LMFDB - Embedded newform 1287.1.ba.c.142.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1287,1,Mod(142,1287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1287, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3, 3]))

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

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

chi := DirichletCharacter("1287.142");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1287 = 3^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1287.ba (of order $6$, degree $2$, 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:	$0.642296671259$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{15}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{15} + \cdots)$

Embedding invariants

Embedding label			142.2
Root			$0.669131 - 0.743145i$ of defining polynomial
Character	$\chi$	$=$	1287.142
Dual form			1287.1.ba.c.571.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.669131 + 1.15897i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.395472 - 0.684977i) q^{4} +(0.895472 - 0.994522i) q^{6} +(0.809017 - 1.40126i) q^{7} -0.279773 q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})$	\(q+(-0.669131 + 1.15897i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.395472 - 0.684977i) q^{4} +(0.895472 - 0.994522i) q^{6} +(0.809017 - 1.40126i) q^{7} -0.279773 q^{8} +(0.913545 + 0.406737i) q^{9} +(-0.500000 + 0.866025i) q^{11} +(0.244415 + 0.752232i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(1.08268 + 1.87525i) q^{14} +(0.582676 - 1.00922i) q^{16} +(-1.08268 + 0.786610i) q^{18} -1.95630 q^{19} +(-1.08268 + 1.20243i) q^{21} +(-0.669131 - 1.15897i) q^{22} +(-0.913545 - 1.58231i) q^{23} +(0.273659 + 0.0581680i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.33826 q^{26} +(-0.809017 - 0.587785i) q^{27} -1.27977 q^{28} +(0.639886 + 1.10832i) q^{32} +(0.669131 - 0.743145i) q^{33} +(-0.0826761 - 0.786610i) q^{36} +(1.30902 - 2.26728i) q^{38} +(0.309017 + 0.951057i) q^{39} +(-0.913545 - 1.58231i) q^{41} +(-0.669131 - 2.05937i) q^{42} +0.790943 q^{44} +2.44512 q^{46} +(-0.779773 + 0.866025i) q^{48} +(-0.809017 - 1.40126i) q^{49} +(-0.669131 - 1.15897i) q^{50} +(-0.395472 + 0.684977i) q^{52} +0.618034 q^{53} +(1.22256 - 0.544320i) q^{54} +(-0.226341 + 0.392034i) q^{56} +(1.91355 + 0.406737i) q^{57} +(1.30902 - 0.951057i) q^{63} -0.547318 q^{64} +(0.413545 + 1.27276i) q^{66} +(0.564602 + 1.73767i) q^{69} +(-0.255585 - 0.113794i) q^{72} +0.618034 q^{73} +(0.669131 - 0.743145i) q^{75} +(0.773659 + 1.34002i) q^{76} +(0.809017 + 1.40126i) q^{77} +(-1.30902 - 0.278240i) q^{78} +(0.669131 + 0.743145i) q^{81} +2.44512 q^{82} +(0.104528 - 0.181049i) q^{83} +(1.25181 + 0.266080i) q^{84} +(0.139886 - 0.242290i) q^{88} -1.61803 q^{91} +(-0.722562 + 1.25151i) q^{92} +(-0.395472 - 1.21714i) q^{96} +2.16535 q^{98} +(-0.809017 + 0.587785i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + q^{3} - 5 q^{4} + 9 q^{6} + 2 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) $ 8 * q - q^2 + q^3 - 5 * q^4 + 9 * q^6 + 2 * q^7 - 2 * q^8 + q^9	$ 8 q - q^{2} + q^{3} - 5 q^{4} + 9 q^{6} + 2 q^{7} - 2 q^{8} + q^{9} - 4 q^{11} - 4 q^{13} - 2 q^{14} - 6 q^{16} + 2 q^{18} + 2 q^{19} + 2 q^{21} - q^{22} - q^{23} - 4 q^{24} - 4 q^{25} + 2 q^{26} - 2 q^{27} - 10 q^{28} + 5 q^{32} + q^{33} + 10 q^{36} + 6 q^{38} - 2 q^{39} - q^{41} - q^{42} + 10 q^{44} - 2 q^{46} - 6 q^{48} - 2 q^{49} - q^{50} - 5 q^{52} - 4 q^{53} - q^{54} - 8 q^{56} + 9 q^{57} + 6 q^{63} + 8 q^{64} - 3 q^{66} + 2 q^{69} - 4 q^{72} - 4 q^{73} + q^{75} + 2 q^{77} - 6 q^{78} + q^{81} - 2 q^{82} - q^{83} - 5 q^{84} + q^{88} - 4 q^{91} + 5 q^{92} - 5 q^{96} - 4 q^{98} - 2 q^{99}+O(q^{100}) $ 8 * q - q^2 + q^3 - 5 * q^4 + 9 * q^6 + 2 * q^7 - 2 * q^8 + q^9 - 4 * q^11 - 4 * q^13 - 2 * q^14 - 6 * q^16 + 2 * q^18 + 2 * q^19 + 2 * q^21 - q^22 - q^23 - 4 * q^24 - 4 * q^25 + 2 * q^26 - 2 * q^27 - 10 * q^28 + 5 * q^32 + q^33 + 10 * q^36 + 6 * q^38 - 2 * q^39 - q^41 - q^42 + 10 * q^44 - 2 * q^46 - 6 * q^48 - 2 * q^49 - q^50 - 5 * q^52 - 4 * q^53 - q^54 - 8 * q^56 + 9 * q^57 + 6 * q^63 + 8 * q^64 - 3 * q^66 + 2 * q^69 - 4 * q^72 - 4 * q^73 + q^75 + 2 * q^77 - 6 * q^78 + q^81 - 2 * q^82 - q^83 - 5 * q^84 + q^88 - 4 * q^91 + 5 * q^92 - 5 * q^96 - 4 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1287\mathbb{Z}\right)^\times$.

$n$	$496$	$937$	$1145$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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	+	1.15897i	−0.669131	+	1.15897i	0.309017	+	0.951057i	$0.400000\pi$
$2$	−0.669131	+	1.15897i	−0.669131	+	1.15897i	−0.978148	+	0.207912i	$0.933333\pi$
$3$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$3$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$4$	−0.395472	−	0.684977i	−0.395472	−	0.684977i
$5$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$5$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$6$	0.895472	−	0.994522i	0.895472	−	0.994522i
$7$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$7$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$8$	−0.279773			−0.279773
$9$	0.913545	+	0.406737i	0.913545	+	0.406737i
$10$		0			0
$11$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$11$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$12$	0.244415	+	0.752232i	0.244415	+	0.752232i
$13$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$13$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$14$	1.08268	+	1.87525i	1.08268	+	1.87525i
$15$		0			0
$16$	0.582676	−	1.00922i	0.582676	−	1.00922i
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$	−1.08268	+	0.786610i	−1.08268	+	0.786610i
$19$	−1.95630			−1.95630			−0.978148	−	0.207912i	$-0.933333\pi$
$19$	−1.95630			−1.95630			−0.978148	+	0.207912i	$0.933333\pi$
$20$		0			0
$21$	−1.08268	+	1.20243i	−1.08268	+	1.20243i
$22$	−0.669131	−	1.15897i	−0.669131	−	1.15897i
$23$	−0.913545	−	1.58231i	−0.913545	−	1.58231i	−0.809017	−	0.587785i	$-0.800000\pi$
$23$	−0.913545	−	1.58231i	−0.913545	−	1.58231i	−0.104528	−	0.994522i	$-0.533333\pi$
$24$	0.273659	+	0.0581680i	0.273659	+	0.0581680i
$25$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$26$	1.33826			1.33826
$27$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$28$	−1.27977			−1.27977
$29$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$29$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$30$		0			0
$31$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$31$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$32$	0.639886	+	1.10832i	0.639886	+	1.10832i
$33$	0.669131	−	0.743145i	0.669131	−	0.743145i
$34$		0			0
$35$		0			0
$36$	−0.0826761	−	0.786610i	−0.0826761	−	0.786610i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	1.30902	−	2.26728i	1.30902	−	2.26728i
$39$	0.309017	+	0.951057i	0.309017	+	0.951057i
$40$		0			0
$41$	−0.913545	−	1.58231i	−0.913545	−	1.58231i	−0.809017	−	0.587785i	$-0.800000\pi$
$41$	−0.913545	−	1.58231i	−0.913545	−	1.58231i	−0.104528	−	0.994522i	$-0.533333\pi$
$42$	−0.669131	−	2.05937i	−0.669131	−	2.05937i
$43$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$43$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$44$	0.790943			0.790943
$45$		0			0
$46$	2.44512			2.44512
$47$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$47$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$48$	−0.779773	+	0.866025i	−0.779773	+	0.866025i
$49$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$50$	−0.669131	−	1.15897i	−0.669131	−	1.15897i
$51$		0			0
$52$	−0.395472	+	0.684977i	−0.395472	+	0.684977i
$53$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$53$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$54$	1.22256	−	0.544320i	1.22256	−	0.544320i
$55$		0			0
$56$	−0.226341	+	0.392034i	−0.226341	+	0.392034i
$57$	1.91355	+	0.406737i	1.91355	+	0.406737i
$58$		0			0
$59$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$59$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$60$		0			0
$61$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$61$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$62$		0			0
$63$	1.30902	−	0.951057i	1.30902	−	0.951057i
$64$	−0.547318			−0.547318
$65$		0			0
$66$	0.413545	+	1.27276i	0.413545	+	1.27276i
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$		0			0
$69$	0.564602	+	1.73767i	0.564602	+	1.73767i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	−0.255585	−	0.113794i	−0.255585	−	0.113794i
$73$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$73$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$74$		0			0
$75$	0.669131	−	0.743145i	0.669131	−	0.743145i
$76$	0.773659	+	1.34002i	0.773659	+	1.34002i
$77$	0.809017	+	1.40126i	0.809017	+	1.40126i
$78$	−1.30902	−	0.278240i	−1.30902	−	0.278240i
$79$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$		0			0
$81$	0.669131	+	0.743145i	0.669131	+	0.743145i
$82$	2.44512			2.44512
$83$	0.104528	−	0.181049i	0.104528	−	0.181049i	−0.809017	−	0.587785i	$-0.800000\pi$
$83$	0.104528	−	0.181049i	0.104528	−	0.181049i	0.913545	+	0.406737i	$0.133333\pi$
$84$	1.25181	+	0.266080i	1.25181	+	0.266080i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	0.139886	−	0.242290i	0.139886	−	0.242290i
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$		0			0
$91$	−1.61803			−1.61803
$92$	−0.722562	+	1.25151i	−0.722562	+	1.25151i
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.395472	−	1.21714i	−0.395472	−	1.21714i
$97$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$97$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$98$	2.16535			2.16535
$99$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$100$	0.790943			0.790943
$101$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$101$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$102$		0			0
$103$	−0.913545	−	1.58231i	−0.913545	−	1.58231i	−0.809017	−	0.587785i	$-0.800000\pi$
$103$	−0.913545	−	1.58231i	−0.913545	−	1.58231i	−0.104528	−	0.994522i	$-0.533333\pi$
$104$	0.139886	+	0.242290i	0.139886	+	0.242290i
$105$		0			0
$106$	−0.413545	+	0.716282i	−0.413545	+	0.716282i
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$	−0.0826761	+	0.786610i	−0.0826761	+	0.786610i
$109$	1.33826			1.33826			0.669131	−	0.743145i	$-0.266667\pi$
$109$	1.33826			1.33826			0.669131	+	0.743145i	$0.266667\pi$
$110$		0			0
$111$		0			0
$112$	−0.942790	−	1.63296i	−0.942790	−	1.63296i
$113$	−0.669131	−	1.15897i	−0.669131	−	1.15897i	−0.978148	−	0.207912i	$-0.933333\pi$
$113$	−0.669131	−	1.15897i	−0.669131	−	1.15897i	0.309017	−	0.951057i	$-0.400000\pi$
$114$	−1.75181	+	1.94558i	−1.75181	+	1.94558i
$115$		0			0
$116$		0			0
$117$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$122$		0			0
$123$	0.564602	+	1.73767i	0.564602	+	1.73767i
$124$		0			0
$125$		0			0
$126$	0.226341	+	2.15349i	0.226341	+	2.15349i
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	−0.273659	+	0.473991i	−0.273659	+	0.473991i
$129$		0			0
$130$		0			0
$131$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$131$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$132$	−0.773659	−	0.164446i	−0.773659	−	0.164446i
$133$	−1.58268	+	2.74128i	−1.58268	+	2.74128i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$	−2.39169	−	0.508370i	−2.39169	−	0.508370i
$139$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$139$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.00000			1.00000
$144$	0.942790	−	0.684977i	0.942790	−	0.684977i
$145$		0			0
$146$	−0.413545	+	0.716282i	−0.413545	+	0.716282i
$147$	0.500000	+	1.53884i	0.500000	+	1.53884i
$148$		0			0
$149$	0.104528	+	0.181049i	0.104528	+	0.181049i	0.913545	−	0.406737i	$-0.133333\pi$
$149$	0.104528	+	0.181049i	0.104528	+	0.181049i	−0.809017	+	0.587785i	$0.800000\pi$
$150$	0.413545	+	1.27276i	0.413545	+	1.27276i
$151$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$151$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$152$	0.547318			0.547318
$153$		0			0
$154$	−2.16535			−2.16535
$155$		0			0
$156$	0.529244	−	0.587785i	0.529244	−	0.587785i
$157$	0.809017	+	1.40126i	0.809017	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$157$	0.809017	+	1.40126i	0.809017	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$158$		0			0
$159$	−0.604528	−	0.128496i	−0.604528	−	0.128496i
$160$		0			0
$161$	−2.95630			−2.95630
$162$	−1.30902	+	0.278240i	−1.30902	+	0.278240i
$163$		0			0		1.00000			$0$
$163$		0			0		−1.00000			$\pi$
$164$	−0.722562	+	1.25151i	−0.722562	+	1.25151i
$165$		0			0
$166$	0.139886	+	0.242290i	0.139886	+	0.242290i
$167$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$167$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$168$	0.302903	−	0.336408i	0.302903	−	0.336408i
$169$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$170$		0			0
$171$	−1.78716	−	0.795697i	−1.78716	−	0.795697i
$172$		0			0
$173$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$173$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$174$		0			0
$175$	0.809017	+	1.40126i	0.809017	+	1.40126i
$176$	0.582676	+	1.00922i	0.582676	+	1.00922i
$177$		0			0
$178$		0			0
$179$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$179$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$180$		0			0
$181$	−1.95630			−1.95630			−0.978148	−	0.207912i	$-0.933333\pi$
$181$	−1.95630			−1.95630			−0.978148	+	0.207912i	$0.933333\pi$
$182$	1.08268	−	1.87525i	1.08268	−	1.87525i
$183$		0			0
$184$	0.255585	+	0.442686i	0.255585	+	0.442686i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−1.47815	+	0.658114i	−1.47815	+	0.658114i
$190$		0			0
$191$	−0.669131	+	1.15897i	−0.669131	+	1.15897i	0.309017	+	0.951057i	$0.400000\pi$
$191$	−0.669131	+	1.15897i	−0.669131	+	1.15897i	−0.978148	+	0.207912i	$0.933333\pi$
$192$	0.535358	+	0.113794i	0.535358	+	0.113794i
$193$	0.104528	+	0.181049i	0.104528	+	0.181049i	0.913545	−	0.406737i	$-0.133333\pi$
$193$	0.104528	+	0.181049i	0.104528	+	0.181049i	−0.809017	+	0.587785i	$0.800000\pi$
$194$		0			0
$195$		0			0
$196$	−0.639886	+	1.10832i	−0.639886	+	1.10832i
$197$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$197$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$198$	−0.139886	−	1.33093i	−0.139886	−	1.33093i
$199$	1.33826			1.33826			0.669131	−	0.743145i	$-0.266667\pi$
$199$	1.33826			1.33826			0.669131	+	0.743145i	$0.266667\pi$
$200$	0.139886	−	0.242290i	0.139886	−	0.242290i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$	2.44512			2.44512
$207$	−0.190983	−	1.81708i	−0.190983	−	1.81708i
$208$	−1.16535			−1.16535
$209$	0.978148	−	1.69420i	0.978148	−	1.69420i
$210$		0			0
$211$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$211$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$212$	−0.244415	−	0.423339i	−0.244415	−	0.423339i
$213$		0			0
$214$		0			0
$215$		0			0
$216$	0.226341	+	0.164446i	0.226341	+	0.164446i
$217$		0			0
$218$	−0.895472	+	1.55100i	−0.895472	+	1.55100i
$219$	−0.604528	−	0.128496i	−0.604528	−	0.128496i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$223$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$224$	2.07072			2.07072
$225$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$226$	1.79094			1.79094
$227$	0.978148	−	1.69420i	0.978148	−	1.69420i	0.309017	−	0.951057i	$-0.400000\pi$
$227$	0.978148	−	1.69420i	0.978148	−	1.69420i	0.669131	−	0.743145i	$-0.266667\pi$
$228$	−0.478148	−	1.47159i	−0.478148	−	1.47159i
$229$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$229$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$230$		0			0
$231$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$232$		0			0
$233$		0			0		1.00000			$0$
$233$		0			0		−1.00000			$\pi$
$234$	1.22256	+	0.544320i	1.22256	+	0.544320i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.978148	+	1.69420i	0.978148	+	1.69420i	0.669131	+	0.743145i	$0.266667\pi$
$239$	0.978148	+	1.69420i	0.978148	+	1.69420i	0.309017	+	0.951057i	$0.400000\pi$
$240$		0			0
$241$	−0.913545	+	1.58231i	−0.913545	+	1.58231i	−0.104528	+	0.994522i	$0.533333\pi$
$241$	−0.913545	+	1.58231i	−0.913545	+	1.58231i	−0.809017	+	0.587785i	$0.800000\pi$
$242$	1.33826			1.33826
$243$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$244$		0			0
$245$		0			0
$246$	−2.39169	−	0.508370i	−2.39169	−	0.508370i
$247$	0.978148	+	1.69420i	0.978148	+	1.69420i
$248$		0			0
$249$	−0.139886	+	0.155360i	−0.139886	+	0.155360i
$250$		0			0
$251$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$251$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$252$	−1.16913	−	0.520530i	−1.16913	−	0.520530i
$253$	1.82709			1.82709
$254$		0			0
$255$		0			0
$256$	−0.639886	−	1.10832i	−0.639886	−	1.10832i
$257$	0.104528	+	0.181049i	0.104528	+	0.181049i	0.913545	−	0.406737i	$-0.133333\pi$
$257$	0.104528	+	0.181049i	0.104528	+	0.181049i	−0.809017	+	0.587785i	$0.800000\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$	−0.187205	+	0.207912i	−0.187205	+	0.207912i
$265$		0			0
$266$	−2.11803	−	3.66854i	−2.11803	−	3.66854i
$267$		0			0
$268$		0			0
$269$	−0.209057			−0.209057			−0.104528	−	0.994522i	$-0.533333\pi$
$269$	−0.209057			−0.209057			−0.104528	+	0.994522i	$0.533333\pi$
$270$		0			0
$271$	1.33826			1.33826			0.669131	−	0.743145i	$-0.266667\pi$
$271$	1.33826			1.33826			0.669131	+	0.743145i	$0.266667\pi$
$272$		0			0
$273$	1.58268	+	0.336408i	1.58268	+	0.336408i
$274$		0			0
$275$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$276$	0.966977	−	1.07394i	0.966977	−	1.07394i
$277$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$277$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$281$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$282$		0			0
$283$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$283$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$284$		0			0
$285$		0			0
$286$	−0.669131	+	1.15897i	−0.669131	+	1.15897i
$287$	−2.95630			−2.95630
$288$	0.133773	+	1.27276i	0.133773	+	1.27276i
$289$	1.00000			1.00000
$290$		0			0
$291$		0			0
$292$	−0.244415	−	0.423339i	−0.244415	−	0.423339i
$293$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$293$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$294$	−2.11803	−	0.450202i	−2.11803	−	0.450202i
$295$		0			0
$296$		0			0
$297$	0.913545	−	0.406737i	0.913545	−	0.406737i
$298$	−0.279773			−0.279773
$299$	−0.913545	+	1.58231i	−0.913545	+	1.58231i
$300$	−0.773659	−	0.164446i	−0.773659	−	0.164446i
$301$		0			0
$302$	0.669131	+	1.15897i	0.669131	+	1.15897i
$303$		0			0
$304$	−1.13989	+	1.97434i	−1.13989	+	1.97434i
$305$		0			0
$306$		0			0
$307$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$307$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$308$	0.639886	−	1.10832i	0.639886	−	1.10832i
$309$	0.564602	+	1.73767i	0.564602	+	1.73767i
$310$		0			0
$311$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$311$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$312$	−0.0864545	−	0.266080i	−0.0864545	−	0.266080i
$313$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$313$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$314$	−2.16535			−2.16535
$315$		0			0
$316$		0			0
$317$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$317$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$318$	0.553432	−	0.614648i	0.553432	−	0.614648i
$319$		0			0
$320$		0			0
$321$		0			0
$322$	1.97815	−	3.42625i	1.97815	−	3.42625i
$323$		0			0
$324$	0.244415	−	0.752232i	0.244415	−	0.752232i
$325$	1.00000			1.00000
$326$		0			0
$327$	−1.30902	−	0.278240i	−1.30902	−	0.278240i
$328$	0.255585	+	0.442686i	0.255585	+	0.442686i
$329$		0			0
$330$		0			0
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$	−0.165352			−0.165352
$333$		0			0
$334$	0.827091			0.827091
$335$		0			0
$336$	0.582676	+	1.79329i	0.582676	+	1.79329i
$337$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$337$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$338$	−0.669131	−	1.15897i	−0.669131	−	1.15897i
$339$	0.413545	+	1.27276i	0.413545	+	1.27276i
$340$		0			0
$341$		0			0
$342$	2.11803	−	1.53884i	2.11803	−	1.53884i
$343$	−1.00000			−1.00000
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$347$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$348$		0			0
$349$	0.104528	−	0.181049i	0.104528	−	0.181049i	−0.809017	−	0.587785i	$-0.800000\pi$
$349$	0.104528	−	0.181049i	0.104528	−	0.181049i	0.913545	+	0.406737i	$0.133333\pi$
$350$	−2.16535			−2.16535
$351$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$352$	−1.27977			−1.27977
$353$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$353$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.669131	−	1.15897i	0.669131	−	1.15897i
$359$	1.82709			1.82709			0.913545	−	0.406737i	$-0.133333\pi$
$359$	1.82709			1.82709			0.913545	+	0.406737i	$0.133333\pi$
$360$		0			0
$361$	2.82709			2.82709
$362$	1.30902	−	2.26728i	1.30902	−	2.26728i
$363$	0.309017	+	0.951057i	0.309017	+	0.951057i
$364$	0.639886	+	1.10832i	0.639886	+	1.10832i
$365$		0			0
$366$		0			0
$367$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$367$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$368$	−2.12920			−2.12920
$369$	−0.190983	−	1.81708i	−0.190983	−	1.81708i
$370$		0			0
$371$	0.500000	−	0.866025i	0.500000	−	0.866025i
$372$		0			0
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$	0.226341	−	2.15349i	0.226341	−	2.15349i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$	−0.895472	−	1.55100i	−0.895472	−	1.55100i
$383$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$383$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$384$	0.366227	−	0.406737i	0.366227	−	0.406737i
$385$		0			0
$386$	−0.279773			−0.279773
$387$		0			0
$388$		0			0
$389$	0.978148	−	1.69420i	0.978148	−	1.69420i	0.309017	−	0.951057i	$-0.400000\pi$
$389$	0.978148	−	1.69420i	0.978148	−	1.69420i	0.669131	−	0.743145i	$-0.266667\pi$
$390$		0			0
$391$		0			0
$392$	0.226341	+	0.392034i	0.226341	+	0.392034i
$393$		0			0
$394$	−0.413545	+	0.716282i	−0.413545	+	0.716282i
$395$		0			0
$396$	0.722562	+	0.321706i	0.722562	+	0.321706i
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$	−0.895472	+	1.55100i	−0.895472	+	1.55100i
$399$	2.11803	−	2.35232i	2.11803	−	2.35232i
$400$	0.582676	+	1.00922i	0.582676	+	1.00922i
$401$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$401$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$409$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$410$		0			0
$411$		0			0
$412$	−0.722562	+	1.25151i	−0.722562	+	1.25151i
$413$		0			0
$414$	2.23373	+	0.994522i	2.23373	+	0.994522i
$415$		0			0
$416$	0.639886	−	1.10832i	0.639886	−	1.10832i
$417$		0			0
$418$	1.30902	+	2.26728i	1.30902	+	2.26728i
$419$	0.104528	+	0.181049i	0.104528	+	0.181049i	0.913545	−	0.406737i	$-0.133333\pi$
$419$	0.104528	+	0.181049i	0.104528	+	0.181049i	−0.809017	+	0.587785i	$0.800000\pi$
$420$		0			0
$421$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$421$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$422$		0			0
$423$		0			0
$424$	−0.172909			−0.172909
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$430$		0			0
$431$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$431$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$432$	−1.06460	+	0.473991i	−1.06460	+	0.473991i
$433$	−1.95630			−1.95630			−0.978148	−	0.207912i	$-0.933333\pi$
$433$	−1.95630			−1.95630			−0.978148	+	0.207912i	$0.933333\pi$
$434$		0			0
$435$		0			0
$436$	−0.529244	−	0.916678i	−0.529244	−	0.916678i
$437$	1.78716	+	3.09546i	1.78716	+	3.09546i
$438$	0.553432	−	0.614648i	0.553432	−	0.614648i
$439$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$439$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$440$		0			0
$441$	−0.169131	−	1.60917i	−0.169131	−	1.60917i
$442$		0			0
$443$	0.104528	−	0.181049i	0.104528	−	0.181049i	−0.809017	−	0.587785i	$-0.800000\pi$
$443$	0.104528	−	0.181049i	0.104528	−	0.181049i	0.913545	+	0.406737i	$0.133333\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i
$448$	−0.442790	+	0.766934i	−0.442790	+	0.766934i
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	−0.139886	−	1.33093i	−0.139886	−	1.33093i
$451$	1.82709			1.82709
$452$	−0.529244	+	0.916678i	−0.529244	+	0.916678i
$453$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$454$	1.30902	+	2.26728i	1.30902	+	2.26728i
$455$		0			0
$456$	−0.535358	−	0.113794i	−0.535358	−	0.113794i
$457$	−0.669131	+	1.15897i	−0.669131	+	1.15897i	0.309017	+	0.951057i	$0.400000\pi$
$457$	−0.669131	+	1.15897i	−0.669131	+	1.15897i	−0.978148	+	0.207912i	$0.933333\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.978148	−	1.69420i	0.978148	−	1.69420i	0.309017	−	0.951057i	$-0.400000\pi$
$461$	0.978148	−	1.69420i	0.978148	−	1.69420i	0.669131	−	0.743145i	$-0.266667\pi$
$462$	2.11803	+	0.450202i	2.11803	+	0.450202i
$463$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$463$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.00000			2.00000			1.00000			$0$
$467$	2.00000			2.00000			1.00000			$0$
$468$	−0.639886	+	0.464905i	−0.639886	+	0.464905i
$469$		0			0
$470$		0			0
$471$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	0.978148	−	1.69420i	0.978148	−	1.69420i
$476$		0			0
$477$	0.564602	+	0.251377i	0.564602	+	0.251377i
$478$	−2.61803			−2.61803
$479$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$479$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$480$		0			0
$481$		0			0
$482$	−1.22256	−	2.11754i	−1.22256	−	2.11754i
$483$	2.89169	+	0.614648i	2.89169	+	0.614648i
$484$	−0.395472	+	0.684977i	−0.395472	+	0.684977i
$485$		0			0
$486$	1.33826			1.33826
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$491$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$492$	0.966977	−	1.07394i	0.966977	−	1.07394i
$493$		0			0
$494$	−2.61803			−2.61803
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.0864545	−	0.266080i	−0.0864545	−	0.266080i
$499$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$499$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$500$		0			0
$501$	0.190983	+	0.587785i	0.190983	+	0.587785i
$502$	1.08268	−	1.87525i	1.08268	−	1.87525i
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$	−0.366227	+	0.266080i	−0.366227	+	0.266080i
$505$		0			0
$506$	−1.22256	+	2.11754i	−1.22256	+	2.11754i
$507$	0.669131	−	0.743145i	0.669131	−	0.743145i
$508$		0			0
$509$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$509$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$510$		0			0
$511$	0.500000	−	0.866025i	0.500000	−	0.866025i
$512$	1.16535			1.16535
$513$	1.58268	+	1.14988i	1.58268	+	1.14988i
$514$	−0.279773			−0.279773
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.82709			1.82709			0.913545	−	0.406737i	$-0.133333\pi$
$521$	1.82709			1.82709			0.913545	+	0.406737i	$0.133333\pi$
$522$		0			0
$523$		0			0		1.00000			$0$
$523$		0			0		−1.00000			$\pi$
$524$		0			0
$525$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$526$		0			0
$527$		0			0
$528$	−0.360114	−	1.10832i	−0.360114	−	1.10832i
$529$	−1.16913	+	2.02499i	−1.16913	+	2.02499i
$530$		0			0
$531$		0			0
$532$	2.50361			2.50361
$533$	−0.913545	+	1.58231i	−0.913545	+	1.58231i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.978148	+	0.207912i	0.978148	+	0.207912i
$538$	0.139886	−	0.242290i	0.139886	−	0.242290i
$539$	1.61803			1.61803
$540$		0			0
$541$	−0.209057			−0.209057			−0.104528	−	0.994522i	$-0.533333\pi$
$541$	−0.209057			−0.209057			−0.104528	+	0.994522i	$0.533333\pi$
$542$	−0.895472	+	1.55100i	−0.895472	+	1.55100i
$543$	1.91355	+	0.406737i	1.91355	+	0.406737i
$544$		0			0
$545$		0			0
$546$	−1.44890	+	1.60917i	−1.44890	+	1.60917i
$547$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$547$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$548$		0			0
$549$		0			0
$550$	1.33826			1.33826
$551$		0			0
$552$	−0.157960	−	0.486152i	−0.157960	−	0.486152i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$557$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.413545	−	0.716282i	−0.413545	−	0.716282i
$563$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$563$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	1.58268	−	0.336408i	1.58268	−	0.336408i
$568$		0			0
$569$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$569$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$570$		0			0
$571$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$571$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$572$	−0.395472	−	0.684977i	−0.395472	−	0.684977i
$573$	0.895472	−	0.994522i	0.895472	−	0.994522i
$574$	1.97815	−	3.42625i	1.97815	−	3.42625i
$575$	1.82709			1.82709
$576$	−0.500000	−	0.222614i	−0.500000	−	0.222614i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	−0.669131	+	1.15897i	−0.669131	+	1.15897i
$579$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i
$580$		0			0
$581$	−0.169131	−	0.292943i	−0.169131	−	0.292943i
$582$		0			0
$583$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$584$	−0.172909			−0.172909
$585$		0			0
$586$	−1.33826			−1.33826
$587$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$587$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$588$	0.856335	−	0.951057i	0.856335	−	0.951057i
$589$		0			0
$590$		0			0
$591$	−0.604528	−	0.128496i	−0.604528	−	0.128496i
$592$		0			0
$593$	−0.209057			−0.209057			−0.104528	−	0.994522i	$-0.533333\pi$
$593$	−0.209057			−0.209057			−0.104528	+	0.994522i	$0.533333\pi$
$594$	−0.139886	+	1.33093i	−0.139886	+	1.33093i
$595$		0			0
$596$	0.0826761	−	0.143199i	0.0826761	−	0.143199i
$597$	−1.30902	−	0.278240i	−1.30902	−	0.278240i
$598$	−1.22256	−	2.11754i	−1.22256	−	2.11754i
$599$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$599$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$600$	−0.187205	+	0.207912i	−0.187205	+	0.207912i
$601$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$601$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$602$		0			0
$603$		0			0
$604$	−0.790943			−0.790943
$605$		0			0
$606$		0			0
$607$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$607$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$608$	−1.25181	−	2.16819i	−1.25181	−	2.16819i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.95630			−1.95630			−0.978148	−	0.207912i	$-0.933333\pi$
$613$	−1.95630			−1.95630			−0.978148	+	0.207912i	$0.933333\pi$
$614$	0.669131	−	1.15897i	0.669131	−	1.15897i
$615$		0			0
$616$	−0.226341	−	0.392034i	−0.226341	−	0.392034i
$617$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$617$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$618$	−2.39169	−	0.508370i	−2.39169	−	0.508370i
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$		0			0
$621$	−0.190983	+	1.81708i	−0.190983	+	1.81708i
$622$	0.827091			0.827091
$623$		0			0
$624$	1.13989	+	0.242290i	1.13989	+	0.242290i
$625$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$626$	1.08268	+	1.87525i	1.08268	+	1.87525i
$627$	−1.30902	+	1.45381i	−1.30902	+	1.45381i
$628$	0.639886	−	1.10832i	0.639886	−	1.10832i
$629$		0			0
$630$		0			0
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	0.151057	+	0.464905i	0.151057	+	0.464905i
$637$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$641$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$642$		0			0
$643$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$643$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$644$	1.16913	+	2.02499i	1.16913	+	2.02499i
$645$		0			0
$646$		0			0
$647$	−1.95630			−1.95630			−0.978148	−	0.207912i	$-0.933333\pi$
$647$	−1.95630			−1.95630			−0.978148	+	0.207912i	$0.933333\pi$
$648$	−0.187205	−	0.207912i	−0.187205	−	0.207912i
$649$		0			0
$650$	−0.669131	+	1.15897i	−0.669131	+	1.15897i
$651$		0			0
$652$		0			0
$653$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$653$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$654$	1.19837	−	1.33093i	1.19837	−	1.33093i
$655$		0			0
$656$	−2.12920			−2.12920
$657$	0.564602	+	0.251377i	0.564602	+	0.251377i
$658$		0			0
$659$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$659$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$660$		0			0
$661$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$661$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$662$		0			0
$663$		0			0
$664$	−0.0292442	+	0.0506525i	−0.0292442	+	0.0506525i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−0.244415	+	0.423339i	−0.244415	+	0.423339i
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−2.02547	−	0.430526i	−2.02547	−	0.430526i
$673$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$673$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$674$		0			0
$675$	0.913545	−	0.406737i	0.913545	−	0.406737i
$676$	0.790943			0.790943
$677$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$677$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$678$	−1.75181	−	0.372358i	−1.75181	−	0.372358i
$679$		0			0
$680$		0			0
$681$	−1.30902	+	1.45381i	−1.30902	+	1.45381i
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	0.161739	+	1.53884i	0.161739	+	1.53884i
$685$		0			0
$686$	0.669131	−	1.15897i	0.669131	−	1.15897i
$687$		0			0
$688$		0			0
$689$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$690$		0			0
$691$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$691$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$692$		0			0
$693$	0.169131	+	1.60917i	0.169131	+	1.60917i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$	0.139886	+	0.242290i	0.139886	+	0.242290i
$699$		0			0
$700$	0.639886	−	1.10832i	0.639886	−	1.10832i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	−1.08268	−	0.786610i	−1.08268	−	0.786610i
$703$		0			0
$704$	0.273659	−	0.473991i	0.273659	−	0.473991i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$709$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.395472	+	0.684977i	0.395472	+	0.684977i
$717$	−0.604528	−	1.86055i	−0.604528	−	1.86055i
$718$	−1.22256	+	2.11754i	−1.22256	+	2.11754i
$719$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$719$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$720$		0			0
$721$	−2.95630			−2.95630
$722$	−1.89169	+	3.27651i	−1.89169	+	3.27651i
$723$	1.22256	−	1.35779i	1.22256	−	1.35779i
$724$	0.773659	+	1.34002i	0.773659	+	1.34002i
$725$		0			0
$726$	−1.30902	−	0.278240i	−1.30902	−	0.278240i
$727$	0.104528	−	0.181049i	0.104528	−	0.181049i	−0.809017	−	0.587785i	$-0.800000\pi$
$727$	0.104528	−	0.181049i	0.104528	−	0.181049i	0.913545	+	0.406737i	$0.133333\pi$
$728$	0.452682			0.452682
$729$	0.309017	+	0.951057i	0.309017	+	0.951057i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−0.913545	−	1.58231i	−0.913545	−	1.58231i	−0.809017	−	0.587785i	$-0.800000\pi$
$733$	−0.913545	−	1.58231i	−0.913545	−	1.58231i	−0.104528	−	0.994522i	$-0.533333\pi$
$734$	−0.413545	−	0.716282i	−0.413545	−	0.716282i
$735$		0			0
$736$	1.16913	−	2.02499i	1.16913	−	2.02499i
$737$		0			0
$738$	2.23373	+	0.994522i	2.23373	+	0.994522i
$739$	−0.209057			−0.209057			−0.104528	−	0.994522i	$-0.533333\pi$
$739$	−0.209057			−0.209057			−0.104528	+	0.994522i	$0.533333\pi$
$740$		0			0
$741$	−0.604528	−	1.86055i	−0.604528	−	1.86055i
$742$	0.669131	+	1.15897i	0.669131	+	1.15897i
$743$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$743$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.169131	−	0.122881i	0.169131	−	0.122881i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	0.978148	+	1.69420i	0.978148	+	1.69420i	0.669131	+	0.743145i	$0.266667\pi$
$751$	0.978148	+	1.69420i	0.978148	+	1.69420i	0.309017	+	0.951057i	$0.400000\pi$
$752$		0			0
$753$	1.58268	+	0.336408i	1.58268	+	0.336408i
$754$		0			0
$755$		0			0
$756$	1.03536	+	0.752232i	1.03536	+	0.752232i
$757$	−0.209057			−0.209057			−0.104528	−	0.994522i	$-0.533333\pi$
$757$	−0.209057			−0.209057			−0.104528	+	0.994522i	$0.533333\pi$
$758$		0			0
$759$	−1.78716	−	0.379874i	−1.78716	−	0.379874i
$760$		0			0
$761$	0.809017	+	1.40126i	0.809017	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$761$	0.809017	+	1.40126i	0.809017	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$762$		0			0
$763$	1.08268	−	1.87525i	1.08268	−	1.87525i
$764$	1.05849			1.05849
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.395472	+	1.21714i	0.395472	+	1.21714i
$769$	−0.913545	−	1.58231i	−0.913545	−	1.58231i	−0.809017	−	0.587785i	$-0.800000\pi$
$769$	−0.913545	−	1.58231i	−0.913545	−	1.58231i	−0.104528	−	0.994522i	$-0.533333\pi$
$770$		0			0
$771$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i
$772$	0.0826761	−	0.143199i	0.0826761	−	0.143199i
$773$		0			0		1.00000			$0$
$773$		0			0		−1.00000			$\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$	1.30902	+	2.26728i	1.30902	+	2.26728i
$779$	1.78716	+	3.09546i	1.78716	+	3.09546i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−1.88558			−1.88558
$785$		0			0
$786$		0			0
$787$	−0.913545	−	1.58231i	−0.913545	−	1.58231i	−0.809017	−	0.587785i	$-0.800000\pi$
$787$	−0.913545	−	1.58231i	−0.913545	−	1.58231i	−0.104528	−	0.994522i	$-0.533333\pi$
$788$	−0.244415	−	0.423339i	−0.244415	−	0.423339i
$789$		0			0
$790$		0			0
$791$	−2.16535			−2.16535
$792$	0.226341	−	0.164446i	0.226341	−	0.164446i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.529244	−	0.916678i	−0.529244	−	0.916678i
$797$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$797$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$798$	1.30902	+	4.02874i	1.30902	+	4.02874i
$799$		0			0
$800$	−1.27977			−1.27977
$801$		0			0
$802$		0			0
$803$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.204489	+	0.0434654i	0.204489	+	0.0434654i
$808$		0			0
$809$		0			0		1.00000			$0$
$809$		0			0		−1.00000			$\pi$
$810$		0			0
$811$	1.82709			1.82709			0.913545	−	0.406737i	$-0.133333\pi$
$811$	1.82709			1.82709			0.913545	+	0.406737i	$0.133333\pi$
$812$		0			0
$813$	−1.30902	−	0.278240i	−1.30902	−	0.278240i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−1.33826			−1.33826
$819$	−1.47815	−	0.658114i	−1.47815	−	0.658114i
$820$		0			0
$821$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$821$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$822$		0			0
$823$	0.809017	+	1.40126i	0.809017	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$823$	0.809017	+	1.40126i	0.809017	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$824$	0.255585	+	0.442686i	0.255585	+	0.442686i
$825$	0.309017	+	0.951057i	0.309017	+	0.951057i
$826$		0			0
$827$	−1.95630			−1.95630			−0.978148	−	0.207912i	$-0.933333\pi$
$827$	−1.95630			−1.95630			−0.978148	+	0.207912i	$0.933333\pi$
$828$	−1.16913	+	0.849423i	−1.16913	+	0.849423i
$829$	−0.209057			−0.209057			−0.104528	−	0.994522i	$-0.533333\pi$
$829$	−0.209057			−0.209057			−0.104528	+	0.994522i	$0.533333\pi$
$830$		0			0
$831$		0			0
$832$	0.273659	+	0.473991i	0.273659	+	0.473991i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	−1.54732			−1.54732
$837$		0			0
$838$	−0.279773			−0.279773
$839$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$839$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$840$		0			0
$841$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$842$		0			0
$843$	0.413545	−	0.459289i	0.413545	−	0.459289i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−1.61803			−1.61803
$848$	0.360114	−	0.623735i	0.360114	−	0.623735i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	0.978148	−	1.69420i	0.978148	−	1.69420i	0.309017	−	0.951057i	$-0.400000\pi$
$853$	0.978148	−	1.69420i	0.978148	−	1.69420i	0.669131	−	0.743145i	$-0.266667\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$857$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$858$	0.895472	−	0.994522i	0.895472	−	0.994522i
$859$	−0.669131	−	1.15897i	−0.669131	−	1.15897i	−0.978148	−	0.207912i	$-0.933333\pi$
$859$	−0.669131	−	1.15897i	−0.669131	−	1.15897i	0.309017	−	0.951057i	$-0.400000\pi$
$860$		0			0
$861$	2.89169	+	0.614648i	2.89169	+	0.614648i
$862$	1.08268	−	1.87525i	1.08268	−	1.87525i
$863$		0			0		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$	0.133773	−	1.27276i	0.133773	−	1.27276i
$865$		0			0
$866$	1.30902	−	2.26728i	1.30902	−	2.26728i
$867$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.374409			−0.374409
$873$		0			0
$874$	−4.78339			−4.78339
$875$		0			0
$876$	0.151057	+	0.464905i	0.151057	+	0.464905i
$877$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$877$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$878$		0			0
$879$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$880$		0			0
$881$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$881$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$882$	1.97815	+	0.880728i	1.97815	+	0.880728i
$883$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$883$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$884$		0			0
$885$		0			0
$886$	0.139886	+	0.242290i	0.139886	+	0.242290i
$887$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$887$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$892$		0			0
$893$		0			0
$894$	0.273659	+	0.0581680i	0.273659	+	0.0581680i
$895$		0			0
$896$	0.442790	+	0.766934i	0.442790	+	0.766934i
$897$	1.22256	−	1.35779i	1.22256	−	1.35779i
$898$		0			0
$899$		0			0
$900$	0.722562	+	0.321706i	0.722562	+	0.321706i
$901$		0			0
$902$	−1.22256	+	2.11754i	−1.22256	+	2.11754i
$903$		0			0
$904$	0.187205	+	0.324248i	0.187205	+	0.324248i
$905$		0			0
$906$	−0.413545	−	1.27276i	−0.413545	−	1.27276i
$907$	−0.913545	+	1.58231i	−0.913545	+	1.58231i	−0.104528	+	0.994522i	$0.533333\pi$
$907$	−0.913545	+	1.58231i	−0.913545	+	1.58231i	−0.809017	+	0.587785i	$0.800000\pi$
$908$	−1.54732			−1.54732
$909$		0			0
$910$		0			0
$911$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$911$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$912$	1.52547	−	1.69420i	1.52547	−	1.69420i
$913$	0.104528	+	0.181049i	0.104528	+	0.181049i
$914$	−0.895472	−	1.55100i	−0.895472	−	1.55100i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$	0.978148	+	0.207912i	0.978148	+	0.207912i
$922$	1.30902	+	2.26728i	1.30902	+	2.26728i
$923$		0			0
$924$	−0.856335	+	0.951057i	−0.856335	+	0.951057i
$925$		0			0
$926$		0			0
$927$	−0.190983	−	1.81708i	−0.190983	−	1.81708i
$928$		0			0
$929$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$929$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$930$		0			0
$931$	1.58268	+	2.74128i	1.58268	+	2.74128i
$932$		0			0
$933$	0.190983	+	0.587785i	0.190983	+	0.587785i
$934$	−1.33826	+	2.31794i	−1.33826	+	2.31794i
$935$		0			0
$936$	0.0292442	+	0.278240i	0.0292442	+	0.278240i
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$	−1.08268	+	1.20243i	−1.08268	+	1.20243i
$940$		0			0
$941$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$941$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$942$	2.11803	+	0.450202i	2.11803	+	0.450202i
$943$	−1.66913	+	2.89102i	−1.66913	+	2.89102i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$947$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$948$		0			0
$949$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$950$	1.30902	+	2.26728i	1.30902	+	2.26728i
$951$		0			0
$952$		0			0
$953$		0			0		1.00000			$0$
$953$		0			0		−1.00000			$\pi$
$954$	−0.669131	+	0.486152i	−0.669131	+	0.486152i
$955$		0			0
$956$	0.773659	−	1.34002i	0.773659	−	1.34002i
$957$		0			0
$958$	0.669131	+	1.15897i	0.669131	+	1.15897i
$959$		0			0
$960$		0			0
$961$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$962$		0			0
$963$		0			0
$964$	1.44512			1.44512
$965$		0			0
$966$	−2.64728	+	2.94010i	−2.64728	+	2.94010i
$967$	−0.669131	−	1.15897i	−0.669131	−	1.15897i	−0.978148	−	0.207912i	$-0.933333\pi$
$967$	−0.669131	−	1.15897i	−0.669131	−	1.15897i	0.309017	−	0.951057i	$-0.400000\pi$
$968$	0.139886	+	0.242290i	0.139886	+	0.242290i
$969$		0			0
$970$		0			0
$971$	1.33826			1.33826			0.669131	−	0.743145i	$-0.266667\pi$
$971$	1.33826			1.33826			0.669131	+	0.743145i	$0.266667\pi$
$972$	−0.395472	+	0.684977i	−0.395472	+	0.684977i
$973$		0			0
$974$		0			0
$975$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$976$		0			0
$977$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$977$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	1.22256	+	0.544320i	1.22256	+	0.544320i
$982$		0			0
$983$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$983$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$984$	−0.157960	−	0.486152i	−0.157960	−	0.486152i
$985$		0			0
$986$		0			0
$987$		0			0
$988$	0.773659	−	1.34002i	0.773659	−	1.34002i
$989$		0			0
$990$		0			0
$991$	1.33826			1.33826			0.669131	−	0.743145i	$-0.266667\pi$
$991$	1.33826			1.33826			0.669131	+	0.743145i	$0.266667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	0.161739	+	0.0343786i	0.161739	+	0.0343786i
$997$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$997$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1287.1.ba.c.142.2	✓	8
3.2	odd	2		3861.1.ba.d.2287.3		8
9.4	even	3	inner	1287.1.ba.c.571.2	yes	8
9.5	odd	6		3861.1.ba.d.3574.3		8
11.10	odd	2		1287.1.ba.d.142.3	yes	8
13.12	even	2		1287.1.ba.d.142.3	yes	8
33.32	even	2		3861.1.ba.c.2287.2		8
39.38	odd	2		3861.1.ba.c.2287.2		8
99.32	even	6		3861.1.ba.c.3574.2		8
99.76	odd	6		1287.1.ba.d.571.3	yes	8
117.77	odd	6		3861.1.ba.c.3574.2		8
117.103	even	6		1287.1.ba.d.571.3	yes	8
143.142	odd	2	CM	1287.1.ba.c.142.2	✓	8
429.428	even	2		3861.1.ba.d.2287.3		8
1287.428	even	6		3861.1.ba.d.3574.3		8
1287.571	odd	6	inner	1287.1.ba.c.571.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1287.1.ba.c.142.2	✓	8	1.1	even	1	trivial
1287.1.ba.c.142.2	✓	8	143.142	odd	2	CM
1287.1.ba.c.571.2	yes	8	9.4	even	3	inner
1287.1.ba.c.571.2	yes	8	1287.571	odd	6	inner
1287.1.ba.d.142.3	yes	8	11.10	odd	2
1287.1.ba.d.142.3	yes	8	13.12	even	2
1287.1.ba.d.571.3	yes	8	99.76	odd	6
1287.1.ba.d.571.3	yes	8	117.103	even	6
3861.1.ba.c.2287.2		8	33.32	even	2
3861.1.ba.c.2287.2		8	39.38	odd	2
3861.1.ba.c.3574.2		8	99.32	even	6
3861.1.ba.c.3574.2		8	117.77	odd	6
3861.1.ba.d.2287.3		8	3.2	odd	2
3861.1.ba.d.2287.3		8	429.428	even	2
3861.1.ba.d.3574.3		8	9.5	odd	6
3861.1.ba.d.3574.3		8	1287.428	even	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:	\( N \)	\(=\)	\( 1287 = 3^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1287.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.669131 + 1.15897i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.395472 - 0.684977i) q^{4} +(0.895472 - 0.994522i) q^{6} +(0.809017 - 1.40126i) q^{7} -0.279773 q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})\)	\(q+(-0.669131 + 1.15897i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.395472 - 0.684977i) q^{4} +(0.895472 - 0.994522i) q^{6} +(0.809017 - 1.40126i) q^{7} -0.279773 q^{8} +(0.913545 + 0.406737i) q^{9} +(-0.500000 + 0.866025i) q^{11} +(0.244415 + 0.752232i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(1.08268 + 1.87525i) q^{14} +(0.582676 - 1.00922i) q^{16} +(-1.08268 + 0.786610i) q^{18} -1.95630 q^{19} +(-1.08268 + 1.20243i) q^{21} +(-0.669131 - 1.15897i) q^{22} +(-0.913545 - 1.58231i) q^{23} +(0.273659 + 0.0581680i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.33826 q^{26} +(-0.809017 - 0.587785i) q^{27} -1.27977 q^{28} +(0.639886 + 1.10832i) q^{32} +(0.669131 - 0.743145i) q^{33} +(-0.0826761 - 0.786610i) q^{36} +(1.30902 - 2.26728i) q^{38} +(0.309017 + 0.951057i) q^{39} +(-0.913545 - 1.58231i) q^{41} +(-0.669131 - 2.05937i) q^{42} +0.790943 q^{44} +2.44512 q^{46} +(-0.779773 + 0.866025i) q^{48} +(-0.809017 - 1.40126i) q^{49} +(-0.669131 - 1.15897i) q^{50} +(-0.395472 + 0.684977i) q^{52} +0.618034 q^{53} +(1.22256 - 0.544320i) q^{54} +(-0.226341 + 0.392034i) q^{56} +(1.91355 + 0.406737i) q^{57} +(1.30902 - 0.951057i) q^{63} -0.547318 q^{64} +(0.413545 + 1.27276i) q^{66} +(0.564602 + 1.73767i) q^{69} +(-0.255585 - 0.113794i) q^{72} +0.618034 q^{73} +(0.669131 - 0.743145i) q^{75} +(0.773659 + 1.34002i) q^{76} +(0.809017 + 1.40126i) q^{77} +(-1.30902 - 0.278240i) q^{78} +(0.669131 + 0.743145i) q^{81} +2.44512 q^{82} +(0.104528 - 0.181049i) q^{83} +(1.25181 + 0.266080i) q^{84} +(0.139886 - 0.242290i) q^{88} -1.61803 q^{91} +(-0.722562 + 1.25151i) q^{92} +(-0.395472 - 1.21714i) q^{96} +2.16535 q^{98} +(-0.809017 + 0.587785i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + q^{3} - 5 q^{4} + 9 q^{6} + 2 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) 8 * q - q^2 + q^3 - 5 * q^4 + 9 * q^6 + 2 * q^7 - 2 * q^8 + q^9	\( 8 q - q^{2} + q^{3} - 5 q^{4} + 9 q^{6} + 2 q^{7} - 2 q^{8} + q^{9} - 4 q^{11} - 4 q^{13} - 2 q^{14} - 6 q^{16} + 2 q^{18} + 2 q^{19} + 2 q^{21} - q^{22} - q^{23} - 4 q^{24} - 4 q^{25} + 2 q^{26} - 2 q^{27} - 10 q^{28} + 5 q^{32} + q^{33} + 10 q^{36} + 6 q^{38} - 2 q^{39} - q^{41} - q^{42} + 10 q^{44} - 2 q^{46} - 6 q^{48} - 2 q^{49} - q^{50} - 5 q^{52} - 4 q^{53} - q^{54} - 8 q^{56} + 9 q^{57} + 6 q^{63} + 8 q^{64} - 3 q^{66} + 2 q^{69} - 4 q^{72} - 4 q^{73} + q^{75} + 2 q^{77} - 6 q^{78} + q^{81} - 2 q^{82} - q^{83} - 5 q^{84} + q^{88} - 4 q^{91} + 5 q^{92} - 5 q^{96} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) 8 * q - q^2 + q^3 - 5 * q^4 + 9 * q^6 + 2 * q^7 - 2 * q^8 + q^9 - 4 * q^11 - 4 * q^13 - 2 * q^14 - 6 * q^16 + 2 * q^18 + 2 * q^19 + 2 * q^21 - q^22 - q^23 - 4 * q^24 - 4 * q^25 + 2 * q^26 - 2 * q^27 - 10 * q^28 + 5 * q^32 + q^33 + 10 * q^36 + 6 * q^38 - 2 * q^39 - q^41 - q^42 + 10 * q^44 - 2 * q^46 - 6 * q^48 - 2 * q^49 - q^50 - 5 * q^52 - 4 * q^53 - q^54 - 8 * q^56 + 9 * q^57 + 6 * q^63 + 8 * q^64 - 3 * q^66 + 2 * q^69 - 4 * q^72 - 4 * q^73 + q^75 + 2 * q^77 - 6 * q^78 + q^81 - 2 * q^82 - q^83 - 5 * q^84 + q^88 - 4 * q^91 + 5 * q^92 - 5 * q^96 - 4 * q^98 - 2 * q^99

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