LMFDB - Embedded newform 2303.1.q.b.1409.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2303,1,Mod(46,2303)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2303, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([22, 21]))

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

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

chi := DirichletCharacter("2303.46");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2303 = 7^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2303.q (of order $42$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.14934672409$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{42})$
Coefficient field:	$\Q(\zeta_{210})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{48} - x^{47} + x^{46} + x^{43} - x^{42} + 2 x^{41} - x^{40} + x^{39} + x^{36} - x^{35} + x^{34} + \cdots + 1 $ x^48 - x^47 + x^46 + x^43 - x^42 + 2x^41 - x^40 + x^39 + x^36 - x^35 + x^34 - x^33 + x^32 - x^31 - x^28 - x^26 - x^24 - x^22 - x^20 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 + x^9 - x^8 + 2x^7 - x^6 + x^5 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{105}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{105} - \cdots)$

Embedding invariants

Embedding label			1409.4
Root			$0.946327 + 0.323210i$ of defining polynomial
Character	$\chi$	$=$	2303.1409
Dual form			2303.1.q.b.1033.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50961 - 1.02924i) q^{2} +(0.807672 - 0.749410i) q^{3} +(0.854263 - 2.17663i) q^{4} +(0.447952 - 1.96261i) q^{6} +(-0.999552 + 0.0299155i) q^{7} +(-0.544091 - 2.38382i) q^{8} +(0.0159885 - 0.213352i) q^{9} +O(q^{10})$	\(q+(1.50961 - 1.02924i) q^{2} +(0.807672 - 0.749410i) q^{3} +(0.854263 - 2.17663i) q^{4} +(0.447952 - 1.96261i) q^{6} +(-0.999552 + 0.0299155i) q^{7} +(-0.544091 - 2.38382i) q^{8} +(0.0159885 - 0.213352i) q^{9} +(-0.941222 - 2.39819i) q^{12} +(-1.47815 + 1.07394i) q^{14} +(-1.56082 - 1.44823i) q^{16} +(-0.831324 - 0.125302i) q^{17} +(-0.195453 - 0.338535i) q^{18} +(-0.784892 + 0.773237i) q^{21} +(-2.22591 - 1.51760i) q^{24} +(0.826239 + 0.563320i) q^{25} +(0.539983 + 0.677117i) q^{27} +(-0.788766 + 2.20121i) q^{28} +(-1.42898 - 0.215385i) q^{32} +(-1.38394 + 0.666472i) q^{34} +(-0.450728 - 0.217059i) q^{36} +(0.578021 + 1.47277i) q^{37} +(-0.389039 + 1.97513i) q^{42} +(0.826239 - 0.563320i) q^{47} -2.34594 q^{48} +(0.998210 - 0.0598042i) q^{49} +1.82709 q^{50} +(-0.765340 + 0.521800i) q^{51} +(0.520520 - 1.32626i) q^{53} +(1.51208 + 0.466415i) q^{54} +(0.615161 + 2.36648i) q^{56} +(-1.14635 + 0.353601i) q^{59} +(-0.472459 - 1.20381i) q^{61} +(-0.00959883 + 0.213735i) q^{63} +(-0.460549 + 0.221788i) q^{64} +(-0.982905 + 1.70244i) q^{68} +(-0.557790 - 0.699447i) q^{71} +(-0.517291 + 0.0779691i) q^{72} +(2.38842 + 1.62840i) q^{74} +(1.08949 - 0.164214i) q^{75} +(-0.858449 + 1.48688i) q^{79} +(1.15513 + 0.174108i) q^{81} +(-0.658322 + 0.317031i) q^{83} +(1.01254 + 2.36896i) q^{84} +(-0.120916 + 1.61351i) q^{89} +(0.667511 - 1.70079i) q^{94} +(-1.31556 + 0.896935i) q^{96} -0.209057 q^{97} +(1.44536 - 1.11768i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} - 2 q^{3} + 5 q^{4} - 4 q^{6} - q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 48 * q + q^2 - 2 * q^3 + 5 * q^4 - 4 * q^6 - q^7 + 2 * q^8 + 2 * q^9	$ 48 q + q^{2} - 2 q^{3} + 5 q^{4} - 4 q^{6} - q^{7} + 2 q^{8} + 2 q^{9} - 40 q^{12} - 18 q^{14} + 6 q^{16} + q^{17} - 9 q^{18} + 5 q^{21} + 8 q^{24} + 4 q^{25} - 6 q^{27} - 5 q^{32} + 2 q^{34} - 10 q^{36} + q^{37} + 7 q^{42} + 4 q^{47} + 6 q^{48} - q^{49} + 12 q^{50} + 4 q^{51} + 8 q^{53} - q^{54} - 11 q^{56} - 13 q^{59} + q^{61} - 4 q^{63} - 8 q^{64} - 5 q^{68} + 5 q^{71} - 8 q^{72} + 13 q^{74} + 5 q^{75} - 2 q^{79} + 8 q^{83} + 5 q^{84} - 2 q^{89} + q^{94} + 10 q^{96} + 12 q^{97} + q^{98}+O(q^{100}) $ 48 * q + q^2 - 2 * q^3 + 5 * q^4 - 4 * q^6 - q^7 + 2 * q^8 + 2 * q^9 - 40 * q^12 - 18 * q^14 + 6 * q^16 + q^17 - 9 * q^18 + 5 * q^21 + 8 * q^24 + 4 * q^25 - 6 * q^27 - 5 * q^32 + 2 * q^34 - 10 * q^36 + q^37 + 7 * q^42 + 4 * q^47 + 6 * q^48 - q^49 + 12 * q^50 + 4 * q^51 + 8 * q^53 - q^54 - 11 * q^56 - 13 * q^59 + q^61 - 4 * q^63 - 8 * q^64 - 5 * q^68 + 5 * q^71 - 8 * q^72 + 13 * q^74 + 5 * q^75 - 2 * q^79 + 8 * q^83 + 5 * q^84 - 2 * q^89 + q^94 + 10 * q^96 + 12 * q^97 + q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2303\mathbb{Z}\right)^\times$.

$n$	$99$	$2257$
$\chi(n)$	$-1$	$e\left(\frac{16}{21}\right)$

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 $

$2$	1.50961	−	1.02924i	1.50961	−	1.02924i	0.525684	−	0.850680i	$-0.323810\pi$
$2$	1.50961	−	1.02924i	1.50961	−	1.02924i	0.983930	−	0.178557i	$-0.0571429\pi$
$3$	0.807672	−	0.749410i	0.807672	−	0.749410i	−0.163818	−	0.986491i	$-0.552381\pi$
$3$	0.807672	−	0.749410i	0.807672	−	0.749410i	0.971490	+	0.237080i	$0.0761905\pi$
$4$	0.854263	−	2.17663i	0.854263	−	2.17663i
$5$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$5$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$6$	0.447952	−	1.96261i	0.447952	−	1.96261i
$7$	−0.999552	+	0.0299155i	−0.999552	+	0.0299155i
$7$	−0.999552	+	0.0299155i	−0.999552	+	0.0299155i
$8$	−0.544091	−	2.38382i	−0.544091	−	2.38382i
$9$	0.0159885	−	0.213352i	0.0159885	−	0.213352i
$10$		0			0
$11$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$11$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$12$	−0.941222	−	2.39819i	−0.941222	−	2.39819i
$13$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$13$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$14$	−1.47815	+	1.07394i	−1.47815	+	1.07394i
$15$		0			0
$16$	−1.56082	−	1.44823i	−1.56082	−	1.44823i
$17$	−0.831324	−	0.125302i	−0.831324	−	0.125302i	−0.280427	−	0.959875i	$-0.590476\pi$
$17$	−0.831324	−	0.125302i	−0.831324	−	0.125302i	−0.550897	+	0.834573i	$0.685714\pi$
$18$	−0.195453	−	0.338535i	−0.195453	−	0.338535i
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$		0			0
$21$	−0.784892	+	0.773237i	−0.784892	+	0.773237i
$22$		0			0
$23$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$23$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$24$	−2.22591	−	1.51760i	−2.22591	−	1.51760i
$25$	0.826239	+	0.563320i	0.826239	+	0.563320i
$26$		0			0
$27$	0.539983	+	0.677117i	0.539983	+	0.677117i
$28$	−0.788766	+	2.20121i	−0.788766	+	2.20121i
$29$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$29$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$30$		0			0
$31$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$31$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$32$	−1.42898	−	0.215385i	−1.42898	−	0.215385i
$33$		0			0
$34$	−1.38394	+	0.666472i	−1.38394	+	0.666472i
$35$		0			0
$36$	−0.450728	−	0.217059i	−0.450728	−	0.217059i
$37$	0.578021	+	1.47277i	0.578021	+	1.47277i	0.858449	+	0.512899i	$0.171429\pi$
$37$	0.578021	+	1.47277i	0.578021	+	1.47277i	−0.280427	+	0.959875i	$0.590476\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$41$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$42$	−0.389039	+	1.97513i	−0.389039	+	1.97513i
$43$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$43$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.826239	−	0.563320i	0.826239	−	0.563320i
$47$	0.826239	−	0.563320i	0.826239	−	0.563320i
$48$	−2.34594			−2.34594
$49$	0.998210	−	0.0598042i	0.998210	−	0.0598042i
$50$	1.82709			1.82709
$51$	−0.765340	+	0.521800i	−0.765340	+	0.521800i
$52$		0			0
$53$	0.520520	−	1.32626i	0.520520	−	1.32626i	−0.393025	−	0.919528i	$-0.628571\pi$
$53$	0.520520	−	1.32626i	0.520520	−	1.32626i	0.913545	−	0.406737i	$-0.133333\pi$
$54$	1.51208	+	0.466415i	1.51208	+	0.466415i
$55$		0			0
$56$	0.615161	+	2.36648i	0.615161	+	2.36648i
$57$		0			0
$58$		0			0
$59$	−1.14635	+	0.353601i	−1.14635	+	0.353601i	−0.809017	−	0.587785i	$-0.800000\pi$
$59$	−1.14635	+	0.353601i	−1.14635	+	0.353601i	−0.337330	+	0.941386i	$0.609524\pi$
$60$		0			0
$61$	−0.472459	−	1.20381i	−0.472459	−	1.20381i	−0.946327	−	0.323210i	$-0.895238\pi$
$61$	−0.472459	−	1.20381i	−0.472459	−	1.20381i	0.473869	−	0.880596i	$-0.342857\pi$
$62$		0			0
$63$	−0.00959883	+	0.213735i	−0.00959883	+	0.213735i
$64$	−0.460549	+	0.221788i	−0.460549	+	0.221788i
$65$		0			0
$66$		0			0
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$	−0.982905	+	1.70244i	−0.982905	+	1.70244i
$69$		0			0
$70$		0			0
$71$	−0.557790	−	0.699447i	−0.557790	−	0.699447i	0.420357	−	0.907359i	$-0.361905\pi$
$71$	−0.557790	−	0.699447i	−0.557790	−	0.699447i	−0.978148	+	0.207912i	$0.933333\pi$
$72$	−0.517291	+	0.0779691i	−0.517291	+	0.0779691i
$73$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$73$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$74$	2.38842	+	1.62840i	2.38842	+	1.62840i
$75$	1.08949	−	0.164214i	1.08949	−	0.164214i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.858449	+	1.48688i	−0.858449	+	1.48688i	0.0149594	+	0.999888i	$0.495238\pi$
$79$	−0.858449	+	1.48688i	−0.858449	+	1.48688i	−0.873408	+	0.486989i	$0.838095\pi$
$80$		0			0
$81$	1.15513	+	0.174108i	1.15513	+	0.174108i
$82$		0			0
$83$	−0.658322	+	0.317031i	−0.658322	+	0.317031i	−0.733052	−	0.680173i	$-0.761905\pi$
$83$	−0.658322	+	0.317031i	−0.658322	+	0.317031i	0.0747301	+	0.997204i	$0.476190\pi$
$84$	1.01254	+	2.36896i	1.01254	+	2.36896i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.120916	+	1.61351i	−0.120916	+	1.61351i	0.525684	+	0.850680i	$0.323810\pi$
$89$	−0.120916	+	1.61351i	−0.120916	+	1.61351i	−0.646600	+	0.762830i	$0.723810\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$	0.667511	−	1.70079i	0.667511	−	1.70079i
$95$		0			0
$96$	−1.31556	+	0.896935i	−1.31556	+	0.896935i
$97$	−0.209057			−0.209057			−0.104528	−	0.994522i	$-0.533333\pi$
$97$	−0.209057			−0.209057			−0.104528	+	0.994522i	$0.533333\pi$
$98$	1.44536	−	1.11768i	1.44536	−	1.11768i
$99$		0			0
$100$	1.93196	−	1.31719i	1.93196	−	1.31719i
$101$	−0.843914	+	0.783038i	−0.843914	+	0.783038i	−0.978148	−	0.207912i	$-0.933333\pi$
$101$	−0.843914	+	0.783038i	−0.843914	+	0.783038i	0.134233	+	0.990950i	$0.457143\pi$
$102$	−0.618312	+	1.57543i	−0.618312	+	1.57543i
$103$	−1.76839	−	0.545476i	−1.76839	−	0.545476i	−0.772417	−	0.635116i	$-0.780952\pi$
$103$	−1.76839	−	0.545476i	−1.76839	−	0.545476i	−0.995974	+	0.0896393i	$0.971429\pi$
$104$		0			0
$105$		0			0
$106$	−0.579256	−	2.53789i	−0.579256	−	2.53789i
$107$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$107$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$108$	1.93512	−	0.596905i	1.93512	−	0.596905i
$109$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$109$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$110$		0			0
$111$	1.57056	+	0.756344i	1.57056	+	0.756344i
$112$	1.60344	+	1.40089i	1.60344	+	1.40089i
$113$		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			0
$118$	−1.36660	+	1.71366i	−1.36660	+	1.71366i
$119$	0.834701	+	0.100376i	0.834701	+	0.100376i
$120$		0			0
$121$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$122$	−1.95223	−	1.33101i	−1.95223	−	1.33101i
$123$		0			0
$124$		0			0
$125$		0			0
$126$	0.205493	+	0.332536i	0.205493	+	0.332536i
$127$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$127$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$128$	0.255585	−	0.442686i	0.255585	−	0.442686i
$129$		0			0
$130$		0			0
$131$	0.494561	+	0.458885i	0.494561	+	0.458885i	0.887586	−	0.460642i	$-0.152381\pi$
$131$	0.494561	+	0.458885i	0.494561	+	0.458885i	−0.393025	+	0.919528i	$0.628571\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.153619	+	2.04990i	0.153619	+	2.04990i
$137$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$137$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$138$		0			0
$139$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$139$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$140$		0			0
$141$	0.245172	−	1.07417i	0.245172	−	1.07417i
$142$	−1.56194	−	0.481796i	−1.56194	−	0.481796i
$143$		0			0
$144$	−0.333937	+	0.309848i	−0.333937	+	0.309848i
$145$		0			0
$146$		0			0
$147$	0.761409	−	0.796371i	0.761409	−	0.796371i
$148$	3.69946			3.69946
$149$	−0.270705	+	0.184564i	−0.270705	+	0.184564i	−0.691063	−	0.722795i	$-0.742857\pi$
$149$	−0.270705	+	0.184564i	−0.270705	+	0.184564i	0.420357	+	0.907359i	$0.361905\pi$
$150$	1.47569	−	1.36924i	1.47569	−	1.36924i
$151$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$151$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$152$		0			0
$153$	−0.0400250	+	0.175361i	−0.0400250	+	0.175361i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.905632	−	0.279350i	0.905632	−	0.279350i	0.193256	−	0.981148i	$-0.438095\pi$
$157$	0.905632	−	0.279350i	0.905632	−	0.279350i	0.712376	+	0.701798i	$0.247619\pi$
$158$	0.234423	+	3.12816i	0.234423	+	3.12816i
$159$	−0.573506	−	1.46127i	−0.573506	−	1.46127i
$160$		0			0
$161$		0			0
$162$	1.92299	−	0.926065i	1.92299	−	0.926065i
$163$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$163$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$164$		0			0
$165$		0			0
$166$	−0.667511	+	1.15616i	−0.667511	+	1.15616i
$167$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$167$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$168$	2.27031	+	1.45033i	2.27031	+	1.45033i
$169$	0.623490	+	0.781831i	0.623490	+	0.781831i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.40884	+	0.212348i	−1.40884	+	0.212348i	−0.809017	−	0.587785i	$-0.800000\pi$
$173$	−1.40884	+	0.212348i	−1.40884	+	0.212348i	−0.599822	+	0.800134i	$0.704762\pi$
$174$		0			0
$175$	−0.842721	−	0.538351i	−0.842721	−	0.538351i
$176$		0			0
$177$	−0.660880	+	1.14468i	−0.660880	+	1.14468i
$178$	1.47815	+	2.56023i	1.47815	+	2.56023i
$179$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$179$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$180$		0			0
$181$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$181$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$182$		0			0
$183$	−1.28374	−	0.618215i	−1.28374	−	0.618215i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−0.520312	−	2.27964i	−0.520312	−	2.27964i
$189$	−0.559997	−	0.660660i	−0.559997	−	0.660660i
$190$		0			0
$191$	0.142820	+	0.0440542i	0.142820	+	0.0440542i	0.365341	−	0.930874i	$-0.380952\pi$
$191$	0.142820	+	0.0440542i	0.142820	+	0.0440542i	−0.222521	+	0.974928i	$0.571429\pi$
$192$	−0.205762	+	0.524272i	−0.205762	+	0.524272i
$193$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$193$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$194$	−0.315595	+	0.215169i	−0.315595	+	0.215169i
$195$		0			0
$196$	0.722562	−	2.22382i	0.722562	−	2.22382i
$197$	1.91115			1.91115			0.955573	−	0.294755i	$-0.0952381\pi$
$197$	1.91115			1.91115			0.955573	+	0.294755i	$0.0952381\pi$
$198$		0			0
$199$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$199$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$200$	0.893304	−	2.27610i	0.893304	−	2.27610i
$201$		0			0
$202$	−0.468053	+	2.05067i	−0.468053	+	2.05067i
$203$		0			0
$204$	0.481962	+	2.11161i	0.481962	+	2.11161i
$205$		0			0
$206$	−3.23101	+	0.996635i	−3.23101	+	0.996635i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$211$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$212$	−2.44212	−	2.26596i	−2.44212	−	2.26596i
$213$	−0.974684	−	0.146910i	−0.974684	−	0.146910i
$214$		0			0
$215$		0			0
$216$	1.32033	−	1.65564i	1.32033	−	1.65564i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$	3.14940	−	0.474696i	3.14940	−	0.474696i
$223$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$223$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$224$	1.43479	+	0.172540i	1.43479	+	0.172540i
$225$	0.133396	−	0.167273i	0.133396	−	0.167273i
$226$		0			0
$227$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$227$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$228$		0			0
$229$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$229$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$233$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$234$		0			0
$235$		0			0
$236$	−0.209624	+	2.79724i	−0.209624	+	2.79724i
$237$	0.420936	+	1.84424i	0.420936	+	1.84424i
$238$	1.36339	−	0.707575i	1.36339	−	0.707575i
$239$	0.411799	−	1.80421i	0.411799	−	1.80421i	−0.163818	−	0.986491i	$-0.552381\pi$
$239$	0.411799	−	1.80421i	0.411799	−	1.80421i	0.575617	−	0.817719i	$-0.304762\pi$
$240$		0			0
$241$	−0.204903	+	0.522085i	−0.204903	+	0.522085i	−0.995974	−	0.0896393i	$-0.971429\pi$
$241$	−0.204903	+	0.522085i	−0.204903	+	0.522085i	0.791071	+	0.611724i	$0.209524\pi$
$242$	−1.33935	+	1.24274i	−1.33935	+	1.24274i
$243$	0.347866	−	0.237171i	0.347866	−	0.237171i
$244$	−3.02384			−3.02384
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−0.294122	+	0.749410i	−0.294122	+	0.749410i
$250$		0			0
$251$	0.388703	−	1.70302i	0.388703	−	1.70302i	−0.280427	−	0.959875i	$-0.590476\pi$
$251$	0.388703	−	1.70302i	0.388703	−	1.70302i	0.669131	−	0.743145i	$-0.266667\pi$
$252$	0.457020	+	0.203478i	0.457020	+	0.203478i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.107994	−	1.44108i	−0.107994	−	1.44108i
$257$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$257$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$258$		0			0
$259$	−0.621821	−	1.45482i	−0.621821	−	1.45482i
$260$		0			0
$261$		0			0
$262$	1.21890	+	0.183719i	1.21890	+	0.183719i
$263$	−0.983930	−	1.70422i	−0.983930	−	1.70422i	−0.646600	−	0.762830i	$-0.723810\pi$
$263$	−0.983930	−	1.70422i	−0.983930	−	1.70422i	−0.337330	−	0.941386i	$-0.609524\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.11152	+	1.39380i	1.11152	+	1.39380i
$268$		0			0
$269$	−1.21135	−	0.825886i	−1.21135	−	0.825886i	−0.222521	−	0.974928i	$-0.571429\pi$
$269$	−1.21135	−	0.825886i	−1.21135	−	0.825886i	−0.988831	+	0.149042i	$0.952381\pi$
$270$		0			0
$271$	−1.56447	+	0.235806i	−1.56447	+	0.235806i	−0.873408	−	0.486989i	$-0.838095\pi$
$271$	−1.56447	+	0.235806i	−1.56447	+	0.235806i	−0.691063	+	0.722795i	$0.742857\pi$
$272$	1.11608	+	1.39952i	1.11608	+	1.39952i
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−0.265468	−	0.0400129i	−0.265468	−	0.0400129i	0.0149594	−	0.999888i	$-0.495238\pi$
$277$	−0.265468	−	0.0400129i	−0.265468	−	0.0400129i	−0.280427	+	0.959875i	$0.590476\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$281$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$282$	−0.735460	−	1.87392i	−0.735460	−	1.87392i
$283$	0.0785688	+	1.04843i	0.0785688	+	1.04843i	0.887586	+	0.460642i	$0.152381\pi$
$283$	0.0785688	+	1.04843i	0.0785688	+	1.04843i	−0.809017	+	0.587785i	$0.800000\pi$
$284$	−1.99893	+	0.616589i	−1.99893	+	0.616589i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.0688000	+	0.301432i	−0.0688000	+	0.301432i
$289$	−0.280173	−	0.0864220i	−0.280173	−	0.0864220i
$290$		0			0
$291$	−0.168849	+	0.156669i	−0.168849	+	0.156669i
$292$		0			0
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	0.329778	−	1.98588i	0.329778	−	1.98588i
$295$		0			0
$296$	3.19633	−	2.17922i	3.19633	−	2.17922i
$297$		0			0
$298$	−0.218701	+	0.557240i	−0.218701	+	0.557240i
$299$		0			0
$300$	0.573277	−	2.51169i	0.573277	−	2.51169i
$301$		0			0
$302$		0			0
$303$	−0.0947894	+	1.26488i	−0.0947894	+	1.26488i
$304$		0			0
$305$		0			0
$306$	0.120066	+	0.305923i	0.120066	+	0.305923i
$307$	0.806030	+	0.388164i	0.806030	+	0.388164i	0.791071	−	0.611724i	$-0.209524\pi$
$307$	0.806030	+	0.388164i	0.806030	+	0.388164i	0.0149594	+	0.999888i	$0.495238\pi$
$308$		0			0
$309$	−1.83707	+	0.884684i	−1.83707	+	0.884684i
$310$		0			0
$311$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$311$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$312$		0			0
$313$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$313$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$314$	1.07964	−	1.35382i	1.07964	−	1.35382i
$315$		0			0
$316$	2.50303	+	3.13871i	2.50303	+	3.13871i
$317$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$317$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$318$	−2.36977	−	1.61568i	−2.36977	−	1.61568i
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	1.36575	−	2.36555i	1.36575	−	2.36555i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$330$		0			0
$331$	−0.704350	−	1.79466i	−0.704350	−	1.79466i	−0.599822	−	0.800134i	$-0.704762\pi$
$331$	−0.704350	−	1.79466i	−0.704350	−	1.79466i	−0.104528	−	0.994522i	$-0.533333\pi$
$332$	0.127678	+	1.70375i	0.127678	+	1.70375i
$333$	0.323461	−	0.0997744i	0.323461	−	0.0997744i
$334$		0			0
$335$		0			0
$336$	2.34489	−	0.0701800i	2.34489	−	0.0701800i
$337$	0.375046	−	1.64318i	0.375046	−	1.64318i	−0.337330	−	0.941386i	$-0.609524\pi$
$337$	0.375046	−	1.64318i	0.375046	−	1.64318i	0.712376	−	0.701798i	$-0.247619\pi$
$338$	1.74592	+	0.538545i	1.74592	+	0.538545i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.995974	+	0.0896393i	−0.995974	+	0.0896393i
$344$		0			0
$345$		0			0
$346$	−1.90825	+	1.77059i	−1.90825	+	1.77059i
$347$	−0.638184	+	1.62607i	−0.638184	+	1.62607i	0.134233	+	0.990950i	$0.457143\pi$
$347$	−0.638184	+	1.62607i	−0.638184	+	1.62607i	−0.772417	+	0.635116i	$0.780952\pi$
$348$		0			0
$349$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$349$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$350$	−1.82627	+	0.0546583i	−1.82627	+	0.0546583i
$351$		0			0
$352$		0			0
$353$	1.74592	−	0.538545i	1.74592	−	0.538545i	0.753071	−	0.657939i	$-0.228571\pi$
$353$	1.74592	−	0.538545i	1.74592	−	0.538545i	0.992847	+	0.119394i	$0.0380952\pi$
$354$	0.180471	+	2.40822i	0.180471	+	2.40822i
$355$		0			0
$356$	3.40871	+	1.64155i	3.40871	+	1.64155i
$357$	0.749388	−	0.544462i	0.749388	−	0.544462i
$358$		0			0
$359$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$359$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$360$		0			0
$361$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$362$		0			0
$363$	−0.686957	+	0.861417i	−0.686957	+	0.861417i
$364$		0			0
$365$		0			0
$366$	−2.57423	+	0.388003i	−2.57423	+	0.388003i
$367$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$367$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.480612	+	1.34124i	−0.480612	+	1.34124i
$372$		0			0
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$		0			0
$376$	−1.79240	−	1.66311i	−1.79240	−	1.66311i
$377$		0			0
$378$	−1.52536	−	0.420971i	−1.52536	−	0.420971i
$379$	1.08084	+	0.520506i	1.08084	+	0.520506i	0.887586	−	0.460642i	$-0.152381\pi$
$379$	1.08084	+	0.520506i	1.08084	+	0.520506i	0.193256	+	0.981148i	$0.438095\pi$
$380$		0			0
$381$		0			0
$382$	0.260945	−	0.0804910i	0.260945	−	0.0804910i
$383$	0.149193	−	1.99084i	0.149193	−	1.99084i	0.0149594	−	0.999888i	$-0.495238\pi$
$383$	0.149193	−	1.99084i	0.149193	−	1.99084i	0.134233	−	0.990950i	$-0.457143\pi$
$384$	−0.125325	−	0.549084i	−0.125325	−	0.549084i
$385$		0			0
$386$		0			0
$387$		0			0
$388$	−0.178590	+	0.455039i	−0.178590	+	0.455039i
$389$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$389$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$390$		0			0
$391$		0			0
$392$	−0.685680	−	2.34701i	−0.685680	−	2.34701i
$393$	0.743336			0.743336
$394$	2.88509	−	1.96702i	2.88509	−	1.96702i
$395$		0			0
$396$		0			0
$397$	1.90772	+	0.588455i	1.90772	+	0.588455i	0.971490	+	0.237080i	$0.0761905\pi$
$397$	1.90772	+	0.588455i	1.90772	+	0.588455i	0.936235	+	0.351375i	$0.114286\pi$
$398$		0			0
$399$		0			0
$400$	−0.473793	−	2.07582i	−0.473793	−	2.07582i
$401$	−0.115446	+	1.54051i	−0.115446	+	1.54051i	0.575617	+	0.817719i	$0.304762\pi$
$401$	−0.115446	+	1.54051i	−0.115446	+	1.54051i	−0.691063	+	0.722795i	$0.742857\pi$
$402$		0			0
$403$		0			0
$404$	0.983456	+	2.50581i	0.983456	+	2.50581i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	1.66029	+	1.54053i	1.66029	+	1.54053i
$409$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$409$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$410$		0			0
$411$		0			0
$412$	−2.69797	+	3.38315i	−2.69797	+	3.38315i
$413$	1.13526	−	0.387736i	1.13526	−	0.387736i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$419$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$420$		0			0
$421$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$421$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$422$		0			0
$423$	−0.106975	−	0.185286i	−0.106975	−	0.185286i
$424$	−3.44479	−	0.519218i	−3.44479	−	0.519218i
$425$	−0.616287	−	0.571831i	−0.616287	−	0.571831i
$426$	−1.62260	+	0.781404i	−1.62260	+	0.781404i
$427$	0.508260	+	1.18913i	0.508260	+	1.18913i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.61056	+	0.496793i	−1.61056	+	0.496793i	−0.963963	−	0.266037i	$-0.914286\pi$
$431$	−1.61056	+	0.496793i	−1.61056	+	0.496793i	−0.646600	+	0.762830i	$0.723810\pi$
$432$	0.137805	−	1.83887i	0.137805	−	1.83887i
$433$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$433$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	1.57906	−	1.07659i	1.57906	−	1.07659i	0.623490	−	0.781831i	$-0.285714\pi$
$439$	1.57906	−	1.07659i	1.57906	−	1.07659i	0.955573	−	0.294755i	$-0.0952381\pi$
$440$		0			0
$441$	0.00320056	−	0.213926i	0.00320056	−	0.213926i
$442$		0			0
$443$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$443$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$444$	2.98795	−	2.77241i	2.98795	−	2.77241i
$445$		0			0
$446$		0			0
$447$	−0.0803272	+	0.351936i	−0.0803272	+	0.351936i
$448$	0.453707	−	0.235467i	0.453707	−	0.235467i
$449$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$449$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$450$	0.0292124	−	0.389813i	0.0292124	−	0.389813i
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.46020	+	1.35487i	1.46020	+	1.35487i	0.791071	+	0.611724i	$0.209524\pi$
$457$	1.46020	+	1.35487i	1.46020	+	1.35487i	0.669131	+	0.743145i	$0.266667\pi$
$458$		0			0
$459$	−0.364057	−	0.630565i	−0.364057	−	0.630565i
$460$		0			0
$461$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$461$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$462$		0			0
$463$		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		0.988831	−	0.149042i	$-0.0476190\pi$
$467$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	0.522106	−	0.904313i	0.522106	−	0.904313i
$472$	1.46664	+	2.54029i	1.46664	+	2.54029i
$473$		0			0
$474$	2.53361	+	2.35085i	2.53361	+	2.35085i
$475$		0			0
$476$	0.931536	−	1.73108i	0.931536	−	1.73108i
$477$	−0.274638	−	0.132259i	−0.274638	−	0.132259i
$478$	−1.23530	−	3.14750i	−1.23530	−	3.14750i
$479$	−0.00670551	−	0.0894788i	−0.00670551	−	0.0894788i	0.992847	−	0.119394i	$-0.0380952\pi$
$479$	−0.00670551	−	0.0894788i	−0.00670551	−	0.0894788i	−0.999552	+	0.0299155i	$0.990476\pi$
$480$		0			0
$481$		0			0
$482$	0.228024	+	0.999040i	0.228024	+	0.999040i
$483$		0			0
$484$	−0.520312	+	2.27964i	−0.520312	+	2.27964i
$485$		0			0
$486$	0.281038	−	0.716073i	0.281038	−	0.716073i
$487$	−1.21135	+	1.12397i	−1.21135	+	1.12397i	−0.222521	+	0.974928i	$0.571429\pi$
$487$	−1.21135	+	1.12397i	−1.21135	+	1.12397i	−0.988831	+	0.149042i	$0.952381\pi$
$488$	−2.61259	+	1.78124i	−2.61259	+	1.78124i
$489$		0			0
$490$		0			0
$491$	1.50614			1.50614			0.753071	−	0.657939i	$-0.228571\pi$
$491$	1.50614			1.50614			0.753071	+	0.657939i	$0.228571\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.578465	+	0.682447i	0.578465	+	0.682447i
$498$	0.327310	+	1.43404i	0.327310	+	1.43404i
$499$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$499$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$500$		0			0
$501$		0			0
$502$	−1.16602	−	2.97097i	−1.16602	−	2.97097i
$503$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$503$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$504$	0.514727	−	0.0934092i	0.514727	−	0.0934092i
$505$		0			0
$506$		0			0
$507$	1.08949	+	0.164214i	1.08949	+	0.164214i
$508$		0			0
$509$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$509$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$510$		0			0
$511$		0			0
$512$	−1.32754	−	1.66468i	−1.32754	−	1.66468i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−2.43607	−	1.55622i	−2.43607	−	1.55622i
$519$	−0.978744	+	1.22731i	−0.978744	+	1.22731i
$520$		0			0
$521$	−0.525684	−	0.910511i	−0.525684	−	0.910511i	−0.999552	−	0.0299155i	$-0.990476\pi$
$521$	−0.525684	−	0.910511i	−0.525684	−	0.910511i	0.473869	−	0.880596i	$-0.342857\pi$
$522$		0			0
$523$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.988831	−	0.149042i	$-0.952381\pi$
$523$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.222521	−	0.974928i	$-0.571429\pi$
$524$	1.42131	−	0.684465i	1.42131	−	0.684465i
$525$	−1.08409	+	0.196733i	−1.08409	+	0.196733i
$526$	−3.23940	−	1.56001i	−3.23940	−	1.56001i
$527$		0			0
$528$		0			0
$529$	0.955573	−	0.294755i	0.955573	−	0.294755i
$530$		0			0
$531$	0.0571130	+	0.250229i	0.0571130	+	0.250229i
$532$		0			0
$533$		0			0
$534$	3.11252	+	0.960085i	3.11252	+	0.960085i
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−2.67870			−2.67870
$539$		0			0
$540$		0			0
$541$	−1.65174	+	1.12614i	−1.65174	+	1.12614i	−0.809017	+	0.587785i	$0.800000\pi$
$541$	−1.65174	+	1.12614i	−1.65174	+	1.12614i	−0.842721	+	0.538351i	$0.819048\pi$
$542$	−2.11905	+	1.96619i	−2.11905	+	1.96619i
$543$		0			0
$544$	1.16096	+	0.358109i	1.16096	+	0.358109i
$545$		0			0
$546$		0			0
$547$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$547$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$548$		0			0
$549$	−0.264388	+	0.0815528i	−0.264388	+	0.0815528i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	0.813584	−	1.51189i	0.813584	−	1.51189i
$554$	−0.441937	+	0.212826i	−0.441937	+	0.212826i
$555$		0			0
$556$		0			0
$557$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$557$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$563$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$564$	−2.12862	−	1.45127i	−2.12862	−	1.45127i
$565$		0			0
$566$	1.19769	+	1.50185i	1.19769	+	1.50185i
$567$	−1.15982	−	0.139473i	−1.15982	−	0.139473i
$568$	−1.36387	+	1.71024i	−1.36387	+	1.71024i
$569$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$569$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$570$		0			0
$571$	−1.92128	−	0.289586i	−1.92128	−	0.289586i	−0.925304	−	0.379225i	$-0.876190\pi$
$571$	−1.92128	−	0.289586i	−1.92128	−	0.289586i	−0.995974	+	0.0896393i	$0.971429\pi$
$572$		0			0
$573$	0.148366	−	0.0714495i	0.148366	−	0.0714495i
$574$		0			0
$575$		0			0
$576$	0.0399555	+	0.101805i	0.0399555	+	0.101805i
$577$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$577$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$578$	−0.511902	+	0.157901i	−0.511902	+	0.157901i
$579$		0			0
$580$		0			0
$581$	0.648543	−	0.336583i	0.648543	−	0.336583i
$582$	−0.0936475	+	0.410296i	−0.0936475	+	0.410296i
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$	−1.08296	−	2.33761i	−1.08296	−	2.33761i
$589$		0			0
$590$		0			0
$591$	1.54358	−	1.43223i	1.54358	−	1.43223i
$592$	1.23073	−	3.13584i	1.23073	−	3.13584i
$593$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$593$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$594$		0			0
$595$		0			0
$596$	0.170473	+	0.746890i	0.170473	+	0.746890i
$597$		0			0
$598$		0			0
$599$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$599$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$600$	−0.984237	−	2.50780i	−0.984237	−	2.50780i
$601$	0.708207	+	0.341054i	0.708207	+	0.341054i	0.753071	−	0.657939i	$-0.228571\pi$
$601$	0.708207	+	0.341054i	0.708207	+	0.341054i	−0.0448648	+	0.998993i	$0.514286\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$	1.15876	+	2.00703i	1.15876	+	2.00703i
$607$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$607$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.347504	+	0.236924i	0.347504	+	0.236924i
$613$	1.46672	+	0.999990i	1.46672	+	0.999990i	0.992847	+	0.119394i	$0.0380952\pi$
$613$	1.46672	+	0.999990i	1.46672	+	0.999990i	0.473869	+	0.880596i	$0.342857\pi$
$614$	1.61631	−	0.243619i	1.61631	−	0.243619i
$615$		0			0
$616$		0			0
$617$	−0.349687	+	0.438494i	−0.349687	+	0.438494i	−0.925304	−	0.379225i	$-0.876190\pi$
$617$	−0.349687	+	0.438494i	−0.349687	+	0.438494i	0.575617	+	0.817719i	$0.304762\pi$
$618$	−1.86271	+	3.22631i	−1.86271	+	3.22631i
$619$	0.900969	+	1.56052i	0.900969	+	1.56052i	0.826239	+	0.563320i	$0.190476\pi$
$619$	0.900969	+	1.56052i	0.900969	+	1.56052i	0.0747301	+	0.997204i	$0.476190\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.0725928	−	1.61640i	0.0725928	−	1.61640i
$624$		0			0
$625$	0.365341	+	0.930874i	0.365341	+	0.930874i
$626$		0			0
$627$		0			0
$628$	0.165606	−	2.20986i	0.165606	−	2.20986i
$629$	−0.295982	−	1.29678i	−0.295982	−	1.29678i
$630$		0			0
$631$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$631$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$632$	4.01152	+	1.23739i	4.01152	+	1.23739i
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−3.67056			−3.67056
$637$		0			0
$638$		0			0
$639$	−0.158146	+	0.107822i	−0.158146	+	0.107822i
$640$		0			0
$641$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$641$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$642$		0			0
$643$	−0.395013	+	1.73066i	−0.395013	+	1.73066i	0.251587	+	0.967835i	$0.419048\pi$
$643$	−0.395013	+	1.73066i	−0.395013	+	1.73066i	−0.646600	+	0.762830i	$0.723810\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.89748	−	0.585294i	1.89748	−	0.585294i	0.913545	−	0.406737i	$-0.133333\pi$
$647$	1.89748	−	0.585294i	1.89748	−	0.585294i	0.983930	−	0.178557i	$-0.0571429\pi$
$648$	−0.213454	−	2.84835i	−0.213454	−	2.84835i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.37262	−	1.27360i	−1.37262	−	1.27360i	−0.925304	−	0.379225i	$-0.876190\pi$
$653$	−1.37262	−	1.27360i	−1.37262	−	1.27360i	−0.447313	−	0.894377i	$-0.647619\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$	−0.616333	+	1.72000i	−0.616333	+	1.72000i
$659$	0.167386	+	0.209896i	0.167386	+	0.209896i	0.858449	−	0.512899i	$-0.171429\pi$
$659$	0.167386	+	0.209896i	0.167386	+	0.209896i	−0.691063	+	0.722795i	$0.742857\pi$
$660$		0			0
$661$	1.60537	+	1.09452i	1.60537	+	1.09452i	0.936235	+	0.351375i	$0.114286\pi$
$661$	1.60537	+	1.09452i	1.60537	+	1.09452i	0.669131	+	0.743145i	$0.266667\pi$
$662$	−2.91042	−	1.98429i	−2.91042	−	1.98429i
$663$		0			0
$664$	1.11393	+	1.39683i	1.11393	+	1.39683i
$665$		0			0
$666$	0.385609	−	0.483538i	0.385609	−	0.483538i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	1.28814	−	0.935889i	1.28814	−	0.935889i
$673$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$673$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$674$	−1.12505	−	2.86658i	−1.12505	−	2.86658i
$675$	0.0647211	+	0.863644i	0.0647211	+	0.863644i
$676$	2.23438	−	0.689215i	2.23438	−	0.689215i
$677$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$677$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$678$		0			0
$679$	0.208963	−	0.00625404i	0.208963	−	0.00625404i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.18610	−	1.10054i	1.18610	−	1.10054i	0.193256	−	0.981148i	$-0.438095\pi$
$683$	1.18610	−	1.10054i	1.18610	−	1.10054i	0.992847	−	0.119394i	$-0.0380952\pi$
$684$		0			0
$685$		0			0
$686$	−1.41128	+	1.16041i	−1.41128	+	1.16041i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$691$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$692$	−0.741316	+	3.24792i	−0.741316	+	3.24792i
$693$		0			0
$694$	0.710196	+	3.11157i	0.710196	+	3.11157i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−1.89169	+	1.37440i	−1.89169	+	1.37440i
$701$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$701$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	2.08137	−	2.60996i	2.08137	−	2.60996i
$707$	0.820112	−	0.807934i	0.820112	−	0.807934i
$708$	1.92697	+	2.41634i	1.92697	+	2.41634i
$709$	−1.96352	+	0.295952i	−1.96352	+	0.295952i	−0.963963	+	0.266037i	$0.914286\pi$
$709$	−1.96352	+	0.295952i	−1.96352	+	0.295952i	−0.999552	+	0.0299155i	$0.990476\pi$
$710$		0			0
$711$	0.303502	+	0.206924i	0.303502	+	0.206924i
$712$	3.91211	−	0.589655i	3.91211	−	0.589655i
$713$		0			0
$714$	0.570905	−	1.59322i	0.570905	−	1.59322i
$715$		0			0
$716$		0			0
$717$	−1.01949	−	1.76582i	−1.01949	−	1.76582i
$718$		0			0
$719$	−0.694741	−	0.644625i	−0.694741	−	0.644625i	0.251587	−	0.967835i	$-0.419048\pi$
$719$	−0.694741	−	0.644625i	−0.694741	−	0.644625i	−0.946327	+	0.323210i	$0.895238\pi$
$720$		0			0
$721$	1.78392	+	0.492330i	1.78392	+	0.492330i
$722$	−1.64615	−	0.792745i	−1.64615	−	0.792745i
$723$	0.225761	+	0.575230i	0.225761	+	0.575230i
$724$		0			0
$725$		0			0
$726$	−0.150437	+	2.00745i	−0.150437	+	2.00745i
$727$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$727$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$728$		0			0
$729$	−0.156720	+	0.686636i	−0.156720	+	0.686636i
$730$		0			0
$731$		0			0
$732$	−2.44227	+	2.26609i	−2.44227	+	2.26609i
$733$	−1.27640	+	0.870236i	−1.27640	+	0.870236i	−0.995974	−	0.0896393i	$-0.971429\pi$
$733$	−1.27640	+	0.870236i	−1.27640	+	0.870236i	−0.280427	+	0.959875i	$0.590476\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−0.246481	+	0.628023i	−0.246481	+	0.628023i	−0.999552	−	0.0299155i	$-0.990476\pi$
$739$	−0.246481	+	0.628023i	−0.246481	+	0.628023i	0.753071	+	0.657939i	$0.228571\pi$
$740$		0			0
$741$		0			0
$742$	0.654919	+	2.51942i	0.654919	+	2.51942i
$743$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$743$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.0571135	+	0.145523i	0.0571135	+	0.145523i
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$751$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$752$	−2.10542	−	0.317341i	−2.10542	−	0.317341i
$753$	−0.962316	−	1.66678i	−0.962316	−	1.66678i
$754$		0			0
$755$		0			0
$756$	−1.91639	+	0.654528i	−1.91639	+	0.654528i
$757$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$757$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$758$	2.16738	−	0.326680i	2.16738	−	0.326680i
$759$		0			0
$760$		0			0
$761$	−1.63402	+	0.246289i	−1.63402	+	0.246289i	−0.900969	−	0.433884i	$-0.857143\pi$
$761$	−1.63402	+	0.246289i	−1.63402	+	0.246289i	−0.733052	+	0.680173i	$0.761905\pi$
$762$		0			0
$763$		0			0
$764$	0.217895	−	0.273232i	0.217895	−	0.273232i
$765$		0			0
$766$	−1.82382	−	3.15895i	−1.82382	−	3.15895i
$767$		0			0
$768$	−1.16719	−	1.08299i	−1.16719	−	1.08299i
$769$	1.79468	−	0.864274i	1.79468	−	0.864274i	0.858449	−	0.512899i	$-0.171429\pi$
$769$	1.79468	−	0.864274i	1.79468	−	0.864274i	0.936235	−	0.351375i	$-0.114286\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	0.0200625	+	0.267716i	0.0200625	+	0.267716i	0.998210	+	0.0598042i	$0.0190476\pi$
$773$	0.0200625	+	0.267716i	0.0200625	+	0.267716i	−0.978148	+	0.207912i	$0.933333\pi$
$774$		0			0
$775$		0			0
$776$	0.113746	+	0.498354i	0.113746	+	0.498354i
$777$	−1.59249	−	0.709021i	−1.59249	−	0.709021i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−1.64463	−	1.35229i	−1.64463	−	1.35229i
$785$		0			0
$786$	1.12215	−	0.765069i	1.12215	−	0.765069i
$787$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$787$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$788$	1.63262	−	4.15985i	1.63262	−	4.15985i
$789$	−2.07185	−	0.639081i	−2.07185	−	0.639081i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	3.48559	−	1.07516i	3.48559	−	1.07516i
$795$		0			0
$796$		0			0
$797$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$797$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$798$		0			0
$799$	−0.757458	+	0.364772i	−0.757458	+	0.364772i
$800$	−1.05935	−	0.982935i	−1.05935	−	0.982935i
$801$	0.342312	+	0.0515952i	0.342312	+	0.0515952i
$802$	1.41128	+	2.44440i	1.41128	+	2.44440i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.59730	+	0.240755i	−1.59730	+	0.240755i
$808$	2.32579	+	1.58570i	2.32579	+	1.58570i
$809$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$809$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$810$		0			0
$811$	0.834392	+	1.04629i	0.834392	+	1.04629i	0.998210	+	0.0598042i	$0.0190476\pi$
$811$	0.834392	+	1.04629i	0.834392	+	1.04629i	−0.163818	+	0.986491i	$0.552381\pi$
$812$		0			0
$813$	−1.08686	+	1.36288i	−1.08686	+	1.36288i
$814$		0			0
$815$		0			0
$816$	1.95024	+	0.293952i	1.95024	+	0.293952i
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$821$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$822$		0			0
$823$	1.82624	−	0.563320i	1.82624	−	0.563320i	0.826239	−	0.563320i	$-0.190476\pi$
$823$	1.82624	−	0.563320i	1.82624	−	0.563320i	1.00000			$0$
$824$	−0.338151	+	4.51232i	−0.338151	+	4.51232i
$825$		0			0
$826$	1.31472	−	1.75378i	1.31472	−	1.75378i
$827$	0.421155	−	1.84520i	0.421155	−	1.84520i	−0.104528	−	0.994522i	$-0.533333\pi$
$827$	0.421155	−	1.84520i	0.421155	−	1.84520i	0.525684	−	0.850680i	$-0.323810\pi$
$828$		0			0
$829$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$829$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$830$		0			0
$831$	−0.244397	+	0.166627i	−0.244397	+	0.166627i
$832$		0			0
$833$	−0.837330	−	0.0753611i	−0.837330	−	0.0753611i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$839$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$840$		0			0
$841$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		0			0
$846$	−0.352194	−	0.169608i	−0.352194	−	0.169608i
$847$	0.983930	−	0.178557i	0.983930	−	0.178557i
$848$	−2.73317	+	1.31622i	−2.73317	+	1.31622i
$849$	0.849160	+	0.787906i	0.849160	+	0.787906i
$850$	−1.51891	−	0.228938i	−1.51891	−	0.228938i
$851$		0			0
$852$	−1.15240	+	1.99602i	−1.15240	+	1.99602i
$853$	0.385338	−	0.483198i	0.385338	−	0.483198i	−0.550897	−	0.834573i	$-0.685714\pi$
$853$	0.385338	−	0.483198i	0.385338	−	0.483198i	0.936235	+	0.351375i	$0.114286\pi$
$854$	1.99117	+	1.27201i	1.99117	+	1.27201i
$855$		0			0
$856$		0			0
$857$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$857$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$858$		0			0
$859$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$859$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$860$		0			0
$861$		0			0
$862$	−1.92001	+	2.40762i	−1.92001	+	2.40762i
$863$	0.550897	−	0.954182i	0.550897	−	0.954182i	−0.447313	−	0.894377i	$-0.647619\pi$
$863$	0.550897	−	0.954182i	0.550897	−	0.954182i	0.998210	−	0.0598042i	$-0.0190476\pi$
$864$	−0.625786	−	1.08389i	−0.625786	−	1.08389i
$865$		0			0
$866$		0			0
$867$	−0.291054	+	0.140164i	−0.291054	+	0.140164i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.00334251	+	0.0446026i	−0.00334251	+	0.0446026i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$877$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$878$	1.27571	−	3.25046i	1.27571	−	3.25046i
$879$		0			0
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−0.215349	−	0.326240i	−0.215349	−	0.326240i
$883$	0.386512			0.386512			0.193256	−	0.981148i	$-0.438095\pi$
$883$	0.386512			0.386512			0.193256	+	0.981148i	$0.438095\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$887$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$888$	0.948457	−	4.15546i	0.948457	−	4.15546i
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$	0.240963	+	0.613964i	0.240963	+	0.613964i
$895$		0			0
$896$	−0.242228	+	0.450134i	−0.242228	+	0.450134i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−0.250135	−	0.433247i	−0.250135	−	0.433247i
$901$	−0.598905	+	1.03733i	−0.598905	+	1.03733i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.826239	−	0.563320i	−0.826239	−	0.563320i	0.0747301	−	0.997204i	$-0.476190\pi$
$907$	−0.826239	−	0.563320i	−0.826239	−	0.563320i	−0.900969	+	0.433884i	$0.857143\pi$
$908$		0			0
$909$	0.153570	+	0.192570i	0.153570	+	0.192570i
$910$		0			0
$911$	−0.420644	+	0.527470i	−0.420644	+	0.527470i	−0.946327	−	0.323210i	$-0.895238\pi$
$911$	−0.420644	+	0.527470i	−0.420644	+	0.527470i	0.525684	+	0.850680i	$0.323810\pi$
$912$		0			0
$913$		0			0
$914$	3.59882	+	0.542435i	3.59882	+	0.542435i
$915$		0			0
$916$		0			0
$917$	−0.508067	−	0.443885i	−0.508067	−	0.443885i
$918$	−1.19859	−	0.577208i	−1.19859	−	0.577208i
$919$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$919$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$920$		0			0
$921$	0.941902	−	0.290538i	0.941902	−	0.290538i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.352060	+	1.54247i	−0.352060	+	1.54247i
$926$		0			0
$927$	−0.144652	+	0.368568i	−0.144652	+	0.368568i
$928$		0			0
$929$	1.54711	−	1.05480i	1.54711	−	1.05480i	0.575617	−	0.817719i	$-0.304762\pi$
$929$	1.54711	−	1.05480i	1.54711	−	1.05480i	0.971490	−	0.237080i	$-0.0761905\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$937$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.43923	−	0.443943i	1.43923	−	0.443943i	0.525684	−	0.850680i	$-0.323810\pi$
$941$	1.43923	−	0.443943i	1.43923	−	0.443943i	0.913545	+	0.406737i	$0.133333\pi$
$942$	−0.142575	−	1.90253i	−0.142575	−	1.90253i
$943$		0			0
$944$	2.30133	+	1.10826i	2.30133	+	1.10826i
$945$		0			0
$946$		0			0
$947$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.988831	−	0.149042i	$-0.952381\pi$
$947$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.222521	−	0.974928i	$-0.571429\pi$
$948$	4.37381	+	0.659246i	4.37381	+	0.659246i
$949$		0			0
$950$		0			0
$951$		0			0
$952$	−0.214874	−	2.04439i	−0.214874	−	2.04439i
$953$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$953$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$954$	−0.550724	+	0.0830082i	−0.550724	+	0.0830082i
$955$		0			0
$956$	−3.57531	−	2.43760i	−3.57531	−	2.43760i
$957$		0			0
$958$	−0.102218	−	0.128177i	−0.102218	−	0.128177i
$959$		0			0
$960$		0			0
$961$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$962$		0			0
$963$		0			0
$964$	0.961343	+	0.891996i	0.961343	+	0.891996i
$965$		0			0
$966$		0			0
$967$	−1.35699	−	0.653491i	−1.35699	−	0.653491i	−0.393025	−	0.919528i	$-0.628571\pi$
$967$	−1.35699	−	0.653491i	−1.35699	−	0.653491i	−0.963963	+	0.266037i	$0.914286\pi$
$968$	0.893304	+	2.27610i	0.893304	+	2.27610i
$969$		0			0
$970$		0			0
$971$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$971$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$972$	−0.219064	−	0.959780i	−0.219064	−	0.959780i
$973$		0			0
$974$	−0.671841	+	2.94353i	−0.671841	+	2.94353i
$975$		0			0
$976$	−1.00596	+	2.56315i	−1.00596	+	2.56315i
$977$	−0.535628	+	0.496990i	−0.535628	+	0.496990i	−0.900969	−	0.433884i	$-0.857143\pi$
$977$	−0.535628	+	0.496990i	−0.535628	+	0.496990i	0.365341	+	0.930874i	$0.380952\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	2.27369	−	1.55018i	2.27369	−	1.55018i
$983$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$983$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−0.212928	+	1.08102i	−0.212928	+	1.08102i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.0376022	+	0.501767i	0.0376022	+	0.501767i	0.983930	+	0.178557i	$0.0571429\pi$
$991$	0.0376022	+	0.501767i	0.0376022	+	0.501767i	−0.946327	+	0.323210i	$0.895238\pi$
$992$		0			0
$993$	−1.91382	−	0.921646i	−1.91382	−	0.921646i
$994$	1.57566	+	0.434854i	1.57566	+	0.434854i
$995$		0			0
$996$	1.37993	+	1.28039i	1.37993	+	1.28039i
$997$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$997$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$998$		0			0
$999$	−0.685119	+	1.18666i	−0.685119	+	1.18666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.1.q.b.1409.4	yes	48
47.46	odd	2	CM	2303.1.q.b.1409.4	yes	48
49.4	even	21	inner	2303.1.q.b.1033.4	✓	48
2303.1033	odd	42	inner	2303.1.q.b.1033.4	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.1.q.b.1033.4	✓	48	49.4	even	21	inner
2303.1.q.b.1033.4	✓	48	2303.1033	odd	42	inner
2303.1.q.b.1409.4	yes	48	1.1	even	1	trivial
2303.1.q.b.1409.4	yes	48	47.46	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2303 = 7^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2303.q (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50961 - 1.02924i) q^{2} +(0.807672 - 0.749410i) q^{3} +(0.854263 - 2.17663i) q^{4} +(0.447952 - 1.96261i) q^{6} +(-0.999552 + 0.0299155i) q^{7} +(-0.544091 - 2.38382i) q^{8} +(0.0159885 - 0.213352i) q^{9} +O(q^{10})\)	\(q+(1.50961 - 1.02924i) q^{2} +(0.807672 - 0.749410i) q^{3} +(0.854263 - 2.17663i) q^{4} +(0.447952 - 1.96261i) q^{6} +(-0.999552 + 0.0299155i) q^{7} +(-0.544091 - 2.38382i) q^{8} +(0.0159885 - 0.213352i) q^{9} +(-0.941222 - 2.39819i) q^{12} +(-1.47815 + 1.07394i) q^{14} +(-1.56082 - 1.44823i) q^{16} +(-0.831324 - 0.125302i) q^{17} +(-0.195453 - 0.338535i) q^{18} +(-0.784892 + 0.773237i) q^{21} +(-2.22591 - 1.51760i) q^{24} +(0.826239 + 0.563320i) q^{25} +(0.539983 + 0.677117i) q^{27} +(-0.788766 + 2.20121i) q^{28} +(-1.42898 - 0.215385i) q^{32} +(-1.38394 + 0.666472i) q^{34} +(-0.450728 - 0.217059i) q^{36} +(0.578021 + 1.47277i) q^{37} +(-0.389039 + 1.97513i) q^{42} +(0.826239 - 0.563320i) q^{47} -2.34594 q^{48} +(0.998210 - 0.0598042i) q^{49} +1.82709 q^{50} +(-0.765340 + 0.521800i) q^{51} +(0.520520 - 1.32626i) q^{53} +(1.51208 + 0.466415i) q^{54} +(0.615161 + 2.36648i) q^{56} +(-1.14635 + 0.353601i) q^{59} +(-0.472459 - 1.20381i) q^{61} +(-0.00959883 + 0.213735i) q^{63} +(-0.460549 + 0.221788i) q^{64} +(-0.982905 + 1.70244i) q^{68} +(-0.557790 - 0.699447i) q^{71} +(-0.517291 + 0.0779691i) q^{72} +(2.38842 + 1.62840i) q^{74} +(1.08949 - 0.164214i) q^{75} +(-0.858449 + 1.48688i) q^{79} +(1.15513 + 0.174108i) q^{81} +(-0.658322 + 0.317031i) q^{83} +(1.01254 + 2.36896i) q^{84} +(-0.120916 + 1.61351i) q^{89} +(0.667511 - 1.70079i) q^{94} +(-1.31556 + 0.896935i) q^{96} -0.209057 q^{97} +(1.44536 - 1.11768i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} - 2 q^{3} + 5 q^{4} - 4 q^{6} - q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 48 * q + q^2 - 2 * q^3 + 5 * q^4 - 4 * q^6 - q^7 + 2 * q^8 + 2 * q^9	\( 48 q + q^{2} - 2 q^{3} + 5 q^{4} - 4 q^{6} - q^{7} + 2 q^{8} + 2 q^{9} - 40 q^{12} - 18 q^{14} + 6 q^{16} + q^{17} - 9 q^{18} + 5 q^{21} + 8 q^{24} + 4 q^{25} - 6 q^{27} - 5 q^{32} + 2 q^{34} - 10 q^{36} + q^{37} + 7 q^{42} + 4 q^{47} + 6 q^{48} - q^{49} + 12 q^{50} + 4 q^{51} + 8 q^{53} - q^{54} - 11 q^{56} - 13 q^{59} + q^{61} - 4 q^{63} - 8 q^{64} - 5 q^{68} + 5 q^{71} - 8 q^{72} + 13 q^{74} + 5 q^{75} - 2 q^{79} + 8 q^{83} + 5 q^{84} - 2 q^{89} + q^{94} + 10 q^{96} + 12 q^{97} + q^{98}+O(q^{100}) \) 48 * q + q^2 - 2 * q^3 + 5 * q^4 - 4 * q^6 - q^7 + 2 * q^8 + 2 * q^9 - 40 * q^12 - 18 * q^14 + 6 * q^16 + q^17 - 9 * q^18 + 5 * q^21 + 8 * q^24 + 4 * q^25 - 6 * q^27 - 5 * q^32 + 2 * q^34 - 10 * q^36 + q^37 + 7 * q^42 + 4 * q^47 + 6 * q^48 - q^49 + 12 * q^50 + 4 * q^51 + 8 * q^53 - q^54 - 11 * q^56 - 13 * q^59 + q^61 - 4 * q^63 - 8 * q^64 - 5 * q^68 + 5 * q^71 - 8 * q^72 + 13 * q^74 + 5 * q^75 - 2 * q^79 + 8 * q^83 + 5 * q^84 - 2 * q^89 + q^94 + 10 * q^96 + 12 * q^97 + q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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