LMFDB - Embedded newform 539.2.f.e.148.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(148,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("539.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.f (of order $5$, degree $4$, 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:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
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} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			148.3
Root			$-0.206962 - 0.636964i$ of defining polynomial
Character	$\chi$	$=$	539.148
Dual form			539.2.f.e.295.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.206962 + 0.636964i) q^{2} +(2.54013 + 1.84551i) q^{3} +(1.25514 - 0.911915i) q^{4} +(-0.662464 + 2.03885i) q^{5} +(-0.649815 + 1.99992i) q^{6} +(1.92429 + 1.39808i) q^{8} +(2.11929 + 6.52251i) q^{9} +O(q^{10})$	\(q+(0.206962 + 0.636964i) q^{2} +(2.54013 + 1.84551i) q^{3} +(1.25514 - 0.911915i) q^{4} +(-0.662464 + 2.03885i) q^{5} +(-0.649815 + 1.99992i) q^{6} +(1.92429 + 1.39808i) q^{8} +(2.11929 + 6.52251i) q^{9} -1.43578 q^{10} +(-1.08444 - 3.13432i) q^{11} +4.87118 q^{12} +(-0.781276 - 2.40452i) q^{13} +(-5.44548 + 3.95637i) q^{15} +(0.466573 - 1.43596i) q^{16} +(0.553425 - 1.70327i) q^{17} +(-3.71599 + 2.69983i) q^{18} +(-5.44258 - 3.95427i) q^{19} +(1.02778 + 3.16317i) q^{20} +(1.77201 - 1.33944i) q^{22} -3.16429 q^{23} +(2.30778 + 7.10261i) q^{24} +(0.327016 + 0.237591i) q^{25} +(1.36990 - 0.995290i) q^{26} +(-3.74337 + 11.5209i) q^{27} +(0.747669 - 0.543213i) q^{29} +(-3.64707 - 2.64975i) q^{30} +(-0.927602 - 2.85487i) q^{31} +5.76834 q^{32} +(3.02982 - 9.96294i) q^{33} +1.19946 q^{34} +(8.60800 + 6.25408i) q^{36} +(1.21933 - 0.885898i) q^{37} +(1.39232 - 4.28511i) q^{38} +(2.45303 - 7.54965i) q^{39} +(-4.12526 + 2.99718i) q^{40} +(4.49897 + 3.26870i) q^{41} -8.42985 q^{43} +(-4.21937 - 2.94511i) q^{44} -14.7024 q^{45} +(-0.654888 - 2.01554i) q^{46} +(3.55782 + 2.58491i) q^{47} +(3.83525 - 2.78647i) q^{48} +(-0.0836570 + 0.257470i) q^{50} +(4.54917 - 3.30516i) q^{51} +(-3.17333 - 2.30556i) q^{52} +(0.206244 + 0.634755i) q^{53} -8.11314 q^{54} +(7.10883 - 0.134639i) q^{55} +(-6.52722 - 20.0887i) q^{57} +(0.500747 + 0.363814i) q^{58} +(-0.298010 + 0.216517i) q^{59} +(-3.22698 + 9.93163i) q^{60} +(-1.54863 + 4.76621i) q^{61} +(1.62647 - 1.18170i) q^{62} +(0.260682 + 0.802296i) q^{64} +5.42003 q^{65} +(6.97309 - 0.132068i) q^{66} -0.902129 q^{67} +(-0.858607 - 2.64252i) q^{68} +(-8.03770 - 5.83973i) q^{69} +(-4.59489 + 14.1416i) q^{71} +(-5.04086 + 15.5142i) q^{72} +(6.50301 - 4.72471i) q^{73} +(0.816641 + 0.593325i) q^{74} +(0.392186 + 1.20702i) q^{75} -10.4372 q^{76} +5.31654 q^{78} +(1.25358 + 3.85813i) q^{79} +(2.61863 + 1.90255i) q^{80} +(-14.1255 + 10.2628i) q^{81} +(-1.15092 + 3.54218i) q^{82} +(1.25193 - 3.85305i) q^{83} +(3.10609 + 2.25670i) q^{85} +(-1.74466 - 5.36951i) q^{86} +2.90168 q^{87} +(2.29526 - 7.54749i) q^{88} +8.30727 q^{89} +(-3.04284 - 9.36491i) q^{90} +(-3.97163 + 2.88556i) q^{92} +(2.91246 - 8.96363i) q^{93} +(-0.910159 + 2.80118i) q^{94} +(11.6677 - 8.47707i) q^{95} +(14.6523 + 10.6455i) q^{96} +(-2.63154 - 8.09904i) q^{97} +(18.1454 - 13.7158i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} + 2 q^{3} - 11 q^{4} + 5 q^{5} - 3 q^{6} - 5 q^{8} - 12 q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 + 2 * q^3 - 11 * q^4 + 5 * q^5 - 3 * q^6 - 5 * q^8 - 12 * q^9	$ 16 q - 3 q^{2} + 2 q^{3} - 11 q^{4} + 5 q^{5} - 3 q^{6} - 5 q^{8} - 12 q^{9} - 12 q^{10} - 3 q^{11} - 18 q^{12} + 7 q^{13} - 18 q^{15} + 17 q^{16} + 5 q^{17} + 11 q^{18} - 19 q^{19} - q^{20} - 33 q^{22} + 32 q^{23} + 35 q^{24} + 7 q^{25} + 27 q^{26} - 10 q^{27} + 3 q^{29} - 2 q^{30} + 7 q^{31} + 32 q^{32} + 26 q^{33} + 24 q^{34} + 52 q^{36} + 4 q^{37} + 5 q^{38} + 11 q^{39} + 10 q^{40} + 10 q^{41} - 8 q^{43} - 38 q^{44} - 70 q^{45} - 42 q^{46} + 23 q^{47} + 36 q^{48} + 52 q^{50} - 29 q^{51} - 33 q^{52} + 4 q^{53} - 60 q^{54} + 12 q^{55} - 11 q^{57} + 20 q^{58} - 17 q^{59} - 30 q^{60} + 7 q^{61} - 79 q^{62} + 7 q^{64} - 8 q^{65} - 8 q^{66} - 38 q^{67} + 2 q^{68} - 10 q^{69} - 14 q^{71} + 35 q^{73} - 29 q^{74} - 9 q^{75} - 52 q^{76} - 58 q^{78} + 15 q^{79} + 87 q^{80} - 14 q^{81} - 19 q^{82} - 5 q^{83} + 6 q^{85} - 52 q^{86} + 72 q^{87} + 55 q^{88} - 74 q^{89} + 14 q^{90} - 55 q^{92} + 32 q^{93} + 24 q^{94} + 32 q^{95} + 42 q^{96} - 20 q^{97} + 16 q^{99}+O(q^{100}) $ 16 * q - 3 * q^2 + 2 * q^3 - 11 * q^4 + 5 * q^5 - 3 * q^6 - 5 * q^8 - 12 * q^9 - 12 * q^10 - 3 * q^11 - 18 * q^12 + 7 * q^13 - 18 * q^15 + 17 * q^16 + 5 * q^17 + 11 * q^18 - 19 * q^19 - q^20 - 33 * q^22 + 32 * q^23 + 35 * q^24 + 7 * q^25 + 27 * q^26 - 10 * q^27 + 3 * q^29 - 2 * q^30 + 7 * q^31 + 32 * q^32 + 26 * q^33 + 24 * q^34 + 52 * q^36 + 4 * q^37 + 5 * q^38 + 11 * q^39 + 10 * q^40 + 10 * q^41 - 8 * q^43 - 38 * q^44 - 70 * q^45 - 42 * q^46 + 23 * q^47 + 36 * q^48 + 52 * q^50 - 29 * q^51 - 33 * q^52 + 4 * q^53 - 60 * q^54 + 12 * q^55 - 11 * q^57 + 20 * q^58 - 17 * q^59 - 30 * q^60 + 7 * q^61 - 79 * q^62 + 7 * q^64 - 8 * q^65 - 8 * q^66 - 38 * q^67 + 2 * q^68 - 10 * q^69 - 14 * q^71 + 35 * q^73 - 29 * q^74 - 9 * q^75 - 52 * q^76 - 58 * q^78 + 15 * q^79 + 87 * q^80 - 14 * q^81 - 19 * q^82 - 5 * q^83 + 6 * q^85 - 52 * q^86 + 72 * q^87 + 55 * q^88 - 74 * q^89 + 14 * q^90 - 55 * q^92 + 32 * q^93 + 24 * q^94 + 32 * q^95 + 42 * q^96 - 20 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.206962	+	0.636964i	0.146344	+	0.450402i	0.997181	−	0.0750279i	$-0.0239046\pi$
$2$	0.206962	+	0.636964i	0.146344	+	0.450402i	−0.850837	+	0.525430i	$0.823905\pi$
$3$	2.54013	+	1.84551i	1.46654	+	1.06551i	0.981597	+	0.190964i	$0.0611613\pi$
$3$	2.54013	+	1.84551i	1.46654	+	1.06551i	0.484948	+	0.874543i	$0.338839\pi$
$4$	1.25514	−	0.911915i	0.627572	−	0.455958i
$5$	−0.662464	+	2.03885i	−0.296263	+	0.911803i	0.686531	+	0.727100i	$0.259132\pi$
$5$	−0.662464	+	2.03885i	−0.296263	+	0.911803i	−0.982794	+	0.184703i	$0.940868\pi$
$6$	−0.649815	+	1.99992i	−0.265286	+	0.816465i
$7$		0			0
$7$		0			0
$8$	1.92429	+	1.39808i	0.680340	+	0.494296i
$9$	2.11929	+	6.52251i	0.706431	+	2.17417i
$10$	−1.43578			−0.454034
$11$	−1.08444	−	3.13432i	−0.326971	−	0.945034i
$11$	−1.08444	−	3.13432i	−0.326971	−	0.945034i
$12$	4.87118			1.40619
$13$	−0.781276	−	2.40452i	−0.216687	−	0.666894i	−0.999030	−	0.0440455i	$-0.985975\pi$
$13$	−0.781276	−	2.40452i	−0.216687	−	0.666894i	0.782343	−	0.622848i	$-0.214025\pi$
$14$		0			0
$15$	−5.44548	+	3.95637i	−1.40602	+	1.02153i
$16$	0.466573	−	1.43596i	0.116643	−	0.358991i
$17$	0.553425	−	1.70327i	0.134225	−	0.413103i	−0.861244	−	0.508193i	$-0.830314\pi$
$17$	0.553425	−	1.70327i	0.134225	−	0.413103i	0.995469	+	0.0950899i	$0.0303138\pi$
$18$	−3.71599	+	2.69983i	−0.875868	+	0.636356i
$19$	−5.44258	−	3.95427i	−1.24861	−	0.907171i	−0.250473	−	0.968124i	$-0.580586\pi$
$19$	−5.44258	−	3.95427i	−1.24861	−	0.907171i	−0.998141	+	0.0609525i	$0.980586\pi$
$20$	1.02778	+	3.16317i	0.229818	+	0.707306i
$21$		0			0
$22$	1.77201	−	1.33944i	0.377795	−	0.285569i
$23$	−3.16429			−0.659799			−0.329900	−	0.944016i	$-0.607015\pi$
$23$	−3.16429			−0.659799			−0.329900	+	0.944016i	$0.607015\pi$
$24$	2.30778	+	7.10261i	0.471073	+	1.44982i
$25$	0.327016	+	0.237591i	0.0654031	+	0.0475182i
$26$	1.36990	−	0.995290i	0.268659	−	0.195192i
$27$	−3.74337	+	11.5209i	−0.720412	+	2.21720i
$28$		0			0
$29$	0.747669	−	0.543213i	0.138839	−	0.100872i	−0.516198	−	0.856469i	$-0.672653\pi$
$29$	0.747669	−	0.543213i	0.138839	−	0.100872i	0.655037	+	0.755597i	$0.272653\pi$
$30$	−3.64707	−	2.64975i	−0.665862	−	0.483777i
$31$	−0.927602	−	2.85487i	−0.166602	−	0.512749i	0.832549	−	0.553952i	$-0.186881\pi$
$31$	−0.927602	−	2.85487i	−0.166602	−	0.512749i	−0.999151	+	0.0412031i	$0.986881\pi$
$32$	5.76834			1.01971
$33$	3.02982	−	9.96294i	0.527423	−	1.73433i
$34$	1.19946			0.205705
$35$		0			0
$36$	8.60800	+	6.25408i	1.43467	+	1.04235i
$37$	1.21933	−	0.885898i	0.200457	−	0.145641i	−0.483028	−	0.875605i	$-0.660463\pi$
$37$	1.21933	−	0.885898i	0.200457	−	0.145641i	0.683486	+	0.729964i	$0.260463\pi$
$38$	1.39232	−	4.28511i	0.225864	−	0.695137i
$39$	2.45303	−	7.54965i	0.392799	−	1.20891i
$40$	−4.12526	+	2.99718i	−0.652261	+	0.473895i
$41$	4.49897	+	3.26870i	0.702622	+	0.510485i	0.880785	−	0.473516i	$-0.157016\pi$
$41$	4.49897	+	3.26870i	0.702622	+	0.510485i	−0.178163	+	0.984001i	$0.557016\pi$
$42$		0			0
$43$	−8.42985			−1.28554			−0.642770	−	0.766059i	$-0.722215\pi$
$43$	−8.42985			−1.28554			−0.642770	+	0.766059i	$0.722215\pi$
$44$	−4.21937	−	2.94511i	−0.636094	−	0.443992i
$45$	−14.7024			−2.19171
$46$	−0.654888	−	2.01554i	−0.0965579	−	0.297175i
$47$	3.55782	+	2.58491i	0.518961	+	0.377047i	0.816212	−	0.577752i	$-0.196070\pi$
$47$	3.55782	+	2.58491i	0.518961	+	0.377047i	−0.297251	+	0.954799i	$0.596070\pi$
$48$	3.83525	−	2.78647i	0.553570	−	0.402192i
$49$		0			0
$50$	−0.0836570	+	0.257470i	−0.0118309	+	0.0364117i
$51$	4.54917	−	3.30516i	0.637011	−	0.462816i
$52$	−3.17333	−	2.30556i	−0.440062	−	0.319724i
$53$	0.206244	+	0.634755i	0.0283298	+	0.0871903i	0.964222	−	0.265097i	$-0.0854040\pi$
$53$	0.206244	+	0.634755i	0.0283298	+	0.0871903i	−0.935892	+	0.352287i	$0.885404\pi$
$54$	−8.11314			−1.10406
$55$	7.10883	−	0.134639i	0.958555	−	0.0181547i
$56$		0			0
$57$	−6.52722	−	20.0887i	−0.864551	−	2.66081i
$58$	0.500747	+	0.363814i	0.0657513	+	0.0477711i
$59$	−0.298010	+	0.216517i	−0.0387976	+	0.0281881i	−0.607015	−	0.794690i	$-0.707633\pi$
$59$	−0.298010	+	0.216517i	−0.0387976	+	0.0281881i	0.568217	+	0.822878i	$0.307633\pi$
$60$	−3.22698	+	9.93163i	−0.416601	+	1.28217i
$61$	−1.54863	+	4.76621i	−0.198282	+	0.610250i	0.801640	+	0.597807i	$0.203961\pi$
$61$	−1.54863	+	4.76621i	−0.198282	+	0.610250i	−0.999923	+	0.0124435i	$0.996039\pi$
$62$	1.62647	−	1.18170i	0.206562	−	0.150076i
$63$		0			0
$64$	0.260682	+	0.802296i	0.0325852	+	0.100287i
$65$	5.42003			0.672273
$66$	6.97309	−	0.132068i	0.858329	−	0.0162564i
$67$	−0.902129			−0.110213			−0.0551063	−	0.998480i	$-0.517550\pi$
$67$	−0.902129			−0.110213			−0.0551063	+	0.998480i	$0.517550\pi$
$68$	−0.858607	−	2.64252i	−0.104121	−	0.320453i
$69$	−8.03770	−	5.83973i	−0.967625	−	0.703021i
$70$		0			0
$71$	−4.59489	+	14.1416i	−0.545313	+	1.67830i	0.174932	+	0.984580i	$0.444029\pi$
$71$	−4.59489	+	14.1416i	−0.545313	+	1.67830i	−0.720245	+	0.693720i	$0.755971\pi$
$72$	−5.04086	+	15.5142i	−0.594071	+	1.82836i
$73$	6.50301	−	4.72471i	0.761119	−	0.552986i	−0.138134	−	0.990414i	$-0.544110\pi$
$73$	6.50301	−	4.72471i	0.761119	−	0.552986i	0.899254	+	0.437428i	$0.144110\pi$
$74$	0.816641	+	0.593325i	0.0949326	+	0.0689726i
$75$	0.392186	+	1.20702i	0.0452857	+	0.139375i
$76$	−10.4372			−1.19723
$77$		0			0
$78$	5.31654			0.601980
$79$	1.25358	+	3.85813i	0.141039	+	0.434074i	0.996480	−	0.0838261i	$-0.0267140\pi$
$79$	1.25358	+	3.85813i	0.141039	+	0.434074i	−0.855441	+	0.517900i	$0.826714\pi$
$80$	2.61863	+	1.90255i	0.292772	+	0.212711i
$81$	−14.1255	+	10.2628i	−1.56950	+	1.14031i
$82$	−1.15092	+	3.54218i	−0.127098	+	0.391169i
$83$	1.25193	−	3.85305i	0.137418	−	0.422928i	−0.858541	−	0.512745i	$-0.828628\pi$
$83$	1.25193	−	3.85305i	0.137418	−	0.422928i	0.995958	+	0.0898178i	$0.0286285\pi$
$84$		0			0
$85$	3.10609	+	2.25670i	0.336902	+	0.244774i
$86$	−1.74466	−	5.36951i	−0.188132	−	0.579009i
$87$	2.90168			0.311093
$88$	2.29526	−	7.54749i	0.244675	−	0.804566i
$89$	8.30727			0.880569			0.440284	−	0.897858i	$-0.354878\pi$
$89$	8.30727			0.880569			0.440284	+	0.897858i	$0.354878\pi$
$90$	−3.04284	−	9.36491i	−0.320744	−	0.987148i
$91$		0			0
$92$	−3.97163	+	2.88556i	−0.414071	+	0.300840i
$93$	2.91246	−	8.96363i	0.302008	−	0.929485i
$94$	−0.910159	+	2.80118i	−0.0938758	+	0.288920i
$95$	11.6677	−	8.47707i	1.19708	−	0.869729i
$96$	14.6523	+	10.6455i	1.49545	+	1.08651i
$97$	−2.63154	−	8.09904i	−0.267192	−	0.822333i	−0.991180	−	0.132520i	$-0.957693\pi$
$97$	−2.63154	−	8.09904i	−0.267192	−	0.822333i	0.723988	−	0.689812i	$-0.242307\pi$
$98$		0			0
$99$	18.1454	−	13.7158i	1.82368	−	1.37849i
$100$	0.627115			0.0627115
$101$	1.24443	+	3.82997i	0.123826	+	0.381096i	0.993685	−	0.112203i	$-0.0357907\pi$
$101$	1.24443	+	3.82997i	0.123826	+	0.381096i	−0.869860	+	0.493299i	$0.835791\pi$
$102$	3.04678	+	2.21361i	0.301676	+	0.219180i
$103$	−14.2596	+	10.3602i	−1.40504	+	1.02082i	−0.411020	+	0.911626i	$0.634827\pi$
$103$	−14.2596	+	10.3602i	−1.40504	+	1.02082i	−0.994020	+	0.109195i	$0.965173\pi$
$104$	1.85831	−	5.71929i	0.182222	−	0.560822i
$105$		0			0
$106$	−0.361631	+	0.262741i	−0.0351248	+	0.0255196i
$107$	12.4619	+	9.05408i	1.20473	+	0.875291i	0.994742	−	0.102412i	$-0.0326560\pi$
$107$	12.4619	+	9.05408i	1.20473	+	0.875291i	0.209993	+	0.977703i	$0.432656\pi$
$108$	5.80762	+	17.8740i	0.558839	+	1.71993i
$109$	−18.9265			−1.81283			−0.906416	−	0.422386i	$-0.861193\pi$
$109$	−18.9265			−1.81283			−0.906416	+	0.422386i	$0.861193\pi$
$110$	1.55702	+	4.50021i	0.148456	+	0.429078i
$111$	4.73220			0.449161
$112$		0			0
$113$	−1.35965	−	0.987844i	−0.127905	−	0.0929286i	0.521993	−	0.852950i	$-0.325189\pi$
$113$	−1.35965	−	0.987844i	−0.127905	−	0.0929286i	−0.649898	+	0.760021i	$0.725189\pi$
$114$	11.4449	−	8.31521i	1.07191	−	0.778790i
$115$	2.09623	−	6.45152i	0.195474	−	0.601607i
$116$	0.443068	−	1.36362i	0.0411378	−	0.126609i
$117$	14.0278	−	10.1918i	1.29687	−	0.942229i
$118$	−0.199590	−	0.145011i	−0.0183738	−	0.0133493i
$119$		0			0
$120$	−16.0100			−1.46151
$121$	−8.64798	+	6.79797i	−0.786180	+	0.617998i
$122$	−3.35641			−0.303875
$123$	5.39556	+	16.6058i	0.486501	+	1.49730i
$124$	−3.76767	−	2.73737i	−0.338347	−	0.245823i
$125$	−9.37282	+	6.80975i	−0.838330	+	0.609082i
$126$		0			0
$127$	5.42848	−	16.7071i	0.481699	−	1.48252i	−0.355006	−	0.934864i	$-0.615521\pi$
$127$	5.42848	−	16.7071i	0.481699	−	1.48252i	0.836705	−	0.547654i	$-0.184479\pi$
$128$	8.87628	−	6.44900i	0.784560	−	0.570016i
$129$	−21.4129	−	15.5574i	−1.88530	−	1.36975i
$130$	1.12174	+	3.45237i	0.0983833	+	0.302793i
$131$	−6.72557			−0.587616			−0.293808	−	0.955865i	$-0.594923\pi$
$131$	−6.72557			−0.587616			−0.293808	+	0.955865i	$0.594923\pi$
$132$	−5.28250	−	15.2679i	−0.459783	−	1.32890i
$133$		0			0
$134$	−0.186707	−	0.574624i	−0.0161290	−	0.0496400i
$135$	−21.0096	−	15.2644i	−1.80822	−	1.31375i
$136$	3.44625	−	2.50385i	0.295514	−	0.214703i
$137$	4.28533	−	13.1889i	0.366121	−	1.12680i	−0.583156	−	0.812360i	$-0.698182\pi$
$137$	4.28533	−	13.1889i	0.366121	−	1.12680i	0.949276	−	0.314443i	$-0.101818\pi$
$138$	2.05620	−	6.32833i	0.175035	−	0.538703i
$139$	11.5453	−	8.38812i	0.979256	−	0.711471i	0.0217140	−	0.999764i	$-0.493088\pi$
$139$	11.5453	−	8.38812i	0.979256	−	0.711471i	0.957542	+	0.288293i	$0.0930877\pi$
$140$		0			0
$141$	4.26685	+	13.1320i	0.359333	+	1.10591i
$142$	−9.95867			−0.835713
$143$	−6.68930	+	5.05633i	−0.559387	+	0.422832i
$144$	10.3549			0.862908
$145$	0.612229	+	1.88425i	0.0508429	+	0.156478i
$146$	4.35535	+	3.16435i	0.360451	+	0.261883i
$147$		0			0
$148$	0.722575	−	2.22386i	0.0593953	−	0.182800i
$149$	0.810527	−	2.49455i	0.0664010	−	0.204361i	−0.912351	−	0.409409i	$-0.865735\pi$
$149$	0.810527	−	2.49455i	0.0664010	−	0.204361i	0.978752	+	0.205048i	$0.0657349\pi$
$150$	−0.687663	+	0.499616i	−0.0561475	+	0.0407935i
$151$	2.41864	+	1.75724i	0.196826	+	0.143002i	0.681833	−	0.731508i	$-0.261183\pi$
$151$	2.41864	+	1.75724i	0.196826	+	0.143002i	−0.485007	+	0.874510i	$0.661183\pi$
$152$	−4.94474	−	15.2183i	−0.401071	−	1.23437i
$153$	12.2824			0.992977
$154$		0			0
$155$	6.43516			0.516884
$156$	−3.80574	−	11.7128i	−0.304703	−	0.937779i
$157$	9.10524	+	6.61534i	0.726677	+	0.527962i	0.888511	−	0.458856i	$-0.151741\pi$
$157$	9.10524	+	6.61534i	0.726677	+	0.527962i	−0.161833	+	0.986818i	$0.551741\pi$
$158$	−2.19805	+	1.59698i	−0.174867	+	0.127049i
$159$	−0.647561	+	1.99299i	−0.0513549	+	0.158054i
$160$	−3.82131	+	11.7608i	−0.302101	+	0.929773i
$161$		0			0
$162$	−9.46045	−	6.87342i	−0.743283	−	0.540027i
$163$	−5.62502	−	17.3120i	−0.440586	−	1.35598i	−0.887253	−	0.461283i	$-0.847389\pi$
$163$	−5.62502	−	17.3120i	−0.440586	−	1.35598i	0.446667	−	0.894700i	$-0.352611\pi$
$164$	8.62763			0.673705
$165$	18.3058	+	12.7774i	1.42511	+	0.994722i
$166$	2.71336			0.210598
$167$	−6.15909	−	18.9557i	−0.476605	−	1.46684i	−0.843781	−	0.536687i	$-0.819675\pi$
$167$	−6.15909	−	18.9557i	−0.476605	−	1.46684i	0.367176	−	0.930151i	$-0.380325\pi$
$168$		0			0
$169$	5.34590	−	3.88402i	0.411223	−	0.298771i
$170$	−0.794597	+	2.44552i	−0.0609428	+	0.187563i
$171$	14.2573	−	43.8796i	1.09029	−	3.35555i
$172$	−10.5807	+	7.68731i	−0.806769	+	0.586152i
$173$	4.84607	+	3.52088i	0.368440	+	0.267687i	0.756564	−	0.653920i	$-0.226877\pi$
$173$	4.84607	+	3.52088i	0.368440	+	0.267687i	−0.388124	+	0.921607i	$0.626877\pi$
$174$	0.600539	+	1.84827i	0.0455267	+	0.140117i
$175$		0			0
$176$	−5.00675	+	0.0948260i	−0.377398	+	0.00714778i
$177$	−1.15657			−0.0869329
$178$	1.71929	+	5.29143i	0.128866	+	0.396610i
$179$	1.30975	+	0.951588i	0.0978952	+	0.0711251i	0.635656	−	0.771972i	$-0.280730\pi$
$179$	1.30975	+	0.951588i	0.0978952	+	0.0711251i	−0.537761	+	0.843097i	$0.680730\pi$
$180$	−18.4536	+	13.4074i	−1.37545	+	0.999325i
$181$	−0.749929	+	2.30804i	−0.0557418	+	0.171556i	−0.975051	−	0.221980i	$-0.928748\pi$
$181$	−0.749929	+	2.30804i	−0.0557418	+	0.171556i	0.919309	+	0.393535i	$0.128748\pi$
$182$		0			0
$183$	−12.7298	+	9.24876i	−0.941016	+	0.683688i
$184$	−6.08901	−	4.42393i	−0.448888	−	0.326136i
$185$	0.998452	+	3.07292i	0.0734077	+	0.225926i
$186$	6.31228			0.462839
$187$	−5.93874	+	0.112478i	−0.434284	+	0.00822518i
$188$	6.82279			0.497603
$189$		0			0
$190$	7.81436	+	5.67747i	0.566914	+	0.411887i
$191$	−10.2753	+	7.46541i	−0.743492	+	0.540178i	−0.893803	−	0.448460i	$-0.851973\pi$
$191$	−10.2753	+	7.46541i	−0.743492	+	0.540178i	0.150311	+	0.988639i	$0.451973\pi$
$192$	−0.818481	+	2.51903i	−0.0590688	+	0.181795i
$193$	−0.543657	+	1.67320i	−0.0391333	+	0.120440i	−0.968715	−	0.248177i	$-0.920169\pi$
$193$	−0.543657	+	1.67320i	−0.0391333	+	0.120440i	0.929581	+	0.368617i	$0.120169\pi$
$194$	4.61417	−	3.35239i	0.331278	−	0.240688i
$195$	13.7676	+	10.0027i	0.985918	+	0.716311i
$196$		0			0
$197$	−0.903053			−0.0643399			−0.0321699	−	0.999482i	$-0.510242\pi$
$197$	−0.903053			−0.0643399			−0.0321699	+	0.999482i	$0.510242\pi$
$198$	12.4919	+	8.71933i	0.887761	+	0.619656i
$199$	15.6296			1.10795			0.553976	−	0.832533i	$-0.313110\pi$
$199$	15.6296			1.10795			0.553976	+	0.832533i	$0.313110\pi$
$200$	0.297103	+	0.914389i	0.0210084	+	0.0646571i
$201$	−2.29153	−	1.66489i	−0.161632	−	0.117432i
$202$	−2.18200	+	1.58532i	−0.153525	+	0.111543i
$203$		0			0
$204$	2.69583	−	8.29691i	0.188746	−	0.580900i
$205$	−9.64480	+	7.00736i	−0.673622	+	0.489415i
$206$	−9.55028	−	6.93868i	−0.665399	−	0.483441i
$207$	−6.70605	−	20.6391i	−0.466103	−	1.43452i
$208$	−3.81733			−0.264684
$209$	−6.49180	+	21.3470i	−0.449047	+	1.47660i
$210$		0			0
$211$	4.56378	+	14.0459i	0.314184	+	0.966958i	0.976089	+	0.217371i	$0.0697480\pi$
$211$	4.56378	+	14.0459i	0.314184	+	0.966958i	−0.661905	+	0.749587i	$0.730252\pi$
$212$	0.837709	+	0.608631i	0.0575341	+	0.0418010i
$213$	−37.7701	+	27.4416i	−2.58797	+	1.88027i
$214$	−3.18799	+	9.81162i	−0.217926	+	0.670709i
$215$	5.58447	−	17.1872i	0.380858	−	1.17216i
$216$	−23.3105	+	16.9361i	−1.58608	+	1.15235i
$217$		0			0
$218$	−3.91708	−	12.0555i	−0.265298	−	0.816503i
$219$	25.2380			1.70543
$220$	8.79983	−	6.65165i	0.593284	−	0.448454i
$221$	−4.52791			−0.304581
$222$	0.979387	+	3.01424i	0.0657322	+	0.202303i
$223$	−1.49293	−	1.08468i	−0.0999743	−	0.0726356i	0.536675	−	0.843789i	$-0.319680\pi$
$223$	−1.49293	−	1.08468i	−0.0999743	−	0.0726356i	−0.636649	+	0.771153i	$0.719680\pi$
$224$		0			0
$225$	−0.856647	+	2.63649i	−0.0571098	+	0.175766i
$226$	0.347825	−	1.07050i	0.0231370	−	0.0712083i
$227$	−17.7498	+	12.8960i	−1.17809	+	0.855936i	−0.991955	−	0.126588i	$-0.959597\pi$
$227$	−17.7498	+	12.8960i	−1.17809	+	0.855936i	−0.186139	+	0.982523i	$0.559597\pi$
$228$	−26.5118	−	19.2619i	−1.75579	−	1.27565i
$229$	6.25815	+	19.2606i	0.413550	+	1.27278i	0.913541	+	0.406746i	$0.133337\pi$
$229$	6.25815	+	19.2606i	0.413550	+	1.27278i	−0.499991	+	0.866030i	$0.666663\pi$
$230$	4.54323			0.299571
$231$		0			0
$232$	2.19819			0.144318
$233$	6.50870	+	20.0317i	0.426399	+	1.31232i	0.901648	+	0.432470i	$0.142358\pi$
$233$	6.50870	+	20.0317i	0.426399	+	1.31232i	−0.475250	+	0.879851i	$0.657642\pi$
$234$	9.39501	+	6.82587i	0.614171	+	0.446221i
$235$	−7.62718	+	5.54147i	−0.497542	+	0.361486i
$236$	−0.176600	+	0.543519i	−0.0114957	+	0.0353801i
$237$	−3.93597	+	12.1137i	−0.255668	+	0.786867i
$238$		0			0
$239$	−12.5370	−	9.10863i	−0.810948	−	0.589188i	0.103157	−	0.994665i	$-0.467106\pi$
$239$	−12.5370	−	9.10863i	−0.810948	−	0.589188i	−0.914105	+	0.405477i	$0.867106\pi$
$240$	3.14049	+	9.66544i	0.202718	+	0.623902i
$241$	−14.0848			−0.907283			−0.453641	−	0.891184i	$-0.649875\pi$
$241$	−14.0848			−0.907283			−0.453641	+	0.891184i	$0.649875\pi$
$242$	−6.11987	−	4.10153i	−0.393400	−	0.263656i
$243$	−18.4792			−1.18544
$244$	2.40262	+	7.39450i	0.153812	+	0.473384i
$245$		0			0
$246$	−9.46064	+	6.87356i	−0.603188	+	0.438242i
$247$	−5.25596	+	16.1762i	−0.334429	+	1.02927i
$248$	2.20635	−	6.79046i	0.140104	−	0.431195i
$249$	10.2909	−	7.47680i	0.652161	−	0.473823i
$250$	−6.27739	−	4.56079i	−0.397017	−	0.288450i
$251$	0.332894	+	1.02454i	0.0210121	+	0.0646686i	0.961013	−	0.276504i	$-0.0891759\pi$
$251$	0.332894	+	1.02454i	0.0210121	+	0.0646686i	−0.940001	+	0.341173i	$0.889176\pi$
$252$		0			0
$253$	3.43148	+	9.91790i	0.215735	+	0.623533i
$254$	11.7653			0.738223
$255$	3.72509	+	11.4646i	0.233274	+	0.717944i
$256$	7.30978	+	5.31087i	0.456861	+	0.331929i
$257$	10.5828	−	7.68883i	0.660135	−	0.479616i	−0.206574	−	0.978431i	$-0.566231\pi$
$257$	10.5828	−	7.68883i	0.660135	−	0.479616i	0.866708	+	0.498815i	$0.166231\pi$
$258$	5.47784	−	16.8591i	0.341035	−	1.04960i
$259$		0			0
$260$	6.80292	−	4.94261i	0.421899	−	0.306528i
$261$	5.12765	+	3.72545i	0.317393	+	0.230600i
$262$	−1.39194	−	4.28395i	−0.0859943	−	0.264663i
$263$	−9.57216			−0.590245			−0.295122	−	0.955459i	$-0.595360\pi$
$263$	−9.57216			−0.590245			−0.295122	+	0.955459i	$0.595360\pi$
$264$	19.7592	−	14.9357i	1.21610	−	0.919228i
$265$	−1.43080			−0.0878935
$266$		0			0
$267$	21.1015	+	15.3312i	1.29139	+	0.938252i
$268$	−1.13230	+	0.822665i	−0.0691663	+	0.0502523i
$269$	1.47356	−	4.53514i	0.0898444	−	0.276513i	−0.896031	−	0.443991i	$-0.853562\pi$
$269$	1.47356	−	4.53514i	0.0898444	−	0.276513i	0.985876	+	0.167478i	$0.0535623\pi$
$270$	5.37466	−	16.5415i	0.327092	−	1.00668i
$271$	−16.2226	+	11.7864i	−0.985455	+	0.715975i	−0.958921	−	0.283673i	$-0.908447\pi$
$271$	−16.2226	+	11.7864i	−0.985455	+	0.715975i	−0.0265341	+	0.999648i	$0.508447\pi$
$272$	−2.18762	−	1.58940i	−0.132644	−	0.0963713i
$273$		0			0
$274$	9.28776			0.561094
$275$	0.390058	−	1.28263i	0.0235214	−	0.0773453i
$276$	−15.4138			−0.927802
$277$	−3.58535	−	11.0346i	−0.215423	−	0.663004i	−0.999123	−	0.0418647i	$-0.986670\pi$
$277$	−3.58535	−	11.0346i	−0.215423	−	0.663004i	0.783700	−	0.621139i	$-0.213330\pi$
$278$	7.73237	+	5.61789i	0.463757	+	0.336939i
$279$	16.6550	−	12.1006i	0.997111	−	0.724443i
$280$		0			0
$281$	3.73256	−	11.4876i	0.222666	−	0.685295i	−0.775854	−	0.630912i	$-0.782681\pi$
$281$	3.73256	−	11.4876i	0.222666	−	0.685295i	0.998520	−	0.0543830i	$-0.0173192\pi$
$282$	−7.48154	+	5.43566i	−0.445519	+	0.323689i
$283$	17.7929	+	12.9273i	1.05768	+	0.768448i	0.973657	−	0.228017i	$-0.0732240\pi$
$283$	17.7929	+	12.9273i	1.05768	+	0.768448i	0.0840200	+	0.996464i	$0.473224\pi$
$284$	7.12871	+	21.9399i	0.423011	+	1.30189i
$285$	45.2820			2.68227
$286$	−4.60513	−	3.21438i	−0.272307	−	0.190070i
$287$		0			0
$288$	12.2248	+	37.6240i	0.720353	+	2.21702i
$289$	11.1585	+	8.10709i	0.656380	+	0.476888i
$290$	−1.07349	+	0.779936i	−0.0630375	+	0.0457994i
$291$	8.26243	−	25.4291i	0.484352	−	1.49068i
$292$	3.85367	−	11.8604i	0.225519	−	0.694077i
$293$	1.14654	−	0.833014i	0.0669819	−	0.0486652i	−0.553790	−	0.832656i	$-0.686819\pi$
$293$	1.14654	−	0.833014i	0.0669819	−	0.0486652i	0.620772	+	0.783991i	$0.286819\pi$
$294$		0			0
$295$	−0.244025	−	0.751033i	−0.0142077	−	0.0437268i
$296$	3.58491			0.208369
$297$	40.1697	−	0.760800i	2.33088	−	0.0441461i
$298$	1.75669			0.101762
$299$	2.47218	+	7.60859i	0.142970	+	0.440016i
$300$	1.59295	+	1.15735i	0.0919691	+	0.0668195i
$301$		0			0
$302$	−0.618734	+	1.90427i	−0.0356041	+	0.109578i
$303$	−3.90724	+	12.0252i	−0.224465	+	0.690832i
$304$	−8.21755	+	5.97040i	−0.471309	+	0.342426i
$305$	−8.69169	−	6.31488i	−0.497685	−	0.361589i
$306$	2.54200	+	7.82348i	0.145317	+	0.447238i
$307$	−29.4646			−1.68163			−0.840817	−	0.541319i	$-0.817925\pi$
$307$	−29.4646			−1.68163			−0.840817	+	0.541319i	$0.817925\pi$
$308$		0			0
$309$	−55.3411			−3.14825
$310$	1.33183	+	4.09897i	0.0756431	+	0.232806i
$311$	21.7453	+	15.7989i	1.23306	+	0.895873i	0.997116	−	0.0758927i	$-0.0241807\pi$
$311$	21.7453	+	15.7989i	1.23306	+	0.895873i	0.235948	+	0.971766i	$0.424181\pi$
$312$	15.2754	−	11.0982i	0.864797	−	0.628312i
$313$	1.38832	−	4.27281i	0.0784725	−	0.241514i	−0.904123	−	0.427273i	$-0.859474\pi$
$313$	1.38832	−	4.27281i	0.0784725	−	0.241514i	0.982595	+	0.185759i	$0.0594744\pi$
$314$	−2.32930	+	7.16884i	−0.131450	+	0.404561i
$315$		0			0
$316$	5.09172	+	3.69935i	0.286431	+	0.208105i
$317$	−3.38376	−	10.4141i	−0.190051	−	0.584916i	0.809948	−	0.586502i	$-0.199495\pi$
$317$	−3.38376	−	10.4141i	−0.190051	−	0.584916i	−0.999999	+	0.00158586i	$0.999495\pi$
$318$	−1.40348			−0.0787034
$319$	−2.51341	−	1.75436i	−0.140724	−	0.0982250i
$320$	−1.80846			−0.101096
$321$	14.9454	+	45.9971i	0.834169	+	2.56731i
$322$		0			0
$323$	−9.74723	+	7.08177i	−0.542350	+	0.394040i
$324$	−8.37074	+	25.7625i	−0.465041	+	1.43125i
$325$	0.315802	−	0.971940i	0.0175176	−	0.0539135i
$326$	9.86298	−	7.16588i	0.546260	−	0.396881i
$327$	−48.0758	−	34.9291i	−2.65860	−	1.93159i
$328$	4.08744	+	12.5799i	0.225691	+	0.694607i
$329$		0			0
$330$	−4.35016	+	14.3046i	−0.239468	+	0.787443i
$331$	16.5226			0.908166			0.454083	−	0.890959i	$-0.349967\pi$
$331$	16.5226			0.908166			0.454083	+	0.890959i	$0.349967\pi$
$332$	−1.94230	−	5.97779i	−0.106598	−	0.328074i
$333$	8.36241	+	6.07564i	0.458257	+	0.332943i
$334$	10.7994	−	7.84624i	0.590918	−	0.429327i
$335$	0.597628	−	1.83931i	0.0326519	−	0.100492i
$336$		0			0
$337$	9.80588	−	7.12439i	0.534160	−	0.388090i	−0.287751	−	0.957705i	$-0.592908\pi$
$337$	9.80588	−	7.12439i	0.534160	−	0.388090i	0.821912	+	0.569615i	$0.192908\pi$
$338$	3.58038	+	2.60130i	0.194747	+	0.141492i
$339$	−1.63061	−	5.01851i	−0.0885626	−	0.272568i
$340$	5.95651			0.323037
$341$	−7.94214	+	6.00334i	−0.430091	+	0.325099i
$342$	30.9004			1.67090
$343$		0			0
$344$	−16.2215	−	11.7856i	−0.874605	−	0.635437i
$345$	17.2310	−	12.5191i	0.927688	−	0.674005i
$346$	−1.23972	+	3.81547i	−0.0666478	+	0.205121i
$347$	−7.50452	+	23.0965i	−0.402864	+	1.23989i	0.519802	+	0.854287i	$0.326006\pi$
$347$	−7.50452	+	23.0965i	−0.402864	+	1.23989i	−0.922666	+	0.385600i	$0.873994\pi$
$348$	3.64203	−	2.64609i	0.195233	−	0.141845i
$349$	−2.68497	−	1.95074i	−0.143723	−	0.104421i	0.513600	−	0.858030i	$-0.328311\pi$
$349$	−2.68497	−	1.95074i	−0.143723	−	0.104421i	−0.657323	+	0.753609i	$0.728311\pi$
$350$		0			0
$351$	30.6269			1.63474
$352$	−6.25542	−	18.0798i	−0.333415	−	0.963658i
$353$	−20.3272			−1.08191			−0.540955	−	0.841051i	$-0.681937\pi$
$353$	−20.3272			−1.08191			−0.540955	+	0.841051i	$0.681937\pi$
$354$	−0.239366	−	0.736692i	−0.0127221	−	0.0391548i
$355$	−25.7887	−	18.7366i	−1.36872	−	0.994436i
$356$	10.4268	−	7.57553i	0.552620	−	0.401502i
$357$		0			0
$358$	−0.335059	+	1.03121i	−0.0177084	+	0.0545009i
$359$	−23.4949	+	17.0700i	−1.24001	+	0.900921i	−0.997599	−	0.0692529i	$-0.977938\pi$
$359$	−23.4949	+	17.0700i	−1.24001	+	0.900921i	−0.242412	+	0.970173i	$0.577938\pi$
$360$	−28.2917	−	20.5552i	−1.49111	−	1.08335i
$361$	8.11414	+	24.9728i	0.427060	+	1.31436i
$362$	−1.62535			−0.0854264
$363$	−34.5127	+	1.30779i	−1.81145	+	0.0686410i
$364$		0			0
$365$	5.32499	+	16.3886i	0.278723	+	0.857821i
$366$	−8.52572	−	6.19430i	−0.445647	−	0.323781i
$367$	−18.4122	+	13.3773i	−0.961111	+	0.698288i	−0.953409	−	0.301682i	$-0.902452\pi$
$367$	−18.4122	+	13.3773i	−0.961111	+	0.698288i	−0.00770265	+	0.999970i	$0.502452\pi$
$368$	−1.47637	+	4.54380i	−0.0769611	+	0.236862i
$369$	−11.7855	+	36.2719i	−0.613527	+	1.88824i
$370$	−1.75070	+	1.27196i	−0.0910145	+	0.0661259i
$371$		0			0
$372$	−4.51852	−	13.9066i	−0.234274	−	0.721022i
$373$	−22.2412			−1.15160			−0.575802	−	0.817589i	$-0.695310\pi$
$373$	−22.2412			−1.15160			−0.575802	+	0.817589i	$0.695310\pi$
$374$	−1.30074	−	3.75949i	−0.0672597	−	0.194399i
$375$	−36.3756			−1.87843
$376$	3.23238	+	9.94824i	0.166697	+	0.513041i
$377$	−1.89030	−	1.37339i	−0.0973556	−	0.0707330i
$378$		0			0
$379$	10.3430	−	31.8325i	0.531285	−	1.63513i	−0.220258	−	0.975442i	$-0.570690\pi$
$379$	10.3430	−	31.8325i	0.531285	−	1.63513i	0.751543	−	0.659685i	$-0.229310\pi$
$380$	6.91426	−	21.2799i	0.354694	−	1.09164i
$381$	44.6223	−	32.4200i	2.28607	−	1.66093i
$382$	−6.88179	−	4.99992i	−0.352103	−	0.255818i
$383$	1.89919	+	5.84512i	0.0970443	+	0.298672i	0.987781	−	0.155848i	$-0.0498110\pi$
$383$	1.89919	+	5.84512i	0.0970443	+	0.298672i	−0.890737	+	0.454520i	$0.849811\pi$
$384$	34.4486			1.75795
$385$		0			0
$386$	−1.17829			−0.0599733
$387$	−17.8653	−	54.9838i	−0.908145	−	2.79498i
$388$	−10.6886	−	7.76572i	−0.542631	−	0.394245i
$389$	−5.98967	+	4.35175i	−0.303689	+	0.220643i	−0.729184	−	0.684318i	$-0.760100\pi$
$389$	−5.98967	+	4.35175i	−0.303689	+	0.220643i	0.425495	+	0.904961i	$0.360100\pi$
$390$	−3.52202	+	10.8397i	−0.178344	+	0.548887i
$391$	−1.75119	+	5.38962i	−0.0885617	+	0.272565i
$392$		0			0
$393$	−17.0838	−	12.4121i	−0.861765	−	0.626109i
$394$	−0.186898	−	0.575213i	−0.00941578	−	0.0289788i
$395$	−8.69662			−0.437575
$396$	10.2674	−	33.7624i	0.515959	−	1.69663i
$397$	−17.8079			−0.893752			−0.446876	−	0.894596i	$-0.647463\pi$
$397$	−17.8079			−0.893752			−0.446876	+	0.894596i	$0.647463\pi$
$398$	3.23473	+	9.95549i	0.162143	+	0.499024i
$399$		0			0
$400$	0.493749	−	0.358729i	0.0246874	−	0.0179365i
$401$	7.93520	−	24.4220i	0.396265	−	1.21958i	−0.531707	−	0.846929i	$-0.678449\pi$
$401$	7.93520	−	24.4220i	0.396265	−	1.21958i	0.927972	−	0.372650i	$-0.121551\pi$
$402$	0.586217	−	1.80419i	0.0292378	−	0.0899848i
$403$	−6.13987	+	4.46088i	−0.305849	+	0.222212i
$404$	5.05455	+	3.67235i	0.251473	+	0.182706i
$405$	−11.5667	−	35.5985i	−0.574752	−	1.76890i
$406$		0			0
$407$	−4.09899	−	2.86108i	−0.203179	−	0.141819i
$408$	13.3748			0.662152
$409$	−0.413324	−	1.27208i	−0.0204376	−	0.0629003i	0.940318	−	0.340298i	$-0.110528\pi$
$409$	−0.413324	−	1.27208i	−0.0204376	−	0.0629003i	−0.960755	+	0.277398i	$0.910528\pi$
$410$	−6.45955	−	4.69314i	−0.319014	−	0.231778i
$411$	35.2256	−	25.5929i	1.73755	−	1.26240i
$412$	−8.45022	+	26.0071i	−0.416312	+	1.28128i
$413$		0			0
$414$	11.7585	−	8.54303i	0.577897	−	0.419867i
$415$	7.02646	+	5.10502i	0.344915	+	0.250596i
$416$	−4.50666	−	13.8701i	−0.220957	−	0.680037i
$417$	44.8068			2.19420
$418$	−14.9408	+	0.282974i	−0.730780	+	0.0138407i
$419$	−37.4618			−1.83013			−0.915064	−	0.403310i	$-0.867860\pi$
$419$	−37.4618			−1.83013			−0.915064	+	0.403310i	$0.867860\pi$
$420$		0			0
$421$	−6.68374	−	4.85602i	−0.325746	−	0.236668i	0.412878	−	0.910787i	$-0.364524\pi$
$421$	−6.68374	−	4.85602i	−0.325746	−	0.236668i	−0.738623	+	0.674118i	$0.764524\pi$
$422$	−8.00219	+	5.81393i	−0.389541	+	0.283018i
$423$	−9.32003	+	28.6841i	−0.453155	+	1.39467i
$424$	−0.490564	+	1.50980i	−0.0238239	+	0.0733224i
$425$	0.585659	−	0.425506i	0.0284086	−	0.0206401i
$426$	−25.2963	−	18.3788i	−1.22561	−	0.890458i
$427$		0			0
$428$	23.8980			1.15515
$429$	−26.3232	+	0.498552i	−1.27090	+	0.0240703i
$430$	12.1034			0.583679
$431$	10.0914	+	31.0581i	0.486085	+	1.49602i	0.830403	+	0.557164i	$0.188110\pi$
$431$	10.0914	+	31.0581i	0.486085	+	1.49602i	−0.344317	+	0.938853i	$0.611890\pi$
$432$	14.7971	+	10.7507i	0.711923	+	0.517243i
$433$	12.7786	−	9.28422i	0.614102	−	0.446171i	−0.236754	−	0.971570i	$-0.576084\pi$
$433$	12.7786	−	9.28422i	0.614102	−	0.446171i	0.850856	+	0.525398i	$0.176084\pi$
$434$		0			0
$435$	−1.92226	+	5.91611i	−0.0921654	+	0.283656i
$436$	−23.7555	+	17.2594i	−1.13768	+	0.826575i
$437$	17.2219	+	12.5124i	0.823834	+	0.598551i
$438$	5.22331	+	16.0757i	0.249580	+	0.768127i
$439$	20.6942			0.987678			0.493839	−	0.869553i	$-0.335593\pi$
$439$	20.6942			0.987678			0.493839	+	0.869553i	$0.335593\pi$
$440$	13.8677	+	9.67964i	0.661118	+	0.461459i
$441$		0			0
$442$	−0.937107	−	2.88412i	−0.0445737	−	0.137184i
$443$	−24.3477	−	17.6897i	−1.15680	−	0.840462i	−0.167427	−	0.985885i	$-0.553546\pi$
$443$	−24.3477	−	17.6897i	−1.15680	−	0.840462i	−0.989370	+	0.145423i	$0.953546\pi$
$444$	5.93959	−	4.31537i	0.281881	−	0.204798i
$445$	−5.50327	+	16.9373i	−0.260880	+	0.802906i
$446$	0.381922	−	1.17543i	0.0180845	−	0.0556584i
$447$	6.66256	−	4.84063i	0.315128	−	0.228954i
$448$		0			0
$449$	11.2465	+	34.6132i	0.530755	+	1.63350i	0.752647	+	0.658424i	$0.228777\pi$
$449$	11.2465	+	34.6132i	0.530755	+	1.63350i	−0.221892	+	0.975071i	$0.571223\pi$
$450$	−1.85664			−0.0875230
$451$	5.36629	−	17.6460i	0.252689	−	0.830915i
$452$	−2.60739			−0.122641
$453$	2.90064	+	8.92725i	0.136284	+	0.419439i
$454$	−11.8878	−	8.63700i	−0.557922	−	0.405354i
$455$		0			0
$456$	15.5254	−	47.7821i	0.727041	−	2.23760i
$457$	−3.02652	+	9.31466i	−0.141574	+	0.435721i	−0.996555	−	0.0829393i	$-0.973569\pi$
$457$	−3.02652	+	9.31466i	−0.141574	+	0.435721i	0.854980	+	0.518661i	$0.173569\pi$
$458$	−10.9731	+	7.97243i	−0.512740	+	0.372527i
$459$	17.5515	+	12.7519i	0.819233	+	0.595208i
$460$	−3.25217	−	10.0092i	−0.151633	−	0.466680i
$461$	21.8596			1.01810			0.509052	−	0.860736i	$-0.329996\pi$
$461$	21.8596			1.01810			0.509052	+	0.860736i	$0.329996\pi$
$462$		0			0
$463$	6.75889			0.314112			0.157056	−	0.987590i	$-0.449800\pi$
$463$	6.75889			0.314112			0.157056	+	0.987590i	$0.449800\pi$
$464$	−0.431193	−	1.32707i	−0.0200176	−	0.0616079i
$465$	16.3461	+	11.8762i	0.758034	+	0.550744i
$466$	−11.4124	+	8.29161i	−0.528670	+	0.384102i
$467$	9.27768	−	28.5538i	0.429320	−	1.32131i	−0.469477	−	0.882945i	$-0.655558\pi$
$467$	9.27768	−	28.5538i	0.429320	−	1.32131i	0.898797	−	0.438366i	$-0.144442\pi$
$468$	8.31283	−	25.5843i	0.384261	−	1.18263i
$469$		0			0
$470$	−5.10826	−	3.71136i	−0.235626	−	0.171192i
$471$	10.9198	+	33.6077i	0.503157	+	1.54856i
$472$	−0.876166			−0.0403288
$473$	9.14167	+	26.4219i	0.420334	+	1.21488i
$474$	−8.53056			−0.391822
$475$	−0.840312	−	2.58622i	−0.0385562	−	0.118664i
$476$		0			0
$477$	−3.70311	+	2.69046i	−0.169554	+	0.123188i
$478$	3.20720	−	9.87074i	0.146694	−	0.451477i
$479$	1.85519	−	5.70970i	0.0847659	−	0.260883i	−0.899686	−	0.436538i	$-0.856204\pi$
$479$	1.85519	−	5.70970i	0.0847659	−	0.260883i	0.984452	+	0.175655i	$0.0562044\pi$
$480$	−31.4113	+	22.8217i	−1.43372	+	1.04166i
$481$	−3.08280	−	2.23978i	−0.140563	−	0.102125i
$482$	−2.91503	−	8.97153i	−0.132776	−	0.408642i
$483$		0			0
$484$	−4.65528	+	16.4187i	−0.211604	+	0.746303i
$485$	18.2561			0.828965
$486$	−3.82450	−	11.7706i	−0.173483	−	0.533925i
$487$	−5.15120	−	3.74256i	−0.233423	−	0.169592i	0.464925	−	0.885350i	$-0.346081\pi$
$487$	−5.15120	−	3.74256i	−0.233423	−	0.169592i	−0.698348	+	0.715758i	$0.746081\pi$
$488$	−9.64357	+	7.00646i	−0.436544	+	0.317168i
$489$	17.6613	−	54.3559i	0.798671	−	2.45806i
$490$		0			0
$491$	−10.0131	+	7.27496i	−0.451886	+	0.328314i	−0.790340	−	0.612669i	$-0.790096\pi$
$491$	−10.0131	+	7.27496i	−0.451886	+	0.328314i	0.338454	+	0.940983i	$0.390096\pi$
$492$	21.9153	+	15.9224i	0.988019	+	0.717838i
$493$	−0.511458	−	1.57411i	−0.0230349	−	0.0708942i
$494$	−11.3914			−0.512525
$495$	15.9439	+	46.0821i	0.716624	+	2.07124i
$496$	−4.53228			−0.203505
$497$		0			0
$498$	6.89229	+	5.00754i	0.308851	+	0.224393i
$499$	11.5525	−	8.39337i	0.517160	−	0.375739i	−0.298373	−	0.954449i	$-0.596444\pi$
$499$	11.5525	−	8.39337i	0.517160	−	0.375739i	0.815533	+	0.578711i	$0.196444\pi$
$500$	−5.55432	+	17.0944i	−0.248397	+	0.764486i
$501$	19.3381	−	59.5167i	0.863965	−	2.65901i
$502$	−0.583701	+	0.424084i	−0.0260519	+	0.0189278i
$503$	4.79402	+	3.48306i	0.213755	+	0.155302i	0.689511	−	0.724275i	$-0.257826\pi$
$503$	4.79402	+	3.48306i	0.213755	+	0.155302i	−0.475756	+	0.879577i	$0.657826\pi$
$504$		0			0
$505$	−8.63314			−0.384170
$506$	−5.60716	+	4.23836i	−0.249269	+	0.188418i
$507$	20.7473			0.921419
$508$	−8.42197	−	25.9202i	−0.373665	−	1.15002i
$509$	24.9772	+	18.1470i	1.10709	+	0.804351i	0.982204	−	0.187820i	$-0.0601420\pi$
$509$	24.9772	+	18.1470i	1.10709	+	0.804351i	0.124891	+	0.992171i	$0.460142\pi$
$510$	−6.53162	+	4.74550i	−0.289225	+	0.210134i
$511$		0			0
$512$	4.91089	−	15.1142i	0.217033	−	0.667958i
$513$	65.9303	−	47.9012i	2.91090	−	2.11489i
$514$	7.08774	+	5.14955i	0.312627	+	0.227137i
$515$	−11.6765	−	35.9365i	−0.514527	−	1.58355i
$516$	−41.0633			−1.80771
$517$	4.24370	−	13.9545i	0.186637	−	0.613720i
$518$		0			0
$519$	5.81183	+	17.8870i	0.255111	+	0.785151i
$520$	10.4297	+	7.57765i	0.457374	+	0.332302i
$521$	15.2799	−	11.1015i	0.669423	−	0.486365i	−0.200409	−	0.979712i	$-0.564227\pi$
$521$	15.2799	−	11.1015i	0.669423	−	0.486365i	0.869832	+	0.493348i	$0.164227\pi$
$522$	−1.31175	+	4.03716i	−0.0574138	+	0.176702i
$523$	2.45424	−	7.55337i	0.107316	−	0.330286i	−0.882951	−	0.469466i	$-0.844447\pi$
$523$	2.45424	−	7.55337i	0.107316	−	0.330286i	0.990267	+	0.139180i	$0.0444466\pi$
$524$	−8.44156	+	6.13315i	−0.368771	+	0.267928i
$525$		0			0
$526$	−1.98108	−	6.09712i	−0.0863790	−	0.265847i
$527$	−5.37595			−0.234180
$528$	−12.8928	−	8.99914i	−0.561087	−	0.391637i
$529$	−12.9873			−0.564665
$530$	−0.296122	−	0.911370i	−0.0128627	−	0.0395874i
$531$	−2.04380	−	1.48491i	−0.0886935	−	0.0644396i
$532$		0			0
$533$	4.34471	−	13.3716i	0.188190	−	0.579190i
$534$	−5.39818	+	16.6139i	−0.233602	+	0.718954i
$535$	−26.7155	+	19.4099i	−1.15501	+	0.839165i
$536$	−1.73596	−	1.26125i	−0.0749821	−	0.0544777i
$537$	1.57076	+	4.83432i	0.0677835	+	0.208616i
$538$	3.19370			0.137690
$539$		0			0
$540$	−40.2899			−1.73380
$541$	2.34904	+	7.22960i	0.100993	+	0.310825i	0.988769	−	0.149451i	$-0.0477506\pi$
$541$	2.34904	+	7.22960i	0.100993	+	0.310825i	−0.887776	+	0.460276i	$0.847751\pi$
$542$	−10.8650	−	7.89389i	−0.466692	−	0.339072i
$543$	−6.16444	+	4.47873i	−0.264541	+	0.192201i
$544$	3.19234	−	9.82501i	0.136870	−	0.421244i
$545$	12.5381	−	38.5884i	0.537075	−	1.65295i
$546$		0			0
$547$	−17.5548	−	12.7543i	−0.750590	−	0.545335i	0.145420	−	0.989370i	$-0.453547\pi$
$547$	−17.5548	−	12.7543i	−0.750590	−	0.545335i	−0.896010	+	0.444035i	$0.853547\pi$
$548$	−6.64845	−	20.4618i	−0.284008	−	0.874086i
$549$	−34.3697			−1.46686
$550$	0.897714	−	0.0170024i	0.0382787	−	0.000724984i
$551$	−6.21726			−0.264864
$552$	−7.30247	−	22.4747i	−0.310814	−	0.956587i
$553$		0			0
$554$	6.28660	−	4.56749i	0.267092	−	0.194054i
$555$	−3.13491	+	9.64827i	−0.133070	+	0.409546i
$556$	6.84170	−	21.0566i	0.290153	−	0.892999i
$557$	32.8569	−	23.8719i	1.39219	−	1.01149i	0.396571	−	0.918004i	$-0.370200\pi$
$557$	32.8569	−	23.8719i	1.39219	−	1.01149i	0.995621	−	0.0934825i	$-0.0297999\pi$
$558$	11.1546	+	8.10430i	0.472212	+	0.343082i
$559$	6.58604	+	20.2697i	0.278560	+	0.857319i
$560$		0			0
$561$	−15.2928	−	10.6743i	−0.645661	−	0.450670i
$562$	8.08972			0.341244
$563$	7.24004	+	22.2825i	0.305131	+	0.939097i	0.979628	+	0.200820i	$0.0643606\pi$
$563$	7.24004	+	22.2825i	0.305131	+	0.939097i	−0.674497	+	0.738278i	$0.735639\pi$
$564$	17.3308	+	12.5915i	0.729757	+	0.530200i
$565$	2.91479	−	2.11772i	0.122626	−	0.0890931i
$566$	−4.55177	+	14.0089i	−0.191325	+	0.588838i
$567$		0			0
$568$	−28.6130	+	20.7886i	−1.20058	+	0.872269i
$569$	9.01678	+	6.55107i	0.378003	+	0.274635i	0.760522	−	0.649313i	$-0.224943\pi$
$569$	9.01678	+	6.55107i	0.378003	+	0.274635i	−0.382519	+	0.923948i	$0.624943\pi$
$570$	9.37166	+	28.8430i	0.392536	+	1.20810i
$571$	−6.15846			−0.257724			−0.128862	−	0.991663i	$-0.541132\pi$
$571$	−6.15846			−0.257724			−0.128862	+	0.991663i	$0.541132\pi$
$572$	−3.78509	+	12.4465i	−0.158262	+	0.520414i
$573$	−39.8780			−1.66593
$574$		0			0
$575$	−1.03477	−	0.751805i	−0.0431529	−	0.0313524i
$576$	−4.68052	+	3.40060i	−0.195022	+	0.141692i
$577$	4.47585	−	13.7752i	0.186332	−	0.573471i	−0.813637	−	0.581374i	$-0.802515\pi$
$577$	4.47585	−	13.7752i	0.186332	−	0.573471i	0.999969	+	0.00790255i	$0.00251548\pi$
$578$	−2.85455	+	8.78540i	−0.118734	+	0.365424i
$579$	−4.46888	+	3.24683i	−0.185720	+	0.134934i
$580$	2.48671	+	1.80670i	0.103255	+	0.0750192i
$581$		0			0
$582$	17.9075			0.742288
$583$	1.76587	−	1.33479i	0.0731348	−	0.0552814i
$584$	19.1192			0.791159
$585$	11.4866	+	35.3522i	0.474914	+	1.46164i
$586$	0.767891	+	0.557906i	0.0317213	+	0.0230469i
$587$	12.8285	−	9.32048i	0.529491	−	0.384698i	−0.290676	−	0.956821i	$-0.593880\pi$
$587$	12.8285	−	9.32048i	0.529491	−	0.384698i	0.820167	+	0.572124i	$0.193880\pi$
$588$		0			0
$589$	−6.24035	+	19.2058i	−0.257129	+	0.791362i
$590$	0.427877	−	0.310871i	0.0176154	−	0.0127984i
$591$	−2.29387	−	1.66660i	−0.0943573	−	0.0685546i
$592$	−0.703209	−	2.16426i	−0.0289017	−	0.0889503i
$593$	−22.9285			−0.941560			−0.470780	−	0.882251i	$-0.656027\pi$
$593$	−22.9285			−0.941560			−0.470780	+	0.882251i	$0.656027\pi$
$594$	8.79822	+	25.4292i	0.360995	+	1.04337i
$595$		0			0
$596$	−1.25749	−	3.87015i	−0.0515087	−	0.158527i
$597$	39.7012	+	28.8446i	1.62486	+	1.18053i
$598$	−4.33475	+	3.14938i	−0.177261	+	0.128788i
$599$	4.06395	−	12.5075i	0.166048	−	0.511044i	−0.833064	−	0.553177i	$-0.813415\pi$
$599$	4.06395	−	12.5075i	0.166048	−	0.511044i	0.999112	+	0.0421329i	$0.0134153\pi$
$600$	−0.932836	+	2.87097i	−0.0380829	+	0.117207i
$601$	22.1286	−	16.0774i	0.902645	−	0.655810i	−0.0364993	−	0.999334i	$-0.511621\pi$
$601$	22.1286	−	16.0774i	0.902645	−	0.655810i	0.939144	+	0.343524i	$0.111621\pi$
$602$		0			0
$603$	−1.91188	−	5.88415i	−0.0778576	−	0.239621i
$604$	4.63819			0.188725
$605$	−8.13111	−	22.1354i	−0.330577	−	0.899931i
$606$	−8.46830			−0.344001
$607$	14.4850	+	44.5801i	0.587926	+	1.80945i	0.587186	+	0.809452i	$0.300236\pi$
$607$	14.4850	+	44.5801i	0.587926	+	1.80945i	0.000740345		1.00000i	$0.499764\pi$
$608$	−31.3946	−	22.8095i	−1.27322	−	0.925049i
$609$		0			0
$610$	2.22350	−	6.84324i	0.0900270	−	0.277075i
$611$	3.43582	−	10.5744i	0.138999	−	0.427793i
$612$	15.4162	−	11.2005i	0.623164	−	0.452755i
$613$	16.5601	+	12.0316i	0.668857	+	0.485953i	0.869642	−	0.493682i	$-0.164349\pi$
$613$	16.5601	+	12.0316i	0.668857	+	0.485953i	−0.200786	+	0.979635i	$0.564349\pi$
$614$	−6.09806	−	18.7679i	−0.246098	−	0.757411i
$615$	−37.4312			−1.50937
$616$		0			0
$617$	44.1691			1.77818			0.889090	−	0.457733i	$-0.151338\pi$
$617$	44.1691			1.77818			0.889090	+	0.457733i	$0.151338\pi$
$618$	−11.4535	−	35.2503i	−0.460728	−	1.41798i
$619$	0.551413	+	0.400625i	0.0221632	+	0.0161025i	0.598812	−	0.800890i	$-0.295640\pi$
$619$	0.551413	+	0.400625i	0.0221632	+	0.0161025i	−0.576649	+	0.816992i	$0.695640\pi$
$620$	8.07705	−	5.86832i	0.324382	−	0.235677i
$621$	11.8451	−	36.4554i	0.475327	−	1.46291i
$622$	−5.56287	+	17.1208i	−0.223051	+	0.686480i
$623$		0			0
$624$	−9.69651	−	7.04492i	−0.388171	−	0.282023i
$625$	−7.05039	−	21.6989i	−0.282016	−	0.867955i
$626$	3.00896			0.120262
$627$	−55.8861	+	42.2434i	−2.23188	+	1.68704i
$628$	17.4610			0.696770
$629$	−0.834110	−	2.56713i	−0.0332582	−	0.102358i
$630$		0			0
$631$	29.8299	−	21.6727i	1.18751	−	0.862776i	0.194511	−	0.980900i	$-0.437688\pi$
$631$	29.8299	−	21.6727i	1.18751	−	0.862776i	0.992999	+	0.118124i	$0.0376880\pi$
$632$	−2.98172	+	9.17679i	−0.118606	+	0.365033i
$633$	−14.3292	+	44.1009i	−0.569536	+	1.75285i
$634$	5.93312	−	4.31066i	0.235634	−	0.171198i
$635$	30.4672	+	22.1357i	1.20906	+	0.878430i
$636$	1.00465	+	3.09201i	0.0398371	+	0.122606i
$637$		0			0
$638$	0.597281	−	1.96404i	0.0236466	−	0.0777570i
$639$	−101.977			−4.03414
$640$	7.26835	+	22.3697i	0.287307	+	0.884239i
$641$	16.5951	+	12.0570i	0.655466	+	0.476224i	0.865129	−	0.501550i	$-0.167237\pi$
$641$	16.5951	+	12.0570i	0.655466	+	0.476224i	−0.209663	+	0.977774i	$0.567237\pi$
$642$	−26.2054	+	19.0393i	−1.03424	+	0.751422i
$643$	2.35984	−	7.26283i	0.0930629	−	0.286418i	−0.893681	−	0.448703i	$-0.851886\pi$
$643$	2.35984	−	7.26283i	0.0930629	−	0.286418i	0.986744	+	0.162284i	$0.0518862\pi$
$644$		0			0
$645$	45.9045	−	33.3516i	1.80749	−	1.31322i
$646$	−6.52815	−	4.74298i	−0.256846	−	0.186610i
$647$	−4.53724	−	13.9642i	−0.178377	−	0.548989i	0.821394	−	0.570361i	$-0.193197\pi$
$647$	−4.53724	−	13.9642i	−0.178377	−	0.548989i	−0.999772	+	0.0213717i	$0.993197\pi$
$648$	−41.5297			−1.63144
$649$	1.00181	+	0.699260i	0.0393244	+	0.0274483i
$650$	0.684450			0.0268463
$651$		0			0
$652$	−22.8473	−	16.5996i	−0.894770	−	0.650089i
$653$	−0.911790	+	0.662454i	−0.0356811	+	0.0259238i	−0.605483	−	0.795858i	$-0.707020\pi$
$653$	−0.911790	+	0.662454i	−0.0356811	+	0.0259238i	0.569802	+	0.821782i	$0.307020\pi$
$654$	12.2987	−	37.8516i	0.480918	−	1.48011i
$655$	4.45545	−	13.7125i	0.174089	−	0.535790i
$656$	6.79283	−	4.93528i	0.265215	−	0.192690i
$657$	44.5988	+	32.4029i	1.73996	+	1.26416i
$658$		0			0
$659$	10.0215			0.390384			0.195192	−	0.980765i	$-0.437467\pi$
$659$	10.0215			0.390384			0.195192	+	0.980765i	$0.437467\pi$
$660$	34.6284	−	0.655850i	1.34791	−	0.0255289i
$661$	−15.7371			−0.612101			−0.306050	−	0.952015i	$-0.599008\pi$
$661$	−15.7371			−0.612101			−0.306050	+	0.952015i	$0.599008\pi$
$662$	3.41956	+	10.5243i	0.132905	+	0.409040i
$663$	−11.5015	−	8.35632i	−0.446681	−	0.324533i
$664$	7.79597	−	5.66410i	0.302542	−	0.219810i
$665$		0			0
$666$	−2.13927	+	6.58398i	−0.0828949	+	0.255124i
$667$	−2.36584	+	1.71888i	−0.0916056	+	0.0665554i
$668$	−25.0166	−	18.1756i	−0.967920	−	0.703235i
$669$	−1.79046	−	5.51046i	−0.0692230	−	0.213047i
$670$	1.29526			0.0500403
$671$	16.6182	−	0.314744i	0.641540	−	0.0121505i
$672$		0			0
$673$	9.89226	+	30.4452i	0.381319	+	1.17358i	0.939116	+	0.343601i	$0.111647\pi$
$673$	9.89226	+	30.4452i	0.381319	+	1.17358i	−0.557797	+	0.829977i	$0.688353\pi$
$674$	6.56743	+	4.77152i	0.252968	+	0.183792i
$675$	−3.96140	+	2.87813i	−0.152474	+	0.110779i
$676$	3.16797	−	9.75001i	0.121845	−	0.375000i
$677$	4.74033	−	14.5892i	0.182186	−	0.560710i	−0.817703	−	0.575641i	$-0.804753\pi$
$677$	4.74033	−	14.5892i	0.182186	−	0.560710i	0.999889	+	0.0149305i	$0.00475269\pi$
$678$	2.85913	−	2.07728i	0.109804	−	0.0797775i
$679$		0			0
$680$	2.82197	+	8.68512i	0.108218	+	0.333059i
$681$	−68.8864			−2.63973
$682$	−5.46763	−	3.81640i	−0.209367	−	0.146137i
$683$	1.04764			0.0400868			0.0200434	−	0.999799i	$-0.493620\pi$
$683$	1.04764			0.0400868			0.0200434	+	0.999799i	$0.493620\pi$
$684$	−22.1194	−	68.0766i	−0.845758	−	2.60298i
$685$	24.0514	+	17.4743i	0.918955	+	0.667660i
$686$		0			0
$687$	−19.6492	+	60.4739i	−0.749663	+	2.30722i
$688$	−3.93314	+	12.1050i	−0.149950	+	0.461497i
$689$	1.36515	−	0.991838i	0.0520080	−	0.0377860i
$690$	11.5404	+	8.38458i	0.439335	+	0.319195i
$691$	−9.01969	−	27.7597i	−0.343125	−	1.05603i	−0.962580	−	0.270998i	$-0.912646\pi$
$691$	−9.01969	−	27.7597i	−0.343125	−	1.05603i	0.619455	−	0.785032i	$-0.287354\pi$
$692$	9.29326			0.353277
$693$		0			0
$694$	−16.2648			−0.617404
$695$	9.45384	+	29.0959i	0.358605	+	1.10367i
$696$	5.58369	+	4.05679i	0.211649	+	0.153772i
$697$	8.05730	−	5.85397i	0.305192	−	0.221735i
$698$	0.686867	−	2.11396i	0.0259983	−	0.0800145i
$699$	−20.4358	+	62.8950i	−0.772954	+	2.37891i
$700$		0			0
$701$	−10.3380	−	7.51100i	−0.390461	−	0.283687i	0.375183	−	0.926951i	$-0.377580\pi$
$701$	−10.3380	−	7.51100i	−0.390461	−	0.283687i	−0.765644	+	0.643264i	$0.777580\pi$
$702$	6.33860	+	19.5082i	0.239235	+	0.736290i
$703$	−10.1394			−0.382415
$704$	2.23196	−	1.68710i	0.0841202	−	0.0635851i
$705$	−29.6009			−1.11483
$706$	−4.20697	−	12.9477i	−0.158332	−	0.487294i
$707$		0			0
$708$	−1.45166	+	1.05469i	−0.0545567	+	0.0396377i
$709$	11.7646	−	36.2076i	0.441828	−	1.35981i	−0.444098	−	0.895978i	$-0.646476\pi$
$709$	11.7646	−	36.2076i	0.441828	−	1.35981i	0.885925	−	0.463828i	$-0.153524\pi$
$710$	6.59726	−	20.3043i	0.247591	−	0.762006i
$711$	−22.5080	+	16.3530i	−0.844116	+	0.613286i
$712$	15.9856	+	11.6142i	0.599087	+	0.435262i
$713$	2.93520	+	9.03361i	0.109924	+	0.338311i
$714$		0			0
$715$	−5.87770	−	16.9881i	−0.219814	−	0.635321i
$716$	2.51169			0.0938663
$717$	−15.0354	−	46.2742i	−0.561507	−	1.72814i
$718$	−15.7355	−	11.4325i	−0.587245	−	0.426658i
$719$	−31.7696	+	23.0819i	−1.18481	+	0.860811i	−0.992706	−	0.120564i	$-0.961530\pi$
$719$	−31.7696	+	23.0819i	−1.18481	+	0.860811i	−0.192100	+	0.981375i	$0.561530\pi$
$720$	−6.85975	+	21.1121i	−0.255648	+	0.786803i
$721$		0			0
$722$	−14.2274	+	10.3368i	−0.529491	+	0.384697i
$723$	−35.7773	−	25.9937i	−1.33057	−	0.966716i
$724$	1.16347	+	3.58080i	0.0432401	+	0.133079i
$725$	0.373562			0.0138737
$726$	−7.97585	−	21.7127i	−0.296011	−	0.805835i
$727$	28.4699			1.05589			0.527946	−	0.849278i	$-0.322963\pi$
$727$	28.4699			1.05589			0.527946	+	0.849278i	$0.322963\pi$
$728$		0			0
$729$	−4.56314	−	3.31531i	−0.169005	−	0.122789i
$730$	−9.33691	+	6.78366i	−0.345574	+	0.251074i
$731$	−4.66529	+	14.3583i	−0.172552	+	0.531060i
$732$	−7.54368	+	23.2170i	−0.278822	+	0.858127i
$733$	−2.42168	+	1.75946i	−0.0894470	+	0.0649870i	−0.631610	−	0.775286i	$-0.717606\pi$
$733$	−2.42168	+	1.75946i	−0.0894470	+	0.0649870i	0.542163	+	0.840273i	$0.317606\pi$
$734$	−12.3315	−	8.95935i	−0.455163	−	0.330696i
$735$		0			0
$736$	−18.2527			−0.672802
$737$	0.978305	+	2.82757i	0.0360363	+	0.104155i
$738$	−25.5431			−0.940254
$739$	−15.6773	−	48.2498i	−0.576700	−	1.77490i	−0.630318	−	0.776337i	$-0.717075\pi$
$739$	−15.6773	−	48.2498i	−0.576700	−	1.77490i	0.0536180	−	0.998562i	$-0.482925\pi$
$740$	4.05544	+	2.94645i	0.149081	+	0.108314i
$741$	−43.2041	+	31.3896i	−1.58714	+	1.15313i
$742$		0			0
$743$	−0.118625	+	0.365089i	−0.00435191	+	0.0133938i	−0.953209	−	0.302312i	$-0.902241\pi$
$743$	−0.118625	+	0.365089i	−0.00435191	+	0.0133938i	0.948857	+	0.315706i	$0.102241\pi$
$744$	18.1363	−	13.1768i	0.664909	−	0.483085i
$745$	4.54907	+	3.30510i	0.166665	+	0.121089i
$746$	−4.60309	−	14.1668i	−0.168531	−	0.518685i
$747$	27.7848			1.01659
$748$	−7.35141	+	5.55681i	−0.268794	+	0.203177i
$749$		0			0
$750$	−7.52839	−	23.1700i	−0.274898	−	0.846048i
$751$	31.8404	+	23.1334i	1.16187	+	0.844151i	0.990014	−	0.140970i	$-0.0450221\pi$
$751$	31.8404	+	23.1334i	1.16187	+	0.844151i	0.171861	+	0.985121i	$0.445022\pi$
$752$	5.37182	−	3.90285i	0.195890	−	0.142322i
$753$	−1.04521	+	3.21683i	−0.0380897	+	0.117228i
$754$	0.483576	−	1.48830i	0.0176108	−	0.0542005i
$755$	−5.18502	+	3.76714i	−0.188702	+	0.137100i
$756$		0			0
$757$	3.51868	+	10.8294i	0.127889	+	0.393600i	0.994416	−	0.105528i	$-0.0336534\pi$
$757$	3.51868	+	10.8294i	0.127889	+	0.393600i	−0.866528	+	0.499129i	$0.833653\pi$
$758$	22.4168			0.814214
$759$	−9.58720	+	31.5256i	−0.347993	+	1.14431i
$760$	34.3037			1.24433
$761$	2.31196	+	7.11547i	0.0838083	+	0.257936i	0.984176	−	0.177195i	$-0.0567023\pi$
$761$	2.31196	+	7.11547i	0.0838083	+	0.257936i	−0.900367	+	0.435130i	$0.856702\pi$
$762$	29.8855	+	21.7131i	1.08264	+	0.786582i
$763$		0			0
$764$	−6.08911	+	18.7403i	−0.220296	+	0.678002i
$765$	−8.13668	+	25.0421i	−0.294182	+	0.905400i
$766$	−3.33007	+	2.41944i	−0.120320	+	0.0874179i
$767$	0.753447	+	0.547411i	0.0272054	+	0.0197659i
$768$	8.76652	+	26.9806i	0.316335	+	0.973578i
$769$	26.8378			0.967798			0.483899	−	0.875124i	$-0.339220\pi$
$769$	26.8378			0.967798			0.483899	+	0.875124i	$0.339220\pi$
$770$		0			0
$771$	41.0714			1.47915
$772$	0.843453	+	2.59588i	0.0303565	+	0.0934278i
$773$	3.61453	+	2.62611i	0.130006	+	0.0944546i	0.650888	−	0.759174i	$-0.274397\pi$
$773$	3.61453	+	2.62611i	0.130006	+	0.0944546i	−0.520882	+	0.853629i	$0.674397\pi$
$774$	31.3253	−	22.7591i	1.12596	−	0.818060i
$775$	0.374949	−	1.15398i	0.0134686	−	0.0414520i
$776$	6.25926	−	19.2640i	0.224694	−	0.691538i
$777$		0			0
$778$	−4.01155	−	2.91456i	−0.143821	−	0.104492i
$779$	−11.5607	−	35.5803i	−0.414206	−	1.27480i
$780$	26.4020			0.945342
$781$	49.3073	−	0.933862i	1.76435	−	0.0334162i
$782$	−3.79543			−0.135724
$783$	3.45951	+	10.6473i	0.123633	+	0.380503i
$784$		0			0
$785$	−19.5196	+	14.1818i	−0.696685	+	0.506171i
$786$	4.37037	−	13.4506i	0.155886	−	0.479768i
$787$	4.16738	−	12.8259i	0.148551	−	0.457193i	−0.848899	−	0.528554i	$-0.822734\pi$
$787$	4.16738	−	12.8259i	0.148551	−	0.457193i	0.997451	+	0.0713611i	$0.0227343\pi$
$788$	−1.13346	+	0.823508i	−0.0403779	+	0.0293363i
$789$	−24.3145	−	17.6655i	−0.865620	−	0.628910i
$790$	−1.79987	−	5.53944i	−0.0640366	−	0.197084i
$791$		0			0
$792$	54.0930	−	1.02450i	1.92211	−	0.0364041i
$793$	12.6704			0.449937
$794$	−3.68556	−	11.3430i	−0.130796	−	0.402547i
$795$	−3.63442	−	2.64056i	−0.128900	−	0.0936512i
$796$	19.6174	−	14.2529i	0.695320	−	0.505179i
$797$	−16.2250	+	49.9354i	−0.574719	+	1.76880i	0.0624156	+	0.998050i	$0.480120\pi$
$797$	−16.2250	+	49.9354i	−0.574719	+	1.76880i	−0.637134	+	0.770753i	$0.719880\pi$
$798$		0			0
$799$	6.37177	−	4.62936i	0.225417	−	0.163775i
$800$	1.88634	+	1.37050i	0.0666921	+	0.0484546i
$801$	17.6055	+	54.1843i	0.622061	+	1.91451i
$802$	17.1983			0.607292
$803$	−21.8609	−	15.2589i	−0.771454	−	0.538474i
$804$	−4.39443			−0.154980
$805$		0			0
$806$	−4.11214	−	2.98764i	−0.144844	−	0.105235i
$807$	12.1127	−	8.80038i	0.426387	−	0.309788i
$808$	−2.95995	+	9.10980i	−0.104131	+	0.320482i
$809$	−0.398583	+	1.22671i	−0.0140134	+	0.0431289i	−0.957819	−	0.287373i	$-0.907218\pi$
$809$	−0.398583	+	1.22671i	−0.0140134	+	0.0431289i	0.943805	+	0.330502i	$0.107218\pi$
$810$	20.2811	−	14.7351i	0.712606	−	0.517738i
$811$	−27.6585	−	20.0951i	−0.971220	−	0.705633i	−0.0154910	−	0.999880i	$-0.504931\pi$
$811$	−27.6585	−	20.0951i	−0.971220	−	0.705633i	−0.955729	+	0.294247i	$0.904931\pi$
$812$		0			0
$813$	−62.9596			−2.20809
$814$	0.974073	−	3.20304i	0.0341412	−	0.112267i
$815$	39.0231			1.36692
$816$	−2.62358	−	8.07454i	−0.0918436	−	0.282666i
$817$	45.8801	+	33.3339i	1.60514	+	1.16620i
$818$	0.724728	−	0.526545i	0.0253395	−	0.0184102i
$819$		0			0
$820$	−5.71550	+	17.5905i	−0.199594	+	0.614287i
$821$	−32.0856	+	23.3115i	−1.11979	+	0.813578i	−0.984178	−	0.177184i	$-0.943301\pi$
$821$	−32.0856	+	23.3115i	−1.11979	+	0.813578i	−0.135616	+	0.990761i	$0.543301\pi$
$822$	23.5921	+	17.1407i	0.822870	+	0.597850i
$823$	−2.85134	−	8.77554i	−0.0993916	−	0.305896i	0.888982	−	0.457943i	$-0.151414\pi$
$823$	−2.85134	−	8.77554i	−0.0993916	−	0.305896i	−0.988373	+	0.152047i	$0.951414\pi$
$824$	−41.9241			−1.46049
$825$	3.35790	−	2.53818i	0.116907	−	0.0883681i
$826$		0			0
$827$	−7.94043	−	24.4381i	−0.276116	−	0.849797i	−0.988922	−	0.148436i	$-0.952576\pi$
$827$	−7.94043	−	24.4381i	−0.276116	−	0.849797i	0.712806	−	0.701361i	$-0.247424\pi$
$828$	−27.2382	−	19.7897i	−0.946591	−	0.687739i
$829$	8.84945	−	6.42950i	0.307354	−	0.223306i	−0.423406	−	0.905940i	$-0.639166\pi$
$829$	8.84945	−	6.42950i	0.307354	−	0.223306i	0.730760	+	0.682634i	$0.239166\pi$
$830$	−1.79750	+	5.53215i	−0.0623923	+	0.192024i
$831$	11.2572	−	34.6461i	0.390508	−	1.20186i
$832$	1.72547	−	1.25363i	0.0598200	−	0.0434618i
$833$		0			0
$834$	9.27333	+	28.5404i	0.321109	+	0.988272i
$835$	42.7282			1.47867
$836$	11.3185	+	32.7135i	0.391458	+	1.13142i
$837$	36.3630			1.25689
$838$	−7.75317	−	23.8618i	−0.267829	−	0.824293i
$839$	−28.1031	−	20.4181i	−0.970228	−	0.704912i	−0.0147243	−	0.999892i	$-0.504687\pi$
$839$	−28.1031	−	20.4181i	−0.970228	−	0.704912i	−0.955503	+	0.294980i	$0.904687\pi$
$840$		0			0
$841$	−8.69756	+	26.7684i	−0.299916	+	0.923047i
$842$	1.70983	−	5.26232i	0.0589247	−	0.181351i
$843$	30.6818	−	22.2916i	1.05674	−	0.767764i
$844$	18.5369	+	13.4678i	0.638065	+	0.463581i
$845$	4.37749	+	13.4725i	0.150590	+	0.463469i
$846$	−20.1996			−0.694478
$847$		0			0
$848$	1.00771			0.0346050
$849$	21.3388	+	65.6740i	0.732345	+	2.25393i
$850$	0.392241	+	0.284980i	0.0134538	+	0.00977474i
$851$	−3.85832	+	2.80323i	−0.132262	+	0.0960936i
$852$	−22.3825	+	68.8863i	−0.766813	+	2.36001i
$853$	6.37880	−	19.6319i	0.218406	−	0.672185i	−0.780488	−	0.625171i	$-0.785029\pi$
$853$	6.37880	−	19.6319i	0.218406	−	0.672185i	0.998894	−	0.0470143i	$-0.0149706\pi$
$854$		0			0
$855$	80.0191	+	58.1373i	2.73659	+	1.98825i
$856$	11.3220	+	34.8454i	0.386977	+	1.19099i
$857$	34.1512			1.16658			0.583291	−	0.812263i	$-0.301765\pi$
$857$	34.1512			1.16658			0.583291	+	0.812263i	$0.301765\pi$
$858$	−5.76547	−	16.6638i	−0.196830	−	0.568892i
$859$	33.4493			1.14127			0.570637	−	0.821202i	$-0.306696\pi$
$859$	33.4493			1.14127			0.570637	+	0.821202i	$0.306696\pi$
$860$	−8.66399	−	26.6650i	−0.295440	−	0.909269i
$861$		0			0
$862$	−17.6944	+	12.8557i	−0.602673	+	0.437868i
$863$	−10.5171	+	32.3683i	−0.358006	+	1.10183i	0.596240	+	0.802806i	$0.296660\pi$
$863$	−10.5171	+	32.3683i	−0.358006	+	1.10183i	−0.954246	+	0.299022i	$0.903340\pi$
$864$	−21.5930	+	66.4564i	−0.734609	+	2.26089i
$865$	−10.3889	+	7.54799i	−0.353234	+	0.256639i
$866$	8.55841	+	6.21805i	0.290827	+	0.211298i
$867$	13.3822	+	41.1861i	0.454483	+	1.39875i
$868$		0			0
$869$	10.7332	−	8.11305i	0.364099	−	0.275216i
$870$	−4.16619			−0.141247
$871$	0.704812	+	2.16919i	0.0238816	+	0.0735001i
$872$	−36.4202	−	26.4608i	−1.23334	−	0.896076i
$873$	47.2491	−	34.3285i	1.59914	−	1.16184i
$874$	−4.40569	+	13.5593i	−0.149025	+	0.458651i
$875$		0			0
$876$	31.6773	−	23.0149i	1.07028	−	0.777602i
$877$	−6.36458	−	4.62414i	−0.214917	−	0.156146i	0.475119	−	0.879922i	$-0.342405\pi$
$877$	−6.36458	−	4.62414i	−0.214917	−	0.156146i	−0.690035	+	0.723776i	$0.742405\pi$
$878$	4.28291	+	13.1814i	0.144541	+	0.444852i
$879$	4.44971			0.150085
$880$	3.12345	−	10.2708i	0.105292	−	0.346230i
$881$	−13.3289			−0.449063			−0.224531	−	0.974467i	$-0.572085\pi$
$881$	−13.3289			−0.449063			−0.224531	+	0.974467i	$0.572085\pi$
$882$		0			0
$883$	13.8340	+	10.0510i	0.465552	+	0.338243i	0.795705	−	0.605684i	$-0.207100\pi$
$883$	13.8340	+	10.0510i	0.465552	+	0.338243i	−0.330153	+	0.943927i	$0.607100\pi$
$884$	−5.68318	+	4.12908i	−0.191146	+	0.138876i
$885$	0.766184	−	2.35807i	0.0257550	−	0.0792658i
$886$	6.22863	−	19.1697i	0.209255	−	0.644020i
$887$	−21.4539	+	15.5872i	−0.720351	+	0.523366i	−0.886496	−	0.462736i	$-0.846868\pi$
$887$	−21.4539	+	15.5872i	−0.720351	+	0.523366i	0.166145	+	0.986101i	$0.446868\pi$
$888$	9.10614	+	6.61600i	0.305582	+	0.222018i
$889$		0			0
$890$	−11.9274			−0.399808
$891$	47.4850	+	33.1445i	1.59081	+	1.11038i
$892$	−2.86298			−0.0958598
$893$	−9.14231	−	28.1371i	−0.305936	−	0.941573i
$894$	4.46221	+	3.24199i	0.149239	+	0.108428i
$895$	−2.80781	+	2.03999i	−0.0938548	+	0.0681895i
$896$		0			0
$897$	−7.76209	+	23.8892i	−0.259168	+	0.797639i
$898$	−19.7197	+	14.3272i	−0.658056	+	0.478106i
$899$	−2.24434	−	1.63061i	−0.0748529	−	0.0543838i
$900$	1.32904	+	4.09036i	0.0443013	+	0.136345i
$901$	1.19530			0.0398211
$902$	12.3505	−	0.233913i	0.411225	−	0.00778846i
$903$		0			0
$904$	−1.23528	−	3.80180i	−0.0410848	−	0.126446i
$905$	−4.20896	−	3.05799i	−0.139911	−	0.101651i
$906$	−5.08601	+	3.69521i	−0.168972	+	0.122765i
$907$	2.73559	−	8.41928i	0.0908338	−	0.279558i	−0.895312	−	0.445440i	$-0.853047\pi$
$907$	2.73559	−	8.41928i	0.0908338	−	0.279558i	0.986146	+	0.165882i	$0.0530472\pi$
$908$	−10.5185	+	32.3726i	−0.349068	+	1.07432i
$909$	−22.3437	+	16.2337i	−0.741094	+	0.538436i
$910$		0			0
$911$	−17.2740	−	53.1639i	−0.572313	−	1.76140i	−0.645151	−	0.764055i	$-0.723206\pi$
$911$	−17.2740	−	53.1639i	−0.572313	−	1.76140i	0.0728381	−	0.997344i	$-0.476794\pi$
$912$	−31.8921			−1.05605
$913$	−13.4344	+	0.254442i	−0.444613	+	0.00842081i
$914$	−6.55948			−0.216968
$915$	−10.4238	−	32.0812i	−0.344601	−	1.06057i
$916$	25.4189	+	18.4679i	0.839865	+	0.610197i
$917$		0			0
$918$	−4.49001	+	13.8188i	−0.148192	+	0.456090i
$919$	14.9495	−	46.0098i	0.493139	−	1.51772i	−0.326699	−	0.945128i	$-0.605936\pi$
$919$	14.9495	−	46.0098i	0.493139	−	1.51772i	0.819838	−	0.572596i	$-0.194064\pi$
$920$	13.0535	−	9.48392i	0.430361	−	0.312676i
$921$	−74.8439	−	54.3773i	−2.46619	−	1.79179i
$922$	4.52412	+	13.9238i	0.148994	+	0.458556i
$923$	37.5937			1.23741
$924$		0			0
$925$	0.609223			0.0200311
$926$	1.39884	+	4.30517i	0.0459686	+	0.141477i
$927$	−97.7948	−	71.0521i	−3.21200	−	2.33366i
$928$	4.31281	−	3.13344i	0.141575	−	0.102860i
$929$	−0.267082	+	0.821994i	−0.00876267	+	0.0269687i	−0.955342	−	0.295502i	$-0.904513\pi$
$929$	−0.267082	+	0.821994i	−0.00876267	+	0.0269687i	0.946580	+	0.322470i	$0.104513\pi$
$930$	−4.18166	+	12.8698i	−0.137122	+	0.422018i
$931$		0			0
$932$	26.4366	+	19.2073i	0.865959	+	0.629156i
$933$	26.0789	+	80.2625i	0.853784	+	2.62768i
$934$	20.1079			0.657949
$935$	3.70488	−	12.1827i	0.121162	−	0.398418i
$936$	41.2424			1.34805
$937$	−16.5194	−	50.8416i	−0.539667	−	1.66092i	−0.733344	−	0.679858i	$-0.762042\pi$
$937$	−16.5194	−	50.8416i	−0.539667	−	1.66092i	0.193678	−	0.981065i	$-0.437958\pi$
$938$		0			0
$939$	11.4120	−	8.29134i	0.372418	−	0.270578i
$940$	−4.51985	+	13.9107i	−0.147421	+	0.453716i
$941$	−4.23353	+	13.0295i	−0.138009	+	0.424749i	−0.996046	−	0.0888397i	$-0.971684\pi$
$941$	−4.23353	+	13.0295i	−0.138009	+	0.424749i	0.858037	+	0.513588i	$0.171684\pi$
$942$	−19.1469	+	13.9110i	−0.623840	+	0.453246i
$943$	−14.2360	−	10.3431i	−0.463589	−	0.336817i
$944$	0.171867	+	0.528952i	0.00559379	+	0.0172159i
$945$		0			0
$946$	−14.9378	+	11.2912i	−0.485670	+	0.367110i
$947$	31.6444			1.02830			0.514152	−	0.857699i	$-0.328107\pi$
$947$	31.6444			1.02830			0.514152	+	0.857699i	$0.328107\pi$
$948$	6.10643	+	18.7936i	0.198328	+	0.610389i
$949$	−16.4413	−	11.9453i	−0.533707	−	0.387761i
$950$	1.47341	−	1.07050i	0.0478039	−	0.0347315i
$951$	10.6242	−	32.6980i	0.344514	−	1.06031i
$952$		0			0
$953$	−26.4856	+	19.2429i	−0.857951	+	0.623338i	−0.927327	−	0.374253i	$-0.877899\pi$
$953$	−26.4856	+	19.2429i	−0.857951	+	0.623338i	0.0693755	+	0.997591i	$0.477899\pi$
$954$	−2.48013	−	1.80192i	−0.0802972	−	0.0583394i
$955$	−8.41390	−	25.8953i	−0.272268	−	0.837953i
$956$	−24.0420			−0.777573
$957$	−3.14670	−	9.09482i	−0.101718	−	0.293994i
$958$	4.02083			0.129907
$959$		0			0
$960$	−4.59371	−	3.33753i	−0.148261	−	0.107718i
$961$	17.7897	−	12.9250i	0.573862	−	0.416935i
$962$	0.788639	−	2.42718i	0.0254267	−	0.0782555i
$963$	−32.6450	+	100.471i	−1.05197	+	3.23763i
$964$	−17.6785	+	12.8442i	−0.569385	+	0.413683i
$965$	−3.05127	−	2.21688i	−0.0982238	−	0.0713637i
$966$		0			0
$967$	−32.3487			−1.04026			−0.520132	−	0.854086i	$-0.674117\pi$
$967$	−32.3487			−1.04026			−0.520132	+	0.854086i	$0.674117\pi$
$968$	−26.1454	+	0.990723i	−0.840344	+	0.0318430i
$969$	−37.8287			−1.21523
$970$	3.77832	+	11.6285i	0.121314	+	0.373367i
$971$	−23.8069	−	17.2968i	−0.764001	−	0.555079i	0.136134	−	0.990690i	$-0.456532\pi$
$971$	−23.8069	−	17.2968i	−0.764001	−	0.555079i	−0.900135	+	0.435611i	$0.856532\pi$
$972$	−23.1941	+	16.8515i	−0.743950	+	0.540511i
$973$		0			0
$974$	1.31778	−	4.05570i	0.0422243	−	0.129953i
$975$	2.59591	−	1.88604i	0.0831355	−	0.0604015i
$976$	6.12155	+	4.44757i	0.195946	+	0.142363i
$977$	4.23181	+	13.0242i	0.135388	+	0.416681i	0.995650	−	0.0931709i	$-0.0297003\pi$
$977$	4.23181	+	13.0242i	0.135388	+	0.416681i	−0.860262	+	0.509852i	$0.829700\pi$
$978$	38.2780			1.22399
$979$	−9.00874	−	26.0377i	−0.287920	−	0.832168i
$980$		0			0
$981$	−40.1108	−	123.448i	−1.28064	−	3.94141i
$982$	−6.70622	−	4.87236i	−0.214004	−	0.155483i
$983$	13.7791	−	10.0111i	0.439486	−	0.319305i	−0.345945	−	0.938255i	$-0.612442\pi$
$983$	13.7791	−	10.0111i	0.439486	−	0.319305i	0.785431	+	0.618950i	$0.212442\pi$
$984$	−12.8336	+	39.4979i	−0.409122	+	1.25915i
$985$	0.598240	−	1.84119i	0.0190615	−	0.0586653i
$986$	0.896797	−	0.651561i	0.0285598	−	0.0207499i
$987$		0			0
$988$	8.15432	+	25.0964i	0.259423	+	0.798423i
$989$	26.6744			0.848198
$990$	−26.0529	+	19.6929i	−0.828015	+	0.625883i
$991$	23.2202			0.737614			0.368807	−	0.929506i	$-0.379766\pi$
$991$	23.2202			0.737614			0.368807	+	0.929506i	$0.379766\pi$
$992$	−5.35072	−	16.4678i	−0.169886	−	0.522854i
$993$	41.9696	+	30.4927i	1.33187	+	0.967657i
$994$		0			0
$995$	−10.3540	+	31.8665i	−0.328245	+	1.01023i
$996$	6.09839	−	18.7689i	0.193235	−	0.594716i
$997$	−14.8678	+	10.8021i	−0.470868	+	0.342105i	−0.797779	−	0.602949i	$-0.793992\pi$
$997$	−14.8678	+	10.8021i	−0.470868	+	0.342105i	0.326912	+	0.945055i	$0.393992\pi$
$998$	7.73720	+	5.62141i	0.244917	+	0.177943i
$999$	5.64193	+	17.3641i	0.178503	+	0.549375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.f.e.148.3		16
7.2	even	3		539.2.q.f.214.3		32
7.3	odd	6		539.2.q.g.324.2		32
7.4	even	3		539.2.q.f.324.2		32
7.5	odd	6		539.2.q.g.214.3		32
7.6	odd	2		77.2.f.b.71.3	yes	16
11.3	even	5		5929.2.a.bt.1.5		8
11.8	odd	10		5929.2.a.bs.1.4		8
11.9	even	5	inner	539.2.f.e.295.3		16
21.20	even	2		693.2.m.i.379.2		16
77.6	even	10		847.2.f.v.323.3		16
77.9	even	15		539.2.q.f.361.2		32
77.13	even	10		847.2.f.x.372.2		16
77.20	odd	10		77.2.f.b.64.3	✓	16
77.27	odd	10		847.2.f.w.323.2		16
77.31	odd	30		539.2.q.g.471.3		32
77.41	even	10		847.2.a.o.1.4		8
77.48	odd	10		847.2.f.w.729.2		16
77.53	even	15		539.2.q.f.471.3		32
77.62	even	10		847.2.f.v.729.3		16
77.69	odd	10		847.2.a.p.1.5		8
77.75	odd	30		539.2.q.g.361.2		32
77.76	even	2		847.2.f.x.148.2		16
231.20	even	10		693.2.m.i.64.2		16
231.41	odd	10		7623.2.a.cw.1.5		8
231.146	even	10		7623.2.a.ct.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.3	✓	16	77.20	odd	10
77.2.f.b.71.3	yes	16	7.6	odd	2
539.2.f.e.148.3		16	1.1	even	1	trivial
539.2.f.e.295.3		16	11.9	even	5	inner
539.2.q.f.214.3		32	7.2	even	3
539.2.q.f.324.2		32	7.4	even	3
539.2.q.f.361.2		32	77.9	even	15
539.2.q.f.471.3		32	77.53	even	15
539.2.q.g.214.3		32	7.5	odd	6
539.2.q.g.324.2		32	7.3	odd	6
539.2.q.g.361.2		32	77.75	odd	30
539.2.q.g.471.3		32	77.31	odd	30
693.2.m.i.64.2		16	231.20	even	10
693.2.m.i.379.2		16	21.20	even	2
847.2.a.o.1.4		8	77.41	even	10
847.2.a.p.1.5		8	77.69	odd	10
847.2.f.v.323.3		16	77.6	even	10
847.2.f.v.729.3		16	77.62	even	10
847.2.f.w.323.2		16	77.27	odd	10
847.2.f.w.729.2		16	77.48	odd	10
847.2.f.x.148.2		16	77.76	even	2
847.2.f.x.372.2		16	77.13	even	10
5929.2.a.bs.1.4		8	11.8	odd	10
5929.2.a.bt.1.5		8	11.3	even	5
7623.2.a.ct.1.4		8	231.146	even	10
7623.2.a.cw.1.5		8	231.41	odd	10

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:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.206962 + 0.636964i) q^{2} +(2.54013 + 1.84551i) q^{3} +(1.25514 - 0.911915i) q^{4} +(-0.662464 + 2.03885i) q^{5} +(-0.649815 + 1.99992i) q^{6} +(1.92429 + 1.39808i) q^{8} +(2.11929 + 6.52251i) q^{9} +O(q^{10})\)	\(q+(0.206962 + 0.636964i) q^{2} +(2.54013 + 1.84551i) q^{3} +(1.25514 - 0.911915i) q^{4} +(-0.662464 + 2.03885i) q^{5} +(-0.649815 + 1.99992i) q^{6} +(1.92429 + 1.39808i) q^{8} +(2.11929 + 6.52251i) q^{9} -1.43578 q^{10} +(-1.08444 - 3.13432i) q^{11} +4.87118 q^{12} +(-0.781276 - 2.40452i) q^{13} +(-5.44548 + 3.95637i) q^{15} +(0.466573 - 1.43596i) q^{16} +(0.553425 - 1.70327i) q^{17} +(-3.71599 + 2.69983i) q^{18} +(-5.44258 - 3.95427i) q^{19} +(1.02778 + 3.16317i) q^{20} +(1.77201 - 1.33944i) q^{22} -3.16429 q^{23} +(2.30778 + 7.10261i) q^{24} +(0.327016 + 0.237591i) q^{25} +(1.36990 - 0.995290i) q^{26} +(-3.74337 + 11.5209i) q^{27} +(0.747669 - 0.543213i) q^{29} +(-3.64707 - 2.64975i) q^{30} +(-0.927602 - 2.85487i) q^{31} +5.76834 q^{32} +(3.02982 - 9.96294i) q^{33} +1.19946 q^{34} +(8.60800 + 6.25408i) q^{36} +(1.21933 - 0.885898i) q^{37} +(1.39232 - 4.28511i) q^{38} +(2.45303 - 7.54965i) q^{39} +(-4.12526 + 2.99718i) q^{40} +(4.49897 + 3.26870i) q^{41} -8.42985 q^{43} +(-4.21937 - 2.94511i) q^{44} -14.7024 q^{45} +(-0.654888 - 2.01554i) q^{46} +(3.55782 + 2.58491i) q^{47} +(3.83525 - 2.78647i) q^{48} +(-0.0836570 + 0.257470i) q^{50} +(4.54917 - 3.30516i) q^{51} +(-3.17333 - 2.30556i) q^{52} +(0.206244 + 0.634755i) q^{53} -8.11314 q^{54} +(7.10883 - 0.134639i) q^{55} +(-6.52722 - 20.0887i) q^{57} +(0.500747 + 0.363814i) q^{58} +(-0.298010 + 0.216517i) q^{59} +(-3.22698 + 9.93163i) q^{60} +(-1.54863 + 4.76621i) q^{61} +(1.62647 - 1.18170i) q^{62} +(0.260682 + 0.802296i) q^{64} +5.42003 q^{65} +(6.97309 - 0.132068i) q^{66} -0.902129 q^{67} +(-0.858607 - 2.64252i) q^{68} +(-8.03770 - 5.83973i) q^{69} +(-4.59489 + 14.1416i) q^{71} +(-5.04086 + 15.5142i) q^{72} +(6.50301 - 4.72471i) q^{73} +(0.816641 + 0.593325i) q^{74} +(0.392186 + 1.20702i) q^{75} -10.4372 q^{76} +5.31654 q^{78} +(1.25358 + 3.85813i) q^{79} +(2.61863 + 1.90255i) q^{80} +(-14.1255 + 10.2628i) q^{81} +(-1.15092 + 3.54218i) q^{82} +(1.25193 - 3.85305i) q^{83} +(3.10609 + 2.25670i) q^{85} +(-1.74466 - 5.36951i) q^{86} +2.90168 q^{87} +(2.29526 - 7.54749i) q^{88} +8.30727 q^{89} +(-3.04284 - 9.36491i) q^{90} +(-3.97163 + 2.88556i) q^{92} +(2.91246 - 8.96363i) q^{93} +(-0.910159 + 2.80118i) q^{94} +(11.6677 - 8.47707i) q^{95} +(14.6523 + 10.6455i) q^{96} +(-2.63154 - 8.09904i) q^{97} +(18.1454 - 13.7158i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} + 2 q^{3} - 11 q^{4} + 5 q^{5} - 3 q^{6} - 5 q^{8} - 12 q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 + 2 * q^3 - 11 * q^4 + 5 * q^5 - 3 * q^6 - 5 * q^8 - 12 * q^9	\( 16 q - 3 q^{2} + 2 q^{3} - 11 q^{4} + 5 q^{5} - 3 q^{6} - 5 q^{8} - 12 q^{9} - 12 q^{10} - 3 q^{11} - 18 q^{12} + 7 q^{13} - 18 q^{15} + 17 q^{16} + 5 q^{17} + 11 q^{18} - 19 q^{19} - q^{20} - 33 q^{22} + 32 q^{23} + 35 q^{24} + 7 q^{25} + 27 q^{26} - 10 q^{27} + 3 q^{29} - 2 q^{30} + 7 q^{31} + 32 q^{32} + 26 q^{33} + 24 q^{34} + 52 q^{36} + 4 q^{37} + 5 q^{38} + 11 q^{39} + 10 q^{40} + 10 q^{41} - 8 q^{43} - 38 q^{44} - 70 q^{45} - 42 q^{46} + 23 q^{47} + 36 q^{48} + 52 q^{50} - 29 q^{51} - 33 q^{52} + 4 q^{53} - 60 q^{54} + 12 q^{55} - 11 q^{57} + 20 q^{58} - 17 q^{59} - 30 q^{60} + 7 q^{61} - 79 q^{62} + 7 q^{64} - 8 q^{65} - 8 q^{66} - 38 q^{67} + 2 q^{68} - 10 q^{69} - 14 q^{71} + 35 q^{73} - 29 q^{74} - 9 q^{75} - 52 q^{76} - 58 q^{78} + 15 q^{79} + 87 q^{80} - 14 q^{81} - 19 q^{82} - 5 q^{83} + 6 q^{85} - 52 q^{86} + 72 q^{87} + 55 q^{88} - 74 q^{89} + 14 q^{90} - 55 q^{92} + 32 q^{93} + 24 q^{94} + 32 q^{95} + 42 q^{96} - 20 q^{97} + 16 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + 2 * q^3 - 11 * q^4 + 5 * q^5 - 3 * q^6 - 5 * q^8 - 12 * q^9 - 12 * q^10 - 3 * q^11 - 18 * q^12 + 7 * q^13 - 18 * q^15 + 17 * q^16 + 5 * q^17 + 11 * q^18 - 19 * q^19 - q^20 - 33 * q^22 + 32 * q^23 + 35 * q^24 + 7 * q^25 + 27 * q^26 - 10 * q^27 + 3 * q^29 - 2 * q^30 + 7 * q^31 + 32 * q^32 + 26 * q^33 + 24 * q^34 + 52 * q^36 + 4 * q^37 + 5 * q^38 + 11 * q^39 + 10 * q^40 + 10 * q^41 - 8 * q^43 - 38 * q^44 - 70 * q^45 - 42 * q^46 + 23 * q^47 + 36 * q^48 + 52 * q^50 - 29 * q^51 - 33 * q^52 + 4 * q^53 - 60 * q^54 + 12 * q^55 - 11 * q^57 + 20 * q^58 - 17 * q^59 - 30 * q^60 + 7 * q^61 - 79 * q^62 + 7 * q^64 - 8 * q^65 - 8 * q^66 - 38 * q^67 + 2 * q^68 - 10 * q^69 - 14 * q^71 + 35 * q^73 - 29 * q^74 - 9 * q^75 - 52 * q^76 - 58 * q^78 + 15 * q^79 + 87 * q^80 - 14 * q^81 - 19 * q^82 - 5 * q^83 + 6 * q^85 - 52 * q^86 + 72 * q^87 + 55 * q^88 - 74 * q^89 + 14 * q^90 - 55 * q^92 + 32 * q^93 + 24 * q^94 + 32 * q^95 + 42 * q^96 - 20 * q^97 + 16 * q^99

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