LMFDB - Embedded newform 891.2.e.e.298.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(298,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("891.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.e (of order $3$, degree $2$, not 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			298.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	891.298
Dual form			891.2.e.e.595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +(-2.00000 + 3.46410i) q^{7} -3.00000 q^{8} -2.00000 q^{10} +(-0.500000 + 0.866025i) q^{11} +(1.00000 + 1.73205i) q^{13} +(-2.00000 - 3.46410i) q^{14} +(0.500000 - 0.866025i) q^{16} -2.00000 q^{17} +(-1.00000 + 1.73205i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(-4.00000 - 6.92820i) q^{23} +(0.500000 - 0.866025i) q^{25} -2.00000 q^{26} -4.00000 q^{28} +(3.00000 - 5.19615i) q^{29} +(4.00000 + 6.92820i) q^{31} +(-2.50000 - 4.33013i) q^{32} +(1.00000 - 1.73205i) q^{34} -8.00000 q^{35} +6.00000 q^{37} +(-3.00000 - 5.19615i) q^{40} +(1.00000 + 1.73205i) q^{41} -1.00000 q^{44} +8.00000 q^{46} +(-4.00000 + 6.92820i) q^{47} +(-4.50000 - 7.79423i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-1.00000 + 1.73205i) q^{52} +6.00000 q^{53} -2.00000 q^{55} +(6.00000 - 10.3923i) q^{56} +(3.00000 + 5.19615i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-3.00000 + 5.19615i) q^{61} -8.00000 q^{62} +7.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-1.00000 - 1.73205i) q^{68} +(4.00000 - 6.92820i) q^{70} -14.0000 q^{73} +(-3.00000 + 5.19615i) q^{74} +(-2.00000 - 3.46410i) q^{77} +(2.00000 - 3.46410i) q^{79} +2.00000 q^{80} -2.00000 q^{82} +(-6.00000 + 10.3923i) q^{83} +(-2.00000 - 3.46410i) q^{85} +(1.50000 - 2.59808i) q^{88} -6.00000 q^{89} -8.00000 q^{91} +(4.00000 - 6.92820i) q^{92} +(-4.00000 - 6.92820i) q^{94} +(-1.00000 + 1.73205i) q^{97} +9.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{4} + 2 q^{5} - 4 q^{7} - 6 q^{8} - 4 q^{10} - q^{11} + 2 q^{13} - 4 q^{14} + q^{16} - 4 q^{17} - 2 q^{20} - q^{22} - 8 q^{23} + q^{25} - 4 q^{26} - 8 q^{28} + 6 q^{29} + 8 q^{31}+ \cdots + 18 q^{98}+O(q^{100}) $ 2 * q - q^2 + q^4 + 2 * q^5 - 4 * q^7 - 6 * q^8 - 4 * q^10 - q^11 + 2 * q^13 - 4 * q^14 + q^16 - 4 * q^17 - 2 * q^20 - q^22 - 8 * q^23 + q^25 - 4 * q^26 - 8 * q^28 + 6 * q^29 + 8 * q^31 - 5 * q^32 + 2 * q^34 - 16 * q^35 + 12 * q^37 - 6 * q^40 + 2 * q^41 - 2 * q^44 + 16 * q^46 - 8 * q^47 - 9 * q^49 + q^50 - 2 * q^52 + 12 * q^53 - 4 * q^55 + 12 * q^56 + 6 * q^58 + 4 * q^59 - 6 * q^61 - 16 * q^62 + 14 * q^64 - 4 * q^65 + 4 * q^67 - 2 * q^68 + 8 * q^70 - 28 * q^73 - 6 * q^74 - 4 * q^77 + 4 * q^79 + 4 * q^80 - 4 * q^82 - 12 * q^83 - 4 * q^85 + 3 * q^88 - 12 * q^89 - 16 * q^91 + 8 * q^92 - 8 * q^94 - 2 * q^97 + 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i	−0.986869	−	0.161521i	$-0.948360\pi$
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i	0.633316	+	0.773893i	$0.281693\pi$
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	0.998203	−	0.0599153i	$-0.0190830\pi$
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	−0.550990	+	0.834512i	$0.685750\pi$
$6$		0			0
$7$	−2.00000	+	3.46410i	−0.755929	+	1.30931i	0.188982	+	0.981981i	$0.439481\pi$
$7$	−2.00000	+	3.46410i	−0.755929	+	1.30931i	−0.944911	+	0.327327i	$0.893852\pi$
$8$	−3.00000			−1.06066
$9$		0			0
$10$	−2.00000			−0.632456
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$		0			0
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	−0.693375	+	0.720577i	$0.743877\pi$
$14$	−2.00000	−	3.46410i	−0.534522	−	0.925820i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$		0			0
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$	−1.00000	+	1.73205i	−0.223607	+	0.387298i
$21$		0			0
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	−0.894795	−	0.446476i	$-0.852679\pi$
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	0.0607377	−	0.998154i	$-0.480655\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−2.00000			−0.392232
$27$		0			0
$28$	−4.00000			−0.755929
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	−0.440652	−	0.897678i	$-0.645253\pi$
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	0.997738	−	0.0672232i	$-0.0214140\pi$
$30$		0			0
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	0.961625	+	0.274367i	$0.0884683\pi$
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	−0.243204	+	0.969975i	$0.578198\pi$
$32$	−2.50000	−	4.33013i	−0.441942	−	0.765466i
$33$		0			0
$34$	1.00000	−	1.73205i	0.171499	−	0.297044i
$35$	−8.00000			−1.35225
$36$		0			0
$37$	6.00000			0.986394			0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000			0.986394			0.493197	+	0.869918i	$0.335828\pi$
$38$		0			0
$39$		0			0
$40$	−3.00000	−	5.19615i	−0.474342	−	0.821584i
$41$	1.00000	+	1.73205i	0.156174	+	0.270501i	0.933486	−	0.358614i	$-0.116751\pi$
$41$	1.00000	+	1.73205i	0.156174	+	0.270501i	−0.777312	+	0.629115i	$0.783417\pi$
$42$		0			0
$43$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$43$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$44$	−1.00000			−0.150756
$45$		0			0
$46$	8.00000			1.17954
$47$	−4.00000	+	6.92820i	−0.583460	+	1.01058i	0.411606	+	0.911362i	$0.364968\pi$
$47$	−4.00000	+	6.92820i	−0.583460	+	1.01058i	−0.995066	+	0.0992202i	$0.968365\pi$
$48$		0			0
$49$	−4.50000	−	7.79423i	−0.642857	−	1.11346i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$		0			0
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$		0			0
$55$	−2.00000			−0.269680
$56$	6.00000	−	10.3923i	0.801784	−	1.38873i
$57$		0			0
$58$	3.00000	+	5.19615i	0.393919	+	0.682288i
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$		0			0
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	−0.991645	−	0.128994i	$-0.958825\pi$
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	0.607535	+	0.794293i	$0.292159\pi$
$62$	−8.00000			−1.01600
$63$		0			0
$64$	7.00000			0.875000
$65$	−2.00000	+	3.46410i	−0.248069	+	0.429669i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	−1.00000	−	1.73205i	−0.121268	−	0.210042i
$69$		0			0
$70$	4.00000	−	6.92820i	0.478091	−	0.828079i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−14.0000			−1.63858			−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000			−1.63858			−0.819288	+	0.573382i	$0.805631\pi$
$74$	−3.00000	+	5.19615i	−0.348743	+	0.604040i
$75$		0			0
$76$		0			0
$77$	−2.00000	−	3.46410i	−0.227921	−	0.394771i
$78$		0			0
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$	2.00000			0.223607
$81$		0			0
$82$	−2.00000			−0.220863
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	0.322396	+	0.946605i	$0.395512\pi$
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	−0.980982	+	0.194099i	$0.937822\pi$
$84$		0			0
$85$	−2.00000	−	3.46410i	−0.216930	−	0.375735i
$86$		0			0
$87$		0			0
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$		0			0
$91$	−8.00000			−0.838628
$92$	4.00000	−	6.92820i	0.417029	−	0.722315i
$93$		0			0
$94$	−4.00000	−	6.92820i	−0.412568	−	0.714590i
$95$		0			0
$96$		0			0
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$	9.00000			0.909137
$99$		0			0
$100$	1.00000			0.100000
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	−0.911479	−	0.411346i	$-0.865059\pi$
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	0.811976	+	0.583691i	$0.198392\pi$
$102$		0			0
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$	−3.00000	−	5.19615i	−0.294174	−	0.509525i
$105$		0			0
$106$	−3.00000	+	5.19615i	−0.291386	+	0.504695i
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$		0			0
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	1.00000	−	1.73205i	0.0953463	−	0.165145i
$111$		0			0
$112$	2.00000	+	3.46410i	0.188982	+	0.327327i
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	0.971930	−	0.235269i	$-0.0755971\pi$
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	−0.689714	+	0.724082i	$0.742264\pi$
$114$		0			0
$115$	8.00000	−	13.8564i	0.746004	−	1.29212i
$116$	6.00000			0.557086
$117$		0			0
$118$	−4.00000			−0.368230
$119$	4.00000	−	6.92820i	0.366679	−	0.635107i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−3.00000	−	5.19615i	−0.271607	−	0.470438i
$123$		0			0
$124$	−4.00000	+	6.92820i	−0.359211	+	0.622171i
$125$	12.0000			1.07331
$126$		0			0
$127$	−4.00000			−0.354943			−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000			−0.354943			−0.177471	+	0.984126i	$0.556792\pi$
$128$	1.50000	−	2.59808i	0.132583	−	0.229640i
$129$		0			0
$130$	−2.00000	−	3.46410i	−0.175412	−	0.303822i
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	0.999602	+	0.0281993i	$0.00897729\pi$
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	−0.475380	+	0.879781i	$0.657689\pi$
$132$		0			0
$133$		0			0
$134$	−4.00000			−0.345547
$135$		0			0
$136$	6.00000			0.514496
$137$	−1.00000	+	1.73205i	−0.0854358	+	0.147979i	−0.905577	−	0.424182i	$-0.860562\pi$
$137$	−1.00000	+	1.73205i	−0.0854358	+	0.147979i	0.820141	+	0.572161i	$0.193895\pi$
$138$		0			0
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	0.984297	−	0.176522i	$-0.0564848\pi$
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	−0.645021	+	0.764165i	$0.723151\pi$
$140$	−4.00000	−	6.92820i	−0.338062	−	0.585540i
$141$		0			0
$142$		0			0
$143$	−2.00000			−0.167248
$144$		0			0
$145$	12.0000			0.996546
$146$	7.00000	−	12.1244i	0.579324	−	1.00342i
$147$		0			0
$148$	3.00000	+	5.19615i	0.246598	+	0.427121i
$149$	11.0000	+	19.0526i	0.901155	+	1.56085i	0.825997	+	0.563675i	$0.190613\pi$
$149$	11.0000	+	19.0526i	0.901155	+	1.56085i	0.0751583	+	0.997172i	$0.476054\pi$
$150$		0			0
$151$	−10.0000	+	17.3205i	−0.813788	+	1.40952i	0.0964061	+	0.995342i	$0.469265\pi$
$151$	−10.0000	+	17.3205i	−0.813788	+	1.40952i	−0.910195	+	0.414181i	$0.864068\pi$
$152$		0			0
$153$		0			0
$154$	4.00000			0.322329
$155$	−8.00000	+	13.8564i	−0.642575	+	1.11297i
$156$		0			0
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	0.438948	−	0.898513i	$-0.355351\pi$
$158$	2.00000	+	3.46410i	0.159111	+	0.275589i
$159$		0			0
$160$	5.00000	−	8.66025i	0.395285	−	0.684653i
$161$	32.0000			2.52195
$162$		0			0
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$	−1.00000	+	1.73205i	−0.0780869	+	0.135250i
$165$		0			0
$166$	−6.00000	−	10.3923i	−0.465690	−	0.806599i
$167$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$167$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$	4.00000			0.306786
$171$		0			0
$172$		0			0
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		0			0
$175$	2.00000	+	3.46410i	0.151186	+	0.261861i
$176$	0.500000	+	0.866025i	0.0376889	+	0.0652791i
$177$		0			0
$178$	3.00000	−	5.19615i	0.224860	−	0.389468i
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	22.0000			1.63525			0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000			1.63525			0.817624	+	0.575753i	$0.195291\pi$
$182$	4.00000	−	6.92820i	0.296500	−	0.513553i
$183$		0			0
$184$	12.0000	+	20.7846i	0.884652	+	1.53226i
$185$	6.00000	+	10.3923i	0.441129	+	0.764057i
$186$		0			0
$187$	1.00000	−	1.73205i	0.0731272	−	0.126660i
$188$	−8.00000			−0.583460
$189$		0			0
$190$		0			0
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	−0.973674	−	0.227946i	$-0.926799\pi$
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	0.684244	+	0.729253i	$0.260132\pi$
$192$		0			0
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	0.999990	+	0.00447566i	$0.00142465\pi$
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	−0.496119	+	0.868255i	$0.665242\pi$
$194$	−1.00000	−	1.73205i	−0.0717958	−	0.124354i
$195$		0			0
$196$	4.50000	−	7.79423i	0.321429	−	0.556731i
$197$	−14.0000			−0.997459			−0.498729	−	0.866758i	$-0.666200\pi$
$197$	−14.0000			−0.997459			−0.498729	+	0.866758i	$0.666200\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	−1.50000	+	2.59808i	−0.106066	+	0.183712i
$201$		0			0
$202$	−1.00000	−	1.73205i	−0.0703598	−	0.121867i
$203$	12.0000	+	20.7846i	0.842235	+	1.45879i
$204$		0			0
$205$	−2.00000	+	3.46410i	−0.139686	+	0.241943i
$206$	8.00000			0.557386
$207$		0			0
$208$	2.00000			0.138675
$209$		0			0
$210$		0			0
$211$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$211$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$212$	3.00000	+	5.19615i	0.206041	+	0.356873i
$213$		0			0
$214$	6.00000	−	10.3923i	0.410152	−	0.710403i
$215$		0			0
$216$		0			0
$217$	−32.0000			−2.17230
$218$	1.00000	−	1.73205i	0.0677285	−	0.117309i
$219$		0			0
$220$	−1.00000	−	1.73205i	−0.0674200	−	0.116775i
$221$	−2.00000	−	3.46410i	−0.134535	−	0.233021i
$222$		0			0
$223$	−8.00000	+	13.8564i	−0.535720	+	0.927894i	0.463409	+	0.886145i	$0.346626\pi$
$223$	−8.00000	+	13.8564i	−0.535720	+	0.927894i	−0.999128	+	0.0417488i	$0.986707\pi$
$224$	20.0000			1.33631
$225$		0			0
$226$	−6.00000			−0.399114
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	−0.993508	−	0.113761i	$-0.963710\pi$
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	0.595274	+	0.803523i	$0.297043\pi$
$228$		0			0
$229$	−3.00000	−	5.19615i	−0.198246	−	0.343371i	0.749714	−	0.661762i	$-0.230191\pi$
$229$	−3.00000	−	5.19615i	−0.198246	−	0.343371i	−0.947960	+	0.318390i	$0.896858\pi$
$230$	8.00000	+	13.8564i	0.527504	+	0.913664i
$231$		0			0
$232$	−9.00000	+	15.5885i	−0.590879	+	1.02343i
$233$	30.0000			1.96537			0.982683	−	0.185296i	$-0.0593245\pi$
$233$	30.0000			1.96537			0.982683	+	0.185296i	$0.0593245\pi$
$234$		0			0
$235$	−16.0000			−1.04372
$236$	−2.00000	+	3.46410i	−0.130189	+	0.225494i
$237$		0			0
$238$	4.00000	+	6.92820i	0.259281	+	0.449089i
$239$	−12.0000	−	20.7846i	−0.776215	−	1.34444i	−0.934109	−	0.356988i	$-0.883804\pi$
$239$	−12.0000	−	20.7846i	−0.776215	−	1.34444i	0.157893	−	0.987456i	$-0.449530\pi$
$240$		0			0
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	−0.980917	−	0.194429i	$-0.937715\pi$
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	0.658838	+	0.752285i	$0.271048\pi$
$242$	1.00000			0.0642824
$243$		0			0
$244$	−6.00000			−0.384111
$245$	9.00000	−	15.5885i	0.574989	−	0.995910i
$246$		0			0
$247$		0			0
$248$	−12.0000	−	20.7846i	−0.762001	−	1.31982i
$249$		0			0
$250$	−6.00000	+	10.3923i	−0.379473	+	0.657267i
$251$	4.00000			0.252478			0.126239	−	0.992000i	$-0.459709\pi$
$251$	4.00000			0.252478			0.126239	+	0.992000i	$0.459709\pi$
$252$		0			0
$253$	8.00000			0.502956
$254$	2.00000	−	3.46410i	0.125491	−	0.217357i
$255$		0			0
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	7.00000	+	12.1244i	0.436648	+	0.756297i	0.997429	−	0.0716680i	$-0.0228322\pi$
$257$	7.00000	+	12.1244i	0.436648	+	0.756297i	−0.560781	+	0.827964i	$0.689499\pi$
$258$		0			0
$259$	−12.0000	+	20.7846i	−0.745644	+	1.29149i
$260$	−4.00000			−0.248069
$261$		0			0
$262$	−12.0000			−0.741362
$263$	8.00000	−	13.8564i	0.493301	−	0.854423i	−0.506669	−	0.862141i	$-0.669123\pi$
$263$	8.00000	−	13.8564i	0.493301	−	0.854423i	0.999970	+	0.00771799i	$0.00245674\pi$
$264$		0			0
$265$	6.00000	+	10.3923i	0.368577	+	0.638394i
$266$		0			0
$267$		0			0
$268$	−2.00000	+	3.46410i	−0.122169	+	0.211604i
$269$	−2.00000			−0.121942			−0.0609711	−	0.998140i	$-0.519420\pi$
$269$	−2.00000			−0.121942			−0.0609711	+	0.998140i	$0.519420\pi$
$270$		0			0
$271$	20.0000			1.21491			0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000			1.21491			0.607457	+	0.794353i	$0.292190\pi$
$272$	−1.00000	+	1.73205i	−0.0606339	+	0.105021i
$273$		0			0
$274$	−1.00000	−	1.73205i	−0.0604122	−	0.104637i
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$		0			0
$277$	13.0000	−	22.5167i	0.781094	−	1.35290i	−0.150210	−	0.988654i	$-0.547995\pi$
$277$	13.0000	−	22.5167i	0.781094	−	1.35290i	0.931305	−	0.364241i	$-0.118672\pi$
$278$	−8.00000			−0.479808
$279$		0			0
$280$	24.0000			1.43427
$281$	9.00000	−	15.5885i	0.536895	−	0.929929i	−0.462174	−	0.886789i	$-0.652930\pi$
$281$	9.00000	−	15.5885i	0.536895	−	0.929929i	0.999069	−	0.0431402i	$-0.0137362\pi$
$282$		0			0
$283$	−8.00000	−	13.8564i	−0.475551	−	0.823678i	0.524057	−	0.851683i	$-0.324418\pi$
$283$	−8.00000	−	13.8564i	−0.475551	−	0.823678i	−0.999608	+	0.0280052i	$0.991084\pi$
$284$		0			0
$285$		0			0
$286$	1.00000	−	1.73205i	0.0591312	−	0.102418i
$287$	−8.00000			−0.472225
$288$		0			0
$289$	−13.0000			−0.764706
$290$	−6.00000	+	10.3923i	−0.352332	+	0.610257i
$291$		0			0
$292$	−7.00000	−	12.1244i	−0.409644	−	0.709524i
$293$	3.00000	+	5.19615i	0.175262	+	0.303562i	0.940252	−	0.340480i	$-0.110589\pi$
$293$	3.00000	+	5.19615i	0.175262	+	0.303562i	−0.764990	+	0.644042i	$0.777256\pi$
$294$		0			0
$295$	−4.00000	+	6.92820i	−0.232889	+	0.403376i
$296$	−18.0000			−1.04623
$297$		0			0
$298$	−22.0000			−1.27443
$299$	8.00000	−	13.8564i	0.462652	−	0.801337i
$300$		0			0
$301$		0			0
$302$	−10.0000	−	17.3205i	−0.575435	−	0.996683i
$303$		0			0
$304$		0			0
$305$	−12.0000			−0.687118
$306$		0			0
$307$	32.0000			1.82634			0.913168	−	0.407583i	$-0.133628\pi$
$307$	32.0000			1.82634			0.913168	+	0.407583i	$0.133628\pi$
$308$	2.00000	−	3.46410i	0.113961	−	0.197386i
$309$		0			0
$310$	−8.00000	−	13.8564i	−0.454369	−	0.786991i
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	0.974841	+	0.222900i	$0.0715523\pi$
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	−0.294384	+	0.955687i	$0.595114\pi$
$312$		0			0
$313$	11.0000	−	19.0526i	0.621757	−	1.07691i	−0.367402	−	0.930062i	$-0.619753\pi$
$313$	11.0000	−	19.0526i	0.621757	−	1.07691i	0.989158	−	0.146852i	$-0.0469141\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$	4.00000			0.225018
$317$	−11.0000	+	19.0526i	−0.617822	+	1.07010i	0.372061	+	0.928208i	$0.378651\pi$
$317$	−11.0000	+	19.0526i	−0.617822	+	1.07010i	−0.989882	+	0.141890i	$0.954682\pi$
$318$		0			0
$319$	3.00000	+	5.19615i	0.167968	+	0.290929i
$320$	7.00000	+	12.1244i	0.391312	+	0.677772i
$321$		0			0
$322$	−16.0000	+	27.7128i	−0.891645	+	1.54437i
$323$		0			0
$324$		0			0
$325$	2.00000			0.110940
$326$	−2.00000	+	3.46410i	−0.110770	+	0.191859i
$327$		0			0
$328$	−3.00000	−	5.19615i	−0.165647	−	0.286910i
$329$	−16.0000	−	27.7128i	−0.882109	−	1.52786i
$330$		0			0
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	−0.448649	−	0.893708i	$-0.648095\pi$
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	0.998298	−	0.0583130i	$-0.0185721\pi$
$332$	−12.0000			−0.658586
$333$		0			0
$334$		0			0
$335$	−4.00000	+	6.92820i	−0.218543	+	0.378528i
$336$		0			0
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	0.992938	+	0.118633i	$0.0378512\pi$
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	−0.393730	+	0.919226i	$0.628816\pi$
$338$	4.50000	+	7.79423i	0.244768	+	0.423950i
$339$		0			0
$340$	2.00000	−	3.46410i	0.108465	−	0.187867i
$341$	−8.00000			−0.433224
$342$		0			0
$343$	8.00000			0.431959
$344$		0			0
$345$		0			0
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	−2.00000	−	3.46410i	−0.107366	−	0.185963i	0.807337	−	0.590091i	$-0.200908\pi$
$347$	−2.00000	−	3.46410i	−0.107366	−	0.185963i	−0.914702	+	0.404128i	$0.867575\pi$
$348$		0			0
$349$	−3.00000	+	5.19615i	−0.160586	+	0.278144i	−0.935079	−	0.354439i	$-0.884672\pi$
$349$	−3.00000	+	5.19615i	−0.160586	+	0.278144i	0.774493	+	0.632583i	$0.218005\pi$
$350$	−4.00000			−0.213809
$351$		0			0
$352$	5.00000			0.266501
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	−0.999711	−	0.0240566i	$-0.992342\pi$
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	0.520689	+	0.853746i	$0.325675\pi$
$354$		0			0
$355$		0			0
$356$	−3.00000	−	5.19615i	−0.159000	−	0.275396i
$357$		0			0
$358$	−6.00000	+	10.3923i	−0.317110	+	0.549250i
$359$	−8.00000			−0.422224			−0.211112	−	0.977462i	$-0.567708\pi$
$359$	−8.00000			−0.422224			−0.211112	+	0.977462i	$0.567708\pi$
$360$		0			0
$361$	−19.0000			−1.00000
$362$	−11.0000	+	19.0526i	−0.578147	+	1.00138i
$363$		0			0
$364$	−4.00000	−	6.92820i	−0.209657	−	0.363137i
$365$	−14.0000	−	24.2487i	−0.732793	−	1.26924i
$366$		0			0
$367$	16.0000	−	27.7128i	0.835193	−	1.44660i	−0.0586798	−	0.998277i	$-0.518689\pi$
$367$	16.0000	−	27.7128i	0.835193	−	1.44660i	0.893873	−	0.448320i	$-0.147978\pi$
$368$	−8.00000			−0.417029
$369$		0			0
$370$	−12.0000			−0.623850
$371$	−12.0000	+	20.7846i	−0.623009	+	1.07908i
$372$		0			0
$373$	1.00000	+	1.73205i	0.0517780	+	0.0896822i	0.890753	−	0.454488i	$-0.150178\pi$
$373$	1.00000	+	1.73205i	0.0517780	+	0.0896822i	−0.838975	+	0.544170i	$0.816844\pi$
$374$	1.00000	+	1.73205i	0.0517088	+	0.0895622i
$375$		0			0
$376$	12.0000	−	20.7846i	0.618853	−	1.07188i
$377$	12.0000			0.618031
$378$		0			0
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$		0			0
$381$		0			0
$382$	−4.00000	−	6.92820i	−0.204658	−	0.354478i
$383$	8.00000	+	13.8564i	0.408781	+	0.708029i	0.994753	−	0.102302i	$-0.0326207\pi$
$383$	8.00000	+	13.8564i	0.408781	+	0.708029i	−0.585973	+	0.810331i	$0.699287\pi$
$384$		0			0
$385$	4.00000	−	6.92820i	0.203859	−	0.353094i
$386$	−14.0000			−0.712581
$387$		0			0
$388$	−2.00000			−0.101535
$389$	9.00000	−	15.5885i	0.456318	−	0.790366i	−0.542445	−	0.840091i	$-0.682501\pi$
$389$	9.00000	−	15.5885i	0.456318	−	0.790366i	0.998763	+	0.0497253i	$0.0158346\pi$
$390$		0			0
$391$	8.00000	+	13.8564i	0.404577	+	0.700749i
$392$	13.5000	+	23.3827i	0.681853	+	1.18100i
$393$		0			0
$394$	7.00000	−	12.1244i	0.352655	−	0.610816i
$395$	8.00000			0.402524
$396$		0			0
$397$	−2.00000			−0.100377			−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000			−0.100377			−0.0501886	+	0.998740i	$0.515982\pi$
$398$		0			0
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−13.0000	−	22.5167i	−0.649189	−	1.12443i	−0.983317	−	0.181901i	$-0.941775\pi$
$401$	−13.0000	−	22.5167i	−0.649189	−	1.12443i	0.334128	−	0.942528i	$-0.391558\pi$
$402$		0			0
$403$	−8.00000	+	13.8564i	−0.398508	+	0.690237i
$404$	−2.00000			−0.0995037
$405$		0			0
$406$	−24.0000			−1.19110
$407$	−3.00000	+	5.19615i	−0.148704	+	0.257564i
$408$		0			0
$409$	−9.00000	−	15.5885i	−0.445021	−	0.770800i	0.553032	−	0.833160i	$-0.313471\pi$
$409$	−9.00000	−	15.5885i	−0.445021	−	0.770800i	−0.998054	+	0.0623602i	$0.980137\pi$
$410$	−2.00000	−	3.46410i	−0.0987730	−	0.171080i
$411$		0			0
$412$	4.00000	−	6.92820i	0.197066	−	0.341328i
$413$	−16.0000			−0.787309
$414$		0			0
$415$	−24.0000			−1.17811
$416$	5.00000	−	8.66025i	0.245145	−	0.424604i
$417$		0			0
$418$		0			0
$419$	2.00000	+	3.46410i	0.0977064	+	0.169232i	0.910735	−	0.412991i	$-0.135516\pi$
$419$	2.00000	+	3.46410i	0.0977064	+	0.169232i	−0.813029	+	0.582224i	$0.802183\pi$
$420$		0			0
$421$	13.0000	−	22.5167i	0.633581	−	1.09739i	−0.353233	−	0.935536i	$-0.614918\pi$
$421$	13.0000	−	22.5167i	0.633581	−	1.09739i	0.986814	−	0.161859i	$-0.0517491\pi$
$422$		0			0
$423$		0			0
$424$	−18.0000			−0.874157
$425$	−1.00000	+	1.73205i	−0.0485071	+	0.0840168i
$426$		0			0
$427$	−12.0000	−	20.7846i	−0.580721	−	1.00584i
$428$	−6.00000	−	10.3923i	−0.290021	−	0.502331i
$429$		0			0
$430$		0			0
$431$	−24.0000			−1.15604			−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000			−1.15604			−0.578020	+	0.816023i	$0.696174\pi$
$432$		0			0
$433$	34.0000			1.63394			0.816968	−	0.576683i	$-0.195653\pi$
$433$	34.0000			1.63394			0.816968	+	0.576683i	$0.195653\pi$
$434$	16.0000	−	27.7128i	0.768025	−	1.33026i
$435$		0			0
$436$	−1.00000	−	1.73205i	−0.0478913	−	0.0829502i
$437$		0			0
$438$		0			0
$439$	10.0000	−	17.3205i	0.477274	−	0.826663i	−0.522387	−	0.852709i	$-0.674958\pi$
$439$	10.0000	−	17.3205i	0.477274	−	0.826663i	0.999661	+	0.0260459i	$0.00829161\pi$
$440$	6.00000			0.286039
$441$		0			0
$442$	4.00000			0.190261
$443$	−14.0000	+	24.2487i	−0.665160	+	1.15209i	0.314082	+	0.949396i	$0.398303\pi$
$443$	−14.0000	+	24.2487i	−0.665160	+	1.15209i	−0.979242	+	0.202695i	$0.935030\pi$
$444$		0			0
$445$	−6.00000	−	10.3923i	−0.284427	−	0.492642i
$446$	−8.00000	−	13.8564i	−0.378811	−	0.656120i
$447$		0			0
$448$	−14.0000	+	24.2487i	−0.661438	+	1.14564i
$449$	2.00000			0.0943858			0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000			0.0943858			0.0471929	+	0.998886i	$0.484972\pi$
$450$		0			0
$451$	−2.00000			−0.0941763
$452$	−3.00000	+	5.19615i	−0.141108	+	0.244406i
$453$		0			0
$454$	−6.00000	−	10.3923i	−0.281594	−	0.487735i
$455$	−8.00000	−	13.8564i	−0.375046	−	0.649598i
$456$		0			0
$457$	−9.00000	+	15.5885i	−0.421002	+	0.729197i	−0.996038	−	0.0889312i	$-0.971655\pi$
$457$	−9.00000	+	15.5885i	−0.421002	+	0.729197i	0.575036	+	0.818128i	$0.304988\pi$
$458$	6.00000			0.280362
$459$		0			0
$460$	16.0000			0.746004
$461$	15.0000	−	25.9808i	0.698620	−	1.21004i	−0.270326	−	0.962769i	$-0.587131\pi$
$461$	15.0000	−	25.9808i	0.698620	−	1.21004i	0.968945	−	0.247276i	$-0.0795353\pi$
$462$		0			0
$463$	−8.00000	−	13.8564i	−0.371792	−	0.643962i	0.618050	−	0.786139i	$-0.287923\pi$
$463$	−8.00000	−	13.8564i	−0.371792	−	0.643962i	−0.989841	+	0.142177i	$0.954590\pi$
$464$	−3.00000	−	5.19615i	−0.139272	−	0.241225i
$465$		0			0
$466$	−15.0000	+	25.9808i	−0.694862	+	1.20354i
$467$	−12.0000			−0.555294			−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000			−0.555294			−0.277647	+	0.960683i	$0.589555\pi$
$468$		0			0
$469$	−16.0000			−0.738811
$470$	8.00000	−	13.8564i	0.369012	−	0.639148i
$471$		0			0
$472$	−6.00000	−	10.3923i	−0.276172	−	0.478345i
$473$		0			0
$474$		0			0
$475$		0			0
$476$	8.00000			0.366679
$477$		0			0
$478$	24.0000			1.09773
$479$	−4.00000	+	6.92820i	−0.182765	+	0.316558i	−0.942821	−	0.333300i	$-0.891838\pi$
$479$	−4.00000	+	6.92820i	−0.182765	+	0.316558i	0.760056	+	0.649857i	$0.225171\pi$
$480$		0			0
$481$	6.00000	+	10.3923i	0.273576	+	0.473848i
$482$	−5.00000	−	8.66025i	−0.227744	−	0.394464i
$483$		0			0
$484$	0.500000	−	0.866025i	0.0227273	−	0.0393648i
$485$	−4.00000			−0.181631
$486$		0			0
$487$	−16.0000			−0.725029			−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000			−0.725029			−0.362515	+	0.931978i	$0.618082\pi$
$488$	9.00000	−	15.5885i	0.407411	−	0.705656i
$489$		0			0
$490$	9.00000	+	15.5885i	0.406579	+	0.704215i
$491$	−2.00000	−	3.46410i	−0.0902587	−	0.156333i	0.817361	−	0.576126i	$-0.195436\pi$
$491$	−2.00000	−	3.46410i	−0.0902587	−	0.156333i	−0.907620	+	0.419793i	$0.862103\pi$
$492$		0			0
$493$	−6.00000	+	10.3923i	−0.270226	+	0.468046i
$494$		0			0
$495$		0			0
$496$	8.00000			0.359211
$497$		0			0
$498$		0			0
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	0.907314	−	0.420455i	$-0.138129\pi$
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	−0.817781	+	0.575529i	$0.804796\pi$
$500$	6.00000	+	10.3923i	0.268328	+	0.464758i
$501$		0			0
$502$	−2.00000	+	3.46410i	−0.0892644	+	0.154610i
$503$	−32.0000			−1.42681			−0.713405	−	0.700752i	$-0.752848\pi$
$503$	−32.0000			−1.42681			−0.713405	+	0.700752i	$0.752848\pi$
$504$		0			0
$505$	−4.00000			−0.177998
$506$	−4.00000	+	6.92820i	−0.177822	+	0.307996i
$507$		0			0
$508$	−2.00000	−	3.46410i	−0.0887357	−	0.153695i
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	−0.979322	−	0.202306i	$-0.935156\pi$
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	0.314459	−	0.949271i	$-0.398177\pi$
$510$		0			0
$511$	28.0000	−	48.4974i	1.23865	−	2.14540i
$512$	−11.0000			−0.486136
$513$		0			0
$514$	−14.0000			−0.617514
$515$	8.00000	−	13.8564i	0.352522	−	0.610586i
$516$		0			0
$517$	−4.00000	−	6.92820i	−0.175920	−	0.304702i
$518$	−12.0000	−	20.7846i	−0.527250	−	0.913223i
$519$		0			0
$520$	6.00000	−	10.3923i	0.263117	−	0.455733i
$521$	−30.0000			−1.31432			−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000			−1.31432			−0.657162	+	0.753749i	$0.728243\pi$
$522$		0			0
$523$	−16.0000			−0.699631			−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000			−0.699631			−0.349816	+	0.936819i	$0.613756\pi$
$524$	−6.00000	+	10.3923i	−0.262111	+	0.453990i
$525$		0			0
$526$	8.00000	+	13.8564i	0.348817	+	0.604168i
$527$	−8.00000	−	13.8564i	−0.348485	−	0.603595i
$528$		0			0
$529$	−20.5000	+	35.5070i	−0.891304	+	1.54378i
$530$	−12.0000			−0.521247
$531$		0			0
$532$		0			0
$533$	−2.00000	+	3.46410i	−0.0866296	+	0.150047i
$534$		0			0
$535$	−12.0000	−	20.7846i	−0.518805	−	0.898597i
$536$	−6.00000	−	10.3923i	−0.259161	−	0.448879i
$537$		0			0
$538$	1.00000	−	1.73205i	0.0431131	−	0.0746740i
$539$	9.00000			0.387657
$540$		0			0
$541$	46.0000			1.97769			0.988847	−	0.148933i	$-0.0475840\pi$
$541$	46.0000			1.97769			0.988847	+	0.148933i	$0.0475840\pi$
$542$	−10.0000	+	17.3205i	−0.429537	+	0.743980i
$543$		0			0
$544$	5.00000	+	8.66025i	0.214373	+	0.371305i
$545$	−2.00000	−	3.46410i	−0.0856706	−	0.148386i
$546$		0			0
$547$	−4.00000	+	6.92820i	−0.171028	+	0.296229i	−0.938779	−	0.344519i	$-0.888042\pi$
$547$	−4.00000	+	6.92820i	−0.171028	+	0.296229i	0.767752	+	0.640747i	$0.221375\pi$
$548$	−2.00000			−0.0854358
$549$		0			0
$550$	−1.00000			−0.0426401
$551$		0			0
$552$		0			0
$553$	8.00000	+	13.8564i	0.340195	+	0.589234i
$554$	13.0000	+	22.5167i	0.552317	+	0.956641i
$555$		0			0
$556$	−4.00000	+	6.92820i	−0.169638	+	0.293821i
$557$	−14.0000			−0.593199			−0.296600	−	0.955002i	$-0.595853\pi$
$557$	−14.0000			−0.593199			−0.296600	+	0.955002i	$0.595853\pi$
$558$		0			0
$559$		0			0
$560$	−4.00000	+	6.92820i	−0.169031	+	0.292770i
$561$		0			0
$562$	9.00000	+	15.5885i	0.379642	+	0.657559i
$563$	22.0000	+	38.1051i	0.927189	+	1.60594i	0.788002	+	0.615673i	$0.211116\pi$
$563$	22.0000	+	38.1051i	0.927189	+	1.60594i	0.139188	+	0.990266i	$0.455551\pi$
$564$		0			0
$565$	−6.00000	+	10.3923i	−0.252422	+	0.437208i
$566$	16.0000			0.672530
$567$		0			0
$568$		0			0
$569$	21.0000	−	36.3731i	0.880366	−	1.52484i	0.0294311	−	0.999567i	$-0.490630\pi$
$569$	21.0000	−	36.3731i	0.880366	−	1.52484i	0.850935	−	0.525271i	$-0.176036\pi$
$570$		0			0
$571$	8.00000	+	13.8564i	0.334790	+	0.579873i	0.983444	−	0.181210i	$-0.0580014\pi$
$571$	8.00000	+	13.8564i	0.334790	+	0.579873i	−0.648655	+	0.761083i	$0.724668\pi$
$572$	−1.00000	−	1.73205i	−0.0418121	−	0.0724207i
$573$		0			0
$574$	4.00000	−	6.92820i	0.166957	−	0.289178i
$575$	−8.00000			−0.333623
$576$		0			0
$577$	−30.0000			−1.24892			−0.624458	−	0.781058i	$-0.714680\pi$
$577$	−30.0000			−1.24892			−0.624458	+	0.781058i	$0.714680\pi$
$578$	6.50000	−	11.2583i	0.270364	−	0.468285i
$579$		0			0
$580$	6.00000	+	10.3923i	0.249136	+	0.431517i
$581$	−24.0000	−	41.5692i	−0.995688	−	1.72458i
$582$		0			0
$583$	−3.00000	+	5.19615i	−0.124247	+	0.215203i
$584$	42.0000			1.73797
$585$		0			0
$586$	−6.00000			−0.247858
$587$	−14.0000	+	24.2487i	−0.577842	+	1.00085i	0.417885	+	0.908500i	$0.362772\pi$
$587$	−14.0000	+	24.2487i	−0.577842	+	1.00085i	−0.995726	+	0.0923513i	$0.970562\pi$
$588$		0			0
$589$		0			0
$590$	−4.00000	−	6.92820i	−0.164677	−	0.285230i
$591$		0			0
$592$	3.00000	−	5.19615i	0.123299	−	0.213561i
$593$	38.0000			1.56047			0.780236	−	0.625485i	$-0.215099\pi$
$593$	38.0000			1.56047			0.780236	+	0.625485i	$0.215099\pi$
$594$		0			0
$595$	16.0000			0.655936
$596$	−11.0000	+	19.0526i	−0.450578	+	0.780423i
$597$		0			0
$598$	8.00000	+	13.8564i	0.327144	+	0.566631i
$599$	4.00000	+	6.92820i	0.163436	+	0.283079i	0.936099	−	0.351738i	$-0.114409\pi$
$599$	4.00000	+	6.92820i	0.163436	+	0.283079i	−0.772663	+	0.634816i	$0.781076\pi$
$600$		0			0
$601$	−13.0000	+	22.5167i	−0.530281	+	0.918474i	0.469095	+	0.883148i	$0.344580\pi$
$601$	−13.0000	+	22.5167i	−0.530281	+	0.918474i	−0.999376	+	0.0353259i	$0.988753\pi$
$602$		0			0
$603$		0			0
$604$	−20.0000			−0.813788
$605$	1.00000	−	1.73205i	0.0406558	−	0.0704179i
$606$		0			0
$607$	2.00000	+	3.46410i	0.0811775	+	0.140604i	0.903756	−	0.428048i	$-0.140799\pi$
$607$	2.00000	+	3.46410i	0.0811775	+	0.140604i	−0.822578	+	0.568652i	$0.807465\pi$
$608$		0			0
$609$		0			0
$610$	6.00000	−	10.3923i	0.242933	−	0.420772i
$611$	−16.0000			−0.647291
$612$		0			0
$613$	14.0000			0.565455			0.282727	−	0.959200i	$-0.408761\pi$
$613$	14.0000			0.565455			0.282727	+	0.959200i	$0.408761\pi$
$614$	−16.0000	+	27.7128i	−0.645707	+	1.11840i
$615$		0			0
$616$	6.00000	+	10.3923i	0.241747	+	0.418718i
$617$	15.0000	+	25.9808i	0.603877	+	1.04595i	0.992228	+	0.124434i	$0.0397116\pi$
$617$	15.0000	+	25.9808i	0.603877	+	1.04595i	−0.388351	+	0.921512i	$0.626955\pi$
$618$		0			0
$619$	−22.0000	+	38.1051i	−0.884255	+	1.53157i	−0.0376891	+	0.999290i	$0.512000\pi$
$619$	−22.0000	+	38.1051i	−0.884255	+	1.53157i	−0.846566	+	0.532284i	$0.821334\pi$
$620$	−16.0000			−0.642575
$621$		0			0
$622$	−24.0000			−0.962312
$623$	12.0000	−	20.7846i	0.480770	−	0.832718i
$624$		0			0
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$	11.0000	+	19.0526i	0.439648	+	0.761493i
$627$		0			0
$628$	7.00000	−	12.1244i	0.279330	−	0.483814i
$629$	−12.0000			−0.478471
$630$		0			0
$631$	16.0000			0.636950			0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000			0.636950			0.318475	+	0.947931i	$0.396829\pi$
$632$	−6.00000	+	10.3923i	−0.238667	+	0.413384i
$633$		0			0
$634$	−11.0000	−	19.0526i	−0.436866	−	0.756674i
$635$	−4.00000	−	6.92820i	−0.158735	−	0.274937i
$636$		0			0
$637$	9.00000	−	15.5885i	0.356593	−	0.617637i
$638$	−6.00000			−0.237542
$639$		0			0
$640$	6.00000			0.237171
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	−0.987200	−	0.159489i	$-0.949015\pi$
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	0.631721	+	0.775196i	$0.282349\pi$
$642$		0			0
$643$	−10.0000	−	17.3205i	−0.394362	−	0.683054i	0.598658	−	0.801005i	$-0.295701\pi$
$643$	−10.0000	−	17.3205i	−0.394362	−	0.683054i	−0.993019	+	0.117951i	$0.962368\pi$
$644$	16.0000	+	27.7128i	0.630488	+	1.09204i
$645$		0			0
$646$		0			0
$647$	8.00000			0.314512			0.157256	−	0.987558i	$-0.449735\pi$
$647$	8.00000			0.314512			0.157256	+	0.987558i	$0.449735\pi$
$648$		0			0
$649$	−4.00000			−0.157014
$650$	−1.00000	+	1.73205i	−0.0392232	+	0.0679366i
$651$		0			0
$652$	2.00000	+	3.46410i	0.0783260	+	0.135665i
$653$	1.00000	+	1.73205i	0.0391330	+	0.0677804i	0.884929	−	0.465727i	$-0.154207\pi$
$653$	1.00000	+	1.73205i	0.0391330	+	0.0677804i	−0.845796	+	0.533507i	$0.820874\pi$
$654$		0			0
$655$	−12.0000	+	20.7846i	−0.468879	+	0.812122i
$656$	2.00000			0.0780869
$657$		0			0
$658$	32.0000			1.24749
$659$	−2.00000	+	3.46410i	−0.0779089	+	0.134942i	−0.902348	−	0.431009i	$-0.858158\pi$
$659$	−2.00000	+	3.46410i	−0.0779089	+	0.134942i	0.824439	+	0.565951i	$0.191491\pi$
$660$		0			0
$661$	13.0000	+	22.5167i	0.505641	+	0.875797i	0.999979	+	0.00652642i	$0.00207744\pi$
$661$	13.0000	+	22.5167i	0.505641	+	0.875797i	−0.494337	+	0.869270i	$0.664589\pi$
$662$	10.0000	+	17.3205i	0.388661	+	0.673181i
$663$		0			0
$664$	18.0000	−	31.1769i	0.698535	−	1.20990i
$665$		0			0
$666$		0			0
$667$	−48.0000			−1.85857
$668$		0			0
$669$		0			0
$670$	−4.00000	−	6.92820i	−0.154533	−	0.267660i
$671$	−3.00000	−	5.19615i	−0.115814	−	0.200595i
$672$		0			0
$673$	23.0000	−	39.8372i	0.886585	−	1.53561i	0.0426985	−	0.999088i	$-0.486405\pi$
$673$	23.0000	−	39.8372i	0.886585	−	1.53561i	0.843886	−	0.536522i	$-0.180262\pi$
$674$	−22.0000			−0.847408
$675$		0			0
$676$	9.00000			0.346154
$677$	−9.00000	+	15.5885i	−0.345898	+	0.599113i	−0.985517	−	0.169580i	$-0.945759\pi$
$677$	−9.00000	+	15.5885i	−0.345898	+	0.599113i	0.639618	+	0.768693i	$0.279092\pi$
$678$		0			0
$679$	−4.00000	−	6.92820i	−0.153506	−	0.265880i
$680$	6.00000	+	10.3923i	0.230089	+	0.398527i
$681$		0			0
$682$	4.00000	−	6.92820i	0.153168	−	0.265295i
$683$	20.0000			0.765279			0.382639	−	0.923898i	$-0.375015\pi$
$683$	20.0000			0.765279			0.382639	+	0.923898i	$0.375015\pi$
$684$		0			0
$685$	−4.00000			−0.152832
$686$	−4.00000	+	6.92820i	−0.152721	+	0.264520i
$687$		0			0
$688$		0			0
$689$	6.00000	+	10.3923i	0.228582	+	0.395915i
$690$		0			0
$691$	14.0000	−	24.2487i	0.532585	−	0.922464i	−0.466691	−	0.884420i	$-0.654554\pi$
$691$	14.0000	−	24.2487i	0.532585	−	0.922464i	0.999276	−	0.0380440i	$-0.0121127\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	4.00000			0.151838
$695$	−8.00000	+	13.8564i	−0.303457	+	0.525603i
$696$		0			0
$697$	−2.00000	−	3.46410i	−0.0757554	−	0.131212i
$698$	−3.00000	−	5.19615i	−0.113552	−	0.196677i
$699$		0			0
$700$	−2.00000	+	3.46410i	−0.0755929	+	0.130931i
$701$	50.0000			1.88847			0.944237	−	0.329267i	$-0.106802\pi$
$701$	50.0000			1.88847			0.944237	+	0.329267i	$0.106802\pi$
$702$		0			0
$703$		0			0
$704$	−3.50000	+	6.06218i	−0.131911	+	0.228477i
$705$		0			0
$706$	−9.00000	−	15.5885i	−0.338719	−	0.586679i
$707$	−4.00000	−	6.92820i	−0.150435	−	0.260562i
$708$		0			0
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	0.249952	+	0.968258i	$0.419585\pi$
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	−0.963512	+	0.267664i	$0.913748\pi$
$710$		0			0
$711$		0			0
$712$	18.0000			0.674579
$713$	32.0000	−	55.4256i	1.19841	−	2.07571i
$714$		0			0
$715$	−2.00000	−	3.46410i	−0.0747958	−	0.129550i
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$		0			0
$718$	4.00000	−	6.92820i	0.149279	−	0.258558i
$719$	24.0000			0.895049			0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000			0.895049			0.447524	+	0.894272i	$0.352306\pi$
$720$		0			0
$721$	32.0000			1.19174
$722$	9.50000	−	16.4545i	0.353553	−	0.612372i
$723$		0			0
$724$	11.0000	+	19.0526i	0.408812	+	0.708083i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$		0			0
$727$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$727$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$728$	24.0000			0.889499
$729$		0			0
$730$	28.0000			1.03633
$731$		0			0
$732$		0			0
$733$	−15.0000	−	25.9808i	−0.554038	−	0.959621i	−0.997978	−	0.0635649i	$-0.979753\pi$
$733$	−15.0000	−	25.9808i	−0.554038	−	0.959621i	0.443940	−	0.896056i	$-0.353580\pi$
$734$	16.0000	+	27.7128i	0.590571	+	1.02290i
$735$		0			0
$736$	−20.0000	+	34.6410i	−0.737210	+	1.27688i
$737$	−4.00000			−0.147342
$738$		0			0
$739$	8.00000			0.294285			0.147142	−	0.989115i	$-0.452992\pi$
$739$	8.00000			0.294285			0.147142	+	0.989115i	$0.452992\pi$
$740$	−6.00000	+	10.3923i	−0.220564	+	0.382029i
$741$		0			0
$742$	−12.0000	−	20.7846i	−0.440534	−	0.763027i
$743$	−20.0000	−	34.6410i	−0.733729	−	1.27086i	−0.955279	−	0.295707i	$-0.904445\pi$
$743$	−20.0000	−	34.6410i	−0.733729	−	1.27086i	0.221550	−	0.975149i	$-0.428888\pi$
$744$		0			0
$745$	−22.0000	+	38.1051i	−0.806018	+	1.39606i
$746$	−2.00000			−0.0732252
$747$		0			0
$748$	2.00000			0.0731272
$749$	24.0000	−	41.5692i	0.876941	−	1.51891i
$750$		0			0
$751$	4.00000	+	6.92820i	0.145962	+	0.252814i	0.929731	−	0.368238i	$-0.120039\pi$
$751$	4.00000	+	6.92820i	0.145962	+	0.252814i	−0.783769	+	0.621052i	$0.786706\pi$
$752$	4.00000	+	6.92820i	0.145865	+	0.252646i
$753$		0			0
$754$	−6.00000	+	10.3923i	−0.218507	+	0.378465i
$755$	−40.0000			−1.45575
$756$		0			0
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$	−14.0000	+	24.2487i	−0.508503	+	0.880753i
$759$		0			0
$760$		0			0
$761$	−3.00000	−	5.19615i	−0.108750	−	0.188360i	0.806514	−	0.591215i	$-0.201351\pi$
$761$	−3.00000	−	5.19615i	−0.108750	−	0.188360i	−0.915264	+	0.402854i	$0.868018\pi$
$762$		0			0
$763$	4.00000	−	6.92820i	0.144810	−	0.250818i
$764$	−8.00000			−0.289430
$765$		0			0
$766$	−16.0000			−0.578103
$767$	−4.00000	+	6.92820i	−0.144432	+	0.250163i
$768$		0			0
$769$	−1.00000	−	1.73205i	−0.0360609	−	0.0624593i	0.847432	−	0.530904i	$-0.178148\pi$
$769$	−1.00000	−	1.73205i	−0.0360609	−	0.0624593i	−0.883493	+	0.468445i	$0.844814\pi$
$770$	4.00000	+	6.92820i	0.144150	+	0.249675i
$771$		0			0
$772$	−7.00000	+	12.1244i	−0.251936	+	0.436365i
$773$	6.00000			0.215805			0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000			0.215805			0.107903	+	0.994161i	$0.465587\pi$
$774$		0			0
$775$	8.00000			0.287368
$776$	3.00000	−	5.19615i	0.107694	−	0.186531i
$777$		0			0
$778$	9.00000	+	15.5885i	0.322666	+	0.558873i
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−16.0000			−0.572159
$783$		0			0
$784$	−9.00000			−0.321429
$785$	14.0000	−	24.2487i	0.499681	−	0.865474i
$786$		0			0
$787$	4.00000	+	6.92820i	0.142585	+	0.246964i	0.928469	−	0.371409i	$-0.121125\pi$
$787$	4.00000	+	6.92820i	0.142585	+	0.246964i	−0.785885	+	0.618373i	$0.787792\pi$
$788$	−7.00000	−	12.1244i	−0.249365	−	0.431912i
$789$		0			0
$790$	−4.00000	+	6.92820i	−0.142314	+	0.246494i
$791$	−24.0000			−0.853342
$792$		0			0
$793$	−12.0000			−0.426132
$794$	1.00000	−	1.73205i	0.0354887	−	0.0614682i
$795$		0			0
$796$		0			0
$797$	5.00000	+	8.66025i	0.177109	+	0.306762i	0.940889	−	0.338715i	$-0.109992\pi$
$797$	5.00000	+	8.66025i	0.177109	+	0.306762i	−0.763780	+	0.645477i	$0.776659\pi$
$798$		0			0
$799$	8.00000	−	13.8564i	0.283020	−	0.490204i
$800$	−5.00000			−0.176777
$801$		0			0
$802$	26.0000			0.918092
$803$	7.00000	−	12.1244i	0.247025	−	0.427859i
$804$		0			0
$805$	32.0000	+	55.4256i	1.12785	+	1.95350i
$806$	−8.00000	−	13.8564i	−0.281788	−	0.488071i
$807$		0			0
$808$	3.00000	−	5.19615i	0.105540	−	0.182800i
$809$	54.0000			1.89854			0.949269	−	0.314464i	$-0.101825\pi$
$809$	54.0000			1.89854			0.949269	+	0.314464i	$0.101825\pi$
$810$		0			0
$811$	−56.0000			−1.96643			−0.983213	−	0.182462i	$-0.941593\pi$
$811$	−56.0000			−1.96643			−0.983213	+	0.182462i	$0.941593\pi$
$812$	−12.0000	+	20.7846i	−0.421117	+	0.729397i
$813$		0			0
$814$	−3.00000	−	5.19615i	−0.105150	−	0.182125i
$815$	4.00000	+	6.92820i	0.140114	+	0.242684i
$816$		0			0
$817$		0			0
$818$	18.0000			0.629355
$819$		0			0
$820$	−4.00000			−0.139686
$821$	7.00000	−	12.1244i	0.244302	−	0.423143i	−0.717633	−	0.696421i	$-0.754775\pi$
$821$	7.00000	−	12.1244i	0.244302	−	0.423143i	0.961935	+	0.273278i	$0.0881079\pi$
$822$		0			0
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	0.577474	−	0.816409i	$-0.304038\pi$
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	−0.995768	+	0.0919029i	$0.970705\pi$
$824$	12.0000	+	20.7846i	0.418040	+	0.724066i
$825$		0			0
$826$	8.00000	−	13.8564i	0.278356	−	0.482126i
$827$	20.0000			0.695468			0.347734	−	0.937593i	$-0.386951\pi$
$827$	20.0000			0.695468			0.347734	+	0.937593i	$0.386951\pi$
$828$		0			0
$829$	−2.00000			−0.0694629			−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000			−0.0694629			−0.0347314	+	0.999397i	$0.511058\pi$
$830$	12.0000	−	20.7846i	0.416526	−	0.721444i
$831$		0			0
$832$	7.00000	+	12.1244i	0.242681	+	0.420336i
$833$	9.00000	+	15.5885i	0.311832	+	0.540108i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$	−4.00000			−0.138178
$839$	28.0000	−	48.4974i	0.966667	−	1.67432i	0.261600	−	0.965176i	$-0.415750\pi$
$839$	28.0000	−	48.4974i	0.966667	−	1.67432i	0.705067	−	0.709141i	$-0.250917\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	13.0000	+	22.5167i	0.448010	+	0.775975i
$843$		0			0
$844$		0			0
$845$	18.0000			0.619219
$846$		0			0
$847$	4.00000			0.137442
$848$	3.00000	−	5.19615i	0.103020	−	0.178437i
$849$		0			0
$850$	−1.00000	−	1.73205i	−0.0342997	−	0.0594089i
$851$	−24.0000	−	41.5692i	−0.822709	−	1.42497i
$852$		0			0
$853$	17.0000	−	29.4449i	0.582069	−	1.00817i	−0.413165	−	0.910656i	$-0.635577\pi$
$853$	17.0000	−	29.4449i	0.582069	−	1.00817i	0.995234	−	0.0975167i	$-0.0310899\pi$
$854$	24.0000			0.821263
$855$		0			0
$856$	36.0000			1.23045
$857$	5.00000	−	8.66025i	0.170797	−	0.295829i	−0.767902	−	0.640567i	$-0.778699\pi$
$857$	5.00000	−	8.66025i	0.170797	−	0.295829i	0.938699	+	0.344739i	$0.112033\pi$
$858$		0			0
$859$	18.0000	+	31.1769i	0.614152	+	1.06374i	0.990533	+	0.137277i	$0.0438352\pi$
$859$	18.0000	+	31.1769i	0.614152	+	1.06374i	−0.376381	+	0.926465i	$0.622831\pi$
$860$		0			0
$861$		0			0
$862$	12.0000	−	20.7846i	0.408722	−	0.707927i
$863$	48.0000			1.63394			0.816970	−	0.576681i	$-0.195652\pi$
$863$	48.0000			1.63394			0.816970	+	0.576681i	$0.195652\pi$
$864$		0			0
$865$	12.0000			0.408012
$866$	−17.0000	+	29.4449i	−0.577684	+	1.00058i
$867$		0			0
$868$	−16.0000	−	27.7128i	−0.543075	−	0.940634i
$869$	2.00000	+	3.46410i	0.0678454	+	0.117512i
$870$		0			0
$871$	−4.00000	+	6.92820i	−0.135535	+	0.234753i
$872$	6.00000			0.203186
$873$		0			0
$874$		0			0
$875$	−24.0000	+	41.5692i	−0.811348	+	1.40530i
$876$		0			0
$877$	−3.00000	−	5.19615i	−0.101303	−	0.175462i	0.810919	−	0.585159i	$-0.198968\pi$
$877$	−3.00000	−	5.19615i	−0.101303	−	0.175462i	−0.912222	+	0.409697i	$0.865634\pi$
$878$	10.0000	+	17.3205i	0.337484	+	0.584539i
$879$		0			0
$880$	−1.00000	+	1.73205i	−0.0337100	+	0.0583874i
$881$	26.0000			0.875962			0.437981	−	0.898984i	$-0.355694\pi$
$881$	26.0000			0.875962			0.437981	+	0.898984i	$0.355694\pi$
$882$		0			0
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$	2.00000	−	3.46410i	0.0672673	−	0.116510i
$885$		0			0
$886$	−14.0000	−	24.2487i	−0.470339	−	0.814651i
$887$	−4.00000	−	6.92820i	−0.134307	−	0.232626i	0.791026	−	0.611783i	$-0.209547\pi$
$887$	−4.00000	−	6.92820i	−0.134307	−	0.232626i	−0.925332	+	0.379157i	$0.876214\pi$
$888$		0			0
$889$	8.00000	−	13.8564i	0.268311	−	0.464729i
$890$	12.0000			0.402241
$891$		0			0
$892$	−16.0000			−0.535720
$893$		0			0
$894$		0			0
$895$	12.0000	+	20.7846i	0.401116	+	0.694753i
$896$	6.00000	+	10.3923i	0.200446	+	0.347183i
$897$		0			0
$898$	−1.00000	+	1.73205i	−0.0333704	+	0.0577993i
$899$	48.0000			1.60089
$900$		0			0
$901$	−12.0000			−0.399778
$902$	1.00000	−	1.73205i	0.0332964	−	0.0576710i
$903$		0			0
$904$	−9.00000	−	15.5885i	−0.299336	−	0.518464i
$905$	22.0000	+	38.1051i	0.731305	+	1.26666i
$906$		0			0
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	−0.948278	−	0.317441i	$-0.897176\pi$
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	0.749051	+	0.662512i	$0.230510\pi$
$908$	−12.0000			−0.398234
$909$		0			0
$910$	16.0000			0.530395
$911$	−12.0000	+	20.7846i	−0.397578	+	0.688625i	−0.993426	−	0.114472i	$-0.963482\pi$
$911$	−12.0000	+	20.7846i	−0.397578	+	0.688625i	0.595849	+	0.803097i	$0.296816\pi$
$912$		0			0
$913$	−6.00000	−	10.3923i	−0.198571	−	0.343935i
$914$	−9.00000	−	15.5885i	−0.297694	−	0.515620i
$915$		0			0
$916$	3.00000	−	5.19615i	0.0991228	−	0.171686i
$917$	−48.0000			−1.58510
$918$		0			0
$919$	−20.0000			−0.659739			−0.329870	−	0.944027i	$-0.607005\pi$
$919$	−20.0000			−0.659739			−0.329870	+	0.944027i	$0.607005\pi$
$920$	−24.0000	+	41.5692i	−0.791257	+	1.37050i
$921$		0			0
$922$	15.0000	+	25.9808i	0.493999	+	0.855631i
$923$		0			0
$924$		0			0
$925$	3.00000	−	5.19615i	0.0986394	−	0.170848i
$926$	16.0000			0.525793
$927$		0			0
$928$	−30.0000			−0.984798
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	−0.812607	−	0.582812i	$-0.801952\pi$
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	0.911034	+	0.412332i	$0.135286\pi$
$930$		0			0
$931$		0			0
$932$	15.0000	+	25.9808i	0.491341	+	0.851028i
$933$		0			0
$934$	6.00000	−	10.3923i	0.196326	−	0.340047i
$935$	4.00000			0.130814
$936$		0			0
$937$	26.0000			0.849383			0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000			0.849383			0.424691	+	0.905338i	$0.360383\pi$
$938$	8.00000	−	13.8564i	0.261209	−	0.452428i
$939$		0			0
$940$	−8.00000	−	13.8564i	−0.260931	−	0.451946i
$941$	27.0000	+	46.7654i	0.880175	+	1.52451i	0.851146	+	0.524929i	$0.175908\pi$
$941$	27.0000	+	46.7654i	0.880175	+	1.52451i	0.0290288	+	0.999579i	$0.490759\pi$
$942$		0			0
$943$	8.00000	−	13.8564i	0.260516	−	0.451227i
$944$	4.00000			0.130189
$945$		0			0
$946$		0			0
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	−0.946892	−	0.321552i	$-0.895796\pi$
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	0.751918	+	0.659256i	$0.229129\pi$
$948$		0			0
$949$	−14.0000	−	24.2487i	−0.454459	−	0.787146i
$950$		0			0
$951$		0			0
$952$	−12.0000	+	20.7846i	−0.388922	+	0.673633i
$953$	22.0000			0.712650			0.356325	−	0.934362i	$-0.384030\pi$
$953$	22.0000			0.712650			0.356325	+	0.934362i	$0.384030\pi$
$954$		0			0
$955$	−16.0000			−0.517748
$956$	12.0000	−	20.7846i	0.388108	−	0.672222i
$957$		0			0
$958$	−4.00000	−	6.92820i	−0.129234	−	0.223840i
$959$	−4.00000	−	6.92820i	−0.129167	−	0.223723i
$960$		0			0
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	−12.0000			−0.386896
$963$		0			0
$964$	−10.0000			−0.322078
$965$	−14.0000	+	24.2487i	−0.450676	+	0.780594i
$966$		0			0
$967$	−2.00000	−	3.46410i	−0.0643157	−	0.111398i	0.832075	−	0.554664i	$-0.187153\pi$
$967$	−2.00000	−	3.46410i	−0.0643157	−	0.111398i	−0.896390	+	0.443266i	$0.853820\pi$
$968$	1.50000	+	2.59808i	0.0482118	+	0.0835053i
$969$		0			0
$970$	2.00000	−	3.46410i	0.0642161	−	0.111226i
$971$	−52.0000			−1.66876			−0.834380	−	0.551190i	$-0.814174\pi$
$971$	−52.0000			−1.66876			−0.834380	+	0.551190i	$0.814174\pi$
$972$		0			0
$973$	−32.0000			−1.02587
$974$	8.00000	−	13.8564i	0.256337	−	0.443988i
$975$		0			0
$976$	3.00000	+	5.19615i	0.0960277	+	0.166325i
$977$	3.00000	+	5.19615i	0.0959785	+	0.166240i	0.910017	−	0.414572i	$-0.136069\pi$
$977$	3.00000	+	5.19615i	0.0959785	+	0.166240i	−0.814038	+	0.580812i	$0.802735\pi$
$978$		0			0
$979$	3.00000	−	5.19615i	0.0958804	−	0.166070i
$980$	18.0000			0.574989
$981$		0			0
$982$	4.00000			0.127645
$983$	−12.0000	+	20.7846i	−0.382741	+	0.662926i	−0.991453	−	0.130465i	$-0.958353\pi$
$983$	−12.0000	+	20.7846i	−0.382741	+	0.662926i	0.608712	+	0.793391i	$0.291686\pi$
$984$		0			0
$985$	−14.0000	−	24.2487i	−0.446077	−	0.772628i
$986$	−6.00000	−	10.3923i	−0.191079	−	0.330958i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	40.0000			1.27064			0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000			1.27064			0.635321	+	0.772248i	$0.280868\pi$
$992$	20.0000	−	34.6410i	0.635001	−	1.09985i
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	−0.955322	−	0.295567i	$-0.904491\pi$
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	0.733630	+	0.679549i	$0.237825\pi$
$998$	−4.00000			−0.126618
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.e.e.298.1		2
3.2	odd	2		891.2.e.g.298.1		2
9.2	odd	6		99.2.a.b.1.1		1
9.4	even	3	inner	891.2.e.e.595.1		2
9.5	odd	6		891.2.e.g.595.1		2
9.7	even	3		33.2.a.a.1.1	✓	1
36.7	odd	6		528.2.a.g.1.1		1
36.11	even	6		1584.2.a.o.1.1		1
45.2	even	12		2475.2.c.d.199.1		2
45.7	odd	12		825.2.c.a.199.2		2
45.29	odd	6		2475.2.a.g.1.1		1
45.34	even	6		825.2.a.a.1.1		1
45.38	even	12		2475.2.c.d.199.2		2
45.43	odd	12		825.2.c.a.199.1		2
63.20	even	6		4851.2.a.b.1.1		1
63.34	odd	6		1617.2.a.j.1.1		1
72.11	even	6		6336.2.a.n.1.1		1
72.29	odd	6		6336.2.a.x.1.1		1
72.43	odd	6		2112.2.a.j.1.1		1
72.61	even	6		2112.2.a.bb.1.1		1
99.7	odd	30		363.2.e.g.148.1		4
99.16	even	15		363.2.e.e.124.1		4
99.25	even	15		363.2.e.e.130.1		4
99.43	odd	6		363.2.a.b.1.1		1
99.52	odd	30		363.2.e.g.130.1		4
99.61	odd	30		363.2.e.g.124.1		4
99.65	even	6		1089.2.a.j.1.1		1
99.70	even	15		363.2.e.e.148.1		4
99.79	odd	30		363.2.e.g.202.1		4
99.97	even	15		363.2.e.e.202.1		4
117.25	even	6		5577.2.a.a.1.1		1
153.16	even	6		9537.2.a.m.1.1		1
396.43	even	6		5808.2.a.t.1.1		1
495.439	odd	6		9075.2.a.q.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.a.a.1.1	✓	1	9.7	even	3
99.2.a.b.1.1		1	9.2	odd	6
363.2.a.b.1.1		1	99.43	odd	6
363.2.e.e.124.1		4	99.16	even	15
363.2.e.e.130.1		4	99.25	even	15
363.2.e.e.148.1		4	99.70	even	15
363.2.e.e.202.1		4	99.97	even	15
363.2.e.g.124.1		4	99.61	odd	30
363.2.e.g.130.1		4	99.52	odd	30
363.2.e.g.148.1		4	99.7	odd	30
363.2.e.g.202.1		4	99.79	odd	30
528.2.a.g.1.1		1	36.7	odd	6
825.2.a.a.1.1		1	45.34	even	6
825.2.c.a.199.1		2	45.43	odd	12
825.2.c.a.199.2		2	45.7	odd	12
891.2.e.e.298.1		2	1.1	even	1	trivial
891.2.e.e.595.1		2	9.4	even	3	inner
891.2.e.g.298.1		2	3.2	odd	2
891.2.e.g.595.1		2	9.5	odd	6
1089.2.a.j.1.1		1	99.65	even	6
1584.2.a.o.1.1		1	36.11	even	6
1617.2.a.j.1.1		1	63.34	odd	6
2112.2.a.j.1.1		1	72.43	odd	6
2112.2.a.bb.1.1		1	72.61	even	6
2475.2.a.g.1.1		1	45.29	odd	6
2475.2.c.d.199.1		2	45.2	even	12
2475.2.c.d.199.2		2	45.38	even	12
4851.2.a.b.1.1		1	63.20	even	6
5577.2.a.a.1.1		1	117.25	even	6
5808.2.a.t.1.1		1	396.43	even	6
6336.2.a.n.1.1		1	72.11	even	6
6336.2.a.x.1.1		1	72.29	odd	6
9075.2.a.q.1.1		1	495.439	odd	6
9537.2.a.m.1.1		1	153.16	even	6

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +(-2.00000 + 3.46410i) q^{7} -3.00000 q^{8} -2.00000 q^{10} +(-0.500000 + 0.866025i) q^{11} +(1.00000 + 1.73205i) q^{13} +(-2.00000 - 3.46410i) q^{14} +(0.500000 - 0.866025i) q^{16} -2.00000 q^{17} +(-1.00000 + 1.73205i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(-4.00000 - 6.92820i) q^{23} +(0.500000 - 0.866025i) q^{25} -2.00000 q^{26} -4.00000 q^{28} +(3.00000 - 5.19615i) q^{29} +(4.00000 + 6.92820i) q^{31} +(-2.50000 - 4.33013i) q^{32} +(1.00000 - 1.73205i) q^{34} -8.00000 q^{35} +6.00000 q^{37} +(-3.00000 - 5.19615i) q^{40} +(1.00000 + 1.73205i) q^{41} -1.00000 q^{44} +8.00000 q^{46} +(-4.00000 + 6.92820i) q^{47} +(-4.50000 - 7.79423i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-1.00000 + 1.73205i) q^{52} +6.00000 q^{53} -2.00000 q^{55} +(6.00000 - 10.3923i) q^{56} +(3.00000 + 5.19615i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-3.00000 + 5.19615i) q^{61} -8.00000 q^{62} +7.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-1.00000 - 1.73205i) q^{68} +(4.00000 - 6.92820i) q^{70} -14.0000 q^{73} +(-3.00000 + 5.19615i) q^{74} +(-2.00000 - 3.46410i) q^{77} +(2.00000 - 3.46410i) q^{79} +2.00000 q^{80} -2.00000 q^{82} +(-6.00000 + 10.3923i) q^{83} +(-2.00000 - 3.46410i) q^{85} +(1.50000 - 2.59808i) q^{88} -6.00000 q^{89} -8.00000 q^{91} +(4.00000 - 6.92820i) q^{92} +(-4.00000 - 6.92820i) q^{94} +(-1.00000 + 1.73205i) q^{97} +9.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{4} + 2 q^{5} - 4 q^{7} - 6 q^{8} - 4 q^{10} - q^{11} + 2 q^{13} - 4 q^{14} + q^{16} - 4 q^{17} - 2 q^{20} - q^{22} - 8 q^{23} + q^{25} - 4 q^{26} - 8 q^{28} + 6 q^{29} + 8 q^{31}+ \cdots + 18 q^{98}+O(q^{100}) \) 2 * q - q^2 + q^4 + 2 * q^5 - 4 * q^7 - 6 * q^8 - 4 * q^10 - q^11 + 2 * q^13 - 4 * q^14 + q^16 - 4 * q^17 - 2 * q^20 - q^22 - 8 * q^23 + q^25 - 4 * q^26 - 8 * q^28 + 6 * q^29 + 8 * q^31 - 5 * q^32 + 2 * q^34 - 16 * q^35 + 12 * q^37 - 6 * q^40 + 2 * q^41 - 2 * q^44 + 16 * q^46 - 8 * q^47 - 9 * q^49 + q^50 - 2 * q^52 + 12 * q^53 - 4 * q^55 + 12 * q^56 + 6 * q^58 + 4 * q^59 - 6 * q^61 - 16 * q^62 + 14 * q^64 - 4 * q^65 + 4 * q^67 - 2 * q^68 + 8 * q^70 - 28 * q^73 - 6 * q^74 - 4 * q^77 + 4 * q^79 + 4 * q^80 - 4 * q^82 - 12 * q^83 - 4 * q^85 + 3 * q^88 - 12 * q^89 - 16 * q^91 + 8 * q^92 - 8 * q^94 - 2 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more