LMFDB - Embedded newform 864.2.bf.a.241.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(49,864)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("864.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(864, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bf (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			241.11
Character	$\chi$	$=$	864.241
Dual form			864.2.bf.a.337.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.919076 + 1.46809i) q^{3} +(-0.185555 - 0.221136i) q^{5} +(2.62731 - 0.956263i) q^{7} +(-1.31060 - 2.69858i) q^{9} +(-3.08006 + 3.67067i) q^{11} +(3.17478 - 0.559799i) q^{13} +(0.495188 - 0.0691714i) q^{15} +(2.81522 + 4.87610i) q^{17} +(-0.00428975 - 0.00247669i) q^{19} +(-1.01082 + 4.73602i) q^{21} +(-1.84294 - 0.670777i) q^{23} +(0.853770 - 4.84197i) q^{25} +(5.16631 + 0.556122i) q^{27} +(7.88122 + 1.38967i) q^{29} +(5.45972 + 1.98718i) q^{31} +(-2.55808 - 7.89544i) q^{33} +(-0.698975 - 0.403553i) q^{35} +(-8.20717 + 4.73841i) q^{37} +(-2.09603 + 5.17537i) q^{39} +(1.69965 + 9.63917i) q^{41} +(-3.57494 + 4.26045i) q^{43} +(-0.353565 + 0.790555i) q^{45} +(-3.48835 + 1.26966i) q^{47} +(0.626015 - 0.525289i) q^{49} +(-9.74597 - 0.348505i) q^{51} +0.865665i q^{53} +1.38324 q^{55} +(0.00757862 - 0.00402149i) q^{57} +(3.57109 + 4.25586i) q^{59} +(2.43327 + 6.68534i) q^{61} +(-6.02390 - 5.83673i) q^{63} +(-0.712888 - 0.598184i) q^{65} +(0.224950 - 0.0396647i) q^{67} +(2.67857 - 2.08912i) q^{69} +(-0.429923 - 0.744648i) q^{71} +(-2.02670 + 3.51035i) q^{73} +(6.32379 + 5.70356i) q^{75} +(-4.58214 + 12.5893i) q^{77} +(0.797428 - 4.52244i) q^{79} +(-5.56467 + 7.07350i) q^{81} +(4.00250 + 0.705749i) q^{83} +(0.555903 - 1.52733i) q^{85} +(-9.28361 + 10.2932i) q^{87} +(-1.77889 + 3.08112i) q^{89} +(7.80581 - 4.50669i) q^{91} +(-7.93526 + 6.18901i) q^{93} +(0.000248300 + 0.00140818i) q^{95} +(6.04757 + 5.07452i) q^{97} +(13.9423 + 3.50101i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73}+ \cdots - 12 q^{97}+O(q^{100}) $ 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{5}{9}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.919076	+	1.46809i	−0.530629	+	0.847604i
$3$	−0.919076	+	1.46809i	−0.530629	+	0.847604i
$4$		0			0
$5$	−0.185555	−	0.221136i	−0.0829828	−	0.0988950i	0.722956	−	0.690895i	$-0.242783\pi$
$5$	−0.185555	−	0.221136i	−0.0829828	−	0.0988950i	−0.805938	+	0.592000i	$0.798339\pi$
$6$		0			0
$7$	2.62731	−	0.956263i	0.993030	−	0.361433i	0.206137	−	0.978523i	$-0.433911\pi$
$7$	2.62731	−	0.956263i	0.993030	−	0.361433i	0.786893	+	0.617090i	$0.211688\pi$
$8$		0			0
$9$	−1.31060	−	2.69858i	−0.436866	−	0.899527i
$10$		0			0
$11$	−3.08006	+	3.67067i	−0.928672	+	1.10675i	0.0653817	+	0.997860i	$0.479174\pi$
$11$	−3.08006	+	3.67067i	−0.928672	+	1.10675i	−0.994054	+	0.108888i	$0.965271\pi$
$12$		0			0
$13$	3.17478	−	0.559799i	0.880525	−	0.155260i	0.284933	−	0.958547i	$-0.408029\pi$
$13$	3.17478	−	0.559799i	0.880525	−	0.155260i	0.595592	+	0.803287i	$0.296918\pi$
$14$		0			0
$15$	0.495188	−	0.0691714i	0.127857	−	0.0178600i
$16$		0			0
$17$	2.81522	+	4.87610i	0.682791	+	1.18263i	0.974126	+	0.226007i	$0.0725672\pi$
$17$	2.81522	+	4.87610i	0.682791	+	1.18263i	−0.291335	+	0.956621i	$0.594099\pi$
$18$		0			0
$19$	−0.00428975	−	0.00247669i	−0.000984137	−	0.000568192i	0.499508	−	0.866309i	$-0.333514\pi$
$19$	−0.00428975	−	0.00247669i	−0.000984137	−	0.000568192i	−0.500492	+	0.865741i	$0.666848\pi$
$20$		0			0
$21$	−1.01082	+	4.73602i	−0.220578	+	1.03348i
$22$		0			0
$23$	−1.84294	−	0.670777i	−0.384280	−	0.139867i	0.142654	−	0.989773i	$-0.454436\pi$
$23$	−1.84294	−	0.670777i	−0.384280	−	0.139867i	−0.526934	+	0.849906i	$0.676659\pi$
$24$		0			0
$25$	0.853770	−	4.84197i	0.170754	−	0.968395i
$26$		0			0
$27$	5.16631	+	0.556122i	0.994256	+	0.107026i
$28$		0			0
$29$	7.88122	+	1.38967i	1.46351	+	0.258056i	0.847966	−	0.530050i	$-0.177827\pi$
$29$	7.88122	+	1.38967i	1.46351	+	0.258056i	0.615540	+	0.788106i	$0.288938\pi$
$30$		0			0
$31$	5.45972	+	1.98718i	0.980595	+	0.356907i	0.782071	−	0.623189i	$-0.214163\pi$
$31$	5.45972	+	1.98718i	0.980595	+	0.356907i	0.198523	+	0.980096i	$0.436385\pi$
$32$		0			0
$33$	−2.55808	−	7.89544i	−0.445304	−	1.37442i
$34$		0			0
$35$	−0.698975	−	0.403553i	−0.118148	−	0.0682130i
$36$		0			0
$37$	−8.20717	+	4.73841i	−1.34925	+	0.778990i	−0.988143	−	0.153534i	$-0.950934\pi$
$37$	−8.20717	+	4.73841i	−1.34925	+	0.778990i	−0.361107	+	0.932524i	$0.617601\pi$
$38$		0			0
$39$	−2.09603	+	5.17537i	−0.335633	+	0.828722i
$40$		0			0
$41$	1.69965	+	9.63917i	0.265440	+	1.50539i	0.767779	+	0.640715i	$0.221362\pi$
$41$	1.69965	+	9.63917i	0.265440	+	1.50539i	−0.502339	+	0.864671i	$0.667527\pi$
$42$		0			0
$43$	−3.57494	+	4.26045i	−0.545173	+	0.649712i	−0.966339	−	0.257271i	$-0.917177\pi$
$43$	−3.57494	+	4.26045i	−0.545173	+	0.649712i	0.421166	+	0.906984i	$0.361621\pi$
$44$		0			0
$45$	−0.353565	+	0.790555i	−0.0527064	+	0.117849i
$46$		0			0
$47$	−3.48835	+	1.26966i	−0.508829	+	0.185199i	−0.583661	−	0.811998i	$-0.698380\pi$
$47$	−3.48835	+	1.26966i	−0.508829	+	0.185199i	0.0748320	+	0.997196i	$0.476158\pi$
$48$		0			0
$49$	0.626015	−	0.525289i	0.0894307	−	0.0750413i
$50$		0			0
$51$	−9.74597	−	0.348505i	−1.36471	−	0.0488005i
$52$		0			0
$53$			0.865665i			0.118908i	0.998231	+	0.0594541i	$0.0189360\pi$
$53$			0.865665i			0.118908i	−0.998231	+	0.0594541i	$0.981064\pi$
$54$		0			0
$55$	1.38324			0.186516
$56$		0			0
$57$	0.00757862	−	0.00402149i	0.00100381	−	0.000532660i
$58$		0			0
$59$	3.57109	+	4.25586i	0.464916	+	0.554066i	0.946655	−	0.322249i	$-0.104439\pi$
$59$	3.57109	+	4.25586i	0.464916	+	0.554066i	−0.481739	+	0.876315i	$0.659995\pi$
$60$		0			0
$61$	2.43327	+	6.68534i	0.311548	+	0.855970i	0.992345	+	0.123498i	$0.0394113\pi$
$61$	2.43327	+	6.68534i	0.311548	+	0.855970i	−0.680797	+	0.732472i	$0.738366\pi$
$62$		0			0
$63$	−6.02390	−	5.83673i	−0.758940	−	0.735359i
$64$		0			0
$65$	−0.712888	−	0.598184i	−0.0884228	−	0.0741956i
$66$		0			0
$67$	0.224950	−	0.0396647i	0.0274820	−	0.00484582i	−0.159890	−	0.987135i	$-0.551114\pi$
$67$	0.224950	−	0.0396647i	0.0274820	−	0.00484582i	0.187372	+	0.982289i	$0.440003\pi$
$68$		0			0
$69$	2.67857	−	2.08912i	0.322462	−	0.251500i
$70$		0			0
$71$	−0.429923	−	0.744648i	−0.0510224	−	0.0883735i	0.839386	−	0.543535i	$-0.182915\pi$
$71$	−0.429923	−	0.744648i	−0.0510224	−	0.0883735i	−0.890409	+	0.455162i	$0.849581\pi$
$72$		0			0
$73$	−2.02670	+	3.51035i	−0.237208	+	0.410856i	−0.959912	−	0.280301i	$-0.909566\pi$
$73$	−2.02670	+	3.51035i	−0.237208	+	0.410856i	0.722704	+	0.691157i	$0.242899\pi$
$74$		0			0
$75$	6.32379	+	5.70356i	0.730208	+	0.658590i
$76$		0			0
$77$	−4.58214	+	12.5893i	−0.522184	+	1.43469i
$78$		0			0
$79$	0.797428	−	4.52244i	0.0897176	−	0.508814i	−0.906521	−	0.422161i	$-0.861272\pi$
$79$	0.797428	−	4.52244i	0.0897176	−	0.508814i	0.996239	−	0.0866531i	$-0.0276172\pi$
$80$		0			0
$81$	−5.56467	+	7.07350i	−0.618297	+	0.785945i
$82$		0			0
$83$	4.00250	+	0.705749i	0.439332	+	0.0774660i	0.388939	−	0.921263i	$-0.372842\pi$
$83$	4.00250	+	0.705749i	0.439332	+	0.0774660i	0.0503925	+	0.998729i	$0.483953\pi$
$84$		0			0
$85$	0.555903	−	1.52733i	0.0602961	−	0.165662i
$86$		0			0
$87$	−9.28361	+	10.2932i	−0.995308	+	1.10354i
$88$		0			0
$89$	−1.77889	+	3.08112i	−0.188562	+	0.326599i	−0.944771	−	0.327731i	$-0.893716\pi$
$89$	−1.77889	+	3.08112i	−0.188562	+	0.326599i	0.756209	+	0.654330i	$0.227049\pi$
$90$		0			0
$91$	7.80581	−	4.50669i	0.818272	−	0.472429i
$92$		0			0
$93$	−7.93526	+	6.18901i	−0.822848	+	0.641771i
$94$		0			0
$95$	0.000248300		0.00140818i	2.54751e−5		0.000144476i
$96$		0			0
$97$	6.04757	+	5.07452i	0.614038	+	0.515239i	0.895923	−	0.444209i	$-0.146515\pi$
$97$	6.04757	+	5.07452i	0.614038	+	0.515239i	−0.281885	+	0.959448i	$0.590960\pi$
$98$		0			0
$99$	13.9423	+	3.50101i	1.40126	+	0.351865i
$100$		0			0
$101$	−6.35260	−	17.4536i	−0.632107	−	1.73670i	−0.675205	−	0.737630i	$-0.735945\pi$
$101$	−6.35260	−	17.4536i	−0.632107	−	1.73670i	0.0430976	−	0.999071i	$-0.486277\pi$
$102$		0			0
$103$	3.47298	−	2.91418i	0.342203	−	0.287143i	−0.455447	−	0.890263i	$-0.650521\pi$
$103$	3.47298	−	2.91418i	0.342203	−	0.287143i	0.797650	+	0.603120i	$0.206076\pi$
$104$		0			0
$105$	1.23487	−	0.655264i	0.120511	−	0.0639473i
$106$		0			0
$107$		−	3.74905i		−	0.362434i	−0.983443	−	0.181217i	$-0.941996\pi$
$107$		−	3.74905i		−	0.362434i	0.983443	−	0.181217i	$-0.0580036\pi$
$108$		0			0
$109$		−	16.8471i		−	1.61366i	−0.590782	−	0.806831i	$-0.701181\pi$
$109$		−	16.8471i		−	1.61366i	0.590782	−	0.806831i	$-0.298819\pi$
$110$		0			0
$111$	0.586584	−	16.4039i	0.0556761	−	1.55698i
$112$		0			0
$113$	4.67369	−	3.92169i	0.439664	−	0.368921i	−0.395920	−	0.918285i	$-0.629574\pi$
$113$	4.67369	−	3.92169i	0.439664	−	0.368921i	0.835583	+	0.549364i	$0.185130\pi$
$114$		0			0
$115$	0.193635	+	0.532007i	0.0180565	+	0.0496099i
$116$		0			0
$117$	−5.67152	−	7.83372i	−0.524332	−	0.724228i
$118$		0			0
$119$	12.0593	+	10.1189i	1.10547	+	0.927602i
$120$		0			0
$121$	−2.07693	−	11.7789i	−0.188812	−	1.07081i
$122$		0			0
$123$	−15.7133	−	6.36390i	−1.41682	−	0.573813i
$124$		0			0
$125$	−2.47914	+	1.43133i	−0.221741	+	0.128022i
$126$		0			0
$127$	10.6004	−	18.3604i	0.940632	−	1.62922i	0.176362	−	0.984325i	$-0.443567\pi$
$127$	10.6004	−	18.3604i	0.940632	−	1.62922i	0.764270	−	0.644896i	$-0.223099\pi$
$128$		0			0
$129$	−2.96909	−	9.16403i	−0.261414	−	0.806847i
$130$		0			0
$131$	3.62600	−	9.96234i	0.316805	−	0.870414i	−0.674435	−	0.738335i	$-0.735613\pi$
$131$	3.62600	−	9.96234i	0.316805	−	0.870414i	0.991239	−	0.132079i	$-0.0421653\pi$
$132$		0			0
$133$	−0.0136389	−	0.00240490i	−0.00118264	−	0.000208532i
$134$		0			0
$135$	−0.835656	−	1.24565i	−0.0719218	−	0.107208i
$136$		0			0
$137$	−2.46640	+	13.9877i	−0.210719	+	1.19505i	0.677463	+	0.735557i	$0.263079\pi$
$137$	−2.46640	+	13.9877i	−0.210719	+	1.19505i	−0.888182	+	0.459491i	$0.848032\pi$
$138$		0			0
$139$	3.33532	−	9.16372i	0.282898	−	0.777257i	−0.714115	−	0.700028i	$-0.753171\pi$
$139$	3.33532	−	9.16372i	0.282898	−	0.777257i	0.997013	−	0.0772283i	$-0.0246070\pi$
$140$		0			0
$141$	1.34209	−	6.28814i	0.113024	−	0.529557i
$142$		0			0
$143$	−7.72366	+	13.3778i	−0.645885	+	1.11871i
$144$		0			0
$145$	−1.15509	−	2.00068i	−0.0959254	−	0.166148i
$146$		0			0
$147$	0.195818	+	1.40183i	0.0161508	+	0.115621i
$148$		0			0
$149$	1.13973	−	0.200964i	0.0933699	−	0.0164636i	−0.126768	−	0.991932i	$-0.540460\pi$
$149$	1.13973	−	0.200964i	0.0933699	−	0.0164636i	0.220138	+	0.975469i	$0.429349\pi$
$150$		0			0
$151$	15.9973	+	13.4234i	1.30184	+	1.09238i	0.989823	+	0.142303i	$0.0454506\pi$
$151$	15.9973	+	13.4234i	1.30184	+	1.09238i	0.312022	+	0.950075i	$0.398994\pi$
$152$		0			0
$153$	9.46893	−	13.9877i	0.765518	−	1.13084i
$154$		0			0
$155$	−0.573643	−	1.57607i	−0.0460761	−	0.126593i
$156$		0			0
$157$	12.0447	+	14.3543i	0.961268	+	1.14560i	0.989286	+	0.145988i	$0.0466360\pi$
$157$	12.0447	+	14.3543i	0.961268	+	1.14560i	−0.0280180	+	0.999607i	$0.508920\pi$
$158$		0			0
$159$	−1.27088	−	0.795612i	−0.100787	−	0.0630961i
$160$		0			0
$161$	−5.48343			−0.432155
$162$		0			0
$163$		−	11.5772i		−	0.906795i	−0.891308	−	0.453397i	$-0.850212\pi$
$163$		−	11.5772i		−	0.906795i	0.891308	−	0.453397i	$-0.149788\pi$
$164$		0			0
$165$	−1.27130	+	2.03072i	−0.0989706	+	0.158091i
$166$		0			0
$167$	−7.59855	+	6.37594i	−0.587994	+	0.493385i	−0.887561	−	0.460690i	$-0.847602\pi$
$167$	−7.59855	+	6.37594i	−0.587994	+	0.493385i	0.299568	+	0.954075i	$0.403158\pi$
$168$		0			0
$169$	−2.45017	+	0.891789i	−0.188475	+	0.0685991i
$170$		0			0
$171$	−0.00106141	+	0.0148222i	−8.11679e−5	+	0.00113348i
$172$		0			0
$173$	12.8453	−	15.3084i	0.976609	−	1.16388i	−0.00986338	−	0.999951i	$-0.503140\pi$
$173$	12.8453	−	15.3084i	0.976609	−	1.16388i	0.986473	−	0.163926i	$-0.0524159\pi$
$174$		0			0
$175$	−2.38708	−	13.5378i	−0.180446	−	1.02336i
$176$		0			0
$177$	−9.53010	+	1.33123i	−0.716326	+	0.100062i
$178$		0			0
$179$	−18.6622	+	10.7746i	−1.39488	+	0.805335i	−0.993851	−	0.110730i	$-0.964681\pi$
$179$	−18.6622	+	10.7746i	−1.39488	+	0.805335i	−0.401030	+	0.916065i	$0.631348\pi$
$180$		0			0
$181$	−17.9309	−	10.3524i	−1.33280	−	0.769490i	−0.347068	−	0.937840i	$-0.612823\pi$
$181$	−17.9309	−	10.3524i	−1.33280	−	0.769490i	−0.985727	+	0.168350i	$0.946156\pi$
$182$		0			0
$183$	−12.0511	−	2.57208i	−0.890840	−	0.190134i
$184$		0			0
$185$	2.57071	+	0.935664i	0.189003	+	0.0687914i
$186$		0			0
$187$	−26.5696	−	4.68494i	−1.94296	−	0.342596i
$188$		0			0
$189$	14.1053	−	3.47924i	1.02601	−	0.253078i
$190$		0			0
$191$	0.173666	−	0.984911i	0.0125661	−	0.0712657i	−0.977880	−	0.209167i	$-0.932925\pi$
$191$	0.173666	−	0.984911i	0.0125661	−	0.0712657i	0.990446	+	0.137902i	$0.0440358\pi$
$192$		0			0
$193$	18.6207	+	6.77739i	1.34035	+	0.487847i	0.909923	−	0.414778i	$-0.136141\pi$
$193$	18.6207	+	6.77739i	1.34035	+	0.487847i	0.430427	+	0.902625i	$0.358363\pi$
$194$		0			0
$195$	1.53339	−	0.496809i	0.109808	−	0.0355772i
$196$		0			0
$197$	−5.14676	−	2.97148i	−0.366691	−	0.211709i	0.305321	−	0.952250i	$-0.401236\pi$
$197$	−5.14676	−	2.97148i	−0.366691	−	0.211709i	−0.672012	+	0.740540i	$0.734570\pi$
$198$		0			0
$199$	4.22572	+	7.31916i	0.299553	+	0.518842i	0.976034	−	0.217619i	$-0.0698290\pi$
$199$	4.22572	+	7.31916i	0.299553	+	0.518842i	−0.676480	+	0.736461i	$0.736496\pi$
$200$		0			0
$201$	−0.148515	+	0.366702i	−0.0104754	+	0.0258652i
$202$		0			0
$203$	22.0353	−	3.88542i	1.54658	−	0.272703i
$204$		0			0
$205$	1.81619	−	2.16445i	0.126848	−	0.151172i
$206$		0			0
$207$	0.605213	+	5.85245i	0.0420652	+	0.406773i
$208$		0			0
$209$	0.0223038	−	0.00811792i	0.00154279	−	0.000561528i
$210$		0			0
$211$	2.67743	+	3.19083i	0.184322	+	0.219666i	0.850291	−	0.526313i	$-0.176426\pi$
$211$	2.67743	+	3.19083i	0.184322	+	0.219666i	−0.665969	+	0.745980i	$0.731982\pi$
$212$		0			0
$213$	1.48834	+	0.0532216i	0.101980	+	0.00364668i
$214$		0			0
$215$	1.60549			0.109493
$216$		0			0
$217$	16.2446			1.10276
$218$		0			0
$219$	−3.29083	−	6.20168i	−0.222374	−	0.419070i
$220$		0			0
$221$	11.6673	+	13.9046i	0.784829	+	0.935323i
$222$		0			0
$223$	−13.7266	+	4.99606i	−0.919198	+	0.334561i	−0.757919	−	0.652348i	$-0.773784\pi$
$223$	−13.7266	+	4.99606i	−0.919198	+	0.334561i	−0.161279	+	0.986909i	$0.551562\pi$
$224$		0			0
$225$	−14.1854	+	4.04191i	−0.945693	+	0.269461i
$226$		0			0
$227$	13.2187	−	15.7535i	0.877359	−	1.04560i	−0.121237	−	0.992624i	$-0.538686\pi$
$227$	13.2187	−	15.7535i	0.877359	−	1.04560i	0.998596	−	0.0529722i	$-0.0168695\pi$
$228$		0			0
$229$	11.3156	−	1.99525i	0.747759	−	0.131850i	0.213232	−	0.977002i	$-0.431601\pi$
$229$	11.3156	−	1.99525i	0.747759	−	0.131850i	0.534527	+	0.845151i	$0.320490\pi$
$230$		0			0
$231$	−14.2710	−	18.2976i	−0.938962	−	1.20389i
$232$		0			0
$233$	−2.16566	−	3.75103i	−0.141877	−	0.245738i	0.786326	−	0.617811i	$-0.211980\pi$
$233$	−2.16566	−	3.75103i	−0.141877	−	0.245738i	−0.928203	+	0.372073i	$0.878647\pi$
$234$		0			0
$235$	0.928049	+	0.535809i	0.0605392	+	0.0349523i
$236$		0			0
$237$	5.90647	+	5.32717i	0.383666	+	0.346037i
$238$		0			0
$239$	13.2703	+	4.82998i	0.858382	+	0.312426i	0.733453	−	0.679740i	$-0.237907\pi$
$239$	13.2703	+	4.82998i	0.858382	+	0.312426i	0.124929	+	0.992166i	$0.460130\pi$
$240$		0			0
$241$	2.60609	−	14.7799i	0.167873	−	0.952056i	−0.778179	−	0.628042i	$-0.783856\pi$
$241$	2.60609	−	14.7799i	0.167873	−	0.952056i	0.946052	−	0.324014i	$-0.105032\pi$
$242$		0			0
$243$	−5.27021	−	14.6705i	−0.338084	−	0.941116i
$244$		0			0
$245$	−0.232321	−	0.0409644i	−0.0148424	−	0.00261712i
$246$		0			0
$247$	−0.0150055	−	0.00546154i	−0.000954774	−	0.000347509i
$248$		0			0
$249$	−4.71471	+	5.22741i	−0.298783	+	0.331274i
$250$		0			0
$251$	−26.0768	−	15.0554i	−1.64595	−	0.950290i	−0.978658	−	0.205495i	$-0.934120\pi$
$251$	−26.0768	−	15.0554i	−1.64595	−	0.950290i	−0.667293	−	0.744795i	$-0.732547\pi$
$252$		0			0
$253$	8.13857	−	4.69881i	0.511668	−	0.295412i
$254$		0			0
$255$	1.73135	+	2.21985i	0.108421	+	0.139012i
$256$		0			0
$257$	−0.685637	−	3.88844i	−0.0427688	−	0.242554i	0.955927	−	0.293603i	$-0.0948545\pi$
$257$	−0.685637	−	3.88844i	−0.0427688	−	0.242554i	−0.998696	+	0.0510494i	$0.983743\pi$
$258$		0			0
$259$	−17.0316	+	20.2975i	−1.05829	+	1.26123i
$260$		0			0
$261$	−6.57897	−	23.0894i	−0.407228	−	1.42920i
$262$		0			0
$263$	−12.3951	+	4.51144i	−0.764313	+	0.278187i	−0.694616	−	0.719381i	$-0.744425\pi$
$263$	−12.3951	+	4.51144i	−0.764313	+	0.278187i	−0.0696970	+	0.997568i	$0.522203\pi$
$264$		0			0
$265$	0.191430	−	0.160629i	0.0117594	−	0.00986733i
$266$		0			0
$267$	−2.88844	−	5.44336i	−0.176770	−	0.333128i
$268$		0			0
$269$			7.68651i			0.468655i	0.972158	+	0.234327i	$0.0752887\pi$
$269$			7.68651i			0.468655i	−0.972158	+	0.234327i	$0.924711\pi$
$270$		0			0
$271$	−21.3410			−1.29637			−0.648187	−	0.761481i	$-0.724472\pi$
$271$	−21.3410			−1.29637			−0.648187	+	0.761481i	$0.724472\pi$
$272$		0			0
$273$	−0.557898	+	15.6017i	−0.0337655	+	0.944255i
$274$		0			0
$275$	15.1436	+	18.0475i	0.913195	+	1.08830i
$276$		0			0
$277$	−7.73418	−	21.2495i	−0.464702	−	1.27676i	−0.921912	−	0.387400i	$-0.873373\pi$
$277$	−7.73418	−	21.2495i	−0.464702	−	1.27676i	0.457210	−	0.889359i	$-0.348849\pi$
$278$		0			0
$279$	−1.79294	−	17.3379i	−0.107341	−	1.03799i
$280$		0			0
$281$	−24.7061	−	20.7308i	−1.47384	−	1.23670i	−0.912477	−	0.409129i	$-0.865833\pi$
$281$	−24.7061	−	20.7308i	−1.47384	−	1.23670i	−0.561363	−	0.827570i	$-0.689723\pi$
$282$		0			0
$283$	20.0970	−	3.54364i	1.19464	−	0.210648i	0.459261	−	0.888301i	$-0.348114\pi$
$283$	20.0970	−	3.54364i	1.19464	−	0.210648i	0.735381	+	0.677653i	$0.237003\pi$
$284$		0			0
$285$	−0.00229555		0.000929698i	−0.000135977		5.50705e-5i
$286$		0			0
$287$	13.6831	+	23.6998i	0.807687	+	1.39896i
$288$		0			0
$289$	−7.35090	+	12.7321i	−0.432406	+	0.748949i
$290$		0			0
$291$	−13.0080	+	4.21453i	−0.762545	+	0.247060i
$292$		0			0
$293$	−1.43710	+	3.94839i	−0.0839561	+	0.230667i	−0.974566	−	0.224101i	$-0.928056\pi$
$293$	−1.43710	+	3.94839i	−0.0839561	+	0.230667i	0.890610	+	0.454768i	$0.150278\pi$
$294$		0			0
$295$	0.278490	−	1.57939i	0.0162143	−	0.0919558i
$296$		0			0
$297$	−17.9539	+	17.2509i	−1.04179	+	1.00100i
$298$		0			0
$299$	−6.22644	−	1.09789i	−0.360084	−	0.0634926i
$300$		0			0
$301$	−5.31837	+	14.6121i	−0.306546	+	0.842228i
$302$		0			0
$303$	31.4621	+	6.71500i	1.80745	+	0.385767i
$304$		0			0
$305$	1.02686	−	1.77858i	0.0587981	−	0.101841i
$306$		0			0
$307$	16.4700	−	9.50896i	0.939993	−	0.542705i	0.0500346	−	0.998747i	$-0.484067\pi$
$307$	16.4700	−	9.50896i	0.939993	−	0.542705i	0.889958	+	0.456043i	$0.150734\pi$
$308$		0			0
$309$	1.08635	+	7.77702i	0.0618003	+	0.442419i
$310$		0			0
$311$	−3.01498	−	17.0988i	−0.170964	−	0.969585i	−0.942700	−	0.333642i	$-0.891722\pi$
$311$	−3.01498	−	17.0988i	−0.170964	−	0.969585i	0.771736	−	0.635943i	$-0.219389\pi$
$312$		0			0
$313$	0.579959	+	0.486644i	0.0327812	+	0.0275067i	0.659031	−	0.752116i	$-0.270967\pi$
$313$	0.579959	+	0.486644i	0.0327812	+	0.0275067i	−0.626250	+	0.779622i	$0.715411\pi$
$314$		0			0
$315$	−0.172947	+	2.41514i	−0.00974443	+	0.136078i
$316$		0			0
$317$	−6.72476	−	18.4761i	−0.377700	−	1.03772i	−0.972307	−	0.233706i	$-0.924915\pi$
$317$	−6.72476	−	18.4761i	−0.377700	−	1.03772i	0.594607	−	0.804016i	$-0.297308\pi$
$318$		0			0
$319$	−29.3756	+	24.6491i	−1.64472	+	1.38008i
$320$		0			0
$321$	5.50395	+	3.44566i	0.307201	+	0.192318i
$322$		0			0
$323$		−	0.0278897i		−	0.00155182i
$324$		0			0
$325$		−	15.8501i		−	0.879207i
$326$		0			0
$327$	24.7332	+	15.4838i	1.36775	+	0.856256i
$328$		0			0
$329$	−7.95087	+	6.67157i	−0.438345	+	0.367815i
$330$		0			0
$331$	8.42157	+	23.1381i	0.462891	+	1.27178i	0.923301	+	0.384077i	$0.125480\pi$
$331$	8.42157	+	23.1381i	0.462891	+	1.27178i	−0.460409	+	0.887707i	$0.652297\pi$
$332$		0			0
$333$	23.5433	+	15.9376i	1.29016	+	0.873373i
$334$		0			0
$335$	−0.0505119	−	0.0423845i	−0.00275976	−	0.00231571i
$336$		0			0
$337$	−1.71929	−	9.75056i	−0.0936555	−	0.531147i	−0.995151	−	0.0983585i	$-0.968641\pi$
$337$	−1.71929	−	9.75056i	−0.0936555	−	0.531147i	0.901496	−	0.432788i	$-0.142470\pi$
$338$		0			0
$339$	1.46193	+	10.4657i	0.0794012	+	0.568421i
$340$		0			0
$341$	−24.1105	+	13.9202i	−1.30566	+	0.753822i
$342$		0			0
$343$	−8.64332	+	14.9707i	−0.466695	+	0.808340i
$344$		0			0
$345$	−0.959002	−	0.204681i	−0.0516309	−	0.0110197i
$346$		0			0
$347$	−7.12971	+	19.5887i	−0.382743	+	1.05158i	0.587453	+	0.809258i	$0.300131\pi$
$347$	−7.12971	+	19.5887i	−0.382743	+	1.05158i	−0.970196	+	0.242320i	$0.922092\pi$
$348$		0			0
$349$	−14.8725	−	2.62242i	−0.796107	−	0.140375i	−0.239222	−	0.970965i	$-0.576892\pi$
$349$	−14.8725	−	2.62242i	−0.796107	−	0.140375i	−0.556885	+	0.830590i	$0.688004\pi$
$350$		0			0
$351$	16.7132	−	1.12653i	0.892084	−	0.0601297i
$352$		0			0
$353$	−0.616217	+	3.49474i	−0.0327979	+	0.186006i	−0.996805	−	0.0798689i	$-0.974550\pi$
$353$	−0.616217	+	3.49474i	−0.0327979	+	0.186006i	0.964007	+	0.265875i	$0.0856609\pi$
$354$		0			0
$355$	−0.0848941	+	0.233245i	−0.00450571	+	0.0123793i
$356$		0			0
$357$	−25.9390	+	8.40408i	−1.37284	+	0.444791i
$358$		0			0
$359$	11.0808	−	19.1925i	0.584823	−	1.01294i	−0.410074	−	0.912052i	$-0.634497\pi$
$359$	11.0808	−	19.1925i	0.584823	−	1.01294i	0.994897	−	0.100891i	$-0.0321694\pi$
$360$		0			0
$361$	−9.49999	−	16.4545i	−0.499999	−	0.866024i
$362$		0			0
$363$	19.2013	+	7.77655i	1.00781	+	0.408163i
$364$		0			0
$365$	1.15233	−	0.203187i	0.0603158	−	0.0106353i
$366$		0			0
$367$	−13.2887	−	11.1505i	−0.693664	−	0.582053i	0.226299	−	0.974058i	$-0.427337\pi$
$367$	−13.2887	−	11.1505i	−0.693664	−	0.582053i	−0.919963	+	0.392005i	$0.871782\pi$
$368$		0			0
$369$	23.7845	−	17.2197i	1.23817	−	0.896422i
$370$		0			0
$371$	0.827803	+	2.27437i	0.0429774	+	0.118079i
$372$		0			0
$373$	10.6639	+	12.7087i	0.552156	+	0.658034i	0.967867	−	0.251463i	$-0.0809116\pi$
$373$	10.6639	+	12.7087i	0.552156	+	0.658034i	−0.415711	+	0.909497i	$0.636467\pi$
$374$		0			0
$375$	0.177190	−	4.95512i	0.00915004	−	0.255881i
$376$		0			0
$377$	25.7991			1.32872
$378$		0			0
$379$			9.64915i			0.495644i	0.968806	+	0.247822i	$0.0797148\pi$
$379$			9.64915i			0.495644i	−0.968806	+	0.247822i	$0.920285\pi$
$380$		0			0
$381$	17.2122	+	32.4370i	0.881809	+	1.66180i
$382$		0			0
$383$	9.22574	−	7.74132i	0.471414	−	0.395563i	−0.375896	−	0.926662i	$-0.622665\pi$
$383$	9.22574	−	7.74132i	0.471414	−	0.395563i	0.847310	+	0.531099i	$0.178221\pi$
$384$		0			0
$385$	3.63420	−	1.32274i	0.185216	−	0.0674130i
$386$		0			0
$387$	16.1825	+	4.06353i	0.822601	+	0.206561i
$388$		0			0
$389$	−1.86623	+	2.22408i	−0.0946216	+	0.112766i	−0.811277	−	0.584661i	$-0.801227\pi$
$389$	−1.86623	+	2.22408i	−0.0946216	+	0.112766i	0.716656	+	0.697427i	$0.245672\pi$
$390$		0			0
$391$	−1.91751	−	10.8748i	−0.0969729	−	0.549960i
$392$		0			0
$393$	11.2931	+	14.4795i	0.569661	+	0.730392i
$394$		0			0
$395$	−1.14804	+	0.662821i	−0.0577642	+	0.0333502i
$396$		0			0
$397$	3.53148	+	2.03890i	0.177240	+	0.102330i	0.585995	−	0.810314i	$-0.300704\pi$
$397$	3.53148	+	2.03890i	0.177240	+	0.102330i	−0.408755	+	0.912644i	$0.634037\pi$
$398$		0			0
$399$	0.0160658	−	0.0178129i	0.000804296	−	0.000891759i
$400$		0			0
$401$	2.09322	+	0.761870i	0.104530	+	0.0380460i	0.393756	−	0.919215i	$-0.371176\pi$
$401$	2.09322	+	0.761870i	0.104530	+	0.0380460i	−0.289226	+	0.957261i	$0.593398\pi$
$402$		0			0
$403$	18.4458	+	3.25249i	0.918851	+	0.162018i
$404$		0			0
$405$	2.59676	−	0.0819761i	0.129034	−	0.00407343i
$406$		0			0
$407$	7.88541	−	44.7204i	0.390865	−	2.21671i
$408$		0			0
$409$	17.7345	+	6.45483i	0.876914	+	0.319171i	0.740964	−	0.671545i	$-0.234369\pi$
$409$	17.7345	+	6.45483i	0.876914	+	0.319171i	0.135950	+	0.990716i	$0.456591\pi$
$410$		0			0
$411$	−18.2684	−	16.4767i	−0.901114	−	0.812733i
$412$		0			0
$413$	13.4521	+	7.76657i	0.661934	+	0.382168i
$414$		0			0
$415$	−0.586618	−	1.01605i	−0.0287959	−	0.0498760i
$416$		0			0
$417$	10.3878	+	13.3187i	0.508692	+	0.652221i
$418$		0			0
$419$	−13.5715	+	2.39303i	−0.663013	+	0.116907i	−0.495021	−	0.868881i	$-0.664839\pi$
$419$	−13.5715	+	2.39303i	−0.663013	+	0.116907i	−0.167992	+	0.985788i	$0.553728\pi$
$420$		0			0
$421$	−23.8985	+	28.4811i	−1.16474	+	1.38809i	−0.258135	+	0.966109i	$0.583108\pi$
$421$	−23.8985	+	28.4811i	−1.16474	+	1.38809i	−0.906607	+	0.421977i	$0.861336\pi$
$422$		0			0
$423$	7.99810	+	7.74959i	0.388881	+	0.376798i
$424$		0			0
$425$	26.0135	−	9.46814i	1.26184	−	0.459272i
$426$		0			0
$427$	12.7859	+	15.2376i	0.618753	+	0.737401i
$428$		0			0
$429$	−12.5412	−	23.6342i	−0.605494	−	1.14107i
$430$		0			0
$431$	−11.4089			−0.549548			−0.274774	−	0.961509i	$-0.588603\pi$
$431$	−11.4089			−0.549548			−0.274774	+	0.961509i	$0.588603\pi$
$432$		0			0
$433$	−7.51420			−0.361109			−0.180555	−	0.983565i	$-0.557789\pi$
$433$	−7.51420			−0.361109			−0.180555	+	0.983565i	$0.557789\pi$
$434$		0			0
$435$	3.99881	+	0.142993i	0.191728	+	0.00685599i
$436$		0			0
$437$	0.00624447	+	0.00744187i	0.000298713	+	0.000355993i
$438$		0			0
$439$	19.2063	−	6.99052i	0.916667	−	0.333639i	0.159755	−	0.987157i	$-0.448930\pi$
$439$	19.2063	−	6.99052i	0.916667	−	0.333639i	0.756912	+	0.653517i	$0.226707\pi$
$440$		0			0
$441$	−2.23799	−	1.00091i	−0.106571	−	0.0476624i
$442$		0			0
$443$	18.1395	−	21.6178i	0.861832	−	1.02709i	−0.137498	−	0.990502i	$-0.543906\pi$
$443$	18.1395	−	21.6178i	0.861832	−	1.02709i	0.999330	−	0.0365893i	$-0.0116493\pi$
$444$		0			0
$445$	1.01143	−	0.178342i	0.0479463	−	0.00845423i
$446$		0			0
$447$	−0.752460	+	1.85793i	−0.0355901	+	0.0878768i
$448$		0			0
$449$	−5.65025	−	9.78653i	−0.266652	−	0.461855i	0.701343	−	0.712824i	$-0.252584\pi$
$449$	−5.65025	−	9.78653i	−0.266652	−	0.461855i	−0.967995	+	0.250969i	$0.919251\pi$
$450$		0			0
$451$	−40.6172	−	23.4504i	−1.91259	−	1.10423i
$452$		0			0
$453$	−34.4095	+	11.1485i	−1.61670	+	0.523802i
$454$		0			0
$455$	−2.44500	−	0.889907i	−0.114623	−	0.0417195i
$456$		0			0
$457$	−6.59891	+	37.4243i	−0.308684	+	1.75063i	0.296952	+	0.954892i	$0.404030\pi$
$457$	−6.59891	+	37.4243i	−0.308684	+	1.75063i	−0.605636	+	0.795742i	$0.707081\pi$
$458$		0			0
$459$	11.8326	+	26.7570i	0.552297	+	1.24891i
$460$		0			0
$461$	−7.55207	−	1.33163i	−0.351735	−	0.0620204i	−0.00501063	−	0.999987i	$-0.501595\pi$
$461$	−7.55207	−	1.33163i	−0.351735	−	0.0620204i	−0.346724	+	0.937967i	$0.612706\pi$
$462$		0			0
$463$	20.5953	+	7.49607i	0.957144	+	0.348372i	0.772914	−	0.634511i	$-0.218798\pi$
$463$	20.5953	+	7.49607i	0.957144	+	0.348372i	0.184231	+	0.982883i	$0.441021\pi$
$464$		0			0
$465$	2.84104	+	0.606368i	0.131750	+	0.0281196i
$466$		0			0
$467$	−2.10941	−	1.21787i	−0.0976119	−	0.0563563i	0.450399	−	0.892827i	$-0.351282\pi$
$467$	−2.10941	−	1.21787i	−0.0976119	−	0.0563563i	−0.548011	+	0.836471i	$0.684615\pi$
$468$		0			0
$469$	0.553083	−	0.319323i	0.0255390	−	0.0147450i
$470$		0			0
$471$	−32.1434	+	4.49002i	−1.48109	+	0.206889i
$472$		0			0
$473$	−4.62768	−	26.2449i	−0.212781	−	1.20674i
$474$		0			0
$475$	−0.0156545	+	0.0186563i	−0.000718279	+	0.000856012i
$476$		0			0
$477$	2.33607	−	1.13454i	0.106961	−	0.0519469i
$478$		0			0
$479$	−13.6689	+	4.97509i	−0.624550	+	0.227318i	−0.634857	−	0.772629i	$-0.718941\pi$
$479$	−13.6689	+	4.97509i	−0.624550	+	0.227318i	0.0103076	+	0.999947i	$0.496719\pi$
$480$		0			0
$481$	−23.4034	+	19.6378i	−1.06710	+	0.895405i
$482$		0			0
$483$	5.03969	−	8.05018i	0.229314	−	0.366296i
$484$		0			0
$485$		−	2.27894i		−	0.103481i
$486$		0			0
$487$	−2.54679			−0.115406			−0.0577031	−	0.998334i	$-0.518378\pi$
$487$	−2.54679			−0.115406			−0.0577031	+	0.998334i	$0.518378\pi$
$488$		0			0
$489$	16.9964	+	10.6403i	0.768603	+	0.481172i
$490$		0			0
$491$	11.6939	+	13.9362i	0.527738	+	0.628933i	0.962392	−	0.271664i	$-0.0875739\pi$
$491$	11.6939	+	13.9362i	0.527738	+	0.628933i	−0.434654	+	0.900597i	$0.643129\pi$
$492$		0			0
$493$	15.4112	+	42.3419i	0.694085	+	1.90698i
$494$		0			0
$495$	−1.81287	−	3.73278i	−0.0814823	−	0.167776i
$496$		0			0
$497$	−1.84162	−	1.54530i	−0.0826080	−	0.0693163i
$498$		0			0
$499$	−2.03309	+	0.358488i	−0.0910134	+	0.0160481i	−0.218969	−	0.975732i	$-0.570269\pi$
$499$	−2.03309	+	0.358488i	−0.0910134	+	0.0160481i	0.127956	+	0.991780i	$0.459158\pi$
$500$		0			0
$501$	−2.37683	−	17.0154i	−0.106189	−	0.760190i
$502$		0			0
$503$	−15.5785	−	26.9828i	−0.694613	−	1.20310i	−0.970311	−	0.241860i	$-0.922242\pi$
$503$	−15.5785	−	26.9828i	−0.694613	−	1.20310i	0.275699	−	0.961244i	$-0.411091\pi$
$504$		0			0
$505$	−2.68087	+	4.64340i	−0.119297	+	0.206628i
$506$		0			0
$507$	0.942664	−	4.41670i	0.0418652	−	0.196153i
$508$		0			0
$509$	−0.653669	+	1.79594i	−0.0289734	+	0.0796037i	−0.953336	−	0.301911i	$-0.902375\pi$
$509$	−0.653669	+	1.79594i	−0.0289734	+	0.0796037i	0.924363	+	0.381515i	$0.124598\pi$
$510$		0			0
$511$	−1.96796	+	11.1609i	−0.0870574	+	0.493727i
$512$		0			0
$513$	−0.0207848	−	0.0151810i	−0.000917673	−	0.000670256i
$514$		0			0
$515$	−1.28886	−	0.227261i	−0.0567939	−	0.0100143i
$516$		0			0
$517$	6.08384	−	16.7152i	0.267567	−	0.735134i
$518$		0			0
$519$	10.6684	+	32.9277i	0.468290	+	1.44537i
$520$		0			0
$521$	4.36155	−	7.55442i	0.191083	−	0.330965i	−0.754527	−	0.656269i	$-0.772133\pi$
$521$	4.36155	−	7.55442i	0.191083	−	0.330965i	0.945609	+	0.325304i	$0.105467\pi$
$522$		0			0
$523$	−17.9490	+	10.3629i	−0.784855	+	0.453136i	−0.838148	−	0.545443i	$-0.816362\pi$
$523$	−17.9490	+	10.3629i	−0.784855	+	0.453136i	0.0532932	+	0.998579i	$0.483028\pi$
$524$		0			0
$525$	22.0687	+	8.93782i	0.963156	+	0.390078i
$526$		0			0
$527$	5.68063	+	32.2165i	0.247452	+	1.40337i
$528$		0			0
$529$	−14.6725	−	12.3117i	−0.637936	−	0.535292i
$530$		0			0
$531$	6.80452	−	15.2146i	0.295291	−	0.660257i
$532$		0			0
$533$	10.7920	+	29.6508i	0.467453	+	1.28432i
$534$		0			0
$535$	−0.829049	+	0.695655i	−0.0358429	+	0.0300758i
$536$		0			0
$537$	1.33383	−	37.3006i	0.0575590	−	1.60964i
$538$		0			0
$539$			3.91581i			0.168666i
$540$		0			0
$541$			3.63212i			0.156157i	0.996947	+	0.0780785i	$0.0248785\pi$
$541$			3.63212i			0.156157i	−0.996947	+	0.0780785i	$0.975122\pi$
$542$		0			0
$543$	31.6782	−	16.8096i	1.35944	−	0.721369i
$544$		0			0
$545$	−3.72551	+	3.12607i	−0.159583	+	0.133906i
$546$		0			0
$547$	3.43081	+	9.42608i	0.146691	+	0.403030i	0.991177	−	0.132548i	$-0.0423159\pi$
$547$	3.43081	+	9.42608i	0.146691	+	0.403030i	−0.844486	+	0.535578i	$0.820094\pi$
$548$		0			0
$549$	14.8519	−	15.3282i	0.633864	−	0.654190i
$550$		0			0
$551$	−0.0303667	−	0.0254807i	−0.00129367	−	0.00108551i
$552$		0			0
$553$	−2.22955	−	12.6444i	−0.0948101	−	0.537695i
$554$		0			0
$555$	−3.73633	+	2.91410i	−0.158598	+	0.123697i
$556$		0			0
$557$	9.46379	−	5.46392i	0.400994	−	0.231514i	−0.285919	−	0.958254i	$-0.592299\pi$
$557$	9.46379	−	5.46392i	0.400994	−	0.231514i	0.686913	+	0.726740i	$0.258966\pi$
$558$		0			0
$559$	−8.96465	+	15.5272i	−0.379164	+	0.656732i
$560$		0			0
$561$	31.2974	−	34.7008i	1.32138	−	1.46507i
$562$		0			0
$563$	−9.70697	+	26.6697i	−0.409100	+	1.12399i	0.548565	+	0.836108i	$0.315174\pi$
$563$	−9.70697	+	26.6697i	−0.409100	+	1.12399i	−0.957665	+	0.287885i	$0.907048\pi$
$564$		0			0
$565$	−1.73445	−	0.305831i	−0.0729690	−	0.0128664i
$566$		0			0
$567$	−7.85599	+	23.9056i	−0.329921	+	1.00394i
$568$		0			0
$569$	−2.42865	+	13.7735i	−0.101814	+	0.577417i	0.890631	+	0.454727i	$0.150263\pi$
$569$	−2.42865	+	13.7735i	−0.101814	+	0.577417i	−0.992445	+	0.122690i	$0.960848\pi$
$570$		0			0
$571$	5.30577	−	14.5775i	0.222040	−	0.610049i	−0.777790	−	0.628525i	$-0.783659\pi$
$571$	5.30577	−	14.5775i	0.222040	−	0.610049i	0.999829	+	0.0184759i	$0.00588139\pi$
$572$		0			0
$573$	1.28633	+	1.16017i	0.0537372	+	0.0484667i
$574$		0			0
$575$	−4.82133	+	8.35080i	−0.201064	+	0.348252i
$576$		0			0
$577$	−0.198083	−	0.343090i	−0.00824632	−	0.0142830i	0.861873	−	0.507125i	$-0.169292\pi$
$577$	−0.198083	−	0.343090i	−0.00824632	−	0.0142830i	−0.870119	+	0.492841i	$0.835958\pi$
$578$		0			0
$579$	−27.0637	+	21.1080i	−1.12473	+	0.877220i
$580$		0			0
$581$	11.1907	−	1.97322i	0.464268	−	0.0818630i
$582$		0			0
$583$	−3.17757	−	2.66630i	−0.131602	−	0.110427i
$584$		0			0
$585$	−0.679938	+	2.70776i	−0.0281120	+	0.111952i
$586$		0			0
$587$	4.01994	+	11.0447i	0.165921	+	0.455864i	0.994590	−	0.103874i	$-0.0331240\pi$
$587$	4.01994	+	11.0447i	0.165921	+	0.455864i	−0.828670	+	0.559738i	$0.810902\pi$
$588$		0			0
$589$	−0.0184992	−	0.0220465i	−0.000762247	−	0.000908411i
$590$		0			0
$591$	9.09268	−	4.82490i	0.374023	−	0.198470i
$592$		0			0
$593$	−14.1087			−0.579377			−0.289688	−	0.957121i	$-0.593552\pi$
$593$	−14.1087			−0.579377			−0.289688	+	0.957121i	$0.593552\pi$
$594$		0			0
$595$		−	4.54436i		−	0.186301i
$596$		0			0
$597$	−14.6290	−	0.523116i	−0.598724	−	0.0214097i
$598$		0			0
$599$	28.5436	−	23.9509i	1.16626	−	0.978607i	0.166286	−	0.986077i	$-0.446822\pi$
$599$	28.5436	−	23.9509i	1.16626	−	0.978607i	0.999972	+	0.00747033i	$0.00237790\pi$
$600$		0			0
$601$	−11.4635	+	4.17236i	−0.467605	+	0.170194i	−0.565067	−	0.825045i	$-0.691150\pi$
$601$	−11.4635	+	4.17236i	−0.467605	+	0.170194i	0.0974622	+	0.995239i	$0.468927\pi$
$602$		0			0
$603$	−0.401857	−	0.555061i	−0.0163649	−	0.0226038i
$604$		0			0
$605$	−2.21934	+	2.64491i	−0.0902292	+	0.107531i
$606$		0			0
$607$	−7.57443	−	42.9567i	−0.307436	−	1.74356i	−0.611809	−	0.791006i	$-0.709558\pi$
$607$	−7.57443	−	42.9567i	−0.307436	−	1.74356i	0.304372	−	0.952553i	$-0.401553\pi$
$608$		0			0
$609$	−14.5480	+	35.9209i	−0.589514	+	1.45559i
$610$		0			0
$611$	−10.3640	+	5.98365i	−0.419282	+	0.242073i
$612$		0			0
$613$	24.6408	+	14.2264i	0.995233	+	0.574598i	0.906834	−	0.421487i	$-0.138492\pi$
$613$	24.6408	+	14.2264i	0.995233	+	0.574598i	0.0883987	+	0.996085i	$0.471825\pi$
$614$		0			0
$615$	1.50840	+	4.65563i	0.0608245	+	0.187733i
$616$		0			0
$617$	−6.84389	−	2.49097i	−0.275525	−	0.100283i	0.200562	−	0.979681i	$-0.435723\pi$
$617$	−6.84389	−	2.49097i	−0.275525	−	0.100283i	−0.476087	+	0.879398i	$0.657945\pi$
$618$		0			0
$619$	4.70638	+	0.829861i	0.189165	+	0.0333549i	0.267428	−	0.963578i	$-0.413826\pi$
$619$	4.70638	+	0.829861i	0.189165	+	0.0333549i	−0.0782628	+	0.996933i	$0.524937\pi$
$620$		0			0
$621$	−9.14818	−	4.49034i	−0.367104	−	0.180191i
$622$		0			0
$623$	−1.72733	+	9.79616i	−0.0692039	+	0.392475i
$624$		0			0
$625$	−22.3242	−	8.12536i	−0.892970	−	0.325014i
$626$		0			0
$627$	−0.00858103	+	0.0402050i	−0.000342693	+	0.00160563i
$628$		0			0
$629$	−46.2099	−	26.6793i	−1.84251	−	1.06377i
$630$		0			0
$631$	10.2228	+	17.7064i	0.406964	+	0.704882i	0.994548	−	0.104281i	$-0.0332543\pi$
$631$	10.2228	+	17.7064i	0.406964	+	0.704882i	−0.587584	+	0.809163i	$0.699921\pi$
$632$		0			0
$633$	−7.14521	+	0.998094i	−0.283996	+	0.0396707i
$634$		0			0
$635$	−6.02710	+	1.06274i	−0.239178	+	0.0421736i
$636$		0			0
$637$	1.69340	−	2.01812i	0.0670950	−	0.0799607i
$638$		0			0
$639$	−1.44604	+	2.13611i	−0.0572043	+	0.0845034i
$640$		0			0
$641$	17.9357	−	6.52806i	0.708417	−	0.257843i	0.0374167	−	0.999300i	$-0.488087\pi$
$641$	17.9357	−	6.52806i	0.708417	−	0.257843i	0.671000	+	0.741457i	$0.265865\pi$
$642$		0			0
$643$	11.9937	+	14.2935i	0.472984	+	0.563680i	0.948805	−	0.315862i	$-0.102294\pi$
$643$	11.9937	+	14.2935i	0.472984	+	0.563680i	−0.475821	+	0.879542i	$0.657849\pi$
$644$		0			0
$645$	−1.47556	+	2.35700i	−0.0581003	+	0.0928070i
$646$		0			0
$647$	−1.28685			−0.0505911			−0.0252955	−	0.999680i	$-0.508053\pi$
$647$	−1.28685			−0.0505911			−0.0252955	+	0.999680i	$0.508053\pi$
$648$		0			0
$649$	−26.6210			−1.04497
$650$		0			0
$651$	−14.9301	+	23.8487i	−0.585156	+	0.934703i
$652$		0			0
$653$	4.80662	+	5.72830i	0.188097	+	0.224166i	0.851849	−	0.523787i	$-0.175481\pi$
$653$	4.80662	+	5.72830i	0.188097	+	0.224166i	−0.663752	+	0.747953i	$0.731037\pi$
$654$		0			0
$655$	−2.87585	+	1.04672i	−0.112369	+	0.0408989i
$656$		0			0
$657$	12.1292	+	0.868563i	0.473204	+	0.0338859i
$658$		0			0
$659$	15.2256	−	18.1451i	0.593104	−	0.706834i	−0.383095	−	0.923709i	$-0.625142\pi$
$659$	15.2256	−	18.1451i	0.593104	−	0.706834i	0.976199	+	0.216875i	$0.0695864\pi$
$660$		0			0
$661$	4.78633	−	0.843960i	0.186167	−	0.0328262i	−0.0797873	−	0.996812i	$-0.525424\pi$
$661$	4.78633	−	0.843960i	0.186167	−	0.0328262i	0.265954	+	0.963986i	$0.414313\pi$
$662$		0			0
$663$	−31.1364	+	4.34936i	−1.20924	+	0.168915i
$664$		0			0
$665$	0.00199895	+	0.00346229i	7.75161e−5	+	0.000134262i
$666$		0			0
$667$	−13.5925	−	7.84763i	−0.526303	−	0.303861i
$668$		0			0
$669$	5.28107	−	24.7436i	0.204178	−	0.956644i
$670$		0			0
$671$	−32.0343	−	11.6595i	−1.23667	−	0.450111i
$672$		0			0
$673$	−6.24184	+	35.3992i	−0.240605	+	1.36454i	0.589876	+	0.807494i	$0.299176\pi$
$673$	−6.24184	+	35.3992i	−0.240605	+	1.36454i	−0.830482	+	0.557046i	$0.811935\pi$
$674$		0			0
$675$	7.10357	−	24.5403i	0.273416	−	0.944557i
$676$		0			0
$677$	17.6982	+	3.12068i	0.680199	+	0.119937i	0.503064	−	0.864249i	$-0.332206\pi$
$677$	17.6982	+	3.12068i	0.680199	+	0.119937i	0.177135	+	0.984187i	$0.443317\pi$
$678$		0			0
$679$	20.7414	+	7.54926i	0.795983	+	0.289714i
$680$		0			0
$681$	10.9786	+	33.8850i	0.420699	+	1.29848i
$682$		0			0
$683$	5.01354	+	2.89457i	0.191838	+	0.110758i	0.592843	−	0.805318i	$-0.298006\pi$
$683$	5.01354	+	2.89457i	0.191838	+	0.110758i	−0.401005	+	0.916076i	$0.631339\pi$
$684$		0			0
$685$	3.55083	−	2.05007i	0.135670	−	0.0783293i
$686$		0			0
$687$	−7.47072	+	18.4462i	−0.285026	+	0.703767i
$688$		0			0
$689$	0.484598	+	2.74829i	0.0184617	+	0.104702i
$690$		0			0
$691$	8.42802	−	10.0441i	0.320617	−	0.382097i	−0.581530	−	0.813525i	$-0.697546\pi$
$691$	8.42802	−	10.0441i	0.320617	−	0.382097i	0.902147	+	0.431428i	$0.141990\pi$
$692$		0			0
$693$	39.9787	−	4.13427i	1.51866	−	0.157048i
$694$		0			0
$695$	−2.64531	+	0.962815i	−0.100342	+	0.0365217i
$696$		0			0
$697$	−42.2167	+	35.4240i	−1.59907	+	1.34178i
$698$		0			0
$699$	7.49727	+	0.268094i	0.283573	+	0.0101403i
$700$		0			0
$701$		−	3.89204i		−	0.147000i	−0.997295	−	0.0735002i	$-0.976583\pi$
$701$		−	3.89204i		−	0.147000i	0.997295	−	0.0735002i	$-0.0234170\pi$
$702$		0			0
$703$	0.0469423			0.00177046
$704$		0			0
$705$	−1.63957	+	0.870013i	−0.0617496	+	0.0327666i
$706$		0			0
$707$	−33.3805	−	39.7814i	−1.25540	−	1.49613i
$708$		0			0
$709$	−10.4928	−	28.8286i	−0.394064	−	1.08268i	−0.965128	−	0.261777i	$-0.915692\pi$
$709$	−10.4928	−	28.8286i	−0.394064	−	1.08268i	0.571065	−	0.820905i	$-0.306531\pi$
$710$		0			0
$711$	−13.2493	+	3.77517i	−0.496886	+	0.141580i
$712$		0			0
$713$	−8.72901	−	7.32451i	−0.326904	−	0.274305i
$714$		0			0
$715$	4.39147	−	0.774335i	0.164232	−	0.0289585i
$716$		0			0
$717$	−19.2873	+	15.0429i	−0.720296	+	0.561786i
$718$		0			0
$719$	−10.3301	−	17.8922i	−0.385246	−	0.667266i	0.606557	−	0.795040i	$-0.292550\pi$
$719$	−10.3301	−	17.8922i	−0.385246	−	0.667266i	−0.991803	+	0.127774i	$0.959217\pi$
$720$		0			0
$721$	6.33789	−	10.9775i	0.236035	−	0.408825i
$722$		0			0
$723$	19.3031	+	17.4098i	0.717889	+	0.647479i
$724$		0			0
$725$	13.4575	−	36.9742i	0.499799	−	1.37319i
$726$		0			0
$727$	−5.27477	+	29.9147i	−0.195630	+	1.10947i	0.715888	+	0.698215i	$0.246022\pi$
$727$	−5.27477	+	29.9147i	−0.195630	+	1.10947i	−0.911518	+	0.411259i	$0.865089\pi$
$728$		0			0
$729$	26.3815	+	5.74619i	0.977091	+	0.212822i
$730$		0			0
$731$	−30.8386	−	5.43768i	−1.14061	−	0.201120i
$732$		0			0
$733$	12.3847	−	34.0267i	0.457439	−	1.25680i	−0.469946	−	0.882695i	$-0.655727\pi$
$733$	12.3847	−	34.0267i	0.457439	−	1.25680i	0.927385	−	0.374108i	$-0.122051\pi$
$734$		0			0
$735$	0.273660	−	0.303419i	0.0100941	−	0.0111918i
$736$		0			0
$737$	−0.547262	+	0.947886i	−0.0201587	+	0.0349158i
$738$		0			0
$739$	−4.81815	+	2.78176i	−0.177239	+	0.102329i	−0.585995	−	0.810315i	$-0.699296\pi$
$739$	−4.81815	+	2.78176i	−0.177239	+	0.102329i	0.408756	+	0.912644i	$0.365963\pi$
$740$		0			0
$741$	0.0218092	−	0.0170098i	0.000801181	−	0.000624872i
$742$		0			0
$743$	−6.80955	−	38.6189i	−0.249818	−	1.41679i	−0.809032	−	0.587765i	$-0.800008\pi$
$743$	−6.80955	−	38.6189i	−0.249818	−	1.41679i	0.559214	−	0.829024i	$-0.311103\pi$
$744$		0			0
$745$	−0.255922	−	0.214744i	−0.00937627	−	0.00786762i
$746$		0			0
$747$	−3.34115	−	11.7260i	−0.122246	−	0.429033i
$748$		0			0
$749$	−3.58507	−	9.84991i	−0.130996	−	0.359908i
$750$		0			0
$751$	−20.3773	+	17.0986i	−0.743579	+	0.623937i	−0.933796	−	0.357805i	$-0.883525\pi$
$751$	−20.3773	+	17.0986i	−0.743579	+	0.623937i	0.190217	+	0.981742i	$0.439081\pi$
$752$		0			0
$753$	46.0693	−	24.4460i	1.67886	−	0.890863i
$754$		0			0
$755$		−	6.02836i		−	0.219394i
$756$		0			0
$757$			9.99796i			0.363382i	0.983356	+	0.181691i	$0.0581571\pi$
$757$			9.99796i			0.363382i	−0.983356	+	0.181691i	$0.941843\pi$
$758$		0			0
$759$	−0.581682	+	16.2668i	−0.0211137	+	0.590446i
$760$		0			0
$761$	36.4687	−	30.6009i	1.32199	−	1.10928i	0.336112	−	0.941822i	$-0.390888\pi$
$761$	36.4687	−	30.6009i	1.32199	−	1.10928i	0.985879	−	0.167460i	$-0.0535564\pi$
$762$		0			0
$763$	−16.1103	−	44.2627i	−0.583232	−	1.60242i
$764$		0			0
$765$	−4.85019	+	0.501567i	−0.175359	+	0.0181342i
$766$		0			0
$767$	13.7198	+	11.5123i	0.495395	+	0.415685i
$768$		0			0
$769$	−7.87549	−	44.6641i	−0.283998	−	1.61063i	−0.708844	−	0.705365i	$-0.750783\pi$
$769$	−7.87549	−	44.6641i	−0.283998	−	1.61063i	0.424847	−	0.905265i	$-0.360328\pi$
$770$		0			0
$771$	6.33874	+	2.56719i	0.228284	+	0.0924552i
$772$		0			0
$773$	−7.37741	+	4.25935i	−0.265347	+	0.153198i	−0.626771	−	0.779203i	$-0.715624\pi$
$773$	−7.37741	+	4.25935i	−0.265347	+	0.153198i	0.361424	+	0.932401i	$0.382291\pi$
$774$		0			0
$775$	14.2832	−	24.7392i	0.513068	−	0.888659i
$776$		0			0
$777$	−14.1453	−	43.6590i	−0.507458	−	1.56626i
$778$		0			0
$779$	0.0165822	−	0.0455592i	0.000594118	−	0.00163233i
$780$		0			0
$781$	4.05754	+	0.715454i	0.145190	+	0.0256010i
$782$		0			0
$783$	39.9440	+	11.5624i	1.42748	+	0.413206i
$784$		0			0
$785$	0.939296	−	5.32701i	0.0335249	−	0.190129i
$786$		0			0
$787$	−6.01089	+	16.5148i	−0.214265	+	0.588688i	−0.999536	−	0.0304642i	$-0.990301\pi$
$787$	−6.01089	+	16.5148i	−0.214265	+	0.588688i	0.785271	+	0.619152i	$0.212524\pi$
$788$		0			0
$789$	4.76880	−	22.3435i	0.169774	−	0.795449i
$790$		0			0
$791$	8.52906	−	14.7728i	0.303259	−	0.525259i
$792$		0			0
$793$	11.4675	+	19.8623i	0.407224	+	0.705332i
$794$		0			0
$795$	0.0598793	+	0.428666i	0.00212370	+	0.0152032i
$796$		0			0
$797$	−14.0527	+	2.47787i	−0.497773	+	0.0877708i	−0.416898	−	0.908953i	$-0.636883\pi$
$797$	−14.0527	+	2.47787i	−0.497773	+	0.0877708i	−0.0808752	+	0.996724i	$0.525772\pi$
$798$		0			0
$799$	−16.0115	−	13.4352i	−0.566444	−	0.475303i
$800$		0			0
$801$	10.6461	+	0.762359i	0.376160	+	0.0269366i
$802$		0			0
$803$	−6.64299	−	18.2515i	−0.234426	−	0.644080i
$804$		0			0
$805$	1.01748	+	1.21258i	0.0358614	+	0.0427379i
$806$		0			0
$807$	−11.2845	−	7.06449i	−0.397234	−	0.248682i
$808$		0			0
$809$	−41.9742			−1.47573			−0.737867	−	0.674946i	$-0.764167\pi$
$809$	−41.9742			−1.47573			−0.737867	+	0.674946i	$0.764167\pi$
$810$		0			0
$811$		−	34.8911i		−	1.22519i	−0.790397	−	0.612595i	$-0.790125\pi$
$811$		−	34.8911i		−	1.22519i	0.790397	−	0.612595i	$-0.209875\pi$
$812$		0			0
$813$	19.6140	−	31.3306i	0.687893	−	1.09881i
$814$		0			0
$815$	−2.56013	+	2.14820i	−0.0896775	+	0.0752483i
$816$		0			0
$817$	0.0258874	−	0.00942225i	0.000905686	−	0.000329643i
$818$		0			0
$819$	−22.3919	−	15.1582i	−0.782438	−	0.529669i
$820$		0			0
$821$	2.36456	−	2.81797i	0.0825236	−	0.0983478i	−0.723203	−	0.690636i	$-0.757331\pi$
$821$	2.36456	−	2.81797i	0.0825236	−	0.0983478i	0.805726	+	0.592288i	$0.201775\pi$
$822$		0			0
$823$	4.05525	+	22.9985i	0.141357	+	0.801676i	0.970220	+	0.242225i	$0.0778771\pi$
$823$	4.05525	+	22.9985i	0.141357	+	0.801676i	−0.828863	+	0.559452i	$0.811012\pi$
$824$		0			0
$825$	−40.4135	+	5.64525i	−1.40702	+	0.196543i
$826$		0			0
$827$	17.6991	−	10.2186i	0.615456	−	0.355334i	−0.159642	−	0.987175i	$-0.551034\pi$
$827$	17.6991	−	10.2186i	0.615456	−	0.355334i	0.775098	+	0.631841i	$0.217701\pi$
$828$		0			0
$829$	−18.2976	−	10.5641i	−0.635503	−	0.366908i	0.147377	−	0.989080i	$-0.452917\pi$
$829$	−18.2976	−	10.5641i	−0.635503	−	0.366908i	−0.782880	+	0.622173i	$0.786250\pi$
$830$		0			0
$831$	38.3046	+	8.17540i	1.32877	+	0.283602i
$832$		0			0
$833$	4.32373	+	1.57371i	0.149808	+	0.0545258i
$834$		0			0
$835$	2.81990	+	0.497224i	0.0975866	+	0.0172072i
$836$		0			0
$837$	27.1015	+	13.3026i	0.936764	+	0.459806i
$838$		0			0
$839$	5.53919	−	31.4143i	0.191234	−	1.08454i	−0.726446	−	0.687223i	$-0.758829\pi$
$839$	5.53919	−	31.4143i	0.191234	−	1.08454i	0.917680	−	0.397320i	$-0.130060\pi$
$840$		0			0
$841$	32.9314	+	11.9860i	1.13557	+	0.413312i
$842$		0			0
$843$	53.1416	−	17.2176i	1.83029	−	0.593005i
$844$		0			0
$845$	0.651848	+	0.376345i	0.0224242	+	0.0129466i
$846$		0			0
$847$	−16.7204	−	28.9607i	−0.574521	−	0.995100i
$848$		0			0
$849$	−13.2683	+	32.7612i	−0.455366	+	1.12436i
$850$		0			0
$851$	18.3038	−	3.22745i	0.627445	−	0.110636i
$852$		0			0
$853$	−10.1055	+	12.0433i	−0.346006	+	0.412354i	−0.910780	−	0.412891i	$-0.864519\pi$
$853$	−10.1055	+	12.0433i	−0.346006	+	0.412354i	0.564774	+	0.825246i	$0.308963\pi$
$854$		0			0
$855$	0.00347467	−	0.00251562i	0.000118831	−	8.60323e-5i
$856$		0			0
$857$	30.3992	−	11.0644i	1.03842	−	0.377953i	0.234138	−	0.972203i	$-0.424773\pi$
$857$	30.3992	−	11.0644i	1.03842	−	0.377953i	0.804280	+	0.594250i	$0.202551\pi$
$858$		0			0
$859$	−7.62842	−	9.09120i	−0.260278	−	0.310188i	0.620041	−	0.784570i	$-0.287116\pi$
$859$	−7.62842	−	9.09120i	−0.260278	−	0.310188i	−0.880319	+	0.474382i	$0.842672\pi$
$860$		0			0
$861$	−47.3693	−	1.69388i	−1.61434	−	0.0577271i
$862$		0			0
$863$	25.9229			0.882426			0.441213	−	0.897402i	$-0.354548\pi$
$863$	25.9229			0.882426			0.441213	+	0.897402i	$0.354548\pi$
$864$		0			0
$865$	−5.76875			−0.196143
$866$		0			0
$867$	−11.9359	−	22.4936i	−0.405365	−	0.763923i
$868$		0			0
$869$	14.1443	+	16.8565i	0.479811	+	0.571816i
$870$		0			0
$871$	0.691961	−	0.251853i	0.0234462	−	0.00853373i
$872$		0			0
$873$	5.76806	−	22.9705i	0.195219	−	0.777434i
$874$		0			0
$875$	−5.14475	+	6.13128i	−0.173924	+	0.207275i
$876$		0			0
$877$	−23.4419	+	4.13345i	−0.791578	+	0.139577i	−0.554796	−	0.831986i	$-0.687204\pi$
$877$	−23.4419	+	4.13345i	−0.791578	+	0.139577i	−0.236782	+	0.971563i	$0.576093\pi$
$878$		0			0
$879$	−4.47580	−	5.73866i	−0.150965	−	0.193560i
$880$		0			0
$881$	19.7098	+	34.1384i	0.664040	+	1.15015i	0.979545	+	0.201227i	$0.0644930\pi$
$881$	19.7098	+	34.1384i	0.664040	+	1.15015i	−0.315504	+	0.948924i	$0.602174\pi$
$882$		0			0
$883$	39.3493	+	22.7183i	1.32421	+	0.764533i	0.984397	−	0.175960i	$-0.0563031\pi$
$883$	39.3493	+	22.7183i	1.32421	+	0.764533i	0.339812	+	0.940493i	$0.389636\pi$
$884$		0			0
$885$	2.06274	+	1.86043i	0.0693383	+	0.0625377i
$886$		0			0
$887$	3.61326	+	1.31512i	0.121321	+	0.0441573i	0.401967	−	0.915654i	$-0.368327\pi$
$887$	3.61326	+	1.31512i	0.121321	+	0.0441573i	−0.280646	+	0.959811i	$0.590549\pi$
$888$		0			0
$889$	10.2931	−	58.3752i	0.345220	−	1.95784i
$890$		0			0
$891$	−8.82499	−	42.2129i	−0.295648	−	1.41418i
$892$		0			0
$893$	0.0181087	+	0.00319306i	0.000605985	+	0.000106852i
$894$		0			0
$895$	5.84553	+	2.12760i	0.195395	+	0.0711178i
$896$		0			0
$897$	7.33437	−	8.13195i	0.244888	−	0.271518i
$898$		0			0
$899$	40.2677	+	23.2486i	1.34300	+	0.775384i
$900$		0			0
$901$	−4.22107	+	2.43704i	−0.140624	+	0.0811894i
$902$		0			0
$903$	−16.5640	−	21.2375i	−0.551214	−	0.706740i
$904$		0			0
$905$	1.03788	+	5.88612i	0.0345003	+	0.195661i
$906$		0			0
$907$	−6.16891	+	7.35182i	−0.204835	+	0.244113i	−0.858676	−	0.512519i	$-0.828712\pi$
$907$	−6.16891	+	7.35182i	−0.204835	+	0.244113i	0.653840	+	0.756632i	$0.273157\pi$
$908$		0			0
$909$	−38.7743	+	40.0177i	−1.28606	+	1.32730i
$910$		0			0
$911$	−27.8833	+	10.1487i	−0.923814	+	0.336241i	−0.759755	−	0.650210i	$-0.774681\pi$
$911$	−27.8833	+	10.1487i	−0.923814	+	0.336241i	−0.164059	+	0.986451i	$0.552459\pi$
$912$		0			0
$913$	−14.9185	+	12.5181i	−0.493730	+	0.414289i
$914$		0			0
$915$	1.66736	+	3.14219i	0.0551211	+	0.103877i
$916$		0			0
$917$		−	29.6416i		−	0.978851i
$918$		0			0
$919$	18.2259			0.601217			0.300608	−	0.953748i	$-0.402810\pi$
$919$	18.2259			0.601217			0.300608	+	0.953748i	$0.402810\pi$
$920$		0			0
$921$	−1.17715	+	32.9190i	−0.0387883	+	1.08472i
$922$		0			0
$923$	−1.78176	−	2.12342i	−0.0586474	−	0.0698933i
$924$		0			0
$925$	15.9362	+	43.7844i	0.523980	+	1.43962i
$926$		0			0
$927$	−12.4158	−	5.55281i	−0.407789	−	0.182378i
$928$		0			0
$929$	−1.32347	−	1.11052i	−0.0434216	−	0.0364351i	0.620819	−	0.783954i	$-0.286800\pi$
$929$	−1.32347	−	1.11052i	−0.0434216	−	0.0364351i	−0.664240	+	0.747519i	$0.731245\pi$
$930$		0			0
$931$	−0.00398643		0.000702915i	−0.000130650		2.30371e-5i
$932$		0			0
$933$	27.8737	+	11.2888i	0.912543	+	0.369580i
$934$		0			0
$935$	3.89411	+	6.74480i	0.127351	+	0.220579i
$936$		0			0
$937$	−3.54099	+	6.13317i	−0.115679	+	0.200362i	−0.918051	−	0.396462i	$-0.870238\pi$
$937$	−3.54099	+	6.13317i	−0.115679	+	0.200362i	0.802372	+	0.596824i	$0.203571\pi$
$938$		0			0
$939$	−1.24747	+	0.404172i	−0.0407095	+	0.0131897i
$940$		0			0
$941$	−3.52638	+	9.68865i	−0.114957	+	0.315841i	−0.983806	−	0.179235i	$-0.942638\pi$
$941$	−3.52638	+	9.68865i	−0.114957	+	0.315841i	0.868850	+	0.495076i	$0.164860\pi$
$942$		0			0
$943$	3.33338	−	18.9045i	0.108550	−	0.615617i
$944$		0			0
$945$	−3.38670	−	2.47360i	−0.110169	−	0.0804661i
$946$		0			0
$947$	10.4361	+	1.84016i	0.339127	+	0.0597973i	0.340618	−	0.940202i	$-0.389364\pi$
$947$	10.4361	+	1.84016i	0.339127	+	0.0597973i	−0.00149128	+	0.999999i	$0.500475\pi$
$948$		0			0
$949$	−4.46924	+	12.2791i	−0.145078	+	0.398598i
$950$		0			0
$951$	33.3052	+	7.10839i	1.08000	+	0.230505i
$952$		0			0
$953$	−3.01897	+	5.22901i	−0.0977940	+	0.169384i	−0.910771	−	0.412911i	$-0.864512\pi$
$953$	−3.01897	+	5.22901i	−0.0977940	+	0.169384i	0.812977	+	0.582295i	$0.197845\pi$
$954$		0			0
$955$	−0.250024	+	0.144351i	−0.00809058	+	0.00467110i
$956$		0			0
$957$	−9.18871	−	65.7806i	−0.297029	−	2.12638i
$958$		0			0
$959$	6.89588	+	39.1085i	0.222680	+	1.26288i
$960$		0			0
$961$	2.11229	+	1.77242i	0.0681384	+	0.0571749i
$962$		0			0
$963$	−10.1171	+	4.91349i	−0.326019	+	0.158335i
$964$		0			0
$965$	−1.95645	−	5.37529i	−0.0629802	−	0.173037i
$966$		0			0
$967$	−15.4521	+	12.9658i	−0.496906	+	0.416954i	−0.856494	−	0.516158i	$-0.827362\pi$
$967$	−15.4521	+	12.9658i	−0.496906	+	0.416954i	0.359588	+	0.933111i	$0.382917\pi$
$968$		0			0
$969$	0.0409447	+	0.0256328i	0.00131533	+	0.000823443i
$970$		0			0
$971$			31.1328i			0.999100i	0.866285	+	0.499550i	$0.166501\pi$
$971$			31.1328i			0.999100i	−0.866285	+	0.499550i	$0.833499\pi$
$972$		0			0
$973$		−	27.2654i		−	0.874088i
$974$		0			0
$975$	23.2695	+	14.5675i	0.745219	+	0.466533i
$976$		0			0
$977$	−14.4476	+	12.1229i	−0.462219	+	0.387848i	−0.843947	−	0.536427i	$-0.819774\pi$
$977$	−14.4476	+	12.1229i	−0.462219	+	0.387848i	0.381728	+	0.924275i	$0.375329\pi$
$978$		0			0
$979$	−5.83071	−	16.0198i	−0.186350	−	0.511993i
$980$		0			0
$981$	−45.4633	+	22.0798i	−1.45153	+	0.704954i
$982$		0			0
$983$	−24.2461	−	20.3449i	−0.773330	−	0.648901i	0.168229	−	0.985748i	$-0.446195\pi$
$983$	−24.2461	−	20.3449i	−0.773330	−	0.648901i	−0.941559	+	0.336847i	$0.890639\pi$
$984$		0			0
$985$	0.297906	+	1.68951i	0.00949206	+	0.0538322i
$986$		0			0
$987$	−2.48703	−	17.8043i	−0.0791632	−	0.566717i
$988$		0			0
$989$	9.44623	−	5.45378i	0.300373	−	0.173420i
$990$		0			0
$991$	−22.5906	+	39.1281i	−0.717614	+	1.24294i	0.244328	+	0.969693i	$0.421433\pi$
$991$	−22.5906	+	39.1281i	−0.717614	+	1.24294i	−0.961942	+	0.273252i	$0.911901\pi$
$992$		0			0
$993$	−41.7089	−	8.90201i	−1.32359	−	0.282497i
$994$		0			0
$995$	0.834426	−	2.29257i	0.0264531	−	0.0726792i
$996$		0			0
$997$	−20.6197	−	3.63580i	−0.653031	−	0.115147i	−0.162689	−	0.986677i	$-0.552017\pi$
$997$	−20.6197	−	3.63580i	−0.653031	−	0.115147i	−0.490342	+	0.871530i	$0.663128\pi$
$998$		0			0
$999$	−45.0359	+	19.9159i	−1.42487	+	0.630111i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bf.a.241.11		204
4.3	odd	2		216.2.t.a.133.22	yes	204
8.3	odd	2		216.2.t.a.133.17	yes	204
8.5	even	2	inner	864.2.bf.a.241.24		204
12.11	even	2		648.2.t.a.397.13		204
24.11	even	2		648.2.t.a.397.18		204
27.13	even	9	inner	864.2.bf.a.337.24		204
108.67	odd	18		216.2.t.a.13.17	✓	204
108.95	even	18		648.2.t.a.253.18		204
216.13	even	18	inner	864.2.bf.a.337.11		204
216.67	odd	18		216.2.t.a.13.22	yes	204
216.203	even	18		648.2.t.a.253.13		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.17	✓	204	108.67	odd	18
216.2.t.a.13.22	yes	204	216.67	odd	18
216.2.t.a.133.17	yes	204	8.3	odd	2
216.2.t.a.133.22	yes	204	4.3	odd	2
648.2.t.a.253.13		204	216.203	even	18
648.2.t.a.253.18		204	108.95	even	18
648.2.t.a.397.13		204	12.11	even	2
648.2.t.a.397.18		204	24.11	even	2
864.2.bf.a.241.11		204	1.1	even	1	trivial
864.2.bf.a.241.24		204	8.5	even	2	inner
864.2.bf.a.337.11		204	216.13	even	18	inner
864.2.bf.a.337.24		204	27.13	even	9	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bf (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.919076 + 1.46809i) q^{3} +(-0.185555 - 0.221136i) q^{5} +(2.62731 - 0.956263i) q^{7} +(-1.31060 - 2.69858i) q^{9} +(-3.08006 + 3.67067i) q^{11} +(3.17478 - 0.559799i) q^{13} +(0.495188 - 0.0691714i) q^{15} +(2.81522 + 4.87610i) q^{17} +(-0.00428975 - 0.00247669i) q^{19} +(-1.01082 + 4.73602i) q^{21} +(-1.84294 - 0.670777i) q^{23} +(0.853770 - 4.84197i) q^{25} +(5.16631 + 0.556122i) q^{27} +(7.88122 + 1.38967i) q^{29} +(5.45972 + 1.98718i) q^{31} +(-2.55808 - 7.89544i) q^{33} +(-0.698975 - 0.403553i) q^{35} +(-8.20717 + 4.73841i) q^{37} +(-2.09603 + 5.17537i) q^{39} +(1.69965 + 9.63917i) q^{41} +(-3.57494 + 4.26045i) q^{43} +(-0.353565 + 0.790555i) q^{45} +(-3.48835 + 1.26966i) q^{47} +(0.626015 - 0.525289i) q^{49} +(-9.74597 - 0.348505i) q^{51} +0.865665i q^{53} +1.38324 q^{55} +(0.00757862 - 0.00402149i) q^{57} +(3.57109 + 4.25586i) q^{59} +(2.43327 + 6.68534i) q^{61} +(-6.02390 - 5.83673i) q^{63} +(-0.712888 - 0.598184i) q^{65} +(0.224950 - 0.0396647i) q^{67} +(2.67857 - 2.08912i) q^{69} +(-0.429923 - 0.744648i) q^{71} +(-2.02670 + 3.51035i) q^{73} +(6.32379 + 5.70356i) q^{75} +(-4.58214 + 12.5893i) q^{77} +(0.797428 - 4.52244i) q^{79} +(-5.56467 + 7.07350i) q^{81} +(4.00250 + 0.705749i) q^{83} +(0.555903 - 1.52733i) q^{85} +(-9.28361 + 10.2932i) q^{87} +(-1.77889 + 3.08112i) q^{89} +(7.80581 - 4.50669i) q^{91} +(-7.93526 + 6.18901i) q^{93} +(0.000248300 + 0.00140818i) q^{95} +(6.04757 + 5.07452i) q^{97} +(13.9423 + 3.50101i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73}+ \cdots - 12 q^{97}+O(q^{100}) \) 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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