LMFDB - Embedded newform 576.2.bb.e.241.17

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			241.17
Character	$\chi$	$=$	576.241
Dual form			576.2.bb.e.337.17

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

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

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
$3$	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	−0.656378	−	0.754433i	$-0.727912\pi$
$5$	0.646846	−	2.41406i	0.289278	−	1.07960i	0.945656	−	0.325169i	$-0.105421\pi$
$6$		0			0
$7$	2.82197	+	1.62927i	1.06661	+	0.615805i	0.927252	−	0.374438i	$-0.122164\pi$
$7$	2.82197	+	1.62927i	1.06661	+	0.615805i	0.139353	+	0.990243i	$0.455498\pi$
$8$		0			0
$9$	1.73540	−	2.44712i	0.578467	−	0.815706i
$10$		0			0
$11$	1.32906	−	0.356120i	0.400726	−	0.107374i	−0.0528265	−	0.998604i	$-0.516823\pi$
$11$	1.32906	−	0.356120i	0.400726	−	0.107374i	0.453553	+	0.891229i	$0.350156\pi$
$12$		0			0
$13$	−5.32945	−	1.42802i	−1.47812	−	0.396062i	−0.572415	−	0.819964i	$-0.693993\pi$
$13$	−5.32945	−	1.42802i	−1.47812	−	0.396062i	−0.905708	+	0.423903i	$0.860660\pi$
$14$		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
$21$	5.63781	+	0.263051i	1.23027	+	0.0574025i
$22$		0			0
$23$	−2.88877	+	1.66783i	−0.602351	+	0.347767i	−0.769966	−	0.638085i	$-0.779727\pi$
$23$	−2.88877	+	1.66783i	−0.602351	+	0.347767i	0.167615	+	0.985853i	$0.446393\pi$
$24$		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	0.999401	+	0.0346168i	$0.0110211\pi$
$29$	0.814251	+	3.03883i	0.151203	+	0.564296i	−0.848198	+	0.529679i	$0.822312\pi$
$30$		0			0
$31$	−0.621800	−	1.07699i	−0.111679	−	0.193433i	0.804769	−	0.593589i	$-0.202289\pi$
$31$	−0.621800	−	1.07699i	−0.111679	−	0.193433i	−0.916447	+	0.400156i	$0.868956\pi$
$32$		0			0
$33$	1.76189	−	1.60481i	0.306706	−	0.279361i
$34$		0			0
$35$	5.75853	−	5.75853i	0.973369	−	0.973369i
$36$		0			0
$37$	−5.86087	−	5.86087i	−0.963521	−	0.963521i	0.0358368	−	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	$-0.585096\pi$
$41$	2.81108	−	1.62298i	0.439017	−	0.253467i	0.703181	+	0.711011i	$0.251763\pi$
$42$		0			0
$43$	6.03232	−	1.61636i	0.919920	−	0.246492i	0.232369	−	0.972628i	$-0.425352\pi$
$43$	6.03232	−	1.61636i	0.919920	−	0.246492i	0.687551	+	0.726136i	$0.258686\pi$
$44$		0			0
$45$	−4.78496	−	5.77227i	−0.713299	−	0.860480i
$46$		0			0
$47$	−2.17485	+	3.76695i	−0.317234	+	0.549466i	−0.979910	−	0.199441i	$-0.936088\pi$
$47$	−2.17485	+	3.76695i	−0.317234	+	0.549466i	0.662676	+	0.748907i	$0.269421\pi$
$48$		0			0
$49$	1.80902	+	3.13331i	0.258431	+	0.447615i
$50$		0			0
$51$	8.26995	−	4.27367i	1.15803	−	0.598434i
$52$		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
$59$	−0.592405	+	2.21088i	−0.0771245	+	0.287833i	−0.993707	−	0.112014i	$-0.964270\pi$
$59$	−0.592405	+	2.21088i	−0.0771245	+	0.287833i	0.916582	+	0.399846i	$0.130937\pi$
$60$		0			0
$61$	0.615960	+	2.29879i	0.0788656	+	0.294330i	0.994082	−	0.108632i	$-0.0346471\pi$
$61$	0.615960	+	2.29879i	0.0788656	+	0.294330i	−0.915216	+	0.402963i	$0.867980\pi$
$62$		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	0.251954	−	0.967739i	$-0.418927\pi$
$67$	−0.112274	−	0.0300838i	−0.0137165	−	0.00367532i	−0.265671	+	0.964064i	$0.585593\pi$
$68$		0			0
$69$	−3.11884	+	4.86343i	−0.375464	+	0.585488i
$70$		0			0
$71$			3.21118i			0.381097i	0.981678	+	0.190548i	$0.0610266\pi$
$71$			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
$75$	−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	−0.921769	−	0.387740i	$-0.873256\pi$
$79$	−1.11184	+	1.92576i	−0.125092	+	0.216665i	0.796677	+	0.604405i	$0.206589\pi$
$80$		0			0
$81$	−2.97677	−	8.49346i	−0.330752	−	0.943718i
$82$		0			0
$83$	1.54010	+	5.74772i	0.169048	+	0.630895i	0.997489	+	0.0708190i	$0.0225613\pi$
$83$	1.54010	+	5.74772i	0.169048	+	0.630895i	−0.828441	+	0.560076i	$0.810772\pi$
$84$		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	$-0.894784\pi$
$89$		−	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
$93$	−1.81318	−	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	−0.956288	−	0.292428i	$-0.905537\pi$
$97$	−2.21495	+	3.83640i	−0.224894	+	0.389528i	0.731394	+	0.681956i	$0.238870\pi$
$98$		0			0
$99$	1.43498	−	3.87037i	0.144221	−	0.388987i
$100$		0			0
$101$	17.2544	−	4.62330i	1.71688	−	0.460035i	0.739782	−	0.672847i	$-0.234929\pi$
$101$	17.2544	−	4.62330i	1.71688	−	0.460035i	0.977093	+	0.212811i	$0.0682619\pi$
$102$		0			0
$103$	−8.73448	+	5.04285i	−0.860634	+	0.496887i	−0.864224	−	0.503106i	$-0.832190\pi$
$103$	−8.73448	+	5.04285i	−0.860634	+	0.496887i	0.00359067	+	0.999994i	$0.498857\pi$
$104$		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	0.998501	+	0.0547341i	$0.0174311\pi$
$113$	5.81099	+	10.0649i	0.546652	+	0.946828i	−0.451849	+	0.892094i	$0.649236\pi$
$114$		0			0
$115$	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	−0.448082	−	0.893992i	$-0.647893\pi$
$131$	−14.6861	−	3.93512i	−1.28313	−	0.343813i	−0.835047	+	0.550179i	$0.814560\pi$
$132$		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	−0.0818576	−	0.996644i	$-0.526085\pi$
$137$	−11.5397	−	6.66247i	−0.985906	−	0.569213i	−0.904048	+	0.427431i	$0.859419\pi$
$138$		0			0
$139$	−4.34417	+	16.2127i	−0.368468	+	1.37514i	0.494191	+	0.869354i	$0.335465\pi$
$139$	−4.34417	+	16.2127i	−0.368468	+	1.37514i	−0.862658	+	0.505787i	$0.831202\pi$
$140$		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	0.671610	+	0.740905i	$0.265603\pi$
$149$	−3.42362	+	12.7771i	−0.280474	+	1.04674i	−0.952084	+	0.305838i	$0.901063\pi$
$150$		0			0
$151$	−10.3438	−	5.97202i	−0.841769	−	0.485996i	0.0160959	−	0.999870i	$-0.494876\pi$
$151$	−10.3438	−	5.97202i	−0.841769	−	0.485996i	−0.857865	+	0.513875i	$0.828210\pi$
$152$		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	0.785721	−	0.618581i	$-0.212292\pi$
$157$	14.4957	+	3.88412i	1.15689	+	0.309986i	0.371164	+	0.928567i	$0.378959\pi$
$158$		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
$165$	−2.73443	−	5.29137i	−0.212875	−	0.411933i
$166$		0			0
$167$	11.8153	−	6.82158i	0.914297	−	0.527870i	0.0324861	−	0.999472i	$-0.489658\pi$
$167$	11.8153	−	6.82158i	0.914297	−	0.527870i	0.881811	+	0.471602i	$0.156324\pi$
$168$		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	0.995855	−	0.0909602i	$-0.0289936\pi$
$173$	1.15666	+	4.31671i	0.0879391	+	0.328193i	−0.907915	+	0.419153i	$0.862327\pi$
$174$		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
$187$	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	−0.993550	−	0.113395i	$-0.963827\pi$
$191$	−5.50837	+	9.54078i	−0.398572	+	0.690346i	0.594978	+	0.803742i	$0.297161\pi$
$192$		0			0
$193$	−8.22204	−	14.2410i	−0.591836	−	1.02509i	−0.993985	−	0.109515i	$-0.965070\pi$
$193$	−8.22204	−	14.2410i	−0.591836	−	1.02509i	0.402149	−	0.915574i	$-0.368263\pi$
$194$		0			0
$195$	−1.11317	+	23.8579i	−0.0797158	+	1.70850i
$196$		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
$203$	−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	0.0533513	−	0.998576i	$-0.483010\pi$
$211$	−5.80646	−	1.55584i	−0.399733	−	0.107108i	−0.453084	+	0.891468i	$0.649676\pi$
$212$		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	−0.970729	−	0.240179i	$-0.922794\pi$
$223$	−4.14191	+	7.17400i	−0.277363	+	0.480407i	0.693366	+	0.720586i	$0.256127\pi$
$224$		0			0
$225$	−3.39746	+	1.55958i	−0.226497	+	0.103972i
$226$		0			0
$227$	−4.64336	−	17.3293i	−0.308191	−	1.15018i	−0.930164	−	0.367145i	$-0.880335\pi$
$227$	−4.64336	−	17.3293i	−0.308191	−	1.15018i	0.621973	−	0.783039i	$-0.286331\pi$
$228$		0			0
$229$	2.45857	−	9.17552i	0.162467	−	0.606335i	−0.835883	−	0.548908i	$-0.815044\pi$
$229$	2.45857	−	9.17552i	0.162467	−	0.606335i	0.998350	−	0.0574270i	$-0.0182896\pi$
$230$		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
$237$	−0.179511	+	3.84733i	−0.0116605	+	0.249911i
$238$		0			0
$239$	−12.4015	−	21.4800i	−0.802187	−	1.38943i	−0.918174	−	0.396178i	$-0.870336\pi$
$239$	−12.4015	−	21.4800i	−0.802187	−	1.38943i	0.115987	−	0.993251i	$-0.462997\pi$
$240$		0			0
$241$	4.32533	−	7.49168i	0.278619	−	0.482582i	−0.692423	−	0.721492i	$-0.743457\pi$
$241$	4.32533	−	7.49168i	0.278619	−	0.482582i	0.971042	+	0.238910i	$0.0767901\pi$
$242$		0			0
$243$	−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	0.748224	−	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	−0.908201	−	0.418535i	$-0.862544\pi$
$257$	−13.0905	−	22.6734i	−0.816563	−	1.41433i	0.0916380	−	0.995792i	$-0.470790\pi$
$258$		0			0
$259$	−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	0.693617	−	0.720344i	$-0.256016\pi$
$263$	6.75594	+	3.90054i	0.416589	+	0.240518i	−0.277028	+	0.960862i	$0.589349\pi$
$264$		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	−0.545815	−	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
$275$	−1.65615	−	0.443764i	−0.0998695	−	0.0267599i
$276$		0			0
$277$	0.891589	−	0.238901i	0.0535704	−	0.0143541i	−0.231934	−	0.972731i	$-0.574505\pi$
$277$	0.891589	−	0.238901i	0.0535704	−	0.0143541i	0.285505	+	0.958377i	$0.407839\pi$
$278$		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	$-0.0102695\pi$
$281$	24.6632	+	14.2393i	1.47128	+	0.849446i	0.471804	+	0.881703i	$0.343603\pi$
$282$		0			0
$283$	1.71872	−	6.41436i	0.102167	−	0.381294i	−0.895841	−	0.444375i	$-0.853426\pi$
$283$	1.71872	−	6.41436i	0.102167	−	0.381294i	0.998008	+	0.0630806i	$0.0200925\pi$
$284$		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	−0.852156	−	0.523288i	$-0.824705\pi$
$293$	2.52439	−	9.42116i	0.147477	−	0.550390i	0.999633	−	0.0271023i	$-0.00862799\pi$
$294$		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	−0.565164	−	0.824979i	$-0.691187\pi$
$307$	4.55233	−	4.55233i	0.259815	−	0.259815i	0.824979	+	0.565164i	$0.191187\pi$
$308$		0			0
$309$	−9.43010	+	14.7050i	−0.536459	+	0.836540i
$310$		0			0
$311$	−5.56997	+	3.21582i	−0.315844	+	0.182353i	−0.649539	−	0.760329i	$-0.725038\pi$
$311$	−5.56997	+	3.21582i	−0.315844	+	0.182353i	0.333695	+	0.942681i	$0.391705\pi$
$312$		0			0
$313$	2.90181	+	1.67536i	0.164020	+	0.0946969i	0.579763	−	0.814785i	$-0.303145\pi$
$313$	2.90181	+	1.67536i	0.164020	+	0.0946969i	−0.415743	+	0.909482i	$0.636478\pi$
$314$		0			0
$315$	−4.09844	−	24.0852i	−0.230921	−	1.35705i
$316$		0			0
$317$	3.92134	+	14.6346i	0.220244	+	0.821963i	0.984254	+	0.176758i	$0.0565611\pi$
$317$	3.92134	+	14.6346i	0.220244	+	0.821963i	−0.764010	+	0.645204i	$0.776772\pi$
$318$		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	−0.523190	−	0.852216i	$-0.675258\pi$
$331$	−10.0096	+	2.68206i	−0.550177	+	0.147420i	−0.0269876	+	0.999636i	$0.508591\pi$
$332$		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	0.987167	−	0.159689i	$-0.0510490\pi$
$337$	6.52225	+	11.2969i	0.355289	+	0.615379i	−0.631878	+	0.775068i	$0.717716\pi$
$338$		0			0
$339$	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	−0.561562	−	0.827435i	$-0.689799\pi$
$347$	6.30523	−	23.5314i	0.338482	−	1.26323i	0.900044	−	0.435798i	$-0.143534\pi$
$348$		0			0
$349$	−7.44289	−	27.7772i	−0.398409	−	1.48688i	−0.815896	−	0.578199i	$-0.803756\pi$
$349$	−7.44289	−	27.7772i	−0.398409	−	1.48688i	0.417487	−	0.908683i	$-0.362911\pi$
$350$		0			0
$351$	−11.2086	+	26.3876i	−0.598271	+	1.40847i
$352$		0			0
$353$	17.6048	−	30.4924i	0.937010	−	1.62295i	0.165999	−	0.986126i	$-0.446915\pi$
$353$	17.6048	−	30.4924i	0.937010	−	1.62295i	0.771011	−	0.636822i	$-0.219752\pi$
$354$		0			0
$355$	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	$0.153867\pi$
$359$			17.6127i			0.929564i	−0.885425	+	0.464782i	$0.846133\pi$
$360$		0			0
$361$		−	25.4188i		−	1.33783i
$362$		0			0
$363$	−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	−0.562957	−	0.826486i	$-0.690337\pi$
$367$	8.31959	−	14.4100i	0.434279	−	0.752193i	0.997236	+	0.0742925i	$0.0236698\pi$
$368$		0			0
$369$	0.906734	−	9.69556i	0.0472027	−	0.504731i
$370$		0			0
$371$	−0.160221	−	0.597954i	−0.00831828	−	0.0310442i
$372$		0			0
$373$	0.864710	−	3.22714i	0.0447730	−	0.167095i	−0.939919	−	0.341397i	$-0.889100\pi$
$373$	0.864710	−	3.22714i	0.0447730	−	0.167095i	0.984692	+	0.174302i	$0.0557667\pi$
$374$		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
$381$	11.3523	−	5.86656i	0.581598	−	0.300553i
$382$		0			0
$383$	−5.44755	−	9.43544i	−0.278357	−	0.482128i	0.692620	−	0.721303i	$-0.256456\pi$
$383$	−5.44755	−	9.43544i	−0.278357	−	0.482128i	−0.970977	+	0.239175i	$0.923123\pi$
$384$		0			0
$385$	5.60270	−	9.70416i	0.285540	−	0.494570i
$386$		0			0
$387$	6.51308	−	17.5668i	0.331079	−	0.892971i
$388$		0			0
$389$	−13.9149	+	3.72849i	−0.705513	+	0.189042i	−0.593699	−	0.804687i	$-0.702333\pi$
$389$	−13.9149	+	3.72849i	−0.705513	+	0.189042i	−0.111815	+	0.993729i	$0.535666\pi$
$390$		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	0.774446	−	0.632640i	$-0.218029\pi$
$401$	−3.21720	−	5.57235i	−0.160659	−	0.278270i	−0.935105	+	0.354370i	$0.884695\pi$
$402$		0			0
$403$	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	−0.580117	+	0.814533i	$0.696993\pi$
$409$	−31.8642	+	18.3968i	−1.57558	+	0.909663i	−0.995465	+	0.0951294i	$0.969674\pi$
$410$		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	−0.310093	−	0.950706i	$-0.600360\pi$
$419$	−21.5747	−	5.78093i	−1.05399	−	0.282417i	−0.743901	+	0.668290i	$0.767027\pi$
$420$		0			0
$421$	−8.71347	+	2.33477i	−0.424669	+	0.113790i	−0.464822	−	0.885404i	$-0.653882\pi$
$421$	−8.71347	+	2.33477i	−0.424669	+	0.113790i	0.0401539	+	0.999194i	$0.487215\pi$
$422$		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	0.626151	−	0.779701i	$-0.284629\pi$
$439$	5.53112	+	3.19339i	0.263986	+	0.152412i	−0.362166	+	0.932114i	$0.617963\pi$
$440$		0			0
$441$	10.8069	+	1.01067i	0.514616	+	0.0481272i
$442$		0			0
$443$	−16.1600	+	4.33005i	−0.767783	+	0.205727i	−0.621392	−	0.783500i	$-0.713432\pi$
$443$	−16.1600	+	4.33005i	−0.767783	+	0.205727i	−0.146391	+	0.989227i	$0.546766\pi$
$444$		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	0.962875	−	0.269946i	$-0.0870060\pi$
$457$	25.8782	+	14.9408i	1.21053	+	0.698901i	0.247657	+	0.968848i	$0.420339\pi$
$458$		0			0
$459$	3.89351	−	27.6541i	0.181733	−	1.29078i
$460$		0			0
$461$	−7.22887	−	26.9785i	−0.336682	−	1.25651i	−0.902034	−	0.431665i	$-0.857926\pi$
$461$	−7.22887	−	26.9785i	−0.336682	−	1.25651i	0.565352	−	0.824850i	$-0.308740\pi$
$462$		0			0
$463$	−9.00954	−	15.6050i	−0.418709	−	0.725225i	0.577101	−	0.816673i	$-0.304184\pi$
$463$	−9.00954	−	15.6050i	−0.418709	−	0.725225i	−0.995810	+	0.0914480i	$0.970850\pi$
$464$		0			0
$465$	−3.97982	+	3.62500i	−0.184560	+	0.168105i
$466$		0			0
$467$	−3.24566	+	3.24566i	−0.150191	+	0.150191i	−0.778204	−	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
$475$	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	−0.835513	−	0.549471i	$-0.814829\pi$
$479$	1.27156	−	2.20241i	0.0580991	−	0.100631i	0.893612	+	0.448840i	$0.148163\pi$
$480$		0			0
$481$	22.8657	+	39.6046i	1.04259	+	1.80582i
$482$		0			0
$483$	−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	$0.204596\pi$
$487$			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
$491$	−5.87672	+	21.9322i	−0.265213	+	0.989787i	0.696907	+	0.717161i	$0.254559\pi$
$491$	−5.87672	+	21.9322i	−0.265213	+	0.989787i	−0.962120	+	0.272626i	$0.912108\pi$
$492$		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	0.813470	−	0.581606i	$-0.197576\pi$
$499$	27.4125	+	7.34516i	1.22715	+	0.328815i	0.413683	+	0.910421i	$0.364242\pi$
$500$		0			0
$501$	12.7563	−	19.8918i	0.569910	−	0.888701i
$502$		0			0
$503$		−	32.0583i		−	1.42941i	−0.699427	−	0.714704i	$-0.746561\pi$
$503$		−	32.0583i		−	1.42941i	0.699427	−	0.714704i	$-0.253439\pi$
$504$		0			0
$505$		−	44.6437i		−	1.98662i
$506$		0			0
$507$	30.1780	+	1.40806i	1.34025	+	0.0625341i
$508$		0			0
$509$	−26.6932	−	7.15242i	−1.18316	−	0.317025i	−0.386978	−	0.922089i	$-0.626481\pi$
$509$	−26.6932	−	7.15242i	−1.18316	−	0.317025i	−0.796177	+	0.605064i	$0.793148\pi$
$510$		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	$-0.951683\pi$
$521$		−	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
$525$	−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	−0.955078	−	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
$547$	1.09601	+	4.09038i	0.0468622	+	0.174892i	0.985390	−	0.170310i	$-0.0544770\pi$
$547$	1.09601	+	4.09038i	0.0468622	+	0.174892i	−0.938528	+	0.345202i	$0.887810\pi$
$548$		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	−0.622687	−	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
$563$	17.6273	+	4.72321i	0.742901	+	0.199060i	0.610367	−	0.792119i	$-0.291022\pi$
$563$	17.6273	+	4.72321i	0.742901	+	0.199060i	0.132534	+	0.991178i	$0.457689\pi$
$564$		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	0.704896	−	0.709311i	$-0.250994\pi$
$569$	10.5687	+	6.10184i	0.443062	+	0.255802i	−0.261833	+	0.965113i	$0.584327\pi$
$570$		0			0
$571$	2.71820	−	10.1445i	0.113753	−	0.424533i	−0.885437	−	0.464759i	$-0.846141\pi$
$571$	2.71820	−	10.1445i	0.113753	−	0.424533i	0.999191	+	0.0402258i	$0.0128077\pi$
$572$		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	−0.583735	−	0.811944i	$-0.698409\pi$
$587$	−16.5549	+	4.43586i	−0.683292	+	0.183088i	−0.0995570	+	0.995032i	$0.531743\pi$
$588$		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	−0.595547	−	0.803320i	$-0.703065\pi$
$599$	−4.83678	+	2.79252i	−0.197626	+	0.114099i	0.397922	+	0.917419i	$0.369732\pi$
$600$		0			0
$601$	−29.8602	−	17.2398i	−1.21802	−	0.703227i	−0.253529	−	0.967328i	$-0.581591\pi$
$601$	−29.8602	−	17.2398i	−1.21802	−	0.703227i	−0.964495	+	0.264101i	$0.914925\pi$
$602$		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	0.670040	−	0.742325i	$-0.266277\pi$
$607$	−7.58467	−	13.1370i	−0.307852	−	0.533216i	−0.977892	+	0.209109i	$0.932944\pi$
$608$		0			0
$609$	3.79123	+	17.3465i	0.153628	+	0.702917i
$610$		0			0
$611$	16.9700	−	16.9700i	0.686534	−	0.686534i
$612$		0			0
$613$	7.90551	+	7.90551i	0.319301	+	0.319301i	0.848498	−	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	$-0.469055\pi$
$617$	25.0266	−	14.4491i	1.00753	−	0.581700i	0.910468	+	0.413578i	$0.135721\pi$
$618$		0			0
$619$	33.4626	−	8.96627i	1.34497	−	0.360385i	0.486697	−	0.873571i	$-0.338202\pi$
$619$	33.4626	−	8.96627i	1.34497	−	0.360385i	0.858277	+	0.513186i	$0.171535\pi$
$620$		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	$0.206973\pi$
$631$			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
$635$	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	−0.962072	−	0.272796i	$-0.912052\pi$
$641$	−6.19753	+	10.7344i	−0.244788	+	0.423985i	0.717284	+	0.696781i	$0.245385\pi$
$642$		0			0
$643$	26.0383	+	6.97693i	1.02685	+	0.275143i	0.732653	−	0.680602i	$-0.238282\pi$
$643$	26.0383	+	6.97693i	1.02685	+	0.275143i	0.294195	+	0.955745i	$0.404948\pi$
$644$		0			0
$645$	−12.4110	−	24.0164i	−0.488682	−	0.945646i
$646$		0			0
$647$		−	1.44109i		−	0.0566551i	−0.999599	−	0.0283275i	$-0.990982\pi$
$647$		−	1.44109i		−	0.0566551i	0.999599	−	0.0283275i	$-0.00901814\pi$
$648$		0			0
$649$			3.14936i			0.123623i
$650$		0			0
$651$	−3.22229	−	6.23543i	−0.126291	−	0.244386i
$652$		0			0
$653$	−14.4750	−	3.87857i	−0.566451	−	0.151780i	−0.0357824	−	0.999360i	$-0.511392\pi$
$653$	−14.4750	−	3.87857i	−0.566451	−	0.151780i	−0.530668	+	0.847580i	$0.678059\pi$
$654$		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	0.934486	−	0.356000i	$-0.115860\pi$
$659$	−1.35549	−	5.05876i	−0.0528024	−	0.197061i	−0.987289	+	0.158938i	$0.949193\pi$
$660$		0			0
$661$	−5.31043	+	19.8188i	−0.206552	+	0.770862i	0.782419	+	0.622752i	$0.213986\pi$
$661$	−5.31043	+	19.8188i	−0.206552	+	0.770862i	−0.988971	+	0.148110i	$0.952681\pi$
$662$		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	−0.698699	−	0.715416i	$-0.746237\pi$
$673$	7.01009	−	12.1418i	0.270219	−	0.468033i	0.968918	+	0.247383i	$0.0795706\pi$
$674$		0			0
$675$	−3.98764	+	5.10135i	−0.153484	+	0.196351i
$676$		0			0
$677$	−16.2587	+	4.35650i	−0.624872	+	0.167434i	−0.557342	−	0.830283i	$-0.688179\pi$
$677$	−16.2587	+	4.35650i	−0.624872	+	0.167434i	−0.0675306	+	0.997717i	$0.521512\pi$
$678$		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
$691$	−7.57544	−	28.2719i	−0.288183	−	1.07551i	−0.946482	−	0.322757i	$-0.895390\pi$
$691$	−7.57544	−	28.2719i	−0.288183	−	1.07551i	0.658299	−	0.752757i	$-0.271276\pi$
$692$		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	−0.0847476	+	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
$707$	56.2240	+	15.0652i	2.11452	+	0.566584i
$708$		0			0
$709$	−26.0795	+	6.98798i	−0.979437	+	0.262439i	−0.712807	−	0.701360i	$-0.752577\pi$
$709$	−26.0795	+	6.98798i	−0.979437	+	0.262439i	−0.266629	+	0.963799i	$0.585910\pi$
$710$		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	0.248130	−	0.968727i	$-0.420184\pi$
$727$	−12.5849	−	7.26589i	−0.466748	−	0.269477i	−0.714877	+	0.699250i	$0.753517\pi$
$728$		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	0.345137	−	0.938552i	$-0.387832\pi$
$733$	4.73140	+	1.26777i	0.174758	+	0.0468263i	−0.170379	+	0.985379i	$0.554499\pi$
$734$		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
$741$	34.3820	−	53.6144i	1.26306	−	1.96957i
$742$		0			0
$743$	16.0882	−	9.28853i	0.590219	−	0.340763i	−0.174965	−	0.984575i	$-0.555981\pi$
$743$	16.0882	−	9.28853i	0.590219	−	0.340763i	0.765184	+	0.643812i	$0.222648\pi$
$744$		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	−0.986080	−	0.166273i	$-0.946827\pi$
$751$	−17.4576	−	30.2374i	−0.637037	−	1.10338i	0.349043	−	0.937107i	$-0.386507\pi$
$752$		0			0
$753$	3.13473	+	0.998694i	0.114236	+	0.0363944i
$754$		0			0
$755$	−21.1077	+	21.1077i	−0.768187	+	0.768187i
$756$		0			0
$757$	15.4255	+	15.4255i	0.560649	+	0.560649i	0.929492	−	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	$-0.766287\pi$
$761$	−14.7108	+	8.49331i	−0.533268	+	0.307882i	0.209078	+	0.977899i	$0.432954\pi$
$762$		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	−0.933905	−	0.357522i	$-0.883622\pi$
$769$	−21.5351	−	37.2999i	−0.776575	−	1.34507i	0.157330	−	0.987546i	$-0.449712\pi$
$770$		0			0
$771$	−38.1720	−	24.4791i	−1.37473	−	0.881594i
$772$		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
$779$	−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	0.361069	−	0.932539i	$-0.382412\pi$
$787$	5.82094	+	1.55972i	0.207494	+	0.0555978i	−0.153575	+	0.988137i	$0.549079\pi$
$788$		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	0.990939	−	0.134313i	$-0.0428828\pi$
$797$	50.3069	+	13.4797i	1.78196	+	0.477475i	0.791022	+	0.611788i	$0.209549\pi$
$798$		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	$0.0690599\pi$
$809$			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
$813$	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	−0.393157	−	0.919471i	$-0.628617\pi$
$821$	−7.84823	+	2.10293i	−0.273905	+	0.0733926i	0.119252	+	0.992864i	$0.461950\pi$
$822$		0			0
$823$	−11.0255	+	6.36556i	−0.384324	+	0.221890i	−0.679698	−	0.733492i	$-0.737889\pi$
$823$	−11.0255	+	6.36556i	−0.384324	+	0.221890i	0.295374	+	0.955382i	$0.404556\pi$
$824$		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
$835$	−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	−0.231858	−	0.972750i	$-0.574480\pi$
$839$	−34.4751	−	19.9042i	−1.19021	−	0.687169i	−0.958355	+	0.285580i	$0.907814\pi$
$840$		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	0.685489	−	0.728083i	$-0.259589\pi$
$853$	47.9910	−	12.8592i	1.64318	−	0.440289i	0.957692	+	0.287794i	$0.0929219\pi$
$854$		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	$-0.321761\pi$
$857$	1.84308	+	1.06410i	0.0629582	+	0.0363490i	−0.468190	+	0.883628i	$0.655094\pi$
$858$		0			0
$859$	2.44211	−	9.11407i	0.0833237	−	0.310968i	−0.911668	−	0.410928i	$-0.865205\pi$
$859$	2.44211	−	9.11407i	0.0833237	−	0.310968i	0.994991	+	0.0999599i	$0.0318714\pi$
$860$		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	0.530364	−	0.847770i	$-0.322055\pi$
$877$	16.7554	+	4.48959i	0.565789	+	0.151603i	0.0354241	+	0.999372i	$0.488722\pi$
$878$		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
$885$	9.89727	+	0.461791i	0.332693	+	0.0155229i
$886$		0			0
$887$	32.3743	−	18.6913i	1.08702	−	0.627592i	0.154240	−	0.988033i	$-0.450707\pi$
$887$	32.3743	−	18.6913i	1.08702	−	0.627592i	0.932782	+	0.360441i	$0.117374\pi$
$888$		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	0.225460	−	0.974253i	$-0.427612\pi$
$907$	27.3409	−	7.32597i	0.907840	−	0.243255i	0.682380	+	0.730998i	$0.260945\pi$
$908$		0			0
$909$	18.6295	−	50.2468i	0.617902	−	1.66658i
$910$		0			0
$911$	12.2805	−	21.2704i	0.406871	−	0.704721i	−0.587667	−	0.809103i	$-0.699953\pi$
$911$	12.2805	−	21.2704i	0.406871	−	0.704721i	0.994537	+	0.104383i	$0.0332867\pi$
$912$		0			0
$913$	4.09376	+	7.09060i	0.135484	+	0.234665i
$914$		0			0
$915$	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	$0.114611\pi$
$919$			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
$923$	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	−0.852879	−	0.522108i	$-0.825146\pi$
$929$	0.783906	−	1.35776i	0.0257191	−	0.0445468i	0.878598	+	0.477561i	$0.158479\pi$
$930$		0			0
$931$	−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	$0.227445\pi$
$937$			40.1161i			1.31054i	−0.755396	+	0.655269i	$0.772555\pi$
$938$		0			0
$939$	5.79731	+	0.270493i	0.189188	+	0.00882721i
$940$		0			0
$941$	39.9706	+	10.7101i	1.30300	+	0.349139i	0.842586	−	0.538562i	$-0.181032\pi$
$941$	39.9706	+	10.7101i	1.30300	+	0.349139i	0.460419	+	0.887702i	$0.347699\pi$
$942$		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	0.953724	+	0.300685i	$0.0972152\pi$
$947$	8.55860	+	31.9411i	0.278117	+	1.03795i	−0.675606	+	0.737263i	$0.736118\pi$
$948$		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	$0.0319499\pi$
$953$			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
$957$	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	−0.0403133	−	0.999187i	$-0.512836\pi$
$967$	25.0282	−	14.4500i	0.804851	−	0.464681i	0.845165	+	0.534506i	$0.179502\pi$
$968$		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	−0.995264	−	0.0972120i	$-0.969008\pi$
$977$	−18.1859	−	31.4990i	−0.581820	−	1.00774i	0.413444	−	0.910530i	$-0.364326\pi$
$978$		0			0
$979$	−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	−0.999266	−	0.0383018i	$-0.987805\pi$
$983$	−48.0347	−	27.7329i	−1.53207	−	0.884541i	−0.532803	−	0.846239i	$-0.678861\pi$
$984$		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	0.227586	−	0.973758i	$-0.426917\pi$
$997$	28.7828	−	7.71233i	0.911561	−	0.244252i	0.683974	+	0.729506i	$0.260250\pi$
$998$		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.241.17		72
3.2	odd	2		1728.2.bc.e.1585.3		72
4.3	odd	2		144.2.x.e.133.8	yes	72
9.4	even	3	inner	576.2.bb.e.49.12		72
9.5	odd	6		1728.2.bc.e.1009.16		72
12.11	even	2		432.2.y.e.181.11		72
16.3	odd	4		144.2.x.e.61.16	yes	72
16.13	even	4	inner	576.2.bb.e.529.12		72
36.23	even	6		432.2.y.e.37.3		72
36.31	odd	6		144.2.x.e.85.16	yes	72
48.29	odd	4		1728.2.bc.e.721.16		72
48.35	even	4		432.2.y.e.397.3		72
144.13	even	12	inner	576.2.bb.e.337.17		72
144.67	odd	12		144.2.x.e.13.8	✓	72
144.77	odd	12		1728.2.bc.e.145.3		72
144.131	even	12		432.2.y.e.253.11		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.8	✓	72	144.67	odd	12
144.2.x.e.61.16	yes	72	16.3	odd	4
144.2.x.e.85.16	yes	72	36.31	odd	6
144.2.x.e.133.8	yes	72	4.3	odd	2
432.2.y.e.37.3		72	36.23	even	6
432.2.y.e.181.11		72	12.11	even	2
432.2.y.e.253.11		72	144.131	even	12
432.2.y.e.397.3		72	48.35	even	4
576.2.bb.e.49.12		72	9.4	even	3	inner
576.2.bb.e.241.17		72	1.1	even	1	trivial
576.2.bb.e.337.17		72	144.13	even	12	inner
576.2.bb.e.529.12		72	16.13	even	4	inner
1728.2.bc.e.145.3		72	144.77	odd	12
1728.2.bc.e.721.16		72	48.29	odd	4
1728.2.bc.e.1009.16		72	9.5	odd	6
1728.2.bc.e.1585.3		72	3.2	odd	2

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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