LMFDB - Embedded newform 560.2.bs.c.271.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,2,Mod(31,560)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("560.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bs (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 43 x^{10} - 160 x^{9} + 572 x^{8} - 1394 x^{7} + 3039 x^{6} - 4844 x^{5} + \cdots + 657 $ x^12 - 6x^11 + 43x^10 - 160x^9 + 572x^8 - 1394x^7 + 3039x^6 - 4844x^5 + 6526x^4 - 6318x^3 + 4737x^2 - 2196*x + 657
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.1
Root			$0.500000 - 2.35365i$ of defining polynomial
Character	$\chi$	$=$	560.271
Dual form			560.2.bs.c.31.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.60984 - 2.78832i) q^{3} +(0.866025 + 0.500000i) q^{5} +(-0.279599 + 2.63094i) q^{7} +(-3.68317 + 6.37943i) q^{9} +(1.40022 - 0.808417i) q^{11} +5.32414i q^{13} -3.21968i q^{15} +(-4.03609 + 2.33024i) q^{17} +(-2.68317 + 4.64738i) q^{19} +(7.78601 - 3.45577i) q^{21} +(-5.13166 - 2.96277i) q^{23} +(0.500000 + 0.866025i) q^{25} +14.0582 q^{27} +8.25106 q^{29} +(2.66611 + 4.61784i) q^{31} +(-4.50826 - 2.60284i) q^{33} +(-1.55761 + 2.13866i) q^{35} +(3.02810 - 5.24482i) q^{37} +(14.8454 - 8.57102i) q^{39} +2.35034i q^{41} -3.04075i q^{43} +(-6.37943 + 3.68317i) q^{45} +(-1.08102 + 1.87238i) q^{47} +(-6.84365 - 1.47122i) q^{49} +(12.9949 + 7.50263i) q^{51} +(-2.69786 - 4.67282i) q^{53} +1.61683 q^{55} +17.2779 q^{57} +(3.72375 + 6.44972i) q^{59} +(-0.549881 - 0.317474i) q^{61} +(-15.7541 - 11.4739i) q^{63} +(-2.66207 + 4.61084i) q^{65} +(-12.3459 + 7.12793i) q^{67} +19.0783i q^{69} +5.61214i q^{71} +(0.645073 - 0.372433i) q^{73} +(1.60984 - 2.78832i) q^{75} +(1.73539 + 3.90992i) q^{77} +(-0.535453 - 0.309144i) q^{79} +(-11.5819 - 20.0605i) q^{81} -3.11383 q^{83} -4.66048 q^{85} +(-13.2829 - 23.0066i) q^{87} +(-1.96739 - 1.13587i) q^{89} +(-14.0075 - 1.48863i) q^{91} +(8.58403 - 14.8680i) q^{93} +(-4.64738 + 2.68317i) q^{95} -4.11527i q^{97} +11.9101i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} - 2 q^{7} - 10 q^{9} + 6 q^{11} + 2 q^{19} + 12 q^{21} - 18 q^{23} + 6 q^{25} + 20 q^{27} + 16 q^{29} + 4 q^{31} - 6 q^{35} - 4 q^{37} + 24 q^{39} - 12 q^{45} + 12 q^{47} - 8 q^{49} - 12 q^{51}+ \cdots - 12 q^{95}+O(q^{100}) $ 12 * q + 2 * q^3 - 2 * q^7 - 10 * q^9 + 6 * q^11 + 2 * q^19 + 12 * q^21 - 18 * q^23 + 6 * q^25 + 20 * q^27 + 16 * q^29 + 4 * q^31 - 6 * q^35 - 4 * q^37 + 24 * q^39 - 12 * q^45 + 12 * q^47 - 8 * q^49 - 12 * q^51 - 12 * q^53 + 24 * q^55 + 16 * q^57 + 24 * q^59 - 48 * q^61 - 56 * q^63 - 2 * q^65 - 42 * q^67 + 24 * q^73 - 2 * q^75 + 40 * q^77 + 12 * q^79 - 6 * q^81 + 36 * q^83 - 16 * q^85 - 30 * q^87 + 12 * q^89 + 36 * q^91 + 28 * q^93 - 12 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.60984	−	2.78832i	−0.929441	−	1.60984i	−0.784258	−	0.620435i	$-0.786956\pi$
$3$	−1.60984	−	2.78832i	−0.929441	−	1.60984i	−0.145183	−	0.989405i	$-0.546377\pi$
$4$		0			0
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$		0			0
$7$	−0.279599	+	2.63094i	−0.105679	+	0.994400i
$7$	−0.279599	+	2.63094i	−0.105679	+	0.994400i
$8$		0			0
$9$	−3.68317	+	6.37943i	−1.22772	+	2.12648i
$10$		0			0
$11$	1.40022	−	0.808417i	0.422182	−	0.243747i	−0.273828	−	0.961779i	$-0.588290\pi$
$11$	1.40022	−	0.808417i	0.422182	−	0.243747i	0.696011	+	0.718032i	$0.254957\pi$
$12$		0			0
$13$			5.32414i			1.47665i	0.674444	+	0.738326i	$0.264383\pi$
$13$			5.32414i			1.47665i	−0.674444	+	0.738326i	$0.735617\pi$
$14$		0			0
$15$		−	3.21968i		−	0.831318i
$16$		0			0
$17$	−4.03609	+	2.33024i	−0.978897	+	0.565166i	−0.901937	−	0.431868i	$-0.857855\pi$
$17$	−4.03609	+	2.33024i	−0.978897	+	0.565166i	−0.0769599	+	0.997034i	$0.524521\pi$
$18$		0			0
$19$	−2.68317	+	4.64738i	−0.615561	+	1.06618i	0.374725	+	0.927136i	$0.377737\pi$
$19$	−2.68317	+	4.64738i	−0.615561	+	1.06618i	−0.990286	+	0.139047i	$0.955596\pi$
$20$		0			0
$21$	7.78601	−	3.45577i	1.69905	−	0.754111i
$22$		0			0
$23$	−5.13166	−	2.96277i	−1.07003	−	0.617780i	−0.141837	−	0.989890i	$-0.545301\pi$
$23$	−5.13166	−	2.96277i	−1.07003	−	0.617780i	−0.928188	+	0.372110i	$0.878634\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		0			0
$27$	14.0582			2.70550
$28$		0			0
$29$	8.25106			1.53218			0.766092	−	0.642731i	$-0.222199\pi$
$29$	8.25106			1.53218			0.766092	+	0.642731i	$0.222199\pi$
$30$		0			0
$31$	2.66611	+	4.61784i	0.478848	+	0.829389i	0.999706	−	0.0242543i	$-0.00772115\pi$
$31$	2.66611	+	4.61784i	0.478848	+	0.829389i	−0.520858	+	0.853643i	$0.674388\pi$
$32$		0			0
$33$	−4.50826	−	2.60284i	−0.784787	−	0.453097i
$34$		0			0
$35$	−1.55761	+	2.13866i	−0.263284	+	0.361499i
$36$		0			0
$37$	3.02810	−	5.24482i	0.497816	−	0.862243i	−0.502181	−	0.864763i	$-0.667469\pi$
$37$	3.02810	−	5.24482i	0.497816	−	0.862243i	0.999997	+	0.00251999i	$0.000802139\pi$
$38$		0			0
$39$	14.8454	−	8.57102i	2.37717	−	1.37246i
$40$		0			0
$41$			2.35034i			0.367061i	0.983014	+	0.183531i	$0.0587527\pi$
$41$			2.35034i			0.367061i	−0.983014	+	0.183531i	$0.941247\pi$
$42$		0			0
$43$		−	3.04075i		−	0.463710i	−0.972750	−	0.231855i	$-0.925521\pi$
$43$		−	3.04075i		−	0.463710i	0.972750	−	0.231855i	$-0.0744795\pi$
$44$		0			0
$45$	−6.37943	+	3.68317i	−0.950990	+	0.549054i
$46$		0			0
$47$	−1.08102	+	1.87238i	−0.157683	+	0.273115i	−0.934033	−	0.357187i	$-0.883736\pi$
$47$	−1.08102	+	1.87238i	−0.157683	+	0.273115i	0.776350	+	0.630303i	$0.217069\pi$
$48$		0			0
$49$	−6.84365	−	1.47122i	−0.977664	−	0.210174i
$50$		0			0
$51$	12.9949	+	7.50263i	1.81965	+	1.05058i
$52$		0			0
$53$	−2.69786	−	4.67282i	−0.370579	−	0.641862i	0.619076	−	0.785331i	$-0.287507\pi$
$53$	−2.69786	−	4.67282i	−0.370579	−	0.641862i	−0.989655	+	0.143470i	$0.954174\pi$
$54$		0			0
$55$	1.61683			0.218014
$56$		0			0
$57$	17.2779			2.28851
$58$		0			0
$59$	3.72375	+	6.44972i	0.484791	+	0.839682i	0.999847	−	0.0174739i	$-0.00556238\pi$
$59$	3.72375	+	6.44972i	0.484791	+	0.839682i	−0.515056	+	0.857156i	$0.672229\pi$
$60$		0			0
$61$	−0.549881	−	0.317474i	−0.0704050	−	0.0406484i	0.464384	−	0.885634i	$-0.346276\pi$
$61$	−0.549881	−	0.317474i	−0.0704050	−	0.0406484i	−0.534789	+	0.844985i	$0.679609\pi$
$62$		0			0
$63$	−15.7541	−	11.4739i	−1.98483	−	1.44557i
$64$		0			0
$65$	−2.66207	+	4.61084i	−0.330189	+	0.571905i
$66$		0			0
$67$	−12.3459	+	7.12793i	−1.50830	+	0.870815i	−0.508343	+	0.861155i	$0.669742\pi$
$67$	−12.3459	+	7.12793i	−1.50830	+	0.870815i	−0.999953	+	0.00966075i	$0.996925\pi$
$68$		0			0
$69$			19.0783i			2.29676i
$70$		0			0
$71$			5.61214i			0.666039i	0.942920	+	0.333019i	$0.108067\pi$
$71$			5.61214i			0.666039i	−0.942920	+	0.333019i	$0.891933\pi$
$72$		0			0
$73$	0.645073	−	0.372433i	0.0755001	−	0.0435900i	−0.461775	−	0.886997i	$-0.652787\pi$
$73$	0.645073	−	0.372433i	0.0755001	−	0.0435900i	0.537275	+	0.843407i	$0.319454\pi$
$74$		0			0
$75$	1.60984	−	2.78832i	0.185888	−	0.321968i
$76$		0			0
$77$	1.73539	+	3.90992i	0.197766	+	0.445577i
$78$		0			0
$79$	−0.535453	−	0.309144i	−0.0602432	−	0.0347814i	0.469576	−	0.882892i	$-0.344407\pi$
$79$	−0.535453	−	0.309144i	−0.0602432	−	0.0347814i	−0.529819	+	0.848111i	$0.677740\pi$
$80$		0			0
$81$	−11.5819	−	20.0605i	−1.28688	−	2.22895i
$82$		0			0
$83$	−3.11383			−0.341787			−0.170894	−	0.985289i	$-0.554665\pi$
$83$	−3.11383			−0.341787			−0.170894	+	0.985289i	$0.554665\pi$
$84$		0			0
$85$	−4.66048			−0.505500
$86$		0			0
$87$	−13.2829	−	23.0066i	−1.42408	−	2.46657i
$88$		0			0
$89$	−1.96739	−	1.13587i	−0.208543	−	0.120402i	0.392091	−	0.919926i	$-0.371752\pi$
$89$	−1.96739	−	1.13587i	−0.208543	−	0.120402i	−0.600634	+	0.799524i	$0.705085\pi$
$90$		0			0
$91$	−14.0075	−	1.48863i	−1.46838	−	0.156050i
$92$		0			0
$93$	8.58403	−	14.8680i	0.890122	−	1.54174i
$94$		0			0
$95$	−4.64738	+	2.68317i	−0.476811	+	0.275287i
$96$		0			0
$97$		−	4.11527i		−	0.417843i	−0.977932	−	0.208921i	$-0.933005\pi$
$97$		−	4.11527i		−	0.417843i	0.977932	−	0.208921i	$-0.0669953\pi$
$98$		0			0
$99$			11.9101i			1.19701i
$100$		0			0
$101$	−0.154909	+	0.0894366i	−0.0154140	+	0.00889927i	−0.507687	−	0.861541i	$-0.669499\pi$
$101$	−0.154909	+	0.0894366i	−0.0154140	+	0.00889927i	0.492273	+	0.870441i	$0.336166\pi$
$102$		0			0
$103$	−5.16904	+	8.95304i	−0.509320	+	0.882169i	0.490621	+	0.871373i	$0.336770\pi$
$103$	−5.16904	+	8.95304i	−0.509320	+	0.882169i	−0.999942	+	0.0107960i	$0.996563\pi$
$104$		0			0
$105$	8.47077	+	0.900220i	0.826663	+	0.0878525i
$106$		0			0
$107$	0.0940291	+	0.0542877i	0.00909014	+	0.00524819i	0.504538	−	0.863389i	$-0.331663\pi$
$107$	0.0940291	+	0.0542877i	0.00909014	+	0.00524819i	−0.495448	+	0.868638i	$0.664996\pi$
$108$		0			0
$109$	−0.210362	−	0.364357i	−0.0201490	−	0.0348991i	0.855775	−	0.517348i	$-0.173081\pi$
$109$	−0.210362	−	0.364357i	−0.0201490	−	0.0348991i	−0.875924	+	0.482449i	$0.839747\pi$
$110$		0			0
$111$	−19.4990			−1.85076
$112$		0			0
$113$	11.3932			1.07178			0.535889	−	0.844289i	$-0.319977\pi$
$113$	11.3932			1.07178			0.535889	+	0.844289i	$0.319977\pi$
$114$		0			0
$115$	−2.96277	−	5.13166i	−0.276279	−	0.478530i
$116$		0			0
$117$	−33.9650	−	19.6097i	−3.14007	−	1.81292i
$118$		0			0
$119$	−5.00222	−	11.2702i	−0.458553	−	1.03314i
$120$		0			0
$121$	−4.19292	+	7.26236i	−0.381175	+	0.660214i
$122$		0			0
$123$	6.55351	−	3.78367i	0.590910	−	0.341162i
$124$		0			0
$125$			1.00000i			0.0894427i
$126$		0			0
$127$			5.28924i			0.469344i	0.972075	+	0.234672i	$0.0754017\pi$
$127$			5.28924i			0.469344i	−0.972075	+	0.234672i	$0.924598\pi$
$128$		0			0
$129$	−8.47860	+	4.89512i	−0.746499	+	0.430991i
$130$		0			0
$131$	7.47994	−	12.9556i	0.653525	−	1.13194i	−0.328736	−	0.944422i	$-0.606623\pi$
$131$	7.47994	−	12.9556i	0.653525	−	1.13194i	0.982261	−	0.187517i	$-0.0600441\pi$
$132$		0			0
$133$	−11.4768	−	8.35865i	−0.995161	−	0.724787i
$134$		0			0
$135$	12.1748	+	7.02910i	1.04784	+	0.604969i
$136$		0			0
$137$	10.8292	+	18.7568i	0.925203	+	1.60250i	0.791235	+	0.611513i	$0.209439\pi$
$137$	10.8292	+	18.7568i	0.925203	+	1.60250i	0.133968	+	0.990986i	$0.457228\pi$
$138$		0			0
$139$	13.9971			1.18722			0.593610	−	0.804753i	$-0.297702\pi$
$139$	13.9971			1.18722			0.593610	+	0.804753i	$0.297702\pi$
$140$		0			0
$141$	6.96109			0.586229
$142$		0			0
$143$	4.30413	+	7.45497i	0.359929	+	0.623416i
$144$		0			0
$145$	7.14563	+	4.12553i	0.593412	+	0.342607i
$146$		0			0
$147$	6.91495	+	21.4507i	0.570336	+	1.76923i
$148$		0			0
$149$	5.15128	−	8.92228i	0.422010	−	0.730942i	−0.574126	−	0.818767i	$-0.694658\pi$
$149$	5.15128	−	8.92228i	0.422010	−	0.730942i	0.996136	+	0.0878247i	$0.0279915\pi$
$150$		0			0
$151$	1.46828	−	0.847712i	0.119487	−	0.0689858i	−0.439065	−	0.898455i	$-0.644690\pi$
$151$	1.46828	−	0.847712i	0.119487	−	0.0689858i	0.558552	+	0.829469i	$0.311357\pi$
$152$		0			0
$153$		−	34.3307i		−	2.77547i
$154$		0			0
$155$			5.33223i			0.428295i
$156$		0			0
$157$	−11.7709	+	6.79593i	−0.939420	+	0.542374i	−0.889778	−	0.456393i	$-0.849141\pi$
$157$	−11.7709	+	6.79593i	−0.939420	+	0.542374i	−0.0496416	+	0.998767i	$0.515808\pi$
$158$		0			0
$159$	−8.68623	+	15.0450i	−0.688863	+	1.19315i
$160$		0			0
$161$	9.22966	−	12.6727i	0.727399	−	0.998748i
$162$		0			0
$163$	9.81781	+	5.66832i	0.768990	+	0.443977i	0.832514	−	0.554003i	$-0.186901\pi$
$163$	9.81781	+	5.66832i	0.768990	+	0.443977i	−0.0635239	+	0.997980i	$0.520234\pi$
$164$		0			0
$165$	−2.60284	−	4.50826i	−0.202631	−	0.350968i
$166$		0			0
$167$	−5.04821			−0.390642			−0.195321	−	0.980739i	$-0.562575\pi$
$167$	−5.04821			−0.390642			−0.195321	+	0.980739i	$0.562575\pi$
$168$		0			0
$169$	−15.3465			−1.18050
$170$		0			0
$171$	−19.7651	−	34.2342i	−1.51148	−	2.61795i
$172$		0			0
$173$	20.4776	+	11.8227i	1.55688	+	0.898867i	0.997552	+	0.0699224i	$0.0222752\pi$
$173$	20.4776	+	11.8227i	1.55688	+	0.898867i	0.559331	+	0.828945i	$0.311058\pi$
$174$		0			0
$175$	−2.41826	+	1.07333i	−0.182803	+	0.0811360i
$176$		0			0
$177$	11.9893	−	20.7660i	0.901169	−	1.56087i
$178$		0			0
$179$	11.4566	−	6.61449i	0.856309	−	0.494390i	−0.00646563	−	0.999979i	$-0.502058\pi$
$179$	11.4566	−	6.61449i	0.856309	−	0.494390i	0.862774	+	0.505589i	$0.168725\pi$
$180$		0			0
$181$		−	15.3043i		−	1.13756i	−0.822490	−	0.568780i	$-0.807416\pi$
$181$		−	15.3043i		−	1.13756i	0.822490	−	0.568780i	$-0.192584\pi$
$182$		0			0
$183$			2.04433i			0.151121i
$184$		0			0
$185$	5.24482	−	3.02810i	0.385607	−	0.222630i
$186$		0			0
$187$	−3.76761	+	6.52570i	−0.275515	+	0.477206i
$188$		0			0
$189$	−3.93066	+	36.9862i	−0.285914	+	2.69035i
$190$		0			0
$191$	−5.39331	−	3.11383i	−0.390246	−	0.225309i	0.292021	−	0.956412i	$-0.405672\pi$
$191$	−5.39331	−	3.11383i	−0.390246	−	0.225309i	−0.682267	+	0.731103i	$0.739006\pi$
$192$		0			0
$193$	−10.5625	−	18.2948i	−0.760305	−	1.31689i	−0.942694	−	0.333660i	$-0.891716\pi$
$193$	−10.5625	−	18.2948i	−0.760305	−	1.31689i	0.182389	−	0.983226i	$-0.441617\pi$
$194$		0			0
$195$	17.1420			1.22757
$196$		0			0
$197$	−6.90157			−0.491717			−0.245858	−	0.969306i	$-0.579070\pi$
$197$	−6.90157			−0.491717			−0.245858	+	0.969306i	$0.579070\pi$
$198$		0			0
$199$	0.170183	+	0.294765i	0.0120639	+	0.0208954i	0.871994	−	0.489516i	$-0.162827\pi$
$199$	0.170183	+	0.294765i	0.0120639	+	0.0208954i	−0.859930	+	0.510411i	$0.829493\pi$
$200$		0			0
$201$	39.7500	+	22.9497i	2.80375	+	1.61874i
$202$		0			0
$203$	−2.30699	+	21.7080i	−0.161919	+	1.52360i
$204$		0			0
$205$	−1.17517	+	2.03545i	−0.0820774	+	0.142162i
$206$		0			0
$207$	37.8015	−	21.8247i	2.62739	−	1.51692i
$208$		0			0
$209$			8.67648i			0.600164i
$210$		0			0
$211$			14.1037i			0.970938i	0.874254	+	0.485469i	$0.161351\pi$
$211$			14.1037i			0.970938i	−0.874254	+	0.485469i	$0.838649\pi$
$212$		0			0
$213$	15.6485	−	9.03465i	1.07222	−	0.619044i
$214$		0			0
$215$	1.52037	−	2.63337i	0.103689	−	0.179594i
$216$		0			0
$217$	−12.8947	+	5.72323i	−0.875349	+	0.388518i
$218$		0			0
$219$	−2.07693	−	1.19912i	−0.140346	−	0.0810287i
$220$		0			0
$221$	−12.4065	−	21.4887i	−0.834554	−	1.44549i
$222$		0			0
$223$	19.6411			1.31526			0.657632	−	0.753339i	$-0.271558\pi$
$223$	19.6411			1.31526			0.657632	+	0.753339i	$0.271558\pi$
$224$		0			0
$225$	−7.36634			−0.491089
$226$		0			0
$227$	−9.19814	−	15.9316i	−0.610502	−	1.05742i	−0.991156	−	0.132703i	$-0.957634\pi$
$227$	−9.19814	−	15.9316i	−0.610502	−	1.05742i	0.380654	−	0.924718i	$-0.375699\pi$
$228$		0			0
$229$	−1.00128	−	0.578091i	−0.0661666	−	0.0382013i	0.466552	−	0.884494i	$-0.345496\pi$
$229$	−1.00128	−	0.578091i	−0.0661666	−	0.0382013i	−0.532718	+	0.846293i	$0.678829\pi$
$230$		0			0
$231$	8.10842	−	11.1332i	0.533495	−	0.732510i
$232$		0			0
$233$	−1.23369	+	2.13681i	−0.0808217	+	0.139987i	−0.903603	−	0.428371i	$-0.859088\pi$
$233$	−1.23369	+	2.13681i	−0.0808217	+	0.139987i	0.822781	+	0.568358i	$0.192421\pi$
$234$		0			0
$235$	−1.87238	+	1.08102i	−0.122141	+	0.0705181i
$236$		0			0
$237$			1.99069i			0.129309i
$238$		0			0
$239$		−	4.30458i		−	0.278440i	−0.990261	−	0.139220i	$-0.955540\pi$
$239$		−	4.30458i		−	0.278440i	0.990261	−	0.139220i	$-0.0444595\pi$
$240$		0			0
$241$	−24.9319	+	14.3944i	−1.60600	+	0.927227i	−0.615752	+	0.787940i	$0.711148\pi$
$241$	−24.9319	+	14.3944i	−1.60600	+	0.927227i	−0.990252	+	0.139287i	$0.955519\pi$
$242$		0			0
$243$	−16.2028	+	28.0642i	−1.03941	+	1.80032i
$244$		0			0
$245$	−5.19117	−	4.69593i	−0.331651	−	0.300012i
$246$		0			0
$247$	−24.7433	−	14.2856i	−1.57438	−	0.908969i
$248$		0			0
$249$	5.01277	+	8.68237i	0.317671	+	0.550223i
$250$		0			0
$251$	−15.6864			−0.990117			−0.495059	−	0.868860i	$-0.664853\pi$
$251$	−15.6864			−0.990117			−0.495059	+	0.868860i	$0.664853\pi$
$252$		0			0
$253$	−9.58061			−0.602328
$254$		0			0
$255$	7.50263	+	12.9949i	0.469833	+	0.813774i
$256$		0			0
$257$	21.8310	+	12.6041i	1.36178	+	0.786224i	0.989861	−	0.142041i	$-0.0453666\pi$
$257$	21.8310	+	12.6041i	1.36178	+	0.786224i	0.371919	+	0.928265i	$0.378700\pi$
$258$		0			0
$259$	12.9521	+	9.43318i	0.804806	+	0.586149i
$260$		0			0
$261$	−30.3900	+	52.6371i	−1.88110	+	3.25816i
$262$		0			0
$263$	13.8970	−	8.02345i	0.856927	−	0.494747i	−0.00605512	−	0.999982i	$-0.501927\pi$
$263$	13.8970	−	8.02345i	0.856927	−	0.494747i	0.862982	+	0.505235i	$0.168594\pi$
$264$		0			0
$265$		−	5.39571i		−	0.331456i
$266$		0			0
$267$			7.31431i			0.447628i
$268$		0			0
$269$	−2.57670	+	1.48766i	−0.157104	+	0.0907040i	−0.576491	−	0.817104i	$-0.695578\pi$
$269$	−2.57670	+	1.48766i	−0.157104	+	0.0907040i	0.419387	+	0.907808i	$0.362245\pi$
$270$		0			0
$271$	8.68150	−	15.0368i	0.527364	−	0.913421i	−0.472128	−	0.881530i	$-0.656514\pi$
$271$	8.68150	−	15.0368i	0.527364	−	0.913421i	0.999491	−	0.0318904i	$-0.0101528\pi$
$272$		0			0
$273$	18.3990	+	41.4538i	1.11356	+	2.50890i
$274$		0			0
$275$	1.40022	+	0.808417i	0.0844364	+	0.0487494i
$276$		0			0
$277$	11.1292	+	19.2764i	0.668691	+	1.15821i	0.978270	+	0.207333i	$0.0664785\pi$
$277$	11.1292	+	19.2764i	0.668691	+	1.15821i	−0.309579	+	0.950874i	$0.600188\pi$
$278$		0			0
$279$	−39.2790			−2.35157
$280$		0			0
$281$	−32.6620			−1.94845			−0.974226	−	0.225573i	$-0.927575\pi$
$281$	−32.6620			−1.94845			−0.974226	+	0.225573i	$0.927575\pi$
$282$		0			0
$283$	−4.39573	−	7.61363i	−0.261299	−	0.452584i	0.705288	−	0.708921i	$-0.250818\pi$
$283$	−4.39573	−	7.61363i	−0.261299	−	0.452584i	−0.966587	+	0.256337i	$0.917484\pi$
$284$		0			0
$285$	14.9631	+	8.63894i	0.886336	+	0.511727i
$286$		0			0
$287$	−6.18359	−	0.657153i	−0.365006	−	0.0387905i
$288$		0			0
$289$	2.36004	−	4.08771i	0.138826	−	0.240454i
$290$		0			0
$291$	−11.4747	+	6.62493i	−0.672660	+	0.388360i
$292$		0			0
$293$		−	7.59186i		−	0.443521i	−0.975101	−	0.221761i	$-0.928820\pi$
$293$		−	7.59186i		−	0.443521i	0.975101	−	0.221761i	$-0.0711804\pi$
$294$		0			0
$295$			7.44750i			0.433610i
$296$		0			0
$297$	19.6846	−	11.3649i	1.14221	−	0.659458i
$298$		0			0
$299$	15.7742	−	27.3217i	0.912245	−	1.58005i
$300$		0			0
$301$	8.00002	+	0.850191i	0.461113	+	0.0490042i
$302$		0			0
$303$	0.498756	+	0.287957i	0.0286528	+	0.0165427i
$304$		0			0
$305$	−0.317474	−	0.549881i	−0.0181785	−	0.0314861i
$306$		0			0
$307$	−19.2802			−1.10038			−0.550189	−	0.835040i	$-0.685444\pi$
$307$	−19.2802			−1.10038			−0.550189	+	0.835040i	$0.685444\pi$
$308$		0			0
$309$	33.2853			1.89353
$310$		0			0
$311$	6.11946	+	10.5992i	0.347003	+	0.601027i	0.985716	−	0.168419i	$-0.0538661\pi$
$311$	6.11946	+	10.5992i	0.347003	+	0.601027i	−0.638713	+	0.769445i	$0.720533\pi$
$312$		0			0
$313$	−6.34922	−	3.66572i	−0.358879	−	0.207199i	0.309710	−	0.950831i	$-0.399768\pi$
$313$	−6.34922	−	3.66572i	−0.358879	−	0.207199i	−0.668589	+	0.743632i	$0.733101\pi$
$314$		0			0
$315$	−7.90649	−	17.8137i	−0.445480	−	1.00369i
$316$		0			0
$317$	13.4673	−	23.3261i	0.756400	−	1.31012i	−0.188276	−	0.982116i	$-0.560290\pi$
$317$	13.4673	−	23.3261i	0.756400	−	1.31012i	0.944675	−	0.328007i	$-0.106377\pi$
$318$		0			0
$319$	11.5533	−	6.67030i	0.646861	−	0.373465i
$320$		0			0
$321$		−	0.349578i		−	0.0195116i
$322$		0			0
$323$		−	25.0097i		−	1.39158i
$324$		0			0
$325$	−4.61084	+	2.66207i	−0.255764	+	0.147665i
$326$		0			0
$327$	−0.677297	+	1.17311i	−0.0374546	+	0.0648733i
$328$		0			0
$329$	−4.62387	−	3.36762i	−0.254922	−	0.185663i
$330$		0			0
$331$	−2.75467	−	1.59041i	−0.151410	−	0.0874168i	0.422381	−	0.906419i	$-0.361195\pi$
$331$	−2.75467	−	1.59041i	−0.151410	−	0.0874168i	−0.573791	+	0.819002i	$0.694528\pi$
$332$		0			0
$333$	22.3060	+	38.6351i	1.22236	+	2.11719i
$334$		0			0
$335$	−14.2559			−0.778881
$336$		0			0
$337$	−6.57720			−0.358283			−0.179141	−	0.983823i	$-0.557332\pi$
$337$	−6.57720			−0.358283			−0.179141	+	0.983823i	$0.557332\pi$
$338$		0			0
$339$	−18.3411	−	31.7678i	−0.996154	−	1.72539i
$340$		0			0
$341$	7.46629	+	4.31066i	0.404322	+	0.233436i
$342$		0			0
$343$	5.78415	−	17.5939i	0.312315	−	0.949979i
$344$		0			0
$345$	−9.53916	+	16.5223i	−0.513571	+	0.889531i
$346$		0			0
$347$	25.3335	−	14.6263i	1.35997	−	0.785182i	0.370354	−	0.928891i	$-0.379236\pi$
$347$	25.3335	−	14.6263i	1.35997	−	0.785182i	0.989620	+	0.143709i	$0.0459029\pi$
$348$		0			0
$349$		−	28.9652i		−	1.55047i	−0.631673	−	0.775235i	$-0.717631\pi$
$349$		−	28.9652i		−	1.55047i	0.631673	−	0.775235i	$-0.282369\pi$
$350$		0			0
$351$			74.8479i			3.99508i
$352$		0			0
$353$	−2.49898	+	1.44279i	−0.133007	+	0.0767918i	−0.565027	−	0.825072i	$-0.691134\pi$
$353$	−2.49898	+	1.44279i	−0.133007	+	0.0767918i	0.432020	+	0.901864i	$0.357801\pi$
$354$		0			0
$355$	−2.80607	+	4.86026i	−0.148931	+	0.257956i
$356$		0			0
$357$	−23.3723	+	32.0911i	−1.23699	+	1.69844i
$358$		0			0
$359$	27.2434	+	15.7290i	1.43785	+	0.830145i	0.997700	−	0.0677778i	$-0.0215909\pi$
$359$	27.2434	+	15.7290i	1.43785	+	0.830145i	0.440153	+	0.897923i	$0.354924\pi$
$360$		0			0
$361$	−4.89878	−	8.48493i	−0.257830	−	0.446575i
$362$		0			0
$363$	26.9997			1.41712
$364$		0			0
$365$	0.744866			0.0389881
$366$		0			0
$367$	15.9862	+	27.6889i	0.834472	+	1.44535i	0.894460	+	0.447148i	$0.147560\pi$
$367$	15.9862	+	27.6889i	0.834472	+	1.44535i	−0.0599880	+	0.998199i	$0.519106\pi$
$368$		0			0
$369$	−14.9938	−	8.65669i	−0.780548	−	0.450649i
$370$		0			0
$371$	13.0482	−	5.79137i	0.677430	−	0.300673i
$372$		0			0
$373$	17.1833	−	29.7623i	0.889717	−	1.54104i	0.0495076	−	0.998774i	$-0.484235\pi$
$373$	17.1833	−	29.7623i	0.889717	−	1.54104i	0.840210	−	0.542262i	$-0.182432\pi$
$374$		0			0
$375$	2.78832	−	1.60984i	0.143988	−	0.0831318i
$376$		0			0
$377$			43.9298i			2.26250i
$378$		0			0
$379$			28.7064i			1.47455i	0.675595	+	0.737273i	$0.263887\pi$
$379$			28.7064i			1.47455i	−0.675595	+	0.737273i	$0.736113\pi$
$380$		0			0
$381$	14.7481	−	8.51483i	0.755569	−	0.436228i
$382$		0			0
$383$	3.87359	−	6.70926i	0.197931	−	0.342827i	−0.749926	−	0.661521i	$-0.769911\pi$
$383$	3.87359	−	6.70926i	0.197931	−	0.342827i	0.947858	+	0.318694i	$0.103244\pi$
$384$		0			0
$385$	−0.452066	+	4.25379i	−0.0230394	+	0.216793i
$386$		0			0
$387$	19.3983	+	11.1996i	0.986069	+	0.569307i
$388$		0			0
$389$	10.2230	+	17.7067i	0.518325	+	0.897765i	0.999773	+	0.0212909i	$0.00677760\pi$
$389$	10.2230	+	17.7067i	0.518325	+	0.897765i	−0.481448	+	0.876475i	$0.659889\pi$
$390$		0			0
$391$	27.6158			1.39659
$392$		0			0
$393$	−48.1660			−2.42965
$394$		0			0
$395$	−0.309144	−	0.535453i	−0.0155547	−	0.0269416i
$396$		0			0
$397$	−27.8565	−	16.0829i	−1.39808	−	0.807180i	−0.403885	−	0.914810i	$-0.632341\pi$
$397$	−27.8565	−	16.0829i	−1.39808	−	0.807180i	−0.994191	+	0.107630i	$0.965674\pi$
$398$		0			0
$399$	−4.83088	+	45.4570i	−0.241847	+	2.27570i
$400$		0			0
$401$	11.1471	−	19.3073i	0.556660	−	0.964163i	−0.441113	−	0.897452i	$-0.645416\pi$
$401$	11.1471	−	19.3073i	0.556660	−	0.964163i	0.997772	−	0.0667110i	$-0.0212506\pi$
$402$		0			0
$403$	−24.5861	+	14.1948i	−1.22472	+	0.707092i
$404$		0			0
$405$		−	23.1639i		−	1.15102i
$406$		0			0
$407$		−	9.79186i		−	0.485365i
$408$		0			0
$409$	3.45876	−	1.99691i	0.171024	−	0.0987410i	−0.412044	−	0.911164i	$-0.635185\pi$
$409$	3.45876	−	1.99691i	0.171024	−	0.0987410i	0.583069	+	0.812423i	$0.301852\pi$
$410$		0			0
$411$	34.8666	−	60.3908i	1.71984	−	2.97886i
$412$		0			0
$413$	−18.0100	+	7.99361i	−0.886212	+	0.393340i
$414$		0			0
$415$	−2.69666	−	1.55691i	−0.132374	−	0.0764259i
$416$		0			0
$417$	−22.5331	−	39.0285i	−1.10345	−	1.91123i
$418$		0			0
$419$	32.9704			1.61071			0.805354	−	0.592794i	$-0.201975\pi$
$419$	32.9704			1.61071			0.805354	+	0.592794i	$0.201975\pi$
$420$		0			0
$421$	24.0036			1.16986			0.584931	−	0.811083i	$-0.301121\pi$
$421$	24.0036			1.16986			0.584931	+	0.811083i	$0.301121\pi$
$422$		0			0
$423$	−7.96317	−	13.7926i	−0.387182	−	0.670620i
$424$		0			0
$425$	−4.03609	−	2.33024i	−0.195779	−	0.113033i
$426$		0			0
$427$	0.989000	−	1.35794i	0.0478611	−	0.0657151i
$428$		0			0
$429$	13.8579	−	24.0026i	0.669067	−	1.15886i
$430$		0			0
$431$	−6.94578	+	4.01015i	−0.334566	+	0.193162i	−0.657867	−	0.753134i	$-0.728541\pi$
$431$	−6.94578	+	4.01015i	−0.334566	+	0.193162i	0.323300	+	0.946296i	$0.395208\pi$
$432$		0			0
$433$			14.0389i			0.674665i	0.941386	+	0.337333i	$0.109525\pi$
$433$			14.0389i			0.674665i	−0.941386	+	0.337333i	$0.890475\pi$
$434$		0			0
$435$		−	26.5658i		−	1.27373i
$436$		0			0
$437$	27.5382	−	15.8992i	1.31733	−	0.760562i
$438$		0			0
$439$	9.93780	−	17.2128i	0.474305	−	0.821521i	−0.525262	−	0.850941i	$-0.676033\pi$
$439$	9.93780	−	17.2128i	0.474305	−	0.821521i	0.999567	+	0.0294199i	$0.00936601\pi$
$440$		0			0
$441$	34.5918	−	38.2399i	1.64723	−	1.82095i
$442$		0			0
$443$	−3.93609	−	2.27250i	−0.187009	−	0.107970i	0.403572	−	0.914948i	$-0.367768\pi$
$443$	−3.93609	−	2.27250i	−0.187009	−	0.107970i	−0.590582	+	0.806978i	$0.701102\pi$
$444$		0			0
$445$	−1.13587	−	1.96739i	−0.0538456	−	0.0932634i
$446$		0			0
$447$	−33.1710			−1.56893
$448$		0			0
$449$	−6.12285			−0.288955			−0.144477	−	0.989508i	$-0.546150\pi$
$449$	−6.12285			−0.288955			−0.144477	+	0.989508i	$0.546150\pi$
$450$		0			0
$451$	1.90005	+	3.29099i	0.0894701	+	0.154967i
$452$		0			0
$453$	−4.72739	−	2.72936i	−0.222112	−	0.128237i
$454$		0			0
$455$	−11.3865	−	8.29293i	−0.533808	−	0.388778i
$456$		0			0
$457$	−2.62269	+	4.54262i	−0.122684	+	0.212495i	−0.920825	−	0.389975i	$-0.872484\pi$
$457$	−2.62269	+	4.54262i	−0.122684	+	0.212495i	0.798141	+	0.602470i	$0.205817\pi$
$458$		0			0
$459$	−56.7402	+	32.7590i	−2.64841	+	1.52906i
$460$		0			0
$461$		−	12.4847i		−	0.581473i	−0.956803	−	0.290736i	$-0.906100\pi$
$461$		−	12.4847i		−	0.581473i	0.956803	−	0.290736i	$-0.0939002\pi$
$462$		0			0
$463$			2.48748i			0.115603i	0.998328	+	0.0578014i	$0.0184090\pi$
$463$			2.48748i			0.115603i	−0.998328	+	0.0578014i	$0.981591\pi$
$464$		0			0
$465$	14.8680	−	8.58403i	0.689486	−	0.398075i
$466$		0			0
$467$	−13.9669	+	24.1914i	−0.646311	+	1.11944i	0.337686	+	0.941259i	$0.390356\pi$
$467$	−13.9669	+	24.1914i	−0.646311	+	1.11944i	−0.983997	+	0.178185i	$0.942978\pi$
$468$		0			0
$469$	−15.3012	−	34.4743i	−0.706544	−	1.59188i
$470$		0			0
$471$	37.8985	+	21.8807i	1.74627	+	1.00821i
$472$		0			0
$473$	−2.45819	−	4.25772i	−0.113028	−	0.195770i
$474$		0			0
$475$	−5.36634			−0.246224
$476$		0			0
$477$	39.7466			1.81987
$478$		0			0
$479$	−3.29237	−	5.70255i	−0.150432	−	0.260556i	0.780954	−	0.624588i	$-0.214733\pi$
$479$	−3.29237	−	5.70255i	−0.150432	−	0.260556i	−0.931386	+	0.364032i	$0.881400\pi$
$480$		0			0
$481$	27.9242	+	16.1220i	1.27323	+	0.735101i
$482$		0			0
$483$	−50.1938	−	5.33428i	−2.28390	−	0.242718i
$484$		0			0
$485$	2.05764	−	3.56393i	0.0934324	−	0.161830i
$486$		0			0
$487$	1.65409	−	0.954988i	0.0749539	−	0.0432746i	−0.462055	−	0.886851i	$-0.652888\pi$
$487$	1.65409	−	0.954988i	0.0749539	−	0.0432746i	0.537009	+	0.843577i	$0.319554\pi$
$488$		0			0
$489$		−	36.5003i		−	1.65060i
$490$		0			0
$491$		−	1.49744i		−	0.0675784i	−0.999429	−	0.0337892i	$-0.989243\pi$
$491$		−	1.49744i		−	0.0675784i	0.999429	−	0.0337892i	$-0.0107575\pi$
$492$		0			0
$493$	−33.3021	+	19.2270i	−1.49985	+	0.865939i
$494$		0			0
$495$	−5.95507	+	10.3145i	−0.267661	+	0.463602i
$496$		0			0
$497$	−14.7652	−	1.56915i	−0.662309	−	0.0703861i
$498$		0			0
$499$	−36.1503	−	20.8714i	−1.61831	−	0.934333i	−0.987357	−	0.158513i	$-0.949330\pi$
$499$	−36.1503	−	20.8714i	−1.61831	−	0.934333i	−0.630955	−	0.775819i	$-0.717337\pi$
$500$		0			0
$501$	8.12681	+	14.0761i	0.363079	+	0.628872i
$502$		0			0
$503$	19.9860			0.891130			0.445565	−	0.895250i	$-0.353003\pi$
$503$	19.9860			0.891130			0.445565	+	0.895250i	$0.353003\pi$
$504$		0			0
$505$	−0.178873			−0.00795975
$506$		0			0
$507$	24.7054	+	42.7910i	1.09721	+	1.90042i
$508$		0			0
$509$	−19.8929	−	11.4851i	−0.881736	−	0.509070i	−0.0105053	−	0.999945i	$-0.503344\pi$
$509$	−19.8929	−	11.4851i	−0.881736	−	0.509070i	−0.871230	+	0.490875i	$0.836677\pi$
$510$		0			0
$511$	0.799486	+	1.80128i	0.0353672	+	0.0796838i
$512$		0			0
$513$	−37.7205	+	65.3338i	−1.66540	+	2.88456i
$514$		0			0
$515$	−8.95304	+	5.16904i	−0.394518	+	0.227775i
$516$		0			0
$517$			3.49567i			0.153739i
$518$		0			0
$519$		−	76.1309i		−	3.34178i
$520$		0			0
$521$	−34.8762	+	20.1358i	−1.52795	+	0.882165i	−0.528507	+	0.848929i	$0.677248\pi$
$521$	−34.8762	+	20.1358i	−1.52795	+	0.882165i	−0.999448	+	0.0332363i	$0.989419\pi$
$522$		0			0
$523$	11.1304	−	19.2784i	0.486697	−	0.842984i	−0.513186	−	0.858277i	$-0.671535\pi$
$523$	11.1304	−	19.2784i	0.486697	−	0.842984i	0.999883	+	0.0152934i	$0.00486823\pi$
$524$		0			0
$525$	6.88579	+	5.01500i	0.300521	+	0.218872i
$526$		0			0
$527$	−21.5214	−	12.4254i	−0.937486	−	0.541258i
$528$		0			0
$529$	6.05598	+	10.4893i	0.263303	+	0.456055i
$530$		0			0
$531$	−54.8608			−2.38075
$532$		0			0
$533$	−12.5135			−0.542022
$534$		0			0
$535$	0.0542877	+	0.0940291i	0.00234706	+	0.00406523i
$536$		0			0
$537$	−36.8867	−	21.2965i	−1.59178	−	0.919013i
$538$		0			0
$539$	−10.7720	+	3.47250i	−0.463982	+	0.149571i
$540$		0			0
$541$	0.320401	−	0.554951i	0.0137751	−	0.0238592i	−0.859056	−	0.511882i	$-0.828948\pi$
$541$	0.320401	−	0.554951i	0.0137751	−	0.0238592i	0.872831	+	0.488023i	$0.162282\pi$
$542$		0			0
$543$	−42.6734	+	24.6375i	−1.83129	+	1.05730i
$544$		0			0
$545$		−	0.420724i		−	0.0180218i
$546$		0			0
$547$			21.9754i			0.939598i	0.882773	+	0.469799i	$0.155674\pi$
$547$			21.9754i			0.939598i	−0.882773	+	0.469799i	$0.844326\pi$
$548$		0			0
$549$	4.05061	−	2.33862i	0.172876	−	0.0998098i
$550$		0			0
$551$	−22.1390	+	38.3458i	−0.943152	+	1.63359i
$552$		0			0
$553$	0.963051	−	1.32231i	0.0409531	−	0.0562302i
$554$		0			0
$555$	−16.8866	−	9.74950i	−0.716798	−	0.413843i
$556$		0			0
$557$	0.438633	+	0.759735i	0.0185855	+	0.0321910i	0.875169	−	0.483818i	$-0.160750\pi$
$557$	0.438633	+	0.759735i	0.0185855	+	0.0321910i	−0.856583	+	0.516009i	$0.827417\pi$
$558$		0			0
$559$	16.1894			0.684738
$560$		0			0
$561$	24.2610			1.02430
$562$		0			0
$563$	8.69342	+	15.0575i	0.366384	+	0.634596i	0.988997	−	0.147934i	$-0.0472623\pi$
$563$	8.69342	+	15.0575i	0.366384	+	0.634596i	−0.622613	+	0.782530i	$0.713929\pi$
$564$		0			0
$565$	9.86676	+	5.69658i	0.415098	+	0.239657i
$566$		0			0
$567$	56.0162	−	24.8625i	2.35246	−	1.04412i
$568$		0			0
$569$	14.7391	−	25.5289i	0.617897	−	1.07023i	−0.371972	−	0.928244i	$-0.621318\pi$
$569$	14.7391	−	25.5289i	0.617897	−	1.07023i	0.989869	−	0.141985i	$-0.0453485\pi$
$570$		0			0
$571$	16.5518	−	9.55619i	0.692672	−	0.399914i	−0.111940	−	0.993715i	$-0.535707\pi$
$571$	16.5518	−	9.55619i	0.692672	−	0.399914i	0.804612	+	0.593801i	$0.202373\pi$
$572$		0			0
$573$			20.0511i			0.837645i
$574$		0			0
$575$		−	5.92553i		−	0.247112i
$576$		0			0
$577$	−9.56733	+	5.52370i	−0.398293	+	0.229955i	−0.685747	−	0.727840i	$-0.740524\pi$
$577$	−9.56733	+	5.52370i	−0.398293	+	0.229955i	0.287454	+	0.957794i	$0.407191\pi$
$578$		0			0
$579$	−34.0078	+	58.9033i	−1.41332	+	2.44794i
$580$		0			0
$581$	0.870624	−	8.19229i	0.0361196	−	0.339873i
$582$		0			0
$583$	−7.55518	−	4.36199i	−0.312904	−	0.180655i
$584$		0			0
$585$	−19.6097	−	33.9650i	−0.810762	−	1.40428i
$586$		0			0
$587$	−8.71924			−0.359881			−0.179941	−	0.983677i	$-0.557591\pi$
$587$	−8.71924			−0.359881			−0.179941	+	0.983677i	$0.557591\pi$
$588$		0			0
$589$	−28.6145			−1.17904
$590$		0			0
$591$	11.1104	+	19.2438i	0.457022	+	0.791585i
$592$		0			0
$593$	5.61937	+	3.24435i	0.230760	+	0.133229i	0.610923	−	0.791690i	$-0.290799\pi$
$593$	5.61937	+	3.24435i	0.230760	+	0.133229i	−0.380163	+	0.924920i	$0.624132\pi$
$594$		0			0
$595$	1.30307	−	12.2614i	0.0534205	−	0.502669i
$596$		0			0
$597$	0.547934	−	0.949050i	0.0224255	−	0.0388420i
$598$		0			0
$599$	−4.63126	+	2.67386i	−0.189228	+	0.109251i	−0.591621	−	0.806216i	$-0.701512\pi$
$599$	−4.63126	+	2.67386i	−0.189228	+	0.109251i	0.402393	+	0.915467i	$0.368179\pi$
$600$		0			0
$601$			28.4122i			1.15896i	0.814988	+	0.579478i	$0.196744\pi$
$601$			28.4122i			1.15896i	−0.814988	+	0.579478i	$0.803256\pi$
$602$		0			0
$603$		−	105.013i		−	4.27648i
$604$		0			0
$605$	−7.26236	+	4.19292i	−0.295257	+	0.170467i
$606$		0			0
$607$	4.08802	−	7.08065i	0.165927	−	0.287395i	−0.771057	−	0.636766i	$-0.780272\pi$
$607$	4.08802	−	7.08065i	0.165927	−	0.287395i	0.936984	+	0.349372i	$0.113605\pi$
$608$		0			0
$609$	64.2429	−	28.5138i	2.60325	−	1.15544i
$610$		0			0
$611$	−9.96884	−	5.75551i	−0.403296	−	0.232843i
$612$		0			0
$613$	12.1355	+	21.0194i	0.490150	+	0.848964i	0.999936	−	0.0113371i	$-0.00360880\pi$
$613$	12.1355	+	21.0194i	0.490150	+	0.848964i	−0.509786	+	0.860301i	$0.670275\pi$
$614$		0			0
$615$	7.56734			0.305145
$616$		0			0
$617$	34.2542			1.37902			0.689511	−	0.724275i	$-0.257825\pi$
$617$	34.2542			1.37902			0.689511	+	0.724275i	$0.257825\pi$
$618$		0			0
$619$	−16.9691	−	29.3914i	−0.682047	−	1.18134i	−0.974355	−	0.225015i	$-0.927757\pi$
$619$	−16.9691	−	29.3914i	−0.682047	−	1.18134i	0.292309	−	0.956324i	$-0.405577\pi$
$620$		0			0
$621$	−72.1419	−	41.6512i	−2.89496	−	1.67140i
$622$		0			0
$623$	3.53850	−	4.85850i	0.141767	−	0.194652i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	24.1928	−	13.9677i	0.966169	−	0.557818i
$628$		0			0
$629$			28.2248i			1.12540i
$630$		0			0
$631$			15.1185i			0.601857i	0.953647	+	0.300929i	$0.0972966\pi$
$631$			15.1185i			0.601857i	−0.953647	+	0.300929i	$0.902703\pi$
$632$		0			0
$633$	39.3256	−	22.7047i	1.56305	−	0.902430i
$634$		0			0
$635$	−2.64462	+	4.58062i	−0.104949	+	0.181776i
$636$		0			0
$637$	7.83296	−	36.4366i	0.310353	−	1.44367i
$638$		0			0
$639$	−35.8023	−	20.6705i	−1.41632	−	0.817711i
$640$		0			0
$641$	−11.9914	−	20.7696i	−0.473630	−	0.820352i	0.525914	−	0.850538i	$-0.323723\pi$
$641$	−11.9914	−	20.7696i	−0.473630	−	0.820352i	−0.999544	+	0.0301859i	$0.990390\pi$
$642$		0			0
$643$	8.12044			0.320239			0.160119	−	0.987098i	$-0.448812\pi$
$643$	8.12044			0.320239			0.160119	+	0.987098i	$0.448812\pi$
$644$		0			0
$645$	−9.79024			−0.385490
$646$		0			0
$647$	3.47447	+	6.01796i	0.136596	+	0.236590i	0.926206	−	0.377018i	$-0.123051\pi$
$647$	3.47447	+	6.01796i	0.136596	+	0.236590i	−0.789610	+	0.613609i	$0.789717\pi$
$648$		0			0
$649$	10.4281	+	6.02069i	0.409340	+	0.236333i
$650$		0			0
$651$	36.7166	+	26.7411i	1.43904	+	1.04807i
$652$		0			0
$653$	−2.93521	+	5.08394i	−0.114864	+	0.198950i	−0.917725	−	0.397216i	$-0.869976\pi$
$653$	−2.93521	+	5.08394i	−0.114864	+	0.198950i	0.802862	+	0.596166i	$0.203310\pi$
$654$		0			0
$655$	12.9556	−	7.47994i	0.506219	−	0.292265i
$656$		0			0
$657$			5.48693i			0.214066i
$658$		0			0
$659$			27.6988i			1.07899i	0.841988	+	0.539496i	$0.181385\pi$
$659$			27.6988i			1.07899i	−0.841988	+	0.539496i	$0.818615\pi$
$660$		0			0
$661$	2.06615	−	1.19289i	0.0803639	−	0.0463981i	−0.459280	−	0.888292i	$-0.651892\pi$
$661$	2.06615	−	1.19289i	0.0803639	−	0.0463981i	0.539643	+	0.841894i	$0.318559\pi$
$662$		0			0
$663$	−39.9451	+	69.1869i	−1.55134	+	2.68700i
$664$		0			0
$665$	−5.75984	−	12.9772i	−0.223357	−	0.503233i
$666$		0			0
$667$	−42.3417	−	24.4460i	−1.63948	−	0.946552i
$668$		0			0
$669$	−31.6190	−	54.7657i	−1.22246	−	2.11736i
$670$		0			0
$671$	−1.02661			−0.0396317
$672$		0			0
$673$	43.3982			1.67288			0.836440	−	0.548059i	$-0.184633\pi$
$673$	43.3982			1.67288			0.836440	+	0.548059i	$0.184633\pi$
$674$		0			0
$675$	7.02910	+	12.1748i	0.270550	+	0.468607i
$676$		0			0
$677$	31.2191	+	18.0243i	1.19985	+	0.692731i	0.960521	−	0.278208i	$-0.0897404\pi$
$677$	31.2191	+	18.0243i	1.19985	+	0.692731i	0.239325	+	0.970939i	$0.423074\pi$
$678$		0			0
$679$	10.8270	+	1.15063i	0.415503	+	0.0441570i
$680$		0			0
$681$	−29.6151	+	51.2948i	−1.13485	+	1.96562i
$682$		0			0
$683$	22.6823	−	13.0956i	0.867914	−	0.501091i	0.00125979	−	0.999999i	$-0.499599\pi$
$683$	22.6823	−	13.0956i	0.867914	−	0.501091i	0.866655	+	0.498909i	$0.166266\pi$
$684$		0			0
$685$			21.6584i			0.827527i
$686$		0			0
$687$			3.72254i			0.142024i
$688$		0			0
$689$	24.8788	−	14.3638i	0.947806	−	0.547216i
$690$		0			0
$691$	6.74749	−	11.6870i	0.256687	−	0.444595i	−0.708666	−	0.705545i	$-0.750702\pi$
$691$	6.74749	−	11.6870i	0.256687	−	0.444595i	0.965352	+	0.260950i	$0.0840358\pi$
$692$		0			0
$693$	−31.3348	−	3.33007i	−1.19031	−	0.126499i
$694$		0			0
$695$	12.1219	+	6.99856i	0.459808	+	0.265470i
$696$		0			0
$697$	−5.47686	−	9.48619i	−0.207451	−	0.359315i
$698$		0			0
$699$	7.94417			0.300476
$700$		0			0
$701$	−14.6264			−0.552432			−0.276216	−	0.961096i	$-0.589081\pi$
$701$	−14.6264			−0.552432			−0.276216	+	0.961096i	$0.589081\pi$
$702$		0			0
$703$	16.2498	+	28.1454i	0.612872	+	1.06153i
$704$		0			0
$705$	6.02848	+	3.48054i	0.227046	+	0.131085i
$706$		0			0
$707$	−0.191990	−	0.432561i	−0.00722051	−	0.0162681i
$708$		0			0
$709$	−3.63183	+	6.29051i	−0.136396	+	0.236245i	−0.926130	−	0.377205i	$-0.876885\pi$
$709$	−3.63183	+	6.29051i	−0.136396	+	0.236245i	0.789734	+	0.613450i	$0.210219\pi$
$710$		0			0
$711$	3.94433	−	2.27726i	0.147924	−	0.0854039i
$712$		0			0
$713$		−	31.5963i		−	1.18329i
$714$		0			0
$715$			8.60826i			0.321931i
$716$		0			0
$717$	−12.0026	+	6.92968i	−0.448244	+	0.258794i
$718$		0			0
$719$	10.0297	−	17.3719i	0.374043	−	0.647862i	−0.616140	−	0.787636i	$-0.711305\pi$
$719$	10.0297	−	17.3719i	0.374043	−	0.647862i	0.990183	+	0.139775i	$0.0446379\pi$
$720$		0			0
$721$	−22.1096	−	16.1027i	−0.823405	−	0.599695i
$722$		0			0
$723$	80.2727	+	46.3455i	2.98537	+	1.72361i
$724$		0			0
$725$	4.12553	+	7.14563i	0.153218	+	0.265382i
$726$		0			0
$727$	20.9849			0.778287			0.389144	−	0.921177i	$-0.372771\pi$
$727$	20.9849			0.778287			0.389144	+	0.921177i	$0.372771\pi$
$728$		0			0
$729$	34.8443			1.29053
$730$		0			0
$731$	7.08568	+	12.2728i	0.262073	+	0.453924i
$732$		0			0
$733$	11.8703	+	6.85334i	0.438441	+	0.253134i	0.702936	−	0.711253i	$-0.251872\pi$
$733$	11.8703	+	6.85334i	0.438441	+	0.253134i	−0.264495	+	0.964387i	$0.585205\pi$
$734$		0			0
$735$	−4.73684	+	22.0344i	−0.174721	+	0.812749i
$736$		0			0
$737$	−11.5247	+	19.9613i	−0.424517	+	0.735285i
$738$		0			0
$739$	0.459385	−	0.265226i	0.0168987	−	0.00975649i	−0.491527	−	0.870862i	$-0.663561\pi$
$739$	0.459385	−	0.265226i	0.0168987	−	0.00975649i	0.508426	+	0.861106i	$0.330228\pi$
$740$		0			0
$741$			91.9899i			3.37933i
$742$		0			0
$743$		−	22.8953i		−	0.839946i	−0.907537	−	0.419973i	$-0.862040\pi$
$743$		−	22.8953i		−	0.839946i	0.907537	−	0.419973i	$-0.137960\pi$
$744$		0			0
$745$	8.92228	−	5.15128i	0.326887	−	0.188728i
$746$		0			0
$747$	11.4688	−	19.8645i	0.419620	−	0.726803i
$748$		0			0
$749$	−0.169118	+	0.232206i	−0.00617944	+	0.00848462i
$750$		0			0
$751$	8.89236	+	5.13401i	0.324487	+	0.187343i	0.653391	−	0.757021i	$-0.273346\pi$
$751$	8.89236	+	5.13401i	0.324487	+	0.187343i	−0.328904	+	0.944363i	$0.606679\pi$
$752$		0			0
$753$	25.2526	+	43.7388i	0.920256	+	1.59393i
$754$		0			0
$755$	1.69542			0.0617028
$756$		0			0
$757$	24.3589			0.885340			0.442670	−	0.896685i	$-0.354031\pi$
$757$	24.3589			0.885340			0.442670	+	0.896685i	$0.354031\pi$
$758$		0			0
$759$	15.4232	+	26.7138i	0.559828	+	0.969651i
$760$		0			0
$761$	−13.0418	−	7.52970i	−0.472766	−	0.272951i	0.244631	−	0.969616i	$-0.421333\pi$
$761$	−13.0418	−	7.52970i	−0.472766	−	0.272951i	−0.717397	+	0.696665i	$0.754666\pi$
$762$		0			0
$763$	1.01742	−	0.451574i	0.0368330	−	0.0163481i
$764$		0			0
$765$	17.1653	−	29.7312i	0.620614	−	1.07493i
$766$		0			0
$767$	−34.3392	+	19.8258i	−1.23992	+	0.715867i
$768$		0			0
$769$			14.6137i			0.526985i	0.964661	+	0.263492i	$0.0848744\pi$
$769$			14.6137i			0.526985i	−0.964661	+	0.263492i	$0.915126\pi$
$770$		0			0
$771$		−	81.1625i		−	2.92300i
$772$		0			0
$773$	−33.6718	+	19.4404i	−1.21109	+	0.699223i	−0.962997	−	0.269513i	$-0.913137\pi$
$773$	−33.6718	+	19.4404i	−1.21109	+	0.699223i	−0.248093	+	0.968736i	$0.579804\pi$
$774$		0			0
$775$	−2.66611	+	4.61784i	−0.0957696	+	0.165878i
$776$		0			0
$777$	5.45191	−	51.3006i	0.195586	−	1.84040i
$778$		0			0
$779$	−10.9229	−	6.30635i	−0.391354	−	0.225949i
$780$		0			0
$781$	4.53695	+	7.85824i	0.162345	+	0.281190i
$782$		0			0
$783$	115.995			4.14533
$784$		0			0
$785$	−13.5919			−0.485114
$786$		0			0
$787$	−3.07615	−	5.32805i	−0.109653	−	0.189925i	0.805977	−	0.591947i	$-0.201641\pi$
$787$	−3.07615	−	5.32805i	−0.109653	−	0.189925i	−0.915630	+	0.402023i	$0.868307\pi$
$788$		0			0
$789$	−44.7439	−	25.8329i	−1.59293	−	0.919677i
$790$		0			0
$791$	−3.18552	+	29.9747i	−0.113264	+	1.06578i
$792$		0			0
$793$	1.69028	−	2.92764i	0.0600235	−	0.103964i
$794$		0			0
$795$	−15.0450	+	8.68623i	−0.533591	+	0.308069i
$796$		0			0
$797$			47.2913i			1.67514i	0.546327	+	0.837572i	$0.316026\pi$
$797$			47.2913i			1.67514i	−0.546327	+	0.837572i	$0.683974\pi$
$798$		0			0
$799$		−	10.0762i		−	0.356469i
$800$		0			0
$801$	14.4925	−	8.36724i	0.512066	−	0.295642i
$802$		0			0
$803$	0.602163	−	1.04298i	0.0212499	−	0.0368058i
$804$		0			0
$805$	14.3295	−	6.36004i	0.505047	−	0.224162i
$806$		0			0
$807$	8.29614	+	4.78978i	0.292038	+	0.168608i
$808$		0			0
$809$	13.9998	+	24.2484i	0.492208	+	0.852529i	0.999960	−	0.00897419i	$-0.00285661\pi$
$809$	13.9998	+	24.2484i	0.492208	+	0.852529i	−0.507752	+	0.861503i	$0.669523\pi$
$810$		0			0
$811$	−12.1609			−0.427026			−0.213513	−	0.976940i	$-0.568491\pi$
$811$	−12.1609			−0.427026			−0.213513	+	0.976940i	$0.568491\pi$
$812$		0			0
$813$	−55.9033			−1.96061
$814$		0			0
$815$	5.66832	+	9.81781i	0.198552	+	0.343903i
$816$		0			0
$817$	14.1315	+	8.15884i	0.494400	+	0.285442i
$818$		0			0
$819$	61.0885	−	83.8769i	2.13460	−	2.93090i
$820$		0			0
$821$	9.22766	−	15.9828i	0.322048	−	0.557803i	−0.658863	−	0.752263i	$-0.728962\pi$
$821$	9.22766	−	15.9828i	0.322048	−	0.557803i	0.980910	+	0.194460i	$0.0622956\pi$
$822$		0			0
$823$	−26.1593	+	15.1031i	−0.911855	+	0.526460i	−0.881028	−	0.473065i	$-0.843148\pi$
$823$	−26.1593	+	15.1031i	−0.911855	+	0.526460i	−0.0308275	+	0.999525i	$0.509814\pi$
$824$		0			0
$825$		−	5.20569i		−	0.181239i
$826$		0			0
$827$		−	3.28320i		−	0.114168i	−0.998369	−	0.0570841i	$-0.981820\pi$
$827$		−	3.28320i		−	0.114168i	0.998369	−	0.0570841i	$-0.0181803\pi$
$828$		0			0
$829$	32.6939	−	18.8758i	1.13550	−	0.655584i	0.190191	−	0.981747i	$-0.439089\pi$
$829$	32.6939	−	18.8758i	1.13550	−	0.655584i	0.945314	+	0.326163i	$0.105756\pi$
$830$		0			0
$831$	35.8326	−	62.0638i	1.24302	−	2.15297i
$832$		0			0
$833$	31.0499	−	10.0094i	1.07582	−	0.346805i
$834$		0			0
$835$	−4.37188	−	2.52411i	−0.151295	−	0.0873503i
$836$		0			0
$837$	37.4807	+	64.9186i	1.29552	+	2.24391i
$838$		0			0
$839$	−41.6604			−1.43828			−0.719139	−	0.694866i	$-0.755464\pi$
$839$	−41.6604			−1.43828			−0.719139	+	0.694866i	$0.755464\pi$
$840$		0			0
$841$	39.0800			1.34759
$842$		0			0
$843$	52.5806	+	91.0723i	1.81097	+	3.13670i
$844$		0			0
$845$	−13.2905	−	7.67325i	−0.457206	−	0.263968i
$846$		0			0
$847$	−17.9345	−	13.0619i	−0.616235	−	0.448811i
$848$		0			0
$849$	−14.1529	+	24.5135i	−0.485725	+	0.841300i
$850$		0			0
$851$	−31.0783	+	17.9431i	−1.06535	+	0.615081i
$852$		0			0
$853$		−	14.9474i		−	0.511791i	−0.966705	−	0.255895i	$-0.917630\pi$
$853$		−	14.9474i		−	0.511791i	0.966705	−	0.255895i	$-0.0823702\pi$
$854$		0			0
$855$		−	39.5302i		−	1.35191i
$856$		0			0
$857$	−50.5400	+	29.1793i	−1.72641	+	0.996746i	−0.822901	+	0.568185i	$0.807646\pi$
$857$	−50.5400	+	29.1793i	−1.72641	+	0.996746i	−0.903513	+	0.428561i	$0.859021\pi$
$858$		0			0
$859$	−12.6277	+	21.8717i	−0.430850	+	0.746254i	−0.996947	−	0.0780847i	$-0.975120\pi$
$859$	−12.6277	+	21.8717i	−0.430850	+	0.746254i	0.566097	+	0.824339i	$0.308453\pi$
$860$		0			0
$861$	8.12224	+	18.2998i	0.276805	+	0.623654i
$862$		0			0
$863$	−13.7889	−	7.96102i	−0.469379	−	0.270996i	0.246601	−	0.969117i	$-0.420686\pi$
$863$	−13.7889	−	7.96102i	−0.469379	−	0.270996i	−0.715980	+	0.698121i	$0.754020\pi$
$864$		0			0
$865$	11.8227	+	20.4776i	0.401986	+	0.696259i
$866$		0			0
$867$	−15.1972			−0.516122
$868$		0			0
$869$	−0.999670			−0.0339115
$870$		0			0
$871$	−37.9501	−	65.7315i	−1.28589	−	2.22723i
$872$		0			0
$873$	26.2531	+	15.1572i	0.888533	+	0.512995i
$874$		0			0
$875$	−2.63094	−	0.279599i	−0.0889419	−	0.00945218i
$876$		0			0
$877$	−10.4854	+	18.1613i	−0.354068	+	0.613264i	−0.986958	−	0.160978i	$-0.948535\pi$
$877$	−10.4854	+	18.1613i	−0.354068	+	0.613264i	0.632890	+	0.774242i	$0.281869\pi$
$878$		0			0
$879$	−21.1686	+	12.2217i	−0.713998	+	0.412227i
$880$		0			0
$881$			18.5802i			0.625984i	0.949756	+	0.312992i	$0.101331\pi$
$881$			18.5802i			0.625984i	−0.949756	+	0.312992i	$0.898669\pi$
$882$		0			0
$883$			41.4967i			1.39648i	0.715865	+	0.698238i	$0.246032\pi$
$883$			41.4967i			1.39648i	−0.715865	+	0.698238i	$0.753968\pi$
$884$		0			0
$885$	20.7660	−	11.9893i	0.698043	−	0.403015i
$886$		0			0
$887$	18.9466	−	32.8165i	0.636165	−	1.10187i	−0.350102	−	0.936712i	$-0.613853\pi$
$887$	18.9466	−	32.8165i	0.636165	−	1.10187i	0.986267	−	0.165159i	$-0.0528136\pi$
$888$		0			0
$889$	−13.9157	−	1.47887i	−0.466716	−	0.0495997i
$890$		0			0
$891$	−32.4345	−	18.7261i	−1.08660	−	0.627348i
$892$		0			0
$893$	−5.80112	−	10.0478i	−0.194127	−	0.336238i
$894$		0			0
$895$	13.2290			0.442196
$896$		0			0
$897$	−101.576			−3.39151
$898$		0			0
$899$	21.9983	+	38.1021i	0.733683	+	1.27078i
$900$		0			0
$901$	21.7776	+	12.5733i	0.725517	+	0.418878i
$902$		0			0
$903$	−10.5081	−	23.6753i	−0.349689	−	0.787865i
$904$		0			0
$905$	7.65215	−	13.2539i	0.254366	−	0.440575i
$906$		0			0
$907$	−45.2780	+	26.1413i	−1.50343	+	0.868007i	−0.503440	+	0.864030i	$0.667932\pi$
$907$	−45.2780	+	26.1413i	−1.50343	+	0.868007i	−0.999992	+	0.00397669i	$0.998734\pi$
$908$		0			0
$909$		−	1.31764i		−	0.0437034i
$910$		0			0
$911$		−	7.69892i		−	0.255077i	−0.991834	−	0.127538i	$-0.959292\pi$
$911$		−	7.69892i		−	0.255077i	0.991834	−	0.127538i	$-0.0407076\pi$
$912$		0			0
$913$	−4.36005	+	2.51727i	−0.144296	+	0.0833096i
$914$		0			0
$915$	−1.02216	+	1.77044i	−0.0337917	+	0.0585289i
$916$		0			0
$917$	31.9941	+	23.3016i	1.05654	+	0.769488i
$918$		0			0
$919$	38.7913	+	22.3962i	1.27961	+	0.738781i	0.976776	−	0.214263i	$-0.0687350\pi$
$919$	38.7913	+	22.3962i	1.27961	+	0.738781i	0.302831	+	0.953044i	$0.402068\pi$
$920$		0			0
$921$	31.0380	+	53.7594i	1.02274	+	1.77143i
$922$		0			0
$923$	−29.8799			−0.983507
$924$		0			0
$925$	6.05619			0.199126
$926$		0			0
$927$	−38.0769	−	65.9511i	−1.25061	−	2.16612i
$928$		0			0
$929$	23.2991	+	13.4518i	0.764420	+	0.441338i	0.830880	−	0.556451i	$-0.187837\pi$
$929$	23.2991	+	13.4518i	0.764420	+	0.441338i	−0.0664604	+	0.997789i	$0.521171\pi$
$930$		0			0
$931$	25.2000	−	27.8575i	0.825895	−	0.912994i
$932$		0			0
$933$	19.7027	−	34.1261i	0.645038	−	1.11724i
$934$		0			0
$935$	−6.52570	+	3.76761i	−0.213413	+	0.123214i
$936$		0			0
$937$		−	30.0574i		−	0.981933i	−0.871178	−	0.490967i	$-0.836644\pi$
$937$		−	30.0574i		−	0.981933i	0.871178	−	0.490967i	$-0.163356\pi$
$938$		0			0
$939$			23.6049i			0.770317i
$940$		0			0
$941$	21.1093	−	12.1875i	0.688144	−	0.397300i	−0.114773	−	0.993392i	$-0.536614\pi$
$941$	21.1093	−	12.1875i	0.688144	−	0.397300i	0.802916	+	0.596092i	$0.203281\pi$
$942$		0			0
$943$	6.96351	−	12.0611i	0.226763	−	0.392765i
$944$		0			0
$945$	−21.8972	+	30.0657i	−0.712315	+	0.978037i
$946$		0			0
$947$	46.9659	+	27.1158i	1.52619	+	0.881144i	0.999517	+	0.0310743i	$0.00989286\pi$
$947$	46.9659	+	27.1158i	1.52619	+	0.881144i	0.526670	+	0.850070i	$0.323440\pi$
$948$		0			0
$949$	1.98289	+	3.43446i	0.0643672	+	0.111487i
$950$		0			0
$951$	−86.7209			−2.81212
$952$		0			0
$953$	5.63583			0.182562			0.0912812	−	0.995825i	$-0.470904\pi$
$953$	5.63583			0.182562			0.0912812	+	0.995825i	$0.470904\pi$
$954$		0			0
$955$	−3.11383	−	5.39331i	−0.100761	−	0.174523i
$956$		0			0
$957$	−37.1979	−	21.4762i	−1.20244	−	0.694228i
$958$		0			0
$959$	−52.3757	+	23.2466i	−1.69130	+	0.750672i
$960$		0			0
$961$	1.28368	−	2.22340i	0.0414091	−	0.0717227i
$962$		0			0
$963$	−0.692650	+	0.399902i	−0.0223203	+	0.0128867i
$964$		0			0
$965$		−	21.1250i		−	0.680037i
$966$		0			0
$967$		−	1.59534i		−	0.0513027i	−0.999671	−	0.0256513i	$-0.991834\pi$
$967$		−	1.59534i		−	0.0513027i	0.999671	−	0.0256513i	$-0.00816597\pi$
$968$		0			0
$969$	−69.7352	+	40.2616i	−2.24022	+	1.29339i
$970$		0			0
$971$	−6.62035	+	11.4668i	−0.212457	+	0.367986i	−0.952483	−	0.304592i	$-0.901480\pi$
$971$	−6.62035	+	11.4668i	−0.212457	+	0.367986i	0.740026	+	0.672578i	$0.234813\pi$
$972$		0			0
$973$	−3.91358	+	36.8255i	−0.125464	+	1.18057i
$974$		0			0
$975$	14.8454	+	8.57102i	0.475434	+	0.274492i
$976$		0			0
$977$	−3.00596	−	5.20648i	−0.0961693	−	0.166570i	0.813927	−	0.580968i	$-0.197326\pi$
$977$	−3.00596	−	5.20648i	−0.0961693	−	0.166570i	−0.910096	+	0.414397i	$0.863992\pi$
$978$		0			0
$979$	−3.67304			−0.117391
$980$		0			0
$981$	3.09919			0.0989495
$982$		0			0
$983$	9.68346	+	16.7722i	0.308854	+	0.534952i	0.978112	−	0.208079i	$-0.0667211\pi$
$983$	9.68346	+	16.7722i	0.308854	+	0.534952i	−0.669258	+	0.743030i	$0.733388\pi$
$984$		0			0
$985$	−5.97694	−	3.45079i	−0.190441	−	0.109951i
$986$		0			0
$987$	−1.94631	+	18.3142i	−0.0619519	+	0.582946i
$988$		0			0
$989$	−9.00903	+	15.6041i	−0.286471	+	0.496182i
$990$		0			0
$991$	−21.6772	+	12.5153i	−0.688599	+	0.397563i	−0.803087	−	0.595862i	$-0.796811\pi$
$991$	−21.6772	+	12.5153i	−0.688599	+	0.397563i	0.114488	+	0.993425i	$0.463477\pi$
$992$		0			0
$993$			10.2412i			0.324995i
$994$		0			0
$995$			0.340366i			0.0107903i
$996$		0			0
$997$	6.28460	−	3.62841i	0.199035	−	0.114913i	−0.397170	−	0.917745i	$-0.630008\pi$
$997$	6.28460	−	3.62841i	0.199035	−	0.114913i	0.596205	+	0.802832i	$0.296674\pi$
$998$		0			0
$999$	42.5696	−	73.7327i	1.34684	−	2.33280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bs.c.271.1	yes	12
4.3	odd	2		560.2.bs.b.271.6	yes	12
7.2	even	3		3920.2.k.d.2351.11		12
7.3	odd	6		560.2.bs.b.31.6	✓	12
7.5	odd	6		3920.2.k.e.2351.2		12
28.3	even	6	inner	560.2.bs.c.31.1	yes	12
28.19	even	6		3920.2.k.d.2351.12		12
28.23	odd	6		3920.2.k.e.2351.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bs.b.31.6	✓	12	7.3	odd	6
560.2.bs.b.271.6	yes	12	4.3	odd	2
560.2.bs.c.31.1	yes	12	28.3	even	6	inner
560.2.bs.c.271.1	yes	12	1.1	even	1	trivial
3920.2.k.d.2351.11		12	7.2	even	3
3920.2.k.d.2351.12		12	28.19	even	6
3920.2.k.e.2351.1		12	28.23	odd	6
3920.2.k.e.2351.2		12	7.5	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.60984 - 2.78832i) q^{3} +(0.866025 + 0.500000i) q^{5} +(-0.279599 + 2.63094i) q^{7} +(-3.68317 + 6.37943i) q^{9} +(1.40022 - 0.808417i) q^{11} +5.32414i q^{13} -3.21968i q^{15} +(-4.03609 + 2.33024i) q^{17} +(-2.68317 + 4.64738i) q^{19} +(7.78601 - 3.45577i) q^{21} +(-5.13166 - 2.96277i) q^{23} +(0.500000 + 0.866025i) q^{25} +14.0582 q^{27} +8.25106 q^{29} +(2.66611 + 4.61784i) q^{31} +(-4.50826 - 2.60284i) q^{33} +(-1.55761 + 2.13866i) q^{35} +(3.02810 - 5.24482i) q^{37} +(14.8454 - 8.57102i) q^{39} +2.35034i q^{41} -3.04075i q^{43} +(-6.37943 + 3.68317i) q^{45} +(-1.08102 + 1.87238i) q^{47} +(-6.84365 - 1.47122i) q^{49} +(12.9949 + 7.50263i) q^{51} +(-2.69786 - 4.67282i) q^{53} +1.61683 q^{55} +17.2779 q^{57} +(3.72375 + 6.44972i) q^{59} +(-0.549881 - 0.317474i) q^{61} +(-15.7541 - 11.4739i) q^{63} +(-2.66207 + 4.61084i) q^{65} +(-12.3459 + 7.12793i) q^{67} +19.0783i q^{69} +5.61214i q^{71} +(0.645073 - 0.372433i) q^{73} +(1.60984 - 2.78832i) q^{75} +(1.73539 + 3.90992i) q^{77} +(-0.535453 - 0.309144i) q^{79} +(-11.5819 - 20.0605i) q^{81} -3.11383 q^{83} -4.66048 q^{85} +(-13.2829 - 23.0066i) q^{87} +(-1.96739 - 1.13587i) q^{89} +(-14.0075 - 1.48863i) q^{91} +(8.58403 - 14.8680i) q^{93} +(-4.64738 + 2.68317i) q^{95} -4.11527i q^{97} +11.9101i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} - 2 q^{7} - 10 q^{9} + 6 q^{11} + 2 q^{19} + 12 q^{21} - 18 q^{23} + 6 q^{25} + 20 q^{27} + 16 q^{29} + 4 q^{31} - 6 q^{35} - 4 q^{37} + 24 q^{39} - 12 q^{45} + 12 q^{47} - 8 q^{49} - 12 q^{51}+ \cdots - 12 q^{95}+O(q^{100}) \) 12 * q + 2 * q^3 - 2 * q^7 - 10 * q^9 + 6 * q^11 + 2 * q^19 + 12 * q^21 - 18 * q^23 + 6 * q^25 + 20 * q^27 + 16 * q^29 + 4 * q^31 - 6 * q^35 - 4 * q^37 + 24 * q^39 - 12 * q^45 + 12 * q^47 - 8 * q^49 - 12 * q^51 - 12 * q^53 + 24 * q^55 + 16 * q^57 + 24 * q^59 - 48 * q^61 - 56 * q^63 - 2 * q^65 - 42 * q^67 + 24 * q^73 - 2 * q^75 + 40 * q^77 + 12 * q^79 - 6 * q^81 + 36 * q^83 - 16 * q^85 - 30 * q^87 + 12 * q^89 + 36 * q^91 + 28 * q^93 - 12 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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