LMFDB - Embedded newform 576.2.bb.e.529.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(49,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("576.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bb (of order $12$, degree $4$, not 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			529.12
Character	$\chi$	$=$	576.529
Dual form			576.2.bb.e.49.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.795173 + 1.53873i) q^{3} +(-2.41406 - 0.646846i) q^{5} +(-2.82197 - 1.62927i) q^{7} +(-1.73540 + 2.44712i) q^{9} +O(q^{10})$	\(q+(0.795173 + 1.53873i) q^{3} +(-2.41406 - 0.646846i) q^{5} +(-2.82197 - 1.62927i) q^{7} +(-1.73540 + 2.44712i) q^{9} +(-0.356120 - 1.32906i) q^{11} +(1.42802 - 5.32945i) q^{13} +(-0.924273 - 4.22895i) q^{15} +5.37452 q^{17} +(-4.71269 - 4.71269i) q^{19} +(0.263051 - 5.63781i) q^{21} +(2.88877 - 1.66783i) q^{23} +(1.07916 + 0.623053i) q^{25} +(-5.14540 - 0.724438i) q^{27} +(-3.03883 + 0.814251i) q^{29} +(-0.621800 - 1.07699i) q^{31} +(1.76189 - 1.60481i) q^{33} +(5.75853 + 5.75853i) q^{35} +(-5.86087 + 5.86087i) q^{37} +(9.33612 - 2.04049i) q^{39} +(-2.81108 + 1.62298i) q^{41} +(-1.61636 - 6.03232i) q^{43} +(5.77227 - 4.78496i) q^{45} +(-2.17485 + 3.76695i) q^{47} +(1.80902 + 3.13331i) q^{49} +(4.27367 + 8.26995i) q^{51} +(-0.134334 + 0.134334i) q^{53} +3.43879i q^{55} +(3.50417 - 10.9990i) q^{57} +(2.21088 + 0.592405i) q^{59} +(-2.29879 + 0.615960i) q^{61} +(8.88426 - 4.07827i) q^{63} +(-6.89466 + 11.9419i) q^{65} +(0.0300838 - 0.112274i) q^{67} +(4.86343 + 3.11884i) q^{69} -3.21118i q^{71} -9.75441i q^{73} +(-0.100594 + 2.15597i) q^{75} +(-1.16043 + 4.33078i) q^{77} +(-1.11184 + 1.92576i) q^{79} +(-2.97677 - 8.49346i) q^{81} +(-5.74772 + 1.54010i) q^{83} +(-12.9744 - 3.47649i) q^{85} +(-3.66931 - 4.02848i) q^{87} +6.12376i q^{89} +(-12.7129 + 12.7129i) q^{91} +(1.16276 - 1.81318i) q^{93} +(8.32833 + 14.4251i) q^{95} +(-2.21495 + 3.83640i) q^{97} +(3.87037 + 1.43498i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) $ 72 * q - 2 * q^3 + 4 * q^5	$ 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) $ 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	0.795173	+	1.53873i	0.459093	+	0.888388i
$3$	0.795173	+	1.53873i	0.459093	+	0.888388i
$4$		0			0
$5$	−2.41406	−	0.646846i	−1.07960	−	0.289278i	−0.325169	−	0.945656i	$-0.605421\pi$
$5$	−2.41406	−	0.646846i	−1.07960	−	0.289278i	−0.754433	+	0.656378i	$0.772088\pi$
$6$		0			0
$7$	−2.82197	−	1.62927i	−1.06661	−	0.615805i	−0.139353	−	0.990243i	$-0.544502\pi$
$7$	−2.82197	−	1.62927i	−1.06661	−	0.615805i	−0.927252	+	0.374438i	$0.877836\pi$
$8$		0			0
$9$	−1.73540	+	2.44712i	−0.578467	+	0.815706i
$10$		0			0
$11$	−0.356120	−	1.32906i	−0.107374	−	0.400726i	0.891229	−	0.453553i	$-0.149844\pi$
$11$	−0.356120	−	1.32906i	−0.107374	−	0.400726i	−0.998604	+	0.0528265i	$0.983177\pi$
$12$		0			0
$13$	1.42802	−	5.32945i	0.396062	−	1.47812i	−0.423903	−	0.905708i	$-0.639340\pi$
$13$	1.42802	−	5.32945i	0.396062	−	1.47812i	0.819964	−	0.572415i	$-0.193993\pi$
$14$		0			0
$15$	−0.924273	−	4.22895i	−0.238646	−	1.09191i
$16$		0			0
$17$	5.37452			1.30351			0.651756	−	0.758428i	$-0.274032\pi$
$17$	5.37452			1.30351			0.651756	+	0.758428i	$0.274032\pi$
$18$		0			0
$19$	−4.71269	−	4.71269i	−1.08116	−	1.08116i	−0.996401	−	0.0847630i	$-0.972987\pi$
$19$	−4.71269	−	4.71269i	−1.08116	−	1.08116i	−0.0847630	−	0.996401i	$-0.527013\pi$
$20$		0			0
$21$	0.263051	−	5.63781i	0.0574025	−	1.23027i
$22$		0			0
$23$	2.88877	−	1.66783i	0.602351	−	0.347767i	−0.167615	−	0.985853i	$-0.553607\pi$
$23$	2.88877	−	1.66783i	0.602351	−	0.347767i	0.769966	+	0.638085i	$0.220273\pi$
$24$		0			0
$25$	1.07916	+	0.623053i	0.215832	+	0.124611i
$26$		0			0
$27$	−5.14540	−	0.724438i	−0.990234	−	0.139418i
$28$		0			0
$29$	−3.03883	+	0.814251i	−0.564296	+	0.151203i	−0.529679	−	0.848198i	$-0.677688\pi$
$29$	−3.03883	+	0.814251i	−0.564296	+	0.151203i	−0.0346168	+	0.999401i	$0.511021\pi$
$30$		0			0
$31$	−0.621800	−	1.07699i	−0.111679	−	0.193433i	0.804769	−	0.593589i	$-0.202289\pi$
$31$	−0.621800	−	1.07699i	−0.111679	−	0.193433i	−0.916447	+	0.400156i	$0.868956\pi$
$32$		0			0
$33$	1.76189	−	1.60481i	0.306706	−	0.279361i
$34$		0			0
$35$	5.75853	+	5.75853i	0.973369	+	0.973369i
$36$		0			0
$37$	−5.86087	+	5.86087i	−0.963521	+	0.963521i	−0.999358	−	0.0358368i	$-0.988590\pi$
$37$	−5.86087	+	5.86087i	−0.963521	+	0.963521i	0.0358368	+	0.999358i	$0.488590\pi$
$38$		0			0
$39$	9.33612	−	2.04049i	1.49498	−	0.326739i
$40$		0			0
$41$	−2.81108	+	1.62298i	−0.439017	+	0.253467i	−0.703181	−	0.711011i	$-0.748237\pi$
$41$	−2.81108	+	1.62298i	−0.439017	+	0.253467i	0.264163	+	0.964478i	$0.414904\pi$
$42$		0			0
$43$	−1.61636	−	6.03232i	−0.246492	−	0.919920i	−0.972628	−	0.232369i	$-0.925352\pi$
$43$	−1.61636	−	6.03232i	−0.246492	−	0.919920i	0.726136	−	0.687551i	$-0.241314\pi$
$44$		0			0
$45$	5.77227	−	4.78496i	0.860480	−	0.713299i
$46$		0			0
$47$	−2.17485	+	3.76695i	−0.317234	+	0.549466i	−0.979910	−	0.199441i	$-0.936088\pi$
$47$	−2.17485	+	3.76695i	−0.317234	+	0.549466i	0.662676	+	0.748907i	$0.269421\pi$
$48$		0			0
$49$	1.80902	+	3.13331i	0.258431	+	0.447615i
$50$		0			0
$51$	4.27367	+	8.26995i	0.598434	+	1.15803i
$52$		0			0
$53$	−0.134334	+	0.134334i	−0.0184522	+	0.0184522i	−0.716273	−	0.697820i	$-0.754153\pi$
$53$	−0.134334	+	0.134334i	−0.0184522	+	0.0184522i	0.697820	+	0.716273i	$0.254153\pi$
$54$		0			0
$55$			3.43879i			0.463686i
$56$		0			0
$57$	3.50417	−	10.9990i	0.464138	−	1.45685i
$58$		0			0
$59$	2.21088	+	0.592405i	0.287833	+	0.0771245i	0.399846	−	0.916582i	$-0.369063\pi$
$59$	2.21088	+	0.592405i	0.287833	+	0.0771245i	−0.112014	+	0.993707i	$0.535730\pi$
$60$		0			0
$61$	−2.29879	+	0.615960i	−0.294330	+	0.0788656i	−0.402963	−	0.915216i	$-0.632020\pi$
$61$	−2.29879	+	0.615960i	−0.294330	+	0.0788656i	0.108632	+	0.994082i	$0.465353\pi$
$62$		0			0
$63$	8.88426	−	4.07827i	1.11931	−	0.513813i
$64$		0			0
$65$	−6.89466	+	11.9419i	−0.855178	+	1.48121i
$66$		0			0
$67$	0.0300838	−	0.112274i	0.00367532	−	0.0137165i	−0.964064	−	0.265671i	$-0.914407\pi$
$67$	0.0300838	−	0.112274i	0.00367532	−	0.0137165i	0.967739	+	0.251954i	$0.0810733\pi$
$68$		0			0
$69$	4.86343	+	3.11884i	0.585488	+	0.375464i
$70$		0			0
$71$		−	3.21118i		−	0.381097i	−0.981678	−	0.190548i	$-0.938973\pi$
$71$		−	3.21118i		−	0.381097i	0.981678	−	0.190548i	$-0.0610266\pi$
$72$		0			0
$73$		−	9.75441i		−	1.14167i	−0.821066	−	0.570833i	$-0.806620\pi$
$73$		−	9.75441i		−	1.14167i	0.821066	−	0.570833i	$-0.193380\pi$
$74$		0			0
$75$	−0.100594	+	2.15597i	−0.0116156	+	0.248950i
$76$		0			0
$77$	−1.16043	+	4.33078i	−0.132243	+	0.493538i
$78$		0			0
$79$	−1.11184	+	1.92576i	−0.125092	+	0.216665i	−0.921769	−	0.387740i	$-0.873256\pi$
$79$	−1.11184	+	1.92576i	−0.125092	+	0.216665i	0.796677	+	0.604405i	$0.206589\pi$
$80$		0			0
$81$	−2.97677	−	8.49346i	−0.330752	−	0.943718i
$82$		0			0
$83$	−5.74772	+	1.54010i	−0.630895	+	0.169048i	−0.560076	−	0.828441i	$-0.689228\pi$
$83$	−5.74772	+	1.54010i	−0.630895	+	0.169048i	−0.0708190	+	0.997489i	$0.522561\pi$
$84$		0			0
$85$	−12.9744	−	3.47649i	−1.40727	−	0.377078i
$86$		0			0
$87$	−3.66931	−	4.02848i	−0.393391	−	0.431898i
$88$		0			0
$89$			6.12376i			0.649118i	0.945866	+	0.324559i	$0.105216\pi$
$89$			6.12376i			0.649118i	−0.945866	+	0.324559i	$0.894784\pi$
$90$		0			0
$91$	−12.7129	+	12.7129i	−1.33268	+	1.33268i
$92$		0			0
$93$	1.16276	−	1.81318i	0.120573	−	0.188018i
$94$		0			0
$95$	8.32833	+	14.4251i	0.854469	+	1.47998i
$96$		0			0
$97$	−2.21495	+	3.83640i	−0.224894	+	0.389528i	−0.956288	−	0.292428i	$-0.905537\pi$
$97$	−2.21495	+	3.83640i	−0.224894	+	0.389528i	0.731394	+	0.681956i	$0.238870\pi$
$98$		0			0
$99$	3.87037	+	1.43498i	0.388987	+	0.144221i
$100$		0			0
$101$	−4.62330	−	17.2544i	−0.460035	−	1.71688i	−0.672847	−	0.739782i	$-0.734929\pi$
$101$	−4.62330	−	17.2544i	−0.460035	−	1.71688i	0.212811	−	0.977093i	$-0.431738\pi$
$102$		0			0
$103$	8.73448	−	5.04285i	0.860634	−	0.496887i	−0.00359067	−	0.999994i	$-0.501143\pi$
$103$	8.73448	−	5.04285i	0.860634	−	0.496887i	0.864224	+	0.503106i	$0.167810\pi$
$104$		0			0
$105$	−4.28182	+	13.4399i	−0.417863	+	1.31160i
$106$		0			0
$107$	−3.59876	+	3.59876i	−0.347905	+	0.347905i	−0.859329	−	0.511423i	$-0.829118\pi$
$107$	−3.59876	+	3.59876i	−0.347905	+	0.347905i	0.511423	+	0.859329i	$0.329118\pi$
$108$		0			0
$109$	−7.27011	−	7.27011i	−0.696351	−	0.696351i	0.267271	−	0.963621i	$-0.413878\pi$
$109$	−7.27011	−	7.27011i	−0.696351	−	0.696351i	−0.963621	+	0.267271i	$0.913878\pi$
$110$		0			0
$111$	−13.6787	−	4.35791i	−1.29833	−	0.413635i
$112$		0			0
$113$	5.81099	+	10.0649i	0.546652	+	0.946828i	0.998501	+	0.0547341i	$0.0174311\pi$
$113$	5.81099	+	10.0649i	0.546652	+	0.946828i	−0.451849	+	0.892094i	$0.649236\pi$
$114$		0			0
$115$	−8.05251	+	2.15766i	−0.750900	+	0.201203i
$116$		0			0
$117$	10.5636	+	12.7433i	0.976604	+	1.17811i
$118$		0			0
$119$	−15.1667	−	8.75652i	−1.39033	−	0.802709i
$120$		0			0
$121$	7.88670	−	4.55339i	0.716973	−	0.413945i
$122$		0			0
$123$	−4.73263	−	3.03496i	−0.426727	−	0.273653i
$124$		0			0
$125$	6.63394	+	6.63394i	0.593358	+	0.593358i
$126$		0			0
$127$	7.37772			0.654667			0.327333	−	0.944909i	$-0.393850\pi$
$127$	7.37772			0.654667			0.327333	+	0.944909i	$0.393850\pi$
$128$		0			0
$129$	7.99685	−	7.28387i	0.704083	−	0.641309i
$130$		0			0
$131$	3.93512	−	14.6861i	0.343813	−	1.28313i	−0.550179	−	0.835047i	$-0.685440\pi$
$131$	3.93512	−	14.6861i	0.343813	−	1.28313i	0.893992	−	0.448082i	$-0.147893\pi$
$132$		0			0
$133$	5.62085	+	20.9773i	0.487389	+	1.81896i
$134$		0			0
$135$	11.9527	+	5.07712i	1.02873	+	0.436969i
$136$		0			0
$137$	11.5397	+	6.66247i	0.985906	+	0.569213i	0.904048	−	0.427431i	$-0.140581\pi$
$137$	11.5397	+	6.66247i	0.985906	+	0.569213i	0.0818576	+	0.996644i	$0.473915\pi$
$138$		0			0
$139$	16.2127	+	4.34417i	1.37514	+	0.368468i	0.869354	−	0.494191i	$-0.164535\pi$
$139$	16.2127	+	4.34417i	1.37514	+	0.368468i	0.505787	+	0.862658i	$0.331202\pi$
$140$		0			0
$141$	−7.52571	−	0.351138i	−0.633779	−	0.0295712i
$142$		0			0
$143$	−7.59170			−0.634849
$144$		0			0
$145$	7.86261			0.652955
$146$		0			0
$147$	−3.38285	+	5.27511i	−0.279012	+	0.435084i
$148$		0			0
$149$	12.7771	+	3.42362i	1.04674	+	0.280474i	0.740905	−	0.671610i	$-0.234397\pi$
$149$	12.7771	+	3.42362i	1.04674	+	0.280474i	0.305838	+	0.952084i	$0.401063\pi$
$150$		0			0
$151$	10.3438	+	5.97202i	0.841769	+	0.485996i	0.857865	−	0.513875i	$-0.171790\pi$
$151$	10.3438	+	5.97202i	0.841769	+	0.485996i	−0.0160959	+	0.999870i	$0.505124\pi$
$152$		0			0
$153$	−9.32695	+	13.1521i	−0.754039	+	1.06328i
$154$		0			0
$155$	0.804418	+	3.00213i	0.0646124	+	0.241137i
$156$		0			0
$157$	−3.88412	+	14.4957i	−0.309986	+	1.15689i	0.618581	+	0.785721i	$0.287708\pi$
$157$	−3.88412	+	14.4957i	−0.309986	+	1.15689i	−0.928567	+	0.371164i	$0.878959\pi$
$158$		0			0
$159$	−0.313524	−	0.0998858i	−0.0248641	−	0.00792146i
$160$		0			0
$161$	−10.8694			−0.856627
$162$		0			0
$163$	−16.4303	−	16.4303i	−1.28692	−	1.28692i	−0.936646	−	0.350278i	$-0.886087\pi$
$163$	−16.4303	−	16.4303i	−1.28692	−	1.28692i	−0.350278	−	0.936646i	$-0.613913\pi$
$164$		0			0
$165$	−5.29137	+	2.73443i	−0.411933	+	0.212875i
$166$		0			0
$167$	−11.8153	+	6.82158i	−0.914297	+	0.527870i	−0.881811	−	0.471602i	$-0.843676\pi$
$167$	−11.8153	+	6.82158i	−0.914297	+	0.527870i	−0.0324861	+	0.999472i	$0.510342\pi$
$168$		0			0
$169$	−15.1054	−	8.72112i	−1.16196	−	0.670855i
$170$		0			0
$171$	19.7109	−	3.35410i	1.50733	−	0.256494i
$172$		0			0
$173$	−4.31671	+	1.15666i	−0.328193	+	0.0879391i	−0.419153	−	0.907915i	$-0.637673\pi$
$173$	−4.31671	+	1.15666i	−0.328193	+	0.0879391i	0.0909602	+	0.995855i	$0.471006\pi$
$174$		0			0
$175$	−2.03024	−	3.51648i	−0.153472	−	0.265821i
$176$		0			0
$177$	0.846482	+	3.87303i	0.0636255	+	0.291114i
$178$		0			0
$179$	17.9090	+	17.9090i	1.33858	+	1.33858i	0.897435	+	0.441146i	$0.145428\pi$
$179$	17.9090	+	17.9090i	1.33858	+	1.33858i	0.441146	+	0.897435i	$0.354572\pi$
$180$		0			0
$181$	9.03811	−	9.03811i	0.671797	−	0.671797i	−0.286333	−	0.958130i	$-0.592436\pi$
$181$	9.03811	−	9.03811i	0.671797	−	0.671797i	0.958130	+	0.286333i	$0.0924363\pi$
$182$		0			0
$183$	−2.77574	−	3.04744i	−0.205188	−	0.225273i
$184$		0			0
$185$	17.9396	−	10.3574i	1.31894	−	0.761493i
$186$		0			0
$187$	−1.91398	−	7.14305i	−0.139964	−	0.522352i
$188$		0			0
$189$	13.3399	+	10.4276i	0.970334	+	0.758495i
$190$		0			0
$191$	−5.50837	+	9.54078i	−0.398572	+	0.690346i	−0.993550	−	0.113395i	$-0.963827\pi$
$191$	−5.50837	+	9.54078i	−0.398572	+	0.690346i	0.594978	+	0.803742i	$0.297161\pi$
$192$		0			0
$193$	−8.22204	−	14.2410i	−0.591836	−	1.02509i	−0.993985	−	0.109515i	$-0.965070\pi$
$193$	−8.22204	−	14.2410i	−0.591836	−	1.02509i	0.402149	−	0.915574i	$-0.368263\pi$
$194$		0			0
$195$	−23.8579	−	1.11317i	−1.70850	−	0.0797158i
$196$		0			0
$197$	2.20874	−	2.20874i	0.157366	−	0.157366i	−0.624033	−	0.781398i	$-0.714507\pi$
$197$	2.20874	−	2.20874i	0.157366	−	0.157366i	0.781398	+	0.624033i	$0.214507\pi$
$198$		0			0
$199$			11.9387i			0.846312i	0.906057	+	0.423156i	$0.139078\pi$
$199$			11.9387i			0.846312i	−0.906057	+	0.423156i	$0.860922\pi$
$200$		0			0
$201$	0.196682	−	0.0429865i	0.0138729	−	0.00303203i
$202$		0			0
$203$	9.90212	+	2.65326i	0.694992	+	0.186223i
$204$		0			0
$205$	7.83594	−	2.09963i	0.547286	−	0.146645i
$206$		0			0
$207$	−0.931794	+	9.96353i	−0.0647642	+	0.692513i
$208$		0			0
$209$	−4.58515	+	7.94172i	−0.317162	+	0.549340i
$210$		0			0
$211$	1.55584	−	5.80646i	0.107108	−	0.399733i	−0.891468	−	0.453084i	$-0.850324\pi$
$211$	1.55584	−	5.80646i	0.107108	−	0.399733i	0.998576	+	0.0533513i	$0.0169903\pi$
$212$		0			0
$213$	4.94115	−	2.55344i	0.338562	−	0.174959i
$214$		0			0
$215$			15.6079i			1.06445i
$216$		0			0
$217$			4.05231i			0.275089i
$218$		0			0
$219$	15.0094	−	7.75644i	1.01424	−	0.524131i
$220$		0			0
$221$	7.67493	−	28.6432i	0.516271	−	1.92675i
$222$		0			0
$223$	−4.14191	+	7.17400i	−0.277363	+	0.480407i	−0.970729	−	0.240179i	$-0.922794\pi$
$223$	−4.14191	+	7.17400i	−0.277363	+	0.480407i	0.693366	+	0.720586i	$0.256127\pi$
$224$		0			0
$225$	−3.39746	+	1.55958i	−0.226497	+	0.103972i
$226$		0			0
$227$	17.3293	−	4.64336i	1.15018	−	0.308191i	0.367145	−	0.930164i	$-0.380335\pi$
$227$	17.3293	−	4.64336i	1.15018	−	0.308191i	0.783039	+	0.621973i	$0.213669\pi$
$228$		0			0
$229$	−9.17552	−	2.45857i	−0.606335	−	0.162467i	−0.0574270	−	0.998350i	$-0.518290\pi$
$229$	−9.17552	−	2.45857i	−0.606335	−	0.162467i	−0.548908	+	0.835883i	$0.684956\pi$
$230$		0			0
$231$	−7.58666	+	1.65813i	−0.499166	+	0.109097i
$232$		0			0
$233$			6.39614i			0.419025i	0.977806	+	0.209512i	$0.0671877\pi$
$233$			6.39614i			0.419025i	−0.977806	+	0.209512i	$0.932812\pi$
$234$		0			0
$235$	7.68686	−	7.68686i	0.501435	−	0.501435i
$236$		0			0
$237$	−3.84733	−	0.179511i	−0.249911	−	0.0116605i
$238$		0			0
$239$	−12.4015	−	21.4800i	−0.802187	−	1.38943i	−0.918174	−	0.396178i	$-0.870336\pi$
$239$	−12.4015	−	21.4800i	−0.802187	−	1.38943i	0.115987	−	0.993251i	$-0.462997\pi$
$240$		0			0
$241$	4.32533	−	7.49168i	0.278619	−	0.482582i	−0.692423	−	0.721492i	$-0.743457\pi$
$241$	4.32533	−	7.49168i	0.278619	−	0.482582i	0.971042	+	0.238910i	$0.0767901\pi$
$242$		0			0
$243$	10.7021	−	11.3342i	0.686542	−	0.727090i
$244$		0			0
$245$	−2.34031	−	8.73415i	−0.149517	−	0.558005i
$246$		0			0
$247$	−31.8458	+	18.3862i	−2.02630	+	1.16989i
$248$		0			0
$249$	−6.94023	−	7.61957i	−0.439819	−	0.482871i
$250$		0			0
$251$	1.34312	−	1.34312i	0.0847772	−	0.0847772i	−0.663446	−	0.748224i	$-0.730907\pi$
$251$	1.34312	−	1.34312i	0.0847772	−	0.0847772i	0.748224	+	0.663446i	$0.230907\pi$
$252$		0			0
$253$	−3.24540	−	3.24540i	−0.204037	−	0.204037i
$254$		0			0
$255$	−4.96752	−	22.7286i	−0.311078	−	1.42332i
$256$		0			0
$257$	−13.0905	−	22.6734i	−0.816563	−	1.41433i	−0.908201	−	0.418535i	$-0.862544\pi$
$257$	−13.0905	−	22.6734i	−0.816563	−	1.41433i	0.0916380	−	0.995792i	$-0.470790\pi$
$258$		0			0
$259$	26.0881	−	6.99029i	1.62104	−	0.434356i
$260$		0			0
$261$	3.28102	−	8.84942i	0.203090	−	0.547765i
$262$		0			0
$263$	−6.75594	−	3.90054i	−0.416589	−	0.240518i	0.277028	−	0.960862i	$-0.410651\pi$
$263$	−6.75594	−	3.90054i	−0.416589	−	0.240518i	−0.693617	+	0.720344i	$0.743984\pi$
$264$		0			0
$265$	0.411185	−	0.237398i	0.0252589	−	0.0145832i
$266$		0			0
$267$	−9.42284	+	4.86945i	−0.576668	+	0.298005i
$268$		0			0
$269$	4.79063	+	4.79063i	0.292090	+	0.292090i	0.837905	−	0.545815i	$-0.183780\pi$
$269$	4.79063	+	4.79063i	0.292090	+	0.292090i	−0.545815	+	0.837905i	$0.683780\pi$
$270$		0			0
$271$	24.8625			1.51029			0.755144	−	0.655559i	$-0.227567\pi$
$271$	24.8625			1.51029			0.755144	+	0.655559i	$0.227567\pi$
$272$		0			0
$273$	−29.6708	−	9.45283i	−1.79576	−	0.572111i
$274$		0			0
$275$	0.443764	−	1.65615i	0.0267599	−	0.0998695i
$276$		0			0
$277$	−0.238901	−	0.891589i	−0.0143541	−	0.0535704i	0.958377	−	0.285505i	$-0.0921612\pi$
$277$	−0.238901	−	0.891589i	−0.0143541	−	0.0535704i	−0.972731	+	0.231934i	$0.925495\pi$
$278$		0			0
$279$	3.71459	+	0.347390i	0.222387	+	0.0207977i
$280$		0			0
$281$	−24.6632	−	14.2393i	−1.47128	−	0.849446i	−0.471804	−	0.881703i	$-0.656397\pi$
$281$	−24.6632	−	14.2393i	−1.47128	−	0.849446i	−0.999480	+	0.0322571i	$0.989730\pi$
$282$		0			0
$283$	−6.41436	−	1.71872i	−0.381294	−	0.102167i	0.0630806	−	0.998008i	$-0.479907\pi$
$283$	−6.41436	−	1.71872i	−0.381294	−	0.102167i	−0.444375	+	0.895841i	$0.646574\pi$
$284$		0			0
$285$	−15.5739	+	24.2855i	−0.922519	+	1.43855i
$286$		0			0
$287$	10.5771			0.624344
$288$		0			0
$289$	11.8855			0.699145
$290$		0			0
$291$	−7.66447	−	0.357612i	−0.449299	−	0.0209636i
$292$		0			0
$293$	−9.42116	−	2.52439i	−0.550390	−	0.147477i	−0.0271023	−	0.999633i	$-0.508628\pi$
$293$	−9.42116	−	2.52439i	−0.550390	−	0.147477i	−0.523288	+	0.852156i	$0.675295\pi$
$294$		0			0
$295$	−4.95402	−	2.86020i	−0.288434	−	0.166527i
$296$		0			0
$297$	0.869562	+	7.09653i	0.0504571	+	0.411783i
$298$		0			0
$299$	−4.76340	−	17.7773i	−0.275475	−	1.02809i
$300$		0			0
$301$	−5.26694	+	19.6565i	−0.303582	+	1.13298i
$302$		0			0
$303$	22.8736	−	20.8342i	1.31405	−	1.19690i
$304$		0			0
$305$	5.94786			0.340574
$306$		0			0
$307$	4.55233	+	4.55233i	0.259815	+	0.259815i	0.824979	−	0.565164i	$-0.191187\pi$
$307$	4.55233	+	4.55233i	0.259815	+	0.259815i	−0.565164	+	0.824979i	$0.691187\pi$
$308$		0			0
$309$	14.7050	+	9.43010i	0.836540	+	0.536459i
$310$		0			0
$311$	5.56997	−	3.21582i	0.315844	−	0.182353i	−0.333695	−	0.942681i	$-0.608295\pi$
$311$	5.56997	−	3.21582i	0.315844	−	0.182353i	0.649539	+	0.760329i	$0.274962\pi$
$312$		0			0
$313$	−2.90181	−	1.67536i	−0.164020	−	0.0946969i	0.415743	−	0.909482i	$-0.363522\pi$
$313$	−2.90181	−	1.67536i	−0.164020	−	0.0946969i	−0.579763	+	0.814785i	$0.696855\pi$
$314$		0			0
$315$	−24.0852	+	4.09844i	−1.35705	+	0.230921i
$316$		0			0
$317$	−14.6346	+	3.92134i	−0.821963	+	0.220244i	−0.645204	−	0.764010i	$-0.723228\pi$
$317$	−14.6346	+	3.92134i	−0.821963	+	0.220244i	−0.176758	+	0.984254i	$0.556561\pi$
$318$		0			0
$319$	2.16438	+	3.74881i	0.121182	+	0.209893i
$320$		0			0
$321$	−8.39917	−	2.67590i	−0.468796	−	0.149354i
$322$		0			0
$323$	−25.3284	−	25.3284i	−1.40931	−	1.40931i
$324$		0			0
$325$	4.86159	−	4.86159i	0.269672	−	0.269672i
$326$		0			0
$327$	5.40577	−	16.9678i	0.298940	−	0.938319i
$328$		0			0
$329$	12.2747	−	7.08682i	0.676728	−	0.390709i
$330$		0			0
$331$	2.68206	+	10.0096i	0.147420	+	0.550177i	0.999636	+	0.0269876i	$0.00859146\pi$
$331$	2.68206	+	10.0096i	0.147420	+	0.550177i	−0.852216	+	0.523190i	$0.824742\pi$
$332$		0			0
$333$	−4.17128	−	24.5132i	−0.228585	−	1.34331i
$334$		0			0
$335$	−0.145248	+	0.251578i	−0.00793577	+	0.0137452i
$336$		0			0
$337$	6.52225	+	11.2969i	0.355289	+	0.615379i	0.987167	−	0.159689i	$-0.0510490\pi$
$337$	6.52225	+	11.2969i	0.355289	+	0.615379i	−0.631878	+	0.775068i	$0.717716\pi$
$338$		0			0
$339$	−10.8665	+	16.9449i	−0.590187	+	0.920321i
$340$		0			0
$341$	−1.20995	+	1.20995i	−0.0655223	+	0.0655223i
$342$		0			0
$343$			11.0203i			0.595038i
$344$		0			0
$345$	−9.72320	−	10.6750i	−0.523480	−	0.574720i
$346$		0			0
$347$	−23.5314	−	6.30523i	−1.26323	−	0.338482i	−0.435798	−	0.900044i	$-0.643534\pi$
$347$	−23.5314	−	6.30523i	−1.26323	−	0.338482i	−0.827435	+	0.561562i	$0.810201\pi$
$348$		0			0
$349$	27.7772	−	7.44289i	1.48688	−	0.398409i	0.578199	−	0.815896i	$-0.303756\pi$
$349$	27.7772	−	7.44289i	1.48688	−	0.398409i	0.908683	+	0.417487i	$0.137089\pi$
$350$		0			0
$351$	−11.2086	+	26.3876i	−0.598271	+	1.40847i
$352$		0			0
$353$	17.6048	−	30.4924i	0.937010	−	1.62295i	0.165999	−	0.986126i	$-0.446915\pi$
$353$	17.6048	−	30.4924i	0.937010	−	1.62295i	0.771011	−	0.636822i	$-0.219752\pi$
$354$		0			0
$355$	−2.07714	+	7.75199i	−0.110243	+	0.411433i
$356$		0			0
$357$	1.41378	−	30.3005i	0.0748249	−	1.60367i
$358$		0			0
$359$		−	17.6127i		−	0.929564i	−0.885425	−	0.464782i	$-0.846133\pi$
$359$		−	17.6127i		−	0.929564i	0.885425	−	0.464782i	$-0.153867\pi$
$360$		0			0
$361$			25.4188i			1.33783i
$362$		0			0
$363$	13.2777	+	8.51480i	0.696901	+	0.446911i
$364$		0			0
$365$	−6.30960	+	23.5477i	−0.330259	+	1.23255i
$366$		0			0
$367$	8.31959	−	14.4100i	0.434279	−	0.752193i	−0.562957	−	0.826486i	$-0.690337\pi$
$367$	8.31959	−	14.4100i	0.434279	−	0.752193i	0.997236	+	0.0742925i	$0.0236698\pi$
$368$		0			0
$369$	0.906734	−	9.69556i	0.0472027	−	0.504731i
$370$		0			0
$371$	0.597954	−	0.160221i	0.0310442	−	0.00831828i
$372$		0			0
$373$	−3.22714	−	0.864710i	−0.167095	−	0.0447730i	0.174302	−	0.984692i	$-0.444233\pi$
$373$	−3.22714	−	0.864710i	−0.167095	−	0.0447730i	−0.341397	+	0.939919i	$0.610900\pi$
$374$		0			0
$375$	−4.93274	+	15.4830i	−0.254726	+	0.799539i
$376$		0			0
$377$			17.3580i			0.893984i
$378$		0			0
$379$	10.2384	−	10.2384i	0.525910	−	0.525910i	−0.393440	−	0.919350i	$-0.628715\pi$
$379$	10.2384	−	10.2384i	0.525910	−	0.525910i	0.919350	+	0.393440i	$0.128715\pi$
$380$		0			0
$381$	5.86656	+	11.3523i	0.300553	+	0.581598i
$382$		0			0
$383$	−5.44755	−	9.43544i	−0.278357	−	0.482128i	0.692620	−	0.721303i	$-0.256456\pi$
$383$	−5.44755	−	9.43544i	−0.278357	−	0.482128i	−0.970977	+	0.239175i	$0.923123\pi$
$384$		0			0
$385$	5.60270	−	9.70416i	0.285540	−	0.494570i
$386$		0			0
$387$	17.5668	+	6.51308i	0.892971	+	0.331079i
$388$		0			0
$389$	3.72849	+	13.9149i	0.189042	+	0.705513i	0.993729	+	0.111815i	$0.0356663\pi$
$389$	3.72849	+	13.9149i	0.189042	+	0.705513i	−0.804687	+	0.593699i	$0.797667\pi$
$390$		0			0
$391$	15.5258	−	8.96381i	0.785172	−	0.453319i
$392$		0			0
$393$	25.7271	−	5.62287i	1.29776	−	0.283636i
$394$		0			0
$395$	3.92972	−	3.92972i	0.197725	−	0.197725i
$396$		0			0
$397$	15.4247	+	15.4247i	0.774145	+	0.774145i	0.978828	−	0.204683i	$-0.0656165\pi$
$397$	15.4247	+	15.4247i	0.774145	+	0.774145i	−0.204683	+	0.978828i	$0.565616\pi$
$398$		0			0
$399$	−27.8089	+	25.3295i	−1.39219	+	1.26806i
$400$		0			0
$401$	−3.21720	−	5.57235i	−0.160659	−	0.278270i	0.774446	−	0.632640i	$-0.218029\pi$
$401$	−3.21720	−	5.57235i	−0.160659	−	0.278270i	−0.935105	+	0.354370i	$0.884695\pi$
$402$		0			0
$403$	−6.62770	+	1.77589i	−0.330149	+	0.0884633i
$404$		0			0
$405$	1.69214	+	22.4292i	0.0840832	+	1.11452i
$406$		0			0
$407$	9.87661	+	5.70227i	0.489566	+	0.282651i
$408$		0			0
$409$	31.8642	−	18.3968i	1.57558	−	0.909663i	0.580117	−	0.814533i	$-0.303007\pi$
$409$	31.8642	−	18.3968i	1.57558	−	0.909663i	0.995465	−	0.0951294i	$-0.0303265\pi$
$410$		0			0
$411$	−1.07568	+	23.0544i	−0.0530594	+	1.13719i
$412$		0			0
$413$	−5.27387	−	5.27387i	−0.259510	−	0.259510i
$414$		0			0
$415$	14.8716			0.730017
$416$		0			0
$417$	6.20735	+	28.4013i	0.303975	+	1.39082i
$418$		0			0
$419$	5.78093	−	21.5747i	0.282417	−	1.05399i	−0.668290	−	0.743901i	$-0.732973\pi$
$419$	5.78093	−	21.5747i	0.282417	−	1.05399i	0.950706	−	0.310093i	$-0.100360\pi$
$420$		0			0
$421$	2.33477	+	8.71347i	0.113790	+	0.424669i	0.999194	−	0.0401539i	$-0.0127848\pi$
$421$	2.33477	+	8.71347i	0.113790	+	0.424669i	−0.885404	+	0.464822i	$0.846118\pi$
$422$		0			0
$423$	−5.44393	−	11.8593i	−0.264693	−	0.576618i
$424$		0			0
$425$	5.79996	+	3.34861i	0.281340	+	0.162431i
$426$		0			0
$427$	7.49070	+	2.00713i	0.362500	+	0.0971316i
$428$		0			0
$429$	−6.03671	−	11.6816i	−0.291455	−	0.563993i
$430$		0			0
$431$	2.82883			0.136260			0.0681299	−	0.997676i	$-0.478297\pi$
$431$	2.82883			0.136260			0.0681299	+	0.997676i	$0.478297\pi$
$432$		0			0
$433$	−9.90919			−0.476205			−0.238103	−	0.971240i	$-0.576525\pi$
$433$	−9.90919			−0.476205			−0.238103	+	0.971240i	$0.576525\pi$
$434$		0			0
$435$	6.25214	+	12.0985i	0.299767	+	0.580077i
$436$		0			0
$437$	−21.4739	−	5.75390i	−1.02723	−	0.275246i
$438$		0			0
$439$	−5.53112	−	3.19339i	−0.263986	−	0.152412i	0.362166	−	0.932114i	$-0.382037\pi$
$439$	−5.53112	−	3.19339i	−0.263986	−	0.152412i	−0.626151	+	0.779701i	$0.715371\pi$
$440$		0			0
$441$	−10.8069	−	1.01067i	−0.514616	−	0.0481272i
$442$		0			0
$443$	4.33005	+	16.1600i	0.205727	+	0.767783i	0.989227	+	0.146391i	$0.0467658\pi$
$443$	4.33005	+	16.1600i	0.205727	+	0.767783i	−0.783500	+	0.621392i	$0.786568\pi$
$444$		0			0
$445$	3.96113	−	14.7831i	0.187776	−	0.700788i
$446$		0			0
$447$	4.89198	+	22.3830i	0.231383	+	1.05868i
$448$		0			0
$449$	−23.7209			−1.11946			−0.559729	−	0.828676i	$-0.689095\pi$
$449$	−23.7209			−1.11946			−0.559729	+	0.828676i	$0.689095\pi$
$450$		0			0
$451$	3.15812	+	3.15812i	0.148710	+	0.148710i
$452$		0			0
$453$	−0.964205	+	20.6652i	−0.0453023	+	0.970935i
$454$		0			0
$455$	38.9131	−	22.4665i	1.82427	−	1.05324i
$456$		0			0
$457$	−25.8782	−	14.9408i	−1.21053	−	0.698901i	−0.247657	−	0.968848i	$-0.579661\pi$
$457$	−25.8782	−	14.9408i	−1.21053	−	0.698901i	−0.962875	+	0.269946i	$0.912994\pi$
$458$		0			0
$459$	−27.6541	−	3.89351i	−1.29078	−	0.181733i
$460$		0			0
$461$	26.9785	−	7.22887i	1.25651	−	0.336682i	0.431665	−	0.902034i	$-0.357926\pi$
$461$	26.9785	−	7.22887i	1.25651	−	0.336682i	0.824850	+	0.565352i	$0.191260\pi$
$462$		0			0
$463$	−9.00954	−	15.6050i	−0.418709	−	0.725225i	0.577101	−	0.816673i	$-0.304184\pi$
$463$	−9.00954	−	15.6050i	−0.418709	−	0.725225i	−0.995810	+	0.0914480i	$0.970850\pi$
$464$		0			0
$465$	−3.97982	+	3.62500i	−0.184560	+	0.168105i
$466$		0			0
$467$	−3.24566	−	3.24566i	−0.150191	−	0.150191i	0.628012	−	0.778204i	$-0.283869\pi$
$467$	−3.24566	−	3.24566i	−0.150191	−	0.150191i	−0.778204	+	0.628012i	$0.783869\pi$
$468$		0			0
$469$	−0.267820	+	0.267820i	−0.0123668	+	0.0123668i
$470$		0			0
$471$	−25.3936	+	5.54998i	−1.17008	+	0.255730i
$472$		0			0
$473$	−7.44169	+	4.29646i	−0.342169	+	0.197552i
$474$		0			0
$475$	−2.14949	−	8.02199i	−0.0986252	−	0.368074i
$476$		0			0
$477$	−0.0956080	−	0.561856i	−0.00437759	−	0.0257256i
$478$		0			0
$479$	1.27156	−	2.20241i	0.0580991	−	0.100631i	−0.835513	−	0.549471i	$-0.814829\pi$
$479$	1.27156	−	2.20241i	0.0580991	−	0.100631i	0.893612	+	0.448840i	$0.148163\pi$
$480$		0			0
$481$	22.8657	+	39.6046i	1.04259	+	1.80582i
$482$		0			0
$483$	−8.64304	−	16.7251i	−0.393272	−	0.761018i
$484$		0			0
$485$	7.82859	−	7.82859i	0.355478	−	0.355478i
$486$		0			0
$487$		−	26.4554i		−	1.19881i	−0.800447	−	0.599404i	$-0.795404\pi$
$487$		−	26.4554i		−	1.19881i	0.800447	−	0.599404i	$-0.204596\pi$
$488$		0			0
$489$	12.2170	−	38.3469i	0.552470	−	1.73411i
$490$		0			0
$491$	21.9322	+	5.87672i	0.989787	+	0.265213i	0.717161	−	0.696907i	$-0.245441\pi$
$491$	21.9322	+	5.87672i	0.989787	+	0.265213i	0.272626	+	0.962120i	$0.412108\pi$
$492$		0			0
$493$	−16.3322	+	4.37621i	−0.735567	+	0.197095i
$494$		0			0
$495$	−8.41511	−	5.96767i	−0.378231	−	0.268227i
$496$		0			0
$497$	−5.23187	+	9.06186i	−0.234681	+	0.406480i
$498$		0			0
$499$	−7.34516	+	27.4125i	−0.328815	+	1.22715i	0.581606	+	0.813470i	$0.302424\pi$
$499$	−7.34516	+	27.4125i	−0.328815	+	1.22715i	−0.910421	+	0.413683i	$0.864242\pi$
$500$		0			0
$501$	−19.8918	−	12.7563i	−0.888701	−	0.569910i
$502$		0			0
$503$			32.0583i			1.42941i	0.699427	+	0.714704i	$0.253439\pi$
$503$			32.0583i			1.42941i	−0.699427	+	0.714704i	$0.746561\pi$
$504$		0			0
$505$			44.6437i			1.98662i
$506$		0			0
$507$	1.40806	−	30.1780i	0.0625341	−	1.34025i
$508$		0			0
$509$	7.15242	−	26.6932i	0.317025	−	1.18316i	−0.605064	−	0.796177i	$-0.706852\pi$
$509$	7.15242	−	26.6932i	0.317025	−	1.18316i	0.922089	−	0.386978i	$-0.126481\pi$
$510$		0			0
$511$	−15.8925	+	27.5267i	−0.703044	+	1.21771i
$512$		0			0
$513$	20.8346	+	27.6627i	0.919871	+	1.22134i
$514$		0			0
$515$	−24.3475	+	6.52390i	−1.07288	+	0.287477i
$516$		0			0
$517$	5.78101	+	1.54902i	0.254248	+	0.0681256i
$518$		0			0
$519$	−5.21232	−	5.72252i	−0.228795	−	0.251191i
$520$		0			0
$521$			6.90291i			0.302422i	0.988502	+	0.151211i	$0.0483173\pi$
$521$			6.90291i			0.302422i	−0.988502	+	0.151211i	$0.951683\pi$
$522$		0			0
$523$	−14.2754	+	14.2754i	−0.624219	+	0.624219i	−0.946607	−	0.322389i	$-0.895514\pi$
$523$	−14.2754	+	14.2754i	−0.624219	+	0.624219i	0.322389	+	0.946607i	$0.395514\pi$
$524$		0			0
$525$	3.79653	−	5.92020i	0.165694	−	0.258379i
$526$		0			0
$527$	−3.34188	−	5.78830i	−0.145574	−	0.252142i
$528$		0			0
$529$	−5.93666	+	10.2826i	−0.258116	+	0.447069i
$530$		0			0
$531$	−5.28645	+	4.38223i	−0.229413	+	0.190173i
$532$		0			0
$533$	4.63529	+	17.2992i	0.200777	+	0.749310i
$534$		0			0
$535$	11.0155	−	6.35979i	0.476241	−	0.274958i
$536$		0			0
$537$	−13.3164	+	41.7979i	−0.574646	+	1.80371i
$538$		0			0
$539$	3.52012	−	3.52012i	0.151622	−	0.151622i
$540$		0			0
$541$	−15.3215	−	15.3215i	−0.658723	−	0.658723i	0.296355	−	0.955078i	$-0.404229\pi$
$541$	−15.3215	−	15.3215i	−0.658723	−	0.658723i	−0.955078	+	0.296355i	$0.904229\pi$
$542$		0			0
$543$	21.0941	+	6.72038i	0.905234	+	0.288399i
$544$		0			0
$545$	12.8479	+	22.2532i	0.550342	+	0.953220i
$546$		0			0
$547$	−4.09038	+	1.09601i	−0.174892	+	0.0468622i	−0.345202	−	0.938528i	$-0.612190\pi$
$547$	−4.09038	+	1.09601i	−0.174892	+	0.0468622i	0.170310	+	0.985390i	$0.445523\pi$
$548$		0			0
$549$	2.48200	−	6.69436i	0.105929	−	0.285708i
$550$		0			0
$551$	18.1584	+	10.4837i	0.773572	+	0.446622i
$552$		0			0
$553$	6.27515	−	3.62296i	0.266847	−	0.154064i
$554$		0			0
$555$	30.2024	+	19.3683i	1.28202	+	0.822138i
$556$		0			0
$557$	3.77104	+	3.77104i	0.159784	+	0.159784i	0.782471	−	0.622687i	$-0.213959\pi$
$557$	3.77104	+	3.77104i	0.159784	+	0.159784i	−0.622687	+	0.782471i	$0.713959\pi$
$558$		0			0
$559$	−34.4571			−1.45738
$560$		0			0
$561$	9.46931	−	8.62506i	0.399795	−	0.364150i
$562$		0			0
$563$	−4.72321	+	17.6273i	−0.199060	+	0.742901i	0.792119	+	0.610367i	$0.208978\pi$
$563$	−4.72321	+	17.6273i	−0.199060	+	0.742901i	−0.991178	+	0.132534i	$0.957689\pi$
$564$		0			0
$565$	−7.51763	−	28.0562i	−0.316269	−	1.18033i
$566$		0			0
$567$	−5.43775	+	28.8182i	−0.228364	+	1.21025i
$568$		0			0
$569$	−10.5687	−	6.10184i	−0.443062	−	0.255802i	0.261833	−	0.965113i	$-0.415673\pi$
$569$	−10.5687	−	6.10184i	−0.443062	−	0.255802i	−0.704896	+	0.709311i	$0.749006\pi$
$570$		0			0
$571$	−10.1445	−	2.71820i	−0.424533	−	0.113753i	0.0402258	−	0.999191i	$-0.487192\pi$
$571$	−10.1445	−	2.71820i	−0.424533	−	0.113753i	−0.464759	+	0.885437i	$0.653859\pi$
$572$		0			0
$573$	−19.0608	−	0.889348i	−0.796277	−	0.0371531i
$574$		0			0
$575$	4.15660			0.173342
$576$		0			0
$577$	−11.0011			−0.457982			−0.228991	−	0.973429i	$-0.573543\pi$
$577$	−11.0011			−0.457982			−0.228991	+	0.973429i	$0.573543\pi$
$578$		0			0
$579$	15.3752	−	23.9756i	0.638970	−	0.996391i
$580$		0			0
$581$	18.7291	+	5.01846i	0.777016	+	0.208201i
$582$		0			0
$583$	0.226378	+	0.130699i	0.00937560	+	0.00541300i
$584$		0			0
$585$	−17.2582	−	37.5960i	−0.713540	−	1.55440i
$586$		0			0
$587$	4.43586	+	16.5549i	0.183088	+	0.683292i	0.995032	+	0.0995570i	$0.0317426\pi$
$587$	4.43586	+	16.5549i	0.183088	+	0.683292i	−0.811944	+	0.583735i	$0.801591\pi$
$588$		0			0
$589$	−2.14516	+	8.00586i	−0.0883900	+	0.329876i
$590$		0			0
$591$	5.15498	+	1.64233i	0.212048	+	0.0675564i
$592$		0			0
$593$	38.5906			1.58472			0.792362	−	0.610051i	$-0.208851\pi$
$593$	38.5906			1.58472			0.792362	+	0.610051i	$0.208851\pi$
$594$		0			0
$595$	30.9493	+	30.9493i	1.26880	+	1.26880i
$596$		0			0
$597$	−18.3705	+	9.49332i	−0.751853	+	0.388536i
$598$		0			0
$599$	4.83678	−	2.79252i	0.197626	−	0.114099i	−0.397922	−	0.917419i	$-0.630268\pi$
$599$	4.83678	−	2.79252i	0.197626	−	0.114099i	0.595547	+	0.803320i	$0.296935\pi$
$600$		0			0
$601$	29.8602	+	17.2398i	1.21802	+	0.703227i	0.964495	−	0.264101i	$-0.0850753\pi$
$601$	29.8602	+	17.2398i	1.21802	+	0.703227i	0.253529	+	0.967328i	$0.418409\pi$
$602$		0			0
$603$	0.222541	+	0.268460i	0.00906257	+	0.0109325i
$604$		0			0
$605$	−21.9843	+	5.89068i	−0.893790	+	0.239490i
$606$		0			0
$607$	−7.58467	−	13.1370i	−0.307852	−	0.533216i	0.670040	−	0.742325i	$-0.266277\pi$
$607$	−7.58467	−	13.1370i	−0.307852	−	0.533216i	−0.977892	+	0.209109i	$0.932944\pi$
$608$		0			0
$609$	3.79123	+	17.3465i	0.153628	+	0.702917i
$610$		0			0
$611$	16.9700	+	16.9700i	0.686534	+	0.686534i
$612$		0			0
$613$	7.90551	−	7.90551i	0.319301	−	0.319301i	−0.529198	−	0.848498i	$-0.677507\pi$
$613$	7.90551	−	7.90551i	0.319301	−	0.319301i	0.848498	+	0.529198i	$0.177507\pi$
$614$		0			0
$615$	9.46170	+	10.3879i	0.381533	+	0.418879i
$616$		0			0
$617$	−25.0266	+	14.4491i	−1.00753	+	0.581700i	−0.910468	−	0.413578i	$-0.864279\pi$
$617$	−25.0266	+	14.4491i	−1.00753	+	0.581700i	−0.0970648	+	0.995278i	$0.530945\pi$
$618$		0			0
$619$	−8.96627	−	33.4626i	−0.360385	−	1.34497i	−0.873571	−	0.486697i	$-0.838202\pi$
$619$	−8.96627	−	33.4626i	−0.360385	−	1.34497i	0.513186	−	0.858277i	$-0.328465\pi$
$620$		0			0
$621$	−16.0722	+	6.48894i	−0.644953	+	0.260392i
$622$		0			0
$623$	9.97724	−	17.2811i	0.399730	−	0.692352i
$624$		0			0
$625$	−14.8389	−	25.7017i	−0.593555	−	1.02807i
$626$		0			0
$627$	−15.8662	−	0.740291i	−0.633634	−	0.0295644i
$628$		0			0
$629$	−31.4994	+	31.4994i	−1.25596	+	1.25596i
$630$		0			0
$631$		−	30.4132i		−	1.21073i	−0.795948	−	0.605365i	$-0.793027\pi$
$631$		−	30.4132i		−	1.21073i	0.795948	−	0.605365i	$-0.206973\pi$
$632$		0			0
$633$	10.1717	−	2.22312i	0.404291	−	0.0883611i
$634$		0			0
$635$	−17.8103	−	4.77225i	−0.706779	−	0.189381i
$636$		0			0
$637$	19.2821	−	5.16663i	0.763985	−	0.204709i
$638$		0			0
$639$	7.85814	+	5.57269i	0.310863	+	0.220452i
$640$		0			0
$641$	−6.19753	+	10.7344i	−0.244788	+	0.423985i	−0.962072	−	0.272796i	$-0.912052\pi$
$641$	−6.19753	+	10.7344i	−0.244788	+	0.423985i	0.717284	+	0.696781i	$0.245385\pi$
$642$		0			0
$643$	−6.97693	+	26.0383i	−0.275143	+	1.02685i	0.680602	+	0.732653i	$0.261718\pi$
$643$	−6.97693	+	26.0383i	−0.275143	+	1.02685i	−0.955745	+	0.294195i	$0.904948\pi$
$644$		0			0
$645$	−24.0164	+	12.4110i	−0.945646	+	0.488682i
$646$		0			0
$647$			1.44109i			0.0566551i	0.999599	+	0.0283275i	$0.00901814\pi$
$647$			1.44109i			0.0566551i	−0.999599	+	0.0283275i	$0.990982\pi$
$648$		0			0
$649$		−	3.14936i		−	0.123623i
$650$		0			0
$651$	−6.23543	+	3.22229i	−0.244386	+	0.126291i
$652$		0			0
$653$	3.87857	−	14.4750i	0.151780	−	0.566451i	−0.847580	−	0.530668i	$-0.821941\pi$
$653$	3.87857	−	14.4750i	0.151780	−	0.566451i	0.999360	−	0.0357824i	$-0.0113923\pi$
$654$		0			0
$655$	−18.9993	+	32.9077i	−0.742363	+	1.28581i
$656$		0			0
$657$	23.8702	+	16.9278i	0.931264	+	0.660417i
$658$		0			0
$659$	5.05876	−	1.35549i	0.197061	−	0.0528024i	−0.158938	−	0.987289i	$-0.550807\pi$
$659$	5.05876	−	1.35549i	0.197061	−	0.0528024i	0.356000	+	0.934486i	$0.384140\pi$
$660$		0			0
$661$	19.8188	+	5.31043i	0.770862	+	0.206552i	0.622752	−	0.782419i	$-0.286014\pi$
$661$	19.8188	+	5.31043i	0.770862	+	0.206552i	0.148110	+	0.988971i	$0.452681\pi$
$662$		0			0
$663$	50.1772	−	10.9666i	1.94872	−	0.425909i
$664$		0			0
$665$		−	54.2763i		−	2.10474i
$666$		0			0
$667$	−7.42045	+	7.42045i	−0.287321	+	0.287321i
$668$		0			0
$669$	−14.3324	−	0.668728i	−0.554123	−	0.0258545i
$670$		0			0
$671$	1.63729	+	2.83588i	0.0632071	+	0.109478i
$672$		0			0
$673$	7.01009	−	12.1418i	0.270219	−	0.468033i	−0.698699	−	0.715416i	$-0.746237\pi$
$673$	7.01009	−	12.1418i	0.270219	−	0.468033i	0.968918	+	0.247383i	$0.0795706\pi$
$674$		0			0
$675$	−5.10135	−	3.98764i	−0.196351	−	0.153484i
$676$		0			0
$677$	4.35650	+	16.2587i	0.167434	+	0.624872i	0.997717	+	0.0675306i	$0.0215120\pi$
$677$	4.35650	+	16.2587i	0.167434	+	0.624872i	−0.830283	+	0.557342i	$0.811821\pi$
$678$		0			0
$679$	12.5010	−	7.21748i	0.479746	−	0.276982i
$680$		0			0
$681$	20.9247	+	22.9728i	0.801834	+	0.880321i
$682$		0			0
$683$	−26.6987	+	26.6987i	−1.02160	+	1.02160i	−0.0218370	+	0.999762i	$0.506951\pi$
$683$	−26.6987	+	26.6987i	−1.02160	+	1.02160i	−0.999762	+	0.0218370i	$0.993049\pi$
$684$		0			0
$685$	−23.5480	−	23.5480i	−0.899724	−	0.899724i
$686$		0			0
$687$	−3.51303	−	16.0737i	−0.134031	−	0.613248i
$688$		0			0
$689$	0.524096	+	0.907760i	0.0199665	+	0.0345829i
$690$		0			0
$691$	28.2719	−	7.57544i	1.07551	−	0.288183i	0.322757	−	0.946482i	$-0.395390\pi$
$691$	28.2719	−	7.57544i	1.07551	−	0.288183i	0.752757	+	0.658299i	$0.228724\pi$
$692$		0			0
$693$	−8.58412	−	10.3553i	−0.326084	−	0.393367i
$694$		0			0
$695$	−36.3284	−	20.9742i	−1.37801	−	0.795597i
$696$		0			0
$697$	−15.1082	+	8.72273i	−0.572264	+	0.330397i
$698$		0			0
$699$	−9.84195	+	5.08603i	−0.372257	+	0.192371i
$700$		0			0
$701$	−28.6250	−	28.6250i	−1.08115	−	1.08115i	−0.996402	−	0.0847476i	$-0.972992\pi$
$701$	−28.6250	−	28.6250i	−1.08115	−	1.08115i	−0.0847476	−	0.996402i	$-0.527008\pi$
$702$		0			0
$703$	55.2409			2.08345
$704$		0			0
$705$	17.9404	+	5.71565i	0.675675	+	0.215264i
$706$		0			0
$707$	−15.0652	+	56.2240i	−0.566584	+	2.11452i
$708$		0			0
$709$	6.98798	+	26.0795i	0.262439	+	0.979437i	0.963799	+	0.266629i	$0.0859099\pi$
$709$	6.98798	+	26.0795i	0.262439	+	0.979437i	−0.701360	+	0.712807i	$0.747423\pi$
$710$		0			0
$711$	−2.78308	−	6.06276i	−0.104374	−	0.227371i
$712$		0			0
$713$	−3.59248	−	2.07412i	−0.134539	−	0.0776764i
$714$		0			0
$715$	18.3268	+	4.91066i	0.685384	+	0.183648i
$716$		0			0
$717$	23.1907	−	36.1630i	0.866073	−	1.35053i
$718$		0			0
$719$	−3.06518			−0.114312			−0.0571560	−	0.998365i	$-0.518203\pi$
$719$	−3.06518			−0.114312			−0.0571560	+	0.998365i	$0.518203\pi$
$720$		0			0
$721$	−32.8646			−1.22394
$722$		0			0
$723$	14.9671	+	0.698341i	0.556632	+	0.0259716i
$724$		0			0
$725$	−3.78670	−	1.01464i	−0.140635	−	0.0376829i
$726$		0			0
$727$	12.5849	+	7.26589i	0.466748	+	0.269477i	0.714877	−	0.699250i	$-0.246483\pi$
$727$	12.5849	+	7.26589i	0.466748	+	0.269477i	−0.248130	+	0.968727i	$0.579816\pi$
$728$		0			0
$729$	25.9504	+	7.45506i	0.961125	+	0.276113i
$730$		0			0
$731$	−8.68713	−	32.4208i	−0.321305	−	1.19913i
$732$		0			0
$733$	−1.26777	+	4.73140i	−0.0468263	+	0.174758i	−0.985379	−	0.170379i	$-0.945501\pi$
$733$	−1.26777	+	4.73140i	−0.0468263	+	0.174758i	0.938552	+	0.345137i	$0.112168\pi$
$734$		0			0
$735$	11.5786	−	10.5463i	0.427083	−	0.389005i
$736$		0			0
$737$	−0.159933			−0.00589119
$738$		0			0
$739$	−27.6544	−	27.6544i	−1.01728	−	1.01728i	−0.999848	−	0.0174359i	$-0.994450\pi$
$739$	−27.6544	−	27.6544i	−1.01728	−	1.01728i	−0.0174359	−	0.999848i	$-0.505550\pi$
$740$		0			0
$741$	−53.6144	−	34.3820i	−1.96957	−	1.26306i
$742$		0			0
$743$	−16.0882	+	9.28853i	−0.590219	+	0.340763i	−0.765184	−	0.643812i	$-0.777352\pi$
$743$	−16.0882	+	9.28853i	−0.590219	+	0.340763i	0.174965	+	0.984575i	$0.444019\pi$
$744$		0			0
$745$	−28.6302	−	16.5297i	−1.04893	−	0.605600i
$746$		0			0
$747$	6.20580	−	16.7380i	0.227059	−	0.612413i
$748$		0			0
$749$	16.0189	−	4.29226i	0.585320	−	0.156836i
$750$		0			0
$751$	−17.4576	−	30.2374i	−0.637037	−	1.10338i	−0.986080	−	0.166273i	$-0.946827\pi$
$751$	−17.4576	−	30.2374i	−0.637037	−	1.10338i	0.349043	−	0.937107i	$-0.386507\pi$
$752$		0			0
$753$	3.13473	+	0.998694i	0.114236	+	0.0363944i
$754$		0			0
$755$	−21.1077	−	21.1077i	−0.768187	−	0.768187i
$756$		0			0
$757$	15.4255	−	15.4255i	0.560649	−	0.560649i	−0.368843	−	0.929492i	$-0.620246\pi$
$757$	15.4255	−	15.4255i	0.560649	−	0.560649i	0.929492	+	0.368843i	$0.120246\pi$
$758$		0			0
$759$	2.41315	−	7.57446i	0.0875919	−	0.274935i
$760$		0			0
$761$	14.7108	−	8.49331i	0.533268	−	0.307882i	−0.209078	−	0.977899i	$-0.567046\pi$
$761$	14.7108	−	8.49331i	0.533268	−	0.307882i	0.742346	+	0.670017i	$0.233713\pi$
$762$		0			0
$763$	8.67111	+	32.3610i	0.313915	+	1.17155i
$764$		0			0
$765$	31.0232	−	25.7168i	1.12165	−	0.929795i
$766$		0			0
$767$	6.31438	−	10.9368i	0.227999	−	0.394906i
$768$		0			0
$769$	−21.5351	−	37.2999i	−0.776575	−	1.34507i	−0.933905	−	0.357522i	$-0.883622\pi$
$769$	−21.5351	−	37.2999i	−0.776575	−	1.34507i	0.157330	−	0.987546i	$-0.449712\pi$
$770$		0			0
$771$	24.4791	−	38.1720i	0.881594	−	1.37473i
$772$		0			0
$773$	32.8660	−	32.8660i	1.18211	−	1.18211i	0.202909	−	0.979198i	$-0.434961\pi$
$773$	32.8660	−	32.8660i	1.18211	−	1.18211i	0.979198	−	0.202909i	$-0.0650394\pi$
$774$		0			0
$775$		−	1.54966i		−	0.0556653i
$776$		0			0
$777$	31.5008	+	34.5842i	1.13008	+	1.24070i
$778$		0			0
$779$	20.8963	+	5.59915i	0.748689	+	0.200611i
$780$		0			0
$781$	−4.26785	+	1.14357i	−0.152716	+	0.0409200i
$782$		0			0
$783$	16.2259	−	1.98821i	0.579865	−	0.0710528i
$784$		0			0
$785$	18.7530	−	32.4812i	0.669324	−	1.15930i
$786$		0			0
$787$	−1.55972	+	5.82094i	−0.0555978	+	0.207494i	−0.988137	−	0.153575i	$-0.950921\pi$
$787$	−1.55972	+	5.82094i	−0.0555978	+	0.207494i	0.932539	+	0.361069i	$0.117588\pi$
$788$		0			0
$789$	0.629758	−	13.4972i	0.0224200	−	0.480513i
$790$		0			0
$791$		−	37.8706i		−	1.34652i
$792$		0			0
$793$			13.1309i			0.466292i
$794$		0			0
$795$	0.692255	+	0.443932i	0.0245518	+	0.0157447i
$796$		0			0
$797$	−13.4797	+	50.3069i	−0.477475	+	1.78196i	0.134313	+	0.990939i	$0.457117\pi$
$797$	−13.4797	+	50.3069i	−0.477475	+	1.78196i	−0.611788	+	0.791022i	$0.709549\pi$
$798$		0			0
$799$	−11.6888	+	20.2455i	−0.413519	+	0.716236i
$800$		0			0
$801$	−14.9856	−	10.6272i	−0.529489	−	0.375493i
$802$		0			0
$803$	−12.9642	+	3.47374i	−0.457496	+	0.122586i
$804$		0			0
$805$	26.2394	+	7.03082i	0.924816	+	0.247804i
$806$		0			0
$807$	−3.56213	+	11.1809i	−0.125393	+	0.393586i
$808$		0			0
$809$		−	12.2452i		−	0.430520i	−0.976557	−	0.215260i	$-0.930940\pi$
$809$		−	12.2452i		−	0.430520i	0.976557	−	0.215260i	$-0.0690599\pi$
$810$		0			0
$811$	−34.8977	+	34.8977i	−1.22542	+	1.22542i	−0.259747	+	0.965677i	$0.583639\pi$
$811$	−34.8977	+	34.8977i	−1.22542	+	1.22542i	−0.965677	+	0.259747i	$0.916361\pi$
$812$		0			0
$813$	19.7700	+	38.2567i	0.693363	+	1.34172i
$814$		0			0
$815$	29.0360	+	50.2918i	1.01709	+	1.76164i
$816$		0			0
$817$	−20.8110	+	36.0458i	−0.728086	+	1.26108i
$818$		0			0
$819$	−9.04800	−	53.1720i	−0.316163	−	1.85798i
$820$		0			0
$821$	2.10293	+	7.84823i	0.0733926	+	0.273905i	0.992864	−	0.119252i	$-0.0380496\pi$
$821$	2.10293	+	7.84823i	0.0733926	+	0.273905i	−0.919471	+	0.393157i	$0.871383\pi$
$822$		0			0
$823$	11.0255	−	6.36556i	0.384324	−	0.221890i	−0.295374	−	0.955382i	$-0.595444\pi$
$823$	11.0255	−	6.36556i	0.384324	−	0.221890i	0.679698	+	0.733492i	$0.262111\pi$
$824$		0			0
$825$	2.90124	−	0.634090i	0.101008	−	0.0220762i
$826$		0			0
$827$	−7.95914	+	7.95914i	−0.276766	+	0.276766i	−0.831817	−	0.555050i	$-0.812699\pi$
$827$	−7.95914	+	7.95914i	−0.276766	+	0.276766i	0.555050	+	0.831817i	$0.312699\pi$
$828$		0			0
$829$	21.1944	+	21.1944i	0.736113	+	0.736113i	0.971823	−	0.235710i	$-0.0757416\pi$
$829$	21.1944	+	21.1944i	0.736113	+	0.736113i	−0.235710	+	0.971823i	$0.575742\pi$
$830$		0			0
$831$	1.18195	−	1.07657i	0.0410014	−	0.0373459i
$832$		0			0
$833$	9.72259	+	16.8400i	0.336868	+	0.583472i
$834$		0			0
$835$	32.9354	−	8.82503i	1.13978	−	0.305403i
$836$		0			0
$837$	2.41920	+	5.99200i	0.0836198	+	0.207114i
$838$		0			0
$839$	34.4751	+	19.9042i	1.19021	+	0.687169i	0.958355	−	0.285580i	$-0.0921864\pi$
$839$	34.4751	+	19.9042i	1.19021	+	0.687169i	0.231858	+	0.972750i	$0.425520\pi$
$840$		0			0
$841$	−16.5433	+	9.55126i	−0.570458	+	0.329354i
$842$		0			0
$843$	2.29899	−	49.2728i	0.0791815	−	1.69705i
$844$		0			0
$845$	30.8242	+	30.8242i	1.06039	+	1.06039i
$846$		0			0
$847$	−29.6747			−1.01964
$848$		0			0
$849$	−2.45587	−	11.2367i	−0.0842852	−	0.385642i
$850$		0			0
$851$	−7.15576	+	26.7057i	−0.245296	+	0.915459i
$852$		0			0
$853$	−12.8592	−	47.9910i	−0.440289	−	1.64318i	−0.728083	−	0.685489i	$-0.759589\pi$
$853$	−12.8592	−	47.9910i	−0.440289	−	1.64318i	0.287794	−	0.957692i	$-0.407078\pi$
$854$		0			0
$855$	−49.7529	−	4.65292i	−1.70151	−	0.159126i
$856$		0			0
$857$	−1.84308	−	1.06410i	−0.0629582	−	0.0363490i	0.468190	−	0.883628i	$-0.344906\pi$
$857$	−1.84308	−	1.06410i	−0.0629582	−	0.0363490i	−0.531149	+	0.847279i	$0.678239\pi$
$858$		0			0
$859$	−9.11407	−	2.44211i	−0.310968	−	0.0833237i	0.0999599	−	0.994991i	$-0.468129\pi$
$859$	−9.11407	−	2.44211i	−0.310968	−	0.0833237i	−0.410928	+	0.911668i	$0.634795\pi$
$860$		0			0
$861$	8.41059	+	16.2753i	0.286632	+	0.554660i
$862$		0			0
$863$	−1.35198			−0.0460219			−0.0230110	−	0.999735i	$-0.507325\pi$
$863$	−1.35198			−0.0460219			−0.0230110	+	0.999735i	$0.507325\pi$
$864$		0			0
$865$	11.1690			0.379757
$866$		0			0
$867$	9.45100	+	18.2886i	0.320973	+	0.621112i
$868$		0			0
$869$	2.95540	+	0.791896i	0.100255	+	0.0268632i
$870$		0			0
$871$	−0.555400	−	0.320660i	−0.0188190	−	0.0108652i
$872$		0			0
$873$	−5.54431	−	12.0779i	−0.187646	−	0.408776i
$874$		0			0
$875$	−7.91234	−	29.5293i	−0.267486	−	0.998271i
$876$		0			0
$877$	−4.48959	+	16.7554i	−0.151603	+	0.565789i	0.847770	+	0.530364i	$0.177945\pi$
$877$	−4.48959	+	16.7554i	−0.151603	+	0.565789i	−0.999372	+	0.0354241i	$0.988722\pi$
$878$		0			0
$879$	−3.60708	−	16.5040i	−0.121664	−	0.556665i
$880$		0			0
$881$	4.49503			0.151441			0.0757207	−	0.997129i	$-0.475874\pi$
$881$	4.49503			0.151441			0.0757207	+	0.997129i	$0.475874\pi$
$882$		0			0
$883$	−7.21822	−	7.21822i	−0.242913	−	0.242913i	0.575141	−	0.818054i	$-0.304947\pi$
$883$	−7.21822	−	7.21822i	−0.242913	−	0.242913i	−0.818054	+	0.575141i	$0.804947\pi$
$884$		0			0
$885$	0.461791	−	9.89727i	0.0155229	−	0.332693i
$886$		0			0
$887$	−32.3743	+	18.6913i	−1.08702	+	0.627592i	−0.932782	−	0.360441i	$-0.882626\pi$
$887$	−32.3743	+	18.6913i	−1.08702	+	0.627592i	−0.154240	+	0.988033i	$0.549293\pi$
$888$		0			0
$889$	−20.8197	−	12.0203i	−0.698271	−	0.403147i
$890$		0			0
$891$	−10.2282	+	6.98099i	−0.342658	+	0.233872i
$892$		0			0
$893$	28.0018	−	7.50307i	0.937046	−	0.251081i
$894$		0			0
$895$	−31.6491	−	54.8178i	−1.05791	−	1.83236i
$896$		0			0
$897$	23.5667	−	21.4656i	0.786871	−	0.716716i
$898$		0			0
$899$	2.76648	+	2.76648i	0.0922674	+	0.0922674i
$900$		0			0
$901$	−0.721983	+	0.721983i	−0.0240527	+	0.0240527i
$902$		0			0
$903$	−34.4343	+	7.52589i	−1.14590	+	0.250446i
$904$		0			0
$905$	−27.6648	+	15.9723i	−0.919610	+	0.530937i
$906$		0			0
$907$	−7.32597	−	27.3409i	−0.243255	−	0.907840i	−0.974253	−	0.225460i	$-0.927612\pi$
$907$	−7.32597	−	27.3409i	−0.243255	−	0.907840i	0.730998	−	0.682380i	$-0.239055\pi$
$908$		0			0
$909$	50.2468	+	18.6295i	1.66658	+	0.617902i
$910$		0			0
$911$	12.2805	−	21.2704i	0.406871	−	0.704721i	−0.587667	−	0.809103i	$-0.699953\pi$
$911$	12.2805	−	21.2704i	0.406871	−	0.704721i	0.994537	+	0.104383i	$0.0332867\pi$
$912$		0			0
$913$	4.09376	+	7.09060i	0.135484	+	0.234665i
$914$		0			0
$915$	4.72958	+	9.15218i	0.156355	+	0.302562i
$916$		0			0
$917$	−35.0323	+	35.0323i	−1.15687	+	1.15687i
$918$		0			0
$919$		−	21.3619i		−	0.704665i	−0.935875	−	0.352332i	$-0.885389\pi$
$919$		−	21.3619i		−	0.704665i	0.935875	−	0.352332i	$-0.114611\pi$
$920$		0			0
$921$	−3.38493	+	10.6247i	−0.111537	+	0.350096i
$922$		0			0
$923$	−17.1138	−	4.58563i	−0.563308	−	0.150938i
$924$		0			0
$925$	−9.97644	+	2.67318i	−0.328023	+	0.0878936i
$926$		0			0
$927$	−2.81737	+	30.1257i	−0.0925345	+	0.989457i
$928$		0			0
$929$	0.783906	−	1.35776i	0.0257191	−	0.0445468i	−0.852879	−	0.522108i	$-0.825146\pi$
$929$	0.783906	−	1.35776i	0.0257191	−	0.0445468i	0.878598	+	0.477561i	$0.158479\pi$
$930$		0			0
$931$	6.24097	−	23.2916i	0.204540	−	0.763352i
$932$		0			0
$933$	9.37738	+	6.01356i	0.307002	+	0.196875i
$934$		0			0
$935$			18.4818i			0.604420i
$936$		0			0
$937$		−	40.1161i		−	1.31054i	−0.755396	−	0.655269i	$-0.772555\pi$
$937$		−	40.1161i		−	1.31054i	0.755396	−	0.655269i	$-0.227445\pi$
$938$		0			0
$939$	0.270493	−	5.79731i	0.00882721	−	0.189188i
$940$		0			0
$941$	−10.7101	+	39.9706i	−0.349139	+	1.30300i	0.538562	+	0.842586i	$0.318968\pi$
$941$	−10.7101	+	39.9706i	−0.349139	+	1.30300i	−0.887702	+	0.460419i	$0.847699\pi$
$942$		0			0
$943$	−5.41372	+	9.37683i	−0.176295	+	0.305352i
$944$		0			0
$945$	−25.4583	−	33.8017i	−0.828158	−	1.09957i
$946$		0			0
$947$	−31.9411	+	8.55860i	−1.03795	+	0.278117i	−0.737263	−	0.675606i	$-0.763882\pi$
$947$	−31.9411	+	8.55860i	−1.03795	+	0.278117i	−0.300685	+	0.953724i	$0.597215\pi$
$948$		0			0
$949$	−51.9856	−	13.9295i	−1.68752	−	0.452171i
$950$		0			0
$951$	−17.6710	−	19.4007i	−0.573020	−	0.629109i
$952$		0			0
$953$		−	6.18680i		−	0.200410i	−0.994967	−	0.100205i	$-0.968050\pi$
$953$		−	6.18680i		−	0.200410i	0.994967	−	0.100205i	$-0.0319499\pi$
$954$		0			0
$955$	19.4690	−	19.4690i	0.630001	−	0.630001i
$956$		0			0
$957$	−4.04737	+	6.31135i	−0.130833	+	0.204017i
$958$		0			0
$959$	−21.7099	−	37.6026i	−0.701048	−	1.21425i
$960$		0			0
$961$	14.7267	−	25.5074i	0.475056	−	0.822821i
$962$		0			0
$963$	−2.56130	−	15.0519i	−0.0825367	−	0.485040i
$964$		0			0
$965$	10.6368	+	39.6971i	0.342410	+	1.27789i
$966$		0			0
$967$	−25.0282	+	14.4500i	−0.804851	+	0.464681i	−0.845165	−	0.534506i	$-0.820498\pi$
$967$	−25.0282	+	14.4500i	−0.804851	+	0.464681i	0.0403133	+	0.999187i	$0.487164\pi$
$968$		0			0
$969$	18.8332	−	59.1142i	0.605010	−	1.89902i
$970$		0			0
$971$	41.1803	−	41.1803i	1.32154	−	1.32154i	0.409008	−	0.912531i	$-0.365875\pi$
$971$	41.1803	−	41.1803i	1.32154	−	1.32154i	0.912531	−	0.409008i	$-0.134125\pi$
$972$		0			0
$973$	−38.6739	−	38.6739i	−1.23983	−	1.23983i
$974$		0			0
$975$	11.3465	+	3.61489i	0.363379	+	0.115769i
$976$		0			0
$977$	−18.1859	−	31.4990i	−0.581820	−	1.00774i	−0.995264	−	0.0972120i	$-0.969008\pi$
$977$	−18.1859	−	31.4990i	−0.581820	−	1.00774i	0.413444	−	0.910530i	$-0.364326\pi$
$978$		0			0
$979$	8.13884	−	2.18080i	0.260119	−	0.0696986i
$980$		0			0
$981$	30.4074	−	5.17426i	0.970833	−	0.165201i
$982$		0			0
$983$	48.0347	+	27.7329i	1.53207	+	0.884541i	0.999266	+	0.0383018i	$0.0121948\pi$
$983$	48.0347	+	27.7329i	1.53207	+	0.884541i	0.532803	+	0.846239i	$0.321139\pi$
$984$		0			0
$985$	−6.76074	+	3.90331i	−0.215415	+	0.124370i
$986$		0			0
$987$	20.6653	+	13.2523i	0.657782	+	0.421825i
$988$		0			0
$989$	−14.7302	−	14.7302i	−0.468393	−	0.468393i
$990$		0			0
$991$	−15.3724			−0.488321			−0.244161	−	0.969735i	$-0.578512\pi$
$991$	−15.3724			−0.488321			−0.244161	+	0.969735i	$0.578512\pi$
$992$		0			0
$993$	−13.2694	+	12.0863i	−0.421092	+	0.383549i
$994$		0			0
$995$	7.72250	−	28.8208i	0.244820	−	0.913679i
$996$		0			0
$997$	−7.71233	−	28.7828i	−0.244252	−	0.911561i	−0.973758	−	0.227586i	$-0.926917\pi$
$997$	−7.71233	−	28.7828i	−0.244252	−	0.911561i	0.729506	−	0.683974i	$-0.239750\pi$
$998$		0			0
$999$	34.4024	−	25.9107i	1.08844	−	0.819778i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bb.e.529.12		72
3.2	odd	2		1728.2.bc.e.721.16		72
4.3	odd	2		144.2.x.e.61.16	yes	72
9.4	even	3	inner	576.2.bb.e.337.17		72
9.5	odd	6		1728.2.bc.e.145.3		72
12.11	even	2		432.2.y.e.397.3		72
16.5	even	4	inner	576.2.bb.e.241.17		72
16.11	odd	4		144.2.x.e.133.8	yes	72
36.23	even	6		432.2.y.e.253.11		72
36.31	odd	6		144.2.x.e.13.8	✓	72
48.5	odd	4		1728.2.bc.e.1585.3		72
48.11	even	4		432.2.y.e.181.11		72
144.5	odd	12		1728.2.bc.e.1009.16		72
144.59	even	12		432.2.y.e.37.3		72
144.85	even	12	inner	576.2.bb.e.49.12		72
144.139	odd	12		144.2.x.e.85.16	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.8	✓	72	36.31	odd	6
144.2.x.e.61.16	yes	72	4.3	odd	2
144.2.x.e.85.16	yes	72	144.139	odd	12
144.2.x.e.133.8	yes	72	16.11	odd	4
432.2.y.e.37.3		72	144.59	even	12
432.2.y.e.181.11		72	48.11	even	4
432.2.y.e.253.11		72	36.23	even	6
432.2.y.e.397.3		72	12.11	even	2
576.2.bb.e.49.12		72	144.85	even	12	inner
576.2.bb.e.241.17		72	16.5	even	4	inner
576.2.bb.e.337.17		72	9.4	even	3	inner
576.2.bb.e.529.12		72	1.1	even	1	trivial
1728.2.bc.e.145.3		72	9.5	odd	6
1728.2.bc.e.721.16		72	3.2	odd	2
1728.2.bc.e.1009.16		72	144.5	odd	12
1728.2.bc.e.1585.3		72	48.5	odd	4

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.795173 + 1.53873i) q^{3} +(-2.41406 - 0.646846i) q^{5} +(-2.82197 - 1.62927i) q^{7} +(-1.73540 + 2.44712i) q^{9} +O(q^{10})\)	\(q+(0.795173 + 1.53873i) q^{3} +(-2.41406 - 0.646846i) q^{5} +(-2.82197 - 1.62927i) q^{7} +(-1.73540 + 2.44712i) q^{9} +(-0.356120 - 1.32906i) q^{11} +(1.42802 - 5.32945i) q^{13} +(-0.924273 - 4.22895i) q^{15} +5.37452 q^{17} +(-4.71269 - 4.71269i) q^{19} +(0.263051 - 5.63781i) q^{21} +(2.88877 - 1.66783i) q^{23} +(1.07916 + 0.623053i) q^{25} +(-5.14540 - 0.724438i) q^{27} +(-3.03883 + 0.814251i) q^{29} +(-0.621800 - 1.07699i) q^{31} +(1.76189 - 1.60481i) q^{33} +(5.75853 + 5.75853i) q^{35} +(-5.86087 + 5.86087i) q^{37} +(9.33612 - 2.04049i) q^{39} +(-2.81108 + 1.62298i) q^{41} +(-1.61636 - 6.03232i) q^{43} +(5.77227 - 4.78496i) q^{45} +(-2.17485 + 3.76695i) q^{47} +(1.80902 + 3.13331i) q^{49} +(4.27367 + 8.26995i) q^{51} +(-0.134334 + 0.134334i) q^{53} +3.43879i q^{55} +(3.50417 - 10.9990i) q^{57} +(2.21088 + 0.592405i) q^{59} +(-2.29879 + 0.615960i) q^{61} +(8.88426 - 4.07827i) q^{63} +(-6.89466 + 11.9419i) q^{65} +(0.0300838 - 0.112274i) q^{67} +(4.86343 + 3.11884i) q^{69} -3.21118i q^{71} -9.75441i q^{73} +(-0.100594 + 2.15597i) q^{75} +(-1.16043 + 4.33078i) q^{77} +(-1.11184 + 1.92576i) q^{79} +(-2.97677 - 8.49346i) q^{81} +(-5.74772 + 1.54010i) q^{83} +(-12.9744 - 3.47649i) q^{85} +(-3.66931 - 4.02848i) q^{87} +6.12376i q^{89} +(-12.7129 + 12.7129i) q^{91} +(1.16276 - 1.81318i) q^{93} +(8.32833 + 14.4251i) q^{95} +(-2.21495 + 3.83640i) q^{97} +(3.87037 + 1.43498i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) \) 72 * q - 2 * q^3 + 4 * q^5	\( 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) \) 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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