LMFDB - Embedded newform 576.2.bb.e.337.17

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			337.17
Character	$\chi$	$=$	576.337
Dual form			576.2.bb.e.241.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.53873 + 0.795173i) q^{3} +(0.646846 + 2.41406i) q^{5} +(2.82197 - 1.62927i) q^{7} +(1.73540 + 2.44712i) q^{9} +O(q^{10})$	\(q+(1.53873 + 0.795173i) q^{3} +(0.646846 + 2.41406i) q^{5} +(2.82197 - 1.62927i) q^{7} +(1.73540 + 2.44712i) q^{9} +(1.32906 + 0.356120i) q^{11} +(-5.32945 + 1.42802i) q^{13} +(-0.924273 + 4.22895i) q^{15} +5.37452 q^{17} +(-4.71269 - 4.71269i) q^{19} +(5.63781 - 0.263051i) q^{21} +(-2.88877 - 1.66783i) q^{23} +(-1.07916 + 0.623053i) q^{25} +(0.724438 + 5.14540i) q^{27} +(0.814251 - 3.03883i) q^{29} +(-0.621800 + 1.07699i) q^{31} +(1.76189 + 1.60481i) q^{33} +(5.75853 + 5.75853i) q^{35} +(-5.86087 + 5.86087i) q^{37} +(-9.33612 - 2.04049i) q^{39} +(2.81108 + 1.62298i) q^{41} +(6.03232 + 1.61636i) q^{43} +(-4.78496 + 5.77227i) q^{45} +(-2.17485 - 3.76695i) q^{47} +(1.80902 - 3.13331i) q^{49} +(8.26995 + 4.27367i) q^{51} +(-0.134334 + 0.134334i) q^{53} +3.43879i q^{55} +(-3.50417 - 10.9990i) q^{57} +(-0.592405 - 2.21088i) q^{59} +(0.615960 - 2.29879i) q^{61} +(8.88426 + 4.07827i) q^{63} +(-6.89466 - 11.9419i) q^{65} +(-0.112274 + 0.0300838i) q^{67} +(-3.11884 - 4.86343i) q^{69} -3.21118i q^{71} -9.75441i q^{73} +(-2.15597 + 0.100594i) q^{75} +(4.33078 - 1.16043i) q^{77} +(-1.11184 - 1.92576i) q^{79} +(-2.97677 + 8.49346i) q^{81} +(1.54010 - 5.74772i) q^{83} +(3.47649 + 12.9744i) q^{85} +(3.66931 - 4.02848i) q^{87} +6.12376i q^{89} +(-12.7129 + 12.7129i) q^{91} +(-1.81318 + 1.16276i) q^{93} +(8.32833 - 14.4251i) q^{95} +(-2.21495 - 3.83640i) q^{97} +(1.43498 + 3.87037i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

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

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
$3$	1.53873	+	0.795173i	0.888388	+	0.459093i
$3$	1.53873	+	0.795173i	0.888388	+	0.459093i
$4$		0			0
$5$	0.646846	+	2.41406i	0.289278	+	1.07960i	0.945656	+	0.325169i	$0.105421\pi$
$5$	0.646846	+	2.41406i	0.289278	+	1.07960i	−0.656378	+	0.754433i	$0.727912\pi$
$6$		0			0
$7$	2.82197	−	1.62927i	1.06661	−	0.615805i	0.139353	−	0.990243i	$-0.455498\pi$
$7$	2.82197	−	1.62927i	1.06661	−	0.615805i	0.927252	+	0.374438i	$0.122164\pi$
$8$		0			0
$9$	1.73540	+	2.44712i	0.578467	+	0.815706i
$10$		0			0
$11$	1.32906	+	0.356120i	0.400726	+	0.107374i	0.453553	−	0.891229i	$-0.350156\pi$
$11$	1.32906	+	0.356120i	0.400726	+	0.107374i	−0.0528265	+	0.998604i	$0.516823\pi$
$12$		0			0
$13$	−5.32945	+	1.42802i	−1.47812	+	0.396062i	−0.905708	−	0.423903i	$-0.860660\pi$
$13$	−5.32945	+	1.42802i	−1.47812	+	0.396062i	−0.572415	+	0.819964i	$0.693993\pi$
$14$		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
$21$	5.63781	−	0.263051i	1.23027	−	0.0574025i
$22$		0			0
$23$	−2.88877	−	1.66783i	−0.602351	−	0.347767i	0.167615	−	0.985853i	$-0.446393\pi$
$23$	−2.88877	−	1.66783i	−0.602351	−	0.347767i	−0.769966	+	0.638085i	$0.779727\pi$
$24$		0			0
$25$	−1.07916	+	0.623053i	−0.215832	+	0.124611i
$26$		0			0
$27$	0.724438	+	5.14540i	0.139418	+	0.990234i
$28$		0			0
$29$	0.814251	−	3.03883i	0.151203	−	0.564296i	−0.848198	−	0.529679i	$-0.822312\pi$
$29$	0.814251	−	3.03883i	0.151203	−	0.564296i	0.999401	−	0.0346168i	$-0.0110211\pi$
$30$		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	−0.999358	−	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	$-0.251763\pi$
$41$	2.81108	+	1.62298i	0.439017	+	0.253467i	−0.264163	+	0.964478i	$0.585096\pi$
$42$		0			0
$43$	6.03232	+	1.61636i	0.919920	+	0.246492i	0.687551	−	0.726136i	$-0.258686\pi$
$43$	6.03232	+	1.61636i	0.919920	+	0.246492i	0.232369	+	0.972628i	$0.425352\pi$
$44$		0			0
$45$	−4.78496	+	5.77227i	−0.713299	+	0.860480i
$46$		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
$51$	8.26995	+	4.27367i	1.15803	+	0.598434i
$52$		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
$59$	−0.592405	−	2.21088i	−0.0771245	−	0.287833i	0.916582	−	0.399846i	$-0.130937\pi$
$59$	−0.592405	−	2.21088i	−0.0771245	−	0.287833i	−0.993707	+	0.112014i	$0.964270\pi$
$60$		0			0
$61$	0.615960	−	2.29879i	0.0788656	−	0.294330i	−0.915216	−	0.402963i	$-0.867980\pi$
$61$	0.615960	−	2.29879i	0.0788656	−	0.294330i	0.994082	+	0.108632i	$0.0346471\pi$
$62$		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
$67$	−0.112274	+	0.0300838i	−0.0137165	+	0.00367532i	−0.265671	−	0.964064i	$-0.585593\pi$
$67$	−0.112274	+	0.0300838i	−0.0137165	+	0.00367532i	0.251954	+	0.967739i	$0.418927\pi$
$68$		0			0
$69$	−3.11884	−	4.86343i	−0.375464	−	0.585488i
$70$		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
$75$	−2.15597	+	0.100594i	−0.248950	+	0.0116156i
$76$		0			0
$77$	4.33078	−	1.16043i	0.493538	−	0.132243i
$78$		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
$83$	1.54010	−	5.74772i	0.169048	−	0.630895i	−0.828441	−	0.560076i	$-0.810772\pi$
$83$	1.54010	−	5.74772i	0.169048	−	0.630895i	0.997489	−	0.0708190i	$-0.0225613\pi$
$84$		0			0
$85$	3.47649	+	12.9744i	0.377078	+	1.40727i
$86$		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
$93$	−1.81318	+	1.16276i	−0.188018	+	0.120573i
$94$		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
$99$	1.43498	+	3.87037i	0.144221	+	0.388987i
$100$		0			0
$101$	17.2544	+	4.62330i	1.71688	+	0.460035i	0.977093	−	0.212811i	$-0.0682619\pi$
$101$	17.2544	+	4.62330i	1.71688	+	0.460035i	0.739782	+	0.672847i	$0.234929\pi$
$102$		0			0
$103$	−8.73448	−	5.04285i	−0.860634	−	0.496887i	0.00359067	−	0.999994i	$-0.498857\pi$
$103$	−8.73448	−	5.04285i	−0.860634	−	0.496887i	−0.864224	+	0.503106i	$0.832190\pi$
$104$		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	−0.451849	−	0.892094i	$-0.649236\pi$
$113$	5.81099	−	10.0649i	0.546652	−	0.946828i	0.998501	−	0.0547341i	$-0.0174311\pi$
$114$		0			0
$115$	2.15766	−	8.05251i	0.201203	−	0.750900i
$116$		0			0
$117$	−12.7433	−	10.5636i	−1.17811	−	0.976604i
$118$		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
$123$	3.03496	+	4.73263i	0.273653	+	0.426727i
$124$		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
$131$	−14.6861	+	3.93512i	−1.28313	+	0.343813i	−0.835047	−	0.550179i	$-0.814560\pi$
$131$	−14.6861	+	3.93512i	−1.28313	+	0.343813i	−0.448082	+	0.893992i	$0.647893\pi$
$132$		0			0
$133$	−20.9773	−	5.62085i	−1.81896	−	0.487389i
$134$		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	$-0.859419\pi$
$137$	−11.5397	+	6.66247i	−0.985906	+	0.569213i	−0.0818576	+	0.996644i	$0.526085\pi$
$138$		0			0
$139$	−4.34417	−	16.2127i	−0.368468	−	1.37514i	−0.862658	−	0.505787i	$-0.831202\pi$
$139$	−4.34417	−	16.2127i	−0.368468	−	1.37514i	0.494191	−	0.869354i	$-0.335465\pi$
$140$		0			0
$141$	−0.351138	−	7.52571i	−0.0295712	−	0.633779i
$142$		0			0
$143$	−7.59170			−0.634849
$144$		0			0
$145$	7.86261			0.652955
$146$		0			0
$147$	5.27511	−	3.38285i	0.435084	−	0.279012i
$148$		0			0
$149$	−3.42362	−	12.7771i	−0.280474	−	1.04674i	−0.952084	−	0.305838i	$-0.901063\pi$
$149$	−3.42362	−	12.7771i	−0.280474	−	1.04674i	0.671610	−	0.740905i	$-0.265603\pi$
$150$		0			0
$151$	−10.3438	+	5.97202i	−0.841769	+	0.485996i	−0.857865	−	0.513875i	$-0.828210\pi$
$151$	−10.3438	+	5.97202i	−0.841769	+	0.485996i	0.0160959	+	0.999870i	$0.494876\pi$
$152$		0			0
$153$	9.32695	+	13.1521i	0.754039	+	1.06328i
$154$		0			0
$155$	−3.00213	−	0.804418i	−0.241137	−	0.0646124i
$156$		0			0
$157$	14.4957	−	3.88412i	1.15689	−	0.309986i	0.371164	−	0.928567i	$-0.378959\pi$
$157$	14.4957	−	3.88412i	1.15689	−	0.309986i	0.785721	+	0.618581i	$0.212292\pi$
$158$		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
$165$	−2.73443	+	5.29137i	−0.212875	+	0.411933i
$166$		0			0
$167$	11.8153	+	6.82158i	0.914297	+	0.527870i	0.881811	−	0.471602i	$-0.156324\pi$
$167$	11.8153	+	6.82158i	0.914297	+	0.527870i	0.0324861	+	0.999472i	$0.489658\pi$
$168$		0			0
$169$	15.1054	−	8.72112i	1.16196	−	0.670855i
$170$		0			0
$171$	3.35410	−	19.7109i	0.256494	−	1.50733i
$172$		0			0
$173$	1.15666	−	4.31671i	0.0879391	−	0.328193i	−0.907915	−	0.419153i	$-0.862327\pi$
$173$	1.15666	−	4.31671i	0.0879391	−	0.328193i	0.995855	+	0.0909602i	$0.0289936\pi$
$174$		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
$187$	7.14305	+	1.91398i	0.522352	+	0.139964i
$188$		0			0
$189$	10.4276	+	13.3399i	0.758495	+	0.970334i
$190$		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
$195$	−1.11317	−	23.8579i	−0.0797158	−	1.70850i
$196$		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
$203$	−2.65326	−	9.90212i	−0.186223	−	0.694992i
$204$		0			0
$205$	−2.09963	+	7.83594i	−0.146645	+	0.547286i
$206$		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
$211$	−5.80646	+	1.55584i	−0.399733	+	0.107108i	−0.453084	−	0.891468i	$-0.649676\pi$
$211$	−5.80646	+	1.55584i	−0.399733	+	0.107108i	0.0533513	+	0.998576i	$0.483010\pi$
$212$		0			0
$213$	2.55344	−	4.94115i	0.174959	−	0.338562i
$214$		0			0
$215$			15.6079i			1.06445i
$216$		0			0
$217$			4.05231i			0.275089i
$218$		0			0
$219$	7.75644	−	15.0094i	0.524131	−	1.01424i
$220$		0			0
$221$	−28.6432	+	7.67493i	−1.92675	+	0.516271i
$222$		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
$227$	−4.64336	+	17.3293i	−0.308191	+	1.15018i	0.621973	+	0.783039i	$0.286331\pi$
$227$	−4.64336	+	17.3293i	−0.308191	+	1.15018i	−0.930164	+	0.367145i	$0.880335\pi$
$228$		0			0
$229$	2.45857	+	9.17552i	0.162467	+	0.606335i	0.998350	+	0.0574270i	$0.0182896\pi$
$229$	2.45857	+	9.17552i	0.162467	+	0.606335i	−0.835883	+	0.548908i	$0.815044\pi$
$230$		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
$237$	−0.179511	−	3.84733i	−0.0116605	−	0.249911i
$238$		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
$243$	−11.3342	+	10.7021i	−0.727090	+	0.686542i
$244$		0			0
$245$	8.73415	+	2.34031i	0.558005	+	0.149517i
$246$		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	0.0916380	+	0.995792i	$0.470790\pi$
$257$	−13.0905	+	22.6734i	−0.816563	+	1.41433i	−0.908201	+	0.418535i	$0.862544\pi$
$258$		0			0
$259$	−6.99029	+	26.0881i	−0.434356	+	1.62104i
$260$		0			0
$261$	8.84942	−	3.28102i	0.547765	−	0.203090i
$262$		0			0
$263$	6.75594	−	3.90054i	0.416589	−	0.240518i	−0.277028	−	0.960862i	$-0.589349\pi$
$263$	6.75594	−	3.90054i	0.416589	−	0.240518i	0.693617	+	0.720344i	$0.256016\pi$
$264$		0			0
$265$	−0.411185	−	0.237398i	−0.0252589	−	0.0145832i
$266$		0			0
$267$	−4.86945	+	9.42284i	−0.298005	+	0.576668i
$268$		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
$275$	−1.65615	+	0.443764i	−0.0998695	+	0.0267599i
$276$		0			0
$277$	0.891589	+	0.238901i	0.0535704	+	0.0143541i	0.285505	−	0.958377i	$-0.407839\pi$
$277$	0.891589	+	0.238901i	0.0535704	+	0.0143541i	−0.231934	+	0.972731i	$0.574505\pi$
$278$		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	$-0.343603\pi$
$281$	24.6632	−	14.2393i	1.47128	−	0.849446i	0.999480	+	0.0322571i	$0.0102695\pi$
$282$		0			0
$283$	1.71872	+	6.41436i	0.102167	+	0.381294i	0.998008	−	0.0630806i	$-0.0200925\pi$
$283$	1.71872	+	6.41436i	0.102167	+	0.381294i	−0.895841	+	0.444375i	$0.853426\pi$
$284$		0			0
$285$	24.2855	−	15.5739i	1.43855	−	0.922519i
$286$		0			0
$287$	10.5771			0.624344
$288$		0			0
$289$	11.8855			0.699145
$290$		0			0
$291$	−0.357612	−	7.66447i	−0.0209636	−	0.449299i
$292$		0			0
$293$	2.52439	+	9.42116i	0.147477	+	0.550390i	0.999633	+	0.0271023i	$0.00862799\pi$
$293$	2.52439	+	9.42116i	0.147477	+	0.550390i	−0.852156	+	0.523288i	$0.824705\pi$
$294$		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
$299$	17.7773	+	4.76340i	1.02809	+	0.275475i
$300$		0			0
$301$	19.6565	−	5.26694i	1.13298	−	0.303582i
$302$		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
$309$	−9.43010	−	14.7050i	−0.536459	−	0.836540i
$310$		0			0
$311$	−5.56997	−	3.21582i	−0.315844	−	0.182353i	0.333695	−	0.942681i	$-0.391705\pi$
$311$	−5.56997	−	3.21582i	−0.315844	−	0.182353i	−0.649539	+	0.760329i	$0.725038\pi$
$312$		0			0
$313$	2.90181	−	1.67536i	0.164020	−	0.0946969i	−0.415743	−	0.909482i	$-0.636478\pi$
$313$	2.90181	−	1.67536i	0.164020	−	0.0946969i	0.579763	+	0.814785i	$0.303145\pi$
$314$		0			0
$315$	−4.09844	+	24.0852i	−0.230921	+	1.35705i
$316$		0			0
$317$	3.92134	−	14.6346i	0.220244	−	0.821963i	−0.764010	−	0.645204i	$-0.776772\pi$
$317$	3.92134	−	14.6346i	0.220244	−	0.821963i	0.984254	−	0.176758i	$-0.0565611\pi$
$318$		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
$331$	−10.0096	−	2.68206i	−0.550177	−	0.147420i	−0.0269876	−	0.999636i	$-0.508591\pi$
$331$	−10.0096	−	2.68206i	−0.550177	−	0.147420i	−0.523190	+	0.852216i	$0.675258\pi$
$332$		0			0
$333$	−24.5132	−	4.17128i	−1.34331	−	0.228585i
$334$		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
$339$	16.9449	−	10.8665i	0.920321	−	0.590187i
$340$		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
$347$	6.30523	+	23.5314i	0.338482	+	1.26323i	0.900044	+	0.435798i	$0.143534\pi$
$347$	6.30523	+	23.5314i	0.338482	+	1.26323i	−0.561562	+	0.827435i	$0.689799\pi$
$348$		0			0
$349$	−7.44289	+	27.7772i	−0.398409	+	1.48688i	0.417487	+	0.908683i	$0.362911\pi$
$349$	−7.44289	+	27.7772i	−0.398409	+	1.48688i	−0.815896	+	0.578199i	$0.803756\pi$
$350$		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
$355$	7.75199	−	2.07714i	0.411433	−	0.110243i
$356$		0			0
$357$	30.3005	−	1.41378i	1.60367	−	0.0748249i
$358$		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
$363$	−8.51480	−	13.2777i	−0.446911	−	0.696901i
$364$		0			0
$365$	23.5477	−	6.30960i	1.23255	−	0.330259i
$366$		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
$371$	−0.160221	+	0.597954i	−0.00831828	+	0.0310442i
$372$		0			0
$373$	0.864710	+	3.22714i	0.0447730	+	0.167095i	0.984692	−	0.174302i	$-0.0557667\pi$
$373$	0.864710	+	3.22714i	0.0447730	+	0.167095i	−0.939919	+	0.341397i	$0.889100\pi$
$374$		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
$381$	11.3523	+	5.86656i	0.581598	+	0.300553i
$382$		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
$387$	6.51308	+	17.5668i	0.331079	+	0.892971i
$388$		0			0
$389$	−13.9149	−	3.72849i	−0.705513	−	0.189042i	−0.111815	−	0.993729i	$-0.535666\pi$
$389$	−13.9149	−	3.72849i	−0.705513	−	0.189042i	−0.593699	+	0.804687i	$0.702333\pi$
$390$		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	−0.935105	−	0.354370i	$-0.884695\pi$
$401$	−3.21720	+	5.57235i	−0.160659	+	0.278270i	0.774446	+	0.632640i	$0.218029\pi$
$402$		0			0
$403$	1.77589	−	6.62770i	0.0884633	−	0.330149i
$404$		0			0
$405$	−22.4292	−	1.69214i	−1.11452	−	0.0840832i
$406$		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	$-0.969674\pi$
$409$	−31.8642	−	18.3968i	−1.57558	−	0.909663i	−0.580117	−	0.814533i	$-0.696993\pi$
$410$		0			0
$411$	−23.0544	+	1.07568i	−1.13719	+	0.0530594i
$412$		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
$419$	−21.5747	+	5.78093i	−1.05399	+	0.282417i	−0.743901	−	0.668290i	$-0.767027\pi$
$419$	−21.5747	+	5.78093i	−1.05399	+	0.282417i	−0.310093	+	0.950706i	$0.600360\pi$
$420$		0			0
$421$	−8.71347	−	2.33477i	−0.424669	−	0.113790i	0.0401539	−	0.999194i	$-0.487215\pi$
$421$	−8.71347	−	2.33477i	−0.424669	−	0.113790i	−0.464822	+	0.885404i	$0.653882\pi$
$422$		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
$427$	−2.00713	−	7.49070i	−0.0971316	−	0.362500i
$428$		0			0
$429$	−11.6816	−	6.03671i	−0.563993	−	0.291455i
$430$		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
$435$	12.0985	+	6.25214i	0.580077	+	0.299767i
$436$		0			0
$437$	5.75390	+	21.4739i	0.275246	+	1.02723i
$438$		0			0
$439$	5.53112	−	3.19339i	0.263986	−	0.152412i	−0.362166	−	0.932114i	$-0.617963\pi$
$439$	5.53112	−	3.19339i	0.263986	−	0.152412i	0.626151	+	0.779701i	$0.284629\pi$
$440$		0			0
$441$	10.8069	−	1.01067i	0.514616	−	0.0481272i
$442$		0			0
$443$	−16.1600	−	4.33005i	−0.767783	−	0.205727i	−0.146391	−	0.989227i	$-0.546766\pi$
$443$	−16.1600	−	4.33005i	−0.767783	−	0.205727i	−0.621392	+	0.783500i	$0.713432\pi$
$444$		0			0
$445$	−14.7831	+	3.96113i	−0.700788	+	0.187776i
$446$		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
$453$	−20.6652	+	0.964205i	−0.970935	+	0.0453023i
$454$		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	$-0.420339\pi$
$457$	25.8782	−	14.9408i	1.21053	−	0.698901i	0.962875	+	0.269946i	$0.0870060\pi$
$458$		0			0
$459$	3.89351	+	27.6541i	0.181733	+	1.29078i
$460$		0			0
$461$	−7.22887	+	26.9785i	−0.336682	+	1.25651i	0.565352	+	0.824850i	$0.308740\pi$
$461$	−7.22887	+	26.9785i	−0.336682	+	1.25651i	−0.902034	+	0.431665i	$0.857926\pi$
$462$		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	0.628012	−	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
$475$	8.02199	+	2.14949i	0.368074	+	0.0986252i
$476$		0			0
$477$	−0.561856	−	0.0956080i	−0.0257256	−	0.00437759i
$478$		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
$483$	−16.7251	−	8.64304i	−0.761018	−	0.393272i
$484$		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
$491$	−5.87672	−	21.9322i	−0.265213	−	0.989787i	−0.962120	−	0.272626i	$-0.912108\pi$
$491$	−5.87672	−	21.9322i	−0.265213	−	0.989787i	0.696907	−	0.717161i	$-0.254559\pi$
$492$		0			0
$493$	4.37621	−	16.3322i	0.197095	−	0.735567i
$494$		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
$499$	27.4125	−	7.34516i	1.22715	−	0.328815i	0.413683	−	0.910421i	$-0.364242\pi$
$499$	27.4125	−	7.34516i	1.22715	−	0.328815i	0.813470	+	0.581606i	$0.197576\pi$
$500$		0			0
$501$	12.7563	+	19.8918i	0.569910	+	0.888701i
$502$		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
$507$	30.1780	−	1.40806i	1.34025	−	0.0625341i
$508$		0			0
$509$	−26.6932	+	7.15242i	−1.18316	+	0.317025i	−0.796177	−	0.605064i	$-0.793148\pi$
$509$	−26.6932	+	7.15242i	−1.18316	+	0.317025i	−0.386978	+	0.922089i	$0.626481\pi$
$510$		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
$515$	6.52390	−	24.3475i	0.287477	−	1.07288i
$516$		0			0
$517$	−1.54902	−	5.78101i	−0.0681256	−	0.254248i
$518$		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
$525$	−5.92020	+	3.79653i	−0.258379	+	0.165694i
$526$		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
$531$	4.38223	−	5.28645i	0.190173	−	0.229413i
$532$		0			0
$533$	−17.2992	−	4.63529i	−0.749310	−	0.200777i
$534$		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
$547$	1.09601	−	4.09038i	0.0468622	−	0.174892i	−0.938528	−	0.345202i	$-0.887810\pi$
$547$	1.09601	−	4.09038i	0.0468622	−	0.174892i	0.985390	+	0.170310i	$0.0544770\pi$
$548$		0			0
$549$	6.69436	−	2.48200i	0.285708	−	0.105929i
$550$		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
$555$	−19.3683	−	30.2024i	−0.822138	−	1.28202i
$556$		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
$563$	17.6273	−	4.72321i	0.742901	−	0.199060i	0.132534	−	0.991178i	$-0.457689\pi$
$563$	17.6273	−	4.72321i	0.742901	−	0.199060i	0.610367	+	0.792119i	$0.291022\pi$
$564$		0			0
$565$	28.0562	+	7.51763i	1.18033	+	0.316269i
$566$		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	$-0.584327\pi$
$569$	10.5687	−	6.10184i	0.443062	−	0.255802i	0.704896	+	0.709311i	$0.250994\pi$
$570$		0			0
$571$	2.71820	+	10.1445i	0.113753	+	0.424533i	0.999191	−	0.0402258i	$-0.0128077\pi$
$571$	2.71820	+	10.1445i	0.113753	+	0.424533i	−0.885437	+	0.464759i	$0.846141\pi$
$572$		0			0
$573$	−0.889348	−	19.0608i	−0.0371531	−	0.796277i
$574$		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
$579$	−23.9756	+	15.3752i	−0.996391	+	0.638970i
$580$		0			0
$581$	−5.01846	−	18.7291i	−0.208201	−	0.777016i
$582$		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
$587$	−16.5549	−	4.43586i	−0.683292	−	0.183088i	−0.0995570	−	0.995032i	$-0.531743\pi$
$587$	−16.5549	−	4.43586i	−0.683292	−	0.183088i	−0.583735	+	0.811944i	$0.698409\pi$
$588$		0			0
$589$	8.00586	−	2.14516i	0.329876	−	0.0883900i
$590$		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
$597$	−9.49332	+	18.3705i	−0.388536	+	0.751853i
$598$		0			0
$599$	−4.83678	−	2.79252i	−0.197626	−	0.114099i	0.397922	−	0.917419i	$-0.369732\pi$
$599$	−4.83678	−	2.79252i	−0.197626	−	0.114099i	−0.595547	+	0.803320i	$0.703065\pi$
$600$		0			0
$601$	−29.8602	+	17.2398i	−1.21802	+	0.703227i	−0.964495	−	0.264101i	$-0.914925\pi$
$601$	−29.8602	+	17.2398i	−1.21802	+	0.703227i	−0.253529	+	0.967328i	$0.581591\pi$
$602$		0			0
$603$	−0.268460	−	0.222541i	−0.0109325	−	0.00906257i
$604$		0			0
$605$	5.89068	−	21.9843i	0.239490	−	0.893790i
$606$		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	−0.529198	−	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	$-0.135721\pi$
$617$	25.0266	+	14.4491i	1.00753	+	0.581700i	0.0970648	+	0.995278i	$0.469055\pi$
$618$		0			0
$619$	33.4626	+	8.96627i	1.34497	+	0.360385i	0.858277	−	0.513186i	$-0.171535\pi$
$619$	33.4626	+	8.96627i	1.34497	+	0.360385i	0.486697	+	0.873571i	$0.338202\pi$
$620$		0			0
$621$	6.48894	−	16.0722i	0.260392	−	0.644953i
$622$		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
$627$	−0.740291	−	15.8662i	−0.0295644	−	0.633634i
$628$		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
$635$	4.77225	+	17.8103i	0.189381	+	0.706779i
$636$		0			0
$637$	−5.16663	+	19.2821i	−0.204709	+	0.763985i
$638$		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
$643$	26.0383	−	6.97693i	1.02685	−	0.275143i	0.294195	−	0.955745i	$-0.404948\pi$
$643$	26.0383	−	6.97693i	1.02685	−	0.275143i	0.732653	+	0.680602i	$0.238282\pi$
$644$		0			0
$645$	−12.4110	+	24.0164i	−0.488682	+	0.945646i
$646$		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
$651$	−3.22229	+	6.23543i	−0.126291	+	0.244386i
$652$		0			0
$653$	−14.4750	+	3.87857i	−0.566451	+	0.151780i	−0.530668	−	0.847580i	$-0.678059\pi$
$653$	−14.4750	+	3.87857i	−0.566451	+	0.151780i	−0.0357824	+	0.999360i	$0.511392\pi$
$654$		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
$659$	−1.35549	+	5.05876i	−0.0528024	+	0.197061i	−0.987289	−	0.158938i	$-0.949193\pi$
$659$	−1.35549	+	5.05876i	−0.0528024	+	0.197061i	0.934486	+	0.356000i	$0.115860\pi$
$660$		0			0
$661$	−5.31043	−	19.8188i	−0.206552	−	0.770862i	−0.988971	−	0.148110i	$-0.952681\pi$
$661$	−5.31043	−	19.8188i	−0.206552	−	0.770862i	0.782419	−	0.622752i	$-0.213986\pi$
$662$		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
$669$	−0.668728	−	14.3324i	−0.0258545	−	0.554123i
$670$		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
$675$	−3.98764	−	5.10135i	−0.153484	−	0.196351i
$676$		0			0
$677$	−16.2587	−	4.35650i	−0.624872	−	0.167434i	−0.0675306	−	0.997717i	$-0.521512\pi$
$677$	−16.2587	−	4.35650i	−0.624872	−	0.167434i	−0.557342	+	0.830283i	$0.688179\pi$
$678$		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
$691$	−7.57544	+	28.2719i	−0.288183	+	1.07551i	0.658299	+	0.752757i	$0.271276\pi$
$691$	−7.57544	+	28.2719i	−0.288183	+	1.07551i	−0.946482	+	0.322757i	$0.895390\pi$
$692$		0			0
$693$	10.3553	+	8.58412i	0.393367	+	0.326084i
$694$		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
$699$	−5.08603	+	9.84195i	−0.192371	+	0.372257i
$700$		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
$707$	56.2240	−	15.0652i	2.11452	−	0.566584i
$708$		0			0
$709$	−26.0795	−	6.98798i	−0.979437	−	0.262439i	−0.266629	−	0.963799i	$-0.585910\pi$
$709$	−26.0795	−	6.98798i	−0.979437	−	0.262439i	−0.712807	+	0.701360i	$0.752577\pi$
$710$		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
$715$	−4.91066	−	18.3268i	−0.183648	−	0.685384i
$716$		0			0
$717$	−36.1630	+	23.1907i	−1.35053	+	0.866073i
$718$		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
$723$	0.698341	+	14.9671i	0.0259716	+	0.556632i
$724$		0			0
$725$	1.01464	+	3.78670i	0.0376829	+	0.140635i
$726$		0			0
$727$	−12.5849	+	7.26589i	−0.466748	+	0.269477i	−0.714877	−	0.699250i	$-0.753517\pi$
$727$	−12.5849	+	7.26589i	−0.466748	+	0.269477i	0.248130	+	0.968727i	$0.420184\pi$
$728$		0			0
$729$	−25.9504	+	7.45506i	−0.961125	+	0.276113i
$730$		0			0
$731$	32.4208	+	8.68713i	1.19913	+	0.321305i
$732$		0			0
$733$	4.73140	−	1.26777i	0.174758	−	0.0468263i	−0.170379	−	0.985379i	$-0.554499\pi$
$733$	4.73140	−	1.26777i	0.174758	−	0.0468263i	0.345137	+	0.938552i	$0.387832\pi$
$734$		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
$741$	34.3820	+	53.6144i	1.26306	+	1.96957i
$742$		0			0
$743$	16.0882	+	9.28853i	0.590219	+	0.340763i	0.765184	−	0.643812i	$-0.222648\pi$
$743$	16.0882	+	9.28853i	0.590219	+	0.340763i	−0.174965	+	0.984575i	$0.555981\pi$
$744$		0			0
$745$	28.6302	−	16.5297i	1.04893	−	0.605600i
$746$		0			0
$747$	16.7380	−	6.20580i	0.612413	−	0.227059i
$748$		0			0
$749$	−4.29226	+	16.0189i	−0.156836	+	0.585320i
$750$		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	−0.368843	−	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	$-0.432954\pi$
$761$	−14.7108	−	8.49331i	−0.533268	−	0.307882i	−0.742346	+	0.670017i	$0.766287\pi$
$762$		0			0
$763$	−32.3610	−	8.67111i	−1.17155	−	0.313915i
$764$		0			0
$765$	−25.7168	+	31.0232i	−0.929795	+	1.12165i
$766$		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
$771$	−38.1720	+	24.4791i	−1.37473	+	0.881594i
$772$		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
$779$	−5.59915	−	20.8963i	−0.200611	−	0.748689i
$780$		0			0
$781$	1.14357	−	4.26785i	0.0409200	−	0.152716i
$782$		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
$787$	5.82094	−	1.55972i	0.207494	−	0.0555978i	−0.153575	−	0.988137i	$-0.549079\pi$
$787$	5.82094	−	1.55972i	0.207494	−	0.0555978i	0.361069	+	0.932539i	$0.382412\pi$
$788$		0			0
$789$	13.4972	−	0.629758i	0.480513	−	0.0224200i
$790$		0			0
$791$		−	37.8706i		−	1.34652i
$792$		0			0
$793$			13.1309i			0.466292i
$794$		0			0
$795$	−0.443932	−	0.692255i	−0.0157447	−	0.0245518i
$796$		0			0
$797$	50.3069	−	13.4797i	1.78196	−	0.477475i	0.791022	−	0.611788i	$-0.209549\pi$
$797$	50.3069	−	13.4797i	1.78196	−	0.477475i	0.990939	+	0.134313i	$0.0428828\pi$
$798$		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
$803$	3.47374	−	12.9642i	0.122586	−	0.457496i
$804$		0			0
$805$	−7.03082	−	26.2394i	−0.247804	−	0.924816i
$806$		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
$813$	38.2567	+	19.7700i	1.34172	+	0.693363i
$814$		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
$819$	−53.1720	−	9.04800i	−1.85798	−	0.316163i
$820$		0			0
$821$	−7.84823	−	2.10293i	−0.273905	−	0.0733926i	0.119252	−	0.992864i	$-0.461950\pi$
$821$	−7.84823	−	2.10293i	−0.273905	−	0.0733926i	−0.393157	+	0.919471i	$0.628617\pi$
$822$		0			0
$823$	−11.0255	−	6.36556i	−0.384324	−	0.221890i	0.295374	−	0.955382i	$-0.404556\pi$
$823$	−11.0255	−	6.36556i	−0.384324	−	0.221890i	−0.679698	+	0.733492i	$0.737889\pi$
$824$		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
$835$	−8.82503	+	32.9354i	−0.305403	+	1.13978i
$836$		0			0
$837$	−5.99200	−	2.41920i	−0.207114	−	0.0836198i
$838$		0			0
$839$	−34.4751	+	19.9042i	−1.19021	+	0.687169i	−0.958355	−	0.285580i	$-0.907814\pi$
$839$	−34.4751	+	19.9042i	−1.19021	+	0.687169i	−0.231858	+	0.972750i	$0.574480\pi$
$840$		0			0
$841$	16.5433	+	9.55126i	0.570458	+	0.329354i
$842$		0			0
$843$	49.2728	−	2.29899i	1.69705	−	0.0791815i
$844$		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
$851$	26.7057	−	7.15576i	0.915459	−	0.245296i
$852$		0			0
$853$	47.9910	+	12.8592i	1.64318	+	0.440289i	0.957692	−	0.287794i	$-0.0929219\pi$
$853$	47.9910	+	12.8592i	1.64318	+	0.440289i	0.685489	+	0.728083i	$0.259589\pi$
$854$		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	$-0.655094\pi$
$857$	1.84308	−	1.06410i	0.0629582	−	0.0363490i	0.531149	+	0.847279i	$0.321761\pi$
$858$		0			0
$859$	2.44211	+	9.11407i	0.0833237	+	0.310968i	0.994991	−	0.0999599i	$-0.0318714\pi$
$859$	2.44211	+	9.11407i	0.0833237	+	0.310968i	−0.911668	+	0.410928i	$0.865205\pi$
$860$		0			0
$861$	16.2753	+	8.41059i	0.554660	+	0.286632i
$862$		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
$867$	18.2886	+	9.45100i	0.621112	+	0.320973i
$868$		0			0
$869$	−0.791896	−	2.95540i	−0.0268632	−	0.100255i
$870$		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
$875$	29.5293	+	7.91234i	0.998271	+	0.267486i
$876$		0			0
$877$	16.7554	−	4.48959i	0.565789	−	0.151603i	0.0354241	−	0.999372i	$-0.488722\pi$
$877$	16.7554	−	4.48959i	0.565789	−	0.151603i	0.530364	+	0.847770i	$0.322055\pi$
$878$		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
$885$	9.89727	−	0.461791i	0.332693	−	0.0155229i
$886$		0			0
$887$	32.3743	+	18.6913i	1.08702	+	0.627592i	0.932782	−	0.360441i	$-0.117374\pi$
$887$	32.3743	+	18.6913i	1.08702	+	0.627592i	0.154240	+	0.988033i	$0.450707\pi$
$888$		0			0
$889$	20.8197	−	12.0203i	0.698271	−	0.403147i
$890$		0			0
$891$	−6.98099	+	10.2282i	−0.233872	+	0.342658i
$892$		0			0
$893$	−7.50307	+	28.0018i	−0.251081	+	0.937046i
$894$		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
$907$	27.3409	+	7.32597i	0.907840	+	0.243255i	0.682380	−	0.730998i	$-0.260945\pi$
$907$	27.3409	+	7.32597i	0.907840	+	0.243255i	0.225460	+	0.974253i	$0.427612\pi$
$908$		0			0
$909$	18.6295	+	50.2468i	0.617902	+	1.66658i
$910$		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
$915$	9.15218	+	4.72958i	0.302562	+	0.156355i
$916$		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
$923$	4.58563	+	17.1138i	0.150938	+	0.563308i
$924$		0			0
$925$	2.67318	−	9.97644i	0.0878936	−	0.328023i
$926$		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
$931$	−23.2916	+	6.24097i	−0.763352	+	0.204540i
$932$		0			0
$933$	−6.01356	−	9.37738i	−0.196875	−	0.307002i
$934$		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
$939$	5.79731	−	0.270493i	0.189188	−	0.00882721i
$940$		0			0
$941$	39.9706	−	10.7101i	1.30300	−	0.349139i	0.460419	−	0.887702i	$-0.347699\pi$
$941$	39.9706	−	10.7101i	1.30300	−	0.349139i	0.842586	+	0.538562i	$0.181032\pi$
$942$		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
$947$	8.55860	−	31.9411i	0.278117	−	1.03795i	−0.675606	−	0.737263i	$-0.736118\pi$
$947$	8.55860	−	31.9411i	0.278117	−	1.03795i	0.953724	−	0.300685i	$-0.0972152\pi$
$948$		0			0
$949$	13.9295	+	51.9856i	0.452171	+	1.68752i
$950$		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
$957$	6.31135	−	4.04737i	0.204017	−	0.130833i
$958$		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
$963$	−15.0519	−	2.56130i	−0.485040	−	0.0825367i
$964$		0			0
$965$	−39.6971	−	10.6368i	−1.27789	−	0.342410i
$966$		0			0
$967$	25.0282	+	14.4500i	0.804851	+	0.464681i	0.845165	−	0.534506i	$-0.179502\pi$
$967$	25.0282	+	14.4500i	0.804851	+	0.464681i	−0.0403133	+	0.999187i	$0.512836\pi$
$968$		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	0.413444	+	0.910530i	$0.364326\pi$
$977$	−18.1859	+	31.4990i	−0.581820	+	1.00774i	−0.995264	+	0.0972120i	$0.969008\pi$
$978$		0			0
$979$	−2.18080	+	8.13884i	−0.0696986	+	0.260119i
$980$		0			0
$981$	5.17426	−	30.4074i	0.165201	−	0.970833i
$982$		0			0
$983$	−48.0347	+	27.7329i	−1.53207	+	0.884541i	−0.532803	+	0.846239i	$0.678861\pi$
$983$	−48.0347	+	27.7329i	−1.53207	+	0.884541i	−0.999266	+	0.0383018i	$0.987805\pi$
$984$		0			0
$985$	6.76074	+	3.90331i	0.215415	+	0.124370i
$986$		0			0
$987$	−13.2523	−	20.6653i	−0.421825	−	0.657782i
$988$		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
$995$	−28.8208	+	7.72250i	−0.913679	+	0.244820i
$996$		0			0
$997$	28.7828	+	7.71233i	0.911561	+	0.244252i	0.683974	−	0.729506i	$-0.260250\pi$
$997$	28.7828	+	7.71233i	0.911561	+	0.244252i	0.227586	+	0.973758i	$0.426917\pi$
$998$		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.337.17		72
3.2	odd	2		1728.2.bc.e.145.3		72
4.3	odd	2		144.2.x.e.13.8	✓	72
9.2	odd	6		1728.2.bc.e.721.16		72
9.7	even	3	inner	576.2.bb.e.529.12		72
12.11	even	2		432.2.y.e.253.11		72
16.5	even	4	inner	576.2.bb.e.49.12		72
16.11	odd	4		144.2.x.e.85.16	yes	72
36.7	odd	6		144.2.x.e.61.16	yes	72
36.11	even	6		432.2.y.e.397.3		72
48.5	odd	4		1728.2.bc.e.1009.16		72
48.11	even	4		432.2.y.e.37.3		72
144.11	even	12		432.2.y.e.181.11		72
144.43	odd	12		144.2.x.e.133.8	yes	72
144.101	odd	12		1728.2.bc.e.1585.3		72
144.133	even	12	inner	576.2.bb.e.241.17		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.8	✓	72	4.3	odd	2
144.2.x.e.61.16	yes	72	36.7	odd	6
144.2.x.e.85.16	yes	72	16.11	odd	4
144.2.x.e.133.8	yes	72	144.43	odd	12
432.2.y.e.37.3		72	48.11	even	4
432.2.y.e.181.11		72	144.11	even	12
432.2.y.e.253.11		72	12.11	even	2
432.2.y.e.397.3		72	36.11	even	6
576.2.bb.e.49.12		72	16.5	even	4	inner
576.2.bb.e.241.17		72	144.133	even	12	inner
576.2.bb.e.337.17		72	1.1	even	1	trivial
576.2.bb.e.529.12		72	9.7	even	3	inner
1728.2.bc.e.145.3		72	3.2	odd	2
1728.2.bc.e.721.16		72	9.2	odd	6
1728.2.bc.e.1009.16		72	48.5	odd	4
1728.2.bc.e.1585.3		72	144.101	odd	12

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)

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

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