LMFDB - Embedded newform 2888.1.bm.a.235.1

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			235.1
Root			$0.975796 + 0.218681i$ of defining polynomial
Character	$\chi$	$=$	2888.235
Dual form			2888.1.bm.a.467.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.716783 - 0.697297i) q^{2} +(-1.48636 + 0.701431i) q^{3} +(0.0275543 - 0.999620i) q^{4} +(-0.576292 + 1.53921i) q^{6} +(-0.677282 - 0.735724i) q^{8} +(1.08154 - 1.31324i) q^{9} +O(q^{10})$	\(q+(0.716783 - 0.697297i) q^{2} +(-1.48636 + 0.701431i) q^{3} +(0.0275543 - 0.999620i) q^{4} +(-0.576292 + 1.53921i) q^{6} +(-0.677282 - 0.735724i) q^{8} +(1.08154 - 1.31324i) q^{9} +(-1.68060 + 0.280443i) q^{11} +(0.660209 + 1.50512i) q^{12} +(-0.998482 - 0.0550878i) q^{16} +(0.0301416 + 1.09348i) q^{17} +(-0.140490 - 1.69546i) q^{18} +(0.716783 + 0.697297i) q^{19} +(-1.00907 + 1.37289i) q^{22} +(1.52274 + 0.618485i) q^{24} +(0.993931 + 0.110008i) q^{25} +(-0.282943 + 1.11732i) q^{27} +(-0.754107 + 0.656752i) q^{32} +(2.30127 - 1.59566i) q^{33} +(0.784086 + 0.762770i) q^{34} +(-1.28294 - 1.11732i) q^{36} +1.00000 q^{38} +(-0.225748 + 1.62798i) q^{41} +(-0.370244 - 0.322446i) q^{43} +(0.234028 + 1.68769i) q^{44} +(1.52274 - 0.618485i) q^{48} +(0.546948 + 0.837166i) q^{49} +(0.789141 - 0.614213i) q^{50} +(-0.811803 - 1.60417i) q^{51} +(0.576292 + 0.998168i) q^{54} +(-1.55450 - 0.533662i) q^{57} +(-0.264342 + 1.90630i) q^{59} +(-0.0825793 + 0.996584i) q^{64} +(0.536858 - 2.74841i) q^{66} +(1.24067 - 0.278042i) q^{67} +1.09390 q^{68} +(-1.69869 + 0.0937194i) q^{72} +(0.00756937 + 0.274603i) q^{73} +(-1.55450 + 0.533662i) q^{75} +(0.716783 - 0.697297i) q^{76} +(-0.0370120 - 0.189481i) q^{81} +(0.973372 + 1.32432i) q^{82} +(0.493931 + 0.756017i) q^{83} +(-0.490225 + 0.0270465i) q^{86} +(1.34457 + 1.04652i) q^{88} +(0.0301416 - 1.09348i) q^{89} +(0.660209 - 1.50512i) q^{96} +(-0.975796 - 0.218681i) q^{97} +(0.975796 + 0.218681i) q^{98} +(-1.44935 + 2.51035i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2888\mathbb{Z}\right)^\times$.

$n$	$1445$	$2167$	$2529$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{43}{57}\right)$

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 $

$2$	0.716783	−	0.697297i	0.716783	−	0.697297i
$2$	0.716783	−	0.697297i	0.716783	−	0.697297i
$3$	−1.48636	+	0.701431i	−1.48636	+	0.701431i	−0.986361	−	0.164595i	$-0.947368\pi$
$3$	−1.48636	+	0.701431i	−1.48636	+	0.701431i	−0.500000	+	0.866025i	$0.666667\pi$
$4$	0.0275543	−	0.999620i	0.0275543	−	0.999620i
$5$		0			0		−0.998482	−	0.0550878i	$-0.982456\pi$
$5$		0			0		0.998482	+	0.0550878i	$0.0175439\pi$
$6$	−0.576292	+	1.53921i	−0.576292	+	1.53921i
$7$		0			0		−0.879474	−	0.475947i	$-0.842105\pi$
$7$		0			0		0.879474	+	0.475947i	$0.157895\pi$
$8$	−0.677282	−	0.735724i	−0.677282	−	0.735724i
$9$	1.08154	−	1.31324i	1.08154	−	1.31324i
$10$		0			0
$11$	−1.68060	+	0.280443i	−1.68060	+	0.280443i	−0.926494	−	0.376309i	$-0.877193\pi$
$11$	−1.68060	+	0.280443i	−1.68060	+	0.280443i	−0.754107	+	0.656752i	$0.771930\pi$
$12$	0.660209	+	1.50512i	0.660209	+	1.50512i
$13$		0			0		−0.821778	−	0.569808i	$-0.807018\pi$
$13$		0			0		0.821778	+	0.569808i	$0.192982\pi$
$14$		0			0
$15$		0			0
$16$	−0.998482	−	0.0550878i	−0.998482	−	0.0550878i
$17$	0.0301416	+	1.09348i	0.0301416	+	1.09348i	0.851919	+	0.523673i	$0.175439\pi$
$17$	0.0301416	+	1.09348i	0.0301416	+	1.09348i	−0.821778	+	0.569808i	$0.807018\pi$
$18$	−0.140490	−	1.69546i	−0.140490	−	1.69546i
$19$	0.716783	+	0.697297i	0.716783	+	0.697297i
$19$	0.716783	+	0.697297i	0.716783	+	0.697297i
$20$		0			0
$21$		0			0
$22$	−1.00907	+	1.37289i	−1.00907	+	1.37289i
$23$		0			0		−0.904357	−	0.426776i	$-0.859649\pi$
$23$		0			0		0.904357	+	0.426776i	$0.140351\pi$
$24$	1.52274	+	0.618485i	1.52274	+	0.618485i
$25$	0.993931	+	0.110008i	0.993931	+	0.110008i
$26$		0			0
$27$	−0.282943	+	1.11732i	−0.282943	+	1.11732i
$28$		0			0
$29$		0			0		0.851919	−	0.523673i	$-0.175439\pi$
$29$		0			0		−0.851919	+	0.523673i	$0.824561\pi$
$30$		0			0
$31$		0			0		0.245485	−	0.969400i	$-0.421053\pi$
$31$		0			0		−0.245485	+	0.969400i	$0.578947\pi$
$32$	−0.754107	+	0.656752i	−0.754107	+	0.656752i
$33$	2.30127	−	1.59566i	2.30127	−	1.59566i
$34$	0.784086	+	0.762770i	0.784086	+	0.762770i
$35$		0			0
$36$	−1.28294	−	1.11732i	−1.28294	−	1.11732i
$37$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$37$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$38$	1.00000			1.00000
$39$		0			0
$40$		0			0
$41$	−0.225748	+	1.62798i	−0.225748	+	1.62798i	0.451533	+	0.892254i	$0.350877\pi$
$41$	−0.225748	+	1.62798i	−0.225748	+	1.62798i	−0.677282	+	0.735724i	$0.736842\pi$
$42$		0			0
$43$	−0.370244	−	0.322446i	−0.370244	−	0.322446i	0.451533	−	0.892254i	$-0.350877\pi$
$43$	−0.370244	−	0.322446i	−0.370244	−	0.322446i	−0.821778	+	0.569808i	$0.807018\pi$
$44$	0.234028	+	1.68769i	0.234028	+	1.68769i
$45$		0			0
$46$		0			0
$47$		0			0		0.350638	−	0.936511i	$-0.385965\pi$
$47$		0			0		−0.350638	+	0.936511i	$0.614035\pi$
$48$	1.52274	−	0.618485i	1.52274	−	0.618485i
$49$	0.546948	+	0.837166i	0.546948	+	0.837166i
$50$	0.789141	−	0.614213i	0.789141	−	0.614213i
$51$	−0.811803	−	1.60417i	−0.811803	−	1.60417i
$52$		0			0
$53$		0			0		0.350638	−	0.936511i	$-0.385965\pi$
$53$		0			0		−0.350638	+	0.936511i	$0.614035\pi$
$54$	0.576292	+	0.998168i	0.576292	+	0.998168i
$55$		0			0
$56$		0			0
$57$	−1.55450	−	0.533662i	−1.55450	−	0.533662i
$58$		0			0
$59$	−0.264342	+	1.90630i	−0.264342	+	1.90630i	0.137354	+	0.990522i	$0.456140\pi$
$59$	−0.264342	+	1.90630i	−0.264342	+	1.90630i	−0.401695	+	0.915773i	$0.631579\pi$
$60$		0			0
$61$		0			0		−0.298515	−	0.954405i	$-0.596491\pi$
$61$		0			0		0.298515	+	0.954405i	$0.403509\pi$
$62$		0			0
$63$		0			0
$64$	−0.0825793	+	0.996584i	−0.0825793	+	0.996584i
$65$		0			0
$66$	0.536858	−	2.74841i	0.536858	−	2.74841i
$67$	1.24067	−	0.278042i	1.24067	−	0.278042i	0.451533	−	0.892254i	$-0.350877\pi$
$67$	1.24067	−	0.278042i	1.24067	−	0.278042i	0.789141	+	0.614213i	$0.210526\pi$
$68$	1.09390			1.09390
$69$		0			0
$70$		0			0
$71$		0			0		0.298515	−	0.954405i	$-0.403509\pi$
$71$		0			0		−0.298515	+	0.954405i	$0.596491\pi$
$72$	−1.69869	+	0.0937194i	−1.69869	+	0.0937194i
$73$	0.00756937	+	0.274603i	0.00756937	+	0.274603i	0.993931	+	0.110008i	$0.0350877\pi$
$73$	0.00756937	+	0.274603i	0.00756937	+	0.274603i	−0.986361	+	0.164595i	$0.947368\pi$
$74$		0			0
$75$	−1.55450	+	0.533662i	−1.55450	+	0.533662i
$76$	0.716783	−	0.697297i	0.716783	−	0.697297i
$77$		0			0
$78$		0			0
$79$		0			0		−0.754107	−	0.656752i	$-0.771930\pi$
$79$		0			0		0.754107	+	0.656752i	$0.228070\pi$
$80$		0			0
$81$	−0.0370120	−	0.189481i	−0.0370120	−	0.189481i
$82$	0.973372	+	1.32432i	0.973372	+	1.32432i
$83$	0.493931	+	0.756017i	0.493931	+	0.756017i	0.993931	−	0.110008i	$-0.0350877\pi$
$83$	0.493931	+	0.756017i	0.493931	+	0.756017i	−0.500000	+	0.866025i	$0.666667\pi$
$84$		0			0
$85$		0			0
$86$	−0.490225	+	0.0270465i	−0.490225	+	0.0270465i
$87$		0			0
$88$	1.34457	+	1.04652i	1.34457	+	1.04652i
$89$	0.0301416	−	1.09348i	0.0301416	−	1.09348i	−0.821778	−	0.569808i	$-0.807018\pi$
$89$	0.0301416	−	1.09348i	0.0301416	−	1.09348i	0.851919	−	0.523673i	$-0.175439\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.660209	−	1.50512i	0.660209	−	1.50512i
$97$	−0.975796	−	0.218681i	−0.975796	−	0.218681i	−0.298515	−	0.954405i	$-0.596491\pi$
$97$	−0.975796	−	0.218681i	−0.975796	−	0.218681i	−0.677282	+	0.735724i	$0.736842\pi$
$98$	0.975796	+	0.218681i	0.975796	+	0.218681i
$99$	−1.44935	+	2.51035i	−1.44935	+	2.51035i
$100$	0.137354	−	0.990522i	0.137354	−	0.990522i
$101$		0			0		0.635724	−	0.771917i	$-0.280702\pi$
$101$		0			0		−0.635724	+	0.771917i	$0.719298\pi$
$102$	−1.70047	−	0.583771i	−1.70047	−	0.583771i
$103$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$103$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.387445	+	1.52999i	0.387445	+	1.52999i	0.789141	+	0.614213i	$0.210526\pi$
$107$	0.387445	+	1.52999i	0.387445	+	1.52999i	−0.401695	+	0.915773i	$0.631579\pi$
$108$	1.10910	+	0.313622i	1.10910	+	0.313622i
$109$		0			0		−0.350638	−	0.936511i	$-0.614035\pi$
$109$		0			0		0.350638	+	0.936511i	$0.385965\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.26078	+	0.682302i	−1.26078	+	0.682302i	−0.962268	−	0.272103i	$-0.912281\pi$
$113$	−1.26078	+	0.682302i	−1.26078	+	0.682302i	−0.298515	+	0.954405i	$0.596491\pi$
$114$	−1.48636	+	0.701431i	−1.48636	+	0.701431i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	1.13978	+	1.55072i	1.13978	+	1.55072i
$119$		0			0
$120$		0			0
$121$	1.79995	−	0.617925i	1.79995	−	0.617925i
$122$		0			0
$123$	−0.806371	−	2.57811i	−0.806371	−	2.57811i
$124$		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	$0.666667\pi$
$128$	0.635724	+	0.771917i	0.635724	+	0.771917i
$129$	0.776491	+	0.219571i	0.776491	+	0.219571i
$130$		0			0
$131$	1.92161	−	0.543381i	1.92161	−	0.543381i	0.945817	−	0.324699i	$-0.105263\pi$
$131$	1.92161	−	0.543381i	1.92161	−	0.543381i	0.975796	−	0.218681i	$-0.0701754\pi$
$132$	−1.53165	−	2.34436i	−1.53165	−	2.34436i
$133$		0			0
$134$	0.695416	−	1.06441i	0.695416	−	1.06441i
$135$		0			0
$136$	0.784086	−	0.762770i	0.784086	−	0.762770i
$137$	−0.374141	+	0.0838470i	−0.374141	+	0.0838470i	−0.401695	−	0.915773i	$-0.631579\pi$
$137$	−0.374141	+	0.0838470i	−0.374141	+	0.0838470i	0.0275543	+	0.999620i	$0.491228\pi$
$138$		0			0
$139$	−0.381094	+	1.95099i	−0.381094	+	1.95099i	−0.0825793	+	0.996584i	$0.526316\pi$
$139$	−0.381094	+	1.95099i	−0.381094	+	1.95099i	−0.298515	+	0.954405i	$0.596491\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−1.15224	+	1.25167i	−1.15224	+	1.25167i
$145$		0			0
$146$	0.196905	+	0.191552i	0.196905	+	0.191552i
$147$	−1.40018	−	0.860686i	−1.40018	−	0.860686i
$148$		0			0
$149$		0			0		−0.926494	−	0.376309i	$-0.877193\pi$
$149$		0			0		0.926494	+	0.376309i	$0.122807\pi$
$150$	−0.742120	+	1.46647i	−0.742120	+	1.46647i
$151$		0			0		0.789141	−	0.614213i	$-0.210526\pi$
$151$		0			0		−0.789141	+	0.614213i	$0.789474\pi$
$152$	0.0275543	−	0.999620i	0.0275543	−	0.999620i
$153$	1.46861	+	1.14306i	1.46861	+	1.14306i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.904357	−	0.426776i	$-0.140351\pi$
$157$		0			0		−0.904357	+	0.426776i	$0.859649\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.158654	−	0.110008i	−0.158654	−	0.110008i
$163$	−0.290770	−	1.14823i	−0.290770	−	1.14823i	−0.926494	−	0.376309i	$-0.877193\pi$
$163$	−0.290770	−	1.14823i	−0.290770	−	1.14823i	0.635724	−	0.771917i	$-0.280702\pi$
$164$	1.62114	+	0.270520i	1.62114	+	0.270520i
$165$		0			0
$166$	0.881209	+	0.197484i	0.881209	+	0.197484i
$167$		0			0		0.851919	−	0.523673i	$-0.175439\pi$
$167$		0			0		−0.851919	+	0.523673i	$0.824561\pi$
$168$		0			0
$169$	0.350638	+	0.936511i	0.350638	+	0.936511i
$170$		0			0
$171$	1.69095	−	0.187154i	1.69095	−	0.187154i
$172$	−0.332526	+	0.361219i	−0.332526	+	0.361219i
$173$		0			0		−0.926494	−	0.376309i	$-0.877193\pi$
$173$		0			0		0.926494	+	0.376309i	$0.122807\pi$
$174$		0			0
$175$		0			0
$176$	1.69350	−	0.187436i	1.69350	−	0.187436i
$177$	−0.944227	−	3.01886i	−0.944227	−	3.01886i
$178$	−0.740876	−	0.804806i	−0.740876	−	0.804806i
$179$	−1.82026	−	0.624896i	−1.82026	−	0.624896i	−0.998482	−	0.0550878i	$-0.982456\pi$
$179$	−1.82026	−	0.624896i	−1.82026	−	0.624896i	−0.821778	−	0.569808i	$-0.807018\pi$
$180$		0			0
$181$		0			0		−0.716783	−	0.697297i	$-0.754386\pi$
$181$		0			0		0.716783	+	0.697297i	$0.245614\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.357315	−	1.82925i	−0.357315	−	1.82925i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.677282	−	0.735724i	$-0.736842\pi$
$191$		0			0		0.677282	+	0.735724i	$0.263158\pi$
$192$	−0.576292	−	1.53921i	−0.576292	−	1.53921i
$193$	−1.25411	−	1.52278i	−1.25411	−	1.52278i	−0.754107	−	0.656752i	$-0.771930\pi$
$193$	−1.25411	−	1.52278i	−1.25411	−	1.52278i	−0.500000	−	0.866025i	$-0.666667\pi$
$194$	−0.851919	+	0.523673i	−0.851919	+	0.523673i
$195$		0			0
$196$	0.851919	−	0.523673i	0.851919	−	0.523673i
$197$		0			0		−0.986361	−	0.164595i	$-0.947368\pi$
$197$		0			0		0.986361	+	0.164595i	$0.0526316\pi$
$198$	0.711588	+	2.81000i	0.711588	+	2.81000i
$199$		0			0		−0.821778	−	0.569808i	$-0.807018\pi$
$199$		0			0		0.821778	+	0.569808i	$0.192982\pi$
$200$	−0.592235	−	0.805765i	−0.592235	−	0.805765i
$201$	−1.64906	+	1.28352i	−1.64906	+	1.28352i
$202$		0			0
$203$		0			0
$204$	−1.62593	+	0.767293i	−1.62593	+	0.767293i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.40018	−	0.970861i	−1.40018	−	0.970861i
$210$		0			0
$211$	−0.611630	+	1.20861i	−0.611630	+	1.20861i	0.350638	+	0.936511i	$0.385965\pi$
$211$	−0.611630	+	1.20861i	−0.611630	+	1.20861i	−0.962268	+	0.272103i	$0.912281\pi$
$212$		0			0
$213$		0			0
$214$	1.34457	+	0.826503i	1.34457	+	0.826503i
$215$		0			0
$216$	1.01367	−	0.548570i	1.01367	−	0.548570i
$217$		0			0
$218$		0			0
$219$	−0.203866	−	0.402850i	−0.203866	−	0.402850i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.716783	−	0.697297i	$-0.245614\pi$
$223$		0			0		−0.716783	+	0.697297i	$0.754386\pi$
$224$		0			0
$225$	1.21944	−	1.18629i	1.21944	−	1.18629i
$226$	−0.427940	+	1.36820i	−0.427940	+	1.36820i
$227$	1.06742	−	1.63381i	1.06742	−	1.63381i	0.350638	−	0.936511i	$-0.385965\pi$
$227$	1.06742	−	1.63381i	1.06742	−	1.63381i	0.716783	−	0.697297i	$-0.245614\pi$
$228$	−0.576292	+	1.53921i	−0.576292	+	1.53921i
$229$		0			0		−0.546948	−	0.837166i	$-0.684211\pi$
$229$		0			0		0.546948	+	0.837166i	$0.315789\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.635724	−	0.771917i	−0.635724	−	0.771917i	0.350638	−	0.936511i	$-0.385965\pi$
$233$	−0.635724	−	0.771917i	−0.635724	−	0.771917i	−0.986361	+	0.164595i	$0.947368\pi$
$234$		0			0
$235$		0			0
$236$	1.89829	+	0.316768i	1.89829	+	0.316768i
$237$		0			0
$238$		0			0
$239$		0			0		−0.879474	−	0.475947i	$-0.842105\pi$
$239$		0			0		0.879474	+	0.475947i	$0.157895\pi$
$240$		0			0
$241$	−1.67576	−	0.790812i	−1.67576	−	0.790812i	−0.998482	−	0.0550878i	$-0.982456\pi$
$241$	−1.67576	−	0.790812i	−1.67576	−	0.790812i	−0.677282	−	0.735724i	$-0.736842\pi$
$242$	0.859298	−	1.69802i	0.859298	−	1.69802i
$243$	−0.494680	−	0.673037i	−0.494680	−	0.673037i
$244$		0			0
$245$		0			0
$246$	−2.37570	−	1.28566i	−2.37570	−	1.28566i
$247$		0			0
$248$		0			0
$249$	−1.26445	−	0.777256i	−1.26445	−	0.777256i
$250$		0			0
$251$	1.08317	−	1.31522i	1.08317	−	1.31522i	0.137354	−	0.990522i	$-0.456140\pi$
$251$	1.08317	−	1.31522i	1.08317	−	1.31522i	0.945817	−	0.324699i	$-0.105263\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.993931	+	0.110008i	0.993931	+	0.110008i
$257$	0.174638	+	1.25940i	0.174638	+	1.25940i	0.851919	+	0.523673i	$0.175439\pi$
$257$	0.174638	+	1.25940i	0.174638	+	1.25940i	−0.677282	+	0.735724i	$0.736842\pi$
$258$	0.709681	−	0.384060i	0.709681	−	0.384060i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.998482	−	1.72942i	0.998482	−	1.72942i
$263$		0			0		−0.975796	−	0.218681i	$-0.929825\pi$
$263$		0			0		0.975796	+	0.218681i	$0.0701754\pi$
$264$	−2.73258	−	0.612384i	−2.73258	−	0.612384i
$265$		0			0
$266$		0			0
$267$	0.722200	+	1.64645i	0.722200	+	1.64645i
$268$	−0.243750	−	1.24786i	−0.243750	−	1.24786i
$269$		0			0		0.451533	−	0.892254i	$-0.350877\pi$
$269$		0			0		−0.451533	+	0.892254i	$0.649123\pi$
$270$		0			0
$271$		0			0		−0.0275543	−	0.999620i	$-0.508772\pi$
$271$		0			0		0.0275543	+	0.999620i	$0.491228\pi$
$272$	0.0301416	−	1.09348i	0.0301416	−	1.09348i
$273$		0			0
$274$	−0.209712	+	0.320987i	−0.209712	+	0.320987i
$275$	−1.70125	+	0.0938607i	−1.70125	+	0.0938607i
$276$		0			0
$277$		0			0		0.0825793	−	0.996584i	$-0.473684\pi$
$277$		0			0		−0.0825793	+	0.996584i	$0.526316\pi$
$278$	1.08726	+	1.66417i	1.08726	+	1.66417i
$279$		0			0
$280$		0			0
$281$	−0.593406	−	0.0656782i	−0.593406	−	0.0656782i	−0.191711	−	0.981451i	$-0.561404\pi$
$281$	−0.593406	−	0.0656782i	−0.593406	−	0.0656782i	−0.401695	+	0.915773i	$0.631579\pi$
$282$		0			0
$283$	0.821778	−	0.569808i	0.821778	−	0.569808i	−0.0825793	−	0.996584i	$-0.526316\pi$
$283$	0.821778	−	0.569808i	0.821778	−	0.569808i	0.904357	+	0.426776i	$0.140351\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.0468775	+	1.70063i	0.0468775	+	1.70063i
$289$	−0.196311	+	0.0108308i	−0.196311	+	0.0108308i
$290$		0			0
$291$	1.60378	−	0.359415i	1.60378	−	0.359415i
$292$	0.274707			0.274707
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	−1.60378	+	0.359415i	−1.60378	+	0.359415i
$295$		0			0
$296$		0			0
$297$	0.162171	−	1.95711i	0.162171	−	1.95711i
$298$		0			0
$299$		0			0
$300$	0.490626	+	1.56862i	0.490626	+	1.56862i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.677282	−	0.735724i	−0.677282	−	0.735724i
$305$		0			0
$306$	1.84972	−	0.204727i	1.84972	−	0.204727i
$307$	−0.904357	−	1.56639i	−0.904357	−	1.56639i	−0.821778	−	0.569808i	$-0.807018\pi$
$307$	−0.904357	−	1.56639i	−0.904357	−	1.56639i	−0.0825793	−	0.996584i	$-0.526316\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.789141	−	0.614213i	$-0.210526\pi$
$311$		0			0		−0.789141	+	0.614213i	$0.789474\pi$
$312$		0			0
$313$	1.39735	−	0.567555i	1.39735	−	0.567555i	0.451533	−	0.892254i	$-0.350877\pi$
$313$	1.39735	−	0.567555i	1.39735	−	0.567555i	0.945817	+	0.324699i	$0.105263\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.137354	−	0.990522i	$-0.543860\pi$
$317$		0			0		0.137354	+	0.990522i	$0.456140\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−1.64906	−	2.00235i	−1.64906	−	2.00235i
$322$		0			0
$323$	−0.740876	+	0.804806i	−0.740876	+	0.804806i
$324$	−0.190429	+	0.0317769i	−0.190429	+	0.0317769i
$325$		0			0
$326$	−1.00907	−	0.620275i	−1.00907	−	0.620275i
$327$		0			0
$328$	1.35064	−	0.936511i	1.35064	−	0.936511i
$329$		0			0
$330$		0			0
$331$	−0.783946	+	1.78722i	−0.783946	+	1.78722i	−0.191711	+	0.981451i	$0.561404\pi$
$331$	−0.783946	+	1.78722i	−0.783946	+	1.78722i	−0.592235	+	0.805765i	$0.701754\pi$
$332$	0.769340	−	0.472912i	0.769340	−	0.472912i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.84174	−	0.748051i	−1.84174	−	0.748051i	−0.962268	−	0.272103i	$-0.912281\pi$
$337$	−1.84174	−	0.748051i	−1.84174	−	0.748051i	−0.879474	−	0.475947i	$-0.842105\pi$
$338$	0.904357	+	0.426776i	0.904357	+	0.426776i
$339$	1.39539	−	1.89850i	1.39539	−	1.89850i
$340$		0			0
$341$		0			0
$342$	1.08154	−	1.31324i	1.08154	−	1.31324i
$343$		0			0
$344$	0.0135284	+	0.490785i	0.0135284	+	0.490785i
$345$		0			0
$346$		0			0
$347$	−1.63955	+	0.463620i	−1.63955	+	0.463620i	−0.962268	−	0.272103i	$-0.912281\pi$
$347$	−1.63955	+	0.463620i	−1.63955	+	0.463620i	−0.677282	+	0.735724i	$0.736842\pi$
$348$		0			0
$349$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$349$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$350$		0			0
$351$		0			0
$352$	1.08317	−	1.31522i	1.08317	−	1.31522i
$353$	0.802220	+	0.871443i	0.802220	+	0.871443i	0.993931	−	0.110008i	$-0.0350877\pi$
$353$	0.802220	+	0.871443i	0.802220	+	0.871443i	−0.191711	+	0.981451i	$0.561404\pi$
$354$	−2.78185	−	1.50546i	−2.78185	−	1.50546i
$355$		0			0
$356$	−1.09224	−	0.0602603i	−1.09224	−	0.0602603i
$357$		0			0
$358$	−1.74047	+	0.821347i	−1.74047	+	0.821347i
$359$		0			0		0.716783	−	0.697297i	$-0.245614\pi$
$359$		0			0		−0.716783	+	0.697297i	$0.754386\pi$
$360$		0			0
$361$	0.0275543	+	0.999620i	0.0275543	+	0.999620i
$362$		0			0
$363$	−2.24195	+	2.18100i	−2.24195	+	2.18100i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.350638	−	0.936511i	$-0.385965\pi$
$367$		0			0		−0.350638	+	0.936511i	$0.614035\pi$
$368$		0			0
$369$	1.89377	+	2.05719i	1.89377	+	2.05719i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$373$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$374$	−1.53165	−	1.06202i	−1.53165	−	1.06202i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.162906	+	1.96598i	0.162906	+	1.96598i	0.245485	+	0.969400i	$0.421053\pi$
$379$	0.162906	+	1.96598i	0.162906	+	1.96598i	−0.0825793	+	0.996584i	$0.526316\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.592235	−	0.805765i	$-0.298246\pi$
$383$		0			0		−0.592235	+	0.805765i	$0.701754\pi$
$384$	−1.48636	−	0.701431i	−1.48636	−	0.701431i
$385$		0			0
$386$	−1.96075	−	0.217016i	−1.96075	−	0.217016i
$387$	−0.823885	+	0.137482i	−0.823885	+	0.137482i
$388$	−0.245485	+	0.969400i	−0.245485	+	0.969400i
$389$		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
$392$	0.245485	−	0.969400i	0.245485	−	0.969400i
$393$	−2.47507	+	2.15554i	−2.47507	+	2.15554i
$394$		0			0
$395$		0			0
$396$	2.46946	+	1.51797i	2.46946	+	1.51797i
$397$		0			0		−0.754107	−	0.656752i	$-0.771930\pi$
$397$		0			0		0.754107	+	0.656752i	$0.228070\pi$
$398$		0			0
$399$		0			0
$400$	−0.986361	−	0.164595i	−0.986361	−	0.164595i
$401$	−0.243750	−	0.295969i	−0.243750	−	0.295969i	0.635724	−	0.771917i	$-0.280702\pi$
$401$	−0.243750	−	0.295969i	−0.243750	−	0.295969i	−0.879474	+	0.475947i	$0.842105\pi$
$402$	−0.287027	+	2.06989i	−0.287027	+	2.06989i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.630404	+	1.68373i	−0.630404	+	1.68373i
$409$	0.553144	−	0.224668i	0.553144	−	0.224668i	−0.0825793	−	0.996584i	$-0.526316\pi$
$409$	0.553144	−	0.224668i	0.553144	−	0.224668i	0.635724	+	0.771917i	$0.280702\pi$
$410$		0			0
$411$	0.497296	−	0.387061i	0.497296	−	0.387061i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.802041	−	3.16719i	−0.802041	−	3.16719i
$418$	−1.68060	+	0.280443i	−1.68060	+	0.280443i
$419$	−0.431796	+	1.70512i	−0.431796	+	1.70512i	0.245485	+	0.969400i	$0.421053\pi$
$419$	−0.431796	+	1.70512i	−0.431796	+	1.70512i	−0.677282	+	0.735724i	$0.736842\pi$
$420$		0			0
$421$		0			0		−0.350638	−	0.936511i	$-0.614035\pi$
$421$		0			0		0.350638	+	0.936511i	$0.385965\pi$
$422$	0.404357	+	1.29280i	0.404357	+	1.29280i
$423$		0			0
$424$		0			0
$425$	−0.0903332	+	1.09016i	−0.0903332	+	1.09016i
$426$		0			0
$427$		0			0
$428$	1.54008	−	0.345140i	1.54008	−	0.345140i
$429$		0			0
$430$		0			0
$431$		0			0		0.975796	−	0.218681i	$-0.0701754\pi$
$431$		0			0		−0.975796	+	0.218681i	$0.929825\pi$
$432$	0.344064	−	1.10003i	0.344064	−	1.10003i
$433$	0.164908	−	0.00909822i	0.164908	−	0.00909822i	0.0275543	−	0.999620i	$-0.491228\pi$
$433$	0.164908	−	0.00909822i	0.164908	−	0.00909822i	0.137354	+	0.990522i	$0.456140\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.427033	−	0.146601i	−0.427033	−	0.146601i
$439$		0			0		0.821778	−	0.569808i	$-0.192982\pi$
$439$		0			0		−0.821778	+	0.569808i	$0.807018\pi$
$440$		0			0
$441$	1.69095	+	0.187154i	1.69095	+	0.187154i
$442$		0			0
$443$	−0.849008	−	1.15512i	−0.849008	−	1.15512i	−0.986361	−	0.164595i	$-0.947368\pi$
$443$	−0.849008	−	1.15512i	−0.849008	−	1.15512i	0.137354	−	0.990522i	$-0.456140\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	1.42733	+	1.11094i	1.42733	+	1.11094i	0.975796	+	0.218681i	$0.0701754\pi$
$449$	1.42733	+	1.11094i	1.42733	+	1.11094i	0.451533	+	0.892254i	$0.350877\pi$
$450$	0.0468775	−	1.70063i	0.0468775	−	1.70063i
$451$	−0.0771619	−	2.79929i	−0.0771619	−	2.79929i
$452$	0.647302	+	1.27910i	0.647302	+	1.27910i
$453$		0			0
$454$	−0.374141	−	1.91539i	−0.374141	−	1.91539i
$455$		0			0
$456$	0.660209	+	1.50512i	0.660209	+	1.50512i
$457$	0.239824	−	0.546744i	0.239824	−	0.546744i	−0.754107	−	0.656752i	$-0.771930\pi$
$457$	0.239824	−	0.546744i	0.239824	−	0.546744i	0.993931	+	0.110008i	$0.0350877\pi$
$458$		0			0
$459$	−1.23029	−	0.275715i	−1.23029	−	0.275715i
$460$		0			0
$461$		0			0		0.137354	−	0.990522i	$-0.456140\pi$
$461$		0			0		−0.137354	+	0.990522i	$0.543860\pi$
$462$		0			0
$463$		0			0		−0.945817	−	0.324699i	$-0.894737\pi$
$463$		0			0		0.945817	+	0.324699i	$0.105263\pi$
$464$		0			0
$465$		0			0
$466$	−0.993931	−	0.110008i	−0.993931	−	0.110008i
$467$	−0.110349	−	0.251569i	−0.110349	−	0.251569i	0.851919	−	0.523673i	$-0.175439\pi$
$467$	−0.110349	−	0.251569i	−0.110349	−	0.251569i	−0.962268	+	0.272103i	$0.912281\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	1.58154	−	1.09662i	1.58154	−	1.09662i
$473$	0.712661	+	0.438071i	0.712661	+	0.438071i
$474$		0			0
$475$	0.635724	+	0.771917i	0.635724	+	0.771917i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.592235	−	0.805765i	$-0.701754\pi$
$479$		0			0		0.592235	+	0.805765i	$0.298246\pi$
$480$		0			0
$481$		0			0
$482$	−1.75259	+	0.601664i	−1.75259	+	0.601664i
$483$		0			0
$484$	−0.568094	−	1.81630i	−0.568094	−	1.81630i
$485$		0			0
$486$	−0.823885	−	0.137482i	−0.823885	−	0.137482i
$487$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$487$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$488$		0			0
$489$	1.23759	+	1.50272i	1.23759	+	1.50272i
$490$		0			0
$491$	1.88015	−	0.208095i	1.88015	−	0.208095i	0.904357	−	0.426776i	$-0.140351\pi$
$491$	1.88015	−	0.208095i	1.88015	−	0.208095i	0.975796	+	0.218681i	$0.0701754\pi$
$492$	−2.59935	+	0.735026i	−2.59935	+	0.735026i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.44832	+	0.324575i	−1.44832	+	0.324575i
$499$	1.39887	−	1.36084i	1.39887	−	1.36084i	0.546948	−	0.837166i	$-0.315789\pi$
$499$	1.39887	−	1.36084i	1.39887	−	1.36084i	0.851919	−	0.523673i	$-0.175439\pi$
$500$		0			0
$501$		0			0
$502$	−0.140702	−	1.69802i	−0.140702	−	1.69802i
$503$		0			0		−0.451533	−	0.892254i	$-0.649123\pi$
$503$		0			0		0.451533	+	0.892254i	$0.350877\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.17807	−	1.14605i	−1.17807	−	1.14605i
$508$		0			0
$509$		0			0		−0.137354	−	0.990522i	$-0.543860\pi$
$509$		0			0		0.137354	+	0.990522i	$0.456140\pi$
$510$		0			0
$511$		0			0
$512$	0.789141	−	0.614213i	0.789141	−	0.614213i
$513$	−0.981909	+	0.603577i	−0.981909	+	0.603577i
$514$	1.00335	+	0.780939i	1.00335	+	0.780939i
$515$		0			0
$516$	0.240883	−	0.770146i	0.240883	−	0.770146i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.34457	−	1.04652i	1.34457	−	1.04652i	0.350638	−	0.936511i	$-0.385965\pi$
$521$	1.34457	−	1.04652i	1.34457	−	1.04652i	0.993931	−	0.110008i	$-0.0350877\pi$
$522$		0			0
$523$	−0.898940	−	0.623311i	−0.898940	−	0.623311i	0.0275543	−	0.999620i	$-0.491228\pi$
$523$	−0.898940	−	0.623311i	−0.898940	−	0.623311i	−0.926494	+	0.376309i	$0.877193\pi$
$524$	−0.490225	−	1.93586i	−0.490225	−	1.93586i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−2.38568	+	1.46647i	−2.38568	+	1.46647i
$529$	0.635724	+	0.771917i	0.635724	+	0.771917i
$530$		0			0
$531$	2.21753	+	2.40888i	2.21753	+	2.40888i
$532$		0			0
$533$		0			0
$534$	1.66572	+	0.676559i	1.66572	+	0.676559i
$535$		0			0
$536$	−1.04485	−	0.724481i	−1.04485	−	0.724481i
$537$	3.14388	−	0.347965i	3.14388	−	0.347965i
$538$		0			0
$539$	−1.15398	−	1.25355i	−1.15398	−	1.25355i
$540$		0			0
$541$		0			0		−0.716783	−	0.697297i	$-0.754386\pi$
$541$		0			0		0.716783	+	0.697297i	$0.245614\pi$
$542$		0			0
$543$		0			0
$544$	−0.740876	−	0.804806i	−0.740876	−	0.804806i
$545$		0			0
$546$		0			0
$547$	1.62114	+	1.12407i	1.62114	+	1.12407i	0.904357	+	0.426776i	$0.140351\pi$
$547$	1.62114	+	1.12407i	1.62114	+	1.12407i	0.716783	+	0.697297i	$0.245614\pi$
$548$	0.0735059	+	0.376309i	0.0735059	+	0.376309i
$549$		0			0
$550$	−1.15398	+	1.25355i	−1.15398	+	1.25355i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.93975	+	0.434708i	1.93975	+	0.434708i
$557$		0			0		0.851919	−	0.523673i	$-0.175439\pi$
$557$		0			0		−0.851919	+	0.523673i	$0.824561\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	1.81419	+	2.46830i	1.81419	+	2.46830i
$562$	−0.471140	+	0.366703i	−0.471140	+	0.366703i
$563$	0.153019	+	1.84666i	0.153019	+	1.84666i	0.451533	+	0.892254i	$0.350877\pi$
$563$	0.153019	+	1.84666i	0.153019	+	1.84666i	−0.298515	+	0.954405i	$0.596491\pi$
$564$		0			0
$565$		0			0
$566$	0.191711	−	0.981451i	0.191711	−	0.981451i
$567$		0			0
$568$		0			0
$569$	1.49277	+	1.16187i	1.49277	+	1.16187i	0.945817	+	0.324699i	$0.105263\pi$
$569$	1.49277	+	1.16187i	1.49277	+	1.16187i	0.546948	+	0.837166i	$0.315789\pi$
$570$		0			0
$571$	0.216783	−	0.168729i	0.216783	−	0.168729i	−0.500000	−	0.866025i	$-0.666667\pi$
$571$	0.216783	−	0.168729i	0.216783	−	0.168729i	0.716783	+	0.697297i	$0.245614\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	1.21944	+	1.18629i	1.21944	+	1.18629i
$577$	−1.59072	+	0.860853i	−1.59072	+	0.860853i	−0.592235	+	0.805765i	$0.701754\pi$
$577$	−1.59072	+	0.860853i	−1.59072	+	0.860853i	−0.998482	+	0.0550878i	$0.982456\pi$
$578$	−0.133160	+	0.144650i	−0.133160	+	0.144650i
$579$	2.93218	+	1.38373i	2.93218	+	1.38373i
$580$		0			0
$581$		0			0
$582$	0.898940	−	1.37593i	0.898940	−	1.37593i
$583$		0			0
$584$	0.196905	−	0.191552i	0.196905	−	0.191552i
$585$		0			0
$586$		0			0
$587$	0.525072	−	1.67875i	0.525072	−	1.67875i	−0.191711	−	0.981451i	$-0.561404\pi$
$587$	0.525072	−	1.67875i	0.525072	−	1.67875i	0.716783	−	0.697297i	$-0.245614\pi$
$588$	−0.898940	+	1.37593i	−0.898940	+	1.37593i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.91286	−	0.540904i	−1.91286	−	0.540904i	−0.986361	−	0.164595i	$-0.947368\pi$
$593$	−1.91286	−	0.540904i	−1.91286	−	0.540904i	−0.926494	−	0.376309i	$-0.877193\pi$
$594$	−1.24845	−	1.51590i	−1.24845	−	1.51590i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.298515	−	0.954405i	$-0.596491\pi$
$599$		0			0		0.298515	+	0.954405i	$0.403509\pi$
$600$	1.44546	+	0.782246i	1.44546	+	0.782246i
$601$	−0.945817	+	0.324699i	−0.945817	+	0.324699i	−0.754107	−	0.656752i	$-0.771930\pi$
$601$	−0.945817	+	0.324699i	−0.945817	+	0.324699i	−0.191711	+	0.981451i	$0.561404\pi$
$602$		0			0
$603$	0.976704	−	1.93002i	0.976704	−	1.93002i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.879474	−	0.475947i	$-0.842105\pi$
$607$		0			0		0.879474	+	0.475947i	$0.157895\pi$
$608$	−0.998482	−	0.0550878i	−0.998482	−	0.0550878i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	1.18309	−	1.43655i	1.18309	−	1.43655i
$613$		0			0		−0.350638	−	0.936511i	$-0.614035\pi$
$613$		0			0		0.350638	+	0.936511i	$0.385965\pi$
$614$	−1.74047	−	0.492157i	−1.74047	−	0.492157i
$615$		0			0
$616$		0			0
$617$	0.897586	+	0.0993448i	0.897586	+	0.0993448i	0.546948	−	0.837166i	$-0.315789\pi$
$617$	0.897586	+	0.0993448i	0.897586	+	0.0993448i	0.350638	+	0.936511i	$0.385965\pi$
$618$		0			0
$619$	1.19130	−	0.644701i	1.19130	−	0.644701i	0.245485	−	0.969400i	$-0.421053\pi$
$619$	1.19130	−	0.644701i	1.19130	−	0.644701i	0.945817	+	0.324699i	$0.105263\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.975796	+	0.218681i	0.975796	+	0.218681i
$626$	0.605842	−	1.38118i	0.605842	−	1.38118i
$627$	2.76216	+	0.460923i	2.76216	+	0.460923i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.451533	−	0.892254i	$-0.649123\pi$
$631$		0			0		0.451533	+	0.892254i	$0.350877\pi$
$632$		0			0
$633$	0.0613442	−	2.22545i	0.0613442	−	2.22545i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.274830	−	1.40697i	−0.274830	−	1.40697i	−0.821778	−	0.569808i	$-0.807018\pi$
$641$	−0.274830	−	1.40697i	−0.274830	−	1.40697i	0.546948	−	0.837166i	$-0.315789\pi$
$642$	−2.57825	−	0.285361i	−2.57825	−	0.285361i
$643$	1.39735	+	1.21695i	1.39735	+	1.21695i	0.945817	+	0.324699i	$0.105263\pi$
$643$	1.39735	+	1.21695i	1.39735	+	1.21695i	0.451533	+	0.892254i	$0.350877\pi$
$644$		0			0
$645$		0			0
$646$	0.0301416	+	1.09348i	0.0301416	+	1.09348i
$647$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$647$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$648$	−0.114338	+	0.155563i	−0.114338	+	0.155563i
$649$	−0.0903534	−	3.27785i	−0.0903534	−	3.27785i
$650$		0			0
$651$		0			0
$652$	−1.15580	+	0.259021i	−1.15580	+	0.259021i
$653$		0			0		1.00000			$0$
$653$		0			0		−1.00000			$\pi$
$654$		0			0
$655$		0			0
$656$	0.315087	−	1.61307i	0.315087	−	1.61307i
$657$	0.368807	+	0.287054i	0.368807	+	0.287054i
$658$		0			0
$659$	1.62965	−	0.661908i	1.62965	−	0.661908i	0.635724	−	0.771917i	$-0.280702\pi$
$659$	1.62965	−	0.661908i	1.62965	−	0.661908i	0.993931	+	0.110008i	$0.0350877\pi$
$660$		0			0
$661$		0			0		−0.298515	−	0.954405i	$-0.596491\pi$
$661$		0			0		0.298515	+	0.954405i	$0.403509\pi$
$662$	0.684302	+	1.82769i	0.684302	+	1.82769i
$663$		0			0
$664$	0.221690	−	0.875433i	0.221690	−	0.875433i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.0903332	−	0.138265i	−0.0903332	−	0.138265i	0.789141	−	0.614213i	$-0.210526\pi$
$673$	−0.0903332	−	0.138265i	−0.0903332	−	0.138265i	−0.879474	+	0.475947i	$0.842105\pi$
$674$	−1.84174	+	0.748051i	−1.84174	+	0.748051i
$675$	−0.404139	+	1.07941i	−0.404139	+	1.07941i
$676$	0.945817	−	0.324699i	0.945817	−	0.324699i
$677$		0			0		0.677282	−	0.735724i	$-0.263158\pi$
$677$		0			0		−0.677282	+	0.735724i	$0.736842\pi$
$678$	−0.323625	−	2.33381i	−0.323625	−	2.33381i
$679$		0			0
$680$		0			0
$681$	−0.440569	+	3.17715i	−0.440569	+	3.17715i
$682$		0			0
$683$	0.162906	+	0.0271842i	0.162906	+	0.0271842i	0.245485	−	0.969400i	$-0.421053\pi$
$683$	0.162906	+	0.0271842i	0.162906	+	0.0271842i	−0.0825793	+	0.996584i	$0.526316\pi$
$684$	−0.140490	−	1.69546i	−0.140490	−	1.69546i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.351919	+	0.342352i	0.351919	+	0.342352i
$689$		0			0
$690$		0			0
$691$	−0.484275	+	1.91236i	−0.484275	+	1.91236i	−0.0825793	+	0.996584i	$0.526316\pi$
$691$	−0.484275	+	1.91236i	−0.484275	+	1.91236i	−0.401695	+	0.915773i	$0.631579\pi$
$692$		0			0
$693$		0			0
$694$	−0.851919	+	1.47557i	−0.851919	+	1.47557i
$695$		0			0
$696$		0			0
$697$	−1.78697	−	0.197782i	−1.78697	−	0.197782i
$698$		0			0
$699$	1.48636	+	0.701431i	1.48636	+	0.701431i
$700$		0			0
$701$		0			0		−0.998482	−	0.0550878i	$-0.982456\pi$
$701$		0			0		0.998482	+	0.0550878i	$0.0175439\pi$
$702$		0			0
$703$		0			0
$704$	−0.140702	−	1.69802i	−0.140702	−	1.69802i
$705$		0			0
$706$	1.18267	+	0.0652498i	1.18267	+	0.0652498i
$707$		0			0
$708$	−3.04373	+	0.860686i	−3.04373	+	0.860686i
$709$		0			0		−0.821778	−	0.569808i	$-0.807018\pi$
$709$		0			0		0.821778	+	0.569808i	$0.192982\pi$
$710$		0			0
$711$		0			0
$712$	−0.824914	+	0.718419i	−0.824914	+	0.718419i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.674815	+	1.80235i	−0.674815	+	1.80235i
$717$		0			0
$718$		0			0
$719$		0			0		0.904357	−	0.426776i	$-0.140351\pi$
$719$		0			0		−0.904357	+	0.426776i	$0.859649\pi$
$720$		0			0
$721$		0			0
$722$	0.716783	+	0.697297i	0.716783	+	0.697297i
$723$	3.04549			3.04549
$724$		0			0
$725$		0			0
$726$	−0.0861844	+	3.12661i	−0.0861844	+	3.12661i
$727$		0			0		−0.998482	−	0.0550878i	$-0.982456\pi$
$727$		0			0		0.998482	+	0.0550878i	$0.0175439\pi$
$728$		0			0
$729$	1.37716	+	0.745279i	1.37716	+	0.745279i
$730$		0			0
$731$	0.341429	−	0.414574i	0.341429	−	0.414574i
$732$		0			0
$733$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$733$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.00710	+	0.815215i	−2.00710	+	0.815215i
$738$	2.79189	+	0.154033i	2.79189	+	0.154033i
$739$	−0.0326373	−	1.18402i	−0.0326373	−	1.18402i	−0.821778	−	0.569808i	$-0.807018\pi$
$739$	−0.0326373	−	1.18402i	−0.0326373	−	1.18402i	0.789141	−	0.614213i	$-0.210526\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.998482	−	0.0550878i	$-0.982456\pi$
$743$		0			0		0.998482	+	0.0550878i	$0.0175439\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.52704	+	0.169013i	1.52704	+	0.169013i
$748$	−1.83840	+	0.306775i	−1.83840	+	0.306775i
$749$		0			0
$750$		0			0
$751$		0			0		0.851919	−	0.523673i	$-0.175439\pi$
$751$		0			0		−0.851919	+	0.523673i	$0.824561\pi$
$752$		0			0
$753$	−0.687446	+	2.71466i	−0.687446	+	2.71466i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.851919	−	0.523673i	$-0.824561\pi$
$757$		0			0		0.851919	+	0.523673i	$0.175439\pi$
$758$	1.48764	+	1.29559i	1.48764	+	1.29559i
$759$		0			0
$760$		0			0
$761$	−0.270960	−	0.0452153i	−0.270960	−	0.0452153i	0.0275543	−	0.999620i	$-0.491228\pi$
$761$	−0.270960	−	0.0452153i	−0.270960	−	0.0452153i	−0.298515	+	0.954405i	$0.596491\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−1.55450	+	0.533662i	−1.55450	+	0.533662i
$769$	−0.691711	+	1.84748i	−0.691711	+	1.84748i	−0.191711	+	0.981451i	$0.561404\pi$
$769$	−0.691711	+	1.84748i	−0.691711	+	1.84748i	−0.500000	+	0.866025i	$0.666667\pi$
$770$		0			0
$771$	−1.14295	−	1.74942i	−1.14295	−	1.74942i
$772$	−1.55676	+	1.21167i	−1.55676	+	1.21167i
$773$		0			0		−0.451533	−	0.892254i	$-0.649123\pi$
$773$		0			0		0.451533	+	0.892254i	$0.350877\pi$
$774$	−0.494680	+	0.673037i	−0.494680	+	0.673037i
$775$		0			0
$776$	0.500000	+	0.866025i	0.500000	+	0.866025i
$777$		0			0
$778$		0			0
$779$	−1.29700	+	1.00949i	−1.29700	+	1.00949i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$785$		0			0
$786$	−0.271035	+	3.27091i	−0.271035	+	3.27091i
$787$	1.00335	+	0.780939i	1.00335	+	0.780939i	0.975796	−	0.218681i	$-0.0701754\pi$
$787$	1.00335	+	0.780939i	1.00335	+	0.780939i	0.0275543	+	0.999620i	$0.491228\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	2.82854	−	0.633891i	2.82854	−	0.633891i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$797$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$798$		0			0
$799$		0			0
$800$	−0.821778	+	0.569808i	−0.821778	+	0.569808i
$801$	−1.40341	−	1.22223i	−1.40341	−	1.22223i
$802$	−0.381094	−	0.0421795i	−0.381094	−	0.0421795i
$803$	−0.0897314	−	0.459375i	−0.0897314	−	0.459375i
$804$	1.23759	+	1.68380i	1.23759	+	1.68380i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.898940	+	1.37593i	−0.898940	+	1.37593i	0.0275543	+	0.999620i	$0.491228\pi$
$809$	−0.898940	+	1.37593i	−0.898940	+	1.37593i	−0.926494	+	0.376309i	$0.877193\pi$
$810$		0			0
$811$	0.0434885	−	1.57768i	0.0434885	−	1.57768i	−0.592235	−	0.805765i	$-0.701754\pi$
$811$	0.0434885	−	1.57768i	0.0434885	−	1.57768i	0.635724	−	0.771917i	$-0.280702\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.722200	+	1.64645i	0.722200	+	1.64645i
$817$	−0.0405441	−	0.489294i	−0.0405441	−	0.489294i
$818$	0.239824	−	0.546744i	0.239824	−	0.546744i
$819$		0			0
$820$		0			0
$821$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$821$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$822$	0.0865567	−	0.624201i	0.0865567	−	0.624201i
$823$		0			0		0.635724	−	0.771917i	$-0.280702\pi$
$823$		0			0		−0.635724	+	0.771917i	$0.719298\pi$
$824$		0			0
$825$	2.46284	−	1.33282i	2.46284	−	1.33282i
$826$		0			0
$827$	−1.63358	−	0.180805i	−1.63358	−	0.180805i	−0.754107	−	0.656752i	$-0.771930\pi$
$827$	−1.63358	−	0.180805i	−1.63358	−	0.180805i	−0.879474	+	0.475947i	$0.842105\pi$
$828$		0			0
$829$		0			0		−0.245485	−	0.969400i	$-0.578947\pi$
$829$		0			0		0.245485	+	0.969400i	$0.421053\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.898940	+	0.623311i	−0.898940	+	0.623311i
$834$	−2.78336	−	1.71092i	−2.78336	−	1.71092i
$835$		0			0
$836$	−1.00907	+	1.37289i	−1.00907	+	1.37289i
$837$		0			0
$838$	0.879474	+	1.52329i	0.879474	+	1.52329i
$839$		0			0		0.962268	−	0.272103i	$-0.0877193\pi$
$839$		0			0		−0.962268	+	0.272103i	$0.912281\pi$
$840$		0			0
$841$	0.451533	−	0.892254i	0.451533	−	0.892254i
$842$		0			0
$843$	0.928084	−	0.318612i	0.928084	−	0.318612i
$844$	1.19130	+	0.644701i	1.19130	+	0.644701i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.821778	+	1.42336i	−0.821778	+	1.42336i
$850$	0.695416	+	0.844397i	0.695416	+	0.844397i
$851$		0			0
$852$		0			0
$853$		0			0		0.962268	−	0.272103i	$-0.0877193\pi$
$853$		0			0		−0.962268	+	0.272103i	$0.912281\pi$
$854$		0			0
$855$		0			0
$856$	0.863238	−	1.32128i	0.863238	−	1.32128i
$857$	−0.582579	+	1.86261i	−0.582579	+	1.86261i	−0.0825793	+	0.996584i	$0.526316\pi$
$857$	−0.582579	+	1.86261i	−0.582579	+	1.86261i	−0.500000	+	0.866025i	$0.666667\pi$
$858$		0			0
$859$	0.881209	−	0.197484i	0.881209	−	0.197484i	0.245485	−	0.969400i	$-0.421053\pi$
$859$	0.881209	−	0.197484i	0.881209	−	0.197484i	0.635724	+	0.771917i	$0.280702\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$863$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$864$	−0.520430	−	1.02840i	−0.520430	−	1.02840i
$865$		0			0
$866$	0.111859	−	0.121511i	0.111859	−	0.121511i
$867$	0.284191	−	0.153797i	0.284191	−	0.153797i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−1.34255	+	1.04494i	−1.34255	+	1.04494i
$874$		0			0
$875$		0			0
$876$	−0.408314	+	0.192688i	−0.408314	+	0.192688i
$877$		0			0		0.298515	−	0.954405i	$-0.403509\pi$
$877$		0			0		−0.298515	+	0.954405i	$0.596491\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.158927	+	1.91796i	0.158927	+	1.91796i	0.350638	+	0.936511i	$0.385965\pi$
$881$	0.158927	+	1.91796i	0.158927	+	1.91796i	−0.191711	+	0.981451i	$0.561404\pi$
$882$	1.34255	−	1.04494i	1.34255	−	1.04494i
$883$	1.18267	+	1.60908i	1.18267	+	1.60908i	0.635724	+	0.771917i	$0.280702\pi$
$883$	1.18267	+	1.60908i	1.18267	+	1.60908i	0.546948	+	0.837166i	$0.315789\pi$
$884$		0			0
$885$		0			0
$886$	−1.41401	−	0.235957i	−1.41401	−	0.235957i
$887$		0			0		0.851919	−	0.523673i	$-0.175439\pi$
$887$		0			0		−0.851919	+	0.523673i	$0.824561\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.115341	+	0.308062i	0.115341	+	0.308062i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	1.79774	−	0.198973i	1.79774	−	0.198973i
$899$		0			0
$900$	−1.15224	−	1.25167i	−1.15224	−	1.25167i
$901$		0			0
$902$	−2.00724	−	1.95268i	−2.00724	−	1.95268i
$903$		0			0
$904$	1.35589	+	0.465478i	1.35589	+	0.465478i
$905$		0			0
$906$		0			0
$907$	−1.17728	+	0.130301i	−1.17728	+	0.130301i	−0.677282	−	0.735724i	$-0.736842\pi$
$907$	−1.17728	+	0.130301i	−1.17728	+	0.130301i	−0.500000	+	0.866025i	$0.666667\pi$
$908$	−1.60378	−	1.11203i	−1.60378	−	1.11203i
$909$		0			0
$910$		0			0
$911$		0			0		0.677282	−	0.735724i	$-0.263158\pi$
$911$		0			0		−0.677282	+	0.735724i	$0.736842\pi$
$912$	1.52274	+	0.618485i	1.52274	+	0.618485i
$913$	−1.04212	−	1.13204i	−1.04212	−	1.13204i
$914$	−0.209341	−	0.559125i	−0.209341	−	0.559125i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−1.07411	+	0.660251i	−1.07411	+	0.660251i
$919$		0			0		−0.986361	−	0.164595i	$-0.947368\pi$
$919$		0			0		0.986361	+	0.164595i	$0.0526316\pi$
$920$		0			0
$921$	2.44292	+	1.69388i	2.44292	+	1.69388i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.346750	+	0.163635i	−0.346750	+	0.163635i	−0.592235	−	0.805765i	$-0.701754\pi$
$929$	−0.346750	+	0.163635i	−0.346750	+	0.163635i	0.245485	+	0.969400i	$0.421053\pi$
$930$		0			0
$931$	−0.191711	+	0.981451i	−0.191711	+	0.981451i
$932$	−0.789141	+	0.614213i	−0.789141	+	0.614213i
$933$		0			0
$934$	−0.254515	−	0.103375i	−0.254515	−	0.103375i
$935$		0			0
$936$		0			0
$937$	1.02755	+	0.999620i	1.02755	+	0.999620i	1.00000			$0$
$937$	1.02755	+	0.999620i	1.02755	+	0.999620i	0.0275543	+	0.999620i	$0.491228\pi$
$938$		0			0
$939$	−1.67887	+	1.82374i	−1.67887	+	1.82374i
$940$		0			0
$941$		0			0		−0.451533	−	0.892254i	$-0.649123\pi$
$941$		0			0		0.451533	+	0.892254i	$0.350877\pi$
$942$		0			0
$943$		0			0
$944$	0.368954	−	1.88884i	0.368954	−	1.88884i
$945$		0			0
$946$	0.816288	−	0.182934i	0.816288	−	0.182934i
$947$	0.351919	−	0.342352i	0.351919	−	0.342352i	−0.500000	−	0.866025i	$-0.666667\pi$
$947$	0.351919	−	0.342352i	0.351919	−	0.342352i	0.851919	+	0.523673i	$0.175439\pi$
$948$		0			0
$949$		0			0
$950$	0.993931	+	0.110008i	0.993931	+	0.110008i
$951$		0			0
$952$		0			0
$953$	−1.17728	+	0.130301i	−1.17728	+	0.130301i	−0.677282	−	0.735724i	$-0.736842\pi$
$953$	−1.17728	+	0.130301i	−1.17728	+	0.130301i	−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
$961$	−0.879474	−	0.475947i	−0.879474	−	0.475947i
$962$		0			0
$963$	2.42828	+	1.14593i	2.42828	+	1.14593i
$964$	−0.836686	+	1.65334i	−0.836686	+	1.65334i
$965$		0			0
$966$		0			0
$967$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$967$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$968$	−1.67370	−	0.905760i	−1.67370	−	0.905760i
$969$	0.536694	−	1.71591i	0.536694	−	1.71591i
$970$		0			0
$971$	−0.851919	−	0.523673i	−0.851919	−	0.523673i	0.0275543	−	0.999620i	$-0.491228\pi$
$971$	−0.851919	−	0.523673i	−0.851919	−	0.523673i	−0.879474	+	0.475947i	$0.842105\pi$
$972$	−0.686412	+	0.475947i	−0.686412	+	0.475947i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.154019	+	0.351127i	0.154019	+	0.351127i	0.975796	−	0.218681i	$-0.0701754\pi$
$977$	0.154019	+	0.351127i	0.154019	+	0.351127i	−0.821778	+	0.569808i	$0.807018\pi$
$978$	1.93493	+	0.214158i	1.93493	+	0.214158i
$979$	0.256003	+	1.84616i	0.256003	+	1.84616i
$980$		0			0
$981$		0			0
$982$	1.20256	−	1.46018i	1.20256	−	1.46018i
$983$		0			0		0.137354	−	0.990522i	$-0.456140\pi$
$983$		0			0		−0.137354	+	0.990522i	$0.543860\pi$
$984$	−1.35064	+	2.33937i	−1.35064	+	2.33937i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.451533	−	0.892254i	$-0.350877\pi$
$991$		0			0		−0.451533	+	0.892254i	$0.649123\pi$
$992$		0			0
$993$	−0.0883820	−	3.20633i	−0.0883820	−	3.20633i
$994$		0			0
$995$		0			0
$996$	−0.811803	+	1.24256i	−0.811803	+	1.24256i
$997$		0			0		0.998482	−	0.0550878i	$-0.0175439\pi$
$997$		0			0		−0.998482	+	0.0550878i	$0.982456\pi$
$998$	0.0537749	−	1.95085i	0.0537749	−	1.95085i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2888.1.bm.a.235.1	✓	36
8.3	odd	2	CM	2888.1.bm.a.235.1	✓	36
361.106	even	57	inner	2888.1.bm.a.467.1	yes	36
2888.467	odd	114	inner	2888.1.bm.a.467.1	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2888.1.bm.a.235.1	✓	36	1.1	even	1	trivial
2888.1.bm.a.235.1	✓	36	8.3	odd	2	CM
2888.1.bm.a.467.1	yes	36	361.106	even	57	inner
2888.1.bm.a.467.1	yes	36	2888.467	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)

\(f(q)\)	\(=\)	\(q+(0.716783 - 0.697297i) q^{2} +(-1.48636 + 0.701431i) q^{3} +(0.0275543 - 0.999620i) q^{4} +(-0.576292 + 1.53921i) q^{6} +(-0.677282 - 0.735724i) q^{8} +(1.08154 - 1.31324i) q^{9} +O(q^{10})\)	\(q+(0.716783 - 0.697297i) q^{2} +(-1.48636 + 0.701431i) q^{3} +(0.0275543 - 0.999620i) q^{4} +(-0.576292 + 1.53921i) q^{6} +(-0.677282 - 0.735724i) q^{8} +(1.08154 - 1.31324i) q^{9} +(-1.68060 + 0.280443i) q^{11} +(0.660209 + 1.50512i) q^{12} +(-0.998482 - 0.0550878i) q^{16} +(0.0301416 + 1.09348i) q^{17} +(-0.140490 - 1.69546i) q^{18} +(0.716783 + 0.697297i) q^{19} +(-1.00907 + 1.37289i) q^{22} +(1.52274 + 0.618485i) q^{24} +(0.993931 + 0.110008i) q^{25} +(-0.282943 + 1.11732i) q^{27} +(-0.754107 + 0.656752i) q^{32} +(2.30127 - 1.59566i) q^{33} +(0.784086 + 0.762770i) q^{34} +(-1.28294 - 1.11732i) q^{36} +1.00000 q^{38} +(-0.225748 + 1.62798i) q^{41} +(-0.370244 - 0.322446i) q^{43} +(0.234028 + 1.68769i) q^{44} +(1.52274 - 0.618485i) q^{48} +(0.546948 + 0.837166i) q^{49} +(0.789141 - 0.614213i) q^{50} +(-0.811803 - 1.60417i) q^{51} +(0.576292 + 0.998168i) q^{54} +(-1.55450 - 0.533662i) q^{57} +(-0.264342 + 1.90630i) q^{59} +(-0.0825793 + 0.996584i) q^{64} +(0.536858 - 2.74841i) q^{66} +(1.24067 - 0.278042i) q^{67} +1.09390 q^{68} +(-1.69869 + 0.0937194i) q^{72} +(0.00756937 + 0.274603i) q^{73} +(-1.55450 + 0.533662i) q^{75} +(0.716783 - 0.697297i) q^{76} +(-0.0370120 - 0.189481i) q^{81} +(0.973372 + 1.32432i) q^{82} +(0.493931 + 0.756017i) q^{83} +(-0.490225 + 0.0270465i) q^{86} +(1.34457 + 1.04652i) q^{88} +(0.0301416 - 1.09348i) q^{89} +(0.660209 - 1.50512i) q^{96} +(-0.975796 - 0.218681i) q^{97} +(0.975796 + 0.218681i) q^{98} +(-1.44935 + 2.51035i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + q^{2} - 20 q^{3} + q^{4} - q^{6} - 2 q^{8} - 19 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more