LMFDB - Embedded newform 2025.1.y.a.296.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2025,1,Mod(296,2025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2025, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([25, 18]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("2025.296");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2025 = 3^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2025.y (of order $30$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.01060665058$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{30})$
Coefficient field:	$\Q(\zeta_{60})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - x^{10} - x^{8} - x^{6} + x^{2} + 1 $ x^16 + x^14 - x^10 - x^8 - x^6 + x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 675)
Projective image:	$A_{5}$
Projective field:	Galois closure of 5.1.31640625.2

Embedding invariants

Embedding label			296.1
Root			$0.207912 - 0.978148i$ of defining polynomial
Character	$\chi$	$=$	2025.296
Dual form			2025.1.y.a.431.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.128496 - 0.604528i) q^{2} +(0.564602 - 0.251377i) q^{4} +(-0.207912 + 0.978148i) q^{5} +(-0.309017 - 0.535233i) q^{7} +(-0.587785 - 0.809017i) q^{8} +O(q^{10})$	\(q+(-0.128496 - 0.604528i) q^{2} +(0.564602 - 0.251377i) q^{4} +(-0.207912 + 0.978148i) q^{5} +(-0.309017 - 0.535233i) q^{7} +(-0.587785 - 0.809017i) q^{8} +0.618034 q^{10} +(0.207912 + 0.978148i) q^{11} +(-0.283856 + 0.255585i) q^{14} +(0.587785 + 0.809017i) q^{17} +(0.809017 - 0.587785i) q^{19} +(0.128496 + 0.604528i) q^{20} +(0.564602 - 0.251377i) q^{22} +(0.743145 - 0.669131i) q^{23} +(-0.913545 - 0.406737i) q^{25} +(-0.309017 - 0.224514i) q^{28} +(1.60917 + 0.169131i) q^{29} +(-0.866025 - 0.500000i) q^{32} +(0.413545 - 0.459289i) q^{34} +(0.587785 - 0.190983i) q^{35} +(0.500000 + 1.53884i) q^{37} +(-0.459289 - 0.413545i) q^{38} +(0.913545 - 0.406737i) q^{40} +(0.207912 - 0.978148i) q^{41} +(0.363271 + 0.500000i) q^{44} +(-0.500000 - 0.363271i) q^{46} +(-1.60917 - 0.169131i) q^{47} +(0.309017 - 0.535233i) q^{49} +(-0.128496 + 0.604528i) q^{50} +(0.363271 - 0.500000i) q^{53} -1.00000 q^{55} +(-0.251377 + 0.564602i) q^{56} +(-0.104528 - 0.994522i) q^{58} +(0.978148 - 0.207912i) q^{61} +(-0.190983 + 0.587785i) q^{64} +(-0.0646021 - 0.614648i) q^{67} +(0.535233 + 0.309017i) q^{68} +(-0.190983 - 0.330792i) q^{70} +(-0.951057 + 1.30902i) q^{71} +(0.866025 - 0.500000i) q^{74} +(0.309017 - 0.535233i) q^{76} +(0.459289 - 0.413545i) q^{77} +(-0.169131 + 1.60917i) q^{79} -0.618034 q^{82} +(0.251377 - 0.564602i) q^{83} +(-0.913545 + 0.406737i) q^{85} +(0.669131 - 0.743145i) q^{88} +(-0.951057 - 0.309017i) q^{89} +(0.251377 - 0.564602i) q^{92} +(0.104528 + 0.994522i) q^{94} +(0.406737 + 0.913545i) q^{95} +(-0.104528 + 0.994522i) q^{97} +(-0.363271 - 0.118034i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 4 q^{7}+O(q^{10}) $ 16 * q + 4 * q^4 + 4 * q^7	$ 16 q + 4 q^{4} + 4 q^{7} - 8 q^{10} + 4 q^{19} + 4 q^{22} - 2 q^{25} + 4 q^{28} - 6 q^{34} + 8 q^{37} + 2 q^{40} - 8 q^{46} - 4 q^{49} - 16 q^{55} + 2 q^{58} - 2 q^{61} - 12 q^{64} + 4 q^{67} - 12 q^{70} - 4 q^{76} + 6 q^{79} + 8 q^{82} - 2 q^{85} + 2 q^{88} - 2 q^{94} + 2 q^{97}+O(q^{100}) $ 16 * q + 4 * q^4 + 4 * q^7 - 8 * q^10 + 4 * q^19 + 4 * q^22 - 2 * q^25 + 4 * q^28 - 6 * q^34 + 8 * q^37 + 2 * q^40 - 8 * q^46 - 4 * q^49 - 16 * q^55 + 2 * q^58 - 2 * q^61 - 12 * q^64 + 4 * q^67 - 12 * q^70 - 4 * q^76 + 6 * q^79 + 8 * q^82 - 2 * q^85 + 2 * q^88 - 2 * q^94 + 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2025\mathbb{Z}\right)^\times$.

$n$	$326$	$1702$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.128496	−	0.604528i	−0.128496	−	0.604528i	−0.994522	−	0.104528i	$-0.966667\pi$
$2$	−0.128496	−	0.604528i	−0.128496	−	0.604528i	0.866025	−	0.500000i	$-0.166667\pi$
$3$		0			0
$3$		0			0
$4$	0.564602	−	0.251377i	0.564602	−	0.251377i
$5$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$5$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$6$		0			0
$7$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$7$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$8$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$9$		0			0
$10$	0.618034			0.618034
$11$	0.207912	+	0.978148i	0.207912	+	0.978148i	0.951057	+	0.309017i	$0.100000\pi$
$11$	0.207912	+	0.978148i	0.207912	+	0.978148i	−0.743145	+	0.669131i	$0.766667\pi$
$12$		0			0
$13$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$13$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$14$	−0.283856	+	0.255585i	−0.283856	+	0.255585i
$15$		0			0
$16$		0			0
$17$	0.587785	+	0.809017i	0.587785	+	0.809017i	0.994522	−	0.104528i	$-0.0333333\pi$
$17$	0.587785	+	0.809017i	0.587785	+	0.809017i	−0.406737	+	0.913545i	$0.633333\pi$
$18$		0			0
$19$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$19$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$20$	0.128496	+	0.604528i	0.128496	+	0.604528i
$21$		0			0
$22$	0.564602	−	0.251377i	0.564602	−	0.251377i
$23$	0.743145	−	0.669131i	0.743145	−	0.669131i	−0.207912	−	0.978148i	$-0.566667\pi$
$23$	0.743145	−	0.669131i	0.743145	−	0.669131i	0.951057	+	0.309017i	$0.100000\pi$
$24$		0			0
$25$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$26$		0			0
$27$		0			0
$28$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$29$	1.60917	+	0.169131i	1.60917	+	0.169131i	0.866025	−	0.500000i	$-0.166667\pi$
$29$	1.60917	+	0.169131i	1.60917	+	0.169131i	0.743145	+	0.669131i	$0.233333\pi$
$30$		0			0
$31$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$31$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$32$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$33$		0			0
$34$	0.413545	−	0.459289i	0.413545	−	0.459289i
$35$	0.587785	−	0.190983i	0.587785	−	0.190983i
$36$		0			0
$37$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$37$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$38$	−0.459289	−	0.413545i	−0.459289	−	0.413545i
$39$		0			0
$40$	0.913545	−	0.406737i	0.913545	−	0.406737i
$41$	0.207912	−	0.978148i	0.207912	−	0.978148i	−0.743145	−	0.669131i	$-0.766667\pi$
$41$	0.207912	−	0.978148i	0.207912	−	0.978148i	0.951057	−	0.309017i	$-0.100000\pi$
$42$		0			0
$43$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$43$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$44$	0.363271	+	0.500000i	0.363271	+	0.500000i
$45$		0			0
$46$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$47$	−1.60917	−	0.169131i	−1.60917	−	0.169131i	−0.743145	−	0.669131i	$-0.766667\pi$
$47$	−1.60917	−	0.169131i	−1.60917	−	0.169131i	−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$	0.309017	−	0.535233i	0.309017	−	0.535233i
$50$	−0.128496	+	0.604528i	−0.128496	+	0.604528i
$51$		0			0
$52$		0			0
$53$	0.363271	−	0.500000i	0.363271	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$53$	0.363271	−	0.500000i	0.363271	−	0.500000i	0.951057	+	0.309017i	$0.100000\pi$
$54$		0			0
$55$	−1.00000			−1.00000
$56$	−0.251377	+	0.564602i	−0.251377	+	0.564602i
$57$		0			0
$58$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$59$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$59$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$60$		0			0
$61$	0.978148	−	0.207912i	0.978148	−	0.207912i	0.309017	−	0.951057i	$-0.400000\pi$
$61$	0.978148	−	0.207912i	0.978148	−	0.207912i	0.669131	+	0.743145i	$0.266667\pi$
$62$		0			0
$63$		0			0
$64$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$65$		0			0
$66$		0			0
$67$	−0.0646021	−	0.614648i	−0.0646021	−	0.614648i	−0.978148	−	0.207912i	$-0.933333\pi$
$67$	−0.0646021	−	0.614648i	−0.0646021	−	0.614648i	0.913545	−	0.406737i	$-0.133333\pi$
$68$	0.535233	+	0.309017i	0.535233	+	0.309017i
$69$		0			0
$70$	−0.190983	−	0.330792i	−0.190983	−	0.330792i
$71$	−0.951057	+	1.30902i	−0.951057	+	1.30902i			1.00000i	$0.5\pi$
$71$	−0.951057	+	1.30902i	−0.951057	+	1.30902i	−0.951057	+	0.309017i	$0.900000\pi$
$72$		0			0
$73$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$73$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$74$	0.866025	−	0.500000i	0.866025	−	0.500000i
$75$		0			0
$76$	0.309017	−	0.535233i	0.309017	−	0.535233i
$77$	0.459289	−	0.413545i	0.459289	−	0.413545i
$78$		0			0
$79$	−0.169131	+	1.60917i	−0.169131	+	1.60917i	0.500000	+	0.866025i	$0.333333\pi$
$79$	−0.169131	+	1.60917i	−0.169131	+	1.60917i	−0.669131	+	0.743145i	$0.733333\pi$
$80$		0			0
$81$		0			0
$82$	−0.618034			−0.618034
$83$	0.251377	−	0.564602i	0.251377	−	0.564602i	−0.743145	−	0.669131i	$-0.766667\pi$
$83$	0.251377	−	0.564602i	0.251377	−	0.564602i	0.994522	+	0.104528i	$0.0333333\pi$
$84$		0			0
$85$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$86$		0			0
$87$		0			0
$88$	0.669131	−	0.743145i	0.669131	−	0.743145i
$89$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.207912	−	0.978148i	$-0.566667\pi$
$89$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.743145	+	0.669131i	$0.766667\pi$
$90$		0			0
$91$		0			0
$92$	0.251377	−	0.564602i	0.251377	−	0.564602i
$93$		0			0
$94$	0.104528	+	0.994522i	0.104528	+	0.994522i
$95$	0.406737	+	0.913545i	0.406737	+	0.913545i
$96$		0			0
$97$	−0.104528	+	0.994522i	−0.104528	+	0.994522i	0.809017	+	0.587785i	$0.200000\pi$
$97$	−0.104528	+	0.994522i	−0.104528	+	0.994522i	−0.913545	+	0.406737i	$0.866667\pi$
$98$	−0.363271	−	0.118034i	−0.363271	−	0.118034i
$99$		0			0
$100$	−0.618034			−0.618034
$101$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$101$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$102$		0			0
$103$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$103$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$104$		0			0
$105$		0			0
$106$	−0.348943	−	0.155360i	−0.348943	−	0.155360i
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$		0			0
$109$	0.309017	+	0.951057i	0.309017	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$109$	0.309017	+	0.951057i	0.309017	+	0.951057i	−0.669131	+	0.743145i	$0.733333\pi$
$110$	0.128496	+	0.604528i	0.128496	+	0.604528i
$111$		0			0
$112$		0			0
$113$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$113$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$114$		0			0
$115$	0.500000	+	0.866025i	0.500000	+	0.866025i
$116$	0.951057	−	0.309017i	0.951057	−	0.309017i
$117$		0			0
$118$		0			0
$119$	0.251377	−	0.564602i	0.251377	−	0.564602i
$120$		0			0
$121$		0			0
$122$	−0.251377	−	0.564602i	−0.251377	−	0.564602i
$123$		0			0
$124$		0			0
$125$	0.587785	−	0.809017i	0.587785	−	0.809017i
$126$		0			0
$127$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$127$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$128$	−0.614648	−	0.0646021i	−0.614648	−	0.0646021i
$129$		0			0
$130$		0			0
$131$	−1.60917	+	0.169131i	−1.60917	+	0.169131i	−0.866025	−	0.500000i	$-0.833333\pi$
$131$	−1.60917	+	0.169131i	−1.60917	+	0.169131i	−0.743145	+	0.669131i	$0.766667\pi$
$132$		0			0
$133$	−0.564602	−	0.251377i	−0.564602	−	0.251377i
$134$	−0.363271	+	0.118034i	−0.363271	+	0.118034i
$135$		0			0
$136$	0.309017	−	0.951057i	0.309017	−	0.951057i
$137$	−0.743145	−	0.669131i	−0.743145	−	0.669131i	0.207912	−	0.978148i	$-0.433333\pi$
$137$	−0.743145	−	0.669131i	−0.743145	−	0.669131i	−0.951057	+	0.309017i	$0.900000\pi$
$138$		0			0
$139$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	0.309017	−	0.951057i	$-0.400000\pi$
$139$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	−0.978148	+	0.207912i	$0.933333\pi$
$140$	0.283856	−	0.255585i	0.283856	−	0.255585i
$141$		0			0
$142$	0.913545	+	0.406737i	0.913545	+	0.406737i
$143$		0			0
$144$		0			0
$145$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$146$		0			0
$147$		0			0
$148$	0.669131	+	0.743145i	0.669131	+	0.743145i
$149$	0.535233	+	0.309017i	0.535233	+	0.309017i	0.743145	−	0.669131i	$-0.233333\pi$
$149$	0.535233	+	0.309017i	0.535233	+	0.309017i	−0.207912	+	0.978148i	$0.566667\pi$
$150$		0			0
$151$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$151$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$152$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$153$		0			0
$154$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$155$		0			0
$156$		0			0
$157$	−0.809017	+	1.40126i	−0.809017	+	1.40126i	0.104528	+	0.994522i	$0.466667\pi$
$157$	−0.809017	+	1.40126i	−0.809017	+	1.40126i	−0.913545	+	0.406737i	$0.866667\pi$
$158$	0.994522	−	0.104528i	0.994522	−	0.104528i
$159$		0			0
$160$	0.669131	−	0.743145i	0.669131	−	0.743145i
$161$	−0.587785	−	0.190983i	−0.587785	−	0.190983i
$162$		0			0
$163$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$163$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$164$	−0.128496	−	0.604528i	−0.128496	−	0.604528i
$165$		0			0
$166$	−0.373619	−	0.0794152i	−0.373619	−	0.0794152i
$167$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$167$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$168$		0			0
$169$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$170$	0.363271	+	0.500000i	0.363271	+	0.500000i
$171$		0			0
$172$		0			0
$173$	−0.336408	−	1.58268i	−0.336408	−	1.58268i	−0.743145	−	0.669131i	$-0.766667\pi$
$173$	−0.336408	−	1.58268i	−0.336408	−	1.58268i	0.406737	−	0.913545i	$-0.366667\pi$
$174$		0			0
$175$	0.0646021	+	0.614648i	0.0646021	+	0.614648i
$176$		0			0
$177$		0			0
$178$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i
$179$	0.951057	−	1.30902i	0.951057	−	1.30902i		−	1.00000i	$-0.5\pi$
$179$	0.951057	−	1.30902i	0.951057	−	1.30902i	0.951057	−	0.309017i	$-0.100000\pi$
$180$		0			0
$181$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	−0.913545	−	0.406737i	$-0.866667\pi$
$181$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	0.104528	+	0.994522i	$0.466667\pi$
$182$		0			0
$183$		0			0
$184$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$185$	−1.60917	+	0.169131i	−1.60917	+	0.169131i
$186$		0			0
$187$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$188$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$189$		0			0
$190$	0.500000	−	0.363271i	0.500000	−	0.363271i
$191$	−0.459289	−	0.413545i	−0.459289	−	0.413545i	0.406737	−	0.913545i	$-0.366667\pi$
$191$	−0.459289	−	0.413545i	−0.459289	−	0.413545i	−0.866025	+	0.500000i	$0.833333\pi$
$192$		0			0
$193$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$193$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$194$	0.614648	−	0.0646021i	0.614648	−	0.0646021i
$195$		0			0
$196$	0.0399263	−	0.379874i	0.0399263	−	0.379874i
$197$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$197$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	0.207912	+	0.978148i	0.207912	+	0.978148i
$201$		0			0
$202$	0.413545	+	0.459289i	0.413545	+	0.459289i
$203$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$204$		0			0
$205$	0.913545	+	0.406737i	0.913545	+	0.406737i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.743145	+	0.669131i	0.743145	+	0.669131i
$210$		0			0
$211$	−0.413545	−	0.459289i	−0.413545	−	0.459289i	0.500000	−	0.866025i	$-0.333333\pi$
$211$	−0.413545	−	0.459289i	−0.413545	−	0.459289i	−0.913545	+	0.406737i	$0.866667\pi$
$212$	0.0794152	−	0.373619i	0.0794152	−	0.373619i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	0.535233	−	0.309017i	0.535233	−	0.309017i
$219$		0			0
$220$	−0.564602	+	0.251377i	−0.564602	+	0.251377i
$221$		0			0
$222$		0			0
$223$	0.604528	−	0.128496i	0.604528	−	0.128496i	0.104528	−	0.994522i	$-0.466667\pi$
$223$	0.604528	−	0.128496i	0.604528	−	0.128496i	0.500000	+	0.866025i	$0.333333\pi$
$224$			0.618034i			0.618034i
$225$		0			0
$226$		0			0
$227$	0.128496	+	0.604528i	0.128496	+	0.604528i	0.994522	+	0.104528i	$0.0333333\pi$
$227$	0.128496	+	0.604528i	0.128496	+	0.604528i	−0.866025	+	0.500000i	$0.833333\pi$
$228$		0			0
$229$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$229$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$230$	0.459289	−	0.413545i	0.459289	−	0.413545i
$231$		0			0
$232$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$233$	0.587785	+	0.809017i	0.587785	+	0.809017i	0.994522	−	0.104528i	$-0.0333333\pi$
$233$	0.587785	+	0.809017i	0.587785	+	0.809017i	−0.406737	+	0.913545i	$0.633333\pi$
$234$		0			0
$235$	0.500000	−	1.53884i	0.500000	−	1.53884i
$236$		0			0
$237$		0			0
$238$	−0.373619	−	0.0794152i	−0.373619	−	0.0794152i
$239$	0.459289	−	0.413545i	0.459289	−	0.413545i	−0.406737	−	0.913545i	$-0.633333\pi$
$239$	0.459289	−	0.413545i	0.459289	−	0.413545i	0.866025	+	0.500000i	$0.166667\pi$
$240$		0			0
$241$	−1.08268	+	1.20243i	−1.08268	+	1.20243i	−0.104528	+	0.994522i	$0.533333\pi$
$241$	−1.08268	+	1.20243i	−1.08268	+	1.20243i	−0.978148	+	0.207912i	$0.933333\pi$
$242$		0			0
$243$		0			0
$244$	0.500000	−	0.363271i	0.500000	−	0.363271i
$245$	0.459289	+	0.413545i	0.459289	+	0.413545i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	−0.564602	−	0.251377i	−0.564602	−	0.251377i
$251$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$251$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$252$		0			0
$253$	0.809017	+	0.587785i	0.809017	+	0.587785i
$254$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$255$		0			0
$256$	0.104528	+	0.994522i	0.104528	+	0.994522i
$257$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$257$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$258$		0			0
$259$	0.669131	−	0.743145i	0.669131	−	0.743145i
$260$		0			0
$261$		0			0
$262$	0.309017	+	0.951057i	0.309017	+	0.951057i
$263$	0.743145	+	0.669131i	0.743145	+	0.669131i	0.951057	−	0.309017i	$-0.100000\pi$
$263$	0.743145	+	0.669131i	0.743145	+	0.669131i	−0.207912	+	0.978148i	$0.566667\pi$
$264$		0			0
$265$	0.413545	+	0.459289i	0.413545	+	0.459289i
$266$	−0.0794152	+	0.373619i	−0.0794152	+	0.373619i
$267$		0			0
$268$	−0.190983	−	0.330792i	−0.190983	−	0.330792i
$269$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	0.406737	−	0.913545i	$-0.366667\pi$
$269$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	−0.994522	+	0.104528i	$0.966667\pi$
$270$		0			0
$271$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	0.104528	−	0.994522i	$-0.466667\pi$
$271$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	−0.913545	+	0.406737i	$0.866667\pi$
$272$		0			0
$273$		0			0
$274$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$275$	0.207912	−	0.978148i	0.207912	−	0.978148i
$276$		0			0
$277$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$277$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$278$	−0.363271	+	0.500000i	−0.363271	+	0.500000i
$279$		0			0
$280$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$281$	−0.406737	+	0.913545i	−0.406737	+	0.913545i	0.587785	+	0.809017i	$0.300000\pi$
$281$	−0.406737	+	0.913545i	−0.406737	+	0.913545i	−0.994522	+	0.104528i	$0.966667\pi$
$282$		0			0
$283$	0.104528	+	0.994522i	0.104528	+	0.994522i	0.913545	+	0.406737i	$0.133333\pi$
$283$	0.104528	+	0.994522i	0.104528	+	0.994522i	−0.809017	+	0.587785i	$0.800000\pi$
$284$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$285$		0			0
$286$		0			0
$287$	−0.587785	+	0.190983i	−0.587785	+	0.190983i
$288$		0			0
$289$		0			0
$290$	0.994522	+	0.104528i	0.994522	+	0.104528i
$291$		0			0
$292$		0			0
$293$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$293$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$294$		0			0
$295$		0			0
$296$	0.951057	−	1.30902i	0.951057	−	1.30902i
$297$		0			0
$298$	0.118034	−	0.363271i	0.118034	−	0.363271i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$			1.00000i			1.00000i
$306$		0			0
$307$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$307$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$308$	0.155360	−	0.348943i	0.155360	−	0.348943i
$309$		0			0
$310$		0			0
$311$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	−0.951057	−	0.309017i	$-0.900000\pi$
$311$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	0.207912	+	0.978148i	$0.433333\pi$
$312$		0			0
$313$	−0.413545	+	0.459289i	−0.413545	+	0.459289i	−0.913545	−	0.406737i	$-0.866667\pi$
$313$	−0.413545	+	0.459289i	−0.413545	+	0.459289i	0.500000	+	0.866025i	$0.333333\pi$
$314$	0.951057	+	0.309017i	0.951057	+	0.309017i
$315$		0			0
$316$	0.309017	+	0.951057i	0.309017	+	0.951057i
$317$	−0.251377	+	0.564602i	−0.251377	+	0.564602i	−0.994522	−	0.104528i	$-0.966667\pi$
$317$	−0.251377	+	0.564602i	−0.251377	+	0.564602i	0.743145	+	0.669131i	$0.233333\pi$
$318$		0			0
$319$	0.169131	+	1.60917i	0.169131	+	1.60917i
$320$	−0.535233	−	0.309017i	−0.535233	−	0.309017i
$321$		0			0
$322$	−0.0399263	+	0.379874i	−0.0399263	+	0.379874i
$323$	0.951057	+	0.309017i	0.951057	+	0.309017i
$324$		0			0
$325$		0			0
$326$	−0.535233	+	0.309017i	−0.535233	+	0.309017i
$327$		0			0
$328$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$329$	0.406737	+	0.913545i	0.406737	+	0.913545i
$330$		0			0
$331$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$331$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$332$		−	0.381966i		−	0.381966i
$333$		0			0
$334$		0			0
$335$	0.614648	+	0.0646021i	0.614648	+	0.0646021i
$336$		0			0
$337$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$337$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$338$	−0.128496	+	0.604528i	−0.128496	+	0.604528i
$339$		0			0
$340$	−0.413545	+	0.459289i	−0.413545	+	0.459289i
$341$		0			0
$342$		0			0
$343$	−1.00000			−1.00000
$344$		0			0
$345$		0			0
$346$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$347$	0.406737	+	0.913545i	0.406737	+	0.913545i	0.994522	+	0.104528i	$0.0333333\pi$
$347$	0.406737	+	0.913545i	0.406737	+	0.913545i	−0.587785	+	0.809017i	$0.700000\pi$
$348$		0			0
$349$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$349$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$350$	0.363271	−	0.118034i	0.363271	−	0.118034i
$351$		0			0
$352$	0.309017	−	0.951057i	0.309017	−	0.951057i
$353$	0.614648	+	0.0646021i	0.614648	+	0.0646021i	0.406737	−	0.913545i	$-0.366667\pi$
$353$	0.614648	+	0.0646021i	0.614648	+	0.0646021i	0.207912	+	0.978148i	$0.433333\pi$
$354$		0			0
$355$	−1.08268	−	1.20243i	−1.08268	−	1.20243i
$356$	−0.614648	+	0.0646021i	−0.614648	+	0.0646021i
$357$		0			0
$358$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$359$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.207912	−	0.978148i	$-0.433333\pi$
$359$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.743145	+	0.669131i	$0.233333\pi$
$360$		0			0
$361$		0			0
$362$	0.459289	+	0.413545i	0.459289	+	0.413545i
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$	0.913545	+	0.406737i	0.913545	+	0.406737i	0.809017	−	0.587785i	$-0.200000\pi$
$367$	0.913545	+	0.406737i	0.913545	+	0.406737i	0.104528	+	0.994522i	$0.466667\pi$
$368$		0			0
$369$		0			0
$370$	0.309017	+	0.951057i	0.309017	+	0.951057i
$371$	−0.379874	−	0.0399263i	−0.379874	−	0.0399263i
$372$		0			0
$373$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	0.309017	−	0.951057i	$-0.400000\pi$
$373$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	−0.978148	+	0.207912i	$0.933333\pi$
$374$	0.535233	+	0.309017i	0.535233	+	0.309017i
$375$		0			0
$376$	0.809017	+	1.40126i	0.809017	+	1.40126i
$377$		0			0
$378$		0			0
$379$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$379$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$380$	0.459289	+	0.413545i	0.459289	+	0.413545i
$381$		0			0
$382$	−0.190983	+	0.330792i	−0.190983	+	0.330792i
$383$	−1.60917	+	0.169131i	−1.60917	+	0.169131i	−0.866025	−	0.500000i	$-0.833333\pi$
$383$	−1.60917	+	0.169131i	−1.60917	+	0.169131i	−0.743145	+	0.669131i	$0.766667\pi$
$384$		0			0
$385$	0.309017	+	0.535233i	0.309017	+	0.535233i
$386$	0.587785	+	0.190983i	0.587785	+	0.190983i
$387$		0			0
$388$	0.190983	+	0.587785i	0.190983	+	0.587785i
$389$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$389$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$390$		0			0
$391$	0.978148	+	0.207912i	0.978148	+	0.207912i
$392$	−0.614648	+	0.0646021i	−0.614648	+	0.0646021i
$393$		0			0
$394$		0			0
$395$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$396$		0			0
$397$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$397$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	0.535233	+	0.309017i	0.535233	+	0.309017i	0.743145	−	0.669131i	$-0.233333\pi$
$401$	0.535233	+	0.309017i	0.535233	+	0.309017i	−0.207912	+	0.978148i	$0.566667\pi$
$402$		0			0
$403$		0			0
$404$	−0.363271	+	0.500000i	−0.363271	+	0.500000i
$405$		0			0
$406$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$407$	−1.40126	+	0.809017i	−1.40126	+	0.809017i
$408$		0			0
$409$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$409$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$410$	0.128496	−	0.604528i	0.128496	−	0.604528i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	0.500000	+	0.363271i	0.500000	+	0.363271i
$416$		0			0
$417$		0			0
$418$	0.309017	−	0.535233i	0.309017	−	0.535233i
$419$	0.614648	−	0.0646021i	0.614648	−	0.0646021i	0.207912	−	0.978148i	$-0.433333\pi$
$419$	0.614648	−	0.0646021i	0.614648	−	0.0646021i	0.406737	+	0.913545i	$0.366667\pi$
$420$		0			0
$421$	0.104528	−	0.994522i	0.104528	−	0.994522i	−0.809017	−	0.587785i	$-0.800000\pi$
$421$	0.104528	−	0.994522i	0.104528	−	0.994522i	0.913545	−	0.406737i	$-0.133333\pi$
$422$	−0.224514	+	0.309017i	−0.224514	+	0.309017i
$423$		0			0
$424$	−0.618034			−0.618034
$425$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$426$		0			0
$427$	−0.413545	−	0.459289i	−0.413545	−	0.459289i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$431$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$432$		0			0
$433$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	−0.913545	−	0.406737i	$-0.866667\pi$
$433$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	0.104528	+	0.994522i	$0.466667\pi$
$434$		0			0
$435$		0			0
$436$	0.413545	+	0.459289i	0.413545	+	0.459289i
$437$	0.207912	−	0.978148i	0.207912	−	0.978148i
$438$		0			0
$439$	0.978148	−	0.207912i	0.978148	−	0.207912i	0.309017	−	0.951057i	$-0.400000\pi$
$439$	0.978148	−	0.207912i	0.978148	−	0.207912i	0.669131	+	0.743145i	$0.266667\pi$
$440$	0.587785	+	0.809017i	0.587785	+	0.809017i
$441$		0			0
$442$		0			0
$443$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$443$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$444$		0			0
$445$	0.500000	−	0.866025i	0.500000	−	0.866025i
$446$	−0.155360	−	0.348943i	−0.155360	−	0.348943i
$447$		0			0
$448$	0.373619	−	0.0794152i	0.373619	−	0.0794152i
$449$		−	1.61803i		−	1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$449$		−	1.61803i		−	1.61803i	0.587785	−	0.809017i	$-0.300000\pi$
$450$		0			0
$451$	1.00000			1.00000
$452$		0			0
$453$		0			0
$454$	0.348943	−	0.155360i	0.348943	−	0.155360i
$455$		0			0
$456$		0			0
$457$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$457$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$458$		0			0
$459$		0			0
$460$	0.500000	+	0.363271i	0.500000	+	0.363271i
$461$	−0.207912	−	0.978148i	−0.207912	−	0.978148i	−0.951057	−	0.309017i	$-0.900000\pi$
$461$	−0.207912	−	0.978148i	−0.207912	−	0.978148i	0.743145	−	0.669131i	$-0.233333\pi$
$462$		0			0
$463$	0.978148	+	0.207912i	0.978148	+	0.207912i	0.669131	−	0.743145i	$-0.266667\pi$
$463$	0.978148	+	0.207912i	0.978148	+	0.207912i	0.309017	+	0.951057i	$0.400000\pi$
$464$		0			0
$465$		0			0
$466$	0.413545	−	0.459289i	0.413545	−	0.459289i
$467$	−0.951057	−	1.30902i	−0.951057	−	1.30902i	−0.951057	−	0.309017i	$-0.900000\pi$
$467$	−0.951057	−	1.30902i	−0.951057	−	1.30902i		−	1.00000i	$-0.5\pi$
$468$		0			0
$469$	−0.309017	+	0.224514i	−0.309017	+	0.224514i
$470$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$476$		−	0.381966i		−	0.381966i
$477$		0			0
$478$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$479$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$479$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$480$		0			0
$481$		0			0
$482$	0.866025	+	0.500000i	0.866025	+	0.500000i
$483$		0			0
$484$		0			0
$485$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$486$		0			0
$487$	0.309017	+	0.951057i	0.309017	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$487$	0.309017	+	0.951057i	0.309017	+	0.951057i	−0.669131	+	0.743145i	$0.733333\pi$
$488$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$489$		0			0
$490$	0.190983	−	0.330792i	0.190983	−	0.330792i
$491$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$491$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$492$		0			0
$493$	0.809017	+	1.40126i	0.809017	+	1.40126i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.994522	+	0.104528i	0.994522	+	0.104528i
$498$		0			0
$499$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$499$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$500$	0.128496	−	0.604528i	0.128496	−	0.604528i
$501$		0			0
$502$	0.604528	−	0.128496i	0.604528	−	0.128496i
$503$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$503$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$504$		0			0
$505$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$506$	0.251377	−	0.564602i	0.251377	−	0.564602i
$507$		0			0
$508$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$509$	0.128496	−	0.604528i	0.128496	−	0.604528i	−0.866025	−	0.500000i	$-0.833333\pi$
$509$	0.128496	−	0.604528i	0.128496	−	0.604528i	0.994522	−	0.104528i	$-0.0333333\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−0.169131	−	1.60917i	−0.169131	−	1.60917i
$518$	−0.535233	−	0.309017i	−0.535233	−	0.309017i
$519$		0			0
$520$		0			0
$521$	0.363271	−	0.500000i	0.363271	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$521$	0.363271	−	0.500000i	0.363271	−	0.500000i	0.951057	+	0.309017i	$0.100000\pi$
$522$		0			0
$523$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$523$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$524$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$525$		0			0
$526$	0.309017	−	0.535233i	0.309017	−	0.535233i
$527$		0			0
$528$		0			0
$529$		0			0
$530$	0.224514	−	0.309017i	0.224514	−	0.309017i
$531$		0			0
$532$	−0.381966			−0.381966
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−0.459289	+	0.413545i	−0.459289	+	0.413545i
$537$		0			0
$538$	−0.413545	+	0.459289i	−0.413545	+	0.459289i
$539$	0.587785	+	0.190983i	0.587785	+	0.190983i
$540$		0			0
$541$	0.309017	+	0.951057i	0.309017	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$541$	0.309017	+	0.951057i	0.309017	+	0.951057i	−0.669131	+	0.743145i	$0.733333\pi$
$542$	−0.251377	+	0.564602i	−0.251377	+	0.564602i
$543$		0			0
$544$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$545$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$546$		0			0
$547$	0.104528	−	0.994522i	0.104528	−	0.994522i	−0.809017	−	0.587785i	$-0.800000\pi$
$547$	0.104528	−	0.994522i	0.104528	−	0.994522i	0.913545	−	0.406737i	$-0.133333\pi$
$548$	−0.587785	−	0.190983i	−0.587785	−	0.190983i
$549$		0			0
$550$	−0.618034			−0.618034
$551$	1.40126	−	0.809017i	1.40126	−	0.809017i
$552$		0			0
$553$	0.913545	−	0.406737i	0.913545	−	0.406737i
$554$		0			0
$555$		0			0
$556$	−0.564602	−	0.251377i	−0.564602	−	0.251377i
$557$			1.61803i			1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$557$			1.61803i			1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.604528	+	0.128496i	0.604528	+	0.128496i
$563$	0.128496	−	0.604528i	0.128496	−	0.604528i	−0.866025	−	0.500000i	$-0.833333\pi$
$563$	0.128496	−	0.604528i	0.128496	−	0.604528i	0.994522	−	0.104528i	$-0.0333333\pi$
$564$		0			0
$565$		0			0
$566$	0.587785	−	0.190983i	0.587785	−	0.190983i
$567$		0			0
$568$	1.61803			1.61803
$569$	−0.251377	+	0.564602i	−0.251377	+	0.564602i	−0.994522	−	0.104528i	$-0.966667\pi$
$569$	−0.251377	+	0.564602i	−0.251377	+	0.564602i	0.743145	+	0.669131i	$0.233333\pi$
$570$		0			0
$571$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$571$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$572$		0			0
$573$		0			0
$574$	0.190983	+	0.330792i	0.190983	+	0.330792i
$575$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$576$		0			0
$577$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$577$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$578$		0			0
$579$		0			0
$580$	0.104528	+	0.994522i	0.104528	+	0.994522i
$581$	−0.379874	+	0.0399263i	−0.379874	+	0.0399263i
$582$		0			0
$583$	0.564602	+	0.251377i	0.564602	+	0.251377i
$584$		0			0
$585$		0			0
$586$	0.190983	−	0.587785i	0.190983	−	0.587785i
$587$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$587$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$593$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$594$		0			0
$595$	0.500000	+	0.363271i	0.500000	+	0.363271i
$596$	0.379874	+	0.0399263i	0.379874	+	0.0399263i
$597$		0			0
$598$		0			0
$599$	−0.535233	−	0.309017i	−0.535233	−	0.309017i	0.207912	−	0.978148i	$-0.433333\pi$
$599$	−0.535233	−	0.309017i	−0.535233	−	0.309017i	−0.743145	+	0.669131i	$0.766667\pi$
$600$		0			0
$601$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$601$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$607$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$608$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$609$		0			0
$610$	0.604528	−	0.128496i	0.604528	−	0.128496i
$611$		0			0
$612$		0			0
$613$	0.309017	+	0.951057i	0.309017	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$613$	0.309017	+	0.951057i	0.309017	+	0.951057i	−0.669131	+	0.743145i	$0.733333\pi$
$614$	0.207912	+	0.978148i	0.207912	+	0.978148i
$615$		0			0
$616$	−0.604528	−	0.128496i	−0.604528	−	0.128496i
$617$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.406737	−	0.913545i	$-0.366667\pi$
$617$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.587785	+	0.809017i	$0.300000\pi$
$618$		0			0
$619$	−0.564602	−	0.251377i	−0.564602	−	0.251377i	0.104528	−	0.994522i	$-0.466667\pi$
$619$	−0.564602	−	0.251377i	−0.564602	−	0.251377i	−0.669131	+	0.743145i	$0.733333\pi$
$620$		0			0
$621$		0			0
$622$	0.500000	+	0.363271i	0.500000	+	0.363271i
$623$	0.128496	+	0.604528i	0.128496	+	0.604528i
$624$		0			0
$625$	0.669131	+	0.743145i	0.669131	+	0.743145i
$626$	0.330792	+	0.190983i	0.330792	+	0.190983i
$627$		0			0
$628$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$629$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$630$		0			0
$631$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$631$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$632$	1.40126	−	0.809017i	1.40126	−	0.809017i
$633$		0			0
$634$	0.373619	+	0.0794152i	0.373619	+	0.0794152i
$635$	1.40126	+	0.809017i	1.40126	+	0.809017i
$636$		0			0
$637$		0			0
$638$	0.951057	−	0.309017i	0.951057	−	0.309017i
$639$		0			0
$640$	0.190983	−	0.587785i	0.190983	−	0.587785i
$641$	−0.743145	−	0.669131i	−0.743145	−	0.669131i	0.207912	−	0.978148i	$-0.433333\pi$
$641$	−0.743145	−	0.669131i	−0.743145	−	0.669131i	−0.951057	+	0.309017i	$0.900000\pi$
$642$		0			0
$643$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$643$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$644$	−0.379874	+	0.0399263i	−0.379874	+	0.0399263i
$645$		0			0
$646$	0.0646021	−	0.614648i	0.0646021	−	0.614648i
$647$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$647$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.413545	−	0.459289i	−0.413545	−	0.459289i
$653$	0.406737	+	0.913545i	0.406737	+	0.913545i	0.994522	+	0.104528i	$0.0333333\pi$
$653$	0.406737	+	0.913545i	0.406737	+	0.913545i	−0.587785	+	0.809017i	$0.700000\pi$
$654$		0			0
$655$	0.169131	−	1.60917i	0.169131	−	1.60917i
$656$		0			0
$657$		0			0
$658$	0.500000	−	0.363271i	0.500000	−	0.363271i
$659$	−1.20243	−	1.08268i	−1.20243	−	1.08268i	−0.994522	−	0.104528i	$-0.966667\pi$
$659$	−1.20243	−	1.08268i	−1.20243	−	1.08268i	−0.207912	−	0.978148i	$-0.566667\pi$
$660$		0			0
$661$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$661$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$662$		0			0
$663$		0			0
$664$	−0.604528	+	0.128496i	−0.604528	+	0.128496i
$665$	0.363271	−	0.500000i	0.363271	−	0.500000i
$666$		0			0
$667$	1.30902	−	0.951057i	1.30902	−	0.951057i
$668$		0			0
$669$		0			0
$670$	−0.0399263	−	0.379874i	−0.0399263	−	0.379874i
$671$	0.406737	+	0.913545i	0.406737	+	0.913545i
$672$		0			0
$673$	−0.604528	+	0.128496i	−0.604528	+	0.128496i	−0.500000	−	0.866025i	$-0.666667\pi$
$673$	−0.604528	+	0.128496i	−0.604528	+	0.128496i	−0.104528	+	0.994522i	$0.533333\pi$
$674$		0			0
$675$		0			0
$676$	−0.618034			−0.618034
$677$	0.128496	+	0.604528i	0.128496	+	0.604528i	0.994522	+	0.104528i	$0.0333333\pi$
$677$	0.128496	+	0.604528i	0.128496	+	0.604528i	−0.866025	+	0.500000i	$0.833333\pi$
$678$		0			0
$679$	0.564602	−	0.251377i	0.564602	−	0.251377i
$680$	0.866025	+	0.500000i	0.866025	+	0.500000i
$681$		0			0
$682$		0			0
$683$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	0.406737	−	0.913545i	$-0.366667\pi$
$683$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	−0.994522	+	0.104528i	$0.966667\pi$
$684$		0			0
$685$	0.809017	−	0.587785i	0.809017	−	0.587785i
$686$	0.128496	+	0.604528i	0.128496	+	0.604528i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$691$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$692$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$693$		0			0
$694$	0.500000	−	0.363271i	0.500000	−	0.363271i
$695$	0.866025	−	0.500000i	0.866025	−	0.500000i
$696$		0			0
$697$	0.913545	−	0.406737i	0.913545	−	0.406737i
$698$		0			0
$699$		0			0
$700$	0.190983	+	0.330792i	0.190983	+	0.330792i
$701$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$701$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$702$		0			0
$703$	1.30902	+	0.951057i	1.30902	+	0.951057i
$704$	−0.614648	−	0.0646021i	−0.614648	−	0.0646021i
$705$		0			0
$706$	−0.0399263	−	0.379874i	−0.0399263	−	0.379874i
$707$	0.535233	+	0.309017i	0.535233	+	0.309017i
$708$		0			0
$709$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$709$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$710$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$711$		0			0
$712$	0.309017	+	0.951057i	0.309017	+	0.951057i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.207912	−	0.978148i	0.207912	−	0.978148i
$717$		0			0
$718$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$719$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$719$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$725$	−1.40126	−	0.809017i	−1.40126	−	0.809017i
$726$		0			0
$727$	1.95630	−	0.415823i	1.95630	−	0.415823i	0.978148	−	0.207912i	$-0.0666667\pi$
$727$	1.95630	−	0.415823i	1.95630	−	0.415823i	0.978148	−	0.207912i	$-0.0666667\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	0.104528	+	0.994522i	0.104528	+	0.994522i	0.913545	+	0.406737i	$0.133333\pi$
$733$	0.104528	+	0.994522i	0.104528	+	0.994522i	−0.809017	+	0.587785i	$0.800000\pi$
$734$	0.128496	−	0.604528i	0.128496	−	0.604528i
$735$		0			0
$736$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$737$	0.587785	−	0.190983i	0.587785	−	0.190983i
$738$		0			0
$739$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$739$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$740$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$741$		0			0
$742$	0.0246758	+	0.234775i	0.0246758	+	0.234775i
$743$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$743$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$744$		0			0
$745$	−0.413545	+	0.459289i	−0.413545	+	0.459289i
$746$	−0.363271	+	0.500000i	−0.363271	+	0.500000i
$747$		0			0
$748$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$749$		0			0
$750$		0			0
$751$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$751$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$757$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$758$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$759$		0			0
$760$	0.500000	−	0.866025i	0.500000	−	0.866025i
$761$	1.20243	−	1.08268i	1.20243	−	1.08268i	0.207912	−	0.978148i	$-0.433333\pi$
$761$	1.20243	−	1.08268i	1.20243	−	1.08268i	0.994522	−	0.104528i	$-0.0333333\pi$
$762$		0			0
$763$	0.413545	−	0.459289i	0.413545	−	0.459289i
$764$	−0.363271	−	0.118034i	−0.363271	−	0.118034i
$765$		0			0
$766$	0.309017	+	0.951057i	0.309017	+	0.951057i
$767$		0			0
$768$		0			0
$769$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$769$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$770$	0.283856	−	0.255585i	0.283856	−	0.255585i
$771$		0			0
$772$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i
$773$	0.951057	+	0.309017i	0.951057	+	0.309017i	0.743145	−	0.669131i	$-0.233333\pi$
$773$	0.951057	+	0.309017i	0.951057	+	0.309017i	0.207912	+	0.978148i	$0.433333\pi$
$774$		0			0
$775$		0			0
$776$	0.866025	−	0.500000i	0.866025	−	0.500000i
$777$		0			0
$778$		0			0
$779$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$780$		0			0
$781$	−1.47815	−	0.658114i	−1.47815	−	0.658114i
$782$		−	0.618034i		−	0.618034i
$783$		0			0
$784$		0			0
$785$	−1.20243	−	1.08268i	−1.20243	−	1.08268i
$786$		0			0
$787$	−0.604528	−	0.128496i	−0.604528	−	0.128496i	−0.104528	−	0.994522i	$-0.533333\pi$
$787$	−0.604528	−	0.128496i	−0.604528	−	0.128496i	−0.500000	+	0.866025i	$0.666667\pi$
$788$		0			0
$789$		0			0
$790$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$791$		0			0
$792$		0			0
$793$		0			0
$794$	−0.155360	+	0.348943i	−0.155360	+	0.348943i
$795$		0			0
$796$		0			0
$797$	−0.406737	−	0.913545i	−0.406737	−	0.913545i	−0.994522	−	0.104528i	$-0.966667\pi$
$797$	−0.406737	−	0.913545i	−0.406737	−	0.913545i	0.587785	−	0.809017i	$-0.300000\pi$
$798$		0			0
$799$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$800$	0.587785	+	0.809017i	0.587785	+	0.809017i
$801$		0			0
$802$	0.118034	−	0.363271i	0.118034	−	0.363271i
$803$		0			0
$804$		0			0
$805$	0.309017	−	0.535233i	0.309017	−	0.535233i
$806$		0			0
$807$		0			0
$808$	0.913545	+	0.406737i	0.913545	+	0.406737i
$809$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$809$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$810$		0			0
$811$	0.309017	−	0.951057i	0.309017	−	0.951057i	−0.669131	−	0.743145i	$-0.733333\pi$
$811$	0.309017	−	0.951057i	0.309017	−	0.951057i	0.978148	−	0.207912i	$-0.0666667\pi$
$812$	−0.459289	−	0.413545i	−0.459289	−	0.413545i
$813$		0			0
$814$	0.669131	+	0.743145i	0.669131	+	0.743145i
$815$	0.994522	−	0.104528i	0.994522	−	0.104528i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	0.618034			0.618034
$821$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$821$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$822$		0			0
$823$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	0.309017	−	0.951057i	$-0.400000\pi$
$823$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	−0.978148	+	0.207912i	$0.933333\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.53884	+	0.500000i	1.53884	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$827$	1.53884	+	0.500000i	1.53884	+	0.500000i	0.587785	+	0.809017i	$0.300000\pi$
$828$		0			0
$829$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$829$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$830$	0.155360	−	0.348943i	0.155360	−	0.348943i
$831$		0			0
$832$		0			0
$833$	0.614648	−	0.0646021i	0.614648	−	0.0646021i
$834$		0			0
$835$		0			0
$836$	0.587785	+	0.190983i	0.587785	+	0.190983i
$837$		0			0
$838$	−0.118034	−	0.363271i	−0.118034	−	0.363271i
$839$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$839$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$840$		0			0
$841$	1.58268	+	0.336408i	1.58268	+	0.336408i
$842$	−0.614648	+	0.0646021i	−0.614648	+	0.0646021i
$843$		0			0
$844$	−0.348943	−	0.155360i	−0.348943	−	0.155360i
$845$	0.587785	−	0.809017i	0.587785	−	0.809017i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$	−0.564602	+	0.251377i	−0.564602	+	0.251377i
$851$	1.40126	+	0.809017i	1.40126	+	0.809017i
$852$		0			0
$853$	0.169131	−	1.60917i	0.169131	−	1.60917i	−0.500000	−	0.866025i	$-0.666667\pi$
$853$	0.169131	−	1.60917i	0.169131	−	1.60917i	0.669131	−	0.743145i	$-0.266667\pi$
$854$	−0.224514	+	0.309017i	−0.224514	+	0.309017i
$855$		0			0
$856$		0			0
$857$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$857$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$858$		0			0
$859$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$859$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$863$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$864$		0			0
$865$	1.61803			1.61803
$866$	0.459289	+	0.413545i	0.459289	+	0.413545i
$867$		0			0
$868$		0			0
$869$	−1.60917	+	0.169131i	−1.60917	+	0.169131i
$870$		0			0
$871$		0			0
$872$	0.587785	−	0.809017i	0.587785	−	0.809017i
$873$		0			0
$874$	−0.618034			−0.618034
$875$	−0.614648	−	0.0646021i	−0.614648	−	0.0646021i
$876$		0			0
$877$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$877$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$878$	−0.251377	−	0.564602i	−0.251377	−	0.564602i
$879$		0			0
$880$		0			0
$881$	−1.17557	−	1.61803i	−1.17557	−	1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$881$	−1.17557	−	1.61803i	−1.17557	−	1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$882$		0			0
$883$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$883$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$884$		0			0
$885$		0			0
$886$	−0.413545	−	0.459289i	−0.413545	−	0.459289i
$887$	−0.207912	+	0.978148i	−0.207912	+	0.978148i	0.743145	+	0.669131i	$0.233333\pi$
$887$	−0.207912	+	0.978148i	−0.207912	+	0.978148i	−0.951057	+	0.309017i	$0.900000\pi$
$888$		0			0
$889$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$890$	−0.587785	−	0.190983i	−0.587785	−	0.190983i
$891$		0			0
$892$	0.309017	−	0.224514i	0.309017	−	0.224514i
$893$	−1.40126	+	0.809017i	−1.40126	+	0.809017i
$894$		0			0
$895$	1.08268	+	1.20243i	1.08268	+	1.20243i
$896$	0.155360	+	0.348943i	0.155360	+	0.348943i
$897$		0			0
$898$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$899$		0			0
$900$		0			0
$901$	0.618034			0.618034
$902$	−0.128496	−	0.604528i	−0.128496	−	0.604528i
$903$		0			0
$904$		0			0
$905$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$906$		0			0
$907$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$907$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$908$	0.224514	+	0.309017i	0.224514	+	0.309017i
$909$		0			0
$910$		0			0
$911$	−0.336408	−	1.58268i	−0.336408	−	1.58268i	−0.743145	−	0.669131i	$-0.766667\pi$
$911$	−0.336408	−	1.58268i	−0.336408	−	1.58268i	0.406737	−	0.913545i	$-0.366667\pi$
$912$		0			0
$913$	0.604528	+	0.128496i	0.604528	+	0.128496i
$914$	−0.459289	+	0.413545i	−0.459289	+	0.413545i
$915$		0			0
$916$		0			0
$917$	0.587785	+	0.809017i	0.587785	+	0.809017i
$918$		0			0
$919$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$919$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$920$	0.406737	−	0.913545i	0.406737	−	0.913545i
$921$		0			0
$922$	−0.564602	+	0.251377i	−0.564602	+	0.251377i
$923$		0			0
$924$		0			0
$925$	0.169131	−	1.60917i	0.169131	−	1.60917i
$926$		−	0.618034i		−	0.618034i
$927$		0			0
$928$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$929$	−0.614648	−	0.0646021i	−0.614648	−	0.0646021i	−0.207912	−	0.978148i	$-0.566667\pi$
$929$	−0.614648	−	0.0646021i	−0.614648	−	0.0646021i	−0.406737	+	0.913545i	$0.633333\pi$
$930$		0			0
$931$	−0.0646021	−	0.614648i	−0.0646021	−	0.614648i
$932$	0.535233	+	0.309017i	0.535233	+	0.309017i
$933$		0			0
$934$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$935$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$936$		0			0
$937$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$937$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$938$	0.175433	+	0.157960i	0.175433	+	0.157960i
$939$		0			0
$940$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$941$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$941$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$942$		0			0
$943$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.60917	+	0.169131i	1.60917	+	0.169131i	0.866025	−	0.500000i	$-0.166667\pi$
$947$	1.60917	+	0.169131i	1.60917	+	0.169131i	0.743145	+	0.669131i	$0.233333\pi$
$948$		0			0
$949$		0			0
$950$	0.251377	+	0.564602i	0.251377	+	0.564602i
$951$		0			0
$952$	−0.604528	+	0.128496i	−0.604528	+	0.128496i
$953$	0.587785	−	0.809017i	0.587785	−	0.809017i	−0.406737	−	0.913545i	$-0.633333\pi$
$953$	0.587785	−	0.809017i	0.587785	−	0.809017i	0.994522	+	0.104528i	$0.0333333\pi$
$954$		0			0
$955$	0.500000	−	0.363271i	0.500000	−	0.363271i
$956$	0.155360	−	0.348943i	0.155360	−	0.348943i
$957$		0			0
$958$		0			0
$959$	−0.128496	+	0.604528i	−0.128496	+	0.604528i
$960$		0			0
$961$	0.978148	−	0.207912i	0.978148	−	0.207912i
$962$		0			0
$963$		0			0
$964$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$965$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$966$		0			0
$967$	0.169131	+	1.60917i	0.169131	+	1.60917i	0.669131	+	0.743145i	$0.266667\pi$
$967$	0.169131	+	1.60917i	0.169131	+	1.60917i	−0.500000	+	0.866025i	$0.666667\pi$
$968$		0			0
$969$		0			0
$970$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i
$971$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	−0.994522	−	0.104528i	$-0.966667\pi$
$971$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	0.406737	+	0.913545i	$0.366667\pi$
$972$		0			0
$973$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$974$	0.535233	−	0.309017i	0.535233	−	0.309017i
$975$		0			0
$976$		0			0
$977$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	−0.951057	−	0.309017i	$-0.900000\pi$
$977$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	0.207912	+	0.978148i	$0.433333\pi$
$978$		0			0
$979$	0.104528	−	0.994522i	0.104528	−	0.994522i
$980$	0.363271	+	0.118034i	0.363271	+	0.118034i
$981$		0			0
$982$		0			0
$983$	−0.658114	+	1.47815i	−0.658114	+	1.47815i	0.207912	+	0.978148i	$0.433333\pi$
$983$	−0.658114	+	1.47815i	−0.658114	+	1.47815i	−0.866025	+	0.500000i	$0.833333\pi$
$984$		0			0
$985$		0			0
$986$	0.743145	−	0.669131i	0.743145	−	0.669131i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$991$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$992$		0			0
$993$		0			0
$994$	−0.0646021	−	0.614648i	−0.0646021	−	0.614648i
$995$		0			0
$996$		0			0
$997$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i	0.913545	+	0.406737i	$0.133333\pi$
$997$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i	−0.978148	+	0.207912i	$0.933333\pi$
$998$	−0.587785	−	0.190983i	−0.587785	−	0.190983i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2025.1.y.a.296.1		16
3.2	odd	2	inner	2025.1.y.a.296.2		16
9.2	odd	6	inner	2025.1.y.a.1646.2		16
9.4	even	3		675.1.o.a.296.2	yes	8
9.5	odd	6		675.1.o.a.296.1	✓	8
9.7	even	3	inner	2025.1.y.a.1646.1		16
25.6	even	5	inner	2025.1.y.a.1106.2		16
45.4	even	6		3375.1.o.a.2726.1		8
45.13	odd	12		3375.1.m.b.2024.1		8
45.14	odd	6		3375.1.o.a.2726.2		8
45.22	odd	12		3375.1.m.a.2024.2		8
45.23	even	12		3375.1.m.a.2024.1		8
45.32	even	12		3375.1.m.b.2024.2		8
75.56	odd	10	inner	2025.1.y.a.1106.1		16
225.31	even	15		675.1.o.a.431.1	yes	8
225.56	odd	30	inner	2025.1.y.a.431.1		16
225.58	odd	60		3375.1.m.b.1349.1		8
225.67	odd	60		3375.1.m.a.1349.2		8
225.94	even	30		3375.1.o.a.26.2		8
225.106	even	15	inner	2025.1.y.a.431.2		16
225.131	odd	30		675.1.o.a.431.2	yes	8
225.158	even	60		3375.1.m.a.1349.1		8
225.167	even	60		3375.1.m.b.1349.2		8
225.194	odd	30		3375.1.o.a.26.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.1.o.a.296.1	✓	8	9.5	odd	6
675.1.o.a.296.2	yes	8	9.4	even	3
675.1.o.a.431.1	yes	8	225.31	even	15
675.1.o.a.431.2	yes	8	225.131	odd	30
2025.1.y.a.296.1		16	1.1	even	1	trivial
2025.1.y.a.296.2		16	3.2	odd	2	inner
2025.1.y.a.431.1		16	225.56	odd	30	inner
2025.1.y.a.431.2		16	225.106	even	15	inner
2025.1.y.a.1106.1		16	75.56	odd	10	inner
2025.1.y.a.1106.2		16	25.6	even	5	inner
2025.1.y.a.1646.1		16	9.7	even	3	inner
2025.1.y.a.1646.2		16	9.2	odd	6	inner
3375.1.m.a.1349.1		8	225.158	even	60
3375.1.m.a.1349.2		8	225.67	odd	60
3375.1.m.a.2024.1		8	45.23	even	12
3375.1.m.a.2024.2		8	45.22	odd	12
3375.1.m.b.1349.1		8	225.58	odd	60
3375.1.m.b.1349.2		8	225.167	even	60
3375.1.m.b.2024.1		8	45.13	odd	12
3375.1.m.b.2024.2		8	45.32	even	12
3375.1.o.a.26.1		8	225.194	odd	30
3375.1.o.a.26.2		8	225.94	even	30
3375.1.o.a.2726.1		8	45.4	even	6
3375.1.o.a.2726.2		8	45.14	odd	6

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:	\( N \)	\(=\)	\( 2025 = 3^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2025.y (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.128496 - 0.604528i) q^{2} +(0.564602 - 0.251377i) q^{4} +(-0.207912 + 0.978148i) q^{5} +(-0.309017 - 0.535233i) q^{7} +(-0.587785 - 0.809017i) q^{8} +O(q^{10})\)	\(q+(-0.128496 - 0.604528i) q^{2} +(0.564602 - 0.251377i) q^{4} +(-0.207912 + 0.978148i) q^{5} +(-0.309017 - 0.535233i) q^{7} +(-0.587785 - 0.809017i) q^{8} +0.618034 q^{10} +(0.207912 + 0.978148i) q^{11} +(-0.283856 + 0.255585i) q^{14} +(0.587785 + 0.809017i) q^{17} +(0.809017 - 0.587785i) q^{19} +(0.128496 + 0.604528i) q^{20} +(0.564602 - 0.251377i) q^{22} +(0.743145 - 0.669131i) q^{23} +(-0.913545 - 0.406737i) q^{25} +(-0.309017 - 0.224514i) q^{28} +(1.60917 + 0.169131i) q^{29} +(-0.866025 - 0.500000i) q^{32} +(0.413545 - 0.459289i) q^{34} +(0.587785 - 0.190983i) q^{35} +(0.500000 + 1.53884i) q^{37} +(-0.459289 - 0.413545i) q^{38} +(0.913545 - 0.406737i) q^{40} +(0.207912 - 0.978148i) q^{41} +(0.363271 + 0.500000i) q^{44} +(-0.500000 - 0.363271i) q^{46} +(-1.60917 - 0.169131i) q^{47} +(0.309017 - 0.535233i) q^{49} +(-0.128496 + 0.604528i) q^{50} +(0.363271 - 0.500000i) q^{53} -1.00000 q^{55} +(-0.251377 + 0.564602i) q^{56} +(-0.104528 - 0.994522i) q^{58} +(0.978148 - 0.207912i) q^{61} +(-0.190983 + 0.587785i) q^{64} +(-0.0646021 - 0.614648i) q^{67} +(0.535233 + 0.309017i) q^{68} +(-0.190983 - 0.330792i) q^{70} +(-0.951057 + 1.30902i) q^{71} +(0.866025 - 0.500000i) q^{74} +(0.309017 - 0.535233i) q^{76} +(0.459289 - 0.413545i) q^{77} +(-0.169131 + 1.60917i) q^{79} -0.618034 q^{82} +(0.251377 - 0.564602i) q^{83} +(-0.913545 + 0.406737i) q^{85} +(0.669131 - 0.743145i) q^{88} +(-0.951057 - 0.309017i) q^{89} +(0.251377 - 0.564602i) q^{92} +(0.104528 + 0.994522i) q^{94} +(0.406737 + 0.913545i) q^{95} +(-0.104528 + 0.994522i) q^{97} +(-0.363271 - 0.118034i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 4 q^{7}+O(q^{10}) \) 16 * q + 4 * q^4 + 4 * q^7	\( 16 q + 4 q^{4} + 4 q^{7} - 8 q^{10} + 4 q^{19} + 4 q^{22} - 2 q^{25} + 4 q^{28} - 6 q^{34} + 8 q^{37} + 2 q^{40} - 8 q^{46} - 4 q^{49} - 16 q^{55} + 2 q^{58} - 2 q^{61} - 12 q^{64} + 4 q^{67} - 12 q^{70} - 4 q^{76} + 6 q^{79} + 8 q^{82} - 2 q^{85} + 2 q^{88} - 2 q^{94} + 2 q^{97}+O(q^{100}) \) 16 * q + 4 * q^4 + 4 * q^7 - 8 * q^10 + 4 * q^19 + 4 * q^22 - 2 * q^25 + 4 * q^28 - 6 * q^34 + 8 * q^37 + 2 * q^40 - 8 * q^46 - 4 * q^49 - 16 * q^55 + 2 * q^58 - 2 * q^61 - 12 * q^64 + 4 * q^67 - 12 * q^70 - 4 * q^76 + 6 * q^79 + 8 * q^82 - 2 * q^85 + 2 * q^88 - 2 * q^94 + 2 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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