LMFDB - Embedded newform 2695.1.ck.a.1649.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2695,1,Mod(109,2695)]

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

lf = mfeigenbasis(mf)

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")

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

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

Self dual:	no
Analytic conductor:	$1.34498020905$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\Q(\zeta_{21})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + x^{9} - x^{8} + x^{6} - x^{4} + x^{3} - x + 1 $ x^12 - x^11 + x^9 - x^8 + x^6 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{21}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{21} - \cdots)$

Embedding invariants

Embedding label			1649.1
Root			$0.365341 + 0.930874i$ of defining polynomial
Character	$\chi$	$=$	2695.1649
Dual form			2695.1.ck.a.219.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.147791 - 1.97213i) q^{2} +(-2.87863 + 0.433884i) q^{4} +(-0.733052 + 0.680173i) q^{5} +(-0.900969 + 0.433884i) q^{7} +(0.841040 + 3.68484i) q^{8} +(0.826239 + 0.563320i) q^{9} +O(q^{10})$	\(q+(-0.147791 - 1.97213i) q^{2} +(-2.87863 + 0.433884i) q^{4} +(-0.733052 + 0.680173i) q^{5} +(-0.900969 + 0.433884i) q^{7} +(0.841040 + 3.68484i) q^{8} +(0.826239 + 0.563320i) q^{9} +(1.44973 + 1.34515i) q^{10} +(0.826239 - 0.563320i) q^{11} +(-1.48883 - 0.716983i) q^{13} +(0.988831 + 1.71271i) q^{14} +(4.36087 - 1.34515i) q^{16} +(-0.162592 - 0.414278i) q^{17} +(0.988831 - 1.71271i) q^{18} +(1.81507 - 2.27603i) q^{20} +(-1.23305 - 1.54620i) q^{22} +(0.0747301 - 0.997204i) q^{25} +(-1.19395 + 3.04213i) q^{26} +(2.40530 - 1.63991i) q^{28} +(0.500000 - 0.866025i) q^{31} +(-1.91647 - 4.88309i) q^{32} +(-0.792981 + 0.381879i) q^{34} +(0.365341 - 0.930874i) q^{35} +(-2.62285 - 1.26310i) q^{36} +(-3.12285 - 2.12912i) q^{40} +(-0.0332580 + 0.145713i) q^{43} +(-2.13402 + 1.98008i) q^{44} +(-0.988831 + 0.149042i) q^{45} +(0.623490 - 0.781831i) q^{49} -1.97766 q^{50} +(4.59688 + 1.41795i) q^{52} +(-0.222521 + 0.974928i) q^{55} +(-2.35654 - 2.95501i) q^{56} +(-1.21135 - 1.12397i) q^{59} +(-1.78181 - 0.858075i) q^{62} +(-0.988831 - 0.149042i) q^{63} +(-5.23517 + 2.52113i) q^{64} +(1.57906 - 0.487076i) q^{65} +(0.647791 + 1.12201i) q^{68} +(-1.88980 - 0.582926i) q^{70} +(-1.23305 - 1.54620i) q^{71} +(-1.38084 + 3.51833i) q^{72} +(0.142820 - 1.90580i) q^{73} +(-0.500000 + 0.866025i) q^{77} +(-2.28181 + 3.95221i) q^{80} +(0.365341 + 0.930874i) q^{81} +(0.900969 - 0.433884i) q^{83} +(0.400969 + 0.193096i) q^{85} +(0.292280 + 0.0440542i) q^{86} +(2.77064 + 2.57078i) q^{88} +(0.123490 + 0.0841939i) q^{89} +(0.440071 + 1.92808i) q^{90} +1.65248 q^{91} +(-1.63402 - 1.11406i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} + q^{5} - 2 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) $ 12 * q - q^2 + q^5 - 2 * q^7 - 2 * q^8 + q^9	$ 12 q - q^{2} + q^{5} - 2 q^{7} - 2 q^{8} + q^{9} - q^{10} + q^{11} - 5 q^{13} - q^{14} + 13 q^{16} + 2 q^{17} - q^{18} - 5 q^{22} + q^{25} + q^{26} + 6 q^{31} - 7 q^{32} - 3 q^{34} + q^{35} - 6 q^{40} + 2 q^{43} - 7 q^{44} + q^{45} - 2 q^{49} + 2 q^{50} + 14 q^{52} - 2 q^{55} - 9 q^{56} - q^{59} - 2 q^{62} + q^{63} - 9 q^{64} - q^{65} + 7 q^{68} - q^{70} - 5 q^{71} - 6 q^{72} - q^{73} - 6 q^{77} - 8 q^{80} + q^{81} + 2 q^{83} - 4 q^{85} + q^{86} + q^{88} - 8 q^{89} + 2 q^{90} + 2 q^{91} - q^{98} + 12 q^{99}+O(q^{100}) $ 12 * q - q^2 + q^5 - 2 * q^7 - 2 * q^8 + q^9 - q^10 + q^11 - 5 * q^13 - q^14 + 13 * q^16 + 2 * q^17 - q^18 - 5 * q^22 + q^25 + q^26 + 6 * q^31 - 7 * q^32 - 3 * q^34 + q^35 - 6 * q^40 + 2 * q^43 - 7 * q^44 + q^45 - 2 * q^49 + 2 * q^50 + 14 * q^52 - 2 * q^55 - 9 * q^56 - q^59 - 2 * q^62 + q^63 - 9 * q^64 - q^65 + 7 * q^68 - q^70 - 5 * q^71 - 6 * q^72 - q^73 - 6 * q^77 - 8 * q^80 + q^81 + 2 * q^83 - 4 * q^85 + q^86 + q^88 - 8 * q^89 + 2 * q^90 + 2 * q^91 - q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$981$	$1816$	$2157$
$\chi(n)$	$-1$	$e\left(\frac{2}{21}\right)$	$-1$

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 $

$2$	−0.147791	−	1.97213i	−0.147791	−	1.97213i	−0.222521	−	0.974928i	$-0.571429\pi$
$2$	−0.147791	−	1.97213i	−0.147791	−	1.97213i	0.0747301	−	0.997204i	$-0.476190\pi$
$3$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$3$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$4$	−2.87863	+	0.433884i	−2.87863	+	0.433884i
$5$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$5$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$6$		0			0
$7$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$7$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$8$	0.841040	+	3.68484i	0.841040	+	3.68484i
$9$	0.826239	+	0.563320i	0.826239	+	0.563320i
$10$	1.44973	+	1.34515i	1.44973	+	1.34515i
$11$	0.826239	−	0.563320i	0.826239	−	0.563320i
$11$	0.826239	−	0.563320i	0.826239	−	0.563320i
$12$		0			0
$13$	−1.48883	−	0.716983i	−1.48883	−	0.716983i	−0.500000	−	0.866025i	$-0.666667\pi$
$13$	−1.48883	−	0.716983i	−1.48883	−	0.716983i	−0.988831	+	0.149042i	$0.952381\pi$
$14$	0.988831	+	1.71271i	0.988831	+	1.71271i
$15$		0			0
$16$	4.36087	−	1.34515i	4.36087	−	1.34515i
$17$	−0.162592	−	0.414278i	−0.162592	−	0.414278i	0.826239	−	0.563320i	$-0.190476\pi$
$17$	−0.162592	−	0.414278i	−0.162592	−	0.414278i	−0.988831	+	0.149042i	$0.952381\pi$
$18$	0.988831	−	1.71271i	0.988831	−	1.71271i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$	1.81507	−	2.27603i	1.81507	−	2.27603i
$21$		0			0
$22$	−1.23305	−	1.54620i	−1.23305	−	1.54620i
$23$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$23$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$24$		0			0
$25$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$26$	−1.19395	+	3.04213i	−1.19395	+	3.04213i
$27$		0			0
$28$	2.40530	−	1.63991i	2.40530	−	1.63991i
$29$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$29$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$30$		0			0
$31$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$31$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$32$	−1.91647	−	4.88309i	−1.91647	−	4.88309i
$33$		0			0
$34$	−0.792981	+	0.381879i	−0.792981	+	0.381879i
$35$	0.365341	−	0.930874i	0.365341	−	0.930874i
$36$	−2.62285	−	1.26310i	−2.62285	−	1.26310i
$37$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$37$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$38$		0			0
$39$		0			0
$40$	−3.12285	−	2.12912i	−3.12285	−	2.12912i
$41$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$41$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$42$		0			0
$43$	−0.0332580	+	0.145713i	−0.0332580	+	0.145713i	−0.988831	−	0.149042i	$-0.952381\pi$
$43$	−0.0332580	+	0.145713i	−0.0332580	+	0.145713i	0.955573	+	0.294755i	$0.0952381\pi$
$44$	−2.13402	+	1.98008i	−2.13402	+	1.98008i
$45$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$46$		0			0
$47$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$47$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$48$		0			0
$49$	0.623490	−	0.781831i	0.623490	−	0.781831i
$50$	−1.97766			−1.97766
$51$		0			0
$52$	4.59688	+	1.41795i	4.59688	+	1.41795i
$53$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$53$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$54$		0			0
$55$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$56$	−2.35654	−	2.95501i	−2.35654	−	2.95501i
$57$		0			0
$58$		0			0
$59$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.988831	−	0.149042i	$-0.952381\pi$
$59$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.222521	−	0.974928i	$-0.571429\pi$
$60$		0			0
$61$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$61$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$62$	−1.78181	−	0.858075i	−1.78181	−	0.858075i
$63$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$64$	−5.23517	+	2.52113i	−5.23517	+	2.52113i
$65$	1.57906	−	0.487076i	1.57906	−	0.487076i
$66$		0			0
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$	0.647791	+	1.12201i	0.647791	+	1.12201i
$69$		0			0
$70$	−1.88980	−	0.582926i	−1.88980	−	0.582926i
$71$	−1.23305	−	1.54620i	−1.23305	−	1.54620i	−0.733052	−	0.680173i	$-0.761905\pi$
$71$	−1.23305	−	1.54620i	−1.23305	−	1.54620i	−0.500000	−	0.866025i	$-0.666667\pi$
$72$	−1.38084	+	3.51833i	−1.38084	+	3.51833i
$73$	0.142820	−	1.90580i	0.142820	−	1.90580i	−0.222521	−	0.974928i	$-0.571429\pi$
$73$	0.142820	−	1.90580i	0.142820	−	1.90580i	0.365341	−	0.930874i	$-0.380952\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$78$		0			0
$79$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$79$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$80$	−2.28181	+	3.95221i	−2.28181	+	3.95221i
$81$	0.365341	+	0.930874i	0.365341	+	0.930874i
$82$		0			0
$83$	0.900969	−	0.433884i	0.900969	−	0.433884i	0.0747301	−	0.997204i	$-0.476190\pi$
$83$	0.900969	−	0.433884i	0.900969	−	0.433884i	0.826239	+	0.563320i	$0.190476\pi$
$84$		0			0
$85$	0.400969	+	0.193096i	0.400969	+	0.193096i
$86$	0.292280	+	0.0440542i	0.292280	+	0.0440542i
$87$		0			0
$88$	2.77064	+	2.57078i	2.77064	+	2.57078i
$89$	0.123490	+	0.0841939i	0.123490	+	0.0841939i	0.623490	−	0.781831i	$-0.285714\pi$
$89$	0.123490	+	0.0841939i	0.123490	+	0.0841939i	−0.500000	+	0.866025i	$0.666667\pi$
$90$	0.440071	+	1.92808i	0.440071	+	1.92808i
$91$	1.65248			1.65248
$92$		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			$\pi$
$98$	−1.63402	−	1.11406i	−1.63402	−	1.11406i
$99$	1.00000			1.00000
$100$	0.217550	+	2.90301i	0.217550	+	2.90301i
$101$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$101$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$102$		0			0
$103$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$103$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$104$	1.38980	−	6.08911i	1.38980	−	6.08911i
$105$		0			0
$106$		0			0
$107$	1.03030	+	0.702449i	1.03030	+	0.702449i	0.955573	−	0.294755i	$-0.0952381\pi$
$107$	1.03030	+	0.702449i	1.03030	+	0.702449i	0.0747301	+	0.997204i	$0.476190\pi$
$108$		0			0
$109$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$109$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$110$	1.95557	+	0.294755i	1.95557	+	0.294755i
$111$		0			0
$112$	−3.34537	+	3.10405i	−3.34537	+	3.10405i
$113$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$113$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.826239	−	1.43109i	−0.826239	−	1.43109i
$118$	−2.03759	+	2.55506i	−2.03759	+	2.55506i
$119$	0.326239	+	0.302705i	0.326239	+	0.302705i
$120$		0			0
$121$	0.365341	−	0.930874i	0.365341	−	0.930874i
$122$		0			0
$123$		0			0
$124$	−1.06356	+	2.70991i	−1.06356	+	2.70991i
$125$	0.623490	+	0.781831i	0.623490	+	0.781831i
$126$	−0.147791	+	1.97213i	−0.147791	+	1.97213i
$127$	0.777479	−	0.974928i	0.777479	−	0.974928i	−0.222521	−	0.974928i	$-0.571429\pi$
$127$	0.777479	−	0.974928i	0.777479	−	0.974928i	1.00000			$0$
$128$	3.12285	+	5.40894i	3.12285	+	5.40894i
$129$		0			0
$130$	−1.19395	−	3.04213i	−1.19395	−	3.04213i
$131$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$131$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	1.38980	−	0.947549i	1.38980	−	0.947549i
$137$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$137$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$138$		0			0
$139$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$139$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$140$	−0.647791	+	2.83816i	−0.647791	+	2.83816i
$141$		0			0
$142$	−2.86707	+	2.66025i	−2.86707	+	2.66025i
$143$	−1.63402	+	0.246289i	−1.63402	+	0.246289i
$144$	4.36087	+	1.34515i	4.36087	+	1.34515i
$145$		0			0
$146$	−3.77960			−3.77960
$147$		0			0
$148$		0			0
$149$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$149$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$150$		0			0
$151$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$151$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$152$		0			0
$153$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$154$	1.78181	+	0.858075i	1.78181	+	0.858075i
$155$	0.222521	+	0.974928i	0.222521	+	0.974928i
$156$		0			0
$157$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$157$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$158$		0			0
$159$		0			0
$160$	4.72622	+	2.27603i	4.72622	+	2.27603i
$161$		0			0
$162$	1.78181	−	0.858075i	1.78181	−	0.858075i
$163$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$163$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$164$		0			0
$165$		0			0
$166$	−0.988831	−	1.71271i	−0.988831	−	1.71271i
$167$	1.24698	−	1.56366i	1.24698	−	1.56366i	0.623490	−	0.781831i	$-0.285714\pi$
$167$	1.24698	−	1.56366i	1.24698	−	1.56366i	0.623490	−	0.781831i	$-0.285714\pi$
$168$		0			0
$169$	1.07906	+	1.35310i	1.07906	+	1.35310i
$170$	0.321552	−	0.819301i	0.321552	−	0.819301i
$171$		0			0
$172$	0.0325151	−	0.433884i	0.0325151	−	0.433884i
$173$	0.266948	−	0.680173i	0.266948	−	0.680173i	−0.733052	−	0.680173i	$-0.761905\pi$
$173$	0.266948	−	0.680173i	0.266948	−	0.680173i	1.00000			$0$
$174$		0			0
$175$	0.365341	+	0.930874i	0.365341	+	0.930874i
$176$	2.84537	−	3.56798i	2.84537	−	3.56798i
$177$		0			0
$178$	0.147791	−	0.255981i	0.147791	−	0.255981i
$179$	−0.722521	−	1.84095i	−0.722521	−	1.84095i	−0.500000	−	0.866025i	$-0.666667\pi$
$179$	−0.722521	−	1.84095i	−0.722521	−	1.84095i	−0.222521	−	0.974928i	$-0.571429\pi$
$180$	2.78181	−	0.858075i	2.78181	−	0.858075i
$181$	−1.72188	+	0.829215i	−1.72188	+	0.829215i	−0.733052	+	0.680173i	$0.761905\pi$
$181$	−1.72188	+	0.829215i	−1.72188	+	0.829215i	−0.988831	+	0.149042i	$0.952381\pi$
$182$	−0.244221	−	3.25890i	−0.244221	−	3.25890i
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.367711	−	0.250701i	−0.367711	−	0.250701i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.733052	−	0.680173i	0.733052	−	0.680173i	−0.222521	−	0.974928i	$-0.571429\pi$
$191$	0.733052	−	0.680173i	0.733052	−	0.680173i	0.955573	+	0.294755i	$0.0952381\pi$
$192$		0			0
$193$	−0.425270	−	0.131178i	−0.425270	−	0.131178i	0.0747301	−	0.997204i	$-0.476190\pi$
$193$	−0.425270	−	0.131178i	−0.425270	−	0.131178i	−0.500000	+	0.866025i	$0.666667\pi$
$194$		0			0
$195$		0			0
$196$	−1.45557	+	2.52113i	−1.45557	+	2.52113i
$197$	0.730682			0.730682			0.365341	−	0.930874i	$-0.380952\pi$
$197$	0.730682			0.730682			0.365341	+	0.930874i	$0.380952\pi$
$198$	−0.147791	−	1.97213i	−0.147791	−	1.97213i
$199$	0.698220	+	0.215372i	0.698220	+	0.215372i	0.623490	−	0.781831i	$-0.285714\pi$
$199$	0.698220	+	0.215372i	0.698220	+	0.215372i	0.0747301	+	0.997204i	$0.476190\pi$
$200$	3.73738	−	0.563320i	3.73738	−	0.563320i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$	−7.45705	−	1.12397i	−7.45705	−	1.12397i
$209$		0			0
$210$		0			0
$211$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$211$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$212$		0			0
$213$		0			0
$214$	1.23305	−	2.13571i	1.23305	−	2.13571i
$215$	−0.0747301	−	0.129436i	−0.0747301	−	0.129436i
$216$		0			0
$217$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$218$		0			0
$219$		0			0
$220$	0.217550	−	2.90301i	0.217550	−	2.90301i
$221$	−0.0549581	+	0.733365i	−0.0549581	+	0.733365i
$222$		0			0
$223$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$223$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$224$	3.84537	+	3.56798i	3.84537	+	3.56798i
$225$	0.623490	−	0.781831i	0.623490	−	0.781831i
$226$		0			0
$227$	0.733052	−	1.26968i	0.733052	−	1.26968i	−0.222521	−	0.974928i	$-0.571429\pi$
$227$	0.733052	−	1.26968i	0.733052	−	1.26968i	0.955573	−	0.294755i	$-0.0952381\pi$
$228$		0			0
$229$	−1.88980	+	0.582926i	−1.88980	+	0.582926i	−0.900969	+	0.433884i	$0.857143\pi$
$229$	−1.88980	+	0.582926i	−1.88980	+	0.582926i	−0.988831	+	0.149042i	$0.952381\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.97766	−	0.298085i	−1.97766	−	0.298085i	−0.988831	−	0.149042i	$-0.952381\pi$
$233$	−1.97766	−	0.298085i	−1.97766	−	0.298085i	−0.988831	−	0.149042i	$-0.952381\pi$
$234$	−2.70018	+	1.84095i	−2.70018	+	1.84095i
$235$		0			0
$236$	3.97471	+	2.70991i	3.97471	+	2.70991i
$237$		0			0
$238$	0.548760	−	0.688123i	0.548760	−	0.688123i
$239$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$239$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$240$		0			0
$241$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$241$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$242$	−1.88980	−	0.582926i	−1.88980	−	0.582926i
$243$		0			0
$244$		0			0
$245$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$246$		0			0
$247$		0			0
$248$	3.61168	+	1.11406i	3.61168	+	1.11406i
$249$		0			0
$250$	1.44973	−	1.34515i	1.44973	−	1.34515i
$251$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$251$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$252$	2.91115			2.91115
$253$		0			0
$254$	−2.03759	−	1.38921i	−2.03759	−	1.38921i
$255$		0			0
$256$	5.40466	−	3.68484i	5.40466	−	3.68484i
$257$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$257$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$258$		0			0
$259$		0			0
$260$	−4.33420	+	2.08724i	−4.33420	+	2.08724i
$261$		0			0
$262$		0			0
$263$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$263$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.0332580	+	0.443797i	−0.0332580	+	0.443797i	0.955573	+	0.294755i	$0.0952381\pi$
$269$	−0.0332580	+	0.443797i	−0.0332580	+	0.443797i	−0.988831	+	0.149042i	$0.952381\pi$
$270$		0			0
$271$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$271$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$272$	−1.26631	−	1.58790i	−1.26631	−	1.58790i
$273$		0			0
$274$		0			0
$275$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$276$		0			0
$277$	0.698220	+	1.77904i	0.698220	+	1.77904i	0.623490	+	0.781831i	$0.285714\pi$
$277$	0.698220	+	1.77904i	0.698220	+	1.77904i	0.0747301	+	0.997204i	$0.476190\pi$
$278$		0			0
$279$	0.900969	−	0.433884i	0.900969	−	0.433884i
$280$	3.73738	+	0.563320i	3.73738	+	0.563320i
$281$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$281$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$282$		0			0
$283$	−1.48883	+	1.01507i	−1.48883	+	1.01507i	−0.500000	+	0.866025i	$0.666667\pi$
$283$	−1.48883	+	1.01507i	−1.48883	+	1.01507i	−0.988831	+	0.149042i	$0.952381\pi$
$284$	4.22037	+	3.91593i	4.22037	+	3.91593i
$285$		0			0
$286$	0.727208	+	3.18610i	0.727208	+	3.18610i
$287$		0			0
$288$	1.16728	−	5.11418i	1.16728	−	5.11418i
$289$	0.587862	−	0.545456i	0.587862	−	0.545456i
$290$		0			0
$291$		0			0
$292$	0.415770	+	5.54807i	0.415770	+	5.54807i
$293$	−1.46610			−1.46610			−0.733052	−	0.680173i	$-0.761905\pi$
$293$	−1.46610			−1.46610			−0.733052	+	0.680173i	$0.761905\pi$
$294$		0			0
$295$	1.65248			1.65248
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−0.0332580	−	0.145713i	−0.0332580	−	0.145713i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$	−0.870312	−	0.131178i	−0.870312	−	0.131178i
$307$	1.78181	+	0.858075i	1.78181	+	0.858075i	0.955573	+	0.294755i	$0.0952381\pi$
$307$	1.78181	+	0.858075i	1.78181	+	0.858075i	0.826239	+	0.563320i	$0.190476\pi$
$308$	1.06356	−	2.70991i	1.06356	−	2.70991i
$309$		0			0
$310$	1.88980	−	0.582926i	1.88980	−	0.582926i
$311$	−0.535628	−	1.36476i	−0.535628	−	1.36476i	−0.900969	−	0.433884i	$-0.857143\pi$
$311$	−0.535628	−	1.36476i	−0.535628	−	1.36476i	0.365341	−	0.930874i	$-0.380952\pi$
$312$		0			0
$313$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$313$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$314$		0			0
$315$	0.826239	−	0.563320i	0.826239	−	0.563320i
$316$		0			0
$317$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$317$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$318$		0			0
$319$		0			0
$320$	2.12285	−	5.40894i	2.12285	−	5.40894i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−1.45557	−	2.52113i	−1.45557	−	2.52113i
$325$	−0.826239	+	1.43109i	−0.826239	+	1.43109i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.147791	−	0.0222759i	−0.147791	−	0.0222759i	0.0747301	−	0.997204i	$-0.476190\pi$
$331$	−0.147791	−	0.0222759i	−0.147791	−	0.0222759i	−0.222521	+	0.974928i	$0.571429\pi$
$332$	−2.40530	+	1.63991i	−2.40530	+	1.63991i
$333$		0			0
$334$	−3.26804	−	2.22811i	−3.26804	−	2.22811i
$335$		0			0
$336$		0			0
$337$	−0.367711	+	1.61105i	−0.367711	+	1.61105i	0.365341	+	0.930874i	$0.380952\pi$
$337$	−0.367711	+	1.61105i	−0.367711	+	1.61105i	−0.733052	+	0.680173i	$0.761905\pi$
$338$	2.50902	−	2.32803i	2.50902	−	2.32803i
$339$		0			0
$340$	−1.23802	−	0.381879i	−1.23802	−	0.381879i
$341$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i
$342$		0			0
$343$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$344$	−0.564900			−0.564900
$345$		0			0
$346$	−1.38084	−	0.425934i	−1.38084	−	0.425934i
$347$	−0.722521	+	0.108903i	−0.722521	+	0.108903i	−0.500000	−	0.866025i	$-0.666667\pi$
$347$	−0.722521	+	0.108903i	−0.722521	+	0.108903i	−0.222521	+	0.974928i	$0.571429\pi$
$348$		0			0
$349$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$349$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$350$	1.78181	−	0.858075i	1.78181	−	0.858075i
$351$		0			0
$352$	−4.33420	−	2.95501i	−4.33420	−	2.95501i
$353$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$353$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$354$		0			0
$355$	1.95557	+	0.294755i	1.95557	+	0.294755i
$356$	−0.392012	−	0.188783i	−0.392012	−	0.188783i
$357$		0			0
$358$	−3.52382	+	1.69698i	−3.52382	+	1.69698i
$359$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$359$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$360$	−1.38084	−	3.51833i	−1.38084	−	3.51833i
$361$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$362$	1.88980	+	3.27323i	1.88980	+	3.27323i
$363$		0			0
$364$	−4.75687	+	0.716983i	−4.75687	+	0.716983i
$365$	1.19158	+	1.49419i	1.19158	+	1.49419i
$366$		0			0
$367$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$367$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	0.733052	+	1.26968i	0.733052	+	1.26968i	0.955573	+	0.294755i	$0.0952381\pi$
$373$	0.733052	+	1.26968i	0.733052	+	1.26968i	−0.222521	+	0.974928i	$0.571429\pi$
$374$	−0.440071	+	0.762226i	−0.440071	+	0.762226i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.32091	+	0.636119i	1.32091	+	0.636119i	0.955573	−	0.294755i	$-0.0952381\pi$
$379$	1.32091	+	0.636119i	1.32091	+	0.636119i	0.365341	+	0.930874i	$0.380952\pi$
$380$		0			0
$381$		0			0
$382$	−1.44973	−	1.34515i	−1.44973	−	1.34515i
$383$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$383$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$384$		0			0
$385$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$386$	−0.195850	+	0.858075i	−0.195850	+	0.858075i
$387$	−0.109562	+	0.101659i	−0.109562	+	0.101659i
$388$		0			0
$389$	−1.40097	−	0.432142i	−1.40097	−	0.432142i	−0.500000	−	0.866025i	$-0.666667\pi$
$389$	−1.40097	−	0.432142i	−1.40097	−	0.432142i	−0.900969	+	0.433884i	$0.857143\pi$
$390$		0			0
$391$		0			0
$392$	3.40530	+	1.63991i	3.40530	+	1.63991i
$393$		0			0
$394$	−0.107988	−	1.44100i	−0.107988	−	1.44100i
$395$		0			0
$396$	−2.87863	+	0.433884i	−2.87863	+	0.433884i
$397$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$397$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$398$	0.321552	−	1.40881i	0.321552	−	1.40881i
$399$		0			0
$400$	−1.01550	−	4.44920i	−1.01550	−	4.44920i
$401$	0.123490	+	0.0841939i	0.123490	+	0.0841939i	0.623490	−	0.781831i	$-0.285714\pi$
$401$	0.123490	+	0.0841939i	0.123490	+	0.0841939i	−0.500000	+	0.866025i	$0.666667\pi$
$402$		0			0
$403$	−1.36534	+	0.930874i	−1.36534	+	0.930874i
$404$		0			0
$405$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$409$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1.57906	+	0.487076i	1.57906	+	0.487076i
$414$		0			0
$415$	−0.365341	+	0.930874i	−0.365341	+	0.930874i
$416$	−0.647791	+	8.64417i	−0.647791	+	8.64417i
$417$		0			0
$418$		0			0
$419$	1.03030	+	1.29196i	1.03030	+	1.29196i	0.955573	+	0.294755i	$0.0952381\pi$
$419$	1.03030	+	1.29196i	1.03030	+	1.29196i	0.0747301	+	0.997204i	$0.476190\pi$
$420$		0			0
$421$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$421$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.425270	+	0.131178i	−0.425270	+	0.131178i
$426$		0			0
$427$		0			0
$428$	−3.27064	−	1.57506i	−3.27064	−	1.57506i
$429$		0			0
$430$	−0.244221	+	0.166507i	−0.244221	+	0.166507i
$431$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$431$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$432$		0			0
$433$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$433$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$434$	1.97766			1.97766
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$439$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$440$	−3.77960			−3.77960
$441$	0.955573	−	0.294755i	0.955573	−	0.294755i
$442$	1.45442			1.45442
$443$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$443$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$444$		0			0
$445$	−0.147791	+	0.0222759i	−0.147791	+	0.0222759i
$446$		0			0
$447$		0			0
$448$	3.62285	−	4.54291i	3.62285	−	4.54291i
$449$	−0.367711	−	1.61105i	−0.367711	−	1.61105i	−0.733052	−	0.680173i	$-0.761905\pi$
$449$	−0.367711	−	1.61105i	−0.367711	−	1.61105i	0.365341	−	0.930874i	$-0.380952\pi$
$450$	−1.63402	−	1.11406i	−1.63402	−	1.11406i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−2.61232	−	1.25803i	−2.61232	−	1.25803i
$455$	−1.21135	+	1.12397i	−1.21135	+	1.12397i
$456$		0			0
$457$	−0.955573	+	0.294755i	−0.955573	+	0.294755i	−0.733052	−	0.680173i	$-0.761905\pi$
$457$	−0.955573	+	0.294755i	−0.955573	+	0.294755i	−0.222521	+	0.974928i	$0.571429\pi$
$458$	1.42890	+	3.64078i	1.42890	+	3.64078i
$459$		0			0
$460$		0			0
$461$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$461$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$462$		0			0
$463$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$463$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$464$		0			0
$465$		0			0
$466$	−0.295582	+	3.94426i	−0.295582	+	3.94426i
$467$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$467$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$468$	2.99936	+	3.76108i	2.99936	+	3.76108i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	3.12285	−	5.40894i	3.12285	−	5.40894i
$473$	0.0546039	+	0.139129i	0.0546039	+	0.139129i
$474$		0			0
$475$		0			0
$476$	−1.07046	−	0.729827i	−1.07046	−	0.729827i
$477$		0			0
$478$		0			0
$479$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$479$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.647791	+	2.83816i	−0.647791	+	2.83816i
$485$		0			0
$486$		0			0
$487$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$487$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$488$		0			0
$489$		0			0
$490$	1.95557	−	0.294755i	1.95557	−	0.294755i
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$496$	1.01550	−	4.44920i	1.01550	−	4.44920i
$497$	1.78181	+	0.858075i	1.78181	+	0.858075i
$498$		0			0
$499$	0.123490	+	0.0841939i	0.123490	+	0.0841939i	0.623490	−	0.781831i	$-0.285714\pi$
$499$	0.123490	+	0.0841939i	0.123490	+	0.0841939i	−0.500000	+	0.866025i	$0.666667\pi$
$500$	−2.13402	−	1.98008i	−2.13402	−	1.98008i
$501$		0			0
$502$	2.43856	+	0.367554i	2.43856	+	0.367554i
$503$	0.900969	+	0.433884i	0.900969	+	0.433884i	0.826239	−	0.563320i	$-0.190476\pi$
$503$	0.900969	+	0.433884i	0.900969	+	0.433884i	0.0747301	+	0.997204i	$0.476190\pi$
$504$	−0.282450	−	3.76903i	−0.282450	−	3.76903i
$505$		0			0
$506$		0			0
$507$		0			0
$508$	−1.81507	+	3.14379i	−1.81507	+	3.14379i
$509$	0.733052	+	1.26968i	0.733052	+	1.26968i	0.955573	+	0.294755i	$0.0952381\pi$
$509$	0.733052	+	1.26968i	0.733052	+	1.26968i	−0.222521	+	0.974928i	$0.571429\pi$
$510$		0			0
$511$	0.698220	+	1.77904i	0.698220	+	1.77904i
$512$	−4.17161	−	5.23104i	−4.17161	−	5.23104i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	3.12285	+	5.40894i	3.12285	+	5.40894i
$521$	0.988831	−	1.71271i	0.988831	−	1.71271i	0.365341	−	0.930874i	$-0.380952\pi$
$521$	0.988831	−	1.71271i	0.988831	−	1.71271i	0.623490	−	0.781831i	$-0.285714\pi$
$522$		0			0
$523$	0.142820	−	0.0440542i	0.142820	−	0.0440542i	−0.222521	−	0.974928i	$-0.571429\pi$
$523$	0.142820	−	0.0440542i	0.142820	−	0.0440542i	0.365341	+	0.930874i	$0.380952\pi$
$524$		0			0
$525$		0			0
$526$	−1.78181	−	0.858075i	−1.78181	−	0.858075i
$527$	−0.440071	−	0.0663300i	−0.440071	−	0.0663300i
$528$		0			0
$529$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$530$		0			0
$531$	−0.367711	−	1.61105i	−0.367711	−	1.61105i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−1.23305	+	0.185853i	−1.23305	+	0.185853i
$536$		0			0
$537$		0			0
$538$	0.880142			0.880142
$539$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$540$		0			0
$541$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$541$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$542$		0			0
$543$		0			0
$544$	−1.71135	+	1.58790i	−1.71135	+	1.58790i
$545$		0			0
$546$		0			0
$547$	−0.425270	−	1.86323i	−0.425270	−	1.86323i	−0.500000	−	0.866025i	$-0.666667\pi$
$547$	−0.425270	−	1.86323i	−0.425270	−	1.86323i	0.0747301	−	0.997204i	$-0.476190\pi$
$548$		0			0
$549$		0			0
$550$	−1.63402	+	1.11406i	−1.63402	+	1.11406i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	3.40530	−	1.63991i	3.40530	−	1.63991i
$555$		0			0
$556$		0			0
$557$	0.900969	−	1.56052i	0.900969	−	1.56052i	0.0747301	−	0.997204i	$-0.476190\pi$
$557$	0.900969	−	1.56052i	0.900969	−	1.56052i	0.826239	−	0.563320i	$-0.190476\pi$
$558$	−0.988831	−	1.71271i	−0.988831	−	1.71271i
$559$	0.153989	−	0.193096i	0.153989	−	0.193096i
$560$	0.341040	−	4.55086i	0.341040	−	4.55086i
$561$		0			0
$562$		0			0
$563$	0.0546039	−	0.728639i	0.0546039	−	0.728639i	−0.900969	−	0.433884i	$-0.857143\pi$
$563$	0.0546039	−	0.728639i	0.0546039	−	0.728639i	0.955573	−	0.294755i	$-0.0952381\pi$
$564$		0			0
$565$		0			0
$566$	2.22188	+	2.78615i	2.22188	+	2.78615i
$567$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$568$	4.66044	−	5.84401i	4.66044	−	5.84401i
$569$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$569$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$570$		0			0
$571$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$571$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$572$	4.59688	−	1.41795i	4.59688	−	1.41795i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−5.74570	−	0.866025i	−5.74570	−	0.866025i
$577$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$577$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$578$	−1.16259	−	1.07873i	−1.16259	−	1.07873i
$579$		0			0
$580$		0			0
$581$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$582$		0			0
$583$		0			0
$584$	7.14269	−	1.07659i	7.14269	−	1.07659i
$585$	1.57906	+	0.487076i	1.57906	+	0.487076i
$586$	0.216677	+	2.89135i	0.216677	+	2.89135i
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$		0			0
$589$		0			0
$590$	−0.244221	−	3.25890i	−0.244221	−	3.25890i
$591$		0			0
$592$		0			0
$593$	−0.109562	+	0.101659i	−0.109562	+	0.101659i	−0.733052	−	0.680173i	$-0.761905\pi$
$593$	−0.109562	+	0.101659i	−0.109562	+	0.101659i	0.623490	+	0.781831i	$0.285714\pi$
$594$		0			0
$595$	−0.445042			−0.445042
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.21135	+	0.825886i	−1.21135	+	0.825886i	−0.988831	−	0.149042i	$-0.952381\pi$
$599$	−1.21135	+	0.825886i	−1.21135	+	0.825886i	−0.222521	+	0.974928i	$0.571429\pi$
$600$		0			0
$601$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$601$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$602$	−0.282450	+	0.0871242i	−0.282450	+	0.0871242i
$603$		0			0
$604$		0			0
$605$	0.365341	+	0.930874i	0.365341	+	0.930874i
$606$		0			0
$607$	0.733052	+	1.26968i	0.733052	+	1.26968i	0.955573	+	0.294755i	$0.0952381\pi$
$607$	0.733052	+	1.26968i	0.733052	+	1.26968i	−0.222521	+	0.974928i	$0.571429\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.0968189	+	1.29196i	−0.0968189	+	1.29196i
$613$	0.0546039	−	0.728639i	0.0546039	−	0.728639i	−0.900969	−	0.433884i	$-0.857143\pi$
$613$	0.0546039	−	0.728639i	0.0546039	−	0.728639i	0.955573	−	0.294755i	$-0.0952381\pi$
$614$	1.42890	−	3.64078i	1.42890	−	3.64078i
$615$		0			0
$616$	−3.61168	−	1.11406i	−3.61168	−	1.11406i
$617$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$617$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$618$		0			0
$619$	0.900969	−	1.56052i	0.900969	−	1.56052i	0.0747301	−	0.997204i	$-0.476190\pi$
$619$	0.900969	−	1.56052i	0.900969	−	1.56052i	0.826239	−	0.563320i	$-0.190476\pi$
$620$	−1.06356	−	2.70991i	−1.06356	−	2.70991i
$621$		0			0
$622$	−2.61232	+	1.25803i	−2.61232	+	1.25803i
$623$	−0.147791	−	0.0222759i	−0.147791	−	0.0222759i
$624$		0			0
$625$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−1.23305	−	1.54620i	−1.23305	−	1.54620i
$631$	−0.162592	+	0.712362i	−0.162592	+	0.712362i	0.826239	+	0.563320i	$0.190476\pi$
$631$	−0.162592	+	0.712362i	−0.162592	+	0.712362i	−0.988831	+	0.149042i	$0.952381\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.0931869	+	1.24349i	0.0931869	+	1.24349i
$636$		0			0
$637$	−1.48883	+	0.716983i	−1.48883	+	0.716983i
$638$		0			0
$639$	−0.147791	−	1.97213i	−0.147791	−	1.97213i
$640$	−5.96822	−	1.84095i	−5.96822	−	1.84095i
$641$	−1.23305	+	0.185853i	−1.23305	+	0.185853i	−0.733052	−	0.680173i	$-0.761905\pi$
$641$	−1.23305	+	0.185853i	−1.23305	+	0.185853i	−0.500000	+	0.866025i	$0.666667\pi$
$642$		0			0
$643$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$643$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$647$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$648$	−3.12285	+	2.12912i	−3.12285	+	2.12912i
$649$	−1.63402	−	0.246289i	−1.63402	−	0.246289i
$650$	2.94440	+	1.41795i	2.94440	+	1.41795i
$651$		0			0
$652$		0			0
$653$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$653$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	1.19158	−	1.49419i	1.19158	−	1.49419i
$658$		0			0
$659$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$659$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$660$		0			0
$661$	0.0931869	−	1.24349i	0.0931869	−	1.24349i	−0.733052	−	0.680173i	$-0.761905\pi$
$661$	0.0931869	−	1.24349i	0.0931869	−	1.24349i	0.826239	−	0.563320i	$-0.190476\pi$
$662$	−0.0220888	+	0.294755i	−0.0220888	+	0.294755i
$663$		0			0
$664$	2.35654	+	2.95501i	2.35654	+	2.95501i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−2.91115	+	5.04225i	−2.91115	+	5.04225i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.900969	+	0.433884i	0.900969	+	0.433884i	0.826239	−	0.563320i	$-0.190476\pi$
$673$	0.900969	+	0.433884i	0.900969	+	0.433884i	0.0747301	+	0.997204i	$0.476190\pi$
$674$	3.23154	+	0.487076i	3.23154	+	0.487076i
$675$		0			0
$676$	−3.69331	−	3.42689i	−3.69331	−	3.42689i
$677$	−1.48883	−	1.01507i	−1.48883	−	1.01507i	−0.988831	−	0.149042i	$-0.952381\pi$
$677$	−1.48883	−	1.01507i	−1.48883	−	1.01507i	−0.500000	−	0.866025i	$-0.666667\pi$
$678$		0			0
$679$		0			0
$680$	−0.374298	+	1.63991i	−0.374298	+	1.63991i
$681$		0			0
$682$	−1.95557	+	0.294755i	−1.95557	+	0.294755i
$683$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$683$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$684$		0			0
$685$		0			0
$686$	1.95557	+	0.294755i	1.95557	+	0.294755i
$687$		0			0
$688$	0.0509719	+	0.680173i	0.0509719	+	0.680173i
$689$		0			0
$690$		0			0
$691$	0.326239	−	0.302705i	0.326239	−	0.302705i	−0.500000	−	0.866025i	$-0.666667\pi$
$691$	0.326239	−	0.302705i	0.326239	−	0.302705i	0.826239	+	0.563320i	$0.190476\pi$
$692$	−0.473329	+	2.07379i	−0.473329	+	2.07379i
$693$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$694$	0.321552	+	1.40881i	0.321552	+	1.40881i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−1.45557	−	2.52113i	−1.45557	−	2.52113i
$701$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$701$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$702$		0			0
$703$		0			0
$704$	−2.90530	+	5.03213i	−2.90530	+	5.03213i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.365341	+	0.930874i	−0.365341	+	0.930874i	0.623490	+	0.781831i	$0.285714\pi$
$709$	−0.365341	+	0.930874i	−0.365341	+	0.930874i	−0.988831	+	0.149042i	$0.952381\pi$
$710$	0.292280	−	3.90021i	0.292280	−	3.90021i
$711$		0			0
$712$	−0.206381	+	0.525850i	−0.206381	+	0.525850i
$713$		0			0
$714$		0			0
$715$	1.03030	−	1.29196i	1.03030	−	1.29196i
$716$	2.87863	+	4.98593i	2.87863	+	4.98593i
$717$		0			0
$718$		0			0
$719$	−0.425270	+	0.131178i	−0.425270	+	0.131178i	−0.500000	−	0.866025i	$-0.666667\pi$
$719$	−0.425270	+	0.131178i	−0.425270	+	0.131178i	0.0747301	+	0.997204i	$0.476190\pi$
$720$	−4.11168	+	1.98008i	−4.11168	+	1.98008i
$721$		0			0
$722$	1.78181	+	0.858075i	1.78181	+	0.858075i
$723$		0			0
$724$	4.59688	−	3.13410i	4.59688	−	3.13410i
$725$		0			0
$726$		0			0
$727$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$727$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$728$	1.38980	+	6.08911i	1.38980	+	6.08911i
$729$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$730$	2.77064	−	2.57078i	2.77064	−	2.57078i
$731$	0.0657731	−	0.00991370i	0.0657731	−	0.00991370i
$732$		0			0
$733$	0.0931869	+	1.24349i	0.0931869	+	1.24349i	0.826239	+	0.563320i	$0.190476\pi$
$733$	0.0931869	+	1.24349i	0.0931869	+	1.24349i	−0.733052	+	0.680173i	$0.761905\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$739$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.367711	−	1.61105i	−0.367711	−	1.61105i	−0.733052	−	0.680173i	$-0.761905\pi$
$743$	−0.367711	−	1.61105i	−0.367711	−	1.61105i	0.365341	−	0.930874i	$-0.380952\pi$
$744$		0			0
$745$		0			0
$746$	2.39564	−	1.63332i	2.39564	−	1.63332i
$747$	0.988831	+	0.149042i	0.988831	+	0.149042i
$748$	1.16728	+	0.562132i	1.16728	+	0.562132i
$749$	−1.23305	−	0.185853i	−1.23305	−	0.185853i
$750$		0			0
$751$	1.82624	−	0.563320i	1.82624	−	0.563320i	0.826239	−	0.563320i	$-0.190476\pi$
$751$	1.82624	−	0.563320i	1.82624	−	0.563320i	1.00000			$0$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$757$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$758$	1.05929	−	2.69903i	1.05929	−	2.69903i
$759$		0			0
$760$		0			0
$761$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$761$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$762$		0			0
$763$		0			0
$764$	−1.81507	+	2.27603i	−1.81507	+	2.27603i
$765$	0.222521	+	0.385418i	0.222521	+	0.385418i
$766$		0			0
$767$	0.997630	+	2.54192i	0.997630	+	2.54192i
$768$		0			0
$769$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$769$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$770$	−1.88980	+	0.582926i	−1.88980	+	0.582926i
$771$		0			0
$772$	1.28111	+	0.193096i	1.28111	+	0.193096i
$773$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$773$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$774$	0.216677	+	0.201047i	0.216677	+	0.201047i
$775$	−0.826239	−	0.563320i	−0.826239	−	0.563320i
$776$		0			0
$777$		0			0
$778$	−0.645190	+	2.82676i	−0.645190	+	2.82676i
$779$		0			0
$780$		0			0
$781$	−1.88980	−	0.582926i	−1.88980	−	0.582926i
$782$		0			0
$783$		0			0
$784$	1.66728	−	4.24816i	1.66728	−	4.24816i
$785$		0			0
$786$		0			0
$787$	0.698220	+	0.215372i	0.698220	+	0.215372i	0.623490	−	0.781831i	$-0.285714\pi$
$787$	0.698220	+	0.215372i	0.698220	+	0.215372i	0.0747301	+	0.997204i	$0.476190\pi$
$788$	−2.10336	+	0.317031i	−2.10336	+	0.317031i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.841040	+	3.68484i	0.841040	+	3.68484i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−2.10336	−	0.317031i	−2.10336	−	0.317031i
$797$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$797$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$798$		0			0
$799$		0			0
$800$	−5.01265	+	1.54620i	−5.01265	+	1.54620i
$801$	0.0546039	+	0.139129i	0.0546039	+	0.139129i
$802$	0.147791	−	0.255981i	0.147791	−	0.255981i
$803$	−0.955573	−	1.65510i	−0.955573	−	1.65510i
$804$		0			0
$805$		0			0
$806$	2.03759	+	2.55506i	2.03759	+	2.55506i
$807$		0			0
$808$		0			0
$809$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$809$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$810$	−0.722521	+	1.84095i	−0.722521	+	1.84095i
$811$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$811$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	1.36534	+	0.930874i	1.36534	+	0.930874i
$820$		0			0
$821$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$821$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$822$		0			0
$823$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$823$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$824$		0			0
$825$		0			0
$826$	0.727208	−	3.18610i	0.727208	−	3.18610i
$827$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	−0.900969	−	0.433884i	$-0.857143\pi$
$827$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	1.00000			$0$
$828$		0			0
$829$	−1.63402	+	0.246289i	−1.63402	+	0.246289i	−0.900969	−	0.433884i	$-0.857143\pi$
$829$	−1.63402	+	0.246289i	−1.63402	+	0.246289i	−0.733052	+	0.680173i	$0.761905\pi$
$830$	1.88980	+	0.582926i	1.88980	+	0.582926i
$831$		0			0
$832$	9.60189			9.60189
$833$	−0.425270	−	0.131178i	−0.425270	−	0.131178i
$834$		0			0
$835$	0.149460	+	1.99441i	0.149460	+	1.99441i
$836$		0			0
$837$		0			0
$838$	2.39564	−	2.22283i	2.39564	−	2.22283i
$839$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	−0.900969	−	0.433884i	$-0.857143\pi$
$839$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	1.00000			$0$
$840$		0			0
$841$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$842$	0.727208	+	0.495802i	0.727208	+	0.495802i
$843$		0			0
$844$		0			0
$845$	−1.71135	−	0.257945i	−1.71135	−	0.257945i
$846$		0			0
$847$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$848$		0			0
$849$		0			0
$850$	0.321552	+	0.819301i	0.321552	+	0.819301i
$851$		0			0
$852$		0			0
$853$	0.777479	−	0.974928i	0.777479	−	0.974928i	−0.222521	−	0.974928i	$-0.571429\pi$
$853$	0.777479	−	0.974928i	0.777479	−	0.974928i	1.00000			$0$
$854$		0			0
$855$		0			0
$856$	−1.72188	+	4.38729i	−1.72188	+	4.38729i
$857$	−0.147791	+	1.97213i	−0.147791	+	1.97213i	0.0747301	+	0.997204i	$0.476190\pi$
$857$	−0.147791	+	1.97213i	−0.147791	+	1.97213i	−0.222521	+	0.974928i	$0.571429\pi$
$858$		0			0
$859$	−0.162592	+	0.414278i	−0.162592	+	0.414278i	−0.988831	−	0.149042i	$-0.952381\pi$
$859$	−0.162592	+	0.414278i	−0.162592	+	0.414278i	0.826239	+	0.563320i	$0.190476\pi$
$860$	0.271281	+	0.340175i	0.271281	+	0.340175i
$861$		0			0
$862$		0			0
$863$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$863$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$864$		0			0
$865$	0.266948	+	0.680173i	0.266948	+	0.680173i
$866$		0			0
$867$		0			0
$868$	−0.217550	−	2.90301i	−0.217550	−	2.90301i
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$876$		0			0
$877$	0.733052	−	0.680173i	0.733052	−	0.680173i	−0.222521	−	0.974928i	$-0.571429\pi$
$877$	0.733052	−	0.680173i	0.733052	−	0.680173i	0.955573	+	0.294755i	$0.0952381\pi$
$878$		0			0
$879$		0			0
$880$	0.341040	+	4.55086i	0.341040	+	4.55086i
$881$	0.730682			0.730682			0.365341	−	0.930874i	$-0.380952\pi$
$881$	0.730682			0.730682			0.365341	+	0.930874i	$0.380952\pi$
$882$	−0.722521	−	1.84095i	−0.722521	−	1.84095i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$	−0.159991	−	2.13493i	−0.159991	−	2.13493i
$885$		0			0
$886$		0			0
$887$	−1.40097	+	1.29991i	−1.40097	+	1.29991i	−0.500000	+	0.866025i	$0.666667\pi$
$887$	−1.40097	+	1.29991i	−1.40097	+	1.29991i	−0.900969	+	0.433884i	$0.857143\pi$
$888$		0			0
$889$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$890$	0.0657731	+	0.288171i	0.0657731	+	0.288171i
$891$	0.826239	+	0.563320i	0.826239	+	0.563320i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	1.78181	+	0.858075i	1.78181	+	0.858075i
$896$	−5.16044	−	3.51833i	−5.16044	−	3.51833i
$897$		0			0
$898$	−3.12285	+	0.963272i	−3.12285	+	0.963272i
$899$		0			0
$900$	−1.45557	+	2.52113i	−1.45557	+	2.52113i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.698220	−	1.77904i	0.698220	−	1.77904i
$906$		0			0
$907$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$907$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$908$	−1.55929	+	3.97301i	−1.55929	+	3.97301i
$909$		0			0
$910$	2.39564	+	2.22283i	2.39564	+	2.22283i
$911$	0.455573	−	0.571270i	0.455573	−	0.571270i	−0.500000	−	0.866025i	$-0.666667\pi$
$911$	0.455573	−	0.571270i	0.455573	−	0.571270i	0.955573	+	0.294755i	$0.0952381\pi$
$912$		0			0
$913$	0.500000	−	0.866025i	0.500000	−	0.866025i
$914$	0.722521	+	1.84095i	0.722521	+	1.84095i
$915$		0			0
$916$	5.18711	−	2.49798i	5.18711	−	2.49798i
$917$		0			0
$918$		0			0
$919$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$919$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	0.727208	+	3.18610i	0.727208	+	3.18610i
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.0931869	+	1.24349i	0.0931869	+	1.24349i	0.826239	+	0.563320i	$0.190476\pi$
$929$	0.0931869	+	1.24349i	0.0931869	+	1.24349i	−0.733052	+	0.680173i	$0.761905\pi$
$930$		0			0
$931$		0			0
$932$	5.82229			5.82229
$933$		0			0
$934$		0			0
$935$	0.440071	−	0.0663300i	0.440071	−	0.0663300i
$936$	4.57842	−	4.24816i	4.57842	−	4.24816i
$937$	−0.367711	+	1.61105i	−0.367711	+	1.61105i	0.365341	+	0.930874i	$0.380952\pi$
$937$	−0.367711	+	1.61105i	−0.367711	+	1.61105i	−0.733052	+	0.680173i	$0.761905\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$941$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$942$		0			0
$943$		0			0
$944$	−6.79446	−	3.27204i	−6.79446	−	3.27204i
$945$		0			0
$946$	0.266310	−	0.128248i	0.266310	−	0.128248i
$947$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$947$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$948$		0			0
$949$	−1.57906	+	2.73502i	−1.57906	+	2.73502i
$950$		0			0
$951$		0			0
$952$	−0.841040	+	1.45672i	−0.841040	+	1.45672i
$953$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$953$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$954$		0			0
$955$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$		0			0
$962$		0			0
$963$	0.455573	+	1.16078i	0.455573	+	1.16078i
$964$		0			0
$965$	0.400969	−	0.193096i	0.400969	−	0.193096i
$966$		0			0
$967$	−1.72188	−	0.829215i	−1.72188	−	0.829215i	−0.988831	−	0.149042i	$-0.952381\pi$
$967$	−1.72188	−	0.829215i	−1.72188	−	0.829215i	−0.733052	−	0.680173i	$-0.761905\pi$
$968$	3.73738	+	0.563320i	3.73738	+	0.563320i
$969$		0			0
$970$		0			0
$971$	0.603718	+	0.411608i	0.603718	+	0.411608i	0.826239	−	0.563320i	$-0.190476\pi$
$971$	0.603718	+	0.411608i	0.603718	+	0.411608i	−0.222521	+	0.974928i	$0.571429\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$977$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$978$		0			0
$979$	0.149460			0.149460
$980$	−0.647791	−	2.83816i	−0.647791	−	2.83816i
$981$		0			0
$982$		0			0
$983$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$983$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$984$		0			0
$985$	−0.535628	+	0.496990i	−0.535628	+	0.496990i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	1.44973	+	1.34515i	1.44973	+	1.34515i
$991$	−0.367711	+	0.250701i	−0.367711	+	0.250701i	−0.733052	−	0.680173i	$-0.761905\pi$
$991$	−0.367711	+	0.250701i	−0.367711	+	0.250701i	0.365341	+	0.930874i	$0.380952\pi$
$992$	−5.18711	−	0.781831i	−5.18711	−	0.781831i
$993$		0			0
$994$	1.42890	−	3.64078i	1.42890	−	3.64078i
$995$	−0.658322	+	0.317031i	−0.658322	+	0.317031i
$996$		0			0
$997$	0.0546039	+	0.139129i	0.0546039	+	0.139129i	0.955573	−	0.294755i	$-0.0952381\pi$
$997$	0.0546039	+	0.139129i	0.0546039	+	0.139129i	−0.900969	+	0.433884i	$0.857143\pi$
$998$	0.147791	−	0.255981i	0.147791	−	0.255981i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.1.ck.a.1649.1	yes	12
5.4	even	2		2695.1.ck.b.1649.1	yes	12
11.10	odd	2		2695.1.ck.b.1649.1	yes	12
49.23	even	21	inner	2695.1.ck.a.219.1	✓	12
55.54	odd	2	CM	2695.1.ck.a.1649.1	yes	12
245.219	even	42		2695.1.ck.b.219.1	yes	12
539.219	odd	42		2695.1.ck.b.219.1	yes	12
2695.219	odd	42	inner	2695.1.ck.a.219.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2695.1.ck.a.219.1	✓	12	49.23	even	21	inner
2695.1.ck.a.219.1	✓	12	2695.219	odd	42	inner
2695.1.ck.a.1649.1	yes	12	1.1	even	1	trivial
2695.1.ck.a.1649.1	yes	12	55.54	odd	2	CM
2695.1.ck.b.219.1	yes	12	245.219	even	42
2695.1.ck.b.219.1	yes	12	539.219	odd	42
2695.1.ck.b.1649.1	yes	12	5.4	even	2
2695.1.ck.b.1649.1	yes	12	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.147791 - 1.97213i) q^{2} +(-2.87863 + 0.433884i) q^{4} +(-0.733052 + 0.680173i) q^{5} +(-0.900969 + 0.433884i) q^{7} +(0.841040 + 3.68484i) q^{8} +(0.826239 + 0.563320i) q^{9} +O(q^{10})\)	\(q+(-0.147791 - 1.97213i) q^{2} +(-2.87863 + 0.433884i) q^{4} +(-0.733052 + 0.680173i) q^{5} +(-0.900969 + 0.433884i) q^{7} +(0.841040 + 3.68484i) q^{8} +(0.826239 + 0.563320i) q^{9} +(1.44973 + 1.34515i) q^{10} +(0.826239 - 0.563320i) q^{11} +(-1.48883 - 0.716983i) q^{13} +(0.988831 + 1.71271i) q^{14} +(4.36087 - 1.34515i) q^{16} +(-0.162592 - 0.414278i) q^{17} +(0.988831 - 1.71271i) q^{18} +(1.81507 - 2.27603i) q^{20} +(-1.23305 - 1.54620i) q^{22} +(0.0747301 - 0.997204i) q^{25} +(-1.19395 + 3.04213i) q^{26} +(2.40530 - 1.63991i) q^{28} +(0.500000 - 0.866025i) q^{31} +(-1.91647 - 4.88309i) q^{32} +(-0.792981 + 0.381879i) q^{34} +(0.365341 - 0.930874i) q^{35} +(-2.62285 - 1.26310i) q^{36} +(-3.12285 - 2.12912i) q^{40} +(-0.0332580 + 0.145713i) q^{43} +(-2.13402 + 1.98008i) q^{44} +(-0.988831 + 0.149042i) q^{45} +(0.623490 - 0.781831i) q^{49} -1.97766 q^{50} +(4.59688 + 1.41795i) q^{52} +(-0.222521 + 0.974928i) q^{55} +(-2.35654 - 2.95501i) q^{56} +(-1.21135 - 1.12397i) q^{59} +(-1.78181 - 0.858075i) q^{62} +(-0.988831 - 0.149042i) q^{63} +(-5.23517 + 2.52113i) q^{64} +(1.57906 - 0.487076i) q^{65} +(0.647791 + 1.12201i) q^{68} +(-1.88980 - 0.582926i) q^{70} +(-1.23305 - 1.54620i) q^{71} +(-1.38084 + 3.51833i) q^{72} +(0.142820 - 1.90580i) q^{73} +(-0.500000 + 0.866025i) q^{77} +(-2.28181 + 3.95221i) q^{80} +(0.365341 + 0.930874i) q^{81} +(0.900969 - 0.433884i) q^{83} +(0.400969 + 0.193096i) q^{85} +(0.292280 + 0.0440542i) q^{86} +(2.77064 + 2.57078i) q^{88} +(0.123490 + 0.0841939i) q^{89} +(0.440071 + 1.92808i) q^{90} +1.65248 q^{91} +(-1.63402 - 1.11406i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} + q^{5} - 2 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) 12 * q - q^2 + q^5 - 2 * q^7 - 2 * q^8 + q^9	\( 12 q - q^{2} + q^{5} - 2 q^{7} - 2 q^{8} + q^{9} - q^{10} + q^{11} - 5 q^{13} - q^{14} + 13 q^{16} + 2 q^{17} - q^{18} - 5 q^{22} + q^{25} + q^{26} + 6 q^{31} - 7 q^{32} - 3 q^{34} + q^{35} - 6 q^{40} + 2 q^{43} - 7 q^{44} + q^{45} - 2 q^{49} + 2 q^{50} + 14 q^{52} - 2 q^{55} - 9 q^{56} - q^{59} - 2 q^{62} + q^{63} - 9 q^{64} - q^{65} + 7 q^{68} - q^{70} - 5 q^{71} - 6 q^{72} - q^{73} - 6 q^{77} - 8 q^{80} + q^{81} + 2 q^{83} - 4 q^{85} + q^{86} + q^{88} - 8 q^{89} + 2 q^{90} + 2 q^{91} - q^{98} + 12 q^{99}+O(q^{100}) \) 12 * q - q^2 + q^5 - 2 * q^7 - 2 * q^8 + q^9 - q^10 + q^11 - 5 * q^13 - q^14 + 13 * q^16 + 2 * q^17 - q^18 - 5 * q^22 + q^25 + q^26 + 6 * q^31 - 7 * q^32 - 3 * q^34 + q^35 - 6 * q^40 + 2 * q^43 - 7 * q^44 + q^45 - 2 * q^49 + 2 * q^50 + 14 * q^52 - 2 * q^55 - 9 * q^56 - q^59 - 2 * q^62 + q^63 - 9 * q^64 - q^65 + 7 * q^68 - q^70 - 5 * q^71 - 6 * q^72 - q^73 - 6 * q^77 - 8 * q^80 + q^81 + 2 * q^83 - 4 * q^85 + q^86 + q^88 - 8 * q^89 + 2 * q^90 + 2 * q^91 - q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more