LMFDB - Embedded newform 1248.2.ca.b.49.7

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			49.7
Character	$\chi$	$=$	1248.49
Dual form			1248.2.ca.b.433.7

$q$-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 $\left(\mathbb{Z}/1248\mathbb{Z}\right)^\times$.

$n$	$703$	$769$	$833$	$1093$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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	$-0.483594\pi$
$5$	0.230393			0.103035			0.0515174	+	0.998672i	$0.483594\pi$
$6$		0			0
$7$	2.89019	+	1.66865i	1.09239	+	0.630691i	0.934211	−	0.356720i	$-0.116105\pi$
$7$	2.89019	+	1.66865i	1.09239	+	0.630691i	0.158177	+	0.987411i	$0.449438\pi$
$8$		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	$-0.323907\pi$
$11$	−1.57254	−	2.72371i	−0.474138	−	0.821230i	−0.999562	+	0.0296102i	$0.990573\pi$
$12$		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	−0.945917	−	0.324408i	$-0.894835\pi$
$17$	−0.791692	+	1.37125i	−0.192013	+	0.332577i	0.753904	+	0.656985i	$0.228168\pi$
$18$		0			0
$19$	4.02979	−	6.97979i	0.924496	−	1.60127i	0.132127	−	0.991233i	$-0.457819\pi$
$19$	4.02979	−	6.97979i	0.924496	−	1.60127i	0.792369	−	0.610042i	$-0.208847\pi$
$20$		0			0
$21$	−3.33730			−0.728259
$22$		0			0
$23$	3.40824	+	5.90325i	0.710668	+	1.23091i	0.964607	+	0.263692i	$0.0849404\pi$
$23$	3.40824	+	5.90325i	0.710668	+	1.23091i	−0.253939	+	0.967220i	$0.581726\pi$
$24$		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	$-0.775889\pi$
$29$	−3.13808	+	1.81177i	−0.582727	+	0.336437i	0.179490	+	0.983760i	$0.442555\pi$
$30$		0			0
$31$		−	9.62991i		−	1.72958i	−0.502132	−	0.864791i	$-0.667451\pi$
$31$		−	9.62991i		−	1.72958i	0.502132	−	0.864791i	$-0.332549\pi$
$32$		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	$-0.196473\pi$
$37$	−0.568757	−	0.985115i	−0.0935030	−	0.161952i	−0.908983	+	0.416834i	$0.863140\pi$
$38$		0			0
$39$	−0.558542	+	3.56203i	−0.0894383	+	0.570381i
$40$		0			0
$41$	9.84578	−	5.68446i	1.53765	−	0.887764i	0.538677	−	0.842512i	$-0.318924\pi$
$41$	9.84578	−	5.68446i	1.53765	−	0.887764i	0.998976	−	0.0452518i	$-0.0144090\pi$
$42$		0			0
$43$	5.40070	+	3.11810i	0.823599	+	0.475505i	0.851656	−	0.524101i	$-0.175599\pi$
$43$	5.40070	+	3.11810i	0.823599	+	0.475505i	−0.0280568	+	0.999606i	$0.508932\pi$
$44$		0			0
$45$	0.115196	−	0.199526i	0.0171725	−	0.0297436i
$46$		0			0
$47$			8.90552i			1.29900i	0.760360	+	0.649501i	$0.225022\pi$
$47$			8.90552i			1.29900i	−0.760360	+	0.649501i	$0.774978\pi$
$48$		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	$-0.676574\pi$
$59$	3.63171	−	6.29031i	0.472809	−	0.818929i	0.999516	+	0.0311183i	$0.00990686\pi$
$60$		0			0
$61$	2.50714	+	1.44750i	0.321006	+	0.185333i	0.651841	−	0.758356i	$-0.273997\pi$
$61$	2.50714	+	1.44750i	0.321006	+	0.185333i	−0.330835	+	0.943689i	$0.607330\pi$
$62$		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	$-0.141740\pi$
$67$	0.640338	+	1.10910i	0.0782297	+	0.135498i	−0.824257	+	0.566217i	$0.808407\pi$
$68$		0			0
$69$	−5.90325	−	3.40824i	−0.710668	−	0.410304i
$70$		0			0
$71$	0.987337	+	0.570039i	0.117175	+	0.0676512i	0.557442	−	0.830216i	$-0.311783\pi$
$71$	0.987337	+	0.570039i	0.117175	+	0.0676512i	−0.440267	+	0.897867i	$0.645116\pi$
$72$		0			0
$73$		−	0.813566i		−	0.0952207i	−0.998866	−	0.0476104i	$-0.984839\pi$
$73$		−	0.813566i		−	0.0952207i	0.998866	−	0.0476104i	$-0.0151606\pi$
$74$		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	$-0.746129\pi$
$83$	−12.7265			−1.39691			−0.698455	+	0.715654i	$0.746129\pi$
$84$		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	0.139993	−	0.990152i	$-0.455292\pi$
$89$	10.0707	−	5.81429i	1.06749	−	0.616314i	0.927494	+	0.373838i	$0.121959\pi$
$90$		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	0.809416	−	0.587235i	$-0.199784\pi$
$97$	6.94900	+	4.01201i	0.705564	+	0.407358i	−0.103852	+	0.994593i	$0.533117\pi$
$98$		0			0
$99$	−3.14507			−0.316092
$100$		0			0
$101$	9.97844	−	5.76105i	0.992892	−	0.573246i	0.0867543	−	0.996230i	$-0.472350\pi$
$101$	9.97844	−	5.76105i	0.992892	−	0.573246i	0.906137	+	0.422983i	$0.139017\pi$
$102$		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	$-0.689424\pi$
$107$	−1.27986	+	0.738926i	−0.123729	+	0.0714347i	0.436858	+	0.899530i	$0.356091\pi$
$108$		0			0
$109$	1.50562			0.144212			0.0721062	−	0.997397i	$-0.477028\pi$
$109$	1.50562			0.144212			0.0721062	+	0.997397i	$0.477028\pi$
$110$		0			0
$111$	0.985115	+	0.568757i	0.0935030	+	0.0539840i
$112$		0			0
$113$	−0.0381779	+	0.0661261i	−0.00359148	+	0.00622062i	−0.867816	−	0.496886i	$-0.834477\pi$
$113$	−0.0381779	+	0.0661261i	−0.00359148	+	0.00622062i	0.864224	+	0.503107i	$0.167810\pi$
$114$		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	0.693741	−	0.720224i	$-0.255961\pi$
$127$	−3.12007	−	5.40413i	−0.276862	−	0.479539i	−0.970603	+	0.240686i	$0.922628\pi$
$128$		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	0.298744	−	0.954333i	$-0.403432\pi$
$137$	−4.42860	−	2.55686i	−0.378361	−	0.218447i	−0.677105	+	0.735886i	$0.736766\pi$
$138$		0			0
$139$	−4.90809	−	2.83369i	−0.416299	−	0.240350i	0.277194	−	0.960814i	$-0.410596\pi$
$139$	−4.90809	−	2.83369i	−0.416299	−	0.240350i	−0.693492	+	0.720464i	$0.743929\pi$
$140$		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	$-0.953630\pi$
$149$	−4.50412	+	7.80137i	−0.368992	+	0.639113i	0.620416	+	0.784273i	$0.286964\pi$
$150$		0			0
$151$		−	6.17629i		−	0.502619i	−0.967907	−	0.251310i	$-0.919139\pi$
$151$		−	6.17629i		−	0.502619i	0.967907	−	0.251310i	$-0.0808612\pi$
$152$		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	0.108276	+	0.994121i	$0.465467\pi$
$163$	−10.3005	+	17.8410i	−0.806796	+	1.39741i	−0.915072	+	0.403291i	$0.867866\pi$
$164$		0			0
$165$	0.627524	+	0.362301i	0.0488527	+	0.0282051i
$166$		0			0
$167$	7.97855	−	4.60642i	0.617399	−	0.356455i	−0.158457	−	0.987366i	$-0.550652\pi$
$167$	7.97855	−	4.60642i	0.617399	−	0.356455i	0.775856	+	0.630910i	$0.217318\pi$
$168$		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	$-0.356494\pi$
$173$	−1.65613	−	0.956165i	−0.125913	−	0.0726959i	−0.561634	+	0.827386i	$0.689827\pi$
$174$		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	$-0.837435\pi$
$179$	−11.8443	+	6.83830i	−0.885283	+	0.511118i	−0.0128863	+	0.999917i	$0.504102\pi$
$180$		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	0.398183	+	0.917306i	$0.369641\pi$
$191$	−8.22747	+	14.2504i	−0.595318	+	1.03112i	−0.993502	+	0.113816i	$0.963693\pi$
$192$		0			0
$193$	−5.14440	+	2.97012i	−0.370302	+	0.213794i	−0.673590	−	0.739105i	$-0.735249\pi$
$193$	−5.14440	+	2.97012i	−0.370302	+	0.213794i	0.303288	+	0.952899i	$0.401915\pi$
$194$		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	$-0.0759430\pi$
$197$	3.94646	+	6.83547i	0.281174	+	0.487007i	−0.690500	+	0.723332i	$0.742610\pi$
$198$		0			0
$199$	−8.18855	+	14.1830i	−0.580471	+	1.00541i	0.414952	+	0.909843i	$0.363798\pi$
$199$	−8.18855	+	14.1830i	−0.580471	+	1.00541i	−0.995423	+	0.0955625i	$0.969535\pi$
$200$		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	$-0.499994\pi$
$211$	12.5801	−	7.26314i	0.866052	−	0.500016i	0.866034	+	0.499984i	$0.166661\pi$
$212$		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	−0.987045	−	0.160442i	$-0.948708\pi$
$223$	−20.0347	+	11.5670i	−1.34162	+	0.774585i	−0.354576	+	0.935027i	$0.615375\pi$
$224$		0			0
$225$	−2.47346	+	4.28416i	−0.164897	+	0.285611i
$226$		0			0
$227$	10.2158	−	17.6943i	0.678048	−	1.17441i	−0.297519	−	0.954716i	$-0.596159\pi$
$227$	10.2158	−	17.6943i	0.678048	−	1.17441i	0.975568	−	0.219699i	$-0.0705074\pi$
$228$		0			0
$229$	−6.70980			−0.443396			−0.221698	−	0.975115i	$-0.571160\pi$
$229$	−6.70980			−0.443396			−0.221698	+	0.975115i	$0.571160\pi$
$230$		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	$-0.908193\pi$
$239$		−	8.79465i		−	0.568879i	0.958694	−	0.284439i	$-0.0918074\pi$
$240$		0			0
$241$	−16.6492	−	9.61245i	−1.07247	−	0.619192i	−0.143616	−	0.989633i	$-0.545873\pi$
$241$	−16.6492	−	9.61245i	−1.07247	−	0.619192i	−0.928856	+	0.370441i	$0.879206\pi$
$242$		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	$-0.566513\pi$
$251$	−18.3517	−	10.5953i	−1.15835	−	0.668772i	−0.950907	+	0.309476i	$0.899846\pi$
$252$		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	0.934169	−	0.356830i	$-0.116143\pi$
$257$	2.53390	+	4.38885i	0.158061	+	0.273769i	−0.776109	+	0.630599i	$0.782809\pi$
$258$		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	0.770902	−	0.636954i	$-0.219806\pi$
$263$	−2.69479	−	4.66751i	−0.166168	−	0.287811i	−0.937069	+	0.349143i	$0.886473\pi$
$264$		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	$-0.485788\pi$
$269$	−13.0916	−	7.55845i	−0.798210	−	0.460847i	−0.842845	+	0.538156i	$0.819121\pi$
$270$		0			0
$271$	−1.44092	+	0.831915i	−0.0875296	+	0.0505352i	−0.543126	−	0.839651i	$-0.682759\pi$
$271$	−1.44092	+	0.831915i	−0.0875296	+	0.0505352i	0.455596	+	0.890186i	$0.349426\pi$
$272$		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	$-0.494311\pi$
$277$	−13.9650	−	8.06272i	−0.839078	−	0.484442i	−0.856951	+	0.515399i	$0.827644\pi$
$278$		0			0
$279$	−8.33974	−	4.81495i	−0.499287	−	0.288264i
$280$		0			0
$281$		−	23.9271i		−	1.42737i	−0.700466	−	0.713686i	$-0.747024\pi$
$281$		−	23.9271i		−	1.42737i	0.700466	−	0.713686i	$-0.252976\pi$
$282$		0			0
$283$	7.67135	−	4.42906i	0.456015	−	0.263280i	−0.254352	−	0.967112i	$-0.581862\pi$
$283$	7.67135	−	4.42906i	0.456015	−	0.263280i	0.710367	+	0.703831i	$0.248529\pi$
$284$		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	0.255623	+	0.966776i	$0.417719\pi$
$293$	−12.1437	+	21.0335i	−0.709441	+	1.22879i	−0.965065	+	0.262012i	$0.915614\pi$
$294$		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	$-0.124897\pi$
$307$	32.3797			1.84801			0.924004	+	0.382383i	$0.124897\pi$
$308$		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	$-0.819050\pi$
$317$	−30.0086			−1.68545			−0.842725	+	0.538345i	$0.819050\pi$
$318$		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	$-0.789635\pi$
$331$	2.48978	−	4.31242i	0.136851	−	0.237032i	0.926303	+	0.376780i	$0.122969\pi$
$332$		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	$-0.386360\pi$
$347$	−5.35002	−	3.08884i	−0.287204	−	0.165817i	−0.636680	+	0.771128i	$0.719693\pi$
$348$		0			0
$349$	12.8064	+	22.1813i	0.685510	+	1.18734i	0.973276	+	0.229638i	$0.0737542\pi$
$349$	12.8064	+	22.1813i	0.685510	+	1.18734i	−0.287766	+	0.957701i	$0.592912\pi$
$350$		0			0
$351$	2.80553	+	2.26472i	0.149748	+	0.120882i
$352$		0			0
$353$	6.78643	−	3.91815i	0.361205	−	0.208542i	−0.308404	−	0.951255i	$-0.599795\pi$
$353$	6.78643	−	3.91815i	0.361205	−	0.208542i	0.669609	+	0.742713i	$0.266462\pi$
$354$		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	$-0.735800\pi$
$359$		−	27.9638i		−	1.47587i	0.674870	−	0.737937i	$-0.264200\pi$
$360$		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	0.989126	+	0.147069i	$0.0469840\pi$
$367$	11.9144	+	20.6364i	0.621929	+	1.07721i	−0.367198	+	0.930143i	$0.619683\pi$
$368$		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	$-0.231915\pi$
$373$	10.4787	+	6.04988i	0.542567	+	0.313251i	−0.203552	+	0.979064i	$0.565249\pi$
$374$		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	$-0.0474862\pi$
$379$	7.11999	+	12.3322i	0.365729	+	0.633462i	−0.623164	+	0.782092i	$0.714153\pi$
$380$		0			0
$381$	5.40413	+	3.12007i	0.276862	+	0.159846i
$382$		0			0
$383$	−20.4692	−	11.8179i	−1.04593	−	0.603866i	−0.124421	−	0.992230i	$-0.539707\pi$
$383$	−20.4692	−	11.8179i	−1.04593	−	0.603866i	−0.921506	+	0.388363i	$0.873041\pi$
$384$		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	$-0.800033\pi$
$397$	2.08064	−	3.60378i	0.104424	−	0.180868i	0.913503	+	0.406832i	$0.133367\pi$
$398$		0			0
$399$	−13.4486	+	23.2937i	−0.673273	+	1.16614i
$400$		0			0
$401$	−9.32403	+	5.38323i	−0.465620	+	0.268826i	−0.714404	−	0.699733i	$-0.753302\pi$
$401$	−9.32403	+	5.38323i	−0.465620	+	0.268826i	0.248785	+	0.968559i	$0.419969\pi$
$402$		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	0.978135	−	0.207972i	$-0.0666864\pi$
$409$	26.0298	+	15.0283i	1.28709	+	0.743103i	0.308958	+	0.951076i	$0.400020\pi$
$410$		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	$-0.540235\pi$
$419$	13.7149	−	7.91829i	0.670016	−	0.386834i	0.796083	+	0.605188i	$0.206902\pi$
$420$		0			0
$421$	−23.2913			−1.13515			−0.567574	−	0.823322i	$-0.692118\pi$
$421$	−23.2913			−1.13515			−0.567574	+	0.823322i	$0.692118\pi$
$422$		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	−0.657948	−	0.753064i	$-0.728575\pi$
$431$	−6.94958	+	4.01234i	−0.334750	+	0.193268i	0.323198	+	0.946331i	$0.395242\pi$
$432$		0			0
$433$	−15.2699	+	26.4483i	−0.733825	+	1.27102i	0.221412	+	0.975180i	$0.428934\pi$
$433$	−15.2699	+	26.4483i	−0.733825	+	1.27102i	−0.955237	+	0.295842i	$0.904400\pi$
$434$		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	0.967788	−	0.251765i	$-0.0810109\pi$
$439$	5.57038	+	9.64818i	0.265860	+	0.460482i	−0.701929	+	0.712247i	$0.747678\pi$
$440$		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	0.938616	−	0.344963i	$-0.112109\pi$
$449$	23.5031	+	13.5695i	1.10918	+	0.640384i	0.170561	+	0.985347i	$0.445442\pi$
$450$		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	0.0909374	−	0.995857i	$-0.471014\pi$
$457$	21.3528	−	12.3281i	0.998843	−	0.576682i	0.907906	+	0.419174i	$0.137680\pi$
$458$		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	$-0.888067\pi$
$461$	−3.67379	+	6.36319i	−0.171105	+	0.296363i	0.767701	+	0.640808i	$0.221401\pi$
$462$		0			0
$463$		−	13.6798i		−	0.635756i	−0.948132	−	0.317878i	$-0.897030\pi$
$463$		−	13.6798i		−	0.635756i	0.948132	−	0.317878i	$-0.102970\pi$
$464$		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	−0.413856	−	0.910342i	$-0.635818\pi$
$479$	3.66802	−	2.11773i	0.167596	−	0.0967616i	0.581452	+	0.813581i	$0.302485\pi$
$480$		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	0.996632	+	0.0820078i	$0.0261332\pi$
$487$	34.5579	+	19.9520i	1.56597	+	0.904112i	0.569337	+	0.822104i	$0.307200\pi$
$488$		0			0
$489$		−	20.6010i		−	0.931608i
$490$		0			0
$491$	23.5208	−	13.5798i	1.06148	−	0.612846i	0.135639	−	0.990758i	$-0.456691\pi$
$491$	23.5208	−	13.5798i	1.06148	−	0.612846i	0.925841	+	0.377913i	$0.123358\pi$
$492$		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	$-0.591603\pi$
$499$	−12.6803			−0.567649			−0.283825	+	0.958876i	$0.591603\pi$
$500$		0			0
$501$	−4.60642	+	7.97855i	−0.205800	+	0.356455i
$502$		0			0
$503$	3.49953	−	6.06136i	0.156036	−	0.270263i	−0.777400	−	0.629007i	$-0.783462\pi$
$503$	3.49953	−	6.06136i	0.156036	−	0.270263i	0.933436	+	0.358744i	$0.116795\pi$
$504$		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	$-0.276921\pi$
$509$	−7.65922	−	13.2662i	−0.339489	−	0.588012i	−0.984337	+	0.176299i	$0.943587\pi$
$510$		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	$-0.826343\pi$
$523$	−19.0473	+	10.9970i	−0.832879	+	0.480863i	0.0219582	+	0.999759i	$0.493010\pi$
$524$		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	$-0.490502\pi$
$541$	1.38788			0.0596694			0.0298347	+	0.999555i	$0.490502\pi$
$542$		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	0.983087	+	0.183141i	$0.0586266\pi$
$557$	15.3441	+	26.5767i	0.650148	+	1.12609i	−0.332938	+	0.942949i	$0.608040\pi$
$558$		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	$-0.648276\pi$
$563$	−34.3455	−	19.8294i	−1.44749	−	0.835709i	−0.998331	+	0.0577430i	$0.981610\pi$
$564$		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	0.753581	−	0.657355i	$-0.228325\pi$
$569$	−4.59173	−	7.95311i	−0.192495	−	0.333412i	−0.946077	+	0.323943i	$0.894991\pi$
$570$		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	$0.213497\pi$
$577$			29.8603i			1.24310i	−0.783375	+	0.621550i	$0.786503\pi$
$578$		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	−0.946336	−	0.323185i	$-0.895246\pi$
$587$	−18.2451	−	31.6014i	−0.753054	−	1.30433i	0.193282	−	0.981143i	$-0.438087\pi$
$588$		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	$0.182558\pi$
$593$			26.4261i			1.08519i	−0.839995	+	0.542594i	$0.817442\pi$
$594$		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	0.868409	−	0.495849i	$-0.165143\pi$
$601$	0.117332	+	0.203224i	0.00478606	+	0.00828970i	−0.863622	+	0.504139i	$0.831810\pi$
$602$		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	−0.976405	−	0.215949i	$-0.930715\pi$
$607$	−7.42041	+	12.8525i	−0.301185	+	0.521668i	0.675220	+	0.737617i	$0.264049\pi$
$608$		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	$-0.169698\pi$
$613$	−0.235744	−	0.408321i	−0.00952163	−	0.0164919i	−0.870747	+	0.491731i	$0.836364\pi$
$614$		0			0
$615$	−1.30966	+	2.26840i	−0.0528106	+	0.0914706i
$616$		0			0
$617$	−28.2097	−	16.2869i	−1.13568	−	0.655685i	−0.190323	−	0.981721i	$-0.560954\pi$
$617$	−28.2097	−	16.2869i	−1.13568	−	0.655685i	−0.945357	+	0.326036i	$0.894287\pi$
$618$		0			0
$619$	9.28369			0.373143			0.186571	−	0.982441i	$-0.440262\pi$
$619$	9.28369			0.373143			0.186571	+	0.982441i	$0.440262\pi$
$620$		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	0.423287	−	0.905996i	$-0.360876\pi$
$631$	−3.76004	−	2.17086i	−0.149685	−	0.0864205i	−0.572972	+	0.819575i	$0.694210\pi$
$632$		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	0.338026	+	0.941137i	$0.390241\pi$
$641$	−16.3563	+	28.3299i	−0.646035	+	1.11897i	−0.984061	+	0.177829i	$0.943093\pi$
$642$		0			0
$643$	3.40535	−	5.89823i	0.134294	−	0.232604i	−0.791034	−	0.611773i	$-0.790457\pi$
$643$	3.40535	−	5.89823i	0.134294	−	0.232604i	0.925327	+	0.379169i	$0.123790\pi$
$644$		0			0
$645$	−1.43677			−0.0565729
$646$		0			0
$647$	12.5284	+	21.6999i	0.492543	+	0.853110i	0.999963	−	0.00858905i	$-0.00273401\pi$
$647$	12.5284	+	21.6999i	0.492543	+	0.853110i	−0.507420	+	0.861699i	$0.669401\pi$
$648$		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	0.646712	−	0.762734i	$-0.276144\pi$
$653$	41.6685	−	24.0573i	1.63062	−	0.941436i	0.983903	−	0.178702i	$-0.0571898\pi$
$654$		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	$-0.194912\pi$
$659$	18.7319	+	10.8148i	0.729690	+	0.421287i	−0.0886189	+	0.996066i	$0.528245\pi$
$660$		0			0
$661$	10.4554	+	18.1092i	0.406666	+	0.704366i	0.994514	−	0.104605i	$-0.0333579\pi$
$661$	10.4554	+	18.1092i	0.406666	+	0.704366i	−0.587848	+	0.808972i	$0.700025\pi$
$662$		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	0.649866	−	0.760049i	$-0.274825\pi$
$673$	−8.64625	−	14.9757i	−0.333288	−	0.577272i	−0.983155	+	0.182776i	$0.941492\pi$
$674$		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	0.293365	+	0.956001i	$0.405225\pi$
$683$	−17.8037	+	30.8369i	−0.681238	+	1.17994i	−0.974603	+	0.223939i	$0.928108\pi$
$684$		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	0.997089	+	0.0762454i	$0.0242933\pi$
$691$	14.8409	+	25.7052i	0.564575	+	0.977873i	−0.432514	+	0.901627i	$0.642373\pi$
$692$		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	$-0.782154\pi$
$709$	4.26282	−	7.38342i	0.160093	−	0.277290i	0.934902	+	0.354906i	$0.115487\pi$
$710$		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	−0.722273	−	0.691608i	$-0.756903\pi$
$719$	6.37676	−	11.0449i	0.237813	−	0.411904i	0.960086	+	0.279703i	$0.0902361\pi$
$720$		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	$-0.866254\pi$
$733$	−49.4380			−1.82604			−0.913018	+	0.407920i	$0.866254\pi$
$734$		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	−0.999827	−	0.0185956i	$-0.994081\pi$
$739$	−14.0277	−	24.2967i	−0.516018	−	0.893769i	0.483809	−	0.875173i	$-0.339253\pi$
$740$		0			0
$741$	22.6114	+	18.2527i	0.830651	+	0.670530i
$742$		0			0
$743$	2.05615	−	1.18712i	0.0754328	−	0.0435512i	−0.461809	−	0.886979i	$-0.652800\pi$
$743$	2.05615	−	1.18712i	0.0754328	−	0.0435512i	0.537242	+	0.843428i	$0.319466\pi$
$744$		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	0.817156	−	0.576416i	$-0.195549\pi$
$751$	−2.48319	−	4.30101i	−0.0906130	−	0.156946i	−0.907769	+	0.419470i	$0.862216\pi$
$752$		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	$-0.687454\pi$
$757$	−3.10991	+	1.79551i	−0.113032	+	0.0652589i	0.442418	+	0.896809i	$0.354121\pi$
$758$		0			0
$759$			21.4383i			0.778163i
$760$		0			0
$761$	−30.1976	−	17.4346i	−1.09466	−	0.632004i	−0.159849	−	0.987142i	$-0.551101\pi$
$761$	−30.1976	−	17.4346i	−1.09466	−	0.632004i	−0.934814	+	0.355138i	$0.884434\pi$
$762$		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	−0.562356	−	0.826895i	$-0.690105\pi$
$769$	−3.53352	+	2.04008i	−0.127422	+	0.0735670i	0.434934	+	0.900462i	$0.356772\pi$
$770$		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	$-0.919163\pi$
$773$	−7.40633	+	12.8281i	−0.266387	+	0.461396i	0.701539	+	0.712631i	$0.252497\pi$
$774$		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	−0.342378	−	0.939562i	$-0.611232\pi$
$787$	18.0243	−	31.2189i	0.642496	−	1.11283i	0.984874	−	0.173273i	$-0.0554342\pi$
$788$		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	$-0.407947\pi$
$797$	−11.3573	−	6.55713i	−0.402295	−	0.232265i	−0.687474	+	0.726209i	$0.741280\pi$
$798$		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	0.967047	−	0.254599i	$-0.0819436\pi$
$809$	7.48145	+	12.9583i	0.263034	+	0.455588i	−0.704013	+	0.710187i	$0.748610\pi$
$810$		0			0
$811$	−20.9684			−0.736299			−0.368150	−	0.929767i	$-0.620009\pi$
$811$	−20.9684			−0.736299			−0.368150	+	0.929767i	$0.620009\pi$
$812$		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	$-0.0219919\pi$
$821$	12.5793	+	21.7880i	0.439021	+	0.760407i	−0.558593	+	0.829442i	$0.688659\pi$
$822$		0			0
$823$	4.64806	−	8.05068i	0.162021	−	0.280629i	−0.773572	−	0.633708i	$-0.781532\pi$
$823$	4.64806	−	8.05068i	0.162021	−	0.280629i	0.935593	+	0.353079i	$0.114865\pi$
$824$		0			0
$825$	−13.4740	−	7.77921i	−0.469104	−	0.270837i
$826$		0			0
$827$	−22.5483			−0.784080			−0.392040	−	0.919948i	$-0.628231\pi$
$827$	−22.5483			−0.784080			−0.392040	+	0.919948i	$0.628231\pi$
$828$		0			0
$829$	−4.07023	+	2.34995i	−0.141365	+	0.0816171i	−0.569014	−	0.822328i	$-0.692675\pi$
$829$	−4.07023	+	2.34995i	−0.141365	+	0.0816171i	0.427649	+	0.903945i	$0.359342\pi$
$830$		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	0.983757	−	0.179507i	$-0.0574503\pi$
$839$	38.2396	+	22.0776i	1.32018	+	0.762205i	0.336421	+	0.941712i	$0.390784\pi$
$840$		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	$-0.487745\pi$
$853$	2.24836			0.0769825			0.0384912	+	0.999259i	$0.487745\pi$
$854$		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	$0.338205\pi$
$863$			51.3259i			1.74715i	−0.486687	+	0.873577i	$0.661795\pi$
$864$		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	$-0.777067\pi$
$877$	5.20754	−	9.01972i	0.175846	−	0.304574i	0.940454	+	0.339922i	$0.110401\pi$
$878$		0			0
$879$		−	24.2874i		−	0.819192i
$880$		0			0
$881$	−20.8219	−	36.0645i	−0.701507	−	1.21505i	−0.967938	−	0.251191i	$-0.919178\pi$
$881$	−20.8219	−	36.0645i	−0.701507	−	1.21505i	0.266431	−	0.963854i	$-0.414156\pi$
$882$		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	0.570265	−	0.821460i	$-0.306840\pi$
$887$	−12.6955	−	21.9892i	−0.426273	−	0.738326i	−0.996538	+	0.0831341i	$0.973507\pi$
$888$		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	$-0.791185\pi$
$907$	−19.8890	+	11.4829i	−0.660405	+	0.381285i	0.132027	+	0.991246i	$0.457852\pi$
$908$		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	−0.644368	−	0.764715i	$-0.722880\pi$
$919$	10.3095	−	17.8566i	0.340079	−	0.589034i	0.984447	+	0.175682i	$0.0562129\pi$
$920$		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	0.267568	−	0.963539i	$-0.413780\pi$
$929$	−13.2006	−	7.62136i	−0.433097	−	0.250049i	−0.700665	+	0.713490i	$0.747113\pi$
$930$		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	$-0.391634\pi$
$941$	20.4855			0.667807			0.333904	+	0.942607i	$0.391634\pi$
$942$		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	0.996750	+	0.0805608i	$0.0256711\pi$
$947$	17.4837	+	30.2826i	0.568143	+	0.984052i	−0.428607	+	0.903491i	$0.640996\pi$
$948$		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	−0.478459	−	0.878110i	$-0.658804\pi$
$953$	16.0909	−	27.8703i	0.521236	−	0.902808i	0.999695	−	0.0246977i	$-0.00786233\pi$
$954$		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	$0.108272\pi$
$967$			20.7493i			0.667251i	−0.942706	+	0.333626i	$0.891728\pi$
$968$		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	$-0.235290\pi$
$971$	16.3626	+	9.44693i	0.525099	+	0.303166i	−0.213919	+	0.976851i	$0.568623\pi$
$972$		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	0.100218	−	0.994966i	$-0.468046\pi$
$977$	31.6318	−	18.2627i	1.01199	−	0.584274i	0.911774	+	0.410691i	$0.134713\pi$
$978$		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	$-0.791225\pi$
$983$		−	38.2418i		−	1.21972i	0.792508	−	0.609862i	$-0.208775\pi$
$984$		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	−0.999889	−	0.0149201i	$-0.995251\pi$
$991$	−16.1451	−	27.9641i	−0.512866	−	0.888309i	0.487023	−	0.873389i	$-0.338083\pi$
$992$		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	$-0.446087\pi$
$997$	−18.9701	−	10.9524i	−0.600789	−	0.346866i	−0.769352	+	0.638825i	$0.779421\pi$
$998$		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.49.7		48
4.3	odd	2		312.2.bk.b.205.23	yes	48
8.3	odd	2		312.2.bk.b.205.15	✓	48
8.5	even	2	inner	1248.2.ca.b.49.18		48
12.11	even	2		936.2.dg.e.829.2		48
13.4	even	6	inner	1248.2.ca.b.433.18		48
24.11	even	2		936.2.dg.e.829.10		48
52.43	odd	6		312.2.bk.b.277.15	yes	48
104.43	odd	6		312.2.bk.b.277.23	yes	48
104.69	even	6	inner	1248.2.ca.b.433.7		48
156.95	even	6		936.2.dg.e.901.10		48
312.251	even	6		936.2.dg.e.901.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bk.b.205.15	✓	48	8.3	odd	2
312.2.bk.b.205.23	yes	48	4.3	odd	2
312.2.bk.b.277.15	yes	48	52.43	odd	6
312.2.bk.b.277.23	yes	48	104.43	odd	6
936.2.dg.e.829.2		48	12.11	even	2
936.2.dg.e.829.10		48	24.11	even	2
936.2.dg.e.901.2		48	312.251	even	6
936.2.dg.e.901.10		48	156.95	even	6
1248.2.ca.b.49.7		48	1.1	even	1	trivial
1248.2.ca.b.49.18		48	8.5	even	2	inner
1248.2.ca.b.433.7		48	104.69	even	6	inner
1248.2.ca.b.433.18		48	13.4	even	6	inner

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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