LMFDB - Embedded newform 2695.1.ck.c.2034.2

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			2034.2
Root			$-0.149042 + 0.988831i$ of defining polynomial
Character	$\chi$	$=$	2695.2034
Dual form			2695.1.ck.c.1374.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.07659 - 0.332083i) q^{2} +(0.222521 - 0.151712i) q^{4} +(0.988831 + 0.149042i) q^{5} +(-0.974928 + 0.222521i) q^{7} +(-0.513267 + 0.643616i) q^{8} +(-0.733052 + 0.680173i) q^{9} +(1.11406 - 0.167917i) q^{10} +(0.733052 + 0.680173i) q^{11} +(-0.302705 + 1.32624i) q^{13} +(-0.975699 + 0.563320i) q^{14} +(-0.437235 + 1.11406i) q^{16} +(0.116853 - 1.55929i) q^{17} +(-0.563320 + 0.975699i) q^{18} +(0.242647 - 0.116853i) q^{20} +(1.01507 + 0.488831i) q^{22} +(0.955573 + 0.294755i) q^{25} +(0.114533 + 1.52833i) q^{26} +(-0.183183 + 0.197424i) q^{28} +(-0.500000 + 0.866025i) q^{31} +(-0.0392431 + 0.523663i) q^{32} +(-0.392012 - 1.71752i) q^{34} +(-0.997204 + 0.0747301i) q^{35} +(-0.0599289 + 0.262566i) q^{36} +(-0.603460 + 0.559929i) q^{40} +(0.367554 + 0.460898i) q^{43} +(0.266310 + 0.0401398i) q^{44} +(-0.826239 + 0.563320i) q^{45} +(0.900969 - 0.433884i) q^{49} +1.12664 q^{50} +(0.133848 + 0.341040i) q^{52} +(0.623490 + 0.781831i) q^{55} +(0.357180 - 0.741692i) q^{56} +(1.44973 - 0.218511i) q^{59} +(-0.250701 + 1.09839i) q^{62} +(0.563320 - 0.826239i) q^{63} +(-0.134659 - 0.589980i) q^{64} +(-0.496990 + 1.26631i) q^{65} +(-0.210561 - 0.364703i) q^{68} +(-1.04876 + 0.411608i) q^{70} +(-1.48883 - 0.716983i) q^{71} +(-0.0615190 - 0.820914i) q^{72} +(1.77904 + 0.548760i) q^{73} +(-0.866025 - 0.500000i) q^{77} +(-0.598393 + 1.03645i) q^{80} +(0.0747301 - 0.997204i) q^{81} +(-0.385418 - 1.68862i) q^{83} +(0.347948 - 1.52446i) q^{85} +(0.548760 + 0.374138i) q^{86} +(-0.814021 + 0.122694i) q^{88} +(1.40097 - 1.29991i) q^{89} +(-0.702449 + 0.880843i) q^{90} -1.36035i q^{91} +(0.825886 - 0.766310i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2695\mathbb{Z}\right)^\times$.

$n$	$981$	$1816$	$2157$
$\chi(n)$	$-1$	$e\left(\frac{8}{21}\right)$	$-1$

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 $

$2$	1.07659	−	0.332083i	1.07659	−	0.332083i	0.294755	−	0.955573i	$-0.404762\pi$
$2$	1.07659	−	0.332083i	1.07659	−	0.332083i	0.781831	+	0.623490i	$0.214286\pi$
$3$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$3$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$4$	0.222521	−	0.151712i	0.222521	−	0.151712i
$5$	0.988831	+	0.149042i	0.988831	+	0.149042i
$5$	0.988831	+	0.149042i	0.988831	+	0.149042i
$6$		0			0
$7$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$7$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$8$	−0.513267	+	0.643616i	−0.513267	+	0.643616i
$9$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$10$	1.11406	−	0.167917i	1.11406	−	0.167917i
$11$	0.733052	+	0.680173i	0.733052	+	0.680173i
$11$	0.733052	+	0.680173i	0.733052	+	0.680173i
$12$		0			0
$13$	−0.302705	+	1.32624i	−0.302705	+	1.32624i	0.563320	+	0.826239i	$0.309524\pi$
$13$	−0.302705	+	1.32624i	−0.302705	+	1.32624i	−0.866025	+	0.500000i	$0.833333\pi$
$14$	−0.975699	+	0.563320i	−0.975699	+	0.563320i
$15$		0			0
$16$	−0.437235	+	1.11406i	−0.437235	+	1.11406i
$17$	0.116853	−	1.55929i	0.116853	−	1.55929i	−0.563320	−	0.826239i	$-0.690476\pi$
$17$	0.116853	−	1.55929i	0.116853	−	1.55929i	0.680173	−	0.733052i	$-0.261905\pi$
$18$	−0.563320	+	0.975699i	−0.563320	+	0.975699i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$	0.242647	−	0.116853i	0.242647	−	0.116853i
$21$		0			0
$22$	1.01507	+	0.488831i	1.01507	+	0.488831i
$23$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$23$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$24$		0			0
$25$	0.955573	+	0.294755i	0.955573	+	0.294755i
$26$	0.114533	+	1.52833i	0.114533	+	1.52833i
$27$		0			0
$28$	−0.183183	+	0.197424i	−0.183183	+	0.197424i
$29$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$29$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$30$		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			$\pi$
$32$	−0.0392431	+	0.523663i	−0.0392431	+	0.523663i
$33$		0			0
$34$	−0.392012	−	1.71752i	−0.392012	−	1.71752i
$35$	−0.997204	+	0.0747301i	−0.997204	+	0.0747301i
$36$	−0.0599289	+	0.262566i	−0.0599289	+	0.262566i
$37$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$37$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$38$		0			0
$39$		0			0
$40$	−0.603460	+	0.559929i	−0.603460	+	0.559929i
$41$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$41$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$42$		0			0
$43$	0.367554	+	0.460898i	0.367554	+	0.460898i	0.930874	−	0.365341i	$-0.119048\pi$
$43$	0.367554	+	0.460898i	0.367554	+	0.460898i	−0.563320	+	0.826239i	$0.690476\pi$
$44$	0.266310	+	0.0401398i	0.266310	+	0.0401398i
$45$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$46$		0			0
$47$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$47$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$48$		0			0
$49$	0.900969	−	0.433884i	0.900969	−	0.433884i
$50$	1.12664			1.12664
$51$		0			0
$52$	0.133848	+	0.341040i	0.133848	+	0.341040i
$53$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$53$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$54$		0			0
$55$	0.623490	+	0.781831i	0.623490	+	0.781831i
$56$	0.357180	−	0.741692i	0.357180	−	0.741692i
$57$		0			0
$58$		0			0
$59$	1.44973	−	0.218511i	1.44973	−	0.218511i	0.623490	−	0.781831i	$-0.285714\pi$
$59$	1.44973	−	0.218511i	1.44973	−	0.218511i	0.826239	+	0.563320i	$0.190476\pi$
$60$		0			0
$61$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$61$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$62$	−0.250701	+	1.09839i	−0.250701	+	1.09839i
$63$	0.563320	−	0.826239i	0.563320	−	0.826239i
$64$	−0.134659	−	0.589980i	−0.134659	−	0.589980i
$65$	−0.496990	+	1.26631i	−0.496990	+	1.26631i
$66$		0			0
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$	−0.210561	−	0.364703i	−0.210561	−	0.364703i
$69$		0			0
$70$	−1.04876	+	0.411608i	−1.04876	+	0.411608i
$71$	−1.48883	−	0.716983i	−1.48883	−	0.716983i	−0.500000	−	0.866025i	$-0.666667\pi$
$71$	−1.48883	−	0.716983i	−1.48883	−	0.716983i	−0.988831	+	0.149042i	$0.952381\pi$
$72$	−0.0615190	−	0.820914i	−0.0615190	−	0.820914i
$73$	1.77904	+	0.548760i	1.77904	+	0.548760i	0.997204	−	0.0747301i	$-0.0238095\pi$
$73$	1.77904	+	0.548760i	1.77904	+	0.548760i	0.781831	+	0.623490i	$0.214286\pi$
$74$		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	$-0.666667\pi$
$79$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$80$	−0.598393	+	1.03645i	−0.598393	+	1.03645i
$81$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$82$		0			0
$83$	−0.385418	−	1.68862i	−0.385418	−	1.68862i	−0.680173	−	0.733052i	$-0.738095\pi$
$83$	−0.385418	−	1.68862i	−0.385418	−	1.68862i	0.294755	−	0.955573i	$-0.404762\pi$
$84$		0			0
$85$	0.347948	−	1.52446i	0.347948	−	1.52446i
$86$	0.548760	+	0.374138i	0.548760	+	0.374138i
$87$		0			0
$88$	−0.814021	+	0.122694i	−0.814021	+	0.122694i
$89$	1.40097	−	1.29991i	1.40097	−	1.29991i	0.500000	−	0.866025i	$-0.333333\pi$
$89$	1.40097	−	1.29991i	1.40097	−	1.29991i	0.900969	−	0.433884i	$-0.142857\pi$
$90$	−0.702449	+	0.880843i	−0.702449	+	0.880843i
$91$		−	1.36035i		−	1.36035i
$92$		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			$\pi$
$98$	0.825886	−	0.766310i	0.825886	−	0.766310i
$99$	−1.00000			−1.00000
$100$	0.257353	−	0.0793829i	0.257353	−	0.0793829i
$101$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$101$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$102$		0			0
$103$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$103$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$104$	−0.698220	−	0.875540i	−0.698220	−	0.875540i
$105$		0			0
$106$		0			0
$107$	−0.636119	+	0.590232i	−0.636119	+	0.590232i	−0.930874	−	0.365341i	$-0.880952\pi$
$107$	−0.636119	+	0.590232i	−0.636119	+	0.590232i	0.294755	+	0.955573i	$0.404762\pi$
$108$		0			0
$109$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$109$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$110$	0.930874	+	0.634659i	0.930874	+	0.634659i
$111$		0			0
$112$	0.178372	−	1.18342i	0.178372	−	1.18342i
$113$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$113$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.680173	−	1.17809i	−0.680173	−	1.17809i
$118$	1.48819	−	0.716677i	1.48819	−	0.716677i
$119$	0.233052	+	1.54620i	0.233052	+	1.54620i
$120$		0			0
$121$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$122$		0			0
$123$		0			0
$124$	0.0201262	+	0.268565i	0.0201262	+	0.268565i
$125$	0.900969	+	0.433884i	0.900969	+	0.433884i
$126$	0.332083	−	1.07659i	0.332083	−	1.07659i
$127$	0.781831	−	0.376510i	0.781831	−	0.376510i		−	1.00000i	$-0.5\pi$
$127$	0.781831	−	0.376510i	0.781831	−	0.376510i	0.781831	+	0.623490i	$0.214286\pi$
$128$	−0.603460	−	1.04522i	−0.603460	−	1.04522i
$129$		0			0
$130$	−0.114533	+	1.52833i	−0.114533	+	1.52833i
$131$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$131$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.943608	+	0.875540i	0.943608	+	0.875540i
$137$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$137$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$138$		0			0
$139$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$139$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$140$	−0.210561	+	0.167917i	−0.210561	+	0.167917i
$141$		0			0
$142$	−1.84095	−	0.277479i	−1.84095	−	0.277479i
$143$	−1.12397	+	0.766310i	−1.12397	+	0.766310i
$144$	−0.437235	−	1.11406i	−0.437235	−	1.11406i
$145$		0			0
$146$	2.09752			2.09752
$147$		0			0
$148$		0			0
$149$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$149$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$150$		0			0
$151$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$151$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$152$		0			0
$153$	0.974928	+	1.22252i	0.974928	+	1.22252i
$154$	−1.09839	−	0.250701i	−1.09839	−	0.250701i
$155$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$156$		0			0
$157$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$157$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$158$		0			0
$159$		0			0
$160$	−0.116853	+	0.511965i	−0.116853	+	0.511965i
$161$		0			0
$162$	−0.250701	−	1.09839i	−0.250701	−	1.09839i
$163$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$163$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$164$		0			0
$165$		0			0
$166$	−0.975699	−	1.68996i	−0.975699	−	1.68996i
$167$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$167$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$168$		0			0
$169$	−0.766310	−	0.369035i	−0.766310	−	0.369035i
$170$	−0.131651	−	1.75676i	−0.131651	−	1.75676i
$171$		0			0
$172$	0.151712	+	0.0467970i	0.151712	+	0.0467970i
$173$	−0.149042	−	1.98883i	−0.149042	−	1.98883i	−0.149042	−	0.988831i	$-0.547619\pi$
$173$	−0.149042	−	1.98883i	−0.149042	−	1.98883i		−	1.00000i	$-0.5\pi$
$174$		0			0
$175$	−0.997204	−	0.0747301i	−0.997204	−	0.0747301i
$176$	−1.07827	+	0.519266i	−1.07827	+	0.519266i
$177$		0			0
$178$	1.07659	−	1.86470i	1.07659	−	1.86470i
$179$	−0.123490	+	1.64786i	−0.123490	+	1.64786i	0.500000	+	0.866025i	$0.333333\pi$
$179$	−0.123490	+	1.64786i	−0.123490	+	1.64786i	−0.623490	+	0.781831i	$0.714286\pi$
$180$	−0.0983929	+	0.250701i	−0.0983929	+	0.250701i
$181$	0.162592	+	0.712362i	0.162592	+	0.712362i	0.988831	+	0.149042i	$0.0476190\pi$
$181$	0.162592	+	0.712362i	0.162592	+	0.712362i	−0.826239	+	0.563320i	$0.809524\pi$
$182$	−0.451748	−	1.46453i	−0.451748	−	1.46453i
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.14625	−	1.06356i	1.14625	−	1.06356i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.988831	−	0.149042i	−0.988831	−	0.149042i	−0.365341	−	0.930874i	$-0.619048\pi$
$191$	−0.988831	−	0.149042i	−0.988831	−	0.149042i	−0.623490	+	0.781831i	$0.714286\pi$
$192$		0			0
$193$	0.571270	+	1.45557i	0.571270	+	1.45557i	0.866025	+	0.500000i	$0.166667\pi$
$193$	0.571270	+	1.45557i	0.571270	+	1.45557i	−0.294755	+	0.955573i	$0.595238\pi$
$194$		0			0
$195$		0			0
$196$	0.134659	−	0.233236i	0.134659	−	0.233236i
$197$	−1.99441			−1.99441			−0.997204	−	0.0747301i	$-0.976190\pi$
$197$	−1.99441			−1.99441			−0.997204	+	0.0747301i	$0.976190\pi$
$198$	−1.07659	+	0.332083i	−1.07659	+	0.332083i
$199$	0.0546039	+	0.139129i	0.0546039	+	0.139129i	0.955573	−	0.294755i	$-0.0952381\pi$
$199$	0.0546039	+	0.139129i	0.0546039	+	0.139129i	−0.900969	+	0.433884i	$0.857143\pi$
$200$	−0.680173	+	0.463734i	−0.680173	+	0.463734i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$	−1.34515	−	0.917109i	−1.34515	−	0.917109i
$209$		0			0
$210$		0			0
$211$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$211$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$212$		0			0
$213$		0			0
$214$	−0.488831	+	0.846680i	−0.488831	+	0.846680i
$215$	0.294755	+	0.510531i	0.294755	+	0.510531i
$216$		0			0
$217$	0.294755	−	0.955573i	0.294755	−	0.955573i
$218$		0			0
$219$		0			0
$220$	0.257353	+	0.0793829i	0.257353	+	0.0793829i
$221$	2.03262	+	0.626980i	2.03262	+	0.626980i
$222$		0			0
$223$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$223$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$224$	−0.0782667	−	0.519266i	−0.0782667	−	0.519266i
$225$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$226$		0			0
$227$	0.149042	−	0.258149i	0.149042	−	0.258149i	−0.781831	−	0.623490i	$-0.785714\pi$
$227$	0.149042	−	0.258149i	0.149042	−	0.258149i	0.930874	+	0.365341i	$0.119048\pi$
$228$		0			0
$229$	0.603718	−	1.53825i	0.603718	−	1.53825i	−0.222521	−	0.974928i	$-0.571429\pi$
$229$	0.603718	−	1.53825i	0.603718	−	1.53825i	0.826239	−	0.563320i	$-0.190476\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.563320	−	0.826239i	$-0.309524\pi$
$233$		0			0		−0.563320	+	0.826239i	$0.690476\pi$
$234$	−1.12349	−	1.04245i	−1.12349	−	1.04245i
$235$		0			0
$236$	0.289444	−	0.268565i	0.289444	−	0.268565i
$237$		0			0
$238$	0.764367	+	1.58722i	0.764367	+	1.58722i
$239$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$239$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$240$		0			0
$241$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$241$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$242$	0.411608	+	1.04876i	0.411608	+	1.04876i
$243$		0			0
$244$		0			0
$245$	0.955573	−	0.294755i	0.955573	−	0.294755i
$246$		0			0
$247$		0			0
$248$	−0.300754	−	0.766310i	−0.300754	−	0.766310i
$249$		0			0
$250$	1.11406	+	0.167917i	1.11406	+	0.167917i
$251$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$251$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$252$		−	0.269318i		−	0.269318i
$253$		0			0
$254$	0.716677	−	0.664979i	0.716677	−	0.664979i
$255$		0			0
$256$	−0.553170	−	0.513267i	−0.553170	−	0.513267i
$257$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$257$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$258$		0			0
$259$		0			0
$260$	0.0815240	+	0.357180i	0.0815240	+	0.357180i
$261$		0			0
$262$		0			0
$263$	−0.866025	+	1.50000i	−0.866025	+	1.50000i			1.00000i	$0.5\pi$
$263$	−0.866025	+	1.50000i	−0.866025	+	1.50000i	−0.866025	+	0.500000i	$0.833333\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.19158	+	0.367554i	1.19158	+	0.367554i	0.826239	−	0.563320i	$-0.190476\pi$
$269$	1.19158	+	0.367554i	1.19158	+	0.367554i	0.365341	+	0.930874i	$0.380952\pi$
$270$		0			0
$271$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$271$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$272$	1.68605	+	0.811957i	1.68605	+	0.811957i
$273$		0			0
$274$		0			0
$275$	0.500000	+	0.866025i	0.500000	+	0.866025i
$276$		0			0
$277$	0.139129	−	1.85654i	0.139129	−	1.85654i	−0.294755	−	0.955573i	$-0.595238\pi$
$277$	0.139129	−	1.85654i	0.139129	−	1.85654i	0.433884	−	0.900969i	$-0.357143\pi$
$278$		0			0
$279$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$280$	0.463734	−	0.680173i	0.463734	−	0.680173i
$281$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$281$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$282$		0			0
$283$	1.42935	+	1.32624i	1.42935	+	1.32624i	0.866025	+	0.500000i	$0.166667\pi$
$283$	1.42935	+	1.32624i	1.42935	+	1.32624i	0.563320	+	0.826239i	$0.309524\pi$
$284$	−0.440071	+	0.0663300i	−0.440071	+	0.0663300i
$285$		0			0
$286$	−0.955573	+	1.19825i	−0.955573	+	1.19825i
$287$		0			0
$288$	−0.327414	−	0.410564i	−0.327414	−	0.410564i
$289$	−1.42890	−	0.215372i	−1.42890	−	0.215372i
$290$		0			0
$291$		0			0
$292$	0.479126	−	0.147791i	0.479126	−	0.147791i
$293$	0.298085			0.298085			0.149042	−	0.988831i	$-0.452381\pi$
$293$	0.298085			0.298085			0.149042	+	0.988831i	$0.452381\pi$
$294$		0			0
$295$	1.46610			1.46610
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−0.460898	−	0.367554i	−0.460898	−	0.367554i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$	1.45557	+	0.992393i	1.45557	+	0.992393i
$307$	−0.250701	+	1.09839i	−0.250701	+	1.09839i	0.680173	+	0.733052i	$0.261905\pi$
$307$	−0.250701	+	1.09839i	−0.250701	+	1.09839i	−0.930874	+	0.365341i	$0.880952\pi$
$308$	−0.268565	+	0.0201262i	−0.268565	+	0.0201262i
$309$		0			0
$310$	−0.411608	+	1.04876i	−0.411608	+	1.04876i
$311$	−0.147791	+	1.97213i	−0.147791	+	1.97213i	0.0747301	+	0.997204i	$0.476190\pi$
$311$	−0.147791	+	1.97213i	−0.147791	+	1.97213i	−0.222521	+	0.974928i	$0.571429\pi$
$312$		0			0
$313$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$313$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$314$		0			0
$315$	0.680173	−	0.733052i	0.680173	−	0.733052i
$316$		0			0
$317$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$317$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$318$		0			0
$319$		0			0
$320$	−0.0452231	−	0.603460i	−0.0452231	−	0.603460i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.134659	−	0.233236i	−0.134659	−	0.233236i
$325$	−0.680173	+	1.17809i	−0.680173	+	1.17809i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.57906	−	1.07659i	−1.57906	−	1.07659i	−0.955573	−	0.294755i	$-0.904762\pi$
$331$	−1.57906	−	1.07659i	−1.57906	−	1.07659i	−0.623490	−	0.781831i	$-0.714286\pi$
$332$	−0.341948	−	0.317282i	−0.341948	−	0.317282i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.848162	+	1.06356i	0.848162	+	1.06356i	0.997204	+	0.0747301i	$0.0238095\pi$
$337$	0.848162	+	1.06356i	0.848162	+	1.06356i	−0.149042	+	0.988831i	$0.547619\pi$
$338$	−0.947549	−	0.142820i	−0.947549	−	0.142820i
$339$		0			0
$340$	−0.153853	−	0.392012i	−0.153853	−	0.392012i
$341$	−0.955573	+	0.294755i	−0.955573	+	0.294755i
$342$		0			0
$343$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$344$	−0.485294			−0.485294
$345$		0			0
$346$	−0.820914	−	2.09165i	−0.820914	−	2.09165i
$347$	1.64786	−	1.12349i	1.64786	−	1.12349i	0.781831	−	0.623490i	$-0.214286\pi$
$347$	1.64786	−	1.12349i	1.64786	−	1.12349i	0.866025	−	0.500000i	$-0.166667\pi$
$348$		0			0
$349$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$349$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$350$	−1.09839	+	0.250701i	−1.09839	+	0.250701i
$351$		0			0
$352$	−0.384948	+	0.357180i	−0.384948	+	0.357180i
$353$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$353$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$354$		0			0
$355$	−1.36534	−	0.930874i	−1.36534	−	0.930874i
$356$	0.114533	−	0.501801i	0.114533	−	0.501801i
$357$		0			0
$358$	0.414278	+	1.81507i	0.414278	+	1.81507i
$359$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$359$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$360$	0.0615190	−	0.820914i	0.0615190	−	0.820914i
$361$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$362$	0.411608	+	0.712926i	0.411608	+	0.712926i
$363$		0			0
$364$	−0.206381	−	0.302705i	−0.206381	−	0.302705i
$365$	1.67738	+	0.807782i	1.67738	+	0.807782i
$366$		0			0
$367$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$367$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	0.149042	+	0.258149i	0.149042	+	0.258149i	0.930874	−	0.365341i	$-0.119048\pi$
$373$	0.149042	+	0.258149i	0.149042	+	0.258149i	−0.781831	+	0.623490i	$0.785714\pi$
$374$	0.880843	−	1.52566i	0.880843	−	1.52566i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.440071	−	1.92808i	0.440071	−	1.92808i	0.0747301	−	0.997204i	$-0.476190\pi$
$379$	0.440071	−	1.92808i	0.440071	−	1.92808i	0.365341	−	0.930874i	$-0.380952\pi$
$380$		0			0
$381$		0			0
$382$	−1.11406	+	0.167917i	−1.11406	+	0.167917i
$383$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$383$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$384$		0			0
$385$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$386$	1.09839	+	1.37734i	1.09839	+	1.37734i
$387$	−0.582926	−	0.0878620i	−0.582926	−	0.0878620i
$388$		0			0
$389$	−0.722521	−	1.84095i	−0.722521	−	1.84095i	−0.500000	−	0.866025i	$-0.666667\pi$
$389$	−0.722521	−	1.84095i	−0.722521	−	1.84095i	−0.222521	−	0.974928i	$-0.571429\pi$
$390$		0			0
$391$		0			0
$392$	−0.183183	+	0.802576i	−0.183183	+	0.802576i
$393$		0			0
$394$	−2.14715	+	0.662309i	−2.14715	+	0.662309i
$395$		0			0
$396$	−0.222521	+	0.151712i	−0.222521	+	0.151712i
$397$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$397$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$398$	0.104988	+	0.131651i	0.104988	+	0.131651i
$399$		0			0
$400$	−0.746184	+	0.935685i	−0.746184	+	0.935685i
$401$	1.40097	−	1.29991i	1.40097	−	1.29991i	0.500000	−	0.866025i	$-0.333333\pi$
$401$	1.40097	−	1.29991i	1.40097	−	1.29991i	0.900969	−	0.433884i	$-0.142857\pi$
$402$		0			0
$403$	−0.997204	−	0.925270i	−0.997204	−	0.925270i
$404$		0			0
$405$	0.222521	−	0.974928i	0.222521	−	0.974928i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$409$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−1.36476	+	0.535628i	−1.36476	+	0.535628i
$414$		0			0
$415$	−0.129436	−	1.72721i	−0.129436	−	1.72721i
$416$	−0.682623	−	0.210561i	−0.682623	−	0.210561i
$417$		0			0
$418$		0			0
$419$	−1.32091	−	0.636119i	−1.32091	−	0.636119i	−0.365341	−	0.930874i	$-0.619048\pi$
$419$	−1.32091	−	0.636119i	−1.32091	−	0.636119i	−0.955573	+	0.294755i	$0.904762\pi$
$420$		0			0
$421$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.222521	−	0.974928i	$-0.428571\pi$
$421$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.900969	+	0.433884i	$0.142857\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.571270	−	1.45557i	0.571270	−	1.45557i
$426$		0			0
$427$		0			0
$428$	−0.0520043	+	0.227846i	−0.0520043	+	0.227846i
$429$		0			0
$430$	0.486868	+	0.451748i	0.486868	+	0.451748i
$431$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$431$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$432$		0			0
$433$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$433$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$434$		−	1.12664i		−	1.12664i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$439$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$440$	−0.823216			−0.823216
$441$	−0.365341	+	0.930874i	−0.365341	+	0.930874i
$442$	2.39650			2.39650
$443$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$443$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$444$		0			0
$445$	1.57906	−	1.07659i	1.57906	−	1.07659i
$446$		0			0
$447$		0			0
$448$	0.262566	+	0.545223i	0.262566	+	0.545223i
$449$	0.914101	−	1.14625i	0.914101	−	1.14625i	−0.0747301	−	0.997204i	$-0.523810\pi$
$449$	0.914101	−	1.14625i	0.914101	−	1.14625i	0.988831	−	0.149042i	$-0.0476190\pi$
$450$	−0.825886	+	0.766310i	−0.825886	+	0.766310i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.0747301	−	0.327414i	0.0747301	−	0.327414i
$455$	0.202749	−	1.34515i	0.202749	−	1.34515i
$456$		0			0
$457$	−0.632789	+	1.61232i	−0.632789	+	1.61232i	0.149042	+	0.988831i	$0.452381\pi$
$457$	−0.632789	+	1.61232i	−0.632789	+	1.61232i	−0.781831	+	0.623490i	$0.785714\pi$
$458$	0.139129	−	1.85654i	0.139129	−	1.85654i
$459$		0			0
$460$		0			0
$461$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$461$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$462$		0			0
$463$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$463$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$467$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$468$	−0.330084	−	0.158960i	−0.330084	−	0.158960i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.603460	+	1.04522i	−0.603460	+	1.04522i
$473$	−0.0440542	+	0.587862i	−0.0440542	+	0.587862i
$474$		0			0
$475$		0			0
$476$	0.286436	+	0.308705i	0.286436	+	0.308705i
$477$		0			0
$478$		0			0
$479$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$479$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.167917	+	0.210561i	0.167917	+	0.210561i
$485$		0			0
$486$		0			0
$487$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$487$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$488$		0			0
$489$		0			0
$490$	0.930874	−	0.634659i	0.930874	−	0.634659i
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$496$	−0.746184	−	0.935685i	−0.746184	−	0.935685i
$497$	1.61105	+	0.367711i	1.61105	+	0.367711i
$498$		0			0
$499$	−1.40097	+	1.29991i	−1.40097	+	1.29991i	−0.500000	+	0.866025i	$0.666667\pi$
$499$	−1.40097	+	1.29991i	−1.40097	+	1.29991i	−0.900969	+	0.433884i	$0.857143\pi$
$500$	0.266310	−	0.0401398i	0.266310	−	0.0401398i
$501$		0			0
$502$	−1.67738	−	1.14362i	−1.67738	−	1.14362i
$503$	0.385418	−	1.68862i	0.385418	−	1.68862i	−0.294755	−	0.955573i	$-0.595238\pi$
$503$	0.385418	−	1.68862i	0.385418	−	1.68862i	0.680173	−	0.733052i	$-0.261905\pi$
$504$	0.242647	+	0.786643i	0.242647	+	0.786643i
$505$		0			0
$506$		0			0
$507$		0			0
$508$	0.116853	−	0.202395i	0.116853	−	0.202395i
$509$	0.988831	+	1.71271i	0.988831	+	1.71271i	0.623490	+	0.781831i	$0.285714\pi$
$509$	0.988831	+	1.71271i	0.988831	+	1.71271i	0.365341	+	0.930874i	$0.380952\pi$
$510$		0			0
$511$	−1.85654	−	0.139129i	−1.85654	−	0.139129i
$512$	0.321415	+	0.154785i	0.321415	+	0.154785i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−0.559929	−	0.969825i	−0.559929	−	0.969825i
$521$	0.826239	−	1.43109i	0.826239	−	1.43109i	−0.0747301	−	0.997204i	$-0.523810\pi$
$521$	0.826239	−	1.43109i	0.826239	−	1.43109i	0.900969	−	0.433884i	$-0.142857\pi$
$522$		0			0
$523$	0.215372	−	0.548760i	0.215372	−	0.548760i	−0.781831	−	0.623490i	$-0.785714\pi$
$523$	0.215372	−	0.548760i	0.215372	−	0.548760i	0.997204	+	0.0747301i	$0.0238095\pi$
$524$		0			0
$525$		0			0
$526$	−0.434227	+	1.90247i	−0.434227	+	1.90247i
$527$	1.29196	+	0.880843i	1.29196	+	0.880843i
$528$		0			0
$529$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$530$		0			0
$531$	−0.914101	+	1.14625i	−0.914101	+	1.14625i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−0.716983	+	0.488831i	−0.716983	+	0.488831i
$536$		0			0
$537$		0			0
$538$	1.40490			1.40490
$539$	0.955573	+	0.294755i	0.955573	+	0.294755i
$540$		0			0
$541$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$541$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$542$		0			0
$543$		0			0
$544$	0.811957	+	0.122383i	0.811957	+	0.122383i
$545$		0			0
$546$		0			0
$547$	−1.16078	+	1.45557i	−1.16078	+	1.45557i	−0.294755	+	0.955573i	$0.595238\pi$
$547$	−1.16078	+	1.45557i	−1.16078	+	1.45557i	−0.866025	+	0.500000i	$0.833333\pi$
$548$		0			0
$549$		0			0
$550$	0.825886	+	0.766310i	0.825886	+	0.766310i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−0.466742	−	2.04493i	−0.466742	−	2.04493i
$555$		0			0
$556$		0			0
$557$	−0.974928	+	1.68862i	−0.974928	+	1.68862i	−0.294755	+	0.955573i	$0.595238\pi$
$557$	−0.974928	+	1.68862i	−0.974928	+	1.68862i	−0.680173	+	0.733052i	$0.738095\pi$
$558$	−0.563320	−	0.975699i	−0.563320	−	0.975699i
$559$	−0.722521	+	0.347948i	−0.722521	+	0.347948i
$560$	0.352759	−	1.14362i	0.352759	−	1.14362i
$561$		0			0
$562$		0			0
$563$	1.90580	+	0.587862i	1.90580	+	0.587862i	0.974928	+	0.222521i	$0.0714286\pi$
$563$	1.90580	+	0.587862i	1.90580	+	0.587862i	0.930874	+	0.365341i	$0.119048\pi$
$564$		0			0
$565$		0			0
$566$	1.97924	+	0.953150i	1.97924	+	0.953150i
$567$	0.149042	+	0.988831i	0.149042	+	0.988831i
$568$	1.22563	−	0.590232i	1.22563	−	0.590232i
$569$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$569$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$570$		0			0
$571$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$571$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$572$	−0.133848	+	0.341040i	−0.133848	+	0.341040i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.500000	+	0.340894i	0.500000	+	0.340894i
$577$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$577$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$578$	−1.60986	+	0.242647i	−1.60986	+	0.242647i
$579$		0			0
$580$		0			0
$581$	0.751509	+	1.56052i	0.751509	+	1.56052i
$582$		0			0
$583$		0			0
$584$	−1.26631	+	0.863355i	−1.26631	+	0.863355i
$585$	−0.496990	−	1.26631i	−0.496990	−	1.26631i
$586$	0.320914	−	0.0989888i	0.320914	−	0.0989888i
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$		0			0
$589$		0			0
$590$	1.57839	−	0.486868i	1.57839	−	0.486868i
$591$		0			0
$592$		0			0
$593$	−0.582926	−	0.0878620i	−0.582926	−	0.0878620i	−0.149042	−	0.988831i	$-0.547619\pi$
$593$	−0.582926	−	0.0878620i	−0.582926	−	0.0878620i	−0.433884	+	0.900969i	$0.642857\pi$
$594$		0			0
$595$			1.56366i			1.56366i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.44973	−	1.34515i	−1.44973	−	1.34515i	−0.826239	−	0.563320i	$-0.809524\pi$
$599$	−1.44973	−	1.34515i	−1.44973	−	1.34515i	−0.623490	−	0.781831i	$-0.714286\pi$
$600$		0			0
$601$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$601$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$602$	−0.618255	−	0.242647i	−0.618255	−	0.242647i
$603$		0			0
$604$		0			0
$605$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$606$		0			0
$607$	−0.149042	−	0.258149i	−0.149042	−	0.258149i	0.781831	−	0.623490i	$-0.214286\pi$
$607$	−0.149042	−	0.258149i	−0.149042	−	0.258149i	−0.930874	+	0.365341i	$0.880952\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.402413	+	0.124128i	0.402413	+	0.124128i
$613$	1.90580	+	0.587862i	1.90580	+	0.587862i	0.974928	+	0.222521i	$0.0714286\pi$
$613$	1.90580	+	0.587862i	1.90580	+	0.587862i	0.930874	+	0.365341i	$0.119048\pi$
$614$	0.0948562	+	1.26577i	0.0948562	+	1.26577i
$615$		0			0
$616$	0.766310	−	0.300754i	0.766310	−	0.300754i
$617$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$617$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$618$		0			0
$619$	−0.222521	+	0.385418i	−0.222521	+	0.385418i	−0.955573	−	0.294755i	$-0.904762\pi$
$619$	−0.222521	+	0.385418i	−0.222521	+	0.385418i	0.733052	+	0.680173i	$0.238095\pi$
$620$	−0.0201262	+	0.268565i	−0.0201262	+	0.268565i
$621$		0			0
$622$	0.495802	+	2.17225i	0.495802	+	2.17225i
$623$	−1.07659	+	1.57906i	−1.07659	+	1.57906i
$624$		0			0
$625$	0.826239	+	0.563320i	0.826239	+	0.563320i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	0.488831	−	1.01507i	0.488831	−	1.01507i
$631$	0.0931869	+	0.116853i	0.0931869	+	0.116853i	0.826239	−	0.563320i	$-0.190476\pi$
$631$	0.0931869	+	0.116853i	0.0931869	+	0.116853i	−0.733052	+	0.680173i	$0.761905\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.829215	−	0.255779i	0.829215	−	0.255779i
$636$		0			0
$637$	0.302705	+	1.32624i	0.302705	+	1.32624i
$638$		0			0
$639$	1.57906	−	0.487076i	1.57906	−	0.487076i
$640$	−0.440937	−	1.12349i	−0.440937	−	1.12349i
$641$	1.48883	−	1.01507i	1.48883	−	1.01507i	0.500000	−	0.866025i	$-0.333333\pi$
$641$	1.48883	−	1.01507i	1.48883	−	1.01507i	0.988831	−	0.149042i	$-0.0476190\pi$
$642$		0			0
$643$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$643$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$647$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$648$	0.603460	+	0.559929i	0.603460	+	0.559929i
$649$	1.21135	+	0.825886i	1.21135	+	0.825886i
$650$	−0.341040	+	1.49419i	−0.341040	+	1.49419i
$651$		0			0
$652$		0			0
$653$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$653$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−1.67738	+	0.807782i	−1.67738	+	0.807782i
$658$		0			0
$659$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$659$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$660$		0			0
$661$	−1.72188	−	0.531130i	−1.72188	−	0.531130i	−0.733052	−	0.680173i	$-0.761905\pi$
$661$	−1.72188	−	0.531130i	−1.72188	−	0.531130i	−0.988831	+	0.149042i	$0.952381\pi$
$662$	−2.05751	−	0.634659i	−2.05751	−	0.634659i
$663$		0			0
$664$	1.28465	+	0.618654i	1.28465	+	0.618654i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.385418	+	1.68862i	−0.385418	+	1.68862i	0.294755	+	0.955573i	$0.404762\pi$
$673$	−0.385418	+	1.68862i	−0.385418	+	1.68862i	−0.680173	+	0.733052i	$0.738095\pi$
$674$	1.26631	+	0.863355i	1.26631	+	0.863355i
$675$		0			0
$676$	−0.226507	+	0.0341405i	−0.226507	+	0.0341405i
$677$	1.42935	−	1.32624i	1.42935	−	1.32624i	0.563320	−	0.826239i	$-0.309524\pi$
$677$	1.42935	−	1.32624i	1.42935	−	1.32624i	0.866025	−	0.500000i	$-0.166667\pi$
$678$		0			0
$679$		0			0
$680$	0.802576	+	1.00640i	0.802576	+	1.00640i
$681$		0			0
$682$	−0.930874	+	0.634659i	−0.930874	+	0.634659i
$683$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$683$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$684$		0			0
$685$		0			0
$686$	−0.634659	+	0.930874i	−0.634659	+	0.930874i
$687$		0			0
$688$	−0.674173	+	0.207955i	−0.674173	+	0.207955i
$689$		0			0
$690$		0			0
$691$	−1.23305	−	0.185853i	−1.23305	−	0.185853i	−0.500000	−	0.866025i	$-0.666667\pi$
$691$	−1.23305	−	0.185853i	−1.23305	−	0.185853i	−0.733052	+	0.680173i	$0.761905\pi$
$692$	−0.334895	−	0.419945i	−0.334895	−	0.419945i
$693$	0.974928	−	0.222521i	0.974928	−	0.222521i
$694$	1.40097	−	1.75676i	1.40097	−	1.75676i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.233236	+	0.134659i	−0.233236	+	0.134659i
$701$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$701$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$702$		0			0
$703$		0			0
$704$	0.302576	−	0.524077i	0.302576	−	0.524077i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.0747301	+	0.997204i	0.0747301	+	0.997204i	0.900969	+	0.433884i	$0.142857\pi$
$709$	0.0747301	+	0.997204i	0.0747301	+	0.997204i	−0.826239	+	0.563320i	$0.809524\pi$
$710$	−1.77904	−	0.548760i	−1.77904	−	0.548760i
$711$		0			0
$712$	0.117572	+	1.56889i	0.117572	+	1.56889i
$713$		0			0
$714$		0			0
$715$	−1.22563	+	0.590232i	−1.22563	+	0.590232i
$716$	0.222521	+	0.385418i	0.222521	+	0.385418i
$717$		0			0
$718$		0			0
$719$	−0.455573	+	1.16078i	−0.455573	+	1.16078i	0.500000	+	0.866025i	$0.333333\pi$
$719$	−0.455573	+	1.16078i	−0.455573	+	1.16078i	−0.955573	+	0.294755i	$0.904762\pi$
$720$	−0.266310	−	1.16678i	−0.266310	−	1.16678i
$721$		0			0
$722$	−0.250701	+	1.09839i	−0.250701	+	1.09839i
$723$		0			0
$724$	0.144254	+	0.133848i	0.144254	+	0.133848i
$725$		0			0
$726$		0			0
$727$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$727$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$728$	0.875540	+	0.698220i	0.875540	+	0.698220i
$729$	0.623490	+	0.781831i	0.623490	+	0.781831i
$730$	2.07409	+	0.312619i	2.07409	+	0.312619i
$731$	0.761623	−	0.519266i	0.761623	−	0.519266i
$732$		0			0
$733$	−0.829215	+	0.255779i	−0.829215	+	0.255779i	−0.680173	−	0.733052i	$-0.738095\pi$
$733$	−0.829215	+	0.255779i	−0.829215	+	0.255779i	−0.149042	+	0.988831i	$0.547619\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$739$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.848162	−	1.06356i	0.848162	−	1.06356i	−0.149042	−	0.988831i	$-0.547619\pi$
$743$	0.848162	−	1.06356i	0.848162	−	1.06356i	0.997204	−	0.0747301i	$-0.0238095\pi$
$744$		0			0
$745$		0			0
$746$	0.246184	+	0.228425i	0.246184	+	0.228425i
$747$	1.43109	+	0.975699i	1.43109	+	0.975699i
$748$	0.0937086	−	0.410564i	0.0937086	−	0.410564i
$749$	0.488831	−	0.716983i	0.488831	−	0.716983i
$750$		0			0
$751$	0.266948	−	0.680173i	0.266948	−	0.680173i	−0.733052	−	0.680173i	$-0.761905\pi$
$751$	0.266948	−	0.680173i	0.266948	−	0.680173i	1.00000			$0$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$757$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$758$	−0.166507	−	2.22188i	−0.166507	−	2.22188i
$759$		0			0
$760$		0			0
$761$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$761$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$762$		0			0
$763$		0			0
$764$	−0.242647	+	0.116853i	−0.242647	+	0.116853i
$765$	0.781831	+	1.35417i	0.781831	+	1.35417i
$766$		0			0
$767$	−0.149042	+	1.98883i	−0.149042	+	1.98883i
$768$		0			0
$769$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$769$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$770$	−1.04876	−	0.411608i	−1.04876	−	0.411608i
$771$		0			0
$772$	0.347948	+	0.237227i	0.347948	+	0.237227i
$773$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$773$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$774$	−0.656748	+	0.0989888i	−0.656748	+	0.0989888i
$775$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$776$		0			0
$777$		0			0
$778$	−1.38921	−	1.74201i	−1.38921	−	1.74201i
$779$		0			0
$780$		0			0
$781$	−0.603718	−	1.53825i	−0.603718	−	1.53825i
$782$		0			0
$783$		0			0
$784$	0.0894359	+	1.19344i	0.0894359	+	1.19344i
$785$		0			0
$786$		0			0
$787$	−0.728639	−	1.85654i	−0.728639	−	1.85654i	−0.433884	−	0.900969i	$-0.642857\pi$
$787$	−0.728639	−	1.85654i	−0.728639	−	1.85654i	−0.294755	−	0.955573i	$-0.595238\pi$
$788$	−0.443797	+	0.302576i	−0.443797	+	0.302576i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.513267	−	0.643616i	0.513267	−	0.643616i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	0.0332580	+	0.0226749i	0.0332580	+	0.0226749i
$797$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$797$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$798$		0			0
$799$		0			0
$800$	−0.191852	+	0.488831i	−0.191852	+	0.488831i
$801$	−0.142820	+	1.90580i	−0.142820	+	1.90580i
$802$	1.07659	−	1.86470i	1.07659	−	1.86470i
$803$	0.930874	+	1.61232i	0.930874	+	1.61232i
$804$		0			0
$805$		0			0
$806$	−1.38084	−	0.664979i	−1.38084	−	0.664979i
$807$		0			0
$808$		0			0
$809$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$809$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$810$	−0.0841939	−	1.12349i	−0.0841939	−	1.12349i
$811$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$811$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	0.925270	+	0.997204i	0.925270	+	0.997204i
$820$		0			0
$821$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$821$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$822$		0			0
$823$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$823$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$824$		0			0
$825$		0			0
$826$	−1.29141	+	1.02986i	−1.29141	+	1.02986i
$827$	0.974928	+	1.22252i	0.974928	+	1.22252i	0.974928	+	0.222521i	$0.0714286\pi$
$827$	0.974928	+	1.22252i	0.974928	+	1.22252i			1.00000i	$0.5\pi$
$828$		0			0
$829$	1.21135	−	0.825886i	1.21135	−	0.825886i	0.222521	−	0.974928i	$-0.428571\pi$
$829$	1.21135	−	0.825886i	1.21135	−	0.825886i	0.988831	+	0.149042i	$0.0476190\pi$
$830$	−0.712926	−	1.81651i	−0.712926	−	1.81651i
$831$		0			0
$832$	0.823216			0.823216
$833$	−0.571270	−	1.45557i	−0.571270	−	1.45557i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$	−1.63332	−	0.246184i	−1.63332	−	0.246184i
$839$	0.777479	+	0.974928i	0.777479	+	0.974928i	1.00000			$0$
$839$	0.777479	+	0.974928i	0.777479	+	0.974928i	−0.222521	+	0.974928i	$0.571429\pi$
$840$		0			0
$841$	0.623490	−	0.781831i	0.623490	−	0.781831i
$842$	1.02986	−	0.955573i	1.02986	−	0.955573i
$843$		0			0
$844$		0			0
$845$	−0.702749	−	0.479126i	−0.702749	−	0.479126i
$846$		0			0
$847$	−0.294755	−	0.955573i	−0.294755	−	0.955573i
$848$		0			0
$849$		0			0
$850$	0.131651	−	1.75676i	0.131651	−	1.75676i
$851$		0			0
$852$		0			0
$853$	−0.781831	+	0.376510i	−0.781831	+	0.376510i	−0.781831	−	0.623490i	$-0.785714\pi$
$853$	−0.781831	+	0.376510i	−0.781831	+	0.376510i			1.00000i	$0.5\pi$
$854$		0			0
$855$		0			0
$856$	−0.0533842	−	0.712362i	−0.0533842	−	0.712362i
$857$	1.07659	+	0.332083i	1.07659	+	0.332083i	0.781831	−	0.623490i	$-0.214286\pi$
$857$	1.07659	+	0.332083i	1.07659	+	0.332083i	0.294755	+	0.955573i	$0.404762\pi$
$858$		0			0
$859$	−0.0931869	−	1.24349i	−0.0931869	−	1.24349i	−0.826239	−	0.563320i	$-0.809524\pi$
$859$	−0.0931869	−	1.24349i	−0.0931869	−	1.24349i	0.733052	−	0.680173i	$-0.238095\pi$
$860$	0.143043	+	0.0688859i	0.143043	+	0.0688859i
$861$		0			0
$862$		0			0
$863$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$863$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$864$		0			0
$865$	0.149042	−	1.98883i	0.149042	−	1.98883i
$866$		0			0
$867$		0			0
$868$	−0.0793829	−	0.257353i	−0.0793829	−	0.257353i
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$876$		0			0
$877$	−1.71271	−	0.258149i	−1.71271	−	0.258149i	−0.781831	−	0.623490i	$-0.785714\pi$
$877$	−1.71271	−	0.258149i	−1.71271	−	0.258149i	−0.930874	+	0.365341i	$0.880952\pi$
$878$		0			0
$879$		0			0
$880$	−1.14362	+	0.352759i	−1.14362	+	0.352759i
$881$	0.149460			0.149460			0.0747301	−	0.997204i	$-0.476190\pi$
$881$	0.149460			0.149460			0.0747301	+	0.997204i	$0.476190\pi$
$882$	−0.0841939	+	1.12349i	−0.0841939	+	1.12349i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$	0.547421	−	0.168857i	0.547421	−	0.168857i
$885$		0			0
$886$		0			0
$887$	1.84095	+	0.277479i	1.84095	+	0.277479i	0.974928	−	0.222521i	$-0.0714286\pi$
$887$	1.84095	+	0.277479i	1.84095	+	0.277479i	0.866025	+	0.500000i	$0.166667\pi$
$888$		0			0
$889$	−0.678448	+	0.541044i	−0.678448	+	0.541044i
$890$	1.34248	−	1.68342i	1.34248	−	1.68342i
$891$	0.733052	−	0.680173i	0.733052	−	0.680173i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−0.367711	+	1.61105i	−0.367711	+	1.61105i
$896$	0.820914	+	0.884735i	0.820914	+	0.884735i
$897$		0			0
$898$	0.603460	−	1.53759i	0.603460	−	1.53759i
$899$		0			0
$900$	−0.134659	+	0.233236i	−0.134659	+	0.233236i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.0546039	+	0.728639i	0.0546039	+	0.728639i
$906$		0			0
$907$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$907$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$908$	−0.00599930	−	0.0800550i	−0.00599930	−	0.0800550i
$909$		0			0
$910$	−0.228425	−	1.51550i	−0.228425	−	1.51550i
$911$	0.134659	−	0.0648483i	0.134659	−	0.0648483i	−0.365341	−	0.930874i	$-0.619048\pi$
$911$	0.134659	−	0.0648483i	0.134659	−	0.0648483i	0.500000	+	0.866025i	$0.333333\pi$
$912$		0			0
$913$	0.866025	−	1.50000i	0.866025	−	1.50000i
$914$	−0.145828	+	1.94594i	−0.145828	+	1.94594i
$915$		0			0
$916$	−0.0990311	−	0.433884i	−0.0990311	−	0.433884i
$917$		0			0
$918$		0			0
$919$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$919$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.40157	−	1.75751i	1.40157	−	1.75751i
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.72188	+	0.531130i	−1.72188	+	0.531130i	−0.988831	−	0.149042i	$-0.952381\pi$
$929$	−1.72188	+	0.531130i	−1.72188	+	0.531130i	−0.733052	+	0.680173i	$0.761905\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.29196	−	0.880843i	1.29196	−	0.880843i
$936$	1.10735	+	0.166906i	1.10735	+	0.166906i
$937$	−0.848162	−	1.06356i	−0.848162	−	1.06356i	−0.997204	−	0.0747301i	$-0.976190\pi$
$937$	−0.848162	−	1.06356i	−0.848162	−	1.06356i	0.149042	−	0.988831i	$-0.452381\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$941$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$942$		0			0
$943$		0			0
$944$	−0.390438	+	1.71062i	−0.390438	+	1.71062i
$945$		0			0
$946$	0.147791	+	0.647514i	0.147791	+	0.647514i
$947$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$947$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$948$		0			0
$949$	−1.26631	+	2.19331i	−1.26631	+	2.19331i
$950$		0			0
$951$		0			0
$952$	−1.11478	−	0.643616i	−1.11478	−	0.643616i
$953$	−1.75676	−	0.846011i	−1.75676	−	0.846011i	−0.974928	−	0.222521i	$-0.928571\pi$
$953$	−1.75676	−	0.846011i	−1.75676	−	0.846011i	−0.781831	−	0.623490i	$-0.785714\pi$
$954$		0			0
$955$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$		0			0
$962$		0			0
$963$	0.0648483	−	0.865341i	0.0648483	−	0.865341i
$964$		0			0
$965$	0.347948	+	1.52446i	0.347948	+	1.52446i
$966$		0			0
$967$	0.414278	−	1.81507i	0.414278	−	1.81507i	−0.149042	−	0.988831i	$-0.547619\pi$
$967$	0.414278	−	1.81507i	0.414278	−	1.81507i	0.563320	−	0.826239i	$-0.309524\pi$
$968$	−0.680173	−	0.463734i	−0.680173	−	0.463734i
$969$		0			0
$970$		0			0
$971$	0.109562	−	0.101659i	0.109562	−	0.101659i	−0.623490	−	0.781831i	$-0.714286\pi$
$971$	0.109562	−	0.101659i	0.109562	−	0.101659i	0.733052	+	0.680173i	$0.238095\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$977$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$978$		0			0
$979$	1.91115			1.91115
$980$	0.167917	−	0.210561i	0.167917	−	0.210561i
$981$		0			0
$982$		0			0
$983$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$983$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$984$		0			0
$985$	−1.97213	−	0.297251i	−1.97213	−	0.297251i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−1.11406	+	0.167917i	−1.11406	+	0.167917i
$991$	0.914101	+	0.848162i	0.914101	+	0.848162i	0.988831	−	0.149042i	$-0.0476190\pi$
$991$	0.914101	+	0.848162i	0.914101	+	0.848162i	−0.0747301	+	0.997204i	$0.523810\pi$
$992$	−0.433884	−	0.295817i	−0.433884	−	0.295817i
$993$		0			0
$994$	1.85654	−	0.139129i	1.85654	−	0.139129i
$995$	0.0332580	+	0.145713i	0.0332580	+	0.145713i
$996$		0			0
$997$	0.0440542	−	0.587862i	0.0440542	−	0.587862i	−0.930874	−	0.365341i	$-0.880952\pi$
$997$	0.0440542	−	0.587862i	0.0440542	−	0.587862i	0.974928	−	0.222521i	$-0.0714286\pi$
$998$	−1.07659	+	1.86470i	−1.07659	+	1.86470i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.1.ck.c.2034.2	yes	24
5.4	even	2	inner	2695.1.ck.c.2034.1	yes	24
11.10	odd	2	inner	2695.1.ck.c.2034.1	yes	24
49.2	even	21	inner	2695.1.ck.c.1374.2	yes	24
55.54	odd	2	CM	2695.1.ck.c.2034.2	yes	24
245.149	even	42	inner	2695.1.ck.c.1374.1	✓	24
539.296	odd	42	inner	2695.1.ck.c.1374.1	✓	24
2695.1374	odd	42	inner	2695.1.ck.c.1374.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2695.1.ck.c.1374.1	✓	24	245.149	even	42	inner
2695.1.ck.c.1374.1	✓	24	539.296	odd	42	inner
2695.1.ck.c.1374.2	yes	24	49.2	even	21	inner
2695.1.ck.c.1374.2	yes	24	2695.1374	odd	42	inner
2695.1.ck.c.2034.1	yes	24	5.4	even	2	inner
2695.1.ck.c.2034.1	yes	24	11.10	odd	2	inner
2695.1.ck.c.2034.2	yes	24	1.1	even	1	trivial
2695.1.ck.c.2034.2	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)

\(f(q)\)	\(=\)	\(q+(1.07659 - 0.332083i) q^{2} +(0.222521 - 0.151712i) q^{4} +(0.988831 + 0.149042i) q^{5} +(-0.974928 + 0.222521i) q^{7} +(-0.513267 + 0.643616i) q^{8} +(-0.733052 + 0.680173i) q^{9} +(1.11406 - 0.167917i) q^{10} +(0.733052 + 0.680173i) q^{11} +(-0.302705 + 1.32624i) q^{13} +(-0.975699 + 0.563320i) q^{14} +(-0.437235 + 1.11406i) q^{16} +(0.116853 - 1.55929i) q^{17} +(-0.563320 + 0.975699i) q^{18} +(0.242647 - 0.116853i) q^{20} +(1.01507 + 0.488831i) q^{22} +(0.955573 + 0.294755i) q^{25} +(0.114533 + 1.52833i) q^{26} +(-0.183183 + 0.197424i) q^{28} +(-0.500000 + 0.866025i) q^{31} +(-0.0392431 + 0.523663i) q^{32} +(-0.392012 - 1.71752i) q^{34} +(-0.997204 + 0.0747301i) q^{35} +(-0.0599289 + 0.262566i) q^{36} +(-0.603460 + 0.559929i) q^{40} +(0.367554 + 0.460898i) q^{43} +(0.266310 + 0.0401398i) q^{44} +(-0.826239 + 0.563320i) q^{45} +(0.900969 - 0.433884i) q^{49} +1.12664 q^{50} +(0.133848 + 0.341040i) q^{52} +(0.623490 + 0.781831i) q^{55} +(0.357180 - 0.741692i) q^{56} +(1.44973 - 0.218511i) q^{59} +(-0.250701 + 1.09839i) q^{62} +(0.563320 - 0.826239i) q^{63} +(-0.134659 - 0.589980i) q^{64} +(-0.496990 + 1.26631i) q^{65} +(-0.210561 - 0.364703i) q^{68} +(-1.04876 + 0.411608i) q^{70} +(-1.48883 - 0.716983i) q^{71} +(-0.0615190 - 0.820914i) q^{72} +(1.77904 + 0.548760i) q^{73} +(-0.866025 - 0.500000i) q^{77} +(-0.598393 + 1.03645i) q^{80} +(0.0747301 - 0.997204i) q^{81} +(-0.385418 - 1.68862i) q^{83} +(0.347948 - 1.52446i) q^{85} +(0.548760 + 0.374138i) q^{86} +(-0.814021 + 0.122694i) q^{88} +(1.40097 - 1.29991i) q^{89} +(-0.702449 + 0.880843i) q^{90} -1.36035i q^{91} +(0.825886 - 0.766310i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4} - 2 q^{5} + 2 q^{9} - 2 q^{11} - 6 q^{14} - 26 q^{16} + 8 q^{20} + 2 q^{25} + 6 q^{26} - 12 q^{31} - 14 q^{34} - 8 q^{36} - 18 q^{44} - 2 q^{45} + 4 q^{49} - 4 q^{55} + 14 q^{56} - 2 q^{59}+ \cdots - 24 q^{99}+O(q^{100}) \) 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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