LMFDB - Embedded newform 2303.1.q.b.1080.3

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			1080.3
Root			$0.447313 - 0.894377i$ of defining polynomial
Character	$\chi$	$=$	2303.1080
Dual form			2303.1.q.b.1691.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.27881 + 0.394459i) q^{2} +(0.718940 - 1.83183i) q^{3} +(0.653508 + 0.445554i) q^{4} +(1.64197 - 2.05896i) q^{6} +(0.575617 + 0.817719i) q^{7} +(-0.174435 - 0.218735i) q^{8} +(-2.10567 - 1.95378i) q^{9} +O(q^{10})$	\(q+(1.27881 + 0.394459i) q^{2} +(0.718940 - 1.83183i) q^{3} +(0.653508 + 0.445554i) q^{4} +(1.64197 - 2.05896i) q^{6} +(0.575617 + 0.817719i) q^{7} +(-0.174435 - 0.218735i) q^{8} +(-2.10567 - 1.95378i) q^{9} +(1.28601 - 0.876788i) q^{12} +(0.413545 + 1.27276i) q^{14} +(-0.425751 - 1.08480i) q^{16} +(0.0376022 + 0.501767i) q^{17} +(-1.92206 - 3.32910i) q^{18} +(1.91176 - 0.466541i) q^{21} +(-0.526094 + 0.162278i) q^{24} +(0.955573 - 0.294755i) q^{25} +(-3.31985 + 1.59876i) q^{27} +(0.0118320 + 0.790855i) q^{28} +(-0.0956375 - 1.27619i) q^{32} +(-0.149841 + 0.656495i) q^{34} +(-0.505559 - 2.21500i) q^{36} +(-0.991192 + 0.675783i) q^{37} +(2.62880 + 0.157495i) q^{42} +(0.955573 + 0.294755i) q^{47} -2.29325 q^{48} +(-0.337330 + 0.941386i) q^{49} +1.33826 q^{50} +(0.946184 + 0.291859i) q^{51} +(1.60537 + 1.09452i) q^{53} +(-4.87609 + 0.734952i) q^{54} +(0.0784559 - 0.268547i) q^{56} +(0.323976 + 0.0488316i) q^{59} +(-1.44329 + 0.984017i) q^{61} +(0.385581 - 2.84647i) q^{63} +(0.121790 - 0.533596i) q^{64} +(-0.198991 + 0.344662i) q^{68} +(1.16513 - 0.561098i) q^{71} +(-0.0600560 + 0.801392i) q^{72} +(-1.53411 + 0.473211i) q^{74} +(0.147058 - 1.96236i) q^{75} +(0.0448648 - 0.0777082i) q^{79} +(0.327214 + 4.36637i) q^{81} +(-0.367711 + 1.61105i) q^{83} +(1.45722 + 0.546902i) q^{84} +(-0.453051 - 0.420370i) q^{89} +(1.10572 + 0.753869i) q^{94} +(-2.40653 - 0.742315i) q^{96} -1.95630 q^{97} +(-0.802718 + 1.07079i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2303\mathbb{Z}\right)^\times$.

$n$	$99$	$2257$
$\chi(n)$	$-1$	$e\left(\frac{13}{21}\right)$

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 $

$2$	1.27881	+	0.394459i	1.27881	+	0.394459i	0.858449	−	0.512899i	$-0.171429\pi$
$2$	1.27881	+	0.394459i	1.27881	+	0.394459i	0.420357	+	0.907359i	$0.361905\pi$
$3$	0.718940	−	1.83183i	0.718940	−	1.83183i	0.193256	−	0.981148i	$-0.438095\pi$
$3$	0.718940	−	1.83183i	0.718940	−	1.83183i	0.525684	−	0.850680i	$-0.323810\pi$
$4$	0.653508	+	0.445554i	0.653508	+	0.445554i
$5$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$5$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$6$	1.64197	−	2.05896i	1.64197	−	2.05896i
$7$	0.575617	+	0.817719i	0.575617	+	0.817719i
$7$	0.575617	+	0.817719i	0.575617	+	0.817719i
$8$	−0.174435	−	0.218735i	−0.174435	−	0.218735i
$9$	−2.10567	−	1.95378i	−2.10567	−	1.95378i
$10$		0			0
$11$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$11$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$12$	1.28601	−	0.876788i	1.28601	−	0.876788i
$13$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$13$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$14$	0.413545	+	1.27276i	0.413545	+	1.27276i
$15$		0			0
$16$	−0.425751	−	1.08480i	−0.425751	−	1.08480i
$17$	0.0376022	+	0.501767i	0.0376022	+	0.501767i	0.983930	+	0.178557i	$0.0571429\pi$
$17$	0.0376022	+	0.501767i	0.0376022	+	0.501767i	−0.946327	+	0.323210i	$0.895238\pi$
$18$	−1.92206	−	3.32910i	−1.92206	−	3.32910i
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$		0			0
$21$	1.91176	−	0.466541i	1.91176	−	0.466541i
$22$		0			0
$23$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$23$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$24$	−0.526094	+	0.162278i	−0.526094	+	0.162278i
$25$	0.955573	−	0.294755i	0.955573	−	0.294755i
$26$		0			0
$27$	−3.31985	+	1.59876i	−3.31985	+	1.59876i
$28$	0.0118320	+	0.790855i	0.0118320	+	0.790855i
$29$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$29$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$30$		0			0
$31$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$31$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$32$	−0.0956375	−	1.27619i	−0.0956375	−	1.27619i
$33$		0			0
$34$	−0.149841	+	0.656495i	−0.149841	+	0.656495i
$35$		0			0
$36$	−0.505559	−	2.21500i	−0.505559	−	2.21500i
$37$	−0.991192	+	0.675783i	−0.991192	+	0.675783i	−0.946327	−	0.323210i	$-0.895238\pi$
$37$	−0.991192	+	0.675783i	−0.991192	+	0.675783i	−0.0448648	+	0.998993i	$0.514286\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$41$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$42$	2.62880	+	0.157495i	2.62880	+	0.157495i
$43$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$43$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.955573	+	0.294755i	0.955573	+	0.294755i
$47$	0.955573	+	0.294755i	0.955573	+	0.294755i
$48$	−2.29325			−2.29325
$49$	−0.337330	+	0.941386i	−0.337330	+	0.941386i
$50$	1.33826			1.33826
$51$	0.946184	+	0.291859i	0.946184	+	0.291859i
$52$		0			0
$53$	1.60537	+	1.09452i	1.60537	+	1.09452i	0.936235	+	0.351375i	$0.114286\pi$
$53$	1.60537	+	1.09452i	1.60537	+	1.09452i	0.669131	+	0.743145i	$0.266667\pi$
$54$	−4.87609	+	0.734952i	−4.87609	+	0.734952i
$55$		0			0
$56$	0.0784559	−	0.268547i	0.0784559	−	0.268547i
$57$		0			0
$58$		0			0
$59$	0.323976	+	0.0488316i	0.323976	+	0.0488316i	0.309017	−	0.951057i	$-0.400000\pi$
$59$	0.323976	+	0.0488316i	0.323976	+	0.0488316i	0.0149594	+	0.999888i	$0.495238\pi$
$60$		0			0
$61$	−1.44329	+	0.984017i	−1.44329	+	0.984017i	−0.447313	+	0.894377i	$0.647619\pi$
$61$	−1.44329	+	0.984017i	−1.44329	+	0.984017i	−0.995974	+	0.0896393i	$0.971429\pi$
$62$		0			0
$63$	0.385581	−	2.84647i	0.385581	−	2.84647i
$64$	0.121790	−	0.533596i	0.121790	−	0.533596i
$65$		0			0
$66$		0			0
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$	−0.198991	+	0.344662i	−0.198991	+	0.344662i
$69$		0			0
$70$		0			0
$71$	1.16513	−	0.561098i	1.16513	−	0.561098i	0.251587	−	0.967835i	$-0.419048\pi$
$71$	1.16513	−	0.561098i	1.16513	−	0.561098i	0.913545	+	0.406737i	$0.133333\pi$
$72$	−0.0600560	+	0.801392i	−0.0600560	+	0.801392i
$73$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$73$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$74$	−1.53411	+	0.473211i	−1.53411	+	0.473211i
$75$	0.147058	−	1.96236i	0.147058	−	1.96236i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	0.0448648	−	0.0777082i	0.0448648	−	0.0777082i	−0.842721	−	0.538351i	$-0.819048\pi$
$79$	0.0448648	−	0.0777082i	0.0448648	−	0.0777082i	0.887586	+	0.460642i	$0.152381\pi$
$80$		0			0
$81$	0.327214	+	4.36637i	0.327214	+	4.36637i
$82$		0			0
$83$	−0.367711	+	1.61105i	−0.367711	+	1.61105i	0.365341	+	0.930874i	$0.380952\pi$
$83$	−0.367711	+	1.61105i	−0.367711	+	1.61105i	−0.733052	+	0.680173i	$0.761905\pi$
$84$	1.45722	+	0.546902i	1.45722	+	0.546902i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.453051	−	0.420370i	−0.453051	−	0.420370i	0.420357	−	0.907359i	$-0.361905\pi$
$89$	−0.453051	−	0.420370i	−0.453051	−	0.420370i	−0.873408	+	0.486989i	$0.838095\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$	1.10572	+	0.753869i	1.10572	+	0.753869i
$95$		0			0
$96$	−2.40653	−	0.742315i	−2.40653	−	0.742315i
$97$	−1.95630			−1.95630			−0.978148	−	0.207912i	$-0.933333\pi$
$97$	−1.95630			−1.95630			−0.978148	+	0.207912i	$0.933333\pi$
$98$	−0.802718	+	1.07079i	−0.802718	+	1.07079i
$99$		0			0
$100$	0.755804	+	0.233135i	0.755804	+	0.233135i
$101$	0.520520	−	1.32626i	0.520520	−	1.32626i	−0.393025	−	0.919528i	$-0.628571\pi$
$101$	0.520520	−	1.32626i	0.520520	−	1.32626i	0.913545	−	0.406737i	$-0.133333\pi$
$102$	1.09486	+	0.746462i	1.09486	+	0.746462i
$103$	−1.96352	+	0.295952i	−1.96352	+	0.295952i	−0.963963	+	0.266037i	$0.914286\pi$
$103$	−1.96352	+	0.295952i	−1.96352	+	0.295952i	−0.999552	+	0.0299155i	$0.990476\pi$
$104$		0			0
$105$		0			0
$106$	1.62121	+	2.03293i	1.62121	+	2.03293i
$107$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$107$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$108$	−2.88188	−	0.434374i	−2.88188	−	0.434374i
$109$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$109$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$110$		0			0
$111$	0.525312	+	2.30154i	0.525312	+	2.30154i
$112$	0.641989	−	0.972572i	0.641989	−	0.972572i
$113$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$113$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.395041	+	0.190242i	0.395041	+	0.190242i
$119$	−0.388660	+	0.319573i	−0.388660	+	0.319573i
$120$		0			0
$121$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$122$	−2.23384	+	0.689048i	−2.23384	+	0.689048i
$123$		0			0
$124$		0			0
$125$		0			0
$126$	1.61590	−	3.48799i	1.61590	−	3.48799i
$127$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$127$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$128$	−0.273659	+	0.473991i	−0.273659	+	0.473991i
$129$		0			0
$130$		0			0
$131$	0.0109306	+	0.0278506i	0.0109306	+	0.0278506i	0.936235	−	0.351375i	$-0.114286\pi$
$131$	0.0109306	+	0.0278506i	0.0109306	+	0.0278506i	−0.925304	+	0.379225i	$0.876190\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.103195	−	0.0957508i	0.103195	−	0.0957508i
$137$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$137$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$138$		0			0
$139$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$139$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$140$		0			0
$141$	1.22694	−	1.53853i	1.22694	−	1.53853i
$142$	1.71131	−	0.257938i	1.71131	−	0.257938i
$143$		0			0
$144$	−1.22296	+	3.11604i	−1.22296	+	3.11604i
$145$		0			0
$146$		0			0
$147$	1.48194	+	1.29473i	1.48194	+	1.29473i
$148$	−0.948850			−0.948850
$149$	1.00466	+	0.309896i	1.00466	+	0.309896i	0.753071	−	0.657939i	$-0.228571\pi$
$149$	1.00466	+	0.309896i	1.00466	+	0.309896i	0.251587	+	0.967835i	$0.419048\pi$
$150$	0.962129	−	2.45146i	0.962129	−	2.45146i
$151$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$151$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$152$		0			0
$153$	0.901161	−	1.13002i	0.901161	−	1.13002i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	1.96970	+	0.296885i	1.96970	+	0.296885i	0.998210	+	0.0598042i	$0.0190476\pi$
$157$	1.96970	+	0.296885i	1.96970	+	0.296885i	0.971490	+	0.237080i	$0.0761905\pi$
$158$	0.0880261	−	0.0816763i	0.0880261	−	0.0816763i
$159$	3.15913	−	2.15386i	3.15913	−	2.15386i
$160$		0			0
$161$		0			0
$162$	−1.30391	+	5.71281i	−1.30391	+	5.71281i
$163$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$163$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$164$		0			0
$165$		0			0
$166$	−1.10572	+	1.91517i	−1.10572	+	1.91517i
$167$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$167$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$168$	−0.435527	−	0.336787i	−0.435527	−	0.336787i
$169$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.145199	−	1.93755i	0.145199	−	1.93755i	−0.163818	−	0.986491i	$-0.552381\pi$
$173$	0.145199	−	1.93755i	0.145199	−	1.93755i	0.309017	−	0.951057i	$-0.400000\pi$
$174$		0			0
$175$	0.791071	+	0.611724i	0.791071	+	0.611724i
$176$		0			0
$177$	0.322371	−	0.558362i	0.322371	−	0.558362i
$178$	−0.413545	−	0.716282i	−0.413545	−	0.716282i
$179$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$179$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$180$		0			0
$181$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$181$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$182$		0			0
$183$	0.764913	+	3.35130i	0.764913	+	3.35130i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	0.493145	+	0.618384i	0.493145	+	0.618384i
$189$	−3.21830	−	1.79444i	−3.21830	−	1.79444i
$190$		0			0
$191$	1.44973	−	0.218511i	1.44973	−	0.218511i	0.623490	−	0.781831i	$-0.285714\pi$
$191$	1.44973	−	0.218511i	1.44973	−	0.218511i	0.826239	+	0.563320i	$0.190476\pi$
$192$	−0.889896	−	0.606721i	−0.889896	−	0.606721i
$193$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$193$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$194$	−2.50172	−	0.771679i	−2.50172	−	0.771679i
$195$		0			0
$196$	−0.639886	+	0.464905i	−0.639886	+	0.464905i
$197$	−1.97766			−1.97766			−0.988831	−	0.149042i	$-0.952381\pi$
$197$	−1.97766			−1.97766			−0.988831	+	0.149042i	$0.952381\pi$
$198$		0			0
$199$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$199$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$200$	−0.231159	−	0.157602i	−0.231159	−	0.157602i
$201$		0			0
$202$	1.18880	−	1.49071i	1.18880	−	1.49071i
$203$		0			0
$204$	0.488300	+	0.612308i	0.488300	+	0.612308i
$205$		0			0
$206$	−2.62770	−	0.396061i	−2.62770	−	0.396061i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$211$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$212$	0.561451	+	1.43055i	0.561451	+	1.43055i
$213$	−0.190176	−	2.53772i	−0.190176	−	2.53772i
$214$		0			0
$215$		0			0
$216$	0.928804	+	0.447288i	0.928804	+	0.447288i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$	−0.236093	+	3.15044i	−0.236093	+	3.15044i
$223$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$223$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$224$	0.988518	−	0.812804i	0.988518	−	0.812804i
$225$	−2.58801	−	1.24632i	−2.58801	−	1.24632i
$226$		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		−0.365341	−	0.930874i	$-0.619048\pi$
$229$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$233$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$234$		0			0
$235$		0			0
$236$	0.189964	+	0.176261i	0.189964	+	0.176261i
$237$	−0.110093	−	0.138052i	−0.110093	−	0.138052i
$238$	−0.623079	+	0.255362i	−0.623079	+	0.255362i
$239$	1.23806	−	1.55248i	1.23806	−	1.55248i	0.525684	−	0.850680i	$-0.323810\pi$
$239$	1.23806	−	1.55248i	1.23806	−	1.55248i	0.712376	−	0.701798i	$-0.247619\pi$
$240$		0			0
$241$	−1.56378	−	1.06617i	−1.56378	−	1.06617i	−0.963963	−	0.266037i	$-0.914286\pi$
$241$	−1.56378	−	1.06617i	−1.56378	−	1.06617i	−0.599822	−	0.800134i	$-0.704762\pi$
$242$	0.488922	−	1.24575i	0.488922	−	1.24575i
$243$	4.71263	+	1.45365i	4.71263	+	1.45365i
$244$	−1.38163			−1.38163
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$	2.68680	+	1.83183i	2.68680	+	1.83183i
$250$		0			0
$251$	−1.05086	+	1.31773i	−1.05086	+	1.31773i	−0.104528	+	0.994522i	$0.533333\pi$
$251$	−1.05086	+	1.31773i	−1.05086	+	1.31773i	−0.946327	+	0.323210i	$0.895238\pi$
$252$	1.52024	−	1.68840i	1.52024	−	1.68840i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.938140	+	0.870467i	−0.938140	+	0.870467i
$257$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$257$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$258$		0			0
$259$	−1.12315	−	0.421525i	−1.12315	−	0.421525i
$260$		0			0
$261$		0			0
$262$	0.00299213	+	0.0399272i	0.00299213	+	0.0399272i
$263$	−0.858449	−	1.48688i	−0.858449	−	1.48688i	−0.873408	−	0.486989i	$-0.838095\pi$
$263$	−0.858449	−	1.48688i	−0.858449	−	1.48688i	0.0149594	−	0.999888i	$-0.495238\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.09576	+	0.527691i	−1.09576	+	0.527691i
$268$		0			0
$269$	0.698220	−	0.215372i	0.698220	−	0.215372i	0.0747301	−	0.997204i	$-0.476190\pi$
$269$	0.698220	−	0.215372i	0.698220	−	0.215372i	0.623490	+	0.781831i	$0.285714\pi$
$270$		0			0
$271$	−0.0896495	+	1.19629i	−0.0896495	+	1.19629i	0.753071	+	0.657939i	$0.228571\pi$
$271$	−0.0896495	+	1.19629i	−0.0896495	+	1.19629i	−0.842721	+	0.538351i	$0.819048\pi$
$272$	0.528305	−	0.254418i	0.528305	−	0.254418i
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−0.0587416	−	0.783852i	−0.0587416	−	0.783852i	−0.946327	−	0.323210i	$-0.895238\pi$
$277$	−0.0587416	−	0.783852i	−0.0587416	−	0.783852i	0.887586	−	0.460642i	$-0.152381\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$281$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$282$	2.17591	−	1.48351i	2.17591	−	1.48351i
$283$	−0.616287	+	0.571831i	−0.616287	+	0.571831i	−0.925304	−	0.379225i	$-0.876190\pi$
$283$	−0.616287	+	0.571831i	−0.616287	+	0.571831i	0.309017	+	0.951057i	$0.400000\pi$
$284$	1.01142	+	0.152447i	1.01142	+	0.152447i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−2.29202	+	2.87410i	−2.29202	+	2.87410i
$289$	0.738475	−	0.111307i	0.738475	−	0.111307i
$290$		0			0
$291$	−1.40646	+	3.58360i	−1.40646	+	3.58360i
$292$		0			0
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	1.38439	+	2.24027i	1.38439	+	2.24027i
$295$		0			0
$296$	0.320717	+	0.0989280i	0.320717	+	0.0989280i
$297$		0			0
$298$	1.16252	+	0.792594i	1.16252	+	0.792594i
$299$		0			0
$300$	0.970440	−	1.21689i	0.970440	−	1.21689i
$301$		0			0
$302$		0			0
$303$	−2.05527	−	1.90701i	−2.05527	−	1.90701i
$304$		0			0
$305$		0			0
$306$	1.59816	−	1.08961i	1.59816	−	1.08961i
$307$	0.287764	+	1.26078i	0.287764	+	1.26078i	0.887586	+	0.460642i	$0.152381\pi$
$307$	0.287764	+	1.26078i	0.287764	+	1.26078i	−0.599822	+	0.800134i	$0.704762\pi$
$308$		0			0
$309$	−0.869515	+	3.80960i	−0.869515	+	3.80960i
$310$		0			0
$311$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$311$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$312$		0			0
$313$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$313$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$314$	2.40176	+	1.15662i	2.40176	+	1.15662i
$315$		0			0
$316$	0.0639427	−	0.0307932i	0.0639427	−	0.0307932i
$317$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$317$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$318$	4.88953	−	1.50822i	4.88953	−	1.50822i
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−1.73162	+	2.99925i	−1.73162	+	2.99925i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.309017	+	0.951057i	0.309017	+	0.951057i
$330$		0			0
$331$	−1.14197	+	0.778579i	−1.14197	+	0.778579i	−0.978148	−	0.207912i	$-0.933333\pi$
$331$	−1.14197	+	0.778579i	−1.14197	+	0.778579i	−0.163818	+	0.986491i	$0.552381\pi$
$332$	−0.958110	+	0.888996i	−0.958110	+	0.888996i
$333$	3.40745	+	0.513591i	3.40745	+	0.513591i
$334$		0			0
$335$		0			0
$336$	−1.32003	−	1.87523i	−1.32003	−	1.87523i
$337$	0.986449	−	1.23697i	0.986449	−	1.23697i	0.0149594	−	0.999888i	$-0.495238\pi$
$337$	0.986449	−	1.23697i	0.986449	−	1.23697i	0.971490	−	0.237080i	$-0.0761905\pi$
$338$	−1.32331	+	0.199457i	−1.32331	+	0.199457i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.963963	+	0.266037i	−0.963963	+	0.266037i
$344$		0			0
$345$		0			0
$346$	0.949965	−	2.42047i	0.949965	−	2.42047i
$347$	−1.39258	−	0.949443i	−1.39258	−	0.949443i	−0.999552	−	0.0299155i	$-0.990476\pi$
$347$	−1.39258	−	0.949443i	−1.39258	−	0.949443i	−0.393025	−	0.919528i	$-0.628571\pi$
$348$		0			0
$349$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$349$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$350$	0.770326	+	1.09432i	0.770326	+	1.09432i
$351$		0			0
$352$		0			0
$353$	−1.32331	−	0.199457i	−1.32331	−	0.199457i	−0.550897	−	0.834573i	$-0.685714\pi$
$353$	−1.32331	−	0.199457i	−1.32331	−	0.199457i	−0.772417	+	0.635116i	$0.780952\pi$
$354$	0.632501	−	0.586875i	0.632501	−	0.586875i
$355$		0			0
$356$	−0.108775	−	0.476574i	−0.108775	−	0.476574i
$357$	0.305981	+	0.941712i	0.305981	+	0.941712i
$358$		0			0
$359$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$359$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$360$		0			0
$361$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$362$		0			0
$363$	−1.77298	−	0.853822i	−1.77298	−	0.853822i
$364$		0			0
$365$		0			0
$366$	−0.343778	+	4.58739i	−0.343778	+	4.58739i
$367$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$367$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.0290658	+	1.94276i	0.0290658	+	1.94276i
$372$		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
$376$	−0.102212	−	0.260433i	−0.102212	−	0.260433i
$377$		0			0
$378$	−3.40775	−	3.56422i	−3.40775	−	3.56422i
$379$	0.0729058	+	0.319421i	0.0729058	+	0.319421i	0.998210	−	0.0598042i	$-0.0190476\pi$
$379$	0.0729058	+	0.319421i	0.0729058	+	0.319421i	−0.925304	+	0.379225i	$0.876190\pi$
$380$		0			0
$381$		0			0
$382$	1.94012	+	0.292425i	1.94012	+	0.292425i
$383$	0.494561	+	0.458885i	0.494561	+	0.458885i	0.887586	−	0.460642i	$-0.152381\pi$
$383$	0.494561	+	0.458885i	0.494561	+	0.458885i	−0.393025	+	0.919528i	$0.628571\pi$
$384$	0.671527	+	0.842068i	0.671527	+	0.842068i
$385$		0			0
$386$		0			0
$387$		0			0
$388$	−1.27845	−	0.871635i	−1.27845	−	0.871635i
$389$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$389$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$390$		0			0
$391$		0			0
$392$	0.264757	−	0.0904253i	0.264757	−	0.0904253i
$393$	0.0588760			0.0588760
$394$	−2.52905	−	0.780107i	−2.52905	−	0.780107i
$395$		0			0
$396$		0			0
$397$	0.667125	−	0.100553i	0.667125	−	0.100553i	0.193256	−	0.981148i	$-0.438095\pi$
$397$	0.667125	−	0.100553i	0.667125	−	0.100553i	0.473869	+	0.880596i	$0.342857\pi$
$398$		0			0
$399$		0			0
$400$	−0.726585	−	0.911109i	−0.726585	−	0.911109i
$401$	1.46545	+	1.35974i	1.46545	+	1.35974i	0.753071	+	0.657939i	$0.228571\pi$
$401$	1.46545	+	1.35974i	1.46545	+	1.35974i	0.712376	+	0.701798i	$0.247619\pi$
$402$		0			0
$403$		0			0
$404$	0.931087	−	0.634804i	0.931087	−	0.634804i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.101208	−	0.257874i	−0.101208	−	0.257874i
$409$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$409$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$410$		0			0
$411$		0			0
$412$	−1.41504	−	0.681445i	−1.41504	−	0.681445i
$413$	0.146556	+	0.293030i	0.146556	+	0.293030i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$419$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$420$		0			0
$421$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$421$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$422$		0			0
$423$	−1.43623	−	2.48763i	−1.43623	−	2.48763i
$424$	−0.0406228	−	0.542073i	−0.0406228	−	0.542073i
$425$	0.183830	+	0.468391i	0.183830	+	0.468391i
$426$	0.757829	−	3.32027i	0.757829	−	3.32027i
$427$	−1.63543	−	0.613787i	−1.63543	−	0.613787i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.56447	−	0.235806i	−1.56447	−	0.235806i	−0.691063	−	0.722795i	$-0.742857\pi$
$431$	−1.56447	−	0.235806i	−1.56447	−	0.235806i	−0.873408	+	0.486989i	$0.838095\pi$
$432$	3.14775	+	2.92069i	3.14775	+	2.92069i
$433$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$433$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−1.88980	−	0.582926i	−1.88980	−	0.582926i	−0.988831	−	0.149042i	$-0.952381\pi$
$439$	−1.88980	−	0.582926i	−1.88980	−	0.582926i	−0.900969	−	0.433884i	$-0.857143\pi$
$440$		0			0
$441$	2.54956	−	1.32318i	2.54956	−	1.32318i
$442$		0			0
$443$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$443$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$444$	−0.682166	+	1.73813i	−0.682166	+	1.73813i
$445$		0			0
$446$		0			0
$447$	1.28997	−	1.61756i	1.28997	−	1.61756i
$448$	0.506436	−	0.207557i	0.506436	−	0.207557i
$449$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$449$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$450$	−2.81794	−	2.61466i	−2.81794	−	2.61466i
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.704350	−	1.79466i	−0.704350	−	1.79466i	−0.599822	−	0.800134i	$-0.704762\pi$
$457$	−0.704350	−	1.79466i	−0.704350	−	1.79466i	−0.104528	−	0.994522i	$-0.533333\pi$
$458$		0			0
$459$	−0.927036	−	1.60567i	−0.927036	−	1.60567i
$460$		0			0
$461$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$461$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$462$		0			0
$463$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$463$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$467$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	1.95994	−	3.39471i	1.95994	−	3.39471i
$472$	−0.0458318	−	0.0793830i	−0.0458318	−	0.0793830i
$473$		0			0
$474$	−0.0863315	−	0.219969i	−0.0863315	−	0.219969i
$475$		0			0
$476$	−0.396379	+	0.0356748i	−0.396379	+	0.0356748i
$477$	−1.24192	−	5.44122i	−1.24192	−	5.44122i
$478$	2.19563	−	1.49695i	2.19563	−	1.49695i
$479$	−0.196800	+	0.182604i	−0.196800	+	0.182604i	−0.772417	−	0.635116i	$-0.780952\pi$
$479$	−0.196800	+	0.182604i	−0.196800	+	0.182604i	0.575617	+	0.817719i	$0.304762\pi$
$480$		0			0
$481$		0			0
$482$	−1.57922	−	1.98027i	−1.57922	−	1.98027i
$483$		0			0
$484$	0.493145	−	0.618384i	0.493145	−	0.618384i
$485$		0			0
$486$	5.45314	+	3.71789i	5.45314	+	3.71789i
$487$	0.698220	−	1.77904i	0.698220	−	1.77904i	0.0747301	−	0.997204i	$-0.476190\pi$
$487$	0.698220	−	1.77904i	0.698220	−	1.77904i	0.623490	−	0.781831i	$-0.285714\pi$
$488$	0.467000	+	0.144050i	0.467000	+	0.144050i
$489$		0			0
$490$		0			0
$491$	−1.10179			−1.10179			−0.550897	−	0.834573i	$-0.685714\pi$
$491$	−1.10179			−1.10179			−0.550897	+	0.834573i	$0.685714\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.12949	+	0.629774i	1.12949	+	0.629774i
$498$	2.71331	+	3.40239i	2.71331	+	3.40239i
$499$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$499$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$500$		0			0
$501$		0			0
$502$	−1.86363	+	1.27060i	−1.86363	+	1.27060i
$503$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$503$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$504$	−0.689883	+	0.412186i	−0.689883	+	0.412186i
$505$		0			0
$506$		0			0
$507$	0.147058	+	1.96236i	0.147058	+	1.96236i
$508$		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
$512$	−1.04995	+	0.505627i	−1.04995	+	0.505627i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−1.27001	−	0.982085i	−1.27001	−	0.982085i
$519$	−3.44486	−	1.65896i	−3.44486	−	1.65896i
$520$		0			0
$521$	−0.420357	−	0.728080i	−0.420357	−	0.728080i	0.575617	−	0.817719i	$-0.304762\pi$
$521$	−0.420357	−	0.728080i	−0.420357	−	0.728080i	−0.995974	+	0.0896393i	$0.971429\pi$
$522$		0			0
$523$	0.698220	+	1.77904i	0.698220	+	1.77904i	0.623490	+	0.781831i	$0.285714\pi$
$523$	0.698220	+	1.77904i	0.698220	+	1.77904i	0.0747301	+	0.997204i	$0.476190\pi$
$524$	−0.00526575	+	0.0230708i	−0.00526575	+	0.0230708i
$525$	1.68931	−	1.00931i	1.68931	−	1.00931i
$526$	−0.511277	−	2.24005i	−0.511277	−	2.24005i
$527$		0			0
$528$		0			0
$529$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$530$		0			0
$531$	−0.586781	−	0.735800i	−0.586781	−	0.735800i
$532$		0			0
$533$		0			0
$534$	−1.60942	+	0.242581i	−1.60942	+	0.242581i
$535$		0			0
$536$		0			0
$537$		0			0
$538$	0.977843			0.977843
$539$		0			0
$540$		0			0
$541$	1.10009	+	0.339332i	1.10009	+	0.339332i	0.791071	−	0.611724i	$-0.209524\pi$
$541$	1.10009	+	0.339332i	1.10009	+	0.339332i	0.309017	+	0.951057i	$0.400000\pi$
$542$	−0.586532	+	1.49446i	−0.586532	+	1.49446i
$543$		0			0
$544$	0.636755	−	0.0959754i	0.636755	−	0.0959754i
$545$		0			0
$546$		0			0
$547$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$547$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$548$		0			0
$549$	4.96163	+	0.747846i	4.96163	+	0.747846i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	0.0893684	−	0.00804330i	0.0893684	−	0.00804330i
$554$	0.234079	−	1.02557i	0.234079	−	1.02557i
$555$		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		0.955573	−	0.294755i	$-0.0952381\pi$
$563$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$564$	1.48732	−	0.458776i	1.48732	−	0.458776i
$565$		0			0
$566$	−1.01368	+	0.488161i	−1.01368	+	0.488161i
$567$	−3.38211	+	2.78093i	−3.38211	+	2.78093i
$568$	−0.325972	−	0.156980i	−0.325972	−	0.156980i
$569$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$569$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$570$		0			0
$571$	0.0288841	+	0.385431i	0.0288841	+	0.385431i	0.992847	+	0.119394i	$0.0380952\pi$
$571$	0.0288841	+	0.385431i	0.0288841	+	0.385431i	−0.963963	+	0.266037i	$0.914286\pi$
$572$		0			0
$573$	0.641992	−	2.81275i	0.641992	−	2.81275i
$574$		0			0
$575$		0			0
$576$	−1.29898	+	0.885626i	−1.29898	+	0.885626i
$577$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$577$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$578$	0.988273	+	0.148958i	0.988273	+	0.148958i
$579$		0			0
$580$		0			0
$581$	−1.52904	+	0.626662i	−1.52904	+	0.626662i
$582$	−3.21217	+	4.02793i	−3.21217	+	4.02793i
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$	0.391586	+	1.50640i	0.391586	+	1.50640i
$589$		0			0
$590$		0			0
$591$	−1.42182	+	3.62274i	−1.42182	+	3.62274i
$592$	1.15509	+	0.787526i	1.15509	+	0.787526i
$593$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$593$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$594$		0			0
$595$		0			0
$596$	0.518477	+	0.650149i	0.518477	+	0.650149i
$597$		0			0
$598$		0			0
$599$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$599$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$600$	−0.454889	+	0.310138i	−0.454889	+	0.310138i
$601$	−0.416664	−	1.82552i	−0.416664	−	1.82552i	−0.550897	−	0.834573i	$-0.685714\pi$
$601$	−0.416664	−	1.82552i	−0.416664	−	1.82552i	0.134233	−	0.990950i	$-0.457143\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$	−1.87605	−	3.24941i	−1.87605	−	3.24941i
$607$		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
$612$	1.09240	−	0.336961i	1.09240	−	0.336961i
$613$	−1.76839	+	0.545476i	−1.76839	+	0.545476i	−0.995974	−	0.0896393i	$-0.971429\pi$
$613$	−1.76839	+	0.545476i	−1.76839	+	0.545476i	−0.772417	+	0.635116i	$0.780952\pi$
$614$	−0.129331	+	1.72580i	−0.129331	+	1.72580i
$615$		0			0
$616$		0			0
$617$	1.70522	+	0.821192i	1.70522	+	0.821192i	0.992847	+	0.119394i	$0.0380952\pi$
$617$	1.70522	+	0.821192i	1.70522	+	0.821192i	0.712376	+	0.701798i	$0.247619\pi$
$618$	−2.61467	+	4.52874i	−2.61467	+	4.52874i
$619$	0.222521	+	0.385418i	0.222521	+	0.385418i	0.955573	−	0.294755i	$-0.0952381\pi$
$619$	0.222521	+	0.385418i	0.222521	+	0.385418i	−0.733052	+	0.680173i	$0.761905\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.0829607	−	0.612441i	0.0829607	−	0.612441i
$624$		0			0
$625$	0.826239	−	0.563320i	0.826239	−	0.563320i
$626$		0			0
$627$		0			0
$628$	1.15494	+	1.07162i	1.15494	+	1.07162i
$629$	−0.376357	−	0.471936i	−0.376357	−	0.471936i
$630$		0			0
$631$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$631$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$632$	−0.0248235	+	0.00374154i	−0.0248235	+	0.00374154i
$633$		0			0
$634$		0			0
$635$		0			0
$636$	3.02418			3.02418
$637$		0			0
$638$		0			0
$639$	−3.54964	−	1.09492i	−3.54964	−	1.09492i
$640$		0			0
$641$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$641$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$642$		0			0
$643$	−1.15384	+	1.44686i	−1.15384	+	1.44686i	−0.280427	+	0.959875i	$0.590476\pi$
$643$	−1.15384	+	1.44686i	−1.15384	+	1.44686i	−0.873408	+	0.486989i	$0.838095\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.52758	+	0.230246i	1.52758	+	0.230246i	0.858449	−	0.512899i	$-0.171429\pi$
$647$	1.52758	+	0.230246i	1.52758	+	0.230246i	0.669131	+	0.743145i	$0.266667\pi$
$648$	0.898001	−	0.833223i	0.898001	−	0.833223i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.346247	+	0.882224i	0.346247	+	0.882224i	0.992847	+	0.119394i	$0.0380952\pi$
$653$	0.346247	+	0.882224i	0.346247	+	0.882224i	−0.646600	+	0.762830i	$0.723810\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$	0.0200196	+	1.33811i	0.0200196	+	1.33811i
$659$	0.708207	−	0.341054i	0.708207	−	0.341054i	−0.0448648	−	0.998993i	$-0.514286\pi$
$659$	0.708207	−	0.341054i	0.708207	−	0.341054i	0.753071	+	0.657939i	$0.228571\pi$
$660$		0			0
$661$	0.369340	−	0.113926i	0.369340	−	0.113926i	−0.104528	−	0.994522i	$-0.533333\pi$
$661$	0.369340	−	0.113926i	0.369340	−	0.113926i	0.473869	+	0.880596i	$0.342857\pi$
$662$	−1.76747	+	0.545192i	−1.76747	+	0.545192i
$663$		0			0
$664$	0.416534	−	0.200592i	0.416534	−	0.200592i
$665$		0			0
$666$	4.15488	+	2.00088i	4.15488	+	2.00088i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−0.778232	−	2.39515i	−0.778232	−	2.39515i
$673$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$673$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$674$	1.74941	−	1.19273i	1.74941	−	1.19273i
$675$	−2.70112	+	2.50627i	−2.70112	+	2.50627i
$676$	−0.782109	−	0.117884i	−0.782109	−	0.117884i
$677$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$677$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$678$		0			0
$679$	−1.12608	−	1.59970i	−1.12608	−	1.59970i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.225793	−	0.575312i	0.225793	−	0.575312i	−0.772417	−	0.635116i	$-0.780952\pi$
$683$	0.225793	−	0.575312i	0.225793	−	0.575312i	0.998210	+	0.0598042i	$0.0190476\pi$
$684$		0			0
$685$		0			0
$686$	−1.33766	−	0.0400347i	−1.33766	−	0.0400347i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$691$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$692$	0.958171	−	1.20151i	0.958171	−	1.20151i
$693$		0			0
$694$	−1.40632	−	1.76347i	−1.40632	−	1.76347i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	0.244415	+	0.752232i	0.244415	+	0.752232i
$701$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$701$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−1.61358	−	0.777061i	−1.61358	−	0.777061i
$707$	1.38413	−	0.337781i	1.38413	−	0.337781i
$708$	0.459452	−	0.221261i	0.459452	−	0.221261i
$709$	−0.115446	+	1.54051i	−0.115446	+	1.54051i	0.575617	+	0.817719i	$0.304762\pi$
$709$	−0.115446	+	1.54051i	−0.115446	+	1.54051i	−0.691063	+	0.722795i	$0.742857\pi$
$710$		0			0
$711$	−0.246295	+	0.0759719i	−0.246295	+	0.0759719i
$712$	−0.0129215	+	0.172426i	−0.0129215	+	0.172426i
$713$		0			0
$714$	0.0198229	+	1.32496i	0.0198229	+	1.32496i
$715$		0			0
$716$		0			0
$717$	−1.95378	−	3.38405i	−1.95378	−	3.38405i
$718$		0			0
$719$	−0.727741	−	1.85425i	−0.727741	−	1.85425i	−0.447313	−	0.894377i	$-0.647619\pi$
$719$	−0.727741	−	1.85425i	−0.727741	−	1.85425i	−0.280427	−	0.959875i	$-0.590476\pi$
$720$		0			0
$721$	−1.37224	−	1.43525i	−1.37224	−	1.43525i
$722$	−0.297791	−	1.30471i	−0.297791	−	1.30471i
$723$	−3.07731	+	2.09807i	−3.07731	+	2.09807i
$724$		0			0
$725$		0			0
$726$	−1.93050	−	1.79124i	−1.93050	−	1.79124i
$727$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$727$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$728$		0			0
$729$	3.32092	−	4.16431i	3.32092	−	4.16431i
$730$		0			0
$731$		0			0
$732$	−0.993310	+	2.53091i	−0.993310	+	2.53091i
$733$	−1.91029	−	0.589247i	−1.91029	−	0.589247i	−0.963963	−	0.266037i	$-0.914286\pi$
$733$	−1.91029	−	0.589247i	−1.91029	−	0.589247i	−0.946327	−	0.323210i	$-0.895238\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	0.0247201	+	0.0168539i	0.0247201	+	0.0168539i	0.575617	−	0.817719i	$-0.304762\pi$
$739$	0.0247201	+	0.0168539i	0.0247201	+	0.0168539i	−0.550897	+	0.834573i	$0.685714\pi$
$740$		0			0
$741$		0			0
$742$	−0.729171	+	2.49588i	−0.729171	+	2.49588i
$743$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$743$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	3.92190	−	2.67391i	3.92190	−	2.67391i
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$751$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$752$	−0.0870869	−	1.16209i	−0.0870869	−	1.16209i
$753$	1.65836	+	2.87236i	1.65836	+	2.87236i
$754$		0			0
$755$		0			0
$756$	−1.30366	−	2.60660i	−1.30366	−	2.60660i
$757$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$757$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$758$	−0.0327663	+	0.437236i	−0.0327663	+	0.437236i
$759$		0			0
$760$		0			0
$761$	0.142820	−	1.90580i	0.142820	−	1.90580i	−0.222521	−	0.974928i	$-0.571429\pi$
$761$	0.142820	−	1.90580i	0.142820	−	1.90580i	0.365341	−	0.930874i	$-0.380952\pi$
$762$		0			0
$763$		0			0
$764$	1.04477	+	0.503134i	1.04477	+	0.503134i
$765$		0			0
$766$	0.451436	+	0.781909i	0.451436	+	0.781909i
$767$		0			0
$768$	0.920079	+	2.34432i	0.920079	+	2.34432i
$769$	0.429004	−	1.87959i	0.429004	−	1.87959i	−0.0448648	−	0.998993i	$-0.514286\pi$
$769$	0.429004	−	1.87959i	0.429004	−	1.87959i	0.473869	−	0.880596i	$-0.342857\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	0.576215	−	0.534650i	0.576215	−	0.534650i	−0.337330	−	0.941386i	$-0.609524\pi$
$773$	0.576215	−	0.534650i	0.576215	−	0.534650i	0.913545	+	0.406737i	$0.133333\pi$
$774$		0			0
$775$		0			0
$776$	0.341247	+	0.427911i	0.341247	+	0.427911i
$777$	−1.57964	+	1.75436i	−1.57964	+	1.75436i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	1.16483	−	0.0348621i	1.16483	−	0.0348621i
$785$		0			0
$786$	0.0752910	+	0.0232242i	0.0752910	+	0.0232242i
$787$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$787$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$788$	−1.29242	−	0.881155i	−1.29242	−	0.881155i
$789$	−3.34088	+	0.503556i	−3.34088	+	0.503556i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	0.892787	+	0.134566i	0.892787	+	0.134566i
$795$		0			0
$796$		0			0
$797$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$797$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$798$		0			0
$799$	−0.111967	+	0.490558i	−0.111967	+	0.490558i
$800$	−0.467553	−	1.19131i	−0.467553	−	1.19131i
$801$	0.132667	+	1.77032i	0.132667	+	1.77032i
$802$	1.33766	+	2.31690i	1.33766	+	2.31690i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.107453	−	1.43386i	0.107453	−	1.43386i
$808$	−0.380898	+	0.117491i	−0.380898	+	0.117491i
$809$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$809$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$810$		0			0
$811$	0.188354	−	0.0907064i	0.188354	−	0.0907064i	−0.337330	−	0.941386i	$-0.609524\pi$
$811$	0.188354	−	0.0907064i	0.188354	−	0.0907064i	0.525684	+	0.850680i	$0.323810\pi$
$812$		0			0
$813$	2.12694	+	1.02428i	2.12694	+	1.02428i
$814$		0			0
$815$		0			0
$816$	−0.0862312	−	1.15068i	−0.0862312	−	1.15068i
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$821$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$822$		0			0
$823$	1.95557	+	0.294755i	1.95557	+	0.294755i	1.00000			$0$
$823$	1.95557	+	0.294755i	1.95557	+	0.294755i	0.955573	+	0.294755i	$0.0952381\pi$
$824$	0.407242	+	0.377865i	0.407242	+	0.377865i
$825$		0			0
$826$	0.0718280	+	0.432539i	0.0718280	+	0.432539i
$827$	−0.557790	+	0.699447i	−0.557790	+	0.699447i	−0.978148	−	0.207912i	$-0.933333\pi$
$827$	−0.557790	+	0.699447i	−0.557790	+	0.699447i	0.420357	+	0.907359i	$0.361905\pi$
$828$		0			0
$829$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$829$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$830$		0			0
$831$	−1.47811	−	0.455938i	−1.47811	−	0.455938i
$832$		0			0
$833$	−0.485041	−	0.133863i	−0.485041	−	0.133863i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$839$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$840$		0			0
$841$	0.623490	+	0.781831i	0.623490	+	0.781831i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		0			0
$846$	−0.855396	−	3.74773i	−0.855396	−	3.74773i
$847$	0.858449	−	0.512899i	0.858449	−	0.512899i
$848$	0.503844	−	2.20749i	0.503844	−	2.20749i
$849$	0.604423	+	1.54004i	0.604423	+	1.54004i
$850$	0.0503216	+	0.671495i	0.0503216	+	0.671495i
$851$		0			0
$852$	1.00641	−	1.74315i	1.00641	−	1.74315i
$853$	1.45780	+	0.702039i	1.45780	+	0.702039i	0.983930	−	0.178557i	$-0.0571429\pi$
$853$	1.45780	+	0.702039i	1.45780	+	0.702039i	0.473869	+	0.880596i	$0.342857\pi$
$854$	−1.84928	−	1.43003i	−1.84928	−	1.43003i
$855$		0			0
$856$		0			0
$857$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$857$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$858$		0			0
$859$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$859$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$860$		0			0
$861$		0			0
$862$	−1.90764	−	0.918670i	−1.90764	−	0.918670i
$863$	−0.983930	+	1.70422i	−0.983930	+	1.70422i	−0.337330	+	0.941386i	$0.609524\pi$
$863$	−0.983930	+	1.70422i	−0.983930	+	1.70422i	−0.646600	+	0.762830i	$0.723810\pi$
$864$	2.35783	+	4.08387i	2.35783	+	4.08387i
$865$		0			0
$866$		0			0
$867$	0.327023	−	1.43278i	0.327023	−	1.43278i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	4.11931	+	3.82216i	4.11931	+	3.82216i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$877$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$878$	−2.18675	−	1.49090i	−2.18675	−	1.49090i
$879$		0			0
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	3.78234	−	0.686393i	3.78234	−	0.686393i
$883$	1.99642			1.99642			0.998210	−	0.0598042i	$-0.0190476\pi$
$883$	1.99642			1.99642			0.998210	+	0.0598042i	$0.0190476\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$887$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$888$	0.411795	−	0.516375i	0.411795	−	0.516375i
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$	2.28768	−	1.55971i	2.28768	−	1.55971i
$895$		0			0
$896$	−0.545115	+	0.0490612i	−0.545115	+	0.0490612i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−1.13598	−	1.96758i	−1.13598	−	1.96758i
$901$	−0.488828	+	0.846675i	−0.488828	+	0.846675i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.955573	+	0.294755i	−0.955573	+	0.294755i	−0.733052	−	0.680173i	$-0.761905\pi$
$907$	−0.955573	+	0.294755i	−0.955573	+	0.294755i	−0.222521	+	0.974928i	$0.571429\pi$
$908$		0			0
$909$	−3.68727	+	1.77569i	−3.68727	+	1.77569i
$910$		0			0
$911$	−0.0269559	−	0.0129813i	−0.0269559	−	0.0129813i	0.420357	−	0.907359i	$-0.361905\pi$
$911$	−0.0269559	−	0.0129813i	−0.0269559	−	0.0129813i	−0.447313	+	0.894377i	$0.647619\pi$
$912$		0			0
$913$		0			0
$914$	−0.192809	−	2.57285i	−0.192809	−	2.57285i
$915$		0			0
$916$		0			0
$917$	−0.0164822	+	0.0249694i	−0.0164822	+	0.0249694i
$918$	−0.552126	−	2.41902i	−0.552126	−	2.41902i
$919$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$919$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$920$		0			0
$921$	2.51641	+	0.379288i	2.51641	+	0.379288i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.747966	+	0.937919i	−0.747966	+	0.937919i
$926$		0			0
$927$	4.71274	+	3.21309i	4.71274	+	3.21309i
$928$		0			0
$929$	0.905632	+	0.279350i	0.905632	+	0.279350i	0.712376	−	0.701798i	$-0.247619\pi$
$929$	0.905632	+	0.279350i	0.905632	+	0.279350i	0.193256	+	0.981148i	$0.438095\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$937$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.08949	+	0.164214i	1.08949	+	0.164214i	0.669131	−	0.743145i	$-0.266667\pi$
$941$	1.08949	+	0.164214i	1.08949	+	0.164214i	0.420357	+	0.907359i	$0.361905\pi$
$942$	3.84546	−	3.56806i	3.84546	−	3.56806i
$943$		0			0
$944$	−0.0849610	−	0.372238i	−0.0849610	−	0.372238i
$945$		0			0
$946$		0			0
$947$	0.698220	+	1.77904i	0.698220	+	1.77904i	0.623490	+	0.781831i	$0.285714\pi$
$947$	0.698220	+	1.77904i	0.698220	+	1.77904i	0.0747301	+	0.997204i	$0.476190\pi$
$948$	−0.0104369	−	0.139271i	−0.0104369	−	0.139271i
$949$		0			0
$950$		0			0
$951$		0			0
$952$	0.137698	+	0.0292686i	0.137698	+	0.0292686i
$953$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$953$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$954$	0.558162	−	7.44815i	0.558162	−	7.44815i
$955$		0			0
$956$	1.50079	−	0.462934i	1.50079	−	0.462934i
$957$		0			0
$958$	−0.323699	+	0.155885i	−0.323699	+	0.155885i
$959$		0			0
$960$		0			0
$961$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$962$		0			0
$963$		0			0
$964$	−0.546909	−	1.39350i	−0.546909	−	1.39350i
$965$		0			0
$966$		0			0
$967$	0.245172	+	1.07417i	0.245172	+	1.07417i	0.936235	+	0.351375i	$0.114286\pi$
$967$	0.245172	+	1.07417i	0.245172	+	1.07417i	−0.691063	+	0.722795i	$0.742857\pi$
$968$	−0.231159	+	0.157602i	−0.231159	+	0.157602i
$969$		0			0
$970$		0			0
$971$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$971$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$972$	2.43206	+	3.04971i	2.43206	+	3.04971i
$973$		0			0
$974$	1.59465	−	1.99962i	1.59465	−	1.99962i
$975$		0			0
$976$	1.68194	+	1.14673i	1.68194	+	1.14673i
$977$	0.603718	−	1.53825i	0.603718	−	1.53825i	−0.222521	−	0.974928i	$-0.571429\pi$
$977$	0.603718	−	1.53825i	0.603718	−	1.53825i	0.826239	−	0.563320i	$-0.190476\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	−1.40898	−	0.434613i	−1.40898	−	0.434613i
$983$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$983$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	1.96434	+	0.117686i	1.96434	+	0.117686i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.411136	−	0.381478i	0.411136	−	0.381478i	−0.447313	−	0.894377i	$-0.647619\pi$
$991$	0.411136	−	0.381478i	0.411136	−	0.381478i	0.858449	+	0.512899i	$0.171429\pi$
$992$		0			0
$993$	0.605219	+	2.65164i	0.605219	+	2.65164i
$994$	1.19598	+	1.25090i	1.19598	+	1.25090i
$995$		0			0
$996$	0.939665	+	2.39423i	0.939665	+	2.39423i
$997$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$997$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$998$		0			0
$999$	2.21020	−	3.82817i	2.21020	−	3.82817i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.1.q.b.1080.3	✓	48
47.46	odd	2	CM	2303.1.q.b.1080.3	✓	48
49.25	even	21	inner	2303.1.q.b.1691.3	yes	48
2303.1691	odd	42	inner	2303.1.q.b.1691.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.1.q.b.1080.3	✓	48	1.1	even	1	trivial
2303.1.q.b.1080.3	✓	48	47.46	odd	2	CM
2303.1.q.b.1691.3	yes	48	49.25	even	21	inner
2303.1.q.b.1691.3	yes	48	2303.1691	odd	42	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.27881 + 0.394459i) q^{2} +(0.718940 - 1.83183i) q^{3} +(0.653508 + 0.445554i) q^{4} +(1.64197 - 2.05896i) q^{6} +(0.575617 + 0.817719i) q^{7} +(-0.174435 - 0.218735i) q^{8} +(-2.10567 - 1.95378i) q^{9} +O(q^{10})\)	\(q+(1.27881 + 0.394459i) q^{2} +(0.718940 - 1.83183i) q^{3} +(0.653508 + 0.445554i) q^{4} +(1.64197 - 2.05896i) q^{6} +(0.575617 + 0.817719i) q^{7} +(-0.174435 - 0.218735i) q^{8} +(-2.10567 - 1.95378i) q^{9} +(1.28601 - 0.876788i) q^{12} +(0.413545 + 1.27276i) q^{14} +(-0.425751 - 1.08480i) q^{16} +(0.0376022 + 0.501767i) q^{17} +(-1.92206 - 3.32910i) q^{18} +(1.91176 - 0.466541i) q^{21} +(-0.526094 + 0.162278i) q^{24} +(0.955573 - 0.294755i) q^{25} +(-3.31985 + 1.59876i) q^{27} +(0.0118320 + 0.790855i) q^{28} +(-0.0956375 - 1.27619i) q^{32} +(-0.149841 + 0.656495i) q^{34} +(-0.505559 - 2.21500i) q^{36} +(-0.991192 + 0.675783i) q^{37} +(2.62880 + 0.157495i) q^{42} +(0.955573 + 0.294755i) q^{47} -2.29325 q^{48} +(-0.337330 + 0.941386i) q^{49} +1.33826 q^{50} +(0.946184 + 0.291859i) q^{51} +(1.60537 + 1.09452i) q^{53} +(-4.87609 + 0.734952i) q^{54} +(0.0784559 - 0.268547i) q^{56} +(0.323976 + 0.0488316i) q^{59} +(-1.44329 + 0.984017i) q^{61} +(0.385581 - 2.84647i) q^{63} +(0.121790 - 0.533596i) q^{64} +(-0.198991 + 0.344662i) q^{68} +(1.16513 - 0.561098i) q^{71} +(-0.0600560 + 0.801392i) q^{72} +(-1.53411 + 0.473211i) q^{74} +(0.147058 - 1.96236i) q^{75} +(0.0448648 - 0.0777082i) q^{79} +(0.327214 + 4.36637i) q^{81} +(-0.367711 + 1.61105i) q^{83} +(1.45722 + 0.546902i) q^{84} +(-0.453051 - 0.420370i) q^{89} +(1.10572 + 0.753869i) q^{94} +(-2.40653 - 0.742315i) q^{96} -1.95630 q^{97} +(-0.802718 + 1.07079i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} - 2 q^{3} + 5 q^{4} - 4 q^{6} - q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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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