LMFDB - Embedded newform 3332.1.be.b.1359.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3332,1,Mod(407,3332)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3332, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 10, 7]))

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

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

chi := DirichletCharacter("3332.407");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3332 = 2^{2} \cdot 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3332.be (of order $14$, degree $6$, 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:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{7}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{7} - \cdots)$

Embedding invariants

Embedding label			1359.1
Root			$0.900969 - 0.433884i$ of defining polynomial
Character	$\chi$	$=$	3332.1359
Dual form			3332.1.be.b.407.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.222521 - 0.974928i) q^{2} +(0.777479 + 0.974928i) q^{3} +(-0.900969 + 0.433884i) q^{4} +(0.777479 - 0.974928i) q^{6} +(0.623490 + 0.781831i) q^{7} +(0.623490 + 0.781831i) q^{8} +(-0.123490 + 0.541044i) q^{9} +(0.0990311 + 0.433884i) q^{11} +(-1.12349 - 0.541044i) q^{12} +(0.0990311 + 0.433884i) q^{13} +(0.623490 - 0.781831i) q^{14} +(0.623490 - 0.781831i) q^{16} +(-0.900969 - 0.433884i) q^{17} +0.554958 q^{18} +(-0.277479 + 1.21572i) q^{21} +(0.400969 - 0.193096i) q^{22} +(0.400969 - 0.193096i) q^{23} +(-0.277479 + 1.21572i) q^{24} +(-0.222521 + 0.974928i) q^{25} +(0.400969 - 0.193096i) q^{26} +(0.500000 - 0.240787i) q^{27} +(-0.900969 - 0.433884i) q^{28} +1.24698 q^{31} +(-0.900969 - 0.433884i) q^{32} +(-0.346011 + 0.433884i) q^{33} +(-0.222521 + 0.974928i) q^{34} +(-0.123490 - 0.541044i) q^{36} +(-0.346011 + 0.433884i) q^{39} +1.24698 q^{42} +(-0.277479 - 0.347948i) q^{44} +(-0.277479 - 0.347948i) q^{46} +1.24698 q^{48} +(-0.222521 + 0.974928i) q^{49} +1.00000 q^{50} +(-0.277479 - 1.21572i) q^{51} +(-0.277479 - 0.347948i) q^{52} +(-1.12349 + 0.541044i) q^{53} +(-0.346011 - 0.433884i) q^{54} +(-0.222521 + 0.974928i) q^{56} +(-0.277479 - 1.21572i) q^{62} +(-0.500000 + 0.240787i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(0.500000 + 0.240787i) q^{66} +1.00000 q^{68} +(0.500000 + 0.240787i) q^{69} +(-1.12349 + 0.541044i) q^{71} +(-0.500000 + 0.240787i) q^{72} +(-1.12349 + 0.541044i) q^{75} +(-0.277479 + 0.347948i) q^{77} +(0.500000 + 0.240787i) q^{78} -0.445042 q^{79} +(1.12349 + 0.541044i) q^{81} +(-0.277479 - 1.21572i) q^{84} +(-0.277479 + 0.347948i) q^{88} +(-0.277479 + 1.21572i) q^{89} +(-0.277479 + 0.347948i) q^{91} +(-0.277479 + 0.347948i) q^{92} +(0.969501 + 1.21572i) q^{93} +(-0.277479 - 1.21572i) q^{96} +1.00000 q^{98} -0.246980 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} + 5 q^{3} - q^{4} + 5 q^{6} - q^{7} - q^{8} + 4 q^{9} + 5 q^{11} - 2 q^{12} + 5 q^{13} - q^{14} - q^{16} - q^{17} + 4 q^{18} - 2 q^{21} - 2 q^{22} - 2 q^{23} - 2 q^{24} - q^{25} - 2 q^{26}+ \cdots + 8 q^{99}+O(q^{100}) $ 6 * q - q^2 + 5 * q^3 - q^4 + 5 * q^6 - q^7 - q^8 + 4 * q^9 + 5 * q^11 - 2 * q^12 + 5 * q^13 - q^14 - q^16 - q^17 + 4 * q^18 - 2 * q^21 - 2 * q^22 - 2 * q^23 - 2 * q^24 - q^25 - 2 * q^26 + 3 * q^27 - q^28 - 2 * q^31 - q^32 + 3 * q^33 - q^34 + 4 * q^36 + 3 * q^39 - 2 * q^42 - 2 * q^44 - 2 * q^46 - 2 * q^48 - q^49 + 6 * q^50 - 2 * q^51 - 2 * q^52 - 2 * q^53 + 3 * q^54 - q^56 - 2 * q^62 - 3 * q^63 - q^64 + 3 * q^66 + 6 * q^68 + 3 * q^69 - 2 * q^71 - 3 * q^72 - 2 * q^75 - 2 * q^77 + 3 * q^78 - 2 * q^79 + 2 * q^81 - 2 * q^84 - 2 * q^88 - 2 * q^89 - 2 * q^91 - 2 * q^92 - 4 * q^93 - 2 * q^96 + 6 * q^98 + 8 * q^99

Character values

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

$n$	$785$	$885$	$1667$
$\chi(n)$	$-1$	$e\left(\frac{2}{7}\right)$	$-1$

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 $

$2$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$2$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$3$	0.777479	+	0.974928i	0.777479	+	0.974928i	1.00000			$0$
$3$	0.777479	+	0.974928i	0.777479	+	0.974928i	−0.222521	+	0.974928i	$0.571429\pi$
$4$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$5$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$5$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$6$	0.777479	−	0.974928i	0.777479	−	0.974928i
$7$	0.623490	+	0.781831i	0.623490	+	0.781831i
$7$	0.623490	+	0.781831i	0.623490	+	0.781831i
$8$	0.623490	+	0.781831i	0.623490	+	0.781831i
$9$	−0.123490	+	0.541044i	−0.123490	+	0.541044i
$10$		0			0
$11$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	1.00000			$0$
$11$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	−0.900969	+	0.433884i	$0.857143\pi$
$12$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$13$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	1.00000			$0$
$13$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	−0.900969	+	0.433884i	$0.857143\pi$
$14$	0.623490	−	0.781831i	0.623490	−	0.781831i
$15$		0			0
$16$	0.623490	−	0.781831i	0.623490	−	0.781831i
$17$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$17$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$18$	0.554958			0.554958
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$		0			0
$21$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$22$	0.400969	−	0.193096i	0.400969	−	0.193096i
$23$	0.400969	−	0.193096i	0.400969	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$23$	0.400969	−	0.193096i	0.400969	−	0.193096i	0.623490	+	0.781831i	$0.285714\pi$
$24$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$25$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$26$	0.400969	−	0.193096i	0.400969	−	0.193096i
$27$	0.500000	−	0.240787i	0.500000	−	0.240787i
$28$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$29$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$29$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$30$		0			0
$31$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$31$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$32$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$33$	−0.346011	+	0.433884i	−0.346011	+	0.433884i
$34$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$35$		0			0
$36$	−0.123490	−	0.541044i	−0.123490	−	0.541044i
$37$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$37$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$38$		0			0
$39$	−0.346011	+	0.433884i	−0.346011	+	0.433884i
$40$		0			0
$41$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$41$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$42$	1.24698			1.24698
$43$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$43$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$44$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$45$		0			0
$46$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$47$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$47$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$48$	1.24698			1.24698
$49$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$50$	1.00000			1.00000
$51$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$52$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$53$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.900969	−	0.433884i	$-0.857143\pi$
$53$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$54$	−0.346011	−	0.433884i	−0.346011	−	0.433884i
$55$		0			0
$56$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$57$		0			0
$58$		0			0
$59$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$59$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$60$		0			0
$61$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$61$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$62$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$63$	−0.500000	+	0.240787i	−0.500000	+	0.240787i
$64$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$65$		0			0
$66$	0.500000	+	0.240787i	0.500000	+	0.240787i
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$	1.00000			1.00000
$69$	0.500000	+	0.240787i	0.500000	+	0.240787i
$70$		0			0
$71$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.900969	−	0.433884i	$-0.857143\pi$
$71$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$72$	−0.500000	+	0.240787i	−0.500000	+	0.240787i
$73$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$73$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$74$		0			0
$75$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$76$		0			0
$77$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$78$	0.500000	+	0.240787i	0.500000	+	0.240787i
$79$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$79$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$80$		0			0
$81$	1.12349	+	0.541044i	1.12349	+	0.541044i
$82$		0			0
$83$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$83$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$84$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$89$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$89$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$90$		0			0
$91$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$92$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$93$	0.969501	+	1.21572i	0.969501	+	1.21572i
$94$		0			0
$95$		0			0
$96$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	1.00000			1.00000
$99$	−0.246980			−0.246980
$100$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$101$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$101$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$102$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$103$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$103$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$104$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$105$		0			0
$106$	0.777479	+	0.974928i	0.777479	+	0.974928i
$107$	0.400969	−	1.75676i	0.400969	−	1.75676i	−0.222521	−	0.974928i	$-0.571429\pi$
$107$	0.400969	−	1.75676i	0.400969	−	1.75676i	0.623490	−	0.781831i	$-0.285714\pi$
$108$	−0.346011	+	0.433884i	−0.346011	+	0.433884i
$109$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$109$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$110$		0			0
$111$		0			0
$112$	1.00000			1.00000
$113$		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
$117$	−0.246980			−0.246980
$118$		0			0
$119$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$120$		0			0
$121$	0.722521	−	0.347948i	0.722521	−	0.347948i
$122$		0			0
$123$		0			0
$124$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$125$		0			0
$126$	0.346011	+	0.433884i	0.346011	+	0.433884i
$127$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$127$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$128$	1.00000			1.00000
$129$		0			0
$130$		0			0
$131$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$131$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$132$	0.123490	−	0.541044i	0.123490	−	0.541044i
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$137$	0.777479	−	0.974928i	0.777479	−	0.974928i	−0.222521	−	0.974928i	$-0.571429\pi$
$137$	0.777479	−	0.974928i	0.777479	−	0.974928i	1.00000			$0$
$138$	0.123490	−	0.541044i	0.123490	−	0.541044i
$139$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$139$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$140$		0			0
$141$		0			0
$142$	0.777479	+	0.974928i	0.777479	+	0.974928i
$143$	−0.178448	+	0.0859360i	−0.178448	+	0.0859360i
$144$	0.346011	+	0.433884i	0.346011	+	0.433884i
$145$		0			0
$146$		0			0
$147$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$148$		0			0
$149$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	−0.900969	−	0.433884i	$-0.857143\pi$
$149$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	0.623490	−	0.781831i	$-0.285714\pi$
$150$	0.777479	+	0.974928i	0.777479	+	0.974928i
$151$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$151$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$152$		0			0
$153$	0.346011	−	0.433884i	0.346011	−	0.433884i
$154$	0.400969	+	0.193096i	0.400969	+	0.193096i
$155$		0			0
$156$	0.123490	−	0.541044i	0.123490	−	0.541044i
$157$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$157$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$158$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$159$	−1.40097	−	0.674671i	−1.40097	−	0.674671i
$160$		0			0
$161$	0.400969	+	0.193096i	0.400969	+	0.193096i
$162$	0.277479	−	1.21572i	0.277479	−	1.21572i
$163$	1.24698	−	1.56366i	1.24698	−	1.56366i	0.623490	−	0.781831i	$-0.285714\pi$
$163$	1.24698	−	1.56366i	1.24698	−	1.56366i	0.623490	−	0.781831i	$-0.285714\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.62349	+	0.781831i	1.62349	+	0.781831i	1.00000			$0$
$167$	1.62349	+	0.781831i	1.62349	+	0.781831i	0.623490	+	0.781831i	$0.285714\pi$
$168$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$169$	0.722521	−	0.347948i	0.722521	−	0.347948i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$173$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$174$		0			0
$175$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$176$	0.400969	+	0.193096i	0.400969	+	0.193096i
$177$		0			0
$178$	1.24698			1.24698
$179$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$179$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$180$		0			0
$181$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$181$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$182$	0.400969	+	0.193096i	0.400969	+	0.193096i
$183$		0			0
$184$	0.400969	+	0.193096i	0.400969	+	0.193096i
$185$		0			0
$186$	0.969501	−	1.21572i	0.969501	−	1.21572i
$187$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$188$		0			0
$189$	0.500000	+	0.240787i	0.500000	+	0.240787i
$190$		0			0
$191$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$191$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$192$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$193$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$193$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$194$		0			0
$195$		0			0
$196$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	0.0549581	+	0.240787i	0.0549581	+	0.240787i
$199$	0.777479	+	0.974928i	0.777479	+	0.974928i	1.00000			$0$
$199$	0.777479	+	0.974928i	0.777479	+	0.974928i	−0.222521	+	0.974928i	$0.571429\pi$
$200$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$201$		0			0
$202$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$203$		0			0
$204$	0.777479	+	0.974928i	0.777479	+	0.974928i
$205$		0			0
$206$		0			0
$207$	0.0549581	+	0.240787i	0.0549581	+	0.240787i
$208$	0.400969	+	0.193096i	0.400969	+	0.193096i
$209$		0			0
$210$		0			0
$211$	0.400969	−	1.75676i	0.400969	−	1.75676i	−0.222521	−	0.974928i	$-0.571429\pi$
$211$	0.400969	−	1.75676i	0.400969	−	1.75676i	0.623490	−	0.781831i	$-0.285714\pi$
$212$	0.777479	−	0.974928i	0.777479	−	0.974928i
$213$	−1.40097	−	0.674671i	−1.40097	−	0.674671i
$214$	−1.80194			−1.80194
$215$		0			0
$216$	0.500000	+	0.240787i	0.500000	+	0.240787i
$217$	0.777479	+	0.974928i	0.777479	+	0.974928i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$222$		0			0
$223$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$223$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$224$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$225$	−0.500000	−	0.240787i	−0.500000	−	0.240787i
$226$		0			0
$227$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$227$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$228$		0			0
$229$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$229$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$230$		0			0
$231$	−0.554958			−0.554958
$232$		0			0
$233$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$233$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$234$	0.0549581	+	0.240787i	0.0549581	+	0.240787i
$235$		0			0
$236$		0			0
$237$	−0.346011	−	0.433884i	−0.346011	−	0.433884i
$238$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$239$		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		0.900969	−	0.433884i	$-0.142857\pi$
$241$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$242$	−0.500000	−	0.626980i	−0.500000	−	0.626980i
$243$	0.222521	+	0.974928i	0.222521	+	0.974928i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$	0.777479	+	0.974928i	0.777479	+	0.974928i
$249$		0			0
$250$		0			0
$251$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$251$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$252$	0.346011	−	0.433884i	0.346011	−	0.433884i
$253$	0.123490	+	0.154851i	0.123490	+	0.154851i
$254$		0			0
$255$		0			0
$256$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$257$	−1.80194	−	0.867767i	−1.80194	−	0.867767i	−0.900969	−	0.433884i	$-0.857143\pi$
$257$	−1.80194	−	0.867767i	−1.80194	−	0.867767i	−0.900969	−	0.433884i	$-0.857143\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.400969	+	0.193096i	0.400969	+	0.193096i
$263$		0			0		1.00000			$0$
$263$		0			0		−1.00000			$\pi$
$264$	−0.554958			−0.554958
$265$		0			0
$266$		0			0
$267$	−1.40097	+	0.674671i	−1.40097	+	0.674671i
$268$		0			0
$269$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$269$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$270$		0			0
$271$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$271$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$272$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$273$	−0.554958			−0.554958
$274$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$275$	−0.445042			−0.445042
$276$	−0.554958			−0.554958
$277$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$277$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$278$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$279$	−0.153989	+	0.674671i	−0.153989	+	0.674671i
$280$		0			0
$281$	−0.445042	−	1.94986i	−0.445042	−	1.94986i	−0.222521	−	0.974928i	$-0.571429\pi$
$281$	−0.445042	−	1.94986i	−0.445042	−	1.94986i	−0.222521	−	0.974928i	$-0.571429\pi$
$282$		0			0
$283$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	1.00000			$0$
$283$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	−0.900969	+	0.433884i	$0.857143\pi$
$284$	0.777479	−	0.974928i	0.777479	−	0.974928i
$285$		0			0
$286$	0.123490	+	0.154851i	0.123490	+	0.154851i
$287$		0			0
$288$	0.346011	−	0.433884i	0.346011	−	0.433884i
$289$	0.623490	+	0.781831i	0.623490	+	0.781831i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$293$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$294$	0.777479	+	0.974928i	0.777479	+	0.974928i
$295$		0			0
$296$		0			0
$297$	0.153989	+	0.193096i	0.153989	+	0.193096i
$298$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$299$	0.123490	+	0.154851i	0.123490	+	0.154851i
$300$	0.777479	−	0.974928i	0.777479	−	0.974928i
$301$		0			0
$302$		0			0
$303$	0.123490	−	0.541044i	0.123490	−	0.541044i
$304$		0			0
$305$		0			0
$306$	−0.500000	−	0.240787i	−0.500000	−	0.240787i
$307$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$307$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$308$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$309$		0			0
$310$		0			0
$311$	−1.80194	−	0.867767i	−1.80194	−	0.867767i	−0.900969	−	0.433884i	$-0.857143\pi$
$311$	−1.80194	−	0.867767i	−1.80194	−	0.867767i	−0.900969	−	0.433884i	$-0.857143\pi$
$312$	−0.554958			−0.554958
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$	0.400969	+	0.193096i	0.400969	+	0.193096i
$315$		0			0
$316$	0.400969	−	0.193096i	0.400969	−	0.193096i
$317$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$317$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$318$	−0.346011	+	1.51597i	−0.346011	+	1.51597i
$319$		0			0
$320$		0			0
$321$	2.02446	−	0.974928i	2.02446	−	0.974928i
$322$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$323$		0			0
$324$	−1.24698			−1.24698
$325$	−0.445042			−0.445042
$326$	−1.80194	−	0.867767i	−1.80194	−	0.867767i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$331$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$332$		0			0
$333$		0			0
$334$	0.400969	−	1.75676i	0.400969	−	1.75676i
$335$		0			0
$336$	0.777479	+	0.974928i	0.777479	+	0.974928i
$337$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$337$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$338$	−0.500000	−	0.626980i	−0.500000	−	0.626980i
$339$		0			0
$340$		0			0
$341$	0.123490	+	0.541044i	0.123490	+	0.541044i
$342$		0			0
$343$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.62349	−	0.781831i	1.62349	−	0.781831i	0.623490	−	0.781831i	$-0.285714\pi$
$347$	1.62349	−	0.781831i	1.62349	−	0.781831i	1.00000			$0$
$348$		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	$0.857143\pi$
$350$	0.623490	+	0.781831i	0.623490	+	0.781831i
$351$	0.153989	+	0.193096i	0.153989	+	0.193096i
$352$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$353$	1.24698	−	1.56366i	1.24698	−	1.56366i	0.623490	−	0.781831i	$-0.285714\pi$
$353$	1.24698	−	1.56366i	1.24698	−	1.56366i	0.623490	−	0.781831i	$-0.285714\pi$
$354$		0			0
$355$		0			0
$356$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$357$	0.777479	−	0.974928i	0.777479	−	0.974928i
$358$		0			0
$359$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$359$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$360$		0			0
$361$	1.00000			1.00000
$362$		0			0
$363$	0.900969	+	0.433884i	0.900969	+	0.433884i
$364$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$365$		0			0
$366$		0			0
$367$	0.400969	−	1.75676i	0.400969	−	1.75676i	−0.222521	−	0.974928i	$-0.571429\pi$
$367$	0.400969	−	1.75676i	0.400969	−	1.75676i	0.623490	−	0.781831i	$-0.285714\pi$
$368$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$369$		0			0
$370$		0			0
$371$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$372$	−1.40097	−	0.674671i	−1.40097	−	0.674671i
$373$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$373$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$374$	−0.445042			−0.445042
$375$		0			0
$376$		0			0
$377$		0			0
$378$	0.123490	−	0.541044i	0.123490	−	0.541044i
$379$	−0.445042	−	1.94986i	−0.445042	−	1.94986i	−0.222521	−	0.974928i	$-0.571429\pi$
$379$	−0.445042	−	1.94986i	−0.445042	−	1.94986i	−0.222521	−	0.974928i	$-0.571429\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$383$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$384$	0.777479	+	0.974928i	0.777479	+	0.974928i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$389$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$390$		0			0
$391$	−0.445042			−0.445042
$392$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$393$	−0.554958			−0.554958
$394$		0			0
$395$		0			0
$396$	0.222521	−	0.107160i	0.222521	−	0.107160i
$397$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$397$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$398$	0.777479	−	0.974928i	0.777479	−	0.974928i
$399$		0			0
$400$	0.623490	+	0.781831i	0.623490	+	0.781831i
$401$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$401$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$402$		0			0
$403$	0.123490	+	0.541044i	0.123490	+	0.541044i
$404$	0.400969	+	0.193096i	0.400969	+	0.193096i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.777479	−	0.974928i	0.777479	−	0.974928i
$409$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.222521	−	0.974928i	$-0.571429\pi$
$409$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.900969	+	0.433884i	$0.857143\pi$
$410$		0			0
$411$	1.55496			1.55496
$412$		0			0
$413$		0			0
$414$	0.222521	−	0.107160i	0.222521	−	0.107160i
$415$		0			0
$416$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$417$	0.123490	−	0.541044i	0.123490	−	0.541044i
$418$		0			0
$419$	0.400969	−	0.193096i	0.400969	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$419$	0.400969	−	0.193096i	0.400969	−	0.193096i	0.623490	+	0.781831i	$0.285714\pi$
$420$		0			0
$421$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.222521	−	0.974928i	$-0.571429\pi$
$421$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.900969	+	0.433884i	$0.857143\pi$
$422$	−1.80194			−1.80194
$423$		0			0
$424$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$425$	0.623490	−	0.781831i	0.623490	−	0.781831i
$426$	−0.346011	+	1.51597i	−0.346011	+	1.51597i
$427$		0			0
$428$	0.400969	+	1.75676i	0.400969	+	1.75676i
$429$	−0.222521	−	0.107160i	−0.222521	−	0.107160i
$430$		0			0
$431$	1.24698	−	1.56366i	1.24698	−	1.56366i	0.623490	−	0.781831i	$-0.285714\pi$
$431$	1.24698	−	1.56366i	1.24698	−	1.56366i	0.623490	−	0.781831i	$-0.285714\pi$
$432$	0.123490	−	0.541044i	0.123490	−	0.541044i
$433$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$433$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$434$	0.777479	−	0.974928i	0.777479	−	0.974928i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	1.00000			$0$
$439$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	−0.900969	+	0.433884i	$0.857143\pi$
$440$		0			0
$441$	−0.500000	−	0.240787i	−0.500000	−	0.240787i
$442$	−0.445042			−0.445042
$443$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$443$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.969501	−	1.21572i	0.969501	−	1.21572i
$448$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$449$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$449$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$450$	−0.123490	+	0.541044i	−0.123490	+	0.541044i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−0.277479	−	1.21572i	−0.277479	−	1.21572i
$455$		0			0
$456$		0			0
$457$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$457$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$458$	1.62349	+	0.781831i	1.62349	+	0.781831i
$459$	−0.554958			−0.554958
$460$		0			0
$461$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.222521	−	0.974928i	$-0.571429\pi$
$461$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.900969	+	0.433884i	$0.857143\pi$
$462$	0.123490	+	0.541044i	0.123490	+	0.541044i
$463$		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		0.900969	−	0.433884i	$-0.142857\pi$
$467$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$468$	0.222521	−	0.107160i	0.222521	−	0.107160i
$469$		0			0
$470$		0			0
$471$	−0.554958			−0.554958
$472$		0			0
$473$		0			0
$474$	−0.346011	+	0.433884i	−0.346011	+	0.433884i
$475$		0			0
$476$	0.623490	+	0.781831i	0.623490	+	0.781831i
$477$	−0.153989	−	0.674671i	−0.153989	−	0.674671i
$478$		0			0
$479$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	1.00000			$0$
$479$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	−0.900969	+	0.433884i	$0.857143\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	0.123490	+	0.541044i	0.123490	+	0.541044i
$484$	−0.500000	+	0.626980i	−0.500000	+	0.626980i
$485$		0			0
$486$	0.900969	−	0.433884i	0.900969	−	0.433884i
$487$	1.24698	+	1.56366i	1.24698	+	1.56366i	0.623490	+	0.781831i	$0.285714\pi$
$487$	1.24698	+	1.56366i	1.24698	+	1.56366i	0.623490	+	0.781831i	$0.285714\pi$
$488$		0			0
$489$	2.49396			2.49396
$490$		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
$496$	0.777479	−	0.974928i	0.777479	−	0.974928i
$497$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$498$		0			0
$499$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	−0.900969	−	0.433884i	$-0.857143\pi$
$499$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	1.00000			$0$
$500$		0			0
$501$	0.500000	+	2.19064i	0.500000	+	2.19064i
$502$		0			0
$503$	0.400969	+	1.75676i	0.400969	+	1.75676i	0.623490	+	0.781831i	$0.285714\pi$
$503$	0.400969	+	1.75676i	0.400969	+	1.75676i	−0.222521	+	0.974928i	$0.571429\pi$
$504$	−0.500000	−	0.240787i	−0.500000	−	0.240787i
$505$		0			0
$506$	0.123490	−	0.154851i	0.123490	−	0.154851i
$507$	0.900969	+	0.433884i	0.900969	+	0.433884i
$508$		0			0
$509$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$509$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$510$		0			0
$511$		0			0
$512$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$513$		0			0
$514$	−0.445042	+	1.94986i	−0.445042	+	1.94986i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$		0			0
$523$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$523$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$524$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$525$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$526$		0			0
$527$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$528$	0.123490	+	0.541044i	0.123490	+	0.541044i
$529$	−0.500000	+	0.626980i	−0.500000	+	0.626980i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	0.969501	+	1.21572i	0.969501	+	1.21572i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.445042			−0.445042
$540$		0			0
$541$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$541$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$542$		0			0
$543$		0			0
$544$	0.623490	+	0.781831i	0.623490	+	0.781831i
$545$		0			0
$546$	0.123490	+	0.541044i	0.123490	+	0.541044i
$547$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$547$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$548$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$549$		0			0
$550$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$551$		0			0
$552$	0.123490	+	0.541044i	0.123490	+	0.541044i
$553$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$554$		0			0
$555$		0			0
$556$	0.400969	+	0.193096i	0.400969	+	0.193096i
$557$	1.24698			1.24698			0.623490	−	0.781831i	$-0.285714\pi$
$557$	1.24698			1.24698			0.623490	+	0.781831i	$0.285714\pi$
$558$	0.692021			0.692021
$559$		0			0
$560$		0			0
$561$	0.500000	−	0.240787i	0.500000	−	0.240787i
$562$	−1.80194	+	0.867767i	−1.80194	+	0.867767i
$563$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$563$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$564$		0			0
$565$		0			0
$566$	0.400969	−	0.193096i	0.400969	−	0.193096i
$567$	0.277479	+	1.21572i	0.277479	+	1.21572i
$568$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$569$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$569$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$570$		0			0
$571$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.222521	−	0.974928i	$-0.571429\pi$
$571$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.900969	+	0.433884i	$0.857143\pi$
$572$	0.123490	−	0.154851i	0.123490	−	0.154851i
$573$		0			0
$574$		0			0
$575$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$576$	−0.500000	−	0.240787i	−0.500000	−	0.240787i
$577$	0.400969	+	1.75676i	0.400969	+	1.75676i	0.623490	+	0.781831i	$0.285714\pi$
$577$	0.400969	+	1.75676i	0.400969	+	1.75676i	−0.222521	+	0.974928i	$0.571429\pi$
$578$	0.623490	−	0.781831i	0.623490	−	0.781831i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.346011	−	0.433884i	−0.346011	−	0.433884i
$584$		0			0
$585$		0			0
$586$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$	0.777479	−	0.974928i	0.777479	−	0.974928i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$593$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$594$	0.153989	−	0.193096i	0.153989	−	0.193096i
$595$		0			0
$596$	0.777479	+	0.974928i	0.777479	+	0.974928i
$597$	−0.346011	+	1.51597i	−0.346011	+	1.51597i
$598$	0.123490	−	0.154851i	0.123490	−	0.154851i
$599$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$599$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$600$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$601$		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
$606$	−0.554958			−0.554958
$607$	2.00000			2.00000			1.00000			$0$
$607$	2.00000			2.00000			1.00000			$0$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.123490	+	0.541044i	−0.123490	+	0.541044i
$613$	0.400969	−	1.75676i	0.400969	−	1.75676i	−0.222521	−	0.974928i	$-0.571429\pi$
$613$	0.400969	−	1.75676i	0.400969	−	1.75676i	0.623490	−	0.781831i	$-0.285714\pi$
$614$		0			0
$615$		0			0
$616$	−0.445042			−0.445042
$617$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$617$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$618$		0			0
$619$	2.00000			2.00000			1.00000			$0$
$619$	2.00000			2.00000			1.00000			$0$
$620$		0			0
$621$	0.153989	−	0.193096i	0.153989	−	0.193096i
$622$	−0.445042	+	1.94986i	−0.445042	+	1.94986i
$623$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$624$	0.123490	+	0.541044i	0.123490	+	0.541044i
$625$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$626$		0			0
$627$		0			0
$628$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$629$		0			0
$630$		0			0
$631$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$631$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$632$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$633$	2.02446	−	0.974928i	2.02446	−	0.974928i
$634$		0			0
$635$		0			0
$636$	1.55496			1.55496
$637$	−0.445042			−0.445042
$638$		0			0
$639$	−0.153989	−	0.674671i	−0.153989	−	0.674671i
$640$		0			0
$641$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$641$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$642$	−1.40097	−	1.75676i	−1.40097	−	1.75676i
$643$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$643$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$644$	−0.445042			−0.445042
$645$		0			0
$646$		0			0
$647$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$647$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$648$	0.277479	+	1.21572i	0.277479	+	1.21572i
$649$		0			0
$650$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$651$	−0.346011	+	1.51597i	−0.346011	+	1.51597i
$652$	−0.445042	+	1.94986i	−0.445042	+	1.94986i
$653$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$653$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$654$		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
$661$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$661$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$662$		0			0
$663$	0.500000	−	0.240787i	0.500000	−	0.240787i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−1.80194			−1.80194
$669$		0			0
$670$		0			0
$671$		0			0
$672$	0.777479	−	0.974928i	0.777479	−	0.974928i
$673$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$673$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$674$		0			0
$675$	0.123490	+	0.541044i	0.123490	+	0.541044i
$676$	−0.500000	+	0.626980i	−0.500000	+	0.626980i
$677$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$677$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.969501	+	1.21572i	0.969501	+	1.21572i
$682$	0.500000	−	0.240787i	0.500000	−	0.240787i
$683$	0.777479	+	0.974928i	0.777479	+	0.974928i	1.00000			$0$
$683$	0.777479	+	0.974928i	0.777479	+	0.974928i	−0.222521	+	0.974928i	$0.571429\pi$
$684$		0			0
$685$		0			0
$686$	0.623490	+	0.781831i	0.623490	+	0.781831i
$687$	−2.24698			−2.24698
$688$		0			0
$689$	−0.346011	−	0.433884i	−0.346011	−	0.433884i
$690$		0			0
$691$	0.777479	+	0.974928i	0.777479	+	0.974928i	1.00000			$0$
$691$	0.777479	+	0.974928i	0.777479	+	0.974928i	−0.222521	+	0.974928i	$0.571429\pi$
$692$		0			0
$693$	−0.153989	−	0.193096i	−0.153989	−	0.193096i
$694$	−1.12349	−	1.40881i	−1.12349	−	1.40881i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	1.62349	+	0.781831i	1.62349	+	0.781831i
$699$		0			0
$700$	0.623490	−	0.781831i	0.623490	−	0.781831i
$701$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$701$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$702$	0.153989	−	0.193096i	0.153989	−	0.193096i
$703$		0			0
$704$	−0.445042			−0.445042
$705$		0			0
$706$	−1.80194	−	0.867767i	−1.80194	−	0.867767i
$707$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$708$		0			0
$709$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$709$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$710$		0			0
$711$	0.0549581	−	0.240787i	0.0549581	−	0.240787i
$712$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$713$	0.500000	−	0.240787i	0.500000	−	0.240787i
$714$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$719$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$720$		0			0
$721$		0			0
$722$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	0.222521	−	0.974928i	0.222521	−	0.974928i
$727$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$727$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$728$	−0.445042			−0.445042
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−0.445042	−	1.94986i	−0.445042	−	1.94986i	−0.222521	−	0.974928i	$-0.571429\pi$
$733$	−0.445042	−	1.94986i	−0.445042	−	1.94986i	−0.222521	−	0.974928i	$-0.571429\pi$
$734$	−1.80194			−1.80194
$735$		0			0
$736$	−0.445042			−0.445042
$737$		0			0
$738$		0			0
$739$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$739$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$740$		0			0
$741$		0			0
$742$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$743$	0.777479	+	0.974928i	0.777479	+	0.974928i	1.00000			$0$
$743$	0.777479	+	0.974928i	0.777479	+	0.974928i	−0.222521	+	0.974928i	$0.571429\pi$
$744$	−0.346011	+	1.51597i	−0.346011	+	1.51597i
$745$		0			0
$746$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$747$		0			0
$748$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$749$	1.62349	−	0.781831i	1.62349	−	0.781831i
$750$		0			0
$751$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$751$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−0.554958			−0.554958
$757$	−1.80194	+	0.867767i	−1.80194	+	0.867767i	−0.900969	+	0.433884i	$0.857143\pi$
$757$	−1.80194	+	0.867767i	−1.80194	+	0.867767i	−0.900969	+	0.433884i	$0.857143\pi$
$758$	−1.80194	+	0.867767i	−1.80194	+	0.867767i
$759$	−0.0549581	+	0.240787i	−0.0549581	+	0.240787i
$760$		0			0
$761$	1.62349	−	0.781831i	1.62349	−	0.781831i	0.623490	−	0.781831i	$-0.285714\pi$
$761$	1.62349	−	0.781831i	1.62349	−	0.781831i	1.00000			$0$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.777479	−	0.974928i	0.777479	−	0.974928i
$769$	−0.445042	+	1.94986i	−0.445042	+	1.94986i	−0.222521	+	0.974928i	$0.571429\pi$
$769$	−0.445042	+	1.94986i	−0.445042	+	1.94986i	−0.222521	+	0.974928i	$0.571429\pi$
$770$		0			0
$771$	−0.554958	−	2.43143i	−0.554958	−	2.43143i
$772$		0			0
$773$	0.400969	+	1.75676i	0.400969	+	1.75676i	0.623490	+	0.781831i	$0.285714\pi$
$773$	0.400969	+	1.75676i	0.400969	+	1.75676i	−0.222521	+	0.974928i	$0.571429\pi$
$774$		0			0
$775$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$776$		0			0
$777$		0			0
$778$	−1.12349	+	1.40881i	−1.12349	+	1.40881i
$779$		0			0
$780$		0			0
$781$	−0.346011	−	0.433884i	−0.346011	−	0.433884i
$782$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$783$		0			0
$784$	0.623490	+	0.781831i	0.623490	+	0.781831i
$785$		0			0
$786$	0.123490	+	0.541044i	0.123490	+	0.541044i
$787$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$787$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.153989	−	0.193096i	−0.153989	−	0.193096i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$797$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	−0.900969	−	0.433884i	$-0.857143\pi$
$797$	−0.277479	−	1.21572i	−0.277479	−	1.21572i	0.623490	−	0.781831i	$-0.285714\pi$
$798$		0			0
$799$		0			0
$800$	0.623490	−	0.781831i	0.623490	−	0.781831i
$801$	−0.623490	−	0.300257i	−0.623490	−	0.300257i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	0.500000	−	0.240787i	0.500000	−	0.240787i
$807$		0			0
$808$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$809$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$809$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$810$		0			0
$811$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.900969	−	0.433884i	$-0.857143\pi$
$811$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$817$		0			0
$818$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$819$	−0.153989	−	0.193096i	−0.153989	−	0.193096i
$820$		0			0
$821$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$821$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$822$	−0.346011	−	1.51597i	−0.346011	−	1.51597i
$823$	0.777479	−	0.974928i	0.777479	−	0.974928i	−0.222521	−	0.974928i	$-0.571429\pi$
$823$	0.777479	−	0.974928i	0.777479	−	0.974928i	1.00000			$0$
$824$		0			0
$825$	−0.346011	−	0.433884i	−0.346011	−	0.433884i
$826$		0			0
$827$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$827$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$828$	−0.153989	−	0.193096i	−0.153989	−	0.193096i
$829$	1.62349	−	0.781831i	1.62349	−	0.781831i	0.623490	−	0.781831i	$-0.285714\pi$
$829$	1.62349	−	0.781831i	1.62349	−	0.781831i	1.00000			$0$
$830$		0			0
$831$		0			0
$832$	−0.445042			−0.445042
$833$	0.623490	−	0.781831i	0.623490	−	0.781831i
$834$	−0.554958			−0.554958
$835$		0			0
$836$		0			0
$837$	0.623490	−	0.300257i	0.623490	−	0.300257i
$838$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$839$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$839$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$840$		0			0
$841$	0.623490	+	0.781831i	0.623490	+	0.781831i
$842$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$843$	1.55496	−	1.94986i	1.55496	−	1.94986i
$844$	0.400969	+	1.75676i	0.400969	+	1.75676i
$845$		0			0
$846$		0			0
$847$	0.722521	+	0.347948i	0.722521	+	0.347948i
$848$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$849$	−0.346011	+	0.433884i	−0.346011	+	0.433884i
$850$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$851$		0			0
$852$	1.55496			1.55496
$853$		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
$856$	1.62349	−	0.781831i	1.62349	−	0.781831i
$857$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$857$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$858$	−0.0549581	+	0.240787i	−0.0549581	+	0.240787i
$859$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$859$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$860$		0			0
$861$		0			0
$862$	−1.80194	−	0.867767i	−1.80194	−	0.867767i
$863$		0			0		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$	−0.554958			−0.554958
$865$		0			0
$866$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$867$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$868$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$869$	−0.0440730	−	0.193096i	−0.0440730	−	0.193096i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$877$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$878$	0.400969	−	0.193096i	0.400969	−	0.193096i
$879$	−0.346011	−	0.433884i	−0.346011	−	0.433884i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−0.123490	+	0.541044i	−0.123490	+	0.541044i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$885$		0			0
$886$		0			0
$887$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$887$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.123490	+	0.541044i	−0.123490	+	0.541044i
$892$		0			0
$893$		0			0
$894$	−1.40097	−	0.674671i	−1.40097	−	0.674671i
$895$		0			0
$896$	0.623490	+	0.781831i	0.623490	+	0.781831i
$897$	−0.0549581	+	0.240787i	−0.0549581	+	0.240787i
$898$		0			0
$899$		0			0
$900$	0.554958			0.554958
$901$	1.24698			1.24698
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$907$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$908$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$909$	0.222521	−	0.107160i	0.222521	−	0.107160i
$910$		0			0
$911$	0.400969	+	0.193096i	0.400969	+	0.193096i	0.623490	−	0.781831i	$-0.285714\pi$
$911$	0.400969	+	0.193096i	0.400969	+	0.193096i	−0.222521	+	0.974928i	$0.571429\pi$
$912$		0			0
$913$		0			0
$914$	0.400969	+	0.193096i	0.400969	+	0.193096i
$915$		0			0
$916$	0.400969	−	1.75676i	0.400969	−	1.75676i
$917$	−0.445042			−0.445042
$918$	0.123490	+	0.541044i	0.123490	+	0.541044i
$919$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$919$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$920$		0			0
$921$		0			0
$922$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$923$	−0.346011	−	0.433884i	−0.346011	−	0.433884i
$924$	0.500000	−	0.240787i	0.500000	−	0.240787i
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$929$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−0.554958	−	2.43143i	−0.554958	−	2.43143i
$934$		0			0
$935$		0			0
$936$	−0.153989	−	0.193096i	−0.153989	−	0.193096i
$937$	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		0.623490	−	0.781831i	$-0.285714\pi$
$941$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$942$	0.123490	+	0.541044i	0.123490	+	0.541044i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.24698	−	1.56366i	1.24698	−	1.56366i	0.623490	−	0.781831i	$-0.285714\pi$
$947$	1.24698	−	1.56366i	1.24698	−	1.56366i	0.623490	−	0.781831i	$-0.285714\pi$
$948$	0.500000	+	0.240787i	0.500000	+	0.240787i
$949$		0			0
$950$		0			0
$951$		0			0
$952$	0.623490	−	0.781831i	0.623490	−	0.781831i
$953$	1.62349	−	0.781831i	1.62349	−	0.781831i	0.623490	−	0.781831i	$-0.285714\pi$
$953$	1.62349	−	0.781831i	1.62349	−	0.781831i	1.00000			$0$
$954$	−0.623490	+	0.300257i	−0.623490	+	0.300257i
$955$		0			0
$956$		0			0
$957$		0			0
$958$	0.400969	−	0.193096i	0.400969	−	0.193096i
$959$	1.24698			1.24698
$960$		0			0
$961$	0.554958			0.554958
$962$		0			0
$963$	0.900969	+	0.433884i	0.900969	+	0.433884i
$964$		0			0
$965$		0			0
$966$	0.500000	−	0.240787i	0.500000	−	0.240787i
$967$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$967$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$968$	0.722521	+	0.347948i	0.722521	+	0.347948i
$969$		0			0
$970$		0			0
$971$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$971$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$972$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$973$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$974$	1.24698	−	1.56366i	1.24698	−	1.56366i
$975$	−0.346011	−	0.433884i	−0.346011	−	0.433884i
$976$		0			0
$977$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$977$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$978$	−0.554958	−	2.43143i	−0.554958	−	2.43143i
$979$	−0.554958			−0.554958
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	0.623490	−	0.781831i	$-0.285714\pi$
$983$	−0.277479	−	0.347948i	−0.277479	−	0.347948i	−0.900969	+	0.433884i	$0.857143\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.400969	+	1.75676i	0.400969	+	1.75676i	0.623490	+	0.781831i	$0.285714\pi$
$991$	0.400969	+	1.75676i	0.400969	+	1.75676i	−0.222521	+	0.974928i	$0.571429\pi$
$992$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$993$		0			0
$994$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$995$		0			0
$996$		0			0
$997$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$997$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$998$	−0.445042			−0.445042
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3332.1.be.b.1359.1	yes	6
4.3	odd	2		3332.1.be.a.1359.1	yes	6
17.16	even	2		3332.1.be.a.1359.1	yes	6
49.15	even	7	inner	3332.1.be.b.407.1	yes	6
68.67	odd	2	CM	3332.1.be.b.1359.1	yes	6
196.15	odd	14		3332.1.be.a.407.1	✓	6
833.407	even	14		3332.1.be.a.407.1	✓	6
3332.407	odd	14	inner	3332.1.be.b.407.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3332.1.be.a.407.1	✓	6	196.15	odd	14
3332.1.be.a.407.1	✓	6	833.407	even	14
3332.1.be.a.1359.1	yes	6	4.3	odd	2
3332.1.be.a.1359.1	yes	6	17.16	even	2
3332.1.be.b.407.1	yes	6	49.15	even	7	inner
3332.1.be.b.407.1	yes	6	3332.407	odd	14	inner
3332.1.be.b.1359.1	yes	6	1.1	even	1	trivial
3332.1.be.b.1359.1	yes	6	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.be (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.222521 - 0.974928i) q^{2} +(0.777479 + 0.974928i) q^{3} +(-0.900969 + 0.433884i) q^{4} +(0.777479 - 0.974928i) q^{6} +(0.623490 + 0.781831i) q^{7} +(0.623490 + 0.781831i) q^{8} +(-0.123490 + 0.541044i) q^{9} +(0.0990311 + 0.433884i) q^{11} +(-1.12349 - 0.541044i) q^{12} +(0.0990311 + 0.433884i) q^{13} +(0.623490 - 0.781831i) q^{14} +(0.623490 - 0.781831i) q^{16} +(-0.900969 - 0.433884i) q^{17} +0.554958 q^{18} +(-0.277479 + 1.21572i) q^{21} +(0.400969 - 0.193096i) q^{22} +(0.400969 - 0.193096i) q^{23} +(-0.277479 + 1.21572i) q^{24} +(-0.222521 + 0.974928i) q^{25} +(0.400969 - 0.193096i) q^{26} +(0.500000 - 0.240787i) q^{27} +(-0.900969 - 0.433884i) q^{28} +1.24698 q^{31} +(-0.900969 - 0.433884i) q^{32} +(-0.346011 + 0.433884i) q^{33} +(-0.222521 + 0.974928i) q^{34} +(-0.123490 - 0.541044i) q^{36} +(-0.346011 + 0.433884i) q^{39} +1.24698 q^{42} +(-0.277479 - 0.347948i) q^{44} +(-0.277479 - 0.347948i) q^{46} +1.24698 q^{48} +(-0.222521 + 0.974928i) q^{49} +1.00000 q^{50} +(-0.277479 - 1.21572i) q^{51} +(-0.277479 - 0.347948i) q^{52} +(-1.12349 + 0.541044i) q^{53} +(-0.346011 - 0.433884i) q^{54} +(-0.222521 + 0.974928i) q^{56} +(-0.277479 - 1.21572i) q^{62} +(-0.500000 + 0.240787i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(0.500000 + 0.240787i) q^{66} +1.00000 q^{68} +(0.500000 + 0.240787i) q^{69} +(-1.12349 + 0.541044i) q^{71} +(-0.500000 + 0.240787i) q^{72} +(-1.12349 + 0.541044i) q^{75} +(-0.277479 + 0.347948i) q^{77} +(0.500000 + 0.240787i) q^{78} -0.445042 q^{79} +(1.12349 + 0.541044i) q^{81} +(-0.277479 - 1.21572i) q^{84} +(-0.277479 + 0.347948i) q^{88} +(-0.277479 + 1.21572i) q^{89} +(-0.277479 + 0.347948i) q^{91} +(-0.277479 + 0.347948i) q^{92} +(0.969501 + 1.21572i) q^{93} +(-0.277479 - 1.21572i) q^{96} +1.00000 q^{98} -0.246980 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} + 5 q^{3} - q^{4} + 5 q^{6} - q^{7} - q^{8} + 4 q^{9} + 5 q^{11} - 2 q^{12} + 5 q^{13} - q^{14} - q^{16} - q^{17} + 4 q^{18} - 2 q^{21} - 2 q^{22} - 2 q^{23} - 2 q^{24} - q^{25} - 2 q^{26}+ \cdots + 8 q^{99}+O(q^{100}) \) 6 * q - q^2 + 5 * q^3 - q^4 + 5 * q^6 - q^7 - q^8 + 4 * q^9 + 5 * q^11 - 2 * q^12 + 5 * q^13 - q^14 - q^16 - q^17 + 4 * q^18 - 2 * q^21 - 2 * q^22 - 2 * q^23 - 2 * q^24 - q^25 - 2 * q^26 + 3 * q^27 - q^28 - 2 * q^31 - q^32 + 3 * q^33 - q^34 + 4 * q^36 + 3 * q^39 - 2 * q^42 - 2 * q^44 - 2 * q^46 - 2 * q^48 - q^49 + 6 * q^50 - 2 * q^51 - 2 * q^52 - 2 * q^53 + 3 * q^54 - q^56 - 2 * q^62 - 3 * q^63 - q^64 + 3 * q^66 + 6 * q^68 + 3 * q^69 - 2 * q^71 - 3 * q^72 - 2 * q^75 - 2 * q^77 + 3 * q^78 - 2 * q^79 + 2 * q^81 - 2 * q^84 - 2 * q^88 - 2 * q^89 - 2 * q^91 - 2 * q^92 - 4 * q^93 - 2 * q^96 + 6 * q^98 + 8 * q^99

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