LMFDB - Embedded newform 576.2.y.a.527.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [576,2,Mod(47,576)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(576, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("576.47"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.y (of order $12$, degree $4$, 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			527.11
Character	$\chi$	$=$	576.527
Dual form			576.2.y.a.47.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.256373 + 1.71297i) q^{3} +(0.546024 + 2.03779i) q^{5} +(0.0638076 + 0.110518i) q^{7} +(-2.86855 + 0.878321i) q^{9} +(0.181856 - 0.678695i) q^{11} +(0.493860 + 1.84311i) q^{13} +(-3.35069 + 1.45776i) q^{15} +4.32243i q^{17} +(3.97707 + 3.97707i) q^{19} +(-0.172956 + 0.137635i) q^{21} +(-6.81589 - 3.93516i) q^{23} +(0.475689 - 0.274639i) q^{25} +(-2.23996 - 4.68856i) q^{27} +(-0.248377 + 0.926957i) q^{29} +(-4.91353 - 2.83683i) q^{31} +(1.20921 + 0.137514i) q^{33} +(-0.190372 + 0.190372i) q^{35} +(-6.64358 - 6.64358i) q^{37} +(-3.03058 + 1.31849i) q^{39} +(-4.61325 + 7.99038i) q^{41} +(10.8712 + 2.91294i) q^{43} +(-3.35613 - 5.36590i) q^{45} +(5.92267 + 10.2584i) q^{47} +(3.49186 - 6.04807i) q^{49} +(-7.40421 + 1.10816i) q^{51} +(-0.00259022 + 0.00259022i) q^{53} +1.48233 q^{55} +(-5.79299 + 7.83221i) q^{57} +(4.09587 - 1.09748i) q^{59} +(4.44908 + 1.19213i) q^{61} +(-0.280105 - 0.260982i) q^{63} +(-3.48621 + 2.01276i) q^{65} +(-2.01106 + 0.538862i) q^{67} +(4.99340 - 12.6843i) q^{69} +3.80683i q^{71} -1.87674i q^{73} +(0.592403 + 0.744431i) q^{75} +(0.0866118 - 0.0232076i) q^{77} +(3.00919 - 1.73736i) q^{79} +(7.45710 - 5.03901i) q^{81} +(1.47149 + 0.394284i) q^{83} +(-8.80821 + 2.36015i) q^{85} +(-1.65153 - 0.187816i) q^{87} +10.5967 q^{89} +(-0.172185 + 0.172185i) q^{91} +(3.59971 - 9.14402i) q^{93} +(-5.93284 + 10.2760i) q^{95} +(3.31795 + 5.74685i) q^{97} +(0.0744506 + 2.10659i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55}+ \cdots - 46 q^{99}+O(q^{100}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.256373	+	1.71297i	0.148017	+	0.988985i
$3$	0.256373	+	1.71297i	0.148017	+	0.988985i
$4$		0			0
$5$	0.546024	+	2.03779i	0.244189	+	0.911327i	0.973789	+	0.227452i	$0.0730396\pi$
$5$	0.546024	+	2.03779i	0.244189	+	0.911327i	−0.729600	+	0.683874i	$0.760294\pi$
$6$		0			0
$7$	0.0638076	+	0.110518i	0.0241170	+	0.0417719i	0.877832	−	0.478969i	$-0.158989\pi$
$7$	0.0638076	+	0.110518i	0.0241170	+	0.0417719i	−0.853715	+	0.520741i	$0.825656\pi$
$8$		0			0
$9$	−2.86855	+	0.878321i	−0.956182	+	0.292774i
$10$		0			0
$11$	0.181856	−	0.678695i	0.0548316	−	0.204634i	−0.933076	−	0.359680i	$-0.882886\pi$
$11$	0.181856	−	0.678695i	0.0548316	−	0.204634i	0.987907	+	0.155046i	$0.0495525\pi$
$12$		0			0
$13$	0.493860	+	1.84311i	0.136972	+	0.511187i	0.999982	+	0.00599967i	$0.00190977\pi$
$13$	0.493860	+	1.84311i	0.136972	+	0.511187i	−0.863010	+	0.505187i	$0.831424\pi$
$14$		0			0
$15$	−3.35069	+	1.45776i	−0.865144	+	0.376391i
$16$		0			0
$17$			4.32243i			1.04834i	0.851612	+	0.524172i	$0.175625\pi$
$17$			4.32243i			1.04834i	−0.851612	+	0.524172i	$0.824375\pi$
$18$		0			0
$19$	3.97707	+	3.97707i	0.912401	+	0.912401i	0.996461	−	0.0840594i	$-0.0267886\pi$
$19$	3.97707	+	3.97707i	0.912401	+	0.912401i	−0.0840594	+	0.996461i	$0.526789\pi$
$20$		0			0
$21$	−0.172956	+	0.137635i	−0.0377420	+	0.0300343i
$22$		0			0
$23$	−6.81589	−	3.93516i	−1.42121	−	0.820537i	−0.424809	−	0.905283i	$-0.639659\pi$
$23$	−6.81589	−	3.93516i	−1.42121	−	0.820537i	−0.996403	+	0.0847463i	$0.972992\pi$
$24$		0			0
$25$	0.475689	−	0.274639i	0.0951377	−	0.0549278i
$26$		0			0
$27$	−2.23996	−	4.68856i	−0.431080	−	0.902314i
$28$		0			0
$29$	−0.248377	+	0.926957i	−0.0461225	+	0.172132i	−0.985145	−	0.171724i	$-0.945066\pi$
$29$	−0.248377	+	0.926957i	−0.0461225	+	0.172132i	0.939023	+	0.343855i	$0.111733\pi$
$30$		0			0
$31$	−4.91353	−	2.83683i	−0.882496	−	0.509509i	−0.0110152	−	0.999939i	$-0.503506\pi$
$31$	−4.91353	−	2.83683i	−0.882496	−	0.509509i	−0.871480	+	0.490430i	$0.836840\pi$
$32$		0			0
$33$	1.20921	+	0.137514i	0.210496	+	0.0239382i
$34$		0			0
$35$	−0.190372	+	0.190372i	−0.0321787	+	0.0321787i
$36$		0			0
$37$	−6.64358	−	6.64358i	−1.09220	−	1.09220i	−0.995294	−	0.0969037i	$-0.969106\pi$
$37$	−6.64358	−	6.64358i	−1.09220	−	1.09220i	−0.0969037	−	0.995294i	$-0.530894\pi$
$38$		0			0
$39$	−3.03058	+	1.31849i	−0.485281	+	0.211128i
$40$		0			0
$41$	−4.61325	+	7.99038i	−0.720469	+	1.24789i	0.240344	+	0.970688i	$0.422740\pi$
$41$	−4.61325	+	7.99038i	−0.720469	+	1.24789i	−0.960812	+	0.277200i	$0.910593\pi$
$42$		0			0
$43$	10.8712	+	2.91294i	1.65785	+	0.444219i	0.961795	−	0.273772i	$-0.0882713\pi$
$43$	10.8712	+	2.91294i	1.65785	+	0.444219i	0.696053	+	0.717991i	$0.254938\pi$
$44$		0			0
$45$	−3.35613	−	5.36590i	−0.500302	−	0.799902i
$46$		0			0
$47$	5.92267	+	10.2584i	0.863910	+	1.49634i	0.868125	+	0.496345i	$0.165325\pi$
$47$	5.92267	+	10.2584i	0.863910	+	1.49634i	−0.00421475	+	0.999991i	$0.501342\pi$
$48$		0			0
$49$	3.49186	−	6.04807i	0.498837	−	0.864011i
$50$		0			0
$51$	−7.40421	+	1.10816i	−1.03680	+	0.155173i
$52$		0			0
$53$	−0.00259022	+	0.00259022i	−0.000355794	+	0.000355794i	−0.707285	−	0.706929i	$-0.750080\pi$
$53$	−0.00259022	+	0.00259022i	−0.000355794	+	0.000355794i	0.706929	+	0.707285i	$0.250080\pi$
$54$		0			0
$55$	1.48233			0.199878
$56$		0			0
$57$	−5.79299	+	7.83221i	−0.767300	+	1.03740i
$58$		0			0
$59$	4.09587	−	1.09748i	0.533237	−	0.142880i	0.0178541	−	0.999841i	$-0.494317\pi$
$59$	4.09587	−	1.09748i	0.533237	−	0.142880i	0.515382	+	0.856960i	$0.327650\pi$
$60$		0			0
$61$	4.44908	+	1.19213i	0.569646	+	0.152636i	0.532134	−	0.846660i	$-0.321390\pi$
$61$	4.44908	+	1.19213i	0.569646	+	0.152636i	0.0375117	+	0.999296i	$0.488057\pi$
$62$		0			0
$63$	−0.280105	−	0.260982i	−0.0352900	−	0.0328807i
$64$		0			0
$65$	−3.48621	+	2.01276i	−0.432411	+	0.249652i
$66$		0			0
$67$	−2.01106	+	0.538862i	−0.245690	+	0.0658325i	−0.379563	−	0.925166i	$-0.623925\pi$
$67$	−2.01106	+	0.538862i	−0.245690	+	0.0658325i	0.133872	+	0.990999i	$0.457259\pi$
$68$		0			0
$69$	4.99340	−	12.6843i	0.601134	−	1.52701i
$70$		0			0
$71$			3.80683i			0.451788i	0.974152	+	0.225894i	$0.0725303\pi$
$71$			3.80683i			0.451788i	−0.974152	+	0.225894i	$0.927470\pi$
$72$		0			0
$73$		−	1.87674i		−	0.219656i	−0.993951	−	0.109828i	$-0.964970\pi$
$73$		−	1.87674i		−	0.219656i	0.993951	−	0.109828i	$-0.0350300\pi$
$74$		0			0
$75$	0.592403	+	0.744431i	0.0684048	+	0.0859595i
$76$		0			0
$77$	0.0866118	−	0.0232076i	0.00987033	−	0.00264475i
$78$		0			0
$79$	3.00919	−	1.73736i	0.338560	−	0.195468i	−0.321075	−	0.947054i	$-0.604044\pi$
$79$	3.00919	−	1.73736i	0.338560	−	0.195468i	0.659635	+	0.751586i	$0.270711\pi$
$80$		0			0
$81$	7.45710	−	5.03901i	0.828567	−	0.559890i
$82$		0			0
$83$	1.47149	+	0.394284i	0.161517	+	0.0432783i	0.338671	−	0.940905i	$-0.390023\pi$
$83$	1.47149	+	0.394284i	0.161517	+	0.0432783i	−0.177155	+	0.984183i	$0.556689\pi$
$84$		0			0
$85$	−8.80821	+	2.36015i	−0.955384	+	0.255994i
$86$		0			0
$87$	−1.65153	−	0.187816i	−0.177062	−	0.0201360i
$88$		0			0
$89$	10.5967			1.12325			0.561624	−	0.827392i	$-0.310177\pi$
$89$	10.5967			1.12325			0.561624	+	0.827392i	$0.310177\pi$
$90$		0			0
$91$	−0.172185	+	0.172185i	−0.0180499	+	0.0180499i
$92$		0			0
$93$	3.59971	−	9.14402i	0.373272	−	0.948191i
$94$		0			0
$95$	−5.93284	+	10.2760i	−0.608697	+	1.05429i
$96$		0			0
$97$	3.31795	+	5.74685i	0.336886	+	0.583504i	0.983845	−	0.179021i	$-0.0572928\pi$
$97$	3.31795	+	5.74685i	0.336886	+	0.583504i	−0.646959	+	0.762525i	$0.723960\pi$
$98$		0			0
$99$	0.0744506	+	2.10659i	0.00748257	+	0.211721i
$100$		0			0
$101$	12.0922	+	3.24008i	1.20321	+	0.322400i	0.804096	−	0.594499i	$-0.202650\pi$
$101$	12.0922	+	3.24008i	1.20321	+	0.322400i	0.399118	+	0.916899i	$0.369316\pi$
$102$		0			0
$103$	4.21850	−	7.30665i	0.415661	−	0.719946i	−0.579837	−	0.814733i	$-0.696884\pi$
$103$	4.21850	−	7.30665i	0.415661	−	0.719946i	0.995498	+	0.0947868i	$0.0302169\pi$
$104$		0			0
$105$	−0.374908	−	0.277295i	−0.0365873	−	0.0270613i
$106$		0			0
$107$	7.25071	+	7.25071i	0.700953	+	0.700953i	0.964615	−	0.263662i	$-0.0849304\pi$
$107$	7.25071	+	7.25071i	0.700953	+	0.700953i	−0.263662	+	0.964615i	$0.584930\pi$
$108$		0			0
$109$	10.2850	−	10.2850i	0.985128	−	0.985128i	−0.0147630	−	0.999891i	$-0.504699\pi$
$109$	10.2850	−	10.2850i	0.985128	−	0.985128i	0.999891	+	0.0147630i	$0.00469937\pi$
$110$		0			0
$111$	9.67702	−	13.0835i	0.918503	−	1.24183i
$112$		0			0
$113$	−18.2964	−	10.5634i	−1.72118	−	0.993722i	−0.916526	−	0.399976i	$-0.869019\pi$
$113$	−18.2964	−	10.5634i	−1.72118	−	0.993722i	−0.804652	−	0.593747i	$-0.797648\pi$
$114$		0			0
$115$	4.29738	−	16.0380i	0.400732	−	1.49555i
$116$		0			0
$117$	−3.03550	−	4.85328i	−0.280632	−	0.448685i
$118$		0			0
$119$	−0.477707	+	0.275804i	−0.0437913	+	0.0252829i
$120$		0			0
$121$	9.09872	+	5.25315i	0.827157	+	0.477559i
$122$		0			0
$123$	−14.8700	−	5.85384i	−1.34078	−	0.527823i
$124$		0			0
$125$	8.27822	+	8.27822i	0.740426	+	0.740426i
$126$		0			0
$127$		−	13.1109i		−	1.16340i	−0.813403	−	0.581700i	$-0.802388\pi$
$127$		−	13.1109i		−	1.16340i	0.813403	−	0.581700i	$-0.197612\pi$
$128$		0			0
$129$	−2.20269	+	19.3689i	−0.193936	+	1.70534i
$130$		0			0
$131$	−1.27247	−	4.74891i	−0.111176	−	0.414914i	0.887797	−	0.460236i	$-0.152235\pi$
$131$	−1.27247	−	4.74891i	−0.111176	−	0.414914i	−0.998972	+	0.0453222i	$0.985569\pi$
$132$		0			0
$133$	−0.185770	+	0.693305i	−0.0161083	+	0.0601171i
$134$		0			0
$135$	8.33122	−	7.12462i	0.717037	−	0.613190i
$136$		0			0
$137$	−3.41217	−	5.91005i	−0.291521	−	0.504930i	0.682648	−	0.730747i	$-0.260828\pi$
$137$	−3.41217	−	5.91005i	−0.291521	−	0.504930i	−0.974170	+	0.225817i	$0.927495\pi$
$138$		0			0
$139$	2.77132	+	10.3427i	0.235061	+	0.877258i	0.978121	+	0.208035i	$0.0667066\pi$
$139$	2.77132	+	10.3427i	0.235061	+	0.877258i	−0.743061	+	0.669224i	$0.766627\pi$
$140$		0			0
$141$	−16.0539	+	12.7753i	−1.35198	+	1.07588i
$142$		0			0
$143$	1.34072			0.112117
$144$		0			0
$145$	−2.02456			−0.168131
$146$		0			0
$147$	11.2554	+	4.43089i	0.928330	+	0.365453i
$148$		0			0
$149$	−0.0546714	−	0.204036i	−0.00447885	−	0.0167153i	0.963650	−	0.267167i	$-0.0860875\pi$
$149$	−0.0546714	−	0.204036i	−0.00447885	−	0.0167153i	−0.968129	+	0.250452i	$0.919421\pi$
$150$		0			0
$151$	−1.14798	−	1.98835i	−0.0934210	−	0.161810i	0.815528	−	0.578718i	$-0.196447\pi$
$151$	−1.14798	−	1.98835i	−0.0934210	−	0.161810i	−0.908949	+	0.416908i	$0.863114\pi$
$152$		0			0
$153$	−3.79649	−	12.3991i	−0.306928	−	1.00241i
$154$		0			0
$155$	3.09795	−	11.5617i	0.248833	−	0.928658i
$156$		0			0
$157$	4.34480	+	16.2150i	0.346753	+	1.29410i	0.890551	+	0.454883i	$0.150319\pi$
$157$	4.34480	+	16.2150i	0.346753	+	1.29410i	−0.543799	+	0.839216i	$0.683015\pi$
$158$		0			0
$159$	−0.00510103	−	0.00377291i	−0.000404538	−	0.000299211i
$160$		0			0
$161$		−	1.00437i		−	0.0791556i
$162$		0			0
$163$	−0.490399	−	0.490399i	−0.0384110	−	0.0384110i	0.687640	−	0.726051i	$-0.258647\pi$
$163$	−0.490399	−	0.490399i	−0.0384110	−	0.0384110i	−0.726051	+	0.687640i	$0.758647\pi$
$164$		0			0
$165$	0.380031	+	2.53920i	0.0295854	+	0.197676i
$166$		0			0
$167$	−9.34175	−	5.39346i	−0.722887	−	0.417359i	0.0929276	−	0.995673i	$-0.470378\pi$
$167$	−9.34175	−	5.39346i	−0.722887	−	0.417359i	−0.815814	+	0.578314i	$0.803711\pi$
$168$		0			0
$169$	8.10518	−	4.67953i	0.623475	−	0.359963i
$170$		0			0
$171$	−14.9015	−	7.91525i	−1.13955	−	0.605294i
$172$		0			0
$173$	1.23685	−	4.61598i	0.0940358	−	0.350946i	−0.902836	−	0.429986i	$-0.858519\pi$
$173$	1.23685	−	4.61598i	0.0940358	−	0.350946i	0.996871	+	0.0790394i	$0.0251853\pi$
$174$		0			0
$175$	0.0607051	+	0.0350481i	0.00458888	+	0.00264939i
$176$		0			0
$177$	2.93003	+	6.73474i	0.220235	+	0.506214i
$178$		0			0
$179$	3.52882	−	3.52882i	0.263756	−	0.263756i	−0.562822	−	0.826578i	$-0.690284\pi$
$179$	3.52882	−	3.52882i	0.263756	−	0.263756i	0.826578	+	0.562822i	$0.190284\pi$
$180$		0			0
$181$	7.34860	+	7.34860i	0.546217	+	0.546217i	0.925344	−	0.379127i	$-0.123776\pi$
$181$	7.34860	+	7.34860i	0.546217	+	0.546217i	−0.379127	+	0.925344i	$0.623776\pi$
$182$		0			0
$183$	−0.901454	+	7.92677i	−0.0666374	+	0.585964i
$184$		0			0
$185$	9.91065	−	17.1658i	0.728646	−	1.26205i
$186$		0			0
$187$	2.93361	+	0.786059i	0.214527	+	0.0574824i
$188$		0			0
$189$	0.375244	−	0.546722i	0.0272950	−	0.0397681i
$190$		0			0
$191$	−2.58888	−	4.48407i	−0.187325	−	0.324456i	0.757033	−	0.653377i	$-0.226648\pi$
$191$	−2.58888	−	4.48407i	−0.187325	−	0.324456i	−0.944357	+	0.328921i	$0.893315\pi$
$192$		0			0
$193$	13.2173	−	22.8930i	0.951401	−	1.64787i	0.209003	−	0.977915i	$-0.432978\pi$
$193$	13.2173	−	22.8930i	0.951401	−	1.64787i	0.742398	−	0.669960i	$-0.233689\pi$
$194$		0			0
$195$	−4.34158	−	5.45576i	−0.310907	−	0.390695i
$196$		0			0
$197$	−5.14652	+	5.14652i	−0.366674	+	0.366674i	−0.866263	−	0.499588i	$-0.833485\pi$
$197$	−5.14652	+	5.14652i	−0.366674	+	0.366674i	0.499588	+	0.866263i	$0.333485\pi$
$198$		0			0
$199$	1.37436			0.0974261			0.0487130	−	0.998813i	$-0.484488\pi$
$199$	1.37436			0.0974261			0.0487130	+	0.998813i	$0.484488\pi$
$200$		0			0
$201$	−1.43864	−	3.30674i	−0.101474	−	0.233240i
$202$		0			0
$203$	−0.118294	+	0.0316967i	−0.00830260	+	0.00222468i
$204$		0			0
$205$	−18.8017	−	5.03789i	−1.31316	−	0.351861i
$206$		0			0
$207$	23.0080	+	5.30163i	1.59917	+	0.368489i
$208$		0			0
$209$	3.42246	−	1.97596i	0.236737	−	0.136680i
$210$		0			0
$211$	−11.1381	+	2.98444i	−0.766776	+	0.205457i	−0.620947	−	0.783853i	$-0.713252\pi$
$211$	−11.1381	+	2.98444i	−0.766776	+	0.205457i	−0.145829	+	0.989310i	$0.546585\pi$
$212$		0			0
$213$	−6.52100	+	0.975971i	−0.446811	+	0.0668724i
$214$		0			0
$215$			23.7438i			1.61931i
$216$		0			0
$217$		−	0.724045i		−	0.0491514i
$218$		0			0
$219$	3.21481	−	0.481147i	0.217237	−	0.0325129i
$220$		0			0
$221$	−7.96672	+	2.13468i	−0.535900	+	0.143594i
$222$		0			0
$223$	−17.9819	+	10.3819i	−1.20416	+	0.695220i	−0.961477	−	0.274886i	$-0.911360\pi$
$223$	−17.9819	+	10.3819i	−1.20416	+	0.695220i	−0.242680	+	0.970106i	$0.578026\pi$
$224$		0			0
$225$	−1.12331	+	1.20562i	−0.0748876	+	0.0803748i
$226$		0			0
$227$	−7.65406	−	2.05090i	−0.508018	−	0.136123i	−0.00429906	−	0.999991i	$-0.501368\pi$
$227$	−7.65406	−	2.05090i	−0.508018	−	0.136123i	−0.503718	+	0.863868i	$0.668035\pi$
$228$		0			0
$229$	0.448692	−	0.120227i	0.0296504	−	0.00794481i	−0.243963	−	0.969784i	$-0.578448\pi$
$229$	0.448692	−	0.120227i	0.0296504	−	0.00794481i	0.273614	+	0.961840i	$0.411781\pi$
$230$		0			0
$231$	0.0619589	+	0.142414i	0.00407659	+	0.00937014i
$232$		0			0
$233$	−9.13737			−0.598609			−0.299305	−	0.954158i	$-0.596755\pi$
$233$	−9.13737			−0.598609			−0.299305	+	0.954158i	$0.596755\pi$
$234$		0			0
$235$	−17.6705	+	17.6705i	−1.15269	+	1.15269i
$236$		0			0
$237$	3.74752	+	4.70925i	0.243428	+	0.305898i
$238$		0			0
$239$	−3.65824	+	6.33626i	−0.236632	+	0.409859i	−0.959746	−	0.280870i	$-0.909377\pi$
$239$	−3.65824	+	6.33626i	−0.236632	+	0.409859i	0.723114	+	0.690729i	$0.242710\pi$
$240$		0			0
$241$	−1.24858	−	2.16261i	−0.0804282	−	0.139306i	0.823006	−	0.568033i	$-0.192295\pi$
$241$	−1.24858	−	2.16261i	−0.0804282	−	0.139306i	−0.903434	+	0.428727i	$0.858962\pi$
$242$		0			0
$243$	10.5435	+	11.4819i	0.676365	+	0.736567i
$244$		0			0
$245$	14.2313	+	3.81327i	0.909206	+	0.243621i
$246$		0			0
$247$	−5.36605	+	9.29428i	−0.341434	+	0.591381i
$248$		0			0
$249$	−0.298147	+	2.62170i	−0.0188943	+	0.166144i
$250$		0			0
$251$	−2.77626	−	2.77626i	−0.175236	−	0.175236i	0.614039	−	0.789275i	$-0.289544\pi$
$251$	−2.77626	−	2.77626i	−0.175236	−	0.175236i	−0.789275	+	0.614039i	$0.789544\pi$
$252$		0			0
$253$	−3.91028	+	3.91028i	−0.245837	+	0.245837i
$254$		0			0
$255$	−6.30106	−	14.4831i	−0.394588	−	0.906969i
$256$		0			0
$257$	−9.61957	−	5.55386i	−0.600052	−	0.346440i	0.169010	−	0.985614i	$-0.445943\pi$
$257$	−9.61957	−	5.55386i	−0.600052	−	0.346440i	−0.769062	+	0.639174i	$0.779276\pi$
$258$		0			0
$259$	0.310324	−	1.15815i	0.0192826	−	0.0719637i
$260$		0			0
$261$	−0.101684	−	2.87717i	−0.00629409	−	0.178093i
$262$		0			0
$263$	16.6320	−	9.60247i	1.02557	−	0.592114i	0.109858	−	0.993947i	$-0.464960\pi$
$263$	16.6320	−	9.60247i	1.02557	−	0.592114i	0.915713	+	0.401834i	$0.131627\pi$
$264$		0			0
$265$	−0.00669264	−	0.00386400i	−0.000411125	−	0.000237363i
$266$		0			0
$267$	2.71671	+	18.1519i	0.166260	+	1.11088i
$268$		0			0
$269$	−7.66476	−	7.66476i	−0.467329	−	0.467329i	0.433719	−	0.901048i	$-0.357201\pi$
$269$	−7.66476	−	7.66476i	−0.467329	−	0.467329i	−0.901048	+	0.433719i	$0.857201\pi$
$270$		0			0
$271$		−	12.9801i		−	0.788486i	−0.919006	−	0.394243i	$-0.871007\pi$
$271$		−	12.9801i		−	0.788486i	0.919006	−	0.394243i	$-0.128993\pi$
$272$		0			0
$273$	−0.339091	−	0.250804i	−0.0205227	−	0.0151794i
$274$		0			0
$275$	−0.0998893	−	0.372792i	−0.00602355	−	0.0224802i
$276$		0			0
$277$	−6.42631	+	23.9833i	−0.386119	+	1.44102i	0.450276	+	0.892890i	$0.351326\pi$
$277$	−6.42631	+	23.9833i	−0.386119	+	1.44102i	−0.836395	+	0.548127i	$0.815341\pi$
$278$		0			0
$279$	16.5863	+	3.82191i	0.992997	+	0.228812i
$280$		0			0
$281$	−3.69120	−	6.39334i	−0.220198	−	0.381395i	0.734670	−	0.678425i	$-0.237337\pi$
$281$	−3.69120	−	6.39334i	−0.220198	−	0.381395i	−0.954868	+	0.297030i	$0.904004\pi$
$282$		0			0
$283$	−1.60691	−	5.99708i	−0.0955211	−	0.356490i	0.901577	−	0.432619i	$-0.142410\pi$
$283$	−1.60691	−	5.99708i	−0.0955211	−	0.356490i	−0.997098	+	0.0761294i	$0.975744\pi$
$284$		0			0
$285$	−19.1235	−	7.52830i	−1.13278	−	0.445938i
$286$		0			0
$287$	−1.17744			−0.0695022
$288$		0			0
$289$	−1.68344			−0.0990261
$290$		0			0
$291$	−8.99356	+	7.15689i	−0.527212	+	0.419544i
$292$		0			0
$293$	6.43453	+	24.0140i	0.375909	+	1.40291i	0.852012	+	0.523522i	$0.175382\pi$
$293$	6.43453	+	24.0140i	0.375909	+	1.40291i	−0.476103	+	0.879390i	$0.657951\pi$
$294$		0			0
$295$	4.47288	+	7.74726i	0.260421	+	0.451063i
$296$		0			0
$297$	−3.58945	+	0.667607i	−0.208281	+	0.0387385i
$298$		0			0
$299$	3.88683	−	14.5058i	0.224781	−	0.838895i
$300$		0			0
$301$	0.371735	+	1.38734i	0.0214265	+	0.0799647i
$302$		0			0
$303$	−2.45006	+	21.5442i	−0.140753	+	1.23768i
$304$		0			0
$305$			9.71720i			0.556406i
$306$		0			0
$307$	17.3773	+	17.3773i	0.991773	+	0.991773i	0.999966	−	0.00819381i	$-0.00260820\pi$
$307$	17.3773	+	17.3773i	0.991773	+	0.991773i	−0.00819381	+	0.999966i	$0.502608\pi$
$308$		0			0
$309$	13.5976	+	5.35294i	0.773541	+	0.304518i
$310$		0			0
$311$	11.9437	+	6.89568i	0.677264	+	0.391018i	0.798823	−	0.601566i	$-0.205456\pi$
$311$	11.9437	+	6.89568i	0.677264	+	0.391018i	−0.121560	+	0.992584i	$0.538790\pi$
$312$		0			0
$313$	−17.6368	+	10.1826i	−0.996890	+	0.575555i	−0.907327	−	0.420426i	$-0.861881\pi$
$313$	−17.6368	+	10.1826i	−0.996890	+	0.575555i	−0.0895635	+	0.995981i	$0.528547\pi$
$314$		0			0
$315$	0.378883	−	0.713298i	0.0213476	−	0.0401898i
$316$		0			0
$317$	5.44301	−	20.3136i	0.305710	−	1.14092i	−0.626623	−	0.779322i	$-0.715563\pi$
$317$	5.44301	−	20.3136i	0.305710	−	1.14092i	0.932333	−	0.361601i	$-0.117770\pi$
$318$		0			0
$319$	0.583952	+	0.337145i	0.0326950	+	0.0188765i
$320$		0			0
$321$	−10.5614	+	14.2792i	−0.589479	+	0.796985i
$322$		0			0
$323$	−17.1906	+	17.1906i	−0.956511	+	0.956511i
$324$		0			0
$325$	0.741113	+	0.741113i	0.0411096	+	0.0411096i
$326$		0			0
$327$	20.2548	+	14.9812i	1.12009	+	0.828461i
$328$		0			0
$329$	−0.755823	+	1.30912i	−0.0416699	+	0.0721743i
$330$		0			0
$331$	−17.0629	−	4.57199i	−0.937862	−	0.251299i	−0.242658	−	0.970112i	$-0.578019\pi$
$331$	−17.0629	−	4.57199i	−0.937862	−	0.251299i	−0.695204	+	0.718813i	$0.744686\pi$
$332$		0			0
$333$	24.8926	+	13.2222i	1.36411	+	0.724573i
$334$		0			0
$335$	−2.19618	−	3.80389i	−0.119990	−	0.207829i
$336$		0			0
$337$	−4.82538	+	8.35780i	−0.262855	+	0.455279i	−0.966999	−	0.254778i	$-0.917997\pi$
$337$	−4.82538	+	8.35780i	−0.262855	+	0.455279i	0.704144	+	0.710057i	$0.251331\pi$
$338$		0			0
$339$	13.4041	−	34.0493i	0.728012	−	1.84931i
$340$		0			0
$341$	−2.81889	+	2.81889i	−0.152652	+	0.152652i
$342$		0			0
$343$	1.78454			0.0963558
$344$		0			0
$345$	28.5744	+	3.24956i	1.53840	+	0.174950i
$346$		0			0
$347$	−18.4037	+	4.93125i	−0.987960	+	0.264723i	−0.716393	−	0.697696i	$-0.754208\pi$
$347$	−18.4037	+	4.93125i	−0.987960	+	0.264723i	−0.271567	+	0.962420i	$0.587542\pi$
$348$		0			0
$349$	−17.4744	−	4.68226i	−0.935385	−	0.250636i	−0.241236	−	0.970467i	$-0.577553\pi$
$349$	−17.4744	−	4.68226i	−0.935385	−	0.250636i	−0.694150	+	0.719831i	$0.744219\pi$
$350$		0			0
$351$	7.53530	−	6.44398i	0.402205	−	0.343954i
$352$		0			0
$353$	5.65589	−	3.26543i	0.301033	−	0.173801i	−0.341874	−	0.939746i	$-0.611062\pi$
$353$	5.65589	−	3.26543i	0.301033	−	0.173801i	0.642907	+	0.765944i	$0.277728\pi$
$354$		0			0
$355$	−7.75752	+	2.07862i	−0.411726	+	0.110322i
$356$		0			0
$357$	−0.594916	−	0.747590i	−0.0314863	−	0.0395667i
$358$		0			0
$359$		−	22.8075i		−	1.20373i	−0.798597	−	0.601866i	$-0.794424\pi$
$359$		−	22.8075i		−	1.20373i	0.798597	−	0.601866i	$-0.205576\pi$
$360$		0			0
$361$			12.6341i			0.664952i
$362$		0			0
$363$	−6.66583	+	16.9326i	−0.349865	+	0.888732i
$364$		0			0
$365$	3.82440	−	1.02475i	0.200178	−	0.0536377i
$366$		0			0
$367$	−20.7702	+	11.9917i	−1.08419	+	0.625959i	−0.932025	−	0.362395i	$-0.881959\pi$
$367$	−20.7702	+	11.9917i	−1.08419	+	0.625959i	−0.152169	+	0.988355i	$0.548626\pi$
$368$		0			0
$369$	6.21519	−	26.9727i	0.323550	−	1.40414i
$370$		0			0
$371$	−0.000451542	0	0.000120990i	−2.34429e−5	0	6.28150e-6i
$372$		0			0
$373$	−23.1710	+	6.20866i	−1.19975	+	0.321472i	−0.802733	−	0.596338i	$-0.796622\pi$
$373$	−23.1710	+	6.20866i	−1.19975	+	0.321472i	−0.397018	+	0.917811i	$0.629955\pi$
$374$		0			0
$375$	−12.0580	+	16.3027i	−0.622674	+	0.841866i
$376$		0			0
$377$	−1.83115			−0.0943089
$378$		0			0
$379$	−9.96634	+	9.96634i	−0.511936	+	0.511936i	−0.915119	−	0.403183i	$-0.867904\pi$
$379$	−9.96634	+	9.96634i	−0.511936	+	0.511936i	0.403183	+	0.915119i	$0.367904\pi$
$380$		0			0
$381$	22.4585	−	3.36128i	1.15059	−	0.172203i
$382$		0			0
$383$	2.30770	−	3.99705i	0.117918	−	0.204240i	−0.801024	−	0.598632i	$-0.795711\pi$
$383$	2.30770	−	3.99705i	0.117918	−	0.204240i	0.918942	+	0.394392i	$0.129045\pi$
$384$		0			0
$385$	0.0945842	+	0.163825i	0.00482046	+	0.00834927i
$386$		0			0
$387$	−33.7431	+	1.19254i	−1.71526	+	0.0606202i
$388$		0			0
$389$	−12.3565	−	3.31091i	−0.626498	−	0.167870i	−0.0684178	−	0.997657i	$-0.521795\pi$
$389$	−12.3565	−	3.31091i	−0.626498	−	0.167870i	−0.558080	+	0.829787i	$0.688462\pi$
$390$		0			0
$391$	17.0095	−	29.4612i	0.860205	−	1.48992i
$392$		0			0
$393$	7.80852	−	3.39719i	0.393887	−	0.171366i
$394$		0			0
$395$	5.18345	+	5.18345i	0.260808	+	0.260808i
$396$		0			0
$397$	−3.70313	+	3.70313i	−0.185855	+	0.185855i	−0.793901	−	0.608047i	$-0.791953\pi$
$397$	−3.70313	+	3.70313i	−0.185855	+	0.185855i	0.608047	+	0.793901i	$0.291953\pi$
$398$		0			0
$399$	−1.23524	−	0.140475i	−0.0618392	−	0.00703252i
$400$		0			0
$401$	11.5871	+	6.68983i	0.578633	+	0.334074i	0.760590	−	0.649232i	$-0.224910\pi$
$401$	11.5871	+	6.68983i	0.578633	+	0.334074i	−0.181957	+	0.983307i	$0.558243\pi$
$402$		0			0
$403$	2.80199	−	10.4572i	0.139577	−	0.520908i
$404$		0			0
$405$	14.3402	+	12.4446i	0.712570	+	0.618376i
$406$		0			0
$407$	−5.71713	+	3.30079i	−0.283388	+	0.163614i
$408$		0			0
$409$	−24.1053	−	13.9172i	−1.19193	−	0.688161i	−0.233185	−	0.972432i	$-0.574915\pi$
$409$	−24.1053	−	13.9172i	−1.19193	−	0.688161i	−0.958744	+	0.284272i	$0.908248\pi$
$410$		0			0
$411$	9.24896	−	7.36013i	0.456217	−	0.363048i
$412$		0			0
$413$	0.382639	+	0.382639i	0.0188285	+	0.0188285i
$414$		0			0
$415$			3.21387i			0.157763i
$416$		0			0
$417$	−17.0063	+	7.39880i	−0.832802	+	0.362321i
$418$		0			0
$419$	−2.67387	−	9.97902i	−0.130627	−	0.487507i	0.869350	−	0.494196i	$-0.164538\pi$
$419$	−2.67387	−	9.97902i	−0.130627	−	0.487507i	−0.999978	+	0.00668892i	$0.997871\pi$
$420$		0			0
$421$	7.99904	−	29.8528i	0.389849	−	1.45494i	−0.440529	−	0.897738i	$-0.645209\pi$
$421$	7.99904	−	29.8528i	0.389849	−	1.45494i	0.830379	−	0.557199i	$-0.188124\pi$
$422$		0			0
$423$	−25.9996	−	24.2246i	−1.26414	−	1.17784i
$424$		0			0
$425$	1.18711	+	2.05613i	0.0575833	+	0.0997371i
$426$		0			0
$427$	0.152134	+	0.567770i	0.00736226	+	0.0274763i
$428$		0			0
$429$	0.343725	+	2.29662i	0.0165952	+	0.110882i
$430$		0			0
$431$	14.8449			0.715053			0.357526	−	0.933903i	$-0.383620\pi$
$431$	14.8449			0.715053			0.357526	+	0.933903i	$0.383620\pi$
$432$		0			0
$433$	−32.1617			−1.54559			−0.772796	−	0.634654i	$-0.781143\pi$
$433$	−32.1617			−1.54559			−0.772796	+	0.634654i	$0.781143\pi$
$434$		0			0
$435$	−0.519044	−	3.46802i	−0.0248863	−	0.166279i
$436$		0			0
$437$	−11.4569	−	42.7576i	−0.548056	−	2.04537i
$438$		0			0
$439$	0.140035	+	0.242548i	0.00668352	+	0.0115762i	0.869348	−	0.494201i	$-0.164539\pi$
$439$	0.140035	+	0.242548i	0.00668352	+	0.0115762i	−0.862664	+	0.505777i	$0.831206\pi$
$440$		0			0
$441$	−4.70440	+	20.4161i	−0.224019	+	0.972197i
$442$		0			0
$443$	6.50011	−	24.2588i	0.308830	−	1.15257i	−0.620768	−	0.783994i	$-0.713179\pi$
$443$	6.50011	−	24.2588i	0.308830	−	1.15257i	0.929598	−	0.368574i	$-0.120154\pi$
$444$		0			0
$445$	5.78605	+	21.5938i	0.274285	+	1.02365i
$446$		0			0
$447$	0.335492	−	0.145960i	0.0158682	−	0.00690367i
$448$		0			0
$449$			14.2885i			0.674318i	0.941448	+	0.337159i	$0.109466\pi$
$449$			14.2885i			0.674318i	−0.941448	+	0.337159i	$0.890534\pi$
$450$		0			0
$451$	4.58408	+	4.58408i	0.215856	+	0.215856i
$452$		0			0
$453$	3.11168	−	2.47621i	0.146200	−	0.116343i
$454$		0			0
$455$	−0.444893	−	0.256859i	−0.0208569	−	0.0120417i
$456$		0			0
$457$	24.1097	−	13.9198i	1.12781	−	0.651139i	0.184424	−	0.982847i	$-0.440958\pi$
$457$	24.1097	−	13.9198i	1.12781	−	0.651139i	0.943382	+	0.331708i	$0.107625\pi$
$458$		0			0
$459$	20.2660	−	9.68207i	0.945935	−	0.451921i
$460$		0			0
$461$	4.33776	−	16.1887i	0.202030	−	0.753985i	−0.788305	−	0.615285i	$-0.789041\pi$
$461$	4.33776	−	16.1887i	0.202030	−	0.753985i	0.990334	−	0.138700i	$-0.0442923\pi$
$462$		0			0
$463$	26.1951	+	15.1238i	1.21739	+	0.702861i	0.964359	−	0.264597i	$-0.0852389\pi$
$463$	26.1951	+	15.1238i	1.21739	+	0.702861i	0.253032	+	0.967458i	$0.418572\pi$
$464$		0			0
$465$	20.5991	+	2.34259i	0.955261	+	0.108635i
$466$		0			0
$467$	15.9369	−	15.9369i	0.737469	−	0.737469i	−0.234618	−	0.972088i	$-0.575384\pi$
$467$	15.9369	−	15.9369i	0.737469	−	0.737469i	0.972088	+	0.234618i	$0.0753840\pi$
$468$		0			0
$469$	−0.187875	−	0.187875i	−0.00867527	−	0.00867527i
$470$		0			0
$471$	−26.6620	+	11.5996i	−1.22852	+	0.534482i
$472$		0			0
$473$	3.95399	−	6.84851i	0.181805	−	0.314895i
$474$		0			0
$475$	2.98410	+	0.799588i	0.136920	+	0.0366876i
$476$		0			0
$477$	0.00515511	−	0.00970520i	0.000236036	−	0.000444371i
$478$		0			0
$479$	−14.8100	−	25.6516i	−0.676684	−	1.17205i	−0.975973	−	0.217889i	$-0.930083\pi$
$479$	−14.8100	−	25.6516i	−0.676684	−	1.17205i	0.299289	−	0.954163i	$-0.403251\pi$
$480$		0			0
$481$	8.96385	−	15.5258i	0.408716	−	0.707917i
$482$		0			0
$483$	1.72046	−	0.257494i	0.0782837	−	0.0117164i
$484$		0			0
$485$	−9.89919	+	9.89919i	−0.449499	+	0.449499i
$486$		0			0
$487$	−25.6320			−1.16150			−0.580749	−	0.814083i	$-0.697240\pi$
$487$	−25.6320			−1.16150			−0.580749	+	0.814083i	$0.697240\pi$
$488$		0			0
$489$	0.714315	−	0.965765i	0.0323024	−	0.0436734i
$490$		0			0
$491$	5.25069	−	1.40692i	0.236960	−	0.0634933i	−0.138385	−	0.990379i	$-0.544191\pi$
$491$	5.25069	−	1.40692i	0.236960	−	0.0634933i	0.375345	+	0.926885i	$0.377524\pi$
$492$		0			0
$493$	−4.00671	−	1.07360i	−0.180453	−	0.0483523i
$494$		0			0
$495$	−4.25214	+	1.30196i	−0.191119	+	0.0585190i
$496$		0			0
$497$	−0.420724	+	0.242905i	−0.0188720	+	0.0108958i
$498$		0			0
$499$	21.5779	−	5.78179i	0.965961	−	0.258829i	0.258840	−	0.965920i	$-0.416660\pi$
$499$	21.5779	−	5.78179i	0.965961	−	0.258829i	0.707122	+	0.707092i	$0.249993\pi$
$500$		0			0
$501$	6.84387	−	17.3849i	0.305762	−	0.776700i
$502$		0			0
$503$		−	24.7337i		−	1.10282i	−0.834235	−	0.551410i	$-0.814090\pi$
$503$		−	24.7337i		−	1.10282i	0.834235	−	0.551410i	$-0.185910\pi$
$504$		0			0
$505$			26.4104i			1.17525i
$506$		0			0
$507$	10.0938	+	12.6842i	0.448284	+	0.563327i
$508$		0			0
$509$	−8.62284	+	2.31048i	−0.382201	+	0.102410i	−0.444804	−	0.895628i	$-0.646726\pi$
$509$	−8.62284	+	2.31048i	−0.382201	+	0.102410i	0.0626029	+	0.998039i	$0.480060\pi$
$510$		0			0
$511$	0.207414	−	0.119751i	0.00917545	−	0.00529745i
$512$		0			0
$513$	9.73824	−	27.5552i	0.429954	−	1.21659i
$514$		0			0
$515$	17.1928	+	4.60680i	0.757606	+	0.203000i
$516$		0			0
$517$	8.03937	−	2.15414i	0.353571	−	0.0947391i
$518$		0			0
$519$	8.22413	+	0.935271i	0.360999	+	0.0410538i
$520$		0			0
$521$	−14.1129			−0.618299			−0.309149	−	0.951013i	$-0.600044\pi$
$521$	−14.1129			−0.618299			−0.309149	+	0.951013i	$0.600044\pi$
$522$		0			0
$523$	27.5776	−	27.5776i	1.20588	−	1.20588i	0.233534	−	0.972349i	$-0.424971\pi$
$523$	27.5776	−	27.5776i	1.20588	−	1.20588i	0.972349	−	0.233534i	$-0.0750289\pi$
$524$		0			0
$525$	−0.0444733	+	0.112972i	−0.00194097	+	0.00493048i
$526$		0			0
$527$	12.2620	−	21.2384i	0.534141	−	0.925159i
$528$		0			0
$529$	19.4709	+	33.7246i	0.846561	+	1.46629i
$530$		0			0
$531$	−10.7852	+	6.74567i	−0.468039	+	0.292737i
$532$		0			0
$533$	−17.0054	−	4.55660i	−0.736588	−	0.197368i
$534$		0			0
$535$	−10.8164	+	18.7345i	−0.467632	+	0.809962i
$536$		0			0
$537$	6.94946	+	5.14007i	0.299891	+	0.221810i
$538$		0			0
$539$	−3.46978	−	3.46978i	−0.149454	−	0.149454i
$540$		0			0
$541$	7.82995	−	7.82995i	0.336636	−	0.336636i	−0.518464	−	0.855100i	$-0.673496\pi$
$541$	7.82995	−	7.82995i	0.336636	−	0.336636i	0.855100	+	0.518464i	$0.173496\pi$
$542$		0			0
$543$	−10.7040	+	14.4719i	−0.459351	+	0.621050i
$544$		0			0
$545$	26.5746	+	15.3429i	1.13833	+	0.657216i
$546$		0			0
$547$	−5.82566	+	21.7416i	−0.249087	+	0.929606i	0.722198	+	0.691686i	$0.243132\pi$
$547$	−5.82566	+	21.7416i	−0.249087	+	0.929606i	−0.971285	+	0.237919i	$0.923535\pi$
$548$		0			0
$549$	−13.8094	+	0.488049i	−0.589373	+	0.0208294i
$550$		0			0
$551$	−4.67438	+	2.69876i	−0.199135	+	0.114971i
$552$		0			0
$553$	0.384019	+	0.221713i	0.0163301	+	0.00942821i
$554$		0			0
$555$	31.9453	+	12.5758i	1.35600	+	0.533814i
$556$		0			0
$557$	25.5918	+	25.5918i	1.08436	+	1.08436i	0.996097	+	0.0882628i	$0.0281315\pi$
$557$	25.5918	+	25.5918i	1.08436	+	1.08436i	0.0882628	+	0.996097i	$0.471868\pi$
$558$		0			0
$559$			21.4755i			0.908315i
$560$		0			0
$561$	−0.594397	+	5.22672i	−0.0250955	+	0.220672i
$562$		0			0
$563$	−3.04735	−	11.3728i	−0.128430	−	0.479308i	0.871508	−	0.490381i	$-0.163142\pi$
$563$	−3.04735	−	11.3728i	−0.128430	−	0.479308i	−0.999939	+	0.0110721i	$0.996476\pi$
$564$		0			0
$565$	11.5357	−	43.0520i	0.485313	−	1.81121i
$566$		0			0
$567$	1.03272	+	0.502617i	0.0433702	+	0.0211079i
$568$		0			0
$569$	−0.819418	−	1.41927i	−0.0343518	−	0.0594990i	0.848338	−	0.529454i	$-0.177603\pi$
$569$	−0.819418	−	1.41927i	−0.0343518	−	0.0594990i	−0.882690	+	0.469955i	$0.844270\pi$
$570$		0			0
$571$	−8.76233	−	32.7015i	−0.366692	−	1.36851i	−0.865112	−	0.501578i	$-0.832753\pi$
$571$	−8.76233	−	32.7015i	−0.366692	−	1.36851i	0.498420	−	0.866936i	$-0.333914\pi$
$572$		0			0
$573$	7.01737	−	5.58427i	0.293155	−	0.233286i
$574$		0			0
$575$	−4.32299			−0.180281
$576$		0			0
$577$	−16.0429			−0.667873			−0.333936	−	0.942596i	$-0.608377\pi$
$577$	−16.0429			−0.667873			−0.333936	+	0.942596i	$0.608377\pi$
$578$		0			0
$579$	42.6036	+	16.7717i	1.77055	+	0.697007i
$580$		0			0
$581$	0.0503166	+	0.187784i	0.00208749	+	0.00779060i
$582$		0			0
$583$	0.00128692	+	0.00222901i	5.32988e−5	+	9.23163e-5i
$584$		0			0
$585$	8.23249	−	8.83571i	0.340372	−	0.365312i
$586$		0			0
$587$	−9.90974	+	36.9837i	−0.409019	+	1.52648i	0.387502	+	0.921869i	$0.373338\pi$
$587$	−9.90974	+	36.9837i	−0.409019	+	1.52648i	−0.796521	+	0.604611i	$0.793329\pi$
$588$		0			0
$589$	−8.25918	−	30.8237i	−0.340313	−	1.27007i
$590$		0			0
$591$	−10.1353	−	7.49641i	−0.416910	−	0.308361i
$592$		0			0
$593$		−	32.2597i		−	1.32475i	−0.749173	−	0.662374i	$-0.769549\pi$
$593$		−	32.2597i		−	1.32475i	0.749173	−	0.662374i	$-0.230451\pi$
$594$		0			0
$595$	−0.822870	−	0.822870i	−0.0337344	−	0.0337344i
$596$		0			0
$597$	0.352351	+	2.35425i	0.0144207	+	0.0963529i
$598$		0			0
$599$	−11.7417	−	6.77905i	−0.479751	−	0.276984i	0.240562	−	0.970634i	$-0.422668\pi$
$599$	−11.7417	−	6.77905i	−0.479751	−	0.276984i	−0.720313	+	0.693649i	$0.756002\pi$
$600$		0			0
$601$	0.496416	−	0.286606i	0.0202492	−	0.0116909i	−0.489841	−	0.871812i	$-0.662945\pi$
$601$	0.496416	−	0.286606i	0.0202492	−	0.0116909i	0.510090	+	0.860121i	$0.329612\pi$
$602$		0			0
$603$	5.29553	−	3.31211i	0.215651	−	0.134880i
$604$		0			0
$605$	−5.73669	+	21.4096i	−0.233230	+	0.870425i
$606$		0			0
$607$	29.1103	+	16.8068i	1.18155	+	0.682168i	0.956373	−	0.292149i	$-0.0943705\pi$
$607$	29.1103	+	16.8068i	1.18155	+	0.682168i	0.225178	+	0.974318i	$0.427704\pi$
$608$		0			0
$609$	−0.0846230	−	0.194508i	−0.00342910	−	0.00788185i
$610$		0			0
$611$	−15.9823	+	15.9823i	−0.646576	+	0.646576i
$612$		0			0
$613$	26.5621	+	26.5621i	1.07283	+	1.07283i	0.997130	+	0.0757042i	$0.0241205\pi$
$613$	26.5621	+	26.5621i	1.07283	+	1.07283i	0.0757042	+	0.997130i	$0.475880\pi$
$614$		0			0
$615$	3.80951	−	33.4983i	0.153614	−	1.35078i
$616$		0			0
$617$	−11.8730	+	20.5647i	−0.477991	+	0.827904i	−0.999682	−	0.0252305i	$-0.991968\pi$
$617$	−11.8730	+	20.5647i	−0.477991	+	0.827904i	0.521691	+	0.853134i	$0.325301\pi$
$618$		0			0
$619$	17.1798	+	4.60330i	0.690513	+	0.185022i	0.586977	−	0.809603i	$-0.300318\pi$
$619$	17.1798	+	4.60330i	0.690513	+	0.185022i	0.103535	+	0.994626i	$0.466984\pi$
$620$		0			0
$621$	−3.18290	+	40.7713i	−0.127725	+	1.63610i
$622$		0			0
$623$	0.676151	+	1.17113i	0.0270894	+	0.0469202i
$624$		0			0
$625$	−10.9760	+	19.0109i	−0.439038	+	0.760436i
$626$		0			0
$627$	4.26219	+	5.35600i	0.170216	+	0.213898i
$628$		0			0
$629$	28.7164	−	28.7164i	1.14500	−	1.14500i
$630$		0			0
$631$	−16.0572			−0.639228			−0.319614	−	0.947548i	$-0.603553\pi$
$631$	−16.0572			−0.639228			−0.319614	+	0.947548i	$0.603553\pi$
$632$		0			0
$633$	−7.96776	−	18.3141i	−0.316690	−	0.727919i
$634$		0			0
$635$	26.7172	−	7.15884i	1.06024	−	0.284090i
$636$		0			0
$637$	12.8717	+	3.44897i	0.509997	+	0.136653i
$638$		0			0
$639$	−3.34362	−	10.9201i	−0.132272	−	0.431991i
$640$		0			0
$641$	35.3930	−	20.4342i	1.39794	−	0.807102i	0.403764	−	0.914863i	$-0.367702\pi$
$641$	35.3930	−	20.4342i	1.39794	−	0.807102i	0.994177	+	0.107761i	$0.0343683\pi$
$642$		0			0
$643$	−33.2700	+	8.91467i	−1.31204	+	0.351560i	−0.845991	−	0.533198i	$-0.820990\pi$
$643$	−33.2700	+	8.91467i	−1.31204	+	0.351560i	−0.466050	+	0.884758i	$0.654323\pi$
$644$		0			0
$645$	−40.6725	+	6.08728i	−1.60148	+	0.239686i
$646$		0			0
$647$			28.1696i			1.10746i	0.832696	+	0.553730i	$0.186796\pi$
$647$			28.1696i			1.10746i	−0.832696	+	0.553730i	$0.813204\pi$
$648$		0			0
$649$		−	2.97943i		−	0.116953i
$650$		0			0
$651$	1.24027	−	0.185626i	0.0486099	−	0.00727525i
$652$		0			0
$653$	8.11558	−	2.17456i	0.317587	−	0.0850972i	−0.0965042	−	0.995333i	$-0.530766\pi$
$653$	8.11558	−	2.17456i	0.317587	−	0.0850972i	0.414091	+	0.910235i	$0.364099\pi$
$654$		0			0
$655$	8.98247	−	5.18603i	0.350974	−	0.202635i
$656$		0			0
$657$	1.64838	+	5.38352i	0.0643096	+	0.210031i
$658$		0			0
$659$	24.7356	+	6.62788i	0.963562	+	0.258186i	0.706107	−	0.708105i	$-0.250450\pi$
$659$	24.7356	+	6.62788i	0.963562	+	0.258186i	0.257455	+	0.966290i	$0.417116\pi$
$660$		0			0
$661$	20.3200	−	5.44473i	0.790357	−	0.211775i	0.159011	−	0.987277i	$-0.449170\pi$
$661$	20.3200	−	5.44473i	0.790357	−	0.211775i	0.631346	+	0.775501i	$0.282503\pi$
$662$		0			0
$663$	−5.69910	−	13.0995i	−0.221335	−	0.508742i
$664$		0			0
$665$	−1.51424			−0.0587198
$666$		0			0
$667$	5.34063	−	5.34063i	0.206790	−	0.206790i
$668$		0			0
$669$	−22.3939	−	28.1408i	−0.865798	−	1.08799i
$670$		0			0
$671$	1.61818	−	2.80277i	0.0624691	−	0.108200i
$672$		0			0
$673$	−12.5221	−	21.6890i	−0.482693	−	0.836048i	0.517110	−	0.855919i	$-0.327008\pi$
$673$	−12.5221	−	21.6890i	−0.482693	−	0.836048i	−0.999803	+	0.0198709i	$0.993674\pi$
$674$		0			0
$675$	−2.35318	−	1.61511i	−0.0905741	−	0.0621658i
$676$		0			0
$677$	−18.3334	−	4.91241i	−0.704608	−	0.188799i	−0.111314	−	0.993785i	$-0.535506\pi$
$677$	−18.3334	−	4.91241i	−0.704608	−	0.188799i	−0.593294	+	0.804986i	$0.702173\pi$
$678$		0			0
$679$	−0.423420	+	0.733386i	−0.0162494	+	0.0281448i
$680$		0			0
$681$	1.55083	−	13.6370i	0.0594281	−	0.522570i
$682$		0			0
$683$	3.70253	+	3.70253i	0.141673	+	0.141673i	0.774386	−	0.632713i	$-0.218059\pi$
$683$	3.70253	+	3.70253i	0.141673	+	0.141673i	−0.632713	+	0.774386i	$0.718059\pi$
$684$		0			0
$685$	10.1803	−	10.1803i	0.388969	−	0.388969i
$686$		0			0
$687$	0.320978	+	0.737774i	0.0122461	+	0.0281478i
$688$		0			0
$689$	−0.00605326	−	0.00349485i	−0.000230611	−	0.000133143i
$690$		0			0
$691$	2.19392	−	8.18783i	0.0834607	−	0.311480i	−0.911558	−	0.411173i	$-0.865119\pi$
$691$	2.19392	−	8.18783i	0.0834607	−	0.311480i	0.995018	+	0.0996929i	$0.0317860\pi$
$692$		0			0
$693$	−0.228066	+	0.142645i	−0.00866352	+	0.00541863i
$694$		0			0
$695$	−19.5631	+	11.2947i	−0.742070	+	0.428434i
$696$		0			0
$697$	−34.5379	−	19.9405i	−1.30822	−	0.755299i
$698$		0			0
$699$	−2.34258	−	15.6521i	−0.0886045	−	0.592015i
$700$		0			0
$701$	−16.2977	−	16.2977i	−0.615557	−	0.615557i	0.328831	−	0.944389i	$-0.393345\pi$
$701$	−16.2977	−	16.2977i	−0.615557	−	0.615557i	−0.944389	+	0.328831i	$0.893345\pi$
$702$		0			0
$703$		−	52.8439i		−	1.99304i
$704$		0			0
$705$	−34.7992	−	25.7388i	−1.31062	−	0.969378i
$706$		0			0
$707$	0.413484	+	1.54314i	0.0155507	+	0.0580359i
$708$		0			0
$709$	4.99557	−	18.6437i	0.187613	−	0.700180i	−0.806443	−	0.591311i	$-0.798610\pi$
$709$	4.99557	−	18.6437i	0.187613	−	0.700180i	0.994056	−	0.108869i	$-0.0347229\pi$
$710$		0			0
$711$	−7.10604	+	7.62672i	−0.266497	+	0.286024i
$712$		0			0
$713$	22.3267	+	38.6710i	0.836142	+	1.44824i
$714$		0			0
$715$	0.732065	+	2.73210i	0.0273777	+	0.102175i
$716$		0			0
$717$	−11.7917	−	4.64202i	−0.440370	−	0.173359i
$718$		0			0
$719$	−24.2401			−0.904003			−0.452002	−	0.892017i	$-0.649290\pi$
$719$	−24.2401			−0.904003			−0.452002	+	0.892017i	$0.649290\pi$
$720$		0			0
$721$	1.07669			0.0400980
$722$		0			0
$723$	3.38438	−	2.69322i	0.125866	−	0.100162i
$724$		0			0
$725$	0.136428	+	0.509157i	0.00506682	+	0.0189096i
$726$		0			0
$727$	8.10074	+	14.0309i	0.300440	+	0.520377i	0.976236	−	0.216712i	$-0.0695332\pi$
$727$	8.10074	+	14.0309i	0.300440	+	0.520377i	−0.675796	+	0.737089i	$0.736200\pi$
$728$		0			0
$729$	−16.9652	+	21.0044i	−0.628340	+	0.777939i
$730$		0			0
$731$	−12.5910	+	46.9902i	−0.465694	+	1.73800i
$732$		0			0
$733$	−2.15479	−	8.04180i	−0.0795891	−	0.297031i	0.914646	−	0.404257i	$-0.132470\pi$
$733$	−2.15479	−	8.04180i	−0.0795891	−	0.297031i	−0.994235	+	0.107226i	$0.965803\pi$
$734$		0			0
$735$	−2.88349	+	25.3555i	−0.106359	+	0.935251i
$736$		0			0
$737$			1.46289i			0.0538863i
$738$		0			0
$739$	−22.8405	−	22.8405i	−0.840203	−	0.840203i	0.148682	−	0.988885i	$-0.452497\pi$
$739$	−22.8405	−	22.8405i	−0.840203	−	0.840203i	−0.988885	+	0.148682i	$0.952497\pi$
$740$		0			0
$741$	−17.2966	−	6.80909i	−0.635405	−	0.250138i
$742$		0			0
$743$	7.19608	+	4.15466i	0.263999	+	0.152420i	0.626157	−	0.779697i	$-0.284627\pi$
$743$	7.19608	+	4.15466i	0.263999	+	0.152420i	−0.362159	+	0.932116i	$0.617960\pi$
$744$		0			0
$745$	0.385931	−	0.222817i	0.0141394	−	0.00816339i
$746$		0			0
$747$	−4.56734	+	0.161417i	−0.167110	+	0.00590595i
$748$		0			0
$749$	−0.338684	+	1.26399i	−0.0123752	+	0.0461850i
$750$		0			0
$751$	28.0215	+	16.1782i	1.02252	+	0.590352i	0.914833	−	0.403833i	$-0.132322\pi$
$751$	28.0215	+	16.1782i	1.02252	+	0.590352i	0.107687	+	0.994185i	$0.465656\pi$
$752$		0			0
$753$	4.04390	−	5.46742i	0.147368	−	0.199244i
$754$		0			0
$755$	3.42502	−	3.42502i	0.124649	−	0.124649i
$756$		0			0
$757$	3.76265	+	3.76265i	0.136756	+	0.136756i	0.772171	−	0.635415i	$-0.219171\pi$
$757$	3.76265	+	3.76265i	0.136756	+	0.136756i	−0.635415	+	0.772171i	$0.719171\pi$
$758$		0			0
$759$	−7.70069	−	5.69570i	−0.279517	−	0.206741i
$760$		0			0
$761$	−13.1168	+	22.7190i	−0.475485	+	0.823564i	−0.999606	−	0.0280801i	$-0.991061\pi$
$761$	−13.1168	+	22.7190i	−0.475485	+	0.823564i	0.524121	+	0.851644i	$0.324394\pi$
$762$		0			0
$763$	1.79295	+	0.480419i	0.0649090	+	0.0173923i
$764$		0			0
$765$	23.1938	−	14.5066i	0.838572	−	0.524489i
$766$		0			0
$767$	4.04557	+	7.00713i	0.146077	+	0.253013i
$768$		0			0
$769$	−9.31591	+	16.1356i	−0.335940	+	0.581865i	−0.983665	−	0.180009i	$-0.942387\pi$
$769$	−9.31591	+	16.1356i	−0.335940	+	0.581865i	0.647725	+	0.761874i	$0.275721\pi$
$770$		0			0
$771$	7.04741	−	17.9019i	0.253806	−	0.644722i
$772$		0			0
$773$	4.69430	−	4.69430i	0.168842	−	0.168842i	−0.617628	−	0.786470i	$-0.711906\pi$
$773$	4.69430	−	4.69430i	0.168842	−	0.168842i	0.786470	+	0.617628i	$0.211906\pi$
$774$		0			0
$775$	−3.11641			−0.111945
$776$		0			0
$777$	2.06343	+	0.234659i	0.0740252	+	0.00841834i
$778$		0			0
$779$	−50.1255	+	13.4311i	−1.79593	+	0.481218i
$780$		0			0
$781$	2.58368	+	0.692294i	0.0924512	+	0.0247722i
$782$		0			0
$783$	4.90245	−	0.911813i	0.175199	−	0.0325855i
$784$		0			0
$785$	−30.6704	+	17.7076i	−1.09467	+	0.632010i
$786$		0			0
$787$	−43.7964	+	11.7352i	−1.56117	+	0.418315i	−0.933035	−	0.359786i	$-0.882850\pi$
$787$	−43.7964	+	11.7352i	−1.56117	+	0.418315i	−0.628139	+	0.778101i	$0.716183\pi$
$788$		0			0
$789$	20.7128	+	26.0283i	0.737394	+	0.926631i
$790$		0			0
$791$		−	2.69611i		−	0.0958625i
$792$		0			0
$793$			8.78888i			0.312102i
$794$		0			0
$795$	0.00490310	−	0.0124549i	0.000173895	−	0.000441731i
$796$		0			0
$797$	−36.4751	+	9.77347i	−1.29201	+	0.346194i	−0.838425	−	0.545017i	$-0.816523\pi$
$797$	−36.4751	+	9.77347i	−1.29201	+	0.346194i	−0.453589	+	0.891211i	$0.649857\pi$
$798$		0			0
$799$	−44.3411	+	25.6004i	−1.56868	+	0.905676i
$800$		0			0
$801$	−30.3971	+	9.30731i	−1.07403	+	0.328858i
$802$		0			0
$803$	−1.27374	−	0.341296i	−0.0449492	−	0.0120441i
$804$		0			0
$805$	2.04670	−	0.548411i	0.0721366	−	0.0193289i
$806$		0			0
$807$	11.1645	−	15.0946i	0.393008	−	0.531353i
$808$		0			0
$809$	24.0071			0.844045			0.422023	−	0.906585i	$-0.361320\pi$
$809$	24.0071			0.844045			0.422023	+	0.906585i	$0.361320\pi$
$810$		0			0
$811$	0.243845	−	0.243845i	0.00856256	−	0.00856256i	−0.702813	−	0.711375i	$-0.748073\pi$
$811$	0.243845	−	0.243845i	0.00856256	−	0.00856256i	0.711375	+	0.702813i	$0.248073\pi$
$812$		0			0
$813$	22.2346	−	3.32776i	0.779800	−	0.116710i
$814$		0			0
$815$	0.731560	−	1.26710i	0.0256254	−	0.0443846i
$816$		0			0
$817$	31.6507	+	54.8205i	1.10732	+	1.91793i
$818$		0			0
$819$	0.342686	−	0.645154i	0.0119744	−	0.0225435i
$820$		0			0
$821$	−46.3025	−	12.4067i	−1.61597	−	0.432998i	−0.666156	−	0.745813i	$-0.732061\pi$
$821$	−46.3025	−	12.4067i	−1.61597	−	0.432998i	−0.949814	+	0.312815i	$0.898728\pi$
$822$		0			0
$823$	0.737958	−	1.27818i	0.0257236	−	0.0445546i	−0.852877	−	0.522112i	$-0.825144\pi$
$823$	0.737958	−	1.27818i	0.0257236	−	0.0445546i	0.878601	+	0.477557i	$0.158478\pi$
$824$		0			0
$825$	0.612973	−	0.266682i	0.0213410	−	0.00928466i
$826$		0			0
$827$	−11.5464	−	11.5464i	−0.401509	−	0.401509i	0.477256	−	0.878764i	$-0.341632\pi$
$827$	−11.5464	−	11.5464i	−0.401509	−	0.401509i	−0.878764	+	0.477256i	$0.841632\pi$
$828$		0			0
$829$	34.7961	−	34.7961i	1.20852	−	1.20852i	0.237010	−	0.971507i	$-0.423833\pi$
$829$	34.7961	−	34.7961i	1.20852	−	1.20852i	0.971507	−	0.237010i	$-0.0761675\pi$
$830$		0			0
$831$	−42.7303	−	4.85940i	−1.48230	−	0.168571i
$832$		0			0
$833$	26.1424	+	15.0933i	0.905781	+	0.522953i
$834$		0			0
$835$	5.88992	−	21.9815i	0.203829	−	0.760700i
$836$		0			0
$837$	−2.29453	+	29.3917i	−0.0793106	+	1.01593i
$838$		0			0
$839$	41.3065	−	23.8483i	1.42606	−	0.823335i	0.429252	−	0.903185i	$-0.358777\pi$
$839$	41.3065	−	23.8483i	1.42606	−	0.823335i	0.996807	+	0.0798497i	$0.0254440\pi$
$840$		0			0
$841$	24.3172	+	14.0395i	0.838523	+	0.484122i
$842$		0			0
$843$	10.0053	−	7.96200i	0.344601	−	0.274226i
$844$		0			0
$845$	13.9615	+	13.9615i	0.480290	+	0.480290i
$846$		0			0
$847$			1.34076i			0.0460692i
$848$		0			0
$849$	9.86087	−	4.29009i	0.338424	−	0.147236i
$850$		0			0
$851$	19.1384	+	71.4254i	0.656055	+	2.44843i
$852$		0			0
$853$	−11.3911	+	42.5120i	−0.390023	+	1.45558i	0.440072	+	0.897962i	$0.354953\pi$
$853$	−11.3911	+	42.5120i	−0.390023	+	1.45558i	−0.830095	+	0.557622i	$0.811714\pi$
$854$		0			0
$855$	7.99302	−	34.6881i	0.273355	−	1.18631i
$856$		0			0
$857$	−4.36756	−	7.56483i	−0.149193	−	0.258410i	0.781736	−	0.623609i	$-0.214334\pi$
$857$	−4.36756	−	7.56483i	−0.149193	−	0.258410i	−0.930929	+	0.365199i	$0.881001\pi$
$858$		0			0
$859$	−12.9902	−	48.4800i	−0.443219	−	1.65411i	−0.720597	−	0.693354i	$-0.756132\pi$
$859$	−12.9902	−	48.4800i	−0.443219	−	1.65411i	0.277378	−	0.960761i	$-0.410534\pi$
$860$		0			0
$861$	−0.301865	−	2.01693i	−0.0102875	−	0.0687366i
$862$		0			0
$863$	−3.87853			−0.132027			−0.0660134	−	0.997819i	$-0.521028\pi$
$863$	−3.87853			−0.132027			−0.0660134	+	0.997819i	$0.521028\pi$
$864$		0			0
$865$	10.0817			0.342789
$866$		0			0
$867$	−0.431590	−	2.88369i	−0.0146576	−	0.0979353i
$868$		0			0
$869$	−0.631896	−	2.35827i	−0.0214356	−	0.0799988i
$870$		0			0
$871$	−1.98636	−	3.44049i	−0.0673054	−	0.116576i
$872$		0			0
$873$	−14.5653	−	13.5709i	−0.492959	−	0.459305i
$874$		0			0
$875$	−0.386679	+	1.44311i	−0.0130721	+	0.0487859i
$876$		0			0
$877$	5.43592	+	20.2871i	0.183558	+	0.685047i	0.994935	+	0.100524i	$0.0320519\pi$
$877$	5.43592	+	20.2871i	0.183558	+	0.685047i	−0.811377	+	0.584524i	$0.801281\pi$
$878$		0			0
$879$	−39.4856	+	17.1787i	−1.33182	+	0.579424i
$880$		0			0
$881$		−	7.45496i		−	0.251164i	−0.992083	−	0.125582i	$-0.959920\pi$
$881$		−	7.45496i		−	0.251164i	0.992083	−	0.125582i	$-0.0400798\pi$
$882$		0			0
$883$	9.55597	+	9.55597i	0.321584	+	0.321584i	0.849375	−	0.527791i	$-0.176979\pi$
$883$	9.55597	+	9.55597i	0.321584	+	0.321584i	−0.527791	+	0.849375i	$0.676979\pi$
$884$		0			0
$885$	−12.1241	+	9.64811i	−0.407547	+	0.324318i
$886$		0			0
$887$	41.0581	+	23.7049i	1.37860	+	0.795934i	0.991991	−	0.126311i	$-0.0403138\pi$
$887$	41.0581	+	23.7049i	1.37860	+	0.795934i	0.386607	+	0.922245i	$0.373647\pi$
$888$		0			0
$889$	1.44899	−	0.836573i	0.0485975	−	0.0280578i
$890$		0			0
$891$	−2.06383	−	5.97747i	−0.0691409	−	0.200253i
$892$		0			0
$893$	−17.2433	+	64.3530i	−0.577027	+	2.15349i
$894$		0			0
$895$	9.11780	+	5.26416i	0.304774	+	0.175962i
$896$		0			0
$897$	25.8446	+	2.93912i	0.862926	+	0.0981342i
$898$		0			0
$899$	3.85003	−	3.85003i	0.128406	−	0.128406i
$900$		0			0
$901$	−0.0111960	−	0.0111960i	−0.000372994	−	0.000372994i
$902$		0			0
$903$	−2.28116	+	0.992448i	−0.0759124	+	0.0330266i
$904$		0			0
$905$	−10.9624	+	18.9874i	−0.364402	+	0.631162i
$906$		0			0
$907$	−13.6705	−	3.66301i	−0.453923	−	0.121628i	0.0246114	−	0.999697i	$-0.492165\pi$
$907$	−13.6705	−	3.66301i	−0.453923	−	0.121628i	−0.478534	+	0.878069i	$0.658832\pi$
$908$		0			0
$909$	−37.5327	+	1.32647i	−1.24488	+	0.0439963i
$910$		0			0
$911$	20.0062	+	34.6517i	0.662834	+	1.14806i	0.979868	+	0.199648i	$0.0639799\pi$
$911$	20.0062	+	34.6517i	0.662834	+	1.14806i	−0.317034	+	0.948414i	$0.602687\pi$
$912$		0			0
$913$	0.535197	−	0.926988i	0.0177124	−	0.0306788i
$914$		0			0
$915$	−16.6453	+	2.49123i	−0.550277	+	0.0823576i
$916$		0			0
$917$	0.443647	−	0.443647i	0.0146505	−	0.0146505i
$918$		0			0
$919$	18.6876			0.616446			0.308223	−	0.951314i	$-0.400266\pi$
$919$	18.6876			0.616446			0.308223	+	0.951314i	$0.400266\pi$
$920$		0			0
$921$	−25.3117	+	34.2218i	−0.834049	+	1.12765i
$922$		0			0
$923$	−7.01641	+	1.88004i	−0.230948	+	0.0618823i
$924$		0			0
$925$	−4.98486	−	1.33569i	−0.163901	−	0.0439172i
$926$		0			0
$927$	−5.68337	+	24.6647i	−0.186666	+	0.810094i
$928$		0			0
$929$	−8.76538	+	5.06070i	−0.287583	+	0.166036i	−0.636851	−	0.770987i	$-0.719763\pi$
$929$	−8.76538	+	5.06070i	−0.287583	+	0.166036i	0.349268	+	0.937023i	$0.386430\pi$
$930$		0			0
$931$	37.9409	−	10.1662i	1.24346	−	0.333185i
$932$		0			0
$933$	−8.75007	+	22.2270i	−0.286464	+	0.727681i
$934$		0			0
$935$			6.40729i			0.209541i
$936$		0			0
$937$		−	19.1375i		−	0.625194i	−0.949886	−	0.312597i	$-0.898801\pi$
$937$		−	19.1375i		−	0.625194i	0.949886	−	0.312597i	$-0.101199\pi$
$938$		0			0
$939$	−21.9641	−	27.6008i	−0.716772	−	0.900717i
$940$		0			0
$941$	41.4559	−	11.1081i	1.35142	−	0.362113i	0.490764	−	0.871292i	$-0.336718\pi$
$941$	41.4559	−	11.1081i	1.35142	−	0.362113i	0.860660	+	0.509179i	$0.170051\pi$
$942$		0			0
$943$	62.8868	−	36.3077i	2.04788	−	1.18234i
$944$		0			0
$945$	1.31899	+	0.466145i	0.0429069	+	0.0151637i
$946$		0			0
$947$	−45.0535	−	12.0721i	−1.46404	−	0.392289i	−0.563159	−	0.826349i	$-0.690414\pi$
$947$	−45.0535	−	12.0721i	−1.46404	−	0.392289i	−0.900884	+	0.434060i	$0.857081\pi$
$948$		0			0
$949$	3.45904	−	0.926848i	0.112285	−	0.0300867i
$950$		0			0
$951$	36.1920	+	4.11585i	1.17361	+	0.133466i
$952$		0			0
$953$	20.2249			0.655149			0.327575	−	0.944825i	$-0.393769\pi$
$953$	20.2249			0.655149			0.327575	+	0.944825i	$0.393769\pi$
$954$		0			0
$955$	7.72399	−	7.72399i	0.249943	−	0.249943i
$956$		0			0
$957$	−0.427810	+	1.08673i	−0.0138291	+	0.0351289i
$958$		0			0
$959$	0.435445	−	0.754212i	0.0140612	−	0.0243548i
$960$		0			0
$961$	0.595170	+	1.03087i	0.0191990	+	0.0332537i
$962$		0			0
$963$	−27.1675	−	14.4305i	−0.875459	−	0.465018i
$964$		0			0
$965$	53.8680	+	14.4339i	1.73407	+	0.464644i
$966$		0			0
$967$	−15.9815	+	27.6807i	−0.513930	+	0.890152i	0.485940	+	0.873992i	$0.338477\pi$
$967$	−15.9815	+	27.6807i	−0.513930	+	0.890152i	−0.999869	+	0.0161601i	$0.994856\pi$
$968$		0			0
$969$	−33.8542	−	25.0398i	−1.08755	−	0.804395i
$970$		0			0
$971$	4.69660	+	4.69660i	0.150721	+	0.150721i	0.778440	−	0.627719i	$-0.216011\pi$
$971$	4.69660	+	4.69660i	0.150721	+	0.150721i	−0.627719	+	0.778440i	$0.716011\pi$
$972$		0			0
$973$	−0.966226	+	0.966226i	−0.0309758	+	0.0309758i
$974$		0			0
$975$	−1.07950	+	1.45951i	−0.0345718	+	0.0467417i
$976$		0			0
$977$	−22.7888	−	13.1571i	−0.729079	−	0.420934i	0.0890064	−	0.996031i	$-0.471631\pi$
$977$	−22.7888	−	13.1571i	−0.729079	−	0.420934i	−0.818085	+	0.575097i	$0.804964\pi$
$978$		0			0
$979$	1.92707	−	7.19193i	0.0615895	−	0.229855i
$980$		0			0
$981$	−20.4695	+	38.5367i	−0.653542	+	1.23038i
$982$		0			0
$983$	−19.6448	+	11.3420i	−0.626573	+	0.361752i	−0.779424	−	0.626497i	$-0.784488\pi$
$983$	−19.6448	+	11.3420i	−0.626573	+	0.361752i	0.152851	+	0.988249i	$0.451155\pi$
$984$		0			0
$985$	−13.2976	−	7.67740i	−0.423698	−	0.244622i
$986$		0			0
$987$	−2.43627	−	0.959079i	−0.0775472	−	0.0305278i
$988$		0			0
$989$	−62.6343	−	62.6343i	−1.99165	−	1.99165i
$990$		0			0
$991$			13.0577i			0.414793i	0.978257	+	0.207396i	$0.0664990\pi$
$991$			13.0577i			0.414793i	−0.978257	+	0.207396i	$0.933501\pi$
$992$		0			0
$993$	3.45722	−	30.4004i	0.109711	−	0.964728i
$994$		0			0
$995$	0.750435	+	2.80066i	0.0237904	+	0.0887870i
$996$		0			0
$997$	−2.05844	+	7.68222i	−0.0651916	+	0.243298i	−0.990831	−	0.135109i	$-0.956861\pi$
$997$	−2.05844	+	7.68222i	−0.0651916	+	0.243298i	0.925639	+	0.378407i	$0.123528\pi$
$998$		0			0
$999$	−16.2675	+	46.0301i	−0.514680	+	1.45633i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.y.a.527.11		88
3.2	odd	2		1728.2.z.a.719.5		88
4.3	odd	2		144.2.u.a.59.19	yes	88
9.2	odd	6	inner	576.2.y.a.335.22		88
9.7	even	3		1728.2.z.a.143.5		88
12.11	even	2		432.2.v.a.395.4		88
16.3	odd	4	inner	576.2.y.a.239.22		88
16.13	even	4		144.2.u.a.131.19	yes	88
36.7	odd	6		432.2.v.a.251.4		88
36.11	even	6		144.2.u.a.11.19	✓	88
48.29	odd	4		432.2.v.a.179.4		88
48.35	even	4		1728.2.z.a.1583.5		88
144.29	odd	12		144.2.u.a.83.19	yes	88
144.61	even	12		432.2.v.a.35.4		88
144.83	even	12	inner	576.2.y.a.47.11		88
144.115	odd	12		1728.2.z.a.1007.5		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.19	✓	88	36.11	even	6
144.2.u.a.59.19	yes	88	4.3	odd	2
144.2.u.a.83.19	yes	88	144.29	odd	12
144.2.u.a.131.19	yes	88	16.13	even	4
432.2.v.a.35.4		88	144.61	even	12
432.2.v.a.179.4		88	48.29	odd	4
432.2.v.a.251.4		88	36.7	odd	6
432.2.v.a.395.4		88	12.11	even	2
576.2.y.a.47.11		88	144.83	even	12	inner
576.2.y.a.239.22		88	16.3	odd	4	inner
576.2.y.a.335.22		88	9.2	odd	6	inner
576.2.y.a.527.11		88	1.1	even	1	trivial
1728.2.z.a.143.5		88	9.7	even	3
1728.2.z.a.719.5		88	3.2	odd	2
1728.2.z.a.1007.5		88	144.115	odd	12
1728.2.z.a.1583.5		88	48.35	even	4

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.256373 + 1.71297i) q^{3} +(0.546024 + 2.03779i) q^{5} +(0.0638076 + 0.110518i) q^{7} +(-2.86855 + 0.878321i) q^{9} +(0.181856 - 0.678695i) q^{11} +(0.493860 + 1.84311i) q^{13} +(-3.35069 + 1.45776i) q^{15} +4.32243i q^{17} +(3.97707 + 3.97707i) q^{19} +(-0.172956 + 0.137635i) q^{21} +(-6.81589 - 3.93516i) q^{23} +(0.475689 - 0.274639i) q^{25} +(-2.23996 - 4.68856i) q^{27} +(-0.248377 + 0.926957i) q^{29} +(-4.91353 - 2.83683i) q^{31} +(1.20921 + 0.137514i) q^{33} +(-0.190372 + 0.190372i) q^{35} +(-6.64358 - 6.64358i) q^{37} +(-3.03058 + 1.31849i) q^{39} +(-4.61325 + 7.99038i) q^{41} +(10.8712 + 2.91294i) q^{43} +(-3.35613 - 5.36590i) q^{45} +(5.92267 + 10.2584i) q^{47} +(3.49186 - 6.04807i) q^{49} +(-7.40421 + 1.10816i) q^{51} +(-0.00259022 + 0.00259022i) q^{53} +1.48233 q^{55} +(-5.79299 + 7.83221i) q^{57} +(4.09587 - 1.09748i) q^{59} +(4.44908 + 1.19213i) q^{61} +(-0.280105 - 0.260982i) q^{63} +(-3.48621 + 2.01276i) q^{65} +(-2.01106 + 0.538862i) q^{67} +(4.99340 - 12.6843i) q^{69} +3.80683i q^{71} -1.87674i q^{73} +(0.592403 + 0.744431i) q^{75} +(0.0866118 - 0.0232076i) q^{77} +(3.00919 - 1.73736i) q^{79} +(7.45710 - 5.03901i) q^{81} +(1.47149 + 0.394284i) q^{83} +(-8.80821 + 2.36015i) q^{85} +(-1.65153 - 0.187816i) q^{87} +10.5967 q^{89} +(-0.172185 + 0.172185i) q^{91} +(3.59971 - 9.14402i) q^{93} +(-5.93284 + 10.2760i) q^{95} +(3.31795 + 5.74685i) q^{97} +(0.0744506 + 2.10659i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55}+ \cdots - 46 q^{99}+O(q^{100}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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