LMFDB - Embedded newform 1248.2.ca.b.433.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1248,2,Mod(49,1248)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1248, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1248.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1248 = 2^{5} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1248.ca (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$9.96533017226$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			433.18
Character	$\chi$	$=$	1248.433
Dual form			1248.2.ca.b.49.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{3} -0.230393 q^{5} +(2.89019 - 1.66865i) q^{7} +(0.500000 + 0.866025i) q^{9} +(1.57254 - 2.72371i) q^{11} +(-2.26472 - 2.80553i) q^{13} +(-0.199526 - 0.115196i) q^{15} +(-0.791692 - 1.37125i) q^{17} +(-4.02979 - 6.97979i) q^{19} +3.33730 q^{21} +(3.40824 - 5.90325i) q^{23} -4.94692 q^{25} +1.00000i q^{27} +(3.13808 + 1.81177i) q^{29} +9.62991i q^{31} +(2.72371 - 1.57254i) q^{33} +(-0.665879 + 0.384445i) q^{35} +(0.568757 - 0.985115i) q^{37} +(-0.558542 - 3.56203i) q^{39} +(9.84578 + 5.68446i) q^{41} +(-5.40070 + 3.11810i) q^{43} +(-0.115196 - 0.199526i) q^{45} -8.90552i q^{47} +(2.06880 - 3.58326i) q^{49} -1.58338i q^{51} +4.01765i q^{53} +(-0.362301 + 0.627524i) q^{55} -8.05957i q^{57} +(-3.63171 - 6.29031i) q^{59} +(-2.50714 + 1.44750i) q^{61} +(2.89019 + 1.66865i) q^{63} +(0.521776 + 0.646375i) q^{65} +(-0.640338 + 1.10910i) q^{67} +(5.90325 - 3.40824i) q^{69} +(0.987337 - 0.570039i) q^{71} +0.813566i q^{73} +(-4.28416 - 2.47346i) q^{75} -10.4961i q^{77} +15.4710 q^{79} +(-0.500000 + 0.866025i) q^{81} +12.7265 q^{83} +(0.182400 + 0.315926i) q^{85} +(1.81177 + 3.13808i) q^{87} +(10.0707 + 5.81429i) q^{89} +(-11.2269 - 4.32949i) q^{91} +(-4.81495 + 8.33974i) q^{93} +(0.928434 + 1.60809i) q^{95} +(6.94900 - 4.01201i) q^{97} +3.14507 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{7} + 24 q^{9} + 12 q^{17} - 20 q^{23} + 48 q^{25} + 12 q^{33} - 28 q^{39} - 12 q^{41} + 16 q^{49} + 68 q^{55} + 12 q^{63} + 12 q^{65} + 12 q^{71} + 192 q^{79} - 24 q^{81} - 48 q^{89} + 20 q^{95}+ \cdots + 144 q^{97}+O(q^{100}) $ 48 * q + 12 * q^7 + 24 * q^9 + 12 * q^17 - 20 * q^23 + 48 * q^25 + 12 * q^33 - 28 * q^39 - 12 * q^41 + 16 * q^49 + 68 * q^55 + 12 * q^63 + 12 * q^65 + 12 * q^71 + 192 * q^79 - 24 * q^81 - 48 * q^89 + 20 * q^95 + 144 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1248\mathbb{Z}\right)^\times$.

$n$	$703$	$769$	$833$	$1093$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$		0			0
$5$	−0.230393			−0.103035			−0.0515174	−	0.998672i	$-0.516406\pi$
$5$	−0.230393			−0.103035			−0.0515174	+	0.998672i	$0.516406\pi$
$6$		0			0
$7$	2.89019	−	1.66865i	1.09239	−	0.630691i	0.158177	−	0.987411i	$-0.449438\pi$
$7$	2.89019	−	1.66865i	1.09239	−	0.630691i	0.934211	+	0.356720i	$0.116105\pi$
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	1.57254	−	2.72371i	0.474138	−	0.821230i	−0.525424	−	0.850841i	$-0.676093\pi$
$11$	1.57254	−	2.72371i	0.474138	−	0.821230i	0.999562	+	0.0296102i	$0.00942660\pi$
$12$		0			0
$13$	−2.26472	−	2.80553i	−0.628122	−	0.778115i
$13$	−2.26472	−	2.80553i	−0.628122	−	0.778115i
$14$		0			0
$15$	−0.199526	−	0.115196i	−0.0515174	−	0.0297436i
$16$		0			0
$17$	−0.791692	−	1.37125i	−0.192013	−	0.332577i	0.753904	−	0.656985i	$-0.228168\pi$
$17$	−0.791692	−	1.37125i	−0.192013	−	0.332577i	−0.945917	+	0.324408i	$0.894835\pi$
$18$		0			0
$19$	−4.02979	−	6.97979i	−0.924496	−	1.60127i	−0.792369	−	0.610042i	$-0.791153\pi$
$19$	−4.02979	−	6.97979i	−0.924496	−	1.60127i	−0.132127	−	0.991233i	$-0.542181\pi$
$20$		0			0
$21$	3.33730			0.728259
$22$		0			0
$23$	3.40824	−	5.90325i	0.710668	−	1.23091i	−0.253939	−	0.967220i	$-0.581726\pi$
$23$	3.40824	−	5.90325i	0.710668	−	1.23091i	0.964607	−	0.263692i	$-0.0849404\pi$
$24$		0			0
$25$	−4.94692			−0.989384
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$	3.13808	+	1.81177i	0.582727	+	0.336437i	0.762216	−	0.647323i	$-0.224111\pi$
$29$	3.13808	+	1.81177i	0.582727	+	0.336437i	−0.179490	+	0.983760i	$0.557445\pi$
$30$		0			0
$31$			9.62991i			1.72958i	0.502132	+	0.864791i	$0.332549\pi$
$31$			9.62991i			1.72958i	−0.502132	+	0.864791i	$0.667451\pi$
$32$		0			0
$33$	2.72371	−	1.57254i	0.474138	−	0.273743i
$34$		0			0
$35$	−0.665879	+	0.384445i	−0.112554	+	0.0649831i
$36$		0			0
$37$	0.568757	−	0.985115i	0.0935030	−	0.161952i	−0.815480	−	0.578785i	$-0.803527\pi$
$37$	0.568757	−	0.985115i	0.0935030	−	0.161952i	0.908983	+	0.416834i	$0.136860\pi$
$38$		0			0
$39$	−0.558542	−	3.56203i	−0.0894383	−	0.570381i
$40$		0			0
$41$	9.84578	+	5.68446i	1.53765	+	0.887764i	0.998976	+	0.0452518i	$0.0144090\pi$
$41$	9.84578	+	5.68446i	1.53765	+	0.887764i	0.538677	+	0.842512i	$0.318924\pi$
$42$		0			0
$43$	−5.40070	+	3.11810i	−0.823599	+	0.475505i	−0.851656	−	0.524101i	$-0.824401\pi$
$43$	−5.40070	+	3.11810i	−0.823599	+	0.475505i	0.0280568	+	0.999606i	$0.491068\pi$
$44$		0			0
$45$	−0.115196	−	0.199526i	−0.0171725	−	0.0297436i
$46$		0			0
$47$		−	8.90552i		−	1.29900i	−0.760360	−	0.649501i	$-0.774978\pi$
$47$		−	8.90552i		−	1.29900i	0.760360	−	0.649501i	$-0.225022\pi$
$48$		0			0
$49$	2.06880	−	3.58326i	0.295542	−	0.511894i
$50$		0			0
$51$		−	1.58338i		−	0.221718i
$52$		0			0
$53$			4.01765i			0.551867i	0.961177	+	0.275933i	$0.0889869\pi$
$53$			4.01765i			0.551867i	−0.961177	+	0.275933i	$0.911013\pi$
$54$		0			0
$55$	−0.362301	+	0.627524i	−0.0488527	+	0.0846153i
$56$		0			0
$57$		−	8.05957i		−	1.06752i
$58$		0			0
$59$	−3.63171	−	6.29031i	−0.472809	−	0.818929i	0.526707	−	0.850047i	$-0.323426\pi$
$59$	−3.63171	−	6.29031i	−0.472809	−	0.818929i	−0.999516	+	0.0311183i	$0.990093\pi$
$60$		0			0
$61$	−2.50714	+	1.44750i	−0.321006	+	0.185333i	−0.651841	−	0.758356i	$-0.726003\pi$
$61$	−2.50714	+	1.44750i	−0.321006	+	0.185333i	0.330835	+	0.943689i	$0.392670\pi$
$62$		0			0
$63$	2.89019	+	1.66865i	0.364130	+	0.210230i
$64$		0			0
$65$	0.521776	+	0.646375i	0.0647184	+	0.0801730i
$66$		0			0
$67$	−0.640338	+	1.10910i	−0.0782297	+	0.135498i	−0.902486	−	0.430719i	$-0.858260\pi$
$67$	−0.640338	+	1.10910i	−0.0782297	+	0.135498i	0.824257	+	0.566217i	$0.191593\pi$
$68$		0			0
$69$	5.90325	−	3.40824i	0.710668	−	0.410304i
$70$		0			0
$71$	0.987337	−	0.570039i	0.117175	−	0.0676512i	−0.440267	−	0.897867i	$-0.645116\pi$
$71$	0.987337	−	0.570039i	0.117175	−	0.0676512i	0.557442	+	0.830216i	$0.311783\pi$
$72$		0			0
$73$			0.813566i			0.0952207i	0.998866	+	0.0476104i	$0.0151606\pi$
$73$			0.813566i			0.0952207i	−0.998866	+	0.0476104i	$0.984839\pi$
$74$		0			0
$75$	−4.28416	−	2.47346i	−0.494692	−	0.285611i
$76$		0			0
$77$		−	10.4961i		−	1.19614i
$78$		0			0
$79$	15.4710			1.74062			0.870309	−	0.492506i	$-0.163919\pi$
$79$	15.4710			1.74062			0.870309	+	0.492506i	$0.163919\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	12.7265			1.39691			0.698455	−	0.715654i	$-0.253871\pi$
$83$	12.7265			1.39691			0.698455	+	0.715654i	$0.253871\pi$
$84$		0			0
$85$	0.182400	+	0.315926i	0.0197841	+	0.0342670i
$86$		0			0
$87$	1.81177	+	3.13808i	0.194242	+	0.336437i
$88$		0			0
$89$	10.0707	+	5.81429i	1.06749	+	0.616314i	0.927494	−	0.373838i	$-0.121959\pi$
$89$	10.0707	+	5.81429i	1.06749	+	0.616314i	0.139993	+	0.990152i	$0.455292\pi$
$90$		0			0
$91$	−11.2269	−	4.32949i	−1.17690	−	0.453854i
$92$		0			0
$93$	−4.81495	+	8.33974i	−0.499287	+	0.864791i
$94$		0			0
$95$	0.928434	+	1.60809i	0.0952553	+	0.164987i
$96$		0			0
$97$	6.94900	−	4.01201i	0.705564	−	0.407358i	−0.103852	−	0.994593i	$-0.533117\pi$
$97$	6.94900	−	4.01201i	0.705564	−	0.407358i	0.809416	+	0.587235i	$0.199784\pi$
$98$		0			0
$99$	3.14507			0.316092
$100$		0			0
$101$	−9.97844	−	5.76105i	−0.992892	−	0.573246i	−0.0867543	−	0.996230i	$-0.527650\pi$
$101$	−9.97844	−	5.76105i	−0.992892	−	0.573246i	−0.906137	+	0.422983i	$0.860983\pi$
$102$		0			0
$103$	0.570336			0.0561969			0.0280984	−	0.999605i	$-0.491055\pi$
$103$	0.570336			0.0561969			0.0280984	+	0.999605i	$0.491055\pi$
$104$		0			0
$105$	−0.768891			−0.0750361
$106$		0			0
$107$	1.27986	+	0.738926i	0.123729	+	0.0714347i	0.560587	−	0.828096i	$-0.310576\pi$
$107$	1.27986	+	0.738926i	0.123729	+	0.0714347i	−0.436858	+	0.899530i	$0.643909\pi$
$108$		0			0
$109$	−1.50562			−0.144212			−0.0721062	−	0.997397i	$-0.522972\pi$
$109$	−1.50562			−0.144212			−0.0721062	+	0.997397i	$0.522972\pi$
$110$		0			0
$111$	0.985115	−	0.568757i	0.0935030	−	0.0539840i
$112$		0			0
$113$	−0.0381779	−	0.0661261i	−0.00359148	−	0.00622062i	0.864224	−	0.503107i	$-0.167810\pi$
$113$	−0.0381779	−	0.0661261i	−0.00359148	−	0.00622062i	−0.867816	+	0.496886i	$0.834477\pi$
$114$		0			0
$115$	−0.785235	+	1.36007i	−0.0732235	+	0.126827i
$116$		0			0
$117$	1.29730	−	3.36408i	0.119936	−	0.311009i
$118$		0			0
$119$	−4.57628	−	2.64211i	−0.419507	−	0.242202i
$120$		0			0
$121$	0.554258	+	0.960004i	0.0503871	+	0.0872731i
$122$		0			0
$123$	5.68446	+	9.84578i	0.512551	+	0.887764i
$124$		0			0
$125$	2.29170			0.204976
$126$		0			0
$127$	−3.12007	+	5.40413i	−0.276862	+	0.479539i	−0.970603	−	0.240686i	$-0.922628\pi$
$127$	−3.12007	+	5.40413i	−0.276862	+	0.479539i	0.693741	+	0.720224i	$0.255961\pi$
$128$		0			0
$129$	−6.23619			−0.549066
$130$		0			0
$131$			15.7714i			1.37795i	0.724783	+	0.688977i	$0.241940\pi$
$131$			15.7714i			1.37795i	−0.724783	+	0.688977i	$0.758060\pi$
$132$		0			0
$133$	−23.2937	−	13.4486i	−2.01982	−	1.16614i
$134$		0			0
$135$		−	0.230393i		−	0.0198291i
$136$		0			0
$137$	−4.42860	+	2.55686i	−0.378361	+	0.218447i	−0.677105	−	0.735886i	$-0.736766\pi$
$137$	−4.42860	+	2.55686i	−0.378361	+	0.218447i	0.298744	+	0.954333i	$0.403432\pi$
$138$		0			0
$139$	4.90809	−	2.83369i	0.416299	−	0.240350i	−0.277194	−	0.960814i	$-0.589404\pi$
$139$	4.90809	−	2.83369i	0.416299	−	0.240350i	0.693492	+	0.720464i	$0.256071\pi$
$140$		0			0
$141$	4.45276	−	7.71240i	0.374990	−	0.649501i
$142$		0			0
$143$	−11.2028	+	1.75666i	−0.936828	+	0.146899i
$144$		0			0
$145$	−0.722991	−	0.417419i	−0.0600411	−	0.0346648i
$146$		0			0
$147$	3.58326	−	2.06880i	0.295542	−	0.170631i
$148$		0			0
$149$	4.50412	+	7.80137i	0.368992	+	0.639113i	0.989408	−	0.145160i	$-0.0463696\pi$
$149$	4.50412	+	7.80137i	0.368992	+	0.639113i	−0.620416	+	0.784273i	$0.713036\pi$
$150$		0			0
$151$			6.17629i			0.502619i	0.967907	+	0.251310i	$0.0808612\pi$
$151$			6.17629i			0.502619i	−0.967907	+	0.251310i	$0.919139\pi$
$152$		0			0
$153$	0.791692	−	1.37125i	0.0640045	−	0.110859i
$154$		0			0
$155$		−	2.21866i		−	0.178207i
$156$		0			0
$157$			10.0557i			0.802532i	0.915961	+	0.401266i	$0.131430\pi$
$157$			10.0557i			0.802532i	−0.915961	+	0.401266i	$0.868570\pi$
$158$		0			0
$159$	−2.00883	+	3.47939i	−0.159310	+	0.275933i
$160$		0			0
$161$		−	22.7487i		−	1.79285i
$162$		0			0
$163$	10.3005	+	17.8410i	0.806796	+	1.39741i	0.915072	+	0.403291i	$0.132134\pi$
$163$	10.3005	+	17.8410i	0.806796	+	1.39741i	−0.108276	+	0.994121i	$0.534533\pi$
$164$		0			0
$165$	−0.627524	+	0.362301i	−0.0488527	+	0.0282051i
$166$		0			0
$167$	7.97855	+	4.60642i	0.617399	+	0.356455i	0.775856	−	0.630910i	$-0.217318\pi$
$167$	7.97855	+	4.60642i	0.617399	+	0.356455i	−0.158457	+	0.987366i	$0.550652\pi$
$168$		0			0
$169$	−2.74204	+	12.7075i	−0.210926	+	0.977502i
$170$		0			0
$171$	4.02979	−	6.97979i	0.308165	−	0.533758i
$172$		0			0
$173$	1.65613	−	0.956165i	0.125913	−	0.0726959i	−0.435721	−	0.900082i	$-0.643506\pi$
$173$	1.65613	−	0.956165i	0.125913	−	0.0726959i	0.561634	+	0.827386i	$0.310173\pi$
$174$		0			0
$175$	−14.2975	+	8.25468i	−1.08079	+	0.623995i
$176$		0			0
$177$		−	7.26342i		−	0.545952i
$178$		0			0
$179$	11.8443	+	6.83830i	0.885283	+	0.511118i	0.872397	−	0.488799i	$-0.162565\pi$
$179$	11.8443	+	6.83830i	0.885283	+	0.511118i	0.0128863	+	0.999917i	$0.495898\pi$
$180$		0			0
$181$			1.95106i			0.145021i	0.997368	+	0.0725105i	$0.0231011\pi$
$181$			1.95106i			0.145021i	−0.997368	+	0.0725105i	$0.976899\pi$
$182$		0			0
$183$	−2.89499			−0.214004
$184$		0			0
$185$	−0.131037	+	0.226964i	−0.00963407	+	0.0166867i
$186$		0			0
$187$	−4.97986			−0.364163
$188$		0			0
$189$	1.66865	+	2.89019i	0.121377	+	0.210230i
$190$		0			0
$191$	−8.22747	−	14.2504i	−0.595318	−	1.03112i	−0.993502	−	0.113816i	$-0.963693\pi$
$191$	−8.22747	−	14.2504i	−0.595318	−	1.03112i	0.398183	−	0.917306i	$-0.369641\pi$
$192$		0			0
$193$	−5.14440	−	2.97012i	−0.370302	−	0.213794i	0.303288	−	0.952899i	$-0.401915\pi$
$193$	−5.14440	−	2.97012i	−0.370302	−	0.213794i	−0.673590	+	0.739105i	$0.735249\pi$
$194$		0			0
$195$	0.128684	+	0.820665i	0.00921526	+	0.0587691i
$196$		0			0
$197$	−3.94646	+	6.83547i	−0.281174	+	0.487007i	−0.971674	−	0.236325i	$-0.924057\pi$
$197$	−3.94646	+	6.83547i	−0.281174	+	0.487007i	0.690500	+	0.723332i	$0.257390\pi$
$198$		0			0
$199$	−8.18855	−	14.1830i	−0.580471	−	1.00541i	−0.995423	−	0.0955625i	$-0.969535\pi$
$199$	−8.18855	−	14.1830i	−0.580471	−	1.00541i	0.414952	−	0.909843i	$-0.363798\pi$
$200$		0			0
$201$	−1.10910	+	0.640338i	−0.0782297	+	0.0451659i
$202$		0			0
$203$	12.0929			0.848752
$204$		0			0
$205$	−2.26840	−	1.30966i	−0.158432	−	0.0914706i
$206$		0			0
$207$	6.81649			0.473778
$208$		0			0
$209$	−25.3479			−1.75335
$210$		0			0
$211$	−12.5801	−	7.26314i	−0.866052	−	0.500016i	−1.79224e−5	−	1.00000i	$-0.500006\pi$
$211$	−12.5801	−	7.26314i	−0.866052	−	0.500016i	−0.866034	+	0.499984i	$0.833339\pi$
$212$		0			0
$213$	1.14008			0.0781169
$214$		0			0
$215$	1.24428	−	0.718387i	0.0848594	−	0.0489936i
$216$		0			0
$217$	16.0690	+	27.8322i	1.09083	+	1.88938i
$218$		0			0
$219$	−0.406783	+	0.704569i	−0.0274879	+	0.0476104i
$220$		0			0
$221$	−2.05413	+	5.32662i	−0.138175	+	0.358307i
$222$		0			0
$223$	−20.0347	−	11.5670i	−1.34162	−	0.774585i	−0.354576	−	0.935027i	$-0.615375\pi$
$223$	−20.0347	−	11.5670i	−1.34162	−	0.774585i	−0.987045	+	0.160442i	$0.948708\pi$
$224$		0			0
$225$	−2.47346	−	4.28416i	−0.164897	−	0.285611i
$226$		0			0
$227$	−10.2158	−	17.6943i	−0.678048	−	1.17441i	−0.975568	−	0.219699i	$-0.929493\pi$
$227$	−10.2158	−	17.6943i	−0.678048	−	1.17441i	0.297519	−	0.954716i	$-0.403841\pi$
$228$		0			0
$229$	6.70980			0.443396			0.221698	−	0.975115i	$-0.428840\pi$
$229$	6.70980			0.443396			0.221698	+	0.975115i	$0.428840\pi$
$230$		0			0
$231$	5.24803	−	9.08986i	0.345295	−	0.598069i
$232$		0			0
$233$	−9.35304			−0.612738			−0.306369	−	0.951913i	$-0.599114\pi$
$233$	−9.35304			−0.612738			−0.306369	+	0.951913i	$0.599114\pi$
$234$		0			0
$235$			2.05177i			0.133843i
$236$		0			0
$237$	13.3982	+	7.73548i	0.870309	+	0.502473i
$238$		0			0
$239$			8.79465i			0.568879i	0.958694	+	0.284439i	$0.0918074\pi$
$239$			8.79465i			0.568879i	−0.958694	+	0.284439i	$0.908193\pi$
$240$		0			0
$241$	−16.6492	+	9.61245i	−1.07247	+	0.619192i	−0.928856	−	0.370441i	$-0.879206\pi$
$241$	−16.6492	+	9.61245i	−1.07247	+	0.619192i	−0.143616	+	0.989633i	$0.545873\pi$
$242$		0			0
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$		0			0
$245$	−0.476636	+	0.825557i	−0.0304511	+	0.0527429i
$246$		0			0
$247$	−10.4557	+	27.1130i	−0.665280	+	1.72516i
$248$		0			0
$249$	11.0214	+	6.36323i	0.698455	+	0.403253i
$250$		0			0
$251$	18.3517	−	10.5953i	1.15835	−	0.668772i	0.207440	−	0.978248i	$-0.433487\pi$
$251$	18.3517	−	10.5953i	1.15835	−	0.668772i	0.950907	+	0.309476i	$0.100154\pi$
$252$		0			0
$253$	−10.7192	−	18.5661i	−0.673909	−	1.16724i
$254$		0			0
$255$			0.364800i			0.0228447i
$256$		0			0
$257$	2.53390	−	4.38885i	0.158061	−	0.273769i	−0.776109	−	0.630599i	$-0.782809\pi$
$257$	2.53390	−	4.38885i	0.158061	−	0.273769i	0.934169	+	0.356830i	$0.116143\pi$
$258$		0			0
$259$		−	3.79623i		−	0.235886i
$260$		0			0
$261$			3.62354i			0.224292i
$262$		0			0
$263$	−2.69479	+	4.66751i	−0.166168	+	0.287811i	−0.937069	−	0.349143i	$-0.886473\pi$
$263$	−2.69479	+	4.66751i	−0.166168	+	0.287811i	0.770902	+	0.636954i	$0.219806\pi$
$264$		0			0
$265$		−	0.925638i		−	0.0568615i
$266$		0			0
$267$	5.81429	+	10.0707i	0.355829	+	0.616314i
$268$		0			0
$269$	13.0916	−	7.55845i	0.798210	−	0.460847i	−0.0446347	−	0.999003i	$-0.514212\pi$
$269$	13.0916	−	7.55845i	0.798210	−	0.460847i	0.842845	+	0.538156i	$0.180879\pi$
$270$		0			0
$271$	−1.44092	−	0.831915i	−0.0875296	−	0.0505352i	0.455596	−	0.890186i	$-0.349426\pi$
$271$	−1.44092	−	0.831915i	−0.0875296	−	0.0505352i	−0.543126	+	0.839651i	$0.682759\pi$
$272$		0			0
$273$	−7.55807	−	9.36292i	−0.457435	−	0.566670i
$274$		0			0
$275$	−7.77921	+	13.4740i	−0.469104	+	0.812512i
$276$		0			0
$277$	13.9650	−	8.06272i	0.839078	−	0.484442i	−0.0178730	−	0.999840i	$-0.505689\pi$
$277$	13.9650	−	8.06272i	0.839078	−	0.484442i	0.856951	+	0.515399i	$0.172356\pi$
$278$		0			0
$279$	−8.33974	+	4.81495i	−0.499287	+	0.288264i
$280$		0			0
$281$			23.9271i			1.42737i	0.700466	+	0.713686i	$0.252976\pi$
$281$			23.9271i			1.42737i	−0.700466	+	0.713686i	$0.747024\pi$
$282$		0			0
$283$	−7.67135	−	4.42906i	−0.456015	−	0.263280i	0.254352	−	0.967112i	$-0.418138\pi$
$283$	−7.67135	−	4.42906i	−0.456015	−	0.263280i	−0.710367	+	0.703831i	$0.751471\pi$
$284$		0			0
$285$			1.85687i			0.109991i
$286$		0			0
$287$	37.9416			2.23962
$288$		0			0
$289$	7.24645	−	12.5512i	0.426262	−	0.738307i
$290$		0			0
$291$	8.02401			0.470376
$292$		0			0
$293$	12.1437	+	21.0335i	0.709441	+	1.22879i	0.965065	+	0.262012i	$0.0843860\pi$
$293$	12.1437	+	21.0335i	0.709441	+	1.22879i	−0.255623	+	0.966776i	$0.582281\pi$
$294$		0			0
$295$	0.836721	+	1.44924i	0.0487158	+	0.0843782i
$296$		0			0
$297$	2.72371	+	1.57254i	0.158046	+	0.0912478i
$298$		0			0
$299$	−24.2805	+	3.80729i	−1.40418	+	0.220182i
$300$		0			0
$301$	−10.4060	+	18.0238i	−0.599794	+	1.03887i
$302$		0			0
$303$	−5.76105	−	9.97844i	−0.330964	−	0.573246i
$304$		0			0
$305$	0.577627	−	0.333493i	0.0330748	−	0.0190957i
$306$		0			0
$307$	−32.3797			−1.84801			−0.924004	−	0.382383i	$-0.875103\pi$
$307$	−32.3797			−1.84801			−0.924004	+	0.382383i	$0.875103\pi$
$308$		0			0
$309$	0.493925	+	0.285168i	0.0280984	+	0.0162226i
$310$		0			0
$311$	−16.7587			−0.950298			−0.475149	−	0.879905i	$-0.657606\pi$
$311$	−16.7587			−0.950298			−0.475149	+	0.879905i	$0.657606\pi$
$312$		0			0
$313$	−12.2059			−0.689921			−0.344960	−	0.938617i	$-0.612108\pi$
$313$	−12.2059			−0.689921			−0.344960	+	0.938617i	$0.612108\pi$
$314$		0			0
$315$	−0.665879	−	0.384445i	−0.0375180	−	0.0216610i
$316$		0			0
$317$	30.0086			1.68545			0.842725	−	0.538345i	$-0.180950\pi$
$317$	30.0086			1.68545			0.842725	+	0.538345i	$0.180950\pi$
$318$		0			0
$319$	9.86948	−	5.69815i	0.552585	−	0.319035i
$320$		0			0
$321$	0.738926	+	1.27986i	0.0412428	+	0.0714347i
$322$		0			0
$323$	−6.38070	+	11.0517i	−0.355031	+	0.614932i
$324$		0			0
$325$	11.2034	+	13.8788i	0.621453	+	0.769855i
$326$		0			0
$327$	−1.30391	−	0.752810i	−0.0721062	−	0.0416305i
$328$		0			0
$329$	−14.8602	−	25.7386i	−0.819269	−	1.41902i
$330$		0			0
$331$	−2.48978	−	4.31242i	−0.136851	−	0.237032i	0.789452	−	0.613812i	$-0.210365\pi$
$331$	−2.48978	−	4.31242i	−0.136851	−	0.237032i	−0.926303	+	0.376780i	$0.877031\pi$
$332$		0			0
$333$	1.13751			0.0623353
$334$		0			0
$335$	0.147529	−	0.255528i	0.00806038	−	0.0139610i
$336$		0			0
$337$	−14.3686			−0.782707			−0.391353	−	0.920240i	$-0.627993\pi$
$337$	−14.3686			−0.782707			−0.391353	+	0.920240i	$0.627993\pi$
$338$		0			0
$339$		−	0.0763558i		−	0.00414708i
$340$		0			0
$341$	26.2291	+	15.1434i	1.42039	+	0.820060i
$342$		0			0
$343$			9.55273i			0.515799i
$344$		0			0
$345$	−1.36007	+	0.785235i	−0.0732235	+	0.0422756i
$346$		0			0
$347$	5.35002	−	3.08884i	0.287204	−	0.165817i	−0.349476	−	0.936945i	$-0.613640\pi$
$347$	5.35002	−	3.08884i	0.287204	−	0.165817i	0.636680	+	0.771128i	$0.280307\pi$
$348$		0			0
$349$	−12.8064	+	22.1813i	−0.685510	+	1.18734i	0.287766	+	0.957701i	$0.407088\pi$
$349$	−12.8064	+	22.1813i	−0.685510	+	1.18734i	−0.973276	+	0.229638i	$0.926246\pi$
$350$		0			0
$351$	2.80553	−	2.26472i	0.149748	−	0.120882i
$352$		0			0
$353$	6.78643	+	3.91815i	0.361205	+	0.208542i	0.669609	−	0.742713i	$-0.266462\pi$
$353$	6.78643	+	3.91815i	0.361205	+	0.208542i	−0.308404	+	0.951255i	$0.599795\pi$
$354$		0			0
$355$	−0.227475	+	0.131333i	−0.0120731	+	0.00697043i
$356$		0			0
$357$	−2.64211	−	4.57628i	−0.139836	−	0.242202i
$358$		0			0
$359$			27.9638i			1.47587i	0.674870	+	0.737937i	$0.264200\pi$
$359$			27.9638i			1.47587i	−0.674870	+	0.737937i	$0.735800\pi$
$360$		0			0
$361$	−22.9783	+	39.7997i	−1.20939	+	2.09472i
$362$		0			0
$363$			1.10852i			0.0581820i
$364$		0			0
$365$		−	0.187440i		−	0.00981105i
$366$		0			0
$367$	11.9144	−	20.6364i	0.621929	−	1.07721i	−0.367198	−	0.930143i	$-0.619683\pi$
$367$	11.9144	−	20.6364i	0.621929	−	1.07721i	0.989126	−	0.147069i	$-0.0469840\pi$
$368$		0			0
$369$			11.3689i			0.591843i
$370$		0			0
$371$	6.70406	+	11.6118i	0.348057	+	0.602853i
$372$		0			0
$373$	−10.4787	+	6.04988i	−0.542567	+	0.313251i	−0.746118	−	0.665813i	$-0.768085\pi$
$373$	−10.4787	+	6.04988i	−0.542567	+	0.313251i	0.203552	+	0.979064i	$0.434751\pi$
$374$		0			0
$375$	1.98467	+	1.14585i	0.102488	+	0.0591714i
$376$		0			0
$377$	−2.02390	−	12.9071i	−0.104236	−	0.664752i
$378$		0			0
$379$	−7.11999	+	12.3322i	−0.365729	+	0.633462i	−0.988893	−	0.148630i	$-0.952514\pi$
$379$	−7.11999	+	12.3322i	−0.365729	+	0.633462i	0.623164	+	0.782092i	$0.285847\pi$
$380$		0			0
$381$	−5.40413	+	3.12007i	−0.276862	+	0.159846i
$382$		0			0
$383$	−20.4692	+	11.8179i	−1.04593	+	0.603866i	−0.921506	−	0.388363i	$-0.873041\pi$
$383$	−20.4692	+	11.8179i	−1.04593	+	0.603866i	−0.124421	+	0.992230i	$0.539707\pi$
$384$		0			0
$385$			2.41822i			0.123244i
$386$		0			0
$387$	−5.40070	−	3.11810i	−0.274533	−	0.158502i
$388$		0			0
$389$		−	16.4521i		−	0.834152i	−0.908872	−	0.417076i	$-0.863055\pi$
$389$		−	16.4521i		−	0.834152i	0.908872	−	0.417076i	$-0.136945\pi$
$390$		0			0
$391$	−10.7931			−0.545831
$392$		0			0
$393$	−7.88570	+	13.6584i	−0.397781	+	0.688977i
$394$		0			0
$395$	−3.56440			−0.179344
$396$		0			0
$397$	−2.08064	−	3.60378i	−0.104424	−	0.180868i	0.809078	−	0.587701i	$-0.199967\pi$
$397$	−2.08064	−	3.60378i	−0.104424	−	0.180868i	−0.913503	+	0.406832i	$0.866633\pi$
$398$		0			0
$399$	−13.4486	−	23.2937i	−0.673273	−	1.16614i
$400$		0			0
$401$	−9.32403	−	5.38323i	−0.465620	−	0.268826i	0.248785	−	0.968559i	$-0.419969\pi$
$401$	−9.32403	−	5.38323i	−0.465620	−	0.268826i	−0.714404	+	0.699733i	$0.753302\pi$
$402$		0			0
$403$	27.0170	−	21.8091i	1.34581	−	1.08639i
$404$		0			0
$405$	0.115196	−	0.199526i	0.00572416	−	0.00991453i
$406$		0			0
$407$	−1.78878	−	3.09826i	−0.0886666	−	0.153575i
$408$		0			0
$409$	26.0298	−	15.0283i	1.28709	−	0.743103i	0.308958	−	0.951076i	$-0.400020\pi$
$409$	26.0298	−	15.0283i	1.28709	−	0.743103i	0.978135	+	0.207972i	$0.0666864\pi$
$410$		0			0
$411$	−5.11371			−0.252241
$412$		0			0
$413$	−20.9927	−	12.1201i	−1.03298	−	0.596392i
$414$		0			0
$415$	−2.93209			−0.143930
$416$		0			0
$417$	5.66737			0.277532
$418$		0			0
$419$	−13.7149	−	7.91829i	−0.670016	−	0.386834i	0.126067	−	0.992022i	$-0.459765\pi$
$419$	−13.7149	−	7.91829i	−0.670016	−	0.386834i	−0.796083	+	0.605188i	$0.793098\pi$
$420$		0			0
$421$	23.2913			1.13515			0.567574	−	0.823322i	$-0.307882\pi$
$421$	23.2913			1.13515			0.567574	+	0.823322i	$0.307882\pi$
$422$		0			0
$423$	7.71240	−	4.45276i	0.374990	−	0.216500i
$424$		0			0
$425$	3.91643	+	6.78346i	0.189975	+	0.329046i
$426$		0			0
$427$	−4.83073	+	8.36708i	−0.233776	+	0.404911i
$428$		0			0
$429$	−10.5803	−	4.08011i	−0.510820	−	0.196989i
$430$		0			0
$431$	−6.94958	−	4.01234i	−0.334750	−	0.193268i	0.323198	−	0.946331i	$-0.395242\pi$
$431$	−6.94958	−	4.01234i	−0.334750	−	0.193268i	−0.657948	+	0.753064i	$0.728575\pi$
$432$		0			0
$433$	−15.2699	−	26.4483i	−0.733825	−	1.27102i	−0.955237	−	0.295842i	$-0.904400\pi$
$433$	−15.2699	−	26.4483i	−0.733825	−	1.27102i	0.221412	−	0.975180i	$-0.428934\pi$
$434$		0			0
$435$	−0.417419	−	0.722991i	−0.0200137	−	0.0346648i
$436$		0			0
$437$	−54.9379			−2.62804
$438$		0			0
$439$	5.57038	−	9.64818i	0.265860	−	0.460482i	−0.701929	−	0.712247i	$-0.747678\pi$
$439$	5.57038	−	9.64818i	0.265860	−	0.460482i	0.967788	+	0.251765i	$0.0810109\pi$
$440$		0			0
$441$	4.13759			0.197028
$442$		0			0
$443$		−	1.48868i		−	0.0707295i	−0.999374	−	0.0353647i	$-0.988741\pi$
$443$		−	1.48868i		−	0.0707295i	0.999374	−	0.0353647i	$-0.0112593\pi$
$444$		0			0
$445$	−2.32021	−	1.33957i	−0.109988	−	0.0635018i
$446$		0			0
$447$			9.00825i			0.426076i
$448$		0			0
$449$	23.5031	−	13.5695i	1.10918	−	0.640384i	0.170561	−	0.985347i	$-0.445442\pi$
$449$	23.5031	−	13.5695i	1.10918	−	0.640384i	0.938616	+	0.344963i	$0.112109\pi$
$450$		0			0
$451$	30.9657	−	17.8781i	1.45812	−	0.841845i
$452$		0			0
$453$	−3.08814	+	5.34882i	−0.145094	+	0.251310i
$454$		0			0
$455$	2.58661	+	0.997483i	0.121262	+	0.0467627i
$456$		0			0
$457$	21.3528	+	12.3281i	0.998843	+	0.576682i	0.907906	−	0.419174i	$-0.137680\pi$
$457$	21.3528	+	12.3281i	0.998843	+	0.576682i	0.0909374	+	0.995857i	$0.471014\pi$
$458$		0			0
$459$	1.37125	−	0.791692i	0.0640045	−	0.0369530i
$460$		0			0
$461$	3.67379	+	6.36319i	0.171105	+	0.296363i	0.938807	−	0.344445i	$-0.111933\pi$
$461$	3.67379	+	6.36319i	0.171105	+	0.296363i	−0.767701	+	0.640808i	$0.778599\pi$
$462$		0			0
$463$			13.6798i			0.635756i	0.948132	+	0.317878i	$0.102970\pi$
$463$			13.6798i			0.635756i	−0.948132	+	0.317878i	$0.897030\pi$
$464$		0			0
$465$	1.10933	−	1.92142i	0.0514440	−	0.0891036i
$466$		0			0
$467$			29.4078i			1.36083i	0.732826	+	0.680416i	$0.238201\pi$
$467$			29.4078i			1.36083i	−0.732826	+	0.680416i	$0.761799\pi$
$468$		0			0
$469$			4.27400i			0.197355i
$470$		0			0
$471$	−5.02785	+	8.70849i	−0.231671	+	0.401266i
$472$		0			0
$473$			19.6133i			0.901820i
$474$		0			0
$475$	19.9350	+	34.5285i	0.914682	+	1.58428i
$476$		0			0
$477$	−3.47939	+	2.00883i	−0.159310	+	0.0919778i
$478$		0			0
$479$	3.66802	+	2.11773i	0.167596	+	0.0967616i	0.581452	−	0.813581i	$-0.302485\pi$
$479$	3.66802	+	2.11773i	0.167596	+	0.0967616i	−0.413856	+	0.910342i	$0.635818\pi$
$480$		0			0
$481$	−4.05185	+	0.635349i	−0.184749	+	0.0289694i
$482$		0			0
$483$	11.3743	−	19.7009i	0.517550	−	0.896423i
$484$		0			0
$485$	−1.60100	+	0.924338i	−0.0726977	+	0.0419720i
$486$		0			0
$487$	34.5579	−	19.9520i	1.56597	−	0.904112i	0.569337	−	0.822104i	$-0.307200\pi$
$487$	34.5579	−	19.9520i	1.56597	−	0.904112i	0.996632	−	0.0820078i	$-0.0261332\pi$
$488$		0			0
$489$			20.6010i			0.931608i
$490$		0			0
$491$	−23.5208	−	13.5798i	−1.06148	−	0.612846i	−0.135639	−	0.990758i	$-0.543309\pi$
$491$	−23.5208	−	13.5798i	−1.06148	−	0.612846i	−0.925841	+	0.377913i	$0.876642\pi$
$492$		0			0
$493$		−	5.73745i		−	0.258402i
$494$		0			0
$495$	−0.724602			−0.0325685
$496$		0			0
$497$	1.90239	−	3.29504i	0.0853340	−	0.147803i
$498$		0			0
$499$	12.6803			0.567649			0.283825	−	0.958876i	$-0.408397\pi$
$499$	12.6803			0.567649			0.283825	+	0.958876i	$0.408397\pi$
$500$		0			0
$501$	4.60642	+	7.97855i	0.205800	+	0.356455i
$502$		0			0
$503$	3.49953	+	6.06136i	0.156036	+	0.270263i	0.933436	−	0.358744i	$-0.116795\pi$
$503$	3.49953	+	6.06136i	0.156036	+	0.270263i	−0.777400	+	0.629007i	$0.783462\pi$
$504$		0			0
$505$	2.29896	+	1.32731i	0.102302	+	0.0590643i
$506$		0			0
$507$	−8.72844	+	9.63402i	−0.387644	+	0.427862i
$508$		0			0
$509$	7.65922	−	13.2662i	0.339489	−	0.588012i	−0.644848	−	0.764311i	$-0.723079\pi$
$509$	7.65922	−	13.2662i	0.339489	−	0.588012i	0.984337	+	0.176299i	$0.0564126\pi$
$510$		0			0
$511$	1.35756	+	2.35136i	0.0600549	+	0.104018i
$512$		0			0
$513$	6.97979	−	4.02979i	0.308165	−	0.177919i
$514$		0			0
$515$	−0.131401			−0.00579024
$516$		0			0
$517$	−24.2561	−	14.0042i	−1.06678	−	0.615906i
$518$		0			0
$519$	1.91233			0.0839420
$520$		0			0
$521$	30.3448			1.32943			0.664715	−	0.747097i	$-0.268553\pi$
$521$	30.3448			1.32943			0.664715	+	0.747097i	$0.268553\pi$
$522$		0			0
$523$	19.0473	+	10.9970i	0.832879	+	0.480863i	0.854837	−	0.518896i	$-0.173657\pi$
$523$	19.0473	+	10.9970i	0.832879	+	0.480863i	−0.0219582	+	0.999759i	$0.506990\pi$
$524$		0			0
$525$	−16.5094			−0.720528
$526$		0			0
$527$	13.2050	−	7.62392i	0.575219	−	0.332103i
$528$		0			0
$529$	−11.7322	−	20.3208i	−0.510097	−	0.883514i
$530$		0			0
$531$	3.63171	−	6.29031i	0.157603	−	0.272976i
$532$		0			0
$533$	−6.35003	−	40.4964i	−0.275050	−	1.75409i
$534$		0			0
$535$	−0.294870	−	0.170243i	−0.0127483	−	0.00736026i
$536$		0			0
$537$	6.83830	+	11.8443i	0.295094	+	0.511118i
$538$		0			0
$539$	−6.50651	−	11.2696i	−0.280255	−	0.485416i
$540$		0			0
$541$	−1.38788			−0.0596694			−0.0298347	−	0.999555i	$-0.509498\pi$
$541$	−1.38788			−0.0596694			−0.0298347	+	0.999555i	$0.509498\pi$
$542$		0			0
$543$	−0.975528	+	1.68966i	−0.0418639	+	0.0725105i
$544$		0			0
$545$	0.346884			0.0148589
$546$		0			0
$547$		−	2.42593i		−	0.103725i	−0.998654	−	0.0518626i	$-0.983484\pi$
$547$		−	2.42593i		−	0.103725i	0.998654	−	0.0518626i	$-0.0165158\pi$
$548$		0			0
$549$	−2.50714	−	1.44750i	−0.107002	−	0.0617777i
$550$		0			0
$551$		−	29.2042i		−	1.24414i
$552$		0			0
$553$	44.7140	−	25.8156i	1.90143	−	1.09779i
$554$		0			0
$555$	−0.226964	+	0.131037i	−0.00963407	+	0.00556223i
$556$		0			0
$557$	−15.3441	+	26.5767i	−0.650148	+	1.12609i	0.332938	+	0.942949i	$0.391960\pi$
$557$	−15.3441	+	26.5767i	−0.650148	+	1.12609i	−0.983087	+	0.183141i	$0.941373\pi$
$558$		0			0
$559$	20.9790	+	8.09022i	0.887318	+	0.342180i
$560$		0			0
$561$	−4.31268	−	2.48993i	−0.182082	−	0.105125i
$562$		0			0
$563$	34.3455	−	19.8294i	1.44749	−	0.835709i	0.449159	−	0.893452i	$-0.351724\pi$
$563$	34.3455	−	19.8294i	1.44749	−	0.835709i	0.998331	+	0.0577430i	$0.0183904\pi$
$564$		0			0
$565$	0.00879592	+	0.0152350i	0.000370047	+	0.000640941i
$566$		0			0
$567$			3.33730i			0.140154i
$568$		0			0
$569$	−4.59173	+	7.95311i	−0.192495	+	0.333412i	−0.946077	−	0.323943i	$-0.894991\pi$
$569$	−4.59173	+	7.95311i	−0.192495	+	0.333412i	0.753581	+	0.657355i	$0.228325\pi$
$570$		0			0
$571$		−	12.4846i		−	0.522463i	−0.965276	−	0.261232i	$-0.915871\pi$
$571$		−	12.4846i		−	0.522463i	0.965276	−	0.261232i	$-0.0841286\pi$
$572$		0			0
$573$		−	16.4549i		−	0.687415i
$574$		0			0
$575$	−16.8603	+	29.2029i	−0.703123	+	1.21784i
$576$		0			0
$577$		−	29.8603i		−	1.24310i	−0.783375	−	0.621550i	$-0.786503\pi$
$577$		−	29.8603i		−	1.24310i	0.783375	−	0.621550i	$-0.213497\pi$
$578$		0			0
$579$	−2.97012	−	5.14440i	−0.123434	−	0.213794i
$580$		0			0
$581$	36.7819	−	21.2360i	1.52597	−	0.881019i
$582$		0			0
$583$	10.9429	+	6.31790i	0.453210	+	0.261661i
$584$		0			0
$585$	−0.298889	+	0.775059i	−0.0123575	+	0.0320448i
$586$		0			0
$587$	18.2451	−	31.6014i	0.753054	−	1.30433i	−0.193282	−	0.981143i	$-0.561913\pi$
$587$	18.2451	−	31.6014i	0.753054	−	1.30433i	0.946336	−	0.323185i	$-0.104754\pi$
$588$		0			0
$589$	67.2148	−	38.8065i	2.76954	−	1.59899i
$590$		0			0
$591$	−6.83547	+	3.94646i	−0.281174	+	0.162336i
$592$		0			0
$593$		−	26.4261i		−	1.08519i	−0.839995	−	0.542594i	$-0.817442\pi$
$593$		−	26.4261i		−	1.08519i	0.839995	−	0.542594i	$-0.182558\pi$
$594$		0			0
$595$	1.05434	+	0.608724i	0.0432238	+	0.0249553i
$596$		0			0
$597$		−	16.3771i		−	0.670270i
$598$		0			0
$599$	−7.29146			−0.297921			−0.148960	−	0.988843i	$-0.547593\pi$
$599$	−7.29146			−0.297921			−0.148960	+	0.988843i	$0.547593\pi$
$600$		0			0
$601$	0.117332	−	0.203224i	0.00478606	−	0.00828970i	−0.863622	−	0.504139i	$-0.831810\pi$
$601$	0.117332	−	0.203224i	0.00478606	−	0.00828970i	0.868409	+	0.495849i	$0.165143\pi$
$602$		0			0
$603$	−1.28068			−0.0521531
$604$		0			0
$605$	−0.127697	−	0.221178i	−0.00519163	−	0.00899216i
$606$		0			0
$607$	−7.42041	−	12.8525i	−0.301185	−	0.521668i	0.675220	−	0.737617i	$-0.264049\pi$
$607$	−7.42041	−	12.8525i	−0.301185	−	0.521668i	−0.976405	+	0.215949i	$0.930715\pi$
$608$		0			0
$609$	10.4727	+	6.04643i	0.424376	+	0.245014i
$610$		0			0
$611$	−24.9847	+	20.1685i	−1.01077	+	0.815932i
$612$		0			0
$613$	0.235744	−	0.408321i	0.00952163	−	0.0164919i	−0.861225	−	0.508223i	$-0.830302\pi$
$613$	0.235744	−	0.408321i	0.00952163	−	0.0164919i	0.870747	+	0.491731i	$0.163636\pi$
$614$		0			0
$615$	−1.30966	−	2.26840i	−0.0528106	−	0.0914706i
$616$		0			0
$617$	−28.2097	+	16.2869i	−1.13568	+	0.655685i	−0.945357	−	0.326036i	$-0.894287\pi$
$617$	−28.2097	+	16.2869i	−1.13568	+	0.655685i	−0.190323	+	0.981721i	$0.560954\pi$
$618$		0			0
$619$	−9.28369			−0.373143			−0.186571	−	0.982441i	$-0.559738\pi$
$619$	−9.28369			−0.373143			−0.186571	+	0.982441i	$0.559738\pi$
$620$		0			0
$621$	5.90325	+	3.40824i	0.236889	+	0.136768i
$622$		0			0
$623$	38.8081			1.55481
$624$		0			0
$625$	24.2066			0.968264
$626$		0			0
$627$	−21.9520	−	12.6740i	−0.876677	−	0.506150i
$628$		0			0
$629$	−1.80112			−0.0718153
$630$		0			0
$631$	−3.76004	+	2.17086i	−0.149685	+	0.0864205i	−0.572972	−	0.819575i	$-0.694210\pi$
$631$	−3.76004	+	2.17086i	−0.149685	+	0.0864205i	0.423287	+	0.905996i	$0.360876\pi$
$632$		0			0
$633$	−7.26314	−	12.5801i	−0.288684	−	0.500016i
$634$		0			0
$635$	0.718843	−	1.24507i	0.0285264	−	0.0494092i
$636$		0			0
$637$	−14.7382	+	2.31102i	−0.583949	+	0.0915659i
$638$		0			0
$639$	0.987337	+	0.570039i	0.0390585	+	0.0225504i
$640$		0			0
$641$	−16.3563	−	28.3299i	−0.646035	−	1.11897i	−0.984061	−	0.177829i	$-0.943093\pi$
$641$	−16.3563	−	28.3299i	−0.646035	−	1.11897i	0.338026	−	0.941137i	$-0.390241\pi$
$642$		0			0
$643$	−3.40535	−	5.89823i	−0.134294	−	0.232604i	0.791034	−	0.611773i	$-0.209543\pi$
$643$	−3.40535	−	5.89823i	−0.134294	−	0.232604i	−0.925327	+	0.379169i	$0.876210\pi$
$644$		0			0
$645$	1.43677			0.0565729
$646$		0			0
$647$	12.5284	−	21.6999i	0.492543	−	0.853110i	−0.507420	−	0.861699i	$-0.669401\pi$
$647$	12.5284	−	21.6999i	0.492543	−	0.853110i	0.999963	+	0.00858905i	$0.00273401\pi$
$648$		0			0
$649$	−22.8440			−0.896705
$650$		0			0
$651$			32.1379i			1.25958i
$652$		0			0
$653$	−41.6685	−	24.0573i	−1.63062	−	0.941436i	−0.983903	−	0.178702i	$-0.942810\pi$
$653$	−41.6685	−	24.0573i	−1.63062	−	0.941436i	−0.646712	−	0.762734i	$-0.723856\pi$
$654$		0			0
$655$		−	3.63362i		−	0.141977i
$656$		0			0
$657$	−0.704569	+	0.406783i	−0.0274879	+	0.0158701i
$658$		0			0
$659$	−18.7319	+	10.8148i	−0.729690	+	0.421287i	−0.818309	−	0.574779i	$-0.805088\pi$
$659$	−18.7319	+	10.8148i	−0.729690	+	0.421287i	0.0886189	+	0.996066i	$0.471755\pi$
$660$		0			0
$661$	−10.4554	+	18.1092i	−0.406666	+	0.704366i	−0.994514	−	0.104605i	$-0.966642\pi$
$661$	−10.4554	+	18.1092i	−0.406666	+	0.704366i	0.587848	+	0.808972i	$0.299975\pi$
$662$		0			0
$663$	−4.44224	+	3.58593i	−0.172522	+	0.139266i
$664$		0			0
$665$	5.36670	+	3.09847i	0.208112	+	0.120153i
$666$		0			0
$667$	21.3907	−	12.3499i	0.828250	−	0.478190i
$668$		0			0
$669$	−11.5670	−	20.0347i	−0.447207	−	0.774585i
$670$		0			0
$671$			9.10496i			0.351493i
$672$		0			0
$673$	−8.64625	+	14.9757i	−0.333288	+	0.577272i	−0.983155	−	0.182776i	$-0.941492\pi$
$673$	−8.64625	+	14.9757i	−0.333288	+	0.577272i	0.649866	+	0.760049i	$0.274825\pi$
$674$		0			0
$675$		−	4.94692i		−	0.190407i
$676$		0			0
$677$			5.72652i			0.220088i	0.993927	+	0.110044i	$0.0350992\pi$
$677$			5.72652i			0.220088i	−0.993927	+	0.110044i	$0.964901\pi$
$678$		0			0
$679$	13.3893	−	23.1909i	0.513833	−	0.889986i
$680$		0			0
$681$		−	20.4317i		−	0.782943i
$682$		0			0
$683$	17.8037	+	30.8369i	0.681238	+	1.17994i	0.974603	+	0.223939i	$0.0718917\pi$
$683$	17.8037	+	30.8369i	0.681238	+	1.17994i	−0.293365	+	0.956001i	$0.594775\pi$
$684$		0			0
$685$	1.02032	−	0.589081i	0.0389844	−	0.0225076i
$686$		0			0
$687$	5.81086	+	3.35490i	0.221698	+	0.127997i
$688$		0			0
$689$	11.2717	−	9.09887i	0.429416	−	0.346639i
$690$		0			0
$691$	−14.8409	+	25.7052i	−0.564575	+	0.977873i	0.432514	+	0.901627i	$0.357627\pi$
$691$	−14.8409	+	25.7052i	−0.564575	+	0.977873i	−0.997089	+	0.0762454i	$0.975707\pi$
$692$		0			0
$693$	9.08986	−	5.24803i	0.345295	−	0.199356i
$694$		0			0
$695$	−1.13079	+	0.652861i	−0.0428933	+	0.0247644i
$696$		0			0
$697$		−	18.0014i		−	0.681851i
$698$		0			0
$699$	−8.09997	−	4.67652i	−0.306369	−	0.176882i
$700$		0			0
$701$			23.7944i			0.898704i	0.893355	+	0.449352i	$0.148345\pi$
$701$			23.7944i			0.898704i	−0.893355	+	0.449352i	$0.851655\pi$
$702$		0			0
$703$	−9.16787			−0.345773
$704$		0			0
$705$	−1.02588	+	1.77688i	−0.0386370	+	0.0669213i
$706$		0			0
$707$	−38.4528			−1.44617
$708$		0			0
$709$	−4.26282	−	7.38342i	−0.160093	−	0.277290i	0.774809	−	0.632196i	$-0.217846\pi$
$709$	−4.26282	−	7.38342i	−0.160093	−	0.277290i	−0.934902	+	0.354906i	$0.884513\pi$
$710$		0			0
$711$	7.73548	+	13.3982i	0.290103	+	0.502473i
$712$		0			0
$713$	56.8477	+	32.8211i	2.12896	+	1.22916i
$714$		0			0
$715$	2.58105	−	0.404721i	0.0965259	−	0.0151357i
$716$		0			0
$717$	−4.39732	+	7.61639i	−0.164221	+	0.284439i
$718$		0			0
$719$	6.37676	+	11.0449i	0.237813	+	0.411904i	0.960086	−	0.279703i	$-0.0902361\pi$
$719$	6.37676	+	11.0449i	0.237813	+	0.411904i	−0.722273	+	0.691608i	$0.756903\pi$
$720$		0			0
$721$	1.64838	−	0.951692i	0.0613888	−	0.0354429i
$722$		0			0
$723$	−19.2249			−0.714981
$724$		0			0
$725$	−15.5238	−	8.96268i	−0.576540	−	0.332866i
$726$		0			0
$727$	−28.1255			−1.04312			−0.521559	−	0.853216i	$-0.674649\pi$
$727$	−28.1255			−1.04312			−0.521559	+	0.853216i	$0.674649\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	8.55138	+	4.93714i	0.316284	+	0.182607i
$732$		0			0
$733$	49.4380			1.82604			0.913018	−	0.407920i	$-0.133746\pi$
$733$	49.4380			1.82604			0.913018	+	0.407920i	$0.133746\pi$
$734$		0			0
$735$	−0.825557	+	0.476636i	−0.0304511	+	0.0175810i
$736$		0			0
$737$	2.01391	+	3.48819i	0.0741833	+	0.128489i
$738$		0			0
$739$	14.0277	−	24.2967i	0.516018	−	0.893769i	−0.483809	−	0.875173i	$-0.660747\pi$
$739$	14.0277	−	24.2967i	0.516018	−	0.893769i	0.999827	−	0.0185956i	$-0.00591950\pi$
$740$		0			0
$741$	−22.6114	+	18.2527i	−0.830651	+	0.670530i
$742$		0			0
$743$	2.05615	+	1.18712i	0.0754328	+	0.0435512i	0.537242	−	0.843428i	$-0.319466\pi$
$743$	2.05615	+	1.18712i	0.0754328	+	0.0435512i	−0.461809	+	0.886979i	$0.652800\pi$
$744$		0			0
$745$	−1.03772	−	1.79738i	−0.0380191	−	0.0658509i
$746$		0			0
$747$	6.36323	+	11.0214i	0.232818	+	0.403253i
$748$		0			0
$749$	4.93204			0.180213
$750$		0			0
$751$	−2.48319	+	4.30101i	−0.0906130	+	0.156946i	−0.907769	−	0.419470i	$-0.862216\pi$
$751$	−2.48319	+	4.30101i	−0.0906130	+	0.156946i	0.817156	+	0.576416i	$0.195549\pi$
$752$		0			0
$753$	21.1907			0.772231
$754$		0			0
$755$		−	1.42297i		−	0.0517873i
$756$		0			0
$757$	3.10991	+	1.79551i	0.113032	+	0.0652589i	0.555450	−	0.831550i	$-0.312546\pi$
$757$	3.10991	+	1.79551i	0.113032	+	0.0652589i	−0.442418	+	0.896809i	$0.645879\pi$
$758$		0			0
$759$		−	21.4383i		−	0.778163i
$760$		0			0
$761$	−30.1976	+	17.4346i	−1.09466	+	0.632004i	−0.934814	−	0.355138i	$-0.884434\pi$
$761$	−30.1976	+	17.4346i	−1.09466	+	0.632004i	−0.159849	+	0.987142i	$0.551101\pi$
$762$		0			0
$763$	−4.35153	+	2.51236i	−0.157536	+	0.0909534i
$764$		0			0
$765$	−0.182400	+	0.315926i	−0.00659469	+	0.0114223i
$766$		0			0
$767$	−9.42285	+	24.4347i	−0.340239	+	0.882286i
$768$		0			0
$769$	−3.53352	−	2.04008i	−0.127422	−	0.0735670i	0.434934	−	0.900462i	$-0.356772\pi$
$769$	−3.53352	−	2.04008i	−0.127422	−	0.0735670i	−0.562356	+	0.826895i	$0.690105\pi$
$770$		0			0
$771$	4.38885	−	2.53390i	0.158061	−	0.0912563i
$772$		0			0
$773$	7.40633	+	12.8281i	0.266387	+	0.461396i	0.967926	−	0.251235i	$-0.0808367\pi$
$773$	7.40633	+	12.8281i	0.266387	+	0.461396i	−0.701539	+	0.712631i	$0.747503\pi$
$774$		0			0
$775$		−	47.6384i		−	1.71122i
$776$		0			0
$777$	1.89811	−	3.28763i	0.0680944	−	0.117943i
$778$		0			0
$779$		−	91.6287i		−	3.28294i
$780$		0			0
$781$		−	3.58563i		−	0.128304i
$782$		0			0
$783$	−1.81177	+	3.13808i	−0.0647474	+	0.112146i
$784$		0			0
$785$		−	2.31676i		−	0.0826888i
$786$		0			0
$787$	−18.0243	−	31.2189i	−0.642496	−	1.11283i	−0.984874	−	0.173273i	$-0.944566\pi$
$787$	−18.0243	−	31.2189i	−0.642496	−	1.11283i	0.342378	−	0.939562i	$-0.388768\pi$
$788$		0			0
$789$	−4.66751	+	2.69479i	−0.166168	+	0.0959370i
$790$		0			0
$791$	−0.220683	−	0.127411i	−0.00784658	−	0.00453022i
$792$		0			0
$793$	9.73898	+	3.75568i	0.345841	+	0.133368i
$794$		0			0
$795$	0.462819	−	0.801626i	0.0164145	−	0.0284307i
$796$		0			0
$797$	11.3573	−	6.55713i	0.402295	−	0.232265i	−0.285179	−	0.958474i	$-0.592053\pi$
$797$	11.3573	−	6.55713i	0.402295	−	0.232265i	0.687474	+	0.726209i	$0.258720\pi$
$798$		0			0
$799$	−12.2117	+	7.05042i	−0.432019	+	0.249426i
$800$		0			0
$801$			11.6286i			0.410876i
$802$		0			0
$803$	2.21592	+	1.27936i	0.0781982	+	0.0451477i
$804$		0			0
$805$			5.24113i			0.184726i
$806$		0			0
$807$	15.1169			0.532140
$808$		0			0
$809$	7.48145	−	12.9583i	0.263034	−	0.455588i	−0.704013	−	0.710187i	$-0.748610\pi$
$809$	7.48145	−	12.9583i	0.263034	−	0.455588i	0.967047	+	0.254599i	$0.0819436\pi$
$810$		0			0
$811$	20.9684			0.736299			0.368150	−	0.929767i	$-0.379991\pi$
$811$	20.9684			0.736299			0.368150	+	0.929767i	$0.379991\pi$
$812$		0			0
$813$	−0.831915	−	1.44092i	−0.0291765	−	0.0505352i
$814$		0			0
$815$	−2.37316	−	4.11043i	−0.0831281	−	0.143982i
$816$		0			0
$817$	43.5273	+	25.1305i	1.52283	+	0.879206i
$818$		0			0
$819$	−1.86402	−	11.8876i	−0.0651343	−	0.415385i
$820$		0			0
$821$	−12.5793	+	21.7880i	−0.439021	+	0.760407i	−0.997614	−	0.0690347i	$-0.978008\pi$
$821$	−12.5793	+	21.7880i	−0.439021	+	0.760407i	0.558593	+	0.829442i	$0.311341\pi$
$822$		0			0
$823$	4.64806	+	8.05068i	0.162021	+	0.280629i	0.935593	−	0.353079i	$-0.114865\pi$
$823$	4.64806	+	8.05068i	0.162021	+	0.280629i	−0.773572	+	0.633708i	$0.781532\pi$
$824$		0			0
$825$	−13.4740	+	7.77921i	−0.469104	+	0.270837i
$826$		0			0
$827$	22.5483			0.784080			0.392040	−	0.919948i	$-0.371769\pi$
$827$	22.5483			0.784080			0.392040	+	0.919948i	$0.371769\pi$
$828$		0			0
$829$	4.07023	+	2.34995i	0.141365	+	0.0816171i	0.569014	−	0.822328i	$-0.307325\pi$
$829$	4.07023	+	2.34995i	0.141365	+	0.0816171i	−0.427649	+	0.903945i	$0.640658\pi$
$830$		0			0
$831$	16.1254			0.559385
$832$		0			0
$833$	−6.55139			−0.226992
$834$		0			0
$835$	−1.83820	−	1.06129i	−0.0636136	−	0.0367273i
$836$		0			0
$837$	−9.62991			−0.332858
$838$		0			0
$839$	38.2396	−	22.0776i	1.32018	−	0.762205i	0.336421	−	0.941712i	$-0.390784\pi$
$839$	38.2396	−	22.0776i	1.32018	−	0.762205i	0.983757	+	0.179507i	$0.0574503\pi$
$840$		0			0
$841$	−7.93498	−	13.7438i	−0.273620	−	0.473924i
$842$		0			0
$843$	−11.9636	+	20.7215i	−0.412047	+	0.713686i
$844$		0			0
$845$	0.631747	−	2.92772i	0.0217328	−	0.100717i
$846$		0			0
$847$	3.20382	+	1.84973i	0.110085	+	0.0635574i
$848$		0			0
$849$	−4.42906	−	7.67135i	−0.152005	−	0.263280i
$850$		0			0
$851$	−3.87692	−	6.71502i	−0.132899	−	0.230188i
$852$		0			0
$853$	−2.24836			−0.0769825			−0.0384912	−	0.999259i	$-0.512255\pi$
$853$	−2.24836			−0.0769825			−0.0384912	+	0.999259i	$0.512255\pi$
$854$		0			0
$855$	−0.928434	+	1.60809i	−0.0317518	+	0.0549957i
$856$		0			0
$857$	23.3922			0.799062			0.399531	−	0.916720i	$-0.369173\pi$
$857$	23.3922			0.799062			0.399531	+	0.916720i	$0.369173\pi$
$858$		0			0
$859$			23.3254i			0.795854i	0.917417	+	0.397927i	$0.130270\pi$
$859$			23.3254i			0.795854i	−0.917417	+	0.397927i	$0.869730\pi$
$860$		0			0
$861$	32.8584	+	18.9708i	1.11981	+	0.646522i
$862$		0			0
$863$		−	51.3259i		−	1.74715i	−0.486687	−	0.873577i	$-0.661795\pi$
$863$		−	51.3259i		−	1.74715i	0.486687	−	0.873577i	$-0.338205\pi$
$864$		0			0
$865$	−0.381560	+	0.220294i	−0.0129734	+	0.00749021i
$866$		0			0
$867$	12.5512	−	7.24645i	0.426262	−	0.246102i
$868$		0			0
$869$	24.3286	−	42.1384i	0.825292	−	1.42945i
$870$		0			0
$871$	4.56180	−	0.715311i	0.154571	−	0.0242374i
$872$		0			0
$873$	6.94900	+	4.01201i	0.235188	+	0.135786i
$874$		0			0
$875$	6.62344	−	3.82405i	0.223913	−	0.129276i
$876$		0			0
$877$	−5.20754	−	9.01972i	−0.175846	−	0.304574i	0.764608	−	0.644496i	$-0.222933\pi$
$877$	−5.20754	−	9.01972i	−0.175846	−	0.304574i	−0.940454	+	0.339922i	$0.889599\pi$
$878$		0			0
$879$			24.2874i			0.819192i
$880$		0			0
$881$	−20.8219	+	36.0645i	−0.701507	+	1.21505i	0.266431	+	0.963854i	$0.414156\pi$
$881$	−20.8219	+	36.0645i	−0.701507	+	1.21505i	−0.967938	+	0.251191i	$0.919178\pi$
$882$		0			0
$883$			20.2048i			0.679945i	0.940435	+	0.339972i	$0.110418\pi$
$883$			20.2048i			0.679945i	−0.940435	+	0.339972i	$0.889582\pi$
$884$		0			0
$885$			1.67344i			0.0562521i
$886$		0			0
$887$	−12.6955	+	21.9892i	−0.426273	+	0.738326i	−0.996538	−	0.0831341i	$-0.973507\pi$
$887$	−12.6955	+	21.9892i	−0.426273	+	0.738326i	0.570265	+	0.821460i	$0.306840\pi$
$888$		0			0
$889$			20.8253i			0.698457i
$890$		0			0
$891$	1.57254	+	2.72371i	0.0526820	+	0.0912478i
$892$		0			0
$893$	−62.1587	+	35.8873i	−2.08006	+	1.20092i
$894$		0			0
$895$	−2.72884	−	1.57550i	−0.0912150	−	0.0526630i
$896$		0			0
$897$	−22.9312	−	8.84304i	−0.765650	−	0.295260i
$898$		0			0
$899$	−17.4472	+	30.2194i	−0.581896	+	1.00787i
$900$		0			0
$901$	5.50920	−	3.18074i	0.183538	−	0.105966i
$902$		0			0
$903$	−18.0238	+	10.4060i	−0.599794	+	0.346291i
$904$		0			0
$905$		−	0.449510i		−	0.0149422i
$906$		0			0
$907$	19.8890	+	11.4829i	0.660405	+	0.381285i	0.792431	−	0.609961i	$-0.208815\pi$
$907$	19.8890	+	11.4829i	0.660405	+	0.381285i	−0.132027	+	0.991246i	$0.542148\pi$
$908$		0			0
$909$		−	11.5221i		−	0.382164i
$910$		0			0
$911$	−25.4657			−0.843717			−0.421859	−	0.906662i	$-0.638622\pi$
$911$	−25.4657			−0.843717			−0.421859	+	0.906662i	$0.638622\pi$
$912$		0			0
$913$	20.0128	−	34.6632i	0.662328	−	1.14719i
$914$		0			0
$915$	0.666986			0.0220499
$916$		0			0
$917$	26.3170	+	45.5823i	0.869063	+	1.50526i
$918$		0			0
$919$	10.3095	+	17.8566i	0.340079	+	0.589034i	0.984447	−	0.175682i	$-0.0562129\pi$
$919$	10.3095	+	17.8566i	0.340079	+	0.589034i	−0.644368	+	0.764715i	$0.722880\pi$
$920$		0			0
$921$	−28.0417	−	16.1899i	−0.924004	−	0.533474i
$922$		0			0
$923$	−3.83531	−	1.47903i	−0.126241	−	0.0486827i
$924$		0			0
$925$	−2.81359	+	4.87329i	−0.0925104	+	0.160233i
$926$		0			0
$927$	0.285168	+	0.493925i	0.00936615	+	0.0162226i
$928$		0			0
$929$	−13.2006	+	7.62136i	−0.433097	+	0.250049i	−0.700665	−	0.713490i	$-0.747113\pi$
$929$	−13.2006	+	7.62136i	−0.433097	+	0.250049i	0.267568	+	0.963539i	$0.413780\pi$
$930$		0			0
$931$	−33.3472			−1.09291
$932$		0			0
$933$	−14.5134	−	8.37934i	−0.475149	−	0.274327i
$934$		0			0
$935$	1.14732			0.0375215
$936$		0			0
$937$	44.7527			1.46201			0.731004	−	0.682373i	$-0.239052\pi$
$937$	44.7527			1.46201			0.731004	+	0.682373i	$0.239052\pi$
$938$		0			0
$939$	−10.5707	−	6.10297i	−0.344960	−	0.199163i
$940$		0			0
$941$	−20.4855			−0.667807			−0.333904	−	0.942607i	$-0.608366\pi$
$941$	−20.4855			−0.667807			−0.333904	+	0.942607i	$0.608366\pi$
$942$		0			0
$943$	67.1136	−	38.7481i	2.18552	−	1.26181i
$944$		0			0
$945$	−0.384445	−	0.665879i	−0.0125060	−	0.0216610i
$946$		0			0
$947$	−17.4837	+	30.2826i	−0.568143	+	0.984052i	0.428607	+	0.903491i	$0.359004\pi$
$947$	−17.4837	+	30.2826i	−0.568143	+	0.984052i	−0.996750	+	0.0805608i	$0.974329\pi$
$948$		0			0
$949$	2.28249	−	1.84250i	0.0740927	−	0.0598102i
$950$		0			0
$951$	25.9882	+	15.0043i	0.842725	+	0.486547i
$952$		0			0
$953$	16.0909	+	27.8703i	0.521236	+	0.902808i	0.999695	+	0.0246977i	$0.00786233\pi$
$953$	16.0909	+	27.8703i	0.521236	+	0.902808i	−0.478459	+	0.878110i	$0.658804\pi$
$954$		0			0
$955$	1.89555	+	3.28319i	0.0613385	+	0.106241i
$956$		0			0
$957$	11.3963			0.368390
$958$		0			0
$959$	−8.53300	+	14.7796i	−0.275545	+	0.477258i
$960$		0			0
$961$	−61.7351			−1.99145
$962$		0			0
$963$			1.47785i			0.0476231i
$964$		0			0
$965$	1.18523	+	0.684295i	0.0381540	+	0.0220282i
$966$		0			0
$967$		−	20.7493i		−	0.667251i	−0.942706	−	0.333626i	$-0.891728\pi$
$967$		−	20.7493i		−	0.667251i	0.942706	−	0.333626i	$-0.108272\pi$
$968$		0			0
$969$	−11.0517	+	6.38070i	−0.355031	+	0.204977i
$970$		0			0
$971$	−16.3626	+	9.44693i	−0.525099	+	0.303166i	−0.739019	−	0.673685i	$-0.764710\pi$
$971$	−16.3626	+	9.44693i	−0.525099	+	0.303166i	0.213919	+	0.976851i	$0.431377\pi$
$972$		0			0
$973$	9.45687	−	16.3798i	0.303173	−	0.525112i
$974$		0			0
$975$	2.76306	+	17.6211i	0.0884888	+	0.564325i
$976$		0			0
$977$	31.6318	+	18.2627i	1.01199	+	0.584274i	0.911774	−	0.410691i	$-0.134713\pi$
$977$	31.6318	+	18.2627i	1.01199	+	0.584274i	0.100218	+	0.994966i	$0.468046\pi$
$978$		0			0
$979$	31.6729	−	18.2864i	1.01227	−	0.584435i
$980$		0			0
$981$	−0.752810	−	1.30391i	−0.0240354	−	0.0416305i
$982$		0			0
$983$			38.2418i			1.21972i	0.792508	+	0.609862i	$0.208775\pi$
$983$			38.2418i			1.21972i	−0.792508	+	0.609862i	$0.791225\pi$
$984$		0			0
$985$	0.909236	−	1.57484i	0.0289707	−	0.0501787i
$986$		0			0
$987$		−	29.7204i		−	0.946011i
$988$		0			0
$989$			42.5089i			1.35170i
$990$		0			0
$991$	−16.1451	+	27.9641i	−0.512866	+	0.888309i	0.487023	+	0.873389i	$0.338083\pi$
$991$	−16.1451	+	27.9641i	−0.512866	+	0.888309i	−0.999889	+	0.0149201i	$0.995251\pi$
$992$		0			0
$993$		−	4.97955i		−	0.158021i
$994$		0			0
$995$	1.88658	+	3.26766i	0.0598088	+	0.103592i
$996$		0			0
$997$	18.9701	−	10.9524i	0.600789	−	0.346866i	−0.168563	−	0.985691i	$-0.553913\pi$
$997$	18.9701	−	10.9524i	0.600789	−	0.346866i	0.769352	+	0.638825i	$0.220579\pi$
$998$		0			0
$999$	0.985115	+	0.568757i	0.0311677	+	0.0179947i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1248.2.ca.b.433.18		48
4.3	odd	2		312.2.bk.b.277.15	yes	48
8.3	odd	2		312.2.bk.b.277.23	yes	48
8.5	even	2	inner	1248.2.ca.b.433.7		48
12.11	even	2		936.2.dg.e.901.10		48
13.10	even	6	inner	1248.2.ca.b.49.7		48
24.11	even	2		936.2.dg.e.901.2		48
52.23	odd	6		312.2.bk.b.205.23	yes	48
104.75	odd	6		312.2.bk.b.205.15	✓	48
104.101	even	6	inner	1248.2.ca.b.49.18		48
156.23	even	6		936.2.dg.e.829.2		48
312.179	even	6		936.2.dg.e.829.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bk.b.205.15	✓	48	104.75	odd	6
312.2.bk.b.205.23	yes	48	52.23	odd	6
312.2.bk.b.277.15	yes	48	4.3	odd	2
312.2.bk.b.277.23	yes	48	8.3	odd	2
936.2.dg.e.829.2		48	156.23	even	6
936.2.dg.e.829.10		48	312.179	even	6
936.2.dg.e.901.2		48	24.11	even	2
936.2.dg.e.901.10		48	12.11	even	2
1248.2.ca.b.49.7		48	13.10	even	6	inner
1248.2.ca.b.49.18		48	104.101	even	6	inner
1248.2.ca.b.433.7		48	8.5	even	2	inner
1248.2.ca.b.433.18		48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1248.ca (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{3} -0.230393 q^{5} +(2.89019 - 1.66865i) q^{7} +(0.500000 + 0.866025i) q^{9} +(1.57254 - 2.72371i) q^{11} +(-2.26472 - 2.80553i) q^{13} +(-0.199526 - 0.115196i) q^{15} +(-0.791692 - 1.37125i) q^{17} +(-4.02979 - 6.97979i) q^{19} +3.33730 q^{21} +(3.40824 - 5.90325i) q^{23} -4.94692 q^{25} +1.00000i q^{27} +(3.13808 + 1.81177i) q^{29} +9.62991i q^{31} +(2.72371 - 1.57254i) q^{33} +(-0.665879 + 0.384445i) q^{35} +(0.568757 - 0.985115i) q^{37} +(-0.558542 - 3.56203i) q^{39} +(9.84578 + 5.68446i) q^{41} +(-5.40070 + 3.11810i) q^{43} +(-0.115196 - 0.199526i) q^{45} -8.90552i q^{47} +(2.06880 - 3.58326i) q^{49} -1.58338i q^{51} +4.01765i q^{53} +(-0.362301 + 0.627524i) q^{55} -8.05957i q^{57} +(-3.63171 - 6.29031i) q^{59} +(-2.50714 + 1.44750i) q^{61} +(2.89019 + 1.66865i) q^{63} +(0.521776 + 0.646375i) q^{65} +(-0.640338 + 1.10910i) q^{67} +(5.90325 - 3.40824i) q^{69} +(0.987337 - 0.570039i) q^{71} +0.813566i q^{73} +(-4.28416 - 2.47346i) q^{75} -10.4961i q^{77} +15.4710 q^{79} +(-0.500000 + 0.866025i) q^{81} +12.7265 q^{83} +(0.182400 + 0.315926i) q^{85} +(1.81177 + 3.13808i) q^{87} +(10.0707 + 5.81429i) q^{89} +(-11.2269 - 4.32949i) q^{91} +(-4.81495 + 8.33974i) q^{93} +(0.928434 + 1.60809i) q^{95} +(6.94900 - 4.01201i) q^{97} +3.14507 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{7} + 24 q^{9} + 12 q^{17} - 20 q^{23} + 48 q^{25} + 12 q^{33} - 28 q^{39} - 12 q^{41} + 16 q^{49} + 68 q^{55} + 12 q^{63} + 12 q^{65} + 12 q^{71} + 192 q^{79} - 24 q^{81} - 48 q^{89} + 20 q^{95}+ \cdots + 144 q^{97}+O(q^{100}) \) 48 * q + 12 * q^7 + 24 * q^9 + 12 * q^17 - 20 * q^23 + 48 * q^25 + 12 * q^33 - 28 * q^39 - 12 * q^41 + 16 * q^49 + 68 * q^55 + 12 * q^63 + 12 * q^65 + 12 * q^71 + 192 * q^79 - 24 * q^81 - 48 * q^89 + 20 * q^95 + 144 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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