LMFDB - Embedded newform 3784.1.em.a.1571.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3784,1,Mod(203,3784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3784, base_ring=CyclotomicField(210))

chi = DirichletCharacter(H, H._module([105, 105, 84, 170]))

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

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

chi := DirichletCharacter("3784.203");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3784 = 2^{3} \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3784.em (of order $210$, degree $48$, 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:	$1.88846200780$
Analytic rank:	$0$
Dimension:	$48$
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			1571.1
Root			$-0.998210 - 0.0598042i$ of defining polynomial
Character	$\chi$	$=$	3784.1571
Dual form			3784.1.em.a.3283.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.936235 - 0.351375i) q^{2} +(-1.44687 - 0.924293i) q^{3} +(0.753071 - 0.657939i) q^{4} +(-1.67938 - 0.356963i) q^{6} +(0.473869 - 0.880596i) q^{8} +(0.818745 + 1.76730i) q^{9} +O(q^{10})$	\(q+(0.936235 - 0.351375i) q^{2} +(-1.44687 - 0.924293i) q^{3} +(0.753071 - 0.657939i) q^{4} +(-1.67938 - 0.356963i) q^{6} +(0.473869 - 0.880596i) q^{8} +(0.818745 + 1.76730i) q^{9} +(-0.646600 - 0.762830i) q^{11} +(-1.69772 + 0.255890i) q^{12} +(0.134233 - 0.990950i) q^{16} +(-1.83737 + 0.753026i) q^{17} +(1.38752 + 1.36692i) q^{18} +(-1.19106 - 0.143231i) q^{19} +(-0.873408 - 0.486989i) q^{22} +(-1.49955 + 0.836110i) q^{24} +(0.887586 - 0.460642i) q^{25} +(0.218420 - 1.61244i) q^{27} +(-0.222521 - 0.974928i) q^{32} +(0.230465 + 1.70136i) q^{33} +(-1.45562 + 1.35061i) q^{34} +(1.77935 + 0.792216i) q^{36} +(-1.16544 + 0.284412i) q^{38} +(-1.52513 - 0.420908i) q^{41} +(-0.772417 - 0.635116i) q^{43} +(-0.988831 - 0.149042i) q^{44} +(-1.11015 + 1.30970i) q^{48} +(-0.978148 - 0.207912i) q^{49} +(0.669131 - 0.743145i) q^{50} +(3.35445 + 0.608742i) q^{51} +(-0.362079 - 1.58637i) q^{54} +(1.59092 + 1.30813i) q^{57} +(-0.798678 - 1.48419i) q^{59} +(-0.550897 - 0.834573i) q^{64} +(0.813584 + 1.51189i) q^{66} +(0.153250 + 0.142195i) q^{67} +(-0.888227 + 1.77596i) q^{68} +(1.94425 + 0.116483i) q^{72} +(0.659917 + 1.84163i) q^{73} +(-1.70999 - 0.153902i) q^{75} +(-0.991192 + 0.675783i) q^{76} +(-0.546987 + 0.645311i) q^{81} +(-1.57577 + 0.141822i) q^{82} +(0.851044 - 0.699767i) q^{83} +(-0.946327 - 0.323210i) q^{86} +(-0.978148 + 0.207912i) q^{88} +(-0.204903 - 0.522085i) q^{89} +(-0.579161 + 1.61626i) q^{96} +(1.53861 + 0.138478i) q^{97} +(-0.988831 + 0.149042i) q^{98} +(0.818745 - 1.76730i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9}+O(q^{10}) $ 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9	$ 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9} - q^{11} - 2 q^{12} + 2 q^{16} + q^{17} + 2 q^{18} - 22 q^{19} - q^{22} - 25 q^{24} - q^{25} - 2 q^{27} - 8 q^{32} - 6 q^{33} - 13 q^{34} + 9 q^{36} + q^{38} - 2 q^{41} - q^{43} + 4 q^{44} - 2 q^{48} + 6 q^{49} + 6 q^{50} + 8 q^{51} - 6 q^{54} + 7 q^{57} + 3 q^{59} + 2 q^{64} + 4 q^{66} + q^{67} + q^{68} - 3 q^{72} + q^{73} - 20 q^{75} + q^{76} + 7 q^{81} + 3 q^{82} + 10 q^{83} - q^{86} + 6 q^{88} + q^{89} - 2 q^{96} + 3 q^{97} + 4 q^{98} - 3 q^{99}+O(q^{100}) $ 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9 - q^11 - 2 * q^12 + 2 * q^16 + q^17 + 2 * q^18 - 22 * q^19 - q^22 - 25 * q^24 - q^25 - 2 * q^27 - 8 * q^32 - 6 * q^33 - 13 * q^34 + 9 * q^36 + q^38 - 2 * q^41 - q^43 + 4 * q^44 - 2 * q^48 + 6 * q^49 + 6 * q^50 + 8 * q^51 - 6 * q^54 + 7 * q^57 + 3 * q^59 + 2 * q^64 + 4 * q^66 + q^67 + q^68 - 3 * q^72 + q^73 - 20 * q^75 + q^76 + 7 * q^81 + 3 * q^82 + 10 * q^83 - q^86 + 6 * q^88 + q^89 - 2 * q^96 + 3 * q^97 + 4 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3784\mathbb{Z}\right)^\times$.

$n$	$89$	$1377$	$1893$	$2839$
$\chi(n)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.936235	−	0.351375i	0.936235	−	0.351375i
$2$	0.936235	−	0.351375i	0.936235	−	0.351375i
$3$	−1.44687	−	0.924293i	−1.44687	−	0.924293i	−0.999552	−	0.0299155i	$-0.990476\pi$
$3$	−1.44687	−	0.924293i	−1.44687	−	0.924293i	−0.447313	−	0.894377i	$-0.647619\pi$
$4$	0.753071	−	0.657939i	0.753071	−	0.657939i
$5$		0			0		0.971490	−	0.237080i	$-0.0761905\pi$
$5$		0			0		−0.971490	+	0.237080i	$0.923810\pi$
$6$	−1.67938	−	0.356963i	−1.67938	−	0.356963i
$7$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$7$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$8$	0.473869	−	0.880596i	0.473869	−	0.880596i
$9$	0.818745	+	1.76730i	0.818745	+	1.76730i
$10$		0			0
$11$	−0.646600	−	0.762830i	−0.646600	−	0.762830i
$11$	−0.646600	−	0.762830i	−0.646600	−	0.762830i
$12$	−1.69772	+	0.255890i	−1.69772	+	0.255890i
$13$		0			0		0.791071	−	0.611724i	$-0.209524\pi$
$13$		0			0		−0.791071	+	0.611724i	$0.790476\pi$
$14$		0			0
$15$		0			0
$16$	0.134233	−	0.990950i	0.134233	−	0.990950i
$17$	−1.83737	+	0.753026i	−1.83737	+	0.753026i	−0.873408	+	0.486989i	$0.838095\pi$
$17$	−1.83737	+	0.753026i	−1.83737	+	0.753026i	−0.963963	+	0.266037i	$0.914286\pi$
$18$	1.38752	+	1.36692i	1.38752	+	1.36692i
$19$	−1.19106	−	0.143231i	−1.19106	−	0.143231i	−0.500000	−	0.866025i	$-0.666667\pi$
$19$	−1.19106	−	0.143231i	−1.19106	−	0.143231i	−0.691063	+	0.722795i	$0.742857\pi$
$20$		0			0
$21$		0			0
$22$	−0.873408	−	0.486989i	−0.873408	−	0.486989i
$23$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$23$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$24$	−1.49955	+	0.836110i	−1.49955	+	0.836110i
$25$	0.887586	−	0.460642i	0.887586	−	0.460642i
$26$		0			0
$27$	0.218420	−	1.61244i	0.218420	−	1.61244i
$28$		0			0
$29$		0			0		0.842721	−	0.538351i	$-0.180952\pi$
$29$		0			0		−0.842721	+	0.538351i	$0.819048\pi$
$30$		0			0
$31$		0			0		0.163818	−	0.986491i	$-0.447619\pi$
$31$		0			0		−0.163818	+	0.986491i	$0.552381\pi$
$32$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$33$	0.230465	+	1.70136i	0.230465	+	1.70136i
$34$	−1.45562	+	1.35061i	−1.45562	+	1.35061i
$35$		0			0
$36$	1.77935	+	0.792216i	1.77935	+	0.792216i
$37$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$37$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$38$	−1.16544	+	0.284412i	−1.16544	+	0.284412i
$39$		0			0
$40$		0			0
$41$	−1.52513	−	0.420908i	−1.52513	−	0.420908i	−0.599822	−	0.800134i	$-0.704762\pi$
$41$	−1.52513	−	0.420908i	−1.52513	−	0.420908i	−0.925304	+	0.379225i	$0.876190\pi$
$42$		0			0
$43$	−0.772417	−	0.635116i	−0.772417	−	0.635116i
$43$	−0.772417	−	0.635116i	−0.772417	−	0.635116i
$44$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$45$		0			0
$46$		0			0
$47$		0			0		−0.393025	−	0.919528i	$-0.628571\pi$
$47$		0			0		0.393025	+	0.919528i	$0.371429\pi$
$48$	−1.11015	+	1.30970i	−1.11015	+	1.30970i
$49$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$50$	0.669131	−	0.743145i	0.669131	−	0.743145i
$51$	3.35445	+	0.608742i	3.35445	+	0.608742i
$52$		0			0
$53$		0			0		−0.280427	−	0.959875i	$-0.590476\pi$
$53$		0			0		0.280427	+	0.959875i	$0.409524\pi$
$54$	−0.362079	−	1.58637i	−0.362079	−	1.58637i
$55$		0			0
$56$		0			0
$57$	1.59092	+	1.30813i	1.59092	+	1.30813i
$58$		0			0
$59$	−0.798678	−	1.48419i	−0.798678	−	1.48419i	−0.873408	−	0.486989i	$-0.838095\pi$
$59$	−0.798678	−	1.48419i	−0.798678	−	1.48419i	0.0747301	−	0.997204i	$-0.476190\pi$
$60$		0			0
$61$		0			0		−0.163818	−	0.986491i	$-0.552381\pi$
$61$		0			0		0.163818	+	0.986491i	$0.447619\pi$
$62$		0			0
$63$		0			0
$64$	−0.550897	−	0.834573i	−0.550897	−	0.834573i
$65$		0			0
$66$	0.813584	+	1.51189i	0.813584	+	1.51189i
$67$	0.153250	+	0.142195i	0.153250	+	0.142195i	0.753071	−	0.657939i	$-0.228571\pi$
$67$	0.153250	+	0.142195i	0.153250	+	0.142195i	−0.599822	+	0.800134i	$0.704762\pi$
$68$	−0.888227	+	1.77596i	−0.888227	+	1.77596i
$69$		0			0
$70$		0			0
$71$		0			0		−0.575617	−	0.817719i	$-0.695238\pi$
$71$		0			0		0.575617	+	0.817719i	$0.304762\pi$
$72$	1.94425	+	0.116483i	1.94425	+	0.116483i
$73$	0.659917	+	1.84163i	0.659917	+	1.84163i	0.525684	+	0.850680i	$0.323810\pi$
$73$	0.659917	+	1.84163i	0.659917	+	1.84163i	0.134233	+	0.990950i	$0.457143\pi$
$74$		0			0
$75$	−1.70999	−	0.153902i	−1.70999	−	0.153902i
$76$	−0.991192	+	0.675783i	−0.991192	+	0.675783i
$77$		0			0
$78$		0			0
$79$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$79$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$80$		0			0
$81$	−0.546987	+	0.645311i	−0.546987	+	0.645311i
$82$	−1.57577	+	0.141822i	−1.57577	+	0.141822i
$83$	0.851044	−	0.699767i	0.851044	−	0.699767i	−0.104528	−	0.994522i	$-0.533333\pi$
$83$	0.851044	−	0.699767i	0.851044	−	0.699767i	0.955573	+	0.294755i	$0.0952381\pi$
$84$		0			0
$85$		0			0
$86$	−0.946327	−	0.323210i	−0.946327	−	0.323210i
$87$		0			0
$88$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$89$	−0.204903	−	0.522085i	−0.204903	−	0.522085i	0.791071	−	0.611724i	$-0.209524\pi$
$89$	−0.204903	−	0.522085i	−0.204903	−	0.522085i	−0.995974	+	0.0896393i	$0.971429\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.579161	+	1.61626i	−0.579161	+	1.61626i
$97$	1.53861	+	0.138478i	1.53861	+	0.138478i	0.826239	−	0.563320i	$-0.190476\pi$
$97$	1.53861	+	0.138478i	1.53861	+	0.138478i	0.712376	+	0.701798i	$0.247619\pi$
$98$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$99$	0.818745	−	1.76730i	0.818745	−	1.76730i
$100$	0.365341	−	0.930874i	0.365341	−	0.930874i
$101$		0			0		0.0149594	−	0.999888i	$-0.495238\pi$
$101$		0			0		−0.0149594	+	0.999888i	$0.504762\pi$
$102$	3.35445	−	0.608742i	3.35445	−	0.608742i
$103$		0			0		0.525684	−	0.850680i	$-0.323810\pi$
$103$		0			0		−0.525684	+	0.850680i	$0.676190\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.0871715	+	1.94102i	−0.0871715	+	1.94102i	0.193256	+	0.981148i	$0.438095\pi$
$107$	−0.0871715	+	1.94102i	−0.0871715	+	1.94102i	−0.280427	+	0.959875i	$0.590476\pi$
$108$	−0.896402	−	1.35799i	−0.896402	−	1.35799i
$109$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$109$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.380300	−	0.0690144i	0.380300	−	0.0690144i	0.0149594	−	0.999888i	$-0.495238\pi$
$113$	0.380300	−	0.0690144i	0.380300	−	0.0690144i	0.365341	+	0.930874i	$0.380952\pi$
$114$	1.94912	+	0.665704i	1.94912	+	0.665704i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−1.26926	−	1.10892i	−1.26926	−	1.10892i
$119$		0			0
$120$		0			0
$121$	−0.163818	+	0.986491i	−0.163818	+	0.986491i
$122$		0			0
$123$	1.81761	+	2.01866i	1.81761	+	2.01866i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.550897	−	0.834573i	$-0.314286\pi$
$127$		0			0		−0.550897	+	0.834573i	$0.685714\pi$
$128$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$129$	0.530551	+	1.63287i	0.530551	+	1.63287i
$130$		0			0
$131$	0.655517	+	0.821992i	0.655517	+	0.821992i	0.992847	−	0.119394i	$-0.0380952\pi$
$131$	0.655517	+	0.821992i	0.655517	+	0.821992i	−0.337330	+	0.941386i	$0.609524\pi$
$132$	1.29295	+	1.12961i	1.29295	+	1.12961i
$133$		0			0
$134$	0.193441	+	0.0792797i	0.193441	+	0.0792797i
$135$		0			0
$136$	−0.207562	+	1.97482i	−0.207562	+	1.97482i
$137$	−1.29399	−	1.35341i	−1.29399	−	1.35341i	−0.900969	−	0.433884i	$-0.857143\pi$
$137$	−1.29399	−	1.35341i	−1.29399	−	1.35341i	−0.393025	−	0.919528i	$-0.628571\pi$
$138$		0			0
$139$	−0.149393	−	0.00447117i	−0.149393	−	0.00447117i	−0.0448648	−	0.998993i	$-0.514286\pi$
$139$	−0.149393	−	0.00447117i	−0.149393	−	0.00447117i	−0.104528	+	0.994522i	$0.533333\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	1.86120	−	0.574106i	1.86120	−	0.574106i
$145$		0			0
$146$	1.26494	+	1.49232i	1.26494	+	1.49232i
$147$	1.22308	+	1.20492i	1.22308	+	1.20492i
$148$		0			0
$149$		0			0		−0.0149594	−	0.999888i	$-0.504762\pi$
$149$		0			0		0.0149594	+	0.999888i	$0.495238\pi$
$150$	−1.65503	+	0.456758i	−1.65503	+	0.456758i
$151$		0			0		0.0448648	−	0.998993i	$-0.485714\pi$
$151$		0			0		−0.0448648	+	0.998993i	$0.514286\pi$
$152$	−0.690535	+	0.980972i	−0.690535	+	0.980972i
$153$	−2.83516	−	2.63064i	−2.83516	−	2.63064i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.599822	−	0.800134i	$-0.295238\pi$
$157$		0			0		−0.599822	+	0.800134i	$0.704762\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.285362	+	0.796360i	−0.285362	+	0.796360i
$163$	−0.543606	−	1.17340i	−0.543606	−	1.17340i	−0.963963	−	0.266037i	$-0.914286\pi$
$163$	−0.543606	−	1.17340i	−0.543606	−	1.17340i	0.420357	−	0.907359i	$-0.361905\pi$
$164$	−1.42546	+	0.686466i	−1.42546	+	0.686466i
$165$		0			0
$166$	0.550897	−	0.954182i	0.550897	−	0.954182i
$167$		0			0		−0.925304	−	0.379225i	$-0.876190\pi$
$167$		0			0		0.925304	+	0.379225i	$0.123810\pi$
$168$		0			0
$169$	0.251587	−	0.967835i	0.251587	−	0.967835i
$170$		0			0
$171$	−0.722046	−	2.22223i	−0.722046	−	2.22223i
$172$	−0.999552	+	0.0299155i	−0.999552	+	0.0299155i
$173$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$173$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$174$		0			0
$175$		0			0
$176$	−0.842721	+	0.538351i	−0.842721	+	0.538351i
$177$	−0.216249	+	2.88564i	−0.216249	+	2.88564i
$178$	−0.375285	−	0.416796i	−0.375285	−	0.416796i
$179$	−1.53973	−	0.685531i	−1.53973	−	0.685531i	−0.550897	−	0.834573i	$-0.685714\pi$
$179$	−1.53973	−	0.685531i	−1.53973	−	0.685531i	−0.988831	+	0.149042i	$0.952381\pi$
$180$		0			0
$181$		0			0		−0.873408	−	0.486989i	$-0.838095\pi$
$181$		0			0		0.873408	+	0.486989i	$0.161905\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.76247	+	0.914695i	1.76247	+	0.914695i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.193256	−	0.981148i	$-0.561905\pi$
$191$		0			0		0.193256	+	0.981148i	$0.438095\pi$
$192$	0.0256838	+	1.71671i	0.0256838	+	1.71671i
$193$	1.16747	+	0.438157i	1.16747	+	0.438157i	0.858449	−	0.512899i	$-0.171429\pi$
$193$	1.16747	+	0.438157i	1.16747	+	0.438157i	0.309017	+	0.951057i	$0.400000\pi$
$194$	1.48916	−	0.410983i	1.48916	−	0.410983i
$195$		0			0
$196$	−0.873408	+	0.486989i	−0.873408	+	0.486989i
$197$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$197$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$198$	0.145555	−	1.94229i	0.145555	−	1.94229i
$199$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$199$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$200$	0.0149594	−	0.999888i	0.0149594	−	0.999888i
$201$	−0.0903019	−	0.347384i	−0.0903019	−	0.347384i
$202$		0			0
$203$		0			0
$204$	2.92665	−	1.74859i	2.92665	−	1.74859i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.660880	+	1.00119i	0.660880	+	1.00119i
$210$		0			0
$211$	−1.18648	−	0.708891i	−1.18648	−	0.708891i	−0.222521	−	0.974928i	$-0.571429\pi$
$211$	−1.18648	−	0.708891i	−1.18648	−	0.708891i	−0.963963	+	0.266037i	$0.914286\pi$
$212$		0			0
$213$		0			0
$214$	0.600414	+	1.84788i	0.600414	+	1.84788i
$215$		0			0
$216$	−1.31641	−	0.956425i	−1.31641	−	0.956425i
$217$		0			0
$218$		0			0
$219$	0.747394	−	3.27455i	0.747394	−	3.27455i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.473869	−	0.880596i	$-0.342857\pi$
$223$		0			0		−0.473869	+	0.880596i	$0.657143\pi$
$224$		0			0
$225$	1.54080	+	1.19148i	1.54080	+	1.19148i
$226$	0.331801	−	0.198242i	0.331801	−	0.198242i
$227$	1.57562	+	0.817719i	1.57562	+	0.817719i	1.00000			$0$
$227$	1.57562	+	0.817719i	1.57562	+	0.817719i	0.575617	+	0.817719i	$0.304762\pi$
$228$	2.05874	−	0.0616159i	2.05874	−	0.0616159i
$229$		0			0		−0.772417	−	0.635116i	$-0.780952\pi$
$229$		0			0		0.772417	+	0.635116i	$0.219048\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.0133831	+	0.0267587i	−0.0133831	+	0.0267587i	−0.900969	−	0.433884i	$-0.857143\pi$
$233$	−0.0133831	+	0.0267587i	−0.0133831	+	0.0267587i	0.887586	+	0.460642i	$0.152381\pi$
$234$		0			0
$235$		0			0
$236$	−1.57797	−	0.592222i	−1.57797	−	0.592222i
$237$		0			0
$238$		0			0
$239$		0			0		−0.992847	−	0.119394i	$-0.961905\pi$
$239$		0			0		0.992847	+	0.119394i	$0.0380952\pi$
$240$		0			0
$241$	−0.144074	−	1.92253i	−0.144074	−	1.92253i	−0.337330	−	0.941386i	$-0.609524\pi$
$241$	−0.144074	−	1.92253i	−0.144074	−	1.92253i	0.193256	−	0.981148i	$-0.438095\pi$
$242$	0.193256	+	0.981148i	0.193256	+	0.981148i
$243$	−0.167005	+	0.0515143i	−0.167005	+	0.0515143i
$244$		0			0
$245$		0			0
$246$	2.41102	+	1.25128i	2.41102	+	1.25128i
$247$		0			0
$248$		0			0
$249$	−1.87814	+	0.225854i	−1.87814	+	0.225854i
$250$		0			0
$251$	0.978148	−	0.207912i	0.978148	−	0.207912i	0.309017	−	0.951057i	$-0.400000\pi$
$251$	0.978148	−	0.207912i	0.978148	−	0.207912i	0.669131	+	0.743145i	$0.266667\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.963963	−	0.266037i	−0.963963	−	0.266037i
$257$	−1.08268	−	0.786610i	−1.08268	−	0.786610i	−0.104528	−	0.994522i	$-0.533333\pi$
$257$	−1.08268	−	0.786610i	−1.08268	−	0.786610i	−0.978148	+	0.207912i	$0.933333\pi$
$258$	1.07047	+	1.34232i	1.07047	+	1.34232i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.902545	+	0.539246i	0.902545	+	0.539246i
$263$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$263$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$264$	1.60742	+	0.603275i	1.60742	+	0.603275i
$265$		0			0
$266$		0			0
$267$	−0.186092	+	0.944777i	−0.186092	+	0.944777i
$268$	0.208963	+	0.00625404i	0.208963	+	0.00625404i
$269$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$269$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$270$		0			0
$271$		0			0		−0.337330	−	0.941386i	$-0.609524\pi$
$271$		0			0		0.337330	+	0.941386i	$0.390476\pi$
$272$	0.499574	+	1.92182i	0.499574	+	1.92182i
$273$		0			0
$274$	−1.68704	−	0.812434i	−1.68704	−	0.812434i
$275$	−0.925304	−	0.379225i	−0.925304	−	0.379225i
$276$		0			0
$277$		0			0		0.873408	−	0.486989i	$-0.161905\pi$
$277$		0			0		−0.873408	+	0.486989i	$0.838095\pi$
$278$	−0.141438	+	0.0483070i	−0.141438	+	0.0483070i
$279$		0			0
$280$		0			0
$281$	−0.0292650	−	1.95608i	−0.0292650	−	1.95608i	−0.222521	−	0.974928i	$-0.571429\pi$
$281$	−0.0292650	−	1.95608i	−0.0292650	−	1.95608i	0.193256	−	0.981148i	$-0.438095\pi$
$282$		0			0
$283$	1.69631	−	0.880355i	1.69631	−	0.880355i	0.712376	−	0.701798i	$-0.247619\pi$
$283$	1.69631	−	0.880355i	1.69631	−	0.880355i	0.983930	−	0.178557i	$-0.0571429\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	1.54080	−	1.19148i	1.54080	−	1.19148i
$289$	2.09651	−	2.06538i	2.09651	−	2.06538i
$290$		0			0
$291$	−2.09817	−	1.62249i	−2.09817	−	1.62249i
$292$	1.70864	+	0.952694i	1.70864	+	0.952694i
$293$		0			0		−0.983930	−	0.178557i	$-0.942857\pi$
$293$		0			0		0.983930	+	0.178557i	$0.0571429\pi$
$294$	1.56846	+	0.698325i	1.56846	+	0.698325i
$295$		0			0
$296$		0			0
$297$	−1.37125	+	0.875987i	−1.37125	+	0.875987i
$298$		0			0
$299$		0			0
$300$	−1.38900	+	1.00917i	−1.38900	+	1.00917i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.301814	+	1.16106i	−0.301814	+	1.16106i
$305$		0			0
$306$	−3.57872	−	1.46670i	−3.57872	−	1.46670i
$307$	0.873408	−	1.51279i	0.873408	−	1.51279i	0.0149594	−	0.999888i	$-0.495238\pi$
$307$	0.873408	−	1.51279i	0.873408	−	1.51279i	0.858449	−	0.512899i	$-0.171429\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.337330	−	0.941386i	$-0.390476\pi$
$311$		0			0		−0.337330	+	0.941386i	$0.609524\pi$
$312$		0			0
$313$	−0.423935	−	0.847635i	−0.423935	−	0.847635i	−0.999552	−	0.0299155i	$-0.990476\pi$
$313$	−0.423935	−	0.847635i	−0.423935	−	0.847635i	0.575617	−	0.817719i	$-0.304762\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.691063	−	0.722795i	$-0.257143\pi$
$317$		0			0		−0.691063	+	0.722795i	$0.742857\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	1.92020	−	2.72783i	1.92020	−	2.72783i
$322$		0			0
$323$	2.29628	−	0.633733i	2.29628	−	0.633733i
$324$	0.0126548	+	0.845849i	0.0126548	+	0.845849i
$325$		0			0
$326$	−0.921244	−	0.907564i	−0.921244	−	0.907564i
$327$		0			0
$328$	−1.09336	+	1.14356i	−1.09336	+	1.14356i
$329$		0			0
$330$		0			0
$331$	1.64952	+	1.12462i	1.64952	+	1.12462i	0.858449	+	0.512899i	$0.171429\pi$
$331$	1.64952	+	1.12462i	1.64952	+	1.12462i	0.791071	+	0.611724i	$0.209524\pi$
$332$	0.180494	−	1.08691i	0.180494	−	1.08691i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.148927	+	1.41695i	−0.148927	+	1.41695i	0.623490	+	0.781831i	$0.285714\pi$
$337$	−0.148927	+	1.41695i	−0.148927	+	1.41695i	−0.772417	+	0.635116i	$0.780952\pi$
$338$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$339$	−0.614033	−	0.251654i	−0.614033	−	0.251654i
$340$		0			0
$341$		0			0
$342$	−1.45684	−	1.82682i	−1.45684	−	1.82682i
$343$		0			0
$344$	−0.925304	+	0.379225i	−0.925304	+	0.379225i
$345$		0			0
$346$		0			0
$347$	−0.298548	+	0.245480i	−0.298548	+	0.245480i	−0.772417	−	0.635116i	$-0.780952\pi$
$347$	−0.298548	+	0.245480i	−0.298548	+	0.245480i	0.473869	+	0.880596i	$0.342857\pi$
$348$		0			0
$349$		0			0		−0.525684	−	0.850680i	$-0.676190\pi$
$349$		0			0		0.525684	+	0.850680i	$0.323810\pi$
$350$		0			0
$351$		0			0
$352$	−0.599822	+	0.800134i	−0.599822	+	0.800134i
$353$	0.947982	−	0.879599i	0.947982	−	0.879599i	−0.0448648	−	0.998993i	$-0.514286\pi$
$353$	0.947982	−	0.879599i	0.947982	−	0.879599i	0.992847	+	0.119394i	$0.0380952\pi$
$354$	0.811481	+	2.77762i	0.811481	+	2.77762i
$355$		0			0
$356$	−0.497807	−	0.258354i	−0.497807	−	0.258354i
$357$		0			0
$358$	−1.68243	−	0.100796i	−1.68243	−	0.100796i
$359$		0			0		−0.946327	−	0.323210i	$-0.895238\pi$
$359$		0			0		0.946327	+	0.323210i	$0.104762\pi$
$360$		0			0
$361$	0.426625	+	0.104113i	0.426625	+	0.104113i
$362$		0			0
$363$	1.14883	−	1.27590i	1.14883	−	1.27590i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.599822	−	0.800134i	$-0.704762\pi$
$367$		0			0		0.599822	+	0.800134i	$0.295238\pi$
$368$		0			0
$369$	−0.504821	−	3.03997i	−0.504821	−	3.03997i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$373$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$374$	1.97149	+	0.237080i	1.97149	+	0.237080i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.37965	−	1.44300i	−1.37965	−	1.44300i	−0.733052	−	0.680173i	$-0.761905\pi$
$379$	−1.37965	−	1.44300i	−1.37965	−	1.44300i	−0.646600	−	0.762830i	$-0.723810\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.858449	−	0.512899i	$-0.828571\pi$
$383$		0			0		0.858449	+	0.512899i	$0.171429\pi$
$384$	0.627253	+	1.59821i	0.627253	+	1.59821i
$385$		0			0
$386$	1.24698			1.24698
$387$	0.490025	−	1.88509i	0.490025	−	1.88509i
$388$	1.24980	−	0.908031i	1.24980	−	0.908031i
$389$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$389$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$390$		0			0
$391$		0			0
$392$	−0.646600	+	0.762830i	−0.646600	+	0.762830i
$393$	−0.188683	−	1.79520i	−0.188683	−	1.79520i
$394$		0			0
$395$		0			0
$396$	−0.546199	−	1.86958i	−0.546199	−	1.86958i
$397$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$397$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$398$		0			0
$399$		0			0
$400$	−0.337330	−	0.941386i	−0.337330	−	0.941386i
$401$	1.86912	+	0.111981i	1.86912	+	0.111981i	0.955573	−	0.294755i	$-0.0952381\pi$
$401$	1.86912	+	0.111981i	1.86912	+	0.111981i	0.913545	+	0.406737i	$0.133333\pi$
$402$	−0.206606	−	0.293503i	−0.206606	−	0.293503i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	2.12562	−	2.66545i	2.12562	−	2.66545i
$409$	−0.910345	−	1.37911i	−0.910345	−	1.37911i	−0.925304	−	0.379225i	$-0.876190\pi$
$409$	−0.910345	−	1.37911i	−0.910345	−	1.37911i	0.0149594	−	0.999888i	$-0.495238\pi$
$410$		0			0
$411$	0.621287	+	3.15423i	0.621287	+	3.15423i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.212019	+	0.144552i	0.212019	+	0.144552i
$418$	0.970532	+	0.705133i	0.970532	+	0.705133i
$419$	−0.0597394	−	0.261736i	−0.0597394	−	0.261736i	0.936235	−	0.351375i	$-0.114286\pi$
$419$	−0.0597394	−	0.261736i	−0.0597394	−	0.261736i	−0.995974	+	0.0896393i	$0.971429\pi$
$420$		0			0
$421$		0			0		0.193256	−	0.981148i	$-0.438095\pi$
$421$		0			0		−0.193256	+	0.981148i	$0.561905\pi$
$422$	−1.35991	−	0.246788i	−1.35991	−	0.246788i
$423$		0			0
$424$		0			0
$425$	−1.28395	+	1.51475i	−1.28395	+	1.51475i
$426$		0			0
$427$		0			0
$428$	1.21143	+	1.51908i	1.21143	+	1.51908i
$429$		0			0
$430$		0			0
$431$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$431$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$432$	−1.56853	−	0.432887i	−1.56853	−	0.432887i
$433$	0.495087	−	1.90456i	0.495087	−	1.90456i	0.0747301	−	0.997204i	$-0.476190\pi$
$433$	0.495087	−	1.90456i	0.495087	−	1.90456i	0.420357	−	0.907359i	$-0.361905\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.450857	−	3.32836i	−0.450857	−	3.32836i
$439$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$439$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$440$		0			0
$441$	−0.433412	−	1.89890i	−0.433412	−	1.89890i
$442$		0			0
$443$	−0.268346	+	0.00803130i	−0.268346	+	0.00803130i	−0.163818	−	0.986491i	$-0.552381\pi$
$443$	−0.268346	+	0.00803130i	−0.268346	+	0.00803130i	−0.104528	+	0.994522i	$0.533333\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.439476	+	0.245040i	−0.439476	+	0.245040i	−0.691063	−	0.722795i	$-0.742857\pi$
$449$	−0.439476	+	0.245040i	−0.439476	+	0.245040i	0.251587	+	0.967835i	$0.419048\pi$
$450$	1.86120	+	0.574106i	1.86120	+	0.574106i
$451$	0.665065	+	1.43557i	0.665065	+	1.43557i
$452$	0.240986	−	0.302187i	0.240986	−	0.302187i
$453$		0			0
$454$	1.76247	+	0.211945i	1.76247	+	0.211945i
$455$		0			0
$456$	1.90582	−	0.781078i	1.90582	−	0.781078i
$457$	−0.248413	+	1.83386i	−0.248413	+	1.83386i	0.251587	+	0.967835i	$0.419048\pi$
$457$	−0.248413	+	1.83386i	−0.248413	+	1.83386i	−0.500000	+	0.866025i	$0.666667\pi$
$458$		0			0
$459$	0.812891	+	3.12713i	0.812891	+	3.12713i
$460$		0			0
$461$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$461$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$462$		0			0
$463$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$463$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$464$		0			0
$465$		0			0
$466$	−0.00312737	+	0.0297549i	−0.00312737	+	0.0297549i
$467$	−1.61637	−	0.343569i	−1.61637	−	0.343569i	−0.691063	−	0.722795i	$-0.742857\pi$
$467$	−1.61637	−	0.343569i	−1.61637	−	0.343569i	−0.925304	+	0.379225i	$0.876190\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−1.68544			−1.68544
$473$	0.0149594	+	0.999888i	0.0149594	+	0.999888i
$474$		0			0
$475$	−1.12315	+	0.421525i	−1.12315	+	0.421525i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$479$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$480$		0			0
$481$		0			0
$482$	−0.810418	−	1.74932i	−0.810418	−	1.74932i
$483$		0			0
$484$	0.525684	+	0.850680i	0.525684	+	0.850680i
$485$		0			0
$486$	−0.138255	+	0.106911i	−0.138255	+	0.106911i
$487$		0			0		−0.251587	−	0.967835i	$-0.580952\pi$
$487$		0			0		0.251587	+	0.967835i	$0.419048\pi$
$488$		0			0
$489$	−0.298037	+	2.20020i	−0.298037	+	2.20020i
$490$		0			0
$491$	−1.24439	−	1.22591i	−1.24439	−	1.22591i	−0.963963	−	0.266037i	$-0.914286\pi$
$491$	−1.24439	−	1.22591i	−1.24439	−	1.22591i	−0.280427	−	0.959875i	$-0.590476\pi$
$492$	2.69695	+	0.324320i	2.69695	+	0.324320i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.67902	+	0.871382i	−1.67902	+	0.871382i
$499$	−0.812094	+	1.31416i	−0.812094	+	1.31416i	0.134233	+	0.990950i	$0.457143\pi$
$499$	−0.812094	+	1.31416i	−0.812094	+	1.31416i	−0.946327	+	0.323210i	$0.895238\pi$
$500$		0			0
$501$		0			0
$502$	0.842721	−	0.538351i	0.842721	−	0.538351i
$503$		0			0		0.999552	−	0.0299155i	$-0.00952381\pi$
$503$		0			0		−0.999552	+	0.0299155i	$0.990476\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.25857	+	1.16779i	−1.25857	+	1.16779i
$508$		0			0
$509$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$509$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$510$		0			0
$511$		0			0
$512$	−0.995974	+	0.0896393i	−0.995974	+	0.0896393i
$513$	−0.491103	+	1.88923i	−0.491103	+	1.88923i
$514$	−1.29003	−	0.356027i	−1.29003	−	0.356027i
$515$		0			0
$516$	1.47387	+	0.880596i	1.47387	+	0.880596i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.679814	+	0.802014i	−0.679814	+	0.802014i	−0.988831	−	0.149042i	$-0.952381\pi$
$521$	−0.679814	+	0.802014i	−0.679814	+	0.802014i	0.309017	+	0.951057i	$0.400000\pi$
$522$		0			0
$523$	−1.33766	+	1.48562i	−1.33766	+	1.48562i	−0.646600	+	0.762830i	$0.723810\pi$
$523$	−1.33766	+	1.48562i	−1.33766	+	1.48562i	−0.691063	+	0.722795i	$0.742857\pi$
$524$	1.03447	+	0.187729i	1.03447	+	0.187729i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	1.71690			1.71690
$529$	0.826239	+	0.563320i	0.826239	+	0.563320i
$530$		0			0
$531$	1.96909	−	2.62668i	1.96909	−	2.62668i
$532$		0			0
$533$		0			0
$534$	0.157745	+	0.949922i	0.157745	+	0.949922i
$535$		0			0
$536$	0.197836	−	0.0675692i	0.197836	−	0.0675692i
$537$	1.59415	+	2.41503i	1.59415	+	2.41503i
$538$		0			0
$539$	0.473869	+	0.880596i	0.473869	+	0.880596i
$540$		0			0
$541$		0			0		0.447313	−	0.894377i	$-0.352381\pi$
$541$		0			0		−0.447313	+	0.894377i	$0.647619\pi$
$542$		0			0
$543$		0			0
$544$	1.14300	+	1.62374i	1.14300	+	1.62374i
$545$		0			0
$546$		0			0
$547$	1.40186	−	1.38104i	1.40186	−	1.38104i	0.575617	−	0.817719i	$-0.304762\pi$
$547$	1.40186	−	1.38104i	1.40186	−	1.38104i	0.826239	−	0.563320i	$-0.190476\pi$
$548$	−1.86493	−	0.167847i	−1.86493	−	0.167847i
$549$		0			0
$550$	−0.999552	−	0.0299155i	−0.999552	−	0.0299155i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.115446	+	0.0949245i	−0.115446	+	0.0949245i
$557$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$557$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−1.70462	−	2.95248i	−1.70462	−	2.95248i
$562$	−0.714715	−	1.82106i	−0.714715	−	1.82106i
$563$	0.230465	+	0.137696i	0.230465	+	0.137696i	0.623490	−	0.781831i	$-0.285714\pi$
$563$	0.230465	+	0.137696i	0.230465	+	0.137696i	−0.393025	+	0.919528i	$0.628571\pi$
$564$		0			0
$565$		0			0
$566$	1.27881	−	1.42026i	1.27881	−	1.42026i
$567$		0			0
$568$		0			0
$569$	−0.169736	+	0.473681i	−0.169736	+	0.473681i	−0.995974	−	0.0896393i	$-0.971429\pi$
$569$	−0.169736	+	0.473681i	−0.169736	+	0.473681i	0.826239	+	0.563320i	$0.190476\pi$
$570$		0			0
$571$	−1.23305	+	0.185853i	−1.23305	+	0.185853i	−0.733052	−	0.680173i	$-0.761905\pi$
$571$	−1.23305	+	0.185853i	−1.23305	+	0.185853i	−0.500000	+	0.866025i	$0.666667\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	1.02389	−	1.65690i	1.02389	−	1.65690i
$577$	0.315829	+	1.90188i	0.315829	+	1.90188i	0.420357	+	0.907359i	$0.361905\pi$
$577$	0.315829	+	1.90188i	0.315829	+	1.90188i	−0.104528	+	0.994522i	$0.533333\pi$
$578$	1.23710	−	2.67034i	1.23710	−	2.67034i
$579$	−1.28418	−	1.71303i	−1.28418	−	1.71303i
$580$		0			0
$581$		0			0
$582$	−2.53449	−	0.781786i	−2.53449	−	0.781786i
$583$		0			0
$584$	1.93445	+	0.291571i	1.93445	+	0.291571i
$585$		0			0
$586$		0			0
$587$	−1.67989	−	0.573753i	−1.67989	−	0.573753i	−0.691063	−	0.722795i	$-0.742857\pi$
$587$	−1.67989	−	0.573753i	−1.67989	−	0.573753i	−0.988831	+	0.149042i	$0.952381\pi$
$588$	1.71382	+	0.102678i	1.71382	+	0.102678i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.38741	−	1.28733i	1.38741	−	1.28733i	0.473869	−	0.880596i	$-0.342857\pi$
$593$	1.38741	−	1.28733i	1.38741	−	1.28733i	0.913545	−	0.406737i	$-0.133333\pi$
$594$	−0.976011	+	1.30195i	−0.976011	+	1.30195i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.772417	−	0.635116i	$-0.219048\pi$
$599$		0			0		−0.772417	+	0.635116i	$0.780952\pi$
$600$	−0.945834	+	1.43288i	−0.945834	+	1.43288i
$601$	−1.61514	−	1.17347i	−1.61514	−	1.17347i	−0.842721	−	0.538351i	$-0.819048\pi$
$601$	−1.61514	−	1.17347i	−1.61514	−	1.17347i	−0.772417	−	0.635116i	$-0.780952\pi$
$602$		0			0
$603$	−0.125828	+	0.387259i	−0.125828	+	0.387259i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.925304	−	0.379225i	$-0.876190\pi$
$607$		0			0		0.925304	+	0.379225i	$0.123810\pi$
$608$	0.125397	+	1.19307i	0.125397	+	1.19307i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−3.86588	−	0.115701i	−3.86588	−	0.115701i
$613$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$613$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$614$	0.286160	−	1.72322i	0.286160	−	1.72322i
$615$		0			0
$616$		0			0
$617$	1.43923	−	0.443943i	1.43923	−	0.443943i	0.525684	−	0.850680i	$-0.323810\pi$
$617$	1.43923	−	0.443943i	1.43923	−	0.443943i	0.913545	+	0.406737i	$0.133333\pi$
$618$		0			0
$619$	0.508260	+	0.599622i	0.508260	+	0.599622i	0.955573	−	0.294755i	$-0.0952381\pi$
$619$	0.508260	+	0.599622i	0.508260	+	0.599622i	−0.447313	+	0.894377i	$0.647619\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.575617	−	0.817719i	0.575617	−	0.817719i
$626$	−0.694741	−	0.644625i	−0.694741	−	0.644625i
$627$	−0.0308114	−	2.05944i	−0.0308114	−	2.05944i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.842721	−	0.538351i	$-0.180952\pi$
$631$		0			0		−0.842721	+	0.538351i	$0.819048\pi$
$632$		0			0
$633$	1.06146	+	2.12233i	1.06146	+	2.12233i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.128769	+	0.301270i	0.128769	+	0.301270i	0.971490	−	0.237080i	$-0.0761905\pi$
$641$	0.128769	+	0.301270i	0.128769	+	0.301270i	−0.842721	+	0.538351i	$0.819048\pi$
$642$	0.839268	−	3.22860i	0.839268	−	3.22860i
$643$	−0.634211	+	0.960789i	−0.634211	+	0.960789i	0.365341	+	0.930874i	$0.380952\pi$
$643$	−0.634211	+	0.960789i	−0.634211	+	0.960789i	−0.999552	+	0.0299155i	$0.990476\pi$
$644$		0			0
$645$		0			0
$646$	1.92718	−	1.40018i	1.92718	−	1.40018i
$647$		0			0		0.936235	−	0.351375i	$-0.114286\pi$
$647$		0			0		−0.936235	+	0.351375i	$0.885714\pi$
$648$	0.309058	+	0.787466i	0.309058	+	0.787466i
$649$	−0.615761	+	1.56893i	−0.615761	+	1.56893i
$650$		0			0
$651$		0			0
$652$	−1.18140	−	0.525992i	−1.18140	−	0.525992i
$653$		0			0		−0.983930	−	0.178557i	$-0.942857\pi$
$653$		0			0		0.983930	+	0.178557i	$0.0571429\pi$
$654$		0			0
$655$		0			0
$656$	−0.621821	+	1.45482i	−0.621821	+	1.45482i
$657$	−2.71440	+	2.67410i	−2.71440	+	2.67410i
$658$		0			0
$659$	−0.287176	+	0.731713i	−0.287176	+	0.731713i	0.712376	+	0.701798i	$0.247619\pi$
$659$	−0.287176	+	0.731713i	−0.287176	+	0.731713i	−0.999552	+	0.0299155i	$0.990476\pi$
$660$		0			0
$661$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$661$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$662$	1.93950	+	0.473312i	1.93950	+	0.473312i
$663$		0			0
$664$	−0.212928	−	1.08102i	−0.212928	−	1.08102i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.0100925	+	0.674584i	−0.0100925	+	0.674584i	0.936235	+	0.351375i	$0.114286\pi$
$673$	−0.0100925	+	0.674584i	−0.0100925	+	0.674584i	−0.946327	+	0.323210i	$0.895238\pi$
$674$	0.358449	+	1.37892i	0.358449	+	1.37892i
$675$	−0.548893	−	1.53179i	−0.548893	−	1.53179i
$676$	−0.447313	−	0.894377i	−0.447313	−	0.894377i
$677$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$677$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$678$	−0.663304	−	0.0198519i	−0.663304	−	0.0198519i
$679$		0			0
$680$		0			0
$681$	−1.52389	−	2.63946i	−1.52389	−	2.63946i
$682$		0			0
$683$	−0.0332580	+	0.443797i	−0.0332580	+	0.443797i	0.955573	+	0.294755i	$0.0952381\pi$
$683$	−0.0332580	+	0.443797i	−0.0332580	+	0.443797i	−0.988831	+	0.149042i	$0.952381\pi$
$684$	−2.00584	−	1.19844i	−2.00584	−	1.19844i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$689$		0			0
$690$		0			0
$691$	1.82382	−	0.109268i	1.82382	−	0.109268i	0.887586	−	0.460642i	$-0.152381\pi$
$691$	1.82382	−	0.109268i	1.82382	−	0.109268i	0.936235	+	0.351375i	$0.114286\pi$
$692$		0			0
$693$		0			0
$694$	−0.193256	+	0.334729i	−0.193256	+	0.334729i
$695$		0			0
$696$		0			0
$697$	3.11918	−	0.375095i	3.11918	−	0.375095i
$698$		0			0
$699$	0.0440964	−	0.0263464i	0.0440964	−	0.0263464i
$700$		0			0
$701$		0			0		0.999552	−	0.0299155i	$-0.00952381\pi$
$701$		0			0		−0.999552	+	0.0299155i	$0.990476\pi$
$702$		0			0
$703$		0			0
$704$	−0.280427	+	0.959875i	−0.280427	+	0.959875i
$705$		0			0
$706$	0.578465	−	1.15661i	0.578465	−	1.15661i
$707$		0			0
$708$	1.73572	+	2.31537i	1.73572	+	2.31537i
$709$		0			0		−0.936235	−	0.351375i	$-0.885714\pi$
$709$		0			0		0.936235	+	0.351375i	$0.114286\pi$
$710$		0			0
$711$		0			0
$712$	−0.556843	−	0.0669628i	−0.556843	−	0.0669628i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.61056	+	0.496793i	−1.61056	+	0.496793i
$717$		0			0
$718$		0			0
$719$		0			0		−0.887586	−	0.460642i	$-0.847619\pi$
$719$		0			0		0.887586	+	0.460642i	$0.152381\pi$
$720$		0			0
$721$		0			0
$722$	0.436004	−	0.0524314i	0.436004	−	0.0524314i
$723$	−1.56853	+	2.91482i	−1.56853	+	2.91482i
$724$		0			0
$725$		0			0
$726$	0.627253	−	1.59821i	0.627253	−	1.59821i
$727$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$727$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$728$		0			0
$729$	1.10471	+	0.304880i	1.10471	+	0.304880i
$730$		0			0
$731$	1.89748	+	0.585294i	1.89748	+	0.585294i
$732$		0			0
$733$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$733$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.00937930	−	0.208846i	0.00937930	−	0.208846i
$738$	−1.54080	−	2.66874i	−1.54080	−	2.66874i
$739$	0.264152	+	1.95005i	0.264152	+	1.95005i	0.309017	+	0.951057i	$0.400000\pi$
$739$	0.264152	+	1.95005i	0.264152	+	1.95005i	−0.0448648	+	0.998993i	$0.514286\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.447313	−	0.894377i	$-0.647619\pi$
$743$		0			0		0.447313	+	0.894377i	$0.352381\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.93348	+	0.931117i	1.93348	+	0.931117i
$748$	1.92908	−	0.470769i	1.92908	−	0.470769i
$749$		0			0
$750$		0			0
$751$		0			0		0.946327	−	0.323210i	$-0.104762\pi$
$751$		0			0		−0.946327	+	0.323210i	$0.895238\pi$
$752$		0			0
$753$	−1.60742	−	0.603275i	−1.60742	−	0.603275i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.971490	−	0.237080i	$-0.923810\pi$
$757$		0			0		0.971490	+	0.237080i	$0.0761905\pi$
$758$	−1.79871	−	0.866214i	−1.79871	−	0.866214i
$759$		0			0
$760$		0			0
$761$	1.55672	−	1.20379i	1.55672	−	1.20379i	0.669131	−	0.743145i	$-0.266667\pi$
$761$	1.55672	−	1.20379i	1.55672	−	1.20379i	0.887586	−	0.460642i	$-0.152381\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	1.14883	+	1.27590i	1.14883	+	1.27590i
$769$	−0.147791	+	1.97213i	−0.147791	+	1.97213i	0.0747301	+	0.997204i	$0.476190\pi$
$769$	−0.147791	+	1.97213i	−0.147791	+	1.97213i	−0.222521	+	0.974928i	$0.571429\pi$
$770$		0			0
$771$	0.839429	+	2.13883i	0.839429	+	2.13883i
$772$	1.16747	−	0.438157i	1.16747	−	0.438157i
$773$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$773$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$774$	−0.203594	−	1.93707i	−0.203594	−	1.93707i
$775$		0			0
$776$	0.851044	−	1.28928i	0.851044	−	1.28928i
$777$		0			0
$778$		0			0
$779$	1.75623	+	0.719773i	1.75623	+	0.719773i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.337330	+	0.941386i	−0.337330	+	0.941386i
$785$		0			0
$786$	−0.807441	−	1.61443i	−0.807441	−	1.61443i
$787$	−0.422364	+	1.44571i	−0.422364	+	1.44571i	0.420357	+	0.907359i	$0.361905\pi$
$787$	−0.422364	+	1.44571i	−0.422364	+	1.44571i	−0.842721	+	0.538351i	$0.819048\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−1.16830	−	1.55845i	−1.16830	−	1.55845i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.0149594	−	0.999888i	$-0.504762\pi$
$797$		0			0		0.0149594	+	0.999888i	$0.495238\pi$
$798$		0			0
$799$		0			0
$800$	−0.646600	−	0.762830i	−0.646600	−	0.762830i
$801$	0.754915	−	0.789580i	0.754915	−	0.789580i
$802$	1.78928	−	0.551920i	1.78928	−	0.551920i
$803$	0.978148	−	1.69420i	0.978148	−	1.69420i
$804$	−0.296561	−	0.202192i	−0.296561	−	0.202192i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.04084	−	1.08863i	−1.04084	−	1.08863i	−0.995974	−	0.0896393i	$-0.971429\pi$
$809$	−1.04084	−	1.08863i	−1.04084	−	1.08863i	−0.0448648	−	0.998993i	$-0.514286\pi$
$810$		0			0
$811$	−0.139886	−	1.33093i	−0.139886	−	1.33093i	−0.809017	−	0.587785i	$-0.800000\pi$
$811$	−0.139886	−	1.33093i	−0.139886	−	1.33093i	0.669131	−	0.743145i	$-0.266667\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	1.05351	−	3.24237i	1.05351	−	3.24237i
$817$	0.829029	+	0.867096i	0.829029	+	0.867096i
$818$	−1.33688	−	0.971302i	−1.33688	−	0.971302i
$819$		0			0
$820$		0			0
$821$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$821$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$822$	1.68999	+	2.73480i	1.68999	+	2.73480i
$823$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$823$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$824$		0			0
$825$	0.988276	+	1.40394i	0.988276	+	1.40394i
$826$		0			0
$827$	0.189193	+	0.647589i	0.189193	+	0.647589i	0.998210	+	0.0598042i	$0.0190476\pi$
$827$	0.189193	+	0.647589i	0.189193	+	0.647589i	−0.809017	+	0.587785i	$0.800000\pi$
$828$		0			0
$829$		0			0		−0.887586	−	0.460642i	$-0.847619\pi$
$829$		0			0		0.887586	+	0.460642i	$0.152381\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.95378	−	0.354559i	1.95378	−	0.354559i
$834$	0.249292	+	0.0608367i	0.249292	+	0.0608367i
$835$		0			0
$836$	1.15641	+	0.319149i	1.15641	+	0.319149i
$837$		0			0
$838$	−0.147897	−	0.224055i	−0.147897	−	0.224055i
$839$		0			0		0.0448648	−	0.998993i	$-0.485714\pi$
$839$		0			0		−0.0448648	+	0.998993i	$0.514286\pi$
$840$		0			0
$841$	0.420357	−	0.907359i	0.420357	−	0.907359i
$842$		0			0
$843$	−1.76564	+	2.85723i	−1.76564	+	2.85723i
$844$	−1.35991	+	0.246788i	−1.35991	+	0.246788i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−3.26803	−	0.294128i	−3.26803	−	0.294128i
$850$	−0.669834	+	1.86931i	−0.669834	+	1.86931i
$851$		0			0
$852$		0			0
$853$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$853$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$854$		0			0
$855$		0			0
$856$	1.66795	+	0.996553i	1.66795	+	0.996553i
$857$	−0.727741	−	1.85425i	−0.727741	−	1.85425i	−0.447313	−	0.894377i	$-0.647619\pi$
$857$	−0.727741	−	1.85425i	−0.727741	−	1.85425i	−0.280427	−	0.959875i	$-0.590476\pi$
$858$		0			0
$859$	1.05137			1.05137			0.525684	−	0.850680i	$-0.323810\pi$
$859$	1.05137			1.05137			0.525684	+	0.850680i	$0.323810\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.772417	−	0.635116i	$-0.219048\pi$
$863$		0			0		−0.772417	+	0.635116i	$0.780952\pi$
$864$	−1.62062	+	0.145858i	−1.62062	+	0.145858i
$865$		0			0
$866$	−0.205697	−	1.95708i	−0.205697	−	1.95708i
$867$	−4.94238	+	1.05054i	−4.94238	+	1.05054i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	1.01500	+	2.83257i	1.01500	+	2.83257i
$874$		0			0
$875$		0			0
$876$	−1.59161	−	2.95771i	−1.59161	−	2.95771i
$877$		0			0		−0.646600	−	0.762830i	$-0.723810\pi$
$877$		0			0		0.646600	+	0.762830i	$0.276190\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.717783	−	0.900071i	0.717783	−	0.900071i	−0.280427	−	0.959875i	$-0.590476\pi$
$881$	0.717783	−	0.900071i	0.717783	−	0.900071i	0.998210	+	0.0598042i	$0.0190476\pi$
$882$	−1.07300	−	1.62553i	−1.07300	−	1.62553i
$883$	1.88504	−	0.643817i	1.88504	−	0.643817i	0.913545	−	0.406737i	$-0.133333\pi$
$883$	1.88504	−	0.643817i	1.88504	−	0.643817i	0.971490	−	0.237080i	$-0.0761905\pi$
$884$		0			0
$885$		0			0
$886$	−0.248413	+	0.101809i	−0.248413	+	0.101809i
$887$		0			0		−0.473869	−	0.880596i	$-0.657143\pi$
$887$		0			0		0.473869	+	0.880596i	$0.342857\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.845943			0.845943
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.325352	+	0.383836i	−0.325352	+	0.383836i
$899$		0			0
$900$	1.94425	−	0.116483i	1.94425	−	0.116483i
$901$		0			0
$902$	1.12708	+	1.11034i	1.12708	+	1.11034i
$903$		0			0
$904$	0.119439	−	0.367595i	0.119439	−	0.367595i
$905$		0			0
$906$		0			0
$907$	1.99106	−	0.179198i	1.99106	−	0.179198i	0.992847	−	0.119394i	$-0.0380952\pi$
$907$	1.99106	−	0.179198i	1.99106	−	0.179198i	0.998210	−	0.0598042i	$-0.0190476\pi$
$908$	1.72456	−	0.420858i	1.72456	−	0.420858i
$909$		0			0
$910$		0			0
$911$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$911$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$912$	1.50984	−	1.40093i	1.50984	−	1.40093i
$913$	−1.08409	−	0.196733i	−1.08409	−	0.196733i
$914$	0.411799	+	1.80421i	0.411799	+	1.80421i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	1.85985	+	2.64210i	1.85985	+	2.64210i
$919$		0			0		0.134233	−	0.990950i	$-0.457143\pi$
$919$		0			0		−0.134233	+	0.990950i	$0.542857\pi$
$920$		0			0
$921$	−2.66196	+	1.38152i	−2.66196	+	1.38152i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.69062	+	0.692879i	−1.69062	+	0.692879i	−0.999552	−	0.0299155i	$-0.990476\pi$
$929$	−1.69062	+	0.692879i	−1.69062	+	0.692879i	−0.691063	+	0.722795i	$0.742857\pi$
$930$		0			0
$931$	1.13526	+	0.387736i	1.13526	+	0.387736i
$932$	0.00752718	+	0.0289565i	0.00752718	+	0.0289565i
$933$		0			0
$934$	−1.63402	+	0.246289i	−1.63402	+	0.246289i
$935$		0			0
$936$		0			0
$937$	0.211513	+	0.456559i	0.211513	+	0.456559i	0.983930	−	0.178557i	$-0.0571429\pi$
$937$	0.211513	+	0.456559i	0.211513	+	0.456559i	−0.772417	+	0.635116i	$0.780952\pi$
$938$		0			0
$939$	−0.170085	+	1.61825i	−0.170085	+	1.61825i
$940$		0			0
$941$		0			0		0.971490	−	0.237080i	$-0.0761905\pi$
$941$		0			0		−0.971490	+	0.237080i	$0.923810\pi$
$942$		0			0
$943$		0			0
$944$	−1.57797	+	0.592222i	−1.57797	+	0.592222i
$945$		0			0
$946$	0.365341	+	0.930874i	0.365341	+	0.930874i
$947$	−1.89265			−1.89265			−0.946327	−	0.323210i	$-0.895238\pi$
$947$	−1.89265			−1.89265			−0.946327	+	0.323210i	$0.895238\pi$
$948$		0			0
$949$		0			0
$950$	−0.903418	+	0.789292i	−0.903418	+	0.789292i
$951$		0			0
$952$		0			0
$953$	−0.0280624	+	0.266996i	−0.0280624	+	0.266996i	0.971490	+	0.237080i	$0.0761905\pi$
$953$	−0.0280624	+	0.266996i	−0.0280624	+	0.266996i	−0.999552	+	0.0299155i	$0.990476\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.946327	−	0.323210i	−0.946327	−	0.323210i
$962$		0			0
$963$	−3.50174	+	1.43515i	−3.50174	+	1.43515i
$964$	−1.37341	−	1.35301i	−1.37341	−	1.35301i
$965$		0			0
$966$		0			0
$967$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$967$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$968$	0.791071	+	0.611724i	0.791071	+	0.611724i
$969$	−3.90816	−	1.20551i	−3.90816	−	1.20551i
$970$		0			0
$971$	−1.59937	+	0.830049i	−1.59937	+	0.830049i	−0.599822	+	0.800134i	$0.704762\pi$
$971$	−1.59937	+	0.830049i	−1.59937	+	0.830049i	−0.999552	+	0.0299155i	$0.990476\pi$
$972$	−0.0918737	+	0.148673i	−0.0918737	+	0.148673i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.313080	+	1.88533i	−0.313080	+	1.88533i	0.134233	+	0.990950i	$0.457143\pi$
$977$	−0.313080	+	1.88533i	−0.313080	+	1.88533i	−0.447313	+	0.894377i	$0.647619\pi$
$978$	0.494061	+	2.16462i	0.494061	+	2.16462i
$979$	−0.265772	+	0.493886i	−0.265772	+	0.493886i
$980$		0			0
$981$		0			0
$982$	−1.59580	−	0.710494i	−1.59580	−	0.710494i
$983$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$983$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$984$	2.63893	−	0.643999i	2.63893	−	0.643999i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$991$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$992$		0			0
$993$	−1.34715	−	3.15182i	−1.34715	−	3.15182i
$994$		0			0
$995$		0			0
$996$	−1.26577	+	1.40578i	−1.26577	+	1.40578i
$997$		0			0		−0.983930	−	0.178557i	$-0.942857\pi$
$997$		0			0		0.983930	+	0.178557i	$0.0571429\pi$
$998$	−0.298548	+	1.51571i	−0.298548	+	1.51571i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3784.1.em.a.1571.1	✓	48
8.3	odd	2	CM	3784.1.em.a.1571.1	✓	48
11.5	even	5		3784.1.em.b.3635.1	yes	48
43.15	even	21		3784.1.em.b.1219.1	yes	48
88.27	odd	10		3784.1.em.b.3635.1	yes	48
344.187	odd	42		3784.1.em.b.1219.1	yes	48
473.445	even	105	inner	3784.1.em.a.3283.1	yes	48
3784.3283	odd	210	inner	3784.1.em.a.3283.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3784.1.em.a.1571.1	✓	48	1.1	even	1	trivial
3784.1.em.a.1571.1	✓	48	8.3	odd	2	CM
3784.1.em.a.3283.1	yes	48	473.445	even	105	inner
3784.1.em.a.3283.1	yes	48	3784.3283	odd	210	inner
3784.1.em.b.1219.1	yes	48	43.15	even	21
3784.1.em.b.1219.1	yes	48	344.187	odd	42
3784.1.em.b.3635.1	yes	48	11.5	even	5
3784.1.em.b.3635.1	yes	48	88.27	odd	10

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:	\( N \)	\(=\)	\( 3784 = 2^{3} \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3784.em (of order \(210\), degree \(48\), minimal)

\(f(q)\)	\(=\)	\(q+(0.936235 - 0.351375i) q^{2} +(-1.44687 - 0.924293i) q^{3} +(0.753071 - 0.657939i) q^{4} +(-1.67938 - 0.356963i) q^{6} +(0.473869 - 0.880596i) q^{8} +(0.818745 + 1.76730i) q^{9} +O(q^{10})\)	\(q+(0.936235 - 0.351375i) q^{2} +(-1.44687 - 0.924293i) q^{3} +(0.753071 - 0.657939i) q^{4} +(-1.67938 - 0.356963i) q^{6} +(0.473869 - 0.880596i) q^{8} +(0.818745 + 1.76730i) q^{9} +(-0.646600 - 0.762830i) q^{11} +(-1.69772 + 0.255890i) q^{12} +(0.134233 - 0.990950i) q^{16} +(-1.83737 + 0.753026i) q^{17} +(1.38752 + 1.36692i) q^{18} +(-1.19106 - 0.143231i) q^{19} +(-0.873408 - 0.486989i) q^{22} +(-1.49955 + 0.836110i) q^{24} +(0.887586 - 0.460642i) q^{25} +(0.218420 - 1.61244i) q^{27} +(-0.222521 - 0.974928i) q^{32} +(0.230465 + 1.70136i) q^{33} +(-1.45562 + 1.35061i) q^{34} +(1.77935 + 0.792216i) q^{36} +(-1.16544 + 0.284412i) q^{38} +(-1.52513 - 0.420908i) q^{41} +(-0.772417 - 0.635116i) q^{43} +(-0.988831 - 0.149042i) q^{44} +(-1.11015 + 1.30970i) q^{48} +(-0.978148 - 0.207912i) q^{49} +(0.669131 - 0.743145i) q^{50} +(3.35445 + 0.608742i) q^{51} +(-0.362079 - 1.58637i) q^{54} +(1.59092 + 1.30813i) q^{57} +(-0.798678 - 1.48419i) q^{59} +(-0.550897 - 0.834573i) q^{64} +(0.813584 + 1.51189i) q^{66} +(0.153250 + 0.142195i) q^{67} +(-0.888227 + 1.77596i) q^{68} +(1.94425 + 0.116483i) q^{72} +(0.659917 + 1.84163i) q^{73} +(-1.70999 - 0.153902i) q^{75} +(-0.991192 + 0.675783i) q^{76} +(-0.546987 + 0.645311i) q^{81} +(-1.57577 + 0.141822i) q^{82} +(0.851044 - 0.699767i) q^{83} +(-0.946327 - 0.323210i) q^{86} +(-0.978148 + 0.207912i) q^{88} +(-0.204903 - 0.522085i) q^{89} +(-0.579161 + 1.61626i) q^{96} +(1.53861 + 0.138478i) q^{97} +(-0.988831 + 0.149042i) q^{98} +(0.818745 - 1.76730i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9	\( 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9} - q^{11} - 2 q^{12} + 2 q^{16} + q^{17} + 2 q^{18} - 22 q^{19} - q^{22} - 25 q^{24} - q^{25} - 2 q^{27} - 8 q^{32} - 6 q^{33} - 13 q^{34} + 9 q^{36} + q^{38} - 2 q^{41} - q^{43} + 4 q^{44} - 2 q^{48} + 6 q^{49} + 6 q^{50} + 8 q^{51} - 6 q^{54} + 7 q^{57} + 3 q^{59} + 2 q^{64} + 4 q^{66} + q^{67} + q^{68} - 3 q^{72} + q^{73} - 20 q^{75} + q^{76} + 7 q^{81} + 3 q^{82} + 10 q^{83} - q^{86} + 6 q^{88} + q^{89} - 2 q^{96} + 3 q^{97} + 4 q^{98} - 3 q^{99}+O(q^{100}) \) 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9 - q^11 - 2 * q^12 + 2 * q^16 + q^17 + 2 * q^18 - 22 * q^19 - q^22 - 25 * q^24 - q^25 - 2 * q^27 - 8 * q^32 - 6 * q^33 - 13 * q^34 + 9 * q^36 + q^38 - 2 * q^41 - q^43 + 4 * q^44 - 2 * q^48 + 6 * q^49 + 6 * q^50 + 8 * q^51 - 6 * q^54 + 7 * q^57 + 3 * q^59 + 2 * q^64 + 4 * q^66 + q^67 + q^68 - 3 * q^72 + q^73 - 20 * q^75 + q^76 + 7 * q^81 + 3 * q^82 + 10 * q^83 - q^86 + 6 * q^88 + q^89 - 2 * q^96 + 3 * q^97 + 4 * q^98 - 3 * q^99

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