LMFDB - Embedded newform 2695.1.ck.c.2144.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2695, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 40, 21]))

N = Newforms(chi, 1, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2695.109");

S:= CuspForms(chi, 1);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.34498020905$
Analytic rank:	$0$
Dimension:	$24$
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			2144.1
Root			$-0.294755 + 0.955573i$ of defining polynomial
Character	$\chi$	$=$	2695.2144
Dual form			2695.1.ck.c.494.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53825 + 1.04876i) q^{2} +(0.900969 - 2.29563i) q^{4} +(-0.955573 - 0.294755i) q^{5} +(-0.433884 - 0.900969i) q^{7} +(0.607374 + 2.66108i) q^{8} +(0.0747301 - 0.997204i) q^{9} +O(q^{10})$	\(q+(-1.53825 + 1.04876i) q^{2} +(0.900969 - 2.29563i) q^{4} +(-0.955573 - 0.294755i) q^{5} +(-0.433884 - 0.900969i) q^{7} +(0.607374 + 2.66108i) q^{8} +(0.0747301 - 0.997204i) q^{9} +(1.77904 - 0.548760i) q^{10} +(-0.0747301 - 0.997204i) q^{11} +(-1.79690 - 0.865341i) q^{13} +(1.61232 + 0.930874i) q^{14} +(-1.91734 - 1.77904i) q^{16} +(1.92808 + 0.290611i) q^{17} +(0.930874 + 1.61232i) q^{18} +(-1.53759 + 1.92808i) q^{20} +(1.16078 + 1.45557i) q^{22} +(0.826239 + 0.563320i) q^{25} +(3.67161 - 0.553406i) q^{26} +(-2.45921 + 0.184292i) q^{28} +(-0.500000 - 0.866025i) q^{31} +(2.11610 + 0.318951i) q^{32} +(-3.27064 + 1.57506i) q^{34} +(0.149042 + 0.988831i) q^{35} +(-2.22188 - 1.07000i) q^{36} +(0.203977 - 2.72188i) q^{40} +(0.250701 - 1.09839i) q^{43} +(-2.35654 - 0.726897i) q^{44} +(-0.365341 + 0.930874i) q^{45} +(-0.623490 + 0.781831i) q^{49} -1.86175 q^{50} +(-3.60545 + 3.34537i) q^{52} +(-0.222521 + 0.974928i) q^{55} +(2.13402 - 1.70182i) q^{56} +(0.142820 - 0.0440542i) q^{59} +(1.67738 + 0.807782i) q^{62} +(-0.930874 + 0.365341i) q^{63} +(-1.23305 + 0.593806i) q^{64} +(1.46200 + 1.35654i) q^{65} +(2.40427 - 4.16432i) q^{68} +(-1.26631 - 1.36476i) q^{70} +(0.455573 + 0.571270i) q^{71} +(2.69903 - 0.406813i) q^{72} +(-1.12397 - 0.766310i) q^{73} +(-0.866025 + 0.500000i) q^{77} +(1.30778 + 2.26514i) q^{80} +(-0.988831 - 0.149042i) q^{81} +(-1.56052 + 0.751509i) q^{83} +(-1.75676 - 0.846011i) q^{85} +(0.766310 + 1.95253i) q^{86} +(2.60825 - 0.804539i) q^{88} +(-0.123490 + 1.64786i) q^{89} +(-0.414278 - 1.81507i) q^{90} +1.99441i q^{91} +(0.139129 - 1.85654i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4} - 2 q^{5} + 2 q^{9}+O(q^{10}) $ 24 * q + 4 * q^4 - 2 * q^5 + 2 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$981$	$1816$	$2157$
$\chi(n)$	$-1$	$e\left(\frac{16}{21}\right)$	$-1$

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 $

$2$	−1.53825	+	1.04876i	−1.53825	+	1.04876i	−0.563320	+	0.826239i	$0.690476\pi$
$2$	−1.53825	+	1.04876i	−1.53825	+	1.04876i	−0.974928	+	0.222521i	$0.928571\pi$
$3$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$3$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$4$	0.900969	−	2.29563i	0.900969	−	2.29563i
$5$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$5$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$6$		0			0
$7$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$7$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$8$	0.607374	+	2.66108i	0.607374	+	2.66108i
$9$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$10$	1.77904	−	0.548760i	1.77904	−	0.548760i
$11$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i
$11$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i
$12$		0			0
$13$	−1.79690	−	0.865341i	−1.79690	−	0.865341i	−0.930874	−	0.365341i	$-0.880952\pi$
$13$	−1.79690	−	0.865341i	−1.79690	−	0.865341i	−0.866025	−	0.500000i	$-0.833333\pi$
$14$	1.61232	+	0.930874i	1.61232	+	0.930874i
$15$		0			0
$16$	−1.91734	−	1.77904i	−1.91734	−	1.77904i
$17$	1.92808	+	0.290611i	1.92808	+	0.290611i	0.997204	−	0.0747301i	$-0.0238095\pi$
$17$	1.92808	+	0.290611i	1.92808	+	0.290611i	0.930874	+	0.365341i	$0.119048\pi$
$18$	0.930874	+	1.61232i	0.930874	+	1.61232i
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$	−1.53759	+	1.92808i	−1.53759	+	1.92808i
$21$		0			0
$22$	1.16078	+	1.45557i	1.16078	+	1.45557i
$23$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$23$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$24$		0			0
$25$	0.826239	+	0.563320i	0.826239	+	0.563320i
$26$	3.67161	−	0.553406i	3.67161	−	0.553406i
$27$		0			0
$28$	−2.45921	+	0.184292i	−2.45921	+	0.184292i
$29$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$29$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$30$		0			0
$31$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$31$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$32$	2.11610	+	0.318951i	2.11610	+	0.318951i
$33$		0			0
$34$	−3.27064	+	1.57506i	−3.27064	+	1.57506i
$35$	0.149042	+	0.988831i	0.149042	+	0.988831i
$36$	−2.22188	−	1.07000i	−2.22188	−	1.07000i
$37$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$37$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$38$		0			0
$39$		0			0
$40$	0.203977	−	2.72188i	0.203977	−	2.72188i
$41$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$41$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$42$		0			0
$43$	0.250701	−	1.09839i	0.250701	−	1.09839i	−0.680173	−	0.733052i	$-0.738095\pi$
$43$	0.250701	−	1.09839i	0.250701	−	1.09839i	0.930874	−	0.365341i	$-0.119048\pi$
$44$	−2.35654	−	0.726897i	−2.35654	−	0.726897i
$45$	−0.365341	+	0.930874i	−0.365341	+	0.930874i
$46$		0			0
$47$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$47$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$48$		0			0
$49$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$50$	−1.86175			−1.86175
$51$		0			0
$52$	−3.60545	+	3.34537i	−3.60545	+	3.34537i
$53$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$53$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$54$		0			0
$55$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$56$	2.13402	−	1.70182i	2.13402	−	1.70182i
$57$		0			0
$58$		0			0
$59$	0.142820	−	0.0440542i	0.142820	−	0.0440542i	−0.222521	−	0.974928i	$-0.571429\pi$
$59$	0.142820	−	0.0440542i	0.142820	−	0.0440542i	0.365341	+	0.930874i	$0.380952\pi$
$60$		0			0
$61$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$61$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$62$	1.67738	+	0.807782i	1.67738	+	0.807782i
$63$	−0.930874	+	0.365341i	−0.930874	+	0.365341i
$64$	−1.23305	+	0.593806i	−1.23305	+	0.593806i
$65$	1.46200	+	1.35654i	1.46200	+	1.35654i
$66$		0			0
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$	2.40427	−	4.16432i	2.40427	−	4.16432i
$69$		0			0
$70$	−1.26631	−	1.36476i	−1.26631	−	1.36476i
$71$	0.455573	+	0.571270i	0.455573	+	0.571270i	0.955573	−	0.294755i	$-0.0952381\pi$
$71$	0.455573	+	0.571270i	0.455573	+	0.571270i	−0.500000	+	0.866025i	$0.666667\pi$
$72$	2.69903	−	0.406813i	2.69903	−	0.406813i
$73$	−1.12397	−	0.766310i	−1.12397	−	0.766310i	−0.149042	−	0.988831i	$-0.547619\pi$
$73$	−1.12397	−	0.766310i	−1.12397	−	0.766310i	−0.974928	+	0.222521i	$0.928571\pi$
$74$		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	$0.666667\pi$
$80$	1.30778	+	2.26514i	1.30778	+	2.26514i
$81$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$82$		0			0
$83$	−1.56052	+	0.751509i	−1.56052	+	0.751509i	−0.997204	−	0.0747301i	$-0.976190\pi$
$83$	−1.56052	+	0.751509i	−1.56052	+	0.751509i	−0.563320	+	0.826239i	$0.690476\pi$
$84$		0			0
$85$	−1.75676	−	0.846011i	−1.75676	−	0.846011i
$86$	0.766310	+	1.95253i	0.766310	+	1.95253i
$87$		0			0
$88$	2.60825	−	0.804539i	2.60825	−	0.804539i
$89$	−0.123490	+	1.64786i	−0.123490	+	1.64786i	0.500000	+	0.866025i	$0.333333\pi$
$89$	−0.123490	+	1.64786i	−0.123490	+	1.64786i	−0.623490	+	0.781831i	$0.714286\pi$
$90$	−0.414278	−	1.81507i	−0.414278	−	1.81507i
$91$			1.99441i			1.99441i
$92$		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			$\pi$
$98$	0.139129	−	1.85654i	0.139129	−	1.85654i
$99$	−1.00000			−1.00000
$100$	2.03759	−	1.38921i	2.03759	−	1.38921i
$101$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$101$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$102$		0			0
$103$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$103$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$104$	1.21135	−	5.30728i	1.21135	−	5.30728i
$105$		0			0
$106$		0			0
$107$	0.116853	−	1.55929i	0.116853	−	1.55929i	−0.563320	−	0.826239i	$-0.690476\pi$
$107$	0.116853	−	1.55929i	0.116853	−	1.55929i	0.680173	−	0.733052i	$-0.261905\pi$
$108$		0			0
$109$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$109$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$110$	−0.680173	−	1.73305i	−0.680173	−	1.73305i
$111$		0			0
$112$	−0.770951	+	2.49936i	−0.770951	+	2.49936i
$113$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$113$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.997204	+	1.72721i	−0.997204	+	1.72721i
$118$	−0.173490	+	0.217550i	−0.173490	+	0.217550i
$119$	−0.574730	−	1.86323i	−0.574730	−	1.86323i
$120$		0			0
$121$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$122$		0			0
$123$		0			0
$124$	−2.43856	+	0.367554i	−2.43856	+	0.367554i
$125$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$126$	1.04876	−	1.53825i	1.04876	−	1.53825i
$127$	−0.974928	+	1.22252i	−0.974928	+	1.22252i			1.00000i	$0.5\pi$
$127$	−0.974928	+	1.22252i	−0.974928	+	1.22252i	−0.974928	+	0.222521i	$0.928571\pi$
$128$	0.203977	−	0.353298i	0.203977	−	0.353298i
$129$		0			0
$130$	−3.67161	−	0.553406i	−3.67161	−	0.553406i
$131$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$131$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.397726	+	5.30728i	0.397726	+	5.30728i
$137$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$137$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$138$		0			0
$139$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$139$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$140$	2.40427	+	0.548760i	2.40427	+	0.548760i
$141$		0			0
$142$	−1.29991	−	0.400969i	−1.29991	−	0.400969i
$143$	−0.728639	+	1.85654i	−0.728639	+	1.85654i
$144$	−1.91734	+	1.77904i	−1.91734	+	1.77904i
$145$		0			0
$146$	2.53262			2.53262
$147$		0			0
$148$		0			0
$149$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$149$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$150$		0			0
$151$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$151$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$152$		0			0
$153$	0.433884	−	1.90097i	0.433884	−	1.90097i
$154$	0.807782	−	1.67738i	0.807782	−	1.67738i
$155$	0.222521	+	0.974928i	0.222521	+	0.974928i
$156$		0			0
$157$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$157$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$158$		0			0
$159$		0			0
$160$	−1.92808	−	0.928513i	−1.92808	−	0.928513i
$161$		0			0
$162$	1.67738	−	0.807782i	1.67738	−	0.807782i
$163$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$163$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$164$		0			0
$165$		0			0
$166$	1.61232	−	2.79262i	1.61232	−	2.79262i
$167$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$167$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$168$		0			0
$169$	1.85654	+	2.32803i	1.85654	+	2.32803i
$170$	3.58959	−	0.541044i	3.58959	−	0.541044i
$171$		0			0
$172$	−2.29563	−	1.56513i	−2.29563	−	1.56513i
$173$	−0.294755	+	0.0444272i	−0.294755	+	0.0444272i	−0.294755	−	0.955573i	$-0.595238\pi$
$173$	−0.294755	+	0.0444272i	−0.294755	+	0.0444272i			1.00000i	$0.5\pi$
$174$		0			0
$175$	0.149042	−	0.988831i	0.149042	−	0.988831i
$176$	−1.63078	+	2.04493i	−1.63078	+	2.04493i
$177$		0			0
$178$	−1.53825	−	2.66432i	−1.53825	−	2.66432i
$179$	0.722521	+	0.108903i	0.722521	+	0.108903i	0.500000	−	0.866025i	$-0.333333\pi$
$179$	0.722521	+	0.108903i	0.722521	+	0.108903i	0.222521	+	0.974928i	$0.428571\pi$
$180$	1.80778	+	1.67738i	1.80778	+	1.67738i
$181$	−1.32091	+	0.636119i	−1.32091	+	0.636119i	−0.955573	−	0.294755i	$-0.904762\pi$
$181$	−1.32091	+	0.636119i	−1.32091	+	0.636119i	−0.365341	+	0.930874i	$0.619048\pi$
$182$	−2.09165	−	3.06789i	−2.09165	−	3.06789i
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.145713	−	1.94440i	0.145713	−	1.94440i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.955573	+	0.294755i	0.955573	+	0.294755i	0.733052	−	0.680173i	$-0.238095\pi$
$191$	0.955573	+	0.294755i	0.955573	+	0.294755i	0.222521	+	0.974928i	$0.428571\pi$
$192$		0			0
$193$	1.42935	−	1.32624i	1.42935	−	1.32624i	0.563320	−	0.826239i	$-0.309524\pi$
$193$	1.42935	−	1.32624i	1.42935	−	1.32624i	0.866025	−	0.500000i	$-0.166667\pi$
$194$		0			0
$195$		0			0
$196$	1.23305	+	2.13571i	1.23305	+	2.13571i
$197$	0.298085			0.298085			0.149042	−	0.988831i	$-0.452381\pi$
$197$	0.298085			0.298085			0.149042	+	0.988831i	$0.452381\pi$
$198$	1.53825	−	1.04876i	1.53825	−	1.04876i
$199$	1.44973	−	1.34515i	1.44973	−	1.34515i	0.623490	−	0.781831i	$-0.285714\pi$
$199$	1.44973	−	1.34515i	1.44973	−	1.34515i	0.826239	−	0.563320i	$-0.190476\pi$
$200$	−0.997204	+	2.54083i	−0.997204	+	2.54083i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$	1.90580	+	4.85590i	1.90580	+	4.85590i
$209$		0			0
$210$		0			0
$211$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$211$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$212$		0			0
$213$		0			0
$214$	1.45557	+	2.52113i	1.45557	+	2.52113i
$215$	−0.563320	+	0.975699i	−0.563320	+	0.975699i
$216$		0			0
$217$	−0.563320	+	0.826239i	−0.563320	+	0.826239i
$218$		0			0
$219$		0			0
$220$	2.03759	+	1.38921i	2.03759	+	1.38921i
$221$	−3.21308	−	2.19064i	−3.21308	−	2.19064i
$222$		0			0
$223$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$223$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$224$	−0.630777	−	2.04493i	−0.630777	−	2.04493i
$225$	0.623490	−	0.781831i	0.623490	−	0.781831i
$226$		0			0
$227$	0.294755	+	0.510531i	0.294755	+	0.510531i	0.974928	−	0.222521i	$-0.0714286\pi$
$227$	0.294755	+	0.510531i	0.294755	+	0.510531i	−0.680173	+	0.733052i	$0.738095\pi$
$228$		0			0
$229$	−0.535628	−	0.496990i	−0.535628	−	0.496990i	0.365341	−	0.930874i	$-0.380952\pi$
$229$	−0.535628	−	0.496990i	−0.535628	−	0.496990i	−0.900969	+	0.433884i	$0.857143\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.930874	−	0.365341i	$-0.119048\pi$
$233$		0			0		−0.930874	+	0.365341i	$0.880952\pi$
$234$	−0.277479	−	3.70270i	−0.277479	−	3.70270i
$235$		0			0
$236$	0.0275443	−	0.367554i	0.0275443	−	0.367554i
$237$		0			0
$238$	2.83816	+	2.26335i	2.83816	+	2.26335i
$239$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$239$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$240$		0			0
$241$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$241$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$242$	1.36476	−	1.26631i	1.36476	−	1.26631i
$243$		0			0
$244$		0			0
$245$	0.826239	−	0.563320i	0.826239	−	0.563320i
$246$		0			0
$247$		0			0
$248$	2.00088	−	1.85654i	2.00088	−	1.85654i
$249$		0			0
$250$	1.77904	+	0.548760i	1.77904	+	0.548760i
$251$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$251$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$252$			2.46610i			2.46610i
$253$		0			0
$254$	0.217550	−	2.90301i	0.217550	−	2.90301i
$255$		0			0
$256$	−0.0455164	−	0.607374i	−0.0455164	−	0.607374i
$257$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$257$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$258$		0			0
$259$		0			0
$260$	4.43134	−	2.13402i	4.43134	−	2.13402i
$261$		0			0
$262$		0			0
$263$	−0.866025	−	1.50000i	−0.866025	−	1.50000i	−0.866025	−	0.500000i	$-0.833333\pi$
$263$	−0.866025	−	1.50000i	−0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.367711	−	0.250701i	−0.367711	−	0.250701i	0.365341	−	0.930874i	$-0.380952\pi$
$269$	−0.367711	−	0.250701i	−0.367711	−	0.250701i	−0.733052	+	0.680173i	$0.761905\pi$
$270$		0			0
$271$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$271$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$272$	−3.17978	−	3.98732i	−3.17978	−	3.98732i
$273$		0			0
$274$		0			0
$275$	0.500000	−	0.866025i	0.500000	−	0.866025i
$276$		0			0
$277$	1.34515	+	0.202749i	1.34515	+	0.202749i	0.781831	−	0.623490i	$-0.214286\pi$
$277$	1.34515	+	0.202749i	1.34515	+	0.202749i	0.563320	+	0.826239i	$0.309524\pi$
$278$		0			0
$279$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$280$	−2.54083	+	0.997204i	−2.54083	+	0.997204i
$281$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$281$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$282$		0			0
$283$	−0.0648483	−	0.865341i	−0.0648483	−	0.865341i	−0.930874	−	0.365341i	$-0.880952\pi$
$283$	−0.0648483	−	0.865341i	−0.0648483	−	0.865341i	0.866025	−	0.500000i	$-0.166667\pi$
$284$	1.72188	−	0.531130i	1.72188	−	0.531130i
$285$		0			0
$286$	−0.826239	−	3.61999i	−0.826239	−	3.61999i
$287$		0			0
$288$	0.476196	−	2.08635i	0.476196	−	2.08635i
$289$	2.67746	+	0.825886i	2.67746	+	0.825886i
$290$		0			0
$291$		0			0
$292$	−2.77183	+	1.88980i	−2.77183	+	1.88980i
$293$	0.589510			0.589510			0.294755	−	0.955573i	$-0.404762\pi$
$293$	0.589510			0.589510			0.294755	+	0.955573i	$0.404762\pi$
$294$		0			0
$295$	−0.149460			−0.149460
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−1.09839	+	0.250701i	−1.09839	+	0.250701i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$	1.32624	+	3.37920i	1.32624	+	3.37920i
$307$	1.67738	+	0.807782i	1.67738	+	0.807782i	0.997204	+	0.0747301i	$0.0238095\pi$
$307$	1.67738	+	0.807782i	1.67738	+	0.807782i	0.680173	+	0.733052i	$0.261905\pi$
$308$	0.367554	+	2.43856i	0.367554	+	2.43856i
$309$		0			0
$310$	−1.36476	−	1.26631i	−1.36476	−	1.26631i
$311$	−1.88980	−	0.284841i	−1.88980	−	0.284841i	−0.900969	−	0.433884i	$-0.857143\pi$
$311$	−1.88980	−	0.284841i	−1.88980	−	0.284841i	−0.988831	+	0.149042i	$0.952381\pi$
$312$		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
$315$	0.997204	−	0.0747301i	0.997204	−	0.0747301i
$316$		0			0
$317$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$317$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$318$		0			0
$319$		0			0
$320$	1.35330	−	0.203977i	1.35330	−	0.203977i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−1.23305	+	2.13571i	−1.23305	+	2.13571i
$325$	−0.997204	−	1.72721i	−0.997204	−	1.72721i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.603718	−	1.53825i	−0.603718	−	1.53825i	−0.826239	−	0.563320i	$-0.809524\pi$
$331$	−0.603718	−	1.53825i	−0.603718	−	1.53825i	0.222521	−	0.974928i	$-0.428571\pi$
$332$	0.319203	+	4.25947i	0.319203	+	4.25947i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.443797	+	1.94440i	−0.443797	+	1.94440i	−0.149042	+	0.988831i	$0.547619\pi$
$337$	−0.443797	+	1.94440i	−0.443797	+	1.94440i	−0.294755	+	0.955573i	$0.595238\pi$
$338$	−5.29737	−	1.63402i	−5.29737	−	1.63402i
$339$		0			0
$340$	−3.52491	+	3.27064i	−3.52491	+	3.27064i
$341$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$342$		0			0
$343$	0.974928	+	0.222521i	0.974928	+	0.222521i
$344$	3.07518			3.07518
$345$		0			0
$346$	0.406813	−	0.377467i	0.406813	−	0.377467i
$347$	−0.108903	+	0.277479i	−0.108903	+	0.277479i	−0.974928	−	0.222521i	$-0.928571\pi$
$347$	−0.108903	+	0.277479i	−0.108903	+	0.277479i	0.866025	+	0.500000i	$0.166667\pi$
$348$		0			0
$349$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$349$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$350$	0.807782	+	1.67738i	0.807782	+	1.67738i
$351$		0			0
$352$	0.159923	−	2.13402i	0.159923	−	2.13402i
$353$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$353$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$354$		0			0
$355$	−0.266948	−	0.680173i	−0.266948	−	0.680173i
$356$	3.67161	+	1.76815i	3.67161	+	1.76815i
$357$		0			0
$358$	−1.22563	+	0.590232i	−1.22563	+	0.590232i
$359$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$359$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$360$	−2.69903	−	0.406813i	−2.69903	−	0.406813i
$361$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$362$	1.36476	−	2.36383i	1.36476	−	2.36383i
$363$		0			0
$364$	4.57842	+	1.79690i	4.57842	+	1.79690i
$365$	0.848162	+	1.06356i	0.848162	+	1.06356i
$366$		0			0
$367$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$367$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	0.294755	−	0.510531i	0.294755	−	0.510531i	−0.680173	−	0.733052i	$-0.738095\pi$
$373$	0.294755	−	0.510531i	0.294755	−	0.510531i	0.974928	+	0.222521i	$0.0714286\pi$
$374$	1.81507	+	3.14379i	1.81507	+	3.14379i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.72188	−	0.829215i	−1.72188	−	0.829215i	−0.988831	−	0.149042i	$-0.952381\pi$
$379$	−1.72188	−	0.829215i	−1.72188	−	0.829215i	−0.733052	−	0.680173i	$-0.761905\pi$
$380$		0			0
$381$		0			0
$382$	−1.77904	+	0.548760i	−1.77904	+	0.548760i
$383$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$383$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$384$		0			0
$385$	0.974928	−	0.222521i	0.974928	−	0.222521i
$386$	−0.807782	+	3.53912i	−0.807782	+	3.53912i
$387$	−1.07659	−	0.332083i	−1.07659	−	0.332083i
$388$		0			0
$389$	−1.40097	+	1.29991i	−1.40097	+	1.29991i	−0.500000	+	0.866025i	$0.666667\pi$
$389$	−1.40097	+	1.29991i	−1.40097	+	1.29991i	−0.900969	+	0.433884i	$0.857143\pi$
$390$		0			0
$391$		0			0
$392$	−2.45921	−	1.18429i	−2.45921	−	1.18429i
$393$		0			0
$394$	−0.458528	+	0.312619i	−0.458528	+	0.312619i
$395$		0			0
$396$	−0.900969	+	2.29563i	−0.900969	+	2.29563i
$397$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$397$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$398$	−0.819301	+	3.58959i	−0.819301	+	3.58959i
$399$		0			0
$400$	−0.582018	−	2.54999i	−0.582018	−	2.54999i
$401$	−0.123490	+	1.64786i	−0.123490	+	1.64786i	0.500000	+	0.866025i	$0.333333\pi$
$401$	−0.123490	+	1.64786i	−0.123490	+	1.64786i	−0.623490	+	0.781831i	$0.714286\pi$
$402$		0			0
$403$	0.149042	+	1.98883i	0.149042	+	1.98883i
$404$		0			0
$405$	0.900969	+	0.433884i	0.900969	+	0.433884i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$409$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−0.101659	−	0.109562i	−0.101659	−	0.109562i
$414$		0			0
$415$	1.71271	−	0.258149i	1.71271	−	0.258149i
$416$	−3.52642	−	2.40427i	−3.52642	−	2.40427i
$417$		0			0
$418$		0			0
$419$	−0.0931869	−	0.116853i	−0.0931869	−	0.116853i	0.733052	−	0.680173i	$-0.238095\pi$
$419$	−0.0931869	−	0.116853i	−0.0931869	−	0.116853i	−0.826239	+	0.563320i	$0.809524\pi$
$420$		0			0
$421$	0.277479	−	0.347948i	0.277479	−	0.347948i	−0.623490	−	0.781831i	$-0.714286\pi$
$421$	0.277479	−	0.347948i	0.277479	−	0.347948i	0.900969	+	0.433884i	$0.142857\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.42935	+	1.32624i	1.42935	+	1.32624i
$426$		0			0
$427$		0			0
$428$	−3.47428	−	1.67312i	−3.47428	−	1.67312i
$429$		0			0
$430$	−0.156748	−	2.09165i	−0.156748	−	2.09165i
$431$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$431$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$432$		0			0
$433$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$433$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$434$		−	1.86175i		−	1.86175i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$439$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$440$	−2.72951			−2.72951
$441$	0.733052	+	0.680173i	0.733052	+	0.680173i
$442$	7.23998			7.23998
$443$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$443$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$444$		0			0
$445$	0.603718	−	1.53825i	0.603718	−	1.53825i
$446$		0			0
$447$		0			0
$448$	1.07000	+	0.853298i	1.07000	+	0.853298i
$449$	0.0332580	+	0.145713i	0.0332580	+	0.145713i	0.988831	−	0.149042i	$-0.0476190\pi$
$449$	0.0332580	+	0.145713i	0.0332580	+	0.145713i	−0.955573	+	0.294755i	$0.904762\pi$
$450$	−0.139129	+	1.85654i	−0.139129	+	1.85654i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−0.988831	−	0.476196i	−0.988831	−	0.476196i
$455$	0.587862	−	1.90580i	0.587862	−	1.90580i
$456$		0			0
$457$	1.26968	+	1.17809i	1.26968	+	1.17809i	0.974928	+	0.222521i	$0.0714286\pi$
$457$	1.26968	+	1.17809i	1.26968	+	1.17809i	0.294755	+	0.955573i	$0.404762\pi$
$458$	1.34515	+	0.202749i	1.34515	+	0.202749i
$459$		0			0
$460$		0			0
$461$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$461$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$462$		0			0
$463$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$463$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$467$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$468$	3.06658	+	3.84537i	3.06658	+	3.84537i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.203977	+	0.353298i	0.203977	+	0.353298i
$473$	−1.11406	−	0.167917i	−1.11406	−	0.167917i
$474$		0			0
$475$		0			0
$476$	−4.79510	−	0.359343i	−4.79510	−	0.359343i
$477$		0			0
$478$		0			0
$479$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$479$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.548760	+	2.40427i	−0.548760	+	2.40427i
$485$		0			0
$486$		0			0
$487$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$487$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$488$		0			0
$489$		0			0
$490$	−0.680173	+	1.73305i	−0.680173	+	1.73305i
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	0.955573	+	0.294755i	0.955573	+	0.294755i
$496$	−0.582018	+	2.54999i	−0.582018	+	2.54999i
$497$	0.317031	−	0.658322i	0.317031	−	0.658322i
$498$		0			0
$499$	0.123490	−	1.64786i	0.123490	−	1.64786i	−0.500000	−	0.866025i	$-0.666667\pi$
$499$	0.123490	−	1.64786i	0.123490	−	1.64786i	0.623490	−	0.781831i	$-0.285714\pi$
$500$	−2.35654	+	0.726897i	−2.35654	+	0.726897i
$501$		0			0
$502$	−0.848162	−	2.16108i	−0.848162	−	2.16108i
$503$	1.56052	+	0.751509i	1.56052	+	0.751509i	0.997204	−	0.0747301i	$-0.0238095\pi$
$503$	1.56052	+	0.751509i	1.56052	+	0.751509i	0.563320	+	0.826239i	$0.309524\pi$
$504$	−1.53759	−	2.25523i	−1.53759	−	2.25523i
$505$		0			0
$506$		0			0
$507$		0			0
$508$	1.92808	+	3.33953i	1.92808	+	3.33953i
$509$	−0.955573	+	1.65510i	−0.955573	+	1.65510i	−0.222521	+	0.974928i	$0.571429\pi$
$509$	−0.955573	+	1.65510i	−0.955573	+	1.65510i	−0.733052	+	0.680173i	$0.761905\pi$
$510$		0			0
$511$	−0.202749	+	1.34515i	−0.202749	+	1.34515i
$512$	0.961360	+	1.20551i	0.961360	+	1.20551i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−2.72188	+	4.71444i	−2.72188	+	4.71444i
$521$	0.365341	+	0.632789i	0.365341	+	0.632789i	0.988831	−	0.149042i	$-0.0476190\pi$
$521$	0.365341	+	0.632789i	0.365341	+	0.632789i	−0.623490	+	0.781831i	$0.714286\pi$
$522$		0			0
$523$	0.825886	+	0.766310i	0.825886	+	0.766310i	0.974928	−	0.222521i	$-0.0714286\pi$
$523$	0.825886	+	0.766310i	0.825886	+	0.766310i	−0.149042	+	0.988831i	$0.547619\pi$
$524$		0			0
$525$		0			0
$526$	2.90530	+	1.39912i	2.90530	+	1.39912i
$527$	−0.712362	−	1.81507i	−0.712362	−	1.81507i
$528$		0			0
$529$	0.955573	−	0.294755i	0.955573	−	0.294755i
$530$		0			0
$531$	−0.0332580	−	0.145713i	−0.0332580	−	0.145713i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−0.571270	+	1.45557i	−0.571270	+	1.45557i
$536$		0			0
$537$		0			0
$538$	0.828556			0.828556
$539$	0.826239	+	0.563320i	0.826239	+	0.563320i
$540$		0			0
$541$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$541$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$542$		0			0
$543$		0			0
$544$	3.98732	+	1.22993i	3.98732	+	1.22993i
$545$		0			0
$546$		0			0
$547$	−0.302705	−	1.32624i	−0.302705	−	1.32624i	−0.866025	−	0.500000i	$-0.833333\pi$
$547$	−0.302705	−	1.32624i	−0.302705	−	1.32624i	0.563320	−	0.826239i	$-0.309524\pi$
$548$		0			0
$549$		0			0
$550$	0.139129	+	1.85654i	0.139129	+	1.85654i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−2.28181	+	1.09886i	−2.28181	+	1.09886i
$555$		0			0
$556$		0			0
$557$	−0.433884	−	0.751509i	−0.433884	−	0.751509i	0.563320	−	0.826239i	$-0.309524\pi$
$557$	−0.433884	−	0.751509i	−0.433884	−	0.751509i	−0.997204	+	0.0747301i	$0.976190\pi$
$558$	0.930874	−	1.61232i	0.930874	−	1.61232i
$559$	−1.40097	+	1.75676i	−1.40097	+	1.75676i
$560$	1.47340	−	2.16108i	1.47340	−	2.16108i
$561$		0			0
$562$		0			0
$563$	−0.246289	−	0.167917i	−0.246289	−	0.167917i	0.433884	−	0.900969i	$-0.357143\pi$
$563$	−0.246289	−	0.167917i	−0.246289	−	0.167917i	−0.680173	+	0.733052i	$0.738095\pi$
$564$		0			0
$565$		0			0
$566$	1.00729	+	1.26310i	1.00729	+	1.26310i
$567$	0.294755	+	0.955573i	0.294755	+	0.955573i
$568$	−1.24349	+	1.55929i	−1.24349	+	1.55929i
$569$		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		−0.988831	−	0.149042i	$-0.952381\pi$
$571$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$572$	3.60545	+	3.34537i	3.60545	+	3.34537i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.500000	+	1.27398i	0.500000	+	1.27398i
$577$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$577$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$578$	−4.98475	+	1.53759i	−4.98475	+	1.53759i
$579$		0			0
$580$		0			0
$581$	1.35417	+	1.07992i	1.35417	+	1.07992i
$582$		0			0
$583$		0			0
$584$	1.35654	−	3.45641i	1.35654	−	3.45641i
$585$	1.46200	−	1.35654i	1.46200	−	1.35654i
$586$	−0.906813	+	0.618255i	−0.906813	+	0.618255i
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$		0			0
$589$		0			0
$590$	0.229907	−	0.156748i	0.229907	−	0.156748i
$591$		0			0
$592$		0			0
$593$	−1.07659	−	0.332083i	−1.07659	−	0.332083i	−0.294755	−	0.955573i	$-0.595238\pi$
$593$	−1.07659	−	0.332083i	−1.07659	−	0.332083i	−0.781831	+	0.623490i	$0.785714\pi$
$594$		0			0
$595$			1.94986i			1.94986i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−0.142820	−	1.90580i	−0.142820	−	1.90580i	−0.365341	−	0.930874i	$-0.619048\pi$
$599$	−0.142820	−	1.90580i	−0.142820	−	1.90580i	0.222521	−	0.974928i	$-0.428571\pi$
$600$		0			0
$601$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$601$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$602$	1.42668	−	1.53759i	1.42668	−	1.53759i
$603$		0			0
$604$		0			0
$605$	0.988831	+	0.149042i	0.988831	+	0.149042i
$606$		0			0
$607$	−0.294755	+	0.510531i	−0.294755	+	0.510531i	−0.974928	−	0.222521i	$-0.928571\pi$
$607$	−0.294755	+	0.510531i	−0.294755	+	0.510531i	0.680173	+	0.733052i	$0.261905\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−3.97301	−	2.70875i	−3.97301	−	2.70875i
$613$	−0.246289	−	0.167917i	−0.246289	−	0.167917i	0.433884	−	0.900969i	$-0.357143\pi$
$613$	−0.246289	−	0.167917i	−0.246289	−	0.167917i	−0.680173	+	0.733052i	$0.738095\pi$
$614$	−3.42739	+	0.516596i	−3.42739	+	0.516596i
$615$		0			0
$616$	−1.85654	−	2.00088i	−1.85654	−	2.00088i
$617$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$617$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$618$		0			0
$619$	−0.900969	−	1.56052i	−0.900969	−	1.56052i	−0.826239	−	0.563320i	$-0.809524\pi$
$619$	−0.900969	−	1.56052i	−0.900969	−	1.56052i	−0.0747301	−	0.997204i	$-0.523810\pi$
$620$	2.43856	+	0.367554i	2.43856	+	0.367554i
$621$		0			0
$622$	3.20571	−	1.54379i	3.20571	−	1.54379i
$623$	1.53825	−	0.603718i	1.53825	−	0.603718i
$624$		0			0
$625$	0.365341	+	0.930874i	0.365341	+	0.930874i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−1.45557	+	1.16078i	−1.45557	+	1.16078i
$631$	0.440071	−	1.92808i	0.440071	−	1.92808i	0.0747301	−	0.997204i	$-0.476190\pi$
$631$	0.440071	−	1.92808i	0.440071	−	1.92808i	0.365341	−	0.930874i	$-0.380952\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.29196	−	0.880843i	1.29196	−	0.880843i
$636$		0			0
$637$	1.79690	−	0.865341i	1.79690	−	0.865341i
$638$		0			0
$639$	0.603718	−	0.411608i	0.603718	−	0.411608i
$640$	−0.299051	+	0.277479i	−0.299051	+	0.277479i
$641$	−0.455573	+	1.16078i	−0.455573	+	1.16078i	0.500000	+	0.866025i	$0.333333\pi$
$641$	−0.455573	+	1.16078i	−0.455573	+	1.16078i	−0.955573	+	0.294755i	$0.904762\pi$
$642$		0			0
$643$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$643$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$647$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$648$	−0.203977	−	2.72188i	−0.203977	−	2.72188i
$649$	−0.0546039	−	0.139129i	−0.0546039	−	0.139129i
$650$	3.34537	+	1.61105i	3.34537	+	1.61105i
$651$		0			0
$652$		0			0
$653$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$653$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−0.848162	+	1.06356i	−0.848162	+	1.06356i
$658$		0			0
$659$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$659$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$660$		0			0
$661$	1.03030	+	0.702449i	1.03030	+	0.702449i	0.955573	−	0.294755i	$-0.0952381\pi$
$661$	1.03030	+	0.702449i	1.03030	+	0.702449i	0.0747301	+	0.997204i	$0.476190\pi$
$662$	2.54192	+	1.73305i	2.54192	+	1.73305i
$663$		0			0
$664$	−2.94765	−	3.69623i	−2.94765	−	3.69623i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1.56052	−	0.751509i	−1.56052	−	0.751509i	−0.563320	−	0.826239i	$-0.690476\pi$
$673$	−1.56052	−	0.751509i	−1.56052	−	0.751509i	−0.997204	+	0.0747301i	$0.976190\pi$
$674$	−1.35654	−	3.45641i	−1.35654	−	3.45641i
$675$		0			0
$676$	7.01698	−	2.16445i	7.01698	−	2.16445i
$677$	−0.0648483	+	0.865341i	−0.0648483	+	0.865341i	0.866025	+	0.500000i	$0.166667\pi$
$677$	−0.0648483	+	0.865341i	−0.0648483	+	0.865341i	−0.930874	+	0.365341i	$0.880952\pi$
$678$		0			0
$679$		0			0
$680$	1.18429	−	5.18872i	1.18429	−	5.18872i
$681$		0			0
$682$	0.680173	−	1.73305i	0.680173	−	1.73305i
$683$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$683$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$684$		0			0
$685$		0			0
$686$	−1.73305	+	0.680173i	−1.73305	+	0.680173i
$687$		0			0
$688$	−2.43476	+	1.65999i	−2.43476	+	1.65999i
$689$		0			0
$690$		0			0
$691$	−0.425270	−	0.131178i	−0.425270	−	0.131178i	0.0747301	−	0.997204i	$-0.476190\pi$
$691$	−0.425270	−	0.131178i	−0.425270	−	0.131178i	−0.500000	+	0.866025i	$0.666667\pi$
$692$	−0.163577	+	0.716677i	−0.163577	+	0.716677i
$693$	0.433884	+	0.900969i	0.433884	+	0.900969i
$694$	−0.123490	−	0.541044i	−0.123490	−	0.541044i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−2.13571	−	1.23305i	−2.13571	−	1.23305i
$701$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$701$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$702$		0			0
$703$		0			0
$704$	0.684292	+	1.18523i	0.684292	+	1.18523i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.988831	+	0.149042i	−0.988831	+	0.149042i	−0.623490	−	0.781831i	$-0.714286\pi$
$709$	−0.988831	+	0.149042i	−0.988831	+	0.149042i	−0.365341	+	0.930874i	$0.619048\pi$
$710$	1.12397	+	0.766310i	1.12397	+	0.766310i
$711$		0			0
$712$	−4.46008	+	0.672250i	−4.46008	+	0.672250i
$713$		0			0
$714$		0			0
$715$	1.24349	−	1.55929i	1.24349	−	1.55929i
$716$	0.900969	−	1.56052i	0.900969	−	1.56052i
$717$		0			0
$718$		0			0
$719$	−0.326239	−	0.302705i	−0.326239	−	0.302705i	0.500000	−	0.866025i	$-0.333333\pi$
$719$	−0.326239	−	0.302705i	−0.326239	−	0.302705i	−0.826239	+	0.563320i	$0.809524\pi$
$720$	2.35654	−	1.13485i	2.35654	−	1.13485i
$721$		0			0
$722$	1.67738	+	0.807782i	1.67738	+	0.807782i
$723$		0			0
$724$	0.270191	+	3.60545i	0.270191	+	3.60545i
$725$		0			0
$726$		0			0
$727$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$727$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$728$	−5.30728	+	1.21135i	−5.30728	+	1.21135i
$729$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$730$	−2.42010	−	0.746503i	−2.42010	−	0.746503i
$731$	0.802576	−	2.04493i	0.802576	−	2.04493i
$732$		0			0
$733$	−1.29196	+	0.880843i	−1.29196	+	0.880843i	−0.997204	−	0.0747301i	$-0.976190\pi$
$733$	−1.29196	+	0.880843i	−1.29196	+	0.880843i	−0.294755	+	0.955573i	$0.595238\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$739$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.443797	−	1.94440i	−0.443797	−	1.94440i	−0.294755	−	0.955573i	$-0.595238\pi$
$743$	−0.443797	−	1.94440i	−0.443797	−	1.94440i	−0.149042	−	0.988831i	$-0.547619\pi$
$744$		0			0
$745$		0			0
$746$	0.0820177	+	1.09445i	0.0820177	+	1.09445i
$747$	0.632789	+	1.61232i	0.632789	+	1.61232i
$748$	−4.33235	−	2.08635i	−4.33235	−	2.08635i
$749$	−1.45557	+	0.571270i	−1.45557	+	0.571270i
$750$		0			0
$751$	1.07473	+	0.997204i	1.07473	+	0.997204i	1.00000			$0$
$751$	1.07473	+	0.997204i	1.07473	+	0.997204i	0.0747301	+	0.997204i	$0.476190\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$757$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$758$	3.51833	−	0.530303i	3.51833	−	0.530303i
$759$		0			0
$760$		0			0
$761$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$761$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$762$		0			0
$763$		0			0
$764$	1.53759	−	1.92808i	1.53759	−	1.92808i
$765$	−0.974928	+	1.68862i	−0.974928	+	1.68862i
$766$		0			0
$767$	−0.294755	−	0.0444272i	−0.294755	−	0.0444272i
$768$		0			0
$769$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$769$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$770$	−1.26631	+	1.36476i	−1.26631	+	1.36476i
$771$		0			0
$772$	−1.75676	−	4.47615i	−1.75676	−	4.47615i
$773$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$773$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$774$	2.00433	−	0.618255i	2.00433	−	0.618255i
$775$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$776$		0			0
$777$		0			0
$778$	0.791745	−	3.46886i	0.791745	−	3.46886i
$779$		0			0
$780$		0			0
$781$	0.535628	−	0.496990i	0.535628	−	0.496990i
$782$		0			0
$783$		0			0
$784$	2.58635	−	0.389830i	2.58635	−	0.389830i
$785$		0			0
$786$		0			0
$787$	−0.218511	+	0.202749i	−0.218511	+	0.202749i	−0.781831	−	0.623490i	$-0.785714\pi$
$787$	−0.218511	+	0.202749i	−0.218511	+	0.202749i	0.563320	+	0.826239i	$0.309524\pi$
$788$	0.268565	−	0.684292i	0.268565	−	0.684292i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.607374	−	2.66108i	−0.607374	−	2.66108i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−1.78181	−	4.53998i	−1.78181	−	4.53998i
$797$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$797$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$798$		0			0
$799$		0			0
$800$	1.56873	+	1.45557i	1.56873	+	1.45557i
$801$	1.63402	+	0.246289i	1.63402	+	0.246289i
$802$	−1.53825	−	2.66432i	−1.53825	−	2.66432i
$803$	−0.680173	+	1.17809i	−0.680173	+	1.17809i
$804$		0			0
$805$		0			0
$806$	−2.31507	−	2.90301i	−2.31507	−	2.90301i
$807$		0			0
$808$		0			0
$809$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$809$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$810$	−1.84095	+	0.277479i	−1.84095	+	0.277479i
$811$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$811$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	1.98883	+	0.149042i	1.98883	+	0.149042i
$820$		0			0
$821$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$821$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$822$		0			0
$823$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$823$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$824$		0			0
$825$		0			0
$826$	0.271281	+	0.0619180i	0.271281	+	0.0619180i
$827$	0.433884	−	1.90097i	0.433884	−	1.90097i		−	1.00000i	$-0.5\pi$
$827$	0.433884	−	1.90097i	0.433884	−	1.90097i	0.433884	−	0.900969i	$-0.357143\pi$
$828$		0			0
$829$	−0.0546039	+	0.139129i	−0.0546039	+	0.139129i	−0.955573	−	0.294755i	$-0.904762\pi$
$829$	−0.0546039	+	0.139129i	−0.0546039	+	0.139129i	0.900969	+	0.433884i	$0.142857\pi$
$830$	−2.36383	+	2.19331i	−2.36383	+	2.19331i
$831$		0			0
$832$	2.72951			2.72951
$833$	−1.42935	+	1.32624i	−1.42935	+	1.32624i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$	0.265895	+	0.0820177i	0.265895	+	0.0820177i
$839$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	−0.900969	−	0.433884i	$-0.857143\pi$
$839$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	1.00000			$0$
$840$		0			0
$841$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$842$	−0.0619180	+	0.826239i	−0.0619180	+	0.826239i
$843$		0			0
$844$		0			0
$845$	−1.08786	−	2.77183i	−1.08786	−	2.77183i
$846$		0			0
$847$	0.563320	+	0.826239i	0.563320	+	0.826239i
$848$		0			0
$849$		0			0
$850$	−3.58959	−	0.541044i	−3.58959	−	0.541044i
$851$		0			0
$852$		0			0
$853$	0.974928	−	1.22252i	0.974928	−	1.22252i		−	1.00000i	$-0.5\pi$
$853$	0.974928	−	1.22252i	0.974928	−	1.22252i	0.974928	−	0.222521i	$-0.0714286\pi$
$854$		0			0
$855$		0			0
$856$	4.22037	−	0.636119i	4.22037	−	0.636119i
$857$	−1.53825	−	1.04876i	−1.53825	−	1.04876i	−0.974928	−	0.222521i	$-0.928571\pi$
$857$	−1.53825	−	1.04876i	−1.53825	−	1.04876i	−0.563320	−	0.826239i	$-0.690476\pi$
$858$		0			0
$859$	−0.440071	+	0.0663300i	−0.440071	+	0.0663300i	−0.365341	−	0.930874i	$-0.619048\pi$
$859$	−0.440071	+	0.0663300i	−0.440071	+	0.0663300i	−0.0747301	+	0.997204i	$0.523810\pi$
$860$	1.73231	+	2.17225i	1.73231	+	2.17225i
$861$		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
$865$	0.294755	+	0.0444272i	0.294755	+	0.0444272i
$866$		0			0
$867$		0			0
$868$	1.38921	+	2.03759i	1.38921	+	2.03759i
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$876$		0			0
$877$	1.65510	+	0.510531i	1.65510	+	0.510531i	0.974928	−	0.222521i	$-0.0714286\pi$
$877$	1.65510	+	0.510531i	1.65510	+	0.510531i	0.680173	+	0.733052i	$0.261905\pi$
$878$		0			0
$879$		0			0
$880$	2.16108	−	1.47340i	2.16108	−	1.47340i
$881$	−1.97766			−1.97766			−0.988831	−	0.149042i	$-0.952381\pi$
$881$	−1.97766			−1.97766			−0.988831	+	0.149042i	$0.952381\pi$
$882$	−1.84095	−	0.277479i	−1.84095	−	0.277479i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$	−7.92380	+	5.40235i	−7.92380	+	5.40235i
$885$		0			0
$886$		0			0
$887$	1.29991	+	0.400969i	1.29991	+	0.400969i	0.866025	−	0.500000i	$-0.166667\pi$
$887$	1.29991	+	0.400969i	1.29991	+	0.400969i	0.433884	+	0.900969i	$0.357143\pi$
$888$		0			0
$889$	1.52446	+	0.347948i	1.52446	+	0.347948i
$890$	0.684585	+	2.99936i	0.684585	+	2.99936i
$891$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−0.658322	−	0.317031i	−0.658322	−	0.317031i
$896$	−0.406813	−	0.0304864i	−0.406813	−	0.0304864i
$897$		0			0
$898$	−0.203977	−	0.189263i	−0.203977	−	0.189263i
$899$		0			0
$900$	−1.23305	−	2.13571i	−1.23305	−	2.13571i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.44973	−	0.218511i	1.44973	−	0.218511i
$906$		0			0
$907$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$907$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$908$	1.43756	−	0.216677i	1.43756	−	0.216677i
$909$		0			0
$910$	1.09445	+	3.54812i	1.09445	+	3.54812i
$911$	1.23305	−	1.54620i	1.23305	−	1.54620i	0.500000	−	0.866025i	$-0.333333\pi$
$911$	1.23305	−	1.54620i	1.23305	−	1.54620i	0.733052	−	0.680173i	$-0.238095\pi$
$912$		0			0
$913$	0.866025	+	1.50000i	0.866025	+	1.50000i
$914$	−3.18862	−	0.480608i	−3.18862	−	0.480608i
$915$		0			0
$916$	−1.62349	+	0.781831i	−1.62349	+	0.781831i
$917$		0			0
$918$		0			0
$919$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$919$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.324275	−	1.42074i	−0.324275	−	1.42074i
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.03030	−	0.702449i	1.03030	−	0.702449i	0.0747301	−	0.997204i	$-0.476190\pi$
$929$	1.03030	−	0.702449i	1.03030	−	0.702449i	0.955573	+	0.294755i	$0.0952381\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.712362	+	1.81507i	−0.712362	+	1.81507i
$936$	−5.20191	−	1.60458i	−5.20191	−	1.60458i
$937$	0.443797	−	1.94440i	0.443797	−	1.94440i	0.149042	−	0.988831i	$-0.452381\pi$
$937$	0.443797	−	1.94440i	0.443797	−	1.94440i	0.294755	−	0.955573i	$-0.404762\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$941$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$942$		0			0
$943$		0			0
$944$	−0.352209	−	0.169615i	−0.352209	−	0.169615i
$945$		0			0
$946$	1.88980	−	0.910080i	1.88980	−	0.910080i
$947$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$947$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$948$		0			0
$949$	1.35654	+	2.34960i	1.35654	+	2.34960i
$950$		0			0
$951$		0			0
$952$	4.60913	−	2.66108i	4.60913	−	2.66108i
$953$	0.541044	+	0.678448i	0.541044	+	0.678448i	0.974928	−	0.222521i	$-0.0714286\pi$
$953$	0.541044	+	0.678448i	0.541044	+	0.678448i	−0.433884	+	0.900969i	$0.642857\pi$
$954$		0			0
$955$	−0.826239	−	0.563320i	−0.826239	−	0.563320i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$		0			0
$962$		0			0
$963$	−1.54620	−	0.233052i	−1.54620	−	0.233052i
$964$		0			0
$965$	−1.75676	+	0.846011i	−1.75676	+	0.846011i
$966$		0			0
$967$	−1.22563	−	0.590232i	−1.22563	−	0.590232i	−0.294755	−	0.955573i	$-0.595238\pi$
$967$	−1.22563	−	0.590232i	−1.22563	−	0.590232i	−0.930874	+	0.365341i	$0.880952\pi$
$968$	−0.997204	−	2.54083i	−0.997204	−	2.54083i
$969$		0			0
$970$		0			0
$971$	0.147791	−	1.97213i	0.147791	−	1.97213i	−0.0747301	−	0.997204i	$-0.523810\pi$
$971$	0.147791	−	1.97213i	0.147791	−	1.97213i	0.222521	−	0.974928i	$-0.428571\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$977$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$978$		0			0
$979$	1.65248			1.65248
$980$	−0.548760	−	2.40427i	−0.548760	−	2.40427i
$981$		0			0
$982$		0			0
$983$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$983$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$984$		0			0
$985$	−0.284841	−	0.0878620i	−0.284841	−	0.0878620i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−1.77904	+	0.548760i	−1.77904	+	0.548760i
$991$	0.0332580	+	0.443797i	0.0332580	+	0.443797i	0.988831	+	0.149042i	$0.0476190\pi$
$991$	0.0332580	+	0.443797i	0.0332580	+	0.443797i	−0.955573	+	0.294755i	$0.904762\pi$
$992$	−0.781831	−	1.99207i	−0.781831	−	1.99207i
$993$		0			0
$994$	0.202749	+	1.34515i	0.202749	+	1.34515i
$995$	−1.78181	+	0.858075i	−1.78181	+	0.858075i
$996$		0			0
$997$	1.11406	+	0.167917i	1.11406	+	0.167917i	0.680173	−	0.733052i	$-0.261905\pi$
$997$	1.11406	+	0.167917i	1.11406	+	0.167917i	0.433884	+	0.900969i	$0.357143\pi$
$998$	1.53825	+	2.66432i	1.53825	+	2.66432i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.1.ck.c.2144.1	yes	24
5.4	even	2	inner	2695.1.ck.c.2144.2	yes	24
11.10	odd	2	inner	2695.1.ck.c.2144.2	yes	24
49.4	even	21	inner	2695.1.ck.c.494.1	✓	24
55.54	odd	2	CM	2695.1.ck.c.2144.1	yes	24
245.4	even	42	inner	2695.1.ck.c.494.2	yes	24
539.494	odd	42	inner	2695.1.ck.c.494.2	yes	24
2695.494	odd	42	inner	2695.1.ck.c.494.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2695.1.ck.c.494.1	✓	24	49.4	even	21	inner
2695.1.ck.c.494.1	✓	24	2695.494	odd	42	inner
2695.1.ck.c.494.2	yes	24	245.4	even	42	inner
2695.1.ck.c.494.2	yes	24	539.494	odd	42	inner
2695.1.ck.c.2144.1	yes	24	1.1	even	1	trivial
2695.1.ck.c.2144.1	yes	24	55.54	odd	2	CM
2695.1.ck.c.2144.2	yes	24	5.4	even	2	inner
2695.1.ck.c.2144.2	yes	24	11.10	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.53825 + 1.04876i) q^{2} +(0.900969 - 2.29563i) q^{4} +(-0.955573 - 0.294755i) q^{5} +(-0.433884 - 0.900969i) q^{7} +(0.607374 + 2.66108i) q^{8} +(0.0747301 - 0.997204i) q^{9} +O(q^{10})\)	\(q+(-1.53825 + 1.04876i) q^{2} +(0.900969 - 2.29563i) q^{4} +(-0.955573 - 0.294755i) q^{5} +(-0.433884 - 0.900969i) q^{7} +(0.607374 + 2.66108i) q^{8} +(0.0747301 - 0.997204i) q^{9} +(1.77904 - 0.548760i) q^{10} +(-0.0747301 - 0.997204i) q^{11} +(-1.79690 - 0.865341i) q^{13} +(1.61232 + 0.930874i) q^{14} +(-1.91734 - 1.77904i) q^{16} +(1.92808 + 0.290611i) q^{17} +(0.930874 + 1.61232i) q^{18} +(-1.53759 + 1.92808i) q^{20} +(1.16078 + 1.45557i) q^{22} +(0.826239 + 0.563320i) q^{25} +(3.67161 - 0.553406i) q^{26} +(-2.45921 + 0.184292i) q^{28} +(-0.500000 - 0.866025i) q^{31} +(2.11610 + 0.318951i) q^{32} +(-3.27064 + 1.57506i) q^{34} +(0.149042 + 0.988831i) q^{35} +(-2.22188 - 1.07000i) q^{36} +(0.203977 - 2.72188i) q^{40} +(0.250701 - 1.09839i) q^{43} +(-2.35654 - 0.726897i) q^{44} +(-0.365341 + 0.930874i) q^{45} +(-0.623490 + 0.781831i) q^{49} -1.86175 q^{50} +(-3.60545 + 3.34537i) q^{52} +(-0.222521 + 0.974928i) q^{55} +(2.13402 - 1.70182i) q^{56} +(0.142820 - 0.0440542i) q^{59} +(1.67738 + 0.807782i) q^{62} +(-0.930874 + 0.365341i) q^{63} +(-1.23305 + 0.593806i) q^{64} +(1.46200 + 1.35654i) q^{65} +(2.40427 - 4.16432i) q^{68} +(-1.26631 - 1.36476i) q^{70} +(0.455573 + 0.571270i) q^{71} +(2.69903 - 0.406813i) q^{72} +(-1.12397 - 0.766310i) q^{73} +(-0.866025 + 0.500000i) q^{77} +(1.30778 + 2.26514i) q^{80} +(-0.988831 - 0.149042i) q^{81} +(-1.56052 + 0.751509i) q^{83} +(-1.75676 - 0.846011i) q^{85} +(0.766310 + 1.95253i) q^{86} +(2.60825 - 0.804539i) q^{88} +(-0.123490 + 1.64786i) q^{89} +(-0.414278 - 1.81507i) q^{90} +1.99441i q^{91} +(0.139129 - 1.85654i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4} - 2 q^{5} + 2 q^{9}+O(q^{10}) \) 24 * q + 4 * q^4 - 2 * q^5 + 2 * q^9	\( 24 q + 4 q^{4} - 2 q^{5} + 2 q^{9} - 2 q^{11} - 6 q^{14} - 26 q^{16} + 8 q^{20} + 2 q^{25} + 6 q^{26} - 12 q^{31} - 14 q^{34} - 8 q^{36} - 18 q^{44} - 2 q^{45} + 4 q^{49} - 4 q^{55} + 14 q^{56} - 2 q^{59} - 10 q^{64} - 6 q^{70} - 10 q^{71} + 12 q^{80} + 2 q^{81} - 6 q^{86} + 16 q^{89} - 24 q^{99}+O(q^{100}) \) 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

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Database

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