LMFDB - Embedded newform 2940.1.dd.a.1319.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2940,1,Mod(59,2940)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2940, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([21, 21, 21, 13])) N = Newforms(chi, 1, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2940.59"); S:= CuspForms(chi, 1); N := Newforms(S);

Level:	$ N $	$=$	$ 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2940.dd (of order $42$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,-2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$1.46725113714$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{42})$
Coefficient field:	$\Q(\zeta_{84})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} + x^{22} - x^{18} - x^{16} + x^{12} - x^{8} - x^{6} + x^{2} + 1 $ x^24 + x^22 - x^18 - x^16 + x^12 - x^8 - x^6 + x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{42}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{42} - \cdots)$

Embedding invariants

Embedding label			1319.2
Root			$-0.680173 - 0.733052i$ of defining polynomial
Character	$\chi$	$=$	2940.1319
Dual form			2940.1.dd.a.1139.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.563320 - 0.826239i) q^{2} +(-0.433884 + 0.900969i) q^{3} +(-0.365341 - 0.930874i) q^{4} +(-0.955573 + 0.294755i) q^{5} +(0.500000 + 0.866025i) q^{6} +(0.930874 - 0.365341i) q^{7} +(-0.974928 - 0.222521i) q^{8} +(-0.623490 - 0.781831i) q^{9} +(-0.294755 + 0.955573i) q^{10} +(0.997204 + 0.0747301i) q^{12} +(0.222521 - 0.974928i) q^{14} +(0.149042 - 0.988831i) q^{15} +(-0.733052 + 0.680173i) q^{16} +(-0.997204 + 0.0747301i) q^{18} +(0.623490 + 0.781831i) q^{20} +(-0.0747301 + 0.997204i) q^{21} +(0.218511 - 1.44973i) q^{23} +(0.623490 - 0.781831i) q^{24} +(0.826239 - 0.563320i) q^{25} +(0.974928 - 0.222521i) q^{27} +(-0.680173 - 0.733052i) q^{28} +(0.233052 - 0.185853i) q^{29} +(-0.733052 - 0.680173i) q^{30} +(0.149042 + 0.988831i) q^{32} +(-0.781831 + 0.623490i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(0.997204 - 0.0747301i) q^{40} +(-0.0332580 + 0.145713i) q^{41} +(0.781831 + 0.623490i) q^{42} +(-0.443797 - 1.94440i) q^{43} +(0.826239 + 0.563320i) q^{45} +(-1.07473 - 0.997204i) q^{46} +(-1.61105 - 1.09839i) q^{47} +(-0.294755 - 0.955573i) q^{48} +(0.733052 - 0.680173i) q^{49} -1.00000i q^{50} +(0.365341 - 0.930874i) q^{54} +(-0.988831 + 0.149042i) q^{56} +(-0.0222759 - 0.297251i) q^{58} +(-0.974928 + 0.222521i) q^{60} +(1.26631 + 0.496990i) q^{61} +(-0.866025 - 0.500000i) q^{63} +(0.900969 + 0.433884i) q^{64} +(0.866025 - 1.50000i) q^{67} +(1.21135 + 0.825886i) q^{69} +(0.0747301 + 0.997204i) q^{70} +(0.433884 + 0.900969i) q^{72} +(0.149042 + 0.988831i) q^{75} +(0.500000 - 0.866025i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(0.101659 + 0.109562i) q^{82} +(1.67738 + 0.807782i) q^{83} +(0.955573 - 0.294755i) q^{84} +(-1.85654 - 0.728639i) q^{86} +(0.0663300 + 0.290611i) q^{87} +(-0.147791 - 1.97213i) q^{89} +(0.930874 - 0.365341i) q^{90} +(-1.42935 + 0.326239i) q^{92} +(-1.81507 + 0.712362i) q^{94} +(-0.955573 - 0.294755i) q^{96} +(-0.149042 - 0.988831i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{4} - 2 q^{5} + 12 q^{6} + 4 q^{9} + 4 q^{14} + 2 q^{16} - 4 q^{20} - 2 q^{21} - 4 q^{24} + 2 q^{25} - 14 q^{29} + 2 q^{30} - 12 q^{36} + 4 q^{41} + 2 q^{45} - 26 q^{46} - 2 q^{49} + 2 q^{54}+ \cdots - 2 q^{96}+O(q^{100}) $ 24 * q - 2 * q^4 - 2 * q^5 + 12 * q^6 + 4 * q^9 + 4 * q^14 + 2 * q^16 - 4 * q^20 - 2 * q^21 - 4 * q^24 + 2 * q^25 - 14 * q^29 + 2 * q^30 - 12 * q^36 + 4 * q^41 + 2 * q^45 - 26 * q^46 - 2 * q^49 + 2 * q^54 + 2 * q^56 + 6 * q^61 + 4 * q^64 + 2 * q^69 + 2 * q^70 + 12 * q^80 - 4 * q^81 + 2 * q^84 - 6 * q^86 - 2 * q^89 - 2 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2940\mathbb{Z}\right)^\times$.

$n$	$1081$	$1177$	$1471$	$1961$
$\chi(n)$	$e\left(\frac{31}{42}\right)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.563320	−	0.826239i	0.563320	−	0.826239i
$2$	0.563320	−	0.826239i	0.563320	−	0.826239i
$3$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$3$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$4$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$5$	−0.955573	+	0.294755i	−0.955573	+	0.294755i
$5$	−0.955573	+	0.294755i	−0.955573	+	0.294755i
$6$	0.500000	+	0.866025i	0.500000	+	0.866025i
$7$	0.930874	−	0.365341i	0.930874	−	0.365341i
$7$	0.930874	−	0.365341i	0.930874	−	0.365341i
$8$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$9$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$10$	−0.294755	+	0.955573i	−0.294755	+	0.955573i
$11$		0			0		−0.997204	−	0.0747301i	$-0.976190\pi$
$11$		0			0		0.997204	+	0.0747301i	$0.0238095\pi$
$12$	0.997204	+	0.0747301i	0.997204	+	0.0747301i
$13$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$13$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$14$	0.222521	−	0.974928i	0.222521	−	0.974928i
$15$	0.149042	−	0.988831i	0.149042	−	0.988831i
$16$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$17$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$17$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$18$	−0.997204	+	0.0747301i	−0.997204	+	0.0747301i
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$	0.623490	+	0.781831i	0.623490	+	0.781831i
$21$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$22$		0			0
$23$	0.218511	−	1.44973i	0.218511	−	1.44973i	−0.563320	−	0.826239i	$-0.690476\pi$
$23$	0.218511	−	1.44973i	0.218511	−	1.44973i	0.781831	−	0.623490i	$-0.214286\pi$
$24$	0.623490	−	0.781831i	0.623490	−	0.781831i
$25$	0.826239	−	0.563320i	0.826239	−	0.563320i
$26$		0			0
$27$	0.974928	−	0.222521i	0.974928	−	0.222521i
$28$	−0.680173	−	0.733052i	−0.680173	−	0.733052i
$29$	0.233052	−	0.185853i	0.233052	−	0.185853i	−0.500000	−	0.866025i	$-0.666667\pi$
$29$	0.233052	−	0.185853i	0.233052	−	0.185853i	0.733052	+	0.680173i	$0.238095\pi$
$30$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$31$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$31$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$32$	0.149042	+	0.988831i	0.149042	+	0.988831i
$33$		0			0
$34$		0			0
$35$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$36$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$37$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$37$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$38$		0			0
$39$		0			0
$40$	0.997204	−	0.0747301i	0.997204	−	0.0747301i
$41$	−0.0332580	+	0.145713i	−0.0332580	+	0.145713i	−0.988831	−	0.149042i	$-0.952381\pi$
$41$	−0.0332580	+	0.145713i	−0.0332580	+	0.145713i	0.955573	+	0.294755i	$0.0952381\pi$
$42$	0.781831	+	0.623490i	0.781831	+	0.623490i
$43$	−0.443797	−	1.94440i	−0.443797	−	1.94440i	−0.294755	−	0.955573i	$-0.595238\pi$
$43$	−0.443797	−	1.94440i	−0.443797	−	1.94440i	−0.149042	−	0.988831i	$-0.547619\pi$
$44$		0			0
$45$	0.826239	+	0.563320i	0.826239	+	0.563320i
$46$	−1.07473	−	0.997204i	−1.07473	−	0.997204i
$47$	−1.61105	−	1.09839i	−1.61105	−	1.09839i	−0.930874	−	0.365341i	$-0.880952\pi$
$47$	−1.61105	−	1.09839i	−1.61105	−	1.09839i	−0.680173	−	0.733052i	$-0.738095\pi$
$48$	−0.294755	−	0.955573i	−0.294755	−	0.955573i
$49$	0.733052	−	0.680173i	0.733052	−	0.680173i
$50$		−	1.00000i		−	1.00000i
$51$		0			0
$52$		0			0
$53$		0			0		0.930874	−	0.365341i	$-0.119048\pi$
$53$		0			0		−0.930874	+	0.365341i	$0.880952\pi$
$54$	0.365341	−	0.930874i	0.365341	−	0.930874i
$55$		0			0
$56$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$57$		0			0
$58$	−0.0222759	−	0.297251i	−0.0222759	−	0.297251i
$59$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$59$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$60$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$61$	1.26631	+	0.496990i	1.26631	+	0.496990i	0.900969	−	0.433884i	$-0.142857\pi$
$61$	1.26631	+	0.496990i	1.26631	+	0.496990i	0.365341	+	0.930874i	$0.380952\pi$
$62$		0			0
$63$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$64$	0.900969	+	0.433884i	0.900969	+	0.433884i
$65$		0			0
$66$		0			0
$67$	0.866025	−	1.50000i	0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$67$	0.866025	−	1.50000i	0.866025	−	1.50000i	0.866025	−	0.500000i	$-0.166667\pi$
$68$		0			0
$69$	1.21135	+	0.825886i	1.21135	+	0.825886i
$70$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$71$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$71$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$72$	0.433884	+	0.900969i	0.433884	+	0.900969i
$73$		0			0		−0.563320	−	0.826239i	$-0.690476\pi$
$73$		0			0		0.563320	+	0.826239i	$0.309524\pi$
$74$		0			0
$75$	0.149042	+	0.988831i	0.149042	+	0.988831i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$79$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$80$	0.500000	−	0.866025i	0.500000	−	0.866025i
$81$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$82$	0.101659	+	0.109562i	0.101659	+	0.109562i
$83$	1.67738	+	0.807782i	1.67738	+	0.807782i	0.997204	+	0.0747301i	$0.0238095\pi$
$83$	1.67738	+	0.807782i	1.67738	+	0.807782i	0.680173	+	0.733052i	$0.261905\pi$
$84$	0.955573	−	0.294755i	0.955573	−	0.294755i
$85$		0			0
$86$	−1.85654	−	0.728639i	−1.85654	−	0.728639i
$87$	0.0663300	+	0.290611i	0.0663300	+	0.290611i
$88$		0			0
$89$	−0.147791	−	1.97213i	−0.147791	−	1.97213i	−0.222521	−	0.974928i	$-0.571429\pi$
$89$	−0.147791	−	1.97213i	−0.147791	−	1.97213i	0.0747301	−	0.997204i	$-0.476190\pi$
$90$	0.930874	−	0.365341i	0.930874	−	0.365341i
$91$		0			0
$92$	−1.42935	+	0.326239i	−1.42935	+	0.326239i
$93$		0			0
$94$	−1.81507	+	0.712362i	−1.81507	+	0.712362i
$95$		0			0
$96$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$97$		0			0			−	1.00000i	$-0.5\pi$
$97$		0			0				1.00000i	$0.5\pi$
$98$	−0.149042	−	0.988831i	−0.149042	−	0.988831i
$99$		0			0
$100$	−0.826239	−	0.563320i	−0.826239	−	0.563320i
$101$	0.535628	+	0.496990i	0.535628	+	0.496990i	0.900969	−	0.433884i	$-0.142857\pi$
$101$	0.535628	+	0.496990i	0.535628	+	0.496990i	−0.365341	+	0.930874i	$0.619048\pi$
$102$		0			0
$103$	−0.294755	−	0.955573i	−0.294755	−	0.955573i	−0.974928	−	0.222521i	$-0.928571\pi$
$103$	−0.294755	−	0.955573i	−0.294755	−	0.955573i	0.680173	−	0.733052i	$-0.261905\pi$
$104$		0			0
$105$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$106$		0			0
$107$	−0.728639	+	0.0546039i	−0.728639	+	0.0546039i	−0.433884	−	0.900969i	$-0.642857\pi$
$107$	−0.728639	+	0.0546039i	−0.728639	+	0.0546039i	−0.294755	+	0.955573i	$0.595238\pi$
$108$	−0.563320	−	0.826239i	−0.563320	−	0.826239i
$109$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i	0.826239	+	0.563320i	$0.190476\pi$
$109$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i	−0.900969	+	0.433884i	$0.857143\pi$
$110$		0			0
$111$		0			0
$112$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$113$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$113$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$114$		0			0
$115$	0.218511	+	1.44973i	0.218511	+	1.44973i
$116$	−0.258149	−	0.149042i	−0.258149	−	0.149042i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−0.365341	+	0.930874i	−0.365341	+	0.930874i
$121$	0.988831	+	0.149042i	0.988831	+	0.149042i
$122$	1.12397	−	0.766310i	1.12397	−	0.766310i
$123$	−0.116853	−	0.0931869i	−0.116853	−	0.0931869i
$124$		0			0
$125$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$126$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$127$	−0.541044	−	0.678448i	−0.541044	−	0.678448i	0.433884	−	0.900969i	$-0.357143\pi$
$127$	−0.541044	−	0.678448i	−0.541044	−	0.678448i	−0.974928	+	0.222521i	$0.928571\pi$
$128$	0.866025	−	0.500000i	0.866025	−	0.500000i
$129$	1.94440	+	0.443797i	1.94440	+	0.443797i
$130$		0			0
$131$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$131$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$132$		0			0
$133$		0			0
$134$	−0.751509	−	1.56052i	−0.751509	−	1.56052i
$135$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$136$		0			0
$137$		0			0		0.294755	−	0.955573i	$-0.404762\pi$
$137$		0			0		−0.294755	+	0.955573i	$0.595238\pi$
$138$	1.36476	−	0.535628i	1.36476	−	0.535628i
$139$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$139$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$140$	0.866025	+	0.500000i	0.866025	+	0.500000i
$141$	1.68862	−	0.974928i	1.68862	−	0.974928i
$142$		0			0
$143$		0			0
$144$	0.988831	+	0.149042i	0.988831	+	0.149042i
$145$	−0.167917	+	0.246289i	−0.167917	+	0.246289i
$146$		0			0
$147$	0.294755	+	0.955573i	0.294755	+	0.955573i
$148$		0			0
$149$	−1.04876	+	1.53825i	−1.04876	+	1.53825i	−0.222521	+	0.974928i	$0.571429\pi$
$149$	−1.04876	+	1.53825i	−1.04876	+	1.53825i	−0.826239	+	0.563320i	$0.809524\pi$
$150$	0.900969	+	0.433884i	0.900969	+	0.433884i
$151$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$151$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.294755	−	0.955573i	$-0.404762\pi$
$157$		0			0		−0.294755	+	0.955573i	$0.595238\pi$
$158$		0			0
$159$		0			0
$160$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$161$	−0.326239	−	1.42935i	−0.326239	−	1.42935i
$162$	0.680173	+	0.733052i	0.680173	+	0.733052i
$163$	−1.14625	+	1.06356i	−1.14625	+	1.06356i	−0.149042	+	0.988831i	$0.547619\pi$
$163$	−1.14625	+	1.06356i	−1.14625	+	1.06356i	−0.997204	+	0.0747301i	$0.976190\pi$
$164$	0.147791	−	0.0222759i	0.147791	−	0.0222759i
$165$		0			0
$166$	1.61232	−	0.930874i	1.61232	−	0.930874i
$167$	−0.702449	−	0.880843i	−0.702449	−	0.880843i	0.294755	−	0.955573i	$-0.404762\pi$
$167$	−0.702449	−	0.880843i	−0.702449	−	0.880843i	−0.997204	+	0.0747301i	$0.976190\pi$
$168$	0.294755	−	0.955573i	0.294755	−	0.955573i
$169$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$170$		0			0
$171$		0			0
$172$	−1.64786	+	1.12349i	−1.64786	+	1.12349i
$173$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$173$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$174$	0.277479	+	0.108903i	0.277479	+	0.108903i
$175$	0.563320	−	0.826239i	0.563320	−	0.826239i
$176$		0			0
$177$		0			0
$178$	−1.71271	−	0.988831i	−1.71271	−	0.988831i
$179$		0			0		−0.149042	−	0.988831i	$-0.547619\pi$
$179$		0			0		0.149042	+	0.988831i	$0.452381\pi$
$180$	0.222521	−	0.974928i	0.222521	−	0.974928i
$181$	−0.751509	+	1.56052i	−0.751509	+	1.56052i	0.0747301	+	0.997204i	$0.476190\pi$
$181$	−0.751509	+	1.56052i	−0.751509	+	1.56052i	−0.826239	+	0.563320i	$0.809524\pi$
$182$		0			0
$183$	−0.997204	+	0.925270i	−0.997204	+	0.925270i
$184$	−0.535628	+	1.36476i	−0.535628	+	1.36476i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−0.433884	+	1.90097i	−0.433884	+	1.90097i
$189$	0.826239	−	0.563320i	0.826239	−	0.563320i
$190$		0			0
$191$		0			0		−0.294755	−	0.955573i	$-0.595238\pi$
$191$		0			0		0.294755	+	0.955573i	$0.404762\pi$
$192$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$193$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$193$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$194$		0			0
$195$		0			0
$196$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$		0			0
$199$		0			0		0.680173	−	0.733052i	$-0.261905\pi$
$199$		0			0		−0.680173	+	0.733052i	$0.738095\pi$
$200$	−0.930874	+	0.365341i	−0.930874	+	0.365341i
$201$	0.975699	+	1.43109i	0.975699	+	1.43109i
$202$	0.712362	−	0.162592i	0.712362	−	0.162592i
$203$	0.149042	−	0.258149i	0.149042	−	0.258149i
$204$		0			0
$205$	−0.0111692	−	0.149042i	−0.0111692	−	0.149042i
$206$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$207$	−1.26968	+	0.733052i	−1.26968	+	0.733052i
$208$		0			0
$209$		0			0
$210$	−0.930874	−	0.365341i	−0.930874	−	0.365341i
$211$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$211$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$212$		0			0
$213$		0			0
$214$	−0.365341	+	0.632789i	−0.365341	+	0.632789i
$215$	0.997204	+	1.72721i	0.997204	+	1.72721i
$216$	−1.00000			−1.00000
$217$		0			0
$218$	0.781831	+	0.623490i	0.781831	+	0.623490i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	1.40881	+	1.12349i	1.40881	+	1.12349i	0.974928	+	0.222521i	$0.0714286\pi$
$223$	1.40881	+	1.12349i	1.40881	+	1.12349i	0.433884	+	0.900969i	$0.357143\pi$
$224$	0.500000	+	0.866025i	0.500000	+	0.866025i
$225$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$226$		0			0
$227$	−0.433884	+	0.751509i	−0.433884	+	0.751509i	−0.997204	−	0.0747301i	$-0.976190\pi$
$227$	−0.433884	+	0.751509i	−0.433884	+	0.751509i	0.563320	+	0.826239i	$0.309524\pi$
$228$		0			0
$229$	−1.06356	−	1.14625i	−1.06356	−	1.14625i	−0.988831	−	0.149042i	$-0.952381\pi$
$229$	−1.06356	−	1.14625i	−1.06356	−	1.14625i	−0.0747301	−	0.997204i	$-0.523810\pi$
$230$	1.32091	+	0.636119i	1.32091	+	0.636119i
$231$		0			0
$232$	−0.268565	+	0.129334i	−0.268565	+	0.129334i
$233$		0			0		−0.930874	−	0.365341i	$-0.880952\pi$
$233$		0			0		0.930874	+	0.365341i	$0.119048\pi$
$234$		0			0
$235$	1.86323	+	0.574730i	1.86323	+	0.574730i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$239$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$240$	0.563320	+	0.826239i	0.563320	+	0.826239i
$241$	−0.807782	+	0.317031i	−0.807782	+	0.317031i	−0.733052	−	0.680173i	$-0.761905\pi$
$241$	−0.807782	+	0.317031i	−0.807782	+	0.317031i	−0.0747301	+	0.997204i	$0.523810\pi$
$242$	0.680173	−	0.733052i	0.680173	−	0.733052i
$243$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$244$		−	1.36035i		−	1.36035i
$245$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$246$	−0.142820	+	0.0440542i	−0.142820	+	0.0440542i
$247$		0			0
$248$		0			0
$249$	−1.45557	+	1.16078i	−1.45557	+	1.16078i
$250$	0.294755	+	0.955573i	0.294755	+	0.955573i
$251$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$251$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$252$	−0.149042	+	0.988831i	−0.149042	+	0.988831i
$253$		0			0
$254$	−0.865341	+	0.0648483i	−0.865341	+	0.0648483i
$255$		0			0
$256$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$257$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$257$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$258$	1.46200	−	1.35654i	1.46200	−	1.35654i
$259$		0			0
$260$		0			0
$261$	−0.290611	−	0.0663300i	−0.290611	−	0.0663300i
$262$		0			0
$263$	1.71271	+	0.988831i	1.71271	+	0.988831i	0.930874	+	0.365341i	$0.119048\pi$
$263$	1.71271	+	0.988831i	1.71271	+	0.988831i	0.781831	+	0.623490i	$0.214286\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.84095	+	0.722521i	1.84095	+	0.722521i
$268$	−1.71271	−	0.258149i	−1.71271	−	0.258149i
$269$	1.36534	−	0.930874i	1.36534	−	0.930874i	0.365341	−	0.930874i	$-0.380952\pi$
$269$	1.36534	−	0.930874i	1.36534	−	0.930874i	1.00000			$0$
$270$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$271$		0			0		0.149042	−	0.988831i	$-0.452381\pi$
$271$		0			0		−0.149042	+	0.988831i	$0.547619\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	0.326239	−	1.42935i	0.326239	−	1.42935i
$277$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$277$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$278$		0			0
$279$		0			0
$280$	0.900969	−	0.433884i	0.900969	−	0.433884i
$281$	0.846011	+	1.75676i	0.846011	+	1.75676i	0.623490	+	0.781831i	$0.285714\pi$
$281$	0.846011	+	1.75676i	0.846011	+	1.75676i	0.222521	+	0.974928i	$0.428571\pi$
$282$	0.145713	−	1.94440i	0.145713	−	1.94440i
$283$	0.443797	+	0.0332580i	0.443797	+	0.0332580i	0.294755	−	0.955573i	$-0.404762\pi$
$283$	0.443797	+	0.0332580i	0.443797	+	0.0332580i	0.149042	+	0.988831i	$0.452381\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.0222759	+	0.147791i	0.0222759	+	0.147791i
$288$	0.680173	−	0.733052i	0.680173	−	0.733052i
$289$	0.955573	−	0.294755i	0.955573	−	0.294755i
$290$	0.108903	+	0.277479i	0.108903	+	0.277479i
$291$		0			0
$292$		0			0
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	0.955573	+	0.294755i	0.955573	+	0.294755i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	0.680173	+	1.73305i	0.680173	+	1.73305i
$299$		0			0
$300$	0.866025	−	0.500000i	0.866025	−	0.500000i
$301$	−1.12349	−	1.64786i	−1.12349	−	1.64786i
$302$		0			0
$303$	−0.680173	+	0.266948i	−0.680173	+	0.266948i
$304$		0			0
$305$	−1.35654	−	0.101659i	−1.35654	−	0.101659i
$306$		0			0
$307$	0.716983	+	1.48883i	0.716983	+	1.48883i	0.866025	+	0.500000i	$0.166667\pi$
$307$	0.716983	+	1.48883i	0.716983	+	1.48883i	−0.149042	+	0.988831i	$0.547619\pi$
$308$		0			0
$309$	0.988831	+	0.149042i	0.988831	+	0.149042i
$310$		0			0
$311$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$311$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$312$		0			0
$313$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$313$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$314$		0			0
$315$	0.974928	+	0.222521i	0.974928	+	0.222521i
$316$		0			0
$317$		0			0		0.149042	−	0.988831i	$-0.452381\pi$
$317$		0			0		−0.149042	+	0.988831i	$0.547619\pi$
$318$		0			0
$319$		0			0
$320$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$321$	0.266948	−	0.680173i	0.266948	−	0.680173i
$322$	−1.36476	−	0.535628i	−1.36476	−	0.535628i
$323$		0			0
$324$	0.988831	−	0.149042i	0.988831	−	0.149042i
$325$		0			0
$326$	0.233052	+	1.54620i	0.233052	+	1.54620i
$327$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$328$	0.0648483	−	0.134659i	0.0648483	−	0.134659i
$329$	−1.90097	−	0.433884i	−1.90097	−	0.433884i
$330$		0			0
$331$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$331$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$332$	0.139129	−	1.85654i	0.139129	−	1.85654i
$333$		0			0
$334$	−1.12349	+	0.0841939i	−1.12349	+	0.0841939i
$335$	−0.385418	+	1.68862i	−0.385418	+	1.68862i
$336$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$337$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$337$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$338$	0.294755	+	0.955573i	0.294755	+	0.955573i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.433884	−	0.900969i	0.433884	−	0.900969i
$344$			1.99441i			1.99441i
$345$	−1.40097	−	0.432142i	−1.40097	−	0.432142i
$346$		0			0
$347$	0.139129	−	0.0546039i	0.139129	−	0.0546039i	−0.294755	−	0.955573i	$-0.595238\pi$
$347$	0.139129	−	0.0546039i	0.139129	−	0.0546039i	0.433884	+	0.900969i	$0.357143\pi$
$348$	0.246289	−	0.167917i	0.246289	−	0.167917i
$349$	−1.94440	+	0.443797i	−1.94440	+	0.443797i	−0.955573	+	0.294755i	$0.904762\pi$
$349$	−1.94440	+	0.443797i	−1.94440	+	0.443797i	−0.988831	+	0.149042i	$0.952381\pi$
$350$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$351$		0			0
$352$		0			0
$353$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$353$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$354$		0			0
$355$		0			0
$356$	−1.78181	+	0.858075i	−1.78181	+	0.858075i
$357$		0			0
$358$		0			0
$359$		0			0		−0.680173	−	0.733052i	$-0.738095\pi$
$359$		0			0		0.680173	+	0.733052i	$0.261905\pi$
$360$	−0.680173	−	0.733052i	−0.680173	−	0.733052i
$361$	0.500000	−	0.866025i	0.500000	−	0.866025i
$362$	0.866025	+	1.50000i	0.866025	+	1.50000i
$363$	−0.563320	+	0.826239i	−0.563320	+	0.826239i
$364$		0			0
$365$		0			0
$366$	0.202749	+	1.34515i	0.202749	+	1.34515i
$367$	0.930874	+	1.36534i	0.930874	+	1.36534i	0.930874	+	0.365341i	$0.119048\pi$
$367$	0.930874	+	1.36534i	0.930874	+	1.36534i			1.00000i	$0.5\pi$
$368$	0.825886	+	1.21135i	0.825886	+	1.21135i
$369$	0.134659	−	0.0648483i	0.134659	−	0.0648483i
$370$		0			0
$371$		0			0
$372$		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
$375$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$376$	1.32624	+	1.42935i	1.32624	+	1.42935i
$377$		0			0
$378$		−	1.00000i		−	1.00000i
$379$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$379$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$380$		0			0
$381$	0.846011	−	0.193096i	0.846011	−	0.193096i
$382$		0			0
$383$	−0.0222759	−	0.297251i	−0.0222759	−	0.297251i	−0.997204	−	0.0747301i	$-0.976190\pi$
$383$	−0.0222759	−	0.297251i	−0.0222759	−	0.297251i	0.974928	−	0.222521i	$-0.0714286\pi$
$384$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$385$		0			0
$386$		0			0
$387$	−1.24349	+	1.55929i	−1.24349	+	1.55929i
$388$		0			0
$389$	−1.06356	+	1.14625i	−1.06356	+	1.14625i	−0.0747301	+	0.997204i	$0.523810\pi$
$389$	−1.06356	+	1.14625i	−1.06356	+	1.14625i	−0.988831	+	0.149042i	$0.952381\pi$
$390$		0			0
$391$		0			0
$392$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.294755	−	0.955573i	$-0.595238\pi$
$397$		0			0		0.294755	+	0.955573i	$0.404762\pi$
$398$		0			0
$399$		0			0
$400$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$401$	0.587862	−	0.0440542i	0.587862	−	0.0440542i	0.222521	−	0.974928i	$-0.428571\pi$
$401$	0.587862	−	0.0440542i	0.587862	−	0.0440542i	0.365341	+	0.930874i	$0.380952\pi$
$402$	1.73205			1.73205
$403$		0			0
$404$	0.266948	−	0.680173i	0.266948	−	0.680173i
$405$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i
$406$	−0.129334	−	0.268565i	−0.129334	−	0.268565i
$407$		0			0
$408$		0			0
$409$	0.167917	+	1.11406i	0.167917	+	1.11406i	0.900969	+	0.433884i	$0.142857\pi$
$409$	0.167917	+	1.11406i	0.167917	+	1.11406i	−0.733052	+	0.680173i	$0.761905\pi$
$410$	−0.129436	−	0.0747301i	−0.129436	−	0.0747301i
$411$		0			0
$412$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$413$		0			0
$414$	−0.109562	+	1.46200i	−0.109562	+	1.46200i
$415$	−1.84095	−	0.277479i	−1.84095	−	0.277479i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$419$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$420$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$421$	−1.19158	−	1.49419i	−1.19158	−	1.49419i	−0.826239	−	0.563320i	$-0.809524\pi$
$421$	−1.19158	−	1.49419i	−1.19158	−	1.49419i	−0.365341	−	0.930874i	$-0.619048\pi$
$422$		0			0
$423$	0.145713	+	1.94440i	0.145713	+	1.94440i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.36035			1.36035
$428$	0.317031	+	0.658322i	0.317031	+	0.658322i
$429$		0			0
$430$	1.98883	+	0.149042i	1.98883	+	0.149042i
$431$		0			0		0.294755	−	0.955573i	$-0.404762\pi$
$431$		0			0		−0.294755	+	0.955573i	$0.595238\pi$
$432$	−0.563320	+	0.826239i	−0.563320	+	0.826239i
$433$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$433$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$434$		0			0
$435$	−0.149042	−	0.258149i	−0.149042	−	0.258149i
$436$	0.955573	−	0.294755i	0.955573	−	0.294755i
$437$		0			0
$438$		0			0
$439$		0			0		0.563320	−	0.826239i	$-0.309524\pi$
$439$		0			0		−0.563320	+	0.826239i	$0.690476\pi$
$440$		0			0
$441$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$442$		0			0
$443$	1.11406	−	1.63402i	1.11406	−	1.63402i	0.433884	−	0.900969i	$-0.357143\pi$
$443$	1.11406	−	1.63402i	1.11406	−	1.63402i	0.680173	−	0.733052i	$-0.261905\pi$
$444$		0			0
$445$	0.722521	+	1.84095i	0.722521	+	1.84095i
$446$	1.72188	−	0.531130i	1.72188	−	0.531130i
$447$	−0.930874	−	1.61232i	−0.930874	−	1.61232i
$448$	0.997204	+	0.0747301i	0.997204	+	0.0747301i
$449$	1.32624	+	0.302705i	1.32624	+	0.302705i	0.826239	−	0.563320i	$-0.190476\pi$
$449$	1.32624	+	0.302705i	1.32624	+	0.302705i	0.500000	+	0.866025i	$0.333333\pi$
$450$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.376510	+	0.781831i	0.376510	+	0.781831i
$455$		0			0
$456$		0			0
$457$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$457$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$458$	−1.54620	+	0.233052i	−1.54620	+	0.233052i
$459$		0			0
$460$	1.26968	−	0.733052i	1.26968	−	0.733052i
$461$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$461$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$462$		0			0
$463$	1.16078	−	1.45557i	1.16078	−	1.45557i	0.294755	−	0.955573i	$-0.404762\pi$
$463$	1.16078	−	1.45557i	1.16078	−	1.45557i	0.866025	−	0.500000i	$-0.166667\pi$
$464$	−0.0444272	+	0.294755i	−0.0444272	+	0.294755i
$465$		0			0
$466$		0			0
$467$	1.71271	+	0.258149i	1.71271	+	0.258149i	0.930874	−	0.365341i	$-0.119048\pi$
$467$	1.71271	+	0.258149i	1.71271	+	0.258149i	0.781831	+	0.623490i	$0.214286\pi$
$468$		0			0
$469$	0.258149	−	1.71271i	0.258149	−	1.71271i
$470$	1.52446	−	1.21572i	1.52446	−	1.21572i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$479$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$480$	1.00000			1.00000
$481$		0			0
$482$	−0.193096	+	0.846011i	−0.193096	+	0.846011i
$483$	1.42935	+	0.326239i	1.42935	+	0.326239i
$484$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$485$		0			0
$486$	−0.955573	+	0.294755i	−0.955573	+	0.294755i
$487$	−1.42935	−	1.32624i	−1.42935	−	1.32624i	−0.866025	−	0.500000i	$-0.833333\pi$
$487$	−1.42935	−	1.32624i	−1.42935	−	1.32624i	−0.563320	−	0.826239i	$-0.690476\pi$
$488$	−1.12397	−	0.766310i	−1.12397	−	0.766310i
$489$	−0.460898	−	1.49419i	−0.460898	−	1.49419i
$490$	0.433884	+	0.900969i	0.433884	+	0.900969i
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$	−0.0440542	+	0.142820i	−0.0440542	+	0.142820i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.139129	+	1.85654i	0.139129	+	1.85654i
$499$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$499$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$500$	0.955573	+	0.294755i	0.955573	+	0.294755i
$501$	1.09839	−	0.250701i	1.09839	−	0.250701i
$502$		0			0
$503$	−1.79690	+	0.865341i	−1.79690	+	0.865341i	−0.866025	+	0.500000i	$0.833333\pi$
$503$	−1.79690	+	0.865341i	−1.79690	+	0.865341i	−0.930874	+	0.365341i	$0.880952\pi$
$504$	0.733052	+	0.680173i	0.733052	+	0.680173i
$505$	−0.658322	−	0.317031i	−0.658322	−	0.317031i
$506$		0			0
$507$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$508$	−0.433884	+	0.751509i	−0.433884	+	0.751509i
$509$	−0.733052	−	1.26968i	−0.733052	−	1.26968i	−0.955573	−	0.294755i	$-0.904762\pi$
$509$	−0.733052	−	1.26968i	−0.733052	−	1.26968i	0.222521	−	0.974928i	$-0.428571\pi$
$510$		0			0
$511$		0			0
$512$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$513$		0			0
$514$		0			0
$515$	0.563320	+	0.826239i	0.563320	+	0.826239i
$516$	−0.297251	−	1.97213i	−0.297251	−	1.97213i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.623490	−	1.07992i	0.623490	−	1.07992i	−0.365341	−	0.930874i	$-0.619048\pi$
$521$	0.623490	−	1.07992i	0.623490	−	1.07992i	0.988831	−	0.149042i	$-0.0476190\pi$
$522$	−0.218511	+	0.202749i	−0.218511	+	0.202749i
$523$	−0.848162	−	0.914101i	−0.848162	−	0.914101i	0.149042	−	0.988831i	$-0.452381\pi$
$523$	−0.848162	−	0.914101i	−0.848162	−	0.914101i	−0.997204	+	0.0747301i	$0.976190\pi$
$524$		0			0
$525$	0.500000	+	0.866025i	0.500000	+	0.866025i
$526$	1.78181	−	0.858075i	1.78181	−	0.858075i
$527$		0			0
$528$		0			0
$529$	−1.09839	−	0.338809i	−1.09839	−	0.338809i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	1.63402	−	1.11406i	1.63402	−	1.11406i
$535$	0.680173	−	0.266948i	0.680173	−	0.266948i
$536$	−1.17809	+	1.26968i	−1.17809	+	1.26968i
$537$		0			0
$538$		−	1.65248i		−	1.65248i
$539$		0			0
$540$	0.781831	+	0.623490i	0.781831	+	0.623490i
$541$	1.57906	+	1.07659i	1.57906	+	1.07659i	0.955573	+	0.294755i	$0.0952381\pi$
$541$	1.57906	+	1.07659i	1.57906	+	1.07659i	0.623490	+	0.781831i	$0.285714\pi$
$542$		0			0
$543$	−1.07992	−	1.35417i	−1.07992	−	1.35417i
$544$		0			0
$545$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$546$		0			0
$547$	−0.302705	+	1.32624i	−0.302705	+	1.32624i	0.563320	+	0.826239i	$0.309524\pi$
$547$	−0.302705	+	1.32624i	−0.302705	+	1.32624i	−0.866025	+	0.500000i	$0.833333\pi$
$548$		0			0
$549$	−0.400969	−	1.29991i	−0.400969	−	1.29991i
$550$		0			0
$551$		0			0
$552$	−0.997204	−	1.07473i	−0.997204	−	1.07473i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$557$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$558$		0			0
$559$		0			0
$560$	0.149042	−	0.988831i	0.149042	−	0.988831i
$561$		0			0
$562$	1.92808	+	0.290611i	1.92808	+	0.290611i
$563$	0.246289	−	0.167917i	0.246289	−	0.167917i	−0.433884	−	0.900969i	$-0.642857\pi$
$563$	0.246289	−	0.167917i	0.246289	−	0.167917i	0.680173	+	0.733052i	$0.261905\pi$
$564$	−1.52446	−	1.21572i	−1.52446	−	1.21572i
$565$		0			0
$566$	0.277479	−	0.347948i	0.277479	−	0.347948i
$567$	0.149042	+	0.988831i	0.149042	+	0.988831i
$568$		0			0
$569$	0.751509	−	0.433884i	0.751509	−	0.433884i	−0.0747301	−	0.997204i	$-0.523810\pi$
$569$	0.751509	−	0.433884i	0.751509	−	0.433884i	0.826239	+	0.563320i	$0.190476\pi$
$570$		0			0
$571$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$571$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$572$		0			0
$573$		0			0
$574$	0.134659	+	0.0648483i	0.134659	+	0.0648483i
$575$	−0.636119	−	1.32091i	−0.636119	−	1.32091i
$576$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$577$		0			0		−0.997204	−	0.0747301i	$-0.976190\pi$
$577$		0			0		0.997204	+	0.0747301i	$0.0238095\pi$
$578$	0.294755	−	0.955573i	0.294755	−	0.955573i
$579$		0			0
$580$	0.290611	+	0.0663300i	0.290611	+	0.0663300i
$581$	1.85654	+	0.139129i	1.85654	+	0.139129i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.56366			−1.56366			−0.781831	−	0.623490i	$-0.785714\pi$
$587$	−1.56366			−1.56366			−0.781831	+	0.623490i	$0.785714\pi$
$588$	0.781831	−	0.623490i	0.781831	−	0.623490i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$593$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$594$		0			0
$595$		0			0
$596$	1.81507	+	0.414278i	1.81507	+	0.414278i
$597$		0			0
$598$		0			0
$599$		0			0		−0.997204	−	0.0747301i	$-0.976190\pi$
$599$		0			0		0.997204	+	0.0747301i	$0.0238095\pi$
$600$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$601$	0.678448	+	1.40881i	0.678448	+	1.40881i	0.900969	+	0.433884i	$0.142857\pi$
$601$	0.678448	+	1.40881i	0.678448	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$602$	−1.99441			−1.99441
$603$	−1.71271	+	0.258149i	−1.71271	+	0.258149i
$604$		0			0
$605$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$606$	−0.162592	+	0.712362i	−0.162592	+	0.712362i
$607$	−1.71271	+	0.988831i	−1.71271	+	0.988831i	−0.781831	+	0.623490i	$0.785714\pi$
$607$	−1.71271	+	0.988831i	−1.71271	+	0.988831i	−0.930874	+	0.365341i	$0.880952\pi$
$608$		0			0
$609$	0.167917	+	0.246289i	0.167917	+	0.246289i
$610$	−0.848162	+	1.06356i	−0.848162	+	1.06356i
$611$		0			0
$612$		0			0
$613$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$613$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$614$	1.63402	+	0.246289i	1.63402	+	0.246289i
$615$	0.139129	+	0.0546039i	0.139129	+	0.0546039i
$616$		0			0
$617$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$617$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$618$	0.680173	−	0.733052i	0.680173	−	0.733052i
$619$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$619$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$620$		0			0
$621$	−0.109562	−	1.46200i	−0.109562	−	1.46200i
$622$		0			0
$623$	−0.858075	−	1.78181i	−0.858075	−	1.78181i
$624$		0			0
$625$	0.365341	−	0.930874i	0.365341	−	0.930874i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	0.733052	−	0.680173i	0.733052	−	0.680173i
$631$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$631$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.716983	+	0.488831i	0.716983	+	0.488831i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−0.680173	+	0.733052i	−0.680173	+	0.733052i
$641$	0.548760	−	0.215372i	0.548760	−	0.215372i	−0.0747301	−	0.997204i	$-0.523810\pi$
$641$	0.548760	−	0.215372i	0.548760	−	0.215372i	0.623490	+	0.781831i	$0.285714\pi$
$642$	−0.411608	−	0.603718i	−0.411608	−	0.603718i
$643$	−1.75676	+	0.400969i	−1.75676	+	0.400969i	−0.974928	−	0.222521i	$-0.928571\pi$
$643$	−1.75676	+	0.400969i	−1.75676	+	0.400969i	−0.781831	+	0.623490i	$0.785714\pi$
$644$	−1.21135	+	0.825886i	−1.21135	+	0.825886i
$645$	−1.98883	+	0.149042i	−1.98883	+	0.149042i
$646$		0			0
$647$	1.07659	+	0.332083i	1.07659	+	0.332083i	0.781831	−	0.623490i	$-0.214286\pi$
$647$	1.07659	+	0.332083i	1.07659	+	0.332083i	0.294755	+	0.955573i	$0.404762\pi$
$648$	0.433884	−	0.900969i	0.433884	−	0.900969i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	1.40881	+	0.678448i	1.40881	+	0.678448i
$653$		0			0		−0.680173	−	0.733052i	$-0.738095\pi$
$653$		0			0		0.680173	+	0.733052i	$0.261905\pi$
$654$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$655$		0			0
$656$	−0.0747301	−	0.129436i	−0.0747301	−	0.129436i
$657$		0			0
$658$	−1.42935	+	1.32624i	−1.42935	+	1.32624i
$659$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$659$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$660$		0			0
$661$	−1.04876	−	1.53825i	−1.04876	−	1.53825i	−0.826239	−	0.563320i	$-0.809524\pi$
$661$	−1.04876	−	1.53825i	−1.04876	−	1.53825i	−0.222521	−	0.974928i	$-0.571429\pi$
$662$		0			0
$663$		0			0
$664$	−1.45557	−	1.16078i	−1.45557	−	1.16078i
$665$		0			0
$666$		0			0
$667$	−0.218511	−	0.378473i	−0.218511	−	0.378473i
$668$	−0.563320	+	0.975699i	−0.563320	+	0.975699i
$669$	−1.62349	+	0.781831i	−1.62349	+	0.781831i
$670$	1.17809	+	1.26968i	1.17809	+	1.26968i
$671$		0			0
$672$	−0.997204	+	0.0747301i	−0.997204	+	0.0747301i
$673$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$673$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$674$		0			0
$675$	0.680173	−	0.733052i	0.680173	−	0.733052i
$676$	0.955573	+	0.294755i	0.955573	+	0.294755i
$677$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$677$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.488831	−	0.716983i	−0.488831	−	0.716983i
$682$		0			0
$683$	1.12397	−	1.21135i	1.12397	−	1.21135i	0.149042	−	0.988831i	$-0.452381\pi$
$683$	1.12397	−	1.21135i	1.12397	−	1.21135i	0.974928	−	0.222521i	$-0.0714286\pi$
$684$		0			0
$685$		0			0
$686$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$687$	1.49419	−	0.460898i	1.49419	−	0.460898i
$688$	1.64786	+	1.12349i	1.64786	+	1.12349i
$689$		0			0
$690$	−1.14625	+	0.914101i	−1.14625	+	0.914101i
$691$		0			0		−0.294755	−	0.955573i	$-0.595238\pi$
$691$		0			0		0.294755	+	0.955573i	$0.404762\pi$
$692$		0			0
$693$		0			0
$694$	0.0332580	−	0.145713i	0.0332580	−	0.145713i
$695$		0			0
$696$		−	0.298085i		−	0.298085i
$697$		0			0
$698$	−0.728639	+	1.85654i	−0.728639	+	1.85654i
$699$		0			0
$700$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$701$	0.255779	−	0.531130i	0.255779	−	0.531130i	−0.733052	−	0.680173i	$-0.761905\pi$
$701$	0.255779	−	0.531130i	0.255779	−	0.531130i	0.988831	+	0.149042i	$0.0476190\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−1.32624	+	1.42935i	−1.32624	+	1.42935i
$706$		0			0
$707$	0.680173	+	0.266948i	0.680173	+	0.266948i
$708$		0			0
$709$	−0.722521	−	0.108903i	−0.722521	−	0.108903i	−0.222521	−	0.974928i	$-0.571429\pi$
$709$	−0.722521	−	0.108903i	−0.722521	−	0.108903i	−0.500000	+	0.866025i	$0.666667\pi$
$710$		0			0
$711$		0			0
$712$	−0.294755	+	1.95557i	−0.294755	+	1.95557i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$719$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$720$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$721$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$722$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$723$	0.0648483	−	0.865341i	0.0648483	−	0.865341i
$724$	1.72721	+	0.129436i	1.72721	+	0.129436i
$725$	0.0878620	−	0.284841i	0.0878620	−	0.284841i
$726$	0.365341	+	0.930874i	0.365341	+	0.930874i
$727$	−0.712362	−	0.162592i	−0.712362	−	0.162592i	−0.149042	−	0.988831i	$-0.547619\pi$
$727$	−0.712362	−	0.162592i	−0.712362	−	0.162592i	−0.563320	+	0.826239i	$0.690476\pi$
$728$		0			0
$729$	0.900969	−	0.433884i	0.900969	−	0.433884i
$730$		0			0
$731$		0			0
$732$	1.22563	+	0.590232i	1.22563	+	0.590232i
$733$		0			0		0.563320	−	0.826239i	$-0.309524\pi$
$733$		0			0		−0.563320	+	0.826239i	$0.690476\pi$
$734$	1.65248			1.65248
$735$	−0.563320	−	0.826239i	−0.563320	−	0.826239i
$736$	1.46610			1.46610
$737$		0			0
$738$	0.0222759	−	0.147791i	0.0222759	−	0.147791i
$739$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$739$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.61105	−	0.367711i	−1.61105	−	0.367711i	−0.680173	−	0.733052i	$-0.738095\pi$
$743$	−1.61105	−	0.367711i	−1.61105	−	0.367711i	−0.930874	+	0.365341i	$0.880952\pi$
$744$		0			0
$745$	0.548760	−	1.77904i	0.548760	−	1.77904i
$746$		0			0
$747$	−0.414278	−	1.81507i	−0.414278	−	1.81507i
$748$		0			0
$749$	−0.658322	+	0.317031i	−0.658322	+	0.317031i
$750$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$751$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$751$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$752$	1.92808	−	0.290611i	1.92808	−	0.290611i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−0.826239	−	0.563320i	−0.826239	−	0.563320i
$757$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$757$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.78181	+	0.268565i	1.78181	+	0.268565i	0.955573	−	0.294755i	$-0.0952381\pi$
$761$	1.78181	+	0.268565i	1.78181	+	0.268565i	0.826239	+	0.563320i	$0.190476\pi$
$762$	0.317031	−	0.807782i	0.317031	−	0.807782i
$763$	0.294755	+	0.955573i	0.294755	+	0.955573i
$764$		0			0
$765$		0			0
$766$	−0.258149	−	0.149042i	−0.258149	−	0.149042i
$767$		0			0
$768$	0.866025	+	0.500000i	0.866025	+	0.500000i
$769$	−0.376510	+	0.781831i	−0.376510	+	0.781831i	0.623490	+	0.781831i	$0.285714\pi$
$769$	−0.376510	+	0.781831i	−0.376510	+	0.781831i	−1.00000			$\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$773$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$774$	0.587862	+	1.90580i	0.587862	+	1.90580i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	0.347948	+	1.52446i	0.347948	+	1.52446i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.185853	−	0.233052i	0.185853	−	0.233052i
$784$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$785$		0			0
$786$		0			0
$787$	1.34515	−	1.44973i	1.34515	−	1.44973i	0.563320	−	0.826239i	$-0.309524\pi$
$787$	1.34515	−	1.44973i	1.34515	−	1.44973i	0.781831	−	0.623490i	$-0.214286\pi$
$788$		0			0
$789$	−1.63402	+	1.11406i	−1.63402	+	1.11406i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$797$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$798$		0			0
$799$		0			0
$800$	0.680173	+	0.733052i	0.680173	+	0.733052i
$801$	−1.44973	+	1.34515i	−1.44973	+	1.34515i
$802$	0.294755	−	0.510531i	0.294755	−	0.510531i
$803$		0			0
$804$	0.975699	−	1.43109i	0.975699	−	1.43109i
$805$	0.733052	+	1.26968i	0.733052	+	1.26968i
$806$		0			0
$807$	0.246289	+	1.63402i	0.246289	+	1.63402i
$808$	−0.411608	−	0.603718i	−0.411608	−	0.603718i
$809$	0.975699	+	1.43109i	0.975699	+	1.43109i	0.900969	+	0.433884i	$0.142857\pi$
$809$	0.975699	+	1.43109i	0.975699	+	1.43109i	0.0747301	+	0.997204i	$0.476190\pi$
$810$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$811$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$811$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$812$	−0.294755	−	0.0444272i	−0.294755	−	0.0444272i
$813$		0			0
$814$		0			0
$815$	0.781831	−	1.35417i	0.781831	−	1.35417i
$816$		0			0
$817$		0			0
$818$	1.01507	+	0.488831i	1.01507	+	0.488831i
$819$		0			0
$820$	−0.134659	+	0.0648483i	−0.134659	+	0.0648483i
$821$	0.807782	+	0.317031i	0.807782	+	0.317031i	0.733052	−	0.680173i	$-0.238095\pi$
$821$	0.807782	+	0.317031i	0.807782	+	0.317031i	0.0747301	+	0.997204i	$0.476190\pi$
$822$		0			0
$823$	1.07659	+	0.332083i	1.07659	+	0.332083i	0.781831	−	0.623490i	$-0.214286\pi$
$823$	1.07659	+	0.332083i	1.07659	+	0.332083i	0.294755	+	0.955573i	$0.404762\pi$
$824$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$825$		0			0
$826$		0			0
$827$	1.86323	−	0.425270i	1.86323	−	0.425270i	0.866025	−	0.500000i	$-0.166667\pi$
$827$	1.86323	−	0.425270i	1.86323	−	0.425270i	0.997204	+	0.0747301i	$0.0238095\pi$
$828$	1.14625	+	0.914101i	1.14625	+	0.914101i
$829$	−1.45557	+	0.571270i	−1.45557	+	0.571270i	−0.955573	−	0.294755i	$-0.904762\pi$
$829$	−1.45557	+	0.571270i	−1.45557	+	0.571270i	−0.500000	+	0.866025i	$0.666667\pi$
$830$	−1.26631	+	1.36476i	−1.26631	+	1.36476i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	0.930874	+	0.634659i	0.930874	+	0.634659i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$839$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$840$			1.00000i			1.00000i
$841$	−0.202749	+	0.888301i	−0.202749	+	0.888301i
$842$	−1.90580	+	0.142820i	−1.90580	+	0.142820i
$843$	−1.94986			−1.94986
$844$		0			0
$845$	0.365341	−	0.930874i	0.365341	−	0.930874i
$846$	1.68862	+	0.974928i	1.68862	+	0.974928i
$847$	0.974928	−	0.222521i	0.974928	−	0.222521i
$848$		0			0
$849$	−0.222521	+	0.385418i	−0.222521	+	0.385418i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$853$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$854$	0.766310	−	1.12397i	0.766310	−	1.12397i
$855$		0			0
$856$	0.722521	+	0.108903i	0.722521	+	0.108903i
$857$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$857$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$858$		0			0
$859$		0			0		0.149042	−	0.988831i	$-0.452381\pi$
$859$		0			0		−0.149042	+	0.988831i	$0.547619\pi$
$860$	1.24349	−	1.55929i	1.24349	−	1.55929i
$861$	−0.142820	−	0.0440542i	−0.142820	−	0.0440542i
$862$		0			0
$863$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$863$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$864$	0.365341	+	0.930874i	0.365341	+	0.930874i
$865$		0			0
$866$		0			0
$867$	−0.149042	+	0.988831i	−0.149042	+	0.988831i
$868$		0			0
$869$		0			0
$870$	−0.297251	−	0.0222759i	−0.297251	−	0.0222759i
$871$		0			0
$872$	0.294755	−	0.955573i	0.294755	−	0.955573i
$873$		0			0
$874$		0			0
$875$	−0.294755	+	0.955573i	−0.294755	+	0.955573i
$876$		0			0
$877$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$877$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$881$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$882$	−0.680173	+	0.733052i	−0.680173	+	0.733052i
$883$	−0.867767			−0.867767			−0.433884	−	0.900969i	$-0.642857\pi$
$883$	−0.867767			−0.867767			−0.433884	+	0.900969i	$0.642857\pi$
$884$		0			0
$885$		0			0
$886$	−0.722521	−	1.84095i	−0.722521	−	1.84095i
$887$	−1.29991	+	0.400969i	−1.29991	+	0.400969i	−0.866025	−	0.500000i	$-0.833333\pi$
$887$	−1.29991	+	0.400969i	−1.29991	+	0.400969i	−0.433884	+	0.900969i	$0.642857\pi$
$888$		0			0
$889$	−0.751509	−	0.433884i	−0.751509	−	0.433884i
$890$	1.92808	+	0.440071i	1.92808	+	0.440071i
$891$		0			0
$892$	0.531130	−	1.72188i	0.531130	−	1.72188i
$893$		0			0
$894$	−1.85654	−	0.139129i	−1.85654	−	0.139129i
$895$		0			0
$896$	0.623490	−	0.781831i	0.623490	−	0.781831i
$897$		0			0
$898$	0.997204	−	0.925270i	0.997204	−	0.925270i
$899$		0			0
$900$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$901$		0			0
$902$		0			0
$903$	1.97213	−	0.297251i	1.97213	−	0.297251i
$904$		0			0
$905$	0.258149	−	1.71271i	0.258149	−	1.71271i
$906$		0			0
$907$	0.487076	−	0.332083i	0.487076	−	0.332083i	−0.294755	−	0.955573i	$-0.595238\pi$
$907$	0.487076	−	0.332083i	0.487076	−	0.332083i	0.781831	+	0.623490i	$0.214286\pi$
$908$	0.858075	+	0.129334i	0.858075	+	0.129334i
$909$	0.0546039	−	0.728639i	0.0546039	−	0.728639i
$910$		0			0
$911$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$911$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	0.680173	−	1.17809i	0.680173	−	1.17809i
$916$	−0.678448	+	1.40881i	−0.678448	+	1.40881i
$917$		0			0
$918$		0			0
$919$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$919$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$920$	0.109562	−	1.46200i	0.109562	−	1.46200i
$921$	−1.65248			−1.65248
$922$	−0.443797	+	0.0332580i	−0.443797	+	0.0332580i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−0.548760	−	1.77904i	−0.548760	−	1.77904i
$927$	−0.563320	+	0.826239i	−0.563320	+	0.826239i
$928$	0.218511	+	0.202749i	0.218511	+	0.202749i
$929$	1.21135	+	0.825886i	1.21135	+	0.825886i	0.988831	−	0.149042i	$-0.0476190\pi$
$929$	1.21135	+	0.825886i	1.21135	+	0.825886i	0.222521	+	0.974928i	$0.428571\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	1.17809	−	1.26968i	1.17809	−	1.26968i
$935$		0			0
$936$		0			0
$937$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$937$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$938$	−1.26968	−	1.17809i	−1.26968	−	1.17809i
$939$		0			0
$940$	−0.145713	−	1.94440i	−0.145713	−	1.94440i
$941$	1.19158	+	0.367554i	1.19158	+	0.367554i	0.826239	−	0.563320i	$-0.190476\pi$
$941$	1.19158	+	0.367554i	1.19158	+	0.367554i	0.365341	+	0.930874i	$0.380952\pi$
$942$		0			0
$943$	0.203977	+	0.0800550i	0.203977	+	0.0800550i
$944$		0			0
$945$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$946$		0			0
$947$	1.12397	+	1.21135i	1.12397	+	1.21135i	0.974928	+	0.222521i	$0.0714286\pi$
$947$	1.12397	+	1.21135i	1.12397	+	1.21135i	0.149042	+	0.988831i	$0.452381\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$953$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	0.563320	−	0.826239i	0.563320	−	0.826239i
$961$	0.500000	+	0.866025i	0.500000	+	0.866025i
$962$		0			0
$963$	0.496990	+	0.535628i	0.496990	+	0.535628i
$964$	0.590232	+	0.636119i	0.590232	+	0.636119i
$965$		0			0
$966$	1.07473	−	0.997204i	1.07473	−	0.997204i
$967$	−0.531130	+	0.255779i	−0.531130	+	0.255779i	−0.680173	−	0.733052i	$-0.738095\pi$
$967$	−0.531130	+	0.255779i	−0.531130	+	0.255779i	0.149042	+	0.988831i	$0.452381\pi$
$968$	−0.930874	−	0.365341i	−0.930874	−	0.365341i
$969$		0			0
$970$		0			0
$971$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$971$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$972$	−0.294755	+	0.955573i	−0.294755	+	0.955573i
$973$		0			0
$974$	−1.90097	+	0.433884i	−1.90097	+	0.433884i
$975$		0			0
$976$	−1.26631	+	0.496990i	−1.26631	+	0.496990i
$977$		0			0		0.680173	−	0.733052i	$-0.261905\pi$
$977$		0			0		−0.680173	+	0.733052i	$0.738095\pi$
$978$	−1.49419	−	0.460898i	−1.49419	−	0.460898i
$979$		0			0
$980$	0.988831	+	0.149042i	0.988831	+	0.149042i
$981$	0.826239	−	0.563320i	0.826239	−	0.563320i
$982$		0			0
$983$	−0.997204	−	0.925270i	−0.997204	−	0.925270i		−	1.00000i	$-0.5\pi$
$983$	−0.997204	−	0.925270i	−0.997204	−	0.925270i	−0.997204	+	0.0747301i	$0.976190\pi$
$984$	0.0931869	+	0.116853i	0.0931869	+	0.116853i
$985$		0			0
$986$		0			0
$987$	1.21572	−	1.52446i	1.21572	−	1.52446i
$988$		0			0
$989$	−2.91583	+	0.218511i	−2.91583	+	0.218511i
$990$		0			0
$991$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$991$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	1.61232	+	0.930874i	1.61232	+	0.930874i
$997$		0			0		−0.149042	−	0.988831i	$-0.547619\pi$
$997$		0			0		0.149042	+	0.988831i	$0.452381\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2940.1.dd.a.1319.2	yes	24
3.2	odd	2		2940.1.dd.b.1319.1	yes	24
4.3	odd	2	inner	2940.1.dd.a.1319.1	yes	24
5.4	even	2	inner	2940.1.dd.a.1319.1	yes	24
12.11	even	2		2940.1.dd.b.1319.2	yes	24
15.14	odd	2		2940.1.dd.b.1319.2	yes	24
20.19	odd	2	CM	2940.1.dd.a.1319.2	yes	24
49.12	odd	42		2940.1.dd.b.1139.1	yes	24
60.59	even	2		2940.1.dd.b.1319.1	yes	24
147.110	even	42	inner	2940.1.dd.a.1139.2	yes	24
196.159	even	42		2940.1.dd.b.1139.2	yes	24
245.159	odd	42		2940.1.dd.b.1139.2	yes	24
588.551	odd	42	inner	2940.1.dd.a.1139.1	✓	24
735.404	even	42	inner	2940.1.dd.a.1139.1	✓	24
980.159	even	42		2940.1.dd.b.1139.1	yes	24
2940.1139	odd	42	inner	2940.1.dd.a.1139.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2940.1.dd.a.1139.1	✓	24	588.551	odd	42	inner
2940.1.dd.a.1139.1	✓	24	735.404	even	42	inner
2940.1.dd.a.1139.2	yes	24	147.110	even	42	inner
2940.1.dd.a.1139.2	yes	24	2940.1139	odd	42	inner
2940.1.dd.a.1319.1	yes	24	4.3	odd	2	inner
2940.1.dd.a.1319.1	yes	24	5.4	even	2	inner
2940.1.dd.a.1319.2	yes	24	1.1	even	1	trivial
2940.1.dd.a.1319.2	yes	24	20.19	odd	2	CM
2940.1.dd.b.1139.1	yes	24	49.12	odd	42
2940.1.dd.b.1139.1	yes	24	980.159	even	42
2940.1.dd.b.1139.2	yes	24	196.159	even	42
2940.1.dd.b.1139.2	yes	24	245.159	odd	42
2940.1.dd.b.1319.1	yes	24	3.2	odd	2
2940.1.dd.b.1319.1	yes	24	60.59	even	2
2940.1.dd.b.1319.2	yes	24	12.11	even	2
2940.1.dd.b.1319.2	yes	24	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2940.dd (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.563320 - 0.826239i) q^{2} +(-0.433884 + 0.900969i) q^{3} +(-0.365341 - 0.930874i) q^{4} +(-0.955573 + 0.294755i) q^{5} +(0.500000 + 0.866025i) q^{6} +(0.930874 - 0.365341i) q^{7} +(-0.974928 - 0.222521i) q^{8} +(-0.623490 - 0.781831i) q^{9} +(-0.294755 + 0.955573i) q^{10} +(0.997204 + 0.0747301i) q^{12} +(0.222521 - 0.974928i) q^{14} +(0.149042 - 0.988831i) q^{15} +(-0.733052 + 0.680173i) q^{16} +(-0.997204 + 0.0747301i) q^{18} +(0.623490 + 0.781831i) q^{20} +(-0.0747301 + 0.997204i) q^{21} +(0.218511 - 1.44973i) q^{23} +(0.623490 - 0.781831i) q^{24} +(0.826239 - 0.563320i) q^{25} +(0.974928 - 0.222521i) q^{27} +(-0.680173 - 0.733052i) q^{28} +(0.233052 - 0.185853i) q^{29} +(-0.733052 - 0.680173i) q^{30} +(0.149042 + 0.988831i) q^{32} +(-0.781831 + 0.623490i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(0.997204 - 0.0747301i) q^{40} +(-0.0332580 + 0.145713i) q^{41} +(0.781831 + 0.623490i) q^{42} +(-0.443797 - 1.94440i) q^{43} +(0.826239 + 0.563320i) q^{45} +(-1.07473 - 0.997204i) q^{46} +(-1.61105 - 1.09839i) q^{47} +(-0.294755 - 0.955573i) q^{48} +(0.733052 - 0.680173i) q^{49} -1.00000i q^{50} +(0.365341 - 0.930874i) q^{54} +(-0.988831 + 0.149042i) q^{56} +(-0.0222759 - 0.297251i) q^{58} +(-0.974928 + 0.222521i) q^{60} +(1.26631 + 0.496990i) q^{61} +(-0.866025 - 0.500000i) q^{63} +(0.900969 + 0.433884i) q^{64} +(0.866025 - 1.50000i) q^{67} +(1.21135 + 0.825886i) q^{69} +(0.0747301 + 0.997204i) q^{70} +(0.433884 + 0.900969i) q^{72} +(0.149042 + 0.988831i) q^{75} +(0.500000 - 0.866025i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(0.101659 + 0.109562i) q^{82} +(1.67738 + 0.807782i) q^{83} +(0.955573 - 0.294755i) q^{84} +(-1.85654 - 0.728639i) q^{86} +(0.0663300 + 0.290611i) q^{87} +(-0.147791 - 1.97213i) q^{89} +(0.930874 - 0.365341i) q^{90} +(-1.42935 + 0.326239i) q^{92} +(-1.81507 + 0.712362i) q^{94} +(-0.955573 - 0.294755i) q^{96} +(-0.149042 - 0.988831i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{4} - 2 q^{5} + 12 q^{6} + 4 q^{9} + 4 q^{14} + 2 q^{16} - 4 q^{20} - 2 q^{21} - 4 q^{24} + 2 q^{25} - 14 q^{29} + 2 q^{30} - 12 q^{36} + 4 q^{41} + 2 q^{45} - 26 q^{46} - 2 q^{49} + 2 q^{54}+ \cdots - 2 q^{96}+O(q^{100}) \) 24 * q - 2 * q^4 - 2 * q^5 + 12 * q^6 + 4 * q^9 + 4 * q^14 + 2 * q^16 - 4 * q^20 - 2 * q^21 - 4 * q^24 + 2 * q^25 - 14 * q^29 + 2 * q^30 - 12 * q^36 + 4 * q^41 + 2 * q^45 - 26 * q^46 - 2 * q^49 + 2 * q^54 + 2 * q^56 + 6 * q^61 + 4 * q^64 + 2 * q^69 + 2 * q^70 + 12 * q^80 - 4 * q^81 + 2 * q^84 - 6 * q^86 - 2 * q^89 - 2 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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