LMFDB - Embedded newform 2888.1.bm.a.387.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2888,1,Mod(11,2888)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2888, base_ring=CyclotomicField(114))

chi = DirichletCharacter(H, H._module([57, 57, 34]))

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

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

chi := DirichletCharacter("2888.11");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2888 = 2^{3} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2888.bm (of order $114$, degree $36$, 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:	$1.44129975648$
Analytic rank:	$0$
Dimension:	$36$
Coefficient field:	$\Q(\zeta_{57})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{36} - x^{35} + x^{33} - x^{32} + x^{30} - x^{29} + x^{27} - x^{26} + x^{24} - x^{23} + x^{21} + \cdots + 1 $ x^36 - x^35 + x^33 - x^32 + x^30 - x^29 + x^27 - x^26 + x^24 - x^23 + x^21 - x^20 + x^18 - x^16 + x^15 - x^13 + x^12 - x^10 + x^9 - x^7 + x^6 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{57}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{57} - \cdots)$

Embedding invariants

Embedding label			387.1
Root			$-0.191711 - 0.981451i$ of defining polynomial
Character	$\chi$	$=$	2888.387
Dual form			2888.1.bm.a.2291.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.993931 - 0.110008i) q^{2} +(-0.254515 - 0.103375i) q^{3} +(0.975796 - 0.218681i) q^{4} +(-0.264342 - 0.0747488i) q^{6} +(0.945817 - 0.324699i) q^{8} +(-0.662691 - 0.644676i) q^{9} +O(q^{10})$	\(q+(0.993931 - 0.110008i) q^{2} +(-0.254515 - 0.103375i) q^{3} +(0.975796 - 0.218681i) q^{4} +(-0.264342 - 0.0747488i) q^{6} +(0.945817 - 0.324699i) q^{8} +(-0.662691 - 0.644676i) q^{9} +(-0.146562 - 0.578761i) q^{11} +(-0.270960 - 0.0452153i) q^{12} +(0.904357 - 0.426776i) q^{16} +(-0.161161 - 0.0361171i) q^{17} +(-0.729589 - 0.567862i) q^{18} +(0.993931 + 0.110008i) q^{19} +(-0.209341 - 0.559125i) q^{22} +(-0.274290 - 0.0151330i) q^{24} +(0.635724 - 0.771917i) q^{25} +(0.212370 + 0.484154i) q^{27} +(0.851919 - 0.523673i) q^{32} +(-0.0225271 + 0.162454i) q^{33} +(-0.164156 - 0.0181688i) q^{34} +(-0.787630 - 0.484154i) q^{36} +1.00000 q^{38} +(0.124039 - 0.245109i) q^{41} +(-0.684424 - 0.420714i) q^{43} +(-0.269579 - 0.532702i) q^{44} +(-0.274290 + 0.0151330i) q^{48} +(-0.0825793 - 0.996584i) q^{49} +(0.546948 - 0.837166i) q^{50} +(0.0372843 + 0.0258523i) q^{51} +(0.264342 + 0.457854i) q^{54} +(-0.241598 - 0.130746i) q^{57} +(-0.534828 + 1.05685i) q^{59} +(0.789141 - 0.614213i) q^{64} +(-0.00451914 + 0.163946i) q^{66} +(-0.274830 + 1.40697i) q^{67} -0.165159 q^{68} +(-0.836111 - 0.394570i) q^{72} +(0.881209 + 0.197484i) q^{73} +(-0.241598 + 0.130746i) q^{75} +(0.993931 - 0.110008i) q^{76} +(0.0214732 + 0.779007i) q^{81} +(0.0963226 - 0.257266i) q^{82} +(0.135724 + 1.63794i) q^{83} +(-0.726552 - 0.342868i) q^{86} +(-0.326544 - 0.499813i) q^{88} +(-0.161161 + 0.0361171i) q^{89} +(-0.270960 + 0.0452153i) q^{96} +(0.191711 + 0.981451i) q^{97} +(-0.191711 - 0.981451i) q^{98} +(-0.275988 + 0.478025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + q^{2} - 20 q^{3} + q^{4} - q^{6} - 2 q^{8} - 19 q^{9}+O(q^{10}) $ 36 * q + q^2 - 20 * q^3 + q^4 - q^6 - 2 * q^8 - 19 * q^9	$ 36 q + q^{2} - 20 q^{3} + q^{4} - q^{6} - 2 q^{8} - 19 q^{9} + 2 q^{11} + 2 q^{12} + q^{16} + 2 q^{17} + q^{19} - q^{22} - q^{24} + q^{25} + 36 q^{27} + q^{32} + q^{33} + 2 q^{34} + 36 q^{38} - q^{41} + 2 q^{43} - q^{44} - q^{48} - 2 q^{49} - 2 q^{50} - 2 q^{51} + q^{54} + 2 q^{57} - q^{59} - 2 q^{64} + q^{66} - q^{67} - 4 q^{68} - q^{73} + 2 q^{75} + q^{76} - 20 q^{81} - q^{82} - 17 q^{83} + 2 q^{86} + 2 q^{88} + 2 q^{89} + 2 q^{96} - q^{97} + q^{98}+O(q^{100}) $ 36 * q + q^2 - 20 * q^3 + q^4 - q^6 - 2 * q^8 - 19 * q^9 + 2 * q^11 + 2 * q^12 + q^16 + 2 * q^17 + q^19 - q^22 - q^24 + q^25 + 36 * q^27 + q^32 + q^33 + 2 * q^34 + 36 * q^38 - q^41 + 2 * q^43 - q^44 - q^48 - 2 * q^49 - 2 * q^50 - 2 * q^51 + q^54 + 2 * q^57 - q^59 - 2 * q^64 + q^66 - q^67 - 4 * q^68 - q^73 + 2 * q^75 + q^76 - 20 * q^81 - q^82 - 17 * q^83 + 2 * q^86 + 2 * q^88 + 2 * q^89 + 2 * q^96 - q^97 + q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2888\mathbb{Z}\right)^\times$.

$n$	$1445$	$2167$	$2529$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{55}{57}\right)$

Coefficient data

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

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

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

$2$	0.993931	−	0.110008i	0.993931	−	0.110008i
$2$	0.993931	−	0.110008i	0.993931	−	0.110008i
$3$	−0.254515	−	0.103375i	−0.254515	−	0.103375i	0.245485	−	0.969400i	$-0.421053\pi$
$3$	−0.254515	−	0.103375i	−0.254515	−	0.103375i	−0.500000	+	0.866025i	$0.666667\pi$
$4$	0.975796	−	0.218681i	0.975796	−	0.218681i
$5$		0			0		0.904357	−	0.426776i	$-0.140351\pi$
$5$		0			0		−0.904357	+	0.426776i	$0.859649\pi$
$6$	−0.264342	−	0.0747488i	−0.264342	−	0.0747488i
$7$		0			0		0.677282	−	0.735724i	$-0.263158\pi$
$7$		0			0		−0.677282	+	0.735724i	$0.736842\pi$
$8$	0.945817	−	0.324699i	0.945817	−	0.324699i
$9$	−0.662691	−	0.644676i	−0.662691	−	0.644676i
$10$		0			0
$11$	−0.146562	−	0.578761i	−0.146562	−	0.578761i	−0.998482	−	0.0550878i	$-0.982456\pi$
$11$	−0.146562	−	0.578761i	−0.146562	−	0.578761i	0.851919	−	0.523673i	$-0.175439\pi$
$12$	−0.270960	−	0.0452153i	−0.270960	−	0.0452153i
$13$		0			0		−0.137354	−	0.990522i	$-0.543860\pi$
$13$		0			0		0.137354	+	0.990522i	$0.456140\pi$
$14$		0			0
$15$		0			0
$16$	0.904357	−	0.426776i	0.904357	−	0.426776i
$17$	−0.161161	−	0.0361171i	−0.161161	−	0.0361171i	0.137354	−	0.990522i	$-0.456140\pi$
$17$	−0.161161	−	0.0361171i	−0.161161	−	0.0361171i	−0.298515	+	0.954405i	$0.596491\pi$
$18$	−0.729589	−	0.567862i	−0.729589	−	0.567862i
$19$	0.993931	+	0.110008i	0.993931	+	0.110008i
$19$	0.993931	+	0.110008i	0.993931	+	0.110008i
$20$		0			0
$21$		0			0
$22$	−0.209341	−	0.559125i	−0.209341	−	0.559125i
$23$		0			0		0.926494	−	0.376309i	$-0.122807\pi$
$23$		0			0		−0.926494	+	0.376309i	$0.877193\pi$
$24$	−0.274290	−	0.0151330i	−0.274290	−	0.0151330i
$25$	0.635724	−	0.771917i	0.635724	−	0.771917i
$26$		0			0
$27$	0.212370	+	0.484154i	0.212370	+	0.484154i
$28$		0			0
$29$		0			0		−0.298515	−	0.954405i	$-0.596491\pi$
$29$		0			0		0.298515	+	0.954405i	$0.403509\pi$
$30$		0			0
$31$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$31$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$32$	0.851919	−	0.523673i	0.851919	−	0.523673i
$33$	−0.0225271	+	0.162454i	−0.0225271	+	0.162454i
$34$	−0.164156	−	0.0181688i	−0.164156	−	0.0181688i
$35$		0			0
$36$	−0.787630	−	0.484154i	−0.787630	−	0.484154i
$37$		0			0		−0.245485	−	0.969400i	$-0.578947\pi$
$37$		0			0		0.245485	+	0.969400i	$0.421053\pi$
$38$	1.00000			1.00000
$39$		0			0
$40$		0			0
$41$	0.124039	−	0.245109i	0.124039	−	0.245109i	−0.821778	−	0.569808i	$-0.807018\pi$
$41$	0.124039	−	0.245109i	0.124039	−	0.245109i	0.945817	+	0.324699i	$0.105263\pi$
$42$		0			0
$43$	−0.684424	−	0.420714i	−0.684424	−	0.420714i	0.137354	−	0.990522i	$-0.456140\pi$
$43$	−0.684424	−	0.420714i	−0.684424	−	0.420714i	−0.821778	+	0.569808i	$0.807018\pi$
$44$	−0.269579	−	0.532702i	−0.269579	−	0.532702i
$45$		0			0
$46$		0			0
$47$		0			0		−0.962268	−	0.272103i	$-0.912281\pi$
$47$		0			0		0.962268	+	0.272103i	$0.0877193\pi$
$48$	−0.274290	+	0.0151330i	−0.274290	+	0.0151330i
$49$	−0.0825793	−	0.996584i	−0.0825793	−	0.996584i
$50$	0.546948	−	0.837166i	0.546948	−	0.837166i
$51$	0.0372843	+	0.0258523i	0.0372843	+	0.0258523i
$52$		0			0
$53$		0			0		−0.962268	−	0.272103i	$-0.912281\pi$
$53$		0			0		0.962268	+	0.272103i	$0.0877193\pi$
$54$	0.264342	+	0.457854i	0.264342	+	0.457854i
$55$		0			0
$56$		0			0
$57$	−0.241598	−	0.130746i	−0.241598	−	0.130746i
$58$		0			0
$59$	−0.534828	+	1.05685i	−0.534828	+	1.05685i	0.451533	+	0.892254i	$0.350877\pi$
$59$	−0.534828	+	1.05685i	−0.534828	+	1.05685i	−0.986361	+	0.164595i	$0.947368\pi$
$60$		0			0
$61$		0			0		0.754107	−	0.656752i	$-0.228070\pi$
$61$		0			0		−0.754107	+	0.656752i	$0.771930\pi$
$62$		0			0
$63$		0			0
$64$	0.789141	−	0.614213i	0.789141	−	0.614213i
$65$		0			0
$66$	−0.00451914	+	0.163946i	−0.00451914	+	0.163946i
$67$	−0.274830	+	1.40697i	−0.274830	+	1.40697i	0.546948	+	0.837166i	$0.315789\pi$
$67$	−0.274830	+	1.40697i	−0.274830	+	1.40697i	−0.821778	+	0.569808i	$0.807018\pi$
$68$	−0.165159			−0.165159
$69$		0			0
$70$		0			0
$71$		0			0		−0.754107	−	0.656752i	$-0.771930\pi$
$71$		0			0		0.754107	+	0.656752i	$0.228070\pi$
$72$	−0.836111	−	0.394570i	−0.836111	−	0.394570i
$73$	0.881209	+	0.197484i	0.881209	+	0.197484i	0.635724	−	0.771917i	$-0.280702\pi$
$73$	0.881209	+	0.197484i	0.881209	+	0.197484i	0.245485	+	0.969400i	$0.421053\pi$
$74$		0			0
$75$	−0.241598	+	0.130746i	−0.241598	+	0.130746i
$76$	0.993931	−	0.110008i	0.993931	−	0.110008i
$77$		0			0
$78$		0			0
$79$		0			0		−0.851919	−	0.523673i	$-0.824561\pi$
$79$		0			0		0.851919	+	0.523673i	$0.175439\pi$
$80$		0			0
$81$	0.0214732	+	0.779007i	0.0214732	+	0.779007i
$82$	0.0963226	−	0.257266i	0.0963226	−	0.257266i
$83$	0.135724	+	1.63794i	0.135724	+	1.63794i	0.635724	+	0.771917i	$0.280702\pi$
$83$	0.135724	+	1.63794i	0.135724	+	1.63794i	−0.500000	+	0.866025i	$0.666667\pi$
$84$		0			0
$85$		0			0
$86$	−0.726552	−	0.342868i	−0.726552	−	0.342868i
$87$		0			0
$88$	−0.326544	−	0.499813i	−0.326544	−	0.499813i
$89$	−0.161161	+	0.0361171i	−0.161161	+	0.0361171i	−0.298515	−	0.954405i	$-0.596491\pi$
$89$	−0.161161	+	0.0361171i	−0.161161	+	0.0361171i	0.137354	+	0.990522i	$0.456140\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.270960	+	0.0452153i	−0.270960	+	0.0452153i
$97$	0.191711	+	0.981451i	0.191711	+	0.981451i	0.945817	+	0.324699i	$0.105263\pi$
$97$	0.191711	+	0.981451i	0.191711	+	0.981451i	−0.754107	+	0.656752i	$0.771930\pi$
$98$	−0.191711	−	0.981451i	−0.191711	−	0.981451i
$99$	−0.275988	+	0.478025i	−0.275988	+	0.478025i
$100$	0.451533	−	0.892254i	0.451533	−	0.892254i
$101$		0			0		−0.716783	−	0.697297i	$-0.754386\pi$
$101$		0			0		0.716783	+	0.697297i	$0.245614\pi$
$102$	0.0399020	+	0.0215939i	0.0399020	+	0.0215939i
$103$		0			0		−0.677282	−	0.735724i	$-0.736842\pi$
$103$		0			0		0.677282	+	0.735724i	$0.263158\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.439413	+	1.00176i	−0.439413	+	1.00176i	0.546948	+	0.837166i	$0.315789\pi$
$107$	−0.439413	+	1.00176i	−0.439413	+	1.00176i	−0.986361	+	0.164595i	$0.947368\pi$
$108$	0.313105	+	0.425995i	0.313105	+	0.425995i
$109$		0			0		0.962268	−	0.272103i	$-0.0877193\pi$
$109$		0			0		−0.962268	+	0.272103i	$0.912281\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.34634	−	1.46252i	−1.34634	−	1.46252i	−0.754107	−	0.656752i	$-0.771930\pi$
$113$	−1.34634	−	1.46252i	−1.34634	−	1.46252i	−0.592235	−	0.805765i	$-0.701754\pi$
$114$	−0.254515	−	0.103375i	−0.254515	−	0.103375i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.415320	+	1.10927i	−0.415320	+	1.10927i
$119$		0			0
$120$		0			0
$121$	0.565990	−	0.306299i	0.565990	−	0.306299i
$122$		0			0
$123$	−0.0569079	+	0.0495611i	−0.0569079	+	0.0495611i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$127$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$128$	0.716783	−	0.697297i	0.716783	−	0.697297i
$129$	0.130705	+	0.177830i	0.130705	+	0.177830i
$130$		0			0
$131$	−1.07118	+	1.45740i	−1.07118	+	1.45740i	−0.191711	+	0.981451i	$0.561404\pi$
$131$	−1.07118	+	1.45740i	−1.07118	+	1.45740i	−0.879474	+	0.475947i	$0.842105\pi$
$132$	0.0135437	+	0.163448i	0.0135437	+	0.163448i
$133$		0			0
$134$	−0.118383	+	1.42867i	−0.118383	+	1.42867i
$135$		0			0
$136$	−0.164156	+	0.0181688i	−0.164156	+	0.0181688i
$137$	−0.0105649	+	0.0540865i	−0.0105649	+	0.0540865i	−0.986361	−	0.164595i	$-0.947368\pi$
$137$	−0.0105649	+	0.0540865i	−0.0105649	+	0.0540865i	0.975796	+	0.218681i	$0.0701754\pi$
$138$		0			0
$139$	0.0350339	−	1.27096i	0.0350339	−	1.27096i	−0.754107	−	0.656752i	$-0.771930\pi$
$139$	0.0350339	−	1.27096i	0.0350339	−	1.27096i	0.789141	−	0.614213i	$-0.210526\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.874442	−	0.300196i	−0.874442	−	0.300196i
$145$		0			0
$146$	0.897586	+	0.0993448i	0.897586	+	0.0993448i
$147$	−0.0820041	+	0.262182i	−0.0820041	+	0.262182i
$148$		0			0
$149$		0			0		−0.998482	−	0.0550878i	$-0.982456\pi$
$149$		0			0		0.998482	+	0.0550878i	$0.0175439\pi$
$150$	−0.225748	+	0.156530i	−0.225748	+	0.156530i
$151$		0			0		0.546948	−	0.837166i	$-0.315789\pi$
$151$		0			0		−0.546948	+	0.837166i	$0.684211\pi$
$152$	0.975796	−	0.218681i	0.975796	−	0.218681i
$153$	0.0835163	+	0.127831i	0.0835163	+	0.127831i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.926494	−	0.376309i	$-0.877193\pi$
$157$		0			0		0.926494	+	0.376309i	$0.122807\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.107040	+	0.771917i	0.107040	+	0.771917i
$163$	−0.281699	+	0.642209i	−0.281699	+	0.642209i	−0.998482	−	0.0550878i	$-0.982456\pi$
$163$	−0.281699	+	0.642209i	−0.281699	+	0.642209i	0.716783	+	0.697297i	$0.245614\pi$
$164$	0.0674366	−	0.266301i	0.0674366	−	0.266301i
$165$		0			0
$166$	0.315087	+	1.61307i	0.315087	+	1.61307i
$167$		0			0		−0.298515	−	0.954405i	$-0.596491\pi$
$167$		0			0		0.298515	+	0.954405i	$0.403509\pi$
$168$		0			0
$169$	−0.962268	+	0.272103i	−0.962268	+	0.272103i
$170$		0			0
$171$	−0.587749	−	0.713665i	−0.587749	−	0.713665i
$172$	−0.759861	−	0.260861i	−0.759861	−	0.260861i
$173$		0			0		−0.998482	−	0.0550878i	$-0.982456\pi$
$173$		0			0		0.998482	+	0.0550878i	$0.0175439\pi$
$174$		0			0
$175$		0			0
$176$	−0.379546	−	0.460857i	−0.379546	−	0.460857i
$177$	0.245373	−	0.213696i	0.245373	−	0.213696i
$178$	−0.156210	+	0.0536269i	−0.156210	+	0.0536269i
$179$	1.04171	+	0.563746i	1.04171	+	0.563746i	0.904357	−	0.426776i	$-0.140351\pi$
$179$	1.04171	+	0.563746i	1.04171	+	0.563746i	0.137354	+	0.990522i	$0.456140\pi$
$180$		0			0
$181$		0			0		−0.993931	−	0.110008i	$-0.964912\pi$
$181$		0			0		0.993931	+	0.110008i	$0.0350877\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.00271699	+	0.0985672i	0.00271699	+	0.0985672i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$191$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$192$	−0.264342	+	0.0747488i	−0.264342	+	0.0747488i
$193$	0.351919	−	0.342352i	0.351919	−	0.342352i	−0.500000	−	0.866025i	$-0.666667\pi$
$193$	0.351919	−	0.342352i	0.351919	−	0.342352i	0.851919	+	0.523673i	$0.175439\pi$
$194$	0.298515	+	0.954405i	0.298515	+	0.954405i
$195$		0			0
$196$	−0.298515	−	0.954405i	−0.298515	−	0.954405i
$197$		0			0		0.245485	−	0.969400i	$-0.421053\pi$
$197$		0			0		−0.245485	+	0.969400i	$0.578947\pi$
$198$	−0.221726	+	0.505484i	−0.221726	+	0.505484i
$199$		0			0		−0.137354	−	0.990522i	$-0.543860\pi$
$199$		0			0		0.137354	+	0.990522i	$0.456140\pi$
$200$	0.350638	−	0.936511i	0.350638	−	0.936511i
$201$	0.215394	−	0.329685i	0.215394	−	0.329685i
$202$		0			0
$203$		0			0
$204$	0.0420353	+	0.0170733i	0.0420353	+	0.0170733i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.0820041	−	0.591371i	−0.0820041	−	0.591371i
$210$		0			0
$211$	−1.55450	+	1.07787i	−1.55450	+	1.07787i	−0.592235	+	0.805765i	$0.701754\pi$
$211$	−1.55450	+	1.07787i	−1.55450	+	1.07787i	−0.962268	+	0.272103i	$0.912281\pi$
$212$		0			0
$213$		0			0
$214$	−0.326544	+	1.04402i	−0.326544	+	1.04402i
$215$		0			0
$216$	0.358068	+	0.388965i	0.358068	+	0.388965i
$217$		0			0
$218$		0			0
$219$	−0.203866	−	0.141357i	−0.203866	−	0.141357i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.993931	−	0.110008i	$-0.0350877\pi$
$223$		0			0		−0.993931	+	0.110008i	$0.964912\pi$
$224$		0			0
$225$	−0.918925	+	0.101707i	−0.918925	+	0.101707i
$226$	−1.49906	−	1.30553i	−1.49906	−	1.30553i
$227$	0.0316627	−	0.382112i	0.0316627	−	0.382112i	−0.962268	−	0.272103i	$-0.912281\pi$
$227$	0.0316627	−	0.382112i	0.0316627	−	0.382112i	0.993931	−	0.110008i	$-0.0350877\pi$
$228$	−0.264342	−	0.0747488i	−0.264342	−	0.0747488i
$229$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$229$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.716783	+	0.697297i	−0.716783	+	0.697297i	−0.962268	−	0.272103i	$-0.912281\pi$
$233$	−0.716783	+	0.697297i	−0.716783	+	0.697297i	0.245485	+	0.969400i	$0.421053\pi$
$234$		0			0
$235$		0			0
$236$	−0.290770	+	1.14823i	−0.290770	+	1.14823i
$237$		0			0
$238$		0			0
$239$		0			0		0.677282	−	0.735724i	$-0.263158\pi$
$239$		0			0		−0.677282	+	0.735724i	$0.736842\pi$
$240$		0			0
$241$	1.85017	−	0.751476i	1.85017	−	0.751476i	0.904357	−	0.426776i	$-0.140351\pi$
$241$	1.85017	−	0.751476i	1.85017	−	0.751476i	0.945817	−	0.324699i	$-0.105263\pi$
$242$	0.528860	−	0.366703i	0.528860	−	0.366703i
$243$	0.260441	−	0.695607i	0.260441	−	0.695607i
$244$		0			0
$245$		0			0
$246$	−0.0511104	+	0.0555207i	−0.0511104	+	0.0555207i
$247$		0			0
$248$		0			0
$249$	0.134778	−	0.430910i	0.134778	−	0.430910i
$250$		0			0
$251$	−0.427940	−	0.416307i	−0.427940	−	0.416307i	0.451533	−	0.892254i	$-0.350877\pi$
$251$	−0.427940	−	0.416307i	−0.427940	−	0.416307i	−0.879474	+	0.475947i	$0.842105\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.635724	−	0.771917i	0.635724	−	0.771917i
$257$	0.647302	+	1.27910i	0.647302	+	1.27910i	0.945817	+	0.324699i	$0.105263\pi$
$257$	0.647302	+	1.27910i	0.647302	+	1.27910i	−0.298515	+	0.954405i	$0.596491\pi$
$258$	0.149474	+	0.162372i	0.149474	+	0.162372i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.904357	+	1.56639i	−0.904357	+	1.56639i
$263$		0			0		−0.191711	−	0.981451i	$-0.561404\pi$
$263$		0			0		0.191711	+	0.981451i	$0.438596\pi$
$264$	0.0314421	+	0.160966i	0.0314421	+	0.160966i
$265$		0			0
$266$		0			0
$267$	0.0447515	+	0.00746770i	0.0447515	+	0.00746770i
$268$	0.0395009	+	1.43302i	0.0395009	+	1.43302i
$269$		0			0		0.821778	−	0.569808i	$-0.192982\pi$
$269$		0			0		−0.821778	+	0.569808i	$0.807018\pi$
$270$		0			0
$271$		0			0		−0.975796	−	0.218681i	$-0.929825\pi$
$271$		0			0		0.975796	+	0.218681i	$0.0701754\pi$
$272$	−0.161161	+	0.0361171i	−0.161161	+	0.0361171i
$273$		0			0
$274$	−0.00455084	+	0.0549205i	−0.00455084	+	0.0549205i
$275$	−0.539928	−	0.254798i	−0.539928	−	0.254798i
$276$		0			0
$277$		0			0		0.789141	−	0.614213i	$-0.210526\pi$
$277$		0			0		−0.789141	+	0.614213i	$0.789474\pi$
$278$	−0.104995	−	1.26710i	−0.104995	−	1.26710i
$279$		0			0
$280$		0			0
$281$	−0.958807	+	1.16421i	−0.958807	+	1.16421i	0.0275543	+	0.999620i	$0.491228\pi$
$281$	−0.958807	+	1.16421i	−0.958807	+	1.16421i	−0.986361	+	0.164595i	$0.947368\pi$
$282$		0			0
$283$	−0.137354	+	0.990522i	−0.137354	+	0.990522i	0.789141	+	0.614213i	$0.210526\pi$
$283$	−0.137354	+	0.990522i	−0.137354	+	0.990522i	−0.926494	+	0.376309i	$0.877193\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.902159	−	0.202179i	−0.902159	−	0.202179i
$289$	−0.879689	−	0.415135i	−0.879689	−	0.415135i
$290$		0			0
$291$	0.0526643	−	0.269612i	0.0526643	−	0.269612i
$292$	0.903067			0.903067
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	−0.0526643	+	0.269612i	−0.0526643	+	0.269612i
$295$		0			0
$296$		0			0
$297$	0.249084	−	0.193870i	0.249084	−	0.193870i
$298$		0			0
$299$		0			0
$300$	−0.207158	+	0.180414i	−0.207158	+	0.180414i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.945817	−	0.324699i	0.945817	−	0.324699i
$305$		0			0
$306$	0.0970719	+	0.117868i	0.0970719	+	0.117868i
$307$	0.926494	+	1.60473i	0.926494	+	1.60473i	0.789141	+	0.614213i	$0.210526\pi$
$307$	0.926494	+	1.60473i	0.926494	+	1.60473i	0.137354	+	0.990522i	$0.456140\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.546948	−	0.837166i	$-0.315789\pi$
$311$		0			0		−0.546948	+	0.837166i	$0.684211\pi$
$312$		0			0
$313$	−1.70125	+	0.0938607i	−1.70125	+	0.0938607i	−0.879474	−	0.475947i	$-0.842105\pi$
$313$	−1.70125	+	0.0938607i	−1.70125	+	0.0938607i	−0.821778	+	0.569808i	$0.807018\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.451533	−	0.892254i	$-0.649123\pi$
$317$		0			0		0.451533	+	0.892254i	$0.350877\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	0.215394	−	0.209538i	0.215394	−	0.209538i
$322$		0			0
$323$	−0.156210	−	0.0536269i	−0.156210	−	0.0536269i
$324$	0.191308	+	0.755456i	0.191308	+	0.755456i
$325$		0			0
$326$	−0.209341	+	0.669300i	−0.209341	+	0.669300i
$327$		0			0
$328$	0.0377320	−	0.272103i	0.0377320	−	0.272103i
$329$		0			0
$330$		0			0
$331$	0.378192	−	0.0631091i	0.378192	−	0.0631091i	0.0275543	−	0.999620i	$-0.491228\pi$
$331$	0.378192	−	0.0631091i	0.378192	−	0.0631091i	0.350638	+	0.936511i	$0.385965\pi$
$332$	0.490626	+	1.56862i	0.490626	+	1.56862i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.26952	−	0.0700412i	−1.26952	−	0.0700412i	−0.592235	−	0.805765i	$-0.701754\pi$
$337$	−1.26952	−	0.0700412i	−1.26952	−	0.0700412i	−0.677282	+	0.735724i	$0.736842\pi$
$338$	−0.926494	+	0.376309i	−0.926494	+	0.376309i
$339$	0.191476	+	0.511410i	0.191476	+	0.511410i
$340$		0			0
$341$		0			0
$342$	−0.662691	−	0.644676i	−0.662691	−	0.644676i
$343$		0			0
$344$	−0.783946	−	0.175686i	−0.783946	−	0.175686i
$345$		0			0
$346$		0			0
$347$	0.353582	−	0.481066i	0.353582	−	0.481066i	−0.592235	−	0.805765i	$-0.701754\pi$
$347$	0.353582	−	0.481066i	0.353582	−	0.481066i	0.945817	+	0.324699i	$0.105263\pi$
$348$		0			0
$349$		0			0		−0.986361	−	0.164595i	$-0.947368\pi$
$349$		0			0		0.986361	+	0.164595i	$0.0526316\pi$
$350$		0			0
$351$		0			0
$352$	−0.427940	−	0.416307i	−0.427940	−	0.416307i
$353$	0.663278	−	0.227704i	0.663278	−	0.227704i	0.0275543	−	0.999620i	$-0.491228\pi$
$353$	0.663278	−	0.227704i	0.663278	−	0.227704i	0.635724	+	0.771917i	$0.280702\pi$
$354$	0.220376	−	0.239392i	0.220376	−	0.239392i
$355$		0			0
$356$	−0.149362	+	0.0704858i	−0.149362	+	0.0704858i
$357$		0			0
$358$	1.09740	+	0.445727i	1.09740	+	0.445727i
$359$		0			0		0.993931	−	0.110008i	$-0.0350877\pi$
$359$		0			0		−0.993931	+	0.110008i	$0.964912\pi$
$360$		0			0
$361$	0.975796	+	0.218681i	0.975796	+	0.218681i
$362$		0			0
$363$	−0.175716	+	0.0194483i	−0.175716	+	0.0194483i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.962268	−	0.272103i	$-0.912281\pi$
$367$		0			0		0.962268	+	0.272103i	$0.0877193\pi$
$368$		0			0
$369$	−0.240215	+	0.0824661i	−0.240215	+	0.0824661i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.986361	−	0.164595i	$-0.947368\pi$
$373$		0			0		0.986361	+	0.164595i	$0.0526316\pi$
$374$	0.0135437	+	0.0976701i	0.0135437	+	0.0976701i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.387445	+	0.301561i	0.387445	+	0.301561i	0.789141	−	0.614213i	$-0.210526\pi$
$379$	0.387445	+	0.301561i	0.387445	+	0.301561i	−0.401695	+	0.915773i	$0.631579\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.350638	−	0.936511i	$-0.614035\pi$
$383$		0			0		0.350638	+	0.936511i	$0.385965\pi$
$384$	−0.254515	+	0.103375i	−0.254515	+	0.103375i
$385$		0			0
$386$	0.312122	−	0.378989i	0.312122	−	0.378989i
$387$	0.182338	+	0.720035i	0.182338	+	0.720035i
$388$	0.401695	+	0.915773i	0.401695	+	0.915773i
$389$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$389$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$390$		0			0
$391$		0			0
$392$	−0.401695	−	0.915773i	−0.401695	−	0.915773i
$393$	0.423290	−	0.260196i	0.423290	−	0.260196i
$394$		0			0
$395$		0			0
$396$	−0.164773	+	0.526808i	−0.164773	+	0.526808i
$397$		0			0		−0.851919	−	0.523673i	$-0.824561\pi$
$397$		0			0		0.851919	+	0.523673i	$0.175439\pi$
$398$		0			0
$399$		0			0
$400$	0.245485	−	0.969400i	0.245485	−	0.969400i
$401$	0.0395009	−	0.0384271i	0.0395009	−	0.0384271i	−0.677282	−	0.735724i	$-0.736842\pi$
$401$	0.0395009	−	0.0384271i	0.0395009	−	0.0384271i	0.716783	+	0.697297i	$0.245614\pi$
$402$	0.177819	−	0.351379i	0.177819	−	0.351379i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.0436584	+	0.0123454i	0.0436584	+	0.0123454i
$409$	1.50592	−	0.0830841i	1.50592	−	0.0830841i	0.716783	−	0.697297i	$-0.245614\pi$
$409$	1.50592	−	0.0830841i	1.50592	−	0.0830841i	0.789141	+	0.614213i	$0.210526\pi$
$410$		0			0
$411$	0.00828011	−	0.0126737i	0.00828011	−	0.0126737i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.140302	+	0.319857i	−0.140302	+	0.319857i
$418$	−0.146562	−	0.578761i	−0.146562	−	0.578761i
$419$	0.544122	+	1.24047i	0.544122	+	1.24047i	0.945817	+	0.324699i	$0.105263\pi$
$419$	0.544122	+	1.24047i	0.544122	+	1.24047i	−0.401695	+	0.915773i	$0.631579\pi$
$420$		0			0
$421$		0			0		0.962268	−	0.272103i	$-0.0877193\pi$
$421$		0			0		−0.962268	+	0.272103i	$0.912281\pi$
$422$	−1.42649	+	1.24233i	−1.42649	+	1.24233i
$423$		0			0
$424$		0			0
$425$	−0.130333	+	0.101443i	−0.130333	+	0.101443i
$426$		0			0
$427$		0			0
$428$	−0.209712	+	1.07361i	−0.209712	+	1.07361i
$429$		0			0
$430$		0			0
$431$		0			0		0.191711	−	0.981451i	$-0.438596\pi$
$431$		0			0		−0.191711	+	0.981451i	$0.561404\pi$
$432$	0.398684	+	0.347214i	0.398684	+	0.347214i
$433$	1.42733	+	0.673573i	1.42733	+	0.673573i	0.975796	−	0.218681i	$-0.0701754\pi$
$433$	1.42733	+	0.673573i	1.42733	+	0.673573i	0.451533	+	0.892254i	$0.350877\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.218179	−	0.118072i	−0.218179	−	0.118072i
$439$		0			0		0.137354	−	0.990522i	$-0.456140\pi$
$439$		0			0		−0.137354	+	0.990522i	$0.543860\pi$
$440$		0			0
$441$	−0.587749	+	0.713665i	−0.587749	+	0.713665i
$442$		0			0
$443$	0.697019	−	1.86165i	0.697019	−	1.86165i	0.245485	−	0.969400i	$-0.421053\pi$
$443$	0.697019	−	1.86165i	0.697019	−	1.86165i	0.451533	−	0.892254i	$-0.350877\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.01349	−	1.55126i	−1.01349	−	1.55126i	−0.821778	−	0.569808i	$-0.807018\pi$
$449$	−1.01349	−	1.55126i	−1.01349	−	1.55126i	−0.191711	−	0.981451i	$-0.561404\pi$
$450$	−0.902159	+	0.202179i	−0.902159	+	0.202179i
$451$	−0.160039	−	0.0358655i	−0.160039	−	0.0358655i
$452$	−1.63358	−	1.13270i	−1.63358	−	1.13270i
$453$		0			0
$454$	−0.0105649	−	0.383276i	−0.0105649	−	0.383276i
$455$		0			0
$456$	−0.270960	−	0.0452153i	−0.270960	−	0.0452153i
$457$	1.48764	−	0.248244i	1.48764	−	0.248244i	0.635724	−	0.771917i	$-0.280702\pi$
$457$	1.48764	−	0.248244i	1.48764	−	0.248244i	0.851919	+	0.523673i	$0.175439\pi$
$458$		0			0
$459$	−0.0167395	−	0.0856971i	−0.0167395	−	0.0856971i
$460$		0			0
$461$		0			0		0.451533	−	0.892254i	$-0.350877\pi$
$461$		0			0		−0.451533	+	0.892254i	$0.649123\pi$
$462$		0			0
$463$		0			0		−0.879474	−	0.475947i	$-0.842105\pi$
$463$		0			0		0.879474	+	0.475947i	$0.157895\pi$
$464$		0			0
$465$		0			0
$466$	−0.635724	+	0.771917i	−0.635724	+	0.771917i
$467$	−0.890750	−	0.148640i	−0.890750	−	0.148640i	−0.298515	−	0.954405i	$-0.596491\pi$
$467$	−0.890750	−	0.148640i	−0.890750	−	0.148640i	−0.592235	+	0.805765i	$0.701754\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.162691	+	1.17324i	−0.162691	+	1.17324i
$473$	−0.143182	+	0.457779i	−0.143182	+	0.457779i
$474$		0			0
$475$	0.716783	−	0.697297i	0.716783	−	0.697297i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.350638	−	0.936511i	$-0.385965\pi$
$479$		0			0		−0.350638	+	0.936511i	$0.614035\pi$
$480$		0			0
$481$		0			0
$482$	1.75628	−	0.950449i	1.75628	−	0.950449i
$483$		0			0
$484$	0.485310	−	0.422656i	0.485310	−	0.422656i
$485$		0			0
$486$	0.182338	−	0.720035i	0.182338	−	0.720035i
$487$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$487$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$488$		0			0
$489$	0.138085	−	0.134331i	0.138085	−	0.134331i
$490$		0			0
$491$	−1.11820	−	1.35776i	−1.11820	−	1.35776i	−0.926494	−	0.376309i	$-0.877193\pi$
$491$	−1.11820	−	1.35776i	−1.11820	−	1.35776i	−0.191711	−	0.981451i	$-0.561404\pi$
$492$	−0.0446924	+	0.0608063i	−0.0446924	+	0.0608063i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.0865567	−	0.443122i	0.0865567	−	0.443122i
$499$	−0.381094	+	0.0421795i	−0.381094	+	0.0421795i	−0.298515	−	0.954405i	$-0.596491\pi$
$499$	−0.381094	+	0.0421795i	−0.381094	+	0.0421795i	−0.0825793	+	0.996584i	$0.526316\pi$
$500$		0			0
$501$		0			0
$502$	−0.471140	−	0.366703i	−0.471140	−	0.366703i
$503$		0			0		−0.821778	−	0.569808i	$-0.807018\pi$
$503$		0			0		0.821778	+	0.569808i	$0.192982\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.273040	+	0.0302200i	0.273040	+	0.0302200i
$508$		0			0
$509$		0			0		−0.451533	−	0.892254i	$-0.649123\pi$
$509$		0			0		0.451533	+	0.892254i	$0.350877\pi$
$510$		0			0
$511$		0			0
$512$	0.546948	−	0.837166i	0.546948	−	0.837166i
$513$	0.157820	+	0.504578i	0.157820	+	0.504578i
$514$	0.784086	+	1.20013i	0.784086	+	1.20013i
$515$		0			0
$516$	0.166429	+	0.144943i	0.166429	+	0.144943i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.326544	+	0.499813i	−0.326544	+	0.499813i	−0.962268	−	0.272103i	$-0.912281\pi$
$521$	−0.326544	+	0.499813i	−0.326544	+	0.499813i	0.635724	+	0.771917i	$0.280702\pi$
$522$		0			0
$523$	−0.0226851	−	0.163593i	−0.0226851	−	0.163593i	0.975796	−	0.218681i	$-0.0701754\pi$
$523$	−0.0226851	−	0.163593i	−0.0226851	−	0.163593i	−0.998482	+	0.0550878i	$0.982456\pi$
$524$	−0.726552	+	1.65637i	−0.726552	+	1.65637i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.0489589	+	0.156530i	0.0489589	+	0.156530i
$529$	0.716783	−	0.697297i	0.716783	−	0.697297i
$530$		0			0
$531$	1.03575	−	0.355574i	1.03575	−	0.355574i
$532$		0			0
$533$		0			0
$534$	0.0453014	+	0.00249935i	0.0453014	+	0.00249935i
$535$		0			0
$536$	0.196905	+	1.41998i	0.196905	+	1.41998i
$537$	−0.206853	−	0.251168i	−0.206853	−	0.251168i
$538$		0			0
$539$	−0.564681	+	0.193855i	−0.564681	+	0.193855i
$540$		0			0
$541$		0			0		−0.993931	−	0.110008i	$-0.964912\pi$
$541$		0			0		0.993931	+	0.110008i	$0.0350877\pi$
$542$		0			0
$543$		0			0
$544$	−0.156210	+	0.0536269i	−0.156210	+	0.0536269i
$545$		0			0
$546$		0			0
$547$	0.0674366	+	0.486318i	0.0674366	+	0.486318i	0.993931	+	0.110008i	$0.0350877\pi$
$547$	0.0674366	+	0.486318i	0.0674366	+	0.486318i	−0.926494	+	0.376309i	$0.877193\pi$
$548$	0.00151848	+	0.0550878i	0.00151848	+	0.0550878i
$549$		0			0
$550$	−0.564681	−	0.193855i	−0.564681	−	0.193855i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.243750	−	1.24786i	−0.243750	−	1.24786i
$557$		0			0		−0.298515	−	0.954405i	$-0.596491\pi$
$557$		0			0		0.298515	+	0.954405i	$0.403509\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.00949786	−	0.0253676i	0.00949786	−	0.0253676i
$562$	−0.824914	+	1.26263i	−0.824914	+	1.26263i
$563$	−1.57588	−	1.22656i	−1.57588	−	1.22656i	−0.821778	−	0.569808i	$-0.807018\pi$
$563$	−1.57588	−	1.22656i	−1.57588	−	1.22656i	−0.754107	−	0.656752i	$-0.771930\pi$
$564$		0			0
$565$		0			0
$566$	−0.0275543	+	0.999620i	−0.0275543	+	0.999620i
$567$		0			0
$568$		0			0
$569$	−0.962053	−	1.47253i	−0.962053	−	1.47253i	−0.879474	−	0.475947i	$-0.842105\pi$
$569$	−0.962053	−	1.47253i	−0.962053	−	1.47253i	−0.0825793	−	0.996584i	$-0.526316\pi$
$570$		0			0
$571$	0.493931	−	0.756017i	0.493931	−	0.756017i	−0.500000	−	0.866025i	$-0.666667\pi$
$571$	0.493931	−	0.756017i	0.493931	−	0.756017i	0.993931	+	0.110008i	$0.0350877\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.918925	−	0.101707i	−0.918925	−	0.101707i
$577$	1.25499	+	1.36329i	1.25499	+	1.36329i	0.904357	+	0.426776i	$0.140351\pi$
$577$	1.25499	+	1.36329i	1.25499	+	1.36329i	0.350638	+	0.936511i	$0.385965\pi$
$578$	−0.920018	−	0.315843i	−0.920018	−	0.315843i
$579$	−0.124959	+	0.0507541i	−0.124959	+	0.0507541i
$580$		0			0
$581$		0			0
$582$	0.0226851	−	0.273769i	0.0226851	−	0.273769i
$583$		0			0
$584$	0.897586	−	0.0993448i	0.897586	−	0.0993448i
$585$		0			0
$586$		0			0
$587$	1.02149	+	0.889612i	1.02149	+	0.889612i	0.993931	−	0.110008i	$-0.0350877\pi$
$587$	1.02149	+	0.889612i	1.02149	+	0.889612i	0.0275543	+	0.999620i	$0.491228\pi$
$588$	−0.0226851	+	0.273769i	−0.0226851	+	0.273769i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.752996	−	1.02449i	−0.752996	−	1.02449i	−0.998482	−	0.0550878i	$-0.982456\pi$
$593$	−0.752996	−	1.02449i	−0.752996	−	1.02449i	0.245485	−	0.969400i	$-0.421053\pi$
$594$	0.226245	−	0.220095i	0.226245	−	0.220095i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.754107	−	0.656752i	$-0.228070\pi$
$599$		0			0		−0.754107	+	0.656752i	$0.771930\pi$
$600$	−0.186054	+	0.202109i	−0.186054	+	0.202109i
$601$	0.879474	−	0.475947i	0.879474	−	0.475947i	0.0275543	−	0.999620i	$-0.491228\pi$
$601$	0.879474	−	0.475947i	0.879474	−	0.475947i	0.851919	+	0.523673i	$0.175439\pi$
$602$		0			0
$603$	1.08917	−	0.755214i	1.08917	−	0.755214i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.677282	−	0.735724i	$-0.263158\pi$
$607$		0			0		−0.677282	+	0.735724i	$0.736842\pi$
$608$	0.904357	−	0.426776i	0.904357	−	0.426776i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.109449	+	0.106474i	0.109449	+	0.106474i
$613$		0			0		0.962268	−	0.272103i	$-0.0877193\pi$
$613$		0			0		−0.962268	+	0.272103i	$0.912281\pi$
$614$	1.09740	+	1.49307i	1.09740	+	1.49307i
$615$		0			0
$616$		0			0
$617$	−1.04485	+	1.26869i	−1.04485	+	1.26869i	−0.0825793	+	0.996584i	$0.526316\pi$
$617$	−1.04485	+	1.26869i	−1.04485	+	1.26869i	−0.962268	+	0.272103i	$0.912281\pi$
$618$		0			0
$619$	−1.28117	−	1.39172i	−1.28117	−	1.39172i	−0.879474	−	0.475947i	$-0.842105\pi$
$619$	−1.28117	−	1.39172i	−1.28117	−	1.39172i	−0.401695	−	0.915773i	$-0.631579\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.191711	−	0.981451i	−0.191711	−	0.981451i
$626$	−1.68060	+	0.280443i	−1.68060	+	0.280443i
$627$	−0.0402617	+	0.158990i	−0.0402617	+	0.158990i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.821778	−	0.569808i	$-0.807018\pi$
$631$		0			0		0.821778	+	0.569808i	$0.192982\pi$
$632$		0			0
$633$	0.507068	−	0.113637i	0.507068	−	0.113637i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.0547742	+	1.98711i	0.0547742	+	1.98711i	0.137354	+	0.990522i	$0.456140\pi$
$641$	0.0547742	+	1.98711i	0.0547742	+	1.98711i	−0.0825793	+	0.996584i	$0.526316\pi$
$642$	0.191036	−	0.231962i	0.191036	−	0.231962i
$643$	−1.70125	−	1.04576i	−1.70125	−	1.04576i	−0.879474	−	0.475947i	$-0.842105\pi$
$643$	−1.70125	−	1.04576i	−1.70125	−	1.04576i	−0.821778	−	0.569808i	$-0.807018\pi$
$644$		0			0
$645$		0			0
$646$	−0.161161	−	0.0361171i	−0.161161	−	0.0361171i
$647$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$647$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$648$	0.273253	+	0.729826i	0.273253	+	0.729826i
$649$	0.690048	+	0.154643i	0.690048	+	0.154643i
$650$		0			0
$651$		0			0
$652$	−0.134442	+	0.688268i	−0.134442	+	0.688268i
$653$		0			0		1.00000			$0$
$653$		0			0		−1.00000			$\pi$
$654$		0			0
$655$		0			0
$656$	0.00756937	−	0.274603i	0.00756937	−	0.274603i
$657$	−0.456657	−	0.698965i	−0.456657	−	0.698965i
$658$		0			0
$659$	1.35251	−	0.0746198i	1.35251	−	0.0746198i	0.635724	−	0.771917i	$-0.280702\pi$
$659$	1.35251	−	0.0746198i	1.35251	−	0.0746198i	0.716783	+	0.697297i	$0.245614\pi$
$660$		0			0
$661$		0			0		0.754107	−	0.656752i	$-0.228070\pi$
$661$		0			0		−0.754107	+	0.656752i	$0.771930\pi$
$662$	0.368954	−	0.104330i	0.368954	−	0.104330i
$663$		0			0
$664$	0.660209	+	1.50512i	0.660209	+	1.50512i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.130333	−	1.57289i	−0.130333	−	1.57289i	−0.677282	−	0.735724i	$-0.736842\pi$
$673$	−0.130333	−	1.57289i	−0.130333	−	1.57289i	0.546948	−	0.837166i	$-0.315789\pi$
$674$	−1.26952	+	0.0700412i	−1.26952	+	0.0700412i
$675$	0.508735	+	0.143857i	0.508735	+	0.143857i
$676$	−0.879474	+	0.475947i	−0.879474	+	0.475947i
$677$		0			0		−0.945817	−	0.324699i	$-0.894737\pi$
$677$		0			0		0.945817	+	0.324699i	$0.105263\pi$
$678$	0.246573	+	0.487242i	0.246573	+	0.487242i
$679$		0			0
$680$		0			0
$681$	−0.0475594	+	0.0939798i	−0.0475594	+	0.0939798i
$682$		0			0
$683$	0.387445	−	1.52999i	0.387445	−	1.52999i	−0.401695	−	0.915773i	$-0.631579\pi$
$683$	0.387445	−	1.52999i	0.387445	−	1.52999i	0.789141	−	0.614213i	$-0.210526\pi$
$684$	−0.729589	−	0.567862i	−0.729589	−	0.567862i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.798515	−	0.0883796i	−0.798515	−	0.0883796i
$689$		0			0
$690$		0			0
$691$	−0.197221	−	0.449618i	−0.197221	−	0.449618i	0.789141	−	0.614213i	$-0.210526\pi$
$691$	−0.197221	−	0.449618i	−0.197221	−	0.449618i	−0.986361	+	0.164595i	$0.947368\pi$
$692$		0			0
$693$		0			0
$694$	0.298515	−	0.517043i	0.298515	−	0.517043i
$695$		0			0
$696$		0			0
$697$	−0.0288430	+	0.0350221i	−0.0288430	+	0.0350221i
$698$		0			0
$699$	0.254515	−	0.103375i	0.254515	−	0.103375i
$700$		0			0
$701$		0			0		0.904357	−	0.426776i	$-0.140351\pi$
$701$		0			0		−0.904357	+	0.426776i	$0.859649\pi$
$702$		0			0
$703$		0			0
$704$	−0.471140	−	0.366703i	−0.471140	−	0.366703i
$705$		0			0
$706$	0.634203	−	0.299288i	0.634203	−	0.299288i
$707$		0			0
$708$	0.192703	−	0.262182i	0.192703	−	0.262182i
$709$		0			0		−0.137354	−	0.990522i	$-0.543860\pi$
$709$		0			0		0.137354	+	0.990522i	$0.456140\pi$
$710$		0			0
$711$		0			0
$712$	−0.140702	+	0.0864891i	−0.140702	+	0.0864891i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.13978	+	0.322299i	1.13978	+	0.322299i
$717$		0			0
$718$		0			0
$719$		0			0		−0.926494	−	0.376309i	$-0.877193\pi$
$719$		0			0		0.926494	+	0.376309i	$0.122807\pi$
$720$		0			0
$721$		0			0
$722$	0.993931	+	0.110008i	0.993931	+	0.110008i
$723$	−0.548580			−0.548580
$724$		0			0
$725$		0			0
$726$	−0.172510	+	0.0386605i	−0.172510	+	0.0386605i
$727$		0			0		0.904357	−	0.426776i	$-0.140351\pi$
$727$		0			0		−0.904357	+	0.426776i	$0.859649\pi$
$728$		0			0
$729$	0.389613	−	0.423233i	0.389613	−	0.423233i
$730$		0			0
$731$	0.0951077	+	0.0925222i	0.0951077	+	0.0925222i
$732$		0			0
$733$		0			0		−0.245485	−	0.969400i	$-0.578947\pi$
$733$		0			0		0.245485	+	0.969400i	$0.421053\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.854581	−	0.0471486i	0.854581	−	0.0471486i
$738$	−0.229686	+	0.108391i	−0.229686	+	0.108391i
$739$	0.684302	+	0.153356i	0.684302	+	0.153356i	0.546948	−	0.837166i	$-0.315789\pi$
$739$	0.684302	+	0.153356i	0.684302	+	0.153356i	0.137354	+	0.990522i	$0.456140\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.904357	−	0.426776i	$-0.140351\pi$
$743$		0			0		−0.904357	+	0.426776i	$0.859649\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.965999	−	1.17295i	0.965999	−	1.17295i
$748$	0.0242060	+	0.0955874i	0.0242060	+	0.0955874i
$749$		0			0
$750$		0			0
$751$		0			0		−0.298515	−	0.954405i	$-0.596491\pi$
$751$		0			0		0.298515	+	0.954405i	$0.403509\pi$
$752$		0			0
$753$	0.0658814	+	0.150194i	0.0658814	+	0.150194i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.298515	−	0.954405i	$-0.403509\pi$
$757$		0			0		−0.298515	+	0.954405i	$0.596491\pi$
$758$	0.418268	+	0.257108i	0.418268	+	0.257108i
$759$		0			0
$760$		0			0
$761$	0.221690	−	0.875433i	0.221690	−	0.875433i	−0.754107	−	0.656752i	$-0.771930\pi$
$761$	0.221690	−	0.875433i	0.221690	−	0.875433i	0.975796	−	0.218681i	$-0.0701754\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.241598	+	0.130746i	−0.241598	+	0.130746i
$769$	−0.472446	−	0.133595i	−0.472446	−	0.133595i	0.0275543	−	0.999620i	$-0.491228\pi$
$769$	−0.472446	−	0.133595i	−0.472446	−	0.133595i	−0.500000	+	0.866025i	$0.666667\pi$
$770$		0			0
$771$	−0.0325206	−	0.392465i	−0.0325206	−	0.392465i
$772$	0.268536	−	0.411024i	0.268536	−	0.411024i
$773$		0			0		−0.821778	−	0.569808i	$-0.807018\pi$
$773$		0			0		0.821778	+	0.569808i	$0.192982\pi$
$774$	0.260441	+	0.695607i	0.260441	+	0.695607i
$775$		0			0
$776$	0.500000	+	0.866025i	0.500000	+	0.866025i
$777$		0			0
$778$		0			0
$779$	0.150251	−	0.229976i	0.150251	−	0.229976i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$785$		0			0
$786$	0.392098	−	0.305182i	0.392098	−	0.305182i
$787$	0.784086	+	1.20013i	0.784086	+	1.20013i	0.975796	+	0.218681i	$0.0701754\pi$
$787$	0.784086	+	1.20013i	0.784086	+	1.20013i	−0.191711	+	0.981451i	$0.561404\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.105820	+	0.541737i	−0.105820	+	0.541737i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$797$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$798$		0			0
$799$		0			0
$800$	0.137354	−	0.990522i	0.137354	−	0.990522i
$801$	0.130084	+	0.0799623i	0.130084	+	0.0799623i
$802$	0.0350339	−	0.0425393i	0.0350339	−	0.0425393i
$803$	−0.0148561	−	0.538953i	−0.0148561	−	0.538953i
$804$	0.138085	−	0.368808i	0.138085	−	0.368808i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.0226851	+	0.273769i	−0.0226851	+	0.273769i	0.975796	+	0.218681i	$0.0701754\pi$
$809$	−0.0226851	+	0.273769i	−0.0226851	+	0.273769i	−0.998482	+	0.0550878i	$0.982456\pi$
$810$		0			0
$811$	1.06742	−	0.239214i	1.06742	−	0.239214i	0.350638	−	0.936511i	$-0.385965\pi$
$811$	1.06742	−	0.239214i	1.06742	−	0.239214i	0.716783	+	0.697297i	$0.245614\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.0447515	+	0.00746770i	0.0447515	+	0.00746770i
$817$	−0.633988	−	0.493453i	−0.633988	−	0.493453i
$818$	1.48764	−	0.248244i	1.48764	−	0.248244i
$819$		0			0
$820$		0			0
$821$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$821$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$822$	0.00683565	−	0.0135076i	0.00683565	−	0.0135076i
$823$		0			0		−0.716783	−	0.697297i	$-0.754386\pi$
$823$		0			0		0.716783	+	0.697297i	$0.245614\pi$
$824$		0			0
$825$	0.111080	+	0.120665i	0.111080	+	0.120665i
$826$		0			0
$827$	0.174638	−	0.212051i	0.174638	−	0.212051i	−0.677282	−	0.735724i	$-0.736842\pi$
$827$	0.174638	−	0.212051i	0.174638	−	0.212051i	0.851919	+	0.523673i	$0.175439\pi$
$828$		0			0
$829$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$829$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.0226851	+	0.163593i	−0.0226851	+	0.163593i
$834$	−0.104264	+	0.333350i	−0.104264	+	0.333350i
$835$		0			0
$836$	−0.209341	−	0.559125i	−0.209341	−	0.559125i
$837$		0			0
$838$	0.677282	+	1.17309i	0.677282	+	1.17309i
$839$		0			0		0.592235	−	0.805765i	$-0.298246\pi$
$839$		0			0		−0.592235	+	0.805765i	$0.701754\pi$
$840$		0			0
$841$	−0.821778	+	0.569808i	−0.821778	+	0.569808i
$842$		0			0
$843$	0.364381	−	0.197193i	0.364381	−	0.197193i
$844$	−1.28117	+	1.39172i	−1.28117	+	1.39172i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.137354	−	0.237903i	0.137354	−	0.237903i
$850$	−0.118383	+	0.115165i	−0.118383	+	0.115165i
$851$		0			0
$852$		0			0
$853$		0			0		0.592235	−	0.805765i	$-0.298246\pi$
$853$		0			0		−0.592235	+	0.805765i	$0.701754\pi$
$854$		0			0
$855$		0			0
$856$	−0.0903332	+	1.09016i	−0.0903332	+	1.09016i
$857$	0.289141	+	0.251813i	0.289141	+	0.251813i	0.789141	−	0.614213i	$-0.210526\pi$
$857$	0.289141	+	0.251813i	0.289141	+	0.251813i	−0.500000	+	0.866025i	$0.666667\pi$
$858$		0			0
$859$	0.315087	−	1.61307i	0.315087	−	1.61307i	−0.401695	−	0.915773i	$-0.631579\pi$
$859$	0.315087	−	1.61307i	0.315087	−	1.61307i	0.716783	−	0.697297i	$-0.245614\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$863$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$864$	0.434461	+	0.301248i	0.434461	+	0.301248i
$865$		0			0
$866$	1.49277	+	0.512467i	1.49277	+	0.512467i
$867$	0.180979	+	0.196596i	0.180979	+	0.196596i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.505673	−	0.773991i	0.505673	−	0.773991i
$874$		0			0
$875$		0			0
$876$	−0.229844	−	0.0933544i	−0.229844	−	0.0933544i
$877$		0			0		−0.754107	−	0.656752i	$-0.771930\pi$
$877$		0			0		0.754107	+	0.656752i	$0.228070\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.934714	−	0.727517i	−0.934714	−	0.727517i	0.0275543	−	0.999620i	$-0.491228\pi$
$881$	−0.934714	−	0.727517i	−0.934714	−	0.727517i	−0.962268	+	0.272103i	$0.912281\pi$
$882$	−0.505673	+	0.773991i	−0.505673	+	0.773991i
$883$	0.634203	−	1.69388i	0.634203	−	1.69388i	−0.0825793	−	0.996584i	$-0.526316\pi$
$883$	0.634203	−	1.69388i	0.634203	−	1.69388i	0.716783	−	0.697297i	$-0.245614\pi$
$884$		0			0
$885$		0			0
$886$	0.487991	−	1.92703i	0.487991	−	1.92703i
$887$		0			0		−0.298515	−	0.954405i	$-0.596491\pi$
$887$		0			0		0.298515	+	0.954405i	$0.403509\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.447711	−	0.126601i	0.447711	−	0.126601i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−1.17799	−	1.43035i	−1.17799	−	1.43035i
$899$		0			0
$900$	−0.874442	+	0.300196i	−0.874442	+	0.300196i
$901$		0			0
$902$	−0.163013	−	0.0180423i	−0.163013	−	0.0180423i
$903$		0			0
$904$	−1.74827	−	0.946117i	−1.74827	−	0.946117i
$905$		0			0
$906$		0			0
$907$	0.445817	+	0.541326i	0.445817	+	0.541326i	0.945817	−	0.324699i	$-0.105263\pi$
$907$	0.445817	+	0.541326i	0.445817	+	0.541326i	−0.500000	+	0.866025i	$0.666667\pi$
$908$	−0.0526643	−	0.379787i	−0.0526643	−	0.379787i
$909$		0			0
$910$		0			0
$911$		0			0		−0.945817	−	0.324699i	$-0.894737\pi$
$911$		0			0		0.945817	+	0.324699i	$0.105263\pi$
$912$	−0.274290	−	0.0151330i	−0.274290	−	0.0151330i
$913$	0.928084	−	0.318612i	0.928084	−	0.318612i
$914$	1.45131	−	0.410390i	1.45131	−	0.410390i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.0260653	−	0.0833355i	−0.0260653	−	0.0833355i
$919$		0			0		0.245485	−	0.969400i	$-0.421053\pi$
$919$		0			0		−0.245485	+	0.969400i	$0.578947\pi$
$920$		0			0
$921$	−0.0699169	−	0.504204i	−0.0699169	−	0.504204i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.0510579	−	0.0207379i	−0.0510579	−	0.0207379i	0.350638	−	0.936511i	$-0.385965\pi$
$929$	−0.0510579	−	0.0207379i	−0.0510579	−	0.0207379i	−0.401695	+	0.915773i	$0.631579\pi$
$930$		0			0
$931$	0.0275543	−	0.999620i	0.0275543	−	0.999620i
$932$	−0.546948	+	0.837166i	−0.546948	+	0.837166i
$933$		0			0
$934$	−0.901695	−	0.0497479i	−0.901695	−	0.0497479i
$935$		0			0
$936$		0			0
$937$	1.97580	+	0.218681i	1.97580	+	0.218681i	1.00000			$0$
$937$	1.97580	+	0.218681i	1.97580	+	0.218681i	0.975796	+	0.218681i	$0.0701754\pi$
$938$		0			0
$939$	0.442696	+	0.151978i	0.442696	+	0.151978i
$940$		0			0
$941$		0			0		−0.821778	−	0.569808i	$-0.807018\pi$
$941$		0			0		0.821778	+	0.569808i	$0.192982\pi$
$942$		0			0
$943$		0			0
$944$	−0.0326373	+	1.18402i	−0.0326373	+	1.18402i
$945$		0			0
$946$	−0.0919536	+	0.470751i	−0.0919536	+	0.470751i
$947$	−0.798515	+	0.0883796i	−0.798515	+	0.0883796i	−0.500000	−	0.866025i	$-0.666667\pi$
$947$	−0.798515	+	0.0883796i	−0.798515	+	0.0883796i	−0.298515	+	0.954405i	$0.596491\pi$
$948$		0			0
$949$		0			0
$950$	0.635724	−	0.771917i	0.635724	−	0.771917i
$951$		0			0
$952$		0			0
$953$	0.445817	+	0.541326i	0.445817	+	0.541326i	0.945817	−	0.324699i	$-0.105263\pi$
$953$	0.445817	+	0.541326i	0.445817	+	0.541326i	−0.500000	+	0.866025i	$0.666667\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.677282	+	0.735724i	−0.677282	+	0.735724i
$962$		0			0
$963$	0.937007	−	0.380579i	0.937007	−	0.380579i
$964$	1.64106	−	1.13789i	1.64106	−	1.13789i
$965$		0			0
$966$		0			0
$967$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$967$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$968$	0.435868	−	0.473479i	0.435868	−	0.473479i
$969$	0.0342140	+	0.0297970i	0.0342140	+	0.0297970i
$970$		0			0
$971$	0.298515	−	0.954405i	0.298515	−	0.954405i	−0.677282	−	0.735724i	$-0.736842\pi$
$971$	0.298515	−	0.954405i	0.298515	−	0.954405i	0.975796	−	0.218681i	$-0.0701754\pi$
$972$	0.102021	−	0.735724i	0.102021	−	0.735724i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.0543571	−	0.00907059i	−0.0543571	−	0.00907059i	0.137354	−	0.990522i	$-0.456140\pi$
$977$	−0.0543571	−	0.00907059i	−0.0543571	−	0.00907059i	−0.191711	+	0.981451i	$0.561404\pi$
$978$	0.122469	−	0.148706i	0.122469	−	0.148706i
$979$	0.0445233	+	0.0879804i	0.0445233	+	0.0879804i
$980$		0			0
$981$		0			0
$982$	−1.26078	−	1.22651i	−1.26078	−	1.22651i
$983$		0			0		0.451533	−	0.892254i	$-0.350877\pi$
$983$		0			0		−0.451533	+	0.892254i	$0.649123\pi$
$984$	−0.0377320	+	0.0653537i	−0.0377320	+	0.0653537i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.821778	−	0.569808i	$-0.192982\pi$
$991$		0			0		−0.821778	+	0.569808i	$0.807018\pi$
$992$		0			0
$993$	−0.102779	−	0.0230334i	−0.102779	−	0.0230334i
$994$		0			0
$995$		0			0
$996$	0.0372843	−	0.449954i	0.0372843	−	0.449954i
$997$		0			0		−0.904357	−	0.426776i	$-0.859649\pi$
$997$		0			0		0.904357	+	0.426776i	$0.140351\pi$
$998$	−0.374141	+	0.0838470i	−0.374141	+	0.0838470i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2888.1.bm.a.387.1	✓	36
8.3	odd	2	CM	2888.1.bm.a.387.1	✓	36
361.125	even	57	inner	2888.1.bm.a.2291.1	yes	36
2888.2291	odd	114	inner	2888.1.bm.a.2291.1	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2888.1.bm.a.387.1	✓	36	1.1	even	1	trivial
2888.1.bm.a.387.1	✓	36	8.3	odd	2	CM
2888.1.bm.a.2291.1	yes	36	361.125	even	57	inner
2888.1.bm.a.2291.1	yes	36	2888.2291	odd	114	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:	\( N \)	\(=\)	\( 2888 = 2^{3} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2888.bm (of order \(114\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(0.993931 - 0.110008i) q^{2} +(-0.254515 - 0.103375i) q^{3} +(0.975796 - 0.218681i) q^{4} +(-0.264342 - 0.0747488i) q^{6} +(0.945817 - 0.324699i) q^{8} +(-0.662691 - 0.644676i) q^{9} +O(q^{10})\)	\(q+(0.993931 - 0.110008i) q^{2} +(-0.254515 - 0.103375i) q^{3} +(0.975796 - 0.218681i) q^{4} +(-0.264342 - 0.0747488i) q^{6} +(0.945817 - 0.324699i) q^{8} +(-0.662691 - 0.644676i) q^{9} +(-0.146562 - 0.578761i) q^{11} +(-0.270960 - 0.0452153i) q^{12} +(0.904357 - 0.426776i) q^{16} +(-0.161161 - 0.0361171i) q^{17} +(-0.729589 - 0.567862i) q^{18} +(0.993931 + 0.110008i) q^{19} +(-0.209341 - 0.559125i) q^{22} +(-0.274290 - 0.0151330i) q^{24} +(0.635724 - 0.771917i) q^{25} +(0.212370 + 0.484154i) q^{27} +(0.851919 - 0.523673i) q^{32} +(-0.0225271 + 0.162454i) q^{33} +(-0.164156 - 0.0181688i) q^{34} +(-0.787630 - 0.484154i) q^{36} +1.00000 q^{38} +(0.124039 - 0.245109i) q^{41} +(-0.684424 - 0.420714i) q^{43} +(-0.269579 - 0.532702i) q^{44} +(-0.274290 + 0.0151330i) q^{48} +(-0.0825793 - 0.996584i) q^{49} +(0.546948 - 0.837166i) q^{50} +(0.0372843 + 0.0258523i) q^{51} +(0.264342 + 0.457854i) q^{54} +(-0.241598 - 0.130746i) q^{57} +(-0.534828 + 1.05685i) q^{59} +(0.789141 - 0.614213i) q^{64} +(-0.00451914 + 0.163946i) q^{66} +(-0.274830 + 1.40697i) q^{67} -0.165159 q^{68} +(-0.836111 - 0.394570i) q^{72} +(0.881209 + 0.197484i) q^{73} +(-0.241598 + 0.130746i) q^{75} +(0.993931 - 0.110008i) q^{76} +(0.0214732 + 0.779007i) q^{81} +(0.0963226 - 0.257266i) q^{82} +(0.135724 + 1.63794i) q^{83} +(-0.726552 - 0.342868i) q^{86} +(-0.326544 - 0.499813i) q^{88} +(-0.161161 + 0.0361171i) q^{89} +(-0.270960 + 0.0452153i) q^{96} +(0.191711 + 0.981451i) q^{97} +(-0.191711 - 0.981451i) q^{98} +(-0.275988 + 0.478025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + q^{2} - 20 q^{3} + q^{4} - q^{6} - 2 q^{8} - 19 q^{9}+O(q^{10}) \) 36 * q + q^2 - 20 * q^3 + q^4 - q^6 - 2 * q^8 - 19 * q^9	\( 36 q + q^{2} - 20 q^{3} + q^{4} - q^{6} - 2 q^{8} - 19 q^{9} + 2 q^{11} + 2 q^{12} + q^{16} + 2 q^{17} + q^{19} - q^{22} - q^{24} + q^{25} + 36 q^{27} + q^{32} + q^{33} + 2 q^{34} + 36 q^{38} - q^{41} + 2 q^{43} - q^{44} - q^{48} - 2 q^{49} - 2 q^{50} - 2 q^{51} + q^{54} + 2 q^{57} - q^{59} - 2 q^{64} + q^{66} - q^{67} - 4 q^{68} - q^{73} + 2 q^{75} + q^{76} - 20 q^{81} - q^{82} - 17 q^{83} + 2 q^{86} + 2 q^{88} + 2 q^{89} + 2 q^{96} - q^{97} + q^{98}+O(q^{100}) \) 36 * q + q^2 - 20 * q^3 + q^4 - q^6 - 2 * q^8 - 19 * q^9 + 2 * q^11 + 2 * q^12 + q^16 + 2 * q^17 + q^19 - q^22 - q^24 + q^25 + 36 * q^27 + q^32 + q^33 + 2 * q^34 + 36 * q^38 - q^41 + 2 * q^43 - q^44 - q^48 - 2 * q^49 - 2 * q^50 - 2 * q^51 + q^54 + 2 * q^57 - q^59 - 2 * q^64 + q^66 - q^67 - 4 * q^68 - q^73 + 2 * q^75 + q^76 - 20 * q^81 - q^82 - 17 * q^83 + 2 * q^86 + 2 * q^88 + 2 * q^89 + 2 * q^96 - q^97 + q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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