LMFDB - Embedded newform 3784.1.em.b.427.1

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			427.1
Root			$0.925304 - 0.379225i$ of defining polynomial
Character	$\chi$	$=$	3784.427
Dual form			3784.1.em.b.1347.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.691063 + 0.722795i) q^{2} +(-0.579195 - 0.937274i) q^{3} +(-0.0448648 - 0.998993i) q^{4} +(1.07772 + 0.229076i) q^{6} +(0.753071 + 0.657939i) q^{8} +(-0.0957026 + 0.191352i) q^{9} +O(q^{10})$	\(q+(-0.691063 + 0.722795i) q^{2} +(-0.579195 - 0.937274i) q^{3} +(-0.0448648 - 0.998993i) q^{4} +(1.07772 + 0.229076i) q^{6} +(0.753071 + 0.657939i) q^{8} +(-0.0957026 + 0.191352i) q^{9} +(0.525684 + 0.850680i) q^{11} +(-0.910345 + 0.620663i) q^{12} +(-0.995974 + 0.0896393i) q^{16} +(1.02182 + 1.45159i) q^{17} +(-0.0721717 - 0.201410i) q^{18} +(-1.20067 + 1.18284i) q^{19} +(-0.978148 - 0.207912i) q^{22} +(0.180494 - 1.08691i) q^{24} +(-0.999552 + 0.0299155i) q^{25} +(-0.862579 + 0.0776335i) q^{27} +(0.623490 - 0.781831i) q^{32} +(0.492847 - 0.985420i) q^{33} +(-1.75534 - 0.264576i) q^{34} +(0.195453 + 0.0870213i) q^{36} +(-0.0252132 - 1.68525i) q^{38} +(-1.71874 + 0.311906i) q^{41} +(-0.925304 + 0.379225i) q^{43} +(0.826239 - 0.563320i) q^{44} +(0.660880 + 0.881582i) q^{48} +(-0.978148 - 0.207912i) q^{49} +(0.669131 - 0.743145i) q^{50} +(0.768707 - 1.79848i) q^{51} +(0.539983 - 0.677117i) q^{54} +(1.80407 + 0.440261i) q^{57} +(-0.973871 + 0.850846i) q^{59} +(0.134233 + 0.990950i) q^{64} +(0.371668 + 1.03721i) q^{66} +(-1.80668 + 0.272314i) q^{67} +(1.40429 - 1.08592i) q^{68} +(-0.197969 + 0.0811353i) q^{72} +(1.32869 - 0.159781i) q^{73} +(0.606975 + 0.919528i) q^{75} +(1.23552 + 1.14639i) q^{76} +(0.700697 + 0.934696i) q^{81} +(0.962316 - 1.45785i) q^{82} +(-1.34272 + 0.327675i) q^{83} +(0.365341 - 0.930874i) q^{86} +(-0.163818 + 0.986491i) q^{88} +(0.0628267 - 0.838364i) q^{89} +(-1.09391 - 0.131548i) q^{96} +(1.01949 + 1.54447i) q^{97} +(0.826239 - 0.563320i) q^{98} +(-0.213089 + 0.0191783i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 2 q^{19} + 6 q^{22} + 10 q^{24} - q^{25} - 2 q^{27} - 8 q^{32} - 25 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} - 8 q^{57} + 3 q^{59} + 2 q^{64} - 2 q^{66} + q^{67} + q^{68} - 3 q^{72} + q^{73} + 50 q^{75} + q^{76} - 28 q^{81} + 3 q^{82} - 25 q^{83} + 4 q^{86} - q^{88} + q^{89} - 2 q^{96} + 3 q^{97} + 4 q^{98} - 8 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 - 2 * q^19 + 6 * q^22 + 10 * q^24 - q^25 - 2 * q^27 - 8 * q^32 - 25 * 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 - 8 * q^57 + 3 * q^59 + 2 * q^64 - 2 * q^66 + q^67 + q^68 - 3 * q^72 + q^73 + 50 * q^75 + q^76 - 28 * q^81 + 3 * q^82 - 25 * q^83 + 4 * q^86 - q^88 + q^89 - 2 * q^96 + 3 * q^97 + 4 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$89$	$1377$	$1893$	$2839$
$\chi(n)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$-1$

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 $

$2$	−0.691063	+	0.722795i	−0.691063	+	0.722795i
$2$	−0.691063	+	0.722795i	−0.691063	+	0.722795i
$3$	−0.579195	−	0.937274i	−0.579195	−	0.937274i	−0.999552	−	0.0299155i	$-0.990476\pi$
$3$	−0.579195	−	0.937274i	−0.579195	−	0.937274i	0.420357	−	0.907359i	$-0.361905\pi$
$4$	−0.0448648	−	0.998993i	−0.0448648	−	0.998993i
$5$		0			0		−0.0149594	−	0.999888i	$-0.504762\pi$
$5$		0			0		0.0149594	+	0.999888i	$0.495238\pi$
$6$	1.07772	+	0.229076i	1.07772	+	0.229076i
$7$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$7$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$8$	0.753071	+	0.657939i	0.753071	+	0.657939i
$9$	−0.0957026	+	0.191352i	−0.0957026	+	0.191352i
$10$		0			0
$11$	0.525684	+	0.850680i	0.525684	+	0.850680i
$11$	0.525684	+	0.850680i	0.525684	+	0.850680i
$12$	−0.910345	+	0.620663i	−0.910345	+	0.620663i
$13$		0			0		−0.420357	−	0.907359i	$-0.638095\pi$
$13$		0			0		0.420357	+	0.907359i	$0.361905\pi$
$14$		0			0
$15$		0			0
$16$	−0.995974	+	0.0896393i	−0.995974	+	0.0896393i
$17$	1.02182	+	1.45159i	1.02182	+	1.45159i	0.887586	+	0.460642i	$0.152381\pi$
$17$	1.02182	+	1.45159i	1.02182	+	1.45159i	0.134233	+	0.990950i	$0.457143\pi$
$18$	−0.0721717	−	0.201410i	−0.0721717	−	0.201410i
$19$	−1.20067	+	1.18284i	−1.20067	+	1.18284i	−0.222521	+	0.974928i	$0.571429\pi$
$19$	−1.20067	+	1.18284i	−1.20067	+	1.18284i	−0.978148	+	0.207912i	$0.933333\pi$
$20$		0			0
$21$		0			0
$22$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$23$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$23$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$24$	0.180494	−	1.08691i	0.180494	−	1.08691i
$25$	−0.999552	+	0.0299155i	−0.999552	+	0.0299155i
$26$		0			0
$27$	−0.862579	+	0.0776335i	−0.862579	+	0.0776335i
$28$		0			0
$29$		0			0		0.525684	−	0.850680i	$-0.323810\pi$
$29$		0			0		−0.525684	+	0.850680i	$0.676190\pi$
$30$		0			0
$31$		0			0		−0.280427	−	0.959875i	$-0.590476\pi$
$31$		0			0		0.280427	+	0.959875i	$0.409524\pi$
$32$	0.623490	−	0.781831i	0.623490	−	0.781831i
$33$	0.492847	−	0.985420i	0.492847	−	0.985420i
$34$	−1.75534	−	0.264576i	−1.75534	−	0.264576i
$35$		0			0
$36$	0.195453	+	0.0870213i	0.195453	+	0.0870213i
$37$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$37$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$38$	−0.0252132	−	1.68525i	−0.0252132	−	1.68525i
$39$		0			0
$40$		0			0
$41$	−1.71874	+	0.311906i	−1.71874	+	0.311906i	−0.946327	−	0.323210i	$-0.895238\pi$
$41$	−1.71874	+	0.311906i	−1.71874	+	0.311906i	−0.772417	+	0.635116i	$0.780952\pi$
$42$		0			0
$43$	−0.925304	+	0.379225i	−0.925304	+	0.379225i
$43$	−0.925304	+	0.379225i	−0.925304	+	0.379225i
$44$	0.826239	−	0.563320i	0.826239	−	0.563320i
$45$		0			0
$46$		0			0
$47$		0			0		−0.963963	−	0.266037i	$-0.914286\pi$
$47$		0			0		0.963963	+	0.266037i	$0.0857143\pi$
$48$	0.660880	+	0.881582i	0.660880	+	0.881582i
$49$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$50$	0.669131	−	0.743145i	0.669131	−	0.743145i
$51$	0.768707	−	1.79848i	0.768707	−	1.79848i
$52$		0			0
$53$		0			0		0.873408	−	0.486989i	$-0.161905\pi$
$53$		0			0		−0.873408	+	0.486989i	$0.838095\pi$
$54$	0.539983	−	0.677117i	0.539983	−	0.677117i
$55$		0			0
$56$		0			0
$57$	1.80407	+	0.440261i	1.80407	+	0.440261i
$58$		0			0
$59$	−0.973871	+	0.850846i	−0.973871	+	0.850846i	−0.988831	−	0.149042i	$-0.952381\pi$
$59$	−0.973871	+	0.850846i	−0.973871	+	0.850846i	0.0149594	+	0.999888i	$0.495238\pi$
$60$		0			0
$61$		0			0		0.280427	−	0.959875i	$-0.409524\pi$
$61$		0			0		−0.280427	+	0.959875i	$0.590476\pi$
$62$		0			0
$63$		0			0
$64$	0.134233	+	0.990950i	0.134233	+	0.990950i
$65$		0			0
$66$	0.371668	+	1.03721i	0.371668	+	1.03721i
$67$	−1.80668	+	0.272314i	−1.80668	+	0.272314i	−0.963963	−	0.266037i	$-0.914286\pi$
$67$	−1.80668	+	0.272314i	−1.80668	+	0.272314i	−0.842721	+	0.538351i	$0.819048\pi$
$68$	1.40429	−	1.08592i	1.40429	−	1.08592i
$69$		0			0
$70$		0			0
$71$		0			0		−0.998210	−	0.0598042i	$-0.980952\pi$
$71$		0			0		0.998210	+	0.0598042i	$0.0190476\pi$
$72$	−0.197969	+	0.0811353i	−0.197969	+	0.0811353i
$73$	1.32869	−	0.159781i	1.32869	−	0.159781i	0.575617	−	0.817719i	$-0.304762\pi$
$73$	1.32869	−	0.159781i	1.32869	−	0.159781i	0.753071	+	0.657939i	$0.228571\pi$
$74$		0			0
$75$	0.606975	+	0.919528i	0.606975	+	0.919528i
$76$	1.23552	+	1.14639i	1.23552	+	1.14639i
$77$		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
$81$	0.700697	+	0.934696i	0.700697	+	0.934696i
$82$	0.962316	−	1.45785i	0.962316	−	1.45785i
$83$	−1.34272	+	0.327675i	−1.34272	+	0.327675i	−0.842721	−	0.538351i	$-0.819048\pi$
$83$	−1.34272	+	0.327675i	−1.34272	+	0.327675i	−0.500000	+	0.866025i	$0.666667\pi$
$84$		0			0
$85$		0			0
$86$	0.365341	−	0.930874i	0.365341	−	0.930874i
$87$		0			0
$88$	−0.163818	+	0.986491i	−0.163818	+	0.986491i
$89$	0.0628267	−	0.838364i	0.0628267	−	0.838364i	−0.873408	−	0.486989i	$-0.838095\pi$
$89$	0.0628267	−	0.838364i	0.0628267	−	0.838364i	0.936235	−	0.351375i	$-0.114286\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−1.09391	−	0.131548i	−1.09391	−	0.131548i
$97$	1.01949	+	1.54447i	1.01949	+	1.54447i	0.826239	+	0.563320i	$0.190476\pi$
$97$	1.01949	+	1.54447i	1.01949	+	1.54447i	0.193256	+	0.981148i	$0.438095\pi$
$98$	0.826239	−	0.563320i	0.826239	−	0.563320i
$99$	−0.213089	+	0.0191783i	−0.213089	+	0.0191783i
$100$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$101$		0			0		−0.772417	−	0.635116i	$-0.780952\pi$
$101$		0			0		0.772417	+	0.635116i	$0.219048\pi$
$102$	0.768707	+	1.79848i	0.768707	+	1.79848i
$103$		0			0		−0.946327	−	0.323210i	$-0.895238\pi$
$103$		0			0		0.946327	+	0.323210i	$0.104762\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.545534	−	1.01377i	0.545534	−	1.01377i	−0.447313	−	0.894377i	$-0.647619\pi$
$107$	0.545534	−	1.01377i	0.545534	−	1.01377i	0.992847	−	0.119394i	$-0.0380952\pi$
$108$	0.116255	+	0.858227i	0.116255	+	0.858227i
$109$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$109$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.559963	−	1.31010i	−0.559963	−	1.31010i	−0.925304	−	0.379225i	$-0.876190\pi$
$113$	−0.559963	−	1.31010i	−0.559963	−	1.31010i	0.365341	−	0.930874i	$-0.380952\pi$
$114$	−1.56494	+	0.999722i	−1.56494	+	0.999722i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.0580192	−	1.29190i	0.0580192	−	1.29190i
$119$		0			0
$120$		0			0
$121$	−0.447313	+	0.894377i	−0.447313	+	0.894377i
$122$		0			0
$123$	1.28783	+	1.43028i	1.28783	+	1.43028i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.134233	−	0.990950i	$-0.457143\pi$
$127$		0			0		−0.134233	+	0.990950i	$0.542857\pi$
$128$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$129$	0.891370	+	0.647618i	0.891370	+	0.647618i
$130$		0			0
$131$	1.08084	+	0.520506i	1.08084	+	0.520506i	0.887586	−	0.460642i	$-0.152381\pi$
$131$	1.08084	+	0.520506i	1.08084	+	0.520506i	0.193256	+	0.981148i	$0.438095\pi$
$132$	−1.00654	−	0.448140i	−1.00654	−	0.448140i
$133$		0			0
$134$	1.05170	−	1.49405i	1.05170	−	1.49405i
$135$		0			0
$136$	−0.185556	+	1.76545i	−0.185556	+	1.76545i
$137$	0.230465	−	0.137696i	0.230465	−	0.137696i	−0.393025	−	0.919528i	$-0.628571\pi$
$137$	0.230465	−	0.137696i	0.230465	−	0.137696i	0.623490	+	0.781831i	$0.285714\pi$
$138$		0			0
$139$	0.369340	+	1.87512i	0.369340	+	1.87512i	0.473869	+	0.880596i	$0.342857\pi$
$139$	0.369340	+	1.87512i	0.369340	+	1.87512i	−0.104528	+	0.994522i	$0.533333\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.0781647	−	0.199160i	0.0781647	−	0.199160i
$145$		0			0
$146$	−0.802718	+	1.07079i	−0.802718	+	1.07079i
$147$	0.371668	+	1.03721i	0.371668	+	1.03721i
$148$		0			0
$149$		0			0		0.772417	−	0.635116i	$-0.219048\pi$
$149$		0			0		−0.772417	+	0.635116i	$0.780952\pi$
$150$	−1.08409	−	0.196733i	−1.08409	−	0.196733i
$151$		0			0		0.473869	−	0.880596i	$-0.342857\pi$
$151$		0			0		−0.473869	+	0.880596i	$0.657143\pi$
$152$	−1.68243	+	0.100796i	−1.68243	+	0.100796i
$153$	−0.375556	+	0.0566059i	−0.375556	+	0.0566059i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.251587	−	0.967835i	$-0.580952\pi$
$157$		0			0		0.251587	+	0.967835i	$0.419048\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−1.15982	−	0.139473i	−1.15982	−	0.139473i
$163$	0.846609	−	1.69275i	0.846609	−	1.69275i	0.134233	−	0.990950i	$-0.457143\pi$
$163$	0.846609	−	1.69275i	0.846609	−	1.69275i	0.712376	−	0.701798i	$-0.247619\pi$
$164$	0.388703	+	1.70302i	0.388703	+	1.70302i
$165$		0			0
$166$	0.691063	−	1.19696i	0.691063	−	1.19696i
$167$		0			0		0.575617	−	0.817719i	$-0.304762\pi$
$167$		0			0		−0.575617	+	0.817719i	$0.695238\pi$
$168$		0			0
$169$	−0.646600	+	0.762830i	−0.646600	+	0.762830i
$170$		0			0
$171$	−0.111432	−	0.342951i	−0.111432	−	0.342951i
$172$	0.420357	+	0.907359i	0.420357	+	0.907359i
$173$		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
$176$	−0.599822	−	0.800134i	−0.599822	−	0.800134i
$177$	1.36154	+	0.419979i	1.36154	+	0.419979i
$178$	0.562548	+	0.624773i	0.562548	+	0.624773i
$179$	−1.18140	−	0.525992i	−1.18140	−	0.525992i	−0.280427	−	0.959875i	$-0.590476\pi$
$179$	−1.18140	−	0.525992i	−1.18140	−	0.525992i	−0.900969	+	0.433884i	$0.857143\pi$
$180$		0			0
$181$		0			0		−0.163818	−	0.986491i	$-0.552381\pi$
$181$		0			0		0.163818	+	0.986491i	$0.447619\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.697687	+	1.63232i	−0.697687	+	1.63232i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.887586	−	0.460642i	$-0.847619\pi$
$191$		0			0		0.887586	+	0.460642i	$0.152381\pi$
$192$	0.851044	−	0.699767i	0.851044	−	0.699767i
$193$	1.24525	+	1.30243i	1.24525	+	1.30243i	0.936235	+	0.351375i	$0.114286\pi$
$193$	1.24525	+	1.30243i	1.24525	+	1.30243i	0.309017	+	0.951057i	$0.400000\pi$
$194$	−1.82087	−	0.330439i	−1.82087	−	0.330439i
$195$		0			0
$196$	−0.163818	+	0.986491i	−0.163818	+	0.986491i
$197$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$197$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$198$	0.133396	−	0.167273i	0.133396	−	0.167273i
$199$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$199$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$200$	−0.772417	−	0.635116i	−0.772417	−	0.635116i
$201$	1.30166	+	1.53564i	1.30166	+	1.53564i
$202$		0			0
$203$		0			0
$204$	−1.83116	−	0.687245i	−1.83116	−	0.687245i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.63739	−	0.399585i	−1.63739	−	0.399585i
$210$		0			0
$211$	−1.86493	+	0.699921i	−1.86493	+	0.699921i	−0.900969	+	0.433884i	$0.857143\pi$
$211$	−1.86493	+	0.699921i	−1.86493	+	0.699921i	−0.963963	+	0.266037i	$0.914286\pi$
$212$		0			0
$213$		0			0
$214$	0.355751	+	1.09489i	0.355751	+	1.09489i
$215$		0			0
$216$	−0.700661	−	0.509060i	−0.700661	−	0.509060i
$217$		0			0
$218$		0			0
$219$	−0.919328	−	1.15280i	−0.919328	−	1.15280i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$223$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$224$		0			0
$225$	0.0899354	−	0.194129i	0.0899354	−	0.194129i
$226$	1.33390	+	0.500622i	1.33390	+	0.500622i
$227$	0.674358	+	0.0201828i	0.674358	+	0.0201828i	0.365341	−	0.930874i	$-0.380952\pi$
$227$	0.674358	+	0.0201828i	0.674358	+	0.0201828i	0.309017	+	0.951057i	$0.400000\pi$
$228$	0.358878	−	1.82200i	0.358878	−	1.82200i
$229$		0			0		−0.971490	−	0.237080i	$-0.923810\pi$
$229$		0			0		0.971490	+	0.237080i	$0.0761905\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.57931	−	1.22126i	1.57931	−	1.22126i	0.753071	−	0.657939i	$-0.228571\pi$
$233$	1.57931	−	1.22126i	1.57931	−	1.22126i	0.826239	−	0.563320i	$-0.190476\pi$
$234$		0			0
$235$		0			0
$236$	0.893682	+	0.934718i	0.893682	+	0.934718i
$237$		0			0
$238$		0			0
$239$		0			0		0.712376	−	0.701798i	$-0.247619\pi$
$239$		0			0		−0.712376	+	0.701798i	$0.752381\pi$
$240$		0			0
$241$	0.905632	−	0.279350i	0.905632	−	0.279350i	0.193256	−	0.981148i	$-0.438095\pi$
$241$	0.905632	−	0.279350i	0.905632	−	0.279350i	0.712376	+	0.701798i	$0.247619\pi$
$242$	−0.337330	−	0.941386i	−0.337330	−	0.941386i
$243$	0.153817	−	0.391920i	0.153817	−	0.391920i
$244$		0			0
$245$		0			0
$246$	−1.92377	−	0.0575763i	−1.92377	−	0.0575763i
$247$		0			0
$248$		0			0
$249$	1.08482	+	1.06871i	1.08482	+	1.06871i
$250$		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
$256$	0.983930	−	0.178557i	0.983930	−	0.178557i
$257$	1.58268	+	1.14988i	1.58268	+	1.14988i	0.913545	+	0.406737i	$0.133333\pi$
$257$	1.58268	+	1.14988i	1.58268	+	1.14988i	0.669131	+	0.743145i	$0.266667\pi$
$258$	−1.08409	+	0.196733i	−1.08409	+	0.196733i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−1.12315	+	0.421525i	−1.12315	+	0.421525i
$263$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$263$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$264$	1.01949	−	0.417828i	1.01949	−	0.417828i
$265$		0			0
$266$		0			0
$267$	−0.822165	+	0.426690i	−0.822165	+	0.426690i
$268$	0.353096	+	1.79265i	0.353096	+	1.79265i
$269$		0			0		−0.936235	−	0.351375i	$-0.885714\pi$
$269$		0			0		0.936235	+	0.351375i	$0.114286\pi$
$270$		0			0
$271$		0			0		0.992847	−	0.119394i	$-0.0380952\pi$
$271$		0			0		−0.992847	+	0.119394i	$0.961905\pi$
$272$	−1.14783	−	1.35415i	−1.14783	−	1.35415i
$273$		0			0
$274$	−0.0597394	+	0.261736i	−0.0597394	+	0.261736i
$275$	−0.550897	−	0.834573i	−0.550897	−	0.834573i
$276$		0			0
$277$		0			0		0.163818	−	0.986491i	$-0.447619\pi$
$277$		0			0		−0.163818	+	0.986491i	$0.552381\pi$
$278$	−1.61056	−	1.02887i	−1.61056	−	1.02887i
$279$		0			0
$280$		0			0
$281$	−1.03370	+	0.849951i	−1.03370	+	0.849951i	−0.988831	−	0.149042i	$-0.952381\pi$
$281$	−1.03370	+	0.849951i	−1.03370	+	0.849951i	−0.0448648	+	0.998993i	$0.514286\pi$
$282$		0			0
$283$	−0.730355	+	0.0218587i	−0.730355	+	0.0218587i	−0.393025	−	0.919528i	$-0.628571\pi$
$283$	−0.730355	+	0.0218587i	−0.730355	+	0.0218587i	−0.337330	+	0.941386i	$0.609524\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.0899354	+	0.194129i	0.0899354	+	0.194129i
$289$	−0.725676	+	2.02514i	−0.725676	+	2.02514i
$290$		0			0
$291$	0.857104	−	1.85009i	0.857104	−	1.85009i
$292$	−0.219231	−	1.32018i	−0.219231	−	1.32018i
$293$		0			0		0.393025	−	0.919528i	$-0.371429\pi$
$293$		0			0		−0.393025	+	0.919528i	$0.628571\pi$
$294$	−1.00654	−	0.448140i	−1.00654	−	0.448140i
$295$		0			0
$296$		0			0
$297$	−0.519485	−	0.692968i	−0.519485	−	0.692968i
$298$		0			0
$299$		0			0
$300$	0.891370	−	0.647618i	0.891370	−	0.647618i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	1.08981	−	1.28570i	1.08981	−	1.28570i
$305$		0			0
$306$	0.218618	−	0.310568i	0.218618	−	0.310568i
$307$	0.447313	−	0.774769i	0.447313	−	0.774769i	−0.550897	−	0.834573i	$-0.685714\pi$
$307$	0.447313	−	0.774769i	0.447313	−	0.774769i	0.998210	+	0.0598042i	$0.0190476\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.992847	−	0.119394i	$-0.961905\pi$
$311$		0			0		0.992847	+	0.119394i	$0.0380952\pi$
$312$		0			0
$313$	−0.621821	−	0.480846i	−0.621821	−	0.480846i	0.251587	−	0.967835i	$-0.419048\pi$
$313$	−0.621821	−	0.480846i	−0.621821	−	0.480846i	−0.873408	+	0.486989i	$0.838095\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.858449	−	0.512899i	$-0.828571\pi$
$317$		0			0		0.858449	+	0.512899i	$0.171429\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−1.26615	+	0.0758570i	−1.26615	+	0.0758570i
$322$		0			0
$323$	−2.94387	−	0.534233i	−2.94387	−	0.534233i
$324$	0.902318	−	0.741927i	0.902318	−	0.741927i
$325$		0			0
$326$	0.638449	+	1.78172i	0.638449	+	1.78172i
$327$		0			0
$328$	−1.49955	−	0.895941i	−1.49955	−	0.895941i
$329$		0			0
$330$		0			0
$331$	−1.42431	+	1.32156i	−1.42431	+	1.32156i	−0.550897	+	0.834573i	$0.685714\pi$
$331$	−1.42431	+	1.32156i	−1.42431	+	1.32156i	−0.873408	+	0.486989i	$0.838095\pi$
$332$	0.387586	+	1.32667i	0.387586	+	1.32667i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.208963	−	1.98815i	0.208963	−	1.98815i	0.0747301	−	0.997204i	$-0.476190\pi$
$337$	0.208963	−	1.98815i	0.208963	−	1.98815i	0.134233	−	0.990950i	$-0.457143\pi$
$338$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$339$	−0.903594	+	1.28364i	−0.903594	+	1.28364i
$340$		0			0
$341$		0			0
$342$	0.324890	+	0.156459i	0.324890	+	0.156459i
$343$		0			0
$344$	−0.946327	−	0.323210i	−0.946327	−	0.323210i
$345$		0			0
$346$		0			0
$347$	1.38413	−	0.337781i	1.38413	−	0.337781i	0.525684	−	0.850680i	$-0.323810\pi$
$347$	1.38413	−	0.337781i	1.38413	−	0.337781i	0.858449	+	0.512899i	$0.171429\pi$
$348$		0			0
$349$		0			0		0.946327	−	0.323210i	$-0.104762\pi$
$349$		0			0		−0.946327	+	0.323210i	$0.895238\pi$
$350$		0			0
$351$		0			0
$352$	0.992847	+	0.119394i	0.992847	+	0.119394i
$353$	1.87152	+	0.282086i	1.87152	+	0.282086i	0.983930	−	0.178557i	$-0.0571429\pi$
$353$	1.87152	+	0.282086i	1.87152	+	0.282086i	0.887586	+	0.460642i	$0.152381\pi$
$354$	−1.24447	+	0.693881i	−1.24447	+	0.693881i
$355$		0			0
$356$	−0.840338	−	0.0251504i	−0.840338	−	0.0251504i
$357$		0			0
$358$	1.19660	−	0.490414i	1.19660	−	0.490414i
$359$		0			0		0.842721	−	0.538351i	$-0.180952\pi$
$359$		0			0		−0.842721	+	0.538351i	$0.819048\pi$
$360$		0			0
$361$	0.0275360	−	1.84051i	0.0275360	−	1.84051i
$362$		0			0
$363$	1.09736	−	0.0987640i	1.09736	−	0.0987640i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.251587	−	0.967835i	$-0.419048\pi$
$367$		0			0		−0.251587	+	0.967835i	$0.580952\pi$
$368$		0			0
$369$	0.104804	−	0.358735i	0.104804	−	0.358735i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$373$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$374$	−0.697687	−	1.63232i	−0.697687	−	1.63232i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.66795	−	0.996553i	1.66795	−	0.996553i	0.712376	−	0.701798i	$-0.247619\pi$
$379$	1.66795	−	0.996553i	1.66795	−	0.996553i	0.955573	−	0.294755i	$-0.0952381\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.936235	−	0.351375i	$-0.114286\pi$
$383$		0			0		−0.936235	+	0.351375i	$0.885714\pi$
$384$	−0.0823372	+	1.09871i	−0.0823372	+	1.09871i
$385$		0			0
$386$	−1.80194			−1.80194
$387$	0.0159885	−	0.213352i	0.0159885	−	0.213352i
$388$	1.49717	−	1.08776i	1.49717	−	1.08776i
$389$		0			0		−0.473869	−	0.880596i	$-0.657143\pi$
$389$		0			0		0.473869	+	0.880596i	$0.342857\pi$
$390$		0			0
$391$		0			0
$392$	−0.599822	−	0.800134i	−0.599822	−	0.800134i
$393$	−0.138162	−	1.31452i	−0.138162	−	1.31452i
$394$		0			0
$395$		0			0
$396$	0.0287192	+	0.212014i	0.0287192	+	0.212014i
$397$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$397$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$398$		0			0
$399$		0			0
$400$	0.992847	−	0.119394i	0.992847	−	0.119394i
$401$	−0.248413	+	0.101809i	−0.248413	+	0.101809i	−0.500000	−	0.866025i	$-0.666667\pi$
$401$	−0.248413	+	0.101809i	−0.248413	+	0.101809i	0.251587	+	0.967835i	$0.419048\pi$
$402$	−2.00947	−	0.120390i	−2.00947	−	0.120390i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	1.76218	−	0.848622i	1.76218	−	0.848622i
$409$	−0.196800	−	1.45284i	−0.196800	−	1.45284i	−0.772417	−	0.635116i	$-0.780952\pi$
$409$	−0.196800	−	1.45284i	−0.196800	−	1.45284i	0.575617	−	0.817719i	$-0.304762\pi$
$410$		0			0
$411$	−0.262543	−	0.136256i	−0.262543	−	0.136256i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.54358	−	1.43223i	1.54358	−	1.43223i
$418$	1.42036	−	0.907359i	1.42036	−	0.907359i
$419$	1.07047	−	1.34232i	1.07047	−	1.34232i	0.134233	−	0.990950i	$-0.457143\pi$
$419$	1.07047	−	1.34232i	1.07047	−	1.34232i	0.936235	−	0.351375i	$-0.114286\pi$
$420$		0			0
$421$		0			0		0.887586	−	0.460642i	$-0.152381\pi$
$421$		0			0		−0.887586	+	0.460642i	$0.847619\pi$
$422$	0.782886	−	1.83165i	0.782886	−	1.83165i
$423$		0			0
$424$		0			0
$425$	−1.06479	−	1.42037i	−1.06479	−	1.42037i
$426$		0			0
$427$		0			0
$428$	−1.03723	−	0.499502i	−1.03723	−	0.499502i
$429$		0			0
$430$		0			0
$431$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$431$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$432$	0.852147	−	0.154642i	0.852147	−	0.154642i
$433$	−0.973871	+	1.14893i	−0.973871	+	1.14893i	0.0149594	+	0.999888i	$0.495238\pi$
$433$	−0.973871	+	1.14893i	−0.973871	+	1.14893i	−0.988831	+	0.149042i	$0.952381\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	1.46855	+	0.132172i	1.46855	+	0.132172i
$439$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$439$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$440$		0			0
$441$	0.133396	−	0.167273i	0.133396	−	0.167273i
$442$		0			0
$443$	0.331801	−	1.68453i	0.331801	−	1.68453i	−0.337330	−	0.941386i	$-0.609524\pi$
$443$	0.331801	−	1.68453i	0.331801	−	1.68453i	0.669131	−	0.743145i	$-0.266667\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.172233	+	1.03716i	−0.172233	+	1.03716i	0.753071	+	0.657939i	$0.228571\pi$
$449$	−0.172233	+	1.03716i	−0.172233	+	1.03716i	−0.925304	+	0.379225i	$0.876190\pi$
$450$	0.0781647	+	0.199160i	0.0781647	+	0.199160i
$451$	−1.16885	−	1.29814i	−1.16885	−	1.29814i
$452$	−1.28366	+	0.618177i	−1.28366	+	0.618177i
$453$		0			0
$454$	−0.480612	+	0.473475i	−0.480612	+	0.473475i
$455$		0			0
$456$	1.06893	+	1.51851i	1.06893	+	1.51851i
$457$	−0.0297984	+	0.00268190i	−0.0297984	+	0.00268190i	−0.104528	−	0.994522i	$-0.533333\pi$
$457$	−0.0297984	+	0.00268190i	−0.0297984	+	0.00268190i	0.0747301	+	0.997204i	$0.476190\pi$
$458$		0			0
$459$	−0.994092	−	1.17279i	−0.994092	−	1.17279i
$460$		0			0
$461$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$461$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$462$		0			0
$463$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$463$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$464$		0			0
$465$		0			0
$466$	−0.208683	+	1.98548i	−0.208683	+	1.98548i
$467$	1.43407	+	0.304820i	1.43407	+	0.304820i	0.858449	−	0.512899i	$-0.171429\pi$
$467$	1.43407	+	0.304820i	1.43407	+	0.304820i	0.575617	+	0.817719i	$0.304762\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−1.29320			−1.29320
$473$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$474$		0			0
$475$	1.16475	−	1.21823i	1.16475	−	1.21823i
$476$		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
$482$	−0.423935	+	0.847635i	−0.423935	+	0.847635i
$483$		0			0
$484$	0.913545	+	0.406737i	0.913545	+	0.406737i
$485$		0			0
$486$	0.176980	+	0.382019i	0.176980	+	0.382019i
$487$		0			0		−0.646600	−	0.762830i	$-0.723810\pi$
$487$		0			0		0.646600	+	0.762830i	$0.276190\pi$
$488$		0			0
$489$	−2.07692	+	0.186926i	−2.07692	+	0.186926i
$490$		0			0
$491$	0.301784	+	0.842189i	0.301784	+	0.842189i	0.992847	+	0.119394i	$0.0380952\pi$
$491$	0.301784	+	0.842189i	0.301784	+	0.842189i	−0.691063	+	0.722795i	$0.742857\pi$
$492$	1.37106	−	1.35070i	1.37106	−	1.35070i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.52214	+	0.0455558i	−1.52214	+	0.0455558i
$499$	1.75128	+	0.598135i	1.75128	+	0.598135i	0.998210	−	0.0598042i	$-0.0190476\pi$
$499$	1.75128	+	0.598135i	1.75128	+	0.598135i	0.753071	+	0.657939i	$0.228571\pi$
$500$		0			0
$501$		0			0
$502$	−0.525684	+	0.850680i	−0.525684	+	0.850680i
$503$		0			0		0.193256	−	0.981148i	$-0.438095\pi$
$503$		0			0		−0.193256	+	0.981148i	$0.561905\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.08949	+	0.164214i	1.08949	+	0.164214i
$508$		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
$512$	−0.550897	+	0.834573i	−0.550897	+	0.834573i
$513$	0.943843	−	1.11350i	0.943843	−	1.11350i
$514$	−1.92486	+	0.349310i	−1.92486	+	0.349310i
$515$		0			0
$516$	0.606975	−	0.919528i	0.606975	−	0.919528i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.719573	+	0.959875i	0.719573	+	0.959875i	1.00000			$0$
$521$	0.719573	+	0.959875i	0.719573	+	0.959875i	−0.280427	+	0.959875i	$0.590476\pi$
$522$		0			0
$523$	1.32869	−	1.47566i	1.32869	−	1.47566i	0.575617	−	0.817719i	$-0.304762\pi$
$523$	1.32869	−	1.47566i	1.32869	−	1.47566i	0.753071	−	0.657939i	$-0.228571\pi$
$524$	0.471490	−	1.10311i	0.471490	−	1.10311i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.402531	+	1.02563i	−0.402531	+	1.02563i
$529$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$530$		0			0
$531$	−0.0696090	−	0.267780i	−0.0696090	−	0.267780i
$532$		0			0
$533$		0			0
$534$	0.259758	−	0.889127i	0.259758	−	0.889127i
$535$		0			0
$536$	−1.53973	−	0.983616i	−1.53973	−	0.983616i
$537$	0.191261	+	1.41194i	0.191261	+	1.41194i
$538$		0			0
$539$	−0.337330	−	0.941386i	−0.337330	−	0.941386i
$540$		0			0
$541$		0			0		0.791071	−	0.611724i	$-0.209524\pi$
$541$		0			0		−0.791071	+	0.611724i	$0.790476\pi$
$542$		0			0
$543$		0			0
$544$	1.77199	+	0.106163i	1.77199	+	0.106163i
$545$		0			0
$546$		0			0
$547$	−0.508067	+	1.41786i	−0.508067	+	1.41786i	0.365341	+	0.930874i	$0.380952\pi$
$547$	−0.508067	+	1.41786i	−0.508067	+	1.41786i	−0.873408	+	0.486989i	$0.838095\pi$
$548$	−0.147897	−	0.224055i	−0.147897	−	0.224055i
$549$		0			0
$550$	0.983930	+	0.178557i	0.983930	+	0.178557i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.85666	−	0.453095i	1.85666	−	0.453095i
$557$		0			0		−0.473869	−	0.880596i	$-0.657143\pi$
$557$		0			0		0.473869	+	0.880596i	$0.342857\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	1.93403	−	0.291508i	1.93403	−	0.291508i
$562$	0.100008	−	1.33452i	0.100008	−	1.33452i
$563$	1.60742	−	0.603275i	1.60742	−	0.603275i	0.623490	−	0.781831i	$-0.285714\pi$
$563$	1.60742	−	0.603275i	1.60742	−	0.603275i	0.983930	+	0.178557i	$0.0571429\pi$
$564$		0			0
$565$		0			0
$566$	0.488922	−	0.543003i	0.488922	−	0.543003i
$567$		0			0
$568$		0			0
$569$	1.04385	+	0.125527i	1.04385	+	0.125527i	0.623490	−	0.781831i	$-0.285714\pi$
$569$	1.04385	+	0.125527i	1.04385	+	0.125527i	0.420357	+	0.907359i	$0.361905\pi$
$570$		0			0
$571$	−1.48883	+	1.01507i	−1.48883	+	1.01507i	−0.500000	+	0.866025i	$0.666667\pi$
$571$	−1.48883	+	1.01507i	−1.48883	+	1.01507i	−0.988831	+	0.149042i	$0.952381\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.202467	−	0.0691507i	−0.202467	−	0.0691507i
$577$	−0.265772	+	0.909710i	−0.265772	+	0.909710i	0.712376	+	0.701798i	$0.247619\pi$
$577$	−0.265772	+	0.909710i	−0.265772	+	0.909710i	−0.978148	+	0.207912i	$0.933333\pi$
$578$	−0.962275	−	1.92402i	−0.962275	−	1.92402i
$579$	0.499491	−	1.92150i	0.499491	−	1.92150i
$580$		0			0
$581$		0			0
$582$	0.744926	+	1.89804i	0.744926	+	1.89804i
$583$		0			0
$584$	1.10572	+	0.753869i	1.10572	+	0.753869i
$585$		0			0
$586$		0			0
$587$	0.568550	−	0.363204i	0.568550	−	0.363204i	−0.222521	−	0.974928i	$-0.571429\pi$
$587$	0.568550	−	0.363204i	0.568550	−	0.363204i	0.791071	+	0.611724i	$0.209524\pi$
$588$	1.01949	−	0.417828i	1.01949	−	0.417828i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.497553	−	0.0749941i	−0.497553	−	0.0749941i	−0.104528	−	0.994522i	$-0.533333\pi$
$593$	−0.497553	−	0.0749941i	−0.497553	−	0.0749941i	−0.393025	+	0.919528i	$0.628571\pi$
$594$	0.859870	+	0.103403i	0.859870	+	0.103403i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.971490	−	0.237080i	$-0.0761905\pi$
$599$		0			0		−0.971490	+	0.237080i	$0.923810\pi$
$600$	−0.147897	+	1.09182i	−0.147897	+	1.09182i
$601$	−1.57190	−	1.14206i	−1.57190	−	1.14206i	−0.925304	−	0.379225i	$-0.876190\pi$
$601$	−1.57190	−	1.14206i	−1.57190	−	1.14206i	−0.646600	−	0.762830i	$-0.723810\pi$
$602$		0			0
$603$	0.120797	−	0.371774i	0.120797	−	0.371774i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.575617	−	0.817719i	$-0.304762\pi$
$607$		0			0		−0.575617	+	0.817719i	$0.695238\pi$
$608$	0.176177	+	1.67621i	0.176177	+	1.67621i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.0733982	+	0.372638i	0.0733982	+	0.372638i
$613$		0			0		0.0448648	−	0.998993i	$-0.485714\pi$
$613$		0			0		−0.0448648	+	0.998993i	$0.514286\pi$
$614$	0.250878	+	0.858730i	0.250878	+	0.858730i
$615$		0			0
$616$		0			0
$617$	−0.704350	+	1.79466i	−0.704350	+	1.79466i	−0.104528	+	0.994522i	$0.533333\pi$
$617$	−0.704350	+	1.79466i	−0.704350	+	1.79466i	−0.599822	+	0.800134i	$0.704762\pi$
$618$		0			0
$619$	0.0538218	−	0.0717957i	0.0538218	−	0.0717957i	−0.772417	−	0.635116i	$-0.780952\pi$
$619$	0.0538218	−	0.0717957i	0.0538218	−	0.0717957i	0.826239	+	0.563320i	$0.190476\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.998210	−	0.0598042i	0.998210	−	0.0598042i
$626$	0.777271	−	0.117155i	0.777271	−	0.117155i
$627$	0.573848	+	1.76612i	0.573848	+	1.76612i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.525684	−	0.850680i	$-0.323810\pi$
$631$		0			0		−0.525684	+	0.850680i	$0.676190\pi$
$632$		0			0
$633$	1.73618	+	1.34256i	1.73618	+	1.34256i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.52513	−	0.420908i	−1.52513	−	0.420908i	−0.599822	−	0.800134i	$-0.704762\pi$
$641$	−1.52513	−	0.420908i	−1.52513	−	0.420908i	−0.925304	+	0.379225i	$0.876190\pi$
$642$	0.820162	−	0.967590i	0.820162	−	0.967590i
$643$	−0.207368	+	1.53085i	−0.207368	+	1.53085i	0.525684	+	0.850680i	$0.323810\pi$
$643$	−0.207368	+	1.53085i	−0.207368	+	1.53085i	−0.733052	+	0.680173i	$0.761905\pi$
$644$		0			0
$645$		0			0
$646$	2.42054	−	1.75862i	2.42054	−	1.75862i
$647$		0			0		0.691063	−	0.722795i	$-0.257143\pi$
$647$		0			0		−0.691063	+	0.722795i	$0.742857\pi$
$648$	−0.0872979	+	1.16491i	−0.0872979	+	1.16491i
$649$	−1.23575	−	0.381177i	−1.23575	−	0.381177i
$650$		0			0
$651$		0			0
$652$	−1.72903	−	0.769812i	−1.72903	−	0.769812i
$653$		0			0		0.393025	−	0.919528i	$-0.371429\pi$
$653$		0			0		−0.393025	+	0.919528i	$0.628571\pi$
$654$		0			0
$655$		0			0
$656$	1.68387	−	0.464718i	1.68387	−	0.464718i
$657$	−0.0965846	+	0.269539i	−0.0965846	+	0.269539i
$658$		0			0
$659$	−0.00670551	−	0.0894788i	−0.00670551	−	0.0894788i	0.992847	−	0.119394i	$-0.0380952\pi$
$659$	−0.00670551	−	0.0894788i	−0.00670551	−	0.0894788i	−0.999552	+	0.0299155i	$0.990476\pi$
$660$		0			0
$661$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$661$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$662$	0.0290658	−	1.94276i	0.0290658	−	1.94276i
$663$		0			0
$664$	−1.22675	−	0.636666i	−1.22675	−	0.636666i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.298548	−	0.245480i	−0.298548	−	0.245480i	0.473869	−	0.880596i	$-0.342857\pi$
$673$	−0.298548	−	0.245480i	−0.298548	−	0.245480i	−0.772417	+	0.635116i	$0.780952\pi$
$674$	1.29262	+	1.52498i	1.29262	+	1.52498i
$675$	0.859870	−	0.103403i	0.859870	−	0.103403i
$676$	0.791071	+	0.611724i	0.791071	+	0.611724i
$677$		0			0		−0.936235	−	0.351375i	$-0.885714\pi$
$677$		0			0		0.936235	+	0.351375i	$0.114286\pi$
$678$	−0.303370	−	1.54019i	−0.303370	−	1.54019i
$679$		0			0
$680$		0			0
$681$	−0.371668	−	0.643748i	−0.371668	−	0.643748i
$682$		0			0
$683$	1.19158	+	0.367554i	1.19158	+	0.367554i	0.826239	−	0.563320i	$-0.190476\pi$
$683$	1.19158	+	0.367554i	1.19158	+	0.367554i	0.365341	+	0.930874i	$0.380952\pi$
$684$	−0.337606	+	0.126706i	−0.337606	+	0.126706i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.887586	−	0.460642i	0.887586	−	0.460642i
$689$		0			0
$690$		0			0
$691$	0.193441	+	0.0792797i	0.193441	+	0.0792797i	0.473869	−	0.880596i	$-0.342857\pi$
$691$	0.193441	+	0.0792797i	0.193441	+	0.0792797i	−0.280427	+	0.959875i	$0.590476\pi$
$692$		0			0
$693$		0			0
$694$	−0.712376	+	1.23387i	−0.712376	+	1.23387i
$695$		0			0
$696$		0			0
$697$	−2.20901	−	2.17620i	−2.20901	−	2.17620i
$698$		0			0
$699$	−2.05938	−	0.772899i	−2.05938	−	0.772899i
$700$		0			0
$701$		0			0		0.193256	−	0.981148i	$-0.438095\pi$
$701$		0			0		−0.193256	+	0.981148i	$0.561905\pi$
$702$		0			0
$703$		0			0
$704$	−0.772417	+	0.635116i	−0.772417	+	0.635116i
$705$		0			0
$706$	−1.49722	+	1.15778i	−1.49722	+	1.15778i
$707$		0			0
$708$	0.358471	−	1.37901i	0.358471	−	1.37901i
$709$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$709$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$710$		0			0
$711$		0			0
$712$	0.598905	−	0.590012i	0.598905	−	0.590012i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.472459	+	1.20381i	−0.472459	+	1.20381i
$717$		0			0
$718$		0			0
$719$		0			0		−0.999552	−	0.0299155i	$-0.990476\pi$
$719$		0			0		0.999552	+	0.0299155i	$0.00952381\pi$
$720$		0			0
$721$		0			0
$722$	1.31128	+	1.29181i	1.31128	+	1.29181i
$723$	−0.786366	−	0.687027i	−0.786366	−	0.687027i
$724$		0			0
$725$		0			0
$726$	−0.686957	+	0.861417i	−0.686957	+	0.861417i
$727$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$727$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$728$		0			0
$729$	0.692976	−	0.125757i	0.692976	−	0.125757i
$730$		0			0
$731$	−1.49597	−	0.955665i	−1.49597	−	0.955665i
$732$		0			0
$733$		0			0		−0.473869	−	0.880596i	$-0.657143\pi$
$733$		0			0		0.473869	+	0.880596i	$0.342857\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.18140	−	1.39376i	−1.18140	−	1.39376i
$738$	0.186866	+	0.323661i	0.186866	+	0.323661i
$739$	−1.50008	−	0.135010i	−1.50008	−	0.135010i	−0.691063	−	0.722795i	$-0.742857\pi$
$739$	−1.50008	−	0.135010i	−1.50008	−	0.135010i	−0.809017	+	0.587785i	$0.800000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.791071	−	0.611724i	$-0.790476\pi$
$743$		0			0		0.791071	+	0.611724i	$0.209524\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.0658007	−	0.288292i	0.0658007	−	0.288292i
$748$	1.66198	+	0.623751i	1.66198	+	0.623751i
$749$		0			0
$750$		0			0
$751$		0			0		−0.842721	−	0.538351i	$-0.819048\pi$
$751$		0			0		0.842721	+	0.538351i	$0.180952\pi$
$752$		0			0
$753$	−0.761409	−	0.796371i	−0.761409	−	0.796371i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.0149594	−	0.999888i	$-0.495238\pi$
$757$		0			0		−0.0149594	+	0.999888i	$0.504762\pi$
$758$	−0.432354	+	1.89427i	−0.432354	+	1.89427i
$759$		0			0
$760$		0			0
$761$	0.633118	+	1.36661i	0.633118	+	1.36661i	0.913545	+	0.406737i	$0.133333\pi$
$761$	0.633118	+	1.36661i	0.633118	+	1.36661i	−0.280427	+	0.959875i	$0.590476\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.737244	−	0.818792i	−0.737244	−	0.818792i
$769$	1.57906	+	0.487076i	1.57906	+	0.487076i	0.955573	−	0.294755i	$-0.0952381\pi$
$769$	1.57906	+	0.487076i	1.57906	+	0.487076i	0.623490	+	0.781831i	$0.285714\pi$
$770$		0			0
$771$	0.161076	−	2.14941i	0.161076	−	2.14941i
$772$	1.24525	−	1.30243i	1.24525	−	1.30243i
$773$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$773$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$774$	0.143160	+	0.158996i	0.143160	+	0.158996i
$775$		0			0
$776$	−0.248413	+	1.83386i	−0.248413	+	1.83386i
$777$		0			0
$778$		0			0
$779$	1.69471	−	2.40749i	1.69471	−	2.40749i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.992847	+	0.119394i	0.992847	+	0.119394i
$785$		0			0
$786$	1.04561	+	0.808553i	1.04561	+	0.808553i
$787$	1.68387	+	0.938878i	1.68387	+	0.938878i	0.971490	+	0.237080i	$0.0761905\pi$
$787$	1.68387	+	0.938878i	1.68387	+	0.938878i	0.712376	+	0.701798i	$0.247619\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.173089	−	0.125757i	−0.173089	−	0.125757i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.772417	−	0.635116i	$-0.219048\pi$
$797$		0			0		−0.772417	+	0.635116i	$0.780952\pi$
$798$		0			0
$799$		0			0
$800$	−0.599822	+	0.800134i	−0.599822	+	0.800134i
$801$	0.154410	+	0.0922556i	0.154410	+	0.0922556i
$802$	0.0980818	−	0.249908i	0.0980818	−	0.249908i
$803$	0.834392	+	1.04629i	0.834392	+	1.04629i
$804$	1.47569	−	1.36924i	1.47569	−	1.36924i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.65503	+	0.988832i	−1.65503	+	0.988832i	−0.691063	+	0.722795i	$0.742857\pi$
$809$	−1.65503	+	0.988832i	−1.65503	+	0.988832i	−0.963963	+	0.266037i	$0.914286\pi$
$810$		0			0
$811$	0.204489	+	1.94558i	0.204489	+	1.94558i	0.309017	+	0.951057i	$0.400000\pi$
$811$	0.204489	+	1.94558i	0.204489	+	1.94558i	−0.104528	+	0.994522i	$0.533333\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.604398	+	1.86015i	−0.604398	+	1.86015i
$817$	0.662421	−	1.54981i	0.662421	−	1.54981i
$818$	1.18610	+	0.861754i	1.18610	+	0.861754i
$819$		0			0
$820$		0			0
$821$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$821$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$822$	0.279919	−	0.0956037i	0.279919	−	0.0956037i
$823$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$823$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$824$		0			0
$825$	−0.463147	+	0.999722i	−0.463147	+	0.999722i
$826$		0			0
$827$	−0.337583	+	0.188227i	−0.337583	+	0.188227i	−0.646600	−	0.762830i	$-0.723810\pi$
$827$	−0.337583	+	0.188227i	−0.337583	+	0.188227i	0.309017	+	0.951057i	$0.400000\pi$
$828$		0			0
$829$		0			0		−0.999552	−	0.0299155i	$-0.990476\pi$
$829$		0			0		0.999552	+	0.0299155i	$0.00952381\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.697687	−	1.63232i	−0.697687	−	1.63232i
$834$	−0.0314999	+	2.10545i	−0.0314999	+	2.10545i
$835$		0			0
$836$	−0.325722	+	1.65367i	−0.325722	+	1.65367i
$837$		0			0
$838$	0.230465	+	1.70136i	0.230465	+	1.70136i
$839$		0			0		0.473869	−	0.880596i	$-0.342857\pi$
$839$		0			0		−0.473869	+	0.880596i	$0.657143\pi$
$840$		0			0
$841$	−0.447313	−	0.894377i	−0.447313	−	0.894377i
$842$		0			0
$843$	1.39535	+	0.476569i	1.39535	+	0.476569i
$844$	0.782886	+	1.83165i	0.782886	+	1.83165i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.443506	+	0.671882i	0.443506	+	0.671882i
$850$	1.76247	+	0.211945i	1.76247	+	0.211945i
$851$		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
$856$	1.07783	−	0.404515i	1.07783	−	0.404515i
$857$	0.139930	−	1.86723i	0.139930	−	1.86723i	−0.280427	−	0.959875i	$-0.590476\pi$
$857$	0.139930	−	1.86723i	0.139930	−	1.86723i	0.420357	−	0.907359i	$-0.361905\pi$
$858$		0			0
$859$	−1.19964			−1.19964			−0.599822	−	0.800134i	$-0.704762\pi$
$859$	−1.19964			−1.19964			−0.599822	+	0.800134i	$0.704762\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.971490	−	0.237080i	$-0.0761905\pi$
$863$		0			0		−0.971490	+	0.237080i	$0.923810\pi$
$864$	−0.477113	+	0.722795i	−0.477113	+	0.722795i
$865$		0			0
$866$	−0.157435	−	1.49789i	−0.157435	−	1.49789i
$867$	2.31842	−	0.492796i	2.31842	−	0.492796i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.393105	+	0.0472727i	−0.393105	+	0.0472727i
$874$		0			0
$875$		0			0
$876$	−1.11039	+	0.970123i	−1.11039	+	0.970123i
$877$		0			0		0.599822	−	0.800134i	$-0.295238\pi$
$877$		0			0		−0.599822	+	0.800134i	$0.704762\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.39185	−	0.670278i	1.39185	−	0.670278i	0.420357	−	0.907359i	$-0.361905\pi$
$881$	1.39185	−	0.670278i	1.39185	−	0.670278i	0.971490	+	0.237080i	$0.0761905\pi$
$882$	0.0287192	+	0.212014i	0.0287192	+	0.212014i
$883$	−1.57797	−	1.00805i	−1.57797	−	1.00805i	−0.978148	−	0.207912i	$-0.933333\pi$
$883$	−1.57797	−	1.00805i	−1.57797	−	1.00805i	−0.599822	−	0.800134i	$-0.704762\pi$
$884$		0			0
$885$		0			0
$886$	0.988276	+	1.40394i	0.988276	+	1.40394i
$887$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$887$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.426782	+	1.08742i	−0.426782	+	1.08742i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.630633	−	0.841234i	−0.630633	−	0.841234i
$899$		0			0
$900$	−0.197969	−	0.0811353i	−0.197969	−	0.0811353i
$901$		0			0
$902$	1.74603	+	0.0522568i	1.74603	+	0.0522568i
$903$		0			0
$904$	0.440273	−	1.35502i	0.440273	−	1.35502i
$905$		0			0
$906$		0			0
$907$	−1.09391	+	1.65721i	−1.09391	+	1.65721i	−0.447313	+	0.894377i	$0.647619\pi$
$907$	−1.09391	+	1.65721i	−1.09391	+	1.65721i	−0.646600	+	0.762830i	$0.723810\pi$
$908$	−0.0100925	−	0.674584i	−0.0100925	−	0.674584i
$909$		0			0
$910$		0			0
$911$		0			0		−0.995974	−	0.0896393i	$-0.971429\pi$
$911$		0			0		0.995974	+	0.0896393i	$0.0285714\pi$
$912$	−1.83627	−	0.276773i	−1.83627	−	0.276773i
$913$	−0.984593	−	0.969973i	−0.984593	−	0.969973i
$914$	0.0186541	−	0.0233915i	0.0186541	−	0.0233915i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	1.53466	+	0.0919438i	1.53466	+	0.0919438i
$919$		0			0		0.995974	−	0.0896393i	$-0.0285714\pi$
$919$		0			0		−0.995974	+	0.0896393i	$0.971429\pi$
$920$		0			0
$921$	−0.985253	+	0.0294875i	−0.985253	+	0.0294875i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.120337	−	0.170950i	−0.120337	−	0.170950i	0.753071	−	0.657939i	$-0.228571\pi$
$929$	−0.120337	−	0.170950i	−0.120337	−	0.170950i	−0.873408	+	0.486989i	$0.838095\pi$
$930$		0			0
$931$	1.42036	−	0.907359i	1.42036	−	0.907359i
$932$	−1.29088	−	1.52293i	−1.29088	−	1.52293i
$933$		0			0
$934$	−1.21135	+	0.825886i	−1.21135	+	0.825886i
$935$		0			0
$936$		0			0
$937$	−0.470291	+	0.940319i	−0.470291	+	0.940319i	0.525684	+	0.850680i	$0.323810\pi$
$937$	−0.470291	+	0.940319i	−0.470291	+	0.940319i	−0.995974	+	0.0896393i	$0.971429\pi$
$938$		0			0
$939$	−0.0905285	+	0.861321i	−0.0905285	+	0.861321i
$940$		0			0
$941$		0			0		−0.0149594	−	0.999888i	$-0.504762\pi$
$941$		0			0		0.0149594	+	0.999888i	$0.495238\pi$
$942$		0			0
$943$		0			0
$944$	0.893682	−	0.934718i	0.893682	−	0.934718i
$945$		0			0
$946$	0.983930	−	0.178557i	0.983930	−	0.178557i
$947$	0.503174			0.503174			0.251587	−	0.967835i	$-0.419048\pi$
$947$	0.503174			0.503174			0.251587	+	0.967835i	$0.419048\pi$
$948$		0			0
$949$		0			0
$950$	0.0756171	+	1.68374i	0.0756171	+	1.68374i
$951$		0			0
$952$		0			0
$953$	−0.179465	+	1.70749i	−0.179465	+	1.70749i	0.420357	+	0.907359i	$0.361905\pi$
$953$	−0.179465	+	1.70749i	−0.179465	+	1.70749i	−0.599822	+	0.800134i	$0.704762\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.842721	+	0.538351i	−0.842721	+	0.538351i
$962$		0			0
$963$	0.141778	+	0.201410i	0.141778	+	0.201410i
$964$	−0.319700	−	0.892187i	−0.319700	−	0.892187i
$965$		0			0
$966$		0			0
$967$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$967$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$968$	−0.925304	+	0.379225i	−0.925304	+	0.379225i
$969$	1.20435	+	3.06864i	1.20435	+	3.06864i
$970$		0			0
$971$	0.444843	−	0.0133136i	0.444843	−	0.0133136i	0.193256	−	0.981148i	$-0.438095\pi$
$971$	0.444843	−	0.0133136i	0.444843	−	0.0133136i	0.251587	+	0.967835i	$0.419048\pi$
$972$	−0.398426	−	0.136079i	−0.398426	−	0.136079i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.204903	−	0.701364i	−0.204903	−	0.701364i	−0.995974	−	0.0896393i	$-0.971429\pi$
$977$	−0.204903	−	0.701364i	−0.204903	−	0.701364i	0.791071	−	0.611724i	$-0.209524\pi$
$978$	1.30017	−	1.63037i	1.30017	−	1.63037i
$979$	0.746206	−	0.387269i	0.746206	−	0.387269i
$980$		0			0
$981$		0			0
$982$	−0.817282	−	0.363877i	−0.817282	−	0.363877i
$983$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$983$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$984$	0.0287913	+	1.92442i	0.0287913	+	1.92442i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$991$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$992$		0			0
$993$	2.06362	+	0.569522i	2.06362	+	0.569522i
$994$		0			0
$995$		0			0
$996$	1.01896	−	1.13167i	1.01896	−	1.13167i
$997$		0			0		0.393025	−	0.919528i	$-0.371429\pi$
$997$		0			0		−0.393025	+	0.919528i	$0.628571\pi$
$998$	−1.64257	+	0.852469i	−1.64257	+	0.852469i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3784.1.em.b.427.1	yes	48
8.3	odd	2	CM	3784.1.em.b.427.1	yes	48
11.5	even	5		3784.1.em.a.2491.1	✓	48
43.14	even	21		3784.1.em.a.3067.1	yes	48
88.27	odd	10		3784.1.em.a.2491.1	✓	48
344.315	odd	42		3784.1.em.a.3067.1	yes	48
473.401	even	105	inner	3784.1.em.b.1347.1	yes	48
3784.1347	odd	210	inner	3784.1.em.b.1347.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3784.1.em.a.2491.1	✓	48	11.5	even	5
3784.1.em.a.2491.1	✓	48	88.27	odd	10
3784.1.em.a.3067.1	yes	48	43.14	even	21
3784.1.em.a.3067.1	yes	48	344.315	odd	42
3784.1.em.b.427.1	yes	48	1.1	even	1	trivial
3784.1.em.b.427.1	yes	48	8.3	odd	2	CM
3784.1.em.b.1347.1	yes	48	473.401	even	105	inner
3784.1.em.b.1347.1	yes	48	3784.1347	odd	210	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:	\( N \)	\(=\)	\( 3784 = 2^{3} \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3784.em (of order \(210\), degree \(48\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.691063 + 0.722795i) q^{2} +(-0.579195 - 0.937274i) q^{3} +(-0.0448648 - 0.998993i) q^{4} +(1.07772 + 0.229076i) q^{6} +(0.753071 + 0.657939i) q^{8} +(-0.0957026 + 0.191352i) q^{9} +O(q^{10})\)	\(q+(-0.691063 + 0.722795i) q^{2} +(-0.579195 - 0.937274i) q^{3} +(-0.0448648 - 0.998993i) q^{4} +(1.07772 + 0.229076i) q^{6} +(0.753071 + 0.657939i) q^{8} +(-0.0957026 + 0.191352i) q^{9} +(0.525684 + 0.850680i) q^{11} +(-0.910345 + 0.620663i) q^{12} +(-0.995974 + 0.0896393i) q^{16} +(1.02182 + 1.45159i) q^{17} +(-0.0721717 - 0.201410i) q^{18} +(-1.20067 + 1.18284i) q^{19} +(-0.978148 - 0.207912i) q^{22} +(0.180494 - 1.08691i) q^{24} +(-0.999552 + 0.0299155i) q^{25} +(-0.862579 + 0.0776335i) q^{27} +(0.623490 - 0.781831i) q^{32} +(0.492847 - 0.985420i) q^{33} +(-1.75534 - 0.264576i) q^{34} +(0.195453 + 0.0870213i) q^{36} +(-0.0252132 - 1.68525i) q^{38} +(-1.71874 + 0.311906i) q^{41} +(-0.925304 + 0.379225i) q^{43} +(0.826239 - 0.563320i) q^{44} +(0.660880 + 0.881582i) q^{48} +(-0.978148 - 0.207912i) q^{49} +(0.669131 - 0.743145i) q^{50} +(0.768707 - 1.79848i) q^{51} +(0.539983 - 0.677117i) q^{54} +(1.80407 + 0.440261i) q^{57} +(-0.973871 + 0.850846i) q^{59} +(0.134233 + 0.990950i) q^{64} +(0.371668 + 1.03721i) q^{66} +(-1.80668 + 0.272314i) q^{67} +(1.40429 - 1.08592i) q^{68} +(-0.197969 + 0.0811353i) q^{72} +(1.32869 - 0.159781i) q^{73} +(0.606975 + 0.919528i) q^{75} +(1.23552 + 1.14639i) q^{76} +(0.700697 + 0.934696i) q^{81} +(0.962316 - 1.45785i) q^{82} +(-1.34272 + 0.327675i) q^{83} +(0.365341 - 0.930874i) q^{86} +(-0.163818 + 0.986491i) q^{88} +(0.0628267 - 0.838364i) q^{89} +(-1.09391 - 0.131548i) q^{96} +(1.01949 + 1.54447i) q^{97} +(0.826239 - 0.563320i) q^{98} +(-0.213089 + 0.0191783i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9	\( 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9} - q^{11} - 2 q^{12} + 2 q^{16} + q^{17} + 2 q^{18} - 2 q^{19} + 6 q^{22} + 10 q^{24} - q^{25} - 2 q^{27} - 8 q^{32} - 25 q^{33} - 13 q^{34} + 9 q^{36} + q^{38} - 2 q^{41} - q^{43} + 4 q^{44} - 2 q^{48} + 6 q^{49} + 6 q^{50} + 8 q^{51} - 6 q^{54} - 8 q^{57} + 3 q^{59} + 2 q^{64} - 2 q^{66} + q^{67} + q^{68} - 3 q^{72} + q^{73} + 50 q^{75} + q^{76} - 28 q^{81} + 3 q^{82} - 25 q^{83} + 4 q^{86} - q^{88} + q^{89} - 2 q^{96} + 3 q^{97} + 4 q^{98} - 8 q^{99}+O(q^{100}) \) 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 - 2 * q^19 + 6 * q^22 + 10 * q^24 - q^25 - 2 * q^27 - 8 * q^32 - 25 * 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 - 8 * q^57 + 3 * q^59 + 2 * q^64 - 2 * q^66 + q^67 + q^68 - 3 * q^72 + q^73 + 50 * q^75 + q^76 - 28 * q^81 + 3 * q^82 - 25 * q^83 + 4 * q^86 - q^88 + q^89 - 2 * q^96 + 3 * q^97 + 4 * q^98 - 8 * q^99

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