LMFDB - Embedded newform 880.2.bd.e.593.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(417,880)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("880.417"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 1, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.bd (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,4,0,-8,0,0,0,0,0,-4,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 25 $ x^4 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			593.1
Root			$-1.58114 + 1.58114i$ of defining polynomial
Character	$\chi$	$=$	880.593
Dual form			880.2.bd.e.417.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.00000i) q^{3} +(-2.00000 - 1.00000i) q^{5} -1.00000i q^{9} +(-1.00000 - 3.16228i) q^{11} +(-3.16228 + 3.16228i) q^{13} +(-1.00000 - 3.00000i) q^{15} +(-3.16228 - 3.16228i) q^{17} -6.32456 q^{19} +(1.00000 + 1.00000i) q^{23} +(3.00000 + 4.00000i) q^{25} +(4.00000 - 4.00000i) q^{27} -6.32456 q^{29} -2.00000 q^{31} +(2.16228 - 4.16228i) q^{33} +(3.00000 - 3.00000i) q^{37} -6.32456 q^{39} -6.32456i q^{41} +(-1.00000 + 2.00000i) q^{45} +(-3.00000 + 3.00000i) q^{47} -7.00000i q^{49} -6.32456i q^{51} +(-1.00000 - 1.00000i) q^{53} +(-1.16228 + 7.32456i) q^{55} +(-6.32456 - 6.32456i) q^{57} -6.00000i q^{59} +6.32456i q^{61} +(9.48683 - 3.16228i) q^{65} +(-3.00000 + 3.00000i) q^{67} +2.00000i q^{69} +8.00000 q^{71} +(3.16228 - 3.16228i) q^{73} +(-1.00000 + 7.00000i) q^{75} +6.32456 q^{79} +5.00000 q^{81} +(6.32456 - 6.32456i) q^{83} +(3.16228 + 9.48683i) q^{85} +(-6.32456 - 6.32456i) q^{87} +6.00000i q^{89} +(-2.00000 - 2.00000i) q^{93} +(12.6491 + 6.32456i) q^{95} +(-7.00000 + 7.00000i) q^{97} +(-3.16228 + 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 8 q^{5} - 4 q^{11} - 4 q^{15} + 4 q^{23} + 12 q^{25} + 16 q^{27} - 8 q^{31} - 4 q^{33} + 12 q^{37} - 4 q^{45} - 12 q^{47} - 4 q^{53} + 8 q^{55} - 12 q^{67} + 32 q^{71} - 4 q^{75} + 20 q^{81}+ \cdots - 28 q^{97}+O(q^{100}) $ 4 * q + 4 * q^3 - 8 * q^5 - 4 * q^11 - 4 * q^15 + 4 * q^23 + 12 * q^25 + 16 * q^27 - 8 * q^31 - 4 * q^33 + 12 * q^37 - 4 * q^45 - 12 * q^47 - 4 * q^53 + 8 * q^55 - 12 * q^67 + 32 * q^71 - 4 * q^75 + 20 * q^81 - 8 * q^93 - 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.00000	+	1.00000i	0.577350	+	0.577350i	0.934172	−	0.356822i	$-0.116140\pi$
$3$	1.00000	+	1.00000i	0.577350	+	0.577350i	−0.356822	+	0.934172i	$0.616140\pi$
$4$		0			0
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$		0			0
$7$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$7$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−1.00000	−	3.16228i	−0.301511	−	0.953463i
$11$	−1.00000	−	3.16228i	−0.301511	−	0.953463i
$12$		0			0
$13$	−3.16228	+	3.16228i	−0.877058	+	0.877058i	−0.993229	−	0.116171i	$-0.962938\pi$
$13$	−3.16228	+	3.16228i	−0.877058	+	0.877058i	0.116171	+	0.993229i	$0.462938\pi$
$14$		0			0
$15$	−1.00000	−	3.00000i	−0.258199	−	0.774597i
$16$		0			0
$17$	−3.16228	−	3.16228i	−0.766965	−	0.766965i	0.210606	−	0.977571i	$-0.432456\pi$
$17$	−3.16228	−	3.16228i	−0.766965	−	0.766965i	−0.977571	+	0.210606i	$0.932456\pi$
$18$		0			0
$19$	−6.32456			−1.45095			−0.725476	−	0.688247i	$-0.758380\pi$
$19$	−6.32456			−1.45095			−0.725476	+	0.688247i	$0.758380\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.00000	+	1.00000i	0.208514	+	0.208514i	0.803636	−	0.595121i	$-0.202896\pi$
$23$	1.00000	+	1.00000i	0.208514	+	0.208514i	−0.595121	+	0.803636i	$0.702896\pi$
$24$		0			0
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$		0			0
$27$	4.00000	−	4.00000i	0.769800	−	0.769800i
$28$		0			0
$29$	−6.32456			−1.17444			−0.587220	−	0.809427i	$-0.699778\pi$
$29$	−6.32456			−1.17444			−0.587220	+	0.809427i	$0.699778\pi$
$30$		0			0
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$		0			0
$33$	2.16228	−	4.16228i	0.376404	−	0.724560i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.00000	−	3.00000i	0.493197	−	0.493197i	−0.416115	−	0.909312i	$-0.636609\pi$
$37$	3.00000	−	3.00000i	0.493197	−	0.493197i	0.909312	+	0.416115i	$0.136609\pi$
$38$		0			0
$39$	−6.32456			−1.01274
$40$		0			0
$41$		−	6.32456i		−	0.987730i	−0.869539	−	0.493865i	$-0.835584\pi$
$41$		−	6.32456i		−	0.987730i	0.869539	−	0.493865i	$-0.164416\pi$
$42$		0			0
$43$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$43$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$44$		0			0
$45$	−1.00000	+	2.00000i	−0.149071	+	0.298142i
$46$		0			0
$47$	−3.00000	+	3.00000i	−0.437595	+	0.437595i	−0.891202	−	0.453607i	$-0.850137\pi$
$47$	−3.00000	+	3.00000i	−0.437595	+	0.437595i	0.453607	+	0.891202i	$0.350137\pi$
$48$		0			0
$49$		−	7.00000i		−	1.00000i
$50$		0			0
$51$		−	6.32456i		−	0.885615i
$52$		0			0
$53$	−1.00000	−	1.00000i	−0.137361	−	0.137361i	0.635083	−	0.772444i	$-0.280966\pi$
$53$	−1.00000	−	1.00000i	−0.137361	−	0.137361i	−0.772444	+	0.635083i	$0.780966\pi$
$54$		0			0
$55$	−1.16228	+	7.32456i	−0.156721	+	0.987643i
$56$		0			0
$57$	−6.32456	−	6.32456i	−0.837708	−	0.837708i
$58$		0			0
$59$		−	6.00000i		−	0.781133i	−0.920575	−	0.390567i	$-0.872279\pi$
$59$		−	6.00000i		−	0.781133i	0.920575	−	0.390567i	$-0.127721\pi$
$60$		0			0
$61$			6.32456i			0.809776i	0.914366	+	0.404888i	$0.132690\pi$
$61$			6.32456i			0.809776i	−0.914366	+	0.404888i	$0.867310\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	9.48683	−	3.16228i	1.17670	−	0.392232i
$66$		0			0
$67$	−3.00000	+	3.00000i	−0.366508	+	0.366508i	−0.866202	−	0.499694i	$-0.833446\pi$
$67$	−3.00000	+	3.00000i	−0.366508	+	0.366508i	0.499694	+	0.866202i	$0.333446\pi$
$68$		0			0
$69$			2.00000i			0.240772i
$70$		0			0
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$		0			0
$73$	3.16228	−	3.16228i	0.370117	−	0.370117i	−0.497403	−	0.867520i	$-0.665713\pi$
$73$	3.16228	−	3.16228i	0.370117	−	0.370117i	0.867520	+	0.497403i	$0.165713\pi$
$74$		0			0
$75$	−1.00000	+	7.00000i	−0.115470	+	0.808290i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	6.32456			0.711568			0.355784	−	0.934568i	$-0.384214\pi$
$79$	6.32456			0.711568			0.355784	+	0.934568i	$0.384214\pi$
$80$		0			0
$81$	5.00000			0.555556
$82$		0			0
$83$	6.32456	−	6.32456i	0.694210	−	0.694210i	−0.268945	−	0.963155i	$-0.586675\pi$
$83$	6.32456	−	6.32456i	0.694210	−	0.694210i	0.963155	+	0.268945i	$0.0866751\pi$
$84$		0			0
$85$	3.16228	+	9.48683i	0.342997	+	1.02899i
$86$		0			0
$87$	−6.32456	−	6.32456i	−0.678064	−	0.678064i
$88$		0			0
$89$			6.00000i			0.635999i	0.948091	+	0.317999i	$0.103011\pi$
$89$			6.00000i			0.635999i	−0.948091	+	0.317999i	$0.896989\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−2.00000	−	2.00000i	−0.207390	−	0.207390i
$94$		0			0
$95$	12.6491	+	6.32456i	1.29777	+	0.648886i
$96$		0			0
$97$	−7.00000	+	7.00000i	−0.710742	+	0.710742i	−0.966691	−	0.255948i	$-0.917612\pi$
$97$	−7.00000	+	7.00000i	−0.710742	+	0.710742i	0.255948	+	0.966691i	$0.417612\pi$
$98$		0			0
$99$	−3.16228	+	1.00000i	−0.317821	+	0.100504i
$100$		0			0
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$		0			0
$103$	−9.00000	−	9.00000i	−0.886796	−	0.886796i	0.107418	−	0.994214i	$-0.465742\pi$
$103$	−9.00000	−	9.00000i	−0.886796	−	0.886796i	−0.994214	+	0.107418i	$0.965742\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$107$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$108$		0			0
$109$	−12.6491			−1.21157			−0.605783	−	0.795630i	$-0.707140\pi$
$109$	−12.6491			−1.21157			−0.605783	+	0.795630i	$0.707140\pi$
$110$		0			0
$111$	6.00000			0.569495
$112$		0			0
$113$	9.00000	+	9.00000i	0.846649	+	0.846649i	0.989713	−	0.143065i	$-0.0456957\pi$
$113$	9.00000	+	9.00000i	0.846649	+	0.846649i	−0.143065	+	0.989713i	$0.545696\pi$
$114$		0			0
$115$	−1.00000	−	3.00000i	−0.0932505	−	0.279751i
$116$		0			0
$117$	3.16228	+	3.16228i	0.292353	+	0.292353i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−9.00000	+	6.32456i	−0.818182	+	0.574960i
$122$		0			0
$123$	6.32456	−	6.32456i	0.570266	−	0.570266i
$124$		0			0
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$	6.32456	+	6.32456i	0.561214	+	0.561214i	0.929652	−	0.368439i	$-0.120108\pi$
$127$	6.32456	+	6.32456i	0.561214	+	0.561214i	−0.368439	+	0.929652i	$0.620108\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$			12.6491i			1.10516i	0.833461	+	0.552579i	$0.186356\pi$
$131$			12.6491i			1.10516i	−0.833461	+	0.552579i	$0.813644\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−12.0000	+	4.00000i	−1.03280	+	0.344265i
$136$		0			0
$137$	13.0000	−	13.0000i	1.11066	−	1.11066i	0.117604	−	0.993061i	$-0.462479\pi$
$137$	13.0000	−	13.0000i	1.11066	−	1.11066i	0.993061	−	0.117604i	$-0.0375215\pi$
$138$		0			0
$139$	−12.6491			−1.07288			−0.536442	−	0.843937i	$-0.680232\pi$
$139$	−12.6491			−1.07288			−0.536442	+	0.843937i	$0.680232\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$		0			0
$143$	13.1623	+	6.83772i	1.10068	+	0.571799i
$144$		0			0
$145$	12.6491	+	6.32456i	1.05045	+	0.525226i
$146$		0			0
$147$	7.00000	−	7.00000i	0.577350	−	0.577350i
$148$		0			0
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$		0			0
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$		0			0
$153$	−3.16228	+	3.16228i	−0.255655	+	0.255655i
$154$		0			0
$155$	4.00000	+	2.00000i	0.321288	+	0.160644i
$156$		0			0
$157$	−7.00000	+	7.00000i	−0.558661	+	0.558661i	−0.928926	−	0.370265i	$-0.879267\pi$
$157$	−7.00000	+	7.00000i	−0.558661	+	0.558661i	0.370265	+	0.928926i	$0.379267\pi$
$158$		0			0
$159$		−	2.00000i		−	0.158610i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	1.00000	+	1.00000i	0.0783260	+	0.0783260i	0.745184	−	0.666858i	$-0.232361\pi$
$163$	1.00000	+	1.00000i	0.0783260	+	0.0783260i	−0.666858	+	0.745184i	$0.732361\pi$
$164$		0			0
$165$	−8.48683	+	6.16228i	−0.660699	+	0.479733i
$166$		0			0
$167$	−12.6491	−	12.6491i	−0.978818	−	0.978818i	0.0209627	−	0.999780i	$-0.493327\pi$
$167$	−12.6491	−	12.6491i	−0.978818	−	0.978818i	−0.999780	+	0.0209627i	$0.993327\pi$
$168$		0			0
$169$		−	7.00000i		−	0.538462i
$170$		0			0
$171$			6.32456i			0.483651i
$172$		0			0
$173$	3.16228	−	3.16228i	0.240424	−	0.240424i	−0.576602	−	0.817025i	$-0.695622\pi$
$173$	3.16228	−	3.16228i	0.240424	−	0.240424i	0.817025	+	0.576602i	$0.195622\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	6.00000	−	6.00000i	0.450988	−	0.450988i
$178$		0			0
$179$			4.00000i			0.298974i	0.988764	+	0.149487i	$0.0477622\pi$
$179$			4.00000i			0.298974i	−0.988764	+	0.149487i	$0.952238\pi$
$180$		0			0
$181$	−8.00000			−0.594635			−0.297318	−	0.954779i	$-0.596092\pi$
$181$	−8.00000			−0.594635			−0.297318	+	0.954779i	$0.596092\pi$
$182$		0			0
$183$	−6.32456	+	6.32456i	−0.467525	+	0.467525i
$184$		0			0
$185$	−9.00000	+	3.00000i	−0.661693	+	0.220564i
$186$		0			0
$187$	−6.83772	+	13.1623i	−0.500024	+	0.962521i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−22.0000			−1.59186			−0.795932	−	0.605386i	$-0.793019\pi$
$191$	−22.0000			−1.59186			−0.795932	+	0.605386i	$0.793019\pi$
$192$		0			0
$193$	15.8114	−	15.8114i	1.13813	−	1.13813i	0.149343	−	0.988785i	$-0.452284\pi$
$193$	15.8114	−	15.8114i	1.13813	−	1.13813i	0.988785	−	0.149343i	$-0.0477159\pi$
$194$		0			0
$195$	12.6491	+	6.32456i	0.905822	+	0.452911i
$196$		0			0
$197$	3.16228	+	3.16228i	0.225303	+	0.225303i	0.810727	−	0.585424i	$-0.199072\pi$
$197$	3.16228	+	3.16228i	0.225303	+	0.225303i	−0.585424	+	0.810727i	$0.699072\pi$
$198$		0			0
$199$		−	6.00000i		−	0.425329i	−0.977125	−	0.212664i	$-0.931786\pi$
$199$		−	6.00000i		−	0.425329i	0.977125	−	0.212664i	$-0.0682141\pi$
$200$		0			0
$201$	−6.00000			−0.423207
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−6.32456	+	12.6491i	−0.441726	+	0.883452i
$206$		0			0
$207$	1.00000	−	1.00000i	0.0695048	−	0.0695048i
$208$		0			0
$209$	6.32456	+	20.0000i	0.437479	+	1.38343i
$210$		0			0
$211$			25.2982i			1.74160i	0.491636	+	0.870801i	$0.336399\pi$
$211$			25.2982i			1.74160i	−0.491636	+	0.870801i	$0.663601\pi$
$212$		0			0
$213$	8.00000	+	8.00000i	0.548151	+	0.548151i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$	6.32456			0.427374
$220$		0			0
$221$	20.0000			1.34535
$222$		0			0
$223$	11.0000	+	11.0000i	0.736614	+	0.736614i	0.971921	−	0.235307i	$-0.0756095\pi$
$223$	11.0000	+	11.0000i	0.736614	+	0.736614i	−0.235307	+	0.971921i	$0.575609\pi$
$224$		0			0
$225$	4.00000	−	3.00000i	0.266667	−	0.200000i
$226$		0			0
$227$	6.32456	+	6.32456i	0.419775	+	0.419775i	0.885126	−	0.465351i	$-0.154072\pi$
$227$	6.32456	+	6.32456i	0.419775	+	0.419775i	−0.465351	+	0.885126i	$0.654072\pi$
$228$		0			0
$229$		−	4.00000i		−	0.264327i	−0.991228	−	0.132164i	$-0.957808\pi$
$229$		−	4.00000i		−	0.264327i	0.991228	−	0.132164i	$-0.0421925\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	9.48683	−	9.48683i	0.621503	−	0.621503i	−0.324413	−	0.945916i	$-0.605167\pi$
$233$	9.48683	−	9.48683i	0.621503	−	0.621503i	0.945916	+	0.324413i	$0.105167\pi$
$234$		0			0
$235$	9.00000	−	3.00000i	0.587095	−	0.195698i
$236$		0			0
$237$	6.32456	+	6.32456i	0.410824	+	0.410824i
$238$		0			0
$239$	18.9737			1.22730			0.613652	−	0.789576i	$-0.289700\pi$
$239$	18.9737			1.22730			0.613652	+	0.789576i	$0.289700\pi$
$240$		0			0
$241$		−	6.32456i		−	0.407400i	−0.979033	−	0.203700i	$-0.934703\pi$
$241$		−	6.32456i		−	0.407400i	0.979033	−	0.203700i	$-0.0652968\pi$
$242$		0			0
$243$	−7.00000	−	7.00000i	−0.449050	−	0.449050i
$244$		0			0
$245$	−7.00000	+	14.0000i	−0.447214	+	0.894427i
$246$		0			0
$247$	20.0000	−	20.0000i	1.27257	−	1.27257i
$248$		0			0
$249$	12.6491			0.801605
$250$		0			0
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	2.16228	−	4.16228i	0.135941	−	0.261680i
$254$		0			0
$255$	−6.32456	+	12.6491i	−0.396059	+	0.792118i
$256$		0			0
$257$	−7.00000	+	7.00000i	−0.436648	+	0.436648i	−0.890882	−	0.454234i	$-0.849913\pi$
$257$	−7.00000	+	7.00000i	−0.436648	+	0.436648i	0.454234	+	0.890882i	$0.349913\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$			6.32456i			0.391480i
$262$		0			0
$263$	18.9737	−	18.9737i	1.16997	−	1.16997i	0.187749	−	0.982217i	$-0.439881\pi$
$263$	18.9737	−	18.9737i	1.16997	−	1.16997i	0.982217	−	0.187749i	$-0.0601193\pi$
$264$		0			0
$265$	1.00000	+	3.00000i	0.0614295	+	0.184289i
$266$		0			0
$267$	−6.00000	+	6.00000i	−0.367194	+	0.367194i
$268$		0			0
$269$		−	24.0000i		−	1.46331i	−0.681677	−	0.731653i	$-0.738749\pi$
$269$		−	24.0000i		−	1.46331i	0.681677	−	0.731653i	$-0.261251\pi$
$270$		0			0
$271$		−	12.6491i		−	0.768379i	−0.923254	−	0.384189i	$-0.874481\pi$
$271$		−	12.6491i		−	0.768379i	0.923254	−	0.384189i	$-0.125519\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	9.64911	−	13.4868i	0.581863	−	0.813287i
$276$		0			0
$277$	9.48683	+	9.48683i	0.570009	+	0.570009i	0.932131	−	0.362122i	$-0.117948\pi$
$277$	9.48683	+	9.48683i	0.570009	+	0.570009i	−0.362122	+	0.932131i	$0.617948\pi$
$278$		0			0
$279$			2.00000i			0.119737i
$280$		0			0
$281$			18.9737i			1.13187i	0.824448	+	0.565937i	$0.191485\pi$
$281$			18.9737i			1.13187i	−0.824448	+	0.565937i	$0.808515\pi$
$282$		0			0
$283$	6.32456	−	6.32456i	0.375956	−	0.375956i	−0.493685	−	0.869641i	$-0.664350\pi$
$283$	6.32456	−	6.32456i	0.375956	−	0.375956i	0.869641	+	0.493685i	$0.164350\pi$
$284$		0			0
$285$	6.32456	+	18.9737i	0.374634	+	1.12390i
$286$		0			0
$287$		0			0
$288$		0			0
$289$			3.00000i			0.176471i
$290$		0			0
$291$	−14.0000			−0.820695
$292$		0			0
$293$	15.8114	−	15.8114i	0.923711	−	0.923711i	−0.0735783	−	0.997289i	$-0.523442\pi$
$293$	15.8114	−	15.8114i	0.923711	−	0.923711i	0.997289	+	0.0735783i	$0.0234419\pi$
$294$		0			0
$295$	−6.00000	+	12.0000i	−0.349334	+	0.698667i
$296$		0			0
$297$	−16.6491	−	8.64911i	−0.966079	−	0.501872i
$298$		0			0
$299$	−6.32456			−0.365758
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	6.32456	−	12.6491i	0.362143	−	0.724286i
$306$		0			0
$307$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$307$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$308$		0			0
$309$		−	18.0000i		−	1.02398i
$310$		0			0
$311$	8.00000			0.453638			0.226819	−	0.973937i	$-0.427167\pi$
$311$	8.00000			0.453638			0.226819	+	0.973937i	$0.427167\pi$
$312$		0			0
$313$	9.00000	+	9.00000i	0.508710	+	0.508710i	0.914130	−	0.405420i	$-0.132875\pi$
$313$	9.00000	+	9.00000i	0.508710	+	0.508710i	−0.405420	+	0.914130i	$0.632875\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−17.0000	+	17.0000i	−0.954815	+	0.954815i	−0.999022	−	0.0442073i	$-0.985924\pi$
$317$	−17.0000	+	17.0000i	−0.954815	+	0.954815i	0.0442073	+	0.999022i	$0.485924\pi$
$318$		0			0
$319$	6.32456	+	20.0000i	0.354107	+	1.11979i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	20.0000	+	20.0000i	1.11283	+	1.11283i
$324$		0			0
$325$	−22.1359	−	3.16228i	−1.22788	−	0.175412i
$326$		0			0
$327$	−12.6491	−	12.6491i	−0.699497	−	0.699497i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	18.0000			0.989369			0.494685	−	0.869072i	$-0.335284\pi$
$331$	18.0000			0.989369			0.494685	+	0.869072i	$0.335284\pi$
$332$		0			0
$333$	−3.00000	−	3.00000i	−0.164399	−	0.164399i
$334$		0			0
$335$	9.00000	−	3.00000i	0.491723	−	0.163908i
$336$		0			0
$337$	−9.48683	−	9.48683i	−0.516781	−	0.516781i	0.399815	−	0.916596i	$-0.369074\pi$
$337$	−9.48683	−	9.48683i	−0.516781	−	0.516781i	−0.916596	+	0.399815i	$0.869074\pi$
$338$		0			0
$339$			18.0000i			0.977626i
$340$		0			0
$341$	2.00000	+	6.32456i	0.108306	+	0.342494i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	2.00000	−	4.00000i	0.107676	−	0.215353i
$346$		0			0
$347$	−18.9737	−	18.9737i	−1.01856	−	1.01856i	−0.999824	−	0.0187353i	$-0.994036\pi$
$347$	−18.9737	−	18.9737i	−1.01856	−	1.01856i	−0.0187353	−	0.999824i	$-0.505964\pi$
$348$		0			0
$349$	−31.6228			−1.69273			−0.846364	−	0.532605i	$-0.821213\pi$
$349$	−31.6228			−1.69273			−0.846364	+	0.532605i	$0.821213\pi$
$350$		0			0
$351$			25.2982i			1.35032i
$352$		0			0
$353$	−21.0000	−	21.0000i	−1.11772	−	1.11772i	−0.992076	−	0.125642i	$-0.959901\pi$
$353$	−21.0000	−	21.0000i	−1.11772	−	1.11772i	−0.125642	−	0.992076i	$-0.540099\pi$
$354$		0			0
$355$	−16.0000	−	8.00000i	−0.849192	−	0.424596i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−18.9737			−1.00139			−0.500696	−	0.865623i	$-0.666923\pi$
$359$	−18.9737			−1.00139			−0.500696	+	0.865623i	$0.666923\pi$
$360$		0			0
$361$	21.0000			1.10526
$362$		0			0
$363$	−15.3246	−	2.67544i	−0.804331	−	0.140424i
$364$		0			0
$365$	−9.48683	+	3.16228i	−0.496564	+	0.165521i
$366$		0			0
$367$	−3.00000	+	3.00000i	−0.156599	+	0.156599i	−0.781058	−	0.624459i	$-0.785320\pi$
$367$	−3.00000	+	3.00000i	−0.156599	+	0.156599i	0.624459	+	0.781058i	$0.285320\pi$
$368$		0			0
$369$	−6.32456			−0.329243
$370$		0			0
$371$		0			0
$372$		0			0
$373$	3.16228	−	3.16228i	0.163737	−	0.163737i	−0.620483	−	0.784220i	$-0.713063\pi$
$373$	3.16228	−	3.16228i	0.163737	−	0.163737i	0.784220	+	0.620483i	$0.213063\pi$
$374$		0			0
$375$	9.00000	−	13.0000i	0.464758	−	0.671317i
$376$		0			0
$377$	20.0000	−	20.0000i	1.03005	−	1.03005i
$378$		0			0
$379$		−	26.0000i		−	1.33553i	−0.744372	−	0.667765i	$-0.767251\pi$
$379$		−	26.0000i		−	1.33553i	0.744372	−	0.667765i	$-0.232749\pi$
$380$		0			0
$381$			12.6491i			0.648034i
$382$		0			0
$383$	−19.0000	−	19.0000i	−0.970855	−	0.970855i	0.0287325	−	0.999587i	$-0.490853\pi$
$383$	−19.0000	−	19.0000i	−0.970855	−	0.970855i	−0.999587	+	0.0287325i	$0.990853\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$			16.0000i			0.811232i	0.914044	+	0.405616i	$0.132943\pi$
$389$			16.0000i			0.811232i	−0.914044	+	0.405616i	$0.867057\pi$
$390$		0			0
$391$		−	6.32456i		−	0.319847i
$392$		0			0
$393$	−12.6491	+	12.6491i	−0.638063	+	0.638063i
$394$		0			0
$395$	−12.6491	−	6.32456i	−0.636446	−	0.318223i
$396$		0			0
$397$	13.0000	−	13.0000i	0.652451	−	0.652451i	−0.301131	−	0.953583i	$-0.597364\pi$
$397$	13.0000	−	13.0000i	0.652451	−	0.652451i	0.953583	+	0.301131i	$0.0973643\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	12.0000			0.599251			0.299626	−	0.954057i	$-0.403138\pi$
$401$	12.0000			0.599251			0.299626	+	0.954057i	$0.403138\pi$
$402$		0			0
$403$	6.32456	−	6.32456i	0.315049	−	0.315049i
$404$		0			0
$405$	−10.0000	−	5.00000i	−0.496904	−	0.248452i
$406$		0			0
$407$	−12.4868	−	6.48683i	−0.618949	−	0.321540i
$408$		0			0
$409$	−12.6491			−0.625458			−0.312729	−	0.949842i	$-0.601243\pi$
$409$	−12.6491			−0.625458			−0.312729	+	0.949842i	$0.601243\pi$
$410$		0			0
$411$	26.0000			1.28249
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−18.9737	+	6.32456i	−0.931381	+	0.310460i
$416$		0			0
$417$	−12.6491	−	12.6491i	−0.619430	−	0.619430i
$418$		0			0
$419$		−	36.0000i		−	1.75872i	−0.476162	−	0.879358i	$-0.657972\pi$
$419$		−	36.0000i		−	1.75872i	0.476162	−	0.879358i	$-0.342028\pi$
$420$		0			0
$421$	−28.0000			−1.36464			−0.682318	−	0.731055i	$-0.739028\pi$
$421$	−28.0000			−1.36464			−0.682318	+	0.731055i	$0.739028\pi$
$422$		0			0
$423$	3.00000	+	3.00000i	0.145865	+	0.145865i
$424$		0			0
$425$	3.16228	−	22.1359i	0.153393	−	1.07375i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	6.32456	+	20.0000i	0.305352	+	0.965609i
$430$		0			0
$431$		−	18.9737i		−	0.913929i	−0.889485	−	0.456965i	$-0.848937\pi$
$431$		−	18.9737i		−	0.913929i	0.889485	−	0.456965i	$-0.151063\pi$
$432$		0			0
$433$	−1.00000	−	1.00000i	−0.0480569	−	0.0480569i	0.682670	−	0.730727i	$-0.260819\pi$
$433$	−1.00000	−	1.00000i	−0.0480569	−	0.0480569i	−0.730727	+	0.682670i	$0.760819\pi$
$434$		0			0
$435$	6.32456	+	18.9737i	0.303239	+	0.909718i
$436$		0			0
$437$	−6.32456	−	6.32456i	−0.302545	−	0.302545i
$438$		0			0
$439$	−12.6491			−0.603709			−0.301855	−	0.953354i	$-0.597606\pi$
$439$	−12.6491			−0.603709			−0.301855	+	0.953354i	$0.597606\pi$
$440$		0			0
$441$	−7.00000			−0.333333
$442$		0			0
$443$	11.0000	+	11.0000i	0.522626	+	0.522626i	0.918364	−	0.395738i	$-0.129511\pi$
$443$	11.0000	+	11.0000i	0.522626	+	0.522626i	−0.395738	+	0.918364i	$0.629511\pi$
$444$		0			0
$445$	6.00000	−	12.0000i	0.284427	−	0.568855i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			6.00000i			0.283158i	0.989927	+	0.141579i	$0.0452178\pi$
$449$			6.00000i			0.283158i	−0.989927	+	0.141579i	$0.954782\pi$
$450$		0			0
$451$	−20.0000	+	6.32456i	−0.941763	+	0.297812i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−15.8114	−	15.8114i	−0.739626	−	0.739626i	0.232880	−	0.972505i	$-0.425185\pi$
$457$	−15.8114	−	15.8114i	−0.739626	−	0.739626i	−0.972505	+	0.232880i	$0.925185\pi$
$458$		0			0
$459$	−25.2982			−1.18082
$460$		0			0
$461$		−	25.2982i		−	1.17826i	−0.808040	−	0.589128i	$-0.799471\pi$
$461$		−	25.2982i		−	1.17826i	0.808040	−	0.589128i	$-0.200529\pi$
$462$		0			0
$463$	−9.00000	−	9.00000i	−0.418265	−	0.418265i	0.466340	−	0.884606i	$-0.345572\pi$
$463$	−9.00000	−	9.00000i	−0.418265	−	0.418265i	−0.884606	+	0.466340i	$0.845572\pi$
$464$		0			0
$465$	2.00000	+	6.00000i	0.0927478	+	0.278243i
$466$		0			0
$467$	7.00000	−	7.00000i	0.323921	−	0.323921i	−0.526348	−	0.850269i	$-0.676439\pi$
$467$	7.00000	−	7.00000i	0.323921	−	0.323921i	0.850269	+	0.526348i	$0.176439\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−14.0000			−0.645086
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−18.9737	−	25.2982i	−0.870572	−	1.16076i
$476$		0			0
$477$	−1.00000	+	1.00000i	−0.0457869	+	0.0457869i
$478$		0			0
$479$	6.32456			0.288976			0.144488	−	0.989507i	$-0.453846\pi$
$479$	6.32456			0.288976			0.144488	+	0.989507i	$0.453846\pi$
$480$		0			0
$481$			18.9737i			0.865125i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	21.0000	−	7.00000i	0.953561	−	0.317854i
$486$		0			0
$487$	−3.00000	+	3.00000i	−0.135943	+	0.135943i	−0.771804	−	0.635861i	$-0.780645\pi$
$487$	−3.00000	+	3.00000i	−0.135943	+	0.135943i	0.635861	+	0.771804i	$0.280645\pi$
$488$		0			0
$489$			2.00000i			0.0904431i
$490$		0			0
$491$			6.32456i			0.285423i	0.989764	+	0.142712i	$0.0455821\pi$
$491$			6.32456i			0.285423i	−0.989764	+	0.142712i	$0.954418\pi$
$492$		0			0
$493$	20.0000	+	20.0000i	0.900755	+	0.900755i
$494$		0			0
$495$	7.32456	+	1.16228i	0.329214	+	0.0522405i
$496$		0			0
$497$		0			0
$498$		0			0
$499$			34.0000i			1.52205i	0.648723	+	0.761025i	$0.275303\pi$
$499$			34.0000i			1.52205i	−0.648723	+	0.761025i	$0.724697\pi$
$500$		0			0
$501$		−	25.2982i		−	1.13024i
$502$		0			0
$503$	−6.32456	+	6.32456i	−0.281998	+	0.281998i	−0.833905	−	0.551907i	$-0.813900\pi$
$503$	−6.32456	+	6.32456i	−0.281998	+	0.281998i	0.551907	+	0.833905i	$0.313900\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	7.00000	−	7.00000i	0.310881	−	0.310881i
$508$		0			0
$509$		−	4.00000i		−	0.177297i	−0.996063	−	0.0886484i	$-0.971745\pi$
$509$		−	4.00000i		−	0.177297i	0.996063	−	0.0886484i	$-0.0282548\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−25.2982	+	25.2982i	−1.11694	+	1.11694i
$514$		0			0
$515$	9.00000	+	27.0000i	0.396587	+	1.18976i
$516$		0			0
$517$	12.4868	+	6.48683i	0.549170	+	0.285291i
$518$		0			0
$519$	6.32456			0.277617
$520$		0			0
$521$	−28.0000			−1.22670			−0.613351	−	0.789810i	$-0.710179\pi$
$521$	−28.0000			−1.22670			−0.613351	+	0.789810i	$0.710179\pi$
$522$		0			0
$523$	−18.9737	+	18.9737i	−0.829660	+	0.829660i	−0.987470	−	0.157809i	$-0.949557\pi$
$523$	−18.9737	+	18.9737i	−0.829660	+	0.829660i	0.157809	+	0.987470i	$0.449557\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.32456	+	6.32456i	0.275502	+	0.275502i
$528$		0			0
$529$		−	21.0000i		−	0.913043i
$530$		0			0
$531$	−6.00000			−0.260378
$532$		0			0
$533$	20.0000	+	20.0000i	0.866296	+	0.866296i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−4.00000	+	4.00000i	−0.172613	+	0.172613i
$538$		0			0
$539$	−22.1359	+	7.00000i	−0.953463	+	0.301511i
$540$		0			0
$541$		−	37.9473i		−	1.63148i	−0.578416	−	0.815742i	$-0.696329\pi$
$541$		−	37.9473i		−	1.63148i	0.578416	−	0.815742i	$-0.303671\pi$
$542$		0			0
$543$	−8.00000	−	8.00000i	−0.343313	−	0.343313i
$544$		0			0
$545$	25.2982	+	12.6491i	1.08366	+	0.541828i
$546$		0			0
$547$	12.6491	+	12.6491i	0.540837	+	0.540837i	0.923774	−	0.382937i	$-0.125088\pi$
$547$	12.6491	+	12.6491i	0.540837	+	0.540837i	−0.382937	+	0.923774i	$0.625088\pi$
$548$		0			0
$549$	6.32456			0.269925
$550$		0			0
$551$	40.0000			1.70406
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−12.0000	−	6.00000i	−0.509372	−	0.254686i
$556$		0			0
$557$	−15.8114	−	15.8114i	−0.669950	−	0.669950i	0.287754	−	0.957704i	$-0.407091\pi$
$557$	−15.8114	−	15.8114i	−0.669950	−	0.669950i	−0.957704	+	0.287754i	$0.907091\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−20.0000	+	6.32456i	−0.844401	+	0.267023i
$562$		0			0
$563$	18.9737	−	18.9737i	0.799645	−	0.799645i	−0.183395	−	0.983039i	$-0.558709\pi$
$563$	18.9737	−	18.9737i	0.799645	−	0.799645i	0.983039	+	0.183395i	$0.0587086\pi$
$564$		0			0
$565$	−9.00000	−	27.0000i	−0.378633	−	1.13590i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	37.9473			1.59083			0.795417	−	0.606062i	$-0.207252\pi$
$569$	37.9473			1.59083			0.795417	+	0.606062i	$0.207252\pi$
$570$		0			0
$571$		−	44.2719i		−	1.85272i	−0.376638	−	0.926360i	$-0.622920\pi$
$571$		−	44.2719i		−	1.85272i	0.376638	−	0.926360i	$-0.377080\pi$
$572$		0			0
$573$	−22.0000	−	22.0000i	−0.919063	−	0.919063i
$574$		0			0
$575$	−1.00000	+	7.00000i	−0.0417029	+	0.291920i
$576$		0			0
$577$	23.0000	−	23.0000i	0.957503	−	0.957503i	−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	23.0000	−	23.0000i	0.957503	−	0.957503i	0.999133	+	0.0416305i	$0.0132552\pi$
$578$		0			0
$579$	31.6228			1.31420
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−2.16228	+	4.16228i	−0.0895524	+	0.172384i
$584$		0			0
$585$	−3.16228	−	9.48683i	−0.130744	−	0.392232i
$586$		0			0
$587$	7.00000	−	7.00000i	0.288921	−	0.288921i	−0.547733	−	0.836653i	$-0.684509\pi$
$587$	7.00000	−	7.00000i	0.288921	−	0.288921i	0.836653	+	0.547733i	$0.184509\pi$
$588$		0			0
$589$	12.6491			0.521198
$590$		0			0
$591$			6.32456i			0.260157i
$592$		0			0
$593$	−15.8114	+	15.8114i	−0.649296	+	0.649296i	−0.952823	−	0.303527i	$-0.901836\pi$
$593$	−15.8114	+	15.8114i	−0.649296	+	0.649296i	0.303527	+	0.952823i	$0.401836\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	6.00000	−	6.00000i	0.245564	−	0.245564i
$598$		0			0
$599$		−	16.0000i		−	0.653742i	−0.945069	−	0.326871i	$-0.894006\pi$
$599$		−	16.0000i		−	0.653742i	0.945069	−	0.326871i	$-0.105994\pi$
$600$		0			0
$601$			31.6228i			1.28992i	0.764216	+	0.644960i	$0.223126\pi$
$601$			31.6228i			1.28992i	−0.764216	+	0.644960i	$0.776874\pi$
$602$		0			0
$603$	3.00000	+	3.00000i	0.122169	+	0.122169i
$604$		0			0
$605$	24.3246	−	3.64911i	0.988934	−	0.148357i
$606$		0			0
$607$	31.6228	+	31.6228i	1.28353	+	1.28353i	0.938646	+	0.344883i	$0.112082\pi$
$607$	31.6228	+	31.6228i	1.28353	+	1.28353i	0.344883	+	0.938646i	$0.387918\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	18.9737i		−	0.767592i
$612$		0			0
$613$	28.4605	−	28.4605i	1.14951	−	1.14951i	0.162859	−	0.986649i	$-0.447928\pi$
$613$	28.4605	−	28.4605i	1.14951	−	1.14951i	0.986649	−	0.162859i	$-0.0520717\pi$
$614$		0			0
$615$	−18.9737	+	6.32456i	−0.765092	+	0.255031i
$616$		0			0
$617$	−17.0000	+	17.0000i	−0.684394	+	0.684394i	−0.960987	−	0.276593i	$-0.910795\pi$
$617$	−17.0000	+	17.0000i	−0.684394	+	0.684394i	0.276593	+	0.960987i	$0.410795\pi$
$618$		0			0
$619$		−	36.0000i		−	1.44696i	−0.690344	−	0.723481i	$-0.742541\pi$
$619$		−	36.0000i		−	1.44696i	0.690344	−	0.723481i	$-0.257459\pi$
$620$		0			0
$621$	8.00000			0.321029
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$		0			0
$627$	−13.6754	+	26.3246i	−0.546145	+	1.05130i
$628$		0			0
$629$	−18.9737			−0.756530
$630$		0			0
$631$	−32.0000			−1.27390			−0.636950	−	0.770905i	$-0.719804\pi$
$631$	−32.0000			−1.27390			−0.636950	+	0.770905i	$0.719804\pi$
$632$		0			0
$633$	−25.2982	+	25.2982i	−1.00551	+	1.00551i
$634$		0			0
$635$	−6.32456	−	18.9737i	−0.250982	−	0.752947i
$636$		0			0
$637$	22.1359	+	22.1359i	0.877058	+	0.877058i
$638$		0			0
$639$		−	8.00000i		−	0.316475i
$640$		0			0
$641$	−8.00000			−0.315981			−0.157991	−	0.987441i	$-0.550502\pi$
$641$	−8.00000			−0.315981			−0.157991	+	0.987441i	$0.550502\pi$
$642$		0			0
$643$	11.0000	+	11.0000i	0.433798	+	0.433798i	0.889918	−	0.456120i	$-0.150761\pi$
$643$	11.0000	+	11.0000i	0.433798	+	0.433798i	−0.456120	+	0.889918i	$0.650761\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−13.0000	+	13.0000i	−0.511083	+	0.511083i	−0.914858	−	0.403775i	$-0.867698\pi$
$647$	−13.0000	+	13.0000i	−0.511083	+	0.511083i	0.403775	+	0.914858i	$0.367698\pi$
$648$		0			0
$649$	−18.9737	+	6.00000i	−0.744782	+	0.235521i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.00000	−	1.00000i	−0.0391330	−	0.0391330i	0.687270	−	0.726403i	$-0.258809\pi$
$653$	−1.00000	−	1.00000i	−0.0391330	−	0.0391330i	−0.726403	+	0.687270i	$0.758809\pi$
$654$		0			0
$655$	12.6491	−	25.2982i	0.494242	−	0.988483i
$656$		0			0
$657$	−3.16228	−	3.16228i	−0.123372	−	0.123372i
$658$		0			0
$659$	12.6491			0.492739			0.246370	−	0.969176i	$-0.420762\pi$
$659$	12.6491			0.492739			0.246370	+	0.969176i	$0.420762\pi$
$660$		0			0
$661$	42.0000			1.63361			0.816805	−	0.576913i	$-0.195743\pi$
$661$	42.0000			1.63361			0.816805	+	0.576913i	$0.195743\pi$
$662$		0			0
$663$	20.0000	+	20.0000i	0.776736	+	0.776736i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−6.32456	−	6.32456i	−0.244888	−	0.244888i
$668$		0			0
$669$			22.0000i			0.850569i
$670$		0			0
$671$	20.0000	−	6.32456i	0.772091	−	0.244157i
$672$		0			0
$673$	−28.4605	+	28.4605i	−1.09707	+	1.09707i	−0.102320	+	0.994752i	$0.532627\pi$
$673$	−28.4605	+	28.4605i	−1.09707	+	1.09707i	−0.994752	+	0.102320i	$0.967373\pi$
$674$		0			0
$675$	28.0000	+	4.00000i	1.07772	+	0.153960i
$676$		0			0
$677$	9.48683	+	9.48683i	0.364609	+	0.364609i	0.865506	−	0.500898i	$-0.166997\pi$
$677$	9.48683	+	9.48683i	0.364609	+	0.364609i	−0.500898	+	0.865506i	$0.666997\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$			12.6491i			0.484715i
$682$		0			0
$683$	−29.0000	−	29.0000i	−1.10965	−	1.10965i	−0.993196	−	0.116459i	$-0.962846\pi$
$683$	−29.0000	−	29.0000i	−1.10965	−	1.10965i	−0.116459	−	0.993196i	$-0.537154\pi$
$684$		0			0
$685$	−39.0000	+	13.0000i	−1.49011	+	0.496704i
$686$		0			0
$687$	4.00000	−	4.00000i	0.152610	−	0.152610i
$688$		0			0
$689$	6.32456			0.240946
$690$		0			0
$691$	28.0000			1.06517			0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000			1.06517			0.532585	+	0.846376i	$0.321221\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	25.2982	+	12.6491i	0.959616	+	0.479808i
$696$		0			0
$697$	−20.0000	+	20.0000i	−0.757554	+	0.757554i
$698$		0			0
$699$	18.9737			0.717650
$700$		0			0
$701$		−	31.6228i		−	1.19438i	−0.802101	−	0.597188i	$-0.796285\pi$
$701$		−	31.6228i		−	1.19438i	0.802101	−	0.597188i	$-0.203715\pi$
$702$		0			0
$703$	−18.9737	+	18.9737i	−0.715605	+	0.715605i
$704$		0			0
$705$	12.0000	+	6.00000i	0.451946	+	0.225973i
$706$		0			0
$707$		0			0
$708$		0			0
$709$			6.00000i			0.225335i	0.993633	+	0.112667i	$0.0359394\pi$
$709$			6.00000i			0.225335i	−0.993633	+	0.112667i	$0.964061\pi$
$710$		0			0
$711$		−	6.32456i		−	0.237189i
$712$		0			0
$713$	−2.00000	−	2.00000i	−0.0749006	−	0.0749006i
$714$		0			0
$715$	−19.4868	−	26.8377i	−0.728766	−	1.00367i
$716$		0			0
$717$	18.9737	+	18.9737i	0.708585	+	0.708585i
$718$		0			0
$719$			24.0000i			0.895049i	0.894272	+	0.447524i	$0.147694\pi$
$719$			24.0000i			0.895049i	−0.894272	+	0.447524i	$0.852306\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	6.32456	−	6.32456i	0.235213	−	0.235213i
$724$		0			0
$725$	−18.9737	−	25.2982i	−0.704664	−	0.939552i
$726$		0			0
$727$	−23.0000	+	23.0000i	−0.853023	+	0.853023i	−0.990504	−	0.137482i	$-0.956099\pi$
$727$	−23.0000	+	23.0000i	−0.853023	+	0.853023i	0.137482	+	0.990504i	$0.456099\pi$
$728$		0			0
$729$		−	29.0000i		−	1.07407i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	9.48683	−	9.48683i	0.350404	−	0.350404i	−0.509856	−	0.860260i	$-0.670301\pi$
$733$	9.48683	−	9.48683i	0.350404	−	0.350404i	0.860260	+	0.509856i	$0.170301\pi$
$734$		0			0
$735$	−21.0000	+	7.00000i	−0.774597	+	0.258199i
$736$		0			0
$737$	12.4868	+	6.48683i	0.459958	+	0.238946i
$738$		0			0
$739$	−12.6491			−0.465305			−0.232653	−	0.972560i	$-0.574740\pi$
$739$	−12.6491			−0.465305			−0.232653	+	0.972560i	$0.574740\pi$
$740$		0			0
$741$	40.0000			1.46944
$742$		0			0
$743$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$743$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−6.32456	−	6.32456i	−0.231403	−	0.231403i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	8.00000			0.291924			0.145962	−	0.989290i	$-0.453372\pi$
$751$	8.00000			0.291924			0.145962	+	0.989290i	$0.453372\pi$
$752$		0			0
$753$	−12.0000	−	12.0000i	−0.437304	−	0.437304i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−27.0000	+	27.0000i	−0.981332	+	0.981332i	−0.999829	−	0.0184972i	$-0.994112\pi$
$757$	−27.0000	+	27.0000i	−0.981332	+	0.981332i	0.0184972	+	0.999829i	$0.494112\pi$
$758$		0			0
$759$	6.32456	−	2.00000i	0.229567	−	0.0725954i
$760$		0			0
$761$			37.9473i			1.37559i	0.725905	+	0.687795i	$0.241421\pi$
$761$			37.9473i			1.37559i	−0.725905	+	0.687795i	$0.758579\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	9.48683	−	3.16228i	0.342997	−	0.114332i
$766$		0			0
$767$	18.9737	+	18.9737i	0.685099	+	0.685099i
$768$		0			0
$769$	6.32456			0.228069			0.114035	−	0.993477i	$-0.463623\pi$
$769$	6.32456			0.228069			0.114035	+	0.993477i	$0.463623\pi$
$770$		0			0
$771$	−14.0000			−0.504198
$772$		0			0
$773$	−11.0000	−	11.0000i	−0.395643	−	0.395643i	0.481050	−	0.876693i	$-0.340255\pi$
$773$	−11.0000	−	11.0000i	−0.395643	−	0.395643i	−0.876693	+	0.481050i	$0.840255\pi$
$774$		0			0
$775$	−6.00000	−	8.00000i	−0.215526	−	0.287368i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			40.0000i			1.43315i
$780$		0			0
$781$	−8.00000	−	25.2982i	−0.286263	−	0.905242i
$782$		0			0
$783$	−25.2982	+	25.2982i	−0.904085	+	0.904085i
$784$		0			0
$785$	21.0000	−	7.00000i	0.749522	−	0.249841i
$786$		0			0
$787$	25.2982	+	25.2982i	0.901784	+	0.901784i	0.995590	−	0.0938063i	$-0.0299034\pi$
$787$	25.2982	+	25.2982i	0.901784	+	0.901784i	−0.0938063	+	0.995590i	$0.529903\pi$
$788$		0			0
$789$	37.9473			1.35096
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−20.0000	−	20.0000i	−0.710221	−	0.710221i
$794$		0			0
$795$	−2.00000	+	4.00000i	−0.0709327	+	0.141865i
$796$		0			0
$797$	13.0000	−	13.0000i	0.460484	−	0.460484i	−0.438330	−	0.898814i	$-0.644430\pi$
$797$	13.0000	−	13.0000i	0.460484	−	0.460484i	0.898814	+	0.438330i	$0.144430\pi$
$798$		0			0
$799$	18.9737			0.671240
$800$		0			0
$801$	6.00000			0.212000
$802$		0			0
$803$	−13.1623	−	6.83772i	−0.464487	−	0.241298i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	24.0000	−	24.0000i	0.844840	−	0.844840i
$808$		0			0
$809$	18.9737			0.667079			0.333539	−	0.942736i	$-0.391757\pi$
$809$	18.9737			0.667079			0.333539	+	0.942736i	$0.391757\pi$
$810$		0			0
$811$		−	6.32456i		−	0.222085i	−0.993816	−	0.111043i	$-0.964581\pi$
$811$		−	6.32456i		−	0.222085i	0.993816	−	0.111043i	$-0.0354190\pi$
$812$		0			0
$813$	12.6491	−	12.6491i	0.443624	−	0.443624i
$814$		0			0
$815$	−1.00000	−	3.00000i	−0.0350285	−	0.105085i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$		−	18.9737i		−	0.662186i	−0.943598	−	0.331093i	$-0.892583\pi$
$821$		−	18.9737i		−	0.662186i	0.943598	−	0.331093i	$-0.107417\pi$
$822$		0			0
$823$	11.0000	+	11.0000i	0.383436	+	0.383436i	0.872338	−	0.488903i	$-0.162603\pi$
$823$	11.0000	+	11.0000i	0.383436	+	0.383436i	−0.488903	+	0.872338i	$0.662603\pi$
$824$		0			0
$825$	23.1359	−	3.83772i	0.805490	−	0.133612i
$826$		0			0
$827$	6.32456	+	6.32456i	0.219926	+	0.219926i	0.808467	−	0.588541i	$-0.200297\pi$
$827$	6.32456	+	6.32456i	0.219926	+	0.219926i	−0.588541	+	0.808467i	$0.700297\pi$
$828$		0			0
$829$			6.00000i			0.208389i	0.994557	+	0.104194i	$0.0332264\pi$
$829$			6.00000i			0.208389i	−0.994557	+	0.104194i	$0.966774\pi$
$830$		0			0
$831$			18.9737i			0.658189i
$832$		0			0
$833$	−22.1359	+	22.1359i	−0.766965	+	0.766965i
$834$		0			0
$835$	12.6491	+	37.9473i	0.437741	+	1.31322i
$836$		0			0
$837$	−8.00000	+	8.00000i	−0.276520	+	0.276520i
$838$		0			0
$839$		−	6.00000i		−	0.207143i	−0.994622	−	0.103572i	$-0.966973\pi$
$839$		−	6.00000i		−	0.207143i	0.994622	−	0.103572i	$-0.0330271\pi$
$840$		0			0
$841$	11.0000			0.379310
$842$		0			0
$843$	−18.9737	+	18.9737i	−0.653488	+	0.653488i
$844$		0			0
$845$	−7.00000	+	14.0000i	−0.240807	+	0.481615i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	12.6491			0.434116
$850$		0			0
$851$	6.00000			0.205677
$852$		0			0
$853$	−9.48683	+	9.48683i	−0.324823	+	0.324823i	−0.850614	−	0.525791i	$-0.823769\pi$
$853$	−9.48683	+	9.48683i	−0.324823	+	0.324823i	0.525791	+	0.850614i	$0.323769\pi$
$854$		0			0
$855$	6.32456	−	12.6491i	0.216295	−	0.432590i
$856$		0			0
$857$	15.8114	+	15.8114i	0.540107	+	0.540107i	0.923560	−	0.383453i	$-0.125265\pi$
$857$	15.8114	+	15.8114i	0.540107	+	0.540107i	−0.383453	+	0.923560i	$0.625265\pi$
$858$		0			0
$859$			44.0000i			1.50126i	0.660722	+	0.750630i	$0.270250\pi$
$859$			44.0000i			1.50126i	−0.660722	+	0.750630i	$0.729750\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.00000	+	1.00000i	0.0340404	+	0.0340404i	0.723922	−	0.689882i	$-0.242337\pi$
$863$	1.00000	+	1.00000i	0.0340404	+	0.0340404i	−0.689882	+	0.723922i	$0.742337\pi$
$864$		0			0
$865$	−9.48683	+	3.16228i	−0.322562	+	0.107521i
$866$		0			0
$867$	−3.00000	+	3.00000i	−0.101885	+	0.101885i
$868$		0			0
$869$	−6.32456	−	20.0000i	−0.214546	−	0.678454i
$870$		0			0
$871$		−	18.9737i		−	0.642898i
$872$		0			0
$873$	7.00000	+	7.00000i	0.236914	+	0.236914i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	41.1096	+	41.1096i	1.38817	+	1.38817i	0.829157	+	0.559016i	$0.188821\pi$
$877$	41.1096	+	41.1096i	1.38817	+	1.38817i	0.559016	+	0.829157i	$0.311179\pi$
$878$		0			0
$879$	31.6228			1.06661
$880$		0			0
$881$	2.00000			0.0673817			0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000			0.0673817			0.0336909	+	0.999432i	$0.489274\pi$
$882$		0			0
$883$	−19.0000	−	19.0000i	−0.639401	−	0.639401i	0.311007	−	0.950408i	$-0.399334\pi$
$883$	−19.0000	−	19.0000i	−0.639401	−	0.639401i	−0.950408	+	0.311007i	$0.899334\pi$
$884$		0			0
$885$	−18.0000	+	6.00000i	−0.605063	+	0.201688i
$886$		0			0
$887$	−6.32456	−	6.32456i	−0.212358	−	0.212358i	0.592911	−	0.805268i	$-0.297979\pi$
$887$	−6.32456	−	6.32456i	−0.212358	−	0.212358i	−0.805268	+	0.592911i	$0.797979\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−5.00000	−	15.8114i	−0.167506	−	0.529701i
$892$		0			0
$893$	18.9737	−	18.9737i	0.634930	−	0.634930i
$894$		0			0
$895$	4.00000	−	8.00000i	0.133705	−	0.267411i
$896$		0			0
$897$	−6.32456	−	6.32456i	−0.211171	−	0.211171i
$898$		0			0
$899$	12.6491			0.421871
$900$		0			0
$901$			6.32456i			0.210701i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	16.0000	+	8.00000i	0.531858	+	0.265929i
$906$		0			0
$907$	17.0000	−	17.0000i	0.564476	−	0.564476i	−0.366100	−	0.930576i	$-0.619307\pi$
$907$	17.0000	−	17.0000i	0.564476	−	0.564476i	0.930576	+	0.366100i	$0.119307\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−42.0000			−1.39152			−0.695761	−	0.718273i	$-0.744933\pi$
$911$	−42.0000			−1.39152			−0.695761	+	0.718273i	$0.744933\pi$
$912$		0			0
$913$	−26.3246	−	13.6754i	−0.871216	−	0.452591i
$914$		0			0
$915$	18.9737	−	6.32456i	0.627250	−	0.209083i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−37.9473			−1.25177			−0.625883	−	0.779917i	$-0.715261\pi$
$919$	−37.9473			−1.25177			−0.625883	+	0.779917i	$0.715261\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−25.2982	+	25.2982i	−0.832701	+	0.832701i
$924$		0			0
$925$	21.0000	+	3.00000i	0.690476	+	0.0986394i
$926$		0			0
$927$	−9.00000	+	9.00000i	−0.295599	+	0.295599i
$928$		0			0
$929$		−	4.00000i		−	0.131236i	−0.997845	−	0.0656179i	$-0.979098\pi$
$929$		−	4.00000i		−	0.131236i	0.997845	−	0.0656179i	$-0.0209018\pi$
$930$		0			0
$931$			44.2719i			1.45095i
$932$		0			0
$933$	8.00000	+	8.00000i	0.261908	+	0.261908i
$934$		0			0
$935$	26.8377	−	19.4868i	0.877687	−	0.637288i
$936$		0			0
$937$	−9.48683	−	9.48683i	−0.309921	−	0.309921i	0.534958	−	0.844879i	$-0.320328\pi$
$937$	−9.48683	−	9.48683i	−0.309921	−	0.309921i	−0.844879	+	0.534958i	$0.820328\pi$
$938$		0			0
$939$			18.0000i			0.587408i
$940$		0			0
$941$		−	37.9473i		−	1.23705i	−0.785766	−	0.618524i	$-0.787731\pi$
$941$		−	37.9473i		−	1.23705i	0.785766	−	0.618524i	$-0.212269\pi$
$942$		0			0
$943$	6.32456	−	6.32456i	0.205956	−	0.205956i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	7.00000	−	7.00000i	0.227469	−	0.227469i	−0.584165	−	0.811635i	$-0.698578\pi$
$947$	7.00000	−	7.00000i	0.227469	−	0.227469i	0.811635	+	0.584165i	$0.198578\pi$
$948$		0			0
$949$			20.0000i			0.649227i
$950$		0			0
$951$	−34.0000			−1.10253
$952$		0			0
$953$	−9.48683	+	9.48683i	−0.307309	+	0.307309i	−0.843865	−	0.536556i	$-0.819725\pi$
$953$	−9.48683	+	9.48683i	−0.307309	+	0.307309i	0.536556	+	0.843865i	$0.319725\pi$
$954$		0			0
$955$	44.0000	+	22.0000i	1.42381	+	0.711903i
$956$		0			0
$957$	−13.6754	+	26.3246i	−0.442064	+	0.850952i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−27.0000			−0.870968
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−47.4342	+	15.8114i	−1.52696	+	0.508987i
$966$		0			0
$967$	18.9737	+	18.9737i	0.610152	+	0.610152i	0.942986	−	0.332834i	$-0.108005\pi$
$967$	18.9737	+	18.9737i	0.610152	+	0.610152i	−0.332834	+	0.942986i	$0.608005\pi$
$968$		0			0
$969$			40.0000i			1.28499i
$970$		0			0
$971$	−42.0000			−1.34784			−0.673922	−	0.738802i	$-0.735392\pi$
$971$	−42.0000			−1.34784			−0.673922	+	0.738802i	$0.735392\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−18.9737	−	25.2982i	−0.607644	−	0.810191i
$976$		0			0
$977$	−17.0000	+	17.0000i	−0.543878	+	0.543878i	−0.924663	−	0.380785i	$-0.875654\pi$
$977$	−17.0000	+	17.0000i	−0.543878	+	0.543878i	0.380785	+	0.924663i	$0.375654\pi$
$978$		0			0
$979$	18.9737	−	6.00000i	0.606401	−	0.191761i
$980$		0			0
$981$			12.6491i			0.403855i
$982$		0			0
$983$	−29.0000	−	29.0000i	−0.924956	−	0.924956i	0.0724180	−	0.997374i	$-0.476928\pi$
$983$	−29.0000	−	29.0000i	−0.924956	−	0.924956i	−0.997374	+	0.0724180i	$0.976928\pi$
$984$		0			0
$985$	−3.16228	−	9.48683i	−0.100759	−	0.302276i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	58.0000			1.84243			0.921215	−	0.389053i	$-0.127198\pi$
$991$	58.0000			1.84243			0.921215	+	0.389053i	$0.127198\pi$
$992$		0			0
$993$	18.0000	+	18.0000i	0.571213	+	0.571213i
$994$		0			0
$995$	−6.00000	+	12.0000i	−0.190213	+	0.380426i
$996$		0			0
$997$	34.7851	+	34.7851i	1.10165	+	1.10165i	0.994211	+	0.107442i	$0.0342661\pi$
$997$	34.7851	+	34.7851i	1.10165	+	1.10165i	0.107442	+	0.994211i	$0.465734\pi$
$998$		0			0
$999$		−	24.0000i		−	0.759326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bd.e.593.1		4
4.3	odd	2		55.2.e.a.43.2	yes	4
5.2	odd	4	inner	880.2.bd.e.417.1		4
11.10	odd	2	inner	880.2.bd.e.593.2		4
12.11	even	2		495.2.k.b.208.1		4
20.3	even	4		275.2.e.b.32.2		4
20.7	even	4		55.2.e.a.32.1	✓	4
20.19	odd	2		275.2.e.b.43.1		4
44.3	odd	10		605.2.m.b.233.2		16
44.7	even	10		605.2.m.b.578.2		16
44.15	odd	10		605.2.m.b.578.1		16
44.19	even	10		605.2.m.b.233.1		16
44.27	odd	10		605.2.m.b.118.1		16
44.31	odd	10		605.2.m.b.403.1		16
44.35	even	10		605.2.m.b.403.2		16
44.39	even	10		605.2.m.b.118.2		16
44.43	even	2		55.2.e.a.43.1	yes	4
55.32	even	4	inner	880.2.bd.e.417.2		4
60.47	odd	4		495.2.k.b.307.2		4
132.131	odd	2		495.2.k.b.208.2		4
220.7	odd	20		605.2.m.b.457.2		16
220.27	even	20		605.2.m.b.602.2		16
220.43	odd	4		275.2.e.b.32.1		4
220.47	even	20		605.2.m.b.112.2		16
220.87	odd	4		55.2.e.a.32.2	yes	4
220.107	odd	20		605.2.m.b.112.1		16
220.127	odd	20		605.2.m.b.602.1		16
220.147	even	20		605.2.m.b.457.1		16
220.167	odd	20		605.2.m.b.282.1		16
220.207	even	20		605.2.m.b.282.2		16
220.219	even	2		275.2.e.b.43.2		4
660.527	even	4		495.2.k.b.307.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.e.a.32.1	✓	4	20.7	even	4
55.2.e.a.32.2	yes	4	220.87	odd	4
55.2.e.a.43.1	yes	4	44.43	even	2
55.2.e.a.43.2	yes	4	4.3	odd	2
275.2.e.b.32.1		4	220.43	odd	4
275.2.e.b.32.2		4	20.3	even	4
275.2.e.b.43.1		4	20.19	odd	2
275.2.e.b.43.2		4	220.219	even	2
495.2.k.b.208.1		4	12.11	even	2
495.2.k.b.208.2		4	132.131	odd	2
495.2.k.b.307.1		4	660.527	even	4
495.2.k.b.307.2		4	60.47	odd	4
605.2.m.b.112.1		16	220.107	odd	20
605.2.m.b.112.2		16	220.47	even	20
605.2.m.b.118.1		16	44.27	odd	10
605.2.m.b.118.2		16	44.39	even	10
605.2.m.b.233.1		16	44.19	even	10
605.2.m.b.233.2		16	44.3	odd	10
605.2.m.b.282.1		16	220.167	odd	20
605.2.m.b.282.2		16	220.207	even	20
605.2.m.b.403.1		16	44.31	odd	10
605.2.m.b.403.2		16	44.35	even	10
605.2.m.b.457.1		16	220.147	even	20
605.2.m.b.457.2		16	220.7	odd	20
605.2.m.b.578.1		16	44.15	odd	10
605.2.m.b.578.2		16	44.7	even	10
605.2.m.b.602.1		16	220.127	odd	20
605.2.m.b.602.2		16	220.27	even	20
880.2.bd.e.417.1		4	5.2	odd	4	inner
880.2.bd.e.417.2		4	55.32	even	4	inner
880.2.bd.e.593.1		4	1.1	even	1	trivial
880.2.bd.e.593.2		4	11.10	odd	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bd (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{3} +(-2.00000 - 1.00000i) q^{5} -1.00000i q^{9} +(-1.00000 - 3.16228i) q^{11} +(-3.16228 + 3.16228i) q^{13} +(-1.00000 - 3.00000i) q^{15} +(-3.16228 - 3.16228i) q^{17} -6.32456 q^{19} +(1.00000 + 1.00000i) q^{23} +(3.00000 + 4.00000i) q^{25} +(4.00000 - 4.00000i) q^{27} -6.32456 q^{29} -2.00000 q^{31} +(2.16228 - 4.16228i) q^{33} +(3.00000 - 3.00000i) q^{37} -6.32456 q^{39} -6.32456i q^{41} +(-1.00000 + 2.00000i) q^{45} +(-3.00000 + 3.00000i) q^{47} -7.00000i q^{49} -6.32456i q^{51} +(-1.00000 - 1.00000i) q^{53} +(-1.16228 + 7.32456i) q^{55} +(-6.32456 - 6.32456i) q^{57} -6.00000i q^{59} +6.32456i q^{61} +(9.48683 - 3.16228i) q^{65} +(-3.00000 + 3.00000i) q^{67} +2.00000i q^{69} +8.00000 q^{71} +(3.16228 - 3.16228i) q^{73} +(-1.00000 + 7.00000i) q^{75} +6.32456 q^{79} +5.00000 q^{81} +(6.32456 - 6.32456i) q^{83} +(3.16228 + 9.48683i) q^{85} +(-6.32456 - 6.32456i) q^{87} +6.00000i q^{89} +(-2.00000 - 2.00000i) q^{93} +(12.6491 + 6.32456i) q^{95} +(-7.00000 + 7.00000i) q^{97} +(-3.16228 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 8 q^{5} - 4 q^{11} - 4 q^{15} + 4 q^{23} + 12 q^{25} + 16 q^{27} - 8 q^{31} - 4 q^{33} + 12 q^{37} - 4 q^{45} - 12 q^{47} - 4 q^{53} + 8 q^{55} - 12 q^{67} + 32 q^{71} - 4 q^{75} + 20 q^{81}+ \cdots - 28 q^{97}+O(q^{100}) \) 4 * q + 4 * q^3 - 8 * q^5 - 4 * q^11 - 4 * q^15 + 4 * q^23 + 12 * q^25 + 16 * q^27 - 8 * q^31 - 4 * q^33 + 12 * q^37 - 4 * q^45 - 12 * q^47 - 4 * q^53 + 8 * q^55 - 12 * q^67 + 32 * q^71 - 4 * q^75 + 20 * q^81 - 8 * q^93 - 28 * q^97

Introduction

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