LMFDB - Embedded newform 546.2.c.d.337.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(337,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("546.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.c (of order $2$, degree $1$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	546.337
Dual form			546.2.c.d.337.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -3.00000i q^{5} +1.00000i q^{6} +1.00000i q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -3.00000i q^{5} +1.00000i q^{6} +1.00000i q^{7} -1.00000i q^{8} +1.00000 q^{9} +3.00000 q^{10} -5.00000i q^{11} -1.00000 q^{12} +(-3.00000 - 2.00000i) q^{13} -1.00000 q^{14} -3.00000i q^{15} +1.00000 q^{16} +3.00000 q^{17} +1.00000i q^{18} -1.00000i q^{19} +3.00000i q^{20} +1.00000i q^{21} +5.00000 q^{22} -1.00000 q^{23} -1.00000i q^{24} -4.00000 q^{25} +(2.00000 - 3.00000i) q^{26} +1.00000 q^{27} -1.00000i q^{28} +5.00000 q^{29} +3.00000 q^{30} +1.00000i q^{32} -5.00000i q^{33} +3.00000i q^{34} +3.00000 q^{35} -1.00000 q^{36} -7.00000i q^{37} +1.00000 q^{38} +(-3.00000 - 2.00000i) q^{39} -3.00000 q^{40} -1.00000 q^{42} -1.00000 q^{43} +5.00000i q^{44} -3.00000i q^{45} -1.00000i q^{46} +8.00000i q^{47} +1.00000 q^{48} -1.00000 q^{49} -4.00000i q^{50} +3.00000 q^{51} +(3.00000 + 2.00000i) q^{52} +14.0000 q^{53} +1.00000i q^{54} -15.0000 q^{55} +1.00000 q^{56} -1.00000i q^{57} +5.00000i q^{58} +14.0000i q^{59} +3.00000i q^{60} -3.00000 q^{61} +1.00000i q^{63} -1.00000 q^{64} +(-6.00000 + 9.00000i) q^{65} +5.00000 q^{66} +8.00000i q^{67} -3.00000 q^{68} -1.00000 q^{69} +3.00000i q^{70} -10.0000i q^{71} -1.00000i q^{72} +11.0000i q^{73} +7.00000 q^{74} -4.00000 q^{75} +1.00000i q^{76} +5.00000 q^{77} +(2.00000 - 3.00000i) q^{78} -3.00000i q^{80} +1.00000 q^{81} +6.00000i q^{83} -1.00000i q^{84} -9.00000i q^{85} -1.00000i q^{86} +5.00000 q^{87} -5.00000 q^{88} -16.0000i q^{89} +3.00000 q^{90} +(2.00000 - 3.00000i) q^{91} +1.00000 q^{92} -8.00000 q^{94} -3.00000 q^{95} +1.00000i q^{96} -2.00000i q^{97} -1.00000i q^{98} -5.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} - 2 q^{4} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^3 - 2 * q^4 + 2 * q^9	$ 2 q + 2 q^{3} - 2 q^{4} + 2 q^{9} + 6 q^{10} - 2 q^{12} - 6 q^{13} - 2 q^{14} + 2 q^{16} + 6 q^{17} + 10 q^{22} - 2 q^{23} - 8 q^{25} + 4 q^{26} + 2 q^{27} + 10 q^{29} + 6 q^{30} + 6 q^{35} - 2 q^{36} + 2 q^{38} - 6 q^{39} - 6 q^{40} - 2 q^{42} - 2 q^{43} + 2 q^{48} - 2 q^{49} + 6 q^{51} + 6 q^{52} + 28 q^{53} - 30 q^{55} + 2 q^{56} - 6 q^{61} - 2 q^{64} - 12 q^{65} + 10 q^{66} - 6 q^{68} - 2 q^{69} + 14 q^{74} - 8 q^{75} + 10 q^{77} + 4 q^{78} + 2 q^{81} + 10 q^{87} - 10 q^{88} + 6 q^{90} + 4 q^{91} + 2 q^{92} - 16 q^{94} - 6 q^{95}+O(q^{100}) $ 2 * q + 2 * q^3 - 2 * q^4 + 2 * q^9 + 6 * q^10 - 2 * q^12 - 6 * q^13 - 2 * q^14 + 2 * q^16 + 6 * q^17 + 10 * q^22 - 2 * q^23 - 8 * q^25 + 4 * q^26 + 2 * q^27 + 10 * q^29 + 6 * q^30 + 6 * q^35 - 2 * q^36 + 2 * q^38 - 6 * q^39 - 6 * q^40 - 2 * q^42 - 2 * q^43 + 2 * q^48 - 2 * q^49 + 6 * q^51 + 6 * q^52 + 28 * q^53 - 30 * q^55 + 2 * q^56 - 6 * q^61 - 2 * q^64 - 12 * q^65 + 10 * q^66 - 6 * q^68 - 2 * q^69 + 14 * q^74 - 8 * q^75 + 10 * q^77 + 4 * q^78 + 2 * q^81 + 10 * q^87 - 10 * q^88 + 6 * q^90 + 4 * q^91 + 2 * q^92 - 16 * q^94 - 6 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−1.00000			−0.500000
$5$		−	3.00000i		−	1.34164i	−0.741620	−	0.670820i	$-0.765942\pi$
$5$		−	3.00000i		−	1.34164i	0.741620	−	0.670820i	$-0.234058\pi$
$6$			1.00000i			0.408248i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		−	1.00000i		−	0.353553i
$9$	1.00000			0.333333
$10$	3.00000			0.948683
$11$		−	5.00000i		−	1.50756i	−0.657129	−	0.753778i	$-0.728229\pi$
$11$		−	5.00000i		−	1.50756i	0.657129	−	0.753778i	$-0.271771\pi$
$12$	−1.00000			−0.288675
$13$	−3.00000	−	2.00000i	−0.832050	−	0.554700i
$13$	−3.00000	−	2.00000i	−0.832050	−	0.554700i
$14$	−1.00000			−0.267261
$15$		−	3.00000i		−	0.774597i
$16$	1.00000			0.250000
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$			1.00000i			0.235702i
$19$		−	1.00000i		−	0.229416i	−0.993399	−	0.114708i	$-0.963407\pi$
$19$		−	1.00000i		−	0.229416i	0.993399	−	0.114708i	$-0.0365932\pi$
$20$			3.00000i			0.670820i
$21$			1.00000i			0.218218i
$22$	5.00000			1.06600
$23$	−1.00000			−0.208514			−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000			−0.208514			−0.104257	+	0.994550i	$0.533247\pi$
$24$		−	1.00000i		−	0.204124i
$25$	−4.00000			−0.800000
$26$	2.00000	−	3.00000i	0.392232	−	0.588348i
$27$	1.00000			0.192450
$28$		−	1.00000i		−	0.188982i
$29$	5.00000			0.928477			0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000			0.928477			0.464238	+	0.885710i	$0.346328\pi$
$30$	3.00000			0.547723
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$			1.00000i			0.176777i
$33$		−	5.00000i		−	0.870388i
$34$			3.00000i			0.514496i
$35$	3.00000			0.507093
$36$	−1.00000			−0.166667
$37$		−	7.00000i		−	1.15079i	−0.817875	−	0.575396i	$-0.804848\pi$
$37$		−	7.00000i		−	1.15079i	0.817875	−	0.575396i	$-0.195152\pi$
$38$	1.00000			0.162221
$39$	−3.00000	−	2.00000i	−0.480384	−	0.320256i
$40$	−3.00000			−0.474342
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$	−1.00000			−0.154303
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$			5.00000i			0.753778i
$45$		−	3.00000i		−	0.447214i
$46$		−	1.00000i		−	0.147442i
$47$			8.00000i			1.16692i	0.812142	+	0.583460i	$0.198301\pi$
$47$			8.00000i			1.16692i	−0.812142	+	0.583460i	$0.801699\pi$
$48$	1.00000			0.144338
$49$	−1.00000			−0.142857
$50$		−	4.00000i		−	0.565685i
$51$	3.00000			0.420084
$52$	3.00000	+	2.00000i	0.416025	+	0.277350i
$53$	14.0000			1.92305			0.961524	−	0.274721i	$-0.0885855\pi$
$53$	14.0000			1.92305			0.961524	+	0.274721i	$0.0885855\pi$
$54$			1.00000i			0.136083i
$55$	−15.0000			−2.02260
$56$	1.00000			0.133631
$57$		−	1.00000i		−	0.132453i
$58$			5.00000i			0.656532i
$59$			14.0000i			1.82264i	0.411693	+	0.911322i	$0.364937\pi$
$59$			14.0000i			1.82264i	−0.411693	+	0.911322i	$0.635063\pi$
$60$			3.00000i			0.387298i
$61$	−3.00000			−0.384111			−0.192055	−	0.981384i	$-0.561515\pi$
$61$	−3.00000			−0.384111			−0.192055	+	0.981384i	$0.561515\pi$
$62$		0			0
$63$			1.00000i			0.125988i
$64$	−1.00000			−0.125000
$65$	−6.00000	+	9.00000i	−0.744208	+	1.11631i
$66$	5.00000			0.615457
$67$			8.00000i			0.977356i	0.872464	+	0.488678i	$0.162521\pi$
$67$			8.00000i			0.977356i	−0.872464	+	0.488678i	$0.837479\pi$
$68$	−3.00000			−0.363803
$69$	−1.00000			−0.120386
$70$			3.00000i			0.358569i
$71$		−	10.0000i		−	1.18678i	−0.804914	−	0.593391i	$-0.797789\pi$
$71$		−	10.0000i		−	1.18678i	0.804914	−	0.593391i	$-0.202211\pi$
$72$		−	1.00000i		−	0.117851i
$73$			11.0000i			1.28745i	0.765256	+	0.643726i	$0.222612\pi$
$73$			11.0000i			1.28745i	−0.765256	+	0.643726i	$0.777388\pi$
$74$	7.00000			0.813733
$75$	−4.00000			−0.461880
$76$			1.00000i			0.114708i
$77$	5.00000			0.569803
$78$	2.00000	−	3.00000i	0.226455	−	0.339683i
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$		−	3.00000i		−	0.335410i
$81$	1.00000			0.111111
$82$		0			0
$83$			6.00000i			0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$			6.00000i			0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$		−	1.00000i		−	0.109109i
$85$		−	9.00000i		−	0.976187i
$86$		−	1.00000i		−	0.107833i
$87$	5.00000			0.536056
$88$	−5.00000			−0.533002
$89$		−	16.0000i		−	1.69600i	−0.529999	−	0.847998i	$-0.677808\pi$
$89$		−	16.0000i		−	1.69600i	0.529999	−	0.847998i	$-0.322192\pi$
$90$	3.00000			0.316228
$91$	2.00000	−	3.00000i	0.209657	−	0.314485i
$92$	1.00000			0.104257
$93$		0			0
$94$	−8.00000			−0.825137
$95$	−3.00000			−0.307794
$96$			1.00000i			0.102062i
$97$		−	2.00000i		−	0.203069i	−0.994832	−	0.101535i	$-0.967625\pi$
$97$		−	2.00000i		−	0.203069i	0.994832	−	0.101535i	$-0.0323753\pi$
$98$		−	1.00000i		−	0.101015i
$99$		−	5.00000i		−	0.502519i
$100$	4.00000			0.400000
$101$	−18.0000			−1.79107			−0.895533	−	0.444994i	$-0.853206\pi$
$101$	−18.0000			−1.79107			−0.895533	+	0.444994i	$0.853206\pi$
$102$			3.00000i			0.297044i
$103$	−11.0000			−1.08386			−0.541931	−	0.840423i	$-0.682307\pi$
$103$	−11.0000			−1.08386			−0.541931	+	0.840423i	$0.682307\pi$
$104$	−2.00000	+	3.00000i	−0.196116	+	0.294174i
$105$	3.00000			0.292770
$106$			14.0000i			1.35980i
$107$	18.0000			1.74013			0.870063	−	0.492941i	$-0.164078\pi$
$107$	18.0000			1.74013			0.870063	+	0.492941i	$0.164078\pi$
$108$	−1.00000			−0.0962250
$109$			9.00000i			0.862044i	0.902342	+	0.431022i	$0.141847\pi$
$109$			9.00000i			0.862044i	−0.902342	+	0.431022i	$0.858153\pi$
$110$		−	15.0000i		−	1.43019i
$111$		−	7.00000i		−	0.664411i
$112$			1.00000i			0.0944911i
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$	1.00000			0.0936586
$115$			3.00000i			0.279751i
$116$	−5.00000			−0.464238
$117$	−3.00000	−	2.00000i	−0.277350	−	0.184900i
$118$	−14.0000			−1.28880
$119$			3.00000i			0.275010i
$120$	−3.00000			−0.273861
$121$	−14.0000			−1.27273
$122$		−	3.00000i		−	0.271607i
$123$		0			0
$124$		0			0
$125$		−	3.00000i		−	0.268328i
$126$	−1.00000			−0.0890871
$127$	−12.0000			−1.06483			−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000			−1.06483			−0.532414	+	0.846484i	$0.678715\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−1.00000			−0.0880451
$130$	−9.00000	−	6.00000i	−0.789352	−	0.526235i
$131$	7.00000			0.611593			0.305796	−	0.952097i	$-0.401077\pi$
$131$	7.00000			0.611593			0.305796	+	0.952097i	$0.401077\pi$
$132$			5.00000i			0.435194i
$133$	1.00000			0.0867110
$134$	−8.00000			−0.691095
$135$		−	3.00000i		−	0.258199i
$136$		−	3.00000i		−	0.257248i
$137$			3.00000i			0.256307i	0.991754	+	0.128154i	$0.0409051\pi$
$137$			3.00000i			0.256307i	−0.991754	+	0.128154i	$0.959095\pi$
$138$		−	1.00000i		−	0.0851257i
$139$	20.0000			1.69638			0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000			1.69638			0.848189	+	0.529694i	$0.177693\pi$
$140$	−3.00000			−0.253546
$141$			8.00000i			0.673722i
$142$	10.0000			0.839181
$143$	−10.0000	+	15.0000i	−0.836242	+	1.25436i
$144$	1.00000			0.0833333
$145$		−	15.0000i		−	1.24568i
$146$	−11.0000			−0.910366
$147$	−1.00000			−0.0824786
$148$			7.00000i			0.575396i
$149$		−	6.00000i		−	0.491539i	−0.969328	−	0.245770i	$-0.920959\pi$
$149$		−	6.00000i		−	0.491539i	0.969328	−	0.245770i	$-0.0790407\pi$
$150$		−	4.00000i		−	0.326599i
$151$			15.0000i			1.22068i	0.792139	+	0.610341i	$0.208968\pi$
$151$			15.0000i			1.22068i	−0.792139	+	0.610341i	$0.791032\pi$
$152$	−1.00000			−0.0811107
$153$	3.00000			0.242536
$154$			5.00000i			0.402911i
$155$		0			0
$156$	3.00000	+	2.00000i	0.240192	+	0.160128i
$157$	13.0000			1.03751			0.518756	−	0.854922i	$-0.326395\pi$
$157$	13.0000			1.03751			0.518756	+	0.854922i	$0.326395\pi$
$158$		0			0
$159$	14.0000			1.11027
$160$	3.00000			0.237171
$161$		−	1.00000i		−	0.0788110i
$162$			1.00000i			0.0785674i
$163$		−	4.00000i		−	0.313304i	−0.987654	−	0.156652i	$-0.949930\pi$
$163$		−	4.00000i		−	0.313304i	0.987654	−	0.156652i	$-0.0500701\pi$
$164$		0			0
$165$	−15.0000			−1.16775
$166$	−6.00000			−0.465690
$167$		−	7.00000i		−	0.541676i	−0.962625	−	0.270838i	$-0.912699\pi$
$167$		−	7.00000i		−	0.541676i	0.962625	−	0.270838i	$-0.0873008\pi$
$168$	1.00000			0.0771517
$169$	5.00000	+	12.0000i	0.384615	+	0.923077i
$170$	9.00000			0.690268
$171$		−	1.00000i		−	0.0764719i
$172$	1.00000			0.0762493
$173$	−26.0000			−1.97674			−0.988372	−	0.152057i	$-0.951410\pi$
$173$	−26.0000			−1.97674			−0.988372	+	0.152057i	$0.951410\pi$
$174$			5.00000i			0.379049i
$175$		−	4.00000i		−	0.302372i
$176$		−	5.00000i		−	0.376889i
$177$			14.0000i			1.05230i
$178$	16.0000			1.19925
$179$	10.0000			0.747435			0.373718	−	0.927543i	$-0.378083\pi$
$179$	10.0000			0.747435			0.373718	+	0.927543i	$0.378083\pi$
$180$			3.00000i			0.223607i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	3.00000	+	2.00000i	0.222375	+	0.148250i
$183$	−3.00000			−0.221766
$184$			1.00000i			0.0737210i
$185$	−21.0000			−1.54395
$186$		0			0
$187$		−	15.0000i		−	1.09691i
$188$		−	8.00000i		−	0.583460i
$189$			1.00000i			0.0727393i
$190$		−	3.00000i		−	0.217643i
$191$	17.0000			1.23008			0.615038	−	0.788497i	$-0.289140\pi$
$191$	17.0000			1.23008			0.615038	+	0.788497i	$0.289140\pi$
$192$	−1.00000			−0.0721688
$193$			16.0000i			1.15171i	0.817554	+	0.575853i	$0.195330\pi$
$193$			16.0000i			1.15171i	−0.817554	+	0.575853i	$0.804670\pi$
$194$	2.00000			0.143592
$195$	−6.00000	+	9.00000i	−0.429669	+	0.644503i
$196$	1.00000			0.0714286
$197$		−	2.00000i		−	0.142494i	−0.997459	−	0.0712470i	$-0.977302\pi$
$197$		−	2.00000i		−	0.142494i	0.997459	−	0.0712470i	$-0.0226979\pi$
$198$	5.00000			0.355335
$199$	−5.00000			−0.354441			−0.177220	−	0.984171i	$-0.556711\pi$
$199$	−5.00000			−0.354441			−0.177220	+	0.984171i	$0.556711\pi$
$200$			4.00000i			0.282843i
$201$			8.00000i			0.564276i
$202$		−	18.0000i		−	1.26648i
$203$			5.00000i			0.350931i
$204$	−3.00000			−0.210042
$205$		0			0
$206$		−	11.0000i		−	0.766406i
$207$	−1.00000			−0.0695048
$208$	−3.00000	−	2.00000i	−0.208013	−	0.138675i
$209$	−5.00000			−0.345857
$210$			3.00000i			0.207020i
$211$	−13.0000			−0.894957			−0.447478	−	0.894295i	$-0.647678\pi$
$211$	−13.0000			−0.894957			−0.447478	+	0.894295i	$0.647678\pi$
$212$	−14.0000			−0.961524
$213$		−	10.0000i		−	0.685189i
$214$			18.0000i			1.23045i
$215$			3.00000i			0.204598i
$216$		−	1.00000i		−	0.0680414i
$217$		0			0
$218$	−9.00000			−0.609557
$219$			11.0000i			0.743311i
$220$	15.0000			1.01130
$221$	−9.00000	−	6.00000i	−0.605406	−	0.403604i
$222$	7.00000			0.469809
$223$			16.0000i			1.07144i	0.844396	+	0.535720i	$0.179960\pi$
$223$			16.0000i			1.07144i	−0.844396	+	0.535720i	$0.820040\pi$
$224$	−1.00000			−0.0668153
$225$	−4.00000			−0.266667
$226$		−	6.00000i		−	0.399114i
$227$			8.00000i			0.530979i	0.964114	+	0.265489i	$0.0855335\pi$
$227$			8.00000i			0.530979i	−0.964114	+	0.265489i	$0.914466\pi$
$228$			1.00000i			0.0662266i
$229$		−	26.0000i		−	1.71813i	−0.511868	−	0.859064i	$-0.671046\pi$
$229$		−	26.0000i		−	1.71813i	0.511868	−	0.859064i	$-0.328954\pi$
$230$	−3.00000			−0.197814
$231$	5.00000			0.328976
$232$		−	5.00000i		−	0.328266i
$233$	14.0000			0.917170			0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000			0.917170			0.458585	+	0.888650i	$0.348356\pi$
$234$	2.00000	−	3.00000i	0.130744	−	0.196116i
$235$	24.0000			1.56559
$236$		−	14.0000i		−	0.911322i
$237$		0			0
$238$	−3.00000			−0.194461
$239$			4.00000i			0.258738i	0.991596	+	0.129369i	$0.0412952\pi$
$239$			4.00000i			0.258738i	−0.991596	+	0.129369i	$0.958705\pi$
$240$		−	3.00000i		−	0.193649i
$241$			10.0000i			0.644157i	0.946713	+	0.322078i	$0.104381\pi$
$241$			10.0000i			0.644157i	−0.946713	+	0.322078i	$0.895619\pi$
$242$		−	14.0000i		−	0.899954i
$243$	1.00000			0.0641500
$244$	3.00000			0.192055
$245$			3.00000i			0.191663i
$246$		0			0
$247$	−2.00000	+	3.00000i	−0.127257	+	0.190885i
$248$		0			0
$249$			6.00000i			0.380235i
$250$	3.00000			0.189737
$251$	17.0000			1.07303			0.536515	−	0.843891i	$-0.319740\pi$
$251$	17.0000			1.07303			0.536515	+	0.843891i	$0.319740\pi$
$252$		−	1.00000i		−	0.0629941i
$253$			5.00000i			0.314347i
$254$		−	12.0000i		−	0.752947i
$255$		−	9.00000i		−	0.563602i
$256$	1.00000			0.0625000
$257$	18.0000			1.12281			0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000			1.12281			0.561405	+	0.827541i	$0.310261\pi$
$258$		−	1.00000i		−	0.0622573i
$259$	7.00000			0.434959
$260$	6.00000	−	9.00000i	0.372104	−	0.558156i
$261$	5.00000			0.309492
$262$			7.00000i			0.432461i
$263$	24.0000			1.47990			0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000			1.47990			0.739952	+	0.672660i	$0.234848\pi$
$264$	−5.00000			−0.307729
$265$		−	42.0000i		−	2.58004i
$266$			1.00000i			0.0613139i
$267$		−	16.0000i		−	0.979184i
$268$		−	8.00000i		−	0.488678i
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$	3.00000			0.182574
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$	3.00000			0.181902
$273$	2.00000	−	3.00000i	0.121046	−	0.181568i
$274$	−3.00000			−0.181237
$275$			20.0000i			1.20605i
$276$	1.00000			0.0601929
$277$	28.0000			1.68236			0.841178	−	0.540758i	$-0.181862\pi$
$277$	28.0000			1.68236			0.841178	+	0.540758i	$0.181862\pi$
$278$			20.0000i			1.19952i
$279$		0			0
$280$		−	3.00000i		−	0.179284i
$281$		−	10.0000i		−	0.596550i	−0.954480	−	0.298275i	$-0.903589\pi$
$281$		−	10.0000i		−	0.596550i	0.954480	−	0.298275i	$-0.0964112\pi$
$282$	−8.00000			−0.476393
$283$	14.0000			0.832214			0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000			0.832214			0.416107	+	0.909316i	$0.363394\pi$
$284$			10.0000i			0.593391i
$285$	−3.00000			−0.177705
$286$	−15.0000	−	10.0000i	−0.886969	−	0.591312i
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	−8.00000			−0.470588
$290$	15.0000			0.880830
$291$		−	2.00000i		−	0.117242i
$292$		−	11.0000i		−	0.643726i
$293$			6.00000i			0.350524i	0.984522	+	0.175262i	$0.0560772\pi$
$293$			6.00000i			0.350524i	−0.984522	+	0.175262i	$0.943923\pi$
$294$		−	1.00000i		−	0.0583212i
$295$	42.0000			2.44533
$296$	−7.00000			−0.406867
$297$		−	5.00000i		−	0.290129i
$298$	6.00000			0.347571
$299$	3.00000	+	2.00000i	0.173494	+	0.115663i
$300$	4.00000			0.230940
$301$		−	1.00000i		−	0.0576390i
$302$	−15.0000			−0.863153
$303$	−18.0000			−1.03407
$304$		−	1.00000i		−	0.0573539i
$305$			9.00000i			0.515339i
$306$			3.00000i			0.171499i
$307$			8.00000i			0.456584i	0.973593	+	0.228292i	$0.0733141\pi$
$307$			8.00000i			0.456584i	−0.973593	+	0.228292i	$0.926686\pi$
$308$	−5.00000			−0.284901
$309$	−11.0000			−0.625768
$310$		0			0
$311$	−8.00000			−0.453638			−0.226819	−	0.973937i	$-0.572833\pi$
$311$	−8.00000			−0.453638			−0.226819	+	0.973937i	$0.572833\pi$
$312$	−2.00000	+	3.00000i	−0.113228	+	0.169842i
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$			13.0000i			0.733632i
$315$	3.00000			0.169031
$316$		0			0
$317$			8.00000i			0.449325i	0.974437	+	0.224662i	$0.0721279\pi$
$317$			8.00000i			0.449325i	−0.974437	+	0.224662i	$0.927872\pi$
$318$			14.0000i			0.785081i
$319$		−	25.0000i		−	1.39973i
$320$			3.00000i			0.167705i
$321$	18.0000			1.00466
$322$	1.00000			0.0557278
$323$		−	3.00000i		−	0.166924i
$324$	−1.00000			−0.0555556
$325$	12.0000	+	8.00000i	0.665640	+	0.443760i
$326$	4.00000			0.221540
$327$			9.00000i			0.497701i
$328$		0			0
$329$	−8.00000			−0.441054
$330$		−	15.0000i		−	0.825723i
$331$			20.0000i			1.09930i	0.835395	+	0.549650i	$0.185239\pi$
$331$			20.0000i			1.09930i	−0.835395	+	0.549650i	$0.814761\pi$
$332$		−	6.00000i		−	0.329293i
$333$		−	7.00000i		−	0.383598i
$334$	7.00000			0.383023
$335$	24.0000			1.31126
$336$			1.00000i			0.0545545i
$337$	33.0000			1.79762			0.898812	−	0.438334i	$-0.144431\pi$
$337$	33.0000			1.79762			0.898812	+	0.438334i	$0.144431\pi$
$338$	−12.0000	+	5.00000i	−0.652714	+	0.271964i
$339$	−6.00000			−0.325875
$340$			9.00000i			0.488094i
$341$		0			0
$342$	1.00000			0.0540738
$343$		−	1.00000i		−	0.0539949i
$344$			1.00000i			0.0539164i
$345$			3.00000i			0.161515i
$346$		−	26.0000i		−	1.39777i
$347$	28.0000			1.50312			0.751559	−	0.659665i	$-0.229302\pi$
$347$	28.0000			1.50312			0.751559	+	0.659665i	$0.229302\pi$
$348$	−5.00000			−0.268028
$349$		−	16.0000i		−	0.856460i	−0.903670	−	0.428230i	$-0.859137\pi$
$349$		−	16.0000i		−	0.856460i	0.903670	−	0.428230i	$-0.140863\pi$
$350$	4.00000			0.213809
$351$	−3.00000	−	2.00000i	−0.160128	−	0.106752i
$352$	5.00000			0.266501
$353$		−	24.0000i		−	1.27739i	−0.769460	−	0.638696i	$-0.779474\pi$
$353$		−	24.0000i		−	1.27739i	0.769460	−	0.638696i	$-0.220526\pi$
$354$	−14.0000			−0.744092
$355$	−30.0000			−1.59223
$356$			16.0000i			0.847998i
$357$			3.00000i			0.158777i
$358$			10.0000i			0.528516i
$359$			34.0000i			1.79445i	0.441572	+	0.897226i	$0.354421\pi$
$359$			34.0000i			1.79445i	−0.441572	+	0.897226i	$0.645579\pi$
$360$	−3.00000			−0.158114
$361$	18.0000			0.947368
$362$			2.00000i			0.105118i
$363$	−14.0000			−0.734809
$364$	−2.00000	+	3.00000i	−0.104828	+	0.157243i
$365$	33.0000			1.72730
$366$		−	3.00000i		−	0.156813i
$367$	−32.0000			−1.67039			−0.835193	−	0.549957i	$-0.814644\pi$
$367$	−32.0000			−1.67039			−0.835193	+	0.549957i	$0.814644\pi$
$368$	−1.00000			−0.0521286
$369$		0			0
$370$		−	21.0000i		−	1.09174i
$371$			14.0000i			0.726844i
$372$		0			0
$373$	−26.0000			−1.34623			−0.673114	−	0.739538i	$-0.735044\pi$
$373$	−26.0000			−1.34623			−0.673114	+	0.739538i	$0.735044\pi$
$374$	15.0000			0.775632
$375$		−	3.00000i		−	0.154919i
$376$	8.00000			0.412568
$377$	−15.0000	−	10.0000i	−0.772539	−	0.515026i
$378$	−1.00000			−0.0514344
$379$			4.00000i			0.205466i	0.994709	+	0.102733i	$0.0327588\pi$
$379$			4.00000i			0.205466i	−0.994709	+	0.102733i	$0.967241\pi$
$380$	3.00000			0.153897
$381$	−12.0000			−0.614779
$382$			17.0000i			0.869796i
$383$			31.0000i			1.58403i	0.610504	+	0.792013i	$0.290967\pi$
$383$			31.0000i			1.58403i	−0.610504	+	0.792013i	$0.709033\pi$
$384$		−	1.00000i		−	0.0510310i
$385$		−	15.0000i		−	0.764471i
$386$	−16.0000			−0.814379
$387$	−1.00000			−0.0508329
$388$			2.00000i			0.101535i
$389$	−30.0000			−1.52106			−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000			−1.52106			−0.760530	+	0.649303i	$0.775061\pi$
$390$	−9.00000	−	6.00000i	−0.455733	−	0.303822i
$391$	−3.00000			−0.151717
$392$			1.00000i			0.0505076i
$393$	7.00000			0.353103
$394$	2.00000			0.100759
$395$		0			0
$396$			5.00000i			0.251259i
$397$		−	12.0000i		−	0.602263i	−0.953583	−	0.301131i	$-0.902636\pi$
$397$		−	12.0000i		−	0.602263i	0.953583	−	0.301131i	$-0.0973643\pi$
$398$		−	5.00000i		−	0.250627i
$399$	1.00000			0.0500626
$400$	−4.00000			−0.200000
$401$		−	30.0000i		−	1.49813i	−0.662497	−	0.749064i	$-0.730503\pi$
$401$		−	30.0000i		−	1.49813i	0.662497	−	0.749064i	$-0.269497\pi$
$402$	−8.00000			−0.399004
$403$		0			0
$404$	18.0000			0.895533
$405$		−	3.00000i		−	0.149071i
$406$	−5.00000			−0.248146
$407$	−35.0000			−1.73489
$408$		−	3.00000i		−	0.148522i
$409$			19.0000i			0.939490i	0.882802	+	0.469745i	$0.155654\pi$
$409$			19.0000i			0.939490i	−0.882802	+	0.469745i	$0.844346\pi$
$410$		0			0
$411$			3.00000i			0.147979i
$412$	11.0000			0.541931
$413$	−14.0000			−0.688895
$414$		−	1.00000i		−	0.0491473i
$415$	18.0000			0.883585
$416$	2.00000	−	3.00000i	0.0980581	−	0.147087i
$417$	20.0000			0.979404
$418$		−	5.00000i		−	0.244558i
$419$	−35.0000			−1.70986			−0.854931	−	0.518742i	$-0.826401\pi$
$419$	−35.0000			−1.70986			−0.854931	+	0.518742i	$0.826401\pi$
$420$	−3.00000			−0.146385
$421$		−	30.0000i		−	1.46211i	−0.682318	−	0.731055i	$-0.739028\pi$
$421$		−	30.0000i		−	1.46211i	0.682318	−	0.731055i	$-0.260972\pi$
$422$		−	13.0000i		−	0.632830i
$423$			8.00000i			0.388973i
$424$		−	14.0000i		−	0.679900i
$425$	−12.0000			−0.582086
$426$	10.0000			0.484502
$427$		−	3.00000i		−	0.145180i
$428$	−18.0000			−0.870063
$429$	−10.0000	+	15.0000i	−0.482805	+	0.724207i
$430$	−3.00000			−0.144673
$431$		−	30.0000i		−	1.44505i	−0.691345	−	0.722525i	$-0.742982\pi$
$431$		−	30.0000i		−	1.44505i	0.691345	−	0.722525i	$-0.257018\pi$
$432$	1.00000			0.0481125
$433$	4.00000			0.192228			0.0961139	−	0.995370i	$-0.469359\pi$
$433$	4.00000			0.192228			0.0961139	+	0.995370i	$0.469359\pi$
$434$		0			0
$435$		−	15.0000i		−	0.719195i
$436$		−	9.00000i		−	0.431022i
$437$			1.00000i			0.0478365i
$438$	−11.0000			−0.525600
$439$	−15.0000			−0.715911			−0.357955	−	0.933739i	$-0.616526\pi$
$439$	−15.0000			−0.715911			−0.357955	+	0.933739i	$0.616526\pi$
$440$			15.0000i			0.715097i
$441$	−1.00000			−0.0476190
$442$	6.00000	−	9.00000i	0.285391	−	0.428086i
$443$	−6.00000			−0.285069			−0.142534	−	0.989790i	$-0.545525\pi$
$443$	−6.00000			−0.285069			−0.142534	+	0.989790i	$0.545525\pi$
$444$			7.00000i			0.332205i
$445$	−48.0000			−2.27542
$446$	−16.0000			−0.757622
$447$		−	6.00000i		−	0.283790i
$448$		−	1.00000i		−	0.0472456i
$449$		−	21.0000i		−	0.991051i	−0.868593	−	0.495526i	$-0.834975\pi$
$449$		−	21.0000i		−	0.991051i	0.868593	−	0.495526i	$-0.165025\pi$
$450$		−	4.00000i		−	0.188562i
$451$		0			0
$452$	6.00000			0.282216
$453$			15.0000i			0.704761i
$454$	−8.00000			−0.375459
$455$	−9.00000	−	6.00000i	−0.421927	−	0.281284i
$456$	−1.00000			−0.0468293
$457$			8.00000i			0.374224i	0.982339	+	0.187112i	$0.0599128\pi$
$457$			8.00000i			0.374224i	−0.982339	+	0.187112i	$0.940087\pi$
$458$	26.0000			1.21490
$459$	3.00000			0.140028
$460$		−	3.00000i		−	0.139876i
$461$			15.0000i			0.698620i	0.937007	+	0.349310i	$0.113584\pi$
$461$			15.0000i			0.698620i	−0.937007	+	0.349310i	$0.886416\pi$
$462$			5.00000i			0.232621i
$463$			11.0000i			0.511213i	0.966781	+	0.255607i	$0.0822752\pi$
$463$			11.0000i			0.511213i	−0.966781	+	0.255607i	$0.917725\pi$
$464$	5.00000			0.232119
$465$		0			0
$466$			14.0000i			0.648537i
$467$	−7.00000			−0.323921			−0.161961	−	0.986797i	$-0.551782\pi$
$467$	−7.00000			−0.323921			−0.161961	+	0.986797i	$0.551782\pi$
$468$	3.00000	+	2.00000i	0.138675	+	0.0924500i
$469$	−8.00000			−0.369406
$470$			24.0000i			1.10704i
$471$	13.0000			0.599008
$472$	14.0000			0.644402
$473$			5.00000i			0.229900i
$474$		0			0
$475$			4.00000i			0.183533i
$476$		−	3.00000i		−	0.137505i
$477$	14.0000			0.641016
$478$	−4.00000			−0.182956
$479$		−	21.0000i		−	0.959514i	−0.877401	−	0.479757i	$-0.840725\pi$
$479$		−	21.0000i		−	0.959514i	0.877401	−	0.479757i	$-0.159275\pi$
$480$	3.00000			0.136931
$481$	−14.0000	+	21.0000i	−0.638345	+	0.957518i
$482$	−10.0000			−0.455488
$483$		−	1.00000i		−	0.0455016i
$484$	14.0000			0.636364
$485$	−6.00000			−0.272446
$486$			1.00000i			0.0453609i
$487$		−	32.0000i		−	1.45006i	−0.688718	−	0.725029i	$-0.741826\pi$
$487$		−	32.0000i		−	1.45006i	0.688718	−	0.725029i	$-0.258174\pi$
$488$			3.00000i			0.135804i
$489$		−	4.00000i		−	0.180886i
$490$	−3.00000			−0.135526
$491$	−28.0000			−1.26362			−0.631811	−	0.775122i	$-0.717688\pi$
$491$	−28.0000			−1.26362			−0.631811	+	0.775122i	$0.717688\pi$
$492$		0			0
$493$	15.0000			0.675566
$494$	−3.00000	−	2.00000i	−0.134976	−	0.0899843i
$495$	−15.0000			−0.674200
$496$		0			0
$497$	10.0000			0.448561
$498$	−6.00000			−0.268866
$499$			14.0000i			0.626726i	0.949633	+	0.313363i	$0.101456\pi$
$499$			14.0000i			0.626726i	−0.949633	+	0.313363i	$0.898544\pi$
$500$			3.00000i			0.134164i
$501$		−	7.00000i		−	0.312737i
$502$			17.0000i			0.758747i
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$	1.00000			0.0445435
$505$			54.0000i			2.40297i
$506$	−5.00000			−0.222277
$507$	5.00000	+	12.0000i	0.222058	+	0.532939i
$508$	12.0000			0.532414
$509$		−	1.00000i		−	0.0443242i	−0.999754	−	0.0221621i	$-0.992945\pi$
$509$		−	1.00000i		−	0.0443242i	0.999754	−	0.0221621i	$-0.00705500\pi$
$510$	9.00000			0.398527
$511$	−11.0000			−0.486611
$512$			1.00000i			0.0441942i
$513$		−	1.00000i		−	0.0441511i
$514$			18.0000i			0.793946i
$515$			33.0000i			1.45415i
$516$	1.00000			0.0440225
$517$	40.0000			1.75920
$518$			7.00000i			0.307562i
$519$	−26.0000			−1.14127
$520$	9.00000	+	6.00000i	0.394676	+	0.263117i
$521$	27.0000			1.18289			0.591446	−	0.806345i	$-0.298557\pi$
$521$	27.0000			1.18289			0.591446	+	0.806345i	$0.298557\pi$
$522$			5.00000i			0.218844i
$523$	−16.0000			−0.699631			−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000			−0.699631			−0.349816	+	0.936819i	$0.613756\pi$
$524$	−7.00000			−0.305796
$525$		−	4.00000i		−	0.174574i
$526$			24.0000i			1.04645i
$527$		0			0
$528$		−	5.00000i		−	0.217597i
$529$	−22.0000			−0.956522
$530$	42.0000			1.82436
$531$			14.0000i			0.607548i
$532$	−1.00000			−0.0433555
$533$		0			0
$534$	16.0000			0.692388
$535$		−	54.0000i		−	2.33462i
$536$	8.00000			0.345547
$537$	10.0000			0.431532
$538$		0			0
$539$			5.00000i			0.215365i
$540$			3.00000i			0.129099i
$541$			15.0000i			0.644900i	0.946586	+	0.322450i	$0.104506\pi$
$541$			15.0000i			0.644900i	−0.946586	+	0.322450i	$0.895494\pi$
$542$		0			0
$543$	2.00000			0.0858282
$544$			3.00000i			0.128624i
$545$	27.0000			1.15655
$546$	3.00000	+	2.00000i	0.128388	+	0.0855921i
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$		−	3.00000i		−	0.128154i
$549$	−3.00000			−0.128037
$550$	−20.0000			−0.852803
$551$		−	5.00000i		−	0.213007i
$552$			1.00000i			0.0425628i
$553$		0			0
$554$			28.0000i			1.18961i
$555$	−21.0000			−0.891400
$556$	−20.0000			−0.848189
$557$		−	22.0000i		−	0.932170i	−0.884740	−	0.466085i	$-0.845664\pi$
$557$		−	22.0000i		−	0.932170i	0.884740	−	0.466085i	$-0.154336\pi$
$558$		0			0
$559$	3.00000	+	2.00000i	0.126886	+	0.0845910i
$560$	3.00000			0.126773
$561$		−	15.0000i		−	0.633300i
$562$	10.0000			0.421825
$563$	9.00000			0.379305			0.189652	−	0.981851i	$-0.439264\pi$
$563$	9.00000			0.379305			0.189652	+	0.981851i	$0.439264\pi$
$564$		−	8.00000i		−	0.336861i
$565$			18.0000i			0.757266i
$566$			14.0000i			0.588464i
$567$			1.00000i			0.0419961i
$568$	−10.0000			−0.419591
$569$	−30.0000			−1.25767			−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000			−1.25767			−0.628833	+	0.777541i	$0.716467\pi$
$570$		−	3.00000i		−	0.125656i
$571$	32.0000			1.33916			0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000			1.33916			0.669579	+	0.742741i	$0.266474\pi$
$572$	10.0000	−	15.0000i	0.418121	−	0.627182i
$573$	17.0000			0.710185
$574$		0			0
$575$	4.00000			0.166812
$576$	−1.00000			−0.0416667
$577$			38.0000i			1.58196i	0.611842	+	0.790980i	$0.290429\pi$
$577$			38.0000i			1.58196i	−0.611842	+	0.790980i	$0.709571\pi$
$578$		−	8.00000i		−	0.332756i
$579$			16.0000i			0.664937i
$580$			15.0000i			0.622841i
$581$	−6.00000			−0.248922
$582$	2.00000			0.0829027
$583$		−	70.0000i		−	2.89910i
$584$	11.0000			0.455183
$585$	−6.00000	+	9.00000i	−0.248069	+	0.372104i
$586$	−6.00000			−0.247858
$587$			8.00000i			0.330195i	0.986277	+	0.165098i	$0.0527939\pi$
$587$			8.00000i			0.330195i	−0.986277	+	0.165098i	$0.947206\pi$
$588$	1.00000			0.0412393
$589$		0			0
$590$			42.0000i			1.72911i
$591$		−	2.00000i		−	0.0822690i
$592$		−	7.00000i		−	0.287698i
$593$		−	24.0000i		−	0.985562i	−0.870153	−	0.492781i	$-0.835980\pi$
$593$		−	24.0000i		−	0.985562i	0.870153	−	0.492781i	$-0.164020\pi$
$594$	5.00000			0.205152
$595$	9.00000			0.368964
$596$			6.00000i			0.245770i
$597$	−5.00000			−0.204636
$598$	−2.00000	+	3.00000i	−0.0817861	+	0.122679i
$599$	−45.0000			−1.83865			−0.919325	−	0.393499i	$-0.871265\pi$
$599$	−45.0000			−1.83865			−0.919325	+	0.393499i	$0.871265\pi$
$600$			4.00000i			0.163299i
$601$	−48.0000			−1.95796			−0.978980	−	0.203954i	$-0.934621\pi$
$601$	−48.0000			−1.95796			−0.978980	+	0.203954i	$0.934621\pi$
$602$	1.00000			0.0407570
$603$			8.00000i			0.325785i
$604$		−	15.0000i		−	0.610341i
$605$			42.0000i			1.70754i
$606$		−	18.0000i		−	0.731200i
$607$	23.0000			0.933541			0.466771	−	0.884378i	$-0.345417\pi$
$607$	23.0000			0.933541			0.466771	+	0.884378i	$0.345417\pi$
$608$	1.00000			0.0405554
$609$			5.00000i			0.202610i
$610$	−9.00000			−0.364399
$611$	16.0000	−	24.0000i	0.647291	−	0.970936i
$612$	−3.00000			−0.121268
$613$		−	39.0000i		−	1.57520i	−0.616190	−	0.787598i	$-0.711325\pi$
$613$		−	39.0000i		−	1.57520i	0.616190	−	0.787598i	$-0.288675\pi$
$614$	−8.00000			−0.322854
$615$		0			0
$616$		−	5.00000i		−	0.201456i
$617$		−	17.0000i		−	0.684394i	−0.939628	−	0.342197i	$-0.888829\pi$
$617$		−	17.0000i		−	0.684394i	0.939628	−	0.342197i	$-0.111171\pi$
$618$		−	11.0000i		−	0.442485i
$619$		−	11.0000i		−	0.442127i	−0.975259	−	0.221064i	$-0.929047\pi$
$619$		−	11.0000i		−	0.442127i	0.975259	−	0.221064i	$-0.0709529\pi$
$620$		0			0
$621$	−1.00000			−0.0401286
$622$		−	8.00000i		−	0.320771i
$623$	16.0000			0.641026
$624$	−3.00000	−	2.00000i	−0.120096	−	0.0800641i
$625$	−29.0000			−1.16000
$626$		−	6.00000i		−	0.239808i
$627$	−5.00000			−0.199681
$628$	−13.0000			−0.518756
$629$		−	21.0000i		−	0.837325i
$630$			3.00000i			0.119523i
$631$			35.0000i			1.39333i	0.717398	+	0.696664i	$0.245333\pi$
$631$			35.0000i			1.39333i	−0.717398	+	0.696664i	$0.754667\pi$
$632$		0			0
$633$	−13.0000			−0.516704
$634$	−8.00000			−0.317721
$635$			36.0000i			1.42862i
$636$	−14.0000			−0.555136
$637$	3.00000	+	2.00000i	0.118864	+	0.0792429i
$638$	25.0000			0.989759
$639$		−	10.0000i		−	0.395594i
$640$	−3.00000			−0.118585
$641$	−8.00000			−0.315981			−0.157991	−	0.987441i	$-0.550502\pi$
$641$	−8.00000			−0.315981			−0.157991	+	0.987441i	$0.550502\pi$
$642$			18.0000i			0.710403i
$643$		−	19.0000i		−	0.749287i	−0.927169	−	0.374643i	$-0.877765\pi$
$643$		−	19.0000i		−	0.749287i	0.927169	−	0.374643i	$-0.122235\pi$
$644$			1.00000i			0.0394055i
$645$			3.00000i			0.118125i
$646$	3.00000			0.118033
$647$	−2.00000			−0.0786281			−0.0393141	−	0.999227i	$-0.512517\pi$
$647$	−2.00000			−0.0786281			−0.0393141	+	0.999227i	$0.512517\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	70.0000			2.74774
$650$	−8.00000	+	12.0000i	−0.313786	+	0.470679i
$651$		0			0
$652$			4.00000i			0.156652i
$653$	−1.00000			−0.0391330			−0.0195665	−	0.999809i	$-0.506229\pi$
$653$	−1.00000			−0.0391330			−0.0195665	+	0.999809i	$0.506229\pi$
$654$	−9.00000			−0.351928
$655$		−	21.0000i		−	0.820538i
$656$		0			0
$657$			11.0000i			0.429151i
$658$		−	8.00000i		−	0.311872i
$659$	−30.0000			−1.16863			−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000			−1.16863			−0.584317	+	0.811525i	$0.698638\pi$
$660$	15.0000			0.583874
$661$			50.0000i			1.94477i	0.233373	+	0.972387i	$0.425024\pi$
$661$			50.0000i			1.94477i	−0.233373	+	0.972387i	$0.574976\pi$
$662$	−20.0000			−0.777322
$663$	−9.00000	−	6.00000i	−0.349531	−	0.233021i
$664$	6.00000			0.232845
$665$		−	3.00000i		−	0.116335i
$666$	7.00000			0.271244
$667$	−5.00000			−0.193601
$668$			7.00000i			0.270838i
$669$			16.0000i			0.618596i
$670$			24.0000i			0.927201i
$671$			15.0000i			0.579069i
$672$	−1.00000			−0.0385758
$673$	−11.0000			−0.424019			−0.212009	−	0.977268i	$-0.568001\pi$
$673$	−11.0000			−0.424019			−0.212009	+	0.977268i	$0.568001\pi$
$674$			33.0000i			1.27111i
$675$	−4.00000			−0.153960
$676$	−5.00000	−	12.0000i	−0.192308	−	0.461538i
$677$	8.00000			0.307465			0.153732	−	0.988113i	$-0.450871\pi$
$677$	8.00000			0.307465			0.153732	+	0.988113i	$0.450871\pi$
$678$		−	6.00000i		−	0.230429i
$679$	2.00000			0.0767530
$680$	−9.00000			−0.345134
$681$			8.00000i			0.306561i
$682$		0			0
$683$			1.00000i			0.0382639i	0.999817	+	0.0191320i	$0.00609027\pi$
$683$			1.00000i			0.0382639i	−0.999817	+	0.0191320i	$0.993910\pi$
$684$			1.00000i			0.0382360i
$685$	9.00000			0.343872
$686$	1.00000			0.0381802
$687$		−	26.0000i		−	0.991962i
$688$	−1.00000			−0.0381246
$689$	−42.0000	−	28.0000i	−1.60007	−	1.06672i
$690$	−3.00000			−0.114208
$691$		−	40.0000i		−	1.52167i	−0.648944	−	0.760836i	$-0.724789\pi$
$691$		−	40.0000i		−	1.52167i	0.648944	−	0.760836i	$-0.275211\pi$
$692$	26.0000			0.988372
$693$	5.00000			0.189934
$694$			28.0000i			1.06287i
$695$		−	60.0000i		−	2.27593i
$696$		−	5.00000i		−	0.189525i
$697$		0			0
$698$	16.0000			0.605609
$699$	14.0000			0.529529
$700$			4.00000i			0.151186i
$701$	2.00000			0.0755390			0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000			0.0755390			0.0377695	+	0.999286i	$0.487975\pi$
$702$	2.00000	−	3.00000i	0.0754851	−	0.113228i
$703$	−7.00000			−0.264010
$704$			5.00000i			0.188445i
$705$	24.0000			0.903892
$706$	24.0000			0.903252
$707$		−	18.0000i		−	0.676960i
$708$		−	14.0000i		−	0.526152i
$709$		−	26.0000i		−	0.976450i	−0.872718	−	0.488225i	$-0.837644\pi$
$709$		−	26.0000i		−	0.976450i	0.872718	−	0.488225i	$-0.162356\pi$
$710$		−	30.0000i		−	1.12588i
$711$		0			0
$712$	−16.0000			−0.599625
$713$		0			0
$714$	−3.00000			−0.112272
$715$	45.0000	+	30.0000i	1.68290	+	1.12194i
$716$	−10.0000			−0.373718
$717$			4.00000i			0.149383i
$718$	−34.0000			−1.26887
$719$	−20.0000			−0.745874			−0.372937	−	0.927857i	$-0.621649\pi$
$719$	−20.0000			−0.745874			−0.372937	+	0.927857i	$0.621649\pi$
$720$		−	3.00000i		−	0.111803i
$721$		−	11.0000i		−	0.409661i
$722$			18.0000i			0.669891i
$723$			10.0000i			0.371904i
$724$	−2.00000			−0.0743294
$725$	−20.0000			−0.742781
$726$		−	14.0000i		−	0.519589i
$727$	−7.00000			−0.259616			−0.129808	−	0.991539i	$-0.541436\pi$
$727$	−7.00000			−0.259616			−0.129808	+	0.991539i	$0.541436\pi$
$728$	−3.00000	−	2.00000i	−0.111187	−	0.0741249i
$729$	1.00000			0.0370370
$730$			33.0000i			1.22138i
$731$	−3.00000			−0.110959
$732$	3.00000			0.110883
$733$			36.0000i			1.32969i	0.746981	+	0.664845i	$0.231502\pi$
$733$			36.0000i			1.32969i	−0.746981	+	0.664845i	$0.768498\pi$
$734$		−	32.0000i		−	1.18114i
$735$			3.00000i			0.110657i
$736$		−	1.00000i		−	0.0368605i
$737$	40.0000			1.47342
$738$		0			0
$739$			24.0000i			0.882854i	0.897297	+	0.441427i	$0.145528\pi$
$739$			24.0000i			0.882854i	−0.897297	+	0.441427i	$0.854472\pi$
$740$	21.0000			0.771975
$741$	−2.00000	+	3.00000i	−0.0734718	+	0.110208i
$742$	−14.0000			−0.513956
$743$		−	4.00000i		−	0.146746i	−0.997305	−	0.0733729i	$-0.976624\pi$
$743$		−	4.00000i		−	0.146746i	0.997305	−	0.0733729i	$-0.0233763\pi$
$744$		0			0
$745$	−18.0000			−0.659469
$746$		−	26.0000i		−	0.951928i
$747$			6.00000i			0.219529i
$748$			15.0000i			0.548454i
$749$			18.0000i			0.657706i
$750$	3.00000			0.109545
$751$	−48.0000			−1.75154			−0.875772	−	0.482724i	$-0.839647\pi$
$751$	−48.0000			−1.75154			−0.875772	+	0.482724i	$0.839647\pi$
$752$			8.00000i			0.291730i
$753$	17.0000			0.619514
$754$	10.0000	−	15.0000i	0.364179	−	0.546268i
$755$	45.0000			1.63772
$756$		−	1.00000i		−	0.0363696i
$757$	18.0000			0.654221			0.327111	−	0.944986i	$-0.393925\pi$
$757$	18.0000			0.654221			0.327111	+	0.944986i	$0.393925\pi$
$758$	−4.00000			−0.145287
$759$			5.00000i			0.181489i
$760$			3.00000i			0.108821i
$761$			30.0000i			1.08750i	0.839248	+	0.543750i	$0.182996\pi$
$761$			30.0000i			1.08750i	−0.839248	+	0.543750i	$0.817004\pi$
$762$		−	12.0000i		−	0.434714i
$763$	−9.00000			−0.325822
$764$	−17.0000			−0.615038
$765$		−	9.00000i		−	0.325396i
$766$	−31.0000			−1.12008
$767$	28.0000	−	42.0000i	1.01102	−	1.51653i
$768$	1.00000			0.0360844
$769$		−	1.00000i		−	0.0360609i	−0.999837	−	0.0180305i	$-0.994260\pi$
$769$		−	1.00000i		−	0.0360609i	0.999837	−	0.0180305i	$-0.00573959\pi$
$770$	15.0000			0.540562
$771$	18.0000			0.648254
$772$		−	16.0000i		−	0.575853i
$773$		−	9.00000i		−	0.323708i	−0.986815	−	0.161854i	$-0.948253\pi$
$773$		−	9.00000i		−	0.323708i	0.986815	−	0.161854i	$-0.0517473\pi$
$774$		−	1.00000i		−	0.0359443i
$775$		0			0
$776$	−2.00000			−0.0717958
$777$	7.00000			0.251124
$778$		−	30.0000i		−	1.07555i
$779$		0			0
$780$	6.00000	−	9.00000i	0.214834	−	0.322252i
$781$	−50.0000			−1.78914
$782$		−	3.00000i		−	0.107280i
$783$	5.00000			0.178685
$784$	−1.00000			−0.0357143
$785$		−	39.0000i		−	1.39197i
$786$			7.00000i			0.249682i
$787$			13.0000i			0.463400i	0.972787	+	0.231700i	$0.0744288\pi$
$787$			13.0000i			0.463400i	−0.972787	+	0.231700i	$0.925571\pi$
$788$			2.00000i			0.0712470i
$789$	24.0000			0.854423
$790$		0			0
$791$		−	6.00000i		−	0.213335i
$792$	−5.00000			−0.177667
$793$	9.00000	+	6.00000i	0.319599	+	0.213066i
$794$	12.0000			0.425864
$795$		−	42.0000i		−	1.48959i
$796$	5.00000			0.177220
$797$	18.0000			0.637593			0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000			0.637593			0.318796	+	0.947823i	$0.396721\pi$
$798$			1.00000i			0.0353996i
$799$			24.0000i			0.849059i
$800$		−	4.00000i		−	0.141421i
$801$		−	16.0000i		−	0.565332i
$802$	30.0000			1.05934
$803$	55.0000			1.94091
$804$		−	8.00000i		−	0.282138i
$805$	−3.00000			−0.105736
$806$		0			0
$807$		0			0
$808$			18.0000i			0.633238i
$809$		0			0			−	1.00000i	$-0.5\pi$
$809$		0			0				1.00000i	$0.5\pi$
$810$	3.00000			0.105409
$811$			35.0000i			1.22902i	0.788911	+	0.614508i	$0.210645\pi$
$811$			35.0000i			1.22902i	−0.788911	+	0.614508i	$0.789355\pi$
$812$		−	5.00000i		−	0.175466i
$813$		0			0
$814$		−	35.0000i		−	1.22675i
$815$	−12.0000			−0.420342
$816$	3.00000			0.105021
$817$			1.00000i			0.0349856i
$818$	−19.0000			−0.664319
$819$	2.00000	−	3.00000i	0.0698857	−	0.104828i
$820$		0			0
$821$		−	20.0000i		−	0.698005i	−0.937122	−	0.349002i	$-0.886521\pi$
$821$		−	20.0000i		−	0.698005i	0.937122	−	0.349002i	$-0.113479\pi$
$822$	−3.00000			−0.104637
$823$	44.0000			1.53374			0.766872	−	0.641800i	$-0.221812\pi$
$823$	44.0000			1.53374			0.766872	+	0.641800i	$0.221812\pi$
$824$			11.0000i			0.383203i
$825$			20.0000i			0.696311i
$826$		−	14.0000i		−	0.487122i
$827$			23.0000i			0.799788i	0.916561	+	0.399894i	$0.130953\pi$
$827$			23.0000i			0.799788i	−0.916561	+	0.399894i	$0.869047\pi$
$828$	1.00000			0.0347524
$829$	−25.0000			−0.868286			−0.434143	−	0.900844i	$-0.642949\pi$
$829$	−25.0000			−0.868286			−0.434143	+	0.900844i	$0.642949\pi$
$830$			18.0000i			0.624789i
$831$	28.0000			0.971309
$832$	3.00000	+	2.00000i	0.104006	+	0.0693375i
$833$	−3.00000			−0.103944
$834$			20.0000i			0.692543i
$835$	−21.0000			−0.726735
$836$	5.00000			0.172929
$837$		0			0
$838$		−	35.0000i		−	1.20905i
$839$		−	36.0000i		−	1.24286i	−0.783470	−	0.621429i	$-0.786552\pi$
$839$		−	36.0000i		−	1.24286i	0.783470	−	0.621429i	$-0.213448\pi$
$840$		−	3.00000i		−	0.103510i
$841$	−4.00000			−0.137931
$842$	30.0000			1.03387
$843$		−	10.0000i		−	0.344418i
$844$	13.0000			0.447478
$845$	36.0000	−	15.0000i	1.23844	−	0.516016i
$846$	−8.00000			−0.275046
$847$		−	14.0000i		−	0.481046i
$848$	14.0000			0.480762
$849$	14.0000			0.480479
$850$		−	12.0000i		−	0.411597i
$851$			7.00000i			0.239957i
$852$			10.0000i			0.342594i
$853$			16.0000i			0.547830i	0.961754	+	0.273915i	$0.0883186\pi$
$853$			16.0000i			0.547830i	−0.961754	+	0.273915i	$0.911681\pi$
$854$	3.00000			0.102658
$855$	−3.00000			−0.102598
$856$		−	18.0000i		−	0.615227i
$857$	−42.0000			−1.43469			−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000			−1.43469			−0.717346	+	0.696717i	$0.754643\pi$
$858$	−15.0000	−	10.0000i	−0.512092	−	0.341394i
$859$	−50.0000			−1.70598			−0.852989	−	0.521929i	$-0.825213\pi$
$859$	−50.0000			−1.70598			−0.852989	+	0.521929i	$0.825213\pi$
$860$		−	3.00000i		−	0.102299i
$861$		0			0
$862$	30.0000			1.02180
$863$		−	24.0000i		−	0.816970i	−0.912765	−	0.408485i	$-0.866057\pi$
$863$		−	24.0000i		−	0.816970i	0.912765	−	0.408485i	$-0.133943\pi$
$864$			1.00000i			0.0340207i
$865$			78.0000i			2.65208i
$866$			4.00000i			0.135926i
$867$	−8.00000			−0.271694
$868$		0			0
$869$		0			0
$870$	15.0000			0.508548
$871$	16.0000	−	24.0000i	0.542139	−	0.813209i
$872$	9.00000			0.304778
$873$		−	2.00000i		−	0.0676897i
$874$	−1.00000			−0.0338255
$875$	3.00000			0.101419
$876$		−	11.0000i		−	0.371656i
$877$			38.0000i			1.28317i	0.767052	+	0.641584i	$0.221723\pi$
$877$			38.0000i			1.28317i	−0.767052	+	0.641584i	$0.778277\pi$
$878$		−	15.0000i		−	0.506225i
$879$			6.00000i			0.202375i
$880$	−15.0000			−0.505650
$881$	7.00000			0.235836			0.117918	−	0.993023i	$-0.462378\pi$
$881$	7.00000			0.235836			0.117918	+	0.993023i	$0.462378\pi$
$882$		−	1.00000i		−	0.0336718i
$883$	−41.0000			−1.37976			−0.689880	−	0.723924i	$-0.742337\pi$
$883$	−41.0000			−1.37976			−0.689880	+	0.723924i	$0.742337\pi$
$884$	9.00000	+	6.00000i	0.302703	+	0.201802i
$885$	42.0000			1.41181
$886$		−	6.00000i		−	0.201574i
$887$	−2.00000			−0.0671534			−0.0335767	−	0.999436i	$-0.510690\pi$
$887$	−2.00000			−0.0671534			−0.0335767	+	0.999436i	$0.510690\pi$
$888$	−7.00000			−0.234905
$889$		−	12.0000i		−	0.402467i
$890$		−	48.0000i		−	1.60896i
$891$		−	5.00000i		−	0.167506i
$892$		−	16.0000i		−	0.535720i
$893$	8.00000			0.267710
$894$	6.00000			0.200670
$895$		−	30.0000i		−	1.00279i
$896$	1.00000			0.0334077
$897$	3.00000	+	2.00000i	0.100167	+	0.0667781i
$898$	21.0000			0.700779
$899$		0			0
$900$	4.00000			0.133333
$901$	42.0000			1.39922
$902$		0			0
$903$		−	1.00000i		−	0.0332779i
$904$			6.00000i			0.199557i
$905$		−	6.00000i		−	0.199447i
$906$	−15.0000			−0.498342
$907$	−12.0000			−0.398453			−0.199227	−	0.979953i	$-0.563843\pi$
$907$	−12.0000			−0.398453			−0.199227	+	0.979953i	$0.563843\pi$
$908$		−	8.00000i		−	0.265489i
$909$	−18.0000			−0.597022
$910$	6.00000	−	9.00000i	0.198898	−	0.298347i
$911$	47.0000			1.55718			0.778590	−	0.627533i	$-0.215935\pi$
$911$	47.0000			1.55718			0.778590	+	0.627533i	$0.215935\pi$
$912$		−	1.00000i		−	0.0331133i
$913$	30.0000			0.992855
$914$	−8.00000			−0.264616
$915$			9.00000i			0.297531i
$916$			26.0000i			0.859064i
$917$			7.00000i			0.231160i
$918$			3.00000i			0.0990148i
$919$	10.0000			0.329870			0.164935	−	0.986304i	$-0.447259\pi$
$919$	10.0000			0.329870			0.164935	+	0.986304i	$0.447259\pi$
$920$	3.00000			0.0989071
$921$			8.00000i			0.263609i
$922$	−15.0000			−0.493999
$923$	−20.0000	+	30.0000i	−0.658308	+	0.987462i
$924$	−5.00000			−0.164488
$925$			28.0000i			0.920634i
$926$	−11.0000			−0.361482
$927$	−11.0000			−0.361287
$928$			5.00000i			0.164133i
$929$			54.0000i			1.77168i	0.463988	+	0.885841i	$0.346418\pi$
$929$			54.0000i			1.77168i	−0.463988	+	0.885841i	$0.653582\pi$
$930$		0			0
$931$			1.00000i			0.0327737i
$932$	−14.0000			−0.458585
$933$	−8.00000			−0.261908
$934$		−	7.00000i		−	0.229047i
$935$	−45.0000			−1.47166
$936$	−2.00000	+	3.00000i	−0.0653720	+	0.0980581i
$937$	−32.0000			−1.04539			−0.522697	−	0.852518i	$-0.675074\pi$
$937$	−32.0000			−1.04539			−0.522697	+	0.852518i	$0.675074\pi$
$938$		−	8.00000i		−	0.261209i
$939$	−6.00000			−0.195803
$940$	−24.0000			−0.782794
$941$		−	30.0000i		−	0.977972i	−0.872292	−	0.488986i	$-0.837367\pi$
$941$		−	30.0000i		−	0.977972i	0.872292	−	0.488986i	$-0.162633\pi$
$942$			13.0000i			0.423563i
$943$		0			0
$944$			14.0000i			0.455661i
$945$	3.00000			0.0975900
$946$	−5.00000			−0.162564
$947$		−	57.0000i		−	1.85225i	−0.377215	−	0.926126i	$-0.623118\pi$
$947$		−	57.0000i		−	1.85225i	0.377215	−	0.926126i	$-0.376882\pi$
$948$		0			0
$949$	22.0000	−	33.0000i	0.714150	−	1.07123i
$950$	−4.00000			−0.129777
$951$			8.00000i			0.259418i
$952$	3.00000			0.0972306
$953$	54.0000			1.74923			0.874616	−	0.484817i	$-0.161114\pi$
$953$	54.0000			1.74923			0.874616	+	0.484817i	$0.161114\pi$
$954$			14.0000i			0.453267i
$955$		−	51.0000i		−	1.65032i
$956$		−	4.00000i		−	0.129369i
$957$		−	25.0000i		−	0.808135i
$958$	21.0000			0.678479
$959$	−3.00000			−0.0968751
$960$			3.00000i			0.0968246i
$961$	31.0000			1.00000
$962$	−21.0000	−	14.0000i	−0.677067	−	0.451378i
$963$	18.0000			0.580042
$964$		−	10.0000i		−	0.322078i
$965$	48.0000			1.54517
$966$	1.00000			0.0321745
$967$		−	17.0000i		−	0.546683i	−0.961917	−	0.273342i	$-0.911871\pi$
$967$		−	17.0000i		−	0.546683i	0.961917	−	0.273342i	$-0.0881289\pi$
$968$			14.0000i			0.449977i
$969$		−	3.00000i		−	0.0963739i
$970$		−	6.00000i		−	0.192648i
$971$	−28.0000			−0.898563			−0.449281	−	0.893390i	$-0.648320\pi$
$971$	−28.0000			−0.898563			−0.449281	+	0.893390i	$0.648320\pi$
$972$	−1.00000			−0.0320750
$973$			20.0000i			0.641171i
$974$	32.0000			1.02535
$975$	12.0000	+	8.00000i	0.384308	+	0.256205i
$976$	−3.00000			−0.0960277
$977$			3.00000i			0.0959785i	0.998848	+	0.0479893i	$0.0152813\pi$
$977$			3.00000i			0.0959785i	−0.998848	+	0.0479893i	$0.984719\pi$
$978$	4.00000			0.127906
$979$	−80.0000			−2.55681
$980$		−	3.00000i		−	0.0958315i
$981$			9.00000i			0.287348i
$982$		−	28.0000i		−	0.893516i
$983$			11.0000i			0.350846i	0.984493	+	0.175423i	$0.0561292\pi$
$983$			11.0000i			0.350846i	−0.984493	+	0.175423i	$0.943871\pi$
$984$		0			0
$985$	−6.00000			−0.191176
$986$			15.0000i			0.477697i
$987$	−8.00000			−0.254643
$988$	2.00000	−	3.00000i	0.0636285	−	0.0954427i
$989$	1.00000			0.0317982
$990$		−	15.0000i		−	0.476731i
$991$	−28.0000			−0.889449			−0.444725	−	0.895667i	$-0.646698\pi$
$991$	−28.0000			−0.889449			−0.444725	+	0.895667i	$0.646698\pi$
$992$		0			0
$993$			20.0000i			0.634681i
$994$			10.0000i			0.317181i
$995$			15.0000i			0.475532i
$996$		−	6.00000i		−	0.190117i
$997$	38.0000			1.20347			0.601736	−	0.798695i	$-0.294476\pi$
$997$	38.0000			1.20347			0.601736	+	0.798695i	$0.294476\pi$
$998$	−14.0000			−0.443162
$999$		−	7.00000i		−	0.221470i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.c.d.337.2	yes	2
3.2	odd	2		1638.2.c.g.883.1		2
4.3	odd	2		4368.2.h.b.337.1		2
7.6	odd	2		3822.2.c.a.883.2		2
13.5	odd	4		7098.2.a.x.1.1		1
13.8	odd	4		7098.2.a.p.1.1		1
13.12	even	2	inner	546.2.c.d.337.1	✓	2
39.38	odd	2		1638.2.c.g.883.2		2
52.51	odd	2		4368.2.h.b.337.2		2
91.90	odd	2		3822.2.c.a.883.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.c.d.337.1	✓	2	13.12	even	2	inner
546.2.c.d.337.2	yes	2	1.1	even	1	trivial
1638.2.c.g.883.1		2	3.2	odd	2
1638.2.c.g.883.2		2	39.38	odd	2
3822.2.c.a.883.1		2	91.90	odd	2
3822.2.c.a.883.2		2	7.6	odd	2
4368.2.h.b.337.1		2	4.3	odd	2
4368.2.h.b.337.2		2	52.51	odd	2
7098.2.a.p.1.1		1	13.8	odd	4
7098.2.a.x.1.1		1	13.5	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -3.00000i q^{5} +1.00000i q^{6} +1.00000i q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -3.00000i q^{5} +1.00000i q^{6} +1.00000i q^{7} -1.00000i q^{8} +1.00000 q^{9} +3.00000 q^{10} -5.00000i q^{11} -1.00000 q^{12} +(-3.00000 - 2.00000i) q^{13} -1.00000 q^{14} -3.00000i q^{15} +1.00000 q^{16} +3.00000 q^{17} +1.00000i q^{18} -1.00000i q^{19} +3.00000i q^{20} +1.00000i q^{21} +5.00000 q^{22} -1.00000 q^{23} -1.00000i q^{24} -4.00000 q^{25} +(2.00000 - 3.00000i) q^{26} +1.00000 q^{27} -1.00000i q^{28} +5.00000 q^{29} +3.00000 q^{30} +1.00000i q^{32} -5.00000i q^{33} +3.00000i q^{34} +3.00000 q^{35} -1.00000 q^{36} -7.00000i q^{37} +1.00000 q^{38} +(-3.00000 - 2.00000i) q^{39} -3.00000 q^{40} -1.00000 q^{42} -1.00000 q^{43} +5.00000i q^{44} -3.00000i q^{45} -1.00000i q^{46} +8.00000i q^{47} +1.00000 q^{48} -1.00000 q^{49} -4.00000i q^{50} +3.00000 q^{51} +(3.00000 + 2.00000i) q^{52} +14.0000 q^{53} +1.00000i q^{54} -15.0000 q^{55} +1.00000 q^{56} -1.00000i q^{57} +5.00000i q^{58} +14.0000i q^{59} +3.00000i q^{60} -3.00000 q^{61} +1.00000i q^{63} -1.00000 q^{64} +(-6.00000 + 9.00000i) q^{65} +5.00000 q^{66} +8.00000i q^{67} -3.00000 q^{68} -1.00000 q^{69} +3.00000i q^{70} -10.0000i q^{71} -1.00000i q^{72} +11.0000i q^{73} +7.00000 q^{74} -4.00000 q^{75} +1.00000i q^{76} +5.00000 q^{77} +(2.00000 - 3.00000i) q^{78} -3.00000i q^{80} +1.00000 q^{81} +6.00000i q^{83} -1.00000i q^{84} -9.00000i q^{85} -1.00000i q^{86} +5.00000 q^{87} -5.00000 q^{88} -16.0000i q^{89} +3.00000 q^{90} +(2.00000 - 3.00000i) q^{91} +1.00000 q^{92} -8.00000 q^{94} -3.00000 q^{95} +1.00000i q^{96} -2.00000i q^{97} -1.00000i q^{98} -5.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} - 2 q^{4} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^3 - 2 * q^4 + 2 * q^9	\( 2 q + 2 q^{3} - 2 q^{4} + 2 q^{9} + 6 q^{10} - 2 q^{12} - 6 q^{13} - 2 q^{14} + 2 q^{16} + 6 q^{17} + 10 q^{22} - 2 q^{23} - 8 q^{25} + 4 q^{26} + 2 q^{27} + 10 q^{29} + 6 q^{30} + 6 q^{35} - 2 q^{36} + 2 q^{38} - 6 q^{39} - 6 q^{40} - 2 q^{42} - 2 q^{43} + 2 q^{48} - 2 q^{49} + 6 q^{51} + 6 q^{52} + 28 q^{53} - 30 q^{55} + 2 q^{56} - 6 q^{61} - 2 q^{64} - 12 q^{65} + 10 q^{66} - 6 q^{68} - 2 q^{69} + 14 q^{74} - 8 q^{75} + 10 q^{77} + 4 q^{78} + 2 q^{81} + 10 q^{87} - 10 q^{88} + 6 q^{90} + 4 q^{91} + 2 q^{92} - 16 q^{94} - 6 q^{95}+O(q^{100}) \) 2 * q + 2 * q^3 - 2 * q^4 + 2 * q^9 + 6 * q^10 - 2 * q^12 - 6 * q^13 - 2 * q^14 + 2 * q^16 + 6 * q^17 + 10 * q^22 - 2 * q^23 - 8 * q^25 + 4 * q^26 + 2 * q^27 + 10 * q^29 + 6 * q^30 + 6 * q^35 - 2 * q^36 + 2 * q^38 - 6 * q^39 - 6 * q^40 - 2 * q^42 - 2 * q^43 + 2 * q^48 - 2 * q^49 + 6 * q^51 + 6 * q^52 + 28 * q^53 - 30 * q^55 + 2 * q^56 - 6 * q^61 - 2 * q^64 - 12 * q^65 + 10 * q^66 - 6 * q^68 - 2 * q^69 + 14 * q^74 - 8 * q^75 + 10 * q^77 + 4 * q^78 + 2 * q^81 + 10 * q^87 - 10 * q^88 + 6 * q^90 + 4 * q^91 + 2 * q^92 - 16 * q^94 - 6 * q^95

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