LMFDB - Embedded newform 576.2.y.a.335.22

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			335.22
Character	$\chi$	$=$	576.335
Dual form			576.2.y.a.239.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.71297 + 0.256373i) q^{3} +(2.03779 + 0.546024i) q^{5} +(0.0638076 - 0.110518i) q^{7} +(2.86855 + 0.878321i) q^{9} +O(q^{10})$	\(q+(1.71297 + 0.256373i) q^{3} +(2.03779 + 0.546024i) q^{5} +(0.0638076 - 0.110518i) q^{7} +(2.86855 + 0.878321i) q^{9} +(0.678695 - 0.181856i) q^{11} +(-1.84311 - 0.493860i) q^{13} +(3.35069 + 1.45776i) q^{15} -4.32243i q^{17} +(3.97707 + 3.97707i) q^{19} +(0.137635 - 0.172956i) q^{21} +(-6.81589 + 3.93516i) q^{23} +(-0.475689 - 0.274639i) q^{25} +(4.68856 + 2.23996i) q^{27} +(-0.926957 + 0.248377i) q^{29} +(4.91353 - 2.83683i) q^{31} +(1.20921 - 0.137514i) q^{33} +(0.190372 - 0.190372i) q^{35} +(-6.64358 - 6.64358i) q^{37} +(-3.03058 - 1.31849i) q^{39} +(4.61325 + 7.99038i) q^{41} +(-2.91294 - 10.8712i) q^{43} +(5.36590 + 3.35613i) q^{45} +(-5.92267 + 10.2584i) q^{47} +(3.49186 + 6.04807i) q^{49} +(1.10816 - 7.40421i) q^{51} +(0.00259022 - 0.00259022i) q^{53} +1.48233 q^{55} +(5.79299 + 7.83221i) q^{57} +(1.09748 - 4.09587i) q^{59} +(-1.19213 - 4.44908i) q^{61} +(0.280105 - 0.260982i) q^{63} +(-3.48621 - 2.01276i) q^{65} +(0.538862 - 2.01106i) q^{67} +(-12.6843 + 4.99340i) q^{69} -3.80683i q^{71} -1.87674i q^{73} +(-0.744431 - 0.592403i) q^{75} +(0.0232076 - 0.0866118i) q^{77} +(-3.00919 - 1.73736i) q^{79} +(7.45710 + 5.03901i) q^{81} +(0.394284 + 1.47149i) q^{83} +(2.36015 - 8.80821i) q^{85} +(-1.65153 + 0.187816i) q^{87} -10.5967 q^{89} +(-0.172185 + 0.172185i) q^{91} +(9.14402 - 3.59971i) q^{93} +(5.93284 + 10.2760i) q^{95} +(3.31795 - 5.74685i) q^{97} +(2.10659 + 0.0744506i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.71297	+	0.256373i	0.988985	+	0.148017i
$3$	1.71297	+	0.256373i	0.988985	+	0.148017i
$4$		0			0
$5$	2.03779	+	0.546024i	0.911327	+	0.244189i	0.683874	−	0.729600i	$-0.260294\pi$
$5$	2.03779	+	0.546024i	0.911327	+	0.244189i	0.227452	+	0.973789i	$0.426960\pi$
$6$		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
$11$	0.678695	−	0.181856i	0.204634	−	0.0548316i	−0.155046	−	0.987907i	$-0.549553\pi$
$11$	0.678695	−	0.181856i	0.204634	−	0.0548316i	0.359680	+	0.933076i	$0.382886\pi$
$12$		0			0
$13$	−1.84311	−	0.493860i	−0.511187	−	0.136972i	−0.00599967	−	0.999982i	$-0.501910\pi$
$13$	−1.84311	−	0.493860i	−0.511187	−	0.136972i	−0.505187	+	0.863010i	$0.668576\pi$
$14$		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	0.996461	−	0.0840594i	$-0.0267886\pi$
$19$	3.97707	+	3.97707i	0.912401	+	0.912401i	−0.0840594	+	0.996461i	$0.526789\pi$
$20$		0			0
$21$	0.137635	−	0.172956i	0.0300343	−	0.0377420i
$22$		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
$27$	4.68856	+	2.23996i	0.902314	+	0.431080i
$28$		0			0
$29$	−0.926957	+	0.248377i	−0.172132	+	0.0461225i	−0.343855	−	0.939023i	$-0.611733\pi$
$29$	−0.926957	+	0.248377i	−0.172132	+	0.0461225i	0.171724	+	0.985145i	$0.445066\pi$
$30$		0			0
$31$	4.91353	−	2.83683i	0.882496	−	0.509509i	0.0110152	−	0.999939i	$-0.496494\pi$
$31$	4.91353	−	2.83683i	0.882496	−	0.509509i	0.871480	+	0.490430i	$0.163160\pi$
$32$		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	0.960812	+	0.277200i	$0.0894066\pi$
$41$	4.61325	+	7.99038i	0.720469	+	1.24789i	−0.240344	+	0.970688i	$0.577260\pi$
$42$		0			0
$43$	−2.91294	−	10.8712i	−0.444219	−	1.65785i	−0.717991	−	0.696053i	$-0.754938\pi$
$43$	−2.91294	−	10.8712i	−0.444219	−	1.65785i	0.273772	−	0.961795i	$-0.411729\pi$
$44$		0			0
$45$	5.36590	+	3.35613i	0.799902	+	0.500302i
$46$		0			0
$47$	−5.92267	+	10.2584i	−0.863910	+	1.49634i	0.00421475	+	0.999991i	$0.498658\pi$
$47$	−5.92267	+	10.2584i	−0.863910	+	1.49634i	−0.868125	+	0.496345i	$0.834675\pi$
$48$		0			0
$49$	3.49186	+	6.04807i	0.498837	+	0.864011i
$50$		0			0
$51$	1.10816	−	7.40421i	0.155173	−	1.03680i
$52$		0			0
$53$	0.00259022	−	0.00259022i	0.000355794	−	0.000355794i	−0.706929	−	0.707285i	$-0.749920\pi$
$53$	0.00259022	−	0.00259022i	0.000355794	−	0.000355794i	0.707285	+	0.706929i	$0.249920\pi$
$54$		0			0
$55$	1.48233			0.199878
$56$		0			0
$57$	5.79299	+	7.83221i	0.767300	+	1.03740i
$58$		0			0
$59$	1.09748	−	4.09587i	0.142880	−	0.533237i	−0.856960	−	0.515382i	$-0.827650\pi$
$59$	1.09748	−	4.09587i	0.142880	−	0.533237i	0.999841	−	0.0178541i	$-0.00568344\pi$
$60$		0			0
$61$	−1.19213	−	4.44908i	−0.152636	−	0.569646i	−0.999296	−	0.0375117i	$-0.988057\pi$
$61$	−1.19213	−	4.44908i	−0.152636	−	0.569646i	0.846660	−	0.532134i	$-0.178610\pi$
$62$		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
$67$	0.538862	−	2.01106i	0.0658325	−	0.245690i	−0.925166	−	0.379563i	$-0.876075\pi$
$67$	0.538862	−	2.01106i	0.0658325	−	0.245690i	0.990999	+	0.133872i	$0.0427412\pi$
$68$		0			0
$69$	−12.6843	+	4.99340i	−1.52701	+	0.601134i
$70$		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	$-0.964970\pi$
$73$		−	1.87674i		−	0.219656i	0.993951	−	0.109828i	$-0.0350300\pi$
$74$		0			0
$75$	−0.744431	−	0.592403i	−0.0859595	−	0.0684048i
$76$		0			0
$77$	0.0232076	−	0.0866118i	0.00264475	−	0.00987033i
$78$		0			0
$79$	−3.00919	−	1.73736i	−0.338560	−	0.195468i	0.321075	−	0.947054i	$-0.395956\pi$
$79$	−3.00919	−	1.73736i	−0.338560	−	0.195468i	−0.659635	+	0.751586i	$0.729289\pi$
$80$		0			0
$81$	7.45710	+	5.03901i	0.828567	+	0.559890i
$82$		0			0
$83$	0.394284	+	1.47149i	0.0432783	+	0.161517i	0.984183	−	0.177155i	$-0.0566892\pi$
$83$	0.394284	+	1.47149i	0.0432783	+	0.161517i	−0.940905	+	0.338671i	$0.890023\pi$
$84$		0			0
$85$	2.36015	−	8.80821i	0.255994	−	0.955384i
$86$		0			0
$87$	−1.65153	+	0.187816i	−0.177062	+	0.0201360i
$88$		0			0
$89$	−10.5967			−1.12325			−0.561624	−	0.827392i	$-0.689823\pi$
$89$	−10.5967			−1.12325			−0.561624	+	0.827392i	$0.689823\pi$
$90$		0			0
$91$	−0.172185	+	0.172185i	−0.0180499	+	0.0180499i
$92$		0			0
$93$	9.14402	−	3.59971i	0.948191	−	0.373272i
$94$		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
$99$	2.10659	+	0.0744506i	0.211721	+	0.00748257i
$100$		0			0
$101$	3.24008	+	12.0922i	0.322400	+	1.20321i	0.916899	+	0.399118i	$0.130684\pi$
$101$	3.24008	+	12.0922i	0.322400	+	1.20321i	−0.594499	+	0.804096i	$0.702650\pi$
$102$		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	$-0.415070\pi$
$107$	−7.25071	−	7.25071i	−0.700953	−	0.700953i	−0.964615	+	0.263662i	$0.915070\pi$
$108$		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	−0.804652	+	0.593747i	$0.797648\pi$
$113$	−18.2964	+	10.5634i	−1.72118	+	0.993722i	−0.916526	+	0.399976i	$0.869019\pi$
$114$		0			0
$115$	−16.0380	+	4.29738i	−1.49555	+	0.400732i
$116$		0			0
$117$	−4.85328	−	3.03550i	−0.448685	−	0.280632i
$118$		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
$123$	5.85384	+	14.8700i	0.527823	+	1.34078i
$124$		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
$131$	−4.74891	−	1.27247i	−0.414914	−	0.111176i	0.0453222	−	0.998972i	$-0.485569\pi$
$131$	−4.74891	−	1.27247i	−0.414914	−	0.111176i	−0.460236	+	0.887797i	$0.652235\pi$
$132$		0			0
$133$	0.693305	−	0.185770i	0.0601171	−	0.0161083i
$134$		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	$-0.739172\pi$
$137$	3.41217	−	5.91005i	0.291521	−	0.504930i	0.974170	+	0.225817i	$0.0725053\pi$
$138$		0			0
$139$	−10.3427	−	2.77132i	−0.877258	−	0.235061i	−0.208035	−	0.978121i	$-0.566707\pi$
$139$	−10.3427	−	2.77132i	−0.877258	−	0.235061i	−0.669224	+	0.743061i	$0.733373\pi$
$140$		0			0
$141$	−12.7753	+	16.0539i	−1.07588	+	1.35198i
$142$		0			0
$143$	−1.34072			−0.112117
$144$		0			0
$145$	−2.02456			−0.168131
$146$		0			0
$147$	4.43089	+	11.2554i	0.365453	+	0.928330i
$148$		0			0
$149$	−0.204036	−	0.0546714i	−0.0167153	−	0.00447885i	0.250452	−	0.968129i	$-0.419421\pi$
$149$	−0.204036	−	0.0546714i	−0.0167153	−	0.00447885i	−0.267167	+	0.963650i	$0.586088\pi$
$150$		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
$155$	11.5617	−	3.09795i	0.928658	−	0.248833i
$156$		0			0
$157$	−16.2150	−	4.34480i	−1.29410	−	0.346753i	−0.454883	−	0.890551i	$-0.650319\pi$
$157$	−16.2150	−	4.34480i	−1.29410	−	0.346753i	−0.839216	+	0.543799i	$0.816985\pi$
$158$		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
$165$	2.53920	+	0.380031i	0.197676	+	0.0295854i
$166$		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
$171$	7.91525	+	14.9015i	0.605294	+	1.13955i
$172$		0			0
$173$	4.61598	−	1.23685i	0.350946	−	0.0940358i	−0.0790394	−	0.996871i	$-0.525185\pi$
$173$	4.61598	−	1.23685i	0.350946	−	0.0940358i	0.429986	+	0.902836i	$0.358519\pi$
$174$		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	$-0.809716\pi$
$179$	−3.52882	+	3.52882i	−0.263756	+	0.263756i	0.562822	+	0.826578i	$0.309716\pi$
$180$		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
$187$	−0.786059	−	2.93361i	−0.0574824	−	0.214527i
$188$		0			0
$189$	0.546722	−	0.375244i	0.0397681	−	0.0272950i
$190$		0			0
$191$	2.58888	−	4.48407i	0.187325	−	0.324456i	−0.757033	−	0.653377i	$-0.773352\pi$
$191$	2.58888	−	4.48407i	0.187325	−	0.324456i	0.944357	+	0.328921i	$0.106685\pi$
$192$		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
$195$	−5.45576	−	4.34158i	−0.390695	−	0.310907i
$196$		0			0
$197$	5.14652	−	5.14652i	0.366674	−	0.366674i	−0.499588	−	0.866263i	$-0.666515\pi$
$197$	5.14652	−	5.14652i	0.366674	−	0.366674i	0.866263	+	0.499588i	$0.166515\pi$
$198$		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
$203$	−0.0316967	+	0.118294i	−0.00222468	+	0.00830260i
$204$		0			0
$205$	5.03789	+	18.8017i	0.351861	+	1.31316i
$206$		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
$211$	2.98444	−	11.1381i	0.205457	−	0.766776i	−0.783853	−	0.620947i	$-0.786748\pi$
$211$	2.98444	−	11.1381i	0.205457	−	0.766776i	0.989310	−	0.145829i	$-0.0465850\pi$
$212$		0			0
$213$	0.975971	−	6.52100i	0.0668724	−	0.446811i
$214$		0			0
$215$		−	23.7438i		−	1.61931i
$216$		0			0
$217$		−	0.724045i		−	0.0491514i
$218$		0			0
$219$	0.481147	−	3.21481i	0.0325129	−	0.217237i
$220$		0			0
$221$	−2.13468	+	7.96672i	−0.143594	+	0.535900i
$222$		0			0
$223$	17.9819	+	10.3819i	1.20416	+	0.695220i	0.961477	−	0.274886i	$-0.0886402\pi$
$223$	17.9819	+	10.3819i	1.20416	+	0.695220i	0.242680	+	0.970106i	$0.421974\pi$
$224$		0			0
$225$	−1.12331	−	1.20562i	−0.0748876	−	0.0803748i
$226$		0			0
$227$	−2.05090	−	7.65406i	−0.136123	−	0.508018i	−0.999991	−	0.00429906i	$-0.998632\pi$
$227$	−2.05090	−	7.65406i	−0.136123	−	0.508018i	0.863868	−	0.503718i	$-0.168035\pi$
$228$		0			0
$229$	−0.120227	+	0.448692i	−0.00794481	+	0.0296504i	−0.969784	−	0.243963i	$-0.921552\pi$
$229$	−0.120227	+	0.448692i	−0.00794481	+	0.0296504i	0.961840	+	0.273614i	$0.0882190\pi$
$230$		0			0
$231$	0.0619589	−	0.142414i	0.00407659	−	0.00937014i
$232$		0			0
$233$	9.13737			0.598609			0.299305	−	0.954158i	$-0.403245\pi$
$233$	9.13737			0.598609			0.299305	+	0.954158i	$0.403245\pi$
$234$		0			0
$235$	−17.6705	+	17.6705i	−1.15269	+	1.15269i
$236$		0			0
$237$	−4.70925	−	3.74752i	−0.305898	−	0.243428i
$238$		0			0
$239$	3.65824	+	6.33626i	0.236632	+	0.409859i	0.959746	−	0.280870i	$-0.0906231\pi$
$239$	3.65824	+	6.33626i	0.236632	+	0.409859i	−0.723114	+	0.690729i	$0.757290\pi$
$240$		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
$243$	11.4819	+	10.5435i	0.736567	+	0.676365i
$244$		0			0
$245$	3.81327	+	14.2313i	0.243621	+	0.909206i
$246$		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	$-0.210456\pi$
$251$	2.77626	+	2.77626i	0.175236	+	0.175236i	−0.614039	+	0.789275i	$0.710456\pi$
$252$		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
$259$	−1.15815	+	0.310324i	−0.0719637	+	0.0192826i
$260$		0			0
$261$	−2.87717	−	0.101684i	−0.178093	−	0.00629409i
$262$		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
$267$	−18.1519	−	2.71671i	−1.11088	−	0.166260i
$268$		0			0
$269$	7.66476	+	7.66476i	0.467329	+	0.467329i	0.901048	−	0.433719i	$-0.142799\pi$
$269$	7.66476	+	7.66476i	0.467329	+	0.467329i	−0.433719	+	0.901048i	$0.642799\pi$
$270$		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
$275$	−0.372792	−	0.0998893i	−0.0224802	−	0.00602355i
$276$		0			0
$277$	23.9833	−	6.42631i	1.44102	−	0.386119i	0.548127	−	0.836395i	$-0.315341\pi$
$277$	23.9833	−	6.42631i	1.44102	−	0.386119i	0.892890	+	0.450276i	$0.148674\pi$
$278$		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	$-0.762663\pi$
$281$	3.69120	−	6.39334i	0.220198	−	0.381395i	0.954868	+	0.297030i	$0.0959962\pi$
$282$		0			0
$283$	5.99708	+	1.60691i	0.356490	+	0.0955211i	0.432619	−	0.901577i	$-0.357590\pi$
$283$	5.99708	+	1.60691i	0.356490	+	0.0955211i	−0.0761294	+	0.997098i	$0.524256\pi$
$284$		0			0
$285$	7.52830	+	19.1235i	0.445938	+	1.13278i
$286$		0			0
$287$	1.17744			0.0695022
$288$		0			0
$289$	−1.68344			−0.0990261
$290$		0			0
$291$	7.15689	−	8.99356i	0.419544	−	0.527212i
$292$		0			0
$293$	24.0140	+	6.43453i	1.40291	+	0.375909i	0.879390	−	0.476103i	$-0.157951\pi$
$293$	24.0140	+	6.43453i	1.40291	+	0.375909i	0.523522	+	0.852012i	$0.324618\pi$
$294$		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
$299$	14.5058	−	3.88683i	0.838895	−	0.224781i
$300$		0			0
$301$	−1.38734	−	0.371735i	−0.0799647	−	0.0214265i
$302$		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
$309$	5.35294	+	13.5976i	0.304518	+	0.773541i
$310$		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	0.907327	−	0.420426i	$-0.138119\pi$
$313$	17.6368	+	10.1826i	0.996890	+	0.575555i	0.0895635	+	0.995981i	$0.471453\pi$
$314$		0			0
$315$	0.713298	−	0.378883i	0.0401898	−	0.0213476i
$316$		0			0
$317$	20.3136	−	5.44301i	1.14092	−	0.305710i	0.361601	−	0.932333i	$-0.382230\pi$
$317$	20.3136	−	5.44301i	1.14092	−	0.305710i	0.779322	+	0.626623i	$0.215563\pi$
$318$		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
$331$	4.57199	+	17.0629i	0.251299	+	0.937862i	0.970112	+	0.242658i	$0.0780193\pi$
$331$	4.57199	+	17.0629i	0.251299	+	0.937862i	−0.718813	+	0.695204i	$0.755314\pi$
$332$		0			0
$333$	−13.2222	−	24.8926i	−0.724573	−	1.36411i
$334$		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
$339$	−34.0493	+	13.4041i	−1.84931	+	0.728012i
$340$		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
$347$	−4.93125	+	18.4037i	−0.264723	+	0.987960i	0.697696	+	0.716393i	$0.254208\pi$
$347$	−4.93125	+	18.4037i	−0.264723	+	0.987960i	−0.962420	+	0.271567i	$0.912458\pi$
$348$		0			0
$349$	4.68226	+	17.4744i	0.250636	+	0.935385i	0.970467	+	0.241236i	$0.0775527\pi$
$349$	4.68226	+	17.4744i	0.250636	+	0.935385i	−0.719831	+	0.694150i	$0.755781\pi$
$350$		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
$355$	2.07862	−	7.75752i	0.110322	−	0.411726i
$356$		0			0
$357$	−0.747590	−	0.594916i	−0.0395667	−	0.0314863i
$358$		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
$363$	−16.9326	+	6.66583i	−0.888732	+	0.349865i
$364$		0			0
$365$	1.02475	−	3.82440i	0.0536377	−	0.200178i
$366$		0			0
$367$	20.7702	+	11.9917i	1.08419	+	0.625959i	0.932025	−	0.362395i	$-0.118041\pi$
$367$	20.7702	+	11.9917i	1.08419	+	0.625959i	0.152169	+	0.988355i	$0.451374\pi$
$368$		0			0
$369$	6.21519	+	26.9727i	0.323550	+	1.40414i
$370$		0			0
$371$	−0.000120990	0	0.000451542i	−6.28150e−6	0	2.34429e-5i
$372$		0			0
$373$	6.20866	−	23.1710i	0.321472	−	1.19975i	−0.596338	−	0.802733i	$-0.703378\pi$
$373$	6.20866	−	23.1710i	0.321472	−	1.19975i	0.917811	−	0.397018i	$-0.129955\pi$
$374$		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
$381$	3.36128	−	22.4585i	0.172203	−	1.15059i
$382$		0			0
$383$	−2.30770	−	3.99705i	−0.117918	−	0.204240i	0.801024	−	0.598632i	$-0.204289\pi$
$383$	−2.30770	−	3.99705i	−0.117918	−	0.204240i	−0.918942	+	0.394392i	$0.870955\pi$
$384$		0			0
$385$	0.0945842	−	0.163825i	0.00482046	−	0.00834927i
$386$		0			0
$387$	1.19254	−	33.7431i	0.0606202	−	1.71526i
$388$		0			0
$389$	−3.31091	−	12.3565i	−0.167870	−	0.626498i	−0.997657	−	0.0684178i	$-0.978205\pi$
$389$	−3.31091	−	12.3565i	−0.167870	−	0.626498i	0.829787	−	0.558080i	$-0.188462\pi$
$390$		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	−0.181957	−	0.983307i	$-0.558243\pi$
$401$	11.5871	−	6.68983i	0.578633	−	0.334074i	0.760590	+	0.649232i	$0.224910\pi$
$402$		0			0
$403$	−10.4572	+	2.80199i	−0.520908	+	0.139577i
$404$		0			0
$405$	12.4446	+	14.3402i	0.618376	+	0.712570i
$406$		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	$-0.425085\pi$
$409$	24.1053	−	13.9172i	1.19193	−	0.688161i	0.958744	+	0.284272i	$0.0917518\pi$
$410$		0			0
$411$	7.36013	−	9.24896i	0.363048	−	0.456217i
$412$		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
$419$	−9.97902	−	2.67387i	−0.487507	−	0.130627i	0.00668892	−	0.999978i	$-0.497871\pi$
$419$	−9.97902	−	2.67387i	−0.487507	−	0.130627i	−0.494196	+	0.869350i	$0.664538\pi$
$420$		0			0
$421$	−29.8528	+	7.99904i	−1.45494	+	0.389849i	−0.897738	−	0.440529i	$-0.854791\pi$
$421$	−29.8528	+	7.99904i	−1.45494	+	0.389849i	−0.557199	+	0.830379i	$0.688124\pi$
$422$		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
$427$	−0.567770	−	0.152134i	−0.0274763	−	0.00736226i
$428$		0			0
$429$	−2.29662	−	0.343725i	−0.110882	−	0.0165952i
$430$		0			0
$431$	−14.8449			−0.715053			−0.357526	−	0.933903i	$-0.616380\pi$
$431$	−14.8449			−0.715053			−0.357526	+	0.933903i	$0.616380\pi$
$432$		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
$435$	−3.46802	−	0.519044i	−0.166279	−	0.0248863i
$436$		0			0
$437$	−42.7576	−	11.4569i	−2.04537	−	0.548056i
$438$		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
$443$	24.2588	−	6.50011i	1.15257	−	0.308830i	0.368574	−	0.929598i	$-0.379846\pi$
$443$	24.2588	−	6.50011i	1.15257	−	0.308830i	0.783994	+	0.620768i	$0.213179\pi$
$444$		0			0
$445$	−21.5938	−	5.78605i	−1.02365	−	0.274285i
$446$		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
$453$	−2.47621	+	3.11168i	−0.116343	+	0.146200i
$454$		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	$-0.559042\pi$
$457$	−24.1097	−	13.9198i	−1.12781	−	0.651139i	−0.943382	+	0.331708i	$0.892375\pi$
$458$		0			0
$459$	9.68207	−	20.2660i	0.451921	−	0.945935i
$460$		0			0
$461$	16.1887	−	4.33776i	0.753985	−	0.202030i	0.138700	−	0.990334i	$-0.455708\pi$
$461$	16.1887	−	4.33776i	0.753985	−	0.202030i	0.615285	+	0.788305i	$0.289041\pi$
$462$		0			0
$463$	−26.1951	+	15.1238i	−1.21739	+	0.702861i	−0.964359	−	0.264597i	$-0.914761\pi$
$463$	−26.1951	+	15.1238i	−1.21739	+	0.702861i	−0.253032	+	0.967458i	$0.581428\pi$
$464$		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	$-0.924616\pi$
$467$	−15.9369	+	15.9369i	−0.737469	+	0.737469i	0.234618	+	0.972088i	$0.424616\pi$
$468$		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
$475$	−0.799588	−	2.98410i	−0.0366876	−	0.136920i
$476$		0			0
$477$	0.00970520	−	0.00515511i	0.000444371	−	0.000236036i
$478$		0			0
$479$	14.8100	−	25.6516i	0.676684	−	1.17205i	−0.299289	−	0.954163i	$-0.596749\pi$
$479$	14.8100	−	25.6516i	0.676684	−	1.17205i	0.975973	−	0.217889i	$-0.0699172\pi$
$480$		0			0
$481$	8.96385	+	15.5258i	0.408716	+	0.707917i
$482$		0			0
$483$	−0.257494	+	1.72046i	−0.0117164	+	0.0782837i
$484$		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
$491$	1.40692	−	5.25069i	0.0634933	−	0.236960i	−0.926885	−	0.375345i	$-0.877524\pi$
$491$	1.40692	−	5.25069i	0.0634933	−	0.236960i	0.990379	+	0.138385i	$0.0441910\pi$
$492$		0			0
$493$	1.07360	+	4.00671i	0.0483523	+	0.180453i
$494$		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
$499$	−5.78179	+	21.5779i	−0.258829	+	0.965961i	0.707092	+	0.707122i	$0.250007\pi$
$499$	−5.78179	+	21.5779i	−0.258829	+	0.965961i	−0.965920	+	0.258840i	$0.916660\pi$
$500$		0			0
$501$	−17.3849	+	6.84387i	−0.776700	+	0.305762i
$502$		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
$507$	−12.6842	−	10.0938i	−0.563327	−	0.448284i
$508$		0			0
$509$	−2.31048	+	8.62284i	−0.102410	+	0.382201i	−0.998039	−	0.0626029i	$-0.980060\pi$
$509$	−2.31048	+	8.62284i	−0.102410	+	0.382201i	0.895628	+	0.444804i	$0.146726\pi$
$510$		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
$515$	4.60680	+	17.1928i	0.203000	+	0.757606i
$516$		0			0
$517$	−2.15414	+	8.03937i	−0.0947391	+	0.353571i
$518$		0			0
$519$	8.22413	−	0.935271i	0.360999	−	0.0410538i
$520$		0			0
$521$	14.1129			0.618299			0.309149	−	0.951013i	$-0.399956\pi$
$521$	14.1129			0.618299			0.309149	+	0.951013i	$0.399956\pi$
$522$		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
$525$	−0.112972	+	0.0444733i	−0.00493048	+	0.00194097i
$526$		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
$531$	6.74567	−	10.7852i	0.292737	−	0.468039i
$532$		0			0
$533$	−4.55660	−	17.0054i	−0.197368	−	0.736588i
$534$		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
$547$	21.7416	−	5.82566i	0.929606	−	0.249087i	0.237919	−	0.971285i	$-0.423535\pi$
$547$	21.7416	−	5.82566i	0.929606	−	0.249087i	0.691686	+	0.722198i	$0.256868\pi$
$548$		0			0
$549$	0.488049	−	13.8094i	0.0208294	−	0.589373i
$550$		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
$555$	−12.5758	−	31.9453i	−0.533814	−	1.35600i
$556$		0			0
$557$	−25.5918	−	25.5918i	−1.08436	−	1.08436i	−0.996097	−	0.0882628i	$-0.971868\pi$
$557$	−25.5918	−	25.5918i	−1.08436	−	1.08436i	−0.0882628	−	0.996097i	$-0.528132\pi$
$558$		0			0
$559$			21.4755i			0.908315i
$560$		0			0
$561$	−0.594397	−	5.22672i	−0.0250955	−	0.220672i
$562$		0			0
$563$	−11.3728	−	3.04735i	−0.479308	−	0.128430i	0.0110721	−	0.999939i	$-0.496476\pi$
$563$	−11.3728	−	3.04735i	−0.479308	−	0.128430i	−0.490381	+	0.871508i	$0.663142\pi$
$564$		0			0
$565$	−43.0520	+	11.5357i	−1.81121	+	0.485313i
$566$		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	$-0.822397\pi$
$569$	0.819418	−	1.41927i	0.0343518	−	0.0594990i	0.882690	+	0.469955i	$0.155730\pi$
$570$		0			0
$571$	32.7015	+	8.76233i	1.36851	+	0.366692i	0.866936	−	0.498420i	$-0.166086\pi$
$571$	32.7015	+	8.76233i	1.36851	+	0.366692i	0.501578	+	0.865112i	$0.332753\pi$
$572$		0			0
$573$	5.58427	−	7.01737i	0.233286	−	0.293155i
$574$		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
$579$	16.7717	+	42.6036i	0.697007	+	1.77055i
$580$		0			0
$581$	0.187784	+	0.0503166i	0.00779060	+	0.00208749i
$582$		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
$587$	−36.9837	+	9.90974i	−1.52648	+	0.409019i	−0.921869	−	0.387502i	$-0.873338\pi$
$587$	−36.9837	+	9.90974i	−1.52648	+	0.409019i	−0.604611	+	0.796521i	$0.706671\pi$
$588$		0			0
$589$	30.8237	+	8.25918i	1.27007	+	0.340313i
$590$		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
$597$	2.35425	+	0.352351i	0.0963529	+	0.0144207i
$598$		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	0.489841	−	0.871812i	$-0.337055\pi$
$601$	−0.496416	−	0.286606i	−0.0202492	−	0.0116909i	−0.510090	+	0.860121i	$0.670388\pi$
$602$		0			0
$603$	3.31211	−	5.29553i	0.134880	−	0.215651i
$604$		0			0
$605$	−21.4096	+	5.73669i	−0.870425	+	0.233230i
$606$		0			0
$607$	−29.1103	+	16.8068i	−1.18155	+	0.682168i	−0.956373	−	0.292149i	$-0.905630\pi$
$607$	−29.1103	+	16.8068i	−1.18155	+	0.682168i	−0.225178	+	0.974318i	$0.572296\pi$
$608$		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	$-0.00803196\pi$
$617$	11.8730	+	20.5647i	0.477991	+	0.827904i	−0.521691	+	0.853134i	$0.674699\pi$
$618$		0			0
$619$	−4.60330	−	17.1798i	−0.185022	−	0.690513i	−0.994626	−	0.103535i	$-0.966984\pi$
$619$	−4.60330	−	17.1798i	−0.185022	−	0.690513i	0.809603	−	0.586977i	$-0.199682\pi$
$620$		0			0
$621$	−40.7713	+	3.18290i	−1.63610	+	0.127725i
$622$		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
$627$	5.35600	+	4.26219i	0.213898	+	0.170216i
$628$		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
$635$	7.15884	−	26.7172i	0.284090	−	1.06024i
$636$		0			0
$637$	−3.44897	−	12.8717i	−0.136653	−	0.509997i
$638$		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
$643$	8.91467	−	33.2700i	0.351560	−	1.31204i	−0.533198	−	0.845991i	$-0.679010\pi$
$643$	8.91467	−	33.2700i	0.351560	−	1.31204i	0.884758	−	0.466050i	$-0.154323\pi$
$644$		0			0
$645$	6.08728	−	40.6725i	0.239686	−	1.60148i
$646$		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
$651$	0.185626	−	1.24027i	0.00727525	−	0.0486099i
$652$		0			0
$653$	2.17456	−	8.11558i	0.0850972	−	0.317587i	−0.910235	−	0.414091i	$-0.864099\pi$
$653$	2.17456	−	8.11558i	0.0850972	−	0.317587i	0.995333	+	0.0965042i	$0.0307661\pi$
$654$		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
$659$	6.62788	+	24.7356i	0.258186	+	0.963562i	0.966290	+	0.257455i	$0.0828838\pi$
$659$	6.62788	+	24.7356i	0.258186	+	0.963562i	−0.708105	+	0.706107i	$0.750450\pi$
$660$		0			0
$661$	−5.44473	+	20.3200i	−0.211775	+	0.790357i	0.775501	+	0.631346i	$0.217497\pi$
$661$	−5.44473	+	20.3200i	−0.211775	+	0.790357i	−0.987277	+	0.159011i	$0.949170\pi$
$662$		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
$669$	28.1408	+	22.3939i	1.08799	+	0.865798i
$670$		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
$675$	−1.61511	−	2.35318i	−0.0621658	−	0.0905741i
$676$		0			0
$677$	−4.91241	−	18.3334i	−0.188799	−	0.704608i	−0.993785	−	0.111314i	$-0.964494\pi$
$677$	−4.91241	−	18.3334i	−0.188799	−	0.704608i	0.804986	−	0.593294i	$-0.202173\pi$
$678$		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	$-0.281941\pi$
$683$	−3.70253	−	3.70253i	−0.141673	−	0.141673i	−0.774386	+	0.632713i	$0.781941\pi$
$684$		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
$691$	−8.18783	+	2.19392i	−0.311480	+	0.0834607i	−0.411173	−	0.911558i	$-0.634881\pi$
$691$	−8.18783	+	2.19392i	−0.311480	+	0.0834607i	0.0996929	+	0.995018i	$0.468214\pi$
$692$		0			0
$693$	0.142645	−	0.228066i	0.00541863	−	0.00866352i
$694$		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
$699$	15.6521	+	2.34258i	0.592015	+	0.0886045i
$700$		0			0
$701$	16.2977	+	16.2977i	0.615557	+	0.615557i	0.944389	−	0.328831i	$-0.106655\pi$
$701$	16.2977	+	16.2977i	0.615557	+	0.615557i	−0.328831	+	0.944389i	$0.606655\pi$
$702$		0			0
$703$		−	52.8439i		−	1.99304i
$704$		0			0
$705$	−34.7992	+	25.7388i	−1.31062	+	0.969378i
$706$		0			0
$707$	1.54314	+	0.413484i	0.0580359	+	0.0155507i
$708$		0			0
$709$	−18.6437	+	4.99557i	−0.700180	+	0.187613i	−0.591311	−	0.806443i	$-0.701390\pi$
$709$	−18.6437	+	4.99557i	−0.700180	+	0.187613i	−0.108869	+	0.994056i	$0.534723\pi$
$710$		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
$715$	−2.73210	−	0.732065i	−0.102175	−	0.0273777i
$716$		0			0
$717$	4.64202	+	11.7917i	0.173359	+	0.440370i
$718$		0			0
$719$	24.2401			0.904003			0.452002	−	0.892017i	$-0.350710\pi$
$719$	24.2401			0.904003			0.452002	+	0.892017i	$0.350710\pi$
$720$		0			0
$721$	1.07669			0.0400980
$722$		0			0
$723$	−2.69322	+	3.38438i	−0.100162	+	0.125866i
$724$		0			0
$725$	0.509157	+	0.136428i	0.0189096	+	0.00506682i
$726$		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
$731$	−46.9902	+	12.5910i	−1.73800	+	0.465694i
$732$		0			0
$733$	8.04180	+	2.15479i	0.297031	+	0.0795891i	0.404257	−	0.914646i	$-0.367530\pi$
$733$	8.04180	+	2.15479i	0.297031	+	0.0795891i	−0.107226	+	0.994235i	$0.534197\pi$
$734$		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
$741$	−6.80909	−	17.2966i	−0.250138	−	0.635405i
$742$		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
$747$	−0.161417	+	4.56734i	−0.00590595	+	0.167110i
$748$		0			0
$749$	−1.26399	+	0.338684i	−0.0461850	+	0.0123752i
$750$		0			0
$751$	−28.0215	+	16.1782i	−1.02252	+	0.590352i	−0.914833	−	0.403833i	$-0.867678\pi$
$751$	−28.0215	+	16.1782i	−1.02252	+	0.590352i	−0.107687	+	0.994185i	$0.534344\pi$
$752$		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	$-0.00893934\pi$
$761$	13.1168	+	22.7190i	0.475485	+	0.823564i	−0.524121	+	0.851644i	$0.675606\pi$
$762$		0			0
$763$	−0.480419	−	1.79295i	−0.0173923	−	0.0649090i
$764$		0			0
$765$	14.5066	−	23.1938i	0.524489	−	0.838572i
$766$		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
$771$	−17.9019	+	7.04741i	−0.644722	+	0.253806i
$772$		0			0
$773$	−4.69430	+	4.69430i	−0.168842	+	0.168842i	−0.786470	−	0.617628i	$-0.788094\pi$
$773$	−4.69430	+	4.69430i	−0.168842	+	0.168842i	0.617628	+	0.786470i	$0.288094\pi$
$774$		0			0
$775$	−3.11641			−0.111945
$776$		0			0
$777$	−2.06343	+	0.234659i	−0.0740252	+	0.00841834i
$778$		0			0
$779$	−13.4311	+	50.1255i	−0.481218	+	1.79593i
$780$		0			0
$781$	−0.692294	−	2.58368i	−0.0247722	−	0.0924512i
$782$		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
$787$	11.7352	−	43.7964i	0.418315	−	1.56117i	−0.359786	−	0.933035i	$-0.617150\pi$
$787$	11.7352	−	43.7964i	0.418315	−	1.56117i	0.778101	−	0.628139i	$-0.216183\pi$
$788$		0			0
$789$	26.0283	+	20.7128i	0.926631	+	0.737394i
$790$		0			0
$791$			2.69611i			0.0958625i
$792$		0			0
$793$			8.78888i			0.312102i
$794$		0			0
$795$	0.0124549	−	0.00490310i	0.000441731	−	0.000173895i
$796$		0			0
$797$	−9.77347	+	36.4751i	−0.346194	+	1.29201i	0.545017	+	0.838425i	$0.316523\pi$
$797$	−9.77347	+	36.4751i	−0.346194	+	1.29201i	−0.891211	+	0.453589i	$0.850143\pi$
$798$		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
$803$	−0.341296	−	1.27374i	−0.0120441	−	0.0449492i
$804$		0			0
$805$	−0.548411	+	2.04670i	−0.0193289	+	0.0721366i
$806$		0			0
$807$	11.1645	+	15.0946i	0.393008	+	0.531353i
$808$		0			0
$809$	−24.0071			−0.844045			−0.422023	−	0.906585i	$-0.638680\pi$
$809$	−24.0071			−0.844045			−0.422023	+	0.906585i	$0.638680\pi$
$810$		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
$813$	3.32776	−	22.2346i	0.116710	−	0.779800i
$814$		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
$819$	−0.645154	+	0.342686i	−0.0225435	+	0.0119744i
$820$		0			0
$821$	−12.4067	−	46.3025i	−0.432998	−	1.61597i	−0.745813	−	0.666156i	$-0.767939\pi$
$821$	−12.4067	−	46.3025i	−0.432998	−	1.61597i	0.312815	−	0.949814i	$-0.398728\pi$
$822$		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	$-0.158368\pi$
$827$	11.5464	+	11.5464i	0.401509	+	0.401509i	−0.477256	+	0.878764i	$0.658368\pi$
$828$		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
$835$	−21.9815	+	5.88992i	−0.760700	+	0.203829i
$836$		0			0
$837$	29.3917	−	2.29453i	1.01593	−	0.0793106i
$838$		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
$843$	7.96200	−	10.0053i	0.274226	−	0.344601i
$844$		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
$851$	71.4254	+	19.1384i	2.44843	+	0.656055i
$852$		0			0
$853$	42.5120	−	11.3911i	1.45558	−	0.390023i	0.557622	−	0.830095i	$-0.311714\pi$
$853$	42.5120	−	11.3911i	1.45558	−	0.390023i	0.897962	+	0.440072i	$0.145047\pi$
$854$		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	$-0.785666\pi$
$857$	4.36756	−	7.56483i	0.149193	−	0.258410i	0.930929	+	0.365199i	$0.118999\pi$
$858$		0			0
$859$	48.4800	+	12.9902i	1.65411	+	0.443219i	0.960761	−	0.277378i	$-0.0894655\pi$
$859$	48.4800	+	12.9902i	1.65411	+	0.443219i	0.693354	+	0.720597i	$0.256132\pi$
$860$		0			0
$861$	2.01693	+	0.301865i	0.0687366	+	0.0102875i
$862$		0			0
$863$	3.87853			0.132027			0.0660134	−	0.997819i	$-0.478972\pi$
$863$	3.87853			0.132027			0.0660134	+	0.997819i	$0.478972\pi$
$864$		0			0
$865$	10.0817			0.342789
$866$		0			0
$867$	−2.88369	−	0.431590i	−0.0979353	−	0.0146576i
$868$		0			0
$869$	−2.35827	−	0.631896i	−0.0799988	−	0.0214356i
$870$		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
$875$	−1.44311	+	0.386679i	−0.0487859	+	0.0130721i
$876$		0			0
$877$	−20.2871	−	5.43592i	−0.685047	−	0.183558i	−0.100524	−	0.994935i	$-0.532052\pi$
$877$	−20.2871	−	5.43592i	−0.685047	−	0.183558i	−0.584524	+	0.811377i	$0.698719\pi$
$878$		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	0.849375	−	0.527791i	$-0.176979\pi$
$883$	9.55597	+	9.55597i	0.321584	+	0.321584i	−0.527791	+	0.849375i	$0.676979\pi$
$884$		0			0
$885$	9.64811	−	12.1241i	0.324318	−	0.407547i
$886$		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
$891$	5.97747	+	2.06383i	0.200253	+	0.0691409i
$892$		0			0
$893$	−64.3530	+	17.2433i	−2.15349	+	0.577027i
$894$		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
$907$	3.66301	+	13.6705i	0.121628	+	0.453923i	0.999697	−	0.0246114i	$-0.00783484\pi$
$907$	3.66301	+	13.6705i	0.121628	+	0.453923i	−0.878069	+	0.478534i	$0.841168\pi$
$908$		0			0
$909$	−1.32647	+	37.5327i	−0.0439963	+	1.24488i
$910$		0			0
$911$	−20.0062	+	34.6517i	−0.662834	+	1.14806i	0.317034	+	0.948414i	$0.397313\pi$
$911$	−20.0062	+	34.6517i	−0.662834	+	1.14806i	−0.979868	+	0.199648i	$0.936020\pi$
$912$		0			0
$913$	0.535197	+	0.926988i	0.0177124	+	0.0306788i
$914$		0			0
$915$	2.49123	−	16.6453i	0.0823576	−	0.550277i
$916$		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
$923$	−1.88004	+	7.01641i	−0.0618823	+	0.230948i
$924$		0			0
$925$	1.33569	+	4.98486i	0.0439172	+	0.163901i
$926$		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
$931$	−10.1662	+	37.9409i	−0.333185	+	1.24346i
$932$		0			0
$933$	22.2270	−	8.75007i	0.727681	−	0.286464i
$934$		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
$939$	27.6008	+	21.9641i	0.900717	+	0.716772i
$940$		0			0
$941$	11.1081	−	41.4559i	0.362113	−	1.35142i	−0.509179	−	0.860660i	$-0.670051\pi$
$941$	11.1081	−	41.4559i	0.362113	−	1.35142i	0.871292	−	0.490764i	$-0.163282\pi$
$942$		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
$947$	−12.0721	−	45.0535i	−0.392289	−	1.46404i	−0.826349	−	0.563159i	$-0.809586\pi$
$947$	−12.0721	−	45.0535i	−0.392289	−	1.46404i	0.434060	−	0.900884i	$-0.357081\pi$
$948$		0			0
$949$	−0.926848	+	3.45904i	−0.0300867	+	0.112285i
$950$		0			0
$951$	36.1920	−	4.11585i	1.17361	−	0.133466i
$952$		0			0
$953$	−20.2249			−0.655149			−0.327575	−	0.944825i	$-0.606231\pi$
$953$	−20.2249			−0.655149			−0.327575	+	0.944825i	$0.606231\pi$
$954$		0			0
$955$	7.72399	−	7.72399i	0.249943	−	0.249943i
$956$		0			0
$957$	−1.08673	+	0.427810i	−0.0351289	+	0.0138291i
$958$		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
$963$	−14.4305	−	27.1675i	−0.465018	−	0.875459i
$964$		0			0
$965$	14.4339	+	53.8680i	0.464644	+	1.73407i
$966$		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	$-0.283989\pi$
$971$	−4.69660	−	4.69660i	−0.150721	−	0.150721i	−0.778440	+	0.627719i	$0.783989\pi$
$972$		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
$979$	−7.19193	+	1.92707i	−0.229855	+	0.0615895i
$980$		0			0
$981$	38.5367	−	20.4695i	1.23038	−	0.653542i
$982$		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
$987$	0.959079	+	2.43627i	0.0305278	+	0.0775472i
$988$		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
$995$	2.80066	+	0.750435i	0.0887870	+	0.0237904i
$996$		0			0
$997$	7.68222	−	2.05844i	0.243298	−	0.0651916i	−0.135109	−	0.990831i	$-0.543139\pi$
$997$	7.68222	−	2.05844i	0.243298	−	0.0651916i	0.378407	+	0.925639i	$0.376472\pi$
$998$		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.335.22		88
3.2	odd	2		1728.2.z.a.143.5		88
4.3	odd	2		144.2.u.a.11.19	✓	88
9.4	even	3		1728.2.z.a.719.5		88
9.5	odd	6	inner	576.2.y.a.527.11		88
12.11	even	2		432.2.v.a.251.4		88
16.3	odd	4	inner	576.2.y.a.47.11		88
16.13	even	4		144.2.u.a.83.19	yes	88
36.23	even	6		144.2.u.a.59.19	yes	88
36.31	odd	6		432.2.v.a.395.4		88
48.29	odd	4		432.2.v.a.35.4		88
48.35	even	4		1728.2.z.a.1007.5		88
144.13	even	12		432.2.v.a.179.4		88
144.67	odd	12		1728.2.z.a.1583.5		88
144.77	odd	12		144.2.u.a.131.19	yes	88
144.131	even	12	inner	576.2.y.a.239.22		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.19	✓	88	4.3	odd	2
144.2.u.a.59.19	yes	88	36.23	even	6
144.2.u.a.83.19	yes	88	16.13	even	4
144.2.u.a.131.19	yes	88	144.77	odd	12
432.2.v.a.35.4		88	48.29	odd	4
432.2.v.a.179.4		88	144.13	even	12
432.2.v.a.251.4		88	12.11	even	2
432.2.v.a.395.4		88	36.31	odd	6
576.2.y.a.47.11		88	16.3	odd	4	inner
576.2.y.a.239.22		88	144.131	even	12	inner
576.2.y.a.335.22		88	1.1	even	1	trivial
576.2.y.a.527.11		88	9.5	odd	6	inner
1728.2.z.a.143.5		88	3.2	odd	2
1728.2.z.a.719.5		88	9.4	even	3
1728.2.z.a.1007.5		88	48.35	even	4
1728.2.z.a.1583.5		88	144.67	odd	12

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)

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