LMFDB - Embedded newform 3332.1.cc.a.2447.1

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:	$12$
Coefficient field:	$\Q(\zeta_{21})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + x^{9} - x^{8} + x^{6} - x^{4} + x^{3} - x + 1 $ x^12 - x^11 + x^9 - x^8 + x^6 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{21}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{21} + \cdots)$

Embedding invariants

Embedding label			2447.1
Root			$0.955573 + 0.294755i$ of defining polynomial
Character	$\chi$	$=$	3332.2447
Dual form			3332.1.cc.a.2515.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.365341 - 0.930874i) q^{2} +(-0.0111692 + 0.149042i) q^{3} +(-0.733052 - 0.680173i) q^{4} +(0.134659 + 0.0648483i) q^{6} +(0.900969 - 0.433884i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(0.966742 + 0.145713i) q^{9} +O(q^{10})$	\(q+(0.365341 - 0.930874i) q^{2} +(-0.0111692 + 0.149042i) q^{3} +(-0.733052 - 0.680173i) q^{4} +(0.134659 + 0.0648483i) q^{6} +(0.900969 - 0.433884i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(0.966742 + 0.145713i) q^{9} +(0.722521 - 0.108903i) q^{11} +(0.109562 - 0.101659i) q^{12} +(0.455573 + 0.571270i) q^{13} +(-0.0747301 - 0.997204i) q^{14} +(0.0747301 + 0.997204i) q^{16} +(0.955573 + 0.294755i) q^{17} +(0.488831 - 0.846680i) q^{18} +(0.0546039 + 0.139129i) q^{21} +(0.162592 - 0.712362i) q^{22} +(-1.19158 + 0.367554i) q^{23} +(-0.0546039 - 0.139129i) q^{24} +(0.365341 + 0.930874i) q^{25} +(0.698220 - 0.215372i) q^{26} +(-0.0657731 + 0.288171i) q^{27} +(-0.955573 - 0.294755i) q^{28} +(-0.900969 + 1.56052i) q^{31} +(0.955573 + 0.294755i) q^{32} +(0.00816111 + 0.108903i) q^{33} +(0.623490 - 0.781831i) q^{34} +(-0.609562 - 0.764367i) q^{36} +(-0.0902318 + 0.0615190i) q^{39} +0.149460 q^{42} +(-0.603718 - 0.411608i) q^{44} +(-0.0931869 + 1.24349i) q^{46} -0.149460 q^{48} +(0.623490 - 0.781831i) q^{49} +1.00000 q^{50} +(-0.0546039 + 0.139129i) q^{51} +(0.0546039 - 0.728639i) q^{52} +(-1.21135 - 1.12397i) q^{53} +(0.244221 + 0.166507i) q^{54} +(-0.623490 + 0.781831i) q^{56} +(1.12349 + 1.40881i) q^{62} +(0.934227 - 0.288171i) q^{63} +(0.623490 - 0.781831i) q^{64} +(0.104356 + 0.0321896i) q^{66} +(-0.500000 - 0.866025i) q^{68} +(-0.0414721 - 0.181701i) q^{69} +(0.367711 - 1.61105i) q^{71} +(-0.934227 + 0.288171i) q^{72} +(-0.142820 + 0.0440542i) q^{75} +(0.603718 - 0.411608i) q^{77} +(0.0243010 + 0.106470i) q^{78} +(-0.988831 - 1.71271i) q^{79} +(0.892012 + 0.275149i) q^{81} +(0.0546039 - 0.139129i) q^{84} +(-0.603718 + 0.411608i) q^{88} +(-0.147791 - 0.0222759i) q^{89} +(0.658322 + 0.317031i) q^{91} +(1.12349 + 0.541044i) q^{92} +(-0.222521 - 0.151712i) q^{93} +(-0.0546039 + 0.139129i) q^{96} +(-0.500000 - 0.866025i) q^{98} +0.714360 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} - 13 q^{3} + q^{4} + 5 q^{6} + 2 q^{7} - 2 q^{8} + 14 q^{9}+O(q^{10}) $ 12 * q + q^2 - 13 * q^3 + q^4 + 5 * q^6 + 2 * q^7 - 2 * q^8 + 14 * q^9	$ 12 q + q^{2} - 13 q^{3} + q^{4} + 5 q^{6} + 2 q^{7} - 2 q^{8} + 14 q^{9} + 8 q^{11} + q^{12} - 5 q^{13} - q^{14} + q^{16} + q^{17} - 7 q^{18} - q^{21} - 2 q^{22} - 2 q^{23} + q^{24} + q^{25} - q^{26} - 12 q^{27} - q^{28} - 2 q^{31} + q^{32} - 6 q^{33} - 2 q^{34} - 7 q^{36} + 6 q^{39} + 2 q^{42} + q^{44} - 2 q^{46} - 2 q^{48} - 2 q^{49} + 12 q^{50} + q^{51} - q^{52} - q^{53} + 6 q^{54} + 2 q^{56} + 4 q^{62} - 2 q^{64} + 15 q^{66} - 6 q^{68} - 3 q^{69} - 2 q^{71} + q^{75} - q^{77} + 9 q^{78} + q^{79} + 13 q^{81} - q^{84} + q^{88} - q^{89} - 2 q^{91} + 4 q^{92} - 2 q^{93} + q^{96} - 6 q^{98} + 14 q^{99}+O(q^{100}) $ 12 * q + q^2 - 13 * q^3 + q^4 + 5 * q^6 + 2 * q^7 - 2 * q^8 + 14 * q^9 + 8 * q^11 + q^12 - 5 * q^13 - q^14 + q^16 + q^17 - 7 * q^18 - q^21 - 2 * q^22 - 2 * q^23 + q^24 + q^25 - q^26 - 12 * q^27 - q^28 - 2 * q^31 + q^32 - 6 * q^33 - 2 * q^34 - 7 * q^36 + 6 * q^39 + 2 * q^42 + q^44 - 2 * q^46 - 2 * q^48 - 2 * q^49 + 12 * q^50 + q^51 - q^52 - q^53 + 6 * q^54 + 2 * q^56 + 4 * q^62 - 2 * q^64 + 15 * q^66 - 6 * q^68 - 3 * q^69 - 2 * q^71 + q^75 - q^77 + 9 * q^78 + q^79 + 13 * q^81 - q^84 + q^88 - q^89 - 2 * q^91 + 4 * q^92 - 2 * q^93 + q^96 - 6 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$885$	$1667$
$\chi(n)$	$-1$	$e\left(\frac{11}{21}\right)$	$-1$

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 $

$2$	0.365341	−	0.930874i	0.365341	−	0.930874i
$2$	0.365341	−	0.930874i	0.365341	−	0.930874i
$3$	−0.0111692	+	0.149042i	−0.0111692	+	0.149042i	0.988831	+	0.149042i	$0.0476190\pi$
$3$	−0.0111692	+	0.149042i	−0.0111692	+	0.149042i	−1.00000			$\pi$
$4$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$5$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$5$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$6$	0.134659	+	0.0648483i	0.134659	+	0.0648483i
$7$	0.900969	−	0.433884i	0.900969	−	0.433884i
$7$	0.900969	−	0.433884i	0.900969	−	0.433884i
$8$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$9$	0.966742	+	0.145713i	0.966742	+	0.145713i
$10$		0			0
$11$	0.722521	−	0.108903i	0.722521	−	0.108903i	0.222521	−	0.974928i	$-0.428571\pi$
$11$	0.722521	−	0.108903i	0.722521	−	0.108903i	0.500000	+	0.866025i	$0.333333\pi$
$12$	0.109562	−	0.101659i	0.109562	−	0.101659i
$13$	0.455573	+	0.571270i	0.455573	+	0.571270i	0.955573	−	0.294755i	$-0.0952381\pi$
$13$	0.455573	+	0.571270i	0.455573	+	0.571270i	−0.500000	+	0.866025i	$0.666667\pi$
$14$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i
$15$		0			0
$16$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$17$	0.955573	+	0.294755i	0.955573	+	0.294755i
$17$	0.955573	+	0.294755i	0.955573	+	0.294755i
$18$	0.488831	−	0.846680i	0.488831	−	0.846680i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$		0			0
$21$	0.0546039	+	0.139129i	0.0546039	+	0.139129i
$22$	0.162592	−	0.712362i	0.162592	−	0.712362i
$23$	−1.19158	+	0.367554i	−1.19158	+	0.367554i	−0.826239	−	0.563320i	$-0.809524\pi$
$23$	−1.19158	+	0.367554i	−1.19158	+	0.367554i	−0.365341	+	0.930874i	$0.619048\pi$
$24$	−0.0546039	−	0.139129i	−0.0546039	−	0.139129i
$25$	0.365341	+	0.930874i	0.365341	+	0.930874i
$26$	0.698220	−	0.215372i	0.698220	−	0.215372i
$27$	−0.0657731	+	0.288171i	−0.0657731	+	0.288171i
$28$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$29$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$29$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$30$		0			0
$31$	−0.900969	+	1.56052i	−0.900969	+	1.56052i	−0.0747301	+	0.997204i	$0.523810\pi$
$31$	−0.900969	+	1.56052i	−0.900969	+	1.56052i	−0.826239	+	0.563320i	$0.809524\pi$
$32$	0.955573	+	0.294755i	0.955573	+	0.294755i
$33$	0.00816111	+	0.108903i	0.00816111	+	0.108903i
$34$	0.623490	−	0.781831i	0.623490	−	0.781831i
$35$		0			0
$36$	−0.609562	−	0.764367i	−0.609562	−	0.764367i
$37$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$37$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$38$		0			0
$39$	−0.0902318	+	0.0615190i	−0.0902318	+	0.0615190i
$40$		0			0
$41$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$41$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$42$	0.149460			0.149460
$43$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$43$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$44$	−0.603718	−	0.411608i	−0.603718	−	0.411608i
$45$		0			0
$46$	−0.0931869	+	1.24349i	−0.0931869	+	1.24349i
$47$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$47$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$48$	−0.149460			−0.149460
$49$	0.623490	−	0.781831i	0.623490	−	0.781831i
$50$	1.00000			1.00000
$51$	−0.0546039	+	0.139129i	−0.0546039	+	0.139129i
$52$	0.0546039	−	0.728639i	0.0546039	−	0.728639i
$53$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.988831	−	0.149042i	$-0.952381\pi$
$53$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.222521	−	0.974928i	$-0.571429\pi$
$54$	0.244221	+	0.166507i	0.244221	+	0.166507i
$55$		0			0
$56$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$57$		0			0
$58$		0			0
$59$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$59$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$60$		0			0
$61$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$61$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$62$	1.12349	+	1.40881i	1.12349	+	1.40881i
$63$	0.934227	−	0.288171i	0.934227	−	0.288171i
$64$	0.623490	−	0.781831i	0.623490	−	0.781831i
$65$		0			0
$66$	0.104356	+	0.0321896i	0.104356	+	0.0321896i
$67$		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
$69$	−0.0414721	−	0.181701i	−0.0414721	−	0.181701i
$70$		0			0
$71$	0.367711	−	1.61105i	0.367711	−	1.61105i	−0.365341	−	0.930874i	$-0.619048\pi$
$71$	0.367711	−	1.61105i	0.367711	−	1.61105i	0.733052	−	0.680173i	$-0.238095\pi$
$72$	−0.934227	+	0.288171i	−0.934227	+	0.288171i
$73$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$73$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$74$		0			0
$75$	−0.142820	+	0.0440542i	−0.142820	+	0.0440542i
$76$		0			0
$77$	0.603718	−	0.411608i	0.603718	−	0.411608i
$78$	0.0243010	+	0.106470i	0.0243010	+	0.106470i
$79$	−0.988831	−	1.71271i	−0.988831	−	1.71271i	−0.623490	−	0.781831i	$-0.714286\pi$
$79$	−0.988831	−	1.71271i	−0.988831	−	1.71271i	−0.365341	−	0.930874i	$-0.619048\pi$
$80$		0			0
$81$	0.892012	+	0.275149i	0.892012	+	0.275149i
$82$		0			0
$83$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$83$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$84$	0.0546039	−	0.139129i	0.0546039	−	0.139129i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−0.603718	+	0.411608i	−0.603718	+	0.411608i
$89$	−0.147791	−	0.0222759i	−0.147791	−	0.0222759i	0.0747301	−	0.997204i	$-0.476190\pi$
$89$	−0.147791	−	0.0222759i	−0.147791	−	0.0222759i	−0.222521	+	0.974928i	$0.571429\pi$
$90$		0			0
$91$	0.658322	+	0.317031i	0.658322	+	0.317031i
$92$	1.12349	+	0.541044i	1.12349	+	0.541044i
$93$	−0.222521	−	0.151712i	−0.222521	−	0.151712i
$94$		0			0
$95$		0			0
$96$	−0.0546039	+	0.139129i	−0.0546039	+	0.139129i
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$99$	0.714360			0.714360
$100$	0.365341	−	0.930874i	0.365341	−	0.930874i
$101$	0.0931869	−	1.24349i	0.0931869	−	1.24349i	−0.733052	−	0.680173i	$-0.761905\pi$
$101$	0.0931869	−	1.24349i	0.0931869	−	1.24349i	0.826239	−	0.563320i	$-0.190476\pi$
$102$	0.109562	+	0.101659i	0.109562	+	0.101659i
$103$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$103$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$104$	−0.658322	−	0.317031i	−0.658322	−	0.317031i
$105$		0			0
$106$	−1.48883	+	0.716983i	−1.48883	+	0.716983i
$107$	−1.44973	−	0.218511i	−1.44973	−	0.218511i	−0.623490	−	0.781831i	$-0.714286\pi$
$107$	−1.44973	−	0.218511i	−1.44973	−	0.218511i	−0.826239	+	0.563320i	$0.809524\pi$
$108$	0.244221	−	0.166507i	0.244221	−	0.166507i
$109$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$109$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$110$		0			0
$111$		0			0
$112$	0.500000	+	0.866025i	0.500000	+	0.866025i
$113$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$113$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.357180	+	0.618654i	0.357180	+	0.618654i
$118$		0			0
$119$	0.988831	−	0.149042i	0.988831	−	0.149042i
$120$		0			0
$121$	−0.445396	+	0.137386i	−0.445396	+	0.137386i
$122$		0			0
$123$		0			0
$124$	1.72188	−	0.531130i	1.72188	−	0.531130i
$125$		0			0
$126$	0.0730607	−	0.974928i	0.0730607	−	0.974928i
$127$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$127$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$128$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$129$		0			0
$130$		0			0
$131$	−0.0931869	−	1.24349i	−0.0931869	−	1.24349i	−0.826239	−	0.563320i	$-0.809524\pi$
$131$	−0.0931869	−	1.24349i	−0.0931869	−	1.24349i	0.733052	−	0.680173i	$-0.238095\pi$
$132$	0.0680900	−	0.0853822i	0.0680900	−	0.0853822i
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$137$	0.123490	−	0.0841939i	0.123490	−	0.0841939i	−0.500000	−	0.866025i	$-0.666667\pi$
$137$	0.123490	−	0.0841939i	0.123490	−	0.0841939i	0.623490	+	0.781831i	$0.285714\pi$
$138$	−0.184292	−	0.0277776i	−0.184292	−	0.0277776i
$139$	−1.78181	+	0.858075i	−1.78181	+	0.858075i	−0.826239	+	0.563320i	$0.809524\pi$
$139$	−1.78181	+	0.858075i	−1.78181	+	0.858075i	−0.955573	+	0.294755i	$0.904762\pi$
$140$		0			0
$141$		0			0
$142$	−1.36534	−	0.930874i	−1.36534	−	0.930874i
$143$	0.391374	+	0.363142i	0.391374	+	0.363142i
$144$	−0.0730607	+	0.974928i	−0.0730607	+	0.974928i
$145$		0			0
$146$		0			0
$147$	0.109562	+	0.101659i	0.109562	+	0.101659i
$148$		0			0
$149$	0.0546039	−	0.139129i	0.0546039	−	0.139129i	−0.900969	−	0.433884i	$-0.857143\pi$
$149$	0.0546039	−	0.139129i	0.0546039	−	0.139129i	0.955573	+	0.294755i	$0.0952381\pi$
$150$	−0.0111692	+	0.149042i	−0.0111692	+	0.149042i
$151$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$151$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$152$		0			0
$153$	0.880843	+	0.424191i	0.880843	+	0.424191i
$154$	−0.162592	−	0.712362i	−0.162592	−	0.712362i
$155$		0			0
$156$	0.107988	+	0.0162766i	0.107988	+	0.0162766i
$157$	−1.63402	+	1.11406i	−1.63402	+	1.11406i	−0.733052	+	0.680173i	$0.761905\pi$
$157$	−1.63402	+	1.11406i	−1.63402	+	1.11406i	−0.900969	+	0.433884i	$0.857143\pi$
$158$	−1.95557	+	0.294755i	−1.95557	+	0.294755i
$159$	0.181049	−	0.167989i	0.181049	−	0.167989i
$160$		0			0
$161$	−0.914101	+	0.848162i	−0.914101	+	0.848162i
$162$	0.582018	−	0.729827i	0.582018	−	0.729827i
$163$	−0.149460	−	1.99441i	−0.149460	−	1.99441i	−0.0747301	−	0.997204i	$-0.523810\pi$
$163$	−0.149460	−	1.99441i	−0.149460	−	1.99441i	−0.0747301	−	0.997204i	$-0.523810\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.425270	+	1.86323i	0.425270	+	1.86323i	0.500000	+	0.866025i	$0.333333\pi$
$167$	0.425270	+	1.86323i	0.425270	+	1.86323i	−0.0747301	+	0.997204i	$0.523810\pi$
$168$	−0.109562	−	0.101659i	−0.109562	−	0.101659i
$169$	0.103718	−	0.454418i	0.103718	−	0.454418i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$173$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$174$		0			0
$175$	0.733052	+	0.680173i	0.733052	+	0.680173i
$176$	0.162592	+	0.712362i	0.162592	+	0.712362i
$177$		0			0
$178$	−0.0747301	+	0.129436i	−0.0747301	+	0.129436i
$179$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$179$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$180$		0			0
$181$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$181$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$182$	0.535628	−	0.496990i	0.535628	−	0.496990i
$183$		0			0
$184$	0.914101	−	0.848162i	0.914101	−	0.848162i
$185$		0			0
$186$	−0.222521	+	0.151712i	−0.222521	+	0.151712i
$187$	0.722521	+	0.108903i	0.722521	+	0.108903i
$188$		0			0
$189$	0.0657731	+	0.288171i	0.0657731	+	0.288171i
$190$		0			0
$191$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$191$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$192$	0.109562	+	0.101659i	0.109562	+	0.101659i
$193$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$193$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$194$		0			0
$195$		0			0
$196$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	0.260985	−	0.664979i	0.260985	−	0.664979i
$199$	−0.123490	+	1.64786i	−0.123490	+	1.64786i	0.500000	+	0.866025i	$0.333333\pi$
$199$	−0.123490	+	1.64786i	−0.123490	+	1.64786i	−0.623490	+	0.781831i	$0.714286\pi$
$200$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$201$		0			0
$202$	−1.12349	−	0.541044i	−1.12349	−	0.541044i
$203$		0			0
$204$	0.134659	−	0.0648483i	0.134659	−	0.0648483i
$205$		0			0
$206$		0			0
$207$	−1.20551	+	0.181701i	−1.20551	+	0.181701i
$208$	−0.535628	+	0.496990i	−0.535628	+	0.496990i
$209$		0			0
$210$		0			0
$211$	0.277479	−	0.347948i	0.277479	−	0.347948i	−0.623490	−	0.781831i	$-0.714286\pi$
$211$	0.277479	−	0.347948i	0.277479	−	0.347948i	0.900969	+	0.433884i	$0.142857\pi$
$212$	0.123490	+	1.64786i	0.123490	+	1.64786i
$213$	0.236007	+	0.0727985i	0.236007	+	0.0727985i
$214$	−0.733052	+	1.26968i	−0.733052	+	1.26968i
$215$		0			0
$216$	−0.0657731	−	0.288171i	−0.0657731	−	0.288171i
$217$	−0.134659	+	1.79690i	−0.134659	+	1.79690i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.266948	+	0.680173i	0.266948	+	0.680173i
$222$		0			0
$223$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$223$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$224$	0.988831	−	0.149042i	0.988831	−	0.149042i
$225$	0.217550	+	0.953150i	0.217550	+	0.953150i
$226$		0			0
$227$	0.826239	−	1.43109i	0.826239	−	1.43109i	−0.0747301	−	0.997204i	$-0.523810\pi$
$227$	0.826239	−	1.43109i	0.826239	−	1.43109i	0.900969	−	0.433884i	$-0.142857\pi$
$228$		0			0
$229$	−0.0332580	−	0.443797i	−0.0332580	−	0.443797i	−0.988831	−	0.149042i	$-0.952381\pi$
$229$	−0.0332580	−	0.443797i	−0.0332580	−	0.443797i	0.955573	−	0.294755i	$-0.0952381\pi$
$230$		0			0
$231$	0.0546039	+	0.0945768i	0.0546039	+	0.0945768i
$232$		0			0
$233$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$233$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$234$	0.706381	−	0.106470i	0.706381	−	0.106470i
$235$		0			0
$236$		0			0
$237$	0.266310	−	0.128248i	0.266310	−	0.128248i
$238$	0.222521	−	0.974928i	0.222521	−	0.974928i
$239$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$239$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$240$		0			0
$241$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$241$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$242$	−0.0348320	+	0.464800i	−0.0348320	+	0.464800i
$243$	−0.158960	+	0.405024i	−0.158960	+	0.405024i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$	0.134659	−	1.79690i	0.134659	−	1.79690i
$249$		0			0
$250$		0			0
$251$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$251$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$252$	−0.880843	−	0.424191i	−0.880843	−	0.424191i
$253$	−0.820914	+	0.395331i	−0.820914	+	0.395331i
$254$		0			0
$255$		0			0
$256$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$257$	0.733052	−	0.680173i	0.733052	−	0.680173i	−0.222521	−	0.974928i	$-0.571429\pi$
$257$	0.733052	−	0.680173i	0.733052	−	0.680173i	0.955573	+	0.294755i	$0.0952381\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−1.19158	−	0.367554i	−1.19158	−	0.367554i
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$	−0.0546039	−	0.0945768i	−0.0546039	−	0.0945768i
$265$		0			0
$266$		0			0
$267$	0.00497075	−	0.0217783i	0.00497075	−	0.0217783i
$268$		0			0
$269$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$269$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$270$		0			0
$271$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$271$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$272$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$273$	−0.0546039	+	0.0945768i	−0.0546039	+	0.0945768i
$274$	−0.0332580	−	0.145713i	−0.0332580	−	0.145713i
$275$	0.365341	+	0.632789i	0.365341	+	0.632789i
$276$	−0.0931869	+	0.161404i	−0.0931869	+	0.161404i
$277$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$277$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$278$	0.147791	+	1.97213i	0.147791	+	1.97213i
$279$	−1.09839	+	1.37734i	−1.09839	+	1.37734i
$280$		0			0
$281$	−0.623490	−	0.781831i	−0.623490	−	0.781831i	0.365341	−	0.930874i	$-0.380952\pi$
$281$	−0.623490	−	0.781831i	−0.623490	−	0.781831i	−0.988831	+	0.149042i	$0.952381\pi$
$282$		0			0
$283$	0.722521	−	0.108903i	0.722521	−	0.108903i	0.222521	−	0.974928i	$-0.428571\pi$
$283$	0.722521	−	0.108903i	0.722521	−	0.108903i	0.500000	+	0.866025i	$0.333333\pi$
$284$	−1.36534	+	0.930874i	−1.36534	+	0.930874i
$285$		0			0
$286$	0.481024	−	0.231649i	0.481024	−	0.231649i
$287$		0			0
$288$	0.880843	+	0.424191i	0.880843	+	0.424191i
$289$	0.826239	+	0.563320i	0.826239	+	0.563320i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.97766			−1.97766			−0.988831	−	0.149042i	$-0.952381\pi$
$293$	−1.97766			−1.97766			−0.988831	+	0.149042i	$0.952381\pi$
$294$	0.134659	−	0.0648483i	0.134659	−	0.0648483i
$295$		0			0
$296$		0			0
$297$	−0.0161399	+	0.215372i	−0.0161399	+	0.215372i
$298$	−0.109562	−	0.101659i	−0.109562	−	0.101659i
$299$	−0.752824	−	0.513267i	−0.752824	−	0.513267i
$300$	0.134659	+	0.0648483i	0.134659	+	0.0648483i
$301$		0			0
$302$		0			0
$303$	0.184292	+	0.0277776i	0.184292	+	0.0277776i
$304$		0			0
$305$		0			0
$306$	0.716677	−	0.664979i	0.716677	−	0.664979i
$307$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$307$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$308$	−0.722521	−	0.108903i	−0.722521	−	0.108903i
$309$		0			0
$310$		0			0
$311$	0.955573	+	0.294755i	0.955573	+	0.294755i	0.733052	−	0.680173i	$-0.238095\pi$
$311$	0.955573	+	0.294755i	0.955573	+	0.294755i	0.222521	+	0.974928i	$0.428571\pi$
$312$	0.0546039	−	0.0945768i	0.0546039	−	0.0945768i
$313$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$313$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$314$	0.440071	+	1.92808i	0.440071	+	1.92808i
$315$		0			0
$316$	−0.440071	+	1.92808i	−0.440071	+	1.92808i
$317$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$317$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$318$	−0.0902318	−	0.229907i	−0.0902318	−	0.229907i
$319$		0			0
$320$		0			0
$321$	0.0487597	−	0.213630i	0.0487597	−	0.213630i
$322$	0.455573	+	1.16078i	0.455573	+	1.16078i
$323$		0			0
$324$	−0.466742	−	0.808421i	−0.466742	−	0.808421i
$325$	−0.365341	+	0.632789i	−0.365341	+	0.632789i
$326$	−1.91115	−	0.589510i	−1.91115	−	0.589510i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$331$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$332$		0			0
$333$		0			0
$334$	1.88980	+	0.284841i	1.88980	+	0.284841i
$335$		0			0
$336$	−0.134659	+	0.0648483i	−0.134659	+	0.0648483i
$337$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$337$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$338$	−0.385113	−	0.262566i	−0.385113	−	0.262566i
$339$		0			0
$340$		0			0
$341$	−0.481024	+	1.22563i	−0.481024	+	1.22563i
$342$		0			0
$343$	0.222521	−	0.974928i	0.222521	−	0.974928i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−0.326239	−	0.302705i	−0.326239	−	0.302705i	0.500000	−	0.866025i	$-0.333333\pi$
$347$	−0.326239	−	0.302705i	−0.326239	−	0.302705i	−0.826239	+	0.563320i	$0.809524\pi$
$348$		0			0
$349$	0.400969	+	0.193096i	0.400969	+	0.193096i	0.623490	−	0.781831i	$-0.285714\pi$
$349$	0.400969	+	0.193096i	0.400969	+	0.193096i	−0.222521	+	0.974928i	$0.571429\pi$
$350$	0.900969	−	0.433884i	0.900969	−	0.433884i
$351$	−0.194588	+	0.0937086i	−0.194588	+	0.0937086i
$352$	0.722521	+	0.108903i	0.722521	+	0.108903i
$353$	−0.826239	+	0.563320i	−0.826239	+	0.563320i	−0.900969	−	0.433884i	$-0.857143\pi$
$353$	−0.826239	+	0.563320i	−0.826239	+	0.563320i	0.0747301	+	0.997204i	$0.476190\pi$
$354$		0			0
$355$		0			0
$356$	0.0931869	+	0.116853i	0.0931869	+	0.116853i
$357$	0.0111692	+	0.149042i	0.0111692	+	0.149042i
$358$		0			0
$359$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$359$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$360$		0			0
$361$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$362$		0			0
$363$	−0.0155017	−	0.0679173i	−0.0155017	−	0.0679173i
$364$	−0.266948	−	0.680173i	−0.266948	−	0.680173i
$365$		0			0
$366$		0			0
$367$	0.535628	+	1.36476i	0.535628	+	1.36476i	0.900969	+	0.433884i	$0.142857\pi$
$367$	0.535628	+	1.36476i	0.535628	+	1.36476i	−0.365341	+	0.930874i	$0.619048\pi$
$368$	−0.455573	−	1.16078i	−0.455573	−	1.16078i
$369$		0			0
$370$		0			0
$371$	−1.57906	−	0.487076i	−1.57906	−	0.487076i
$372$	0.0599289	+	0.262566i	0.0599289	+	0.262566i
$373$	−0.365341	−	0.632789i	−0.365341	−	0.632789i	0.623490	−	0.781831i	$-0.285714\pi$
$373$	−0.365341	−	0.632789i	−0.365341	−	0.632789i	−0.988831	+	0.149042i	$0.952381\pi$
$374$	0.365341	−	0.632789i	0.365341	−	0.632789i
$375$		0			0
$376$		0			0
$377$		0			0
$378$	0.292280	+	0.0440542i	0.292280	+	0.0440542i
$379$	0.623490	+	0.781831i	0.623490	+	0.781831i	0.988831	−	0.149042i	$-0.0476190\pi$
$379$	0.623490	+	0.781831i	0.623490	+	0.781831i	−0.365341	+	0.930874i	$0.619048\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$383$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$384$	0.134659	−	0.0648483i	0.134659	−	0.0648483i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	0.142820	−	1.90580i	0.142820	−	1.90580i	−0.222521	−	0.974928i	$-0.571429\pi$
$389$	0.142820	−	1.90580i	0.142820	−	1.90580i	0.365341	−	0.930874i	$-0.380952\pi$
$390$		0			0
$391$	−1.24698			−1.24698
$392$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$393$	0.186374			0.186374
$394$		0			0
$395$		0			0
$396$	−0.523663	−	0.485888i	−0.523663	−	0.485888i
$397$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$397$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$398$	1.48883	+	0.716983i	1.48883	+	0.716983i
$399$		0			0
$400$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$401$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$401$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$402$		0			0
$403$	−1.30194	+	0.196236i	−1.30194	+	0.196236i
$404$	−0.914101	+	0.848162i	−0.914101	+	0.848162i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.0111692	−	0.149042i	−0.0111692	−	0.149042i
$409$	1.57906	+	0.487076i	1.57906	+	0.487076i	0.955573	−	0.294755i	$-0.0952381\pi$
$409$	1.57906	+	0.487076i	1.57906	+	0.487076i	0.623490	+	0.781831i	$0.285714\pi$
$410$		0			0
$411$	0.0111692	+	0.0193456i	0.0111692	+	0.0193456i
$412$		0			0
$413$		0			0
$414$	−0.271281	+	1.18856i	−0.271281	+	1.18856i
$415$		0			0
$416$	0.266948	+	0.680173i	0.266948	+	0.680173i
$417$	−0.107988	−	0.275149i	−0.107988	−	0.275149i
$418$		0			0
$419$	−0.440071	+	1.92808i	−0.440071	+	1.92808i	−0.0747301	+	0.997204i	$0.523810\pi$
$419$	−0.440071	+	1.92808i	−0.440071	+	1.92808i	−0.365341	+	0.930874i	$0.619048\pi$
$420$		0			0
$421$	0.400969	+	1.75676i	0.400969	+	1.75676i	0.623490	+	0.781831i	$0.285714\pi$
$421$	0.400969	+	1.75676i	0.400969	+	1.75676i	−0.222521	+	0.974928i	$0.571429\pi$
$422$	−0.222521	−	0.385418i	−0.222521	−	0.385418i
$423$		0			0
$424$	1.57906	+	0.487076i	1.57906	+	0.487076i
$425$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$426$	0.153989	−	0.193096i	0.153989	−	0.193096i
$427$		0			0
$428$	0.914101	+	1.14625i	0.914101	+	1.14625i
$429$	−0.0584948	+	0.0542752i	−0.0584948	+	0.0542752i
$430$		0			0
$431$	0.826239	−	0.563320i	0.826239	−	0.563320i	−0.0747301	−	0.997204i	$-0.523810\pi$
$431$	0.826239	−	0.563320i	0.826239	−	0.563320i	0.900969	+	0.433884i	$0.142857\pi$
$432$	−0.292280	−	0.0440542i	−0.292280	−	0.0440542i
$433$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.900969	−	0.433884i	$-0.857143\pi$
$433$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$434$	1.62349	+	0.781831i	1.62349	+	0.781831i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	0.722521	−	1.84095i	0.722521	−	1.84095i	0.222521	−	0.974928i	$-0.428571\pi$
$439$	0.722521	−	1.84095i	0.722521	−	1.84095i	0.500000	−	0.866025i	$-0.333333\pi$
$440$		0			0
$441$	0.716677	−	0.664979i	0.716677	−	0.664979i
$442$	0.730682			0.730682
$443$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$443$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.0201262	+	0.00969225i	0.0201262	+	0.00969225i
$448$	0.222521	−	0.974928i	0.222521	−	0.974928i
$449$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$449$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$450$	0.966742	+	0.145713i	0.966742	+	0.145713i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−1.03030	−	1.29196i	−1.03030	−	1.29196i
$455$		0			0
$456$		0			0
$457$	0.0931869	+	1.24349i	0.0931869	+	1.24349i	0.826239	+	0.563320i	$0.190476\pi$
$457$	0.0931869	+	1.24349i	0.0931869	+	1.24349i	−0.733052	+	0.680173i	$0.761905\pi$
$458$	−0.425270	−	0.131178i	−0.425270	−	0.131178i
$459$	−0.147791	+	0.255981i	−0.147791	+	0.255981i
$460$		0			0
$461$	−0.367711	−	1.61105i	−0.367711	−	1.61105i	−0.733052	−	0.680173i	$-0.761905\pi$
$461$	−0.367711	−	1.61105i	−0.367711	−	1.61105i	0.365341	−	0.930874i	$-0.380952\pi$
$462$	0.107988	−	0.0162766i	0.107988	−	0.0162766i
$463$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$463$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$467$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$468$	0.158960	−	0.696449i	0.158960	−	0.696449i
$469$		0			0
$470$		0			0
$471$	−0.147791	−	0.255981i	−0.147791	−	0.255981i
$472$		0			0
$473$		0			0
$474$	−0.0220888	−	0.294755i	−0.0220888	−	0.294755i
$475$		0			0
$476$	−0.826239	−	0.563320i	−0.826239	−	0.563320i
$477$	−1.00729	−	1.26310i	−1.00729	−	1.26310i
$478$		0			0
$479$	1.23305	−	0.185853i	1.23305	−	0.185853i	0.500000	−	0.866025i	$-0.333333\pi$
$479$	1.23305	−	0.185853i	1.23305	−	0.185853i	0.733052	+	0.680173i	$0.238095\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−0.116202	−	0.145713i	−0.116202	−	0.145713i
$484$	0.419945	+	0.202235i	0.419945	+	0.202235i
$485$		0			0
$486$	0.318951	+	0.295943i	0.318951	+	0.295943i
$487$	0.0747301	−	0.997204i	0.0747301	−	0.997204i	−0.826239	−	0.563320i	$-0.809524\pi$
$487$	0.0747301	−	0.997204i	0.0747301	−	0.997204i	0.900969	−	0.433884i	$-0.142857\pi$
$488$		0			0
$489$	0.298920			0.298920
$490$		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
$496$	−1.62349	−	0.781831i	−1.62349	−	0.781831i
$497$	−0.367711	−	1.61105i	−0.367711	−	1.61105i
$498$		0			0
$499$	−1.95557	−	0.294755i	−1.95557	−	0.294755i	−0.955573	−	0.294755i	$-0.904762\pi$
$499$	−1.95557	−	0.294755i	−1.95557	−	0.294755i	−1.00000			$\pi$
$500$		0			0
$501$	−0.282450	+	0.0425725i	−0.282450	+	0.0425725i
$502$		0			0
$503$	0.914101	+	1.14625i	0.914101	+	1.14625i	0.988831	+	0.149042i	$0.0476190\pi$
$503$	0.914101	+	1.14625i	0.914101	+	1.14625i	−0.0747301	+	0.997204i	$0.523810\pi$
$504$	−0.716677	+	0.664979i	−0.716677	+	0.664979i
$505$		0			0
$506$	0.0680900	+	0.908598i	0.0680900	+	0.908598i
$507$	0.0665690	+	0.0205338i	0.0665690	+	0.0205338i
$508$		0			0
$509$	−0.623490	−	1.07992i	−0.623490	−	1.07992i	−0.988831	−	0.149042i	$-0.952381\pi$
$509$	−0.623490	−	1.07992i	−0.623490	−	1.07992i	0.365341	−	0.930874i	$-0.380952\pi$
$510$		0			0
$511$		0			0
$512$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$513$		0			0
$514$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$515$		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		−0.0747301	−	0.997204i	$-0.523810\pi$
$523$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$524$	−0.777479	+	0.974928i	−0.777479	+	0.974928i
$525$	−0.109562	+	0.101659i	−0.109562	+	0.101659i
$526$		0			0
$527$	−1.32091	+	1.22563i	−1.32091	+	1.22563i
$528$	−0.107988	+	0.0162766i	−0.107988	+	0.0162766i
$529$	0.458528	−	0.312619i	0.458528	−	0.312619i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−0.0184568	−	0.0125836i	−0.0184568	−	0.0125836i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.365341	−	0.632789i	0.365341	−	0.632789i
$540$		0			0
$541$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$541$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$542$		0			0
$543$		0			0
$544$	0.826239	+	0.563320i	0.826239	+	0.563320i
$545$		0			0
$546$	0.0680900	+	0.0853822i	0.0680900	+	0.0853822i
$547$	1.72188	−	0.829215i	1.72188	−	0.829215i	0.733052	−	0.680173i	$-0.238095\pi$
$547$	1.72188	−	0.829215i	1.72188	−	0.829215i	0.988831	−	0.149042i	$-0.0476190\pi$
$548$	−0.147791	−	0.0222759i	−0.147791	−	0.0222759i
$549$		0			0
$550$	0.722521	−	0.108903i	0.722521	−	0.108903i
$551$		0			0
$552$	0.116202	+	0.145713i	0.116202	+	0.145713i
$553$	−1.63402	−	1.11406i	−1.63402	−	1.11406i
$554$		0			0
$555$		0			0
$556$	1.88980	+	0.582926i	1.88980	+	0.582926i
$557$	−0.826239	+	1.43109i	−0.826239	+	1.43109i	0.0747301	+	0.997204i	$0.476190\pi$
$557$	−0.826239	+	1.43109i	−0.826239	+	1.43109i	−0.900969	+	0.433884i	$0.857143\pi$
$558$	0.880843	+	1.52566i	0.880843	+	1.52566i
$559$		0			0
$560$		0			0
$561$	−0.0243010	+	0.106470i	−0.0243010	+	0.106470i
$562$	−0.955573	+	0.294755i	−0.955573	+	0.294755i
$563$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$563$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$564$		0			0
$565$		0			0
$566$	0.162592	−	0.712362i	0.162592	−	0.712362i
$567$	0.923058	−	0.139129i	0.923058	−	0.139129i
$568$	0.367711	+	1.61105i	0.367711	+	1.61105i
$569$	−0.365341	−	0.632789i	−0.365341	−	0.632789i	0.623490	−	0.781831i	$-0.285714\pi$
$569$	−0.365341	−	0.632789i	−0.365341	−	0.632789i	−0.988831	+	0.149042i	$0.952381\pi$
$570$		0			0
$571$	1.72188	+	0.531130i	1.72188	+	0.531130i	0.988831	−	0.149042i	$-0.0476190\pi$
$571$	1.72188	+	0.531130i	1.72188	+	0.531130i	0.733052	+	0.680173i	$0.238095\pi$
$572$	−0.0398981	−	0.532403i	−0.0398981	−	0.532403i
$573$		0			0
$574$		0			0
$575$	−0.777479	−	0.974928i	−0.777479	−	0.974928i
$576$	0.716677	−	0.664979i	0.716677	−	0.664979i
$577$	1.44973	−	0.218511i	1.44973	−	0.218511i	0.623490	−	0.781831i	$-0.285714\pi$
$577$	1.44973	−	0.218511i	1.44973	−	0.218511i	0.826239	+	0.563320i	$0.190476\pi$
$578$	0.826239	−	0.563320i	0.826239	−	0.563320i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.997630	−	0.680173i	−0.997630	−	0.680173i
$584$		0			0
$585$		0			0
$586$	−0.722521	+	1.84095i	−0.722521	+	1.84095i
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$	−0.0111692	−	0.149042i	−0.0111692	−	0.149042i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.21135	−	0.825886i	−1.21135	−	0.825886i	−0.222521	−	0.974928i	$-0.571429\pi$
$593$	−1.21135	−	0.825886i	−1.21135	−	0.825886i	−0.988831	+	0.149042i	$0.952381\pi$
$594$	0.194588	+	0.0937086i	0.194588	+	0.0937086i
$595$		0			0
$596$	−0.134659	+	0.0648483i	−0.134659	+	0.0648483i
$597$	−0.244221	−	0.0368104i	−0.244221	−	0.0368104i
$598$	−0.752824	+	0.513267i	−0.752824	+	0.513267i
$599$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$599$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$600$	0.109562	−	0.101659i	0.109562	−	0.101659i
$601$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$601$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$	0.0931869	−	0.161404i	0.0931869	−	0.161404i
$607$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$607$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.357180	−	0.910080i	−0.357180	−	0.910080i
$613$	0.698220	+	1.77904i	0.698220	+	1.77904i	0.623490	+	0.781831i	$0.285714\pi$
$613$	0.698220	+	1.77904i	0.698220	+	1.77904i	0.0747301	+	0.997204i	$0.476190\pi$
$614$		0			0
$615$		0			0
$616$	−0.365341	+	0.632789i	−0.365341	+	0.632789i
$617$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$617$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$618$		0			0
$619$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$619$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$620$		0			0
$621$	−0.0275443	−	0.367554i	−0.0275443	−	0.367554i
$622$	0.623490	−	0.781831i	0.623490	−	0.781831i
$623$	−0.142820	+	0.0440542i	−0.142820	+	0.0440542i
$624$	−0.0680900	−	0.0853822i	−0.0680900	−	0.0853822i
$625$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$626$		0			0
$627$		0			0
$628$	1.95557	+	0.294755i	1.95557	+	0.294755i
$629$		0			0
$630$		0			0
$631$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$631$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$632$	1.63402	+	1.11406i	1.63402	+	1.11406i
$633$	0.0487597	+	0.0452424i	0.0487597	+	0.0452424i
$634$		0			0
$635$		0			0
$636$	−0.246980			−0.246980
$637$	0.730682			0.730682
$638$		0			0
$639$	0.590232	−	1.50389i	0.590232	−	1.50389i
$640$		0			0
$641$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$641$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$642$	−0.181049	−	0.123437i	−0.181049	−	0.123437i
$643$	1.72188	+	0.829215i	1.72188	+	0.829215i	0.988831	+	0.149042i	$0.0476190\pi$
$643$	1.72188	+	0.829215i	1.72188	+	0.829215i	0.733052	+	0.680173i	$0.238095\pi$
$644$	1.24698			1.24698
$645$		0			0
$646$		0			0
$647$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$647$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$648$	−0.923058	+	0.139129i	−0.923058	+	0.139129i
$649$		0			0
$650$	0.455573	+	0.571270i	0.455573	+	0.571270i
$651$	−0.266310	−	0.0401398i	−0.266310	−	0.0401398i
$652$	−1.24698	+	1.56366i	−1.24698	+	1.56366i
$653$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$653$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$659$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$660$		0			0
$661$	−0.658322	−	1.67738i	−0.658322	−	1.67738i	−0.733052	−	0.680173i	$-0.761905\pi$
$661$	−0.658322	−	1.67738i	−0.658322	−	1.67738i	0.0747301	−	0.997204i	$-0.476190\pi$
$662$		0			0
$663$	−0.104356	+	0.0321896i	−0.104356	+	0.0321896i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.955573	−	1.65510i	0.955573	−	1.65510i
$669$		0			0
$670$		0			0
$671$		0			0
$672$	0.0111692	+	0.149042i	0.0111692	+	0.149042i
$673$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$673$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$674$		0			0
$675$	−0.292280	+	0.0440542i	−0.292280	+	0.0440542i
$676$	−0.385113	+	0.262566i	−0.385113	+	0.262566i
$677$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$677$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.204064	+	0.139129i	0.204064	+	0.139129i
$682$	0.965168	+	0.895545i	0.965168	+	0.895545i
$683$	−0.123490	+	1.64786i	−0.123490	+	1.64786i	0.500000	+	0.866025i	$0.333333\pi$
$683$	−0.123490	+	1.64786i	−0.123490	+	1.64786i	−0.623490	+	0.781831i	$0.714286\pi$
$684$		0			0
$685$		0			0
$686$	−0.826239	−	0.563320i	−0.826239	−	0.563320i
$687$	0.0665160			0.0665160
$688$		0			0
$689$	0.0902318	−	1.20406i	0.0902318	−	1.20406i
$690$		0			0
$691$	1.48883	+	1.01507i	1.48883	+	1.01507i	0.988831	+	0.149042i	$0.0476190\pi$
$691$	1.48883	+	1.01507i	1.48883	+	1.01507i	0.500000	+	0.866025i	$0.333333\pi$
$692$		0			0
$693$	0.643616	−	0.309949i	0.643616	−	0.309949i
$694$	−0.400969	+	0.193096i	−0.400969	+	0.193096i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	0.326239	−	0.302705i	0.326239	−	0.302705i
$699$		0			0
$700$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i
$701$	1.03030	−	1.29196i	1.03030	−	1.29196i	0.0747301	−	0.997204i	$-0.476190\pi$
$701$	1.03030	−	1.29196i	1.03030	−	1.29196i	0.955573	−	0.294755i	$-0.0952381\pi$
$702$	0.0161399	+	0.215372i	0.0161399	+	0.215372i
$703$		0			0
$704$	0.365341	−	0.632789i	0.365341	−	0.632789i
$705$		0			0
$706$	0.222521	+	0.974928i	0.222521	+	0.974928i
$707$	−0.455573	−	1.16078i	−0.455573	−	1.16078i
$708$		0			0
$709$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$709$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$710$		0			0
$711$	−0.706381	−	1.79983i	−0.706381	−	1.79983i
$712$	0.142820	−	0.0440542i	0.142820	−	0.0440542i
$713$	0.500000	−	2.19064i	0.500000	−	2.19064i
$714$	0.142820	+	0.0440542i	0.142820	+	0.0440542i
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−0.0546039	−	0.728639i	−0.0546039	−	0.728639i	−0.955573	−	0.294755i	$-0.904762\pi$
$719$	−0.0546039	−	0.728639i	−0.0546039	−	0.728639i	0.900969	−	0.433884i	$-0.142857\pi$
$720$		0			0
$721$		0			0
$722$	0.623490	+	0.781831i	0.623490	+	0.781831i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	−0.0688859	−	0.0103829i	−0.0688859	−	0.0103829i
$727$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$727$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$728$	−0.730682			−0.730682
$729$	0.782450	+	0.376808i	0.782450	+	0.376808i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−0.365341	+	0.930874i	−0.365341	+	0.930874i	0.623490	+	0.781831i	$0.285714\pi$
$733$	−0.365341	+	0.930874i	−0.365341	+	0.930874i	−0.988831	+	0.149042i	$0.952381\pi$
$734$	1.46610			1.46610
$735$		0			0
$736$	−1.24698			−1.24698
$737$		0			0
$738$		0			0
$739$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$739$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$740$		0			0
$741$		0			0
$742$	−1.03030	+	1.29196i	−1.03030	+	1.29196i
$743$	0.134659	−	0.0648483i	0.134659	−	0.0648483i	−0.365341	−	0.930874i	$-0.619048\pi$
$743$	0.134659	−	0.0648483i	0.134659	−	0.0648483i	0.500000	+	0.866025i	$0.333333\pi$
$744$	0.266310	+	0.0401398i	0.266310	+	0.0401398i
$745$		0			0
$746$	−0.722521	+	0.108903i	−0.722521	+	0.108903i
$747$		0			0
$748$	−0.455573	−	0.571270i	−0.455573	−	0.571270i
$749$	−1.40097	+	0.432142i	−1.40097	+	0.432142i
$750$		0			0
$751$	0.147791	+	1.97213i	0.147791	+	1.97213i	0.222521	+	0.974928i	$0.428571\pi$
$751$	0.147791	+	1.97213i	0.147791	+	1.97213i	−0.0747301	+	0.997204i	$0.523810\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$	0.147791	−	0.255981i	0.147791	−	0.255981i
$757$	0.222521	−	0.974928i	0.222521	−	0.974928i	−0.733052	−	0.680173i	$-0.761905\pi$
$757$	0.222521	−	0.974928i	0.222521	−	0.974928i	0.955573	−	0.294755i	$-0.0952381\pi$
$758$	0.955573	−	0.294755i	0.955573	−	0.294755i
$759$	−0.0497521	−	0.126766i	−0.0497521	−	0.126766i
$760$		0			0
$761$	1.82624	−	0.563320i	1.82624	−	0.563320i	0.826239	−	0.563320i	$-0.190476\pi$
$761$	1.82624	−	0.563320i	1.82624	−	0.563320i	1.00000			$0$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.0111692	−	0.149042i	−0.0111692	−	0.149042i
$769$	−0.623490	+	0.781831i	−0.623490	+	0.781831i	−0.988831	−	0.149042i	$-0.952381\pi$
$769$	−0.623490	+	0.781831i	−0.623490	+	0.781831i	0.365341	+	0.930874i	$0.380952\pi$
$770$		0			0
$771$	0.0931869	+	0.116853i	0.0931869	+	0.116853i
$772$		0			0
$773$	−1.88980	+	0.284841i	−1.88980	+	0.284841i	−0.988831	−	0.149042i	$-0.952381\pi$
$773$	−1.88980	+	0.284841i	−1.88980	+	0.284841i	−0.900969	+	0.433884i	$0.857143\pi$
$774$		0			0
$775$	−1.78181	−	0.268565i	−1.78181	−	0.268565i
$776$		0			0
$777$		0			0
$778$	−1.72188	−	0.829215i	−1.72188	−	0.829215i
$779$		0			0
$780$		0			0
$781$	0.0902318	−	1.20406i	0.0902318	−	1.20406i
$782$	−0.455573	+	1.16078i	−0.455573	+	1.16078i
$783$		0			0
$784$	0.826239	+	0.563320i	0.826239	+	0.563320i
$785$		0			0
$786$	0.0680900	−	0.173490i	0.0680900	−	0.173490i
$787$	0.0332580	−	0.443797i	0.0332580	−	0.443797i	−0.955573	−	0.294755i	$-0.904762\pi$
$787$	0.0332580	−	0.443797i	0.0332580	−	0.443797i	0.988831	−	0.149042i	$-0.0476190\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.643616	+	0.309949i	−0.643616	+	0.309949i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	1.21135	−	1.12397i	1.21135	−	1.12397i
$797$	1.03030	+	1.29196i	1.03030	+	1.29196i	0.955573	+	0.294755i	$0.0952381\pi$
$797$	1.03030	+	1.29196i	1.03030	+	1.29196i	0.0747301	+	0.997204i	$0.476190\pi$
$798$		0			0
$799$		0			0
$800$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$801$	−0.139630	−	0.0430701i	−0.139630	−	0.0430701i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−0.292981	+	1.28363i	−0.292981	+	1.28363i
$807$		0			0
$808$	0.455573	+	1.16078i	0.455573	+	1.16078i
$809$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$809$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$810$		0			0
$811$	0.367711	−	1.61105i	0.367711	−	1.61105i	−0.365341	−	0.930874i	$-0.619048\pi$
$811$	0.367711	−	1.61105i	0.367711	−	1.61105i	0.733052	−	0.680173i	$-0.238095\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.142820	−	0.0440542i	−0.142820	−	0.0440542i
$817$		0			0
$818$	1.03030	−	1.29196i	1.03030	−	1.29196i
$819$	0.590232	+	0.402413i	0.590232	+	0.402413i
$820$		0			0
$821$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$821$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$822$	0.0220888	−	0.00332936i	0.0220888	−	0.00332936i
$823$	−0.123490	+	0.0841939i	−0.123490	+	0.0841939i	−0.623490	−	0.781831i	$-0.714286\pi$
$823$	−0.123490	+	0.0841939i	−0.123490	+	0.0841939i	0.500000	+	0.866025i	$0.333333\pi$
$824$		0			0
$825$	−0.0983929	+	0.0473835i	−0.0983929	+	0.0473835i
$826$		0			0
$827$	−1.32091	−	0.636119i	−1.32091	−	0.636119i	−0.365341	−	0.930874i	$-0.619048\pi$
$827$	−1.32091	−	0.636119i	−1.32091	−	0.636119i	−0.955573	+	0.294755i	$0.904762\pi$
$828$	1.00729	+	0.686757i	1.00729	+	0.686757i
$829$	1.07473	+	0.997204i	1.07473	+	0.997204i	1.00000			$0$
$829$	1.07473	+	0.997204i	1.07473	+	0.997204i	0.0747301	+	0.997204i	$0.476190\pi$
$830$		0			0
$831$		0			0
$832$	0.730682			0.730682
$833$	0.826239	−	0.563320i	0.826239	−	0.563320i
$834$	−0.295582			−0.295582
$835$		0			0
$836$		0			0
$837$	−0.390438	−	0.362273i	−0.390438	−	0.362273i
$838$	1.63402	+	1.11406i	1.63402	+	1.11406i
$839$	−0.400969	−	0.193096i	−0.400969	−	0.193096i	0.222521	−	0.974928i	$-0.428571\pi$
$839$	−0.400969	−	0.193096i	−0.400969	−	0.193096i	−0.623490	+	0.781831i	$0.714286\pi$
$840$		0			0
$841$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$842$	1.78181	+	0.268565i	1.78181	+	0.268565i
$843$	0.123490	−	0.0841939i	0.123490	−	0.0841939i
$844$	−0.440071	+	0.0663300i	−0.440071	+	0.0663300i
$845$		0			0
$846$		0			0
$847$	−0.341678	+	0.317031i	−0.341678	+	0.317031i
$848$	1.03030	−	1.29196i	1.03030	−	1.29196i
$849$	0.00816111	+	0.108903i	0.00816111	+	0.108903i
$850$	0.955573	+	0.294755i	0.955573	+	0.294755i
$851$		0			0
$852$	−0.123490	−	0.213891i	−0.123490	−	0.213891i
$853$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$853$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$854$		0			0
$855$		0			0
$856$	1.40097	−	0.432142i	1.40097	−	0.432142i
$857$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$857$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$858$	0.0291528	+	0.0742802i	0.0291528	+	0.0742802i
$859$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$859$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$860$		0			0
$861$		0			0
$862$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$863$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$863$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$864$	−0.147791	+	0.255981i	−0.147791	+	0.255981i
$865$		0			0
$866$	0.0931869	+	1.24349i	0.0931869	+	1.24349i
$867$	−0.0931869	+	0.116853i	−0.0931869	+	0.116853i
$868$	1.32091	−	1.22563i	1.32091	−	1.22563i
$869$	−0.900969	−	1.12978i	−0.900969	−	1.12978i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$877$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$878$	−1.44973	−	1.34515i	−1.44973	−	1.34515i
$879$	0.0220888	−	0.294755i	0.0220888	−	0.294755i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−0.357180	−	0.910080i	−0.357180	−	0.910080i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$	0.266948	−	0.680173i	0.266948	−	0.680173i
$885$		0			0
$886$		0			0
$887$	−0.603718	−	0.411608i	−0.603718	−	0.411608i	0.222521	−	0.974928i	$-0.428571\pi$
$887$	−0.603718	−	0.411608i	−0.603718	−	0.411608i	−0.826239	+	0.563320i	$0.809524\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.674462	+	0.101659i	0.674462	+	0.101659i
$892$		0			0
$893$		0			0
$894$	0.0163752	−	0.0151939i	0.0163752	−	0.0151939i
$895$		0			0
$896$	−0.826239	−	0.563320i	−0.826239	−	0.563320i
$897$	0.0849068	−	0.106470i	0.0849068	−	0.106470i
$898$		0			0
$899$		0			0
$900$	0.488831	−	0.846680i	0.488831	−	0.846680i
$901$	−0.826239	−	1.43109i	−0.826239	−	1.43109i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	0.658322	+	1.67738i	0.658322	+	1.67738i	0.733052	+	0.680173i	$0.238095\pi$
$907$	0.658322	+	1.67738i	0.658322	+	1.67738i	−0.0747301	+	0.997204i	$0.523810\pi$
$908$	−1.57906	+	0.487076i	−1.57906	+	0.487076i
$909$	0.271281	−	1.18856i	0.271281	−	1.18856i
$910$		0			0
$911$	0.277479	+	1.21572i	0.277479	+	1.21572i	0.900969	+	0.433884i	$0.142857\pi$
$911$	0.277479	+	1.21572i	0.277479	+	1.21572i	−0.623490	+	0.781831i	$0.714286\pi$
$912$		0			0
$913$		0			0
$914$	1.19158	+	0.367554i	1.19158	+	0.367554i
$915$		0			0
$916$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$917$	−0.623490	−	1.07992i	−0.623490	−	1.07992i
$918$	0.184292	+	0.231095i	0.184292	+	0.231095i
$919$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$919$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$920$		0			0
$921$		0			0
$922$	−1.63402	−	0.246289i	−1.63402	−	0.246289i
$923$	1.08786	−	0.523887i	1.08786	−	0.523887i
$924$	0.0243010	−	0.106470i	0.0243010	−	0.106470i
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$929$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−0.0546039	+	0.139129i	−0.0546039	+	0.139129i
$934$		0			0
$935$		0			0
$936$	−0.590232	−	0.402413i	−0.590232	−	0.402413i
$937$	1.62349	+	0.781831i	1.62349	+	0.781831i	1.00000			$0$
$937$	1.62349	+	0.781831i	1.62349	+	0.781831i	0.623490	+	0.781831i	$0.285714\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$941$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$942$	−0.292280	+	0.0440542i	−0.292280	+	0.0440542i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.0747301	+	0.997204i	0.0747301	+	0.997204i	0.900969	+	0.433884i	$0.142857\pi$
$947$	0.0747301	+	0.997204i	0.0747301	+	0.997204i	−0.826239	+	0.563320i	$0.809524\pi$
$948$	−0.282450	−	0.0871242i	−0.282450	−	0.0871242i
$949$		0			0
$950$		0			0
$951$		0			0
$952$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$953$	−0.425270	+	1.86323i	−0.425270	+	1.86323i	0.0747301	+	0.997204i	$0.476190\pi$
$953$	−0.425270	+	1.86323i	−0.425270	+	1.86323i	−0.500000	+	0.866025i	$0.666667\pi$
$954$	−1.54379	+	0.476196i	−1.54379	+	0.476196i
$955$		0			0
$956$		0			0
$957$		0			0
$958$	0.277479	−	1.21572i	0.277479	−	1.21572i
$959$	0.0747301	−	0.129436i	0.0747301	−	0.129436i
$960$		0			0
$961$	−1.12349	−	1.94594i	−1.12349	−	1.94594i
$962$		0			0
$963$	−1.36967	−	0.422488i	−1.36967	−	0.422488i
$964$		0			0
$965$		0			0
$966$	−0.178094	+	0.0549346i	−0.178094	+	0.0549346i
$967$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$967$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$968$	0.341678	−	0.317031i	0.341678	−	0.317031i
$969$		0			0
$970$		0			0
$971$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$971$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$972$	0.392012	−	0.188783i	0.392012	−	0.188783i
$973$	−1.23305	+	1.54620i	−1.23305	+	1.54620i
$974$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$975$	−0.0902318	−	0.0615190i	−0.0902318	−	0.0615190i
$976$		0			0
$977$	0.0931869	−	1.24349i	0.0931869	−	1.24349i	−0.733052	−	0.680173i	$-0.761905\pi$
$977$	0.0931869	−	1.24349i	0.0931869	−	1.24349i	0.826239	−	0.563320i	$-0.190476\pi$
$978$	0.109208	−	0.278257i	0.109208	−	0.278257i
$979$	−0.109208			−0.109208
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−0.0546039	+	0.728639i	−0.0546039	+	0.728639i	0.900969	+	0.433884i	$0.142857\pi$
$983$	−0.0546039	+	0.728639i	−0.0546039	+	0.728639i	−0.955573	+	0.294755i	$0.904762\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	1.88980	−	0.284841i	1.88980	−	0.284841i	0.900969	−	0.433884i	$-0.142857\pi$
$991$	1.88980	−	0.284841i	1.88980	−	0.284841i	0.988831	+	0.149042i	$0.0476190\pi$
$992$	−1.32091	+	1.22563i	−1.32091	+	1.22563i
$993$		0			0
$994$	−1.63402	−	0.246289i	−1.63402	−	0.246289i
$995$		0			0
$996$		0			0
$997$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$997$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$998$	−0.988831	+	1.71271i	−0.988831	+	1.71271i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3332.1.cc.a.2447.1	✓	12
4.3	odd	2		3332.1.cc.b.2447.1	yes	12
17.16	even	2		3332.1.cc.b.2447.1	yes	12
49.16	even	21	inner	3332.1.cc.a.2515.1	yes	12
68.67	odd	2	CM	3332.1.cc.a.2447.1	✓	12
196.163	odd	42		3332.1.cc.b.2515.1	yes	12
833.16	even	42		3332.1.cc.b.2515.1	yes	12
3332.2515	odd	42	inner	3332.1.cc.a.2515.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3332.1.cc.a.2447.1	✓	12	1.1	even	1	trivial
3332.1.cc.a.2447.1	✓	12	68.67	odd	2	CM
3332.1.cc.a.2515.1	yes	12	49.16	even	21	inner
3332.1.cc.a.2515.1	yes	12	3332.2515	odd	42	inner
3332.1.cc.b.2447.1	yes	12	4.3	odd	2
3332.1.cc.b.2447.1	yes	12	17.16	even	2
3332.1.cc.b.2515.1	yes	12	196.163	odd	42
3332.1.cc.b.2515.1	yes	12	833.16	even	42

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)

\(f(q)\)	\(=\)	\(q+(0.365341 - 0.930874i) q^{2} +(-0.0111692 + 0.149042i) q^{3} +(-0.733052 - 0.680173i) q^{4} +(0.134659 + 0.0648483i) q^{6} +(0.900969 - 0.433884i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(0.966742 + 0.145713i) q^{9} +O(q^{10})\)	\(q+(0.365341 - 0.930874i) q^{2} +(-0.0111692 + 0.149042i) q^{3} +(-0.733052 - 0.680173i) q^{4} +(0.134659 + 0.0648483i) q^{6} +(0.900969 - 0.433884i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(0.966742 + 0.145713i) q^{9} +(0.722521 - 0.108903i) q^{11} +(0.109562 - 0.101659i) q^{12} +(0.455573 + 0.571270i) q^{13} +(-0.0747301 - 0.997204i) q^{14} +(0.0747301 + 0.997204i) q^{16} +(0.955573 + 0.294755i) q^{17} +(0.488831 - 0.846680i) q^{18} +(0.0546039 + 0.139129i) q^{21} +(0.162592 - 0.712362i) q^{22} +(-1.19158 + 0.367554i) q^{23} +(-0.0546039 - 0.139129i) q^{24} +(0.365341 + 0.930874i) q^{25} +(0.698220 - 0.215372i) q^{26} +(-0.0657731 + 0.288171i) q^{27} +(-0.955573 - 0.294755i) q^{28} +(-0.900969 + 1.56052i) q^{31} +(0.955573 + 0.294755i) q^{32} +(0.00816111 + 0.108903i) q^{33} +(0.623490 - 0.781831i) q^{34} +(-0.609562 - 0.764367i) q^{36} +(-0.0902318 + 0.0615190i) q^{39} +0.149460 q^{42} +(-0.603718 - 0.411608i) q^{44} +(-0.0931869 + 1.24349i) q^{46} -0.149460 q^{48} +(0.623490 - 0.781831i) q^{49} +1.00000 q^{50} +(-0.0546039 + 0.139129i) q^{51} +(0.0546039 - 0.728639i) q^{52} +(-1.21135 - 1.12397i) q^{53} +(0.244221 + 0.166507i) q^{54} +(-0.623490 + 0.781831i) q^{56} +(1.12349 + 1.40881i) q^{62} +(0.934227 - 0.288171i) q^{63} +(0.623490 - 0.781831i) q^{64} +(0.104356 + 0.0321896i) q^{66} +(-0.500000 - 0.866025i) q^{68} +(-0.0414721 - 0.181701i) q^{69} +(0.367711 - 1.61105i) q^{71} +(-0.934227 + 0.288171i) q^{72} +(-0.142820 + 0.0440542i) q^{75} +(0.603718 - 0.411608i) q^{77} +(0.0243010 + 0.106470i) q^{78} +(-0.988831 - 1.71271i) q^{79} +(0.892012 + 0.275149i) q^{81} +(0.0546039 - 0.139129i) q^{84} +(-0.603718 + 0.411608i) q^{88} +(-0.147791 - 0.0222759i) q^{89} +(0.658322 + 0.317031i) q^{91} +(1.12349 + 0.541044i) q^{92} +(-0.222521 - 0.151712i) q^{93} +(-0.0546039 + 0.139129i) q^{96} +(-0.500000 - 0.866025i) q^{98} +0.714360 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} - 13 q^{3} + q^{4} + 5 q^{6} + 2 q^{7} - 2 q^{8} + 14 q^{9}+O(q^{10}) \) 12 * q + q^2 - 13 * q^3 + q^4 + 5 * q^6 + 2 * q^7 - 2 * q^8 + 14 * q^9	\( 12 q + q^{2} - 13 q^{3} + q^{4} + 5 q^{6} + 2 q^{7} - 2 q^{8} + 14 q^{9} + 8 q^{11} + q^{12} - 5 q^{13} - q^{14} + q^{16} + q^{17} - 7 q^{18} - q^{21} - 2 q^{22} - 2 q^{23} + q^{24} + q^{25} - q^{26} - 12 q^{27} - q^{28} - 2 q^{31} + q^{32} - 6 q^{33} - 2 q^{34} - 7 q^{36} + 6 q^{39} + 2 q^{42} + q^{44} - 2 q^{46} - 2 q^{48} - 2 q^{49} + 12 q^{50} + q^{51} - q^{52} - q^{53} + 6 q^{54} + 2 q^{56} + 4 q^{62} - 2 q^{64} + 15 q^{66} - 6 q^{68} - 3 q^{69} - 2 q^{71} + q^{75} - q^{77} + 9 q^{78} + q^{79} + 13 q^{81} - q^{84} + q^{88} - q^{89} - 2 q^{91} + 4 q^{92} - 2 q^{93} + q^{96} - 6 q^{98} + 14 q^{99}+O(q^{100}) \) 12 * q + q^2 - 13 * q^3 + q^4 + 5 * q^6 + 2 * q^7 - 2 * q^8 + 14 * q^9 + 8 * q^11 + q^12 - 5 * q^13 - q^14 + q^16 + q^17 - 7 * q^18 - q^21 - 2 * q^22 - 2 * q^23 + q^24 + q^25 - q^26 - 12 * q^27 - q^28 - 2 * q^31 + q^32 - 6 * q^33 - 2 * q^34 - 7 * q^36 + 6 * q^39 + 2 * q^42 + q^44 - 2 * q^46 - 2 * q^48 - 2 * q^49 + 12 * q^50 + q^51 - q^52 - q^53 + 6 * q^54 + 2 * q^56 + 4 * q^62 - 2 * q^64 + 15 * q^66 - 6 * q^68 - 3 * q^69 - 2 * q^71 + q^75 - q^77 + 9 * q^78 + q^79 + 13 * q^81 - q^84 + q^88 - q^89 - 2 * q^91 + 4 * q^92 - 2 * q^93 + q^96 - 6 * q^98 + 14 * q^99

Introduction

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