LMFDB - Embedded newform 882.2.l.a.509.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(227,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, 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("882.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.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:	$7.04280545828$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			509.5
Root			$-0.0967785 + 1.72934i$ of defining polynomial
Character	$\chi$	$=$	882.509
Dual form			882.2.l.a.227.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-1.54605 + 0.780860i) q^{3} -1.00000 q^{4} +(0.183299 + 0.317483i) q^{5} +(-0.780860 - 1.54605i) q^{6} -1.00000i q^{8} +(1.78052 - 2.41449i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-1.54605 + 0.780860i) q^{3} -1.00000 q^{4} +(0.183299 + 0.317483i) q^{5} +(-0.780860 - 1.54605i) q^{6} -1.00000i q^{8} +(1.78052 - 2.41449i) q^{9} +(-0.317483 + 0.183299i) q^{10} +(-0.579764 - 0.334727i) q^{11} +(1.54605 - 0.780860i) q^{12} +(0.867380 + 0.500782i) q^{13} +(-0.531299 - 0.347713i) q^{15} +1.00000 q^{16} +(-2.49453 - 4.32065i) q^{17} +(2.41449 + 1.78052i) q^{18} +(-5.50552 - 3.17861i) q^{19} +(-0.183299 - 0.317483i) q^{20} +(0.334727 - 0.579764i) q^{22} +(6.66371 - 3.84729i) q^{23} +(0.780860 + 1.54605i) q^{24} +(2.43280 - 4.21374i) q^{25} +(-0.500782 + 0.867380i) q^{26} +(-0.867380 + 5.12325i) q^{27} +(1.58394 - 0.914490i) q^{29} +(0.347713 - 0.531299i) q^{30} +6.32588i q^{31} +1.00000i q^{32} +(1.15772 + 0.0647887i) q^{33} +(4.32065 - 2.49453i) q^{34} +(-1.78052 + 2.41449i) q^{36} +(2.58394 - 4.47552i) q^{37} +(3.17861 - 5.50552i) q^{38} +(-1.73205 - 0.0969299i) q^{39} +(0.317483 - 0.183299i) q^{40} +(2.15928 - 3.73998i) q^{41} +(2.24922 + 3.89576i) q^{43} +(0.579764 + 0.334727i) q^{44} +(1.09293 + 0.122710i) q^{45} +(3.84729 + 6.66371i) q^{46} +8.32901 q^{47} +(-1.54605 + 0.780860i) q^{48} +(4.21374 + 2.43280i) q^{50} +(7.23048 + 4.73205i) q^{51} +(-0.867380 - 0.500782i) q^{52} +(-5.12325 - 0.867380i) q^{54} -0.245420i q^{55} +(10.9938 + 0.615242i) q^{57} +(0.914490 + 1.58394i) q^{58} +8.72695 q^{59} +(0.531299 + 0.347713i) q^{60} +4.95771i q^{61} -6.32588 q^{62} -1.00000 q^{64} +0.367172i q^{65} +(-0.0647887 + 1.15772i) q^{66} -10.8907 q^{67} +(2.49453 + 4.32065i) q^{68} +(-7.29820 + 11.1515i) q^{69} +5.49843i q^{71} +(-2.41449 - 1.78052i) q^{72} +(-3.52744 + 2.03657i) q^{73} +(4.47552 + 2.58394i) q^{74} +(-0.470886 + 8.41431i) q^{75} +(5.50552 + 3.17861i) q^{76} +(0.0969299 - 1.73205i) q^{78} +8.35568 q^{79} +(0.183299 + 0.317483i) q^{80} +(-2.65953 - 8.59808i) q^{81} +(3.73998 + 2.15928i) q^{82} +(-8.50712 - 14.7348i) q^{83} +(0.914490 - 1.58394i) q^{85} +(-3.89576 + 2.24922i) q^{86} +(-1.73476 + 2.65068i) q^{87} +(-0.334727 + 0.579764i) q^{88} +(5.35566 - 9.27628i) q^{89} +(-0.122710 + 1.09293i) q^{90} +(-6.66371 + 3.84729i) q^{92} +(-4.93962 - 9.78010i) q^{93} +8.32901i q^{94} -2.33055i q^{95} +(-0.780860 - 1.54605i) q^{96} +(14.9093 - 8.60787i) q^{97} +(-1.84047 + 0.803848i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 12 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 - 12 * q^9	$ 16 q - 16 q^{4} - 12 q^{9} + 12 q^{11} + 16 q^{16} + 12 q^{18} + 48 q^{23} - 8 q^{25} - 12 q^{29} + 12 q^{30} + 12 q^{36} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} + 60 q^{50} + 24 q^{51} + 48 q^{57} - 12 q^{58} - 16 q^{64} + 56 q^{67} - 12 q^{72} - 36 q^{74} - 24 q^{78} + 8 q^{79} - 12 q^{85} + 24 q^{86} - 48 q^{92} + 84 q^{93} - 72 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 - 12 * q^9 + 12 * q^11 + 16 * q^16 + 12 * q^18 + 48 * q^23 - 8 * q^25 - 12 * q^29 + 12 * q^30 + 12 * q^36 + 4 * q^37 + 4 * q^43 - 12 * q^44 - 12 * q^46 + 60 * q^50 + 24 * q^51 + 48 * q^57 - 12 * q^58 - 16 * q^64 + 56 * q^67 - 12 * q^72 - 36 * q^74 - 24 * q^78 + 8 * q^79 - 12 * q^85 + 24 * q^86 - 48 * q^92 + 84 * q^93 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.54605	+	0.780860i	−0.892610	+	0.450830i
$3$	−1.54605	+	0.780860i	−0.892610	+	0.450830i
$4$	−1.00000			−0.500000
$5$	0.183299	+	0.317483i	0.0819738	+	0.141983i	0.904098	−	0.427326i	$-0.140544\pi$
$5$	0.183299	+	0.317483i	0.0819738	+	0.141983i	−0.822124	+	0.569309i	$0.807211\pi$
$6$	−0.780860	−	1.54605i	−0.318785	−	0.631171i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	1.78052	−	2.41449i	0.593505	−	0.804830i
$10$	−0.317483	+	0.183299i	−0.100397	+	0.0579643i
$11$	−0.579764	−	0.334727i	−0.174805	−	0.100924i	0.410044	−	0.912066i	$-0.365513\pi$
$11$	−0.579764	−	0.334727i	−0.174805	−	0.100924i	−0.584850	+	0.811142i	$0.698847\pi$
$12$	1.54605	−	0.780860i	0.446305	−	0.225415i
$13$	0.867380	+	0.500782i	0.240568	+	0.138892i	0.615438	−	0.788185i	$-0.288979\pi$
$13$	0.867380	+	0.500782i	0.240568	+	0.138892i	−0.374870	+	0.927077i	$0.622313\pi$
$14$		0			0
$15$	−0.531299	−	0.347713i	−0.137181	−	0.0897791i
$16$	1.00000			0.250000
$17$	−2.49453	−	4.32065i	−0.605013	−	1.04791i	−0.992049	−	0.125848i	$-0.959835\pi$
$17$	−2.49453	−	4.32065i	−0.605013	−	1.04791i	0.387037	−	0.922064i	$-0.373499\pi$
$18$	2.41449	+	1.78052i	0.569101	+	0.419672i
$19$	−5.50552	−	3.17861i	−1.26305	−	0.729224i	−0.289389	−	0.957212i	$-0.593452\pi$
$19$	−5.50552	−	3.17861i	−1.26305	−	0.729224i	−0.973664	+	0.227988i	$0.926785\pi$
$20$	−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	$-0.370321\pi$
$23$	6.66371	−	3.84729i	1.38948	−	0.802216i	0.993256	+	0.115938i	$0.0369875\pi$
$24$	0.780860	+	1.54605i	0.159392	+	0.315585i
$25$	2.43280	−	4.21374i	0.486561	−	0.842748i
$26$	−0.500782	+	0.867380i	−0.0982115	+	0.170107i
$27$	−0.867380	+	5.12325i	−0.166927	+	0.985969i
$28$		0			0
$29$	1.58394	−	0.914490i	0.294131	−	0.169817i	−0.345672	−	0.938355i	$-0.612349\pi$
$29$	1.58394	−	0.914490i	0.294131	−	0.169817i	0.639803	+	0.768539i	$0.279016\pi$
$30$	0.347713	−	0.531299i	0.0634834	−	0.0970014i
$31$			6.32588i			1.13616i	0.822973	+	0.568081i	$0.192314\pi$
$31$			6.32588i			1.13616i	−0.822973	+	0.568081i	$0.807686\pi$
$32$			1.00000i			0.176777i
$33$	1.15772	+	0.0647887i	0.201532	+	0.0112783i
$34$	4.32065	−	2.49453i	0.740986	−	0.427809i
$35$		0			0
$36$	−1.78052	+	2.41449i	−0.296753	+	0.402415i
$37$	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	$0.0270119\pi$
$38$	3.17861	−	5.50552i	0.515639	−	0.893113i
$39$	−1.73205	−	0.0969299i	−0.277350	−	0.0155212i
$40$	0.317483	−	0.183299i	0.0501985	−	0.0289821i
$41$	2.15928	−	3.73998i	0.337223	−	0.584087i	−0.646686	−	0.762756i	$-0.723846\pi$
$41$	2.15928	−	3.73998i	0.337223	−	0.584087i	0.983909	+	0.178669i	$0.0571790\pi$
$42$		0			0
$43$	2.24922	+	3.89576i	0.343002	+	0.594098i	0.984989	−	0.172618i	$-0.0552228\pi$
$43$	2.24922	+	3.89576i	0.343002	+	0.594098i	−0.641986	+	0.766716i	$0.721889\pi$
$44$	0.579764	+	0.334727i	0.0874027	+	0.0504619i
$45$	1.09293	+	0.122710i	0.162924	+	0.0182926i
$46$	3.84729	+	6.66371i	0.567252	+	0.982510i
$47$	8.32901			1.21491			0.607455	−	0.794354i	$-0.292190\pi$
$47$	8.32901			1.21491			0.607455	+	0.794354i	$0.292190\pi$
$48$	−1.54605	+	0.780860i	−0.223153	+	0.112707i
$49$		0			0
$50$	4.21374	+	2.43280i	0.595913	+	0.344050i
$51$	7.23048	+	4.73205i	1.01247	+	0.662620i
$52$	−0.867380	−	0.500782i	−0.120284	−	0.0694460i
$53$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$53$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$54$	−5.12325	−	0.867380i	−0.697185	−	0.118036i
$55$		−	0.245420i		−	0.0330925i
$56$		0			0
$57$	10.9938	+	0.615242i	1.45617	+	0.0814909i
$58$	0.914490	+	1.58394i	0.120078	+	0.207982i
$59$	8.72695			1.13615			0.568076	−	0.822976i	$-0.307688\pi$
$59$	8.72695			1.13615			0.568076	+	0.822976i	$0.307688\pi$
$60$	0.531299	+	0.347713i	0.0685904	+	0.0448895i
$61$			4.95771i			0.634770i	0.948297	+	0.317385i	$0.102805\pi$
$61$			4.95771i			0.634770i	−0.948297	+	0.317385i	$0.897195\pi$
$62$	−6.32588			−0.803387
$63$		0			0
$64$	−1.00000			−0.125000
$65$			0.367172i			0.0455420i
$66$	−0.0647887	+	1.15772i	−0.00797493	+	0.142505i
$67$	−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
$69$	−7.29820	+	11.1515i	−0.878600	+	1.34248i
$70$		0			0
$71$			5.49843i			0.652544i	0.945276	+	0.326272i	$0.105793\pi$
$71$			5.49843i			0.652544i	−0.945276	+	0.326272i	$0.894207\pi$
$72$	−2.41449	−	1.78052i	−0.284550	−	0.209836i
$73$	−3.52744	+	2.03657i	−0.412856	+	0.238363i	−0.692016	−	0.721882i	$-0.743277\pi$
$73$	−3.52744	+	2.03657i	−0.412856	+	0.238363i	0.279160	+	0.960245i	$0.409944\pi$
$74$	4.47552	+	2.58394i	0.520269	+	0.300377i
$75$	−0.470886	+	8.41431i	−0.0543732	+	0.971601i
$76$	5.50552	+	3.17861i	0.631526	+	0.364612i
$77$		0			0
$78$	0.0969299	−	1.73205i	0.0109751	−	0.196116i
$79$	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
$81$	−2.65953	−	8.59808i	−0.295503	−	0.955342i
$82$	3.73998	+	2.15928i	0.413012	+	0.238453i
$83$	−8.50712	−	14.7348i	−0.933778	−	1.61735i	−0.776798	−	0.629750i	$-0.783158\pi$
$83$	−8.50712	−	14.7348i	−0.933778	−	1.61735i	−0.156980	−	0.987602i	$-0.550176\pi$
$84$		0			0
$85$	0.914490	−	1.58394i	0.0991904	−	0.171803i
$86$	−3.89576	+	2.24922i	−0.420090	+	0.242539i
$87$	−1.73476	+	2.65068i	−0.185986	+	0.284183i
$88$	−0.334727	+	0.579764i	−0.0356820	+	0.0618030i
$89$	5.35566	−	9.27628i	0.567699	−	0.983283i	−0.429094	−	0.903260i	$-0.641167\pi$
$89$	5.35566	−	9.27628i	0.567699	−	0.983283i	0.996793	−	0.0800234i	$-0.0254995\pi$
$90$	−0.122710	+	1.09293i	−0.0129348	+	0.115205i
$91$		0			0
$92$	−6.66371	+	3.84729i	−0.694740	+	0.401108i
$93$	−4.93962	−	9.78010i	−0.512215	−	1.01415i
$94$			8.32901i			0.859071i
$95$		−	2.33055i		−	0.239109i
$96$	−0.780860	−	1.54605i	−0.0796962	−	0.157793i
$97$	14.9093	−	8.60787i	1.51381	−	0.873997i	0.513937	−	0.857828i	$-0.328186\pi$
$97$	14.9093	−	8.60787i	1.51381	−	0.873997i	0.999869	−	0.0161687i	$-0.00514689\pi$
$98$		0			0
$99$	−1.84047	+	0.803848i	−0.184974	+	0.0807897i
$100$	−2.43280	+	4.21374i	−0.243280	+	0.421374i
$101$	7.86586	−	13.6241i	0.782683	−	1.35565i	−0.147691	−	0.989034i	$-0.547184\pi$
$101$	7.86586	−	13.6241i	0.782683	−	1.35565i	0.930374	−	0.366613i	$-0.119483\pi$
$102$	−4.73205	+	7.23048i	−0.468543	+	0.715925i
$103$	−9.91124	+	5.72226i	−0.976584	+	0.563831i	−0.901237	−	0.433327i	$-0.857340\pi$
$103$	−9.91124	+	5.72226i	−0.976584	+	0.563831i	−0.0753467	+	0.997157i	$0.524006\pi$
$104$	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	$0.846238\pi$
$108$	0.867380	−	5.12325i	0.0834637	−	0.492985i
$109$	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	$0.664497\pi$
$110$	0.245420			0.0233999
$111$	−0.500140	+	8.93706i	−0.0474712	+	0.848268i
$112$		0			0
$113$	3.60226	+	2.07976i	0.338872	+	0.195648i	0.659773	−	0.751465i	$-0.270652\pi$
$113$	3.60226	+	2.07976i	0.338872	+	0.195648i	−0.320901	+	0.947113i	$0.603986\pi$
$114$	−0.615242	+	10.9938i	−0.0576227	+	1.02967i
$115$	2.44290	+	1.41041i	0.227802	+	0.131521i
$116$	−1.58394	+	0.914490i	−0.147065	+	0.0849083i
$117$	2.75352	−	1.20263i	0.254563	−	0.111183i
$118$			8.72695i			0.803381i
$119$		0			0
$120$	−0.347713	+	0.531299i	−0.0317417	+	0.0485007i
$121$	−5.27592	−	9.13815i	−0.479629	−	0.830741i
$122$	−4.95771			−0.448850
$123$	−0.417944	+	7.46828i	−0.0376847	+	0.673392i
$124$		−	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
$129$	−6.51943	−	4.26670i	−0.574004	−	0.375662i
$130$	−0.367172			−0.0322031
$131$	−6.76607	−	11.7192i	−0.591154	−	1.02391i	−0.994077	−	0.108675i	$-0.965339\pi$
$131$	−6.76607	−	11.7192i	−0.591154	−	1.02391i	0.402923	−	0.915234i	$-0.367994\pi$
$132$	−1.15772	−	0.0647887i	−0.100766	−	0.00563913i
$133$		0			0
$134$		−	10.8907i		−	0.940817i
$135$	−1.78554	+	0.663707i	−0.153674	+	0.0571228i
$136$	−4.32065	+	2.49453i	−0.370493	+	0.213904i
$137$	−7.78428	−	4.49425i	−0.665056	−	0.383970i	0.129145	−	0.991626i	$-0.458777\pi$
$137$	−7.78428	−	4.49425i	−0.665056	−	0.383970i	−0.794201	+	0.607656i	$0.792110\pi$
$138$	−11.1515	−	7.29820i	−0.949280	−	0.621264i
$139$	8.05336	+	4.64961i	0.683077	+	0.394375i	0.801014	−	0.598646i	$-0.204294\pi$
$139$	8.05336	+	4.64961i	0.683077	+	0.394375i	−0.117936	+	0.993021i	$0.537628\pi$
$140$		0			0
$141$	−12.8770	+	6.50379i	−1.08444	+	0.547718i
$142$	−5.49843			−0.461418
$143$	−0.335250	−	0.580671i	−0.0280351	−	0.0485581i
$144$	1.78052	−	2.41449i	0.148376	−	0.201208i
$145$	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	$-0.629657\pi$
$149$	2.45268	−	1.41606i	0.200931	−	0.116008i	0.597090	+	0.802174i	$0.296324\pi$
$150$	−8.41431	−	0.470886i	−0.687026	−	0.0384477i
$151$	8.27592	−	14.3343i	0.673484	−	1.16651i	−0.303425	−	0.952855i	$-0.598130\pi$
$151$	8.27592	−	14.3343i	0.673484	−	1.16651i	0.976909	−	0.213654i	$-0.0685365\pi$
$152$	−3.17861	+	5.50552i	−0.257820	+	0.446556i
$153$	−14.8737	−	1.66997i	−1.20247	−	0.135009i
$154$		0			0
$155$	−2.00836	+	1.15953i	−0.161315	+	0.0931355i
$156$	1.73205	+	0.0969299i	0.138675	+	0.00776060i
$157$			2.83456i			0.226222i	0.993582	+	0.113111i	$0.0360816\pi$
$157$			2.83456i			0.226222i	−0.993582	+	0.113111i	$0.963918\pi$
$158$			8.35568i			0.664742i
$159$		0			0
$160$	−0.317483	+	0.183299i	−0.0250993	+	0.0144911i
$161$		0			0
$162$	8.59808	−	2.65953i	0.675529	−	0.208952i
$163$	−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	$0.746867\pi$
$164$	−2.15928	+	3.73998i	−0.168611	+	0.292044i
$165$	0.191639	+	0.379431i	0.0149191	+	0.0295387i
$166$	14.7348	−	8.50712i	1.14364	−	0.660281i
$167$	9.67422	−	16.7562i	0.748614	−	1.29664i	−0.199874	−	0.979822i	$-0.564053\pi$
$167$	9.67422	−	16.7562i	0.748614	−	1.29664i	0.948487	−	0.316815i	$-0.102614\pi$
$168$		0			0
$169$	−5.99843	−	10.3896i	−0.461418	−	0.799199i
$170$	1.58394	+	0.914490i	0.121483	+	0.0701382i
$171$	−17.4774	+	7.63345i	−1.33653	+	0.583745i
$172$	−2.24922	−	3.89576i	−0.171501	−	0.297049i
$173$	−4.83654			−0.367715			−0.183858	−	0.982953i	$-0.558859\pi$
$173$	−4.83654			−0.367715			−0.183858	+	0.982953i	$0.558859\pi$
$174$	−2.65068	−	1.73476i	−0.200948	−	0.131512i
$175$		0			0
$176$	−0.579764	−	0.334727i	−0.0437013	−	0.0252310i
$177$	−13.4923	+	6.81453i	−1.01414	+	0.512211i
$178$	9.27628	+	5.35566i	0.695286	+	0.401424i
$179$	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	$0.289682\pi$
$180$	−1.09293	−	0.122710i	−0.0814620	−	0.00914628i
$181$		−	5.66796i		−	0.421296i	−0.977562	−	0.210648i	$-0.932443\pi$
$181$		−	5.66796i		−	0.421296i	0.977562	−	0.210648i	$-0.0675574\pi$
$182$		0			0
$183$	−3.87128	−	7.66485i	−0.286173	−	0.566602i
$184$	−3.84729	−	6.66371i	−0.283626	−	0.491255i
$185$	1.89454			0.139289
$186$	9.78010	−	4.93962i	0.717111	−	0.362191i
$187$			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	$0.543935\pi$
$192$	1.54605	−	0.780860i	0.111576	−	0.0563537i
$193$	−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
$195$	−0.286710	−	0.567664i	−0.0205317	−	0.0406513i
$196$		0			0
$197$		−	18.8258i		−	1.34129i	−0.741780	−	0.670643i	$-0.766018\pi$
$197$		−	18.8258i		−	1.34129i	0.741780	−	0.670643i	$-0.233982\pi$
$198$	−0.803848	−	1.84047i	−0.0571270	−	0.130797i
$199$	4.64541	−	2.68203i	0.329305	−	0.190124i	−0.326228	−	0.945291i	$-0.605778\pi$
$199$	4.64541	−	2.68203i	0.329305	−	0.190124i	0.655532	+	0.755167i	$0.272444\pi$
$200$	−4.21374	−	2.43280i	−0.297956	−	0.172025i
$201$	16.8376	−	8.50414i	1.18763	−	0.599836i
$202$	13.6241	+	7.86586i	0.958587	+	0.553440i
$203$		0			0
$204$	−7.23048	−	4.73205i	−0.506235	−	0.331310i
$205$	1.58318			0.110574
$206$	−5.72226	−	9.91124i	−0.398689	−	0.690549i
$207$	2.57558	−	22.9396i	0.179015	−	1.59441i
$208$	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	−0.893149	−	0.449762i	$-0.851509\pi$
$211$	−0.828981	+	1.43584i	−0.0570694	+	0.0988471i	0.836079	+	0.548609i	$0.184842\pi$
$212$		0			0
$213$	−4.29351	−	8.50083i	−0.294186	−	0.582467i
$214$	5.53088	−	9.57976i	0.378083	−	0.654859i
$215$	−0.824559	+	1.42818i	−0.0562344	+	0.0974009i
$216$	5.12325	+	0.867380i	0.348593	+	0.0590178i
$217$		0			0
$218$	−9.14811	+	5.28166i	−0.619588	+	0.357719i
$219$	3.86331	−	5.90307i	0.261059	−	0.398893i
$220$			0.245420i			0.0165462i
$221$		−	4.99687i		−	0.336126i
$222$	−8.93706	−	0.500140i	−0.599816	−	0.0335672i
$223$	−14.7546	+	8.51860i	−0.988044	+	0.570448i	−0.904689	−	0.426072i	$-0.859897\pi$
$223$	−14.7546	+	8.51860i	−0.988044	+	0.570448i	−0.0833551	+	0.996520i	$0.526564\pi$
$224$		0			0
$225$	−5.84239	−	13.3766i	−0.389492	−	0.891774i
$226$	−2.07976	+	3.60226i	−0.138344	+	0.239619i
$227$	−2.55512	+	4.42560i	−0.169589	+	0.293737i	−0.938276	−	0.345889i	$-0.887577\pi$
$227$	−2.55512	+	4.42560i	−0.169589	+	0.293737i	0.768686	+	0.639626i	$0.220911\pi$
$228$	−10.9938	−	0.615242i	−0.728084	−	0.0407454i
$229$	−13.2215	+	7.63345i	−0.873703	+	0.504433i	−0.868577	−	0.495554i	$-0.834965\pi$
$229$	−13.2215	+	7.63345i	−0.873703	+	0.504433i	−0.00512595	+	0.999987i	$0.501632\pi$
$230$	−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	$0.775026\pi$
$234$	1.20263	+	2.75352i	0.0786184	+	0.180003i
$235$	1.52670	+	2.64432i	0.0995909	+	0.172496i
$236$	−8.72695			−0.568076
$237$	−12.9183	+	6.52461i	−0.839131	+	0.423819i
$238$		0			0
$239$	−16.6117	−	9.59076i	−1.07452	−	0.620375i	−0.145108	−	0.989416i	$-0.546353\pi$
$239$	−16.6117	−	9.59076i	−1.07452	−	0.620375i	−0.929413	+	0.369041i	$0.879686\pi$
$240$	−0.531299	−	0.347713i	−0.0342952	−	0.0224448i
$241$	17.9140	+	10.3426i	1.15394	+	0.666227i	0.949844	−	0.312724i	$-0.101241\pi$
$241$	17.9140	+	10.3426i	1.15394	+	0.666227i	0.204095	+	0.978951i	$0.434575\pi$
$242$	9.13815	−	5.27592i	0.587423	−	0.339149i
$243$	10.8256	+	11.2163i	0.694465	+	0.719526i
$244$		−	4.95771i		−	0.317385i
$245$		0			0
$246$	−7.46828	−	0.417944i	−0.476160	−	0.0266471i
$247$	−3.18359	−	5.51413i	−0.202567	−	0.350856i
$248$	6.32588			0.401694
$249$	24.6582	+	16.1378i	1.56265	+	1.02269i
$250$			3.61671i			0.228741i
$251$	1.81200			0.114373			0.0571864	−	0.998364i	$-0.481787\pi$
$251$	1.81200			0.114373			0.0571864	+	0.998364i	$0.481787\pi$
$252$		0			0
$253$	−5.15117			−0.323851
$254$		−	1.66945i		−	0.104751i
$255$	−0.177006	+	3.16294i	−0.0110845	+	0.198071i
$256$	1.00000			0.0625000
$257$	−3.22773	−	5.59059i	−0.201340	−	0.348731i	0.747620	−	0.664126i	$-0.231196\pi$
$257$	−3.22773	−	5.59059i	−0.201340	−	0.348731i	−0.948960	+	0.315395i	$0.897863\pi$
$258$	4.26670	−	6.51943i	0.265633	−	0.405882i
$259$		0			0
$260$		−	0.367172i		−	0.0227710i
$261$	0.612209	−	5.45268i	0.0378948	−	0.337513i
$262$	11.7192	−	6.76607i	0.724013	−	0.418009i
$263$	7.63888	+	4.41031i	0.471034	+	0.271951i	0.716672	−	0.697410i	$-0.245664\pi$
$263$	7.63888	+	4.41031i	0.471034	+	0.271951i	−0.245639	+	0.969361i	$0.578998\pi$
$264$	0.0647887	−	1.15772i	0.00398747	−	0.0712525i
$265$		0			0
$266$		0			0
$267$	−1.03663	+	18.5236i	−0.0634404	+	1.13362i
$268$	10.8907			0.665258
$269$	7.13267	+	12.3541i	0.434886	+	0.753245i	0.997286	−	0.0736199i	$-0.0234552\pi$
$269$	7.13267	+	12.3541i	0.434886	+	0.753245i	−0.562400	+	0.826865i	$0.690122\pi$
$270$	−0.663707	−	1.78554i	−0.0403919	−	0.108664i
$271$	2.64381	+	1.52641i	0.160600	+	0.0927226i	0.578146	−	0.815933i	$-0.303776\pi$
$271$	2.64381	+	1.52641i	0.160600	+	0.0927226i	−0.417546	+	0.908656i	$0.637110\pi$
$272$	−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
$276$	7.29820	−	11.1515i	0.439300	−	0.671242i
$277$	−0.632828	+	1.09609i	−0.0380230	+	0.0658577i	−0.884411	−	0.466710i	$-0.845439\pi$
$277$	−0.632828	+	1.09609i	−0.0380230	+	0.0658577i	0.846388	+	0.532567i	$0.178773\pi$
$278$	−4.64961	+	8.05336i	−0.278865	+	0.483009i
$279$	15.2738	+	11.2633i	0.914417	+	0.674318i
$280$		0			0
$281$	9.11639	−	5.26335i	0.543838	−	0.313985i	−0.202795	−	0.979221i	$-0.565002\pi$
$281$	9.11639	−	5.26335i	0.543838	−	0.313985i	0.746633	+	0.665236i	$0.231669\pi$
$282$	−6.50379	−	12.8770i	−0.387295	−	0.766816i
$283$		−	19.8718i		−	1.18125i	−0.806945	−	0.590627i	$-0.798881\pi$
$283$		−	19.8718i		−	1.18125i	0.806945	−	0.590627i	$-0.201119\pi$
$284$		−	5.49843i		−	0.326272i
$285$	1.81983	+	3.60313i	0.107797	+	0.213431i
$286$	0.580671	−	0.335250i	0.0343358	−	0.0198238i
$287$		0			0
$288$	2.41449	+	1.78052i	0.142275	+	0.104918i
$289$	−3.94537	+	6.83358i	−0.232081	+	0.401975i
$290$	−0.335250	+	0.580671i	−0.0196866	+	0.0340982i
$291$	−16.3289	+	24.9502i	−0.957215	+	1.46261i
$292$	3.52744	−	2.03657i	0.206428	−	0.119181i
$293$	−6.70606	+	11.6152i	−0.391772	+	0.678569i	−0.992683	−	0.120747i	$-0.961471\pi$
$293$	−6.70606	+	11.6152i	−0.391772	+	0.678569i	0.600911	+	0.799316i	$0.294804\pi$
$294$		0			0
$295$	1.59964	+	2.77066i	0.0931348	+	0.161314i
$296$	−4.47552	−	2.58394i	−0.260134	−	0.150189i
$297$	2.21776	−	2.67994i	0.128688	−	0.155506i
$298$	1.41606	+	2.45268i	0.0820299	+	0.142080i
$299$	7.70663			0.445686
$300$	0.470886	−	8.41431i	0.0271866	−	0.485800i
$301$		0			0
$302$	14.3343	+	8.27592i	0.824847	+	0.476225i
$303$	−1.52249	+	27.2056i	−0.0874649	+	1.56292i
$304$	−5.50552	−	3.17861i	−0.315763	−	0.182306i
$305$	−1.57399	+	0.908744i	−0.0901265	+	0.0520346i
$306$	1.66997	−	14.8737i	0.0954660	−	0.850275i
$307$		−	0.653728i		−	0.0373102i	−0.999826	−	0.0186551i	$-0.994062\pi$
$307$		−	0.653728i		−	0.0373102i	0.999826	−	0.0186551i	$-0.00593845\pi$
$308$		0			0
$309$	10.8550	−	16.5862i	0.617517	−	0.943554i
$310$	−1.15953	−	2.00836i	−0.0658567	−	0.114067i
$311$	9.24493			0.524232			0.262116	−	0.965036i	$-0.415580\pi$
$311$	9.24493			0.524232			0.262116	+	0.965036i	$0.415580\pi$
$312$	−0.0969299	+	1.73205i	−0.00548757	+	0.0980581i
$313$			6.16414i			0.348418i	0.984709	+	0.174209i	$0.0557368\pi$
$313$			6.16414i			0.348418i	−0.984709	+	0.174209i	$0.944263\pi$
$314$	−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
$321$	19.1296	+	1.07054i	1.06771	+	0.0597517i
$322$		0			0
$323$			31.7166i			1.76476i
$324$	2.65953	+	8.59808i	0.147752	+	0.477671i
$325$	4.22033	−	2.43661i	0.234102	−	0.135159i
$326$	−21.4151	−	12.3640i	−1.18608	−	0.684781i
$327$	−15.3091	−	10.0192i	−0.846594	−	0.554061i
$328$	−3.73998	−	2.15928i	−0.206506	−	0.119226i
$329$		0			0
$330$	−0.379431	+	0.191639i	−0.0208870	+	0.0105494i
$331$	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
$333$	−6.20535	−	14.2076i	−0.340051	−	0.778574i
$334$	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	−0.744664	−	0.667439i	$-0.767390\pi$
$337$	3.77592	−	6.54008i	0.205687	−	0.356261i	0.950351	+	0.311179i	$0.100724\pi$
$338$	10.3896	−	5.99843i	0.565119	−	0.326272i
$339$	−7.19326	−	0.402553i	−0.390684	−	0.0218637i
$340$	−0.914490	+	1.58394i	−0.0495952	+	0.0859014i
$341$	2.11744	−	3.66751i	0.114666	−	0.198607i
$342$	−7.63345	−	17.4774i	−0.412770	−	0.945069i
$343$		0			0
$344$	3.89576	−	2.24922i	0.210045	−	0.121270i
$345$	−4.87817	−	0.272995i	−0.262632	−	0.0146975i
$346$		−	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	$0.905203\pi$
$348$	1.73476	−	2.65068i	0.0929929	−	0.142091i
$349$	−1.02562	+	0.592145i	−0.0549004	+	0.0316968i	−0.527199	−	0.849742i	$-0.676758\pi$
$349$	−1.02562	+	0.592145i	−0.0549004	+	0.0316968i	0.472299	+	0.881439i	$0.343424\pi$
$350$		0			0
$351$	−3.31798	+	4.00943i	−0.177101	+	0.214008i
$352$	0.334727	−	0.579764i	0.0178410	−	0.0309015i
$353$	−16.7912	+	29.0832i	−0.893706	+	1.54794i	−0.0583086	+	0.998299i	$0.518571\pi$
$353$	−16.7912	+	29.0832i	−0.893706	+	1.54794i	−0.835398	+	0.549646i	$0.814763\pi$
$354$	−6.81453	−	13.4923i	−0.362188	−	0.717106i
$355$	−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	$-0.247211\pi$
$359$	8.77122	+	5.06407i	0.462927	+	0.267271i	−0.250347	+	0.968156i	$0.580545\pi$
$360$	0.122710	−	1.09293i	0.00646739	−	0.0576023i
$361$	10.7072	+	18.5453i	0.563534	+	0.976070i
$362$	5.66796			0.297901
$363$	15.2924	+	10.0083i	0.802644	+	0.525297i
$364$		0			0
$365$	−1.29315	−	0.746603i	−0.0676868	−	0.0390790i
$366$	7.66485	−	3.87128i	0.400648	−	0.202355i
$367$	−15.5903	−	9.00104i	−0.813805	−	0.469850i	0.0344706	−	0.999406i	$-0.489025\pi$
$367$	−15.5903	−	9.00104i	−0.813805	−	0.469850i	−0.848275	+	0.529555i	$0.822359\pi$
$368$	6.66371	−	3.84729i	0.347370	−	0.200554i
$369$	−5.18552	−	11.8727i	−0.269947	−	0.618066i
$370$			1.89454i			0.0984923i
$371$		0			0
$372$	4.93962	+	9.78010i	0.256108	+	0.507074i
$373$	−8.20451	−	14.2106i	−0.424814	−	0.735799i	0.571589	−	0.820540i	$-0.306327\pi$
$373$	−8.20451	−	14.2106i	−0.424814	−	0.735799i	−0.996403	+	0.0847411i	$0.972994\pi$
$374$	−3.33994			−0.172704
$375$	−5.59160	+	2.82415i	−0.288749	+	0.145838i
$376$		−	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
$381$	2.58105	−	1.30361i	0.132231	−	0.0667859i
$382$	−27.3777			−1.40076
$383$	4.28721	+	7.42567i	0.219066	+	0.379434i	0.954523	−	0.298138i	$-0.0963655\pi$
$383$	4.28721	+	7.42567i	0.219066	+	0.379434i	−0.735456	+	0.677572i	$0.763032\pi$
$384$	0.780860	+	1.54605i	0.0398481	+	0.0788963i
$385$		0			0
$386$		−	10.0283i		−	0.510425i
$387$	13.4110	+	1.50575i	0.681721	+	0.0765414i
$388$	−14.9093	+	8.60787i	−0.756903	+	0.436998i
$389$	30.7906	+	17.7770i	1.56115	+	0.901328i	0.997142	+	0.0755559i	$0.0240731\pi$
$389$	30.7906	+	17.7770i	1.56115	+	0.901328i	0.564004	+	0.825772i	$0.309260\pi$
$390$	0.567664	−	0.286710i	0.0287448	−	0.0145181i
$391$	−33.2456	−	19.1944i	−1.68130	−	0.970702i
$392$		0			0
$393$	19.6117	+	12.8350i	0.989279	+	0.647442i
$394$	18.8258			0.948433
$395$	1.53159	+	2.65279i	0.0770626	+	0.133476i
$396$	1.84047	−	0.803848i	0.0924872	−	0.0403949i
$397$	−3.10066	−	1.79017i	−0.155618	−	0.0898460i	0.420169	−	0.907446i	$-0.361971\pi$
$397$	−3.10066	−	1.79017i	−0.155618	−	0.0898460i	−0.575787	+	0.817600i	$0.695304\pi$
$398$	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	$-0.668184\pi$
$401$	−0.165300	+	0.0954357i	−0.00825467	+	0.00476583i	0.495867	+	0.868398i	$0.334850\pi$
$402$	8.50414	+	16.8376i	0.424148	+	0.839782i
$403$	−3.16789	+	5.48694i	−0.157804	+	0.273324i
$404$	−7.86586	+	13.6241i	−0.391341	+	0.677823i
$405$	2.24226	−	2.42037i	0.111419	−	0.120269i
$406$		0			0
$407$	−2.99615	+	1.72983i	−0.148514	+	0.0857445i
$408$	4.73205	−	7.23048i	0.234271	−	0.357962i
$409$		−	3.47371i		−	0.171764i	−0.996305	−	0.0858819i	$-0.972629\pi$
$409$		−	3.47371i		−	0.171764i	0.996305	−	0.0858819i	$-0.0273708\pi$
$410$			1.58318i			0.0781875i
$411$	15.5442	+	0.869894i	0.766740	+	0.0429087i
$412$	9.91124	−	5.72226i	0.488292	−	0.281915i
$413$		0			0
$414$	22.9396	+	2.57558i	1.12742	+	0.126583i
$415$	3.11870	−	5.40174i	0.153091	−	0.265161i
$416$	−0.500782	+	0.867380i	−0.0245529	+	0.0425268i
$417$	−16.0816	−	0.899965i	−0.787518	−	0.0440715i
$418$	−3.68569	+	2.12793i	−0.180273	+	0.104081i
$419$	−0.703955	+	1.21929i	−0.0343905	+	0.0595660i	−0.882708	−	0.469921i	$-0.844282\pi$
$419$	−0.703955	+	1.21929i	−0.0343905	+	0.0595660i	0.848318	+	0.529487i	$0.177616\pi$
$420$		0			0
$421$	15.1930	+	26.3151i	0.740463	+	1.28252i	0.952285	+	0.305211i	$0.0987268\pi$
$421$	15.1930	+	26.3151i	0.740463	+	1.28252i	−0.211822	+	0.977308i	$0.567940\pi$
$422$	−1.43584	−	0.828981i	−0.0698954	−	0.0403541i
$423$	14.8299	−	20.1103i	0.721056	−	0.977797i
$424$		0			0
$425$	−24.2748			−1.17750
$426$	8.50083	−	4.29351i	0.411867	−	0.208021i
$427$		0			0
$428$	9.57976	+	5.53088i	0.463055	+	0.267345i
$429$	0.971735	+	0.635960i	0.0469158	+	0.0307044i
$430$	−1.42818	−	0.824559i	−0.0688728	−	0.0397638i
$431$	−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	$0.561461\pi$
$432$	−0.867380	+	5.12325i	−0.0417319	+	0.246492i
$433$		−	8.15047i		−	0.391686i	−0.980635	−	0.195843i	$-0.937256\pi$
$433$		−	8.15047i		−	0.391686i	0.980635	−	0.195843i	$-0.0627444\pi$
$434$		0			0
$435$	−1.15953	−	0.0648900i	−0.0555951	−	0.00311124i
$436$	−5.28166	−	9.14811i	−0.252946	−	0.438115i
$437$	−48.9162			−2.33998
$438$	5.90307	+	3.86331i	0.282060	+	0.184596i
$439$		−	12.2404i		−	0.584203i	−0.956387	−	0.292101i	$-0.905646\pi$
$439$		−	12.2404i		−	0.584203i	0.956387	−	0.292101i	$-0.0943545\pi$
$440$	−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	$0.939072\pi$
$444$	0.500140	−	8.93706i	0.0237356	−	0.424134i
$445$	3.92675			0.186146
$446$	−8.51860	−	14.7546i	−0.403367	−	0.698653i
$447$	−2.68622	+	4.10449i	−0.127054	+	0.194136i
$448$		0			0
$449$			14.5183i			0.685163i	0.939488	+	0.342581i	$0.111301\pi$
$449$			14.5183i			0.685163i	−0.939488	+	0.342581i	$0.888699\pi$
$450$	13.3766	−	5.84239i	0.630579	−	0.275413i
$451$	−2.50374	+	1.44554i	−0.117897	+	0.0680677i
$452$	−3.60226	−	2.07976i	−0.169436	−	0.0978239i
$453$	−1.60186	+	28.6238i	−0.0752620	+	1.34486i
$454$	−4.42560	−	2.55512i	−0.207704	−	0.119918i
$455$		0			0
$456$	0.615242	−	10.9938i	0.0288114	−	0.514833i
$457$	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
$459$	24.2995	−	9.03245i	1.13420	−	0.421598i
$460$	−2.44290	−	1.41041i	−0.113901	−	0.0657607i
$461$	16.1635	+	27.9960i	0.752810	+	1.30391i	0.946456	+	0.322834i	$0.104636\pi$
$461$	16.1635	+	27.9960i	0.752810	+	1.30391i	−0.193645	+	0.981072i	$0.562031\pi$
$462$		0			0
$463$	−4.72516	+	8.18421i	−0.219597	+	0.380353i	−0.954685	−	0.297619i	$-0.903807\pi$
$463$	−4.72516	+	8.18421i	−0.219597	+	0.380353i	0.735088	+	0.677972i	$0.237141\pi$
$464$	1.58394	−	0.914490i	0.0735327	−	0.0424541i
$465$	2.19959	−	3.36093i	0.102003	−	0.155859i
$466$	5.09651	−	8.82741i	0.236091	−	0.408922i
$467$	10.3312	−	17.8941i	0.478069	−	0.828039i	−0.521615	−	0.853181i	$-0.674670\pi$
$467$	10.3312	−	17.8941i	0.478069	−	0.828039i	0.999684	+	0.0251414i	$0.00800361\pi$
$468$	−2.75352	+	1.20263i	−0.127281	+	0.0555916i
$469$		0			0
$470$	−2.64432	+	1.52670i	−0.121973	+	0.0704214i
$471$	−2.21339	−	4.38235i	−0.101988	−	0.201928i
$472$		−	8.72695i		−	0.401691i
$473$		−	3.01149i		−	0.138469i
$474$	−6.52461	−	12.9183i	−0.299685	−	0.593356i
$475$	−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	$-0.758764\pi$
$479$	5.08042	−	8.79955i	0.232131	−	0.402062i	0.958435	+	0.285311i	$0.0920970\pi$
$480$	0.347713	−	0.531299i	0.0158708	−	0.0242504i
$481$	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
$486$	−11.2163	+	10.8256i	−0.508782	+	0.491061i
$487$	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	$0.583122\pi$
$488$	4.95771			0.224425
$489$	2.39315	−	42.7634i	0.108222	−	1.93383i
$490$		0			0
$491$	17.8314	+	10.2950i	0.804720	+	0.464605i	0.845119	−	0.534578i	$-0.179529\pi$
$491$	17.8314	+	10.2950i	0.804720	+	0.464605i	−0.0403987	+	0.999184i	$0.512863\pi$
$492$	0.417944	−	7.46828i	0.0188424	−	0.336696i
$493$	−7.90239	−	4.56245i	−0.355906	−	0.205482i
$494$	5.51413	−	3.18359i	0.248093	−	0.143236i
$495$	−0.592565	−	0.436975i	−0.0266338	−	0.0196406i
$496$			6.32588i			0.284040i
$497$		0			0
$498$	−16.1378	+	24.6582i	−0.723150	+	1.10496i
$499$	12.5766	+	21.7834i	0.563007	+	0.975157i	0.997232	+	0.0743527i	$0.0236891\pi$
$499$	12.5766	+	21.7834i	0.563007	+	0.975157i	−0.434225	+	0.900805i	$0.642978\pi$
$500$	−3.61671			−0.161744
$501$	−1.87251	+	33.4601i	−0.0836577	+	1.49489i
$502$			1.81200i			0.0808737i
$503$	31.1553			1.38915			0.694574	−	0.719421i	$-0.255593\pi$
$503$	31.1553			1.38915			0.694574	+	0.719421i	$0.255593\pi$
$504$		0			0
$505$	5.76722			0.256638
$506$		−	5.15117i		−	0.228997i
$507$	17.3867	+	11.3789i	0.772169	+	0.505352i
$508$	1.66945			0.0740700
$509$	2.41674	+	4.18591i	0.107120	+	0.185537i	0.914602	−	0.404354i	$-0.132504\pi$
$509$	2.41674	+	4.18591i	0.107120	+	0.185537i	−0.807482	+	0.589892i	$0.799170\pi$
$510$	−3.16294	−	0.177006i	−0.140057	−	0.00783796i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	21.0602	−	25.4491i	0.929830	−	1.12360i
$514$	5.59059	−	3.22773i	0.246590	−	0.142369i
$515$	−3.63344	−	2.09777i	−0.160109	−	0.0924387i
$516$	6.51943	+	4.26670i	0.287002	+	0.187831i
$517$	−4.82886	−	2.78794i	−0.212373	−	0.122613i
$518$		0			0
$519$	7.47751	−	3.77666i	0.328226	−	0.165777i
$520$	0.367172			0.0161015
$521$	8.76611	+	15.1834i	0.384050	+	0.665195i	0.991637	−	0.129059i	$-0.0411956\pi$
$521$	8.76611	+	15.1834i	0.384050	+	0.665195i	−0.607587	+	0.794253i	$0.707862\pi$
$522$	5.45268	+	0.612209i	0.238657	+	0.0267956i
$523$	−16.5427	−	9.55094i	−0.723362	−	0.417633i	0.0926268	−	0.995701i	$-0.470474\pi$
$523$	−16.5427	−	9.55094i	−0.723362	−	0.417633i	−0.815989	+	0.578068i	$0.803807\pi$
$524$	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
$528$	1.15772	+	0.0647887i	0.0503831	+	0.00281957i
$529$	18.1033	−	31.3559i	0.787101	−	1.36330i
$530$		0			0
$531$	15.5385	−	21.0711i	0.674312	−	0.914410i
$532$		0			0
$533$	3.74584	−	2.16266i	0.162250	−	0.0936752i
$534$	−18.5236	−	1.03663i	−0.801593	−	0.0448592i
$535$		−	4.05522i		−	0.175322i
$536$			10.8907i			0.470408i
$537$	−3.46952	+	5.30136i	−0.149721	+	0.228771i
$538$	−12.3541	+	7.13267i	−0.532625	+	0.307511i
$539$		0			0
$540$	1.78554	−	0.663707i	0.0768372	−	0.0285614i
$541$	−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	$0.261565\pi$
$542$	−1.52641	+	2.64381i	−0.0655648	+	0.113562i
$543$	4.42588	+	8.76293i	0.189933	+	0.376053i
$544$	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	0.952147	−	0.305640i	$-0.0988703\pi$
$547$	4.94380	+	8.56292i	0.211382	+	0.366124i	−0.740765	+	0.671764i	$0.765537\pi$
$548$	7.78428	+	4.49425i	0.332528	+	0.191985i
$549$	11.9704	+	8.82729i	0.510882	+	0.376739i
$550$	−1.62865	−	2.82090i	−0.0694458	−	0.120284i
$551$	−11.6272			−0.495337
$552$	11.1515	+	7.29820i	0.474640	+	0.310632i
$553$		0			0
$554$	−1.09609	−	0.632828i	−0.0465684	−	0.0268863i
$555$	−2.92904	+	1.47937i	−0.124331	+	0.0627957i
$556$	−8.05336	−	4.64961i	−0.341539	−	0.197187i
$557$	−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	$0.419206\pi$
$558$	−11.2633	+	15.2738i	−0.476815	+	0.646590i
$559$			4.50547i			0.190561i
$560$		0			0
$561$	−2.60803	−	5.16371i	−0.110111	−	0.218012i
$562$	5.26335	+	9.11639i	0.222021	+	0.384552i
$563$	24.3333			1.02553			0.512763	−	0.858530i	$-0.328622\pi$
$563$	24.3333			1.02553			0.512763	+	0.858530i	$0.328622\pi$
$564$	12.8770	−	6.50379i	0.542221	−	0.273859i
$565$			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	$-0.0634990\pi$
$570$	−3.60313	+	1.81983i	−0.150919	+	0.0762243i
$571$	−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
$573$	−21.3781	−	42.3272i	−0.893084	−	1.76824i
$574$		0			0
$575$		−	37.4388i		−	1.56131i
$576$	−1.78052	+	2.41449i	−0.0741882	+	0.100604i
$577$	29.0806	−	16.7897i	1.21064	−	0.698964i	0.247742	−	0.968826i	$-0.420312\pi$
$577$	29.0806	−	16.7897i	1.21064	−	0.698964i	0.962899	+	0.269862i	$0.0869782\pi$
$578$	−6.83358	−	3.94537i	−0.284239	−	0.164106i
$579$	15.5042	−	7.83067i	0.644331	−	0.325432i
$580$	−0.580671	−	0.335250i	−0.0241110	−	0.0139205i
$581$		0			0
$582$	−24.9502	−	16.3289i	−1.03422	−	0.676853i
$583$		0			0
$584$	2.03657	+	3.52744i	0.0842739	+	0.145967i
$585$	0.886533	+	0.653755i	0.0366536	+	0.0270294i
$586$	−11.6152	−	6.70606i	−0.479821	−	0.277025i
$587$	9.65855	+	16.7291i	0.398651	+	0.690484i	0.993560	−	0.113310i	$-0.0361452\pi$
$587$	9.65855	+	16.7291i	0.398651	+	0.690484i	−0.594909	+	0.803793i	$0.702812\pi$
$588$		0			0
$589$	20.1075	−	34.8272i	0.828516	−	1.43503i
$590$	−2.77066	+	1.59964i	−0.114066	+	0.0658562i
$591$	14.7003	+	29.1056i	0.604692	+	1.19725i
$592$	2.58394	−	4.47552i	0.106199	−	0.183943i
$593$	0.366598	−	0.634967i	0.0150544	−	0.0260750i	−0.858400	−	0.512981i	$-0.828541\pi$
$593$	0.366598	−	0.634967i	0.0150544	−	0.0260750i	0.873454	+	0.486906i	$0.161875\pi$
$594$	2.67994	+	2.21776i	0.109959	+	0.0909959i
$595$		0			0
$596$	−2.45268	+	1.41606i	−0.100466	+	0.0580039i
$597$	−5.08773	+	7.77396i	−0.208227	+	0.318167i
$598$			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	$-0.216447\pi$
$600$	8.41431	+	0.470886i	0.343513	+	0.0192238i
$601$	0.786931	−	0.454335i	0.0320996	−	0.0185327i	−0.483864	−	0.875143i	$-0.660767\pi$
$601$	0.786931	−	0.454335i	0.0320996	−	0.0185327i	0.515964	+	0.856610i	$0.327434\pi$
$602$		0			0
$603$	−19.3911	+	26.2956i	−0.789668	+	1.07084i
$604$	−8.27592	+	14.3343i	−0.336742	+	0.583255i
$605$	1.93414	−	3.35003i	0.0786340	−	0.136198i
$606$	−27.2056	−	1.52249i	−1.10515	−	0.0618470i
$607$	38.7783	−	22.3887i	1.57396	−	0.908728i	0.578287	−	0.815833i	$-0.303721\pi$
$607$	38.7783	−	22.3887i	1.57396	−	0.908728i	0.995676	−	0.0928949i	$-0.0296121\pi$
$608$	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
$612$	14.8737	+	1.66997i	0.601235	+	0.0675046i
$613$	−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	$0.952776\pi$
$614$	0.653728			0.0263823
$615$	−2.44766	+	1.23624i	−0.0986993	+	0.0498500i
$616$		0			0
$617$	−19.7393	−	11.3965i	−0.794674	−	0.458805i	0.0469315	−	0.998898i	$-0.485056\pi$
$617$	−19.7393	−	11.3965i	−0.794674	−	0.458805i	−0.841605	+	0.540093i	$0.818389\pi$
$618$	16.5862	+	10.8550i	0.667193	+	0.436650i
$619$	−38.4228	−	22.1834i	−1.54434	−	0.891626i	−0.998557	−	0.0537011i	$-0.982898\pi$
$619$	−38.4228	−	22.1834i	−1.54434	−	0.891626i	−0.545785	−	0.837925i	$-0.683768\pi$
$620$	2.00836	−	1.15953i	0.0806577	−	0.0465677i
$621$	13.9307	+	37.4769i	0.559018	+	1.50390i
$622$			9.24493i			0.370688i
$623$		0			0
$624$	−1.73205	−	0.0969299i	−0.0693375	−	0.00388030i
$625$	−11.5011	−	19.9204i	−0.460043	−	0.796818i
$626$	−6.16414			−0.246368
$627$	−6.16789	−	4.03663i	−0.246322	−	0.161207i
$628$		−	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
$633$	0.160455	−	2.86719i	0.00637751	−	0.113960i
$634$	20.6548			0.820308
$635$	−0.306009	−	0.530024i	−0.0121436	−	0.0210333i
$636$		0			0
$637$		0			0
$638$		−	1.22442i		−	0.0484751i
$639$	13.2759	+	9.79005i	0.525187	+	0.387288i
$640$	0.317483	−	0.183299i	0.0125496	−	0.00724553i
$641$	10.2270	+	5.90456i	0.403942	+	0.233216i	0.688184	−	0.725537i	$-0.258408\pi$
$641$	10.2270	+	5.90456i	0.403942	+	0.233216i	−0.284241	+	0.958753i	$0.591742\pi$
$642$	−1.07054	+	19.1296i	−0.0422508	+	0.754985i
$643$	−25.3714	−	14.6482i	−1.00055	−	0.577668i	−0.0921392	−	0.995746i	$-0.529370\pi$
$643$	−25.3714	−	14.6482i	−1.00055	−	0.577668i	−0.908411	+	0.418078i	$0.862704\pi$
$644$		0			0
$645$	0.159599	−	2.85189i	0.00628421	−	0.112293i
$646$	−31.7166			−1.24787
$647$	−14.0841	−	24.3945i	−0.553705	−	0.959045i	−0.998003	−	0.0631660i	$-0.979880\pi$
$647$	−14.0841	−	24.3945i	−0.553705	−	0.959045i	0.444298	−	0.895879i	$-0.353453\pi$
$648$	−8.59808	+	2.65953i	−0.337764	+	0.104476i
$649$	−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	−0.528929	+	0.848666i	$0.677406\pi$
$653$	−39.0555	+	22.5487i	−1.52836	+	0.882399i	−0.999431	+	0.0337326i	$0.989261\pi$
$654$	10.0192	−	15.3091i	0.391780	−	0.598632i
$655$	2.48043	−	4.29623i	0.0969184	−	0.167868i
$656$	2.15928	−	3.73998i	0.0843057	−	0.146022i
$657$	−1.36339	+	12.1431i	−0.0531909	+	0.473748i
$658$		0			0
$659$	27.5435	−	15.9022i	1.07294	−	0.619463i	0.143958	−	0.989584i	$-0.454017\pi$
$659$	27.5435	−	15.9022i	1.07294	−	0.619463i	0.928984	+	0.370121i	$0.120684\pi$
$660$	−0.191639	−	0.379431i	−0.00745953	−	0.0147693i
$661$			19.7724i			0.769056i	0.923113	+	0.384528i	$0.125636\pi$
$661$			19.7724i			0.769056i	−0.923113	+	0.384528i	$0.874364\pi$
$662$			10.7114i			0.416309i
$663$	3.90185	+	7.72539i	0.151535	+	0.300029i
$664$	−14.7348	+	8.50712i	−0.571820	+	0.330140i
$665$		0			0
$666$	14.2076	−	6.20535i	0.550535	−	0.240452i
$667$	7.03663	−	12.1878i	0.272459	−	0.471913i
$668$	−9.67422	+	16.7562i	−0.374307	+	0.648318i
$669$	16.1595	−	24.6915i	0.624763	−	0.954627i
$670$	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	0.847230	−	0.531227i	$-0.178269\pi$
$673$	−0.945369	−	1.63743i	−0.0364413	−	0.0631182i	−0.883671	+	0.468109i	$0.844936\pi$
$674$	6.54008	+	3.77592i	0.251914	+	0.145443i
$675$	19.4779	+	16.1188i	0.749703	+	0.620411i
$676$	5.99843	+	10.3896i	0.230709	+	0.399600i
$677$	21.1322			0.812175			0.406088	−	0.913834i	$-0.366893\pi$
$677$	21.1322			0.812175			0.406088	+	0.913834i	$0.366893\pi$
$678$	0.402553	−	7.19326i	0.0154599	−	0.276255i
$679$		0			0
$680$	−1.58394	−	0.914490i	−0.0607415	−	0.0350691i
$681$	0.494561	−	8.83737i	0.0189516	−	0.338649i
$682$	3.66751	+	2.11744i	0.140436	+	0.0810810i
$683$	−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	$0.386685\pi$
$684$	17.4774	−	7.63345i	0.668265	−	0.291872i
$685$		−	3.29517i		−	0.125902i
$686$		0			0
$687$	14.4804	−	22.1258i	0.552463	−	0.844153i
$688$	2.24922	+	3.89576i	0.0857506	+	0.148524i
$689$		0			0
$690$	0.272995	−	4.87817i	0.0103927	−	0.185709i
$691$			18.1370i			0.689964i	0.938609	+	0.344982i	$0.112115\pi$
$691$			18.1370i			0.689964i	−0.938609	+	0.344982i	$0.887885\pi$
$692$	4.83654			0.183858
$693$		0			0
$694$	−10.9320			−0.414972
$695$			3.40908i			0.129314i
$696$	2.65068	+	1.73476i	0.100474	+	0.0657559i
$697$	−21.5456			−0.816097
$698$	−0.592145	−	1.02562i	−0.0224130	−	0.0388205i
$699$	17.6272	+	0.986465i	0.666724	+	0.0373115i
$700$		0			0
$701$			35.6167i			1.34523i	0.739995	+	0.672613i	$0.234828\pi$
$701$			35.6167i			1.34523i	−0.739995	+	0.672613i	$0.765172\pi$
$702$	−4.00943	−	3.31798i	−0.151326	−	0.125229i
$703$	−28.4519	+	16.4267i	−1.07308	+	0.619545i
$704$	0.579764	+	0.334727i	0.0218507	+	0.0126155i
$705$	−4.42519	−	2.89610i	−0.166662	−	0.109074i
$706$	−29.0832	−	16.7912i	−1.09456	−	0.631946i
$707$		0			0
$708$	13.4923	−	6.81453i	0.507071	−	0.256106i
$709$	−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
$711$	14.8774	−	20.1747i	0.557947	−	0.756611i
$712$	−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
$717$	33.1715	+	1.85636i	1.23881	+	0.0693270i
$718$	−5.06407	+	8.77122i	−0.188989	+	0.327339i
$719$	−12.8915	+	22.3287i	−0.480770	+	0.832718i	−0.999757	−	0.0220642i	$-0.992976\pi$
$719$	−12.8915	+	22.3287i	−0.480770	+	0.832718i	0.518986	+	0.854782i	$0.326310\pi$
$720$	1.09293	+	0.122710i	0.0407310	+	0.00457314i
$721$		0			0
$722$	−18.5453	+	10.7072i	−0.690186	+	0.398479i
$723$	−35.7719	−	2.00189i	−1.33037	−	0.0744510i
$724$			5.66796i			0.210648i
$725$		−	8.89910i		−	0.330504i
$726$	−10.0083	+	15.2924i	−0.371441	+	0.567555i
$727$	−1.32423	+	0.764544i	−0.0491129	+	0.0283554i	−0.524355	−	0.851499i	$-0.675694\pi$
$727$	−1.32423	+	0.764544i	−0.0491129	+	0.0283554i	0.475242	+	0.879855i	$0.342360\pi$
$728$		0			0
$729$	−25.4953	−	8.88761i	−0.944270	−	0.329171i
$730$	0.746603	−	1.29315i	0.0276330	−	0.0478618i
$731$	11.2215	−	19.4362i	0.415042	−	0.718873i
$732$	3.87128	+	7.66485i	0.143087	+	0.283301i
$733$	−17.9908	+	10.3870i	−0.664504	+	0.383651i	−0.793991	−	0.607930i	$-0.792000\pi$
$733$	−17.9908	+	10.3870i	−0.664504	+	0.383651i	0.129487	+	0.991581i	$0.458667\pi$
$734$	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
$738$	11.8727	−	5.18552i	0.437039	−	0.190882i
$739$	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	$0.763270\pi$
$740$	−1.89454			−0.0696446
$741$	9.22773	+	6.03917i	0.338989	+	0.221854i
$742$		0			0
$743$	−37.5906	−	21.7029i	−1.37907	−	0.796204i	−0.387019	−	0.922072i	$-0.626495\pi$
$743$	−37.5906	−	21.7029i	−1.37907	−	0.796204i	−0.992047	+	0.125868i	$0.959828\pi$
$744$	−9.78010	+	4.93962i	−0.358556	+	0.181095i
$745$	0.899148	+	0.519124i	0.0329422	+	0.0190192i
$746$	14.2106	−	8.20451i	0.520288	−	0.300389i
$747$	−50.7240	−	5.69512i	−1.85590	−	0.208374i
$748$		−	3.33994i		−	0.122120i
$749$		0			0
$750$	−2.82415	−	5.59160i	−0.103123	−	0.204176i
$751$	−1.15691	−	2.00383i	−0.0422164	−	0.0731209i	0.844145	−	0.536115i	$-0.180109\pi$
$751$	−1.15691	−	2.00383i	−0.0422164	−	0.0731209i	−0.886362	+	0.462994i	$0.846775\pi$
$752$	8.32901			0.303728
$753$	−2.80144	+	1.41492i	−0.102090	+	0.0515626i
$754$			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
$759$	7.96394	−	4.02234i	0.289073	−	0.146002i
$760$	−2.33055			−0.0845378
$761$	−11.6690	−	20.2112i	−0.422999	−	0.732656i	0.573232	−	0.819393i	$-0.305689\pi$
$761$	−11.6690	−	20.2112i	−0.422999	−	0.732656i	−0.996231	+	0.0867370i	$0.972356\pi$
$762$	1.30361	+	2.58105i	0.0472248	+	0.0935016i
$763$		0			0
$764$		−	27.3777i		−	0.990490i
$765$	−2.19615	−	5.02826i	−0.0794021	−	0.181797i
$766$	−7.42567	+	4.28721i	−0.268300	+	0.154903i
$767$	7.56959	+	4.37030i	0.273322	+	0.157803i
$768$	−1.54605	+	0.780860i	−0.0557881	+	0.0281769i
$769$	15.8266	+	9.13748i	0.570721	+	0.329506i	0.757437	−	0.652908i	$-0.226451\pi$
$769$	15.8266	+	9.13748i	0.570721	+	0.329506i	−0.186716	+	0.982414i	$0.559784\pi$
$770$		0			0
$771$	9.35568	+	6.12290i	0.336937	+	0.220511i
$772$	10.0283			0.360925
$773$	−0.219254	−	0.379758i	−0.00788600	−	0.0136590i	0.862055	−	0.506814i	$-0.169177\pi$
$773$	−0.219254	−	0.379758i	−0.00788600	−	0.0136590i	−0.869941	+	0.493155i	$0.835844\pi$
$774$	−1.50575	+	13.4110i	−0.0541229	+	0.482050i
$775$	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
$780$	0.286710	+	0.567664i	0.0102659	+	0.0203256i
$781$	1.84047	−	3.18779i	0.0658573	−	0.114068i
$782$	19.1944	−	33.2456i	0.686390	−	1.18886i
$783$	3.31128	+	8.90814i	0.118335	+	0.318351i
$784$		0			0
$785$	−0.899924	+	0.519571i	−0.0321197	+	0.0185443i
$786$	−12.8350	+	19.6117i	−0.457810	+	0.699526i
$787$		−	38.2572i		−	1.36372i	−0.731481	−	0.681861i	$-0.761171\pi$
$787$		−	38.2572i		−	1.36372i	0.731481	−	0.681861i	$-0.238829\pi$
$788$			18.8258i			0.670643i
$789$	−15.2539	−	0.853646i	−0.543053	−	0.0303906i
$790$	−2.65279	+	1.53159i	−0.0943820	+	0.0544915i
$791$		0			0
$792$	0.803848	+	1.84047i	0.0285635	+	0.0653983i
$793$	−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	0.362832	+	0.931855i	$0.381810\pi$
$797$	−17.6613	+	30.5902i	−0.625594	+	1.08356i	−0.988426	+	0.151706i	$0.951523\pi$
$798$		0			0
$799$	−20.7770	−	35.9868i	−0.735036	−	1.27312i
$800$	4.21374	+	2.43280i	0.148978	+	0.0860126i
$801$	−12.8616	−	29.4477i	−0.454444	−	1.04048i
$802$	−0.0954357	−	0.165300i	−0.00336995	−	0.00583693i
$803$	2.72678			0.0962259
$804$	−16.8376	+	8.50414i	−0.593816	+	0.299918i
$805$		0			0
$806$	−5.48694	−	3.16789i	−0.193269	−	0.111584i
$807$	−20.6743	−	13.5305i	−0.727769	−	0.476295i
$808$	−13.6241	−	7.86586i	−0.479293	−	0.276720i
$809$	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	$0.208348\pi$
$810$	2.42037	+	2.24226i	0.0850433	+	0.0787849i
$811$			17.0184i			0.597598i	0.954316	+	0.298799i	$0.0965860\pi$
$811$			17.0184i			0.597598i	−0.954316	+	0.298799i	$0.903414\pi$
$812$		0			0
$813$	−5.27937	−	0.295447i	−0.185156	−	0.0103618i
$814$	−1.72983	−	2.99615i	−0.0606305	−	0.105015i
$815$	−9.06527			−0.317542
$816$	7.23048	+	4.73205i	0.253118	+	0.165655i
$817$		−	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	$-0.142469\pi$
$822$	−0.869894	+	15.5442i	−0.0303410	+	0.542167i
$823$	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
$825$	3.08950	−	4.72069i	0.107562	−	0.164353i
$826$		0			0
$827$			49.7585i			1.73027i	0.501537	+	0.865136i	$0.332768\pi$
$827$			49.7585i			1.73027i	−0.501537	+	0.865136i	$0.667232\pi$
$828$	−2.57558	+	22.9396i	−0.0895077	+	0.797207i
$829$	−37.3422	+	21.5595i	−1.29695	+	0.748793i	−0.979876	−	0.199609i	$-0.936033\pi$
$829$	−37.3422	+	21.5595i	−1.29695	+	0.748793i	−0.317071	+	0.948402i	$0.602699\pi$
$830$	5.40174	+	3.11870i	0.187497	+	0.108252i
$831$	0.122488	−	2.18876i	0.00424907	−	0.0759271i
$832$	−0.867380	−	0.500782i	−0.0300710	−	0.0173615i
$833$		0			0
$834$	0.899965	−	16.0816i	0.0311632	−	0.556859i
$835$	7.09310			0.245467
$836$	−2.12793	−	3.68569i	−0.0735961	−	0.127472i
$837$	−32.4090	−	5.48694i	−1.12022	−	0.189656i
$838$	−1.21929	−	0.703955i	−0.0421195	−	0.0243177i
$839$	−14.9985	−	25.9782i	−0.517807	−	0.896868i	−0.999786	−	0.0206851i	$-0.993415\pi$
$839$	−14.9985	−	25.9782i	−0.517807	−	0.896868i	0.481979	−	0.876183i	$-0.339918\pi$
$840$		0			0
$841$	−12.8274	+	22.2177i	−0.442325	+	0.766129i
$842$	−26.3151	+	15.1930i	−0.906878	+	0.523586i
$843$	−9.98442	+	15.2560i	−0.343882	+	0.525445i
$844$	0.828981	−	1.43584i	0.0285347	−	0.0494235i
$845$	2.19901	−	3.80881i	0.0756484	−	0.131027i
$846$	20.1103	+	14.8299i	0.691407	+	0.509863i
$847$		0			0
$848$		0			0
$849$	15.5171	+	30.7226i	0.532544	+	1.05440i
$850$		−	24.2748i		−	0.832619i
$851$		−	39.7648i		−	1.36312i
$852$	4.29351	+	8.50083i	0.147093	+	0.291234i
$853$	25.7693	−	14.8779i	0.882325	−	0.509411i	0.0109007	−	0.999941i	$-0.496530\pi$
$853$	25.7693	−	14.8779i	0.882325	−	0.509411i	0.871424	+	0.490530i	$0.163197\pi$
$854$		0			0
$855$	−5.62708	−	4.14957i	−0.192442	−	0.141912i
$856$	−5.53088	+	9.57976i	−0.189042	+	0.327430i
$857$	−22.9296	+	39.7152i	−0.783260	+	1.35665i	0.146773	+	0.989170i	$0.453111\pi$
$857$	−22.9296	+	39.7152i	−0.783260	+	1.35665i	−0.930033	+	0.367476i	$0.880222\pi$
$858$	−0.635960	+	0.971735i	−0.0217113	+	0.0331745i
$859$	−3.24073	+	1.87104i	−0.110572	+	0.0638390i	−0.554266	−	0.832339i	$-0.687001\pi$
$859$	−3.24073	+	1.87104i	−0.110572	+	0.0638390i	0.443694	+	0.896178i	$0.353668\pi$
$860$	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	$0.846106\pi$
$864$	−5.12325	−	0.867380i	−0.174296	−	0.0295089i
$865$	−0.886533	−	1.53552i	−0.0301430	−	0.0522092i
$866$	8.15047			0.276964
$867$	0.763654	−	13.6458i	0.0259350	−	0.463436i
$868$		0			0
$869$	−4.84432	−	2.79687i	−0.164332	−	0.0948773i
$870$	0.0648900	−	1.15953i	0.00219998	−	0.0393117i
$871$	−9.44641	−	5.45389i	−0.320080	−	0.184798i
$872$	9.14811	−	5.28166i	0.309794	−	0.178860i
$873$	5.76257	−	51.3247i	0.195033	−	1.73708i
$874$		−	48.9162i		−	1.65462i
$875$		0			0
$876$	−3.86331	+	5.90307i	−0.130529	+	0.199446i
$877$	10.1962	+	17.6603i	0.344300	+	0.596344i	0.985226	−	0.171258i	$-0.0547831\pi$
$877$	10.1962	+	17.6603i	0.344300	+	0.596344i	−0.640927	+	0.767602i	$0.721450\pi$
$878$	12.2404			0.413094
$879$	1.29800	−	23.1942i	0.0437806	−	0.782320i
$880$		−	0.245420i		−	0.00827312i
$881$	−21.2010			−0.714280			−0.357140	−	0.934051i	$-0.616248\pi$
$881$	−21.2010			−0.714280			−0.357140	+	0.934051i	$0.616248\pi$
$882$		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
$885$	−4.63662	−	3.03447i	−0.155858	−	0.102003i
$886$	−8.00836			−0.269046
$887$	3.09606	+	5.36253i	0.103955	+	0.180056i	0.913311	−	0.407263i	$-0.133517\pi$
$887$	3.09606	+	5.36253i	0.103955	+	0.180056i	−0.809356	+	0.587319i	$0.800183\pi$
$888$	8.93706	+	0.500140i	0.299908	+	0.0167836i
$889$		0			0
$890$			3.92675i			0.131625i
$891$	−1.33611	+	5.87507i	−0.0447613	+	0.196822i
$892$	14.7546	−	8.51860i	0.494022	−	0.285224i
$893$	−45.8555	−	26.4747i	−1.53450	−	0.885941i
$894$	−4.10449	−	2.68622i	−0.137275	−	0.0898405i
$895$	1.16134	+	0.670501i	0.0388194	+	0.0224124i
$896$		0			0
$897$	−11.9148	+	6.01779i	−0.397824	+	0.200928i
$898$	−14.5183			−0.484483
$899$	5.78495	+	10.0198i	0.192939	+	0.334180i
$900$	5.84239	+	13.3766i	0.194746	+	0.445887i
$901$		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
$906$	−28.6238	−	1.60186i	−0.950963	−	0.0532183i
$907$	0.0645566	−	0.111815i	0.00214357	−	0.00371277i	−0.864952	−	0.501855i	$-0.832651\pi$
$907$	0.0645566	−	0.111815i	0.00214357	−	0.00371277i	0.867095	+	0.498142i	$0.165984\pi$
$908$	2.55512	−	4.42560i	0.0847946	−	0.146869i
$909$	−18.8899	−	43.2499i	−0.626539	−	1.43451i
$910$		0			0
$911$	29.6682	−	17.1290i	0.982952	−	0.567508i	0.0797919	−	0.996812i	$-0.474574\pi$
$911$	29.6682	−	17.1290i	0.982952	−	0.567508i	0.903160	+	0.429304i	$0.141241\pi$
$912$	10.9938	+	0.615242i	0.364042	+	0.0203727i
$913$			11.3902i			0.376962i
$914$			9.95501i			0.329283i
$915$	1.72386	−	2.63403i	0.0569891	−	0.0870783i
$916$	13.2215	−	7.63345i	0.436851	−	0.252216i
$917$		0			0
$918$	9.03245	+	24.2995i	0.298115	+	0.802002i
$919$	−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	$0.242486\pi$
$920$	1.41041	−	2.44290i	0.0464999	−	0.0805401i
$921$	0.510470	+	1.01069i	0.0168206	+	0.0333035i
$922$	−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
$927$	−3.83079	+	34.1192i	−0.125819	+	1.12062i
$928$	0.914490	+	1.58394i	0.0300196	+	0.0519955i
$929$	11.7473			0.385415			0.192708	−	0.981256i	$-0.438273\pi$
$929$	11.7473			0.385415			0.192708	+	0.981256i	$0.438273\pi$
$930$	3.36093	+	2.19959i	0.110209	+	0.0721274i
$931$		0			0
$932$	8.82741	+	5.09651i	0.289152	+	0.166942i
$933$	−14.2931	+	7.21899i	−0.467935	+	0.236339i
$934$	17.8941	+	10.3312i	0.585512	+	0.338046i
$935$	−1.06038	+	0.612209i	−0.0346780	+	0.0200214i
$936$	−1.20263	−	2.75352i	−0.0393092	−	0.0900016i
$937$		−	2.63611i		−	0.0861179i	−0.999073	−	0.0430589i	$-0.986290\pi$
$937$		−	2.63611i		−	0.0861179i	0.999073	−	0.0430589i	$-0.0137103\pi$
$938$		0			0
$939$	−4.81333	−	9.53004i	−0.157077	−	0.311001i
$940$	−1.52670	−	2.64432i	−0.0497954	−	0.0862482i
$941$	−11.9311			−0.388944			−0.194472	−	0.980908i	$-0.562299\pi$
$941$	−11.9311			−0.388944			−0.194472	+	0.980908i	$0.562299\pi$
$942$	4.38235	−	2.21339i	0.142785	−	0.0721162i
$943$		−	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	$0.959866\pi$
$948$	12.9183	−	6.52461i	0.419566	−	0.211910i
$949$	−4.07951			−0.132427
$950$	−15.4659	−	26.7877i	−0.501779	−	0.869107i
$951$	16.1285	+	31.9333i	0.523003	+	1.03551i
$952$		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
$957$	1.89301	−	0.956098i	0.0611922	−	0.0309063i
$958$	8.79955	+	5.08042i	0.284301	+	0.164141i
$959$		0			0
$960$	0.531299	+	0.347713i	0.0171476	+	0.0112224i
$961$	−9.01672			−0.290862
$962$	2.58799	+	4.48252i	0.0834400	+	0.144522i
$963$	−30.4112	+	13.2824i	−0.979986	+	0.428020i
$964$	−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	−0.900458	−	0.434942i	$-0.856769\pi$
$967$	−2.28741	+	3.96191i	−0.0735581	+	0.127406i	0.826900	+	0.562349i	$0.190102\pi$
$968$	−9.13815	+	5.27592i	−0.293711	+	0.169574i
$969$	−24.7662	−	49.0353i	−0.795605	−	1.57524i
$970$	−3.15563	+	5.46571i	−0.101321	+	0.175493i
$971$	−12.9222	+	22.3820i	−0.414694	+	0.718271i	−0.995396	−	0.0958449i	$-0.969445\pi$
$971$	−12.9222	+	22.3820i	−0.414694	+	0.718271i	0.580702	+	0.814116i	$0.302778\pi$
$972$	−10.8256	−	11.2163i	−0.347233	−	0.359763i
$973$		0			0
$974$	−27.0457	+	15.6148i	−0.866599	+	0.500331i
$975$	−4.62218	+	7.06260i	−0.148028	+	0.226184i
$976$			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	$0.839910\pi$
$978$	42.7634	+	2.39315i	1.36742	+	0.0765244i
$979$	−6.21003	+	3.58536i	−0.198474	+	0.114589i
$980$		0			0
$981$	31.4921	+	3.53583i	1.00547	+	0.112890i
$982$	−10.2950	+	17.8314i	−0.328526	+	0.569023i
$983$	6.30293	−	10.9170i	0.201032	−	0.348198i	−0.747829	−	0.663891i	$-0.768904\pi$
$983$	6.30293	−	10.9170i	0.201032	−	0.348198i	0.948861	+	0.315693i	$0.102237\pi$
$984$	7.46828	+	0.417944i	0.238080	+	0.0133236i
$985$	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
$990$	0.436975	−	0.592565i	0.0138880	−	0.0188330i
$991$	−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	$-0.473204\pi$
$992$	−6.32588			−0.200847
$993$	−16.5603	+	8.36407i	−0.525524	+	0.265426i
$994$		0			0
$995$	1.70300	+	0.983227i	0.0539887	+	0.0311704i
$996$	−24.6582	−	16.1378i	−0.781325	−	0.511345i
$997$	35.1469	+	20.2921i	1.11311	+	0.642656i	0.939634	−	0.342181i	$-0.111166\pi$
$997$	35.1469	+	20.2921i	1.11311	+	0.642656i	0.173479	+	0.984837i	$0.444499\pi$
$998$	−21.7834	+	12.5766i	−0.689540	+	0.398106i
$999$	20.6879	+	17.1202i	0.654537	+	0.541658i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.6	✓	16	7.5	odd	6
126.2.m.a.41.7	yes	16	7.2	even	3
126.2.m.a.83.6	yes	16	63.2	odd	6
126.2.m.a.83.7	yes	16	63.47	even	6
378.2.m.a.125.2		16	21.2	odd	6
378.2.m.a.125.3		16	21.5	even	6
378.2.m.a.251.2		16	63.61	odd	6
378.2.m.a.251.3		16	63.16	even	3
882.2.l.a.227.1		16	63.38	even	6	inner
882.2.l.a.227.4		16	63.11	odd	6	inner
882.2.l.a.509.5		16	1.1	even	1	trivial
882.2.l.a.509.8		16	7.6	odd	2	inner
882.2.t.b.803.1		16	9.2	odd	6
882.2.t.b.803.4		16	63.20	even	6
882.2.t.b.815.1		16	7.3	odd	6
882.2.t.b.815.4		16	7.4	even	3
1008.2.cc.b.209.4		16	252.47	odd	6
1008.2.cc.b.209.5		16	252.191	even	6
1008.2.cc.b.545.4		16	28.23	odd	6
1008.2.cc.b.545.5		16	28.19	even	6
1134.2.d.a.1133.4		16	63.5	even	6
1134.2.d.a.1133.5		16	63.23	odd	6
1134.2.d.a.1133.12		16	63.58	even	3
1134.2.d.a.1133.13		16	63.40	odd	6
2646.2.l.b.521.6		16	63.52	odd	6
2646.2.l.b.521.7		16	63.25	even	3
2646.2.l.b.1097.2		16	3.2	odd	2
2646.2.l.b.1097.3		16	21.20	even	2
2646.2.t.a.1979.6		16	9.7	even	3
2646.2.t.a.1979.7		16	63.34	odd	6
2646.2.t.a.2285.6		16	21.17	even	6
2646.2.t.a.2285.7		16	21.11	odd	6
3024.2.cc.b.881.4		16	84.23	even	6
3024.2.cc.b.881.5		16	84.47	odd	6
3024.2.cc.b.2897.4		16	252.187	even	6
3024.2.cc.b.2897.5		16	252.79	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.54605 + 0.780860i) q^{3} -1.00000 q^{4} +(0.183299 + 0.317483i) q^{5} +(-0.780860 - 1.54605i) q^{6} -1.00000i q^{8} +(1.78052 - 2.41449i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-1.54605 + 0.780860i) q^{3} -1.00000 q^{4} +(0.183299 + 0.317483i) q^{5} +(-0.780860 - 1.54605i) q^{6} -1.00000i q^{8} +(1.78052 - 2.41449i) q^{9} +(-0.317483 + 0.183299i) q^{10} +(-0.579764 - 0.334727i) q^{11} +(1.54605 - 0.780860i) q^{12} +(0.867380 + 0.500782i) q^{13} +(-0.531299 - 0.347713i) q^{15} +1.00000 q^{16} +(-2.49453 - 4.32065i) q^{17} +(2.41449 + 1.78052i) q^{18} +(-5.50552 - 3.17861i) q^{19} +(-0.183299 - 0.317483i) q^{20} +(0.334727 - 0.579764i) q^{22} +(6.66371 - 3.84729i) q^{23} +(0.780860 + 1.54605i) q^{24} +(2.43280 - 4.21374i) q^{25} +(-0.500782 + 0.867380i) q^{26} +(-0.867380 + 5.12325i) q^{27} +(1.58394 - 0.914490i) q^{29} +(0.347713 - 0.531299i) q^{30} +6.32588i q^{31} +1.00000i q^{32} +(1.15772 + 0.0647887i) q^{33} +(4.32065 - 2.49453i) q^{34} +(-1.78052 + 2.41449i) q^{36} +(2.58394 - 4.47552i) q^{37} +(3.17861 - 5.50552i) q^{38} +(-1.73205 - 0.0969299i) q^{39} +(0.317483 - 0.183299i) q^{40} +(2.15928 - 3.73998i) q^{41} +(2.24922 + 3.89576i) q^{43} +(0.579764 + 0.334727i) q^{44} +(1.09293 + 0.122710i) q^{45} +(3.84729 + 6.66371i) q^{46} +8.32901 q^{47} +(-1.54605 + 0.780860i) q^{48} +(4.21374 + 2.43280i) q^{50} +(7.23048 + 4.73205i) q^{51} +(-0.867380 - 0.500782i) q^{52} +(-5.12325 - 0.867380i) q^{54} -0.245420i q^{55} +(10.9938 + 0.615242i) q^{57} +(0.914490 + 1.58394i) q^{58} +8.72695 q^{59} +(0.531299 + 0.347713i) q^{60} +4.95771i q^{61} -6.32588 q^{62} -1.00000 q^{64} +0.367172i q^{65} +(-0.0647887 + 1.15772i) q^{66} -10.8907 q^{67} +(2.49453 + 4.32065i) q^{68} +(-7.29820 + 11.1515i) q^{69} +5.49843i q^{71} +(-2.41449 - 1.78052i) q^{72} +(-3.52744 + 2.03657i) q^{73} +(4.47552 + 2.58394i) q^{74} +(-0.470886 + 8.41431i) q^{75} +(5.50552 + 3.17861i) q^{76} +(0.0969299 - 1.73205i) q^{78} +8.35568 q^{79} +(0.183299 + 0.317483i) q^{80} +(-2.65953 - 8.59808i) q^{81} +(3.73998 + 2.15928i) q^{82} +(-8.50712 - 14.7348i) q^{83} +(0.914490 - 1.58394i) q^{85} +(-3.89576 + 2.24922i) q^{86} +(-1.73476 + 2.65068i) q^{87} +(-0.334727 + 0.579764i) q^{88} +(5.35566 - 9.27628i) q^{89} +(-0.122710 + 1.09293i) q^{90} +(-6.66371 + 3.84729i) q^{92} +(-4.93962 - 9.78010i) q^{93} +8.32901i q^{94} -2.33055i q^{95} +(-0.780860 - 1.54605i) q^{96} +(14.9093 - 8.60787i) q^{97} +(-1.84047 + 0.803848i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 12 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 - 12 * q^9	\( 16 q - 16 q^{4} - 12 q^{9} + 12 q^{11} + 16 q^{16} + 12 q^{18} + 48 q^{23} - 8 q^{25} - 12 q^{29} + 12 q^{30} + 12 q^{36} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} + 60 q^{50} + 24 q^{51} + 48 q^{57} - 12 q^{58} - 16 q^{64} + 56 q^{67} - 12 q^{72} - 36 q^{74} - 24 q^{78} + 8 q^{79} - 12 q^{85} + 24 q^{86} - 48 q^{92} + 84 q^{93} - 72 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 - 12 * q^9 + 12 * q^11 + 16 * q^16 + 12 * q^18 + 48 * q^23 - 8 * q^25 - 12 * q^29 + 12 * q^30 + 12 * q^36 + 4 * q^37 + 4 * q^43 - 12 * q^44 - 12 * q^46 + 60 * q^50 + 24 * q^51 + 48 * q^57 - 12 * q^58 - 16 * q^64 + 56 * q^67 - 12 * q^72 - 36 * q^74 - 24 * q^78 + 8 * q^79 - 12 * q^85 + 24 * q^86 - 48 * q^92 + 84 * q^93 - 72 * q^99

Introduction

L-functions

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