LMFDB - Embedded newform 3332.1.cc.c.1019.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("3332.135");

S:= CuspForms(chi, 1);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.66288462209$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{42})$
Coefficient field:	$\Q(\zeta_{84})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} + x^{22} - x^{18} - x^{16} + x^{12} - x^{8} - x^{6} + x^{2} + 1 $ x^24 + x^22 - x^18 - x^16 + x^12 - x^8 - x^6 + x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{42}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{42} - \cdots)$

Embedding invariants

Embedding label			1019.2
Root			$0.997204 - 0.0747301i$ of defining polynomial
Character	$\chi$	$=$	3332.1019
Dual form			3332.1.cc.c.1563.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.988831 + 0.149042i) q^{2} +(0.930874 - 0.634659i) q^{3} +(0.955573 + 0.294755i) q^{4} +(1.01507 - 0.488831i) q^{6} +(-0.433884 + 0.900969i) q^{7} +(0.900969 + 0.433884i) q^{8} +(0.0983929 - 0.250701i) q^{9} +O(q^{10})$	\(q+(0.988831 + 0.149042i) q^{2} +(0.930874 - 0.634659i) q^{3} +(0.955573 + 0.294755i) q^{4} +(1.01507 - 0.488831i) q^{6} +(-0.433884 + 0.900969i) q^{7} +(0.900969 + 0.433884i) q^{8} +(0.0983929 - 0.250701i) q^{9} +(0.108903 + 0.277479i) q^{11} +(1.07659 - 0.332083i) q^{12} +(1.23305 - 1.54620i) q^{13} +(-0.563320 + 0.826239i) q^{14} +(0.826239 + 0.563320i) q^{16} +(-0.733052 - 0.680173i) q^{17} +(0.134659 - 0.233236i) q^{18} +(0.167917 + 1.11406i) q^{21} +(0.0663300 + 0.290611i) q^{22} +(-1.14625 + 1.06356i) q^{23} +(1.11406 - 0.167917i) q^{24} +(-0.988831 + 0.149042i) q^{25} +(1.44973 - 1.34515i) q^{26} +(0.183183 + 0.802576i) q^{27} +(-0.680173 + 0.733052i) q^{28} +(0.433884 - 0.751509i) q^{31} +(0.733052 + 0.680173i) q^{32} +(0.277479 + 0.189182i) q^{33} +(-0.623490 - 0.781831i) q^{34} +(0.167917 - 0.210561i) q^{36} +(0.166507 - 2.22188i) q^{39} +1.12664i q^{42} +(0.0222759 + 0.297251i) q^{44} +(-1.29196 + 0.880843i) q^{46} +1.12664 q^{48} +(-0.623490 - 0.781831i) q^{49} -1.00000 q^{50} +(-1.11406 - 0.167917i) q^{51} +(1.63402 - 1.11406i) q^{52} +(0.142820 + 0.0440542i) q^{53} +(0.0615190 + 0.820914i) q^{54} +(-0.781831 + 0.623490i) q^{56} +(0.541044 - 0.678448i) q^{62} +(0.183183 + 0.197424i) q^{63} +(0.623490 + 0.781831i) q^{64} +(0.246184 + 0.228425i) q^{66} +(-0.500000 - 0.866025i) q^{68} +(-0.392012 + 1.71752i) q^{69} +(-0.443797 - 1.94440i) q^{71} +(0.197424 - 0.183183i) q^{72} +(-0.825886 + 0.766310i) q^{75} +(-0.297251 - 0.0222759i) q^{77} +(0.495802 - 2.17225i) q^{78} +(-0.930874 - 1.61232i) q^{79} +(0.877306 + 0.814021i) q^{81} +(-0.167917 + 1.11406i) q^{84} +(-0.0222759 + 0.297251i) q^{88} +(-0.603718 + 1.53825i) q^{89} +(0.858075 + 1.78181i) q^{91} +(-1.40881 + 0.678448i) q^{92} +(-0.0730607 - 0.974928i) q^{93} +(1.11406 + 0.167917i) q^{96} +(-0.500000 - 0.866025i) q^{98} +0.0802795 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} + 2 q^{4} + 4 q^{8} - 24 q^{9}+O(q^{10}) $ 24 * q - 2 * q^2 + 2 * q^4 + 4 * q^8 - 24 * q^9	$ 24 q - 2 q^{2} + 2 q^{4} + 4 q^{8} - 24 q^{9} + 10 q^{13} + 2 q^{16} + 2 q^{17} + 10 q^{18} + 6 q^{21} + 2 q^{25} - 2 q^{26} - 2 q^{32} + 8 q^{33} + 4 q^{34} + 6 q^{36} + 4 q^{49} - 24 q^{50} + 2 q^{52} - 2 q^{53} - 4 q^{64} - 22 q^{66} - 12 q^{68} - 14 q^{69} - 4 q^{72} - 6 q^{77} + 30 q^{81} - 6 q^{84} + 2 q^{89} - 12 q^{98}+O(q^{100}) $ 24 * q - 2 * q^2 + 2 * q^4 + 4 * q^8 - 24 * q^9 + 10 * q^13 + 2 * q^16 + 2 * q^17 + 10 * q^18 + 6 * q^21 + 2 * q^25 - 2 * q^26 - 2 * q^32 + 8 * q^33 + 4 * q^34 + 6 * q^36 + 4 * q^49 - 24 * q^50 + 2 * q^52 - 2 * q^53 - 4 * q^64 - 22 * q^66 - 12 * q^68 - 14 * q^69 - 4 * q^72 - 6 * q^77 + 30 * q^81 - 6 * q^84 + 2 * q^89 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$885$	$1667$
$\chi(n)$	$-1$	$e\left(\frac{17}{21}\right)$	$-1$

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 $

$2$	0.988831	+	0.149042i	0.988831	+	0.149042i
$2$	0.988831	+	0.149042i	0.988831	+	0.149042i
$3$	0.930874	−	0.634659i	0.930874	−	0.634659i		−	1.00000i	$-0.5\pi$
$3$	0.930874	−	0.634659i	0.930874	−	0.634659i	0.930874	+	0.365341i	$0.119048\pi$
$4$	0.955573	+	0.294755i	0.955573	+	0.294755i
$5$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$5$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$6$	1.01507	−	0.488831i	1.01507	−	0.488831i
$7$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$7$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$8$	0.900969	+	0.433884i	0.900969	+	0.433884i
$9$	0.0983929	−	0.250701i	0.0983929	−	0.250701i
$10$		0			0
$11$	0.108903	+	0.277479i	0.108903	+	0.277479i	0.974928	−	0.222521i	$-0.0714286\pi$
$11$	0.108903	+	0.277479i	0.108903	+	0.277479i	−0.866025	+	0.500000i	$0.833333\pi$
$12$	1.07659	−	0.332083i	1.07659	−	0.332083i
$13$	1.23305	−	1.54620i	1.23305	−	1.54620i	0.500000	−	0.866025i	$-0.333333\pi$
$13$	1.23305	−	1.54620i	1.23305	−	1.54620i	0.733052	−	0.680173i	$-0.238095\pi$
$14$	−0.563320	+	0.826239i	−0.563320	+	0.826239i
$15$		0			0
$16$	0.826239	+	0.563320i	0.826239	+	0.563320i
$17$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$17$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$18$	0.134659	−	0.233236i	0.134659	−	0.233236i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$		0			0
$21$	0.167917	+	1.11406i	0.167917	+	1.11406i
$22$	0.0663300	+	0.290611i	0.0663300	+	0.290611i
$23$	−1.14625	+	1.06356i	−1.14625	+	1.06356i	−0.149042	+	0.988831i	$0.547619\pi$
$23$	−1.14625	+	1.06356i	−1.14625	+	1.06356i	−0.997204	+	0.0747301i	$0.976190\pi$
$24$	1.11406	−	0.167917i	1.11406	−	0.167917i
$25$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$26$	1.44973	−	1.34515i	1.44973	−	1.34515i
$27$	0.183183	+	0.802576i	0.183183	+	0.802576i
$28$	−0.680173	+	0.733052i	−0.680173	+	0.733052i
$29$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$29$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$30$		0			0
$31$	0.433884	−	0.751509i	0.433884	−	0.751509i	−0.563320	−	0.826239i	$-0.690476\pi$
$31$	0.433884	−	0.751509i	0.433884	−	0.751509i	0.997204	+	0.0747301i	$0.0238095\pi$
$32$	0.733052	+	0.680173i	0.733052	+	0.680173i
$33$	0.277479	+	0.189182i	0.277479	+	0.189182i
$34$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$35$		0			0
$36$	0.167917	−	0.210561i	0.167917	−	0.210561i
$37$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$37$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$38$		0			0
$39$	0.166507	−	2.22188i	0.166507	−	2.22188i
$40$		0			0
$41$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$41$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$42$			1.12664i			1.12664i
$43$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$43$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$44$	0.0222759	+	0.297251i	0.0222759	+	0.297251i
$45$		0			0
$46$	−1.29196	+	0.880843i	−1.29196	+	0.880843i
$47$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$47$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$48$	1.12664			1.12664
$49$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$50$	−1.00000			−1.00000
$51$	−1.11406	−	0.167917i	−1.11406	−	0.167917i
$52$	1.63402	−	1.11406i	1.63402	−	1.11406i
$53$	0.142820	+	0.0440542i	0.142820	+	0.0440542i	0.365341	−	0.930874i	$-0.380952\pi$
$53$	0.142820	+	0.0440542i	0.142820	+	0.0440542i	−0.222521	+	0.974928i	$0.571429\pi$
$54$	0.0615190	+	0.820914i	0.0615190	+	0.820914i
$55$		0			0
$56$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$57$		0			0
$58$		0			0
$59$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$59$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$60$		0			0
$61$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$61$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$62$	0.541044	−	0.678448i	0.541044	−	0.678448i
$63$	0.183183	+	0.197424i	0.183183	+	0.197424i
$64$	0.623490	+	0.781831i	0.623490	+	0.781831i
$65$		0			0
$66$	0.246184	+	0.228425i	0.246184	+	0.228425i
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$69$	−0.392012	+	1.71752i	−0.392012	+	1.71752i
$70$		0			0
$71$	−0.443797	−	1.94440i	−0.443797	−	1.94440i	−0.294755	−	0.955573i	$-0.595238\pi$
$71$	−0.443797	−	1.94440i	−0.443797	−	1.94440i	−0.149042	−	0.988831i	$-0.547619\pi$
$72$	0.197424	−	0.183183i	0.197424	−	0.183183i
$73$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$73$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$74$		0			0
$75$	−0.825886	+	0.766310i	−0.825886	+	0.766310i
$76$		0			0
$77$	−0.297251	−	0.0222759i	−0.297251	−	0.0222759i
$78$	0.495802	−	2.17225i	0.495802	−	2.17225i
$79$	−0.930874	−	1.61232i	−0.930874	−	1.61232i	−0.781831	−	0.623490i	$-0.785714\pi$
$79$	−0.930874	−	1.61232i	−0.930874	−	1.61232i	−0.149042	−	0.988831i	$-0.547619\pi$
$80$		0			0
$81$	0.877306	+	0.814021i	0.877306	+	0.814021i
$82$		0			0
$83$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$83$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$84$	−0.167917	+	1.11406i	−0.167917	+	1.11406i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−0.0222759	+	0.297251i	−0.0222759	+	0.297251i
$89$	−0.603718	+	1.53825i	−0.603718	+	1.53825i	0.222521	+	0.974928i	$0.428571\pi$
$89$	−0.603718	+	1.53825i	−0.603718	+	1.53825i	−0.826239	+	0.563320i	$0.809524\pi$
$90$		0			0
$91$	0.858075	+	1.78181i	0.858075	+	1.78181i
$92$	−1.40881	+	0.678448i	−1.40881	+	0.678448i
$93$	−0.0730607	−	0.974928i	−0.0730607	−	0.974928i
$94$		0			0
$95$		0			0
$96$	1.11406	+	0.167917i	1.11406	+	0.167917i
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$99$	0.0802795			0.0802795
$100$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$101$	−1.03030	+	0.702449i	−1.03030	+	0.702449i	−0.955573	−	0.294755i	$-0.904762\pi$
$101$	−1.03030	+	0.702449i	−1.03030	+	0.702449i	−0.0747301	+	0.997204i	$0.523810\pi$
$102$	−1.07659	−	0.332083i	−1.07659	−	0.332083i
$103$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$103$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$104$	1.78181	−	0.858075i	1.78181	−	0.858075i
$105$		0			0
$106$	0.134659	+	0.0648483i	0.134659	+	0.0648483i
$107$	−0.215372	+	0.548760i	−0.215372	+	0.548760i	−0.997204	−	0.0747301i	$-0.976190\pi$
$107$	−0.215372	+	0.548760i	−0.215372	+	0.548760i	0.781831	+	0.623490i	$0.214286\pi$
$108$	−0.0615190	+	0.820914i	−0.0615190	+	0.820914i
$109$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$109$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$110$		0			0
$111$		0			0
$112$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$113$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$113$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.266310	−	0.461262i	−0.266310	−	0.461262i
$118$		0			0
$119$	0.930874	−	0.365341i	0.930874	−	0.365341i
$120$		0			0
$121$	0.667917	−	0.619736i	0.667917	−	0.619736i
$122$		0			0
$123$		0			0
$124$	0.636119	−	0.590232i	0.636119	−	0.590232i
$125$		0			0
$126$	0.151712	+	0.222521i	0.151712	+	0.222521i
$127$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$127$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$128$	0.500000	+	0.866025i	0.500000	+	0.866025i
$129$		0			0
$130$		0			0
$131$	1.29196	+	0.880843i	1.29196	+	0.880843i	0.997204	−	0.0747301i	$-0.0238095\pi$
$131$	1.29196	+	0.880843i	1.29196	+	0.880843i	0.294755	+	0.955573i	$0.404762\pi$
$132$	0.209389	+	0.262566i	0.209389	+	0.262566i
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$137$	−0.123490	+	1.64786i	−0.123490	+	1.64786i	0.500000	+	0.866025i	$0.333333\pi$
$137$	−0.123490	+	1.64786i	−0.123490	+	1.64786i	−0.623490	+	0.781831i	$0.714286\pi$
$138$	−0.643616	+	1.63991i	−0.643616	+	1.63991i
$139$	−1.67738	−	0.807782i	−1.67738	−	0.807782i	−0.997204	−	0.0747301i	$-0.976190\pi$
$139$	−1.67738	−	0.807782i	−1.67738	−	0.807782i	−0.680173	−	0.733052i	$-0.738095\pi$
$140$		0			0
$141$		0			0
$142$	−0.149042	−	1.98883i	−0.149042	−	1.98883i
$143$	0.563320	+	0.173761i	0.563320	+	0.173761i
$144$	0.222521	−	0.151712i	0.222521	−	0.151712i
$145$		0			0
$146$		0			0
$147$	−1.07659	−	0.332083i	−1.07659	−	0.332083i
$148$		0			0
$149$	−1.63402	−	0.246289i	−1.63402	−	0.246289i	−0.733052	−	0.680173i	$-0.761905\pi$
$149$	−1.63402	−	0.246289i	−1.63402	−	0.246289i	−0.900969	+	0.433884i	$0.857143\pi$
$150$	−0.930874	+	0.634659i	−0.930874	+	0.634659i
$151$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$151$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$152$		0			0
$153$	−0.242647	+	0.116853i	−0.242647	+	0.116853i
$154$	−0.290611	−	0.0663300i	−0.290611	−	0.0663300i
$155$		0			0
$156$	0.814021	−	2.07409i	0.814021	−	2.07409i
$157$	0.0546039	−	0.728639i	0.0546039	−	0.728639i	−0.900969	−	0.433884i	$-0.857143\pi$
$157$	0.0546039	−	0.728639i	0.0546039	−	0.728639i	0.955573	−	0.294755i	$-0.0952381\pi$
$158$	−0.680173	−	1.73305i	−0.680173	−	1.73305i
$159$	0.160907	−	0.0496332i	0.160907	−	0.0496332i
$160$		0			0
$161$	−0.460898	−	1.49419i	−0.460898	−	1.49419i
$162$	0.746184	+	0.935685i	0.746184	+	0.935685i
$163$		0			0		0.563320	−	0.826239i	$-0.309524\pi$
$163$		0			0		−0.563320	+	0.826239i	$0.690476\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.302705	−	1.32624i	0.302705	−	1.32624i	−0.563320	−	0.826239i	$-0.690476\pi$
$167$	0.302705	−	1.32624i	0.302705	−	1.32624i	0.866025	−	0.500000i	$-0.166667\pi$
$168$	−0.332083	+	1.07659i	−0.332083	+	1.07659i
$169$	−0.647791	−	2.83816i	−0.647791	−	2.83816i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$173$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$174$		0			0
$175$	0.294755	−	0.955573i	0.294755	−	0.955573i
$176$	−0.0663300	+	0.290611i	−0.0663300	+	0.290611i
$177$		0			0
$178$	−0.826239	+	1.43109i	−0.826239	+	1.43109i
$179$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$179$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$180$		0			0
$181$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$181$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$182$	0.582926	+	1.88980i	0.582926	+	1.88980i
$183$		0			0
$184$	−1.49419	+	0.460898i	−1.49419	+	0.460898i
$185$		0			0
$186$	0.0730607	−	0.974928i	0.0730607	−	0.974928i
$187$	0.108903	−	0.277479i	0.108903	−	0.277479i
$188$		0			0
$189$	−0.802576	−	0.183183i	−0.802576	−	0.183183i
$190$		0			0
$191$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$191$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$192$	1.07659	+	0.332083i	1.07659	+	0.332083i
$193$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$193$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$194$		0			0
$195$		0			0
$196$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	0.0793829	+	0.0119650i	0.0793829	+	0.0119650i
$199$	−1.64786	+	1.12349i	−1.64786	+	1.12349i	−0.781831	+	0.623490i	$0.785714\pi$
$199$	−1.64786	+	1.12349i	−1.64786	+	1.12349i	−0.866025	+	0.500000i	$0.833333\pi$
$200$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$201$		0			0
$202$	−1.12349	+	0.541044i	−1.12349	+	0.541044i
$203$		0			0
$204$	−1.01507	−	0.488831i	−1.01507	−	0.488831i
$205$		0			0
$206$		0			0
$207$	0.153853	+	0.392012i	0.153853	+	0.392012i
$208$	1.88980	−	0.582926i	1.88980	−	0.582926i
$209$		0			0
$210$		0			0
$211$	1.21572	+	1.52446i	1.21572	+	1.52446i	0.781831	+	0.623490i	$0.214286\pi$
$211$	1.21572	+	1.52446i	1.21572	+	1.52446i	0.433884	+	0.900969i	$0.357143\pi$
$212$	0.123490	+	0.0841939i	0.123490	+	0.0841939i
$213$	−1.64715	−	1.52833i	−1.64715	−	1.52833i
$214$	−0.294755	+	0.510531i	−0.294755	+	0.510531i
$215$		0			0
$216$	−0.183183	+	0.802576i	−0.183183	+	0.802576i
$217$	0.488831	+	0.716983i	0.488831	+	0.716983i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.95557	+	0.294755i	−1.95557	+	0.294755i
$222$		0			0
$223$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$223$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$224$	−0.930874	+	0.365341i	−0.930874	+	0.365341i
$225$	−0.0599289	+	0.262566i	−0.0599289	+	0.262566i
$226$		0			0
$227$	0.997204	−	1.72721i	0.997204	−	1.72721i	0.433884	−	0.900969i	$-0.357143\pi$
$227$	0.997204	−	1.72721i	0.997204	−	1.72721i	0.563320	−	0.826239i	$-0.309524\pi$
$228$		0			0
$229$	0.367711	+	0.250701i	0.367711	+	0.250701i	0.733052	−	0.680173i	$-0.238095\pi$
$229$	0.367711	+	0.250701i	0.367711	+	0.250701i	−0.365341	+	0.930874i	$0.619048\pi$
$230$		0			0
$231$	−0.290841	+	0.167917i	−0.290841	+	0.167917i
$232$		0			0
$233$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$233$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$234$	−0.194588	−	0.495802i	−0.194588	−	0.495802i
$235$		0			0
$236$		0			0
$237$	−1.88980	−	0.910080i	−1.88980	−	0.910080i
$238$	0.974928	−	0.222521i	0.974928	−	0.222521i
$239$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$239$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$240$		0			0
$241$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$241$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$242$	0.752824	−	0.513267i	0.752824	−	0.513267i
$243$	0.519266	+	0.0782667i	0.519266	+	0.0782667i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$	0.716983	−	0.488831i	0.716983	−	0.488831i
$249$		0			0
$250$		0			0
$251$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$251$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$252$	0.116853	+	0.242647i	0.116853	+	0.242647i
$253$	−0.419945	−	0.202235i	−0.419945	−	0.202235i
$254$		0			0
$255$		0			0
$256$	0.365341	+	0.930874i	0.365341	+	0.930874i
$257$	0.955573	−	0.294755i	0.955573	−	0.294755i	0.222521	−	0.974928i	$-0.428571\pi$
$257$	0.955573	−	0.294755i	0.955573	−	0.294755i	0.733052	+	0.680173i	$0.238095\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	1.14625	+	1.06356i	1.14625	+	1.06356i
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$	0.167917	+	0.290841i	0.167917	+	0.290841i
$265$		0			0
$266$		0			0
$267$	0.414278	+	1.81507i	0.414278	+	1.81507i
$268$		0			0
$269$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$269$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$270$		0			0
$271$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$271$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$272$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$273$	1.92960	+	1.11406i	1.92960	+	1.11406i
$274$	−0.367711	+	1.61105i	−0.367711	+	1.61105i
$275$	−0.149042	−	0.258149i	−0.149042	−	0.258149i
$276$	−0.880843	+	1.52566i	−0.880843	+	1.52566i
$277$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$277$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$278$	−1.53825	−	1.04876i	−1.53825	−	1.04876i
$279$	−0.145713	−	0.182718i	−0.145713	−	0.182718i
$280$		0			0
$281$	−0.623490	+	0.781831i	−0.623490	+	0.781831i	−0.988831	−	0.149042i	$-0.952381\pi$
$281$	−0.623490	+	0.781831i	−0.623490	+	0.781831i	0.365341	+	0.930874i	$0.380952\pi$
$282$		0			0
$283$	−0.108903	−	0.277479i	−0.108903	−	0.277479i	0.866025	−	0.500000i	$-0.166667\pi$
$283$	−0.108903	−	0.277479i	−0.108903	−	0.277479i	−0.974928	+	0.222521i	$0.928571\pi$
$284$	0.149042	−	1.98883i	0.149042	−	1.98883i
$285$		0			0
$286$	0.531130	+	0.255779i	0.531130	+	0.255779i
$287$		0			0
$288$	0.242647	−	0.116853i	0.242647	−	0.116853i
$289$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.730682			0.730682			0.365341	−	0.930874i	$-0.380952\pi$
$293$	0.730682			0.730682			0.365341	+	0.930874i	$0.380952\pi$
$294$	−1.01507	−	0.488831i	−1.01507	−	0.488831i
$295$		0			0
$296$		0			0
$297$	−0.202749	+	0.138232i	−0.202749	+	0.138232i
$298$	−1.57906	−	0.487076i	−1.57906	−	0.487076i
$299$	0.231095	+	3.08375i	0.231095	+	3.08375i
$300$	−1.01507	+	0.488831i	−1.01507	+	0.488831i
$301$		0			0
$302$		0			0
$303$	−0.513267	+	1.30778i	−0.513267	+	1.30778i
$304$		0			0
$305$		0			0
$306$	−0.257353	+	0.0793829i	−0.257353	+	0.0793829i
$307$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$307$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$308$	−0.277479	−	0.108903i	−0.277479	−	0.108903i
$309$		0			0
$310$		0			0
$311$	1.26968	+	1.17809i	1.26968	+	1.17809i	0.974928	+	0.222521i	$0.0714286\pi$
$311$	1.26968	+	1.17809i	1.26968	+	1.17809i	0.294755	+	0.955573i	$0.404762\pi$
$312$	1.11406	−	1.92960i	1.11406	−	1.92960i
$313$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$313$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$314$	0.162592	−	0.712362i	0.162592	−	0.712362i
$315$		0			0
$316$	−0.414278	−	1.81507i	−0.414278	−	1.81507i
$317$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$317$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$318$	0.166507	−	0.0250969i	0.166507	−	0.0250969i
$319$		0			0
$320$		0			0
$321$	0.147791	+	0.647514i	0.147791	+	0.647514i
$322$	−0.233052	−	1.54620i	−0.233052	−	1.54620i
$323$		0			0
$324$	0.598393	+	1.03645i	0.598393	+	1.03645i
$325$	−0.988831	+	1.71271i	−0.988831	+	1.71271i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$331$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$332$		0			0
$333$		0			0
$334$	0.496990	−	1.26631i	0.496990	−	1.26631i
$335$		0			0
$336$	−0.488831	+	1.01507i	−0.488831	+	1.01507i
$337$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$337$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$338$	−0.217550	−	2.90301i	−0.217550	−	2.90301i
$339$		0			0
$340$		0			0
$341$	0.255779	+	0.0385525i	0.255779	+	0.0385525i
$342$		0			0
$343$	0.974928	−	0.222521i	0.974928	−	0.222521i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.86323	+	0.574730i	1.86323	+	0.574730i	0.997204	+	0.0747301i	$0.0238095\pi$
$347$	1.86323	+	0.574730i	1.86323	+	0.574730i	0.866025	+	0.500000i	$0.166667\pi$
$348$		0			0
$349$	0.400969	−	0.193096i	0.400969	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$349$	0.400969	−	0.193096i	0.400969	−	0.193096i	0.623490	+	0.781831i	$0.285714\pi$
$350$	0.433884	−	0.900969i	0.433884	−	0.900969i
$351$	1.46682	+	0.706381i	1.46682	+	0.706381i
$352$	−0.108903	+	0.277479i	−0.108903	+	0.277479i
$353$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i	0.826239	+	0.563320i	$0.190476\pi$
$353$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i	−0.900969	+	0.433884i	$0.857143\pi$
$354$		0			0
$355$		0			0
$356$	−1.03030	+	1.29196i	−1.03030	+	1.29196i
$357$	0.634659	−	0.930874i	0.634659	−	0.930874i
$358$		0			0
$359$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$359$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$360$		0			0
$361$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$362$		0			0
$363$	0.228425	−	1.00080i	0.228425	−	1.00080i
$364$	0.294755	+	1.95557i	0.294755	+	1.95557i
$365$		0			0
$366$		0			0
$367$	−0.582926	+	0.0878620i	−0.582926	+	0.0878620i	−0.433884	−	0.900969i	$-0.642857\pi$
$367$	−0.582926	+	0.0878620i	−0.582926	+	0.0878620i	−0.149042	+	0.988831i	$0.547619\pi$
$368$	−1.54620	+	0.233052i	−1.54620	+	0.233052i
$369$		0			0
$370$		0			0
$371$	−0.101659	+	0.109562i	−0.101659	+	0.109562i
$372$	0.217550	−	0.953150i	0.217550	−	0.953150i
$373$	−0.988831	−	1.71271i	−0.988831	−	1.71271i	−0.623490	−	0.781831i	$-0.714286\pi$
$373$	−0.988831	−	1.71271i	−0.988831	−	1.71271i	−0.365341	−	0.930874i	$-0.619048\pi$
$374$	0.149042	−	0.258149i	0.149042	−	0.258149i
$375$		0			0
$376$		0			0
$377$		0			0
$378$	−0.766310	−	0.300754i	−0.766310	−	0.300754i
$379$	−1.07992	+	1.35417i	−1.07992	+	1.35417i	−0.149042	+	0.988831i	$0.547619\pi$
$379$	−1.07992	+	1.35417i	−1.07992	+	1.35417i	−0.930874	+	0.365341i	$0.880952\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$383$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$384$	1.01507	+	0.488831i	1.01507	+	0.488831i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.21135	−	0.825886i	1.21135	−	0.825886i	0.222521	−	0.974928i	$-0.428571\pi$
$389$	1.21135	−	0.825886i	1.21135	−	0.825886i	0.988831	+	0.149042i	$0.0476190\pi$
$390$		0			0
$391$	1.56366			1.56366
$392$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$393$	1.76169			1.76169
$394$		0			0
$395$		0			0
$396$	0.0767129	+	0.0236628i	0.0767129	+	0.0236628i
$397$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$397$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$398$	−1.79690	+	0.865341i	−1.79690	+	0.865341i
$399$		0			0
$400$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$401$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$401$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$402$		0			0
$403$	−0.626980	−	1.59752i	−0.626980	−	1.59752i
$404$	−1.19158	+	0.367554i	−1.19158	+	0.367554i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.930874	−	0.634659i	−0.930874	−	0.634659i
$409$	−0.109562	−	0.101659i	−0.109562	−	0.101659i	0.623490	−	0.781831i	$-0.285714\pi$
$409$	−0.109562	−	0.101659i	−0.109562	−	0.101659i	−0.733052	+	0.680173i	$0.761905\pi$
$410$		0			0
$411$	0.930874	+	1.61232i	0.930874	+	1.61232i
$412$		0			0
$413$		0			0
$414$	0.0937086	+	0.410564i	0.0937086	+	0.410564i
$415$		0			0
$416$	1.95557	−	0.294755i	1.95557	−	0.294755i
$417$	−2.07409	+	0.312619i	−2.07409	+	0.312619i
$418$		0			0
$419$	−0.414278	−	1.81507i	−0.414278	−	1.81507i	−0.563320	−	0.826239i	$-0.690476\pi$
$419$	−0.414278	−	1.81507i	−0.414278	−	1.81507i	0.149042	−	0.988831i	$-0.452381\pi$
$420$		0			0
$421$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	0.222521	+	0.974928i	$0.428571\pi$
$421$	−0.400969	+	1.75676i	−0.400969	+	1.75676i	−0.623490	+	0.781831i	$0.714286\pi$
$422$	0.974928	+	1.68862i	0.974928	+	1.68862i
$423$		0			0
$424$	0.109562	+	0.101659i	0.109562	+	0.101659i
$425$	0.826239	+	0.563320i	0.826239	+	0.563320i
$426$	−1.40097	−	1.75676i	−1.40097	−	1.75676i
$427$		0			0
$428$	−0.367554	+	0.460898i	−0.367554	+	0.460898i
$429$	0.634659	−	0.195766i	0.634659	−	0.195766i
$430$		0			0
$431$	−0.129436	+	1.72721i	−0.129436	+	1.72721i	0.433884	+	0.900969i	$0.357143\pi$
$431$	−0.129436	+	1.72721i	−0.129436	+	1.72721i	−0.563320	+	0.826239i	$0.690476\pi$
$432$	−0.300754	+	0.766310i	−0.300754	+	0.766310i
$433$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.900969	−	0.433884i	$-0.142857\pi$
$433$	1.12349	+	0.541044i	1.12349	+	0.541044i	0.222521	+	0.974928i	$0.428571\pi$
$434$	0.376510	+	0.781831i	0.376510	+	0.781831i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	1.84095	+	0.277479i	1.84095	+	0.277479i	0.974928	−	0.222521i	$-0.0714286\pi$
$439$	1.84095	+	0.277479i	1.84095	+	0.277479i	0.866025	+	0.500000i	$0.166667\pi$
$440$		0			0
$441$	−0.257353	+	0.0793829i	−0.257353	+	0.0793829i
$442$	−1.97766			−1.97766
$443$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$443$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−1.67738	+	0.807782i	−1.67738	+	0.807782i
$448$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$449$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$449$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$450$	−0.0983929	+	0.250701i	−0.0983929	+	0.250701i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	1.24349	−	1.55929i	1.24349	−	1.55929i
$455$		0			0
$456$		0			0
$457$	−1.03030	−	0.702449i	−1.03030	−	0.702449i	−0.0747301	−	0.997204i	$-0.523810\pi$
$457$	−1.03030	−	0.702449i	−1.03030	−	0.702449i	−0.955573	+	0.294755i	$0.904762\pi$
$458$	0.326239	+	0.302705i	0.326239	+	0.302705i
$459$	0.411608	−	0.712926i	0.411608	−	0.712926i
$460$		0			0
$461$	−0.0332580	+	0.145713i	−0.0332580	+	0.145713i	−0.988831	−	0.149042i	$-0.952381\pi$
$461$	−0.0332580	+	0.145713i	−0.0332580	+	0.145713i	0.955573	+	0.294755i	$0.0952381\pi$
$462$	−0.312619	+	0.122694i	−0.312619	+	0.122694i
$463$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$463$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$467$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$468$	−0.118519	−	0.519266i	−0.118519	−	0.519266i
$469$		0			0
$470$		0			0
$471$	−0.411608	−	0.712926i	−0.411608	−	0.712926i
$472$		0			0
$473$		0			0
$474$	−1.73305	−	1.18157i	−1.73305	−	1.18157i
$475$		0			0
$476$	0.997204	−	0.0747301i	0.997204	−	0.0747301i
$477$	0.0250969	−	0.0314705i	0.0250969	−	0.0314705i
$478$		0			0
$479$	−0.571270	−	1.45557i	−0.571270	−	1.45557i	−0.866025	−	0.500000i	$-0.833333\pi$
$479$	−0.571270	−	1.45557i	−0.571270	−	1.45557i	0.294755	−	0.955573i	$-0.404762\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−1.37734	−	1.09839i	−1.37734	−	1.09839i
$484$	0.820914	−	0.395331i	0.820914	−	0.395331i
$485$		0			0
$486$	0.501801	+	0.154785i	0.501801	+	0.154785i
$487$	1.43109	−	0.975699i	1.43109	−	0.975699i	0.433884	−	0.900969i	$-0.357143\pi$
$487$	1.43109	−	0.975699i	1.43109	−	0.975699i	0.997204	−	0.0747301i	$-0.0238095\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.781831	−	0.376510i	0.781831	−	0.376510i
$497$	1.94440	+	0.443797i	1.94440	+	0.443797i
$498$		0			0
$499$	−0.680173	+	1.73305i	−0.680173	+	1.73305i			1.00000i	$0.5\pi$
$499$	−0.680173	+	1.73305i	−0.680173	+	1.73305i	−0.680173	+	0.733052i	$0.738095\pi$
$500$		0			0
$501$	−0.559929	−	1.42668i	−0.559929	−	1.42668i
$502$		0			0
$503$	−0.367554	+	0.460898i	−0.367554	+	0.460898i	−0.930874	−	0.365341i	$-0.880952\pi$
$503$	−0.367554	+	0.460898i	−0.367554	+	0.460898i	0.563320	+	0.826239i	$0.309524\pi$
$504$	0.0793829	+	0.257353i	0.0793829	+	0.257353i
$505$		0			0
$506$	−0.385113	−	0.262566i	−0.385113	−	0.262566i
$507$	−2.40427	−	2.23084i	−2.40427	−	2.23084i
$508$		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
$514$	0.988831	−	0.149042i	0.988831	−	0.149042i
$515$		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		−0.826239	−	0.563320i	$-0.809524\pi$
$523$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$524$	0.974928	+	1.22252i	0.974928	+	1.22252i
$525$	−0.332083	−	1.07659i	−0.332083	−	1.07659i
$526$		0			0
$527$	−0.829215	+	0.255779i	−0.829215	+	0.255779i
$528$	0.122694	+	0.312619i	0.122694	+	0.312619i
$529$	0.107988	−	1.44100i	0.107988	−	1.44100i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	0.139129	+	1.85654i	0.139129	+	1.85654i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.149042	−	0.258149i	0.149042	−	0.258149i
$540$		0			0
$541$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$541$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$542$		0			0
$543$		0			0
$544$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i
$545$		0			0
$546$	1.74201	+	1.38921i	1.74201	+	1.38921i
$547$	1.22563	+	0.590232i	1.22563	+	0.590232i	0.930874	−	0.365341i	$-0.119048\pi$
$547$	1.22563	+	0.590232i	1.22563	+	0.590232i	0.294755	+	0.955573i	$0.404762\pi$
$548$	−0.603718	+	1.53825i	−0.603718	+	1.53825i
$549$		0			0
$550$	−0.108903	−	0.277479i	−0.108903	−	0.277479i
$551$		0			0
$552$	−1.09839	+	1.37734i	−1.09839	+	1.37734i
$553$	1.85654	−	0.139129i	1.85654	−	0.139129i
$554$		0			0
$555$		0			0
$556$	−1.36476	−	1.26631i	−1.36476	−	1.26631i
$557$	0.0747301	−	0.129436i	0.0747301	−	0.129436i	−0.826239	−	0.563320i	$-0.809524\pi$
$557$	0.0747301	−	0.129436i	0.0747301	−	0.129436i	0.900969	+	0.433884i	$0.142857\pi$
$558$	−0.116853	−	0.202395i	−0.116853	−	0.202395i
$559$		0			0
$560$		0			0
$561$	−0.0747301	−	0.327414i	−0.0747301	−	0.327414i
$562$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$563$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$563$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$564$		0			0
$565$		0			0
$566$	−0.0663300	−	0.290611i	−0.0663300	−	0.290611i
$567$	−1.11406	+	0.437235i	−1.11406	+	0.437235i
$568$	0.443797	−	1.94440i	0.443797	−	1.94440i
$569$	0.988831	+	1.71271i	0.988831	+	1.71271i	0.623490	+	0.781831i	$0.285714\pi$
$569$	0.988831	+	1.71271i	0.988831	+	1.71271i	0.365341	+	0.930874i	$0.380952\pi$
$570$		0			0
$571$	0.636119	+	0.590232i	0.636119	+	0.590232i	0.930874	−	0.365341i	$-0.119048\pi$
$571$	0.636119	+	0.590232i	0.636119	+	0.590232i	−0.294755	+	0.955573i	$0.595238\pi$
$572$	0.487076	+	0.332083i	0.487076	+	0.332083i
$573$		0			0
$574$		0			0
$575$	0.974928	−	1.22252i	0.974928	−	1.22252i
$576$	0.257353	−	0.0793829i	0.257353	−	0.0793829i
$577$	−0.698220	−	1.77904i	−0.698220	−	1.77904i	−0.623490	−	0.781831i	$-0.714286\pi$
$577$	−0.698220	−	1.77904i	−0.698220	−	1.77904i	−0.0747301	−	0.997204i	$-0.523810\pi$
$578$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	0.00332936	+	0.0444272i	0.00332936	+	0.0444272i
$584$		0			0
$585$		0			0
$586$	0.722521	+	0.108903i	0.722521	+	0.108903i
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$	−0.930874	−	0.634659i	−0.930874	−	0.634659i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.142820	+	1.90580i	0.142820	+	1.90580i	0.365341	+	0.930874i	$0.380952\pi$
$593$	0.142820	+	1.90580i	0.142820	+	1.90580i	−0.222521	+	0.974928i	$0.571429\pi$
$594$	−0.221087	+	0.106470i	−0.221087	+	0.106470i
$595$		0			0
$596$	−1.48883	−	0.716983i	−1.48883	−	0.716983i
$597$	−0.820914	+	2.09165i	−0.820914	+	2.09165i
$598$	−0.231095	+	3.08375i	−0.231095	+	3.08375i
$599$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$599$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$600$	−1.07659	+	0.332083i	−1.07659	+	0.332083i
$601$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$601$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$	−0.702449	+	1.21668i	−0.702449	+	1.21668i
$607$	−0.866025	−	1.50000i	−0.866025	−	1.50000i	−0.866025	−	0.500000i	$-0.833333\pi$
$607$	−0.866025	−	1.50000i	−0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.266310	+	0.0401398i	−0.266310	+	0.0401398i
$613$	1.44973	−	0.218511i	1.44973	−	0.218511i	0.623490	−	0.781831i	$-0.285714\pi$
$613$	1.44973	−	0.218511i	1.44973	−	0.218511i	0.826239	+	0.563320i	$0.190476\pi$
$614$		0			0
$615$		0			0
$616$	−0.258149	−	0.149042i	−0.258149	−	0.149042i
$617$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$617$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$618$		0			0
$619$	0.866025	−	1.50000i	0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$619$	0.866025	−	1.50000i	0.866025	−	1.50000i	0.866025	−	0.500000i	$-0.166667\pi$
$620$		0			0
$621$	−1.06356	−	0.725124i	−1.06356	−	0.725124i
$622$	1.07992	+	1.35417i	1.07992	+	1.35417i
$623$	−1.12397	−	1.21135i	−1.12397	−	1.21135i
$624$	1.38921	−	1.74201i	1.38921	−	1.74201i
$625$	0.955573	−	0.294755i	0.955573	−	0.294755i
$626$		0			0
$627$		0			0
$628$	0.266948	−	0.680173i	0.266948	−	0.680173i
$629$		0			0
$630$		0			0
$631$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$631$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$632$	−0.139129	−	1.85654i	−0.139129	−	1.85654i
$633$	2.09919	+	0.647514i	2.09919	+	0.647514i
$634$		0			0
$635$		0			0
$636$	0.168388			0.168388
$637$	−1.97766			−1.97766
$638$		0			0
$639$	−0.531130	−	0.0800550i	−0.531130	−	0.0800550i
$640$		0			0
$641$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$641$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$642$	0.0496332	+	0.662309i	0.0496332	+	0.662309i
$643$	1.22563	−	0.590232i	1.22563	−	0.590232i	0.294755	−	0.955573i	$-0.404762\pi$
$643$	1.22563	−	0.590232i	1.22563	−	0.590232i	0.930874	+	0.365341i	$0.119048\pi$
$644$		−	1.56366i		−	1.56366i
$645$		0			0
$646$		0			0
$647$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$647$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$648$	0.437235	+	1.11406i	0.437235	+	1.11406i
$649$		0			0
$650$	−1.23305	+	1.54620i	−1.23305	+	1.54620i
$651$	0.910080	+	0.357180i	0.910080	+	0.357180i
$652$		0			0
$653$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$653$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$659$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$660$		0			0
$661$	1.78181	−	0.268565i	1.78181	−	0.268565i	0.826239	−	0.563320i	$-0.190476\pi$
$661$	1.78181	−	0.268565i	1.78181	−	0.268565i	0.955573	+	0.294755i	$0.0952381\pi$
$662$		0			0
$663$	−1.63332	+	1.51550i	−1.63332	+	1.51550i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.680173	−	1.17809i	0.680173	−	1.17809i
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−0.634659	+	0.930874i	−0.634659	+	0.930874i
$673$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$673$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$674$		0			0
$675$	−0.300754	−	0.766310i	−0.300754	−	0.766310i
$676$	0.217550	−	2.90301i	0.217550	−	2.90301i
$677$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$677$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.167917	−	2.24070i	−0.167917	−	2.24070i
$682$	0.247176	+	0.0762438i	0.247176	+	0.0762438i
$683$	−1.64786	+	1.12349i	−1.64786	+	1.12349i	−0.781831	+	0.623490i	$0.785714\pi$
$683$	−1.64786	+	1.12349i	−1.64786	+	1.12349i	−0.866025	+	0.500000i	$0.833333\pi$
$684$		0			0
$685$		0			0
$686$	0.997204	−	0.0747301i	0.997204	−	0.0747301i
$687$	0.501402			0.501402
$688$		0			0
$689$	0.244221	−	0.166507i	0.244221	−	0.166507i
$690$		0			0
$691$	0.0648483	+	0.865341i	0.0648483	+	0.865341i	0.930874	+	0.365341i	$0.119048\pi$
$691$	0.0648483	+	0.865341i	0.0648483	+	0.865341i	−0.866025	+	0.500000i	$0.833333\pi$
$692$		0			0
$693$	−0.0348320	+	0.0723293i	−0.0348320	+	0.0723293i
$694$	1.75676	+	0.846011i	1.75676	+	0.846011i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	0.425270	−	0.131178i	0.425270	−	0.131178i
$699$		0			0
$700$	0.563320	−	0.826239i	0.563320	−	0.826239i
$701$	−0.0931869	−	0.116853i	−0.0931869	−	0.116853i	0.733052	−	0.680173i	$-0.238095\pi$
$701$	−0.0931869	−	0.116853i	−0.0931869	−	0.116853i	−0.826239	+	0.563320i	$0.809524\pi$
$702$	1.34515	+	0.917109i	1.34515	+	0.917109i
$703$		0			0
$704$	−0.149042	+	0.258149i	−0.149042	+	0.258149i
$705$		0			0
$706$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$707$	−0.185853	−	1.23305i	−0.185853	−	1.23305i
$708$		0			0
$709$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$709$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$710$		0			0
$711$	−0.495802	+	0.0747301i	−0.495802	+	0.0747301i
$712$	−1.21135	+	1.12397i	−1.21135	+	1.12397i
$713$	0.301938	+	1.32288i	0.301938	+	1.32288i
$714$	0.766310	−	0.825886i	0.766310	−	0.825886i
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	0.246289	+	0.167917i	0.246289	+	0.167917i	0.680173	−	0.733052i	$-0.261905\pi$
$719$	0.246289	+	0.167917i	0.246289	+	0.167917i	−0.433884	+	0.900969i	$0.642857\pi$
$720$		0			0
$721$		0			0
$722$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	0.375035	−	0.955573i	0.375035	−	0.955573i
$727$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$727$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$728$			1.97766i			1.97766i
$729$	−0.545223	+	0.262566i	−0.545223	+	0.262566i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	0.988831	+	0.149042i	0.988831	+	0.149042i	0.623490	−	0.781831i	$-0.285714\pi$
$733$	0.988831	+	0.149042i	0.988831	+	0.149042i	0.365341	+	0.930874i	$0.380952\pi$
$734$	−0.589510			−0.589510
$735$		0			0
$736$	−1.56366			−1.56366
$737$		0			0
$738$		0			0
$739$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$739$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$740$		0			0
$741$		0			0
$742$	−0.116853	+	0.0931869i	−0.116853	+	0.0931869i
$743$	1.01507	+	0.488831i	1.01507	+	0.488831i	0.866025	−	0.500000i	$-0.166667\pi$
$743$	1.01507	+	0.488831i	1.01507	+	0.488831i	0.149042	+	0.988831i	$0.452381\pi$
$744$	0.357180	−	0.910080i	0.357180	−	0.910080i
$745$		0			0
$746$	−0.722521	−	1.84095i	−0.722521	−	1.84095i
$747$		0			0
$748$	0.185853	−	0.233052i	0.185853	−	0.233052i
$749$	−0.400969	−	0.432142i	−0.400969	−	0.432142i
$750$		0			0
$751$	−1.53825	−	1.04876i	−1.53825	−	1.04876i	−0.974928	−	0.222521i	$-0.928571\pi$
$751$	−1.53825	−	1.04876i	−1.53825	−	1.04876i	−0.563320	−	0.826239i	$-0.690476\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−0.712926	−	0.411608i	−0.712926	−	0.411608i
$757$	−0.222521	−	0.974928i	−0.222521	−	0.974928i	−0.955573	−	0.294755i	$-0.904762\pi$
$757$	−0.222521	−	0.974928i	−0.222521	−	0.974928i	0.733052	−	0.680173i	$-0.238095\pi$
$758$	−1.26968	+	1.17809i	−1.26968	+	1.17809i
$759$	−0.519266	+	0.0782667i	−0.519266	+	0.0782667i
$760$		0			0
$761$	−1.07473	+	0.997204i	−1.07473	+	0.997204i	−0.0747301	+	0.997204i	$0.523810\pi$
$761$	−1.07473	+	0.997204i	−1.07473	+	0.997204i	−1.00000			$1.00000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.930874	+	0.634659i	0.930874	+	0.634659i
$769$	0.623490	+	0.781831i	0.623490	+	0.781831i	0.988831	−	0.149042i	$-0.0476190\pi$
$769$	0.623490	+	0.781831i	0.623490	+	0.781831i	−0.365341	+	0.930874i	$0.619048\pi$
$770$		0			0
$771$	0.702449	−	0.880843i	0.702449	−	0.880843i
$772$		0			0
$773$	0.535628	+	1.36476i	0.535628	+	1.36476i	0.900969	+	0.433884i	$0.142857\pi$
$773$	0.535628	+	1.36476i	0.535628	+	1.36476i	−0.365341	+	0.930874i	$0.619048\pi$
$774$		0			0
$775$	−0.317031	+	0.807782i	−0.317031	+	0.807782i
$776$		0			0
$777$		0			0
$778$	1.32091	−	0.636119i	1.32091	−	0.636119i
$779$		0			0
$780$		0			0
$781$	0.491201	−	0.334895i	0.491201	−	0.334895i
$782$	1.54620	+	0.233052i	1.54620	+	0.233052i
$783$		0			0
$784$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i
$785$		0			0
$786$	1.74201	+	0.262566i	1.74201	+	0.262566i
$787$	1.61105	−	1.09839i	1.61105	−	1.09839i	0.680173	−	0.733052i	$-0.261905\pi$
$787$	1.61105	−	1.09839i	1.61105	−	1.09839i	0.930874	−	0.365341i	$-0.119048\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.0723293	+	0.0348320i	0.0723293	+	0.0348320i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−1.90580	+	0.587862i	−1.90580	+	0.587862i
$797$	0.0931869	−	0.116853i	0.0931869	−	0.116853i	−0.733052	−	0.680173i	$-0.761905\pi$
$797$	0.0931869	−	0.116853i	0.0931869	−	0.116853i	0.826239	+	0.563320i	$0.190476\pi$
$798$		0			0
$799$		0			0
$800$	−0.826239	−	0.563320i	−0.826239	−	0.563320i
$801$	0.326239	+	0.302705i	0.326239	+	0.302705i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−0.381879	−	1.67312i	−0.381879	−	1.67312i
$807$		0			0
$808$	−1.23305	+	0.185853i	−1.23305	+	0.185853i
$809$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$809$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$810$		0			0
$811$	−0.443797	−	1.94440i	−0.443797	−	1.94440i	−0.294755	−	0.955573i	$-0.595238\pi$
$811$	−0.443797	−	1.94440i	−0.443797	−	1.94440i	−0.149042	−	0.988831i	$-0.547619\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.825886	−	0.766310i	−0.825886	−	0.766310i
$817$		0			0
$818$	−0.0931869	−	0.116853i	−0.0931869	−	0.116853i
$819$	0.531130	−	0.0398027i	0.531130	−	0.0398027i
$820$		0			0
$821$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$821$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$822$	0.680173	+	1.73305i	0.680173	+	1.73305i
$823$	0.0841939	−	1.12349i	0.0841939	−	1.12349i	−0.781831	−	0.623490i	$-0.785714\pi$
$823$	0.0841939	−	1.12349i	0.0841939	−	1.12349i	0.866025	−	0.500000i	$-0.166667\pi$
$824$		0			0
$825$	−0.302576	−	0.145713i	−0.302576	−	0.145713i
$826$		0			0
$827$	−0.531130	+	0.255779i	−0.531130	+	0.255779i	−0.680173	−	0.733052i	$-0.738095\pi$
$827$	−0.531130	+	0.255779i	−0.531130	+	0.255779i	0.149042	+	0.988831i	$0.452381\pi$
$828$	0.0314705	+	0.419945i	0.0314705	+	0.419945i
$829$	1.82624	+	0.563320i	1.82624	+	0.563320i	1.00000			$0$
$829$	1.82624	+	0.563320i	1.82624	+	0.563320i	0.826239	+	0.563320i	$0.190476\pi$
$830$		0			0
$831$		0			0
$832$	1.97766			1.97766
$833$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$834$	−2.09752			−2.09752
$835$		0			0
$836$		0			0
$837$	0.682623	+	0.210561i	0.682623	+	0.210561i
$838$	−0.139129	−	1.85654i	−0.139129	−	1.85654i
$839$	−1.75676	+	0.846011i	−1.75676	+	0.846011i	−0.781831	+	0.623490i	$0.785714\pi$
$839$	−1.75676	+	0.846011i	−1.75676	+	0.846011i	−0.974928	+	0.222521i	$0.928571\pi$
$840$		0			0
$841$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$842$	−0.658322	+	1.67738i	−0.658322	+	1.67738i
$843$	−0.0841939	+	1.12349i	−0.0841939	+	1.12349i
$844$	0.712362	+	1.81507i	0.712362	+	1.81507i
$845$		0			0
$846$		0			0
$847$	0.268565	+	0.870666i	0.268565	+	0.870666i
$848$	0.0931869	+	0.116853i	0.0931869	+	0.116853i
$849$	−0.277479	−	0.189182i	−0.277479	−	0.189182i
$850$	0.733052	+	0.680173i	0.733052	+	0.680173i
$851$		0			0
$852$	−1.12349	−	1.94594i	−1.12349	−	1.94594i
$853$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$853$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$854$		0			0
$855$		0			0
$856$	−0.432142	+	0.400969i	−0.432142	+	0.400969i
$857$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$857$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$858$	0.656748	−	0.0989888i	0.656748	−	0.0989888i
$859$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$859$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$860$		0			0
$861$		0			0
$862$	−0.385418	+	1.68862i	−0.385418	+	1.68862i
$863$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$863$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$864$	−0.411608	+	0.712926i	−0.411608	+	0.712926i
$865$		0			0
$866$	1.03030	+	0.702449i	1.03030	+	0.702449i
$867$	0.702449	+	0.880843i	0.702449	+	0.880843i
$868$	0.255779	+	0.829215i	0.255779	+	0.829215i
$869$	0.346011	−	0.433884i	0.346011	−	0.433884i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$877$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$878$	1.77904	+	0.548760i	1.77904	+	0.548760i
$879$	0.680173	−	0.463734i	0.680173	−	0.463734i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−0.266310	+	0.0401398i	−0.266310	+	0.0401398i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$	−1.95557	−	0.294755i	−1.95557	−	0.294755i
$885$		0			0
$886$		0			0
$887$	0.0222759	+	0.297251i	0.0222759	+	0.297251i	0.997204	+	0.0747301i	$0.0238095\pi$
$887$	0.0222759	+	0.297251i	0.0222759	+	0.297251i	−0.974928	+	0.222521i	$0.928571\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.130333	+	0.332083i	−0.130333	+	0.332083i
$892$		0			0
$893$		0			0
$894$	−1.77904	+	0.548760i	−1.77904	+	0.548760i
$895$		0			0
$896$	−0.997204	+	0.0747301i	−0.997204	+	0.0747301i
$897$	2.17225	+	2.72391i	2.17225	+	2.72391i
$898$		0			0
$899$		0			0
$900$	−0.134659	+	0.233236i	−0.134659	+	0.233236i
$901$	−0.0747301	−	0.129436i	−0.0747301	−	0.129436i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	0.858075	−	0.129334i	0.858075	−	0.129334i	0.294755	−	0.955573i	$-0.404762\pi$
$907$	0.858075	−	0.129334i	0.858075	−	0.129334i	0.563320	+	0.826239i	$0.309524\pi$
$908$	1.46200	−	1.35654i	1.46200	−	1.35654i
$909$	0.0747301	+	0.327414i	0.0747301	+	0.327414i
$910$		0			0
$911$	0.347948	−	1.52446i	0.347948	−	1.52446i	−0.433884	−	0.900969i	$-0.642857\pi$
$911$	0.347948	−	1.52446i	0.347948	−	1.52446i	0.781831	−	0.623490i	$-0.214286\pi$
$912$		0			0
$913$		0			0
$914$	−0.914101	−	0.848162i	−0.914101	−	0.848162i
$915$		0			0
$916$	0.277479	+	0.347948i	0.277479	+	0.347948i
$917$	−1.35417	+	0.781831i	−1.35417	+	0.781831i
$918$	0.513267	−	0.643616i	0.513267	−	0.643616i
$919$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$919$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$920$		0			0
$921$		0			0
$922$	−0.0546039	+	0.139129i	−0.0546039	+	0.139129i
$923$	−3.55366	−	1.71135i	−3.55366	−	1.71135i
$924$	−0.327414	+	0.0747301i	−0.327414	+	0.0747301i
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$929$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	1.92960	+	0.290841i	1.92960	+	0.290841i
$934$		0			0
$935$		0			0
$936$	−0.0398027	−	0.531130i	−0.0398027	−	0.531130i
$937$	1.62349	−	0.781831i	1.62349	−	0.781831i	0.623490	−	0.781831i	$-0.285714\pi$
$937$	1.62349	−	0.781831i	1.62349	−	0.781831i	1.00000			$0$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$941$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$942$	−0.300754	−	0.766310i	−0.300754	−	0.766310i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.43109	−	0.975699i	−1.43109	−	0.975699i	−0.997204	−	0.0747301i	$-0.976190\pi$
$947$	−1.43109	−	0.975699i	−1.43109	−	0.975699i	−0.433884	−	0.900969i	$-0.642857\pi$
$948$	−1.53759	−	1.42668i	−1.53759	−	1.42668i
$949$		0			0
$950$		0			0
$951$		0			0
$952$	0.997204	+	0.0747301i	0.997204	+	0.0747301i
$953$	−0.326239	−	1.42935i	−0.326239	−	1.42935i	−0.826239	−	0.563320i	$-0.809524\pi$
$953$	−0.326239	−	1.42935i	−0.326239	−	1.42935i	0.500000	−	0.866025i	$-0.333333\pi$
$954$	0.0295070	−	0.0273785i	0.0295070	−	0.0273785i
$955$		0			0
$956$		0			0
$957$		0			0
$958$	−0.347948	−	1.52446i	−0.347948	−	1.52446i
$959$	−1.43109	−	0.826239i	−1.43109	−	0.826239i
$960$		0			0
$961$	0.123490	+	0.213891i	0.123490	+	0.213891i
$962$		0			0
$963$	0.116384	+	0.107988i	0.116384	+	0.107988i
$964$		0			0
$965$		0			0
$966$	−1.19825	−	1.29141i	−1.19825	−	1.29141i
$967$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$967$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$968$	0.870666	−	0.268565i	0.870666	−	0.268565i
$969$		0			0
$970$		0			0
$971$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$971$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$972$	0.473127	+	0.227846i	0.473127	+	0.227846i
$973$	1.45557	−	1.16078i	1.45557	−	1.16078i
$974$	1.56052	−	0.751509i	1.56052	−	0.751509i
$975$	0.166507	+	2.22188i	0.166507	+	2.22188i
$976$		0			0
$977$	1.03030	−	0.702449i	1.03030	−	0.702449i	0.0747301	−	0.997204i	$-0.476190\pi$
$977$	1.03030	−	0.702449i	1.03030	−	0.702449i	0.955573	+	0.294755i	$0.0952381\pi$
$978$		0			0
$979$	−0.492578			−0.492578
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−0.246289	+	0.167917i	−0.246289	+	0.167917i	−0.680173	−	0.733052i	$-0.738095\pi$
$983$	−0.246289	+	0.167917i	−0.246289	+	0.167917i	0.433884	+	0.900969i	$0.357143\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−0.496990	−	1.26631i	−0.496990	−	1.26631i	−0.930874	−	0.365341i	$-0.880952\pi$
$991$	−0.496990	−	1.26631i	−0.496990	−	1.26631i	0.433884	−	0.900969i	$-0.357143\pi$
$992$	0.829215	−	0.255779i	0.829215	−	0.255779i
$993$		0			0
$994$	1.85654	+	0.728639i	1.85654	+	0.728639i
$995$		0			0
$996$		0			0
$997$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$997$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$998$	−0.930874	+	1.61232i	−0.930874	+	1.61232i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3332.1.cc.c.1019.2	yes	24
4.3	odd	2	inner	3332.1.cc.c.1019.1	✓	24
17.16	even	2	inner	3332.1.cc.c.1019.1	✓	24
49.44	even	21	inner	3332.1.cc.c.1563.2	yes	24
68.67	odd	2	CM	3332.1.cc.c.1019.2	yes	24
196.191	odd	42	inner	3332.1.cc.c.1563.1	yes	24
833.730	even	42	inner	3332.1.cc.c.1563.1	yes	24
3332.1563	odd	42	inner	3332.1.cc.c.1563.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3332.1.cc.c.1019.1	✓	24	4.3	odd	2	inner
3332.1.cc.c.1019.1	✓	24	17.16	even	2	inner
3332.1.cc.c.1019.2	yes	24	1.1	even	1	trivial
3332.1.cc.c.1019.2	yes	24	68.67	odd	2	CM
3332.1.cc.c.1563.1	yes	24	196.191	odd	42	inner
3332.1.cc.c.1563.1	yes	24	833.730	even	42	inner
3332.1.cc.c.1563.2	yes	24	49.44	even	21	inner
3332.1.cc.c.1563.2	yes	24	3332.1563	odd	42	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.988831 + 0.149042i) q^{2} +(0.930874 - 0.634659i) q^{3} +(0.955573 + 0.294755i) q^{4} +(1.01507 - 0.488831i) q^{6} +(-0.433884 + 0.900969i) q^{7} +(0.900969 + 0.433884i) q^{8} +(0.0983929 - 0.250701i) q^{9} +O(q^{10})\)	\(q+(0.988831 + 0.149042i) q^{2} +(0.930874 - 0.634659i) q^{3} +(0.955573 + 0.294755i) q^{4} +(1.01507 - 0.488831i) q^{6} +(-0.433884 + 0.900969i) q^{7} +(0.900969 + 0.433884i) q^{8} +(0.0983929 - 0.250701i) q^{9} +(0.108903 + 0.277479i) q^{11} +(1.07659 - 0.332083i) q^{12} +(1.23305 - 1.54620i) q^{13} +(-0.563320 + 0.826239i) q^{14} +(0.826239 + 0.563320i) q^{16} +(-0.733052 - 0.680173i) q^{17} +(0.134659 - 0.233236i) q^{18} +(0.167917 + 1.11406i) q^{21} +(0.0663300 + 0.290611i) q^{22} +(-1.14625 + 1.06356i) q^{23} +(1.11406 - 0.167917i) q^{24} +(-0.988831 + 0.149042i) q^{25} +(1.44973 - 1.34515i) q^{26} +(0.183183 + 0.802576i) q^{27} +(-0.680173 + 0.733052i) q^{28} +(0.433884 - 0.751509i) q^{31} +(0.733052 + 0.680173i) q^{32} +(0.277479 + 0.189182i) q^{33} +(-0.623490 - 0.781831i) q^{34} +(0.167917 - 0.210561i) q^{36} +(0.166507 - 2.22188i) q^{39} +1.12664i q^{42} +(0.0222759 + 0.297251i) q^{44} +(-1.29196 + 0.880843i) q^{46} +1.12664 q^{48} +(-0.623490 - 0.781831i) q^{49} -1.00000 q^{50} +(-1.11406 - 0.167917i) q^{51} +(1.63402 - 1.11406i) q^{52} +(0.142820 + 0.0440542i) q^{53} +(0.0615190 + 0.820914i) q^{54} +(-0.781831 + 0.623490i) q^{56} +(0.541044 - 0.678448i) q^{62} +(0.183183 + 0.197424i) q^{63} +(0.623490 + 0.781831i) q^{64} +(0.246184 + 0.228425i) q^{66} +(-0.500000 - 0.866025i) q^{68} +(-0.392012 + 1.71752i) q^{69} +(-0.443797 - 1.94440i) q^{71} +(0.197424 - 0.183183i) q^{72} +(-0.825886 + 0.766310i) q^{75} +(-0.297251 - 0.0222759i) q^{77} +(0.495802 - 2.17225i) q^{78} +(-0.930874 - 1.61232i) q^{79} +(0.877306 + 0.814021i) q^{81} +(-0.167917 + 1.11406i) q^{84} +(-0.0222759 + 0.297251i) q^{88} +(-0.603718 + 1.53825i) q^{89} +(0.858075 + 1.78181i) q^{91} +(-1.40881 + 0.678448i) q^{92} +(-0.0730607 - 0.974928i) q^{93} +(1.11406 + 0.167917i) q^{96} +(-0.500000 - 0.866025i) q^{98} +0.0802795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 2 q^{4} + 4 q^{8} - 24 q^{9}+O(q^{10}) \) 24 * q - 2 * q^2 + 2 * q^4 + 4 * q^8 - 24 * q^9	\( 24 q - 2 q^{2} + 2 q^{4} + 4 q^{8} - 24 q^{9} + 10 q^{13} + 2 q^{16} + 2 q^{17} + 10 q^{18} + 6 q^{21} + 2 q^{25} - 2 q^{26} - 2 q^{32} + 8 q^{33} + 4 q^{34} + 6 q^{36} + 4 q^{49} - 24 q^{50} + 2 q^{52} - 2 q^{53} - 4 q^{64} - 22 q^{66} - 12 q^{68} - 14 q^{69} - 4 q^{72} - 6 q^{77} + 30 q^{81} - 6 q^{84} + 2 q^{89} - 12 q^{98}+O(q^{100}) \) 24 * q - 2 * q^2 + 2 * q^4 + 4 * q^8 - 24 * q^9 + 10 * q^13 + 2 * q^16 + 2 * q^17 + 10 * q^18 + 6 * q^21 + 2 * q^25 - 2 * q^26 - 2 * q^32 + 8 * q^33 + 4 * q^34 + 6 * q^36 + 4 * q^49 - 24 * q^50 + 2 * q^52 - 2 * q^53 - 4 * q^64 - 22 * q^66 - 12 * q^68 - 14 * q^69 - 4 * q^72 - 6 * q^77 + 30 * q^81 - 6 * q^84 + 2 * q^89 - 12 * q^98

Introduction

L-functions

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