LMFDB - Embedded newform 864.2.bf.a.337.24

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			337.24
Character	$\chi$	$=$	864.337
Dual form			864.2.bf.a.241.24

$q$-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 $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{4}{9}\right)$	$1$

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	$-0.757217\pi$
$5$	0.185555	−	0.221136i	0.0829828	−	0.0988950i	0.805938	+	0.592000i	$0.201661\pi$
$6$		0			0
$7$	2.62731	+	0.956263i	0.993030	+	0.361433i	0.786893	−	0.617090i	$-0.211688\pi$
$7$	2.62731	+	0.956263i	0.993030	+	0.361433i	0.206137	+	0.978523i	$0.433911\pi$
$8$		0			0
$9$	−1.31060	+	2.69858i	−0.436866	+	0.899527i
$10$		0			0
$11$	3.08006	+	3.67067i	0.928672	+	1.10675i	0.994054	+	0.108888i	$0.0347291\pi$
$11$	3.08006	+	3.67067i	0.928672	+	1.10675i	−0.0653817	+	0.997860i	$0.520826\pi$
$12$		0			0
$13$	−3.17478	−	0.559799i	−0.880525	−	0.155260i	−0.284933	−	0.958547i	$-0.591971\pi$
$13$	−3.17478	−	0.559799i	−0.880525	−	0.155260i	−0.595592	+	0.803287i	$0.703082\pi$
$14$		0			0
$15$	0.495188	+	0.0691714i	0.127857	+	0.0178600i
$16$		0			0
$17$	2.81522	−	4.87610i	0.682791	−	1.18263i	−0.291335	−	0.956621i	$-0.594099\pi$
$17$	2.81522	−	4.87610i	0.682791	−	1.18263i	0.974126	−	0.226007i	$-0.0725672\pi$
$18$		0			0
$19$	0.00428975	−	0.00247669i	0.000984137	−	0.000568192i	−0.499508	−	0.866309i	$-0.666486\pi$
$19$	0.00428975	−	0.00247669i	0.000984137	−	0.000568192i	0.500492	+	0.865741i	$0.333152\pi$
$20$		0			0
$21$	1.01082	+	4.73602i	0.220578	+	1.03348i
$22$		0			0
$23$	−1.84294	+	0.670777i	−0.384280	+	0.139867i	−0.526934	−	0.849906i	$-0.676659\pi$
$23$	−1.84294	+	0.670777i	−0.384280	+	0.139867i	0.142654	+	0.989773i	$0.454436\pi$
$24$		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	$-0.822173\pi$
$29$	−7.88122	+	1.38967i	−1.46351	+	0.258056i	−0.615540	+	0.788106i	$0.711062\pi$
$30$		0			0
$31$	5.45972	−	1.98718i	0.980595	−	0.356907i	0.198523	−	0.980096i	$-0.436385\pi$
$31$	5.45972	−	1.98718i	0.980595	−	0.356907i	0.782071	+	0.623189i	$0.214163\pi$
$32$		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	$-0.0490656\pi$
$37$	8.20717	+	4.73841i	1.34925	+	0.778990i	0.361107	+	0.932524i	$0.382399\pi$
$38$		0			0
$39$	−2.09603	−	5.17537i	−0.335633	−	0.828722i
$40$		0			0
$41$	1.69965	−	9.63917i	0.265440	−	1.50539i	−0.502339	−	0.864671i	$-0.667527\pi$
$41$	1.69965	−	9.63917i	0.265440	−	1.50539i	0.767779	−	0.640715i	$-0.221362\pi$
$42$		0			0
$43$	3.57494	+	4.26045i	0.545173	+	0.649712i	0.966339	−	0.257271i	$-0.0828234\pi$
$43$	3.57494	+	4.26045i	0.545173	+	0.649712i	−0.421166	+	0.906984i	$0.638379\pi$
$44$		0			0
$45$	0.353565	+	0.790555i	0.0527064	+	0.117849i
$46$		0			0
$47$	−3.48835	−	1.26966i	−0.508829	−	0.185199i	0.0748320	−	0.997196i	$-0.476158\pi$
$47$	−3.48835	−	1.26966i	−0.508829	−	0.185199i	−0.583661	+	0.811998i	$0.698380\pi$
$48$		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	$-0.895561\pi$
$59$	−3.57109	+	4.25586i	−0.464916	+	0.554066i	0.481739	+	0.876315i	$0.340005\pi$
$60$		0			0
$61$	−2.43327	+	6.68534i	−0.311548	+	0.855970i	0.680797	+	0.732472i	$0.261634\pi$
$61$	−2.43327	+	6.68534i	−0.311548	+	0.855970i	−0.992345	+	0.123498i	$0.960589\pi$
$62$		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	$-0.448886\pi$
$67$	−0.224950	−	0.0396647i	−0.0274820	−	0.00484582i	−0.187372	+	0.982289i	$0.559997\pi$
$68$		0			0
$69$	−2.67857	−	2.08912i	−0.322462	−	0.251500i
$70$		0			0
$71$	−0.429923	+	0.744648i	−0.0510224	+	0.0883735i	−0.890409	−	0.455162i	$-0.849581\pi$
$71$	−0.429923	+	0.744648i	−0.0510224	+	0.0883735i	0.839386	+	0.543535i	$0.182915\pi$
$72$		0			0
$73$	−2.02670	−	3.51035i	−0.237208	−	0.410856i	0.722704	−	0.691157i	$-0.242899\pi$
$73$	−2.02670	−	3.51035i	−0.237208	−	0.410856i	−0.959912	+	0.280301i	$0.909566\pi$
$74$		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	0.996239	+	0.0866531i	$0.0276172\pi$
$79$	0.797428	+	4.52244i	0.0897176	+	0.508814i	−0.906521	+	0.422161i	$0.861272\pi$
$80$		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	$-0.627158\pi$
$83$	−4.00250	+	0.705749i	−0.439332	+	0.0774660i	−0.0503925	+	0.998729i	$0.516047\pi$
$84$		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	0.756209	−	0.654330i	$-0.227049\pi$
$89$	−1.77889	−	3.08112i	−0.188562	−	0.326599i	−0.944771	+	0.327731i	$0.893716\pi$
$90$		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	−0.281885	−	0.959448i	$-0.590960\pi$
$97$	6.04757	−	5.07452i	0.614038	−	0.515239i	0.895923	+	0.444209i	$0.146515\pi$
$98$		0			0
$99$	−13.9423	+	3.50101i	−1.40126	+	0.351865i
$100$		0			0
$101$	6.35260	−	17.4536i	0.632107	−	1.73670i	−0.0430976	−	0.999071i	$-0.513723\pi$
$101$	6.35260	−	17.4536i	0.632107	−	1.73670i	0.675205	−	0.737630i	$-0.264055\pi$
$102$		0			0
$103$	3.47298	+	2.91418i	0.342203	+	0.287143i	0.797650	−	0.603120i	$-0.206076\pi$
$103$	3.47298	+	2.91418i	0.342203	+	0.287143i	−0.455447	+	0.890263i	$0.650521\pi$
$104$		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	0.835583	−	0.549364i	$-0.185130\pi$
$113$	4.67369	+	3.92169i	0.439664	+	0.368921i	−0.395920	+	0.918285i	$0.629574\pi$
$114$		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	0.764270	+	0.644896i	$0.223099\pi$
$127$	10.6004	+	18.3604i	0.940632	+	1.62922i	0.176362	+	0.984325i	$0.443567\pi$
$128$		0			0
$129$	−2.96909	+	9.16403i	−0.261414	+	0.806847i
$130$		0			0
$131$	−3.62600	−	9.96234i	−0.316805	−	0.870414i	−0.991239	−	0.132079i	$-0.957835\pi$
$131$	−3.62600	−	9.96234i	−0.316805	−	0.870414i	0.674435	−	0.738335i	$-0.264387\pi$
$132$		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	−0.888182	−	0.459491i	$-0.848032\pi$
$137$	−2.46640	−	13.9877i	−0.210719	−	1.19505i	0.677463	−	0.735557i	$-0.263079\pi$
$138$		0			0
$139$	−3.33532	−	9.16372i	−0.282898	−	0.777257i	−0.997013	−	0.0772283i	$-0.975393\pi$
$139$	−3.33532	−	9.16372i	−0.282898	−	0.777257i	0.714115	−	0.700028i	$-0.246829\pi$
$140$		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	$-0.459540\pi$
$149$	−1.13973	−	0.200964i	−0.0933699	−	0.0164636i	−0.220138	+	0.975469i	$0.570651\pi$
$150$		0			0
$151$	15.9973	−	13.4234i	1.30184	−	1.09238i	0.312022	−	0.950075i	$-0.398994\pi$
$151$	15.9973	−	13.4234i	1.30184	−	1.09238i	0.989823	−	0.142303i	$-0.0454506\pi$
$152$		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	0.0280180	+	0.999607i	$0.491080\pi$
$157$	−12.0447	+	14.3543i	−0.961268	+	1.14560i	−0.989286	+	0.145988i	$0.953364\pi$
$158$		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	0.299568	−	0.954075i	$-0.403158\pi$
$167$	−7.59855	−	6.37594i	−0.587994	−	0.493385i	−0.887561	+	0.460690i	$0.847602\pi$
$168$		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	−0.986473	−	0.163926i	$-0.947584\pi$
$173$	−12.8453	−	15.3084i	−0.976609	−	1.16388i	0.00986338	−	0.999951i	$-0.496860\pi$
$174$		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	$-0.0353188\pi$
$179$	18.6622	+	10.7746i	1.39488	+	0.805335i	0.401030	+	0.916065i	$0.368652\pi$
$180$		0			0
$181$	17.9309	−	10.3524i	1.33280	−	0.769490i	0.347068	−	0.937840i	$-0.387177\pi$
$181$	17.9309	−	10.3524i	1.33280	−	0.769490i	0.985727	+	0.168350i	$0.0538440\pi$
$182$		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	0.990446	−	0.137902i	$-0.0440358\pi$
$191$	0.173666	+	0.984911i	0.0125661	+	0.0712657i	−0.977880	+	0.209167i	$0.932925\pi$
$192$		0			0
$193$	18.6207	−	6.77739i	1.34035	−	0.487847i	0.430427	−	0.902625i	$-0.358363\pi$
$193$	18.6207	−	6.77739i	1.34035	−	0.487847i	0.909923	+	0.414778i	$0.136141\pi$
$194$		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	$-0.598764\pi$
$197$	5.14676	−	2.97148i	0.366691	−	0.211709i	0.672012	+	0.740540i	$0.265430\pi$
$198$		0			0
$199$	4.22572	−	7.31916i	0.299553	−	0.518842i	−0.676480	−	0.736461i	$-0.736496\pi$
$199$	4.22572	−	7.31916i	0.299553	−	0.518842i	0.976034	+	0.217619i	$0.0698290\pi$
$200$		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	$-0.823574\pi$
$211$	−2.67743	+	3.19083i	−0.184322	+	0.219666i	0.665969	+	0.745980i	$0.268018\pi$
$212$		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	−0.161279	−	0.986909i	$-0.551562\pi$
$223$	−13.7266	−	4.99606i	−0.919198	−	0.334561i	−0.757919	+	0.652348i	$0.773784\pi$
$224$		0			0
$225$	−14.1854	−	4.04191i	−0.945693	−	0.269461i
$226$		0			0
$227$	−13.2187	−	15.7535i	−0.877359	−	1.04560i	−0.998596	−	0.0529722i	$-0.983131\pi$
$227$	−13.2187	−	15.7535i	−0.877359	−	1.04560i	0.121237	−	0.992624i	$-0.461314\pi$
$228$		0			0
$229$	−11.3156	−	1.99525i	−0.747759	−	0.131850i	−0.213232	−	0.977002i	$-0.568399\pi$
$229$	−11.3156	−	1.99525i	−0.747759	−	0.131850i	−0.534527	+	0.845151i	$0.679510\pi$
$230$		0			0
$231$	−14.2710	+	18.2976i	−0.938962	+	1.20389i
$232$		0			0
$233$	−2.16566	+	3.75103i	−0.141877	+	0.245738i	−0.928203	−	0.372073i	$-0.878647\pi$
$233$	−2.16566	+	3.75103i	−0.141877	+	0.245738i	0.786326	+	0.617811i	$0.211980\pi$
$234$		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	0.124929	−	0.992166i	$-0.460130\pi$
$239$	13.2703	−	4.82998i	0.858382	−	0.312426i	0.733453	+	0.679740i	$0.237907\pi$
$240$		0			0
$241$	2.60609	+	14.7799i	0.167873	+	0.952056i	0.946052	+	0.324014i	$0.105032\pi$
$241$	2.60609	+	14.7799i	0.167873	+	0.952056i	−0.778179	+	0.628042i	$0.783856\pi$
$242$		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	0.667293	−	0.744795i	$-0.267453\pi$
$251$	26.0768	−	15.0554i	1.64595	−	0.950290i	0.978658	−	0.205495i	$-0.0658804\pi$
$252$		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	−0.998696	−	0.0510494i	$-0.983743\pi$
$257$	−0.685637	+	3.88844i	−0.0427688	+	0.242554i	0.955927	+	0.293603i	$0.0948545\pi$
$258$		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	−0.0696970	−	0.997568i	$-0.522203\pi$
$263$	−12.3951	−	4.51144i	−0.764313	−	0.278187i	−0.694616	+	0.719381i	$0.744425\pi$
$264$		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	−0.457210	−	0.889359i	$-0.651151\pi$
$277$	7.73418	−	21.2495i	0.464702	−	1.27676i	0.921912	−	0.387400i	$-0.126627\pi$
$278$		0			0
$279$	−1.79294	+	17.3379i	−0.107341	+	1.03799i
$280$		0			0
$281$	−24.7061	+	20.7308i	−1.47384	+	1.23670i	−0.561363	+	0.827570i	$0.689723\pi$
$281$	−24.7061	+	20.7308i	−1.47384	+	1.23670i	−0.912477	+	0.409129i	$0.865833\pi$
$282$		0			0
$283$	−20.0970	−	3.54364i	−1.19464	−	0.210648i	−0.459261	−	0.888301i	$-0.651886\pi$
$283$	−20.0970	−	3.54364i	−1.19464	−	0.210648i	−0.735381	+	0.677653i	$0.762997\pi$
$284$		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	$-0.0719444\pi$
$293$	1.43710	+	3.94839i	0.0839561	+	0.230667i	−0.890610	+	0.454768i	$0.849722\pi$
$294$		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	$-0.515933\pi$
$307$	−16.4700	−	9.50896i	−0.939993	−	0.542705i	−0.889958	+	0.456043i	$0.849266\pi$
$308$		0			0
$309$	−1.08635	+	7.77702i	−0.0618003	+	0.442419i
$310$		0			0
$311$	−3.01498	+	17.0988i	−0.170964	+	0.969585i	0.771736	+	0.635943i	$0.219389\pi$
$311$	−3.01498	+	17.0988i	−0.170964	+	0.969585i	−0.942700	+	0.333642i	$0.891722\pi$
$312$		0			0
$313$	0.579959	−	0.486644i	0.0327812	−	0.0275067i	−0.626250	−	0.779622i	$-0.715411\pi$
$313$	0.579959	−	0.486644i	0.0327812	−	0.0275067i	0.659031	+	0.752116i	$0.270967\pi$
$314$		0			0
$315$	0.172947	+	2.41514i	0.00974443	+	0.136078i
$316$		0			0
$317$	6.72476	−	18.4761i	0.377700	−	1.03772i	−0.594607	−	0.804016i	$-0.702692\pi$
$317$	6.72476	−	18.4761i	0.377700	−	1.03772i	0.972307	−	0.233706i	$-0.0750853\pi$
$318$		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	0.460409	+	0.887707i	$0.347703\pi$
$331$	−8.42157	+	23.1381i	−0.462891	+	1.27178i	−0.923301	+	0.384077i	$0.874520\pi$
$332$		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	0.901496	+	0.432788i	$0.142470\pi$
$337$	−1.71929	+	9.75056i	−0.0936555	+	0.531147i	−0.995151	+	0.0983585i	$0.968641\pi$
$338$		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	0.970196	+	0.242320i	$0.0779084\pi$
$347$	7.12971	+	19.5887i	0.382743	+	1.05158i	−0.587453	+	0.809258i	$0.699869\pi$
$348$		0			0
$349$	14.8725	−	2.62242i	0.796107	−	0.140375i	0.239222	−	0.970965i	$-0.423108\pi$
$349$	14.8725	−	2.62242i	0.796107	−	0.140375i	0.556885	+	0.830590i	$0.311996\pi$
$350$		0			0
$351$	16.7132	+	1.12653i	0.892084	+	0.0601297i
$352$		0			0
$353$	−0.616217	−	3.49474i	−0.0327979	−	0.186006i	0.964007	−	0.265875i	$-0.0856609\pi$
$353$	−0.616217	−	3.49474i	−0.0327979	−	0.186006i	−0.996805	+	0.0798689i	$0.974550\pi$
$354$		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	0.994897	+	0.100891i	$0.0321694\pi$
$359$	11.0808	+	19.1925i	0.584823	+	1.01294i	−0.410074	+	0.912052i	$0.634497\pi$
$360$		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	−0.919963	−	0.392005i	$-0.871782\pi$
$367$	−13.2887	+	11.1505i	−0.693664	+	0.582053i	0.226299	+	0.974058i	$0.427337\pi$
$368$		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	$-0.919088\pi$
$373$	−10.6639	+	12.7087i	−0.552156	+	0.658034i	0.415711	+	0.909497i	$0.363533\pi$
$374$		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	0.847310	−	0.531099i	$-0.178221\pi$
$383$	9.22574	+	7.74132i	0.471414	+	0.395563i	−0.375896	+	0.926662i	$0.622665\pi$
$384$		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	$-0.198773\pi$
$389$	1.86623	+	2.22408i	0.0946216	+	0.112766i	−0.716656	+	0.697427i	$0.754328\pi$
$390$		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	$-0.699296\pi$
$397$	−3.53148	+	2.03890i	−0.177240	+	0.102330i	0.408755	+	0.912644i	$0.365963\pi$
$398$		0			0
$399$	0.0160658	+	0.0178129i	0.000804296	+	0.000891759i
$400$		0			0
$401$	2.09322	−	0.761870i	0.104530	−	0.0380460i	−0.289226	−	0.957261i	$-0.593398\pi$
$401$	2.09322	−	0.761870i	0.104530	−	0.0380460i	0.393756	+	0.919215i	$0.371176\pi$
$402$		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	0.135950	−	0.990716i	$-0.456591\pi$
$409$	17.7345	−	6.45483i	0.876914	−	0.319171i	0.740964	+	0.671545i	$0.234369\pi$
$410$		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	$-0.335161\pi$
$419$	13.5715	+	2.39303i	0.663013	+	0.116907i	0.167992	+	0.985788i	$0.446272\pi$
$420$		0			0
$421$	23.8985	+	28.4811i	1.16474	+	1.38809i	0.906607	+	0.421977i	$0.138664\pi$
$421$	23.8985	+	28.4811i	1.16474	+	1.38809i	0.258135	+	0.966109i	$0.416892\pi$
$422$		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	0.756912	−	0.653517i	$-0.226707\pi$
$439$	19.2063	+	6.99052i	0.916667	+	0.333639i	0.159755	+	0.987157i	$0.448930\pi$
$440$		0			0
$441$	−2.23799	+	1.00091i	−0.106571	+	0.0476624i
$442$		0			0
$443$	−18.1395	−	21.6178i	−0.861832	−	1.02709i	−0.999330	−	0.0365893i	$-0.988351\pi$
$443$	−18.1395	−	21.6178i	−0.861832	−	1.02709i	0.137498	−	0.990502i	$-0.456094\pi$
$444$		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	−0.967995	−	0.250969i	$-0.919251\pi$
$449$	−5.65025	+	9.78653i	−0.266652	+	0.461855i	0.701343	+	0.712824i	$0.252584\pi$
$450$		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	−0.605636	−	0.795742i	$-0.707081\pi$
$457$	−6.59891	−	37.4243i	−0.308684	−	1.75063i	0.296952	−	0.954892i	$-0.404030\pi$
$458$		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	$-0.498405\pi$
$461$	7.55207	−	1.33163i	0.351735	−	0.0620204i	0.346724	+	0.937967i	$0.387294\pi$
$462$		0			0
$463$	20.5953	−	7.49607i	0.957144	−	0.348372i	0.184231	−	0.982883i	$-0.441021\pi$
$463$	20.5953	−	7.49607i	0.957144	−	0.348372i	0.772914	+	0.634511i	$0.218798\pi$
$464$		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	$-0.648718\pi$
$467$	2.10941	−	1.21787i	0.0976119	−	0.0563563i	0.548011	+	0.836471i	$0.315385\pi$
$468$		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	0.0103076	−	0.999947i	$-0.496719\pi$
$479$	−13.6689	−	4.97509i	−0.624550	−	0.227318i	−0.634857	+	0.772629i	$0.718941\pi$
$480$		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	$-0.912426\pi$
$491$	−11.6939	+	13.9362i	−0.527738	+	0.628933i	0.434654	+	0.900597i	$0.356871\pi$
$492$		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	$-0.429731\pi$
$499$	2.03309	+	0.358488i	0.0910134	+	0.0160481i	−0.127956	+	0.991780i	$0.540842\pi$
$500$		0			0
$501$	2.37683	−	17.0154i	0.106189	−	0.760190i
$502$		0			0
$503$	−15.5785	+	26.9828i	−0.694613	+	1.20310i	0.275699	+	0.961244i	$0.411091\pi$
$503$	−15.5785	+	26.9828i	−0.694613	+	1.20310i	−0.970311	+	0.241860i	$0.922242\pi$
$504$		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	$-0.0976247\pi$
$509$	0.653669	+	1.79594i	0.0289734	+	0.0796037i	−0.924363	+	0.381515i	$0.875402\pi$
$510$		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	0.945609	−	0.325304i	$-0.105467\pi$
$521$	4.36155	+	7.55442i	0.191083	+	0.330965i	−0.754527	+	0.656269i	$0.772133\pi$
$522$		0			0
$523$	17.9490	+	10.3629i	0.784855	+	0.453136i	0.838148	−	0.545443i	$-0.183638\pi$
$523$	17.9490	+	10.3629i	0.784855	+	0.453136i	−0.0532932	+	0.998579i	$0.516972\pi$
$524$		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	$-0.957684\pi$
$547$	−3.43081	+	9.42608i	−0.146691	+	0.403030i	0.844486	+	0.535578i	$0.179906\pi$
$548$		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	$-0.407701\pi$
$557$	−9.46379	−	5.46392i	−0.400994	−	0.231514i	−0.686913	+	0.726740i	$0.741034\pi$
$558$		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	0.957665	+	0.287885i	$0.0929521\pi$
$563$	9.70697	+	26.6697i	0.409100	+	1.12399i	−0.548565	+	0.836108i	$0.684826\pi$
$564$		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	−0.992445	−	0.122690i	$-0.960848\pi$
$569$	−2.42865	−	13.7735i	−0.101814	−	0.577417i	0.890631	−	0.454727i	$-0.150263\pi$
$570$		0			0
$571$	−5.30577	−	14.5775i	−0.222040	−	0.610049i	0.777790	−	0.628525i	$-0.216341\pi$
$571$	−5.30577	−	14.5775i	−0.222040	−	0.610049i	−0.999829	+	0.0184759i	$0.994119\pi$
$572$		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	−0.870119	−	0.492841i	$-0.835958\pi$
$577$	−0.198083	+	0.343090i	−0.00824632	+	0.0142830i	0.861873	+	0.507125i	$0.169292\pi$
$578$		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	$-0.966876\pi$
$587$	−4.01994	+	11.0447i	−0.165921	+	0.455864i	0.828670	+	0.559738i	$0.189098\pi$
$588$		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	0.999972	−	0.00747033i	$-0.00237790\pi$
$599$	28.5436	+	23.9509i	1.16626	+	0.978607i	0.166286	+	0.986077i	$0.446822\pi$
$600$		0			0
$601$	−11.4635	−	4.17236i	−0.467605	−	0.170194i	0.0974622	−	0.995239i	$-0.468927\pi$
$601$	−11.4635	−	4.17236i	−0.467605	−	0.170194i	−0.565067	+	0.825045i	$0.691150\pi$
$602$		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	0.304372	+	0.952553i	$0.401553\pi$
$607$	−7.57443	+	42.9567i	−0.307436	+	1.74356i	−0.611809	+	0.791006i	$0.709558\pi$
$608$		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	$-0.861508\pi$
$613$	−24.6408	+	14.2264i	−0.995233	+	0.574598i	−0.0883987	+	0.996085i	$0.528175\pi$
$614$		0			0
$615$	1.50840	−	4.65563i	0.0608245	−	0.187733i
$616$		0			0
$617$	−6.84389	+	2.49097i	−0.275525	+	0.100283i	−0.476087	−	0.879398i	$-0.657945\pi$
$617$	−6.84389	+	2.49097i	−0.275525	+	0.100283i	0.200562	+	0.979681i	$0.435723\pi$
$618$		0			0
$619$	−4.70638	+	0.829861i	−0.189165	+	0.0333549i	−0.267428	−	0.963578i	$-0.586174\pi$
$619$	−4.70638	+	0.829861i	−0.189165	+	0.0333549i	0.0782628	+	0.996933i	$0.475063\pi$
$620$		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	−0.587584	−	0.809163i	$-0.699921\pi$
$631$	10.2228	−	17.7064i	0.406964	−	0.704882i	0.994548	+	0.104281i	$0.0332543\pi$
$632$		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	0.671000	−	0.741457i	$-0.265865\pi$
$641$	17.9357	+	6.52806i	0.708417	+	0.257843i	0.0374167	+	0.999300i	$0.488087\pi$
$642$		0			0
$643$	−11.9937	+	14.2935i	−0.472984	+	0.563680i	−0.948805	−	0.315862i	$-0.897706\pi$
$643$	−11.9937	+	14.2935i	−0.472984	+	0.563680i	0.475821	+	0.879542i	$0.342151\pi$
$644$		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	$-0.824519\pi$
$653$	−4.80662	+	5.72830i	−0.188097	+	0.224166i	0.663752	+	0.747953i	$0.268963\pi$
$654$		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	$-0.374858\pi$
$659$	−15.2256	−	18.1451i	−0.593104	−	0.706834i	−0.976199	+	0.216875i	$0.930414\pi$
$660$		0			0
$661$	−4.78633	−	0.843960i	−0.186167	−	0.0328262i	0.0797873	−	0.996812i	$-0.474576\pi$
$661$	−4.78633	−	0.843960i	−0.186167	−	0.0328262i	−0.265954	+	0.963986i	$0.585687\pi$
$662$		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	−0.830482	−	0.557046i	$-0.811935\pi$
$673$	−6.24184	−	35.3992i	−0.240605	−	1.36454i	0.589876	−	0.807494i	$-0.299176\pi$
$674$		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	$-0.667794\pi$
$677$	−17.6982	+	3.12068i	−0.680199	+	0.119937i	−0.177135	+	0.984187i	$0.556683\pi$
$678$		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	$-0.701994\pi$
$683$	−5.01354	+	2.89457i	−0.191838	+	0.110758i	0.401005	+	0.916076i	$0.368661\pi$
$684$		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	$-0.302454\pi$
$691$	−8.42802	−	10.0441i	−0.320617	−	0.382097i	−0.902147	+	0.431428i	$0.858010\pi$
$692$		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	−0.571065	−	0.820905i	$-0.693469\pi$
$709$	10.4928	−	28.8286i	0.394064	−	1.08268i	0.965128	−	0.261777i	$-0.0843084\pi$
$710$		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	−0.991803	−	0.127774i	$-0.959217\pi$
$719$	−10.3301	+	17.8922i	−0.385246	+	0.667266i	0.606557	+	0.795040i	$0.292550\pi$
$720$		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	−0.911518	−	0.411259i	$-0.865089\pi$
$727$	−5.27477	−	29.9147i	−0.195630	−	1.10947i	0.715888	−	0.698215i	$-0.246022\pi$
$728$		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	−0.927385	−	0.374108i	$-0.877949\pi$
$733$	−12.3847	−	34.0267i	−0.457439	−	1.25680i	0.469946	−	0.882695i	$-0.344273\pi$
$734$		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	$-0.300704\pi$
$739$	4.81815	+	2.78176i	0.177239	+	0.102329i	−0.408756	+	0.912644i	$0.634037\pi$
$740$		0			0
$741$	−0.0218092	−	0.0170098i	−0.000801181	−	0.000624872i
$742$		0			0
$743$	−6.80955	+	38.6189i	−0.249818	+	1.41679i	0.559214	+	0.829024i	$0.311103\pi$
$743$	−6.80955	+	38.6189i	−0.249818	+	1.41679i	−0.809032	+	0.587765i	$0.800008\pi$
$744$		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	0.190217	−	0.981742i	$-0.439081\pi$
$751$	−20.3773	−	17.0986i	−0.743579	−	0.623937i	−0.933796	+	0.357805i	$0.883525\pi$
$752$		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	0.985879	+	0.167460i	$0.0535564\pi$
$761$	36.4687	+	30.6009i	1.32199	+	1.10928i	0.336112	+	0.941822i	$0.390888\pi$
$762$		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	0.424847	+	0.905265i	$0.360328\pi$
$769$	−7.87549	+	44.6641i	−0.283998	+	1.61063i	−0.708844	+	0.705365i	$0.750783\pi$
$770$		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	$-0.284376\pi$
$773$	7.37741	+	4.25935i	0.265347	+	0.153198i	−0.361424	+	0.932401i	$0.617709\pi$
$774$		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	$-0.00969856\pi$
$787$	6.01089	+	16.5148i	0.214265	+	0.588688i	−0.785271	+	0.619152i	$0.787476\pi$
$788$		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	$-0.363117\pi$
$797$	14.0527	+	2.47787i	0.497773	+	0.0877708i	0.0808752	+	0.996724i	$0.474228\pi$
$798$		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	$-0.242669\pi$
$821$	−2.36456	−	2.81797i	−0.0825236	−	0.0983478i	−0.805726	+	0.592288i	$0.798225\pi$
$822$		0			0
$823$	4.05525	−	22.9985i	0.141357	−	0.801676i	−0.828863	−	0.559452i	$-0.811012\pi$
$823$	4.05525	−	22.9985i	0.141357	−	0.801676i	0.970220	−	0.242225i	$-0.0778771\pi$
$824$		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	$-0.448966\pi$
$827$	−17.6991	−	10.2186i	−0.615456	−	0.355334i	−0.775098	+	0.631841i	$0.782299\pi$
$828$		0			0
$829$	18.2976	−	10.5641i	0.635503	−	0.366908i	−0.147377	−	0.989080i	$-0.547083\pi$
$829$	18.2976	−	10.5641i	0.635503	−	0.366908i	0.782880	+	0.622173i	$0.213750\pi$
$830$		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	0.917680	+	0.397320i	$0.130060\pi$
$839$	5.53919	+	31.4143i	0.191234	+	1.08454i	−0.726446	+	0.687223i	$0.758829\pi$
$840$		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	$-0.135481\pi$
$853$	10.1055	+	12.0433i	0.346006	+	0.412354i	−0.564774	+	0.825246i	$0.691037\pi$
$854$		0			0
$855$	0.00347467	+	0.00251562i	0.000118831	+	8.60323e-5i
$856$		0			0
$857$	30.3992	+	11.0644i	1.03842	+	0.377953i	0.804280	−	0.594250i	$-0.202551\pi$
$857$	30.3992	+	11.0644i	1.03842	+	0.377953i	0.234138	+	0.972203i	$0.424773\pi$
$858$		0			0
$859$	7.62842	−	9.09120i	0.260278	−	0.310188i	−0.620041	−	0.784570i	$-0.712884\pi$
$859$	7.62842	−	9.09120i	0.260278	−	0.310188i	0.880319	+	0.474382i	$0.157328\pi$
$860$		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	$-0.312796\pi$
$877$	23.4419	+	4.13345i	0.791578	+	0.139577i	0.236782	+	0.971563i	$0.423907\pi$
$878$		0			0
$879$	−4.47580	+	5.73866i	−0.150965	+	0.193560i
$880$		0			0
$881$	19.7098	−	34.1384i	0.664040	−	1.15015i	−0.315504	−	0.948924i	$-0.602174\pi$
$881$	19.7098	−	34.1384i	0.664040	−	1.15015i	0.979545	−	0.201227i	$-0.0644930\pi$
$882$		0			0
$883$	−39.3493	+	22.7183i	−1.32421	+	0.764533i	−0.984397	−	0.175960i	$-0.943697\pi$
$883$	−39.3493	+	22.7183i	−1.32421	+	0.764533i	−0.339812	+	0.940493i	$0.610364\pi$
$884$		0			0
$885$	−2.06274	+	1.86043i	−0.0693383	+	0.0625377i
$886$		0			0
$887$	3.61326	−	1.31512i	0.121321	−	0.0441573i	−0.280646	−	0.959811i	$-0.590549\pi$
$887$	3.61326	−	1.31512i	0.121321	−	0.0441573i	0.401967	+	0.915654i	$0.368327\pi$
$888$		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	$-0.171288\pi$
$907$	6.16891	+	7.35182i	0.204835	+	0.244113i	−0.653840	+	0.756632i	$0.726843\pi$
$908$		0			0
$909$	38.7743	+	40.0177i	1.28606	+	1.32730i
$910$		0			0
$911$	−27.8833	−	10.1487i	−0.923814	−	0.336241i	−0.164059	−	0.986451i	$-0.552459\pi$
$911$	−27.8833	−	10.1487i	−0.923814	−	0.336241i	−0.759755	+	0.650210i	$0.774681\pi$
$912$		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	−0.664240	−	0.747519i	$-0.731245\pi$
$929$	−1.32347	+	1.11052i	−0.0434216	+	0.0364351i	0.620819	+	0.783954i	$0.286800\pi$
$930$		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	0.802372	−	0.596824i	$-0.203571\pi$
$937$	−3.54099	−	6.13317i	−0.115679	−	0.200362i	−0.918051	+	0.396462i	$0.870238\pi$
$938$		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	$-0.0573624\pi$
$941$	3.52638	+	9.68865i	0.114957	+	0.315841i	−0.868850	+	0.495076i	$0.835140\pi$
$942$		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	$-0.610636\pi$
$947$	−10.4361	+	1.84016i	−0.339127	+	0.0597973i	0.00149128	+	0.999999i	$0.499525\pi$
$948$		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	0.812977	−	0.582295i	$-0.197845\pi$
$953$	−3.01897	−	5.22901i	−0.0977940	−	0.169384i	−0.910771	+	0.412911i	$0.864512\pi$
$954$		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	0.359588	−	0.933111i	$-0.382917\pi$
$967$	−15.4521	−	12.9658i	−0.496906	−	0.416954i	−0.856494	+	0.516158i	$0.827362\pi$
$968$		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	0.381728	−	0.924275i	$-0.375329\pi$
$977$	−14.4476	−	12.1229i	−0.462219	−	0.387848i	−0.843947	+	0.536427i	$0.819774\pi$
$978$		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	−0.941559	−	0.336847i	$-0.890639\pi$
$983$	−24.2461	+	20.3449i	−0.773330	+	0.648901i	0.168229	+	0.985748i	$0.446195\pi$
$984$		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	−0.961942	−	0.273252i	$-0.911901\pi$
$991$	−22.5906	−	39.1281i	−0.717614	−	1.24294i	0.244328	−	0.969693i	$-0.421433\pi$
$992$		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	$-0.447983\pi$
$997$	20.6197	−	3.63580i	0.653031	−	0.115147i	0.490342	+	0.871530i	$0.336872\pi$
$998$		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.337.24		204
4.3	odd	2		216.2.t.a.13.17	✓	204
8.3	odd	2		216.2.t.a.13.22	yes	204
8.5	even	2	inner	864.2.bf.a.337.11		204
12.11	even	2		648.2.t.a.253.18		204
24.11	even	2		648.2.t.a.253.13		204
27.25	even	9	inner	864.2.bf.a.241.11		204
108.79	odd	18		216.2.t.a.133.22	yes	204
108.83	even	18		648.2.t.a.397.13		204
216.83	even	18		648.2.t.a.397.18		204
216.133	even	18	inner	864.2.bf.a.241.24		204
216.187	odd	18		216.2.t.a.133.17	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.17	✓	204	4.3	odd	2
216.2.t.a.13.22	yes	204	8.3	odd	2
216.2.t.a.133.17	yes	204	216.187	odd	18
216.2.t.a.133.22	yes	204	108.79	odd	18
648.2.t.a.253.13		204	24.11	even	2
648.2.t.a.253.18		204	12.11	even	2
648.2.t.a.397.13		204	108.83	even	18
648.2.t.a.397.18		204	216.83	even	18
864.2.bf.a.241.11		204	27.25	even	9	inner
864.2.bf.a.241.24		204	216.133	even	18	inner
864.2.bf.a.337.11		204	8.5	even	2	inner
864.2.bf.a.337.24		204	1.1	even	1	trivial

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

Related objects

Downloads

Learn more