LMFDB - Embedded newform 1860.1.df.a.1739.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1860,1,Mod(179,1860)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1860.179"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1860, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([15, 15, 15, 13])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1860.df (of order $30$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-1,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$0.928260923497$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{30}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{30} + \cdots)$

Embedding invariants

Embedding label			1739.1
Root			$-0.104528 - 0.994522i$ of defining polynomial
Character	$\chi$	$=$	1860.1739
Dual form			1860.1.df.a.1199.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.669131 + 0.743145i) q^{2} +(0.104528 - 0.994522i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.669131 + 0.743145i) q^{6} +(0.809017 + 0.587785i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(-0.309017 - 0.951057i) q^{10} -1.00000 q^{12} +(0.809017 + 0.587785i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(-1.28716 - 1.15897i) q^{17} +(0.809017 - 0.587785i) q^{18} +(0.809017 - 1.81708i) q^{19} +(0.913545 + 0.406737i) q^{20} +(0.190983 + 0.587785i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.309017 + 0.951057i) q^{27} +(-0.978148 + 0.207912i) q^{30} +(0.809017 - 0.587785i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.72256 - 0.181049i) q^{34} +(-0.104528 + 0.994522i) q^{36} +(0.809017 + 1.81708i) q^{38} +(-0.913545 + 0.406737i) q^{40} +(0.669131 - 0.743145i) q^{45} +(-0.564602 - 0.251377i) q^{46} +(0.873619 - 1.20243i) q^{47} +(0.104528 + 0.994522i) q^{48} +(-0.913545 + 0.406737i) q^{49} +(0.978148 + 0.207912i) q^{50} +(-1.28716 + 1.15897i) q^{51} +(0.244415 - 1.14988i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-1.72256 - 0.994522i) q^{57} +(0.500000 - 0.866025i) q^{60} -0.813473i q^{61} +(-0.104528 + 0.994522i) q^{62} +(0.309017 + 0.951057i) q^{64} +(-1.01807 + 1.40126i) q^{68} +(0.604528 - 0.128496i) q^{69} +(-0.669131 - 0.743145i) q^{72} +(-0.913545 + 0.406737i) q^{75} +(-1.89169 - 0.614648i) q^{76} +(-0.139886 + 0.155360i) q^{79} +(0.309017 - 0.951057i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-0.139886 - 1.33093i) q^{83} +(1.64728 - 0.535233i) q^{85} +(0.104528 + 0.994522i) q^{90} +(0.564602 - 0.251377i) q^{92} +(-0.500000 - 0.866025i) q^{93} +(0.309017 + 1.45381i) q^{94} +(1.16913 + 1.60917i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(0.309017 - 0.951057i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - q^{3} + q^{4} - 4 q^{5} + q^{6} + 2 q^{8} + q^{9} + 2 q^{10} - 8 q^{12} + 2 q^{15} + q^{16} + 3 q^{17} + 2 q^{18} + 2 q^{19} + q^{20} + 6 q^{23} + q^{24} - 4 q^{25} + 2 q^{27} + q^{30}+ \cdots - 2 q^{98}+O(q^{100}) $ 8 * q - q^2 - q^3 + q^4 - 4 * q^5 + q^6 + 2 * q^8 + q^9 + 2 * q^10 - 8 * q^12 + 2 * q^15 + q^16 + 3 * q^17 + 2 * q^18 + 2 * q^19 + q^20 + 6 * q^23 + q^24 - 4 * q^25 + 2 * q^27 + q^30 + 2 * q^31 + 4 * q^32 + 3 * q^34 + q^36 + 2 * q^38 - q^40 + q^45 - 2 * q^46 - q^48 - q^49 - q^50 + 3 * q^51 - 4 * q^54 - 3 * q^57 + 4 * q^60 + q^62 - 2 * q^64 + 3 * q^69 - q^72 - q^75 - q^79 - 2 * q^80 + q^81 - q^83 - q^90 + 2 * q^92 - 4 * q^93 - 2 * q^94 + 5 * q^95 - 2 * q^96 - 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1860\mathbb{Z}\right)^\times$.

$n$	$931$	$1117$	$1241$	$1801$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{1}{30}\right)$

Coefficient data

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

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

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

$2$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$2$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$3$	0.104528	−	0.994522i	0.104528	−	0.994522i
$3$	0.104528	−	0.994522i	0.104528	−	0.994522i
$4$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$5$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$5$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$6$	0.669131	+	0.743145i	0.669131	+	0.743145i
$7$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$7$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$8$	0.809017	+	0.587785i	0.809017	+	0.587785i
$9$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$10$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$11$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$11$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$12$	−1.00000			−1.00000
$13$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$13$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$14$		0			0
$15$	0.809017	+	0.587785i	0.809017	+	0.587785i
$16$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$17$	−1.28716	−	1.15897i	−1.28716	−	1.15897i	−0.978148	−	0.207912i	$-0.933333\pi$
$17$	−1.28716	−	1.15897i	−1.28716	−	1.15897i	−0.309017	−	0.951057i	$-0.600000\pi$
$18$	0.809017	−	0.587785i	0.809017	−	0.587785i
$19$	0.809017	−	1.81708i	0.809017	−	1.81708i	0.309017	−	0.951057i	$-0.400000\pi$
$19$	0.809017	−	1.81708i	0.809017	−	1.81708i	0.500000	−	0.866025i	$-0.333333\pi$
$20$	0.913545	+	0.406737i	0.913545	+	0.406737i
$21$		0			0
$22$		0			0
$23$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$23$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$24$	0.669131	−	0.743145i	0.669131	−	0.743145i
$25$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$26$		0			0
$27$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$28$		0			0
$29$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$29$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$30$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$31$	0.809017	−	0.587785i	0.809017	−	0.587785i
$31$	0.809017	−	0.587785i	0.809017	−	0.587785i
$32$	0.500000	−	0.866025i	0.500000	−	0.866025i
$33$		0			0
$34$	1.72256	−	0.181049i	1.72256	−	0.181049i
$35$		0			0
$36$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$37$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$37$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$38$	0.809017	+	1.81708i	0.809017	+	1.81708i
$39$		0			0
$40$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$41$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$41$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$42$		0			0
$43$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$43$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$44$		0			0
$45$	0.669131	−	0.743145i	0.669131	−	0.743145i
$46$	−0.564602	−	0.251377i	−0.564602	−	0.251377i
$47$	0.873619	−	1.20243i	0.873619	−	1.20243i	−0.104528	−	0.994522i	$-0.533333\pi$
$47$	0.873619	−	1.20243i	0.873619	−	1.20243i	0.978148	−	0.207912i	$-0.0666667\pi$
$48$	0.104528	+	0.994522i	0.104528	+	0.994522i
$49$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$50$	0.978148	+	0.207912i	0.978148	+	0.207912i
$51$	−1.28716	+	1.15897i	−1.28716	+	1.15897i
$52$		0			0
$53$	0.244415	−	1.14988i	0.244415	−	1.14988i	−0.669131	−	0.743145i	$-0.733333\pi$
$53$	0.244415	−	1.14988i	0.244415	−	1.14988i	0.913545	−	0.406737i	$-0.133333\pi$
$54$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$55$		0			0
$56$		0			0
$57$	−1.72256	−	0.994522i	−1.72256	−	0.994522i
$58$		0			0
$59$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$59$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$60$	0.500000	−	0.866025i	0.500000	−	0.866025i
$61$		−	0.813473i		−	0.813473i	−0.913545	−	0.406737i	$-0.866667\pi$
$61$		−	0.813473i		−	0.813473i	0.913545	−	0.406737i	$-0.133333\pi$
$62$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$63$		0			0
$64$	0.309017	+	0.951057i	0.309017	+	0.951057i
$65$		0			0
$66$		0			0
$67$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$67$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$68$	−1.01807	+	1.40126i	−1.01807	+	1.40126i
$69$	0.604528	−	0.128496i	0.604528	−	0.128496i
$70$		0			0
$71$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$71$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$72$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$73$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$73$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$74$		0			0
$75$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$76$	−1.89169	−	0.614648i	−1.89169	−	0.614648i
$77$		0			0
$78$		0			0
$79$	−0.139886	+	0.155360i	−0.139886	+	0.155360i	−0.809017	−	0.587785i	$-0.800000\pi$
$79$	−0.139886	+	0.155360i	−0.139886	+	0.155360i	0.669131	+	0.743145i	$0.266667\pi$
$80$	0.309017	−	0.951057i	0.309017	−	0.951057i
$81$	0.913545	+	0.406737i	0.913545	+	0.406737i
$82$		0			0
$83$	−0.139886	−	1.33093i	−0.139886	−	1.33093i	−0.809017	−	0.587785i	$-0.800000\pi$
$83$	−0.139886	−	1.33093i	−0.139886	−	1.33093i	0.669131	−	0.743145i	$-0.266667\pi$
$84$		0			0
$85$	1.64728	−	0.535233i	1.64728	−	0.535233i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$89$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$90$	0.104528	+	0.994522i	0.104528	+	0.994522i
$91$		0			0
$92$	0.564602	−	0.251377i	0.564602	−	0.251377i
$93$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$94$	0.309017	+	1.45381i	0.309017	+	1.45381i
$95$	1.16913	+	1.60917i	1.16913	+	1.60917i
$96$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$97$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$97$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$98$	0.309017	−	0.951057i	0.309017	−	0.951057i
$99$		0			0
$100$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$101$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$101$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$102$		−	1.73205i		−	1.73205i
$103$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$103$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$104$		0			0
$105$		0			0
$106$	0.690983	+	0.951057i	0.690983	+	0.951057i
$107$	−1.41355	−	1.27276i	−1.41355	−	1.27276i	−0.913545	−	0.406737i	$-0.866667\pi$
$107$	−1.41355	−	1.27276i	−1.41355	−	1.27276i	−0.500000	−	0.866025i	$-0.666667\pi$
$108$	0.978148	+	0.207912i	0.978148	+	0.207912i
$109$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$109$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	0.309017	−	0.951057i	$-0.400000\pi$
$113$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	−0.978148	+	0.207912i	$0.933333\pi$
$114$	1.89169	−	0.614648i	1.89169	−	0.614648i
$115$	−0.604528	−	0.128496i	−0.604528	−	0.128496i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.309017	+	0.951057i	0.309017	+	0.951057i
$121$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$122$	0.604528	+	0.544320i	0.604528	+	0.544320i
$123$		0			0
$124$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$125$	1.00000			1.00000
$126$		0			0
$127$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$127$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$128$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$129$		0			0
$130$		0			0
$131$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$131$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$136$	−0.360114	−	1.69420i	−0.360114	−	1.69420i
$137$	0.169131	+	0.379874i	0.169131	+	0.379874i	0.978148	−	0.207912i	$-0.0666667\pi$
$137$	0.169131	+	0.379874i	0.169131	+	0.379874i	−0.809017	+	0.587785i	$0.800000\pi$
$138$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$139$	1.08268	+	0.786610i	1.08268	+	0.786610i	0.978148	−	0.207912i	$-0.0666667\pi$
$139$	1.08268	+	0.786610i	1.08268	+	0.786610i	0.104528	+	0.994522i	$0.466667\pi$
$140$		0			0
$141$	−1.10453	−	0.994522i	−1.10453	−	0.994522i
$142$		0			0
$143$		0			0
$144$	1.00000			1.00000
$145$		0			0
$146$		0			0
$147$	0.309017	+	0.951057i	0.309017	+	0.951057i
$148$		0			0
$149$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$149$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$150$	0.309017	−	0.951057i	0.309017	−	0.951057i
$151$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$151$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$152$	1.72256	−	0.994522i	1.72256	−	0.994522i
$153$	1.01807	+	1.40126i	1.01807	+	1.40126i
$154$		0			0
$155$	0.104528	+	0.994522i	0.104528	+	0.994522i
$156$		0			0
$157$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$157$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$158$	−0.0218524	−	0.207912i	−0.0218524	−	0.207912i
$159$	−1.11803	−	0.363271i	−1.11803	−	0.363271i
$160$	0.500000	+	0.866025i	0.500000	+	0.866025i
$161$		0			0
$162$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$163$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$163$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$164$		0			0
$165$		0			0
$166$	1.08268	+	0.786610i	1.08268	+	0.786610i
$167$	1.78716	+	0.795697i	1.78716	+	0.795697i	0.978148	+	0.207912i	$0.0666667\pi$
$167$	1.78716	+	0.795697i	1.78716	+	0.795697i	0.809017	+	0.587785i	$0.200000\pi$
$168$		0			0
$169$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$170$	−0.704489	+	1.58231i	−0.704489	+	1.58231i
$171$	−1.16913	+	1.60917i	−1.16913	+	1.60917i
$172$		0			0
$173$	0.564602	−	0.251377i	0.564602	−	0.251377i	−0.104528	−	0.994522i	$-0.533333\pi$
$173$	0.564602	−	0.251377i	0.564602	−	0.251377i	0.669131	+	0.743145i	$0.266667\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$179$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$180$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$181$	1.64728	+	0.951057i	1.64728	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$181$	1.64728	+	0.951057i	1.64728	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$182$		0			0
$183$	−0.809017	−	0.0850311i	−0.809017	−	0.0850311i
$184$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$185$		0			0
$186$	0.978148	+	0.207912i	0.978148	+	0.207912i
$187$		0			0
$188$	−1.28716	−	0.743145i	−1.28716	−	0.743145i
$189$		0			0
$190$	−1.97815	−	0.207912i	−1.97815	−	0.207912i
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$	0.978148	−	0.207912i	0.978148	−	0.207912i
$193$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$193$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$194$		0			0
$195$		0			0
$196$	0.500000	+	0.866025i	0.500000	+	0.866025i
$197$	−1.10453	+	0.994522i	−1.10453	+	0.994522i	−0.104528	+	0.994522i	$0.533333\pi$
$197$	−1.10453	+	0.994522i	−1.10453	+	0.994522i	−1.00000			$\pi$
$198$		0			0
$199$	−0.913545	+	0.406737i	−0.913545	+	0.406737i	−0.809017	−	0.587785i	$-0.800000\pi$
$199$	−0.913545	+	0.406737i	−0.913545	+	0.406737i	−0.104528	+	0.994522i	$0.533333\pi$
$200$	0.104528	−	0.994522i	0.104528	−	0.994522i
$201$		0			0
$202$		0			0
$203$		0			0
$204$	1.28716	+	1.15897i	1.28716	+	1.15897i
$205$		0			0
$206$		0			0
$207$	−0.0646021	−	0.614648i	−0.0646021	−	0.614648i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	1.64728	−	0.951057i	1.64728	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$211$	1.64728	−	0.951057i	1.64728	−	0.951057i	0.978148	−	0.207912i	$-0.0666667\pi$
$212$	−1.16913	−	0.122881i	−1.16913	−	0.122881i
$213$		0			0
$214$	1.89169	−	0.198825i	1.89169	−	0.198825i
$215$		0			0
$216$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$217$		0			0
$218$	1.58268	−	0.336408i	1.58268	−	0.336408i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$223$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$224$		0			0
$225$	0.309017	+	0.951057i	0.309017	+	0.951057i
$226$	1.00000			1.00000
$227$	1.72256	−	0.181049i	1.72256	−	0.181049i	0.809017	−	0.587785i	$-0.200000\pi$
$227$	1.72256	−	0.181049i	1.72256	−	0.181049i	0.913545	+	0.406737i	$0.133333\pi$
$228$	−0.809017	+	1.81708i	−0.809017	+	1.81708i
$229$	−0.478148	+	1.07394i	−0.478148	+	1.07394i	0.500000	+	0.866025i	$0.333333\pi$
$229$	−0.478148	+	1.07394i	−0.478148	+	1.07394i	−0.978148	+	0.207912i	$0.933333\pi$
$230$	0.500000	−	0.363271i	0.500000	−	0.363271i
$231$		0			0
$232$		0			0
$233$	1.47815	+	1.07394i	1.47815	+	1.07394i	0.978148	+	0.207912i	$0.0666667\pi$
$233$	1.47815	+	1.07394i	1.47815	+	1.07394i	0.500000	+	0.866025i	$0.333333\pi$
$234$		0			0
$235$	0.604528	+	1.35779i	0.604528	+	1.35779i
$236$		0			0
$237$	0.139886	+	0.155360i	0.139886	+	0.155360i
$238$		0			0
$239$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$239$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$240$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$241$	0.413545	+	1.94558i	0.413545	+	1.94558i	0.309017	+	0.951057i	$0.400000\pi$
$241$	0.413545	+	1.94558i	0.413545	+	1.94558i	0.104528	+	0.994522i	$0.466667\pi$
$242$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$243$	0.500000	−	0.866025i	0.500000	−	0.866025i
$244$	−0.809017	+	0.0850311i	−0.809017	+	0.0850311i
$245$	0.104528	−	0.994522i	0.104528	−	0.994522i
$246$		0			0
$247$		0			0
$248$	1.00000			1.00000
$249$	−1.33826			−1.33826
$250$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$251$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$251$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−0.360114	−	1.69420i	−0.360114	−	1.69420i
$256$	0.913545	−	0.406737i	0.913545	−	0.406737i
$257$	−0.204489	−	0.0434654i	−0.204489	−	0.0434654i	0.104528	−	0.994522i	$-0.466667\pi$
$257$	−0.204489	−	0.0434654i	−0.204489	−	0.0434654i	−0.309017	+	0.951057i	$0.600000\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.169131	−	0.122881i	−0.169131	−	0.122881i	0.500000	−	0.866025i	$-0.333333\pi$
$263$	−0.169131	−	0.122881i	−0.169131	−	0.122881i	−0.669131	+	0.743145i	$0.733333\pi$
$264$		0			0
$265$	0.873619	+	0.786610i	0.873619	+	0.786610i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$269$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$270$	1.00000			1.00000
$271$	−0.564602	−	1.73767i	−0.564602	−	1.73767i	−0.669131	−	0.743145i	$-0.733333\pi$
$271$	−0.564602	−	1.73767i	−0.564602	−	1.73767i	0.104528	−	0.994522i	$-0.466667\pi$
$272$	1.50000	+	0.866025i	1.50000	+	0.866025i
$273$		0			0
$274$	−0.395472	−	0.128496i	−0.395472	−	0.128496i
$275$		0			0
$276$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$277$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$277$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$278$	−1.30902	+	0.278240i	−1.30902	+	0.278240i
$279$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$280$		0			0
$281$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$281$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$282$	1.47815	−	0.155360i	1.47815	−	0.155360i
$283$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$283$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$284$		0			0
$285$	1.72256	−	0.994522i	1.72256	−	0.994522i
$286$		0			0
$287$		0			0
$288$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$289$	0.209057	+	1.98904i	0.209057	+	1.98904i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.22256	+	1.35779i	−1.22256	+	1.35779i	−0.309017	+	0.951057i	$0.600000\pi$
$293$	−1.22256	+	1.35779i	−1.22256	+	1.35779i	−0.913545	+	0.406737i	$0.866667\pi$
$294$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	0.500000	+	0.866025i	0.500000	+	0.866025i
$301$		0			0
$302$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$303$		0			0
$304$	−0.413545	+	1.94558i	−0.413545	+	1.94558i
$305$	0.704489	+	0.406737i	0.704489	+	0.406737i
$306$	−1.72256	−	0.181049i	−1.72256	−	0.181049i
$307$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$307$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$308$		0			0
$309$		0			0
$310$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$313$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$314$		0			0
$315$		0			0
$316$	0.169131	+	0.122881i	0.169131	+	0.122881i
$317$	1.30902	−	0.278240i	1.30902	−	0.278240i	0.500000	−	0.866025i	$-0.333333\pi$
$317$	1.30902	−	0.278240i	1.30902	−	0.278240i	0.809017	+	0.587785i	$0.200000\pi$
$318$	1.01807	−	0.587785i	1.01807	−	0.587785i
$319$		0			0
$320$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$321$	−1.41355	+	1.27276i	−1.41355	+	1.27276i
$322$		0			0
$323$	−3.14728	+	1.40126i	−3.14728	+	1.40126i
$324$	0.309017	−	0.951057i	0.309017	−	0.951057i
$325$		0			0
$326$		0			0
$327$	−1.08268	+	1.20243i	−1.08268	+	1.20243i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.190983	−	1.81708i	−0.190983	−	1.81708i	−0.500000	−	0.866025i	$-0.666667\pi$
$331$	−0.190983	−	1.81708i	−0.190983	−	1.81708i	0.309017	−	0.951057i	$-0.400000\pi$
$332$	−1.30902	+	0.278240i	−1.30902	+	0.278240i
$333$		0			0
$334$	−1.78716	+	0.795697i	−1.78716	+	0.795697i
$335$		0			0
$336$		0			0
$337$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$337$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$338$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$339$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$340$	−0.704489	−	1.58231i	−0.704489	−	1.58231i
$341$		0			0
$342$	−0.413545	−	1.94558i	−0.413545	−	1.94558i
$343$		0			0
$344$		0			0
$345$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$346$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$347$	−0.978148	−	1.69420i	−0.978148	−	1.69420i	−0.669131	−	0.743145i	$-0.733333\pi$
$347$	−0.978148	−	1.69420i	−0.978148	−	1.69420i	−0.309017	−	0.951057i	$-0.600000\pi$
$348$		0			0
$349$	−0.413545	−	1.27276i	−0.413545	−	1.27276i	−0.913545	−	0.406737i	$-0.866667\pi$
$349$	−0.413545	−	1.27276i	−0.413545	−	1.27276i	0.500000	−	0.866025i	$-0.333333\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.604528	+	1.35779i	−0.604528	+	1.35779i	0.309017	+	0.951057i	$0.400000\pi$
$353$	−0.604528	+	1.35779i	−0.604528	+	1.35779i	−0.913545	+	0.406737i	$0.866667\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$359$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$360$	0.978148	−	0.207912i	0.978148	−	0.207912i
$361$	−1.97815	−	2.19696i	−1.97815	−	2.19696i
$362$	−1.80902	+	0.587785i	−1.80902	+	0.587785i
$363$	0.978148	+	0.207912i	0.978148	+	0.207912i
$364$		0			0
$365$		0			0
$366$	0.604528	−	0.544320i	0.604528	−	0.544320i
$367$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$367$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$368$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$		0			0
$375$	0.104528	−	0.994522i	0.104528	−	0.994522i
$376$	1.41355	−	0.459289i	1.41355	−	0.459289i
$377$		0			0
$378$		0			0
$379$	−0.244415	−	1.14988i	−0.244415	−	1.14988i	−0.913545	−	0.406737i	$-0.866667\pi$
$379$	−0.244415	−	1.14988i	−0.244415	−	1.14988i	0.669131	−	0.743145i	$-0.266667\pi$
$380$	1.47815	−	1.33093i	1.47815	−	1.33093i
$381$		0			0
$382$		0			0
$383$	1.22256	+	1.35779i	1.22256	+	1.35779i	0.913545	+	0.406737i	$0.133333\pi$
$383$	1.22256	+	1.35779i	1.22256	+	1.35779i	0.309017	+	0.951057i	$0.400000\pi$
$384$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$389$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$390$		0			0
$391$	0.435398	−	0.977920i	0.435398	−	0.977920i
$392$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$393$		0			0
$394$		−	1.48629i		−	1.48629i
$395$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i
$396$		0			0
$397$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$397$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$398$	0.309017	−	0.951057i	0.309017	−	0.951057i
$399$		0			0
$400$	0.669131	+	0.743145i	0.669131	+	0.743145i
$401$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$401$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$406$		0			0
$407$		0			0
$408$	−1.72256	+	0.181049i	−1.72256	+	0.181049i
$409$	−1.28716	+	0.743145i	−1.28716	+	0.743145i	−0.978148	−	0.207912i	$-0.933333\pi$
$409$	−1.28716	+	0.743145i	−1.28716	+	0.743145i	−0.309017	+	0.951057i	$0.600000\pi$
$410$		0			0
$411$	0.395472	−	0.128496i	0.395472	−	0.128496i
$412$		0			0
$413$		0			0
$414$	0.500000	+	0.363271i	0.500000	+	0.363271i
$415$	1.22256	+	0.544320i	1.22256	+	0.544320i
$416$		0			0
$417$	0.895472	−	0.994522i	0.895472	−	0.994522i
$418$		0			0
$419$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$419$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$420$		0			0
$421$	0.913545	−	0.406737i	0.913545	−	0.406737i	0.104528	−	0.994522i	$-0.466667\pi$
$421$	0.913545	−	0.406737i	0.913545	−	0.406737i	0.809017	+	0.587785i	$0.200000\pi$
$422$	−0.395472	+	1.86055i	−0.395472	+	1.86055i
$423$	−1.10453	+	0.994522i	−1.10453	+	0.994522i
$424$	0.873619	−	0.786610i	0.873619	−	0.786610i
$425$	−0.360114	+	1.69420i	−0.360114	+	1.69420i
$426$		0			0
$427$		0			0
$428$	−1.11803	+	1.53884i	−1.11803	+	1.53884i
$429$		0			0
$430$		0			0
$431$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$431$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$432$	0.104528	−	0.994522i	0.104528	−	0.994522i
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$		0			0
$435$		0			0
$436$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$437$	1.22256	+	0.128496i	1.22256	+	0.128496i
$438$		0			0
$439$	1.64728	+	0.951057i	1.64728	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$439$	1.64728	+	0.951057i	1.64728	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$440$		0			0
$441$	0.978148	−	0.207912i	0.978148	−	0.207912i
$442$		0			0
$443$	−0.169131	+	0.795697i	−0.169131	+	0.795697i	0.809017	+	0.587785i	$0.200000\pi$
$443$	−0.169131	+	0.795697i	−0.169131	+	0.795697i	−0.978148	+	0.207912i	$0.933333\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$449$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$450$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$451$		0			0
$452$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$453$	1.47815	+	0.658114i	1.47815	+	0.658114i
$454$	−1.01807	+	1.40126i	−1.01807	+	1.40126i
$455$		0			0
$456$	−0.809017	−	1.81708i	−0.809017	−	1.81708i
$457$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$457$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$458$	−0.478148	−	1.07394i	−0.478148	−	1.07394i
$459$	1.50000	−	0.866025i	1.50000	−	0.866025i
$460$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i
$461$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$461$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$462$		0			0
$463$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$463$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$464$		0			0
$465$	1.00000			1.00000
$466$	−1.78716	+	0.379874i	−1.78716	+	0.379874i
$467$	−0.690983	−	0.951057i	−0.690983	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$467$	−0.690983	−	0.951057i	−0.690983	−	0.951057i	−1.00000			$\pi$
$468$		0			0
$469$		0			0
$470$	−1.41355	−	0.459289i	−1.41355	−	0.459289i
$471$		0			0
$472$		0			0
$473$		0			0
$474$	−0.209057			−0.209057
$475$	−1.97815	+	0.207912i	−1.97815	+	0.207912i
$476$		0			0
$477$	−0.478148	+	1.07394i	−0.478148	+	1.07394i
$478$		0			0
$479$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$479$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$480$	0.913545	−	0.406737i	0.913545	−	0.406737i
$481$		0			0
$482$	−1.72256	−	0.994522i	−1.72256	−	0.994522i
$483$		0			0
$484$	1.00000			1.00000
$485$		0			0
$486$	0.309017	+	0.951057i	0.309017	+	0.951057i
$487$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$487$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$488$	0.478148	−	0.658114i	0.478148	−	0.658114i
$489$		0			0
$490$	0.669131	+	0.743145i	0.669131	+	0.743145i
$491$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$491$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$497$		0			0
$498$	0.895472	−	0.994522i	0.895472	−	0.994522i
$499$	−0.169131	+	1.60917i	−0.169131	+	1.60917i	0.500000	+	0.866025i	$0.333333\pi$
$499$	−0.169131	+	1.60917i	−0.169131	+	1.60917i	−0.669131	+	0.743145i	$0.733333\pi$
$500$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$501$	0.978148	−	1.69420i	0.978148	−	1.69420i
$502$		0			0
$503$	−0.244415	−	1.14988i	−0.244415	−	1.14988i	−0.913545	−	0.406737i	$-0.866667\pi$
$503$	−0.244415	−	1.14988i	−0.244415	−	1.14988i	0.669131	−	0.743145i	$-0.266667\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.669131	+	0.743145i	0.669131	+	0.743145i
$508$		0			0
$509$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$509$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$510$	1.50000	+	0.866025i	1.50000	+	0.866025i
$511$		0			0
$512$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$513$	1.47815	+	1.33093i	1.47815	+	1.33093i
$514$	0.169131	−	0.122881i	0.169131	−	0.122881i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$520$		0			0
$521$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$521$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$522$		0			0
$523$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$523$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$524$		0			0
$525$		0			0
$526$	0.204489	−	0.0434654i	0.204489	−	0.0434654i
$527$	−1.72256	−	0.181049i	−1.72256	−	0.181049i
$528$		0			0
$529$	0.500000	−	0.363271i	0.500000	−	0.363271i
$530$	−1.16913	+	0.122881i	−1.16913	+	0.122881i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	1.80902	−	0.587785i	1.80902	−	0.587785i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$541$	1.30902	−	1.45381i	1.30902	−	1.45381i	0.500000	−	0.866025i	$-0.333333\pi$
$541$	1.30902	−	1.45381i	1.30902	−	1.45381i	0.809017	−	0.587785i	$-0.200000\pi$
$542$	1.66913	+	0.743145i	1.66913	+	0.743145i
$543$	1.11803	−	1.53884i	1.11803	−	1.53884i
$544$	−1.64728	+	0.535233i	−1.64728	+	0.535233i
$545$	1.47815	−	0.658114i	1.47815	−	0.658114i
$546$		0			0
$547$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$547$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$548$	0.360114	−	0.207912i	0.360114	−	0.207912i
$549$	−0.169131	+	0.795697i	−0.169131	+	0.795697i
$550$		0			0
$551$		0			0
$552$	0.564602	+	0.251377i	0.564602	+	0.251377i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.669131	−	1.15897i	0.669131	−	1.15897i
$557$			0.813473i			0.813473i	0.913545	+	0.406737i	$0.133333\pi$
$557$			0.813473i			0.813473i	−0.913545	+	0.406737i	$0.866667\pi$
$558$	0.309017	−	0.951057i	0.309017	−	0.951057i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.704489	+	0.406737i	0.704489	+	0.406737i	0.809017	−	0.587785i	$-0.200000\pi$
$563$	0.704489	+	0.406737i	0.704489	+	0.406737i	−0.104528	+	0.994522i	$0.533333\pi$
$564$	−0.873619	+	1.20243i	−0.873619	+	1.20243i
$565$	0.978148	−	0.207912i	0.978148	−	0.207912i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$569$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$570$	−0.413545	+	1.94558i	−0.413545	+	1.94558i
$571$	1.47815	−	0.658114i	1.47815	−	0.658114i	0.500000	−	0.866025i	$-0.333333\pi$
$571$	1.47815	−	0.658114i	1.47815	−	0.658114i	0.978148	+	0.207912i	$0.0666667\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.413545	−	0.459289i	0.413545	−	0.459289i
$576$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$577$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$577$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$578$	−1.61803	−	1.17557i	−1.61803	−	1.17557i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−0.190983	−	1.81708i	−0.190983	−	1.81708i
$587$	−0.169131	+	0.122881i	−0.169131	+	0.122881i	−0.669131	−	0.743145i	$-0.733333\pi$
$587$	−0.169131	+	0.122881i	−0.169131	+	0.122881i	0.500000	+	0.866025i	$0.333333\pi$
$588$	0.913545	−	0.406737i	0.913545	−	0.406737i
$589$	−0.413545	−	1.94558i	−0.413545	−	1.94558i
$590$		0			0
$591$	0.873619	+	1.20243i	0.873619	+	1.20243i
$592$		0			0
$593$	0.413545	−	1.27276i	0.413545	−	1.27276i	−0.500000	−	0.866025i	$-0.666667\pi$
$593$	0.413545	−	1.27276i	0.413545	−	1.27276i	0.913545	−	0.406737i	$-0.133333\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.309017	+	0.951057i	0.309017	+	0.951057i
$598$		0			0
$599$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$599$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$600$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$601$	−0.169131	+	0.379874i	−0.169131	+	0.379874i	−0.978148	−	0.207912i	$-0.933333\pi$
$601$	−0.169131	+	0.379874i	−0.169131	+	0.379874i	0.809017	+	0.587785i	$0.200000\pi$
$602$		0			0
$603$		0			0
$604$	1.58268	+	0.336408i	1.58268	+	0.336408i
$605$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$606$		0			0
$607$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$607$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$608$	−1.16913	−	1.60917i	−1.16913	−	1.60917i
$609$		0			0
$610$	−0.773659	+	0.251377i	−0.773659	+	0.251377i
$611$		0			0
$612$	1.28716	−	1.15897i	1.28716	−	1.15897i
$613$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$613$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.169131	−	1.60917i	0.169131	−	1.60917i	−0.500000	−	0.866025i	$-0.666667\pi$
$617$	0.169131	−	1.60917i	0.169131	−	1.60917i	0.669131	−	0.743145i	$-0.266667\pi$
$618$		0			0
$619$	−1.95630			−1.95630			−0.978148	−	0.207912i	$-0.933333\pi$
$619$	−1.95630			−1.95630			−0.978148	+	0.207912i	$0.933333\pi$
$620$	0.978148	−	0.207912i	0.978148	−	0.207912i
$621$	−0.618034			−0.618034
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	1.30902	+	1.45381i	1.30902	+	1.45381i	0.809017	+	0.587785i	$0.200000\pi$
$631$	1.30902	+	1.45381i	1.30902	+	1.45381i	0.500000	+	0.866025i	$0.333333\pi$
$632$	−0.204489	+	0.0434654i	−0.204489	+	0.0434654i
$633$	−0.773659	−	1.73767i	−0.773659	−	1.73767i
$634$	−0.669131	+	1.15897i	−0.669131	+	1.15897i
$635$		0			0
$636$	−0.244415	+	1.14988i	−0.244415	+	1.14988i
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.809017	−	0.587785i	0.809017	−	0.587785i
$641$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$641$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$642$		−	1.90211i		−	1.90211i
$643$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$643$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$644$		0			0
$645$		0			0
$646$	1.06460	−	3.27651i	1.06460	−	3.27651i
$647$	−0.564602	+	1.73767i	−0.564602	+	1.73767i	0.104528	+	0.994522i	$0.466667\pi$
$647$	−0.564602	+	1.73767i	−0.564602	+	1.73767i	−0.669131	+	0.743145i	$0.733333\pi$
$648$	0.500000	+	0.866025i	0.500000	+	0.866025i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	−0.913545	−	0.406737i	$-0.866667\pi$
$653$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	0.104528	+	0.994522i	$0.466667\pi$
$654$	−0.169131	−	1.60917i	−0.169131	−	1.60917i
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$659$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$660$		0			0
$661$	−0.139886	−	1.33093i	−0.139886	−	1.33093i	−0.809017	−	0.587785i	$-0.800000\pi$
$661$	−0.139886	−	1.33093i	−0.139886	−	1.33093i	0.669131	−	0.743145i	$-0.266667\pi$
$662$	1.47815	+	1.07394i	1.47815	+	1.07394i
$663$		0			0
$664$	0.669131	−	1.15897i	0.669131	−	1.15897i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.604528	−	1.86055i	0.604528	−	1.86055i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$673$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$674$		0			0
$675$	0.978148	−	0.207912i	0.978148	−	0.207912i
$676$	0.809017	+	0.587785i	0.809017	+	0.587785i
$677$	1.64728	+	0.951057i	1.64728	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$677$	1.64728	+	0.951057i	1.64728	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$678$	0.104528	−	0.994522i	0.104528	−	0.994522i
$679$		0			0
$680$	1.64728	+	0.535233i	1.64728	+	0.535233i
$681$		−	1.73205i		−	1.73205i
$682$		0			0
$683$			1.98904i			1.98904i	0.104528	+	0.994522i	$0.466667\pi$
$683$			1.98904i			1.98904i	−0.104528	+	0.994522i	$0.533333\pi$
$684$	1.72256	+	0.994522i	1.72256	+	0.994522i
$685$	−0.413545	−	0.0434654i	−0.413545	−	0.0434654i
$686$		0			0
$687$	1.01807	+	0.587785i	1.01807	+	0.587785i
$688$		0			0
$689$		0			0
$690$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$691$	−0.0864545	+	0.406737i	−0.0864545	+	0.406737i	0.913545	+	0.406737i	$0.133333\pi$
$691$	−0.0864545	+	0.406737i	−0.0864545	+	0.406737i	−1.00000			$\pi$
$692$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$693$		0			0
$694$	1.91355	+	0.406737i	1.91355	+	0.406737i
$695$	−1.22256	+	0.544320i	−1.22256	+	0.544320i
$696$		0			0
$697$		0			0
$698$	1.22256	+	0.544320i	1.22256	+	0.544320i
$699$	1.22256	−	1.35779i	1.22256	−	1.35779i
$700$		0			0
$701$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$701$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	1.41355	−	0.459289i	1.41355	−	0.459289i
$706$	−0.604528	−	1.35779i	−0.604528	−	1.35779i
$707$		0			0
$708$		0			0
$709$	−0.395472	−	0.128496i	−0.395472	−	0.128496i	0.104528	−	0.994522i	$-0.466667\pi$
$709$	−0.395472	−	0.128496i	−0.395472	−	0.128496i	−0.500000	+	0.866025i	$0.666667\pi$
$710$		0			0
$711$	0.169131	−	0.122881i	0.169131	−	0.122881i
$712$		0			0
$713$	0.500000	+	0.363271i	0.500000	+	0.363271i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$719$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$720$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$721$		0			0
$722$	2.95630			2.95630
$723$	1.97815	−	0.207912i	1.97815	−	0.207912i
$724$	0.773659	−	1.73767i	0.773659	−	1.73767i
$725$		0			0
$726$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$727$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$727$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$728$		0			0
$729$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$730$		0			0
$731$		0			0
$732$			0.813473i			0.813473i
$733$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$733$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$734$		0			0
$735$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$736$	0.604528	+	0.128496i	0.604528	+	0.128496i
$737$		0			0
$738$		0			0
$739$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$739$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$743$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$744$	0.104528	−	0.994522i	0.104528	−	0.994522i
$745$		0			0
$746$		0			0
$747$	−0.139886	+	1.33093i	−0.139886	+	1.33093i
$748$		0			0
$749$		0			0
$750$	0.669131	+	0.743145i	0.669131	+	0.743145i
$751$	0.0864545	+	0.406737i	0.0864545	+	0.406737i	1.00000			$0$
$751$	0.0864545	+	0.406737i	0.0864545	+	0.406737i	−0.913545	+	0.406737i	$0.866667\pi$
$752$	−0.604528	+	1.35779i	−0.604528	+	1.35779i
$753$		0			0
$754$		0			0
$755$	−1.08268	−	1.20243i	−1.08268	−	1.20243i
$756$		0			0
$757$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$757$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$758$	1.01807	+	0.587785i	1.01807	+	0.587785i
$759$		0			0
$760$			1.98904i			1.98904i
$761$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$761$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1.72256	+	0.181049i	−1.72256	+	0.181049i
$766$	−1.82709			−1.82709
$767$		0			0
$768$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$769$	−0.104528	−	0.181049i	−0.104528	−	0.181049i	0.809017	−	0.587785i	$-0.200000\pi$
$769$	−0.104528	−	0.181049i	−0.104528	−	0.181049i	−0.913545	+	0.406737i	$0.866667\pi$
$770$		0			0
$771$	−0.0646021	+	0.198825i	−0.0646021	+	0.198825i
$772$		0			0
$773$	−1.11803	−	1.53884i	−1.11803	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$773$	−1.11803	−	1.53884i	−1.11803	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$774$		0			0
$775$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	0.435398	+	0.977920i	0.435398	+	0.977920i
$783$		0			0
$784$	0.809017	−	0.587785i	0.809017	−	0.587785i
$785$		0			0
$786$		0			0
$787$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$787$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$788$	1.10453	+	0.994522i	1.10453	+	0.994522i
$789$	−0.139886	+	0.155360i	−0.139886	+	0.155360i
$790$	0.190983	+	0.0850311i	0.190983	+	0.0850311i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	0.873619	−	0.786610i	0.873619	−	0.786610i
$796$	0.500000	+	0.866025i	0.500000	+	0.866025i
$797$	−0.0864545	+	0.406737i	−0.0864545	+	0.406737i	0.913545	+	0.406737i	$0.133333\pi$
$797$	−0.0864545	+	0.406737i	−0.0864545	+	0.406737i	−1.00000			$\pi$
$798$		0			0
$799$	−2.51807	+	0.535233i	−2.51807	+	0.535233i
$800$	−1.00000			−1.00000
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$809$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$810$	0.104528	−	0.994522i	0.104528	−	0.994522i
$811$	−1.01807	−	0.587785i	−1.01807	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$811$	−1.01807	−	0.587785i	−1.01807	−	0.587785i	−0.913545	+	0.406737i	$0.866667\pi$
$812$		0			0
$813$	−1.78716	+	0.379874i	−1.78716	+	0.379874i
$814$		0			0
$815$		0			0
$816$	1.01807	−	1.40126i	1.01807	−	1.40126i
$817$		0			0
$818$	0.309017	−	1.45381i	0.309017	−	1.45381i
$819$		0			0
$820$		0			0
$821$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$821$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$822$	−0.169131	+	0.379874i	−0.169131	+	0.379874i
$823$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$823$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.190983	−	1.81708i	−0.190983	−	1.81708i	−0.500000	−	0.866025i	$-0.666667\pi$
$827$	−0.190983	−	1.81708i	−0.190983	−	1.81708i	0.309017	−	0.951057i	$-0.400000\pi$
$828$	−0.604528	+	0.128496i	−0.604528	+	0.128496i
$829$	1.89169	−	0.614648i	1.89169	−	0.614648i	0.913545	−	0.406737i	$-0.133333\pi$
$829$	1.89169	−	0.614648i	1.89169	−	0.614648i	0.978148	−	0.207912i	$-0.0666667\pi$
$830$	−1.22256	+	0.544320i	−1.22256	+	0.544320i
$831$		0			0
$832$		0			0
$833$	1.64728	+	0.535233i	1.64728	+	0.535233i
$834$	0.139886	+	1.33093i	0.139886	+	1.33093i
$835$	−1.58268	+	1.14988i	−1.58268	+	1.14988i
$836$		0			0
$837$	0.309017	+	0.951057i	0.309017	+	0.951057i
$838$		0			0
$839$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$839$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$840$		0			0
$841$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$842$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$843$		0			0
$844$	−1.11803	−	1.53884i	−1.11803	−	1.53884i
$845$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$846$		−	1.48629i		−	1.48629i
$847$		0			0
$848$			1.17557i			1.17557i
$849$		0			0
$850$	−1.01807	−	1.40126i	−1.01807	−	1.40126i
$851$		0			0
$852$		0			0
$853$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$853$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$854$		0			0
$855$	−0.809017	−	1.81708i	−0.809017	−	1.81708i
$856$	−0.395472	−	1.86055i	−0.395472	−	1.86055i
$857$	0.413545	+	0.459289i	0.413545	+	0.459289i	0.913545	−	0.406737i	$-0.133333\pi$
$857$	0.413545	+	0.459289i	0.413545	+	0.459289i	−0.500000	+	0.866025i	$0.666667\pi$
$858$		0			0
$859$	−0.204489	−	0.0434654i	−0.204489	−	0.0434654i	0.104528	−	0.994522i	$-0.466667\pi$
$859$	−0.204489	−	0.0434654i	−0.204489	−	0.0434654i	−0.309017	+	0.951057i	$0.600000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$863$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$864$	0.669131	+	0.743145i	0.669131	+	0.743145i
$865$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i
$866$		0			0
$867$	2.00000			2.00000
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$873$		0			0
$874$	−0.913545	+	0.822560i	−0.913545	+	0.822560i
$875$		0			0
$876$		0			0
$877$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$877$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$878$	−1.80902	+	0.587785i	−1.80902	+	0.587785i
$879$	1.22256	+	1.35779i	1.22256	+	1.35779i
$880$		0			0
$881$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$881$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$882$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$883$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$883$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$884$		0			0
$885$		0			0
$886$	−0.478148	−	0.658114i	−0.478148	−	0.658114i
$887$	0.773659	−	1.73767i	0.773659	−	1.73767i	0.104528	−	0.994522i	$-0.466667\pi$
$887$	0.773659	−	1.73767i	0.773659	−	1.73767i	0.669131	−	0.743145i	$-0.266667\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.47815	−	2.56023i	−1.47815	−	2.56023i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	0.913545	−	0.406737i	0.913545	−	0.406737i
$901$	−1.64728	+	1.19682i	−1.64728	+	1.19682i
$902$		0			0
$903$		0			0
$904$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$905$	−1.64728	+	0.951057i	−1.64728	+	0.951057i
$906$	−1.47815	+	0.658114i	−1.47815	+	0.658114i
$907$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$907$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$908$	−0.360114	−	1.69420i	−0.360114	−	1.69420i
$909$		0			0
$910$		0			0
$911$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$911$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$912$	1.89169	+	0.614648i	1.89169	+	0.614648i
$913$		0			0
$914$		0			0
$915$	0.478148	−	0.658114i	0.478148	−	0.658114i
$916$	1.11803	+	0.363271i	1.11803	+	0.363271i
$917$		0			0
$918$	−0.360114	+	1.69420i	−0.360114	+	1.69420i
$919$	0.604528	−	0.544320i	0.604528	−	0.544320i	−0.309017	−	0.951057i	$-0.600000\pi$
$919$	0.604528	−	0.544320i	0.604528	−	0.544320i	0.913545	+	0.406737i	$0.133333\pi$
$920$	−0.413545	−	0.459289i	−0.413545	−	0.459289i
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0			−	1.00000i	$-0.5\pi$
$929$		0			0				1.00000i	$0.5\pi$
$930$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$931$			1.98904i			1.98904i
$932$	0.913545	−	1.58231i	0.913545	−	1.58231i
$933$		0			0
$934$	1.16913	+	0.122881i	1.16913	+	0.122881i
$935$		0			0
$936$		0			0
$937$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$937$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$938$		0			0
$939$		0			0
$940$	1.28716	−	0.743145i	1.28716	−	0.743145i
$941$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$941$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.30902	+	1.45381i	−1.30902	+	1.45381i	−0.500000	+	0.866025i	$0.666667\pi$
$947$	−1.30902	+	1.45381i	−1.30902	+	1.45381i	−0.809017	+	0.587785i	$0.800000\pi$
$948$	0.139886	−	0.155360i	0.139886	−	0.155360i
$949$		0			0
$950$	1.16913	−	1.60917i	1.16913	−	1.60917i
$951$	−0.139886	−	1.33093i	−0.139886	−	1.33093i
$952$		0			0
$953$	−0.773659	+	0.251377i	−0.773659	+	0.251377i	−0.669131	−	0.743145i	$-0.733333\pi$
$953$	−0.773659	+	0.251377i	−0.773659	+	0.251377i	−0.104528	+	0.994522i	$0.533333\pi$
$954$	−0.478148	−	1.07394i	−0.478148	−	1.07394i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$961$	0.309017	−	0.951057i	0.309017	−	0.951057i
$962$		0			0
$963$	1.11803	+	1.53884i	1.11803	+	1.53884i
$964$	1.89169	−	0.614648i	1.89169	−	0.614648i
$965$		0			0
$966$		0			0
$967$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$967$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$968$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$969$	1.06460	+	3.27651i	1.06460	+	3.27651i
$970$		0			0
$971$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$971$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$972$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.169131	+	0.795697i	0.169131	+	0.795697i
$977$	0.169131	+	0.122881i	0.169131	+	0.122881i	0.669131	−	0.743145i	$-0.266667\pi$
$977$	0.169131	+	0.122881i	0.169131	+	0.122881i	−0.500000	+	0.866025i	$0.666667\pi$
$978$		0			0
$979$		0			0
$980$	−1.00000			−1.00000
$981$	1.08268	+	1.20243i	1.08268	+	1.20243i
$982$		0			0
$983$	−0.204489	−	0.0434654i	−0.204489	−	0.0434654i	0.104528	−	0.994522i	$-0.466667\pi$
$983$	−0.204489	−	0.0434654i	−0.204489	−	0.0434654i	−0.309017	+	0.951057i	$0.600000\pi$
$984$		0			0
$985$	−0.309017	−	1.45381i	−0.309017	−	1.45381i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−1.33826			−1.33826			−0.669131	−	0.743145i	$-0.733333\pi$
$991$	−1.33826			−1.33826			−0.669131	+	0.743145i	$0.733333\pi$
$992$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$993$	−1.82709			−1.82709
$994$		0			0
$995$	0.104528	−	0.994522i	0.104528	−	0.994522i
$996$	0.139886	+	1.33093i	0.139886	+	1.33093i
$997$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$997$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$998$	−1.08268	−	1.20243i	−1.08268	−	1.20243i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1860.1.df.a.1739.1	yes	8
3.2	odd	2		1860.1.df.d.1739.1	yes	8
4.3	odd	2		1860.1.df.b.1739.1	yes	8
5.4	even	2		1860.1.df.d.1739.1	yes	8
12.11	even	2		1860.1.df.c.1739.1	yes	8
15.14	odd	2	CM	1860.1.df.a.1739.1	yes	8
20.19	odd	2		1860.1.df.c.1739.1	yes	8
31.21	odd	30		1860.1.df.b.1199.1	yes	8
60.59	even	2		1860.1.df.b.1739.1	yes	8
93.83	even	30		1860.1.df.c.1199.1	yes	8
124.83	even	30	inner	1860.1.df.a.1199.1	✓	8
155.114	odd	30		1860.1.df.c.1199.1	yes	8
372.83	odd	30		1860.1.df.d.1199.1	yes	8
465.269	even	30		1860.1.df.b.1199.1	yes	8
620.579	even	30		1860.1.df.d.1199.1	yes	8
1860.1199	odd	30	inner	1860.1.df.a.1199.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1860.1.df.a.1199.1	✓	8	124.83	even	30	inner
1860.1.df.a.1199.1	✓	8	1860.1199	odd	30	inner
1860.1.df.a.1739.1	yes	8	1.1	even	1	trivial
1860.1.df.a.1739.1	yes	8	15.14	odd	2	CM
1860.1.df.b.1199.1	yes	8	31.21	odd	30
1860.1.df.b.1199.1	yes	8	465.269	even	30
1860.1.df.b.1739.1	yes	8	4.3	odd	2
1860.1.df.b.1739.1	yes	8	60.59	even	2
1860.1.df.c.1199.1	yes	8	93.83	even	30
1860.1.df.c.1199.1	yes	8	155.114	odd	30
1860.1.df.c.1739.1	yes	8	12.11	even	2
1860.1.df.c.1739.1	yes	8	20.19	odd	2
1860.1.df.d.1199.1	yes	8	372.83	odd	30
1860.1.df.d.1199.1	yes	8	620.579	even	30
1860.1.df.d.1739.1	yes	8	3.2	odd	2
1860.1.df.d.1739.1	yes	8	5.4	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1860.df (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.669131 + 0.743145i) q^{2} +(0.104528 - 0.994522i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.669131 + 0.743145i) q^{6} +(0.809017 + 0.587785i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(-0.309017 - 0.951057i) q^{10} -1.00000 q^{12} +(0.809017 + 0.587785i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(-1.28716 - 1.15897i) q^{17} +(0.809017 - 0.587785i) q^{18} +(0.809017 - 1.81708i) q^{19} +(0.913545 + 0.406737i) q^{20} +(0.190983 + 0.587785i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.309017 + 0.951057i) q^{27} +(-0.978148 + 0.207912i) q^{30} +(0.809017 - 0.587785i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.72256 - 0.181049i) q^{34} +(-0.104528 + 0.994522i) q^{36} +(0.809017 + 1.81708i) q^{38} +(-0.913545 + 0.406737i) q^{40} +(0.669131 - 0.743145i) q^{45} +(-0.564602 - 0.251377i) q^{46} +(0.873619 - 1.20243i) q^{47} +(0.104528 + 0.994522i) q^{48} +(-0.913545 + 0.406737i) q^{49} +(0.978148 + 0.207912i) q^{50} +(-1.28716 + 1.15897i) q^{51} +(0.244415 - 1.14988i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-1.72256 - 0.994522i) q^{57} +(0.500000 - 0.866025i) q^{60} -0.813473i q^{61} +(-0.104528 + 0.994522i) q^{62} +(0.309017 + 0.951057i) q^{64} +(-1.01807 + 1.40126i) q^{68} +(0.604528 - 0.128496i) q^{69} +(-0.669131 - 0.743145i) q^{72} +(-0.913545 + 0.406737i) q^{75} +(-1.89169 - 0.614648i) q^{76} +(-0.139886 + 0.155360i) q^{79} +(0.309017 - 0.951057i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-0.139886 - 1.33093i) q^{83} +(1.64728 - 0.535233i) q^{85} +(0.104528 + 0.994522i) q^{90} +(0.564602 - 0.251377i) q^{92} +(-0.500000 - 0.866025i) q^{93} +(0.309017 + 1.45381i) q^{94} +(1.16913 + 1.60917i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(0.309017 - 0.951057i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - q^{3} + q^{4} - 4 q^{5} + q^{6} + 2 q^{8} + q^{9} + 2 q^{10} - 8 q^{12} + 2 q^{15} + q^{16} + 3 q^{17} + 2 q^{18} + 2 q^{19} + q^{20} + 6 q^{23} + q^{24} - 4 q^{25} + 2 q^{27} + q^{30}+ \cdots - 2 q^{98}+O(q^{100}) \) 8 * q - q^2 - q^3 + q^4 - 4 * q^5 + q^6 + 2 * q^8 + q^9 + 2 * q^10 - 8 * q^12 + 2 * q^15 + q^16 + 3 * q^17 + 2 * q^18 + 2 * q^19 + q^20 + 6 * q^23 + q^24 - 4 * q^25 + 2 * q^27 + q^30 + 2 * q^31 + 4 * q^32 + 3 * q^34 + q^36 + 2 * q^38 - q^40 + q^45 - 2 * q^46 - q^48 - q^49 - q^50 + 3 * q^51 - 4 * q^54 - 3 * q^57 + 4 * q^60 + q^62 - 2 * q^64 + 3 * q^69 - q^72 - q^75 - q^79 - 2 * q^80 + q^81 - q^83 - q^90 + 2 * q^92 - 4 * q^93 - 2 * q^94 + 5 * q^95 - 2 * q^96 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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