LMFDB - Embedded newform 580.1.y.c.299.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [580,1,Mod(179,580)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(580, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 7, 11]))

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

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

chi := DirichletCharacter("580.179");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 580 = 2^{2} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	580.y (of order $14$, degree $6$, 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:	$0.289457707327$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{14})$
Coefficient field:	$\Q(\zeta_{28})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{14}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{14} + \cdots)$

Embedding invariants

Embedding label			299.1
Root			$0.974928 - 0.222521i$ of defining polynomial
Character	$\chi$	$=$	580.299
Dual form			580.1.y.c.419.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.433884 - 0.900969i) q^{2} +(1.40881 - 1.12349i) q^{3} +(-0.623490 + 0.781831i) q^{4} +(-0.900969 + 0.433884i) q^{5} +(-1.62349 - 0.781831i) q^{6} +(-0.974928 - 1.22252i) q^{7} +(0.974928 + 0.222521i) q^{8} +(0.500000 - 2.19064i) q^{9} +O(q^{10})$	\(q+(-0.433884 - 0.900969i) q^{2} +(1.40881 - 1.12349i) q^{3} +(-0.623490 + 0.781831i) q^{4} +(-0.900969 + 0.433884i) q^{5} +(-1.62349 - 0.781831i) q^{6} +(-0.974928 - 1.22252i) q^{7} +(0.974928 + 0.222521i) q^{8} +(0.500000 - 2.19064i) q^{9} +(0.781831 + 0.623490i) q^{10} +1.80194i q^{12} +(-0.678448 + 1.40881i) q^{14} +(-0.781831 + 1.62349i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(-2.19064 + 0.500000i) q^{18} +(0.222521 - 0.974928i) q^{20} +(-2.74698 - 0.626980i) q^{21} +(0.781831 + 0.376510i) q^{23} +(1.62349 - 0.781831i) q^{24} +(0.623490 - 0.781831i) q^{25} +(-0.974928 - 2.02446i) q^{27} +1.56366 q^{28} +(0.623490 + 0.781831i) q^{29} +1.80194 q^{30} +(-0.781831 + 0.623490i) q^{32} +(1.40881 + 0.678448i) q^{35} +(1.40097 + 1.75676i) q^{36} +(-0.974928 + 0.222521i) q^{40} +1.94986i q^{41} +(0.626980 + 2.74698i) q^{42} +(0.193096 - 0.400969i) q^{43} +(0.500000 + 2.19064i) q^{45} -0.867767i q^{46} +(1.21572 - 0.277479i) q^{47} +(-1.40881 - 1.12349i) q^{48} +(-0.321552 + 1.40881i) q^{49} +(-0.974928 - 0.222521i) q^{50} +(-1.40097 + 1.75676i) q^{54} +(-0.678448 - 1.40881i) q^{56} +(0.433884 - 0.900969i) q^{58} +(-0.781831 - 1.62349i) q^{60} +(-3.16557 + 1.52446i) q^{63} +(0.900969 + 0.433884i) q^{64} +(1.52446 - 0.347948i) q^{69} -1.56366i q^{70} +(0.974928 - 2.02446i) q^{72} -1.80194i q^{75} +(0.623490 + 0.781831i) q^{80} +(-1.62349 - 0.781831i) q^{81} +(1.75676 - 0.846011i) q^{82} +(-1.21572 + 1.52446i) q^{83} +(2.20291 - 1.75676i) q^{84} -0.445042 q^{86} +(1.75676 + 0.400969i) q^{87} +(-0.678448 - 1.40881i) q^{89} +(1.75676 - 1.40097i) q^{90} +(-0.781831 + 0.376510i) q^{92} +(-0.777479 - 0.974928i) q^{94} +(-0.400969 + 1.75676i) q^{96} +(1.40881 - 0.321552i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{4} - 2 q^{5} - 10 q^{6} + 6 q^{9}+O(q^{10}) $ 12 * q + 2 * q^4 - 2 * q^5 - 10 * q^6 + 6 * q^9	$ 12 q + 2 q^{4} - 2 q^{5} - 10 q^{6} + 6 q^{9} - 2 q^{16} + 2 q^{20} - 14 q^{21} + 10 q^{24} - 2 q^{25} - 2 q^{29} + 4 q^{30} + 8 q^{36} + 6 q^{45} - 12 q^{49} - 8 q^{54} + 2 q^{64} - 2 q^{80} - 10 q^{81} - 4 q^{86} - 10 q^{94} + 4 q^{96}+O(q^{100}) $ 12 * q + 2 * q^4 - 2 * q^5 - 10 * q^6 + 6 * q^9 - 2 * q^16 + 2 * q^20 - 14 * q^21 + 10 * q^24 - 2 * q^25 - 2 * q^29 + 4 * q^30 + 8 * q^36 + 6 * q^45 - 12 * q^49 - 8 * q^54 + 2 * q^64 - 2 * q^80 - 10 * q^81 - 4 * q^86 - 10 * q^94 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/580\mathbb{Z}\right)^\times$.

$n$	$117$	$291$	$321$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{14}\right)$

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 $

$2$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$2$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$3$	1.40881	−	1.12349i	1.40881	−	1.12349i	0.433884	−	0.900969i	$-0.357143\pi$
$3$	1.40881	−	1.12349i	1.40881	−	1.12349i	0.974928	−	0.222521i	$-0.0714286\pi$
$4$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$5$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$5$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$6$	−1.62349	−	0.781831i	−1.62349	−	0.781831i
$7$	−0.974928	−	1.22252i	−0.974928	−	1.22252i	−0.974928	−	0.222521i	$-0.928571\pi$
$7$	−0.974928	−	1.22252i	−0.974928	−	1.22252i		−	1.00000i	$-0.5\pi$
$8$	0.974928	+	0.222521i	0.974928	+	0.222521i
$9$	0.500000	−	2.19064i	0.500000	−	2.19064i
$10$	0.781831	+	0.623490i	0.781831	+	0.623490i
$11$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$11$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$12$			1.80194i			1.80194i
$13$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$13$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$14$	−0.678448	+	1.40881i	−0.678448	+	1.40881i
$15$	−0.781831	+	1.62349i	−0.781831	+	1.62349i
$16$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$	−2.19064	+	0.500000i	−2.19064	+	0.500000i
$19$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$19$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$20$	0.222521	−	0.974928i	0.222521	−	0.974928i
$21$	−2.74698	−	0.626980i	−2.74698	−	0.626980i
$22$		0			0
$23$	0.781831	+	0.376510i	0.781831	+	0.376510i	0.781831	−	0.623490i	$-0.214286\pi$
$23$	0.781831	+	0.376510i	0.781831	+	0.376510i			1.00000i	$0.5\pi$
$24$	1.62349	−	0.781831i	1.62349	−	0.781831i
$25$	0.623490	−	0.781831i	0.623490	−	0.781831i
$26$		0			0
$27$	−0.974928	−	2.02446i	−0.974928	−	2.02446i
$28$	1.56366			1.56366
$29$	0.623490	+	0.781831i	0.623490	+	0.781831i
$29$	0.623490	+	0.781831i	0.623490	+	0.781831i
$30$	1.80194			1.80194
$31$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$31$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$32$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$33$		0			0
$34$		0			0
$35$	1.40881	+	0.678448i	1.40881	+	0.678448i
$36$	1.40097	+	1.75676i	1.40097	+	1.75676i
$37$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$37$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$38$		0			0
$39$		0			0
$40$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$41$			1.94986i			1.94986i	0.222521	+	0.974928i	$0.428571\pi$
$41$			1.94986i			1.94986i	−0.222521	+	0.974928i	$0.571429\pi$
$42$	0.626980	+	2.74698i	0.626980	+	2.74698i
$43$	0.193096	−	0.400969i	0.193096	−	0.400969i	−0.781831	−	0.623490i	$-0.785714\pi$
$43$	0.193096	−	0.400969i	0.193096	−	0.400969i	0.974928	+	0.222521i	$0.0714286\pi$
$44$		0			0
$45$	0.500000	+	2.19064i	0.500000	+	2.19064i
$46$		−	0.867767i		−	0.867767i
$47$	1.21572	−	0.277479i	1.21572	−	0.277479i	0.433884	−	0.900969i	$-0.357143\pi$
$47$	1.21572	−	0.277479i	1.21572	−	0.277479i	0.781831	+	0.623490i	$0.214286\pi$
$48$	−1.40881	−	1.12349i	−1.40881	−	1.12349i
$49$	−0.321552	+	1.40881i	−0.321552	+	1.40881i
$50$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$51$		0			0
$52$		0			0
$53$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$53$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$54$	−1.40097	+	1.75676i	−1.40097	+	1.75676i
$55$		0			0
$56$	−0.678448	−	1.40881i	−0.678448	−	1.40881i
$57$		0			0
$58$	0.433884	−	0.900969i	0.433884	−	0.900969i
$59$		0			0		1.00000			$0$
$59$		0			0		−1.00000			$\pi$
$60$	−0.781831	−	1.62349i	−0.781831	−	1.62349i
$61$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$61$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$62$		0			0
$63$	−3.16557	+	1.52446i	−3.16557	+	1.52446i
$64$	0.900969	+	0.433884i	0.900969	+	0.433884i
$65$		0			0
$66$		0			0
$67$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$67$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$68$		0			0
$69$	1.52446	−	0.347948i	1.52446	−	0.347948i
$70$		−	1.56366i		−	1.56366i
$71$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$71$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$72$	0.974928	−	2.02446i	0.974928	−	2.02446i
$73$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$73$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$74$		0			0
$75$		−	1.80194i		−	1.80194i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$79$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$80$	0.623490	+	0.781831i	0.623490	+	0.781831i
$81$	−1.62349	−	0.781831i	−1.62349	−	0.781831i
$82$	1.75676	−	0.846011i	1.75676	−	0.846011i
$83$	−1.21572	+	1.52446i	−1.21572	+	1.52446i	−0.433884	+	0.900969i	$0.642857\pi$
$83$	−1.21572	+	1.52446i	−1.21572	+	1.52446i	−0.781831	+	0.623490i	$0.785714\pi$
$84$	2.20291	−	1.75676i	2.20291	−	1.75676i
$85$		0			0
$86$	−0.445042			−0.445042
$87$	1.75676	+	0.400969i	1.75676	+	0.400969i
$88$		0			0
$89$	−0.678448	−	1.40881i	−0.678448	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$89$	−0.678448	−	1.40881i	−0.678448	−	1.40881i	0.222521	−	0.974928i	$-0.428571\pi$
$90$	1.75676	−	1.40097i	1.75676	−	1.40097i
$91$		0			0
$92$	−0.781831	+	0.376510i	−0.781831	+	0.376510i
$93$		0			0
$94$	−0.777479	−	0.974928i	−0.777479	−	0.974928i
$95$		0			0
$96$	−0.400969	+	1.75676i	−0.400969	+	1.75676i
$97$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$97$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$98$	1.40881	−	0.321552i	1.40881	−	0.321552i
$99$		0			0
$100$	0.222521	+	0.974928i	0.222521	+	0.974928i
$101$	−0.376510	+	0.781831i	−0.376510	+	0.781831i	0.623490	+	0.781831i	$0.285714\pi$
$101$	−0.376510	+	0.781831i	−0.376510	+	0.781831i	−1.00000			$\pi$
$102$		0			0
$103$	−0.433884	−	1.90097i	−0.433884	−	1.90097i	−0.433884	−	0.900969i	$-0.642857\pi$
$103$	−0.433884	−	1.90097i	−0.433884	−	1.90097i		−	1.00000i	$-0.5\pi$
$104$		0			0
$105$	2.74698	−	0.626980i	2.74698	−	0.626980i
$106$		0			0
$107$	−0.193096	+	0.846011i	−0.193096	+	0.846011i	0.781831	+	0.623490i	$0.214286\pi$
$107$	−0.193096	+	0.846011i	−0.193096	+	0.846011i	−0.974928	+	0.222521i	$0.928571\pi$
$108$	2.19064	+	0.500000i	2.19064	+	0.500000i
$109$	0.277479	+	0.347948i	0.277479	+	0.347948i	0.900969	−	0.433884i	$-0.142857\pi$
$109$	0.277479	+	0.347948i	0.277479	+	0.347948i	−0.623490	+	0.781831i	$0.714286\pi$
$110$		0			0
$111$		0			0
$112$	−0.974928	+	1.22252i	−0.974928	+	1.22252i
$113$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$113$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$114$		0			0
$115$	−0.867767			−0.867767
$116$	−1.00000			−1.00000
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−1.12349	+	1.40881i	−1.12349	+	1.40881i
$121$	0.900969	−	0.433884i	0.900969	−	0.433884i
$122$		0			0
$123$	2.19064	+	2.74698i	2.19064	+	2.74698i
$124$		0			0
$125$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$126$	2.74698	+	2.19064i	2.74698	+	2.19064i
$127$	−1.21572	+	0.277479i	−1.21572	+	0.277479i	−0.781831	−	0.623490i	$-0.785714\pi$
$127$	−1.21572	+	0.277479i	−1.21572	+	0.277479i	−0.433884	+	0.900969i	$0.642857\pi$
$128$		−	1.00000i		−	1.00000i
$129$	−0.178448	−	0.781831i	−0.178448	−	0.781831i
$130$		0			0
$131$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$131$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	1.75676	+	1.40097i	1.75676	+	1.40097i
$136$		0			0
$137$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$137$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$138$	−0.974928	−	1.22252i	−0.974928	−	1.22252i
$139$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$139$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$140$	−1.40881	+	0.678448i	−1.40881	+	0.678448i
$141$	1.40097	−	1.75676i	1.40097	−	1.75676i
$142$		0			0
$143$		0			0
$144$	−2.24698			−2.24698
$145$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$146$		0			0
$147$	1.12978	+	2.34601i	1.12978	+	2.34601i
$148$		0			0
$149$	0.777479	−	0.974928i	0.777479	−	0.974928i	−0.222521	−	0.974928i	$-0.571429\pi$
$149$	0.777479	−	0.974928i	0.777479	−	0.974928i	1.00000			$0$
$150$	−1.62349	+	0.781831i	−1.62349	+	0.781831i
$151$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$151$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0			−	1.00000i	$-0.5\pi$
$157$		0			0				1.00000i	$0.5\pi$
$158$		0			0
$159$		0			0
$160$	0.433884	−	0.900969i	0.433884	−	0.900969i
$161$	−0.301938	−	1.32288i	−0.301938	−	1.32288i
$162$			1.80194i			1.80194i
$163$	0.433884	−	0.0990311i	0.433884	−	0.0990311i		−	1.00000i	$-0.5\pi$
$163$	0.433884	−	0.0990311i	0.433884	−	0.0990311i	0.433884	+	0.900969i	$0.357143\pi$
$164$	−1.52446	−	1.21572i	−1.52446	−	1.21572i
$165$		0			0
$166$	1.90097	+	0.433884i	1.90097	+	0.433884i
$167$	−1.21572	−	1.52446i	−1.21572	−	1.52446i	−0.781831	−	0.623490i	$-0.785714\pi$
$167$	−1.21572	−	1.52446i	−1.21572	−	1.52446i	−0.433884	−	0.900969i	$-0.642857\pi$
$168$	−2.53859	−	1.22252i	−2.53859	−	1.22252i
$169$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$170$		0			0
$171$		0			0
$172$	0.193096	+	0.400969i	0.193096	+	0.400969i
$173$		0			0		1.00000			$0$
$173$		0			0		−1.00000			$\pi$
$174$	−0.400969	−	1.75676i	−0.400969	−	1.75676i
$175$	−1.56366			−1.56366
$176$		0			0
$177$		0			0
$178$	−0.974928	+	1.22252i	−0.974928	+	1.22252i
$179$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$179$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$180$	−2.02446	−	0.974928i	−2.02446	−	0.974928i
$181$	1.12349	+	1.40881i	1.12349	+	1.40881i	0.900969	+	0.433884i	$0.142857\pi$
$181$	1.12349	+	1.40881i	1.12349	+	1.40881i	0.222521	+	0.974928i	$0.428571\pi$
$182$		0			0
$183$		0			0
$184$	0.678448	+	0.541044i	0.678448	+	0.541044i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−0.541044	+	1.12349i	−0.541044	+	1.12349i
$189$	−1.52446	+	3.16557i	−1.52446	+	3.16557i
$190$		0			0
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$	1.75676	−	0.400969i	1.75676	−	0.400969i
$193$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$193$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$194$		0			0
$195$		0			0
$196$	−0.900969	−	1.12978i	−0.900969	−	1.12978i
$197$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$197$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$198$		0			0
$199$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$199$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$200$	0.781831	−	0.623490i	0.781831	−	0.623490i
$201$		0			0
$202$	0.867767			0.867767
$203$	0.347948	−	1.52446i	0.347948	−	1.52446i
$204$		0			0
$205$	−0.846011	−	1.75676i	−0.846011	−	1.75676i
$206$	−1.52446	+	1.21572i	−1.52446	+	1.21572i
$207$	1.21572	−	1.52446i	1.21572	−	1.52446i
$208$		0			0
$209$		0			0
$210$	−1.75676	−	2.20291i	−1.75676	−	2.20291i
$211$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$211$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$212$		0			0
$213$		0			0
$214$	0.846011	−	0.193096i	0.846011	−	0.193096i
$215$			0.445042i			0.445042i
$216$	−0.500000	−	2.19064i	−0.500000	−	2.19064i
$217$		0			0
$218$	0.193096	−	0.400969i	0.193096	−	0.400969i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.347948	+	1.52446i	−0.347948	+	1.52446i	0.433884	+	0.900969i	$0.357143\pi$
$223$	−0.347948	+	1.52446i	−0.347948	+	1.52446i	−0.781831	+	0.623490i	$0.785714\pi$
$224$	1.52446	+	0.347948i	1.52446	+	0.347948i
$225$	−1.40097	−	1.75676i	−1.40097	−	1.75676i
$226$		0			0
$227$	−1.75676	+	0.846011i	−1.75676	+	0.846011i	−0.781831	+	0.623490i	$0.785714\pi$
$227$	−1.75676	+	0.846011i	−1.75676	+	0.846011i	−0.974928	+	0.222521i	$0.928571\pi$
$228$		0			0
$229$	−1.52446	+	1.21572i	−1.52446	+	1.21572i	−0.623490	+	0.781831i	$0.714286\pi$
$229$	−1.52446	+	1.21572i	−1.52446	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$230$	0.376510	+	0.781831i	0.376510	+	0.781831i
$231$		0			0
$232$	0.433884	+	0.900969i	0.433884	+	0.900969i
$233$		0			0		1.00000			$0$
$233$		0			0		−1.00000			$\pi$
$234$		0			0
$235$	−0.974928	+	0.777479i	−0.974928	+	0.777479i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$239$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$240$	1.75676	+	0.400969i	1.75676	+	0.400969i
$241$	0.400969	−	1.75676i	0.400969	−	1.75676i	−0.222521	−	0.974928i	$-0.571429\pi$
$241$	0.400969	−	1.75676i	0.400969	−	1.75676i	0.623490	−	0.781831i	$-0.285714\pi$
$242$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$243$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$244$		0			0
$245$	−0.321552	−	1.40881i	−0.321552	−	1.40881i
$246$	1.52446	−	3.16557i	1.52446	−	3.16557i
$247$		0			0
$248$		0			0
$249$			3.51352i			3.51352i
$250$	0.974928	−	0.222521i	0.974928	−	0.222521i
$251$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$251$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$252$	0.781831	−	3.42543i	0.781831	−	3.42543i
$253$		0			0
$254$	0.777479	+	0.974928i	0.777479	+	0.974928i
$255$		0			0
$256$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$257$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$257$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$258$	−0.626980	+	0.500000i	−0.626980	+	0.500000i
$259$		0			0
$260$		0			0
$261$	2.02446	−	0.974928i	2.02446	−	0.974928i
$262$		0			0
$263$	−0.541044	−	1.12349i	−0.541044	−	1.12349i	−0.974928	−	0.222521i	$-0.928571\pi$
$263$	−0.541044	−	1.12349i	−0.541044	−	1.12349i	0.433884	−	0.900969i	$-0.357143\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−2.53859	−	1.22252i	−2.53859	−	1.22252i
$268$		0			0
$269$	0.846011	+	0.193096i	0.846011	+	0.193096i	0.623490	−	0.781831i	$-0.285714\pi$
$269$	0.846011	+	0.193096i	0.846011	+	0.193096i	0.222521	+	0.974928i	$0.428571\pi$
$270$	0.500000	−	2.19064i	0.500000	−	2.19064i
$271$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$271$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−0.678448	+	1.40881i	−0.678448	+	1.40881i
$277$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$277$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$278$		0			0
$279$		0			0
$280$	1.22252	+	0.974928i	1.22252	+	0.974928i
$281$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	0.222521	+	0.974928i	$0.428571\pi$
$281$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	−0.623490	+	0.781831i	$0.714286\pi$
$282$	−2.19064	−	0.500000i	−2.19064	−	0.500000i
$283$	0.541044	+	0.678448i	0.541044	+	0.678448i	0.974928	−	0.222521i	$-0.0714286\pi$
$283$	0.541044	+	0.678448i	0.541044	+	0.678448i	−0.433884	+	0.900969i	$0.642857\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.38374	−	1.90097i	2.38374	−	1.90097i
$288$	0.974928	+	2.02446i	0.974928	+	2.02446i
$289$	−1.00000			−1.00000
$290$			1.00000i			1.00000i
$291$		0			0
$292$		0			0
$293$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$293$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$294$	1.62349	−	2.03579i	1.62349	−	2.03579i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	−1.21572	−	0.277479i	−1.21572	−	0.277479i
$299$		0			0
$300$	1.40881	+	1.12349i	1.40881	+	1.12349i
$301$	−0.678448	+	0.154851i	−0.678448	+	0.154851i
$302$		0			0
$303$	0.347948	+	1.52446i	0.347948	+	1.52446i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			1.80194i			1.80194i	0.433884	+	0.900969i	$0.357143\pi$
$307$			1.80194i			1.80194i	−0.433884	+	0.900969i	$0.642857\pi$
$308$		0			0
$309$	−2.74698	−	2.19064i	−2.74698	−	2.19064i
$310$		0			0
$311$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$311$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$312$		0			0
$313$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$313$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$314$		0			0
$315$	2.19064	−	2.74698i	2.19064	−	2.74698i
$316$		0			0
$317$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$317$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$318$		0			0
$319$		0			0
$320$	−1.00000			−1.00000
$321$	0.678448	+	1.40881i	0.678448	+	1.40881i
$322$	−1.06086	+	0.846011i	−1.06086	+	0.846011i
$323$		0			0
$324$	1.62349	−	0.781831i	1.62349	−	0.781831i
$325$		0			0
$326$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$327$	0.781831	+	0.178448i	0.781831	+	0.178448i
$328$	−0.433884	+	1.90097i	−0.433884	+	1.90097i
$329$	−1.52446	−	1.21572i	−1.52446	−	1.21572i
$330$		0			0
$331$		0			0			−	1.00000i	$-0.5\pi$
$331$		0			0				1.00000i	$0.5\pi$
$332$	−0.433884	−	1.90097i	−0.433884	−	1.90097i
$333$		0			0
$334$	−0.846011	+	1.75676i	−0.846011	+	1.75676i
$335$		0			0
$336$			2.81762i			2.81762i
$337$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$337$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$338$	0.781831	+	0.623490i	0.781831	+	0.623490i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.626980	−	0.301938i	0.626980	−	0.301938i
$344$	0.277479	−	0.347948i	0.277479	−	0.347948i
$345$	−1.22252	+	0.974928i	−1.22252	+	0.974928i
$346$		0			0
$347$		0			0			−	1.00000i	$-0.5\pi$
$347$		0			0				1.00000i	$0.5\pi$
$348$	−1.40881	+	1.12349i	−1.40881	+	1.12349i
$349$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$349$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$350$	0.678448	+	1.40881i	0.678448	+	1.40881i
$351$		0			0
$352$		0			0
$353$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$353$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$354$		0			0
$355$		0			0
$356$	1.52446	+	0.347948i	1.52446	+	0.347948i
$357$		0			0
$358$		0			0
$359$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$359$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$360$			2.24698i			2.24698i
$361$	0.222521	+	0.974928i	0.222521	+	0.974928i
$362$	0.781831	−	1.62349i	0.781831	−	1.62349i
$363$	0.781831	−	1.62349i	0.781831	−	1.62349i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	0.974928	+	0.777479i	0.974928	+	0.777479i	0.974928	−	0.222521i	$-0.0714286\pi$
$367$	0.974928	+	0.777479i	0.974928	+	0.777479i			1.00000i	$0.5\pi$
$368$	0.193096	−	0.846011i	0.193096	−	0.846011i
$369$	4.27144	+	0.974928i	4.27144	+	0.974928i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$373$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$374$		0			0
$375$	0.781831	+	1.62349i	0.781831	+	1.62349i
$376$	1.24698			1.24698
$377$		0			0
$378$	3.51352			3.51352
$379$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$379$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$380$		0			0
$381$	−1.40097	+	1.75676i	−1.40097	+	1.75676i
$382$		0			0
$383$	0.781831	+	0.376510i	0.781831	+	0.376510i	0.781831	−	0.623490i	$-0.214286\pi$
$383$	0.781831	+	0.376510i	0.781831	+	0.376510i			1.00000i	$0.5\pi$
$384$	−1.12349	−	1.40881i	−1.12349	−	1.40881i
$385$		0			0
$386$		0			0
$387$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$388$		0			0
$389$			0.867767i			0.867767i	0.900969	+	0.433884i	$0.142857\pi$
$389$			0.867767i			0.867767i	−0.900969	+	0.433884i	$0.857143\pi$
$390$		0			0
$391$		0			0
$392$	−0.626980	+	1.30194i	−0.626980	+	1.30194i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$397$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$398$		0			0
$399$		0			0
$400$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$401$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.222521	−	0.974928i	$-0.428571\pi$
$401$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.900969	+	0.433884i	$0.142857\pi$
$402$		0			0
$403$		0			0
$404$	−0.376510	−	0.781831i	−0.376510	−	0.781831i
$405$	1.80194			1.80194
$406$	−1.52446	+	0.347948i	−1.52446	+	0.347948i
$407$		0			0
$408$		0			0
$409$	1.22252	−	0.974928i	1.22252	−	0.974928i	0.222521	−	0.974928i	$-0.428571\pi$
$409$	1.22252	−	0.974928i	1.22252	−	0.974928i	1.00000			$0$
$410$	−1.21572	+	1.52446i	−1.21572	+	1.52446i
$411$		0			0
$412$	1.75676	+	0.846011i	1.75676	+	0.846011i
$413$		0			0
$414$	−1.90097	−	0.433884i	−1.90097	−	0.433884i
$415$	0.433884	−	1.90097i	0.433884	−	1.90097i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$419$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$420$	−1.22252	+	2.53859i	−1.22252	+	2.53859i
$421$	0.846011	−	1.75676i	0.846011	−	1.75676i	0.222521	−	0.974928i	$-0.428571\pi$
$421$	0.846011	−	1.75676i	0.846011	−	1.75676i	0.623490	−	0.781831i	$-0.285714\pi$
$422$		0			0
$423$		−	2.80194i		−	2.80194i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.541044	−	0.678448i	−0.541044	−	0.678448i
$429$		0			0
$430$	0.400969	−	0.193096i	0.400969	−	0.193096i
$431$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$431$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$432$	−1.75676	+	1.40097i	−1.75676	+	1.40097i
$433$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$433$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$434$		0			0
$435$	−1.75676	+	0.400969i	−1.75676	+	0.400969i
$436$	−0.445042			−0.445042
$437$		0			0
$438$		0			0
$439$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$439$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$440$		0			0
$441$	2.92543	+	1.40881i	2.92543	+	1.40881i
$442$		0			0
$443$	−1.94986	−	0.445042i	−1.94986	−	0.445042i	−0.974928	−	0.222521i	$-0.928571\pi$
$443$	−1.94986	−	0.445042i	−1.94986	−	0.445042i	−0.974928	−	0.222521i	$-0.928571\pi$
$444$		0			0
$445$	1.22252	+	0.974928i	1.22252	+	0.974928i
$446$	1.52446	−	0.347948i	1.52446	−	0.347948i
$447$		−	2.24698i		−	2.24698i
$448$	−0.347948	−	1.52446i	−0.347948	−	1.52446i
$449$	0.678448	−	1.40881i	0.678448	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$449$	0.678448	−	1.40881i	0.678448	−	1.40881i	0.900969	−	0.433884i	$-0.142857\pi$
$450$	−0.974928	+	2.02446i	−0.974928	+	2.02446i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	1.52446	+	1.21572i	1.52446	+	1.21572i
$455$		0			0
$456$		0			0
$457$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$457$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$458$	1.75676	+	0.846011i	1.75676	+	0.846011i
$459$		0			0
$460$	0.541044	−	0.678448i	0.541044	−	0.678448i
$461$	1.52446	−	1.21572i	1.52446	−	1.21572i	0.623490	−	0.781831i	$-0.285714\pi$
$461$	1.52446	−	1.21572i	1.52446	−	1.21572i	0.900969	−	0.433884i	$-0.142857\pi$
$462$		0			0
$463$	1.94986			1.94986			0.974928	−	0.222521i	$-0.0714286\pi$
$463$	1.94986			1.94986			0.974928	+	0.222521i	$0.0714286\pi$
$464$	0.623490	−	0.781831i	0.623490	−	0.781831i
$465$		0			0
$466$		0			0
$467$	−0.347948	+	0.277479i	−0.347948	+	0.277479i	−0.781831	−	0.623490i	$-0.785714\pi$
$467$	−0.347948	+	0.277479i	−0.347948	+	0.277479i	0.433884	+	0.900969i	$0.357143\pi$
$468$		0			0
$469$		0			0
$470$	1.12349	+	0.541044i	1.12349	+	0.541044i
$471$		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		0.433884	−	0.900969i	$-0.357143\pi$
$479$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$480$	−0.400969	−	1.75676i	−0.400969	−	1.75676i
$481$		0			0
$482$	−1.75676	+	0.400969i	−1.75676	+	0.400969i
$483$	−1.91161	−	1.52446i	−1.91161	−	1.52446i
$484$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$485$		0			0
$486$	0.623490	+	0.781831i	0.623490	+	0.781831i
$487$	−1.40881	−	0.678448i	−1.40881	−	0.678448i	−0.433884	−	0.900969i	$-0.642857\pi$
$487$	−1.40881	−	0.678448i	−1.40881	−	0.678448i	−0.974928	+	0.222521i	$0.928571\pi$
$488$		0			0
$489$	0.500000	−	0.626980i	0.500000	−	0.626980i
$490$	−1.12978	+	0.900969i	−1.12978	+	0.900969i
$491$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$491$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$492$	−3.51352			−3.51352
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	3.16557	−	1.52446i	3.16557	−	1.52446i
$499$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$499$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$500$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$501$	−3.42543	−	0.781831i	−3.42543	−	0.781831i
$502$		0			0
$503$	−0.347948	−	0.277479i	−0.347948	−	0.277479i	0.433884	−	0.900969i	$-0.357143\pi$
$503$	−0.347948	−	0.277479i	−0.347948	−	0.277479i	−0.781831	+	0.623490i	$0.785714\pi$
$504$	−3.42543	+	0.781831i	−3.42543	+	0.781831i
$505$		−	0.867767i		−	0.867767i
$506$		0			0
$507$	−0.781831	+	1.62349i	−0.781831	+	1.62349i
$508$	0.541044	−	1.12349i	0.541044	−	1.12349i
$509$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i	0.900969	−	0.433884i	$-0.142857\pi$
$509$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i	−1.00000			$\pi$
$510$		0			0
$511$		0			0
$512$	0.781831	+	0.623490i	0.781831	+	0.623490i
$513$		0			0
$514$		0			0
$515$	1.21572	+	1.52446i	1.21572	+	1.52446i
$516$	0.722521	+	0.347948i	0.722521	+	0.347948i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.24698			−1.24698			−0.623490	−	0.781831i	$-0.714286\pi$
$521$	−1.24698			−1.24698			−0.623490	+	0.781831i	$0.714286\pi$
$522$	−1.75676	−	1.40097i	−1.75676	−	1.40097i
$523$	−1.94986			−1.94986			−0.974928	−	0.222521i	$-0.928571\pi$
$523$	−1.94986			−1.94986			−0.974928	+	0.222521i	$0.928571\pi$
$524$		0			0
$525$	−2.20291	+	1.75676i	−2.20291	+	1.75676i
$526$	−0.777479	+	0.974928i	−0.777479	+	0.974928i
$527$		0			0
$528$		0			0
$529$	−0.153989	−	0.193096i	−0.153989	−	0.193096i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$			2.81762i			2.81762i
$535$	−0.193096	−	0.846011i	−0.193096	−	0.846011i
$536$		0			0
$537$		0			0
$538$	−0.193096	−	0.846011i	−0.193096	−	0.846011i
$539$		0			0
$540$	−2.19064	+	0.500000i	−2.19064	+	0.500000i
$541$	1.22252	+	0.974928i	1.22252	+	0.974928i	1.00000			$0$
$541$	1.22252	+	0.974928i	1.22252	+	0.974928i	0.222521	+	0.974928i	$0.428571\pi$
$542$		0			0
$543$	3.16557	+	0.722521i	3.16557	+	0.722521i
$544$		0			0
$545$	−0.400969	−	0.193096i	−0.400969	−	0.193096i
$546$		0			0
$547$	1.21572	−	1.52446i	1.21572	−	1.52446i	0.433884	−	0.900969i	$-0.357143\pi$
$547$	1.21572	−	1.52446i	1.21572	−	1.52446i	0.781831	−	0.623490i	$-0.214286\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$	1.56366			1.56366
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$557$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$558$		0			0
$559$		0			0
$560$	0.347948	−	1.52446i	0.347948	−	1.52446i
$561$		0			0
$562$	1.75676	−	0.400969i	1.75676	−	0.400969i
$563$		−	1.24698i		−	1.24698i	−0.781831	−	0.623490i	$-0.785714\pi$
$563$		−	1.24698i		−	1.24698i	0.781831	−	0.623490i	$-0.214286\pi$
$564$	0.500000	+	2.19064i	0.500000	+	2.19064i
$565$		0			0
$566$	0.376510	−	0.781831i	0.376510	−	0.781831i
$567$	0.626980	+	2.74698i	0.626980	+	2.74698i
$568$		0			0
$569$	−0.846011	+	0.193096i	−0.846011	+	0.193096i	−0.623490	−	0.781831i	$-0.714286\pi$
$569$	−0.846011	+	0.193096i	−0.846011	+	0.193096i	−0.222521	+	0.974928i	$0.571429\pi$
$570$		0			0
$571$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$571$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$572$		0			0
$573$		0			0
$574$	−2.74698	−	1.32288i	−2.74698	−	1.32288i
$575$	0.781831	−	0.376510i	0.781831	−	0.376510i
$576$	1.40097	−	1.75676i	1.40097	−	1.75676i
$577$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$577$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$578$	0.433884	+	0.900969i	0.433884	+	0.900969i
$579$		0			0
$580$	0.900969	−	0.433884i	0.900969	−	0.433884i
$581$	3.04892			3.04892
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.541044	+	0.678448i	0.541044	+	0.678448i	0.974928	−	0.222521i	$-0.0714286\pi$
$587$	0.541044	+	0.678448i	0.541044	+	0.678448i	−0.433884	+	0.900969i	$0.642857\pi$
$588$	−2.53859	−	0.579417i	−2.53859	−	0.579417i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$593$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$594$		0			0
$595$		0			0
$596$	0.277479	+	1.21572i	0.277479	+	1.21572i
$597$		0			0
$598$		0			0
$599$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$599$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$600$	0.400969	−	1.75676i	0.400969	−	1.75676i
$601$	−1.52446	−	0.347948i	−1.52446	−	0.347948i	−0.623490	−	0.781831i	$-0.714286\pi$
$601$	−1.52446	−	0.347948i	−1.52446	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$602$	0.433884	+	0.544073i	0.433884	+	0.544073i
$603$		0			0
$604$		0			0
$605$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$606$	1.22252	−	0.974928i	1.22252	−	0.974928i
$607$	0.781831	+	1.62349i	0.781831	+	1.62349i	0.781831	+	0.623490i	$0.214286\pi$
$607$	0.781831	+	1.62349i	0.781831	+	1.62349i			1.00000i	$0.5\pi$
$608$		0			0
$609$	−1.22252	−	2.53859i	−1.22252	−	2.53859i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$613$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$614$	1.62349	−	0.781831i	1.62349	−	0.781831i
$615$	−3.16557	−	1.52446i	−3.16557	−	1.52446i
$616$		0			0
$617$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$617$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$618$	−0.781831	+	3.42543i	−0.781831	+	3.42543i
$619$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$619$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$620$		0			0
$621$		−	1.94986i		−	1.94986i
$622$		0			0
$623$	−1.06086	+	2.20291i	−1.06086	+	2.20291i
$624$		0			0
$625$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−3.42543	−	0.781831i	−3.42543	−	0.781831i
$631$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$631$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.974928	−	0.777479i	0.974928	−	0.777479i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.433884	+	0.900969i	0.433884	+	0.900969i
$641$	0.678448	−	0.541044i	0.678448	−	0.541044i	−0.222521	−	0.974928i	$-0.571429\pi$
$641$	0.678448	−	0.541044i	0.678448	−	0.541044i	0.900969	+	0.433884i	$0.142857\pi$
$642$	0.974928	−	1.22252i	0.974928	−	1.22252i
$643$	0.781831	−	0.376510i	0.781831	−	0.376510i		−	1.00000i	$-0.5\pi$
$643$	0.781831	−	0.376510i	0.781831	−	0.376510i	0.781831	+	0.623490i	$0.214286\pi$
$644$	1.22252	+	0.588735i	1.22252	+	0.588735i
$645$	0.500000	+	0.626980i	0.500000	+	0.626980i
$646$		0			0
$647$	−0.347948	+	1.52446i	−0.347948	+	1.52446i	0.433884	+	0.900969i	$0.357143\pi$
$647$	−0.347948	+	1.52446i	−0.347948	+	1.52446i	−0.781831	+	0.623490i	$0.785714\pi$
$648$	−1.40881	−	1.12349i	−1.40881	−	1.12349i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.193096	+	0.400969i	−0.193096	+	0.400969i
$653$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$653$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$654$	−0.178448	−	0.781831i	−0.178448	−	0.781831i
$655$		0			0
$656$	1.90097	−	0.433884i	1.90097	−	0.433884i
$657$		0			0
$658$	−0.433884	+	1.90097i	−0.433884	+	1.90097i
$659$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$659$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$660$		0			0
$661$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−0.623490	−	0.781831i	$-0.714286\pi$
$661$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−1.00000			$\pi$
$662$		0			0
$663$		0			0
$664$	−1.52446	+	1.21572i	−1.52446	+	1.21572i
$665$		0			0
$666$		0			0
$667$	0.193096	+	0.846011i	0.193096	+	0.846011i
$668$	1.94986			1.94986
$669$	1.22252	+	2.53859i	1.22252	+	2.53859i
$670$		0			0
$671$		0			0
$672$	2.53859	−	1.22252i	2.53859	−	1.22252i
$673$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$673$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$674$		0			0
$675$	−2.19064	−	0.500000i	−2.19064	−	0.500000i
$676$	0.222521	−	0.974928i	0.222521	−	0.974928i
$677$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$677$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−1.52446	+	3.16557i	−1.52446	+	3.16557i
$682$		0			0
$683$	0.347948	+	1.52446i	0.347948	+	1.52446i	0.781831	+	0.623490i	$0.214286\pi$
$683$	0.347948	+	1.52446i	0.347948	+	1.52446i	−0.433884	+	0.900969i	$0.642857\pi$
$684$		0			0
$685$		0			0
$686$	−0.544073	−	0.433884i	−0.544073	−	0.433884i
$687$	−0.781831	+	3.42543i	−0.781831	+	3.42543i
$688$	−0.433884	−	0.0990311i	−0.433884	−	0.0990311i
$689$		0			0
$690$	1.40881	+	0.678448i	1.40881	+	0.678448i
$691$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$691$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$	1.62349	+	0.781831i	1.62349	+	0.781831i
$697$		0			0
$698$	0.193096	+	0.400969i	0.193096	+	0.400969i
$699$		0			0
$700$	0.974928	−	1.22252i	0.974928	−	1.22252i
$701$	−1.62349	+	0.781831i	−1.62349	+	0.781831i	−0.623490	+	0.781831i	$0.714286\pi$
$701$	−1.62349	+	0.781831i	−1.62349	+	0.781831i	−1.00000			$1.00000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−0.500000	+	2.19064i	−0.500000	+	2.19064i
$706$		0			0
$707$	1.32288	−	0.301938i	1.32288	−	0.301938i
$708$		0			0
$709$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	−0.623490	−	0.781831i	$-0.714286\pi$
$709$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	0.222521	−	0.974928i	$-0.428571\pi$
$710$		0			0
$711$		0			0
$712$	−0.347948	−	1.52446i	−0.347948	−	1.52446i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$719$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$720$	2.02446	−	0.974928i	2.02446	−	0.974928i
$721$	−1.90097	+	2.38374i	−1.90097	+	2.38374i
$722$	0.781831	−	0.623490i	0.781831	−	0.623490i
$723$	−1.40881	−	2.92543i	−1.40881	−	2.92543i
$724$	−1.80194			−1.80194
$725$	1.00000			1.00000
$726$	−1.80194			−1.80194
$727$	0.193096	+	0.400969i	0.193096	+	0.400969i	0.974928	−	0.222521i	$-0.0714286\pi$
$727$	0.193096	+	0.400969i	0.193096	+	0.400969i	−0.781831	+	0.623490i	$0.785714\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$733$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$734$	0.277479	−	1.21572i	0.277479	−	1.21572i
$735$	−2.03579	−	1.62349i	−2.03579	−	1.62349i
$736$	−0.846011	+	0.193096i	−0.846011	+	0.193096i
$737$		0			0
$738$	−0.974928	−	4.27144i	−0.974928	−	4.27144i
$739$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$739$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.433884	+	0.0990311i	−0.433884	+	0.0990311i	−0.433884	−	0.900969i	$-0.642857\pi$
$743$	−0.433884	+	0.0990311i	−0.433884	+	0.0990311i			1.00000i	$0.5\pi$
$744$		0			0
$745$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$746$		0			0
$747$	2.73169	+	3.42543i	2.73169	+	3.42543i
$748$		0			0
$749$	1.22252	−	0.588735i	1.22252	−	0.588735i
$750$	1.12349	−	1.40881i	1.12349	−	1.40881i
$751$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$751$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$752$	−0.541044	−	1.12349i	−0.541044	−	1.12349i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−1.52446	−	3.16557i	−1.52446	−	3.16557i
$757$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$757$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$761$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$762$	2.19064	+	0.500000i	2.19064	+	0.500000i
$763$	0.154851	−	0.678448i	0.154851	−	0.678448i
$764$		0			0
$765$		0			0
$766$		−	0.867767i		−	0.867767i
$767$		0			0
$768$	−0.781831	+	1.62349i	−0.781831	+	1.62349i
$769$	0.678448	−	1.40881i	0.678448	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$769$	0.678448	−	1.40881i	0.678448	−	1.40881i	0.900969	−	0.433884i	$-0.142857\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$773$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$774$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	0.781831	−	0.376510i	0.781831	−	0.376510i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.974928	−	2.02446i	0.974928	−	2.02446i
$784$	1.44504			1.44504
$785$		0			0
$786$		0			0
$787$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$787$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$788$		0			0
$789$	−2.02446	−	0.974928i	−2.02446	−	0.974928i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$797$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$798$		0			0
$799$		0			0
$800$			1.00000i			1.00000i
$801$	−3.42543	+	0.781831i	−3.42543	+	0.781831i
$802$	−0.974928	−	0.777479i	−0.974928	−	0.777479i
$803$		0			0
$804$		0			0
$805$	0.846011	+	1.06086i	0.846011	+	1.06086i
$806$		0			0
$807$	1.40881	−	0.678448i	1.40881	−	0.678448i
$808$	−0.541044	+	0.678448i	−0.541044	+	0.678448i
$809$	0.678448	−	0.541044i	0.678448	−	0.541044i	−0.222521	−	0.974928i	$-0.571429\pi$
$809$	0.678448	−	0.541044i	0.678448	−	0.541044i	0.900969	+	0.433884i	$0.142857\pi$
$810$	−0.781831	−	1.62349i	−0.781831	−	1.62349i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	0.974928	+	1.22252i	0.974928	+	1.22252i
$813$		0			0
$814$		0			0
$815$	−0.347948	+	0.277479i	−0.347948	+	0.277479i
$816$		0			0
$817$		0			0
$818$	−1.40881	−	0.678448i	−1.40881	−	0.678448i
$819$		0			0
$820$	1.90097	+	0.433884i	1.90097	+	0.433884i
$821$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	−0.900969	−	0.433884i	$-0.857143\pi$
$821$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	1.00000			$0$
$822$		0			0
$823$	1.21572	−	0.277479i	1.21572	−	0.277479i	0.433884	−	0.900969i	$-0.357143\pi$
$823$	1.21572	−	0.277479i	1.21572	−	0.277479i	0.781831	+	0.623490i	$0.214286\pi$
$824$		−	1.94986i		−	1.94986i
$825$		0			0
$826$		0			0
$827$	0.541044	−	1.12349i	0.541044	−	1.12349i	−0.433884	−	0.900969i	$-0.642857\pi$
$827$	0.541044	−	1.12349i	0.541044	−	1.12349i	0.974928	−	0.222521i	$-0.0714286\pi$
$828$	0.433884	+	1.90097i	0.433884	+	1.90097i
$829$		−	0.867767i		−	0.867767i	−0.900969	−	0.433884i	$-0.857143\pi$
$829$		−	0.867767i		−	0.867767i	0.900969	−	0.433884i	$-0.142857\pi$
$830$	−1.90097	+	0.433884i	−1.90097	+	0.433884i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.75676	+	0.846011i	1.75676	+	0.846011i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$839$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$840$	2.81762			2.81762
$841$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$842$	−1.94986			−1.94986
$843$	1.40881	+	2.92543i	1.40881	+	2.92543i
$844$		0			0
$845$	0.623490	−	0.781831i	0.623490	−	0.781831i
$846$	−2.52446	+	1.21572i	−2.52446	+	1.21572i
$847$	−1.40881	−	0.678448i	−1.40881	−	0.678448i
$848$		0			0
$849$	1.52446	+	0.347948i	1.52446	+	0.347948i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0			−	1.00000i	$-0.5\pi$
$853$		0			0				1.00000i	$0.5\pi$
$854$		0			0
$855$		0			0
$856$	−0.376510	+	0.781831i	−0.376510	+	0.781831i
$857$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$857$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$858$		0			0
$859$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$859$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$860$	−0.347948	−	0.277479i	−0.347948	−	0.277479i
$861$	1.22252	−	5.35621i	1.22252	−	5.35621i
$862$		0			0
$863$	−1.21572	−	1.52446i	−1.21572	−	1.52446i	−0.781831	−	0.623490i	$-0.785714\pi$
$863$	−1.21572	−	1.52446i	−1.21572	−	1.52446i	−0.433884	−	0.900969i	$-0.642857\pi$
$864$	2.02446	+	0.974928i	2.02446	+	0.974928i
$865$		0			0
$866$		0			0
$867$	−1.40881	+	1.12349i	−1.40881	+	1.12349i
$868$		0			0
$869$		0			0
$870$	1.12349	+	1.40881i	1.12349	+	1.40881i
$871$		0			0
$872$	0.193096	+	0.400969i	0.193096	+	0.400969i
$873$		0			0
$874$		0			0
$875$	1.40881	−	0.678448i	1.40881	−	0.678448i
$876$		0			0
$877$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$877$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.90097	−	0.433884i	1.90097	−	0.433884i	0.900969	−	0.433884i	$-0.142857\pi$
$881$	1.90097	−	0.433884i	1.90097	−	0.433884i	1.00000			$0$
$882$		−	3.24698i		−	3.24698i
$883$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$883$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$884$		0			0
$885$		0			0
$886$	0.445042	+	1.94986i	0.445042	+	1.94986i
$887$		−	1.24698i		−	1.24698i	−0.781831	−	0.623490i	$-0.785714\pi$
$887$		−	1.24698i		−	1.24698i	0.781831	−	0.623490i	$-0.214286\pi$
$888$		0			0
$889$	1.52446	+	1.21572i	1.52446	+	1.21572i
$890$	0.347948	−	1.52446i	0.347948	−	1.52446i
$891$		0			0
$892$	−0.974928	−	1.22252i	−0.974928	−	1.22252i
$893$		0			0
$894$	−2.02446	+	0.974928i	−2.02446	+	0.974928i
$895$		0			0
$896$	−1.22252	+	0.974928i	−1.22252	+	0.974928i
$897$		0			0
$898$	−1.56366			−1.56366
$899$		0			0
$900$	2.24698			2.24698
$901$		0			0
$902$		0			0
$903$	−0.781831	+	0.980386i	−0.781831	+	0.980386i
$904$		0			0
$905$	−1.62349	−	0.781831i	−1.62349	−	0.781831i
$906$		0			0
$907$	0.433884	+	0.0990311i	0.433884	+	0.0990311i	0.433884	−	0.900969i	$-0.357143\pi$
$907$	0.433884	+	0.0990311i	0.433884	+	0.0990311i			1.00000i	$0.5\pi$
$908$	0.433884	−	1.90097i	0.433884	−	1.90097i
$909$	1.52446	+	1.21572i	1.52446	+	1.21572i
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		−	1.94986i		−	1.94986i
$917$		0			0
$918$		0			0
$919$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$919$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$920$	−0.846011	−	0.193096i	−0.846011	−	0.193096i
$921$	2.02446	+	2.53859i	2.02446	+	2.53859i
$922$	−1.75676	−	0.846011i	−1.75676	−	0.846011i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−0.846011	−	1.75676i	−0.846011	−	1.75676i
$927$	−4.38129			−4.38129
$928$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$929$	−1.80194			−1.80194			−0.900969	−	0.433884i	$-0.857143\pi$
$929$	−1.80194			−1.80194			−0.900969	+	0.433884i	$0.857143\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	0.400969	+	0.193096i	0.400969	+	0.193096i
$935$		0			0
$936$		0			0
$937$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$937$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$938$		0			0
$939$		0			0
$940$		−	1.24698i		−	1.24698i
$941$	0.400969	+	1.75676i	0.400969	+	1.75676i	0.623490	+	0.781831i	$0.285714\pi$
$941$	0.400969	+	1.75676i	0.400969	+	1.75676i	−0.222521	+	0.974928i	$0.571429\pi$
$942$		0			0
$943$	−0.734141	+	1.52446i	−0.734141	+	1.52446i
$944$		0			0
$945$		−	3.51352i		−	3.51352i
$946$		0			0
$947$	1.40881	+	1.12349i	1.40881	+	1.12349i	0.974928	+	0.222521i	$0.0714286\pi$
$947$	1.40881	+	1.12349i	1.40881	+	1.12349i	0.433884	+	0.900969i	$0.357143\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$953$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−1.40881	+	1.12349i	−1.40881	+	1.12349i
$961$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$962$		0			0
$963$	1.75676	+	0.846011i	1.75676	+	0.846011i
$964$	1.12349	+	1.40881i	1.12349	+	1.40881i
$965$		0			0
$966$	−0.544073	+	2.38374i	−0.544073	+	2.38374i
$967$	0.347948	+	0.277479i	0.347948	+	0.277479i	0.781831	−	0.623490i	$-0.214286\pi$
$967$	0.347948	+	0.277479i	0.347948	+	0.277479i	−0.433884	+	0.900969i	$0.642857\pi$
$968$	0.974928	−	0.222521i	0.974928	−	0.222521i
$969$		0			0
$970$		0			0
$971$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$971$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$972$	0.433884	−	0.900969i	0.433884	−	0.900969i
$973$		0			0
$974$			1.56366i			1.56366i
$975$		0			0
$976$		0			0
$977$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$977$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$978$	−0.781831	−	0.178448i	−0.781831	−	0.178448i
$979$		0			0
$980$	1.30194	+	0.626980i	1.30194	+	0.626980i
$981$	0.900969	−	0.433884i	0.900969	−	0.433884i
$982$		0			0
$983$	−1.56366	+	1.24698i	−1.56366	+	1.24698i	−0.781831	+	0.623490i	$0.785714\pi$
$983$	−1.56366	+	1.24698i	−1.56366	+	1.24698i	−0.781831	+	0.623490i	$0.785714\pi$
$984$	1.52446	+	3.16557i	1.52446	+	3.16557i
$985$		0			0
$986$		0			0
$987$	−3.51352			−3.51352
$988$		0			0
$989$	0.301938	−	0.240787i	0.301938	−	0.240787i
$990$		0			0
$991$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$991$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−2.74698	−	2.19064i	−2.74698	−	2.19064i
$997$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$997$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	580.1.y.c.299.1	✓	12
4.3	odd	2	inner	580.1.y.c.299.2	yes	12
5.2	odd	4		2900.1.be.b.2851.1		6
5.3	odd	4		2900.1.be.a.2851.1		6
5.4	even	2	inner	580.1.y.c.299.2	yes	12
20.3	even	4		2900.1.be.b.2851.1		6
20.7	even	4		2900.1.be.a.2851.1		6
20.19	odd	2	CM	580.1.y.c.299.1	✓	12
29.13	even	14	inner	580.1.y.c.419.1	yes	12
116.71	odd	14	inner	580.1.y.c.419.2	yes	12
145.13	odd	28		2900.1.be.b.651.1		6
145.42	odd	28		2900.1.be.a.651.1		6
145.129	even	14	inner	580.1.y.c.419.2	yes	12
580.187	even	28		2900.1.be.b.651.1		6
580.303	even	28		2900.1.be.a.651.1		6
580.419	odd	14	inner	580.1.y.c.419.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
580.1.y.c.299.1	✓	12	1.1	even	1	trivial
580.1.y.c.299.1	✓	12	20.19	odd	2	CM
580.1.y.c.299.2	yes	12	4.3	odd	2	inner
580.1.y.c.299.2	yes	12	5.4	even	2	inner
580.1.y.c.419.1	yes	12	29.13	even	14	inner
580.1.y.c.419.1	yes	12	580.419	odd	14	inner
580.1.y.c.419.2	yes	12	116.71	odd	14	inner
580.1.y.c.419.2	yes	12	145.129	even	14	inner
2900.1.be.a.651.1		6	145.42	odd	28
2900.1.be.a.651.1		6	580.303	even	28
2900.1.be.a.2851.1		6	5.3	odd	4
2900.1.be.a.2851.1		6	20.7	even	4
2900.1.be.b.651.1		6	145.13	odd	28
2900.1.be.b.651.1		6	580.187	even	28
2900.1.be.b.2851.1		6	5.2	odd	4
2900.1.be.b.2851.1		6	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 580 = 2^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	580.y (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.433884 - 0.900969i) q^{2} +(1.40881 - 1.12349i) q^{3} +(-0.623490 + 0.781831i) q^{4} +(-0.900969 + 0.433884i) q^{5} +(-1.62349 - 0.781831i) q^{6} +(-0.974928 - 1.22252i) q^{7} +(0.974928 + 0.222521i) q^{8} +(0.500000 - 2.19064i) q^{9} +O(q^{10})\)	\(q+(-0.433884 - 0.900969i) q^{2} +(1.40881 - 1.12349i) q^{3} +(-0.623490 + 0.781831i) q^{4} +(-0.900969 + 0.433884i) q^{5} +(-1.62349 - 0.781831i) q^{6} +(-0.974928 - 1.22252i) q^{7} +(0.974928 + 0.222521i) q^{8} +(0.500000 - 2.19064i) q^{9} +(0.781831 + 0.623490i) q^{10} +1.80194i q^{12} +(-0.678448 + 1.40881i) q^{14} +(-0.781831 + 1.62349i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(-2.19064 + 0.500000i) q^{18} +(0.222521 - 0.974928i) q^{20} +(-2.74698 - 0.626980i) q^{21} +(0.781831 + 0.376510i) q^{23} +(1.62349 - 0.781831i) q^{24} +(0.623490 - 0.781831i) q^{25} +(-0.974928 - 2.02446i) q^{27} +1.56366 q^{28} +(0.623490 + 0.781831i) q^{29} +1.80194 q^{30} +(-0.781831 + 0.623490i) q^{32} +(1.40881 + 0.678448i) q^{35} +(1.40097 + 1.75676i) q^{36} +(-0.974928 + 0.222521i) q^{40} +1.94986i q^{41} +(0.626980 + 2.74698i) q^{42} +(0.193096 - 0.400969i) q^{43} +(0.500000 + 2.19064i) q^{45} -0.867767i q^{46} +(1.21572 - 0.277479i) q^{47} +(-1.40881 - 1.12349i) q^{48} +(-0.321552 + 1.40881i) q^{49} +(-0.974928 - 0.222521i) q^{50} +(-1.40097 + 1.75676i) q^{54} +(-0.678448 - 1.40881i) q^{56} +(0.433884 - 0.900969i) q^{58} +(-0.781831 - 1.62349i) q^{60} +(-3.16557 + 1.52446i) q^{63} +(0.900969 + 0.433884i) q^{64} +(1.52446 - 0.347948i) q^{69} -1.56366i q^{70} +(0.974928 - 2.02446i) q^{72} -1.80194i q^{75} +(0.623490 + 0.781831i) q^{80} +(-1.62349 - 0.781831i) q^{81} +(1.75676 - 0.846011i) q^{82} +(-1.21572 + 1.52446i) q^{83} +(2.20291 - 1.75676i) q^{84} -0.445042 q^{86} +(1.75676 + 0.400969i) q^{87} +(-0.678448 - 1.40881i) q^{89} +(1.75676 - 1.40097i) q^{90} +(-0.781831 + 0.376510i) q^{92} +(-0.777479 - 0.974928i) q^{94} +(-0.400969 + 1.75676i) q^{96} +(1.40881 - 0.321552i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{4} - 2 q^{5} - 10 q^{6} + 6 q^{9}+O(q^{10}) \) 12 * q + 2 * q^4 - 2 * q^5 - 10 * q^6 + 6 * q^9	\( 12 q + 2 q^{4} - 2 q^{5} - 10 q^{6} + 6 q^{9} - 2 q^{16} + 2 q^{20} - 14 q^{21} + 10 q^{24} - 2 q^{25} - 2 q^{29} + 4 q^{30} + 8 q^{36} + 6 q^{45} - 12 q^{49} - 8 q^{54} + 2 q^{64} - 2 q^{80} - 10 q^{81} - 4 q^{86} - 10 q^{94} + 4 q^{96}+O(q^{100}) \) 12 * q + 2 * q^4 - 2 * q^5 - 10 * q^6 + 6 * q^9 - 2 * q^16 + 2 * q^20 - 14 * q^21 + 10 * q^24 - 2 * q^25 - 2 * q^29 + 4 * q^30 + 8 * q^36 + 6 * q^45 - 12 * q^49 - 8 * q^54 + 2 * q^64 - 2 * q^80 - 10 * q^81 - 4 * q^86 - 10 * q^94 + 4 * q^96

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