LMFDB - Embedded newform 2695.1.ck.a.1759.1

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			1759.1
Root			$-0.733052 + 0.680173i$ of defining polynomial
Character	$\chi$	$=$	2695.1759
Dual form			2695.1.ck.a.1264.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.88980 + 0.284841i) q^{2} +(2.53464 - 0.781831i) q^{4} +(0.0747301 - 0.997204i) q^{5} +(0.623490 - 0.781831i) q^{7} +(-2.84537 + 1.37026i) q^{8} +(0.365341 + 0.930874i) q^{9} +O(q^{10})$	\(q+(-1.88980 + 0.284841i) q^{2} +(2.53464 - 0.781831i) q^{4} +(0.0747301 - 0.997204i) q^{5} +(0.623490 - 0.781831i) q^{7} +(-2.84537 + 1.37026i) q^{8} +(0.365341 + 0.930874i) q^{9} +(0.142820 + 1.90580i) q^{10} +(0.365341 - 0.930874i) q^{11} +(0.455573 + 0.571270i) q^{13} +(-0.955573 + 1.65510i) q^{14} +(2.79530 - 1.90580i) q^{16} +(1.32091 - 1.22563i) q^{17} +(-0.955573 - 1.65510i) q^{18} +(-0.590232 - 2.58597i) q^{20} +(-0.425270 + 1.86323i) q^{22} +(-0.988831 - 0.149042i) q^{25} +(-1.02366 - 0.949820i) q^{26} +(0.969059 - 2.46912i) q^{28} +(0.500000 + 0.866025i) q^{31} +(-2.42463 + 2.24973i) q^{32} +(-2.14715 + 2.69244i) q^{34} +(-0.733052 - 0.680173i) q^{35} +(1.65379 + 2.07379i) q^{36} +(1.15379 + 2.93982i) q^{40} +(1.78181 + 0.858075i) q^{43} +(0.198220 - 2.64506i) q^{44} +(0.955573 - 0.294755i) q^{45} +(-0.222521 - 0.974928i) q^{49} +1.91115 q^{50} +(1.60135 + 1.09178i) q^{52} +(-0.900969 - 0.433884i) q^{55} +(-0.702749 + 3.07894i) q^{56} +(0.0546039 + 0.728639i) q^{59} +(-1.19158 - 1.49419i) q^{62} +(0.955573 + 0.294755i) q^{63} +(1.83189 - 2.29711i) q^{64} +(0.603718 - 0.411608i) q^{65} +(2.38980 - 4.13925i) q^{68} +(1.57906 + 1.07659i) q^{70} +(-0.425270 + 1.86323i) q^{71} +(-2.31507 - 2.14807i) q^{72} +(-1.63402 - 0.246289i) q^{73} +(-0.500000 - 0.866025i) q^{77} +(-1.69158 - 2.92990i) q^{80} +(-0.733052 + 0.680173i) q^{81} +(-0.623490 + 0.781831i) q^{83} +(-1.12349 - 1.40881i) q^{85} +(-3.61168 - 1.11406i) q^{86} +(0.236007 + 3.14929i) q^{88} +(-0.722521 - 1.84095i) q^{89} +(-1.72188 + 0.829215i) q^{90} +0.730682 q^{91} +(0.698220 + 1.77904i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2695\mathbb{Z}\right)^\times$.

$n$	$981$	$1816$	$2157$
$\chi(n)$	$-1$	$e\left(\frac{4}{21}\right)$	$-1$

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 $

$2$	−1.88980	+	0.284841i	−1.88980	+	0.284841i	−0.988831	−	0.149042i	$-0.952381\pi$
$2$	−1.88980	+	0.284841i	−1.88980	+	0.284841i	−0.900969	+	0.433884i	$0.857143\pi$
$3$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$3$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$4$	2.53464	−	0.781831i	2.53464	−	0.781831i
$5$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$5$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$6$		0			0
$7$	0.623490	−	0.781831i	0.623490	−	0.781831i
$7$	0.623490	−	0.781831i	0.623490	−	0.781831i
$8$	−2.84537	+	1.37026i	−2.84537	+	1.37026i
$9$	0.365341	+	0.930874i	0.365341	+	0.930874i
$10$	0.142820	+	1.90580i	0.142820	+	1.90580i
$11$	0.365341	−	0.930874i	0.365341	−	0.930874i
$11$	0.365341	−	0.930874i	0.365341	−	0.930874i
$12$		0			0
$13$	0.455573	+	0.571270i	0.455573	+	0.571270i	0.955573	−	0.294755i	$-0.0952381\pi$
$13$	0.455573	+	0.571270i	0.455573	+	0.571270i	−0.500000	+	0.866025i	$0.666667\pi$
$14$	−0.955573	+	1.65510i	−0.955573	+	1.65510i
$15$		0			0
$16$	2.79530	−	1.90580i	2.79530	−	1.90580i
$17$	1.32091	−	1.22563i	1.32091	−	1.22563i	0.365341	−	0.930874i	$-0.380952\pi$
$17$	1.32091	−	1.22563i	1.32091	−	1.22563i	0.955573	−	0.294755i	$-0.0952381\pi$
$18$	−0.955573	−	1.65510i	−0.955573	−	1.65510i
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$	−0.590232	−	2.58597i	−0.590232	−	2.58597i
$21$		0			0
$22$	−0.425270	+	1.86323i	−0.425270	+	1.86323i
$23$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$23$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$24$		0			0
$25$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$26$	−1.02366	−	0.949820i	−1.02366	−	0.949820i
$27$		0			0
$28$	0.969059	−	2.46912i	0.969059	−	2.46912i
$29$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$29$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$30$		0			0
$31$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$31$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$32$	−2.42463	+	2.24973i	−2.42463	+	2.24973i
$33$		0			0
$34$	−2.14715	+	2.69244i	−2.14715	+	2.69244i
$35$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$36$	1.65379	+	2.07379i	1.65379	+	2.07379i
$37$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$37$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$38$		0			0
$39$		0			0
$40$	1.15379	+	2.93982i	1.15379	+	2.93982i
$41$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$41$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$42$		0			0
$43$	1.78181	+	0.858075i	1.78181	+	0.858075i	0.955573	+	0.294755i	$0.0952381\pi$
$43$	1.78181	+	0.858075i	1.78181	+	0.858075i	0.826239	+	0.563320i	$0.190476\pi$
$44$	0.198220	−	2.64506i	0.198220	−	2.64506i
$45$	0.955573	−	0.294755i	0.955573	−	0.294755i
$46$		0			0
$47$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$47$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$48$		0			0
$49$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$50$	1.91115			1.91115
$51$		0			0
$52$	1.60135	+	1.09178i	1.60135	+	1.09178i
$53$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$53$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$54$		0			0
$55$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$56$	−0.702749	+	3.07894i	−0.702749	+	3.07894i
$57$		0			0
$58$		0			0
$59$	0.0546039	+	0.728639i	0.0546039	+	0.728639i	0.955573	+	0.294755i	$0.0952381\pi$
$59$	0.0546039	+	0.728639i	0.0546039	+	0.728639i	−0.900969	+	0.433884i	$0.857143\pi$
$60$		0			0
$61$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$61$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$62$	−1.19158	−	1.49419i	−1.19158	−	1.49419i
$63$	0.955573	+	0.294755i	0.955573	+	0.294755i
$64$	1.83189	−	2.29711i	1.83189	−	2.29711i
$65$	0.603718	−	0.411608i	0.603718	−	0.411608i
$66$		0			0
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$	2.38980	−	4.13925i	2.38980	−	4.13925i
$69$		0			0
$70$	1.57906	+	1.07659i	1.57906	+	1.07659i
$71$	−0.425270	+	1.86323i	−0.425270	+	1.86323i	0.0747301	+	0.997204i	$0.476190\pi$
$71$	−0.425270	+	1.86323i	−0.425270	+	1.86323i	−0.500000	+	0.866025i	$0.666667\pi$
$72$	−2.31507	−	2.14807i	−2.31507	−	2.14807i
$73$	−1.63402	−	0.246289i	−1.63402	−	0.246289i	−0.733052	−	0.680173i	$-0.761905\pi$
$73$	−1.63402	−	0.246289i	−1.63402	−	0.246289i	−0.900969	+	0.433884i	$0.857143\pi$
$74$		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	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$	−1.69158	−	2.92990i	−1.69158	−	2.92990i
$81$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$82$		0			0
$83$	−0.623490	+	0.781831i	−0.623490	+	0.781831i	−0.988831	−	0.149042i	$-0.952381\pi$
$83$	−0.623490	+	0.781831i	−0.623490	+	0.781831i	0.365341	+	0.930874i	$0.380952\pi$
$84$		0			0
$85$	−1.12349	−	1.40881i	−1.12349	−	1.40881i
$86$	−3.61168	−	1.11406i	−3.61168	−	1.11406i
$87$		0			0
$88$	0.236007	+	3.14929i	0.236007	+	3.14929i
$89$	−0.722521	−	1.84095i	−0.722521	−	1.84095i	−0.500000	−	0.866025i	$-0.666667\pi$
$89$	−0.722521	−	1.84095i	−0.722521	−	1.84095i	−0.222521	−	0.974928i	$-0.571429\pi$
$90$	−1.72188	+	0.829215i	−1.72188	+	0.829215i
$91$	0.730682			0.730682
$92$		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			$\pi$
$98$	0.698220	+	1.77904i	0.698220	+	1.77904i
$99$	1.00000			1.00000
$100$	−2.62285	+	0.395331i	−2.62285	+	0.395331i
$101$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$101$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$102$		0			0
$103$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$103$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$104$	−2.07906	−	1.00122i	−2.07906	−	1.00122i
$105$		0			0
$106$		0			0
$107$	−0.162592	−	0.414278i	−0.162592	−	0.414278i	0.826239	−	0.563320i	$-0.190476\pi$
$107$	−0.162592	−	0.414278i	−0.162592	−	0.414278i	−0.988831	+	0.149042i	$0.952381\pi$
$108$		0			0
$109$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$109$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$110$	1.82624	+	0.563320i	1.82624	+	0.563320i
$111$		0			0
$112$	0.252824	−	3.37370i	0.252824	−	3.37370i
$113$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$113$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.365341	+	0.632789i	−0.365341	+	0.632789i
$118$	−0.310737	−	1.36143i	−0.310737	−	1.36143i
$119$	−0.134659	−	1.79690i	−0.134659	−	1.79690i
$120$		0			0
$121$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$122$		0			0
$123$		0			0
$124$	1.94440	+	1.80414i	1.94440	+	1.80414i
$125$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$126$	−1.88980	−	0.284841i	−1.88980	−	0.284841i
$127$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	1.00000			$0$
$127$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	−0.900969	+	0.433884i	$0.857143\pi$
$128$	−1.15379	+	1.99843i	−1.15379	+	1.99843i
$129$		0			0
$130$	−1.02366	+	0.949820i	−1.02366	+	0.949820i
$131$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$131$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−2.07906	+	5.29737i	−2.07906	+	5.29737i
$137$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$137$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$138$		0			0
$139$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$139$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$140$	−2.38980	−	1.15087i	−2.38980	−	1.15087i
$141$		0			0
$142$	0.272950	−	3.64226i	0.272950	−	3.64226i
$143$	0.698220	−	0.215372i	0.698220	−	0.215372i
$144$	2.79530	+	1.90580i	2.79530	+	1.90580i
$145$		0			0
$146$	3.15813			3.15813
$147$		0			0
$148$		0			0
$149$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$149$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$150$		0			0
$151$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$151$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$152$		0			0
$153$	1.62349	+	0.781831i	1.62349	+	0.781831i
$154$	1.19158	+	1.49419i	1.19158	+	1.49419i
$155$	0.900969	−	0.433884i	0.900969	−	0.433884i
$156$		0			0
$157$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$157$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$158$		0			0
$159$		0			0
$160$	2.06225	+	2.58597i	2.06225	+	2.58597i
$161$		0			0
$162$	1.19158	−	1.49419i	1.19158	−	1.49419i
$163$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$163$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$164$		0			0
$165$		0			0
$166$	0.955573	−	1.65510i	0.955573	−	1.65510i
$167$	−0.445042	−	1.94986i	−0.445042	−	1.94986i	−0.222521	−	0.974928i	$-0.571429\pi$
$167$	−0.445042	−	1.94986i	−0.445042	−	1.94986i	−0.222521	−	0.974928i	$-0.571429\pi$
$168$		0			0
$169$	0.103718	−	0.454418i	0.103718	−	0.454418i
$170$	2.52446	+	2.34236i	2.52446	+	2.34236i
$171$		0			0
$172$	5.18711	+	0.781831i	5.18711	+	0.781831i
$173$	1.07473	+	0.997204i	1.07473	+	0.997204i	1.00000			$0$
$173$	1.07473	+	0.997204i	1.07473	+	0.997204i	0.0747301	+	0.997204i	$0.476190\pi$
$174$		0			0
$175$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$176$	−0.752824	−	3.29834i	−0.752824	−	3.29834i
$177$		0			0
$178$	1.88980	+	3.27323i	1.88980	+	3.27323i
$179$	−1.40097	+	1.29991i	−1.40097	+	1.29991i	−0.500000	+	0.866025i	$0.666667\pi$
$179$	−1.40097	+	1.29991i	−1.40097	+	1.29991i	−0.900969	+	0.433884i	$0.857143\pi$
$180$	2.19158	−	1.49419i	2.19158	−	1.49419i
$181$	1.03030	−	1.29196i	1.03030	−	1.29196i	0.0747301	−	0.997204i	$-0.476190\pi$
$181$	1.03030	−	1.29196i	1.03030	−	1.29196i	0.955573	−	0.294755i	$-0.0952381\pi$
$182$	−1.38084	+	0.208129i	−1.38084	+	0.208129i
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.658322	−	1.67738i	−0.658322	−	1.67738i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i	0.826239	+	0.563320i	$0.190476\pi$
$191$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i	−0.900969	+	0.433884i	$0.857143\pi$
$192$		0			0
$193$	−1.48883	−	1.01507i	−1.48883	−	1.01507i	−0.988831	−	0.149042i	$-0.952381\pi$
$193$	−1.48883	−	1.01507i	−1.48883	−	1.01507i	−0.500000	−	0.866025i	$-0.666667\pi$
$194$		0			0
$195$		0			0
$196$	−1.32624	−	2.29711i	−1.32624	−	2.29711i
$197$	−1.46610			−1.46610			−0.733052	−	0.680173i	$-0.761905\pi$
$197$	−1.46610			−1.46610			−0.733052	+	0.680173i	$0.761905\pi$
$198$	−1.88980	+	0.284841i	−1.88980	+	0.284841i
$199$	−1.21135	−	0.825886i	−1.21135	−	0.825886i	−0.222521	−	0.974928i	$-0.571429\pi$
$199$	−1.21135	−	0.825886i	−1.21135	−	0.825886i	−0.988831	+	0.149042i	$0.952381\pi$
$200$	3.01782	−	0.930874i	3.01782	−	0.930874i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$	2.36219	+	0.728639i	2.36219	+	0.728639i
$209$		0			0
$210$		0			0
$211$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$211$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$212$		0			0
$213$		0			0
$214$	0.425270	+	0.736589i	0.425270	+	0.736589i
$215$	0.988831	−	1.71271i	0.988831	−	1.71271i
$216$		0			0
$217$	0.988831	+	0.149042i	0.988831	+	0.149042i
$218$		0			0
$219$		0			0
$220$	−2.62285	−	0.395331i	−2.62285	−	0.395331i
$221$	1.30194	+	0.196236i	1.30194	+	0.196236i
$222$		0			0
$223$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$223$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$224$	0.247176	+	3.29834i	0.247176	+	3.29834i
$225$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$226$		0			0
$227$	−0.0747301	−	0.129436i	−0.0747301	−	0.129436i	0.826239	−	0.563320i	$-0.190476\pi$
$227$	−0.0747301	−	0.129436i	−0.0747301	−	0.129436i	−0.900969	+	0.433884i	$0.857143\pi$
$228$		0			0
$229$	1.57906	−	1.07659i	1.57906	−	1.07659i	0.623490	−	0.781831i	$-0.285714\pi$
$229$	1.57906	−	1.07659i	1.57906	−	1.07659i	0.955573	−	0.294755i	$-0.0952381\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.91115	+	0.589510i	1.91115	+	0.589510i	0.955573	+	0.294755i	$0.0952381\pi$
$233$	1.91115	+	0.589510i	1.91115	+	0.589510i	0.955573	+	0.294755i	$0.0952381\pi$
$234$	0.510177	−	1.29991i	0.510177	−	1.29991i
$235$		0			0
$236$	0.708074	+	1.80414i	0.708074	+	1.80414i
$237$		0			0
$238$	0.766310	+	3.35742i	0.766310	+	3.35742i
$239$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$239$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$240$		0			0
$241$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$241$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$242$	1.57906	+	1.07659i	1.57906	+	1.07659i
$243$		0			0
$244$		0			0
$245$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$246$		0			0
$247$		0			0
$248$	−2.60937	−	1.77904i	−2.60937	−	1.77904i
$249$		0			0
$250$	0.142820	−	1.90580i	0.142820	−	1.90580i
$251$	0.400969	+	0.193096i	0.400969	+	0.193096i	0.623490	−	0.781831i	$-0.285714\pi$
$251$	0.400969	+	0.193096i	0.400969	+	0.193096i	−0.222521	+	0.974928i	$0.571429\pi$
$252$	2.65248			2.65248
$253$		0			0
$254$	−0.310737	−	0.791745i	−0.310737	−	0.791745i
$255$		0			0
$256$	0.537787	−	1.37026i	0.537787	−	1.37026i
$257$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$257$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$258$		0			0
$259$		0			0
$260$	1.20840	−	1.51528i	1.20840	−	1.51528i
$261$		0			0
$262$		0			0
$263$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$263$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.78181	+	0.268565i	1.78181	+	0.268565i	0.955573	−	0.294755i	$-0.0952381\pi$
$269$	1.78181	+	0.268565i	1.78181	+	0.268565i	0.826239	+	0.563320i	$0.190476\pi$
$270$		0			0
$271$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$271$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$272$	1.35654	−	5.94340i	1.35654	−	5.94340i
$273$		0			0
$274$		0			0
$275$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$276$		0			0
$277$	−1.21135	+	1.12397i	−1.21135	+	1.12397i	−0.222521	+	0.974928i	$0.571429\pi$
$277$	−1.21135	+	1.12397i	−1.21135	+	1.12397i	−0.988831	+	0.149042i	$0.952381\pi$
$278$		0			0
$279$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$280$	3.01782	+	0.930874i	3.01782	+	0.930874i
$281$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$281$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$282$		0			0
$283$	0.455573	−	1.16078i	0.455573	−	1.16078i	−0.500000	−	0.866025i	$-0.666667\pi$
$283$	0.455573	−	1.16078i	0.455573	−	1.16078i	0.955573	−	0.294755i	$-0.0952381\pi$
$284$	0.378827	+	5.05510i	0.378827	+	5.05510i
$285$		0			0
$286$	−1.25815	+	0.605893i	−1.25815	+	0.605893i
$287$		0			0
$288$	−2.98003	−	1.43511i	−2.98003	−	1.43511i
$289$	0.167917	−	2.24070i	0.167917	−	2.24070i
$290$		0			0
$291$		0			0
$292$	−4.33420	+	0.653276i	−4.33420	+	0.653276i
$293$	0.149460			0.149460			0.0747301	−	0.997204i	$-0.476190\pi$
$293$	0.149460			0.149460			0.0747301	+	0.997204i	$0.476190\pi$
$294$		0			0
$295$	0.730682			0.730682
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	1.78181	−	0.858075i	1.78181	−	0.858075i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$	−3.29077	−	1.01507i	−3.29077	−	1.01507i
$307$	1.19158	+	1.49419i	1.19158	+	1.49419i	0.826239	+	0.563320i	$0.190476\pi$
$307$	1.19158	+	1.49419i	1.19158	+	1.49419i	0.365341	+	0.930874i	$0.380952\pi$
$308$	−1.94440	−	1.80414i	−1.94440	−	1.80414i
$309$		0			0
$310$	−1.57906	+	1.07659i	−1.57906	+	1.07659i
$311$	−0.109562	+	0.101659i	−0.109562	+	0.101659i	−0.733052	−	0.680173i	$-0.761905\pi$
$311$	−0.109562	+	0.101659i	−0.109562	+	0.101659i	0.623490	+	0.781831i	$0.285714\pi$
$312$		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
$315$	0.365341	−	0.930874i	0.365341	−	0.930874i
$316$		0			0
$317$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$317$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$318$		0			0
$319$		0			0
$320$	−2.15379	−	1.99843i	−2.15379	−	1.99843i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−1.32624	+	2.29711i	−1.32624	+	2.29711i
$325$	−0.365341	−	0.632789i	−0.365341	−	0.632789i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.88980	−	0.582926i	−1.88980	−	0.582926i	−0.988831	−	0.149042i	$-0.952381\pi$
$331$	−1.88980	−	0.582926i	−1.88980	−	0.582926i	−0.900969	−	0.433884i	$-0.857143\pi$
$332$	−0.969059	+	2.46912i	−0.969059	+	2.46912i
$333$		0			0
$334$	1.39644	+	3.55807i	1.39644	+	3.55807i
$335$		0			0
$336$		0			0
$337$	−0.658322	−	0.317031i	−0.658322	−	0.317031i	0.0747301	−	0.997204i	$-0.476190\pi$
$337$	−0.658322	−	0.317031i	−0.658322	−	0.317031i	−0.733052	+	0.680173i	$0.761905\pi$
$338$	−0.0665690	+	0.888301i	−0.0665690	+	0.888301i
$339$		0			0
$340$	−3.94909	−	2.69244i	−3.94909	−	2.69244i
$341$	0.988831	−	0.149042i	0.988831	−	0.149042i
$342$		0			0
$343$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$344$	−6.24570			−6.24570
$345$		0			0
$346$	−2.31507	−	1.57839i	−2.31507	−	1.57839i
$347$	−1.40097	+	0.432142i	−1.40097	+	0.432142i	−0.900969	−	0.433884i	$-0.857143\pi$
$347$	−1.40097	+	0.432142i	−1.40097	+	0.432142i	−0.500000	+	0.866025i	$0.666667\pi$
$348$		0			0
$349$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$349$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$350$	1.19158	−	1.49419i	1.19158	−	1.49419i
$351$		0			0
$352$	1.20840	+	3.07894i	1.20840	+	3.07894i
$353$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$353$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$354$		0			0
$355$	1.82624	+	0.563320i	1.82624	+	0.563320i
$356$	−3.27064	−	4.10126i	−3.27064	−	4.10126i
$357$		0			0
$358$	2.27728	−	2.85562i	2.27728	−	2.85562i
$359$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$359$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$360$	−2.31507	+	2.14807i	−2.31507	+	2.14807i
$361$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$362$	−1.57906	+	2.73502i	−1.57906	+	2.73502i
$363$		0			0
$364$	1.85201	−	0.571270i	1.85201	−	0.571270i
$365$	−0.367711	+	1.61105i	−0.367711	+	1.61105i
$366$		0			0
$367$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$367$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−0.0747301	+	0.129436i	−0.0747301	+	0.129436i	−0.900969	−	0.433884i	$-0.857143\pi$
$373$	−0.0747301	+	0.129436i	−0.0747301	+	0.129436i	0.826239	+	0.563320i	$0.190476\pi$
$374$	1.72188	+	2.98239i	1.72188	+	2.98239i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.0931869	+	0.116853i	0.0931869	+	0.116853i	0.826239	−	0.563320i	$-0.190476\pi$
$379$	0.0931869	+	0.116853i	0.0931869	+	0.116853i	−0.733052	+	0.680173i	$0.761905\pi$
$380$		0			0
$381$		0			0
$382$	−0.142820	−	1.90580i	−0.142820	−	1.90580i
$383$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$383$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$384$		0			0
$385$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$386$	3.10273	+	1.49419i	3.10273	+	1.49419i
$387$	−0.147791	+	1.97213i	−0.147791	+	1.97213i
$388$		0			0
$389$	0.123490	+	0.0841939i	0.123490	+	0.0841939i	0.623490	−	0.781831i	$-0.285714\pi$
$389$	0.123490	+	0.0841939i	0.123490	+	0.0841939i	−0.500000	+	0.866025i	$0.666667\pi$
$390$		0			0
$391$		0			0
$392$	1.96906	+	2.46912i	1.96906	+	2.46912i
$393$		0			0
$394$	2.77064	−	0.417607i	2.77064	−	0.417607i
$395$		0			0
$396$	2.53464	−	0.781831i	2.53464	−	0.781831i
$397$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$397$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$398$	2.52446	+	1.21572i	2.52446	+	1.21572i
$399$		0			0
$400$	−3.04812	+	1.46790i	−3.04812	+	1.46790i
$401$	−0.722521	−	1.84095i	−0.722521	−	1.84095i	−0.500000	−	0.866025i	$-0.666667\pi$
$401$	−0.722521	−	1.84095i	−0.722521	−	1.84095i	−0.222521	−	0.974928i	$-0.571429\pi$
$402$		0			0
$403$	−0.266948	+	0.680173i	−0.266948	+	0.680173i
$404$		0			0
$405$	0.623490	+	0.781831i	0.623490	+	0.781831i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$409$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.603718	+	0.411608i	0.603718	+	0.411608i
$414$		0			0
$415$	0.733052	+	0.680173i	0.733052	+	0.680173i
$416$	−2.38980	−	0.360204i	−2.38980	−	0.360204i
$417$		0			0
$418$		0			0
$419$	−0.162592	+	0.712362i	−0.162592	+	0.712362i	0.826239	+	0.563320i	$0.190476\pi$
$419$	−0.162592	+	0.712362i	−0.162592	+	0.712362i	−0.988831	+	0.149042i	$0.952381\pi$
$420$		0			0
$421$	0.400969	+	1.75676i	0.400969	+	1.75676i	0.623490	+	0.781831i	$0.285714\pi$
$421$	0.400969	+	1.75676i	0.400969	+	1.75676i	−0.222521	+	0.974928i	$0.571429\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.48883	+	1.01507i	−1.48883	+	1.01507i
$426$		0			0
$427$		0			0
$428$	−0.736007	−	0.922924i	−0.736007	−	0.922924i
$429$		0			0
$430$	−1.38084	+	3.51833i	−1.38084	+	3.51833i
$431$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$431$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$432$		0			0
$433$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$433$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$434$	−1.91115			−1.91115
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$439$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$440$	3.15813			3.15813
$441$	0.826239	−	0.563320i	0.826239	−	0.563320i
$442$	−2.51630			−2.51630
$443$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$443$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$444$		0			0
$445$	−1.88980	+	0.582926i	−1.88980	+	0.582926i
$446$		0			0
$447$		0			0
$448$	−0.653793	−	2.86445i	−0.653793	−	2.86445i
$449$	−0.658322	+	0.317031i	−0.658322	+	0.317031i	−0.733052	−	0.680173i	$-0.761905\pi$
$449$	−0.658322	+	0.317031i	−0.658322	+	0.317031i	0.0747301	+	0.997204i	$0.476190\pi$
$450$	0.698220	+	1.77904i	0.698220	+	1.77904i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.178094	+	0.223322i	0.178094	+	0.223322i
$455$	0.0546039	−	0.728639i	0.0546039	−	0.728639i
$456$		0			0
$457$	−0.826239	+	0.563320i	−0.826239	+	0.563320i	−0.900969	−	0.433884i	$-0.857143\pi$
$457$	−0.826239	+	0.563320i	−0.826239	+	0.563320i	0.0747301	+	0.997204i	$0.476190\pi$
$458$	−2.67746	+	2.48432i	−2.67746	+	2.48432i
$459$		0			0
$460$		0			0
$461$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$461$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$462$		0			0
$463$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$463$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$464$		0			0
$465$		0			0
$466$	−3.77960	−	0.569683i	−3.77960	−	0.569683i
$467$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$467$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$468$	−0.431272	+	1.88953i	−0.431272	+	1.88953i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−1.15379	−	1.99843i	−1.15379	−	1.99843i
$473$	1.44973	−	1.34515i	1.44973	−	1.34515i
$474$		0			0
$475$		0			0
$476$	−1.74618	−	4.44920i	−1.74618	−	4.44920i
$477$		0			0
$478$		0			0
$479$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$479$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−2.38980	−	1.15087i	−2.38980	−	1.15087i
$485$		0			0
$486$		0			0
$487$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$487$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$488$		0			0
$489$		0			0
$490$	1.82624	−	0.563320i	1.82624	−	0.563320i
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$496$	3.04812	+	1.46790i	3.04812	+	1.46790i
$497$	1.19158	+	1.49419i	1.19158	+	1.49419i
$498$		0			0
$499$	−0.722521	−	1.84095i	−0.722521	−	1.84095i	−0.500000	−	0.866025i	$-0.666667\pi$
$499$	−0.722521	−	1.84095i	−0.722521	−	1.84095i	−0.222521	−	0.974928i	$-0.571429\pi$
$500$	0.198220	+	2.64506i	0.198220	+	2.64506i
$501$		0			0
$502$	−0.812753	−	0.250701i	−0.812753	−	0.250701i
$503$	−0.623490	−	0.781831i	−0.623490	−	0.781831i	0.365341	−	0.930874i	$-0.380952\pi$
$503$	−0.623490	−	0.781831i	−0.623490	−	0.781831i	−0.988831	+	0.149042i	$0.952381\pi$
$504$	−3.12285	+	0.470694i	−3.12285	+	0.470694i
$505$		0			0
$506$		0			0
$507$		0			0
$508$	0.590232	+	1.02231i	0.590232	+	1.02231i
$509$	−0.0747301	+	0.129436i	−0.0747301	+	0.129436i	−0.900969	−	0.433884i	$-0.857143\pi$
$509$	−0.0747301	+	0.129436i	−0.0747301	+	0.129436i	0.826239	+	0.563320i	$0.190476\pi$
$510$		0			0
$511$	−1.21135	+	1.12397i	−1.21135	+	1.12397i
$512$	−0.112517	+	0.492970i	−0.112517	+	0.492970i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−1.15379	+	1.99843i	−1.15379	+	1.99843i
$521$	−0.955573	−	1.65510i	−0.955573	−	1.65510i	−0.733052	−	0.680173i	$-0.761905\pi$
$521$	−0.955573	−	1.65510i	−0.955573	−	1.65510i	−0.222521	−	0.974928i	$-0.571429\pi$
$522$		0			0
$523$	−1.63402	+	1.11406i	−1.63402	+	1.11406i	−0.733052	+	0.680173i	$0.761905\pi$
$523$	−1.63402	+	1.11406i	−1.63402	+	1.11406i	−0.900969	+	0.433884i	$0.857143\pi$
$524$		0			0
$525$		0			0
$526$	−1.19158	−	1.49419i	−1.19158	−	1.49419i
$527$	1.72188	+	0.531130i	1.72188	+	0.531130i
$528$		0			0
$529$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$530$		0			0
$531$	−0.658322	+	0.317031i	−0.658322	+	0.317031i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−0.425270	+	0.131178i	−0.425270	+	0.131178i
$536$		0			0
$537$		0			0
$538$	−3.44377			−3.44377
$539$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$540$		0			0
$541$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$541$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$542$		0			0
$543$		0			0
$544$	−0.445396	+	5.94340i	−0.445396	+	5.94340i
$545$		0			0
$546$		0			0
$547$	−1.48883	+	0.716983i	−1.48883	+	0.716983i	−0.988831	−	0.149042i	$-0.952381\pi$
$547$	−1.48883	+	0.716983i	−1.48883	+	0.716983i	−0.500000	+	0.866025i	$0.666667\pi$
$548$		0			0
$549$		0			0
$550$	0.698220	−	1.77904i	0.698220	−	1.77904i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	1.96906	−	2.46912i	1.96906	−	2.46912i
$555$		0			0
$556$		0			0
$557$	−0.623490	−	1.07992i	−0.623490	−	1.07992i	−0.988831	−	0.149042i	$-0.952381\pi$
$557$	−0.623490	−	1.07992i	−0.623490	−	1.07992i	0.365341	−	0.930874i	$-0.380952\pi$
$558$	0.955573	−	1.65510i	0.955573	−	1.65510i
$559$	0.321552	+	1.40881i	0.321552	+	1.40881i
$560$	−3.34537	−	0.504234i	−3.34537	−	0.504234i
$561$		0			0
$562$		0			0
$563$	1.44973	+	0.218511i	1.44973	+	0.218511i	0.826239	−	0.563320i	$-0.190476\pi$
$563$	1.44973	+	0.218511i	1.44973	+	0.218511i	0.623490	+	0.781831i	$0.285714\pi$
$564$		0			0
$565$		0			0
$566$	−0.530303	+	2.32341i	−0.530303	+	2.32341i
$567$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$568$	−1.34306	−	5.88431i	−1.34306	−	5.88431i
$569$		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		0.733052	−	0.680173i	$-0.238095\pi$
$571$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$572$	1.60135	−	1.09178i	1.60135	−	1.09178i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	2.80759	+	0.866025i	2.80759	+	0.866025i
$577$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$577$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$578$	0.320914	+	4.28230i	0.320914	+	4.28230i
$579$		0			0
$580$		0			0
$581$	0.222521	+	0.974928i	0.222521	+	0.974928i
$582$		0			0
$583$		0			0
$584$	4.98688	−	1.53825i	4.98688	−	1.53825i
$585$	0.603718	+	0.411608i	0.603718	+	0.411608i
$586$	−0.282450	+	0.0425725i	−0.282450	+	0.0425725i
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$		0			0
$589$		0			0
$590$	−1.38084	+	0.208129i	−1.38084	+	0.208129i
$591$		0			0
$592$		0			0
$593$	−0.147791	+	1.97213i	−0.147791	+	1.97213i	0.0747301	+	0.997204i	$0.476190\pi$
$593$	−0.147791	+	1.97213i	−0.147791	+	1.97213i	−0.222521	+	0.974928i	$0.571429\pi$
$594$		0			0
$595$	−1.80194			−1.80194
$596$		0			0
$597$		0			0
$598$		0			0
$599$	0.0546039	−	0.139129i	0.0546039	−	0.139129i	−0.900969	−	0.433884i	$-0.857143\pi$
$599$	0.0546039	−	0.139129i	0.0546039	−	0.139129i	0.955573	+	0.294755i	$0.0952381\pi$
$600$		0			0
$601$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$601$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$602$	−3.12285	+	2.12912i	−3.12285	+	2.12912i
$603$		0			0
$604$		0			0
$605$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$606$		0			0
$607$	−0.0747301	+	0.129436i	−0.0747301	+	0.129436i	−0.900969	−	0.433884i	$-0.857143\pi$
$607$	−0.0747301	+	0.129436i	−0.0747301	+	0.129436i	0.826239	+	0.563320i	$0.190476\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	4.72622	+	0.712362i	4.72622	+	0.712362i
$613$	1.44973	+	0.218511i	1.44973	+	0.218511i	0.826239	−	0.563320i	$-0.190476\pi$
$613$	1.44973	+	0.218511i	1.44973	+	0.218511i	0.623490	+	0.781831i	$0.285714\pi$
$614$	−2.67746	−	2.48432i	−2.67746	−	2.48432i
$615$		0			0
$616$	2.60937	+	1.77904i	2.60937	+	1.77904i
$617$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$617$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$618$		0			0
$619$	−0.623490	−	1.07992i	−0.623490	−	1.07992i	−0.988831	−	0.149042i	$-0.952381\pi$
$619$	−0.623490	−	1.07992i	−0.623490	−	1.07992i	0.365341	−	0.930874i	$-0.380952\pi$
$620$	1.94440	−	1.80414i	1.94440	−	1.80414i
$621$		0			0
$622$	0.178094	−	0.223322i	0.178094	−	0.223322i
$623$	−1.88980	−	0.582926i	−1.88980	−	0.582926i
$624$		0			0
$625$	0.955573	+	0.294755i	0.955573	+	0.294755i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−0.425270	+	1.86323i	−0.425270	+	1.86323i
$631$	1.32091	+	0.636119i	1.32091	+	0.636119i	0.955573	−	0.294755i	$-0.0952381\pi$
$631$	1.32091	+	0.636119i	1.32091	+	0.636119i	0.365341	+	0.930874i	$0.380952\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.440071	−	0.0663300i	0.440071	−	0.0663300i
$636$		0			0
$637$	0.455573	−	0.571270i	0.455573	−	0.571270i
$638$		0			0
$639$	−1.88980	+	0.284841i	−1.88980	+	0.284841i
$640$	1.90662	+	1.29991i	1.90662	+	1.29991i
$641$	−0.425270	+	0.131178i	−0.425270	+	0.131178i	−0.500000	−	0.866025i	$-0.666667\pi$
$641$	−0.425270	+	0.131178i	−0.425270	+	0.131178i	0.0747301	+	0.997204i	$0.476190\pi$
$642$		0			0
$643$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$643$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$647$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$648$	1.15379	−	2.93982i	1.15379	−	2.93982i
$649$	0.698220	+	0.215372i	0.698220	+	0.215372i
$650$	0.870666	+	1.09178i	0.870666	+	1.09178i
$651$		0			0
$652$		0			0
$653$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$653$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−0.367711	−	1.61105i	−0.367711	−	1.61105i
$658$		0			0
$659$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$659$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$660$		0			0
$661$	0.440071	+	0.0663300i	0.440071	+	0.0663300i	0.365341	−	0.930874i	$-0.380952\pi$
$661$	0.440071	+	0.0663300i	0.440071	+	0.0663300i	0.0747301	+	0.997204i	$0.476190\pi$
$662$	3.73738	+	0.563320i	3.73738	+	0.563320i
$663$		0			0
$664$	0.702749	−	3.07894i	0.702749	−	3.07894i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−2.65248	−	4.59423i	−2.65248	−	4.59423i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.623490	−	0.781831i	−0.623490	−	0.781831i	0.365341	−	0.930874i	$-0.380952\pi$
$673$	−0.623490	−	0.781831i	−0.623490	−	0.781831i	−0.988831	+	0.149042i	$0.952381\pi$
$674$	1.33440	+	0.411608i	1.33440	+	0.411608i
$675$		0			0
$676$	−0.0923910	−	1.23287i	−0.0923910	−	1.23287i
$677$	0.455573	+	1.16078i	0.455573	+	1.16078i	0.955573	+	0.294755i	$0.0952381\pi$
$677$	0.455573	+	1.16078i	0.455573	+	1.16078i	−0.500000	+	0.866025i	$0.666667\pi$
$678$		0			0
$679$		0			0
$680$	5.12718	+	2.46912i	5.12718	+	2.46912i
$681$		0			0
$682$	−1.82624	+	0.563320i	−1.82624	+	0.563320i
$683$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$683$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$684$		0			0
$685$		0			0
$686$	1.82624	+	0.563320i	1.82624	+	0.563320i
$687$		0			0
$688$	6.61601	−	0.997204i	6.61601	−	0.997204i
$689$		0			0
$690$		0			0
$691$	−0.134659	+	1.79690i	−0.134659	+	1.79690i	0.365341	+	0.930874i	$0.380952\pi$
$691$	−0.134659	+	1.79690i	−0.134659	+	1.79690i	−0.500000	+	0.866025i	$0.666667\pi$
$692$	3.50369	+	1.68729i	3.50369	+	1.68729i
$693$	0.623490	−	0.781831i	0.623490	−	0.781831i
$694$	2.52446	−	1.21572i	2.52446	−	1.21572i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−1.32624	+	2.29711i	−1.32624	+	2.29711i
$701$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$701$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$702$		0			0
$703$		0			0
$704$	−1.46906	−	2.54448i	−1.46906	−	2.54448i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.733052	+	0.680173i	0.733052	+	0.680173i	0.955573	−	0.294755i	$-0.0952381\pi$
$709$	0.733052	+	0.680173i	0.733052	+	0.680173i	−0.222521	+	0.974928i	$0.571429\pi$
$710$	−3.61168	−	0.544374i	−3.61168	−	0.544374i
$711$		0			0
$712$	4.57842	+	4.24816i	4.57842	+	4.24816i
$713$		0			0
$714$		0			0
$715$	−0.162592	−	0.712362i	−0.162592	−	0.712362i
$716$	−2.53464	+	4.39012i	−2.53464	+	4.39012i
$717$		0			0
$718$		0			0
$719$	−1.48883	+	1.01507i	−1.48883	+	1.01507i	−0.500000	+	0.866025i	$0.666667\pi$
$719$	−1.48883	+	1.01507i	−1.48883	+	1.01507i	−0.988831	+	0.149042i	$0.952381\pi$
$720$	2.10937	−	2.64506i	2.10937	−	2.64506i
$721$		0			0
$722$	1.19158	+	1.49419i	1.19158	+	1.49419i
$723$		0			0
$724$	1.60135	−	4.08017i	1.60135	−	4.08017i
$725$		0			0
$726$		0			0
$727$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$727$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$728$	−2.07906	+	1.00122i	−2.07906	+	1.00122i
$729$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$730$	0.236007	−	3.14929i	0.236007	−	3.14929i
$731$	3.40530	−	1.05040i	3.40530	−	1.05040i
$732$		0			0
$733$	0.440071	−	0.0663300i	0.440071	−	0.0663300i	0.0747301	−	0.997204i	$-0.476190\pi$
$733$	0.440071	−	0.0663300i	0.440071	−	0.0663300i	0.365341	+	0.930874i	$0.380952\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$739$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.658322	+	0.317031i	−0.658322	+	0.317031i	−0.733052	−	0.680173i	$-0.761905\pi$
$743$	−0.658322	+	0.317031i	−0.658322	+	0.317031i	0.0747301	+	0.997204i	$0.476190\pi$
$744$		0			0
$745$		0			0
$746$	0.104356	−	0.265895i	0.104356	−	0.265895i
$747$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$748$	−2.98003	−	3.73684i	−2.98003	−	3.73684i
$749$	−0.425270	−	0.131178i	−0.425270	−	0.131178i
$750$		0			0
$751$	1.36534	−	0.930874i	1.36534	−	0.930874i	0.365341	−	0.930874i	$-0.380952\pi$
$751$	1.36534	−	0.930874i	1.36534	−	0.930874i	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	$-0.428571\pi$
$757$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$758$	−0.209389	−	0.194285i	−0.209389	−	0.194285i
$759$		0			0
$760$		0			0
$761$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$761$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$762$		0			0
$763$		0			0
$764$	0.590232	+	2.58597i	0.590232	+	2.58597i
$765$	0.900969	−	1.56052i	0.900969	−	1.56052i
$766$		0			0
$767$	−0.391374	+	0.363142i	−0.391374	+	0.363142i
$768$		0			0
$769$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$769$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$770$	1.57906	−	1.07659i	1.57906	−	1.07659i
$771$		0			0
$772$	−4.56726	−	1.40881i	−4.56726	−	1.40881i
$773$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$773$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$774$	−0.282450	−	3.76903i	−0.282450	−	3.76903i
$775$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$776$		0			0
$777$		0			0
$778$	−0.257353	−	0.123935i	−0.257353	−	0.123935i
$779$		0			0
$780$		0			0
$781$	1.57906	+	1.07659i	1.57906	+	1.07659i
$782$		0			0
$783$		0			0
$784$	−2.48003	−	2.30113i	−2.48003	−	2.30113i
$785$		0			0
$786$		0			0
$787$	−1.21135	−	0.825886i	−1.21135	−	0.825886i	−0.222521	−	0.974928i	$-0.571429\pi$
$787$	−1.21135	−	0.825886i	−1.21135	−	0.825886i	−0.988831	+	0.149042i	$0.952381\pi$
$788$	−3.71604	+	1.14625i	−3.71604	+	1.14625i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−2.84537	+	1.37026i	−2.84537	+	1.37026i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−3.71604	−	1.14625i	−3.71604	−	1.14625i
$797$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$797$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$798$		0			0
$799$		0			0
$800$	2.73286	−	1.86323i	2.73286	−	1.86323i
$801$	1.44973	−	1.34515i	1.44973	−	1.34515i
$802$	1.88980	+	3.27323i	1.88980	+	3.27323i
$803$	−0.826239	+	1.43109i	−0.826239	+	1.43109i
$804$		0			0
$805$		0			0
$806$	0.310737	−	1.36143i	0.310737	−	1.36143i
$807$		0			0
$808$		0			0
$809$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$809$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$810$	−1.40097	−	1.29991i	−1.40097	−	1.29991i
$811$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$811$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	0.266948	+	0.680173i	0.266948	+	0.680173i
$820$		0			0
$821$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$821$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$822$		0			0
$823$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$823$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$824$		0			0
$825$		0			0
$826$	−1.25815	−	0.605893i	−1.25815	−	0.605893i
$827$	1.62349	+	0.781831i	1.62349	+	0.781831i	1.00000			$0$
$827$	1.62349	+	0.781831i	1.62349	+	0.781831i	0.623490	+	0.781831i	$0.285714\pi$
$828$		0			0
$829$	0.698220	−	0.215372i	0.698220	−	0.215372i	0.0747301	−	0.997204i	$-0.476190\pi$
$829$	0.698220	−	0.215372i	0.698220	−	0.215372i	0.623490	+	0.781831i	$0.285714\pi$
$830$	−1.57906	−	1.07659i	−1.57906	−	1.07659i
$831$		0			0
$832$	2.14683			2.14683
$833$	−1.48883	−	1.01507i	−1.48883	−	1.01507i
$834$		0			0
$835$	−1.97766	+	0.298085i	−1.97766	+	0.298085i
$836$		0			0
$837$		0			0
$838$	0.104356	−	1.39254i	0.104356	−	1.39254i
$839$	1.62349	+	0.781831i	1.62349	+	0.781831i	1.00000			$0$
$839$	1.62349	+	0.781831i	1.62349	+	0.781831i	0.623490	+	0.781831i	$0.285714\pi$
$840$		0			0
$841$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$842$	−1.25815	−	3.20571i	−1.25815	−	3.20571i
$843$		0			0
$844$		0			0
$845$	−0.445396	−	0.137386i	−0.445396	−	0.137386i
$846$		0			0
$847$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$848$		0			0
$849$		0			0
$850$	2.52446	−	2.34236i	2.52446	−	2.34236i
$851$		0			0
$852$		0			0
$853$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	1.00000			$0$
$853$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	−0.900969	+	0.433884i	$0.857143\pi$
$854$		0			0
$855$		0			0
$856$	1.03030	+	0.955981i	1.03030	+	0.955981i
$857$	−1.88980	−	0.284841i	−1.88980	−	0.284841i	−0.900969	−	0.433884i	$-0.857143\pi$
$857$	−1.88980	−	0.284841i	−1.88980	−	0.284841i	−0.988831	+	0.149042i	$0.952381\pi$
$858$		0			0
$859$	1.32091	+	1.22563i	1.32091	+	1.22563i	0.955573	+	0.294755i	$0.0952381\pi$
$859$	1.32091	+	1.22563i	1.32091	+	1.22563i	0.365341	+	0.930874i	$0.380952\pi$
$860$	1.16728	−	5.11418i	1.16728	−	5.11418i
$861$		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
$865$	1.07473	−	0.997204i	1.07473	−	0.997204i
$866$		0			0
$867$		0			0
$868$	2.62285	−	0.395331i	2.62285	−	0.395331i
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.623490	+	0.781831i	0.623490	+	0.781831i
$876$		0			0
$877$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i	0.826239	+	0.563320i	$0.190476\pi$
$877$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i	−0.900969	+	0.433884i	$0.857143\pi$
$878$		0			0
$879$		0			0
$880$	−3.34537	+	0.504234i	−3.34537	+	0.504234i
$881$	−1.46610			−1.46610			−0.733052	−	0.680173i	$-0.761905\pi$
$881$	−1.46610			−1.46610			−0.733052	+	0.680173i	$0.761905\pi$
$882$	−1.40097	+	1.29991i	−1.40097	+	1.29991i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$	3.45336	−	0.520510i	3.45336	−	0.520510i
$885$		0			0
$886$		0			0
$887$	0.123490	−	1.64786i	0.123490	−	1.64786i	−0.500000	−	0.866025i	$-0.666667\pi$
$887$	0.123490	−	1.64786i	0.123490	−	1.64786i	0.623490	−	0.781831i	$-0.285714\pi$
$888$		0			0
$889$	0.400969	+	0.193096i	0.400969	+	0.193096i
$890$	3.40530	−	1.63991i	3.40530	−	1.63991i
$891$	0.365341	+	0.930874i	0.365341	+	0.930874i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	1.19158	+	1.49419i	1.19158	+	1.49419i
$896$	0.843056	+	2.14807i	0.843056	+	2.14807i
$897$		0			0
$898$	1.15379	−	0.786643i	1.15379	−	0.786643i
$899$		0			0
$900$	−1.32624	−	2.29711i	−1.32624	−	2.29711i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.21135	−	1.12397i	−1.21135	−	1.12397i
$906$		0			0
$907$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$907$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$908$	−0.290611	−	0.269648i	−0.290611	−	0.269648i
$909$		0			0
$910$	0.104356	+	1.39254i	0.104356	+	1.39254i
$911$	0.326239	+	1.42935i	0.326239	+	1.42935i	0.826239	+	0.563320i	$0.190476\pi$
$911$	0.326239	+	1.42935i	0.326239	+	1.42935i	−0.500000	+	0.866025i	$0.666667\pi$
$912$		0			0
$913$	0.500000	+	0.866025i	0.500000	+	0.866025i
$914$	1.40097	−	1.29991i	1.40097	−	1.29991i
$915$		0			0
$916$	3.16064	−	3.96332i	3.16064	−	3.96332i
$917$		0			0
$918$		0			0
$919$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$919$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−1.25815	+	0.605893i	−1.25815	+	0.605893i
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.440071	−	0.0663300i	0.440071	−	0.0663300i	0.0747301	−	0.997204i	$-0.476190\pi$
$929$	0.440071	−	0.0663300i	0.440071	−	0.0663300i	0.365341	+	0.930874i	$0.380952\pi$
$930$		0			0
$931$		0			0
$932$	5.30496			5.30496
$933$		0			0
$934$		0			0
$935$	−1.72188	+	0.531130i	−1.72188	+	0.531130i
$936$	0.172446	−	2.30113i	0.172446	−	2.30113i
$937$	−0.658322	−	0.317031i	−0.658322	−	0.317031i	0.0747301	−	0.997204i	$-0.476190\pi$
$937$	−0.658322	−	0.317031i	−0.658322	−	0.317031i	−0.733052	+	0.680173i	$0.761905\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$941$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$942$		0			0
$943$		0			0
$944$	1.54128	+	1.93270i	1.54128	+	1.93270i
$945$		0			0
$946$	−2.35654	+	2.95501i	−2.35654	+	2.95501i
$947$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$947$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$948$		0			0
$949$	−0.603718	−	1.04567i	−0.603718	−	1.04567i
$950$		0			0
$951$		0			0
$952$	2.84537	+	4.92833i	2.84537	+	4.92833i
$953$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$953$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$954$		0			0
$955$	0.988831	+	0.149042i	0.988831	+	0.149042i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$		0			0
$962$		0			0
$963$	0.326239	−	0.302705i	0.326239	−	0.302705i
$964$		0			0
$965$	−1.12349	+	1.40881i	−1.12349	+	1.40881i
$966$		0			0
$967$	1.03030	+	1.29196i	1.03030	+	1.29196i	0.955573	+	0.294755i	$0.0952381\pi$
$967$	1.03030	+	1.29196i	1.03030	+	1.29196i	0.0747301	+	0.997204i	$0.476190\pi$
$968$	3.01782	+	0.930874i	3.01782	+	0.930874i
$969$		0			0
$970$		0			0
$971$	−0.535628	−	1.36476i	−0.535628	−	1.36476i	−0.900969	−	0.433884i	$-0.857143\pi$
$971$	−0.535628	−	1.36476i	−0.535628	−	1.36476i	0.365341	−	0.930874i	$-0.380952\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$977$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$978$		0			0
$979$	−1.97766			−1.97766
$980$	−2.38980	+	1.15087i	−2.38980	+	1.15087i
$981$		0			0
$982$		0			0
$983$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$983$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$984$		0			0
$985$	−0.109562	+	1.46200i	−0.109562	+	1.46200i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	0.142820	+	1.90580i	0.142820	+	1.90580i
$991$	−0.658322	+	1.67738i	−0.658322	+	1.67738i	0.0747301	+	0.997204i	$0.476190\pi$
$991$	−0.658322	+	1.67738i	−0.658322	+	1.67738i	−0.733052	+	0.680173i	$0.761905\pi$
$992$	−3.16064	−	0.974928i	−3.16064	−	0.974928i
$993$		0			0
$994$	−2.67746	−	2.48432i	−2.67746	−	2.48432i
$995$	−0.914101	+	1.14625i	−0.914101	+	1.14625i
$996$		0			0
$997$	1.44973	−	1.34515i	1.44973	−	1.34515i	0.623490	−	0.781831i	$-0.285714\pi$
$997$	1.44973	−	1.34515i	1.44973	−	1.34515i	0.826239	−	0.563320i	$-0.190476\pi$
$998$	1.88980	+	3.27323i	1.88980	+	3.27323i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.1.ck.a.1759.1	yes	12
5.4	even	2		2695.1.ck.b.1759.1	yes	12
11.10	odd	2		2695.1.ck.b.1759.1	yes	12
49.39	even	21	inner	2695.1.ck.a.1264.1	✓	12
55.54	odd	2	CM	2695.1.ck.a.1759.1	yes	12
245.39	even	42		2695.1.ck.b.1264.1	yes	12
539.186	odd	42		2695.1.ck.b.1264.1	yes	12
2695.1264	odd	42	inner	2695.1.ck.a.1264.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2695.1.ck.a.1264.1	✓	12	49.39	even	21	inner
2695.1.ck.a.1264.1	✓	12	2695.1264	odd	42	inner
2695.1.ck.a.1759.1	yes	12	1.1	even	1	trivial
2695.1.ck.a.1759.1	yes	12	55.54	odd	2	CM
2695.1.ck.b.1264.1	yes	12	245.39	even	42
2695.1.ck.b.1264.1	yes	12	539.186	odd	42
2695.1.ck.b.1759.1	yes	12	5.4	even	2
2695.1.ck.b.1759.1	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)

\(f(q)\)	\(=\)	\(q+(-1.88980 + 0.284841i) q^{2} +(2.53464 - 0.781831i) q^{4} +(0.0747301 - 0.997204i) q^{5} +(0.623490 - 0.781831i) q^{7} +(-2.84537 + 1.37026i) q^{8} +(0.365341 + 0.930874i) q^{9} +O(q^{10})\)	\(q+(-1.88980 + 0.284841i) q^{2} +(2.53464 - 0.781831i) q^{4} +(0.0747301 - 0.997204i) q^{5} +(0.623490 - 0.781831i) q^{7} +(-2.84537 + 1.37026i) q^{8} +(0.365341 + 0.930874i) q^{9} +(0.142820 + 1.90580i) q^{10} +(0.365341 - 0.930874i) q^{11} +(0.455573 + 0.571270i) q^{13} +(-0.955573 + 1.65510i) q^{14} +(2.79530 - 1.90580i) q^{16} +(1.32091 - 1.22563i) q^{17} +(-0.955573 - 1.65510i) q^{18} +(-0.590232 - 2.58597i) q^{20} +(-0.425270 + 1.86323i) q^{22} +(-0.988831 - 0.149042i) q^{25} +(-1.02366 - 0.949820i) q^{26} +(0.969059 - 2.46912i) q^{28} +(0.500000 + 0.866025i) q^{31} +(-2.42463 + 2.24973i) q^{32} +(-2.14715 + 2.69244i) q^{34} +(-0.733052 - 0.680173i) q^{35} +(1.65379 + 2.07379i) q^{36} +(1.15379 + 2.93982i) q^{40} +(1.78181 + 0.858075i) q^{43} +(0.198220 - 2.64506i) q^{44} +(0.955573 - 0.294755i) q^{45} +(-0.222521 - 0.974928i) q^{49} +1.91115 q^{50} +(1.60135 + 1.09178i) q^{52} +(-0.900969 - 0.433884i) q^{55} +(-0.702749 + 3.07894i) q^{56} +(0.0546039 + 0.728639i) q^{59} +(-1.19158 - 1.49419i) q^{62} +(0.955573 + 0.294755i) q^{63} +(1.83189 - 2.29711i) q^{64} +(0.603718 - 0.411608i) q^{65} +(2.38980 - 4.13925i) q^{68} +(1.57906 + 1.07659i) q^{70} +(-0.425270 + 1.86323i) q^{71} +(-2.31507 - 2.14807i) q^{72} +(-1.63402 - 0.246289i) q^{73} +(-0.500000 - 0.866025i) q^{77} +(-1.69158 - 2.92990i) q^{80} +(-0.733052 + 0.680173i) q^{81} +(-0.623490 + 0.781831i) q^{83} +(-1.12349 - 1.40881i) q^{85} +(-3.61168 - 1.11406i) q^{86} +(0.236007 + 3.14929i) q^{88} +(-0.722521 - 1.84095i) q^{89} +(-1.72188 + 0.829215i) q^{90} +0.730682 q^{91} +(0.698220 + 1.77904i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} + q^{5} - 2 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) 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

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