LMFDB - Embedded newform 513.2.m.c.107.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [513,2,Mod(107,513)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(513, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("513.107"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.m (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,-8,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.2
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	513.107
Dual form			513.2.m.c.350.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22474 + 2.12132i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(1.22474 - 0.707107i) q^{5} +2.00000 q^{7} -4.89898 q^{8} +(3.00000 + 1.73205i) q^{10} +5.65685i q^{11} +(-1.50000 - 0.866025i) q^{13} +(2.44949 + 4.24264i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(1.22474 - 0.707107i) q^{17} +(-3.50000 - 2.59808i) q^{19} +5.65685i q^{20} +(-12.0000 + 6.92820i) q^{22} +(2.44949 + 1.41421i) q^{23} +(-1.50000 + 2.59808i) q^{25} -4.24264i q^{26} +(-4.00000 + 6.92820i) q^{28} +(3.67423 - 6.36396i) q^{29} -1.73205i q^{31} +(3.00000 + 1.73205i) q^{34} +(2.44949 - 1.41421i) q^{35} -5.19615i q^{37} +(1.22474 - 10.6066i) q^{38} +(-6.00000 + 3.46410i) q^{40} +(-5.50000 - 9.52628i) q^{43} +(-19.5959 - 11.3137i) q^{44} +6.92820i q^{46} +(9.79796 + 5.65685i) q^{47} -3.00000 q^{49} -7.34847 q^{50} +(6.00000 - 3.46410i) q^{52} +(1.22474 - 2.12132i) q^{53} +(4.00000 + 6.92820i) q^{55} -9.79796 q^{56} +18.0000 q^{58} +(-3.67423 - 6.36396i) q^{59} +(6.50000 - 11.2583i) q^{61} +(3.67423 - 2.12132i) q^{62} -8.00000 q^{64} -2.44949 q^{65} +(12.0000 + 6.92820i) q^{67} +5.65685i q^{68} +(6.00000 + 3.46410i) q^{70} +(2.44949 + 4.24264i) q^{71} +(2.00000 + 3.46410i) q^{73} +(11.0227 - 6.36396i) q^{74} +(16.0000 - 6.92820i) q^{76} +11.3137i q^{77} +(-10.5000 + 6.06218i) q^{79} +(-4.89898 - 2.82843i) q^{80} +1.41421i q^{83} +(1.00000 - 1.73205i) q^{85} +(13.4722 - 23.3345i) q^{86} -27.7128i q^{88} +(4.89898 - 8.48528i) q^{89} +(-3.00000 - 1.73205i) q^{91} +(-9.79796 + 5.65685i) q^{92} +27.7128i q^{94} +(-6.12372 - 0.707107i) q^{95} +(-1.50000 + 0.866025i) q^{97} +(-3.67423 - 6.36396i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{4} + 8 q^{7} + 12 q^{10} - 6 q^{13} - 8 q^{16} - 14 q^{19} - 48 q^{22} - 6 q^{25} - 16 q^{28} + 12 q^{34} - 24 q^{40} - 22 q^{43} - 12 q^{49} + 24 q^{52} + 16 q^{55} + 72 q^{58} + 26 q^{61} - 32 q^{64}+ \cdots - 6 q^{97}+O(q^{100}) $ 4 * q - 8 * q^4 + 8 * q^7 + 12 * q^10 - 6 * q^13 - 8 * q^16 - 14 * q^19 - 48 * q^22 - 6 * q^25 - 16 * q^28 + 12 * q^34 - 24 * q^40 - 22 * q^43 - 12 * q^49 + 24 * q^52 + 16 * q^55 + 72 * q^58 + 26 * q^61 - 32 * q^64 + 48 * q^67 + 24 * q^70 + 8 * q^73 + 64 * q^76 - 42 * q^79 + 4 * q^85 - 12 * q^91 - 6 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.22474	+	2.12132i	0.866025	+	1.50000i	0.866025	+	0.500000i	$0.166667\pi$
$2$	1.22474	+	2.12132i	0.866025	+	1.50000i			1.00000i	$0.5\pi$
$3$		0			0
$3$		0			0
$4$	−2.00000	+	3.46410i	−1.00000	+	1.73205i
$5$	1.22474	−	0.707107i	0.547723	−	0.316228i	−0.200480	−	0.979698i	$-0.564250\pi$
$5$	1.22474	−	0.707107i	0.547723	−	0.316228i	0.748203	+	0.663470i	$0.230917\pi$
$6$		0			0
$7$	2.00000			0.755929			0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000			0.755929			0.377964	+	0.925820i	$0.376624\pi$
$8$	−4.89898			−1.73205
$9$		0			0
$10$	3.00000	+	1.73205i	0.948683	+	0.547723i
$11$			5.65685i			1.70561i	0.522233	+	0.852803i	$0.325099\pi$
$11$			5.65685i			1.70561i	−0.522233	+	0.852803i	$0.674901\pi$
$12$		0			0
$13$	−1.50000	−	0.866025i	−0.416025	−	0.240192i	0.277350	−	0.960769i	$-0.410544\pi$
$13$	−1.50000	−	0.866025i	−0.416025	−	0.240192i	−0.693375	+	0.720577i	$0.743877\pi$
$14$	2.44949	+	4.24264i	0.654654	+	1.13389i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	1.22474	−	0.707107i	0.297044	−	0.171499i	−0.344070	−	0.938944i	$-0.611806\pi$
$17$	1.22474	−	0.707107i	0.297044	−	0.171499i	0.641114	+	0.767445i	$0.278472\pi$
$18$		0			0
$19$	−3.50000	−	2.59808i	−0.802955	−	0.596040i
$19$	−3.50000	−	2.59808i	−0.802955	−	0.596040i
$20$			5.65685i			1.26491i
$21$		0			0
$22$	−12.0000	+	6.92820i	−2.55841	+	1.47710i
$23$	2.44949	+	1.41421i	0.510754	+	0.294884i	0.733144	−	0.680074i	$-0.238052\pi$
$23$	2.44949	+	1.41421i	0.510754	+	0.294884i	−0.222390	+	0.974958i	$0.571386\pi$
$24$		0			0
$25$	−1.50000	+	2.59808i	−0.300000	+	0.519615i
$26$		−	4.24264i		−	0.832050i
$27$		0			0
$28$	−4.00000	+	6.92820i	−0.755929	+	1.30931i
$29$	3.67423	−	6.36396i	0.682288	−	1.18176i	−0.291993	−	0.956421i	$-0.594318\pi$
$29$	3.67423	−	6.36396i	0.682288	−	1.18176i	0.974281	−	0.225337i	$-0.0723484\pi$
$30$		0			0
$31$		−	1.73205i		−	0.311086i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$		−	1.73205i		−	0.311086i	0.987829	−	0.155543i	$-0.0497126\pi$
$32$		0			0
$33$		0			0
$34$	3.00000	+	1.73205i	0.514496	+	0.297044i
$35$	2.44949	−	1.41421i	0.414039	−	0.239046i
$36$		0			0
$37$		−	5.19615i		−	0.854242i	−0.904194	−	0.427121i	$-0.859528\pi$
$37$		−	5.19615i		−	0.854242i	0.904194	−	0.427121i	$-0.140472\pi$
$38$	1.22474	−	10.6066i	0.198680	−	1.72062i
$39$		0			0
$40$	−6.00000	+	3.46410i	−0.948683	+	0.547723i
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$		0			0
$43$	−5.50000	−	9.52628i	−0.838742	−	1.45274i	−0.890947	−	0.454108i	$-0.849958\pi$
$43$	−5.50000	−	9.52628i	−0.838742	−	1.45274i	0.0522047	−	0.998636i	$-0.483375\pi$
$44$	−19.5959	−	11.3137i	−2.95420	−	1.70561i
$45$		0			0
$46$			6.92820i			1.02151i
$47$	9.79796	+	5.65685i	1.42918	+	0.825137i	0.997056	−	0.0766776i	$-0.0244312\pi$
$47$	9.79796	+	5.65685i	1.42918	+	0.825137i	0.432123	+	0.901815i	$0.357765\pi$
$48$		0			0
$49$	−3.00000			−0.428571
$50$	−7.34847			−1.03923
$51$		0			0
$52$	6.00000	−	3.46410i	0.832050	−	0.480384i
$53$	1.22474	−	2.12132i	0.168232	−	0.291386i	−0.769567	−	0.638567i	$-0.779528\pi$
$53$	1.22474	−	2.12132i	0.168232	−	0.291386i	0.937798	+	0.347181i	$0.112861\pi$
$54$		0			0
$55$	4.00000	+	6.92820i	0.539360	+	0.934199i
$56$	−9.79796			−1.30931
$57$		0			0
$58$	18.0000			2.36352
$59$	−3.67423	−	6.36396i	−0.478345	−	0.828517i	0.521347	−	0.853345i	$-0.325430\pi$
$59$	−3.67423	−	6.36396i	−0.478345	−	0.828517i	−0.999692	+	0.0248275i	$0.992096\pi$
$60$		0			0
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	0.896258	−	0.443533i	$-0.146275\pi$
$62$	3.67423	−	2.12132i	0.466628	−	0.269408i
$63$		0			0
$64$	−8.00000			−1.00000
$65$	−2.44949			−0.303822
$66$		0			0
$67$	12.0000	+	6.92820i	1.46603	+	0.846415i	0.999279	−	0.0379722i	$-0.0120898\pi$
$67$	12.0000	+	6.92820i	1.46603	+	0.846415i	0.466755	+	0.884387i	$0.345423\pi$
$68$			5.65685i			0.685994i
$69$		0			0
$70$	6.00000	+	3.46410i	0.717137	+	0.414039i
$71$	2.44949	+	4.24264i	0.290701	+	0.503509i	0.973976	−	0.226653i	$-0.0727782\pi$
$71$	2.44949	+	4.24264i	0.290701	+	0.503509i	−0.683275	+	0.730161i	$0.739445\pi$
$72$		0			0
$73$	2.00000	+	3.46410i	0.234082	+	0.405442i	0.959006	−	0.283387i	$-0.0914581\pi$
$73$	2.00000	+	3.46410i	0.234082	+	0.405442i	−0.724923	+	0.688830i	$0.758125\pi$
$74$	11.0227	−	6.36396i	1.28136	−	0.739795i
$75$		0			0
$76$	16.0000	−	6.92820i	1.83533	−	0.794719i
$77$			11.3137i			1.28932i
$78$		0			0
$79$	−10.5000	+	6.06218i	−1.18134	+	0.682048i	−0.956325	−	0.292306i	$-0.905577\pi$
$79$	−10.5000	+	6.06218i	−1.18134	+	0.682048i	−0.225018	+	0.974355i	$0.572244\pi$
$80$	−4.89898	−	2.82843i	−0.547723	−	0.316228i
$81$		0			0
$82$		0			0
$83$			1.41421i			0.155230i	0.996983	+	0.0776151i	$0.0247305\pi$
$83$			1.41421i			0.155230i	−0.996983	+	0.0776151i	$0.975269\pi$
$84$		0			0
$85$	1.00000	−	1.73205i	0.108465	−	0.187867i
$86$	13.4722	−	23.3345i	1.45274	−	2.51623i
$87$		0			0
$88$		−	27.7128i		−	2.95420i
$89$	4.89898	−	8.48528i	0.519291	−	0.899438i	−0.480458	−	0.877018i	$-0.659529\pi$
$89$	4.89898	−	8.48528i	0.519291	−	0.899438i	0.999749	−	0.0224202i	$-0.00713717\pi$
$90$		0			0
$91$	−3.00000	−	1.73205i	−0.314485	−	0.181568i
$92$	−9.79796	+	5.65685i	−1.02151	+	0.589768i
$93$		0			0
$94$			27.7128i			2.85836i
$95$	−6.12372	−	0.707107i	−0.628281	−	0.0725476i
$96$		0			0
$97$	−1.50000	+	0.866025i	−0.152302	+	0.0879316i	−0.574214	−	0.818705i	$-0.694692\pi$
$97$	−1.50000	+	0.866025i	−0.152302	+	0.0879316i	0.421912	+	0.906637i	$0.361359\pi$
$98$	−3.67423	−	6.36396i	−0.371154	−	0.642857i
$99$		0			0
$100$	−6.00000	−	10.3923i	−0.600000	−	1.03923i
$101$	9.79796	+	5.65685i	0.974933	+	0.562878i	0.900737	−	0.434366i	$-0.143027\pi$
$101$	9.79796	+	5.65685i	0.974933	+	0.562878i	0.0741967	+	0.997244i	$0.476361\pi$
$102$		0			0
$103$		−	17.3205i		−	1.70664i	−0.521387	−	0.853320i	$-0.674585\pi$
$103$		−	17.3205i		−	1.70664i	0.521387	−	0.853320i	$-0.325415\pi$
$104$	7.34847	+	4.24264i	0.720577	+	0.416025i
$105$		0			0
$106$	6.00000			0.582772
$107$	7.34847			0.710403			0.355202	−	0.934790i	$-0.384412\pi$
$107$	7.34847			0.710403			0.355202	+	0.934790i	$0.384412\pi$
$108$		0			0
$109$	−3.00000	+	1.73205i	−0.287348	+	0.165900i	−0.636745	−	0.771074i	$-0.719720\pi$
$109$	−3.00000	+	1.73205i	−0.287348	+	0.165900i	0.349397	+	0.936975i	$0.386386\pi$
$110$	−9.79796	+	16.9706i	−0.934199	+	1.61808i
$111$		0			0
$112$	−4.00000	−	6.92820i	−0.377964	−	0.654654i
$113$	−17.1464			−1.61300			−0.806500	−	0.591234i	$-0.798641\pi$
$113$	−17.1464			−1.61300			−0.806500	+	0.591234i	$0.798641\pi$
$114$		0			0
$115$	4.00000			0.373002
$116$	14.6969	+	25.4558i	1.36458	+	2.36352i
$117$		0			0
$118$	9.00000	−	15.5885i	0.828517	−	1.43503i
$119$	2.44949	−	1.41421i	0.224544	−	0.129641i
$120$		0			0
$121$	−21.0000			−1.90909
$122$	31.8434			2.88296
$123$		0			0
$124$	6.00000	+	3.46410i	0.538816	+	0.311086i
$125$			11.3137i			1.01193i
$126$		0			0
$127$	6.00000	+	3.46410i	0.532414	+	0.307389i	0.741999	−	0.670401i	$-0.233878\pi$
$127$	6.00000	+	3.46410i	0.532414	+	0.307389i	−0.209585	+	0.977790i	$0.567211\pi$
$128$	−9.79796	−	16.9706i	−0.866025	−	1.50000i
$129$		0			0
$130$	−3.00000	−	5.19615i	−0.263117	−	0.455733i
$131$	−17.1464	+	9.89949i	−1.49809	+	0.864923i	−0.999998	−	0.00220084i	$-0.999299\pi$
$131$	−17.1464	+	9.89949i	−1.49809	+	0.864923i	−0.498093	+	0.867124i	$0.665966\pi$
$132$		0			0
$133$	−7.00000	−	5.19615i	−0.606977	−	0.450564i
$134$			33.9411i			2.93207i
$135$		0			0
$136$	−6.00000	+	3.46410i	−0.514496	+	0.297044i
$137$	−12.2474	−	7.07107i	−1.04637	−	0.604122i	−0.124739	−	0.992190i	$-0.539809\pi$
$137$	−12.2474	−	7.07107i	−1.04637	−	0.604122i	−0.921631	+	0.388067i	$0.873143\pi$
$138$		0			0
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	−0.296866	−	0.954919i	$-0.595942\pi$
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	0.975417	−	0.220366i	$-0.0707252\pi$
$140$			11.3137i			0.956183i
$141$		0			0
$142$	−6.00000	+	10.3923i	−0.503509	+	0.872103i
$143$	4.89898	−	8.48528i	0.409673	−	0.709575i
$144$		0			0
$145$		−	10.3923i		−	0.863034i
$146$	−4.89898	+	8.48528i	−0.405442	+	0.702247i
$147$		0			0
$148$	18.0000	+	10.3923i	1.47959	+	0.854242i
$149$	−6.12372	+	3.53553i	−0.501675	+	0.289642i	−0.729405	−	0.684082i	$-0.760203\pi$
$149$	−6.12372	+	3.53553i	−0.501675	+	0.289642i	0.227730	+	0.973724i	$0.426870\pi$
$150$		0			0
$151$			1.73205i			0.140952i	0.997513	+	0.0704761i	$0.0224519\pi$
$151$			1.73205i			0.140952i	−0.997513	+	0.0704761i	$0.977548\pi$
$152$	17.1464	+	12.7279i	1.39076	+	1.03237i
$153$		0			0
$154$	−24.0000	+	13.8564i	−1.93398	+	1.11658i
$155$	−1.22474	−	2.12132i	−0.0983739	−	0.170389i
$156$		0			0
$157$	−2.50000	−	4.33013i	−0.199522	−	0.345582i	0.748852	−	0.662738i	$-0.230606\pi$
$157$	−2.50000	−	4.33013i	−0.199522	−	0.345582i	−0.948373	+	0.317156i	$0.897272\pi$
$158$	−25.7196	−	14.8492i	−2.04614	−	1.18134i
$159$		0			0
$160$		0			0
$161$	4.89898	+	2.82843i	0.386094	+	0.222911i
$162$		0			0
$163$	17.0000			1.33154			0.665771	−	0.746156i	$-0.268103\pi$
$163$	17.0000			1.33154			0.665771	+	0.746156i	$0.268103\pi$
$164$		0			0
$165$		0			0
$166$	−3.00000	+	1.73205i	−0.232845	+	0.134433i
$167$	−1.22474	+	2.12132i	−0.0947736	+	0.164153i	−0.909514	−	0.415673i	$-0.863546\pi$
$167$	−1.22474	+	2.12132i	−0.0947736	+	0.164153i	0.814740	+	0.579826i	$0.196879\pi$
$168$		0			0
$169$	−5.00000	−	8.66025i	−0.384615	−	0.666173i
$170$	4.89898			0.375735
$171$		0			0
$172$	44.0000			3.35497
$173$	1.22474	+	2.12132i	0.0931156	+	0.161281i	0.908821	−	0.417187i	$-0.136984\pi$
$173$	1.22474	+	2.12132i	0.0931156	+	0.161281i	−0.815705	+	0.578468i	$0.803651\pi$
$174$		0			0
$175$	−3.00000	+	5.19615i	−0.226779	+	0.392792i
$176$	19.5959	−	11.3137i	1.47710	−	0.852803i
$177$		0			0
$178$	24.0000			1.79888
$179$	14.6969			1.09850			0.549250	−	0.835658i	$-0.314913\pi$
$179$	14.6969			1.09850			0.549250	+	0.835658i	$0.314913\pi$
$180$		0			0
$181$	10.5000	+	6.06218i	0.780459	+	0.450598i	0.836593	−	0.547825i	$-0.184544\pi$
$181$	10.5000	+	6.06218i	0.780459	+	0.450598i	−0.0561340	+	0.998423i	$0.517877\pi$
$182$		−	8.48528i		−	0.628971i
$183$		0			0
$184$	−12.0000	−	6.92820i	−0.884652	−	0.510754i
$185$	−3.67423	−	6.36396i	−0.270135	−	0.467888i
$186$		0			0
$187$	4.00000	+	6.92820i	0.292509	+	0.506640i
$188$	−39.1918	+	22.6274i	−2.85836	+	1.65027i
$189$		0			0
$190$	−6.00000	−	13.8564i	−0.435286	−	1.00525i
$191$		−	19.7990i		−	1.43260i	−0.697790	−	0.716302i	$-0.745833\pi$
$191$		−	19.7990i		−	1.43260i	0.697790	−	0.716302i	$-0.254167\pi$
$192$		0			0
$193$	−9.00000	+	5.19615i	−0.647834	+	0.374027i	−0.787626	−	0.616154i	$-0.788690\pi$
$193$	−9.00000	+	5.19615i	−0.647834	+	0.374027i	0.139792	+	0.990181i	$0.455357\pi$
$194$	−3.67423	−	2.12132i	−0.263795	−	0.152302i
$195$		0			0
$196$	6.00000	−	10.3923i	0.428571	−	0.742307i
$197$			5.65685i			0.403034i	0.979485	+	0.201517i	$0.0645872\pi$
$197$			5.65685i			0.403034i	−0.979485	+	0.201517i	$0.935413\pi$
$198$		0			0
$199$	−7.00000	+	12.1244i	−0.496217	+	0.859473i	−0.999990	−	0.00436292i	$-0.998611\pi$
$199$	−7.00000	+	12.1244i	−0.496217	+	0.859473i	0.503774	+	0.863836i	$0.331945\pi$
$200$	7.34847	−	12.7279i	0.519615	−	0.900000i
$201$		0			0
$202$			27.7128i			1.94987i
$203$	7.34847	−	12.7279i	0.515761	−	0.893325i
$204$		0			0
$205$		0			0
$206$	36.7423	−	21.2132i	2.55996	−	1.47799i
$207$		0			0
$208$			6.92820i			0.480384i
$209$	14.6969	−	19.7990i	1.01661	−	1.36952i
$210$		0			0
$211$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$211$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$212$	4.89898	+	8.48528i	0.336463	+	0.582772i
$213$		0			0
$214$	9.00000	+	15.5885i	0.615227	+	1.06561i
$215$	−13.4722	−	7.77817i	−0.918796	−	0.530467i
$216$		0			0
$217$		−	3.46410i		−	0.235159i
$218$	−7.34847	−	4.24264i	−0.497701	−	0.287348i
$219$		0			0
$220$	−32.0000			−2.15744
$221$	−2.44949			−0.164771
$222$		0			0
$223$	16.5000	−	9.52628i	1.10492	−	0.637927i	0.167412	−	0.985887i	$-0.446459\pi$
$223$	16.5000	−	9.52628i	1.10492	−	0.637927i	0.937509	+	0.347960i	$0.113126\pi$
$224$		0			0
$225$		0			0
$226$	−21.0000	−	36.3731i	−1.39690	−	2.41950i
$227$	−26.9444			−1.78836			−0.894181	−	0.447706i	$-0.852241\pi$
$227$	−26.9444			−1.78836			−0.894181	+	0.447706i	$0.852241\pi$
$228$		0			0
$229$	−19.0000			−1.25556			−0.627778	−	0.778393i	$-0.716035\pi$
$229$	−19.0000			−1.25556			−0.627778	+	0.778393i	$0.716035\pi$
$230$	4.89898	+	8.48528i	0.323029	+	0.559503i
$231$		0			0
$232$	−18.0000	+	31.1769i	−1.18176	+	2.04686i
$233$	−20.8207	+	12.0208i	−1.36401	+	0.787510i	−0.990155	−	0.139978i	$-0.955297\pi$
$233$	−20.8207	+	12.0208i	−1.36401	+	0.787510i	−0.373852	+	0.927488i	$0.621963\pi$
$234$		0			0
$235$	16.0000			1.04372
$236$	29.3939			1.91338
$237$		0			0
$238$	6.00000	+	3.46410i	0.388922	+	0.224544i
$239$		−	2.82843i		−	0.182956i	−0.995807	−	0.0914779i	$-0.970841\pi$
$239$		−	2.82843i		−	0.182956i	0.995807	−	0.0914779i	$-0.0291591\pi$
$240$		0			0
$241$	−9.00000	−	5.19615i	−0.579741	−	0.334714i	0.181289	−	0.983430i	$-0.441973\pi$
$241$	−9.00000	−	5.19615i	−0.579741	−	0.334714i	−0.761030	+	0.648716i	$0.775306\pi$
$242$	−25.7196	−	44.5477i	−1.65332	−	2.86364i
$243$		0			0
$244$	26.0000	+	45.0333i	1.66448	+	2.88296i
$245$	−3.67423	+	2.12132i	−0.234738	+	0.135526i
$246$		0			0
$247$	3.00000	+	6.92820i	0.190885	+	0.440831i
$248$			8.48528i			0.538816i
$249$		0			0
$250$	−24.0000	+	13.8564i	−1.51789	+	0.876356i
$251$	13.4722	+	7.77817i	0.850357	+	0.490954i	0.860771	−	0.508992i	$-0.169982\pi$
$251$	13.4722	+	7.77817i	0.850357	+	0.490954i	−0.0104141	+	0.999946i	$0.503315\pi$
$252$		0			0
$253$	−8.00000	+	13.8564i	−0.502956	+	0.871145i
$254$			16.9706i			1.06483i
$255$		0			0
$256$	16.0000	−	27.7128i	1.00000	−	1.73205i
$257$	2.44949	−	4.24264i	0.152795	−	0.264649i	−0.779459	−	0.626453i	$-0.784506\pi$
$257$	2.44949	−	4.24264i	0.152795	−	0.264649i	0.932254	+	0.361805i	$0.117839\pi$
$258$		0			0
$259$		−	10.3923i		−	0.645746i
$260$	4.89898	−	8.48528i	0.303822	−	0.526235i
$261$		0			0
$262$	−42.0000	−	24.2487i	−2.59477	−	1.49809i
$263$	−20.8207	+	12.0208i	−1.28386	+	0.741235i	−0.977551	−	0.210698i	$-0.932426\pi$
$263$	−20.8207	+	12.0208i	−1.28386	+	0.741235i	−0.306306	+	0.951933i	$0.599093\pi$
$264$		0			0
$265$		−	3.46410i		−	0.212798i
$266$	2.44949	−	21.2132i	0.150188	−	1.30066i
$267$		0			0
$268$	−48.0000	+	27.7128i	−2.93207	+	1.69283i
$269$	−8.57321	−	14.8492i	−0.522718	−	0.905374i	−0.999651	−	0.0264343i	$-0.991585\pi$
$269$	−8.57321	−	14.8492i	−0.522718	−	0.905374i	0.476932	−	0.878940i	$-0.341749\pi$
$270$		0			0
$271$	6.50000	+	11.2583i	0.394847	+	0.683895i	0.993082	−	0.117426i	$-0.0374643\pi$
$271$	6.50000	+	11.2583i	0.394847	+	0.683895i	−0.598235	+	0.801321i	$0.704131\pi$
$272$	−4.89898	−	2.82843i	−0.297044	−	0.171499i
$273$		0			0
$274$		−	34.6410i		−	2.09274i
$275$	−14.6969	−	8.48528i	−0.886259	−	0.511682i
$276$		0			0
$277$	−16.0000			−0.961347			−0.480673	−	0.876900i	$-0.659608\pi$
$277$	−16.0000			−0.961347			−0.480673	+	0.876900i	$0.659608\pi$
$278$	39.1918			2.35057
$279$		0			0
$280$	−12.0000	+	6.92820i	−0.717137	+	0.414039i
$281$	−11.0227	+	19.0919i	−0.657559	+	1.13893i	0.323686	+	0.946164i	$0.395078\pi$
$281$	−11.0227	+	19.0919i	−0.657559	+	1.13893i	−0.981246	+	0.192762i	$0.938256\pi$
$282$		0			0
$283$	8.00000	+	13.8564i	0.475551	+	0.823678i	0.999608	−	0.0280052i	$-0.00891551\pi$
$283$	8.00000	+	13.8564i	0.475551	+	0.823678i	−0.524057	+	0.851683i	$0.675582\pi$
$284$	−19.5959			−1.16280
$285$		0			0
$286$	24.0000			1.41915
$287$		0			0
$288$		0			0
$289$	−7.50000	+	12.9904i	−0.441176	+	0.764140i
$290$	22.0454	−	12.7279i	1.29455	−	0.747409i
$291$		0			0
$292$	−16.0000			−0.936329
$293$	−2.44949			−0.143101			−0.0715504	−	0.997437i	$-0.522795\pi$
$293$	−2.44949			−0.143101			−0.0715504	+	0.997437i	$0.522795\pi$
$294$		0			0
$295$	−9.00000	−	5.19615i	−0.524000	−	0.302532i
$296$			25.4558i			1.47959i
$297$		0			0
$298$	−15.0000	−	8.66025i	−0.868927	−	0.501675i
$299$	−2.44949	−	4.24264i	−0.141658	−	0.245358i
$300$		0			0
$301$	−11.0000	−	19.0526i	−0.634029	−	1.09817i
$302$	−3.67423	+	2.12132i	−0.211428	+	0.122068i
$303$		0			0
$304$	−2.00000	+	17.3205i	−0.114708	+	0.993399i
$305$		−	18.3848i		−	1.05271i
$306$		0			0
$307$	15.0000	−	8.66025i	0.856095	−	0.494267i	−0.00660752	−	0.999978i	$-0.502103\pi$
$307$	15.0000	−	8.66025i	0.856095	−	0.494267i	0.862703	+	0.505711i	$0.168770\pi$
$308$	−39.1918	−	22.6274i	−2.23316	−	1.28932i
$309$		0			0
$310$	3.00000	−	5.19615i	0.170389	−	0.295122i
$311$		−	7.07107i		−	0.400963i	−0.979697	−	0.200482i	$-0.935749\pi$
$311$		−	7.07107i		−	0.400963i	0.979697	−	0.200482i	$-0.0642507\pi$
$312$		0			0
$313$	−2.50000	+	4.33013i	−0.141308	+	0.244753i	−0.927990	−	0.372606i	$-0.878464\pi$
$313$	−2.50000	+	4.33013i	−0.141308	+	0.244753i	0.786681	+	0.617359i	$0.211798\pi$
$314$	6.12372	−	10.6066i	0.345582	−	0.598565i
$315$		0			0
$316$		−	48.4974i		−	2.72819i
$317$	7.34847	−	12.7279i	0.412731	−	0.714871i	−0.582456	−	0.812862i	$-0.697908\pi$
$317$	7.34847	−	12.7279i	0.412731	−	0.714871i	0.995187	+	0.0979908i	$0.0312416\pi$
$318$		0			0
$319$	36.0000	+	20.7846i	2.01561	+	1.16371i
$320$	−9.79796	+	5.65685i	−0.547723	+	0.316228i
$321$		0			0
$322$			13.8564i			0.772187i
$323$	−6.12372	−	0.707107i	−0.340733	−	0.0393445i
$324$		0			0
$325$	4.50000	−	2.59808i	0.249615	−	0.144115i
$326$	20.8207	+	36.0624i	1.15315	+	1.99731i
$327$		0			0
$328$		0			0
$329$	19.5959	+	11.3137i	1.08036	+	0.623745i
$330$		0			0
$331$			12.1244i			0.666415i	0.942854	+	0.333207i	$0.108131\pi$
$331$			12.1244i			0.666415i	−0.942854	+	0.333207i	$0.891869\pi$
$332$	−4.89898	−	2.82843i	−0.268866	−	0.155230i
$333$		0			0
$334$	−6.00000			−0.328305
$335$	19.5959			1.07064
$336$		0			0
$337$	9.00000	−	5.19615i	0.490261	−	0.283052i	−0.234422	−	0.972135i	$-0.575320\pi$
$337$	9.00000	−	5.19615i	0.490261	−	0.283052i	0.724683	+	0.689083i	$0.241986\pi$
$338$	12.2474	−	21.2132i	0.666173	−	1.15385i
$339$		0			0
$340$	4.00000	+	6.92820i	0.216930	+	0.375735i
$341$	9.79796			0.530589
$342$		0			0
$343$	−20.0000			−1.07990
$344$	26.9444	+	46.6690i	1.45274	+	2.51623i
$345$		0			0
$346$	−3.00000	+	5.19615i	−0.161281	+	0.279347i
$347$	−9.79796	+	5.65685i	−0.525982	+	0.303676i	−0.739379	−	0.673290i	$-0.764881\pi$
$347$	−9.79796	+	5.65685i	−0.525982	+	0.303676i	0.213397	+	0.976966i	$0.431547\pi$
$348$		0			0
$349$	11.0000			0.588817			0.294408	−	0.955680i	$-0.404877\pi$
$349$	11.0000			0.588817			0.294408	+	0.955680i	$0.404877\pi$
$350$	−14.6969			−0.785584
$351$		0			0
$352$		0			0
$353$			18.3848i			0.978523i	0.872137	+	0.489261i	$0.162734\pi$
$353$			18.3848i			0.978523i	−0.872137	+	0.489261i	$0.837266\pi$
$354$		0			0
$355$	6.00000	+	3.46410i	0.318447	+	0.183855i
$356$	19.5959	+	33.9411i	1.03858	+	1.79888i
$357$		0			0
$358$	18.0000	+	31.1769i	0.951330	+	1.64775i
$359$	−13.4722	+	7.77817i	−0.711035	+	0.410516i	−0.811444	−	0.584430i	$-0.801318\pi$
$359$	−13.4722	+	7.77817i	−0.711035	+	0.410516i	0.100409	+	0.994946i	$0.467985\pi$
$360$		0			0
$361$	5.50000	+	18.1865i	0.289474	+	0.957186i
$362$			29.6985i			1.56092i
$363$		0			0
$364$	12.0000	−	6.92820i	0.628971	−	0.363137i
$365$	4.89898	+	2.82843i	0.256424	+	0.148047i
$366$		0			0
$367$	−11.5000	+	19.9186i	−0.600295	+	1.03974i	0.392481	+	0.919760i	$0.371617\pi$
$367$	−11.5000	+	19.9186i	−0.600295	+	1.03974i	−0.992776	+	0.119982i	$0.961716\pi$
$368$		−	11.3137i		−	0.589768i
$369$		0			0
$370$	9.00000	−	15.5885i	0.467888	−	0.810405i
$371$	2.44949	−	4.24264i	0.127171	−	0.220267i
$372$		0			0
$373$			8.66025i			0.448411i	0.974542	+	0.224205i	$0.0719787\pi$
$373$			8.66025i			0.448411i	−0.974542	+	0.224205i	$0.928021\pi$
$374$	−9.79796	+	16.9706i	−0.506640	+	0.877527i
$375$		0			0
$376$	−48.0000	−	27.7128i	−2.47541	−	1.42918i
$377$	−11.0227	+	6.36396i	−0.567698	+	0.327761i
$378$		0			0
$379$			20.7846i			1.06763i	0.845600	+	0.533817i	$0.179243\pi$
$379$			20.7846i			1.06763i	−0.845600	+	0.533817i	$0.820757\pi$
$380$	14.6969	−	19.7990i	0.753937	−	1.01567i
$381$		0			0
$382$	42.0000	−	24.2487i	2.14891	−	1.24067i
$383$	18.3712	+	31.8198i	0.938723	+	1.62592i	0.767856	+	0.640622i	$0.221323\pi$
$383$	18.3712	+	31.8198i	0.938723	+	1.62592i	0.170867	+	0.985294i	$0.445343\pi$
$384$		0			0
$385$	8.00000	+	13.8564i	0.407718	+	0.706188i
$386$	−22.0454	−	12.7279i	−1.12208	−	0.647834i
$387$		0			0
$388$		−	6.92820i		−	0.351726i
$389$	13.4722	+	7.77817i	0.683067	+	0.394369i	0.801010	−	0.598651i	$-0.204296\pi$
$389$	13.4722	+	7.77817i	0.683067	+	0.394369i	−0.117942	+	0.993020i	$0.537630\pi$
$390$		0			0
$391$	4.00000			0.202289
$392$	14.6969			0.742307
$393$		0			0
$394$	−12.0000	+	6.92820i	−0.604551	+	0.349038i
$395$	−8.57321	+	14.8492i	−0.431365	+	0.747146i
$396$		0			0
$397$	−8.50000	−	14.7224i	−0.426603	−	0.738898i	0.569966	−	0.821668i	$-0.306956\pi$
$397$	−8.50000	−	14.7224i	−0.426603	−	0.738898i	−0.996569	+	0.0827707i	$0.973623\pi$
$398$	−34.2929			−1.71895
$399$		0			0
$400$	12.0000			0.600000
$401$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$401$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$402$		0			0
$403$	−1.50000	+	2.59808i	−0.0747203	+	0.129419i
$404$	−39.1918	+	22.6274i	−1.94987	+	1.12576i
$405$		0			0
$406$	36.0000			1.78665
$407$	29.3939			1.45700
$408$		0			0
$409$	−10.5000	−	6.06218i	−0.519192	−	0.299755i	0.217412	−	0.976080i	$-0.430238\pi$
$409$	−10.5000	−	6.06218i	−0.519192	−	0.299755i	−0.736604	+	0.676324i	$0.763572\pi$
$410$		0			0
$411$		0			0
$412$	60.0000	+	34.6410i	2.95599	+	1.70664i
$413$	−7.34847	−	12.7279i	−0.361595	−	0.626300i
$414$		0			0
$415$	1.00000	+	1.73205i	0.0490881	+	0.0850230i
$416$		0			0
$417$		0			0
$418$	60.0000	+	6.92820i	2.93470	+	0.338869i
$419$			22.6274i			1.10542i	0.833373	+	0.552711i	$0.186407\pi$
$419$			22.6274i			1.10542i	−0.833373	+	0.552711i	$0.813593\pi$
$420$		0			0
$421$	16.5000	−	9.52628i	0.804161	−	0.464282i	−0.0407632	−	0.999169i	$-0.512979\pi$
$421$	16.5000	−	9.52628i	0.804161	−	0.464282i	0.844924	+	0.534886i	$0.179646\pi$
$422$		0			0
$423$		0			0
$424$	−6.00000	+	10.3923i	−0.291386	+	0.504695i
$425$			4.24264i			0.205798i
$426$		0			0
$427$	13.0000	−	22.5167i	0.629114	−	1.08966i
$428$	−14.6969	+	25.4558i	−0.710403	+	1.23045i
$429$		0			0
$430$		−	38.1051i		−	1.83759i
$431$	12.2474	−	21.2132i	0.589939	−	1.02180i	−0.404301	−	0.914626i	$-0.632485\pi$
$431$	12.2474	−	21.2132i	0.589939	−	1.02180i	0.994240	−	0.107178i	$-0.0341815\pi$
$432$		0			0
$433$	−25.5000	−	14.7224i	−1.22545	−	0.707515i	−0.259377	−	0.965776i	$-0.583517\pi$
$433$	−25.5000	−	14.7224i	−1.22545	−	0.707515i	−0.966075	+	0.258261i	$0.916850\pi$
$434$	7.34847	−	4.24264i	0.352738	−	0.203653i
$435$		0			0
$436$		−	13.8564i		−	0.663602i
$437$	−4.89898	−	11.3137i	−0.234350	−	0.541208i
$438$		0			0
$439$	−1.50000	+	0.866025i	−0.0715911	+	0.0413331i	−0.535368	−	0.844619i	$-0.679827\pi$
$439$	−1.50000	+	0.866025i	−0.0715911	+	0.0413331i	0.463777	+	0.885952i	$0.346494\pi$
$440$	−19.5959	−	33.9411i	−0.934199	−	1.61808i
$441$		0			0
$442$	−3.00000	−	5.19615i	−0.142695	−	0.247156i
$443$	−8.57321	−	4.94975i	−0.407326	−	0.235170i	0.282314	−	0.959322i	$-0.408898\pi$
$443$	−8.57321	−	4.94975i	−0.407326	−	0.235170i	−0.689640	+	0.724152i	$0.742231\pi$
$444$		0			0
$445$		−	13.8564i		−	0.656857i
$446$	40.4166	+	23.3345i	1.91378	+	1.10492i
$447$		0			0
$448$	−16.0000			−0.755929
$449$	14.6969			0.693591			0.346796	−	0.937941i	$-0.387270\pi$
$449$	14.6969			0.693591			0.346796	+	0.937941i	$0.387270\pi$
$450$		0			0
$451$		0			0
$452$	34.2929	−	59.3970i	1.61300	−	2.79380i
$453$		0			0
$454$	−33.0000	−	57.1577i	−1.54877	−	2.68254i
$455$	−4.89898			−0.229668
$456$		0			0
$457$	−13.0000			−0.608114			−0.304057	−	0.952654i	$-0.598341\pi$
$457$	−13.0000			−0.608114			−0.304057	+	0.952654i	$0.598341\pi$
$458$	−23.2702	−	40.3051i	−1.08734	−	1.88333i
$459$		0			0
$460$	−8.00000	+	13.8564i	−0.373002	+	0.646058i
$461$	4.89898	−	2.82843i	0.228168	−	0.131733i	−0.381559	−	0.924345i	$-0.624613\pi$
$461$	4.89898	−	2.82843i	0.228168	−	0.131733i	0.609727	+	0.792612i	$0.291279\pi$
$462$		0			0
$463$	−19.0000			−0.883005			−0.441502	−	0.897260i	$-0.645554\pi$
$463$	−19.0000			−0.883005			−0.441502	+	0.897260i	$0.645554\pi$
$464$	−29.3939			−1.36458
$465$		0			0
$466$	−51.0000	−	29.4449i	−2.36253	−	1.36401i
$467$			35.3553i			1.63605i	0.575183	+	0.818025i	$0.304931\pi$
$467$			35.3553i			1.63605i	−0.575183	+	0.818025i	$0.695069\pi$
$468$		0			0
$469$	24.0000	+	13.8564i	1.10822	+	0.639829i
$470$	19.5959	+	33.9411i	0.903892	+	1.56559i
$471$		0			0
$472$	18.0000	+	31.1769i	0.828517	+	1.43503i
$473$	53.8888	−	31.1127i	2.47781	−	1.43056i
$474$		0			0
$475$	12.0000	−	5.19615i	0.550598	−	0.238416i
$476$			11.3137i			0.518563i
$477$		0			0
$478$	6.00000	−	3.46410i	0.274434	−	0.158444i
$479$	20.8207	+	12.0208i	0.951320	+	0.549245i	0.893491	−	0.449081i	$-0.148249\pi$
$479$	20.8207	+	12.0208i	0.951320	+	0.549245i	0.0578295	+	0.998326i	$0.481582\pi$
$480$		0			0
$481$	−4.50000	+	7.79423i	−0.205182	+	0.355386i
$482$		−	25.4558i		−	1.15948i
$483$		0			0
$484$	42.0000	−	72.7461i	1.90909	−	3.30664i
$485$	−1.22474	+	2.12132i	−0.0556128	+	0.0963242i
$486$		0			0
$487$		−	5.19615i		−	0.235460i	−0.993046	−	0.117730i	$-0.962438\pi$
$487$		−	5.19615i		−	0.235460i	0.993046	−	0.117730i	$-0.0375618\pi$
$488$	−31.8434	+	55.1543i	−1.44148	+	2.49672i
$489$		0			0
$490$	−9.00000	−	5.19615i	−0.406579	−	0.234738i
$491$	23.2702	−	13.4350i	1.05017	−	0.606314i	0.127471	−	0.991842i	$-0.459314\pi$
$491$	23.2702	−	13.4350i	1.05017	−	0.606314i	0.922696	+	0.385528i	$0.125981\pi$
$492$		0			0
$493$		−	10.3923i		−	0.468046i
$494$	−11.0227	+	14.8492i	−0.495935	+	0.668099i
$495$		0			0
$496$	−6.00000	+	3.46410i	−0.269408	+	0.155543i
$497$	4.89898	+	8.48528i	0.219749	+	0.380617i
$498$		0			0
$499$	3.50000	+	6.06218i	0.156682	+	0.271380i	0.933670	−	0.358134i	$-0.116587\pi$
$499$	3.50000	+	6.06218i	0.156682	+	0.271380i	−0.776989	+	0.629515i	$0.783254\pi$
$500$	−39.1918	−	22.6274i	−1.75271	−	1.01193i
$501$		0			0
$502$			38.1051i			1.70071i
$503$	−12.2474	−	7.07107i	−0.546087	−	0.315283i	0.201455	−	0.979498i	$-0.435433\pi$
$503$	−12.2474	−	7.07107i	−0.546087	−	0.315283i	−0.747542	+	0.664214i	$0.768766\pi$
$504$		0			0
$505$	16.0000			0.711991
$506$	−39.1918			−1.74229
$507$		0			0
$508$	−24.0000	+	13.8564i	−1.06483	+	0.614779i
$509$	−8.57321	+	14.8492i	−0.380001	+	0.658181i	−0.991062	−	0.133402i	$-0.957410\pi$
$509$	−8.57321	+	14.8492i	−0.380001	+	0.658181i	0.611061	+	0.791584i	$0.290743\pi$
$510$		0			0
$511$	4.00000	+	6.92820i	0.176950	+	0.306486i
$512$	39.1918			1.73205
$513$		0			0
$514$	12.0000			0.529297
$515$	−12.2474	−	21.2132i	−0.539687	−	0.934765i
$516$		0			0
$517$	−32.0000	+	55.4256i	−1.40736	+	2.43762i
$518$	22.0454	−	12.7279i	0.968620	−	0.559233i
$519$		0			0
$520$	12.0000			0.526235
$521$	7.34847			0.321942			0.160971	−	0.986959i	$-0.448537\pi$
$521$	7.34847			0.321942			0.160971	+	0.986959i	$0.448537\pi$
$522$		0			0
$523$	1.50000	+	0.866025i	0.0655904	+	0.0378686i	0.532437	−	0.846470i	$-0.321276\pi$
$523$	1.50000	+	0.866025i	0.0655904	+	0.0378686i	−0.466846	+	0.884339i	$0.654610\pi$
$524$		−	79.1960i		−	3.45969i
$525$		0			0
$526$	−51.0000	−	29.4449i	−2.22371	−	1.28386i
$527$	−1.22474	−	2.12132i	−0.0533507	−	0.0924062i
$528$		0			0
$529$	−7.50000	−	12.9904i	−0.326087	−	0.564799i
$530$	7.34847	−	4.24264i	0.319197	−	0.184289i
$531$		0			0
$532$	32.0000	−	13.8564i	1.38738	−	0.600751i
$533$		0			0
$534$		0			0
$535$	9.00000	−	5.19615i	0.389104	−	0.224649i
$536$	−58.7878	−	33.9411i	−2.53924	−	1.46603i
$537$		0			0
$538$	21.0000	−	36.3731i	0.905374	−	1.56815i
$539$		−	16.9706i		−	0.730974i
$540$		0			0
$541$	0.500000	−	0.866025i	0.0214967	−	0.0372333i	−0.855077	−	0.518501i	$-0.826490\pi$
$541$	0.500000	−	0.866025i	0.0214967	−	0.0372333i	0.876574	+	0.481268i	$0.159824\pi$
$542$	−15.9217	+	27.5772i	−0.683895	+	1.18454i
$543$		0			0
$544$		0			0
$545$	−2.44949	+	4.24264i	−0.104925	+	0.181735i
$546$		0			0
$547$	−22.5000	−	12.9904i	−0.962031	−	0.555429i	−0.0652331	−	0.997870i	$-0.520779\pi$
$547$	−22.5000	−	12.9904i	−0.962031	−	0.555429i	−0.896797	+	0.442441i	$0.854112\pi$
$548$	48.9898	−	28.2843i	2.09274	−	1.20824i
$549$		0			0
$550$		−	41.5692i		−	1.77252i
$551$	−29.3939	+	12.7279i	−1.25222	+	0.542228i
$552$		0			0
$553$	−21.0000	+	12.1244i	−0.893011	+	0.515580i
$554$	−19.5959	−	33.9411i	−0.832551	−	1.44202i
$555$		0			0
$556$	32.0000	+	55.4256i	1.35710	+	2.35057i
$557$	−1.22474	−	0.707107i	−0.0518941	−	0.0299611i	0.473828	−	0.880617i	$-0.342872\pi$
$557$	−1.22474	−	0.707107i	−0.0518941	−	0.0299611i	−0.525723	+	0.850656i	$0.676205\pi$
$558$		0			0
$559$			19.0526i			0.805837i
$560$	−9.79796	−	5.65685i	−0.414039	−	0.239046i
$561$		0			0
$562$	−54.0000			−2.27785
$563$	−17.1464			−0.722636			−0.361318	−	0.932443i	$-0.617673\pi$
$563$	−17.1464			−0.722636			−0.361318	+	0.932443i	$0.617673\pi$
$564$		0			0
$565$	−21.0000	+	12.1244i	−0.883477	+	0.510075i
$566$	−19.5959	+	33.9411i	−0.823678	+	1.42665i
$567$		0			0
$568$	−12.0000	−	20.7846i	−0.503509	−	0.872103i
$569$	2.44949			0.102688			0.0513440	−	0.998681i	$-0.483650\pi$
$569$	2.44949			0.102688			0.0513440	+	0.998681i	$0.483650\pi$
$570$		0			0
$571$	35.0000			1.46470			0.732352	−	0.680926i	$-0.238422\pi$
$571$	35.0000			1.46470			0.732352	+	0.680926i	$0.238422\pi$
$572$	19.5959	+	33.9411i	0.819346	+	1.41915i
$573$		0			0
$574$		0			0
$575$	−7.34847	+	4.24264i	−0.306452	+	0.176930i
$576$		0			0
$577$	17.0000			0.707719			0.353860	−	0.935299i	$-0.384869\pi$
$577$	17.0000			0.707719			0.353860	+	0.935299i	$0.384869\pi$
$578$	−36.7423			−1.52828
$579$		0			0
$580$	36.0000	+	20.7846i	1.49482	+	0.863034i
$581$			2.82843i			0.117343i
$582$		0			0
$583$	12.0000	+	6.92820i	0.496989	+	0.286937i
$584$	−9.79796	−	16.9706i	−0.405442	−	0.702247i
$585$		0			0
$586$	−3.00000	−	5.19615i	−0.123929	−	0.214651i
$587$	1.22474	−	0.707107i	0.0505506	−	0.0291854i	−0.474512	−	0.880249i	$-0.657375\pi$
$587$	1.22474	−	0.707107i	0.0505506	−	0.0291854i	0.525062	+	0.851064i	$0.324042\pi$
$588$		0			0
$589$	−4.50000	+	6.06218i	−0.185419	+	0.249788i
$590$		−	25.4558i		−	1.04800i
$591$		0			0
$592$	−18.0000	+	10.3923i	−0.739795	+	0.427121i
$593$	9.79796	+	5.65685i	0.402354	+	0.232299i	0.687499	−	0.726185i	$-0.258708\pi$
$593$	9.79796	+	5.65685i	0.402354	+	0.232299i	−0.285145	+	0.958484i	$0.592042\pi$
$594$		0			0
$595$	2.00000	−	3.46410i	0.0819920	−	0.142014i
$596$		−	28.2843i		−	1.15857i
$597$		0			0
$598$	6.00000	−	10.3923i	0.245358	−	0.424973i
$599$	20.8207	−	36.0624i	0.850709	−	1.47347i	−0.0298600	−	0.999554i	$-0.509506\pi$
$599$	20.8207	−	36.0624i	0.850709	−	1.47347i	0.880569	−	0.473918i	$-0.157161\pi$
$600$		0			0
$601$			12.1244i			0.494563i	0.968944	+	0.247281i	$0.0795372\pi$
$601$			12.1244i			0.494563i	−0.968944	+	0.247281i	$0.920463\pi$
$602$	26.9444	−	46.6690i	1.09817	−	1.90209i
$603$		0			0
$604$	−6.00000	−	3.46410i	−0.244137	−	0.140952i
$605$	−25.7196	+	14.8492i	−1.04565	+	0.603708i
$606$		0			0
$607$		−	6.92820i		−	0.281207i	−0.990066	−	0.140604i	$-0.955096\pi$
$607$		−	6.92820i		−	0.281207i	0.990066	−	0.140604i	$-0.0449043\pi$
$608$		0			0
$609$		0			0
$610$	39.0000	−	22.5167i	1.57906	−	0.911673i
$611$	−9.79796	−	16.9706i	−0.396383	−	0.686555i
$612$		0			0
$613$	15.5000	+	26.8468i	0.626039	+	1.08433i	0.988339	+	0.152270i	$0.0486583\pi$
$613$	15.5000	+	26.8468i	0.626039	+	1.08433i	−0.362300	+	0.932062i	$0.618008\pi$
$614$	36.7423	+	21.2132i	1.48280	+	0.856095i
$615$		0			0
$616$		−	55.4256i		−	2.23316i
$617$	2.44949	+	1.41421i	0.0986127	+	0.0569341i	0.548495	−	0.836154i	$-0.315201\pi$
$617$	2.44949	+	1.41421i	0.0986127	+	0.0569341i	−0.449883	+	0.893088i	$0.648534\pi$
$618$		0			0
$619$	47.0000			1.88909			0.944545	−	0.328383i	$-0.106504\pi$
$619$	47.0000			1.88909			0.944545	+	0.328383i	$0.106504\pi$
$620$	9.79796			0.393496
$621$		0			0
$622$	15.0000	−	8.66025i	0.601445	−	0.347245i
$623$	9.79796	−	16.9706i	0.392547	−	0.679911i
$624$		0			0
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	−12.2474			−0.489506
$627$		0			0
$628$	20.0000			0.798087
$629$	−3.67423	−	6.36396i	−0.146501	−	0.253748i
$630$		0			0
$631$	−11.5000	+	19.9186i	−0.457808	+	0.792946i	−0.998845	−	0.0480524i	$-0.984699\pi$
$631$	−11.5000	+	19.9186i	−0.457808	+	0.792946i	0.541037	+	0.840999i	$0.318032\pi$
$632$	51.4393	−	29.6985i	2.04614	−	1.18134i
$633$		0			0
$634$	36.0000			1.42974
$635$	9.79796			0.388820
$636$		0			0
$637$	4.50000	+	2.59808i	0.178296	+	0.102940i
$638$			101.823i			4.03123i
$639$		0			0
$640$	−24.0000	−	13.8564i	−0.948683	−	0.547723i
$641$	19.5959	+	33.9411i	0.773992	+	1.34059i	0.935359	+	0.353699i	$0.115076\pi$
$641$	19.5959	+	33.9411i	0.773992	+	1.34059i	−0.161367	+	0.986894i	$0.551590\pi$
$642$		0			0
$643$	3.50000	+	6.06218i	0.138027	+	0.239069i	0.926750	−	0.375680i	$-0.122591\pi$
$643$	3.50000	+	6.06218i	0.138027	+	0.239069i	−0.788723	+	0.614749i	$0.789257\pi$
$644$	−19.5959	+	11.3137i	−0.772187	+	0.445823i
$645$		0			0
$646$	−6.00000	−	13.8564i	−0.236067	−	0.545173i
$647$			9.89949i			0.389189i	0.980884	+	0.194595i	$0.0623391\pi$
$647$			9.89949i			0.389189i	−0.980884	+	0.194595i	$0.937661\pi$
$648$		0			0
$649$	36.0000	−	20.7846i	1.41312	−	0.815867i
$650$	11.0227	+	6.36396i	0.432346	+	0.249615i
$651$		0			0
$652$	−34.0000	+	58.8897i	−1.33154	+	2.30630i
$653$		−	28.2843i		−	1.10685i	−0.832899	−	0.553425i	$-0.813321\pi$
$653$		−	28.2843i		−	1.10685i	0.832899	−	0.553425i	$-0.186679\pi$
$654$		0			0
$655$	−14.0000	+	24.2487i	−0.547025	+	0.947476i
$656$		0			0
$657$		0			0
$658$			55.4256i			2.16072i
$659$	7.34847	−	12.7279i	0.286256	−	0.495809i	−0.686657	−	0.726981i	$-0.740923\pi$
$659$	7.34847	−	12.7279i	0.286256	−	0.495809i	0.972913	+	0.231172i	$0.0742560\pi$
$660$		0			0
$661$	−19.5000	−	11.2583i	−0.758462	−	0.437898i	0.0702812	−	0.997527i	$-0.477610\pi$
$661$	−19.5000	−	11.2583i	−0.758462	−	0.437898i	−0.828743	+	0.559629i	$0.810944\pi$
$662$	−25.7196	+	14.8492i	−0.999622	+	0.577132i
$663$		0			0
$664$		−	6.92820i		−	0.268866i
$665$	−12.2474	−	1.41421i	−0.474936	−	0.0548408i
$666$		0			0
$667$	18.0000	−	10.3923i	0.696963	−	0.402392i
$668$	−4.89898	−	8.48528i	−0.189547	−	0.328305i
$669$		0			0
$670$	24.0000	+	41.5692i	0.927201	+	1.60596i
$671$	63.6867	+	36.7696i	2.45860	+	1.41947i
$672$		0			0
$673$		−	24.2487i		−	0.934719i	−0.884067	−	0.467360i	$-0.845205\pi$
$673$		−	24.2487i		−	0.934719i	0.884067	−	0.467360i	$-0.154795\pi$
$674$	22.0454	+	12.7279i	0.849157	+	0.490261i
$675$		0			0
$676$	40.0000			1.53846
$677$	−41.6413			−1.60041			−0.800203	−	0.599729i	$-0.795275\pi$
$677$	−41.6413			−1.60041			−0.800203	+	0.599729i	$0.795275\pi$
$678$		0			0
$679$	−3.00000	+	1.73205i	−0.115129	+	0.0664700i
$680$	−4.89898	+	8.48528i	−0.187867	+	0.325396i
$681$		0			0
$682$	12.0000	+	20.7846i	0.459504	+	0.795884i
$683$	51.4393			1.96827			0.984135	−	0.177423i	$-0.0567759\pi$
$683$	51.4393			1.96827			0.984135	+	0.177423i	$0.0567759\pi$
$684$		0			0
$685$	−20.0000			−0.764161
$686$	−24.4949	−	42.4264i	−0.935220	−	1.61985i
$687$		0			0
$688$	−22.0000	+	38.1051i	−0.838742	+	1.45274i
$689$	−3.67423	+	2.12132i	−0.139977	+	0.0808159i
$690$		0			0
$691$	−22.0000			−0.836919			−0.418460	−	0.908235i	$-0.637430\pi$
$691$	−22.0000			−0.836919			−0.418460	+	0.908235i	$0.637430\pi$
$692$	−9.79796			−0.372463
$693$		0			0
$694$	−24.0000	−	13.8564i	−0.911028	−	0.525982i
$695$		−	22.6274i		−	0.858307i
$696$		0			0
$697$		0			0
$698$	13.4722	+	23.3345i	0.509930	+	0.883225i
$699$		0			0
$700$	−12.0000	−	20.7846i	−0.453557	−	0.785584i
$701$	41.6413	−	24.0416i	1.57277	−	0.908040i	0.576944	−	0.816784i	$-0.304245\pi$
$701$	41.6413	−	24.0416i	1.57277	−	0.908040i	0.995827	−	0.0912559i	$-0.0290881\pi$
$702$		0			0
$703$	−13.5000	+	18.1865i	−0.509162	+	0.685918i
$704$		−	45.2548i		−	1.70561i
$705$		0			0
$706$	−39.0000	+	22.5167i	−1.46778	+	0.847426i
$707$	19.5959	+	11.3137i	0.736980	+	0.425496i
$708$		0			0
$709$	20.0000	−	34.6410i	0.751116	−	1.30097i	−0.196167	−	0.980571i	$-0.562849\pi$
$709$	20.0000	−	34.6410i	0.751116	−	1.30097i	0.947282	−	0.320400i	$-0.103817\pi$
$710$			16.9706i			0.636894i
$711$		0			0
$712$	−24.0000	+	41.5692i	−0.899438	+	1.55787i
$713$	2.44949	−	4.24264i	0.0917341	−	0.158888i
$714$		0			0
$715$		−	13.8564i		−	0.518200i
$716$	−29.3939	+	50.9117i	−1.09850	+	1.90266i
$717$		0			0
$718$	−33.0000	−	19.0526i	−1.23155	−	0.711035i
$719$	−13.4722	+	7.77817i	−0.502428	+	0.290077i	−0.729716	−	0.683751i	$-0.760348\pi$
$719$	−13.4722	+	7.77817i	−0.502428	+	0.290077i	0.227288	+	0.973828i	$0.427014\pi$
$720$		0			0
$721$		−	34.6410i		−	1.29010i
$722$	−31.8434	+	33.9411i	−1.18509	+	1.26316i
$723$		0			0
$724$	−42.0000	+	24.2487i	−1.56092	+	0.901196i
$725$	11.0227	+	19.0919i	0.409373	+	0.709055i
$726$		0			0
$727$	−11.5000	−	19.9186i	−0.426511	−	0.738739i	0.570049	−	0.821611i	$-0.306924\pi$
$727$	−11.5000	−	19.9186i	−0.426511	−	0.738739i	−0.996560	+	0.0828714i	$0.973591\pi$
$728$	14.6969	+	8.48528i	0.544705	+	0.314485i
$729$		0			0
$730$			13.8564i			0.512849i
$731$	−13.4722	−	7.77817i	−0.498287	−	0.287686i
$732$		0			0
$733$	−10.0000			−0.369358			−0.184679	−	0.982799i	$-0.559125\pi$
$733$	−10.0000			−0.369358			−0.184679	+	0.982799i	$0.559125\pi$
$734$	−56.3383			−2.07948
$735$		0			0
$736$		0			0
$737$	−39.1918	+	67.8823i	−1.44365	+	2.50047i
$738$		0			0
$739$	0.500000	+	0.866025i	0.0183928	+	0.0318573i	0.875075	−	0.483987i	$-0.160812\pi$
$739$	0.500000	+	0.866025i	0.0183928	+	0.0318573i	−0.856683	+	0.515844i	$0.827478\pi$
$740$	29.3939			1.08054
$741$		0			0
$742$	12.0000			0.440534
$743$	−14.6969	−	25.4558i	−0.539178	−	0.933884i	−0.998949	−	0.0458464i	$-0.985402\pi$
$743$	−14.6969	−	25.4558i	−0.539178	−	0.933884i	0.459770	−	0.888038i	$-0.347932\pi$
$744$		0			0
$745$	−5.00000	+	8.66025i	−0.183186	+	0.317287i
$746$	−18.3712	+	10.6066i	−0.672616	+	0.388335i
$747$		0			0
$748$	−32.0000			−1.17004
$749$	14.6969			0.537014
$750$		0			0
$751$	16.5000	+	9.52628i	0.602094	+	0.347619i	0.769865	−	0.638207i	$-0.220324\pi$
$751$	16.5000	+	9.52628i	0.602094	+	0.347619i	−0.167771	+	0.985826i	$0.553657\pi$
$752$		−	45.2548i		−	1.65027i
$753$		0			0
$754$	−27.0000	−	15.5885i	−0.983282	−	0.567698i
$755$	1.22474	+	2.12132i	0.0445730	+	0.0772028i
$756$		0			0
$757$	0.500000	+	0.866025i	0.0181728	+	0.0314762i	0.874969	−	0.484179i	$-0.160882\pi$
$757$	0.500000	+	0.866025i	0.0181728	+	0.0314762i	−0.856796	+	0.515656i	$0.827548\pi$
$758$	−44.0908	+	25.4558i	−1.60145	+	0.924598i
$759$		0			0
$760$	30.0000	+	3.46410i	1.08821	+	0.125656i
$761$		−	7.07107i		−	0.256326i	−0.991753	−	0.128163i	$-0.959092\pi$
$761$		−	7.07107i		−	0.256326i	0.991753	−	0.128163i	$-0.0409081\pi$
$762$		0			0
$763$	−6.00000	+	3.46410i	−0.217215	+	0.125409i
$764$	68.5857	+	39.5980i	2.48134	+	1.43260i
$765$		0			0
$766$	−45.0000	+	77.9423i	−1.62592	+	2.81617i
$767$			12.7279i			0.459579i
$768$		0			0
$769$	9.50000	−	16.4545i	0.342579	−	0.593364i	−0.642332	−	0.766426i	$-0.722033\pi$
$769$	9.50000	−	16.4545i	0.342579	−	0.593364i	0.984911	+	0.173063i	$0.0553663\pi$
$770$	−19.5959	+	33.9411i	−0.706188	+	1.22315i
$771$		0			0
$772$		−	41.5692i		−	1.49611i
$773$	−6.12372	+	10.6066i	−0.220255	+	0.381493i	−0.954885	−	0.296975i	$-0.904022\pi$
$773$	−6.12372	+	10.6066i	−0.220255	+	0.381493i	0.734630	+	0.678468i	$0.237356\pi$
$774$		0			0
$775$	4.50000	+	2.59808i	0.161645	+	0.0933257i
$776$	7.34847	−	4.24264i	0.263795	−	0.152302i
$777$		0			0
$778$			38.1051i			1.36613i
$779$		0			0
$780$		0			0
$781$	−24.0000	+	13.8564i	−0.858788	+	0.495821i
$782$	4.89898	+	8.48528i	0.175187	+	0.303433i
$783$		0			0
$784$	6.00000	+	10.3923i	0.214286	+	0.371154i
$785$	−6.12372	−	3.53553i	−0.218565	−	0.126189i
$786$		0			0
$787$		−	1.73205i		−	0.0617409i	−0.999523	−	0.0308705i	$-0.990172\pi$
$787$		−	1.73205i		−	0.0617409i	0.999523	−	0.0308705i	$-0.00982794\pi$
$788$	−19.5959	−	11.3137i	−0.698076	−	0.403034i
$789$		0			0
$790$	−42.0000			−1.49429
$791$	−34.2929			−1.21931
$792$		0			0
$793$	−19.5000	+	11.2583i	−0.692465	+	0.399795i
$794$	20.8207	−	36.0624i	0.738898	−	1.27981i
$795$		0			0
$796$	−28.0000	−	48.4974i	−0.992434	−	1.71895i
$797$	−9.79796			−0.347062			−0.173531	−	0.984828i	$-0.555518\pi$
$797$	−9.79796			−0.347062			−0.173531	+	0.984828i	$0.555518\pi$
$798$		0			0
$799$	16.0000			0.566039
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−19.5959	+	11.3137i	−0.691525	+	0.399252i
$804$		0			0
$805$	8.00000			0.281963
$806$	−7.34847			−0.258839
$807$		0			0
$808$	−48.0000	−	27.7128i	−1.68863	−	0.974933i
$809$			5.65685i			0.198884i	0.995043	+	0.0994422i	$0.0317058\pi$
$809$			5.65685i			0.198884i	−0.995043	+	0.0994422i	$0.968294\pi$
$810$		0			0
$811$	−48.0000	−	27.7128i	−1.68551	−	0.973128i	−0.957885	−	0.287151i	$-0.907292\pi$
$811$	−48.0000	−	27.7128i	−1.68551	−	0.973128i	−0.727623	−	0.685978i	$-0.759375\pi$
$812$	29.3939	+	50.9117i	1.03152	+	1.78665i
$813$		0			0
$814$	36.0000	+	62.3538i	1.26180	+	2.18550i
$815$	20.8207	−	12.0208i	0.729316	−	0.421071i
$816$		0			0
$817$	−5.50000	+	47.6314i	−0.192421	+	1.66641i
$818$		−	29.6985i		−	1.03838i
$819$		0			0
$820$		0			0
$821$	−1.22474	−	0.707107i	−0.0427439	−	0.0246782i	0.478476	−	0.878101i	$-0.341189\pi$
$821$	−1.22474	−	0.707107i	−0.0427439	−	0.0246782i	−0.521220	+	0.853423i	$0.674523\pi$
$822$		0			0
$823$	3.50000	−	6.06218i	0.122002	−	0.211314i	−0.798555	−	0.601922i	$-0.794402\pi$
$823$	3.50000	−	6.06218i	0.122002	−	0.211314i	0.920557	+	0.390608i	$0.127735\pi$
$824$			84.8528i			2.95599i
$825$		0			0
$826$	18.0000	−	31.1769i	0.626300	−	1.08478i
$827$	−20.8207	+	36.0624i	−0.724005	+	1.25401i	0.235377	+	0.971904i	$0.424368\pi$
$827$	−20.8207	+	36.0624i	−0.724005	+	1.25401i	−0.959382	+	0.282110i	$0.908966\pi$
$828$		0			0
$829$		−	10.3923i		−	0.360940i	−0.983581	−	0.180470i	$-0.942238\pi$
$829$		−	10.3923i		−	0.360940i	0.983581	−	0.180470i	$-0.0577618\pi$
$830$	−2.44949	+	4.24264i	−0.0850230	+	0.147264i
$831$		0			0
$832$	12.0000	+	6.92820i	0.416025	+	0.240192i
$833$	−3.67423	+	2.12132i	−0.127305	+	0.0734994i
$834$		0			0
$835$			3.46410i			0.119880i
$836$	39.1918	+	90.5097i	1.35548	+	3.13034i
$837$		0			0
$838$	−48.0000	+	27.7128i	−1.65813	+	0.957323i
$839$	19.5959	+	33.9411i	0.676526	+	1.17178i	0.976020	+	0.217680i	$0.0698488\pi$
$839$	19.5959	+	33.9411i	0.676526	+	1.17178i	−0.299494	+	0.954098i	$0.596818\pi$
$840$		0			0
$841$	−12.5000	−	21.6506i	−0.431034	−	0.746574i
$842$	40.4166	+	23.3345i	1.39285	+	0.804161i
$843$		0			0
$844$		0			0
$845$	−12.2474	−	7.07107i	−0.421325	−	0.243252i
$846$		0			0
$847$	−42.0000			−1.44314
$848$	−9.79796			−0.336463
$849$		0			0
$850$	−9.00000	+	5.19615i	−0.308697	+	0.178227i
$851$	7.34847	−	12.7279i	0.251902	−	0.436308i
$852$		0			0
$853$	8.00000	+	13.8564i	0.273915	+	0.474434i	0.969861	−	0.243660i	$-0.0783480\pi$
$853$	8.00000	+	13.8564i	0.273915	+	0.474434i	−0.695946	+	0.718094i	$0.745015\pi$
$854$	63.6867			2.17932
$855$		0			0
$856$	−36.0000			−1.23045
$857$	−6.12372	−	10.6066i	−0.209182	−	0.362315i	0.742275	−	0.670096i	$-0.233747\pi$
$857$	−6.12372	−	10.6066i	−0.209182	−	0.362315i	−0.951457	+	0.307781i	$0.900414\pi$
$858$		0			0
$859$	18.5000	−	32.0429i	0.631212	−	1.09329i	−0.356092	−	0.934451i	$-0.615891\pi$
$859$	18.5000	−	32.0429i	0.631212	−	1.09329i	0.987304	−	0.158840i	$-0.0507755\pi$
$860$	53.8888	−	31.1127i	1.83759	−	1.06093i
$861$		0			0
$862$	60.0000			2.04361
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$		0			0
$865$	3.00000	+	1.73205i	0.102003	+	0.0588915i
$866$		−	72.1249i		−	2.45090i
$867$		0			0
$868$	12.0000	+	6.92820i	0.407307	+	0.235159i
$869$	−34.2929	−	59.3970i	−1.16331	−	2.01490i
$870$		0			0
$871$	−12.0000	−	20.7846i	−0.406604	−	0.704260i
$872$	14.6969	−	8.48528i	0.497701	−	0.287348i
$873$		0			0
$874$	18.0000	−	24.2487i	0.608859	−	0.820225i
$875$			22.6274i			0.764946i
$876$		0			0
$877$	13.5000	−	7.79423i	0.455863	−	0.263192i	−0.254440	−	0.967088i	$-0.581891\pi$
$877$	13.5000	−	7.79423i	0.455863	−	0.263192i	0.710303	+	0.703896i	$0.248558\pi$
$878$	−3.67423	−	2.12132i	−0.123999	−	0.0715911i
$879$		0			0
$880$	16.0000	−	27.7128i	0.539360	−	0.934199i
$881$		−	15.5563i		−	0.524107i	−0.965053	−	0.262053i	$-0.915600\pi$
$881$		−	15.5563i		−	0.524107i	0.965053	−	0.262053i	$-0.0843996\pi$
$882$		0			0
$883$	6.50000	−	11.2583i	0.218742	−	0.378873i	−0.735681	−	0.677328i	$-0.763138\pi$
$883$	6.50000	−	11.2583i	0.218742	−	0.378873i	0.954424	+	0.298455i	$0.0964712\pi$
$884$	4.89898	−	8.48528i	0.164771	−	0.285391i
$885$		0			0
$886$		−	24.2487i		−	0.814651i
$887$	−1.22474	+	2.12132i	−0.0411229	+	0.0712270i	−0.885854	−	0.463964i	$-0.846427\pi$
$887$	−1.22474	+	2.12132i	−0.0411229	+	0.0712270i	0.844731	+	0.535191i	$0.179760\pi$
$888$		0			0
$889$	12.0000	+	6.92820i	0.402467	+	0.232364i
$890$	29.3939	−	16.9706i	0.985285	−	0.568855i
$891$		0			0
$892$			76.2102i			2.55171i
$893$	−19.5959	−	45.2548i	−0.655752	−	1.51440i
$894$		0			0
$895$	18.0000	−	10.3923i	0.601674	−	0.347376i
$896$	−19.5959	−	33.9411i	−0.654654	−	1.13389i
$897$		0			0
$898$	18.0000	+	31.1769i	0.600668	+	1.04039i
$899$	−11.0227	−	6.36396i	−0.367628	−	0.212250i
$900$		0			0
$901$		−	3.46410i		−	0.115406i
$902$		0			0
$903$		0			0
$904$	84.0000			2.79380
$905$	17.1464			0.569967
$906$		0			0
$907$	7.50000	−	4.33013i	0.249033	−	0.143780i	−0.370288	−	0.928917i	$-0.620741\pi$
$907$	7.50000	−	4.33013i	0.249033	−	0.143780i	0.619322	+	0.785137i	$0.287408\pi$
$908$	53.8888	−	93.3381i	1.78836	−	3.09753i
$909$		0			0
$910$	−6.00000	−	10.3923i	−0.198898	−	0.344502i
$911$	−56.3383			−1.86657			−0.933285	−	0.359137i	$-0.883071\pi$
$911$	−56.3383			−1.86657			−0.933285	+	0.359137i	$0.883071\pi$
$912$		0			0
$913$	−8.00000			−0.264761
$914$	−15.9217	−	27.5772i	−0.526642	−	0.912172i
$915$		0			0
$916$	38.0000	−	65.8179i	1.25556	−	2.17469i
$917$	−34.2929	+	19.7990i	−1.13245	+	0.653820i
$918$		0			0
$919$	−37.0000			−1.22052			−0.610259	−	0.792202i	$-0.708935\pi$
$919$	−37.0000			−1.22052			−0.610259	+	0.792202i	$0.708935\pi$
$920$	−19.5959			−0.646058
$921$		0			0
$922$	12.0000	+	6.92820i	0.395199	+	0.228168i
$923$		−	8.48528i		−	0.279296i
$924$		0			0
$925$	13.5000	+	7.79423i	0.443877	+	0.256273i
$926$	−23.2702	−	40.3051i	−0.764705	−	1.32451i
$927$		0			0
$928$		0			0
$929$	4.89898	−	2.82843i	0.160730	−	0.0927977i	−0.417477	−	0.908687i	$-0.637086\pi$
$929$	4.89898	−	2.82843i	0.160730	−	0.0927977i	0.578208	+	0.815890i	$0.303752\pi$
$930$		0			0
$931$	10.5000	+	7.79423i	0.344124	+	0.255446i
$932$		−	96.1665i		−	3.15004i
$933$		0			0
$934$	−75.0000	+	43.3013i	−2.45407	+	1.41686i
$935$	9.79796	+	5.65685i	0.320428	+	0.184999i
$936$		0			0
$937$	18.5000	−	32.0429i	0.604369	−	1.04680i	−0.387782	−	0.921751i	$-0.626759\pi$
$937$	18.5000	−	32.0429i	0.604369	−	1.04680i	0.992151	−	0.125046i	$-0.0399079\pi$
$938$			67.8823i			2.21643i
$939$		0			0
$940$	−32.0000	+	55.4256i	−1.04372	+	1.80778i
$941$	−8.57321	+	14.8492i	−0.279479	+	0.484071i	−0.971255	−	0.238040i	$-0.923495\pi$
$941$	−8.57321	+	14.8492i	−0.279479	+	0.484071i	0.691777	+	0.722112i	$0.256828\pi$
$942$		0			0
$943$		0			0
$944$	−14.6969	+	25.4558i	−0.478345	+	0.828517i
$945$		0			0
$946$	132.000	+	76.2102i	4.29169	+	2.47781i
$947$	−6.12372	+	3.53553i	−0.198994	+	0.114889i	−0.596186	−	0.802846i	$-0.703318\pi$
$947$	−6.12372	+	3.53553i	−0.198994	+	0.114889i	0.397192	+	0.917736i	$0.369985\pi$
$948$		0			0
$949$		−	6.92820i		−	0.224899i
$950$	25.7196	+	19.0919i	0.834455	+	0.619422i
$951$		0			0
$952$	−12.0000	+	6.92820i	−0.388922	+	0.224544i
$953$	−8.57321	−	14.8492i	−0.277714	−	0.481014i	0.693103	−	0.720839i	$-0.256243\pi$
$953$	−8.57321	−	14.8492i	−0.277714	−	0.481014i	−0.970816	+	0.239825i	$0.922910\pi$
$954$		0			0
$955$	−14.0000	−	24.2487i	−0.453029	−	0.784670i
$956$	9.79796	+	5.65685i	0.316889	+	0.182956i
$957$		0			0
$958$			58.8897i			1.90264i
$959$	−24.4949	−	14.1421i	−0.790981	−	0.456673i
$960$		0			0
$961$	28.0000			0.903226
$962$	−22.0454			−0.710772
$963$		0			0
$964$	36.0000	−	20.7846i	1.15948	−	0.669427i
$965$	−7.34847	+	12.7279i	−0.236556	+	0.409726i
$966$		0			0
$967$	−1.00000	−	1.73205i	−0.0321578	−	0.0556990i	0.849499	−	0.527591i	$-0.176905\pi$
$967$	−1.00000	−	1.73205i	−0.0321578	−	0.0556990i	−0.881656	+	0.471892i	$0.843571\pi$
$968$	102.879			3.30664
$969$		0			0
$970$	−6.00000			−0.192648
$971$	−30.6186	−	53.0330i	−0.982598	−	1.70191i	−0.652157	−	0.758084i	$-0.726136\pi$
$971$	−30.6186	−	53.0330i	−0.982598	−	1.70191i	−0.330441	−	0.943827i	$-0.607197\pi$
$972$		0			0
$973$	16.0000	−	27.7128i	0.512936	−	0.888432i
$974$	11.0227	−	6.36396i	0.353190	−	0.203914i
$975$		0			0
$976$	−52.0000			−1.66448
$977$	−31.8434			−1.01876			−0.509380	−	0.860542i	$-0.670125\pi$
$977$	−31.8434			−1.01876			−0.509380	+	0.860542i	$0.670125\pi$
$978$		0			0
$979$	48.0000	+	27.7128i	1.53409	+	0.885705i
$980$		−	16.9706i		−	0.542105i
$981$		0			0
$982$	57.0000	+	32.9090i	1.81894	+	1.05017i
$983$	1.22474	+	2.12132i	0.0390633	+	0.0676596i	0.884896	−	0.465789i	$-0.154229\pi$
$983$	1.22474	+	2.12132i	0.0390633	+	0.0676596i	−0.845833	+	0.533448i	$0.820896\pi$
$984$		0			0
$985$	4.00000	+	6.92820i	0.127451	+	0.220751i
$986$	22.0454	−	12.7279i	0.702069	−	0.405340i
$987$		0			0
$988$	−30.0000	−	3.46410i	−0.954427	−	0.110208i
$989$		−	31.1127i		−	0.989326i
$990$		0			0
$991$	−25.5000	+	14.7224i	−0.810034	+	0.467673i	−0.846968	−	0.531644i	$-0.821574\pi$
$991$	−25.5000	+	14.7224i	−0.810034	+	0.467673i	0.0369336	+	0.999318i	$0.488241\pi$
$992$		0			0
$993$		0			0
$994$	−12.0000	+	20.7846i	−0.380617	+	0.659248i
$995$			19.7990i			0.627670i
$996$		0			0
$997$	18.5000	−	32.0429i	0.585901	−	1.01481i	−0.408862	−	0.912596i	$-0.634074\pi$
$997$	18.5000	−	32.0429i	0.585901	−	1.01481i	0.994762	−	0.102214i	$-0.0325925\pi$
$998$	−8.57321	+	14.8492i	−0.271380	+	0.470045i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.m.c.107.2	yes	4
3.2	odd	2	inner	513.2.m.c.107.1	✓	4
19.8	odd	6	inner	513.2.m.c.350.1	yes	4
57.8	even	6	inner	513.2.m.c.350.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
513.2.m.c.107.1	✓	4	3.2	odd	2	inner
513.2.m.c.107.2	yes	4	1.1	even	1	trivial
513.2.m.c.350.1	yes	4	19.8	odd	6	inner
513.2.m.c.350.2	yes	4	57.8	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 + 2.12132i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(1.22474 - 0.707107i) q^{5} +2.00000 q^{7} -4.89898 q^{8} +(3.00000 + 1.73205i) q^{10} +5.65685i q^{11} +(-1.50000 - 0.866025i) q^{13} +(2.44949 + 4.24264i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(1.22474 - 0.707107i) q^{17} +(-3.50000 - 2.59808i) q^{19} +5.65685i q^{20} +(-12.0000 + 6.92820i) q^{22} +(2.44949 + 1.41421i) q^{23} +(-1.50000 + 2.59808i) q^{25} -4.24264i q^{26} +(-4.00000 + 6.92820i) q^{28} +(3.67423 - 6.36396i) q^{29} -1.73205i q^{31} +(3.00000 + 1.73205i) q^{34} +(2.44949 - 1.41421i) q^{35} -5.19615i q^{37} +(1.22474 - 10.6066i) q^{38} +(-6.00000 + 3.46410i) q^{40} +(-5.50000 - 9.52628i) q^{43} +(-19.5959 - 11.3137i) q^{44} +6.92820i q^{46} +(9.79796 + 5.65685i) q^{47} -3.00000 q^{49} -7.34847 q^{50} +(6.00000 - 3.46410i) q^{52} +(1.22474 - 2.12132i) q^{53} +(4.00000 + 6.92820i) q^{55} -9.79796 q^{56} +18.0000 q^{58} +(-3.67423 - 6.36396i) q^{59} +(6.50000 - 11.2583i) q^{61} +(3.67423 - 2.12132i) q^{62} -8.00000 q^{64} -2.44949 q^{65} +(12.0000 + 6.92820i) q^{67} +5.65685i q^{68} +(6.00000 + 3.46410i) q^{70} +(2.44949 + 4.24264i) q^{71} +(2.00000 + 3.46410i) q^{73} +(11.0227 - 6.36396i) q^{74} +(16.0000 - 6.92820i) q^{76} +11.3137i q^{77} +(-10.5000 + 6.06218i) q^{79} +(-4.89898 - 2.82843i) q^{80} +1.41421i q^{83} +(1.00000 - 1.73205i) q^{85} +(13.4722 - 23.3345i) q^{86} -27.7128i q^{88} +(4.89898 - 8.48528i) q^{89} +(-3.00000 - 1.73205i) q^{91} +(-9.79796 + 5.65685i) q^{92} +27.7128i q^{94} +(-6.12372 - 0.707107i) q^{95} +(-1.50000 + 0.866025i) q^{97} +(-3.67423 - 6.36396i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{4} + 8 q^{7} + 12 q^{10} - 6 q^{13} - 8 q^{16} - 14 q^{19} - 48 q^{22} - 6 q^{25} - 16 q^{28} + 12 q^{34} - 24 q^{40} - 22 q^{43} - 12 q^{49} + 24 q^{52} + 16 q^{55} + 72 q^{58} + 26 q^{61} - 32 q^{64}+ \cdots - 6 q^{97}+O(q^{100}) \) 4 * q - 8 * q^4 + 8 * q^7 + 12 * q^10 - 6 * q^13 - 8 * q^16 - 14 * q^19 - 48 * q^22 - 6 * q^25 - 16 * q^28 + 12 * q^34 - 24 * q^40 - 22 * q^43 - 12 * q^49 + 24 * q^52 + 16 * q^55 + 72 * q^58 + 26 * q^61 - 32 * q^64 + 48 * q^67 + 24 * q^70 + 8 * q^73 + 64 * q^76 - 42 * q^79 + 4 * q^85 - 12 * q^91 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more