LMFDB - Embedded newform 2695.1.ck.c.604.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2695,1,Mod(109,2695)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2695, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([21, 40, 21])) N = Newforms(chi, 1, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2695.109"); S:= CuspForms(chi, 1); N := Newforms(S);

Level:	$ N $	$=$	$ 2695 = 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2695.ck (of order $42$, degree $12$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.34498020905$
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:	$\Z[a_1, \ldots, a_{4}]$
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			604.2
Root			$0.563320 + 0.826239i$ of defining polynomial
Character	$\chi$	$=$	2695.604
Dual form			2695.1.ck.c.879.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.496990 + 1.26631i) q^{2} +(-0.623490 + 0.578514i) q^{4} +(-0.826239 + 0.563320i) q^{5} +(-0.781831 + 0.623490i) q^{7} +(0.183183 + 0.0882162i) q^{8} +(-0.988831 + 0.149042i) q^{9} +(-1.12397 - 0.766310i) q^{10} +(0.988831 + 0.149042i) q^{11} +(-0.185853 + 0.233052i) q^{13} +(-1.17809 - 0.680173i) q^{14} +(-0.0842299 + 1.12397i) q^{16} +(-0.829215 + 0.255779i) q^{17} +(-0.680173 - 1.17809i) q^{18} +(0.189263 - 0.829215i) q^{20} +(0.302705 + 1.32624i) q^{22} +(0.365341 - 0.930874i) q^{25} +(-0.387483 - 0.119523i) q^{26} +(0.126766 - 0.841040i) q^{28} +(-0.500000 - 0.866025i) q^{31} +(-1.27087 + 0.392012i) q^{32} +(-0.736007 - 0.922924i) q^{34} +(0.294755 - 0.955573i) q^{35} +(0.530303 - 0.664979i) q^{36} +(-0.201047 + 0.0303029i) q^{40} +(-1.67738 + 0.807782i) q^{43} +(-0.702749 + 0.479126i) q^{44} +(0.733052 - 0.680173i) q^{45} +(0.222521 - 0.974928i) q^{49} +1.36035 q^{50} +(-0.0189465 - 0.252824i) q^{52} +(-0.900969 + 0.433884i) q^{55} +(-0.198220 + 0.0452424i) q^{56} +(-1.63402 - 1.11406i) q^{59} +(0.848162 - 1.06356i) q^{62} +(0.680173 - 0.733052i) q^{63} +(-0.425270 - 0.533272i) q^{64} +(0.0222759 - 0.297251i) q^{65} +(0.369035 - 0.639188i) q^{68} +(1.35654 - 0.101659i) q^{70} +(0.326239 + 1.42935i) q^{71} +(-0.194285 - 0.0599289i) q^{72} +(-0.728639 + 1.85654i) q^{73} +(-0.866025 + 0.500000i) q^{77} +(-0.563561 - 0.976116i) q^{80} +(0.955573 - 0.294755i) q^{81} +(1.07992 + 1.35417i) q^{83} +(0.541044 - 0.678448i) q^{85} +(-1.85654 - 1.72262i) q^{86} +(0.167989 + 0.114533i) q^{88} +(0.722521 - 0.108903i) q^{89} +(1.22563 + 0.590232i) q^{90} -0.298085i q^{91} +(1.34515 - 0.202749i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4} - 2 q^{5} + 2 q^{9} - 2 q^{11} - 6 q^{14} - 26 q^{16} + 8 q^{20} + 2 q^{25} + 6 q^{26} - 12 q^{31} - 14 q^{34} - 8 q^{36} - 18 q^{44} - 2 q^{45} + 4 q^{49} - 4 q^{55} + 14 q^{56} - 2 q^{59}+ \cdots - 24 q^{99}+O(q^{100}) $ 24 * q + 4 * q^4 - 2 * q^5 + 2 * q^9 - 2 * q^11 - 6 * q^14 - 26 * q^16 + 8 * q^20 + 2 * q^25 + 6 * q^26 - 12 * q^31 - 14 * q^34 - 8 * q^36 - 18 * q^44 - 2 * q^45 + 4 * q^49 - 4 * q^55 + 14 * q^56 - 2 * q^59 - 10 * q^64 - 6 * q^70 - 10 * q^71 + 12 * q^80 + 2 * q^81 - 6 * q^86 + 16 * q^89 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2695\mathbb{Z}\right)^\times$.

$n$	$981$	$1816$	$2157$
$\chi(n)$	$-1$	$e\left(\frac{10}{21}\right)$	$-1$

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 $

$2$	0.496990	+	1.26631i	0.496990	+	1.26631i	0.930874	+	0.365341i	$0.119048\pi$
$2$	0.496990	+	1.26631i	0.496990	+	1.26631i	−0.433884	+	0.900969i	$0.642857\pi$
$3$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$3$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$4$	−0.623490	+	0.578514i	−0.623490	+	0.578514i
$5$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$5$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$6$		0			0
$7$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$7$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$8$	0.183183	+	0.0882162i	0.183183	+	0.0882162i
$9$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$10$	−1.12397	−	0.766310i	−1.12397	−	0.766310i
$11$	0.988831	+	0.149042i	0.988831	+	0.149042i
$11$	0.988831	+	0.149042i	0.988831	+	0.149042i
$12$		0			0
$13$	−0.185853	+	0.233052i	−0.185853	+	0.233052i	−0.866025	−	0.500000i	$-0.833333\pi$
$13$	−0.185853	+	0.233052i	−0.185853	+	0.233052i	0.680173	+	0.733052i	$0.261905\pi$
$14$	−1.17809	−	0.680173i	−1.17809	−	0.680173i
$15$		0			0
$16$	−0.0842299	+	1.12397i	−0.0842299	+	1.12397i
$17$	−0.829215	+	0.255779i	−0.829215	+	0.255779i	−0.680173	−	0.733052i	$-0.738095\pi$
$17$	−0.829215	+	0.255779i	−0.829215	+	0.255779i	−0.149042	+	0.988831i	$0.547619\pi$
$18$	−0.680173	−	1.17809i	−0.680173	−	1.17809i
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$	0.189263	−	0.829215i	0.189263	−	0.829215i
$21$		0			0
$22$	0.302705	+	1.32624i	0.302705	+	1.32624i
$23$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$23$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$24$		0			0
$25$	0.365341	−	0.930874i	0.365341	−	0.930874i
$26$	−0.387483	−	0.119523i	−0.387483	−	0.119523i
$27$		0			0
$28$	0.126766	−	0.841040i	0.126766	−	0.841040i
$29$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$29$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$30$		0			0
$31$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$31$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$32$	−1.27087	+	0.392012i	−1.27087	+	0.392012i
$33$		0			0
$34$	−0.736007	−	0.922924i	−0.736007	−	0.922924i
$35$	0.294755	−	0.955573i	0.294755	−	0.955573i
$36$	0.530303	−	0.664979i	0.530303	−	0.664979i
$37$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$37$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$38$		0			0
$39$		0			0
$40$	−0.201047	+	0.0303029i	−0.201047	+	0.0303029i
$41$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$41$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$42$		0			0
$43$	−1.67738	+	0.807782i	−1.67738	+	0.807782i	−0.680173	+	0.733052i	$0.738095\pi$
$43$	−1.67738	+	0.807782i	−1.67738	+	0.807782i	−0.997204	+	0.0747301i	$0.976190\pi$
$44$	−0.702749	+	0.479126i	−0.702749	+	0.479126i
$45$	0.733052	−	0.680173i	0.733052	−	0.680173i
$46$		0			0
$47$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$47$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$48$		0			0
$49$	0.222521	−	0.974928i	0.222521	−	0.974928i
$50$	1.36035			1.36035
$51$		0			0
$52$	−0.0189465	−	0.252824i	−0.0189465	−	0.252824i
$53$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$53$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$54$		0			0
$55$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$56$	−0.198220	+	0.0452424i	−0.198220	+	0.0452424i
$57$		0			0
$58$		0			0
$59$	−1.63402	−	1.11406i	−1.63402	−	1.11406i	−0.900969	−	0.433884i	$-0.857143\pi$
$59$	−1.63402	−	1.11406i	−1.63402	−	1.11406i	−0.733052	−	0.680173i	$-0.761905\pi$
$60$		0			0
$61$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$61$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$62$	0.848162	−	1.06356i	0.848162	−	1.06356i
$63$	0.680173	−	0.733052i	0.680173	−	0.733052i
$64$	−0.425270	−	0.533272i	−0.425270	−	0.533272i
$65$	0.0222759	−	0.297251i	0.0222759	−	0.297251i
$66$		0			0
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$	0.369035	−	0.639188i	0.369035	−	0.639188i
$69$		0			0
$70$	1.35654	−	0.101659i	1.35654	−	0.101659i
$71$	0.326239	+	1.42935i	0.326239	+	1.42935i	0.826239	+	0.563320i	$0.190476\pi$
$71$	0.326239	+	1.42935i	0.326239	+	1.42935i	−0.500000	+	0.866025i	$0.666667\pi$
$72$	−0.194285	−	0.0599289i	−0.194285	−	0.0599289i
$73$	−0.728639	+	1.85654i	−0.728639	+	1.85654i	−0.294755	+	0.955573i	$0.595238\pi$
$73$	−0.728639	+	1.85654i	−0.728639	+	1.85654i	−0.433884	+	0.900969i	$0.642857\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$78$		0			0
$79$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$	−0.563561	−	0.976116i	−0.563561	−	0.976116i
$81$	0.955573	−	0.294755i	0.955573	−	0.294755i
$82$		0			0
$83$	1.07992	+	1.35417i	1.07992	+	1.35417i	0.930874	+	0.365341i	$0.119048\pi$
$83$	1.07992	+	1.35417i	1.07992	+	1.35417i	0.149042	+	0.988831i	$0.452381\pi$
$84$		0			0
$85$	0.541044	−	0.678448i	0.541044	−	0.678448i
$86$	−1.85654	−	1.72262i	−1.85654	−	1.72262i
$87$		0			0
$88$	0.167989	+	0.114533i	0.167989	+	0.114533i
$89$	0.722521	−	0.108903i	0.722521	−	0.108903i	0.222521	−	0.974928i	$-0.428571\pi$
$89$	0.722521	−	0.108903i	0.722521	−	0.108903i	0.500000	+	0.866025i	$0.333333\pi$
$90$	1.22563	+	0.590232i	1.22563	+	0.590232i
$91$		−	0.298085i		−	0.298085i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	1.34515	−	0.202749i	1.34515	−	0.202749i
$99$	−1.00000			−1.00000
$100$	0.310737	+	0.791745i	0.310737	+	0.791745i
$101$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$101$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$102$		0			0
$103$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$103$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$104$	−0.0546039	+	0.0262959i	−0.0546039	+	0.0262959i
$105$		0			0
$106$		0			0
$107$	1.92808	−	0.290611i	1.92808	−	0.290611i	0.930874	−	0.365341i	$-0.119048\pi$
$107$	1.92808	−	0.290611i	1.92808	−	0.290611i	0.997204	+	0.0747301i	$0.0238095\pi$
$108$		0			0
$109$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$109$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$110$	−0.997204	−	0.925270i	−0.997204	−	0.925270i
$111$		0			0
$112$	−0.634930	−	0.931272i	−0.634930	−	0.931272i
$113$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$113$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.149042	−	0.258149i	0.149042	−	0.258149i
$118$	0.598649	−	2.62285i	0.598649	−	2.62285i
$119$	0.488831	−	0.716983i	0.488831	−	0.716983i
$120$		0			0
$121$	0.955573	+	0.294755i	0.955573	+	0.294755i
$122$		0			0
$123$		0			0
$124$	0.812753	+	0.250701i	0.812753	+	0.250701i
$125$	0.222521	+	0.974928i	0.222521	+	0.974928i
$126$	1.26631	+	0.496990i	1.26631	+	0.496990i
$127$	−0.433884	+	1.90097i	−0.433884	+	1.90097i			1.00000i	$0.5\pi$
$127$	−0.433884	+	1.90097i	−0.433884	+	1.90097i	−0.433884	+	0.900969i	$0.642857\pi$
$128$	−0.201047	+	0.348223i	−0.201047	+	0.348223i
$129$		0			0
$130$	0.387483	−	0.119523i	0.387483	−	0.119523i
$131$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$131$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.174462	−	0.0262959i	−0.174462	−	0.0262959i
$137$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$137$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$138$		0			0
$139$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$139$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$140$	0.369035	+	0.766310i	0.369035	+	0.766310i
$141$		0			0
$142$	−1.64786	+	1.12349i	−1.64786	+	1.12349i
$143$	−0.218511	+	0.202749i	−0.218511	+	0.202749i
$144$	−0.0842299	−	1.12397i	−0.0842299	−	1.12397i
$145$		0			0
$146$	−2.71308			−2.71308
$147$		0			0
$148$		0			0
$149$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$149$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$150$		0			0
$151$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$151$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$152$		0			0
$153$	0.781831	−	0.376510i	0.781831	−	0.376510i
$154$	−1.06356	−	0.848162i	−1.06356	−	0.848162i
$155$	0.900969	+	0.433884i	0.900969	+	0.433884i
$156$		0			0
$157$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$157$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$158$		0			0
$159$		0			0
$160$	0.829215	−	1.03980i	0.829215	−	1.03980i
$161$		0			0
$162$	0.848162	+	1.06356i	0.848162	+	1.06356i
$163$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$163$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$164$		0			0
$165$		0			0
$166$	−1.17809	+	2.04052i	−1.17809	+	2.04052i
$167$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$167$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$168$		0			0
$169$	0.202749	+	0.888301i	0.202749	+	0.888301i
$170$	1.12802	+	0.347948i	1.12802	+	0.347948i
$171$		0			0
$172$	0.578514	−	1.47403i	0.578514	−	1.47403i
$173$	0.563320	+	0.173761i	0.563320	+	0.173761i	0.563320	−	0.826239i	$-0.309524\pi$
$173$	0.563320	+	0.173761i	0.563320	+	0.173761i			1.00000i	$0.5\pi$
$174$		0			0
$175$	0.294755	+	0.955573i	0.294755	+	0.955573i
$176$	−0.250808	+	1.09886i	−0.250808	+	1.09886i
$177$		0			0
$178$	0.496990	+	0.860812i	0.496990	+	0.860812i
$179$	1.40097	−	0.432142i	1.40097	−	0.432142i	0.500000	−	0.866025i	$-0.333333\pi$
$179$	1.40097	−	0.432142i	1.40097	−	0.432142i	0.900969	+	0.433884i	$0.142857\pi$
$180$	−0.0635609	+	0.848162i	−0.0635609	+	0.848162i
$181$	−0.0931869	−	0.116853i	−0.0931869	−	0.116853i	0.733052	−	0.680173i	$-0.238095\pi$
$181$	−0.0931869	−	0.116853i	−0.0931869	−	0.116853i	−0.826239	+	0.563320i	$0.809524\pi$
$182$	0.377467	−	0.148145i	0.377467	−	0.148145i
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.858075	+	0.129334i	−0.858075	+	0.129334i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.826239	−	0.563320i	0.826239	−	0.563320i	−0.0747301	−	0.997204i	$-0.523810\pi$
$191$	0.826239	−	0.563320i	0.826239	−	0.563320i	0.900969	+	0.433884i	$0.142857\pi$
$192$		0			0
$193$	−0.0648483	−	0.865341i	−0.0648483	−	0.865341i	−0.930874	−	0.365341i	$-0.880952\pi$
$193$	−0.0648483	−	0.865341i	−0.0648483	−	0.865341i	0.866025	−	0.500000i	$-0.166667\pi$
$194$		0			0
$195$		0			0
$196$	0.425270	+	0.736589i	0.425270	+	0.736589i
$197$	0.589510			0.589510			0.294755	−	0.955573i	$-0.404762\pi$
$197$	0.589510			0.589510			0.294755	+	0.955573i	$0.404762\pi$
$198$	−0.496990	−	1.26631i	−0.496990	−	1.26631i
$199$	0.142820	+	1.90580i	0.142820	+	1.90580i	0.365341	+	0.930874i	$0.380952\pi$
$199$	0.142820	+	1.90580i	0.142820	+	1.90580i	−0.222521	+	0.974928i	$0.571429\pi$
$200$	0.149042	−	0.138291i	0.149042	−	0.138291i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$	−0.246289	−	0.228523i	−0.246289	−	0.228523i
$209$		0			0
$210$		0			0
$211$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$211$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$212$		0			0
$213$		0			0
$214$	1.32624	+	2.29711i	1.32624	+	2.29711i
$215$	0.930874	−	1.61232i	0.930874	−	1.61232i
$216$		0			0
$217$	0.930874	+	0.365341i	0.930874	+	0.365341i
$218$		0			0
$219$		0			0
$220$	0.310737	−	0.791745i	0.310737	−	0.791745i
$221$	0.0945021	−	0.240787i	0.0945021	−	0.240787i
$222$		0			0
$223$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$223$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$224$	0.749192	−	1.09886i	0.749192	−	1.09886i
$225$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$226$		0			0
$227$	−0.563320	−	0.975699i	−0.563320	−	0.975699i	−0.997204	−	0.0747301i	$-0.976190\pi$
$227$	−0.563320	−	0.975699i	−0.563320	−	0.975699i	0.433884	−	0.900969i	$-0.357143\pi$
$228$		0			0
$229$	−0.109562	+	1.46200i	−0.109562	+	1.46200i	0.623490	+	0.781831i	$0.285714\pi$
$229$	−0.109562	+	1.46200i	−0.109562	+	1.46200i	−0.733052	+	0.680173i	$0.761905\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.680173	−	0.733052i	$-0.261905\pi$
$233$		0			0		−0.680173	+	0.733052i	$0.738095\pi$
$234$	0.400969	+	0.0604363i	0.400969	+	0.0604363i
$235$		0			0
$236$	1.66329	−	0.250701i	1.66329	−	0.250701i
$237$		0			0
$238$	1.15087	+	0.262678i	1.15087	+	0.262678i
$239$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$239$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$240$		0			0
$241$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$241$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$242$	0.101659	+	1.35654i	0.101659	+	1.35654i
$243$		0			0
$244$		0			0
$245$	0.365341	+	0.930874i	0.365341	+	0.930874i
$246$		0			0
$247$		0			0
$248$	−0.0151939	−	0.202749i	−0.0151939	−	0.202749i
$249$		0			0
$250$	−1.12397	+	0.766310i	−1.12397	+	0.766310i
$251$	0.400969	−	0.193096i	0.400969	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$251$	0.400969	−	0.193096i	0.400969	−	0.193096i	0.623490	+	0.781831i	$0.285714\pi$
$252$			0.850540i			0.850540i
$253$		0			0
$254$	−2.62285	+	0.395331i	−2.62285	+	0.395331i
$255$		0			0
$256$	−1.21534	−	0.183183i	−1.21534	−	0.183183i
$257$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$257$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$258$		0			0
$259$		0			0
$260$	0.158075	+	0.198220i	0.158075	+	0.198220i
$261$		0			0
$262$		0			0
$263$	−0.866025	−	1.50000i	−0.866025	−	1.50000i	−0.866025	−	0.500000i	$-0.833333\pi$
$263$	−0.866025	−	1.50000i	−0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.658322	+	1.67738i	−0.658322	+	1.67738i	0.0747301	+	0.997204i	$0.476190\pi$
$269$	−0.658322	+	1.67738i	−0.658322	+	1.67738i	−0.733052	+	0.680173i	$0.761905\pi$
$270$		0			0
$271$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$271$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$272$	−0.217643	−	0.953557i	−0.217643	−	0.953557i
$273$		0			0
$274$		0			0
$275$	0.500000	−	0.866025i	0.500000	−	0.866025i
$276$		0			0
$277$	−1.90580	+	0.587862i	−1.90580	+	0.587862i	−0.930874	+	0.365341i	$0.880952\pi$
$277$	−1.90580	+	0.587862i	−1.90580	+	0.587862i	−0.974928	+	0.222521i	$0.928571\pi$
$278$		0			0
$279$	0.623490	+	0.781831i	0.623490	+	0.781831i
$280$	0.138291	−	0.149042i	0.138291	−	0.149042i
$281$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$281$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$282$		0			0
$283$	1.54620	+	0.233052i	1.54620	+	0.233052i	0.866025	−	0.500000i	$-0.166667\pi$
$283$	1.54620	+	0.233052i	1.54620	+	0.233052i	0.680173	+	0.733052i	$0.261905\pi$
$284$	−1.03030	−	0.702449i	−1.03030	−	0.702449i
$285$		0			0
$286$	−0.365341	−	0.175939i	−0.365341	−	0.175939i
$287$		0			0
$288$	1.19825	−	0.577047i	1.19825	−	0.577047i
$289$	−0.204064	+	0.139129i	−0.204064	+	0.139129i
$290$		0			0
$291$		0			0
$292$	−0.619736	−	1.57906i	−0.619736	−	1.57906i
$293$	−1.12664			−1.12664			−0.563320	−	0.826239i	$-0.690476\pi$
$293$	−1.12664			−1.12664			−0.563320	+	0.826239i	$0.690476\pi$
$294$		0			0
$295$	1.97766			1.97766
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	0.807782	−	1.67738i	0.807782	−	1.67738i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$	0.865341	+	0.802919i	0.865341	+	0.802919i
$307$	0.848162	−	1.06356i	0.848162	−	1.06356i	−0.149042	−	0.988831i	$-0.547619\pi$
$307$	0.848162	−	1.06356i	0.848162	−	1.06356i	0.997204	−	0.0747301i	$-0.0238095\pi$
$308$	0.250701	−	0.812753i	0.250701	−	0.812753i
$309$		0			0
$310$	−0.101659	+	1.35654i	−0.101659	+	1.35654i
$311$	1.57906	−	0.487076i	1.57906	−	0.487076i	0.623490	−	0.781831i	$-0.285714\pi$
$311$	1.57906	−	0.487076i	1.57906	−	0.487076i	0.955573	+	0.294755i	$0.0952381\pi$
$312$		0			0
$313$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$313$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$314$		0			0
$315$	−0.149042	+	0.988831i	−0.149042	+	0.988831i
$316$		0			0
$317$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$317$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$318$		0			0
$319$		0			0
$320$	0.651777	+	0.201047i	0.651777	+	0.201047i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.425270	+	0.736589i	−0.425270	+	0.736589i
$325$	0.149042	+	0.258149i	0.149042	+	0.258149i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.535628	+	0.496990i	0.535628	+	0.496990i	0.900969	−	0.433884i	$-0.142857\pi$
$331$	0.535628	+	0.496990i	0.535628	+	0.496990i	−0.365341	+	0.930874i	$0.619048\pi$
$332$	−1.45672	−	0.219566i	−1.45672	−	0.219566i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.268565	−	0.129334i	0.268565	−	0.129334i	−0.294755	−	0.955573i	$-0.595238\pi$
$337$	0.268565	−	0.129334i	0.268565	−	0.129334i	0.563320	+	0.826239i	$0.309524\pi$
$338$	−1.02410	+	0.698220i	−1.02410	+	0.698220i
$339$		0			0
$340$	0.0551561	+	0.736007i	0.0551561	+	0.736007i
$341$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$342$		0			0
$343$	0.433884	+	0.900969i	0.433884	+	0.900969i
$344$	−0.378526			−0.378526
$345$		0			0
$346$	0.0599289	+	0.799695i	0.0599289	+	0.799695i
$347$	0.432142	−	0.400969i	0.432142	−	0.400969i	−0.433884	−	0.900969i	$-0.642857\pi$
$347$	0.432142	−	0.400969i	0.432142	−	0.400969i	0.866025	+	0.500000i	$0.166667\pi$
$348$		0			0
$349$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$349$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$350$	−1.06356	+	0.848162i	−1.06356	+	0.848162i
$351$		0			0
$352$	−1.31510	+	0.198220i	−1.31510	+	0.198220i
$353$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$353$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$354$		0			0
$355$	−1.07473	−	0.997204i	−1.07473	−	0.997204i
$356$	−0.387483	+	0.485888i	−0.387483	+	0.485888i
$357$		0			0
$358$	1.24349	+	1.55929i	1.24349	+	1.55929i
$359$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$359$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$360$	0.194285	−	0.0599289i	0.194285	−	0.0599289i
$361$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$362$	0.101659	−	0.176078i	0.101659	−	0.176078i
$363$		0			0
$364$	0.172446	+	0.185853i	0.172446	+	0.185853i
$365$	−0.443797	−	1.94440i	−0.443797	−	1.94440i
$366$		0			0
$367$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$367$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−0.563320	+	0.975699i	−0.563320	+	0.975699i	0.433884	+	0.900969i	$0.357143\pi$
$373$	−0.563320	+	0.975699i	−0.563320	+	0.975699i	−0.997204	+	0.0747301i	$0.976190\pi$
$374$	−0.590232	−	1.02231i	−0.590232	−	1.02231i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.03030	−	1.29196i	1.03030	−	1.29196i	0.0747301	−	0.997204i	$-0.476190\pi$
$379$	1.03030	−	1.29196i	1.03030	−	1.29196i	0.955573	−	0.294755i	$-0.0952381\pi$
$380$		0			0
$381$		0			0
$382$	1.12397	+	0.766310i	1.12397	+	0.766310i
$383$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$383$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$384$		0			0
$385$	0.433884	−	0.900969i	0.433884	−	0.900969i
$386$	1.06356	−	0.512184i	1.06356	−	0.512184i
$387$	1.53825	−	1.04876i	1.53825	−	1.04876i
$388$		0			0
$389$	0.123490	+	1.64786i	0.123490	+	1.64786i	0.623490	+	0.781831i	$0.285714\pi$
$389$	0.123490	+	1.64786i	0.123490	+	1.64786i	−0.500000	+	0.866025i	$0.666667\pi$
$390$		0			0
$391$		0			0
$392$	0.126766	−	0.158960i	0.126766	−	0.158960i
$393$		0			0
$394$	0.292981	+	0.746503i	0.292981	+	0.746503i
$395$		0			0
$396$	0.623490	−	0.578514i	0.623490	−	0.578514i
$397$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$397$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$398$	−2.34236	+	1.12802i	−2.34236	+	1.12802i
$399$		0			0
$400$	1.01550	+	0.489040i	1.01550	+	0.489040i
$401$	0.722521	−	0.108903i	0.722521	−	0.108903i	0.222521	−	0.974928i	$-0.428571\pi$
$401$	0.722521	−	0.108903i	0.722521	−	0.108903i	0.500000	+	0.866025i	$0.333333\pi$
$402$		0			0
$403$	0.294755	+	0.0444272i	0.294755	+	0.0444272i
$404$		0			0
$405$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$409$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1.97213	−	0.147791i	1.97213	−	0.147791i
$414$		0			0
$415$	−1.65510	−	0.510531i	−1.65510	−	0.510531i
$416$	0.144836	−	0.369035i	0.144836	−	0.369035i
$417$		0			0
$418$		0			0
$419$	−0.440071	−	1.92808i	−0.440071	−	1.92808i	−0.365341	−	0.930874i	$-0.619048\pi$
$419$	−0.440071	−	1.92808i	−0.440071	−	1.92808i	−0.0747301	−	0.997204i	$-0.523810\pi$
$420$		0			0
$421$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	0.222521	+	0.974928i	$0.428571\pi$
$421$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	−0.623490	+	0.781831i	$0.714286\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.0648483	+	0.865341i	−0.0648483	+	0.865341i
$426$		0			0
$427$		0			0
$428$	−1.03401	+	1.29661i	−1.03401	+	1.29661i
$429$		0			0
$430$	2.50433	+	0.377467i	2.50433	+	0.377467i
$431$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$431$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$432$		0			0
$433$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$433$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$434$			1.36035i			1.36035i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$439$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$440$	−0.203317			−0.203317
$441$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$442$	0.351878			0.351878
$443$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$443$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$444$		0			0
$445$	−0.535628	+	0.496990i	−0.535628	+	0.496990i
$446$		0			0
$447$		0			0
$448$	0.664979	+	0.151777i	0.664979	+	0.151777i
$449$	−1.78181	−	0.858075i	−1.78181	−	0.858075i	−0.955573	−	0.294755i	$-0.904762\pi$
$449$	−1.78181	−	0.858075i	−1.78181	−	0.858075i	−0.826239	−	0.563320i	$-0.809524\pi$
$450$	−1.34515	+	0.202749i	−1.34515	+	0.202749i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.955573	−	1.19825i	0.955573	−	1.19825i
$455$	0.167917	+	0.246289i	0.167917	+	0.246289i
$456$		0			0
$457$	−0.129436	+	1.72721i	−0.129436	+	1.72721i	0.433884	+	0.900969i	$0.357143\pi$
$457$	−0.129436	+	1.72721i	−0.129436	+	1.72721i	−0.563320	+	0.826239i	$0.690476\pi$
$458$	−1.90580	+	0.587862i	−1.90580	+	0.587862i
$459$		0			0
$460$		0			0
$461$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$461$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$462$		0			0
$463$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$463$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$467$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$468$	0.0564163	+	0.247176i	0.0564163	+	0.247176i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.201047	−	0.348223i	−0.201047	−	0.348223i
$473$	−1.77904	+	0.548760i	−1.77904	+	0.548760i
$474$		0			0
$475$		0			0
$476$	0.110004	+	0.729827i	0.110004	+	0.729827i
$477$		0			0
$478$		0			0
$479$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$479$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.766310	+	0.369035i	−0.766310	+	0.369035i
$485$		0			0
$486$		0			0
$487$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$487$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$488$		0			0
$489$		0			0
$490$	−0.997204	+	0.925270i	−0.997204	+	0.925270i
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	0.826239	−	0.563320i	0.826239	−	0.563320i
$496$	1.01550	−	0.489040i	1.01550	−	0.489040i
$497$	−1.14625	−	0.914101i	−1.14625	−	0.914101i
$498$		0			0
$499$	−0.722521	+	0.108903i	−0.722521	+	0.108903i	−0.500000	−	0.866025i	$-0.666667\pi$
$499$	−0.722521	+	0.108903i	−0.722521	+	0.108903i	−0.222521	+	0.974928i	$0.571429\pi$
$500$	−0.702749	−	0.479126i	−0.702749	−	0.479126i
$501$		0			0
$502$	0.443797	+	0.411784i	0.443797	+	0.411784i
$503$	−1.07992	+	1.35417i	−1.07992	+	1.35417i	−0.149042	+	0.988831i	$0.547619\pi$
$503$	−1.07992	+	1.35417i	−1.07992	+	1.35417i	−0.930874	+	0.365341i	$0.880952\pi$
$504$	0.189263	−	0.0742802i	0.189263	−	0.0742802i
$505$		0			0
$506$		0			0
$507$		0			0
$508$	−0.829215	−	1.43624i	−0.829215	−	1.43624i
$509$	−0.826239	+	1.43109i	−0.826239	+	1.43109i	0.0747301	+	0.997204i	$0.476190\pi$
$509$	−0.826239	+	1.43109i	−0.826239	+	1.43109i	−0.900969	+	0.433884i	$0.857143\pi$
$510$		0			0
$511$	−0.587862	−	1.90580i	−0.587862	−	1.90580i
$512$	−0.282571	−	1.23802i	−0.282571	−	1.23802i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	0.0303029	−	0.0524862i	0.0303029	−	0.0524862i
$521$	−0.733052	−	1.26968i	−0.733052	−	1.26968i	−0.955573	−	0.294755i	$-0.904762\pi$
$521$	−0.733052	−	1.26968i	−0.733052	−	1.26968i	0.222521	−	0.974928i	$-0.428571\pi$
$522$		0			0
$523$	0.139129	−	1.85654i	0.139129	−	1.85654i	−0.294755	−	0.955573i	$-0.595238\pi$
$523$	0.139129	−	1.85654i	0.139129	−	1.85654i	0.433884	−	0.900969i	$-0.357143\pi$
$524$		0			0
$525$		0			0
$526$	1.46906	−	1.84214i	1.46906	−	1.84214i
$527$	0.636119	+	0.590232i	0.636119	+	0.590232i
$528$		0			0
$529$	0.826239	+	0.563320i	0.826239	+	0.563320i
$530$		0			0
$531$	1.78181	+	0.858075i	1.78181	+	0.858075i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−1.42935	+	1.32624i	−1.42935	+	1.32624i
$536$		0			0
$537$		0			0
$538$	−2.45126			−2.45126
$539$	0.365341	−	0.930874i	0.365341	−	0.930874i
$540$		0			0
$541$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$541$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$542$		0			0
$543$		0			0
$544$	0.953557	−	0.650124i	0.953557	−	0.650124i
$545$		0			0
$546$		0			0
$547$	−1.79690	−	0.865341i	−1.79690	−	0.865341i	−0.930874	−	0.365341i	$-0.880952\pi$
$547$	−1.79690	−	0.865341i	−1.79690	−	0.865341i	−0.866025	−	0.500000i	$-0.833333\pi$
$548$		0			0
$549$		0			0
$550$	1.34515	+	0.202749i	1.34515	+	0.202749i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−1.69158	−	2.12117i	−1.69158	−	2.12117i
$555$		0			0
$556$		0			0
$557$	−0.781831	−	1.35417i	−0.781831	−	1.35417i	−0.930874	−	0.365341i	$-0.880952\pi$
$557$	−0.781831	−	1.35417i	−0.781831	−	1.35417i	0.149042	−	0.988831i	$-0.452381\pi$
$558$	−0.680173	+	1.17809i	−0.680173	+	1.17809i
$559$	0.123490	−	0.541044i	0.123490	−	0.541044i
$560$	1.04921	+	0.411784i	1.04921	+	0.411784i
$561$		0			0
$562$		0			0
$563$	−0.215372	+	0.548760i	−0.215372	+	0.548760i	−0.997204	−	0.0747301i	$-0.976190\pi$
$563$	−0.215372	+	0.548760i	−0.215372	+	0.548760i	0.781831	+	0.623490i	$0.214286\pi$
$564$		0			0
$565$		0			0
$566$	0.473329	+	2.07379i	0.473329	+	2.07379i
$567$	−0.563320	+	0.826239i	−0.563320	+	0.826239i
$568$	−0.0663300	+	0.290611i	−0.0663300	+	0.290611i
$569$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$569$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$570$		0			0
$571$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$571$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$572$	0.0189465	−	0.252824i	0.0189465	−	0.252824i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.500000	+	0.463932i	0.500000	+	0.463932i
$577$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$577$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$578$	−0.277598	−	0.189263i	−0.277598	−	0.189263i
$579$		0			0
$580$		0			0
$581$	−1.68862	−	0.385418i	−1.68862	−	0.385418i
$582$		0			0
$583$		0			0
$584$	−0.297251	+	0.275809i	−0.297251	+	0.275809i
$585$	0.0222759	+	0.297251i	0.0222759	+	0.297251i
$586$	−0.559929	−	1.42668i	−0.559929	−	1.42668i
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$		0			0
$589$		0			0
$590$	0.982878	+	2.50433i	0.982878	+	2.50433i
$591$		0			0
$592$		0			0
$593$	1.53825	−	1.04876i	1.53825	−	1.04876i	0.563320	−	0.826239i	$-0.309524\pi$
$593$	1.53825	−	1.04876i	1.53825	−	1.04876i	0.974928	−	0.222521i	$-0.0714286\pi$
$594$		0			0
$595$			0.867767i			0.867767i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	1.63402	+	0.246289i	1.63402	+	0.246289i	0.900969	−	0.433884i	$-0.142857\pi$
$599$	1.63402	+	0.246289i	1.63402	+	0.246289i	0.733052	+	0.680173i	$0.238095\pi$
$600$		0			0
$601$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$601$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$602$	2.52554	+	0.189263i	2.52554	+	0.189263i
$603$		0			0
$604$		0			0
$605$	−0.955573	+	0.294755i	−0.955573	+	0.294755i
$606$		0			0
$607$	0.563320	−	0.975699i	0.563320	−	0.975699i	−0.433884	−	0.900969i	$-0.642857\pi$
$607$	0.563320	−	0.975699i	0.563320	−	0.975699i	0.997204	−	0.0747301i	$-0.0238095\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.269648	+	0.687051i	−0.269648	+	0.687051i
$613$	−0.215372	+	0.548760i	−0.215372	+	0.548760i	−0.997204	−	0.0747301i	$-0.976190\pi$
$613$	−0.215372	+	0.548760i	−0.215372	+	0.548760i	0.781831	+	0.623490i	$0.214286\pi$
$614$	1.76833	+	0.545456i	1.76833	+	0.545456i
$615$		0			0
$616$	−0.202749	+	0.0151939i	−0.202749	+	0.0151939i
$617$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$617$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$618$		0			0
$619$	0.623490	+	1.07992i	0.623490	+	1.07992i	0.988831	+	0.149042i	$0.0476190\pi$
$619$	0.623490	+	1.07992i	0.623490	+	1.07992i	−0.365341	+	0.930874i	$0.619048\pi$
$620$	−0.812753	+	0.250701i	−0.812753	+	0.250701i
$621$		0			0
$622$	1.40157	+	1.75751i	1.40157	+	1.75751i
$623$	−0.496990	+	0.535628i	−0.496990	+	0.535628i
$624$		0			0
$625$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−1.32624	+	0.302705i	−1.32624	+	0.302705i
$631$	−1.72188	+	0.829215i	−1.72188	+	0.829215i	−0.733052	+	0.680173i	$0.761905\pi$
$631$	−1.72188	+	0.829215i	−1.72188	+	0.829215i	−0.988831	+	0.149042i	$0.952381\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.712362	−	1.81507i	−0.712362	−	1.81507i
$636$		0			0
$637$	0.185853	+	0.233052i	0.185853	+	0.233052i
$638$		0			0
$639$	−0.535628	−	1.36476i	−0.535628	−	1.36476i
$640$	−0.0300485	−	0.400969i	−0.0300485	−	0.400969i
$641$	−0.326239	+	0.302705i	−0.326239	+	0.302705i	−0.826239	−	0.563320i	$-0.809524\pi$
$641$	−0.326239	+	0.302705i	−0.326239	+	0.302705i	0.500000	+	0.866025i	$0.333333\pi$
$642$		0			0
$643$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$643$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$647$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$648$	0.201047	+	0.0303029i	0.201047	+	0.0303029i
$649$	−1.44973	−	1.34515i	−1.44973	−	1.34515i
$650$	−0.252824	+	0.317031i	−0.252824	+	0.317031i
$651$		0			0
$652$		0			0
$653$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$653$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	0.443797	−	1.94440i	0.443797	−	1.94440i
$658$		0			0
$659$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$659$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$660$		0			0
$661$	−0.162592	+	0.414278i	−0.162592	+	0.414278i	−0.988831	−	0.149042i	$-0.952381\pi$
$661$	−0.162592	+	0.414278i	−0.162592	+	0.414278i	0.826239	+	0.563320i	$0.190476\pi$
$662$	−0.363142	+	0.925270i	−0.363142	+	0.925270i
$663$		0			0
$664$	0.0783621	+	0.343327i	0.0783621	+	0.343327i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.07992	−	1.35417i	1.07992	−	1.35417i	0.149042	−	0.988831i	$-0.452381\pi$
$673$	1.07992	−	1.35417i	1.07992	−	1.35417i	0.930874	−	0.365341i	$-0.119048\pi$
$674$	0.297251	+	0.275809i	0.297251	+	0.275809i
$675$		0			0
$676$	−0.640307	−	0.436554i	−0.640307	−	0.436554i
$677$	1.54620	−	0.233052i	1.54620	−	0.233052i	0.680173	−	0.733052i	$-0.261905\pi$
$677$	1.54620	−	0.233052i	1.54620	−	0.233052i	0.866025	+	0.500000i	$0.166667\pi$
$678$		0			0
$679$		0			0
$680$	0.158960	−	0.0765511i	0.158960	−	0.0765511i
$681$		0			0
$682$	0.997204	−	0.925270i	0.997204	−	0.925270i
$683$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$683$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$684$		0			0
$685$		0			0
$686$	−0.925270	+	0.997204i	−0.925270	+	0.997204i
$687$		0			0
$688$	−0.766638	−	1.95336i	−0.766638	−	1.95336i
$689$		0			0
$690$		0			0
$691$	−1.48883	+	1.01507i	−1.48883	+	1.01507i	−0.500000	+	0.866025i	$0.666667\pi$
$691$	−1.48883	+	1.01507i	−1.48883	+	1.01507i	−0.988831	+	0.149042i	$0.952381\pi$
$692$	−0.451748	+	0.217550i	−0.451748	+	0.217550i
$693$	0.781831	−	0.623490i	0.781831	−	0.623490i
$694$	0.722521	+	0.347948i	0.722521	+	0.347948i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.736589	−	0.425270i	−0.736589	−	0.425270i
$701$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$701$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$702$		0			0
$703$		0			0
$704$	−0.341040	−	0.590699i	−0.341040	−	0.590699i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.955573	+	0.294755i	0.955573	+	0.294755i	0.733052	−	0.680173i	$-0.238095\pi$
$709$	0.955573	+	0.294755i	0.955573	+	0.294755i	0.222521	+	0.974928i	$0.428571\pi$
$710$	0.728639	−	1.85654i	0.728639	−	1.85654i
$711$		0			0
$712$	0.141960	+	0.0437890i	0.141960	+	0.0437890i
$713$		0			0
$714$		0			0
$715$	0.0663300	−	0.290611i	0.0663300	−	0.290611i
$716$	−0.623490	+	1.07992i	−0.623490	+	1.07992i
$717$		0			0
$718$		0			0
$719$	0.134659	−	1.79690i	0.134659	−	1.79690i	−0.365341	−	0.930874i	$-0.619048\pi$
$719$	0.134659	−	1.79690i	0.134659	−	1.79690i	0.500000	−	0.866025i	$-0.333333\pi$
$720$	0.702749	+	0.881219i	0.702749	+	0.881219i
$721$		0			0
$722$	0.848162	−	1.06356i	0.848162	−	1.06356i
$723$		0			0
$724$	0.125702	+	0.0189465i	0.125702	+	0.0189465i
$725$		0			0
$726$		0			0
$727$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$727$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$728$	0.0262959	−	0.0546039i	0.0262959	−	0.0546039i
$729$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$730$	2.24165	−	1.52833i	2.24165	−	1.52833i
$731$	1.18429	−	1.09886i	1.18429	−	1.09886i
$732$		0			0
$733$	0.712362	+	1.81507i	0.712362	+	1.81507i	0.563320	+	0.826239i	$0.309524\pi$
$733$	0.712362	+	1.81507i	0.712362	+	1.81507i	0.149042	+	0.988831i	$0.452381\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$739$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.268565	+	0.129334i	0.268565	+	0.129334i	0.563320	−	0.826239i	$-0.309524\pi$
$743$	0.268565	+	0.129334i	0.268565	+	0.129334i	−0.294755	+	0.955573i	$0.595238\pi$
$744$		0			0
$745$		0			0
$746$	−1.51550	−	0.228425i	−1.51550	−	0.228425i
$747$	−1.26968	−	1.17809i	−1.26968	−	1.17809i
$748$	0.460180	−	0.577047i	0.460180	−	0.577047i
$749$	−1.32624	+	1.42935i	−1.32624	+	1.42935i
$750$		0			0
$751$	0.0111692	−	0.149042i	0.0111692	−	0.149042i	−0.988831	−	0.149042i	$-0.952381\pi$
$751$	0.0111692	−	0.149042i	0.0111692	−	0.149042i	1.00000			$0$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$757$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$758$	2.14807	+	0.662592i	2.14807	+	0.662592i
$759$		0			0
$760$		0			0
$761$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$761$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$762$		0			0
$763$		0			0
$764$	−0.189263	+	0.829215i	−0.189263	+	0.829215i
$765$	−0.433884	+	0.751509i	−0.433884	+	0.751509i
$766$		0			0
$767$	0.563320	−	0.173761i	0.563320	−	0.173761i
$768$		0			0
$769$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$769$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$770$	1.35654	+	0.101659i	1.35654	+	0.101659i
$771$		0			0
$772$	0.541044	+	0.502016i	0.541044	+	0.502016i
$773$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$773$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$774$	2.09255	+	1.42668i	2.09255	+	1.42668i
$775$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$776$		0			0
$777$		0			0
$778$	−2.02532	+	0.975345i	−2.02532	+	0.975345i
$779$		0			0
$780$		0			0
$781$	0.109562	+	1.46200i	0.109562	+	1.46200i
$782$		0			0
$783$		0			0
$784$	1.07705	+	0.332225i	1.07705	+	0.332225i
$785$		0			0
$786$		0			0
$787$	0.0440542	+	0.587862i	0.0440542	+	0.587862i	0.974928	+	0.222521i	$0.0714286\pi$
$787$	0.0440542	+	0.587862i	0.0440542	+	0.587862i	−0.930874	+	0.365341i	$0.880952\pi$
$788$	−0.367554	+	0.341040i	−0.367554	+	0.341040i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.183183	−	0.0882162i	−0.183183	−	0.0882162i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−1.19158	−	1.10562i	−1.19158	−	1.10562i
$797$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$797$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$798$		0			0
$799$		0			0
$800$	−0.0993879	+	1.32624i	−0.0993879	+	1.32624i
$801$	−0.698220	+	0.215372i	−0.698220	+	0.215372i
$802$	0.496990	+	0.860812i	0.496990	+	0.860812i
$803$	−0.997204	+	1.72721i	−0.997204	+	1.72721i
$804$		0			0
$805$		0			0
$806$	0.0902318	+	0.395331i	0.0902318	+	0.395331i
$807$		0			0
$808$		0			0
$809$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$809$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$810$	−1.29991	−	0.400969i	−1.29991	−	0.400969i
$811$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$811$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	0.0444272	+	0.294755i	0.0444272	+	0.294755i
$820$		0			0
$821$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$821$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$822$		0			0
$823$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$823$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$824$		0			0
$825$		0			0
$826$	1.16728	+	2.42388i	1.16728	+	2.42388i
$827$	0.781831	−	0.376510i	0.781831	−	0.376510i		−	1.00000i	$-0.5\pi$
$827$	0.781831	−	0.376510i	0.781831	−	0.376510i	0.781831	+	0.623490i	$0.214286\pi$
$828$		0			0
$829$	−1.44973	+	1.34515i	−1.44973	+	1.34515i	−0.623490	+	0.781831i	$0.714286\pi$
$829$	−1.44973	+	1.34515i	−1.44973	+	1.34515i	−0.826239	+	0.563320i	$0.809524\pi$
$830$	−0.176078	−	2.34960i	−0.176078	−	2.34960i
$831$		0			0
$832$	0.203317			0.203317
$833$	0.0648483	+	0.865341i	0.0648483	+	0.865341i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$	2.22283	−	1.51550i	2.22283	−	1.51550i
$839$	1.62349	−	0.781831i	1.62349	−	0.781831i	0.623490	−	0.781831i	$-0.285714\pi$
$839$	1.62349	−	0.781831i	1.62349	−	0.781831i	1.00000			$0$
$840$		0			0
$841$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$842$	−2.42388	+	0.365341i	−2.42388	+	0.365341i
$843$		0			0
$844$		0			0
$845$	−0.667917	−	0.619736i	−0.667917	−	0.619736i
$846$		0			0
$847$	−0.930874	+	0.365341i	−0.930874	+	0.365341i
$848$		0			0
$849$		0			0
$850$	−1.12802	+	0.347948i	−1.12802	+	0.347948i
$851$		0			0
$852$		0			0
$853$	0.433884	−	1.90097i	0.433884	−	1.90097i		−	1.00000i	$-0.5\pi$
$853$	0.433884	−	1.90097i	0.433884	−	1.90097i	0.433884	−	0.900969i	$-0.357143\pi$
$854$		0			0
$855$		0			0
$856$	0.378827	+	0.116853i	0.378827	+	0.116853i
$857$	0.496990	−	1.26631i	0.496990	−	1.26631i	−0.433884	−	0.900969i	$-0.642857\pi$
$857$	0.496990	−	1.26631i	0.496990	−	1.26631i	0.930874	−	0.365341i	$-0.119048\pi$
$858$		0			0
$859$	1.72188	+	0.531130i	1.72188	+	0.531130i	0.988831	−	0.149042i	$-0.0476190\pi$
$859$	1.72188	+	0.531130i	1.72188	+	0.531130i	0.733052	+	0.680173i	$0.238095\pi$
$860$	0.352360	+	1.54379i	0.352360	+	1.54379i
$861$		0			0
$862$		0			0
$863$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$863$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$864$		0			0
$865$	−0.563320	+	0.173761i	−0.563320	+	0.173761i
$866$		0			0
$867$		0			0
$868$	−0.791745	+	0.310737i	−0.791745	+	0.310737i
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$876$		0			0
$877$	1.43109	−	0.975699i	1.43109	−	0.975699i	0.433884	−	0.900969i	$-0.357143\pi$
$877$	1.43109	−	0.975699i	1.43109	−	0.975699i	0.997204	−	0.0747301i	$-0.0238095\pi$
$878$		0			0
$879$		0			0
$880$	−0.411784	−	1.04921i	−0.411784	−	1.04921i
$881$	1.91115			1.91115			0.955573	−	0.294755i	$-0.0952381\pi$
$881$	1.91115			1.91115			0.955573	+	0.294755i	$0.0952381\pi$
$882$	−1.29991	+	0.400969i	−1.29991	+	0.400969i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$	0.0803778	+	0.204799i	0.0803778	+	0.204799i
$885$		0			0
$886$		0			0
$887$	1.64786	−	1.12349i	1.64786	−	1.12349i	0.781831	−	0.623490i	$-0.214286\pi$
$887$	1.64786	−	1.12349i	1.64786	−	1.12349i	0.866025	−	0.500000i	$-0.166667\pi$
$888$		0			0
$889$	−0.846011	−	1.75676i	−0.846011	−	1.75676i
$890$	−0.895545	−	0.431272i	−0.895545	−	0.431272i
$891$	0.988831	−	0.149042i	0.988831	−	0.149042i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−0.914101	+	1.14625i	−0.914101	+	1.14625i
$896$	−0.0599289	−	0.397602i	−0.0599289	−	0.397602i
$897$		0			0
$898$	0.201047	−	2.68278i	0.201047	−	2.68278i
$899$		0			0
$900$	−0.425270	−	0.736589i	−0.425270	−	0.736589i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.142820	+	0.0440542i	0.142820	+	0.0440542i
$906$		0			0
$907$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$907$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$908$	0.915680	+	0.282450i	0.915680	+	0.282450i
$909$		0			0
$910$	−0.228425	+	0.335038i	−0.228425	+	0.335038i
$911$	0.425270	−	1.86323i	0.425270	−	1.86323i	−0.0747301	−	0.997204i	$-0.523810\pi$
$911$	0.425270	−	1.86323i	0.425270	−	1.86323i	0.500000	−	0.866025i	$-0.333333\pi$
$912$		0			0
$913$	0.866025	+	1.50000i	0.866025	+	1.50000i
$914$	−2.25151	+	0.694498i	−2.25151	+	0.694498i
$915$		0			0
$916$	−0.777479	−	0.974928i	−0.777479	−	0.974928i
$917$		0			0
$918$		0			0
$919$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$919$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.393744	−	0.189617i	−0.393744	−	0.189617i
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.162592	−	0.414278i	−0.162592	−	0.414278i	0.826239	−	0.563320i	$-0.190476\pi$
$929$	−0.162592	−	0.414278i	−0.162592	−	0.414278i	−0.988831	+	0.149042i	$0.952381\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.636119	−	0.590232i	0.636119	−	0.590232i
$936$	0.0500749	−	0.0341405i	0.0500749	−	0.0341405i
$937$	−0.268565	+	0.129334i	−0.268565	+	0.129334i	−0.563320	−	0.826239i	$-0.690476\pi$
$937$	−0.268565	+	0.129334i	−0.268565	+	0.129334i	0.294755	+	0.955573i	$0.404762\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$941$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$942$		0			0
$943$		0			0
$944$	1.38980	−	1.74275i	1.38980	−	1.74275i
$945$		0			0
$946$	−1.57906	−	1.98008i	−1.57906	−	1.98008i
$947$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$947$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$948$		0			0
$949$	−0.297251	−	0.514854i	−0.297251	−	0.514854i
$950$		0			0
$951$		0			0
$952$	0.152795	−	0.0882162i	0.152795	−	0.0882162i
$953$	−0.347948	−	1.52446i	−0.347948	−	1.52446i	−0.781831	−	0.623490i	$-0.785714\pi$
$953$	−0.347948	−	1.52446i	−0.347948	−	1.52446i	0.433884	−	0.900969i	$-0.357143\pi$
$954$		0			0
$955$	−0.365341	+	0.930874i	−0.365341	+	0.930874i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$		0			0
$962$		0			0
$963$	−1.86323	+	0.574730i	−1.86323	+	0.574730i
$964$		0			0
$965$	0.541044	+	0.678448i	0.541044	+	0.678448i
$966$		0			0
$967$	1.24349	−	1.55929i	1.24349	−	1.55929i	0.563320	−	0.826239i	$-0.309524\pi$
$967$	1.24349	−	1.55929i	1.24349	−	1.55929i	0.680173	−	0.733052i	$-0.261905\pi$
$968$	0.149042	+	0.138291i	0.149042	+	0.138291i
$969$		0			0
$970$		0			0
$971$	1.88980	−	0.284841i	1.88980	−	0.284841i	0.900969	−	0.433884i	$-0.142857\pi$
$971$	1.88980	−	0.284841i	1.88980	−	0.284841i	0.988831	+	0.149042i	$0.0476190\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$977$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$978$		0			0
$979$	0.730682			0.730682
$980$	−0.766310	−	0.369035i	−0.766310	−	0.369035i
$981$		0			0
$982$		0			0
$983$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$983$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$984$		0			0
$985$	−0.487076	+	0.332083i	−0.487076	+	0.332083i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	1.12397	+	0.766310i	1.12397	+	0.766310i
$991$	−1.78181	−	0.268565i	−1.78181	−	0.268565i	−0.826239	−	0.563320i	$-0.809524\pi$
$991$	−1.78181	−	0.268565i	−1.78181	−	0.268565i	−0.955573	+	0.294755i	$0.904762\pi$
$992$	0.974928	+	0.904601i	0.974928	+	0.904601i
$993$		0			0
$994$	0.587862	−	1.90580i	0.587862	−	1.90580i
$995$	−1.19158	−	1.49419i	−1.19158	−	1.49419i
$996$		0			0
$997$	1.77904	−	0.548760i	1.77904	−	0.548760i	0.781831	−	0.623490i	$-0.214286\pi$
$997$	1.77904	−	0.548760i	1.77904	−	0.548760i	0.997204	+	0.0747301i	$0.0238095\pi$
$998$	−0.496990	−	0.860812i	−0.496990	−	0.860812i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.1.ck.c.604.2	yes	24
5.4	even	2	inner	2695.1.ck.c.604.1	✓	24
11.10	odd	2	inner	2695.1.ck.c.604.1	✓	24
49.46	even	21	inner	2695.1.ck.c.879.2	yes	24
55.54	odd	2	CM	2695.1.ck.c.604.2	yes	24
245.144	even	42	inner	2695.1.ck.c.879.1	yes	24
539.340	odd	42	inner	2695.1.ck.c.879.1	yes	24
2695.879	odd	42	inner	2695.1.ck.c.879.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2695.1.ck.c.604.1	✓	24	5.4	even	2	inner
2695.1.ck.c.604.1	✓	24	11.10	odd	2	inner
2695.1.ck.c.604.2	yes	24	1.1	even	1	trivial
2695.1.ck.c.604.2	yes	24	55.54	odd	2	CM
2695.1.ck.c.879.1	yes	24	245.144	even	42	inner
2695.1.ck.c.879.1	yes	24	539.340	odd	42	inner
2695.1.ck.c.879.2	yes	24	49.46	even	21	inner
2695.1.ck.c.879.2	yes	24	2695.879	odd	42	inner

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:	\( N \)	\(=\)	\( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2695.ck (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.496990 + 1.26631i) q^{2} +(-0.623490 + 0.578514i) q^{4} +(-0.826239 + 0.563320i) q^{5} +(-0.781831 + 0.623490i) q^{7} +(0.183183 + 0.0882162i) q^{8} +(-0.988831 + 0.149042i) q^{9} +(-1.12397 - 0.766310i) q^{10} +(0.988831 + 0.149042i) q^{11} +(-0.185853 + 0.233052i) q^{13} +(-1.17809 - 0.680173i) q^{14} +(-0.0842299 + 1.12397i) q^{16} +(-0.829215 + 0.255779i) q^{17} +(-0.680173 - 1.17809i) q^{18} +(0.189263 - 0.829215i) q^{20} +(0.302705 + 1.32624i) q^{22} +(0.365341 - 0.930874i) q^{25} +(-0.387483 - 0.119523i) q^{26} +(0.126766 - 0.841040i) q^{28} +(-0.500000 - 0.866025i) q^{31} +(-1.27087 + 0.392012i) q^{32} +(-0.736007 - 0.922924i) q^{34} +(0.294755 - 0.955573i) q^{35} +(0.530303 - 0.664979i) q^{36} +(-0.201047 + 0.0303029i) q^{40} +(-1.67738 + 0.807782i) q^{43} +(-0.702749 + 0.479126i) q^{44} +(0.733052 - 0.680173i) q^{45} +(0.222521 - 0.974928i) q^{49} +1.36035 q^{50} +(-0.0189465 - 0.252824i) q^{52} +(-0.900969 + 0.433884i) q^{55} +(-0.198220 + 0.0452424i) q^{56} +(-1.63402 - 1.11406i) q^{59} +(0.848162 - 1.06356i) q^{62} +(0.680173 - 0.733052i) q^{63} +(-0.425270 - 0.533272i) q^{64} +(0.0222759 - 0.297251i) q^{65} +(0.369035 - 0.639188i) q^{68} +(1.35654 - 0.101659i) q^{70} +(0.326239 + 1.42935i) q^{71} +(-0.194285 - 0.0599289i) q^{72} +(-0.728639 + 1.85654i) q^{73} +(-0.866025 + 0.500000i) q^{77} +(-0.563561 - 0.976116i) q^{80} +(0.955573 - 0.294755i) q^{81} +(1.07992 + 1.35417i) q^{83} +(0.541044 - 0.678448i) q^{85} +(-1.85654 - 1.72262i) q^{86} +(0.167989 + 0.114533i) q^{88} +(0.722521 - 0.108903i) q^{89} +(1.22563 + 0.590232i) q^{90} -0.298085i q^{91} +(1.34515 - 0.202749i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4} - 2 q^{5} + 2 q^{9} - 2 q^{11} - 6 q^{14} - 26 q^{16} + 8 q^{20} + 2 q^{25} + 6 q^{26} - 12 q^{31} - 14 q^{34} - 8 q^{36} - 18 q^{44} - 2 q^{45} + 4 q^{49} - 4 q^{55} + 14 q^{56} - 2 q^{59}+ \cdots - 24 q^{99}+O(q^{100}) \) 24 * q + 4 * q^4 - 2 * q^5 + 2 * q^9 - 2 * q^11 - 6 * q^14 - 26 * q^16 + 8 * q^20 + 2 * q^25 + 6 * q^26 - 12 * q^31 - 14 * q^34 - 8 * q^36 - 18 * q^44 - 2 * q^45 + 4 * q^49 - 4 * q^55 + 14 * q^56 - 2 * q^59 - 10 * q^64 - 6 * q^70 - 10 * q^71 + 12 * q^80 + 2 * q^81 - 6 * q^86 + 16 * q^89 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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