LMFDB - Embedded newform 280.2.b.b.141.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(141,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 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("280.141");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.b (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:	$2.23581125660$
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			141.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	280.141
Dual form			280.2.b.b.141.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{3} +2.00000i q^{4} +1.00000i q^{5} +(-2.00000 + 2.00000i) q^{6} +1.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{3} +2.00000i q^{4} +1.00000i q^{5} +(-2.00000 + 2.00000i) q^{6} +1.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} -1.00000 q^{9} +(-1.00000 + 1.00000i) q^{10} -4.00000i q^{11} -4.00000 q^{12} -6.00000i q^{13} +(1.00000 + 1.00000i) q^{14} -2.00000 q^{15} -4.00000 q^{16} +(-1.00000 - 1.00000i) q^{18} +8.00000i q^{19} -2.00000 q^{20} +2.00000i q^{21} +(4.00000 - 4.00000i) q^{22} +8.00000 q^{23} +(-4.00000 - 4.00000i) q^{24} -1.00000 q^{25} +(6.00000 - 6.00000i) q^{26} +4.00000i q^{27} +2.00000i q^{28} +(-2.00000 - 2.00000i) q^{30} -8.00000 q^{31} +(-4.00000 - 4.00000i) q^{32} +8.00000 q^{33} +1.00000i q^{35} -2.00000i q^{36} -10.0000i q^{37} +(-8.00000 + 8.00000i) q^{38} +12.0000 q^{39} +(-2.00000 - 2.00000i) q^{40} -2.00000 q^{41} +(-2.00000 + 2.00000i) q^{42} +4.00000i q^{43} +8.00000 q^{44} -1.00000i q^{45} +(8.00000 + 8.00000i) q^{46} +8.00000 q^{47} -8.00000i q^{48} +1.00000 q^{49} +(-1.00000 - 1.00000i) q^{50} +12.0000 q^{52} -2.00000i q^{53} +(-4.00000 + 4.00000i) q^{54} +4.00000 q^{55} +(-2.00000 + 2.00000i) q^{56} -16.0000 q^{57} +4.00000i q^{59} -4.00000i q^{60} +2.00000i q^{61} +(-8.00000 - 8.00000i) q^{62} -1.00000 q^{63} -8.00000i q^{64} +6.00000 q^{65} +(8.00000 + 8.00000i) q^{66} -12.0000i q^{67} +16.0000i q^{69} +(-1.00000 + 1.00000i) q^{70} +2.00000 q^{71} +(2.00000 - 2.00000i) q^{72} +4.00000 q^{73} +(10.0000 - 10.0000i) q^{74} -2.00000i q^{75} -16.0000 q^{76} -4.00000i q^{77} +(12.0000 + 12.0000i) q^{78} -2.00000 q^{79} -4.00000i q^{80} -11.0000 q^{81} +(-2.00000 - 2.00000i) q^{82} -6.00000i q^{83} -4.00000 q^{84} +(-4.00000 + 4.00000i) q^{86} +(8.00000 + 8.00000i) q^{88} +2.00000 q^{89} +(1.00000 - 1.00000i) q^{90} -6.00000i q^{91} +16.0000i q^{92} -16.0000i q^{93} +(8.00000 + 8.00000i) q^{94} -8.00000 q^{95} +(8.00000 - 8.00000i) q^{96} -16.0000 q^{97} +(1.00000 + 1.00000i) q^{98} +4.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 4 q^{6} + 2 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 4 * q^6 + 2 * q^7 - 4 * q^8 - 2 * q^9	$ 2 q + 2 q^{2} - 4 q^{6} + 2 q^{7} - 4 q^{8} - 2 q^{9} - 2 q^{10} - 8 q^{12} + 2 q^{14} - 4 q^{15} - 8 q^{16} - 2 q^{18} - 4 q^{20} + 8 q^{22} + 16 q^{23} - 8 q^{24} - 2 q^{25} + 12 q^{26} - 4 q^{30} - 16 q^{31} - 8 q^{32} + 16 q^{33} - 16 q^{38} + 24 q^{39} - 4 q^{40} - 4 q^{41} - 4 q^{42} + 16 q^{44} + 16 q^{46} + 16 q^{47} + 2 q^{49} - 2 q^{50} + 24 q^{52} - 8 q^{54} + 8 q^{55} - 4 q^{56} - 32 q^{57} - 16 q^{62} - 2 q^{63} + 12 q^{65} + 16 q^{66} - 2 q^{70} + 4 q^{71} + 4 q^{72} + 8 q^{73} + 20 q^{74} - 32 q^{76} + 24 q^{78} - 4 q^{79} - 22 q^{81} - 4 q^{82} - 8 q^{84} - 8 q^{86} + 16 q^{88} + 4 q^{89} + 2 q^{90} + 16 q^{94} - 16 q^{95} + 16 q^{96} - 32 q^{97} + 2 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 4 * q^6 + 2 * q^7 - 4 * q^8 - 2 * q^9 - 2 * q^10 - 8 * q^12 + 2 * q^14 - 4 * q^15 - 8 * q^16 - 2 * q^18 - 4 * q^20 + 8 * q^22 + 16 * q^23 - 8 * q^24 - 2 * q^25 + 12 * q^26 - 4 * q^30 - 16 * q^31 - 8 * q^32 + 16 * q^33 - 16 * q^38 + 24 * q^39 - 4 * q^40 - 4 * q^41 - 4 * q^42 + 16 * q^44 + 16 * q^46 + 16 * q^47 + 2 * q^49 - 2 * q^50 + 24 * q^52 - 8 * q^54 + 8 * q^55 - 4 * q^56 - 32 * q^57 - 16 * q^62 - 2 * q^63 + 12 * q^65 + 16 * q^66 - 2 * q^70 + 4 * q^71 + 4 * q^72 + 8 * q^73 + 20 * q^74 - 32 * q^76 + 24 * q^78 - 4 * q^79 - 22 * q^81 - 4 * q^82 - 8 * q^84 - 8 * q^86 + 16 * q^88 + 4 * q^89 + 2 * q^90 + 16 * q^94 - 16 * q^95 + 16 * q^96 - 32 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$1$	$-1$	$1$

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
$3$			2.00000i			1.15470i	0.816497	+	0.577350i	$0.195913\pi$
$3$			2.00000i			1.15470i	−0.816497	+	0.577350i	$0.804087\pi$
$4$			2.00000i			1.00000i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−2.00000	+	2.00000i	−0.816497	+	0.816497i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$	−1.00000			−0.333333
$10$	−1.00000	+	1.00000i	−0.316228	+	0.316228i
$11$		−	4.00000i		−	1.20605i	−0.797724	−	0.603023i	$-0.793963\pi$
$11$		−	4.00000i		−	1.20605i	0.797724	−	0.603023i	$-0.206037\pi$
$12$	−4.00000			−1.15470
$13$		−	6.00000i		−	1.66410i	−0.554700	−	0.832050i	$-0.687167\pi$
$13$		−	6.00000i		−	1.66410i	0.554700	−	0.832050i	$-0.312833\pi$
$14$	1.00000	+	1.00000i	0.267261	+	0.267261i
$15$	−2.00000			−0.516398
$16$	−4.00000			−1.00000
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$	−1.00000	−	1.00000i	−0.235702	−	0.235702i
$19$			8.00000i			1.83533i	0.397360	+	0.917663i	$0.369927\pi$
$19$			8.00000i			1.83533i	−0.397360	+	0.917663i	$0.630073\pi$
$20$	−2.00000			−0.447214
$21$			2.00000i			0.436436i
$22$	4.00000	−	4.00000i	0.852803	−	0.852803i
$23$	8.00000			1.66812			0.834058	−	0.551677i	$-0.186012\pi$
$23$	8.00000			1.66812			0.834058	+	0.551677i	$0.186012\pi$
$24$	−4.00000	−	4.00000i	−0.816497	−	0.816497i
$25$	−1.00000			−0.200000
$26$	6.00000	−	6.00000i	1.17670	−	1.17670i
$27$			4.00000i			0.769800i
$28$			2.00000i			0.377964i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$	−2.00000	−	2.00000i	−0.365148	−	0.365148i
$31$	−8.00000			−1.43684			−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000			−1.43684			−0.718421	+	0.695608i	$0.755135\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$	8.00000			1.39262
$34$		0			0
$35$			1.00000i			0.169031i
$36$		−	2.00000i		−	0.333333i
$37$		−	10.0000i		−	1.64399i	−0.569495	−	0.821995i	$-0.692861\pi$
$37$		−	10.0000i		−	1.64399i	0.569495	−	0.821995i	$-0.307139\pi$
$38$	−8.00000	+	8.00000i	−1.29777	+	1.29777i
$39$	12.0000			1.92154
$40$	−2.00000	−	2.00000i	−0.316228	−	0.316228i
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$	−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	$0.901344\pi$
$44$	8.00000			1.20605
$45$		−	1.00000i		−	0.149071i
$46$	8.00000	+	8.00000i	1.17954	+	1.17954i
$47$	8.00000			1.16692			0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000			1.16692			0.583460	+	0.812142i	$0.301699\pi$
$48$		−	8.00000i		−	1.15470i
$49$	1.00000			0.142857
$50$	−1.00000	−	1.00000i	−0.141421	−	0.141421i
$51$		0			0
$52$	12.0000			1.66410
$53$		−	2.00000i		−	0.274721i	−0.990521	−	0.137361i	$-0.956138\pi$
$53$		−	2.00000i		−	0.274721i	0.990521	−	0.137361i	$-0.0438619\pi$
$54$	−4.00000	+	4.00000i	−0.544331	+	0.544331i
$55$	4.00000			0.539360
$56$	−2.00000	+	2.00000i	−0.267261	+	0.267261i
$57$	−16.0000			−2.11925
$58$		0			0
$59$			4.00000i			0.520756i	0.965507	+	0.260378i	$0.0838471\pi$
$59$			4.00000i			0.520756i	−0.965507	+	0.260378i	$0.916153\pi$
$60$		−	4.00000i		−	0.516398i
$61$			2.00000i			0.256074i	0.991769	+	0.128037i	$0.0408676\pi$
$61$			2.00000i			0.256074i	−0.991769	+	0.128037i	$0.959132\pi$
$62$	−8.00000	−	8.00000i	−1.01600	−	1.01600i
$63$	−1.00000			−0.125988
$64$		−	8.00000i		−	1.00000i
$65$	6.00000			0.744208
$66$	8.00000	+	8.00000i	0.984732	+	0.984732i
$67$		−	12.0000i		−	1.46603i	−0.680211	−	0.733017i	$-0.738112\pi$
$67$		−	12.0000i		−	1.46603i	0.680211	−	0.733017i	$-0.261888\pi$
$68$		0			0
$69$			16.0000i			1.92617i
$70$	−1.00000	+	1.00000i	−0.119523	+	0.119523i
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$	2.00000	−	2.00000i	0.235702	−	0.235702i
$73$	4.00000			0.468165			0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000			0.468165			0.234082	+	0.972217i	$0.424791\pi$
$74$	10.0000	−	10.0000i	1.16248	−	1.16248i
$75$		−	2.00000i		−	0.230940i
$76$	−16.0000			−1.83533
$77$		−	4.00000i		−	0.455842i
$78$	12.0000	+	12.0000i	1.35873	+	1.35873i
$79$	−2.00000			−0.225018			−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000			−0.225018			−0.112509	+	0.993651i	$0.535889\pi$
$80$		−	4.00000i		−	0.447214i
$81$	−11.0000			−1.22222
$82$	−2.00000	−	2.00000i	−0.220863	−	0.220863i
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$	−4.00000			−0.436436
$85$		0			0
$86$	−4.00000	+	4.00000i	−0.431331	+	0.431331i
$87$		0			0
$88$	8.00000	+	8.00000i	0.852803	+	0.852803i
$89$	2.00000			0.212000			0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000			0.212000			0.106000	+	0.994366i	$0.466196\pi$
$90$	1.00000	−	1.00000i	0.105409	−	0.105409i
$91$		−	6.00000i		−	0.628971i
$92$			16.0000i			1.66812i
$93$		−	16.0000i		−	1.65912i
$94$	8.00000	+	8.00000i	0.825137	+	0.825137i
$95$	−8.00000			−0.820783
$96$	8.00000	−	8.00000i	0.816497	−	0.816497i
$97$	−16.0000			−1.62455			−0.812277	−	0.583272i	$-0.801772\pi$
$97$	−16.0000			−1.62455			−0.812277	+	0.583272i	$0.801772\pi$
$98$	1.00000	+	1.00000i	0.101015	+	0.101015i
$99$			4.00000i			0.402015i
$100$		−	2.00000i		−	0.200000i
$101$		−	2.00000i		−	0.199007i	−0.995037	−	0.0995037i	$-0.968274\pi$
$101$		−	2.00000i		−	0.199007i	0.995037	−	0.0995037i	$-0.0317255\pi$
$102$		0			0
$103$	−8.00000			−0.788263			−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000			−0.788263			−0.394132	+	0.919054i	$0.628955\pi$
$104$	12.0000	+	12.0000i	1.17670	+	1.17670i
$105$	−2.00000			−0.195180
$106$	2.00000	−	2.00000i	0.194257	−	0.194257i
$107$			8.00000i			0.773389i	0.922208	+	0.386695i	$0.126383\pi$
$107$			8.00000i			0.773389i	−0.922208	+	0.386695i	$0.873617\pi$
$108$	−8.00000			−0.769800
$109$		−	4.00000i		−	0.383131i	−0.981480	−	0.191565i	$-0.938644\pi$
$109$		−	4.00000i		−	0.383131i	0.981480	−	0.191565i	$-0.0613564\pi$
$110$	4.00000	+	4.00000i	0.381385	+	0.381385i
$111$	20.0000			1.89832
$112$	−4.00000			−0.377964
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$	−16.0000	−	16.0000i	−1.49854	−	1.49854i
$115$			8.00000i			0.746004i
$116$		0			0
$117$			6.00000i			0.554700i
$118$	−4.00000	+	4.00000i	−0.368230	+	0.368230i
$119$		0			0
$120$	4.00000	−	4.00000i	0.365148	−	0.365148i
$121$	−5.00000			−0.454545
$122$	−2.00000	+	2.00000i	−0.181071	+	0.181071i
$123$		−	4.00000i		−	0.360668i
$124$		−	16.0000i		−	1.43684i
$125$		−	1.00000i		−	0.0894427i
$126$	−1.00000	−	1.00000i	−0.0890871	−	0.0890871i
$127$	−12.0000			−1.06483			−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000			−1.06483			−0.532414	+	0.846484i	$0.678715\pi$
$128$	8.00000	−	8.00000i	0.707107	−	0.707107i
$129$	−8.00000			−0.704361
$130$	6.00000	+	6.00000i	0.526235	+	0.526235i
$131$		−	12.0000i		−	1.04844i	−0.851581	−	0.524222i	$-0.824356\pi$
$131$		−	12.0000i		−	1.04844i	0.851581	−	0.524222i	$-0.175644\pi$
$132$			16.0000i			1.39262i
$133$			8.00000i			0.693688i
$134$	12.0000	−	12.0000i	1.03664	−	1.03664i
$135$	−4.00000			−0.344265
$136$		0			0
$137$	22.0000			1.87959			0.939793	−	0.341743i	$-0.111017\pi$
$137$	22.0000			1.87959			0.939793	+	0.341743i	$0.111017\pi$
$138$	−16.0000	+	16.0000i	−1.36201	+	1.36201i
$139$			4.00000i			0.339276i	0.985506	+	0.169638i	$0.0542598\pi$
$139$			4.00000i			0.339276i	−0.985506	+	0.169638i	$0.945740\pi$
$140$	−2.00000			−0.169031
$141$			16.0000i			1.34744i
$142$	2.00000	+	2.00000i	0.167836	+	0.167836i
$143$	−24.0000			−2.00698
$144$	4.00000			0.333333
$145$		0			0
$146$	4.00000	+	4.00000i	0.331042	+	0.331042i
$147$			2.00000i			0.164957i
$148$	20.0000			1.64399
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$	2.00000	−	2.00000i	0.163299	−	0.163299i
$151$	−2.00000			−0.162758			−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000			−0.162758			−0.0813788	+	0.996683i	$0.525932\pi$
$152$	−16.0000	−	16.0000i	−1.29777	−	1.29777i
$153$		0			0
$154$	4.00000	−	4.00000i	0.322329	−	0.322329i
$155$		−	8.00000i		−	0.642575i
$156$			24.0000i			1.92154i
$157$		−	2.00000i		−	0.159617i	−0.996810	−	0.0798087i	$-0.974569\pi$
$157$		−	2.00000i		−	0.159617i	0.996810	−	0.0798087i	$-0.0254309\pi$
$158$	−2.00000	−	2.00000i	−0.159111	−	0.159111i
$159$	4.00000			0.317221
$160$	4.00000	−	4.00000i	0.316228	−	0.316228i
$161$	8.00000			0.630488
$162$	−11.0000	−	11.0000i	−0.864242	−	0.864242i
$163$			16.0000i			1.25322i	0.779334	+	0.626608i	$0.215557\pi$
$163$			16.0000i			1.25322i	−0.779334	+	0.626608i	$0.784443\pi$
$164$		−	4.00000i		−	0.312348i
$165$			8.00000i			0.622799i
$166$	6.00000	−	6.00000i	0.465690	−	0.465690i
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$	−4.00000	−	4.00000i	−0.308607	−	0.308607i
$169$	−23.0000			−1.76923
$170$		0			0
$171$		−	8.00000i		−	0.611775i
$172$	−8.00000			−0.609994
$173$		−	14.0000i		−	1.06440i	−0.846619	−	0.532200i	$-0.821365\pi$
$173$		−	14.0000i		−	1.06440i	0.846619	−	0.532200i	$-0.178635\pi$
$174$		0			0
$175$	−1.00000			−0.0755929
$176$			16.0000i			1.20605i
$177$	−8.00000			−0.601317
$178$	2.00000	+	2.00000i	0.149906	+	0.149906i
$179$			12.0000i			0.896922i	0.893802	+	0.448461i	$0.148028\pi$
$179$			12.0000i			0.896922i	−0.893802	+	0.448461i	$0.851972\pi$
$180$	2.00000			0.149071
$181$			2.00000i			0.148659i	0.997234	+	0.0743294i	$0.0236816\pi$
$181$			2.00000i			0.148659i	−0.997234	+	0.0743294i	$0.976318\pi$
$182$	6.00000	−	6.00000i	0.444750	−	0.444750i
$183$	−4.00000			−0.295689
$184$	−16.0000	+	16.0000i	−1.17954	+	1.17954i
$185$	10.0000			0.735215
$186$	16.0000	−	16.0000i	1.17318	−	1.17318i
$187$		0			0
$188$			16.0000i			1.16692i
$189$			4.00000i			0.290957i
$190$	−8.00000	−	8.00000i	−0.580381	−	0.580381i
$191$	−2.00000			−0.144715			−0.0723575	−	0.997379i	$-0.523052\pi$
$191$	−2.00000			−0.144715			−0.0723575	+	0.997379i	$0.523052\pi$
$192$	16.0000			1.15470
$193$	−2.00000			−0.143963			−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000			−0.143963			−0.0719816	+	0.997406i	$0.522932\pi$
$194$	−16.0000	−	16.0000i	−1.14873	−	1.14873i
$195$			12.0000i			0.859338i
$196$			2.00000i			0.142857i
$197$			10.0000i			0.712470i	0.934396	+	0.356235i	$0.115940\pi$
$197$			10.0000i			0.712470i	−0.934396	+	0.356235i	$0.884060\pi$
$198$	−4.00000	+	4.00000i	−0.284268	+	0.284268i
$199$	−24.0000			−1.70131			−0.850657	−	0.525720i	$-0.823796\pi$
$199$	−24.0000			−1.70131			−0.850657	+	0.525720i	$0.823796\pi$
$200$	2.00000	−	2.00000i	0.141421	−	0.141421i
$201$	24.0000			1.69283
$202$	2.00000	−	2.00000i	0.140720	−	0.140720i
$203$		0			0
$204$		0			0
$205$		−	2.00000i		−	0.139686i
$206$	−8.00000	−	8.00000i	−0.557386	−	0.557386i
$207$	−8.00000			−0.556038
$208$			24.0000i			1.66410i
$209$	32.0000			2.21349
$210$	−2.00000	−	2.00000i	−0.138013	−	0.138013i
$211$		−	12.0000i		−	0.826114i	−0.910705	−	0.413057i	$-0.864461\pi$
$211$		−	12.0000i		−	0.826114i	0.910705	−	0.413057i	$-0.135539\pi$
$212$	4.00000			0.274721
$213$			4.00000i			0.274075i
$214$	−8.00000	+	8.00000i	−0.546869	+	0.546869i
$215$	−4.00000			−0.272798
$216$	−8.00000	−	8.00000i	−0.544331	−	0.544331i
$217$	−8.00000			−0.543075
$218$	4.00000	−	4.00000i	0.270914	−	0.270914i
$219$			8.00000i			0.540590i
$220$			8.00000i			0.539360i
$221$		0			0
$222$	20.0000	+	20.0000i	1.34231	+	1.34231i
$223$	−8.00000			−0.535720			−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000			−0.535720			−0.267860	+	0.963458i	$0.586316\pi$
$224$	−4.00000	−	4.00000i	−0.267261	−	0.267261i
$225$	1.00000			0.0666667
$226$	−6.00000	−	6.00000i	−0.399114	−	0.399114i
$227$		−	18.0000i		−	1.19470i	−0.801980	−	0.597351i	$-0.796220\pi$
$227$		−	18.0000i		−	1.19470i	0.801980	−	0.597351i	$-0.203780\pi$
$228$		−	32.0000i		−	2.11925i
$229$			10.0000i			0.660819i	0.943838	+	0.330409i	$0.107187\pi$
$229$			10.0000i			0.660819i	−0.943838	+	0.330409i	$0.892813\pi$
$230$	−8.00000	+	8.00000i	−0.527504	+	0.527504i
$231$	8.00000			0.526361
$232$		0			0
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$	−6.00000	+	6.00000i	−0.392232	+	0.392232i
$235$			8.00000i			0.521862i
$236$	−8.00000			−0.520756
$237$		−	4.00000i		−	0.259828i
$238$		0			0
$239$	−2.00000			−0.129369			−0.0646846	−	0.997906i	$-0.520604\pi$
$239$	−2.00000			−0.129369			−0.0646846	+	0.997906i	$0.520604\pi$
$240$	8.00000			0.516398
$241$	18.0000			1.15948			0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000			1.15948			0.579741	+	0.814801i	$0.303154\pi$
$242$	−5.00000	−	5.00000i	−0.321412	−	0.321412i
$243$		−	10.0000i		−	0.641500i
$244$	−4.00000			−0.256074
$245$			1.00000i			0.0638877i
$246$	4.00000	−	4.00000i	0.255031	−	0.255031i
$247$	48.0000			3.05417
$248$	16.0000	−	16.0000i	1.01600	−	1.01600i
$249$	12.0000			0.760469
$250$	1.00000	−	1.00000i	0.0632456	−	0.0632456i
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$		−	2.00000i		−	0.125988i
$253$		−	32.0000i		−	2.01182i
$254$	−12.0000	−	12.0000i	−0.752947	−	0.752947i
$255$		0			0
$256$	16.0000			1.00000
$257$	16.0000			0.998053			0.499026	−	0.866587i	$-0.333691\pi$
$257$	16.0000			0.998053			0.499026	+	0.866587i	$0.333691\pi$
$258$	−8.00000	−	8.00000i	−0.498058	−	0.498058i
$259$		−	10.0000i		−	0.621370i
$260$			12.0000i			0.744208i
$261$		0			0
$262$	12.0000	−	12.0000i	0.741362	−	0.741362i
$263$	−12.0000			−0.739952			−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000			−0.739952			−0.369976	+	0.929041i	$0.620634\pi$
$264$	−16.0000	+	16.0000i	−0.984732	+	0.984732i
$265$	2.00000			0.122859
$266$	−8.00000	+	8.00000i	−0.490511	+	0.490511i
$267$			4.00000i			0.244796i
$268$	24.0000			1.46603
$269$			14.0000i			0.853595i	0.904347	+	0.426798i	$0.140358\pi$
$269$			14.0000i			0.853595i	−0.904347	+	0.426798i	$0.859642\pi$
$270$	−4.00000	−	4.00000i	−0.243432	−	0.243432i
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$		0			0
$273$	12.0000			0.726273
$274$	22.0000	+	22.0000i	1.32907	+	1.32907i
$275$			4.00000i			0.241209i
$276$	−32.0000			−1.92617
$277$			22.0000i			1.32185i	0.750451	+	0.660926i	$0.229836\pi$
$277$			22.0000i			1.32185i	−0.750451	+	0.660926i	$0.770164\pi$
$278$	−4.00000	+	4.00000i	−0.239904	+	0.239904i
$279$	8.00000			0.478947
$280$	−2.00000	−	2.00000i	−0.119523	−	0.119523i
$281$	−22.0000			−1.31241			−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000			−1.31241			−0.656205	+	0.754583i	$0.727839\pi$
$282$	−16.0000	+	16.0000i	−0.952786	+	0.952786i
$283$		−	2.00000i		−	0.118888i	−0.998232	−	0.0594438i	$-0.981067\pi$
$283$		−	2.00000i		−	0.118888i	0.998232	−	0.0594438i	$-0.0189327\pi$
$284$			4.00000i			0.237356i
$285$		−	16.0000i		−	0.947758i
$286$	−24.0000	−	24.0000i	−1.41915	−	1.41915i
$287$	−2.00000			−0.118056
$288$	4.00000	+	4.00000i	0.235702	+	0.235702i
$289$	−17.0000			−1.00000
$290$		0			0
$291$		−	32.0000i		−	1.87587i
$292$			8.00000i			0.468165i
$293$		−	22.0000i		−	1.28525i	−0.766179	−	0.642627i	$-0.777845\pi$
$293$		−	22.0000i		−	1.28525i	0.766179	−	0.642627i	$-0.222155\pi$
$294$	−2.00000	+	2.00000i	−0.116642	+	0.116642i
$295$	−4.00000			−0.232889
$296$	20.0000	+	20.0000i	1.16248	+	1.16248i
$297$	16.0000			0.928414
$298$		0			0
$299$		−	48.0000i		−	2.77591i
$300$	4.00000			0.230940
$301$			4.00000i			0.230556i
$302$	−2.00000	−	2.00000i	−0.115087	−	0.115087i
$303$	4.00000			0.229794
$304$		−	32.0000i		−	1.83533i
$305$	−2.00000			−0.114520
$306$		0			0
$307$			2.00000i			0.114146i	0.998370	+	0.0570730i	$0.0181768\pi$
$307$			2.00000i			0.114146i	−0.998370	+	0.0570730i	$0.981823\pi$
$308$	8.00000			0.455842
$309$		−	16.0000i		−	0.910208i
$310$	8.00000	−	8.00000i	0.454369	−	0.454369i
$311$	20.0000			1.13410			0.567048	−	0.823685i	$-0.308085\pi$
$311$	20.0000			1.13410			0.567048	+	0.823685i	$0.308085\pi$
$312$	−24.0000	+	24.0000i	−1.35873	+	1.35873i
$313$	12.0000			0.678280			0.339140	−	0.940736i	$-0.389864\pi$
$313$	12.0000			0.678280			0.339140	+	0.940736i	$0.389864\pi$
$314$	2.00000	−	2.00000i	0.112867	−	0.112867i
$315$		−	1.00000i		−	0.0563436i
$316$		−	4.00000i		−	0.225018i
$317$			18.0000i			1.01098i	0.862832	+	0.505490i	$0.168688\pi$
$317$			18.0000i			1.01098i	−0.862832	+	0.505490i	$0.831312\pi$
$318$	4.00000	+	4.00000i	0.224309	+	0.224309i
$319$		0			0
$320$	8.00000			0.447214
$321$	−16.0000			−0.893033
$322$	8.00000	+	8.00000i	0.445823	+	0.445823i
$323$		0			0
$324$		−	22.0000i		−	1.22222i
$325$			6.00000i			0.332820i
$326$	−16.0000	+	16.0000i	−0.886158	+	0.886158i
$327$	8.00000			0.442401
$328$	4.00000	−	4.00000i	0.220863	−	0.220863i
$329$	8.00000			0.441054
$330$	−8.00000	+	8.00000i	−0.440386	+	0.440386i
$331$			20.0000i			1.09930i	0.835395	+	0.549650i	$0.185239\pi$
$331$			20.0000i			1.09930i	−0.835395	+	0.549650i	$0.814761\pi$
$332$	12.0000			0.658586
$333$			10.0000i			0.547997i
$334$		0			0
$335$	12.0000			0.655630
$336$		−	8.00000i		−	0.436436i
$337$	30.0000			1.63420			0.817102	−	0.576493i	$-0.195579\pi$
$337$	30.0000			1.63420			0.817102	+	0.576493i	$0.195579\pi$
$338$	−23.0000	−	23.0000i	−1.25104	−	1.25104i
$339$		−	12.0000i		−	0.651751i
$340$		0			0
$341$			32.0000i			1.73290i
$342$	8.00000	−	8.00000i	0.432590	−	0.432590i
$343$	1.00000			0.0539949
$344$	−8.00000	−	8.00000i	−0.431331	−	0.431331i
$345$	−16.0000			−0.861411
$346$	14.0000	−	14.0000i	0.752645	−	0.752645i
$347$		−	16.0000i		−	0.858925i	−0.903085	−	0.429463i	$-0.858703\pi$
$347$		−	16.0000i		−	0.858925i	0.903085	−	0.429463i	$-0.141297\pi$
$348$		0			0
$349$		−	2.00000i		−	0.107058i	−0.998566	−	0.0535288i	$-0.982953\pi$
$349$		−	2.00000i		−	0.107058i	0.998566	−	0.0535288i	$-0.0170469\pi$
$350$	−1.00000	−	1.00000i	−0.0534522	−	0.0534522i
$351$	24.0000			1.28103
$352$	−16.0000	+	16.0000i	−0.852803	+	0.852803i
$353$	−24.0000			−1.27739			−0.638696	−	0.769460i	$-0.720526\pi$
$353$	−24.0000			−1.27739			−0.638696	+	0.769460i	$0.720526\pi$
$354$	−8.00000	−	8.00000i	−0.425195	−	0.425195i
$355$			2.00000i			0.106149i
$356$			4.00000i			0.212000i
$357$		0			0
$358$	−12.0000	+	12.0000i	−0.634220	+	0.634220i
$359$	6.00000			0.316668			0.158334	−	0.987386i	$-0.449388\pi$
$359$	6.00000			0.316668			0.158334	+	0.987386i	$0.449388\pi$
$360$	2.00000	+	2.00000i	0.105409	+	0.105409i
$361$	−45.0000			−2.36842
$362$	−2.00000	+	2.00000i	−0.105118	+	0.105118i
$363$		−	10.0000i		−	0.524864i
$364$	12.0000			0.628971
$365$			4.00000i			0.209370i
$366$	−4.00000	−	4.00000i	−0.209083	−	0.209083i
$367$		0			0			−	1.00000i	$-0.5\pi$
$367$		0			0				1.00000i	$0.5\pi$
$368$	−32.0000			−1.66812
$369$	2.00000			0.104116
$370$	10.0000	+	10.0000i	0.519875	+	0.519875i
$371$		−	2.00000i		−	0.103835i
$372$	32.0000			1.65912
$373$			34.0000i			1.76045i	0.474554	+	0.880227i	$0.342610\pi$
$373$			34.0000i			1.76045i	−0.474554	+	0.880227i	$0.657390\pi$
$374$		0			0
$375$	2.00000			0.103280
$376$	−16.0000	+	16.0000i	−0.825137	+	0.825137i
$377$		0			0
$378$	−4.00000	+	4.00000i	−0.205738	+	0.205738i
$379$			12.0000i			0.616399i	0.951322	+	0.308199i	$0.0997264\pi$
$379$			12.0000i			0.616399i	−0.951322	+	0.308199i	$0.900274\pi$
$380$		−	16.0000i		−	0.820783i
$381$		−	24.0000i		−	1.22956i
$382$	−2.00000	−	2.00000i	−0.102329	−	0.102329i
$383$		0			0			−	1.00000i	$-0.5\pi$
$383$		0			0				1.00000i	$0.5\pi$
$384$	16.0000	+	16.0000i	0.816497	+	0.816497i
$385$	4.00000			0.203859
$386$	−2.00000	−	2.00000i	−0.101797	−	0.101797i
$387$		−	4.00000i		−	0.203331i
$388$		−	32.0000i		−	1.62455i
$389$			20.0000i			1.01404i	0.861934	+	0.507020i	$0.169253\pi$
$389$			20.0000i			1.01404i	−0.861934	+	0.507020i	$0.830747\pi$
$390$	−12.0000	+	12.0000i	−0.607644	+	0.607644i
$391$		0			0
$392$	−2.00000	+	2.00000i	−0.101015	+	0.101015i
$393$	24.0000			1.21064
$394$	−10.0000	+	10.0000i	−0.503793	+	0.503793i
$395$		−	2.00000i		−	0.100631i
$396$	−8.00000			−0.402015
$397$		−	2.00000i		−	0.100377i	−0.998740	−	0.0501886i	$-0.984018\pi$
$397$		−	2.00000i		−	0.100377i	0.998740	−	0.0501886i	$-0.0159822\pi$
$398$	−24.0000	−	24.0000i	−1.20301	−	1.20301i
$399$	−16.0000			−0.801002
$400$	4.00000			0.200000
$401$	−18.0000			−0.898877			−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000			−0.898877			−0.449439	+	0.893311i	$0.648376\pi$
$402$	24.0000	+	24.0000i	1.19701	+	1.19701i
$403$			48.0000i			2.39105i
$404$	4.00000			0.199007
$405$		−	11.0000i		−	0.546594i
$406$		0			0
$407$	−40.0000			−1.98273
$408$		0			0
$409$	−6.00000			−0.296681			−0.148340	−	0.988936i	$-0.547393\pi$
$409$	−6.00000			−0.296681			−0.148340	+	0.988936i	$0.547393\pi$
$410$	2.00000	−	2.00000i	0.0987730	−	0.0987730i
$411$			44.0000i			2.17036i
$412$		−	16.0000i		−	0.788263i
$413$			4.00000i			0.196827i
$414$	−8.00000	−	8.00000i	−0.393179	−	0.393179i
$415$	6.00000			0.294528
$416$	−24.0000	+	24.0000i	−1.17670	+	1.17670i
$417$	−8.00000			−0.391762
$418$	32.0000	+	32.0000i	1.56517	+	1.56517i
$419$			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
$421$			4.00000i			0.194948i	0.995238	+	0.0974740i	$0.0310763\pi$
$421$			4.00000i			0.194948i	−0.995238	+	0.0974740i	$0.968924\pi$
$422$	12.0000	−	12.0000i	0.584151	−	0.584151i
$423$	−8.00000			−0.388973
$424$	4.00000	+	4.00000i	0.194257	+	0.194257i
$425$		0			0
$426$	−4.00000	+	4.00000i	−0.193801	+	0.193801i
$427$			2.00000i			0.0967868i
$428$	−16.0000			−0.773389
$429$		−	48.0000i		−	2.31746i
$430$	−4.00000	−	4.00000i	−0.192897	−	0.192897i
$431$	−18.0000			−0.867029			−0.433515	−	0.901146i	$-0.642727\pi$
$431$	−18.0000			−0.867029			−0.433515	+	0.901146i	$0.642727\pi$
$432$		−	16.0000i		−	0.769800i
$433$	20.0000			0.961139			0.480569	−	0.876957i	$-0.340430\pi$
$433$	20.0000			0.961139			0.480569	+	0.876957i	$0.340430\pi$
$434$	−8.00000	−	8.00000i	−0.384012	−	0.384012i
$435$		0			0
$436$	8.00000			0.383131
$437$			64.0000i			3.06154i
$438$	−8.00000	+	8.00000i	−0.382255	+	0.382255i
$439$	−28.0000			−1.33637			−0.668184	−	0.743996i	$-0.732928\pi$
$439$	−28.0000			−1.33637			−0.668184	+	0.743996i	$0.732928\pi$
$440$	−8.00000	+	8.00000i	−0.381385	+	0.381385i
$441$	−1.00000			−0.0476190
$442$		0			0
$443$			20.0000i			0.950229i	0.879924	+	0.475114i	$0.157593\pi$
$443$			20.0000i			0.950229i	−0.879924	+	0.475114i	$0.842407\pi$
$444$			40.0000i			1.89832i
$445$			2.00000i			0.0948091i
$446$	−8.00000	−	8.00000i	−0.378811	−	0.378811i
$447$		0			0
$448$		−	8.00000i		−	0.377964i
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$	1.00000	+	1.00000i	0.0471405	+	0.0471405i
$451$			8.00000i			0.376705i
$452$		−	12.0000i		−	0.564433i
$453$		−	4.00000i		−	0.187936i
$454$	18.0000	−	18.0000i	0.844782	−	0.844782i
$455$	6.00000			0.281284
$456$	32.0000	−	32.0000i	1.49854	−	1.49854i
$457$	−6.00000			−0.280668			−0.140334	−	0.990104i	$-0.544818\pi$
$457$	−6.00000			−0.280668			−0.140334	+	0.990104i	$0.544818\pi$
$458$	−10.0000	+	10.0000i	−0.467269	+	0.467269i
$459$		0			0
$460$	−16.0000			−0.746004
$461$		−	26.0000i		−	1.21094i	−0.795868	−	0.605470i	$-0.792985\pi$
$461$		−	26.0000i		−	1.21094i	0.795868	−	0.605470i	$-0.207015\pi$
$462$	8.00000	+	8.00000i	0.372194	+	0.372194i
$463$	20.0000			0.929479			0.464739	−	0.885448i	$-0.346148\pi$
$463$	20.0000			0.929479			0.464739	+	0.885448i	$0.346148\pi$
$464$		0			0
$465$	16.0000			0.741982
$466$	18.0000	+	18.0000i	0.833834	+	0.833834i
$467$			26.0000i			1.20314i	0.798821	+	0.601568i	$0.205457\pi$
$467$			26.0000i			1.20314i	−0.798821	+	0.601568i	$0.794543\pi$
$468$	−12.0000			−0.554700
$469$		−	12.0000i		−	0.554109i
$470$	−8.00000	+	8.00000i	−0.369012	+	0.369012i
$471$	4.00000			0.184310
$472$	−8.00000	−	8.00000i	−0.368230	−	0.368230i
$473$	16.0000			0.735681
$474$	4.00000	−	4.00000i	0.183726	−	0.183726i
$475$		−	8.00000i		−	0.367065i
$476$		0			0
$477$			2.00000i			0.0915737i
$478$	−2.00000	−	2.00000i	−0.0914779	−	0.0914779i
$479$	28.0000			1.27935			0.639676	−	0.768644i	$-0.279068\pi$
$479$	28.0000			1.27935			0.639676	+	0.768644i	$0.279068\pi$
$480$	8.00000	+	8.00000i	0.365148	+	0.365148i
$481$	−60.0000			−2.73576
$482$	18.0000	+	18.0000i	0.819878	+	0.819878i
$483$			16.0000i			0.728025i
$484$		−	10.0000i		−	0.454545i
$485$		−	16.0000i		−	0.726523i
$486$	10.0000	−	10.0000i	0.453609	−	0.453609i
$487$	−12.0000			−0.543772			−0.271886	−	0.962329i	$-0.587647\pi$
$487$	−12.0000			−0.543772			−0.271886	+	0.962329i	$0.587647\pi$
$488$	−4.00000	−	4.00000i	−0.181071	−	0.181071i
$489$	−32.0000			−1.44709
$490$	−1.00000	+	1.00000i	−0.0451754	+	0.0451754i
$491$			28.0000i			1.26362i	0.775122	+	0.631811i	$0.217688\pi$
$491$			28.0000i			1.26362i	−0.775122	+	0.631811i	$0.782312\pi$
$492$	8.00000			0.360668
$493$		0			0
$494$	48.0000	+	48.0000i	2.15962	+	2.15962i
$495$	−4.00000			−0.179787
$496$	32.0000			1.43684
$497$	2.00000			0.0897123
$498$	12.0000	+	12.0000i	0.537733	+	0.537733i
$499$		−	28.0000i		−	1.25345i	−0.779240	−	0.626726i	$-0.784395\pi$
$499$		−	28.0000i		−	1.25345i	0.779240	−	0.626726i	$-0.215605\pi$
$500$	2.00000			0.0894427
$501$		0			0
$502$		0			0
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$	2.00000	−	2.00000i	0.0890871	−	0.0890871i
$505$	2.00000			0.0889988
$506$	32.0000	−	32.0000i	1.42257	−	1.42257i
$507$		−	46.0000i		−	2.04293i
$508$		−	24.0000i		−	1.06483i
$509$			30.0000i			1.32973i	0.746965	+	0.664863i	$0.231510\pi$
$509$			30.0000i			1.32973i	−0.746965	+	0.664863i	$0.768490\pi$
$510$		0			0
$511$	4.00000			0.176950
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$	−32.0000			−1.41283
$514$	16.0000	+	16.0000i	0.705730	+	0.705730i
$515$		−	8.00000i		−	0.352522i
$516$		−	16.0000i		−	0.704361i
$517$		−	32.0000i		−	1.40736i
$518$	10.0000	−	10.0000i	0.439375	−	0.439375i
$519$	28.0000			1.22906
$520$	−12.0000	+	12.0000i	−0.526235	+	0.526235i
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$		0			0
$523$		−	34.0000i		−	1.48672i	−0.668894	−	0.743358i	$-0.733232\pi$
$523$		−	34.0000i		−	1.48672i	0.668894	−	0.743358i	$-0.266768\pi$
$524$	24.0000			1.04844
$525$		−	2.00000i		−	0.0872872i
$526$	−12.0000	−	12.0000i	−0.523225	−	0.523225i
$527$		0			0
$528$	−32.0000			−1.39262
$529$	41.0000			1.78261
$530$	2.00000	+	2.00000i	0.0868744	+	0.0868744i
$531$		−	4.00000i		−	0.173585i
$532$	−16.0000			−0.693688
$533$			12.0000i			0.519778i
$534$	−4.00000	+	4.00000i	−0.173097	+	0.173097i
$535$	−8.00000			−0.345870
$536$	24.0000	+	24.0000i	1.03664	+	1.03664i
$537$	−24.0000			−1.03568
$538$	−14.0000	+	14.0000i	−0.603583	+	0.603583i
$539$		−	4.00000i		−	0.172292i
$540$		−	8.00000i		−	0.344265i
$541$		−	40.0000i		−	1.71973i	−0.510518	−	0.859867i	$-0.670546\pi$
$541$		−	40.0000i		−	1.71973i	0.510518	−	0.859867i	$-0.329454\pi$
$542$	−8.00000	−	8.00000i	−0.343629	−	0.343629i
$543$	−4.00000			−0.171656
$544$		0			0
$545$	4.00000			0.171341
$546$	12.0000	+	12.0000i	0.513553	+	0.513553i
$547$		−	32.0000i		−	1.36822i	−0.729378	−	0.684111i	$-0.760191\pi$
$547$		−	32.0000i		−	1.36822i	0.729378	−	0.684111i	$-0.239809\pi$
$548$			44.0000i			1.87959i
$549$		−	2.00000i		−	0.0853579i
$550$	−4.00000	+	4.00000i	−0.170561	+	0.170561i
$551$		0			0
$552$	−32.0000	−	32.0000i	−1.36201	−	1.36201i
$553$	−2.00000			−0.0850487
$554$	−22.0000	+	22.0000i	−0.934690	+	0.934690i
$555$			20.0000i			0.848953i
$556$	−8.00000			−0.339276
$557$		−	42.0000i		−	1.77960i	−0.456354	−	0.889799i	$-0.650845\pi$
$557$		−	42.0000i		−	1.77960i	0.456354	−	0.889799i	$-0.349155\pi$
$558$	8.00000	+	8.00000i	0.338667	+	0.338667i
$559$	24.0000			1.01509
$560$		−	4.00000i		−	0.169031i
$561$		0			0
$562$	−22.0000	−	22.0000i	−0.928014	−	0.928014i
$563$			30.0000i			1.26435i	0.774826	+	0.632175i	$0.217837\pi$
$563$			30.0000i			1.26435i	−0.774826	+	0.632175i	$0.782163\pi$
$564$	−32.0000			−1.34744
$565$		−	6.00000i		−	0.252422i
$566$	2.00000	−	2.00000i	0.0840663	−	0.0840663i
$567$	−11.0000			−0.461957
$568$	−4.00000	+	4.00000i	−0.167836	+	0.167836i
$569$	−22.0000			−0.922288			−0.461144	−	0.887325i	$-0.652561\pi$
$569$	−22.0000			−0.922288			−0.461144	+	0.887325i	$0.652561\pi$
$570$	16.0000	−	16.0000i	0.670166	−	0.670166i
$571$			20.0000i			0.836974i	0.908223	+	0.418487i	$0.137439\pi$
$571$			20.0000i			0.836974i	−0.908223	+	0.418487i	$0.862561\pi$
$572$		−	48.0000i		−	2.00698i
$573$		−	4.00000i		−	0.167102i
$574$	−2.00000	−	2.00000i	−0.0834784	−	0.0834784i
$575$	−8.00000			−0.333623
$576$			8.00000i			0.333333i
$577$	−44.0000			−1.83174			−0.915872	−	0.401470i	$-0.868499\pi$
$577$	−44.0000			−1.83174			−0.915872	+	0.401470i	$0.868499\pi$
$578$	−17.0000	−	17.0000i	−0.707107	−	0.707107i
$579$		−	4.00000i		−	0.166234i
$580$		0			0
$581$		−	6.00000i		−	0.248922i
$582$	32.0000	−	32.0000i	1.32644	−	1.32644i
$583$	−8.00000			−0.331326
$584$	−8.00000	+	8.00000i	−0.331042	+	0.331042i
$585$	−6.00000			−0.248069
$586$	22.0000	−	22.0000i	0.908812	−	0.908812i
$587$			42.0000i			1.73353i	0.498721	+	0.866763i	$0.333803\pi$
$587$			42.0000i			1.73353i	−0.498721	+	0.866763i	$0.666197\pi$
$588$	−4.00000			−0.164957
$589$		−	64.0000i		−	2.63707i
$590$	−4.00000	−	4.00000i	−0.164677	−	0.164677i
$591$	−20.0000			−0.822690
$592$			40.0000i			1.64399i
$593$	4.00000			0.164260			0.0821302	−	0.996622i	$-0.473828\pi$
$593$	4.00000			0.164260			0.0821302	+	0.996622i	$0.473828\pi$
$594$	16.0000	+	16.0000i	0.656488	+	0.656488i
$595$		0			0
$596$		0			0
$597$		−	48.0000i		−	1.96451i
$598$	48.0000	−	48.0000i	1.96287	−	1.96287i
$599$	−30.0000			−1.22577			−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000			−1.22577			−0.612883	+	0.790173i	$0.709990\pi$
$600$	4.00000	+	4.00000i	0.163299	+	0.163299i
$601$	10.0000			0.407909			0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000			0.407909			0.203954	+	0.978980i	$0.434621\pi$
$602$	−4.00000	+	4.00000i	−0.163028	+	0.163028i
$603$			12.0000i			0.488678i
$604$		−	4.00000i		−	0.162758i
$605$		−	5.00000i		−	0.203279i
$606$	4.00000	+	4.00000i	0.162489	+	0.162489i
$607$	32.0000			1.29884			0.649420	−	0.760430i	$-0.275012\pi$
$607$	32.0000			1.29884			0.649420	+	0.760430i	$0.275012\pi$
$608$	32.0000	−	32.0000i	1.29777	−	1.29777i
$609$		0			0
$610$	−2.00000	−	2.00000i	−0.0809776	−	0.0809776i
$611$		−	48.0000i		−	1.94187i
$612$		0			0
$613$		−	10.0000i		−	0.403896i	−0.979396	−	0.201948i	$-0.935273\pi$
$613$		−	10.0000i		−	0.403896i	0.979396	−	0.201948i	$-0.0647272\pi$
$614$	−2.00000	+	2.00000i	−0.0807134	+	0.0807134i
$615$	4.00000			0.161296
$616$	8.00000	+	8.00000i	0.322329	+	0.322329i
$617$	18.0000			0.724653			0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000			0.724653			0.362326	+	0.932051i	$0.381983\pi$
$618$	16.0000	−	16.0000i	0.643614	−	0.643614i
$619$		−	8.00000i		−	0.321547i	−0.986991	−	0.160774i	$-0.948601\pi$
$619$		−	8.00000i		−	0.321547i	0.986991	−	0.160774i	$-0.0513989\pi$
$620$	16.0000			0.642575
$621$			32.0000i			1.28412i
$622$	20.0000	+	20.0000i	0.801927	+	0.801927i
$623$	2.00000			0.0801283
$624$	−48.0000			−1.92154
$625$	1.00000			0.0400000
$626$	12.0000	+	12.0000i	0.479616	+	0.479616i
$627$			64.0000i			2.55591i
$628$	4.00000			0.159617
$629$		0			0
$630$	1.00000	−	1.00000i	0.0398410	−	0.0398410i
$631$	18.0000			0.716569			0.358284	−	0.933613i	$-0.383362\pi$
$631$	18.0000			0.716569			0.358284	+	0.933613i	$0.383362\pi$
$632$	4.00000	−	4.00000i	0.159111	−	0.159111i
$633$	24.0000			0.953914
$634$	−18.0000	+	18.0000i	−0.714871	+	0.714871i
$635$		−	12.0000i		−	0.476205i
$636$			8.00000i			0.317221i
$637$		−	6.00000i		−	0.237729i
$638$		0			0
$639$	−2.00000			−0.0791188
$640$	8.00000	+	8.00000i	0.316228	+	0.316228i
$641$	38.0000			1.50091			0.750455	−	0.660922i	$-0.229834\pi$
$641$	38.0000			1.50091			0.750455	+	0.660922i	$0.229834\pi$
$642$	−16.0000	−	16.0000i	−0.631470	−	0.631470i
$643$			6.00000i			0.236617i	0.992977	+	0.118308i	$0.0377472\pi$
$643$			6.00000i			0.236617i	−0.992977	+	0.118308i	$0.962253\pi$
$644$			16.0000i			0.630488i
$645$		−	8.00000i		−	0.315000i
$646$		0			0
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$	22.0000	−	22.0000i	0.864242	−	0.864242i
$649$	16.0000			0.628055
$650$	−6.00000	+	6.00000i	−0.235339	+	0.235339i
$651$		−	16.0000i		−	0.627089i
$652$	−32.0000			−1.25322
$653$			30.0000i			1.17399i	0.809590	+	0.586995i	$0.199689\pi$
$653$			30.0000i			1.17399i	−0.809590	+	0.586995i	$0.800311\pi$
$654$	8.00000	+	8.00000i	0.312825	+	0.312825i
$655$	12.0000			0.468879
$656$	8.00000			0.312348
$657$	−4.00000			−0.156055
$658$	8.00000	+	8.00000i	0.311872	+	0.311872i
$659$			12.0000i			0.467454i	0.972302	+	0.233727i	$0.0750921\pi$
$659$			12.0000i			0.467454i	−0.972302	+	0.233727i	$0.924908\pi$
$660$	−16.0000			−0.622799
$661$		−	2.00000i		−	0.0777910i	−0.999243	−	0.0388955i	$-0.987616\pi$
$661$		−	2.00000i		−	0.0777910i	0.999243	−	0.0388955i	$-0.0123839\pi$
$662$	−20.0000	+	20.0000i	−0.777322	+	0.777322i
$663$		0			0
$664$	12.0000	+	12.0000i	0.465690	+	0.465690i
$665$	−8.00000			−0.310227
$666$	−10.0000	+	10.0000i	−0.387492	+	0.387492i
$667$		0			0
$668$		0			0
$669$		−	16.0000i		−	0.618596i
$670$	12.0000	+	12.0000i	0.463600	+	0.463600i
$671$	8.00000			0.308837
$672$	8.00000	−	8.00000i	0.308607	−	0.308607i
$673$	−14.0000			−0.539660			−0.269830	−	0.962908i	$-0.586968\pi$
$673$	−14.0000			−0.539660			−0.269830	+	0.962908i	$0.586968\pi$
$674$	30.0000	+	30.0000i	1.15556	+	1.15556i
$675$		−	4.00000i		−	0.153960i
$676$		−	46.0000i		−	1.76923i
$677$			14.0000i			0.538064i	0.963131	+	0.269032i	$0.0867037\pi$
$677$			14.0000i			0.538064i	−0.963131	+	0.269032i	$0.913296\pi$
$678$	12.0000	−	12.0000i	0.460857	−	0.460857i
$679$	−16.0000			−0.614024
$680$		0			0
$681$	36.0000			1.37952
$682$	−32.0000	+	32.0000i	−1.22534	+	1.22534i
$683$		−	24.0000i		−	0.918334i	−0.888350	−	0.459167i	$-0.848148\pi$
$683$		−	24.0000i		−	0.918334i	0.888350	−	0.459167i	$-0.151852\pi$
$684$	16.0000			0.611775
$685$			22.0000i			0.840577i
$686$	1.00000	+	1.00000i	0.0381802	+	0.0381802i
$687$	−20.0000			−0.763048
$688$		−	16.0000i		−	0.609994i
$689$	−12.0000			−0.457164
$690$	−16.0000	−	16.0000i	−0.609110	−	0.609110i
$691$			36.0000i			1.36950i	0.728776	+	0.684752i	$0.240090\pi$
$691$			36.0000i			1.36950i	−0.728776	+	0.684752i	$0.759910\pi$
$692$	28.0000			1.06440
$693$			4.00000i			0.151947i
$694$	16.0000	−	16.0000i	0.607352	−	0.607352i
$695$	−4.00000			−0.151729
$696$		0			0
$697$		0			0
$698$	2.00000	−	2.00000i	0.0757011	−	0.0757011i
$699$			36.0000i			1.36165i
$700$		−	2.00000i		−	0.0755929i
$701$			16.0000i			0.604312i	0.953259	+	0.302156i	$0.0977063\pi$
$701$			16.0000i			0.604312i	−0.953259	+	0.302156i	$0.902294\pi$
$702$	24.0000	+	24.0000i	0.905822	+	0.905822i
$703$	80.0000			3.01726
$704$	−32.0000			−1.20605
$705$	−16.0000			−0.602595
$706$	−24.0000	−	24.0000i	−0.903252	−	0.903252i
$707$		−	2.00000i		−	0.0752177i
$708$		−	16.0000i		−	0.601317i
$709$			40.0000i			1.50223i	0.660171	+	0.751116i	$0.270484\pi$
$709$			40.0000i			1.50223i	−0.660171	+	0.751116i	$0.729516\pi$
$710$	−2.00000	+	2.00000i	−0.0750587	+	0.0750587i
$711$	2.00000			0.0750059
$712$	−4.00000	+	4.00000i	−0.149906	+	0.149906i
$713$	−64.0000			−2.39682
$714$		0			0
$715$		−	24.0000i		−	0.897549i
$716$	−24.0000			−0.896922
$717$		−	4.00000i		−	0.149383i
$718$	6.00000	+	6.00000i	0.223918	+	0.223918i
$719$	−36.0000			−1.34257			−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000			−1.34257			−0.671287	+	0.741198i	$0.734258\pi$
$720$			4.00000i			0.149071i
$721$	−8.00000			−0.297936
$722$	−45.0000	−	45.0000i	−1.67473	−	1.67473i
$723$			36.0000i			1.33885i
$724$	−4.00000			−0.148659
$725$		0			0
$726$	10.0000	−	10.0000i	0.371135	−	0.371135i
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$	12.0000	+	12.0000i	0.444750	+	0.444750i
$729$	−13.0000			−0.481481
$730$	−4.00000	+	4.00000i	−0.148047	+	0.148047i
$731$		0			0
$732$		−	8.00000i		−	0.295689i
$733$			6.00000i			0.221615i	0.993842	+	0.110808i	$0.0353437\pi$
$733$			6.00000i			0.221615i	−0.993842	+	0.110808i	$0.964656\pi$
$734$		0			0
$735$	−2.00000			−0.0737711
$736$	−32.0000	−	32.0000i	−1.17954	−	1.17954i
$737$	−48.0000			−1.76810
$738$	2.00000	+	2.00000i	0.0736210	+	0.0736210i
$739$		−	12.0000i		−	0.441427i	−0.975339	−	0.220714i	$-0.929161\pi$
$739$		−	12.0000i		−	0.441427i	0.975339	−	0.220714i	$-0.0708386\pi$
$740$			20.0000i			0.735215i
$741$			96.0000i			3.52665i
$742$	2.00000	−	2.00000i	0.0734223	−	0.0734223i
$743$	36.0000			1.32071			0.660356	−	0.750953i	$-0.270405\pi$
$743$	36.0000			1.32071			0.660356	+	0.750953i	$0.270405\pi$
$744$	32.0000	+	32.0000i	1.17318	+	1.17318i
$745$		0			0
$746$	−34.0000	+	34.0000i	−1.24483	+	1.24483i
$747$			6.00000i			0.219529i
$748$		0			0
$749$			8.00000i			0.292314i
$750$	2.00000	+	2.00000i	0.0730297	+	0.0730297i
$751$	50.0000			1.82453			0.912263	−	0.409605i	$-0.134333\pi$
$751$	50.0000			1.82453			0.912263	+	0.409605i	$0.134333\pi$
$752$	−32.0000			−1.16692
$753$		0			0
$754$		0			0
$755$		−	2.00000i		−	0.0727875i
$756$	−8.00000			−0.290957
$757$			38.0000i			1.38113i	0.723269	+	0.690567i	$0.242639\pi$
$757$			38.0000i			1.38113i	−0.723269	+	0.690567i	$0.757361\pi$
$758$	−12.0000	+	12.0000i	−0.435860	+	0.435860i
$759$	64.0000			2.32305
$760$	16.0000	−	16.0000i	0.580381	−	0.580381i
$761$	34.0000			1.23250			0.616250	−	0.787551i	$-0.288651\pi$
$761$	34.0000			1.23250			0.616250	+	0.787551i	$0.288651\pi$
$762$	24.0000	−	24.0000i	0.869428	−	0.869428i
$763$		−	4.00000i		−	0.144810i
$764$		−	4.00000i		−	0.144715i
$765$		0			0
$766$		0			0
$767$	24.0000			0.866590
$768$			32.0000i			1.15470i
$769$	42.0000			1.51456			0.757279	−	0.653091i	$-0.226528\pi$
$769$	42.0000			1.51456			0.757279	+	0.653091i	$0.226528\pi$
$770$	4.00000	+	4.00000i	0.144150	+	0.144150i
$771$			32.0000i			1.15245i
$772$		−	4.00000i		−	0.143963i
$773$			6.00000i			0.215805i	0.994161	+	0.107903i	$0.0344134\pi$
$773$			6.00000i			0.215805i	−0.994161	+	0.107903i	$0.965587\pi$
$774$	4.00000	−	4.00000i	0.143777	−	0.143777i
$775$	8.00000			0.287368
$776$	32.0000	−	32.0000i	1.14873	−	1.14873i
$777$	20.0000			0.717496
$778$	−20.0000	+	20.0000i	−0.717035	+	0.717035i
$779$		−	16.0000i		−	0.573259i
$780$	−24.0000			−0.859338
$781$		−	8.00000i		−	0.286263i
$782$		0			0
$783$		0			0
$784$	−4.00000			−0.142857
$785$	2.00000			0.0713831
$786$	24.0000	+	24.0000i	0.856052	+	0.856052i
$787$		−	46.0000i		−	1.63972i	−0.572562	−	0.819861i	$-0.694050\pi$
$787$		−	46.0000i		−	1.63972i	0.572562	−	0.819861i	$-0.305950\pi$
$788$	−20.0000			−0.712470
$789$		−	24.0000i		−	0.854423i
$790$	2.00000	−	2.00000i	0.0711568	−	0.0711568i
$791$	−6.00000			−0.213335
$792$	−8.00000	−	8.00000i	−0.284268	−	0.284268i
$793$	12.0000			0.426132
$794$	2.00000	−	2.00000i	0.0709773	−	0.0709773i
$795$			4.00000i			0.141865i
$796$		−	48.0000i		−	1.70131i
$797$		−	18.0000i		−	0.637593i	−0.947823	−	0.318796i	$-0.896721\pi$
$797$		−	18.0000i		−	0.637593i	0.947823	−	0.318796i	$-0.103279\pi$
$798$	−16.0000	−	16.0000i	−0.566394	−	0.566394i
$799$		0			0
$800$	4.00000	+	4.00000i	0.141421	+	0.141421i
$801$	−2.00000			−0.0706665
$802$	−18.0000	−	18.0000i	−0.635602	−	0.635602i
$803$		−	16.0000i		−	0.564628i
$804$			48.0000i			1.69283i
$805$			8.00000i			0.281963i
$806$	−48.0000	+	48.0000i	−1.69073	+	1.69073i
$807$	−28.0000			−0.985647
$808$	4.00000	+	4.00000i	0.140720	+	0.140720i
$809$	−38.0000			−1.33601			−0.668004	−	0.744157i	$-0.732851\pi$
$809$	−38.0000			−1.33601			−0.668004	+	0.744157i	$0.732851\pi$
$810$	11.0000	−	11.0000i	0.386501	−	0.386501i
$811$		−	20.0000i		−	0.702295i	−0.936320	−	0.351147i	$-0.885792\pi$
$811$		−	20.0000i		−	0.702295i	0.936320	−	0.351147i	$-0.114208\pi$
$812$		0			0
$813$		−	16.0000i		−	0.561144i
$814$	−40.0000	−	40.0000i	−1.40200	−	1.40200i
$815$	−16.0000			−0.560456
$816$		0			0
$817$	−32.0000			−1.11954
$818$	−6.00000	−	6.00000i	−0.209785	−	0.209785i
$819$			6.00000i			0.209657i
$820$	4.00000			0.139686
$821$		−	44.0000i		−	1.53561i	−0.640683	−	0.767805i	$-0.721349\pi$
$821$		−	44.0000i		−	1.53561i	0.640683	−	0.767805i	$-0.278651\pi$
$822$	−44.0000	+	44.0000i	−1.53468	+	1.53468i
$823$		0			0			−	1.00000i	$-0.5\pi$
$823$		0			0				1.00000i	$0.5\pi$
$824$	16.0000	−	16.0000i	0.557386	−	0.557386i
$825$	−8.00000			−0.278524
$826$	−4.00000	+	4.00000i	−0.139178	+	0.139178i
$827$			28.0000i			0.973655i	0.873498	+	0.486828i	$0.161846\pi$
$827$			28.0000i			0.973655i	−0.873498	+	0.486828i	$0.838154\pi$
$828$		−	16.0000i		−	0.556038i
$829$			2.00000i			0.0694629i	0.999397	+	0.0347314i	$0.0110576\pi$
$829$			2.00000i			0.0694629i	−0.999397	+	0.0347314i	$0.988942\pi$
$830$	6.00000	+	6.00000i	0.208263	+	0.208263i
$831$	−44.0000			−1.52634
$832$	−48.0000			−1.66410
$833$		0			0
$834$	−8.00000	−	8.00000i	−0.277017	−	0.277017i
$835$		0			0
$836$			64.0000i			2.21349i
$837$		−	32.0000i		−	1.10608i
$838$	−4.00000	+	4.00000i	−0.138178	+	0.138178i
$839$	−20.0000			−0.690477			−0.345238	−	0.938515i	$-0.612202\pi$
$839$	−20.0000			−0.690477			−0.345238	+	0.938515i	$0.612202\pi$
$840$	4.00000	−	4.00000i	0.138013	−	0.138013i
$841$	29.0000			1.00000
$842$	−4.00000	+	4.00000i	−0.137849	+	0.137849i
$843$		−	44.0000i		−	1.51544i
$844$	24.0000			0.826114
$845$		−	23.0000i		−	0.791224i
$846$	−8.00000	−	8.00000i	−0.275046	−	0.275046i
$847$	−5.00000			−0.171802
$848$			8.00000i			0.274721i
$849$	4.00000			0.137280
$850$		0			0
$851$		−	80.0000i		−	2.74236i
$852$	−8.00000			−0.274075
$853$		−	10.0000i		−	0.342393i	−0.985237	−	0.171197i	$-0.945237\pi$
$853$		−	10.0000i		−	0.342393i	0.985237	−	0.171197i	$-0.0547634\pi$
$854$	−2.00000	+	2.00000i	−0.0684386	+	0.0684386i
$855$	8.00000			0.273594
$856$	−16.0000	−	16.0000i	−0.546869	−	0.546869i
$857$	12.0000			0.409912			0.204956	−	0.978771i	$-0.434295\pi$
$857$	12.0000			0.409912			0.204956	+	0.978771i	$0.434295\pi$
$858$	48.0000	−	48.0000i	1.63869	−	1.63869i
$859$			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
$862$	−18.0000	−	18.0000i	−0.613082	−	0.613082i
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$	16.0000	−	16.0000i	0.544331	−	0.544331i
$865$	14.0000			0.476014
$866$	20.0000	+	20.0000i	0.679628	+	0.679628i
$867$		−	34.0000i		−	1.15470i
$868$		−	16.0000i		−	0.543075i
$869$			8.00000i			0.271381i
$870$		0			0
$871$	−72.0000			−2.43963
$872$	8.00000	+	8.00000i	0.270914	+	0.270914i
$873$	16.0000			0.541518
$874$	−64.0000	+	64.0000i	−2.16483	+	2.16483i
$875$		−	1.00000i		−	0.0338062i
$876$	−16.0000			−0.540590
$877$			22.0000i			0.742887i	0.928456	+	0.371444i	$0.121137\pi$
$877$			22.0000i			0.742887i	−0.928456	+	0.371444i	$0.878863\pi$
$878$	−28.0000	−	28.0000i	−0.944954	−	0.944954i
$879$	44.0000			1.48408
$880$	−16.0000			−0.539360
$881$	6.00000			0.202145			0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000			0.202145			0.101073	+	0.994879i	$0.467773\pi$
$882$	−1.00000	−	1.00000i	−0.0336718	−	0.0336718i
$883$			40.0000i			1.34611i	0.739594	+	0.673054i	$0.235018\pi$
$883$			40.0000i			1.34611i	−0.739594	+	0.673054i	$0.764982\pi$
$884$		0			0
$885$		−	8.00000i		−	0.268917i
$886$	−20.0000	+	20.0000i	−0.671913	+	0.671913i
$887$	−8.00000			−0.268614			−0.134307	−	0.990940i	$-0.542881\pi$
$887$	−8.00000			−0.268614			−0.134307	+	0.990940i	$0.542881\pi$
$888$	−40.0000	+	40.0000i	−1.34231	+	1.34231i
$889$	−12.0000			−0.402467
$890$	−2.00000	+	2.00000i	−0.0670402	+	0.0670402i
$891$			44.0000i			1.47406i
$892$		−	16.0000i		−	0.535720i
$893$			64.0000i			2.14168i
$894$		0			0
$895$	−12.0000			−0.401116
$896$	8.00000	−	8.00000i	0.267261	−	0.267261i
$897$	96.0000			3.20535
$898$	−6.00000	−	6.00000i	−0.200223	−	0.200223i
$899$		0			0
$900$			2.00000i			0.0666667i
$901$		0			0
$902$	−8.00000	+	8.00000i	−0.266371	+	0.266371i
$903$	−8.00000			−0.266223
$904$	12.0000	−	12.0000i	0.399114	−	0.399114i
$905$	−2.00000			−0.0664822
$906$	4.00000	−	4.00000i	0.132891	−	0.132891i
$907$		−	44.0000i		−	1.46100i	−0.682915	−	0.730498i	$-0.739288\pi$
$907$		−	44.0000i		−	1.46100i	0.682915	−	0.730498i	$-0.260712\pi$
$908$	36.0000			1.19470
$909$			2.00000i			0.0663358i
$910$	6.00000	+	6.00000i	0.198898	+	0.198898i
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$	64.0000			2.11925
$913$	−24.0000			−0.794284
$914$	−6.00000	−	6.00000i	−0.198462	−	0.198462i
$915$		−	4.00000i		−	0.132236i
$916$	−20.0000			−0.660819
$917$		−	12.0000i		−	0.396275i
$918$		0			0
$919$	−14.0000			−0.461817			−0.230909	−	0.972975i	$-0.574170\pi$
$919$	−14.0000			−0.461817			−0.230909	+	0.972975i	$0.574170\pi$
$920$	−16.0000	−	16.0000i	−0.527504	−	0.527504i
$921$	−4.00000			−0.131804
$922$	26.0000	−	26.0000i	0.856264	−	0.856264i
$923$		−	12.0000i		−	0.394985i
$924$			16.0000i			0.526361i
$925$			10.0000i			0.328798i
$926$	20.0000	+	20.0000i	0.657241	+	0.657241i
$927$	8.00000			0.262754
$928$		0			0
$929$	46.0000			1.50921			0.754606	−	0.656179i	$-0.227828\pi$
$929$	46.0000			1.50921			0.754606	+	0.656179i	$0.227828\pi$
$930$	16.0000	+	16.0000i	0.524661	+	0.524661i
$931$			8.00000i			0.262189i
$932$			36.0000i			1.17922i
$933$			40.0000i			1.30954i
$934$	−26.0000	+	26.0000i	−0.850746	+	0.850746i
$935$		0			0
$936$	−12.0000	−	12.0000i	−0.392232	−	0.392232i
$937$	−32.0000			−1.04539			−0.522697	−	0.852518i	$-0.675074\pi$
$937$	−32.0000			−1.04539			−0.522697	+	0.852518i	$0.675074\pi$
$938$	12.0000	−	12.0000i	0.391814	−	0.391814i
$939$			24.0000i			0.783210i
$940$	−16.0000			−0.521862
$941$		−	22.0000i		−	0.717180i	−0.933495	−	0.358590i	$-0.883258\pi$
$941$		−	22.0000i		−	0.717180i	0.933495	−	0.358590i	$-0.116742\pi$
$942$	4.00000	+	4.00000i	0.130327	+	0.130327i
$943$	−16.0000			−0.521032
$944$		−	16.0000i		−	0.520756i
$945$	−4.00000			−0.130120
$946$	16.0000	+	16.0000i	0.520205	+	0.520205i
$947$		−	12.0000i		−	0.389948i	−0.980808	−	0.194974i	$-0.937538\pi$
$947$		−	12.0000i		−	0.389948i	0.980808	−	0.194974i	$-0.0624622\pi$
$948$	8.00000			0.259828
$949$		−	24.0000i		−	0.779073i
$950$	8.00000	−	8.00000i	0.259554	−	0.259554i
$951$	−36.0000			−1.16738
$952$		0			0
$953$	−14.0000			−0.453504			−0.226752	−	0.973952i	$-0.572811\pi$
$953$	−14.0000			−0.453504			−0.226752	+	0.973952i	$0.572811\pi$
$954$	−2.00000	+	2.00000i	−0.0647524	+	0.0647524i
$955$		−	2.00000i		−	0.0647185i
$956$		−	4.00000i		−	0.129369i
$957$		0			0
$958$	28.0000	+	28.0000i	0.904639	+	0.904639i
$959$	22.0000			0.710417
$960$			16.0000i			0.516398i
$961$	33.0000			1.06452
$962$	−60.0000	−	60.0000i	−1.93448	−	1.93448i
$963$		−	8.00000i		−	0.257796i
$964$			36.0000i			1.15948i
$965$		−	2.00000i		−	0.0643823i
$966$	−16.0000	+	16.0000i	−0.514792	+	0.514792i
$967$	40.0000			1.28631			0.643157	−	0.765735i	$-0.277624\pi$
$967$	40.0000			1.28631			0.643157	+	0.765735i	$0.277624\pi$
$968$	10.0000	−	10.0000i	0.321412	−	0.321412i
$969$		0			0
$970$	16.0000	−	16.0000i	0.513729	−	0.513729i
$971$			12.0000i			0.385098i	0.981287	+	0.192549i	$0.0616755\pi$
$971$			12.0000i			0.385098i	−0.981287	+	0.192549i	$0.938325\pi$
$972$	20.0000			0.641500
$973$			4.00000i			0.128234i
$974$	−12.0000	−	12.0000i	−0.384505	−	0.384505i
$975$	−12.0000			−0.384308
$976$		−	8.00000i		−	0.256074i
$977$	50.0000			1.59964			0.799821	−	0.600239i	$-0.204928\pi$
$977$	50.0000			1.59964			0.799821	+	0.600239i	$0.204928\pi$
$978$	−32.0000	−	32.0000i	−1.02325	−	1.02325i
$979$		−	8.00000i		−	0.255681i
$980$	−2.00000			−0.0638877
$981$			4.00000i			0.127710i
$982$	−28.0000	+	28.0000i	−0.893516	+	0.893516i
$983$	−8.00000			−0.255160			−0.127580	−	0.991828i	$-0.540721\pi$
$983$	−8.00000			−0.255160			−0.127580	+	0.991828i	$0.540721\pi$
$984$	8.00000	+	8.00000i	0.255031	+	0.255031i
$985$	−10.0000			−0.318626
$986$		0			0
$987$			16.0000i			0.509286i
$988$			96.0000i			3.05417i
$989$			32.0000i			1.01754i
$990$	−4.00000	−	4.00000i	−0.127128	−	0.127128i
$991$	50.0000			1.58830			0.794151	−	0.607720i	$-0.207916\pi$
$991$	50.0000			1.58830			0.794151	+	0.607720i	$0.207916\pi$
$992$	32.0000	+	32.0000i	1.01600	+	1.01600i
$993$	−40.0000			−1.26936
$994$	2.00000	+	2.00000i	0.0634361	+	0.0634361i
$995$		−	24.0000i		−	0.760851i
$996$			24.0000i			0.760469i
$997$			10.0000i			0.316703i	0.987383	+	0.158352i	$0.0506179\pi$
$997$			10.0000i			0.316703i	−0.987383	+	0.158352i	$0.949382\pi$
$998$	28.0000	−	28.0000i	0.886325	−	0.886325i
$999$	40.0000			1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.b.b.141.2	yes	2
4.3	odd	2		1120.2.b.a.561.1		2
8.3	odd	2		1120.2.b.a.561.2		2
8.5	even	2	inner	280.2.b.b.141.1	✓	2
16.3	odd	4		8960.2.a.t.1.1		1
16.5	even	4		8960.2.a.n.1.1		1
16.11	odd	4		8960.2.a.b.1.1		1
16.13	even	4		8960.2.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.b.b.141.1	✓	2	8.5	even	2	inner
280.2.b.b.141.2	yes	2	1.1	even	1	trivial
1120.2.b.a.561.1		2	4.3	odd	2
1120.2.b.a.561.2		2	8.3	odd	2
8960.2.a.b.1.1		1	16.11	odd	4
8960.2.a.f.1.1		1	16.13	even	4
8960.2.a.n.1.1		1	16.5	even	4
8960.2.a.t.1.1		1	16.3	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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{3} +2.00000i q^{4} +1.00000i q^{5} +(-2.00000 + 2.00000i) q^{6} +1.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{3} +2.00000i q^{4} +1.00000i q^{5} +(-2.00000 + 2.00000i) q^{6} +1.00000 q^{7} +(-2.00000 + 2.00000i) q^{8} -1.00000 q^{9} +(-1.00000 + 1.00000i) q^{10} -4.00000i q^{11} -4.00000 q^{12} -6.00000i q^{13} +(1.00000 + 1.00000i) q^{14} -2.00000 q^{15} -4.00000 q^{16} +(-1.00000 - 1.00000i) q^{18} +8.00000i q^{19} -2.00000 q^{20} +2.00000i q^{21} +(4.00000 - 4.00000i) q^{22} +8.00000 q^{23} +(-4.00000 - 4.00000i) q^{24} -1.00000 q^{25} +(6.00000 - 6.00000i) q^{26} +4.00000i q^{27} +2.00000i q^{28} +(-2.00000 - 2.00000i) q^{30} -8.00000 q^{31} +(-4.00000 - 4.00000i) q^{32} +8.00000 q^{33} +1.00000i q^{35} -2.00000i q^{36} -10.0000i q^{37} +(-8.00000 + 8.00000i) q^{38} +12.0000 q^{39} +(-2.00000 - 2.00000i) q^{40} -2.00000 q^{41} +(-2.00000 + 2.00000i) q^{42} +4.00000i q^{43} +8.00000 q^{44} -1.00000i q^{45} +(8.00000 + 8.00000i) q^{46} +8.00000 q^{47} -8.00000i q^{48} +1.00000 q^{49} +(-1.00000 - 1.00000i) q^{50} +12.0000 q^{52} -2.00000i q^{53} +(-4.00000 + 4.00000i) q^{54} +4.00000 q^{55} +(-2.00000 + 2.00000i) q^{56} -16.0000 q^{57} +4.00000i q^{59} -4.00000i q^{60} +2.00000i q^{61} +(-8.00000 - 8.00000i) q^{62} -1.00000 q^{63} -8.00000i q^{64} +6.00000 q^{65} +(8.00000 + 8.00000i) q^{66} -12.0000i q^{67} +16.0000i q^{69} +(-1.00000 + 1.00000i) q^{70} +2.00000 q^{71} +(2.00000 - 2.00000i) q^{72} +4.00000 q^{73} +(10.0000 - 10.0000i) q^{74} -2.00000i q^{75} -16.0000 q^{76} -4.00000i q^{77} +(12.0000 + 12.0000i) q^{78} -2.00000 q^{79} -4.00000i q^{80} -11.0000 q^{81} +(-2.00000 - 2.00000i) q^{82} -6.00000i q^{83} -4.00000 q^{84} +(-4.00000 + 4.00000i) q^{86} +(8.00000 + 8.00000i) q^{88} +2.00000 q^{89} +(1.00000 - 1.00000i) q^{90} -6.00000i q^{91} +16.0000i q^{92} -16.0000i q^{93} +(8.00000 + 8.00000i) q^{94} -8.00000 q^{95} +(8.00000 - 8.00000i) q^{96} -16.0000 q^{97} +(1.00000 + 1.00000i) q^{98} +4.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 4 q^{6} + 2 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 4 * q^6 + 2 * q^7 - 4 * q^8 - 2 * q^9	\( 2 q + 2 q^{2} - 4 q^{6} + 2 q^{7} - 4 q^{8} - 2 q^{9} - 2 q^{10} - 8 q^{12} + 2 q^{14} - 4 q^{15} - 8 q^{16} - 2 q^{18} - 4 q^{20} + 8 q^{22} + 16 q^{23} - 8 q^{24} - 2 q^{25} + 12 q^{26} - 4 q^{30} - 16 q^{31} - 8 q^{32} + 16 q^{33} - 16 q^{38} + 24 q^{39} - 4 q^{40} - 4 q^{41} - 4 q^{42} + 16 q^{44} + 16 q^{46} + 16 q^{47} + 2 q^{49} - 2 q^{50} + 24 q^{52} - 8 q^{54} + 8 q^{55} - 4 q^{56} - 32 q^{57} - 16 q^{62} - 2 q^{63} + 12 q^{65} + 16 q^{66} - 2 q^{70} + 4 q^{71} + 4 q^{72} + 8 q^{73} + 20 q^{74} - 32 q^{76} + 24 q^{78} - 4 q^{79} - 22 q^{81} - 4 q^{82} - 8 q^{84} - 8 q^{86} + 16 q^{88} + 4 q^{89} + 2 q^{90} + 16 q^{94} - 16 q^{95} + 16 q^{96} - 32 q^{97} + 2 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 4 * q^6 + 2 * q^7 - 4 * q^8 - 2 * q^9 - 2 * q^10 - 8 * q^12 + 2 * q^14 - 4 * q^15 - 8 * q^16 - 2 * q^18 - 4 * q^20 + 8 * q^22 + 16 * q^23 - 8 * q^24 - 2 * q^25 + 12 * q^26 - 4 * q^30 - 16 * q^31 - 8 * q^32 + 16 * q^33 - 16 * q^38 + 24 * q^39 - 4 * q^40 - 4 * q^41 - 4 * q^42 + 16 * q^44 + 16 * q^46 + 16 * q^47 + 2 * q^49 - 2 * q^50 + 24 * q^52 - 8 * q^54 + 8 * q^55 - 4 * q^56 - 32 * q^57 - 16 * q^62 - 2 * q^63 + 12 * q^65 + 16 * q^66 - 2 * q^70 + 4 * q^71 + 4 * q^72 + 8 * q^73 + 20 * q^74 - 32 * q^76 + 24 * q^78 - 4 * q^79 - 22 * q^81 - 4 * q^82 - 8 * q^84 - 8 * q^86 + 16 * q^88 + 4 * q^89 + 2 * q^90 + 16 * q^94 - 16 * q^95 + 16 * q^96 - 32 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more