LMFDB - Embedded newform 3784.1.em.b.203.1

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			203.1
Root			$-0.791071 + 0.611724i$ of defining polynomial
Character	$\chi$	$=$	3784.203
Dual form			3784.1.em.b.1659.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.691063 - 0.722795i) q^{2} +(1.10130 + 0.0329607i) q^{3} +(-0.0448648 + 0.998993i) q^{4} +(-0.737244 - 0.818792i) q^{6} +(0.753071 - 0.657939i) q^{8} +(0.213567 + 0.0127951i) q^{9} +O(q^{10})$	\(q+(-0.691063 - 0.722795i) q^{2} +(1.10130 + 0.0329607i) q^{3} +(-0.0448648 + 0.998993i) q^{4} +(-0.737244 - 0.818792i) q^{6} +(0.753071 - 0.657939i) q^{8} +(0.213567 + 0.0127951i) q^{9} +(-0.999552 - 0.0299155i) q^{11} +(-0.0823372 + 1.09871i) q^{12} +(-0.995974 - 0.0896393i) q^{16} +(-0.708488 - 1.52930i) q^{17} +(-0.138340 - 0.163207i) q^{18} +(0.446610 - 1.71807i) q^{19} +(0.669131 + 0.743145i) q^{22} +(0.851044 - 0.699767i) q^{24} +(0.525684 - 0.850680i) q^{25} +(-0.862579 - 0.0776335i) q^{27} +(0.623490 + 0.781831i) q^{32} +(-1.09982 - 0.0658919i) q^{33} +(-0.615761 + 1.56893i) q^{34} +(-0.0223639 + 0.212778i) q^{36} +(-1.55045 + 0.864489i) q^{38} +(0.0294380 + 0.00534221i) q^{41} +(0.791071 - 0.611724i) q^{43} +(0.0747301 - 0.997204i) q^{44} +(-1.09391 - 0.131548i) q^{48} +(0.669131 + 0.743145i) q^{49} +(-0.978148 + 0.207912i) q^{50} +(-0.729851 - 1.70757i) q^{51} +(0.539983 + 0.677117i) q^{54} +(0.548480 - 1.87739i) q^{57} +(-0.508067 - 0.443885i) q^{59} +(0.134233 - 0.990950i) q^{64} +(0.712420 + 0.840481i) q^{66} +(-0.0763771 - 0.194606i) q^{67} +(1.55955 - 0.639162i) q^{68} +(0.169250 - 0.130878i) q^{72} +(1.17343 - 1.56530i) q^{73} +(0.606975 - 0.919528i) q^{75} +(1.69631 + 0.523241i) q^{76} +(-1.15982 - 0.139473i) q^{81} +(-0.0164822 - 0.0249694i) q^{82} +(0.387586 + 1.32667i) q^{83} +(-0.988831 - 0.149042i) q^{86} +(-0.772417 + 0.635116i) q^{88} +(0.951194 - 0.648513i) q^{89} +(0.660880 + 0.881582i) q^{96} +(-0.871597 + 1.32041i) q^{97} +(0.0747301 - 0.997204i) q^{98} +(-0.213089 - 0.0191783i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3784\mathbb{Z}\right)^\times$.

$n$	$89$	$1377$	$1893$	$2839$
$\chi(n)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$-1$

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
$3$	1.10130	+	0.0329607i	1.10130	+	0.0329607i	0.575617	−	0.817719i	$-0.304762\pi$
$3$	1.10130	+	0.0329607i	1.10130	+	0.0329607i	0.525684	+	0.850680i	$0.323810\pi$
$4$	−0.0448648	+	0.998993i	−0.0448648	+	0.998993i
$5$		0			0		0.873408	−	0.486989i	$-0.161905\pi$
$5$		0			0		−0.873408	+	0.486989i	$0.838095\pi$
$6$	−0.737244	−	0.818792i	−0.737244	−	0.818792i
$7$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$7$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$8$	0.753071	−	0.657939i	0.753071	−	0.657939i
$9$	0.213567	+	0.0127951i	0.213567	+	0.0127951i
$10$		0			0
$11$	−0.999552	−	0.0299155i	−0.999552	−	0.0299155i
$11$	−0.999552	−	0.0299155i	−0.999552	−	0.0299155i
$12$	−0.0823372	+	1.09871i	−0.0823372	+	1.09871i
$13$		0			0		−0.575617	−	0.817719i	$-0.695238\pi$
$13$		0			0		0.575617	+	0.817719i	$0.304762\pi$
$14$		0			0
$15$		0			0
$16$	−0.995974	−	0.0896393i	−0.995974	−	0.0896393i
$17$	−0.708488	−	1.52930i	−0.708488	−	1.52930i	−0.842721	−	0.538351i	$-0.819048\pi$
$17$	−0.708488	−	1.52930i	−0.708488	−	1.52930i	0.134233	−	0.990950i	$-0.457143\pi$
$18$	−0.138340	−	0.163207i	−0.138340	−	0.163207i
$19$	0.446610	−	1.71807i	0.446610	−	1.71807i	−0.222521	−	0.974928i	$-0.571429\pi$
$19$	0.446610	−	1.71807i	0.446610	−	1.71807i	0.669131	−	0.743145i	$-0.266667\pi$
$20$		0			0
$21$		0			0
$22$	0.669131	+	0.743145i	0.669131	+	0.743145i
$23$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$23$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$24$	0.851044	−	0.699767i	0.851044	−	0.699767i
$25$	0.525684	−	0.850680i	0.525684	−	0.850680i
$26$		0			0
$27$	−0.862579	−	0.0776335i	−0.862579	−	0.0776335i
$28$		0			0
$29$		0			0		0.999552	−	0.0299155i	$-0.00952381\pi$
$29$		0			0		−0.999552	+	0.0299155i	$0.990476\pi$
$30$		0			0
$31$		0			0		0.971490	−	0.237080i	$-0.0761905\pi$
$31$		0			0		−0.971490	+	0.237080i	$0.923810\pi$
$32$	0.623490	+	0.781831i	0.623490	+	0.781831i
$33$	−1.09982	−	0.0658919i	−1.09982	−	0.0658919i
$34$	−0.615761	+	1.56893i	−0.615761	+	1.56893i
$35$		0			0
$36$	−0.0223639	+	0.212778i	−0.0223639	+	0.212778i
$37$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$37$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$38$	−1.55045	+	0.864489i	−1.55045	+	0.864489i
$39$		0			0
$40$		0			0
$41$	0.0294380	+	0.00534221i	0.0294380	+	0.00534221i	0.193256	−	0.981148i	$-0.438095\pi$
$41$	0.0294380	+	0.00534221i	0.0294380	+	0.00534221i	−0.163818	+	0.986491i	$0.552381\pi$
$42$		0			0
$43$	0.791071	−	0.611724i	0.791071	−	0.611724i
$43$	0.791071	−	0.611724i	0.791071	−	0.611724i
$44$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$45$		0			0
$46$		0			0
$47$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$47$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$48$	−1.09391	−	0.131548i	−1.09391	−	0.131548i
$49$	0.669131	+	0.743145i	0.669131	+	0.743145i
$50$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$51$	−0.729851	−	1.70757i	−0.729851	−	1.70757i
$52$		0			0
$53$		0			0		−0.0149594	−	0.999888i	$-0.504762\pi$
$53$		0			0		0.0149594	+	0.999888i	$0.495238\pi$
$54$	0.539983	+	0.677117i	0.539983	+	0.677117i
$55$		0			0
$56$		0			0
$57$	0.548480	−	1.87739i	0.548480	−	1.87739i
$58$		0			0
$59$	−0.508067	−	0.443885i	−0.508067	−	0.443885i	0.365341	−	0.930874i	$-0.380952\pi$
$59$	−0.508067	−	0.443885i	−0.508067	−	0.443885i	−0.873408	+	0.486989i	$0.838095\pi$
$60$		0			0
$61$		0			0		−0.971490	−	0.237080i	$-0.923810\pi$
$61$		0			0		0.971490	+	0.237080i	$0.0761905\pi$
$62$		0			0
$63$		0			0
$64$	0.134233	−	0.990950i	0.134233	−	0.990950i
$65$		0			0
$66$	0.712420	+	0.840481i	0.712420	+	0.840481i
$67$	−0.0763771	−	0.194606i	−0.0763771	−	0.194606i	0.887586	−	0.460642i	$-0.152381\pi$
$67$	−0.0763771	−	0.194606i	−0.0763771	−	0.194606i	−0.963963	+	0.266037i	$0.914286\pi$
$68$	1.55955	−	0.639162i	1.55955	−	0.639162i
$69$		0			0
$70$		0			0
$71$		0			0		0.447313	−	0.894377i	$-0.352381\pi$
$71$		0			0		−0.447313	+	0.894377i	$0.647619\pi$
$72$	0.169250	−	0.130878i	0.169250	−	0.130878i
$73$	1.17343	−	1.56530i	1.17343	−	1.56530i	0.420357	−	0.907359i	$-0.361905\pi$
$73$	1.17343	−	1.56530i	1.17343	−	1.56530i	0.753071	−	0.657939i	$-0.228571\pi$
$74$		0			0
$75$	0.606975	−	0.919528i	0.606975	−	0.919528i
$76$	1.69631	+	0.523241i	1.69631	+	0.523241i
$77$		0			0
$78$		0			0
$79$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$79$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$80$		0			0
$81$	−1.15982	−	0.139473i	−1.15982	−	0.139473i
$82$	−0.0164822	−	0.0249694i	−0.0164822	−	0.0249694i
$83$	0.387586	+	1.32667i	0.387586	+	1.32667i	0.887586	+	0.460642i	$0.152381\pi$
$83$	0.387586	+	1.32667i	0.387586	+	1.32667i	−0.500000	+	0.866025i	$0.666667\pi$
$84$		0			0
$85$		0			0
$86$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$87$		0			0
$88$	−0.772417	+	0.635116i	−0.772417	+	0.635116i
$89$	0.951194	−	0.648513i	0.951194	−	0.648513i	0.0149594	−	0.999888i	$-0.495238\pi$
$89$	0.951194	−	0.648513i	0.951194	−	0.648513i	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
$96$	0.660880	+	0.881582i	0.660880	+	0.881582i
$97$	−0.871597	+	1.32041i	−0.871597	+	1.32041i	0.0747301	+	0.997204i	$0.476190\pi$
$97$	−0.871597	+	1.32041i	−0.871597	+	1.32041i	−0.946327	+	0.323210i	$0.895238\pi$
$98$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$99$	−0.213089	−	0.0191783i	−0.213089	−	0.0191783i
$100$	0.826239	+	0.563320i	0.826239	+	0.563320i
$101$		0			0		−0.163818	−	0.986491i	$-0.552381\pi$
$101$		0			0		0.163818	+	0.986491i	$0.447619\pi$
$102$	−0.729851	+	1.70757i	−0.729851	+	1.70757i
$103$		0			0		0.193256	−	0.981148i	$-0.438095\pi$
$103$		0			0		−0.193256	+	0.981148i	$0.561905\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.398388	+	0.740329i	0.398388	+	0.740329i	0.998210	−	0.0598042i	$-0.0190476\pi$
$107$	0.398388	+	0.740329i	0.398388	+	0.740329i	−0.599822	+	0.800134i	$0.704762\pi$
$108$	0.116255	−	0.858227i	0.116255	−	0.858227i
$109$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$109$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.197760	+	0.462682i	−0.197760	+	0.462682i	−0.988831	−	0.149042i	$-0.952381\pi$
$113$	−0.197760	+	0.462682i	−0.197760	+	0.462682i	0.791071	+	0.611724i	$0.209524\pi$
$114$	−1.73601	+	0.900958i	−1.73601	+	0.900958i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.0302685	+	0.673981i	0.0302685	+	0.673981i
$119$		0			0
$120$		0			0
$121$	0.998210	+	0.0598042i	0.998210	+	0.0598042i
$122$		0			0
$123$	0.0322440	+	0.00685368i	0.0322440	+	0.00685368i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$127$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$128$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$129$	0.891370	−	0.647618i	0.891370	−	0.647618i
$130$		0			0
$131$	−1.78905	+	0.861560i	−1.78905	+	0.861560i	−0.842721	+	0.538351i	$0.819048\pi$
$131$	−1.78905	+	0.861560i	−1.78905	+	0.861560i	−0.946327	+	0.323210i	$0.895238\pi$
$132$	0.115169	−	1.09576i	0.115169	−	1.09576i
$133$		0			0
$134$	−0.0878786	+	0.189690i	−0.0878786	+	0.189690i
$135$		0			0
$136$	−1.53973	−	0.685531i	−1.53973	−	0.685531i
$137$	0.230465	+	0.137696i	0.230465	+	0.137696i	0.623490	−	0.781831i	$-0.285714\pi$
$137$	0.230465	+	0.137696i	0.230465	+	0.137696i	−0.393025	+	0.919528i	$0.628571\pi$
$138$		0			0
$139$	1.38741	−	0.473859i	1.38741	−	0.473859i	0.473869	−	0.880596i	$-0.342857\pi$
$139$	1.38741	−	0.473859i	1.38741	−	0.473859i	0.913545	+	0.406737i	$0.133333\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.211560	−	0.0318876i	−0.211560	−	0.0318876i
$145$		0			0
$146$	−1.94230	+	0.233570i	−1.94230	+	0.233570i
$147$	0.712420	+	0.840481i	0.712420	+	0.840481i
$148$		0			0
$149$		0			0		0.163818	−	0.986491i	$-0.447619\pi$
$149$		0			0		−0.163818	+	0.986491i	$0.552381\pi$
$150$	−1.08409	+	0.196733i	−1.08409	+	0.196733i
$151$		0			0		−0.473869	−	0.880596i	$-0.657143\pi$
$151$		0			0		0.473869	+	0.880596i	$0.342857\pi$
$152$	−0.794058	−	1.58767i	−0.794058	−	1.58767i
$153$	−0.131742	−	0.335673i	−0.131742	−	0.335673i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.712376	−	0.701798i	$-0.752381\pi$
$157$		0			0		0.712376	+	0.701798i	$0.247619\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.700697	+	0.934696i	0.700697	+	0.934696i
$163$	0.385820	+	0.0231150i	0.385820	+	0.0231150i	0.251587	−	0.967835i	$-0.419048\pi$
$163$	0.385820	+	0.0231150i	0.385820	+	0.0231150i	0.134233	+	0.990950i	$0.457143\pi$
$164$	−0.00665756	+	0.0291687i	−0.00665756	+	0.0291687i
$165$		0			0
$166$	0.691063	−	1.19696i	0.691063	−	1.19696i
$167$		0			0		0.420357	−	0.907359i	$-0.361905\pi$
$167$		0			0		−0.420357	+	0.907359i	$0.638095\pi$
$168$		0			0
$169$	−0.337330	+	0.941386i	−0.337330	+	0.941386i
$170$		0			0
$171$	0.117364	−	0.361209i	0.117364	−	0.361209i
$172$	0.575617	+	0.817719i	0.575617	+	0.817719i
$173$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$173$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$174$		0			0
$175$		0			0
$176$	0.992847	+	0.119394i	0.992847	+	0.119394i
$177$	−0.544904	−	0.505597i	−0.544904	−	0.505597i
$178$	−1.12608	−	0.239355i	−1.12608	−	0.239355i
$179$	0.0705212	−	0.670964i	0.0705212	−	0.670964i	−0.900969	−	0.433884i	$-0.857143\pi$
$179$	0.0705212	−	0.670964i	0.0705212	−	0.670964i	0.971490	−	0.237080i	$-0.0761905\pi$
$180$		0			0
$181$		0			0		−0.772417	−	0.635116i	$-0.780952\pi$
$181$		0			0		0.772417	+	0.635116i	$0.219048\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.662421	+	1.54981i	0.662421	+	1.54981i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.842721	−	0.538351i	$-0.819048\pi$
$191$		0			0		0.842721	+	0.538351i	$0.180952\pi$
$192$	0.180494	−	1.08691i	0.180494	−	1.08691i
$193$	1.24525	−	1.30243i	1.24525	−	1.30243i	0.309017	−	0.951057i	$-0.400000\pi$
$193$	1.24525	−	1.30243i	1.24525	−	1.30243i	0.936235	−	0.351375i	$-0.114286\pi$
$194$	1.55672	−	0.282502i	1.55672	−	0.282502i
$195$		0			0
$196$	−0.772417	+	0.635116i	−0.772417	+	0.635116i
$197$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$197$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$198$	0.133396	+	0.167273i	0.133396	+	0.167273i
$199$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$199$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$200$	−0.163818	−	0.986491i	−0.163818	−	0.986491i
$201$	−0.0776998	−	0.216837i	−0.0776998	−	0.216837i
$202$		0			0
$203$		0			0
$204$	1.73860	−	0.652506i	1.73860	−	0.652506i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.497807	+	1.70394i	−0.497807	+	1.70394i
$210$		0			0
$211$	−1.86493	−	0.699921i	−1.86493	−	0.699921i	−0.963963	−	0.266037i	$-0.914286\pi$
$211$	−1.86493	−	0.699921i	−1.86493	−	0.699921i	−0.900969	−	0.433884i	$-0.857143\pi$
$212$		0			0
$213$		0			0
$214$	0.259795	−	0.799567i	0.259795	−	0.799567i
$215$		0			0
$216$	−0.700661	+	0.509060i	−0.700661	+	0.509060i
$217$		0			0
$218$		0			0
$219$	1.34389	−	1.68519i	1.34389	−	1.68519i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$223$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$224$		0			0
$225$	0.123153	−	0.174951i	0.123153	−	0.174951i
$226$	0.471089	−	0.176803i	0.471089	−	0.176803i
$227$	−0.679814	−	1.10010i	−0.679814	−	1.10010i	−0.988831	−	0.149042i	$-0.952381\pi$
$227$	−0.679814	−	1.10010i	−0.679814	−	1.10010i	0.309017	−	0.951057i	$-0.400000\pi$
$228$	1.85090	+	0.632157i	1.85090	+	0.632157i
$229$		0			0		0.280427	−	0.959875i	$-0.409524\pi$
$229$		0			0		−0.280427	+	0.959875i	$0.590476\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.827802	−	0.339265i	0.827802	−	0.339265i	0.0747301	−	0.997204i	$-0.476190\pi$
$233$	0.827802	−	0.339265i	0.827802	−	0.339265i	0.753071	+	0.657939i	$0.228571\pi$
$234$		0			0
$235$		0			0
$236$	0.466232	−	0.487641i	0.466232	−	0.487641i
$237$		0			0
$238$		0			0
$239$		0			0		0.251587	−	0.967835i	$-0.419048\pi$
$239$		0			0		−0.251587	+	0.967835i	$0.580952\pi$
$240$		0			0
$241$	−0.694741	+	0.644625i	−0.694741	+	0.644625i	−0.946327	−	0.323210i	$-0.895238\pi$
$241$	−0.694741	+	0.644625i	−0.694741	+	0.644625i	0.251587	+	0.967835i	$0.419048\pi$
$242$	−0.646600	−	0.762830i	−0.646600	−	0.762830i
$243$	−0.416321	−	0.0627503i	−0.416321	−	0.0627503i
$244$		0			0
$245$		0			0
$246$	−0.0173288	−	0.0280421i	−0.0173288	−	0.0280421i
$247$		0			0
$248$		0			0
$249$	0.383121	+	1.47384i	0.383121	+	1.47384i
$250$		0			0
$251$	−0.669131	+	0.743145i	−0.669131	+	0.743145i	−0.978148	−	0.207912i	$-0.933333\pi$
$251$	−0.669131	+	0.743145i	−0.669131	+	0.743145i	0.309017	+	0.951057i	$0.400000\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.983930	+	0.178557i	0.983930	+	0.178557i
$257$	−1.08268	+	0.786610i	−1.08268	+	0.786610i	−0.978148	−	0.207912i	$-0.933333\pi$
$257$	−1.08268	+	0.786610i	−1.08268	+	0.786610i	−0.104528	+	0.994522i	$0.533333\pi$
$258$	−1.08409	−	0.196733i	−1.08409	−	0.196733i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	1.85908	+	0.697723i	1.85908	+	0.697723i
$263$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$263$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$264$	−0.871597	+	0.673994i	−0.871597	+	0.673994i
$265$		0			0
$266$		0			0
$267$	1.06893	−	0.682856i	1.06893	−	0.682856i
$268$	0.197836	−	0.0675692i	0.197836	−	0.0675692i
$269$		0			0		0.936235	−	0.351375i	$-0.114286\pi$
$269$		0			0		−0.936235	+	0.351375i	$0.885714\pi$
$270$		0			0
$271$		0			0		0.599822	−	0.800134i	$-0.295238\pi$
$271$		0			0		−0.599822	+	0.800134i	$0.704762\pi$
$272$	0.568550	+	1.58665i	0.568550	+	1.58665i
$273$		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		0.772417	−	0.635116i	$-0.219048\pi$
$277$		0			0		−0.772417	+	0.635116i	$0.780952\pi$
$278$	−1.30129	−	0.675350i	−1.30129	−	0.675350i
$279$		0			0
$280$		0			0
$281$	0.320476	−	1.92987i	0.320476	−	1.92987i	−0.0448648	−	0.998993i	$-0.514286\pi$
$281$	0.320476	−	1.92987i	0.320476	−	1.92987i	0.365341	−	0.930874i	$-0.380952\pi$
$282$		0			0
$283$	−1.03962	+	1.68236i	−1.03962	+	1.68236i	−0.393025	+	0.919528i	$0.628571\pi$
$283$	−1.03962	+	1.68236i	−1.03962	+	1.68236i	−0.646600	+	0.762830i	$0.723810\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.123153	+	0.174951i	0.123153	+	0.174951i
$289$	−1.19021	+	1.40415i	−1.19021	+	1.40415i
$290$		0			0
$291$	−1.00341	+	1.42544i	−1.00341	+	1.42544i
$292$	1.51108	+	1.24247i	1.51108	+	1.24247i
$293$		0			0		−0.393025	−	0.919528i	$-0.628571\pi$
$293$		0			0		0.393025	+	0.919528i	$0.371429\pi$
$294$	0.115169	−	1.09576i	0.115169	−	1.09576i
$295$		0			0
$296$		0			0
$297$	0.859870	+	0.103403i	0.859870	+	0.103403i
$298$		0			0
$299$		0			0
$300$	0.891370	+	0.647618i	0.891370	+	0.647618i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.598819	+	1.67112i	−0.598819	+	1.67112i
$305$		0			0
$306$	−0.151581	+	0.327194i	−0.151581	+	0.327194i
$307$	−0.998210	+	1.72895i	−0.998210	+	1.72895i	−0.447313	+	0.894377i	$0.647619\pi$
$307$	−0.998210	+	1.72895i	−0.998210	+	1.72895i	−0.550897	+	0.834573i	$0.685714\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.599822	−	0.800134i	$-0.704762\pi$
$311$		0			0		0.599822	+	0.800134i	$0.295238\pi$
$312$		0			0
$313$	0.727336	+	0.298090i	0.727336	+	0.298090i	0.712376	−	0.701798i	$-0.247619\pi$
$313$	0.727336	+	0.298090i	0.727336	+	0.298090i	0.0149594	+	0.999888i	$0.495238\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$317$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	0.414344	+	0.828457i	0.414344	+	0.828457i
$322$		0			0
$323$	−2.94387	+	0.534233i	−2.94387	+	0.534233i
$324$	0.191368	−	1.15239i	0.191368	−	1.15239i
$325$		0			0
$326$	−0.249918	−	0.294843i	−0.249918	−	0.294843i
$327$		0			0
$328$	0.0256838	−	0.0153453i	0.0256838	−	0.0153453i
$329$		0			0
$330$		0			0
$331$	−0.535938	+	0.165315i	−0.535938	+	0.165315i	−0.550897	−	0.834573i	$-0.685714\pi$
$331$	−0.535938	+	0.165315i	−0.535938	+	0.165315i	0.0149594	+	0.999888i	$0.495238\pi$
$332$	−1.34272	+	0.327675i	−1.34272	+	0.327675i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.960472	+	0.427630i	0.960472	+	0.427630i	0.826239	−	0.563320i	$-0.190476\pi$
$337$	0.960472	+	0.427630i	0.960472	+	0.427630i	0.134233	+	0.990950i	$0.457143\pi$
$338$	0.913545	−	0.406737i	0.913545	−	0.406737i
$339$	−0.233043	+	0.503034i	−0.233043	+	0.503034i
$340$		0			0
$341$		0			0
$342$	−0.342186	+	0.164788i	−0.342186	+	0.164788i
$343$		0			0
$344$	0.193256	−	0.981148i	0.193256	−	0.981148i
$345$		0			0
$346$		0			0
$347$	−0.141104	−	0.482984i	−0.141104	−	0.482984i	0.858449	−	0.512899i	$-0.171429\pi$
$347$	−0.141104	−	0.482984i	−0.141104	−	0.482984i	−0.999552	+	0.0299155i	$0.990476\pi$
$348$		0			0
$349$		0			0		−0.193256	−	0.981148i	$-0.561905\pi$
$349$		0			0		0.193256	+	0.981148i	$0.438095\pi$
$350$		0			0
$351$		0			0
$352$	−0.599822	−	0.800134i	−0.599822	−	0.800134i
$353$	0.141209	−	0.359794i	0.141209	−	0.359794i	−0.842721	−	0.538351i	$-0.819048\pi$
$353$	0.141209	−	0.359794i	0.141209	−	0.359794i	0.983930	+	0.178557i	$0.0571429\pi$
$354$	0.0111199	+	0.743253i	0.0111199	+	0.743253i
$355$		0			0
$356$	0.605185	+	0.979332i	0.605185	+	0.979332i
$357$		0			0
$358$	−0.533704	+	0.412706i	−0.533704	+	0.412706i
$359$		0			0		0.887586	−	0.460642i	$-0.152381\pi$
$359$		0			0		−0.887586	+	0.460642i	$0.847619\pi$
$360$		0			0
$361$	−1.87891	−	1.04763i	−1.87891	−	1.04763i
$362$		0			0
$363$	1.09736	+	0.0987640i	1.09736	+	0.0987640i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.712376	−	0.701798i	$-0.247619\pi$
$367$		0			0		−0.712376	+	0.701798i	$0.752381\pi$
$368$		0			0
$369$	0.00621863	+	0.00151758i	0.00621863	+	0.00151758i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$373$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$374$	0.662421	−	1.54981i	0.662421	−	1.54981i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.481465	−	0.287662i	−0.481465	−	0.287662i	0.251587	−	0.967835i	$-0.419048\pi$
$379$	−0.481465	−	0.287662i	−0.481465	−	0.287662i	−0.733052	+	0.680173i	$0.761905\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.936235	−	0.351375i	$-0.885714\pi$
$383$		0			0		0.936235	+	0.351375i	$0.114286\pi$
$384$	−0.910345	+	0.620663i	−0.910345	+	0.620663i
$385$		0			0
$386$	−1.80194			−1.80194
$387$	0.176774	−	0.120522i	0.176774	−	0.120522i
$388$	−1.27998	−	0.929960i	−1.27998	−	0.929960i
$389$		0			0		0.473869	−	0.880596i	$-0.342857\pi$
$389$		0			0		−0.473869	+	0.880596i	$0.657143\pi$
$390$		0			0
$391$		0			0
$392$	0.992847	+	0.119394i	0.992847	+	0.119394i
$393$	−1.99868	+	0.889869i	−1.99868	+	0.889869i
$394$		0			0
$395$		0			0
$396$	0.0287192	−	0.212014i	0.0287192	−	0.212014i
$397$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$397$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$398$		0			0
$399$		0			0
$400$	−0.599822	+	0.800134i	−0.599822	+	0.800134i
$401$	0.212376	−	0.164228i	0.212376	−	0.164228i	−0.500000	−	0.866025i	$-0.666667\pi$
$401$	0.212376	−	0.164228i	0.212376	−	0.164228i	0.712376	+	0.701798i	$0.247619\pi$
$402$	−0.103033	+	0.206009i	−0.103033	+	0.206009i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−1.67311	−	0.805726i	−1.67311	−	0.805726i
$409$	0.256539	−	1.89385i	0.256539	−	1.89385i	−0.163818	−	0.986491i	$-0.552381\pi$
$409$	0.256539	−	1.89385i	0.256539	−	1.89385i	0.420357	−	0.907359i	$-0.361905\pi$
$410$		0			0
$411$	0.249272	+	0.159241i	0.249272	+	0.159241i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.54358	−	0.476131i	1.54358	−	0.476131i
$418$	1.57562	−	0.817719i	1.57562	−	0.817719i
$419$	1.07047	+	1.34232i	1.07047	+	1.34232i	0.936235	+	0.351375i	$0.114286\pi$
$419$	1.07047	+	1.34232i	1.07047	+	1.34232i	0.134233	+	0.990950i	$0.457143\pi$
$420$		0			0
$421$		0			0		0.842721	−	0.538351i	$-0.180952\pi$
$421$		0			0		−0.842721	+	0.538351i	$0.819048\pi$
$422$	0.782886	+	1.83165i	0.782886	+	1.83165i
$423$		0			0
$424$		0			0
$425$	−1.67339	−	0.201232i	−1.67339	−	0.201232i
$426$		0			0
$427$		0			0
$428$	−0.757458	+	0.364772i	−0.757458	+	0.364772i
$429$		0			0
$430$		0			0
$431$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$431$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$432$	0.852147	+	0.154642i	0.852147	+	0.154642i
$433$	−0.508067	+	1.41786i	−0.508067	+	1.41786i	0.365341	+	0.930874i	$0.380952\pi$
$433$	−0.508067	+	1.41786i	−0.508067	+	1.41786i	−0.873408	+	0.486989i	$0.838095\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−2.14676	+	0.193212i	−2.14676	+	0.193212i
$439$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$439$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$440$		0			0
$441$	0.133396	+	0.167273i	0.133396	+	0.167273i
$442$		0			0
$443$	−1.62475	−	0.554918i	−1.62475	−	0.554918i	−0.646600	−	0.762830i	$-0.723810\pi$
$443$	−1.62475	−	0.554918i	−1.62475	−	0.554918i	−0.978148	+	0.207912i	$0.933333\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	1.54414	−	1.26966i	1.54414	−	1.26966i	0.753071	−	0.657939i	$-0.228571\pi$
$449$	1.54414	−	1.26966i	1.54414	−	1.26966i	0.791071	−	0.611724i	$-0.209524\pi$
$450$	−0.211560	+	0.0318876i	−0.211560	+	0.0318876i
$451$	−0.0292650	−	0.00622047i	−0.0292650	−	0.00622047i
$452$	−0.453344	−	0.218319i	−0.453344	−	0.218319i
$453$		0			0
$454$	−0.325352	+	1.25160i	−0.325352	+	1.25160i
$455$		0			0
$456$	−0.822165	−	1.77468i	−0.822165	−	1.77468i
$457$	1.73978	+	0.156583i	1.73978	+	0.156583i	0.913545	−	0.406737i	$-0.133333\pi$
$457$	1.73978	+	0.156583i	1.73978	+	0.156583i	0.826239	+	0.563320i	$0.190476\pi$
$458$		0			0
$459$	0.492401	+	1.37414i	0.492401	+	1.37414i
$460$		0			0
$461$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$461$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$462$		0			0
$463$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$463$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$464$		0			0
$465$		0			0
$466$	−0.817282	−	0.363877i	−0.817282	−	0.363877i
$467$	1.27881	+	1.42026i	1.27881	+	1.42026i	0.858449	+	0.512899i	$0.171429\pi$
$467$	1.27881	+	1.42026i	1.27881	+	1.42026i	0.420357	+	0.907359i	$0.361905\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.674660			−0.674660
$473$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$474$		0			0
$475$	−1.22675	−	1.28308i	−1.22675	−	1.28308i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$479$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$480$		0			0
$481$		0			0
$482$	0.946041	+	0.0566786i	0.946041	+	0.0566786i
$483$		0			0
$484$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$485$		0			0
$486$	0.242348	+	0.344279i	0.242348	+	0.344279i
$487$		0			0		−0.337330	−	0.941386i	$-0.609524\pi$
$487$		0			0		0.337330	+	0.941386i	$0.390476\pi$
$488$		0			0
$489$	0.424142	+	0.0381735i	0.424142	+	0.0381735i
$490$		0			0
$491$	−1.29088	−	1.52293i	−1.29088	−	1.52293i	−0.691063	−	0.722795i	$-0.742857\pi$
$491$	−1.29088	−	1.52293i	−1.29088	−	1.52293i	−0.599822	−	0.800134i	$-0.704762\pi$
$492$	−0.00829340	+	0.0319041i	−0.00829340	+	0.0319041i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.800520	−	1.29543i	0.800520	−	1.29543i
$499$	0.305758	−	1.55232i	0.305758	−	1.55232i	−0.447313	−	0.894377i	$-0.647619\pi$
$499$	0.305758	−	1.55232i	0.305758	−	1.55232i	0.753071	−	0.657939i	$-0.228571\pi$
$500$		0			0
$501$		0			0
$502$	0.999552	−	0.0299155i	0.999552	−	0.0299155i
$503$		0			0		−0.946327	−	0.323210i	$-0.895238\pi$
$503$		0			0		0.946327	+	0.323210i	$0.104762\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.402531	+	1.02563i	−0.402531	+	1.02563i
$508$		0			0
$509$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$509$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$510$		0			0
$511$		0			0
$512$	−0.550897	−	0.834573i	−0.550897	−	0.834573i
$513$	−0.518616	+	1.44730i	−0.518616	+	1.44730i
$514$	1.31675	+	0.238956i	1.31675	+	0.238956i
$515$		0			0
$516$	0.606975	+	0.919528i	0.606975	+	0.919528i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.97149	+	0.237080i	1.97149	+	0.237080i	1.00000			$0$
$521$	1.97149	+	0.237080i	1.97149	+	0.237080i	0.971490	+	0.237080i	$0.0761905\pi$
$522$		0			0
$523$	1.17343	−	0.249420i	1.17343	−	0.249420i	0.420357	−	0.907359i	$-0.361905\pi$
$523$	1.17343	−	0.249420i	1.17343	−	0.249420i	0.753071	+	0.657939i	$0.228571\pi$
$524$	−0.780427	−	1.82590i	−0.780427	−	1.82590i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	1.08949	+	0.164214i	1.08949	+	0.164214i
$529$	0.955573	−	0.294755i	0.955573	−	0.294755i
$530$		0			0
$531$	−0.102827	−	0.101300i	−0.102827	−	0.101300i
$532$		0			0
$533$		0			0
$534$	−1.23226	−	0.300718i	−1.23226	−	0.300718i
$535$		0			0
$536$	−0.185556	−	0.0963005i	−0.185556	−	0.0963005i
$537$	0.0997805	−	0.736609i	0.0997805	−	0.736609i
$538$		0			0
$539$	−0.646600	−	0.762830i	−0.646600	−	0.762830i
$540$		0			0
$541$		0			0		0.925304	−	0.379225i	$-0.123810\pi$
$541$		0			0		−0.925304	+	0.379225i	$0.876190\pi$
$542$		0			0
$543$		0			0
$544$	0.753920	−	1.50742i	0.753920	−	1.50742i
$545$		0			0
$546$		0			0
$547$	−0.973871	+	1.14893i	−0.973871	+	1.14893i	0.0149594	+	0.999888i	$0.495238\pi$
$547$	−0.973871	+	1.14893i	−0.973871	+	1.14893i	−0.988831	+	0.149042i	$0.952381\pi$
$548$	−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
$556$	0.411136	+	1.40728i	0.411136	+	1.40728i
$557$		0			0		0.473869	−	0.880596i	$-0.342857\pi$
$557$		0			0		−0.473869	+	0.880596i	$0.657143\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.678442	+	1.72864i	0.678442	+	1.72864i
$562$	−1.61637	+	1.10202i	−1.61637	+	1.10202i
$563$	1.60742	+	0.603275i	1.60742	+	0.603275i	0.983930	−	0.178557i	$-0.0571429\pi$
$563$	1.60742	+	0.603275i	1.60742	+	0.603275i	0.623490	+	0.781831i	$0.285714\pi$
$564$		0			0
$565$		0			0
$566$	1.93445	−	0.411179i	1.93445	−	0.411179i
$567$		0			0
$568$		0			0
$569$	1.19911	+	1.59955i	1.19911	+	1.59955i	0.623490	+	0.781831i	$0.285714\pi$
$569$	1.19911	+	1.59955i	1.19911	+	1.59955i	0.575617	+	0.817719i	$0.304762\pi$
$570$		0			0
$571$	−0.134659	+	1.79690i	−0.134659	+	1.79690i	0.365341	+	0.930874i	$0.380952\pi$
$571$	−0.134659	+	1.79690i	−0.134659	+	1.79690i	−0.500000	+	0.866025i	$0.666667\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.0413471	−	0.209917i	0.0413471	−	0.209917i
$577$	0.920717	+	0.224690i	0.920717	+	0.224690i	0.669131	−	0.743145i	$-0.266667\pi$
$577$	0.920717	+	0.224690i	0.920717	+	0.224690i	0.251587	+	0.967835i	$0.419048\pi$
$578$	1.83742	−	0.110082i	1.83742	−	0.110082i
$579$	1.41433	−	1.39332i	1.41433	−	1.39332i
$580$		0			0
$581$		0			0
$582$	1.72372	−	0.259810i	1.72372	−	0.259810i
$583$		0			0
$584$	−0.146194	−	1.95083i	−0.146194	−	1.95083i
$585$		0			0
$586$		0			0
$587$	−1.14783	+	0.595702i	−1.14783	+	0.595702i	−0.925304	−	0.379225i	$-0.876190\pi$
$587$	−1.14783	+	0.595702i	−1.14783	+	0.595702i	−0.222521	+	0.974928i	$0.571429\pi$
$588$	−0.871597	+	0.673994i	−0.871597	+	0.673994i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.520520	−	1.32626i	0.520520	−	1.32626i	−0.393025	−	0.919528i	$-0.628571\pi$
$593$	0.520520	−	1.32626i	0.520520	−	1.32626i	0.913545	−	0.406737i	$-0.133333\pi$
$594$	−0.519485	−	0.692968i	−0.519485	−	0.692968i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.280427	−	0.959875i	$-0.590476\pi$
$599$		0			0		0.280427	+	0.959875i	$0.409524\pi$
$600$	−0.147897	−	1.09182i	−0.147897	−	1.09182i
$601$	0.453741	−	0.329662i	0.453741	−	0.329662i	−0.337330	−	0.941386i	$-0.609524\pi$
$601$	0.453741	−	0.329662i	0.453741	−	0.329662i	0.791071	+	0.611724i	$0.209524\pi$
$602$		0			0
$603$	−0.0138216	−	0.0425386i	−0.0138216	−	0.0425386i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.420357	−	0.907359i	$-0.361905\pi$
$607$		0			0		−0.420357	+	0.907359i	$0.638095\pi$
$608$	1.62170	−	0.722027i	1.62170	−	0.722027i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.341246	−	0.116549i	0.341246	−	0.116549i
$613$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$613$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$614$	1.93950	−	0.473312i	1.93950	−	0.473312i
$615$		0			0
$616$		0			0
$617$	1.90639	+	0.287342i	1.90639	+	0.287342i	0.992847	−	0.119394i	$-0.0380952\pi$
$617$	1.90639	+	0.287342i	1.90639	+	0.287342i	0.913545	+	0.406737i	$0.133333\pi$
$618$		0			0
$619$	−0.0890878	+	0.0107132i	−0.0890878	+	0.0107132i	−0.163818	−	0.986491i	$-0.552381\pi$
$619$	−0.0890878	+	0.0107132i	−0.0890878	+	0.0107132i	0.0747301	+	0.997204i	$0.476190\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.447313	−	0.894377i	−0.447313	−	0.894377i
$626$	−0.287176	−	0.731713i	−0.287176	−	0.731713i
$627$	−0.604398	+	1.86015i	−0.604398	+	1.86015i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.999552	−	0.0299155i	$-0.00952381\pi$
$631$		0			0		−0.999552	+	0.0299155i	$0.990476\pi$
$632$		0			0
$633$	−2.03078	−	0.832293i	−2.03078	−	0.832293i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.78392	−	0.492330i	1.78392	−	0.492330i	0.791071	−	0.611724i	$-0.209524\pi$
$641$	1.78392	−	0.492330i	1.78392	−	0.492330i	0.992847	+	0.119394i	$0.0380952\pi$
$642$	0.312467	−	0.872001i	0.312467	−	0.872001i
$643$	−0.0439796	−	0.324671i	−0.0439796	−	0.324671i	−0.999552	−	0.0299155i	$-0.990476\pi$
$643$	−0.0439796	−	0.324671i	−0.0439796	−	0.324671i	0.955573	−	0.294755i	$-0.0952381\pi$
$644$		0			0
$645$		0			0
$646$	2.42054	+	1.75862i	2.42054	+	1.75862i
$647$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$647$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$648$	−0.965192	+	0.658057i	−0.965192	+	0.658057i
$649$	0.494561	+	0.458885i	0.494561	+	0.458885i
$650$		0			0
$651$		0			0
$652$	−0.0404015	+	0.384394i	−0.0404015	+	0.384394i
$653$		0			0		−0.393025	−	0.919528i	$-0.628571\pi$
$653$		0			0		0.393025	+	0.919528i	$0.371429\pi$
$654$		0			0
$655$		0			0
$656$	−0.0288406	−	0.00795951i	−0.0288406	−	0.00795951i
$657$	0.270634	−	0.319282i	0.270634	−	0.319282i
$658$		0			0
$659$	−0.0741381	−	0.0505465i	−0.0741381	−	0.0505465i	0.525684	−	0.850680i	$-0.323810\pi$
$659$	−0.0741381	−	0.0505465i	−0.0741381	−	0.0505465i	−0.599822	+	0.800134i	$0.704762\pi$
$660$		0			0
$661$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$661$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$662$	0.489855	+	0.273130i	0.489855	+	0.273130i
$663$		0			0
$664$	1.16475	+	0.744068i	1.16475	+	0.744068i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.310051	+	1.86709i	0.310051	+	1.86709i	0.473869	+	0.880596i	$0.342857\pi$
$673$	0.310051	+	1.86709i	0.310051	+	1.86709i	−0.163818	+	0.986491i	$0.552381\pi$
$674$	−0.354658	−	0.989743i	−0.354658	−	0.989743i
$675$	−0.519485	+	0.692968i	−0.519485	+	0.692968i
$676$	−0.925304	−	0.379225i	−0.925304	−	0.379225i
$677$		0			0		0.936235	−	0.351375i	$-0.114286\pi$
$677$		0			0		−0.936235	+	0.351375i	$0.885714\pi$
$678$	0.524638	−	0.179185i	0.524638	−	0.179185i
$679$		0			0
$680$		0			0
$681$	−0.712420	−	1.23395i	−0.712420	−	1.23395i
$682$		0			0
$683$	−0.914101	−	0.848162i	−0.914101	−	0.848162i	0.0747301	−	0.997204i	$-0.476190\pi$
$683$	−0.914101	−	0.848162i	−0.914101	−	0.848162i	−0.988831	+	0.149042i	$0.952381\pi$
$684$	0.355580	+	0.133451i	0.355580	+	0.133451i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.842721	+	0.538351i	−0.842721	+	0.538351i
$689$		0			0
$690$		0			0
$691$	1.44536	+	1.11768i	1.44536	+	1.11768i	0.971490	+	0.237080i	$0.0761905\pi$
$691$	1.44536	+	1.11768i	1.44536	+	1.11768i	0.473869	+	0.880596i	$0.342857\pi$
$692$		0			0
$693$		0			0
$694$	−0.251587	+	0.435761i	−0.251587	+	0.435761i
$695$		0			0
$696$		0			0
$697$	−0.0126866	−	0.0488044i	−0.0126866	−	0.0488044i
$698$		0			0
$699$	0.922841	−	0.346348i	0.922841	−	0.346348i
$700$		0			0
$701$		0			0		−0.946327	−	0.323210i	$-0.895238\pi$
$701$		0			0		0.946327	+	0.323210i	$0.104762\pi$
$702$		0			0
$703$		0			0
$704$	−0.163818	+	0.986491i	−0.163818	+	0.986491i
$705$		0			0
$706$	−0.357641	+	0.146575i	−0.357641	+	0.146575i
$707$		0			0
$708$	0.529535	−	0.521672i	0.529535	−	0.521672i
$709$		0			0		0.691063	−	0.722795i	$-0.257143\pi$
$709$		0			0		−0.691063	+	0.722795i	$0.742857\pi$
$710$		0			0
$711$		0			0
$712$	0.289635	−	1.11420i	0.289635	−	1.11420i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.667125	+	0.100553i	0.667125	+	0.100553i
$717$		0			0
$718$		0			0
$719$		0			0		−0.525684	−	0.850680i	$-0.676190\pi$
$719$		0			0		0.525684	+	0.850680i	$0.323810\pi$
$720$		0			0
$721$		0			0
$722$	0.541222	+	2.08204i	0.541222	+	2.08204i
$723$	−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	$-0.285714\pi$
$727$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$728$		0			0
$729$	0.692976	+	0.125757i	0.692976	+	0.125757i
$730$		0			0
$731$	−1.49597	−	0.776386i	−1.49597	−	0.776386i
$732$		0			0
$733$		0			0		0.473869	−	0.880596i	$-0.342857\pi$
$733$		0			0		−0.473869	+	0.880596i	$0.657143\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.0705212	+	0.196803i	0.0705212	+	0.196803i
$738$	−0.00320056	−	0.00554354i	−0.00320056	−	0.00554354i
$739$	−1.50008	+	0.135010i	−1.50008	+	0.135010i	−0.809017	−	0.587785i	$-0.800000\pi$
$739$	−1.50008	+	0.135010i	−1.50008	+	0.135010i	−0.691063	+	0.722795i	$0.742857\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.925304	−	0.379225i	$-0.876190\pi$
$743$		0			0		0.925304	+	0.379225i	$0.123810\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.0658007	+	0.288292i	0.0658007	+	0.288292i
$748$	−1.57797	+	0.592222i	−1.57797	+	0.592222i
$749$		0			0
$750$		0			0
$751$		0			0		−0.887586	−	0.460642i	$-0.847619\pi$
$751$		0			0		0.887586	+	0.460642i	$0.152381\pi$
$752$		0			0
$753$	−0.761409	+	0.796371i	−0.761409	+	0.796371i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.873408	−	0.486989i	$-0.838095\pi$
$757$		0			0		0.873408	+	0.486989i	$0.161905\pi$
$758$	0.124802	+	0.546793i	0.124802	+	0.546793i
$759$		0			0
$760$		0			0
$761$	0.866962	+	1.23160i	0.866962	+	1.23160i	0.971490	+	0.237080i	$0.0761905\pi$
$761$	0.866962	+	1.23160i	0.866962	+	1.23160i	−0.104528	+	0.994522i	$0.533333\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	1.07772	+	0.229076i	1.07772	+	0.229076i
$769$	−0.109562	−	0.101659i	−0.109562	−	0.101659i	0.623490	−	0.781831i	$-0.285714\pi$
$769$	−0.109562	−	0.101659i	−0.109562	−	0.101659i	−0.733052	+	0.680173i	$0.761905\pi$
$770$		0			0
$771$	−1.21828	+	0.830609i	−1.21828	+	0.830609i
$772$	1.24525	+	1.30243i	1.24525	+	1.30243i
$773$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$773$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$774$	−0.209275	−	0.0444827i	−0.209275	−	0.0444827i
$775$		0			0
$776$	0.212376	+	1.56782i	0.212376	+	1.56782i
$777$		0			0
$778$		0			0
$779$	0.0223256	−	0.0481908i	0.0223256	−	0.0481908i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.599822	−	0.800134i	−0.599822	−	0.800134i
$785$		0			0
$786$	2.02440	+	0.829679i	2.02440	+	0.829679i
$787$	−0.0288406	+	1.92771i	−0.0288406	+	1.92771i	0.251587	+	0.967835i	$0.419048\pi$
$787$	−0.0288406	+	1.92771i	−0.0288406	+	1.92771i	−0.280427	+	0.959875i	$0.590476\pi$
$788$		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		0.163818	−	0.986491i	$-0.447619\pi$
$797$		0			0		−0.163818	+	0.986491i	$0.552381\pi$
$798$		0			0
$799$		0			0
$800$	0.992847	−	0.119394i	0.992847	−	0.119394i
$801$	0.211441	−	0.126330i	0.211441	−	0.126330i
$802$	−0.265468	−	0.0400129i	−0.265468	−	0.0400129i
$803$	−1.21973	+	1.52949i	−1.21973	+	1.52949i
$804$	0.220104	−	0.0678932i	0.220104	−	0.0678932i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.65503	−	0.988832i	−1.65503	−	0.988832i	−0.963963	−	0.266037i	$-0.914286\pi$
$809$	−1.65503	−	0.988832i	−1.65503	−	0.988832i	−0.691063	−	0.722795i	$-0.742857\pi$
$810$		0			0
$811$	1.22256	−	0.544320i	1.22256	−	0.544320i	0.309017	−	0.951057i	$-0.400000\pi$
$811$	1.22256	−	0.544320i	1.22256	−	0.544320i	0.913545	+	0.406737i	$0.133333\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.573848	+	1.76612i	0.573848	+	1.76612i
$817$	−0.697687	−	1.63232i	−0.697687	−	1.63232i
$818$	−1.54615	+	1.12334i	−1.54615	+	1.12334i
$819$		0			0
$820$		0			0
$821$		0			0		0.0448648	−	0.998993i	$-0.485714\pi$
$821$		0			0		−0.0448648	+	0.998993i	$0.514286\pi$
$822$	−0.0571641	−	0.290219i	−0.0571641	−	0.290219i
$823$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$823$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$824$		0			0
$825$	−0.634211	+	0.900958i	−0.634211	+	0.900958i
$826$		0			0
$827$	−0.0283130	−	1.89244i	−0.0283130	−	1.89244i	−0.337330	−	0.941386i	$-0.609524\pi$
$827$	−0.0283130	−	1.89244i	−0.0283130	−	1.89244i	0.309017	−	0.951057i	$-0.400000\pi$
$828$		0			0
$829$		0			0		−0.525684	−	0.850680i	$-0.676190\pi$
$829$		0			0		0.525684	+	0.850680i	$0.323810\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.662421	−	1.54981i	0.662421	−	1.54981i
$834$	−1.41085	−	0.786655i	−1.41085	−	0.786655i
$835$		0			0
$836$	−1.67989	−	0.573753i	−1.67989	−	0.573753i
$837$		0			0
$838$	0.230465	−	1.70136i	0.230465	−	1.70136i
$839$		0			0		−0.473869	−	0.880596i	$-0.657143\pi$
$839$		0			0		0.473869	+	0.880596i	$0.342857\pi$
$840$		0			0
$841$	0.998210	−	0.0598042i	0.998210	−	0.0598042i
$842$		0			0
$843$	0.416550	−	2.11480i	0.416550	−	2.11480i
$844$	0.782886	−	1.83165i	0.782886	−	1.83165i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−1.20039	+	1.81851i	−1.20039	+	1.81851i
$850$	1.01096	+	1.34858i	1.01096	+	1.34858i
$851$		0			0
$852$		0			0
$853$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$853$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$854$		0			0
$855$		0			0
$856$	0.787106	+	0.295406i	0.787106	+	0.295406i
$857$	1.54711	−	1.05480i	1.54711	−	1.05480i	0.575617	−	0.817719i	$-0.304762\pi$
$857$	1.54711	−	1.05480i	1.54711	−	1.05480i	0.971490	−	0.237080i	$-0.0761905\pi$
$858$		0			0
$859$	1.98569			1.98569			0.992847	−	0.119394i	$-0.0380952\pi$
$859$	1.98569			1.98569			0.992847	+	0.119394i	$0.0380952\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.280427	−	0.959875i	$-0.590476\pi$
$863$		0			0		0.280427	+	0.959875i	$0.409524\pi$
$864$	−0.477113	−	0.722795i	−0.477113	−	0.722795i
$865$		0			0
$866$	1.37593	−	0.612604i	1.37593	−	0.612604i
$867$	−1.35706	+	1.50716i	−1.35706	+	1.50716i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.203039	+	0.270845i	−0.203039	+	0.270845i
$874$		0			0
$875$		0			0
$876$	1.62320	+	1.41814i	1.62320	+	1.41814i
$877$		0			0		0.992847	−	0.119394i	$-0.0380952\pi$
$877$		0			0		−0.992847	+	0.119394i	$0.961905\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.295190	+	0.142156i	0.295190	+	0.142156i	0.575617	−	0.817719i	$-0.304762\pi$
$881$	0.295190	+	0.142156i	0.295190	+	0.142156i	−0.280427	+	0.959875i	$0.590476\pi$
$882$	0.0287192	−	0.212014i	0.0287192	−	0.212014i
$883$	1.66198	+	0.862539i	1.66198	+	0.862539i	0.992847	+	0.119394i	$0.0380952\pi$
$883$	1.66198	+	0.862539i	1.66198	+	0.862539i	0.669131	+	0.743145i	$0.266667\pi$
$884$		0			0
$885$		0			0
$886$	0.721710	+	1.55784i	0.721710	+	1.55784i
$887$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$887$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.15513	+	0.174108i	1.15513	+	0.174108i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−1.98481	−	0.238682i	−1.98481	−	0.238682i
$899$		0			0
$900$	0.169250	+	0.130878i	0.169250	+	0.130878i
$901$		0			0
$902$	0.0157278	+	0.0254513i	0.0157278	+	0.0254513i
$903$		0			0
$904$	0.155489	+	0.478546i	0.155489	+	0.478546i
$905$		0			0
$906$		0			0
$907$	0.660880	+	1.00119i	0.660880	+	1.00119i	0.998210	+	0.0598042i	$0.0190476\pi$
$907$	0.660880	+	1.00119i	0.660880	+	1.00119i	−0.337330	+	0.941386i	$0.609524\pi$
$908$	1.12949	−	0.629774i	1.12949	−	0.629774i
$909$		0			0
$910$		0			0
$911$		0			0		0.995974	−	0.0896393i	$-0.0285714\pi$
$911$		0			0		−0.995974	+	0.0896393i	$0.971429\pi$
$912$	−0.714561	+	1.82067i	−0.714561	+	1.82067i
$913$	−0.347724	−	1.33767i	−0.347724	−	1.33767i
$914$	−1.08912	−	1.36572i	−1.08912	−	1.36572i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.652944	−	1.30553i	0.652944	−	1.30553i
$919$		0			0		−0.995974	−	0.0896393i	$-0.971429\pi$
$919$		0			0		0.995974	+	0.0896393i	$0.0285714\pi$
$920$		0			0
$921$	−1.15632	+	1.87119i	−1.15632	+	1.87119i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.768031	+	1.65783i	0.768031	+	1.65783i	0.753071	+	0.657939i	$0.228571\pi$
$929$	0.768031	+	1.65783i	0.768031	+	1.65783i	0.0149594	+	0.999888i	$0.495238\pi$
$930$		0			0
$931$	1.57562	−	0.817719i	1.57562	−	0.817719i
$932$	0.301784	+	0.842189i	0.301784	+	0.842189i
$933$		0			0
$934$	0.142820	−	1.90580i	0.142820	−	1.90580i
$935$		0			0
$936$		0			0
$937$	−1.99553	−	0.119555i	−1.99553	−	0.119555i	−0.999552	−	0.0299155i	$-0.990476\pi$
$937$	−1.99553	−	0.119555i	−1.99553	−	0.119555i	−0.995974	−	0.0896393i	$-0.971429\pi$
$938$		0			0
$939$	0.791190	+	0.352260i	0.791190	+	0.352260i
$940$		0			0
$941$		0			0		0.873408	−	0.486989i	$-0.161905\pi$
$941$		0			0		−0.873408	+	0.486989i	$0.838095\pi$
$942$		0			0
$943$		0			0
$944$	0.466232	+	0.487641i	0.466232	+	0.487641i
$945$		0			0
$946$	0.983930	+	0.178557i	0.983930	+	0.178557i
$947$	1.42475			1.42475			0.712376	−	0.701798i	$-0.247619\pi$
$947$	1.42475			1.42475			0.712376	+	0.701798i	$0.247619\pi$
$948$		0			0
$949$		0			0
$950$	−0.0796428	+	1.77338i	−0.0796428	+	1.77338i
$951$		0			0
$952$		0			0
$953$	1.56846	+	0.698325i	1.56846	+	0.698325i	0.992847	−	0.119394i	$-0.0380952\pi$
$953$	1.56846	+	0.698325i	1.56846	+	0.698325i	0.575617	+	0.817719i	$0.304762\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.887586	−	0.460642i	0.887586	−	0.460642i
$962$		0			0
$963$	0.0756100	+	0.163207i	0.0756100	+	0.163207i
$964$	−0.612807	−	0.722962i	−0.612807	−	0.722962i
$965$		0			0
$966$		0			0
$967$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$967$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$968$	0.791071	−	0.611724i	0.791071	−	0.611724i
$969$	−3.25969	+	0.491319i	−3.25969	+	0.491319i
$970$		0			0
$971$	−0.233951	+	0.378588i	−0.233951	+	0.378588i	−0.946327	−	0.323210i	$-0.895238\pi$
$971$	−0.233951	+	0.378588i	−0.233951	+	0.378588i	0.712376	+	0.701798i	$0.247619\pi$
$972$	0.0813653	−	0.413086i	0.0813653	−	0.413086i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.92128	+	0.468865i	−1.92128	+	0.468865i	−0.925304	+	0.379225i	$0.876190\pi$
$977$	−1.92128	+	0.468865i	−1.92128	+	0.468865i	−0.995974	+	0.0896393i	$0.971429\pi$
$978$	−0.265517	−	0.332948i	−0.265517	−	0.332948i
$979$	−0.970169	+	0.619768i	−0.970169	+	0.619768i
$980$		0			0
$981$		0			0
$982$	−0.208683	+	1.98548i	−0.208683	+	1.98548i
$983$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$983$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$984$	0.0287913	−	0.0160533i	0.0287913	−	0.0160533i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$991$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$992$		0			0
$993$	−0.595677	+	0.164397i	−0.595677	+	0.164397i
$994$		0			0
$995$		0			0
$996$	−1.48954	+	0.316612i	−1.48954	+	0.316612i
$997$		0			0		−0.393025	−	0.919528i	$-0.628571\pi$
$997$		0			0		0.393025	+	0.919528i	$0.371429\pi$
$998$	−1.33330	+	0.851747i	−1.33330	+	0.851747i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3784.1.em.b.203.1	yes	48
8.3	odd	2	CM	3784.1.em.b.203.1	yes	48
11.9	even	5		3784.1.em.a.1923.1	✓	48
43.25	even	21		3784.1.em.a.3723.1	yes	48
88.75	odd	10		3784.1.em.a.1923.1	✓	48
344.283	odd	42		3784.1.em.a.3723.1	yes	48
473.240	even	105	inner	3784.1.em.b.1659.1	yes	48
3784.1659	odd	210	inner	3784.1.em.b.1659.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3784.1.em.a.1923.1	✓	48	11.9	even	5
3784.1.em.a.1923.1	✓	48	88.75	odd	10
3784.1.em.a.3723.1	yes	48	43.25	even	21
3784.1.em.a.3723.1	yes	48	344.283	odd	42
3784.1.em.b.203.1	yes	48	1.1	even	1	trivial
3784.1.em.b.203.1	yes	48	8.3	odd	2	CM
3784.1.em.b.1659.1	yes	48	473.240	even	105	inner
3784.1.em.b.1659.1	yes	48	3784.1659	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)

\(f(q)\)	\(=\)	\(q+(-0.691063 - 0.722795i) q^{2} +(1.10130 + 0.0329607i) q^{3} +(-0.0448648 + 0.998993i) q^{4} +(-0.737244 - 0.818792i) q^{6} +(0.753071 - 0.657939i) q^{8} +(0.213567 + 0.0127951i) q^{9} +O(q^{10})\)	\(q+(-0.691063 - 0.722795i) q^{2} +(1.10130 + 0.0329607i) q^{3} +(-0.0448648 + 0.998993i) q^{4} +(-0.737244 - 0.818792i) q^{6} +(0.753071 - 0.657939i) q^{8} +(0.213567 + 0.0127951i) q^{9} +(-0.999552 - 0.0299155i) q^{11} +(-0.0823372 + 1.09871i) q^{12} +(-0.995974 - 0.0896393i) q^{16} +(-0.708488 - 1.52930i) q^{17} +(-0.138340 - 0.163207i) q^{18} +(0.446610 - 1.71807i) q^{19} +(0.669131 + 0.743145i) q^{22} +(0.851044 - 0.699767i) q^{24} +(0.525684 - 0.850680i) q^{25} +(-0.862579 - 0.0776335i) q^{27} +(0.623490 + 0.781831i) q^{32} +(-1.09982 - 0.0658919i) q^{33} +(-0.615761 + 1.56893i) q^{34} +(-0.0223639 + 0.212778i) q^{36} +(-1.55045 + 0.864489i) q^{38} +(0.0294380 + 0.00534221i) q^{41} +(0.791071 - 0.611724i) q^{43} +(0.0747301 - 0.997204i) q^{44} +(-1.09391 - 0.131548i) q^{48} +(0.669131 + 0.743145i) q^{49} +(-0.978148 + 0.207912i) q^{50} +(-0.729851 - 1.70757i) q^{51} +(0.539983 + 0.677117i) q^{54} +(0.548480 - 1.87739i) q^{57} +(-0.508067 - 0.443885i) q^{59} +(0.134233 - 0.990950i) q^{64} +(0.712420 + 0.840481i) q^{66} +(-0.0763771 - 0.194606i) q^{67} +(1.55955 - 0.639162i) q^{68} +(0.169250 - 0.130878i) q^{72} +(1.17343 - 1.56530i) q^{73} +(0.606975 - 0.919528i) q^{75} +(1.69631 + 0.523241i) q^{76} +(-1.15982 - 0.139473i) q^{81} +(-0.0164822 - 0.0249694i) q^{82} +(0.387586 + 1.32667i) q^{83} +(-0.988831 - 0.149042i) q^{86} +(-0.772417 + 0.635116i) q^{88} +(0.951194 - 0.648513i) q^{89} +(0.660880 + 0.881582i) q^{96} +(-0.871597 + 1.32041i) q^{97} +(0.0747301 - 0.997204i) q^{98} +(-0.213089 - 0.0191783i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 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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