LMFDB - Embedded newform 484.3.f.a.457.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [484,3,Mod(161,484)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("484.161"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(484, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 484 = 2^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	484.f (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-5,0,-1,0,-15] 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:	$13.1880447950$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 19x^{6} - 37x^{5} + 229x^{4} + 196x^{3} + 1496x^{2} + 2952x + 26896 $ x^8 - x^7 + 19x^6 - 37x^5 + 229x^4 + 196x^3 + 1496x^2 + 2952x + 26896
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			457.1
Root			$-1.37056 + 4.21816i$ of defining polynomial
Character	$\chi$	$=$	484.457
Dual form			484.3.f.a.233.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.08818 - 2.97024i) q^{3} +(1.46509 - 4.50908i) q^{5} +(3.91877 + 5.39373i) q^{7} +(5.10976 + 15.7262i) q^{9} +(-14.3229 + 4.65378i) q^{13} +(-19.3826 + 14.0823i) q^{15} +(16.9976 + 5.52287i) q^{17} +(-19.0249 + 26.1855i) q^{19} -33.6902i q^{21} -3.58879 q^{23} +(2.04012 + 1.48224i) q^{25} +(11.7671 - 36.2153i) q^{27} +(7.50529 + 10.3301i) q^{29} +(6.76473 + 20.8197i) q^{31} +(30.0621 - 9.76777i) q^{35} +(22.4250 - 16.2927i) q^{37} +(72.3773 + 23.5168i) q^{39} +(29.1270 - 40.0899i) q^{41} -16.8760i q^{43} +78.3970 q^{45} +(63.0835 + 45.8328i) q^{47} +(1.40631 - 4.32817i) q^{49} +(-53.0852 - 73.0655i) q^{51} +(3.06043 + 9.41904i) q^{53} +(155.554 - 50.5426i) q^{57} +(-29.6620 + 21.5507i) q^{59} +(26.9171 + 8.74590i) q^{61} +(-64.7990 + 89.1881i) q^{63} +71.4011i q^{65} -30.7234 q^{67} +(14.6716 + 10.6595i) q^{69} +(-12.6835 + 39.0359i) q^{71} +(36.3001 + 49.9628i) q^{73} +(-3.93780 - 12.1193i) q^{75} +(-118.204 + 38.4068i) q^{79} +(-35.2762 + 25.6296i) q^{81} +(2.94344 + 0.956381i) q^{83} +(49.8061 - 68.5522i) q^{85} -64.5240i q^{87} +60.4914 q^{89} +(-81.2293 - 59.0165i) q^{91} +(34.1840 - 105.207i) q^{93} +(90.1993 + 124.149i) q^{95} +(14.8226 + 45.6193i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{3} - q^{5} - 15 q^{7} - q^{9} + 15 q^{13} - 63 q^{15} + 75 q^{17} + 30 q^{19} + 100 q^{23} + 51 q^{25} + 100 q^{27} - 125 q^{29} + 73 q^{31} + 155 q^{35} - 75 q^{37} + 185 q^{39} + 155 q^{41}+ \cdots - 90 q^{97}+O(q^{100}) $ 8 * q - 5 * q^3 - q^5 - 15 * q^7 - q^9 + 15 * q^13 - 63 * q^15 + 75 * q^17 + 30 * q^19 + 100 * q^23 + 51 * q^25 + 100 * q^27 - 125 * q^29 + 73 * q^31 + 155 * q^35 - 75 * q^37 + 185 * q^39 + 155 * q^41 + 332 * q^45 + 45 * q^47 + 87 * q^49 - 150 * q^51 - 85 * q^53 + 310 * q^57 - 178 * q^59 + 145 * q^61 + 110 * q^63 + 10 * q^67 + 124 * q^69 + 207 * q^71 - 65 * q^73 + 192 * q^75 - 235 * q^79 - 12 * q^81 - 210 * q^83 - 105 * q^85 + 18 * q^89 - 195 * q^91 - 335 * q^93 + 255 * q^95 - 90 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/484\mathbb{Z}\right)^\times$.

$n$	$243$	$365$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−4.08818	−	2.97024i	−1.36273	−	0.990079i	−0.998266	−	0.0588599i	$-0.981253\pi$
$3$	−4.08818	−	2.97024i	−1.36273	−	0.990079i	−0.364460	−	0.931219i	$-0.618747\pi$
$4$		0			0
$5$	1.46509	−	4.50908i	0.293018	−	0.901816i	−0.690862	−	0.722986i	$-0.742769\pi$
$5$	1.46509	−	4.50908i	0.293018	−	0.901816i	0.983880	−	0.178829i	$-0.0572310\pi$
$6$		0			0
$7$	3.91877	+	5.39373i	0.559825	+	0.770533i	0.991304	−	0.131590i	$-0.0420083\pi$
$7$	3.91877	+	5.39373i	0.559825	+	0.770533i	−0.431479	+	0.902123i	$0.642008\pi$
$8$		0			0
$9$	5.10976	+	15.7262i	0.567751	+	1.74736i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	−14.3229	+	4.65378i	−1.10176	+	0.357983i	−0.802779	−	0.596276i	$-0.796646\pi$
$13$	−14.3229	+	4.65378i	−1.10176	+	0.357983i	−0.298980	+	0.954260i	$0.596646\pi$
$14$		0			0
$15$	−19.3826	+	14.0823i	−1.29217	+	0.938818i
$16$		0			0
$17$	16.9976	+	5.52287i	0.999861	+	0.324874i	0.762810	−	0.646623i	$-0.223819\pi$
$17$	16.9976	+	5.52287i	0.999861	+	0.324874i	0.237051	+	0.971497i	$0.423819\pi$
$18$		0			0
$19$	−19.0249	+	26.1855i	−1.00131	+	1.37818i	−0.0767906	+	0.997047i	$0.524467\pi$
$19$	−19.0249	+	26.1855i	−1.00131	+	1.37818i	−0.924519	+	0.381137i	$0.875533\pi$
$20$		0			0
$21$		−	33.6902i		−	1.60430i
$22$		0			0
$23$	−3.58879			−0.156034			−0.0780171	−	0.996952i	$-0.524859\pi$
$23$	−3.58879			−0.156034			−0.0780171	+	0.996952i	$0.524859\pi$
$24$		0			0
$25$	2.04012	+	1.48224i	0.0816049	+	0.0592894i
$26$		0			0
$27$	11.7671	−	36.2153i	0.435817	−	1.34131i
$28$		0			0
$29$	7.50529	+	10.3301i	0.258803	+	0.356212i	0.918570	−	0.395258i	$-0.129345\pi$
$29$	7.50529	+	10.3301i	0.258803	+	0.356212i	−0.659767	+	0.751470i	$0.729345\pi$
$30$		0			0
$31$	6.76473	+	20.8197i	0.218217	+	0.671603i	0.998910	+	0.0466876i	$0.0148665\pi$
$31$	6.76473	+	20.8197i	0.218217	+	0.671603i	−0.780692	+	0.624915i	$0.785133\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	30.0621	−	9.76777i	0.858917	−	0.279079i
$36$		0			0
$37$	22.4250	−	16.2927i	0.606082	−	0.440345i	−0.241950	−	0.970289i	$-0.577787\pi$
$37$	22.4250	−	16.2927i	0.606082	−	0.440345i	0.848033	+	0.529944i	$0.177787\pi$
$38$		0			0
$39$	72.3773	+	23.5168i	1.85583	+	0.602995i
$40$		0			0
$41$	29.1270	−	40.0899i	0.710416	−	0.977803i	−0.289372	−	0.957217i	$-0.593447\pi$
$41$	29.1270	−	40.0899i	0.710416	−	0.977803i	0.999788	−	0.0205868i	$-0.00655345\pi$
$42$		0			0
$43$		−	16.8760i		−	0.392466i	−0.980557	−	0.196233i	$-0.937129\pi$
$43$		−	16.8760i		−	0.392466i	0.980557	−	0.196233i	$-0.0628708\pi$
$44$		0			0
$45$	78.3970			1.74215
$46$		0			0
$47$	63.0835	+	45.8328i	1.34220	+	0.975166i	0.999360	+	0.0357732i	$0.0113894\pi$
$47$	63.0835	+	45.8328i	1.34220	+	0.975166i	0.342842	+	0.939393i	$0.388611\pi$
$48$		0			0
$49$	1.40631	−	4.32817i	0.0287001	−	0.0883299i
$50$		0			0
$51$	−53.0852	−	73.0655i	−1.04089	−	1.43266i
$52$		0			0
$53$	3.06043	+	9.41904i	0.0577440	+	0.177718i	0.975768	−	0.218806i	$-0.0702163\pi$
$53$	3.06043	+	9.41904i	0.0577440	+	0.177718i	−0.918024	+	0.396524i	$0.870216\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	155.554	−	50.5426i	2.72902	−	0.886713i
$58$		0			0
$59$	−29.6620	+	21.5507i	−0.502746	+	0.365267i	−0.810065	−	0.586340i	$-0.800568\pi$
$59$	−29.6620	+	21.5507i	−0.502746	+	0.365267i	0.307319	+	0.951607i	$0.400568\pi$
$60$		0			0
$61$	26.9171	+	8.74590i	0.441264	+	0.143375i	0.521219	−	0.853423i	$-0.325478\pi$
$61$	26.9171	+	8.74590i	0.441264	+	0.143375i	−0.0799547	+	0.996799i	$0.525478\pi$
$62$		0			0
$63$	−64.7990	+	89.1881i	−1.02855	+	1.41568i
$64$		0			0
$65$			71.4011i			1.09848i
$66$		0			0
$67$	−30.7234			−0.458558			−0.229279	−	0.973361i	$-0.573637\pi$
$67$	−30.7234			−0.458558			−0.229279	+	0.973361i	$0.573637\pi$
$68$		0			0
$69$	14.6716	+	10.6595i	0.212632	+	0.154486i
$70$		0			0
$71$	−12.6835	+	39.0359i	−0.178641	+	0.549802i	−0.999781	−	0.0209255i	$-0.993339\pi$
$71$	−12.6835	+	39.0359i	−0.178641	+	0.549802i	0.821140	+	0.570727i	$0.193339\pi$
$72$		0			0
$73$	36.3001	+	49.9628i	0.497261	+	0.684422i	0.981707	−	0.190400i	$-0.0609785\pi$
$73$	36.3001	+	49.9628i	0.497261	+	0.684422i	−0.484445	+	0.874822i	$0.660979\pi$
$74$		0			0
$75$	−3.93780	−	12.1193i	−0.0525039	−	0.161591i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−118.204	+	38.4068i	−1.49625	+	0.486161i	−0.938922	−	0.344130i	$-0.888174\pi$
$79$	−118.204	+	38.4068i	−1.49625	+	0.486161i	−0.557329	+	0.830292i	$0.688174\pi$
$80$		0			0
$81$	−35.2762	+	25.6296i	−0.435508	+	0.316415i
$82$		0			0
$83$	2.94344	+	0.956381i	0.0354631	+	0.0115227i	0.326695	−	0.945130i	$-0.394065\pi$
$83$	2.94344	+	0.956381i	0.0354631	+	0.0115227i	−0.291232	+	0.956653i	$0.594065\pi$
$84$		0			0
$85$	49.8061	−	68.5522i	0.585954	−	0.806496i
$86$		0			0
$87$		−	64.5240i		−	0.741655i
$88$		0			0
$89$	60.4914			0.679678			0.339839	−	0.940484i	$-0.389627\pi$
$89$	60.4914			0.679678			0.339839	+	0.940484i	$0.389627\pi$
$90$		0			0
$91$	−81.2293	−	59.0165i	−0.892630	−	0.648533i
$92$		0			0
$93$	34.1840	−	105.207i	0.367570	−	1.13126i
$94$		0			0
$95$	90.1993	+	124.149i	0.949467	+	1.30683i
$96$		0			0
$97$	14.8226	+	45.6193i	0.152810	+	0.470302i	0.997932	−	0.0642712i	$-0.0204723\pi$
$97$	14.8226	+	45.6193i	0.152810	+	0.470302i	−0.845122	+	0.534574i	$0.820472\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−83.6741	+	27.1874i	−0.828456	+	0.269182i	−0.692395	−	0.721519i	$-0.743444\pi$
$101$	−83.6741	+	27.1874i	−0.828456	+	0.269182i	−0.136061	+	0.990700i	$0.543444\pi$
$102$		0			0
$103$	10.0570	−	7.30685i	0.0976409	−	0.0709403i	−0.537894	−	0.843013i	$-0.680780\pi$
$103$	10.0570	−	7.30685i	0.0976409	−	0.0709403i	0.635535	+	0.772072i	$0.280780\pi$
$104$		0			0
$105$	−151.912	−	49.3591i	−1.44678	−	0.470087i
$106$		0			0
$107$	−0.698862	+	0.961900i	−0.00653142	+	0.00898972i	−0.812270	−	0.583281i	$-0.801769\pi$
$107$	−0.698862	+	0.961900i	−0.00653142	+	0.00898972i	0.805739	+	0.592271i	$0.201769\pi$
$108$		0			0
$109$		−	145.212i		−	1.33222i	−0.745855	−	0.666108i	$-0.767959\pi$
$109$		−	145.212i		−	1.33222i	0.745855	−	0.666108i	$-0.232041\pi$
$110$		0			0
$111$	−140.071			−1.26190
$112$		0			0
$113$	−47.0926	−	34.2148i	−0.416749	−	0.302786i	0.359580	−	0.933114i	$-0.382920\pi$
$113$	−47.0926	−	34.2148i	−0.416749	−	0.302786i	−0.776328	+	0.630329i	$0.782920\pi$
$114$		0			0
$115$	−5.25789	+	16.1821i	−0.0457208	+	0.140714i
$116$		0			0
$117$	−146.373	−	201.465i	−1.25105	−	1.72192i
$118$		0			0
$119$	36.8210	+	113.323i	0.309420	+	0.952298i
$120$		0			0
$121$		0			0
$122$		0			0
$123$	−238.153	+	77.3807i	−1.93620	+	0.629111i
$124$		0			0
$125$	105.564	−	76.6966i	0.844510	−	0.613572i
$126$		0			0
$127$	37.6191	+	12.2232i	0.296213	+	0.0962455i	0.453353	−	0.891331i	$-0.350228\pi$
$127$	37.6191	+	12.2232i	0.296213	+	0.0962455i	−0.157140	+	0.987576i	$0.550228\pi$
$128$		0			0
$129$	−50.1258	+	68.9922i	−0.388572	+	0.534823i
$130$		0			0
$131$			130.281i			0.994510i	0.867605	+	0.497255i	$0.165659\pi$
$131$			130.281i			0.994510i	−0.867605	+	0.497255i	$0.834341\pi$
$132$		0			0
$133$	−215.792			−1.62249
$134$		0			0
$135$	−146.058	−	106.117i	−1.08191	−	0.786053i
$136$		0			0
$137$	−63.6741	+	195.969i	−0.464774	+	1.43043i	0.394492	+	0.918899i	$0.370921\pi$
$137$	−63.6741	+	195.969i	−0.464774	+	1.43043i	−0.859266	+	0.511528i	$0.829079\pi$
$138$		0			0
$139$	125.901	+	173.288i	0.905765	+	1.24668i	0.968592	+	0.248655i	$0.0799884\pi$
$139$	125.901	+	173.288i	0.905765	+	1.24668i	−0.0628270	+	0.998024i	$0.520012\pi$
$140$		0			0
$141$	−121.762	−	374.746i	−0.863562	−	2.65777i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	57.5753	−	18.7074i	0.397071	−	0.129016i
$146$		0			0
$147$	−18.6049	+	13.5173i	−0.126564	+	0.0919542i
$148$		0			0
$149$	−57.1220	−	18.5601i	−0.383369	−	0.124564i	0.110991	−	0.993821i	$-0.464598\pi$
$149$	−57.1220	−	18.5601i	−0.383369	−	0.124564i	−0.494360	+	0.869257i	$0.664598\pi$
$150$		0			0
$151$	75.8544	−	104.405i	0.502347	−	0.691422i	−0.480258	−	0.877127i	$-0.659457\pi$
$151$	75.8544	−	104.405i	0.502347	−	0.691422i	0.982605	+	0.185706i	$0.0594571\pi$
$152$		0			0
$153$			295.529i			1.93156i
$154$		0			0
$155$	103.789			0.669604
$156$		0			0
$157$	220.735	+	160.374i	1.40596	+	1.02149i	0.993895	+	0.110332i	$0.0351913\pi$
$157$	220.735	+	160.374i	1.40596	+	1.02149i	0.412062	+	0.911156i	$0.364809\pi$
$158$		0			0
$159$	15.4652	−	47.5969i	0.0972653	−	0.299352i
$160$		0			0
$161$	−14.0636	−	19.3569i	−0.0873518	−	0.120229i
$162$		0			0
$163$	−4.45141	−	13.7000i	−0.0273093	−	0.0840492i	0.936473	−	0.350740i	$-0.114070\pi$
$163$	−4.45141	−	13.7000i	−0.0273093	−	0.0840492i	−0.963782	+	0.266691i	$0.914070\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	154.632	−	50.2429i	0.925938	−	0.300855i	0.193037	−	0.981191i	$-0.438166\pi$
$167$	154.632	−	50.2429i	0.925938	−	0.300855i	0.732900	+	0.680336i	$0.238166\pi$
$168$		0			0
$169$	46.7629	−	33.9752i	0.276704	−	0.201037i
$170$		0			0
$171$	−509.011	−	165.388i	−2.97667	−	0.967180i
$172$		0			0
$173$	65.8448	−	90.6276i	0.380606	−	0.523859i	−0.575139	−	0.818056i	$-0.695052\pi$
$173$	65.8448	−	90.6276i	0.380606	−	0.523859i	0.955745	+	0.294197i	$0.0950521\pi$
$174$		0			0
$175$			16.8124i			0.0960709i
$176$		0			0
$177$	185.275			1.04675
$178$		0			0
$179$	−127.140	−	92.3729i	−0.710281	−	0.516050i	0.172983	−	0.984925i	$-0.444659\pi$
$179$	−127.140	−	92.3729i	−0.710281	−	0.516050i	−0.883264	+	0.468875i	$0.844659\pi$
$180$		0			0
$181$	−105.272	+	323.994i	−0.581614	+	1.79002i	0.0308474	+	0.999524i	$0.490179\pi$
$181$	−105.272	+	323.994i	−0.581614	+	1.79002i	−0.612462	+	0.790500i	$0.709821\pi$
$182$		0			0
$183$	−84.0646	−	115.705i	−0.459369	−	0.632268i
$184$		0			0
$185$	−40.6106	−	124.987i	−0.219517	−	0.675603i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	241.448	−	78.4512i	1.27750	−	0.415085i
$190$		0			0
$191$	−25.1761	+	18.2915i	−0.131812	+	0.0957671i	−0.651738	−	0.758444i	$-0.725960\pi$
$191$	−25.1761	+	18.2915i	−0.131812	+	0.0957671i	0.519926	+	0.854212i	$0.325960\pi$
$192$		0			0
$193$	47.6999	+	15.4986i	0.247150	+	0.0803038i	0.429972	−	0.902842i	$-0.358523\pi$
$193$	47.6999	+	15.4986i	0.247150	+	0.0803038i	−0.182822	+	0.983146i	$0.558523\pi$
$194$		0			0
$195$	212.078	−	291.901i	1.08758	−	1.49693i
$196$		0			0
$197$			225.831i			1.14635i	0.819432	+	0.573176i	$0.194289\pi$
$197$			225.831i			1.14635i	−0.819432	+	0.573176i	$0.805711\pi$
$198$		0			0
$199$	46.4242			0.233287			0.116644	−	0.993174i	$-0.462786\pi$
$199$	46.4242			0.233287			0.116644	+	0.993174i	$0.462786\pi$
$200$		0			0
$201$	125.603	+	91.2558i	0.624889	+	0.454009i
$202$		0			0
$203$	−26.3065	+	80.9630i	−0.129589	+	0.398832i
$204$		0			0
$205$	−138.095	−	190.071i	−0.673634	−	0.927178i
$206$		0			0
$207$	−18.3378	−	56.4380i	−0.0885885	−	0.272648i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−101.556	+	32.9975i	−0.481307	+	0.156386i	−0.539614	−	0.841913i	$-0.681430\pi$
$211$	−101.556	+	32.9975i	−0.481307	+	0.156386i	0.0583069	+	0.998299i	$0.481430\pi$
$212$		0			0
$213$	167.799	−	121.913i	0.787787	−	0.572361i
$214$		0			0
$215$	−76.0953	−	24.7249i	−0.353932	−	0.114999i
$216$		0			0
$217$	−85.7863	+	118.075i	−0.395329	+	0.544123i
$218$		0			0
$219$		−	312.077i		−	1.42501i
$220$		0			0
$221$	−269.157			−1.21791
$222$		0			0
$223$	108.118	+	78.5527i	0.484836	+	0.352254i	0.803195	−	0.595716i	$-0.203132\pi$
$223$	108.118	+	78.5527i	0.484836	+	0.352254i	−0.318359	+	0.947970i	$0.603132\pi$
$224$		0			0
$225$	−12.8854	+	39.6573i	−0.0572685	+	0.176254i
$226$		0			0
$227$	106.721	+	146.889i	0.470137	+	0.647088i	0.976572	−	0.215190i	$-0.0690372\pi$
$227$	106.721	+	146.889i	0.470137	+	0.647088i	−0.506436	+	0.862278i	$0.669037\pi$
$228$		0			0
$229$	−81.2785	−	250.150i	−0.354928	−	1.09236i	−0.956051	−	0.293200i	$-0.905280\pi$
$229$	−81.2785	−	250.150i	−0.354928	−	1.09236i	0.601123	−	0.799156i	$-0.294720\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	156.952	−	50.9968i	0.673614	−	0.218870i	0.0478167	−	0.998856i	$-0.484774\pi$
$233$	156.952	−	50.9968i	0.673614	−	0.218870i	0.625797	+	0.779986i	$0.284774\pi$
$234$		0			0
$235$	299.087	−	217.299i	1.27271	−	0.924677i
$236$		0			0
$237$	597.316	+	194.080i	2.52032	+	0.818901i
$238$		0			0
$239$	−178.104	+	245.140i	−0.745207	+	1.02569i	0.253096	+	0.967441i	$0.418551\pi$
$239$	−178.104	+	245.140i	−0.745207	+	1.02569i	−0.998302	+	0.0582476i	$0.981449\pi$
$240$		0			0
$241$			289.642i			1.20183i	0.799311	+	0.600917i	$0.205198\pi$
$241$			289.642i			1.20183i	−0.799311	+	0.600917i	$0.794802\pi$
$242$		0			0
$243$	−122.370			−0.503579
$244$		0			0
$245$	−17.4557	−	12.6823i	−0.0712477	−	0.0517645i
$246$		0			0
$247$	150.629	−	463.589i	0.609835	−	1.87688i
$248$		0			0
$249$	−9.19263	−	12.6526i	−0.0369182	−	0.0508135i
$250$		0			0
$251$	83.2179	+	256.118i	0.331545	+	1.02039i	0.968399	+	0.249407i	$0.0802356\pi$
$251$	83.2179	+	256.118i	0.331545	+	1.02039i	−0.636853	+	0.770985i	$0.719764\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−407.232	+	132.318i	−1.59699	+	0.518893i
$256$		0			0
$257$	−406.941	+	295.660i	−1.58343	+	1.15043i	−0.670795	+	0.741643i	$0.734047\pi$
$257$	−406.941	+	295.660i	−1.58343	+	1.15043i	−0.912631	+	0.408784i	$0.865953\pi$
$258$		0			0
$259$	175.757	+	57.1070i	0.678600	+	0.220490i
$260$		0			0
$261$	−124.104	+	170.814i	−0.475494	+	0.654461i
$262$		0			0
$263$		−	178.603i		−	0.679099i	−0.940588	−	0.339550i	$-0.889725\pi$
$263$		−	178.603i		−	0.679099i	0.940588	−	0.339550i	$-0.110275\pi$
$264$		0			0
$265$	46.9550			0.177189
$266$		0			0
$267$	−247.300	−	179.674i	−0.926215	−	0.672935i
$268$		0			0
$269$	32.5941	−	100.314i	0.121168	−	0.372916i	−0.872016	−	0.489478i	$-0.837187\pi$
$269$	32.5941	−	100.314i	0.121168	−	0.372916i	0.993183	+	0.116562i	$0.0371874\pi$
$270$		0			0
$271$	−86.3298	−	118.823i	−0.318560	−	0.438460i	0.619467	−	0.785023i	$-0.287349\pi$
$271$	−86.3298	−	118.823i	−0.318560	−	0.438460i	−0.938027	+	0.346563i	$0.887349\pi$
$272$		0			0
$273$	156.787	+	482.540i	0.574311	+	1.76755i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−247.480	+	80.4113i	−0.893431	+	0.290293i	−0.719523	−	0.694469i	$-0.755640\pi$
$277$	−247.480	+	80.4113i	−0.893431	+	0.290293i	−0.173908	+	0.984762i	$0.555640\pi$
$278$		0			0
$279$	−292.849	+	212.767i	−1.04964	+	0.762606i
$280$		0			0
$281$	−487.119	−	158.275i	−1.73352	−	0.563255i	−0.739570	−	0.673080i	$-0.764971\pi$
$281$	−487.119	−	158.275i	−1.73352	−	0.563255i	−0.993951	+	0.109824i	$0.964971\pi$
$282$		0			0
$283$	105.155	−	144.733i	0.371572	−	0.511425i	−0.581755	−	0.813364i	$-0.697634\pi$
$283$	105.155	−	144.733i	0.371572	−	0.511425i	0.953327	+	0.301939i	$0.0976339\pi$
$284$		0			0
$285$		−	775.456i		−	2.72090i
$286$		0			0
$287$	330.377			1.15114
$288$		0			0
$289$	24.6116	+	17.8814i	0.0851613	+	0.0618733i
$290$		0			0
$291$	74.9027	−	230.527i	0.257397	−	0.792188i
$292$		0			0
$293$	305.694	+	420.752i	1.04332	+	1.43601i	0.894456	+	0.447155i	$0.147563\pi$
$293$	305.694	+	420.752i	1.04332	+	1.43601i	0.148867	+	0.988857i	$0.452437\pi$
$294$		0			0
$295$	53.7164	+	165.322i	0.182090	+	0.560414i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	51.4017	−	16.7014i	0.171912	−	0.0558576i
$300$		0			0
$301$	91.0247	−	66.1333i	0.302408	−	0.219712i
$302$		0			0
$303$	422.828	+	137.385i	1.39547	+	0.453416i
$304$		0			0
$305$	78.8719	−	108.558i	0.258596	−	0.355927i
$306$		0			0
$307$		−	453.784i		−	1.47812i	−0.673638	−	0.739061i	$-0.735269\pi$
$307$		−	453.784i		−	1.47812i	0.673638	−	0.739061i	$-0.264731\pi$
$308$		0			0
$309$	−62.8180			−0.203294
$310$		0			0
$311$	−328.234	−	238.476i	−1.05541	−	0.766803i	−0.0821789	−	0.996618i	$-0.526188\pi$
$311$	−328.234	−	238.476i	−1.05541	−	0.766803i	−0.973234	+	0.229815i	$0.926188\pi$
$312$		0			0
$313$	5.16035	−	15.8819i	0.0164867	−	0.0507409i	−0.942475	−	0.334277i	$-0.891508\pi$
$313$	5.16035	−	15.8819i	0.0164867	−	0.0507409i	0.958961	+	0.283537i	$0.0915077\pi$
$314$		0			0
$315$	307.220	+	422.852i	0.975301	+	1.34239i
$316$		0			0
$317$	173.836	+	535.013i	0.548380	+	1.68774i	0.712815	+	0.701352i	$0.247420\pi$
$317$	173.836	+	535.013i	0.548380	+	1.68774i	−0.164436	+	0.986388i	$0.552580\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	5.71414	−	1.85664i	0.0178011	−	0.00578392i
$322$		0			0
$323$	−467.997	+	340.020i	−1.44891	+	1.05269i
$324$		0			0
$325$	−36.1184	−	11.7356i	−0.111134	−	0.0361095i
$326$		0			0
$327$	−431.313	+	593.651i	−1.31900	+	1.81545i
$328$		0			0
$329$			519.864i			1.58013i
$330$		0			0
$331$	167.684			0.506597			0.253298	−	0.967388i	$-0.418485\pi$
$331$	167.684			0.506597			0.253298	+	0.967388i	$0.418485\pi$
$332$		0			0
$333$	370.810	+	269.409i	1.11354	+	0.809036i
$334$		0			0
$335$	−45.0125	+	138.534i	−0.134366	+	0.413535i
$336$		0			0
$337$	−103.280	−	142.152i	−0.306467	−	0.421816i	0.627808	−	0.778368i	$-0.283952\pi$
$337$	−103.280	−	142.152i	−0.306467	−	0.421816i	−0.934276	+	0.356552i	$0.883952\pi$
$338$		0			0
$339$	90.8971	+	279.752i	0.268133	+	0.825228i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	339.551	−	110.327i	0.989944	−	0.321652i
$344$		0			0
$345$	69.5599	−	50.5382i	0.201623	−	0.146488i
$346$		0			0
$347$	459.695	+	149.364i	1.32477	+	0.430443i	0.884130	−	0.467241i	$-0.154752\pi$
$347$	459.695	+	149.364i	1.32477	+	0.430443i	0.440639	+	0.897685i	$0.354752\pi$
$348$		0			0
$349$	−94.6593	+	130.287i	−0.271230	+	0.373316i	−0.922804	−	0.385269i	$-0.874109\pi$
$349$	−94.6593	+	130.287i	−0.271230	+	0.373316i	0.651574	+	0.758585i	$0.274109\pi$
$350$		0			0
$351$			573.468i			1.63381i
$352$		0			0
$353$	522.647			1.48059			0.740294	−	0.672284i	$-0.234687\pi$
$353$	522.647			1.48059			0.740294	+	0.672284i	$0.234687\pi$
$354$		0			0
$355$	157.434	+	114.382i	0.443475	+	0.322203i
$356$		0			0
$357$	186.067	−	572.654i	0.521195	−	1.60407i
$358$		0			0
$359$	−336.373	−	462.978i	−0.936972	−	1.28963i	−0.957077	−	0.289833i	$-0.906400\pi$
$359$	−336.373	−	462.978i	−0.936972	−	1.28963i	0.0201051	−	0.999798i	$-0.493600\pi$
$360$		0			0
$361$	−212.179	−	653.020i	−0.587754	−	1.80892i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	278.469	−	90.4800i	0.762928	−	0.247890i
$366$		0			0
$367$	−136.244	+	98.9867i	−0.371236	+	0.269719i	−0.757723	−	0.652576i	$-0.773688\pi$
$367$	−136.244	+	98.9867i	−0.371236	+	0.269719i	0.386487	+	0.922295i	$0.373688\pi$
$368$		0			0
$369$	779.295	+	253.208i	2.11191	+	0.686201i
$370$		0			0
$371$	−38.8106	+	53.4182i	−0.104611	+	0.143984i
$372$		0			0
$373$		−	500.543i		−	1.34194i	−0.741486	−	0.670969i	$-0.765878\pi$
$373$		−	500.543i		−	1.34194i	0.741486	−	0.670969i	$-0.234122\pi$
$374$		0			0
$375$	−659.370			−1.75832
$376$		0			0
$377$	−155.571	−	113.029i	−0.412656	−	0.299812i
$378$		0			0
$379$	16.1149	−	49.5966i	0.0425195	−	0.130862i	−0.927543	−	0.373716i	$-0.878084\pi$
$379$	16.1149	−	49.5966i	0.0425195	−	0.130862i	0.970063	+	0.242854i	$0.0780836\pi$
$380$		0			0
$381$	−117.488	−	161.708i	−0.308367	−	0.424431i
$382$		0			0
$383$	−76.3632	−	235.022i	−0.199382	−	0.613634i	−0.999897	−	0.0143222i	$-0.995441\pi$
$383$	−76.3632	−	235.022i	−0.199382	−	0.613634i	0.800516	−	0.599312i	$-0.204559\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	265.396	−	86.2324i	0.685778	−	0.222823i
$388$		0			0
$389$	199.368	−	144.850i	0.512515	−	0.372364i	−0.301262	−	0.953542i	$-0.597408\pi$
$389$	199.368	−	144.850i	0.512515	−	0.372364i	0.813777	+	0.581177i	$0.197408\pi$
$390$		0			0
$391$	−61.0009	−	19.8204i	−0.156013	−	0.0506915i
$392$		0			0
$393$	386.965	−	532.611i	0.984643	−	1.35524i
$394$		0			0
$395$			589.260i			1.49180i
$396$		0			0
$397$	50.7517			0.127838			0.0639191	−	0.997955i	$-0.479640\pi$
$397$	50.7517			0.127838			0.0639191	+	0.997955i	$0.479640\pi$
$398$		0			0
$399$	882.195	+	640.952i	2.21102	+	1.60640i
$400$		0			0
$401$	14.8571	−	45.7254i	0.0370501	−	0.114028i	−0.930821	−	0.365475i	$-0.880906\pi$
$401$	14.8571	−	45.7254i	0.0370501	−	0.114028i	0.967871	+	0.251447i	$0.0809064\pi$
$402$		0			0
$403$	−193.781	−	266.716i	−0.480845	−	0.661827i
$404$		0			0
$405$	63.8833	+	196.613i	0.157737	+	0.485463i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	486.442	−	158.055i	1.18934	−	0.386441i	0.353514	−	0.935429i	$-0.384987\pi$
$409$	486.442	−	158.055i	1.18934	−	0.386441i	0.835830	+	0.548988i	$0.184987\pi$
$410$		0			0
$411$	842.384	−	612.028i	2.04960	−	1.48912i
$412$		0			0
$413$	−232.478	−	75.5366i	−0.562900	−	0.182897i
$414$		0			0
$415$	8.62479	−	11.8710i	0.0207826	−	0.0286048i
$416$		0			0
$417$		−	1082.39i		−	2.59566i
$418$		0			0
$419$	790.955			1.88772			0.943860	−	0.330345i	$-0.107165\pi$
$419$	790.955			1.88772			0.943860	+	0.330345i	$0.107165\pi$
$420$		0			0
$421$	−333.136	−	242.038i	−0.791297	−	0.574911i	0.117051	−	0.993126i	$-0.462656\pi$
$421$	−333.136	−	242.038i	−0.791297	−	0.574911i	−0.908348	+	0.418215i	$0.862656\pi$
$422$		0			0
$423$	−398.436	+	1226.26i	−0.941928	+	2.89896i
$424$		0			0
$425$	26.4911	+	36.4618i	0.0623319	+	0.0857925i
$426$		0			0
$427$	58.3090	+	179.457i	0.136555	+	0.420274i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	268.338	−	87.1884i	0.622595	−	0.202293i	0.0193028	−	0.999814i	$-0.493855\pi$
$431$	268.338	−	87.1884i	0.622595	−	0.202293i	0.603292	+	0.797520i	$0.293855\pi$
$432$		0			0
$433$	44.9013	−	32.6227i	0.103698	−	0.0753411i	−0.534728	−	0.845024i	$-0.679586\pi$
$433$	44.9013	−	32.6227i	0.103698	−	0.0753411i	0.638426	+	0.769683i	$0.279586\pi$
$434$		0			0
$435$	−290.944	−	94.5333i	−0.668836	−	0.217318i
$436$		0			0
$437$	68.2762	−	93.9742i	0.156239	−	0.215044i
$438$		0			0
$439$		−	232.914i		−	0.530556i	−0.964172	−	0.265278i	$-0.914536\pi$
$439$		−	232.914i		−	0.530556i	0.964172	−	0.265278i	$-0.0854638\pi$
$440$		0			0
$441$	75.2516			0.170638
$442$		0			0
$443$	344.202	+	250.077i	0.776979	+	0.564508i	0.904071	−	0.427383i	$-0.140564\pi$
$443$	344.202	+	250.077i	0.776979	+	0.564508i	−0.127092	+	0.991891i	$0.540564\pi$
$444$		0			0
$445$	88.6252	−	272.760i	0.199158	−	0.612944i
$446$		0			0
$447$	178.397	+	245.543i	0.399099	+	0.549313i
$448$		0			0
$449$	14.2766	+	43.9388i	0.0317964	+	0.0978592i	0.965695	−	0.259678i	$-0.0836165\pi$
$449$	14.2766	+	43.9388i	0.0317964	+	0.0978592i	−0.933899	+	0.357537i	$0.883616\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−620.213	+	201.519i	−1.36912	+	0.444855i
$454$		0			0
$455$	−385.118	+	279.805i	−0.846414	+	0.614956i
$456$		0			0
$457$	−147.110	−	47.7990i	−0.321904	−	0.104593i	0.143608	−	0.989635i	$-0.454130\pi$
$457$	−147.110	−	47.7990i	−0.321904	−	0.104593i	−0.465512	+	0.885042i	$0.654130\pi$
$458$		0			0
$459$	400.024	−	550.586i	0.871513	−	1.19953i
$460$		0			0
$461$			775.943i			1.68317i	0.540123	+	0.841586i	$0.318378\pi$
$461$			775.943i			1.68317i	−0.540123	+	0.841586i	$0.681622\pi$
$462$		0			0
$463$	−829.285			−1.79111			−0.895557	−	0.444948i	$-0.853222\pi$
$463$	−829.285			−1.79111			−0.895557	+	0.444948i	$0.853222\pi$
$464$		0			0
$465$	−424.306	−	308.277i	−0.912487	−	0.662960i
$466$		0			0
$467$	241.774	−	744.104i	0.517718	−	1.59337i	−0.260565	−	0.965456i	$-0.583909\pi$
$467$	241.774	−	744.104i	0.517718	−	1.59337i	0.778282	−	0.627914i	$-0.216091\pi$
$468$		0			0
$469$	−120.398	−	165.714i	−0.256712	−	0.353334i
$470$		0			0
$471$	−426.058	−	1311.27i	−0.904582	−	2.78402i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−77.6261	+	25.2223i	−0.163423	+	0.0530995i
$476$		0			0
$477$	−132.488	+	96.2580i	−0.277752	+	0.201799i
$478$		0			0
$479$	−77.2103	−	25.0872i	−0.161191	−	0.0523740i	0.227310	−	0.973822i	$-0.427007\pi$
$479$	−77.2103	−	25.0872i	−0.161191	−	0.0523740i	−0.388501	+	0.921448i	$0.627007\pi$
$480$		0			0
$481$	−245.368	+	337.720i	−0.510121	+	0.702121i
$482$		0			0
$483$			120.907i			0.250325i
$484$		0			0
$485$	227.418			0.468902
$486$		0			0
$487$	235.675	+	171.228i	0.483933	+	0.351598i	0.802846	−	0.596186i	$-0.203318\pi$
$487$	235.675	+	171.228i	0.483933	+	0.351598i	−0.318913	+	0.947784i	$0.603318\pi$
$488$		0			0
$489$	−22.4942	+	69.2299i	−0.0460003	+	0.141574i
$490$		0			0
$491$	−176.504	−	242.937i	−0.359479	−	0.494780i	0.590524	−	0.807020i	$-0.298921\pi$
$491$	−176.504	−	242.937i	−0.359479	−	0.494780i	−0.950003	+	0.312239i	$0.898921\pi$
$492$		0			0
$493$	70.5202	+	217.039i	0.143043	+	0.440241i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−260.253	+	84.5614i	−0.523648	+	0.170144i
$498$		0			0
$499$	−248.898	+	180.835i	−0.498794	+	0.362395i	−0.808556	−	0.588419i	$-0.799750\pi$
$499$	−248.898	+	180.835i	−0.498794	+	0.362395i	0.309762	+	0.950814i	$0.399750\pi$
$500$		0			0
$501$	−781.395	−	253.891i	−1.55967	−	0.506768i
$502$		0			0
$503$	−470.986	+	648.257i	−0.936354	+	1.28878i	0.0209742	+	0.999780i	$0.493323\pi$
$503$	−470.986	+	648.257i	−0.936354	+	1.28878i	−0.957329	+	0.289001i	$0.906677\pi$
$504$		0			0
$505$			417.125i			0.825990i
$506$		0			0
$507$	−292.090			−0.576114
$508$		0			0
$509$	−438.219	−	318.385i	−0.860941	−	0.625510i	0.0671999	−	0.997740i	$-0.478593\pi$
$509$	−438.219	−	318.385i	−0.860941	−	0.625510i	−0.928141	+	0.372229i	$0.878593\pi$
$510$		0			0
$511$	−127.234	+	391.586i	−0.248990	+	0.766312i
$512$		0			0
$513$	724.448	+	997.117i	1.41218	+	1.94370i
$514$		0			0
$515$	−18.2127	−	56.0531i	−0.0353645	−	0.108841i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−538.371	+	174.927i	−1.03732	+	0.337047i
$520$		0			0
$521$	−577.263	+	419.406i	−1.10799	+	0.805002i	−0.982346	−	0.187073i	$-0.940100\pi$
$521$	−577.263	+	419.406i	−1.10799	+	0.805002i	−0.125644	+	0.992075i	$0.540100\pi$
$522$		0			0
$523$	432.518	+	140.534i	0.826994	+	0.268707i	0.691779	−	0.722110i	$-0.256827\pi$
$523$	432.518	+	140.534i	0.826994	+	0.268707i	0.135215	+	0.990816i	$0.456827\pi$
$524$		0			0
$525$	49.9368	−	68.7321i	0.0951178	−	0.130918i
$526$		0			0
$527$			391.246i			0.742403i
$528$		0			0
$529$	−516.121			−0.975653
$530$		0			0
$531$	−490.477	−	356.353i	−0.923686	−	0.671097i
$532$		0			0
$533$	−230.613	+	709.754i	−0.432670	+	1.33162i
$534$		0			0
$535$	3.31339	+	4.56049i	0.00619325	+	0.00852428i
$536$		0			0
$537$	245.403	+	755.274i	0.456989	+	1.40647i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−768.411	+	249.672i	−1.42035	+	0.461500i	−0.915714	−	0.401830i	$-0.868374\pi$
$541$	−768.411	+	249.672i	−1.42035	+	0.461500i	−0.504638	+	0.863331i	$0.668374\pi$
$542$		0			0
$543$	1392.71	−	1011.86i	2.56485	−	1.86347i
$544$		0			0
$545$	−654.771	−	212.748i	−1.20141	−	0.390363i
$546$		0			0
$547$	−100.382	+	138.164i	−0.183514	+	0.252585i	−0.890856	−	0.454287i	$-0.849894\pi$
$547$	−100.382	+	138.164i	−0.183514	+	0.252585i	0.707342	+	0.706872i	$0.249894\pi$
$548$		0			0
$549$			467.994i			0.852447i
$550$		0			0
$551$	−413.287			−0.750067
$552$		0			0
$553$	−670.370	−	487.052i	−1.21224	−	0.880745i
$554$		0			0
$555$	−205.216	+	631.591i	−0.369759	+	1.13800i
$556$		0			0
$557$	13.9618	+	19.2168i	0.0250661	+	0.0345005i	0.821366	−	0.570401i	$-0.193212\pi$
$557$	13.9618	+	19.2168i	0.0250661	+	0.0345005i	−0.796300	+	0.604902i	$0.793212\pi$
$558$		0			0
$559$	78.5373	+	241.713i	0.140496	+	0.432402i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	568.487	−	184.713i	1.00975	−	0.328086i	0.242993	−	0.970028i	$-0.421871\pi$
$563$	568.487	−	184.713i	1.00975	−	0.328086i	0.766753	+	0.641942i	$0.221871\pi$
$564$		0			0
$565$	−223.272	+	162.217i	−0.395172	+	0.287109i
$566$		0			0
$567$	−276.478	−	89.8333i	−0.487616	−	0.158436i
$568$		0			0
$569$	239.476	−	329.610i	0.420871	−	0.579279i	−0.544957	−	0.838464i	$-0.683454\pi$
$569$	239.476	−	329.610i	0.420871	−	0.579279i	0.965828	+	0.259185i	$0.0834539\pi$
$570$		0			0
$571$		−	1036.11i		−	1.81456i	−0.420530	−	0.907279i	$-0.638156\pi$
$571$		−	1036.11i		−	1.81456i	0.420530	−	0.907279i	$-0.361844\pi$
$572$		0			0
$573$	157.255			0.274441
$574$		0			0
$575$	−7.32156	−	5.31943i	−0.0127332	−	0.00925118i
$576$		0			0
$577$	212.646	−	654.458i	0.368538	−	1.13424i	−0.579198	−	0.815187i	$-0.696634\pi$
$577$	212.646	−	654.458i	0.368538	−	1.13424i	0.947736	−	0.319056i	$-0.103366\pi$
$578$		0			0
$579$	−148.971	−	205.041i	−0.257290	−	0.354130i
$580$		0			0
$581$	6.37621	+	19.6239i	0.0109745	+	0.0337762i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−1122.87	+	364.842i	−1.91943	+	0.623662i
$586$		0			0
$587$	−485.538	+	352.764i	−0.827152	+	0.600961i	−0.918752	−	0.394835i	$-0.870802\pi$
$587$	−485.538	+	352.764i	−0.827152	+	0.600961i	0.0915999	+	0.995796i	$0.470802\pi$
$588$		0			0
$589$	−673.872	−	218.954i	−1.14410	−	0.371739i
$590$		0			0
$591$	670.773	−	923.239i	1.13498	−	1.56216i
$592$		0			0
$593$		−	468.857i		−	0.790652i	−0.918541	−	0.395326i	$-0.870632\pi$
$593$		−	468.857i		−	0.790652i	0.918541	−	0.395326i	$-0.129368\pi$
$594$		0			0
$595$	564.931			0.949463
$596$		0			0
$597$	−189.790	−	137.891i	−0.317907	−	0.230973i
$598$		0			0
$599$	158.477	−	487.741i	0.264569	−	0.814259i	−0.727224	−	0.686400i	$-0.759190\pi$
$599$	158.477	−	487.741i	0.264569	−	0.814259i	0.991792	−	0.127858i	$-0.0408102\pi$
$600$		0			0
$601$	−298.113	−	410.318i	−0.496028	−	0.682725i	0.485457	−	0.874260i	$-0.338653\pi$
$601$	−298.113	−	410.318i	−0.496028	−	0.682725i	−0.981486	+	0.191536i	$0.938653\pi$
$602$		0			0
$603$	−156.989	−	483.163i	−0.260347	−	0.801265i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−320.774	+	104.226i	−0.528458	+	0.171707i	−0.561081	−	0.827761i	$-0.689614\pi$
$607$	−320.774	+	104.226i	−0.528458	+	0.171707i	0.0326221	+	0.999468i	$0.489614\pi$
$608$		0			0
$609$	348.025	−	252.855i	0.571469	−	0.415197i
$610$		0			0
$611$	−1116.83	−	362.881i	−1.82788	−	0.593913i
$612$		0			0
$613$	198.216	−	272.820i	0.323353	−	0.445058i	−0.616134	−	0.787641i	$-0.711302\pi$
$613$	198.216	−	272.820i	0.323353	−	0.445058i	0.939487	+	0.342584i	$0.111302\pi$
$614$		0			0
$615$			1187.22i			1.93044i
$616$		0			0
$617$	−269.856			−0.437369			−0.218684	−	0.975796i	$-0.570177\pi$
$617$	−269.856			−0.437369			−0.218684	+	0.975796i	$0.570177\pi$
$618$		0			0
$619$	−439.905	−	319.610i	−0.710671	−	0.516333i	0.172719	−	0.984971i	$-0.444745\pi$
$619$	−439.905	−	319.610i	−0.710671	−	0.516333i	−0.883390	+	0.468639i	$0.844745\pi$
$620$		0			0
$621$	−42.2295	+	129.969i	−0.0680024	+	0.209290i
$622$		0			0
$623$	237.052	+	326.274i	0.380501	+	0.523714i
$624$		0			0
$625$	−171.689	−	528.405i	−0.274703	−	0.845448i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	471.155	−	153.088i	0.749055	−	0.243383i
$630$		0			0
$631$	−91.5704	+	66.5298i	−0.145119	+	0.105435i	−0.657976	−	0.753039i	$-0.728587\pi$
$631$	−91.5704	+	66.5298i	−0.145119	+	0.105435i	0.512857	+	0.858474i	$0.328587\pi$
$632$		0			0
$633$	513.189	+	166.745i	0.810724	+	0.263420i
$634$		0			0
$635$	110.230	−	151.719i	0.173591	−	0.238928i
$636$		0			0
$637$			68.5364i			0.107592i
$638$		0			0
$639$	−678.697			−1.06212
$640$		0			0
$641$	426.791	+	310.082i	0.665821	+	0.483747i	0.868624	−	0.495472i	$-0.165005\pi$
$641$	426.791	+	310.082i	0.665821	+	0.483747i	−0.202803	+	0.979220i	$0.565005\pi$
$642$		0			0
$643$	90.5922	−	278.814i	0.140890	−	0.433614i	−0.855570	−	0.517688i	$-0.826793\pi$
$643$	90.5922	−	278.814i	0.140890	−	0.433614i	0.996460	+	0.0840733i	$0.0267930\pi$
$644$		0			0
$645$	237.653	+	327.101i	0.368454	+	0.507133i
$646$		0			0
$647$	−205.130	−	631.325i	−0.317048	−	0.975773i	−0.974903	−	0.222629i	$-0.928536\pi$
$647$	−205.130	−	631.325i	−0.317048	−	0.975773i	0.657855	−	0.753144i	$-0.271464\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	701.420	−	227.905i	1.07745	−	0.350085i
$652$		0			0
$653$	642.435	−	466.756i	0.983821	−	0.714788i	0.0252618	−	0.999681i	$-0.491958\pi$
$653$	642.435	−	466.756i	0.983821	−	0.714788i	0.958559	+	0.284893i	$0.0919581\pi$
$654$		0			0
$655$	587.446	+	190.873i	0.896864	+	0.291409i
$656$		0			0
$657$	−600.241	+	826.160i	−0.913608	+	1.25747i
$658$		0			0
$659$			187.489i			0.284505i	0.989830	+	0.142253i	$0.0454346\pi$
$659$			187.489i			0.284505i	−0.989830	+	0.142253i	$0.954565\pi$
$660$		0			0
$661$	74.1929			0.112243			0.0561217	−	0.998424i	$-0.482127\pi$
$661$	74.1929			0.112243			0.0561217	+	0.998424i	$0.482127\pi$
$662$		0			0
$663$	1100.36	+	799.460i	1.65967	+	1.20582i
$664$		0			0
$665$	−316.154	+	973.021i	−0.475419	+	1.46319i
$666$		0			0
$667$	−26.9349	−	37.0727i	−0.0403821	−	0.0555812i
$668$		0			0
$669$	−208.688	−	642.275i	−0.311940	−	0.960052i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−898.412	+	291.912i	−1.33494	+	0.433747i	−0.887598	−	0.460618i	$-0.847628\pi$
$673$	−898.412	+	291.912i	−1.33494	+	0.433747i	−0.447338	+	0.894365i	$0.647628\pi$
$674$		0			0
$675$	77.6858	−	56.4420i	0.115090	−	0.0836178i
$676$		0			0
$677$	688.441	+	223.688i	1.01690	+	0.330411i	0.769599	−	0.638528i	$-0.220456\pi$
$677$	688.441	+	223.688i	1.01690	+	0.330411i	0.247301	+	0.968939i	$0.420456\pi$
$678$		0			0
$679$	−187.972	+	258.721i	−0.276836	+	0.381032i
$680$		0			0
$681$		−	917.495i		−	1.34728i
$682$		0			0
$683$	660.998			0.967787			0.483893	−	0.875127i	$-0.339222\pi$
$683$	660.998			0.967787			0.483893	+	0.875127i	$0.339222\pi$
$684$		0			0
$685$	790.350	+	574.223i	1.15380	+	0.838281i
$686$		0			0
$687$	−410.722	+	1264.07i	−0.597849	+	1.83999i
$688$		0			0
$689$	−87.6683	−	120.665i	−0.127240	−	0.175131i
$690$		0			0
$691$	−124.898	−	384.395i	−0.180749	−	0.556288i	0.819100	−	0.573650i	$-0.194473\pi$
$691$	−124.898	−	384.395i	−0.180749	−	0.556288i	−0.999849	+	0.0173622i	$0.994473\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	965.827	−	313.816i	1.38968	−	0.451534i
$696$		0			0
$697$	716.502	−	520.569i	1.02798	−	0.746871i
$698$		0			0
$699$	−793.121	−	257.701i	−1.13465	−	0.368670i
$700$		0			0
$701$	−233.239	+	321.027i	−0.332724	+	0.457955i	−0.942299	−	0.334773i	$-0.891340\pi$
$701$	−233.239	+	321.027i	−0.332724	+	0.457955i	0.609575	+	0.792729i	$0.291340\pi$
$702$		0			0
$703$			897.178i			1.27621i
$704$		0			0
$705$	−1868.15			−2.64986
$706$		0			0
$707$	−474.541	−	344.774i	−0.671204	−	0.487658i
$708$		0			0
$709$	−4.25048	+	13.0816i	−0.00599503	+	0.0184508i	−0.954009	−	0.299777i	$-0.903088\pi$
$709$	−4.25048	+	13.0816i	−0.00599503	+	0.0184508i	0.948014	+	0.318228i	$0.103088\pi$
$710$		0			0
$711$	−1207.99	−	1662.65i	−1.69900	−	2.33847i
$712$		0			0
$713$	−24.2772	−	74.7174i	−0.0340493	−	0.104793i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1456.25	−	473.163i	2.03103	−	0.659920i
$718$		0			0
$719$	−84.0118	+	61.0381i	−0.116845	+	0.0848931i	−0.644673	−	0.764458i	$-0.723007\pi$
$719$	−84.0118	+	61.0381i	−0.116845	+	0.0848931i	0.527828	+	0.849351i	$0.323007\pi$
$720$		0			0
$721$	78.8223	+	25.6109i	0.109324	+	0.0355214i
$722$		0			0
$723$	860.306	−	1184.11i	1.18991	−	1.63777i
$724$		0			0
$725$			32.1994i			0.0444129i
$726$		0			0
$727$	1381.61			1.90043			0.950214	−	0.311599i	$-0.100864\pi$
$727$	1381.61			1.90043			0.950214	+	0.311599i	$0.100864\pi$
$728$		0			0
$729$	817.755	+	594.134i	1.12175	+	0.814998i
$730$		0			0
$731$	93.2040	−	286.852i	0.127502	−	0.392411i
$732$		0			0
$733$	418.254	+	575.678i	0.570606	+	0.785372i	0.992626	−	0.121214i	$-0.0386789\pi$
$733$	418.254	+	575.678i	0.570606	+	0.785372i	−0.422020	+	0.906586i	$0.638679\pi$
$734$		0			0
$735$	33.6925	+	103.695i	0.0458402	+	0.141082i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	339.005	−	110.149i	0.458734	−	0.149052i	−0.0705286	−	0.997510i	$-0.522469\pi$
$739$	339.005	−	110.149i	0.458734	−	0.149052i	0.529263	+	0.848458i	$0.322469\pi$
$740$		0			0
$741$	−1992.77	+	1447.83i	−2.68930	+	1.95389i
$742$		0			0
$743$	204.751	+	66.5275i	0.275573	+	0.0895391i	0.443543	−	0.896253i	$-0.353721\pi$
$743$	204.751	+	66.5275i	0.275573	+	0.0895391i	−0.167970	+	0.985792i	$0.553721\pi$
$744$		0			0
$745$	−167.378	+	230.376i	−0.224668	+	0.309229i
$746$		0			0
$747$			51.1760i			0.0685087i
$748$		0			0
$749$	−7.92691			−0.0105833
$750$		0			0
$751$	−15.0409	−	10.9279i	−0.0200279	−	0.0145511i	0.577726	−	0.816231i	$-0.303940\pi$
$751$	−15.0409	−	10.9279i	−0.0200279	−	0.0145511i	−0.597754	+	0.801679i	$0.703940\pi$
$752$		0			0
$753$	420.522	−	1294.23i	0.558463	−	1.71877i
$754$		0			0
$755$	−359.635	−	494.996i	−0.476338	−	0.655623i
$756$		0			0
$757$	99.0402	+	304.814i	0.130833	+	0.402661i	0.994919	−	0.100683i	$-0.0321028\pi$
$757$	99.0402	+	304.814i	0.130833	+	0.402661i	−0.864086	+	0.503344i	$0.832103\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	7.81819	−	2.54029i	0.0102736	−	0.00333809i	−0.303876	−	0.952712i	$-0.598281\pi$
$761$	7.81819	−	2.54029i	0.0102736	−	0.00333809i	0.314149	+	0.949374i	$0.398281\pi$
$762$		0			0
$763$	783.232	−	569.051i	1.02652	−	0.745808i
$764$		0			0
$765$	1332.56	+	432.976i	1.74191	+	0.565982i
$766$		0			0
$767$	324.553	−	446.709i	0.423146	−	0.582411i
$768$		0			0
$769$			32.0029i			0.0416162i	0.999783	+	0.0208081i	$0.00662391\pi$
$769$			32.0029i			0.0416162i	−0.999783	+	0.0208081i	$0.993376\pi$
$770$		0			0
$771$	2541.83			3.29679
$772$		0			0
$773$	−730.274	−	530.575i	−0.944728	−	0.686385i	0.00482645	−	0.999988i	$-0.498464\pi$
$773$	−730.274	−	530.575i	−0.944728	−	0.686385i	−0.949554	+	0.313604i	$0.898464\pi$
$774$		0			0
$775$	−17.0588	+	52.5016i	−0.0220114	+	0.0677440i
$776$		0			0
$777$	−548.906	−	755.505i	−0.706443	−	0.972335i
$778$		0			0
$779$	495.637	+	1525.41i	0.636247	+	1.95817i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	462.424	−	150.251i	0.590580	−	0.191891i
$784$		0			0
$785$	1046.53	−	760.351i	1.33316	−	0.968600i
$786$		0			0
$787$	−803.354	−	261.026i	−1.02078	−	0.331672i	−0.249641	−	0.968338i	$-0.580313\pi$
$787$	−803.354	−	261.026i	−1.02078	−	0.331672i	−0.771139	+	0.636667i	$0.780313\pi$
$788$		0			0
$789$	−530.493	+	730.161i	−0.672362	+	0.925426i
$790$		0			0
$791$		−	388.085i		−	0.490626i
$792$		0			0
$793$	−426.232			−0.537493
$794$		0			0
$795$	−191.960	−	139.467i	−0.241460	−	0.175431i
$796$		0			0
$797$	−132.202	+	406.875i	−0.165874	+	0.510508i	−0.999100	−	0.0424253i	$-0.986492\pi$
$797$	−132.202	+	406.875i	−0.165874	+	0.510508i	0.833226	+	0.552933i	$0.186492\pi$
$798$		0			0
$799$	819.141	+	1127.45i	1.02521	+	1.41108i
$800$		0			0
$801$	309.096	+	951.300i	0.385888	+	1.18764i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−107.886	+	35.0544i	−0.134020	+	0.0435459i
$806$		0			0
$807$	−431.208	+	313.291i	−0.534334	+	0.388217i
$808$		0			0
$809$	633.173	+	205.731i	0.782662	+	0.254302i	0.672976	−	0.739664i	$-0.265016\pi$
$809$	633.173	+	205.731i	0.782662	+	0.254302i	0.109686	+	0.993966i	$0.465016\pi$
$810$		0			0
$811$	382.500	−	526.466i	0.471640	−	0.649156i	−0.505232	−	0.862984i	$-0.668593\pi$
$811$	382.500	−	526.466i	0.471640	−	0.649156i	0.976871	+	0.213828i	$0.0685930\pi$
$812$		0			0
$813$			742.189i			0.912901i
$814$		0			0
$815$	−68.2962			−0.0837990
$816$		0			0
$817$	441.907	+	321.064i	0.540890	+	0.392979i
$818$		0			0
$819$	513.045	−	1578.99i	0.626428	−	1.92795i
$820$		0			0
$821$	725.856	+	999.055i	0.884112	+	1.21688i	0.975265	+	0.221039i	$0.0709449\pi$
$821$	725.856	+	999.055i	0.884112	+	1.21688i	−0.0911526	+	0.995837i	$0.529055\pi$
$822$		0			0
$823$	210.770	+	648.683i	0.256100	+	0.788193i	0.993611	+	0.112859i	$0.0360008\pi$
$823$	210.770	+	648.683i	0.256100	+	0.788193i	−0.737512	+	0.675335i	$0.763999\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−207.534	+	67.4319i	−0.250948	+	0.0815379i	−0.431790	−	0.901974i	$-0.642118\pi$
$827$	−207.534	+	67.4319i	−0.250948	+	0.0815379i	0.180842	+	0.983512i	$0.442118\pi$
$828$		0			0
$829$	−1026.39	+	745.718i	−1.23811	+	0.899539i	−0.997471	−	0.0710752i	$-0.977357\pi$
$829$	−1026.39	+	745.718i	−1.23811	+	0.899539i	−0.240639	+	0.970615i	$0.577357\pi$
$830$		0			0
$831$	1250.58	+	406.340i	1.50492	+	0.488977i
$832$		0			0
$833$	47.8078	−	65.8018i	0.0573923	−	0.0789937i
$834$		0			0
$835$		−	770.856i		−	0.923181i
$836$		0			0
$837$	833.592			0.995928
$838$		0			0
$839$	−734.509	−	533.652i	−0.875458	−	0.636058i	0.0565879	−	0.998398i	$-0.481978\pi$
$839$	−734.509	−	533.652i	−0.875458	−	0.636058i	−0.932046	+	0.362340i	$0.881978\pi$
$840$		0			0
$841$	209.501	−	644.777i	0.249109	−	0.766679i
$842$		0			0
$843$	1521.32	+	2093.92i	1.80465	+	2.48389i
$844$		0			0
$845$	−84.6852	−	260.634i	−0.100219	−	0.308443i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−859.784	+	279.361i	−1.01270	+	0.329047i
$850$		0			0
$851$	−80.4787	+	58.4712i	−0.0945696	+	0.0687088i
$852$		0			0
$853$	−18.1669	−	5.90278i	−0.0212976	−	0.00692003i	0.298349	−	0.954457i	$-0.403564\pi$
$853$	−18.1669	−	5.90278i	−0.0212976	−	0.00692003i	−0.319646	+	0.947537i	$0.603564\pi$
$854$		0			0
$855$	−1491.49	+	2052.86i	−1.74444	+	2.40101i
$856$		0			0
$857$		−	488.737i		−	0.570289i	−0.958485	−	0.285144i	$-0.907958\pi$
$857$		−	488.737i		−	0.570289i	0.958485	−	0.285144i	$-0.0920415\pi$
$858$		0			0
$859$	−1449.51			−1.68744			−0.843721	−	0.536782i	$-0.819640\pi$
$859$	−1449.51			−1.68744			−0.843721	+	0.536782i	$0.819640\pi$
$860$		0			0
$861$	−1350.64	−	981.297i	−1.56869	−	1.13972i
$862$		0			0
$863$	10.0403	−	30.9007i	0.0116341	−	0.0358062i	−0.945071	−	0.326865i	$-0.894008\pi$
$863$	10.0403	−	30.9007i	0.0116341	−	0.0358062i	0.956705	+	0.291059i	$0.0940076\pi$
$864$		0			0
$865$	−312.178	−	429.677i	−0.360900	−	0.496736i
$866$		0			0
$867$	−47.5048	−	146.205i	−0.0547921	−	0.168633i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	440.047	−	142.980i	0.505221	−	0.164156i
$872$		0			0
$873$	−641.679	+	466.207i	−0.735028	+	0.534029i
$874$		0			0
$875$	827.361	+	268.826i	0.945555	+	0.307230i
$876$		0			0
$877$	71.7460	−	98.7499i	0.0818084	−	0.112600i	−0.766151	−	0.642660i	$-0.777831\pi$
$877$	71.7460	−	98.7499i	0.0818084	−	0.112600i	0.847960	+	0.530060i	$0.177831\pi$
$878$		0			0
$879$		−	2628.09i		−	2.98986i
$880$		0			0
$881$	−545.388			−0.619055			−0.309528	−	0.950890i	$-0.600171\pi$
$881$	−545.388			−0.619055			−0.309528	+	0.950890i	$0.600171\pi$
$882$		0			0
$883$	823.342	+	598.193i	0.932438	+	0.677456i	0.946588	−	0.322444i	$-0.104505\pi$
$883$	823.342	+	598.193i	0.932438	+	0.677456i	−0.0141509	+	0.999900i	$0.504505\pi$
$884$		0			0
$885$	271.444	−	835.417i	0.306716	−	0.943974i
$886$		0			0
$887$	−894.768	−	1231.54i	−1.00876	−	1.38844i	−0.919794	−	0.392401i	$-0.871645\pi$
$887$	−894.768	−	1231.54i	−1.00876	−	1.38844i	−0.0889633	−	0.996035i	$-0.528355\pi$
$888$		0			0
$889$	81.4921	+	250.807i	0.0916671	+	0.282122i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−2400.31	+	779.908i	−2.68792	+	0.873357i
$894$		0			0
$895$	−602.788	+	437.951i	−0.673507	+	0.489331i
$896$		0			0
$897$	−259.747	−	84.3968i	−0.289573	−	0.0940879i
$898$		0			0
$899$	−164.299	+	226.138i	−0.182758	+	0.251544i
$900$		0			0
$901$			177.004i			0.196453i
$902$		0			0
$903$	−568.557			−0.629631
$904$		0			0
$905$	1306.68	+	949.361i	1.44385	+	1.04902i
$906$		0			0
$907$	−193.968	+	596.971i	−0.213856	+	0.658182i	0.785377	+	0.619018i	$0.212469\pi$
$907$	−193.968	+	596.971i	−0.213856	+	0.658182i	−0.999233	+	0.0391635i	$0.987531\pi$
$908$		0			0
$909$	−855.109	−	1176.96i	−0.940713	−	1.29478i
$910$		0			0
$911$	221.708	+	682.348i	0.243368	+	0.749010i	0.995901	+	0.0904550i	$0.0288321\pi$
$911$	221.708	+	682.348i	0.243368	+	0.749010i	−0.752532	+	0.658555i	$0.771168\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−644.885	+	209.536i	−0.704792	+	0.229001i
$916$		0			0
$917$	−702.699	+	510.541i	−0.766302	+	0.556751i
$918$		0			0
$919$	847.124	+	275.247i	0.921789	+	0.299507i	0.731200	−	0.682163i	$-0.238960\pi$
$919$	847.124	+	275.247i	0.921789	+	0.299507i	0.190588	+	0.981670i	$0.438960\pi$
$920$		0			0
$921$	−1347.84	+	1855.15i	−1.46346	+	2.01428i
$922$		0			0
$923$		−	618.133i		−	0.669700i
$924$		0			0
$925$	69.8995			0.0755670
$926$		0			0
$927$	166.298	+	120.823i	0.179394	+	0.130337i
$928$		0			0
$929$	−250.632	+	771.367i	−0.269787	+	0.830320i	0.720765	+	0.693180i	$0.243791\pi$
$929$	−250.632	+	771.367i	−0.269787	+	0.830320i	−0.990552	+	0.137140i	$0.956209\pi$
$930$		0			0
$931$	86.5804	+	119.168i	0.0929972	+	0.128000i
$932$		0			0
$933$	633.549	+	1949.86i	0.679045	+	2.08988i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	1399.40	−	454.693i	1.49349	−	0.485265i	0.555380	−	0.831596i	$-0.312573\pi$
$937$	1399.40	−	454.693i	1.49349	−	0.485265i	0.938112	+	0.346331i	$0.112573\pi$
$938$		0			0
$939$	−68.2695	+	49.6007i	−0.0727044	+	0.0528229i
$940$		0			0
$941$	130.287	+	42.3328i	0.138456	+	0.0449871i	0.377425	−	0.926040i	$-0.376810\pi$
$941$	130.287	+	42.3328i	0.138456	+	0.0449871i	−0.238969	+	0.971027i	$0.576810\pi$
$942$		0			0
$943$	−104.531	+	143.874i	−0.110849	+	0.152571i
$944$		0			0
$945$		−	1203.65i		−	1.27370i
$946$		0			0
$947$	−862.357			−0.910620			−0.455310	−	0.890333i	$-0.650472\pi$
$947$	−862.357			−0.910620			−0.455310	+	0.890333i	$0.650472\pi$
$948$		0			0
$949$	−752.437	−	546.677i	−0.792873	−	0.576056i
$950$		0			0
$951$	878.442	−	2703.57i	0.923703	−	2.84287i
$952$		0			0
$953$	875.727	+	1205.33i	0.918916	+	1.26478i	0.964029	+	0.265797i	$0.0856351\pi$
$953$	875.727	+	1205.33i	0.918916	+	1.26478i	−0.0451134	+	0.998982i	$0.514365\pi$
$954$		0			0
$955$	45.5926	+	140.320i	0.0477410	+	0.146932i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1306.53	+	424.516i	−1.36238	+	0.442665i
$960$		0			0
$961$	389.767	−	283.183i	0.405585	−	0.294675i
$962$		0			0
$963$	−18.6981	−	6.07537i	−0.0194165	−	0.00630879i
$964$		0			0
$965$	139.769	−	192.376i	0.144838	−	0.199353i
$966$		0			0
$967$			961.962i			0.994790i	0.867524	+	0.497395i	$0.165710\pi$
$967$			961.962i			0.994790i	−0.867524	+	0.497395i	$0.834290\pi$
$968$		0			0
$969$	2923.19			3.01671
$970$		0			0
$971$	827.337	+	601.095i	0.852046	+	0.619048i	0.925709	−	0.378235i	$-0.123469\pi$
$971$	827.337	+	601.095i	0.852046	+	0.619048i	−0.0736633	+	0.997283i	$0.523469\pi$
$972$		0			0
$973$	−441.292	+	1358.16i	−0.453537	+	1.39584i
$974$		0			0
$975$	112.801	+	155.257i	0.115693	+	0.159238i
$976$		0			0
$977$	−363.804	−	1119.67i	−0.372368	−	1.14603i	−0.945237	−	0.326384i	$-0.894170\pi$
$977$	−363.804	−	1119.67i	−0.372368	−	1.14603i	0.572869	−	0.819647i	$-0.305830\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	2283.63	−	741.996i	2.32786	−	0.756367i
$982$		0			0
$983$	287.961	−	209.216i	0.292941	−	0.212834i	−0.431601	−	0.902065i	$-0.642051\pi$
$983$	287.961	−	209.216i	0.292941	−	0.212834i	0.724542	+	0.689230i	$0.242051\pi$
$984$		0			0
$985$	1018.29	+	330.863i	1.03380	+	0.335901i
$986$		0			0
$987$	1544.12	−	2125.30i	1.56446	−	2.15329i
$988$		0			0
$989$			60.5645i			0.0612381i
$990$		0			0
$991$	−370.283			−0.373646			−0.186823	−	0.982394i	$-0.559819\pi$
$991$	−370.283			−0.373646			−0.186823	+	0.982394i	$0.559819\pi$
$992$		0			0
$993$	−685.521	−	498.060i	−0.690353	−	0.501571i
$994$		0			0
$995$	68.0155	−	209.330i	0.0683573	−	0.210382i
$996$		0			0
$997$	−16.4378	−	22.6247i	−0.0164872	−	0.0226927i	0.800694	−	0.599074i	$-0.204464\pi$
$997$	−16.4378	−	22.6247i	−0.0164872	−	0.0226927i	−0.817181	+	0.576381i	$0.804464\pi$
$998$		0			0
$999$	−326.170	−	1003.85i	−0.326496	−	1.00485i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	484.3.f.a.457.1		8
11.2	odd	10	inner	484.3.f.a.233.1		8
11.3	even	5		484.3.d.c.241.7		8
11.4	even	5		484.3.f.d.481.2		8
11.5	even	5		484.3.f.e.161.2		8
11.6	odd	10		484.3.f.d.161.2		8
11.7	odd	10		484.3.f.e.481.2		8
11.8	odd	10		484.3.d.c.241.8		8
11.9	even	5		44.3.f.a.13.1	✓	8
11.10	odd	2		44.3.f.a.17.1	yes	8
33.8	even	10		4356.3.f.g.1693.4		8
33.14	odd	10		4356.3.f.g.1693.3		8
33.20	odd	10		396.3.t.a.145.1		8
33.32	even	2		396.3.t.a.325.1		8
44.31	odd	10		176.3.n.c.145.2		8
44.43	even	2		176.3.n.c.17.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.3.f.a.13.1	✓	8	11.9	even	5
44.3.f.a.17.1	yes	8	11.10	odd	2
176.3.n.c.17.2		8	44.43	even	2
176.3.n.c.145.2		8	44.31	odd	10
396.3.t.a.145.1		8	33.20	odd	10
396.3.t.a.325.1		8	33.32	even	2
484.3.d.c.241.7		8	11.3	even	5
484.3.d.c.241.8		8	11.8	odd	10
484.3.f.a.233.1		8	11.2	odd	10	inner
484.3.f.a.457.1		8	1.1	even	1	trivial
484.3.f.d.161.2		8	11.6	odd	10
484.3.f.d.481.2		8	11.4	even	5
484.3.f.e.161.2		8	11.5	even	5
484.3.f.e.481.2		8	11.7	odd	10
4356.3.f.g.1693.3		8	33.14	odd	10
4356.3.f.g.1693.4		8	33.8	even	10

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:	\( N \)	\(=\)	\( 484 = 2^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	484.f (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.08818 - 2.97024i) q^{3} +(1.46509 - 4.50908i) q^{5} +(3.91877 + 5.39373i) q^{7} +(5.10976 + 15.7262i) q^{9} +(-14.3229 + 4.65378i) q^{13} +(-19.3826 + 14.0823i) q^{15} +(16.9976 + 5.52287i) q^{17} +(-19.0249 + 26.1855i) q^{19} -33.6902i q^{21} -3.58879 q^{23} +(2.04012 + 1.48224i) q^{25} +(11.7671 - 36.2153i) q^{27} +(7.50529 + 10.3301i) q^{29} +(6.76473 + 20.8197i) q^{31} +(30.0621 - 9.76777i) q^{35} +(22.4250 - 16.2927i) q^{37} +(72.3773 + 23.5168i) q^{39} +(29.1270 - 40.0899i) q^{41} -16.8760i q^{43} +78.3970 q^{45} +(63.0835 + 45.8328i) q^{47} +(1.40631 - 4.32817i) q^{49} +(-53.0852 - 73.0655i) q^{51} +(3.06043 + 9.41904i) q^{53} +(155.554 - 50.5426i) q^{57} +(-29.6620 + 21.5507i) q^{59} +(26.9171 + 8.74590i) q^{61} +(-64.7990 + 89.1881i) q^{63} +71.4011i q^{65} -30.7234 q^{67} +(14.6716 + 10.6595i) q^{69} +(-12.6835 + 39.0359i) q^{71} +(36.3001 + 49.9628i) q^{73} +(-3.93780 - 12.1193i) q^{75} +(-118.204 + 38.4068i) q^{79} +(-35.2762 + 25.6296i) q^{81} +(2.94344 + 0.956381i) q^{83} +(49.8061 - 68.5522i) q^{85} -64.5240i q^{87} +60.4914 q^{89} +(-81.2293 - 59.0165i) q^{91} +(34.1840 - 105.207i) q^{93} +(90.1993 + 124.149i) q^{95} +(14.8226 + 45.6193i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{3} - q^{5} - 15 q^{7} - q^{9} + 15 q^{13} - 63 q^{15} + 75 q^{17} + 30 q^{19} + 100 q^{23} + 51 q^{25} + 100 q^{27} - 125 q^{29} + 73 q^{31} + 155 q^{35} - 75 q^{37} + 185 q^{39} + 155 q^{41}+ \cdots - 90 q^{97}+O(q^{100}) \) 8 * q - 5 * q^3 - q^5 - 15 * q^7 - q^9 + 15 * q^13 - 63 * q^15 + 75 * q^17 + 30 * q^19 + 100 * q^23 + 51 * q^25 + 100 * q^27 - 125 * q^29 + 73 * q^31 + 155 * q^35 - 75 * q^37 + 185 * q^39 + 155 * q^41 + 332 * q^45 + 45 * q^47 + 87 * q^49 - 150 * q^51 - 85 * q^53 + 310 * q^57 - 178 * q^59 + 145 * q^61 + 110 * q^63 + 10 * q^67 + 124 * q^69 + 207 * q^71 - 65 * q^73 + 192 * q^75 - 235 * q^79 - 12 * q^81 - 210 * q^83 - 105 * q^85 + 18 * q^89 - 195 * q^91 - 335 * q^93 + 255 * q^95 - 90 * q^97

Introduction

L-functions

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