LMFDB - Embedded newform 2646.2.l.b.521.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(521,2646)]

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, 1]))

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

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

chi := DirichletCharacter("2646.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.l (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:	$\Z[a_1, \ldots, a_{25}]$
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			521.6
Root			$0.0967785 + 1.72934i$ of defining polynomial
Character	$\chi$	$=$	2646.521
Dual form			2646.2.l.b.1097.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(-0.183299 + 0.317483i) q^{5} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(-0.183299 + 0.317483i) q^{5} -1.00000i q^{8} +(-0.317483 - 0.183299i) q^{10} +(0.579764 - 0.334727i) q^{11} +(0.867380 - 0.500782i) q^{13} +1.00000 q^{16} +(2.49453 - 4.32065i) q^{17} +(-5.50552 + 3.17861i) q^{19} +(0.183299 - 0.317483i) q^{20} +(0.334727 + 0.579764i) q^{22} +(-6.66371 - 3.84729i) q^{23} +(2.43280 + 4.21374i) q^{25} +(0.500782 + 0.867380i) q^{26} +(-1.58394 - 0.914490i) q^{29} -6.32588i q^{31} +1.00000i q^{32} +(4.32065 + 2.49453i) q^{34} +(2.58394 + 4.47552i) q^{37} +(-3.17861 - 5.50552i) q^{38} +(0.317483 + 0.183299i) q^{40} +(-2.15928 - 3.73998i) q^{41} +(2.24922 - 3.89576i) q^{43} +(-0.579764 + 0.334727i) q^{44} +(3.84729 - 6.66371i) q^{46} -8.32901 q^{47} +(-4.21374 + 2.43280i) q^{50} +(-0.867380 + 0.500782i) q^{52} +0.245420i q^{55} +(0.914490 - 1.58394i) q^{58} -8.72695 q^{59} -4.95771i q^{61} +6.32588 q^{62} -1.00000 q^{64} +0.367172i q^{65} -10.8907 q^{67} +(-2.49453 + 4.32065i) q^{68} +5.49843i q^{71} +(-3.52744 - 2.03657i) q^{73} +(-4.47552 + 2.58394i) q^{74} +(5.50552 - 3.17861i) q^{76} +8.35568 q^{79} +(-0.183299 + 0.317483i) q^{80} +(3.73998 - 2.15928i) q^{82} +(8.50712 - 14.7348i) q^{83} +(0.914490 + 1.58394i) q^{85} +(3.89576 + 2.24922i) q^{86} +(-0.334727 - 0.579764i) q^{88} +(-5.35566 - 9.27628i) q^{89} +(6.66371 + 3.84729i) q^{92} -8.32901i q^{94} -2.33055i q^{95} +(14.9093 + 8.60787i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4}+O(q^{10}) $ 16 * q - 16 * q^4	$ 16 q - 16 q^{4} - 12 q^{11} + 16 q^{16} - 48 q^{23} - 8 q^{25} + 12 q^{29} + 4 q^{37} + 4 q^{43} + 12 q^{44} - 12 q^{46} - 60 q^{50} - 12 q^{58} - 16 q^{64} + 56 q^{67} + 36 q^{74} + 8 q^{79} - 12 q^{85} - 24 q^{86} + 48 q^{92}+O(q^{100}) $ 16 * q - 16 * q^4 - 12 * q^11 + 16 * q^16 - 48 * q^23 - 8 * q^25 + 12 * q^29 + 4 * q^37 + 4 * q^43 + 12 * q^44 - 12 * q^46 - 60 * q^50 - 12 * q^58 - 16 * q^64 + 56 * q^67 + 36 * q^74 + 8 * q^79 - 12 * q^85 - 24 * q^86 + 48 * q^92

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−0.183299	+	0.317483i	−0.0819738	+	0.141983i	−0.904098	−	0.427326i	$-0.859456\pi$
$5$	−0.183299	+	0.317483i	−0.0819738	+	0.141983i	0.822124	+	0.569309i	$0.192789\pi$
$6$		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
$11$	0.579764	−	0.334727i	0.174805	−	0.100924i	−0.410044	−	0.912066i	$-0.634487\pi$
$11$	0.579764	−	0.334727i	0.174805	−	0.100924i	0.584850	+	0.811142i	$0.301153\pi$
$12$		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
$16$	1.00000			0.250000
$17$	2.49453	−	4.32065i	0.605013	−	1.04791i	−0.387037	−	0.922064i	$-0.626501\pi$
$17$	2.49453	−	4.32065i	0.605013	−	1.04791i	0.992049	−	0.125848i	$-0.0401653\pi$
$18$		0			0
$19$	−5.50552	+	3.17861i	−1.26305	+	0.729224i	−0.973664	−	0.227988i	$-0.926785\pi$
$19$	−5.50552	+	3.17861i	−1.26305	+	0.729224i	−0.289389	+	0.957212i	$0.593452\pi$
$20$	0.183299	−	0.317483i	0.0409869	−	0.0709914i
$21$		0			0
$22$	0.334727	+	0.579764i	0.0713640	+	0.123606i
$23$	−6.66371	−	3.84729i	−1.38948	−	0.802216i	−0.396223	−	0.918154i	$-0.629679\pi$
$23$	−6.66371	−	3.84729i	−1.38948	−	0.802216i	−0.993256	+	0.115938i	$0.963012\pi$
$24$		0			0
$25$	2.43280	+	4.21374i	0.486561	+	0.842748i
$26$	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
$31$		−	6.32588i		−	1.13616i	−0.822973	−	0.568081i	$-0.807686\pi$
$31$		−	6.32588i		−	1.13616i	0.822973	−	0.568081i	$-0.192314\pi$
$32$			1.00000i			0.176777i
$33$		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	0.996402	−	0.0847585i	$-0.0270119\pi$
$37$	2.58394	+	4.47552i	0.424798	+	0.735771i	−0.571604	+	0.820530i	$0.693679\pi$
$38$	−3.17861	−	5.50552i	−0.515639	−	0.893113i
$39$		0			0
$40$	0.317483	+	0.183299i	0.0501985	+	0.0289821i
$41$	−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
$47$	−8.32901			−1.21491			−0.607455	−	0.794354i	$-0.707810\pi$
$47$	−8.32901			−1.21491			−0.607455	+	0.794354i	$0.707810\pi$
$48$		0			0
$49$		0			0
$50$	−4.21374	+	2.43280i	−0.595913	+	0.344050i
$51$		0			0
$52$	−0.867380	+	0.500782i	−0.120284	+	0.0694460i
$53$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$53$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$54$		0			0
$55$			0.245420i			0.0330925i
$56$		0			0
$57$		0			0
$58$	0.914490	−	1.58394i	0.120078	−	0.207982i
$59$	−8.72695			−1.13615			−0.568076	−	0.822976i	$-0.692312\pi$
$59$	−8.72695			−1.13615			−0.568076	+	0.822976i	$0.692312\pi$
$60$		0			0
$61$		−	4.95771i		−	0.634770i	−0.948297	−	0.317385i	$-0.897195\pi$
$61$		−	4.95771i		−	0.634770i	0.948297	−	0.317385i	$-0.102805\pi$
$62$	6.32588			0.803387
$63$		0			0
$64$	−1.00000			−0.125000
$65$			0.367172i			0.0455420i
$66$		0			0
$67$	−10.8907			−1.33052			−0.665258	−	0.746614i	$-0.731678\pi$
$67$	−10.8907			−1.33052			−0.665258	+	0.746614i	$0.731678\pi$
$68$	−2.49453	+	4.32065i	−0.302506	+	0.523956i
$69$		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	$-0.409944\pi$
$73$	−3.52744	−	2.03657i	−0.412856	−	0.238363i	−0.692016	+	0.721882i	$0.743277\pi$
$74$	−4.47552	+	2.58394i	−0.520269	+	0.300377i
$75$		0			0
$76$	5.50552	−	3.17861i	0.631526	−	0.364612i
$77$		0			0
$78$		0			0
$79$	8.35568			0.940087			0.470044	−	0.882643i	$-0.344238\pi$
$79$	8.35568			0.940087			0.470044	+	0.882643i	$0.344238\pi$
$80$	−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
$86$	3.89576	+	2.24922i	0.420090	+	0.242539i
$87$		0			0
$88$	−0.334727	−	0.579764i	−0.0356820	−	0.0618030i
$89$	−5.35566	−	9.27628i	−0.567699	−	0.983283i	−0.996793	−	0.0800234i	$-0.974500\pi$
$89$	−5.35566	−	9.27628i	−0.567699	−	0.983283i	0.429094	−	0.903260i	$-0.358833\pi$
$90$		0			0
$91$		0			0
$92$	6.66371	+	3.84729i	0.694740	+	0.401108i
$93$		0			0
$94$		−	8.32901i		−	0.859071i
$95$		−	2.33055i		−	0.239109i
$96$		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
$101$	−7.86586	−	13.6241i	−0.782683	−	1.35565i	−0.930374	−	0.366613i	$-0.880517\pi$
$101$	−7.86586	−	13.6241i	−0.782683	−	1.35565i	0.147691	−	0.989034i	$-0.452816\pi$
$102$		0			0
$103$	−9.91124	−	5.72226i	−0.976584	−	0.563831i	−0.0753467	−	0.997157i	$-0.524006\pi$
$103$	−9.91124	−	5.72226i	−0.976584	−	0.563831i	−0.901237	+	0.433327i	$0.857340\pi$
$104$	−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	$-0.487095\pi$
$107$	9.57976	−	5.53088i	0.926111	−	0.534690i	0.885579	+	0.464488i	$0.153762\pi$
$108$		0			0
$109$	5.28166	−	9.14811i	0.505891	−	0.876230i	−0.494085	−	0.869413i	$-0.664497\pi$
$109$	5.28166	−	9.14811i	0.505891	−	0.876230i	0.999977	−	0.00681630i	$-0.00216971\pi$
$110$	−0.245420			−0.0233999
$111$		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
$115$	2.44290	−	1.41041i	0.227802	−	0.131521i
$116$	1.58394	+	0.914490i	0.147065	+	0.0849083i
$117$		0			0
$118$		−	8.72695i		−	0.803381i
$119$		0			0
$120$		0			0
$121$	−5.27592	+	9.13815i	−0.479629	+	0.830741i
$122$	4.95771			0.448850
$123$		0			0
$124$			6.32588i			0.568081i
$125$	−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	$0.523599\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−0.367172			−0.0322031
$131$	6.76607	−	11.7192i	0.591154	−	1.02391i	−0.402923	−	0.915234i	$-0.632006\pi$
$131$	6.76607	−	11.7192i	0.591154	−	1.02391i	0.994077	−	0.108675i	$-0.0346609\pi$
$132$		0			0
$133$		0			0
$134$		−	10.8907i		−	0.940817i
$135$		0			0
$136$	−4.32065	−	2.49453i	−0.370493	−	0.213904i
$137$	7.78428	−	4.49425i	0.665056	−	0.383970i	−0.129145	−	0.991626i	$-0.541223\pi$
$137$	7.78428	−	4.49425i	0.665056	−	0.383970i	0.794201	+	0.607656i	$0.207890\pi$
$138$		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
$142$	−5.49843			−0.461418
$143$	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
$149$	−2.45268	−	1.41606i	−0.200931	−	0.116008i	0.396158	−	0.918182i	$-0.370343\pi$
$149$	−2.45268	−	1.41606i	−0.200931	−	0.116008i	−0.597090	+	0.802174i	$0.703676\pi$
$150$		0			0
$151$	8.27592	+	14.3343i	0.673484	+	1.16651i	0.976909	+	0.213654i	$0.0685365\pi$
$151$	8.27592	+	14.3343i	0.673484	+	1.16651i	−0.303425	+	0.952855i	$0.598130\pi$
$152$	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
$157$		−	2.83456i		−	0.226222i	−0.993582	−	0.113111i	$-0.963918\pi$
$157$		−	2.83456i		−	0.226222i	0.993582	−	0.113111i	$-0.0360816\pi$
$158$			8.35568i			0.664742i
$159$		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	−0.700113	−	0.714032i	$-0.746867\pi$
$163$	−12.3640	−	21.4151i	−0.968426	−	1.67736i	−0.268313	−	0.963332i	$-0.586466\pi$
$164$	2.15928	+	3.73998i	0.168611	+	0.292044i
$165$		0			0
$166$	14.7348	+	8.50712i	1.14364	+	0.660281i
$167$	−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
$173$	4.83654			0.367715			0.183858	−	0.982953i	$-0.441141\pi$
$173$	4.83654			0.367715			0.183858	+	0.982953i	$0.441141\pi$
$174$		0			0
$175$		0			0
$176$	0.579764	−	0.334727i	0.0437013	−	0.0252310i
$177$		0			0
$178$	9.27628	−	5.35566i	0.695286	−	0.401424i
$179$	−3.16789	−	1.82898i	−0.236779	−	0.136704i	0.376916	−	0.926247i	$-0.376984\pi$
$179$	−3.16789	−	1.82898i	−0.236779	−	0.136704i	−0.613695	+	0.789543i	$0.710318\pi$
$180$		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
$184$	−3.84729	+	6.66371i	−0.283626	+	0.491255i
$185$	−1.89454			−0.139289
$186$		0			0
$187$		−	3.33994i		−	0.244241i
$188$	8.32901			0.607455
$189$		0			0
$190$	2.33055			0.169076
$191$			27.3777i			1.98098i	0.137587	+	0.990490i	$0.456065\pi$
$191$			27.3777i			1.98098i	−0.137587	+	0.990490i	$0.543935\pi$
$192$		0			0
$193$	−10.0283			−0.721850			−0.360925	−	0.932595i	$-0.617539\pi$
$193$	−10.0283			−0.721850			−0.360925	+	0.932595i	$0.617539\pi$
$194$	−8.60787	+	14.9093i	−0.618009	+	1.07042i
$195$		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	$-0.272444\pi$
$199$	4.64541	+	2.68203i	0.329305	+	0.190124i	−0.326228	+	0.945291i	$0.605778\pi$
$200$	4.21374	−	2.43280i	0.297956	−	0.172025i
$201$		0			0
$202$	13.6241	−	7.86586i	0.958587	−	0.553440i
$203$		0			0
$204$		0			0
$205$	1.58318			0.110574
$206$	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
$214$	5.53088	+	9.57976i	0.378083	+	0.654859i
$215$	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
$220$		−	0.245420i		−	0.0165462i
$221$		−	4.99687i		−	0.336126i
$222$		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
$227$	2.55512	+	4.42560i	0.169589	+	0.293737i	0.938276	−	0.345889i	$-0.112423\pi$
$227$	2.55512	+	4.42560i	0.169589	+	0.293737i	−0.768686	+	0.639626i	$0.779089\pi$
$228$		0			0
$229$	−13.2215	−	7.63345i	−0.873703	−	0.504433i	−0.00512595	−	0.999987i	$-0.501632\pi$
$229$	−13.2215	−	7.63345i	−0.873703	−	0.504433i	−0.868577	+	0.495554i	$0.834965\pi$
$230$	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	$-0.558307\pi$
$233$	8.82741	−	5.09651i	0.578303	−	0.333883i	0.760459	+	0.649386i	$0.224974\pi$
$234$		0			0
$235$	1.52670	−	2.64432i	0.0995909	−	0.172496i
$236$	8.72695			0.568076
$237$		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
$241$	17.9140	−	10.3426i	1.15394	−	0.666227i	0.204095	−	0.978951i	$-0.434575\pi$
$241$	17.9140	−	10.3426i	1.15394	−	0.666227i	0.949844	+	0.312724i	$0.101241\pi$
$242$	−9.13815	−	5.27592i	−0.587423	−	0.339149i
$243$		0			0
$244$			4.95771i			0.317385i
$245$		0			0
$246$		0			0
$247$	−3.18359	+	5.51413i	−0.202567	+	0.350856i
$248$	−6.32588			−0.401694
$249$		0			0
$250$		−	3.61671i		−	0.228741i
$251$	−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
$254$		−	1.66945i		−	0.104751i
$255$		0			0
$256$	1.00000			0.0625000
$257$	3.22773	−	5.59059i	0.201340	−	0.348731i	−0.747620	−	0.664126i	$-0.768804\pi$
$257$	3.22773	−	5.59059i	0.201340	−	0.348731i	0.948960	+	0.315395i	$0.102137\pi$
$258$		0			0
$259$		0			0
$260$		−	0.367172i		−	0.0227710i
$261$		0			0
$262$	11.7192	+	6.76607i	0.724013	+	0.418009i
$263$	−7.63888	+	4.41031i	−0.471034	+	0.271951i	−0.716672	−	0.697410i	$-0.754336\pi$
$263$	−7.63888	+	4.41031i	−0.471034	+	0.271951i	0.245639	+	0.969361i	$0.421002\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	10.8907			0.665258
$269$	−7.13267	+	12.3541i	−0.434886	+	0.753245i	−0.997286	−	0.0736199i	$-0.976545\pi$
$269$	−7.13267	+	12.3541i	−0.434886	+	0.753245i	0.562400	+	0.826865i	$0.309878\pi$
$270$		0			0
$271$	2.64381	−	1.52641i	0.160600	−	0.0927226i	−0.417546	−	0.908656i	$-0.637110\pi$
$271$	2.64381	−	1.52641i	0.160600	−	0.0927226i	0.578146	+	0.815933i	$0.303776\pi$
$272$	2.49453	−	4.32065i	0.151253	−	0.261978i
$273$		0			0
$274$	4.49425	+	7.78428i	0.271508	+	0.470265i
$275$	2.82090	+	1.62865i	0.170107	+	0.0982112i
$276$		0			0
$277$	−0.632828	−	1.09609i	−0.0380230	−	0.0658577i	0.846388	−	0.532567i	$-0.178773\pi$
$277$	−0.632828	−	1.09609i	−0.0380230	−	0.0658577i	−0.884411	+	0.466710i	$0.845439\pi$
$278$	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
$283$			19.8718i			1.18125i	0.806945	+	0.590627i	$0.201119\pi$
$283$			19.8718i			1.18125i	−0.806945	+	0.590627i	$0.798881\pi$
$284$		−	5.49843i		−	0.326272i
$285$		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
$290$	0.335250	+	0.580671i	0.0196866	+	0.0340982i
$291$		0			0
$292$	3.52744	+	2.03657i	0.206428	+	0.119181i
$293$	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
$299$	−7.70663			−0.445686
$300$		0			0
$301$		0			0
$302$	−14.3343	+	8.27592i	−0.824847	+	0.476225i
$303$		0			0
$304$	−5.50552	+	3.17861i	−0.315763	+	0.182306i
$305$	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
$310$	−1.15953	+	2.00836i	−0.0658567	+	0.114067i
$311$	−9.24493			−0.524232			−0.262116	−	0.965036i	$-0.584420\pi$
$311$	−9.24493			−0.524232			−0.262116	+	0.965036i	$0.584420\pi$
$312$		0			0
$313$		−	6.16414i		−	0.348418i	−0.984709	−	0.174209i	$-0.944263\pi$
$313$		−	6.16414i		−	0.348418i	0.984709	−	0.174209i	$-0.0557368\pi$
$314$	2.83456			0.159963
$315$		0			0
$316$	−8.35568			−0.470044
$317$		−	20.6548i		−	1.16009i	−0.814584	−	0.580045i	$-0.803035\pi$
$317$		−	20.6548i		−	1.16009i	0.814584	−	0.580045i	$-0.196965\pi$
$318$		0			0
$319$	−1.22442			−0.0685542
$320$	0.183299	−	0.317483i	0.0102467	−	0.0177479i
$321$		0			0
$322$		0			0
$323$			31.7166i			1.76476i
$324$		0			0
$325$	4.22033	+	2.43661i	0.234102	+	0.135159i
$326$	21.4151	−	12.3640i	1.18608	−	0.684781i
$327$		0			0
$328$	−3.73998	+	2.15928i	−0.206506	+	0.119226i
$329$		0			0
$330$		0			0
$331$	10.7114			0.588750			0.294375	−	0.955690i	$-0.404889\pi$
$331$	10.7114			0.588750			0.294375	+	0.955690i	$0.404889\pi$
$332$	−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	$0.767390\pi$
$338$	−10.3896	−	5.99843i	−0.565119	−	0.326272i
$339$		0			0
$340$	−0.914490	−	1.58394i	−0.0495952	−	0.0859014i
$341$	−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
$346$			4.83654i			0.260014i
$347$			10.9320i			0.586859i	0.955981	+	0.293430i	$0.0947967\pi$
$347$			10.9320i			0.586859i	−0.955981	+	0.293430i	$0.905203\pi$
$348$		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
$353$	16.7912	+	29.0832i	0.893706	+	1.54794i	0.835398	+	0.549646i	$0.185237\pi$
$353$	16.7912	+	29.0832i	0.893706	+	1.54794i	0.0583086	+	0.998299i	$0.481429\pi$
$354$		0			0
$355$	−1.74566	−	1.00786i	−0.0926501	−	0.0534915i
$356$	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	$-0.752789\pi$
$359$	−8.77122	+	5.06407i	−0.462927	+	0.267271i	0.250347	+	0.968156i	$0.419455\pi$
$360$		0			0
$361$	10.7072	−	18.5453i	0.563534	−	0.976070i
$362$	−5.66796			−0.297901
$363$		0			0
$364$		0			0
$365$	1.29315	−	0.746603i	0.0676868	−	0.0390790i
$366$		0			0
$367$	−15.5903	+	9.00104i	−0.813805	+	0.469850i	−0.848275	−	0.529555i	$-0.822359\pi$
$367$	−15.5903	+	9.00104i	−0.813805	+	0.469850i	0.0344706	+	0.999406i	$0.489025\pi$
$368$	−6.66371	−	3.84729i	−0.347370	−	0.200554i
$369$		0			0
$370$		−	1.89454i		−	0.0984923i
$371$		0			0
$372$		0			0
$373$	−8.20451	+	14.2106i	−0.424814	+	0.735799i	−0.996403	−	0.0847411i	$-0.972994\pi$
$373$	−8.20451	+	14.2106i	−0.424814	+	0.735799i	0.571589	+	0.820540i	$0.306327\pi$
$374$	3.33994			0.172704
$375$		0			0
$376$			8.32901i			0.429536i
$377$	−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	$0.523843\pi$
$380$			2.33055i			0.119555i
$381$		0			0
$382$	−27.3777			−1.40076
$383$	−4.28721	+	7.42567i	−0.219066	+	0.379434i	−0.954523	−	0.298138i	$-0.903634\pi$
$383$	−4.28721	+	7.42567i	−0.219066	+	0.379434i	0.735456	+	0.677572i	$0.236968\pi$
$384$		0			0
$385$		0			0
$386$		−	10.0283i		−	0.510425i
$387$		0			0
$388$	−14.9093	−	8.60787i	−0.756903	−	0.436998i
$389$	−30.7906	+	17.7770i	−1.56115	+	0.901328i	−0.564004	+	0.825772i	$0.690740\pi$
$389$	−30.7906	+	17.7770i	−1.56115	+	0.901328i	−0.997142	+	0.0755559i	$0.975927\pi$
$390$		0			0
$391$	−33.2456	+	19.1944i	−1.68130	+	0.970702i
$392$		0			0
$393$		0			0
$394$	18.8258			0.948433
$395$	−1.53159	+	2.65279i	−0.0770626	+	0.133476i
$396$		0			0
$397$	−3.10066	+	1.79017i	−0.155618	+	0.0898460i	−0.575787	−	0.817600i	$-0.695304\pi$
$397$	−3.10066	+	1.79017i	−0.155618	+	0.0898460i	0.420169	+	0.907446i	$0.361971\pi$
$398$	−2.68203	+	4.64541i	−0.134438	+	0.232853i
$399$		0			0
$400$	2.43280	+	4.21374i	0.121640	+	0.210687i
$401$	0.165300	+	0.0954357i	0.00825467	+	0.00476583i	0.504122	−	0.863633i	$-0.331816\pi$
$401$	0.165300	+	0.0954357i	0.00825467	+	0.00476583i	−0.495867	+	0.868398i	$0.665150\pi$
$402$		0			0
$403$	−3.16789	−	5.48694i	−0.157804	−	0.273324i
$404$	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
$409$			3.47371i			0.171764i	0.996305	+	0.0858819i	$0.0273708\pi$
$409$			3.47371i			0.171764i	−0.996305	+	0.0858819i	$0.972629\pi$
$410$			1.58318i			0.0781875i
$411$		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
$416$	0.500782	+	0.867380i	0.0245529	+	0.0425268i
$417$		0			0
$418$	−3.68569	−	2.12793i	−0.180273	−	0.104081i
$419$	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
$425$	24.2748			1.17750
$426$		0			0
$427$		0			0
$428$	−9.57976	+	5.53088i	−0.463055	+	0.267345i
$429$		0			0
$430$	−1.42818	+	0.824559i	−0.0688728	+	0.0397638i
$431$	23.6206	+	13.6373i	1.13776	+	0.656888i	0.945876	−	0.324529i	$-0.105206\pi$
$431$	23.6206	+	13.6373i	1.13776	+	0.656888i	0.191887	+	0.981417i	$0.438539\pi$
$432$		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
$436$	−5.28166	+	9.14811i	−0.252946	+	0.438115i
$437$	48.9162			2.33998
$438$		0			0
$439$			12.2404i			0.584203i	0.956387	+	0.292101i	$0.0943545\pi$
$439$			12.2404i			0.584203i	−0.956387	+	0.292101i	$0.905646\pi$
$440$	0.245420			0.0117000
$441$		0			0
$442$	4.99687			0.237677
$443$			8.00836i			0.380489i	0.981737	+	0.190244i	$0.0609280\pi$
$443$			8.00836i			0.380489i	−0.981737	+	0.190244i	$0.939072\pi$
$444$		0			0
$445$	3.92675			0.186146
$446$	8.51860	−	14.7546i	0.403367	−	0.698653i
$447$		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
$452$	3.60226	−	2.07976i	0.169436	−	0.0978239i
$453$		0			0
$454$	−4.42560	+	2.55512i	−0.207704	+	0.119918i
$455$		0			0
$456$		0			0
$457$	9.95501			0.465676			0.232838	−	0.972516i	$-0.425199\pi$
$457$	9.95501			0.465676			0.232838	+	0.972516i	$0.425199\pi$
$458$	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	$0.903807\pi$
$464$	−1.58394	−	0.914490i	−0.0735327	−	0.0424541i
$465$		0			0
$466$	5.09651	+	8.82741i	0.236091	+	0.408922i
$467$	−10.3312	−	17.8941i	−0.478069	−	0.828039i	0.521615	−	0.853181i	$-0.325330\pi$
$467$	−10.3312	−	17.8941i	−0.478069	−	0.828039i	−0.999684	+	0.0251414i	$0.991996\pi$
$468$		0			0
$469$		0			0
$470$	2.64432	+	1.52670i	0.121973	+	0.0704214i
$471$		0			0
$472$			8.72695i			0.401691i
$473$		−	3.01149i		−	0.138469i
$474$		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
$479$	−5.08042	−	8.79955i	−0.232131	−	0.402062i	0.726304	−	0.687373i	$-0.241236\pi$
$479$	−5.08042	−	8.79955i	−0.232131	−	0.402062i	−0.958435	+	0.285311i	$0.907903\pi$
$480$		0			0
$481$	4.48252	+	2.58799i	0.204386	+	0.118002i
$482$	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	−0.258179	−	0.966097i	$-0.583122\pi$
$487$	15.6148	−	27.0457i	0.707575	−	1.22556i	0.965754	−	0.259459i	$-0.0835443\pi$
$488$	−4.95771			−0.224425
$489$		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
$493$	−7.90239	+	4.56245i	−0.355906	+	0.205482i
$494$	−5.51413	−	3.18359i	−0.248093	−	0.143236i
$495$		0			0
$496$		−	6.32588i		−	0.284040i
$497$		0			0
$498$		0			0
$499$	12.5766	−	21.7834i	0.563007	−	0.975157i	−0.434225	−	0.900805i	$-0.642978\pi$
$499$	12.5766	−	21.7834i	0.563007	−	0.975157i	0.997232	−	0.0743527i	$-0.0236891\pi$
$500$	3.61671			0.161744
$501$		0			0
$502$		−	1.81200i		−	0.0808737i
$503$	−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
$506$		−	5.15117i		−	0.228997i
$507$		0			0
$508$	1.66945			0.0740700
$509$	−2.41674	+	4.18591i	−0.107120	+	0.185537i	−0.914602	−	0.404354i	$-0.867496\pi$
$509$	−2.41674	+	4.18591i	−0.107120	+	0.185537i	0.807482	+	0.589892i	$0.200830\pi$
$510$		0			0
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	5.59059	+	3.22773i	0.246590	+	0.142369i
$515$	3.63344	−	2.09777i	0.160109	−	0.0924387i
$516$		0			0
$517$	−4.82886	+	2.78794i	−0.212373	+	0.122613i
$518$		0			0
$519$		0			0
$520$	0.367172			0.0161015
$521$	−8.76611	+	15.1834i	−0.384050	+	0.665195i	−0.991637	−	0.129059i	$-0.958804\pi$
$521$	−8.76611	+	15.1834i	−0.384050	+	0.665195i	0.607587	+	0.794253i	$0.292138\pi$
$522$		0			0
$523$	−16.5427	+	9.55094i	−0.723362	+	0.417633i	−0.815989	−	0.578068i	$-0.803807\pi$
$523$	−16.5427	+	9.55094i	−0.723362	+	0.417633i	0.0926268	+	0.995701i	$0.470474\pi$
$524$	−6.76607	+	11.7192i	−0.295577	+	0.511955i
$525$		0			0
$526$	−4.41031	−	7.63888i	−0.192299	−	0.333071i
$527$	−27.3319	−	15.7801i	−1.19060	−	0.687392i
$528$		0			0
$529$	18.1033	+	31.3559i	0.787101	+	1.36330i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−3.74584	−	2.16266i	−0.162250	−	0.0936752i
$534$		0			0
$535$			4.05522i			0.175322i
$536$			10.8907i			0.470408i
$537$		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	0.680954	−	0.732326i	$-0.261565\pi$
$541$	−6.83211	−	11.8336i	−0.293735	−	0.508765i	−0.974690	+	0.223561i	$0.928232\pi$
$542$	1.52641	+	2.64381i	0.0655648	+	0.113562i
$543$		0			0
$544$	4.32065	+	2.49453i	0.185247	+	0.106952i
$545$	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
$551$	11.6272			0.495337
$552$		0			0
$553$		0			0
$554$	1.09609	−	0.632828i	0.0465684	−	0.0268863i
$555$		0			0
$556$	−8.05336	+	4.64961i	−0.341539	+	0.197187i
$557$	10.8946	+	6.29002i	0.461621	+	0.266517i	0.712725	−	0.701443i	$-0.247461\pi$
$557$	10.8946	+	6.29002i	0.461621	+	0.266517i	−0.251105	+	0.967960i	$0.580794\pi$
$558$		0			0
$559$		−	4.50547i		−	0.190561i
$560$		0			0
$561$		0			0
$562$	5.26335	−	9.11639i	0.222021	−	0.384552i
$563$	−24.3333			−1.02553			−0.512763	−	0.858530i	$-0.671378\pi$
$563$	−24.3333			−1.02553			−0.512763	+	0.858530i	$0.671378\pi$
$564$		0			0
$565$		−	1.52487i		−	0.0641520i
$566$	−19.8718			−0.835272
$567$		0			0
$568$	5.49843			0.230709
$569$		−	9.45406i		−	0.396335i	−0.980168	−	0.198167i	$-0.936501\pi$
$569$		−	9.45406i		−	0.396335i	0.980168	−	0.198167i	$-0.0634990\pi$
$570$		0			0
$571$	−31.5686			−1.32110			−0.660551	−	0.750781i	$-0.729677\pi$
$571$	−31.5686			−1.32110			−0.660551	+	0.750781i	$0.729677\pi$
$572$	−0.335250	+	0.580671i	−0.0140175	+	0.0242791i
$573$		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	$-0.0869782\pi$
$577$	29.0806	+	16.7897i	1.21064	+	0.698964i	0.247742	+	0.968826i	$0.420312\pi$
$578$	6.83358	−	3.94537i	0.284239	−	0.164106i
$579$		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
$590$	2.77066	+	1.59964i	0.114066	+	0.0658562i
$591$		0			0
$592$	2.58394	+	4.47552i	0.106199	+	0.183943i
$593$	−0.366598	−	0.634967i	−0.0150544	−	0.0260750i	0.858400	−	0.512981i	$-0.171459\pi$
$593$	−0.366598	−	0.634967i	−0.0150544	−	0.0260750i	−0.873454	+	0.486906i	$0.838125\pi$
$594$		0			0
$595$		0			0
$596$	2.45268	+	1.41606i	0.100466	+	0.0580039i
$597$		0			0
$598$		−	7.70663i		−	0.315147i
$599$		−	30.7783i		−	1.25757i	−0.777580	−	0.628785i	$-0.783553\pi$
$599$		−	30.7783i		−	1.25757i	0.777580	−	0.628785i	$-0.216447\pi$
$600$		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
$605$	−1.93414	−	3.35003i	−0.0786340	−	0.136198i
$606$		0			0
$607$	38.7783	+	22.3887i	1.57396	+	0.908728i	0.995676	+	0.0928949i	$0.0296121\pi$
$607$	38.7783	+	22.3887i	1.57396	+	0.908728i	0.578287	+	0.815833i	$0.303721\pi$
$608$	−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	−0.989015	−	0.147815i	$-0.952776\pi$
$613$	−9.07402	+	15.7167i	−0.366496	+	0.634790i	0.622519	+	0.782605i	$0.286109\pi$
$614$	−0.653728			−0.0263823
$615$		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
$619$	−38.4228	+	22.1834i	−1.54434	+	0.891626i	−0.545785	+	0.837925i	$0.683768\pi$
$619$	−38.4228	+	22.1834i	−1.54434	+	0.891626i	−0.998557	+	0.0537011i	$0.982898\pi$
$620$	−2.00836	−	1.15953i	−0.0806577	−	0.0465677i
$621$		0			0
$622$		−	9.24493i		−	0.370688i
$623$		0			0
$624$		0			0
$625$	−11.5011	+	19.9204i	−0.460043	+	0.796818i
$626$	6.16414			0.246368
$627$		0			0
$628$			2.83456i			0.113111i
$629$	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	$0.724524\pi$
$632$		−	8.35568i		−	0.332371i
$633$		0			0
$634$	20.6548			0.820308
$635$	0.306009	−	0.530024i	0.0121436	−	0.0210333i
$636$		0			0
$637$		0			0
$638$		−	1.22442i		−	0.0484751i
$639$		0			0
$640$	0.317483	+	0.183299i	0.0125496	+	0.00724553i
$641$	−10.2270	+	5.90456i	−0.403942	+	0.233216i	−0.688184	−	0.725537i	$-0.741592\pi$
$641$	−10.2270	+	5.90456i	−0.403942	+	0.233216i	0.284241	+	0.958753i	$0.408258\pi$
$642$		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
$646$	−31.7166			−1.24787
$647$	14.0841	−	24.3945i	0.553705	−	0.959045i	−0.444298	−	0.895879i	$-0.646547\pi$
$647$	14.0841	−	24.3945i	0.553705	−	0.959045i	0.998003	−	0.0631660i	$-0.0201198\pi$
$648$		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
$653$	39.0555	+	22.5487i	1.52836	+	0.882399i	0.999431	+	0.0337326i	$0.0107394\pi$
$653$	39.0555	+	22.5487i	1.52836	+	0.882399i	0.528929	+	0.848666i	$0.322594\pi$
$654$		0			0
$655$	2.48043	+	4.29623i	0.0969184	+	0.167868i
$656$	−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
$661$		−	19.7724i		−	0.769056i	−0.923113	−	0.384528i	$-0.874364\pi$
$661$		−	19.7724i		−	0.769056i	0.923113	−	0.384528i	$-0.125636\pi$
$662$			10.7114i			0.416309i
$663$		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
$668$	9.67422	+	16.7562i	0.374307	+	0.648318i
$669$		0			0
$670$	3.45763	+	1.99626i	0.133580	+	0.0771223i
$671$	−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
$677$	−21.1322			−0.812175			−0.406088	−	0.913834i	$-0.633107\pi$
$677$	−21.1322			−0.812175			−0.406088	+	0.913834i	$0.633107\pi$
$678$		0			0
$679$		0			0
$680$	1.58394	−	0.914490i	0.0607415	−	0.0350691i
$681$		0			0
$682$	3.66751	−	2.11744i	0.140436	−	0.0810810i
$683$	7.55150	+	4.35986i	0.288950	+	0.166825i	0.637468	−	0.770477i	$-0.279982\pi$
$683$	7.55150	+	4.35986i	0.288950	+	0.166825i	−0.348518	+	0.937302i	$0.613315\pi$
$684$		0			0
$685$			3.29517i			0.125902i
$686$		0			0
$687$		0			0
$688$	2.24922	−	3.89576i	0.0857506	−	0.148524i
$689$		0			0
$690$		0			0
$691$		−	18.1370i		−	0.689964i	−0.938609	−	0.344982i	$-0.887885\pi$
$691$		−	18.1370i		−	0.689964i	0.938609	−	0.344982i	$-0.112115\pi$
$692$	−4.83654			−0.183858
$693$		0			0
$694$	−10.9320			−0.414972
$695$			3.40908i			0.129314i
$696$		0			0
$697$	−21.5456			−0.816097
$698$	0.592145	−	1.02562i	0.0224130	−	0.0388205i
$699$		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
$704$	−0.579764	+	0.334727i	−0.0218507	+	0.0126155i
$705$		0			0
$706$	−29.0832	+	16.7912i	−1.09456	+	0.631946i
$707$		0			0
$708$		0			0
$709$	−3.60770			−0.135490			−0.0677449	−	0.997703i	$-0.521580\pi$
$709$	−3.60770			−0.135490			−0.0677449	+	0.997703i	$0.521580\pi$
$710$	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
$716$	3.16789	+	1.82898i	0.118390	+	0.0683522i
$717$		0			0
$718$	−5.06407	−	8.77122i	−0.188989	−	0.327339i
$719$	12.8915	+	22.3287i	0.480770	+	0.832718i	0.999757	−	0.0220642i	$-0.00702381\pi$
$719$	12.8915	+	22.3287i	0.480770	+	0.832718i	−0.518986	+	0.854782i	$0.673690\pi$
$720$		0			0
$721$		0			0
$722$	18.5453	+	10.7072i	0.690186	+	0.398479i
$723$		0			0
$724$		−	5.66796i		−	0.210648i
$725$		−	8.89910i		−	0.330504i
$726$		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
$731$	−11.2215	−	19.4362i	−0.415042	−	0.718873i
$732$		0			0
$733$	−17.9908	−	10.3870i	−0.664504	−	0.383651i	0.129487	−	0.991581i	$-0.458667\pi$
$733$	−17.9908	−	10.3870i	−0.664504	−	0.383651i	−0.793991	+	0.607930i	$0.792000\pi$
$734$	−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	−0.735961	−	0.677023i	$-0.763270\pi$
$739$	5.93544	−	10.2805i	0.218339	−	0.378174i	0.954300	+	0.298850i	$0.0966029\pi$
$740$	1.89454			0.0696446
$741$		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
$745$	0.899148	−	0.519124i	0.0329422	−	0.0190192i
$746$	−14.2106	−	8.20451i	−0.520288	−	0.300389i
$747$		0			0
$748$			3.33994i			0.122120i
$749$		0			0
$750$		0			0
$751$	−1.15691	+	2.00383i	−0.0422164	+	0.0731209i	−0.886362	−	0.462994i	$-0.846775\pi$
$751$	−1.15691	+	2.00383i	−0.0422164	+	0.0731209i	0.844145	+	0.536115i	$0.180109\pi$
$752$	−8.32901			−0.303728
$753$		0			0
$754$		−	1.83184i		−	0.0667118i
$755$	−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	$0.588450\pi$
$758$		−	2.91372i		−	0.105831i
$759$		0			0
$760$	−2.33055			−0.0845378
$761$	11.6690	−	20.2112i	0.422999	−	0.732656i	−0.573232	−	0.819393i	$-0.694311\pi$
$761$	11.6690	−	20.2112i	0.422999	−	0.732656i	0.996231	+	0.0867370i	$0.0276440\pi$
$762$		0			0
$763$		0			0
$764$		−	27.3777i		−	0.990490i
$765$		0			0
$766$	−7.42567	−	4.28721i	−0.268300	−	0.154903i
$767$	−7.56959	+	4.37030i	−0.273322	+	0.157803i
$768$		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
$772$	10.0283			0.360925
$773$	0.219254	−	0.379758i	0.00788600	−	0.0136590i	−0.862055	−	0.506814i	$-0.830823\pi$
$773$	0.219254	−	0.379758i	0.00788600	−	0.0136590i	0.869941	+	0.493155i	$0.164156\pi$
$774$		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
$779$	23.7759	+	13.7270i	0.851861	+	0.491822i
$780$		0			0
$781$	1.84047	+	3.18779i	0.0658573	+	0.114068i
$782$	−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
$787$			38.2572i			1.36372i	0.731481	+	0.681861i	$0.238829\pi$
$787$			38.2572i			1.36372i	−0.731481	+	0.681861i	$0.761171\pi$
$788$			18.8258i			0.670643i
$789$		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
$794$	−1.79017	−	3.10066i	−0.0635307	−	0.110038i
$795$		0			0
$796$	−4.64541	−	2.68203i	−0.164652	−	0.0950620i
$797$	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
$803$	−2.72678			−0.0962259
$804$		0			0
$805$		0			0
$806$	5.48694	−	3.16789i	0.193269	−	0.111584i
$807$		0			0
$808$	−13.6241	+	7.86586i	−0.479293	+	0.276720i
$809$	−18.8506	−	10.8834i	−0.662754	−	0.382641i	0.130572	−	0.991439i	$-0.458319\pi$
$809$	−18.8506	−	10.8834i	−0.662754	−	0.382641i	−0.793325	+	0.608798i	$0.791652\pi$
$810$		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
$814$	−1.72983	+	2.99615i	−0.0606305	+	0.105015i
$815$	9.06527			0.317542
$816$		0			0
$817$			28.5976i			1.00050i
$818$	−3.47371			−0.121455
$819$		0			0
$820$	−1.58318			−0.0552869
$821$		−	24.8013i		−	0.865572i	−0.901497	−	0.432786i	$-0.857531\pi$
$821$		−	24.8013i		−	0.865572i	0.901497	−	0.432786i	$-0.142469\pi$
$822$		0			0
$823$	21.3144			0.742973			0.371486	−	0.928438i	$-0.378848\pi$
$823$	21.3144			0.742973			0.371486	+	0.928438i	$0.378848\pi$
$824$	−5.72226	+	9.91124i	−0.199344	+	0.345274i
$825$		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	$-0.602699\pi$
$829$	−37.3422	−	21.5595i	−1.29695	−	0.748793i	−0.979876	+	0.199609i	$0.936033\pi$
$830$	−5.40174	+	3.11870i	−0.187497	+	0.108252i
$831$		0			0
$832$	−0.867380	+	0.500782i	−0.0300710	+	0.0173615i
$833$		0			0
$834$		0			0
$835$	7.09310			0.245467
$836$	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
$842$	26.3151	+	15.1930i	0.906878	+	0.523586i
$843$		0			0
$844$	0.828981	+	1.43584i	0.0285347	+	0.0494235i
$845$	−2.19901	−	3.80881i	−0.0756484	−	0.131027i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$			24.2748i			0.832619i
$851$		−	39.7648i		−	1.36312i
$852$		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
$857$	22.9296	+	39.7152i	0.783260	+	1.35665i	0.930033	+	0.367476i	$0.119778\pi$
$857$	22.9296	+	39.7152i	0.783260	+	1.35665i	−0.146773	+	0.989170i	$0.546889\pi$
$858$		0			0
$859$	−3.24073	−	1.87104i	−0.110572	−	0.0638390i	0.443694	−	0.896178i	$-0.353668\pi$
$859$	−3.24073	−	1.87104i	−0.110572	−	0.0638390i	−0.554266	+	0.832339i	$0.687001\pi$
$860$	−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	$-0.487227\pi$
$863$	27.1883	−	15.6972i	0.925502	−	0.534339i	0.885386	+	0.464856i	$0.153894\pi$
$864$		0			0
$865$	−0.886533	+	1.53552i	−0.0301430	+	0.0522092i
$866$	−8.15047			−0.276964
$867$		0			0
$868$		0			0
$869$	4.84432	−	2.79687i	0.164332	−	0.0948773i
$870$		0			0
$871$	−9.44641	+	5.45389i	−0.320080	+	0.184798i
$872$	−9.14811	−	5.28166i	−0.309794	−	0.178860i
$873$		0			0
$874$			48.9162i			1.65462i
$875$		0			0
$876$		0			0
$877$	10.1962	−	17.6603i	0.344300	−	0.596344i	−0.640927	−	0.767602i	$-0.721450\pi$
$877$	10.1962	−	17.6603i	0.344300	−	0.596344i	0.985226	+	0.171258i	$0.0547831\pi$
$878$	−12.2404			−0.413094
$879$		0			0
$880$			0.245420i			0.00827312i
$881$	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	$0.274869\pi$
$884$			4.99687i			0.168063i
$885$		0			0
$886$	−8.00836			−0.269046
$887$	−3.09606	+	5.36253i	−0.103955	+	0.180056i	−0.913311	−	0.407263i	$-0.866483\pi$
$887$	−3.09606	+	5.36253i	−0.103955	+	0.180056i	0.809356	+	0.587319i	$0.199817\pi$
$888$		0			0
$889$		0			0
$890$			3.92675i			0.131625i
$891$		0			0
$892$	14.7546	+	8.51860i	0.494022	+	0.285224i
$893$	45.8555	−	26.4747i	1.53450	−	0.885941i
$894$		0			0
$895$	1.16134	−	0.670501i	0.0388194	−	0.0224124i
$896$		0			0
$897$		0			0
$898$	−14.5183			−0.484483
$899$	−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
$905$	−1.79948	−	1.03893i	−0.0598168	−	0.0345353i
$906$		0			0
$907$	0.0645566	+	0.111815i	0.00214357	+	0.00371277i	0.867095	−	0.498142i	$-0.165984\pi$
$907$	0.0645566	+	0.111815i	0.00214357	+	0.00371277i	−0.864952	+	0.501855i	$0.832651\pi$
$908$	−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
$913$		−	11.3902i		−	0.376962i
$914$			9.95501i			0.329283i
$915$		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	0.723601	−	0.690218i	$-0.242486\pi$
$919$	−7.15271	−	12.3889i	−0.235946	−	0.408671i	−0.959547	+	0.281548i	$0.909152\pi$
$920$	−1.41041	−	2.44290i	−0.0464999	−	0.0805401i
$921$		0			0
$922$	−27.9960	−	16.1635i	−0.922001	−	0.532317i
$923$	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
$929$	−11.7473			−0.385415			−0.192708	−	0.981256i	$-0.561727\pi$
$929$	−11.7473			−0.385415			−0.192708	+	0.981256i	$0.561727\pi$
$930$		0			0
$931$		0			0
$932$	−8.82741	+	5.09651i	−0.289152	+	0.166942i
$933$		0			0
$934$	17.8941	−	10.3312i	0.585512	−	0.338046i
$935$	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
$940$	−1.52670	+	2.64432i	−0.0497954	+	0.0862482i
$941$	11.9311			0.388944			0.194472	−	0.980908i	$-0.437701\pi$
$941$	11.9311			0.388944			0.194472	+	0.980908i	$0.437701\pi$
$942$		0			0
$943$			33.2295i			1.08210i
$944$	−8.72695			−0.284038
$945$		0			0
$946$	3.01149			0.0979121
$947$			7.73957i			0.251502i	0.992062	+	0.125751i	$0.0401341\pi$
$947$			7.73957i			0.251502i	−0.992062	+	0.125751i	$0.959866\pi$
$948$		0			0
$949$	−4.07951			−0.132427
$950$	15.4659	−	26.7877i	0.501779	−	0.869107i
$951$		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
$956$	−16.6117	+	9.59076i	−0.537260	+	0.310187i
$957$		0			0
$958$	8.79955	−	5.08042i	0.284301	−	0.164141i
$959$		0			0
$960$		0			0
$961$	−9.01672			−0.290862
$962$	−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	$0.856769\pi$
$968$	9.13815	+	5.27592i	0.293711	+	0.169574i
$969$		0			0
$970$	−3.15563	−	5.46571i	−0.101321	−	0.175493i
$971$	12.9222	+	22.3820i	0.414694	+	0.718271i	0.995396	−	0.0958449i	$-0.0305553\pi$
$971$	12.9222	+	22.3820i	0.414694	+	0.718271i	−0.580702	+	0.814116i	$0.697222\pi$
$972$		0			0
$973$		0			0
$974$	27.0457	+	15.6148i	0.866599	+	0.500331i
$975$		0			0
$976$		−	4.95771i		−	0.158693i
$977$			30.1319i			0.964004i	0.876170	+	0.482002i	$0.160090\pi$
$977$			30.1319i			0.964004i	−0.876170	+	0.482002i	$0.839910\pi$
$978$		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
$983$	−6.30293	−	10.9170i	−0.201032	−	0.348198i	0.747829	−	0.663891i	$-0.231096\pi$
$983$	−6.30293	−	10.9170i	−0.201032	−	0.348198i	−0.948861	+	0.315693i	$0.897763\pi$
$984$		0			0
$985$	5.97689	+	3.45076i	0.190440	+	0.109950i
$986$	−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	0.0840815	+	0.996459i	$0.473204\pi$
$991$	−25.8426	+	44.7607i	−0.820918	+	1.42187i	−0.904999	+	0.425413i	$0.860129\pi$
$992$	6.32588			0.200847
$993$		0			0
$994$		0			0
$995$	−1.70300	+	0.983227i	−0.0539887	+	0.0311704i
$996$		0			0
$997$	35.1469	−	20.2921i	1.11311	−	0.642656i	0.173479	−	0.984837i	$-0.444499\pi$
$997$	35.1469	−	20.2921i	1.11311	−	0.642656i	0.939634	+	0.342181i	$0.111166\pi$
$998$	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.l.b.521.6		16
3.2	odd	2		882.2.l.a.227.1		16
7.2	even	3		2646.2.t.a.1979.7		16
7.3	odd	6		378.2.m.a.251.3		16
7.4	even	3		378.2.m.a.251.2		16
7.5	odd	6		2646.2.t.a.1979.6		16
7.6	odd	2	inner	2646.2.l.b.521.7		16
9.4	even	3		882.2.t.b.815.1		16
9.5	odd	6		2646.2.t.a.2285.6		16
21.2	odd	6		882.2.t.b.803.4		16
21.5	even	6		882.2.t.b.803.1		16
21.11	odd	6		126.2.m.a.83.7	yes	16
21.17	even	6		126.2.m.a.83.6	yes	16
21.20	even	2		882.2.l.a.227.4		16
28.3	even	6		3024.2.cc.b.2897.5		16
28.11	odd	6		3024.2.cc.b.2897.4		16
63.4	even	3		126.2.m.a.41.6	✓	16
63.5	even	6	inner	2646.2.l.b.1097.2		16
63.11	odd	6		1134.2.d.a.1133.4		16
63.13	odd	6		882.2.t.b.815.4		16
63.23	odd	6	inner	2646.2.l.b.1097.3		16
63.25	even	3		1134.2.d.a.1133.13		16
63.31	odd	6		126.2.m.a.41.7	yes	16
63.32	odd	6		378.2.m.a.125.3		16
63.38	even	6		1134.2.d.a.1133.5		16
63.40	odd	6		882.2.l.a.509.5		16
63.41	even	6		2646.2.t.a.2285.7		16
63.52	odd	6		1134.2.d.a.1133.12		16
63.58	even	3		882.2.l.a.509.8		16
63.59	even	6		378.2.m.a.125.2		16
84.11	even	6		1008.2.cc.b.209.4		16
84.59	odd	6		1008.2.cc.b.209.5		16
252.31	even	6		1008.2.cc.b.545.4		16
252.59	odd	6		3024.2.cc.b.881.4		16
252.67	odd	6		1008.2.cc.b.545.5		16
252.95	even	6		3024.2.cc.b.881.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.6	✓	16	63.4	even	3
126.2.m.a.41.7	yes	16	63.31	odd	6
126.2.m.a.83.6	yes	16	21.17	even	6
126.2.m.a.83.7	yes	16	21.11	odd	6
378.2.m.a.125.2		16	63.59	even	6
378.2.m.a.125.3		16	63.32	odd	6
378.2.m.a.251.2		16	7.4	even	3
378.2.m.a.251.3		16	7.3	odd	6
882.2.l.a.227.1		16	3.2	odd	2
882.2.l.a.227.4		16	21.20	even	2
882.2.l.a.509.5		16	63.40	odd	6
882.2.l.a.509.8		16	63.58	even	3
882.2.t.b.803.1		16	21.5	even	6
882.2.t.b.803.4		16	21.2	odd	6
882.2.t.b.815.1		16	9.4	even	3
882.2.t.b.815.4		16	63.13	odd	6
1008.2.cc.b.209.4		16	84.11	even	6
1008.2.cc.b.209.5		16	84.59	odd	6
1008.2.cc.b.545.4		16	252.31	even	6
1008.2.cc.b.545.5		16	252.67	odd	6
1134.2.d.a.1133.4		16	63.11	odd	6
1134.2.d.a.1133.5		16	63.38	even	6
1134.2.d.a.1133.12		16	63.52	odd	6
1134.2.d.a.1133.13		16	63.25	even	3
2646.2.l.b.521.6		16	1.1	even	1	trivial
2646.2.l.b.521.7		16	7.6	odd	2	inner
2646.2.l.b.1097.2		16	63.5	even	6	inner
2646.2.l.b.1097.3		16	63.23	odd	6	inner
2646.2.t.a.1979.6		16	7.5	odd	6
2646.2.t.a.1979.7		16	7.2	even	3
2646.2.t.a.2285.6		16	9.5	odd	6
2646.2.t.a.2285.7		16	63.41	even	6
3024.2.cc.b.881.4		16	252.59	odd	6
3024.2.cc.b.881.5		16	252.95	even	6
3024.2.cc.b.2897.4		16	28.11	odd	6
3024.2.cc.b.2897.5		16	28.3	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.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-0.183299 + 0.317483i) q^{5} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-0.183299 + 0.317483i) q^{5} -1.00000i q^{8} +(-0.317483 - 0.183299i) q^{10} +(0.579764 - 0.334727i) q^{11} +(0.867380 - 0.500782i) q^{13} +1.00000 q^{16} +(2.49453 - 4.32065i) q^{17} +(-5.50552 + 3.17861i) q^{19} +(0.183299 - 0.317483i) q^{20} +(0.334727 + 0.579764i) q^{22} +(-6.66371 - 3.84729i) q^{23} +(2.43280 + 4.21374i) q^{25} +(0.500782 + 0.867380i) q^{26} +(-1.58394 - 0.914490i) q^{29} -6.32588i q^{31} +1.00000i q^{32} +(4.32065 + 2.49453i) q^{34} +(2.58394 + 4.47552i) q^{37} +(-3.17861 - 5.50552i) q^{38} +(0.317483 + 0.183299i) q^{40} +(-2.15928 - 3.73998i) q^{41} +(2.24922 - 3.89576i) q^{43} +(-0.579764 + 0.334727i) q^{44} +(3.84729 - 6.66371i) q^{46} -8.32901 q^{47} +(-4.21374 + 2.43280i) q^{50} +(-0.867380 + 0.500782i) q^{52} +0.245420i q^{55} +(0.914490 - 1.58394i) q^{58} -8.72695 q^{59} -4.95771i q^{61} +6.32588 q^{62} -1.00000 q^{64} +0.367172i q^{65} -10.8907 q^{67} +(-2.49453 + 4.32065i) q^{68} +5.49843i q^{71} +(-3.52744 - 2.03657i) q^{73} +(-4.47552 + 2.58394i) q^{74} +(5.50552 - 3.17861i) q^{76} +8.35568 q^{79} +(-0.183299 + 0.317483i) q^{80} +(3.73998 - 2.15928i) q^{82} +(8.50712 - 14.7348i) q^{83} +(0.914490 + 1.58394i) q^{85} +(3.89576 + 2.24922i) q^{86} +(-0.334727 - 0.579764i) q^{88} +(-5.35566 - 9.27628i) q^{89} +(6.66371 + 3.84729i) q^{92} -8.32901i q^{94} -2.33055i q^{95} +(14.9093 + 8.60787i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4}+O(q^{10}) \) 16 * q - 16 * q^4	\( 16 q - 16 q^{4} - 12 q^{11} + 16 q^{16} - 48 q^{23} - 8 q^{25} + 12 q^{29} + 4 q^{37} + 4 q^{43} + 12 q^{44} - 12 q^{46} - 60 q^{50} - 12 q^{58} - 16 q^{64} + 56 q^{67} + 36 q^{74} + 8 q^{79} - 12 q^{85} - 24 q^{86} + 48 q^{92}+O(q^{100}) \) 16 * q - 16 * q^4 - 12 * q^11 + 16 * q^16 - 48 * q^23 - 8 * q^25 + 12 * q^29 + 4 * q^37 + 4 * q^43 + 12 * q^44 - 12 * q^46 - 60 * q^50 - 12 * q^58 - 16 * q^64 + 56 * q^67 + 36 * q^74 + 8 * q^79 - 12 * q^85 - 24 * q^86 + 48 * q^92

Introduction

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