LMFDB - Embedded newform 576.2.bb.e.49.12

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			49.12
Character	$\chi$	$=$	576.49
Dual form			576.2.bb.e.529.12

$q$-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 $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

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

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	−0.754433	−	0.656378i	$-0.772088\pi$
$5$	−2.41406	+	0.646846i	−1.07960	+	0.289278i	−0.325169	+	0.945656i	$0.605421\pi$
$6$		0			0
$7$	−2.82197	+	1.62927i	−1.06661	+	0.615805i	−0.927252	−	0.374438i	$-0.877836\pi$
$7$	−2.82197	+	1.62927i	−1.06661	+	0.615805i	−0.139353	+	0.990243i	$0.544502\pi$
$8$		0			0
$9$	−1.73540	−	2.44712i	−0.578467	−	0.815706i
$10$		0			0
$11$	−0.356120	+	1.32906i	−0.107374	+	0.400726i	−0.998604	−	0.0528265i	$-0.983177\pi$
$11$	−0.356120	+	1.32906i	−0.107374	+	0.400726i	0.891229	+	0.453553i	$0.149844\pi$
$12$		0			0
$13$	1.42802	+	5.32945i	0.396062	+	1.47812i	0.819964	+	0.572415i	$0.193993\pi$
$13$	1.42802	+	5.32945i	0.396062	+	1.47812i	−0.423903	+	0.905708i	$0.639340\pi$
$14$		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	−0.0847630	+	0.996401i	$0.527013\pi$
$19$	−4.71269	+	4.71269i	−1.08116	+	1.08116i	−0.996401	+	0.0847630i	$0.972987\pi$
$20$		0			0
$21$	0.263051	+	5.63781i	0.0574025	+	1.23027i
$22$		0			0
$23$	2.88877	+	1.66783i	0.602351	+	0.347767i	0.769966	−	0.638085i	$-0.220273\pi$
$23$	2.88877	+	1.66783i	0.602351	+	0.347767i	−0.167615	+	0.985853i	$0.553607\pi$
$24$		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	−0.0346168	−	0.999401i	$-0.511021\pi$
$29$	−3.03883	−	0.814251i	−0.564296	−	0.151203i	−0.529679	+	0.848198i	$0.677688\pi$
$30$		0			0
$31$	−0.621800	+	1.07699i	−0.111679	+	0.193433i	−0.916447	−	0.400156i	$-0.868956\pi$
$31$	−0.621800	+	1.07699i	−0.111679	+	0.193433i	0.804769	+	0.593589i	$0.202289\pi$
$32$		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	0.0358368	−	0.999358i	$-0.488590\pi$
$37$	−5.86087	−	5.86087i	−0.963521	−	0.963521i	−0.999358	+	0.0358368i	$0.988590\pi$
$38$		0			0
$39$	9.33612	+	2.04049i	1.49498	+	0.326739i
$40$		0			0
$41$	−2.81108	−	1.62298i	−0.439017	−	0.253467i	0.264163	−	0.964478i	$-0.414904\pi$
$41$	−2.81108	−	1.62298i	−0.439017	−	0.253467i	−0.703181	+	0.711011i	$0.748237\pi$
$42$		0			0
$43$	−1.61636	+	6.03232i	−0.246492	+	0.919920i	0.726136	+	0.687551i	$0.241314\pi$
$43$	−1.61636	+	6.03232i	−0.246492	+	0.919920i	−0.972628	+	0.232369i	$0.925352\pi$
$44$		0			0
$45$	5.77227	+	4.78496i	0.860480	+	0.713299i
$46$		0			0
$47$	−2.17485	−	3.76695i	−0.317234	−	0.549466i	0.662676	−	0.748907i	$-0.269421\pi$
$47$	−2.17485	−	3.76695i	−0.317234	−	0.549466i	−0.979910	+	0.199441i	$0.936088\pi$
$48$		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	0.697820	−	0.716273i	$-0.254153\pi$
$53$	−0.134334	−	0.134334i	−0.0184522	−	0.0184522i	−0.716273	+	0.697820i	$0.754153\pi$
$54$		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	−0.112014	−	0.993707i	$-0.535730\pi$
$59$	2.21088	−	0.592405i	0.287833	−	0.0771245i	0.399846	+	0.916582i	$0.369063\pi$
$60$		0			0
$61$	−2.29879	−	0.615960i	−0.294330	−	0.0788656i	0.108632	−	0.994082i	$-0.465353\pi$
$61$	−2.29879	−	0.615960i	−0.294330	−	0.0788656i	−0.402963	+	0.915216i	$0.632020\pi$
$62$		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	0.967739	−	0.251954i	$-0.0810733\pi$
$67$	0.0300838	+	0.112274i	0.00367532	+	0.0137165i	−0.964064	+	0.265671i	$0.914407\pi$
$68$		0			0
$69$	4.86343	−	3.11884i	0.585488	−	0.375464i
$70$		0			0
$71$			3.21118i			0.381097i	0.981678	+	0.190548i	$0.0610266\pi$
$71$			3.21118i			0.381097i	−0.981678	+	0.190548i	$0.938973\pi$
$72$		0			0
$73$			9.75441i			1.14167i	0.821066	+	0.570833i	$0.193380\pi$
$73$			9.75441i			1.14167i	−0.821066	+	0.570833i	$0.806620\pi$
$74$		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	0.796677	−	0.604405i	$-0.206589\pi$
$79$	−1.11184	−	1.92576i	−0.125092	−	0.216665i	−0.921769	+	0.387740i	$0.873256\pi$
$80$		0			0
$81$	−2.97677	+	8.49346i	−0.330752	+	0.943718i
$82$		0			0
$83$	−5.74772	−	1.54010i	−0.630895	−	0.169048i	−0.0708190	−	0.997489i	$-0.522561\pi$
$83$	−5.74772	−	1.54010i	−0.630895	−	0.169048i	−0.560076	+	0.828441i	$0.689228\pi$
$84$		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	$-0.894784\pi$
$89$		−	6.12376i		−	0.649118i	0.945866	−	0.324559i	$-0.105216\pi$
$90$		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	0.731394	−	0.681956i	$-0.238870\pi$
$97$	−2.21495	−	3.83640i	−0.224894	−	0.389528i	−0.956288	+	0.292428i	$0.905537\pi$
$98$		0			0
$99$	3.87037	−	1.43498i	0.388987	−	0.144221i
$100$		0			0
$101$	−4.62330	+	17.2544i	−0.460035	+	1.71688i	0.212811	+	0.977093i	$0.431738\pi$
$101$	−4.62330	+	17.2544i	−0.460035	+	1.71688i	−0.672847	+	0.739782i	$0.734929\pi$
$102$		0			0
$103$	8.73448	+	5.04285i	0.860634	+	0.496887i	0.864224	−	0.503106i	$-0.167810\pi$
$103$	8.73448	+	5.04285i	0.860634	+	0.496887i	−0.00359067	+	0.999994i	$0.501143\pi$
$104$		0			0
$105$	−4.28182	−	13.4399i	−0.417863	−	1.31160i
$106$		0			0
$107$	−3.59876	−	3.59876i	−0.347905	−	0.347905i	0.511423	−	0.859329i	$-0.329118\pi$
$107$	−3.59876	−	3.59876i	−0.347905	−	0.347905i	−0.859329	+	0.511423i	$0.829118\pi$
$108$		0			0
$109$	−7.27011	+	7.27011i	−0.696351	+	0.696351i	−0.963621	−	0.267271i	$-0.913878\pi$
$109$	−7.27011	+	7.27011i	−0.696351	+	0.696351i	0.267271	+	0.963621i	$0.413878\pi$
$110$		0			0
$111$	−13.6787	+	4.35791i	−1.29833	+	0.413635i
$112$		0			0
$113$	5.81099	−	10.0649i	0.546652	−	0.946828i	−0.451849	−	0.892094i	$-0.649236\pi$
$113$	5.81099	−	10.0649i	0.546652	−	0.946828i	0.998501	−	0.0547341i	$-0.0174311\pi$
$114$		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	0.893992	+	0.448082i	$0.147893\pi$
$131$	3.93512	+	14.6861i	0.343813	+	1.28313i	−0.550179	+	0.835047i	$0.685440\pi$
$132$		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	0.0818576	−	0.996644i	$-0.473915\pi$
$137$	11.5397	−	6.66247i	0.985906	−	0.569213i	0.904048	+	0.427431i	$0.140581\pi$
$138$		0			0
$139$	16.2127	−	4.34417i	1.37514	−	0.368468i	0.505787	−	0.862658i	$-0.331202\pi$
$139$	16.2127	−	4.34417i	1.37514	−	0.368468i	0.869354	+	0.494191i	$0.164535\pi$
$140$		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	0.305838	−	0.952084i	$-0.401063\pi$
$149$	12.7771	−	3.42362i	1.04674	−	0.280474i	0.740905	+	0.671610i	$0.234397\pi$
$150$		0			0
$151$	10.3438	−	5.97202i	0.841769	−	0.485996i	−0.0160959	−	0.999870i	$-0.505124\pi$
$151$	10.3438	−	5.97202i	0.841769	−	0.485996i	0.857865	+	0.513875i	$0.171790\pi$
$152$		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	−0.928567	−	0.371164i	$-0.878959\pi$
$157$	−3.88412	−	14.4957i	−0.309986	−	1.15689i	0.618581	−	0.785721i	$-0.287708\pi$
$158$		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	−0.350278	+	0.936646i	$0.613913\pi$
$163$	−16.4303	+	16.4303i	−1.28692	+	1.28692i	−0.936646	+	0.350278i	$0.886087\pi$
$164$		0			0
$165$	−5.29137	−	2.73443i	−0.411933	−	0.212875i
$166$		0			0
$167$	−11.8153	−	6.82158i	−0.914297	−	0.527870i	−0.0324861	−	0.999472i	$-0.510342\pi$
$167$	−11.8153	−	6.82158i	−0.914297	−	0.527870i	−0.881811	+	0.471602i	$0.843676\pi$
$168$		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	0.0909602	−	0.995855i	$-0.471006\pi$
$173$	−4.31671	−	1.15666i	−0.328193	−	0.0879391i	−0.419153	+	0.907915i	$0.637673\pi$
$174$		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	0.441146	−	0.897435i	$-0.354572\pi$
$179$	17.9090	−	17.9090i	1.33858	−	1.33858i	0.897435	−	0.441146i	$-0.145428\pi$
$180$		0			0
$181$	9.03811	+	9.03811i	0.671797	+	0.671797i	0.958130	−	0.286333i	$-0.0924363\pi$
$181$	9.03811	+	9.03811i	0.671797	+	0.671797i	−0.286333	+	0.958130i	$0.592436\pi$
$182$		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	0.594978	−	0.803742i	$-0.297161\pi$
$191$	−5.50837	−	9.54078i	−0.398572	−	0.690346i	−0.993550	+	0.113395i	$0.963827\pi$
$192$		0			0
$193$	−8.22204	+	14.2410i	−0.591836	+	1.02509i	0.402149	+	0.915574i	$0.368263\pi$
$193$	−8.22204	+	14.2410i	−0.591836	+	1.02509i	−0.993985	+	0.109515i	$0.965070\pi$
$194$		0			0
$195$	−23.8579	+	1.11317i	−1.70850	+	0.0797158i
$196$		0			0
$197$	2.20874	+	2.20874i	0.157366	+	0.157366i	0.781398	−	0.624033i	$-0.214507\pi$
$197$	2.20874	+	2.20874i	0.157366	+	0.157366i	−0.624033	+	0.781398i	$0.714507\pi$
$198$		0			0
$199$		−	11.9387i		−	0.846312i	−0.906057	−	0.423156i	$-0.860922\pi$
$199$		−	11.9387i		−	0.846312i	0.906057	−	0.423156i	$-0.139078\pi$
$200$		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	0.998576	−	0.0533513i	$-0.0169903\pi$
$211$	1.55584	+	5.80646i	0.107108	+	0.399733i	−0.891468	+	0.453084i	$0.850324\pi$
$212$		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	0.693366	−	0.720586i	$-0.256127\pi$
$223$	−4.14191	−	7.17400i	−0.277363	−	0.480407i	−0.970729	+	0.240179i	$0.922794\pi$
$224$		0			0
$225$	−3.39746	−	1.55958i	−0.226497	−	0.103972i
$226$		0			0
$227$	17.3293	+	4.64336i	1.15018	+	0.308191i	0.783039	−	0.621973i	$-0.213669\pi$
$227$	17.3293	+	4.64336i	1.15018	+	0.308191i	0.367145	+	0.930164i	$0.380335\pi$
$228$		0			0
$229$	−9.17552	+	2.45857i	−0.606335	+	0.162467i	−0.548908	−	0.835883i	$-0.684956\pi$
$229$	−9.17552	+	2.45857i	−0.606335	+	0.162467i	−0.0574270	+	0.998350i	$0.518290\pi$
$230$		0			0
$231$	−7.58666	−	1.65813i	−0.499166	−	0.109097i
$232$		0			0
$233$		−	6.39614i		−	0.419025i	−0.977806	−	0.209512i	$-0.932812\pi$
$233$		−	6.39614i		−	0.419025i	0.977806	−	0.209512i	$-0.0671877\pi$
$234$		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	0.115987	+	0.993251i	$0.462997\pi$
$239$	−12.4015	+	21.4800i	−0.802187	+	1.38943i	−0.918174	+	0.396178i	$0.870336\pi$
$240$		0			0
$241$	4.32533	+	7.49168i	0.278619	+	0.482582i	0.971042	−	0.238910i	$-0.0767901\pi$
$241$	4.32533	+	7.49168i	0.278619	+	0.482582i	−0.692423	+	0.721492i	$0.743457\pi$
$242$		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	0.748224	−	0.663446i	$-0.230907\pi$
$251$	1.34312	+	1.34312i	0.0847772	+	0.0847772i	−0.663446	+	0.748224i	$0.730907\pi$
$252$		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	0.0916380	+	0.995792i	$0.470790\pi$
$257$	−13.0905	+	22.6734i	−0.816563	+	1.41433i	−0.908201	+	0.418535i	$0.862544\pi$
$258$		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	−0.693617	−	0.720344i	$-0.743984\pi$
$263$	−6.75594	+	3.90054i	−0.416589	+	0.240518i	0.277028	+	0.960862i	$0.410651\pi$
$264$		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	−0.545815	−	0.837905i	$-0.683780\pi$
$269$	4.79063	−	4.79063i	0.292090	−	0.292090i	0.837905	+	0.545815i	$0.183780\pi$
$270$		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	−0.972731	−	0.231934i	$-0.925495\pi$
$277$	−0.238901	+	0.891589i	−0.0143541	+	0.0535704i	0.958377	+	0.285505i	$0.0921612\pi$
$278$		0			0
$279$	3.71459	−	0.347390i	0.222387	−	0.0207977i
$280$		0			0
$281$	−24.6632	+	14.2393i	−1.47128	+	0.849446i	−0.999480	−	0.0322571i	$-0.989730\pi$
$281$	−24.6632	+	14.2393i	−1.47128	+	0.849446i	−0.471804	+	0.881703i	$0.656397\pi$
$282$		0			0
$283$	−6.41436	+	1.71872i	−0.381294	+	0.102167i	−0.444375	−	0.895841i	$-0.646574\pi$
$283$	−6.41436	+	1.71872i	−0.381294	+	0.102167i	0.0630806	+	0.998008i	$0.479907\pi$
$284$		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	−0.523288	−	0.852156i	$-0.675295\pi$
$293$	−9.42116	+	2.52439i	−0.550390	+	0.147477i	−0.0271023	+	0.999633i	$0.508628\pi$
$294$		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	−0.565164	−	0.824979i	$-0.691187\pi$
$307$	4.55233	−	4.55233i	0.259815	−	0.259815i	0.824979	+	0.565164i	$0.191187\pi$
$308$		0			0
$309$	14.7050	−	9.43010i	0.836540	−	0.536459i
$310$		0			0
$311$	5.56997	+	3.21582i	0.315844	+	0.182353i	0.649539	−	0.760329i	$-0.274962\pi$
$311$	5.56997	+	3.21582i	0.315844	+	0.182353i	−0.333695	+	0.942681i	$0.608295\pi$
$312$		0			0
$313$	−2.90181	+	1.67536i	−0.164020	+	0.0946969i	−0.579763	−	0.814785i	$-0.696855\pi$
$313$	−2.90181	+	1.67536i	−0.164020	+	0.0946969i	0.415743	+	0.909482i	$0.363522\pi$
$314$		0			0
$315$	−24.0852	−	4.09844i	−1.35705	−	0.230921i
$316$		0			0
$317$	−14.6346	−	3.92134i	−0.821963	−	0.220244i	−0.176758	−	0.984254i	$-0.556561\pi$
$317$	−14.6346	−	3.92134i	−0.821963	−	0.220244i	−0.645204	+	0.764010i	$0.723228\pi$
$318$		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	−0.852216	−	0.523190i	$-0.824742\pi$
$331$	2.68206	−	10.0096i	0.147420	−	0.550177i	0.999636	−	0.0269876i	$-0.00859146\pi$
$332$		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	−0.631878	−	0.775068i	$-0.717716\pi$
$337$	6.52225	−	11.2969i	0.355289	−	0.615379i	0.987167	+	0.159689i	$0.0510490\pi$
$338$		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	−0.827435	−	0.561562i	$-0.810201\pi$
$347$	−23.5314	+	6.30523i	−1.26323	+	0.338482i	−0.435798	+	0.900044i	$0.643534\pi$
$348$		0			0
$349$	27.7772	+	7.44289i	1.48688	+	0.398409i	0.908683	−	0.417487i	$-0.137089\pi$
$349$	27.7772	+	7.44289i	1.48688	+	0.398409i	0.578199	+	0.815896i	$0.303756\pi$
$350$		0			0
$351$	−11.2086	−	26.3876i	−0.598271	−	1.40847i
$352$		0			0
$353$	17.6048	+	30.4924i	0.937010	+	1.62295i	0.771011	+	0.636822i	$0.219752\pi$
$353$	17.6048	+	30.4924i	0.937010	+	1.62295i	0.165999	+	0.986126i	$0.446915\pi$
$354$		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	$0.153867\pi$
$359$			17.6127i			0.929564i	−0.885425	+	0.464782i	$0.846133\pi$
$360$		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	0.997236	−	0.0742925i	$-0.0236698\pi$
$367$	8.31959	+	14.4100i	0.434279	+	0.752193i	−0.562957	+	0.826486i	$0.690337\pi$
$368$		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	−0.341397	−	0.939919i	$-0.610900\pi$
$373$	−3.22714	+	0.864710i	−0.167095	+	0.0447730i	0.174302	+	0.984692i	$0.444233\pi$
$374$		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	0.919350	−	0.393440i	$-0.128715\pi$
$379$	10.2384	+	10.2384i	0.525910	+	0.525910i	−0.393440	+	0.919350i	$0.628715\pi$
$380$		0			0
$381$	5.86656	−	11.3523i	0.300553	−	0.581598i
$382$		0			0
$383$	−5.44755	+	9.43544i	−0.278357	+	0.482128i	−0.970977	−	0.239175i	$-0.923123\pi$
$383$	−5.44755	+	9.43544i	−0.278357	+	0.482128i	0.692620	+	0.721303i	$0.256456\pi$
$384$		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	−0.804687	−	0.593699i	$-0.797667\pi$
$389$	3.72849	−	13.9149i	0.189042	−	0.705513i	0.993729	−	0.111815i	$-0.0356663\pi$
$390$		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	−0.204683	−	0.978828i	$-0.565616\pi$
$397$	15.4247	−	15.4247i	0.774145	−	0.774145i	0.978828	+	0.204683i	$0.0656165\pi$
$398$		0			0
$399$	−27.8089	−	25.3295i	−1.39219	−	1.26806i
$400$		0			0
$401$	−3.21720	+	5.57235i	−0.160659	+	0.278270i	−0.935105	−	0.354370i	$-0.884695\pi$
$401$	−3.21720	+	5.57235i	−0.160659	+	0.278270i	0.774446	+	0.632640i	$0.218029\pi$
$402$		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	0.995465	+	0.0951294i	$0.0303265\pi$
$409$	31.8642	+	18.3968i	1.57558	+	0.909663i	0.580117	+	0.814533i	$0.303007\pi$
$410$		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	0.950706	+	0.310093i	$0.100360\pi$
$419$	5.78093	+	21.5747i	0.282417	+	1.05399i	−0.668290	+	0.743901i	$0.732973\pi$
$420$		0			0
$421$	2.33477	−	8.71347i	0.113790	−	0.424669i	−0.885404	−	0.464822i	$-0.846118\pi$
$421$	2.33477	−	8.71347i	0.113790	−	0.424669i	0.999194	+	0.0401539i	$0.0127848\pi$
$422$		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	−0.626151	−	0.779701i	$-0.715371\pi$
$439$	−5.53112	+	3.19339i	−0.263986	+	0.152412i	0.362166	+	0.932114i	$0.382037\pi$
$440$		0			0
$441$	−10.8069	+	1.01067i	−0.514616	+	0.0481272i
$442$		0			0
$443$	4.33005	−	16.1600i	0.205727	−	0.767783i	−0.783500	−	0.621392i	$-0.786568\pi$
$443$	4.33005	−	16.1600i	0.205727	−	0.767783i	0.989227	−	0.146391i	$-0.0467658\pi$
$444$		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	−0.962875	−	0.269946i	$-0.912994\pi$
$457$	−25.8782	+	14.9408i	−1.21053	+	0.698901i	−0.247657	+	0.968848i	$0.579661\pi$
$458$		0			0
$459$	−27.6541	+	3.89351i	−1.29078	+	0.181733i
$460$		0			0
$461$	26.9785	+	7.22887i	1.25651	+	0.336682i	0.824850	−	0.565352i	$-0.191260\pi$
$461$	26.9785	+	7.22887i	1.25651	+	0.336682i	0.431665	+	0.902034i	$0.357926\pi$
$462$		0			0
$463$	−9.00954	+	15.6050i	−0.418709	+	0.725225i	−0.995810	−	0.0914480i	$-0.970850\pi$
$463$	−9.00954	+	15.6050i	−0.418709	+	0.725225i	0.577101	+	0.816673i	$0.304184\pi$
$464$		0			0
$465$	−3.97982	−	3.62500i	−0.184560	−	0.168105i
$466$		0			0
$467$	−3.24566	+	3.24566i	−0.150191	+	0.150191i	−0.778204	−	0.628012i	$-0.783869\pi$
$467$	−3.24566	+	3.24566i	−0.150191	+	0.150191i	0.628012	+	0.778204i	$0.283869\pi$
$468$		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	0.893612	−	0.448840i	$-0.148163\pi$
$479$	1.27156	+	2.20241i	0.0580991	+	0.100631i	−0.835513	+	0.549471i	$0.814829\pi$
$480$		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	$0.204596\pi$
$487$			26.4554i			1.19881i	−0.800447	+	0.599404i	$0.795404\pi$
$488$		0			0
$489$	12.2170	+	38.3469i	0.552470	+	1.73411i
$490$		0			0
$491$	21.9322	−	5.87672i	0.989787	−	0.265213i	0.272626	−	0.962120i	$-0.412108\pi$
$491$	21.9322	−	5.87672i	0.989787	−	0.265213i	0.717161	+	0.696907i	$0.245441\pi$
$492$		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	−0.910421	−	0.413683i	$-0.864242\pi$
$499$	−7.34516	−	27.4125i	−0.328815	−	1.22715i	0.581606	−	0.813470i	$-0.302424\pi$
$500$		0			0
$501$	−19.8918	+	12.7563i	−0.888701	+	0.569910i
$502$		0			0
$503$		−	32.0583i		−	1.42941i	−0.699427	−	0.714704i	$-0.746561\pi$
$503$		−	32.0583i		−	1.42941i	0.699427	−	0.714704i	$-0.253439\pi$
$504$		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	0.922089	+	0.386978i	$0.126481\pi$
$509$	7.15242	+	26.6932i	0.317025	+	1.18316i	−0.605064	+	0.796177i	$0.706852\pi$
$510$		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	$-0.951683\pi$
$521$		−	6.90291i		−	0.302422i	0.988502	−	0.151211i	$-0.0483173\pi$
$522$		0			0
$523$	−14.2754	−	14.2754i	−0.624219	−	0.624219i	0.322389	−	0.946607i	$-0.395514\pi$
$523$	−14.2754	−	14.2754i	−0.624219	−	0.624219i	−0.946607	+	0.322389i	$0.895514\pi$
$524$		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	−0.955078	−	0.296355i	$-0.904229\pi$
$541$	−15.3215	+	15.3215i	−0.658723	+	0.658723i	0.296355	+	0.955078i	$0.404229\pi$
$542$		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	0.170310	−	0.985390i	$-0.445523\pi$
$547$	−4.09038	−	1.09601i	−0.174892	−	0.0468622i	−0.345202	+	0.938528i	$0.612190\pi$
$548$		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	−0.622687	−	0.782471i	$-0.713959\pi$
$557$	3.77104	−	3.77104i	0.159784	−	0.159784i	0.782471	+	0.622687i	$0.213959\pi$
$558$		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	−0.991178	−	0.132534i	$-0.957689\pi$
$563$	−4.72321	−	17.6273i	−0.199060	−	0.742901i	0.792119	−	0.610367i	$-0.208978\pi$
$564$		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	−0.704896	−	0.709311i	$-0.749006\pi$
$569$	−10.5687	+	6.10184i	−0.443062	+	0.255802i	0.261833	+	0.965113i	$0.415673\pi$
$570$		0			0
$571$	−10.1445	+	2.71820i	−0.424533	+	0.113753i	−0.464759	−	0.885437i	$-0.653859\pi$
$571$	−10.1445	+	2.71820i	−0.424533	+	0.113753i	0.0402258	+	0.999191i	$0.487192\pi$
$572$		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	−0.811944	−	0.583735i	$-0.801591\pi$
$587$	4.43586	−	16.5549i	0.183088	−	0.683292i	0.995032	−	0.0995570i	$-0.0317426\pi$
$588$		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	0.595547	−	0.803320i	$-0.296935\pi$
$599$	4.83678	+	2.79252i	0.197626	+	0.114099i	−0.397922	+	0.917419i	$0.630268\pi$
$600$		0			0
$601$	29.8602	−	17.2398i	1.21802	−	0.703227i	0.253529	−	0.967328i	$-0.418409\pi$
$601$	29.8602	−	17.2398i	1.21802	−	0.703227i	0.964495	+	0.264101i	$0.0850753\pi$
$602$		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	−0.977892	−	0.209109i	$-0.932944\pi$
$607$	−7.58467	+	13.1370i	−0.307852	+	0.533216i	0.670040	+	0.742325i	$0.266277\pi$
$608$		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	0.848498	−	0.529198i	$-0.177507\pi$
$613$	7.90551	+	7.90551i	0.319301	+	0.319301i	−0.529198	+	0.848498i	$0.677507\pi$
$614$		0			0
$615$	9.46170	−	10.3879i	0.381533	−	0.418879i
$616$		0			0
$617$	−25.0266	−	14.4491i	−1.00753	−	0.581700i	−0.0970648	−	0.995278i	$-0.530945\pi$
$617$	−25.0266	−	14.4491i	−1.00753	−	0.581700i	−0.910468	+	0.413578i	$0.864279\pi$
$618$		0			0
$619$	−8.96627	+	33.4626i	−0.360385	+	1.34497i	0.513186	+	0.858277i	$0.328465\pi$
$619$	−8.96627	+	33.4626i	−0.360385	+	1.34497i	−0.873571	+	0.486697i	$0.838202\pi$
$620$		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	$0.206973\pi$
$631$			30.4132i			1.21073i	−0.795948	+	0.605365i	$0.793027\pi$
$632$		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	0.717284	−	0.696781i	$-0.245385\pi$
$641$	−6.19753	−	10.7344i	−0.244788	−	0.423985i	−0.962072	+	0.272796i	$0.912052\pi$
$642$		0			0
$643$	−6.97693	−	26.0383i	−0.275143	−	1.02685i	−0.955745	−	0.294195i	$-0.904948\pi$
$643$	−6.97693	−	26.0383i	−0.275143	−	1.02685i	0.680602	−	0.732653i	$-0.261718\pi$
$644$		0			0
$645$	−24.0164	−	12.4110i	−0.945646	−	0.488682i
$646$		0			0
$647$		−	1.44109i		−	0.0566551i	−0.999599	−	0.0283275i	$-0.990982\pi$
$647$		−	1.44109i		−	0.0566551i	0.999599	−	0.0283275i	$-0.00901814\pi$
$648$		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	0.999360	+	0.0357824i	$0.0113923\pi$
$653$	3.87857	+	14.4750i	0.151780	+	0.566451i	−0.847580	+	0.530668i	$0.821941\pi$
$654$		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	0.356000	−	0.934486i	$-0.384140\pi$
$659$	5.05876	+	1.35549i	0.197061	+	0.0528024i	−0.158938	+	0.987289i	$0.550807\pi$
$660$		0			0
$661$	19.8188	−	5.31043i	0.770862	−	0.206552i	0.148110	−	0.988971i	$-0.452681\pi$
$661$	19.8188	−	5.31043i	0.770862	−	0.206552i	0.622752	+	0.782419i	$0.286014\pi$
$662$		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	0.968918	−	0.247383i	$-0.0795706\pi$
$673$	7.01009	+	12.1418i	0.270219	+	0.468033i	−0.698699	+	0.715416i	$0.746237\pi$
$674$		0			0
$675$	−5.10135	+	3.98764i	−0.196351	+	0.153484i
$676$		0			0
$677$	4.35650	−	16.2587i	0.167434	−	0.624872i	−0.830283	−	0.557342i	$-0.811821\pi$
$677$	4.35650	−	16.2587i	0.167434	−	0.624872i	0.997717	−	0.0675306i	$-0.0215120\pi$
$678$		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	−0.999762	−	0.0218370i	$-0.993049\pi$
$683$	−26.6987	−	26.6987i	−1.02160	−	1.02160i	−0.0218370	−	0.999762i	$-0.506951\pi$
$684$		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	0.752757	−	0.658299i	$-0.228724\pi$
$691$	28.2719	+	7.57544i	1.07551	+	0.288183i	0.322757	+	0.946482i	$0.395390\pi$
$692$		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	−0.0847476	+	0.996402i	$0.527008\pi$
$701$	−28.6250	+	28.6250i	−1.08115	+	1.08115i	−0.996402	+	0.0847476i	$0.972992\pi$
$702$		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	−0.701360	−	0.712807i	$-0.747423\pi$
$709$	6.98798	−	26.0795i	0.262439	−	0.979437i	0.963799	−	0.266629i	$-0.0859099\pi$
$710$		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	−0.248130	−	0.968727i	$-0.579816\pi$
$727$	12.5849	−	7.26589i	0.466748	−	0.269477i	0.714877	+	0.699250i	$0.246483\pi$
$728$		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	0.938552	−	0.345137i	$-0.112168\pi$
$733$	−1.26777	−	4.73140i	−0.0468263	−	0.174758i	−0.985379	+	0.170379i	$0.945501\pi$
$734$		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	−0.0174359	+	0.999848i	$0.505550\pi$
$739$	−27.6544	+	27.6544i	−1.01728	+	1.01728i	−0.999848	+	0.0174359i	$0.994450\pi$
$740$		0			0
$741$	−53.6144	+	34.3820i	−1.96957	+	1.26306i
$742$		0			0
$743$	−16.0882	−	9.28853i	−0.590219	−	0.340763i	0.174965	−	0.984575i	$-0.444019\pi$
$743$	−16.0882	−	9.28853i	−0.590219	−	0.340763i	−0.765184	+	0.643812i	$0.777352\pi$
$744$		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	0.349043	+	0.937107i	$0.386507\pi$
$751$	−17.4576	+	30.2374i	−0.637037	+	1.10338i	−0.986080	+	0.166273i	$0.946827\pi$
$752$		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	0.929492	−	0.368843i	$-0.120246\pi$
$757$	15.4255	+	15.4255i	0.560649	+	0.560649i	−0.368843	+	0.929492i	$0.620246\pi$
$758$		0			0
$759$	2.41315	+	7.57446i	0.0875919	+	0.274935i
$760$		0			0
$761$	14.7108	+	8.49331i	0.533268	+	0.307882i	0.742346	−	0.670017i	$-0.233713\pi$
$761$	14.7108	+	8.49331i	0.533268	+	0.307882i	−0.209078	+	0.977899i	$0.567046\pi$
$762$		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	0.157330	+	0.987546i	$0.449712\pi$
$769$	−21.5351	+	37.2999i	−0.776575	+	1.34507i	−0.933905	+	0.357522i	$0.883622\pi$
$770$		0			0
$771$	24.4791	+	38.1720i	0.881594	+	1.37473i
$772$		0			0
$773$	32.8660	+	32.8660i	1.18211	+	1.18211i	0.979198	+	0.202909i	$0.0650394\pi$
$773$	32.8660	+	32.8660i	1.18211	+	1.18211i	0.202909	+	0.979198i	$0.434961\pi$
$774$		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	0.932539	−	0.361069i	$-0.117588\pi$
$787$	−1.55972	−	5.82094i	−0.0555978	−	0.207494i	−0.988137	+	0.153575i	$0.950921\pi$
$788$		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	−0.611788	−	0.791022i	$-0.709549\pi$
$797$	−13.4797	−	50.3069i	−0.477475	−	1.78196i	0.134313	−	0.990939i	$-0.457117\pi$
$798$		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	$0.0690599\pi$
$809$			12.2452i			0.430520i	−0.976557	+	0.215260i	$0.930940\pi$
$810$		0			0
$811$	−34.8977	−	34.8977i	−1.22542	−	1.22542i	−0.965677	−	0.259747i	$-0.916361\pi$
$811$	−34.8977	−	34.8977i	−1.22542	−	1.22542i	−0.259747	−	0.965677i	$-0.583639\pi$
$812$		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	−0.919471	−	0.393157i	$-0.871383\pi$
$821$	2.10293	−	7.84823i	0.0733926	−	0.273905i	0.992864	+	0.119252i	$0.0380496\pi$
$822$		0			0
$823$	11.0255	+	6.36556i	0.384324	+	0.221890i	0.679698	−	0.733492i	$-0.262111\pi$
$823$	11.0255	+	6.36556i	0.384324	+	0.221890i	−0.295374	+	0.955382i	$0.595444\pi$
$824$		0			0
$825$	2.90124	+	0.634090i	0.101008	+	0.0220762i
$826$		0			0
$827$	−7.95914	−	7.95914i	−0.276766	−	0.276766i	0.555050	−	0.831817i	$-0.312699\pi$
$827$	−7.95914	−	7.95914i	−0.276766	−	0.276766i	−0.831817	+	0.555050i	$0.812699\pi$
$828$		0			0
$829$	21.1944	−	21.1944i	0.736113	−	0.736113i	−0.235710	−	0.971823i	$-0.575742\pi$
$829$	21.1944	−	21.1944i	0.736113	−	0.736113i	0.971823	+	0.235710i	$0.0757416\pi$
$830$		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	0.231858	−	0.972750i	$-0.425520\pi$
$839$	34.4751	−	19.9042i	1.19021	−	0.687169i	0.958355	+	0.285580i	$0.0921864\pi$
$840$		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	0.287794	+	0.957692i	$0.407078\pi$
$853$	−12.8592	+	47.9910i	−0.440289	+	1.64318i	−0.728083	+	0.685489i	$0.759589\pi$
$854$		0			0
$855$	−49.7529	+	4.65292i	−1.70151	+	0.159126i
$856$		0			0
$857$	−1.84308	+	1.06410i	−0.0629582	+	0.0363490i	−0.531149	−	0.847279i	$-0.678239\pi$
$857$	−1.84308	+	1.06410i	−0.0629582	+	0.0363490i	0.468190	+	0.883628i	$0.344906\pi$
$858$		0			0
$859$	−9.11407	+	2.44211i	−0.310968	+	0.0833237i	−0.410928	−	0.911668i	$-0.634795\pi$
$859$	−9.11407	+	2.44211i	−0.310968	+	0.0833237i	0.0999599	+	0.994991i	$0.468129\pi$
$860$		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	−0.999372	−	0.0354241i	$-0.988722\pi$
$877$	−4.48959	−	16.7554i	−0.151603	−	0.565789i	0.847770	−	0.530364i	$-0.177945\pi$
$878$		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	−0.818054	−	0.575141i	$-0.804947\pi$
$883$	−7.21822	+	7.21822i	−0.242913	+	0.242913i	0.575141	+	0.818054i	$0.304947\pi$
$884$		0			0
$885$	0.461791	+	9.89727i	0.0155229	+	0.332693i
$886$		0			0
$887$	−32.3743	−	18.6913i	−1.08702	−	0.627592i	−0.154240	−	0.988033i	$-0.549293\pi$
$887$	−32.3743	−	18.6913i	−1.08702	−	0.627592i	−0.932782	+	0.360441i	$0.882626\pi$
$888$		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	0.730998	+	0.682380i	$0.239055\pi$
$907$	−7.32597	+	27.3409i	−0.243255	+	0.907840i	−0.974253	+	0.225460i	$0.927612\pi$
$908$		0			0
$909$	50.2468	−	18.6295i	1.66658	−	0.617902i
$910$		0			0
$911$	12.2805	+	21.2704i	0.406871	+	0.704721i	0.994537	−	0.104383i	$-0.0332867\pi$
$911$	12.2805	+	21.2704i	0.406871	+	0.704721i	−0.587667	+	0.809103i	$0.699953\pi$
$912$		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	$0.114611\pi$
$919$			21.3619i			0.704665i	−0.935875	+	0.352332i	$0.885389\pi$
$920$		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	0.878598	−	0.477561i	$-0.158479\pi$
$929$	0.783906	+	1.35776i	0.0257191	+	0.0445468i	−0.852879	+	0.522108i	$0.825146\pi$
$930$		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	$0.227445\pi$
$937$			40.1161i			1.31054i	−0.755396	+	0.655269i	$0.772555\pi$
$938$		0			0
$939$	0.270493	+	5.79731i	0.00882721	+	0.189188i
$940$		0			0
$941$	−10.7101	−	39.9706i	−0.349139	−	1.30300i	−0.887702	−	0.460419i	$-0.847699\pi$
$941$	−10.7101	−	39.9706i	−0.349139	−	1.30300i	0.538562	−	0.842586i	$-0.318968\pi$
$942$		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	−0.300685	−	0.953724i	$-0.597215\pi$
$947$	−31.9411	−	8.55860i	−1.03795	−	0.278117i	−0.737263	+	0.675606i	$0.763882\pi$
$948$		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	$0.0319499\pi$
$953$			6.18680i			0.200410i	−0.994967	+	0.100205i	$0.968050\pi$
$954$		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	0.0403133	−	0.999187i	$-0.487164\pi$
$967$	−25.0282	−	14.4500i	−0.804851	−	0.464681i	−0.845165	+	0.534506i	$0.820498\pi$
$968$		0			0
$969$	18.8332	+	59.1142i	0.605010	+	1.89902i
$970$		0			0
$971$	41.1803	+	41.1803i	1.32154	+	1.32154i	0.912531	+	0.409008i	$0.134125\pi$
$971$	41.1803	+	41.1803i	1.32154	+	1.32154i	0.409008	+	0.912531i	$0.365875\pi$
$972$		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	0.413444	+	0.910530i	$0.364326\pi$
$977$	−18.1859	+	31.4990i	−0.581820	+	1.00774i	−0.995264	+	0.0972120i	$0.969008\pi$
$978$		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	0.532803	−	0.846239i	$-0.321139\pi$
$983$	48.0347	−	27.7329i	1.53207	−	0.884541i	0.999266	−	0.0383018i	$-0.0121948\pi$
$984$		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	0.729506	+	0.683974i	$0.239750\pi$
$997$	−7.71233	+	28.7828i	−0.244252	+	0.911561i	−0.973758	+	0.227586i	$0.926917\pi$
$998$		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.49.12		72
3.2	odd	2		1728.2.bc.e.1009.16		72
4.3	odd	2		144.2.x.e.85.16	yes	72
9.2	odd	6		1728.2.bc.e.1585.3		72
9.7	even	3	inner	576.2.bb.e.241.17		72
12.11	even	2		432.2.y.e.37.3		72
16.3	odd	4		144.2.x.e.13.8	✓	72
16.13	even	4	inner	576.2.bb.e.337.17		72
36.7	odd	6		144.2.x.e.133.8	yes	72
36.11	even	6		432.2.y.e.181.11		72
48.29	odd	4		1728.2.bc.e.145.3		72
48.35	even	4		432.2.y.e.253.11		72
144.29	odd	12		1728.2.bc.e.721.16		72
144.61	even	12	inner	576.2.bb.e.529.12		72
144.83	even	12		432.2.y.e.397.3		72
144.115	odd	12		144.2.x.e.61.16	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.8	✓	72	16.3	odd	4
144.2.x.e.61.16	yes	72	144.115	odd	12
144.2.x.e.85.16	yes	72	4.3	odd	2
144.2.x.e.133.8	yes	72	36.7	odd	6
432.2.y.e.37.3		72	12.11	even	2
432.2.y.e.181.11		72	36.11	even	6
432.2.y.e.253.11		72	48.35	even	4
432.2.y.e.397.3		72	144.83	even	12
576.2.bb.e.49.12		72	1.1	even	1	trivial
576.2.bb.e.241.17		72	9.7	even	3	inner
576.2.bb.e.337.17		72	16.13	even	4	inner
576.2.bb.e.529.12		72	144.61	even	12	inner
1728.2.bc.e.145.3		72	48.29	odd	4
1728.2.bc.e.721.16		72	144.29	odd	12
1728.2.bc.e.1009.16		72	3.2	odd	2
1728.2.bc.e.1585.3		72	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:	\( k \)	\(=\)	\( 2 \)
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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