LMFDB - Embedded newform 279.2.h.b.253.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [279,2,Mod(118,279)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(279, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("279.118"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 279 = 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	279.h (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.22782621639$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 93)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			253.1
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	279.253
Dual form			279.2.h.b.118.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.41421 q^{2} +(-0.292893 - 0.507306i) q^{5} +(-0.414214 + 0.717439i) q^{7} +2.82843 q^{8} +(0.414214 + 0.717439i) q^{10} +(-0.707107 - 1.22474i) q^{11} +(-0.914214 - 1.58346i) q^{13} +(0.585786 - 1.01461i) q^{14} -4.00000 q^{16} +(3.41421 - 5.91359i) q^{17} +(1.91421 - 3.31552i) q^{19} +(1.00000 + 1.73205i) q^{22} -3.65685 q^{23} +(2.32843 - 4.03295i) q^{25} +(1.29289 + 2.23936i) q^{26} +3.41421 q^{29} +(2.00000 - 5.19615i) q^{31} +(-4.82843 + 8.36308i) q^{34} +0.485281 q^{35} +(-0.500000 + 0.866025i) q^{37} +(-2.70711 + 4.68885i) q^{38} +(-0.828427 - 1.43488i) q^{40} +(-2.12132 - 3.67423i) q^{41} +(2.74264 - 4.75039i) q^{43} +5.17157 q^{46} -0.585786 q^{47} +(3.15685 + 5.46783i) q^{49} +(-3.29289 + 5.70346i) q^{50} +(-0.707107 - 1.22474i) q^{53} +(-0.414214 + 0.717439i) q^{55} +(-1.17157 + 2.02922i) q^{56} -4.82843 q^{58} +(-4.24264 + 7.34847i) q^{59} -12.4853 q^{61} +(-2.82843 + 7.34847i) q^{62} +8.00000 q^{64} +(-0.535534 + 0.927572i) q^{65} +(7.24264 + 12.5446i) q^{67} -0.686292 q^{70} +(3.00000 + 5.19615i) q^{71} +(-1.91421 - 3.31552i) q^{73} +(0.707107 - 1.22474i) q^{74} +1.17157 q^{77} +(-7.82843 + 13.5592i) q^{79} +(1.17157 + 2.02922i) q^{80} +(3.00000 + 5.19615i) q^{82} +(-3.70711 - 6.42090i) q^{83} -4.00000 q^{85} +(-3.87868 + 6.71807i) q^{86} +(-2.00000 - 3.46410i) q^{88} +17.8995 q^{89} +1.51472 q^{91} +0.828427 q^{94} -2.24264 q^{95} -11.4853 q^{97} +(-4.46447 - 7.73268i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{5} + 4 q^{7} - 4 q^{10} + 2 q^{13} + 8 q^{14} - 16 q^{16} + 8 q^{17} + 2 q^{19} + 4 q^{22} + 8 q^{23} - 2 q^{25} + 8 q^{26} + 8 q^{29} + 8 q^{31} - 8 q^{34} - 32 q^{35} - 2 q^{37} - 8 q^{38}+ \cdots - 32 q^{98}+O(q^{100}) $ 4 * q - 4 * q^5 + 4 * q^7 - 4 * q^10 + 2 * q^13 + 8 * q^14 - 16 * q^16 + 8 * q^17 + 2 * q^19 + 4 * q^22 + 8 * q^23 - 2 * q^25 + 8 * q^26 + 8 * q^29 + 8 * q^31 - 8 * q^34 - 32 * q^35 - 2 * q^37 - 8 * q^38 + 8 * q^40 - 6 * q^43 + 32 * q^46 - 8 * q^47 - 10 * q^49 - 16 * q^50 + 4 * q^55 - 16 * q^56 - 8 * q^58 - 16 * q^61 + 32 * q^64 + 12 * q^65 + 12 * q^67 - 48 * q^70 + 12 * q^71 - 2 * q^73 + 16 * q^77 - 20 * q^79 + 16 * q^80 + 12 * q^82 - 12 * q^83 - 16 * q^85 - 24 * q^86 - 8 * q^88 + 32 * q^89 + 40 * q^91 - 8 * q^94 + 8 * q^95 - 12 * q^97 - 32 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/279\mathbb{Z}\right)^\times$.

$n$	$127$	$218$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.41421			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$2$	−1.41421			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.292893	−	0.507306i	−0.130986	−	0.226874i	0.793071	−	0.609129i	$-0.208481\pi$
$5$	−0.292893	−	0.507306i	−0.130986	−	0.226874i	−0.924057	+	0.382255i	$0.875148\pi$
$6$		0			0
$7$	−0.414214	+	0.717439i	−0.156558	+	0.271166i	−0.933625	−	0.358251i	$-0.883373\pi$
$7$	−0.414214	+	0.717439i	−0.156558	+	0.271166i	0.777067	+	0.629418i	$0.216706\pi$
$8$	2.82843			1.00000
$9$		0			0
$10$	0.414214	+	0.717439i	0.130986	+	0.226874i
$11$	−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	$0.914934\pi$
$14$	0.585786	−	1.01461i	0.156558	−	0.271166i
$15$		0			0
$16$	−4.00000			−1.00000
$17$	3.41421	−	5.91359i	0.828068	−	1.43426i	−0.0714831	−	0.997442i	$-0.522773\pi$
$17$	3.41421	−	5.91359i	0.828068	−	1.43426i	0.899551	−	0.436815i	$-0.143893\pi$
$18$		0			0
$19$	1.91421	−	3.31552i	0.439151	−	0.760631i	−0.558473	−	0.829522i	$-0.688613\pi$
$19$	1.91421	−	3.31552i	0.439151	−	0.760631i	0.997624	+	0.0688910i	$0.0219461\pi$
$20$		0			0
$21$		0			0
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$	−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
$26$	1.29289	+	2.23936i	0.253557	+	0.439174i
$27$		0			0
$28$		0			0
$29$	3.41421			0.634004			0.317002	−	0.948425i	$-0.397324\pi$
$29$	3.41421			0.634004			0.317002	+	0.948425i	$0.397324\pi$
$30$		0			0
$31$	2.00000	−	5.19615i	0.359211	−	0.933257i
$31$	2.00000	−	5.19615i	0.359211	−	0.933257i
$32$		0			0
$33$		0			0
$34$	−4.82843	+	8.36308i	−0.828068	+	1.43426i
$35$	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	$0.192861\pi$
$38$	−2.70711	+	4.68885i	−0.439151	+	0.760631i
$39$		0			0
$40$	−0.828427	−	1.43488i	−0.130986	−	0.226874i
$41$	−2.12132	−	3.67423i	−0.331295	−	0.573819i	0.651471	−	0.758673i	$-0.274152\pi$
$41$	−2.12132	−	3.67423i	−0.331295	−	0.573819i	−0.982766	+	0.184854i	$0.940819\pi$
$42$		0			0
$43$	2.74264	−	4.75039i	0.418249	−	0.724428i	−0.577515	−	0.816380i	$-0.695977\pi$
$43$	2.74264	−	4.75039i	0.418249	−	0.724428i	0.995763	+	0.0919522i	$0.0293107\pi$
$44$		0			0
$45$		0			0
$46$	5.17157			0.762507
$47$	−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
$50$	−3.29289	+	5.70346i	−0.465685	+	0.806591i
$51$		0			0
$52$		0			0
$53$	−0.707107	−	1.22474i	−0.0971286	−	0.168232i	0.813366	−	0.581752i	$-0.197632\pi$
$53$	−0.707107	−	1.22474i	−0.0971286	−	0.168232i	−0.910495	+	0.413520i	$0.864299\pi$
$54$		0			0
$55$	−0.414214	+	0.717439i	−0.0558525	+	0.0967394i
$56$	−1.17157	+	2.02922i	−0.156558	+	0.271166i
$57$		0			0
$58$	−4.82843			−0.634004
$59$	−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	$0.794790\pi$
$62$	−2.82843	+	7.34847i	−0.359211	+	0.933257i
$63$		0			0
$64$	8.00000			1.00000
$65$	−0.535534	+	0.927572i	−0.0664248	+	0.115051i
$66$		0			0
$67$	7.24264	+	12.5446i	0.884829	+	1.53257i	0.845909	+	0.533327i	$0.179059\pi$
$67$	7.24264	+	12.5446i	0.884829	+	1.53257i	0.0389203	+	0.999242i	$0.487608\pi$
$68$		0			0
$69$		0			0
$70$	−0.686292			−0.0820275
$71$	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	$0.905259\pi$
$74$	0.707107	−	1.22474i	0.0821995	−	0.142374i
$75$		0			0
$76$		0			0
$77$	1.17157			0.133513
$78$		0			0
$79$	−7.82843	+	13.5592i	−0.880767	+	1.52553i	−0.0302770	+	0.999542i	$0.509639\pi$
$79$	−7.82843	+	13.5592i	−0.880767	+	1.52553i	−0.850490	+	0.525991i	$0.823694\pi$
$80$	1.17157	+	2.02922i	0.130986	+	0.226874i
$81$		0			0
$82$	3.00000	+	5.19615i	0.331295	+	0.573819i
$83$	−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
$86$	−3.87868	+	6.71807i	−0.418249	+	0.724428i
$87$		0			0
$88$	−2.00000	−	3.46410i	−0.213201	−	0.369274i
$89$	17.8995			1.89734			0.948671	−	0.316264i	$-0.102428\pi$
$89$	17.8995			1.89734			0.948671	+	0.316264i	$0.102428\pi$
$90$		0			0
$91$	1.51472			0.158786
$92$		0			0
$93$		0			0
$94$	0.828427			0.0854457
$95$	−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	$0.698151\pi$
$98$	−4.46447	−	7.73268i	−0.450979	−	0.781119i
$99$		0			0
$100$		0			0
$101$	15.4142			1.53377			0.766886	−	0.641784i	$-0.221805\pi$
$101$	15.4142			1.53377			0.766886	+	0.641784i	$0.221805\pi$
$102$		0			0
$103$	−8.15685	−	14.1281i	−0.803719	−	1.39208i	−0.917153	−	0.398536i	$-0.869518\pi$
$103$	−8.15685	−	14.1281i	−0.803719	−	1.39208i	0.113434	−	0.993546i	$-0.463815\pi$
$104$	−2.58579	−	4.47871i	−0.253557	−	0.439174i
$105$		0			0
$106$	1.00000	+	1.73205i	0.0971286	+	0.168232i
$107$	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	$0.349903\pi$
$110$	0.585786	−	1.01461i	0.0558525	−	0.0967394i
$111$		0			0
$112$	1.65685	−	2.86976i	0.156558	−	0.271166i
$113$	−7.82843	−	13.5592i	−0.736436	−	1.27555i	−0.954090	−	0.299519i	$-0.903174\pi$
$113$	−7.82843	−	13.5592i	−0.736436	−	1.27555i	0.217654	−	0.976026i	$-0.430160\pi$
$114$		0			0
$115$	1.07107	+	1.85514i	0.0998776	+	0.172993i
$116$		0			0
$117$		0			0
$118$	6.00000	−	10.3923i	0.552345	−	0.956689i
$119$	2.82843	+	4.89898i	0.259281	+	0.449089i
$120$		0			0
$121$	4.50000	−	7.79423i	0.409091	−	0.708566i
$122$	17.6569			1.59858
$123$		0			0
$124$		0			0
$125$	−5.65685			−0.505964
$126$		0			0
$127$	−2.67157	+	4.62730i	−0.237064	+	0.410606i	−0.959870	−	0.280444i	$-0.909518\pi$
$127$	−2.67157	+	4.62730i	−0.237064	+	0.410606i	0.722807	+	0.691050i	$0.242852\pi$
$128$	−11.3137			−1.00000
$129$		0			0
$130$	0.757359	−	1.31178i	0.0664248	−	0.115051i
$131$	−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
$134$	−10.2426	−	17.7408i	−0.884829	−	1.53257i
$135$		0			0
$136$	9.65685	−	16.7262i	0.828068	−	1.43426i
$137$	−7.70711	−	13.3491i	−0.658463	−	1.14049i	−0.981014	−	0.193939i	$-0.937874\pi$
$137$	−7.70711	−	13.3491i	−0.658463	−	1.14049i	0.322551	−	0.946552i	$-0.395460\pi$
$138$		0			0
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$		0			0
$141$		0			0
$142$	−4.24264	−	7.34847i	−0.356034	−	0.616670i
$143$	−1.29289	+	2.23936i	−0.108117	+	0.187264i
$144$		0			0
$145$	−1.00000	−	1.73205i	−0.0830455	−	0.143839i
$146$	2.70711	+	4.68885i	0.224042	+	0.388052i
$147$		0			0
$148$		0			0
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$		0			0
$151$	6.31371			0.513802			0.256901	−	0.966438i	$-0.417299\pi$
$151$	6.31371			0.513802			0.256901	+	0.966438i	$0.417299\pi$
$152$	5.41421	−	9.37769i	0.439151	−	0.760631i
$153$		0			0
$154$	−1.65685			−0.133513
$155$	−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	$0.398871\pi$
$158$	11.0711	−	19.1757i	0.880767	−	1.52553i
$159$		0			0
$160$		0			0
$161$	1.51472	−	2.62357i	0.119377	−	0.206766i
$162$		0			0
$163$	−4.65685			−0.364753			−0.182376	−	0.983229i	$-0.558379\pi$
$163$	−4.65685			−0.364753			−0.182376	+	0.983229i	$0.558379\pi$
$164$		0			0
$165$		0			0
$166$	5.24264	+	9.08052i	0.406908	+	0.704785i
$167$	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
$170$	5.65685			0.433861
$171$		0			0
$172$		0			0
$173$	4.65685	+	8.06591i	0.354054	+	0.613240i	0.986956	−	0.160993i	$-0.0514695\pi$
$173$	4.65685	+	8.06591i	0.354054	+	0.613240i	−0.632902	+	0.774232i	$0.718136\pi$
$174$		0			0
$175$	1.92893	+	3.34101i	0.145814	+	0.252557i
$176$	2.82843	+	4.89898i	0.213201	+	0.369274i
$177$		0			0
$178$	−25.3137			−1.89734
$179$	−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	$0.839423\pi$
$182$	−2.14214			−0.158786
$183$		0			0
$184$	−10.3431			−0.762507
$185$	0.585786			0.0430679
$186$		0			0
$187$	−9.65685			−0.706179
$188$		0			0
$189$		0			0
$190$	3.17157			0.230090
$191$	−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	$0.998966\pi$
$194$	16.2426			1.16615
$195$		0			0
$196$		0			0
$197$	1.41421	+	2.44949i	0.100759	+	0.174519i	0.911997	−	0.410196i	$-0.134540\pi$
$197$	1.41421	+	2.44949i	0.100759	+	0.174519i	−0.811239	+	0.584715i	$0.801206\pi$
$198$		0			0
$199$	6.07107	+	10.5154i	0.430367	+	0.745417i	0.996905	−	0.0786187i	$-0.0250510\pi$
$199$	6.07107	+	10.5154i	0.430367	+	0.745417i	−0.566538	+	0.824035i	$0.691718\pi$
$200$	6.58579	−	11.4069i	0.465685	−	0.806591i
$201$		0			0
$202$	−21.7990			−1.53377
$203$	−1.41421	+	2.44949i	−0.0992583	+	0.171920i
$204$		0			0
$205$	−1.24264	+	2.15232i	−0.0867898	+	0.150324i
$206$	11.5355	+	19.9801i	0.803719	+	1.39208i
$207$		0			0
$208$	3.65685	+	6.33386i	0.253557	+	0.439174i
$209$	−5.41421			−0.374509
$210$		0			0
$211$	2.74264	−	4.75039i	0.188811	−	0.327031i	−0.756043	−	0.654522i	$-0.772870\pi$
$211$	2.74264	−	4.75039i	0.188811	−	0.327031i	0.944854	+	0.327491i	$0.106203\pi$
$212$		0			0
$213$		0			0
$214$	−2.75736	+	4.77589i	−0.188489	+	0.326473i
$215$	−3.21320			−0.219139
$216$		0			0
$217$	2.89949	+	3.58719i	0.196831	+	0.243515i
$218$	−13.4142			−0.908525
$219$		0			0
$220$		0			0
$221$	−12.4853			−0.839851
$222$		0			0
$223$	−8.32843	+	14.4253i	−0.557713	+	0.965987i	0.439974	+	0.898010i	$0.354988\pi$
$223$	−8.32843	+	14.4253i	−0.557713	+	0.965987i	−0.997687	+	0.0679764i	$0.978346\pi$
$224$		0			0
$225$		0			0
$226$	11.0711	+	19.1757i	0.736436	+	1.27555i
$227$	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	$0.0427681\pi$
$230$	−1.51472	−	2.62357i	−0.0998776	−	0.172993i
$231$		0			0
$232$	9.65685			0.634004
$233$	−24.0000			−1.57229			−0.786146	−	0.618041i	$-0.787927\pi$
$233$	−24.0000			−1.57229			−0.786146	+	0.618041i	$0.787927\pi$
$234$		0			0
$235$	0.171573	+	0.297173i	0.0111922	+	0.0193854i
$236$		0			0
$237$		0			0
$238$	−4.00000	−	6.92820i	−0.259281	−	0.449089i
$239$	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	$0.105072\pi$
$242$	−6.36396	+	11.0227i	−0.409091	+	0.708566i
$243$		0			0
$244$		0			0
$245$	1.84924	−	3.20298i	0.118144	−	0.204631i
$246$		0			0
$247$	−7.00000			−0.445399
$248$	5.65685	−	14.6969i	0.359211	−	0.933257i
$249$		0			0
$250$	8.00000			0.505964
$251$	−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
$254$	3.77817	−	6.54399i	0.237064	−	0.410606i
$255$		0			0
$256$		0			0
$257$	5.12132	+	8.87039i	0.319459	+	0.553320i	0.980375	−	0.197140i	$-0.0631654\pi$
$257$	5.12132	+	8.87039i	0.319459	+	0.553320i	−0.660916	+	0.750460i	$0.729832\pi$
$258$		0			0
$259$	−0.414214	−	0.717439i	−0.0257380	−	0.0445795i
$260$		0			0
$261$		0			0
$262$	11.4853	−	19.8931i	0.709563	−	1.22900i
$263$	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
$266$	−2.24264	−	3.88437i	−0.137505	−	0.238166i
$267$		0			0
$268$		0			0
$269$	−9.89949	−	17.1464i	−0.603583	−	1.04544i	−0.992274	−	0.124068i	$-0.960406\pi$
$269$	−9.89949	−	17.1464i	−0.603583	−	1.04544i	0.388691	−	0.921368i	$-0.372927\pi$
$270$		0			0
$271$	−28.4558			−1.72857			−0.864285	−	0.503003i	$-0.832228\pi$
$271$	−28.4558			−1.72857			−0.864285	+	0.503003i	$0.832228\pi$
$272$	−13.6569	+	23.6544i	−0.828068	+	1.43426i
$273$		0			0
$274$	10.8995	+	18.8785i	0.658463	+	1.14049i
$275$	−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	$0.389312\pi$
$278$	−19.7990			−1.18746
$279$		0			0
$280$	1.37258			0.0820275
$281$	20.0416			1.19558			0.597792	−	0.801651i	$-0.296045\pi$
$281$	20.0416			1.19558			0.597792	+	0.801651i	$0.296045\pi$
$282$		0			0
$283$	15.4853			0.920504			0.460252	−	0.887788i	$-0.347759\pi$
$283$	15.4853			0.920504			0.460252	+	0.887788i	$0.347759\pi$
$284$		0			0
$285$		0			0
$286$	1.82843	−	3.16693i	0.108117	−	0.187264i
$287$	3.51472			0.207467
$288$		0			0
$289$	−14.8137	−	25.6581i	−0.871395	−	1.50930i
$290$	1.41421	+	2.44949i	0.0830455	+	0.143839i
$291$		0			0
$292$		0			0
$293$	6.41421	−	11.1097i	0.374722	−	0.649038i	−0.615563	−	0.788088i	$-0.711071\pi$
$293$	6.41421	−	11.1097i	0.374722	−	0.649038i	0.990285	+	0.139049i	$0.0444047\pi$
$294$		0			0
$295$	4.97056			0.289397
$296$	−1.41421	+	2.44949i	−0.0821995	+	0.142374i
$297$		0			0
$298$	4.24264	−	7.34847i	0.245770	−	0.425685i
$299$	3.34315	+	5.79050i	0.193339	+	0.334873i
$300$		0			0
$301$	2.27208	+	3.93535i	0.130960	+	0.226830i
$302$	−8.92893			−0.513802
$303$		0			0
$304$	−7.65685	+	13.2621i	−0.439151	+	0.760631i
$305$	3.65685	+	6.33386i	0.209391	+	0.362676i
$306$		0			0
$307$	−3.84315	+	6.65652i	−0.219340	+	0.379908i	−0.954606	−	0.297870i	$-0.903724\pi$
$307$	−3.84315	+	6.65652i	−0.219340	+	0.379908i	0.735266	+	0.677778i	$0.237057\pi$
$308$		0			0
$309$		0			0
$310$	4.55635	−	0.717439i	0.258783	−	0.0407478i
$311$	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	$0.115290\pi$
$314$	−11.0711			−0.624777
$315$		0			0
$316$		0			0
$317$	−11.1213	+	19.2627i	−0.624636	+	1.08190i	0.363976	+	0.931408i	$0.381419\pi$
$317$	−11.1213	+	19.2627i	−0.624636	+	1.08190i	−0.988611	+	0.150492i	$0.951914\pi$
$318$		0			0
$319$	−2.41421	−	4.18154i	−0.135170	−	0.234121i
$320$	−2.34315	−	4.05845i	−0.130986	−	0.226874i
$321$		0			0
$322$	−2.14214	+	3.71029i	−0.119377	+	0.206766i
$323$	−13.0711	−	22.6398i	−0.727294	−	1.25971i
$324$		0			0
$325$	−8.51472			−0.472312
$326$	6.58579			0.364753
$327$		0			0
$328$	−6.00000	−	10.3923i	−0.331295	−	0.573819i
$329$	0.242641	−	0.420266i	0.0133772	−	0.0231700i
$330$		0			0
$331$	−1.50000	−	2.59808i	−0.0824475	−	0.142803i	0.821853	−	0.569699i	$-0.192940\pi$
$331$	−1.50000	−	2.59808i	−0.0824475	−	0.142803i	−0.904301	+	0.426896i	$0.859607\pi$
$332$		0			0
$333$		0			0
$334$	−8.41421	+	14.5738i	−0.460405	+	0.797445i
$335$	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	$0.330625\pi$
$338$	−6.82843	+	11.8272i	−0.371417	+	0.643314i
$339$		0			0
$340$		0			0
$341$	−7.77817	+	1.22474i	−0.421212	+	0.0663237i
$342$		0			0
$343$	−11.0294			−0.595534
$344$	7.75736	−	13.4361i	0.418249	−	0.724428i
$345$		0			0
$346$	−6.58579	−	11.4069i	−0.354054	−	0.613240i
$347$	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	$0.152765\pi$
$350$	−2.72792	−	4.72490i	−0.145814	−	0.252557i
$351$		0			0
$352$		0			0
$353$	13.5858	−	23.5313i	0.723098	−	1.25244i	−0.236653	−	0.971594i	$-0.576051\pi$
$353$	13.5858	−	23.5313i	0.723098	−	1.25244i	0.959752	−	0.280849i	$-0.0906161\pi$
$354$		0			0
$355$	1.75736	−	3.04384i	0.0932709	−	0.161550i
$356$		0			0
$357$		0			0
$358$	9.72792	−	16.8493i	0.514137	−	0.890511i
$359$	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
$362$	0.363961	+	0.630399i	0.0191294	+	0.0331330i
$363$		0			0
$364$		0			0
$365$	−1.12132	+	1.94218i	−0.0586926	+	0.101659i
$366$		0			0
$367$	−9.57107	−	16.5776i	−0.499606	−	0.865342i	0.500394	−	0.865798i	$-0.333188\pi$
$367$	−9.57107	−	16.5776i	−0.499606	−	0.865342i	−1.00000		0.000455270i	$0.999855\pi$
$368$	14.6274			0.762507
$369$		0			0
$370$	−0.828427			−0.0430679
$371$	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	$0.776444\pi$
$374$	13.6569			0.706179
$375$		0			0
$376$	−1.65685			−0.0854457
$377$	−3.12132	−	5.40629i	−0.160756	−	0.278438i
$378$		0			0
$379$	−4.91421	+	8.51167i	−0.252426	+	0.437215i	−0.964193	−	0.265201i	$-0.914562\pi$
$379$	−4.91421	+	8.51167i	−0.252426	+	0.437215i	0.711767	+	0.702416i	$0.247895\pi$
$380$		0			0
$381$		0			0
$382$	2.17157	+	3.76127i	0.111107	+	0.192444i
$383$	−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
$386$	9.87868	−	17.1104i	0.502812	−	0.870895i
$387$		0			0
$388$		0			0
$389$	−8.65685	+	14.9941i	−0.438920	+	0.760232i	−0.997606	−	0.0691473i	$-0.977972\pi$
$389$	−8.65685	+	14.9941i	−0.438920	+	0.760232i	0.558687	+	0.829379i	$0.311305\pi$
$390$		0			0
$391$	−12.4853	+	21.6251i	−0.631408	+	1.09363i
$392$	8.92893	+	15.4654i	0.450979	+	0.781119i
$393$		0			0
$394$	−2.00000	−	3.46410i	−0.100759	−	0.174519i
$395$	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	$0.238941\pi$
$398$	−8.58579	−	14.8710i	−0.430367	−	0.745417i
$399$		0			0
$400$	−9.31371	+	16.1318i	−0.465685	+	0.806591i
$401$	14.8284			0.740496			0.370248	−	0.928933i	$-0.379273\pi$
$401$	14.8284			0.740496			0.370248	+	0.928933i	$0.379273\pi$
$402$		0			0
$403$	−10.0563	+	1.58346i	−0.500942	+	0.0788780i
$404$		0			0
$405$		0			0
$406$	2.00000	−	3.46410i	0.0992583	−	0.171920i
$407$	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	$0.115173\pi$
$410$	1.75736	−	3.04384i	0.0867898	−	0.150324i
$411$		0			0
$412$		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
$417$		0			0
$418$	7.65685			0.374509
$419$	−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	$0.653228\pi$
$422$	−3.87868	+	6.71807i	−0.188811	+	0.327031i
$423$		0			0
$424$	−2.00000	−	3.46410i	−0.0971286	−	0.168232i
$425$	−15.8995	−	27.5387i	−0.771239	−	1.33582i
$426$		0			0
$427$	5.17157	−	8.95743i	0.250270	−	0.433480i
$428$		0			0
$429$		0			0
$430$	4.54416			0.219139
$431$	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	$0.529323\pi$
$434$	−4.10051	−	5.07306i	−0.196831	−	0.243515i
$435$		0			0
$436$		0			0
$437$	−7.00000	+	12.1244i	−0.334855	+	0.579987i
$438$		0			0
$439$	1.74264	+	3.01834i	0.0831717	+	0.144058i	0.904611	−	0.426239i	$-0.140162\pi$
$439$	1.74264	+	3.01834i	0.0831717	+	0.144058i	−0.821439	+	0.570296i	$0.806828\pi$
$440$	−1.17157	+	2.02922i	−0.0558525	+	0.0967394i
$441$		0			0
$442$	17.6569			0.839851
$443$	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
$446$	11.7782	−	20.4004i	0.557713	−	0.965987i
$447$		0			0
$448$	−3.31371	+	5.73951i	−0.156558	+	0.271166i
$449$	18.3431			0.865667			0.432833	−	0.901474i	$-0.357514\pi$
$449$	18.3431			0.865667			0.432833	+	0.901474i	$0.357514\pi$
$450$		0			0
$451$	−3.00000	+	5.19615i	−0.141264	+	0.244677i
$452$		0			0
$453$		0			0
$454$	−7.65685	−	13.2621i	−0.359354	−	0.622419i
$455$	−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	$0.188360\pi$
$458$	−8.12132	+	14.0665i	−0.379484	+	0.657286i
$459$		0			0
$460$		0			0
$461$	−3.55635			−0.165636			−0.0828178	−	0.996565i	$-0.526392\pi$
$461$	−3.55635			−0.165636			−0.0828178	+	0.996565i	$0.526392\pi$
$462$		0			0
$463$	36.4558			1.69425			0.847123	−	0.531396i	$-0.178332\pi$
$463$	36.4558			1.69425			0.847123	+	0.531396i	$0.178332\pi$
$464$	−13.6569			−0.634004
$465$		0			0
$466$	33.9411			1.57229
$467$	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
$470$	−0.242641	−	0.420266i	−0.0111922	−	0.0193854i
$471$		0			0
$472$	−12.0000	+	20.7846i	−0.552345	+	0.956689i
$473$	−7.75736			−0.356684
$474$		0			0
$475$	−8.91421	−	15.4399i	−0.409012	−	0.708430i
$476$		0			0
$477$		0			0
$478$	−18.2426	−	31.5972i	−0.834399	−	1.44522i
$479$	−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
$482$	−4.22183	+	7.31242i	−0.192299	+	0.333071i
$483$		0			0
$484$		0			0
$485$	3.36396	+	5.82655i	0.152750	+	0.264570i
$486$		0			0
$487$	−3.25736	−	5.64191i	−0.147605	−	0.255659i	0.782737	−	0.622353i	$-0.213823\pi$
$487$	−3.25736	−	5.64191i	−0.147605	−	0.255659i	−0.930342	+	0.366693i	$0.880490\pi$
$488$	−35.3137			−1.59858
$489$		0			0
$490$	−2.61522	+	4.52970i	−0.118144	+	0.204631i
$491$	−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
$494$	9.89949			0.445399
$495$		0			0
$496$	−8.00000	+	20.7846i	−0.359211	+	0.933257i
$497$	−4.97056			−0.222960
$498$		0			0
$499$	3.92893	−	6.80511i	0.175883	−	0.304639i	−0.764583	−	0.644525i	$-0.777055\pi$
$499$	3.92893	−	6.80511i	0.175883	−	0.304639i	0.940467	+	0.339886i	$0.110389\pi$
$500$		0			0
$501$		0			0
$502$	17.7279	−	30.7057i	0.791236	−	1.37046i
$503$	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
$506$	−3.65685	−	6.33386i	−0.162567	−	0.281574i
$507$		0			0
$508$		0			0
$509$	13.2426	+	22.9369i	0.586970	+	1.01666i	0.994627	+	0.103526i	$0.0330126\pi$
$509$	13.2426	+	22.9369i	0.586970	+	1.01666i	−0.407657	+	0.913135i	$0.633654\pi$
$510$		0			0
$511$	3.17157			0.140302
$512$	22.6274			1.00000
$513$		0			0
$514$	−7.24264	−	12.5446i	−0.319459	−	0.553320i
$515$	−4.77817	+	8.27604i	−0.210552	+	0.364686i
$516$		0			0
$517$	0.414214	+	0.717439i	0.0182171	+	0.0315529i
$518$	0.585786	+	1.01461i	0.0257380	+	0.0445795i
$519$		0			0
$520$	−1.51472	+	2.62357i	−0.0664248	+	0.115051i
$521$	9.94975	−	17.2335i	0.435906	−	0.755012i	−0.561463	−	0.827502i	$-0.689761\pi$
$521$	9.94975	−	17.2335i	0.435906	−	0.755012i	0.997369	+	0.0724900i	$0.0230946\pi$
$522$		0			0
$523$	6.00000			0.262362			0.131181	−	0.991358i	$-0.458123\pi$
$523$	6.00000			0.262362			0.131181	+	0.991358i	$0.458123\pi$
$524$		0			0
$525$		0			0
$526$	−18.1421			−0.791035
$527$	−23.8995	−	29.5680i	−1.04108	−	1.28800i
$528$		0			0
$529$	−9.62742			−0.418583
$530$	0.585786	−	1.01461i	0.0254449	−	0.0440719i
$531$		0			0
$532$		0			0
$533$	−3.87868	+	6.71807i	−0.168004	+	0.290992i
$534$		0			0
$535$	−2.28427			−0.0987577
$536$	20.4853	+	35.4815i	0.884829	+	1.53257i
$537$		0			0
$538$	14.0000	+	24.2487i	0.603583	+	1.04544i
$539$	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	$0.862721\pi$
$542$	40.2426			1.72857
$543$		0			0
$544$		0			0
$545$	−2.77817	−	4.81194i	−0.119004	−	0.206121i
$546$		0			0
$547$	0.500000	+	0.866025i	0.0213785	+	0.0370286i	0.876517	−	0.481371i	$-0.159861\pi$
$547$	0.500000	+	0.866025i	0.0213785	+	0.0370286i	−0.855138	+	0.518400i	$0.826528\pi$
$548$		0			0
$549$		0			0
$550$	9.31371			0.397138
$551$	6.53553	−	11.3199i	0.278423	−	0.482243i
$552$		0			0
$553$	−6.48528	−	11.2328i	−0.275782	−	0.477669i
$554$	−16.0416			−0.681544
$555$		0			0
$556$		0			0
$557$	4.62742			0.196070			0.0980350	−	0.995183i	$-0.468744\pi$
$557$	4.62742			0.196070			0.0980350	+	0.995183i	$0.468744\pi$
$558$		0			0
$559$	−10.0294			−0.424200
$560$	−1.94113			−0.0820275
$561$		0			0
$562$	−28.3431			−1.19558
$563$	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
$566$	−21.8995			−0.920504
$567$		0			0
$568$	8.48528	+	14.6969i	0.356034	+	0.616670i
$569$	4.07107	+	7.05130i	0.170668	+	0.295606i	0.938654	−	0.344861i	$-0.112074\pi$
$569$	4.07107	+	7.05130i	0.170668	+	0.295606i	−0.767986	+	0.640467i	$0.778741\pi$
$570$		0			0
$571$	−0.742641	−	1.28629i	−0.0310785	−	0.0538296i	0.850068	−	0.526673i	$-0.176561\pi$
$571$	−0.742641	−	1.28629i	−0.0310785	−	0.0538296i	−0.881146	+	0.472844i	$0.843228\pi$
$572$		0			0
$573$		0			0
$574$	−4.97056			−0.207467
$575$	−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	$0.182198\pi$
$578$	20.9497	+	36.2860i	0.871395	+	1.50930i
$579$		0			0
$580$		0			0
$581$	6.14214			0.254819
$582$		0			0
$583$	−1.00000	+	1.73205i	−0.0414158	+	0.0717342i
$584$	−5.41421	−	9.37769i	−0.224042	−	0.388052i
$585$		0			0
$586$	−9.07107	+	15.7116i	−0.374722	+	0.649038i
$587$	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
$590$	−7.02944			−0.289397
$591$		0			0
$592$	2.00000	−	3.46410i	0.0821995	−	0.142374i
$593$	36.0000			1.47834			0.739171	−	0.673517i	$-0.235217\pi$
$593$	36.0000			1.47834			0.739171	+	0.673517i	$0.235217\pi$
$594$		0			0
$595$	1.65685	−	2.86976i	0.0679244	−	0.117649i
$596$		0			0
$597$		0			0
$598$	−4.72792	−	8.18900i	−0.193339	−	0.334873i
$599$	−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	$0.121259\pi$
$602$	−3.21320	−	5.56543i	−0.130960	−	0.226830i
$603$		0			0
$604$		0			0
$605$	−5.27208			−0.214340
$606$		0			0
$607$	20.2279	+	35.0358i	0.821026	+	1.42206i	0.904919	+	0.425584i	$0.139931\pi$
$607$	20.2279	+	35.0358i	0.821026	+	1.42206i	−0.0838929	+	0.996475i	$0.526735\pi$
$608$		0			0
$609$		0			0
$610$	−5.17157	−	8.95743i	−0.209391	−	0.362676i
$611$	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	$0.893327\pi$
$614$	5.43503	−	9.41375i	0.219340	−	0.379908i
$615$		0			0
$616$	3.31371			0.133513
$617$	−16.6066	+	28.7635i	−0.668557	+	1.15797i	0.309751	+	0.950818i	$0.399754\pi$
$617$	−16.6066	+	28.7635i	−0.668557	+	1.15797i	−0.978308	+	0.207156i	$0.933579\pi$
$618$		0			0
$619$	29.4853			1.18511			0.592557	−	0.805529i	$-0.298119\pi$
$619$	29.4853			1.18511			0.592557	+	0.805529i	$0.298119\pi$
$620$		0			0
$621$		0			0
$622$	−28.1421			−1.12840
$623$	−7.41421	+	12.8418i	−0.297044	+	0.514496i
$624$		0			0
$625$	−9.98528	−	17.2950i	−0.399411	−	0.691801i
$626$	−4.02082	+	6.96426i	−0.160704	+	0.278348i
$627$		0			0
$628$		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	$-0.840030\pi$
$631$	−21.4853	−	37.2136i	−0.855316	−	1.48145i	0.0210364	−	0.999779i	$-0.493303\pi$
$632$	−22.1421	+	38.3513i	−0.880767	+	1.52553i
$633$		0			0
$634$	15.7279	−	27.2416i	0.624636	−	1.08190i
$635$	3.12994			0.124208
$636$		0			0
$637$	5.77208	−	9.99753i	0.228698	−	0.396117i
$638$	3.41421	+	5.91359i	0.135170	+	0.234121i
$639$		0			0
$640$	3.31371	+	5.73951i	0.130986	+	0.226874i
$641$	−22.0919	−	38.2643i	−0.872577	−	1.51135i	−0.859322	−	0.511435i	$-0.829114\pi$
$641$	−22.0919	−	38.2643i	−0.872577	−	1.51135i	−0.0132552	−	0.999912i	$-0.504219\pi$
$642$		0			0
$643$	35.7696			1.41061			0.705307	−	0.708902i	$-0.250809\pi$
$643$	35.7696			1.41061			0.705307	+	0.708902i	$0.250809\pi$
$644$		0			0
$645$		0			0
$646$	18.4853	+	32.0174i	0.727294	+	1.25971i
$647$	−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
$650$	12.0416			0.472312
$651$		0			0
$652$		0			0
$653$	−41.0122			−1.60493			−0.802466	−	0.596698i	$-0.796479\pi$
$653$	−41.0122			−1.60493			−0.802466	+	0.596698i	$0.796479\pi$
$654$		0			0
$655$	9.51472			0.371771
$656$	8.48528	+	14.6969i	0.331295	+	0.573819i
$657$		0			0
$658$	−0.343146	+	0.594346i	−0.0133772	+	0.0231700i
$659$	−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	$0.414196\pi$
$662$	2.12132	+	3.67423i	0.0824475	+	0.142803i
$663$		0			0
$664$	−10.4853	−	18.1610i	−0.406908	−	0.704785i
$665$	0.928932	−	1.60896i	0.0360224	−	0.0623927i
$666$		0			0
$667$	−12.4853			−0.483432
$668$		0			0
$669$		0			0
$670$	−6.00000	+	10.3923i	−0.231800	+	0.401490i
$671$	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	$0.755977\pi$
$674$	−26.3431			−1.01470
$675$		0			0
$676$		0			0
$677$	8.94975	+	15.5014i	0.343967	+	0.595768i	0.985165	−	0.171607i	$-0.0548959\pi$
$677$	8.94975	+	15.5014i	0.343967	+	0.595768i	−0.641199	+	0.767375i	$0.721563\pi$
$678$		0			0
$679$	4.75736	−	8.23999i	0.182571	−	0.316222i
$680$	−11.3137			−0.433861
$681$		0			0
$682$	11.0000	−	1.73205i	0.421212	−	0.0663237i
$683$	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
$686$	15.5980			0.595534
$687$		0			0
$688$	−10.9706	+	19.0016i	−0.418249	+	0.724428i
$689$	−1.29289	+	2.23936i	−0.0492553	+	0.0853127i
$690$		0			0
$691$	7.48528	+	12.9649i	0.284754	+	0.493208i	0.972549	−	0.232697i	$-0.0747549\pi$
$691$	7.48528	+	12.9649i	0.284754	+	0.493208i	−0.687796	+	0.725904i	$0.741422\pi$
$692$		0			0
$693$		0			0
$694$	−12.3137	+	21.3280i	−0.467422	+	0.809599i
$695$	−4.10051	−	7.10228i	−0.155541	−	0.269405i
$696$		0			0
$697$	−28.9706			−1.09734
$698$	−46.8701			−1.77406
$699$		0			0
$700$		0			0
$701$	−18.0000	+	31.1769i	−0.679851	+	1.17754i	0.295175	+	0.955443i	$0.404622\pi$
$701$	−18.0000	+	31.1769i	−0.679851	+	1.17754i	−0.975026	+	0.222093i	$0.928711\pi$
$702$		0			0
$703$	1.91421	+	3.31552i	0.0721959	+	0.125047i
$704$	−5.65685	−	9.79796i	−0.213201	−	0.369274i
$705$		0			0
$706$	−19.2132	+	33.2782i	−0.723098	+	1.25244i
$707$	−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	$0.622359\pi$
$710$	−2.48528	+	4.30463i	−0.0932709	+	0.161550i
$711$		0			0
$712$	50.6274			1.89734
$713$	−7.31371	+	19.0016i	−0.273901	+	0.711614i
$714$		0			0
$715$	1.51472			0.0566473
$716$		0			0
$717$		0			0
$718$	−12.7574	−	22.0964i	−0.476100	−	0.824630i
$719$	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
$722$	−3.07107	−	5.31925i	−0.114293	−	0.197962i
$723$		0			0
$724$		0			0
$725$	7.94975	−	13.7694i	0.295246	−	0.511381i
$726$		0			0
$727$	2.50000	−	4.33013i	0.0927199	−	0.160596i	−0.815935	−	0.578144i	$-0.803777\pi$
$727$	2.50000	−	4.33013i	0.0927199	−	0.160596i	0.908655	+	0.417548i	$0.137111\pi$
$728$	4.28427			0.158786
$729$		0			0
$730$	1.58579	−	2.74666i	0.0586926	−	0.101659i
$731$	−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	$0.868851\pi$
$734$	13.5355	+	23.4442i	0.499606	+	0.865342i
$735$		0			0
$736$		0			0
$737$	10.2426	−	17.7408i	0.377293	−	0.653490i
$738$		0			0
$739$	0.843146	+	1.46037i	0.0310156	+	0.0537206i	0.881117	−	0.472899i	$-0.156793\pi$
$739$	0.843146	+	1.46037i	0.0310156	+	0.0537206i	−0.850101	+	0.526620i	$0.823459\pi$
$740$		0			0
$741$		0			0
$742$	−1.65685			−0.0608250
$743$	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
$746$	41.6985			1.52669
$747$		0			0
$748$		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	$-0.569044\pi$
$751$	20.2279	−	35.0358i	0.738127	−	1.27847i	0.953338	−	0.301906i	$-0.0976230\pi$
$752$	2.34315			0.0854457
$753$		0			0
$754$	4.41421	+	7.64564i	0.160756	+	0.278438i
$755$	−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	$-0.538513\pi$
$758$	6.94975	−	12.0373i	0.252426	−	0.437215i
$759$		0			0
$760$	−6.34315			−0.230090
$761$	20.5355	−	35.5686i	0.744413	−	1.28936i	−0.206056	−	0.978540i	$-0.566063\pi$
$761$	20.5355	−	35.5686i	0.744413	−	1.28936i	0.950469	−	0.310820i	$-0.100604\pi$
$762$		0			0
$763$	−3.92893	+	6.80511i	−0.142237	+	0.246362i
$764$		0			0
$765$		0			0
$766$	4.51472	+	7.81972i	0.163123	+	0.282538i
$767$	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	$0.287089\pi$
$770$	0.485281	+	0.840532i	0.0174883	+	0.0302907i
$771$		0			0
$772$		0			0
$773$	11.8579			0.426498			0.213249	−	0.976998i	$-0.431595\pi$
$773$	11.8579			0.426498			0.213249	+	0.976998i	$0.431595\pi$
$774$		0			0
$775$	−16.2990	−	20.1648i	−0.585477	−	0.724340i
$776$	−32.4853			−1.16615
$777$		0			0
$778$	12.2426	−	21.2049i	0.438920	−	0.760232i
$779$	−16.2426			−0.581953
$780$		0			0
$781$	4.24264	−	7.34847i	0.151814	−	0.262949i
$782$	17.6569	−	30.5826i	0.631408	−	1.09363i
$783$		0			0
$784$	−12.6274	−	21.8713i	−0.450979	−	0.781119i
$785$	−2.29289	−	3.97141i	−0.0818369	−	0.141746i
$786$		0			0
$787$	−10.7426	+	18.6068i	−0.382934	+	0.663261i	−0.991480	−	0.130258i	$-0.958420\pi$
$787$	−10.7426	+	18.6068i	−0.382934	+	0.663261i	0.608546	+	0.793518i	$0.291753\pi$
$788$		0			0
$789$		0			0
$790$	−12.9706			−0.461472
$791$	12.9706			0.461180
$792$		0			0
$793$	11.4142	+	19.7700i	0.405331	+	0.702053i
$794$	6.34315	−	10.9867i	0.225110	−	0.389902i
$795$		0			0
$796$		0			0
$797$	−0.343146	−	0.594346i	−0.0121548	−	0.0210528i	0.859884	−	0.510489i	$-0.170536\pi$
$797$	−0.343146	−	0.594346i	−0.0121548	−	0.0210528i	−0.872039	+	0.489437i	$0.837202\pi$
$798$		0			0
$799$	−2.00000	+	3.46410i	−0.0707549	+	0.122551i
$800$		0			0
$801$		0			0
$802$	−20.9706			−0.740496
$803$	−2.70711	+	4.68885i	−0.0955317	+	0.165466i
$804$		0			0
$805$	−1.77460			−0.0625465
$806$	14.2218	−	2.23936i	0.500942	−	0.0788780i
$807$		0			0
$808$	43.5980			1.53377
$809$	−8.46447	+	14.6609i	−0.297595	+	0.515449i	−0.975585	−	0.219621i	$-0.929518\pi$
$809$	−8.46447	+	14.6609i	−0.297595	+	0.515449i	0.677990	+	0.735071i	$0.262851\pi$
$810$		0			0
$811$	−9.50000	−	16.4545i	−0.333590	−	0.577795i	0.649623	−	0.760257i	$-0.274927\pi$
$811$	−9.50000	−	16.4545i	−0.333590	−	0.577795i	−0.983213	+	0.182462i	$0.941593\pi$
$812$		0			0
$813$		0			0
$814$	−2.00000			−0.0701000
$815$	1.36396	+	2.36245i	0.0477775	+	0.0827530i
$816$		0			0
$817$	−10.5000	−	18.1865i	−0.367348	−	0.636266i
$818$	−4.60660	+	7.97887i	−0.161066	+	0.278975i
$819$		0			0
$820$		0			0
$821$	37.7990			1.31919			0.659597	−	0.751620i	$-0.270727\pi$
$821$	37.7990			1.31919			0.659597	+	0.751620i	$0.270727\pi$
$822$		0			0
$823$	17.2426	−	29.8651i	0.601041	−	1.04103i	−0.391623	−	0.920126i	$-0.628086\pi$
$823$	17.2426	−	29.8651i	0.601041	−	1.04103i	0.992664	−	0.120907i	$-0.0385804\pi$
$824$	−23.0711	−	39.9603i	−0.803719	−	1.39208i
$825$		0			0
$826$	4.97056	+	8.60927i	0.172948	+	0.299555i
$827$	−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	$0.416454\pi$
$830$	3.07107	−	5.31925i	0.106598	−	0.184634i
$831$		0			0
$832$	−7.31371	−	12.6677i	−0.253557	−	0.439174i
$833$	43.1127			1.49377
$834$		0			0
$835$	−6.97056			−0.241226
$836$		0			0
$837$		0			0
$838$	32.4853			1.12219
$839$	−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
$842$	−15.5563	−	26.9444i	−0.536107	−	0.928565i
$843$		0			0
$844$		0			0
$845$	−5.65685			−0.194602
$846$		0			0
$847$	3.72792	+	6.45695i	0.128093	+	0.221863i
$848$	2.82843	+	4.89898i	0.0971286	+	0.168232i
$849$		0			0
$850$	22.4853	+	38.9456i	0.771239	+	1.33582i
$851$	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	$0.447296\pi$
$854$	−7.31371	+	12.6677i	−0.250270	+	0.433480i
$855$		0			0
$856$	5.51472	−	9.55177i	0.188489	−	0.326473i
$857$	−6.34315	−	10.9867i	−0.216678	−	0.375297i	0.737113	−	0.675770i	$-0.236189\pi$
$857$	−6.34315	−	10.9867i	−0.216678	−	0.375297i	−0.953790	+	0.300473i	$0.902855\pi$
$858$		0			0
$859$	−22.8137	−	39.5145i	−0.778394	−	1.34822i	−0.932867	−	0.360220i	$-0.882701\pi$
$859$	−22.8137	−	39.5145i	−0.778394	−	1.34822i	0.154474	−	0.987997i	$-0.450632\pi$
$860$		0			0
$861$		0			0
$862$	−3.07107	+	5.31925i	−0.104601	+	0.181174i
$863$	−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
$866$	5.41421			0.183982
$867$		0			0
$868$		0			0
$869$	22.1421			0.751121
$870$		0			0
$871$	13.2426	−	22.9369i	0.448710	−	0.777188i
$872$	26.8284			0.908525
$873$		0			0
$874$	9.89949	−	17.1464i	0.334855	−	0.579987i
$875$	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	$0.667466\pi$
$878$	−2.46447	−	4.26858i	−0.0831717	−	0.144058i
$879$		0			0
$880$	1.65685	−	2.86976i	0.0558525	−	0.0967394i
$881$	0.313708	+	0.543359i	0.0105691	+	0.0183062i	0.871262	−	0.490819i	$-0.163302\pi$
$881$	0.313708	+	0.543359i	0.0105691	+	0.0183062i	−0.860692	+	0.509125i	$0.829969\pi$
$882$		0			0
$883$	−36.9411			−1.24317			−0.621584	−	0.783348i	$-0.713511\pi$
$883$	−36.9411			−1.24317			−0.621584	+	0.783348i	$0.713511\pi$
$884$		0			0
$885$		0			0
$886$	−5.75736	−	9.97204i	−0.193422	−	0.335017i
$887$	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
$890$	7.41421	+	12.8418i	0.248525	+	0.430458i
$891$		0			0
$892$		0			0
$893$	−1.12132	+	1.94218i	−0.0375236	+	0.0649927i
$894$		0			0
$895$	8.05887			0.269378
$896$	4.68629	−	8.11689i	0.156558	−	0.271166i
$897$		0			0
$898$	−25.9411			−0.865667
$899$	6.82843	−	17.7408i	0.227741	−	0.591688i
$900$		0			0
$901$	−9.65685			−0.321716
$902$	4.24264	−	7.34847i	0.141264	−	0.244677i
$903$		0			0
$904$	−22.1421	−	38.3513i	−0.736436	−	1.27555i
$905$	−0.150758	+	0.261120i	−0.00501135	+	0.00867992i
$906$		0			0
$907$	−25.5147			−0.847202			−0.423601	−	0.905849i	$-0.639234\pi$
$907$	−25.5147			−0.847202			−0.423601	+	0.905849i	$0.639234\pi$
$908$		0			0
$909$		0			0
$910$	0.627417	+	1.08672i	0.0207987	+	0.0360244i
$911$	−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
$914$	−50.1838			−1.65993
$915$		0			0
$916$		0			0
$917$	−6.72792	−	11.6531i	−0.222176	−	0.384819i
$918$		0			0
$919$	14.7426	+	25.5350i	0.486315	+	0.842322i	0.999876	−	0.0157308i	$-0.00500748\pi$
$919$	14.7426	+	25.5350i	0.486315	+	0.842322i	−0.513561	+	0.858053i	$0.671674\pi$
$920$	3.02944	+	5.24714i	0.0998776	+	0.172993i
$921$		0			0
$922$	5.02944			0.165636
$923$	5.48528	−	9.50079i	0.180550	−	0.312722i
$924$		0			0
$925$	2.32843	+	4.03295i	0.0765582	+	0.132603i
$926$	−51.5563			−1.69425
$927$		0			0
$928$		0			0
$929$	0.343146			0.0112582			0.00562912	−	0.999984i	$-0.498208\pi$
$929$	0.343146			0.0112582			0.00562912	+	0.999984i	$0.498208\pi$
$930$		0			0
$931$	24.1716			0.792191
$932$		0			0
$933$		0			0
$934$	−13.1716			−0.430987
$935$	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	$0.0413455\pi$
$938$	16.9706			0.554109
$939$		0			0
$940$		0			0
$941$	13.0711	+	22.6398i	0.426105	+	0.738035i	0.996523	−	0.0833195i	$-0.0265522\pi$
$941$	13.0711	+	22.6398i	0.426105	+	0.738035i	−0.570418	+	0.821354i	$0.693219\pi$
$942$		0			0
$943$	7.75736	+	13.4361i	0.252614	+	0.437541i
$944$	16.9706	−	29.3939i	0.552345	−	0.956689i
$945$		0			0
$946$	10.9706			0.356684
$947$	−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
$950$	12.6066	+	21.8353i	0.409012	+	0.708430i
$951$		0			0
$952$	8.00000	+	13.8564i	0.259281	+	0.449089i
$953$	−11.8995			−0.385462			−0.192731	−	0.981252i	$-0.561735\pi$
$953$	−11.8995			−0.385462			−0.192731	+	0.981252i	$0.561735\pi$
$954$		0			0
$955$	−0.899495	+	1.55797i	−0.0291070	+	0.0504148i
$956$		0			0
$957$		0			0
$958$	8.24264	−	14.2767i	0.266308	−	0.461258i
$959$	12.7696			0.412350
$960$		0			0
$961$	−23.0000	−	20.7846i	−0.741935	−	0.670471i
$962$	−2.58579			−0.0833691
$963$		0			0
$964$		0			0
$965$	8.18377			0.263445
$966$		0			0
$967$	5.97056	−	10.3413i	0.192000	−	0.332554i	−0.753913	−	0.656975i	$-0.771836\pi$
$967$	5.97056	−	10.3413i	0.192000	−	0.332554i	0.945913	+	0.324420i	$0.105169\pi$
$968$	12.7279	−	22.0454i	0.409091	−	0.708566i
$969$		0			0
$970$	−4.75736	−	8.23999i	−0.152750	−	0.264570i
$971$	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
$974$	4.60660	+	7.97887i	0.147605	+	0.255659i
$975$		0			0
$976$	49.9411			1.59858
$977$	−12.0000			−0.383914			−0.191957	−	0.981403i	$-0.561483\pi$
$977$	−12.0000			−0.383914			−0.191957	+	0.981403i	$0.561483\pi$
$978$		0			0
$979$	−12.6569	−	21.9223i	−0.404515	−	0.700640i
$980$		0			0
$981$		0			0
$982$	22.8284	+	39.5400i	0.728484	+	1.26177i
$983$	−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
$986$	−16.4853	+	28.5533i	−0.524998	+	0.909324i
$987$		0			0
$988$		0			0
$989$	−10.0294	+	17.3715i	−0.318918	+	0.552381i
$990$		0			0
$991$	45.1421			1.43399			0.716994	−	0.697080i	$-0.245518\pi$
$991$	45.1421			1.43399			0.716994	+	0.697080i	$0.245518\pi$
$992$		0			0
$993$		0			0
$994$	7.02944			0.222960
$995$	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	$0.735901\pi$
$998$	−5.55635	+	9.62388i	−0.175883	+	0.304639i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	279.2.h.b.253.1		4
3.2	odd	2		93.2.e.a.67.2	yes	4
12.11	even	2		1488.2.q.g.625.1		4
31.5	even	3		8649.2.a.h.1.1		2
31.25	even	3	inner	279.2.h.b.118.1		4
31.26	odd	6		8649.2.a.i.1.1		2
93.5	odd	6		2883.2.a.b.1.2		2
93.26	even	6		2883.2.a.c.1.2		2
93.56	odd	6		93.2.e.a.25.2	✓	4
372.335	even	6		1488.2.q.g.769.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.e.a.25.2	✓	4	93.56	odd	6
93.2.e.a.67.2	yes	4	3.2	odd	2
279.2.h.b.118.1		4	31.25	even	3	inner
279.2.h.b.253.1		4	1.1	even	1	trivial
1488.2.q.g.625.1		4	12.11	even	2
1488.2.q.g.769.1		4	372.335	even	6
2883.2.a.b.1.2		2	93.5	odd	6
2883.2.a.c.1.2		2	93.26	even	6
8649.2.a.h.1.1		2	31.5	even	3
8649.2.a.i.1.1		2	31.26	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:	\( N \)	\(=\)	\( 279 = 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	279.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +(-0.292893 - 0.507306i) q^{5} +(-0.414214 + 0.717439i) q^{7} +2.82843 q^{8} +(0.414214 + 0.717439i) q^{10} +(-0.707107 - 1.22474i) q^{11} +(-0.914214 - 1.58346i) q^{13} +(0.585786 - 1.01461i) q^{14} -4.00000 q^{16} +(3.41421 - 5.91359i) q^{17} +(1.91421 - 3.31552i) q^{19} +(1.00000 + 1.73205i) q^{22} -3.65685 q^{23} +(2.32843 - 4.03295i) q^{25} +(1.29289 + 2.23936i) q^{26} +3.41421 q^{29} +(2.00000 - 5.19615i) q^{31} +(-4.82843 + 8.36308i) q^{34} +0.485281 q^{35} +(-0.500000 + 0.866025i) q^{37} +(-2.70711 + 4.68885i) q^{38} +(-0.828427 - 1.43488i) q^{40} +(-2.12132 - 3.67423i) q^{41} +(2.74264 - 4.75039i) q^{43} +5.17157 q^{46} -0.585786 q^{47} +(3.15685 + 5.46783i) q^{49} +(-3.29289 + 5.70346i) q^{50} +(-0.707107 - 1.22474i) q^{53} +(-0.414214 + 0.717439i) q^{55} +(-1.17157 + 2.02922i) q^{56} -4.82843 q^{58} +(-4.24264 + 7.34847i) q^{59} -12.4853 q^{61} +(-2.82843 + 7.34847i) q^{62} +8.00000 q^{64} +(-0.535534 + 0.927572i) q^{65} +(7.24264 + 12.5446i) q^{67} -0.686292 q^{70} +(3.00000 + 5.19615i) q^{71} +(-1.91421 - 3.31552i) q^{73} +(0.707107 - 1.22474i) q^{74} +1.17157 q^{77} +(-7.82843 + 13.5592i) q^{79} +(1.17157 + 2.02922i) q^{80} +(3.00000 + 5.19615i) q^{82} +(-3.70711 - 6.42090i) q^{83} -4.00000 q^{85} +(-3.87868 + 6.71807i) q^{86} +(-2.00000 - 3.46410i) q^{88} +17.8995 q^{89} +1.51472 q^{91} +0.828427 q^{94} -2.24264 q^{95} -11.4853 q^{97} +(-4.46447 - 7.73268i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{5} + 4 q^{7} - 4 q^{10} + 2 q^{13} + 8 q^{14} - 16 q^{16} + 8 q^{17} + 2 q^{19} + 4 q^{22} + 8 q^{23} - 2 q^{25} + 8 q^{26} + 8 q^{29} + 8 q^{31} - 8 q^{34} - 32 q^{35} - 2 q^{37} - 8 q^{38}+ \cdots - 32 q^{98}+O(q^{100}) \) 4 * q - 4 * q^5 + 4 * q^7 - 4 * q^10 + 2 * q^13 + 8 * q^14 - 16 * q^16 + 8 * q^17 + 2 * q^19 + 4 * q^22 + 8 * q^23 - 2 * q^25 + 8 * q^26 + 8 * q^29 + 8 * q^31 - 8 * q^34 - 32 * q^35 - 2 * q^37 - 8 * q^38 + 8 * q^40 - 6 * q^43 + 32 * q^46 - 8 * q^47 - 10 * q^49 - 16 * q^50 + 4 * q^55 - 16 * q^56 - 8 * q^58 - 16 * q^61 + 32 * q^64 + 12 * q^65 + 12 * q^67 - 48 * q^70 + 12 * q^71 - 2 * q^73 + 16 * q^77 - 20 * q^79 + 16 * q^80 + 12 * q^82 - 12 * q^83 - 16 * q^85 - 24 * q^86 - 8 * q^88 + 32 * q^89 + 40 * q^91 - 8 * q^94 + 8 * q^95 - 12 * q^97 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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