LMFDB - Embedded newform 2695.1.ck.c.1759.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.34498020905$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{42})$
Coefficient field:	$\Q(\zeta_{84})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} + x^{22} - x^{18} - x^{16} + x^{12} - x^{8} - x^{6} + x^{2} + 1 $ x^24 + x^22 - x^18 - x^16 + x^12 - x^8 - x^6 + x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{42}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{42} - \cdots)$

Embedding invariants

Embedding label			1759.2
Root			$0.997204 + 0.0747301i$ of defining polynomial
Character	$\chi$	$=$	2695.1759
Dual form			2695.1.ck.c.1264.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.582926 - 0.0878620i) q^{2} +(-0.623490 + 0.192321i) q^{4} +(-0.0747301 + 0.997204i) q^{5} +(0.781831 + 0.623490i) q^{7} +(-0.877681 + 0.422669i) q^{8} +(0.365341 + 0.930874i) q^{9} +(0.0440542 + 0.587862i) q^{10} +(-0.365341 + 0.930874i) q^{11} +(-1.16078 - 1.45557i) q^{13} +(0.510531 + 0.294755i) q^{14} +(0.0646156 - 0.0440542i) q^{16} +(-0.636119 + 0.590232i) q^{17} +(0.294755 + 0.510531i) q^{18} +(-0.145190 - 0.636119i) q^{20} +(-0.131178 + 0.574730i) q^{22} +(-0.988831 - 0.149042i) q^{25} +(-0.804539 - 0.746503i) q^{26} +(-0.607374 - 0.238377i) q^{28} +(-0.500000 - 0.866025i) q^{31} +(0.747900 - 0.693950i) q^{32} +(-0.318951 + 0.399952i) q^{34} +(-0.680173 + 0.733052i) q^{35} +(-0.406813 - 0.510127i) q^{36} +(-0.355898 - 0.906813i) q^{40} +(-0.268565 - 0.129334i) q^{43} +(0.0487597 - 0.650653i) q^{44} +(-0.955573 + 0.294755i) q^{45} +(0.222521 + 0.974928i) q^{49} -0.589510 q^{50} +(1.00367 + 0.684292i) q^{52} +(-0.900969 - 0.433884i) q^{55} +(-0.949729 - 0.216769i) q^{56} +(0.0546039 + 0.728639i) q^{59} +(-0.367554 - 0.460898i) q^{62} +(-0.294755 + 0.955573i) q^{63} +(0.326239 - 0.409090i) q^{64} +(1.53825 - 1.04876i) q^{65} +(0.283099 - 0.490343i) q^{68} +(-0.332083 + 0.487076i) q^{70} +(-0.425270 + 1.86323i) q^{71} +(-0.714104 - 0.662592i) q^{72} +(1.11406 + 0.167917i) q^{73} +(-0.866025 + 0.500000i) q^{77} +(0.0391023 + 0.0677271i) q^{80} +(-0.733052 + 0.680173i) q^{81} +(1.07992 - 1.35417i) q^{83} +(-0.541044 - 0.678448i) q^{85} +(-0.167917 - 0.0517955i) q^{86} +(-0.0727985 - 0.971429i) q^{88} +(0.722521 + 1.84095i) q^{89} +(-0.531130 + 0.255779i) q^{90} -1.86175i q^{91} +(0.215372 + 0.548760i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4} - 2 q^{5} + 2 q^{9} - 2 q^{11} - 6 q^{14} - 26 q^{16} + 8 q^{20} + 2 q^{25} + 6 q^{26} - 12 q^{31} - 14 q^{34} - 8 q^{36} - 18 q^{44} - 2 q^{45} + 4 q^{49} - 4 q^{55} + 14 q^{56} - 2 q^{59}+ \cdots - 24 q^{99}+O(q^{100}) $ 24 * q + 4 * q^4 - 2 * q^5 + 2 * q^9 - 2 * q^11 - 6 * q^14 - 26 * q^16 + 8 * q^20 + 2 * q^25 + 6 * q^26 - 12 * q^31 - 14 * q^34 - 8 * q^36 - 18 * q^44 - 2 * q^45 + 4 * q^49 - 4 * q^55 + 14 * q^56 - 2 * q^59 - 10 * q^64 - 6 * q^70 - 10 * q^71 + 12 * q^80 + 2 * q^81 - 6 * q^86 + 16 * q^89 - 24 * q^99

Character values

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

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

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 $

$2$	0.582926	−	0.0878620i	0.582926	−	0.0878620i	0.149042	−	0.988831i	$-0.452381\pi$
$2$	0.582926	−	0.0878620i	0.582926	−	0.0878620i	0.433884	+	0.900969i	$0.357143\pi$
$3$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$3$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$4$	−0.623490	+	0.192321i	−0.623490	+	0.192321i
$5$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$5$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$6$		0			0
$7$	0.781831	+	0.623490i	0.781831	+	0.623490i
$7$	0.781831	+	0.623490i	0.781831	+	0.623490i
$8$	−0.877681	+	0.422669i	−0.877681	+	0.422669i
$9$	0.365341	+	0.930874i	0.365341	+	0.930874i
$10$	0.0440542	+	0.587862i	0.0440542	+	0.587862i
$11$	−0.365341	+	0.930874i	−0.365341	+	0.930874i
$11$	−0.365341	+	0.930874i	−0.365341	+	0.930874i
$12$		0			0
$13$	−1.16078	−	1.45557i	−1.16078	−	1.45557i	−0.866025	−	0.500000i	$-0.833333\pi$
$13$	−1.16078	−	1.45557i	−1.16078	−	1.45557i	−0.294755	−	0.955573i	$-0.595238\pi$
$14$	0.510531	+	0.294755i	0.510531	+	0.294755i
$15$		0			0
$16$	0.0646156	−	0.0440542i	0.0646156	−	0.0440542i
$17$	−0.636119	+	0.590232i	−0.636119	+	0.590232i	−0.930874	−	0.365341i	$-0.880952\pi$
$17$	−0.636119	+	0.590232i	−0.636119	+	0.590232i	0.294755	+	0.955573i	$0.404762\pi$
$18$	0.294755	+	0.510531i	0.294755	+	0.510531i
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$	−0.145190	−	0.636119i	−0.145190	−	0.636119i
$21$		0			0
$22$	−0.131178	+	0.574730i	−0.131178	+	0.574730i
$23$		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
$26$	−0.804539	−	0.746503i	−0.804539	−	0.746503i
$27$		0			0
$28$	−0.607374	−	0.238377i	−0.607374	−	0.238377i
$29$		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	0.500000	−	0.866025i	$-0.333333\pi$
$31$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$32$	0.747900	−	0.693950i	0.747900	−	0.693950i
$33$		0			0
$34$	−0.318951	+	0.399952i	−0.318951	+	0.399952i
$35$	−0.680173	+	0.733052i	−0.680173	+	0.733052i
$36$	−0.406813	−	0.510127i	−0.406813	−	0.510127i
$37$		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
$40$	−0.355898	−	0.906813i	−0.355898	−	0.906813i
$41$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$41$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$42$		0			0
$43$	−0.268565	−	0.129334i	−0.268565	−	0.129334i	0.294755	−	0.955573i	$-0.404762\pi$
$43$	−0.268565	−	0.129334i	−0.268565	−	0.129334i	−0.563320	+	0.826239i	$0.690476\pi$
$44$	0.0487597	−	0.650653i	0.0487597	−	0.650653i
$45$	−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
$50$	−0.589510			−0.589510
$51$		0			0
$52$	1.00367	+	0.684292i	1.00367	+	0.684292i
$53$		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
$56$	−0.949729	−	0.216769i	−0.949729	−	0.216769i
$57$		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	$0.0952381\pi$
$62$	−0.367554	−	0.460898i	−0.367554	−	0.460898i
$63$	−0.294755	+	0.955573i	−0.294755	+	0.955573i
$64$	0.326239	−	0.409090i	0.326239	−	0.409090i
$65$	1.53825	−	1.04876i	1.53825	−	1.04876i
$66$		0			0
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$	0.283099	−	0.490343i	0.283099	−	0.490343i
$69$		0			0
$70$	−0.332083	+	0.487076i	−0.332083	+	0.487076i
$71$	−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	$0.666667\pi$
$72$	−0.714104	−	0.662592i	−0.714104	−	0.662592i
$73$	1.11406	+	0.167917i	1.11406	+	0.167917i	0.680173	−	0.733052i	$-0.261905\pi$
$73$	1.11406	+	0.167917i	1.11406	+	0.167917i	0.433884	+	0.900969i	$0.357143\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$78$		0			0
$79$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$	0.0391023	+	0.0677271i	0.0391023	+	0.0677271i
$81$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$82$		0			0
$83$	1.07992	−	1.35417i	1.07992	−	1.35417i	0.149042	−	0.988831i	$-0.452381\pi$
$83$	1.07992	−	1.35417i	1.07992	−	1.35417i	0.930874	−	0.365341i	$-0.119048\pi$
$84$		0			0
$85$	−0.541044	−	0.678448i	−0.541044	−	0.678448i
$86$	−0.167917	−	0.0517955i	−0.167917	−	0.0517955i
$87$		0			0
$88$	−0.0727985	−	0.971429i	−0.0727985	−	0.971429i
$89$	0.722521	+	1.84095i	0.722521	+	1.84095i	0.500000	+	0.866025i	$0.333333\pi$
$89$	0.722521	+	1.84095i	0.722521	+	1.84095i	0.222521	+	0.974928i	$0.428571\pi$
$90$	−0.531130	+	0.255779i	−0.531130	+	0.255779i
$91$		−	1.86175i		−	1.86175i
$92$		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			$\pi$
$98$	0.215372	+	0.548760i	0.215372	+	0.548760i
$99$	−1.00000			−1.00000
$100$	0.645190	−	0.0972467i	0.645190	−	0.0972467i
$101$		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	$0.523810\pi$
$104$	1.63402	+	0.786903i	1.63402	+	0.786903i
$105$		0			0
$106$		0			0
$107$	0.712362	+	1.81507i	0.712362	+	1.81507i	0.563320	+	0.826239i	$0.309524\pi$
$107$	0.712362	+	1.81507i	0.712362	+	1.81507i	0.149042	+	0.988831i	$0.452381\pi$
$108$		0			0
$109$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$109$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$110$	−0.563320	−	0.173761i	−0.563320	−	0.173761i
$111$		0			0
$112$	0.0779858	+	0.00584423i	0.0779858	+	0.00584423i
$113$		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
$117$	0.930874	−	1.61232i	0.930874	−	1.61232i
$118$	0.0958497	+	0.419945i	0.0958497	+	0.419945i
$119$	−0.865341	+	0.0648483i	−0.865341	+	0.0648483i
$120$		0			0
$121$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$122$		0			0
$123$		0			0
$124$	0.478300	+	0.443797i	0.478300	+	0.443797i
$125$	0.222521	−	0.974928i	0.222521	−	0.974928i
$126$	−0.0878620	+	0.582926i	−0.0878620	+	0.582926i
$127$	0.433884	+	1.90097i	0.433884	+	1.90097i	0.433884	+	0.900969i	$0.357143\pi$
$127$	0.433884	+	1.90097i	0.433884	+	1.90097i			1.00000i	$0.500000\pi$
$128$	−0.355898	+	0.616433i	−0.355898	+	0.616433i
$129$		0			0
$130$	0.804539	−	0.746503i	0.804539	−	0.746503i
$131$		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
$136$	0.308837	−	0.786903i	0.308837	−	0.786903i
$137$		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	$0.857143\pi$
$140$	0.283099	−	0.587862i	0.283099	−	0.587862i
$141$		0			0
$142$	−0.0841939	+	1.12349i	−0.0841939	+	1.12349i
$143$	1.77904	−	0.548760i	1.77904	−	0.548760i
$144$	0.0646156	+	0.0440542i	0.0646156	+	0.0440542i
$145$		0			0
$146$	0.664166			0.664166
$147$		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
$153$	−0.781831	−	0.376510i	−0.781831	−	0.376510i
$154$	−0.460898	+	0.367554i	−0.460898	+	0.367554i
$155$	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
$160$	0.636119	+	0.797667i	0.636119	+	0.797667i
$161$		0			0
$162$	−0.367554	+	0.460898i	−0.367554	+	0.460898i
$163$		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
$166$	0.510531	−	0.884266i	0.510531	−	0.884266i
$167$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$167$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$168$		0			0
$169$	−0.548760	+	2.40427i	−0.548760	+	2.40427i
$170$	−0.374998	−	0.347948i	−0.374998	−	0.347948i
$171$		0			0
$172$	0.192321	+	0.0289877i	0.192321	+	0.0289877i
$173$	0.997204	+	0.925270i	0.997204	+	0.925270i	0.997204	−	0.0747301i	$-0.0238095\pi$
$173$	0.997204	+	0.925270i	0.997204	+	0.925270i			1.00000i	$0.5\pi$
$174$		0			0
$175$	−0.680173	−	0.733052i	−0.680173	−	0.733052i
$176$	0.0174021	+	0.0762438i	0.0174021	+	0.0762438i
$177$		0			0
$178$	0.582926	+	1.00966i	0.582926	+	1.00966i
$179$	1.40097	−	1.29991i	1.40097	−	1.29991i	0.500000	−	0.866025i	$-0.333333\pi$
$179$	1.40097	−	1.29991i	1.40097	−	1.29991i	0.900969	−	0.433884i	$-0.142857\pi$
$180$	0.539102	−	0.367554i	0.539102	−	0.367554i
$181$	−1.03030	+	1.29196i	−1.03030	+	1.29196i	−0.0747301	+	0.997204i	$0.523810\pi$
$181$	−1.03030	+	1.29196i	−1.03030	+	1.29196i	−0.955573	+	0.294755i	$0.904762\pi$
$182$	−0.163577	−	1.08526i	−0.163577	−	1.08526i
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.317031	−	0.807782i	−0.317031	−	0.807782i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.0747301	−	0.997204i	0.0747301	−	0.997204i	−0.826239	−	0.563320i	$-0.809524\pi$
$191$	0.0747301	−	0.997204i	0.0747301	−	0.997204i	0.900969	−	0.433884i	$-0.142857\pi$
$192$		0			0
$193$	0.716983	+	0.488831i	0.716983	+	0.488831i	0.866025	−	0.500000i	$-0.166667\pi$
$193$	0.716983	+	0.488831i	0.716983	+	0.488831i	−0.149042	+	0.988831i	$0.547619\pi$
$194$		0			0
$195$		0			0
$196$	−0.326239	−	0.565062i	−0.326239	−	0.565062i
$197$	−1.36035			−1.36035			−0.680173	−	0.733052i	$-0.738095\pi$
$197$	−1.36035			−1.36035			−0.680173	+	0.733052i	$0.738095\pi$
$198$	−0.582926	+	0.0878620i	−0.582926	+	0.0878620i
$199$	−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	$0.952381\pi$
$200$	0.930874	−	0.287137i	0.930874	−	0.287137i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$	−0.139129	−	0.0429155i	−0.139129	−	0.0429155i
$209$		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
$214$	0.574730	+	0.995462i	0.574730	+	0.995462i
$215$	0.149042	−	0.258149i	0.149042	−	0.258149i
$216$		0			0
$217$	0.149042	−	0.988831i	0.149042	−	0.988831i
$218$		0			0
$219$		0			0
$220$	0.645190	+	0.0972467i	0.645190	+	0.0972467i
$221$	1.59752	+	0.240787i	1.59752	+	0.240787i
$222$		0			0
$223$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$223$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$224$	1.01740	−	0.0762438i	1.01740	−	0.0762438i
$225$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$226$		0			0
$227$	−0.997204	−	1.72721i	−0.997204	−	1.72721i	−0.563320	−	0.826239i	$-0.690476\pi$
$227$	−0.997204	−	1.72721i	−0.997204	−	1.72721i	−0.433884	−	0.900969i	$-0.642857\pi$
$228$		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
$233$		0			0		0.294755	−	0.955573i	$-0.404762\pi$
$233$		0			0		−0.294755	+	0.955573i	$0.595238\pi$
$234$	0.400969	−	1.02165i	0.400969	−	1.02165i
$235$		0			0
$236$	−0.174178	−	0.443797i	−0.174178	−	0.443797i
$237$		0			0
$238$	−0.498732	+	0.113832i	−0.498732	+	0.113832i
$239$		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	$0.904762\pi$
$242$	−0.487076	−	0.332083i	−0.487076	−	0.332083i
$243$		0			0
$244$		0			0
$245$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$246$		0			0
$247$		0			0
$248$	0.804883	+	0.548760i	0.804883	+	0.548760i
$249$		0			0
$250$	0.0440542	−	0.587862i	0.0440542	−	0.587862i
$251$	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	$0.571429\pi$
$252$		−	0.652478i		−	0.652478i
$253$		0			0
$254$	0.419945	+	1.07000i	0.419945	+	1.07000i
$255$		0			0
$256$	−0.344464	+	0.877681i	−0.344464	+	0.877681i
$257$		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
$260$	−0.757383	+	0.949729i	−0.757383	+	0.949729i
$261$		0			0
$262$		0			0
$263$	−0.866025	−	1.50000i	−0.866025	−	1.50000i	−0.866025	−	0.500000i	$-0.833333\pi$
$263$	−0.866025	−	1.50000i	−0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	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	$0.238095\pi$
$272$	−0.0151010	+	0.0661618i	−0.0151010	+	0.0661618i
$273$		0			0
$274$		0			0
$275$	0.500000	−	0.866025i	0.500000	−	0.866025i
$276$		0			0
$277$	0.825886	−	0.766310i	0.825886	−	0.766310i	−0.149042	−	0.988831i	$-0.547619\pi$
$277$	0.825886	−	0.766310i	0.825886	−	0.766310i	0.974928	+	0.222521i	$0.0714286\pi$
$278$		0			0
$279$	0.623490	−	0.781831i	0.623490	−	0.781831i
$280$	0.287137	−	0.930874i	0.287137	−	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
$283$	0.571270	−	1.45557i	0.571270	−	1.45557i	−0.294755	−	0.955573i	$-0.595238\pi$
$283$	0.571270	−	1.45557i	0.571270	−	1.45557i	0.866025	−	0.500000i	$-0.166667\pi$
$284$	−0.0931869	−	1.24349i	−0.0931869	−	1.24349i
$285$		0			0
$286$	0.988831	−	0.476196i	0.988831	−	0.476196i
$287$		0			0
$288$	0.919218	+	0.442672i	0.919218	+	0.442672i
$289$	−0.0184568	+	0.246289i	−0.0184568	+	0.246289i
$290$		0			0
$291$		0			0
$292$	−0.726897	+	0.109562i	−0.726897	+	0.109562i
$293$	−1.99441			−1.99441			−0.997204	−	0.0747301i	$-0.976190\pi$
$293$	−1.99441			−1.99441			−0.997204	+	0.0747301i	$0.976190\pi$
$294$		0			0
$295$	−0.730682			−0.730682
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−0.129334	−	0.268565i	−0.129334	−	0.268565i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$	−0.488831	−	0.150784i	−0.488831	−	0.150784i
$307$	−0.367554	−	0.460898i	−0.367554	−	0.460898i	0.563320	−	0.826239i	$-0.309524\pi$
$307$	−0.367554	−	0.460898i	−0.367554	−	0.460898i	−0.930874	+	0.365341i	$0.880952\pi$
$308$	0.443797	−	0.478300i	0.443797	−	0.478300i
$309$		0			0
$310$	0.487076	−	0.332083i	0.487076	−	0.332083i
$311$	−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
$315$	−0.930874	−	0.365341i	−0.930874	−	0.365341i
$316$		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
$320$	0.383567	+	0.355898i	0.383567	+	0.355898i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.326239	−	0.565062i	0.326239	−	0.565062i
$325$	0.930874	+	1.61232i	0.930874	+	1.61232i
$326$		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	$0.0476190\pi$
$331$	1.88980	+	0.582926i	1.88980	+	0.582926i	0.900969	+	0.433884i	$0.142857\pi$
$332$	−0.412881	+	1.05200i	−0.412881	+	1.05200i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.67738	+	0.807782i	1.67738	+	0.807782i	0.997204	+	0.0747301i	$0.0238095\pi$
$337$	1.67738	+	0.807782i	1.67738	+	0.807782i	0.680173	+	0.733052i	$0.261905\pi$
$338$	−0.108642	+	1.44973i	−0.108642	+	1.44973i
$339$		0			0
$340$	0.467815	+	0.318951i	0.467815	+	0.318951i
$341$	0.988831	−	0.149042i	0.988831	−	0.149042i
$342$		0			0
$343$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$344$	0.290380			0.290380
$345$		0			0
$346$	0.662592	+	0.451748i	0.662592	+	0.451748i
$347$	1.29991	−	0.400969i	1.29991	−	0.400969i	0.433884	−	0.900969i	$-0.357143\pi$
$347$	1.29991	−	0.400969i	1.29991	−	0.400969i	0.866025	+	0.500000i	$0.166667\pi$
$348$		0			0
$349$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$349$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$350$	−0.460898	−	0.367554i	−0.460898	−	0.367554i
$351$		0			0
$352$	0.372741	+	0.949729i	0.372741	+	0.949729i
$353$		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
$356$	−0.804539	−	1.00886i	−0.804539	−	1.00886i
$357$		0			0
$358$	0.702449	−	0.880843i	0.702449	−	0.880843i
$359$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$359$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$360$	0.714104	−	0.662592i	0.714104	−	0.662592i
$361$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$362$	−0.487076	+	0.843641i	−0.487076	+	0.843641i
$363$		0			0
$364$	0.358053	+	1.16078i	0.358053	+	1.16078i
$365$	−0.250701	+	1.09839i	−0.250701	+	1.09839i
$366$		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
$373$	−0.997204	+	1.72721i	−0.997204	+	1.72721i	−0.433884	+	0.900969i	$0.642857\pi$
$373$	−0.997204	+	1.72721i	−0.997204	+	1.72721i	−0.563320	+	0.826239i	$0.690476\pi$
$374$	−0.255779	−	0.443022i	−0.255779	−	0.443022i
$375$		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
$382$	−0.0440542	−	0.587862i	−0.0440542	−	0.587862i
$383$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$383$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$384$		0			0
$385$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$386$	0.460898	+	0.221957i	0.460898	+	0.221957i
$387$	0.0222759	−	0.297251i	0.0222759	−	0.297251i
$388$		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
$392$	−0.607374	−	0.761623i	−0.607374	−	0.761623i
$393$		0			0
$394$	−0.792981	+	0.119523i	−0.792981	+	0.119523i
$395$		0			0
$396$	0.623490	−	0.192321i	0.623490	−	0.192321i
$397$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$397$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$398$	−0.778692	−	0.374998i	−0.778692	−	0.374998i
$399$		0			0
$400$	−0.0704598	+	0.0339317i	−0.0704598	+	0.0339317i
$401$	0.722521	+	1.84095i	0.722521	+	1.84095i	0.500000	+	0.866025i	$0.333333\pi$
$401$	0.722521	+	1.84095i	0.722521	+	1.84095i	0.222521	+	0.974928i	$0.428571\pi$
$402$		0			0
$403$	−0.680173	+	1.73305i	−0.680173	+	1.73305i
$404$		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
$413$	−0.411608	+	0.603718i	−0.411608	+	0.603718i
$414$		0			0
$415$	1.26968	+	1.17809i	1.26968	+	1.17809i
$416$	−1.87824	−	0.283099i	−1.87824	−	0.283099i
$417$		0			0
$418$		0			0
$419$	0.162592	−	0.712362i	0.162592	−	0.712362i	−0.826239	−	0.563320i	$-0.809524\pi$
$419$	0.162592	−	0.712362i	0.162592	−	0.712362i	0.988831	−	0.149042i	$-0.0476190\pi$
$420$		0			0
$421$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	−0.623490	−	0.781831i	$-0.714286\pi$
$421$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	0.222521	−	0.974928i	$-0.428571\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.716983	−	0.488831i	0.716983	−	0.488831i
$426$		0			0
$427$		0			0
$428$	−0.793227	−	0.994675i	−0.793227	−	0.994675i
$429$		0			0
$430$	0.0641992	−	0.163577i	0.0641992	−	0.163577i
$431$		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	$0.857143\pi$
$434$		−	0.589510i		−	0.589510i
$435$		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	$0.952381\pi$
$440$	0.974153			0.974153
$441$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$442$	0.952392			0.952392
$443$		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
$448$	0.510127	−	0.116433i	0.510127	−	0.116433i
$449$	0.658322	−	0.317031i	0.658322	−	0.317031i	−0.0747301	−	0.997204i	$-0.523810\pi$
$449$	0.658322	−	0.317031i	0.658322	−	0.317031i	0.733052	+	0.680173i	$0.238095\pi$
$450$	−0.215372	−	0.548760i	−0.215372	−	0.548760i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−0.733052	−	0.919218i	−0.733052	−	0.919218i
$455$	1.85654	+	0.139129i	1.85654	+	0.139129i
$456$		0			0
$457$	−1.43109	+	0.975699i	−1.43109	+	0.975699i	−0.433884	+	0.900969i	$0.642857\pi$
$457$	−1.43109	+	0.975699i	−1.43109	+	0.975699i	−0.997204	+	0.0747301i	$0.976190\pi$
$458$	0.825886	−	0.766310i	0.825886	−	0.766310i
$459$		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
$466$		0			0
$467$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$467$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$468$	−0.270307	+	1.18429i	−0.270307	+	1.18429i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.355898	−	0.616433i	−0.355898	−	0.616433i
$473$	0.218511	−	0.202749i	0.218511	−	0.202749i
$474$		0			0
$475$		0			0
$476$	0.527060	−	0.206856i	0.527060	−	0.206856i
$477$		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
$484$	0.587862	+	0.283099i	0.587862	+	0.283099i
$485$		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
$490$	−0.563320	+	0.173761i	−0.563320	+	0.173761i
$491$		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
$496$	−0.0704598	−	0.0339317i	−0.0704598	−	0.0339317i
$497$	−1.49419	+	1.19158i	−1.49419	+	1.19158i
$498$		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	$-0.571429\pi$
$500$	0.0487597	+	0.650653i	0.0487597	+	0.650653i
$501$		0			0
$502$	0.250701	+	0.0773310i	0.250701	+	0.0773310i
$503$	−1.07992	−	1.35417i	−1.07992	−	1.35417i	−0.930874	−	0.365341i	$-0.880952\pi$
$503$	−1.07992	−	1.35417i	−1.07992	−	1.35417i	−0.149042	−	0.988831i	$-0.547619\pi$
$504$	−0.145190	−	0.963272i	−0.145190	−	0.963272i
$505$		0			0
$506$		0			0
$507$		0			0
$508$	−0.636119	−	1.10179i	−0.636119	−	1.10179i
$509$	−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
$511$	0.766310	+	0.825886i	0.766310	+	0.825886i
$512$	0.0347070	−	0.152061i	0.0347070	−	0.152061i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−0.906813	+	1.57065i	−0.906813	+	1.57065i
$521$	0.955573	+	1.65510i	0.955573	+	1.65510i	0.733052	+	0.680173i	$0.238095\pi$
$521$	0.955573	+	1.65510i	0.955573	+	1.65510i	0.222521	+	0.974928i	$0.428571\pi$
$522$		0			0
$523$	0.246289	−	0.167917i	0.246289	−	0.167917i	−0.433884	−	0.900969i	$-0.642857\pi$
$523$	0.246289	−	0.167917i	0.246289	−	0.167917i	0.680173	+	0.733052i	$0.261905\pi$
$524$		0			0
$525$		0			0
$526$	−0.636622	−	0.798298i	−0.636622	−	0.798298i
$527$	0.829215	+	0.255779i	0.829215	+	0.255779i
$528$		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
$535$	−1.86323	+	0.574730i	−1.86323	+	0.574730i
$536$		0			0
$537$		0			0
$538$	1.06226			1.06226
$539$	−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
$544$	−0.0661618	+	0.882868i	−0.0661618	+	0.882868i
$545$		0			0
$546$		0			0
$547$	−1.01507	+	0.488831i	−1.01507	+	0.488831i	−0.866025	−	0.500000i	$-0.833333\pi$
$547$	−1.01507	+	0.488831i	−1.01507	+	0.488831i	−0.149042	+	0.988831i	$0.547619\pi$
$548$		0			0
$549$		0			0
$550$	0.215372	−	0.548760i	0.215372	−	0.548760i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	0.414101	−	0.519266i	0.414101	−	0.519266i
$555$		0			0
$556$		0			0
$557$	0.781831	+	1.35417i	0.781831	+	1.35417i	0.930874	+	0.365341i	$0.119048\pi$
$557$	0.781831	+	1.35417i	0.781831	+	1.35417i	−0.149042	+	0.988831i	$0.547619\pi$
$558$	0.294755	−	0.510531i	0.294755	−	0.510531i
$559$	0.123490	+	0.541044i	0.123490	+	0.541044i
$560$	−0.0116558	+	0.0773310i	−0.0116558	+	0.0773310i
$561$		0			0
$562$		0			0
$563$	−1.34515	−	0.202749i	−1.34515	−	0.202749i	−0.563320	−	0.826239i	$-0.690476\pi$
$563$	−1.34515	−	0.202749i	−1.34515	−	0.202749i	−0.781831	+	0.623490i	$0.785714\pi$
$564$		0			0
$565$		0			0
$566$	0.205119	−	0.898684i	0.205119	−	0.898684i
$567$	−0.997204	+	0.0747301i	−0.997204	+	0.0747301i
$568$	−0.414278	−	1.81507i	−0.414278	−	1.81507i
$569$		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	$0.761905\pi$
$572$	−1.00367	+	0.684292i	−1.00367	+	0.684292i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.500000	+	0.154230i	0.500000	+	0.154230i
$577$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$577$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$578$	0.0108805	+	0.145190i	0.0108805	+	0.145190i
$579$		0			0
$580$		0			0
$581$	1.68862	−	0.385418i	1.68862	−	0.385418i
$582$		0			0
$583$		0			0
$584$	−1.04876	+	0.323500i	−1.04876	+	0.323500i
$585$	1.53825	+	1.04876i	1.53825	+	1.04876i
$586$	−1.16259	+	0.175233i	−1.16259	+	0.175233i
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$		0			0
$589$		0			0
$590$	−0.425934	+	0.0641992i	−0.425934	+	0.0641992i
$591$		0			0
$592$		0			0
$593$	0.0222759	−	0.297251i	0.0222759	−	0.297251i	−0.974928	−	0.222521i	$-0.928571\pi$
$593$	0.0222759	−	0.297251i	0.0222759	−	0.297251i	0.997204	−	0.0747301i	$-0.0238095\pi$
$594$		0			0
$595$		−	0.867767i		−	0.867767i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−0.0546039	+	0.139129i	−0.0546039	+	0.139129i	−0.955573	−	0.294755i	$-0.904762\pi$
$599$	−0.0546039	+	0.139129i	−0.0546039	+	0.139129i	0.900969	+	0.433884i	$0.142857\pi$
$600$		0			0
$601$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$601$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$602$	−0.0989888	−	0.145190i	−0.0989888	−	0.145190i
$603$		0			0
$604$		0			0
$605$	0.733052	−	0.680173i	0.733052	−	0.680173i
$606$		0			0
$607$	0.997204	−	1.72721i	0.997204	−	1.72721i	0.433884	−	0.900969i	$-0.357143\pi$
$607$	0.997204	−	1.72721i	0.997204	−	1.72721i	0.563320	−	0.826239i	$-0.309524\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.559875	+	0.0843876i	0.559875	+	0.0843876i
$613$	−1.34515	−	0.202749i	−1.34515	−	0.202749i	−0.563320	−	0.826239i	$-0.690476\pi$
$613$	−1.34515	−	0.202749i	−1.34515	−	0.202749i	−0.781831	+	0.623490i	$0.785714\pi$
$614$	−0.254752	−	0.236375i	−0.254752	−	0.236375i
$615$		0			0
$616$	0.548760	−	0.804883i	0.548760	−	0.804883i
$617$		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	$0.0476190\pi$
$619$	0.623490	+	1.07992i	0.623490	+	1.07992i	−0.365341	+	0.930874i	$0.619048\pi$
$620$	−0.478300	+	0.443797i	−0.478300	+	0.443797i
$621$		0			0
$622$	−0.0549346	+	0.0688859i	−0.0549346	+	0.0688859i
$623$	−0.582926	+	1.88980i	−0.582926	+	1.88980i
$624$		0			0
$625$	0.955573	+	0.294755i	0.955573	+	0.294755i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−0.574730	−	0.131178i	−0.574730	−	0.131178i
$631$	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
$635$	−1.92808	+	0.290611i	−1.92808	+	0.290611i
$636$		0			0
$637$	1.16078	−	1.45557i	1.16078	−	1.45557i
$638$		0			0
$639$	−1.88980	+	0.284841i	−1.88980	+	0.284841i
$640$	−0.588113	−	0.400969i	−0.588113	−	0.400969i
$641$	0.425270	−	0.131178i	0.425270	−	0.131178i	−0.0747301	−	0.997204i	$-0.523810\pi$
$641$	0.425270	−	0.131178i	0.425270	−	0.131178i	0.500000	+	0.866025i	$0.333333\pi$
$642$		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	$0.476190\pi$
$648$	0.355898	−	0.906813i	0.355898	−	0.906813i
$649$	−0.698220	−	0.215372i	−0.698220	−	0.215372i
$650$	0.684292	+	0.858075i	0.684292	+	0.858075i
$651$		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
$657$	0.250701	+	1.09839i	0.250701	+	1.09839i
$658$		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	$0.476190\pi$
$662$	1.15283	+	0.173761i	1.15283	+	0.173761i
$663$		0			0
$664$	−0.375456	+	1.64498i	−0.375456	+	1.64498i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.07992	+	1.35417i	1.07992	+	1.35417i	0.930874	+	0.365341i	$0.119048\pi$
$673$	1.07992	+	1.35417i	1.07992	+	1.35417i	0.149042	+	0.988831i	$0.452381\pi$
$674$	1.04876	+	0.323500i	1.04876	+	0.323500i
$675$		0			0
$676$	−0.120246	−	1.60458i	−0.120246	−	1.60458i
$677$	0.571270	+	1.45557i	0.571270	+	1.45557i	0.866025	+	0.500000i	$0.166667\pi$
$677$	0.571270	+	1.45557i	0.571270	+	1.45557i	−0.294755	+	0.955573i	$0.595238\pi$
$678$		0			0
$679$		0			0
$680$	0.761623	+	0.366778i	0.761623	+	0.366778i
$681$		0			0
$682$	0.563320	−	0.173761i	0.563320	−	0.173761i
$683$		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
$686$	−0.173761	+	0.563320i	−0.173761	+	0.563320i
$687$		0			0
$688$	−0.0230512	+	0.00347441i	−0.0230512	+	0.00347441i
$689$		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	$0.666667\pi$
$692$	−0.799695	−	0.385113i	−0.799695	−	0.385113i
$693$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$694$	0.722521	−	0.347948i	0.722521	−	0.347948i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	0.565062	+	0.326239i	0.565062	+	0.326239i
$701$		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
$704$	0.261623	+	0.453145i	0.261623	+	0.453145i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.733052	−	0.680173i	−0.733052	−	0.680173i	0.222521	−	0.974928i	$-0.428571\pi$
$709$	−0.733052	−	0.680173i	−0.733052	−	0.680173i	−0.955573	+	0.294755i	$0.904762\pi$
$710$	−1.11406	−	0.167917i	−1.11406	−	0.167917i
$711$		0			0
$712$	−1.41226	−	1.31038i	−1.41226	−	1.31038i
$713$		0			0
$714$		0			0
$715$	0.414278	+	1.81507i	0.414278	+	1.81507i
$716$	−0.623490	+	1.07992i	−0.623490	+	1.07992i
$717$		0			0
$718$		0			0
$719$	1.48883	−	1.01507i	1.48883	−	1.01507i	0.500000	−	0.866025i	$-0.333333\pi$
$719$	1.48883	−	1.01507i	1.48883	−	1.01507i	0.988831	−	0.149042i	$-0.0476190\pi$
$720$	−0.0487597	+	0.0611427i	−0.0487597	+	0.0611427i
$721$		0			0
$722$	−0.367554	−	0.460898i	−0.367554	−	0.460898i
$723$		0			0
$724$	0.393912	−	1.00367i	0.393912	−	1.00367i
$725$		0			0
$726$		0			0
$727$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$727$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$728$	0.786903	+	1.63402i	0.786903	+	1.63402i
$729$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$730$	−0.0496332	+	0.662309i	−0.0496332	+	0.662309i
$731$	0.247176	−	0.0762438i	0.247176	−	0.0762438i
$732$		0			0
$733$	1.92808	−	0.290611i	1.92808	−	0.290611i	0.930874	−	0.365341i	$-0.119048\pi$
$733$	1.92808	−	0.290611i	1.92808	−	0.290611i	0.997204	+	0.0747301i	$0.0238095\pi$
$734$		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
$743$	1.67738	−	0.807782i	1.67738	−	0.807782i	0.680173	−	0.733052i	$-0.261905\pi$
$743$	1.67738	−	0.807782i	1.67738	−	0.807782i	0.997204	−	0.0747301i	$-0.0238095\pi$
$744$		0			0
$745$		0			0
$746$	−0.429540	+	1.09445i	−0.429540	+	1.09445i
$747$	1.65510	+	0.510531i	1.65510	+	0.510531i
$748$	0.353019	+	0.442672i	0.353019	+	0.442672i
$749$	−0.574730	+	1.86323i	−0.574730	+	1.86323i
$750$		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	$0.571429\pi$
$758$	0.0645880	+	0.0599289i	0.0645880	+	0.0599289i
$759$		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
$764$	0.145190	+	0.636119i	0.145190	+	0.636119i
$765$	0.433884	−	0.751509i	0.433884	−	0.751509i
$766$		0			0
$767$	0.997204	−	0.925270i	0.997204	−	0.925270i
$768$		0			0
$769$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$769$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$770$	−0.332083	−	0.487076i	−0.332083	−	0.487076i
$771$		0			0
$772$	−0.541044	−	0.166890i	−0.541044	−	0.166890i
$773$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$773$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$774$	−0.0131319	−	0.175233i	−0.0131319	−	0.175233i
$775$	0.365341	+	0.930874i	0.365341	+	0.930874i
$776$		0			0
$777$		0			0
$778$	0.0793829	+	0.0382288i	0.0793829	+	0.0382288i
$779$		0			0
$780$		0			0
$781$	−1.57906	−	1.07659i	−1.57906	−	1.07659i
$782$		0			0
$783$		0			0
$784$	0.0573280	+	0.0531926i	0.0573280	+	0.0531926i
$785$		0			0
$786$		0			0
$787$	−1.12397	−	0.766310i	−1.12397	−	0.766310i	−0.149042	−	0.988831i	$-0.547619\pi$
$787$	−1.12397	−	0.766310i	−1.12397	−	0.766310i	−0.974928	+	0.222521i	$0.928571\pi$
$788$	0.848162	−	0.261623i	0.848162	−	0.261623i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.877681	−	0.422669i	0.877681	−	0.422669i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	0.914101	+	0.281963i	0.914101	+	0.281963i
$797$		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
$800$	−0.842974	+	0.574730i	−0.842974	+	0.574730i
$801$	−1.44973	+	1.34515i	−1.44973	+	1.34515i
$802$	0.582926	+	1.00966i	0.582926	+	1.00966i
$803$	−0.563320	+	0.975699i	−0.563320	+	0.975699i
$804$		0			0
$805$		0			0
$806$	−0.244221	+	1.07000i	−0.244221	+	1.07000i
$807$		0			0
$808$		0			0
$809$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$809$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$810$	−0.432142	−	0.400969i	−0.432142	−	0.400969i
$811$		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
$819$	1.73305	−	0.680173i	1.73305	−	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
$826$	−0.186893	+	0.388088i	−0.186893	+	0.388088i
$827$	−0.781831	−	0.376510i	−0.781831	−	0.376510i		−	1.00000i	$-0.5\pi$
$827$	−0.781831	−	0.376510i	−0.781831	−	0.376510i	−0.781831	+	0.623490i	$0.785714\pi$
$828$		0			0
$829$	−0.698220	+	0.215372i	−0.698220	+	0.215372i	−0.623490	−	0.781831i	$-0.714286\pi$
$829$	−0.698220	+	0.215372i	−0.698220	+	0.215372i	−0.0747301	+	0.997204i	$0.523810\pi$
$830$	0.843641	+	0.575185i	0.843641	+	0.575185i
$831$		0			0
$832$	−0.974153			−0.974153
$833$	−0.716983	−	0.488831i	−0.716983	−	0.488831i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$	0.0321896	−	0.429540i	0.0321896	−	0.429540i
$839$	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
$842$	−0.388088	−	0.988831i	−0.388088	−	0.988831i
$843$		0			0
$844$		0			0
$845$	−2.35654	−	0.726897i	−2.35654	−	0.726897i
$846$		0			0
$847$	−0.149042	−	0.988831i	−0.149042	−	0.988831i
$848$		0			0
$849$		0			0
$850$	0.374998	−	0.347948i	0.374998	−	0.347948i
$851$		0			0
$852$		0			0
$853$	−0.433884	−	1.90097i	−0.433884	−	1.90097i	−0.433884	−	0.900969i	$-0.642857\pi$
$853$	−0.433884	−	1.90097i	−0.433884	−	1.90097i		−	1.00000i	$-0.5\pi$
$854$		0			0
$855$		0			0
$856$	−1.39240	−	1.29196i	−1.39240	−	1.29196i
$857$	0.582926	+	0.0878620i	0.582926	+	0.0878620i	0.433884	−	0.900969i	$-0.357143\pi$
$857$	0.582926	+	0.0878620i	0.582926	+	0.0878620i	0.149042	+	0.988831i	$0.452381\pi$
$858$		0			0
$859$	−1.32091	−	1.22563i	−1.32091	−	1.22563i	−0.955573	−	0.294755i	$-0.904762\pi$
$859$	−1.32091	−	1.22563i	−1.32091	−	1.22563i	−0.365341	−	0.930874i	$-0.619048\pi$
$860$	−0.0432789	+	0.189617i	−0.0432789	+	0.189617i
$861$		0			0
$862$		0			0
$863$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$863$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$864$		0			0
$865$	−0.997204	+	0.925270i	−0.997204	+	0.925270i
$866$		0			0
$867$		0			0
$868$	0.0972467	+	0.645190i	0.0972467	+	0.645190i
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.781831	−	0.623490i	0.781831	−	0.623490i
$876$		0			0
$877$	0.129436	−	1.72721i	0.129436	−	1.72721i	−0.433884	−	0.900969i	$-0.642857\pi$
$877$	0.129436	−	1.72721i	0.129436	−	1.72721i	0.563320	−	0.826239i	$-0.309524\pi$
$878$		0			0
$879$		0			0
$880$	−0.0773310	+	0.0116558i	−0.0773310	+	0.0116558i
$881$	−1.46610			−1.46610			−0.733052	−	0.680173i	$-0.761905\pi$
$881$	−1.46610			−1.46610			−0.733052	+	0.680173i	$0.761905\pi$
$882$	−0.432142	+	0.400969i	−0.432142	+	0.400969i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$	−1.04235	+	0.157108i	−1.04235	+	0.157108i
$885$		0			0
$886$		0			0
$887$	0.0841939	−	1.12349i	0.0841939	−	1.12349i	−0.781831	−	0.623490i	$-0.785714\pi$
$887$	0.0841939	−	1.12349i	0.0841939	−	1.12349i	0.866025	−	0.500000i	$-0.166667\pi$
$888$		0			0
$889$	−0.846011	+	1.75676i	−0.846011	+	1.75676i
$890$	−1.05040	+	0.505844i	−1.05040	+	0.505844i
$891$	−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
$896$	−0.662592	+	0.260048i	−0.662592	+	0.260048i
$897$		0			0
$898$	0.355898	−	0.242647i	0.355898	−	0.242647i
$899$		0			0
$900$	0.326239	+	0.565062i	0.326239	+	0.565062i
$901$		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	$0.0476190\pi$
$908$	0.953925	+	0.885113i	0.953925	+	0.885113i
$909$		0			0
$910$	1.09445	−	0.0820177i	1.09445	−	0.0820177i
$911$	−0.326239	−	1.42935i	−0.326239	−	1.42935i	−0.826239	−	0.563320i	$-0.809524\pi$
$911$	−0.326239	−	1.42935i	−0.326239	−	1.42935i	0.500000	−	0.866025i	$-0.333333\pi$
$912$		0			0
$913$	0.866025	+	1.50000i	0.866025	+	1.50000i
$914$	−0.748491	+	0.694498i	−0.748491	+	0.694498i
$915$		0			0
$916$	−0.777479	+	0.974928i	−0.777479	+	0.974928i
$917$		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
$923$	3.20571	−	1.54379i	3.20571	−	1.54379i
$924$		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
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.829215	−	0.255779i	0.829215	−	0.255779i
$936$	−0.135532	+	1.80855i	−0.135532	+	1.80855i
$937$	−1.67738	−	0.807782i	−1.67738	−	0.807782i	−0.997204	−	0.0747301i	$-0.976190\pi$
$937$	−1.67738	−	0.807782i	−1.67738	−	0.807782i	−0.680173	−	0.733052i	$-0.738095\pi$
$938$		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
$944$	0.0356278	+	0.0446759i	0.0356278	+	0.0446759i
$945$		0			0
$946$	0.109562	−	0.137386i	0.109562	−	0.137386i
$947$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$947$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$948$		0			0
$949$	−1.04876	−	1.81651i	−1.04876	−	1.81651i
$950$		0			0
$951$		0			0
$952$	0.732084	−	0.422669i	0.732084	−	0.422669i
$953$	0.347948	−	1.52446i	0.347948	−	1.52446i	−0.433884	−	0.900969i	$-0.642857\pi$
$953$	0.347948	−	1.52446i	0.347948	−	1.52446i	0.781831	−	0.623490i	$-0.214286\pi$
$954$		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
$963$	−1.42935	+	1.32624i	−1.42935	+	1.32624i
$964$		0			0
$965$	−0.541044	+	0.678448i	−0.541044	+	0.678448i
$966$		0			0
$967$	0.702449	+	0.880843i	0.702449	+	0.880843i	0.997204	−	0.0747301i	$-0.0238095\pi$
$967$	0.702449	+	0.880843i	0.702449	+	0.880843i	−0.294755	+	0.955573i	$0.595238\pi$
$968$	0.930874	+	0.287137i	0.930874	+	0.287137i
$969$		0			0
$970$		0			0
$971$	0.535628	+	1.36476i	0.535628	+	1.36476i	0.900969	+	0.433884i	$0.142857\pi$
$971$	0.535628	+	1.36476i	0.535628	+	1.36476i	−0.365341	+	0.930874i	$0.619048\pi$
$972$		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
$980$	0.587862	−	0.283099i	0.587862	−	0.283099i
$981$		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
$985$	0.101659	−	1.35654i	0.101659	−	1.35654i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−0.0440542	−	0.587862i	−0.0440542	−	0.587862i
$991$	0.658322	−	1.67738i	0.658322	−	1.67738i	−0.0747301	−	0.997204i	$-0.523810\pi$
$991$	0.658322	−	1.67738i	0.658322	−	1.67738i	0.733052	−	0.680173i	$-0.238095\pi$
$992$	−0.974928	−	0.300725i	−0.974928	−	0.300725i
$993$		0			0
$994$	−0.766310	+	0.825886i	−0.766310	+	0.825886i
$995$	0.914101	−	1.14625i	0.914101	−	1.14625i
$996$		0			0
$997$	−0.218511	+	0.202749i	−0.218511	+	0.202749i	−0.781831	−	0.623490i	$-0.785714\pi$
$997$	−0.218511	+	0.202749i	−0.218511	+	0.202749i	0.563320	+	0.826239i	$0.309524\pi$
$998$	−0.582926	−	1.00966i	−0.582926	−	1.00966i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.1.ck.c.1759.2	yes	24
5.4	even	2	inner	2695.1.ck.c.1759.1	yes	24
11.10	odd	2	inner	2695.1.ck.c.1759.1	yes	24
49.39	even	21	inner	2695.1.ck.c.1264.2	yes	24
55.54	odd	2	CM	2695.1.ck.c.1759.2	yes	24
245.39	even	42	inner	2695.1.ck.c.1264.1	✓	24
539.186	odd	42	inner	2695.1.ck.c.1264.1	✓	24
2695.1264	odd	42	inner	2695.1.ck.c.1264.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2695.1.ck.c.1264.1	✓	24	245.39	even	42	inner
2695.1.ck.c.1264.1	✓	24	539.186	odd	42	inner
2695.1.ck.c.1264.2	yes	24	49.39	even	21	inner
2695.1.ck.c.1264.2	yes	24	2695.1264	odd	42	inner
2695.1.ck.c.1759.1	yes	24	5.4	even	2	inner
2695.1.ck.c.1759.1	yes	24	11.10	odd	2	inner
2695.1.ck.c.1759.2	yes	24	1.1	even	1	trivial
2695.1.ck.c.1759.2	yes	24	55.54	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.582926 - 0.0878620i) q^{2} +(-0.623490 + 0.192321i) q^{4} +(-0.0747301 + 0.997204i) q^{5} +(0.781831 + 0.623490i) q^{7} +(-0.877681 + 0.422669i) q^{8} +(0.365341 + 0.930874i) q^{9} +(0.0440542 + 0.587862i) q^{10} +(-0.365341 + 0.930874i) q^{11} +(-1.16078 - 1.45557i) q^{13} +(0.510531 + 0.294755i) q^{14} +(0.0646156 - 0.0440542i) q^{16} +(-0.636119 + 0.590232i) q^{17} +(0.294755 + 0.510531i) q^{18} +(-0.145190 - 0.636119i) q^{20} +(-0.131178 + 0.574730i) q^{22} +(-0.988831 - 0.149042i) q^{25} +(-0.804539 - 0.746503i) q^{26} +(-0.607374 - 0.238377i) q^{28} +(-0.500000 - 0.866025i) q^{31} +(0.747900 - 0.693950i) q^{32} +(-0.318951 + 0.399952i) q^{34} +(-0.680173 + 0.733052i) q^{35} +(-0.406813 - 0.510127i) q^{36} +(-0.355898 - 0.906813i) q^{40} +(-0.268565 - 0.129334i) q^{43} +(0.0487597 - 0.650653i) q^{44} +(-0.955573 + 0.294755i) q^{45} +(0.222521 + 0.974928i) q^{49} -0.589510 q^{50} +(1.00367 + 0.684292i) q^{52} +(-0.900969 - 0.433884i) q^{55} +(-0.949729 - 0.216769i) q^{56} +(0.0546039 + 0.728639i) q^{59} +(-0.367554 - 0.460898i) q^{62} +(-0.294755 + 0.955573i) q^{63} +(0.326239 - 0.409090i) q^{64} +(1.53825 - 1.04876i) q^{65} +(0.283099 - 0.490343i) q^{68} +(-0.332083 + 0.487076i) q^{70} +(-0.425270 + 1.86323i) q^{71} +(-0.714104 - 0.662592i) q^{72} +(1.11406 + 0.167917i) q^{73} +(-0.866025 + 0.500000i) q^{77} +(0.0391023 + 0.0677271i) q^{80} +(-0.733052 + 0.680173i) q^{81} +(1.07992 - 1.35417i) q^{83} +(-0.541044 - 0.678448i) q^{85} +(-0.167917 - 0.0517955i) q^{86} +(-0.0727985 - 0.971429i) q^{88} +(0.722521 + 1.84095i) q^{89} +(-0.531130 + 0.255779i) q^{90} -1.86175i q^{91} +(0.215372 + 0.548760i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4} - 2 q^{5} + 2 q^{9} - 2 q^{11} - 6 q^{14} - 26 q^{16} + 8 q^{20} + 2 q^{25} + 6 q^{26} - 12 q^{31} - 14 q^{34} - 8 q^{36} - 18 q^{44} - 2 q^{45} + 4 q^{49} - 4 q^{55} + 14 q^{56} - 2 q^{59}+ \cdots - 24 q^{99}+O(q^{100}) \) 24 * q + 4 * q^4 - 2 * q^5 + 2 * q^9 - 2 * q^11 - 6 * q^14 - 26 * q^16 + 8 * q^20 + 2 * q^25 + 6 * q^26 - 12 * q^31 - 14 * q^34 - 8 * q^36 - 18 * q^44 - 2 * q^45 + 4 * q^49 - 4 * q^55 + 14 * q^56 - 2 * q^59 - 10 * q^64 - 6 * q^70 - 10 * q^71 + 12 * q^80 + 2 * q^81 - 6 * q^86 + 16 * q^89 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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