LMFDB - Embedded newform 1488.2.q.g.625.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1488,2,Mod(625,1488)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1488, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1488.625"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1488 = 2^{4} \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1488.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-2,0,4,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$11.8817398208$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 93)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			625.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1488.625
Dual form			1488.2.q.g.769.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{3} +(0.292893 + 0.507306i) q^{5} +(0.414214 - 0.717439i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-0.707107 - 1.22474i) q^{11} +(-0.914214 - 1.58346i) q^{13} -0.585786 q^{15} +(-3.41421 + 5.91359i) q^{17} +(-1.91421 + 3.31552i) q^{19} +(0.414214 + 0.717439i) q^{21} -3.65685 q^{23} +(2.32843 - 4.03295i) q^{25} +1.00000 q^{27} -3.41421 q^{29} +(-2.00000 + 5.19615i) q^{31} +1.41421 q^{33} +0.485281 q^{35} +(-0.500000 + 0.866025i) q^{37} +1.82843 q^{39} +(2.12132 + 3.67423i) q^{41} +(-2.74264 + 4.75039i) q^{43} +(0.292893 - 0.507306i) q^{45} -0.585786 q^{47} +(3.15685 + 5.46783i) q^{49} +(-3.41421 - 5.91359i) q^{51} +(0.707107 + 1.22474i) q^{53} +(0.414214 - 0.717439i) q^{55} +(-1.91421 - 3.31552i) q^{57} +(-4.24264 + 7.34847i) q^{59} -12.4853 q^{61} -0.828427 q^{63} +(0.535534 - 0.927572i) q^{65} +(-7.24264 - 12.5446i) q^{67} +(1.82843 - 3.16693i) q^{69} +(3.00000 + 5.19615i) q^{71} +(-1.91421 - 3.31552i) q^{73} +(2.32843 + 4.03295i) q^{75} -1.17157 q^{77} +(7.82843 - 13.5592i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-3.70711 - 6.42090i) q^{83} -4.00000 q^{85} +(1.70711 - 2.95680i) q^{87} -17.8995 q^{89} -1.51472 q^{91} +(-3.50000 - 4.33013i) q^{93} -2.24264 q^{95} -11.4853 q^{97} +(-0.707107 + 1.22474i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 4 q^{5} - 4 q^{7} - 2 q^{9} + 2 q^{13} - 8 q^{15} - 8 q^{17} - 2 q^{19} - 4 q^{21} + 8 q^{23} - 2 q^{25} + 4 q^{27} - 8 q^{29} - 8 q^{31} - 32 q^{35} - 2 q^{37} - 4 q^{39} + 6 q^{43} + 4 q^{45}+ \cdots - 12 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 + 4 * q^5 - 4 * q^7 - 2 * q^9 + 2 * q^13 - 8 * q^15 - 8 * q^17 - 2 * q^19 - 4 * q^21 + 8 * q^23 - 2 * q^25 + 4 * q^27 - 8 * q^29 - 8 * q^31 - 32 * q^35 - 2 * q^37 - 4 * q^39 + 6 * q^43 + 4 * q^45 - 8 * q^47 - 10 * q^49 - 8 * q^51 - 4 * q^55 - 2 * q^57 - 16 * q^61 + 8 * q^63 - 12 * q^65 - 12 * q^67 - 4 * q^69 + 12 * q^71 - 2 * q^73 - 2 * q^75 - 16 * q^77 + 20 * q^79 - 2 * q^81 - 12 * q^83 - 16 * q^85 + 4 * q^87 - 32 * q^89 - 40 * q^91 - 14 * q^93 + 8 * q^95 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1488\mathbb{Z}\right)^\times$.

$n$	$373$	$497$	$559$	$1057$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$	0.292893	+	0.507306i	0.130986	+	0.226874i	0.924057	−	0.382255i	$-0.124852\pi$
$5$	0.292893	+	0.507306i	0.130986	+	0.226874i	−0.793071	+	0.609129i	$0.791519\pi$
$6$		0			0
$7$	0.414214	−	0.717439i	0.156558	−	0.271166i	−0.777067	−	0.629418i	$-0.783294\pi$
$7$	0.414214	−	0.717439i	0.156558	−	0.271166i	0.933625	+	0.358251i	$0.116627\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−0.707107	−	1.22474i	−0.213201	−	0.369274i	0.739514	−	0.673141i	$-0.235055\pi$
$11$	−0.707107	−	1.22474i	−0.213201	−	0.369274i	−0.952714	+	0.303867i	$0.901722\pi$
$12$		0			0
$13$	−0.914214	−	1.58346i	−0.253557	−	0.439174i	0.710945	−	0.703247i	$-0.248267\pi$
$13$	−0.914214	−	1.58346i	−0.253557	−	0.439174i	−0.964503	+	0.264073i	$0.914934\pi$
$14$		0			0
$15$	−0.585786			−0.151249
$16$		0			0
$17$	−3.41421	+	5.91359i	−0.828068	+	1.43426i	0.0714831	+	0.997442i	$0.477227\pi$
$17$	−3.41421	+	5.91359i	−0.828068	+	1.43426i	−0.899551	+	0.436815i	$0.856107\pi$
$18$		0			0
$19$	−1.91421	+	3.31552i	−0.439151	+	0.760631i	−0.997624	−	0.0688910i	$-0.978054\pi$
$19$	−1.91421	+	3.31552i	−0.439151	+	0.760631i	0.558473	+	0.829522i	$0.311387\pi$
$20$		0			0
$21$	0.414214	+	0.717439i	0.0903888	+	0.156558i
$22$		0			0
$23$	−3.65685			−0.762507			−0.381253	−	0.924471i	$-0.624507\pi$
$23$	−3.65685			−0.762507			−0.381253	+	0.924471i	$0.624507\pi$
$24$		0			0
$25$	2.32843	−	4.03295i	0.465685	−	0.806591i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−3.41421			−0.634004			−0.317002	−	0.948425i	$-0.602676\pi$
$29$	−3.41421			−0.634004			−0.317002	+	0.948425i	$0.602676\pi$
$30$		0			0
$31$	−2.00000	+	5.19615i	−0.359211	+	0.933257i
$31$	−2.00000	+	5.19615i	−0.359211	+	0.933257i
$32$		0			0
$33$	1.41421			0.246183
$34$		0			0
$35$	0.485281			0.0820275
$36$		0			0
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	0.821995	+	0.569495i	$0.192861\pi$
$38$		0			0
$39$	1.82843			0.292783
$40$		0			0
$41$	2.12132	+	3.67423i	0.331295	+	0.573819i	0.982766	−	0.184854i	$-0.0591813\pi$
$41$	2.12132	+	3.67423i	0.331295	+	0.573819i	−0.651471	+	0.758673i	$0.725848\pi$
$42$		0			0
$43$	−2.74264	+	4.75039i	−0.418249	+	0.724428i	−0.995763	−	0.0919522i	$-0.970689\pi$
$43$	−2.74264	+	4.75039i	−0.418249	+	0.724428i	0.577515	+	0.816380i	$0.304023\pi$
$44$		0			0
$45$	0.292893	−	0.507306i	0.0436619	−	0.0756247i
$46$		0			0
$47$	−0.585786			−0.0854457			−0.0427229	−	0.999087i	$-0.513603\pi$
$47$	−0.585786			−0.0854457			−0.0427229	+	0.999087i	$0.513603\pi$
$48$		0			0
$49$	3.15685	+	5.46783i	0.450979	+	0.781119i
$50$		0			0
$51$	−3.41421	−	5.91359i	−0.478086	−	0.828068i
$52$		0			0
$53$	0.707107	+	1.22474i	0.0971286	+	0.168232i	0.910495	−	0.413520i	$-0.135701\pi$
$53$	0.707107	+	1.22474i	0.0971286	+	0.168232i	−0.813366	+	0.581752i	$0.802368\pi$
$54$		0			0
$55$	0.414214	−	0.717439i	0.0558525	−	0.0967394i
$56$		0			0
$57$	−1.91421	−	3.31552i	−0.253544	−	0.439151i
$58$		0			0
$59$	−4.24264	+	7.34847i	−0.552345	+	0.956689i	0.445760	+	0.895152i	$0.352933\pi$
$59$	−4.24264	+	7.34847i	−0.552345	+	0.956689i	−0.998105	+	0.0615367i	$0.980400\pi$
$60$		0			0
$61$	−12.4853			−1.59858			−0.799288	−	0.600948i	$-0.794790\pi$
$61$	−12.4853			−1.59858			−0.799288	+	0.600948i	$0.794790\pi$
$62$		0			0
$63$	−0.828427			−0.104372
$64$		0			0
$65$	0.535534	−	0.927572i	0.0664248	−	0.115051i
$66$		0			0
$67$	−7.24264	−	12.5446i	−0.884829	−	1.53257i	−0.845909	−	0.533327i	$-0.820941\pi$
$67$	−7.24264	−	12.5446i	−0.884829	−	1.53257i	−0.0389203	−	0.999242i	$-0.512392\pi$
$68$		0			0
$69$	1.82843	−	3.16693i	0.220117	−	0.381253i
$70$		0			0
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$		0			0
$73$	−1.91421	−	3.31552i	−0.224042	−	0.388052i	0.731990	−	0.681316i	$-0.238592\pi$
$73$	−1.91421	−	3.31552i	−0.224042	−	0.388052i	−0.956032	+	0.293264i	$0.905259\pi$
$74$		0			0
$75$	2.32843	+	4.03295i	0.268864	+	0.465685i
$76$		0			0
$77$	−1.17157			−0.133513
$78$		0			0
$79$	7.82843	−	13.5592i	0.880767	−	1.52553i	0.0302770	−	0.999542i	$-0.490361\pi$
$79$	7.82843	−	13.5592i	0.880767	−	1.52553i	0.850490	−	0.525991i	$-0.176306\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−3.70711	−	6.42090i	−0.406908	−	0.704785i	0.587634	−	0.809127i	$-0.300060\pi$
$83$	−3.70711	−	6.42090i	−0.406908	−	0.704785i	−0.994541	+	0.104342i	$0.966726\pi$
$84$		0			0
$85$	−4.00000			−0.433861
$86$		0			0
$87$	1.70711	−	2.95680i	0.183021	−	0.317002i
$88$		0			0
$89$	−17.8995			−1.89734			−0.948671	−	0.316264i	$-0.897572\pi$
$89$	−17.8995			−1.89734			−0.948671	+	0.316264i	$0.897572\pi$
$90$		0			0
$91$	−1.51472			−0.158786
$92$		0			0
$93$	−3.50000	−	4.33013i	−0.362933	−	0.449013i
$94$		0			0
$95$	−2.24264			−0.230090
$96$		0			0
$97$	−11.4853			−1.16615			−0.583077	−	0.812417i	$-0.698151\pi$
$97$	−11.4853			−1.16615			−0.583077	+	0.812417i	$0.698151\pi$
$98$		0			0
$99$	−0.707107	+	1.22474i	−0.0710669	+	0.123091i
$100$		0			0
$101$	−15.4142			−1.53377			−0.766886	−	0.641784i	$-0.778195\pi$
$101$	−15.4142			−1.53377			−0.766886	+	0.641784i	$0.778195\pi$
$102$		0			0
$103$	8.15685	+	14.1281i	0.803719	+	1.39208i	0.917153	+	0.398536i	$0.130482\pi$
$103$	8.15685	+	14.1281i	0.803719	+	1.39208i	−0.113434	+	0.993546i	$0.536185\pi$
$104$		0			0
$105$	−0.242641	+	0.420266i	−0.0236793	+	0.0410138i
$106$		0			0
$107$	1.94975	−	3.37706i	0.188489	−	0.326473i	−0.756258	−	0.654274i	$-0.772974\pi$
$107$	1.94975	−	3.37706i	0.188489	−	0.326473i	0.944747	+	0.327801i	$0.106308\pi$
$108$		0			0
$109$	9.48528			0.908525			0.454263	−	0.890868i	$-0.349903\pi$
$109$	9.48528			0.908525			0.454263	+	0.890868i	$0.349903\pi$
$110$		0			0
$111$	−0.500000	−	0.866025i	−0.0474579	−	0.0821995i
$112$		0			0
$113$	7.82843	+	13.5592i	0.736436	+	1.27555i	0.954090	+	0.299519i	$0.0968263\pi$
$113$	7.82843	+	13.5592i	0.736436	+	1.27555i	−0.217654	+	0.976026i	$0.569840\pi$
$114$		0			0
$115$	−1.07107	−	1.85514i	−0.0998776	−	0.172993i
$116$		0			0
$117$	−0.914214	+	1.58346i	−0.0845191	+	0.146391i
$118$		0			0
$119$	2.82843	+	4.89898i	0.259281	+	0.449089i
$120$		0			0
$121$	4.50000	−	7.79423i	0.409091	−	0.708566i
$122$		0			0
$123$	−4.24264			−0.382546
$124$		0			0
$125$	5.65685			0.505964
$126$		0			0
$127$	2.67157	−	4.62730i	0.237064	−	0.410606i	−0.722807	−	0.691050i	$-0.757148\pi$
$127$	2.67157	−	4.62730i	0.237064	−	0.410606i	0.959870	+	0.280444i	$0.0904816\pi$
$128$		0			0
$129$	−2.74264	−	4.75039i	−0.241476	−	0.418249i
$130$		0			0
$131$	−8.12132	+	14.0665i	−0.709563	+	1.22900i	0.255456	+	0.966821i	$0.417774\pi$
$131$	−8.12132	+	14.0665i	−0.709563	+	1.22900i	−0.965019	+	0.262179i	$0.915559\pi$
$132$		0			0
$133$	1.58579	+	2.74666i	0.137505	+	0.238166i
$134$		0			0
$135$	0.292893	+	0.507306i	0.0252082	+	0.0436619i
$136$		0			0
$137$	7.70711	+	13.3491i	0.658463	+	1.14049i	0.981014	+	0.193939i	$0.0621262\pi$
$137$	7.70711	+	13.3491i	0.658463	+	1.14049i	−0.322551	+	0.946552i	$0.604540\pi$
$138$		0			0
$139$	−14.0000			−1.18746			−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000			−1.18746			−0.593732	+	0.804663i	$0.702346\pi$
$140$		0			0
$141$	0.292893	−	0.507306i	0.0246661	−	0.0427229i
$142$		0			0
$143$	−1.29289	+	2.23936i	−0.108117	+	0.187264i
$144$		0			0
$145$	−1.00000	−	1.73205i	−0.0830455	−	0.143839i
$146$		0			0
$147$	−6.31371			−0.520746
$148$		0			0
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$		0			0
$151$	−6.31371			−0.513802			−0.256901	−	0.966438i	$-0.582701\pi$
$151$	−6.31371			−0.513802			−0.256901	+	0.966438i	$0.582701\pi$
$152$		0			0
$153$	6.82843			0.552046
$154$		0			0
$155$	−3.22183	+	0.507306i	−0.258783	+	0.0407478i
$156$		0			0
$157$	7.82843			0.624777			0.312388	−	0.949955i	$-0.398871\pi$
$157$	7.82843			0.624777			0.312388	+	0.949955i	$0.398871\pi$
$158$		0			0
$159$	−1.41421			−0.112154
$160$		0			0
$161$	−1.51472	+	2.62357i	−0.119377	+	0.206766i
$162$		0			0
$163$	4.65685			0.364753			0.182376	−	0.983229i	$-0.441621\pi$
$163$	4.65685			0.364753			0.182376	+	0.983229i	$0.441621\pi$
$164$		0			0
$165$	0.414214	+	0.717439i	0.0322465	+	0.0558525i
$166$		0			0
$167$	5.94975	−	10.3053i	0.460405	−	0.797445i	−0.538576	−	0.842577i	$-0.681037\pi$
$167$	5.94975	−	10.3053i	0.460405	−	0.797445i	0.998981	+	0.0451317i	$0.0143708\pi$
$168$		0			0
$169$	4.82843	−	8.36308i	0.371417	−	0.643314i
$170$		0			0
$171$	3.82843			0.292767
$172$		0			0
$173$	−4.65685	−	8.06591i	−0.354054	−	0.613240i	0.632902	−	0.774232i	$-0.281864\pi$
$173$	−4.65685	−	8.06591i	−0.354054	−	0.613240i	−0.986956	+	0.160993i	$0.948530\pi$
$174$		0			0
$175$	−1.92893	−	3.34101i	−0.145814	−	0.252557i
$176$		0			0
$177$	−4.24264	−	7.34847i	−0.318896	−	0.552345i
$178$		0			0
$179$	−6.87868	+	11.9142i	−0.514137	+	0.890511i	0.485729	+	0.874110i	$0.338554\pi$
$179$	−6.87868	+	11.9142i	−0.514137	+	0.890511i	−0.999865	+	0.0164013i	$0.994779\pi$
$180$		0			0
$181$	−0.257359	−	0.445759i	−0.0191294	−	0.0331330i	0.856302	−	0.516475i	$-0.172756\pi$
$181$	−0.257359	−	0.445759i	−0.0191294	−	0.0331330i	−0.875432	+	0.483342i	$0.839423\pi$
$182$		0			0
$183$	6.24264	−	10.8126i	0.461469	−	0.799288i
$184$		0			0
$185$	−0.585786			−0.0430679
$186$		0			0
$187$	9.65685			0.706179
$188$		0			0
$189$	0.414214	−	0.717439i	0.0301296	−	0.0521860i
$190$		0			0
$191$	−1.53553	−	2.65962i	−0.111107	−	0.192444i	0.805110	−	0.593126i	$-0.202106\pi$
$191$	−1.53553	−	2.65962i	−0.111107	−	0.192444i	−0.916217	+	0.400682i	$0.868773\pi$
$192$		0			0
$193$	−6.98528	+	12.0989i	−0.502812	+	0.870895i	0.497183	+	0.867646i	$0.334368\pi$
$193$	−6.98528	+	12.0989i	−0.502812	+	0.870895i	−0.999995	+	0.00324955i	$0.998966\pi$
$194$		0			0
$195$	0.535534	+	0.927572i	0.0383504	+	0.0664248i
$196$		0			0
$197$	−1.41421	−	2.44949i	−0.100759	−	0.174519i	0.811239	−	0.584715i	$-0.198794\pi$
$197$	−1.41421	−	2.44949i	−0.100759	−	0.174519i	−0.911997	+	0.410196i	$0.865460\pi$
$198$		0			0
$199$	−6.07107	−	10.5154i	−0.430367	−	0.745417i	0.566538	−	0.824035i	$-0.308282\pi$
$199$	−6.07107	−	10.5154i	−0.430367	−	0.745417i	−0.996905	+	0.0786187i	$0.974949\pi$
$200$		0			0
$201$	14.4853			1.02171
$202$		0			0
$203$	−1.41421	+	2.44949i	−0.0992583	+	0.171920i
$204$		0			0
$205$	−1.24264	+	2.15232i	−0.0867898	+	0.150324i
$206$		0			0
$207$	1.82843	+	3.16693i	0.127084	+	0.220117i
$208$		0			0
$209$	5.41421			0.374509
$210$		0			0
$211$	−2.74264	+	4.75039i	−0.188811	+	0.327031i	−0.944854	−	0.327491i	$-0.893797\pi$
$211$	−2.74264	+	4.75039i	−0.188811	+	0.327031i	0.756043	+	0.654522i	$0.227130\pi$
$212$		0			0
$213$	−6.00000			−0.411113
$214$		0			0
$215$	−3.21320			−0.219139
$216$		0			0
$217$	2.89949	+	3.58719i	0.196831	+	0.243515i
$218$		0			0
$219$	3.82843			0.258701
$220$		0			0
$221$	12.4853			0.839851
$222$		0			0
$223$	8.32843	−	14.4253i	0.557713	−	0.965987i	−0.439974	−	0.898010i	$-0.645012\pi$
$223$	8.32843	−	14.4253i	0.557713	−	0.965987i	0.997687	−	0.0679764i	$-0.0216542\pi$
$224$		0			0
$225$	−4.65685			−0.310457
$226$		0			0
$227$	5.41421	+	9.37769i	0.359354	+	0.622419i	0.987853	−	0.155391i	$-0.0496637\pi$
$227$	5.41421	+	9.37769i	0.359354	+	0.622419i	−0.628499	+	0.777810i	$0.716330\pi$
$228$		0			0
$229$	5.74264	−	9.94655i	0.379484	−	0.657286i	−0.611503	−	0.791242i	$-0.709435\pi$
$229$	5.74264	−	9.94655i	0.379484	−	0.657286i	0.990987	+	0.133956i	$0.0427681\pi$
$230$		0			0
$231$	0.585786	−	1.01461i	0.0385419	−	0.0667566i
$232$		0			0
$233$	24.0000			1.57229			0.786146	−	0.618041i	$-0.212073\pi$
$233$	24.0000			1.57229			0.786146	+	0.618041i	$0.212073\pi$
$234$		0			0
$235$	−0.171573	−	0.297173i	−0.0111922	−	0.0193854i
$236$		0			0
$237$	7.82843	+	13.5592i	0.508511	+	0.880767i
$238$		0			0
$239$	12.8995	+	22.3426i	0.834399	+	1.44522i	0.894519	+	0.447030i	$0.147518\pi$
$239$	12.8995	+	22.3426i	0.834399	+	1.44522i	−0.0601199	+	0.998191i	$0.519148\pi$
$240$		0			0
$241$	2.98528	−	5.17066i	0.192299	−	0.333071i	−0.753713	−	0.657204i	$-0.771739\pi$
$241$	2.98528	−	5.17066i	0.192299	−	0.333071i	0.946012	+	0.324132i	$0.105072\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	−1.84924	+	3.20298i	−0.118144	+	0.204631i
$246$		0			0
$247$	7.00000			0.445399
$248$		0			0
$249$	7.41421			0.469857
$250$		0			0
$251$	−12.5355	+	21.7122i	−0.791236	+	1.37046i	0.133966	+	0.990986i	$0.457229\pi$
$251$	−12.5355	+	21.7122i	−0.791236	+	1.37046i	−0.925202	+	0.379475i	$0.876105\pi$
$252$		0			0
$253$	2.58579	+	4.47871i	0.162567	+	0.281574i
$254$		0			0
$255$	2.00000	−	3.46410i	0.125245	−	0.216930i
$256$		0			0
$257$	−5.12132	−	8.87039i	−0.319459	−	0.553320i	0.660916	−	0.750460i	$-0.270168\pi$
$257$	−5.12132	−	8.87039i	−0.319459	−	0.553320i	−0.980375	+	0.197140i	$0.936835\pi$
$258$		0			0
$259$	0.414214	+	0.717439i	0.0257380	+	0.0445795i
$260$		0			0
$261$	1.70711	+	2.95680i	0.105667	+	0.183021i
$262$		0			0
$263$	12.8284			0.791035			0.395517	−	0.918459i	$-0.370565\pi$
$263$	12.8284			0.791035			0.395517	+	0.918459i	$0.370565\pi$
$264$		0			0
$265$	−0.414214	+	0.717439i	−0.0254449	+	0.0440719i
$266$		0			0
$267$	8.94975	−	15.5014i	0.547716	−	0.948671i
$268$		0			0
$269$	9.89949	+	17.1464i	0.603583	+	1.04544i	0.992274	+	0.124068i	$0.0395941\pi$
$269$	9.89949	+	17.1464i	0.603583	+	1.04544i	−0.388691	+	0.921368i	$0.627073\pi$
$270$		0			0
$271$	28.4558			1.72857			0.864285	−	0.503003i	$-0.167772\pi$
$271$	28.4558			1.72857			0.864285	+	0.503003i	$0.167772\pi$
$272$		0			0
$273$	0.757359	−	1.31178i	0.0458375	−	0.0793928i
$274$		0			0
$275$	−6.58579			−0.397138
$276$		0			0
$277$	11.3431			0.681544			0.340772	−	0.940146i	$-0.389312\pi$
$277$	11.3431			0.681544			0.340772	+	0.940146i	$0.389312\pi$
$278$		0			0
$279$	5.50000	−	0.866025i	0.329276	−	0.0518476i
$280$		0			0
$281$	−20.0416			−1.19558			−0.597792	−	0.801651i	$-0.703955\pi$
$281$	−20.0416			−1.19558			−0.597792	+	0.801651i	$0.703955\pi$
$282$		0			0
$283$	−15.4853			−0.920504			−0.460252	−	0.887788i	$-0.652241\pi$
$283$	−15.4853			−0.920504			−0.460252	+	0.887788i	$0.652241\pi$
$284$		0			0
$285$	1.12132	−	1.94218i	0.0664213	−	0.115045i
$286$		0			0
$287$	3.51472			0.207467
$288$		0			0
$289$	−14.8137	−	25.6581i	−0.871395	−	1.50930i
$290$		0			0
$291$	5.74264	−	9.94655i	0.336640	−	0.583077i
$292$		0			0
$293$	−6.41421	+	11.1097i	−0.374722	+	0.649038i	−0.990285	−	0.139049i	$-0.955595\pi$
$293$	−6.41421	+	11.1097i	−0.374722	+	0.649038i	0.615563	+	0.788088i	$0.288929\pi$
$294$		0			0
$295$	−4.97056			−0.289397
$296$		0			0
$297$	−0.707107	−	1.22474i	−0.0410305	−	0.0710669i
$298$		0			0
$299$	3.34315	+	5.79050i	0.193339	+	0.334873i
$300$		0			0
$301$	2.27208	+	3.93535i	0.130960	+	0.226830i
$302$		0			0
$303$	7.70711	−	13.3491i	0.442762	−	0.766886i
$304$		0			0
$305$	−3.65685	−	6.33386i	−0.209391	−	0.362676i
$306$		0			0
$307$	3.84315	−	6.65652i	0.219340	−	0.379908i	−0.735266	−	0.677778i	$-0.762943\pi$
$307$	3.84315	−	6.65652i	0.219340	−	0.379908i	0.954606	+	0.297870i	$0.0962763\pi$
$308$		0			0
$309$	−16.3137			−0.928054
$310$		0			0
$311$	19.8995			1.12840			0.564198	−	0.825639i	$-0.309185\pi$
$311$	19.8995			1.12840			0.564198	+	0.825639i	$0.309185\pi$
$312$		0			0
$313$	2.84315	−	4.92447i	0.160704	−	0.278348i	−0.774417	−	0.632675i	$-0.781957\pi$
$313$	2.84315	−	4.92447i	0.160704	−	0.278348i	0.935121	+	0.354327i	$0.115290\pi$
$314$		0			0
$315$	−0.242641	−	0.420266i	−0.0136713	−	0.0236793i
$316$		0			0
$317$	11.1213	−	19.2627i	0.624636	−	1.08190i	−0.363976	−	0.931408i	$-0.618581\pi$
$317$	11.1213	−	19.2627i	0.624636	−	1.08190i	0.988611	−	0.150492i	$-0.0480858\pi$
$318$		0			0
$319$	2.41421	+	4.18154i	0.135170	+	0.234121i
$320$		0			0
$321$	1.94975	+	3.37706i	0.108824	+	0.188489i
$322$		0			0
$323$	−13.0711	−	22.6398i	−0.727294	−	1.25971i
$324$		0			0
$325$	−8.51472			−0.472312
$326$		0			0
$327$	−4.74264	+	8.21449i	−0.262269	+	0.454263i
$328$		0			0
$329$	−0.242641	+	0.420266i	−0.0133772	+	0.0231700i
$330$		0			0
$331$	1.50000	+	2.59808i	0.0824475	+	0.142803i	0.904301	−	0.426896i	$-0.140393\pi$
$331$	1.50000	+	2.59808i	0.0824475	+	0.142803i	−0.821853	+	0.569699i	$0.807060\pi$
$332$		0			0
$333$	1.00000			0.0547997
$334$		0			0
$335$	4.24264	−	7.34847i	0.231800	−	0.401490i
$336$		0			0
$337$	18.6274			1.01470			0.507350	−	0.861740i	$-0.330625\pi$
$337$	18.6274			1.01470			0.507350	+	0.861740i	$0.330625\pi$
$338$		0			0
$339$	−15.6569			−0.850364
$340$		0			0
$341$	7.77817	−	1.22474i	0.421212	−	0.0663237i
$342$		0			0
$343$	11.0294			0.595534
$344$		0			0
$345$	2.14214			0.115329
$346$		0			0
$347$	8.70711	−	15.0812i	0.467422	−	0.809599i	−0.531885	−	0.846816i	$-0.678516\pi$
$347$	8.70711	−	15.0812i	0.467422	−	0.809599i	0.999307	+	0.0372179i	$0.0118495\pi$
$348$		0			0
$349$	33.1421			1.77406			0.887029	−	0.461714i	$-0.152765\pi$
$349$	33.1421			1.77406			0.887029	+	0.461714i	$0.152765\pi$
$350$		0			0
$351$	−0.914214	−	1.58346i	−0.0487971	−	0.0845191i
$352$		0			0
$353$	−13.5858	+	23.5313i	−0.723098	+	1.25244i	0.236653	+	0.971594i	$0.423949\pi$
$353$	−13.5858	+	23.5313i	−0.723098	+	1.25244i	−0.959752	+	0.280849i	$0.909384\pi$
$354$		0			0
$355$	−1.75736	+	3.04384i	−0.0932709	+	0.161550i
$356$		0			0
$357$	−5.65685			−0.299392
$358$		0			0
$359$	9.02082	+	15.6245i	0.476100	+	0.824630i	0.999625	−	0.0273804i	$-0.00871654\pi$
$359$	9.02082	+	15.6245i	0.476100	+	0.824630i	−0.523525	+	0.852011i	$0.675383\pi$
$360$		0			0
$361$	2.17157	+	3.76127i	0.114293	+	0.197962i
$362$		0			0
$363$	4.50000	+	7.79423i	0.236189	+	0.409091i
$364$		0			0
$365$	1.12132	−	1.94218i	0.0586926	−	0.101659i
$366$		0			0
$367$	9.57107	+	16.5776i	0.499606	+	0.865342i	1.00000		0.000455270i	$-0.000144917\pi$
$367$	9.57107	+	16.5776i	0.499606	+	0.865342i	−0.500394	+	0.865798i	$0.666812\pi$
$368$		0			0
$369$	2.12132	−	3.67423i	0.110432	−	0.191273i
$370$		0			0
$371$	1.17157			0.0608250
$372$		0			0
$373$	−29.4853			−1.52669			−0.763345	−	0.645991i	$-0.776444\pi$
$373$	−29.4853			−1.52669			−0.763345	+	0.645991i	$0.776444\pi$
$374$		0			0
$375$	−2.82843	+	4.89898i	−0.146059	+	0.252982i
$376$		0			0
$377$	3.12132	+	5.40629i	0.160756	+	0.278438i
$378$		0			0
$379$	4.91421	−	8.51167i	0.252426	−	0.437215i	−0.711767	−	0.702416i	$-0.752105\pi$
$379$	4.91421	−	8.51167i	0.252426	−	0.437215i	0.964193	+	0.265201i	$0.0854382\pi$
$380$		0			0
$381$	2.67157	+	4.62730i	0.136869	+	0.237064i
$382$		0			0
$383$	−3.19239	−	5.52938i	−0.163123	−	0.282538i	0.772864	−	0.634572i	$-0.218824\pi$
$383$	−3.19239	−	5.52938i	−0.163123	−	0.282538i	−0.935987	+	0.352034i	$0.885490\pi$
$384$		0			0
$385$	−0.343146	−	0.594346i	−0.0174883	−	0.0302907i
$386$		0			0
$387$	5.48528			0.278833
$388$		0			0
$389$	8.65685	−	14.9941i	0.438920	−	0.760232i	−0.558687	−	0.829379i	$-0.688695\pi$
$389$	8.65685	−	14.9941i	0.438920	−	0.760232i	0.997606	+	0.0691473i	$0.0220278\pi$
$390$		0			0
$391$	12.4853	−	21.6251i	0.631408	−	1.09363i
$392$		0			0
$393$	−8.12132	−	14.0665i	−0.409666	−	0.709563i
$394$		0			0
$395$	9.17157			0.461472
$396$		0			0
$397$	−4.48528	+	7.76874i	−0.225110	+	0.389902i	−0.956352	−	0.292216i	$-0.905607\pi$
$397$	−4.48528	+	7.76874i	−0.225110	+	0.389902i	0.731243	+	0.682118i	$0.238941\pi$
$398$		0			0
$399$	−3.17157			−0.158777
$400$		0			0
$401$	−14.8284			−0.740496			−0.370248	−	0.928933i	$-0.620727\pi$
$401$	−14.8284			−0.740496			−0.370248	+	0.928933i	$0.620727\pi$
$402$		0			0
$403$	10.0563	−	1.58346i	0.500942	−	0.0788780i
$404$		0			0
$405$	−0.585786			−0.0291080
$406$		0			0
$407$	1.41421			0.0701000
$408$		0			0
$409$	3.25736	−	5.64191i	0.161066	−	0.278975i	−0.774185	−	0.632959i	$-0.781840\pi$
$409$	3.25736	−	5.64191i	0.161066	−	0.278975i	0.935251	+	0.353985i	$0.115173\pi$
$410$		0			0
$411$	−15.4142			−0.760327
$412$		0			0
$413$	3.51472	+	6.08767i	0.172948	+	0.299555i
$414$		0			0
$415$	2.17157	−	3.76127i	0.106598	−	0.184634i
$416$		0			0
$417$	7.00000	−	12.1244i	0.342791	−	0.593732i
$418$		0			0
$419$	−22.9706			−1.12219			−0.561093	−	0.827753i	$-0.689619\pi$
$419$	−22.9706			−1.12219			−0.561093	+	0.827753i	$0.689619\pi$
$420$		0			0
$421$	11.0000	+	19.0526i	0.536107	+	0.928565i	0.999109	+	0.0422075i	$0.0134391\pi$
$421$	11.0000	+	19.0526i	0.536107	+	0.928565i	−0.463002	+	0.886357i	$0.653228\pi$
$422$		0			0
$423$	0.292893	+	0.507306i	0.0142410	+	0.0246661i
$424$		0			0
$425$	15.8995	+	27.5387i	0.771239	+	1.33582i
$426$		0			0
$427$	−5.17157	+	8.95743i	−0.250270	+	0.433480i
$428$		0			0
$429$	−1.29289	−	2.23936i	−0.0624215	−	0.108117i
$430$		0			0
$431$	2.17157	−	3.76127i	0.104601	−	0.181174i	−0.808974	−	0.587844i	$-0.799977\pi$
$431$	2.17157	−	3.76127i	0.104601	−	0.181174i	0.913575	+	0.406670i	$0.133310\pi$
$432$		0			0
$433$	−3.82843			−0.183982			−0.0919912	−	0.995760i	$-0.529323\pi$
$433$	−3.82843			−0.183982			−0.0919912	+	0.995760i	$0.529323\pi$
$434$		0			0
$435$	2.00000			0.0958927
$436$		0			0
$437$	7.00000	−	12.1244i	0.334855	−	0.579987i
$438$		0			0
$439$	−1.74264	−	3.01834i	−0.0831717	−	0.144058i	0.821439	−	0.570296i	$-0.193172\pi$
$439$	−1.74264	−	3.01834i	−0.0831717	−	0.144058i	−0.904611	+	0.426239i	$0.859838\pi$
$440$		0			0
$441$	3.15685	−	5.46783i	0.150326	−	0.260373i
$442$		0			0
$443$	4.07107	+	7.05130i	0.193422	+	0.335017i	0.946382	−	0.323049i	$-0.104708\pi$
$443$	4.07107	+	7.05130i	0.193422	+	0.335017i	−0.752960	+	0.658066i	$0.771375\pi$
$444$		0			0
$445$	−5.24264	−	9.08052i	−0.248525	−	0.430458i
$446$		0			0
$447$	3.00000	+	5.19615i	0.141895	+	0.245770i
$448$		0			0
$449$	−18.3431			−0.865667			−0.432833	−	0.901474i	$-0.642486\pi$
$449$	−18.3431			−0.865667			−0.432833	+	0.901474i	$0.642486\pi$
$450$		0			0
$451$	3.00000	−	5.19615i	0.141264	−	0.244677i
$452$		0			0
$453$	3.15685	−	5.46783i	0.148322	−	0.256901i
$454$		0			0
$455$	−0.443651	−	0.768426i	−0.0207987	−	0.0360244i
$456$		0			0
$457$	35.4853			1.65993			0.829966	−	0.557814i	$-0.188360\pi$
$457$	35.4853			1.65993			0.829966	+	0.557814i	$0.188360\pi$
$458$		0			0
$459$	−3.41421	+	5.91359i	−0.159362	+	0.276023i
$460$		0			0
$461$	3.55635			0.165636			0.0828178	−	0.996565i	$-0.473608\pi$
$461$	3.55635			0.165636			0.0828178	+	0.996565i	$0.473608\pi$
$462$		0			0
$463$	−36.4558			−1.69425			−0.847123	−	0.531396i	$-0.821668\pi$
$463$	−36.4558			−1.69425			−0.847123	+	0.531396i	$0.821668\pi$
$464$		0			0
$465$	1.17157	−	3.04384i	0.0543304	−	0.141154i
$466$		0			0
$467$	9.31371			0.430987			0.215494	−	0.976505i	$-0.430864\pi$
$467$	9.31371			0.430987			0.215494	+	0.976505i	$0.430864\pi$
$468$		0			0
$469$	−12.0000			−0.554109
$470$		0			0
$471$	−3.91421	+	6.77962i	−0.180357	+	0.312388i
$472$		0			0
$473$	7.75736			0.356684
$474$		0			0
$475$	8.91421	+	15.4399i	0.409012	+	0.708430i
$476$		0			0
$477$	0.707107	−	1.22474i	0.0323762	−	0.0560772i
$478$		0			0
$479$	−5.82843	+	10.0951i	−0.266308	+	0.461258i	−0.967905	−	0.251315i	$-0.919137\pi$
$479$	−5.82843	+	10.0951i	−0.266308	+	0.461258i	0.701598	+	0.712573i	$0.252470\pi$
$480$		0			0
$481$	1.82843			0.0833691
$482$		0			0
$483$	−1.51472	−	2.62357i	−0.0689221	−	0.119377i
$484$		0			0
$485$	−3.36396	−	5.82655i	−0.152750	−	0.264570i
$486$		0			0
$487$	3.25736	+	5.64191i	0.147605	+	0.255659i	0.930342	−	0.366693i	$-0.119510\pi$
$487$	3.25736	+	5.64191i	0.147605	+	0.255659i	−0.782737	+	0.622353i	$0.786177\pi$
$488$		0			0
$489$	−2.32843	+	4.03295i	−0.105295	+	0.182376i
$490$		0			0
$491$	−16.1421	−	27.9590i	−0.728484	−	1.26177i	−0.957524	−	0.288355i	$-0.906892\pi$
$491$	−16.1421	−	27.9590i	−0.728484	−	1.26177i	0.229039	−	0.973417i	$-0.426442\pi$
$492$		0			0
$493$	11.6569	−	20.1903i	0.524998	−	0.909324i
$494$		0			0
$495$	−0.828427			−0.0372350
$496$		0			0
$497$	4.97056			0.222960
$498$		0			0
$499$	−3.92893	+	6.80511i	−0.175883	+	0.304639i	−0.940467	−	0.339886i	$-0.889611\pi$
$499$	−3.92893	+	6.80511i	−0.175883	+	0.304639i	0.764583	+	0.644525i	$0.222945\pi$
$500$		0			0
$501$	5.94975	+	10.3053i	0.265815	+	0.460405i
$502$		0			0
$503$	3.89949	−	6.75412i	0.173870	−	0.301151i	−0.765900	−	0.642960i	$-0.777706\pi$
$503$	3.89949	−	6.75412i	0.173870	−	0.301151i	0.939770	+	0.341809i	$0.111039\pi$
$504$		0			0
$505$	−4.51472	−	7.81972i	−0.200902	−	0.347973i
$506$		0			0
$507$	4.82843	+	8.36308i	0.214438	+	0.371417i
$508$		0			0
$509$	−13.2426	−	22.9369i	−0.586970	−	1.01666i	−0.994627	−	0.103526i	$-0.966987\pi$
$509$	−13.2426	−	22.9369i	−0.586970	−	1.01666i	0.407657	−	0.913135i	$-0.366346\pi$
$510$		0			0
$511$	−3.17157			−0.140302
$512$		0			0
$513$	−1.91421	+	3.31552i	−0.0845146	+	0.146384i
$514$		0			0
$515$	−4.77817	+	8.27604i	−0.210552	+	0.364686i
$516$		0			0
$517$	0.414214	+	0.717439i	0.0182171	+	0.0315529i
$518$		0			0
$519$	9.31371			0.408826
$520$		0			0
$521$	−9.94975	+	17.2335i	−0.435906	+	0.755012i	−0.997369	−	0.0724900i	$-0.976905\pi$
$521$	−9.94975	+	17.2335i	−0.435906	+	0.755012i	0.561463	+	0.827502i	$0.310239\pi$
$522$		0			0
$523$	−6.00000			−0.262362			−0.131181	−	0.991358i	$-0.541877\pi$
$523$	−6.00000			−0.262362			−0.131181	+	0.991358i	$0.541877\pi$
$524$		0			0
$525$	3.85786			0.168371
$526$		0			0
$527$	−23.8995	−	29.5680i	−1.04108	−	1.28800i
$528$		0			0
$529$	−9.62742			−0.418583
$530$		0			0
$531$	8.48528			0.368230
$532$		0			0
$533$	3.87868	−	6.71807i	0.168004	−	0.290992i
$534$		0			0
$535$	2.28427			0.0987577
$536$		0			0
$537$	−6.87868	−	11.9142i	−0.296837	−	0.514137i
$538$		0			0
$539$	4.46447	−	7.73268i	0.192298	−	0.333070i
$540$		0			0
$541$	−18.9853	+	32.8835i	−0.816241	+	1.41377i	0.0921924	+	0.995741i	$0.470613\pi$
$541$	−18.9853	+	32.8835i	−0.816241	+	1.41377i	−0.908433	+	0.418030i	$0.862721\pi$
$542$		0			0
$543$	0.514719			0.0220887
$544$		0			0
$545$	2.77817	+	4.81194i	0.119004	+	0.206121i
$546$		0			0
$547$	−0.500000	−	0.866025i	−0.0213785	−	0.0370286i	0.855138	−	0.518400i	$-0.173472\pi$
$547$	−0.500000	−	0.866025i	−0.0213785	−	0.0370286i	−0.876517	+	0.481371i	$0.840139\pi$
$548$		0			0
$549$	6.24264	+	10.8126i	0.266429	+	0.461469i
$550$		0			0
$551$	6.53553	−	11.3199i	0.278423	−	0.482243i
$552$		0			0
$553$	−6.48528	−	11.2328i	−0.275782	−	0.477669i
$554$		0			0
$555$	0.292893	−	0.507306i	0.0124326	−	0.0215339i
$556$		0			0
$557$	−4.62742			−0.196070			−0.0980350	−	0.995183i	$-0.531256\pi$
$557$	−4.62742			−0.196070			−0.0980350	+	0.995183i	$0.531256\pi$
$558$		0			0
$559$	10.0294			0.424200
$560$		0			0
$561$	−4.82843	+	8.36308i	−0.203856	+	0.353090i
$562$		0			0
$563$	11.6777	+	20.2263i	0.492155	+	0.852438i	0.999959	−	0.00903495i	$-0.00287595\pi$
$563$	11.6777	+	20.2263i	0.492155	+	0.852438i	−0.507804	+	0.861473i	$0.669543\pi$
$564$		0			0
$565$	−4.58579	+	7.94282i	−0.192925	+	0.334157i
$566$		0			0
$567$	0.414214	+	0.717439i	0.0173953	+	0.0301296i
$568$		0			0
$569$	−4.07107	−	7.05130i	−0.170668	−	0.295606i	0.767986	−	0.640467i	$-0.221259\pi$
$569$	−4.07107	−	7.05130i	−0.170668	−	0.295606i	−0.938654	+	0.344861i	$0.887926\pi$
$570$		0			0
$571$	0.742641	+	1.28629i	0.0310785	+	0.0538296i	0.881146	−	0.472844i	$-0.156772\pi$
$571$	0.742641	+	1.28629i	0.0310785	+	0.0538296i	−0.850068	+	0.526673i	$0.823439\pi$
$572$		0			0
$573$	3.07107			0.128296
$574$		0			0
$575$	−8.51472	+	14.7479i	−0.355088	+	0.615031i
$576$		0			0
$577$	−1.17157	+	2.02922i	−0.0487732	+	0.0844777i	−0.889381	−	0.457166i	$-0.848864\pi$
$577$	−1.17157	+	2.02922i	−0.0487732	+	0.0844777i	0.840608	+	0.541644i	$0.182198\pi$
$578$		0			0
$579$	−6.98528	−	12.0989i	−0.290298	−	0.502812i
$580$		0			0
$581$	−6.14214			−0.254819
$582$		0			0
$583$	1.00000	−	1.73205i	0.0414158	−	0.0717342i
$584$		0			0
$585$	−1.07107			−0.0442832
$586$		0			0
$587$	16.6274			0.686287			0.343143	−	0.939283i	$-0.388508\pi$
$587$	16.6274			0.686287			0.343143	+	0.939283i	$0.388508\pi$
$588$		0			0
$589$	−13.3995	−	16.5776i	−0.552117	−	0.683067i
$590$		0			0
$591$	2.82843			0.116346
$592$		0			0
$593$	−36.0000			−1.47834			−0.739171	−	0.673517i	$-0.764783\pi$
$593$	−36.0000			−1.47834			−0.739171	+	0.673517i	$0.764783\pi$
$594$		0			0
$595$	−1.65685	+	2.86976i	−0.0679244	+	0.117649i
$596$		0			0
$597$	12.1421			0.496945
$598$		0			0
$599$	−11.2635	−	19.5089i	−0.460212	−	0.797111i	0.538759	−	0.842460i	$-0.318893\pi$
$599$	−11.2635	−	19.5089i	−0.460212	−	0.797111i	−0.998971	+	0.0453489i	$0.985560\pi$
$600$		0			0
$601$	3.48528	−	6.03668i	0.142168	−	0.246241i	−0.786145	−	0.618042i	$-0.787926\pi$
$601$	3.48528	−	6.03668i	0.142168	−	0.246241i	0.928313	+	0.371801i	$0.121259\pi$
$602$		0			0
$603$	−7.24264	+	12.5446i	−0.294943	+	0.510856i
$604$		0			0
$605$	5.27208			0.214340
$606$		0			0
$607$	−20.2279	−	35.0358i	−0.821026	−	1.42206i	−0.904919	−	0.425584i	$-0.860069\pi$
$607$	−20.2279	−	35.0358i	−0.821026	−	1.42206i	0.0838929	−	0.996475i	$-0.473265\pi$
$608$		0			0
$609$	−1.41421	−	2.44949i	−0.0573068	−	0.0992583i
$610$		0			0
$611$	0.535534	+	0.927572i	0.0216654	+	0.0375255i
$612$		0			0
$613$	−18.7426	+	32.4632i	−0.757008	+	1.31118i	0.187362	+	0.982291i	$0.440006\pi$
$613$	−18.7426	+	32.4632i	−0.757008	+	1.31118i	−0.944370	+	0.328886i	$0.893327\pi$
$614$		0			0
$615$	−1.24264	−	2.15232i	−0.0501081	−	0.0867898i
$616$		0			0
$617$	16.6066	−	28.7635i	0.668557	−	1.15797i	−0.309751	−	0.950818i	$-0.600246\pi$
$617$	16.6066	−	28.7635i	0.668557	−	1.15797i	0.978308	−	0.207156i	$-0.0664209\pi$
$618$		0			0
$619$	−29.4853			−1.18511			−0.592557	−	0.805529i	$-0.701881\pi$
$619$	−29.4853			−1.18511			−0.592557	+	0.805529i	$0.701881\pi$
$620$		0			0
$621$	−3.65685			−0.146745
$622$		0			0
$623$	−7.41421	+	12.8418i	−0.297044	+	0.514496i
$624$		0			0
$625$	−9.98528	−	17.2950i	−0.399411	−	0.691801i
$626$		0			0
$627$	−2.70711	+	4.68885i	−0.108111	+	0.187254i
$628$		0			0
$629$	−3.41421	−	5.91359i	−0.136134	−	0.235790i
$630$		0			0
$631$	21.4853	+	37.2136i	0.855316	+	1.48145i	0.876352	+	0.481671i	$0.159970\pi$
$631$	21.4853	+	37.2136i	0.855316	+	1.48145i	−0.0210364	+	0.999779i	$0.506697\pi$
$632$		0			0
$633$	−2.74264	−	4.75039i	−0.109010	−	0.188811i
$634$		0			0
$635$	3.12994			0.124208
$636$		0			0
$637$	5.77208	−	9.99753i	0.228698	−	0.396117i
$638$		0			0
$639$	3.00000	−	5.19615i	0.118678	−	0.205557i
$640$		0			0
$641$	22.0919	+	38.2643i	0.872577	+	1.51135i	0.859322	+	0.511435i	$0.170886\pi$
$641$	22.0919	+	38.2643i	0.872577	+	1.51135i	0.0132552	+	0.999912i	$0.495781\pi$
$642$		0			0
$643$	−35.7696			−1.41061			−0.705307	−	0.708902i	$-0.749191\pi$
$643$	−35.7696			−1.41061			−0.705307	+	0.708902i	$0.749191\pi$
$644$		0			0
$645$	1.60660	−	2.78272i	0.0632599	−	0.109569i
$646$		0			0
$647$	−14.4437			−0.567839			−0.283919	−	0.958848i	$-0.591635\pi$
$647$	−14.4437			−0.567839			−0.283919	+	0.958848i	$0.591635\pi$
$648$		0			0
$649$	12.0000			0.471041
$650$		0			0
$651$	−4.55635	+	0.717439i	−0.178577	+	0.0281186i
$652$		0			0
$653$	41.0122			1.60493			0.802466	−	0.596698i	$-0.203521\pi$
$653$	41.0122			1.60493			0.802466	+	0.596698i	$0.203521\pi$
$654$		0			0
$655$	−9.51472			−0.371771
$656$		0			0
$657$	−1.91421	+	3.31552i	−0.0746806	+	0.129351i
$658$		0			0
$659$	−1.61522			−0.0629202			−0.0314601	−	0.999505i	$-0.510016\pi$
$659$	−1.61522			−0.0629202			−0.0314601	+	0.999505i	$0.510016\pi$
$660$		0			0
$661$	24.8848	+	43.1017i	0.967906	+	1.67646i	0.701597	+	0.712574i	$0.252471\pi$
$661$	24.8848	+	43.1017i	0.967906	+	1.67646i	0.266309	+	0.963888i	$0.414196\pi$
$662$		0			0
$663$	−6.24264	+	10.8126i	−0.242444	+	0.419925i
$664$		0			0
$665$	−0.928932	+	1.60896i	−0.0360224	+	0.0623927i
$666$		0			0
$667$	12.4853			0.483432
$668$		0			0
$669$	8.32843	+	14.4253i	0.321996	+	0.557713i
$670$		0			0
$671$	8.82843	+	15.2913i	0.340818	+	0.590313i
$672$		0			0
$673$	6.24264	+	10.8126i	0.240636	+	0.416794i	0.960896	−	0.276911i	$-0.0893106\pi$
$673$	6.24264	+	10.8126i	0.240636	+	0.416794i	−0.720260	+	0.693705i	$0.755977\pi$
$674$		0			0
$675$	2.32843	−	4.03295i	0.0896212	−	0.155228i
$676$		0			0
$677$	−8.94975	−	15.5014i	−0.343967	−	0.595768i	0.641199	−	0.767375i	$-0.278437\pi$
$677$	−8.94975	−	15.5014i	−0.343967	−	0.595768i	−0.985165	+	0.171607i	$0.945104\pi$
$678$		0			0
$679$	−4.75736	+	8.23999i	−0.182571	+	0.316222i
$680$		0			0
$681$	−10.8284			−0.414946
$682$		0			0
$683$	23.6569			0.905204			0.452602	−	0.891713i	$-0.350496\pi$
$683$	23.6569			0.905204			0.452602	+	0.891713i	$0.350496\pi$
$684$		0			0
$685$	−4.51472	+	7.81972i	−0.172499	+	0.298776i
$686$		0			0
$687$	5.74264	+	9.94655i	0.219095	+	0.379484i
$688$		0			0
$689$	1.29289	−	2.23936i	0.0492553	−	0.0853127i
$690$		0			0
$691$	−7.48528	−	12.9649i	−0.284754	−	0.493208i	0.687796	−	0.725904i	$-0.258578\pi$
$691$	−7.48528	−	12.9649i	−0.284754	−	0.493208i	−0.972549	+	0.232697i	$0.925245\pi$
$692$		0			0
$693$	0.585786	+	1.01461i	0.0222522	+	0.0385419i
$694$		0			0
$695$	−4.10051	−	7.10228i	−0.155541	−	0.269405i
$696$		0			0
$697$	−28.9706			−1.09734
$698$		0			0
$699$	−12.0000	+	20.7846i	−0.453882	+	0.786146i
$700$		0			0
$701$	18.0000	−	31.1769i	0.679851	−	1.17754i	−0.295175	−	0.955443i	$-0.595378\pi$
$701$	18.0000	−	31.1769i	0.679851	−	1.17754i	0.975026	−	0.222093i	$-0.0712887\pi$
$702$		0			0
$703$	−1.91421	−	3.31552i	−0.0721959	−	0.125047i
$704$		0			0
$705$	0.343146			0.0129236
$706$		0			0
$707$	−6.38478	+	11.0588i	−0.240124	+	0.415907i
$708$		0			0
$709$	−19.9706			−0.750010			−0.375005	−	0.927023i	$-0.622359\pi$
$709$	−19.9706			−0.750010			−0.375005	+	0.927023i	$0.622359\pi$
$710$		0			0
$711$	−15.6569			−0.587178
$712$		0			0
$713$	7.31371	−	19.0016i	0.273901	−	0.711614i
$714$		0			0
$715$	−1.51472			−0.0566473
$716$		0			0
$717$	−25.7990			−0.963481
$718$		0			0
$719$	12.4142	−	21.5020i	0.462972	−	0.801891i	−0.536135	−	0.844132i	$-0.680116\pi$
$719$	12.4142	−	21.5020i	0.462972	−	0.801891i	0.999107	+	0.0422409i	$0.0134497\pi$
$720$		0			0
$721$	13.5147			0.503314
$722$		0			0
$723$	2.98528	+	5.17066i	0.111024	+	0.192299i
$724$		0			0
$725$	−7.94975	+	13.7694i	−0.295246	+	0.511381i
$726$		0			0
$727$	−2.50000	+	4.33013i	−0.0927199	+	0.160596i	−0.908655	−	0.417548i	$-0.862889\pi$
$727$	−2.50000	+	4.33013i	−0.0927199	+	0.160596i	0.815935	+	0.578144i	$0.196223\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−18.7279	−	32.4377i	−0.692677	−	1.19975i
$732$		0			0
$733$	−3.01472	−	5.22165i	−0.111351	−	0.192866i	0.804964	−	0.593324i	$-0.202185\pi$
$733$	−3.01472	−	5.22165i	−0.111351	−	0.192866i	−0.916315	+	0.400458i	$0.868851\pi$
$734$		0			0
$735$	−1.84924	−	3.20298i	−0.0682103	−	0.118144i
$736$		0			0
$737$	−10.2426	+	17.7408i	−0.377293	+	0.653490i
$738$		0			0
$739$	−0.843146	−	1.46037i	−0.0310156	−	0.0537206i	0.850101	−	0.526620i	$-0.176541\pi$
$739$	−0.843146	−	1.46037i	−0.0310156	−	0.0537206i	−0.881117	+	0.472899i	$0.843207\pi$
$740$		0			0
$741$	−3.50000	+	6.06218i	−0.128576	+	0.222700i
$742$		0			0
$743$	17.7990			0.652982			0.326491	−	0.945200i	$-0.394134\pi$
$743$	17.7990			0.652982			0.326491	+	0.945200i	$0.394134\pi$
$744$		0			0
$745$	3.51472			0.128769
$746$		0			0
$747$	−3.70711	+	6.42090i	−0.135636	+	0.234928i
$748$		0			0
$749$	−1.61522	−	2.79765i	−0.0590190	−	0.102224i
$750$		0			0
$751$	−20.2279	+	35.0358i	−0.738127	+	1.27847i	0.215210	+	0.976568i	$0.430956\pi$
$751$	−20.2279	+	35.0358i	−0.738127	+	1.27847i	−0.953338	+	0.301906i	$0.902377\pi$
$752$		0			0
$753$	−12.5355	−	21.7122i	−0.456820	−	0.791236i
$754$		0			0
$755$	−1.84924	−	3.20298i	−0.0673008	−	0.116568i
$756$		0			0
$757$	−25.3137	−	43.8446i	−0.920042	−	1.59356i	−0.799346	−	0.600871i	$-0.794821\pi$
$757$	−25.3137	−	43.8446i	−0.920042	−	1.59356i	−0.120696	−	0.992690i	$-0.538513\pi$
$758$		0			0
$759$	−5.17157			−0.187716
$760$		0			0
$761$	−20.5355	+	35.5686i	−0.744413	+	1.28936i	0.206056	+	0.978540i	$0.433937\pi$
$761$	−20.5355	+	35.5686i	−0.744413	+	1.28936i	−0.950469	+	0.310820i	$0.899396\pi$
$762$		0			0
$763$	3.92893	−	6.80511i	0.142237	−	0.246362i
$764$		0			0
$765$	2.00000	+	3.46410i	0.0723102	+	0.125245i
$766$		0			0
$767$	15.5147			0.560204
$768$		0			0
$769$	−10.2426	+	17.7408i	−0.369359	+	0.639749i	−0.989465	−	0.144769i	$-0.953756\pi$
$769$	−10.2426	+	17.7408i	−0.369359	+	0.639749i	0.620106	+	0.784518i	$0.287089\pi$
$770$		0			0
$771$	10.2426			0.368880
$772$		0			0
$773$	−11.8579			−0.426498			−0.213249	−	0.976998i	$-0.568405\pi$
$773$	−11.8579			−0.426498			−0.213249	+	0.976998i	$0.568405\pi$
$774$		0			0
$775$	16.2990	+	20.1648i	0.585477	+	0.724340i
$776$		0			0
$777$	−0.828427			−0.0297197
$778$		0			0
$779$	−16.2426			−0.581953
$780$		0			0
$781$	4.24264	−	7.34847i	0.151814	−	0.262949i
$782$		0			0
$783$	−3.41421			−0.122014
$784$		0			0
$785$	2.29289	+	3.97141i	0.0818369	+	0.141746i
$786$		0			0
$787$	10.7426	−	18.6068i	0.382934	−	0.663261i	−0.608546	−	0.793518i	$-0.708247\pi$
$787$	10.7426	−	18.6068i	0.382934	−	0.663261i	0.991480	+	0.130258i	$0.0415804\pi$
$788$		0			0
$789$	−6.41421	+	11.1097i	−0.228352	+	0.395517i
$790$		0			0
$791$	12.9706			0.461180
$792$		0			0
$793$	11.4142	+	19.7700i	0.405331	+	0.702053i
$794$		0			0
$795$	−0.414214	−	0.717439i	−0.0146906	−	0.0254449i
$796$		0			0
$797$	0.343146	+	0.594346i	0.0121548	+	0.0210528i	0.872039	−	0.489437i	$-0.162798\pi$
$797$	0.343146	+	0.594346i	0.0121548	+	0.0210528i	−0.859884	+	0.510489i	$0.829464\pi$
$798$		0			0
$799$	2.00000	−	3.46410i	0.0707549	−	0.122551i
$800$		0			0
$801$	8.94975	+	15.5014i	0.316224	+	0.547716i
$802$		0			0
$803$	−2.70711	+	4.68885i	−0.0955317	+	0.165466i
$804$		0			0
$805$	−1.77460			−0.0625465
$806$		0			0
$807$	−19.7990			−0.696957
$808$		0			0
$809$	8.46447	−	14.6609i	0.297595	−	0.515449i	−0.677990	−	0.735071i	$-0.737149\pi$
$809$	8.46447	−	14.6609i	0.297595	−	0.515449i	0.975585	+	0.219621i	$0.0704822\pi$
$810$		0			0
$811$	9.50000	+	16.4545i	0.333590	+	0.577795i	0.983213	−	0.182462i	$-0.0584065\pi$
$811$	9.50000	+	16.4545i	0.333590	+	0.577795i	−0.649623	+	0.760257i	$0.725073\pi$
$812$		0			0
$813$	−14.2279	+	24.6435i	−0.498995	+	0.864285i
$814$		0			0
$815$	1.36396	+	2.36245i	0.0477775	+	0.0827530i
$816$		0			0
$817$	−10.5000	−	18.1865i	−0.367348	−	0.636266i
$818$		0			0
$819$	0.757359	+	1.31178i	0.0264643	+	0.0458375i
$820$		0			0
$821$	−37.7990			−1.31919			−0.659597	−	0.751620i	$-0.729273\pi$
$821$	−37.7990			−1.31919			−0.659597	+	0.751620i	$0.729273\pi$
$822$		0			0
$823$	−17.2426	+	29.8651i	−0.601041	+	1.04103i	0.391623	+	0.920126i	$0.371914\pi$
$823$	−17.2426	+	29.8651i	−0.601041	+	1.04103i	−0.992664	+	0.120907i	$0.961420\pi$
$824$		0			0
$825$	3.29289	−	5.70346i	0.114644	−	0.198569i
$826$		0			0
$827$	−21.3640	−	37.0035i	−0.742898	−	1.28674i	−0.951171	−	0.308666i	$-0.900118\pi$
$827$	−21.3640	−	37.0035i	−0.742898	−	1.28674i	0.208273	−	0.978071i	$-0.433216\pi$
$828$		0			0
$829$	14.9411			0.518927			0.259463	−	0.965753i	$-0.416454\pi$
$829$	14.9411			0.518927			0.259463	+	0.965753i	$0.416454\pi$
$830$		0			0
$831$	−5.67157	+	9.82345i	−0.196745	+	0.340772i
$832$		0			0
$833$	−43.1127			−1.49377
$834$		0			0
$835$	6.97056			0.241226
$836$		0			0
$837$	−2.00000	+	5.19615i	−0.0691301	+	0.179605i
$838$		0			0
$839$	−7.11270			−0.245558			−0.122779	−	0.992434i	$-0.539181\pi$
$839$	−7.11270			−0.245558			−0.122779	+	0.992434i	$0.539181\pi$
$840$		0			0
$841$	−17.3431			−0.598040
$842$		0			0
$843$	10.0208	−	17.3566i	0.345135	−	0.597792i
$844$		0			0
$845$	5.65685			0.194602
$846$		0			0
$847$	−3.72792	−	6.45695i	−0.128093	−	0.221863i
$848$		0			0
$849$	7.74264	−	13.4106i	0.265727	−	0.460252i
$850$		0			0
$851$	1.82843	−	3.16693i	0.0626777	−	0.108561i
$852$		0			0
$853$	9.62742			0.329636			0.164818	−	0.986324i	$-0.447296\pi$
$853$	9.62742			0.329636			0.164818	+	0.986324i	$0.447296\pi$
$854$		0			0
$855$	1.12132	+	1.94218i	0.0383483	+	0.0664213i
$856$		0			0
$857$	6.34315	+	10.9867i	0.216678	+	0.375297i	0.953790	−	0.300473i	$-0.0971446\pi$
$857$	6.34315	+	10.9867i	0.216678	+	0.375297i	−0.737113	+	0.675770i	$0.763811\pi$
$858$		0			0
$859$	22.8137	+	39.5145i	0.778394	+	1.34822i	0.932867	+	0.360220i	$0.117299\pi$
$859$	22.8137	+	39.5145i	0.778394	+	1.34822i	−0.154474	+	0.987997i	$0.549368\pi$
$860$		0			0
$861$	−1.75736	+	3.04384i	−0.0598906	+	0.103734i
$862$		0			0
$863$	−6.94975	−	12.0373i	−0.236572	−	0.409755i	0.723156	−	0.690684i	$-0.242691\pi$
$863$	−6.94975	−	12.0373i	−0.236572	−	0.409755i	−0.959728	+	0.280929i	$0.909357\pi$
$864$		0			0
$865$	2.72792	−	4.72490i	0.0927521	−	0.160651i
$866$		0			0
$867$	29.6274			1.00620
$868$		0			0
$869$	−22.1421			−0.751121
$870$		0			0
$871$	−13.2426	+	22.9369i	−0.448710	+	0.777188i
$872$		0			0
$873$	5.74264	+	9.94655i	0.194359	+	0.336640i
$874$		0			0
$875$	2.34315	−	4.05845i	0.0792128	−	0.137201i
$876$		0			0
$877$	14.7426	+	25.5350i	0.497824	+	0.862256i	0.999997	−	0.00251127i	$-0.000799362\pi$
$877$	14.7426	+	25.5350i	0.497824	+	0.862256i	−0.502173	+	0.864767i	$0.667466\pi$
$878$		0			0
$879$	−6.41421	−	11.1097i	−0.216346	−	0.374722i
$880$		0			0
$881$	−0.313708	−	0.543359i	−0.0105691	−	0.0183062i	0.860692	−	0.509125i	$-0.170031\pi$
$881$	−0.313708	−	0.543359i	−0.0105691	−	0.0183062i	−0.871262	+	0.490819i	$0.836698\pi$
$882$		0			0
$883$	36.9411			1.24317			0.621584	−	0.783348i	$-0.286489\pi$
$883$	36.9411			1.24317			0.621584	+	0.783348i	$0.286489\pi$
$884$		0			0
$885$	2.48528	−	4.30463i	0.0835418	−	0.144699i
$886$		0			0
$887$	8.12132	−	14.0665i	0.272687	−	0.472308i	−0.696862	−	0.717205i	$-0.745421\pi$
$887$	8.12132	−	14.0665i	0.272687	−	0.472308i	0.969549	+	0.244897i	$0.0787542\pi$
$888$		0			0
$889$	−2.21320	−	3.83338i	−0.0742285	−	0.128567i
$890$		0			0
$891$	1.41421			0.0473779
$892$		0			0
$893$	1.12132	−	1.94218i	0.0375236	−	0.0649927i
$894$		0			0
$895$	−8.05887			−0.269378
$896$		0			0
$897$	−6.68629			−0.223249
$898$		0			0
$899$	6.82843	−	17.7408i	0.227741	−	0.591688i
$900$		0			0
$901$	−9.65685			−0.321716
$902$		0			0
$903$	−4.54416			−0.151220
$904$		0			0
$905$	0.150758	−	0.261120i	0.00501135	−	0.00867992i
$906$		0			0
$907$	25.5147			0.847202			0.423601	−	0.905849i	$-0.360766\pi$
$907$	25.5147			0.847202			0.423601	+	0.905849i	$0.360766\pi$
$908$		0			0
$909$	7.70711	+	13.3491i	0.255629	+	0.442762i
$910$		0			0
$911$	−14.8284	+	25.6836i	−0.491288	+	0.850935i	−0.999950	−	0.0100310i	$-0.996807\pi$
$911$	−14.8284	+	25.6836i	−0.491288	+	0.850935i	0.508662	+	0.860966i	$0.330140\pi$
$912$		0			0
$913$	−5.24264	+	9.08052i	−0.173506	+	0.300521i
$914$		0			0
$915$	7.31371			0.241784
$916$		0			0
$917$	6.72792	+	11.6531i	0.222176	+	0.384819i
$918$		0			0
$919$	−14.7426	−	25.5350i	−0.486315	−	0.842322i	0.513561	−	0.858053i	$-0.328326\pi$
$919$	−14.7426	−	25.5350i	−0.486315	−	0.842322i	−0.999876	+	0.0157308i	$0.994993\pi$
$920$		0			0
$921$	3.84315	+	6.65652i	0.126636	+	0.219340i
$922$		0			0
$923$	5.48528	−	9.50079i	0.180550	−	0.312722i
$924$		0			0
$925$	2.32843	+	4.03295i	0.0765582	+	0.132603i
$926$		0			0
$927$	8.15685	−	14.1281i	0.267906	−	0.464027i
$928$		0			0
$929$	−0.343146			−0.0112582			−0.00562912	−	0.999984i	$-0.501792\pi$
$929$	−0.343146			−0.0112582			−0.00562912	+	0.999984i	$0.501792\pi$
$930$		0			0
$931$	−24.1716			−0.792191
$932$		0			0
$933$	−9.94975	+	17.2335i	−0.325740	+	0.564198i
$934$		0			0
$935$	2.82843	+	4.89898i	0.0924995	+	0.160214i
$936$		0			0
$937$	11.7426	−	20.3389i	0.383615	−	0.664441i	−0.607961	−	0.793967i	$-0.708012\pi$
$937$	11.7426	−	20.3389i	0.383615	−	0.664441i	0.991576	+	0.129526i	$0.0413455\pi$
$938$		0			0
$939$	2.84315	+	4.92447i	0.0927826	+	0.160704i
$940$		0			0
$941$	−13.0711	−	22.6398i	−0.426105	−	0.738035i	0.570418	−	0.821354i	$-0.306781\pi$
$941$	−13.0711	−	22.6398i	−0.426105	−	0.738035i	−0.996523	+	0.0833195i	$0.973448\pi$
$942$		0			0
$943$	−7.75736	−	13.4361i	−0.252614	−	0.437541i
$944$		0			0
$945$	0.485281			0.0157862
$946$		0			0
$947$	−17.3848	+	30.1113i	−0.564929	+	0.978486i	0.432127	+	0.901813i	$0.357763\pi$
$947$	−17.3848	+	30.1113i	−0.564929	+	0.978486i	−0.997056	+	0.0766735i	$0.975570\pi$
$948$		0			0
$949$	−3.50000	+	6.06218i	−0.113615	+	0.196787i
$950$		0			0
$951$	11.1213	+	19.2627i	0.360634	+	0.624636i
$952$		0			0
$953$	11.8995			0.385462			0.192731	−	0.981252i	$-0.438265\pi$
$953$	11.8995			0.385462			0.192731	+	0.981252i	$0.438265\pi$
$954$		0			0
$955$	0.899495	−	1.55797i	0.0291070	−	0.0504148i
$956$		0			0
$957$	−4.82843			−0.156081
$958$		0			0
$959$	12.7696			0.412350
$960$		0			0
$961$	−23.0000	−	20.7846i	−0.741935	−	0.670471i
$962$		0			0
$963$	−3.89949			−0.125659
$964$		0			0
$965$	−8.18377			−0.263445
$966$		0			0
$967$	−5.97056	+	10.3413i	−0.192000	+	0.332554i	−0.945913	−	0.324420i	$-0.894831\pi$
$967$	−5.97056	+	10.3413i	−0.192000	+	0.332554i	0.753913	+	0.656975i	$0.228164\pi$
$968$		0			0
$969$	26.1421			0.839806
$970$		0			0
$971$	19.9706	+	34.5900i	0.640886	+	1.11005i	0.985235	+	0.171205i	$0.0547662\pi$
$971$	19.9706	+	34.5900i	0.640886	+	1.11005i	−0.344350	+	0.938842i	$0.611901\pi$
$972$		0			0
$973$	−5.79899	+	10.0441i	−0.185907	+	0.322001i
$974$		0			0
$975$	4.25736	−	7.37396i	0.136345	−	0.236156i
$976$		0			0
$977$	12.0000			0.383914			0.191957	−	0.981403i	$-0.438517\pi$
$977$	12.0000			0.383914			0.191957	+	0.981403i	$0.438517\pi$
$978$		0			0
$979$	12.6569	+	21.9223i	0.404515	+	0.700640i
$980$		0			0
$981$	−4.74264	−	8.21449i	−0.151421	−	0.262269i
$982$		0			0
$983$	−29.0416	−	50.3016i	−0.926284	−	1.60437i	−0.789483	−	0.613773i	$-0.789651\pi$
$983$	−29.0416	−	50.3016i	−0.926284	−	1.60437i	−0.136801	−	0.990598i	$-0.543682\pi$
$984$		0			0
$985$	0.828427	−	1.43488i	0.0263959	−	0.0457190i
$986$		0			0
$987$	−0.242641	−	0.420266i	−0.00772334	−	0.0133772i
$988$		0			0
$989$	10.0294	−	17.3715i	0.318918	−	0.552381i
$990$		0			0
$991$	−45.1421			−1.43399			−0.716994	−	0.697080i	$-0.754482\pi$
$991$	−45.1421			−1.43399			−0.716994	+	0.697080i	$0.754482\pi$
$992$		0			0
$993$	−3.00000			−0.0952021
$994$		0			0
$995$	3.55635	−	6.15978i	0.112744	−	0.195278i
$996$		0			0
$997$	9.51472	+	16.4800i	0.301334	+	0.521926i	0.976438	−	0.215796i	$-0.0692347\pi$
$997$	9.51472	+	16.4800i	0.301334	+	0.521926i	−0.675104	+	0.737722i	$0.735901\pi$
$998$		0			0
$999$	−0.500000	+	0.866025i	−0.0158193	+	0.0273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1488.2.q.g.625.1		4
4.3	odd	2		93.2.e.a.67.2	yes	4
12.11	even	2		279.2.h.b.253.1		4
31.25	even	3	inner	1488.2.q.g.769.1		4
124.67	odd	6		2883.2.a.b.1.2		2
124.87	odd	6		93.2.e.a.25.2	✓	4
124.119	even	6		2883.2.a.c.1.2		2
372.119	odd	6		8649.2.a.i.1.1		2
372.191	even	6		8649.2.a.h.1.1		2
372.335	even	6		279.2.h.b.118.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.e.a.25.2	✓	4	124.87	odd	6
93.2.e.a.67.2	yes	4	4.3	odd	2
279.2.h.b.118.1		4	372.335	even	6
279.2.h.b.253.1		4	12.11	even	2
1488.2.q.g.625.1		4	1.1	even	1	trivial
1488.2.q.g.769.1		4	31.25	even	3	inner
2883.2.a.b.1.2		2	124.67	odd	6
2883.2.a.c.1.2		2	124.119	even	6
8649.2.a.h.1.1		2	372.191	even	6
8649.2.a.i.1.1		2	372.119	odd	6

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:	\( N \)	\(=\)	\( 1488 = 2^{4} \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1488.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(0.292893 + 0.507306i) q^{5} +(0.414214 - 0.717439i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-0.707107 - 1.22474i) q^{11} +(-0.914214 - 1.58346i) q^{13} -0.585786 q^{15} +(-3.41421 + 5.91359i) q^{17} +(-1.91421 + 3.31552i) q^{19} +(0.414214 + 0.717439i) q^{21} -3.65685 q^{23} +(2.32843 - 4.03295i) q^{25} +1.00000 q^{27} -3.41421 q^{29} +(-2.00000 + 5.19615i) q^{31} +1.41421 q^{33} +0.485281 q^{35} +(-0.500000 + 0.866025i) q^{37} +1.82843 q^{39} +(2.12132 + 3.67423i) q^{41} +(-2.74264 + 4.75039i) q^{43} +(0.292893 - 0.507306i) q^{45} -0.585786 q^{47} +(3.15685 + 5.46783i) q^{49} +(-3.41421 - 5.91359i) q^{51} +(0.707107 + 1.22474i) q^{53} +(0.414214 - 0.717439i) q^{55} +(-1.91421 - 3.31552i) q^{57} +(-4.24264 + 7.34847i) q^{59} -12.4853 q^{61} -0.828427 q^{63} +(0.535534 - 0.927572i) q^{65} +(-7.24264 - 12.5446i) q^{67} +(1.82843 - 3.16693i) q^{69} +(3.00000 + 5.19615i) q^{71} +(-1.91421 - 3.31552i) q^{73} +(2.32843 + 4.03295i) q^{75} -1.17157 q^{77} +(7.82843 - 13.5592i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-3.70711 - 6.42090i) q^{83} -4.00000 q^{85} +(1.70711 - 2.95680i) q^{87} -17.8995 q^{89} -1.51472 q^{91} +(-3.50000 - 4.33013i) q^{93} -2.24264 q^{95} -11.4853 q^{97} +(-0.707107 + 1.22474i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 4 q^{5} - 4 q^{7} - 2 q^{9} + 2 q^{13} - 8 q^{15} - 8 q^{17} - 2 q^{19} - 4 q^{21} + 8 q^{23} - 2 q^{25} + 4 q^{27} - 8 q^{29} - 8 q^{31} - 32 q^{35} - 2 q^{37} - 4 q^{39} + 6 q^{43} + 4 q^{45}+ \cdots - 12 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 + 4 * q^5 - 4 * q^7 - 2 * q^9 + 2 * q^13 - 8 * q^15 - 8 * q^17 - 2 * q^19 - 4 * q^21 + 8 * q^23 - 2 * q^25 + 4 * q^27 - 8 * q^29 - 8 * q^31 - 32 * q^35 - 2 * q^37 - 4 * q^39 + 6 * q^43 + 4 * q^45 - 8 * q^47 - 10 * q^49 - 8 * q^51 - 4 * q^55 - 2 * q^57 - 16 * q^61 + 8 * q^63 - 12 * q^65 - 12 * q^67 - 4 * q^69 + 12 * q^71 - 2 * q^73 - 2 * q^75 - 16 * q^77 + 20 * q^79 - 2 * q^81 - 12 * q^83 - 16 * q^85 + 4 * q^87 - 32 * q^89 - 40 * q^91 - 14 * q^93 + 8 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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