LMFDB - Embedded newform 3332.1.cc.c.2923.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3332,1,Mod(135,3332)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3332, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([21, 32, 21])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

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:traces = [24,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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			2923.1
Root			$0.680173 + 0.733052i$ of defining polynomial
Character	$\chi$	$=$	3332.2923
Dual form			3332.1.cc.c.611.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0747301 - 0.997204i) q^{2} +(-0.563320 - 0.173761i) q^{3} +(-0.988831 + 0.149042i) q^{4} +(-0.131178 + 0.574730i) q^{6} +(-0.974928 + 0.222521i) q^{7} +(0.222521 + 0.974928i) q^{8} +(-0.539102 - 0.367554i) q^{9} +(-1.64786 + 1.12349i) q^{11} +(0.582926 + 0.0878620i) q^{12} +(0.134659 + 0.0648483i) q^{13} +(0.294755 + 0.955573i) q^{14} +(0.955573 - 0.294755i) q^{16} +(0.365341 + 0.930874i) q^{17} +(-0.326239 + 0.565062i) q^{18} +(0.587862 + 0.0440542i) q^{21} +(1.24349 + 1.55929i) q^{22} +(0.317031 - 0.807782i) q^{23} +(0.0440542 - 0.587862i) q^{24} +(0.0747301 - 0.997204i) q^{25} +(0.0546039 - 0.139129i) q^{26} +(0.607374 + 0.761623i) q^{27} +(0.930874 - 0.365341i) q^{28} +(0.974928 - 1.68862i) q^{31} +(-0.365341 - 0.930874i) q^{32} +(1.12349 - 0.346551i) q^{33} +(0.900969 - 0.433884i) q^{34} +(0.587862 + 0.283099i) q^{36} +(-0.0645880 - 0.0599289i) q^{39} -0.589510i q^{42} +(1.46200 - 1.35654i) q^{44} +(-0.829215 - 0.255779i) q^{46} -0.589510 q^{48} +(0.900969 - 0.433884i) q^{49} -1.00000 q^{50} +(-0.0440542 - 0.587862i) q^{51} +(-0.142820 - 0.0440542i) q^{52} +(1.44973 - 0.218511i) q^{53} +(0.714104 - 0.662592i) q^{54} +(-0.433884 - 0.900969i) q^{56} +(-1.75676 - 0.846011i) q^{62} +(0.607374 + 0.238377i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(-0.429540 - 1.09445i) q^{66} +(-0.500000 - 0.866025i) q^{68} +(-0.318951 + 0.399952i) q^{69} +(0.848162 + 1.06356i) q^{71} +(0.238377 - 0.607374i) q^{72} +(-0.215372 + 0.548760i) q^{75} +(1.35654 - 1.46200i) q^{77} +(-0.0549346 + 0.0688859i) q^{78} +(0.563320 + 0.975699i) q^{79} +(0.0285713 + 0.0727985i) q^{81} +(-0.587862 + 0.0440542i) q^{84} +(-1.46200 - 1.35654i) q^{88} +(-1.57906 - 1.07659i) q^{89} +(-0.145713 - 0.0332580i) q^{91} +(-0.193096 + 0.846011i) q^{92} +(-0.842614 + 0.781831i) q^{93} +(0.0440542 + 0.587862i) q^{96} +(-0.500000 - 0.866025i) q^{98} +1.30131 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

Character values

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

$n$	$785$	$885$	$1667$
$\chi(n)$	$-1$	$e\left(\frac{2}{21}\right)$	$-1$

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 $

$2$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i
$2$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i
$3$	−0.563320	−	0.173761i	−0.563320	−	0.173761i		−	1.00000i	$-0.5\pi$
$3$	−0.563320	−	0.173761i	−0.563320	−	0.173761i	−0.563320	+	0.826239i	$0.690476\pi$
$4$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$5$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$5$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$6$	−0.131178	+	0.574730i	−0.131178	+	0.574730i
$7$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$7$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$8$	0.222521	+	0.974928i	0.222521	+	0.974928i
$9$	−0.539102	−	0.367554i	−0.539102	−	0.367554i
$10$		0			0
$11$	−1.64786	+	1.12349i	−1.64786	+	1.12349i	−0.781831	+	0.623490i	$0.785714\pi$
$11$	−1.64786	+	1.12349i	−1.64786	+	1.12349i	−0.866025	+	0.500000i	$0.833333\pi$
$12$	0.582926	+	0.0878620i	0.582926	+	0.0878620i
$13$	0.134659	+	0.0648483i	0.134659	+	0.0648483i	0.500000	−	0.866025i	$-0.333333\pi$
$13$	0.134659	+	0.0648483i	0.134659	+	0.0648483i	−0.365341	+	0.930874i	$0.619048\pi$
$14$	0.294755	+	0.955573i	0.294755	+	0.955573i
$15$		0			0
$16$	0.955573	−	0.294755i	0.955573	−	0.294755i
$17$	0.365341	+	0.930874i	0.365341	+	0.930874i
$17$	0.365341	+	0.930874i	0.365341	+	0.930874i
$18$	−0.326239	+	0.565062i	−0.326239	+	0.565062i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$		0			0
$21$	0.587862	+	0.0440542i	0.587862	+	0.0440542i
$22$	1.24349	+	1.55929i	1.24349	+	1.55929i
$23$	0.317031	−	0.807782i	0.317031	−	0.807782i	−0.680173	−	0.733052i	$-0.738095\pi$
$23$	0.317031	−	0.807782i	0.317031	−	0.807782i	0.997204	−	0.0747301i	$-0.0238095\pi$
$24$	0.0440542	−	0.587862i	0.0440542	−	0.587862i
$25$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$26$	0.0546039	−	0.139129i	0.0546039	−	0.139129i
$27$	0.607374	+	0.761623i	0.607374	+	0.761623i
$28$	0.930874	−	0.365341i	0.930874	−	0.365341i
$29$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$29$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$30$		0			0
$31$	0.974928	−	1.68862i	0.974928	−	1.68862i	0.294755	−	0.955573i	$-0.404762\pi$
$31$	0.974928	−	1.68862i	0.974928	−	1.68862i	0.680173	−	0.733052i	$-0.261905\pi$
$32$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$33$	1.12349	−	0.346551i	1.12349	−	0.346551i
$34$	0.900969	−	0.433884i	0.900969	−	0.433884i
$35$		0			0
$36$	0.587862	+	0.283099i	0.587862	+	0.283099i
$37$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$37$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$38$		0			0
$39$	−0.0645880	−	0.0599289i	−0.0645880	−	0.0599289i
$40$		0			0
$41$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$41$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$42$		−	0.589510i		−	0.589510i
$43$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$43$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$44$	1.46200	−	1.35654i	1.46200	−	1.35654i
$45$		0			0
$46$	−0.829215	−	0.255779i	−0.829215	−	0.255779i
$47$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$47$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$48$	−0.589510			−0.589510
$49$	0.900969	−	0.433884i	0.900969	−	0.433884i
$50$	−1.00000			−1.00000
$51$	−0.0440542	−	0.587862i	−0.0440542	−	0.587862i
$52$	−0.142820	−	0.0440542i	−0.142820	−	0.0440542i
$53$	1.44973	−	0.218511i	1.44973	−	0.218511i	0.623490	−	0.781831i	$-0.285714\pi$
$53$	1.44973	−	0.218511i	1.44973	−	0.218511i	0.826239	+	0.563320i	$0.190476\pi$
$54$	0.714104	−	0.662592i	0.714104	−	0.662592i
$55$		0			0
$56$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$57$		0			0
$58$		0			0
$59$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$59$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$60$		0			0
$61$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$61$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$62$	−1.75676	−	0.846011i	−1.75676	−	0.846011i
$63$	0.607374	+	0.238377i	0.607374	+	0.238377i
$64$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$65$		0			0
$66$	−0.429540	−	1.09445i	−0.429540	−	1.09445i
$67$		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
$69$	−0.318951	+	0.399952i	−0.318951	+	0.399952i
$70$		0			0
$71$	0.848162	+	1.06356i	0.848162	+	1.06356i	0.997204	+	0.0747301i	$0.0238095\pi$
$71$	0.848162	+	1.06356i	0.848162	+	1.06356i	−0.149042	+	0.988831i	$0.547619\pi$
$72$	0.238377	−	0.607374i	0.238377	−	0.607374i
$73$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$73$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$74$		0			0
$75$	−0.215372	+	0.548760i	−0.215372	+	0.548760i
$76$		0			0
$77$	1.35654	−	1.46200i	1.35654	−	1.46200i
$78$	−0.0549346	+	0.0688859i	−0.0549346	+	0.0688859i
$79$	0.563320	+	0.975699i	0.563320	+	0.975699i	0.997204	+	0.0747301i	$0.0238095\pi$
$79$	0.563320	+	0.975699i	0.563320	+	0.975699i	−0.433884	+	0.900969i	$0.642857\pi$
$80$		0			0
$81$	0.0285713	+	0.0727985i	0.0285713	+	0.0727985i
$82$		0			0
$83$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$83$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$84$	−0.587862	+	0.0440542i	−0.587862	+	0.0440542i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−1.46200	−	1.35654i	−1.46200	−	1.35654i
$89$	−1.57906	−	1.07659i	−1.57906	−	1.07659i	−0.955573	−	0.294755i	$-0.904762\pi$
$89$	−1.57906	−	1.07659i	−1.57906	−	1.07659i	−0.623490	−	0.781831i	$-0.714286\pi$
$90$		0			0
$91$	−0.145713	−	0.0332580i	−0.145713	−	0.0332580i
$92$	−0.193096	+	0.846011i	−0.193096	+	0.846011i
$93$	−0.842614	+	0.781831i	−0.842614	+	0.781831i
$94$		0			0
$95$		0			0
$96$	0.0440542	+	0.587862i	0.0440542	+	0.587862i
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$99$	1.30131			1.30131
$100$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$101$	1.72188	+	0.531130i	1.72188	+	0.531130i	0.988831	−	0.149042i	$-0.0476190\pi$
$101$	1.72188	+	0.531130i	1.72188	+	0.531130i	0.733052	+	0.680173i	$0.238095\pi$
$102$	−0.582926	+	0.0878620i	−0.582926	+	0.0878620i
$103$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$103$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$104$	−0.0332580	+	0.145713i	−0.0332580	+	0.145713i
$105$		0			0
$106$	−0.326239	−	1.42935i	−0.326239	−	1.42935i
$107$	−0.246289	−	0.167917i	−0.246289	−	0.167917i	0.433884	−	0.900969i	$-0.357143\pi$
$107$	−0.246289	−	0.167917i	−0.246289	−	0.167917i	−0.680173	+	0.733052i	$0.738095\pi$
$108$	−0.714104	−	0.662592i	−0.714104	−	0.662592i
$109$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$109$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$110$		0			0
$111$		0			0
$112$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$113$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$113$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.0487597	−	0.0844543i	−0.0487597	−	0.0844543i
$118$		0			0
$119$	−0.563320	−	0.826239i	−0.563320	−	0.826239i
$120$		0			0
$121$	1.08786	−	2.77183i	1.08786	−	2.77183i
$122$		0			0
$123$		0			0
$124$	−0.712362	+	1.81507i	−0.712362	+	1.81507i
$125$		0			0
$126$	0.192321	−	0.623490i	0.192321	−	0.623490i
$127$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$127$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$128$	0.500000	+	0.866025i	0.500000	+	0.866025i
$129$		0			0
$130$		0			0
$131$	0.829215	−	0.255779i	0.829215	−	0.255779i	0.149042	−	0.988831i	$-0.452381\pi$
$131$	0.829215	−	0.255779i	0.829215	−	0.255779i	0.680173	+	0.733052i	$0.261905\pi$
$132$	−1.05929	+	0.510127i	−1.05929	+	0.510127i
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$137$	1.40097	+	1.29991i	1.40097	+	1.29991i	0.900969	+	0.433884i	$0.142857\pi$
$137$	1.40097	+	1.29991i	1.40097	+	1.29991i	0.500000	+	0.866025i	$0.333333\pi$
$138$	0.422669	+	0.288171i	0.422669	+	0.288171i
$139$	0.250701	+	1.09839i	0.250701	+	1.09839i	0.930874	+	0.365341i	$0.119048\pi$
$139$	0.250701	+	1.09839i	0.250701	+	1.09839i	−0.680173	+	0.733052i	$0.738095\pi$
$140$		0			0
$141$		0			0
$142$	0.997204	−	0.925270i	0.997204	−	0.925270i
$143$	−0.294755	+	0.0444272i	−0.294755	+	0.0444272i
$144$	−0.623490	−	0.192321i	−0.623490	−	0.192321i
$145$		0			0
$146$		0			0
$147$	−0.582926	+	0.0878620i	−0.582926	+	0.0878620i
$148$		0			0
$149$	0.142820	+	1.90580i	0.142820	+	1.90580i	0.365341	+	0.930874i	$0.380952\pi$
$149$	0.142820	+	1.90580i	0.142820	+	1.90580i	−0.222521	+	0.974928i	$0.571429\pi$
$150$	0.563320	+	0.173761i	0.563320	+	0.173761i
$151$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$151$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$152$		0			0
$153$	0.145190	−	0.636119i	0.145190	−	0.636119i
$154$	−1.55929	−	1.24349i	−1.55929	−	1.24349i
$155$		0			0
$156$	0.0727985	+	0.0496332i	0.0727985	+	0.0496332i
$157$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.988831	−	0.149042i	$-0.952381\pi$
$157$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.222521	−	0.974928i	$-0.571429\pi$
$158$	0.930874	−	0.634659i	0.930874	−	0.634659i
$159$	−0.854630	−	0.128815i	−0.854630	−	0.128815i
$160$		0			0
$161$	−0.129334	+	0.858075i	−0.129334	+	0.858075i
$162$	0.0704598	−	0.0339317i	0.0704598	−	0.0339317i
$163$		0			0		−0.294755	−	0.955573i	$-0.595238\pi$
$163$		0			0		0.294755	+	0.955573i	$0.404762\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.16078	−	1.45557i	1.16078	−	1.45557i	0.294755	−	0.955573i	$-0.404762\pi$
$167$	1.16078	−	1.45557i	1.16078	−	1.45557i	0.866025	−	0.500000i	$-0.166667\pi$
$168$	0.0878620	+	0.582926i	0.0878620	+	0.582926i
$169$	−0.609562	−	0.764367i	−0.609562	−	0.764367i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$173$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$174$		0			0
$175$	0.149042	+	0.988831i	0.149042	+	0.988831i
$176$	−1.24349	+	1.55929i	−1.24349	+	1.55929i
$177$		0			0
$178$	−0.955573	+	1.65510i	−0.955573	+	1.65510i
$179$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$179$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$180$		0			0
$181$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$181$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$182$	−0.0222759	+	0.147791i	−0.0222759	+	0.147791i
$183$		0			0
$184$	0.858075	+	0.129334i	0.858075	+	0.129334i
$185$		0			0
$186$	0.842614	+	0.781831i	0.842614	+	0.781831i
$187$	−1.64786	−	1.12349i	−1.64786	−	1.12349i
$188$		0			0
$189$	−0.761623	−	0.607374i	−0.761623	−	0.607374i
$190$		0			0
$191$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$191$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$192$	0.582926	−	0.0878620i	0.582926	−	0.0878620i
$193$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$193$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$194$		0			0
$195$		0			0
$196$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	−0.0972467	−	1.29767i	−0.0972467	−	1.29767i
$199$	−1.29991	−	0.400969i	−1.29991	−	0.400969i	−0.433884	−	0.900969i	$-0.642857\pi$
$199$	−1.29991	−	0.400969i	−1.29991	−	0.400969i	−0.866025	+	0.500000i	$0.833333\pi$
$200$	0.988831	−	0.149042i	0.988831	−	0.149042i
$201$		0			0
$202$	0.400969	−	1.75676i	0.400969	−	1.75676i
$203$		0			0
$204$	0.131178	+	0.574730i	0.131178	+	0.574730i
$205$		0			0
$206$		0			0
$207$	−0.467815	+	0.318951i	−0.467815	+	0.318951i
$208$	0.147791	+	0.0222759i	0.147791	+	0.0222759i
$209$		0			0
$210$		0			0
$211$	1.40881	−	0.678448i	1.40881	−	0.678448i	0.433884	−	0.900969i	$-0.357143\pi$
$211$	1.40881	−	0.678448i	1.40881	−	0.678448i	0.974928	+	0.222521i	$0.0714286\pi$
$212$	−1.40097	+	0.432142i	−1.40097	+	0.432142i
$213$	−0.292981	−	0.746503i	−0.292981	−	0.746503i
$214$	−0.149042	+	0.258149i	−0.149042	+	0.258149i
$215$		0			0
$216$	−0.607374	+	0.761623i	−0.607374	+	0.761623i
$217$	−0.574730	+	1.86323i	−0.574730	+	1.86323i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.0111692	+	0.149042i	−0.0111692	+	0.149042i
$222$		0			0
$223$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$223$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$224$	0.563320	+	0.826239i	0.563320	+	0.826239i
$225$	−0.406813	+	0.510127i	−0.406813	+	0.510127i
$226$		0			0
$227$	0.680173	−	1.17809i	0.680173	−	1.17809i	−0.294755	−	0.955573i	$-0.595238\pi$
$227$	0.680173	−	1.17809i	0.680173	−	1.17809i	0.974928	−	0.222521i	$-0.0714286\pi$
$228$		0			0
$229$	−1.19158	+	0.367554i	−1.19158	+	0.367554i	−0.826239	−	0.563320i	$-0.809524\pi$
$229$	−1.19158	+	0.367554i	−1.19158	+	0.367554i	−0.365341	+	0.930874i	$0.619048\pi$
$230$		0			0
$231$	−1.01821	+	0.587862i	−1.01821	+	0.587862i
$232$		0			0
$233$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$233$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$234$	−0.0805743	+	0.0549346i	−0.0805743	+	0.0549346i
$235$		0			0
$236$		0			0
$237$	−0.147791	−	0.647514i	−0.147791	−	0.647514i
$238$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$239$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$239$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$240$		0			0
$241$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$241$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$242$	−2.84537	−	0.877681i	−2.84537	−	0.877681i
$243$	−0.0762438	−	1.01740i	−0.0762438	−	1.01740i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$	1.86323	+	0.574730i	1.86323	+	0.574730i
$249$		0			0
$250$		0			0
$251$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$251$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$252$	−0.636119	−	0.145190i	−0.636119	−	0.145190i
$253$	0.385113	+	1.68729i	0.385113	+	1.68729i
$254$		0			0
$255$		0			0
$256$	0.826239	−	0.563320i	0.826239	−	0.563320i
$257$	−0.988831	−	0.149042i	−0.988831	−	0.149042i	−0.365341	−	0.930874i	$-0.619048\pi$
$257$	−0.988831	−	0.149042i	−0.988831	−	0.149042i	−0.623490	+	0.781831i	$0.714286\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.317031	−	0.807782i	−0.317031	−	0.807782i
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$	0.587862	+	1.01821i	0.587862	+	1.01821i
$265$		0			0
$266$		0			0
$267$	0.702449	+	0.880843i	0.702449	+	0.880843i
$268$		0			0
$269$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$269$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$270$		0			0
$271$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$271$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$272$	0.623490	+	0.781831i	0.623490	+	0.781831i
$273$	0.0763040	+	0.0440542i	0.0763040	+	0.0440542i
$274$	1.19158	−	1.49419i	1.19158	−	1.49419i
$275$	0.997204	+	1.72721i	0.997204	+	1.72721i
$276$	0.255779	−	0.443022i	0.255779	−	0.443022i
$277$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$277$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$278$	1.07659	−	0.332083i	1.07659	−	0.332083i
$279$	−1.14625	+	0.552003i	−1.14625	+	0.552003i
$280$		0			0
$281$	0.900969	+	0.433884i	0.900969	+	0.433884i	0.826239	−	0.563320i	$-0.190476\pi$
$281$	0.900969	+	0.433884i	0.900969	+	0.433884i	0.0747301	+	0.997204i	$0.476190\pi$
$282$		0			0
$283$	1.64786	−	1.12349i	1.64786	−	1.12349i	0.781831	−	0.623490i	$-0.214286\pi$
$283$	1.64786	−	1.12349i	1.64786	−	1.12349i	0.866025	−	0.500000i	$-0.166667\pi$
$284$	−0.997204	−	0.925270i	−0.997204	−	0.925270i
$285$		0			0
$286$	0.0663300	+	0.290611i	0.0663300	+	0.290611i
$287$		0			0
$288$	−0.145190	+	0.636119i	−0.145190	+	0.636119i
$289$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.65248			1.65248			0.826239	−	0.563320i	$-0.190476\pi$
$293$	1.65248			1.65248			0.826239	+	0.563320i	$0.190476\pi$
$294$	0.131178	+	0.574730i	0.131178	+	0.574730i
$295$		0			0
$296$		0			0
$297$	−1.85654	−	0.572667i	−1.85654	−	0.572667i
$298$	1.88980	−	0.284841i	1.88980	−	0.284841i
$299$	0.0950744	−	0.0882162i	0.0950744	−	0.0882162i
$300$	0.131178	−	0.574730i	0.131178	−	0.574730i
$301$		0			0
$302$		0			0
$303$	−0.877681	−	0.598393i	−0.877681	−	0.598393i
$304$		0			0
$305$		0			0
$306$	−0.645190	−	0.0972467i	−0.645190	−	0.0972467i
$307$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$307$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$308$	−1.12349	+	1.64786i	−1.12349	+	1.64786i
$309$		0			0
$310$		0			0
$311$	−0.632789	−	1.61232i	−0.632789	−	1.61232i	−0.781831	−	0.623490i	$-0.785714\pi$
$311$	−0.632789	−	1.61232i	−0.632789	−	1.61232i	0.149042	−	0.988831i	$-0.452381\pi$
$312$	0.0440542	−	0.0763040i	0.0440542	−	0.0763040i
$313$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$313$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$314$	−1.03030	+	1.29196i	−1.03030	+	1.29196i
$315$		0			0
$316$	−0.702449	−	0.880843i	−0.702449	−	0.880843i
$317$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$317$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$318$	−0.0645880	+	0.861867i	−0.0645880	+	0.861867i
$319$		0			0
$320$		0			0
$321$	0.109562	+	0.137386i	0.109562	+	0.137386i
$322$	0.865341	+	0.0648483i	0.865341	+	0.0648483i
$323$		0			0
$324$	−0.0391023	−	0.0677271i	−0.0391023	−	0.0677271i
$325$	0.0747301	−	0.129436i	0.0747301	−	0.129436i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$331$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$332$		0			0
$333$		0			0
$334$	−1.53825	−	1.04876i	−1.53825	−	1.04876i
$335$		0			0
$336$	0.574730	−	0.131178i	0.574730	−	0.131178i
$337$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$337$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$338$	−0.716677	+	0.664979i	−0.716677	+	0.664979i
$339$		0			0
$340$		0			0
$341$	0.290611	+	3.87793i	0.290611	+	3.87793i
$342$		0			0
$343$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.54620	−	0.233052i	1.54620	−	0.233052i	0.680173	−	0.733052i	$-0.261905\pi$
$347$	1.54620	−	0.233052i	1.54620	−	0.233052i	0.866025	+	0.500000i	$0.166667\pi$
$348$		0			0
$349$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	0.623490	+	0.781831i	$0.285714\pi$
$349$	−0.277479	+	1.21572i	−0.277479	+	1.21572i	−0.900969	+	0.433884i	$0.857143\pi$
$350$	0.974928	−	0.222521i	0.974928	−	0.222521i
$351$	0.0323984	+	0.141947i	0.0323984	+	0.141947i
$352$	1.64786	+	1.12349i	1.64786	+	1.12349i
$353$	0.733052	+	0.680173i	0.733052	+	0.680173i	0.955573	−	0.294755i	$-0.0952381\pi$
$353$	0.733052	+	0.680173i	0.733052	+	0.680173i	−0.222521	+	0.974928i	$0.571429\pi$
$354$		0			0
$355$		0			0
$356$	1.72188	+	0.829215i	1.72188	+	0.829215i
$357$	0.173761	+	0.563320i	0.173761	+	0.563320i
$358$		0			0
$359$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$359$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$360$		0			0
$361$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$362$		0			0
$363$	−1.09445	+	1.37240i	−1.09445	+	1.37240i
$364$	0.149042	+	0.0111692i	0.149042	+	0.0111692i
$365$		0			0
$366$		0			0
$367$	0.0222759	−	0.297251i	0.0222759	−	0.297251i	−0.974928	−	0.222521i	$-0.928571\pi$
$367$	0.0222759	−	0.297251i	0.0222759	−	0.297251i	0.997204	−	0.0747301i	$-0.0238095\pi$
$368$	0.0648483	−	0.865341i	0.0648483	−	0.865341i
$369$		0			0
$370$		0			0
$371$	−1.36476	+	0.535628i	−1.36476	+	0.535628i
$372$	0.716677	−	0.898684i	0.716677	−	0.898684i
$373$	0.0747301	+	0.129436i	0.0747301	+	0.129436i	0.900969	−	0.433884i	$-0.142857\pi$
$373$	0.0747301	+	0.129436i	0.0747301	+	0.129436i	−0.826239	+	0.563320i	$0.809524\pi$
$374$	−0.997204	+	1.72721i	−0.997204	+	1.72721i
$375$		0			0
$376$		0			0
$377$		0			0
$378$	−0.548760	+	0.804883i	−0.548760	+	0.804883i
$379$	1.56052	+	0.751509i	1.56052	+	0.751509i	0.997204	−	0.0747301i	$-0.0238095\pi$
$379$	1.56052	+	0.751509i	1.56052	+	0.751509i	0.563320	+	0.826239i	$0.309524\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$383$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$384$	−0.131178	−	0.574730i	−0.131178	−	0.574730i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−0.698220	−	0.215372i	−0.698220	−	0.215372i	−0.0747301	−	0.997204i	$-0.523810\pi$
$389$	−0.698220	−	0.215372i	−0.698220	−	0.215372i	−0.623490	+	0.781831i	$0.714286\pi$
$390$		0			0
$391$	0.867767			0.867767
$392$	0.623490	+	0.781831i	0.623490	+	0.781831i
$393$	−0.511558			−0.511558
$394$		0			0
$395$		0			0
$396$	−1.28677	+	0.193950i	−1.28677	+	0.193950i
$397$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$397$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$398$	−0.302705	+	1.32624i	−0.302705	+	1.32624i
$399$		0			0
$400$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$401$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$401$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$402$		0			0
$403$	0.240787	−	0.164166i	0.240787	−	0.164166i
$404$	−1.78181	−	0.268565i	−1.78181	−	0.268565i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.563320	−	0.173761i	0.563320	−	0.173761i
$409$	−0.535628	−	1.36476i	−0.535628	−	1.36476i	−0.900969	−	0.433884i	$-0.857143\pi$
$409$	−0.535628	−	1.36476i	−0.535628	−	1.36476i	0.365341	−	0.930874i	$-0.380952\pi$
$410$		0			0
$411$	−0.563320	−	0.975699i	−0.563320	−	0.975699i
$412$		0			0
$413$		0			0
$414$	0.353019	+	0.442672i	0.353019	+	0.442672i
$415$		0			0
$416$	0.0111692	−	0.149042i	0.0111692	−	0.149042i
$417$	0.0496332	−	0.662309i	0.0496332	−	0.662309i
$418$		0			0
$419$	−0.702449	−	0.880843i	−0.702449	−	0.880843i	0.294755	−	0.955573i	$-0.404762\pi$
$419$	−0.702449	−	0.880843i	−0.702449	−	0.880843i	−0.997204	+	0.0747301i	$0.976190\pi$
$420$		0			0
$421$	0.277479	−	0.347948i	0.277479	−	0.347948i	−0.623490	−	0.781831i	$-0.714286\pi$
$421$	0.277479	−	0.347948i	0.277479	−	0.347948i	0.900969	+	0.433884i	$0.142857\pi$
$422$	−0.781831	−	1.35417i	−0.781831	−	1.35417i
$423$		0			0
$424$	0.535628	+	1.36476i	0.535628	+	1.36476i
$425$	0.955573	−	0.294755i	0.955573	−	0.294755i
$426$	−0.722521	+	0.347948i	−0.722521	+	0.347948i
$427$		0			0
$428$	0.268565	+	0.129334i	0.268565	+	0.129334i
$429$	0.173761	+	0.0261903i	0.173761	+	0.0261903i
$430$		0			0
$431$	1.26968	+	1.17809i	1.26968	+	1.17809i	0.974928	+	0.222521i	$0.0714286\pi$
$431$	1.26968	+	1.17809i	1.26968	+	1.17809i	0.294755	+	0.955573i	$0.404762\pi$
$432$	0.804883	+	0.548760i	0.804883	+	0.548760i
$433$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	−0.623490	−	0.781831i	$-0.714286\pi$
$433$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	0.222521	−	0.974928i	$-0.428571\pi$
$434$	1.90097	+	0.433884i	1.90097	+	0.433884i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	0.0841939	+	1.12349i	0.0841939	+	1.12349i	0.866025	+	0.500000i	$0.166667\pi$
$439$	0.0841939	+	1.12349i	0.0841939	+	1.12349i	−0.781831	+	0.623490i	$0.785714\pi$
$440$		0			0
$441$	−0.645190	−	0.0972467i	−0.645190	−	0.0972467i
$442$	0.149460			0.149460
$443$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$443$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.250701	−	1.09839i	0.250701	−	1.09839i
$448$	0.781831	−	0.623490i	0.781831	−	0.623490i
$449$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$449$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$450$	0.539102	+	0.367554i	0.539102	+	0.367554i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−1.22563	−	0.590232i	−1.22563	−	0.590232i
$455$		0			0
$456$		0			0
$457$	1.72188	−	0.531130i	1.72188	−	0.531130i	0.733052	−	0.680173i	$-0.238095\pi$
$457$	1.72188	−	0.531130i	1.72188	−	0.531130i	0.988831	+	0.149042i	$0.0476190\pi$
$458$	0.455573	+	1.16078i	0.455573	+	1.16078i
$459$	−0.487076	+	0.843641i	−0.487076	+	0.843641i
$460$		0			0
$461$	−0.914101	+	1.14625i	−0.914101	+	1.14625i	0.0747301	+	0.997204i	$0.476190\pi$
$461$	−0.914101	+	1.14625i	−0.914101	+	1.14625i	−0.988831	+	0.149042i	$0.952381\pi$
$462$	0.662309	+	0.971429i	0.662309	+	0.971429i
$463$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$463$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$467$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$468$	0.0608024	+	0.0762438i	0.0608024	+	0.0762438i
$469$		0			0
$470$		0			0
$471$	0.487076	+	0.843641i	0.487076	+	0.843641i
$472$		0			0
$473$		0			0
$474$	−0.634659	+	0.195766i	−0.634659	+	0.195766i
$475$		0			0
$476$	0.680173	+	0.733052i	0.680173	+	0.733052i
$477$	−0.861867	−	0.415053i	−0.861867	−	0.415053i
$478$		0			0
$479$	−0.716983	+	0.488831i	−0.716983	+	0.488831i	−0.866025	−	0.500000i	$-0.833333\pi$
$479$	−0.716983	+	0.488831i	−0.716983	+	0.488831i	0.149042	+	0.988831i	$0.452381\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	0.221957	−	0.460898i	0.221957	−	0.460898i
$484$	−0.662592	+	2.90301i	−0.662592	+	2.90301i
$485$		0			0
$486$	−1.00886	+	0.152061i	−1.00886	+	0.152061i
$487$	1.65510	+	0.510531i	1.65510	+	0.510531i	0.974928	−	0.222521i	$-0.0714286\pi$
$487$	1.65510	+	0.510531i	1.65510	+	0.510531i	0.680173	+	0.733052i	$0.261905\pi$
$488$		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
$496$	0.433884	−	1.90097i	0.433884	−	1.90097i
$497$	−1.06356	−	0.848162i	−1.06356	−	0.848162i
$498$		0			0
$499$	0.930874	+	0.634659i	0.930874	+	0.634659i	0.930874	−	0.365341i	$-0.119048\pi$
$499$	0.930874	+	0.634659i	0.930874	+	0.634659i			1.00000i	$0.5\pi$
$500$		0			0
$501$	−0.906813	+	0.618255i	−0.906813	+	0.618255i
$502$		0			0
$503$	0.268565	+	0.129334i	0.268565	+	0.129334i	0.563320	−	0.826239i	$-0.309524\pi$
$503$	0.268565	+	0.129334i	0.268565	+	0.129334i	−0.294755	+	0.955573i	$0.595238\pi$
$504$	−0.0972467	+	0.645190i	−0.0972467	+	0.645190i
$505$		0			0
$506$	1.65379	−	0.510127i	1.65379	−	0.510127i
$507$	0.210561	+	0.536501i	0.210561	+	0.536501i
$508$		0			0
$509$	0.900969	+	1.56052i	0.900969	+	1.56052i	0.826239	+	0.563320i	$0.190476\pi$
$509$	0.900969	+	1.56052i	0.900969	+	1.56052i	0.0747301	+	0.997204i	$0.476190\pi$
$510$		0			0
$511$		0			0
$512$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$513$		0			0
$514$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$515$		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		0.955573	−	0.294755i	$-0.0952381\pi$
$523$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$524$	−0.781831	+	0.376510i	−0.781831	+	0.376510i
$525$	0.0878620	−	0.582926i	0.0878620	−	0.582926i
$526$		0			0
$527$	1.92808	+	0.290611i	1.92808	+	0.290611i
$528$	0.971429	−	0.662309i	0.971429	−	0.662309i
$529$	0.181049	+	0.167989i	0.181049	+	0.167989i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	0.825886	−	0.766310i	0.825886	−	0.766310i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.997204	+	1.72721i	−0.997204	+	1.72721i
$540$		0			0
$541$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$541$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$542$		0			0
$543$		0			0
$544$	0.733052	−	0.680173i	0.733052	−	0.680173i
$545$		0			0
$546$	0.0382288	−	0.0793829i	0.0382288	−	0.0793829i
$547$	−0.414278	−	1.81507i	−0.414278	−	1.81507i	−0.563320	−	0.826239i	$-0.690476\pi$
$547$	−0.414278	−	1.81507i	−0.414278	−	1.81507i	0.149042	−	0.988831i	$-0.452381\pi$
$548$	−1.57906	−	1.07659i	−1.57906	−	1.07659i
$549$		0			0
$550$	1.64786	−	1.12349i	1.64786	−	1.12349i
$551$		0			0
$552$	−0.460898	−	0.221957i	−0.460898	−	0.221957i
$553$	−0.766310	−	0.825886i	−0.766310	−	0.825886i
$554$		0			0
$555$		0			0
$556$	−0.411608	−	1.04876i	−0.411608	−	1.04876i
$557$	−0.733052	+	1.26968i	−0.733052	+	1.26968i	0.222521	+	0.974928i	$0.428571\pi$
$557$	−0.733052	+	1.26968i	−0.733052	+	1.26968i	−0.955573	+	0.294755i	$0.904762\pi$
$558$	0.636119	+	1.10179i	0.636119	+	1.10179i
$559$		0			0
$560$		0			0
$561$	0.733052	+	0.919218i	0.733052	+	0.919218i
$562$	0.365341	−	0.930874i	0.365341	−	0.930874i
$563$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$563$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$564$		0			0
$565$		0			0
$566$	−1.24349	−	1.55929i	−1.24349	−	1.55929i
$567$	−0.0440542	−	0.0646156i	−0.0440542	−	0.0646156i
$568$	−0.848162	+	1.06356i	−0.848162	+	1.06356i
$569$	−0.0747301	−	0.129436i	−0.0747301	−	0.129436i	0.826239	−	0.563320i	$-0.190476\pi$
$569$	−0.0747301	−	0.129436i	−0.0747301	−	0.129436i	−0.900969	+	0.433884i	$0.857143\pi$
$570$		0			0
$571$	−0.712362	−	1.81507i	−0.712362	−	1.81507i	−0.563320	−	0.826239i	$-0.690476\pi$
$571$	−0.712362	−	1.81507i	−0.712362	−	1.81507i	−0.149042	−	0.988831i	$-0.547619\pi$
$572$	0.284841	−	0.0878620i	0.284841	−	0.0878620i
$573$		0			0
$574$		0			0
$575$	−0.781831	−	0.376510i	−0.781831	−	0.376510i
$576$	0.645190	+	0.0972467i	0.645190	+	0.0972467i
$577$	1.63402	−	1.11406i	1.63402	−	1.11406i	0.733052	−	0.680173i	$-0.238095\pi$
$577$	1.63402	−	1.11406i	1.63402	−	1.11406i	0.900969	−	0.433884i	$-0.142857\pi$
$578$	0.733052	+	0.680173i	0.733052	+	0.680173i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−2.14345	+	1.98883i	−2.14345	+	1.98883i
$584$		0			0
$585$		0			0
$586$	−0.123490	−	1.64786i	−0.123490	−	1.64786i
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$	0.563320	−	0.173761i	0.563320	−	0.173761i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.44973	−	1.34515i	1.44973	−	1.34515i	0.623490	−	0.781831i	$-0.285714\pi$
$593$	1.44973	−	1.34515i	1.44973	−	1.34515i	0.826239	−	0.563320i	$-0.190476\pi$
$594$	−0.432326	+	1.89415i	−0.432326	+	1.89415i
$595$		0			0
$596$	−0.425270	−	1.86323i	−0.425270	−	1.86323i
$597$	0.662592	+	0.451748i	0.662592	+	0.451748i
$598$	−0.0950744	−	0.0882162i	−0.0950744	−	0.0882162i
$599$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$599$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$600$	−0.582926	−	0.0878620i	−0.582926	−	0.0878620i
$601$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$601$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$	−0.531130	+	0.919945i	−0.531130	+	0.919945i
$607$	−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
$612$	−0.0487597	+	0.650653i	−0.0487597	+	0.650653i
$613$	0.0546039	−	0.728639i	0.0546039	−	0.728639i	−0.900969	−	0.433884i	$-0.857143\pi$
$613$	0.0546039	−	0.728639i	0.0546039	−	0.728639i	0.955573	−	0.294755i	$-0.0952381\pi$
$614$		0			0
$615$		0			0
$616$	1.72721	+	0.997204i	1.72721	+	0.997204i
$617$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$617$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$618$		0			0
$619$	0.866025	−	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
$621$	0.807782	−	0.249168i	0.807782	−	0.249168i
$622$	−1.56052	+	0.751509i	−1.56052	+	0.751509i
$623$	1.77904	+	0.698220i	1.77904	+	0.698220i
$624$	−0.0793829	−	0.0382288i	−0.0793829	−	0.0382288i
$625$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$626$		0			0
$627$		0			0
$628$	1.36534	+	0.930874i	1.36534	+	0.930874i
$629$		0			0
$630$		0			0
$631$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$631$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$632$	−0.825886	+	0.766310i	−0.825886	+	0.766310i
$633$	−0.911500	+	0.137386i	−0.911500	+	0.137386i
$634$		0			0
$635$		0			0
$636$	0.864283			0.864283
$637$	0.149460			0.149460
$638$		0			0
$639$	−0.0663300	−	0.885113i	−0.0663300	−	0.885113i
$640$		0			0
$641$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$641$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$642$	0.128815	−	0.119523i	0.128815	−	0.119523i
$643$	−0.414278	+	1.81507i	−0.414278	+	1.81507i	0.149042	+	0.988831i	$0.452381\pi$
$643$	−0.414278	+	1.81507i	−0.414278	+	1.81507i	−0.563320	+	0.826239i	$0.690476\pi$
$644$		−	0.867767i		−	0.867767i
$645$		0			0
$646$		0			0
$647$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$647$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$648$	−0.0646156	+	0.0440542i	−0.0646156	+	0.0440542i
$649$		0			0
$650$	−0.134659	−	0.0648483i	−0.134659	−	0.0648483i
$651$	0.647514	−	0.949729i	0.647514	−	0.949729i
$652$		0			0
$653$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$653$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$659$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$660$		0			0
$661$	−0.0332580	+	0.443797i	−0.0332580	+	0.443797i	0.955573	+	0.294755i	$0.0952381\pi$
$661$	−0.0332580	+	0.443797i	−0.0332580	+	0.443797i	−0.988831	+	0.149042i	$0.952381\pi$
$662$		0			0
$663$	0.0321896	−	0.0820177i	0.0321896	−	0.0820177i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−0.930874	+	1.61232i	−0.930874	+	1.61232i
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−0.173761	−	0.563320i	−0.173761	−	0.563320i
$673$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$673$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$674$		0			0
$675$	0.804883	−	0.548760i	0.804883	−	0.548760i
$676$	0.716677	+	0.664979i	0.716677	+	0.664979i
$677$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$677$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.587862	+	0.545456i	−0.587862	+	0.545456i
$682$	3.84537	−	0.579597i	3.84537	−	0.579597i
$683$	−1.29991	−	0.400969i	−1.29991	−	0.400969i	−0.433884	−	0.900969i	$-0.642857\pi$
$683$	−1.29991	−	0.400969i	−1.29991	−	0.400969i	−0.866025	+	0.500000i	$0.833333\pi$
$684$		0			0
$685$		0			0
$686$	0.680173	+	0.733052i	0.680173	+	0.733052i
$687$	0.735107			0.735107
$688$		0			0
$689$	0.209389	+	0.0645880i	0.209389	+	0.0645880i
$690$		0			0
$691$	−1.42935	+	1.32624i	−1.42935	+	1.32624i	−0.563320	+	0.826239i	$0.690476\pi$
$691$	−1.42935	+	1.32624i	−1.42935	+	1.32624i	−0.866025	+	0.500000i	$0.833333\pi$
$692$		0			0
$693$	−1.26868	+	0.289568i	−1.26868	+	0.289568i
$694$	−0.347948	−	1.52446i	−0.347948	−	1.52446i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	1.23305	+	0.185853i	1.23305	+	0.185853i
$699$		0			0
$700$	−0.294755	−	0.955573i	−0.294755	−	0.955573i
$701$	−1.32091	+	0.636119i	−1.32091	+	0.636119i	−0.955573	−	0.294755i	$-0.904762\pi$
$701$	−1.32091	+	0.636119i	−1.32091	+	0.636119i	−0.365341	+	0.930874i	$0.619048\pi$
$702$	0.139129	−	0.0429155i	0.139129	−	0.0429155i
$703$		0			0
$704$	0.997204	−	1.72721i	0.997204	−	1.72721i
$705$		0			0
$706$	0.623490	−	0.781831i	0.623490	−	0.781831i
$707$	−1.79690	−	0.134659i	−1.79690	−	0.134659i
$708$		0			0
$709$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$709$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$710$		0			0
$711$	0.0549346	−	0.733052i	0.0549346	−	0.733052i
$712$	0.698220	−	1.77904i	0.698220	−	1.77904i
$713$	−1.05496	−	1.32288i	−1.05496	−	1.32288i
$714$	0.548760	−	0.215372i	0.548760	−	0.215372i
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.90580	+	0.587862i	−1.90580	+	0.587862i	−0.930874	+	0.365341i	$0.880952\pi$
$719$	−1.90580	+	0.587862i	−1.90580	+	0.587862i	−0.974928	+	0.222521i	$0.928571\pi$
$720$		0			0
$721$		0			0
$722$	0.900969	+	0.433884i	0.900969	+	0.433884i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	1.45035	+	0.988831i	1.45035	+	0.988831i
$727$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$727$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$728$		−	0.149460i		−	0.149460i
$729$	−0.116433	+	0.510127i	−0.116433	+	0.510127i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i	−0.900969	−	0.433884i	$-0.857143\pi$
$733$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i	0.826239	−	0.563320i	$-0.190476\pi$
$734$	−0.298085			−0.298085
$735$		0			0
$736$	−0.867767			−0.867767
$737$		0			0
$738$		0			0
$739$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$739$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$740$		0			0
$741$		0			0
$742$	0.636119	+	1.32091i	0.636119	+	1.32091i
$743$	−0.131178	−	0.574730i	−0.131178	−	0.574730i	−0.997204	−	0.0747301i	$-0.976190\pi$
$743$	−0.131178	−	0.574730i	−0.131178	−	0.574730i	0.866025	−	0.500000i	$-0.166667\pi$
$744$	−0.949729	−	0.647514i	−0.949729	−	0.647514i
$745$		0			0
$746$	0.123490	−	0.0841939i	0.123490	−	0.0841939i
$747$		0			0
$748$	1.79690	+	0.865341i	1.79690	+	0.865341i
$749$	0.277479	+	0.108903i	0.277479	+	0.108903i
$750$		0			0
$751$	1.07659	−	0.332083i	1.07659	−	0.332083i	0.294755	−	0.955573i	$-0.404762\pi$
$751$	1.07659	−	0.332083i	1.07659	−	0.332083i	0.781831	+	0.623490i	$0.214286\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$	0.843641	+	0.487076i	0.843641	+	0.487076i
$757$	0.623490	+	0.781831i	0.623490	+	0.781831i	0.988831	−	0.149042i	$-0.0476190\pi$
$757$	0.623490	+	0.781831i	0.623490	+	0.781831i	−0.365341	+	0.930874i	$0.619048\pi$
$758$	0.632789	−	1.61232i	0.632789	−	1.61232i
$759$	0.0762438	−	1.01740i	0.0762438	−	1.01740i
$760$		0			0
$761$	−0.266948	+	0.680173i	−0.266948	+	0.680173i	0.733052	+	0.680173i	$0.238095\pi$
$761$	−0.266948	+	0.680173i	−0.266948	+	0.680173i	−1.00000			$\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.563320	+	0.173761i	−0.563320	+	0.173761i
$769$	−0.900969	+	0.433884i	−0.900969	+	0.433884i	−0.826239	−	0.563320i	$-0.809524\pi$
$769$	−0.900969	+	0.433884i	−0.900969	+	0.433884i	−0.0747301	+	0.997204i	$0.523810\pi$
$770$		0			0
$771$	0.531130	+	0.255779i	0.531130	+	0.255779i
$772$		0			0
$773$	−0.603718	+	0.411608i	−0.603718	+	0.411608i	−0.826239	−	0.563320i	$-0.809524\pi$
$773$	−0.603718	+	0.411608i	−0.603718	+	0.411608i	0.222521	+	0.974928i	$0.428571\pi$
$774$		0			0
$775$	−1.61105	−	1.09839i	−1.61105	−	1.09839i
$776$		0			0
$777$		0			0
$778$	−0.162592	+	0.712362i	−0.162592	+	0.712362i
$779$		0			0
$780$		0			0
$781$	−2.59255	−	0.799695i	−2.59255	−	0.799695i
$782$	−0.0648483	−	0.865341i	−0.0648483	−	0.865341i
$783$		0			0
$784$	0.733052	−	0.680173i	0.733052	−	0.680173i
$785$		0			0
$786$	0.0382288	+	0.510127i	0.0382288	+	0.510127i
$787$	−1.49419	−	0.460898i	−1.49419	−	0.460898i	−0.563320	−	0.826239i	$-0.690476\pi$
$787$	−1.49419	−	0.460898i	−1.49419	−	0.460898i	−0.930874	+	0.365341i	$0.880952\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.289568	+	1.26868i	0.289568	+	1.26868i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	1.34515	+	0.202749i	1.34515	+	0.202749i
$797$	1.32091	+	0.636119i	1.32091	+	0.636119i	0.955573	−	0.294755i	$-0.0952381\pi$
$797$	1.32091	+	0.636119i	1.32091	+	0.636119i	0.365341	+	0.930874i	$0.380952\pi$
$798$		0			0
$799$		0			0
$800$	−0.955573	+	0.294755i	−0.955573	+	0.294755i
$801$	0.455573	+	1.16078i	0.455573	+	1.16078i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−0.181701	−	0.227846i	−0.181701	−	0.227846i
$807$		0			0
$808$	−0.134659	+	1.79690i	−0.134659	+	1.79690i
$809$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$809$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$810$		0			0
$811$	0.848162	+	1.06356i	0.848162	+	1.06356i	0.997204	+	0.0747301i	$0.0238095\pi$
$811$	0.848162	+	1.06356i	0.848162	+	1.06356i	−0.149042	+	0.988831i	$0.547619\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.215372	−	0.548760i	−0.215372	−	0.548760i
$817$		0			0
$818$	−1.32091	+	0.636119i	−1.32091	+	0.636119i
$819$	0.0663300	+	0.0714868i	0.0663300	+	0.0714868i
$820$		0			0
$821$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$821$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$822$	−0.930874	+	0.634659i	−0.930874	+	0.634659i
$823$	0.432142	+	0.400969i	0.432142	+	0.400969i	0.866025	−	0.500000i	$-0.166667\pi$
$823$	0.432142	+	0.400969i	0.432142	+	0.400969i	−0.433884	+	0.900969i	$0.642857\pi$
$824$		0			0
$825$	−0.261623	−	1.14625i	−0.261623	−	1.14625i
$826$		0			0
$827$	−0.0663300	+	0.290611i	−0.0663300	+	0.290611i	−0.997204	−	0.0747301i	$-0.976190\pi$
$827$	−0.0663300	+	0.290611i	−0.0663300	+	0.290611i	0.930874	+	0.365341i	$0.119048\pi$
$828$	0.415053	−	0.385113i	0.415053	−	0.385113i
$829$	1.95557	−	0.294755i	1.95557	−	0.294755i	0.955573	−	0.294755i	$-0.0952381\pi$
$829$	1.95557	−	0.294755i	1.95557	−	0.294755i	1.00000			$0$
$830$		0			0
$831$		0			0
$832$	−0.149460			−0.149460
$833$	0.733052	+	0.680173i	0.733052	+	0.680173i
$834$	−0.664166			−0.664166
$835$		0			0
$836$		0			0
$837$	1.87824	−	0.283099i	1.87824	−	0.283099i
$838$	−0.825886	+	0.766310i	−0.825886	+	0.766310i
$839$	0.347948	−	1.52446i	0.347948	−	1.52446i	−0.433884	−	0.900969i	$-0.642857\pi$
$839$	0.347948	−	1.52446i	0.347948	−	1.52446i	0.781831	−	0.623490i	$-0.214286\pi$
$840$		0			0
$841$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$842$	−0.367711	−	0.250701i	−0.367711	−	0.250701i
$843$	−0.432142	−	0.400969i	−0.432142	−	0.400969i
$844$	−1.29196	+	0.880843i	−1.29196	+	0.880843i
$845$		0			0
$846$		0			0
$847$	−0.443797	+	2.94440i	−0.443797	+	2.94440i
$848$	1.32091	−	0.636119i	1.32091	−	0.636119i
$849$	−1.12349	+	0.346551i	−1.12349	+	0.346551i
$850$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$851$		0			0
$852$	0.400969	+	0.694498i	0.400969	+	0.694498i
$853$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$853$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$854$		0			0
$855$		0			0
$856$	0.108903	−	0.277479i	0.108903	−	0.277479i
$857$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$857$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$858$	0.0131319	−	0.175233i	0.0131319	−	0.175233i
$859$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$859$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$860$		0			0
$861$		0			0
$862$	1.07992	−	1.35417i	1.07992	−	1.35417i
$863$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$863$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$864$	0.487076	−	0.843641i	0.487076	−	0.843641i
$865$		0			0
$866$	−1.72188	+	0.531130i	−1.72188	+	0.531130i
$867$	0.531130	−	0.255779i	0.531130	−	0.255779i
$868$	0.290611	−	1.92808i	0.290611	−	1.92808i
$869$	−2.02446	−	0.974928i	−2.02446	−	0.974928i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$877$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$878$	1.11406	−	0.167917i	1.11406	−	0.167917i
$879$	−0.930874	−	0.287137i	−0.930874	−	0.287137i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−0.0487597	+	0.650653i	−0.0487597	+	0.650653i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$	−0.0111692	−	0.149042i	−0.0111692	−	0.149042i
$885$		0			0
$886$		0			0
$887$	1.46200	−	1.35654i	1.46200	−	1.35654i	0.680173	−	0.733052i	$-0.261905\pi$
$887$	1.46200	−	1.35654i	1.46200	−	1.35654i	0.781831	−	0.623490i	$-0.214286\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.128870	−	0.0878620i	−0.128870	−	0.0878620i
$892$		0			0
$893$		0			0
$894$	−1.11406	−	0.167917i	−1.11406	−	0.167917i
$895$		0			0
$896$	−0.680173	−	0.733052i	−0.680173	−	0.733052i
$897$	−0.0688859	+	0.0331737i	−0.0688859	+	0.0331737i
$898$		0			0
$899$		0			0
$900$	0.326239	−	0.565062i	0.326239	−	0.565062i
$901$	0.733052	+	1.26968i	0.733052	+	1.26968i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.145713	+	1.94440i	−0.145713	+	1.94440i	0.149042	+	0.988831i	$0.452381\pi$
$907$	−0.145713	+	1.94440i	−0.145713	+	1.94440i	−0.294755	+	0.955573i	$0.595238\pi$
$908$	−0.496990	+	1.26631i	−0.496990	+	1.26631i
$909$	−0.733052	−	0.919218i	−0.733052	−	0.919218i
$910$		0			0
$911$	−0.541044	+	0.678448i	−0.541044	+	0.678448i	−0.974928	−	0.222521i	$-0.928571\pi$
$911$	−0.541044	+	0.678448i	−0.541044	+	0.678448i	0.433884	+	0.900969i	$0.357143\pi$
$912$		0			0
$913$		0			0
$914$	−0.658322	−	1.67738i	−0.658322	−	1.67738i
$915$		0			0
$916$	1.12349	−	0.541044i	1.12349	−	0.541044i
$917$	−0.751509	+	0.433884i	−0.751509	+	0.433884i
$918$	0.877681	+	0.422669i	0.877681	+	0.422669i
$919$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$919$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$920$		0			0
$921$		0			0
$922$	1.21135	+	0.825886i	1.21135	+	0.825886i
$923$	0.0452424	+	0.198220i	0.0452424	+	0.198220i
$924$	0.919218	−	0.733052i	0.919218	−	0.733052i
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$929$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	0.0763040	+	1.01821i	0.0763040	+	1.01821i
$934$		0			0
$935$		0			0
$936$	0.0714868	−	0.0663300i	0.0714868	−	0.0663300i
$937$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	−0.900969	−	0.433884i	$-0.857143\pi$
$937$	0.0990311	−	0.433884i	0.0990311	−	0.433884i	1.00000			$0$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$941$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$942$	0.804883	−	0.548760i	0.804883	−	0.548760i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.65510	+	0.510531i	−1.65510	+	0.510531i	−0.974928	−	0.222521i	$-0.928571\pi$
$947$	−1.65510	+	0.510531i	−1.65510	+	0.510531i	−0.680173	+	0.733052i	$0.738095\pi$
$948$	0.242647	+	0.618255i	0.242647	+	0.618255i
$949$		0			0
$950$		0			0
$951$		0			0
$952$	0.680173	−	0.733052i	0.680173	−	0.733052i
$953$	−0.455573	−	0.571270i	−0.455573	−	0.571270i	0.500000	−	0.866025i	$-0.333333\pi$
$953$	−0.455573	−	0.571270i	−0.455573	−	0.571270i	−0.955573	+	0.294755i	$0.904762\pi$
$954$	−0.349485	+	0.890474i	−0.349485	+	0.890474i
$955$		0			0
$956$		0			0
$957$		0			0
$958$	0.541044	+	0.678448i	0.541044	+	0.678448i
$959$	−1.65510	−	0.955573i	−1.65510	−	0.955573i
$960$		0			0
$961$	−1.40097	−	2.42655i	−1.40097	−	2.42655i
$962$		0			0
$963$	0.0710564	+	0.181049i	0.0710564	+	0.181049i
$964$		0			0
$965$		0			0
$966$	−0.476196	−	0.186893i	−0.476196	−	0.186893i
$967$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$967$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$968$	2.94440	+	0.443797i	2.94440	+	0.443797i
$969$		0			0
$970$		0			0
$971$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$971$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$972$	0.227028	+	0.994675i	0.227028	+	0.994675i
$973$	−0.488831	−	1.01507i	−0.488831	−	1.01507i
$974$	0.385418	−	1.68862i	0.385418	−	1.68862i
$975$	−0.0645880	+	0.0599289i	−0.0645880	+	0.0599289i
$976$		0			0
$977$	−1.72188	−	0.531130i	−1.72188	−	0.531130i	−0.733052	−	0.680173i	$-0.761905\pi$
$977$	−1.72188	−	0.531130i	−1.72188	−	0.531130i	−0.988831	+	0.149042i	$0.952381\pi$
$978$		0			0
$979$	3.81160			3.81160
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.90580	+	0.587862i	1.90580	+	0.587862i	0.974928	+	0.222521i	$0.0714286\pi$
$983$	1.90580	+	0.587862i	1.90580	+	0.587862i	0.930874	+	0.365341i	$0.119048\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	1.53825	−	1.04876i	1.53825	−	1.04876i	0.563320	−	0.826239i	$-0.309524\pi$
$991$	1.53825	−	1.04876i	1.53825	−	1.04876i	0.974928	−	0.222521i	$-0.0714286\pi$
$992$	−1.92808	−	0.290611i	−1.92808	−	0.290611i
$993$		0			0
$994$	−0.766310	+	1.12397i	−0.766310	+	1.12397i
$995$		0			0
$996$		0			0
$997$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$997$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$998$	0.563320	−	0.975699i	0.563320	−	0.975699i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3332.1.cc.c.2923.1	yes	24
4.3	odd	2	inner	3332.1.cc.c.2923.2	yes	24
17.16	even	2	inner	3332.1.cc.c.2923.2	yes	24
49.23	even	21	inner	3332.1.cc.c.611.1	✓	24
68.67	odd	2	CM	3332.1.cc.c.2923.1	yes	24
196.23	odd	42	inner	3332.1.cc.c.611.2	yes	24
833.611	even	42	inner	3332.1.cc.c.611.2	yes	24
3332.611	odd	42	inner	3332.1.cc.c.611.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3332.1.cc.c.611.1	✓	24	49.23	even	21	inner
3332.1.cc.c.611.1	✓	24	3332.611	odd	42	inner
3332.1.cc.c.611.2	yes	24	196.23	odd	42	inner
3332.1.cc.c.611.2	yes	24	833.611	even	42	inner
3332.1.cc.c.2923.1	yes	24	1.1	even	1	trivial
3332.1.cc.c.2923.1	yes	24	68.67	odd	2	CM
3332.1.cc.c.2923.2	yes	24	4.3	odd	2	inner
3332.1.cc.c.2923.2	yes	24	17.16	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.0747301 - 0.997204i) q^{2} +(-0.563320 - 0.173761i) q^{3} +(-0.988831 + 0.149042i) q^{4} +(-0.131178 + 0.574730i) q^{6} +(-0.974928 + 0.222521i) q^{7} +(0.222521 + 0.974928i) q^{8} +(-0.539102 - 0.367554i) q^{9} +(-1.64786 + 1.12349i) q^{11} +(0.582926 + 0.0878620i) q^{12} +(0.134659 + 0.0648483i) q^{13} +(0.294755 + 0.955573i) q^{14} +(0.955573 - 0.294755i) q^{16} +(0.365341 + 0.930874i) q^{17} +(-0.326239 + 0.565062i) q^{18} +(0.587862 + 0.0440542i) q^{21} +(1.24349 + 1.55929i) q^{22} +(0.317031 - 0.807782i) q^{23} +(0.0440542 - 0.587862i) q^{24} +(0.0747301 - 0.997204i) q^{25} +(0.0546039 - 0.139129i) q^{26} +(0.607374 + 0.761623i) q^{27} +(0.930874 - 0.365341i) q^{28} +(0.974928 - 1.68862i) q^{31} +(-0.365341 - 0.930874i) q^{32} +(1.12349 - 0.346551i) q^{33} +(0.900969 - 0.433884i) q^{34} +(0.587862 + 0.283099i) q^{36} +(-0.0645880 - 0.0599289i) q^{39} -0.589510i q^{42} +(1.46200 - 1.35654i) q^{44} +(-0.829215 - 0.255779i) q^{46} -0.589510 q^{48} +(0.900969 - 0.433884i) q^{49} -1.00000 q^{50} +(-0.0440542 - 0.587862i) q^{51} +(-0.142820 - 0.0440542i) q^{52} +(1.44973 - 0.218511i) q^{53} +(0.714104 - 0.662592i) q^{54} +(-0.433884 - 0.900969i) q^{56} +(-1.75676 - 0.846011i) q^{62} +(0.607374 + 0.238377i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(-0.429540 - 1.09445i) q^{66} +(-0.500000 - 0.866025i) q^{68} +(-0.318951 + 0.399952i) q^{69} +(0.848162 + 1.06356i) q^{71} +(0.238377 - 0.607374i) q^{72} +(-0.215372 + 0.548760i) q^{75} +(1.35654 - 1.46200i) q^{77} +(-0.0549346 + 0.0688859i) q^{78} +(0.563320 + 0.975699i) q^{79} +(0.0285713 + 0.0727985i) q^{81} +(-0.587862 + 0.0440542i) q^{84} +(-1.46200 - 1.35654i) q^{88} +(-1.57906 - 1.07659i) q^{89} +(-0.145713 - 0.0332580i) q^{91} +(-0.193096 + 0.846011i) q^{92} +(-0.842614 + 0.781831i) q^{93} +(0.0440542 + 0.587862i) q^{96} +(-0.500000 - 0.866025i) q^{98} +1.30131 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 2 q^{4} + 4 q^{8} - 24 q^{9} + 10 q^{13} + 2 q^{16} + 2 q^{17} + 10 q^{18} + 6 q^{21} + 2 q^{25} - 2 q^{26} - 2 q^{32} + 8 q^{33} + 4 q^{34} + 6 q^{36} + 4 q^{49} - 24 q^{50} + 2 q^{52}+ \cdots - 12 q^{98}+O(q^{100}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more