LMFDB - Embedded newform 3332.1.cc.c.1971.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3332,1,Mod(135,3332)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3332, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 32, 21]))

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

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

chi := DirichletCharacter("3332.135");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3332 = 2^{2} \cdot 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3332.cc (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:	$1.66288462209$
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:	$\Z[a_1, a_2, a_3]$
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			1971.2
Root			$-0.930874 - 0.365341i$ of defining polynomial
Character	$\chi$	$=$	3332.1971
Dual form			3332.1.cc.c.1087.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.733052 - 0.680173i) q^{2} +(0.294755 - 0.0444272i) q^{3} +(0.0747301 - 0.997204i) q^{4} +(0.185853 - 0.233052i) q^{6} +(0.781831 - 0.623490i) q^{7} +(-0.623490 - 0.781831i) q^{8} +(-0.870666 + 0.268565i) q^{9} +O(q^{10})$	\(q+(0.733052 - 0.680173i) q^{2} +(0.294755 - 0.0444272i) q^{3} +(0.0747301 - 0.997204i) q^{4} +(0.185853 - 0.233052i) q^{6} +(0.781831 - 0.623490i) q^{7} +(-0.623490 - 0.781831i) q^{8} +(-0.870666 + 0.268565i) q^{9} +(-1.29991 - 0.400969i) q^{11} +(-0.0222759 - 0.297251i) q^{12} +(-0.326239 - 1.42935i) q^{13} +(0.149042 - 0.988831i) q^{14} +(-0.988831 - 0.149042i) q^{16} +(0.826239 - 0.563320i) q^{17} +(-0.455573 + 0.789075i) q^{18} +(0.202749 - 0.218511i) q^{21} +(-1.22563 + 0.590232i) q^{22} +(1.61105 + 1.09839i) q^{23} +(-0.218511 - 0.202749i) q^{24} +(-0.733052 - 0.680173i) q^{25} +(-1.21135 - 0.825886i) q^{26} +(-0.513267 + 0.247176i) q^{27} +(-0.563320 - 0.826239i) q^{28} +(-0.781831 + 1.35417i) q^{31} +(-0.826239 + 0.563320i) q^{32} +(-0.400969 - 0.0604363i) q^{33} +(0.222521 - 0.974928i) q^{34} +(0.202749 + 0.888301i) q^{36} +(-0.159662 - 0.406813i) q^{39} -0.298085i q^{42} +(-0.496990 + 1.26631i) q^{44} +(1.92808 - 0.290611i) q^{46} -0.298085 q^{48} +(0.222521 - 0.974928i) q^{49} -1.00000 q^{50} +(0.218511 - 0.202749i) q^{51} +(-1.44973 + 0.218511i) q^{52} +(0.0546039 - 0.728639i) q^{53} +(-0.208129 + 0.530303i) q^{54} +(-0.974928 - 0.222521i) q^{56} +(0.347948 + 1.52446i) q^{62} +(-0.513267 + 0.752824i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(-0.335038 + 0.228425i) q^{66} +(-0.500000 - 0.866025i) q^{68} +(0.523663 + 0.252183i) q^{69} +(1.67738 - 0.807782i) q^{71} +(0.752824 + 0.513267i) q^{72} +(-0.246289 - 0.167917i) q^{75} +(-1.26631 + 0.496990i) q^{77} +(-0.393744 - 0.189617i) q^{78} +(-0.294755 - 0.510531i) q^{79} +(0.612517 - 0.417607i) q^{81} +(-0.202749 - 0.218511i) q^{84} +(0.496990 + 1.26631i) q^{88} +(1.88980 - 0.582926i) q^{89} +(-1.14625 - 0.914101i) q^{91} +(1.21572 - 1.52446i) q^{92} +(-0.170287 + 0.433884i) q^{93} +(-0.218511 + 0.202749i) q^{96} +(-0.500000 - 0.866025i) q^{98} +1.23947 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} + 2 q^{4} + 4 q^{8} - 24 q^{9}+O(q^{10}) $ 24 * q - 2 * q^2 + 2 * q^4 + 4 * q^8 - 24 * q^9	$ 24 q - 2 q^{2} + 2 q^{4} + 4 q^{8} - 24 q^{9} + 10 q^{13} + 2 q^{16} + 2 q^{17} + 10 q^{18} + 6 q^{21} + 2 q^{25} - 2 q^{26} - 2 q^{32} + 8 q^{33} + 4 q^{34} + 6 q^{36} + 4 q^{49} - 24 q^{50} + 2 q^{52} - 2 q^{53} - 4 q^{64} - 22 q^{66} - 12 q^{68} - 14 q^{69} - 4 q^{72} - 6 q^{77} + 30 q^{81} - 6 q^{84} + 2 q^{89} - 12 q^{98}+O(q^{100}) $ 24 * q - 2 * q^2 + 2 * q^4 + 4 * q^8 - 24 * q^9 + 10 * q^13 + 2 * q^16 + 2 * q^17 + 10 * q^18 + 6 * q^21 + 2 * q^25 - 2 * q^26 - 2 * q^32 + 8 * q^33 + 4 * q^34 + 6 * q^36 + 4 * q^49 - 24 * q^50 + 2 * q^52 - 2 * q^53 - 4 * q^64 - 22 * q^66 - 12 * q^68 - 14 * q^69 - 4 * q^72 - 6 * q^77 + 30 * q^81 - 6 * q^84 + 2 * q^89 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3332\mathbb{Z}\right)^\times$.

$n$	$785$	$885$	$1667$
$\chi(n)$	$-1$	$e\left(\frac{20}{21}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.733052	−	0.680173i	0.733052	−	0.680173i
$2$	0.733052	−	0.680173i	0.733052	−	0.680173i
$3$	0.294755	−	0.0444272i	0.294755	−	0.0444272i		−	1.00000i	$-0.5\pi$
$3$	0.294755	−	0.0444272i	0.294755	−	0.0444272i	0.294755	+	0.955573i	$0.404762\pi$
$4$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$5$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$5$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$6$	0.185853	−	0.233052i	0.185853	−	0.233052i
$7$	0.781831	−	0.623490i	0.781831	−	0.623490i
$7$	0.781831	−	0.623490i	0.781831	−	0.623490i
$8$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$9$	−0.870666	+	0.268565i	−0.870666	+	0.268565i
$10$		0			0
$11$	−1.29991	−	0.400969i	−1.29991	−	0.400969i	−0.433884	−	0.900969i	$-0.642857\pi$
$11$	−1.29991	−	0.400969i	−1.29991	−	0.400969i	−0.866025	+	0.500000i	$0.833333\pi$
$12$	−0.0222759	−	0.297251i	−0.0222759	−	0.297251i
$13$	−0.326239	−	1.42935i	−0.326239	−	1.42935i	−0.826239	−	0.563320i	$-0.809524\pi$
$13$	−0.326239	−	1.42935i	−0.326239	−	1.42935i	0.500000	−	0.866025i	$-0.333333\pi$
$14$	0.149042	−	0.988831i	0.149042	−	0.988831i
$15$		0			0
$16$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$17$	0.826239	−	0.563320i	0.826239	−	0.563320i
$17$	0.826239	−	0.563320i	0.826239	−	0.563320i
$18$	−0.455573	+	0.789075i	−0.455573	+	0.789075i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$		0			0
$21$	0.202749	−	0.218511i	0.202749	−	0.218511i
$22$	−1.22563	+	0.590232i	−1.22563	+	0.590232i
$23$	1.61105	+	1.09839i	1.61105	+	1.09839i	0.930874	+	0.365341i	$0.119048\pi$
$23$	1.61105	+	1.09839i	1.61105	+	1.09839i	0.680173	+	0.733052i	$0.261905\pi$
$24$	−0.218511	−	0.202749i	−0.218511	−	0.202749i
$25$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$26$	−1.21135	−	0.825886i	−1.21135	−	0.825886i
$27$	−0.513267	+	0.247176i	−0.513267	+	0.247176i
$28$	−0.563320	−	0.826239i	−0.563320	−	0.826239i
$29$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$29$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$30$		0			0
$31$	−0.781831	+	1.35417i	−0.781831	+	1.35417i	0.149042	+	0.988831i	$0.452381\pi$
$31$	−0.781831	+	1.35417i	−0.781831	+	1.35417i	−0.930874	+	0.365341i	$0.880952\pi$
$32$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$33$	−0.400969	−	0.0604363i	−0.400969	−	0.0604363i
$34$	0.222521	−	0.974928i	0.222521	−	0.974928i
$35$		0			0
$36$	0.202749	+	0.888301i	0.202749	+	0.888301i
$37$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$37$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$38$		0			0
$39$	−0.159662	−	0.406813i	−0.159662	−	0.406813i
$40$		0			0
$41$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$41$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$42$		−	0.298085i		−	0.298085i
$43$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$43$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$44$	−0.496990	+	1.26631i	−0.496990	+	1.26631i
$45$		0			0
$46$	1.92808	−	0.290611i	1.92808	−	0.290611i
$47$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$47$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$48$	−0.298085			−0.298085
$49$	0.222521	−	0.974928i	0.222521	−	0.974928i
$50$	−1.00000			−1.00000
$51$	0.218511	−	0.202749i	0.218511	−	0.202749i
$52$	−1.44973	+	0.218511i	−1.44973	+	0.218511i
$53$	0.0546039	−	0.728639i	0.0546039	−	0.728639i	−0.900969	−	0.433884i	$-0.857143\pi$
$53$	0.0546039	−	0.728639i	0.0546039	−	0.728639i	0.955573	−	0.294755i	$-0.0952381\pi$
$54$	−0.208129	+	0.530303i	−0.208129	+	0.530303i
$55$		0			0
$56$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$57$		0			0
$58$		0			0
$59$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$59$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$60$		0			0
$61$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$61$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$62$	0.347948	+	1.52446i	0.347948	+	1.52446i
$63$	−0.513267	+	0.752824i	−0.513267	+	0.752824i
$64$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$65$		0			0
$66$	−0.335038	+	0.228425i	−0.335038	+	0.228425i
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$69$	0.523663	+	0.252183i	0.523663	+	0.252183i
$70$		0			0
$71$	1.67738	−	0.807782i	1.67738	−	0.807782i	0.680173	−	0.733052i	$-0.261905\pi$
$71$	1.67738	−	0.807782i	1.67738	−	0.807782i	0.997204	−	0.0747301i	$-0.0238095\pi$
$72$	0.752824	+	0.513267i	0.752824	+	0.513267i
$73$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$73$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$74$		0			0
$75$	−0.246289	−	0.167917i	−0.246289	−	0.167917i
$76$		0			0
$77$	−1.26631	+	0.496990i	−1.26631	+	0.496990i
$78$	−0.393744	−	0.189617i	−0.393744	−	0.189617i
$79$	−0.294755	−	0.510531i	−0.294755	−	0.510531i	0.680173	−	0.733052i	$-0.261905\pi$
$79$	−0.294755	−	0.510531i	−0.294755	−	0.510531i	−0.974928	+	0.222521i	$0.928571\pi$
$80$		0			0
$81$	0.612517	−	0.417607i	0.612517	−	0.417607i
$82$		0			0
$83$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$83$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$84$	−0.202749	−	0.218511i	−0.202749	−	0.218511i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	0.496990	+	1.26631i	0.496990	+	1.26631i
$89$	1.88980	−	0.582926i	1.88980	−	0.582926i	0.900969	−	0.433884i	$-0.142857\pi$
$89$	1.88980	−	0.582926i	1.88980	−	0.582926i	0.988831	−	0.149042i	$-0.0476190\pi$
$90$		0			0
$91$	−1.14625	−	0.914101i	−1.14625	−	0.914101i
$92$	1.21572	−	1.52446i	1.21572	−	1.52446i
$93$	−0.170287	+	0.433884i	−0.170287	+	0.433884i
$94$		0			0
$95$		0			0
$96$	−0.218511	+	0.202749i	−0.218511	+	0.202749i
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$99$	1.23947			1.23947
$100$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$101$	−0.440071	+	0.0663300i	−0.440071	+	0.0663300i	−0.365341	−	0.930874i	$-0.619048\pi$
$101$	−0.440071	+	0.0663300i	−0.440071	+	0.0663300i	−0.0747301	+	0.997204i	$0.523810\pi$
$102$	0.0222759	−	0.297251i	0.0222759	−	0.297251i
$103$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$103$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$104$	−0.914101	+	1.14625i	−0.914101	+	1.14625i
$105$		0			0
$106$	−0.455573	−	0.571270i	−0.455573	−	0.571270i
$107$	1.90580	−	0.587862i	1.90580	−	0.587862i	0.930874	−	0.365341i	$-0.119048\pi$
$107$	1.90580	−	0.587862i	1.90580	−	0.587862i	0.974928	−	0.222521i	$-0.0714286\pi$
$108$	0.208129	+	0.530303i	0.208129	+	0.530303i
$109$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$109$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$110$		0			0
$111$		0			0
$112$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$113$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$113$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.667917	+	1.15687i	0.667917	+	1.15687i
$118$		0			0
$119$	0.294755	−	0.955573i	0.294755	−	0.955573i
$120$		0			0
$121$	0.702749	+	0.479126i	0.702749	+	0.479126i
$122$		0			0
$123$		0			0
$124$	1.29196	+	0.880843i	1.29196	+	0.880843i
$125$		0			0
$126$	0.135799	+	0.900969i	0.135799	+	0.900969i
$127$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$127$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$128$	0.500000	+	0.866025i	0.500000	+	0.866025i
$129$		0			0
$130$		0			0
$131$	−1.92808	−	0.290611i	−1.92808	−	0.290611i	−0.930874	−	0.365341i	$-0.880952\pi$
$131$	−1.92808	−	0.290611i	−1.92808	−	0.290611i	−0.997204	+	0.0747301i	$0.976190\pi$
$132$	−0.0902318	+	0.395331i	−0.0902318	+	0.395331i
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$137$	0.722521	+	1.84095i	0.722521	+	1.84095i	0.500000	+	0.866025i	$0.333333\pi$
$137$	0.722521	+	1.84095i	0.722521	+	1.84095i	0.222521	+	0.974928i	$0.428571\pi$
$138$	0.555400	−	0.171318i	0.555400	−	0.171318i
$139$	0.367554	+	0.460898i	0.367554	+	0.460898i	0.930874	−	0.365341i	$-0.119048\pi$
$139$	0.367554	+	0.460898i	0.367554	+	0.460898i	−0.563320	+	0.826239i	$0.690476\pi$
$140$		0			0
$141$		0			0
$142$	0.680173	−	1.73305i	0.680173	−	1.73305i
$143$	−0.149042	+	1.98883i	−0.149042	+	1.98883i
$144$	0.900969	−	0.135799i	0.900969	−	0.135799i
$145$		0			0
$146$		0			0
$147$	0.0222759	−	0.297251i	0.0222759	−	0.297251i
$148$		0			0
$149$	1.44973	−	1.34515i	1.44973	−	1.34515i	0.623490	−	0.781831i	$-0.285714\pi$
$149$	1.44973	−	1.34515i	1.44973	−	1.34515i	0.826239	−	0.563320i	$-0.190476\pi$
$150$	−0.294755	+	0.0444272i	−0.294755	+	0.0444272i
$151$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$151$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$152$		0			0
$153$	−0.568090	+	0.712362i	−0.568090	+	0.712362i
$154$	−0.590232	+	1.22563i	−0.590232	+	1.22563i
$155$		0			0
$156$	−0.417607	+	0.128815i	−0.417607	+	0.128815i
$157$	0.698220	+	1.77904i	0.698220	+	1.77904i	0.623490	+	0.781831i	$0.285714\pi$
$157$	0.698220	+	1.77904i	0.698220	+	1.77904i	0.0747301	+	0.997204i	$0.476190\pi$
$158$	−0.563320	−	0.173761i	−0.563320	−	0.173761i
$159$	−0.0162766	−	0.217196i	−0.0162766	−	0.217196i
$160$		0			0
$161$	1.94440	−	0.145713i	1.94440	−	0.145713i
$162$	0.164962	−	0.722745i	0.164962	−	0.722745i
$163$		0			0		0.149042	−	0.988831i	$-0.452381\pi$
$163$		0			0		−0.149042	+	0.988831i	$0.547619\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.01507	+	0.488831i	1.01507	+	0.488831i	0.866025	−	0.500000i	$-0.166667\pi$
$167$	1.01507	+	0.488831i	1.01507	+	0.488831i	0.149042	+	0.988831i	$0.452381\pi$
$168$	−0.297251	−	0.0222759i	−0.297251	−	0.0222759i
$169$	−1.03563	+	0.498732i	−1.03563	+	0.498732i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$173$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$174$		0			0
$175$	−0.997204	−	0.0747301i	−0.997204	−	0.0747301i
$176$	1.22563	+	0.590232i	1.22563	+	0.590232i
$177$		0			0
$178$	0.988831	−	1.71271i	0.988831	−	1.71271i
$179$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$179$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$180$		0			0
$181$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$181$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$182$	−1.46200	+	0.109562i	−1.46200	+	0.109562i
$183$		0			0
$184$	−0.145713	−	1.94440i	−0.145713	−	1.94440i
$185$		0			0
$186$	0.170287	+	0.433884i	0.170287	+	0.433884i
$187$	−1.29991	+	0.400969i	−1.29991	+	0.400969i
$188$		0			0
$189$	−0.247176	+	0.513267i	−0.247176	+	0.513267i
$190$		0			0
$191$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$191$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$192$	−0.0222759	+	0.297251i	−0.0222759	+	0.297251i
$193$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$193$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$194$		0			0
$195$		0			0
$196$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	0.908598	−	0.843056i	0.908598	−	0.843056i
$199$	−1.84095	+	0.277479i	−1.84095	+	0.277479i	−0.974928	−	0.222521i	$-0.928571\pi$
$199$	−1.84095	+	0.277479i	−1.84095	+	0.277479i	−0.866025	+	0.500000i	$0.833333\pi$
$200$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$201$		0			0
$202$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$203$		0			0
$204$	−0.185853	−	0.233052i	−0.185853	−	0.233052i
$205$		0			0
$206$		0			0
$207$	−1.69767	−	0.523663i	−1.69767	−	0.523663i
$208$	0.109562	+	1.46200i	0.109562	+	1.46200i
$209$		0			0
$210$		0			0
$211$	0.193096	−	0.846011i	0.193096	−	0.846011i	−0.781831	−	0.623490i	$-0.785714\pi$
$211$	0.193096	−	0.846011i	0.193096	−	0.846011i	0.974928	−	0.222521i	$-0.0714286\pi$
$212$	−0.722521	−	0.108903i	−0.722521	−	0.108903i
$213$	0.458528	−	0.312619i	0.458528	−	0.312619i
$214$	0.997204	−	1.72721i	0.997204	−	1.72721i
$215$		0			0
$216$	0.513267	+	0.247176i	0.513267	+	0.247176i
$217$	0.233052	+	1.54620i	0.233052	+	1.54620i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.07473	−	0.997204i	−1.07473	−	0.997204i
$222$		0			0
$223$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$223$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$224$	−0.294755	+	0.955573i	−0.294755	+	0.955573i
$225$	0.820914	+	0.395331i	0.820914	+	0.395331i
$226$		0			0
$227$	−0.930874	+	1.61232i	−0.930874	+	1.61232i	−0.149042	+	0.988831i	$0.547619\pi$
$227$	−0.930874	+	1.61232i	−0.930874	+	1.61232i	−0.781831	+	0.623490i	$0.785714\pi$
$228$		0			0
$229$	−1.78181	−	0.268565i	−1.78181	−	0.268565i	−0.826239	−	0.563320i	$-0.809524\pi$
$229$	−1.78181	−	0.268565i	−1.78181	−	0.268565i	−0.955573	+	0.294755i	$0.904762\pi$
$230$		0			0
$231$	−0.351172	+	0.202749i	−0.351172	+	0.202749i
$232$		0			0
$233$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$233$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$234$	1.27649	+	0.393744i	1.27649	+	0.393744i
$235$		0			0
$236$		0			0
$237$	−0.109562	−	0.137386i	−0.109562	−	0.137386i
$238$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$239$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$239$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$240$		0			0
$241$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$241$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$242$	0.841040	−	0.126766i	0.841040	−	0.126766i
$243$	0.579597	−	0.537787i	0.579597	−	0.537787i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$	1.54620	−	0.233052i	1.54620	−	0.233052i
$249$		0			0
$250$		0			0
$251$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$251$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$252$	0.712362	+	0.568090i	0.712362	+	0.568090i
$253$	−1.65379	−	2.07379i	−1.65379	−	2.07379i
$254$		0			0
$255$		0			0
$256$	0.955573	+	0.294755i	0.955573	+	0.294755i
$257$	0.0747301	+	0.997204i	0.0747301	+	0.997204i	0.900969	+	0.433884i	$0.142857\pi$
$257$	0.0747301	+	0.997204i	0.0747301	+	0.997204i	−0.826239	+	0.563320i	$0.809524\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−1.61105	+	1.09839i	−1.61105	+	1.09839i
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$	0.202749	+	0.351172i	0.202749	+	0.351172i
$265$		0			0
$266$		0			0
$267$	0.531130	−	0.255779i	0.531130	−	0.255779i
$268$		0			0
$269$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$269$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$270$		0			0
$271$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$271$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$272$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$273$	−0.378473	−	0.218511i	−0.378473	−	0.218511i
$274$	1.78181	+	0.858075i	1.78181	+	0.858075i
$275$	0.680173	+	1.17809i	0.680173	+	1.17809i
$276$	0.290611	−	0.503353i	0.290611	−	0.503353i
$277$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$277$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$278$	0.582926	+	0.0878620i	0.582926	+	0.0878620i
$279$	0.317031	−	1.38900i	0.317031	−	1.38900i
$280$		0			0
$281$	0.222521	+	0.974928i	0.222521	+	0.974928i	0.955573	+	0.294755i	$0.0952381\pi$
$281$	0.222521	+	0.974928i	0.222521	+	0.974928i	−0.733052	+	0.680173i	$0.761905\pi$
$282$		0			0
$283$	1.29991	+	0.400969i	1.29991	+	0.400969i	0.866025	−	0.500000i	$-0.166667\pi$
$283$	1.29991	+	0.400969i	1.29991	+	0.400969i	0.433884	+	0.900969i	$0.357143\pi$
$284$	−0.680173	−	1.73305i	−0.680173	−	1.73305i
$285$		0			0
$286$	1.24349	+	1.55929i	1.24349	+	1.55929i
$287$		0			0
$288$	0.568090	−	0.712362i	0.568090	−	0.712362i
$289$	0.365341	−	0.930874i	0.365341	−	0.930874i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.91115			1.91115			0.955573	−	0.294755i	$-0.0952381\pi$
$293$	1.91115			1.91115			0.955573	+	0.294755i	$0.0952381\pi$
$294$	−0.185853	−	0.233052i	−0.185853	−	0.233052i
$295$		0			0
$296$		0			0
$297$	0.766310	−	0.115503i	0.766310	−	0.115503i
$298$	0.147791	−	1.97213i	0.147791	−	1.97213i
$299$	1.04440	−	2.66108i	1.04440	−	2.66108i
$300$	−0.185853	+	0.233052i	−0.185853	+	0.233052i
$301$		0			0
$302$		0			0
$303$	−0.126766	+	0.0391023i	−0.126766	+	0.0391023i
$304$		0			0
$305$		0			0
$306$	0.0680900	+	0.908598i	0.0680900	+	0.908598i
$307$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$307$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$308$	0.400969	+	1.29991i	0.400969	+	1.29991i
$309$		0			0
$310$		0			0
$311$	−1.43109	+	0.975699i	−1.43109	+	0.975699i	−0.433884	+	0.900969i	$0.642857\pi$
$311$	−1.43109	+	0.975699i	−1.43109	+	0.975699i	−0.997204	+	0.0747301i	$0.976190\pi$
$312$	−0.218511	+	0.378473i	−0.218511	+	0.378473i
$313$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$313$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$314$	1.72188	+	0.829215i	1.72188	+	0.829215i
$315$		0			0
$316$	−0.531130	+	0.255779i	−0.531130	+	0.255779i
$317$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$317$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$318$	−0.159662	−	0.148145i	−0.159662	−	0.148145i
$319$		0			0
$320$		0			0
$321$	0.535628	−	0.257945i	0.535628	−	0.257945i
$322$	1.32624	−	1.42935i	1.32624	−	1.42935i
$323$		0			0
$324$	−0.370666	−	0.642012i	−0.370666	−	0.642012i
$325$	−0.733052	+	1.26968i	−0.733052	+	1.26968i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$331$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$332$		0			0
$333$		0			0
$334$	1.07659	−	0.332083i	1.07659	−	0.332083i
$335$		0			0
$336$	−0.233052	+	0.185853i	−0.233052	+	0.185853i
$337$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$337$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$338$	−0.419945	+	1.07000i	−0.419945	+	1.07000i
$339$		0			0
$340$		0			0
$341$	1.55929	−	1.44681i	1.55929	−	1.44681i
$342$		0			0
$343$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−0.0648483	+	0.865341i	−0.0648483	+	0.865341i	0.866025	+	0.500000i	$0.166667\pi$
$347$	−0.0648483	+	0.865341i	−0.0648483	+	0.865341i	−0.930874	+	0.365341i	$0.880952\pi$
$348$		0			0
$349$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$349$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$350$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$351$	0.520748	+	0.652997i	0.520748	+	0.652997i
$352$	1.29991	−	0.400969i	1.29991	−	0.400969i
$353$	−0.365341	−	0.930874i	−0.365341	−	0.930874i	−0.988831	−	0.149042i	$-0.952381\pi$
$353$	−0.365341	−	0.930874i	−0.365341	−	0.930874i	0.623490	−	0.781831i	$-0.285714\pi$
$354$		0			0
$355$		0			0
$356$	−0.440071	−	1.92808i	−0.440071	−	1.92808i
$357$	0.0444272	−	0.294755i	0.0444272	−	0.294755i
$358$		0			0
$359$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$359$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$360$		0			0
$361$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$362$		0			0
$363$	0.228425	+	0.110004i	0.228425	+	0.110004i
$364$	−0.997204	+	1.07473i	−0.997204	+	1.07473i
$365$		0			0
$366$		0			0
$367$	1.46200	+	1.35654i	1.46200	+	1.35654i	0.781831	+	0.623490i	$0.214286\pi$
$367$	1.46200	+	1.35654i	1.46200	+	1.35654i	0.680173	+	0.733052i	$0.261905\pi$
$368$	−1.42935	−	1.32624i	−1.42935	−	1.32624i
$369$		0			0
$370$		0			0
$371$	−0.411608	−	0.603718i	−0.411608	−	0.603718i
$372$	0.419945	+	0.202235i	0.419945	+	0.202235i
$373$	−0.733052	−	1.26968i	−0.733052	−	1.26968i	−0.955573	−	0.294755i	$-0.904762\pi$
$373$	−0.733052	−	1.26968i	−0.733052	−	1.26968i	0.222521	−	0.974928i	$-0.428571\pi$
$374$	−0.680173	+	1.17809i	−0.680173	+	1.17809i
$375$		0			0
$376$		0			0
$377$		0			0
$378$	0.167917	+	0.544374i	0.167917	+	0.544374i
$379$	0.385418	+	1.68862i	0.385418	+	1.68862i	0.680173	+	0.733052i	$0.261905\pi$
$379$	0.385418	+	1.68862i	0.385418	+	1.68862i	−0.294755	+	0.955573i	$0.595238\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$383$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$384$	0.185853	+	0.233052i	0.185853	+	0.233052i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.63402	−	0.246289i	1.63402	−	0.246289i	0.733052	−	0.680173i	$-0.238095\pi$
$389$	1.63402	−	0.246289i	1.63402	−	0.246289i	0.900969	+	0.433884i	$0.142857\pi$
$390$		0			0
$391$	1.94986			1.94986
$392$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$393$	−0.581222			−0.581222
$394$		0			0
$395$		0			0
$396$	0.0926259	−	1.23601i	0.0926259	−	1.23601i
$397$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$397$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$398$	−1.16078	+	1.45557i	−1.16078	+	1.45557i
$399$		0			0
$400$	0.623490	+	0.781831i	0.623490	+	0.781831i
$401$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$401$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$402$		0			0
$403$	2.19064	+	0.675724i	2.19064	+	0.675724i
$404$	0.0332580	+	0.443797i	0.0332580	+	0.443797i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.294755	−	0.0444272i	−0.294755	−	0.0444272i
$409$	0.603718	−	0.411608i	0.603718	−	0.411608i	−0.222521	−	0.974928i	$-0.571429\pi$
$409$	0.603718	−	0.411608i	0.603718	−	0.411608i	0.826239	+	0.563320i	$0.190476\pi$
$410$		0			0
$411$	0.294755	+	0.510531i	0.294755	+	0.510531i
$412$		0			0
$413$		0			0
$414$	−1.60066	+	0.770839i	−1.60066	+	0.770839i
$415$		0			0
$416$	1.07473	+	0.997204i	1.07473	+	0.997204i
$417$	0.128815	+	0.119523i	0.128815	+	0.119523i
$418$		0			0
$419$	−0.531130	+	0.255779i	−0.531130	+	0.255779i	−0.680173	−	0.733052i	$-0.738095\pi$
$419$	−0.531130	+	0.255779i	−0.531130	+	0.255779i	0.149042	+	0.988831i	$0.452381\pi$
$420$		0			0
$421$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.900969	−	0.433884i	$-0.142857\pi$
$421$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.222521	+	0.974928i	$0.428571\pi$
$422$	−0.433884	−	0.751509i	−0.433884	−	0.751509i
$423$		0			0
$424$	−0.603718	+	0.411608i	−0.603718	+	0.411608i
$425$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$426$	0.123490	−	0.541044i	0.123490	−	0.541044i
$427$		0			0
$428$	−0.443797	−	1.94440i	−0.443797	−	1.94440i
$429$	0.0444272	+	0.592840i	0.0444272	+	0.592840i
$430$		0			0
$431$	−0.632789	−	1.61232i	−0.632789	−	1.61232i	−0.781831	−	0.623490i	$-0.785714\pi$
$431$	−0.632789	−	1.61232i	−0.632789	−	1.61232i	0.149042	−	0.988831i	$-0.452381\pi$
$432$	0.544374	−	0.167917i	0.544374	−	0.167917i
$433$	0.277479	+	0.347948i	0.277479	+	0.347948i	0.900969	−	0.433884i	$-0.142857\pi$
$433$	0.277479	+	0.347948i	0.277479	+	0.347948i	−0.623490	+	0.781831i	$0.714286\pi$
$434$	1.22252	+	0.974928i	1.22252	+	0.974928i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	0.432142	−	0.400969i	0.432142	−	0.400969i	−0.433884	−	0.900969i	$-0.642857\pi$
$439$	0.432142	−	0.400969i	0.432142	−	0.400969i	0.866025	+	0.500000i	$0.166667\pi$
$440$		0			0
$441$	0.0680900	+	0.908598i	0.0680900	+	0.908598i
$442$	−1.46610			−1.46610
$443$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$443$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.367554	−	0.460898i	0.367554	−	0.460898i
$448$	0.433884	+	0.900969i	0.433884	+	0.900969i
$449$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$449$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$450$	0.870666	−	0.268565i	0.870666	−	0.268565i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.414278	+	1.81507i	0.414278	+	1.81507i
$455$		0			0
$456$		0			0
$457$	−0.440071	−	0.0663300i	−0.440071	−	0.0663300i	−0.0747301	−	0.997204i	$-0.523810\pi$
$457$	−0.440071	−	0.0663300i	−0.440071	−	0.0663300i	−0.365341	+	0.930874i	$0.619048\pi$
$458$	−1.48883	+	1.01507i	−1.48883	+	1.01507i
$459$	−0.284841	+	0.493360i	−0.284841	+	0.493360i
$460$		0			0
$461$	−0.658322	−	0.317031i	−0.658322	−	0.317031i	0.0747301	−	0.997204i	$-0.476190\pi$
$461$	−0.658322	−	0.317031i	−0.658322	−	0.317031i	−0.733052	+	0.680173i	$0.761905\pi$
$462$	−0.119523	+	0.387483i	−0.119523	+	0.387483i
$463$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$463$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$467$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$468$	1.20354	−	0.579597i	1.20354	−	0.579597i
$469$		0			0
$470$		0			0
$471$	0.284841	+	0.493360i	0.284841	+	0.493360i
$472$		0			0
$473$		0			0
$474$	−0.173761	−	0.0261903i	−0.173761	−	0.0261903i
$475$		0			0
$476$	−0.930874	−	0.365341i	−0.930874	−	0.365341i
$477$	0.148145	+	0.649066i	0.148145	+	0.649066i
$478$		0			0
$479$	−1.86323	−	0.574730i	−1.86323	−	0.574730i	−0.997204	−	0.0747301i	$-0.976190\pi$
$479$	−1.86323	−	0.574730i	−1.86323	−	0.574730i	−0.866025	−	0.500000i	$-0.833333\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	0.566649	−	0.129334i	0.566649	−	0.129334i
$484$	0.530303	−	0.664979i	0.530303	−	0.664979i
$485$		0			0
$486$	0.0590863	−	0.788452i	0.0590863	−	0.788452i
$487$	−1.71271	+	0.258149i	−1.71271	+	0.258149i	−0.930874	−	0.365341i	$-0.880952\pi$
$487$	−1.71271	+	0.258149i	−1.71271	+	0.258149i	−0.781831	+	0.623490i	$0.785714\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.974928	−	1.22252i	0.974928	−	1.22252i
$497$	0.807782	−	1.67738i	0.807782	−	1.67738i
$498$		0			0
$499$	−0.563320	+	0.173761i	−0.563320	+	0.173761i	−0.563320	−	0.826239i	$-0.690476\pi$
$499$	−0.563320	+	0.173761i	−0.563320	+	0.173761i			1.00000i	$0.5\pi$
$500$		0			0
$501$	0.320914	+	0.0989888i	0.320914	+	0.0989888i
$502$		0			0
$503$	−0.443797	−	1.94440i	−0.443797	−	1.94440i	−0.294755	−	0.955573i	$-0.595238\pi$
$503$	−0.443797	−	1.94440i	−0.443797	−	1.94440i	−0.149042	−	0.988831i	$-0.547619\pi$
$504$	0.908598	−	0.0680900i	0.908598	−	0.0680900i
$505$		0			0
$506$	−2.62285	−	0.395331i	−2.62285	−	0.395331i
$507$	−0.283099	+	0.193014i	−0.283099	+	0.193014i
$508$		0			0
$509$	0.222521	+	0.385418i	0.222521	+	0.385418i	0.955573	−	0.294755i	$-0.0952381\pi$
$509$	0.222521	+	0.385418i	0.222521	+	0.385418i	−0.733052	+	0.680173i	$0.761905\pi$
$510$		0			0
$511$		0			0
$512$	0.900969	−	0.433884i	0.900969	−	0.433884i
$513$		0			0
$514$	0.733052	+	0.680173i	0.733052	+	0.680173i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$521$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$522$		0			0
$523$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$523$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$524$	−0.433884	+	1.90097i	−0.433884	+	1.90097i
$525$	−0.297251	+	0.0222759i	−0.297251	+	0.0222759i
$526$		0			0
$527$	0.116853	+	1.55929i	0.116853	+	1.55929i
$528$	0.387483	+	0.119523i	0.387483	+	0.119523i
$529$	1.02366	+	2.60825i	1.02366	+	2.60825i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	0.215372	−	0.548760i	0.215372	−	0.548760i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.680173	+	1.17809i	−0.680173	+	1.17809i
$540$		0			0
$541$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$541$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$542$		0			0
$543$		0			0
$544$	−0.365341	+	0.930874i	−0.365341	+	0.930874i
$545$		0			0
$546$	−0.426066	+	0.0972467i	−0.426066	+	0.0972467i
$547$	−0.702449	−	0.880843i	−0.702449	−	0.880843i	0.294755	−	0.955573i	$-0.404762\pi$
$547$	−0.702449	−	0.880843i	−0.702449	−	0.880843i	−0.997204	+	0.0747301i	$0.976190\pi$
$548$	1.88980	−	0.582926i	1.88980	−	0.582926i
$549$		0			0
$550$	1.29991	+	0.400969i	1.29991	+	0.400969i
$551$		0			0
$552$	−0.129334	−	0.566649i	−0.129334	−	0.566649i
$553$	−0.548760	−	0.215372i	−0.548760	−	0.215372i
$554$		0			0
$555$		0			0
$556$	0.487076	−	0.332083i	0.487076	−	0.332083i
$557$	0.365341	−	0.632789i	0.365341	−	0.632789i	−0.623490	−	0.781831i	$-0.714286\pi$
$557$	0.365341	−	0.632789i	0.365341	−	0.632789i	0.988831	+	0.149042i	$0.0476190\pi$
$558$	−0.712362	−	1.23385i	−0.712362	−	1.23385i
$559$		0			0
$560$		0			0
$561$	−0.365341	+	0.175939i	−0.365341	+	0.175939i
$562$	0.826239	+	0.563320i	0.826239	+	0.563320i
$563$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$563$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$564$		0			0
$565$		0			0
$566$	1.22563	−	0.590232i	1.22563	−	0.590232i
$567$	0.218511	−	0.708397i	0.218511	−	0.708397i
$568$	−1.67738	−	0.807782i	−1.67738	−	0.807782i
$569$	0.733052	+	1.26968i	0.733052	+	1.26968i	0.955573	+	0.294755i	$0.0952381\pi$
$569$	0.733052	+	1.26968i	0.733052	+	1.26968i	−0.222521	+	0.974928i	$0.571429\pi$
$570$		0			0
$571$	1.29196	−	0.880843i	1.29196	−	0.880843i	0.294755	−	0.955573i	$-0.404762\pi$
$571$	1.29196	−	0.880843i	1.29196	−	0.880843i	0.997204	+	0.0747301i	$0.0238095\pi$
$572$	1.97213	+	0.297251i	1.97213	+	0.297251i
$573$		0			0
$574$		0			0
$575$	−0.433884	−	1.90097i	−0.433884	−	1.90097i
$576$	−0.0680900	−	0.908598i	−0.0680900	−	0.908598i
$577$	−0.142820	−	0.0440542i	−0.142820	−	0.0440542i	0.222521	−	0.974928i	$-0.428571\pi$
$577$	−0.142820	−	0.0440542i	−0.142820	−	0.0440542i	−0.365341	+	0.930874i	$0.619048\pi$
$578$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.363142	+	0.925270i	−0.363142	+	0.925270i
$584$		0			0
$585$		0			0
$586$	1.40097	−	1.29991i	1.40097	−	1.29991i
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$	−0.294755	−	0.0444272i	−0.294755	−	0.0444272i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.0546039	−	0.139129i	0.0546039	−	0.139129i	−0.900969	−	0.433884i	$-0.857143\pi$
$593$	0.0546039	−	0.139129i	0.0546039	−	0.139129i	0.955573	+	0.294755i	$0.0952381\pi$
$594$	0.483183	−	0.605893i	0.483183	−	0.605893i
$595$		0			0
$596$	−1.23305	−	1.54620i	−1.23305	−	1.54620i
$597$	−0.530303	+	0.163577i	−0.530303	+	0.163577i
$598$	−1.04440	−	2.66108i	−1.04440	−	2.66108i
$599$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$599$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$600$	0.0222759	+	0.297251i	0.0222759	+	0.297251i
$601$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$601$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$	−0.0663300	+	0.114887i	−0.0663300	+	0.114887i
$607$	−0.866025	−	1.50000i	−0.866025	−	1.50000i	−0.866025	−	0.500000i	$-0.833333\pi$
$607$	−0.866025	−	1.50000i	−0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.667917	+	0.619736i	0.667917	+	0.619736i
$613$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.988831	−	0.149042i	$-0.952381\pi$
$613$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.222521	−	0.974928i	$-0.571429\pi$
$614$		0			0
$615$		0			0
$616$	1.17809	+	0.680173i	1.17809	+	0.680173i
$617$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$617$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$618$		0			0
$619$	0.866025	−	1.50000i	0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$619$	0.866025	−	1.50000i	0.866025	−	1.50000i	0.866025	−	0.500000i	$-0.166667\pi$
$620$		0			0
$621$	−1.09839	−	0.165556i	−1.09839	−	0.165556i
$622$	−0.385418	+	1.68862i	−0.385418	+	1.68862i
$623$	1.11406	−	1.63402i	1.11406	−	1.63402i
$624$	0.0972467	+	0.426066i	0.0972467	+	0.426066i
$625$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$626$		0			0
$627$		0			0
$628$	1.82624	−	0.563320i	1.82624	−	0.563320i
$629$		0			0
$630$		0			0
$631$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$631$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$632$	−0.215372	+	0.548760i	−0.215372	+	0.548760i
$633$	0.0193303	−	0.257945i	0.0193303	−	0.257945i
$634$		0			0
$635$		0			0
$636$	−0.217805			−0.217805
$637$	−1.46610			−1.46610
$638$		0			0
$639$	−1.24349	+	1.15379i	−1.24349	+	1.15379i
$640$		0			0
$641$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$641$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$642$	0.217196	−	0.553406i	0.217196	−	0.553406i
$643$	−0.702449	+	0.880843i	−0.702449	+	0.880843i	−0.997204	−	0.0747301i	$-0.976190\pi$
$643$	−0.702449	+	0.880843i	−0.702449	+	0.880843i	0.294755	+	0.955573i	$0.404762\pi$
$644$		−	1.94986i		−	1.94986i
$645$		0			0
$646$		0			0
$647$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$647$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$648$	−0.708397	−	0.218511i	−0.708397	−	0.218511i
$649$		0			0
$650$	0.326239	+	1.42935i	0.326239	+	1.42935i
$651$	0.137386	+	0.445396i	0.137386	+	0.445396i
$652$		0			0
$653$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$653$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$659$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$660$		0			0
$661$	−0.914101	−	0.848162i	−0.914101	−	0.848162i	0.0747301	−	0.997204i	$-0.476190\pi$
$661$	−0.914101	−	0.848162i	−0.914101	−	0.848162i	−0.988831	+	0.149042i	$0.952381\pi$
$662$		0			0
$663$	−0.361085	−	0.246184i	−0.361085	−	0.246184i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.563320	−	0.975699i	0.563320	−	0.975699i
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−0.0444272	+	0.294755i	−0.0444272	+	0.294755i
$673$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$673$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$674$		0			0
$675$	0.544374	+	0.167917i	0.544374	+	0.167917i
$676$	0.419945	+	1.07000i	0.419945	+	1.07000i
$677$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$677$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.202749	+	0.516596i	−0.202749	+	0.516596i
$682$	0.158960	−	2.12117i	0.158960	−	2.12117i
$683$	−1.84095	+	0.277479i	−1.84095	+	0.277479i	−0.974928	−	0.222521i	$-0.928571\pi$
$683$	−1.84095	+	0.277479i	−1.84095	+	0.277479i	−0.866025	+	0.500000i	$0.833333\pi$
$684$		0			0
$685$		0			0
$686$	−0.930874	−	0.365341i	−0.930874	−	0.365341i
$687$	−0.537130			−0.537130
$688$		0			0
$689$	−1.05929	+	0.159662i	−1.05929	+	0.159662i
$690$		0			0
$691$	−0.571270	+	1.45557i	−0.571270	+	1.45557i	0.294755	+	0.955573i	$0.404762\pi$
$691$	−0.571270	+	1.45557i	−0.571270	+	1.45557i	−0.866025	+	0.500000i	$0.833333\pi$
$692$		0			0
$693$	0.969059	−	0.772799i	0.969059	−	0.772799i
$694$	0.541044	+	0.678448i	0.541044	+	0.678448i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	0.134659	+	1.79690i	0.134659	+	1.79690i
$699$		0			0
$700$	−0.149042	+	0.988831i	−0.149042	+	0.988831i
$701$	0.162592	−	0.712362i	0.162592	−	0.712362i	−0.826239	−	0.563320i	$-0.809524\pi$
$701$	0.162592	−	0.712362i	0.162592	−	0.712362i	0.988831	−	0.149042i	$-0.0476190\pi$
$702$	0.825886	+	0.124482i	0.825886	+	0.124482i
$703$		0			0
$704$	0.680173	−	1.17809i	0.680173	−	1.17809i
$705$		0			0
$706$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$707$	−0.302705	+	0.326239i	−0.302705	+	0.326239i
$708$		0			0
$709$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$709$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$710$		0			0
$711$	0.393744	+	0.365341i	0.393744	+	0.365341i
$712$	−1.63402	−	1.11406i	−1.63402	−	1.11406i
$713$	−2.74698	+	1.32288i	−2.74698	+	1.32288i
$714$	−0.167917	−	0.246289i	−0.167917	−	0.246289i
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	1.34515	+	0.202749i	1.34515	+	0.202749i	0.781831	−	0.623490i	$-0.214286\pi$
$719$	1.34515	+	0.202749i	1.34515	+	0.202749i	0.563320	+	0.826239i	$0.309524\pi$
$720$		0			0
$721$		0			0
$722$	0.222521	+	0.974928i	0.222521	+	0.974928i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	0.242269	−	0.0747301i	0.242269	−	0.0747301i
$727$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$727$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$728$			1.46610i			1.46610i
$729$	−0.315266	+	0.395331i	−0.315266	+	0.395331i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	0.733052	−	0.680173i	0.733052	−	0.680173i	−0.222521	−	0.974928i	$-0.571429\pi$
$733$	0.733052	−	0.680173i	0.733052	−	0.680173i	0.955573	+	0.294755i	$0.0952381\pi$
$734$	1.99441			1.99441
$735$		0			0
$736$	−1.94986			−1.94986
$737$		0			0
$738$		0			0
$739$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$739$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$740$		0			0
$741$		0			0
$742$	−0.712362	−	0.162592i	−0.712362	−	0.162592i
$743$	0.185853	+	0.233052i	0.185853	+	0.233052i	0.866025	−	0.500000i	$-0.166667\pi$
$743$	0.185853	+	0.233052i	0.185853	+	0.233052i	−0.680173	+	0.733052i	$0.738095\pi$
$744$	0.445396	−	0.137386i	0.445396	−	0.137386i
$745$		0			0
$746$	−1.40097	−	0.432142i	−1.40097	−	0.432142i
$747$		0			0
$748$	0.302705	+	1.32624i	0.302705	+	1.32624i
$749$	1.12349	−	1.64786i	1.12349	−	1.64786i
$750$		0			0
$751$	0.582926	+	0.0878620i	0.582926	+	0.0878620i	0.433884	−	0.900969i	$-0.357143\pi$
$751$	0.582926	+	0.0878620i	0.582926	+	0.0878620i	0.149042	+	0.988831i	$0.452381\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$	0.493360	+	0.284841i	0.493360	+	0.284841i
$757$	−0.900969	+	0.433884i	−0.900969	+	0.433884i	−0.826239	−	0.563320i	$-0.809524\pi$
$757$	−0.900969	+	0.433884i	−0.900969	+	0.433884i	−0.0747301	+	0.997204i	$0.523810\pi$
$758$	1.43109	+	0.975699i	1.43109	+	0.975699i
$759$	−0.579597	−	0.537787i	−0.579597	−	0.537787i
$760$		0			0
$761$	−1.36534	−	0.930874i	−1.36534	−	0.930874i	−0.365341	−	0.930874i	$-0.619048\pi$
$761$	−1.36534	−	0.930874i	−1.36534	−	0.930874i	−1.00000			$\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.294755	+	0.0444272i	0.294755	+	0.0444272i
$769$	−0.222521	+	0.974928i	−0.222521	+	0.974928i	0.733052	+	0.680173i	$0.238095\pi$
$769$	−0.222521	+	0.974928i	−0.222521	+	0.974928i	−0.955573	+	0.294755i	$0.904762\pi$
$770$		0			0
$771$	0.0663300	+	0.290611i	0.0663300	+	0.290611i
$772$		0			0
$773$	−1.57906	−	0.487076i	−1.57906	−	0.487076i	−0.623490	−	0.781831i	$-0.714286\pi$
$773$	−1.57906	−	0.487076i	−1.57906	−	0.487076i	−0.955573	+	0.294755i	$0.904762\pi$
$774$		0			0
$775$	1.49419	−	0.460898i	1.49419	−	0.460898i
$776$		0			0
$777$		0			0
$778$	1.03030	−	1.29196i	1.03030	−	1.29196i
$779$		0			0
$780$		0			0
$781$	−2.50433	+	0.377467i	−2.50433	+	0.377467i
$782$	1.42935	−	1.32624i	1.42935	−	1.32624i
$783$		0			0
$784$	−0.365341	+	0.930874i	−0.365341	+	0.930874i
$785$		0			0
$786$	−0.426066	+	0.395331i	−0.426066	+	0.395331i
$787$	0.858075	−	0.129334i	0.858075	−	0.129334i	0.294755	−	0.955573i	$-0.404762\pi$
$787$	0.858075	−	0.129334i	0.858075	−	0.129334i	0.563320	+	0.826239i	$0.309524\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.772799	−	0.969059i	−0.772799	−	0.969059i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	0.139129	+	1.85654i	0.139129	+	1.85654i
$797$	−0.162592	−	0.712362i	−0.162592	−	0.712362i	−0.988831	−	0.149042i	$-0.952381\pi$
$797$	−0.162592	−	0.712362i	−0.162592	−	0.712362i	0.826239	−	0.563320i	$-0.190476\pi$
$798$		0			0
$799$		0			0
$800$	0.988831	+	0.149042i	0.988831	+	0.149042i
$801$	−1.48883	+	1.01507i	−1.48883	+	1.01507i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	2.06546	−	0.994675i	2.06546	−	0.994675i
$807$		0			0
$808$	0.326239	+	0.302705i	0.326239	+	0.302705i
$809$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$809$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$810$		0			0
$811$	1.67738	−	0.807782i	1.67738	−	0.807782i	0.680173	−	0.733052i	$-0.261905\pi$
$811$	1.67738	−	0.807782i	1.67738	−	0.807782i	0.997204	−	0.0747301i	$-0.0238095\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.246289	+	0.167917i	−0.246289	+	0.167917i
$817$		0			0
$818$	0.162592	−	0.712362i	0.162592	−	0.712362i
$819$	1.24349	+	0.488035i	1.24349	+	0.488035i
$820$		0			0
$821$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$821$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$822$	0.563320	+	0.173761i	0.563320	+	0.173761i
$823$	−0.108903	−	0.277479i	−0.108903	−	0.277479i	0.866025	−	0.500000i	$-0.166667\pi$
$823$	−0.108903	−	0.277479i	−0.108903	−	0.277479i	−0.974928	+	0.222521i	$0.928571\pi$
$824$		0			0
$825$	0.252824	+	0.317031i	0.252824	+	0.317031i
$826$		0			0
$827$	−1.24349	+	1.55929i	−1.24349	+	1.55929i	−0.563320	+	0.826239i	$0.690476\pi$
$827$	−1.24349	+	1.55929i	−1.24349	+	1.55929i	−0.680173	+	0.733052i	$0.738095\pi$
$828$	−0.649066	+	1.65379i	−0.649066	+	1.65379i
$829$	0.0111692	−	0.149042i	0.0111692	−	0.149042i	−0.988831	−	0.149042i	$-0.952381\pi$
$829$	0.0111692	−	0.149042i	0.0111692	−	0.149042i	1.00000			$0$
$830$		0			0
$831$		0			0
$832$	1.46610			1.46610
$833$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$834$	0.175724			0.175724
$835$		0			0
$836$		0			0
$837$	0.0665690	−	0.888301i	0.0665690	−	0.888301i
$838$	−0.215372	+	0.548760i	−0.215372	+	0.548760i
$839$	−0.541044	+	0.678448i	−0.541044	+	0.678448i	−0.974928	−	0.222521i	$-0.928571\pi$
$839$	−0.541044	+	0.678448i	−0.541044	+	0.678448i	0.433884	+	0.900969i	$0.357143\pi$
$840$		0			0
$841$	0.623490	+	0.781831i	0.623490	+	0.781831i
$842$	1.19158	−	0.367554i	1.19158	−	0.367554i
$843$	0.108903	+	0.277479i	0.108903	+	0.277479i
$844$	−0.829215	−	0.255779i	−0.829215	−	0.255779i
$845$		0			0
$846$		0			0
$847$	0.848162	−	0.0635609i	0.848162	−	0.0635609i
$848$	−0.162592	+	0.712362i	−0.162592	+	0.712362i
$849$	0.400969	+	0.0604363i	0.400969	+	0.0604363i
$850$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$851$		0			0
$852$	−0.277479	−	0.480608i	−0.277479	−	0.480608i
$853$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$853$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$854$		0			0
$855$		0			0
$856$	−1.64786	−	1.12349i	−1.64786	−	1.12349i
$857$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$857$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$858$	0.435801	+	0.404364i	0.435801	+	0.404364i
$859$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$859$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$860$		0			0
$861$		0			0
$862$	−1.56052	−	0.751509i	−1.56052	−	0.751509i
$863$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$863$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$864$	0.284841	−	0.493360i	0.284841	−	0.493360i
$865$		0			0
$866$	0.440071	+	0.0663300i	0.440071	+	0.0663300i
$867$	0.0663300	−	0.290611i	0.0663300	−	0.290611i
$868$	1.55929	−	0.116853i	1.55929	−	0.116853i
$869$	0.178448	+	0.781831i	0.178448	+	0.781831i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$877$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$878$	0.0440542	−	0.587862i	0.0440542	−	0.587862i
$879$	0.563320	−	0.0849068i	0.563320	−	0.0849068i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	0.667917	+	0.619736i	0.667917	+	0.619736i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$	−1.07473	+	0.997204i	−1.07473	+	0.997204i
$885$		0			0
$886$		0			0
$887$	−0.496990	+	1.26631i	−0.496990	+	1.26631i	0.433884	+	0.900969i	$0.357143\pi$
$887$	−0.496990	+	1.26631i	−0.496990	+	1.26631i	−0.930874	+	0.365341i	$0.880952\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.963664	+	0.297251i	−0.963664	+	0.297251i
$892$		0			0
$893$		0			0
$894$	−0.0440542	−	0.587862i	−0.0440542	−	0.587862i
$895$		0			0
$896$	0.930874	+	0.365341i	0.930874	+	0.365341i
$897$	0.189617	−	0.830767i	0.189617	−	0.830767i
$898$		0			0
$899$		0			0
$900$	0.455573	−	0.789075i	0.455573	−	0.789075i
$901$	−0.365341	−	0.632789i	−0.365341	−	0.632789i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−1.14625	−	1.06356i	−1.14625	−	1.06356i	−0.997204	−	0.0747301i	$-0.976190\pi$
$907$	−1.14625	−	1.06356i	−1.14625	−	1.06356i	−0.149042	−	0.988831i	$-0.547619\pi$
$908$	1.53825	+	1.04876i	1.53825	+	1.04876i
$909$	0.365341	−	0.175939i	0.365341	−	0.175939i
$910$		0			0
$911$	1.75676	+	0.846011i	1.75676	+	0.846011i	0.974928	+	0.222521i	$0.0714286\pi$
$911$	1.75676	+	0.846011i	1.75676	+	0.846011i	0.781831	+	0.623490i	$0.214286\pi$
$912$		0			0
$913$		0			0
$914$	−0.367711	+	0.250701i	−0.367711	+	0.250701i
$915$		0			0
$916$	−0.400969	+	1.75676i	−0.400969	+	1.75676i
$917$	−1.68862	+	0.974928i	−1.68862	+	0.974928i
$918$	0.126766	+	0.555400i	0.126766	+	0.555400i
$919$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$919$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$920$		0			0
$921$		0			0
$922$	−0.698220	+	0.215372i	−0.698220	+	0.215372i
$923$	−1.70182	−	2.13402i	−1.70182	−	2.13402i
$924$	0.175939	+	0.365341i	0.175939	+	0.365341i
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$929$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−0.378473	+	0.351172i	−0.378473	+	0.351172i
$934$		0			0
$935$		0			0
$936$	0.488035	−	1.24349i	0.488035	−	1.24349i
$937$	0.777479	−	0.974928i	0.777479	−	0.974928i	−0.222521	−	0.974928i	$-0.571429\pi$
$937$	0.777479	−	0.974928i	0.777479	−	0.974928i	1.00000			$0$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$941$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$942$	0.544374	+	0.167917i	0.544374	+	0.167917i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.71271	+	0.258149i	1.71271	+	0.258149i	0.930874	−	0.365341i	$-0.119048\pi$
$947$	1.71271	+	0.258149i	1.71271	+	0.258149i	0.781831	+	0.623490i	$0.214286\pi$
$948$	−0.145190	+	0.0989888i	−0.145190	+	0.0989888i
$949$		0			0
$950$		0			0
$951$		0			0
$952$	−0.930874	+	0.365341i	−0.930874	+	0.365341i
$953$	1.48883	−	0.716983i	1.48883	−	0.716983i	0.500000	−	0.866025i	$-0.333333\pi$
$953$	1.48883	−	0.716983i	1.48883	−	0.716983i	0.988831	+	0.149042i	$0.0476190\pi$
$954$	0.550075	+	0.375035i	0.550075	+	0.375035i
$955$		0			0
$956$		0			0
$957$		0			0
$958$	−1.75676	+	0.846011i	−1.75676	+	0.846011i
$959$	1.71271	+	0.988831i	1.71271	+	0.988831i
$960$		0			0
$961$	−0.722521	−	1.25144i	−0.722521	−	1.25144i
$962$		0			0
$963$	−1.50144	+	1.02366i	−1.50144	+	1.02366i
$964$		0			0
$965$		0			0
$966$	0.327414	−	0.480228i	0.327414	−	0.480228i
$967$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$967$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$968$	−0.0635609	−	0.848162i	−0.0635609	−	0.848162i
$969$		0			0
$970$		0			0
$971$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$971$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$972$	−0.492970	−	0.618165i	−0.492970	−	0.618165i
$973$	0.574730	+	0.131178i	0.574730	+	0.131178i
$974$	−1.07992	+	1.35417i	−1.07992	+	1.35417i
$975$	−0.159662	+	0.406813i	−0.159662	+	0.406813i
$976$		0			0
$977$	0.440071	−	0.0663300i	0.440071	−	0.0663300i	0.0747301	−	0.997204i	$-0.476190\pi$
$977$	0.440071	−	0.0663300i	0.440071	−	0.0663300i	0.365341	+	0.930874i	$0.380952\pi$
$978$		0			0
$979$	−2.69030			−2.69030
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1.34515	+	0.202749i	−1.34515	+	0.202749i	−0.781831	−	0.623490i	$-0.785714\pi$
$983$	−1.34515	+	0.202749i	−1.34515	+	0.202749i	−0.563320	+	0.826239i	$0.690476\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−1.07659	−	0.332083i	−1.07659	−	0.332083i	−0.294755	−	0.955573i	$-0.595238\pi$
$991$	−1.07659	−	0.332083i	−1.07659	−	0.332083i	−0.781831	+	0.623490i	$0.785714\pi$
$992$	−0.116853	−	1.55929i	−0.116853	−	1.55929i
$993$		0			0
$994$	−0.548760	−	1.77904i	−0.548760	−	1.77904i
$995$		0			0
$996$		0			0
$997$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$997$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$998$	−0.294755	+	0.510531i	−0.294755	+	0.510531i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3332.1.cc.c.1971.2	yes	24
4.3	odd	2	inner	3332.1.cc.c.1971.1	yes	24
17.16	even	2	inner	3332.1.cc.c.1971.1	yes	24
49.9	even	21	inner	3332.1.cc.c.1087.2	yes	24
68.67	odd	2	CM	3332.1.cc.c.1971.2	yes	24
196.107	odd	42	inner	3332.1.cc.c.1087.1	✓	24
833.254	even	42	inner	3332.1.cc.c.1087.1	✓	24
3332.1087	odd	42	inner	3332.1.cc.c.1087.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3332.1.cc.c.1087.1	✓	24	196.107	odd	42	inner
3332.1.cc.c.1087.1	✓	24	833.254	even	42	inner
3332.1.cc.c.1087.2	yes	24	49.9	even	21	inner
3332.1.cc.c.1087.2	yes	24	3332.1087	odd	42	inner
3332.1.cc.c.1971.1	yes	24	4.3	odd	2	inner
3332.1.cc.c.1971.1	yes	24	17.16	even	2	inner
3332.1.cc.c.1971.2	yes	24	1.1	even	1	trivial
3332.1.cc.c.1971.2	yes	24	68.67	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3332.cc (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.733052 - 0.680173i) q^{2} +(0.294755 - 0.0444272i) q^{3} +(0.0747301 - 0.997204i) q^{4} +(0.185853 - 0.233052i) q^{6} +(0.781831 - 0.623490i) q^{7} +(-0.623490 - 0.781831i) q^{8} +(-0.870666 + 0.268565i) q^{9} +O(q^{10})\)	\(q+(0.733052 - 0.680173i) q^{2} +(0.294755 - 0.0444272i) q^{3} +(0.0747301 - 0.997204i) q^{4} +(0.185853 - 0.233052i) q^{6} +(0.781831 - 0.623490i) q^{7} +(-0.623490 - 0.781831i) q^{8} +(-0.870666 + 0.268565i) q^{9} +(-1.29991 - 0.400969i) q^{11} +(-0.0222759 - 0.297251i) q^{12} +(-0.326239 - 1.42935i) q^{13} +(0.149042 - 0.988831i) q^{14} +(-0.988831 - 0.149042i) q^{16} +(0.826239 - 0.563320i) q^{17} +(-0.455573 + 0.789075i) q^{18} +(0.202749 - 0.218511i) q^{21} +(-1.22563 + 0.590232i) q^{22} +(1.61105 + 1.09839i) q^{23} +(-0.218511 - 0.202749i) q^{24} +(-0.733052 - 0.680173i) q^{25} +(-1.21135 - 0.825886i) q^{26} +(-0.513267 + 0.247176i) q^{27} +(-0.563320 - 0.826239i) q^{28} +(-0.781831 + 1.35417i) q^{31} +(-0.826239 + 0.563320i) q^{32} +(-0.400969 - 0.0604363i) q^{33} +(0.222521 - 0.974928i) q^{34} +(0.202749 + 0.888301i) q^{36} +(-0.159662 - 0.406813i) q^{39} -0.298085i q^{42} +(-0.496990 + 1.26631i) q^{44} +(1.92808 - 0.290611i) q^{46} -0.298085 q^{48} +(0.222521 - 0.974928i) q^{49} -1.00000 q^{50} +(0.218511 - 0.202749i) q^{51} +(-1.44973 + 0.218511i) q^{52} +(0.0546039 - 0.728639i) q^{53} +(-0.208129 + 0.530303i) q^{54} +(-0.974928 - 0.222521i) q^{56} +(0.347948 + 1.52446i) q^{62} +(-0.513267 + 0.752824i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(-0.335038 + 0.228425i) q^{66} +(-0.500000 - 0.866025i) q^{68} +(0.523663 + 0.252183i) q^{69} +(1.67738 - 0.807782i) q^{71} +(0.752824 + 0.513267i) q^{72} +(-0.246289 - 0.167917i) q^{75} +(-1.26631 + 0.496990i) q^{77} +(-0.393744 - 0.189617i) q^{78} +(-0.294755 - 0.510531i) q^{79} +(0.612517 - 0.417607i) q^{81} +(-0.202749 - 0.218511i) q^{84} +(0.496990 + 1.26631i) q^{88} +(1.88980 - 0.582926i) q^{89} +(-1.14625 - 0.914101i) q^{91} +(1.21572 - 1.52446i) q^{92} +(-0.170287 + 0.433884i) q^{93} +(-0.218511 + 0.202749i) q^{96} +(-0.500000 - 0.866025i) q^{98} +1.23947 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 2 q^{4} + 4 q^{8} - 24 q^{9}+O(q^{10}) \) 24 * q - 2 * q^2 + 2 * q^4 + 4 * q^8 - 24 * q^9	\( 24 q - 2 q^{2} + 2 q^{4} + 4 q^{8} - 24 q^{9} + 10 q^{13} + 2 q^{16} + 2 q^{17} + 10 q^{18} + 6 q^{21} + 2 q^{25} - 2 q^{26} - 2 q^{32} + 8 q^{33} + 4 q^{34} + 6 q^{36} + 4 q^{49} - 24 q^{50} + 2 q^{52} - 2 q^{53} - 4 q^{64} - 22 q^{66} - 12 q^{68} - 14 q^{69} - 4 q^{72} - 6 q^{77} + 30 q^{81} - 6 q^{84} + 2 q^{89} - 12 q^{98}+O(q^{100}) \) 24 * q - 2 * q^2 + 2 * q^4 + 4 * q^8 - 24 * q^9 + 10 * q^13 + 2 * q^16 + 2 * q^17 + 10 * q^18 + 6 * q^21 + 2 * q^25 - 2 * q^26 - 2 * q^32 + 8 * q^33 + 4 * q^34 + 6 * q^36 + 4 * q^49 - 24 * q^50 + 2 * q^52 - 2 * q^53 - 4 * q^64 - 22 * q^66 - 12 * q^68 - 14 * q^69 - 4 * q^72 - 6 * q^77 + 30 * q^81 - 6 * q^84 + 2 * q^89 - 12 * q^98

Introduction

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