LMFDB - Embedded newform 576.3.t.c.31.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,3,Mod(31,576)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("576.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	576.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$15.6948632272$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.15
Character	$\chi$	$=$	576.31
Dual form			576.3.t.c.223.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.88051 + 0.838238i) q^{3} +(4.68159 + 2.70292i) q^{5} +(3.20912 - 1.85279i) q^{7} +(7.59471 + 4.82911i) q^{9} +O(q^{10})$	\(q+(2.88051 + 0.838238i) q^{3} +(4.68159 + 2.70292i) q^{5} +(3.20912 - 1.85279i) q^{7} +(7.59471 + 4.82911i) q^{9} +(-4.29408 - 7.43757i) q^{11} +(-7.57334 - 4.37247i) q^{13} +(11.2197 + 11.7101i) q^{15} +22.5120 q^{17} +30.6473 q^{19} +(10.7970 - 2.64697i) q^{21} +(7.00399 + 4.04376i) q^{23} +(2.11152 + 3.65726i) q^{25} +(17.8287 + 20.2765i) q^{27} +(-36.6865 + 21.1810i) q^{29} +(-41.0307 - 23.6891i) q^{31} +(-6.13471 - 25.0235i) q^{33} +20.0317 q^{35} +37.3885i q^{37} +(-18.1499 - 18.9432i) q^{39} +(8.06112 - 13.9623i) q^{41} +(-3.00223 - 5.20002i) q^{43} +(22.5026 + 43.1358i) q^{45} +(25.5341 - 14.7421i) q^{47} +(-17.6344 + 30.5436i) q^{49} +(64.8462 + 18.8705i) q^{51} +67.7934i q^{53} -46.4262i q^{55} +(88.2800 + 25.6898i) q^{57} +(9.44141 - 16.3530i) q^{59} +(-16.5085 + 9.53118i) q^{61} +(33.3197 + 1.42582i) q^{63} +(-23.6369 - 40.9402i) q^{65} +(-19.3353 + 33.4896i) q^{67} +(16.7855 + 17.5191i) q^{69} -88.7130i q^{71} -84.8312 q^{73} +(3.01660 + 12.3047i) q^{75} +(-27.5605 - 15.9120i) q^{77} +(86.5191 - 49.9518i) q^{79} +(34.3593 + 73.3515i) q^{81} +(-17.6268 - 30.5306i) q^{83} +(105.392 + 60.8482i) q^{85} +(-123.431 + 30.2600i) q^{87} -61.8287 q^{89} -32.4050 q^{91} +(-98.3325 - 102.630i) q^{93} +(143.478 + 82.8372i) q^{95} +(68.6165 + 118.847i) q^{97} +(3.30453 - 77.2228i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 18 q^{5} + 18 q^{9}+O(q^{10}) $ 32 * q + 18 * q^5 + 18 * q^9	$ 32 q + 18 q^{5} + 18 q^{9} + 30 q^{13} - 36 q^{17} - 102 q^{21} + 86 q^{25} + 162 q^{29} + 12 q^{33} - 36 q^{41} - 186 q^{45} + 138 q^{49} - 162 q^{57} + 42 q^{61} - 198 q^{65} + 474 q^{69} - 196 q^{73} - 666 q^{77} + 462 q^{81} - 180 q^{85} + 792 q^{89} - 174 q^{93} + 64 q^{97}+O(q^{100}) $ 32 * q + 18 * q^5 + 18 * q^9 + 30 * q^13 - 36 * q^17 - 102 * q^21 + 86 * q^25 + 162 * q^29 + 12 * q^33 - 36 * q^41 - 186 * q^45 + 138 * q^49 - 162 * q^57 + 42 * q^61 - 198 * q^65 + 474 * q^69 - 196 * q^73 - 666 * q^77 + 462 * q^81 - 180 * q^85 + 792 * q^89 - 174 * q^93 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.88051	+	0.838238i	0.960171	+	0.279413i
$3$	2.88051	+	0.838238i	0.960171	+	0.279413i
$4$		0			0
$5$	4.68159	+	2.70292i	0.936318	+	0.540583i	0.888804	−	0.458287i	$-0.151537\pi$
$5$	4.68159	+	2.70292i	0.936318	+	0.540583i	0.0475137	+	0.998871i	$0.484870\pi$
$6$		0			0
$7$	3.20912	−	1.85279i	0.458446	−	0.264684i	−0.252945	−	0.967481i	$-0.581399\pi$
$7$	3.20912	−	1.85279i	0.458446	−	0.264684i	0.711391	+	0.702797i	$0.248066\pi$
$8$		0			0
$9$	7.59471	+	4.82911i	0.843857	+	0.536568i
$10$		0			0
$11$	−4.29408	−	7.43757i	−0.390371	−	0.676143i	0.602127	−	0.798400i	$-0.294320\pi$
$11$	−4.29408	−	7.43757i	−0.390371	−	0.676143i	−0.992498	+	0.122257i	$0.960987\pi$
$12$		0			0
$13$	−7.57334	−	4.37247i	−0.582565	−	0.336344i	0.179587	−	0.983742i	$-0.442524\pi$
$13$	−7.57334	−	4.37247i	−0.582565	−	0.336344i	−0.762152	+	0.647398i	$0.775857\pi$
$14$		0			0
$15$	11.2197	+	11.7101i	0.747979	+	0.780672i
$16$		0			0
$17$	22.5120			1.32424			0.662119	−	0.749399i	$-0.269657\pi$
$17$	22.5120			1.32424			0.662119	+	0.749399i	$0.269657\pi$
$18$		0			0
$19$	30.6473			1.61302			0.806509	−	0.591222i	$-0.201354\pi$
$19$	30.6473			1.61302			0.806509	+	0.591222i	$0.201354\pi$
$20$		0			0
$21$	10.7970	−	2.64697i	0.514143	−	0.126046i
$22$		0			0
$23$	7.00399	+	4.04376i	0.304521	+	0.175816i	0.644472	−	0.764628i	$-0.277077\pi$
$23$	7.00399	+	4.04376i	0.304521	+	0.175816i	−0.339951	+	0.940443i	$0.610410\pi$
$24$		0			0
$25$	2.11152	+	3.65726i	0.0844608	+	0.146290i
$26$		0			0
$27$	17.8287	+	20.2765i	0.660323	+	0.750982i
$28$		0			0
$29$	−36.6865	+	21.1810i	−1.26505	+	0.730379i	−0.974048	−	0.226343i	$-0.927323\pi$
$29$	−36.6865	+	21.1810i	−1.26505	+	0.730379i	−0.291005	+	0.956721i	$0.593990\pi$
$30$		0			0
$31$	−41.0307	−	23.6891i	−1.32357	−	0.764165i	−0.339276	−	0.940687i	$-0.610182\pi$
$31$	−41.0307	−	23.6891i	−1.32357	−	0.764165i	−0.984297	+	0.176522i	$0.943515\pi$
$32$		0			0
$33$	−6.13471	−	25.0235i	−0.185900	−	0.758288i
$34$		0			0
$35$	20.0317			0.572335
$36$		0			0
$37$			37.3885i			1.01050i	0.862973	+	0.505250i	$0.168600\pi$
$37$			37.3885i			1.01050i	−0.862973	+	0.505250i	$0.831400\pi$
$38$		0			0
$39$	−18.1499	−	18.9432i	−0.465383	−	0.485724i
$40$		0			0
$41$	8.06112	−	13.9623i	0.196613	−	0.340543i	−0.750815	−	0.660512i	$-0.770339\pi$
$41$	8.06112	−	13.9623i	0.196613	−	0.340543i	0.947428	+	0.319969i	$0.103673\pi$
$42$		0			0
$43$	−3.00223	−	5.20002i	−0.0698194	−	0.120931i	0.829002	−	0.559245i	$-0.188909\pi$
$43$	−3.00223	−	5.20002i	−0.0698194	−	0.120931i	−0.898822	+	0.438314i	$0.855576\pi$
$44$		0			0
$45$	22.5026	+	43.1358i	0.500059	+	0.958573i
$46$		0			0
$47$	25.5341	−	14.7421i	0.543279	−	0.313662i	−0.203128	−	0.979152i	$-0.565111\pi$
$47$	25.5341	−	14.7421i	0.543279	−	0.313662i	0.746407	+	0.665490i	$0.231777\pi$
$48$		0			0
$49$	−17.6344	+	30.5436i	−0.359885	+	0.623339i
$50$		0			0
$51$	64.8462	+	18.8705i	1.27149	+	0.370009i
$52$		0			0
$53$			67.7934i			1.27912i	0.768741	+	0.639561i	$0.220884\pi$
$53$			67.7934i			1.27912i	−0.768741	+	0.639561i	$0.779116\pi$
$54$		0			0
$55$		−	46.4262i		−	0.844113i
$56$		0			0
$57$	88.2800	+	25.6898i	1.54877	+	0.450698i
$58$		0			0
$59$	9.44141	−	16.3530i	0.160024	−	0.277170i	−0.774853	−	0.632141i	$-0.782176\pi$
$59$	9.44141	−	16.3530i	0.160024	−	0.277170i	0.934877	+	0.354972i	$0.115510\pi$
$60$		0			0
$61$	−16.5085	+	9.53118i	−0.270631	+	0.156249i	−0.629174	−	0.777264i	$-0.716607\pi$
$61$	−16.5085	+	9.53118i	−0.270631	+	0.156249i	0.358543	+	0.933513i	$0.383273\pi$
$62$		0			0
$63$	33.3197	+	1.42582i	0.528884	+	0.0226321i
$64$		0			0
$65$	−23.6369	−	40.9402i	−0.363644	−	0.629850i
$66$		0			0
$67$	−19.3353	+	33.4896i	−0.288586	+	0.499845i	−0.973472	−	0.228804i	$-0.926518\pi$
$67$	−19.3353	+	33.4896i	−0.288586	+	0.499845i	0.684887	+	0.728650i	$0.259852\pi$
$68$		0			0
$69$	16.7855	+	17.5191i	0.243268	+	0.253900i
$70$		0			0
$71$		−	88.7130i		−	1.24948i	−0.780833	−	0.624740i	$-0.785205\pi$
$71$		−	88.7130i		−	1.24948i	0.780833	−	0.624740i	$-0.214795\pi$
$72$		0			0
$73$	−84.8312			−1.16207			−0.581036	−	0.813878i	$-0.697352\pi$
$73$	−84.8312			−1.16207			−0.581036	+	0.813878i	$0.697352\pi$
$74$		0			0
$75$	3.01660	+	12.3047i	0.0402214	+	0.164063i
$76$		0			0
$77$	−27.5605	−	15.9120i	−0.357928	−	0.206650i
$78$		0			0
$79$	86.5191	−	49.9518i	1.09518	−	0.632302i	0.160228	−	0.987080i	$-0.448777\pi$
$79$	86.5191	−	49.9518i	1.09518	−	0.632302i	0.934950	+	0.354778i	$0.115444\pi$
$80$		0			0
$81$	34.3593	+	73.3515i	0.424189	+	0.905573i
$82$		0			0
$83$	−17.6268	−	30.5306i	−0.212371	−	0.367838i	0.740085	−	0.672514i	$-0.234785\pi$
$83$	−17.6268	−	30.5306i	−0.212371	−	0.367838i	−0.952456	+	0.304675i	$0.901452\pi$
$84$		0			0
$85$	105.392	+	60.8482i	1.23991	+	0.715861i
$86$		0			0
$87$	−123.431	+	30.2600i	−1.41874	+	0.347817i
$88$		0			0
$89$	−61.8287			−0.694705			−0.347352	−	0.937735i	$-0.612919\pi$
$89$	−61.8287			−0.694705			−0.347352	+	0.937735i	$0.612919\pi$
$90$		0			0
$91$	−32.4050			−0.356099
$92$		0			0
$93$	−98.3325	−	102.630i	−1.05734	−	1.10355i
$94$		0			0
$95$	143.478	+	82.8372i	1.51030	+	0.871970i
$96$		0			0
$97$	68.6165	+	118.847i	0.707387	+	1.22523i	0.965823	+	0.259201i	$0.0834593\pi$
$97$	68.6165	+	118.847i	0.707387	+	1.22523i	−0.258437	+	0.966028i	$0.583207\pi$
$98$		0			0
$99$	3.30453	−	77.2228i	0.0333791	−	0.780029i
$100$		0			0
$101$	5.56099	−	3.21064i	0.0550593	−	0.0317885i	−0.472218	−	0.881482i	$-0.656546\pi$
$101$	5.56099	−	3.21064i	0.0550593	−	0.0317885i	0.527277	+	0.849693i	$0.323213\pi$
$102$		0			0
$103$	−151.438	−	87.4326i	−1.47027	−	0.848860i	−0.470826	−	0.882226i	$-0.656044\pi$
$103$	−151.438	−	87.4326i	−1.47027	−	0.848860i	−0.999443	+	0.0333656i	$0.989377\pi$
$104$		0			0
$105$	57.7016	+	16.7914i	0.549539	+	0.159918i
$106$		0			0
$107$	134.762			1.25945			0.629727	−	0.776816i	$-0.283167\pi$
$107$	134.762			1.25945			0.629727	+	0.776816i	$0.283167\pi$
$108$		0			0
$109$			142.960i			1.31156i	0.754951	+	0.655781i	$0.227660\pi$
$109$			142.960i			1.31156i	−0.754951	+	0.655781i	$0.772340\pi$
$110$		0			0
$111$	−31.3405	+	107.698i	−0.282346	+	0.970253i
$112$		0			0
$113$	99.4454	−	172.245i	0.880048	−	1.52429i	0.0287618	−	0.999586i	$-0.490844\pi$
$113$	99.4454	−	172.245i	0.880048	−	1.52429i	0.851286	−	0.524702i	$-0.175823\pi$
$114$		0			0
$115$	21.8599	+	37.8624i	0.190086	+	0.329238i
$116$		0			0
$117$	−36.4022	−	69.7802i	−0.311130	−	0.596412i
$118$		0			0
$119$	72.2439	−	41.7100i	0.607091	−	0.350504i
$120$		0			0
$121$	23.6217	−	40.9140i	0.195221	−	0.338132i
$122$		0			0
$123$	34.9239	−	33.4614i	0.283934	−	0.272044i
$124$		0			0
$125$		−	112.317i		−	0.898534i
$126$		0			0
$127$			67.5444i			0.531845i	0.963994	+	0.265923i	$0.0856766\pi$
$127$			67.5444i			0.531845i	−0.963994	+	0.265923i	$0.914323\pi$
$128$		0			0
$129$	−4.28912	−	17.4953i	−0.0332490	−	0.135623i
$130$		0			0
$131$	1.27927	−	2.21576i	0.00976542	−	0.0169142i	−0.861101	−	0.508433i	$-0.830225\pi$
$131$	1.27927	−	2.21576i	0.00976542	−	0.0169142i	0.870867	+	0.491519i	$0.163558\pi$
$132$		0			0
$133$	98.3510	−	56.7830i	0.739481	−	0.426940i
$134$		0			0
$135$	28.6611	+	143.116i	0.212304	+	1.06012i
$136$		0			0
$137$	−103.918	−	179.992i	−0.758528	−	1.31381i	−0.943601	−	0.331084i	$-0.892586\pi$
$137$	−103.918	−	179.992i	−0.758528	−	1.31381i	0.185074	−	0.982725i	$-0.440748\pi$
$138$		0			0
$139$	−99.6746	+	172.642i	−0.717084	+	1.24203i	0.245067	+	0.969506i	$0.421190\pi$
$139$	−99.6746	+	172.642i	−0.717084	+	1.24203i	−0.962150	+	0.272519i	$0.912143\pi$
$140$		0			0
$141$	85.9087	−	21.0612i	0.609282	−	0.149370i
$142$		0			0
$143$			75.1030i			0.525196i
$144$		0			0
$145$	−229.002			−1.57932
$146$		0			0
$147$	−76.3988	+	73.1995i	−0.519720	+	0.497956i
$148$		0			0
$149$	−219.773	−	126.886i	−1.47499	−	0.851584i	−0.475383	−	0.879779i	$-0.657691\pi$
$149$	−219.773	−	126.886i	−1.47499	−	0.851584i	−0.999602	+	0.0281952i	$0.991024\pi$
$150$		0			0
$151$	−134.447	+	77.6229i	−0.890376	+	0.514059i	−0.874065	−	0.485808i	$-0.838525\pi$
$151$	−134.447	+	77.6229i	−0.890376	+	0.514059i	−0.0163104	+	0.999867i	$0.505192\pi$
$152$		0			0
$153$	170.973	+	108.713i	1.11747	+	0.710544i
$154$		0			0
$155$	−128.059	−	221.805i	−0.826190	−	1.43100i
$156$		0			0
$157$	−91.7065	−	52.9467i	−0.584118	−	0.337240i	0.178651	−	0.983913i	$-0.442827\pi$
$157$	−91.7065	−	52.9467i	−0.584118	−	0.337240i	−0.762768	+	0.646672i	$0.776160\pi$
$158$		0			0
$159$	−56.8270	+	195.280i	−0.357403	+	1.22818i
$160$		0			0
$161$	29.9689			0.186142
$162$		0			0
$163$	−291.191			−1.78645			−0.893224	−	0.449612i	$-0.851562\pi$
$163$	−291.191			−1.78645			−0.893224	+	0.449612i	$0.851562\pi$
$164$		0			0
$165$	38.9162	−	133.731i	0.235856	−	0.810493i
$166$		0			0
$167$	34.2561	+	19.7777i	0.205126	+	0.118430i	0.599044	−	0.800716i	$-0.295547\pi$
$167$	34.2561	+	19.7777i	0.205126	+	0.118430i	−0.393918	+	0.919146i	$0.628881\pi$
$168$		0			0
$169$	−46.2630	−	80.1298i	−0.273745	−	0.474141i
$170$		0			0
$171$	232.758	+	147.999i	1.36116	+	0.865493i
$172$		0			0
$173$	136.994	−	79.0933i	0.791871	−	0.457187i	−0.0487498	−	0.998811i	$-0.515524\pi$
$173$	136.994	−	79.0933i	0.791871	−	0.457187i	0.840621	+	0.541624i	$0.182190\pi$
$174$		0			0
$175$	13.5522	+	7.82439i	0.0774414	+	0.0447108i
$176$		0			0
$177$	40.9038	−	39.1909i	0.231095	−	0.221418i
$178$		0			0
$179$	−160.813			−0.898395			−0.449198	−	0.893432i	$-0.648290\pi$
$179$	−160.813			−0.898395			−0.449198	+	0.893432i	$0.648290\pi$
$180$		0			0
$181$		−	106.168i		−	0.586564i	−0.956026	−	0.293282i	$-0.905253\pi$
$181$		−	106.168i		−	0.586564i	0.956026	−	0.293282i	$-0.0947475\pi$
$182$		0			0
$183$	−55.5423	+	13.6166i	−0.303510	+	0.0744079i
$184$		0			0
$185$	−101.058	+	175.038i	−0.546259	+	0.946149i
$186$		0			0
$187$	−96.6686	−	167.435i	−0.516944	−	0.895374i
$188$		0			0
$189$	94.7826	+	32.0369i	0.501495	+	0.169508i
$190$		0			0
$191$	234.885	−	135.611i	1.22977	−	0.710005i	0.262785	−	0.964854i	$-0.415359\pi$
$191$	234.885	−	135.611i	1.22977	−	0.710005i	0.966981	+	0.254849i	$0.0820258\pi$
$192$		0			0
$193$	−164.832	+	285.498i	−0.854052	+	1.47926i	0.0234692	+	0.999725i	$0.492529\pi$
$193$	−164.832	+	285.498i	−0.854052	+	1.47926i	−0.877521	+	0.479537i	$0.840804\pi$
$194$		0			0
$195$	−33.7686	−	137.742i	−0.173172	−	0.706370i
$196$		0			0
$197$			209.728i			1.06461i	0.846553	+	0.532304i	$0.178674\pi$
$197$			209.728i			1.06461i	−0.846553	+	0.532304i	$0.821326\pi$
$198$		0			0
$199$		−	374.629i		−	1.88256i	−0.337633	−	0.941278i	$-0.609626\pi$
$199$		−	374.629i		−	1.88256i	0.337633	−	0.941278i	$-0.390374\pi$
$200$		0			0
$201$	−83.7677	+	80.2598i	−0.416755	+	0.399303i
$202$		0			0
$203$	−78.4877	+	135.945i	−0.386639	+	0.669678i
$204$		0			0
$205$	75.4777	−	43.5771i	0.368184	−	0.212571i
$206$		0			0
$207$	33.6656	+	64.5342i	0.162636	+	0.311760i
$208$		0			0
$209$	−131.602	−	227.942i	−0.629676	−	1.09063i
$210$		0			0
$211$	29.4939	−	51.0849i	0.139781	−	0.242108i	−0.787632	−	0.616145i	$-0.788693\pi$
$211$	29.4939	−	51.0849i	0.139781	−	0.242108i	0.927414	+	0.374037i	$0.122027\pi$
$212$		0			0
$213$	74.3626	−	255.539i	0.349120	−	1.19971i
$214$		0			0
$215$		−	32.4592i		−	0.150973i
$216$		0			0
$217$	−175.564			−0.809049
$218$		0			0
$219$	−244.358	−	71.1088i	−1.11579	−	0.324698i
$220$		0			0
$221$	−170.491	−	98.4333i	−0.771454	−	0.445399i
$222$		0			0
$223$	−92.5698	+	53.4452i	−0.415111	+	0.239664i	−0.692983	−	0.720954i	$-0.743704\pi$
$223$	−92.5698	+	53.4452i	−0.415111	+	0.239664i	0.277872	+	0.960618i	$0.410371\pi$
$224$		0			0
$225$	−1.62493	+	37.9726i	−0.00722191	+	0.168767i
$226$		0			0
$227$	−141.975	−	245.908i	−0.625441	−	1.08329i	−0.988455	−	0.151511i	$-0.951586\pi$
$227$	−141.975	−	245.908i	−0.625441	−	1.08329i	0.363015	−	0.931783i	$-0.381747\pi$
$228$		0			0
$229$	69.8998	+	40.3567i	0.305239	+	0.176230i	0.644794	−	0.764356i	$-0.276943\pi$
$229$	69.8998	+	40.3567i	0.305239	+	0.176230i	−0.339555	+	0.940586i	$0.610276\pi$
$230$		0			0
$231$	−66.0502	−	68.9371i	−0.285932	−	0.298429i
$232$		0			0
$233$	216.622			0.929706			0.464853	−	0.885388i	$-0.346107\pi$
$233$	216.622			0.929706			0.464853	+	0.885388i	$0.346107\pi$
$234$		0			0
$235$	159.387			0.678242
$236$		0			0
$237$	291.091	−	71.3633i	1.22823	−	0.301111i
$238$		0			0
$239$	268.969	+	155.289i	1.12539	+	0.649746i	0.942772	−	0.333437i	$-0.108208\pi$
$239$	268.969	+	155.289i	1.12539	+	0.649746i	0.182621	+	0.983183i	$0.441542\pi$
$240$		0			0
$241$	−65.8918	−	114.128i	−0.273410	−	0.473560i	0.696323	−	0.717729i	$-0.254818\pi$
$241$	−65.8918	−	114.128i	−0.273410	−	0.473560i	−0.969733	+	0.244169i	$0.921485\pi$
$242$		0			0
$243$	37.4866	+	240.091i	0.154266	+	0.988029i
$244$		0			0
$245$	−165.114	+	95.3284i	−0.673933	+	0.389096i
$246$		0			0
$247$	−232.103	−	134.005i	−0.939687	−	0.542529i
$248$		0			0
$249$	−25.1824	−	102.719i	−0.101134	−	0.412527i
$250$		0			0
$251$	−149.518			−0.595690			−0.297845	−	0.954614i	$-0.596268\pi$
$251$	−149.518			−0.595690			−0.297845	+	0.954614i	$0.596268\pi$
$252$		0			0
$253$		−	69.4569i		−	0.274533i
$254$		0			0
$255$	252.578	+	263.618i	0.990503	+	1.03379i
$256$		0			0
$257$	15.2518	−	26.4170i	0.0593457	−	0.102790i	−0.834826	−	0.550514i	$-0.814432\pi$
$257$	15.2518	−	26.4170i	0.0593457	−	0.102790i	0.894172	+	0.447724i	$0.147765\pi$
$258$		0			0
$259$	69.2729	+	119.984i	0.267463	+	0.463259i
$260$		0			0
$261$	−380.909	−	16.2999i	−1.45942	−	0.0624518i
$262$		0			0
$263$	−403.401	+	232.904i	−1.53384	+	0.885565i	−0.534665	+	0.845064i	$0.679562\pi$
$263$	−403.401	+	232.904i	−1.53384	+	0.885565i	−0.999179	+	0.0405010i	$0.987105\pi$
$264$		0			0
$265$	−183.240	+	317.381i	−0.691472	+	1.19766i
$266$		0			0
$267$	−178.098	−	51.8272i	−0.667035	−	0.194109i
$268$		0			0
$269$			219.580i			0.816281i	0.912919	+	0.408141i	$0.133823\pi$
$269$			219.580i			0.816281i	−0.912919	+	0.408141i	$0.866177\pi$
$270$		0			0
$271$		−	64.9447i		−	0.239648i	−0.992795	−	0.119824i	$-0.961767\pi$
$271$		−	64.9447i		−	0.239648i	0.992795	−	0.119824i	$-0.0382331\pi$
$272$		0			0
$273$	−93.3431	−	27.1631i	−0.341916	−	0.0994987i
$274$		0			0
$275$	18.1341	−	31.4091i	0.0659421	−	0.114215i
$276$		0			0
$277$	−69.5974	+	40.1821i	−0.251254	+	0.145062i	−0.620338	−	0.784334i	$-0.713005\pi$
$277$	−69.5974	+	40.1821i	−0.251254	+	0.145062i	0.369084	+	0.929396i	$0.379671\pi$
$278$		0			0
$279$	−197.219	−	378.054i	−0.706880	−	1.35503i
$280$		0			0
$281$	−126.131	−	218.464i	−0.448863	−	0.777454i	0.549449	−	0.835527i	$-0.314838\pi$
$281$	−126.131	−	218.464i	−0.448863	−	0.777454i	−0.998312	+	0.0580735i	$0.981504\pi$
$282$		0			0
$283$	−34.9136	+	60.4722i	−0.123370	+	0.213683i	−0.921095	−	0.389339i	$-0.872703\pi$
$283$	−34.9136	+	60.4722i	−0.123370	+	0.213683i	0.797725	+	0.603022i	$0.206037\pi$
$284$		0			0
$285$	343.854	+	358.882i	1.20650	+	1.25924i
$286$		0			0
$287$		−	59.7421i		−	0.208161i
$288$		0			0
$289$	217.792			0.753606
$290$		0			0
$291$	98.0284	+	399.858i	0.336867	+	1.37408i
$292$		0			0
$293$	−24.7753	−	14.3040i	−0.0845573	−	0.0488192i	0.457125	−	0.889402i	$-0.348879\pi$
$293$	−24.7753	−	14.3040i	−0.0845573	−	0.0488192i	−0.541682	+	0.840583i	$0.682212\pi$
$294$		0			0
$295$	88.4017	−	51.0387i	0.299667	−	0.173013i
$296$		0			0
$297$	74.2499	−	219.671i	0.250000	−	0.739634i
$298$		0			0
$299$	−35.3624	−	61.2495i	−0.118269	−	0.204848i
$300$		0			0
$301$	−19.2691	−	11.1250i	−0.0640169	−	0.0369601i
$302$		0			0
$303$	18.7098	−	4.58685i	0.0617485	−	0.0151381i
$304$		0			0
$305$	−103.048			−0.337862
$306$		0			0
$307$	−47.6097			−0.155081			−0.0775403	−	0.996989i	$-0.524707\pi$
$307$	−47.6097			−0.155081			−0.0775403	+	0.996989i	$0.524707\pi$
$308$		0			0
$309$	−362.929	−	378.792i	−1.17453	−	1.22586i
$310$		0			0
$311$	86.7564	+	50.0888i	0.278959	+	0.161057i	0.632952	−	0.774191i	$-0.281843\pi$
$311$	86.7564	+	50.0888i	0.278959	+	0.161057i	−0.353993	+	0.935248i	$0.615176\pi$
$312$		0			0
$313$	37.8673	+	65.5880i	0.120982	+	0.209546i	0.920155	−	0.391554i	$-0.128062\pi$
$313$	37.8673	+	65.5880i	0.120982	+	0.209546i	−0.799173	+	0.601101i	$0.794729\pi$
$314$		0			0
$315$	152.135	+	96.7354i	0.482969	+	0.307097i
$316$		0			0
$317$	516.193	−	298.024i	1.62837	−	0.940140i	0.643790	−	0.765202i	$-0.277361\pi$
$317$	516.193	−	298.024i	1.62837	−	0.940140i	0.984580	−	0.174938i	$-0.0559724\pi$
$318$		0			0
$319$	315.070	+	181.906i	0.987681	+	0.570238i
$320$		0			0
$321$	388.183	+	112.962i	1.20929	+	0.351908i
$322$		0			0
$323$	689.934			2.13602
$324$		0			0
$325$		−	36.9302i		−	0.113631i
$326$		0			0
$327$	−119.835	+	411.799i	−0.366467	+	1.25932i
$328$		0			0
$329$	54.6280	−	94.6185i	0.166043	−	0.287594i
$330$		0			0
$331$	22.7216	+	39.3550i	0.0686453	+	0.118897i	0.898305	−	0.439372i	$-0.144799\pi$
$331$	22.7216	+	39.3550i	0.0686453	+	0.118897i	−0.829660	+	0.558269i	$0.811466\pi$
$332$		0			0
$333$	−180.553	+	283.955i	−0.542202	+	0.852717i
$334$		0			0
$335$	−181.039	+	104.523i	−0.540416	+	0.312009i
$336$		0			0
$337$	207.173	−	358.834i	0.614757	−	1.06479i	−0.375670	−	0.926753i	$-0.622587\pi$
$337$	207.173	−	358.834i	0.614757	−	1.06479i	0.990427	−	0.138037i	$-0.0440793\pi$
$338$		0			0
$339$	430.836	−	412.794i	1.27090	−	1.21768i
$340$		0			0
$341$			406.892i			1.19323i
$342$		0			0
$343$			312.264i			0.910391i
$344$		0			0
$345$	31.2299	+	127.387i	0.0905216	+	0.369238i
$346$		0			0
$347$	−60.6510	+	105.051i	−0.174787	+	0.302739i	−0.940087	−	0.340933i	$-0.889257\pi$
$347$	−60.6510	+	105.051i	−0.174787	+	0.302739i	0.765301	+	0.643673i	$0.222590\pi$
$348$		0			0
$349$	−540.498	+	312.057i	−1.54871	+	0.894145i	−0.550464	+	0.834859i	$0.685549\pi$
$349$	−540.498	+	312.057i	−1.54871	+	0.894145i	−0.998241	+	0.0592867i	$0.981117\pi$
$350$		0			0
$351$	−46.3646	−	231.516i	−0.132093	−	0.659591i
$352$		0			0
$353$	224.611	+	389.037i	0.636291	+	1.10209i	0.986240	+	0.165319i	$0.0528654\pi$
$353$	224.611	+	389.037i	0.636291	+	1.10209i	−0.349950	+	0.936769i	$0.613801\pi$
$354$		0			0
$355$	239.784	−	415.318i	0.675448	−	1.16991i
$356$		0			0
$357$	243.062	−	59.5887i	0.680847	−	0.166915i
$358$		0			0
$359$		−	587.133i		−	1.63547i	−0.575596	−	0.817734i	$-0.695230\pi$
$359$		−	587.133i		−	1.63547i	0.575596	−	0.817734i	$-0.304770\pi$
$360$		0			0
$361$	578.259			1.60182
$362$		0			0
$363$	102.338	−	98.0526i	0.281923	−	0.270117i
$364$		0			0
$365$	−397.145	−	229.292i	−1.08807	−	0.628197i
$366$		0			0
$367$	45.6070	−	26.3312i	0.124270	−	0.0717471i	−0.436577	−	0.899667i	$-0.643809\pi$
$367$	45.6070	−	26.3312i	0.124270	−	0.0717471i	0.560846	+	0.827920i	$0.310476\pi$
$368$		0			0
$369$	128.647	−	67.1114i	0.348638	−	0.181874i
$370$		0			0
$371$	125.607	+	217.557i	0.338563	+	0.586408i
$372$		0			0
$373$	544.620	+	314.436i	1.46011	+	0.842993i	0.999016	−	0.0443601i	$-0.0141249\pi$
$373$	544.620	+	314.436i	1.46011	+	0.842993i	0.461091	+	0.887353i	$0.347458\pi$
$374$		0			0
$375$	94.1482	−	323.530i	0.251062	−	0.862747i
$376$		0			0
$377$	370.453			0.982634
$378$		0			0
$379$	116.102			0.306337			0.153168	−	0.988200i	$-0.451052\pi$
$379$	116.102			0.306337			0.153168	+	0.988200i	$0.451052\pi$
$380$		0			0
$381$	−56.6183	+	194.562i	−0.148604	+	0.510663i
$382$		0			0
$383$	−76.6891	−	44.2765i	−0.200233	−	0.115604i	0.396531	−	0.918021i	$-0.370214\pi$
$383$	−76.6891	−	44.2765i	−0.200233	−	0.115604i	−0.596764	+	0.802417i	$0.703547\pi$
$384$		0			0
$385$	−86.0179	−	148.987i	−0.223423	−	0.386980i
$386$		0			0
$387$	2.31038	−	53.9908i	0.00596999	−	0.139511i
$388$		0			0
$389$	−80.9245	+	46.7218i	−0.208032	+	0.120107i	−0.600396	−	0.799702i	$-0.704991\pi$
$389$	−80.9245	+	46.7218i	−0.208032	+	0.120107i	0.392364	+	0.919810i	$0.371657\pi$
$390$		0			0
$391$	157.674	+	91.0332i	0.403259	+	0.232822i
$392$		0			0
$393$	5.54229	−	5.31020i	0.0141025	−	0.0135119i
$394$		0			0
$395$	540.063			1.36725
$396$		0			0
$397$			102.633i			0.258521i	0.991611	+	0.129261i	$0.0412604\pi$
$397$			102.633i			0.258521i	−0.991611	+	0.129261i	$0.958740\pi$
$398$		0			0
$399$	330.899	−	81.1225i	0.829321	−	0.203315i
$400$		0			0
$401$	−349.487	+	605.329i	−0.871538	+	1.50955i	−0.0111320	+	0.999938i	$0.503543\pi$
$401$	−349.487	+	605.329i	−0.871538	+	1.50955i	−0.860406	+	0.509610i	$0.829790\pi$
$402$		0			0
$403$	207.160	+	358.812i	0.514045	+	0.890351i
$404$		0			0
$405$	−37.4065	+	436.272i	−0.0923618	+	1.07721i
$406$		0			0
$407$	278.080	−	160.549i	0.683242	−	0.394470i
$408$		0			0
$409$	62.9855	−	109.094i	0.153999	−	0.266734i	−0.778695	−	0.627402i	$-0.784118\pi$
$409$	62.9855	−	109.094i	0.153999	−	0.266734i	0.932694	+	0.360669i	$0.117451\pi$
$410$		0			0
$411$	−148.462	−	605.577i	−0.361222	−	1.47342i
$412$		0			0
$413$		−	69.9717i		−	0.169423i
$414$		0			0
$415$		−	190.575i		−	0.459218i
$416$		0			0
$417$	−431.829	+	413.745i	−1.03556	+	0.992195i
$418$		0			0
$419$	−283.272	+	490.642i	−0.676068	+	1.17098i	0.300088	+	0.953912i	$0.402984\pi$
$419$	−283.272	+	490.642i	−0.676068	+	1.17098i	−0.976156	+	0.217072i	$0.930349\pi$
$420$		0			0
$421$	502.553	−	290.149i	1.19371	−	0.689190i	0.234566	−	0.972100i	$-0.424633\pi$
$421$	502.553	−	290.149i	1.19371	−	0.689190i	0.959146	+	0.282910i	$0.0912999\pi$
$422$		0			0
$423$	265.116	+	11.3449i	0.626751	+	0.0268200i
$424$		0			0
$425$	47.5346	+	82.3324i	0.111846	+	0.193723i
$426$		0			0
$427$	−35.3185	+	61.1734i	−0.0827131	+	0.143263i
$428$		0			0
$429$	−62.9542	+	216.335i	−0.146746	+	0.504278i
$430$		0			0
$431$			141.791i			0.328982i	0.986379	+	0.164491i	$0.0525981\pi$
$431$			141.791i			0.328982i	−0.986379	+	0.164491i	$0.947402\pi$
$432$		0			0
$433$	374.678			0.865306			0.432653	−	0.901561i	$-0.357578\pi$
$433$	374.678			0.865306			0.432653	+	0.901561i	$0.357578\pi$
$434$		0			0
$435$	−659.643	−	191.958i	−1.51642	−	0.441283i
$436$		0			0
$437$	214.654	+	123.930i	0.491198	+	0.283593i
$438$		0			0
$439$	−83.4436	+	48.1762i	−0.190076	+	0.109741i	−0.592018	−	0.805924i	$-0.701669\pi$
$439$	−83.4436	+	48.1762i	−0.190076	+	0.109741i	0.401942	+	0.915665i	$0.368335\pi$
$440$		0			0
$441$	−281.426	+	146.812i	−0.638155	+	0.332906i
$442$		0			0
$443$	86.8023	+	150.346i	0.195942	+	0.339382i	0.947209	−	0.320617i	$-0.103890\pi$
$443$	86.8023	+	150.346i	0.195942	+	0.339382i	−0.751267	+	0.659999i	$0.770557\pi$
$444$		0			0
$445$	−289.457	−	167.118i	−0.650464	−	0.375546i
$446$		0			0
$447$	−526.698	−	549.719i	−1.17830	−	1.22980i
$448$		0			0
$449$	306.677			0.683023			0.341511	−	0.939878i	$-0.389061\pi$
$449$	306.677			0.683023			0.341511	+	0.939878i	$0.389061\pi$
$450$		0			0
$451$	−138.460			−0.307008
$452$		0			0
$453$	−452.342	+	110.895i	−0.998548	+	0.244802i
$454$		0			0
$455$	−151.707	−	87.5881i	−0.333422	−	0.192501i
$456$		0			0
$457$	−20.9864	−	36.3496i	−0.0459222	−	0.0795396i	0.842151	−	0.539242i	$-0.181289\pi$
$457$	−20.9864	−	36.3496i	−0.0459222	−	0.0795396i	−0.888073	+	0.459703i	$0.847956\pi$
$458$		0			0
$459$	401.361	+	456.465i	0.874425	+	0.994478i
$460$		0			0
$461$	785.389	−	453.445i	1.70366	−	0.983611i	0.761681	−	0.647952i	$-0.224374\pi$
$461$	785.389	−	453.445i	1.70366	−	0.983611i	0.941983	−	0.335659i	$-0.108959\pi$
$462$		0			0
$463$	214.087	+	123.603i	0.462390	+	0.266961i	0.713049	−	0.701115i	$-0.247314\pi$
$463$	214.087	+	123.603i	0.462390	+	0.266961i	−0.250659	+	0.968076i	$0.580647\pi$
$464$		0			0
$465$	−182.951	−	746.258i	−0.393443	−	1.60486i
$466$		0			0
$467$	398.622			0.853579			0.426790	−	0.904351i	$-0.359644\pi$
$467$	398.622			0.853579			0.426790	+	0.904351i	$0.359644\pi$
$468$		0			0
$469$			143.296i			0.305536i
$470$		0			0
$471$	−219.780	−	229.386i	−0.466624	−	0.487018i
$472$		0			0
$473$	−25.7837	+	44.6587i	−0.0545110	+	0.0944158i
$474$		0			0
$475$	64.7124	+	112.085i	0.136237	+	0.235969i
$476$		0			0
$477$	−327.382	+	514.872i	−0.686336	+	1.07940i
$478$		0			0
$479$	−362.856	+	209.495i	−0.757529	+	0.437360i	−0.828408	−	0.560125i	$-0.810753\pi$
$479$	−362.856	+	209.495i	−0.757529	+	0.437360i	0.0708788	+	0.997485i	$0.477420\pi$
$480$		0			0
$481$	163.480	−	283.156i	0.339875	−	0.588682i
$482$		0			0
$483$	86.3258	+	25.1211i	0.178728	+	0.0520105i
$484$		0			0
$485$			741.859i			1.52961i
$486$		0			0
$487$			214.949i			0.441375i	0.975345	+	0.220687i	$0.0708300\pi$
$487$			214.949i			0.441375i	−0.975345	+	0.220687i	$0.929170\pi$
$488$		0			0
$489$	−838.779	−	244.087i	−1.71530	−	0.499156i
$490$		0			0
$491$	−227.048	+	393.259i	−0.462420	+	0.800935i	−0.999081	−	0.0428630i	$-0.986352\pi$
$491$	−227.048	+	393.259i	−0.462420	+	0.800935i	0.536661	+	0.843798i	$0.319685\pi$
$492$		0			0
$493$	−825.889	+	476.827i	−1.67523	+	0.967195i
$494$		0			0
$495$	224.197	−	352.594i	0.452924	−	0.712311i
$496$		0			0
$497$	−164.366	−	284.691i	−0.330717	−	0.572819i
$498$		0			0
$499$	−32.7193	+	56.6714i	−0.0655697	+	0.113570i	−0.896947	−	0.442139i	$-0.854220\pi$
$499$	−32.7193	+	56.6714i	−0.0655697	+	0.113570i	0.831377	+	0.555709i	$0.187553\pi$
$500$		0			0
$501$	82.0966	+	85.6848i	0.163865	+	0.171028i
$502$		0			0
$503$		−	360.623i		−	0.716945i	−0.933540	−	0.358473i	$-0.883298\pi$
$503$		−	360.623i		−	0.716945i	0.933540	−	0.358473i	$-0.116702\pi$
$504$		0			0
$505$	34.7124			0.0687373
$506$		0			0
$507$	−66.0933	−	269.594i	−0.130361	−	0.531745i
$508$		0			0
$509$	239.032	+	138.005i	0.469612	+	0.271130i	0.716077	−	0.698021i	$-0.245936\pi$
$509$	239.032	+	138.005i	0.469612	+	0.271130i	−0.246465	+	0.969152i	$0.579269\pi$
$510$		0			0
$511$	−272.234	+	157.174i	−0.532747	+	0.307582i
$512$		0			0
$513$	546.403	+	621.421i	1.06511	+	1.21135i
$514$		0			0
$515$	−472.646	−	818.647i	−0.917760	−	1.58961i
$516$		0			0
$517$	−219.291	−	126.608i	−0.424161	−	0.244889i
$518$		0			0
$519$	460.911	−	112.996i	0.888076	−	0.217719i
$520$		0			0
$521$	13.0126			0.0249761			0.0124881	−	0.999922i	$-0.496025\pi$
$521$	13.0126			0.0249761			0.0124881	+	0.999922i	$0.496025\pi$
$522$		0			0
$523$	693.412			1.32584			0.662918	−	0.748692i	$-0.269318\pi$
$523$	693.412			1.32584			0.662918	+	0.748692i	$0.269318\pi$
$524$		0			0
$525$	32.4787	+	33.8983i	0.0618642	+	0.0645681i
$526$		0			0
$527$	−923.686	−	533.290i	−1.75272	−	1.01194i
$528$		0			0
$529$	−231.796	−	401.483i	−0.438178	−	0.758946i
$530$		0			0
$531$	150.675	−	78.6028i	0.283758	−	0.148028i
$532$		0			0
$533$	−122.099	+	70.4940i	−0.229079	+	0.132259i
$534$		0			0
$535$	630.898	+	364.249i	1.17925	+	0.680840i
$536$		0			0
$537$	−463.223	−	134.799i	−0.862613	−	0.251023i
$538$		0			0
$539$	302.894			0.561955
$540$		0			0
$541$		−	166.049i		−	0.306930i	−0.988154	−	0.153465i	$-0.950957\pi$
$541$		−	166.049i		−	0.306930i	0.988154	−	0.153465i	$-0.0490432\pi$
$542$		0			0
$543$	88.9941	−	305.819i	0.163893	−	0.563202i
$544$		0			0
$545$	−386.410	+	669.281i	−0.709008	+	1.22804i
$546$		0			0
$547$	−230.803	−	399.762i	−0.421943	−	0.730827i	0.574187	−	0.818725i	$-0.305318\pi$
$547$	−230.803	−	399.762i	−0.421943	−	0.730827i	−0.996129	+	0.0878979i	$0.971985\pi$
$548$		0			0
$549$	−171.404	−	7.33476i	−0.312212	−	0.0133602i
$550$		0			0
$551$	−1124.34	+	649.141i	−2.04055	+	1.17811i
$552$		0			0
$553$	185.100	−	320.603i	0.334720	−	0.579752i
$554$		0			0
$555$	−437.822	+	419.487i	−0.788868	+	0.755833i
$556$		0			0
$557$		−	661.847i		−	1.18823i	−0.804378	−	0.594117i	$-0.797501\pi$
$557$		−	661.847i		−	1.18823i	0.804378	−	0.594117i	$-0.202499\pi$
$558$		0			0
$559$			52.5087i			0.0939334i
$560$		0			0
$561$	−138.105	−	563.330i	−0.246176	−	1.00415i
$562$		0			0
$563$	−403.894	+	699.564i	−0.717395	+	1.24257i	0.244633	+	0.969616i	$0.421333\pi$
$563$	−403.894	+	699.564i	−0.717395	+	1.24257i	−0.962028	+	0.272950i	$0.912001\pi$
$564$		0			0
$565$	931.125	−	537.585i	1.64801	−	0.951479i
$566$		0			0
$567$	246.168	+	171.733i	0.434159	+	0.302880i
$568$		0			0
$569$	397.986	+	689.332i	0.699449	+	1.21148i	0.968658	+	0.248399i	$0.0799043\pi$
$569$	397.986	+	689.332i	0.699449	+	1.21148i	−0.269209	+	0.963082i	$0.586762\pi$
$570$		0			0
$571$	276.839	−	479.499i	0.484832	−	0.839754i	−0.515016	−	0.857180i	$-0.672214\pi$
$571$	276.839	−	479.499i	0.484832	−	0.839754i	0.999848	+	0.0174269i	$0.00554742\pi$
$572$		0			0
$573$	790.264	−	193.740i	1.37917	−	0.338115i
$574$		0			0
$575$			34.1539i			0.0593980i
$576$		0			0
$577$	−20.3945			−0.0353457			−0.0176728	−	0.999844i	$-0.505626\pi$
$577$	−20.3945			−0.0353457			−0.0176728	+	0.999844i	$0.505626\pi$
$578$		0			0
$579$	−714.116	+	684.211i	−1.23336	+	1.18171i
$580$		0			0
$581$	−113.133	−	65.3175i	−0.194722	−	0.112423i
$582$		0			0
$583$	504.219	−	291.111i	0.864869	−	0.499332i
$584$		0			0
$585$	18.1899	−	425.074i	0.0310938	−	0.726623i
$586$		0			0
$587$	−147.822	−	256.035i	−0.251826	−	0.436175i	0.712203	−	0.701974i	$-0.247698\pi$
$587$	−147.822	−	256.035i	−0.251826	−	0.436175i	−0.964029	+	0.265799i	$0.914364\pi$
$588$		0			0
$589$	−1257.48	−	726.008i	−2.13495	−	1.23261i
$590$		0			0
$591$	−175.802	+	604.123i	−0.297465	+	1.02221i
$592$		0			0
$593$	−323.469			−0.545479			−0.272740	−	0.962088i	$-0.587930\pi$
$593$	−323.469			−0.545479			−0.272740	+	0.962088i	$0.587930\pi$
$594$		0			0
$595$	450.955			0.757907
$596$		0			0
$597$	314.028	−	1079.12i	0.526010	−	1.80758i
$598$		0			0
$599$	888.894	+	513.203i	1.48396	+	0.856767i	0.999834	−	0.0182299i	$-0.00580308\pi$
$599$	888.894	+	513.203i	1.48396	+	0.856767i	0.484129	+	0.874996i	$0.339136\pi$
$600$		0			0
$601$	510.511	+	884.231i	0.849436	+	1.47127i	0.881712	+	0.471787i	$0.156391\pi$
$601$	510.511	+	884.231i	0.849436	+	1.47127i	−0.0322765	+	0.999479i	$0.510276\pi$
$602$		0			0
$603$	−308.571	+	160.972i	−0.511726	+	0.266952i
$604$		0			0
$605$	221.174	−	127.695i	0.365577	−	0.211066i
$606$		0			0
$607$	−121.280	−	70.0213i	−0.199803	−	0.115356i	0.396761	−	0.917922i	$-0.370134\pi$
$607$	−121.280	−	70.0213i	−0.199803	−	0.115356i	−0.596564	+	0.802566i	$0.703468\pi$
$608$		0			0
$609$	−340.039	+	325.799i	−0.558356	+	0.534974i
$610$		0			0
$611$	−257.838			−0.421993
$612$		0			0
$613$		−	345.844i		−	0.564182i	−0.959388	−	0.282091i	$-0.908972\pi$
$613$		−	345.844i		−	0.564182i	0.959388	−	0.282091i	$-0.0910280\pi$
$614$		0			0
$615$	253.942	−	62.2560i	0.412915	−	0.101229i
$616$		0			0
$617$	−269.562	+	466.895i	−0.436891	+	0.756718i	−0.997448	−	0.0713982i	$-0.977254\pi$
$617$	−269.562	+	466.895i	−0.436891	+	0.756718i	0.560557	+	0.828116i	$0.310587\pi$
$618$		0			0
$619$	−459.468	−	795.823i	−0.742275	−	1.28566i	−0.951457	−	0.307782i	$-0.900413\pi$
$619$	−459.468	−	795.823i	−0.742275	−	1.28566i	0.209182	−	0.977877i	$-0.432920\pi$
$620$		0			0
$621$	42.8790	+	214.111i	0.0690483	+	0.344785i
$622$		0			0
$623$	−198.416	+	114.555i	−0.318485	+	0.183877i
$624$		0			0
$625$	356.371	−	617.253i	0.570194	−	0.987604i
$626$		0			0
$627$	−188.012	−	766.903i	−0.299860	−	1.22313i
$628$		0			0
$629$			841.691i			1.33814i
$630$		0			0
$631$			994.901i			1.57671i	0.615224	+	0.788353i	$0.289066\pi$
$631$			994.901i			1.57671i	−0.615224	+	0.788353i	$0.710934\pi$
$632$		0			0
$633$	127.779	−	122.428i	0.201862	−	0.193409i
$634$		0			0
$635$	−182.567	+	316.215i	−0.287507	+	0.497976i
$636$		0			0
$637$	267.102	−	154.211i	0.419313	−	0.242090i
$638$		0			0
$639$	428.405	−	673.750i	0.670431	−	1.05438i
$640$		0			0
$641$	250.304	+	433.539i	0.390490	+	0.676348i	0.992514	−	0.122130i	$-0.0389724\pi$
$641$	250.304	+	433.539i	0.390490	+	0.676348i	−0.602025	+	0.798478i	$0.705639\pi$
$642$		0			0
$643$	103.501	−	179.269i	0.160965	−	0.278800i	−0.774250	−	0.632880i	$-0.781873\pi$
$643$	103.501	−	179.269i	0.160965	−	0.278800i	0.935215	+	0.354080i	$0.115206\pi$
$644$		0			0
$645$	27.2085	−	93.4991i	0.0421837	−	0.144960i
$646$		0			0
$647$			997.131i			1.54116i	0.637343	+	0.770580i	$0.280033\pi$
$647$			997.131i			1.54116i	−0.637343	+	0.770580i	$0.719967\pi$
$648$		0			0
$649$	−162.169			−0.249875
$650$		0			0
$651$	−505.713	−	147.164i	−0.776825	−	0.226058i
$652$		0			0
$653$	−595.912	−	344.050i	−0.912576	−	0.526876i	−0.0313170	−	0.999510i	$-0.509970\pi$
$653$	−595.912	−	344.050i	−0.912576	−	0.526876i	−0.881259	+	0.472633i	$0.843303\pi$
$654$		0			0
$655$	11.9780	−	6.91552i	0.0182871	−	0.0105580i
$656$		0			0
$657$	−644.269	−	409.660i	−0.980623	−	0.623531i
$658$		0			0
$659$	135.776	+	235.170i	0.206033	+	0.356859i	0.950461	−	0.310843i	$-0.100611\pi$
$659$	135.776	+	235.170i	0.206033	+	0.356859i	−0.744428	+	0.667702i	$0.767278\pi$
$660$		0			0
$661$	170.446	+	98.4072i	0.257861	+	0.148876i	0.623359	−	0.781936i	$-0.285768\pi$
$661$	170.446	+	98.4072i	0.257861	+	0.148876i	−0.365497	+	0.930812i	$0.619101\pi$
$662$		0			0
$663$	−408.592	−	426.451i	−0.616278	−	0.643214i
$664$		0			0
$665$	613.919			0.923186
$666$		0			0
$667$	−342.603			−0.513648
$668$		0			0
$669$	−311.448	+	76.3540i	−0.465543	+	0.114132i
$670$		0			0
$671$	141.778	+	81.8554i	0.211293	+	0.121990i
$672$		0			0
$673$	362.042	+	627.076i	0.537953	+	0.931762i	0.999014	+	0.0443934i	$0.0141355\pi$
$673$	362.042	+	627.076i	0.537953	+	0.931762i	−0.461061	+	0.887368i	$0.652531\pi$
$674$		0			0
$675$	−36.5107	+	108.018i	−0.0540899	+	0.160027i
$676$		0			0
$677$	744.406	−	429.783i	1.09957	−	0.634834i	0.163458	−	0.986550i	$-0.447735\pi$
$677$	744.406	−	429.783i	1.09957	−	0.634834i	0.936107	+	0.351716i	$0.114402\pi$
$678$		0			0
$679$	440.397	+	254.264i	0.648597	+	0.374468i
$680$		0			0
$681$	−202.831	−	827.350i	−0.297844	−	1.21490i
$682$		0			0
$683$	−314.972			−0.461160			−0.230580	−	0.973053i	$-0.574062\pi$
$683$	−314.972			−0.461160			−0.230580	+	0.973053i	$0.574062\pi$
$684$		0			0
$685$		−	1123.53i		−	1.64019i
$686$		0			0
$687$	167.519	+	174.841i	0.243841	+	0.254499i
$688$		0			0
$689$	296.425	−	513.423i	0.430225	−	0.745171i
$690$		0			0
$691$	50.6901	+	87.7979i	0.0733577	+	0.127059i	0.900371	−	0.435123i	$-0.143295\pi$
$691$	50.6901	+	87.7979i	0.0733577	+	0.127059i	−0.827013	+	0.562182i	$0.809962\pi$
$692$		0			0
$693$	−132.473	−	253.940i	−0.191159	−	0.366436i
$694$		0			0
$695$	−933.272	+	538.825i	−1.34284	+	0.775287i
$696$		0			0
$697$	181.472	−	314.319i	0.260362	−	0.450960i
$698$		0			0
$699$	623.981	+	181.581i	0.892677	+	0.259772i
$700$		0			0
$701$		−	606.296i		−	0.864902i	−0.901657	−	0.432451i	$-0.857649\pi$
$701$		−	606.296i		−	0.864902i	0.901657	−	0.432451i	$-0.142351\pi$
$702$		0			0
$703$			1145.86i			1.62995i
$704$		0			0
$705$	459.116	+	133.604i	0.651229	+	0.189510i
$706$		0			0
$707$	11.8973	−	20.6067i	0.0168278	−	0.0291466i
$708$		0			0
$709$	414.361	−	239.231i	0.584430	−	0.337421i	−0.178462	−	0.983947i	$-0.557112\pi$
$709$	414.361	−	239.231i	0.584430	−	0.337421i	0.762892	+	0.646526i	$0.223779\pi$
$710$		0			0
$711$	898.311	+	38.4407i	1.26345	+	0.0540656i
$712$		0			0
$713$	−191.586	−	331.837i	−0.268704	−	0.465409i
$714$		0			0
$715$	−202.997	+	351.602i	−0.283912	+	0.491750i
$716$		0			0
$717$	644.600	+	672.773i	0.899023	+	0.938317i
$718$		0			0
$719$		−	528.537i		−	0.735100i	−0.930004	−	0.367550i	$-0.880197\pi$
$719$		−	528.537i		−	0.735100i	0.930004	−	0.367550i	$-0.119803\pi$
$720$		0			0
$721$	−647.976			−0.898719
$722$		0			0
$723$	−94.1359	−	383.980i	−0.130202	−	0.531093i
$724$		0			0
$725$	−154.929	−	89.4481i	−0.213695	−	0.123377i
$726$		0			0
$727$	−141.893	+	81.9220i	−0.195176	+	0.112685i	−0.594403	−	0.804167i	$-0.702612\pi$
$727$	−141.893	+	81.9220i	−0.195176	+	0.112685i	0.399227	+	0.916852i	$0.369278\pi$
$728$		0			0
$729$	−93.2730	+	723.008i	−0.127947	+	0.991781i
$730$		0			0
$731$	−67.5864	−	117.063i	−0.0924575	−	0.160141i
$732$		0			0
$733$	−280.898	−	162.176i	−0.383216	−	0.221250i	0.296000	−	0.955188i	$-0.404347\pi$
$733$	−280.898	−	162.176i	−0.383216	−	0.221250i	−0.679217	+	0.733938i	$0.737680\pi$
$734$		0			0
$735$	−555.520	+	136.190i	−0.755810	+	0.185293i
$736$		0			0
$737$	332.109			0.450623
$738$		0			0
$739$	−103.528			−0.140093			−0.0700463	−	0.997544i	$-0.522315\pi$
$739$	−103.528			−0.140093			−0.0700463	+	0.997544i	$0.522315\pi$
$740$		0			0
$741$	−556.247	−	580.559i	−0.750671	−	0.783481i
$742$		0			0
$743$	350.394	+	202.300i	0.471593	+	0.272274i	0.716906	−	0.697169i	$-0.245557\pi$
$743$	350.394	+	202.300i	0.471593	+	0.272274i	−0.245313	+	0.969444i	$0.578891\pi$
$744$		0			0
$745$	−685.924	−	1188.06i	−0.920704	−	1.59471i
$746$		0			0
$747$	13.5648	−	316.993i	0.0181590	−	0.424354i
$748$		0			0
$749$	432.466	−	249.685i	0.577392	−	0.333357i
$750$		0			0
$751$	−761.157	−	439.454i	−1.01353	−	0.585159i	−0.101303	−	0.994856i	$-0.532301\pi$
$751$	−761.157	−	439.454i	−1.01353	−	0.585159i	−0.912222	+	0.409696i	$0.865635\pi$
$752$		0			0
$753$	−430.689	−	125.332i	−0.571965	−	0.166443i
$754$		0			0
$755$	−839.233			−1.11157
$756$		0			0
$757$		−	447.570i		−	0.591242i	−0.955305	−	0.295621i	$-0.904473\pi$
$757$		−	447.570i		−	0.591242i	0.955305	−	0.295621i	$-0.0955266\pi$
$758$		0			0
$759$	58.2215	−	200.072i	0.0767081	−	0.263599i
$760$		0			0
$761$	−413.080	+	715.475i	−0.542812	+	0.940177i	0.455930	+	0.890016i	$0.349307\pi$
$761$	−413.080	+	715.475i	−0.542812	+	0.940177i	−0.998741	+	0.0501613i	$0.984026\pi$
$762$		0			0
$763$	264.875	+	458.777i	0.347149	+	0.601280i
$764$		0			0
$765$	506.580	+	971.075i	0.662197	+	1.26938i
$766$		0			0
$767$	−143.006	+	82.5646i	−0.186449	+	0.107646i
$768$		0			0
$769$	−341.441	+	591.392i	−0.444006	+	0.769041i	−0.997982	−	0.0634916i	$-0.979776\pi$
$769$	−341.441	+	591.392i	−0.444006	+	0.769041i	0.553977	+	0.832532i	$0.313110\pi$
$770$		0			0
$771$	66.0769	−	63.3098i	0.0857028	−	0.0821138i
$772$		0			0
$773$			552.034i			0.714144i	0.934077	+	0.357072i	$0.116225\pi$
$773$			552.034i			0.714144i	−0.934077	+	0.357072i	$0.883775\pi$
$774$		0			0
$775$		−	200.080i		−	0.258168i
$776$		0			0
$777$	98.9662	+	403.683i	0.127370	+	0.519541i
$778$		0			0
$779$	247.052	−	427.906i	0.317140	−	0.549302i
$780$		0			0
$781$	−659.810	+	380.941i	−0.844827	+	0.487761i
$782$		0			0
$783$	−1083.55	−	366.245i	−1.38384	−	0.467746i
$784$		0			0
$785$	−286.221	−	495.750i	−0.364613	−	0.631528i
$786$		0			0
$787$	170.612	−	295.509i	0.216788	−	0.375488i	−0.737036	−	0.675853i	$-0.763775\pi$
$787$	170.612	−	295.509i	0.216788	−	0.375488i	0.953824	+	0.300365i	$0.0971086\pi$
$788$		0			0
$789$	−1357.23	+	332.736i	−1.72019	+	0.421719i
$790$		0			0
$791$		−	737.005i		−	0.931738i
$792$		0			0
$793$	166.699			0.210213
$794$		0			0
$795$	−793.866	+	760.621i	−0.998574	+	0.956757i
$796$		0			0
$797$	299.674	+	173.017i	0.376003	+	0.217085i	0.676078	−	0.736830i	$-0.263678\pi$
$797$	299.674	+	173.017i	0.376003	+	0.217085i	−0.300075	+	0.953916i	$0.597012\pi$
$798$		0			0
$799$	574.825	−	331.875i	0.719430	−	0.415363i
$800$		0			0
$801$	−469.571	−	298.578i	−0.586231	−	0.372756i
$802$		0			0
$803$	364.273	+	630.938i	0.453639	+	0.785727i
$804$		0			0
$805$	140.302	+	81.0034i	0.174288	+	0.100625i
$806$		0			0
$807$	−184.060	+	632.502i	−0.228079	+	0.783770i
$808$		0			0
$809$	−1245.47			−1.53952			−0.769760	−	0.638334i	$-0.779624\pi$
$809$	−1245.47			−1.53952			−0.769760	+	0.638334i	$0.779624\pi$
$810$		0			0
$811$	−952.597			−1.17460			−0.587298	−	0.809371i	$-0.699808\pi$
$811$	−952.597			−1.17460			−0.587298	+	0.809371i	$0.699808\pi$
$812$		0			0
$813$	54.4392	−	187.074i	0.0669608	−	0.230104i
$814$		0			0
$815$	−1363.24	−	787.065i	−1.67268	−	0.965724i
$816$		0			0
$817$	−92.0105	−	159.367i	−0.112620	−	0.195063i
$818$		0			0
$819$	−246.107	−	156.488i	−0.300497	−	0.191071i
$820$		0			0
$821$	−144.870	+	83.6406i	−0.176455	+	0.101876i	−0.585626	−	0.810581i	$-0.699151\pi$
$821$	−144.870	+	83.6406i	−0.176455	+	0.101876i	0.409171	+	0.912458i	$0.365818\pi$
$822$		0			0
$823$	35.7978	+	20.6679i	0.0434967	+	0.0251129i	0.521591	−	0.853196i	$-0.325339\pi$
$823$	35.7978	+	20.6679i	0.0434967	+	0.0251129i	−0.478094	+	0.878309i	$0.658672\pi$
$824$		0			0
$825$	78.5638	−	75.2738i	0.0952289	−	0.0912410i
$826$		0			0
$827$	117.866			0.142523			0.0712614	−	0.997458i	$-0.477298\pi$
$827$	117.866			0.142523			0.0712614	+	0.997458i	$0.477298\pi$
$828$		0			0
$829$			1069.61i			1.29024i	0.764083	+	0.645118i	$0.223192\pi$
$829$			1069.61i			1.29024i	−0.764083	+	0.645118i	$0.776808\pi$
$830$		0			0
$831$	−234.159	+	57.4058i	−0.281779	+	0.0690804i
$832$		0			0
$833$	−396.985	+	687.599i	−0.476573	+	0.825449i
$834$		0			0
$835$	106.915	+	185.183i	0.128042	+	0.221776i
$836$		0			0
$837$	−251.194	−	1254.31i	−0.300112	−	1.49857i
$838$		0			0
$839$	769.066	−	444.021i	0.916646	−	0.529226i	0.0340827	−	0.999419i	$-0.489149\pi$
$839$	769.066	−	444.021i	0.916646	−	0.529226i	0.882564	+	0.470193i	$0.155816\pi$
$840$		0			0
$841$	476.768	−	825.787i	0.566906	−	0.981911i
$842$		0			0
$843$	−180.195	−	735.017i	−0.213755	−	0.871907i
$844$		0			0
$845$		−	500.180i		−	0.591929i
$846$		0			0
$847$		−	175.064i		−	0.206687i
$848$		0			0
$849$	−151.259	+	144.925i	−0.178162	+	0.170701i
$850$		0			0
$851$	−151.190	+	261.869i	−0.177662	+	0.307719i
$852$		0			0
$853$	−495.638	+	286.157i	−0.581053	+	0.335471i	−0.761552	−	0.648104i	$-0.775562\pi$
$853$	−495.638	+	286.157i	−0.581053	+	0.335471i	0.180499	+	0.983575i	$0.442229\pi$
$854$		0			0
$855$	689.646	+	1322.00i	0.806603	+	1.54620i
$856$		0			0
$857$	−353.763	−	612.736i	−0.412792	−	0.714977i	0.582402	−	0.812901i	$-0.302113\pi$
$857$	−353.763	−	612.736i	−0.412792	−	0.714977i	−0.995194	+	0.0979239i	$0.968780\pi$
$858$		0			0
$859$	−439.087	+	760.520i	−0.511160	+	0.885355i	0.488756	+	0.872420i	$0.337451\pi$
$859$	−439.087	+	760.520i	−0.511160	+	0.885355i	−0.999916	+	0.0129349i	$0.995883\pi$
$860$		0			0
$861$	50.0781	−	172.088i	0.0581628	−	0.199870i
$862$		0			0
$863$			126.329i			0.146384i	0.997318	+	0.0731920i	$0.0233186\pi$
$863$			126.329i			0.146384i	−0.997318	+	0.0731920i	$0.976681\pi$
$864$		0			0
$865$	855.131			0.988591
$866$		0			0
$867$	627.353	+	182.562i	0.723590	+	0.210567i
$868$		0			0
$869$	−743.041	−	428.995i	−0.855053	−	0.493665i
$870$		0			0
$871$	292.865	−	169.086i	0.336240	−	0.194128i
$872$		0			0
$873$	−52.8042	+	1233.97i	−0.0604859	+	1.41348i
$874$		0			0
$875$	−208.099	−	360.438i	−0.237828	−	0.411929i
$876$		0			0
$877$	1313.43	+	758.310i	1.49764	+	0.864663i	0.999996	−	0.00271779i	$-0.000865102\pi$
$877$	1313.43	+	758.310i	1.49764	+	0.864663i	0.497644	+	0.867381i	$0.334198\pi$
$878$		0			0
$879$	−59.3754	−	61.9705i	−0.0675488	−	0.0705012i
$880$		0			0
$881$	902.446			1.02434			0.512171	−	0.858883i	$-0.328841\pi$
$881$	902.446			1.02434			0.512171	+	0.858883i	$0.328841\pi$
$882$		0			0
$883$	331.022			0.374883			0.187442	−	0.982276i	$-0.439980\pi$
$883$	331.022			0.374883			0.187442	+	0.982276i	$0.439980\pi$
$884$		0			0
$885$	297.425	−	72.9161i	0.336073	−	0.0823910i
$886$		0			0
$887$	1009.21	+	582.668i	1.13778	+	0.656898i	0.945880	−	0.324517i	$-0.105202\pi$
$887$	1009.21	+	582.668i	1.13778	+	0.656898i	0.191900	+	0.981414i	$0.438535\pi$
$888$		0			0
$889$	125.145	+	216.758i	0.140771	+	0.243822i
$890$		0			0
$891$	398.015	−	570.527i	0.446706	−	0.640323i
$892$		0			0
$893$	782.552	−	451.807i	0.876318	−	0.505942i
$894$		0			0
$895$	−752.859	−	434.664i	−0.841184	−	0.485658i
$896$		0			0
$897$	−50.5202	−	206.072i	−0.0563213	−	0.229735i
$898$		0			0
$899$	2007.04			2.23252
$900$		0			0
$901$			1526.17i			1.69386i
$902$		0			0
$903$	−46.1794	−	48.1978i	−0.0511400	−	0.0533752i
$904$		0			0
$905$	286.963	−	497.035i	0.317087	−	0.549210i
$906$		0			0
$907$	−563.443	−	975.912i	−0.621216	−	1.07598i	−0.989260	−	0.146169i	$-0.953306\pi$
$907$	−563.443	−	975.912i	−0.621216	−	1.07598i	0.368043	−	0.929809i	$-0.380028\pi$
$908$		0			0
$909$	57.7386	+	2.47076i	0.0635189	+	0.00271811i
$910$		0			0
$911$	1459.37	−	842.565i	1.60194	−	0.924880i	0.610839	−	0.791755i	$-0.290832\pi$
$911$	1459.37	−	842.565i	1.60194	−	0.924880i	0.991099	−	0.133125i	$-0.0425011\pi$
$912$		0			0
$913$	−151.382	+	262.202i	−0.165807	+	0.287187i
$914$		0			0
$915$	−296.831	−	86.3787i	−0.324405	−	0.0944029i
$916$		0			0
$917$		−	9.48086i		−	0.0103390i
$918$		0			0
$919$		−	63.1127i		−	0.0686754i	−0.999410	−	0.0343377i	$-0.989068\pi$
$919$		−	63.1127i		−	0.0686754i	0.999410	−	0.0343377i	$-0.0109322\pi$
$920$		0			0
$921$	−137.140	−	39.9083i	−0.148904	−	0.0433315i
$922$		0			0
$923$	−387.895	+	671.854i	−0.420255	+	0.727903i
$924$		0			0
$925$	−136.739	+	78.9465i	−0.147826	+	0.0853476i
$926$		0			0
$927$	−727.904	−	1395.34i	−0.785226	−	1.50522i
$928$		0			0
$929$	156.502	+	271.070i	0.168463	+	0.291787i	0.937880	−	0.346960i	$-0.112786\pi$
$929$	156.502	+	271.070i	0.168463	+	0.291787i	−0.769416	+	0.638748i	$0.779453\pi$
$930$		0			0
$931$	−540.446	+	936.080i	−0.580500	+	1.00546i
$932$		0			0
$933$	207.917	+	217.004i	0.222847	+	0.232587i
$934$		0			0
$935$		−	1045.15i		−	1.11781i
$936$		0			0
$937$	−758.852			−0.809874			−0.404937	−	0.914345i	$-0.632707\pi$
$937$	−758.852			−0.809874			−0.404937	+	0.914345i	$0.632707\pi$
$938$		0			0
$939$	54.0988	+	220.669i	0.0576132	+	0.235004i
$940$		0			0
$941$	857.559	+	495.112i	0.911328	+	0.526155i	0.880858	−	0.473380i	$-0.156966\pi$
$941$	857.559	+	495.112i	0.911328	+	0.526155i	0.0304697	+	0.999536i	$0.490300\pi$
$942$		0			0
$943$	112.920	−	65.1944i	0.119746	−	0.0691351i
$944$		0			0
$945$	357.140	+	406.173i	0.377926	+	0.429813i
$946$		0			0
$947$	−505.117	−	874.888i	−0.533386	−	0.923852i	−0.999240	−	0.0389901i	$-0.987586\pi$
$947$	−505.117	−	874.888i	−0.533386	−	0.923852i	0.465853	−	0.884862i	$-0.345747\pi$
$948$		0			0
$949$	642.456	+	370.922i	0.676982	+	0.390856i
$950$		0			0
$951$	1736.72	−	425.770i	1.82620	−	0.447708i
$952$		0			0
$953$	149.903			0.157296			0.0786482	−	0.996902i	$-0.474940\pi$
$953$	149.903			0.157296			0.0786482	+	0.996902i	$0.474940\pi$
$954$		0			0
$955$	1466.18			1.53527
$956$		0			0
$957$	755.083	+	788.086i	0.789011	+	0.823496i
$958$		0			0
$959$	−666.973	−	385.077i	−0.695488	−	0.401540i
$960$		0			0
$961$	641.848	+	1111.71i	0.667896	+	1.15683i
$962$		0			0
$963$	1023.48	+	650.779i	1.06280	+	0.675783i
$964$		0			0
$965$	−1543.35	+	891.055i	−1.59933	+	0.923373i
$966$		0			0
$967$	−0.110033	−	0.0635276i	−0.000113788	−	6.56955e-5i	0.499943	−	0.866058i	$-0.333354\pi$
$967$	−0.110033	−	0.0635276i	−0.000113788	−	6.56955e-5i	−0.500057	+	0.865993i	$0.666688\pi$
$968$		0			0
$969$	1987.36	+	578.329i	2.05094	+	0.596831i
$970$		0			0
$971$	632.194			0.651075			0.325538	−	0.945529i	$-0.394455\pi$
$971$	632.194			0.651075			0.325538	+	0.945529i	$0.394455\pi$
$972$		0			0
$973$			738.704i			0.759202i
$974$		0			0
$975$	30.9563	−	106.378i	0.0317501	−	0.109106i
$976$		0			0
$977$	844.653	−	1462.98i	0.864538	−	1.49742i	−0.00296803	−	0.999996i	$-0.500945\pi$
$977$	844.653	−	1462.98i	0.864538	−	1.49742i	0.867506	−	0.497427i	$-0.165722\pi$
$978$		0			0
$979$	265.498	+	459.856i	0.271193	+	0.469720i
$980$		0			0
$981$	−690.371	+	1085.74i	−0.703742	+	1.10677i
$982$		0			0
$983$	626.800	−	361.883i	0.637640	−	0.368141i	−0.146065	−	0.989275i	$-0.546661\pi$
$983$	626.800	−	361.883i	0.637640	−	0.368141i	0.783705	+	0.621134i	$0.213328\pi$
$984$		0			0
$985$	−566.877	+	981.859i	−0.575509	+	0.996811i
$986$		0			0
$987$	236.670	−	226.759i	0.239787	−	0.229745i
$988$		0			0
$989$		−	48.5612i		−	0.0491013i
$990$		0			0
$991$		−	1005.63i		−	1.01476i	−0.861721	−	0.507382i	$-0.830613\pi$
$991$		−	1005.63i		−	1.01476i	0.861721	−	0.507382i	$-0.169387\pi$
$992$		0			0
$993$	32.4610	+	132.409i	0.0326899	+	0.133342i
$994$		0			0
$995$	1012.59	−	1753.86i	1.01768	−	1.76267i
$996$		0			0
$997$	1119.16	−	646.149i	1.12253	−	0.648093i	0.180484	−	0.983578i	$-0.442233\pi$
$997$	1119.16	−	646.149i	1.12253	−	0.648093i	0.942046	+	0.335485i	$0.108900\pi$
$998$		0			0
$999$	−758.108	+	666.589i	−0.758867	+	0.667256i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.3.t.c.31.15	yes	32
3.2	odd	2		1728.3.t.a.415.6		32
4.3	odd	2	inner	576.3.t.c.31.2	yes	32
8.3	odd	2		576.3.t.a.31.15	yes	32
8.5	even	2		576.3.t.a.31.2	✓	32
9.2	odd	6		1728.3.t.c.991.12		32
9.7	even	3		576.3.t.a.223.15	yes	32
12.11	even	2		1728.3.t.a.415.5		32
24.5	odd	2		1728.3.t.c.415.11		32
24.11	even	2		1728.3.t.c.415.12		32
36.7	odd	6		576.3.t.a.223.2	yes	32
36.11	even	6		1728.3.t.c.991.11		32
72.11	even	6		1728.3.t.a.991.6		32
72.29	odd	6		1728.3.t.a.991.5		32
72.43	odd	6	inner	576.3.t.c.223.15	yes	32
72.61	even	6	inner	576.3.t.c.223.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
576.3.t.a.31.2	✓	32	8.5	even	2
576.3.t.a.31.15	yes	32	8.3	odd	2
576.3.t.a.223.2	yes	32	36.7	odd	6
576.3.t.a.223.15	yes	32	9.7	even	3
576.3.t.c.31.2	yes	32	4.3	odd	2	inner
576.3.t.c.31.15	yes	32	1.1	even	1	trivial
576.3.t.c.223.2	yes	32	72.61	even	6	inner
576.3.t.c.223.15	yes	32	72.43	odd	6	inner
1728.3.t.a.415.5		32	12.11	even	2
1728.3.t.a.415.6		32	3.2	odd	2
1728.3.t.a.991.5		32	72.29	odd	6
1728.3.t.a.991.6		32	72.11	even	6
1728.3.t.c.415.11		32	24.5	odd	2
1728.3.t.c.415.12		32	24.11	even	2
1728.3.t.c.991.11		32	36.11	even	6
1728.3.t.c.991.12		32	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	576.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.88051 + 0.838238i) q^{3} +(4.68159 + 2.70292i) q^{5} +(3.20912 - 1.85279i) q^{7} +(7.59471 + 4.82911i) q^{9} +O(q^{10})\)	\(q+(2.88051 + 0.838238i) q^{3} +(4.68159 + 2.70292i) q^{5} +(3.20912 - 1.85279i) q^{7} +(7.59471 + 4.82911i) q^{9} +(-4.29408 - 7.43757i) q^{11} +(-7.57334 - 4.37247i) q^{13} +(11.2197 + 11.7101i) q^{15} +22.5120 q^{17} +30.6473 q^{19} +(10.7970 - 2.64697i) q^{21} +(7.00399 + 4.04376i) q^{23} +(2.11152 + 3.65726i) q^{25} +(17.8287 + 20.2765i) q^{27} +(-36.6865 + 21.1810i) q^{29} +(-41.0307 - 23.6891i) q^{31} +(-6.13471 - 25.0235i) q^{33} +20.0317 q^{35} +37.3885i q^{37} +(-18.1499 - 18.9432i) q^{39} +(8.06112 - 13.9623i) q^{41} +(-3.00223 - 5.20002i) q^{43} +(22.5026 + 43.1358i) q^{45} +(25.5341 - 14.7421i) q^{47} +(-17.6344 + 30.5436i) q^{49} +(64.8462 + 18.8705i) q^{51} +67.7934i q^{53} -46.4262i q^{55} +(88.2800 + 25.6898i) q^{57} +(9.44141 - 16.3530i) q^{59} +(-16.5085 + 9.53118i) q^{61} +(33.3197 + 1.42582i) q^{63} +(-23.6369 - 40.9402i) q^{65} +(-19.3353 + 33.4896i) q^{67} +(16.7855 + 17.5191i) q^{69} -88.7130i q^{71} -84.8312 q^{73} +(3.01660 + 12.3047i) q^{75} +(-27.5605 - 15.9120i) q^{77} +(86.5191 - 49.9518i) q^{79} +(34.3593 + 73.3515i) q^{81} +(-17.6268 - 30.5306i) q^{83} +(105.392 + 60.8482i) q^{85} +(-123.431 + 30.2600i) q^{87} -61.8287 q^{89} -32.4050 q^{91} +(-98.3325 - 102.630i) q^{93} +(143.478 + 82.8372i) q^{95} +(68.6165 + 118.847i) q^{97} +(3.30453 - 77.2228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 18 q^{5} + 18 q^{9}+O(q^{10}) \) 32 * q + 18 * q^5 + 18 * q^9	\( 32 q + 18 q^{5} + 18 q^{9} + 30 q^{13} - 36 q^{17} - 102 q^{21} + 86 q^{25} + 162 q^{29} + 12 q^{33} - 36 q^{41} - 186 q^{45} + 138 q^{49} - 162 q^{57} + 42 q^{61} - 198 q^{65} + 474 q^{69} - 196 q^{73} - 666 q^{77} + 462 q^{81} - 180 q^{85} + 792 q^{89} - 174 q^{93} + 64 q^{97}+O(q^{100}) \) 32 * q + 18 * q^5 + 18 * q^9 + 30 * q^13 - 36 * q^17 - 102 * q^21 + 86 * q^25 + 162 * q^29 + 12 * q^33 - 36 * q^41 - 186 * q^45 + 138 * q^49 - 162 * q^57 + 42 * q^61 - 198 * q^65 + 474 * q^69 - 196 * q^73 - 666 * q^77 + 462 * q^81 - 180 * q^85 + 792 * q^89 - 174 * q^93 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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