LMFDB - Embedded newform 3332.1.cc.b.1087.1

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 = [12,1,13] 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:	$12$
Coefficient field:	$\Q(\zeta_{21})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + x^{9} - x^{8} + x^{6} - x^{4} + x^{3} - x + 1 $ x^12 - x^11 + x^9 - x^8 + x^6 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{21}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{21} + \cdots)$

Embedding invariants

Embedding label			1087.1
Root			$0.826239 + 0.563320i$ of defining polynomial
Character	$\chi$	$=$	3332.1087
Dual form			3332.1.cc.b.1971.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.733052 - 0.680173i) q^{2} +(1.95557 + 0.294755i) q^{3} +(0.0747301 + 0.997204i) q^{4} +(-1.23305 - 1.54620i) q^{6} +(0.623490 - 0.781831i) q^{7} +(0.623490 - 0.781831i) q^{8} +(2.78181 + 0.858075i) q^{9} +(-1.40097 + 0.432142i) q^{11} +(-0.147791 + 1.97213i) q^{12} +(0.326239 - 1.42935i) q^{13} +(-0.988831 + 0.149042i) q^{14} +(-0.988831 + 0.149042i) q^{16} +(0.826239 + 0.563320i) q^{17} +(-1.45557 - 2.52113i) q^{18} +(1.44973 - 1.34515i) q^{21} +(1.32091 + 0.636119i) q^{22} +(-0.367711 + 0.250701i) q^{23} +(1.44973 - 1.34515i) q^{24} +(-0.733052 + 0.680173i) q^{25} +(-1.21135 + 0.825886i) q^{26} +(3.40530 + 1.63991i) q^{27} +(0.826239 + 0.563320i) q^{28} +(-0.623490 - 1.07992i) q^{31} +(0.826239 + 0.563320i) q^{32} +(-2.86707 + 0.432142i) q^{33} +(-0.222521 - 0.974928i) q^{34} +(-0.647791 + 2.83816i) q^{36} +(1.05929 - 2.69903i) q^{39} -1.97766 q^{42} +(-0.535628 - 1.36476i) q^{44} +(0.440071 + 0.0663300i) q^{46} -1.97766 q^{48} +(-0.222521 - 0.974928i) q^{49} +1.00000 q^{50} +(1.44973 + 1.34515i) q^{51} +(1.44973 + 0.218511i) q^{52} +(0.0546039 + 0.728639i) q^{53} +(-1.38084 - 3.51833i) q^{54} +(-0.222521 - 0.974928i) q^{56} +(-0.277479 + 1.21572i) q^{62} +(2.40530 - 1.63991i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(2.39564 + 1.63332i) q^{66} +(-0.500000 + 0.866025i) q^{68} +(-0.792981 + 0.381879i) q^{69} +(-0.658322 - 0.317031i) q^{71} +(2.40530 - 1.63991i) q^{72} +(-1.63402 + 1.11406i) q^{75} +(-0.535628 + 1.36476i) q^{77} +(-2.61232 + 1.25803i) q^{78} +(-0.955573 + 1.65510i) q^{79} +(3.77064 + 2.57078i) q^{81} +(1.44973 + 1.34515i) q^{84} +(-0.535628 + 1.36476i) q^{88} +(-1.88980 - 0.582926i) q^{89} +(-0.914101 - 1.14625i) q^{91} +(-0.277479 - 0.347948i) q^{92} +(-0.900969 - 2.29563i) q^{93} +(1.44973 + 1.34515i) q^{96} +(-0.500000 + 0.866025i) q^{98} -4.26804 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} + 13 q^{3} + q^{4} - 5 q^{6} - 2 q^{7} - 2 q^{8} + 14 q^{9} - 8 q^{11} - q^{12} - 5 q^{13} + q^{14} + q^{16} + q^{17} - 7 q^{18} - q^{21} + 2 q^{22} + 2 q^{23} - q^{24} + q^{25} - q^{26}+ \cdots - 14 q^{99}+O(q^{100}) $ 12 * q + q^2 + 13 * q^3 + q^4 - 5 * q^6 - 2 * q^7 - 2 * q^8 + 14 * q^9 - 8 * q^11 - q^12 - 5 * q^13 + q^14 + q^16 + q^17 - 7 * q^18 - q^21 + 2 * q^22 + 2 * q^23 - q^24 + q^25 - q^26 + 12 * q^27 + q^28 + 2 * q^31 + q^32 - 6 * q^33 - 2 * q^34 - 7 * q^36 - 6 * q^39 + 2 * q^42 - q^44 + 2 * q^46 + 2 * q^48 - 2 * q^49 + 12 * q^50 - q^51 - q^52 - q^53 - 6 * q^54 - 2 * q^56 - 4 * q^62 - 2 * q^64 + 15 * q^66 - 6 * q^68 - 3 * q^69 + 2 * q^71 - q^75 - q^77 - 9 * q^78 - q^79 + 13 * q^81 - q^84 - q^88 - q^89 + 2 * q^91 - 4 * q^92 - 2 * q^93 - q^96 - 6 * q^98 - 14 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$2$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$3$	1.95557	+	0.294755i	1.95557	+	0.294755i	1.00000			$0$
$3$	1.95557	+	0.294755i	1.95557	+	0.294755i	0.955573	+	0.294755i	$0.0952381\pi$
$4$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$5$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$5$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$6$	−1.23305	−	1.54620i	−1.23305	−	1.54620i
$7$	0.623490	−	0.781831i	0.623490	−	0.781831i
$7$	0.623490	−	0.781831i	0.623490	−	0.781831i
$8$	0.623490	−	0.781831i	0.623490	−	0.781831i
$9$	2.78181	+	0.858075i	2.78181	+	0.858075i
$10$		0			0
$11$	−1.40097	+	0.432142i	−1.40097	+	0.432142i	−0.900969	−	0.433884i	$-0.857143\pi$
$11$	−1.40097	+	0.432142i	−1.40097	+	0.432142i	−0.500000	+	0.866025i	$0.666667\pi$
$12$	−0.147791	+	1.97213i	−0.147791	+	1.97213i
$13$	0.326239	−	1.42935i	0.326239	−	1.42935i	−0.500000	−	0.866025i	$-0.666667\pi$
$13$	0.326239	−	1.42935i	0.326239	−	1.42935i	0.826239	−	0.563320i	$-0.190476\pi$
$14$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$15$		0			0
$16$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$17$	0.826239	+	0.563320i	0.826239	+	0.563320i
$17$	0.826239	+	0.563320i	0.826239	+	0.563320i
$18$	−1.45557	−	2.52113i	−1.45557	−	2.52113i
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$		0			0
$21$	1.44973	−	1.34515i	1.44973	−	1.34515i
$22$	1.32091	+	0.636119i	1.32091	+	0.636119i
$23$	−0.367711	+	0.250701i	−0.367711	+	0.250701i	−0.733052	−	0.680173i	$-0.761905\pi$
$23$	−0.367711	+	0.250701i	−0.367711	+	0.250701i	0.365341	+	0.930874i	$0.380952\pi$
$24$	1.44973	−	1.34515i	1.44973	−	1.34515i
$25$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$26$	−1.21135	+	0.825886i	−1.21135	+	0.825886i
$27$	3.40530	+	1.63991i	3.40530	+	1.63991i
$28$	0.826239	+	0.563320i	0.826239	+	0.563320i
$29$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$29$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$30$		0			0
$31$	−0.623490	−	1.07992i	−0.623490	−	1.07992i	−0.988831	−	0.149042i	$-0.952381\pi$
$31$	−0.623490	−	1.07992i	−0.623490	−	1.07992i	0.365341	−	0.930874i	$-0.380952\pi$
$32$	0.826239	+	0.563320i	0.826239	+	0.563320i
$33$	−2.86707	+	0.432142i	−2.86707	+	0.432142i
$34$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$35$		0			0
$36$	−0.647791	+	2.83816i	−0.647791	+	2.83816i
$37$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$37$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$38$		0			0
$39$	1.05929	−	2.69903i	1.05929	−	2.69903i
$40$		0			0
$41$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$41$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$42$	−1.97766			−1.97766
$43$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$43$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$44$	−0.535628	−	1.36476i	−0.535628	−	1.36476i
$45$		0			0
$46$	0.440071	+	0.0663300i	0.440071	+	0.0663300i
$47$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$47$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$48$	−1.97766			−1.97766
$49$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$50$	1.00000			1.00000
$51$	1.44973	+	1.34515i	1.44973	+	1.34515i
$52$	1.44973	+	0.218511i	1.44973	+	0.218511i
$53$	0.0546039	+	0.728639i	0.0546039	+	0.728639i	0.955573	+	0.294755i	$0.0952381\pi$
$53$	0.0546039	+	0.728639i	0.0546039	+	0.728639i	−0.900969	+	0.433884i	$0.857143\pi$
$54$	−1.38084	−	3.51833i	−1.38084	−	3.51833i
$55$		0			0
$56$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$57$		0			0
$58$		0			0
$59$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$59$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$60$		0			0
$61$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$61$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$62$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$63$	2.40530	−	1.63991i	2.40530	−	1.63991i
$64$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$65$		0			0
$66$	2.39564	+	1.63332i	2.39564	+	1.63332i
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$69$	−0.792981	+	0.381879i	−0.792981	+	0.381879i
$70$		0			0
$71$	−0.658322	−	0.317031i	−0.658322	−	0.317031i	0.0747301	−	0.997204i	$-0.476190\pi$
$71$	−0.658322	−	0.317031i	−0.658322	−	0.317031i	−0.733052	+	0.680173i	$0.761905\pi$
$72$	2.40530	−	1.63991i	2.40530	−	1.63991i
$73$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$73$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$74$		0			0
$75$	−1.63402	+	1.11406i	−1.63402	+	1.11406i
$76$		0			0
$77$	−0.535628	+	1.36476i	−0.535628	+	1.36476i
$78$	−2.61232	+	1.25803i	−2.61232	+	1.25803i
$79$	−0.955573	+	1.65510i	−0.955573	+	1.65510i	−0.222521	+	0.974928i	$0.571429\pi$
$79$	−0.955573	+	1.65510i	−0.955573	+	1.65510i	−0.733052	+	0.680173i	$0.761905\pi$
$80$		0			0
$81$	3.77064	+	2.57078i	3.77064	+	2.57078i
$82$		0			0
$83$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$83$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$84$	1.44973	+	1.34515i	1.44973	+	1.34515i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−0.535628	+	1.36476i	−0.535628	+	1.36476i
$89$	−1.88980	−	0.582926i	−1.88980	−	0.582926i	−0.988831	−	0.149042i	$-0.952381\pi$
$89$	−1.88980	−	0.582926i	−1.88980	−	0.582926i	−0.900969	−	0.433884i	$-0.857143\pi$
$90$		0			0
$91$	−0.914101	−	1.14625i	−0.914101	−	1.14625i
$92$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$93$	−0.900969	−	2.29563i	−0.900969	−	2.29563i
$94$		0			0
$95$		0			0
$96$	1.44973	+	1.34515i	1.44973	+	1.34515i
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$99$	−4.26804			−4.26804
$100$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$101$	0.440071	+	0.0663300i	0.440071	+	0.0663300i	0.365341	−	0.930874i	$-0.380952\pi$
$101$	0.440071	+	0.0663300i	0.440071	+	0.0663300i	0.0747301	+	0.997204i	$0.476190\pi$
$102$	−0.147791	−	1.97213i	−0.147791	−	1.97213i
$103$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$103$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$104$	−0.914101	−	1.14625i	−0.914101	−	1.14625i
$105$		0			0
$106$	0.455573	−	0.571270i	0.455573	−	0.571270i
$107$	0.142820	+	0.0440542i	0.142820	+	0.0440542i	0.365341	−	0.930874i	$-0.380952\pi$
$107$	0.142820	+	0.0440542i	0.142820	+	0.0440542i	−0.222521	+	0.974928i	$0.571429\pi$
$108$	−1.38084	+	3.51833i	−1.38084	+	3.51833i
$109$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$109$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$110$		0			0
$111$		0			0
$112$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$113$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$113$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	2.13402	−	3.69623i	2.13402	−	3.69623i
$118$		0			0
$119$	0.955573	−	0.294755i	0.955573	−	0.294755i
$120$		0			0
$121$	0.949729	−	0.647514i	0.949729	−	0.647514i
$122$		0			0
$123$		0			0
$124$	1.03030	−	0.702449i	1.03030	−	0.702449i
$125$		0			0
$126$	−2.87863	−	0.433884i	−2.87863	−	0.433884i
$127$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$127$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$128$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$129$		0			0
$130$		0			0
$131$	0.440071	−	0.0663300i	0.440071	−	0.0663300i	0.0747301	−	0.997204i	$-0.476190\pi$
$131$	0.440071	−	0.0663300i	0.440071	−	0.0663300i	0.365341	+	0.930874i	$0.380952\pi$
$132$	−0.645190	−	2.82676i	−0.645190	−	2.82676i
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.955573	−	0.294755i	0.955573	−	0.294755i
$137$	−0.722521	+	1.84095i	−0.722521	+	1.84095i	−0.222521	+	0.974928i	$0.571429\pi$
$137$	−0.722521	+	1.84095i	−0.722521	+	1.84095i	−0.500000	+	0.866025i	$0.666667\pi$
$138$	0.841040	+	0.259426i	0.841040	+	0.259426i
$139$	1.19158	−	1.49419i	1.19158	−	1.49419i	0.365341	−	0.930874i	$-0.380952\pi$
$139$	1.19158	−	1.49419i	1.19158	−	1.49419i	0.826239	−	0.563320i	$-0.190476\pi$
$140$		0			0
$141$		0			0
$142$	0.266948	+	0.680173i	0.266948	+	0.680173i
$143$	0.160629	+	2.14345i	0.160629	+	2.14345i
$144$	−2.87863	−	0.433884i	−2.87863	−	0.433884i
$145$		0			0
$146$		0			0
$147$	−0.147791	−	1.97213i	−0.147791	−	1.97213i
$148$		0			0
$149$	1.44973	+	1.34515i	1.44973	+	1.34515i	0.826239	+	0.563320i	$0.190476\pi$
$149$	1.44973	+	1.34515i	1.44973	+	1.34515i	0.623490	+	0.781831i	$0.285714\pi$
$150$	1.95557	+	0.294755i	1.95557	+	0.294755i
$151$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$151$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$152$		0			0
$153$	1.81507	+	2.27603i	1.81507	+	2.27603i
$154$	1.32091	−	0.636119i	1.32091	−	0.636119i
$155$		0			0
$156$	2.77064	+	0.854630i	2.77064	+	0.854630i
$157$	0.698220	−	1.77904i	0.698220	−	1.77904i	0.0747301	−	0.997204i	$-0.476190\pi$
$157$	0.698220	−	1.77904i	0.698220	−	1.77904i	0.623490	−	0.781831i	$-0.285714\pi$
$158$	1.82624	−	0.563320i	1.82624	−	0.563320i
$159$	−0.107988	+	1.44100i	−0.107988	+	1.44100i
$160$		0			0
$161$	−0.0332580	+	0.443797i	−0.0332580	+	0.443797i
$162$	−1.01550	−	4.44920i	−1.01550	−	4.44920i
$163$	−1.97766	+	0.298085i	−1.97766	+	0.298085i	−0.988831	+	0.149042i	$0.952381\pi$
$163$	−1.97766	+	0.298085i	−1.97766	+	0.298085i	−0.988831	+	0.149042i	$0.952381\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.48883	+	0.716983i	−1.48883	+	0.716983i	−0.988831	−	0.149042i	$-0.952381\pi$
$167$	−1.48883	+	0.716983i	−1.48883	+	0.716983i	−0.500000	+	0.866025i	$0.666667\pi$
$168$	−0.147791	−	1.97213i	−0.147791	−	1.97213i
$169$	−1.03563	−	0.498732i	−1.03563	−	0.498732i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$173$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$174$		0			0
$175$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$176$	1.32091	−	0.636119i	1.32091	−	0.636119i
$177$		0			0
$178$	0.988831	+	1.71271i	0.988831	+	1.71271i
$179$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$179$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$180$		0			0
$181$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$181$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$182$	−0.109562	+	1.46200i	−0.109562	+	1.46200i
$183$		0			0
$184$	−0.0332580	+	0.443797i	−0.0332580	+	0.443797i
$185$		0			0
$186$	−0.900969	+	2.29563i	−0.900969	+	2.29563i
$187$	−1.40097	−	0.432142i	−1.40097	−	0.432142i
$188$		0			0
$189$	3.40530	−	1.63991i	3.40530	−	1.63991i
$190$		0			0
$191$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$191$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$192$	−0.147791	−	1.97213i	−0.147791	−	1.97213i
$193$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$193$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$194$		0			0
$195$		0			0
$196$	0.955573	−	0.294755i	0.955573	−	0.294755i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	3.12870	+	2.90301i	3.12870	+	2.90301i
$199$	−0.722521	−	0.108903i	−0.722521	−	0.108903i	−0.222521	−	0.974928i	$-0.571429\pi$
$199$	−0.722521	−	0.108903i	−0.722521	−	0.108903i	−0.500000	+	0.866025i	$0.666667\pi$
$200$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$201$		0			0
$202$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$203$		0			0
$204$	−1.23305	+	1.54620i	−1.23305	+	1.54620i
$205$		0			0
$206$		0			0
$207$	−1.23802	+	0.381879i	−1.23802	+	0.381879i
$208$	−0.109562	+	1.46200i	−0.109562	+	1.46200i
$209$		0			0
$210$		0			0
$211$	0.400969	+	1.75676i	0.400969	+	1.75676i	0.623490	+	0.781831i	$0.285714\pi$
$211$	0.400969	+	1.75676i	0.400969	+	1.75676i	−0.222521	+	0.974928i	$0.571429\pi$
$212$	−0.722521	+	0.108903i	−0.722521	+	0.108903i
$213$	−1.19395	−	0.814021i	−1.19395	−	0.814021i
$214$	−0.0747301	−	0.129436i	−0.0747301	−	0.129436i
$215$		0			0
$216$	3.40530	−	1.63991i	3.40530	−	1.63991i
$217$	−1.23305	−	0.185853i	−1.23305	−	0.185853i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.07473	−	0.997204i	1.07473	−	0.997204i
$222$		0			0
$223$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$223$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$224$	0.955573	−	0.294755i	0.955573	−	0.294755i
$225$	−2.62285	+	1.26310i	−2.62285	+	1.26310i
$226$		0			0
$227$	−0.365341	−	0.632789i	−0.365341	−	0.632789i	0.623490	−	0.781831i	$-0.285714\pi$
$227$	−0.365341	−	0.632789i	−0.365341	−	0.632789i	−0.988831	+	0.149042i	$0.952381\pi$
$228$		0			0
$229$	1.78181	−	0.268565i	1.78181	−	0.268565i	0.826239	−	0.563320i	$-0.190476\pi$
$229$	1.78181	−	0.268565i	1.78181	−	0.268565i	0.955573	+	0.294755i	$0.0952381\pi$
$230$		0			0
$231$	−1.44973	+	2.51100i	−1.44973	+	2.51100i
$232$		0			0
$233$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$233$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$234$	−4.07842	+	1.25803i	−4.07842	+	1.25803i
$235$		0			0
$236$		0			0
$237$	−2.35654	+	2.95501i	−2.35654	+	2.95501i
$238$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$239$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$239$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$240$		0			0
$241$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$241$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$242$	−1.13662	−	0.171318i	−1.13662	−	0.171318i
$243$	3.84537	+	3.56798i	3.84537	+	3.56798i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−1.23305	−	0.185853i	−1.23305	−	0.185853i
$249$		0			0
$250$		0			0
$251$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$251$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$252$	1.81507	+	2.27603i	1.81507	+	2.27603i
$253$	0.406813	−	0.510127i	0.406813	−	0.510127i
$254$		0			0
$255$		0			0
$256$	0.955573	−	0.294755i	0.955573	−	0.294755i
$257$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i	0.826239	+	0.563320i	$0.190476\pi$
$257$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i	−0.900969	+	0.433884i	$0.857143\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.367711	−	0.250701i	−0.367711	−	0.250701i
$263$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$263$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$264$	−1.44973	+	2.51100i	−1.44973	+	2.51100i
$265$		0			0
$266$		0			0
$267$	−3.52382	−	1.69698i	−3.52382	−	1.69698i
$268$		0			0
$269$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$269$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$270$		0			0
$271$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$271$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$272$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$273$	−1.44973	−	2.51100i	−1.44973	−	2.51100i
$274$	1.78181	−	0.858075i	1.78181	−	0.858075i
$275$	0.733052	−	1.26968i	0.733052	−	1.26968i
$276$	−0.440071	−	0.762226i	−0.440071	−	0.762226i
$277$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$277$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$278$	−1.88980	+	0.284841i	−1.88980	+	0.284841i
$279$	−0.807782	−	3.53912i	−0.807782	−	3.53912i
$280$		0			0
$281$	0.222521	−	0.974928i	0.222521	−	0.974928i	−0.733052	−	0.680173i	$-0.761905\pi$
$281$	0.222521	−	0.974928i	0.222521	−	0.974928i	0.955573	−	0.294755i	$-0.0952381\pi$
$282$		0			0
$283$	−1.40097	+	0.432142i	−1.40097	+	0.432142i	−0.900969	−	0.433884i	$-0.857143\pi$
$283$	−1.40097	+	0.432142i	−1.40097	+	0.432142i	−0.500000	+	0.866025i	$0.666667\pi$
$284$	0.266948	−	0.680173i	0.266948	−	0.680173i
$285$		0			0
$286$	1.34017	−	1.68052i	1.34017	−	1.68052i
$287$		0			0
$288$	1.81507	+	2.27603i	1.81507	+	2.27603i
$289$	0.365341	+	0.930874i	0.365341	+	0.930874i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.91115			1.91115			0.955573	−	0.294755i	$-0.0952381\pi$
$293$	1.91115			1.91115			0.955573	+	0.294755i	$0.0952381\pi$
$294$	−1.23305	+	1.54620i	−1.23305	+	1.54620i
$295$		0			0
$296$		0			0
$297$	−5.47939	−	0.825886i	−5.47939	−	0.825886i
$298$	−0.147791	−	1.97213i	−0.147791	−	1.97213i
$299$	0.238377	+	0.607374i	0.238377	+	0.607374i
$300$	−1.23305	−	1.54620i	−1.23305	−	1.54620i
$301$		0			0
$302$		0			0
$303$	0.841040	+	0.259426i	0.841040	+	0.259426i
$304$		0			0
$305$		0			0
$306$	0.217550	−	2.90301i	0.217550	−	2.90301i
$307$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$307$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$308$	−1.40097	−	0.432142i	−1.40097	−	0.432142i
$309$		0			0
$310$		0			0
$311$	−0.826239	−	0.563320i	−0.826239	−	0.563320i	0.0747301	−	0.997204i	$-0.476190\pi$
$311$	−0.826239	−	0.563320i	−0.826239	−	0.563320i	−0.900969	+	0.433884i	$0.857143\pi$
$312$	−1.44973	−	2.51100i	−1.44973	−	2.51100i
$313$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$313$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$314$	−1.72188	+	0.829215i	−1.72188	+	0.829215i
$315$		0			0
$316$	−1.72188	−	0.829215i	−1.72188	−	0.829215i
$317$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$317$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$318$	1.05929	−	0.982878i	1.05929	−	0.982878i
$319$		0			0
$320$		0			0
$321$	0.266310	+	0.128248i	0.266310	+	0.128248i
$322$	0.326239	−	0.302705i	0.326239	−	0.302705i
$323$		0			0
$324$	−2.28181	+	3.95221i	−2.28181	+	3.95221i
$325$	0.733052	+	1.26968i	0.733052	+	1.26968i
$326$	1.65248	+	1.12664i	1.65248	+	1.12664i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$331$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$332$		0			0
$333$		0			0
$334$	1.57906	+	0.487076i	1.57906	+	0.487076i
$335$		0			0
$336$	−1.23305	+	1.54620i	−1.23305	+	1.54620i
$337$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$337$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$338$	0.419945	+	1.07000i	0.419945	+	1.07000i
$339$		0			0
$340$		0			0
$341$	1.34017	+	1.24349i	1.34017	+	1.24349i
$342$		0			0
$343$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−0.134659	−	1.79690i	−0.134659	−	1.79690i	−0.500000	−	0.866025i	$-0.666667\pi$
$347$	−0.134659	−	1.79690i	−0.134659	−	1.79690i	0.365341	−	0.930874i	$-0.380952\pi$
$348$		0			0
$349$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$349$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$350$	0.623490	−	0.781831i	0.623490	−	0.781831i
$351$	3.45493	−	4.33235i	3.45493	−	4.33235i
$352$	−1.40097	−	0.432142i	−1.40097	−	0.432142i
$353$	−0.365341	+	0.930874i	−0.365341	+	0.930874i	0.623490	+	0.781831i	$0.285714\pi$
$353$	−0.365341	+	0.930874i	−0.365341	+	0.930874i	−0.988831	+	0.149042i	$0.952381\pi$
$354$		0			0
$355$		0			0
$356$	0.440071	−	1.92808i	0.440071	−	1.92808i
$357$	1.95557	−	0.294755i	1.95557	−	0.294755i
$358$		0			0
$359$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$359$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$360$		0			0
$361$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$362$		0			0
$363$	2.04812	−	0.986323i	2.04812	−	0.986323i
$364$	1.07473	−	0.997204i	1.07473	−	0.997204i
$365$		0			0
$366$		0			0
$367$	−0.109562	+	0.101659i	−0.109562	+	0.101659i	−0.733052	−	0.680173i	$-0.761905\pi$
$367$	−0.109562	+	0.101659i	−0.109562	+	0.101659i	0.623490	+	0.781831i	$0.285714\pi$
$368$	0.326239	−	0.302705i	0.326239	−	0.302705i
$369$		0			0
$370$		0			0
$371$	0.603718	+	0.411608i	0.603718	+	0.411608i
$372$	2.22188	−	1.07000i	2.22188	−	1.07000i
$373$	0.733052	−	1.26968i	0.733052	−	1.26968i	−0.222521	−	0.974928i	$-0.571429\pi$
$373$	0.733052	−	1.26968i	0.733052	−	1.26968i	0.955573	−	0.294755i	$-0.0952381\pi$
$374$	0.733052	+	1.26968i	0.733052	+	1.26968i
$375$		0			0
$376$		0			0
$377$		0			0
$378$	−3.61168	−	1.11406i	−3.61168	−	1.11406i
$379$	0.222521	−	0.974928i	0.222521	−	0.974928i	−0.733052	−	0.680173i	$-0.761905\pi$
$379$	0.222521	−	0.974928i	0.222521	−	0.974928i	0.955573	−	0.294755i	$-0.0952381\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$383$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$384$	−1.23305	+	1.54620i	−1.23305	+	1.54620i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.63402	−	0.246289i	−1.63402	−	0.246289i	−0.733052	−	0.680173i	$-0.761905\pi$
$389$	−1.63402	−	0.246289i	−1.63402	−	0.246289i	−0.900969	+	0.433884i	$0.857143\pi$
$390$		0			0
$391$	−0.445042			−0.445042
$392$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$393$	0.880142			0.880142
$394$		0			0
$395$		0			0
$396$	−0.318951	−	4.25611i	−0.318951	−	4.25611i
$397$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$397$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$398$	0.455573	+	0.571270i	0.455573	+	0.571270i
$399$		0			0
$400$	0.623490	−	0.781831i	0.623490	−	0.781831i
$401$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$401$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$402$		0			0
$403$	−1.74698	+	0.538872i	−1.74698	+	0.538872i
$404$	−0.0332580	+	0.443797i	−0.0332580	+	0.443797i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	1.95557	−	0.294755i	1.95557	−	0.294755i
$409$	0.603718	+	0.411608i	0.603718	+	0.411608i	0.826239	−	0.563320i	$-0.190476\pi$
$409$	0.603718	+	0.411608i	0.603718	+	0.411608i	−0.222521	+	0.974928i	$0.571429\pi$
$410$		0			0
$411$	−1.95557	+	3.38715i	−1.95557	+	3.38715i
$412$		0			0
$413$		0			0
$414$	1.16728	+	0.562132i	1.16728	+	0.562132i
$415$		0			0
$416$	1.07473	−	0.997204i	1.07473	−	0.997204i
$417$	2.77064	−	2.57078i	2.77064	−	2.57078i
$418$		0			0
$419$	−1.72188	−	0.829215i	−1.72188	−	0.829215i	−0.988831	−	0.149042i	$-0.952381\pi$
$419$	−1.72188	−	0.829215i	−1.72188	−	0.829215i	−0.733052	−	0.680173i	$-0.761905\pi$
$420$		0			0
$421$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.900969	−	0.433884i	$-0.857143\pi$
$421$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$422$	0.900969	−	1.56052i	0.900969	−	1.56052i
$423$		0			0
$424$	0.603718	+	0.411608i	0.603718	+	0.411608i
$425$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$426$	0.321552	+	1.40881i	0.321552	+	1.40881i
$427$		0			0
$428$	−0.0332580	+	0.145713i	−0.0332580	+	0.145713i
$429$	−0.317671	+	4.23902i	−0.317671	+	4.23902i
$430$		0			0
$431$	−0.365341	+	0.930874i	−0.365341	+	0.930874i	0.623490	+	0.781831i	$0.285714\pi$
$431$	−0.365341	+	0.930874i	−0.365341	+	0.930874i	−0.988831	+	0.149042i	$0.952381\pi$
$432$	−3.61168	−	1.11406i	−3.61168	−	1.11406i
$433$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	−0.900969	−	0.433884i	$-0.857143\pi$
$433$	−0.277479	+	0.347948i	−0.277479	+	0.347948i	0.623490	+	0.781831i	$0.285714\pi$
$434$	0.777479	+	0.974928i	0.777479	+	0.974928i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−1.40097	−	1.29991i	−1.40097	−	1.29991i	−0.900969	−	0.433884i	$-0.857143\pi$
$439$	−1.40097	−	1.29991i	−1.40097	−	1.29991i	−0.500000	−	0.866025i	$-0.666667\pi$
$440$		0			0
$441$	0.217550	−	2.90301i	0.217550	−	2.90301i
$442$	−1.46610			−1.46610
$443$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$443$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	2.43856	+	3.05786i	2.43856	+	3.05786i
$448$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$449$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$449$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$450$	2.78181	+	0.858075i	2.78181	+	0.858075i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−0.162592	+	0.712362i	−0.162592	+	0.712362i
$455$		0			0
$456$		0			0
$457$	0.440071	−	0.0663300i	0.440071	−	0.0663300i	0.0747301	−	0.997204i	$-0.476190\pi$
$457$	0.440071	−	0.0663300i	0.440071	−	0.0663300i	0.365341	+	0.930874i	$0.380952\pi$
$458$	−1.48883	−	1.01507i	−1.48883	−	1.01507i
$459$	1.88980	+	3.27323i	1.88980	+	3.27323i
$460$		0			0
$461$	−0.658322	+	0.317031i	−0.658322	+	0.317031i	−0.733052	−	0.680173i	$-0.761905\pi$
$461$	−0.658322	+	0.317031i	−0.658322	+	0.317031i	0.0747301	+	0.997204i	$0.476190\pi$
$462$	2.77064	−	0.854630i	2.77064	−	0.854630i
$463$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$463$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$467$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$468$	3.84537	+	1.85183i	3.84537	+	1.85183i
$469$		0			0
$470$		0			0
$471$	1.88980	−	3.27323i	1.88980	−	3.27323i
$472$		0			0
$473$		0			0
$474$	3.73738	−	0.563320i	3.73738	−	0.563320i
$475$		0			0
$476$	0.365341	+	0.930874i	0.365341	+	0.930874i
$477$	−0.473329	+	2.07379i	−0.473329	+	2.07379i
$478$		0			0
$479$	−0.425270	+	0.131178i	−0.425270	+	0.131178i	−0.500000	−	0.866025i	$-0.666667\pi$
$479$	−0.425270	+	0.131178i	−0.425270	+	0.131178i	0.0747301	+	0.997204i	$0.476190\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−0.195850	+	0.858075i	−0.195850	+	0.858075i
$484$	0.716677	+	0.898684i	0.716677	+	0.898684i
$485$		0			0
$486$	−0.392012	−	5.23104i	−0.392012	−	5.23104i
$487$	0.988831	+	0.149042i	0.988831	+	0.149042i	0.623490	−	0.781831i	$-0.285714\pi$
$487$	0.988831	+	0.149042i	0.988831	+	0.149042i	0.365341	+	0.930874i	$0.380952\pi$
$488$		0			0
$489$	−3.95532			−3.95532
$490$		0			0
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.777479	+	0.974928i	0.777479	+	0.974928i
$497$	−0.658322	+	0.317031i	−0.658322	+	0.317031i
$498$		0			0
$499$	1.82624	+	0.563320i	1.82624	+	0.563320i	1.00000			$0$
$499$	1.82624	+	0.563320i	1.82624	+	0.563320i	0.826239	+	0.563320i	$0.190476\pi$
$500$		0			0
$501$	−3.12285	+	0.963272i	−3.12285	+	0.963272i
$502$		0			0
$503$	−0.0332580	+	0.145713i	−0.0332580	+	0.145713i	−0.988831	−	0.149042i	$-0.952381\pi$
$503$	−0.0332580	+	0.145713i	−0.0332580	+	0.145713i	0.955573	+	0.294755i	$0.0952381\pi$
$504$	0.217550	−	2.90301i	0.217550	−	2.90301i
$505$		0			0
$506$	−0.645190	+	0.0972467i	−0.645190	+	0.0972467i
$507$	−1.87824	−	1.28056i	−1.87824	−	1.28056i
$508$		0			0
$509$	0.222521	−	0.385418i	0.222521	−	0.385418i	−0.733052	−	0.680173i	$-0.761905\pi$
$509$	0.222521	−	0.385418i	0.222521	−	0.385418i	0.955573	+	0.294755i	$0.0952381\pi$
$510$		0			0
$511$		0			0
$512$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$513$		0			0
$514$	0.733052	−	0.680173i	0.733052	−	0.680173i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$521$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$522$		0			0
$523$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$523$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$524$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$525$	−0.147791	+	1.97213i	−0.147791	+	1.97213i
$526$		0			0
$527$	0.0931869	−	1.24349i	0.0931869	−	1.24349i
$528$	2.77064	−	0.854630i	2.77064	−	0.854630i
$529$	−0.292981	+	0.746503i	−0.292981	+	0.746503i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	1.42890	+	3.64078i	1.42890	+	3.64078i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.733052	+	1.26968i	0.733052	+	1.26968i
$540$		0			0
$541$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$541$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$542$		0			0
$543$		0			0
$544$	0.365341	+	0.930874i	0.365341	+	0.930874i
$545$		0			0
$546$	−0.645190	+	2.82676i	−0.645190	+	2.82676i
$547$	1.03030	−	1.29196i	1.03030	−	1.29196i	0.0747301	−	0.997204i	$-0.476190\pi$
$547$	1.03030	−	1.29196i	1.03030	−	1.29196i	0.955573	−	0.294755i	$-0.0952381\pi$
$548$	−1.88980	−	0.582926i	−1.88980	−	0.582926i
$549$		0			0
$550$	−1.40097	+	0.432142i	−1.40097	+	0.432142i
$551$		0			0
$552$	−0.195850	+	0.858075i	−0.195850	+	0.858075i
$553$	0.698220	+	1.77904i	0.698220	+	1.77904i
$554$		0			0
$555$		0			0
$556$	1.57906	+	1.07659i	1.57906	+	1.07659i
$557$	−0.365341	−	0.632789i	−0.365341	−	0.632789i	0.623490	−	0.781831i	$-0.285714\pi$
$557$	−0.365341	−	0.632789i	−0.365341	−	0.632789i	−0.988831	+	0.149042i	$0.952381\pi$
$558$	−1.81507	+	3.14379i	−1.81507	+	3.14379i
$559$		0			0
$560$		0			0
$561$	−2.61232	−	1.25803i	−2.61232	−	1.25803i
$562$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$563$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$563$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$564$		0			0
$565$		0			0
$566$	1.32091	+	0.636119i	1.32091	+	0.636119i
$567$	4.36087	−	1.34515i	4.36087	−	1.34515i
$568$	−0.658322	+	0.317031i	−0.658322	+	0.317031i
$569$	0.733052	−	1.26968i	0.733052	−	1.26968i	−0.222521	−	0.974928i	$-0.571429\pi$
$569$	0.733052	−	1.26968i	0.733052	−	1.26968i	0.955573	−	0.294755i	$-0.0952381\pi$
$570$		0			0
$571$	1.03030	+	0.702449i	1.03030	+	0.702449i	0.955573	−	0.294755i	$-0.0952381\pi$
$571$	1.03030	+	0.702449i	1.03030	+	0.702449i	0.0747301	+	0.997204i	$0.476190\pi$
$572$	−2.12545	+	0.320360i	−2.12545	+	0.320360i
$573$		0			0
$574$		0			0
$575$	0.0990311	−	0.433884i	0.0990311	−	0.433884i
$576$	0.217550	−	2.90301i	0.217550	−	2.90301i
$577$	0.142820	−	0.0440542i	0.142820	−	0.0440542i	−0.222521	−	0.974928i	$-0.571429\pi$
$577$	0.142820	−	0.0440542i	0.142820	−	0.0440542i	0.365341	+	0.930874i	$0.380952\pi$
$578$	0.365341	−	0.930874i	0.365341	−	0.930874i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.391374	−	0.997204i	−0.391374	−	0.997204i
$584$		0			0
$585$		0			0
$586$	−1.40097	−	1.29991i	−1.40097	−	1.29991i
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$	1.95557	−	0.294755i	1.95557	−	0.294755i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.0546039	+	0.139129i	0.0546039	+	0.139129i	0.955573	−	0.294755i	$-0.0952381\pi$
$593$	0.0546039	+	0.139129i	0.0546039	+	0.139129i	−0.900969	+	0.433884i	$0.857143\pi$
$594$	3.45493	+	4.33235i	3.45493	+	4.33235i
$595$		0			0
$596$	−1.23305	+	1.54620i	−1.23305	+	1.54620i
$597$	−1.38084	−	0.425934i	−1.38084	−	0.425934i
$598$	0.238377	−	0.607374i	0.238377	−	0.607374i
$599$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$599$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$600$	−0.147791	+	1.97213i	−0.147791	+	1.97213i
$601$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$601$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$	−0.440071	−	0.762226i	−0.440071	−	0.762226i
$607$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$607$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−2.13402	+	1.98008i	−2.13402	+	1.98008i
$613$	−1.21135	+	1.12397i	−1.21135	+	1.12397i	−0.222521	+	0.974928i	$0.571429\pi$
$613$	−1.21135	+	1.12397i	−1.21135	+	1.12397i	−0.988831	+	0.149042i	$0.952381\pi$
$614$		0			0
$615$		0			0
$616$	0.733052	+	1.26968i	0.733052	+	1.26968i
$617$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$617$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$618$		0			0
$619$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$619$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$620$		0			0
$621$	−1.66329	+	0.250701i	−1.66329	+	0.250701i
$622$	0.222521	+	0.974928i	0.222521	+	0.974928i
$623$	−1.63402	+	1.11406i	−1.63402	+	1.11406i
$624$	−0.645190	+	2.82676i	−0.645190	+	2.82676i
$625$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$626$		0			0
$627$		0			0
$628$	1.82624	+	0.563320i	1.82624	+	0.563320i
$629$		0			0
$630$		0			0
$631$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$631$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$632$	0.698220	+	1.77904i	0.698220	+	1.77904i
$633$	0.266310	+	3.55366i	0.266310	+	3.55366i
$634$		0			0
$635$		0			0
$636$	−1.44504			−1.44504
$637$	−1.46610			−1.46610
$638$		0			0
$639$	−1.55929	−	1.44681i	−1.55929	−	1.44681i
$640$		0			0
$641$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$641$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$642$	−0.107988	−	0.275149i	−0.107988	−	0.275149i
$643$	1.03030	+	1.29196i	1.03030	+	1.29196i	0.955573	+	0.294755i	$0.0952381\pi$
$643$	1.03030	+	1.29196i	1.03030	+	1.29196i	0.0747301	+	0.997204i	$0.476190\pi$
$644$	−0.445042			−0.445042
$645$		0			0
$646$		0			0
$647$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$647$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$648$	4.36087	−	1.34515i	4.36087	−	1.34515i
$649$		0			0
$650$	0.326239	−	1.42935i	0.326239	−	1.42935i
$651$	−2.35654	−	0.726897i	−2.35654	−	0.726897i
$652$	−0.445042	−	1.94986i	−0.445042	−	1.94986i
$653$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$653$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$659$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$660$		0			0
$661$	−0.914101	+	0.848162i	−0.914101	+	0.848162i	−0.988831	−	0.149042i	$-0.952381\pi$
$661$	−0.914101	+	0.848162i	−0.914101	+	0.848162i	0.0747301	+	0.997204i	$0.476190\pi$
$662$		0			0
$663$	2.39564	−	1.63332i	2.39564	−	1.63332i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−0.826239	−	1.43109i	−0.826239	−	1.43109i
$669$		0			0
$670$		0			0
$671$		0			0
$672$	1.95557	−	0.294755i	1.95557	−	0.294755i
$673$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$673$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$674$		0			0
$675$	−3.61168	+	1.11406i	−3.61168	+	1.11406i
$676$	0.419945	−	1.07000i	0.419945	−	1.07000i
$677$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$677$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.527933	−	1.34515i	−0.527933	−	1.34515i
$682$	−0.136622	−	1.82309i	−0.136622	−	1.82309i
$683$	−0.722521	−	0.108903i	−0.722521	−	0.108903i	−0.222521	−	0.974928i	$-0.571429\pi$
$683$	−0.722521	−	0.108903i	−0.722521	−	0.108903i	−0.500000	+	0.866025i	$0.666667\pi$
$684$		0			0
$685$		0			0
$686$	0.365341	+	0.930874i	0.365341	+	0.930874i
$687$	3.56362			3.56362
$688$		0			0
$689$	1.05929	+	0.159662i	1.05929	+	0.159662i
$690$		0			0
$691$	0.455573	+	1.16078i	0.455573	+	1.16078i	0.955573	+	0.294755i	$0.0952381\pi$
$691$	0.455573	+	1.16078i	0.455573	+	1.16078i	−0.500000	+	0.866025i	$0.666667\pi$
$692$		0			0
$693$	−2.66108	+	3.33689i	−2.66108	+	3.33689i
$694$	−1.12349	+	1.40881i	−1.12349	+	1.40881i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−0.134659	+	1.79690i	−0.134659	+	1.79690i
$699$		0			0
$700$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$701$	−0.162592	−	0.712362i	−0.162592	−	0.712362i	−0.988831	−	0.149042i	$-0.952381\pi$
$701$	−0.162592	−	0.712362i	−0.162592	−	0.712362i	0.826239	−	0.563320i	$-0.190476\pi$
$702$	−5.47939	+	0.825886i	−5.47939	+	0.825886i
$703$		0			0
$704$	0.733052	+	1.26968i	0.733052	+	1.26968i
$705$		0			0
$706$	0.900969	−	0.433884i	0.900969	−	0.433884i
$707$	0.326239	−	0.302705i	0.326239	−	0.302705i
$708$		0			0
$709$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$709$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$710$		0			0
$711$	−4.07842	+	3.78422i	−4.07842	+	3.78422i
$712$	−1.63402	+	1.11406i	−1.63402	+	1.11406i
$713$	0.500000	+	0.240787i	0.500000	+	0.240787i
$714$	−1.63402	−	1.11406i	−1.63402	−	1.11406i
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	1.44973	−	0.218511i	1.44973	−	0.218511i	0.623490	−	0.781831i	$-0.285714\pi$
$719$	1.44973	−	0.218511i	1.44973	−	0.218511i	0.826239	+	0.563320i	$0.190476\pi$
$720$		0			0
$721$		0			0
$722$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	−2.17225	−	0.670050i	−2.17225	−	0.670050i
$727$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$727$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$728$	−1.46610			−1.46610
$729$	3.62285	+	4.54291i	3.62285	+	4.54291i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	0.733052	+	0.680173i	0.733052	+	0.680173i	0.955573	−	0.294755i	$-0.0952381\pi$
$733$	0.733052	+	0.680173i	0.733052	+	0.680173i	−0.222521	+	0.974928i	$0.571429\pi$
$734$	0.149460			0.149460
$735$		0			0
$736$	−0.445042			−0.445042
$737$		0			0
$738$		0			0
$739$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$739$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$740$		0			0
$741$		0			0
$742$	−0.162592	−	0.712362i	−0.162592	−	0.712362i
$743$	−1.23305	+	1.54620i	−1.23305	+	1.54620i	−0.500000	+	0.866025i	$0.666667\pi$
$743$	−1.23305	+	1.54620i	−1.23305	+	1.54620i	−0.733052	+	0.680173i	$0.761905\pi$
$744$	−2.35654	−	0.726897i	−2.35654	−	0.726897i
$745$		0			0
$746$	−1.40097	+	0.432142i	−1.40097	+	0.432142i
$747$		0			0
$748$	0.326239	−	1.42935i	0.326239	−	1.42935i
$749$	0.123490	−	0.0841939i	0.123490	−	0.0841939i
$750$		0			0
$751$	−1.88980	+	0.284841i	−1.88980	+	0.284841i	−0.988831	−	0.149042i	$-0.952381\pi$
$751$	−1.88980	+	0.284841i	−1.88980	+	0.284841i	−0.900969	+	0.433884i	$0.857143\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$	1.88980	+	3.27323i	1.88980	+	3.27323i
$757$	0.900969	+	0.433884i	0.900969	+	0.433884i	0.826239	−	0.563320i	$-0.190476\pi$
$757$	0.900969	+	0.433884i	0.900969	+	0.433884i	0.0747301	+	0.997204i	$0.476190\pi$
$758$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$759$	0.945915	−	0.877681i	0.945915	−	0.877681i
$760$		0			0
$761$	1.36534	−	0.930874i	1.36534	−	0.930874i	0.365341	−	0.930874i	$-0.380952\pi$
$761$	1.36534	−	0.930874i	1.36534	−	0.930874i	1.00000			$0$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	1.95557	−	0.294755i	1.95557	−	0.294755i
$769$	0.222521	+	0.974928i	0.222521	+	0.974928i	0.955573	+	0.294755i	$0.0952381\pi$
$769$	0.222521	+	0.974928i	0.222521	+	0.974928i	−0.733052	+	0.680173i	$0.761905\pi$
$770$		0			0
$771$	−0.440071	+	1.92808i	−0.440071	+	1.92808i
$772$		0			0
$773$	1.57906	−	0.487076i	1.57906	−	0.487076i	0.623490	−	0.781831i	$-0.285714\pi$
$773$	1.57906	−	0.487076i	1.57906	−	0.487076i	0.955573	+	0.294755i	$0.0952381\pi$
$774$		0			0
$775$	1.19158	+	0.367554i	1.19158	+	0.367554i
$776$		0			0
$777$		0			0
$778$	1.03030	+	1.29196i	1.03030	+	1.29196i
$779$		0			0
$780$		0			0
$781$	1.05929	+	0.159662i	1.05929	+	0.159662i
$782$	0.326239	+	0.302705i	0.326239	+	0.302705i
$783$		0			0
$784$	0.365341	+	0.930874i	0.365341	+	0.930874i
$785$		0			0
$786$	−0.645190	−	0.598649i	−0.645190	−	0.598649i
$787$	1.78181	+	0.268565i	1.78181	+	0.268565i	0.955573	−	0.294755i	$-0.0952381\pi$
$787$	1.78181	+	0.268565i	1.78181	+	0.268565i	0.826239	+	0.563320i	$0.190476\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−2.66108	+	3.33689i	−2.66108	+	3.33689i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	0.0546039	−	0.728639i	0.0546039	−	0.728639i
$797$	−0.162592	+	0.712362i	−0.162592	+	0.712362i	0.826239	+	0.563320i	$0.190476\pi$
$797$	−0.162592	+	0.712362i	−0.162592	+	0.712362i	−0.988831	+	0.149042i	$0.952381\pi$
$798$		0			0
$799$		0			0
$800$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$801$	−4.75687	−	3.24318i	−4.75687	−	3.24318i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	1.64715	+	0.793227i	1.64715	+	0.793227i
$807$		0			0
$808$	0.326239	−	0.302705i	0.326239	−	0.302705i
$809$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$809$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$810$		0			0
$811$	−0.658322	−	0.317031i	−0.658322	−	0.317031i	0.0747301	−	0.997204i	$-0.476190\pi$
$811$	−0.658322	−	0.317031i	−0.658322	−	0.317031i	−0.733052	+	0.680173i	$0.761905\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−1.63402	−	1.11406i	−1.63402	−	1.11406i
$817$		0			0
$818$	−0.162592	−	0.712362i	−0.162592	−	0.712362i
$819$	−1.55929	−	3.97301i	−1.55929	−	3.97301i
$820$		0			0
$821$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$821$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$822$	3.73738	−	1.15283i	3.73738	−	1.15283i
$823$	−0.722521	+	1.84095i	−0.722521	+	1.84095i	−0.222521	+	0.974928i	$0.571429\pi$
$823$	−0.722521	+	1.84095i	−0.722521	+	1.84095i	−0.500000	+	0.866025i	$0.666667\pi$
$824$		0			0
$825$	1.80778	−	2.26689i	1.80778	−	2.26689i
$826$		0			0
$827$	0.0931869	+	0.116853i	0.0931869	+	0.116853i	0.826239	−	0.563320i	$-0.190476\pi$
$827$	0.0931869	+	0.116853i	0.0931869	+	0.116853i	−0.733052	+	0.680173i	$0.761905\pi$
$828$	−0.473329	−	1.20602i	−0.473329	−	1.20602i
$829$	0.0111692	+	0.149042i	0.0111692	+	0.149042i	1.00000			$0$
$829$	0.0111692	+	0.149042i	0.0111692	+	0.149042i	−0.988831	+	0.149042i	$0.952381\pi$
$830$		0			0
$831$		0			0
$832$	−1.46610			−1.46610
$833$	0.365341	−	0.930874i	0.365341	−	0.930874i
$834$	−3.77960			−3.77960
$835$		0			0
$836$		0			0
$837$	−0.352209	−	4.69990i	−0.352209	−	4.69990i
$838$	0.698220	+	1.77904i	0.698220	+	1.77904i
$839$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.900969	−	0.433884i	$-0.857143\pi$
$839$	−1.12349	−	1.40881i	−1.12349	−	1.40881i	−0.222521	−	0.974928i	$-0.571429\pi$
$840$		0			0
$841$	0.623490	−	0.781831i	0.623490	−	0.781831i
$842$	1.19158	+	0.367554i	1.19158	+	0.367554i
$843$	0.722521	−	1.84095i	0.722521	−	1.84095i
$844$	−1.72188	+	0.531130i	−1.72188	+	0.531130i
$845$		0			0
$846$		0			0
$847$	0.0858993	−	1.14625i	0.0858993	−	1.14625i
$848$	−0.162592	−	0.712362i	−0.162592	−	0.712362i
$849$	−2.86707	+	0.432142i	−2.86707	+	0.432142i
$850$	0.826239	+	0.563320i	0.826239	+	0.563320i
$851$		0			0
$852$	0.722521	−	1.25144i	0.722521	−	1.25144i
$853$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$853$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$854$		0			0
$855$		0			0
$856$	0.123490	−	0.0841939i	0.123490	−	0.0841939i
$857$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$857$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$858$	3.11613	−	2.89135i	3.11613	−	2.89135i
$859$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$859$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$860$		0			0
$861$		0			0
$862$	0.900969	−	0.433884i	0.900969	−	0.433884i
$863$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$863$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$864$	1.88980	+	3.27323i	1.88980	+	3.27323i
$865$		0			0
$866$	0.440071	−	0.0663300i	0.440071	−	0.0663300i
$867$	0.440071	+	1.92808i	0.440071	+	1.92808i
$868$	0.0931869	−	1.24349i	0.0931869	−	1.24349i
$869$	0.623490	−	2.73169i	0.623490	−	2.73169i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$877$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$878$	0.142820	+	1.90580i	0.142820	+	1.90580i
$879$	3.73738	+	0.563320i	3.73738	+	0.563320i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−2.13402	+	1.98008i	−2.13402	+	1.98008i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$	1.07473	+	0.997204i	1.07473	+	0.997204i
$885$		0			0
$886$		0			0
$887$	−0.535628	−	1.36476i	−0.535628	−	1.36476i	−0.900969	−	0.433884i	$-0.857143\pi$
$887$	−0.535628	−	1.36476i	−0.535628	−	1.36476i	0.365341	−	0.930874i	$-0.380952\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−6.39349	−	1.97213i	−6.39349	−	1.97213i
$892$		0			0
$893$		0			0
$894$	0.292280	−	3.90021i	0.292280	−	3.90021i
$895$		0			0
$896$	0.365341	+	0.930874i	0.365341	+	0.930874i
$897$	0.287137	+	1.25803i	0.287137	+	1.25803i
$898$		0			0
$899$		0			0
$900$	−1.45557	−	2.52113i	−1.45557	−	2.52113i
$901$	−0.365341	+	0.632789i	−0.365341	+	0.632789i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.914101	+	0.848162i	−0.914101	+	0.848162i	−0.988831	−	0.149042i	$-0.952381\pi$
$907$	−0.914101	+	0.848162i	−0.914101	+	0.848162i	0.0747301	+	0.997204i	$0.476190\pi$
$908$	0.603718	−	0.411608i	0.603718	−	0.411608i
$909$	1.16728	+	0.562132i	1.16728	+	0.562132i
$910$		0			0
$911$	0.400969	−	0.193096i	0.400969	−	0.193096i	−0.222521	−	0.974928i	$-0.571429\pi$
$911$	0.400969	−	0.193096i	0.400969	−	0.193096i	0.623490	+	0.781831i	$0.285714\pi$
$912$		0			0
$913$		0			0
$914$	−0.367711	−	0.250701i	−0.367711	−	0.250701i
$915$		0			0
$916$	0.400969	+	1.75676i	0.400969	+	1.75676i
$917$	0.222521	−	0.385418i	0.222521	−	0.385418i
$918$	0.841040	−	3.68484i	0.841040	−	3.68484i
$919$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$919$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$920$		0			0
$921$		0			0
$922$	0.698220	+	0.215372i	0.698220	+	0.215372i
$923$	−0.667917	+	0.837541i	−0.667917	+	0.837541i
$924$	−2.61232	−	1.25803i	−2.61232	−	1.25803i
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$929$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−1.44973	−	1.34515i	−1.44973	−	1.34515i
$934$		0			0
$935$		0			0
$936$	−1.55929	−	3.97301i	−1.55929	−	3.97301i
$937$	0.777479	+	0.974928i	0.777479	+	0.974928i	1.00000			$0$
$937$	0.777479	+	0.974928i	0.777479	+	0.974928i	−0.222521	+	0.974928i	$0.571429\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$941$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$942$	−3.61168	+	1.11406i	−3.61168	+	1.11406i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.988831	−	0.149042i	0.988831	−	0.149042i	0.365341	−	0.930874i	$-0.380952\pi$
$947$	0.988831	−	0.149042i	0.988831	−	0.149042i	0.623490	+	0.781831i	$0.285714\pi$
$948$	−3.12285	−	2.12912i	−3.12285	−	2.12912i
$949$		0			0
$950$		0			0
$951$		0			0
$952$	0.365341	−	0.930874i	0.365341	−	0.930874i
$953$	−1.48883	−	0.716983i	−1.48883	−	0.716983i	−0.500000	−	0.866025i	$-0.666667\pi$
$953$	−1.48883	−	0.716983i	−1.48883	−	0.716983i	−0.988831	+	0.149042i	$0.952381\pi$
$954$	1.75751	−	1.19825i	1.75751	−	1.19825i
$955$		0			0
$956$		0			0
$957$		0			0
$958$	0.400969	+	0.193096i	0.400969	+	0.193096i
$959$	0.988831	+	1.71271i	0.988831	+	1.71271i
$960$		0			0
$961$	−0.277479	+	0.480608i	−0.277479	+	0.480608i
$962$		0			0
$963$	0.359497	+	0.245101i	0.359497	+	0.245101i
$964$		0			0
$965$		0			0
$966$	0.727208	−	0.495802i	0.727208	−	0.495802i
$967$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$967$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$968$	0.0858993	−	1.14625i	0.0858993	−	1.14625i
$969$		0			0
$970$		0			0
$971$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$971$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$972$	−3.27064	+	4.10126i	−3.27064	+	4.10126i
$973$	−0.425270	−	1.86323i	−0.425270	−	1.86323i
$974$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$975$	1.05929	+	2.69903i	1.05929	+	2.69903i
$976$		0			0
$977$	0.440071	+	0.0663300i	0.440071	+	0.0663300i	0.365341	−	0.930874i	$-0.380952\pi$
$977$	0.440071	+	0.0663300i	0.440071	+	0.0663300i	0.0747301	+	0.997204i	$0.476190\pi$
$978$	2.89946	+	2.69030i	2.89946	+	2.69030i
$979$	2.89946			2.89946
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.44973	+	0.218511i	1.44973	+	0.218511i	0.826239	−	0.563320i	$-0.190476\pi$
$983$	1.44973	+	0.218511i	1.44973	+	0.218511i	0.623490	+	0.781831i	$0.285714\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	1.57906	−	0.487076i	1.57906	−	0.487076i	0.623490	−	0.781831i	$-0.285714\pi$
$991$	1.57906	−	0.487076i	1.57906	−	0.487076i	0.955573	+	0.294755i	$0.0952381\pi$
$992$	0.0931869	−	1.24349i	0.0931869	−	1.24349i
$993$		0			0
$994$	0.698220	+	0.215372i	0.698220	+	0.215372i
$995$		0			0
$996$		0			0
$997$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$997$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$998$	−0.955573	−	1.65510i	−0.955573	−	1.65510i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3332.1.cc.b.1087.1	yes	12
4.3	odd	2		3332.1.cc.a.1087.1	✓	12
17.16	even	2		3332.1.cc.a.1087.1	✓	12
49.11	even	21	inner	3332.1.cc.b.1971.1	yes	12
68.67	odd	2	CM	3332.1.cc.b.1087.1	yes	12
196.11	odd	42		3332.1.cc.a.1971.1	yes	12
833.305	even	42		3332.1.cc.a.1971.1	yes	12
3332.1971	odd	42	inner	3332.1.cc.b.1971.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3332.1.cc.a.1087.1	✓	12	4.3	odd	2
3332.1.cc.a.1087.1	✓	12	17.16	even	2
3332.1.cc.a.1971.1	yes	12	196.11	odd	42
3332.1.cc.a.1971.1	yes	12	833.305	even	42
3332.1.cc.b.1087.1	yes	12	1.1	even	1	trivial
3332.1.cc.b.1087.1	yes	12	68.67	odd	2	CM
3332.1.cc.b.1971.1	yes	12	49.11	even	21	inner
3332.1.cc.b.1971.1	yes	12	3332.1971	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 $\F_{q}$
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)

\(f(q)\)	\(=\)	\(q+(-0.733052 - 0.680173i) q^{2} +(1.95557 + 0.294755i) q^{3} +(0.0747301 + 0.997204i) q^{4} +(-1.23305 - 1.54620i) q^{6} +(0.623490 - 0.781831i) q^{7} +(0.623490 - 0.781831i) q^{8} +(2.78181 + 0.858075i) q^{9} +(-1.40097 + 0.432142i) q^{11} +(-0.147791 + 1.97213i) q^{12} +(0.326239 - 1.42935i) q^{13} +(-0.988831 + 0.149042i) q^{14} +(-0.988831 + 0.149042i) q^{16} +(0.826239 + 0.563320i) q^{17} +(-1.45557 - 2.52113i) q^{18} +(1.44973 - 1.34515i) q^{21} +(1.32091 + 0.636119i) q^{22} +(-0.367711 + 0.250701i) q^{23} +(1.44973 - 1.34515i) q^{24} +(-0.733052 + 0.680173i) q^{25} +(-1.21135 + 0.825886i) q^{26} +(3.40530 + 1.63991i) q^{27} +(0.826239 + 0.563320i) q^{28} +(-0.623490 - 1.07992i) q^{31} +(0.826239 + 0.563320i) q^{32} +(-2.86707 + 0.432142i) q^{33} +(-0.222521 - 0.974928i) q^{34} +(-0.647791 + 2.83816i) q^{36} +(1.05929 - 2.69903i) q^{39} -1.97766 q^{42} +(-0.535628 - 1.36476i) q^{44} +(0.440071 + 0.0663300i) q^{46} -1.97766 q^{48} +(-0.222521 - 0.974928i) q^{49} +1.00000 q^{50} +(1.44973 + 1.34515i) q^{51} +(1.44973 + 0.218511i) q^{52} +(0.0546039 + 0.728639i) q^{53} +(-1.38084 - 3.51833i) q^{54} +(-0.222521 - 0.974928i) q^{56} +(-0.277479 + 1.21572i) q^{62} +(2.40530 - 1.63991i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(2.39564 + 1.63332i) q^{66} +(-0.500000 + 0.866025i) q^{68} +(-0.792981 + 0.381879i) q^{69} +(-0.658322 - 0.317031i) q^{71} +(2.40530 - 1.63991i) q^{72} +(-1.63402 + 1.11406i) q^{75} +(-0.535628 + 1.36476i) q^{77} +(-2.61232 + 1.25803i) q^{78} +(-0.955573 + 1.65510i) q^{79} +(3.77064 + 2.57078i) q^{81} +(1.44973 + 1.34515i) q^{84} +(-0.535628 + 1.36476i) q^{88} +(-1.88980 - 0.582926i) q^{89} +(-0.914101 - 1.14625i) q^{91} +(-0.277479 - 0.347948i) q^{92} +(-0.900969 - 2.29563i) q^{93} +(1.44973 + 1.34515i) q^{96} +(-0.500000 + 0.866025i) q^{98} -4.26804 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} + 13 q^{3} + q^{4} - 5 q^{6} - 2 q^{7} - 2 q^{8} + 14 q^{9} - 8 q^{11} - q^{12} - 5 q^{13} + q^{14} + q^{16} + q^{17} - 7 q^{18} - q^{21} + 2 q^{22} + 2 q^{23} - q^{24} + q^{25} - q^{26}+ \cdots - 14 q^{99}+O(q^{100}) \) 12 * q + q^2 + 13 * q^3 + q^4 - 5 * q^6 - 2 * q^7 - 2 * q^8 + 14 * q^9 - 8 * q^11 - q^12 - 5 * q^13 + q^14 + q^16 + q^17 - 7 * q^18 - q^21 + 2 * q^22 + 2 * q^23 - q^24 + q^25 - q^26 + 12 * q^27 + q^28 + 2 * q^31 + q^32 - 6 * q^33 - 2 * q^34 - 7 * q^36 - 6 * q^39 + 2 * q^42 - q^44 + 2 * q^46 + 2 * q^48 - 2 * q^49 + 12 * q^50 - q^51 - q^52 - q^53 - 6 * q^54 - 2 * q^56 - 4 * q^62 - 2 * q^64 + 15 * q^66 - 6 * q^68 - 3 * q^69 + 2 * q^71 - q^75 - q^77 - 9 * q^78 - q^79 + 13 * q^81 - q^84 - q^88 - q^89 + 2 * q^91 - 4 * q^92 - 2 * q^93 - q^96 - 6 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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