LMFDB - Embedded newform 1782.2.i.f.593.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1782,2,Mod(593,1782)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1782, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1782.593"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1782 = 2 \cdot 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1782.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,2,0,-2,0,0,0,-4,0,0,-6,0,0,0,0,-2,0,0,0,0,0,6,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(25)] == traces)

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

Self dual:	no
Analytic conductor:	$14.2293416402$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			593.1
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1782.593
Dual form			1782.2.i.f.1187.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.22474 + 0.707107i) q^{5} +(3.67423 + 2.12132i) q^{7} -1.00000 q^{8} +1.41421i q^{10} +(-2.72474 + 1.89097i) q^{11} +(3.67423 - 2.12132i) q^{13} +(3.67423 - 2.12132i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.22474 + 0.707107i) q^{20} +(0.275255 + 3.30518i) q^{22} +(-1.22474 + 0.707107i) q^{23} +(-1.50000 + 2.59808i) q^{25} -4.24264i q^{26} -4.24264i q^{28} +(-3.00000 + 5.19615i) q^{29} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} -6.00000 q^{35} +2.00000 q^{37} +(1.22474 - 0.707107i) q^{40} +(3.00000 + 5.19615i) q^{41} +(-7.34847 - 4.24264i) q^{43} +(3.00000 + 1.41421i) q^{44} +1.41421i q^{46} +(8.57321 + 4.94975i) q^{47} +(5.50000 + 9.52628i) q^{49} +(1.50000 + 2.59808i) q^{50} +(-3.67423 - 2.12132i) q^{52} +7.07107i q^{53} +(2.00000 - 4.24264i) q^{55} +(-3.67423 - 2.12132i) q^{56} +(3.00000 + 5.19615i) q^{58} +(9.79796 - 5.65685i) q^{59} +(3.67423 + 2.12132i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-3.00000 + 5.19615i) q^{70} +7.07107i q^{71} +(1.00000 - 1.73205i) q^{74} +(-14.0227 + 1.16781i) q^{77} +(3.67423 + 2.12132i) q^{79} -1.41421i q^{80} +6.00000 q^{82} +(6.00000 - 10.3923i) q^{83} +(-7.34847 + 4.24264i) q^{86} +(2.72474 - 1.89097i) q^{88} -5.65685i q^{89} +18.0000 q^{91} +(1.22474 + 0.707107i) q^{92} +(8.57321 - 4.94975i) q^{94} +(-4.00000 + 6.92820i) q^{97} +11.0000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 6 q^{11} - 2 q^{16} + 6 q^{22} - 6 q^{25} - 12 q^{29} + 8 q^{31} + 2 q^{32} - 24 q^{35} + 8 q^{37} + 12 q^{41} + 12 q^{44} + 22 q^{49} + 6 q^{50} + 8 q^{55} + 12 q^{58}+ \cdots + 44 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 6 * q^11 - 2 * q^16 + 6 * q^22 - 6 * q^25 - 12 * q^29 + 8 * q^31 + 2 * q^32 - 24 * q^35 + 8 * q^37 + 12 * q^41 + 12 * q^44 + 22 * q^49 + 6 * q^50 + 8 * q^55 + 12 * q^58 + 16 * q^62 + 4 * q^64 - 12 * q^65 + 8 * q^67 - 12 * q^70 + 4 * q^74 - 12 * q^77 + 24 * q^82 + 24 * q^83 + 6 * q^88 + 72 * q^91 - 16 * q^97 + 44 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1782\mathbb{Z}\right)^\times$.

$n$	$1135$	$1541$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.22474	+	0.707107i	−0.547723	+	0.316228i	−0.748203	−	0.663470i	$-0.769083\pi$
$5$	−1.22474	+	0.707107i	−0.547723	+	0.316228i	0.200480	+	0.979698i	$0.435750\pi$
$6$		0			0
$7$	3.67423	+	2.12132i	1.38873	+	0.801784i	0.993172	−	0.116657i	$-0.0372179\pi$
$7$	3.67423	+	2.12132i	1.38873	+	0.801784i	0.395558	+	0.918441i	$0.370551\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$			1.41421i			0.447214i
$11$	−2.72474	+	1.89097i	−0.821541	+	0.570149i
$11$	−2.72474	+	1.89097i	−0.821541	+	0.570149i
$12$		0			0
$13$	3.67423	−	2.12132i	1.01905	−	0.588348i	0.105221	−	0.994449i	$-0.466445\pi$
$13$	3.67423	−	2.12132i	1.01905	−	0.588348i	0.913828	+	0.406100i	$0.133112\pi$
$14$	3.67423	−	2.12132i	0.981981	−	0.566947i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$		0			0
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	1.22474	+	0.707107i	0.273861	+	0.158114i
$21$		0			0
$22$	0.275255	+	3.30518i	0.0586846	+	0.704667i
$23$	−1.22474	+	0.707107i	−0.255377	+	0.147442i	−0.622224	−	0.782839i	$-0.713771\pi$
$23$	−1.22474	+	0.707107i	−0.255377	+	0.147442i	0.366847	+	0.930281i	$0.380437\pi$
$24$		0			0
$25$	−1.50000	+	2.59808i	−0.300000	+	0.519615i
$26$		−	4.24264i		−	0.832050i
$27$		0			0
$28$		−	4.24264i		−	0.801784i
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$		0			0
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$		0			0
$35$	−6.00000			−1.01419
$36$		0			0
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$		0			0
$39$		0			0
$40$	1.22474	−	0.707107i	0.193649	−	0.111803i
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	0.999353	−	0.0359748i	$-0.0114536\pi$
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	−0.530831	+	0.847477i	$0.678120\pi$
$42$		0			0
$43$	−7.34847	−	4.24264i	−1.12063	−	0.646997i	−0.179069	−	0.983836i	$-0.557309\pi$
$43$	−7.34847	−	4.24264i	−1.12063	−	0.646997i	−0.941562	+	0.336840i	$0.890642\pi$
$44$	3.00000	+	1.41421i	0.452267	+	0.213201i
$45$		0			0
$46$			1.41421i			0.208514i
$47$	8.57321	+	4.94975i	1.25053	+	0.721995i	0.971215	−	0.238204i	$-0.0765587\pi$
$47$	8.57321	+	4.94975i	1.25053	+	0.721995i	0.279317	+	0.960199i	$0.409892\pi$
$48$		0			0
$49$	5.50000	+	9.52628i	0.785714	+	1.36090i
$50$	1.50000	+	2.59808i	0.212132	+	0.367423i
$51$		0			0
$52$	−3.67423	−	2.12132i	−0.509525	−	0.294174i
$53$			7.07107i			0.971286i	0.874157	+	0.485643i	$0.161414\pi$
$53$			7.07107i			0.971286i	−0.874157	+	0.485643i	$0.838586\pi$
$54$		0			0
$55$	2.00000	−	4.24264i	0.269680	−	0.572078i
$56$	−3.67423	−	2.12132i	−0.490990	−	0.283473i
$57$		0			0
$58$	3.00000	+	5.19615i	0.393919	+	0.682288i
$59$	9.79796	−	5.65685i	1.27559	−	0.736460i	0.299552	−	0.954080i	$-0.403163\pi$
$59$	9.79796	−	5.65685i	1.27559	−	0.736460i	0.976034	+	0.217620i	$0.0698294\pi$
$60$		0			0
$61$	3.67423	+	2.12132i	0.470438	+	0.271607i	0.716423	−	0.697666i	$-0.245778\pi$
$61$	3.67423	+	2.12132i	0.470438	+	0.271607i	−0.245985	+	0.969274i	$0.579112\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.00000	+	5.19615i	−0.372104	+	0.644503i
$66$		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	$0.754762\pi$
$68$		0			0
$69$		0			0
$70$	−3.00000	+	5.19615i	−0.358569	+	0.621059i
$71$			7.07107i			0.839181i	0.907713	+	0.419591i	$0.137826\pi$
$71$			7.07107i			0.839181i	−0.907713	+	0.419591i	$0.862174\pi$
$72$		0			0
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$		0			0
$76$		0			0
$77$	−14.0227	+	1.16781i	−1.59804	+	0.133084i
$78$		0			0
$79$	3.67423	+	2.12132i	0.413384	+	0.238667i	0.692243	−	0.721665i	$-0.256623\pi$
$79$	3.67423	+	2.12132i	0.413384	+	0.238667i	−0.278859	+	0.960332i	$0.589956\pi$
$80$		−	1.41421i		−	0.158114i
$81$		0			0
$82$	6.00000			0.662589
$83$	6.00000	−	10.3923i	0.658586	−	1.14070i	−0.322396	−	0.946605i	$-0.604488\pi$
$83$	6.00000	−	10.3923i	0.658586	−	1.14070i	0.980982	−	0.194099i	$-0.0621783\pi$
$84$		0			0
$85$		0			0
$86$	−7.34847	+	4.24264i	−0.792406	+	0.457496i
$87$		0			0
$88$	2.72474	−	1.89097i	0.290459	−	0.201578i
$89$		−	5.65685i		−	0.599625i	−0.953998	−	0.299813i	$-0.903076\pi$
$89$		−	5.65685i		−	0.599625i	0.953998	−	0.299813i	$-0.0969242\pi$
$90$		0			0
$91$	18.0000			1.88691
$92$	1.22474	+	0.707107i	0.127688	+	0.0737210i
$93$		0			0
$94$	8.57321	−	4.94975i	0.884260	−	0.510527i
$95$		0			0
$96$		0			0
$97$	−4.00000	+	6.92820i	−0.406138	+	0.703452i	−0.994453	−	0.105180i	$-0.966458\pi$
$97$	−4.00000	+	6.92820i	−0.406138	+	0.703452i	0.588315	+	0.808632i	$0.299792\pi$
$98$	11.0000			1.11117
$99$		0			0
$100$	3.00000			0.300000
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	−0.975796	−	0.218685i	$-0.929823\pi$
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	0.677284	+	0.735721i	$0.263157\pi$
$102$		0			0
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	0.947576	−	0.319531i	$-0.103525\pi$
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	−0.750510	+	0.660859i	$0.770192\pi$
$104$	−3.67423	+	2.12132i	−0.360288	+	0.208013i
$105$		0			0
$106$	6.12372	+	3.53553i	0.594789	+	0.343401i
$107$	−18.0000			−1.74013			−0.870063	−	0.492941i	$-0.835922\pi$
$107$	−18.0000			−1.74013			−0.870063	+	0.492941i	$0.835922\pi$
$108$		0			0
$109$		−	12.7279i		−	1.21911i	−0.792742	−	0.609557i	$-0.791347\pi$
$109$		−	12.7279i		−	1.21911i	0.792742	−	0.609557i	$-0.208653\pi$
$110$	−2.67423	−	3.85337i	−0.254978	−	0.367405i
$111$		0			0
$112$	−3.67423	+	2.12132i	−0.347183	+	0.200446i
$113$	9.79796	−	5.65685i	0.921714	−	0.532152i	0.0375328	−	0.999295i	$-0.488050\pi$
$113$	9.79796	−	5.65685i	0.921714	−	0.532152i	0.884182	+	0.467143i	$0.154717\pi$
$114$		0			0
$115$	1.00000	−	1.73205i	0.0932505	−	0.161515i
$116$	6.00000			0.557086
$117$		0			0
$118$		−	11.3137i		−	1.04151i
$119$		0			0
$120$		0			0
$121$	3.84847	−	10.3048i	0.349861	−	0.936802i
$122$	3.67423	−	2.12132i	0.332650	−	0.192055i
$123$		0			0
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$		−	11.3137i		−	1.01193i
$126$		0			0
$127$			12.7279i			1.12942i	0.825289	+	0.564710i	$0.191012\pi$
$127$			12.7279i			1.12942i	−0.825289	+	0.564710i	$0.808988\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	3.00000	+	5.19615i	0.263117	+	0.455733i
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	−0.999602	−	0.0281993i	$-0.991023\pi$
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	0.475380	−	0.879781i	$-0.342311\pi$
$132$		0			0
$133$		0			0
$134$	4.00000			0.345547
$135$		0			0
$136$		0			0
$137$	−2.44949	−	1.41421i	−0.209274	−	0.120824i	0.391700	−	0.920093i	$-0.371887\pi$
$137$	−2.44949	−	1.41421i	−0.209274	−	0.120824i	−0.600974	+	0.799269i	$0.705220\pi$
$138$		0			0
$139$	14.6969	−	8.48528i	1.24658	−	0.719712i	0.276153	−	0.961114i	$-0.410940\pi$
$139$	14.6969	−	8.48528i	1.24658	−	0.719712i	0.970425	+	0.241402i	$0.0776071\pi$
$140$	3.00000	+	5.19615i	0.253546	+	0.439155i
$141$		0			0
$142$	6.12372	+	3.53553i	0.513892	+	0.296695i
$143$	−6.00000	+	12.7279i	−0.501745	+	1.06436i
$144$		0			0
$145$		−	8.48528i		−	0.704664i
$146$		0			0
$147$		0			0
$148$	−1.00000	−	1.73205i	−0.0821995	−	0.142374i
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	3.67423	+	2.12132i	0.299005	+	0.172631i	0.641996	−	0.766708i	$-0.278107\pi$
$151$	3.67423	+	2.12132i	0.299005	+	0.172631i	−0.342991	+	0.939339i	$0.611440\pi$
$152$		0			0
$153$		0			0
$154$	−6.00000	+	12.7279i	−0.483494	+	1.02565i
$155$	−4.89898	−	2.82843i	−0.393496	−	0.227185i
$156$		0			0
$157$	11.0000	+	19.0526i	0.877896	+	1.52056i	0.853646	+	0.520854i	$0.174386\pi$
$157$	11.0000	+	19.0526i	0.877896	+	1.52056i	0.0242497	+	0.999706i	$0.492280\pi$
$158$	3.67423	−	2.12132i	0.292306	−	0.168763i
$159$		0			0
$160$	−1.22474	−	0.707107i	−0.0968246	−	0.0559017i
$161$	−6.00000			−0.472866
$162$		0			0
$163$	2.00000			0.156652			0.0783260	−	0.996928i	$-0.475042\pi$
$163$	2.00000			0.156652			0.0783260	+	0.996928i	$0.475042\pi$
$164$	3.00000	−	5.19615i	0.234261	−	0.405751i
$165$		0			0
$166$	−6.00000	−	10.3923i	−0.465690	−	0.806599i
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	0.534875	−	0.844931i	$-0.320359\pi$
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	−0.999169	+	0.0407502i	$0.987025\pi$
$168$		0			0
$169$	2.50000	−	4.33013i	0.192308	−	0.333087i
$170$		0			0
$171$		0			0
$172$			8.48528i			0.646997i
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$		0			0
$175$	−11.0227	+	6.36396i	−0.833238	+	0.481070i
$176$	−0.275255	−	3.30518i	−0.0207481	−	0.249138i
$177$		0			0
$178$	−4.89898	−	2.82843i	−0.367194	−	0.212000i
$179$		−	5.65685i		−	0.422813i	−0.977398	−	0.211407i	$-0.932196\pi$
$179$		−	5.65685i		−	0.422813i	0.977398	−	0.211407i	$-0.0678044\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	9.00000	−	15.5885i	0.667124	−	1.15549i
$183$		0			0
$184$	1.22474	−	0.707107i	0.0902894	−	0.0521286i
$185$	−2.44949	+	1.41421i	−0.180090	+	0.103975i
$186$		0			0
$187$		0			0
$188$		−	9.89949i		−	0.721995i
$189$		0			0
$190$		0			0
$191$	8.57321	+	4.94975i	0.620336	+	0.358151i	0.777000	−	0.629501i	$-0.216741\pi$
$191$	8.57321	+	4.94975i	0.620336	+	0.358151i	−0.156664	+	0.987652i	$0.550074\pi$
$192$		0			0
$193$	−7.34847	+	4.24264i	−0.528954	+	0.305392i	−0.740591	−	0.671957i	$-0.765454\pi$
$193$	−7.34847	+	4.24264i	−0.528954	+	0.305392i	0.211636	+	0.977349i	$0.432121\pi$
$194$	4.00000	+	6.92820i	0.287183	+	0.497416i
$195$		0			0
$196$	5.50000	−	9.52628i	0.392857	−	0.680449i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$	1.50000	−	2.59808i	0.106066	−	0.183712i
$201$		0			0
$202$	3.00000	+	5.19615i	0.211079	+	0.365600i
$203$	−22.0454	+	12.7279i	−1.54728	+	0.893325i
$204$		0			0
$205$	−7.34847	−	4.24264i	−0.513239	−	0.296319i
$206$	4.00000			0.278693
$207$		0			0
$208$			4.24264i			0.294174i
$209$		0			0
$210$		0			0
$211$	−7.34847	+	4.24264i	−0.505889	+	0.292075i	−0.731142	−	0.682225i	$-0.761012\pi$
$211$	−7.34847	+	4.24264i	−0.505889	+	0.292075i	0.225253	+	0.974300i	$0.427679\pi$
$212$	6.12372	−	3.53553i	0.420579	−	0.242821i
$213$		0			0
$214$	−9.00000	+	15.5885i	−0.615227	+	1.06561i
$215$	12.0000			0.818393
$216$		0			0
$217$			16.9706i			1.15204i
$218$	−11.0227	−	6.36396i	−0.746552	−	0.431022i
$219$		0			0
$220$	−4.67423	+	0.389270i	−0.315137	+	0.0262445i
$221$		0			0
$222$		0			0
$223$	−4.00000	+	6.92820i	−0.267860	+	0.463947i	−0.968309	−	0.249756i	$-0.919650\pi$
$223$	−4.00000	+	6.92820i	−0.267860	+	0.463947i	0.700449	+	0.713702i	$0.252983\pi$
$224$			4.24264i			0.283473i
$225$		0			0
$226$		−	11.3137i		−	0.752577i
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	−0.948242	−	0.317547i	$-0.897141\pi$
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	0.749125	+	0.662428i	$0.230474\pi$
$228$		0			0
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	0.536515	−	0.843891i	$-0.319740\pi$
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	−0.999088	+	0.0426906i	$0.986407\pi$
$230$	−1.00000	−	1.73205i	−0.0659380	−	0.114208i
$231$		0			0
$232$	3.00000	−	5.19615i	0.196960	−	0.341144i
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$		0			0
$235$	−14.0000			−0.913259
$236$	−9.79796	−	5.65685i	−0.637793	−	0.368230i
$237$		0			0
$238$		0			0
$239$	−6.00000	−	10.3923i	−0.388108	−	0.672222i	0.604087	−	0.796918i	$-0.293538\pi$
$239$	−6.00000	−	10.3923i	−0.388108	−	0.672222i	−0.992195	+	0.124696i	$0.960204\pi$
$240$		0			0
$241$	−7.34847	−	4.24264i	−0.473357	−	0.273293i	0.244287	−	0.969703i	$-0.421446\pi$
$241$	−7.34847	−	4.24264i	−0.473357	−	0.273293i	−0.717644	+	0.696410i	$0.754779\pi$
$242$	−7.00000	−	8.48528i	−0.449977	−	0.545455i
$243$		0			0
$244$		−	4.24264i		−	0.271607i
$245$	−13.4722	−	7.77817i	−0.860707	−	0.496929i
$246$		0			0
$247$		0			0
$248$	−2.00000	−	3.46410i	−0.127000	−	0.219971i
$249$		0			0
$250$	−9.79796	−	5.65685i	−0.619677	−	0.357771i
$251$		−	5.65685i		−	0.357057i	−0.983935	−	0.178529i	$-0.942866\pi$
$251$		−	5.65685i		−	0.357057i	0.983935	−	0.178529i	$-0.0571337\pi$
$252$		0			0
$253$	2.00000	−	4.24264i	0.125739	−	0.266733i
$254$	11.0227	+	6.36396i	0.691626	+	0.399310i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.79796	−	5.65685i	0.611180	−	0.352865i	−0.162247	−	0.986750i	$-0.551874\pi$
$257$	9.79796	−	5.65685i	0.611180	−	0.352865i	0.773427	+	0.633885i	$0.218541\pi$
$258$		0			0
$259$	7.34847	+	4.24264i	0.456612	+	0.263625i
$260$	6.00000			0.372104
$261$		0			0
$262$	−12.0000			−0.741362
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	−0.619586	−	0.784929i	$-0.712699\pi$
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	0.989561	+	0.144112i	$0.0460326\pi$
$264$		0			0
$265$	−5.00000	−	8.66025i	−0.307148	−	0.531995i
$266$		0			0
$267$		0			0
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$			7.07107i			0.431131i	0.976489	+	0.215565i	$0.0691594\pi$
$269$			7.07107i			0.431131i	−0.976489	+	0.215565i	$0.930841\pi$
$270$		0			0
$271$		−	12.7279i		−	0.773166i	−0.922255	−	0.386583i	$-0.873655\pi$
$271$		−	12.7279i		−	0.773166i	0.922255	−	0.386583i	$-0.126345\pi$
$272$		0			0
$273$		0			0
$274$	−2.44949	+	1.41421i	−0.147979	+	0.0854358i
$275$	−0.825765	−	9.91555i	−0.0497955	−	0.597930i
$276$		0			0
$277$	−18.3712	−	10.6066i	−1.10382	−	0.637289i	−0.166596	−	0.986025i	$-0.553278\pi$
$277$	−18.3712	−	10.6066i	−1.10382	−	0.637289i	−0.937221	+	0.348736i	$0.886611\pi$
$278$		−	16.9706i		−	1.01783i
$279$		0			0
$280$	6.00000			0.358569
$281$	6.00000	−	10.3923i	0.357930	−	0.619953i	−0.629685	−	0.776851i	$-0.716816\pi$
$281$	6.00000	−	10.3923i	0.357930	−	0.619953i	0.987615	+	0.156898i	$0.0501493\pi$
$282$		0			0
$283$	−7.34847	+	4.24264i	−0.436821	+	0.252199i	−0.702248	−	0.711932i	$-0.747820\pi$
$283$	−7.34847	+	4.24264i	−0.436821	+	0.252199i	0.265427	+	0.964131i	$0.414487\pi$
$284$	6.12372	−	3.53553i	0.363376	−	0.209795i
$285$		0			0
$286$	8.02270	+	11.5601i	0.474392	+	0.683564i
$287$			25.4558i			1.50261i
$288$		0			0
$289$	−17.0000			−1.00000
$290$	−7.34847	−	4.24264i	−0.431517	−	0.249136i
$291$		0			0
$292$		0			0
$293$	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
$295$	−8.00000	+	13.8564i	−0.465778	+	0.806751i
$296$	−2.00000			−0.116248
$297$		0			0
$298$	6.00000			0.347571
$299$	−3.00000	+	5.19615i	−0.173494	+	0.300501i
$300$		0			0
$301$	−18.0000	−	31.1769i	−1.03750	−	1.79701i
$302$	3.67423	−	2.12132i	0.211428	−	0.122068i
$303$		0			0
$304$		0			0
$305$	−6.00000			−0.343559
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$	8.02270	+	11.5601i	0.457136	+	0.658699i
$309$		0			0
$310$	−4.89898	+	2.82843i	−0.278243	+	0.160644i
$311$	−23.2702	+	13.4350i	−1.31953	+	0.761831i	−0.983653	−	0.180075i	$-0.942366\pi$
$311$	−23.2702	+	13.4350i	−1.31953	+	0.761831i	−0.335876	+	0.941906i	$0.609032\pi$
$312$		0			0
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	−0.689412	−	0.724370i	$-0.742131\pi$
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	0.972028	+	0.234863i	$0.0754642\pi$
$314$	22.0000			1.24153
$315$		0			0
$316$		−	4.24264i		−	0.238667i
$317$	8.57321	+	4.94975i	0.481520	+	0.278006i	0.721050	−	0.692883i	$-0.243660\pi$
$317$	8.57321	+	4.94975i	0.481520	+	0.278006i	−0.239530	+	0.970889i	$0.576993\pi$
$318$		0			0
$319$	−1.65153	−	19.8311i	−0.0924680	−	1.11033i
$320$	−1.22474	+	0.707107i	−0.0684653	+	0.0395285i
$321$		0			0
$322$	−3.00000	+	5.19615i	−0.167183	+	0.289570i
$323$		0			0
$324$		0			0
$325$			12.7279i			0.706018i
$326$	1.00000	−	1.73205i	0.0553849	−	0.0959294i
$327$		0			0
$328$	−3.00000	−	5.19615i	−0.165647	−	0.286910i
$329$	21.0000	+	36.3731i	1.15777	+	2.00531i
$330$		0			0
$331$	5.00000	−	8.66025i	0.274825	−	0.476011i	−0.695266	−	0.718752i	$-0.744713\pi$
$331$	5.00000	−	8.66025i	0.274825	−	0.476011i	0.970091	+	0.242742i	$0.0780468\pi$
$332$	−12.0000			−0.658586
$333$		0			0
$334$	−12.0000			−0.656611
$335$	−4.89898	−	2.82843i	−0.267660	−	0.154533i
$336$		0			0
$337$	−29.3939	+	16.9706i	−1.60119	+	0.924445i	−0.609936	+	0.792451i	$0.708805\pi$
$337$	−29.3939	+	16.9706i	−1.60119	+	0.924445i	−0.991250	+	0.131995i	$0.957862\pi$
$338$	−2.50000	−	4.33013i	−0.135982	−	0.235528i
$339$		0			0
$340$		0			0
$341$	−12.0000	−	5.65685i	−0.649836	−	0.306336i
$342$		0			0
$343$			16.9706i			0.916324i
$344$	7.34847	+	4.24264i	0.396203	+	0.228748i
$345$		0			0
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$		0			0
$349$	25.7196	+	14.8492i	1.37674	+	0.794862i	0.991766	−	0.128065i	$-0.0408767\pi$
$349$	25.7196	+	14.8492i	1.37674	+	0.794862i	0.384975	+	0.922927i	$0.374210\pi$
$350$			12.7279i			0.680336i
$351$		0			0
$352$	−3.00000	−	1.41421i	−0.159901	−	0.0753778i
$353$	19.5959	+	11.3137i	1.04299	+	0.602168i	0.920677	−	0.390324i	$-0.127637\pi$
$353$	19.5959	+	11.3137i	1.04299	+	0.602168i	0.122308	+	0.992492i	$0.460970\pi$
$354$		0			0
$355$	−5.00000	−	8.66025i	−0.265372	−	0.459639i
$356$	−4.89898	+	2.82843i	−0.259645	+	0.149906i
$357$		0			0
$358$	−4.89898	−	2.82843i	−0.258919	−	0.149487i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	19.0000			1.00000
$362$	1.00000	−	1.73205i	0.0525588	−	0.0910346i
$363$		0			0
$364$	−9.00000	−	15.5885i	−0.471728	−	0.817057i
$365$		0			0
$366$		0			0
$367$	14.0000	−	24.2487i	0.730794	−	1.26577i	−0.225750	−	0.974185i	$-0.572483\pi$
$367$	14.0000	−	24.2487i	0.730794	−	1.26577i	0.956544	−	0.291587i	$-0.0941834\pi$
$368$		−	1.41421i		−	0.0737210i
$369$		0			0
$370$			2.82843i			0.147043i
$371$	−15.0000	+	25.9808i	−0.778761	+	1.34885i
$372$		0			0
$373$	25.7196	−	14.8492i	1.33171	−	0.768865i	0.346151	−	0.938179i	$-0.387489\pi$
$373$	25.7196	−	14.8492i	1.33171	−	0.768865i	0.985562	+	0.169314i	$0.0541553\pi$
$374$		0			0
$375$		0			0
$376$	−8.57321	−	4.94975i	−0.442130	−	0.255264i
$377$			25.4558i			1.31104i
$378$		0			0
$379$	2.00000			0.102733			0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000			0.102733			0.0513665	+	0.998680i	$0.483642\pi$
$380$		0			0
$381$		0			0
$382$	8.57321	−	4.94975i	0.438644	−	0.253251i
$383$	−1.22474	+	0.707107i	−0.0625815	+	0.0361315i	−0.530964	−	0.847394i	$-0.678170\pi$
$383$	−1.22474	+	0.707107i	−0.0625815	+	0.0361315i	0.468383	+	0.883526i	$0.344837\pi$
$384$		0			0
$385$	16.3485	−	11.3458i	0.833195	−	0.578236i
$386$			8.48528i			0.431889i
$387$		0			0
$388$	8.00000			0.406138
$389$	8.57321	+	4.94975i	0.434679	+	0.250962i	0.701338	−	0.712829i	$-0.252586\pi$
$389$	8.57321	+	4.94975i	0.434679	+	0.250962i	−0.266659	+	0.963791i	$0.585920\pi$
$390$		0			0
$391$		0			0
$392$	−5.50000	−	9.52628i	−0.277792	−	0.481150i
$393$		0			0
$394$	9.00000	−	15.5885i	0.453413	−	0.785335i
$395$	−6.00000			−0.301893
$396$		0			0
$397$	−34.0000			−1.70641			−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−34.0000			−1.70641			−0.853206	+	0.521575i	$0.825345\pi$
$398$	−8.00000	+	13.8564i	−0.401004	+	0.694559i
$399$		0			0
$400$	−1.50000	−	2.59808i	−0.0750000	−	0.129904i
$401$	31.8434	−	18.3848i	1.59018	−	0.918092i	0.596907	−	0.802310i	$-0.296396\pi$
$401$	31.8434	−	18.3848i	1.59018	−	0.918092i	0.993275	−	0.115782i	$-0.0369373\pi$
$402$		0			0
$403$	14.6969	+	8.48528i	0.732107	+	0.422682i
$404$	6.00000			0.298511
$405$		0			0
$406$			25.4558i			1.26335i
$407$	−5.44949	+	3.78194i	−0.270121	+	0.187464i
$408$		0			0
$409$	−7.34847	+	4.24264i	−0.363358	+	0.209785i	−0.670553	−	0.741862i	$-0.733943\pi$
$409$	−7.34847	+	4.24264i	−0.363358	+	0.209785i	0.307195	+	0.951647i	$0.400610\pi$
$410$	−7.34847	+	4.24264i	−0.362915	+	0.209529i
$411$		0			0
$412$	2.00000	−	3.46410i	0.0985329	−	0.170664i
$413$	48.0000			2.36193
$414$		0			0
$415$			16.9706i			0.833052i
$416$	3.67423	+	2.12132i	0.180144	+	0.104006i
$417$		0			0
$418$		0			0
$419$	9.79796	−	5.65685i	0.478662	−	0.276355i	−0.241197	−	0.970476i	$-0.577540\pi$
$419$	9.79796	−	5.65685i	0.478662	−	0.276355i	0.719859	+	0.694121i	$0.244207\pi$
$420$		0			0
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	−0.718076	−	0.695965i	$-0.754977\pi$
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	0.961761	+	0.273890i	$0.0883103\pi$
$422$			8.48528i			0.413057i
$423$		0			0
$424$		−	7.07107i		−	0.343401i
$425$		0			0
$426$		0			0
$427$	9.00000	+	15.5885i	0.435541	+	0.754378i
$428$	9.00000	+	15.5885i	0.435031	+	0.753497i
$429$		0			0
$430$	6.00000	−	10.3923i	0.289346	−	0.501161i
$431$	−36.0000			−1.73406			−0.867029	−	0.498257i	$-0.833974\pi$
$431$	−36.0000			−1.73406			−0.867029	+	0.498257i	$0.833974\pi$
$432$		0			0
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$	14.6969	+	8.48528i	0.705476	+	0.407307i
$435$		0			0
$436$	−11.0227	+	6.36396i	−0.527892	+	0.304778i
$437$		0			0
$438$		0			0
$439$	−18.3712	−	10.6066i	−0.876808	−	0.506225i	−0.00720355	−	0.999974i	$-0.502293\pi$
$439$	−18.3712	−	10.6066i	−0.876808	−	0.506225i	−0.869605	+	0.493749i	$0.835626\pi$
$440$	−2.00000	+	4.24264i	−0.0953463	+	0.202260i
$441$		0			0
$442$		0			0
$443$	−24.4949	−	14.1421i	−1.16379	−	0.671913i	−0.211579	−	0.977361i	$-0.567861\pi$
$443$	−24.4949	−	14.1421i	−1.16379	−	0.671913i	−0.952209	+	0.305448i	$0.901194\pi$
$444$		0			0
$445$	4.00000	+	6.92820i	0.189618	+	0.328428i
$446$	4.00000	+	6.92820i	0.189405	+	0.328060i
$447$		0			0
$448$	3.67423	+	2.12132i	0.173591	+	0.100223i
$449$		−	31.1127i		−	1.46830i	−0.678988	−	0.734150i	$-0.737581\pi$
$449$		−	31.1127i		−	1.46830i	0.678988	−	0.734150i	$-0.262419\pi$
$450$		0			0
$451$	−18.0000	−	8.48528i	−0.847587	−	0.399556i
$452$	−9.79796	−	5.65685i	−0.460857	−	0.266076i
$453$		0			0
$454$	3.00000	+	5.19615i	0.140797	+	0.243868i
$455$	−22.0454	+	12.7279i	−1.03350	+	0.596694i
$456$		0			0
$457$	−7.34847	−	4.24264i	−0.343747	−	0.198462i	0.318181	−	0.948030i	$-0.396928\pi$
$457$	−7.34847	−	4.24264i	−0.343747	−	0.198462i	−0.661928	+	0.749568i	$0.730261\pi$
$458$	−14.0000			−0.654177
$459$		0			0
$460$	−2.00000			−0.0932505
$461$	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
$463$	−16.0000	−	27.7128i	−0.743583	−	1.28792i	−0.950854	−	0.309640i	$-0.899791\pi$
$463$	−16.0000	−	27.7128i	−0.743583	−	1.28792i	0.207271	−	0.978284i	$-0.433542\pi$
$464$	−3.00000	−	5.19615i	−0.139272	−	0.241225i
$465$		0			0
$466$	−9.00000	+	15.5885i	−0.416917	+	0.722121i
$467$		−	31.1127i		−	1.43972i	−0.694117	−	0.719862i	$-0.744205\pi$
$467$		−	31.1127i		−	1.43972i	0.694117	−	0.719862i	$-0.255795\pi$
$468$		0			0
$469$			16.9706i			0.783628i
$470$	−7.00000	+	12.1244i	−0.322886	+	0.559255i
$471$		0			0
$472$	−9.79796	+	5.65685i	−0.450988	+	0.260378i
$473$	28.0454	−	2.33562i	1.28953	−	0.107392i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−12.0000			−0.548867
$479$	6.00000	−	10.3923i	0.274147	−	0.474837i	−0.695773	−	0.718262i	$-0.744938\pi$
$479$	6.00000	−	10.3923i	0.274147	−	0.474837i	0.969920	+	0.243426i	$0.0782712\pi$
$480$		0			0
$481$	7.34847	−	4.24264i	0.335061	−	0.193448i
$482$	−7.34847	+	4.24264i	−0.334714	+	0.193247i
$483$		0			0
$484$	−10.8485	+	1.81954i	−0.493112	+	0.0827062i
$485$		−	11.3137i		−	0.513729i
$486$		0			0
$487$	20.0000			0.906287			0.453143	−	0.891438i	$-0.350303\pi$
$487$	20.0000			0.906287			0.453143	+	0.891438i	$0.350303\pi$
$488$	−3.67423	−	2.12132i	−0.166325	−	0.0960277i
$489$		0			0
$490$	−13.4722	+	7.77817i	−0.608612	+	0.351382i
$491$	3.00000	+	5.19615i	0.135388	+	0.234499i	0.925746	−	0.378147i	$-0.123439\pi$
$491$	3.00000	+	5.19615i	0.135388	+	0.234499i	−0.790358	+	0.612646i	$0.790105\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−4.00000			−0.179605
$497$	−15.0000	+	25.9808i	−0.672842	+	1.16540i
$498$		0			0
$499$	−7.00000	−	12.1244i	−0.313363	−	0.542761i	0.665725	−	0.746197i	$-0.268122\pi$
$499$	−7.00000	−	12.1244i	−0.313363	−	0.542761i	−0.979088	+	0.203436i	$0.934789\pi$
$500$	−9.79796	+	5.65685i	−0.438178	+	0.252982i
$501$		0			0
$502$	−4.89898	−	2.82843i	−0.218652	−	0.126239i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$		−	8.48528i		−	0.377590i
$506$	−2.67423	−	3.85337i	−0.118884	−	0.171303i
$507$		0			0
$508$	11.0227	−	6.36396i	0.489053	−	0.282355i
$509$	−1.22474	+	0.707107i	−0.0542859	+	0.0313420i	−0.526897	−	0.849929i	$-0.676645\pi$
$509$	−1.22474	+	0.707107i	−0.0542859	+	0.0313420i	0.472611	+	0.881271i	$0.343311\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$		−	11.3137i		−	0.499026i
$515$	−4.89898	−	2.82843i	−0.215875	−	0.124635i
$516$		0			0
$517$	−32.7196	+	2.72489i	−1.43901	+	0.119840i
$518$	7.34847	−	4.24264i	0.322873	−	0.186411i
$519$		0			0
$520$	3.00000	−	5.19615i	0.131559	−	0.227866i
$521$			19.7990i			0.867409i	0.901055	+	0.433705i	$0.142794\pi$
$521$			19.7990i			0.867409i	−0.901055	+	0.433705i	$0.857206\pi$
$522$		0			0
$523$		−	25.4558i		−	1.11311i	−0.830812	−	0.556553i	$-0.812124\pi$
$523$		−	25.4558i		−	1.11311i	0.830812	−	0.556553i	$-0.187876\pi$
$524$	−6.00000	+	10.3923i	−0.262111	+	0.453990i
$525$		0			0
$526$	−6.00000	−	10.3923i	−0.261612	−	0.453126i
$527$		0			0
$528$		0			0
$529$	−10.5000	+	18.1865i	−0.456522	+	0.790719i
$530$	−10.0000			−0.434372
$531$		0			0
$532$		0			0
$533$	22.0454	+	12.7279i	0.954893	+	0.551308i
$534$		0			0
$535$	22.0454	−	12.7279i	0.953106	−	0.550276i
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$		0			0
$538$	6.12372	+	3.53553i	0.264013	+	0.152428i
$539$	−33.0000	−	15.5563i	−1.42141	−	0.670059i
$540$		0			0
$541$		−	12.7279i		−	0.547216i	−0.961841	−	0.273608i	$-0.911783\pi$
$541$		−	12.7279i		−	0.547216i	0.961841	−	0.273608i	$-0.0882171\pi$
$542$	−11.0227	−	6.36396i	−0.473466	−	0.273356i
$543$		0			0
$544$		0			0
$545$	9.00000	+	15.5885i	0.385518	+	0.667736i
$546$		0			0
$547$	−29.3939	−	16.9706i	−1.25679	−	0.725609i	−0.284342	−	0.958723i	$-0.591775\pi$
$547$	−29.3939	−	16.9706i	−1.25679	−	0.725609i	−0.972449	+	0.233114i	$0.925108\pi$
$548$			2.82843i			0.120824i
$549$		0			0
$550$	−9.00000	−	4.24264i	−0.383761	−	0.180907i
$551$		0			0
$552$		0			0
$553$	9.00000	+	15.5885i	0.382719	+	0.662889i
$554$	−18.3712	+	10.6066i	−0.780516	+	0.450631i
$555$		0			0
$556$	−14.6969	−	8.48528i	−0.623289	−	0.359856i
$557$	18.0000			0.762684			0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000			0.762684			0.381342	+	0.924434i	$0.375462\pi$
$558$		0			0
$559$	−36.0000			−1.52264
$560$	3.00000	−	5.19615i	0.126773	−	0.219578i
$561$		0			0
$562$	−6.00000	−	10.3923i	−0.253095	−	0.438373i
$563$	−15.0000	−	25.9808i	−0.632175	−	1.09496i	−0.987106	−	0.160066i	$-0.948829\pi$
$563$	−15.0000	−	25.9808i	−0.632175	−	1.09496i	0.354932	−	0.934892i	$-0.384504\pi$
$564$		0			0
$565$	−8.00000	+	13.8564i	−0.336563	+	0.582943i
$566$			8.48528i			0.356663i
$567$		0			0
$568$		−	7.07107i		−	0.296695i
$569$	−12.0000	+	20.7846i	−0.503066	+	0.871336i	0.496928	+	0.867792i	$0.334461\pi$
$569$	−12.0000	+	20.7846i	−0.503066	+	0.871336i	−0.999994	+	0.00354413i	$0.998872\pi$
$570$		0			0
$571$	−29.3939	+	16.9706i	−1.23010	+	0.710196i	−0.967050	−	0.254587i	$-0.918060\pi$
$571$	−29.3939	+	16.9706i	−1.23010	+	0.710196i	−0.263046	+	0.964783i	$0.584727\pi$
$572$	14.0227	−	1.16781i	0.586319	−	0.0488285i
$573$		0			0
$574$	22.0454	+	12.7279i	0.920158	+	0.531253i
$575$		−	4.24264i		−	0.176930i
$576$		0			0
$577$	20.0000			0.832611			0.416305	−	0.909225i	$-0.363325\pi$
$577$	20.0000			0.832611			0.416305	+	0.909225i	$0.363325\pi$
$578$	−8.50000	+	14.7224i	−0.353553	+	0.612372i
$579$		0			0
$580$	−7.34847	+	4.24264i	−0.305129	+	0.176166i
$581$	44.0908	−	25.4558i	1.82920	−	1.05609i
$582$		0			0
$583$	−13.3712	−	19.2669i	−0.553777	−	0.797952i
$584$		0			0
$585$		0			0
$586$	6.00000			0.247858
$587$	−24.4949	−	14.1421i	−1.01101	−	0.583708i	−0.0995246	−	0.995035i	$-0.531732\pi$
$587$	−24.4949	−	14.1421i	−1.01101	−	0.583708i	−0.911488	+	0.411327i	$0.865066\pi$
$588$		0			0
$589$		0			0
$590$	8.00000	+	13.8564i	0.329355	+	0.570459i
$591$		0			0
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	36.0000			1.47834			0.739171	−	0.673517i	$-0.235217\pi$
$593$	36.0000			1.47834			0.739171	+	0.673517i	$0.235217\pi$
$594$		0			0
$595$		0			0
$596$	3.00000	−	5.19615i	0.122885	−	0.212843i
$597$		0			0
$598$	3.00000	+	5.19615i	0.122679	+	0.212486i
$599$	20.8207	−	12.0208i	0.850709	−	0.491157i	−0.0101809	−	0.999948i	$-0.503241\pi$
$599$	20.8207	−	12.0208i	0.850709	−	0.491157i	0.860890	+	0.508791i	$0.169907\pi$
$600$		0			0
$601$	−29.3939	−	16.9706i	−1.19900	−	0.692244i	−0.238669	−	0.971101i	$-0.576711\pi$
$601$	−29.3939	−	16.9706i	−1.19900	−	0.692244i	−0.960333	+	0.278857i	$0.910044\pi$
$602$	−36.0000			−1.46725
$603$		0			0
$604$		−	4.24264i		−	0.172631i
$605$	2.57321	+	15.3421i	0.104616	+	0.623743i
$606$		0			0
$607$	3.67423	−	2.12132i	0.149133	−	0.0861017i	−0.423577	−	0.905860i	$-0.639226\pi$
$607$	3.67423	−	2.12132i	0.149133	−	0.0861017i	0.572709	+	0.819758i	$0.305892\pi$
$608$		0			0
$609$		0			0
$610$	−3.00000	+	5.19615i	−0.121466	+	0.210386i
$611$	42.0000			1.69914
$612$		0			0
$613$		−	12.7279i		−	0.514076i	−0.966401	−	0.257038i	$-0.917253\pi$
$613$		−	12.7279i		−	0.514076i	0.966401	−	0.257038i	$-0.0827465\pi$
$614$		0			0
$615$		0			0
$616$	14.0227	−	1.16781i	0.564991	−	0.0470523i
$617$	−34.2929	+	19.7990i	−1.38058	+	0.797077i	−0.992228	−	0.124434i	$-0.960288\pi$
$617$	−34.2929	+	19.7990i	−1.38058	+	0.797077i	−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	$0.821334\pi$
$620$			5.65685i			0.227185i
$621$		0			0
$622$			26.8701i			1.07739i
$623$	12.0000	−	20.7846i	0.480770	−	0.832718i
$624$		0			0
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	−5.00000	−	8.66025i	−0.199840	−	0.346133i
$627$		0			0
$628$	11.0000	−	19.0526i	0.438948	−	0.760280i
$629$		0			0
$630$		0			0
$631$	20.0000			0.796187			0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000			0.796187			0.398094	+	0.917345i	$0.369672\pi$
$632$	−3.67423	−	2.12132i	−0.146153	−	0.0843816i
$633$		0			0
$634$	8.57321	−	4.94975i	0.340486	−	0.196580i
$635$	−9.00000	−	15.5885i	−0.357154	−	0.618609i
$636$		0			0
$637$	40.4166	+	23.3345i	1.60136	+	0.924547i
$638$	−18.0000	−	8.48528i	−0.712627	−	0.335936i
$639$		0			0
$640$			1.41421i			0.0559017i
$641$	41.6413	+	24.0416i	1.64473	+	0.949587i	0.979118	+	0.203292i	$0.0651642\pi$
$641$	41.6413	+	24.0416i	1.64473	+	0.949587i	0.665615	+	0.746295i	$0.268169\pi$
$642$		0			0
$643$	2.00000	+	3.46410i	0.0788723	+	0.136611i	0.902764	−	0.430137i	$-0.141535\pi$
$643$	2.00000	+	3.46410i	0.0788723	+	0.136611i	−0.823891	+	0.566748i	$0.808201\pi$
$644$	3.00000	+	5.19615i	0.118217	+	0.204757i
$645$		0			0
$646$		0			0
$647$			7.07107i			0.277992i	0.990293	+	0.138996i	$0.0443876\pi$
$647$			7.07107i			0.277992i	−0.990293	+	0.138996i	$0.955612\pi$
$648$		0			0
$649$	−16.0000	+	33.9411i	−0.628055	+	1.33231i
$650$	11.0227	+	6.36396i	0.432346	+	0.249615i
$651$		0			0
$652$	−1.00000	−	1.73205i	−0.0391630	−	0.0678323i
$653$	−23.2702	+	13.4350i	−0.910631	+	0.525753i	−0.880634	−	0.473797i	$-0.842883\pi$
$653$	−23.2702	+	13.4350i	−0.910631	+	0.525753i	−0.0299972	+	0.999550i	$0.509550\pi$
$654$		0			0
$655$	14.6969	+	8.48528i	0.574257	+	0.331547i
$656$	−6.00000			−0.234261
$657$		0			0
$658$	42.0000			1.63733
$659$	15.0000	−	25.9808i	0.584317	−	1.01207i	−0.410643	−	0.911796i	$-0.634696\pi$
$659$	15.0000	−	25.9808i	0.584317	−	1.01207i	0.994960	−	0.100271i	$-0.0319709\pi$
$660$		0			0
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	0.996682	−	0.0813955i	$-0.0259377\pi$
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	−0.568831	+	0.822454i	$0.692604\pi$
$662$	−5.00000	−	8.66025i	−0.194331	−	0.336590i
$663$		0			0
$664$	−6.00000	+	10.3923i	−0.232845	+	0.403300i
$665$		0			0
$666$		0			0
$667$		−	8.48528i		−	0.328551i
$668$	−6.00000	+	10.3923i	−0.232147	+	0.402090i
$669$		0			0
$670$	−4.89898	+	2.82843i	−0.189264	+	0.109272i
$671$	−14.0227	+	1.16781i	−0.541340	+	0.0450828i
$672$		0			0
$673$	36.7423	+	21.2132i	1.41631	+	0.817709i	0.995973	−	0.0896575i	$-0.0285772\pi$
$673$	36.7423	+	21.2132i	1.41631	+	0.817709i	0.420341	+	0.907366i	$0.361911\pi$
$674$			33.9411i			1.30736i
$675$		0			0
$676$	−5.00000			−0.192308
$677$	15.0000	−	25.9808i	0.576497	−	0.998522i	−0.419380	−	0.907811i	$-0.637753\pi$
$677$	15.0000	−	25.9808i	0.576497	−	0.998522i	0.995877	−	0.0907112i	$-0.0289140\pi$
$678$		0			0
$679$	−29.3939	+	16.9706i	−1.12803	+	0.651270i
$680$		0			0
$681$		0			0
$682$	−10.8990	+	7.56388i	−0.417343	+	0.289636i
$683$		−	5.65685i		−	0.216454i	−0.994126	−	0.108227i	$-0.965483\pi$
$683$		−	5.65685i		−	0.216454i	0.994126	−	0.108227i	$-0.0345173\pi$
$684$		0			0
$685$	4.00000			0.152832
$686$	14.6969	+	8.48528i	0.561132	+	0.323970i
$687$		0			0
$688$	7.34847	−	4.24264i	0.280158	−	0.161749i
$689$	15.0000	+	25.9808i	0.571454	+	0.989788i
$690$		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
$694$	−12.0000			−0.455514
$695$	−12.0000	+	20.7846i	−0.455186	+	0.788405i
$696$		0			0
$697$		0			0
$698$	25.7196	−	14.8492i	0.973503	−	0.562052i
$699$		0			0
$700$	11.0227	+	6.36396i	0.416619	+	0.240535i
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$		0			0
$703$		0			0
$704$	−2.72474	+	1.89097i	−0.102693	+	0.0712686i
$705$		0			0
$706$	19.5959	−	11.3137i	0.737502	−	0.425797i
$707$	−22.0454	+	12.7279i	−0.829103	+	0.478683i
$708$		0			0
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	−0.756730	−	0.653727i	$-0.773204\pi$
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	0.944509	+	0.328484i	$0.106538\pi$
$710$	−10.0000			−0.375293
$711$		0			0
$712$			5.65685i			0.212000i
$713$	−4.89898	−	2.82843i	−0.183468	−	0.105925i
$714$		0			0
$715$	−1.65153	−	19.8311i	−0.0617637	−	0.741641i
$716$	−4.89898	+	2.82843i	−0.183083	+	0.105703i
$717$		0			0
$718$		0			0
$719$			32.5269i			1.21305i	0.795065	+	0.606525i	$0.207437\pi$
$719$			32.5269i			1.21305i	−0.795065	+	0.606525i	$0.792563\pi$
$720$		0			0
$721$			16.9706i			0.632017i
$722$	9.50000	−	16.4545i	0.353553	−	0.612372i
$723$		0			0
$724$	−1.00000	−	1.73205i	−0.0371647	−	0.0643712i
$725$	−9.00000	−	15.5885i	−0.334252	−	0.578941i
$726$		0			0
$727$	−22.0000	+	38.1051i	−0.815935	+	1.41324i	0.0927199	+	0.995692i	$0.470444\pi$
$727$	−22.0000	+	38.1051i	−0.815935	+	1.41324i	−0.908655	+	0.417548i	$0.862889\pi$
$728$	−18.0000			−0.667124
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	3.67423	−	2.12132i	0.135711	−	0.0783528i	−0.430607	−	0.902539i	$-0.641701\pi$
$733$	3.67423	−	2.12132i	0.135711	−	0.0783528i	0.566318	+	0.824187i	$0.308367\pi$
$734$	−14.0000	−	24.2487i	−0.516749	−	0.895036i
$735$		0			0
$736$	−1.22474	−	0.707107i	−0.0451447	−	0.0260643i
$737$	−12.0000	−	5.65685i	−0.442026	−	0.208373i
$738$		0			0
$739$			25.4558i			0.936408i	0.883620	+	0.468204i	$0.155099\pi$
$739$			25.4558i			0.936408i	−0.883620	+	0.468204i	$0.844901\pi$
$740$	2.44949	+	1.41421i	0.0900450	+	0.0519875i
$741$		0			0
$742$	15.0000	+	25.9808i	0.550667	+	0.953784i
$743$	12.0000	+	20.7846i	0.440237	+	0.762513i	0.997707	−	0.0676840i	$-0.0215610\pi$
$743$	12.0000	+	20.7846i	0.440237	+	0.762513i	−0.557470	+	0.830197i	$0.688228\pi$
$744$		0			0
$745$	−7.34847	−	4.24264i	−0.269227	−	0.155438i
$746$		−	29.6985i		−	1.08734i
$747$		0			0
$748$		0			0
$749$	−66.1362	−	38.1838i	−2.41656	−	1.39520i
$750$		0			0
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	0.956963	+	0.290209i	$0.0937250\pi$
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	−0.227153	+	0.973859i	$0.572942\pi$
$752$	−8.57321	+	4.94975i	−0.312633	+	0.180499i
$753$		0			0
$754$	22.0454	+	12.7279i	0.802846	+	0.463524i
$755$	−6.00000			−0.218362
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	1.00000	−	1.73205i	0.0363216	−	0.0629109i
$759$		0			0
$760$		0			0
$761$	12.0000	+	20.7846i	0.435000	+	0.753442i	0.997296	−	0.0734946i	$-0.0234152\pi$
$761$	12.0000	+	20.7846i	0.435000	+	0.753442i	−0.562296	+	0.826936i	$0.690082\pi$
$762$		0			0
$763$	27.0000	−	46.7654i	0.977466	−	1.69302i
$764$		−	9.89949i		−	0.358151i
$765$		0			0
$766$			1.41421i			0.0510976i
$767$	24.0000	−	41.5692i	0.866590	−	1.50098i
$768$		0			0
$769$	36.7423	−	21.2132i	1.32496	−	0.764968i	0.340447	−	0.940264i	$-0.389422\pi$
$769$	36.7423	−	21.2132i	1.32496	−	0.764968i	0.984516	+	0.175296i	$0.0560882\pi$
$770$	−1.65153	−	19.8311i	−0.0595170	−	0.714663i
$771$		0			0
$772$	7.34847	+	4.24264i	0.264477	+	0.152696i
$773$		−	18.3848i		−	0.661254i	−0.943761	−	0.330627i	$-0.892740\pi$
$773$		−	18.3848i		−	0.661254i	0.943761	−	0.330627i	$-0.107260\pi$
$774$		0			0
$775$	−12.0000			−0.431053
$776$	4.00000	−	6.92820i	0.143592	−	0.248708i
$777$		0			0
$778$	8.57321	−	4.94975i	0.307365	−	0.177457i
$779$		0			0
$780$		0			0
$781$	−13.3712	−	19.2669i	−0.478458	−	0.689422i
$782$		0			0
$783$		0			0
$784$	−11.0000			−0.392857
$785$	−26.9444	−	15.5563i	−0.961686	−	0.555230i
$786$		0			0
$787$	36.7423	−	21.2132i	1.30972	−	0.756169i	0.327673	−	0.944791i	$-0.393735\pi$
$787$	36.7423	−	21.2132i	1.30972	−	0.756169i	0.982050	+	0.188622i	$0.0604021\pi$
$788$	−9.00000	−	15.5885i	−0.320612	−	0.555316i
$789$		0			0
$790$	−3.00000	+	5.19615i	−0.106735	+	0.184871i
$791$	48.0000			1.70668
$792$		0			0
$793$	18.0000			0.639199
$794$	−17.0000	+	29.4449i	−0.603307	+	1.04496i
$795$		0			0
$796$	8.00000	+	13.8564i	0.283552	+	0.491127i
$797$	−1.22474	+	0.707107i	−0.0433827	+	0.0250470i	−0.521534	−	0.853230i	$-0.674640\pi$
$797$	−1.22474	+	0.707107i	−0.0433827	+	0.0250470i	0.478152	+	0.878277i	$0.341307\pi$
$798$		0			0
$799$		0			0
$800$	−3.00000			−0.106066
$801$		0			0
$802$		−	36.7696i		−	1.29838i
$803$		0			0
$804$		0			0
$805$	7.34847	−	4.24264i	0.259000	−	0.149533i
$806$	14.6969	−	8.48528i	0.517678	−	0.298881i
$807$		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
$811$		−	25.4558i		−	0.893876i	−0.894565	−	0.446938i	$-0.852515\pi$
$811$		−	25.4558i		−	0.893876i	0.894565	−	0.446938i	$-0.147485\pi$
$812$	22.0454	+	12.7279i	0.773642	+	0.446663i
$813$		0			0
$814$	0.550510	+	6.61037i	0.0192954	+	0.231693i
$815$	−2.44949	+	1.41421i	−0.0858019	+	0.0495377i
$816$		0			0
$817$		0			0
$818$			8.48528i			0.296681i
$819$		0			0
$820$			8.48528i			0.296319i
$821$	15.0000	−	25.9808i	0.523504	−	0.906735i	−0.476122	−	0.879379i	$-0.657958\pi$
$821$	15.0000	−	25.9808i	0.523504	−	0.906735i	0.999626	−	0.0273557i	$-0.00870868\pi$
$822$		0			0
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	0.969448	+	0.245295i	$0.0788849\pi$
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	−0.272292	+	0.962215i	$0.587782\pi$
$824$	−2.00000	−	3.46410i	−0.0696733	−	0.120678i
$825$		0			0
$826$	24.0000	−	41.5692i	0.835067	−	1.44638i
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$		0			0
$829$	2.00000			0.0694629			0.0347314	−	0.999397i	$-0.488942\pi$
$829$	2.00000			0.0694629			0.0347314	+	0.999397i	$0.488942\pi$
$830$	14.6969	+	8.48528i	0.510138	+	0.294528i
$831$		0			0
$832$	3.67423	−	2.12132i	0.127381	−	0.0735436i
$833$		0			0
$834$		0			0
$835$	14.6969	+	8.48528i	0.508609	+	0.293645i
$836$		0			0
$837$		0			0
$838$		−	11.3137i		−	0.390826i
$839$	−13.4722	−	7.77817i	−0.465112	−	0.268532i	0.249079	−	0.968483i	$-0.419872\pi$
$839$	−13.4722	−	7.77817i	−0.465112	−	0.268532i	−0.714191	+	0.699951i	$0.753205\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	−5.00000	−	8.66025i	−0.172311	−	0.298452i
$843$		0			0
$844$	7.34847	+	4.24264i	0.252945	+	0.146038i
$845$			7.07107i			0.243252i
$846$		0			0
$847$	36.0000	−	29.6985i	1.23697	−	1.02045i
$848$	−6.12372	−	3.53553i	−0.210290	−	0.121411i
$849$		0			0
$850$		0			0
$851$	−2.44949	+	1.41421i	−0.0839674	+	0.0484786i
$852$		0			0
$853$	−18.3712	−	10.6066i	−0.629017	−	0.363163i	0.151354	−	0.988480i	$-0.451637\pi$
$853$	−18.3712	−	10.6066i	−0.629017	−	0.363163i	−0.780371	+	0.625316i	$0.784970\pi$
$854$	18.0000			0.615947
$855$		0			0
$856$	18.0000			0.615227
$857$	−3.00000	+	5.19615i	−0.102478	+	0.177497i	−0.912705	−	0.408619i	$-0.866010\pi$
$857$	−3.00000	+	5.19615i	−0.102478	+	0.177497i	0.810227	+	0.586116i	$0.199344\pi$
$858$		0			0
$859$	11.0000	+	19.0526i	0.375315	+	0.650065i	0.990374	−	0.138416i	$-0.0442012\pi$
$859$	11.0000	+	19.0526i	0.375315	+	0.650065i	−0.615059	+	0.788481i	$0.710868\pi$
$860$	−6.00000	−	10.3923i	−0.204598	−	0.354375i
$861$		0			0
$862$	−18.0000	+	31.1769i	−0.613082	+	1.06189i
$863$			7.07107i			0.240702i	0.992731	+	0.120351i	$0.0384020\pi$
$863$			7.07107i			0.240702i	−0.992731	+	0.120351i	$0.961598\pi$
$864$		0			0
$865$		−	8.48528i		−	0.288508i
$866$	1.00000	−	1.73205i	0.0339814	−	0.0588575i
$867$		0			0
$868$	14.6969	−	8.48528i	0.498847	−	0.288009i
$869$	−14.0227	+	1.16781i	−0.475688	+	0.0396152i
$870$		0			0
$871$	14.6969	+	8.48528i	0.497987	+	0.287513i
$872$			12.7279i			0.431022i
$873$		0			0
$874$		0			0
$875$	24.0000	−	41.5692i	0.811348	−	1.40530i
$876$		0			0
$877$	25.7196	−	14.8492i	0.868491	−	0.501423i	0.00164425	−	0.999999i	$-0.499477\pi$
$877$	25.7196	−	14.8492i	0.868491	−	0.501423i	0.866846	+	0.498575i	$0.166143\pi$
$878$	−18.3712	+	10.6066i	−0.619997	+	0.357955i
$879$		0			0
$880$	2.67423	+	3.85337i	0.0901484	+	0.129897i
$881$		−	5.65685i		−	0.190584i	−0.995449	−	0.0952921i	$-0.969621\pi$
$881$		−	5.65685i		−	0.190584i	0.995449	−	0.0952921i	$-0.0303785\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$		0			0
$885$		0			0
$886$	−24.4949	+	14.1421i	−0.822922	+	0.475114i
$887$	−24.0000	−	41.5692i	−0.805841	−	1.39576i	−0.915722	−	0.401813i	$-0.868380\pi$
$887$	−24.0000	−	41.5692i	−0.805841	−	1.39576i	0.109881	−	0.993945i	$-0.464953\pi$
$888$		0			0
$889$	−27.0000	+	46.7654i	−0.905551	+	1.56846i
$890$	8.00000			0.268161
$891$		0			0
$892$	8.00000			0.267860
$893$		0			0
$894$		0			0
$895$	4.00000	+	6.92820i	0.133705	+	0.231584i
$896$	3.67423	−	2.12132i	0.122748	−	0.0708683i
$897$		0			0
$898$	−26.9444	−	15.5563i	−0.899146	−	0.519122i
$899$	−24.0000			−0.800445
$900$		0			0
$901$		0			0
$902$	−16.3485	+	11.3458i	−0.544344	+	0.377774i
$903$		0			0
$904$	−9.79796	+	5.65685i	−0.325875	+	0.188144i
$905$	−2.44949	+	1.41421i	−0.0814238	+	0.0470100i
$906$		0			0
$907$	−22.0000	+	38.1051i	−0.730498	+	1.26526i	0.226173	+	0.974087i	$0.427379\pi$
$907$	−22.0000	+	38.1051i	−0.730498	+	1.26526i	−0.956671	+	0.291172i	$0.905955\pi$
$908$	6.00000			0.199117
$909$		0			0
$910$			25.4558i			0.843853i
$911$	8.57321	+	4.94975i	0.284043	+	0.163992i	0.635252	−	0.772305i	$-0.280896\pi$
$911$	8.57321	+	4.94975i	0.284043	+	0.163992i	−0.351209	+	0.936297i	$0.614229\pi$
$912$		0			0
$913$	3.30306	+	39.6622i	0.109315	+	1.31263i
$914$	−7.34847	+	4.24264i	−0.243066	+	0.140334i
$915$		0			0
$916$	−7.00000	+	12.1244i	−0.231287	+	0.400600i
$917$		−	50.9117i		−	1.68125i
$918$		0			0
$919$		−	38.1838i		−	1.25957i	−0.776771	−	0.629783i	$-0.783144\pi$
$919$		−	38.1838i		−	1.25957i	0.776771	−	0.629783i	$-0.216856\pi$
$920$	−1.00000	+	1.73205i	−0.0329690	+	0.0571040i
$921$		0			0
$922$	−15.0000	−	25.9808i	−0.493999	−	0.855631i
$923$	15.0000	+	25.9808i	0.493731	+	0.855167i
$924$		0			0
$925$	−3.00000	+	5.19615i	−0.0986394	+	0.170848i
$926$	−32.0000			−1.05159
$927$		0			0
$928$	−6.00000			−0.196960
$929$	−2.44949	−	1.41421i	−0.0803652	−	0.0463988i	0.459279	−	0.888292i	$-0.348108\pi$
$929$	−2.44949	−	1.41421i	−0.0803652	−	0.0463988i	−0.539644	+	0.841893i	$0.681441\pi$
$930$		0			0
$931$		0			0
$932$	9.00000	+	15.5885i	0.294805	+	0.510617i
$933$		0			0
$934$	−26.9444	−	15.5563i	−0.881647	−	0.509019i
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$	14.6969	+	8.48528i	0.479872	+	0.277054i
$939$		0			0
$940$	7.00000	+	12.1244i	0.228315	+	0.395453i
$941$	21.0000	+	36.3731i	0.684580	+	1.18573i	0.973568	+	0.228395i	$0.0733479\pi$
$941$	21.0000	+	36.3731i	0.684580	+	1.18573i	−0.288988	+	0.957333i	$0.593319\pi$
$942$		0			0
$943$	−7.34847	−	4.24264i	−0.239299	−	0.138159i
$944$			11.3137i			0.368230i
$945$		0			0
$946$	12.0000	−	25.4558i	0.390154	−	0.827641i
$947$	41.6413	+	24.0416i	1.35316	+	0.781248i	0.988691	−	0.149967i	$-0.0479167\pi$
$947$	41.6413	+	24.0416i	1.35316	+	0.781248i	0.364470	+	0.931215i	$0.381250\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	54.0000			1.74923			0.874616	−	0.484817i	$-0.161114\pi$
$953$	54.0000			1.74923			0.874616	+	0.484817i	$0.161114\pi$
$954$		0			0
$955$	−14.0000			−0.453029
$956$	−6.00000	+	10.3923i	−0.194054	+	0.336111i
$957$		0			0
$958$	−6.00000	−	10.3923i	−0.193851	−	0.335760i
$959$	−6.00000	−	10.3923i	−0.193750	−	0.335585i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		−	8.48528i		−	0.273576i
$963$		0			0
$964$			8.48528i			0.273293i
$965$	6.00000	−	10.3923i	0.193147	−	0.334540i
$966$		0			0
$967$	3.67423	−	2.12132i	0.118155	−	0.0682171i	−0.439758	−	0.898117i	$-0.644936\pi$
$967$	3.67423	−	2.12132i	0.118155	−	0.0682171i	0.557913	+	0.829899i	$0.311602\pi$
$968$	−3.84847	+	10.3048i	−0.123694	+	0.331209i
$969$		0			0
$970$	−9.79796	−	5.65685i	−0.314594	−	0.181631i
$971$			45.2548i			1.45230i	0.687538	+	0.726148i	$0.258691\pi$
$971$			45.2548i			1.45230i	−0.687538	+	0.726148i	$0.741309\pi$
$972$		0			0
$973$	72.0000			2.30821
$974$	10.0000	−	17.3205i	0.320421	−	0.554985i
$975$		0			0
$976$	−3.67423	+	2.12132i	−0.117609	+	0.0679018i
$977$	−12.2474	+	7.07107i	−0.391831	+	0.226224i	−0.682953	−	0.730462i	$-0.739305\pi$
$977$	−12.2474	+	7.07107i	−0.391831	+	0.226224i	0.291122	+	0.956686i	$0.405971\pi$
$978$		0			0
$979$	10.6969	+	15.4135i	0.341876	+	0.492617i
$980$			15.5563i			0.496929i
$981$		0			0
$982$	6.00000			0.191468
$983$	8.57321	+	4.94975i	0.273443	+	0.157872i	0.630451	−	0.776229i	$-0.282870\pi$
$983$	8.57321	+	4.94975i	0.273443	+	0.157872i	−0.357008	+	0.934101i	$0.616203\pi$
$984$		0			0
$985$	−22.0454	+	12.7279i	−0.702425	+	0.405545i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	12.0000			0.381578
$990$		0			0
$991$	20.0000			0.635321			0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000			0.635321			0.317660	+	0.948205i	$0.397103\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$		0			0
$994$	15.0000	+	25.9808i	0.475771	+	0.824060i
$995$	19.5959	−	11.3137i	0.621232	−	0.358669i
$996$		0			0
$997$	25.7196	+	14.8492i	0.814549	+	0.470280i	0.848533	−	0.529142i	$-0.177486\pi$
$997$	25.7196	+	14.8492i	0.814549	+	0.470280i	−0.0339839	+	0.999422i	$0.510820\pi$
$998$	−14.0000			−0.443162
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1782.2.i.f.593.1		4
3.2	odd	2		1782.2.i.c.593.2		4
9.2	odd	6		66.2.b.b.65.2	yes	2
9.4	even	3	inner	1782.2.i.f.1187.2		4
9.5	odd	6		1782.2.i.c.1187.1		4
9.7	even	3		66.2.b.a.65.1	✓	2
11.10	odd	2		1782.2.i.c.593.1		4
33.32	even	2	inner	1782.2.i.f.593.2		4
36.7	odd	6		528.2.b.b.65.2		2
36.11	even	6		528.2.b.c.65.1		2
45.2	even	12		1650.2.f.a.1649.4		4
45.7	odd	12		1650.2.f.b.1649.1		4
45.29	odd	6		1650.2.d.a.1451.1		2
45.34	even	6		1650.2.d.b.1451.2		2
45.38	even	12		1650.2.f.a.1649.1		4
45.43	odd	12		1650.2.f.b.1649.4		4
72.11	even	6		2112.2.b.b.65.2		2
72.29	odd	6		2112.2.b.i.65.1		2
72.43	odd	6		2112.2.b.d.65.1		2
72.61	even	6		2112.2.b.g.65.2		2
99.2	even	30		726.2.h.i.161.2		8
99.7	odd	30		726.2.h.e.215.1		8
99.16	even	15		726.2.h.i.239.2		8
99.20	odd	30		726.2.h.e.161.2		8
99.25	even	15		726.2.h.i.233.2		8
99.29	even	30		726.2.h.i.215.2		8
99.32	even	6	inner	1782.2.i.f.1187.1		4
99.38	odd	30		726.2.h.e.239.1		8
99.43	odd	6		66.2.b.b.65.1	yes	2
99.47	odd	30		726.2.h.e.233.1		8
99.52	odd	30		726.2.h.e.233.2		8
99.61	odd	30		726.2.h.e.239.2		8
99.65	even	6		66.2.b.a.65.2	yes	2
99.70	even	15		726.2.h.i.215.1		8
99.74	even	30		726.2.h.i.233.1		8
99.76	odd	6		1782.2.i.c.1187.2		4
99.79	odd	30		726.2.h.e.161.1		8
99.83	even	30		726.2.h.i.239.1		8
99.92	odd	30		726.2.h.e.215.2		8
99.97	even	15		726.2.h.i.161.1		8
396.43	even	6		528.2.b.c.65.2		2
396.263	odd	6		528.2.b.b.65.1		2
495.43	even	12		1650.2.f.a.1649.2		4
495.142	even	12		1650.2.f.a.1649.3		4
495.164	even	6		1650.2.d.b.1451.1		2
495.263	odd	12		1650.2.f.b.1649.3		4
495.362	odd	12		1650.2.f.b.1649.2		4
495.439	odd	6		1650.2.d.a.1451.2		2
792.43	even	6		2112.2.b.b.65.1		2
792.461	even	6		2112.2.b.g.65.1		2
792.637	odd	6		2112.2.b.i.65.2		2
792.659	odd	6		2112.2.b.d.65.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.b.a.65.1	✓	2	9.7	even	3
66.2.b.a.65.2	yes	2	99.65	even	6
66.2.b.b.65.1	yes	2	99.43	odd	6
66.2.b.b.65.2	yes	2	9.2	odd	6
528.2.b.b.65.1		2	396.263	odd	6
528.2.b.b.65.2		2	36.7	odd	6
528.2.b.c.65.1		2	36.11	even	6
528.2.b.c.65.2		2	396.43	even	6
726.2.h.e.161.1		8	99.79	odd	30
726.2.h.e.161.2		8	99.20	odd	30
726.2.h.e.215.1		8	99.7	odd	30
726.2.h.e.215.2		8	99.92	odd	30
726.2.h.e.233.1		8	99.47	odd	30
726.2.h.e.233.2		8	99.52	odd	30
726.2.h.e.239.1		8	99.38	odd	30
726.2.h.e.239.2		8	99.61	odd	30
726.2.h.i.161.1		8	99.97	even	15
726.2.h.i.161.2		8	99.2	even	30
726.2.h.i.215.1		8	99.70	even	15
726.2.h.i.215.2		8	99.29	even	30
726.2.h.i.233.1		8	99.74	even	30
726.2.h.i.233.2		8	99.25	even	15
726.2.h.i.239.1		8	99.83	even	30
726.2.h.i.239.2		8	99.16	even	15
1650.2.d.a.1451.1		2	45.29	odd	6
1650.2.d.a.1451.2		2	495.439	odd	6
1650.2.d.b.1451.1		2	495.164	even	6
1650.2.d.b.1451.2		2	45.34	even	6
1650.2.f.a.1649.1		4	45.38	even	12
1650.2.f.a.1649.2		4	495.43	even	12
1650.2.f.a.1649.3		4	495.142	even	12
1650.2.f.a.1649.4		4	45.2	even	12
1650.2.f.b.1649.1		4	45.7	odd	12
1650.2.f.b.1649.2		4	495.362	odd	12
1650.2.f.b.1649.3		4	495.263	odd	12
1650.2.f.b.1649.4		4	45.43	odd	12
1782.2.i.c.593.1		4	11.10	odd	2
1782.2.i.c.593.2		4	3.2	odd	2
1782.2.i.c.1187.1		4	9.5	odd	6
1782.2.i.c.1187.2		4	99.76	odd	6
1782.2.i.f.593.1		4	1.1	even	1	trivial
1782.2.i.f.593.2		4	33.32	even	2	inner
1782.2.i.f.1187.1		4	99.32	even	6	inner
1782.2.i.f.1187.2		4	9.4	even	3	inner
2112.2.b.b.65.1		2	792.43	even	6
2112.2.b.b.65.2		2	72.11	even	6
2112.2.b.d.65.1		2	72.43	odd	6
2112.2.b.d.65.2		2	792.659	odd	6
2112.2.b.g.65.1		2	792.461	even	6
2112.2.b.g.65.2		2	72.61	even	6
2112.2.b.i.65.1		2	72.29	odd	6
2112.2.b.i.65.2		2	792.637	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1782 = 2 \cdot 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1782.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.22474 + 0.707107i) q^{5} +(3.67423 + 2.12132i) q^{7} -1.00000 q^{8} +1.41421i q^{10} +(-2.72474 + 1.89097i) q^{11} +(3.67423 - 2.12132i) q^{13} +(3.67423 - 2.12132i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.22474 + 0.707107i) q^{20} +(0.275255 + 3.30518i) q^{22} +(-1.22474 + 0.707107i) q^{23} +(-1.50000 + 2.59808i) q^{25} -4.24264i q^{26} -4.24264i q^{28} +(-3.00000 + 5.19615i) q^{29} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} -6.00000 q^{35} +2.00000 q^{37} +(1.22474 - 0.707107i) q^{40} +(3.00000 + 5.19615i) q^{41} +(-7.34847 - 4.24264i) q^{43} +(3.00000 + 1.41421i) q^{44} +1.41421i q^{46} +(8.57321 + 4.94975i) q^{47} +(5.50000 + 9.52628i) q^{49} +(1.50000 + 2.59808i) q^{50} +(-3.67423 - 2.12132i) q^{52} +7.07107i q^{53} +(2.00000 - 4.24264i) q^{55} +(-3.67423 - 2.12132i) q^{56} +(3.00000 + 5.19615i) q^{58} +(9.79796 - 5.65685i) q^{59} +(3.67423 + 2.12132i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-3.00000 + 5.19615i) q^{70} +7.07107i q^{71} +(1.00000 - 1.73205i) q^{74} +(-14.0227 + 1.16781i) q^{77} +(3.67423 + 2.12132i) q^{79} -1.41421i q^{80} +6.00000 q^{82} +(6.00000 - 10.3923i) q^{83} +(-7.34847 + 4.24264i) q^{86} +(2.72474 - 1.89097i) q^{88} -5.65685i q^{89} +18.0000 q^{91} +(1.22474 + 0.707107i) q^{92} +(8.57321 - 4.94975i) q^{94} +(-4.00000 + 6.92820i) q^{97} +11.0000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 6 q^{11} - 2 q^{16} + 6 q^{22} - 6 q^{25} - 12 q^{29} + 8 q^{31} + 2 q^{32} - 24 q^{35} + 8 q^{37} + 12 q^{41} + 12 q^{44} + 22 q^{49} + 6 q^{50} + 8 q^{55} + 12 q^{58}+ \cdots + 44 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 6 * q^11 - 2 * q^16 + 6 * q^22 - 6 * q^25 - 12 * q^29 + 8 * q^31 + 2 * q^32 - 24 * q^35 + 8 * q^37 + 12 * q^41 + 12 * q^44 + 22 * q^49 + 6 * q^50 + 8 * q^55 + 12 * q^58 + 16 * q^62 + 4 * q^64 - 12 * q^65 + 8 * q^67 - 12 * q^70 + 4 * q^74 - 12 * q^77 + 24 * q^82 + 24 * q^83 + 6 * q^88 + 72 * q^91 - 16 * q^97 + 44 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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