LMFDB - Embedded newform 882.2.t.b.815.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(803,882)]

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, 5]))

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

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

chi := DirichletCharacter("882.803");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.04280545828$
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			815.1
Root			$-0.0967785 - 1.72934i$ of defining polynomial
Character	$\chi$	$=$	882.815
Dual form			882.2.t.b.803.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.44927 - 0.948485i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.366598 q^{5} +(0.780860 + 1.54605i) q^{6} -1.00000i q^{8} +(1.20075 + 2.74922i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.44927 - 0.948485i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.366598 q^{5} +(0.780860 + 1.54605i) q^{6} -1.00000i q^{8} +(1.20075 + 2.74922i) q^{9} +(-0.317483 - 0.183299i) q^{10} +0.669453i q^{11} +(0.0967785 - 1.72934i) q^{12} +(-0.867380 - 0.500782i) q^{13} +(-0.531299 - 0.347713i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.49453 - 4.32065i) q^{17} +(0.334727 - 2.98127i) q^{18} +(-5.50552 + 3.17861i) q^{19} +(0.183299 + 0.317483i) q^{20} +(0.334727 - 0.579764i) q^{22} +7.69459i q^{23} +(-0.948485 + 1.44927i) q^{24} -4.86561 q^{25} +(0.500782 + 0.867380i) q^{26} +(0.867380 - 5.12325i) q^{27} +(1.58394 - 0.914490i) q^{29} +(0.286262 + 0.566778i) q^{30} +(-5.47837 + 3.16294i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.634967 - 0.970217i) q^{33} +(-4.32065 + 2.49453i) q^{34} +(-1.78052 + 2.41449i) q^{36} +(2.58394 + 4.47552i) q^{37} +6.35722 q^{38} +(0.782082 + 1.54846i) q^{39} -0.366598i q^{40} +(-2.15928 + 3.73998i) q^{41} +(2.24922 + 3.89576i) q^{43} +(-0.579764 + 0.334727i) q^{44} +(0.440193 + 1.00786i) q^{45} +(3.84729 - 6.66371i) q^{46} +(4.16450 - 7.21313i) q^{47} +(1.54605 - 0.780860i) q^{48} +(4.21374 + 2.43280i) q^{50} +(-7.71332 + 3.89576i) q^{51} -1.00156i q^{52} +(-3.31280 + 4.00317i) q^{54} +0.245420i q^{55} +(10.9938 + 0.615242i) q^{57} -1.82898 q^{58} +(4.36348 + 7.55776i) q^{59} +(0.0354788 - 0.633975i) q^{60} +(4.29351 + 2.47886i) q^{61} +6.32588 q^{62} -1.00000 q^{64} +(-0.317980 - 0.183586i) q^{65} +(-1.03501 + 0.522749i) q^{66} +(5.44537 + 9.43166i) q^{67} +4.98906 q^{68} +(7.29820 - 11.1515i) q^{69} +5.49843i q^{71} +(2.74922 - 1.20075i) q^{72} +(-3.52744 - 2.03657i) q^{73} -5.16789i q^{74} +(7.05156 + 4.61495i) q^{75} +(-5.50552 - 3.17861i) q^{76} +(0.0969299 - 1.73205i) q^{78} +(-4.17784 + 7.23623i) q^{79} +(-0.183299 + 0.317483i) q^{80} +(-6.11639 + 6.60226i) q^{81} +(3.73998 - 2.15928i) q^{82} +(8.50712 + 14.7348i) q^{83} +(0.914490 - 1.58394i) q^{85} -4.49843i q^{86} +(-3.16294 - 0.177006i) q^{87} +0.669453 q^{88} +(-5.35566 - 9.27628i) q^{89} +(0.122710 - 1.09293i) q^{90} +(-6.66371 + 3.84729i) q^{92} +(10.9396 + 0.612209i) q^{93} +(-7.21313 + 4.16450i) q^{94} +(-2.01831 + 1.16527i) q^{95} +(-1.72934 - 0.0967785i) q^{96} +(-14.9093 + 8.60787i) q^{97} +(-1.84047 + 0.803848i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} - 8 q^{16} + 16 q^{25} - 12 q^{29} + 12 q^{30} + 12 q^{36} + 4 q^{37} + 36 q^{39} + 4 q^{43} + 12 q^{44} - 12 q^{46} + 60 q^{50} - 36 q^{51} + 48 q^{57} + 24 q^{58} - 24 q^{60} - 16 q^{64} - 84 q^{65} - 28 q^{67} + 12 q^{72} - 24 q^{78} - 4 q^{79} - 36 q^{81} - 12 q^{85} - 48 q^{92} + 12 q^{93} - 12 q^{95} - 72 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 - 8 * q^16 + 16 * q^25 - 12 * q^29 + 12 * q^30 + 12 * q^36 + 4 * q^37 + 36 * q^39 + 4 * q^43 + 12 * q^44 - 12 * q^46 + 60 * q^50 - 36 * q^51 + 48 * q^57 + 24 * q^58 - 24 * q^60 - 16 * q^64 - 84 * q^65 - 28 * q^67 + 12 * q^72 - 24 * q^78 - 4 * q^79 - 36 * q^81 - 12 * q^85 - 48 * q^92 + 12 * q^93 - 12 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.44927	−	0.948485i	−0.836735	−	0.547608i
$3$	−1.44927	−	0.948485i	−0.836735	−	0.547608i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.366598			0.163948			0.0819738	−	0.996634i	$-0.473878\pi$
$5$	0.366598			0.163948			0.0819738	+	0.996634i	$0.473878\pi$
$6$	0.780860	+	1.54605i	0.318785	+	0.631171i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	1.20075	+	2.74922i	0.400251	+	0.916406i
$10$	−0.317483	−	0.183299i	−0.100397	−	0.0579643i
$11$			0.669453i			0.201848i	0.994894	+	0.100924i	$0.0321799\pi$
$11$			0.669453i			0.201848i	−0.994894	+	0.100924i	$0.967820\pi$
$12$	0.0967785	−	1.72934i	0.0279375	−	0.499219i
$13$	−0.867380	−	0.500782i	−0.240568	−	0.138892i	0.374870	−	0.927077i	$-0.377687\pi$
$13$	−0.867380	−	0.500782i	−0.240568	−	0.138892i	−0.615438	+	0.788185i	$0.711021\pi$
$14$		0			0
$15$	−0.531299	−	0.347713i	−0.137181	−	0.0897791i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	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	$-0.0401653\pi$
$18$	0.334727	−	2.98127i	0.0788958	−	0.702692i
$19$	−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
$23$			7.69459i			1.60443i	0.597034	+	0.802216i	$0.296346\pi$
$23$			7.69459i			1.60443i	−0.597034	+	0.802216i	$0.703654\pi$
$24$	−0.948485	+	1.44927i	−0.193609	+	0.295830i
$25$	−4.86561			−0.973121
$26$	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	$0.279016\pi$
$30$	0.286262	+	0.566778i	0.0522640	+	0.103479i
$31$	−5.47837	+	3.16294i	−0.983944	+	0.568081i	−0.903459	−	0.428675i	$-0.858980\pi$
$31$	−5.47837	+	3.16294i	−0.983944	+	0.568081i	−0.0804857	+	0.996756i	$0.525647\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	0.634967	−	0.970217i	0.110533	−	0.168893i
$34$	−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	0.996402	−	0.0847585i	$-0.0270119\pi$
$37$	2.58394	+	4.47552i	0.424798	+	0.735771i	−0.571604	+	0.820530i	$0.693679\pi$
$38$	6.35722			1.03128
$39$	0.782082	+	1.54846i	0.125233	+	0.247953i
$40$		−	0.366598i		−	0.0579643i
$41$	−2.15928	+	3.73998i	−0.337223	+	0.584087i	−0.983909	−	0.178669i	$-0.942821\pi$
$41$	−2.15928	+	3.73998i	−0.337223	+	0.584087i	0.646686	+	0.762756i	$0.276154\pi$
$42$		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
$45$	0.440193	+	1.00786i	0.0656202	+	0.150243i
$46$	3.84729	−	6.66371i	0.567252	−	0.982510i
$47$	4.16450	−	7.21313i	0.607455	−	1.05214i	−0.384203	−	0.923249i	$-0.625524\pi$
$47$	4.16450	−	7.21313i	0.607455	−	1.05214i	0.991658	−	0.128895i	$-0.0411429\pi$
$48$	1.54605	−	0.780860i	0.223153	−	0.112707i
$49$		0			0
$50$	4.21374	+	2.43280i	0.595913	+	0.344050i
$51$	−7.71332	+	3.89576i	−1.08008	+	0.545515i
$52$		−	1.00156i		−	0.138892i
$53$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$53$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$54$	−3.31280	+	4.00317i	−0.450815	+	0.544763i
$55$			0.245420i			0.0330925i
$56$		0			0
$57$	10.9938	+	0.615242i	1.45617	+	0.0814909i
$58$	−1.82898			−0.240157
$59$	4.36348	+	7.55776i	0.568076	+	0.983937i	0.996756	+	0.0804804i	$0.0256455\pi$
$59$	4.36348	+	7.55776i	0.568076	+	0.983937i	−0.428680	+	0.903456i	$0.641021\pi$
$60$	0.0354788	−	0.633975i	0.00458029	−	0.0818458i
$61$	4.29351	+	2.47886i	0.549727	+	0.317385i	0.749012	−	0.662556i	$-0.230529\pi$
$61$	4.29351	+	2.47886i	0.549727	+	0.317385i	−0.199285	+	0.979942i	$0.563862\pi$
$62$	6.32588			0.803387
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.317980	−	0.183586i	−0.0394406	−	0.0227710i
$66$	−1.03501	+	0.522749i	−0.127400	+	0.0643460i
$67$	5.44537	+	9.43166i	0.665258	+	1.15226i	0.979215	+	0.202823i	$0.0650117\pi$
$67$	5.44537	+	9.43166i	0.665258	+	1.15226i	−0.313958	+	0.949437i	$0.601655\pi$
$68$	4.98906			0.605013
$69$	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	$0.894207\pi$
$72$	2.74922	−	1.20075i	0.323998	−	0.141510i
$73$	−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	$0.743277\pi$
$74$		−	5.16789i		−	0.600755i
$75$	7.05156	+	4.61495i	0.814244	+	0.532889i
$76$	−5.50552	−	3.17861i	−0.631526	−	0.364612i
$77$		0			0
$78$	0.0969299	−	1.73205i	0.0109751	−	0.196116i
$79$	−4.17784	+	7.23623i	−0.470044	+	0.814140i	−0.999413	−	0.0342518i	$-0.989095\pi$
$79$	−4.17784	+	7.23623i	−0.470044	+	0.814140i	0.529370	+	0.848391i	$0.322429\pi$
$80$	−0.183299	+	0.317483i	−0.0204935	+	0.0354957i
$81$	−6.11639	+	6.60226i	−0.679599	+	0.733584i
$82$	3.73998	−	2.15928i	0.413012	−	0.238453i
$83$	8.50712	+	14.7348i	0.933778	+	1.61735i	0.776798	+	0.629750i	$0.216842\pi$
$83$	8.50712	+	14.7348i	0.933778	+	1.61735i	0.156980	+	0.987602i	$0.449824\pi$
$84$		0			0
$85$	0.914490	−	1.58394i	0.0991904	−	0.171803i
$86$		−	4.49843i		−	0.485079i
$87$	−3.16294	−	0.177006i	−0.339103	−	0.0189770i
$88$	0.669453			0.0713640
$89$	−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	$-0.358833\pi$
$90$	0.122710	−	1.09293i	0.0129348	−	0.115205i
$91$		0			0
$92$	−6.66371	+	3.84729i	−0.694740	+	0.401108i
$93$	10.9396	+	0.612209i	1.13439	+	0.0634831i
$94$	−7.21313	+	4.16450i	−0.743978	+	0.429536i
$95$	−2.01831	+	1.16527i	−0.207074	+	0.119555i
$96$	−1.72934	−	0.0967785i	−0.176501	−	0.00987741i
$97$	−14.9093	+	8.60787i	−1.51381	+	0.873997i	−0.513937	+	0.857828i	$0.671814\pi$
$97$	−14.9093	+	8.60787i	−1.51381	+	0.873997i	−0.999869	+	0.0161687i	$0.994853\pi$
$98$		0			0
$99$	−1.84047	+	0.803848i	−0.184974	+	0.0807897i
$100$	−2.43280	−	4.21374i	−0.243280	−	0.421374i
$101$	15.7317			1.56537			0.782683	−	0.622421i	$-0.213851\pi$
$101$	15.7317			1.56537			0.782683	+	0.622421i	$0.213851\pi$
$102$	8.62781	+	0.482834i	0.854280	+	0.0478077i
$103$			11.4445i			1.12766i	0.825890	+	0.563831i	$0.190673\pi$
$103$			11.4445i			1.12766i	−0.825890	+	0.563831i	$0.809327\pi$
$104$	−0.500782	+	0.867380i	−0.0491057	+	0.0850537i
$105$		0			0
$106$		0			0
$107$	9.57976	−	5.53088i	0.926111	−	0.534690i	0.0405313	−	0.999178i	$-0.487095\pi$
$107$	9.57976	−	5.53088i	0.926111	−	0.534690i	0.885579	+	0.464488i	$0.153762\pi$
$108$	4.87055	−	1.81045i	0.468669	−	0.174211i
$109$	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	$-0.00216971\pi$
$110$	0.122710	−	0.212540i	0.0117000	−	0.0202649i
$111$	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	$0.603986\pi$
$114$	−9.21332	−	6.02973i	−0.862906	−	0.564736i
$115$			2.82082i			0.263043i
$116$	1.58394	+	0.914490i	0.147065	+	0.0849083i
$117$	0.335250	−	2.98593i	0.0309939	−	0.276050i
$118$		−	8.72695i		−	0.803381i
$119$		0			0
$120$	−0.347713	+	0.531299i	−0.0317417	+	0.0485007i
$121$	10.5518			0.959257
$122$	−2.47886	−	4.29351i	−0.224425	−	0.388716i
$123$	6.67669	−	3.37219i	0.602017	−	0.304060i
$124$	−5.47837	−	3.16294i	−0.491972	−	0.284040i
$125$	−3.61671			−0.323489
$126$		0			0
$127$	−1.66945			−0.148140			−0.0740700	−	0.997253i	$-0.523599\pi$
$127$	−1.66945			−0.148140			−0.0740700	+	0.997253i	$0.523599\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	0.435352	−	7.77934i	0.0383306	−	0.684933i
$130$	0.183586	+	0.317980i	0.0161015	+	0.0278887i
$131$	−13.5321			−1.18231			−0.591154	−	0.806558i	$-0.701328\pi$
$131$	−13.5321			−1.18231			−0.591154	+	0.806558i	$0.701328\pi$
$132$	1.15772	+	0.0647887i	0.100766	+	0.00563913i
$133$		0			0
$134$		−	10.8907i		−	0.940817i
$135$	0.317980	−	1.87817i	0.0273674	−	0.161647i
$136$	−4.32065	−	2.49453i	−0.370493	−	0.213904i
$137$			8.98851i			0.767940i	0.923346	+	0.383970i	$0.125443\pi$
$137$			8.98851i			0.767940i	−0.923346	+	0.383970i	$0.874557\pi$
$138$	−11.8962	+	6.00839i	−1.01267	+	0.511468i
$139$	−8.05336	−	4.64961i	−0.683077	−	0.394375i	0.117936	−	0.993021i	$-0.462372\pi$
$139$	−8.05336	−	4.64961i	−0.683077	−	0.394375i	−0.801014	+	0.598646i	$0.795706\pi$
$140$		0			0
$141$	−12.8770	+	6.50379i	−1.08444	+	0.547718i
$142$	2.74922	−	4.76178i	0.230709	−	0.399600i
$143$	0.335250	−	0.580671i	0.0280351	−	0.0485581i
$144$	−2.98127	−	0.334727i	−0.248439	−	0.0278939i
$145$	0.580671	−	0.335250i	0.0482221	−	0.0278410i
$146$	2.03657	+	3.52744i	0.168548	+	0.291933i
$147$		0			0
$148$	−2.58394	+	4.47552i	−0.212399	+	0.367886i
$149$			2.83211i			0.232016i	0.993248	+	0.116008i	$0.0370098\pi$
$149$			2.83211i			0.232016i	−0.993248	+	0.116008i	$0.962990\pi$
$150$	−3.79936	−	7.52245i	−0.310216	−	0.614205i
$151$	−16.5518			−1.34697			−0.673484	−	0.739201i	$-0.735203\pi$
$151$	−16.5518			−1.34697			−0.673484	+	0.739201i	$0.735203\pi$
$152$	3.17861	+	5.50552i	0.257820	+	0.446556i
$153$	14.8737	+	1.66997i	1.20247	+	0.135009i
$154$		0			0
$155$	−2.00836	+	1.15953i	−0.161315	+	0.0931355i
$156$	−0.949969	+	1.45154i	−0.0760584	+	0.116216i
$157$	−2.45480	+	1.41728i	−0.195914	+	0.113111i	−0.594748	−	0.803912i	$-0.702748\pi$
$157$	−2.45480	+	1.41728i	−0.195914	+	0.113111i	0.398834	+	0.917023i	$0.369415\pi$
$158$	7.23623	−	4.17784i	0.575684	−	0.332371i
$159$		0			0
$160$	0.317483	−	0.183299i	0.0250993	−	0.0144911i
$161$		0			0
$162$	8.59808	−	2.65953i	0.675529	−	0.208952i
$163$	−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	$-0.586466\pi$
$164$	−4.31856			−0.337223
$165$	0.232778	−	0.355680i	0.0181217	−	0.0276896i
$166$		−	17.0142i		−	1.32056i
$167$	−9.67422	+	16.7562i	−0.748614	+	1.29664i	0.199874	+	0.979822i	$0.435947\pi$
$167$	−9.67422	+	16.7562i	−0.748614	+	1.29664i	−0.948487	+	0.316815i	$0.897386\pi$
$168$		0			0
$169$	−5.99843	−	10.3896i	−0.461418	−	0.799199i
$170$	−1.58394	+	0.914490i	−0.121483	+	0.0701382i
$171$	−15.3495	−	11.3191i	−1.17380	−	0.865596i
$172$	−2.24922	+	3.89576i	−0.171501	+	0.297049i
$173$	−2.41827	+	4.18856i	−0.183858	+	0.318451i	−0.943191	−	0.332251i	$-0.892192\pi$
$173$	−2.41827	+	4.18856i	−0.183858	+	0.318451i	0.759333	+	0.650702i	$0.225525\pi$
$174$	2.65068	+	1.73476i	0.200948	+	0.131512i
$175$		0			0
$176$	−0.579764	−	0.334727i	−0.0437013	−	0.0252310i
$177$	0.844581	−	15.0919i	0.0634826	−	1.13438i
$178$			10.7113i			0.802847i
$179$	−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	$0.710318\pi$
$180$	−0.652734	+	0.885148i	−0.0486519	+	0.0659750i
$181$			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
$183$	−3.87128	−	7.66485i	−0.286173	−	0.566602i
$184$	7.69459			0.567252
$185$	0.947269	+	1.64072i	0.0696446	+	0.120628i
$186$	−9.16789	−	6.00000i	−0.672222	−	0.439941i
$187$	2.89248	+	1.66997i	0.211519	+	0.122120i
$188$	8.32901			0.607455
$189$		0			0
$190$	2.33055			0.169076
$191$	−23.7098	−	13.6888i	−1.71558	−	0.990490i	−0.926583	−	0.376091i	$-0.877268\pi$
$191$	−23.7098	−	13.6888i	−1.71558	−	0.990490i	−0.788996	−	0.614398i	$-0.789399\pi$
$192$	1.44927	+	0.948485i	0.104592	+	0.0684510i
$193$	5.01413	+	8.68473i	0.360925	+	0.625141i	0.988113	−	0.153727i	$-0.0491276\pi$
$193$	5.01413	+	8.68473i	0.360925	+	0.625141i	−0.627188	+	0.778868i	$0.715794\pi$
$194$	17.2157			1.23602
$195$	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	$-0.233982\pi$
$198$	1.99582	+	0.224084i	0.141837	+	0.0159250i
$199$	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	$0.605778\pi$
$200$			4.86561i			0.344050i
$201$	1.05399	−	18.8338i	0.0743427	−	1.32844i
$202$	−13.6241	−	7.86586i	−0.958587	−	0.553440i
$203$		0			0
$204$	−7.23048	−	4.73205i	−0.506235	−	0.331310i
$205$	−0.791588	+	1.37107i	−0.0552869	+	0.0957597i
$206$	5.72226	−	9.91124i	0.398689	−	0.690549i
$207$	−21.1541	+	9.23929i	−1.47031	+	0.642175i
$208$	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
$213$	5.21518	−	7.96870i	0.357338	−	0.546006i
$214$	−11.0618			−0.756166
$215$	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
$219$	3.18055	+	6.29726i	0.214922	+	0.425530i
$220$	−0.212540	+	0.122710i	−0.0143295	+	0.00827312i
$221$	−4.32741	+	2.49843i	−0.291093	+	0.168063i
$222$	−4.90166	+	7.48965i	−0.328978	+	0.502672i
$223$	14.7546	−	8.51860i	0.988044	−	0.570448i	0.0833551	−	0.996520i	$-0.473436\pi$
$223$	14.7546	−	8.51860i	0.988044	−	0.570448i	0.904689	+	0.426072i	$0.140103\pi$
$224$		0			0
$225$	−5.84239	−	13.3766i	−0.389492	−	0.891774i
$226$	−2.07976	−	3.60226i	−0.138344	−	0.239619i
$227$	−5.11024			−0.339179			−0.169589	−	0.985515i	$-0.554244\pi$
$227$	−5.11024			−0.339179			−0.169589	+	0.985515i	$0.554244\pi$
$228$	4.96410	+	9.82856i	0.328756	+	0.650912i
$229$			15.2669i			1.00887i	0.863451	+	0.504433i	$0.168298\pi$
$229$			15.2669i			1.00887i	−0.863451	+	0.504433i	$0.831702\pi$
$230$	1.41041	−	2.44290i	0.0929997	−	0.161080i
$231$		0			0
$232$	−0.914490	−	1.58394i	−0.0600392	−	0.103991i
$233$	8.82741	−	5.09651i	0.578303	−	0.333883i	−0.182156	−	0.983270i	$-0.558307\pi$
$233$	8.82741	−	5.09651i	0.578303	−	0.333883i	0.760459	+	0.649386i	$0.224974\pi$
$234$	−1.78330	+	2.41827i	−0.116578	+	0.158087i
$235$	1.52670	−	2.64432i	0.0995909	−	0.172496i
$236$	−4.36348	+	7.55776i	−0.284038	+	0.491968i
$237$	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	$0.879686\pi$
$240$	0.566778	−	0.286262i	0.0365853	−	0.0184781i
$241$			20.6853i			1.33245i	0.745749	+	0.666227i	$0.232092\pi$
$241$			20.6853i			1.33245i	−0.745749	+	0.666227i	$0.767908\pi$
$242$	−9.13815	−	5.27592i	−0.587423	−	0.339149i
$243$	15.1264	−	3.76713i	0.970361	−	0.241662i
$244$			4.95771i			0.317385i
$245$		0			0
$246$	−7.46828	−	0.417944i	−0.476160	−	0.0266471i
$247$	6.36717			0.405133
$248$	3.16294	+	5.47837i	0.200847	+	0.347877i
$249$	1.64661	−	29.4235i	0.104350	−	1.86464i
$250$	3.13216	+	1.80836i	0.198096	+	0.114370i
$251$	−1.81200			−0.114373			−0.0571864	−	0.998364i	$-0.518213\pi$
$251$	−1.81200			−0.114373			−0.0571864	+	0.998364i	$0.518213\pi$
$252$		0			0
$253$	−5.15117			−0.323851
$254$	1.44579	+	0.834727i	0.0907169	+	0.0523754i
$255$	−2.82769	+	1.42818i	−0.177077	+	0.0894360i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.45545			−0.402680			−0.201340	−	0.979521i	$-0.564530\pi$
$257$	−6.45545			−0.402680			−0.201340	+	0.979521i	$0.564530\pi$
$258$	−4.26670	+	6.51943i	−0.265633	+	0.405882i
$259$		0			0
$260$		−	0.367172i		−	0.0227710i
$261$	4.41606	+	3.25653i	0.273347	+	0.201574i
$262$	11.7192	+	6.76607i	0.724013	+	0.418009i
$263$		−	8.82062i		−	0.543903i	−0.962311	−	0.271951i	$-0.912331\pi$
$263$		−	8.82062i		−	0.543903i	0.962311	−	0.271951i	$-0.0876690\pi$
$264$	−0.970217	−	0.634967i	−0.0597127	−	0.0390795i
$265$		0			0
$266$		0			0
$267$	−1.03663	+	18.5236i	−0.0634404	+	1.13362i
$268$	−5.44537	+	9.43166i	−0.332629	+	0.576130i
$269$	−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	$0.309878\pi$
$270$	−1.21446	+	1.46755i	−0.0739100	+	0.0893126i
$271$	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
$275$		−	3.25730i		−	0.196422i
$276$	13.3066	+	0.744670i	0.800963	+	0.0448239i
$277$	1.26566			0.0760459			0.0380230	−	0.999277i	$-0.487894\pi$
$277$	1.26566			0.0760459			0.0380230	+	0.999277i	$0.487894\pi$
$278$	4.64961	+	8.05336i	0.278865	+	0.483009i
$279$	−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	$0.231669\pi$
$282$	14.4037	+	0.806068i	0.857729	+	0.0480007i
$283$	17.2094	−	9.93588i	1.02300	−	0.590627i	0.108025	−	0.994148i	$-0.465547\pi$
$283$	17.2094	−	9.93588i	1.02300	−	0.590627i	0.914970	+	0.403522i	$0.132214\pi$
$284$	−4.76178	+	2.74922i	−0.282560	+	0.163136i
$285$	4.03032	+	0.225547i	0.238735	+	0.0133602i
$286$	−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
$290$	−0.670501			−0.0393732
$291$	29.7719	+	1.66611i	1.74526	+	0.0976692i
$292$		−	4.07314i		−	0.238363i
$293$	6.70606	−	11.6152i	0.391772	−	0.678569i	−0.600911	−	0.799316i	$-0.705196\pi$
$293$	6.70606	−	11.6152i	0.391772	−	0.678569i	0.992683	+	0.120747i	$0.0385289\pi$
$294$		0			0
$295$	1.59964	+	2.77066i	0.0931348	+	0.161314i
$296$	4.47552	−	2.58394i	0.260134	−	0.150189i
$297$	3.42977	+	0.580671i	0.199016	+	0.0336939i
$298$	1.41606	−	2.45268i	0.0820299	−	0.142080i
$299$	3.85331	−	6.67413i	0.222843	−	0.385975i
$300$	−0.470886	+	8.41431i	−0.0271866	+	0.485800i
$301$		0			0
$302$	14.3343	+	8.27592i	0.824847	+	0.476225i
$303$	−22.7995	−	14.9213i	−1.30980	−	0.857207i
$304$		−	6.35722i		−	0.364612i
$305$	1.57399	+	0.908744i	0.0901265	+	0.0520346i
$306$	−12.0460	−	8.88310i	−0.688626	−	0.507813i
$307$			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
$309$	10.8550	−	16.5862i	0.617517	−	0.943554i
$310$	2.31905			0.131713
$311$	4.62246	+	8.00634i	0.262116	+	0.453998i	0.966804	−	0.255519i	$-0.0822464\pi$
$311$	4.62246	+	8.00634i	0.262116	+	0.453998i	−0.704688	+	0.709517i	$0.748913\pi$
$312$	1.54846	−	0.782082i	0.0876646	−	0.0442767i
$313$	5.33830	+	3.08207i	0.301739	+	0.174209i	0.643224	−	0.765678i	$-0.277597\pi$
$313$	5.33830	+	3.08207i	0.301739	+	0.174209i	−0.341485	+	0.939887i	$0.610930\pi$
$314$	2.83456			0.159963
$315$		0			0
$316$	−8.35568			−0.470044
$317$	17.8876	+	10.3274i	1.00467	+	0.580045i	0.909626	−	0.415428i	$-0.136368\pi$
$317$	17.8876	+	10.3274i	1.00467	+	0.580045i	0.0950420	+	0.995473i	$0.469701\pi$
$318$		0			0
$319$	0.612209	+	1.06038i	0.0342771	+	0.0593697i
$320$	−0.366598			−0.0204935
$321$	−19.1296	−	1.07054i	−1.06771	−	0.0597517i
$322$		0			0
$323$			31.7166i			1.76476i
$324$	−8.77592	−	1.99582i	−0.487551	−	0.110879i
$325$	4.22033	+	2.43661i	0.234102	+	0.135159i
$326$			24.7281i			1.36956i
$327$	−16.3314	+	8.24848i	−0.903128	+	0.456142i
$328$	3.73998	+	2.15928i	0.206506	+	0.119226i
$329$		0			0
$330$	−0.379431	+	0.191639i	−0.0208870	+	0.0105494i
$331$	−5.35568	+	9.27631i	−0.294375	+	0.509872i	−0.974839	−	0.222909i	$-0.928445\pi$
$331$	−5.35568	+	9.27631i	−0.294375	+	0.509872i	0.680464	+	0.732781i	$0.261778\pi$
$332$	−8.50712	+	14.7348i	−0.466889	+	0.808676i
$333$	−9.20151	+	12.4778i	−0.504239	+	0.683780i
$334$	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	$0.100724\pi$
$338$			11.9969i			0.652544i
$339$	−3.24801	−	6.43082i	−0.176408	−	0.349274i
$340$	1.82898			0.0991904
$341$	−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
$345$	2.67551	−	4.08812i	0.144044	−	0.220097i
$346$	4.18856	−	2.41827i	0.225179	−	0.130007i
$347$	9.46737	−	5.46599i	0.508235	−	0.293430i	−0.223873	−	0.974618i	$-0.571870\pi$
$347$	9.46737	−	5.46599i	0.508235	−	0.293430i	0.732108	+	0.681189i	$0.238537\pi$
$348$	−1.42818	−	2.82769i	−0.0765584	−	0.151580i
$349$	1.02562	−	0.592145i	0.0549004	−	0.0316968i	−0.472299	−	0.881439i	$-0.656576\pi$
$349$	1.02562	−	0.592145i	0.0549004	−	0.0316968i	0.527199	+	0.849742i	$0.323242\pi$
$350$		0			0
$351$	−3.31798	+	4.00943i	−0.177101	+	0.214008i
$352$	0.334727	+	0.579764i	0.0178410	+	0.0309015i
$353$	−33.5824			−1.78741			−0.893706	−	0.448653i	$-0.851904\pi$
$353$	−33.5824			−1.78741			−0.893706	+	0.448653i	$0.851904\pi$
$354$	−8.27738	+	12.6477i	−0.439938	+	0.672217i
$355$			2.01572i			0.106983i
$356$	5.35566	−	9.27628i	0.283849	−	0.491642i
$357$		0			0
$358$	1.82898	+	3.16789i	0.0966646	+	0.167428i
$359$	−8.77122	+	5.06407i	−0.462927	+	0.267271i	−0.713274	−	0.700885i	$-0.752789\pi$
$359$	−8.77122	+	5.06407i	−0.462927	+	0.267271i	0.250347	+	0.968156i	$0.419455\pi$
$360$	1.00786	−	0.440193i	0.0531188	−	0.0232002i
$361$	10.7072	−	18.5453i	0.563534	−	0.976070i
$362$	2.83398	−	4.90860i	0.148951	−	0.257990i
$363$	−15.2924	−	10.0083i	−0.802644	−	0.525297i
$364$		0			0
$365$	−1.29315	−	0.746603i	−0.0676868	−	0.0390790i
$366$	−0.479800	+	8.57360i	−0.0250795	+	0.448149i
$367$		−	18.0021i		−	0.939701i	−0.882746	−	0.469850i	$-0.844308\pi$
$367$		−	18.0021i		−	0.939701i	0.882746	−	0.469850i	$-0.155692\pi$
$368$	−6.66371	−	3.84729i	−0.347370	−	0.200554i
$369$	−12.8748	−	1.44554i	−0.670235	−	0.0752517i
$370$		−	1.89454i		−	0.0984923i
$371$		0			0
$372$	4.93962	+	9.78010i	0.256108	+	0.507074i
$373$	16.4090			0.849627			0.424814	−	0.905281i	$-0.360340\pi$
$373$	16.4090			0.849627			0.424814	+	0.905281i	$0.360340\pi$
$374$	−1.66997	−	2.89248i	−0.0863522	−	0.149566i
$375$	5.24158	+	3.43040i	0.270674	+	0.177145i
$376$	−7.21313	−	4.16450i	−0.371989	−	0.214768i
$377$	−1.83184			−0.0943447
$378$		0			0
$379$	−2.91372			−0.149668			−0.0748339	−	0.997196i	$-0.523843\pi$
$379$	−2.91372			−0.149668			−0.0748339	+	0.997196i	$0.523843\pi$
$380$	−2.01831	−	1.16527i	−0.103537	−	0.0597773i
$381$	2.41948	+	1.58345i	0.123954	+	0.0811227i
$382$	13.6888	+	23.7098i	0.700382	+	1.21310i
$383$	8.57443			0.438133			0.219066	−	0.975710i	$-0.429699\pi$
$383$	8.57443			0.438133			0.219066	+	0.975710i	$0.429699\pi$
$384$	−0.780860	−	1.54605i	−0.0398481	−	0.0788963i
$385$		0			0
$386$		−	10.0283i		−	0.510425i
$387$	−8.00953	+	10.8614i	−0.407147	+	0.552117i
$388$	−14.9093	−	8.60787i	−0.756903	−	0.436998i
$389$		−	35.5539i		−	1.80266i	−0.433137	−	0.901328i	$-0.642594\pi$
$389$		−	35.5539i		−	1.80266i	0.433137	−	0.901328i	$-0.357406\pi$
$390$	0.0355343	−	0.634967i	0.00179935	−	0.0321528i
$391$	33.2456	+	19.1944i	1.68130	+	0.970702i
$392$		0			0
$393$	19.6117	+	12.8350i	0.989279	+	0.647442i
$394$	−9.41292	+	16.3037i	−0.474216	+	0.821367i
$395$	−1.53159	+	2.65279i	−0.0770626	+	0.133476i
$396$	−1.61639	−	1.19197i	−0.0812266	−	0.0598989i
$397$	−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
$401$		−	0.190871i		−	0.00953167i	−0.999989	−	0.00476583i	$-0.998483\pi$
$401$		−	0.190871i		−	0.00953167i	0.999989	−	0.00476583i	$-0.00151702\pi$
$402$	−10.3297	+	15.7836i	−0.515199	+	0.787214i
$403$	6.33577			0.315607
$404$	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
$408$	3.89576	+	7.71332i	0.192869	+	0.381866i
$409$	3.00832	−	1.73685i	0.148752	−	0.0858819i	−0.423777	−	0.905767i	$-0.639296\pi$
$409$	3.00832	−	1.73685i	0.148752	−	0.0858819i	0.572529	+	0.819885i	$0.305963\pi$
$410$	1.37107	−	0.791588i	0.0677124	−	0.0390938i
$411$	8.52547	−	13.0268i	0.420530	−	0.642562i
$412$	−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
$416$	−1.00156			−0.0491057
$417$	7.26139	+	14.3770i	0.355592	+	0.704046i
$418$			4.25587i			0.208161i
$419$	0.703955	−	1.21929i	0.0343905	−	0.0595660i	−0.848318	−	0.529487i	$-0.822384\pi$
$419$	0.703955	−	1.21929i	0.0343905	−	0.0595660i	0.882708	+	0.469921i	$0.155718\pi$
$420$		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
$423$	24.8310	+	2.78794i	1.20732	+	0.135554i
$424$		0			0
$425$	−12.1374	+	21.0226i	−0.588751	+	1.01975i
$426$	−8.50083	+	4.29351i	−0.411867	+	0.208021i
$427$		0			0
$428$	9.57976	+	5.53088i	0.463055	+	0.267345i
$429$	−1.03663	+	0.523567i	−0.0500487	+	0.0252781i
$430$		−	1.64912i		−	0.0795275i
$431$	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	$0.438539\pi$
$432$	4.00317	+	3.31280i	0.192603	+	0.159387i
$433$			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
$435$	−1.15953	−	0.0648900i	−0.0555951	−	0.00311124i
$436$	10.5633			0.505891
$437$	−24.4581	−	42.3627i	−1.16999	−	2.02648i
$438$	0.394192	−	7.04387i	0.0188352	−	0.336569i
$439$	−10.6005	−	6.12020i	−0.505934	−	0.292101i	0.225226	−	0.974306i	$-0.427688\pi$
$439$	−10.6005	−	6.12020i	−0.505934	−	0.292101i	−0.731161	+	0.682205i	$0.761021\pi$
$440$	0.245420			0.0117000
$441$		0			0
$442$	4.99687			0.237677
$443$	−6.93544	−	4.00418i	−0.329513	−	0.190244i	0.326112	−	0.945331i	$-0.394261\pi$
$443$	−6.93544	−	4.00418i	−0.329513	−	0.190244i	−0.655625	+	0.755087i	$0.727595\pi$
$444$	7.98979	−	4.03540i	0.379179	−	0.191511i
$445$	−1.96337	−	3.40067i	−0.0930729	−	0.161207i
$446$	−17.0372			−0.806735
$447$	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	$0.888699\pi$
$450$	−1.62865	+	14.5057i	−0.0767752	+	0.683804i
$451$	−2.50374	−	1.44554i	−0.117897	−	0.0680677i
$452$			4.15953i			0.195648i
$453$	23.9880	+	15.6992i	1.12706	+	0.737611i
$454$	4.42560	+	2.55512i	0.207704	+	0.119918i
$455$		0			0
$456$	0.615242	−	10.9938i	0.0288114	−	0.514833i
$457$	−4.97751	+	8.62130i	−0.232838	+	0.403287i	−0.958642	−	0.284614i	$-0.908135\pi$
$457$	−4.97751	+	8.62130i	−0.232838	+	0.403287i	0.725804	+	0.687901i	$0.241468\pi$
$458$	7.63345	−	13.2215i	0.356688	−	0.617801i
$459$	−19.9721	−	16.5277i	−0.932216	−	0.771449i
$460$	−2.44290	+	1.41041i	−0.113901	+	0.0657607i
$461$	−16.1635	−	27.9960i	−0.752810	−	1.30391i	−0.946456	−	0.322834i	$-0.895364\pi$
$461$	−16.1635	−	27.9960i	−0.752810	−	1.30391i	0.193645	−	0.981072i	$-0.437969\pi$
$462$		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	$0.237141\pi$
$464$			1.82898i			0.0849083i
$465$	4.01045	+	0.224435i	0.185980	+	0.0104079i
$466$	−10.1930			−0.472183
$467$	−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	$0.991996\pi$
$468$	2.75352	−	1.20263i	0.127281	−	0.0555916i
$469$		0			0
$470$	−2.64432	+	1.52670i	−0.121973	+	0.0704214i
$471$	4.90192	+	0.274324i	0.225869	+	0.0126402i
$472$	7.55776	−	4.36348i	0.347874	−	0.200845i
$473$	−2.60803	+	1.50575i	−0.119917	+	0.0692343i
$474$	−14.4499	−	0.808650i	−0.663704	−	0.0371425i
$475$	26.7877	−	15.4659i	1.22910	−	0.709623i
$476$		0			0
$477$		0			0
$478$	9.59076	+	16.6117i	0.438671	+	0.759801i
$479$	10.1608			0.464261			0.232131	−	0.972685i	$-0.425430\pi$
$479$	10.1608			0.464261			0.232131	+	0.972685i	$0.425430\pi$
$480$	−0.633975	−	0.0354788i	−0.0289368	−	0.00161938i
$481$		−	5.17597i		−	0.236004i
$482$	10.3426	−	17.9140i	0.471094	−	0.815958i
$483$		0			0
$484$	5.27592	+	9.13815i	0.239814	+	0.415371i
$485$	−5.46571	+	3.15563i	−0.248185	+	0.143290i
$486$	−14.9834	−	4.30078i	−0.679662	−	0.195087i
$487$	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	$-0.0835443\pi$
$488$	2.47886	−	4.29351i	0.112213	−	0.194358i
$489$	−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	$0.512863\pi$
$492$	6.25875	+	4.09609i	0.282166	+	0.184666i
$493$		−	9.12490i		−	0.410965i
$494$	−5.51413	−	3.18359i	−0.248093	−	0.143236i
$495$	−0.674714	+	0.294689i	−0.0303261	+	0.0132453i
$496$		−	6.32588i		−	0.284040i
$497$		0			0
$498$	−16.1378	+	24.6582i	−0.723150	+	1.10496i
$499$	−25.1533			−1.12601			−0.563007	−	0.826452i	$-0.690356\pi$
$499$	−25.1533			−1.12601			−0.563007	+	0.826452i	$0.690356\pi$
$500$	−1.80836	−	3.13216i	−0.0808722	−	0.140075i
$501$	29.9136	−	15.1084i	1.33644	−	0.674995i
$502$	1.56924	+	0.906002i	0.0700387	+	0.0404369i
$503$	−31.1553			−1.38915			−0.694574	−	0.719421i	$-0.744407\pi$
$503$	−31.1553			−1.38915			−0.694574	+	0.719421i	$0.744407\pi$
$504$		0			0
$505$	5.76722			0.256638
$506$	4.46104	+	2.57558i	0.198317	+	0.114499i
$507$	−1.16104	+	20.7467i	−0.0515635	+	0.921394i
$508$	−0.834727	−	1.44579i	−0.0370350	−	0.0641465i
$509$	4.83347			0.214240			0.107120	−	0.994246i	$-0.465837\pi$
$509$	4.83347			0.214240			0.107120	+	0.994246i	$0.465837\pi$
$510$	3.16294	+	0.177006i	0.140057	+	0.00783796i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	11.5094	+	30.9632i	0.508154	+	1.36706i
$514$	5.59059	+	3.22773i	0.246590	+	0.142369i
$515$			4.19554i			0.184877i
$516$	6.95479	−	3.51265i	0.306167	−	0.154636i
$517$	4.82886	+	2.78794i	0.212373	+	0.122613i
$518$		0			0
$519$	7.47751	−	3.77666i	0.328226	−	0.165777i
$520$	−0.183586	+	0.317980i	−0.00805077	+	0.0139443i
$521$	−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	$0.292138\pi$
$522$	−2.19615	−	5.02826i	−0.0961230	−	0.220081i
$523$	−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
$527$			31.5602i			1.37478i
$528$	0.522749	+	1.03501i	0.0227497	+	0.0450428i
$529$	−36.2067			−1.57420
$530$		0			0
$531$	−15.5385	+	21.0711i	−0.674312	+	0.914410i
$532$		0			0
$533$	3.74584	−	2.16266i	0.162250	−	0.0936752i
$534$	10.1595	−	15.5236i	0.439646	−	0.671770i
$535$	3.51192	−	2.02761i	0.151834	−	0.0876612i
$536$	9.43166	−	5.44537i	0.407386	−	0.235204i
$537$	2.85636	+	5.65538i	0.123261	+	0.244047i
$538$	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	0.680954	−	0.732326i	$-0.261565\pi$
$541$	−6.83211	−	11.8336i	−0.293735	−	0.508765i	−0.974690	+	0.223561i	$0.928232\pi$
$542$	−3.05281			−0.131130
$543$	5.37598	−	8.21439i	0.230705	−	0.352513i
$544$		−	4.98906i		−	0.213904i
$545$	1.93625	−	3.35368i	0.0829397	−	0.143656i
$546$		0			0
$547$	4.94380	+	8.56292i	0.211382	+	0.366124i	0.952147	−	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
$549$	−1.65948	+	14.7803i	−0.0708249	+	0.630807i
$550$	−1.62865	+	2.82090i	−0.0694458	+	0.120284i
$551$	−5.81362	+	10.0695i	−0.247669	+	0.428975i
$552$	−11.1515	−	7.29820i	−0.474640	−	0.310632i
$553$		0			0
$554$	−1.09609	−	0.632828i	−0.0465684	−	0.0268863i
$555$	0.183350	−	3.27631i	0.00778279	−	0.139072i
$556$		−	9.29922i		−	0.394375i
$557$	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	$0.580794\pi$
$558$	7.59581	+	17.3912i	0.321556	+	0.736229i
$559$		−	4.50547i		−	0.190561i
$560$		0			0
$561$	−2.60803	−	5.16371i	−0.110111	−	0.218012i
$562$	−10.5267			−0.444042
$563$	12.1666	+	21.0732i	0.512763	+	0.888132i	0.999890	+	0.0148007i	$0.00471137\pi$
$563$	12.1666	+	21.0732i	0.512763	+	0.888132i	−0.487127	+	0.873331i	$0.661955\pi$
$564$	−12.0710	−	7.89994i	−0.508279	−	0.332647i
$565$	1.32058	+	0.762437i	0.0555572	+	0.0320760i
$566$	−19.8718			−0.835272
$567$		0			0
$568$	5.49843			0.230709
$569$	8.18746	+	4.72703i	0.343236	+	0.198167i	0.661702	−	0.749767i	$-0.269834\pi$
$569$	8.18746	+	4.72703i	0.343236	+	0.198167i	−0.318466	+	0.947934i	$0.603168\pi$
$570$	−3.37759	−	2.21049i	−0.141471	−	0.0925872i
$571$	15.7843	+	27.3392i	0.660551	+	1.14411i	0.980471	+	0.196664i	$0.0630108\pi$
$571$	15.7843	+	27.3392i	0.660551	+	1.14411i	−0.319920	+	0.947445i	$0.603656\pi$
$572$	0.670501			0.0280351
$573$	21.3781	+	42.3272i	0.893084	+	1.76824i
$574$		0			0
$575$		−	37.4388i		−	1.56131i
$576$	−1.20075	−	2.74922i	−0.0500313	−	0.114551i
$577$	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	$0.420312\pi$
$578$			7.89074i			0.328211i
$579$	0.970520	−	17.3423i	0.0403334	−	0.720723i
$580$	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
$585$	0.122902	−	1.09464i	0.00508138	−	0.0452577i
$586$	−11.6152	+	6.70606i	−0.479821	+	0.277025i
$587$	−9.65855	−	16.7291i	−0.398651	−	0.690484i	0.594909	−	0.803793i	$-0.297188\pi$
$587$	−9.65855	−	16.7291i	−0.398651	−	0.690484i	−0.993560	+	0.113310i	$0.963855\pi$
$588$		0			0
$589$	20.1075	−	34.8272i	0.828516	−	1.43503i
$590$		−	3.19928i		−	0.131712i
$591$	−17.8560	+	27.2837i	−0.734499	+	1.12230i
$592$	−5.16789			−0.212399
$593$	−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	$0.838125\pi$
$594$	−2.67994	−	2.21776i	−0.109959	−	0.0909959i
$595$		0			0
$596$	−2.45268	+	1.41606i	−0.100466	+	0.0580039i
$597$	−4.18858	−	8.29308i	−0.171427	−	0.339413i
$598$	−6.67413	+	3.85331i	−0.272926	+	0.157574i
$599$	−26.6548	+	15.3892i	−1.08909	+	0.628785i	−0.933333	−	0.359011i	$-0.883114\pi$
$599$	−26.6548	+	15.3892i	−1.08909	+	0.628785i	−0.155754	+	0.987796i	$0.549781\pi$
$600$	4.61495	−	7.05156i	0.188405	−	0.287879i
$601$	−0.786931	+	0.454335i	−0.0320996	+	0.0185327i	−0.515964	−	0.856610i	$-0.672566\pi$
$601$	−0.786931	+	0.454335i	−0.0320996	+	0.0185327i	0.483864	+	0.875143i	$0.339233\pi$
$602$		0			0
$603$	−19.3911	+	26.2956i	−0.789668	+	1.07084i
$604$	−8.27592	−	14.3343i	−0.336742	−	0.583255i
$605$	3.86828			0.157268
$606$	12.2843	+	24.3220i	0.499015	+	0.988013i
$607$		−	44.7773i		−	1.81746i	−0.417389	−	0.908728i	$-0.637055\pi$
$607$		−	44.7773i		−	1.81746i	0.417389	−	0.908728i	$-0.362945\pi$
$608$	−3.17861	+	5.50552i	−0.128910	+	0.223278i
$609$		0			0
$610$	−0.908744	−	1.57399i	−0.0367940	−	0.0637290i
$611$	−7.22442	+	4.17102i	−0.292269	+	0.168741i
$612$	5.99063	+	13.7160i	0.242157	+	0.554437i
$613$	−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	$0.286109\pi$
$614$	0.326864	−	0.566145i	0.0131912	−	0.0228478i
$615$	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	$0.818389\pi$
$618$	−17.6937	+	8.93656i	−0.711747	+	0.359481i
$619$		−	44.3668i		−	1.78325i	−0.452772	−	0.891626i	$-0.649565\pi$
$619$		−	44.3668i		−	1.78325i	0.452772	−	0.891626i	$-0.350435\pi$
$620$	−2.00836	−	1.15953i	−0.0806577	−	0.0465677i
$621$	39.4213	+	6.67413i	1.58192	+	0.267824i
$622$		−	9.24493i		−	0.370688i
$623$		0			0
$624$	−1.73205	−	0.0969299i	−0.0693375	−	0.00388030i
$625$	23.0021			0.920086
$626$	−3.08207	−	5.33830i	−0.123184	−	0.213361i
$627$	−0.411876	+	7.35986i	−0.0164487	+	0.293924i
$628$	−2.45480	−	1.41728i	−0.0979571	−	0.0565555i
$629$	25.7829			1.02803
$630$		0			0
$631$	−32.5707			−1.29662			−0.648310	−	0.761377i	$-0.724524\pi$
$631$	−32.5707			−1.29662			−0.648310	+	0.761377i	$0.724524\pi$
$632$	7.23623	+	4.17784i	0.287842	+	0.166186i
$633$	2.56328	−	1.29464i	0.101881	−	0.0514571i
$634$	−10.3274	−	17.8876i	−0.410154	−	0.710408i
$635$	−0.612018			−0.0242872
$636$		0			0
$637$		0			0
$638$		−	1.22442i		−	0.0484751i
$639$	−15.1164	+	6.60226i	−0.597995	+	0.261181i
$640$	0.317483	+	0.183299i	0.0125496	+	0.00724553i
$641$		−	11.8091i		−	0.466433i	−0.972425	−	0.233216i	$-0.925075\pi$
$641$		−	11.8091i		−	0.466433i	0.972425	−	0.233216i	$-0.0749250\pi$
$642$	16.0314	+	10.4919i	0.632711	+	0.414083i
$643$	25.3714	+	14.6482i	1.00055	+	0.577668i	0.908411	−	0.418078i	$-0.137296\pi$
$643$	25.3714	+	14.6482i	1.00055	+	0.577668i	0.0921392	+	0.995746i	$0.470630\pi$
$644$		0			0
$645$	0.159599	−	2.85189i	0.00628421	−	0.112293i
$646$	15.8583	−	27.4674i	0.623936	−	1.08069i
$647$	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	$-0.0201198\pi$
$648$	6.60226	+	6.11639i	0.259361	+	0.240274i
$649$	−5.05957	+	2.92114i	−0.198605	+	0.114665i
$650$	−2.43661	−	4.22033i	−0.0955717	−	0.165535i
$651$		0			0
$652$	12.3640	−	21.4151i	0.484213	−	0.838682i
$653$		−	45.0974i		−	1.76480i	−0.470502	−	0.882399i	$-0.655927\pi$
$653$		−	45.0974i		−	1.76480i	0.470502	−	0.882399i	$-0.344073\pi$
$654$	18.2676	+	1.02230i	0.714321	+	0.0399752i
$655$	−4.96086			−0.193837
$656$	−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	$0.120684\pi$
$660$	0.424416	+	0.0237514i	0.0165204	+	0.000924522i
$661$	−17.1234	+	9.88619i	−0.666022	+	0.384528i	−0.794568	−	0.607175i	$-0.792302\pi$
$661$	−17.1234	+	9.88619i	−0.666022	+	0.384528i	0.128546	+	0.991704i	$0.458969\pi$
$662$	9.27631	−	5.35568i	0.360534	−	0.208154i
$663$	8.64131	+	0.483589i	0.335601	+	0.0187810i
$664$	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
$668$	−19.3484			−0.748614
$669$	−29.4632	−	1.64883i	−1.13911	−	0.0637476i
$670$		−	3.99252i		−	0.154245i
$671$	−1.65948	+	2.87430i	−0.0640635	+	0.110961i
$672$		0			0
$673$	−0.945369	−	1.63743i	−0.0364413	−	0.0631182i	0.847230	−	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
$675$	−4.22033	+	24.9277i	−0.162441	+	0.959467i
$676$	5.99843	−	10.3896i	0.230709	−	0.399600i
$677$	10.5661	−	18.3010i	0.406088	−	0.703364i	−0.588360	−	0.808599i	$-0.700226\pi$
$677$	10.5661	−	18.3010i	0.406088	−	0.703364i	0.994447	+	0.105235i	$0.0335595\pi$
$678$	−0.402553	+	7.19326i	−0.0154599	+	0.276255i
$679$		0			0
$680$	−1.58394	−	0.914490i	−0.0607415	−	0.0350691i
$681$	7.40610	+	4.84699i	0.283803	+	0.185737i
$682$			4.23488i			0.162162i
$683$	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	$0.613315\pi$
$684$	2.12793	−	18.9526i	0.0813635	−	0.724670i
$685$			3.29517i			0.125902i
$686$		0			0
$687$	14.4804	−	22.1258i	0.552463	−	0.844153i
$688$	−4.49843			−0.171501
$689$		0			0
$690$	−4.36112	+	2.20267i	−0.166025	+	0.0838541i
$691$	15.7071	+	9.06850i	0.597526	+	0.344982i	0.768068	−	0.640369i	$-0.221218\pi$
$691$	15.7071	+	9.06850i	0.597526	+	0.344982i	−0.170542	+	0.985350i	$0.554552\pi$
$692$	−4.83654			−0.183858
$693$		0			0
$694$	−10.9320			−0.414972
$695$	−2.95235	−	1.70454i	−0.111989	−	0.0646568i
$696$	−0.177006	+	3.16294i	−0.00670939	+	0.119891i
$697$	10.7728	+	18.6590i	0.408048	+	0.706760i
$698$	−1.18429			−0.0448260
$699$	−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	$0.765172\pi$
$702$	4.87817	−	1.81328i	0.184115	−	0.0684379i
$703$	−28.4519	−	16.4267i	−1.07308	−	0.619545i
$704$		−	0.669453i		−	0.0252310i
$705$	−4.72069	+	2.38428i	−0.177792	+	0.0897970i
$706$	29.0832	+	16.7912i	1.09456	+	0.631946i
$707$		0			0
$708$	13.4923	−	6.81453i	0.507071	−	0.256106i
$709$	1.80385	−	3.12436i	0.0677449	−	0.117338i	−0.830163	−	0.557520i	$-0.811753\pi$
$709$	1.80385	−	3.12436i	0.0677449	−	0.117338i	0.897908	+	0.440183i	$0.145086\pi$
$710$	1.00786	−	1.74566i	0.0378242	−	0.0655135i
$711$	−24.9105	−	2.79687i	−0.934217	−	0.104891i
$712$	−9.27628	+	5.35566i	−0.347643	+	0.200712i
$713$	−24.3375	−	42.1538i	−0.911447	−	1.57867i
$714$		0			0
$715$	0.122902	−	0.212873i	0.00459628	−	0.00796099i
$716$		−	3.65796i		−	0.136704i
$717$	14.9781	+	29.6555i	0.559367	+	1.10751i
$718$	10.1281			0.377978
$719$	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	$0.673690\pi$
$720$	−1.09293	−	0.122710i	−0.0407310	−	0.00457314i
$721$		0			0
$722$	−18.5453	+	10.7072i	−0.690186	+	0.398479i
$723$	19.6197	−	29.9785i	0.729663	−	1.11491i
$724$	−4.90860	+	2.83398i	−0.182427	+	0.105324i
$725$	−7.70685	+	4.44955i	−0.286225	+	0.165252i
$726$	8.23950	+	16.3136i	0.305797	+	0.605455i
$727$	1.32423	−	0.764544i	0.0491129	−	0.0283554i	−0.475242	−	0.879855i	$-0.657640\pi$
$727$	1.32423	−	0.764544i	0.0491129	−	0.0283554i	0.524355	+	0.851499i	$0.324306\pi$
$728$		0			0
$729$	−25.4953	−	8.88761i	−0.944270	−	0.329171i
$730$	0.746603	+	1.29315i	0.0276330	+	0.0478618i
$731$	22.4430			0.830083
$732$	4.70232	−	7.18505i	0.173803	−	0.265567i
$733$			20.7739i			0.767303i	0.923478	+	0.383651i	$0.125334\pi$
$733$			20.7739i			0.767303i	−0.923478	+	0.383651i	$0.874666\pi$
$734$	−9.00104	+	15.5903i	−0.332234	+	0.575447i
$735$		0			0
$736$	3.84729	+	6.66371i	0.141813	+	0.245628i
$737$	−6.31405	+	3.64542i	−0.232581	+	0.134281i
$738$	10.4271	+	7.68927i	0.383828	+	0.283046i
$739$	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	$0.0966029\pi$
$740$	−0.947269	+	1.64072i	−0.0348223	+	0.0603140i
$741$	−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	$0.959828\pi$
$744$	0.612209	−	10.9396i	0.0224447	−	0.401066i
$745$			1.03825i			0.0380384i
$746$	−14.2106	−	8.20451i	−0.520288	−	0.300389i
$747$	−30.2941	+	41.0807i	−1.10840	+	1.50307i
$748$			3.33994i			0.122120i
$749$		0			0
$750$	−2.82415	−	5.59160i	−0.103123	−	0.204176i
$751$	2.31383			0.0844327			0.0422164	−	0.999108i	$-0.486558\pi$
$751$	2.31383			0.0844327			0.0422164	+	0.999108i	$0.486558\pi$
$752$	4.16450	+	7.21313i	0.151864	+	0.263036i
$753$	2.62608	+	1.71866i	0.0956997	+	0.0626314i
$754$	1.58642	+	0.915921i	0.0577741	+	0.0333559i
$755$	−6.06787			−0.220832
$756$		0			0
$757$	−15.0946			−0.548624			−0.274312	−	0.961641i	$-0.588450\pi$
$757$	−15.0946			−0.548624			−0.274312	+	0.961641i	$0.588450\pi$
$758$	2.52336	+	1.45686i	0.0916525	+	0.0529156i
$759$	7.46542	+	4.88581i	0.270978	+	0.177343i
$760$	1.16527	+	2.01831i	0.0422689	+	0.0732119i
$761$	−23.3379			−0.845998			−0.422999	−	0.906130i	$-0.639023\pi$
$761$	−23.3379			−0.845998			−0.422999	+	0.906130i	$0.639023\pi$
$762$	−1.30361	−	2.58105i	−0.0472248	−	0.0935016i
$763$		0			0
$764$		−	27.3777i		−	0.990490i
$765$	5.45268	+	0.612209i	0.197142	+	0.0221345i
$766$	−7.42567	−	4.28721i	−0.268300	−	0.154903i
$767$		−	8.74061i		−	0.315605i
$768$	−0.0967785	+	1.72934i	−0.00349219	+	0.0624024i
$769$	−15.8266	−	9.13748i	−0.570721	−	0.329506i	0.186716	−	0.982414i	$-0.440216\pi$
$769$	−15.8266	−	9.13748i	−0.570721	−	0.329506i	−0.757437	+	0.652908i	$0.773549\pi$
$770$		0			0
$771$	9.35568	+	6.12290i	0.336937	+	0.220511i
$772$	−5.01413	+	8.68473i	−0.180463	+	0.312570i
$773$	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	$0.164156\pi$
$774$	12.3672	−	5.40150i	0.444529	−	0.194153i
$775$	26.6556	−	15.3896i	0.957497	−	0.552811i
$776$	8.60787	+	14.9093i	0.309004	+	0.535211i
$777$		0			0
$778$	−17.7770	+	30.7906i	−0.637335	+	1.10390i
$779$		−	27.4541i		−	0.983644i
$780$	−0.348257	+	0.532130i	−0.0124696	+	0.0190533i
$781$	−3.68095			−0.131715
$782$	−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
$786$	−10.5667	−	20.9213i	−0.376902	−	0.746238i
$787$	33.1317	−	19.1286i	1.18102	−	0.681861i	0.224769	−	0.974412i	$-0.427837\pi$
$787$	33.1317	−	19.1286i	1.18102	−	0.681861i	0.956250	+	0.292551i	$0.0945040\pi$
$788$	16.3037	−	9.41292i	0.580794	−	0.335322i
$789$	−8.36623	+	12.7834i	−0.297846	+	0.455102i
$790$	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
$794$	3.58034			0.127061
$795$		0			0
$796$			5.36406i			0.190124i
$797$	17.6613	−	30.5902i	0.625594	−	1.08356i	−0.362832	−	0.931855i	$-0.618190\pi$
$797$	17.6613	−	30.5902i	0.625594	−	1.08356i	0.988426	−	0.151706i	$-0.0484767\pi$
$798$		0			0
$799$	−20.7770	−	35.9868i	−0.735036	−	1.27312i
$800$	−4.21374	+	2.43280i	−0.148978	+	0.0860126i
$801$	19.0717	−	25.8624i	0.673864	−	0.913802i
$802$	−0.0954357	+	0.165300i	−0.00336995	+	0.00583693i
$803$	1.36339	−	2.36146i	0.0481130	−	0.0833341i
$804$	16.8376	−	8.50414i	0.593816	−	0.299918i
$805$		0			0
$806$	−5.48694	−	3.16789i	−0.193269	−	0.111584i
$807$	22.0549	−	11.1392i	0.776368	−	0.392119i
$808$		−	15.7317i		−	0.553440i
$809$	−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	$0.791652\pi$
$810$	3.15204	−	0.974978i	0.110751	−	0.0342572i
$811$		−	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
$813$	−5.27937	−	0.295447i	−0.185156	−	0.0103618i
$814$	3.45966			0.121261
$815$	−4.53263	−	7.85075i	−0.158771	−	0.275000i
$816$	0.482834	−	8.62781i	0.0169026	−	0.302034i
$817$	−24.7662	−	14.2988i	−0.866460	−	0.500251i
$818$	−3.47371			−0.121455
$819$		0			0
$820$	−1.58318			−0.0552869
$821$	21.4786	+	12.4007i	0.749608	+	0.432786i	0.825552	−	0.564326i	$-0.190864\pi$
$821$	21.4786	+	12.4007i	0.749608	+	0.432786i	−0.0759445	+	0.997112i	$0.524197\pi$
$822$	−13.8966	+	7.01877i	−0.484701	+	0.244808i
$823$	−10.6572	−	18.4588i	−0.371486	−	0.643433i	0.618308	−	0.785936i	$-0.287818\pi$
$823$	−10.6572	−	18.4588i	−0.371486	−	0.643433i	−0.989794	+	0.142503i	$0.954485\pi$
$824$	11.4445			0.398689
$825$	−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	$0.667232\pi$
$828$	−18.5785	−	13.7003i	−0.645648	−	0.476119i
$829$	−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	$0.936033\pi$
$830$		−	6.23739i		−	0.216503i
$831$	−1.83427	−	1.20046i	−0.0636303	−	0.0416434i
$832$	0.867380	+	0.500782i	0.0300710	+	0.0173615i
$833$		0			0
$834$	0.899965	−	16.0816i	0.0311632	−	0.556859i
$835$	−3.54655	+	6.14281i	−0.122733	+	0.212581i
$836$	2.12793	−	3.68569i	0.0735961	−	0.127472i
$837$	11.4527	+	30.8105i	0.395863	+	1.06497i
$838$	−1.21929	+	0.703955i	−0.0421195	+	0.0243177i
$839$	14.9985	+	25.9782i	0.517807	+	0.896868i	0.999786	+	0.0206851i	$0.00658476\pi$
$839$	14.9985	+	25.9782i	0.517807	+	0.896868i	−0.481979	+	0.876183i	$0.660082\pi$
$840$		0			0
$841$	−12.8274	+	22.2177i	−0.442325	+	0.766129i
$842$		−	30.3860i		−	1.04717i
$843$	−18.2043	−	1.01876i	−0.626989	−	0.0350879i
$844$	−1.65796			−0.0570694
$845$	−2.19901	−	3.80881i	−0.0756484	−	0.131027i
$846$	−20.1103	−	14.8299i	−0.691407	−	0.509863i
$847$		0			0
$848$		0			0
$849$	−34.3651	−	1.92316i	−1.17941	−	0.0660026i
$850$	21.0226	−	12.1374i	0.721069	−	0.416310i
$851$	−34.4373	+	19.8824i	−1.18050	+	0.681559i
$852$	9.50869	+	0.532130i	0.325762	+	0.0182305i
$853$	−25.7693	+	14.8779i	−0.882325	+	0.509411i	−0.871424	−	0.490530i	$-0.836803\pi$
$853$	−25.7693	+	14.8779i	−0.882325	+	0.509411i	−0.0109007	+	0.999941i	$0.503470\pi$
$854$		0			0
$855$	−5.62708	−	4.14957i	−0.192442	−	0.141912i
$856$	−5.53088	−	9.57976i	−0.189042	−	0.327430i
$857$	−45.8592			−1.56652			−0.783260	−	0.621694i	$-0.786445\pi$
$857$	−45.8592			−1.56652			−0.783260	+	0.621694i	$0.786445\pi$
$858$	1.15953	+	0.0648900i	0.0395856	+	0.00221531i
$859$			3.74208i			0.127678i	0.997960	+	0.0638390i	$0.0203344\pi$
$859$			3.74208i			0.127678i	−0.997960	+	0.0638390i	$0.979666\pi$
$860$	−0.824559	+	1.42818i	−0.0281172	+	0.0487005i
$861$		0			0
$862$	−13.6373	−	23.6206i	−0.464490	−	0.804520i
$863$	27.1883	−	15.6972i	0.925502	−	0.534339i	0.0401159	−	0.999195i	$-0.487227\pi$
$863$	27.1883	−	15.6972i	0.925502	−	0.534339i	0.885386	+	0.464856i	$0.153894\pi$
$864$	−1.81045	−	4.87055i	−0.0615927	−	0.165700i
$865$	−0.886533	+	1.53552i	−0.0301430	+	0.0522092i
$866$	4.07523	−	7.05851i	0.138482	−	0.239858i
$867$	−0.763654	+	13.6458i	−0.0259350	+	0.463436i
$868$		0			0
$869$	−4.84432	−	2.79687i	−0.164332	−	0.0948773i
$870$	0.971735	+	0.635960i	0.0329449	+	0.0215611i
$871$		−	10.9078i		−	0.369596i
$872$	−9.14811	−	5.28166i	−0.309794	−	0.178860i
$873$	−41.5672	−	30.6529i	−1.40684	−	1.03744i
$874$			48.9162i			1.65462i
$875$		0			0
$876$	−3.86331	+	5.90307i	−0.130529	+	0.199446i
$877$	−20.3923			−0.688599			−0.344300	−	0.938860i	$-0.611884\pi$
$877$	−20.3923			−0.688599			−0.344300	+	0.938860i	$0.611884\pi$
$878$	6.12020	+	10.6005i	0.206547	+	0.357750i
$879$	−20.7357	+	10.4730i	−0.699399	+	0.353245i
$880$	−0.212540	−	0.122710i	−0.00716473	−	0.00413656i
$881$	21.2010			0.714280			0.357140	−	0.934051i	$-0.383752\pi$
$881$	21.2010			0.714280			0.357140	+	0.934051i	$0.383752\pi$
$882$		0			0
$883$	38.6157			1.29952			0.649761	−	0.760139i	$-0.274869\pi$
$883$	38.6157			1.29952			0.649761	+	0.760139i	$0.274869\pi$
$884$	−4.32741	−	2.49843i	−0.145547	−	0.0840314i
$885$	0.309622	−	5.53267i	0.0104078	−	0.185979i
$886$	4.00418	+	6.93544i	0.134523	+	0.233001i
$887$	6.19211			0.207911			0.103955	−	0.994582i	$-0.466850\pi$
$887$	6.19211			0.207911			0.103955	+	0.994582i	$0.466850\pi$
$888$	−8.93706	−	0.500140i	−0.299908	−	0.0167836i
$889$		0			0
$890$			3.92675i			0.131625i
$891$	−4.41990	−	4.09464i	−0.148072	−	0.137176i
$892$	14.7546	+	8.51860i	0.494022	+	0.285224i
$893$			52.9494i			1.77188i
$894$	−4.37858	+	2.21148i	−0.146441	+	0.0739631i
$895$	−1.16134	−	0.670501i	−0.0388194	−	0.0224124i
$896$		0			0
$897$	−11.9148	+	6.01779i	−0.397824	+	0.200928i
$898$	7.25917	−	12.5733i	0.242242	−	0.419575i
$899$	−5.78495	+	10.0198i	−0.192939	+	0.334180i
$900$	8.66329	−	11.7480i	0.288776	−	0.391599i
$901$		0			0
$902$	1.44554	+	2.50374i	0.0481311	+	0.0833656i
$903$		0			0
$904$	2.07976	−	3.60226i	0.0691719	−	0.119809i
$905$			2.07786i			0.0690705i
$906$	−12.9247	−	25.5899i	−0.429393	−	0.850167i
$907$	−0.129113			−0.00428714			−0.00214357	−	0.999998i	$-0.500682\pi$
$907$	−0.129113			−0.00428714			−0.00214357	+	0.999998i	$0.500682\pi$
$908$	−2.55512	−	4.42560i	−0.0847946	−	0.146869i
$909$	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	$0.141241\pi$
$912$	−6.02973	+	9.21332i	−0.199664	+	0.305083i
$913$	−9.86424	+	5.69512i	−0.326459	+	0.188481i
$914$	8.62130	−	4.97751i	0.285167	−	0.164641i
$915$	−1.41920	−	2.80992i	−0.0469174	−	0.0928931i
$916$	−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	0.723601	−	0.690218i	$-0.242486\pi$
$919$	−7.15271	−	12.3889i	−0.235946	−	0.408671i	−0.959547	+	0.281548i	$0.909152\pi$
$920$	2.82082			0.0929997
$921$	0.620051	−	0.947427i	0.0204314	−	0.0312188i
$922$			32.3270i			1.06463i
$923$	2.75352	−	4.76923i	0.0906332	−	0.156981i
$924$		0			0
$925$	−12.5725	−	21.7761i	−0.413380	−	0.715995i
$926$	8.18421	−	4.72516i	0.268950	−	0.155278i
$927$	−31.4635	+	13.7420i	−1.03340	+	0.451347i
$928$	0.914490	−	1.58394i	0.0300196	−	0.0519955i
$929$	5.87364	−	10.1734i	0.192708	−	0.333780i	−0.753439	−	0.657518i	$-0.771606\pi$
$929$	5.87364	−	10.1734i	0.192708	−	0.333780i	0.946147	+	0.323738i	$0.104940\pi$
$930$	−3.36093	−	2.19959i	−0.110209	−	0.0721274i
$931$		0			0
$932$	8.82741	+	5.09651i	0.289152	+	0.166942i
$933$	0.894710	−	15.9877i	0.0292915	−	0.523413i
$934$			20.6623i			0.676091i
$935$	1.06038	+	0.612209i	0.0346780	+	0.0200214i
$936$	−2.98593	−	0.335250i	−0.0975983	−	0.0109580i
$937$			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
$939$	−4.81333	−	9.53004i	−0.157077	−	0.311001i
$940$	3.05340			0.0995909
$941$	−5.96557	−	10.3327i	−0.194472	−	0.336836i	0.752255	−	0.658872i	$-0.228966\pi$
$941$	−5.96557	−	10.3327i	−0.194472	−	0.336836i	−0.946727	+	0.322036i	$0.895633\pi$
$942$	−4.10803	−	2.68853i	−0.133847	−	0.0875972i
$943$	−28.7776	−	16.6148i	−0.937128	−	0.541051i
$944$	−8.72695			−0.284038
$945$		0			0
$946$	3.01149			0.0979121
$947$	−6.70267	−	3.86979i	−0.217807	−	0.125751i	0.387127	−	0.922026i	$-0.373467\pi$
$947$	−6.70267	−	3.86979i	−0.217807	−	0.125751i	−0.604935	+	0.796275i	$0.706801\pi$
$948$	12.1096	+	7.92524i	0.393302	+	0.257400i
$949$	2.03976	+	3.53296i	0.0662133	+	0.114685i
$950$	−30.9317			−1.00356
$951$	−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
$956$		−	19.1815i		−	0.620375i
$957$	0.118497	−	2.11744i	0.00383047	−	0.0684471i
$958$	−8.79955	−	5.08042i	−0.284301	−	0.164141i
$959$		0			0
$960$	0.531299	+	0.347713i	0.0171476	+	0.0112224i
$961$	4.50836	−	7.80871i	0.145431	−	0.251894i
$962$	−2.58799	+	4.48252i	−0.0834400	+	0.144522i
$963$	26.7085	+	19.6956i	0.860670	+	0.634683i
$964$	−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	$0.190102\pi$
$968$		−	10.5518i		−	0.339149i
$969$	30.0827	−	45.9658i	0.966396	−	1.47663i
$970$	6.31126			0.202642
$971$	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	$0.697222\pi$
$972$	10.8256	+	11.2163i	0.347233	+	0.359763i
$973$		0			0
$974$	−27.0457	+	15.6148i	−0.866599	+	0.500331i
$975$	−3.80530	−	7.53422i	−0.121867	−	0.241288i
$976$	−4.29351	+	2.47886i	−0.137432	+	0.0793463i
$977$	26.0950	−	15.0659i	0.834852	−	0.482002i	−0.0206590	−	0.999787i	$-0.506576\pi$
$977$	26.0950	−	15.0659i	0.834852	−	0.482002i	0.855511	+	0.517785i	$0.173243\pi$
$978$	23.4542	−	35.8376i	0.749983	−	1.14596i
$979$	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
$983$	12.6059			0.402064			0.201032	−	0.979585i	$-0.435570\pi$
$983$	12.6059			0.402064			0.201032	+	0.979585i	$0.435570\pi$
$984$	−3.37219	−	6.67669i	−0.107502	−	0.212845i
$985$		−	6.90152i		−	0.219901i
$986$	−4.56245	+	7.90239i	−0.145298	+	0.251663i
$987$		0			0
$988$	3.18359	+	5.51413i	0.101283	+	0.175428i
$989$	−29.9762	+	17.3068i	−0.953189	+	0.550324i
$990$	0.731664	+	0.0821487i	0.0232538	+	0.00261086i
$991$	−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	$0.860129\pi$
$992$	−3.16294	+	5.47837i	−0.100423	+	0.173938i
$993$	16.5603	−	8.36407i	0.525524	−	0.265426i
$994$		0			0
$995$	1.70300	+	0.983227i	0.0539887	+	0.0311704i
$996$	26.3048	−	13.2857i	0.833500	−	0.420975i
$997$			40.5841i			1.28531i	0.766155	+	0.642656i	$0.222168\pi$
$997$			40.5841i			1.28531i	−0.766155	+	0.642656i	$0.777832\pi$
$998$	21.7834	+	12.5766i	0.689540	+	0.398106i
$999$	25.1705	−	9.35620i	0.796358	−	0.296017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.t.b.815.1		16
3.2	odd	2		2646.2.t.a.2285.6		16
7.2	even	3		882.2.l.a.509.8		16
7.3	odd	6		126.2.m.a.41.7	yes	16
7.4	even	3		126.2.m.a.41.6	✓	16
7.5	odd	6		882.2.l.a.509.5		16
7.6	odd	2	inner	882.2.t.b.815.4		16
9.2	odd	6		882.2.l.a.227.1		16
9.7	even	3		2646.2.l.b.521.6		16
21.2	odd	6		2646.2.l.b.1097.3		16
21.5	even	6		2646.2.l.b.1097.2		16
21.11	odd	6		378.2.m.a.125.3		16
21.17	even	6		378.2.m.a.125.2		16
21.20	even	2		2646.2.t.a.2285.7		16
28.3	even	6		1008.2.cc.b.545.4		16
28.11	odd	6		1008.2.cc.b.545.5		16
63.2	odd	6	inner	882.2.t.b.803.4		16
63.4	even	3		1134.2.d.a.1133.13		16
63.11	odd	6		126.2.m.a.83.7	yes	16
63.16	even	3		2646.2.t.a.1979.7		16
63.20	even	6		882.2.l.a.227.4		16
63.25	even	3		378.2.m.a.251.2		16
63.31	odd	6		1134.2.d.a.1133.12		16
63.32	odd	6		1134.2.d.a.1133.4		16
63.34	odd	6		2646.2.l.b.521.7		16
63.38	even	6		126.2.m.a.83.6	yes	16
63.47	even	6	inner	882.2.t.b.803.1		16
63.52	odd	6		378.2.m.a.251.3		16
63.59	even	6		1134.2.d.a.1133.5		16
63.61	odd	6		2646.2.t.a.1979.6		16
84.11	even	6		3024.2.cc.b.881.5		16
84.59	odd	6		3024.2.cc.b.881.4		16
252.11	even	6		1008.2.cc.b.209.4		16
252.115	even	6		3024.2.cc.b.2897.5		16
252.151	odd	6		3024.2.cc.b.2897.4		16
252.227	odd	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	7.4	even	3
126.2.m.a.41.7	yes	16	7.3	odd	6
126.2.m.a.83.6	yes	16	63.38	even	6
126.2.m.a.83.7	yes	16	63.11	odd	6
378.2.m.a.125.2		16	21.17	even	6
378.2.m.a.125.3		16	21.11	odd	6
378.2.m.a.251.2		16	63.25	even	3
378.2.m.a.251.3		16	63.52	odd	6
882.2.l.a.227.1		16	9.2	odd	6
882.2.l.a.227.4		16	63.20	even	6
882.2.l.a.509.5		16	7.5	odd	6
882.2.l.a.509.8		16	7.2	even	3
882.2.t.b.803.1		16	63.47	even	6	inner
882.2.t.b.803.4		16	63.2	odd	6	inner
882.2.t.b.815.1		16	1.1	even	1	trivial
882.2.t.b.815.4		16	7.6	odd	2	inner
1008.2.cc.b.209.4		16	252.11	even	6
1008.2.cc.b.209.5		16	252.227	odd	6
1008.2.cc.b.545.4		16	28.3	even	6
1008.2.cc.b.545.5		16	28.11	odd	6
1134.2.d.a.1133.4		16	63.32	odd	6
1134.2.d.a.1133.5		16	63.59	even	6
1134.2.d.a.1133.12		16	63.31	odd	6
1134.2.d.a.1133.13		16	63.4	even	3
2646.2.l.b.521.6		16	9.7	even	3
2646.2.l.b.521.7		16	63.34	odd	6
2646.2.l.b.1097.2		16	21.5	even	6
2646.2.l.b.1097.3		16	21.2	odd	6
2646.2.t.a.1979.6		16	63.61	odd	6
2646.2.t.a.1979.7		16	63.16	even	3
2646.2.t.a.2285.6		16	3.2	odd	2
2646.2.t.a.2285.7		16	21.20	even	2
3024.2.cc.b.881.4		16	84.59	odd	6
3024.2.cc.b.881.5		16	84.11	even	6
3024.2.cc.b.2897.4		16	252.151	odd	6
3024.2.cc.b.2897.5		16	252.115	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.44927 - 0.948485i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.366598 q^{5} +(0.780860 + 1.54605i) q^{6} -1.00000i q^{8} +(1.20075 + 2.74922i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.44927 - 0.948485i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.366598 q^{5} +(0.780860 + 1.54605i) q^{6} -1.00000i q^{8} +(1.20075 + 2.74922i) q^{9} +(-0.317483 - 0.183299i) q^{10} +0.669453i q^{11} +(0.0967785 - 1.72934i) q^{12} +(-0.867380 - 0.500782i) q^{13} +(-0.531299 - 0.347713i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.49453 - 4.32065i) q^{17} +(0.334727 - 2.98127i) q^{18} +(-5.50552 + 3.17861i) q^{19} +(0.183299 + 0.317483i) q^{20} +(0.334727 - 0.579764i) q^{22} +7.69459i q^{23} +(-0.948485 + 1.44927i) q^{24} -4.86561 q^{25} +(0.500782 + 0.867380i) q^{26} +(0.867380 - 5.12325i) q^{27} +(1.58394 - 0.914490i) q^{29} +(0.286262 + 0.566778i) q^{30} +(-5.47837 + 3.16294i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.634967 - 0.970217i) q^{33} +(-4.32065 + 2.49453i) q^{34} +(-1.78052 + 2.41449i) q^{36} +(2.58394 + 4.47552i) q^{37} +6.35722 q^{38} +(0.782082 + 1.54846i) q^{39} -0.366598i q^{40} +(-2.15928 + 3.73998i) q^{41} +(2.24922 + 3.89576i) q^{43} +(-0.579764 + 0.334727i) q^{44} +(0.440193 + 1.00786i) q^{45} +(3.84729 - 6.66371i) q^{46} +(4.16450 - 7.21313i) q^{47} +(1.54605 - 0.780860i) q^{48} +(4.21374 + 2.43280i) q^{50} +(-7.71332 + 3.89576i) q^{51} -1.00156i q^{52} +(-3.31280 + 4.00317i) q^{54} +0.245420i q^{55} +(10.9938 + 0.615242i) q^{57} -1.82898 q^{58} +(4.36348 + 7.55776i) q^{59} +(0.0354788 - 0.633975i) q^{60} +(4.29351 + 2.47886i) q^{61} +6.32588 q^{62} -1.00000 q^{64} +(-0.317980 - 0.183586i) q^{65} +(-1.03501 + 0.522749i) q^{66} +(5.44537 + 9.43166i) q^{67} +4.98906 q^{68} +(7.29820 - 11.1515i) q^{69} +5.49843i q^{71} +(2.74922 - 1.20075i) q^{72} +(-3.52744 - 2.03657i) q^{73} -5.16789i q^{74} +(7.05156 + 4.61495i) q^{75} +(-5.50552 - 3.17861i) q^{76} +(0.0969299 - 1.73205i) q^{78} +(-4.17784 + 7.23623i) q^{79} +(-0.183299 + 0.317483i) q^{80} +(-6.11639 + 6.60226i) q^{81} +(3.73998 - 2.15928i) q^{82} +(8.50712 + 14.7348i) q^{83} +(0.914490 - 1.58394i) q^{85} -4.49843i q^{86} +(-3.16294 - 0.177006i) q^{87} +0.669453 q^{88} +(-5.35566 - 9.27628i) q^{89} +(0.122710 - 1.09293i) q^{90} +(-6.66371 + 3.84729i) q^{92} +(10.9396 + 0.612209i) q^{93} +(-7.21313 + 4.16450i) q^{94} +(-2.01831 + 1.16527i) q^{95} +(-1.72934 - 0.0967785i) q^{96} +(-14.9093 + 8.60787i) q^{97} +(-1.84047 + 0.803848i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} - 8 q^{16} + 16 q^{25} - 12 q^{29} + 12 q^{30} + 12 q^{36} + 4 q^{37} + 36 q^{39} + 4 q^{43} + 12 q^{44} - 12 q^{46} + 60 q^{50} - 36 q^{51} + 48 q^{57} + 24 q^{58} - 24 q^{60} - 16 q^{64} - 84 q^{65} - 28 q^{67} + 12 q^{72} - 24 q^{78} - 4 q^{79} - 36 q^{81} - 12 q^{85} - 48 q^{92} + 12 q^{93} - 12 q^{95} - 72 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 - 8 * q^16 + 16 * q^25 - 12 * q^29 + 12 * q^30 + 12 * q^36 + 4 * q^37 + 36 * q^39 + 4 * q^43 + 12 * q^44 - 12 * q^46 + 60 * q^50 - 36 * q^51 + 48 * q^57 + 24 * q^58 - 24 * q^60 - 16 * q^64 - 84 * q^65 - 28 * q^67 + 12 * q^72 - 24 * q^78 - 4 * q^79 - 36 * q^81 - 12 * q^85 - 48 * q^92 + 12 * q^93 - 12 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

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