.8876	−	15.8876i	1.13774	−	1.13774i
$196$		0			0
$197$	−10.6443	−	10.6443i	−0.758376	−	0.758376i	0.217651	−	0.976027i	$-0.430161\pi$
$197$	−10.6443	−	10.6443i	−0.758376	−	0.758376i	−0.976027	+	0.217651i	$0.930161\pi$
$198$		0			0
$199$		−	19.7485i		−	1.39993i	−0.714176	−	0.699966i	$-0.753198\pi$
$199$		−	19.7485i		−	1.39993i	0.714176	−	0.699966i	$-0.246802\pi$
$200$		0			0
$201$		−	8.79565i		−	0.620397i
$202$		0			0
$203$	−6.07560	−	6.07560i	−0.426424	−	0.426424i
$204$		0			0
$205$	8.63405	−	8.63405i	0.603028	−	0.603028i
$206$		0			0
$207$	−4.00000			−0.278019
$208$		0			0
$209$	−6.67271			−0.461561
$210$		0			0
$211$	0.663643	−	0.663643i	0.0456870	−	0.0456870i	−0.683894	−	0.729581i	$-0.739715\pi$
$211$	0.663643	−	0.663643i	0.0456870	−	0.0456870i	0.729581	+	0.683894i	$0.239715\pi$
$212$		0			0
$213$	4.86709	+	4.86709i	0.333488	+	0.333488i
$214$		0			0
$215$		−	12.2104i		−	0.832742i
$216$		0			0
$217$		−	12.8149i		−	0.869929i
$218$		0			0
$219$	−2.47568	−	2.47568i	−0.167291	−	0.167291i
$220$		0			0
$221$	5.11933	−	5.11933i	0.344364	−	0.344364i
$222$		0			0
$223$	−26.2783			−1.75973			−0.879863	−	0.475228i	$-0.842366\pi$
$223$	−26.2783			−1.75973			−0.879863	+	0.475228i	$0.842366\pi$
$224$		0			0
$225$	11.2195			0.747964
$226$		0			0
$227$	7.71326	−	7.71326i	0.511947	−	0.511947i	−0.403176	−	0.915123i	$-0.632094\pi$
$227$	7.71326	−	7.71326i	0.511947	−	0.511947i	0.915123	+	0.403176i	$0.132094\pi$
$228$		0			0
$229$	13.3360	+	13.3360i	0.881267	+	0.881267i	0.993663	−	0.112397i	$-0.0358528\pi$
$229$	13.3360	+	13.3360i	0.881267	+	0.881267i	−0.112397	+	0.993663i	$0.535853\pi$
$230$		0			0
$231$		−	7.06147i		−	0.464610i
$232$		0			0
$233$		−	19.7662i		−	1.29493i	−0.762096	−	0.647464i	$-0.775830\pi$
$233$		−	19.7662i		−	1.29493i	0.762096	−	0.647464i	$-0.224170\pi$
$234$		0			0
$235$	27.5004	+	27.5004i	1.79393	+	1.79393i
$236$		0			0
$237$	5.78592	−	5.78592i	0.375836	−	0.375836i
$238$		0			0
$239$	14.3515			0.928319			0.464160	−	0.885752i	$-0.346356\pi$
$239$	14.3515			0.928319			0.464160	+	0.885752i	$0.346356\pi$
$240$		0			0
$241$	−21.7534			−1.40126			−0.700629	−	0.713525i	$-0.747097\pi$
$241$	−21.7534			−1.40126			−0.700629	+	0.713525i	$0.747097\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	40.6687	+	40.6687i	2.59822	+	2.59822i
$246$		0			0
$247$			24.3197i			1.54743i
$248$		0			0
$249$		−	4.12612i		−	0.261482i
$250$		0			0
$251$	6.73925	+	6.73925i	0.425377	+	0.425377i	0.887050	−	0.461673i	$-0.152751\pi$
$251$	6.73925	+	6.73925i	0.425377	+	0.425377i	−0.461673	+	0.887050i	$0.652751\pi$
$252$		0			0
$253$	4.32957	−	4.32957i	0.272198	−	0.272198i
$254$		0			0
$255$	5.22625			0.327281
$256$		0			0
$257$	−1.20435			−0.0751253			−0.0375627	−	0.999294i	$-0.511959\pi$
$257$	−1.20435			−0.0751253			−0.0375627	+	0.999294i	$0.511959\pi$
$258$		0			0
$259$	12.9723	−	12.9723i	0.806059	−	0.806059i
$260$		0			0
$261$	1.31703	+	1.31703i	0.0815218	+	0.0815218i
$262$		0			0
$263$			27.5777i			1.70052i	0.526367	+	0.850258i	$0.323554\pi$
$263$			27.5777i			1.70052i	−0.526367	+	0.850258i	$0.676446\pi$
$264$		0			0
$265$			34.5946i			2.12513i
$266$		0			0
$267$	−5.64725	−	5.64725i	−0.345606	−	0.345606i
$268$		0			0
$269$	−10.3694	+	10.3694i	−0.632235	+	0.632235i	−0.948628	−	0.316393i	$-0.897528\pi$
$269$	−10.3694	+	10.3694i	−0.632235	+	0.632235i	0.316393	+	0.948628i	$0.397528\pi$
$270$		0			0
$271$	20.3574			1.23663			0.618313	−	0.785932i	$-0.287816\pi$
$271$	20.3574			1.23663			0.618313	+	0.785932i	$0.287816\pi$
$272$		0			0
$273$	−25.7366			−1.55765
$274$		0			0
$275$	−12.1439	+	12.1439i	−0.732302	+	0.732302i
$276$		0			0
$277$	16.8371	+	16.8371i	1.01164	+	1.01164i	0.999931	+	0.0117134i	$0.00372858\pi$
$277$	16.8371	+	16.8371i	1.01164	+	1.01164i	0.0117134	+	0.999931i	$0.496271\pi$
$278$		0			0
$279$			2.77791i			0.166309i
$280$		0			0
$281$		−	17.1116i		−	1.02079i	−0.859939	−	0.510397i	$-0.829498\pi$
$281$		−	17.1116i		−	1.02079i	0.859939	−	0.510397i	$-0.170502\pi$
$282$		0			0
$283$	−1.60218	−	1.60218i	−0.0952394	−	0.0952394i	0.657882	−	0.753121i	$-0.271453\pi$
$283$	−1.60218	−	1.60218i	−0.0952394	−	0.0952394i	−0.753121	+	0.657882i	$0.771453\pi$
$284$		0			0
$285$	−12.4138	+	12.4138i	−0.735332	+	0.735332i
$286$		0			0
$287$	−13.9864			−0.825592
$288$		0			0
$289$	−15.3160			−0.900941
$290$		0			0
$291$	0.993212	−	0.993212i	0.0582231	−	0.0582231i
$292$		0			0
$293$	2.76030	+	2.76030i	0.161259	+	0.161259i	0.783124	−	0.621865i	$-0.213625\pi$
$293$	2.76030	+	2.76030i	0.161259	+	0.161259i	−0.621865	+	0.783124i	$0.713625\pi$
$294$		0			0
$295$			23.0935i			1.34456i
$296$		0			0
$297$			1.53073i			0.0888222i
$298$		0			0
$299$	−15.7798	−	15.7798i	−0.912569	−	0.912569i
$300$		0			0
$301$	−9.88989	+	9.88989i	−0.570044	+	0.570044i
$302$		0			0
$303$	−0.457942			−0.0263081
$304$		0			0
$305$	30.7981			1.76349
$306$		0			0
$307$	−18.5490	+	18.5490i	−1.05865	+	1.05865i	−0.0604798	+	0.998169i	$0.519263\pi$
$307$	−18.5490	+	18.5490i	−1.05865	+	1.05865i	−0.998169	+	0.0604798i	$0.980737\pi$
$308$		0			0
$309$	−5.49820	−	5.49820i	−0.312782	−	0.312782i
$310$		0			0
$311$		−	9.12522i		−	0.517444i	−0.965952	−	0.258722i	$-0.916699\pi$
$311$		−	9.12522i		−	0.517444i	0.965952	−	0.258722i	$-0.0833013\pi$
$312$		0			0
$313$		−	9.28093i		−	0.524589i	−0.964988	−	0.262295i	$-0.915521\pi$
$313$		−	9.28093i		−	0.524589i	0.964988	−	0.262295i	$-0.0844792\pi$
$314$		0			0
$315$	−13.1371	−	13.1371i	−0.740190	−	0.740190i
$316$		0			0
$317$	−22.8857	+	22.8857i	−1.28539	+	1.28539i	−0.347830	+	0.937558i	$0.613081\pi$
$317$	−22.8857	+	22.8857i	−1.28539	+	1.28539i	−0.937558	+	0.347830i	$0.886919\pi$
$318$		0			0
$319$	−2.85108			−0.159630
$320$		0			0
$321$	14.7047			0.820739
$322$		0			0
$323$	−4.00000	+	4.00000i	−0.222566	+	0.222566i
$324$		0			0
$325$	44.2602	+	44.2602i	2.45511	+	2.45511i
$326$		0			0
$327$			1.09372i			0.0604827i
$328$		0			0
$329$		−	44.5483i		−	2.45603i
$330$		0			0
$331$	15.4457	+	15.4457i	0.848973	+	0.848973i	0.990005	−	0.141032i	$-0.0450420\pi$
$331$	15.4457	+	15.4457i	0.848973	+	0.848973i	−0.141032	+	0.990005i	$0.545042\pi$
$332$		0			0
$333$	−2.81204	+	2.81204i	−0.154099	+	0.154099i
$334$		0			0
$335$	35.4231			1.93537
$336$		0			0
$337$	28.8722			1.57277			0.786385	−	0.617736i	$-0.211950\pi$
$337$	28.8722			1.57277			0.786385	+	0.617736i	$0.211950\pi$
$338$		0			0
$339$	−5.41421	+	5.41421i	−0.294060	+	0.294060i
$340$		0			0
$341$	−3.00679	−	3.00679i	−0.162827	−	0.162827i
$342$		0			0
$343$		−	33.5879i		−	1.81357i
$344$		0			0
$345$		−	16.1094i		−	0.867299i
$346$		0			0
$347$	−15.5349	−	15.5349i	−0.833957	−	0.833957i	0.154099	−	0.988055i	$-0.450753\pi$
$347$	−15.5349	−	15.5349i	−0.833957	−	0.833957i	−0.988055	+	0.154099i	$0.950753\pi$
$348$		0			0
$349$	14.2031	−	14.2031i	0.760273	−	0.760273i	−0.216098	−	0.976372i	$-0.569333\pi$
$349$	14.2031	−	14.2031i	0.760273	−	0.760273i	0.976372	+	0.216098i	$0.0693332\pi$
$350$		0			0
$351$	5.57900			0.297785
$352$		0			0
$353$	−36.9570			−1.96702			−0.983511	−	0.180849i	$-0.942116\pi$
$353$	−36.9570			−1.96702			−0.983511	+	0.180849i	$0.942116\pi$
$354$		0			0
$355$	−19.6014	+	19.6014i	−1.04034	+	1.04034i
$356$		0			0
$357$	−4.23304	−	4.23304i	−0.224036	−	0.224036i
$358$		0			0
$359$			22.5264i			1.18890i	0.804134	+	0.594449i	$0.202630\pi$
$359$			22.5264i			1.18890i	−0.804134	+	0.594449i	$0.797370\pi$
$360$		0			0
$361$		−	0.00228335i		−	0.000120176i
$362$		0			0
$363$	6.12132	+	6.12132i	0.321286	+	0.321286i
$364$		0			0
$365$	9.97041	−	9.97041i	0.521875	−	0.521875i
$366$		0			0
$367$	−0.535798			−0.0279684			−0.0139842	−	0.999902i	$-0.504451\pi$
$367$	−0.535798			−0.0279684			−0.0139842	+	0.999902i	$0.504451\pi$
$368$		0			0
$369$	3.03188			0.157833
$370$		0			0
$371$	28.0202	−	28.0202i	1.45474	−	1.45474i
$372$		0			0
$373$	−6.24943	−	6.24943i	−0.323583	−	0.323583i	0.526557	−	0.850140i	$-0.323483\pi$
$373$	−6.24943	−	6.24943i	−0.323583	−	0.323583i	−0.850140	+	0.526557i	$0.823483\pi$
$374$		0			0
$375$			25.0479i			1.29347i
$376$		0			0
$377$			10.3912i			0.535174i
$378$		0			0
$379$	17.4576	+	17.4576i	0.896735	+	0.896735i	0.995146	−	0.0984108i	$-0.0313759\pi$
$379$	17.4576	+	17.4576i	0.896735	+	0.896735i	−0.0984108	+	0.995146i	$0.531376\pi$
$380$		0			0
$381$	0.636994	−	0.636994i	0.0326342	−	0.0326342i
$382$		0			0
$383$	−31.1290			−1.59062			−0.795308	−	0.606205i	$-0.792691\pi$
$383$	−31.1290			−1.59062			−0.795308	+	0.606205i	$0.792691\pi$
$384$		0			0
$385$	28.4389			1.44938
$386$		0			0
$387$	2.14386	−	2.14386i	0.108979	−	0.108979i
$388$		0			0
$389$	−14.3977	−	14.3977i	−0.729992	−	0.729992i	0.240626	−	0.970618i	$-0.422647\pi$
$389$	−14.3977	−	14.3977i	−0.729992	−	0.729992i	−0.970618	+	0.240626i	$0.922647\pi$
$390$		0			0
$391$		−	5.19077i		−	0.262509i
$392$		0			0
$393$		−	15.7206i		−	0.793000i
$394$		0			0
$395$	23.3019	+	23.3019i	1.17244	+	1.17244i
$396$		0			0
$397$	−2.54622	+	2.54622i	−0.127791	+	0.127791i	−0.768110	−	0.640318i	$-0.778802\pi$
$397$	−2.54622	+	2.54622i	−0.127791	+	0.127791i	0.640318	+	0.768110i	$0.278802\pi$
$398$		0			0
$399$	20.1094			1.00673
$400$		0			0
$401$	18.0160			0.899677			0.449838	−	0.893110i	$-0.351482\pi$
$401$	18.0160			0.899677			0.449838	+	0.893110i	$0.351482\pi$
$402$		0			0
$403$	−10.9587	+	10.9587i	−0.545892	+	0.545892i
$404$		0			0
$405$	2.84776	+	2.84776i	0.141506	+	0.141506i
$406$		0			0
$407$		−	6.08746i		−	0.301744i
$408$		0			0
$409$		−	25.1572i		−	1.24395i	−0.783039	−	0.621973i	$-0.786331\pi$
$409$		−	25.1572i		−	1.24395i	0.783039	−	0.621973i	$-0.213669\pi$
$410$		0			0
$411$	−1.24718	−	1.24718i	−0.0615187	−	0.0615187i
$412$		0			0
$413$	18.7047	−	18.7047i	0.920400	−	0.920400i
$414$		0			0
$415$	16.6173			0.815711
$416$		0			0
$417$	18.3752			0.899836
$418$		0			0
$419$	4.61631	−	4.61631i	0.225522	−	0.225522i	−0.585297	−	0.810819i	$-0.699022\pi$
$419$	4.61631	−	4.61631i	0.225522	−	0.225522i	0.810819	+	0.585297i	$0.199022\pi$
$420$		0			0
$421$	14.0543	+	14.0543i	0.684965	+	0.684965i	0.961115	−	0.276150i	$-0.0890586\pi$
$421$	14.0543	+	14.0543i	0.684965	+	0.684965i	−0.276150	+	0.961115i	$0.589059\pi$
$422$		0			0
$423$			9.65685i			0.469532i
$424$		0			0
$425$			14.5594i			0.706236i
$426$		0			0
$427$	−24.9451	−	24.9451i	−1.20718	−	1.20718i
$428$		0			0
$429$	−6.03866	+	6.03866i	−0.291549	+	0.291549i
$430$		0			0
$431$	−34.7368			−1.67321			−0.836606	−	0.547805i	$-0.815463\pi$
$431$	−34.7368			−1.67321			−0.836606	+	0.547805i	$0.815463\pi$
$432$		0			0
$433$	27.0935			1.30203			0.651015	−	0.759065i	$-0.274343\pi$
$433$	27.0935			1.30203			0.651015	+	0.759065i	$0.274343\pi$
$434$		0			0
$435$	−5.30411	+	5.30411i	−0.254313	+	0.254313i
$436$		0			0
$437$	12.3296	+	12.3296i	0.589803	+	0.589803i
$438$		0			0
$439$			3.52976i			0.168466i	0.996446	+	0.0842331i	$0.0268440\pi$
$439$			3.52976i			0.168466i	−0.996446	+	0.0842331i	$0.973156\pi$
$440$		0			0
$441$			14.2809i			0.680044i
$442$		0			0
$443$	4.04283	+	4.04283i	0.192080	+	0.192080i	0.796594	−	0.604514i	$-0.206633\pi$
$443$	4.04283	+	4.04283i	0.192080	+	0.192080i	−0.604514	+	0.796594i	$0.706633\pi$
$444$		0			0
$445$	22.7434	−	22.7434i	1.07814	−	1.07814i
$446$		0			0
$447$	1.68419			0.0796596
$448$		0			0
$449$	28.9346			1.36551			0.682754	−	0.730648i	$-0.260782\pi$
$449$	28.9346			1.36551			0.682754	+	0.730648i	$0.260782\pi$
$450$		0			0
$451$	−3.28168	+	3.28168i	−0.154528	+	0.154528i
$452$		0			0
$453$	7.29156	+	7.29156i	0.342588	+	0.342588i
$454$		0			0
$455$		−	103.650i		−	4.85919i
$456$		0			0
$457$			33.6233i			1.57283i	0.617697	+	0.786416i	$0.288066\pi$
$457$			33.6233i			1.57283i	−0.617697	+	0.786416i	$0.711934\pi$
$458$		0			0
$459$	0.917608	+	0.917608i	0.0428303	+	0.0428303i
$460$		0			0
$461$	−3.73161	+	3.73161i	−0.173799	+	0.173799i	−0.788646	−	0.614847i	$-0.789218\pi$
$461$	−3.73161	+	3.73161i	−0.173799	+	0.173799i	0.614847	+	0.788646i	$0.289218\pi$
$462$		0			0
$463$	−11.1430			−0.517857			−0.258929	−	0.965896i	$-0.583369\pi$
$463$	−11.1430			−0.517857			−0.258929	+	0.965896i	$0.583369\pi$
$464$		0			0
$465$	−11.1876			−0.518812
$466$		0			0
$467$	18.7392	−	18.7392i	0.867149	−	0.867149i	−0.125007	−	0.992156i	$-0.539895\pi$
$467$	18.7392	−	18.7392i	0.867149	−	0.867149i	0.992156	+	0.125007i	$0.0398953\pi$
$468$		0			0
$469$	−28.6912	−	28.6912i	−1.32484	−	1.32484i
$470$		0			0
$471$		−	13.6337i		−	0.628207i
$472$		0			0
$473$			4.64099i			0.213393i
$474$		0			0
$475$	−34.5828	−	34.5828i	−1.58677	−	1.58677i
$476$		0			0
$477$	−6.07401	+	6.07401i	−0.278110	+	0.278110i
$478$		0			0
$479$	−22.4170			−1.02426			−0.512130	−	0.858908i	$-0.671143\pi$
$479$	−22.4170			−1.02426			−0.512130	+	0.858908i	$0.671143\pi$
$480$		0			0
$481$	−22.1867			−1.01163
$482$		0			0
$483$	−13.0479	+	13.0479i	−0.593700	+	0.593700i
$484$		0			0
$485$	4.00000	+	4.00000i	0.181631	+	0.181631i
$486$		0			0
$487$		−	7.42235i		−	0.336339i	−0.985758	−	0.168169i	$-0.946214\pi$
$487$		−	7.42235i		−	0.336339i	0.985758	−	0.168169i	$-0.0537856\pi$
$488$		0			0
$489$			3.17476i			0.143568i
$490$		0			0
$491$	−12.2832	−	12.2832i	−0.554334	−	0.554334i	0.373355	−	0.927689i	$-0.378207\pi$
$491$	−12.2832	−	12.2832i	−0.554334	−	0.554334i	−0.927689	+	0.373355i	$0.878207\pi$
$492$		0			0
$493$	−1.70910	+	1.70910i	−0.0769738	+	0.0769738i
$494$		0			0
$495$	−6.16478			−0.277086
$496$		0			0
$497$	31.7526			1.42430
$498$		0			0
$499$	26.3707	−	26.3707i	1.18051	−	1.18051i	0.200902	−	0.979611i	$-0.435613\pi$
$499$	26.3707	−	26.3707i	1.18051	−	1.18051i	0.979611	−	0.200902i	$-0.0643873\pi$
$500$		0			0
$501$	−13.0228	−	13.0228i	−0.581816	−	0.581816i
$502$		0			0
$503$			13.8672i			0.618310i	0.951012	+	0.309155i	$0.100046\pi$
$503$			13.8672i			0.618310i	−0.951012	+	0.309155i	$0.899954\pi$
$504$		0			0
$505$		−	1.84429i		−	0.0820697i
$506$		0			0
$507$	12.8165	+	12.8165i	0.569199	+	0.569199i
$508$		0			0
$509$	24.4879	−	24.4879i	1.08540	−	1.08540i	0.0894100	−	0.995995i	$-0.471502\pi$
$509$	24.4879	−	24.4879i	1.08540	−	1.08540i	0.995995	−	0.0894100i	$-0.0284981\pi$
$510$		0			0
$511$	−16.1512			−0.714487
$512$		0			0
$513$	−4.35916			−0.192462
$514$		0			0
$515$	22.1431	−	22.1431i	0.975742	−	0.975742i
$516$		0			0
$517$	−10.4525	−	10.4525i	−0.459701	−	0.459701i
$518$		0			0
$519$		−	11.0341i		−	0.484344i
$520$		0			0
$521$		−	34.8437i		−	1.52653i	−0.646086	−	0.763265i	$-0.723595\pi$
$521$		−	34.8437i		−	1.52653i	0.646086	−	0.763265i	$-0.276405\pi$
$522$		0			0
$523$	18.0665	+	18.0665i	0.789994	+	0.789994i	0.981493	−	0.191499i	$-0.0613347\pi$
$523$	18.0665	+	18.0665i	0.789994	+	0.789994i	−0.191499	+	0.981493i	$0.561335\pi$
$524$		0			0
$525$	36.5976	−	36.5976i	1.59725	−	1.59725i
$526$		0			0
$527$	−3.60488			−0.157031
$528$		0			0
$529$	7.00000			0.304348
$530$		0			0
$531$	−4.05468	+	4.05468i	−0.175958	+	0.175958i
$532$		0			0
$533$	11.9606	+	11.9606i	0.518071	+	0.518071i
$534$		0			0
$535$			59.2210i			2.56035i
$536$		0			0
$537$			0.795649i			0.0343348i
$538$		0			0
$539$	−15.4576	−	15.4576i	−0.665805	−	0.665805i
$540$		0			0
$541$	−23.2451	+	23.2451i	−0.999384	+	0.999384i	−1.00000		0.000615813i	$-0.999804\pi$
$541$	−23.2451	+	23.2451i	−0.999384	+	0.999384i	0.000615813		1.00000i	$0.499804\pi$
$542$		0			0
$543$	5.24943			0.225275
$544$		0			0
$545$	−4.40477			−0.188680
$546$		0			0
$547$	−22.9395	+	22.9395i	−0.980823	+	0.980823i	−0.999820	−	0.0189970i	$-0.993953\pi$
$547$	−22.9395	+	22.9395i	−0.980823	+	0.980823i	0.0189970	+	0.999820i	$0.493953\pi$
$548$		0			0
$549$	5.40743	+	5.40743i	0.230783	+	0.230783i
$550$		0			0
$551$		−	8.11918i		−	0.345889i
$552$		0			0
$553$		−	37.7470i		−	1.60517i
$554$		0			0
$555$	−11.3250	−	11.3250i	−0.480721	−	0.480721i
$556$		0			0
$557$	−1.59117	+	1.59117i	−0.0674199	+	0.0674199i	−0.740013	−	0.672593i	$-0.765181\pi$
$557$	−1.59117	+	1.59117i	−0.0674199	+	0.0674199i	0.672593	+	0.740013i	$0.265181\pi$
$558$		0			0
$559$	16.9148			0.715421
$560$		0			0
$561$	−1.98642			−0.0838668
$562$		0			0
$563$	0.973034	−	0.973034i	0.0410085	−	0.0410085i	−0.686305	−	0.727314i	$-0.740769\pi$
$563$	0.973034	−	0.973034i	0.0410085	−	0.0410085i	0.727314	+	0.686305i	$0.240769\pi$
$564$		0			0
$565$	−21.8049	−	21.8049i	−0.917338	−	0.917338i
$566$		0			0
$567$		−	4.61313i		−	0.193733i
$568$		0			0
$569$			15.5043i			0.649975i	0.945718	+	0.324988i	$0.105360\pi$
$569$			15.5043i			0.649975i	−0.945718	+	0.324988i	$0.894640\pi$
$570$		0			0
$571$	−5.27261	−	5.27261i	−0.220652	−	0.220652i	0.588121	−	0.808773i	$-0.299868\pi$
$571$	−5.27261	−	5.27261i	−0.220652	−	0.220652i	−0.808773	+	0.588121i	$0.799868\pi$
$572$		0			0
$573$	−17.6819	+	17.6819i	−0.738674	+	0.738674i
$574$		0			0
$575$	44.8779			1.87154
$576$		0			0
$577$	−25.9355			−1.07971			−0.539855	−	0.841758i	$-0.681521\pi$
$577$	−25.9355			−1.07971			−0.539855	+	0.841758i	$0.681521\pi$
$578$		0			0
$579$	−16.2195	+	16.2195i	−0.674058	+	0.674058i
$580$		0			0
$581$	−13.4593	−	13.4593i	−0.558386	−	0.558386i
$582$		0			0
$583$		−	13.1489i		−	0.544573i
$584$		0			0
$585$			22.4685i			0.928959i
$586$		0			0
$587$	23.7753	+	23.7753i	0.981311	+	0.981311i	0.999829	−	0.0185175i	$-0.00589465\pi$
$587$	23.7753	+	23.7753i	0.981311	+	0.981311i	−0.0185175	+	0.999829i	$0.505895\pi$
$588$		0			0
$589$	8.56261	−	8.56261i	0.352816	−	0.352816i
$590$		0			0
$591$	15.0533			0.619211
$592$		0			0
$593$	−44.0302			−1.80810			−0.904052	−	0.427422i	$-0.859422\pi$
$593$	−44.0302			−1.80810			−0.904052	+	0.427422i	$0.859422\pi$
$594$		0			0
$595$	17.0479	−	17.0479i	0.698895	−	0.698895i
$596$		0			0
$597$	13.9643	+	13.9643i	0.571520	+	0.571520i
$598$		0			0
$599$		−	6.09578i		−	0.249067i	−0.992215	−	0.124533i	$-0.960257\pi$
$599$		−	6.09578i		−	0.249067i	0.992215	−	0.124533i	$-0.0397434\pi$
$600$		0			0
$601$		−	11.8126i		−	0.481845i	−0.970544	−	0.240922i	$-0.922550\pi$
$601$		−	11.8126i		−	0.481845i	0.970544	−	0.240922i	$-0.0774499\pi$
$602$		0			0
$603$	6.21946	+	6.21946i	0.253276	+	0.253276i
$604$		0			0
$605$	−24.6526	+	24.6526i	−1.00227	+	1.00227i
$606$		0			0
$607$	4.66330			0.189277			0.0946387	−	0.995512i	$-0.469830\pi$
$607$	4.66330			0.189277			0.0946387	+	0.995512i	$0.469830\pi$
$608$		0			0
$609$	8.59220			0.348174
$610$		0			0
$611$	−38.0958	+	38.0958i	−1.54119	+	1.54119i
$612$		0			0
$613$	−20.2031	−	20.2031i	−0.815994	−	0.815994i	0.169530	−	0.985525i	$-0.445775\pi$
$613$	−20.2031	−	20.2031i	−0.815994	−	0.815994i	−0.985525	+	0.169530i	$0.945775\pi$
$614$		0			0
$615$			12.2104i			0.492371i
$616$		0			0
$617$			21.2482i			0.855418i	0.903916	+	0.427709i	$0.140679\pi$
$617$			21.2482i			0.855418i	−0.903916	+	0.427709i	$0.859321\pi$
$618$		0			0
$619$	−8.09016	−	8.09016i	−0.325171	−	0.325171i	0.525576	−	0.850747i	$-0.323850\pi$
$619$	−8.09016	−	8.09016i	−0.325171	−	0.325171i	−0.850747	+	0.525576i	$0.823850\pi$
$620$		0			0
$621$	2.82843	−	2.82843i	0.113501	−	0.113501i
$622$		0			0
$623$	−36.8424			−1.47606
$624$		0			0
$625$	−44.7790			−1.79116
$626$		0			0
$627$	4.71832	−	4.71832i	0.188432	−	0.188432i
$628$		0			0
$629$	−3.64916	−	3.64916i	−0.145502	−	0.145502i
$630$		0			0
$631$			16.9427i			0.674478i	0.941419	+	0.337239i	$0.109493\pi$
$631$			16.9427i			0.674478i	−0.941419	+	0.337239i	$0.890507\pi$
$632$		0			0
$633$			0.938533i			0.0373033i
$634$		0			0
$635$	2.56539	+	2.56539i	0.101804	+	0.101804i
$636$		0			0
$637$	−56.3375	+	56.3375i	−2.23217	+	2.23217i
$638$		0			0
$639$	−6.88311			−0.272291
$640$		0			0
$641$	−27.8596			−1.10039			−0.550193	−	0.835037i	$-0.685446\pi$
$641$	−27.8596			−1.10039			−0.550193	+	0.835037i	$0.685446\pi$
$642$		0			0
$643$	−14.5745	+	14.5745i	−0.574761	+	0.574761i	−0.933455	−	0.358694i	$-0.883222\pi$
$643$	−14.5745	+	14.5745i	−0.574761	+	0.574761i	0.358694	+	0.933455i	$0.383222\pi$
$644$		0			0
$645$	8.63405	+	8.63405i	0.339965	+	0.339965i
$646$		0			0
$647$			11.7142i			0.460534i	0.973127	+	0.230267i	$0.0739600\pi$
$647$			11.7142i			0.460534i	−0.973127	+	0.230267i	$0.926040\pi$
$648$		0			0
$649$		−	8.77751i		−	0.344547i
$650$		0			0
$651$	9.06147	+	9.06147i	0.355147	+	0.355147i
$652$		0			0
$653$	−36.0932	+	36.0932i	−1.41244	+	1.41244i	−0.670781	+	0.741655i	$0.734041\pi$
$653$	−36.0932	+	36.0932i	−1.41244	+	1.41244i	−0.741655	+	0.670781i	$0.765959\pi$
$654$		0			0
$655$	63.3122			2.47381
$656$		0			0
$657$	3.50114			0.136593
$658$		0			0
$659$	−4.01920	+	4.01920i	−0.156566	+	0.156566i	−0.781043	−	0.624477i	$-0.785312\pi$
$659$	−4.01920	+	4.01920i	−0.156566	+	0.156566i	0.624477	+	0.781043i	$0.285312\pi$
$660$		0			0
$661$	25.6405	+	25.6405i	0.997299	+	0.997299i	0.999996	−	0.00269784i	$-0.000858751\pi$
$661$	25.6405	+	25.6405i	0.997299	+	0.997299i	−0.00269784	+	0.999996i	$0.500859\pi$
$662$		0			0
$663$			7.23983i			0.281172i
$664$		0			0
$665$			80.9872i			3.14055i
$666$		0			0
$667$	5.26810	+	5.26810i	0.203982	+	0.203982i
$668$		0			0
$669$	18.5816	−	18.5816i	0.718405	−	0.718405i
$670$		0			0
$671$	−11.7059			−0.451902
$672$		0			0
$673$	17.6569			0.680622			0.340311	−	0.940313i	$-0.389468\pi$
$673$	17.6569			0.680622			0.340311	+	0.940313i	$0.389468\pi$
$674$		0			0
$675$	−7.93336	+	7.93336i	−0.305355	+	0.305355i
$676$		0			0
$677$	−12.7891	−	12.7891i	−0.491527	−	0.491527i	0.417260	−	0.908787i	$-0.362990\pi$
$677$	−12.7891	−	12.7891i	−0.491527	−	0.491527i	−0.908787	+	0.417260i	$0.862990\pi$
$678$		0			0
$679$		−	6.47966i		−	0.248666i
$680$		0			0
$681$			10.9082i			0.418003i
$682$		0			0
$683$	14.3860	+	14.3860i	0.550464	+	0.550464i	0.926575	−	0.376111i	$-0.122739\pi$
$683$	14.3860	+	14.3860i	0.550464	+	0.550464i	−0.376111	+	0.926575i	$0.622739\pi$
$684$		0			0
$685$	5.02280	−	5.02280i	0.191911	−	0.191911i
$686$		0			0
$687$	−18.8599			−0.719551
$688$		0			0
$689$	−47.9233			−1.82573
$690$		0			0
$691$	14.2212	−	14.2212i	0.540999	−	0.540999i	−0.382822	−	0.923822i	$-0.625048\pi$
$691$	14.2212	−	14.2212i	0.540999	−	0.540999i	0.923822	+	0.382822i	$0.125048\pi$
$692$		0			0
$693$	4.99321	+	4.99321i	0.189676	+	0.189676i
$694$		0			0
$695$			74.0031i			2.80710i
$696$		0			0
$697$			3.93444i			0.149028i
$698$		0			0
$699$	13.9768	+	13.9768i	0.528652	+	0.528652i
$700$		0			0
$701$	14.0900	−	14.0900i	0.532173	−	0.532173i	−0.389046	−	0.921219i	$-0.627195\pi$
$701$	14.0900	−	14.0900i	0.532173	−	0.532173i	0.921219	+	0.389046i	$0.127195\pi$
$702$		0			0
$703$	17.3356			0.653825
$704$		0			0
$705$	−38.8914			−1.46474
$706$		0			0
$707$	−1.49379	+	1.49379i	−0.0561799	+	0.0561799i
$708$		0			0
$709$	2.33445	+	2.33445i	0.0876720	+	0.0876720i	0.749583	−	0.661911i	$-0.230254\pi$
$709$	2.33445	+	2.33445i	0.0876720	+	0.0876720i	−0.661911	+	0.749583i	$0.730254\pi$
$710$		0			0
$711$			8.18252i			0.306869i
$712$		0			0
$713$			11.1116i			0.416134i
$714$		0			0
$715$	−24.3197	−	24.3197i	−0.909507	−	0.909507i
$716$		0			0
$717$	−10.1480	+	10.1480i	−0.378985	+	0.378985i
$718$		0			0
$719$	40.2104			1.49959			0.749797	−	0.661668i	$-0.230151\pi$
$719$	40.2104			1.49959			0.749797	+	0.661668i	$0.230151\pi$
$720$		0			0
$721$	−35.8699			−1.33587
$722$		0			0
$723$	15.3820	−	15.3820i	0.572061	−	0.572061i
$724$		0			0
$725$	−14.7763	−	14.7763i	−0.548779	−	0.548779i
$726$		0			0
$727$		−	39.4272i		−	1.46227i	−0.682230	−	0.731137i	$-0.738990\pi$
$727$		−	39.4272i		−	1.46227i	0.682230	−	0.731137i	$-0.261010\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	2.78207	+	2.78207i	0.102899	+	0.102899i
$732$		0			0
$733$	14.6633	−	14.6633i	0.541600	−	0.541600i	−0.382398	−	0.923998i	$-0.624902\pi$
$733$	14.6633	−	14.6633i	0.541600	−	0.541600i	0.923998	+	0.382398i	$0.124902\pi$
$734$		0			0
$735$	−57.5142			−2.12144
$736$		0			0
$737$	−13.4638			−0.495945
$738$		0			0
$739$	9.86619	−	9.86619i	0.362934	−	0.362934i	−0.501958	−	0.864892i	$-0.667387\pi$
$739$	9.86619	−	9.86619i	0.362934	−	0.362934i	0.864892	+	0.501958i	$0.167387\pi$
$740$		0			0
$741$	−17.1967	−	17.1967i	−0.631735	−	0.631735i
$742$		0			0
$743$		−	5.02418i		−	0.184319i	−0.995744	−	0.0921597i	$-0.970623\pi$
$743$		−	5.02418i		−	0.184319i	0.995744	−	0.0921597i	$-0.0293770\pi$
$744$		0			0
$745$			6.78282i			0.248503i
$746$		0			0
$747$	2.91761	+	2.91761i	0.106750	+	0.106750i
$748$		0			0
$749$	47.9665	−	47.9665i	1.75266	−	1.75266i
$750$		0			0
$751$	5.44425			0.198664			0.0993318	−	0.995054i	$-0.468329\pi$
$751$	5.44425			0.198664			0.0993318	+	0.995054i	$0.468329\pi$
$752$		0			0
$753$	−9.53073			−0.347319
$754$		0			0
$755$	−29.3656	+	29.3656i	−1.06872	+	1.06872i
$756$		0			0
$757$	−10.4438	−	10.4438i	−0.379587	−	0.379587i	0.491366	−	0.870953i	$-0.336498\pi$
$757$	−10.4438	−	10.4438i	−0.379587	−	0.379587i	−0.870953	+	0.491366i	$0.836498\pi$
$758$		0			0
$759$			6.12293i			0.222248i
$760$		0			0
$761$		−	1.96584i		−	0.0712617i	−0.999365	−	0.0356308i	$-0.988656\pi$
$761$		−	1.96584i		−	0.0712617i	0.999365	−	0.0356308i	$-0.0113441\pi$
$762$		0			0
$763$	3.56767	+	3.56767i	0.129158	+	0.129158i
$764$		0			0
$765$	−3.69552	+	3.69552i	−0.133612	+	0.133612i
$766$		0			0
$767$	−31.9910			−1.15513
$768$		0			0
$769$	−7.09244			−0.255760			−0.127880	−	0.991790i	$-0.540817\pi$
$769$	−7.09244			−0.255760			−0.127880	+	0.991790i	$0.540817\pi$
$770$		0			0
$771$	0.851604	−	0.851604i	0.0306698	−	0.0306698i
$772$		0			0
$773$	19.4946	+	19.4946i	0.701173	+	0.701173i	0.964662	−	0.263489i	$-0.0848733\pi$
$773$	19.4946	+	19.4946i	0.701173	+	0.701173i	−0.263489	+	0.964662i	$0.584873\pi$
$774$		0			0
$775$		−	31.1667i		−	1.11954i
$776$		0			0
$777$			18.3456i			0.658144i
$778$		0			0
$779$	−9.34543	−	9.34543i	−0.334835	−	0.334835i
$780$		0			0
$781$	7.45022	−	7.45022i	0.266590	−	0.266590i
$782$		0			0
$783$	−1.86256			−0.0665623
$784$		0			0
$785$	54.9074			1.95973
$786$		0			0
$787$	20.9678	−	20.9678i	0.747421	−	0.747421i	−0.226573	−	0.973994i	$-0.572752\pi$
$787$	20.9678	−	20.9678i	0.747421	−	0.747421i	0.973994	+	0.226573i	$0.0727523\pi$
$788$		0			0
$789$	−19.5004	−	19.5004i	−0.694232	−	0.694232i
$790$		0			0
$791$			35.3220i			1.25591i
$792$		0			0
$793$			42.6640i			1.51504i
$794$		0			0
$795$	−24.4621	−	24.4621i	−0.867581	−	0.867581i
$796$		0			0
$797$	3.84548	−	3.84548i	0.136214	−	0.136214i	−0.635712	−	0.771926i	$-0.719294\pi$
$797$	3.84548	−	3.84548i	0.136214	−	0.136214i	0.771926	+	0.635712i	$0.219294\pi$
$798$		0			0
$799$	−12.5316			−0.443337
$800$		0			0
$801$	7.98642			0.282186
$802$		0			0
$803$	−3.78961	+	3.78961i	−0.133732	+	0.133732i
$804$		0			0
$805$	−52.5483	−	52.5483i	−1.85208	−	1.85208i
$806$		0			0
$807$		−	14.6646i		−	0.516218i
$808$		0			0
$809$		−	17.1548i		−	0.603131i	−0.953445	−	0.301566i	$-0.902491\pi$
$809$		−	17.1548i		−	0.603131i	0.953445	−	0.301566i	$-0.0975092\pi$
$810$		0			0
$811$	6.69364	+	6.69364i	0.235045	+	0.235045i	0.814795	−	0.579749i	$-0.196850\pi$
$811$	6.69364	+	6.69364i	0.235045	+	0.235045i	−0.579749	+	0.814795i	$0.696850\pi$
$812$		0			0
$813$	−14.3949	+	14.3949i	−0.504851	+	0.504851i
$814$		0			0
$815$	−12.7858			−0.447868
$816$		0			0
$817$	−13.2164			−0.462384
$818$		0			0
$819$	18.1985	−	18.1985i	0.635908	−	0.635908i
$820$		0			0
$821$	−13.5197	−	13.5197i	−0.471842	−	0.471842i	0.430668	−	0.902510i	$-0.358278\pi$
$821$	−13.5197	−	13.5197i	−0.471842	−	0.471842i	−0.902510	+	0.430668i	$0.858278\pi$
$822$		0			0
$823$		−	10.5257i		−	0.366902i	−0.983029	−	0.183451i	$-0.941273\pi$
$823$		−	10.5257i		−	0.366902i	0.983029	−	0.183451i	$-0.0587268\pi$
$824$		0			0
$825$		−	17.1740i		−	0.597922i
$826$		0			0
$827$	−19.0807	−	19.0807i	−0.663500	−	0.663500i	0.292703	−	0.956203i	$-0.405445\pi$
$827$	−19.0807	−	19.0807i	−0.663500	−	0.663500i	−0.956203	+	0.292703i	$0.905445\pi$
$828$		0			0
$829$	8.81792	−	8.81792i	0.306259	−	0.306259i	−0.537197	−	0.843457i	$-0.680517\pi$
$829$	8.81792	−	8.81792i	0.306259	−	0.306259i	0.843457	+	0.537197i	$0.180517\pi$
$830$		0			0
$831$	−23.8113			−0.826005
$832$		0			0
$833$	−18.5323			−0.642105
$834$		0			0
$835$	52.4473	−	52.4473i	1.81501	−	1.81501i
$836$		0			0
$837$	−1.96428	−	1.96428i	−0.0678954	−	0.0678954i
$838$		0			0
$839$			29.4631i			1.01718i	0.861009	+	0.508590i	$0.169833\pi$
$839$			29.4631i			1.01718i	−0.861009	+	0.508590i	$0.830167\pi$
$840$		0			0
$841$			25.5309i			0.880375i
$842$		0			0
$843$	12.0998	+	12.0998i	0.416738	+	0.416738i
$844$		0			0
$845$	−51.6163	+	51.6163i	−1.77565	+	1.77565i
$846$		0			0
$847$	39.9352			1.37219
$848$		0			0
$849$	2.26582			0.0777627
$850$		0			0
$851$	−11.2482	+	11.2482i	−0.385582	+	0.385582i
$852$		0			0
$853$	−11.4520	−	11.4520i	−0.392108	−	0.392108i	0.483330	−	0.875438i	$-0.339427\pi$
$853$	−11.4520	−	11.4520i	−0.392108	−	0.392108i	−0.875438	+	0.483330i	$0.839427\pi$
$854$		0			0
$855$		−	17.5558i		−	0.600396i
$856$		0			0
$857$		−	28.3592i		−	0.968730i	−0.874866	−	0.484365i	$-0.839051\pi$
$857$		−	28.3592i		−	0.968730i	0.874866	−	0.484365i	$-0.160949\pi$
$858$		0			0
$859$	1.77881	+	1.77881i	0.0606923	+	0.0606923i	0.736801	−	0.676109i	$-0.236335\pi$
$859$	1.77881	+	1.77881i	0.0606923	+	0.0606923i	−0.676109	+	0.736801i	$0.736335\pi$
$860$		0			0
$861$	9.88989	−	9.88989i	0.337047	−	0.337047i
$862$		0			0
$863$	13.8944			0.472971			0.236485	−	0.971635i	$-0.424004\pi$
$863$	13.8944			0.472971			0.236485	+	0.971635i	$0.424004\pi$
$864$		0			0
$865$	44.4382			1.51094
$866$		0			0
$867$	10.8300	−	10.8300i	0.367807	−	0.367807i
$868$		0			0
$869$	−8.85670	−	8.85670i	−0.300443	−	0.300443i
$870$		0			0
$871$			49.0709i			1.66270i
$872$		0			0
$873$			1.40461i			0.0475390i
$874$		0			0
$875$	81.7055	+	81.7055i	2.76215	+	2.76215i
$876$		0			0
$877$	−18.8950	+	18.8950i	−0.638038	+	0.638038i	−0.950071	−	0.312033i	$-0.898990\pi$
$877$	−18.8950	+	18.8950i	−0.638038	+	0.638038i	0.312033	+	0.950071i	$0.398990\pi$
$878$		0			0
$879$	−3.90366			−0.131667
$880$		0			0
$881$	−11.5460			−0.388995			−0.194497	−	0.980903i	$-0.562308\pi$
$881$	−11.5460			−0.388995			−0.194497	+	0.980903i	$0.562308\pi$
$882$		0			0
$883$	37.6088	−	37.6088i	1.26564	−	1.26564i	0.317316	−	0.948320i	$-0.397218\pi$
$883$	37.6088	−	37.6088i	1.26564	−	1.26564i	0.948320	−	0.317316i	$-0.102782\pi$
$884$		0			0
$885$	−16.3296	−	16.3296i	−0.548912	−	0.548912i
$886$		0			0
$887$		−	44.8123i		−	1.50465i	−0.658792	−	0.752325i	$-0.728932\pi$
$887$		−	44.8123i		−	1.50465i	0.658792	−	0.752325i	$-0.271068\pi$
$888$		0			0
$889$		−	4.15571i		−	0.139378i
$890$		0			0
$891$	−1.08239	−	1.08239i	−0.0362615	−	0.0362615i
$892$		0			0
$893$	29.7662	−	29.7662i	0.996088	−	0.996088i
$894$		0			0
$895$	−3.20435			−0.107110
$896$		0			0
$897$	22.3160			0.745109
$898$		0			0
$899$	3.65858	−	3.65858i	0.122020	−	0.122020i
$900$		0			0
$901$	−7.88220	−	7.88220i	−0.262594	−	0.262594i
$902$		0			0
$903$		−	13.9864i		−	0.465439i
$904$		0			0
$905$			21.1412i			0.702758i
$906$		0			0
$907$	20.7392	+	20.7392i	0.688635	+	0.688635i	0.961930	−	0.273295i	$-0.0881135\pi$
$907$	20.7392	+	20.7392i	0.688635	+	0.688635i	−0.273295	+	0.961930i	$0.588113\pi$
$908$		0			0
$909$	0.323814	−	0.323814i	0.0107402	−	0.0107402i
$910$		0			0
$911$	−4.91483			−0.162835			−0.0814177	−	0.996680i	$-0.525945\pi$
$911$	−4.91483			−0.162835			−0.0814177	+	0.996680i	$0.525945\pi$
$912$		0			0
$913$	−6.31599			−0.209029
$914$		0			0
$915$	−21.7775	+	21.7775i	−0.719943	+	0.719943i
$916$		0			0
$917$	−51.2802	−	51.2802i	−1.69342	−	1.69342i
$918$		0			0
$919$		−	18.9465i		−	0.624986i	−0.949920	−	0.312493i	$-0.898836\pi$
$919$		−	18.9465i		−	0.624986i	0.949920	−	0.312493i	$-0.101164\pi$
$920$		0			0
$921$		−	26.2323i		−	0.864383i
$922$		0			0
$923$	−27.1535	−	27.1535i	−0.893768	−	0.893768i
$924$		0			0
$925$	31.5496	−	31.5496i	1.03734	−	1.03734i
$926$		0			0
$927$	7.77563			0.255385
$928$		0			0
$929$	−8.40296			−0.275692			−0.137846	−	0.990454i	$-0.544018\pi$
$929$	−8.40296			−0.275692			−0.137846	+	0.990454i	$0.544018\pi$
$930$		0			0
$931$	44.0194	−	44.0194i	1.44268	−	1.44268i
$932$		0			0
$933$	6.45250	+	6.45250i	0.211245	+	0.211245i
$934$		0			0
$935$		−	8.00000i		−	0.261628i
$936$		0			0
$937$			43.8100i			1.43121i	0.698505	+	0.715605i	$0.253849\pi$
$937$			43.8100i			1.43121i	−0.698505	+	0.715605i	$0.746151\pi$
$938$		0			0
$939$	6.56261	+	6.56261i	0.214163	+	0.214163i
$940$		0			0
$941$	11.6929	−	11.6929i	0.381179	−	0.381179i	−0.490348	−	0.871527i	$-0.663130\pi$
$941$	11.6929	−	11.6929i	0.381179	−	0.381179i	0.871527	+	0.490348i	$0.163130\pi$
$942$		0			0
$943$	12.1275			0.394926
$944$		0			0
$945$	18.5786			0.604363
$946$		0			0
$947$	−33.0671	+	33.0671i	−1.07454	+	1.07454i	−0.0775474	+	0.996989i	$0.524709\pi$
$947$	−33.0671	+	33.0671i	−1.07454	+	1.07454i	−0.996989	+	0.0775474i	$0.975291\pi$
$948$		0			0
$949$	13.8118	+	13.8118i	0.448351	+	0.448351i
$950$		0			0
$951$		−	32.3652i		−	1.04951i
$952$		0			0
$953$		−	43.4436i		−	1.40728i	−0.710558	−	0.703639i	$-0.751557\pi$
$953$		−	43.4436i		−	1.40728i	0.710558	−	0.703639i	$-0.248443\pi$
$954$		0			0
$955$	−71.2112	−	71.2112i	−2.30434	−	2.30434i
$956$		0			0
$957$	2.01602	−	2.01602i	0.0651685	−	0.0651685i
$958$		0			0
$959$	−8.13651			−0.262742
$960$		0			0
$961$	−23.2832			−0.751071
$962$		0			0
$963$	−10.3978	+	10.3978i	−0.335065	+	0.335065i
$964$		0			0
$965$	−65.3213	−	65.3213i	−2.10277	−	2.10277i
$966$		0			0
$967$		−	41.3718i		−	1.33043i	−0.746653	−	0.665214i	$-0.768340\pi$
$967$		−	41.3718i		−	1.33043i	0.746653	−	0.665214i	$-0.231660\pi$
$968$		0			0
$969$		−	5.65685i		−	0.181724i
$970$		0			0
$971$	−38.9998	−	38.9998i	−1.25156	−	1.25156i	−0.955019	−	0.296544i	$-0.904166\pi$
$971$	−38.9998	−	38.9998i	−1.25156	−	1.25156i	−0.296544	−	0.955019i	$-0.595834\pi$
$972$		0			0
$973$	59.9393	−	59.9393i	1.92157	−	1.92157i
$974$		0			0
$975$	−62.5934			−2.00459
$976$		0			0
$977$	46.9120			1.50085			0.750424	−	0.660957i	$-0.229849\pi$
$977$	46.9120			1.50085			0.750424	+	0.660957i	$0.229849\pi$
$978$		0			0
$979$	−8.64444	+	8.64444i	−0.276278	+	0.276278i
$980$		0			0
$981$	−0.773374	−	0.773374i	−0.0246919	−	0.0246919i
$982$		0			0
$983$			4.71195i			0.150288i	0.997173	+	0.0751439i	$0.0239416\pi$
$983$			4.71195i			0.150288i	−0.997173	+	0.0751439i	$0.976058\pi$
$984$		0			0
$985$			60.6249i			1.93167i
$986$		0			0
$987$	31.5004	+	31.5004i	1.00267	+	1.00267i
$988$		0			0
$989$	8.57544	−	8.57544i	0.272683	−	0.272683i
$990$		0			0
$991$	−13.3733			−0.424817			−0.212408	−	0.977181i	$-0.568131\pi$
$991$	−13.3733			−0.424817			−0.212408	+	0.977181i	$0.568131\pi$
$992$		0			0
$993$	−21.8435			−0.693184
$994$		0			0
$995$	−56.2389	+	56.2389i	−1.78289	+	1.78289i
$996$		0			0
$997$	17.5677	+	17.5677i	0.556375	+	0.556375i	0.928273	−	0.371899i	$-0.121293\pi$
$997$	17.5677	+	17.5677i	0.556375	+	0.556375i	−0.371899	+	0.928273i	$0.621293\pi$
$998$		0			0
$999$		−	3.97682i		−	0.125821i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1536.2.j.e.385.1	✓	8
3.2	odd	2		4608.2.k.bh.3457.4		8
4.3	odd	2		1536.2.j.f.385.3	yes	8
8.3	odd	2		1536.2.j.i.385.2	yes	8
8.5	even	2		1536.2.j.j.385.4	yes	8
12.11	even	2		4608.2.k.bj.3457.4		8
16.3	odd	4		1536.2.j.f.1153.3	yes	8
16.5	even	4		1536.2.j.j.1153.4	yes	8
16.11	odd	4		1536.2.j.i.1153.2	yes	8
16.13	even	4	inner	1536.2.j.e.1153.1	yes	8
24.5	odd	2		4608.2.k.be.3457.1		8
24.11	even	2		4608.2.k.bc.3457.1		8
32.3	odd	8		3072.2.a.p.1.4		4
32.5	even	8		3072.2.d.e.1537.1		8
32.11	odd	8		3072.2.d.j.1537.4		8
32.13	even	8		3072.2.a.s.1.1		4
32.19	odd	8		3072.2.a.j.1.1		4
32.21	even	8		3072.2.d.e.1537.8		8
32.27	odd	8		3072.2.d.j.1537.5		8
32.29	even	8		3072.2.a.m.1.4		4
48.5	odd	4		4608.2.k.be.1153.1		8
48.11	even	4		4608.2.k.bc.1153.1		8
48.29	odd	4		4608.2.k.bh.1153.4		8
48.35	even	4		4608.2.k.bj.1153.4		8
96.29	odd	8		9216.2.a.bl.1.1		4
96.35	even	8		9216.2.a.z.1.1		4
96.77	odd	8		9216.2.a.bm.1.4		4
96.83	even	8		9216.2.a.ba.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1536.2.j.e.385.1	✓	8	1.1	even	1	trivial
1536.2.j.e.1153.1	yes	8	16.13	even	4	inner
1536.2.j.f.385.3	yes	8	4.3	odd	2
1536.2.j.f.1153.3	yes	8	16.3	odd	4
1536.2.j.i.385.2	yes	8	8.3	odd	2
1536.2.j.i.1153.2	yes	8	16.11	odd	4
1536.2.j.j.385.4	yes	8	8.5	even	2
1536.2.j.j.1153.4	yes	8	16.5	even	4
3072.2.a.j.1.1		4	32.19	odd	8
3072.2.a.m.1.4		4	32.29	even	8
3072.2.a.p.1.4		4	32.3	odd	8
3072.2.a.s.1.1		4	32.13	even	8
3072.2.d.e.1537.1		8	32.5	even	8
3072.2.d.e.1537.8		8	32.21	even	8
3072.2.d.j.1537.4		8	32.11	odd	8
3072.2.d.j.1537.5		8	32.27	odd	8
4608.2.k.bc.1153.1		8	48.11	even	4
4608.2.k.bc.3457.1		8	24.11	even	2
4608.2.k.be.1153.1		8	48.5	odd	4
4608.2.k.be.3457.1		8	24.5	odd	2
4608.2.k.bh.1153.4		8	48.29	odd	4
4608.2.k.bh.3457.4		8	3.2	odd	2
4608.2.k.bj.1153.4		8	48.35	even	4
4608.2.k.bj.3457.4		8	12.11	even	2
9216.2.a.z.1.1		4	96.35	even	8
9216.2.a.ba.1.4		4	96.83	even	8
9216.2.a.bl.1.1		4	96.29	odd	8
9216.2.a.bm.1.4		4	96.77	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1536 = 2^{9} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1536.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-2.84776 - 2.84776i) q^{5} +4.61313i q^{7} -1.00000i q^{9} +(1.08239 + 1.08239i) q^{11} +(3.94495 - 3.94495i) q^{13} +4.02734 q^{15} +1.29769 q^{17} +(-3.08239 + 3.08239i) q^{19} +(-3.26197 - 3.26197i) q^{21} -4.00000i q^{23} +11.2195i q^{25} +(0.707107 + 0.707107i) q^{27} +(-1.31703 + 1.31703i) q^{29} -2.77791 q^{31} -1.53073 q^{33} +(13.1371 - 13.1371i) q^{35} +(-2.81204 - 2.81204i) q^{37} +5.57900i q^{39} +3.03188i q^{41} +(2.14386 + 2.14386i) q^{43} +(-2.84776 + 2.84776i) q^{45} -9.65685 q^{47} -14.2809 q^{49} +(-0.917608 + 0.917608i) q^{51} +(-6.07401 - 6.07401i) q^{53} -6.16478i q^{55} -4.35916i q^{57} +(-4.05468 - 4.05468i) q^{59} +(-5.40743 + 5.40743i) q^{61} +4.61313 q^{63} -22.4685 q^{65} +(-6.21946 + 6.21946i) q^{67} +(2.82843 + 2.82843i) q^{69} -6.88311i q^{71} +3.50114i q^{73} +(-7.93336 - 7.93336i) q^{75} +(-4.99321 + 4.99321i) q^{77} -8.18252 q^{79} -1.00000 q^{81} +(-2.91761 + 2.91761i) q^{83} +(-3.69552 - 3.69552i) q^{85} -1.86256i q^{87} +7.98642i q^{89} +(18.1985 + 18.1985i) q^{91} +(1.96428 - 1.96428i) q^{93} +17.5558 q^{95} -1.40461 q^{97} +(1.08239 - 1.08239i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{5} + 8 q^{13} - 16 q^{19} - 8 q^{29} + 16 q^{31} + 32 q^{35} + 8 q^{37} - 16 q^{43} - 8 q^{45} - 32 q^{47} - 8 q^{49} - 16 q^{51} + 8 q^{53} + 32 q^{59} + 8 q^{61} + 16 q^{63} - 16 q^{65} + 32 q^{67}+ \cdots - 32 q^{97}+O(q^{100}) \) 8 * q - 8 * q^5 + 8 * q^13 - 16 * q^19 - 8 * q^29 + 16 * q^31 + 32 * q^35 + 8 * q^37 - 16 * q^43 - 8 * q^45 - 32 * q^47 - 8 * q^49 - 16 * q^51 + 8 * q^53 + 32 * q^59 + 8 * q^61 + 16 * q^63 - 16 * q^65 + 32 * q^67 - 16 * q^75 - 48 * q^79 - 8 * q^81 - 32 * q^83 + 48 * q^91 + 64 * q^95 - 32 * q^97

Introduction

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