LMFDB - Embedded newform 576.2.y.a.47.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(47,576)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

N = Newforms(chi, 2, names="a")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$88$
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			47.11
Character	$\chi$	$=$	576.47
Dual form			576.2.y.a.527.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	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	−0.729600	−	0.683874i	$-0.760294\pi$
$5$	0.546024	−	2.03779i	0.244189	−	0.911327i	0.973789	−	0.227452i	$-0.0730396\pi$
$6$		0			0
$7$	0.0638076	−	0.110518i	0.0241170	−	0.0417719i	−0.853715	−	0.520741i	$-0.825656\pi$
$7$	0.0638076	−	0.110518i	0.0241170	−	0.0417719i	0.877832	+	0.478969i	$0.158989\pi$
$8$		0			0
$9$	−2.86855	−	0.878321i	−0.956182	−	0.292774i
$10$		0			0
$11$	0.181856	+	0.678695i	0.0548316	+	0.204634i	0.987907	−	0.155046i	$-0.0495525\pi$
$11$	0.181856	+	0.678695i	0.0548316	+	0.204634i	−0.933076	+	0.359680i	$0.882886\pi$
$12$		0			0
$13$	0.493860	−	1.84311i	0.136972	−	0.511187i	−0.863010	−	0.505187i	$-0.831424\pi$
$13$	0.493860	−	1.84311i	0.136972	−	0.511187i	0.999982	−	0.00599967i	$-0.00190977\pi$
$14$		0			0
$15$	−3.35069	−	1.45776i	−0.865144	−	0.376391i
$16$		0			0
$17$		−	4.32243i		−	1.04834i	−0.851612	−	0.524172i	$-0.824375\pi$
$17$		−	4.32243i		−	1.04834i	0.851612	−	0.524172i	$-0.175625\pi$
$18$		0			0
$19$	3.97707	−	3.97707i	0.912401	−	0.912401i	−0.0840594	−	0.996461i	$-0.526789\pi$
$19$	3.97707	−	3.97707i	0.912401	−	0.912401i	0.996461	+	0.0840594i	$0.0267886\pi$
$20$		0			0
$21$	−0.172956	−	0.137635i	−0.0377420	−	0.0300343i
$22$		0			0
$23$	−6.81589	+	3.93516i	−1.42121	+	0.820537i	−0.996403	−	0.0847463i	$-0.972992\pi$
$23$	−6.81589	+	3.93516i	−1.42121	+	0.820537i	−0.424809	+	0.905283i	$0.639659\pi$
$24$		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	0.939023	−	0.343855i	$-0.111733\pi$
$29$	−0.248377	−	0.926957i	−0.0461225	−	0.172132i	−0.985145	+	0.171724i	$0.945066\pi$
$30$		0			0
$31$	−4.91353	+	2.83683i	−0.882496	+	0.509509i	−0.871480	−	0.490430i	$-0.836840\pi$
$31$	−4.91353	+	2.83683i	−0.882496	+	0.509509i	−0.0110152	+	0.999939i	$0.503506\pi$
$32$		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	−0.0969037	+	0.995294i	$0.530894\pi$
$37$	−6.64358	+	6.64358i	−1.09220	+	1.09220i	−0.995294	+	0.0969037i	$0.969106\pi$
$38$		0			0
$39$	−3.03058	−	1.31849i	−0.485281	−	0.211128i
$40$		0			0
$41$	−4.61325	−	7.99038i	−0.720469	−	1.24789i	−0.960812	−	0.277200i	$-0.910593\pi$
$41$	−4.61325	−	7.99038i	−0.720469	−	1.24789i	0.240344	−	0.970688i	$-0.422740\pi$
$42$		0			0
$43$	10.8712	−	2.91294i	1.65785	−	0.444219i	0.696053	−	0.717991i	$-0.254938\pi$
$43$	10.8712	−	2.91294i	1.65785	−	0.444219i	0.961795	+	0.273772i	$0.0882713\pi$
$44$		0			0
$45$	−3.35613	+	5.36590i	−0.500302	+	0.799902i
$46$		0			0
$47$	5.92267	−	10.2584i	0.863910	−	1.49634i	−0.00421475	−	0.999991i	$-0.501342\pi$
$47$	5.92267	−	10.2584i	0.863910	−	1.49634i	0.868125	−	0.496345i	$-0.165325\pi$
$48$		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	0.706929	−	0.707285i	$-0.250080\pi$
$53$	−0.00259022	−	0.00259022i	−0.000355794	−	0.000355794i	−0.707285	+	0.706929i	$0.750080\pi$
$54$		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	0.515382	−	0.856960i	$-0.327650\pi$
$59$	4.09587	+	1.09748i	0.533237	+	0.142880i	0.0178541	+	0.999841i	$0.494317\pi$
$60$		0			0
$61$	4.44908	−	1.19213i	0.569646	−	0.152636i	0.0375117	−	0.999296i	$-0.488057\pi$
$61$	4.44908	−	1.19213i	0.569646	−	0.152636i	0.532134	+	0.846660i	$0.321390\pi$
$62$		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	0.133872	−	0.990999i	$-0.457259\pi$
$67$	−2.01106	−	0.538862i	−0.245690	−	0.0658325i	−0.379563	+	0.925166i	$0.623925\pi$
$68$		0			0
$69$	4.99340	+	12.6843i	0.601134	+	1.52701i
$70$		0			0
$71$		−	3.80683i		−	0.451788i	−0.974152	−	0.225894i	$-0.927470\pi$
$71$		−	3.80683i		−	0.451788i	0.974152	−	0.225894i	$-0.0725303\pi$
$72$		0			0
$73$			1.87674i			0.219656i	0.993951	+	0.109828i	$0.0350300\pi$
$73$			1.87674i			0.219656i	−0.993951	+	0.109828i	$0.964970\pi$
$74$		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	0.659635	−	0.751586i	$-0.270711\pi$
$79$	3.00919	+	1.73736i	0.338560	+	0.195468i	−0.321075	+	0.947054i	$0.604044\pi$
$80$		0			0
$81$	7.45710	+	5.03901i	0.828567	+	0.559890i
$82$		0			0
$83$	1.47149	−	0.394284i	0.161517	−	0.0432783i	−0.177155	−	0.984183i	$-0.556689\pi$
$83$	1.47149	−	0.394284i	0.161517	−	0.0432783i	0.338671	+	0.940905i	$0.390023\pi$
$84$		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	−0.646959	−	0.762525i	$-0.723960\pi$
$97$	3.31795	−	5.74685i	0.336886	−	0.583504i	0.983845	+	0.179021i	$0.0572928\pi$
$98$		0			0
$99$	0.0744506	−	2.10659i	0.00748257	−	0.211721i
$100$		0			0
$101$	12.0922	−	3.24008i	1.20321	−	0.322400i	0.399118	−	0.916899i	$-0.369316\pi$
$101$	12.0922	−	3.24008i	1.20321	−	0.322400i	0.804096	+	0.594499i	$0.202650\pi$
$102$		0			0
$103$	4.21850	+	7.30665i	0.415661	+	0.719946i	0.995498	−	0.0947868i	$-0.0302169\pi$
$103$	4.21850	+	7.30665i	0.415661	+	0.719946i	−0.579837	+	0.814733i	$0.696884\pi$
$104$		0			0
$105$	−0.374908	+	0.277295i	−0.0365873	+	0.0270613i
$106$		0			0
$107$	7.25071	−	7.25071i	0.700953	−	0.700953i	−0.263662	−	0.964615i	$-0.584930\pi$
$107$	7.25071	−	7.25071i	0.700953	−	0.700953i	0.964615	+	0.263662i	$0.0849304\pi$
$108$		0			0
$109$	10.2850	+	10.2850i	0.985128	+	0.985128i	0.999891	−	0.0147630i	$-0.00469937\pi$
$109$	10.2850	+	10.2850i	0.985128	+	0.985128i	−0.0147630	+	0.999891i	$0.504699\pi$
$110$		0			0
$111$	9.67702	+	13.0835i	0.918503	+	1.24183i
$112$		0			0
$113$	−18.2964	+	10.5634i	−1.72118	+	0.993722i	−0.804652	+	0.593747i	$0.797648\pi$
$113$	−18.2964	+	10.5634i	−1.72118	+	0.993722i	−0.916526	+	0.399976i	$0.869019\pi$
$114$		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	$0.197612\pi$
$127$			13.1109i			1.16340i	−0.813403	+	0.581700i	$0.802388\pi$
$128$		0			0
$129$	−2.20269	−	19.3689i	−0.193936	−	1.70534i
$130$		0			0
$131$	−1.27247	+	4.74891i	−0.111176	+	0.414914i	−0.998972	−	0.0453222i	$-0.985569\pi$
$131$	−1.27247	+	4.74891i	−0.111176	+	0.414914i	0.887797	+	0.460236i	$0.152235\pi$
$132$		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	−0.974170	−	0.225817i	$-0.927495\pi$
$137$	−3.41217	+	5.91005i	−0.291521	+	0.504930i	0.682648	+	0.730747i	$0.260828\pi$
$138$		0			0
$139$	2.77132	−	10.3427i	0.235061	−	0.877258i	−0.743061	−	0.669224i	$-0.766627\pi$
$139$	2.77132	−	10.3427i	0.235061	−	0.877258i	0.978121	−	0.208035i	$-0.0667066\pi$
$140$		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	−0.968129	−	0.250452i	$-0.919421\pi$
$149$	−0.0546714	+	0.204036i	−0.00447885	+	0.0167153i	0.963650	+	0.267167i	$0.0860875\pi$
$150$		0			0
$151$	−1.14798	+	1.98835i	−0.0934210	+	0.161810i	−0.908949	−	0.416908i	$-0.863114\pi$
$151$	−1.14798	+	1.98835i	−0.0934210	+	0.161810i	0.815528	+	0.578718i	$0.196447\pi$
$152$		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	−0.543799	−	0.839216i	$-0.683015\pi$
$157$	4.34480	−	16.2150i	0.346753	−	1.29410i	0.890551	−	0.454883i	$-0.150319\pi$
$158$		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	−0.726051	−	0.687640i	$-0.758647\pi$
$163$	−0.490399	+	0.490399i	−0.0384110	+	0.0384110i	0.687640	+	0.726051i	$0.258647\pi$
$164$		0			0
$165$	0.380031	−	2.53920i	0.0295854	−	0.197676i
$166$		0			0
$167$	−9.34175	+	5.39346i	−0.722887	+	0.417359i	−0.815814	−	0.578314i	$-0.803711\pi$
$167$	−9.34175	+	5.39346i	−0.722887	+	0.417359i	0.0929276	+	0.995673i	$0.470378\pi$
$168$		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	0.996871	−	0.0790394i	$-0.0251853\pi$
$173$	1.23685	+	4.61598i	0.0940358	+	0.350946i	−0.902836	+	0.429986i	$0.858519\pi$
$174$		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	0.826578	−	0.562822i	$-0.190284\pi$
$179$	3.52882	+	3.52882i	0.263756	+	0.263756i	−0.562822	+	0.826578i	$0.690284\pi$
$180$		0			0
$181$	7.34860	−	7.34860i	0.546217	−	0.546217i	−0.379127	−	0.925344i	$-0.623776\pi$
$181$	7.34860	−	7.34860i	0.546217	−	0.546217i	0.925344	+	0.379127i	$0.123776\pi$
$182$		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	−0.944357	−	0.328921i	$-0.893315\pi$
$191$	−2.58888	+	4.48407i	−0.187325	+	0.324456i	0.757033	+	0.653377i	$0.226648\pi$
$192$		0			0
$193$	13.2173	+	22.8930i	0.951401	+	1.64787i	0.742398	+	0.669960i	$0.233689\pi$
$193$	13.2173	+	22.8930i	0.951401	+	1.64787i	0.209003	+	0.977915i	$0.432978\pi$
$194$		0			0
$195$	−4.34158	+	5.45576i	−0.310907	+	0.390695i
$196$		0			0
$197$	−5.14652	−	5.14652i	−0.366674	−	0.366674i	0.499588	−	0.866263i	$-0.333485\pi$
$197$	−5.14652	−	5.14652i	−0.366674	−	0.366674i	−0.866263	+	0.499588i	$0.833485\pi$
$198$		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	−0.145829	−	0.989310i	$-0.546585\pi$
$211$	−11.1381	−	2.98444i	−0.766776	−	0.205457i	−0.620947	+	0.783853i	$0.713252\pi$
$212$		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	−0.242680	−	0.970106i	$-0.578026\pi$
$223$	−17.9819	−	10.3819i	−1.20416	−	0.695220i	−0.961477	+	0.274886i	$0.911360\pi$
$224$		0			0
$225$	−1.12331	−	1.20562i	−0.0748876	−	0.0803748i
$226$		0			0
$227$	−7.65406	+	2.05090i	−0.508018	+	0.136123i	−0.503718	−	0.863868i	$-0.668035\pi$
$227$	−7.65406	+	2.05090i	−0.508018	+	0.136123i	−0.00429906	+	0.999991i	$0.501368\pi$
$228$		0			0
$229$	0.448692	+	0.120227i	0.0296504	+	0.00794481i	0.273614	−	0.961840i	$-0.411781\pi$
$229$	0.448692	+	0.120227i	0.0296504	+	0.00794481i	−0.243963	+	0.969784i	$0.578448\pi$
$230$		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	0.723114	−	0.690729i	$-0.242710\pi$
$239$	−3.65824	−	6.33626i	−0.236632	−	0.409859i	−0.959746	+	0.280870i	$0.909377\pi$
$240$		0			0
$241$	−1.24858	+	2.16261i	−0.0804282	+	0.139306i	−0.903434	−	0.428727i	$-0.858962\pi$
$241$	−1.24858	+	2.16261i	−0.0804282	+	0.139306i	0.823006	+	0.568033i	$0.192295\pi$
$242$		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	−0.789275	−	0.614039i	$-0.789544\pi$
$251$	−2.77626	+	2.77626i	−0.175236	+	0.175236i	0.614039	+	0.789275i	$0.289544\pi$
$252$		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	−0.769062	−	0.639174i	$-0.779276\pi$
$257$	−9.61957	+	5.55386i	−0.600052	+	0.346440i	0.169010	+	0.985614i	$0.445943\pi$
$258$		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	0.915713	−	0.401834i	$-0.131627\pi$
$263$	16.6320	+	9.60247i	1.02557	+	0.592114i	0.109858	+	0.993947i	$0.464960\pi$
$264$		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	−0.901048	−	0.433719i	$-0.857201\pi$
$269$	−7.66476	+	7.66476i	−0.467329	+	0.467329i	0.433719	+	0.901048i	$0.357201\pi$
$270$		0			0
$271$			12.9801i			0.788486i	0.919006	+	0.394243i	$0.128993\pi$
$271$			12.9801i			0.788486i	−0.919006	+	0.394243i	$0.871007\pi$
$272$		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	−0.836395	−	0.548127i	$-0.815341\pi$
$277$	−6.42631	−	23.9833i	−0.386119	−	1.44102i	0.450276	−	0.892890i	$-0.351326\pi$
$278$		0			0
$279$	16.5863	−	3.82191i	0.992997	−	0.228812i
$280$		0			0
$281$	−3.69120	+	6.39334i	−0.220198	+	0.381395i	−0.954868	−	0.297030i	$-0.904004\pi$
$281$	−3.69120	+	6.39334i	−0.220198	+	0.381395i	0.734670	+	0.678425i	$0.237337\pi$
$282$		0			0
$283$	−1.60691	+	5.99708i	−0.0955211	+	0.356490i	−0.997098	−	0.0761294i	$-0.975744\pi$
$283$	−1.60691	+	5.99708i	−0.0955211	+	0.356490i	0.901577	+	0.432619i	$0.142410\pi$
$284$		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	−0.476103	−	0.879390i	$-0.657951\pi$
$293$	6.43453	−	24.0140i	0.375909	−	1.40291i	0.852012	−	0.523522i	$-0.175382\pi$
$294$		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	−0.00819381	−	0.999966i	$-0.502608\pi$
$307$	17.3773	−	17.3773i	0.991773	−	0.991773i	0.999966	+	0.00819381i	$0.00260820\pi$
$308$		0			0
$309$	13.5976	−	5.35294i	0.773541	−	0.304518i
$310$		0			0
$311$	11.9437	−	6.89568i	0.677264	−	0.391018i	−0.121560	−	0.992584i	$-0.538790\pi$
$311$	11.9437	−	6.89568i	0.677264	−	0.391018i	0.798823	+	0.601566i	$0.205456\pi$
$312$		0			0
$313$	−17.6368	−	10.1826i	−0.996890	−	0.575555i	−0.0895635	−	0.995981i	$-0.528547\pi$
$313$	−17.6368	−	10.1826i	−0.996890	−	0.575555i	−0.907327	+	0.420426i	$0.861881\pi$
$314$		0			0
$315$	0.378883	+	0.713298i	0.0213476	+	0.0401898i
$316$		0			0
$317$	5.44301	+	20.3136i	0.305710	+	1.14092i	0.932333	+	0.361601i	$0.117770\pi$
$317$	5.44301	+	20.3136i	0.305710	+	1.14092i	−0.626623	+	0.779322i	$0.715563\pi$
$318$		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	−0.695204	−	0.718813i	$-0.744686\pi$
$331$	−17.0629	+	4.57199i	−0.937862	+	0.251299i	−0.242658	+	0.970112i	$0.578019\pi$
$332$		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	0.704144	−	0.710057i	$-0.251331\pi$
$337$	−4.82538	−	8.35780i	−0.262855	−	0.455279i	−0.966999	+	0.254778i	$0.917997\pi$
$338$		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	−0.271567	−	0.962420i	$-0.587542\pi$
$347$	−18.4037	−	4.93125i	−0.987960	−	0.264723i	−0.716393	+	0.697696i	$0.754208\pi$
$348$		0			0
$349$	−17.4744	+	4.68226i	−0.935385	+	0.250636i	−0.694150	−	0.719831i	$-0.744219\pi$
$349$	−17.4744	+	4.68226i	−0.935385	+	0.250636i	−0.241236	+	0.970467i	$0.577553\pi$
$350$		0			0
$351$	7.53530	+	6.44398i	0.402205	+	0.343954i
$352$		0			0
$353$	5.65589	+	3.26543i	0.301033	+	0.173801i	0.642907	−	0.765944i	$-0.277728\pi$
$353$	5.65589	+	3.26543i	0.301033	+	0.173801i	−0.341874	+	0.939746i	$0.611062\pi$
$354$		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	$0.205576\pi$
$359$			22.8075i			1.20373i	−0.798597	+	0.601866i	$0.794424\pi$
$360$		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	−0.152169	−	0.988355i	$-0.548626\pi$
$367$	−20.7702	−	11.9917i	−1.08419	−	0.625959i	−0.932025	+	0.362395i	$0.881959\pi$
$368$		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	−0.397018	−	0.917811i	$-0.629955\pi$
$373$	−23.1710	−	6.20866i	−1.19975	−	0.321472i	−0.802733	+	0.596338i	$0.796622\pi$
$374$		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	0.403183	−	0.915119i	$-0.367904\pi$
$379$	−9.96634	−	9.96634i	−0.511936	−	0.511936i	−0.915119	+	0.403183i	$0.867904\pi$
$380$		0			0
$381$	22.4585	+	3.36128i	1.15059	+	0.172203i
$382$		0			0
$383$	2.30770	+	3.99705i	0.117918	+	0.204240i	0.918942	−	0.394392i	$-0.129045\pi$
$383$	2.30770	+	3.99705i	0.117918	+	0.204240i	−0.801024	+	0.598632i	$0.795711\pi$
$384$		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	−0.558080	−	0.829787i	$-0.688462\pi$
$389$	−12.3565	+	3.31091i	−0.626498	+	0.167870i	−0.0684178	+	0.997657i	$0.521795\pi$
$390$		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	0.608047	−	0.793901i	$-0.291953\pi$
$397$	−3.70313	−	3.70313i	−0.185855	−	0.185855i	−0.793901	+	0.608047i	$0.791953\pi$
$398$		0			0
$399$	−1.23524	+	0.140475i	−0.0618392	+	0.00703252i
$400$		0			0
$401$	11.5871	−	6.68983i	0.578633	−	0.334074i	−0.181957	−	0.983307i	$-0.558243\pi$
$401$	11.5871	−	6.68983i	0.578633	−	0.334074i	0.760590	+	0.649232i	$0.224910\pi$
$402$		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	−0.958744	−	0.284272i	$-0.908248\pi$
$409$	−24.1053	+	13.9172i	−1.19193	+	0.688161i	−0.233185	+	0.972432i	$0.574915\pi$
$410$		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	−0.999978	−	0.00668892i	$-0.997871\pi$
$419$	−2.67387	+	9.97902i	−0.130627	+	0.487507i	0.869350	+	0.494196i	$0.164538\pi$
$420$		0			0
$421$	7.99904	+	29.8528i	0.389849	+	1.45494i	0.830379	+	0.557199i	$0.188124\pi$
$421$	7.99904	+	29.8528i	0.389849	+	1.45494i	−0.440529	+	0.897738i	$0.645209\pi$
$422$		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	−0.862664	−	0.505777i	$-0.831206\pi$
$439$	0.140035	−	0.242548i	0.00668352	−	0.0115762i	0.869348	+	0.494201i	$0.164539\pi$
$440$		0			0
$441$	−4.70440	−	20.4161i	−0.224019	−	0.972197i
$442$		0			0
$443$	6.50011	+	24.2588i	0.308830	+	1.15257i	0.929598	+	0.368574i	$0.120154\pi$
$443$	6.50011	+	24.2588i	0.308830	+	1.15257i	−0.620768	+	0.783994i	$0.713179\pi$
$444$		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	$-0.890534\pi$
$449$		−	14.2885i		−	0.674318i	0.941448	−	0.337159i	$-0.109466\pi$
$450$		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	0.943382	−	0.331708i	$-0.107625\pi$
$457$	24.1097	+	13.9198i	1.12781	+	0.651139i	0.184424	+	0.982847i	$0.440958\pi$
$458$		0			0
$459$	20.2660	+	9.68207i	0.945935	+	0.451921i
$460$		0			0
$461$	4.33776	+	16.1887i	0.202030	+	0.753985i	0.990334	+	0.138700i	$0.0442923\pi$
$461$	4.33776	+	16.1887i	0.202030	+	0.753985i	−0.788305	+	0.615285i	$0.789041\pi$
$462$		0			0
$463$	26.1951	−	15.1238i	1.21739	−	0.702861i	0.253032	−	0.967458i	$-0.418572\pi$
$463$	26.1951	−	15.1238i	1.21739	−	0.702861i	0.964359	+	0.264597i	$0.0852389\pi$
$464$		0			0
$465$	20.5991	−	2.34259i	0.955261	−	0.108635i
$466$		0			0
$467$	15.9369	+	15.9369i	0.737469	+	0.737469i	0.972088	−	0.234618i	$-0.0753840\pi$
$467$	15.9369	+	15.9369i	0.737469	+	0.737469i	−0.234618	+	0.972088i	$0.575384\pi$
$468$		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	0.299289	+	0.954163i	$0.403251\pi$
$479$	−14.8100	+	25.6516i	−0.676684	+	1.17205i	−0.975973	+	0.217889i	$0.930083\pi$
$480$		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	0.375345	−	0.926885i	$-0.377524\pi$
$491$	5.25069	+	1.40692i	0.236960	+	0.0634933i	−0.138385	+	0.990379i	$0.544191\pi$
$492$		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	0.707122	−	0.707092i	$-0.249993\pi$
$499$	21.5779	+	5.78179i	0.965961	+	0.258829i	0.258840	+	0.965920i	$0.416660\pi$
$500$		0			0
$501$	6.84387	+	17.3849i	0.305762	+	0.776700i
$502$		0			0
$503$			24.7337i			1.10282i	0.834235	+	0.551410i	$0.185910\pi$
$503$			24.7337i			1.10282i	−0.834235	+	0.551410i	$0.814090\pi$
$504$		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	0.0626029	−	0.998039i	$-0.480060\pi$
$509$	−8.62284	−	2.31048i	−0.382201	−	0.102410i	−0.444804	+	0.895628i	$0.646726\pi$
$510$		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	0.972349	+	0.233534i	$0.0750289\pi$
$523$	27.5776	+	27.5776i	1.20588	+	1.20588i	0.233534	+	0.972349i	$0.424971\pi$
$524$		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	0.855100	−	0.518464i	$-0.173496\pi$
$541$	7.82995	+	7.82995i	0.336636	+	0.336636i	−0.518464	+	0.855100i	$0.673496\pi$
$542$		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	−0.971285	−	0.237919i	$-0.923535\pi$
$547$	−5.82566	−	21.7416i	−0.249087	−	0.929606i	0.722198	−	0.691686i	$-0.243132\pi$
$548$		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	0.0882628	−	0.996097i	$-0.471868\pi$
$557$	25.5918	−	25.5918i	1.08436	−	1.08436i	0.996097	−	0.0882628i	$-0.0281315\pi$
$558$		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	−0.999939	−	0.0110721i	$-0.996476\pi$
$563$	−3.04735	+	11.3728i	−0.128430	+	0.479308i	0.871508	+	0.490381i	$0.163142\pi$
$564$		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	−0.882690	−	0.469955i	$-0.844270\pi$
$569$	−0.819418	+	1.41927i	−0.0343518	+	0.0594990i	0.848338	+	0.529454i	$0.177603\pi$
$570$		0			0
$571$	−8.76233	+	32.7015i	−0.366692	+	1.36851i	0.498420	+	0.866936i	$0.333914\pi$
$571$	−8.76233	+	32.7015i	−0.366692	+	1.36851i	−0.865112	+	0.501578i	$0.832753\pi$
$572$		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	−0.796521	−	0.604611i	$-0.793329\pi$
$587$	−9.90974	−	36.9837i	−0.409019	−	1.52648i	0.387502	−	0.921869i	$-0.373338\pi$
$588$		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	$0.230451\pi$
$593$			32.2597i			1.32475i	−0.749173	+	0.662374i	$0.769549\pi$
$594$		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	−0.720313	−	0.693649i	$-0.756002\pi$
$599$	−11.7417	+	6.77905i	−0.479751	+	0.276984i	0.240562	+	0.970634i	$0.422668\pi$
$600$		0			0
$601$	0.496416	+	0.286606i	0.0202492	+	0.0116909i	0.510090	−	0.860121i	$-0.329612\pi$
$601$	0.496416	+	0.286606i	0.0202492	+	0.0116909i	−0.489841	+	0.871812i	$0.662945\pi$
$602$		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	0.225178	−	0.974318i	$-0.427704\pi$
$607$	29.1103	−	16.8068i	1.18155	−	0.682168i	0.956373	+	0.292149i	$0.0943705\pi$
$608$		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	0.0757042	−	0.997130i	$-0.475880\pi$
$613$	26.5621	−	26.5621i	1.07283	−	1.07283i	0.997130	−	0.0757042i	$-0.0241205\pi$
$614$		0			0
$615$	3.80951	+	33.4983i	0.153614	+	1.35078i
$616$		0			0
$617$	−11.8730	−	20.5647i	−0.477991	−	0.827904i	0.521691	−	0.853134i	$-0.325301\pi$
$617$	−11.8730	−	20.5647i	−0.477991	−	0.827904i	−0.999682	+	0.0252305i	$0.991968\pi$
$618$		0			0
$619$	17.1798	−	4.60330i	0.690513	−	0.185022i	0.103535	−	0.994626i	$-0.466984\pi$
$619$	17.1798	−	4.60330i	0.690513	−	0.185022i	0.586977	+	0.809603i	$0.300318\pi$
$620$		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	0.994177	−	0.107761i	$-0.0343683\pi$
$641$	35.3930	+	20.4342i	1.39794	+	0.807102i	0.403764	+	0.914863i	$0.367702\pi$
$642$		0			0
$643$	−33.2700	−	8.91467i	−1.31204	−	0.351560i	−0.466050	−	0.884758i	$-0.654323\pi$
$643$	−33.2700	−	8.91467i	−1.31204	−	0.351560i	−0.845991	+	0.533198i	$0.820990\pi$
$644$		0			0
$645$	−40.6725	−	6.08728i	−1.60148	−	0.239686i
$646$		0			0
$647$		−	28.1696i		−	1.10746i	−0.832696	−	0.553730i	$-0.813204\pi$
$647$		−	28.1696i		−	1.10746i	0.832696	−	0.553730i	$-0.186796\pi$
$648$		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	0.414091	−	0.910235i	$-0.364099\pi$
$653$	8.11558	+	2.17456i	0.317587	+	0.0850972i	−0.0965042	+	0.995333i	$0.530766\pi$
$654$		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	0.257455	−	0.966290i	$-0.417116\pi$
$659$	24.7356	−	6.62788i	0.963562	−	0.258186i	0.706107	+	0.708105i	$0.250450\pi$
$660$		0			0
$661$	20.3200	+	5.44473i	0.790357	+	0.211775i	0.631346	−	0.775501i	$-0.282503\pi$
$661$	20.3200	+	5.44473i	0.790357	+	0.211775i	0.159011	+	0.987277i	$0.449170\pi$
$662$		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	−0.999803	−	0.0198709i	$-0.993674\pi$
$673$	−12.5221	+	21.6890i	−0.482693	+	0.836048i	0.517110	+	0.855919i	$0.327008\pi$
$674$		0			0
$675$	−2.35318	+	1.61511i	−0.0905741	+	0.0621658i
$676$		0			0
$677$	−18.3334	+	4.91241i	−0.704608	+	0.188799i	−0.593294	−	0.804986i	$-0.702173\pi$
$677$	−18.3334	+	4.91241i	−0.704608	+	0.188799i	−0.111314	+	0.993785i	$0.535506\pi$
$678$		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	−0.632713	−	0.774386i	$-0.718059\pi$
$683$	3.70253	−	3.70253i	0.141673	−	0.141673i	0.774386	+	0.632713i	$0.218059\pi$
$684$		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	0.995018	−	0.0996929i	$-0.0317860\pi$
$691$	2.19392	+	8.18783i	0.0834607	+	0.311480i	−0.911558	+	0.411173i	$0.865119\pi$
$692$		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	−0.944389	−	0.328831i	$-0.893345\pi$
$701$	−16.2977	+	16.2977i	−0.615557	+	0.615557i	0.328831	+	0.944389i	$0.393345\pi$
$702$		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	0.994056	+	0.108869i	$0.0347229\pi$
$709$	4.99557	+	18.6437i	0.187613	+	0.700180i	−0.806443	+	0.591311i	$0.798610\pi$
$710$		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	−0.675796	−	0.737089i	$-0.736200\pi$
$727$	8.10074	−	14.0309i	0.300440	−	0.520377i	0.976236	+	0.216712i	$0.0695332\pi$
$728$		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	−0.994235	−	0.107226i	$-0.965803\pi$
$733$	−2.15479	+	8.04180i	−0.0795891	+	0.297031i	0.914646	+	0.404257i	$0.132470\pi$
$734$		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	−0.988885	−	0.148682i	$-0.952497\pi$
$739$	−22.8405	+	22.8405i	−0.840203	+	0.840203i	0.148682	+	0.988885i	$0.452497\pi$
$740$		0			0
$741$	−17.2966	+	6.80909i	−0.635405	+	0.250138i
$742$		0			0
$743$	7.19608	−	4.15466i	0.263999	−	0.152420i	−0.362159	−	0.932116i	$-0.617960\pi$
$743$	7.19608	−	4.15466i	0.263999	−	0.152420i	0.626157	+	0.779697i	$0.284627\pi$
$744$		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	0.107687	−	0.994185i	$-0.465656\pi$
$751$	28.0215	−	16.1782i	1.02252	−	0.590352i	0.914833	+	0.403833i	$0.132322\pi$
$752$		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	−0.635415	−	0.772171i	$-0.719171\pi$
$757$	3.76265	−	3.76265i	0.136756	−	0.136756i	0.772171	+	0.635415i	$0.219171\pi$
$758$		0			0
$759$	−7.70069	+	5.69570i	−0.279517	+	0.206741i
$760$		0			0
$761$	−13.1168	−	22.7190i	−0.475485	−	0.823564i	0.524121	−	0.851644i	$-0.324394\pi$
$761$	−13.1168	−	22.7190i	−0.475485	−	0.823564i	−0.999606	+	0.0280801i	$0.991061\pi$
$762$		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	0.647725	−	0.761874i	$-0.275721\pi$
$769$	−9.31591	−	16.1356i	−0.335940	−	0.581865i	−0.983665	+	0.180009i	$0.942387\pi$
$770$		0			0
$771$	7.04741	+	17.9019i	0.253806	+	0.644722i
$772$		0			0
$773$	4.69430	+	4.69430i	0.168842	+	0.168842i	0.786470	−	0.617628i	$-0.211906\pi$
$773$	4.69430	+	4.69430i	0.168842	+	0.168842i	−0.617628	+	0.786470i	$0.711906\pi$
$774$		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	−0.628139	−	0.778101i	$-0.716183\pi$
$787$	−43.7964	−	11.7352i	−1.56117	−	0.418315i	−0.933035	+	0.359786i	$0.882850\pi$
$788$		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	−0.453589	−	0.891211i	$-0.649857\pi$
$797$	−36.4751	−	9.77347i	−1.29201	−	0.346194i	−0.838425	+	0.545017i	$0.816523\pi$
$798$		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	0.711375	−	0.702813i	$-0.248073\pi$
$811$	0.243845	+	0.243845i	0.00856256	+	0.00856256i	−0.702813	+	0.711375i	$0.748073\pi$
$812$		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	−0.949814	−	0.312815i	$-0.898728\pi$
$821$	−46.3025	+	12.4067i	−1.61597	+	0.432998i	−0.666156	+	0.745813i	$0.732061\pi$
$822$		0			0
$823$	0.737958	+	1.27818i	0.0257236	+	0.0445546i	0.878601	−	0.477557i	$-0.158478\pi$
$823$	0.737958	+	1.27818i	0.0257236	+	0.0445546i	−0.852877	+	0.522112i	$0.825144\pi$
$824$		0			0
$825$	0.612973	+	0.266682i	0.0213410	+	0.00928466i
$826$		0			0
$827$	−11.5464	+	11.5464i	−0.401509	+	0.401509i	−0.878764	−	0.477256i	$-0.841632\pi$
$827$	−11.5464	+	11.5464i	−0.401509	+	0.401509i	0.477256	+	0.878764i	$0.341632\pi$
$828$		0			0
$829$	34.7961	+	34.7961i	1.20852	+	1.20852i	0.971507	+	0.237010i	$0.0761675\pi$
$829$	34.7961	+	34.7961i	1.20852	+	1.20852i	0.237010	+	0.971507i	$0.423833\pi$
$830$		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	0.996807	−	0.0798497i	$-0.0254440\pi$
$839$	41.3065	+	23.8483i	1.42606	+	0.823335i	0.429252	+	0.903185i	$0.358777\pi$
$840$		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	−0.830095	−	0.557622i	$-0.811714\pi$
$853$	−11.3911	−	42.5120i	−0.390023	−	1.45558i	0.440072	−	0.897962i	$-0.354953\pi$
$854$		0			0
$855$	7.99302	+	34.6881i	0.273355	+	1.18631i
$856$		0			0
$857$	−4.36756	+	7.56483i	−0.149193	+	0.258410i	−0.930929	−	0.365199i	$-0.881001\pi$
$857$	−4.36756	+	7.56483i	−0.149193	+	0.258410i	0.781736	+	0.623609i	$0.214334\pi$
$858$		0			0
$859$	−12.9902	+	48.4800i	−0.443219	+	1.65411i	0.277378	+	0.960761i	$0.410534\pi$
$859$	−12.9902	+	48.4800i	−0.443219	+	1.65411i	−0.720597	+	0.693354i	$0.756132\pi$
$860$		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	−0.811377	−	0.584524i	$-0.801281\pi$
$877$	5.43592	−	20.2871i	0.183558	−	0.685047i	0.994935	−	0.100524i	$-0.0320519\pi$
$878$		0			0
$879$	−39.4856	−	17.1787i	−1.33182	−	0.579424i
$880$		0			0
$881$			7.45496i			0.251164i	0.992083	+	0.125582i	$0.0400798\pi$
$881$			7.45496i			0.251164i	−0.992083	+	0.125582i	$0.959920\pi$
$882$		0			0
$883$	9.55597	−	9.55597i	0.321584	−	0.321584i	−0.527791	−	0.849375i	$-0.676979\pi$
$883$	9.55597	−	9.55597i	0.321584	−	0.321584i	0.849375	+	0.527791i	$0.176979\pi$
$884$		0			0
$885$	−12.1241	−	9.64811i	−0.407547	−	0.324318i
$886$		0			0
$887$	41.0581	−	23.7049i	1.37860	−	0.795934i	0.386607	−	0.922245i	$-0.373647\pi$
$887$	41.0581	−	23.7049i	1.37860	−	0.795934i	0.991991	+	0.126311i	$0.0403138\pi$
$888$		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	−0.478534	−	0.878069i	$-0.658832\pi$
$907$	−13.6705	+	3.66301i	−0.453923	+	0.121628i	0.0246114	+	0.999697i	$0.492165\pi$
$908$		0			0
$909$	−37.5327	−	1.32647i	−1.24488	−	0.0439963i
$910$		0			0
$911$	20.0062	−	34.6517i	0.662834	−	1.14806i	−0.317034	−	0.948414i	$-0.602687\pi$
$911$	20.0062	−	34.6517i	0.662834	−	1.14806i	0.979868	−	0.199648i	$-0.0639799\pi$
$912$		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	0.349268	−	0.937023i	$-0.386430\pi$
$929$	−8.76538	−	5.06070i	−0.287583	−	0.166036i	−0.636851	+	0.770987i	$0.719763\pi$
$930$		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	$0.101199\pi$
$937$			19.1375i			0.625194i	−0.949886	+	0.312597i	$0.898801\pi$
$938$		0			0
$939$	−21.9641	+	27.6008i	−0.716772	+	0.900717i
$940$		0			0
$941$	41.4559	+	11.1081i	1.35142	+	0.362113i	0.860660	−	0.509179i	$-0.170051\pi$
$941$	41.4559	+	11.1081i	1.35142	+	0.362113i	0.490764	+	0.871292i	$0.336718\pi$
$942$		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	−0.900884	−	0.434060i	$-0.857081\pi$
$947$	−45.0535	+	12.0721i	−1.46404	+	0.392289i	−0.563159	+	0.826349i	$0.690414\pi$
$948$		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	−0.999869	−	0.0161601i	$-0.994856\pi$
$967$	−15.9815	−	27.6807i	−0.513930	−	0.890152i	0.485940	−	0.873992i	$-0.338477\pi$
$968$		0			0
$969$	−33.8542	+	25.0398i	−1.08755	+	0.804395i
$970$		0			0
$971$	4.69660	−	4.69660i	0.150721	−	0.150721i	−0.627719	−	0.778440i	$-0.716011\pi$
$971$	4.69660	−	4.69660i	0.150721	−	0.150721i	0.778440	+	0.627719i	$0.216011\pi$
$972$		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	−0.818085	−	0.575097i	$-0.804964\pi$
$977$	−22.7888	+	13.1571i	−0.729079	+	0.420934i	0.0890064	+	0.996031i	$0.471631\pi$
$978$		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	0.152851	−	0.988249i	$-0.451155\pi$
$983$	−19.6448	−	11.3420i	−0.626573	−	0.361752i	−0.779424	+	0.626497i	$0.784488\pi$
$984$		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	$-0.933501\pi$
$991$		−	13.0577i		−	0.414793i	0.978257	−	0.207396i	$-0.0664990\pi$
$992$		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	0.925639	−	0.378407i	$-0.123528\pi$
$997$	−2.05844	−	7.68222i	−0.0651916	−	0.243298i	−0.990831	+	0.135109i	$0.956861\pi$
$998$		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.47.11		88
3.2	odd	2		1728.2.z.a.1007.5		88
4.3	odd	2		144.2.u.a.83.19	yes	88
9.4	even	3		1728.2.z.a.1583.5		88
9.5	odd	6	inner	576.2.y.a.239.22		88
12.11	even	2		432.2.v.a.35.4		88
16.5	even	4		144.2.u.a.11.19	✓	88
16.11	odd	4	inner	576.2.y.a.335.22		88
36.23	even	6		144.2.u.a.131.19	yes	88
36.31	odd	6		432.2.v.a.179.4		88
48.5	odd	4		432.2.v.a.251.4		88
48.11	even	4		1728.2.z.a.143.5		88
144.5	odd	12		144.2.u.a.59.19	yes	88
144.59	even	12	inner	576.2.y.a.527.11		88
144.85	even	12		432.2.v.a.395.4		88
144.139	odd	12		1728.2.z.a.719.5		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.19	✓	88	16.5	even	4
144.2.u.a.59.19	yes	88	144.5	odd	12
144.2.u.a.83.19	yes	88	4.3	odd	2
144.2.u.a.131.19	yes	88	36.23	even	6
432.2.v.a.35.4		88	12.11	even	2
432.2.v.a.179.4		88	36.31	odd	6
432.2.v.a.251.4		88	48.5	odd	4
432.2.v.a.395.4		88	144.85	even	12
576.2.y.a.47.11		88	1.1	even	1	trivial
576.2.y.a.239.22		88	9.5	odd	6	inner
576.2.y.a.335.22		88	16.11	odd	4	inner
576.2.y.a.527.11		88	144.59	even	12	inner
1728.2.z.a.143.5		88	48.11	even	4
1728.2.z.a.719.5		88	144.139	odd	12
1728.2.z.a.1007.5		88	3.2	odd	2
1728.2.z.a.1583.5		88	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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