LMFDB - Embedded newform 1320.2.w.a.661.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1320,2,Mod(661,1320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1320, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1320.661");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1320.w (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:	$10.5402530668$
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			661.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1320.661
Dual form			1320.2.w.a.661.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.00000i) q^{2} -1.00000i q^{3} +2.00000i q^{4} -1.00000i q^{5} +(1.00000 - 1.00000i) q^{6} -2.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} -1.00000 q^{9} +(1.00000 - 1.00000i) q^{10} +1.00000i q^{11} +2.00000 q^{12} +4.00000i q^{13} +(-2.00000 - 2.00000i) q^{14} -1.00000 q^{15} -4.00000 q^{16} +2.00000 q^{17} +(-1.00000 - 1.00000i) q^{18} +4.00000i q^{19} +2.00000 q^{20} +2.00000i q^{21} +(-1.00000 + 1.00000i) q^{22} +(2.00000 + 2.00000i) q^{24} -1.00000 q^{25} +(-4.00000 + 4.00000i) q^{26} +1.00000i q^{27} -4.00000i q^{28} +6.00000i q^{29} +(-1.00000 - 1.00000i) q^{30} -6.00000 q^{31} +(-4.00000 - 4.00000i) q^{32} +1.00000 q^{33} +(2.00000 + 2.00000i) q^{34} +2.00000i q^{35} -2.00000i q^{36} +4.00000i q^{37} +(-4.00000 + 4.00000i) q^{38} +4.00000 q^{39} +(2.00000 + 2.00000i) q^{40} +2.00000 q^{41} +(-2.00000 + 2.00000i) q^{42} +4.00000i q^{43} -2.00000 q^{44} +1.00000i q^{45} +4.00000i q^{48} -3.00000 q^{49} +(-1.00000 - 1.00000i) q^{50} -2.00000i q^{51} -8.00000 q^{52} +14.0000i q^{53} +(-1.00000 + 1.00000i) q^{54} +1.00000 q^{55} +(4.00000 - 4.00000i) q^{56} +4.00000 q^{57} +(-6.00000 + 6.00000i) q^{58} -2.00000i q^{60} -12.0000i q^{61} +(-6.00000 - 6.00000i) q^{62} +2.00000 q^{63} -8.00000i q^{64} +4.00000 q^{65} +(1.00000 + 1.00000i) q^{66} +4.00000i q^{67} +4.00000i q^{68} +(-2.00000 + 2.00000i) q^{70} -8.00000 q^{71} +(2.00000 - 2.00000i) q^{72} +10.0000 q^{73} +(-4.00000 + 4.00000i) q^{74} +1.00000i q^{75} -8.00000 q^{76} -2.00000i q^{77} +(4.00000 + 4.00000i) q^{78} +6.00000 q^{79} +4.00000i q^{80} +1.00000 q^{81} +(2.00000 + 2.00000i) q^{82} -4.00000 q^{84} -2.00000i q^{85} +(-4.00000 + 4.00000i) q^{86} +6.00000 q^{87} +(-2.00000 - 2.00000i) q^{88} +6.00000 q^{89} +(-1.00000 + 1.00000i) q^{90} -8.00000i q^{91} +6.00000i q^{93} +4.00000 q^{95} +(-4.00000 + 4.00000i) q^{96} +6.00000 q^{97} +(-3.00000 - 3.00000i) q^{98} -1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{6} - 4 q^{7} - 4 q^{8} - 2 q^{9} + 2 q^{10} + 4 q^{12} - 4 q^{14} - 2 q^{15} - 8 q^{16} + 4 q^{17} - 2 q^{18} + 4 q^{20} - 2 q^{22} + 4 q^{24} - 2 q^{25} - 8 q^{26} - 2 q^{30} - 12 q^{31}+ \cdots - 6 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^6 - 4 * q^7 - 4 * q^8 - 2 * q^9 + 2 * q^10 + 4 * q^12 - 4 * q^14 - 2 * q^15 - 8 * q^16 + 4 * q^17 - 2 * q^18 + 4 * q^20 - 2 * q^22 + 4 * q^24 - 2 * q^25 - 8 * q^26 - 2 * q^30 - 12 * q^31 - 8 * q^32 + 2 * q^33 + 4 * q^34 - 8 * q^38 + 8 * q^39 + 4 * q^40 + 4 * q^41 - 4 * q^42 - 4 * q^44 - 6 * q^49 - 2 * q^50 - 16 * q^52 - 2 * q^54 + 2 * q^55 + 8 * q^56 + 8 * q^57 - 12 * q^58 - 12 * q^62 + 4 * q^63 + 8 * q^65 + 2 * q^66 - 4 * q^70 - 16 * q^71 + 4 * q^72 + 20 * q^73 - 8 * q^74 - 16 * q^76 + 8 * q^78 + 12 * q^79 + 2 * q^81 + 4 * q^82 - 8 * q^84 - 8 * q^86 + 12 * q^87 - 4 * q^88 + 12 * q^89 - 2 * q^90 + 8 * q^95 - 8 * q^96 + 12 * q^97 - 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1320\mathbb{Z}\right)^\times$.

$n$	$661$	$881$	$991$	$1057$	$1201$
$\chi(n)$	$-1$	$1$	$1$	$1$	$1$

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 $

$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$			2.00000i			1.00000i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	1.00000	−	1.00000i	0.408248	−	0.408248i
$7$	−2.00000			−0.755929			−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000			−0.755929			−0.377964	+	0.925820i	$0.623376\pi$
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$	−1.00000			−0.333333
$10$	1.00000	−	1.00000i	0.316228	−	0.316228i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	2.00000			0.577350
$13$			4.00000i			1.10940i	0.832050	+	0.554700i	$0.187167\pi$
$13$			4.00000i			1.10940i	−0.832050	+	0.554700i	$0.812833\pi$
$14$	−2.00000	−	2.00000i	−0.534522	−	0.534522i
$15$	−1.00000			−0.258199
$16$	−4.00000			−1.00000
$17$	2.00000			0.485071			0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000			0.485071			0.242536	+	0.970143i	$0.422021\pi$
$18$	−1.00000	−	1.00000i	−0.235702	−	0.235702i
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$	2.00000			0.447214
$21$			2.00000i			0.436436i
$22$	−1.00000	+	1.00000i	−0.213201	+	0.213201i
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$	2.00000	+	2.00000i	0.408248	+	0.408248i
$25$	−1.00000			−0.200000
$26$	−4.00000	+	4.00000i	−0.784465	+	0.784465i
$27$			1.00000i			0.192450i
$28$		−	4.00000i		−	0.755929i
$29$			6.00000i			1.11417i	0.830455	+	0.557086i	$0.188081\pi$
$29$			6.00000i			1.11417i	−0.830455	+	0.557086i	$0.811919\pi$
$30$	−1.00000	−	1.00000i	−0.182574	−	0.182574i
$31$	−6.00000			−1.07763			−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000			−1.07763			−0.538816	+	0.842424i	$0.681128\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$	1.00000			0.174078
$34$	2.00000	+	2.00000i	0.342997	+	0.342997i
$35$			2.00000i			0.338062i
$36$		−	2.00000i		−	0.333333i
$37$			4.00000i			0.657596i	0.944400	+	0.328798i	$0.106644\pi$
$37$			4.00000i			0.657596i	−0.944400	+	0.328798i	$0.893356\pi$
$38$	−4.00000	+	4.00000i	−0.648886	+	0.648886i
$39$	4.00000			0.640513
$40$	2.00000	+	2.00000i	0.316228	+	0.316228i
$41$	2.00000			0.312348			0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000			0.312348			0.156174	+	0.987730i	$0.450084\pi$
$42$	−2.00000	+	2.00000i	−0.308607	+	0.308607i
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$	−2.00000			−0.301511
$45$			1.00000i			0.149071i
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$			4.00000i			0.577350i
$49$	−3.00000			−0.428571
$50$	−1.00000	−	1.00000i	−0.141421	−	0.141421i
$51$		−	2.00000i		−	0.280056i
$52$	−8.00000			−1.10940
$53$			14.0000i			1.92305i	0.274721	+	0.961524i	$0.411414\pi$
$53$			14.0000i			1.92305i	−0.274721	+	0.961524i	$0.588586\pi$
$54$	−1.00000	+	1.00000i	−0.136083	+	0.136083i
$55$	1.00000			0.134840
$56$	4.00000	−	4.00000i	0.534522	−	0.534522i
$57$	4.00000			0.529813
$58$	−6.00000	+	6.00000i	−0.787839	+	0.787839i
$59$		0			0		1.00000			$0$
$59$		0			0		−1.00000			$\pi$
$60$		−	2.00000i		−	0.258199i
$61$		−	12.0000i		−	1.53644i	−0.640184	−	0.768221i	$-0.721142\pi$
$61$		−	12.0000i		−	1.53644i	0.640184	−	0.768221i	$-0.278858\pi$
$62$	−6.00000	−	6.00000i	−0.762001	−	0.762001i
$63$	2.00000			0.251976
$64$		−	8.00000i		−	1.00000i
$65$	4.00000			0.496139
$66$	1.00000	+	1.00000i	0.123091	+	0.123091i
$67$			4.00000i			0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$67$			4.00000i			0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$68$			4.00000i			0.485071i
$69$		0			0
$70$	−2.00000	+	2.00000i	−0.239046	+	0.239046i
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$	2.00000	−	2.00000i	0.235702	−	0.235702i
$73$	10.0000			1.17041			0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000			1.17041			0.585206	+	0.810885i	$0.301014\pi$
$74$	−4.00000	+	4.00000i	−0.464991	+	0.464991i
$75$			1.00000i			0.115470i
$76$	−8.00000			−0.917663
$77$		−	2.00000i		−	0.227921i
$78$	4.00000	+	4.00000i	0.452911	+	0.452911i
$79$	6.00000			0.675053			0.337526	−	0.941316i	$-0.390410\pi$
$79$	6.00000			0.675053			0.337526	+	0.941316i	$0.390410\pi$
$80$			4.00000i			0.447214i
$81$	1.00000			0.111111
$82$	2.00000	+	2.00000i	0.220863	+	0.220863i
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$	−4.00000			−0.436436
$85$		−	2.00000i		−	0.216930i
$86$	−4.00000	+	4.00000i	−0.431331	+	0.431331i
$87$	6.00000			0.643268
$88$	−2.00000	−	2.00000i	−0.213201	−	0.213201i
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$	−1.00000	+	1.00000i	−0.105409	+	0.105409i
$91$		−	8.00000i		−	0.838628i
$92$		0			0
$93$			6.00000i			0.622171i
$94$		0			0
$95$	4.00000			0.410391
$96$	−4.00000	+	4.00000i	−0.408248	+	0.408248i
$97$	6.00000			0.609208			0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000			0.609208			0.304604	+	0.952479i	$0.401476\pi$
$98$	−3.00000	−	3.00000i	−0.303046	−	0.303046i
$99$		−	1.00000i		−	0.100504i
$100$		−	2.00000i		−	0.200000i
$101$			2.00000i			0.199007i	0.995037	+	0.0995037i	$0.0317255\pi$
$101$			2.00000i			0.199007i	−0.995037	+	0.0995037i	$0.968274\pi$
$102$	2.00000	−	2.00000i	0.198030	−	0.198030i
$103$	−10.0000			−0.985329			−0.492665	−	0.870219i	$-0.663977\pi$
$103$	−10.0000			−0.985329			−0.492665	+	0.870219i	$0.663977\pi$
$104$	−8.00000	−	8.00000i	−0.784465	−	0.784465i
$105$	2.00000			0.195180
$106$	−14.0000	+	14.0000i	−1.35980	+	1.35980i
$107$		−	20.0000i		−	1.93347i	−0.255774	−	0.966736i	$-0.582330\pi$
$107$		−	20.0000i		−	1.93347i	0.255774	−	0.966736i	$-0.417670\pi$
$108$	−2.00000			−0.192450
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$	1.00000	+	1.00000i	0.0953463	+	0.0953463i
$111$	4.00000			0.379663
$112$	8.00000			0.755929
$113$	−2.00000			−0.188144			−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000			−0.188144			−0.0940721	+	0.995565i	$0.529988\pi$
$114$	4.00000	+	4.00000i	0.374634	+	0.374634i
$115$		0			0
$116$	−12.0000			−1.11417
$117$		−	4.00000i		−	0.369800i
$118$		0			0
$119$	−4.00000			−0.366679
$120$	2.00000	−	2.00000i	0.182574	−	0.182574i
$121$	−1.00000			−0.0909091
$122$	12.0000	−	12.0000i	1.08643	−	1.08643i
$123$		−	2.00000i		−	0.180334i
$124$		−	12.0000i		−	1.07763i
$125$			1.00000i			0.0894427i
$126$	2.00000	+	2.00000i	0.178174	+	0.178174i
$127$	6.00000			0.532414			0.266207	−	0.963916i	$-0.414230\pi$
$127$	6.00000			0.532414			0.266207	+	0.963916i	$0.414230\pi$
$128$	8.00000	−	8.00000i	0.707107	−	0.707107i
$129$	4.00000			0.352180
$130$	4.00000	+	4.00000i	0.350823	+	0.350823i
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$			2.00000i			0.174078i
$133$		−	8.00000i		−	0.693688i
$134$	−4.00000	+	4.00000i	−0.345547	+	0.345547i
$135$	1.00000			0.0860663
$136$	−4.00000	+	4.00000i	−0.342997	+	0.342997i
$137$	6.00000			0.512615			0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000			0.512615			0.256307	+	0.966595i	$0.417494\pi$
$138$		0			0
$139$		−	12.0000i		−	1.01783i	−0.860818	−	0.508913i	$-0.830047\pi$
$139$		−	12.0000i		−	1.01783i	0.860818	−	0.508913i	$-0.169953\pi$
$140$	−4.00000			−0.338062
$141$		0			0
$142$	−8.00000	−	8.00000i	−0.671345	−	0.671345i
$143$	−4.00000			−0.334497
$144$	4.00000			0.333333
$145$	6.00000			0.498273
$146$	10.0000	+	10.0000i	0.827606	+	0.827606i
$147$			3.00000i			0.247436i
$148$	−8.00000			−0.657596
$149$		−	2.00000i		−	0.163846i	−0.996639	−	0.0819232i	$-0.973894\pi$
$149$		−	2.00000i		−	0.163846i	0.996639	−	0.0819232i	$-0.0261062\pi$
$150$	−1.00000	+	1.00000i	−0.0816497	+	0.0816497i
$151$	−22.0000			−1.79033			−0.895167	−	0.445730i	$-0.852944\pi$
$151$	−22.0000			−1.79033			−0.895167	+	0.445730i	$0.852944\pi$
$152$	−8.00000	−	8.00000i	−0.648886	−	0.648886i
$153$	−2.00000			−0.161690
$154$	2.00000	−	2.00000i	0.161165	−	0.161165i
$155$			6.00000i			0.481932i
$156$			8.00000i			0.640513i
$157$		−	4.00000i		−	0.319235i	−0.987179	−	0.159617i	$-0.948974\pi$
$157$		−	4.00000i		−	0.319235i	0.987179	−	0.159617i	$-0.0510260\pi$
$158$	6.00000	+	6.00000i	0.477334	+	0.477334i
$159$	14.0000			1.11027
$160$	−4.00000	+	4.00000i	−0.316228	+	0.316228i
$161$		0			0
$162$	1.00000	+	1.00000i	0.0785674	+	0.0785674i
$163$		−	4.00000i		−	0.313304i	−0.987654	−	0.156652i	$-0.949930\pi$
$163$		−	4.00000i		−	0.313304i	0.987654	−	0.156652i	$-0.0500701\pi$
$164$			4.00000i			0.312348i
$165$		−	1.00000i		−	0.0778499i
$166$		0			0
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$	−4.00000	−	4.00000i	−0.308607	−	0.308607i
$169$	−3.00000			−0.230769
$170$	2.00000	−	2.00000i	0.153393	−	0.153393i
$171$		−	4.00000i		−	0.305888i
$172$	−8.00000			−0.609994
$173$			18.0000i			1.36851i	0.729241	+	0.684257i	$0.239873\pi$
$173$			18.0000i			1.36851i	−0.729241	+	0.684257i	$0.760127\pi$
$174$	6.00000	+	6.00000i	0.454859	+	0.454859i
$175$	2.00000			0.151186
$176$		−	4.00000i		−	0.301511i
$177$		0			0
$178$	6.00000	+	6.00000i	0.449719	+	0.449719i
$179$			24.0000i			1.79384i	0.442189	+	0.896922i	$0.354202\pi$
$179$			24.0000i			1.79384i	−0.442189	+	0.896922i	$0.645798\pi$
$180$	−2.00000			−0.149071
$181$		−	20.0000i		−	1.48659i	−0.668965	−	0.743294i	$-0.733262\pi$
$181$		−	20.0000i		−	1.48659i	0.668965	−	0.743294i	$-0.266738\pi$
$182$	8.00000	−	8.00000i	0.592999	−	0.592999i
$183$	−12.0000			−0.887066
$184$		0			0
$185$	4.00000			0.294086
$186$	−6.00000	+	6.00000i	−0.439941	+	0.439941i
$187$			2.00000i			0.146254i
$188$		0			0
$189$		−	2.00000i		−	0.145479i
$190$	4.00000	+	4.00000i	0.290191	+	0.290191i
$191$	4.00000			0.289430			0.144715	−	0.989473i	$-0.453773\pi$
$191$	4.00000			0.289430			0.144715	+	0.989473i	$0.453773\pi$
$192$	−8.00000			−0.577350
$193$	18.0000			1.29567			0.647834	−	0.761781i	$-0.275675\pi$
$193$	18.0000			1.29567			0.647834	+	0.761781i	$0.275675\pi$
$194$	6.00000	+	6.00000i	0.430775	+	0.430775i
$195$		−	4.00000i		−	0.286446i
$196$		−	6.00000i		−	0.428571i
$197$			18.0000i			1.28245i	0.767354	+	0.641223i	$0.221573\pi$
$197$			18.0000i			1.28245i	−0.767354	+	0.641223i	$0.778427\pi$
$198$	1.00000	−	1.00000i	0.0710669	−	0.0710669i
$199$	2.00000			0.141776			0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000			0.141776			0.0708881	+	0.997484i	$0.477417\pi$
$200$	2.00000	−	2.00000i	0.141421	−	0.141421i
$201$	4.00000			0.282138
$202$	−2.00000	+	2.00000i	−0.140720	+	0.140720i
$203$		−	12.0000i		−	0.842235i
$204$	4.00000			0.280056
$205$		−	2.00000i		−	0.139686i
$206$	−10.0000	−	10.0000i	−0.696733	−	0.696733i
$207$		0			0
$208$		−	16.0000i		−	1.10940i
$209$	−4.00000			−0.276686
$210$	2.00000	+	2.00000i	0.138013	+	0.138013i
$211$		−	20.0000i		−	1.37686i	−0.725304	−	0.688428i	$-0.758301\pi$
$211$		−	20.0000i		−	1.37686i	0.725304	−	0.688428i	$-0.241699\pi$
$212$	−28.0000			−1.92305
$213$			8.00000i			0.548151i
$214$	20.0000	−	20.0000i	1.36717	−	1.36717i
$215$	4.00000			0.272798
$216$	−2.00000	−	2.00000i	−0.136083	−	0.136083i
$217$	12.0000			0.814613
$218$		0			0
$219$		−	10.0000i		−	0.675737i
$220$			2.00000i			0.134840i
$221$			8.00000i			0.538138i
$222$	4.00000	+	4.00000i	0.268462	+	0.268462i
$223$	10.0000			0.669650			0.334825	−	0.942280i	$-0.391323\pi$
$223$	10.0000			0.669650			0.334825	+	0.942280i	$0.391323\pi$
$224$	8.00000	+	8.00000i	0.534522	+	0.534522i
$225$	1.00000			0.0666667
$226$	−2.00000	−	2.00000i	−0.133038	−	0.133038i
$227$		0			0		1.00000			$0$
$227$		0			0		−1.00000			$\pi$
$228$			8.00000i			0.529813i
$229$		−	20.0000i		−	1.32164i	−0.750546	−	0.660819i	$-0.770209\pi$
$229$		−	20.0000i		−	1.32164i	0.750546	−	0.660819i	$-0.229791\pi$
$230$		0			0
$231$	−2.00000			−0.131590
$232$	−12.0000	−	12.0000i	−0.787839	−	0.787839i
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$	4.00000	−	4.00000i	0.261488	−	0.261488i
$235$		0			0
$236$		0			0
$237$		−	6.00000i		−	0.389742i
$238$	−4.00000	−	4.00000i	−0.259281	−	0.259281i
$239$	8.00000			0.517477			0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000			0.517477			0.258738	+	0.965947i	$0.416693\pi$
$240$	4.00000			0.258199
$241$	10.0000			0.644157			0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000			0.644157			0.322078	+	0.946713i	$0.395619\pi$
$242$	−1.00000	−	1.00000i	−0.0642824	−	0.0642824i
$243$		−	1.00000i		−	0.0641500i
$244$	24.0000			1.53644
$245$			3.00000i			0.191663i
$246$	2.00000	−	2.00000i	0.127515	−	0.127515i
$247$	−16.0000			−1.01806
$248$	12.0000	−	12.0000i	0.762001	−	0.762001i
$249$		0			0
$250$	−1.00000	+	1.00000i	−0.0632456	+	0.0632456i
$251$			4.00000i			0.252478i	0.992000	+	0.126239i	$0.0402906\pi$
$251$			4.00000i			0.252478i	−0.992000	+	0.126239i	$0.959709\pi$
$252$			4.00000i			0.251976i
$253$		0			0
$254$	6.00000	+	6.00000i	0.376473	+	0.376473i
$255$	−2.00000			−0.125245
$256$	16.0000			1.00000
$257$	22.0000			1.37232			0.686161	−	0.727450i	$-0.259294\pi$
$257$	22.0000			1.37232			0.686161	+	0.727450i	$0.259294\pi$
$258$	4.00000	+	4.00000i	0.249029	+	0.249029i
$259$		−	8.00000i		−	0.497096i
$260$			8.00000i			0.496139i
$261$		−	6.00000i		−	0.371391i
$262$		0			0
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$	−2.00000	+	2.00000i	−0.123091	+	0.123091i
$265$	14.0000			0.860013
$266$	8.00000	−	8.00000i	0.490511	−	0.490511i
$267$		−	6.00000i		−	0.367194i
$268$	−8.00000			−0.488678
$269$			18.0000i			1.09748i	0.835993	+	0.548740i	$0.184892\pi$
$269$			18.0000i			1.09748i	−0.835993	+	0.548740i	$0.815108\pi$
$270$	1.00000	+	1.00000i	0.0608581	+	0.0608581i
$271$	−22.0000			−1.33640			−0.668202	−	0.743980i	$-0.732936\pi$
$271$	−22.0000			−1.33640			−0.668202	+	0.743980i	$0.732936\pi$
$272$	−8.00000			−0.485071
$273$	−8.00000			−0.484182
$274$	6.00000	+	6.00000i	0.362473	+	0.362473i
$275$		−	1.00000i		−	0.0603023i
$276$		0			0
$277$		−	12.0000i		−	0.721010i	−0.932757	−	0.360505i	$-0.882604\pi$
$277$		−	12.0000i		−	0.721010i	0.932757	−	0.360505i	$-0.117396\pi$
$278$	12.0000	−	12.0000i	0.719712	−	0.719712i
$279$	6.00000			0.359211
$280$	−4.00000	−	4.00000i	−0.239046	−	0.239046i
$281$	22.0000			1.31241			0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000			1.31241			0.656205	+	0.754583i	$0.272161\pi$
$282$		0			0
$283$		−	4.00000i		−	0.237775i	−0.992908	−	0.118888i	$-0.962067\pi$
$283$		−	4.00000i		−	0.237775i	0.992908	−	0.118888i	$-0.0379328\pi$
$284$		−	16.0000i		−	0.949425i
$285$		−	4.00000i		−	0.236940i
$286$	−4.00000	−	4.00000i	−0.236525	−	0.236525i
$287$	−4.00000			−0.236113
$288$	4.00000	+	4.00000i	0.235702	+	0.235702i
$289$	−13.0000			−0.764706
$290$	6.00000	+	6.00000i	0.352332	+	0.352332i
$291$		−	6.00000i		−	0.351726i
$292$			20.0000i			1.17041i
$293$		−	14.0000i		−	0.817889i	−0.912559	−	0.408944i	$-0.865897\pi$
$293$		−	14.0000i		−	0.817889i	0.912559	−	0.408944i	$-0.134103\pi$
$294$	−3.00000	+	3.00000i	−0.174964	+	0.174964i
$295$		0			0
$296$	−8.00000	−	8.00000i	−0.464991	−	0.464991i
$297$	−1.00000			−0.0580259
$298$	2.00000	−	2.00000i	0.115857	−	0.115857i
$299$		0			0
$300$	−2.00000			−0.115470
$301$		−	8.00000i		−	0.461112i
$302$	−22.0000	−	22.0000i	−1.26596	−	1.26596i
$303$	2.00000			0.114897
$304$		−	16.0000i		−	0.917663i
$305$	−12.0000			−0.687118
$306$	−2.00000	−	2.00000i	−0.114332	−	0.114332i
$307$			20.0000i			1.14146i	0.821138	+	0.570730i	$0.193340\pi$
$307$			20.0000i			1.14146i	−0.821138	+	0.570730i	$0.806660\pi$
$308$	4.00000			0.227921
$309$			10.0000i			0.568880i
$310$	−6.00000	+	6.00000i	−0.340777	+	0.340777i
$311$	20.0000			1.13410			0.567048	−	0.823685i	$-0.308085\pi$
$311$	20.0000			1.13410			0.567048	+	0.823685i	$0.308085\pi$
$312$	−8.00000	+	8.00000i	−0.452911	+	0.452911i
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$	4.00000	−	4.00000i	0.225733	−	0.225733i
$315$		−	2.00000i		−	0.112687i
$316$			12.0000i			0.675053i
$317$			34.0000i			1.90963i	0.297200	+	0.954815i	$0.403947\pi$
$317$			34.0000i			1.90963i	−0.297200	+	0.954815i	$0.596053\pi$
$318$	14.0000	+	14.0000i	0.785081	+	0.785081i
$319$	−6.00000			−0.335936
$320$	−8.00000			−0.447214
$321$	−20.0000			−1.11629
$322$		0			0
$323$			8.00000i			0.445132i
$324$			2.00000i			0.111111i
$325$		−	4.00000i		−	0.221880i
$326$	4.00000	−	4.00000i	0.221540	−	0.221540i
$327$		0			0
$328$	−4.00000	+	4.00000i	−0.220863	+	0.220863i
$329$		0			0
$330$	1.00000	−	1.00000i	0.0550482	−	0.0550482i
$331$		−	12.0000i		−	0.659580i	−0.944054	−	0.329790i	$-0.893022\pi$
$331$		−	12.0000i		−	0.659580i	0.944054	−	0.329790i	$-0.106978\pi$
$332$		0			0
$333$		−	4.00000i		−	0.219199i
$334$		0			0
$335$	4.00000			0.218543
$336$		−	8.00000i		−	0.436436i
$337$	−2.00000			−0.108947			−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000			−0.108947			−0.0544735	+	0.998515i	$0.517348\pi$
$338$	−3.00000	−	3.00000i	−0.163178	−	0.163178i
$339$			2.00000i			0.108625i
$340$	4.00000			0.216930
$341$		−	6.00000i		−	0.324918i
$342$	4.00000	−	4.00000i	0.216295	−	0.216295i
$343$	20.0000			1.07990
$344$	−8.00000	−	8.00000i	−0.431331	−	0.431331i
$345$		0			0
$346$	−18.0000	+	18.0000i	−0.967686	+	0.967686i
$347$			16.0000i			0.858925i	0.903085	+	0.429463i	$0.141297\pi$
$347$			16.0000i			0.858925i	−0.903085	+	0.429463i	$0.858703\pi$
$348$			12.0000i			0.643268i
$349$			28.0000i			1.49881i	0.662114	+	0.749403i	$0.269659\pi$
$349$			28.0000i			1.49881i	−0.662114	+	0.749403i	$0.730341\pi$
$350$	2.00000	+	2.00000i	0.106904	+	0.106904i
$351$	−4.00000			−0.213504
$352$	4.00000	−	4.00000i	0.213201	−	0.213201i
$353$	14.0000			0.745145			0.372572	−	0.928003i	$-0.378476\pi$
$353$	14.0000			0.745145			0.372572	+	0.928003i	$0.378476\pi$
$354$		0			0
$355$			8.00000i			0.424596i
$356$			12.0000i			0.635999i
$357$			4.00000i			0.211702i
$358$	−24.0000	+	24.0000i	−1.26844	+	1.26844i
$359$	−12.0000			−0.633336			−0.316668	−	0.948536i	$-0.602564\pi$
$359$	−12.0000			−0.633336			−0.316668	+	0.948536i	$0.602564\pi$
$360$	−2.00000	−	2.00000i	−0.105409	−	0.105409i
$361$	3.00000			0.157895
$362$	20.0000	−	20.0000i	1.05118	−	1.05118i
$363$			1.00000i			0.0524864i
$364$	16.0000			0.838628
$365$		−	10.0000i		−	0.523424i
$366$	−12.0000	−	12.0000i	−0.627250	−	0.627250i
$367$	−34.0000			−1.77479			−0.887393	−	0.461014i	$-0.847486\pi$
$367$	−34.0000			−1.77479			−0.887393	+	0.461014i	$0.847486\pi$
$368$		0			0
$369$	−2.00000			−0.104116
$370$	4.00000	+	4.00000i	0.207950	+	0.207950i
$371$		−	28.0000i		−	1.45369i
$372$	−12.0000			−0.622171
$373$			24.0000i			1.24267i	0.783544	+	0.621336i	$0.213410\pi$
$373$			24.0000i			1.24267i	−0.783544	+	0.621336i	$0.786590\pi$
$374$	−2.00000	+	2.00000i	−0.103418	+	0.103418i
$375$	1.00000			0.0516398
$376$		0			0
$377$	−24.0000			−1.23606
$378$	2.00000	−	2.00000i	0.102869	−	0.102869i
$379$		−	36.0000i		−	1.84920i	−0.380945	−	0.924598i	$-0.624401\pi$
$379$		−	36.0000i		−	1.84920i	0.380945	−	0.924598i	$-0.375599\pi$
$380$			8.00000i			0.410391i
$381$		−	6.00000i		−	0.307389i
$382$	4.00000	+	4.00000i	0.204658	+	0.204658i
$383$	20.0000			1.02195			0.510976	−	0.859595i	$-0.329284\pi$
$383$	20.0000			1.02195			0.510976	+	0.859595i	$0.329284\pi$
$384$	−8.00000	−	8.00000i	−0.408248	−	0.408248i
$385$	−2.00000			−0.101929
$386$	18.0000	+	18.0000i	0.916176	+	0.916176i
$387$		−	4.00000i		−	0.203331i
$388$			12.0000i			0.609208i
$389$			10.0000i			0.507020i	0.967333	+	0.253510i	$0.0815851\pi$
$389$			10.0000i			0.507020i	−0.967333	+	0.253510i	$0.918415\pi$
$390$	4.00000	−	4.00000i	0.202548	−	0.202548i
$391$		0			0
$392$	6.00000	−	6.00000i	0.303046	−	0.303046i
$393$		0			0
$394$	−18.0000	+	18.0000i	−0.906827	+	0.906827i
$395$		−	6.00000i		−	0.301893i
$396$	2.00000			0.100504
$397$			28.0000i			1.40528i	0.711546	+	0.702640i	$0.247995\pi$
$397$			28.0000i			1.40528i	−0.711546	+	0.702640i	$0.752005\pi$
$398$	2.00000	+	2.00000i	0.100251	+	0.100251i
$399$	−8.00000			−0.400501
$400$	4.00000			0.200000
$401$	−34.0000			−1.69788			−0.848939	−	0.528490i	$-0.822758\pi$
$401$	−34.0000			−1.69788			−0.848939	+	0.528490i	$0.822758\pi$
$402$	4.00000	+	4.00000i	0.199502	+	0.199502i
$403$		−	24.0000i		−	1.19553i
$404$	−4.00000			−0.199007
$405$		−	1.00000i		−	0.0496904i
$406$	12.0000	−	12.0000i	0.595550	−	0.595550i
$407$	−4.00000			−0.198273
$408$	4.00000	+	4.00000i	0.198030	+	0.198030i
$409$	10.0000			0.494468			0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000			0.494468			0.247234	+	0.968956i	$0.420478\pi$
$410$	2.00000	−	2.00000i	0.0987730	−	0.0987730i
$411$		−	6.00000i		−	0.295958i
$412$		−	20.0000i		−	0.985329i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	16.0000	−	16.0000i	0.784465	−	0.784465i
$417$	−12.0000			−0.587643
$418$	−4.00000	−	4.00000i	−0.195646	−	0.195646i
$419$			4.00000i			0.195413i	0.995215	+	0.0977064i	$0.0311506\pi$
$419$			4.00000i			0.195413i	−0.995215	+	0.0977064i	$0.968849\pi$
$420$			4.00000i			0.195180i
$421$			12.0000i			0.584844i	0.956289	+	0.292422i	$0.0944612\pi$
$421$			12.0000i			0.584844i	−0.956289	+	0.292422i	$0.905539\pi$
$422$	20.0000	−	20.0000i	0.973585	−	0.973585i
$423$		0			0
$424$	−28.0000	−	28.0000i	−1.35980	−	1.35980i
$425$	−2.00000			−0.0970143
$426$	−8.00000	+	8.00000i	−0.387601	+	0.387601i
$427$			24.0000i			1.16144i
$428$	40.0000			1.93347
$429$			4.00000i			0.193122i
$430$	4.00000	+	4.00000i	0.192897	+	0.192897i
$431$	12.0000			0.578020			0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000			0.578020			0.289010	+	0.957326i	$0.406674\pi$
$432$		−	4.00000i		−	0.192450i
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$	12.0000	+	12.0000i	0.576018	+	0.576018i
$435$		−	6.00000i		−	0.287678i
$436$		0			0
$437$		0			0
$438$	10.0000	−	10.0000i	0.477818	−	0.477818i
$439$	14.0000			0.668184			0.334092	−	0.942541i	$-0.391570\pi$
$439$	14.0000			0.668184			0.334092	+	0.942541i	$0.391570\pi$
$440$	−2.00000	+	2.00000i	−0.0953463	+	0.0953463i
$441$	3.00000			0.142857
$442$	−8.00000	+	8.00000i	−0.380521	+	0.380521i
$443$			8.00000i			0.380091i	0.981775	+	0.190046i	$0.0608636\pi$
$443$			8.00000i			0.380091i	−0.981775	+	0.190046i	$0.939136\pi$
$444$			8.00000i			0.379663i
$445$		−	6.00000i		−	0.284427i
$446$	10.0000	+	10.0000i	0.473514	+	0.473514i
$447$	−2.00000			−0.0945968
$448$			16.0000i			0.755929i
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$	1.00000	+	1.00000i	0.0471405	+	0.0471405i
$451$			2.00000i			0.0941763i
$452$		−	4.00000i		−	0.188144i
$453$			22.0000i			1.03365i
$454$		0			0
$455$	−8.00000			−0.375046
$456$	−8.00000	+	8.00000i	−0.374634	+	0.374634i
$457$	26.0000			1.21623			0.608114	−	0.793849i	$-0.291926\pi$
$457$	26.0000			1.21623			0.608114	+	0.793849i	$0.291926\pi$
$458$	20.0000	−	20.0000i	0.934539	−	0.934539i
$459$			2.00000i			0.0933520i
$460$		0			0
$461$			10.0000i			0.465746i	0.972507	+	0.232873i	$0.0748127\pi$
$461$			10.0000i			0.465746i	−0.972507	+	0.232873i	$0.925187\pi$
$462$	−2.00000	−	2.00000i	−0.0930484	−	0.0930484i
$463$	2.00000			0.0929479			0.0464739	−	0.998920i	$-0.485202\pi$
$463$	2.00000			0.0929479			0.0464739	+	0.998920i	$0.485202\pi$
$464$		−	24.0000i		−	1.11417i
$465$	6.00000			0.278243
$466$	−6.00000	−	6.00000i	−0.277945	−	0.277945i
$467$			32.0000i			1.48078i	0.672176	+	0.740392i	$0.265360\pi$
$467$			32.0000i			1.48078i	−0.672176	+	0.740392i	$0.734640\pi$
$468$	8.00000			0.369800
$469$		−	8.00000i		−	0.369406i
$470$		0			0
$471$	−4.00000			−0.184310
$472$		0			0
$473$	−4.00000			−0.183920
$474$	6.00000	−	6.00000i	0.275589	−	0.275589i
$475$		−	4.00000i		−	0.183533i
$476$		−	8.00000i		−	0.366679i
$477$		−	14.0000i		−	0.641016i
$478$	8.00000	+	8.00000i	0.365911	+	0.365911i
$479$	−12.0000			−0.548294			−0.274147	−	0.961688i	$-0.588395\pi$
$479$	−12.0000			−0.548294			−0.274147	+	0.961688i	$0.588395\pi$
$480$	4.00000	+	4.00000i	0.182574	+	0.182574i
$481$	−16.0000			−0.729537
$482$	10.0000	+	10.0000i	0.455488	+	0.455488i
$483$		0			0
$484$		−	2.00000i		−	0.0909091i
$485$		−	6.00000i		−	0.272446i
$486$	1.00000	−	1.00000i	0.0453609	−	0.0453609i
$487$	−22.0000			−0.996915			−0.498458	−	0.866914i	$-0.666100\pi$
$487$	−22.0000			−0.996915			−0.498458	+	0.866914i	$0.666100\pi$
$488$	24.0000	+	24.0000i	1.08643	+	1.08643i
$489$	−4.00000			−0.180886
$490$	−3.00000	+	3.00000i	−0.135526	+	0.135526i
$491$		−	40.0000i		−	1.80517i	−0.430507	−	0.902587i	$-0.641665\pi$
$491$		−	40.0000i		−	1.80517i	0.430507	−	0.902587i	$-0.358335\pi$
$492$	4.00000			0.180334
$493$			12.0000i			0.540453i
$494$	−16.0000	−	16.0000i	−0.719874	−	0.719874i
$495$	−1.00000			−0.0449467
$496$	24.0000			1.07763
$497$	16.0000			0.717698
$498$		0			0
$499$		−	20.0000i		−	0.895323i	−0.894203	−	0.447661i	$-0.852257\pi$
$499$		−	20.0000i		−	0.895323i	0.894203	−	0.447661i	$-0.147743\pi$
$500$	−2.00000			−0.0894427
$501$		0			0
$502$	−4.00000	+	4.00000i	−0.178529	+	0.178529i
$503$	28.0000			1.24846			0.624229	−	0.781241i	$-0.285413\pi$
$503$	28.0000			1.24846			0.624229	+	0.781241i	$0.285413\pi$
$504$	−4.00000	+	4.00000i	−0.178174	+	0.178174i
$505$	2.00000			0.0889988
$506$		0			0
$507$			3.00000i			0.133235i
$508$			12.0000i			0.532414i
$509$			42.0000i			1.86162i	0.365507	+	0.930809i	$0.380896\pi$
$509$			42.0000i			1.86162i	−0.365507	+	0.930809i	$0.619104\pi$
$510$	−2.00000	−	2.00000i	−0.0885615	−	0.0885615i
$511$	−20.0000			−0.884748
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$	−4.00000			−0.176604
$514$	22.0000	+	22.0000i	0.970378	+	0.970378i
$515$			10.0000i			0.440653i
$516$			8.00000i			0.352180i
$517$		0			0
$518$	8.00000	−	8.00000i	0.351500	−	0.351500i
$519$	18.0000			0.790112
$520$	−8.00000	+	8.00000i	−0.350823	+	0.350823i
$521$	42.0000			1.84005			0.920027	−	0.391856i	$-0.128167\pi$
$521$	42.0000			1.84005			0.920027	+	0.391856i	$0.128167\pi$
$522$	6.00000	−	6.00000i	0.262613	−	0.262613i
$523$			36.0000i			1.57417i	0.616844	+	0.787085i	$0.288411\pi$
$523$			36.0000i			1.57417i	−0.616844	+	0.787085i	$0.711589\pi$
$524$		0			0
$525$		−	2.00000i		−	0.0872872i
$526$		0			0
$527$	−12.0000			−0.522728
$528$	−4.00000			−0.174078
$529$	−23.0000			−1.00000
$530$	14.0000	+	14.0000i	0.608121	+	0.608121i
$531$		0			0
$532$	16.0000			0.693688
$533$			8.00000i			0.346518i
$534$	6.00000	−	6.00000i	0.259645	−	0.259645i
$535$	−20.0000			−0.864675
$536$	−8.00000	−	8.00000i	−0.345547	−	0.345547i
$537$	24.0000			1.03568
$538$	−18.0000	+	18.0000i	−0.776035	+	0.776035i
$539$		−	3.00000i		−	0.129219i
$540$			2.00000i			0.0860663i
$541$		−	16.0000i		−	0.687894i	−0.938989	−	0.343947i	$-0.888236\pi$
$541$		−	16.0000i		−	0.687894i	0.938989	−	0.343947i	$-0.111764\pi$
$542$	−22.0000	−	22.0000i	−0.944981	−	0.944981i
$543$	−20.0000			−0.858282
$544$	−8.00000	−	8.00000i	−0.342997	−	0.342997i
$545$		0			0
$546$	−8.00000	−	8.00000i	−0.342368	−	0.342368i
$547$			44.0000i			1.88130i	0.339372	+	0.940652i	$0.389785\pi$
$547$			44.0000i			1.88130i	−0.339372	+	0.940652i	$0.610215\pi$
$548$			12.0000i			0.512615i
$549$			12.0000i			0.512148i
$550$	1.00000	−	1.00000i	0.0426401	−	0.0426401i
$551$	−24.0000			−1.02243
$552$		0			0
$553$	−12.0000			−0.510292
$554$	12.0000	−	12.0000i	0.509831	−	0.509831i
$555$		−	4.00000i		−	0.169791i
$556$	24.0000			1.01783
$557$		−	22.0000i		−	0.932170i	−0.884740	−	0.466085i	$-0.845664\pi$
$557$		−	22.0000i		−	0.932170i	0.884740	−	0.466085i	$-0.154336\pi$
$558$	6.00000	+	6.00000i	0.254000	+	0.254000i
$559$	−16.0000			−0.676728
$560$		−	8.00000i		−	0.338062i
$561$	2.00000			0.0844401
$562$	22.0000	+	22.0000i	0.928014	+	0.928014i
$563$			16.0000i			0.674320i	0.941447	+	0.337160i	$0.109466\pi$
$563$			16.0000i			0.674320i	−0.941447	+	0.337160i	$0.890534\pi$
$564$		0			0
$565$			2.00000i			0.0841406i
$566$	4.00000	−	4.00000i	0.168133	−	0.168133i
$567$	−2.00000			−0.0839921
$568$	16.0000	−	16.0000i	0.671345	−	0.671345i
$569$	−30.0000			−1.25767			−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000			−1.25767			−0.628833	+	0.777541i	$0.716467\pi$
$570$	4.00000	−	4.00000i	0.167542	−	0.167542i
$571$		−	28.0000i		−	1.17176i	−0.810397	−	0.585882i	$-0.800748\pi$
$571$		−	28.0000i		−	1.17176i	0.810397	−	0.585882i	$-0.199252\pi$
$572$		−	8.00000i		−	0.334497i
$573$		−	4.00000i		−	0.167102i
$574$	−4.00000	−	4.00000i	−0.166957	−	0.166957i
$575$		0			0
$576$			8.00000i			0.333333i
$577$	−34.0000			−1.41544			−0.707719	−	0.706494i	$-0.750276\pi$
$577$	−34.0000			−1.41544			−0.707719	+	0.706494i	$0.750276\pi$
$578$	−13.0000	−	13.0000i	−0.540729	−	0.540729i
$579$		−	18.0000i		−	0.748054i
$580$			12.0000i			0.498273i
$581$		0			0
$582$	6.00000	−	6.00000i	0.248708	−	0.248708i
$583$	−14.0000			−0.579821
$584$	−20.0000	+	20.0000i	−0.827606	+	0.827606i
$585$	−4.00000			−0.165380
$586$	14.0000	−	14.0000i	0.578335	−	0.578335i
$587$		−	28.0000i		−	1.15568i	−0.816149	−	0.577842i	$-0.803895\pi$
$587$		−	28.0000i		−	1.15568i	0.816149	−	0.577842i	$-0.196105\pi$
$588$	−6.00000			−0.247436
$589$		−	24.0000i		−	0.988903i
$590$		0			0
$591$	18.0000			0.740421
$592$		−	16.0000i		−	0.657596i
$593$	14.0000			0.574911			0.287456	−	0.957794i	$-0.407191\pi$
$593$	14.0000			0.574911			0.287456	+	0.957794i	$0.407191\pi$
$594$	−1.00000	−	1.00000i	−0.0410305	−	0.0410305i
$595$			4.00000i			0.163984i
$596$	4.00000			0.163846
$597$		−	2.00000i		−	0.0818546i
$598$		0			0
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$	−2.00000	−	2.00000i	−0.0816497	−	0.0816497i
$601$	−38.0000			−1.55005			−0.775026	−	0.631929i	$-0.782263\pi$
$601$	−38.0000			−1.55005			−0.775026	+	0.631929i	$0.782263\pi$
$602$	8.00000	−	8.00000i	0.326056	−	0.326056i
$603$		−	4.00000i		−	0.162893i
$604$		−	44.0000i		−	1.79033i
$605$			1.00000i			0.0406558i
$606$	2.00000	+	2.00000i	0.0812444	+	0.0812444i
$607$	14.0000			0.568242			0.284121	−	0.958788i	$-0.408298\pi$
$607$	14.0000			0.568242			0.284121	+	0.958788i	$0.408298\pi$
$608$	16.0000	−	16.0000i	0.648886	−	0.648886i
$609$	−12.0000			−0.486265
$610$	−12.0000	−	12.0000i	−0.485866	−	0.485866i
$611$		0			0
$612$		−	4.00000i		−	0.161690i
$613$		−	8.00000i		−	0.323117i	−0.986863	−	0.161558i	$-0.948348\pi$
$613$		−	8.00000i		−	0.323117i	0.986863	−	0.161558i	$-0.0516520\pi$
$614$	−20.0000	+	20.0000i	−0.807134	+	0.807134i
$615$	−2.00000			−0.0806478
$616$	4.00000	+	4.00000i	0.161165	+	0.161165i
$617$	−30.0000			−1.20775			−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000			−1.20775			−0.603877	+	0.797077i	$0.706378\pi$
$618$	−10.0000	+	10.0000i	−0.402259	+	0.402259i
$619$			44.0000i			1.76851i	0.467005	+	0.884255i	$0.345333\pi$
$619$			44.0000i			1.76851i	−0.467005	+	0.884255i	$0.654667\pi$
$620$	−12.0000			−0.481932
$621$		0			0
$622$	20.0000	+	20.0000i	0.801927	+	0.801927i
$623$	−12.0000			−0.480770
$624$	−16.0000			−0.640513
$625$	1.00000			0.0400000
$626$	6.00000	+	6.00000i	0.239808	+	0.239808i
$627$			4.00000i			0.159745i
$628$	8.00000			0.319235
$629$			8.00000i			0.318981i
$630$	2.00000	−	2.00000i	0.0796819	−	0.0796819i
$631$	30.0000			1.19428			0.597141	−	0.802137i	$-0.296303\pi$
$631$	30.0000			1.19428			0.597141	+	0.802137i	$0.296303\pi$
$632$	−12.0000	+	12.0000i	−0.477334	+	0.477334i
$633$	−20.0000			−0.794929
$634$	−34.0000	+	34.0000i	−1.35031	+	1.35031i
$635$		−	6.00000i		−	0.238103i
$636$			28.0000i			1.11027i
$637$		−	12.0000i		−	0.475457i
$638$	−6.00000	−	6.00000i	−0.237542	−	0.237542i
$639$	8.00000			0.316475
$640$	−8.00000	−	8.00000i	−0.316228	−	0.316228i
$641$	−18.0000			−0.710957			−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000			−0.710957			−0.355479	+	0.934684i	$0.615682\pi$
$642$	−20.0000	−	20.0000i	−0.789337	−	0.789337i
$643$		−	28.0000i		−	1.10421i	−0.833774	−	0.552106i	$-0.813824\pi$
$643$		−	28.0000i		−	1.10421i	0.833774	−	0.552106i	$-0.186176\pi$
$644$		0			0
$645$		−	4.00000i		−	0.157500i
$646$	−8.00000	+	8.00000i	−0.314756	+	0.314756i
$647$	−32.0000			−1.25805			−0.629025	−	0.777385i	$-0.716546\pi$
$647$	−32.0000			−1.25805			−0.629025	+	0.777385i	$0.716546\pi$
$648$	−2.00000	+	2.00000i	−0.0785674	+	0.0785674i
$649$		0			0
$650$	4.00000	−	4.00000i	0.156893	−	0.156893i
$651$		−	12.0000i		−	0.470317i
$652$	8.00000			0.313304
$653$		−	26.0000i		−	1.01746i	−0.860927	−	0.508729i	$-0.830115\pi$
$653$		−	26.0000i		−	1.01746i	0.860927	−	0.508729i	$-0.169885\pi$
$654$		0			0
$655$		0			0
$656$	−8.00000			−0.312348
$657$	−10.0000			−0.390137
$658$		0			0
$659$		0			0		1.00000			$0$
$659$		0			0		−1.00000			$\pi$
$660$	2.00000			0.0778499
$661$		−	8.00000i		−	0.311164i	−0.987823	−	0.155582i	$-0.950275\pi$
$661$		−	8.00000i		−	0.311164i	0.987823	−	0.155582i	$-0.0497253\pi$
$662$	12.0000	−	12.0000i	0.466393	−	0.466393i
$663$	8.00000			0.310694
$664$		0			0
$665$	−8.00000			−0.310227
$666$	4.00000	−	4.00000i	0.154997	−	0.154997i
$667$		0			0
$668$		0			0
$669$		−	10.0000i		−	0.386622i
$670$	4.00000	+	4.00000i	0.154533	+	0.154533i
$671$	12.0000			0.463255
$672$	8.00000	−	8.00000i	0.308607	−	0.308607i
$673$	6.00000			0.231283			0.115642	−	0.993291i	$-0.463108\pi$
$673$	6.00000			0.231283			0.115642	+	0.993291i	$0.463108\pi$
$674$	−2.00000	−	2.00000i	−0.0770371	−	0.0770371i
$675$		−	1.00000i		−	0.0384900i
$676$		−	6.00000i		−	0.230769i
$677$		−	18.0000i		−	0.691796i	−0.938272	−	0.345898i	$-0.887574\pi$
$677$		−	18.0000i		−	0.691796i	0.938272	−	0.345898i	$-0.112426\pi$
$678$	−2.00000	+	2.00000i	−0.0768095	+	0.0768095i
$679$	−12.0000			−0.460518
$680$	4.00000	+	4.00000i	0.153393	+	0.153393i
$681$		0			0
$682$	6.00000	−	6.00000i	0.229752	−	0.229752i
$683$		−	8.00000i		−	0.306111i	−0.988218	−	0.153056i	$-0.951089\pi$
$683$		−	8.00000i		−	0.306111i	0.988218	−	0.153056i	$-0.0489114\pi$
$684$	8.00000			0.305888
$685$		−	6.00000i		−	0.229248i
$686$	20.0000	+	20.0000i	0.763604	+	0.763604i
$687$	−20.0000			−0.763048
$688$		−	16.0000i		−	0.609994i
$689$	−56.0000			−2.13343
$690$		0			0
$691$			36.0000i			1.36950i	0.728776	+	0.684752i	$0.240090\pi$
$691$			36.0000i			1.36950i	−0.728776	+	0.684752i	$0.759910\pi$
$692$	−36.0000			−1.36851
$693$			2.00000i			0.0759737i
$694$	−16.0000	+	16.0000i	−0.607352	+	0.607352i
$695$	−12.0000			−0.455186
$696$	−12.0000	+	12.0000i	−0.454859	+	0.454859i
$697$	4.00000			0.151511
$698$	−28.0000	+	28.0000i	−1.05982	+	1.05982i
$699$			6.00000i			0.226941i
$700$			4.00000i			0.151186i
$701$		−	34.0000i		−	1.28416i	−0.766637	−	0.642081i	$-0.778071\pi$
$701$		−	34.0000i		−	1.28416i	0.766637	−	0.642081i	$-0.221929\pi$
$702$	−4.00000	−	4.00000i	−0.150970	−	0.150970i
$703$	−16.0000			−0.603451
$704$	8.00000			0.301511
$705$		0			0
$706$	14.0000	+	14.0000i	0.526897	+	0.526897i
$707$		−	4.00000i		−	0.150435i
$708$		0			0
$709$		−	52.0000i		−	1.95290i	−0.215742	−	0.976450i	$-0.569217\pi$
$709$		−	52.0000i		−	1.95290i	0.215742	−	0.976450i	$-0.430783\pi$
$710$	−8.00000	+	8.00000i	−0.300235	+	0.300235i
$711$	−6.00000			−0.225018
$712$	−12.0000	+	12.0000i	−0.449719	+	0.449719i
$713$		0			0
$714$	−4.00000	+	4.00000i	−0.149696	+	0.149696i
$715$			4.00000i			0.149592i
$716$	−48.0000			−1.79384
$717$		−	8.00000i		−	0.298765i
$718$	−12.0000	−	12.0000i	−0.447836	−	0.447836i
$719$	48.0000			1.79010			0.895049	−	0.445968i	$-0.147140\pi$
$719$	48.0000			1.79010			0.895049	+	0.445968i	$0.147140\pi$
$720$		−	4.00000i		−	0.149071i
$721$	20.0000			0.744839
$722$	3.00000	+	3.00000i	0.111648	+	0.111648i
$723$		−	10.0000i		−	0.371904i
$724$	40.0000			1.48659
$725$		−	6.00000i		−	0.222834i
$726$	−1.00000	+	1.00000i	−0.0371135	+	0.0371135i
$727$	−6.00000			−0.222528			−0.111264	−	0.993791i	$-0.535490\pi$
$727$	−6.00000			−0.222528			−0.111264	+	0.993791i	$0.535490\pi$
$728$	16.0000	+	16.0000i	0.592999	+	0.592999i
$729$	−1.00000			−0.0370370
$730$	10.0000	−	10.0000i	0.370117	−	0.370117i
$731$			8.00000i			0.295891i
$732$		−	24.0000i		−	0.887066i
$733$		−	20.0000i		−	0.738717i	−0.929287	−	0.369358i	$-0.879577\pi$
$733$		−	20.0000i		−	0.738717i	0.929287	−	0.369358i	$-0.120423\pi$
$734$	−34.0000	−	34.0000i	−1.25496	−	1.25496i
$735$	3.00000			0.110657
$736$		0			0
$737$	−4.00000			−0.147342
$738$	−2.00000	−	2.00000i	−0.0736210	−	0.0736210i
$739$			28.0000i			1.03000i	0.857191	+	0.514998i	$0.172207\pi$
$739$			28.0000i			1.03000i	−0.857191	+	0.514998i	$0.827793\pi$
$740$			8.00000i			0.294086i
$741$			16.0000i			0.587775i
$742$	28.0000	−	28.0000i	1.02791	−	1.02791i
$743$	−24.0000			−0.880475			−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000			−0.880475			−0.440237	+	0.897881i	$0.645106\pi$
$744$	−12.0000	−	12.0000i	−0.439941	−	0.439941i
$745$	−2.00000			−0.0732743
$746$	−24.0000	+	24.0000i	−0.878702	+	0.878702i
$747$		0			0
$748$	−4.00000			−0.146254
$749$			40.0000i			1.46157i
$750$	1.00000	+	1.00000i	0.0365148	+	0.0365148i
$751$	10.0000			0.364905			0.182453	−	0.983215i	$-0.441596\pi$
$751$	10.0000			0.364905			0.182453	+	0.983215i	$0.441596\pi$
$752$		0			0
$753$	4.00000			0.145768
$754$	−24.0000	−	24.0000i	−0.874028	−	0.874028i
$755$			22.0000i			0.800662i
$756$	4.00000			0.145479
$757$			16.0000i			0.581530i	0.956795	+	0.290765i	$0.0939098\pi$
$757$			16.0000i			0.581530i	−0.956795	+	0.290765i	$0.906090\pi$
$758$	36.0000	−	36.0000i	1.30758	−	1.30758i
$759$		0			0
$760$	−8.00000	+	8.00000i	−0.290191	+	0.290191i
$761$	−22.0000			−0.797499			−0.398750	−	0.917060i	$-0.630556\pi$
$761$	−22.0000			−0.797499			−0.398750	+	0.917060i	$0.630556\pi$
$762$	6.00000	−	6.00000i	0.217357	−	0.217357i
$763$		0			0
$764$			8.00000i			0.289430i
$765$			2.00000i			0.0723102i
$766$	20.0000	+	20.0000i	0.722629	+	0.722629i
$767$		0			0
$768$		−	16.0000i		−	0.577350i
$769$	18.0000			0.649097			0.324548	−	0.945869i	$-0.394788\pi$
$769$	18.0000			0.649097			0.324548	+	0.945869i	$0.394788\pi$
$770$	−2.00000	−	2.00000i	−0.0720750	−	0.0720750i
$771$		−	22.0000i		−	0.792311i
$772$			36.0000i			1.29567i
$773$			46.0000i			1.65451i	0.561830	+	0.827253i	$0.310097\pi$
$773$			46.0000i			1.65451i	−0.561830	+	0.827253i	$0.689903\pi$
$774$	4.00000	−	4.00000i	0.143777	−	0.143777i
$775$	6.00000			0.215526
$776$	−12.0000	+	12.0000i	−0.430775	+	0.430775i
$777$	−8.00000			−0.286998
$778$	−10.0000	+	10.0000i	−0.358517	+	0.358517i
$779$			8.00000i			0.286630i
$780$	8.00000			0.286446
$781$		−	8.00000i		−	0.286263i
$782$		0			0
$783$	−6.00000			−0.214423
$784$	12.0000			0.428571
$785$	−4.00000			−0.142766
$786$		0			0
$787$			52.0000i			1.85360i	0.375555	+	0.926800i	$0.377452\pi$
$787$			52.0000i			1.85360i	−0.375555	+	0.926800i	$0.622548\pi$
$788$	−36.0000			−1.28245
$789$		0			0
$790$	6.00000	−	6.00000i	0.213470	−	0.213470i
$791$	4.00000			0.142224
$792$	2.00000	+	2.00000i	0.0710669	+	0.0710669i
$793$	48.0000			1.70453
$794$	−28.0000	+	28.0000i	−0.993683	+	0.993683i
$795$		−	14.0000i		−	0.496529i
$796$			4.00000i			0.141776i
$797$			14.0000i			0.495905i	0.968772	+	0.247953i	$0.0797578\pi$
$797$			14.0000i			0.495905i	−0.968772	+	0.247953i	$0.920242\pi$
$798$	−8.00000	−	8.00000i	−0.283197	−	0.283197i
$799$		0			0
$800$	4.00000	+	4.00000i	0.141421	+	0.141421i
$801$	−6.00000			−0.212000
$802$	−34.0000	−	34.0000i	−1.20058	−	1.20058i
$803$			10.0000i			0.352892i
$804$			8.00000i			0.282138i
$805$		0			0
$806$	24.0000	−	24.0000i	0.845364	−	0.845364i
$807$	18.0000			0.633630
$808$	−4.00000	−	4.00000i	−0.140720	−	0.140720i
$809$	−30.0000			−1.05474			−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000			−1.05474			−0.527372	+	0.849635i	$0.676823\pi$
$810$	1.00000	−	1.00000i	0.0351364	−	0.0351364i
$811$			4.00000i			0.140459i	0.997531	+	0.0702295i	$0.0223732\pi$
$811$			4.00000i			0.140459i	−0.997531	+	0.0702295i	$0.977627\pi$
$812$	24.0000			0.842235
$813$			22.0000i			0.771574i
$814$	−4.00000	−	4.00000i	−0.140200	−	0.140200i
$815$	−4.00000			−0.140114
$816$			8.00000i			0.280056i
$817$	−16.0000			−0.559769
$818$	10.0000	+	10.0000i	0.349642	+	0.349642i
$819$			8.00000i			0.279543i
$820$	4.00000			0.139686
$821$		−	54.0000i		−	1.88461i	−0.334751	−	0.942306i	$-0.608652\pi$
$821$		−	54.0000i		−	1.88461i	0.334751	−	0.942306i	$-0.391348\pi$
$822$	6.00000	−	6.00000i	0.209274	−	0.209274i
$823$	10.0000			0.348578			0.174289	−	0.984695i	$-0.444237\pi$
$823$	10.0000			0.348578			0.174289	+	0.984695i	$0.444237\pi$
$824$	20.0000	−	20.0000i	0.696733	−	0.696733i
$825$	−1.00000			−0.0348155
$826$		0			0
$827$			20.0000i			0.695468i	0.937593	+	0.347734i	$0.113049\pi$
$827$			20.0000i			0.695468i	−0.937593	+	0.347734i	$0.886951\pi$
$828$		0			0
$829$			28.0000i			0.972480i	0.873825	+	0.486240i	$0.161632\pi$
$829$			28.0000i			0.972480i	−0.873825	+	0.486240i	$0.838368\pi$
$830$		0			0
$831$	−12.0000			−0.416275
$832$	32.0000			1.10940
$833$	−6.00000			−0.207888
$834$	−12.0000	−	12.0000i	−0.415526	−	0.415526i
$835$		0			0
$836$		−	8.00000i		−	0.276686i
$837$		−	6.00000i		−	0.207390i
$838$	−4.00000	+	4.00000i	−0.138178	+	0.138178i
$839$	24.0000			0.828572			0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000			0.828572			0.414286	+	0.910147i	$0.364031\pi$
$840$	−4.00000	+	4.00000i	−0.138013	+	0.138013i
$841$	−7.00000			−0.241379
$842$	−12.0000	+	12.0000i	−0.413547	+	0.413547i
$843$		−	22.0000i		−	0.757720i
$844$	40.0000			1.37686
$845$			3.00000i			0.103203i
$846$		0			0
$847$	2.00000			0.0687208
$848$		−	56.0000i		−	1.92305i
$849$	−4.00000			−0.137280
$850$	−2.00000	−	2.00000i	−0.0685994	−	0.0685994i
$851$		0			0
$852$	−16.0000			−0.548151
$853$			16.0000i			0.547830i	0.961754	+	0.273915i	$0.0883186\pi$
$853$			16.0000i			0.547830i	−0.961754	+	0.273915i	$0.911681\pi$
$854$	−24.0000	+	24.0000i	−0.821263	+	0.821263i
$855$	−4.00000			−0.136797
$856$	40.0000	+	40.0000i	1.36717	+	1.36717i
$857$	38.0000			1.29806			0.649028	−	0.760765i	$-0.275176\pi$
$857$	38.0000			1.29806			0.649028	+	0.760765i	$0.275176\pi$
$858$	−4.00000	+	4.00000i	−0.136558	+	0.136558i
$859$			20.0000i			0.682391i	0.939992	+	0.341196i	$0.110832\pi$
$859$			20.0000i			0.682391i	−0.939992	+	0.341196i	$0.889168\pi$
$860$			8.00000i			0.272798i
$861$			4.00000i			0.136320i
$862$	12.0000	+	12.0000i	0.408722	+	0.408722i
$863$	28.0000			0.953131			0.476566	−	0.879139i	$-0.341881\pi$
$863$	28.0000			0.953131			0.476566	+	0.879139i	$0.341881\pi$
$864$	4.00000	−	4.00000i	0.136083	−	0.136083i
$865$	18.0000			0.612018
$866$	−2.00000	−	2.00000i	−0.0679628	−	0.0679628i
$867$			13.0000i			0.441503i
$868$			24.0000i			0.814613i
$869$			6.00000i			0.203536i
$870$	6.00000	−	6.00000i	0.203419	−	0.203419i
$871$	−16.0000			−0.542139
$872$		0			0
$873$	−6.00000			−0.203069
$874$		0			0
$875$		−	2.00000i		−	0.0676123i
$876$	20.0000			0.675737
$877$		−	56.0000i		−	1.89099i	−0.325643	−	0.945493i	$-0.605581\pi$
$877$		−	56.0000i		−	1.89099i	0.325643	−	0.945493i	$-0.394419\pi$
$878$	14.0000	+	14.0000i	0.472477	+	0.472477i
$879$	−14.0000			−0.472208
$880$	−4.00000			−0.134840
$881$	−38.0000			−1.28025			−0.640126	−	0.768270i	$-0.721118\pi$
$881$	−38.0000			−1.28025			−0.640126	+	0.768270i	$0.721118\pi$
$882$	3.00000	+	3.00000i	0.101015	+	0.101015i
$883$			36.0000i			1.21150i	0.795656	+	0.605748i	$0.207126\pi$
$883$			36.0000i			1.21150i	−0.795656	+	0.605748i	$0.792874\pi$
$884$	−16.0000			−0.538138
$885$		0			0
$886$	−8.00000	+	8.00000i	−0.268765	+	0.268765i
$887$	24.0000			0.805841			0.402921	−	0.915235i	$-0.367995\pi$
$887$	24.0000			0.805841			0.402921	+	0.915235i	$0.367995\pi$
$888$	−8.00000	+	8.00000i	−0.268462	+	0.268462i
$889$	−12.0000			−0.402467
$890$	6.00000	−	6.00000i	0.201120	−	0.201120i
$891$			1.00000i			0.0335013i
$892$			20.0000i			0.669650i
$893$		0			0
$894$	−2.00000	−	2.00000i	−0.0668900	−	0.0668900i
$895$	24.0000			0.802232
$896$	−16.0000	+	16.0000i	−0.534522	+	0.534522i
$897$		0			0
$898$	6.00000	+	6.00000i	0.200223	+	0.200223i
$899$		−	36.0000i		−	1.20067i
$900$			2.00000i			0.0666667i
$901$			28.0000i			0.932815i
$902$	−2.00000	+	2.00000i	−0.0665927	+	0.0665927i
$903$	−8.00000			−0.266223
$904$	4.00000	−	4.00000i	0.133038	−	0.133038i
$905$	−20.0000			−0.664822
$906$	−22.0000	+	22.0000i	−0.730901	+	0.730901i
$907$		−	20.0000i		−	0.664089i	−0.943264	−	0.332045i	$-0.892262\pi$
$907$		−	20.0000i		−	0.664089i	0.943264	−	0.332045i	$-0.107738\pi$
$908$		0			0
$909$		−	2.00000i		−	0.0663358i
$910$	−8.00000	−	8.00000i	−0.265197	−	0.265197i
$911$	20.0000			0.662630			0.331315	−	0.943520i	$-0.392508\pi$
$911$	20.0000			0.662630			0.331315	+	0.943520i	$0.392508\pi$
$912$	−16.0000			−0.529813
$913$		0			0
$914$	26.0000	+	26.0000i	0.860004	+	0.860004i
$915$			12.0000i			0.396708i
$916$	40.0000			1.32164
$917$		0			0
$918$	−2.00000	+	2.00000i	−0.0660098	+	0.0660098i
$919$	10.0000			0.329870			0.164935	−	0.986304i	$-0.447259\pi$
$919$	10.0000			0.329870			0.164935	+	0.986304i	$0.447259\pi$
$920$		0			0
$921$	20.0000			0.659022
$922$	−10.0000	+	10.0000i	−0.329332	+	0.329332i
$923$		−	32.0000i		−	1.05329i
$924$		−	4.00000i		−	0.131590i
$925$		−	4.00000i		−	0.131519i
$926$	2.00000	+	2.00000i	0.0657241	+	0.0657241i
$927$	10.0000			0.328443
$928$	24.0000	−	24.0000i	0.787839	−	0.787839i
$929$	6.00000			0.196854			0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000			0.196854			0.0984268	+	0.995144i	$0.468619\pi$
$930$	6.00000	+	6.00000i	0.196748	+	0.196748i
$931$		−	12.0000i		−	0.393284i
$932$		−	12.0000i		−	0.393073i
$933$		−	20.0000i		−	0.654771i
$934$	−32.0000	+	32.0000i	−1.04707	+	1.04707i
$935$	2.00000			0.0654070
$936$	8.00000	+	8.00000i	0.261488	+	0.261488i
$937$	14.0000			0.457360			0.228680	−	0.973502i	$-0.426559\pi$
$937$	14.0000			0.457360			0.228680	+	0.973502i	$0.426559\pi$
$938$	8.00000	−	8.00000i	0.261209	−	0.261209i
$939$		−	6.00000i		−	0.195803i
$940$		0			0
$941$		−	6.00000i		−	0.195594i	−0.995206	−	0.0977972i	$-0.968820\pi$
$941$		−	6.00000i		−	0.195594i	0.995206	−	0.0977972i	$-0.0311797\pi$
$942$	−4.00000	−	4.00000i	−0.130327	−	0.130327i
$943$		0			0
$944$		0			0
$945$	−2.00000			−0.0650600
$946$	−4.00000	−	4.00000i	−0.130051	−	0.130051i
$947$			52.0000i			1.68977i	0.534946	+	0.844886i	$0.320332\pi$
$947$			52.0000i			1.68977i	−0.534946	+	0.844886i	$0.679668\pi$
$948$	12.0000			0.389742
$949$			40.0000i			1.29845i
$950$	4.00000	−	4.00000i	0.129777	−	0.129777i
$951$	34.0000			1.10253
$952$	8.00000	−	8.00000i	0.259281	−	0.259281i
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$	14.0000	−	14.0000i	0.453267	−	0.453267i
$955$		−	4.00000i		−	0.129437i
$956$			16.0000i			0.517477i
$957$			6.00000i			0.193952i
$958$	−12.0000	−	12.0000i	−0.387702	−	0.387702i
$959$	−12.0000			−0.387500
$960$			8.00000i			0.258199i
$961$	5.00000			0.161290
$962$	−16.0000	−	16.0000i	−0.515861	−	0.515861i
$963$			20.0000i			0.644491i
$964$			20.0000i			0.644157i
$965$		−	18.0000i		−	0.579441i
$966$		0			0
$967$	18.0000			0.578841			0.289420	−	0.957202i	$-0.406537\pi$
$967$	18.0000			0.578841			0.289420	+	0.957202i	$0.406537\pi$
$968$	2.00000	−	2.00000i	0.0642824	−	0.0642824i
$969$	8.00000			0.256997
$970$	6.00000	−	6.00000i	0.192648	−	0.192648i
$971$		−	12.0000i		−	0.385098i	−0.981287	−	0.192549i	$-0.938325\pi$
$971$		−	12.0000i		−	0.385098i	0.981287	−	0.192549i	$-0.0616755\pi$
$972$	2.00000			0.0641500
$973$			24.0000i			0.769405i
$974$	−22.0000	−	22.0000i	−0.704925	−	0.704925i
$975$	−4.00000			−0.128103
$976$			48.0000i			1.53644i
$977$	58.0000			1.85558			0.927792	−	0.373097i	$-0.121704\pi$
$977$	58.0000			1.85558			0.927792	+	0.373097i	$0.121704\pi$
$978$	−4.00000	−	4.00000i	−0.127906	−	0.127906i
$979$			6.00000i			0.191761i
$980$	−6.00000			−0.191663
$981$		0			0
$982$	40.0000	−	40.0000i	1.27645	−	1.27645i
$983$	4.00000			0.127580			0.0637901	−	0.997963i	$-0.479681\pi$
$983$	4.00000			0.127580			0.0637901	+	0.997963i	$0.479681\pi$
$984$	4.00000	+	4.00000i	0.127515	+	0.127515i
$985$	18.0000			0.573528
$986$	−12.0000	+	12.0000i	−0.382158	+	0.382158i
$987$		0			0
$988$		−	32.0000i		−	1.01806i
$989$		0			0
$990$	−1.00000	−	1.00000i	−0.0317821	−	0.0317821i
$991$	−14.0000			−0.444725			−0.222362	−	0.974964i	$-0.571377\pi$
$991$	−14.0000			−0.444725			−0.222362	+	0.974964i	$0.571377\pi$
$992$	24.0000	+	24.0000i	0.762001	+	0.762001i
$993$	−12.0000			−0.380808
$994$	16.0000	+	16.0000i	0.507489	+	0.507489i
$995$		−	2.00000i		−	0.0634043i
$996$		0			0
$997$		−	40.0000i		−	1.26681i	−0.773819	−	0.633406i	$-0.781656\pi$
$997$		−	40.0000i		−	1.26681i	0.773819	−	0.633406i	$-0.218344\pi$
$998$	20.0000	−	20.0000i	0.633089	−	0.633089i
$999$	−4.00000			−0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1320.2.w.a.661.2	yes	2
4.3	odd	2		5280.2.w.b.2641.2		2
8.3	odd	2		5280.2.w.b.2641.1		2
8.5	even	2	inner	1320.2.w.a.661.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1320.2.w.a.661.1	✓	2	8.5	even	2	inner
1320.2.w.a.661.2	yes	2	1.1	even	1	trivial
5280.2.w.b.2641.1		2	8.3	odd	2
5280.2.w.b.2641.2		2	4.3	odd	2

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:	\( N \)	\(=\)	\( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1320.w (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} -1.00000i q^{3} +2.00000i q^{4} -1.00000i q^{5} +(1.00000 - 1.00000i) q^{6} -2.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} -1.00000 q^{9} +(1.00000 - 1.00000i) q^{10} +1.00000i q^{11} +2.00000 q^{12} +4.00000i q^{13} +(-2.00000 - 2.00000i) q^{14} -1.00000 q^{15} -4.00000 q^{16} +2.00000 q^{17} +(-1.00000 - 1.00000i) q^{18} +4.00000i q^{19} +2.00000 q^{20} +2.00000i q^{21} +(-1.00000 + 1.00000i) q^{22} +(2.00000 + 2.00000i) q^{24} -1.00000 q^{25} +(-4.00000 + 4.00000i) q^{26} +1.00000i q^{27} -4.00000i q^{28} +6.00000i q^{29} +(-1.00000 - 1.00000i) q^{30} -6.00000 q^{31} +(-4.00000 - 4.00000i) q^{32} +1.00000 q^{33} +(2.00000 + 2.00000i) q^{34} +2.00000i q^{35} -2.00000i q^{36} +4.00000i q^{37} +(-4.00000 + 4.00000i) q^{38} +4.00000 q^{39} +(2.00000 + 2.00000i) q^{40} +2.00000 q^{41} +(-2.00000 + 2.00000i) q^{42} +4.00000i q^{43} -2.00000 q^{44} +1.00000i q^{45} +4.00000i q^{48} -3.00000 q^{49} +(-1.00000 - 1.00000i) q^{50} -2.00000i q^{51} -8.00000 q^{52} +14.0000i q^{53} +(-1.00000 + 1.00000i) q^{54} +1.00000 q^{55} +(4.00000 - 4.00000i) q^{56} +4.00000 q^{57} +(-6.00000 + 6.00000i) q^{58} -2.00000i q^{60} -12.0000i q^{61} +(-6.00000 - 6.00000i) q^{62} +2.00000 q^{63} -8.00000i q^{64} +4.00000 q^{65} +(1.00000 + 1.00000i) q^{66} +4.00000i q^{67} +4.00000i q^{68} +(-2.00000 + 2.00000i) q^{70} -8.00000 q^{71} +(2.00000 - 2.00000i) q^{72} +10.0000 q^{73} +(-4.00000 + 4.00000i) q^{74} +1.00000i q^{75} -8.00000 q^{76} -2.00000i q^{77} +(4.00000 + 4.00000i) q^{78} +6.00000 q^{79} +4.00000i q^{80} +1.00000 q^{81} +(2.00000 + 2.00000i) q^{82} -4.00000 q^{84} -2.00000i q^{85} +(-4.00000 + 4.00000i) q^{86} +6.00000 q^{87} +(-2.00000 - 2.00000i) q^{88} +6.00000 q^{89} +(-1.00000 + 1.00000i) q^{90} -8.00000i q^{91} +6.00000i q^{93} +4.00000 q^{95} +(-4.00000 + 4.00000i) q^{96} +6.00000 q^{97} +(-3.00000 - 3.00000i) q^{98} -1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{6} - 4 q^{7} - 4 q^{8} - 2 q^{9} + 2 q^{10} + 4 q^{12} - 4 q^{14} - 2 q^{15} - 8 q^{16} + 4 q^{17} - 2 q^{18} + 4 q^{20} - 2 q^{22} + 4 q^{24} - 2 q^{25} - 8 q^{26} - 2 q^{30} - 12 q^{31}+ \cdots - 6 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^6 - 4 * q^7 - 4 * q^8 - 2 * q^9 + 2 * q^10 + 4 * q^12 - 4 * q^14 - 2 * q^15 - 8 * q^16 + 4 * q^17 - 2 * q^18 + 4 * q^20 - 2 * q^22 + 4 * q^24 - 2 * q^25 - 8 * q^26 - 2 * q^30 - 12 * q^31 - 8 * q^32 + 2 * q^33 + 4 * q^34 - 8 * q^38 + 8 * q^39 + 4 * q^40 + 4 * q^41 - 4 * q^42 - 4 * q^44 - 6 * q^49 - 2 * q^50 - 16 * q^52 - 2 * q^54 + 2 * q^55 + 8 * q^56 + 8 * q^57 - 12 * q^58 - 12 * q^62 + 4 * q^63 + 8 * q^65 + 2 * q^66 - 4 * q^70 - 16 * q^71 + 4 * q^72 + 20 * q^73 - 8 * q^74 - 16 * q^76 + 8 * q^78 + 12 * q^79 + 2 * q^81 + 4 * q^82 - 8 * q^84 - 8 * q^86 + 12 * q^87 - 4 * q^88 + 12 * q^89 - 2 * q^90 + 8 * q^95 - 8 * q^96 + 12 * q^97 - 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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