LMFDB - Embedded newform 65.2.o.a.63.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [65,2,Mod(2,65)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("65.2"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(65, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.o (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.519027613138$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			63.3
Root			$0.131303i$ of defining polynomial
Character	$\chi$	$=$	65.63
Dual form			65.2.o.a.32.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0656513 + 0.113711i) q^{2} +(-0.0890070 + 0.332179i) q^{3} +(0.991380 - 1.71712i) q^{4} +(0.813169 + 2.08297i) q^{5} +(-0.0436159 + 0.0116869i) q^{6} +(-2.40874 - 1.39069i) q^{7} +0.522947 q^{8} +(2.49566 + 1.44087i) q^{9} +(-0.183472 + 0.229216i) q^{10} +(-3.91706 - 1.04957i) q^{11} +(0.482151 + 0.482151i) q^{12} +(-3.52539 + 0.756068i) q^{13} -0.365201i q^{14} +(-0.764295 + 0.0847187i) q^{15} +(-1.94843 - 3.37478i) q^{16} +(-2.34186 + 0.627499i) q^{17} +0.378379i q^{18} +(-0.491577 - 1.83459i) q^{19} +(4.38287 + 0.668703i) q^{20} +(0.676351 - 0.676351i) q^{21} +(-0.137812 - 0.514321i) q^{22} +(7.70544 + 2.06467i) q^{23} +(-0.0465459 + 0.173712i) q^{24} +(-3.67751 + 3.38761i) q^{25} +(-0.317420 - 0.351240i) q^{26} +(-1.43027 + 1.43027i) q^{27} +(-4.77595 + 2.75740i) q^{28} +(3.96565 - 2.28957i) q^{29} +(-0.0598105 - 0.0813472i) q^{30} +(3.87352 + 3.87352i) q^{31} +(0.778780 - 1.34889i) q^{32} +(0.697292 - 1.20775i) q^{33} +(-0.225100 - 0.225100i) q^{34} +(0.938043 - 6.14819i) q^{35} +(4.94829 - 2.85689i) q^{36} +(6.07101 - 3.50510i) q^{37} +(0.176341 - 0.176341i) q^{38} +(0.0626346 - 1.23835i) q^{39} +(0.425244 + 1.08928i) q^{40} +(-1.66178 + 6.20184i) q^{41} +(0.121312 + 0.0325055i) q^{42} +(-1.67299 - 6.24368i) q^{43} +(-5.68554 + 5.68554i) q^{44} +(-0.971891 + 6.37004i) q^{45} +(0.271096 + 1.01174i) q^{46} +0.512375i q^{47} +(1.29445 - 0.346847i) q^{48} +(0.368015 + 0.637420i) q^{49} +(-0.626643 - 0.195774i) q^{50} -0.833767i q^{51} +(-2.19674 + 6.80307i) q^{52} +(-1.32662 - 1.32662i) q^{53} +(-0.256537 - 0.0687390i) q^{54} +(-0.999006 - 9.01260i) q^{55} +(-1.25964 - 0.727255i) q^{56} +0.653165 q^{57} +(0.520700 + 0.300626i) q^{58} +(-2.53667 + 0.679700i) q^{59} +(-0.612235 + 1.39638i) q^{60} +(0.641767 - 1.11157i) q^{61} +(-0.186162 + 0.694764i) q^{62} +(-4.00759 - 6.94135i) q^{63} -7.58920 q^{64} +(-4.44160 - 6.72846i) q^{65} +0.183113 q^{66} +(-1.80814 - 3.13180i) q^{67} +(-1.24418 + 4.64334i) q^{68} +(-1.37168 + 2.37581i) q^{69} +(0.760703 - 0.296970i) q^{70} +(-6.20800 + 1.66343i) q^{71} +(1.30509 + 0.753497i) q^{72} +9.93250 q^{73} +(0.797139 + 0.460228i) q^{74} +(-0.797968 - 1.52311i) q^{75} +(-3.63755 - 0.974678i) q^{76} +(7.97556 + 7.97556i) q^{77} +(0.144927 - 0.0741773i) q^{78} +8.37577i q^{79} +(5.44515 - 6.80278i) q^{80} +(3.97480 + 6.88456i) q^{81} +(-0.814318 + 0.218196i) q^{82} +3.17194i q^{83} +(-0.490855 - 1.83190i) q^{84} +(-3.21139 - 4.36775i) q^{85} +(0.600143 - 0.600143i) q^{86} +(0.407576 + 1.52109i) q^{87} +(-2.04842 - 0.548871i) q^{88} +(-1.61226 + 6.01705i) q^{89} +(-0.788152 + 0.307686i) q^{90} +(9.54319 + 3.08154i) q^{91} +(11.1843 - 11.1843i) q^{92} +(-1.63147 + 0.941930i) q^{93} +(-0.0582629 + 0.0336381i) q^{94} +(3.42165 - 2.51577i) q^{95} +(0.378755 + 0.378755i) q^{96} +(5.88500 - 10.1931i) q^{97} +(-0.0483213 + 0.0836950i) q^{98} +(-8.26335 - 8.26335i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9} - 10 q^{10} - 16 q^{11} + 24 q^{12} + 2 q^{13} + 12 q^{15} - 2 q^{16} - 10 q^{17} + 20 q^{19} + 14 q^{20} + 4 q^{21}+ \cdots - 60 q^{99}+O(q^{100}) $ 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9 - 10 * q^10 - 16 * q^11 + 24 * q^12 + 2 * q^13 + 12 * q^15 - 2 * q^16 - 10 * q^17 + 20 * q^19 + 14 * q^20 + 4 * q^21 + 16 * q^22 - 2 * q^23 - 32 * q^24 - 18 * q^25 - 24 * q^26 + 4 * q^27 + 6 * q^28 + 14 * q^30 - 6 * q^32 - 18 * q^33 - 2 * q^34 - 20 * q^35 + 36 * q^36 + 42 * q^37 + 8 * q^38 - 4 * q^39 - 16 * q^40 + 10 * q^41 - 56 * q^42 - 22 * q^43 + 36 * q^44 + 52 * q^45 + 4 * q^46 + 28 * q^48 - 18 * q^49 + 44 * q^50 + 46 * q^52 - 10 * q^53 + 48 * q^54 + 26 * q^55 - 12 * q^57 - 90 * q^58 + 16 * q^59 - 92 * q^60 - 16 * q^61 - 40 * q^62 - 32 * q^63 - 20 * q^64 + 8 * q^65 - 32 * q^66 - 58 * q^67 + 28 * q^68 + 16 * q^69 + 32 * q^70 - 16 * q^71 - 66 * q^72 + 72 * q^73 - 18 * q^74 - 34 * q^75 - 64 * q^76 + 28 * q^77 + 32 * q^78 - 34 * q^80 - 14 * q^81 + 22 * q^82 + 40 * q^84 - 6 * q^85 + 60 * q^86 + 62 * q^87 + 50 * q^88 + 6 * q^89 - 46 * q^90 + 8 * q^91 - 8 * q^92 + 48 * q^93 + 48 * q^94 + 14 * q^95 + 56 * q^96 - 22 * q^97 + 4 * q^98 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.0656513	+	0.113711i	0.0464225	+	0.0804061i	0.888303	−	0.459258i	$-0.151885\pi$
$2$	0.0656513	+	0.113711i	0.0464225	+	0.0804061i	−0.841881	+	0.539664i	$0.818551\pi$
$3$	−0.0890070	+	0.332179i	−0.0513882	+	0.191783i	−0.986848	−	0.161649i	$-0.948319\pi$
$3$	−0.0890070	+	0.332179i	−0.0513882	+	0.191783i	0.935460	+	0.353432i	$0.114985\pi$
$4$	0.991380	−	1.71712i	0.495690	−	0.858560i
$5$	0.813169	+	2.08297i	0.363660	+	0.931532i
$5$	0.813169	+	2.08297i	0.363660	+	0.931532i
$6$	−0.0436159	+	0.0116869i	−0.0178061	+	0.00477114i
$7$	−2.40874	−	1.39069i	−0.910418	−	0.525630i	−0.0298522	−	0.999554i	$-0.509504\pi$
$7$	−2.40874	−	1.39069i	−0.910418	−	0.525630i	−0.880566	+	0.473924i	$0.842837\pi$
$8$	0.522947			0.184890
$9$	2.49566	+	1.44087i	0.831885	+	0.480289i
$10$	−0.183472	+	0.229216i	−0.0580188	+	0.0724845i
$11$	−3.91706	−	1.04957i	−1.18104	−	0.316459i	−0.385701	−	0.922624i	$-0.626040\pi$
$11$	−3.91706	−	1.04957i	−1.18104	−	0.316459i	−0.795339	+	0.606165i	$0.792707\pi$
$12$	0.482151	+	0.482151i	0.139185	+	0.139185i
$13$	−3.52539	+	0.756068i	−0.977767	+	0.209695i
$13$	−3.52539	+	0.756068i	−0.977767	+	0.209695i
$14$		−	0.365201i		−	0.0976042i
$15$	−0.764295	+	0.0847187i	−0.197340	+	0.0218743i
$16$	−1.94843	−	3.37478i	−0.487107	−	0.843694i
$17$	−2.34186	+	0.627499i	−0.567984	+	0.152191i	−0.531372	−	0.847139i	$-0.678323\pi$
$17$	−2.34186	+	0.627499i	−0.567984	+	0.152191i	−0.0366120	+	0.999330i	$0.511657\pi$
$18$			0.378379i			0.0891849i
$19$	−0.491577	−	1.83459i	−0.112775	−	0.420883i	0.886335	−	0.463044i	$-0.153243\pi$
$19$	−0.491577	−	1.83459i	−0.112775	−	0.420883i	−0.999111	+	0.0421602i	$0.986576\pi$
$20$	4.38287	+	0.668703i	0.980039	+	0.149527i
$21$	0.676351	−	0.676351i	0.147592	−	0.147592i
$22$	−0.137812	−	0.514321i	−0.0293816	−	0.109654i
$23$	7.70544	+	2.06467i	1.60670	+	0.430513i	0.947056	−	0.321069i	$-0.104042\pi$
$23$	7.70544	+	2.06467i	1.60670	+	0.430513i	0.659640	+	0.751582i	$0.270709\pi$
$24$	−0.0465459	+	0.173712i	−0.00950115	+	0.0354588i
$25$	−3.67751	+	3.38761i	−0.735502	+	0.677522i
$26$	−0.317420	−	0.351240i	−0.0622511	−	0.0688838i
$27$	−1.43027	+	1.43027i	−0.275256	+	0.275256i
$28$	−4.77595	+	2.75740i	−0.902570	+	0.521099i
$29$	3.96565	−	2.28957i	0.736403	−	0.425162i	−0.0843571	−	0.996436i	$-0.526884\pi$
$29$	3.96565	−	2.28957i	0.736403	−	0.425162i	0.820760	+	0.571273i	$0.193550\pi$
$30$	−0.0598105	−	0.0813472i	−0.0109198	−	0.0148519i
$31$	3.87352	+	3.87352i	0.695704	+	0.695704i	0.963481	−	0.267777i	$-0.0862890\pi$
$31$	3.87352	+	3.87352i	0.695704	+	0.695704i	−0.267777	+	0.963481i	$0.586289\pi$
$32$	0.778780	−	1.34889i	0.137670	−	0.238452i
$33$	0.697292	−	1.20775i	0.121383	−	0.210242i
$34$	−0.225100	−	0.225100i	−0.0386043	−	0.0386043i
$35$	0.938043	−	6.14819i	0.158558	−	1.03923i
$36$	4.94829	−	2.85689i	0.824714	−	0.476149i
$37$	6.07101	−	3.50510i	0.998067	−	0.576234i	0.0903914	−	0.995906i	$-0.471188\pi$
$37$	6.07101	−	3.50510i	0.998067	−	0.576234i	0.907676	+	0.419672i	$0.137855\pi$
$38$	0.176341	−	0.176341i	0.0286063	−	0.0286063i
$39$	0.0626346	−	1.23835i	0.0100296	−	0.198295i
$40$	0.425244	+	1.08928i	0.0672370	+	0.172230i
$41$	−1.66178	+	6.20184i	−0.259526	+	0.968565i	0.705990	+	0.708222i	$0.250502\pi$
$41$	−1.66178	+	6.20184i	−0.259526	+	0.968565i	−0.965516	+	0.260343i	$0.916164\pi$
$42$	0.121312	+	0.0325055i	0.0187189	+	0.00501570i
$43$	−1.67299	−	6.24368i	−0.255128	−	0.952152i	−0.968019	−	0.250877i	$-0.919281\pi$
$43$	−1.67299	−	6.24368i	−0.255128	−	0.952152i	0.712891	−	0.701275i	$-0.247386\pi$
$44$	−5.68554	+	5.68554i	−0.857128	+	0.857128i
$45$	−0.971891	+	6.37004i	−0.144881	+	0.949590i
$46$	0.271096	+	1.01174i	0.0399709	+	0.149174i
$47$			0.512375i			0.0747376i	0.999302	+	0.0373688i	$0.0118976\pi$
$47$			0.512375i			0.0747376i	−0.999302	+	0.0373688i	$0.988102\pi$
$48$	1.29445	−	0.346847i	0.186838	−	0.0500631i
$49$	0.368015	+	0.637420i	0.0525736	+	0.0910601i
$50$	−0.626643	−	0.195774i	−0.0886207	−	0.0276866i
$51$		−	0.833767i		−	0.116751i
$52$	−2.19674	+	6.80307i	−0.304633	+	0.943415i
$53$	−1.32662	−	1.32662i	−0.182225	−	0.182225i	0.610100	−	0.792325i	$-0.291129\pi$
$53$	−1.32662	−	1.32662i	−0.182225	−	0.182225i	−0.792325	+	0.610100i	$0.791129\pi$
$54$	−0.256537	−	0.0687390i	−0.0349103	−	0.00935419i
$55$	−0.999006	−	9.01260i	−0.134706	−	1.21526i
$56$	−1.25964	−	0.727255i	−0.168327	−	0.0971835i
$57$	0.653165			0.0865138
$58$	0.520700	+	0.300626i	0.0683713	+	0.0394742i
$59$	−2.53667	+	0.679700i	−0.330247	+	0.0884894i	−0.420133	−	0.907463i	$-0.638016\pi$
$59$	−2.53667	+	0.679700i	−0.330247	+	0.0884894i	0.0898858	+	0.995952i	$0.471350\pi$
$60$	−0.612235	+	1.39638i	−0.0790392	+	0.180271i
$61$	0.641767	−	1.11157i	0.0821698	−	0.142322i	−0.822012	−	0.569470i	$-0.807148\pi$
$61$	0.641767	−	1.11157i	0.0821698	−	0.142322i	0.904182	+	0.427148i	$0.140482\pi$
$62$	−0.186162	+	0.694764i	−0.0236425	+	0.0882352i
$63$	−4.00759	−	6.94135i	−0.504909	−	0.874528i
$64$	−7.58920			−0.948650
$65$	−4.44160	−	6.72846i	−0.550913	−	0.834563i
$66$	0.183113			0.0225396
$67$	−1.80814	−	3.13180i	−0.220900	−	0.382610i	0.734181	−	0.678953i	$-0.237566\pi$
$67$	−1.80814	−	3.13180i	−0.220900	−	0.382610i	−0.955082	+	0.296343i	$0.904233\pi$
$68$	−1.24418	+	4.64334i	−0.150879	+	0.563088i
$69$	−1.37168	+	2.37581i	−0.165130	+	0.286014i
$70$	0.760703	−	0.296970i	0.0909214	−	0.0354948i
$71$	−6.20800	+	1.66343i	−0.736754	+	0.197413i	−0.607635	−	0.794216i	$-0.707882\pi$
$71$	−6.20800	+	1.66343i	−0.736754	+	0.197413i	−0.129119	+	0.991629i	$0.541215\pi$
$72$	1.30509	+	0.753497i	0.153807	+	0.0888005i
$73$	9.93250			1.16251			0.581256	−	0.813721i	$-0.302562\pi$
$73$	9.93250			1.16251			0.581256	+	0.813721i	$0.302562\pi$
$74$	0.797139	+	0.460228i	0.0926655	+	0.0535005i
$75$	−0.797968	−	1.52311i	−0.0921414	−	0.175874i
$76$	−3.63755	−	0.974678i	−0.417255	−	0.111803i
$77$	7.97556	+	7.97556i	0.908899	+	0.908899i
$78$	0.144927	−	0.0741773i	0.0164098	−	0.00839892i
$79$			8.37577i			0.942347i	0.882040	+	0.471174i	$0.156169\pi$
$79$			8.37577i			0.942347i	−0.882040	+	0.471174i	$0.843831\pi$
$80$	5.44515	−	6.80278i	0.608786	−	0.760573i
$81$	3.97480	+	6.88456i	0.441645	+	0.764951i
$82$	−0.814318	+	0.218196i	−0.0899264	+	0.0240957i
$83$			3.17194i			0.348166i	0.984731	+	0.174083i	$0.0556961\pi$
$83$			3.17194i			0.348166i	−0.984731	+	0.174083i	$0.944304\pi$
$84$	−0.490855	−	1.83190i	−0.0535567	−	0.199876i
$85$	−3.21139	−	4.36775i	−0.348324	−	0.473749i
$86$	0.600143	−	0.600143i	0.0647151	−	0.0647151i
$87$	0.407576	+	1.52109i	0.0436967	+	0.163078i
$88$	−2.04842	−	0.548871i	−0.218362	−	0.0585099i
$89$	−1.61226	+	6.01705i	−0.170900	+	0.637806i	0.826314	+	0.563210i	$0.190434\pi$
$89$	−1.61226	+	6.01705i	−0.170900	+	0.637806i	−0.997214	+	0.0745967i	$0.976233\pi$
$90$	−0.788152	+	0.307686i	−0.0830785	+	0.0324330i
$91$	9.54319	+	3.08154i	1.00040	+	0.323033i
$92$	11.1843	−	11.1843i	1.16604	−	1.16604i
$93$	−1.63147	+	0.941930i	−0.169176	+	0.0976736i
$94$	−0.0582629	+	0.0336381i	−0.00600936	+	0.00346951i
$95$	3.42165	−	2.51577i	0.351054	−	0.258112i
$96$	0.378755	+	0.378755i	0.0386565	+	0.0386565i
$97$	5.88500	−	10.1931i	0.597531	−	1.03495i	−0.395654	−	0.918400i	$-0.629482\pi$
$97$	5.88500	−	10.1931i	0.597531	−	1.03495i	0.993184	−	0.116554i	$-0.0371847\pi$
$98$	−0.0483213	+	0.0836950i	−0.00488119	+	0.00845447i
$99$	−8.26335	−	8.26335i	−0.830498	−	0.830498i
$100$	2.17112	+	9.67314i	0.217112	+	0.967314i
$101$	0.873807	−	0.504493i	0.0869471	−	0.0501989i	−0.455896	−	0.890033i	$-0.650681\pi$
$101$	0.873807	−	0.504493i	0.0869471	−	0.0501989i	0.542843	+	0.839834i	$0.317348\pi$
$102$	0.0948088	−	0.0547379i	0.00938747	−	0.00541986i
$103$	6.00002	−	6.00002i	0.591200	−	0.591200i	−0.346756	−	0.937955i	$-0.612717\pi$
$103$	6.00002	−	6.00002i	0.591200	−	0.591200i	0.937955	+	0.346756i	$0.112717\pi$
$104$	−1.84359	+	0.395383i	−0.180779	+	0.0387705i
$105$	1.95880	+	0.858830i	0.191160	+	0.0838132i
$106$	0.0637574	−	0.237946i	0.00619267	−	0.0231113i
$107$	−4.78678	−	1.28261i	−0.462755	−	0.123995i	0.0199063	−	0.999802i	$-0.493663\pi$
$107$	−4.78678	−	1.28261i	−0.462755	−	0.123995i	−0.482662	+	0.875807i	$0.660330\pi$
$108$	1.03801	+	3.87389i	0.0998821	+	0.372765i
$109$	6.51002	−	6.51002i	0.623546	−	0.623546i	−0.322890	−	0.946436i	$-0.604654\pi$
$109$	6.51002	−	6.51002i	0.623546	−	0.623546i	0.946436	+	0.322890i	$0.104654\pi$
$110$	0.959249	−	0.705287i	0.0914608	−	0.0672465i
$111$	0.623956	+	2.32864i	0.0592233	+	0.221024i
$112$			10.8386i			1.02415i
$113$	−7.24731	+	1.94191i	−0.681769	+	0.182680i	−0.583051	−	0.812436i	$-0.698141\pi$
$113$	−7.24731	+	1.94191i	−0.681769	+	0.182680i	−0.0987188	+	0.995115i	$0.531474\pi$
$114$	0.0428811	+	0.0742723i	0.00401619	+	0.00695624i
$115$	1.96519	+	17.7291i	0.183255	+	1.65325i
$116$		−	9.07933i		−	0.842995i
$117$	−9.88755	−	3.19273i	−0.914104	−	0.295168i
$118$	−0.243826	−	0.243826i	−0.0224460	−	0.0224460i
$119$	6.51358	+	1.74531i	0.597099	+	0.159992i
$120$	−0.399686	+	0.0443033i	−0.0364861	+	0.00404432i
$121$	4.71551	+	2.72250i	0.428683	+	0.247500i
$122$	0.168531			0.0152581
$123$	−1.91221	−	1.10402i	−0.172418	−	0.0995457i
$124$	10.4914	−	2.81117i	0.942157	−	0.252450i
$125$	−10.0467	−	4.90544i	−0.898606	−	0.438756i
$126$	0.526207	−	0.911417i	0.0468782	−	0.0811955i
$127$	−4.28310	+	15.9847i	−0.380064	+	1.41842i	0.465739	+	0.884922i	$0.345788\pi$
$127$	−4.28310	+	15.9847i	−0.380064	+	1.41842i	−0.845803	+	0.533495i	$0.820878\pi$
$128$	−2.05580	−	3.56075i	−0.181709	−	0.314729i
$129$	2.22292			0.195718
$130$	0.473506	−	0.946793i	0.0415292	−	0.0830392i
$131$	−12.6880			−1.10856			−0.554278	−	0.832332i	$-0.687006\pi$
$131$	−12.6880			−1.10856			−0.554278	+	0.832332i	$0.687006\pi$
$132$	−1.38256	−	2.39467i	−0.120337	−	0.208429i
$133$	−1.36726	+	5.10267i	−0.118556	+	0.442458i
$134$	0.237414	−	0.411213i	0.0205095	−	0.0355234i
$135$	−4.14226	−	1.81616i	−0.356509	−	0.156310i
$136$	−1.22467	+	0.328148i	−0.105014	+	0.0281385i
$137$	−12.9428	−	7.47254i	−1.10578	−	0.638422i	−0.168046	−	0.985779i	$-0.553746\pi$
$137$	−12.9428	−	7.47254i	−1.10578	−	0.638422i	−0.937733	+	0.347357i	$0.887079\pi$
$138$	−0.360209			−0.0306631
$139$	−7.42380	−	4.28613i	−0.629679	−	0.363545i	0.150949	−	0.988542i	$-0.451767\pi$
$139$	−7.42380	−	4.28613i	−0.629679	−	0.363545i	−0.780628	+	0.624996i	$0.785100\pi$
$140$	−9.62722	−	7.70592i	−0.813649	−	0.651269i
$141$	−0.170200	−	0.0456050i	−0.0143334	−	0.00384063i
$142$	−0.596714	−	0.596714i	−0.0500751	−	0.0500751i
$143$	14.6027	+	0.738590i	1.22114	+	0.0617640i
$144$		−	11.2297i		−	0.935809i
$145$	7.99385	+	6.39852i	0.663853	+	0.531368i
$146$	0.652082	+	1.12944i	0.0539666	+	0.0934730i
$147$	−0.244493	+	0.0655118i	−0.0201655	+	0.00540332i
$148$		−	13.8995i		−	1.14253i
$149$	3.14239	+	11.7276i	0.257435	+	0.960759i	0.966720	+	0.255837i	$0.0823511\pi$
$149$	3.14239	+	11.7276i	0.257435	+	0.960759i	−0.709285	+	0.704922i	$0.750982\pi$
$150$	0.120808	−	0.190732i	0.00986390	−	0.0155732i
$151$	1.86999	−	1.86999i	0.152177	−	0.152177i	−0.626912	−	0.779090i	$-0.715682\pi$
$151$	1.86999	−	1.86999i	0.152177	−	0.152177i	0.779090	+	0.626912i	$0.215682\pi$
$152$	−0.257068	−	0.959392i	−0.0208510	−	0.0778170i
$153$	−6.74861	−	1.80829i	−0.545593	−	0.146191i
$154$	−0.383306	+	1.43052i	−0.0308877	+	0.115274i
$155$	−4.91859	+	11.2182i	−0.395071	+	0.901071i
$156$	−2.06431	−	1.33523i	−0.165277	−	0.106904i
$157$	−10.3194	+	10.3194i	−0.823581	+	0.823581i	−0.986620	−	0.163039i	$-0.947870\pi$
$157$	−10.3194	+	10.3194i	−0.823581	+	0.823581i	0.163039	+	0.986620i	$0.447870\pi$
$158$	−0.952420	+	0.549880i	−0.0757705	+	0.0437461i
$159$	0.558753	−	0.322596i	0.0443120	−	0.0255835i
$160$	3.44297	+	0.525301i	0.272191	+	0.0415287i
$161$	−15.6891	−	15.6891i	−1.23647	−	1.23647i
$162$	−0.521902	+	0.903960i	−0.0410045	+	0.0710218i
$163$	−9.34772	+	16.1907i	−0.732170	+	1.26815i	0.223784	+	0.974639i	$0.428159\pi$
$163$	−9.34772	+	16.1907i	−0.732170	+	1.26815i	−0.955954	+	0.293516i	$0.905174\pi$
$164$	9.00186	+	9.00186i	0.702927	+	0.702927i
$165$	3.08271	+	0.470336i	0.239989	+	0.0366156i
$166$	−0.360686	+	0.208242i	−0.0279947	+	0.0161627i
$167$	17.9075	−	10.3389i	1.38572	−	0.800049i	0.392895	−	0.919583i	$-0.371474\pi$
$167$	17.9075	−	10.3389i	1.38572	−	0.800049i	0.992830	+	0.119535i	$0.0381403\pi$
$168$	0.353695	−	0.353695i	0.0272882	−	0.0272882i
$169$	11.8567	−	5.33087i	0.912056	−	0.410067i
$170$	0.285831	−	0.651920i	0.0219223	−	0.0500000i
$171$	1.41659	−	5.28680i	0.108330	−	0.404292i
$172$	−12.3797	−	3.31713i	−0.943944	−	0.252929i
$173$	4.69655	+	17.5278i	0.357072	+	1.33261i	0.877856	+	0.478924i	$0.158973\pi$
$173$	4.69655	+	17.5278i	0.357072	+	1.33261i	−0.520784	+	0.853688i	$0.674360\pi$
$174$	−0.146208	+	0.146208i	−0.0110840	+	0.0110840i
$175$	13.5693	−	3.04560i	1.02574	−	0.230226i
$176$	4.09004	+	15.2642i	0.308298	+	1.15058i
$177$		−	0.903127i		−	0.0678832i
$178$	−0.790055	+	0.211694i	−0.0592171	+	0.0158672i
$179$	−8.68110	−	15.0361i	−0.648856	−	1.12385i	−0.983396	−	0.181470i	$-0.941914\pi$
$179$	−8.68110	−	15.0361i	−0.648856	−	1.12385i	0.334540	−	0.942382i	$-0.391419\pi$
$180$	9.97461	+	7.98398i	0.743464	+	0.595091i
$181$		−	24.9284i		−	1.85291i	−0.376406	−	0.926455i	$-0.622840\pi$
$181$		−	24.9284i		−	1.85291i	0.376406	−	0.926455i	$-0.377160\pi$
$182$	0.276117	+	1.28748i	0.0204672	+	0.0954341i
$183$	0.312119	+	0.312119i	0.0230725	+	0.0230725i
$184$	4.02953	+	1.07971i	0.297061	+	0.0795973i
$185$	12.2378	+	9.79548i	0.899738	+	0.720178i
$186$	−0.214216	−	0.123678i	−0.0157071	−	0.00906850i
$187$	9.83181			0.718973
$188$	0.879810	+	0.507958i	0.0641667	+	0.0370467i
$189$	5.43421	−	1.45609i	0.395280	−	0.105915i
$190$	0.510708	+	0.223918i	0.0370506	+	0.0162447i
$191$	−3.39354	+	5.87779i	−0.245548	+	0.425302i	−0.962286	−	0.272041i	$-0.912301\pi$
$191$	−3.39354	+	5.87779i	−0.245548	+	0.425302i	0.716737	+	0.697343i	$0.245635\pi$
$192$	0.675492	−	2.52097i	0.0487494	−	0.181935i
$193$	−0.597582	−	1.03504i	−0.0430149	−	0.0745040i	0.843716	−	0.536789i	$-0.180363\pi$
$193$	−0.597582	−	1.03504i	−0.0430149	−	0.0745040i	−0.886731	+	0.462285i	$0.847030\pi$
$194$	1.54543			0.110955
$195$	2.63038	−	0.876525i	0.188366	−	0.0627693i
$196$	1.45937			0.104241
$197$	−10.0605	−	17.4253i	−0.716780	−	1.24150i	−0.962269	−	0.272100i	$-0.912282\pi$
$197$	−10.0605	−	17.4253i	−0.716780	−	1.24150i	0.245489	−	0.969399i	$-0.421051\pi$
$198$	0.397137	−	1.48214i	0.0282233	−	0.105331i
$199$	1.08885	−	1.88594i	0.0771862	−	0.133690i	−0.824849	−	0.565354i	$-0.808740\pi$
$199$	1.08885	−	1.88594i	0.0771862	−	0.133690i	0.902035	+	0.431663i	$0.142073\pi$
$200$	−1.92314	+	1.77154i	−0.135987	+	0.125267i
$201$	1.20125	−	0.321875i	0.0847299	−	0.0227033i
$202$	0.114733	+	0.0662412i	0.00807259	+	0.00466071i
$203$	−12.7363			−0.893912
$204$	−1.43168	−	0.826580i	−0.100237	−	0.0578721i
$205$	−14.2695	+	1.58171i	−0.996629	+	0.110472i
$206$	1.07618	+	0.288362i	0.0749810	+	0.0200911i
$207$	16.2552	+	16.2552i	1.12982	+	1.12982i
$208$	9.42052	+	10.4242i	0.653196	+	0.722792i
$209$			7.70215i			0.532769i
$210$	0.0309394	+	0.279122i	0.00213502	+	0.0192612i
$211$	9.97642	+	17.2797i	0.686805	+	1.18958i	0.972866	+	0.231370i	$0.0743208\pi$
$211$	9.97642	+	17.2797i	0.686805	+	1.18958i	−0.286061	+	0.958211i	$0.592346\pi$
$212$	−3.59315	+	0.962781i	−0.246778	+	0.0661240i
$213$		−	2.21022i		−	0.151442i
$214$	−0.168410	−	0.628516i	−0.0115123	−	0.0429645i
$215$	11.6450	−	8.56195i	0.794179	−	0.583920i
$216$	−0.747956	+	0.747956i	−0.0508919	+	0.0508919i
$217$	−3.94345	−	14.7171i	−0.267698	−	0.999064i
$218$	1.16765	+	0.312872i	0.0790835	+	0.0211904i
$219$	−0.884062	+	3.29936i	−0.0597394	+	0.222950i
$220$	−16.4661	−	7.21950i	−1.11015	−	0.486738i
$221$	7.78152	−	3.98278i	0.523442	−	0.267911i
$222$	−0.223829	+	0.223829i	−0.0150224	+	0.0150224i
$223$	11.6164	−	6.70672i	0.777891	−	0.449115i	−0.0577915	−	0.998329i	$-0.518406\pi$
$223$	11.6164	−	6.70672i	0.777891	−	0.449115i	0.835682	+	0.549213i	$0.185073\pi$
$224$	−3.75176	+	2.16608i	−0.250675	+	0.144727i
$225$	−14.0589	+	3.15550i	−0.937260	+	0.210367i
$226$	−0.696612	−	0.696612i	−0.0463380	−	0.0463380i
$227$	−7.34064	+	12.7144i	−0.487215	+	0.843882i	−0.999892	−	0.0147000i	$-0.995321\pi$
$227$	−7.34064	+	12.7144i	−0.487215	+	0.843882i	0.512677	+	0.858582i	$0.328654\pi$
$228$	0.647535	−	1.12156i	0.0428840	−	0.0742773i
$229$	−2.65280	−	2.65280i	−0.175302	−	0.175302i	0.614002	−	0.789304i	$-0.289558\pi$
$229$	−2.65280	−	2.65280i	−0.175302	−	0.175302i	−0.789304	+	0.614002i	$0.789558\pi$
$230$	−1.88698	+	1.38740i	−0.124424	+	0.0914827i
$231$	−3.35919	+	1.93943i	−0.221018	+	0.127605i
$232$	2.07382	−	1.19732i	0.136153	−	0.0786081i
$233$	13.9459	−	13.9459i	0.913629	−	0.913629i	−0.0829267	−	0.996556i	$-0.526427\pi$
$233$	13.9459	−	13.9459i	0.913629	−	0.913629i	0.996556	+	0.0829267i	$0.0264267\pi$
$234$	−0.286080	−	1.33393i	−0.0187017	−	0.0872020i
$235$	−1.06726	+	0.416648i	−0.0696205	+	0.0271791i
$236$	−1.34768	+	5.02962i	−0.0877266	+	0.327400i
$237$	−2.78225	−	0.745502i	−0.180727	−	0.0484256i
$238$	0.229163	+	0.855249i	0.0148545	+	0.0554376i
$239$	10.1890	−	10.1890i	0.659074	−	0.659074i	−0.296087	−	0.955161i	$-0.595682\pi$
$239$	10.1890	−	10.1890i	0.659074	−	0.659074i	0.955161	+	0.296087i	$0.0956818\pi$
$240$	1.77508	+	2.41426i	0.114581	+	0.155840i
$241$	−2.09750	−	7.82799i	−0.135112	−	0.504245i	−0.999997	−	0.00227574i	$-0.999276\pi$
$241$	−2.09750	−	7.82799i	−0.135112	−	0.504245i	0.864885	−	0.501970i	$-0.167391\pi$
$242$			0.714943i			0.0459582i
$243$	−8.50205	+	2.27812i	−0.545407	+	0.146141i
$244$	−1.27247	−	2.20398i	−0.0814615	−	0.141095i
$245$	−1.02847	+	1.28489i	−0.0657064	+	0.0820889i
$246$		−	0.289920i		−	0.0184846i
$247$	3.12007	+	6.09597i	0.198525	+	0.387877i
$248$	2.02564	+	2.02564i	0.128628	+	0.128628i
$249$	−1.05365	−	0.282325i	−0.0667725	−	0.0178916i
$250$	−0.101776	−	1.46448i	−0.00643688	−	0.0926215i
$251$	−4.04904	−	2.33771i	−0.255573	−	0.147555i	0.366740	−	0.930323i	$-0.380474\pi$
$251$	−4.04904	−	2.33771i	−0.255573	−	0.147555i	−0.622313	+	0.782768i	$0.713807\pi$
$252$	−15.8922			−1.00111
$253$	−28.0157	−	16.1749i	−1.76133	−	1.01690i
$254$	−2.09884	+	0.562382i	−0.131693	+	0.0352870i
$255$	1.73671	−	0.677993i	0.108757	−	0.0424576i
$256$	−7.31927	+	12.6773i	−0.457454	+	0.792334i
$257$	−4.49187	+	16.7639i	−0.280195	+	1.04570i	0.672085	+	0.740474i	$0.265399\pi$
$257$	−4.49187	+	16.7639i	−0.280195	+	1.04570i	−0.952280	+	0.305227i	$0.901268\pi$
$258$	0.145938	+	0.252772i	0.00908569	+	0.0157369i
$259$	−19.4980			−1.21154
$260$	−15.9569	+	0.956305i	−0.989604	+	0.0593075i
$261$	13.1959			0.816804
$262$	−0.832984	−	1.44277i	−0.0514619	−	0.0891346i
$263$	0.626777	−	2.33916i	0.0386487	−	0.144239i	−0.943905	−	0.330216i	$-0.892878\pi$
$263$	0.626777	−	2.33916i	0.0386487	−	0.144239i	0.982554	+	0.185977i	$0.0595450\pi$
$264$	0.364647	−	0.631587i	0.0224425	−	0.0388715i
$265$	1.68454	−	3.84207i	0.103480	−	0.236016i
$266$	−0.669994	+	0.179524i	−0.0410800	+	0.0110073i
$267$	−1.85523	−	1.07112i	−0.113538	−	0.0655515i
$268$	−7.17023			−0.437992
$269$	8.42829	+	4.86608i	0.513882	+	0.296690i	0.734428	−	0.678687i	$-0.237451\pi$
$269$	8.42829	+	4.86608i	0.513882	+	0.296690i	−0.220546	+	0.975377i	$0.570784\pi$
$270$	−0.0654271	−	0.590255i	−0.00398177	−	0.0359218i
$271$	−21.1708	−	5.67269i	−1.28603	−	0.344591i	−0.449880	−	0.893089i	$-0.648533\pi$
$271$	−21.1708	−	5.67269i	−1.28603	−	0.344591i	−0.836152	+	0.548498i	$0.815200\pi$
$272$	6.68061	+	6.68061i	0.405071	+	0.405071i
$273$	−1.87303	+	2.89577i	−0.113361	+	0.175260i
$274$		−	1.96233i		−	0.118548i
$275$	17.9606	−	9.40967i	1.08306	−	0.567424i
$276$	2.71970	+	4.71067i	0.163707	+	0.283549i
$277$	17.4408	−	4.67325i	1.04792	−	0.280788i	0.306526	−	0.951862i	$-0.400833\pi$
$277$	17.4408	−	4.67325i	1.04792	−	0.280788i	0.741390	+	0.671074i	$0.234167\pi$
$278$		−	1.12556i		−	0.0675067i
$279$	4.08574	+	15.2482i	0.244607	+	0.912885i
$280$	0.490546	−	3.21517i	0.0293157	−	0.192143i
$281$	11.3739	−	11.3739i	0.678510	−	0.678510i	−0.281153	−	0.959663i	$-0.590717\pi$
$281$	11.3739	−	11.3739i	0.678510	−	0.678510i	0.959663	+	0.281153i	$0.0907168\pi$
$282$	−0.00598805	−	0.0223477i	−0.000356583	−	0.00133079i
$283$	10.9682	+	2.93892i	0.651991	+	0.174700i	0.569629	−	0.821902i	$-0.307087\pi$
$283$	10.9682	+	2.93892i	0.651991	+	0.174700i	0.0823620	+	0.996602i	$0.473754\pi$
$284$	−3.29818	+	12.3090i	−0.195711	+	0.730403i
$285$	0.531134	+	1.36052i	0.0314616	+	0.0805904i
$286$	0.874701	+	1.70899i	0.0517222	+	0.101054i
$287$	12.6276	−	12.6276i	0.745384	−	0.745384i
$288$	3.88713	−	2.24424i	0.229052	−	0.132243i
$289$	−9.63189	+	5.56098i	−0.566582	+	0.327116i
$290$	−0.202778	+	1.32906i	−0.0119075	+	0.0780452i
$291$	2.86213	+	2.86213i	0.167781	+	0.167781i
$292$	9.84688	−	17.0553i	0.576245	−	0.998086i
$293$	−0.349807	+	0.605883i	−0.0204359	+	0.0353961i	−0.876063	−	0.482198i	$-0.839839\pi$
$293$	−0.349807	+	0.605883i	−0.0204359	+	0.0353961i	0.855627	+	0.517594i	$0.173172\pi$
$294$	−0.0235007	−	0.0235007i	−0.00137059	−	0.00137059i
$295$	−3.47854	−	4.73110i	−0.202528	−	0.275455i
$296$	3.17481	−	1.83298i	0.184532	−	0.106540i
$297$	7.10364	−	4.10129i	0.412195	−	0.237981i
$298$	−1.12725	+	1.12725i	−0.0653001	+	0.0653001i
$299$	−28.7257	−	1.45292i	−1.66125	−	0.0840243i
$300$	−3.40646	−	0.139776i	−0.196672	−	0.00806999i
$301$	−4.65320	+	17.3660i	−0.268206	+	1.00096i
$302$	0.335406	+	0.0898718i	0.0193004	+	0.00517154i
$303$	0.0898068	+	0.335163i	0.00515926	+	0.0192546i
$304$	−5.23352	+	5.23352i	−0.300163	+	0.300163i
$305$	2.83724	+	0.432883i	0.162460	+	0.0247868i
$306$	−0.237433	−	0.886110i	−0.0135731	−	0.0506555i
$307$			14.2048i			0.810709i	0.914159	+	0.405355i	$0.132852\pi$
$307$			14.2048i			0.810709i	−0.914159	+	0.405355i	$0.867148\pi$
$308$	21.6018	−	5.78818i	1.23088	−	0.329812i
$309$	1.45904	+	2.52712i	0.0830016	+	0.143763i
$310$	−1.59855	+	0.177192i	−0.0907917	+	0.0100638i
$311$			21.4961i			1.21893i	0.792812	+	0.609466i	$0.208616\pi$
$311$			21.4961i			1.21893i	−0.792812	+	0.609466i	$0.791384\pi$
$312$	0.0327546	−	0.647593i	0.00185436	−	0.0366627i
$313$	−9.36303	−	9.36303i	−0.529230	−	0.529230i	0.391113	−	0.920343i	$-0.372090\pi$
$313$	−9.36303	−	9.36303i	−0.529230	−	0.529230i	−0.920343	+	0.391113i	$0.872090\pi$
$314$	−1.85092	−	0.495953i	−0.104454	−	0.0279882i
$315$	11.1998	−	13.9922i	0.631035	−	0.788369i
$316$	14.3822	+	8.30357i	0.809062	+	0.467112i
$317$	17.3024			0.971798			0.485899	−	0.874015i	$-0.338492\pi$
$317$	17.3024			0.971798			0.485899	+	0.874015i	$0.338492\pi$
$318$	0.0733657	+	0.0423577i	0.00411414	+	0.00237530i
$319$	−17.9368	+	4.80615i	−1.00427	+	0.269093i
$320$	−6.17130	−	15.8081i	−0.344986	−	0.883697i
$321$	0.852114	−	1.47590i	0.0475603	−	0.0823769i
$322$	0.754019	−	2.81404i	0.0420198	−	0.156820i
$323$	2.30240	+	3.98788i	0.128109	+	0.221892i
$324$	15.7622			0.875675
$325$	10.4034	−	14.7231i	0.577076	−	0.816690i
$326$	−2.45476			−0.135957
$327$	1.58305	+	2.74193i	0.0875429	+	0.151629i
$328$	−0.869022	+	3.24323i	−0.0479837	+	0.179078i
$329$	0.712553	−	1.23418i	0.0392843	−	0.0680424i
$330$	0.148901	+	0.381418i	0.00819676	+	0.0209964i
$331$	17.3574	−	4.65090i	0.954049	−	0.255637i	0.251969	−	0.967735i	$-0.418922\pi$
$331$	17.3574	−	4.65090i	0.954049	−	0.255637i	0.702079	+	0.712099i	$0.252255\pi$
$332$	5.44661	+	3.14460i	0.298921	+	0.172582i
$333$	20.2015			1.10704
$334$	2.35130	+	1.35753i	0.128658	+	0.0742805i
$335$	5.05311	−	6.31299i	0.276081	−	0.344915i
$336$	−3.60035	−	0.964712i	−0.196415	−	0.0526293i
$337$	−4.83668	−	4.83668i	−0.263471	−	0.263471i	0.562992	−	0.826462i	$-0.309650\pi$
$337$	−4.83668	−	4.83668i	−0.263471	−	0.263471i	−0.826462	+	0.562992i	$0.809650\pi$
$338$	1.38459	+	0.998266i	0.0753117	+	0.0542985i
$339$		−	2.58024i		−	0.140140i
$340$	−10.6837	+	1.18423i	−0.579403	+	0.0642242i
$341$	−11.1073	−	19.2384i	−0.601493	−	1.04182i
$342$	0.694170	−	0.186002i	0.0375364	−	0.0100579i
$343$			17.4224i			0.940723i
$344$	−0.874884	−	3.26511i	−0.0471706	−	0.176043i
$345$	−6.06415	−	0.925220i	−0.326483	−	0.0498122i
$346$	−1.68477	+	1.68477i	−0.0905740	+	0.0905740i
$347$	4.81456	+	17.9682i	0.258459	+	0.964582i	0.966133	+	0.258043i	$0.0830778\pi$
$347$	4.81456	+	17.9682i	0.258459	+	0.964582i	−0.707674	+	0.706539i	$0.750256\pi$
$348$	3.01596	+	0.808124i	0.161672	+	0.0433200i
$349$	−0.651455	+	2.43126i	−0.0348716	+	0.130143i	−0.981167	−	0.193160i	$-0.938126\pi$
$349$	−0.651455	+	2.43126i	−0.0348716	+	0.130143i	0.946296	+	0.323302i	$0.104793\pi$
$350$	1.23716	+	1.34303i	0.0661290	+	0.0717881i
$351$	3.96088	−	6.12364i	0.211416	−	0.326856i
$352$	−4.46629	+	4.46629i	−0.238054	+	0.238054i
$353$	−28.3377	+	16.3608i	−1.50826	+	0.870795i	−0.508308	+	0.861175i	$0.669729\pi$
$353$	−28.3377	+	16.3608i	−1.50826	+	0.870795i	−0.999954	+	0.00962005i	$0.996938\pi$
$354$	0.102696	−	0.0592915i	0.00545822	−	0.00315131i
$355$	−8.51302	−	11.5784i	−0.451824	−	0.614519i
$356$	8.73364	+	8.73364i	0.462882	+	0.462882i
$357$	−1.15951	+	2.00833i	−0.0613677	+	0.106292i
$358$	1.13985	−	1.97428i	0.0602430	−	0.104344i
$359$	0.699684	+	0.699684i	0.0369279	+	0.0369279i	0.725330	−	0.688402i	$-0.241687\pi$
$359$	0.699684	+	0.699684i	0.0369279	+	0.0369279i	−0.688402	+	0.725330i	$0.741687\pi$
$360$	−0.508247	+	3.33119i	−0.0267870	+	0.175569i
$361$	13.3304	−	7.69632i	0.701601	−	0.405069i
$362$	2.83464	−	1.63658i	0.148985	−	0.0860167i
$363$	−1.32407	+	1.32407i	−0.0694956	+	0.0694956i
$364$	14.7523	−	13.3318i	0.773231	−	0.698778i
$365$	8.07680	+	20.6891i	0.422759	+	1.08292i
$366$	−0.0150005	+	0.0559825i	−0.000784087	+	0.00292625i
$367$	−13.9803	−	3.74601i	−0.729767	−	0.195540i	−0.125241	−	0.992126i	$-0.539971\pi$
$367$	−13.9803	−	3.74601i	−0.729767	−	0.195540i	−0.604525	+	0.796586i	$0.706637\pi$
$368$	−8.04571	−	30.0270i	−0.419411	−	1.56526i
$369$	−13.0833	+	13.0833i	−0.681087	+	0.681087i
$370$	−0.310432	+	2.03466i	−0.0161386	+	0.105777i
$371$	1.35057	+	5.04039i	0.0701180	+	0.261684i
$372$			3.73524i			0.193663i
$373$	9.79493	−	2.62454i	0.507162	−	0.135894i	0.00384023	−	0.999993i	$-0.498778\pi$
$373$	9.79493	−	2.62454i	0.507162	−	0.135894i	0.503322	+	0.864099i	$0.332111\pi$
$374$	0.645471	+	1.11799i	0.0333765	+	0.0578098i
$375$	2.52371	−	2.90069i	0.130324	−	0.149791i
$376$			0.267945i			0.0138182i
$377$	−12.2494	+	11.0699i	−0.630876	+	0.570130i
$378$	0.522337	+	0.522337i	0.0268661	+	0.0268661i
$379$	−1.01470	−	0.271887i	−0.0521215	−	0.0139659i	0.232664	−	0.972557i	$-0.425256\pi$
$379$	−1.01470	−	0.271887i	−0.0521215	−	0.0139659i	−0.284786	+	0.958591i	$0.591922\pi$
$380$	−0.927718	−	8.36948i	−0.0475909	−	0.429345i
$381$	−4.92857	−	2.84551i	−0.252498	−	0.145780i
$382$	−0.891162			−0.0455958
$383$	10.3984	+	6.00353i	0.531334	+	0.306766i	0.741560	−	0.670887i	$-0.234086\pi$
$383$	10.3984	+	6.00353i	0.531334	+	0.306766i	−0.210225	+	0.977653i	$0.567420\pi$
$384$	1.36579	−	0.365961i	0.0696975	−	0.0186754i
$385$	−10.1274	+	23.0983i	−0.516138	+	1.17720i
$386$	0.0784640	−	0.135904i	0.00399371	−	0.00691732i
$387$	4.82111	−	17.9926i	0.245071	−	0.914616i
$388$	−11.6685	−	20.2105i	−0.592380	−	1.02603i
$389$	−7.37166			−0.373758			−0.186879	−	0.982383i	$-0.559837\pi$
$389$	−7.37166			−0.373758			−0.186879	+	0.982383i	$0.559837\pi$
$390$	0.272359	+	0.241560i	0.0137914	+	0.0122318i
$391$	−19.3406			−0.978097
$392$	0.192452	+	0.333337i	0.00972030	+	0.0168361i
$393$	1.12932	−	4.21468i	0.0569667	−	0.212603i
$394$	1.32097	−	2.28798i	0.0665494	−	0.115267i
$395$	−17.4465	+	6.81091i	−0.877826	+	0.342694i
$396$	−22.3813	+	5.99704i	−1.12470	+	0.301363i
$397$	5.24359	+	3.02739i	0.263168	+	0.151940i	0.625779	−	0.780001i	$-0.284781\pi$
$397$	5.24359	+	3.02739i	0.263168	+	0.151940i	−0.362611	+	0.931941i	$0.618115\pi$
$398$	0.285937			0.0143327
$399$	−1.57330	−	0.908347i	−0.0787637	−	0.0454742i
$400$	18.5978	+	5.81026i	0.929890	+	0.290513i
$401$	−2.33226	−	0.624928i	−0.116468	−	0.0312074i	0.200114	−	0.979773i	$-0.435869\pi$
$401$	−2.33226	−	0.624928i	−0.116468	−	0.0312074i	−0.316582	+	0.948565i	$0.602535\pi$
$402$	0.115465	+	0.115465i	0.00575886	+	0.00575886i
$403$	−16.5843	−	10.7270i	−0.826123	−	0.534350i
$404$		−	2.00058i		−	0.0995324i
$405$	−11.1081	+	13.8777i	−0.551967	+	0.689588i
$406$	−0.836154	−	1.44826i	−0.0414976	−	0.0718760i
$407$	−27.4594	+	7.35772i	−1.36111	+	0.364709i
$408$		−	0.436016i		−	0.0215860i
$409$	−5.21187	−	19.4510i	−0.257710	−	0.961788i	−0.966563	−	0.256431i	$-0.917453\pi$
$409$	−5.21187	−	19.4510i	−0.257710	−	0.961788i	0.708852	−	0.705357i	$-0.249213\pi$
$410$	−1.11667	−	1.51877i	−0.0551486	−	0.0750066i
$411$	3.63422	−	3.63422i	0.179263	−	0.179263i
$412$	−4.35446	−	16.2511i	−0.214529	−	0.800632i
$413$	7.05543	+	1.89050i	0.347175	+	0.0930253i
$414$	−0.781227	+	2.91558i	−0.0383952	+	0.143293i
$415$	−6.60706	+	2.57933i	−0.324328	+	0.126614i
$416$	−1.72565	+	5.34416i	−0.0846071	+	0.262019i
$417$	2.08453	−	2.08453i	0.102080	−	0.102080i
$418$	−0.875822	+	0.505656i	−0.0428378	+	0.0247324i
$419$	26.0503	−	15.0401i	1.27264	−	0.734759i	0.297156	−	0.954829i	$-0.403962\pi$
$419$	26.0503	−	15.0401i	1.27264	−	0.734759i	0.975484	+	0.220070i	$0.0706287\pi$
$420$	3.41663	−	2.51208i	0.166715	−	0.122577i
$421$	9.24685	+	9.24685i	0.450664	+	0.450664i	0.895575	−	0.444911i	$-0.146765\pi$
$421$	9.24685	+	9.24685i	0.450664	+	0.450664i	−0.444911	+	0.895575i	$0.646765\pi$
$422$	−1.30993	+	2.26887i	−0.0637664	+	0.110447i
$423$	−0.738265	+	1.27871i	−0.0358957	+	0.0621731i
$424$	−0.693751	−	0.693751i	−0.0336915	−	0.0336915i
$425$	6.48649	−	10.2409i	0.314641	−	0.496758i
$426$	0.251327	−	0.145104i	0.0121769	−	0.00703031i
$427$	−3.09170	+	1.78499i	−0.149618	+	0.0863818i
$428$	−6.94792	+	6.94792i	−0.335840	+	0.335840i
$429$	−1.54509	+	4.78497i	−0.0745976	+	0.231021i
$430$	1.73810	+	0.762061i	0.0838185	+	0.0367499i
$431$	−1.63348	+	6.09624i	−0.0786821	+	0.293646i	−0.994043	−	0.108989i	$-0.965239\pi$
$431$	−1.63348	+	6.09624i	−0.0786821	+	0.293646i	0.915361	+	0.402634i	$0.131905\pi$
$432$	7.61362	+	2.04006i	0.366311	+	0.0981527i
$433$	3.18071	+	11.8706i	0.152855	+	0.570463i	0.999279	+	0.0379543i	$0.0120841\pi$
$433$	3.18071	+	11.8706i	0.152855	+	0.570463i	−0.846424	+	0.532509i	$0.821249\pi$
$434$	1.41461	−	1.41461i	0.0679036	−	0.0679036i
$435$	−2.83696	+	2.08587i	−0.136022	+	0.100010i
$436$	−4.72458	−	17.6324i	−0.226266	−	0.844438i
$437$		−	15.1513i		−	0.724783i
$438$	−0.433215	+	0.116080i	−0.0206998	+	0.00554650i
$439$	17.2223	+	29.8300i	0.821977	+	1.42371i	0.904208	+	0.427093i	$0.140462\pi$
$439$	17.2223	+	29.8300i	0.821977	+	1.42371i	−0.0822306	+	0.996613i	$0.526204\pi$
$440$	−0.522427	−	4.71311i	−0.0249057	−	0.224689i
$441$			2.12104i			0.101002i
$442$	0.963754	+	0.623373i	0.0458411	+	0.0296508i
$443$	−5.39452	−	5.39452i	−0.256301	−	0.256301i	0.567247	−	0.823548i	$-0.308009\pi$
$443$	−5.39452	−	5.39452i	−0.256301	−	0.256301i	−0.823548	+	0.567247i	$0.808009\pi$
$444$	4.61713	+	1.23716i	0.219119	+	0.0587128i
$445$	−13.8444	+	1.53459i	−0.656286	+	0.0727463i
$446$	1.52526	+	0.880610i	0.0722232	+	0.0416981i
$447$	−4.17534			−0.197487
$448$	18.2804	+	10.5542i	0.863668	+	0.498639i
$449$	30.0741	−	8.05832i	1.41928	−	0.380296i	0.534053	−	0.845451i	$-0.320668\pi$
$449$	30.0741	−	8.05832i	1.41928	−	0.380296i	0.885229	+	0.465155i	$0.154002\pi$
$450$	−1.28180	−	1.39149i	−0.0604247	−	0.0655957i
$451$	13.0186	−	22.5489i	0.613021	−	1.06178i
$452$	−3.85034	+	14.3697i	−0.181105	+	0.675892i
$453$	0.454728	+	0.787612i	0.0213650	+	0.0370053i
$454$	−1.92769			−0.0904710
$455$	1.34148	+	22.3840i	0.0628897	+	1.04938i
$456$	0.341570			0.0159955
$457$	1.55375	+	2.69118i	0.0726814	+	0.125888i	0.900076	−	0.435734i	$-0.143511\pi$
$457$	1.55375	+	2.69118i	0.0726814	+	0.125888i	−0.827394	+	0.561622i	$0.810178\pi$
$458$	0.127494	−	0.475812i	0.00595738	−	0.0222333i
$459$	2.45200	−	4.24698i	0.114449	−	0.198232i
$460$	32.3913	+	14.2018i	1.51025	+	0.662163i
$461$	−16.1274	+	4.32132i	−0.751126	+	0.201264i	−0.614018	−	0.789292i	$-0.710448\pi$
$461$	−16.1274	+	4.32132i	−0.751126	+	0.201264i	−0.137109	+	0.990556i	$0.543781\pi$
$462$	−0.441070	−	0.254652i	−0.0205205	−	0.0118475i
$463$	15.6396			0.726832			0.363416	−	0.931627i	$-0.381610\pi$
$463$	15.6396			0.726832			0.363416	+	0.931627i	$0.381610\pi$
$464$	−15.4536	−	8.92212i	−0.717414	−	0.414199i
$465$	−3.28867	−	2.63235i	−0.152508	−	0.122072i
$466$	2.50138	+	0.670243i	0.115874	+	0.0310484i
$467$	−15.0821	−	15.0821i	−0.697916	−	0.697916i	0.266045	−	0.963961i	$-0.414283\pi$
$467$	−15.0821	−	15.0821i	−0.697916	−	0.697916i	−0.963961	+	0.266045i	$0.914283\pi$
$468$	−15.2846	+	13.8129i	−0.706532	+	0.638502i
$469$			10.0582i			0.464447i
$470$	−0.117445	−	0.0940063i	−0.00541732	−	0.00433619i
$471$	−2.50939	−	4.34640i	−0.115627	−	0.200272i
$472$	−1.32655	+	0.355447i	−0.0610592	+	0.0163608i
$473$			26.2128i			1.20527i
$474$	−0.0978863	−	0.365317i	−0.00449607	−	0.0167796i
$475$	8.02265	+	5.08145i	0.368104	+	0.233153i
$476$	9.45433	−	9.45433i	0.433339	−	0.433339i
$477$	−1.39930	−	5.22226i	−0.0640696	−	0.239111i
$478$	1.82753	+	0.489686i	0.0835894	+	0.0223977i
$479$	11.0386	−	41.1964i	0.504364	−	1.88231i	0.0348421	−	0.999393i	$-0.488907\pi$
$479$	11.0386	−	41.1964i	0.504364	−	1.88231i	0.469522	−	0.882921i	$-0.344426\pi$
$480$	−0.480942	+	1.09693i	−0.0219519	+	0.0500676i
$481$	−18.7526	+	16.9469i	−0.855043	+	0.772713i
$482$	0.752428	−	0.752428i	0.0342722	−	0.0342722i
$483$	6.60802	−	3.81514i	0.300675	−	0.173595i
$484$	9.34972	−	5.39806i	0.424987	−	0.245366i
$485$	26.0174	+	3.96953i	1.18139	+	0.180247i
$486$	−0.817218	−	0.817218i	−0.0370698	−	0.0370698i
$487$	7.60834	−	13.1780i	0.344767	−	0.597154i	−0.640545	−	0.767921i	$-0.721291\pi$
$487$	7.60834	−	13.1780i	0.344767	−	0.597154i	0.985311	+	0.170767i	$0.0546247\pi$
$488$	0.335610	−	0.581293i	0.0151923	−	0.0263139i
$489$	−4.54620	−	4.54620i	−0.205586	−	0.205586i
$490$	−0.213627	−	0.0325936i	−0.00965070	−	0.00147243i
$491$	24.2273	−	13.9876i	1.09336	−	0.631254i	0.158894	−	0.987296i	$-0.449207\pi$
$491$	24.2273	−	13.9876i	1.09336	−	0.631254i	0.934470	+	0.356042i	$0.115874\pi$
$492$	−3.79145	+	2.18900i	−0.170932	+	0.0986876i
$493$	−7.85029	+	7.85029i	−0.353559	+	0.353559i
$494$	−0.488345	+	0.754996i	−0.0219717	+	0.0339689i
$495$	10.4928	−	23.9318i	0.471616	−	1.07565i
$496$	5.52498	−	20.6195i	0.248079	−	0.925844i
$497$	17.2668	+	4.62661i	0.774520	+	0.207532i
$498$	−0.0370700	−	0.138347i	−0.00166115	−	0.00619949i
$499$	1.67479	−	1.67479i	0.0749740	−	0.0749740i	−0.668625	−	0.743599i	$-0.733117\pi$
$499$	1.67479	−	1.67479i	0.0749740	−	0.0749740i	0.743599	+	0.668625i	$0.233117\pi$
$500$	−18.3833	+	12.3883i	−0.822128	+	0.554021i
$501$	1.84047	+	6.86873i	0.0822261	+	0.306872i
$502$		−	0.613896i		−	0.0273995i
$503$	−22.3705	+	5.99415i	−0.997451	+	0.267266i	−0.720377	−	0.693583i	$-0.756031\pi$
$503$	−22.3705	+	5.99415i	−0.997451	+	0.267266i	−0.277073	+	0.960849i	$0.589365\pi$
$504$	−2.09575	−	3.62995i	−0.0933523	−	0.161691i
$505$	1.76140	+	1.40987i	0.0783811	+	0.0627386i
$506$		−	4.24760i		−	0.188829i
$507$	0.715468	+	4.41303i	0.0317751	+	0.195990i
$508$	23.2016	+	23.2016i	1.02940	+	1.02940i
$509$	−5.82068	−	1.55965i	−0.257997	−	0.0691301i	0.127502	−	0.991838i	$-0.459304\pi$
$509$	−5.82068	−	1.55965i	−0.257997	−	0.0691301i	−0.385499	+	0.922708i	$0.625971\pi$
$510$	0.191113	+	0.152973i	0.00846262	+	0.00677374i
$511$	−23.9248	−	13.8130i	−1.05837	−	0.611051i
$512$	−10.1453			−0.448362
$513$	3.32705	+	1.92087i	0.146893	+	0.0848086i
$514$	−2.20114	+	0.589794i	−0.0970881	+	0.0260147i
$515$	17.3769	+	7.61882i	0.765717	+	0.335725i
$516$	2.20376	−	3.81703i	0.0970152	−	0.168035i
$517$	0.537776	−	2.00701i	0.0236514	−	0.0882681i
$518$	−1.28007	−	2.21714i	−0.0562429	−	0.0974155i
$519$	−6.24038			−0.273922
$520$	−2.32272	−	3.51863i	−0.101858	−	0.154302i
$521$	27.8183			1.21874			0.609371	−	0.792886i	$-0.291422\pi$
$521$	27.8183			1.21874			0.609371	+	0.792886i	$0.291422\pi$
$522$	0.866326	+	1.50052i	0.0379180	+	0.0656760i
$523$	−0.141761	+	0.529059i	−0.00619877	+	0.0231341i	−0.968956	−	0.247233i	$-0.920479\pi$
$523$	−0.141761	+	0.529059i	−0.00619877	+	0.0231341i	0.962757	+	0.270368i	$0.0871452\pi$
$524$	−12.5786	+	21.7868i	−0.549500	+	0.951762i
$525$	−0.196075	+	4.77850i	−0.00855742	+	0.208551i
$526$	0.307138	−	0.0822974i	0.0133919	−	0.00358834i
$527$	−11.5019	−	6.64060i	−0.501029	−	0.289269i
$528$	−5.43449			−0.236506
$529$	35.1924	+	20.3183i	1.53010	+	0.883406i
$530$	0.547479	−	0.0606856i	0.0237810	−	0.00263601i
$531$	−7.31002	−	1.95871i	−0.317228	−	0.0850010i
$532$	7.40643	+	7.40643i	0.321110	+	0.321110i
$533$	1.16940	−	23.1203i	0.0506524	−	1.00145i
$534$		−	0.281282i		−	0.0121722i
$535$	−1.22082	−	11.0137i	−0.0527805	−	0.476163i
$536$	−0.945563	−	1.63776i	−0.0408421	−	0.0707406i
$537$	5.76736	−	1.54536i	0.248880	−	0.0666871i
$538$			1.27786i			0.0550923i
$539$	−0.772518	−	2.88308i	−0.0332747	−	0.124183i
$540$	−7.22512	+	5.31226i	−0.310919	+	0.228603i
$541$	−29.7507	+	29.7507i	−1.27908	+	1.27908i	−0.337899	+	0.941182i	$0.609716\pi$
$541$	−29.7507	+	29.7507i	−1.27908	+	1.27908i	−0.941182	+	0.337899i	$0.890284\pi$
$542$	−0.744839	−	2.77978i	−0.0319936	−	0.119402i
$543$	8.28067	+	2.21880i	0.355357	+	0.0952177i
$544$	−0.977367	+	3.64758i	−0.0419043	+	0.156389i
$545$	18.8539	+	8.26641i	0.807612	+	0.354094i
$546$	−0.452249	−	0.0228743i	−0.0193545	−	0.000978928i
$547$	−14.2594	+	14.2594i	−0.609688	+	0.609688i	−0.942864	−	0.333176i	$-0.891880\pi$
$547$	−14.2594	+	14.2594i	−0.609688	+	0.609688i	0.333176	+	0.942864i	$0.391880\pi$
$548$	−25.6625	+	14.8162i	−1.09625	+	0.632919i
$549$	3.20326	−	1.84940i	0.136712	−	0.0789306i
$550$	2.24912	+	1.42457i	0.0959029	+	0.0607438i
$551$	−6.14984	−	6.14984i	−0.261992	−	0.261992i
$552$	−0.717314	+	1.24242i	−0.0305309	+	0.0528811i
$553$	11.6481	−	20.1750i	0.495326	−	0.857930i
$554$	1.67641	+	1.67641i	0.0712240	+	0.0712240i
$555$	−4.34309	+	3.19326i	−0.184354	+	0.135546i
$556$	−14.7196	+	8.49837i	−0.624251	+	0.360411i
$557$	−30.4644	+	17.5886i	−1.29082	+	0.745254i	−0.978799	−	0.204822i	$-0.934338\pi$
$557$	−30.4644	+	17.5886i	−1.29082	+	0.745254i	−0.312018	+	0.950076i	$0.601005\pi$
$558$	−1.46566	+	1.46566i	−0.0620463	+	0.0620463i
$559$	10.6186	+	20.7465i	0.449118	+	0.877483i
$560$	−22.5765	+	8.81362i	−0.954030	+	0.372443i
$561$	−0.875100	+	3.26592i	−0.0369468	+	0.137887i
$562$	2.04005	+	0.546631i	0.0860545	+	0.0230582i
$563$	−10.8527	−	40.5028i	−0.457387	−	1.70699i	−0.680975	−	0.732306i	$-0.738444\pi$
$563$	−10.8527	−	40.5028i	−0.457387	−	1.70699i	0.223589	−	0.974684i	$-0.428223\pi$
$564$	−0.247042	+	0.247042i	−0.0104024	+	0.0104024i
$565$	−9.93822	−	13.5168i	−0.418104	−	0.568656i
$566$	0.385887	+	1.44015i	0.0162201	+	0.0605341i
$567$		−	22.1108i		−	0.928566i
$568$	−3.24645	+	0.869884i	−0.136218	+	0.0364995i
$569$	−13.7741	−	23.8575i	−0.577441	−	1.00016i	−0.995772	−	0.0918621i	$-0.970718\pi$
$569$	−13.7741	−	23.8575i	−0.577441	−	1.00016i	0.418331	−	0.908295i	$-0.362615\pi$
$570$	−0.119837	+	0.149716i	−0.00501943	+	0.00627091i
$571$			4.72029i			0.197538i	0.995110	+	0.0987690i	$0.0314905\pi$
$571$			4.72029i			0.197538i	−0.995110	+	0.0987690i	$0.968510\pi$
$572$	15.7451	−	24.3424i	0.658335	−	1.01781i
$573$	−1.65043	−	1.65043i	−0.0689476	−	0.0689476i
$574$	2.26492	+	0.606884i	0.0945360	+	0.0253308i
$575$	−35.3311	+	18.5102i	−1.47341	+	0.771928i
$576$	−18.9400	−	10.9350i	−0.789168	−	0.455626i
$577$	6.73701			0.280465			0.140233	−	0.990119i	$-0.455215\pi$
$577$	6.73701			0.280465			0.140233	+	0.990119i	$0.455215\pi$
$578$	−1.26469	−	0.730170i	−0.0526043	−	0.0303711i
$579$	0.397008	−	0.106378i	0.0164991	−	0.00442092i
$580$	18.9120	−	7.38303i	0.785276	−	0.306564i
$581$	4.41118	−	7.64038i	0.183006	−	0.316977i
$582$	−0.137554	+	0.513359i	−0.00570180	+	0.0212794i
$583$	3.80407	+	6.58884i	0.157548	+	0.272882i
$584$	5.19417			0.214936
$585$	−1.38989	−	23.1917i	−0.0574649	−	0.958858i
$586$	−0.0918611			−0.00379475
$587$	2.59719	+	4.49847i	0.107198	+	0.185672i	0.914634	−	0.404283i	$-0.132479\pi$
$587$	2.59719	+	4.49847i	0.107198	+	0.185672i	−0.807436	+	0.589955i	$0.799146\pi$
$588$	−0.129894	+	0.484772i	−0.00535674	+	0.0199916i
$589$	5.20218	−	9.01044i	0.214352	−	0.371269i
$590$	0.309609	−	0.706152i	0.0127464	−	0.0290718i
$591$	6.68376	−	1.79091i	0.274933	−	0.0736681i
$592$	−23.6578	−	13.6589i	−0.972331	−	0.561375i
$593$	−12.9267			−0.530836			−0.265418	−	0.964133i	$-0.585510\pi$
$593$	−12.9267			−0.530836			−0.265418	+	0.964133i	$0.585510\pi$
$594$	0.932726	+	0.538510i	0.0382702	+	0.0220953i
$595$	1.66122	+	14.9868i	0.0681033	+	0.614399i
$596$	23.2529	+	6.23060i	0.952477	+	0.255215i
$597$	0.529553	+	0.529553i	0.0216732	+	0.0216732i
$598$	−1.72067	−	3.36182i	−0.0703633	−	0.137475i
$599$		−	16.7523i		−	0.684481i	−0.939612	−	0.342241i	$-0.888814\pi$
$599$		−	16.7523i		−	0.684481i	0.939612	−	0.342241i	$-0.111186\pi$
$600$	−0.417294	−	0.796506i	−0.0170360	−	0.0325172i
$601$	−6.28803	−	10.8912i	−0.256494	−	0.444261i	0.708806	−	0.705403i	$-0.249234\pi$
$601$	−6.28803	−	10.8912i	−0.256494	−	0.444261i	−0.965300	+	0.261142i	$0.915901\pi$
$602$	−2.28020	+	0.610977i	−0.0929340	+	0.0249016i
$603$		−	10.4212i		−	0.424384i
$604$	−1.35713	−	5.06486i	−0.0552207	−	0.206086i
$605$	−1.83638	+	12.0361i	−0.0746593	+	0.489337i
$606$	−0.0322160	+	0.0322160i	−0.00130868	+	0.00130868i
$607$	9.69731	+	36.1909i	0.393602	+	1.46894i	0.824149	+	0.566374i	$0.191654\pi$
$607$	9.69731	+	36.1909i	0.393602	+	1.46894i	−0.430547	+	0.902568i	$0.641679\pi$
$608$	−2.85748	−	0.765660i	−0.115886	−	0.0310516i
$609$	1.13362	−	4.23072i	0.0459366	−	0.171438i
$610$	0.137044	+	0.351045i	0.00554877	+	0.0142134i
$611$	−0.387390	−	1.80632i	−0.0156721	−	0.0730760i
$612$	−9.79548	+	9.79548i	−0.395959	+	0.395959i
$613$	14.9776	−	8.64732i	0.604940	−	0.349262i	−0.166043	−	0.986119i	$-0.553099\pi$
$613$	14.9776	−	8.64732i	0.604940	−	0.349262i	0.770982	+	0.636856i	$0.219766\pi$
$614$	−1.61524	+	0.932562i	−0.0651860	+	0.0376351i
$615$	0.744678	−	4.88082i	0.0300283	−	0.196814i
$616$	4.17079	+	4.17079i	0.168046	+	0.168046i
$617$	−6.07005	+	10.5136i	−0.244371	+	0.423263i	−0.961955	−	0.273210i	$-0.911915\pi$
$617$	−6.07005	+	10.5136i	−0.244371	+	0.423263i	0.717584	+	0.696472i	$0.245248\pi$
$618$	−0.191575	+	0.331818i	−0.00770628	+	0.0133477i
$619$	2.99993	+	2.99993i	0.120577	+	0.120577i	0.764821	−	0.644243i	$-0.222828\pi$
$619$	2.99993	+	2.99993i	0.120577	+	0.120577i	−0.644243	+	0.764821i	$0.722828\pi$
$620$	14.3869	+	19.5673i	0.577791	+	0.785843i
$621$	−13.9739	+	8.06784i	−0.560753	+	0.323751i
$622$	−2.44435	+	1.41125i	−0.0980095	+	0.0565858i
$623$	12.2514	−	12.2514i	0.490840	−	0.490840i
$624$	−4.30121	+	2.20147i	−0.172186	+	0.0881291i
$625$	2.04819	−	24.9160i	0.0819276	−	0.996638i
$626$	0.449988	−	1.67938i	0.0179851	−	0.0671215i
$627$	−2.55849	−	0.685545i	−0.102176	−	0.0273780i
$628$	7.48923	+	27.9502i	0.298853	+	1.11533i
$629$	−12.0180	+	12.0180i	−0.479188	+	0.479188i
$630$	2.32635	+	0.354936i	0.0926839	+	0.0141410i
$631$	5.60031	+	20.9006i	0.222945	+	0.832041i	0.983218	+	0.182437i	$0.0583986\pi$
$631$	5.60031	+	20.9006i	0.222945	+	0.832041i	−0.760273	+	0.649604i	$0.774935\pi$
$632$			4.38008i			0.174230i
$633$	−6.62791	+	1.77594i	−0.263436	+	0.0705874i
$634$	1.13592	+	1.96748i	0.0451133	+	0.0781385i
$635$	−36.7786	+	4.07674i	−1.45951	+	0.161781i
$636$		−	1.27926i		−	0.0507260i
$637$	−1.77933	−	1.96891i	−0.0704996	−	0.0780111i
$638$	−1.72409	−	1.72409i	−0.0682572	−	0.0682572i
$639$	−17.8898	−	4.79356i	−0.707710	−	0.189630i
$640$	5.74522	−	7.17766i	0.227100	−	0.283722i
$641$	39.2467	+	22.6591i	1.55015	+	0.894980i	0.998129	+	0.0611509i	$0.0194771\pi$
$641$	39.2467	+	22.6591i	1.55015	+	0.894980i	0.552022	+	0.833829i	$0.313856\pi$
$642$	0.223769			0.00883148
$643$	27.4095	+	15.8249i	1.08092	+	0.624072i	0.931146	−	0.364647i	$-0.118810\pi$
$643$	27.4095	+	15.8249i	1.08092	+	0.624072i	0.149779	+	0.988719i	$0.452144\pi$
$644$	−42.4939	+	11.3862i	−1.67449	+	0.448679i
$645$	1.80761	+	4.63028i	0.0711747	+	0.182317i
$646$	−0.302312	+	0.523619i	−0.0118943	+	0.0206015i
$647$	9.83169	−	36.6924i	0.386524	−	1.44253i	−0.449227	−	0.893418i	$-0.648301\pi$
$647$	9.83169	−	36.6924i	0.386524	−	1.44253i	0.835751	−	0.549109i	$-0.185033\pi$
$648$	2.07861	+	3.60026i	0.0816555	+	0.141431i
$649$	10.6497			0.418038
$650$	2.35718	+	0.216394i	0.0924562	+	0.00848769i
$651$	5.23971			0.205361
$652$	18.5343	+	32.1023i	0.725858	+	1.25722i
$653$	0.713775	−	2.66385i	0.0279322	−	0.104244i	−0.950552	−	0.310564i	$-0.899482\pi$
$653$	0.713775	−	2.66385i	0.0279322	−	0.104244i	0.978485	+	0.206320i	$0.0661487\pi$
$654$	−0.207859	+	0.360022i	−0.00812792	+	0.0140780i
$655$	−10.3175	−	26.4287i	−0.403138	−	1.03265i
$656$	24.1677	−	6.47571i	0.943590	−	0.252834i
$657$	24.7881	+	14.3114i	0.967076	+	0.558342i
$658$	0.187120			0.00729470
$659$	−1.80219	−	1.04050i	−0.0702034	−	0.0405320i	0.464487	−	0.885580i	$-0.346239\pi$
$659$	−1.80219	−	1.04050i	−0.0702034	−	0.0405320i	−0.534691	+	0.845048i	$0.679572\pi$
$660$	3.86376	−	4.82711i	0.150397	−	0.187895i
$661$	36.3010	+	9.72683i	1.41195	+	0.378330i	0.882619	−	0.470089i	$-0.155778\pi$
$661$	36.3010	+	9.72683i	1.41195	+	0.378330i	0.529326	+	0.848418i	$0.322445\pi$
$662$	1.66840	+	1.66840i	0.0648440	+	0.0648440i
$663$	0.630384	+	2.93935i	0.0244821	+	0.114155i
$664$			1.65876i			0.0643723i
$665$	−11.7405	+	1.30138i	−0.455278	+	0.0504655i
$666$	1.32626	+	2.29714i	0.0513914	+	0.0890125i
$667$	35.2843	−	9.45440i	1.36621	−	0.366076i
$668$		−	40.9991i		−	1.58630i
$669$	1.19389	+	4.45566i	0.0461585	+	0.172266i
$670$	1.04960	+	0.160140i	0.0405497	+	0.00618675i
$671$	−3.68052	+	3.68052i	−0.142085	+	0.142085i
$672$	−0.385592	−	1.43905i	−0.0148745	−	0.0555125i
$673$	−17.3908	−	4.65984i	−0.670364	−	0.179624i	−0.0924454	−	0.995718i	$-0.529468\pi$
$673$	−17.3908	−	4.65984i	−0.670364	−	0.179624i	−0.577919	+	0.816094i	$0.696135\pi$
$674$	0.232451	−	0.867519i	0.00895368	−	0.0334156i
$675$	0.414638	−	10.1050i	0.0159594	−	0.388943i
$676$	2.60078	−	25.6443i	0.100030	−	0.986320i
$677$	15.4021	−	15.4021i	0.591952	−	0.591952i	−0.346206	−	0.938158i	$-0.612530\pi$
$677$	15.4021	−	15.4021i	0.591952	−	0.591952i	0.938158	+	0.346206i	$0.112530\pi$
$678$	0.293403	−	0.169396i	0.0112681	−	0.00650563i
$679$	−28.3508	+	16.3684i	−1.08801	+	0.628160i
$680$	−1.67938	−	2.28410i	−0.0644014	−	0.0875913i
$681$	−3.57007	−	3.57007i	−0.136805	−	0.136805i
$682$	1.45841	−	2.52605i	0.0558455	−	0.0967273i
$683$	3.08376	−	5.34122i	0.117997	−	0.204376i	−0.800977	−	0.598695i	$-0.795686\pi$
$683$	3.08376	−	5.34122i	0.117997	−	0.204376i	0.918974	+	0.394319i	$0.129019\pi$
$684$	−7.67369	−	7.67369i	−0.293411	−	0.293411i
$685$	5.04036	−	33.0359i	0.192582	−	1.26224i
$686$	−1.98113	+	1.14381i	−0.0756398	+	0.0436707i
$687$	1.11732	−	0.645085i	0.0426284	−	0.0246115i
$688$	−17.8113	+	17.8113i	−0.679050	+	0.679050i
$689$	5.67986	+	3.67383i	0.216385	+	0.139962i
$690$	−0.292911	−	0.750304i	−0.0111509	−	0.0285636i
$691$	3.39841	−	12.6830i	0.129282	−	0.482486i	−0.870674	−	0.491860i	$-0.836317\pi$
$691$	3.39841	−	12.6830i	0.129282	−	0.482486i	0.999956	+	0.00937405i	$0.00298390\pi$
$692$	34.7534	+	9.31214i	1.32112	+	0.353994i
$693$	8.41252	+	31.3960i	0.319565	+	1.19263i
$694$	−1.72710	+	1.72710i	−0.0655600	+	0.0655600i
$695$	2.89107	−	18.9489i	0.109665	−	0.718773i
$696$	0.213140	+	0.795450i	0.00807906	+	0.0301515i
$697$		−	15.5666i		−	0.589627i
$698$	−0.319231	+	0.0855377i	−0.0120831	+	0.00323765i
$699$	3.39126	+	5.87383i	0.128269	+	0.222169i
$700$	8.22263	−	26.3194i	0.310786	−	0.994780i
$701$			23.2292i			0.877354i	0.898645	+	0.438677i	$0.144553\pi$
$701$			23.2292i			0.877354i	−0.898645	+	0.438677i	$0.855447\pi$
$702$	0.956365	+	0.0483719i	0.0360957	+	0.00182568i
$703$	−9.41478	−	9.41478i	−0.355085	−	0.355085i
$704$	29.7274	+	7.96543i	1.12039	+	0.300208i
$705$	−0.0434078	−	0.391606i	−0.00163483	−	0.0147487i
$706$	−3.72081	−	2.14821i	−0.140034	−	0.0808490i
$707$	−2.80636			−0.105544
$708$	−1.55078	−	0.895342i	−0.0582818	−	0.0336490i
$709$	−2.00482	+	0.537189i	−0.0752925	+	0.0201746i	−0.296269	−	0.955105i	$-0.595742\pi$
$709$	−2.00482	+	0.537189i	−0.0752925	+	0.0201746i	0.220976	+	0.975279i	$0.429076\pi$
$710$	0.757707	−	1.72817i	0.0284362	−	0.0648569i
$711$	−12.0684	+	20.9030i	−0.452599	+	0.783925i
$712$	−0.843128	+	3.14660i	−0.0315976	+	0.117924i
$713$	21.8496	+	37.8447i	0.818275	+	1.41729i
$714$	−0.304493			−0.0113954
$715$	10.3360	+	31.0176i	0.386545	+	1.15999i
$716$	−34.4251			−1.28653
$717$	2.47769	+	4.29148i	0.0925309	+	0.160268i
$718$	−0.0336269	+	0.125497i	−0.00125494	+	0.00468351i
$719$	−3.36848	+	5.83438i	−0.125623	+	0.217586i	−0.921976	−	0.387246i	$-0.873426\pi$
$719$	−3.36848	+	5.83438i	−0.125623	+	0.217586i	0.796353	+	0.604832i	$0.206760\pi$
$720$	23.3911	−	9.13165i	0.871735	−	0.340316i
$721$	−22.7966	+	6.10834i	−0.848991	+	0.227486i
$722$	1.75032	+	1.01055i	0.0651401	+	0.0376086i
$723$	2.78698			0.103649
$724$	−42.8050	−	24.7135i	−1.59083	−	0.918469i
$725$	−6.82756	+	21.8540i	−0.253569	+	0.811637i
$726$	−0.237489	−	0.0636349i	−0.00881403	−	0.00236171i
$727$	−34.4733	−	34.4733i	−1.27854	−	1.27854i	−0.941483	−	0.337062i	$-0.890567\pi$
$727$	−34.4733	−	34.4733i	−1.27854	−	1.27854i	−0.337062	−	0.941483i	$-0.609433\pi$
$728$	4.99058	+	1.61148i	0.184963	+	0.0597254i
$729$			20.8218i			0.771179i
$730$	−1.82233	+	2.27669i	−0.0674475	+	0.0842641i
$731$	7.83580	+	13.5720i	0.289817	+	0.501979i
$732$	0.845374	−	0.226517i	0.0312459	−	0.00837232i
$733$		−	28.7555i		−	1.06211i	−0.847338	−	0.531054i	$-0.821796\pi$
$733$		−	28.7555i		−	1.06211i	0.847338	−	0.531054i	$-0.178204\pi$
$734$	−0.491861	−	1.83565i	−0.0181549	−	0.0677551i
$735$	−0.335273	−	0.456000i	−0.0123667	−	0.0168198i
$736$	8.78585	−	8.78585i	0.323851	−	0.323851i
$737$	3.79556	+	14.1652i	0.139811	+	0.521783i
$738$	−2.34665	−	0.628783i	−0.0863813	−	0.0231458i
$739$	−7.94129	+	29.6373i	−0.292125	+	1.09023i	0.651349	+	0.758778i	$0.274203\pi$
$739$	−7.94129	+	29.6373i	−0.292125	+	1.09023i	−0.943474	+	0.331447i	$0.892463\pi$
$740$	28.9523	−	11.3027i	1.06431	−	0.415494i
$741$	−2.30266	+	0.493837i	−0.0845903	+	0.0181416i
$742$	−0.484483	+	0.484483i	−0.0177859	+	0.0177859i
$743$	45.8676	−	26.4817i	1.68272	−	0.971519i	0.722878	−	0.690976i	$-0.242819\pi$
$743$	45.8676	−	26.4817i	1.68272	−	0.971519i	0.959841	−	0.280543i	$-0.0905146\pi$
$744$	−0.853172	+	0.492579i	−0.0312788	+	0.0180588i
$745$	−21.8728	+	16.0820i	−0.801359	+	0.589198i
$746$	0.941490	+	0.941490i	0.0344704	+	0.0344704i
$747$	−4.57035	+	7.91608i	−0.167220	+	0.289634i
$748$	9.74706	−	16.8824i	0.356388	−	0.617282i
$749$	9.74639	+	9.74639i	0.356125	+	0.356125i
$750$	0.495526	+	0.0965407i	0.0180941	+	0.00352517i
$751$	−40.3780	+	23.3123i	−1.47341	+	0.850676i	−0.999552	−	0.0299230i	$-0.990474\pi$
$751$	−40.3780	+	23.3123i	−1.47341	+	0.850676i	−0.473862	+	0.880599i	$0.657140\pi$
$752$	1.72915	−	0.998326i	0.0630557	−	0.0364052i
$753$	1.13693	−	1.13693i	0.0414321	−	0.0414321i
$754$	−2.06296	−	0.666140i	−0.0751287	−	0.0242594i
$755$	5.41574	+	2.37451i	0.197099	+	0.0864172i
$756$	2.88708	−	10.7747i	0.105002	−	0.391873i
$757$	1.20667	+	0.323327i	0.0438572	+	0.0117515i	0.280681	−	0.959801i	$-0.409440\pi$
$757$	1.20667	+	0.323327i	0.0438572	+	0.0117515i	−0.236824	+	0.971553i	$0.576106\pi$
$758$	−0.0356995	−	0.133232i	−0.00129666	−	0.00483922i
$759$	7.86654	−	7.86654i	0.285537	−	0.285537i
$760$	1.78934	−	1.31561i	0.0649063	−	0.0477223i
$761$	−5.28278	−	19.7156i	−0.191501	−	0.714690i	−0.993145	−	0.116889i	$-0.962708\pi$
$761$	−5.28278	−	19.7156i	−0.191501	−	0.714690i	0.801644	−	0.597801i	$-0.203959\pi$
$762$		−	0.747246i		−	0.0270698i
$763$	−24.7343	+	6.62754i	−0.895442	+	0.239933i
$764$	6.72858	+	11.6542i	0.243432	+	0.421636i
$765$	−1.72116	−	15.5276i	−0.0622288	−	0.561401i
$766$			1.57656i			0.0569633i
$767$	8.42886	−	4.31410i	0.304349	−	0.155773i
$768$	−3.55968	−	3.55968i	−0.128449	−	0.128449i
$769$	−35.6638	−	9.55609i	−1.28607	−	0.344602i	−0.449904	−	0.893077i	$-0.648542\pi$
$769$	−35.6638	−	9.55609i	−1.28607	−	0.344602i	−0.836167	+	0.548476i	$0.815208\pi$
$770$	−3.29141	+	0.364838i	−0.118614	+	0.0131479i
$771$	−5.16879	−	2.98420i	−0.186150	−	0.107473i
$772$	−2.36972			−0.0852882
$773$	−18.5187	−	10.6918i	−0.666072	−	0.384557i	0.128515	−	0.991708i	$-0.458979\pi$
$773$	−18.5187	−	10.6918i	−0.666072	−	0.384557i	−0.794587	+	0.607151i	$0.792312\pi$
$774$	2.36248	−	0.633024i	0.0849175	−	0.0227536i
$775$	−27.3669	−	1.12294i	−0.983047	−	0.0403372i
$776$	3.07754	−	5.33045i	0.110477	−	0.191352i
$777$	1.73545	−	6.47681i	0.0622591	−	0.232354i
$778$	−0.483959	−	0.838242i	−0.0173508	−	0.0300524i
$779$	12.1947			0.436921
$780$	1.10261	−	5.38566i	0.0394798	−	0.192837i
$781$	26.0630			0.932608
$782$	−1.26974	−	2.19925i	−0.0454057	−	0.0786449i
$783$	−2.39725	+	8.94666i	−0.0856708	+	0.319728i
$784$	1.43410	−	2.48393i	0.0512179	−	0.0887120i
$785$	−29.8865	−	13.1036i	−1.06670	−	0.467688i
$786$	0.553399	−	0.148283i	0.0197391	−	0.00528907i
$787$	34.1065	+	19.6914i	1.21577	+	0.701923i	0.964010	−	0.265867i	$-0.0856582\pi$
$787$	34.1065	+	19.6914i	1.21577	+	0.701923i	0.251757	+	0.967790i	$0.418992\pi$
$788$	−39.8950			−1.42120
$789$	0.721232	+	0.416404i	0.0256766	+	0.0148244i
$790$	−1.91986	−	1.53672i	−0.0683056	−	0.0546739i
$791$	20.1575	+	5.40118i	0.716717	+	0.192044i
$792$	−4.32129	−	4.32129i	−0.153550	−	0.153550i
$793$	−1.42205	+	4.40394i	−0.0504986	+	0.156389i
$794$			0.795007i			0.0282138i
$795$	1.12632	+	0.901539i	0.0399464	+	0.0319743i
$796$	−2.15892	−	3.73936i	−0.0765209	−	0.132538i
$797$	−37.8319	+	10.1370i	−1.34007	+	0.359072i	−0.856462	−	0.516210i	$-0.827342\pi$
$797$	−37.8319	+	10.1370i	−1.34007	+	0.359072i	−0.483612	+	0.875282i	$0.660676\pi$
$798$		−	0.238537i		−	0.00844411i
$799$	−0.321515	−	1.19991i	−0.0113744	−	0.0424498i
$800$	1.70553	+	7.59875i	0.0602996	+	0.268656i
$801$	−12.6934	+	12.6934i	−0.448500	+	0.448500i
$802$	−0.0820546	−	0.306232i	−0.00289745	−	0.0108134i
$803$	−38.9062	−	10.4249i	−1.37297	−	0.367887i
$804$	0.638201	−	2.38180i	0.0225076	−	0.0839996i
$805$	19.9220	−	45.4378i	0.702158	−	1.60147i
$806$	0.131003	−	2.59006i	0.00461437	−	0.0912311i
$807$	−2.36658	+	2.36658i	−0.0833077	+	0.0833077i
$808$	0.456954	−	0.263823i	0.0160756	−	0.00928125i
$809$	−23.1644	+	13.3740i	−0.814416	+	0.470203i	−0.848487	−	0.529216i	$-0.822486\pi$
$809$	−23.1644	+	13.3740i	−0.814416	+	0.470203i	0.0340712	+	0.999419i	$0.489153\pi$
$810$	−2.30731	−	0.352032i	−0.0810708	−	0.0123691i
$811$	−7.93739	−	7.93739i	−0.278720	−	0.278720i	0.553878	−	0.832598i	$-0.313147\pi$
$811$	−7.93739	−	7.93739i	−0.278720	−	0.278720i	−0.832598	+	0.553878i	$0.813147\pi$
$812$	−12.6265	+	21.8697i	−0.443103	+	0.767477i
$813$	3.76869	−	6.52757i	0.132174	−	0.228932i
$814$	−2.63940	−	2.63940i	−0.0925109	−	0.0925109i
$815$	−41.3260	−	6.30520i	−1.44759	−	0.220862i
$816$	−2.81378	+	1.62453i	−0.0985019	+	0.0568701i
$817$	−10.6322	+	6.13849i	−0.371973	+	0.214759i
$818$	1.86963	−	1.86963i	0.0653700	−	0.0653700i
$819$	19.3764	+	21.4409i	0.677067	+	0.749207i
$820$	−11.4305	+	26.0706i	−0.399172	+	0.910425i
$821$	6.99144	−	26.0924i	0.244003	−	0.910632i	−0.729879	−	0.683577i	$-0.760424\pi$
$821$	6.99144	−	26.0924i	0.244003	−	0.910632i	0.973882	−	0.227055i	$-0.0729098\pi$
$822$	0.651843	+	0.174661i	0.0227356	+	0.00609200i
$823$	−2.42695	−	9.05749i	−0.0845980	−	0.315724i	0.910640	−	0.413201i	$-0.135589\pi$
$823$	−2.42695	−	9.05749i	−0.0845980	−	0.315724i	−0.995238	+	0.0974771i	$0.968923\pi$
$824$	3.13769	−	3.13769i	0.109307	−	0.109307i
$825$	1.52707	+	6.80365i	0.0531658	+	0.236873i
$826$	0.248227	+	0.926397i	0.00863693	+	0.0322335i
$827$			45.0330i			1.56595i	0.622052	+	0.782976i	$0.286299\pi$
$827$			45.0330i			1.56595i	−0.622052	+	0.782976i	$0.713701\pi$
$828$	44.0273	−	11.7971i	1.53005	−	0.409976i
$829$	−21.0075	−	36.3861i	−0.729622	−	1.26374i	−0.957043	−	0.289946i	$-0.906363\pi$
$829$	−21.0075	−	36.3861i	−0.729622	−	1.26374i	0.227421	−	0.973796i	$-0.426971\pi$
$830$	−0.727061	−	0.581961i	−0.0252366	−	0.0202002i
$831$			6.20942i			0.215402i
$832$	26.7549	−	5.73795i	0.927558	−	0.198928i
$833$	−1.26182	−	1.26182i	−0.0437194	−	0.0437194i
$834$	0.373887	+	0.100183i	0.0129467	+	0.00346905i
$835$	36.0974	+	28.8935i	1.24920	+	0.999901i
$836$	13.2255	+	7.63575i	0.457414	+	0.264088i
$837$	−11.0804			−0.382993
$838$	3.42047	+	1.97481i	0.118158	+	0.0682186i
$839$	5.24673	−	1.40586i	0.181137	−	0.0485356i	−0.167110	−	0.985938i	$-0.553444\pi$
$839$	5.24673	−	1.40586i	0.181137	−	0.0485356i	0.348247	+	0.937403i	$0.386777\pi$
$840$	1.02435	+	0.449122i	0.0353434	+	0.0154962i
$841$	−4.01574	+	6.95547i	−0.138474	+	0.239844i
$842$	−0.444405	+	1.65854i	−0.0153152	+	0.0571571i
$843$	2.76581	+	4.79053i	0.0952596	+	0.164994i
$844$	39.5617			1.36177
$845$	20.7455	+	20.3623i	0.713668	+	0.700484i
$846$	−0.193872			−0.00666546
$847$	−7.57228	−	13.1156i	−0.260187	−	0.450657i
$848$	−1.89222	+	7.06186i	−0.0649791	+	0.242505i
$849$	−1.95249	+	3.38181i	−0.0670093	+	0.116063i
$850$	1.59036	+	0.0652568i	0.0545488	+	0.00223829i
$851$	54.0166	−	14.4737i	1.85167	−	0.496152i
$852$	−3.79522	−	2.19117i	−0.130022	−	0.0750682i
$853$	23.0805			0.790260			0.395130	−	0.918625i	$-0.370700\pi$
$853$	23.0805			0.790260			0.395130	+	0.918625i	$0.370700\pi$
$854$	−0.405948	−	0.234374i	−0.0138912	−	0.00802012i
$855$	12.1642	−	1.34834i	0.416006	−	0.0461123i
$856$	−2.50323	−	0.670738i	−0.0855586	−	0.0229254i
$857$	−37.6679	−	37.6679i	−1.28671	−	1.28671i	−0.936772	−	0.349940i	$-0.886202\pi$
$857$	−37.6679	−	37.6679i	−1.28671	−	1.28671i	−0.349940	−	0.936772i	$-0.613798\pi$
$858$	−0.645543	+	0.138446i	−0.0220385	+	0.00472645i
$859$		−	5.08674i		−	0.173557i	−0.996228	−	0.0867787i	$-0.972343\pi$
$859$		−	5.08674i		−	0.173557i	0.996228	−	0.0867787i	$-0.0276573\pi$
$860$	−3.15731	−	28.4839i	−0.107664	−	0.971294i
$861$	3.07068	+	5.31857i	0.104648	+	0.181256i
$862$	−0.800452	+	0.214481i	−0.0272635	+	0.00730524i
$863$			45.1879i			1.53821i	0.639120	+	0.769107i	$0.279299\pi$
$863$			45.1879i			1.53821i	−0.639120	+	0.769107i	$0.720701\pi$
$864$	0.815407	+	3.04314i	0.0277407	+	0.103530i
$865$	−32.6907	+	24.0358i	−1.11152	+	0.817242i
$866$	−1.14100	+	1.14100i	−0.0387728	+	0.0387728i
$867$	−0.989932	−	3.69447i	−0.0336198	−	0.125471i
$868$	−29.1805	−	7.81890i	−0.990452	−	0.265391i
$869$	8.79099	−	32.8084i	0.298214	−	1.11295i
$870$	−0.423437	−	0.185654i	−0.0143559	−	0.00629427i
$871$	8.74226	+	9.67372i	0.296220	+	0.327782i
$872$	3.40439	−	3.40439i	0.115287	−	0.115287i
$873$	29.3738	−	16.9590i	0.994154	−	0.573975i
$874$	1.72287	−	0.994699i	0.0582769	−	0.0336462i
$875$	17.3780	+	25.7878i	0.587484	+	0.871785i
$876$	4.78896	+	4.78896i	0.161804	+	0.161804i
$877$	−10.1641	+	17.6048i	−0.343218	+	0.594471i	−0.985028	−	0.172392i	$-0.944850\pi$
$877$	−10.1641	+	17.6048i	−0.343218	+	0.594471i	0.641810	+	0.766863i	$0.278184\pi$
$878$	−2.26134	+	3.91675i	−0.0763164	+	0.132184i
$879$	−0.170126	−	0.170126i	−0.00573821	−	0.00573821i
$880$	−28.4690	+	20.9318i	−0.959690	+	0.705612i
$881$	−28.5961	+	16.5100i	−0.963428	+	0.556236i	−0.897227	−	0.441571i	$-0.854421\pi$
$881$	−28.5961	+	16.5100i	−0.963428	+	0.556236i	−0.0662019	+	0.997806i	$0.521088\pi$
$882$	−0.241187	+	0.139249i	−0.00812118	+	0.00468876i
$883$	−15.9555	+	15.9555i	−0.536944	+	0.536944i	−0.922630	−	0.385686i	$-0.873965\pi$
$883$	−15.9555	+	15.9555i	−0.536944	+	0.536944i	0.385686	+	0.922630i	$0.373965\pi$
$884$	0.875535	−	17.3103i	0.0294474	−	0.582207i
$885$	1.88119	−	0.734395i	0.0632353	−	0.0246864i
$886$	0.259261	−	0.967576i	0.00871005	−	0.0325063i
$887$	0.609784	+	0.163391i	0.0204745	+	0.00548614i	0.269042	−	0.963129i	$-0.413293\pi$
$887$	0.609784	+	0.163391i	0.0204745	+	0.00548614i	−0.248567	+	0.968615i	$0.579960\pi$
$888$	0.326296	+	1.21775i	0.0109498	+	0.0408651i
$889$	32.5466	−	32.5466i	1.09158	−	1.09158i
$890$	−1.08340	−	1.47351i	−0.0363157	−	0.0493923i
$891$	−8.34370	−	31.1391i	−0.279524	−	1.04320i
$892$		−	26.5956i		−	0.890488i
$893$	0.939998	−	0.251872i	0.0314558	−	0.00842856i
$894$	−0.274116	−	0.474784i	−0.00916782	−	0.0158791i
$895$	24.2605	−	30.3094i	0.810940	−	1.01313i
$896$			11.4359i			0.382046i
$897$	3.03942	−	9.41274i	0.101483	−	0.314282i
$898$	2.89072	+	2.89072i	0.0964647	+	0.0964647i
$899$	24.2297	+	6.49233i	0.808106	+	0.216531i
$900$	−8.51934	+	27.2691i	−0.283978	+	0.908971i
$901$	3.93920	+	2.27430i	0.131234	+	0.0757679i
$902$	3.41875			0.113832
$903$	−5.35444	−	3.09139i	−0.178185	−	0.102875i
$904$	−3.78996	+	1.01552i	−0.126052	+	0.0337755i
$905$	51.9250	−	20.2710i	1.72604	−	0.673830i
$906$	−0.0597070	+	0.103416i	−0.00198363	+	0.00343575i
$907$	10.1387	−	37.8383i	0.336651	−	1.25640i	−0.565417	−	0.824805i	$-0.691285\pi$
$907$	10.1387	−	37.8383i	0.336651	−	1.25640i	0.902068	−	0.431594i	$-0.142049\pi$
$908$	14.5547	+	25.2095i	0.483015	+	0.836607i
$909$	2.90763			0.0964400
$910$	−2.45724	+	1.62208i	−0.0814568	+	0.0537714i
$911$	6.21630			0.205955			0.102978	−	0.994684i	$-0.467163\pi$
$911$	6.21630			0.205955			0.102978	+	0.994684i	$0.467163\pi$
$912$	−1.27264	−	2.20429i	−0.0421415	−	0.0729912i
$913$	3.32919	−	12.4247i	0.110180	−	0.411198i
$914$	−0.204012	+	0.353358i	−0.00674810	+	0.0116881i
$915$	−0.396328	+	0.903940i	−0.0131022	+	0.0298833i
$916$	−7.18510	+	1.92524i	−0.237402	+	0.0636117i
$917$	30.5621	+	17.6450i	1.00925	+	0.582690i
$918$	0.643907			0.0212521
$919$	19.9013	+	11.4900i	0.656485	+	0.379022i	0.790936	−	0.611899i	$-0.209594\pi$
$919$	19.9013	+	11.4900i	0.656485	+	0.379022i	−0.134452	+	0.990920i	$0.542927\pi$
$920$	1.02769	+	9.27138i	0.0338819	+	0.305668i
$921$	−4.71852	−	1.26432i	−0.155481	−	0.0416609i
$922$	−1.55017	−	1.55017i	−0.0510520	−	0.0510520i
$923$	20.6279	−	10.5579i	0.678977	−	0.347518i
$924$			7.69084i			0.253010i
$925$	−10.4523	+	33.4562i	−0.343669	+	1.10003i
$926$	1.02676	+	1.77840i	0.0337413	+	0.0584417i
$927$	23.6192	−	6.32875i	0.775757	−	0.207863i
$928$		−	7.13229i		−	0.234129i
$929$	−0.280692	−	1.04756i	−0.00920921	−	0.0343692i	0.961168	−	0.275963i	$-0.0889966\pi$
$929$	−0.280692	−	1.04756i	−0.00920921	−	0.0343692i	−0.970378	+	0.241593i	$0.922330\pi$
$930$	0.0834229	−	0.546777i	0.00273554	−	0.0179295i
$931$	0.988497	−	0.988497i	0.0323967	−	0.0323967i
$932$	−10.1211	−	37.7726i	−0.331529	−	1.23728i
$933$	−7.14054	−	1.91330i	−0.233771	−	0.0626387i
$934$	0.724846	−	2.70516i	0.0237177	−	0.0885157i
$935$	7.99493	+	20.4794i	0.261462	+	0.669746i
$936$	−5.17066	−	1.66963i	−0.169008	−	0.0545735i
$937$	−2.17699	+	2.17699i	−0.0711191	+	0.0711191i	−0.741772	−	0.670653i	$-0.766014\pi$
$937$	−2.17699	+	2.17699i	−0.0711191	+	0.0711191i	0.670653	+	0.741772i	$0.266014\pi$
$938$	−1.14374	+	0.660337i	−0.0373443	+	0.0215608i
$939$	3.94358	−	2.27682i	0.128694	−	0.0743014i
$940$	−0.342627	+	2.24567i	−0.0111753	+	0.0732457i
$941$	−22.9413	−	22.9413i	−0.747866	−	0.747866i	0.226212	−	0.974078i	$-0.427366\pi$
$941$	−22.9413	−	22.9413i	−0.747866	−	0.747866i	−0.974078	+	0.226212i	$0.927366\pi$
$942$	0.329490	−	0.570694i	0.0107354	−	0.0185942i
$943$	−25.6095	+	44.3569i	−0.833959	+	1.44446i
$944$	7.23636	+	7.23636i	0.235523	+	0.235523i
$945$	7.45192	+	10.1352i	0.242411	+	0.329699i
$946$	−2.98069	+	1.72090i	−0.0969107	+	0.0559514i
$947$	−23.6413	+	13.6493i	−0.768239	+	0.443543i	−0.832246	−	0.554406i	$-0.812945\pi$
$947$	−23.6413	+	13.6493i	−0.768239	+	0.443543i	0.0640069	+	0.997949i	$0.479612\pi$
$948$	−4.03838	+	4.03838i	−0.131161	+	0.131161i
$949$	−35.0159	+	7.50964i	−1.13666	+	0.243773i
$950$	−0.0511215	+	1.24587i	−0.00165860	+	0.0404214i
$951$	−1.54003	+	5.74748i	−0.0499390	+	0.186375i
$952$	3.40625	+	0.912703i	0.110397	+	0.0295809i
$953$	1.65546	+	6.17827i	0.0536257	+	0.200134i	0.987541	−	0.157360i	$-0.0502982\pi$
$953$	1.65546	+	6.17827i	0.0536257	+	0.200134i	−0.933916	+	0.357493i	$0.883631\pi$
$954$	0.501965	−	0.501965i	0.0162517	−	0.0162517i
$955$	−15.0028	−	2.28901i	−0.485478	−	0.0740705i
$956$	−7.39460	−	27.5970i	−0.239158	−	0.892551i
$957$		−	6.38600i		−	0.206430i
$958$	5.40920	−	1.44939i	0.174763	−	0.0468277i
$959$	20.7839	+	35.9988i	0.671147	+	1.16246i
$960$	5.80039	−	0.642947i	0.187207	−	0.0207510i
$961$		−	0.991728i		−	0.0319912i
$962$	−3.15819	−	1.01979i	−0.101824	−	0.0328794i
$963$	−10.0981	−	10.0981i	−0.325406	−	0.325406i
$964$	−15.5210	−	4.15885i	−0.499899	−	0.133947i
$965$	1.67002	−	2.08641i	0.0537600	−	0.0671638i
$966$	0.867650	+	0.500938i	0.0279162	+	0.0161174i
$967$	−28.4424			−0.914647			−0.457324	−	0.889300i	$-0.651192\pi$
$967$	−28.4424			−0.914647			−0.457324	+	0.889300i	$0.651192\pi$
$968$	2.46596	+	1.42372i	0.0792589	+	0.0457602i
$969$	−1.52962	+	0.409860i	−0.0491384	+	0.0131666i
$970$	1.25670	+	3.21908i	0.0403501	+	0.103358i
$971$	0.619921	−	1.07374i	0.0198942	−	0.0344578i	−0.855907	−	0.517130i	$-0.827000\pi$
$971$	0.619921	−	1.07374i	0.0198942	−	0.0344578i	0.875801	+	0.482672i	$0.160334\pi$
$972$	−4.51696	+	16.8575i	−0.144882	+	0.540705i
$973$	11.9213	+	20.6484i	0.382180	+	0.661956i
$974$	1.99799			0.0640197
$975$	3.96472	+	4.76624i	0.126973	+	0.152642i
$976$	−5.00174			−0.160102
$977$	19.0226	+	32.9480i	0.608586	+	1.05410i	0.991474	+	0.130307i	$0.0415962\pi$
$977$	19.0226	+	32.9480i	0.608586	+	1.05410i	−0.382888	+	0.923795i	$0.625071\pi$
$978$	0.218491	−	0.815418i	0.00698656	−	0.0260742i
$979$	12.6307	−	21.8770i	0.403678	−	0.699192i
$980$	1.18671	+	3.03982i	0.0379082	+	0.0971035i
$981$	25.6268	−	6.86669i	0.818202	−	0.219236i
$982$	3.18111	+	1.83661i	0.101513	+	0.0586087i
$983$	−34.5934			−1.10336			−0.551679	−	0.834056i	$-0.686013\pi$
$983$	−34.5934			−1.10336			−0.551679	+	0.834056i	$0.686013\pi$
$984$	−0.999984	−	0.577341i	−0.0318783	−	0.0184050i
$985$	28.1154	−	35.1254i	0.895831	−	1.11919i
$986$	−1.40805	−	0.377285i	−0.0448414	−	0.0120152i
$987$	0.346545	+	0.346545i	0.0110307	+	0.0110307i
$988$	13.5607	+	0.685885i	0.431423	+	0.0218209i
$989$		−	51.5644i		−	1.63965i
$990$	3.41018	−	0.378003i	0.108383	−	0.0120137i
$991$	−19.7486	−	34.2056i	−0.627335	−	1.08658i	−0.988084	−	0.153913i	$-0.950813\pi$
$991$	−19.7486	−	34.2056i	−0.627335	−	1.08658i	0.360750	−	0.932663i	$-0.382521\pi$
$992$	8.24156	−	2.20832i	0.261670	−	0.0701142i
$993$			6.17972i			0.196107i
$994$	0.607486	+	2.26717i	0.0192683	+	0.0719103i
$995$	4.81376	+	0.734446i	0.152606	+	0.0232835i
$996$	−1.52936	+	1.52936i	−0.0484595	+	0.0484595i
$997$	1.90378	+	7.10500i	0.0602933	+	0.225018i	0.989498	−	0.144549i	$-0.0461730\pi$
$997$	1.90378	+	7.10500i	0.0602933	+	0.225018i	−0.929204	+	0.369566i	$0.879506\pi$
$998$	0.300395	+	0.0804906i	0.00950884	+	0.00254789i
$999$	−3.66995	+	13.6964i	−0.116112	+	0.433336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.o.a.63.3	yes	20
3.2	odd	2		585.2.cf.a.388.3		20
5.2	odd	4		65.2.t.a.37.3	yes	20
5.3	odd	4		325.2.x.b.232.3		20
5.4	even	2		325.2.s.b.193.3		20
13.2	odd	12		845.2.f.e.408.7		20
13.3	even	3		845.2.k.e.268.4		20
13.4	even	6		845.2.o.f.488.3		20
13.5	odd	4		845.2.t.f.418.3		20
13.6	odd	12		65.2.t.a.58.3	yes	20
13.7	odd	12		845.2.t.g.188.3		20
13.8	odd	4		845.2.t.e.418.3		20
13.9	even	3		845.2.o.e.488.3		20
13.10	even	6		845.2.k.d.268.7		20
13.11	odd	12		845.2.f.d.408.4		20
13.12	even	2		845.2.o.g.258.3		20
15.2	even	4		585.2.dp.a.37.3		20
39.32	even	12		585.2.dp.a.253.3		20
65.2	even	12		845.2.k.e.577.4		20
65.7	even	12		845.2.o.g.357.3		20
65.12	odd	4		845.2.t.g.427.3		20
65.17	odd	12		845.2.t.e.657.3		20
65.19	odd	12		325.2.x.b.318.3		20
65.22	odd	12		845.2.t.f.657.3		20
65.32	even	12	inner	65.2.o.a.32.3	✓	20
65.37	even	12		845.2.k.d.577.7		20
65.42	odd	12		845.2.f.e.437.4		20
65.47	even	4		845.2.o.f.587.3		20
65.57	even	4		845.2.o.e.587.3		20
65.58	even	12		325.2.s.b.32.3		20
65.62	odd	12		845.2.f.d.437.7		20
195.32	odd	12		585.2.cf.a.487.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.3	✓	20	65.32	even	12	inner
65.2.o.a.63.3	yes	20	1.1	even	1	trivial
65.2.t.a.37.3	yes	20	5.2	odd	4
65.2.t.a.58.3	yes	20	13.6	odd	12
325.2.s.b.32.3		20	65.58	even	12
325.2.s.b.193.3		20	5.4	even	2
325.2.x.b.232.3		20	5.3	odd	4
325.2.x.b.318.3		20	65.19	odd	12
585.2.cf.a.388.3		20	3.2	odd	2
585.2.cf.a.487.3		20	195.32	odd	12
585.2.dp.a.37.3		20	15.2	even	4
585.2.dp.a.253.3		20	39.32	even	12
845.2.f.d.408.4		20	13.11	odd	12
845.2.f.d.437.7		20	65.62	odd	12
845.2.f.e.408.7		20	13.2	odd	12
845.2.f.e.437.4		20	65.42	odd	12
845.2.k.d.268.7		20	13.10	even	6
845.2.k.d.577.7		20	65.37	even	12
845.2.k.e.268.4		20	13.3	even	3
845.2.k.e.577.4		20	65.2	even	12
845.2.o.e.488.3		20	13.9	even	3
845.2.o.e.587.3		20	65.57	even	4
845.2.o.f.488.3		20	13.4	even	6
845.2.o.f.587.3		20	65.47	even	4
845.2.o.g.258.3		20	13.12	even	2
845.2.o.g.357.3		20	65.7	even	12
845.2.t.e.418.3		20	13.8	odd	4
845.2.t.e.657.3		20	65.17	odd	12
845.2.t.f.418.3		20	13.5	odd	4
845.2.t.f.657.3		20	65.22	odd	12
845.2.t.g.188.3		20	13.7	odd	12
845.2.t.g.427.3		20	65.12	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0656513 + 0.113711i) q^{2} +(-0.0890070 + 0.332179i) q^{3} +(0.991380 - 1.71712i) q^{4} +(0.813169 + 2.08297i) q^{5} +(-0.0436159 + 0.0116869i) q^{6} +(-2.40874 - 1.39069i) q^{7} +0.522947 q^{8} +(2.49566 + 1.44087i) q^{9} +(-0.183472 + 0.229216i) q^{10} +(-3.91706 - 1.04957i) q^{11} +(0.482151 + 0.482151i) q^{12} +(-3.52539 + 0.756068i) q^{13} -0.365201i q^{14} +(-0.764295 + 0.0847187i) q^{15} +(-1.94843 - 3.37478i) q^{16} +(-2.34186 + 0.627499i) q^{17} +0.378379i q^{18} +(-0.491577 - 1.83459i) q^{19} +(4.38287 + 0.668703i) q^{20} +(0.676351 - 0.676351i) q^{21} +(-0.137812 - 0.514321i) q^{22} +(7.70544 + 2.06467i) q^{23} +(-0.0465459 + 0.173712i) q^{24} +(-3.67751 + 3.38761i) q^{25} +(-0.317420 - 0.351240i) q^{26} +(-1.43027 + 1.43027i) q^{27} +(-4.77595 + 2.75740i) q^{28} +(3.96565 - 2.28957i) q^{29} +(-0.0598105 - 0.0813472i) q^{30} +(3.87352 + 3.87352i) q^{31} +(0.778780 - 1.34889i) q^{32} +(0.697292 - 1.20775i) q^{33} +(-0.225100 - 0.225100i) q^{34} +(0.938043 - 6.14819i) q^{35} +(4.94829 - 2.85689i) q^{36} +(6.07101 - 3.50510i) q^{37} +(0.176341 - 0.176341i) q^{38} +(0.0626346 - 1.23835i) q^{39} +(0.425244 + 1.08928i) q^{40} +(-1.66178 + 6.20184i) q^{41} +(0.121312 + 0.0325055i) q^{42} +(-1.67299 - 6.24368i) q^{43} +(-5.68554 + 5.68554i) q^{44} +(-0.971891 + 6.37004i) q^{45} +(0.271096 + 1.01174i) q^{46} +0.512375i q^{47} +(1.29445 - 0.346847i) q^{48} +(0.368015 + 0.637420i) q^{49} +(-0.626643 - 0.195774i) q^{50} -0.833767i q^{51} +(-2.19674 + 6.80307i) q^{52} +(-1.32662 - 1.32662i) q^{53} +(-0.256537 - 0.0687390i) q^{54} +(-0.999006 - 9.01260i) q^{55} +(-1.25964 - 0.727255i) q^{56} +0.653165 q^{57} +(0.520700 + 0.300626i) q^{58} +(-2.53667 + 0.679700i) q^{59} +(-0.612235 + 1.39638i) q^{60} +(0.641767 - 1.11157i) q^{61} +(-0.186162 + 0.694764i) q^{62} +(-4.00759 - 6.94135i) q^{63} -7.58920 q^{64} +(-4.44160 - 6.72846i) q^{65} +0.183113 q^{66} +(-1.80814 - 3.13180i) q^{67} +(-1.24418 + 4.64334i) q^{68} +(-1.37168 + 2.37581i) q^{69} +(0.760703 - 0.296970i) q^{70} +(-6.20800 + 1.66343i) q^{71} +(1.30509 + 0.753497i) q^{72} +9.93250 q^{73} +(0.797139 + 0.460228i) q^{74} +(-0.797968 - 1.52311i) q^{75} +(-3.63755 - 0.974678i) q^{76} +(7.97556 + 7.97556i) q^{77} +(0.144927 - 0.0741773i) q^{78} +8.37577i q^{79} +(5.44515 - 6.80278i) q^{80} +(3.97480 + 6.88456i) q^{81} +(-0.814318 + 0.218196i) q^{82} +3.17194i q^{83} +(-0.490855 - 1.83190i) q^{84} +(-3.21139 - 4.36775i) q^{85} +(0.600143 - 0.600143i) q^{86} +(0.407576 + 1.52109i) q^{87} +(-2.04842 - 0.548871i) q^{88} +(-1.61226 + 6.01705i) q^{89} +(-0.788152 + 0.307686i) q^{90} +(9.54319 + 3.08154i) q^{91} +(11.1843 - 11.1843i) q^{92} +(-1.63147 + 0.941930i) q^{93} +(-0.0582629 + 0.0336381i) q^{94} +(3.42165 - 2.51577i) q^{95} +(0.378755 + 0.378755i) q^{96} +(5.88500 - 10.1931i) q^{97} +(-0.0483213 + 0.0836950i) q^{98} +(-8.26335 - 8.26335i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9} - 10 q^{10} - 16 q^{11} + 24 q^{12} + 2 q^{13} + 12 q^{15} - 2 q^{16} - 10 q^{17} + 20 q^{19} + 14 q^{20} + 4 q^{21}+ \cdots - 60 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9 - 10 * q^10 - 16 * q^11 + 24 * q^12 + 2 * q^13 + 12 * q^15 - 2 * q^16 - 10 * q^17 + 20 * q^19 + 14 * q^20 + 4 * q^21 + 16 * q^22 - 2 * q^23 - 32 * q^24 - 18 * q^25 - 24 * q^26 + 4 * q^27 + 6 * q^28 + 14 * q^30 - 6 * q^32 - 18 * q^33 - 2 * q^34 - 20 * q^35 + 36 * q^36 + 42 * q^37 + 8 * q^38 - 4 * q^39 - 16 * q^40 + 10 * q^41 - 56 * q^42 - 22 * q^43 + 36 * q^44 + 52 * q^45 + 4 * q^46 + 28 * q^48 - 18 * q^49 + 44 * q^50 + 46 * q^52 - 10 * q^53 + 48 * q^54 + 26 * q^55 - 12 * q^57 - 90 * q^58 + 16 * q^59 - 92 * q^60 - 16 * q^61 - 40 * q^62 - 32 * q^63 - 20 * q^64 + 8 * q^65 - 32 * q^66 - 58 * q^67 + 28 * q^68 + 16 * q^69 + 32 * q^70 - 16 * q^71 - 66 * q^72 + 72 * q^73 - 18 * q^74 - 34 * q^75 - 64 * q^76 + 28 * q^77 + 32 * q^78 - 34 * q^80 - 14 * q^81 + 22 * q^82 + 40 * q^84 - 6 * q^85 + 60 * q^86 + 62 * q^87 + 50 * q^88 + 6 * q^89 - 46 * q^90 + 8 * q^91 - 8 * q^92 + 48 * q^93 + 48 * q^94 + 14 * q^95 + 56 * q^96 - 22 * q^97 + 4 * q^98 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more