LMFDB - Embedded newform 2646.2.t.a.1979.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(1979,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("2646.1979");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.t (of order $6$, 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:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1979.7
Root			$-0.0967785 + 1.72934i$ of defining polynomial
Character	$\chi$	$=$	2646.1979
Dual form			2646.2.t.a.2285.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +0.366598 q^{5} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +0.366598 q^{5} -1.00000i q^{8} +(0.317483 - 0.183299i) q^{10} +0.669453i q^{11} +(0.867380 - 0.500782i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(2.49453 + 4.32065i) q^{17} +(5.50552 + 3.17861i) q^{19} +(0.183299 - 0.317483i) q^{20} +(0.334727 + 0.579764i) q^{22} +7.69459i q^{23} -4.86561 q^{25} +(0.500782 - 0.867380i) q^{26} +(-1.58394 - 0.914490i) q^{29} +(5.47837 + 3.16294i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(4.32065 + 2.49453i) q^{34} +(2.58394 - 4.47552i) q^{37} +6.35722 q^{38} -0.366598i q^{40} +(-2.15928 - 3.73998i) q^{41} +(2.24922 - 3.89576i) q^{43} +(0.579764 + 0.334727i) q^{44} +(3.84729 + 6.66371i) q^{46} +(4.16450 + 7.21313i) q^{47} +(-4.21374 + 2.43280i) q^{50} -1.00156i q^{52} +0.245420i q^{55} -1.82898 q^{58} +(4.36348 - 7.55776i) q^{59} +(-4.29351 + 2.47886i) q^{61} +6.32588 q^{62} -1.00000 q^{64} +(0.317980 - 0.183586i) q^{65} +(5.44537 - 9.43166i) q^{67} +4.98906 q^{68} +5.49843i q^{71} +(3.52744 - 2.03657i) q^{73} -5.16789i q^{74} +(5.50552 - 3.17861i) q^{76} +(-4.17784 - 7.23623i) q^{79} +(-0.183299 - 0.317483i) q^{80} +(-3.73998 - 2.15928i) q^{82} +(8.50712 - 14.7348i) q^{83} +(0.914490 + 1.58394i) q^{85} -4.49843i q^{86} +0.669453 q^{88} +(-5.35566 + 9.27628i) q^{89} +(6.66371 + 3.84729i) q^{92} +(7.21313 + 4.16450i) q^{94} +(2.01831 + 1.16527i) q^{95} +(14.9093 + 8.60787i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} - 8 q^{16} + 16 q^{25} + 12 q^{29} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} - 60 q^{50} + 24 q^{58} - 16 q^{64} + 84 q^{65} - 28 q^{67} - 4 q^{79} - 12 q^{85} + 48 q^{92} + 12 q^{95}+O(q^{100}) $ 16 * q + 8 * q^4 - 8 * q^16 + 16 * q^25 + 12 * q^29 + 4 * q^37 + 4 * q^43 - 12 * q^44 - 12 * q^46 - 60 * q^50 + 24 * q^58 - 16 * q^64 + 84 * q^65 - 28 * q^67 - 4 * q^79 - 12 * q^85 + 48 * q^92 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.366598			0.163948			0.0819738	−	0.996634i	$-0.473878\pi$
$5$	0.366598			0.163948			0.0819738	+	0.996634i	$0.473878\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	0.317483	−	0.183299i	0.100397	−	0.0579643i
$11$			0.669453i			0.201848i	0.994894	+	0.100924i	$0.0321799\pi$
$11$			0.669453i			0.201848i	−0.994894	+	0.100924i	$0.967820\pi$
$12$		0			0
$13$	0.867380	−	0.500782i	0.240568	−	0.138892i	−0.374870	−	0.927077i	$-0.622313\pi$
$13$	0.867380	−	0.500782i	0.240568	−	0.138892i	0.615438	+	0.788185i	$0.288979\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.49453	+	4.32065i	0.605013	+	1.04791i	0.992049	+	0.125848i	$0.0401653\pi$
$17$	2.49453	+	4.32065i	0.605013	+	1.04791i	−0.387037	+	0.922064i	$0.626501\pi$
$18$		0			0
$19$	5.50552	+	3.17861i	1.26305	+	0.729224i	0.973664	−	0.227988i	$-0.0732147\pi$
$19$	5.50552	+	3.17861i	1.26305	+	0.729224i	0.289389	+	0.957212i	$0.406548\pi$
$20$	0.183299	−	0.317483i	0.0409869	−	0.0709914i
$21$		0			0
$22$	0.334727	+	0.579764i	0.0713640	+	0.123606i
$23$			7.69459i			1.60443i	0.597034	+	0.802216i	$0.296346\pi$
$23$			7.69459i			1.60443i	−0.597034	+	0.802216i	$0.703654\pi$
$24$		0			0
$25$	−4.86561			−0.973121
$26$	0.500782	−	0.867380i	0.0982115	−	0.170107i
$27$		0			0
$28$		0			0
$29$	−1.58394	−	0.914490i	−0.294131	−	0.169817i	0.345672	−	0.938355i	$-0.387651\pi$
$29$	−1.58394	−	0.914490i	−0.294131	−	0.169817i	−0.639803	+	0.768539i	$0.720984\pi$
$30$		0			0
$31$	5.47837	+	3.16294i	0.983944	+	0.568081i	0.903459	−	0.428675i	$-0.141020\pi$
$31$	5.47837	+	3.16294i	0.983944	+	0.568081i	0.0804857	+	0.996756i	$0.474353\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	4.32065	+	2.49453i	0.740986	+	0.427809i
$35$		0			0
$36$		0			0
$37$	2.58394	−	4.47552i	0.424798	−	0.735771i	−0.571604	−	0.820530i	$-0.693679\pi$
$37$	2.58394	−	4.47552i	0.424798	−	0.735771i	0.996402	+	0.0847585i	$0.0270119\pi$
$38$	6.35722			1.03128
$39$		0			0
$40$		−	0.366598i		−	0.0579643i
$41$	−2.15928	−	3.73998i	−0.337223	−	0.584087i	0.646686	−	0.762756i	$-0.276154\pi$
$41$	−2.15928	−	3.73998i	−0.337223	−	0.584087i	−0.983909	+	0.178669i	$0.942821\pi$
$42$		0			0
$43$	2.24922	−	3.89576i	0.343002	−	0.594098i	−0.641986	−	0.766716i	$-0.721889\pi$
$43$	2.24922	−	3.89576i	0.343002	−	0.594098i	0.984989	+	0.172618i	$0.0552228\pi$
$44$	0.579764	+	0.334727i	0.0874027	+	0.0504619i
$45$		0			0
$46$	3.84729	+	6.66371i	0.567252	+	0.982510i
$47$	4.16450	+	7.21313i	0.607455	+	1.05214i	0.991658	+	0.128895i	$0.0411429\pi$
$47$	4.16450	+	7.21313i	0.607455	+	1.05214i	−0.384203	+	0.923249i	$0.625524\pi$
$48$		0			0
$49$		0			0
$50$	−4.21374	+	2.43280i	−0.595913	+	0.344050i
$51$		0			0
$52$		−	1.00156i		−	0.138892i
$53$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$53$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$54$		0			0
$55$			0.245420i			0.0330925i
$56$		0			0
$57$		0			0
$58$	−1.82898			−0.240157
$59$	4.36348	−	7.55776i	0.568076	−	0.983937i	−0.428680	−	0.903456i	$-0.641021\pi$
$59$	4.36348	−	7.55776i	0.568076	−	0.983937i	0.996756	−	0.0804804i	$-0.0256455\pi$
$60$		0			0
$61$	−4.29351	+	2.47886i	−0.549727	+	0.317385i	−0.749012	−	0.662556i	$-0.769471\pi$
$61$	−4.29351	+	2.47886i	−0.549727	+	0.317385i	0.199285	+	0.979942i	$0.436138\pi$
$62$	6.32588			0.803387
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.317980	−	0.183586i	0.0394406	−	0.0227710i
$66$		0			0
$67$	5.44537	−	9.43166i	0.665258	−	1.15226i	−0.313958	−	0.949437i	$-0.601655\pi$
$67$	5.44537	−	9.43166i	0.665258	−	1.15226i	0.979215	−	0.202823i	$-0.0650117\pi$
$68$	4.98906			0.605013
$69$		0			0
$70$		0			0
$71$			5.49843i			0.652544i	0.945276	+	0.326272i	$0.105793\pi$
$71$			5.49843i			0.652544i	−0.945276	+	0.326272i	$0.894207\pi$
$72$		0			0
$73$	3.52744	−	2.03657i	0.412856	−	0.238363i	−0.279160	−	0.960245i	$-0.590056\pi$
$73$	3.52744	−	2.03657i	0.412856	−	0.238363i	0.692016	+	0.721882i	$0.256723\pi$
$74$		−	5.16789i		−	0.600755i
$75$		0			0
$76$	5.50552	−	3.17861i	0.631526	−	0.364612i
$77$		0			0
$78$		0			0
$79$	−4.17784	−	7.23623i	−0.470044	−	0.814140i	0.529370	−	0.848391i	$-0.322429\pi$
$79$	−4.17784	−	7.23623i	−0.470044	−	0.814140i	−0.999413	+	0.0342518i	$0.989095\pi$
$80$	−0.183299	−	0.317483i	−0.0204935	−	0.0354957i
$81$		0			0
$82$	−3.73998	−	2.15928i	−0.413012	−	0.238453i
$83$	8.50712	−	14.7348i	0.933778	−	1.61735i	0.156980	−	0.987602i	$-0.449824\pi$
$83$	8.50712	−	14.7348i	0.933778	−	1.61735i	0.776798	−	0.629750i	$-0.216842\pi$
$84$		0			0
$85$	0.914490	+	1.58394i	0.0991904	+	0.171803i
$86$		−	4.49843i		−	0.485079i
$87$		0			0
$88$	0.669453			0.0713640
$89$	−5.35566	+	9.27628i	−0.567699	+	0.983283i	0.429094	+	0.903260i	$0.358833\pi$
$89$	−5.35566	+	9.27628i	−0.567699	+	0.983283i	−0.996793	+	0.0800234i	$0.974500\pi$
$90$		0			0
$91$		0			0
$92$	6.66371	+	3.84729i	0.694740	+	0.401108i
$93$		0			0
$94$	7.21313	+	4.16450i	0.743978	+	0.429536i
$95$	2.01831	+	1.16527i	0.207074	+	0.119555i
$96$		0			0
$97$	14.9093	+	8.60787i	1.51381	+	0.873997i	0.999869	+	0.0161687i	$0.00514689\pi$
$97$	14.9093	+	8.60787i	1.51381	+	0.873997i	0.513937	+	0.857828i	$0.328186\pi$
$98$		0			0
$99$		0			0
$100$	−2.43280	+	4.21374i	−0.243280	+	0.421374i
$101$	15.7317			1.56537			0.782683	−	0.622421i	$-0.213851\pi$
$101$	15.7317			1.56537			0.782683	+	0.622421i	$0.213851\pi$
$102$		0			0
$103$			11.4445i			1.12766i	0.825890	+	0.563831i	$0.190673\pi$
$103$			11.4445i			1.12766i	−0.825890	+	0.563831i	$0.809327\pi$
$104$	−0.500782	−	0.867380i	−0.0491057	−	0.0850537i
$105$		0			0
$106$		0			0
$107$	−9.57976	−	5.53088i	−0.926111	−	0.534690i	−0.0405313	−	0.999178i	$-0.512905\pi$
$107$	−9.57976	−	5.53088i	−0.926111	−	0.534690i	−0.885579	+	0.464488i	$0.846238\pi$
$108$		0			0
$109$	5.28166	+	9.14811i	0.505891	+	0.876230i	0.999977	+	0.00681630i	$0.00216971\pi$
$109$	5.28166	+	9.14811i	0.505891	+	0.876230i	−0.494085	+	0.869413i	$0.664497\pi$
$110$	0.122710	+	0.212540i	0.0117000	+	0.0202649i
$111$		0			0
$112$		0			0
$113$	−3.60226	+	2.07976i	−0.338872	+	0.195648i	−0.659773	−	0.751465i	$-0.729348\pi$
$113$	−3.60226	+	2.07976i	−0.338872	+	0.195648i	0.320901	+	0.947113i	$0.396014\pi$
$114$		0			0
$115$			2.82082i			0.263043i
$116$	−1.58394	+	0.914490i	−0.147065	+	0.0849083i
$117$		0			0
$118$		−	8.72695i		−	0.803381i
$119$		0			0
$120$		0			0
$121$	10.5518			0.959257
$122$	−2.47886	+	4.29351i	−0.224425	+	0.388716i
$123$		0			0
$124$	5.47837	−	3.16294i	0.491972	−	0.284040i
$125$	−3.61671			−0.323489
$126$		0			0
$127$	−1.66945			−0.148140			−0.0740700	−	0.997253i	$-0.523599\pi$
$127$	−1.66945			−0.148140			−0.0740700	+	0.997253i	$0.523599\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	0.183586	−	0.317980i	0.0161015	−	0.0278887i
$131$	−13.5321			−1.18231			−0.591154	−	0.806558i	$-0.701328\pi$
$131$	−13.5321			−1.18231			−0.591154	+	0.806558i	$0.701328\pi$
$132$		0			0
$133$		0			0
$134$		−	10.8907i		−	0.940817i
$135$		0			0
$136$	4.32065	−	2.49453i	0.370493	−	0.213904i
$137$			8.98851i			0.767940i	0.923346	+	0.383970i	$0.125443\pi$
$137$			8.98851i			0.767940i	−0.923346	+	0.383970i	$0.874557\pi$
$138$		0			0
$139$	8.05336	−	4.64961i	0.683077	−	0.394375i	−0.117936	−	0.993021i	$-0.537628\pi$
$139$	8.05336	−	4.64961i	0.683077	−	0.394375i	0.801014	+	0.598646i	$0.204294\pi$
$140$		0			0
$141$		0			0
$142$	2.74922	+	4.76178i	0.230709	+	0.399600i
$143$	0.335250	+	0.580671i	0.0280351	+	0.0485581i
$144$		0			0
$145$	−0.580671	−	0.335250i	−0.0482221	−	0.0278410i
$146$	2.03657	−	3.52744i	0.168548	−	0.291933i
$147$		0			0
$148$	−2.58394	−	4.47552i	−0.212399	−	0.367886i
$149$			2.83211i			0.232016i	0.993248	+	0.116008i	$0.0370098\pi$
$149$			2.83211i			0.232016i	−0.993248	+	0.116008i	$0.962990\pi$
$150$		0			0
$151$	−16.5518			−1.34697			−0.673484	−	0.739201i	$-0.735203\pi$
$151$	−16.5518			−1.34697			−0.673484	+	0.739201i	$0.735203\pi$
$152$	3.17861	−	5.50552i	0.257820	−	0.446556i
$153$		0			0
$154$		0			0
$155$	2.00836	+	1.15953i	0.161315	+	0.0931355i
$156$		0			0
$157$	2.45480	+	1.41728i	0.195914	+	0.113111i	0.594748	−	0.803912i	$-0.297252\pi$
$157$	2.45480	+	1.41728i	0.195914	+	0.113111i	−0.398834	+	0.917023i	$0.630585\pi$
$158$	−7.23623	−	4.17784i	−0.575684	−	0.332371i
$159$		0			0
$160$	−0.317483	−	0.183299i	−0.0250993	−	0.0144911i
$161$		0			0
$162$		0			0
$163$	−12.3640	+	21.4151i	−0.968426	+	1.67736i	−0.268313	+	0.963332i	$0.586466\pi$
$163$	−12.3640	+	21.4151i	−0.968426	+	1.67736i	−0.700113	+	0.714032i	$0.746867\pi$
$164$	−4.31856			−0.337223
$165$		0			0
$166$		−	17.0142i		−	1.32056i
$167$	−9.67422	−	16.7562i	−0.748614	−	1.29664i	−0.948487	−	0.316815i	$-0.897386\pi$
$167$	−9.67422	−	16.7562i	−0.748614	−	1.29664i	0.199874	−	0.979822i	$-0.435947\pi$
$168$		0			0
$169$	−5.99843	+	10.3896i	−0.461418	+	0.799199i
$170$	1.58394	+	0.914490i	0.121483	+	0.0701382i
$171$		0			0
$172$	−2.24922	−	3.89576i	−0.171501	−	0.297049i
$173$	−2.41827	−	4.18856i	−0.183858	−	0.318451i	0.759333	−	0.650702i	$-0.225525\pi$
$173$	−2.41827	−	4.18856i	−0.183858	−	0.318451i	−0.943191	+	0.332251i	$0.892192\pi$
$174$		0			0
$175$		0			0
$176$	0.579764	−	0.334727i	0.0437013	−	0.0252310i
$177$		0			0
$178$			10.7113i			0.802847i
$179$	3.16789	−	1.82898i	0.236779	−	0.136704i	−0.376916	−	0.926247i	$-0.623016\pi$
$179$	3.16789	−	1.82898i	0.236779	−	0.136704i	0.613695	+	0.789543i	$0.289682\pi$
$180$		0			0
$181$			5.66796i			0.421296i	0.977562	+	0.210648i	$0.0675574\pi$
$181$			5.66796i			0.421296i	−0.977562	+	0.210648i	$0.932443\pi$
$182$		0			0
$183$		0			0
$184$	7.69459			0.567252
$185$	0.947269	−	1.64072i	0.0696446	−	0.120628i
$186$		0			0
$187$	−2.89248	+	1.66997i	−0.211519	+	0.122120i
$188$	8.32901			0.607455
$189$		0			0
$190$	2.33055			0.169076
$191$	23.7098	−	13.6888i	1.71558	−	0.990490i	0.788996	−	0.614398i	$-0.210601\pi$
$191$	23.7098	−	13.6888i	1.71558	−	0.990490i	0.926583	−	0.376091i	$-0.122732\pi$
$192$		0			0
$193$	5.01413	−	8.68473i	0.360925	−	0.625141i	−0.627188	−	0.778868i	$-0.715794\pi$
$193$	5.01413	−	8.68473i	0.360925	−	0.625141i	0.988113	+	0.153727i	$0.0491276\pi$
$194$	17.2157			1.23602
$195$		0			0
$196$		0			0
$197$		−	18.8258i		−	1.34129i	−0.741780	−	0.670643i	$-0.766018\pi$
$197$		−	18.8258i		−	1.34129i	0.741780	−	0.670643i	$-0.233982\pi$
$198$		0			0
$199$	−4.64541	+	2.68203i	−0.329305	+	0.190124i	−0.655532	−	0.755167i	$-0.727556\pi$
$199$	−4.64541	+	2.68203i	−0.329305	+	0.190124i	0.326228	+	0.945291i	$0.394222\pi$
$200$			4.86561i			0.344050i
$201$		0			0
$202$	13.6241	−	7.86586i	0.958587	−	0.553440i
$203$		0			0
$204$		0			0
$205$	−0.791588	−	1.37107i	−0.0552869	−	0.0957597i
$206$	5.72226	+	9.91124i	0.398689	+	0.690549i
$207$		0			0
$208$	−0.867380	−	0.500782i	−0.0601420	−	0.0347230i
$209$	−2.12793	+	3.68569i	−0.147192	+	0.254944i
$210$		0			0
$211$	−0.828981	−	1.43584i	−0.0570694	−	0.0988471i	0.836079	−	0.548609i	$-0.184842\pi$
$211$	−0.828981	−	1.43584i	−0.0570694	−	0.0988471i	−0.893149	+	0.449762i	$0.851509\pi$
$212$		0			0
$213$		0			0
$214$	−11.0618			−0.756166
$215$	0.824559	−	1.42818i	0.0562344	−	0.0974009i
$216$		0			0
$217$		0			0
$218$	9.14811	+	5.28166i	0.619588	+	0.357719i
$219$		0			0
$220$	0.212540	+	0.122710i	0.0143295	+	0.00827312i
$221$	4.32741	+	2.49843i	0.291093	+	0.168063i
$222$		0			0
$223$	−14.7546	−	8.51860i	−0.988044	−	0.570448i	−0.0833551	−	0.996520i	$-0.526564\pi$
$223$	−14.7546	−	8.51860i	−0.988044	−	0.570448i	−0.904689	+	0.426072i	$0.859897\pi$
$224$		0			0
$225$		0			0
$226$	−2.07976	+	3.60226i	−0.138344	+	0.239619i
$227$	−5.11024			−0.339179			−0.169589	−	0.985515i	$-0.554244\pi$
$227$	−5.11024			−0.339179			−0.169589	+	0.985515i	$0.554244\pi$
$228$		0			0
$229$			15.2669i			1.00887i	0.863451	+	0.504433i	$0.168298\pi$
$229$			15.2669i			1.00887i	−0.863451	+	0.504433i	$0.831702\pi$
$230$	1.41041	+	2.44290i	0.0929997	+	0.161080i
$231$		0			0
$232$	−0.914490	+	1.58394i	−0.0600392	+	0.103991i
$233$	−8.82741	−	5.09651i	−0.578303	−	0.333883i	0.182156	−	0.983270i	$-0.441693\pi$
$233$	−8.82741	−	5.09651i	−0.578303	−	0.333883i	−0.760459	+	0.649386i	$0.775026\pi$
$234$		0			0
$235$	1.52670	+	2.64432i	0.0995909	+	0.172496i
$236$	−4.36348	−	7.55776i	−0.284038	−	0.491968i
$237$		0			0
$238$		0			0
$239$	16.6117	−	9.59076i	1.07452	−	0.620375i	0.145108	−	0.989416i	$-0.453647\pi$
$239$	16.6117	−	9.59076i	1.07452	−	0.620375i	0.929413	+	0.369041i	$0.120314\pi$
$240$		0			0
$241$			20.6853i			1.33245i	0.745749	+	0.666227i	$0.232092\pi$
$241$			20.6853i			1.33245i	−0.745749	+	0.666227i	$0.767908\pi$
$242$	9.13815	−	5.27592i	0.587423	−	0.339149i
$243$		0			0
$244$			4.95771i			0.317385i
$245$		0			0
$246$		0			0
$247$	6.36717			0.405133
$248$	3.16294	−	5.47837i	0.200847	−	0.347877i
$249$		0			0
$250$	−3.13216	+	1.80836i	−0.198096	+	0.114370i
$251$	−1.81200			−0.114373			−0.0571864	−	0.998364i	$-0.518213\pi$
$251$	−1.81200			−0.114373			−0.0571864	+	0.998364i	$0.518213\pi$
$252$		0			0
$253$	−5.15117			−0.323851
$254$	−1.44579	+	0.834727i	−0.0907169	+	0.0523754i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.45545			−0.402680			−0.201340	−	0.979521i	$-0.564530\pi$
$257$	−6.45545			−0.402680			−0.201340	+	0.979521i	$0.564530\pi$
$258$		0			0
$259$		0			0
$260$		−	0.367172i		−	0.0227710i
$261$		0			0
$262$	−11.7192	+	6.76607i	−0.724013	+	0.418009i
$263$		−	8.82062i		−	0.543903i	−0.962311	−	0.271951i	$-0.912331\pi$
$263$		−	8.82062i		−	0.543903i	0.962311	−	0.271951i	$-0.0876690\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−5.44537	−	9.43166i	−0.332629	−	0.576130i
$269$	−7.13267	−	12.3541i	−0.434886	−	0.753245i	0.562400	−	0.826865i	$-0.309878\pi$
$269$	−7.13267	−	12.3541i	−0.434886	−	0.753245i	−0.997286	+	0.0736199i	$0.976545\pi$
$270$		0			0
$271$	−2.64381	−	1.52641i	−0.160600	−	0.0927226i	0.417546	−	0.908656i	$-0.362890\pi$
$271$	−2.64381	−	1.52641i	−0.160600	−	0.0927226i	−0.578146	+	0.815933i	$0.696224\pi$
$272$	2.49453	−	4.32065i	0.151253	−	0.261978i
$273$		0			0
$274$	4.49425	+	7.78428i	0.271508	+	0.470265i
$275$		−	3.25730i		−	0.196422i
$276$		0			0
$277$	1.26566			0.0760459			0.0380230	−	0.999277i	$-0.487894\pi$
$277$	1.26566			0.0760459			0.0380230	+	0.999277i	$0.487894\pi$
$278$	4.64961	−	8.05336i	0.278865	−	0.483009i
$279$		0			0
$280$		0			0
$281$	−9.11639	−	5.26335i	−0.543838	−	0.313985i	0.202795	−	0.979221i	$-0.434998\pi$
$281$	−9.11639	−	5.26335i	−0.543838	−	0.313985i	−0.746633	+	0.665236i	$0.768331\pi$
$282$		0			0
$283$	−17.2094	−	9.93588i	−1.02300	−	0.590627i	−0.108025	−	0.994148i	$-0.534453\pi$
$283$	−17.2094	−	9.93588i	−1.02300	−	0.590627i	−0.914970	+	0.403522i	$0.867786\pi$
$284$	4.76178	+	2.74922i	0.282560	+	0.163136i
$285$		0			0
$286$	0.580671	+	0.335250i	0.0343358	+	0.0198238i
$287$		0			0
$288$		0			0
$289$	−3.94537	+	6.83358i	−0.232081	+	0.401975i
$290$	−0.670501			−0.0393732
$291$		0			0
$292$		−	4.07314i		−	0.238363i
$293$	6.70606	+	11.6152i	0.391772	+	0.678569i	0.992683	−	0.120747i	$-0.0385289\pi$
$293$	6.70606	+	11.6152i	0.391772	+	0.678569i	−0.600911	+	0.799316i	$0.705196\pi$
$294$		0			0
$295$	1.59964	−	2.77066i	0.0931348	−	0.161314i
$296$	−4.47552	−	2.58394i	−0.260134	−	0.150189i
$297$		0			0
$298$	1.41606	+	2.45268i	0.0820299	+	0.142080i
$299$	3.85331	+	6.67413i	0.222843	+	0.385975i
$300$		0			0
$301$		0			0
$302$	−14.3343	+	8.27592i	−0.824847	+	0.476225i
$303$		0			0
$304$		−	6.35722i		−	0.364612i
$305$	−1.57399	+	0.908744i	−0.0901265	+	0.0520346i
$306$		0			0
$307$			0.653728i			0.0373102i	0.999826	+	0.0186551i	$0.00593845\pi$
$307$			0.653728i			0.0373102i	−0.999826	+	0.0186551i	$0.994062\pi$
$308$		0			0
$309$		0			0
$310$	2.31905			0.131713
$311$	4.62246	−	8.00634i	0.262116	−	0.453998i	−0.704688	−	0.709517i	$-0.748913\pi$
$311$	4.62246	−	8.00634i	0.262116	−	0.453998i	0.966804	+	0.255519i	$0.0822464\pi$
$312$		0			0
$313$	−5.33830	+	3.08207i	−0.301739	+	0.174209i	−0.643224	−	0.765678i	$-0.722403\pi$
$313$	−5.33830	+	3.08207i	−0.301739	+	0.174209i	0.341485	+	0.939887i	$0.389070\pi$
$314$	2.83456			0.159963
$315$		0			0
$316$	−8.35568			−0.470044
$317$	−17.8876	+	10.3274i	−1.00467	+	0.580045i	−0.909626	−	0.415428i	$-0.863632\pi$
$317$	−17.8876	+	10.3274i	−1.00467	+	0.580045i	−0.0950420	+	0.995473i	$0.530299\pi$
$318$		0			0
$319$	0.612209	−	1.06038i	0.0342771	−	0.0593697i
$320$	−0.366598			−0.0204935
$321$		0			0
$322$		0			0
$323$			31.7166i			1.76476i
$324$		0			0
$325$	−4.22033	+	2.43661i	−0.234102	+	0.135159i
$326$			24.7281i			1.36956i
$327$		0			0
$328$	−3.73998	+	2.15928i	−0.206506	+	0.119226i
$329$		0			0
$330$		0			0
$331$	−5.35568	−	9.27631i	−0.294375	−	0.509872i	0.680464	−	0.732781i	$-0.261778\pi$
$331$	−5.35568	−	9.27631i	−0.294375	−	0.509872i	−0.974839	+	0.222909i	$0.928445\pi$
$332$	−8.50712	−	14.7348i	−0.466889	−	0.808676i
$333$		0			0
$334$	−16.7562	−	9.67422i	−0.916861	−	0.529350i
$335$	1.99626	−	3.45763i	0.109067	−	0.188910i
$336$		0			0
$337$	3.77592	+	6.54008i	0.205687	+	0.356261i	0.950351	−	0.311179i	$-0.100724\pi$
$337$	3.77592	+	6.54008i	0.205687	+	0.356261i	−0.744664	+	0.667439i	$0.767390\pi$
$338$			11.9969i			0.652544i
$339$		0			0
$340$	1.82898			0.0991904
$341$	−2.11744	+	3.66751i	−0.114666	+	0.198607i
$342$		0			0
$343$		0			0
$344$	−3.89576	−	2.24922i	−0.210045	−	0.121270i
$345$		0			0
$346$	−4.18856	−	2.41827i	−0.225179	−	0.130007i
$347$	−9.46737	−	5.46599i	−0.508235	−	0.293430i	0.223873	−	0.974618i	$-0.428130\pi$
$347$	−9.46737	−	5.46599i	−0.508235	−	0.293430i	−0.732108	+	0.681189i	$0.761463\pi$
$348$		0			0
$349$	−1.02562	−	0.592145i	−0.0549004	−	0.0316968i	0.472299	−	0.881439i	$-0.343424\pi$
$349$	−1.02562	−	0.592145i	−0.0549004	−	0.0316968i	−0.527199	+	0.849742i	$0.676758\pi$
$350$		0			0
$351$		0			0
$352$	0.334727	−	0.579764i	0.0178410	−	0.0309015i
$353$	−33.5824			−1.78741			−0.893706	−	0.448653i	$-0.851904\pi$
$353$	−33.5824			−1.78741			−0.893706	+	0.448653i	$0.851904\pi$
$354$		0			0
$355$			2.01572i			0.106983i
$356$	5.35566	+	9.27628i	0.283849	+	0.491642i
$357$		0			0
$358$	1.82898	−	3.16789i	0.0966646	−	0.167428i
$359$	8.77122	+	5.06407i	0.462927	+	0.267271i	0.713274	−	0.700885i	$-0.247211\pi$
$359$	8.77122	+	5.06407i	0.462927	+	0.267271i	−0.250347	+	0.968156i	$0.580545\pi$
$360$		0			0
$361$	10.7072	+	18.5453i	0.563534	+	0.976070i
$362$	2.83398	+	4.90860i	0.148951	+	0.257990i
$363$		0			0
$364$		0			0
$365$	1.29315	−	0.746603i	0.0676868	−	0.0390790i
$366$		0			0
$367$		−	18.0021i		−	0.939701i	−0.882746	−	0.469850i	$-0.844308\pi$
$367$		−	18.0021i		−	0.939701i	0.882746	−	0.469850i	$-0.155692\pi$
$368$	6.66371	−	3.84729i	0.347370	−	0.200554i
$369$		0			0
$370$		−	1.89454i		−	0.0984923i
$371$		0			0
$372$		0			0
$373$	16.4090			0.849627			0.424814	−	0.905281i	$-0.360340\pi$
$373$	16.4090			0.849627			0.424814	+	0.905281i	$0.360340\pi$
$374$	−1.66997	+	2.89248i	−0.0863522	+	0.149566i
$375$		0			0
$376$	7.21313	−	4.16450i	0.371989	−	0.214768i
$377$	−1.83184			−0.0943447
$378$		0			0
$379$	−2.91372			−0.149668			−0.0748339	−	0.997196i	$-0.523843\pi$
$379$	−2.91372			−0.149668			−0.0748339	+	0.997196i	$0.523843\pi$
$380$	2.01831	−	1.16527i	0.103537	−	0.0597773i
$381$		0			0
$382$	13.6888	−	23.7098i	0.700382	−	1.21310i
$383$	8.57443			0.438133			0.219066	−	0.975710i	$-0.429699\pi$
$383$	8.57443			0.438133			0.219066	+	0.975710i	$0.429699\pi$
$384$		0			0
$385$		0			0
$386$		−	10.0283i		−	0.510425i
$387$		0			0
$388$	14.9093	−	8.60787i	0.756903	−	0.436998i
$389$		−	35.5539i		−	1.80266i	−0.433137	−	0.901328i	$-0.642594\pi$
$389$		−	35.5539i		−	1.80266i	0.433137	−	0.901328i	$-0.357406\pi$
$390$		0			0
$391$	−33.2456	+	19.1944i	−1.68130	+	0.970702i
$392$		0			0
$393$		0			0
$394$	−9.41292	−	16.3037i	−0.474216	−	0.821367i
$395$	−1.53159	−	2.65279i	−0.0770626	−	0.133476i
$396$		0			0
$397$	3.10066	+	1.79017i	0.155618	+	0.0898460i	0.575787	−	0.817600i	$-0.304696\pi$
$397$	3.10066	+	1.79017i	0.155618	+	0.0898460i	−0.420169	+	0.907446i	$0.638029\pi$
$398$	−2.68203	+	4.64541i	−0.134438	+	0.232853i
$399$		0			0
$400$	2.43280	+	4.21374i	0.121640	+	0.210687i
$401$		−	0.190871i		−	0.00953167i	−0.999989	−	0.00476583i	$-0.998483\pi$
$401$		−	0.190871i		−	0.00953167i	0.999989	−	0.00476583i	$-0.00151702\pi$
$402$		0			0
$403$	6.33577			0.315607
$404$	7.86586	−	13.6241i	0.391341	−	0.677823i
$405$		0			0
$406$		0			0
$407$	2.99615	+	1.72983i	0.148514	+	0.0857445i
$408$		0			0
$409$	−3.00832	−	1.73685i	−0.148752	−	0.0858819i	0.423777	−	0.905767i	$-0.360704\pi$
$409$	−3.00832	−	1.73685i	−0.148752	−	0.0858819i	−0.572529	+	0.819885i	$0.694037\pi$
$410$	−1.37107	−	0.791588i	−0.0677124	−	0.0390938i
$411$		0			0
$412$	9.91124	+	5.72226i	0.488292	+	0.281915i
$413$		0			0
$414$		0			0
$415$	3.11870	−	5.40174i	0.153091	−	0.265161i
$416$	−1.00156			−0.0491057
$417$		0			0
$418$			4.25587i			0.208161i
$419$	0.703955	+	1.21929i	0.0343905	+	0.0595660i	0.882708	−	0.469921i	$-0.155718\pi$
$419$	0.703955	+	1.21929i	0.0343905	+	0.0595660i	−0.848318	+	0.529487i	$0.822384\pi$
$420$		0			0
$421$	15.1930	−	26.3151i	0.740463	−	1.28252i	−0.211822	−	0.977308i	$-0.567940\pi$
$421$	15.1930	−	26.3151i	0.740463	−	1.28252i	0.952285	−	0.305211i	$-0.0987268\pi$
$422$	−1.43584	−	0.828981i	−0.0698954	−	0.0403541i
$423$		0			0
$424$		0			0
$425$	−12.1374	−	21.0226i	−0.588751	−	1.01975i
$426$		0			0
$427$		0			0
$428$	−9.57976	+	5.53088i	−0.463055	+	0.267345i
$429$		0			0
$430$		−	1.64912i		−	0.0795275i
$431$	−23.6206	+	13.6373i	−1.13776	+	0.656888i	−0.945876	−	0.324529i	$-0.894794\pi$
$431$	−23.6206	+	13.6373i	−1.13776	+	0.656888i	−0.191887	+	0.981417i	$0.561461\pi$
$432$		0			0
$433$			8.15047i			0.391686i	0.980635	+	0.195843i	$0.0627444\pi$
$433$			8.15047i			0.391686i	−0.980635	+	0.195843i	$0.937256\pi$
$434$		0			0
$435$		0			0
$436$	10.5633			0.505891
$437$	−24.4581	+	42.3627i	−1.16999	+	2.02648i
$438$		0			0
$439$	10.6005	−	6.12020i	0.505934	−	0.292101i	−0.225226	−	0.974306i	$-0.572312\pi$
$439$	10.6005	−	6.12020i	0.505934	−	0.292101i	0.731161	+	0.682205i	$0.238979\pi$
$440$	0.245420			0.0117000
$441$		0			0
$442$	4.99687			0.237677
$443$	6.93544	−	4.00418i	0.329513	−	0.190244i	−0.326112	−	0.945331i	$-0.605739\pi$
$443$	6.93544	−	4.00418i	0.329513	−	0.190244i	0.655625	+	0.755087i	$0.272405\pi$
$444$		0			0
$445$	−1.96337	+	3.40067i	−0.0930729	+	0.161207i
$446$	−17.0372			−0.806735
$447$		0			0
$448$		0			0
$449$			14.5183i			0.685163i	0.939488	+	0.342581i	$0.111301\pi$
$449$			14.5183i			0.685163i	−0.939488	+	0.342581i	$0.888699\pi$
$450$		0			0
$451$	2.50374	−	1.44554i	0.117897	−	0.0680677i
$452$			4.15953i			0.195648i
$453$		0			0
$454$	−4.42560	+	2.55512i	−0.207704	+	0.119918i
$455$		0			0
$456$		0			0
$457$	−4.97751	−	8.62130i	−0.232838	−	0.403287i	0.725804	−	0.687901i	$-0.241468\pi$
$457$	−4.97751	−	8.62130i	−0.232838	−	0.403287i	−0.958642	+	0.284614i	$0.908135\pi$
$458$	7.63345	+	13.2215i	0.356688	+	0.617801i
$459$		0			0
$460$	2.44290	+	1.41041i	0.113901	+	0.0657607i
$461$	−16.1635	+	27.9960i	−0.752810	+	1.30391i	0.193645	+	0.981072i	$0.437969\pi$
$461$	−16.1635	+	27.9960i	−0.752810	+	1.30391i	−0.946456	+	0.322834i	$0.895364\pi$
$462$		0			0
$463$	−4.72516	−	8.18421i	−0.219597	−	0.380353i	0.735088	−	0.677972i	$-0.237141\pi$
$463$	−4.72516	−	8.18421i	−0.219597	−	0.380353i	−0.954685	+	0.297619i	$0.903807\pi$
$464$			1.82898i			0.0849083i
$465$		0			0
$466$	−10.1930			−0.472183
$467$	−10.3312	+	17.8941i	−0.478069	+	0.828039i	−0.999684	−	0.0251414i	$-0.991996\pi$
$467$	−10.3312	+	17.8941i	−0.478069	+	0.828039i	0.521615	+	0.853181i	$0.325330\pi$
$468$		0			0
$469$		0			0
$470$	2.64432	+	1.52670i	0.121973	+	0.0704214i
$471$		0			0
$472$	−7.55776	−	4.36348i	−0.347874	−	0.200845i
$473$	2.60803	+	1.50575i	0.119917	+	0.0692343i
$474$		0			0
$475$	−26.7877	−	15.4659i	−1.22910	−	0.709623i
$476$		0			0
$477$		0			0
$478$	9.59076	−	16.6117i	0.438671	−	0.759801i
$479$	10.1608			0.464261			0.232131	−	0.972685i	$-0.425430\pi$
$479$	10.1608			0.464261			0.232131	+	0.972685i	$0.425430\pi$
$480$		0			0
$481$		−	5.17597i		−	0.236004i
$482$	10.3426	+	17.9140i	0.471094	+	0.815958i
$483$		0			0
$484$	5.27592	−	9.13815i	0.239814	−	0.415371i
$485$	5.46571	+	3.15563i	0.248185	+	0.143290i
$486$		0			0
$487$	15.6148	+	27.0457i	0.707575	+	1.22556i	0.965754	+	0.259459i	$0.0835443\pi$
$487$	15.6148	+	27.0457i	0.707575	+	1.22556i	−0.258179	+	0.966097i	$0.583122\pi$
$488$	2.47886	+	4.29351i	0.112213	+	0.194358i
$489$		0			0
$490$		0			0
$491$	−17.8314	+	10.2950i	−0.804720	+	0.464605i	−0.845119	−	0.534578i	$-0.820471\pi$
$491$	−17.8314	+	10.2950i	−0.804720	+	0.464605i	0.0403987	+	0.999184i	$0.487137\pi$
$492$		0			0
$493$		−	9.12490i		−	0.410965i
$494$	5.51413	−	3.18359i	0.248093	−	0.143236i
$495$		0			0
$496$		−	6.32588i		−	0.284040i
$497$		0			0
$498$		0			0
$499$	−25.1533			−1.12601			−0.563007	−	0.826452i	$-0.690356\pi$
$499$	−25.1533			−1.12601			−0.563007	+	0.826452i	$0.690356\pi$
$500$	−1.80836	+	3.13216i	−0.0808722	+	0.140075i
$501$		0			0
$502$	−1.56924	+	0.906002i	−0.0700387	+	0.0404369i
$503$	−31.1553			−1.38915			−0.694574	−	0.719421i	$-0.744407\pi$
$503$	−31.1553			−1.38915			−0.694574	+	0.719421i	$0.744407\pi$
$504$		0			0
$505$	5.76722			0.256638
$506$	−4.46104	+	2.57558i	−0.198317	+	0.114499i
$507$		0			0
$508$	−0.834727	+	1.44579i	−0.0370350	+	0.0641465i
$509$	4.83347			0.214240			0.107120	−	0.994246i	$-0.465837\pi$
$509$	4.83347			0.214240			0.107120	+	0.994246i	$0.465837\pi$
$510$		0			0
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−5.59059	+	3.22773i	−0.246590	+	0.142369i
$515$			4.19554i			0.184877i
$516$		0			0
$517$	−4.82886	+	2.78794i	−0.212373	+	0.122613i
$518$		0			0
$519$		0			0
$520$	−0.183586	−	0.317980i	−0.00805077	−	0.0139443i
$521$	−8.76611	−	15.1834i	−0.384050	−	0.665195i	0.607587	−	0.794253i	$-0.292138\pi$
$521$	−8.76611	−	15.1834i	−0.384050	−	0.665195i	−0.991637	+	0.129059i	$0.958804\pi$
$522$		0			0
$523$	16.5427	+	9.55094i	0.723362	+	0.417633i	0.815989	−	0.578068i	$-0.196193\pi$
$523$	16.5427	+	9.55094i	0.723362	+	0.417633i	−0.0926268	+	0.995701i	$0.529526\pi$
$524$	−6.76607	+	11.7192i	−0.295577	+	0.511955i
$525$		0			0
$526$	−4.41031	−	7.63888i	−0.192299	−	0.333071i
$527$			31.5602i			1.37478i
$528$		0			0
$529$	−36.2067			−1.57420
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−3.74584	−	2.16266i	−0.162250	−	0.0936752i
$534$		0			0
$535$	−3.51192	−	2.02761i	−0.151834	−	0.0876612i
$536$	−9.43166	−	5.44537i	−0.407386	−	0.235204i
$537$		0			0
$538$	−12.3541	−	7.13267i	−0.532625	−	0.307511i
$539$		0			0
$540$		0			0
$541$	−6.83211	+	11.8336i	−0.293735	+	0.508765i	−0.974690	−	0.223561i	$-0.928232\pi$
$541$	−6.83211	+	11.8336i	−0.293735	+	0.508765i	0.680954	+	0.732326i	$0.261565\pi$
$542$	−3.05281			−0.131130
$543$		0			0
$544$		−	4.98906i		−	0.213904i
$545$	1.93625	+	3.35368i	0.0829397	+	0.143656i
$546$		0			0
$547$	4.94380	−	8.56292i	0.211382	−	0.366124i	−0.740765	−	0.671764i	$-0.765537\pi$
$547$	4.94380	−	8.56292i	0.211382	−	0.366124i	0.952147	+	0.305640i	$0.0988703\pi$
$548$	7.78428	+	4.49425i	0.332528	+	0.191985i
$549$		0			0
$550$	−1.62865	−	2.82090i	−0.0694458	−	0.120284i
$551$	−5.81362	−	10.0695i	−0.247669	−	0.428975i
$552$		0			0
$553$		0			0
$554$	1.09609	−	0.632828i	0.0465684	−	0.0268863i
$555$		0			0
$556$		−	9.29922i		−	0.394375i
$557$	−10.8946	+	6.29002i	−0.461621	+	0.266517i	−0.712725	−	0.701443i	$-0.752539\pi$
$557$	−10.8946	+	6.29002i	−0.461621	+	0.266517i	0.251105	+	0.967960i	$0.419206\pi$
$558$		0			0
$559$		−	4.50547i		−	0.190561i
$560$		0			0
$561$		0			0
$562$	−10.5267			−0.444042
$563$	12.1666	−	21.0732i	0.512763	−	0.888132i	−0.487127	−	0.873331i	$-0.661955\pi$
$563$	12.1666	−	21.0732i	0.512763	−	0.888132i	0.999890	−	0.0148007i	$-0.00471137\pi$
$564$		0			0
$565$	−1.32058	+	0.762437i	−0.0555572	+	0.0320760i
$566$	−19.8718			−0.835272
$567$		0			0
$568$	5.49843			0.230709
$569$	−8.18746	+	4.72703i	−0.343236	+	0.198167i	−0.661702	−	0.749767i	$-0.730166\pi$
$569$	−8.18746	+	4.72703i	−0.343236	+	0.198167i	0.318466	+	0.947934i	$0.396832\pi$
$570$		0			0
$571$	15.7843	−	27.3392i	0.660551	−	1.14411i	−0.319920	−	0.947445i	$-0.603656\pi$
$571$	15.7843	−	27.3392i	0.660551	−	1.14411i	0.980471	−	0.196664i	$-0.0630108\pi$
$572$	0.670501			0.0280351
$573$		0			0
$574$		0			0
$575$		−	37.4388i		−	1.56131i
$576$		0			0
$577$	−29.0806	+	16.7897i	−1.21064	+	0.698964i	−0.962899	−	0.269862i	$-0.913022\pi$
$577$	−29.0806	+	16.7897i	−1.21064	+	0.698964i	−0.247742	+	0.968826i	$0.579688\pi$
$578$			7.89074i			0.328211i
$579$		0			0
$580$	−0.580671	+	0.335250i	−0.0241110	+	0.0139205i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−2.03657	−	3.52744i	−0.0842739	−	0.145967i
$585$		0			0
$586$	11.6152	+	6.70606i	0.479821	+	0.277025i
$587$	−9.65855	+	16.7291i	−0.398651	+	0.690484i	−0.993560	−	0.113310i	$-0.963855\pi$
$587$	−9.65855	+	16.7291i	−0.398651	+	0.690484i	0.594909	+	0.803793i	$0.297188\pi$
$588$		0			0
$589$	20.1075	+	34.8272i	0.828516	+	1.43503i
$590$		−	3.19928i		−	0.131712i
$591$		0			0
$592$	−5.16789			−0.212399
$593$	−0.366598	+	0.634967i	−0.0150544	+	0.0260750i	−0.873454	−	0.486906i	$-0.838125\pi$
$593$	−0.366598	+	0.634967i	−0.0150544	+	0.0260750i	0.858400	+	0.512981i	$0.171459\pi$
$594$		0			0
$595$		0			0
$596$	2.45268	+	1.41606i	0.100466	+	0.0580039i
$597$		0			0
$598$	6.67413	+	3.85331i	0.272926	+	0.157574i
$599$	26.6548	+	15.3892i	1.08909	+	0.628785i	0.933333	−	0.359011i	$-0.116886\pi$
$599$	26.6548	+	15.3892i	1.08909	+	0.628785i	0.155754	+	0.987796i	$0.450219\pi$
$600$		0			0
$601$	0.786931	+	0.454335i	0.0320996	+	0.0185327i	0.515964	−	0.856610i	$-0.327434\pi$
$601$	0.786931	+	0.454335i	0.0320996	+	0.0185327i	−0.483864	+	0.875143i	$0.660767\pi$
$602$		0			0
$603$		0			0
$604$	−8.27592	+	14.3343i	−0.336742	+	0.583255i
$605$	3.86828			0.157268
$606$		0			0
$607$		−	44.7773i		−	1.81746i	−0.417389	−	0.908728i	$-0.637055\pi$
$607$		−	44.7773i		−	1.81746i	0.417389	−	0.908728i	$-0.362945\pi$
$608$	−3.17861	−	5.50552i	−0.128910	−	0.223278i
$609$		0			0
$610$	−0.908744	+	1.57399i	−0.0367940	+	0.0637290i
$611$	7.22442	+	4.17102i	0.292269	+	0.168741i
$612$		0			0
$613$	−9.07402	−	15.7167i	−0.366496	−	0.634790i	0.622519	−	0.782605i	$-0.286109\pi$
$613$	−9.07402	−	15.7167i	−0.366496	−	0.634790i	−0.989015	+	0.147815i	$0.952776\pi$
$614$	0.326864	+	0.566145i	0.0131912	+	0.0228478i
$615$		0			0
$616$		0			0
$617$	19.7393	−	11.3965i	0.794674	−	0.458805i	−0.0469315	−	0.998898i	$-0.514944\pi$
$617$	19.7393	−	11.3965i	0.794674	−	0.458805i	0.841605	+	0.540093i	$0.181611\pi$
$618$		0			0
$619$		−	44.3668i		−	1.78325i	−0.452772	−	0.891626i	$-0.649565\pi$
$619$		−	44.3668i		−	1.78325i	0.452772	−	0.891626i	$-0.350435\pi$
$620$	2.00836	−	1.15953i	0.0806577	−	0.0465677i
$621$		0			0
$622$		−	9.24493i		−	0.370688i
$623$		0			0
$624$		0			0
$625$	23.0021			0.920086
$626$	−3.08207	+	5.33830i	−0.123184	+	0.213361i
$627$		0			0
$628$	2.45480	−	1.41728i	0.0979571	−	0.0565555i
$629$	25.7829			1.02803
$630$		0			0
$631$	−32.5707			−1.29662			−0.648310	−	0.761377i	$-0.724524\pi$
$631$	−32.5707			−1.29662			−0.648310	+	0.761377i	$0.724524\pi$
$632$	−7.23623	+	4.17784i	−0.287842	+	0.166186i
$633$		0			0
$634$	−10.3274	+	17.8876i	−0.410154	+	0.710408i
$635$	−0.612018			−0.0242872
$636$		0			0
$637$		0			0
$638$		−	1.22442i		−	0.0484751i
$639$		0			0
$640$	−0.317483	+	0.183299i	−0.0125496	+	0.00724553i
$641$		−	11.8091i		−	0.466433i	−0.972425	−	0.233216i	$-0.925075\pi$
$641$		−	11.8091i		−	0.466433i	0.972425	−	0.233216i	$-0.0749250\pi$
$642$		0			0
$643$	−25.3714	+	14.6482i	−1.00055	+	0.577668i	−0.908411	−	0.418078i	$-0.862704\pi$
$643$	−25.3714	+	14.6482i	−1.00055	+	0.577668i	−0.0921392	+	0.995746i	$0.529370\pi$
$644$		0			0
$645$		0			0
$646$	15.8583	+	27.4674i	0.623936	+	1.08069i
$647$	14.0841	+	24.3945i	0.553705	+	0.959045i	0.998003	+	0.0631660i	$0.0201198\pi$
$647$	14.0841	+	24.3945i	0.553705	+	0.959045i	−0.444298	+	0.895879i	$0.646547\pi$
$648$		0			0
$649$	5.05957	+	2.92114i	0.198605	+	0.114665i
$650$	−2.43661	+	4.22033i	−0.0955717	+	0.165535i
$651$		0			0
$652$	12.3640	+	21.4151i	0.484213	+	0.838682i
$653$		−	45.0974i		−	1.76480i	−0.470502	−	0.882399i	$-0.655927\pi$
$653$		−	45.0974i		−	1.76480i	0.470502	−	0.882399i	$-0.344073\pi$
$654$		0			0
$655$	−4.96086			−0.193837
$656$	−2.15928	+	3.73998i	−0.0843057	+	0.146022i
$657$		0			0
$658$		0			0
$659$	−27.5435	−	15.9022i	−1.07294	−	0.619463i	−0.143958	−	0.989584i	$-0.545983\pi$
$659$	−27.5435	−	15.9022i	−1.07294	−	0.619463i	−0.928984	+	0.370121i	$0.879316\pi$
$660$		0			0
$661$	17.1234	+	9.88619i	0.666022	+	0.384528i	0.794568	−	0.607175i	$-0.207698\pi$
$661$	17.1234	+	9.88619i	0.666022	+	0.384528i	−0.128546	+	0.991704i	$0.541031\pi$
$662$	−9.27631	−	5.35568i	−0.360534	−	0.208154i
$663$		0			0
$664$	−14.7348	−	8.50712i	−0.571820	−	0.330140i
$665$		0			0
$666$		0			0
$667$	7.03663	−	12.1878i	0.272459	−	0.471913i
$668$	−19.3484			−0.748614
$669$		0			0
$670$		−	3.99252i		−	0.154245i
$671$	−1.65948	−	2.87430i	−0.0640635	−	0.110961i
$672$		0			0
$673$	−0.945369	+	1.63743i	−0.0364413	+	0.0631182i	−0.883671	−	0.468109i	$-0.844936\pi$
$673$	−0.945369	+	1.63743i	−0.0364413	+	0.0631182i	0.847230	+	0.531227i	$0.178269\pi$
$674$	6.54008	+	3.77592i	0.251914	+	0.145443i
$675$		0			0
$676$	5.99843	+	10.3896i	0.230709	+	0.399600i
$677$	10.5661	+	18.3010i	0.406088	+	0.703364i	0.994447	−	0.105235i	$-0.0335595\pi$
$677$	10.5661	+	18.3010i	0.406088	+	0.703364i	−0.588360	+	0.808599i	$0.700226\pi$
$678$		0			0
$679$		0			0
$680$	1.58394	−	0.914490i	0.0607415	−	0.0350691i
$681$		0			0
$682$			4.23488i			0.162162i
$683$	−7.55150	+	4.35986i	−0.288950	+	0.166825i	−0.637468	−	0.770477i	$-0.720018\pi$
$683$	−7.55150	+	4.35986i	−0.288950	+	0.166825i	0.348518	+	0.937302i	$0.386685\pi$
$684$		0			0
$685$			3.29517i			0.125902i
$686$		0			0
$687$		0			0
$688$	−4.49843			−0.171501
$689$		0			0
$690$		0			0
$691$	−15.7071	+	9.06850i	−0.597526	+	0.344982i	−0.768068	−	0.640369i	$-0.778782\pi$
$691$	−15.7071	+	9.06850i	−0.597526	+	0.344982i	0.170542	+	0.985350i	$0.445448\pi$
$692$	−4.83654			−0.183858
$693$		0			0
$694$	−10.9320			−0.414972
$695$	2.95235	−	1.70454i	0.111989	−	0.0646568i
$696$		0			0
$697$	10.7728	−	18.6590i	0.408048	−	0.706760i
$698$	−1.18429			−0.0448260
$699$		0			0
$700$		0			0
$701$			35.6167i			1.34523i	0.739995	+	0.672613i	$0.234828\pi$
$701$			35.6167i			1.34523i	−0.739995	+	0.672613i	$0.765172\pi$
$702$		0			0
$703$	28.4519	−	16.4267i	1.07308	−	0.619545i
$704$		−	0.669453i		−	0.0252310i
$705$		0			0
$706$	−29.0832	+	16.7912i	−1.09456	+	0.631946i
$707$		0			0
$708$		0			0
$709$	1.80385	+	3.12436i	0.0677449	+	0.117338i	0.897908	−	0.440183i	$-0.145086\pi$
$709$	1.80385	+	3.12436i	0.0677449	+	0.117338i	−0.830163	+	0.557520i	$0.811753\pi$
$710$	1.00786	+	1.74566i	0.0378242	+	0.0655135i
$711$		0			0
$712$	9.27628	+	5.35566i	0.347643	+	0.200712i
$713$	−24.3375	+	42.1538i	−0.911447	+	1.57867i
$714$		0			0
$715$	0.122902	+	0.212873i	0.00459628	+	0.00796099i
$716$		−	3.65796i		−	0.136704i
$717$		0			0
$718$	10.1281			0.377978
$719$	12.8915	−	22.3287i	0.480770	−	0.832718i	−0.518986	−	0.854782i	$-0.673690\pi$
$719$	12.8915	−	22.3287i	0.480770	−	0.832718i	0.999757	+	0.0220642i	$0.00702381\pi$
$720$		0			0
$721$		0			0
$722$	18.5453	+	10.7072i	0.690186	+	0.398479i
$723$		0			0
$724$	4.90860	+	2.83398i	0.182427	+	0.105324i
$725$	7.70685	+	4.44955i	0.286225	+	0.165252i
$726$		0			0
$727$	−1.32423	−	0.764544i	−0.0491129	−	0.0283554i	0.475242	−	0.879855i	$-0.342360\pi$
$727$	−1.32423	−	0.764544i	−0.0491129	−	0.0283554i	−0.524355	+	0.851499i	$0.675694\pi$
$728$		0			0
$729$		0			0
$730$	0.746603	−	1.29315i	0.0276330	−	0.0478618i
$731$	22.4430			0.830083
$732$		0			0
$733$			20.7739i			0.767303i	0.923478	+	0.383651i	$0.125334\pi$
$733$			20.7739i			0.767303i	−0.923478	+	0.383651i	$0.874666\pi$
$734$	−9.00104	−	15.5903i	−0.332234	−	0.575447i
$735$		0			0
$736$	3.84729	−	6.66371i	0.141813	−	0.245628i
$737$	6.31405	+	3.64542i	0.232581	+	0.134281i
$738$		0			0
$739$	5.93544	+	10.2805i	0.218339	+	0.378174i	0.954300	−	0.298850i	$-0.0966029\pi$
$739$	5.93544	+	10.2805i	0.218339	+	0.378174i	−0.735961	+	0.677023i	$0.763270\pi$
$740$	−0.947269	−	1.64072i	−0.0348223	−	0.0603140i
$741$		0			0
$742$		0			0
$743$	37.5906	−	21.7029i	1.37907	−	0.796204i	0.387019	−	0.922072i	$-0.373505\pi$
$743$	37.5906	−	21.7029i	1.37907	−	0.796204i	0.992047	+	0.125868i	$0.0401716\pi$
$744$		0			0
$745$			1.03825i			0.0380384i
$746$	14.2106	−	8.20451i	0.520288	−	0.300389i
$747$		0			0
$748$			3.33994i			0.122120i
$749$		0			0
$750$		0			0
$751$	2.31383			0.0844327			0.0422164	−	0.999108i	$-0.486558\pi$
$751$	2.31383			0.0844327			0.0422164	+	0.999108i	$0.486558\pi$
$752$	4.16450	−	7.21313i	0.151864	−	0.263036i
$753$		0			0
$754$	−1.58642	+	0.915921i	−0.0577741	+	0.0333559i
$755$	−6.06787			−0.220832
$756$		0			0
$757$	−15.0946			−0.548624			−0.274312	−	0.961641i	$-0.588450\pi$
$757$	−15.0946			−0.548624			−0.274312	+	0.961641i	$0.588450\pi$
$758$	−2.52336	+	1.45686i	−0.0916525	+	0.0529156i
$759$		0			0
$760$	1.16527	−	2.01831i	0.0422689	−	0.0732119i
$761$	−23.3379			−0.845998			−0.422999	−	0.906130i	$-0.639023\pi$
$761$	−23.3379			−0.845998			−0.422999	+	0.906130i	$0.639023\pi$
$762$		0			0
$763$		0			0
$764$		−	27.3777i		−	0.990490i
$765$		0			0
$766$	7.42567	−	4.28721i	0.268300	−	0.154903i
$767$		−	8.74061i		−	0.315605i
$768$		0			0
$769$	15.8266	−	9.13748i	0.570721	−	0.329506i	−0.186716	−	0.982414i	$-0.559784\pi$
$769$	15.8266	−	9.13748i	0.570721	−	0.329506i	0.757437	+	0.652908i	$0.226451\pi$
$770$		0			0
$771$		0			0
$772$	−5.01413	−	8.68473i	−0.180463	−	0.312570i
$773$	0.219254	+	0.379758i	0.00788600	+	0.0136590i	0.869941	−	0.493155i	$-0.164156\pi$
$773$	0.219254	+	0.379758i	0.00788600	+	0.0136590i	−0.862055	+	0.506814i	$0.830823\pi$
$774$		0			0
$775$	−26.6556	−	15.3896i	−0.957497	−	0.552811i
$776$	8.60787	−	14.9093i	0.309004	−	0.535211i
$777$		0			0
$778$	−17.7770	−	30.7906i	−0.637335	−	1.10390i
$779$		−	27.4541i		−	0.983644i
$780$		0			0
$781$	−3.68095			−0.131715
$782$	−19.1944	+	33.2456i	−0.686390	+	1.18886i
$783$		0			0
$784$		0			0
$785$	0.899924	+	0.519571i	0.0321197	+	0.0185443i
$786$		0			0
$787$	−33.1317	−	19.1286i	−1.18102	−	0.681861i	−0.224769	−	0.974412i	$-0.572163\pi$
$787$	−33.1317	−	19.1286i	−1.18102	−	0.681861i	−0.956250	+	0.292551i	$0.905496\pi$
$788$	−16.3037	−	9.41292i	−0.580794	−	0.335322i
$789$		0			0
$790$	−2.65279	−	1.53159i	−0.0943820	−	0.0544915i
$791$		0			0
$792$		0			0
$793$	−2.48274	+	4.30022i	−0.0881645	+	0.152705i
$794$	3.58034			0.127061
$795$		0			0
$796$			5.36406i			0.190124i
$797$	17.6613	+	30.5902i	0.625594	+	1.08356i	0.988426	+	0.151706i	$0.0484767\pi$
$797$	17.6613	+	30.5902i	0.625594	+	1.08356i	−0.362832	+	0.931855i	$0.618190\pi$
$798$		0			0
$799$	−20.7770	+	35.9868i	−0.735036	+	1.27312i
$800$	4.21374	+	2.43280i	0.148978	+	0.0860126i
$801$		0			0
$802$	−0.0954357	−	0.165300i	−0.00336995	−	0.00583693i
$803$	1.36339	+	2.36146i	0.0481130	+	0.0833341i
$804$		0			0
$805$		0			0
$806$	5.48694	−	3.16789i	0.193269	−	0.111584i
$807$		0			0
$808$		−	15.7317i		−	0.553440i
$809$	18.8506	−	10.8834i	0.662754	−	0.382641i	−0.130572	−	0.991439i	$-0.541681\pi$
$809$	18.8506	−	10.8834i	0.662754	−	0.382641i	0.793325	+	0.608798i	$0.208348\pi$
$810$		0			0
$811$		−	17.0184i		−	0.597598i	−0.954316	−	0.298799i	$-0.903414\pi$
$811$		−	17.0184i		−	0.597598i	0.954316	−	0.298799i	$-0.0965860\pi$
$812$		0			0
$813$		0			0
$814$	3.45966			0.121261
$815$	−4.53263	+	7.85075i	−0.158771	+	0.275000i
$816$		0			0
$817$	24.7662	−	14.2988i	0.866460	−	0.500251i
$818$	−3.47371			−0.121455
$819$		0			0
$820$	−1.58318			−0.0552869
$821$	−21.4786	+	12.4007i	−0.749608	+	0.432786i	−0.825552	−	0.564326i	$-0.809136\pi$
$821$	−21.4786	+	12.4007i	−0.749608	+	0.432786i	0.0759445	+	0.997112i	$0.475803\pi$
$822$		0			0
$823$	−10.6572	+	18.4588i	−0.371486	+	0.643433i	−0.989794	−	0.142503i	$-0.954485\pi$
$823$	−10.6572	+	18.4588i	−0.371486	+	0.643433i	0.618308	+	0.785936i	$0.287818\pi$
$824$	11.4445			0.398689
$825$		0			0
$826$		0			0
$827$			49.7585i			1.73027i	0.501537	+	0.865136i	$0.332768\pi$
$827$			49.7585i			1.73027i	−0.501537	+	0.865136i	$0.667232\pi$
$828$		0			0
$829$	37.3422	−	21.5595i	1.29695	−	0.748793i	0.317071	−	0.948402i	$-0.397301\pi$
$829$	37.3422	−	21.5595i	1.29695	−	0.748793i	0.979876	+	0.199609i	$0.0639673\pi$
$830$		−	6.23739i		−	0.216503i
$831$		0			0
$832$	−0.867380	+	0.500782i	−0.0300710	+	0.0173615i
$833$		0			0
$834$		0			0
$835$	−3.54655	−	6.14281i	−0.122733	−	0.212581i
$836$	2.12793	+	3.68569i	0.0735961	+	0.127472i
$837$		0			0
$838$	1.21929	+	0.703955i	0.0421195	+	0.0243177i
$839$	14.9985	−	25.9782i	0.517807	−	0.896868i	−0.481979	−	0.876183i	$-0.660082\pi$
$839$	14.9985	−	25.9782i	0.517807	−	0.896868i	0.999786	−	0.0206851i	$-0.00658476\pi$
$840$		0			0
$841$	−12.8274	−	22.2177i	−0.442325	−	0.766129i
$842$		−	30.3860i		−	1.04717i
$843$		0			0
$844$	−1.65796			−0.0570694
$845$	−2.19901	+	3.80881i	−0.0756484	+	0.131027i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$	−21.0226	−	12.1374i	−0.721069	−	0.416310i
$851$	34.4373	+	19.8824i	1.18050	+	0.681559i
$852$		0			0
$853$	25.7693	+	14.8779i	0.882325	+	0.509411i	0.871424	−	0.490530i	$-0.163197\pi$
$853$	25.7693	+	14.8779i	0.882325	+	0.509411i	0.0109007	+	0.999941i	$0.496530\pi$
$854$		0			0
$855$		0			0
$856$	−5.53088	+	9.57976i	−0.189042	+	0.327430i
$857$	−45.8592			−1.56652			−0.783260	−	0.621694i	$-0.786445\pi$
$857$	−45.8592			−1.56652			−0.783260	+	0.621694i	$0.786445\pi$
$858$		0			0
$859$			3.74208i			0.127678i	0.997960	+	0.0638390i	$0.0203344\pi$
$859$			3.74208i			0.127678i	−0.997960	+	0.0638390i	$0.979666\pi$
$860$	−0.824559	−	1.42818i	−0.0281172	−	0.0487005i
$861$		0			0
$862$	−13.6373	+	23.6206i	−0.464490	+	0.804520i
$863$	−27.1883	−	15.6972i	−0.925502	−	0.534339i	−0.0401159	−	0.999195i	$-0.512773\pi$
$863$	−27.1883	−	15.6972i	−0.925502	−	0.534339i	−0.885386	+	0.464856i	$0.846106\pi$
$864$		0			0
$865$	−0.886533	−	1.53552i	−0.0301430	−	0.0522092i
$866$	4.07523	+	7.05851i	0.138482	+	0.239858i
$867$		0			0
$868$		0			0
$869$	4.84432	−	2.79687i	0.164332	−	0.0948773i
$870$		0			0
$871$		−	10.9078i		−	0.369596i
$872$	9.14811	−	5.28166i	0.309794	−	0.178860i
$873$		0			0
$874$			48.9162i			1.65462i
$875$		0			0
$876$		0			0
$877$	−20.3923			−0.688599			−0.344300	−	0.938860i	$-0.611884\pi$
$877$	−20.3923			−0.688599			−0.344300	+	0.938860i	$0.611884\pi$
$878$	6.12020	−	10.6005i	0.206547	−	0.357750i
$879$		0			0
$880$	0.212540	−	0.122710i	0.00716473	−	0.00413656i
$881$	21.2010			0.714280			0.357140	−	0.934051i	$-0.383752\pi$
$881$	21.2010			0.714280			0.357140	+	0.934051i	$0.383752\pi$
$882$		0			0
$883$	38.6157			1.29952			0.649761	−	0.760139i	$-0.274869\pi$
$883$	38.6157			1.29952			0.649761	+	0.760139i	$0.274869\pi$
$884$	4.32741	−	2.49843i	0.145547	−	0.0840314i
$885$		0			0
$886$	4.00418	−	6.93544i	0.134523	−	0.233001i
$887$	6.19211			0.207911			0.103955	−	0.994582i	$-0.466850\pi$
$887$	6.19211			0.207911			0.103955	+	0.994582i	$0.466850\pi$
$888$		0			0
$889$		0			0
$890$			3.92675i			0.131625i
$891$		0			0
$892$	−14.7546	+	8.51860i	−0.494022	+	0.285224i
$893$			52.9494i			1.77188i
$894$		0			0
$895$	1.16134	−	0.670501i	0.0388194	−	0.0224124i
$896$		0			0
$897$		0			0
$898$	7.25917	+	12.5733i	0.242242	+	0.419575i
$899$	−5.78495	−	10.0198i	−0.192939	−	0.334180i
$900$		0			0
$901$		0			0
$902$	1.44554	−	2.50374i	0.0481311	−	0.0833656i
$903$		0			0
$904$	2.07976	+	3.60226i	0.0691719	+	0.119809i
$905$			2.07786i			0.0690705i
$906$		0			0
$907$	−0.129113			−0.00428714			−0.00214357	−	0.999998i	$-0.500682\pi$
$907$	−0.129113			−0.00428714			−0.00214357	+	0.999998i	$0.500682\pi$
$908$	−2.55512	+	4.42560i	−0.0847946	+	0.146869i
$909$		0			0
$910$		0			0
$911$	−29.6682	−	17.1290i	−0.982952	−	0.567508i	−0.0797919	−	0.996812i	$-0.525426\pi$
$911$	−29.6682	−	17.1290i	−0.982952	−	0.567508i	−0.903160	+	0.429304i	$0.858759\pi$
$912$		0			0
$913$	9.86424	+	5.69512i	0.326459	+	0.188481i
$914$	−8.62130	−	4.97751i	−0.285167	−	0.164641i
$915$		0			0
$916$	13.2215	+	7.63345i	0.436851	+	0.252216i
$917$		0			0
$918$		0			0
$919$	−7.15271	+	12.3889i	−0.235946	+	0.408671i	−0.959547	−	0.281548i	$-0.909152\pi$
$919$	−7.15271	+	12.3889i	−0.235946	+	0.408671i	0.723601	+	0.690218i	$0.242486\pi$
$920$	2.82082			0.0929997
$921$		0			0
$922$			32.3270i			1.06463i
$923$	2.75352	+	4.76923i	0.0906332	+	0.156981i
$924$		0			0
$925$	−12.5725	+	21.7761i	−0.413380	+	0.715995i
$926$	−8.18421	−	4.72516i	−0.268950	−	0.155278i
$927$		0			0
$928$	0.914490	+	1.58394i	0.0300196	+	0.0519955i
$929$	5.87364	+	10.1734i	0.192708	+	0.333780i	0.946147	−	0.323738i	$-0.104940\pi$
$929$	5.87364	+	10.1734i	0.192708	+	0.333780i	−0.753439	+	0.657518i	$0.771606\pi$
$930$		0			0
$931$		0			0
$932$	−8.82741	+	5.09651i	−0.289152	+	0.166942i
$933$		0			0
$934$			20.6623i			0.676091i
$935$	−1.06038	+	0.612209i	−0.0346780	+	0.0200214i
$936$		0			0
$937$			2.63611i			0.0861179i	0.999073	+	0.0430589i	$0.0137103\pi$
$937$			2.63611i			0.0861179i	−0.999073	+	0.0430589i	$0.986290\pi$
$938$		0			0
$939$		0			0
$940$	3.05340			0.0995909
$941$	−5.96557	+	10.3327i	−0.194472	+	0.336836i	−0.946727	−	0.322036i	$-0.895633\pi$
$941$	−5.96557	+	10.3327i	−0.194472	+	0.336836i	0.752255	+	0.658872i	$0.228966\pi$
$942$		0			0
$943$	28.7776	−	16.6148i	0.937128	−	0.541051i
$944$	−8.72695			−0.284038
$945$		0			0
$946$	3.01149			0.0979121
$947$	6.70267	−	3.86979i	0.217807	−	0.125751i	−0.387127	−	0.922026i	$-0.626533\pi$
$947$	6.70267	−	3.86979i	0.217807	−	0.125751i	0.604935	+	0.796275i	$0.293199\pi$
$948$		0			0
$949$	2.03976	−	3.53296i	0.0662133	−	0.114685i
$950$	−30.9317			−1.00356
$951$		0			0
$952$		0			0
$953$			3.76685i			0.122020i	0.998137	+	0.0610102i	$0.0194322\pi$
$953$			3.76685i			0.122020i	−0.998137	+	0.0610102i	$0.980568\pi$
$954$		0			0
$955$	8.69196	−	5.01830i	0.281265	−	0.162388i
$956$		−	19.1815i		−	0.620375i
$957$		0			0
$958$	8.79955	−	5.08042i	0.284301	−	0.164141i
$959$		0			0
$960$		0			0
$961$	4.50836	+	7.80871i	0.145431	+	0.251894i
$962$	−2.58799	−	4.48252i	−0.0834400	−	0.144522i
$963$		0			0
$964$	17.9140	+	10.3426i	0.576970	+	0.333114i
$965$	1.83817	−	3.18381i	0.0591728	−	0.102490i
$966$		0			0
$967$	−2.28741	−	3.96191i	−0.0735581	−	0.127406i	0.826900	−	0.562349i	$-0.190102\pi$
$967$	−2.28741	−	3.96191i	−0.0735581	−	0.127406i	−0.900458	+	0.434942i	$0.856769\pi$
$968$		−	10.5518i		−	0.339149i
$969$		0			0
$970$	6.31126			0.202642
$971$	12.9222	−	22.3820i	0.414694	−	0.718271i	−0.580702	−	0.814116i	$-0.697222\pi$
$971$	12.9222	−	22.3820i	0.414694	−	0.718271i	0.995396	+	0.0958449i	$0.0305553\pi$
$972$		0			0
$973$		0			0
$974$	27.0457	+	15.6148i	0.866599	+	0.500331i
$975$		0			0
$976$	4.29351	+	2.47886i	0.137432	+	0.0793463i
$977$	−26.0950	−	15.0659i	−0.834852	−	0.482002i	0.0206590	−	0.999787i	$-0.493424\pi$
$977$	−26.0950	−	15.0659i	−0.834852	−	0.482002i	−0.855511	+	0.517785i	$0.826757\pi$
$978$		0			0
$979$	−6.21003	−	3.58536i	−0.198474	−	0.114589i
$980$		0			0
$981$		0			0
$982$	−10.2950	+	17.8314i	−0.328526	+	0.569023i
$983$	12.6059			0.402064			0.201032	−	0.979585i	$-0.435570\pi$
$983$	12.6059			0.402064			0.201032	+	0.979585i	$0.435570\pi$
$984$		0			0
$985$		−	6.90152i		−	0.219901i
$986$	−4.56245	−	7.90239i	−0.145298	−	0.251663i
$987$		0			0
$988$	3.18359	−	5.51413i	0.101283	−	0.175428i
$989$	29.9762	+	17.3068i	0.953189	+	0.550324i
$990$		0			0
$991$	−25.8426	−	44.7607i	−0.820918	−	1.42187i	−0.904999	−	0.425413i	$-0.860129\pi$
$991$	−25.8426	−	44.7607i	−0.820918	−	1.42187i	0.0840815	−	0.996459i	$-0.473204\pi$
$992$	−3.16294	−	5.47837i	−0.100423	−	0.173938i
$993$		0			0
$994$		0			0
$995$	−1.70300	+	0.983227i	−0.0539887	+	0.0311704i
$996$		0			0
$997$			40.5841i			1.28531i	0.766155	+	0.642656i	$0.222168\pi$
$997$			40.5841i			1.28531i	−0.766155	+	0.642656i	$0.777832\pi$
$998$	−21.7834	+	12.5766i	−0.689540	+	0.398106i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.t.a.1979.7		16
3.2	odd	2		882.2.t.b.803.4		16
7.2	even	3		378.2.m.a.251.2		16
7.3	odd	6		2646.2.l.b.521.7		16
7.4	even	3		2646.2.l.b.521.6		16
7.5	odd	6		378.2.m.a.251.3		16
7.6	odd	2	inner	2646.2.t.a.1979.6		16
9.4	even	3		882.2.l.a.509.8		16
9.5	odd	6		2646.2.l.b.1097.3		16
21.2	odd	6		126.2.m.a.83.7	yes	16
21.5	even	6		126.2.m.a.83.6	yes	16
21.11	odd	6		882.2.l.a.227.1		16
21.17	even	6		882.2.l.a.227.4		16
21.20	even	2		882.2.t.b.803.1		16
28.19	even	6		3024.2.cc.b.2897.5		16
28.23	odd	6		3024.2.cc.b.2897.4		16
63.2	odd	6		1134.2.d.a.1133.4		16
63.4	even	3		882.2.t.b.815.1		16
63.5	even	6		378.2.m.a.125.2		16
63.13	odd	6		882.2.l.a.509.5		16
63.16	even	3		1134.2.d.a.1133.13		16
63.23	odd	6		378.2.m.a.125.3		16
63.31	odd	6		882.2.t.b.815.4		16
63.32	odd	6	inner	2646.2.t.a.2285.6		16
63.40	odd	6		126.2.m.a.41.7	yes	16
63.41	even	6		2646.2.l.b.1097.2		16
63.47	even	6		1134.2.d.a.1133.5		16
63.58	even	3		126.2.m.a.41.6	✓	16
63.59	even	6	inner	2646.2.t.a.2285.7		16
63.61	odd	6		1134.2.d.a.1133.12		16
84.23	even	6		1008.2.cc.b.209.4		16
84.47	odd	6		1008.2.cc.b.209.5		16
252.23	even	6		3024.2.cc.b.881.5		16
252.103	even	6		1008.2.cc.b.545.4		16
252.131	odd	6		3024.2.cc.b.881.4		16
252.247	odd	6		1008.2.cc.b.545.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.6	✓	16	63.58	even	3
126.2.m.a.41.7	yes	16	63.40	odd	6
126.2.m.a.83.6	yes	16	21.5	even	6
126.2.m.a.83.7	yes	16	21.2	odd	6
378.2.m.a.125.2		16	63.5	even	6
378.2.m.a.125.3		16	63.23	odd	6
378.2.m.a.251.2		16	7.2	even	3
378.2.m.a.251.3		16	7.5	odd	6
882.2.l.a.227.1		16	21.11	odd	6
882.2.l.a.227.4		16	21.17	even	6
882.2.l.a.509.5		16	63.13	odd	6
882.2.l.a.509.8		16	9.4	even	3
882.2.t.b.803.1		16	21.20	even	2
882.2.t.b.803.4		16	3.2	odd	2
882.2.t.b.815.1		16	63.4	even	3
882.2.t.b.815.4		16	63.31	odd	6
1008.2.cc.b.209.4		16	84.23	even	6
1008.2.cc.b.209.5		16	84.47	odd	6
1008.2.cc.b.545.4		16	252.103	even	6
1008.2.cc.b.545.5		16	252.247	odd	6
1134.2.d.a.1133.4		16	63.2	odd	6
1134.2.d.a.1133.5		16	63.47	even	6
1134.2.d.a.1133.12		16	63.61	odd	6
1134.2.d.a.1133.13		16	63.16	even	3
2646.2.l.b.521.6		16	7.4	even	3
2646.2.l.b.521.7		16	7.3	odd	6
2646.2.l.b.1097.2		16	63.41	even	6
2646.2.l.b.1097.3		16	9.5	odd	6
2646.2.t.a.1979.6		16	7.6	odd	2	inner
2646.2.t.a.1979.7		16	1.1	even	1	trivial
2646.2.t.a.2285.6		16	63.32	odd	6	inner
2646.2.t.a.2285.7		16	63.59	even	6	inner
3024.2.cc.b.881.4		16	252.131	odd	6
3024.2.cc.b.881.5		16	252.23	even	6
3024.2.cc.b.2897.4		16	28.23	odd	6
3024.2.cc.b.2897.5		16	28.19	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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +0.366598 q^{5} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +0.366598 q^{5} -1.00000i q^{8} +(0.317483 - 0.183299i) q^{10} +0.669453i q^{11} +(0.867380 - 0.500782i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(2.49453 + 4.32065i) q^{17} +(5.50552 + 3.17861i) q^{19} +(0.183299 - 0.317483i) q^{20} +(0.334727 + 0.579764i) q^{22} +7.69459i q^{23} -4.86561 q^{25} +(0.500782 - 0.867380i) q^{26} +(-1.58394 - 0.914490i) q^{29} +(5.47837 + 3.16294i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(4.32065 + 2.49453i) q^{34} +(2.58394 - 4.47552i) q^{37} +6.35722 q^{38} -0.366598i q^{40} +(-2.15928 - 3.73998i) q^{41} +(2.24922 - 3.89576i) q^{43} +(0.579764 + 0.334727i) q^{44} +(3.84729 + 6.66371i) q^{46} +(4.16450 + 7.21313i) q^{47} +(-4.21374 + 2.43280i) q^{50} -1.00156i q^{52} +0.245420i q^{55} -1.82898 q^{58} +(4.36348 - 7.55776i) q^{59} +(-4.29351 + 2.47886i) q^{61} +6.32588 q^{62} -1.00000 q^{64} +(0.317980 - 0.183586i) q^{65} +(5.44537 - 9.43166i) q^{67} +4.98906 q^{68} +5.49843i q^{71} +(3.52744 - 2.03657i) q^{73} -5.16789i q^{74} +(5.50552 - 3.17861i) q^{76} +(-4.17784 - 7.23623i) q^{79} +(-0.183299 - 0.317483i) q^{80} +(-3.73998 - 2.15928i) q^{82} +(8.50712 - 14.7348i) q^{83} +(0.914490 + 1.58394i) q^{85} -4.49843i q^{86} +0.669453 q^{88} +(-5.35566 + 9.27628i) q^{89} +(6.66371 + 3.84729i) q^{92} +(7.21313 + 4.16450i) q^{94} +(2.01831 + 1.16527i) q^{95} +(14.9093 + 8.60787i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} - 8 q^{16} + 16 q^{25} + 12 q^{29} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} - 60 q^{50} + 24 q^{58} - 16 q^{64} + 84 q^{65} - 28 q^{67} - 4 q^{79} - 12 q^{85} + 48 q^{92} + 12 q^{95}+O(q^{100}) \) 16 * q + 8 * q^4 - 8 * q^16 + 16 * q^25 + 12 * q^29 + 4 * q^37 + 4 * q^43 - 12 * q^44 - 12 * q^46 - 60 * q^50 + 24 * q^58 - 16 * q^64 + 84 * q^65 - 28 * q^67 - 4 * q^79 - 12 * q^85 + 48 * q^92 + 12 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more