LMFDB - Embedded newform 280.2.bv.e.117.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(117,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 3, 10]))

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

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

chi := DirichletCharacter("280.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bv (of order $12$, 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			117.10
Character	$\chi$	$=$	280.117
Dual form			280.2.bv.e.213.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.910407 - 1.08220i) q^{2} +(-0.0340321 - 0.00911887i) q^{3} +(-0.342320 + 1.97049i) q^{4} +(-1.86153 + 1.23883i) q^{5} +(0.0211146 + 0.0451315i) q^{6} +(1.05182 - 2.42769i) q^{7} +(2.44411 - 1.42349i) q^{8} +(-2.59700 - 1.49938i) q^{9} +O(q^{10})$	\(q+(-0.910407 - 1.08220i) q^{2} +(-0.0340321 - 0.00911887i) q^{3} +(-0.342320 + 1.97049i) q^{4} +(-1.86153 + 1.23883i) q^{5} +(0.0211146 + 0.0451315i) q^{6} +(1.05182 - 2.42769i) q^{7} +(2.44411 - 1.42349i) q^{8} +(-2.59700 - 1.49938i) q^{9} +(3.03542 + 0.886711i) q^{10} +(-3.20347 + 1.84952i) q^{11} +(0.0296185 - 0.0639382i) q^{12} +(-0.508427 + 0.508427i) q^{13} +(-3.58483 + 1.07190i) q^{14} +(0.0746485 - 0.0251850i) q^{15} +(-3.76563 - 1.34907i) q^{16} +(-5.87372 - 1.57386i) q^{17} +(0.741697 + 4.17552i) q^{18} +(-4.54459 - 2.62382i) q^{19} +(-1.80386 - 4.09220i) q^{20} +(-0.0579334 + 0.0730279i) q^{21} +(4.91802 + 1.78298i) q^{22} +(1.86304 + 6.95298i) q^{23} +(-0.0961589 + 0.0261566i) q^{24} +(1.93059 - 4.61225i) q^{25} +(1.01310 + 0.0873452i) q^{26} +(0.149448 + 0.149448i) q^{27} +(4.42367 + 2.90364i) q^{28} -0.813729 q^{29} +(-0.0952157 - 0.0578562i) q^{30} +(-0.863133 + 0.498330i) q^{31} +(1.96829 + 5.30338i) q^{32} +(0.125886 - 0.0337312i) q^{33} +(3.64424 + 7.78940i) q^{34} +(1.04950 + 5.82225i) q^{35} +(3.84351 - 4.60409i) q^{36} +(-0.881982 - 3.29160i) q^{37} +(1.29792 + 7.30691i) q^{38} +(0.0219391 - 0.0126666i) q^{39} +(-2.78633 + 5.67771i) q^{40} -2.91694i q^{41} +(0.131774 - 0.00378949i) q^{42} +(0.934569 + 0.934569i) q^{43} +(-2.54785 - 6.94552i) q^{44} +(6.69188 - 0.426106i) q^{45} +(5.82839 - 8.34623i) q^{46} +(0.946701 + 3.53314i) q^{47} +(0.115850 + 0.0802501i) q^{48} +(-4.78735 - 5.10698i) q^{49} +(-6.74900 + 2.10973i) q^{50} +(0.185543 + 0.107123i) q^{51} +(-0.827805 - 1.17589i) q^{52} +(2.72039 - 10.1526i) q^{53} +(0.0256745 - 0.297792i) q^{54} +(3.67211 - 7.41151i) q^{55} +(-0.885012 - 7.43080i) q^{56} +(0.130736 + 0.130736i) q^{57} +(0.740824 + 0.880619i) q^{58} +(-9.24055 + 5.33503i) q^{59} +(0.0240730 + 0.155715i) q^{60} +(-2.23243 + 3.86669i) q^{61} +(1.32509 + 0.480401i) q^{62} +(-6.37160 + 4.72763i) q^{63} +(3.94738 - 6.95832i) q^{64} +(0.316597 - 1.57631i) q^{65} +(-0.151112 - 0.105525i) q^{66} +(10.0105 + 2.68231i) q^{67} +(5.11196 - 11.0353i) q^{68} -0.253613i q^{69} +(5.34537 - 6.43638i) q^{70} +3.86261 q^{71} +(-8.48171 + 0.0321392i) q^{72} +(3.10790 - 11.5988i) q^{73} +(-2.75921 + 3.95118i) q^{74} +(-0.107761 + 0.139360i) q^{75} +(6.72591 - 8.05687i) q^{76} +(1.12060 + 9.72240i) q^{77} +(-0.0336813 - 0.0122108i) q^{78} +(3.47881 + 2.00849i) q^{79} +(8.68112 - 2.15365i) q^{80} +(4.49441 + 7.78455i) q^{81} +(-3.15671 + 2.65560i) q^{82} +(7.44858 - 7.44858i) q^{83} +(-0.124069 - 0.139156i) q^{84} +(12.8839 - 4.34676i) q^{85} +(0.160554 - 1.86223i) q^{86} +(0.0276929 + 0.00742029i) q^{87} +(-5.19687 + 9.08054i) q^{88} +(-5.26687 + 9.12248i) q^{89} +(-6.55346 - 6.85403i) q^{90} +(0.699530 + 1.76908i) q^{91} +(-14.3385 + 1.29096i) q^{92} +(0.0339184 - 0.00908841i) q^{93} +(2.96168 - 4.24111i) q^{94} +(11.7104 - 0.745660i) q^{95} +(-0.0186242 - 0.198434i) q^{96} +(-4.54133 + 4.54133i) q^{97} +(-1.16835 + 9.83031i) q^{98} +11.0926 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 2 q^{2} + 12 q^{7} + 4 q^{8}+O(q^{10}) $ 160 * q - 2 * q^2 + 12 * q^7 + 4 * q^8	$ 160 q - 2 q^{2} + 12 q^{7} + 4 q^{8} - 6 q^{10} + 6 q^{12} - 8 q^{15} + 4 q^{16} - 12 q^{17} - 28 q^{18} - 24 q^{22} - 16 q^{23} + 20 q^{25} - 12 q^{26} - 46 q^{28} + 32 q^{30} + 48 q^{31} + 18 q^{32} - 12 q^{33} - 32 q^{36} - 48 q^{38} + 54 q^{40} + 6 q^{42} - 64 q^{46} - 132 q^{47} - 12 q^{50} - 20 q^{56} - 88 q^{57} + 6 q^{58} + 34 q^{60} - 32 q^{63} - 28 q^{65} - 180 q^{66} + 60 q^{68} - 108 q^{70} - 160 q^{71} + 52 q^{72} + 84 q^{73} + 48 q^{78} - 48 q^{80} + 16 q^{81} - 90 q^{82} - 84 q^{86} - 12 q^{87} + 44 q^{88} + 36 q^{92} - 20 q^{95} - 48 q^{96} - 94 q^{98}+O(q^{100}) $ 160 * q - 2 * q^2 + 12 * q^7 + 4 * q^8 - 6 * q^10 + 6 * q^12 - 8 * q^15 + 4 * q^16 - 12 * q^17 - 28 * q^18 - 24 * q^22 - 16 * q^23 + 20 * q^25 - 12 * q^26 - 46 * q^28 + 32 * q^30 + 48 * q^31 + 18 * q^32 - 12 * q^33 - 32 * q^36 - 48 * q^38 + 54 * q^40 + 6 * q^42 - 64 * q^46 - 132 * q^47 - 12 * q^50 - 20 * q^56 - 88 * q^57 + 6 * q^58 + 34 * q^60 - 32 * q^63 - 28 * q^65 - 180 * q^66 + 60 * q^68 - 108 * q^70 - 160 * q^71 + 52 * q^72 + 84 * q^73 + 48 * q^78 - 48 * q^80 + 16 * q^81 - 90 * q^82 - 84 * q^86 - 12 * q^87 + 44 * q^88 + 36 * q^92 - 20 * q^95 - 48 * q^96 - 94 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.910407	−	1.08220i	−0.643755	−	0.765232i
$2$	−0.910407	−	1.08220i	−0.643755	−	0.765232i
$3$	−0.0340321	−	0.00911887i	−0.0196484	−	0.00526478i	0.248981	−	0.968508i	$-0.419904\pi$
$3$	−0.0340321	−	0.00911887i	−0.0196484	−	0.00526478i	−0.268630	+	0.963243i	$0.586571\pi$
$4$	−0.342320	+	1.97049i	−0.171160	+	0.985243i
$5$	−1.86153	+	1.23883i	−0.832502	+	0.554022i
$5$	−1.86153	+	1.23883i	−0.832502	+	0.554022i
$6$	0.0211146	+	0.0451315i	0.00861999	+	0.0184248i
$7$	1.05182	−	2.42769i	0.397551	−	0.917580i
$7$	1.05182	−	2.42769i	0.397551	−	0.917580i
$8$	2.44411	−	1.42349i	0.864125	−	0.503278i
$9$	−2.59700	−	1.49938i	−0.865667	−	0.499793i
$10$	3.03542	+	0.886711i	0.959883	+	0.280403i
$11$	−3.20347	+	1.84952i	−0.965883	+	0.557653i	−0.897979	−	0.440039i	$-0.854965\pi$
$11$	−3.20347	+	1.84952i	−0.965883	+	0.557653i	−0.0679041	+	0.997692i	$0.521631\pi$
$12$	0.0296185	−	0.0639382i	0.00855012	−	0.0184574i
$13$	−0.508427	+	0.508427i	−0.141012	+	0.141012i	−0.774089	−	0.633077i	$-0.781792\pi$
$13$	−0.508427	+	0.508427i	−0.141012	+	0.141012i	0.633077	+	0.774089i	$0.281792\pi$
$14$	−3.58483	+	1.07190i	−0.958087	+	0.286478i
$15$	0.0746485	−	0.0251850i	0.0192742	−	0.00650273i
$16$	−3.76563	−	1.34907i	−0.941409	−	0.337268i
$17$	−5.87372	−	1.57386i	−1.42459	−	0.381717i	−0.537478	−	0.843278i	$-0.680623\pi$
$17$	−5.87372	−	1.57386i	−1.42459	−	0.381717i	−0.887108	+	0.461561i	$0.847289\pi$
$18$	0.741697	+	4.17552i	0.174820	+	0.984180i
$19$	−4.54459	−	2.62382i	−1.04260	−	0.601946i	−0.122032	−	0.992526i	$-0.538941\pi$
$19$	−4.54459	−	2.62382i	−1.04260	−	0.601946i	−0.920569	+	0.390580i	$0.872274\pi$
$20$	−1.80386	−	4.09220i	−0.403356	−	0.915043i
$21$	−0.0579334	+	0.0730279i	−0.0126421	+	0.0159360i
$22$	4.91802	+	1.78298i	1.04852	+	0.380133i
$23$	1.86304	+	6.95298i	0.388472	+	1.44980i	0.832621	+	0.553843i	$0.186839\pi$
$23$	1.86304	+	6.95298i	0.388472	+	1.44980i	−0.444149	+	0.895953i	$0.646494\pi$
$24$	−0.0961589	+	0.0261566i	−0.0196283	+	0.00533920i
$25$	1.93059	−	4.61225i	0.386119	−	0.922449i
$26$	1.01310	+	0.0873452i	0.198685	+	0.0171298i
$27$	0.149448	+	0.149448i	0.0287614	+	0.0287614i
$28$	4.42367	+	2.90364i	0.835995	+	0.548737i
$29$	−0.813729			−0.151106			−0.0755528	−	0.997142i	$-0.524072\pi$
$29$	−0.813729			−0.151106			−0.0755528	+	0.997142i	$0.524072\pi$
$30$	−0.0952157	−	0.0578562i	−0.0173839	−	0.0105630i
$31$	−0.863133	+	0.498330i	−0.155023	+	0.0895027i	−0.575505	−	0.817798i	$-0.695194\pi$
$31$	−0.863133	+	0.498330i	−0.155023	+	0.0895027i	0.420482	+	0.907301i	$0.361861\pi$
$32$	1.96829	+	5.30338i	0.347948	+	0.937514i
$33$	0.125886	−	0.0337312i	0.0219140	−	0.00587184i
$34$	3.64424	+	7.78940i	0.624982	+	1.33587i
$35$	1.04950	+	5.82225i	0.177398	+	0.984139i
$36$	3.84351	−	4.60409i	0.640585	−	0.767348i
$37$	−0.881982	−	3.29160i	−0.144997	−	0.541136i	−0.999756	−	0.0221102i	$-0.992962\pi$
$37$	−0.881982	−	3.29160i	−0.144997	−	0.541136i	0.854759	−	0.519026i	$-0.173705\pi$
$38$	1.29792	+	7.30691i	0.210551	+	1.18534i
$39$	0.0219391	−	0.0126666i	0.00351307	−	0.00202827i
$40$	−2.78633	+	5.67771i	−0.440558	+	0.897724i
$41$		−	2.91694i		−	0.455549i	−0.973714	−	0.227775i	$-0.926855\pi$
$41$		−	2.91694i		−	0.455549i	0.973714	−	0.227775i	$-0.0731449\pi$
$42$	0.131774	−	0.00378949i	0.0203332	−	0.000584731i
$43$	0.934569	+	0.934569i	0.142521	+	0.142521i	0.774767	−	0.632247i	$-0.217867\pi$
$43$	0.934569	+	0.934569i	0.142521	+	0.142521i	−0.632247	+	0.774767i	$0.717867\pi$
$44$	−2.54785	−	6.94552i	−0.384103	−	1.04708i
$45$	6.69188	−	0.426106i	0.997566	−	0.0635202i
$46$	5.82839	−	8.34623i	0.859350	−	1.23058i
$47$	0.946701	+	3.53314i	0.138091	+	0.515361i	0.999966	+	0.00824095i	$0.00262321\pi$
$47$	0.946701	+	3.53314i	0.138091	+	0.515361i	−0.861876	+	0.507120i	$0.830710\pi$
$48$	0.115850	+	0.0802501i	0.0167216	+	0.0115831i
$49$	−4.78735	−	5.10698i	−0.683907	−	0.729569i
$50$	−6.74900	+	2.10973i	−0.954453	+	0.298361i
$51$	0.185543	+	0.107123i	0.0259812	+	0.0150003i
$52$	−0.827805	−	1.17589i	−0.114796	−	0.163067i
$53$	2.72039	−	10.1526i	0.373674	−	1.39457i	−0.481598	−	0.876392i	$-0.659943\pi$
$53$	2.72039	−	10.1526i	0.373674	−	1.39457i	0.855272	−	0.518179i	$-0.173390\pi$
$54$	0.0256745	−	0.297792i	0.00349385	−	0.0405244i
$55$	3.67211	−	7.41151i	0.495147	−	0.999367i
$56$	−0.885012	−	7.43080i	−0.118265	−	0.992982i
$57$	0.130736	+	0.130736i	0.0173164	+	0.0173164i
$58$	0.740824	+	0.880619i	0.0972750	+	0.115631i
$59$	−9.24055	+	5.33503i	−1.20302	+	0.694562i	−0.961225	−	0.275766i	$-0.911069\pi$
$59$	−9.24055	+	5.33503i	−1.20302	+	0.694562i	−0.241792	+	0.970328i	$0.577735\pi$
$60$	0.0240730	+	0.155715i	0.00310781	+	0.0201028i
$61$	−2.23243	+	3.86669i	−0.285834	+	0.495079i	−0.972811	−	0.231600i	$-0.925604\pi$
$61$	−2.23243	+	3.86669i	−0.285834	+	0.495079i	0.686977	+	0.726679i	$0.258937\pi$
$62$	1.32509	+	0.480401i	0.168287	+	0.0610109i
$63$	−6.37160	+	4.72763i	−0.802747	+	0.595626i
$64$	3.94738	−	6.95832i	0.493423	−	0.869790i
$65$	0.316597	−	1.57631i	0.0392691	−	0.195517i
$66$	−0.151112	−	0.105525i	−0.0186006	−	0.0129893i
$67$	10.0105	+	2.68231i	1.22298	+	0.327696i	0.811841	−	0.583878i	$-0.198465\pi$
$67$	10.0105	+	2.68231i	1.22298	+	0.327696i	0.411136	+	0.911574i	$0.365132\pi$
$68$	5.11196	−	11.0353i	0.619916	−	1.33823i
$69$		−	0.253613i		−	0.0305314i
$70$	5.34537	−	6.43638i	0.638894	−	0.769295i
$71$	3.86261			0.458408			0.229204	−	0.973378i	$-0.426388\pi$
$71$	3.86261			0.458408			0.229204	+	0.973378i	$0.426388\pi$
$72$	−8.48171	+	0.0321392i	−0.999579	+	0.00378765i
$73$	3.10790	−	11.5988i	0.363752	−	1.35754i	−0.505352	−	0.862913i	$-0.668637\pi$
$73$	3.10790	−	11.5988i	0.363752	−	1.35754i	0.869104	−	0.494629i	$-0.164696\pi$
$74$	−2.75921	+	3.95118i	−0.320752	+	0.459315i
$75$	−0.107761	+	0.139360i	−0.0124431	+	0.0160919i
$76$	6.72591	−	8.05687i	0.771515	−	0.924186i
$77$	1.12060	+	9.72240i	0.127704	+	1.10797i
$78$	−0.0336813	−	0.0122108i	−0.00381366	−	0.00138261i
$79$	3.47881	+	2.00849i	0.391396	+	0.225973i	0.682765	−	0.730638i	$-0.260777\pi$
$79$	3.47881	+	2.00849i	0.391396	+	0.225973i	−0.291369	+	0.956611i	$0.594111\pi$
$80$	8.68112	−	2.15365i	0.970578	−	0.240785i
$81$	4.49441	+	7.78455i	0.499379	+	0.864951i
$82$	−3.15671	+	2.65560i	−0.348601	+	0.293262i
$83$	7.44858	−	7.44858i	0.817588	−	0.817588i	−0.168170	−	0.985758i	$-0.553786\pi$
$83$	7.44858	−	7.44858i	0.817588	−	0.817588i	0.985758	+	0.168170i	$0.0537858\pi$
$84$	−0.124069	−	0.139156i	−0.0135370	−	0.0151832i
$85$	12.8839	−	4.34676i	1.39745	−	0.471473i
$86$	0.160554	−	1.86223i	0.0173130	−	0.200809i
$87$	0.0276929	+	0.00742029i	0.00296899	+	0.000795539i
$88$	−5.19687	+	9.08054i	−0.553989	+	0.967989i
$89$	−5.26687	+	9.12248i	−0.558287	+	0.966981i	0.439353	+	0.898315i	$0.355208\pi$
$89$	−5.26687	+	9.12248i	−0.558287	+	0.966981i	−0.997640	+	0.0686666i	$0.978126\pi$
$90$	−6.55346	−	6.85403i	−0.690795	−	0.722478i
$91$	0.699530	+	1.76908i	0.0733306	+	0.185450i
$92$	−14.3385	+	1.29096i	−1.49489	+	0.134592i
$93$	0.0339184	−	0.00908841i	0.00351718	−	0.000942425i
$94$	2.96168	−	4.24111i	0.305474	−	0.437437i
$95$	11.7104	−	0.745660i	1.20146	−	0.0765031i
$96$	−0.0186242	−	0.198434i	−0.00190082	−	0.0202526i
$97$	−4.54133	+	4.54133i	−0.461102	+	0.461102i	−0.899017	−	0.437914i	$-0.855717\pi$
$97$	−4.54133	+	4.54133i	−0.461102	+	0.461102i	0.437914	+	0.899017i	$0.355717\pi$
$98$	−1.16835	+	9.83031i	−0.118021	+	0.993011i
$99$	11.0926			1.11484
$100$	8.42749	+	5.38307i	0.842749	+	0.538307i
$101$	−5.50275	−	9.53104i	−0.547544	−	0.948374i	−0.998442	−	0.0557988i	$-0.982229\pi$
$101$	−5.50275	−	9.53104i	−0.547544	−	0.948374i	0.450898	−	0.892576i	$-0.351104\pi$
$102$	−0.0529906	−	0.298321i	−0.00524685	−	0.0295382i
$103$	0.967194	−	0.259159i	0.0953005	−	0.0255357i	−0.210854	−	0.977518i	$-0.567624\pi$
$103$	0.967194	−	0.259159i	0.0953005	−	0.0255357i	0.306154	+	0.951982i	$0.400958\pi$
$104$	−0.518915	+	1.96639i	−0.0508838	+	0.192821i
$105$	0.0173755	−	0.207714i	0.00169568	−	0.0202708i
$106$	−13.4639	+	6.29902i	−1.30773	+	0.611815i
$107$	−4.29252	−	16.0199i	−0.414973	−	1.54870i	−0.784889	−	0.619636i	$-0.787280\pi$
$107$	−4.29252	−	16.0199i	−0.414973	−	1.54870i	0.369916	−	0.929065i	$-0.379386\pi$
$108$	−0.345645	+	0.243327i	−0.0332597	+	0.0234141i
$109$	−0.123597	−	0.214076i	−0.0118385	−	0.0205048i	0.860045	−	0.510217i	$-0.170435\pi$
$109$	−0.123597	−	0.214076i	−0.0118385	−	0.0205048i	−0.871884	+	0.489713i	$0.837102\pi$
$110$	−11.3639	+	2.77352i	−1.08350	+	0.264445i
$111$			0.120063i			0.0113959i
$112$	−7.23590	+	7.72281i	−0.683728	+	0.729737i
$113$	−10.8352	+	10.8352i	−1.01929	+	1.01929i	−0.0194757	+	0.999810i	$0.506200\pi$
$113$	−10.8352	+	10.8352i	−1.01929	+	1.01929i	−0.999810	+	0.0194757i	$0.993800\pi$
$114$	0.0224597	−	0.260505i	0.00210354	−	0.0243985i
$115$	−12.0817	−	10.6352i	−1.12662	−	0.991736i
$116$	0.278555	−	1.60344i	0.0258632	−	0.148876i
$117$	2.08271	−	0.558061i	0.192547	−	0.0515928i
$118$	14.1862	+	5.14309i	1.30595	+	0.473459i
$119$	−9.99893	+	12.6041i	−0.916601	+	1.15542i
$120$	0.146599	−	0.167816i	0.0133826	−	0.0153194i
$121$	1.34148	−	2.32351i	0.121953	−	0.211228i
$122$	6.21696	−	1.10432i	0.562857	−	0.0999801i
$123$	−0.0265992	+	0.0992695i	−0.00239837	+	0.00895083i
$124$	−0.686485	−	1.87138i	−0.0616482	−	0.168055i
$125$	2.11994	+	10.9775i	0.189613	+	0.981859i
$126$	10.9170	+	2.59129i	0.972564	+	0.230850i
$127$	7.30879	+	7.30879i	0.648550	+	0.648550i	0.952643	−	0.304092i	$-0.0983531\pi$
$127$	7.30879	+	7.30879i	0.648550	+	0.648550i	−0.304092	+	0.952643i	$0.598353\pi$
$128$	−11.1240	+	2.06304i	−0.983234	+	0.182348i
$129$	−0.0232831	−	0.0403276i	−0.00204997	−	0.00355065i
$130$	−1.99412	+	1.09246i	−0.174896	+	0.0958151i
$131$	−8.42271	+	14.5886i	−0.735896	+	1.27461i	0.218433	+	0.975852i	$0.429905\pi$
$131$	−8.42271	+	14.5886i	−0.735896	+	1.27461i	−0.954329	+	0.298757i	$0.903428\pi$
$132$	0.0233734	+	0.259604i	0.00203439	+	0.0225957i
$133$	−11.1499	+	8.27307i	−0.966820	+	0.717366i
$134$	−6.21083	−	13.2754i	−0.536534	−	1.14682i
$135$	−0.463344	−	0.0930614i	−0.0398783	−	0.00800945i
$136$	−16.5964	+	4.51446i	−1.42313	+	0.387112i
$137$	3.15289	−	11.7668i	0.269370	−	1.00530i	−0.690151	−	0.723665i	$-0.742456\pi$
$137$	3.15289	−	11.7668i	0.269370	−	1.00530i	0.959521	−	0.281637i	$-0.0908773\pi$
$138$	−0.274461	+	0.230891i	−0.0233636	+	0.0196548i
$139$			2.32838i			0.197490i	0.995113	+	0.0987451i	$0.0314829\pi$
$139$			2.32838i			0.197490i	−0.995113	+	0.0987451i	$0.968517\pi$
$140$	−11.8319	+	0.0749626i	−0.999980	+	0.00633550i
$141$		−	0.128873i		−	0.0108531i
$142$	−3.51655	−	4.18012i	−0.295102	−	0.350788i
$143$	0.688383	−	2.56908i	0.0575655	−	0.214837i
$144$	7.75659	+	9.14966i	0.646382	+	0.762472i
$145$	1.51478	−	1.00807i	0.125796	−	0.0837159i
$146$	−15.3817	+	7.19629i	−1.27300	+	0.595569i
$147$	0.116354	+	0.217457i	0.00959669	+	0.0179355i
$148$	6.78798	−	0.611154i	0.557968	−	0.0502365i
$149$	11.3140	−	19.5964i	0.926880	−	1.60540i	0.138370	−	0.990381i	$-0.455814\pi$
$149$	11.3140	−	19.5964i	0.926880	−	1.60540i	0.788510	−	0.615022i	$-0.210853\pi$
$150$	0.248921	−	0.0102552i	0.0203243	−	0.000837333i
$151$	3.17989	+	5.50774i	0.258776	+	0.448213i	0.965914	−	0.258862i	$-0.0833475\pi$
$151$	3.17989	+	5.50774i	0.258776	+	0.448213i	−0.707138	+	0.707075i	$0.750014\pi$
$152$	−14.8425	+	0.0562417i	−1.20388	+	0.00456180i
$153$	12.8942	+	12.8942i	1.04244	+	1.04244i
$154$	9.50139	−	10.0640i	0.765644	−	0.810984i
$155$	0.989401	−	1.99693i	0.0794706	−	0.160397i
$156$	0.0174491	+	0.0475668i	0.00139705	+	0.00380839i
$157$	−4.93723	+	18.4260i	−0.394034	+	1.47056i	0.429385	+	0.903122i	$0.358730\pi$
$157$	−4.93723	+	18.4260i	−0.394034	+	1.47056i	−0.823419	+	0.567434i	$0.807936\pi$
$158$	−0.993538	−	5.59331i	−0.0790416	−	0.444980i
$159$	−0.185161	+	0.320709i	−0.0146842	+	0.0254338i
$160$	−10.2340	−	7.43402i	−0.809071	−	0.587711i
$161$	18.8393	+	2.79039i	1.48474	+	0.219913i
$162$	4.33271	−	11.9510i	0.340410	−	0.938957i
$163$	−2.11633	+	0.567069i	−0.165764	+	0.0444163i	−0.340746	−	0.940155i	$-0.610680\pi$
$163$	−2.11633	+	0.567069i	−0.165764	+	0.0444163i	0.174983	+	0.984572i	$0.444013\pi$
$164$	5.74779	+	0.998525i	0.448827	+	0.0779717i
$165$	−0.192554	+	0.218744i	−0.0149903	+	0.0170292i
$166$	−14.8421	−	1.27963i	−1.15197	−	0.0993183i
$167$	−6.56962	+	6.56962i	−0.508372	+	0.508372i	−0.914027	−	0.405654i	$-0.867044\pi$
$167$	−6.56962	+	6.56962i	−0.508372	+	0.508372i	0.405654	+	0.914027i	$0.367044\pi$
$168$	−0.0376417	+	0.260956i	−0.00290412	+	0.0201332i
$169$			12.4830i			0.960231i
$170$	−16.4336	−	9.98560i	−1.26040	−	0.765861i
$171$	7.86821	+	13.6281i	0.601697	+	1.04217i
$172$	−2.16148	+	1.52164i	−0.164811	+	0.116024i
$173$	−2.76302	−	10.3117i	−0.210069	−	0.783987i	−0.987845	−	0.155445i	$-0.950319\pi$
$173$	−2.76302	−	10.3117i	−0.210069	−	0.783987i	0.777776	−	0.628542i	$-0.216348\pi$
$174$	−0.0171816	−	0.0367248i	−0.00130253	−	0.00278410i
$175$	−9.16646	−	9.53813i	−0.692920	−	0.721015i
$176$	14.5582	−	2.64292i	1.09737	−	0.199217i
$177$	0.363125	−	0.0972990i	0.0272941	−	0.00731344i
$178$	14.6674	−	2.60536i	1.09936	−	0.195280i
$179$	−5.77181	−	9.99707i	−0.431406	−	0.747216i	0.565589	−	0.824687i	$-0.308649\pi$
$179$	−5.77181	−	9.99707i	−0.431406	−	0.747216i	−0.996995	+	0.0774709i	$0.975316\pi$
$180$	−1.45112	+	13.3321i	−0.108160	+	0.993717i
$181$	−16.8772			−1.25447			−0.627236	−	0.778829i	$-0.715814\pi$
$181$	−16.8772			−1.25447			−0.627236	+	0.778829i	$0.715814\pi$
$182$	1.27764	−	2.36761i	0.0947051	−	0.175499i
$183$	0.111234	−	0.111234i	0.00822267	−	0.00822267i
$184$	14.4510	+	14.3418i	1.06534	+	1.05730i
$185$	5.71958	+	5.03479i	0.420512	+	0.370165i
$186$	−0.0407150	−	0.0284324i	−0.00298537	−	0.00208477i
$187$	21.7272	−	5.82178i	1.58885	−	0.425731i
$188$	−7.28607	+	0.655999i	−0.531391	+	0.0478437i
$189$	0.520007	−	0.205622i	0.0378250	−	0.0149568i
$190$	−11.4682	−	11.9941i	−0.831987	−	0.870145i
$191$	−4.62049	+	8.00293i	−0.334327	+	0.579072i	−0.983355	−	0.181693i	$-0.941842\pi$
$191$	−4.62049	+	8.00293i	−0.334327	+	0.579072i	0.649028	+	0.760764i	$0.275176\pi$
$192$	−0.197790	+	0.200810i	−0.0142742	+	0.0144922i
$193$	−9.86516	−	2.64336i	−0.710110	−	0.190273i	−0.114355	−	0.993440i	$-0.536480\pi$
$193$	−9.86516	−	2.64336i	−0.710110	−	0.190273i	−0.595754	+	0.803167i	$0.703147\pi$
$194$	9.04909	+	0.780177i	0.649687	+	0.0560135i
$195$	−0.0251486	+	0.0507581i	−0.00180093	+	0.00363486i
$196$	11.7020	−	7.68519i	0.835860	−	0.548942i
$197$	−3.28423	+	3.28423i	−0.233991	+	0.233991i	−0.814356	−	0.580365i	$-0.802910\pi$
$197$	−3.28423	+	3.28423i	−0.233991	+	0.233991i	0.580365	+	0.814356i	$0.302910\pi$
$198$	−10.0987	−	12.0044i	−0.717686	−	0.853114i
$199$	−12.0609	−	20.8902i	−0.854978	−	1.48087i	−0.876665	−	0.481101i	$-0.840237\pi$
$199$	−12.0609	−	20.8902i	−0.854978	−	1.48087i	0.0216874	−	0.999765i	$-0.493096\pi$
$200$	−1.84688	−	14.0210i	−0.130594	−	0.991436i
$201$	−0.316219	−	0.182569i	−0.0223044	−	0.0128774i
$202$	−5.30477	+	14.6322i	−0.373242	+	1.02952i
$203$	−0.855896	+	1.97548i	−0.0600721	+	0.138652i
$204$	−0.274600	+	0.328940i	−0.0192259	+	0.0230304i
$205$	3.61359	+	5.42997i	0.252384	+	0.379245i
$206$	−1.16100	−	0.810759i	−0.0808909	−	0.0564883i
$207$	5.58682	−	20.8503i	0.388311	−	1.44920i
$208$	2.60046	−	1.22865i	0.180309	−	0.0851913i
$209$	19.4113			1.34271
$210$	−0.240607	+	0.170300i	−0.0166034	+	0.0117518i
$211$			5.70817i			0.392967i	0.980507	+	0.196483i	$0.0629522\pi$
$211$			5.70817i			0.392967i	−0.980507	+	0.196483i	$0.937048\pi$
$212$	19.0744	+	8.83594i	1.31003	+	0.606855i
$213$	−0.131453	−	0.0352227i	−0.00900699	−	0.00241342i
$214$	−13.4288	+	19.2300i	−0.917975	+	1.31453i
$215$	−2.89750	−	0.581956i	−0.197608	−	0.0396890i
$216$	0.578006	+	0.152531i	0.0393284	+	0.0103784i
$217$	0.301930	+	2.61957i	0.0204963	+	0.177828i
$218$	−0.119150	+	0.328653i	−0.00806987	+	0.0222592i
$219$	−0.211537	+	0.366392i	−0.0142943	+	0.0247585i
$220$	13.3472	+	9.77295i	0.899871	+	0.658892i
$221$	3.78655	−	2.18617i	0.254711	−	0.147058i
$222$	0.129932	−	0.109306i	0.00872047	−	0.00733613i
$223$	−18.6221	−	18.6221i	−1.24703	−	1.24703i	−0.957027	−	0.289998i	$-0.906345\pi$
$223$	−18.6221	−	18.6221i	−1.24703	−	1.24703i	−0.289998	−	0.957027i	$-0.593655\pi$
$224$	14.9452	+	0.799803i	0.998571	+	0.0534391i
$225$	−11.9293	+	9.08332i	−0.795284	+	0.605554i
$226$	21.5902	+	1.86142i	1.43616	+	0.123820i
$227$	2.26823	−	8.46516i	0.150548	−	0.561852i	−0.848898	−	0.528557i	$-0.822733\pi$
$227$	2.26823	−	8.46516i	0.150548	−	0.561852i	0.999446	−	0.0332951i	$-0.0106001\pi$
$228$	−0.302366	+	0.212860i	−0.0200247	+	0.0140970i
$229$	8.62824	+	4.98152i	0.570170	+	0.329188i	0.757217	−	0.653163i	$-0.226558\pi$
$229$	8.62824	+	4.98152i	0.570170	+	0.329188i	−0.187047	+	0.982351i	$0.559892\pi$
$230$	−0.510165	+	22.7572i	−0.0336393	+	1.50056i
$231$	0.0505210	−	0.341092i	0.00332404	−	0.0224422i
$232$	−1.98885	+	1.15833i	−0.130574	+	0.0760482i
$233$	−4.72234	−	17.6240i	−0.309371	−	1.15459i	−0.929117	−	0.369785i	$-0.879431\pi$
$233$	−4.72234	−	17.6240i	−0.309371	−	1.15459i	0.619746	−	0.784802i	$-0.287235\pi$
$234$	−2.50005	−	1.74585i	−0.163433	−	0.114130i
$235$	−6.13927	−	5.40424i	−0.400482	−	0.352534i
$236$	−7.34939	−	20.0347i	−0.478405	−	1.30415i
$237$	−0.100076	−	0.100076i	−0.00650063	−	0.00650063i
$238$	22.7433	−	0.654041i	1.47423	−	0.0423952i
$239$		−	12.9234i		−	0.835943i	−0.908460	−	0.417971i	$-0.862741\pi$
$239$		−	12.9234i		−	0.835943i	0.908460	−	0.417971i	$-0.137259\pi$
$240$	−0.315075	−	0.00586890i	−0.0203380	−	0.000378836i
$241$	2.40560	−	1.38887i	0.154958	−	0.0894652i	−0.420516	−	0.907285i	$-0.638151\pi$
$241$	2.40560	−	1.38887i	0.154958	−	0.0894652i	0.575474	+	0.817820i	$0.304818\pi$
$242$	−3.73580	+	0.663589i	−0.240146	+	0.0426571i
$243$	−0.246074	−	0.918360i	−0.0157856	−	0.0589128i
$244$	−6.85505	−	5.72262i	−0.438850	−	0.366353i
$245$	15.2385	+	3.57609i	0.973551	+	0.228468i
$246$	0.131646	−	0.0615899i	0.00839342	−	0.00392683i
$247$	3.64462	−	0.976572i	0.231901	−	0.0621378i
$248$	−1.40023	+	2.44663i	−0.0889146	+	0.155361i
$249$	−0.321413	+	0.185568i	−0.0203687	+	0.0117599i
$250$	9.94988	−	12.2882i	0.629286	−	0.777174i
$251$	13.9354			0.879597			0.439798	−	0.898097i	$-0.355050\pi$
$251$	13.9354			0.879597			0.439798	+	0.898097i	$0.355050\pi$
$252$	−7.13462	−	14.1735i	−0.449439	−	0.892848i
$253$	−18.8279	−	18.8279i	−1.18370	−	1.18370i
$254$	1.25561	−	14.5636i	0.0787841	−	0.913799i
$255$	−0.478102	+	0.0304432i	−0.0299399	+	0.00190643i
$256$	12.3600	+	10.1602i	0.772500	+	0.635014i
$257$	−4.59860	−	17.1622i	−0.286852	−	1.07055i	−0.947475	−	0.319830i	$-0.896374\pi$
$257$	−4.59860	−	17.1622i	−0.286852	−	1.07055i	0.660623	−	0.750718i	$-0.270292\pi$
$258$	−0.0224454	+	0.0619115i	−0.00139739	+	0.00385444i
$259$	−8.91867	−	1.32099i	−0.554179	−	0.0820825i
$260$	2.99772	+	1.16345i	0.185911	+	0.0721543i
$261$	2.11325	+	1.22009i	0.130807	+	0.0755216i
$262$	23.4559	−	4.16645i	1.44911	−	0.257404i
$263$	6.58834	+	1.76534i	0.406255	+	0.108856i	0.456159	−	0.889898i	$-0.349225\pi$
$263$	6.58834	+	1.76534i	0.406255	+	0.108856i	−0.0499041	+	0.998754i	$0.515892\pi$
$264$	0.259665	−	0.261640i	0.0159813	−	0.0161028i
$265$	7.51332	+	22.2695i	0.461539	+	1.36801i
$266$	19.1041	+	4.53460i	1.17135	+	0.278034i
$267$	0.262429	−	0.262429i	0.0160604	−	0.0160604i
$268$	−8.71224	+	18.8074i	−0.532185	+	1.14884i
$269$	−22.9758	+	13.2651i	−1.40086	+	0.808788i	−0.994481	−	0.104916i	$-0.966542\pi$
$269$	−22.9758	+	13.2651i	−1.40086	+	0.808788i	−0.406380	+	0.913704i	$0.633209\pi$
$270$	0.321120	+	0.586155i	0.0195428	+	0.0356723i
$271$	1.19103	+	0.687640i	0.0723498	+	0.0417712i	0.535738	−	0.844384i	$-0.320033\pi$
$271$	1.19103	+	0.687640i	0.0723498	+	0.0417712i	−0.463389	+	0.886155i	$0.653367\pi$
$272$	19.9950	+	13.8506i	1.21238	+	0.839819i
$273$	−0.00767447	−	0.0665843i	−0.000464480	−	0.00402987i
$274$	−15.6044	+	7.30047i	−0.942697	+	0.441037i
$275$	2.34587	+	18.3459i	0.141461	+	1.10630i
$276$	0.499741	+	0.0868168i	0.0300809	+	0.00522576i
$277$	−14.9226	−	3.99849i	−0.896610	−	0.240246i	−0.219050	−	0.975714i	$-0.570296\pi$
$277$	−14.9226	−	3.99849i	−0.896610	−	0.240246i	−0.677560	+	0.735468i	$0.736962\pi$
$278$	2.51977	−	2.11977i	0.151126	−	0.127135i
$279$	2.98874			0.178931
$280$	10.8530	+	12.7363i	0.648590	+	0.761138i
$281$	−28.3438			−1.69085			−0.845426	−	0.534093i	$-0.820653\pi$
$281$	−28.3438			−1.69085			−0.845426	+	0.534093i	$0.820653\pi$
$282$	−0.139466	+	0.117327i	−0.00830510	+	0.00698670i
$283$	8.48792	+	2.27433i	0.504554	+	0.135195i	0.502113	−	0.864802i	$-0.332556\pi$
$283$	8.48792	+	2.27433i	0.504554	+	0.135195i	0.00244149	+	0.999997i	$0.499223\pi$
$284$	−1.32225	+	7.61122i	−0.0784610	+	0.451643i
$285$	−0.405328	−	0.0814090i	−0.0240096	−	0.00482225i
$286$	−3.40697	+	1.59394i	−0.201458	+	0.0942516i
$287$	−7.08142	−	3.06809i	−0.418003	−	0.181104i
$288$	2.84013	−	16.7241i	0.167356	−	0.985477i
$289$	17.3011	+	9.98880i	1.01771	+	0.587577i
$290$	−2.47000	−	0.721542i	−0.145044	−	0.0423704i
$291$	0.195963	−	0.113139i	0.0114875	−	0.00663234i
$292$	21.7915	+	10.0946i	1.27525	+	0.590741i
$293$	11.1478	−	11.1478i	0.651263	−	0.651263i	−0.302034	−	0.953297i	$-0.597666\pi$
$293$	11.1478	−	11.1478i	0.651263	−	0.651263i	0.953297	+	0.302034i	$0.0976657\pi$
$294$	0.129403	−	0.323892i	0.00754692	−	0.0188898i
$295$	10.5924	−	21.3788i	0.616711	−	1.24472i
$296$	−6.84121	−	6.78956i	−0.397637	−	0.394635i
$297$	−0.755162	−	0.202345i	−0.0438189	−	0.0117413i
$298$	−31.5076	+	5.59669i	−1.82519	+	0.324208i
$299$	−4.48231	−	2.58786i	−0.259219	−	0.149660i
$300$	−0.237718	−	0.260046i	−0.0137246	−	0.0150138i
$301$	3.25184	−	1.28585i	0.187433	−	0.0741149i
$302$	3.06549	−	8.45557i	0.176399	−	0.486563i
$303$	0.100358	+	0.374540i	0.00576540	+	0.0215168i
$304$	13.5735	+	16.0113i	0.778496	+	0.918313i
$305$	−0.634432	−	9.96357i	−0.0363275	−	0.570512i
$306$	2.21516	−	25.6932i	0.126633	−	1.46878i
$307$	−14.3040	−	14.3040i	−0.816373	−	0.816373i	0.169207	−	0.985580i	$-0.445879\pi$
$307$	−14.3040	−	14.3040i	−0.816373	−	0.816373i	−0.985580	+	0.169207i	$0.945879\pi$
$308$	−19.5415	−	1.12005i	−1.11348	−	0.0638206i
$309$	−0.0352789			−0.00200695
$310$	−3.06184	+	0.747289i	−0.173901	+	0.0424432i
$311$	−22.1979	+	12.8160i	−1.25873	+	0.726728i	−0.972827	−	0.231531i	$-0.925626\pi$
$311$	−22.1979	+	12.8160i	−1.25873	+	0.726728i	−0.285902	+	0.958259i	$0.592293\pi$
$312$	0.0355911	−	0.0621886i	0.00201495	−	0.00352073i
$313$	2.62831	−	0.704252i	0.148561	−	0.0398067i	−0.183772	−	0.982969i	$-0.558831\pi$
$313$	2.62831	−	0.704252i	0.148561	−	0.0398067i	0.332333	+	0.943162i	$0.392164\pi$
$314$	24.4355	−	11.4321i	1.37898	−	0.645149i
$315$	6.00419	−	16.6940i	0.338298	−	0.940599i
$316$	−5.14857	+	6.16740i	−0.289629	+	0.346943i
$317$	6.88000	+	25.6765i	0.386419	+	1.44214i	0.835917	+	0.548855i	$0.184936\pi$
$317$	6.88000	+	25.6765i	0.386419	+	1.44214i	−0.449498	+	0.893281i	$0.648397\pi$
$318$	0.515643	−	0.0915935i	0.0289158	−	0.00513631i
$319$	2.60676	−	1.50501i	0.145950	−	0.0842645i
$320$	1.27201	+	17.8433i	0.0711077	+	0.997469i
$321$			0.584333i			0.0326143i
$322$	−14.1316	−	22.9283i	−0.787525	−	1.27774i
$323$	22.5641	+	22.5641i	1.25550	+	1.25550i
$324$	−16.8779	+	6.19138i	−0.937660	+	0.343965i
$325$	1.36343	+	3.32656i	0.0756293	+	0.184524i
$326$	2.54041	+	1.77403i	0.140700	+	0.0982546i
$327$	0.00225413	+	0.00841253i	0.000124654	+	0.000465214i
$328$	−4.15222	−	7.12933i	−0.229268	−	0.393651i
$329$	9.57311	+	1.41793i	0.527783	+	0.0781728i
$330$	0.412027	+	0.00923674i	0.0226814	+	0.000508466i
$331$	−1.13962	−	0.657959i	−0.0626391	−	0.0361647i	0.468353	−	0.883541i	$-0.344847\pi$
$331$	−1.13962	−	0.657959i	−0.0626391	−	0.0361647i	−0.530992	+	0.847377i	$0.678181\pi$
$332$	12.1275	+	17.2271i	0.665585	+	0.945461i
$333$	−2.64485	+	9.87072i	−0.144937	+	0.540912i
$334$	13.0907	+	1.12863i	0.716290	+	0.0617557i
$335$	−21.9578	+	7.40813i	−1.19968	+	0.404750i
$336$	0.316676	−	0.196840i	0.0172761	−	0.0107385i
$337$	10.9231	+	10.9231i	0.595020	+	0.595020i	0.938983	−	0.343963i	$-0.111769\pi$
$337$	10.9231	+	10.9231i	0.595020	+	0.595020i	−0.343963	+	0.938983i	$0.611769\pi$
$338$	13.5091	−	11.3646i	0.734799	−	0.618153i
$339$	0.467548	−	0.269939i	0.0253937	−	0.0146611i
$340$	4.15484	+	26.8754i	0.225328	+	1.45753i
$341$	1.84335	−	3.19277i	0.0998228	−	0.172898i
$342$	7.58512	−	20.9221i	0.410156	−	1.13134i
$343$	−17.4336	+	6.25057i	−0.941326	+	0.337499i
$344$	3.61454	+	0.953848i	0.194883	+	0.0514280i
$345$	0.314184	+	0.472109i	0.0169151	+	0.0254175i
$346$	−8.64390	+	12.3780i	−0.464699	+	0.665446i
$347$	−16.5883	−	4.44482i	−0.890506	−	0.238610i	−0.215571	−	0.976488i	$-0.569161\pi$
$347$	−16.5883	−	4.44482i	−0.890506	−	0.238610i	−0.674934	+	0.737878i	$0.735828\pi$
$348$	−0.0241014	+	0.0520284i	−0.00129197	+	0.00278901i
$349$			7.87813i			0.421707i	0.977518	+	0.210853i	$0.0676243\pi$
$349$			7.87813i			0.421707i	−0.977518	+	0.210853i	$0.932376\pi$
$350$	−1.97697	+	18.6035i	−0.105673	+	0.994401i
$351$	−0.151967			−0.00811142
$352$	−16.1141	−	13.3488i	−0.858884	−	0.711494i
$353$	3.15040	−	11.7574i	0.167679	−	0.625785i	−0.830005	−	0.557756i	$-0.811662\pi$
$353$	3.15040	−	11.7574i	0.167679	−	0.625785i	0.997683	−	0.0680288i	$-0.0216710\pi$
$354$	−0.435888	−	0.304392i	−0.0231672	−	0.0161783i
$355$	−7.19037	+	4.78512i	−0.381625	+	0.253968i
$356$	−16.1728	−	13.5011i	−0.857155	−	0.715557i
$357$	0.455220	−	0.337767i	0.0240928	−	0.0178765i
$358$	−5.56415	+	15.3477i	−0.294074	+	0.811149i
$359$	10.2871	+	5.93926i	0.542932	+	0.313462i	0.746266	−	0.665647i	$-0.231845\pi$
$359$	10.2871	+	5.93926i	0.542932	+	0.313462i	−0.203334	+	0.979109i	$0.565178\pi$
$360$	15.7491	−	10.5672i	0.830053	−	0.556942i
$361$	4.26888	+	7.39391i	0.224678	+	0.389153i
$362$	15.3651	+	18.2645i	0.807572	+	0.959962i
$363$	−0.0668412	+	0.0668412i	−0.00350825	+	0.00350825i
$364$	−3.72541	+	0.772824i	−0.195264	+	0.0405070i
$365$	8.58356	+	25.4418i	0.449284	+	1.33168i
$366$	−0.221646	−	0.0191095i	−0.0115856	−	0.000998868i
$367$	11.6889	+	3.13204i	0.610157	+	0.163491i	0.550649	−	0.834737i	$-0.314380\pi$
$367$	11.6889	+	3.13204i	0.610157	+	0.163491i	0.0595078	+	0.998228i	$0.481047\pi$
$368$	2.36453	−	28.6958i	0.123259	−	1.49587i
$369$	−4.37360	+	7.57529i	−0.227680	+	0.394354i
$370$	0.241517	−	10.7734i	0.0125559	−	0.560084i
$371$	−21.7861	−	17.2830i	−1.13108	−	0.897289i
$372$	0.00629765	+	0.0699469i	0.000326518	+	0.00362658i
$373$	−15.7510	+	4.22048i	−0.815558	+	0.218528i	−0.642404	−	0.766367i	$-0.722063\pi$
$373$	−15.7510	+	4.22048i	−0.815558	+	0.218528i	−0.173154	+	0.984895i	$0.555396\pi$
$374$	−26.0809	−	18.2130i	−1.34861	−	0.941771i
$375$	0.0279566	−	0.392919i	0.00144367	−	0.0202903i
$376$	7.34321	+	7.28777i	0.378697	+	0.375838i
$377$	0.413722	−	0.413722i	0.0213078	−	0.0213078i
$378$	−0.695942	−	0.375553i	−0.0357954	−	0.0193164i
$379$	−6.08539			−0.312586			−0.156293	−	0.987711i	$-0.549954\pi$
$379$	−6.08539			−0.312586			−0.156293	+	0.987711i	$0.549954\pi$
$380$	−2.53938	+	23.3304i	−0.130267	+	1.19682i
$381$	−0.182086	−	0.315382i	−0.00932853	−	0.0161575i
$382$	12.8673	−	2.28562i	0.658349	−	0.116942i
$383$	11.5464	−	3.09384i	0.589992	−	0.158088i	0.0485423	−	0.998821i	$-0.484542\pi$
$383$	11.5464	−	3.09384i	0.589992	−	0.158088i	0.541449	+	0.840733i	$0.317876\pi$
$384$	0.397386	+	0.0312291i	0.0202790	+	0.00159365i
$385$	−14.1304	−	16.7103i	−0.720154	−	0.851636i
$386$	6.12066	+	13.0826i	0.311533	+	0.665888i
$387$	−1.02580	−	3.82835i	−0.0521445	−	0.194606i
$388$	−7.39405	−	10.5032i	−0.375376	−	0.533220i
$389$	0.0222488	+	0.0385361i	0.00112806	+	0.00195386i	0.866589	−	0.499023i	$-0.166308\pi$
$389$	0.0222488	+	0.0385361i	0.00112806	+	0.00195386i	−0.865461	+	0.500977i	$0.832974\pi$
$390$	0.0778260	−	0.0189946i	0.00394087	−	0.000961830i
$391$		−	43.7720i		−	2.21365i
$392$	−18.9705	−	5.66733i	−0.958157	−	0.286243i
$393$	0.419674	−	0.419674i	0.0211697	−	0.0211697i
$394$	6.54418	+	0.564213i	0.329691	+	0.0284246i
$395$	−8.96408	+	0.570790i	−0.451032	+	0.0287196i
$396$	−3.79720	+	21.8577i	−0.190816	+	1.09839i
$397$	−9.63496	+	2.58168i	−0.483565	+	0.129571i	−0.492362	−	0.870391i	$-0.663866\pi$
$397$	−9.63496	+	2.58168i	−0.483565	+	0.129571i	0.00879725	+	0.999961i	$0.497200\pi$
$398$	−11.6270	+	32.0709i	−0.582809	+	1.60757i
$399$	0.454896	−	0.179875i	0.0227733	−	0.00900503i
$400$	−13.4922	+	14.7635i	−0.674608	+	0.738176i
$401$	14.0222	−	24.2871i	0.700234	−	1.21284i	−0.268150	−	0.963377i	$-0.586412\pi$
$401$	14.0222	−	24.2871i	0.700234	−	1.21284i	0.968384	−	0.249464i	$-0.0802543\pi$
$402$	0.0903113	+	0.508425i	0.00450432	+	0.0253579i
$403$	0.185476	−	0.692205i	0.00923920	−	0.0344812i
$404$	20.6645	−	7.58043i	1.02810	−	0.377141i
$405$	−18.0102	−	8.92336i	−0.894936	−	0.443406i
$406$	2.91708	−	0.872239i	0.144772	−	0.0432885i
$407$	8.91330	+	8.91330i	0.441816	+	0.441816i
$408$	0.605977	−	0.00229619i	0.0300003	−	0.000113679i
$409$	−15.9610	−	27.6452i	−0.789220	−	1.36697i	−0.926445	−	0.376429i	$-0.877152\pi$
$409$	−15.9610	−	27.6452i	−0.789220	−	1.36697i	0.137225	−	0.990540i	$-0.456182\pi$
$410$	2.58648	−	8.85412i	0.127737	−	0.437274i
$411$	−0.214599	+	0.371697i	−0.0105854	+	0.0183344i
$412$	0.179580	+	1.99456i	0.00884725	+	0.0982649i
$413$	3.23241	+	28.0447i	0.159057	+	1.37999i
$414$	−27.6505	+	12.9362i	−1.35895	+	0.635779i
$415$	−4.63822	+	23.0933i	−0.227681	+	1.13361i
$416$	−3.69712	−	1.69565i	−0.181266	−	0.0831361i
$417$	0.0212322	−	0.0792395i	0.00103974	−	0.00388038i
$418$	−17.6722	−	21.0069i	−0.864374	−	1.02748i
$419$		−	6.51076i		−	0.318071i	−0.987273	−	0.159036i	$-0.949161\pi$
$419$		−	6.51076i		−	0.318071i	0.987273	−	0.159036i	$-0.0508385\pi$
$420$	0.403349	+	0.105343i	0.0196814	+	0.00514020i
$421$		−	39.0821i		−	1.90475i	−0.304935	−	0.952373i	$-0.598635\pi$
$421$		−	39.0821i		−	1.90475i	0.304935	−	0.952373i	$-0.401365\pi$
$422$	6.17739	−	5.19676i	0.300711	−	0.252974i
$423$	2.83893	−	10.5950i	0.138033	−	0.515148i
$424$	−7.80318	−	28.6866i	−0.378956	−	1.39315i
$425$	−18.5988	+	24.0526i	−0.902173	+	1.16672i
$426$	0.0815574	+	0.174325i	0.00395147	+	0.00844609i
$427$	7.03900	+	9.48672i	0.340641	+	0.459094i
$428$	33.0364	−	2.97442i	1.59687	−	0.143774i
$429$	−0.0468542	+	0.0811539i	−0.00226214	+	0.00391815i
$430$	2.00811	+	3.66550i	0.0968398	+	0.176766i
$431$	17.1014	+	29.6205i	0.823745	+	1.42677i	0.902874	+	0.429905i	$0.141453\pi$
$431$	17.1014	+	29.6205i	0.823745	+	1.42677i	−0.0791289	+	0.996864i	$0.525214\pi$
$432$	−0.361151	−	0.764385i	−0.0173759	−	0.0367765i
$433$	5.91505	+	5.91505i	0.284259	+	0.284259i	0.834805	−	0.550546i	$-0.185580\pi$
$433$	5.91505	+	5.91505i	0.284259	+	0.284259i	−0.550546	+	0.834805i	$0.685580\pi$
$434$	2.56002	−	2.71162i	0.122885	−	0.130162i
$435$	−0.0607437	+	0.0204937i	−0.00291244	+	0.000982600i
$436$	0.464144	−	0.170264i	0.0222285	−	0.00815416i
$437$	9.77659	−	36.4867i	0.467678	−	1.74540i
$438$	0.589095	−	0.104641i	0.0281480	−	0.00499992i
$439$	9.47875	−	16.4177i	0.452396	−	0.783573i	−0.546138	−	0.837695i	$-0.683903\pi$
$439$	9.47875	−	16.4177i	0.452396	−	0.783573i	0.998534	+	0.0541223i	$0.0172361\pi$
$440$	−1.57512	−	23.3418i	−0.0750908	−	1.11277i
$441$	4.77545	+	20.4409i	0.227402	+	0.973376i
$442$	−5.81318	−	2.10751i	−0.276505	−	0.100244i
$443$	2.84773	−	0.763046i	0.135300	−	0.0362534i	−0.190534	−	0.981681i	$-0.561022\pi$
$443$	2.84773	−	0.763046i	0.135300	−	0.0362534i	0.325833	+	0.945427i	$0.394355\pi$
$444$	−0.236582	−	0.0410999i	−0.0112277	−	0.00195051i
$445$	−1.49678	−	23.5065i	−0.0709543	−	1.11432i
$446$	−3.19917	+	37.1065i	−0.151485	+	1.75704i
$447$	−0.563737	+	0.563737i	−0.0266638	+	0.0266638i
$448$	−12.7407	−	16.9019i	−0.601941	−	0.798540i
$449$		−	2.93565i		−	0.138542i	−0.997598	−	0.0692710i	$-0.977933\pi$
$449$		−	2.93565i		−	0.138542i	0.997598	−	0.0692710i	$-0.0220673\pi$
$450$	20.6905	+	4.64035i	0.975357	+	0.218748i
$451$	5.39495	+	9.34432i	0.254038	+	0.440007i
$452$	−17.6414	−	25.0596i	−0.829784	−	1.17871i
$453$	−0.0579941	−	0.216437i	−0.00272480	−	0.0101691i
$454$	−11.2260	+	5.25205i	−0.526863	+	0.246491i
$455$	−3.49379	−	2.42659i	−0.163791	−	0.113760i
$456$	0.505633	+	0.133433i	0.0236784	+	0.00624855i
$457$	−12.5646	+	3.36668i	−0.587748	+	0.157487i	−0.540424	−	0.841393i	$-0.681736\pi$
$457$	−12.5646	+	3.36668i	−0.587748	+	0.157487i	−0.0473242	+	0.998880i	$0.515069\pi$
$458$	−2.46420	−	13.8727i	−0.115145	−	0.648229i
$459$	−0.642607	−	1.11303i	−0.0299943	−	0.0519517i
$460$	25.0923	−	20.1662i	1.16993	−	0.940252i
$461$	9.30670			0.433456			0.216728	−	0.976232i	$-0.430461\pi$
$461$	9.30670			0.433456			0.216728	+	0.976232i	$0.430461\pi$
$462$	−0.415125	+	0.255859i	−0.0193134	+	0.0119036i
$463$	2.37029	−	2.37029i	0.110157	−	0.110157i	−0.649880	−	0.760037i	$-0.725181\pi$
$463$	2.37029	−	2.37029i	0.110157	−	0.110157i	0.760037	+	0.649880i	$0.225181\pi$
$464$	3.06421	+	1.09778i	0.142252	+	0.0509631i
$465$	−0.0518812	+	0.0589376i	−0.00240593	+	0.00273316i
$466$	−14.7735	+	21.1555i	−0.684368	+	0.980012i
$467$	36.6918	−	9.83154i	1.69789	−	0.454949i	0.725486	−	0.688237i	$-0.241615\pi$
$467$	36.6918	−	9.83154i	1.69789	−	0.454949i	0.972408	+	0.233288i	$0.0749484\pi$
$468$	0.386698	+	4.29499i	0.0178751	+	0.198536i
$469$	17.0411	−	21.4811i	0.786883	−	0.991905i
$470$	−0.259239	+	11.5640i	−0.0119578	+	0.533407i
$471$	0.336049	−	0.582054i	0.0154843	−	0.0268196i
$472$	−14.9906	+	26.1932i	−0.689999	+	1.20564i
$473$	−4.72237	−	1.26536i	−0.217135	−	0.0581811i
$474$	−0.0171925	+	0.199412i	−0.000789679	+	0.00915930i
$475$	−20.8755	+	15.8952i	−0.957832	+	0.729324i
$476$	−21.4135	−	24.0174i	−0.981485	−	1.10084i
$477$	−22.2875	+	22.2875i	−1.02048	+	1.02048i
$478$	−13.9857	+	11.7655i	−0.639690	+	0.538142i
$479$	18.9602	+	32.8399i	0.866311	+	1.50050i	0.865739	+	0.500496i	$0.166849\pi$
$479$	18.9602	+	32.8399i	0.866311	+	1.50050i	0.000572268		1.00000i	$0.499818\pi$
$480$	0.280495	+	0.346318i	0.0128028	+	0.0158072i
$481$	2.12196	+	1.22512i	0.0967532	+	0.0558605i
$482$	−3.69311	−	1.33890i	−0.168217	−	0.0609854i
$483$	−0.615694	−	0.266755i	−0.0280151	−	0.0121378i
$484$	4.11924	+	3.43875i	0.187238	+	0.156307i
$485$	2.82788	−	14.0798i	0.128408	−	0.639330i
$486$	−0.769823	+	1.10238i	−0.0349199	+	0.0500051i
$487$	−6.94520	+	25.9198i	−0.314717	+	1.17454i	0.609536	+	0.792759i	$0.291356\pi$
$487$	−6.94520	+	25.9198i	−0.314717	+	1.17454i	−0.924253	+	0.381781i	$0.875311\pi$
$488$	0.0478523	+	12.6285i	0.00216617	+	0.571664i
$489$	0.0771942			0.00349084
$490$	−10.0032	−	19.7468i	−0.451898	−	0.892070i
$491$		−	1.05107i		−	0.0474343i	−0.999719	−	0.0237171i	$-0.992450\pi$
$491$		−	1.05107i		−	0.0474343i	0.999719	−	0.0237171i	$-0.00755011\pi$
$492$	−0.186504	−	0.0863952i	−0.00840824	−	0.00389500i
$493$	4.77961	+	1.28069i	0.215263	+	0.0576796i
$494$	−4.37493	−	3.05513i	−0.196837	−	0.137457i
$495$	−20.6491	+	13.7418i	−0.928109	+	0.617648i
$496$	3.92253	−	0.712099i	0.176127	−	0.0319742i
$497$	4.06277	−	9.37722i	0.182240	−	0.420626i
$498$	0.493439	+	0.178892i	0.0221115	+	0.00801632i
$499$	−20.2566	+	35.0855i	−0.906811	+	1.57064i	−0.0883424	+	0.996090i	$0.528157\pi$
$499$	−20.2566	+	35.0855i	−0.906811	+	1.57064i	−0.818468	+	0.574552i	$0.805176\pi$
$500$	−22.3567	+	0.419490i	−0.999824	+	0.0187602i
$501$	0.283485	−	0.163670i	0.0126652	−	0.00731225i
$502$	−12.6869	−	15.0809i	−0.566245	−	0.673096i
$503$	9.89997	+	9.89997i	0.441418	+	0.441418i	0.892488	−	0.451071i	$-0.148958\pi$
$503$	9.89997	+	9.89997i	0.441418	+	0.441418i	−0.451071	+	0.892488i	$0.648958\pi$
$504$	−8.84321	+	20.6248i	−0.393908	+	0.918700i
$505$	22.0509	+	10.9253i	0.981252	+	0.486172i
$506$	−3.23454	+	37.5166i	−0.143793	+	1.66782i
$507$	0.113831	−	0.424823i	0.00505541	−	0.0188670i
$508$	−16.9038	+	11.8999i	−0.749986	+	0.527974i
$509$	22.5228	+	13.0035i	0.998304	+	0.576371i	0.907746	−	0.419520i	$-0.137802\pi$
$509$	22.5228	+	13.0035i	0.998304	+	0.576371i	0.0905578	+	0.995891i	$0.471135\pi$
$510$	0.468213	+	0.489687i	0.0207328	+	0.0216837i
$511$	−24.8894	−	19.7449i	−1.10104	−	0.873463i
$512$	−0.257215	−	22.6260i	−0.0113674	−	0.999935i
$513$	−0.287056	−	1.07131i	−0.0126738	−	0.0472994i
$514$	−14.3864	+	20.6012i	−0.634555	+	0.908679i
$515$	−1.47941	+	1.68062i	−0.0651905	+	0.0740571i
$516$	0.0874352	−	0.0320742i	0.00384912	−	0.00141199i
$517$	−9.56735	−	9.56735i	−0.420772	−	0.420772i
$518$	6.69004	+	10.8544i	0.293943	+	0.476917i
$519$			0.376126i			0.0165101i
$520$	−1.47005	−	4.30335i	−0.0644661	−	0.188714i
$521$	−10.1599	+	5.86583i	−0.445114	+	0.256987i	−0.705764	−	0.708447i	$-0.749396\pi$
$521$	−10.1599	+	5.86583i	−0.445114	+	0.256987i	0.260651	+	0.965433i	$0.416063\pi$
$522$	−0.603540	−	3.39774i	−0.0264162	−	0.148715i
$523$	4.16933	+	15.5602i	0.182312	+	0.680398i	0.995190	+	0.0979639i	$0.0312330\pi$
$523$	4.16933	+	15.5602i	0.182312	+	0.680398i	−0.812878	+	0.582434i	$0.802100\pi$
$524$	−25.8633	−	21.5908i	−1.12984	−	0.943198i
$525$	0.224977	+	0.408190i	0.00981880	+	0.0178149i
$526$	−4.08762	−	8.73709i	−0.178229	−	0.380955i
$527$	5.85410	−	1.56860i	0.255009	−	0.0683293i
$528$	−0.519548	−	0.0428107i	−0.0226104	−	0.00186310i
$529$	−24.9544	+	14.4074i	−1.08497	+	0.626409i
$530$	17.2600	−	28.4053i	0.749725	−	1.23385i
$531$	31.9970			1.38855
$532$	−12.4851	−	24.8028i	−0.541299	−	1.07534i
$533$	1.48305	+	1.48305i	0.0642381	+	0.0642381i
$534$	−0.522919	−	0.0450840i	−0.0226289	−	0.00195098i
$535$	27.8366	+	24.5038i	1.20348	+	1.05939i
$536$	28.2850	−	7.69394i	1.22173	−	0.332328i
$537$	0.105265	+	0.392854i	0.00454251	+	0.0169529i
$538$	35.2729	+	12.7878i	1.52072	+	0.551323i
$539$	24.7816	+	7.50575i	1.06742	+	0.323295i
$540$	0.341988	−	0.881157i	0.0147168	−	0.0379190i
$541$	27.3425	+	15.7862i	1.17554	+	0.678701i	0.954980	−	0.296671i	$-0.0958765\pi$
$541$	27.3425	+	15.7862i	1.17554	+	0.678701i	0.220565	+	0.975372i	$0.429210\pi$
$542$	−0.340154	−	1.91496i	−0.0146109	−	0.0822548i
$543$	0.574366	+	0.153901i	0.0246484	+	0.00660452i
$544$	−3.21441	−	34.2484i	−0.137817	−	1.46839i
$545$	0.495284	+	0.245394i	0.0212156	+	0.0105115i
$546$	−0.0650708	+	0.0689242i	−0.00278477	+	0.00294968i
$547$	−7.88050	+	7.88050i	−0.336946	+	0.336946i	−0.855217	−	0.518271i	$-0.826576\pi$
$547$	−7.88050	+	7.88050i	−0.336946	+	0.336946i	0.518271	+	0.855217i	$0.326576\pi$
$548$	22.1069	+	10.2407i	0.944361	+	0.437462i
$549$	11.5953	−	6.69453i	0.494874	−	0.285716i
$550$	17.7182	−	19.2409i	0.755508	−	0.820435i
$551$	3.69807	+	2.13508i	0.157543	+	0.0909574i
$552$	−0.361015	−	0.619860i	−0.0153658	−	0.0263830i
$553$	8.53507	−	6.33289i	0.362948	−	0.269302i
$554$	9.25843	+	19.7895i	0.393353	+	0.840774i
$555$	−0.148738	−	0.223501i	−0.00631356	−	0.00948707i
$556$	−4.58803	−	0.797049i	−0.194576	−	0.0338024i
$557$	20.3123	+	5.44265i	0.860658	+	0.230613i	0.662044	−	0.749465i	$-0.269689\pi$
$557$	20.3123	+	5.44265i	0.860658	+	0.230613i	0.198614	+	0.980078i	$0.436356\pi$
$558$	−2.72097	−	3.23442i	−0.115188	−	0.136924i
$559$	−0.950321			−0.0401943
$560$	3.90259	−	23.3403i	0.164914	−	0.986308i
$561$	−0.792509			−0.0334598
$562$	25.8044	+	30.6737i	1.08849	+	1.29389i
$563$	−25.2438	−	6.76404i	−1.06390	−	0.285070i	−0.315914	−	0.948788i	$-0.602311\pi$
$563$	−25.2438	−	6.76404i	−1.06390	−	0.285070i	−0.747984	+	0.663717i	$0.768978\pi$
$564$	0.253942	+	0.0441157i	0.0106929	+	0.00185761i
$565$	6.74704	−	33.5929i	0.283850	−	1.41326i
$566$	−5.26617	−	11.2562i	−0.221354	−	0.473134i
$567$	23.6258	−	2.72309i	0.992190	−	0.114359i
$568$	9.44066	−	5.49837i	0.396121	−	0.230706i
$569$	−16.2173	−	9.36309i	−0.679866	−	0.392521i	0.119938	−	0.992781i	$-0.461730\pi$
$569$	−16.2173	−	9.36309i	−0.679866	−	0.392521i	−0.799805	+	0.600260i	$0.795064\pi$
$570$	0.280912	+	0.512762i	0.0117661	+	0.0214772i
$571$	0.183287	−	0.105821i	0.00767030	−	0.00442845i	−0.496160	−	0.868231i	$-0.665257\pi$
$571$	0.183287	−	0.105821i	0.00767030	−	0.00442845i	0.503830	+	0.863803i	$0.331924\pi$
$572$	4.82669	+	2.23590i	0.201814	+	0.0934875i
$573$	0.230223	−	0.230223i	0.00961770	−	0.00961770i
$574$	3.12667	+	10.4567i	0.130505	+	0.436456i
$575$	35.6656	+	4.83055i	1.48736	+	0.201448i
$576$	−20.6845	+	12.1521i	−0.861855	+	0.506339i
$577$	6.96694	+	1.86679i	0.290038	+	0.0777154i	0.400904	−	0.916120i	$-0.368696\pi$
$577$	6.96694	+	1.86679i	0.290038	+	0.0777154i	−0.110867	+	0.993835i	$0.535363\pi$
$578$	−4.94115	−	27.8172i	−0.205525	−	1.15704i
$579$	0.311628	+	0.179918i	0.0129508	+	0.00747715i
$580$	1.46785	+	3.32994i	0.0609494	+	0.138268i
$581$	−10.2483	−	25.9174i	−0.425170	−	1.07523i
$582$	−0.300845	−	0.109069i	−0.0124704	−	0.00452104i
$583$	10.0629	+	37.5551i	0.416761	+	1.55537i
$584$	−8.91472	−	32.7729i	−0.368894	−	1.35615i
$585$	−3.18569	+	3.61898i	−0.131712	+	0.149626i
$586$	−22.2132	−	1.91514i	−0.917620	−	0.0791136i
$587$	8.42362	+	8.42362i	0.347680	+	0.347680i	0.859245	−	0.511565i	$-0.170934\pi$
$587$	8.42362	+	8.42362i	0.347680	+	0.347680i	−0.511565	+	0.859245i	$0.670934\pi$
$588$	−0.468325	+	0.154834i	−0.0193134	+	0.00638523i
$589$	5.23011			0.215503
$590$	−32.7795	+	8.00035i	−1.34951	+	0.329369i
$591$	0.141718	−	0.0818207i	0.00582948	−	0.00336565i
$592$	−1.11939	+	13.5848i	−0.0460066	+	0.558333i
$593$	24.6545	−	6.60616i	1.01244	−	0.271282i	0.285791	−	0.958292i	$-0.407744\pi$
$593$	24.6545	−	6.60616i	1.01244	−	0.271282i	0.726648	+	0.687010i	$0.241077\pi$
$594$	0.468526	+	1.00145i	0.0192239	+	0.0410901i
$595$	2.99890	−	35.8500i	0.122943	−	1.46971i
$596$	34.7415	+	29.0023i	1.42307	+	1.18798i
$597$	0.219965	+	0.820919i	0.00900255	+	0.0335980i
$598$	1.28013	+	7.20676i	0.0523486	+	0.294707i
$599$	−13.3644	+	7.71594i	−0.546055	+	0.315265i	−0.747529	−	0.664229i	$-0.768760\pi$
$599$	−13.3644	+	7.71594i	−0.546055	+	0.315265i	0.201474	+	0.979494i	$0.435427\pi$
$600$	−0.0650029	+	0.494006i	−0.00265373	+	0.0201677i
$601$		−	20.5309i		−	0.837474i	−0.908108	−	0.418737i	$-0.862473\pi$
$601$		−	20.5309i		−	0.837474i	0.908108	−	0.418737i	$-0.137527\pi$
$602$	−4.35204	−	2.34851i	−0.177376	−	0.0957180i
$603$	−21.9755	−	21.9755i	−0.894911	−	0.894911i
$604$	−11.9415	+	4.38053i	−0.485891	+	0.178241i
$605$	0.381233	+	5.98716i	0.0154993	+	0.243413i
$606$	0.313962	−	0.449591i	0.0127538	−	0.0182634i
$607$	2.53104	+	9.44598i	0.102732	+	0.383401i	0.998078	−	0.0619704i	$-0.0197384\pi$
$607$	2.53104	+	9.44598i	0.102732	+	0.383401i	−0.895346	+	0.445371i	$0.853072\pi$
$608$	4.97005	−	29.2661i	0.201562	−	1.18690i
$609$	0.0471421	−	0.0594250i	0.00191029	−	0.00240802i
$610$	−10.2050	+	9.75748i	−0.413188	+	0.395069i
$611$	−2.27767	−	1.31501i	−0.0921447	−	0.0531998i
$612$	−29.8219	+	20.9940i	−1.20548	+	0.848631i
$613$	−5.75742	+	21.4870i	−0.232540	+	0.867852i	0.746702	+	0.665159i	$0.231636\pi$
$613$	−5.75742	+	21.4870i	−0.232540	+	0.867852i	−0.979242	+	0.202693i	$0.935031\pi$
$614$	−2.45736	+	28.5023i	−0.0991708	+	1.15026i
$615$	−0.0734630	−	0.217745i	−0.00296231	−	0.00878033i
$616$	16.5786	+	22.1675i	0.667969	+	0.893153i
$617$	−4.61357	−	4.61357i	−0.185735	−	0.185735i	0.608114	−	0.793849i	$-0.291926\pi$
$617$	−4.61357	−	4.61357i	−0.185735	−	0.185735i	−0.793849	+	0.608114i	$0.791926\pi$
$618$	0.0321181	+	0.0381789i	0.00129198	+	0.00153578i
$619$	27.8132	−	16.0580i	1.11791	−	0.645424i	0.177041	−	0.984203i	$-0.443347\pi$
$619$	27.8132	−	16.0580i	1.11791	−	0.645424i	0.940866	+	0.338780i	$0.110014\pi$
$620$	3.59624	+	2.63319i	0.144428	+	0.105751i
$621$	−0.760682	+	1.31754i	−0.0305251	+	0.0528711i
$622$	34.0786	+	12.3549i	1.36643	+	0.495386i
$623$	16.6068	+	22.3815i	0.665336	+	0.896697i
$624$	−0.0997029	+	0.0181002i	−0.00399131	+	0.000724587i
$625$	−17.5456	−	17.8087i	−0.701825	−	0.712349i
$626$	−3.15497	−	2.20320i	−0.126098	−	0.0880576i
$627$	−0.660607	−	0.177009i	−0.0263821	−	0.00706906i
$628$	−34.6181	−	16.0363i	−1.38141	−	0.639920i
$629$			20.7221i			0.826242i
$630$	−23.5325	+	8.70056i	−0.937558	+	0.346639i
$631$	−6.08715			−0.242326			−0.121163	−	0.992633i	$-0.538662\pi$
$631$	−6.08715			−0.242326			−0.121163	+	0.992633i	$0.538662\pi$
$632$	11.3617	−	0.0430520i	0.451942	−	0.00171252i
$633$	0.0520521	−	0.194261i	0.00206889	−	0.00772119i
$634$	21.5236	−	30.8216i	0.854810	−	1.22408i
$635$	−22.6599	−	4.55118i	−0.899231	−	0.180608i
$636$	−0.568568	−	0.474643i	−0.0225452	−	0.0188208i
$637$	5.03055	+	0.162510i	0.199318	+	0.00643889i
$638$	−4.00193	−	1.45086i	−0.158438	−	0.0574402i
$639$	−10.0312	−	5.79152i	−0.396828	−	0.229109i
$640$	18.1520	−	17.6212i	0.717519	−	0.696539i
$641$	−11.4872	−	19.8965i	−0.453718	−	0.785863i	0.544895	−	0.838504i	$-0.316569\pi$
$641$	−11.4872	−	19.8965i	−0.453718	−	0.785863i	−0.998614	+	0.0526410i	$0.983236\pi$
$642$	0.632366	−	0.531981i	0.0249575	−	0.0209956i
$643$	14.3360	−	14.3360i	0.565358	−	0.565358i	−0.365466	−	0.930825i	$-0.619090\pi$
$643$	14.3360	−	14.3360i	0.565358	−	0.565358i	0.930825	+	0.365466i	$0.119090\pi$
$644$	−11.9475	+	36.1673i	−0.470796	+	1.42519i
$645$	0.0933014	+	0.0462271i	0.00367374	+	0.00182019i
$646$	3.87640	−	44.9615i	0.152515	−	1.76899i
$647$	−27.9501	−	7.48921i	−1.09883	−	0.294431i	−0.336543	−	0.941668i	$-0.609258\pi$
$647$	−27.9501	−	7.48921i	−1.09883	−	0.294431i	−0.762289	+	0.647237i	$0.775924\pi$
$648$	22.0661	+	12.6286i	0.866837	+	0.496098i
$649$	19.7345	−	34.1812i	0.774649	−	1.34173i
$650$	2.35873	−	4.50402i	0.0925172	−	0.176662i
$651$	0.0136122	−	0.0919028i	0.000533505	−	0.00360195i
$652$	−0.392940	−	4.36432i	−0.0153887	−	0.170920i
$653$	12.7040	−	3.40402i	0.497145	−	0.133210i	−0.00152959	−	0.999999i	$-0.500487\pi$
$653$	12.7040	−	3.40402i	0.497145	−	0.133210i	0.498675	+	0.866789i	$0.333820\pi$
$654$	0.00705188	−	0.0100983i	0.000275750	−	0.000394873i
$655$	−2.39364	−	37.5914i	−0.0935272	−	1.46882i
$656$	−3.93516	+	10.9841i	−0.153642	+	0.428858i
$657$	−25.4623	+	25.4623i	−0.993378	+	0.993378i
$658$	−7.18094	−	11.6509i	−0.279942	−	0.454200i
$659$	10.6261			0.413934			0.206967	−	0.978348i	$-0.433641\pi$
$659$	10.6261			0.413934			0.206967	+	0.978348i	$0.433641\pi$
$660$	−0.365116	−	0.454306i	−0.0142121	−	0.0176838i
$661$	15.1865	+	26.3038i	0.590687	+	1.02310i	0.994140	+	0.108099i	$0.0344765\pi$
$661$	15.1865	+	26.3038i	0.590687	+	1.02310i	−0.403453	+	0.915000i	$0.632190\pi$
$662$	0.325472	+	1.83231i	0.0126498	+	0.0712146i
$663$	−0.148800	+	0.0398708i	−0.00577890	+	0.00154845i
$664$	7.60223	−	28.8081i	0.295024	−	1.11797i
$665$	10.5070	−	29.2134i	0.407443	−	1.13285i
$666$	13.0900	−	6.12411i	0.507227	−	0.237304i
$667$	−1.51601	−	5.65784i	−0.0587003	−	0.219072i
$668$	−10.6964	−	15.1943i	−0.413857	−	0.587883i
$669$	0.463936	+	0.803560i	0.0179368	+	0.0310674i
$670$	28.0076	+	17.0183i	1.08203	+	0.657476i
$671$		−	16.5158i		−	0.637584i
$672$	−0.501325	−	0.163503i	−0.0193390	−	0.00630726i
$673$	−8.98864	+	8.98864i	−0.346487	+	0.346487i	−0.858799	−	0.512313i	$-0.828789\pi$
$673$	−8.98864	+	8.98864i	−0.346487	+	0.346487i	0.512313	+	0.858799i	$0.328789\pi$
$674$	1.87654	−	21.7655i	0.0722815	−	0.838376i
$675$	0.977817	−	0.400769i	0.0376362	−	0.0154256i
$676$	−24.5976	−	4.27318i	−0.946061	−	0.164353i
$677$	0.644580	−	0.172715i	0.0247732	−	0.00663796i	−0.246411	−	0.969165i	$-0.579251\pi$
$677$	0.644580	−	0.172715i	0.0247732	−	0.00663796i	0.271184	+	0.962527i	$0.412585\pi$
$678$	−0.717787	−	0.260227i	−0.0275664	−	0.00999395i
$679$	6.24828	+	15.8016i	0.239787	+	0.606410i
$680$	25.3020	−	28.9640i	0.970289	−	1.11072i
$681$	−0.154385	+	0.267403i	−0.00591606	+	0.0102469i
$682$	−5.13341	+	0.911846i	−0.196569	+	0.0349164i
$683$	−6.46135	+	24.1141i	−0.247237	+	0.922700i	0.725009	+	0.688739i	$0.241835\pi$
$683$	−6.46135	+	24.1141i	−0.247237	+	0.922700i	−0.972246	+	0.233961i	$0.924831\pi$
$684$	−29.5475	+	10.8390i	−1.12978	+	0.414440i
$685$	8.70782	+	25.8101i	0.332709	+	0.986152i
$686$	22.6360	+	13.1761i	0.864248	+	0.503066i
$687$	−0.248211	−	0.248211i	−0.00946985	−	0.00946985i
$688$	−2.25844	−	4.78005i	−0.0861024	−	0.182238i
$689$	3.77876	+	6.54500i	0.143959	+	0.249345i
$690$	0.224882	−	0.769821i	0.00856109	−	0.0293066i
$691$	16.9303	−	29.3242i	0.644060	−	1.11554i	−0.340458	−	0.940260i	$-0.610582\pi$
$691$	16.9303	−	29.3242i	0.644060	−	1.11554i	0.984518	−	0.175284i	$-0.0560845\pi$
$692$	21.2650	−	1.91459i	0.808373	−	0.0727816i
$693$	11.6674	−	26.9293i	0.443207	−	1.02296i
$694$	10.2919	+	21.9985i	0.390675	+	0.835050i
$695$	−2.88447	−	4.33434i	−0.109414	−	0.164411i
$696$	0.0782473	−	0.0212844i	0.00296595	−	0.000806783i
$697$	−4.59085	+	17.1333i	−0.173891	+	0.648969i
$698$	8.52572	−	7.17230i	0.322703	−	0.271476i
$699$			0.642845i			0.0243146i
$700$	21.9326	−	14.7973i	0.828975	−	0.559286i
$701$		−	10.3666i		−	0.391540i	−0.980650	−	0.195770i	$-0.937279\pi$
$701$		−	10.3666i		−	0.391540i	0.980650	−	0.195770i	$-0.0627205\pi$
$702$	0.138352	+	0.164459i	0.00522176	+	0.00620712i
$703$	−4.62833	+	17.2731i	−0.174561	+	0.651469i
$704$	0.224262	+	29.5915i	0.00845220	+	1.11527i
$705$	0.159652	+	0.239901i	0.00601283	+	0.00903519i
$706$	−15.5921	+	7.29468i	−0.586815	+	0.274539i
$707$	−28.9263	+	3.33403i	−1.08789	+	0.125389i
$708$	0.0674216	+	0.748840i	0.00253386	+	0.0281431i
$709$	8.98504	−	15.5625i	0.337440	−	0.584464i	−0.646510	−	0.762905i	$-0.723772\pi$
$709$	8.98504	−	15.5625i	0.337440	−	0.584464i	0.983951	+	0.178442i	$0.0571055\pi$
$710$	11.7246	+	3.42502i	0.440017	+	0.128539i
$711$	−6.02298	−	10.4321i	−0.225879	−	0.391234i
$712$	0.112895	+	29.7937i	0.00423094	+	1.11657i
$713$	−5.07293	−	5.07293i	−0.189983	−	0.189983i
$714$	−0.779967	−	0.185135i	−0.0291895	−	0.00692851i
$715$	1.90121	+	5.63521i	0.0711013	+	0.210745i
$716$	21.6749	−	7.95108i	0.810029	−	0.297146i
$717$	−0.117847	+	0.439809i	−0.00440106	+	0.0164250i
$718$	−2.93797	−	16.5398i	−0.109644	−	0.617262i
$719$	5.62399	−	9.74103i	0.209739	−	0.363279i	−0.741893	−	0.670518i	$-0.766072\pi$
$719$	5.62399	−	9.74103i	0.209739	−	0.363279i	0.951632	+	0.307239i	$0.0994051\pi$
$720$	−25.7740	−	7.42327i	−0.960541	−	0.276649i
$721$	0.388157	−	2.62064i	0.0144557	−	0.0975976i
$722$	4.11529	−	11.3512i	0.153155	−	0.422450i
$723$	−0.0945325	+	0.0253299i	−0.00351570	+	0.000942030i
$724$	5.77740	−	33.2563i	0.214715	−	1.23596i
$725$	−1.57098	+	3.75312i	−0.0583447	+	0.139387i
$726$	0.133188	+	0.0114830i	0.00494308	+	0.000426173i
$727$	−6.63131	+	6.63131i	−0.245942	+	0.245942i	−0.819303	−	0.573361i	$-0.805639\pi$
$727$	−6.63131	+	6.63131i	−0.245942	+	0.245942i	0.573361	+	0.819303i	$0.305639\pi$
$728$	4.22799	+	3.32806i	0.156700	+	0.123346i
$729$		−	26.9330i		−	0.997518i
$730$	19.7186	−	32.4515i	0.729817	−	1.20108i
$731$	−4.01852	−	6.96028i	−0.148630	−	0.257435i
$732$	0.181108	+	0.257263i	0.00669394	+	0.00950872i
$733$	1.28045	+	4.77870i	0.0472945	+	0.176505i	0.985533	−	0.169484i	$-0.0542100\pi$
$733$	1.28045	+	4.77870i	0.0472945	+	0.176505i	−0.938238	+	0.345989i	$0.887543\pi$
$734$	−7.25218	−	15.5012i	−0.267683	−	0.572160i
$735$	−0.485988	−	0.260660i	−0.0179259	−	0.00961457i
$736$	−33.2073	+	23.5659i	−1.22404	+	0.868651i
$737$	−37.0293	+	9.92198i	−1.36399	+	0.365481i
$738$	12.1797	−	2.16348i	0.448342	−	0.0796389i
$739$	23.7183	+	41.0812i	0.872491	+	1.51120i	0.859412	+	0.511284i	$0.170830\pi$
$739$	23.7183	+	41.0812i	0.872491	+	1.51120i	0.0130787	+	0.999914i	$0.495837\pi$
$740$	−11.8789	+	9.54684i	−0.436677	+	0.350949i
$741$	−0.132939			−0.00488364
$742$	1.13050	+	39.3115i	0.0415020	+	1.44317i
$743$	19.2803	−	19.2803i	0.707326	−	0.707326i	−0.258646	−	0.965972i	$-0.583276\pi$
$743$	19.2803	−	19.2803i	0.707326	−	0.707326i	0.965972	+	0.258646i	$0.0832764\pi$
$744$	0.0699632	−	0.0704955i	0.00256498	−	0.00258449i
$745$	3.21531	+	50.4955i	0.117800	+	1.85001i
$746$	18.9073	+	13.2034i	0.692244	+	0.483413i
$747$	−30.5122	+	8.17572i	−1.11638	+	0.299134i
$748$	4.03410	+	44.8060i	0.147501	+	1.63827i
$749$	−43.4063	−	6.42914i	−1.58603	−	0.234916i
$750$	−0.450670	+	0.327462i	−0.0164561	+	0.0119572i
$751$	8.95971	−	15.5187i	0.326945	−	0.566285i	−0.654959	−	0.755664i	$-0.727314\pi$
$751$	8.95971	−	15.5187i	0.326945	−	0.566285i	0.981904	+	0.189379i	$0.0606476\pi$
$752$	1.20153	−	14.5817i	0.0438152	−	0.531739i
$753$	−0.474252	−	0.127075i	−0.0172827	−	0.00463089i
$754$	−0.824386	−	0.0710753i	−0.0300224	−	0.00258841i
$755$	−12.7426	−	6.31347i	−0.463752	−	0.229771i
$756$	0.227166	+	1.09506i	0.00826194	+	0.0398268i
$757$	−2.57599	+	2.57599i	−0.0936261	+	0.0936261i	−0.752369	−	0.658742i	$-0.771089\pi$
$757$	−2.57599	+	2.57599i	−0.0936261	+	0.0936261i	0.658742	+	0.752369i	$0.271089\pi$
$758$	5.54018	+	6.58562i	0.201229	+	0.239201i
$759$	0.469064	+	0.812442i	0.0170259	+	0.0294898i
$760$	27.5600	−	18.4920i	0.999708	−	0.670776i
$761$	−24.7066	−	14.2644i	−0.895615	−	0.517084i	−0.0198401	−	0.999803i	$-0.506316\pi$
$761$	−24.7066	−	14.2644i	−0.895615	−	0.517084i	−0.875775	+	0.482720i	$0.839649\pi$
$762$	−0.175534	+	0.484179i	−0.00635894	+	0.0175399i
$763$	−0.649713	+	0.0748855i	−0.0235212	+	0.00271104i
$764$	−14.1880	−	11.8442i	−0.513303	−	0.428508i
$765$	−39.9768	−	8.02923i	−1.44537	−	0.290298i
$766$	−13.8600	−	9.67884i	−0.500784	−	0.349711i
$767$	1.98567	−	7.41063i	0.0716984	−	0.267582i
$768$	−0.327987	−	0.458483i	−0.0118352	−	0.0165441i
$769$	12.9742			0.467862			0.233931	−	0.972253i	$-0.424841\pi$
$769$	12.9742			0.467862			0.233931	+	0.972253i	$0.424841\pi$
$770$	−5.21948	+	30.5052i	−0.188097	+	1.09933i
$771$			0.625999i			0.0225448i
$772$	8.58575	−	18.5343i	0.309008	−	0.667064i
$773$	30.1855	+	8.08817i	1.08570	+	0.290911i	0.756927	−	0.653499i	$-0.226700\pi$
$773$	30.1855	+	8.08817i	1.08570	+	0.290911i	0.328769	+	0.944410i	$0.393366\pi$
$774$	−3.20915	+	4.59548i	−0.115350	+	0.165181i
$775$	0.632062	+	4.94305i	0.0227043	+	0.177560i
$776$	−4.63501	+	17.5640i	−0.166387	+	0.630513i
$777$	0.291475	+	0.126284i	0.0104566	+	0.00453043i
$778$	0.0214483	−	0.0591612i	0.000768960	−	0.00212103i
$779$	−7.65352	+	13.2563i	−0.274216	+	0.474956i
$780$	−0.0914093	−	0.0669305i	−0.00327298	−	0.00239650i
$781$	−12.3738	+	7.14399i	−0.442768	+	0.255632i
$782$	−47.3701	+	39.8503i	−1.69395	+	1.42504i
$783$	−0.121611	−	0.121611i	−0.00434600	−	0.00434600i
$784$	11.1377	+	25.6895i	0.397776	+	0.917483i
$785$	−13.6359	−	40.4170i	−0.486686	−	1.44254i
$786$	−0.836245	−	0.0720978i	−0.0298279	−	0.00257164i
$787$	−7.67662	+	28.6496i	−0.273642	+	1.02125i	0.683104	+	0.730321i	$0.260630\pi$
$787$	−7.67662	+	28.6496i	−0.273642	+	1.02125i	−0.956746	+	0.290925i	$0.906037\pi$
$788$	−5.34727	−	7.59578i	−0.190489	−	0.270588i
$789$	−0.208117	−	0.120157i	−0.00740917	−	0.00427769i
$790$	8.77867	+	9.18129i	0.312331	+	0.326656i
$791$	14.9078	+	37.7010i	0.530059	+	1.34049i
$792$	27.1115	−	15.7901i	0.963364	−	0.561076i
$793$	−0.830900	−	3.10096i	−0.0295061	−	0.110118i
$794$	11.5656	+	8.07659i	0.410449	+	0.286627i
$795$	−0.0526207	−	0.826392i	−0.00186626	−	0.0293091i
$796$	45.2925	−	16.6148i	1.60535	−	0.588897i
$797$	−29.8865	−	29.8865i	−1.05863	−	1.05863i	−0.998170	−	0.0604623i	$-0.980743\pi$
$797$	−29.8865	−	29.8865i	−1.05863	−	1.05863i	−0.0604623	−	0.998170i	$-0.519257\pi$
$798$	−0.608802	−	0.328530i	−0.0215513	−	0.0116298i
$799$		−	22.2426i		−	0.786887i
$800$	28.2605	+	1.16043i	0.999158	+	0.0410273i
$801$	27.3561	−	15.7941i	0.966581	−	0.558056i
$802$	−39.0494	+	6.93634i	−1.37888	+	0.244931i
$803$	11.4963	+	42.9047i	0.405695	+	1.51407i
$804$	0.467998	−	0.560608i	0.0165050	−	0.0197711i
$805$	−38.5267	+	18.1443i	−1.35789	+	0.639502i
$806$	−0.917963	+	0.429466i	−0.0323339	+	0.0151273i
$807$	0.902879	−	0.241926i	0.0317828	−	0.00851618i
$808$	−27.0166	−	15.4619i	−0.950442	−	0.543947i
$809$	−13.5510	+	7.82367i	−0.476428	+	0.275066i	−0.718927	−	0.695086i	$-0.755366\pi$
$809$	−13.5510	+	7.82367i	−0.476428	+	0.275066i	0.242499	+	0.970152i	$0.422033\pi$
$810$	6.73977	+	27.6146i	0.236811	+	0.970278i
$811$	−12.5758			−0.441595			−0.220797	−	0.975320i	$-0.570866\pi$
$811$	−12.5758			−0.441595			−0.220797	+	0.975320i	$0.570866\pi$
$812$	−3.59967	−	2.36278i	−0.126324	−	0.0829173i
$813$	−0.0342627	−	0.0342627i	−0.00120164	−	0.00120164i
$814$	1.53126	−	17.7607i	0.0536706	−	0.622513i
$815$	3.23711	−	3.67739i	0.113391	−	0.128814i
$816$	−0.554170	−	0.653699i	−0.0193998	−	0.0228840i
$817$	−1.79509	−	6.69938i	−0.0628024	−	0.234382i
$818$	−15.3867	+	42.4414i	−0.537984	+	1.48393i
$819$	0.835839	−	5.64316i	0.0292066	−	0.197188i
$820$	−11.9367	+	5.26175i	−0.416847	+	0.183748i
$821$	−7.38962	−	4.26640i	−0.257899	−	0.148898i	0.365477	−	0.930821i	$-0.380906\pi$
$821$	−7.38962	−	4.26640i	−0.257899	−	0.148898i	−0.623376	+	0.781922i	$0.714239\pi$
$822$	0.597623	−	0.106156i	0.0208445	−	0.00370260i
$823$	−15.0138	−	4.02294i	−0.523349	−	0.140231i	−0.0125335	−	0.999921i	$-0.503990\pi$
$823$	−15.0138	−	4.02294i	−0.523349	−	0.140231i	−0.510815	+	0.859691i	$0.670656\pi$
$824$	1.99502	−	2.01020i	0.0694999	−	0.0700287i
$825$	0.0874589	−	0.645740i	0.00304493	−	0.0224818i
$826$	27.4072	−	29.0302i	0.953618	−	1.01009i
$827$	−30.5636	+	30.5636i	−1.06280	+	1.06280i	−0.0649101	+	0.997891i	$0.520676\pi$
$827$	−30.5636	+	30.5636i	−1.06280	+	1.06280i	−0.997891	+	0.0649101i	$0.979324\pi$
$828$	39.1728	+	18.1462i	1.36135	+	0.630625i
$829$	14.0181	−	8.09336i	0.486869	−	0.281094i	−0.236406	−	0.971654i	$-0.575969\pi$
$829$	14.0181	−	8.09336i	0.486869	−	0.281094i	0.723275	+	0.690561i	$0.242636\pi$
$830$	29.2143	−	16.0048i	1.01404	−	0.555534i
$831$	0.471384	+	0.272154i	0.0163521	+	0.00944091i
$832$	1.53084	+	5.54476i	0.0530724	+	0.192230i
$833$	20.0819	+	37.5316i	0.695796	+	1.30039i
$834$	−0.105083	+	0.0491627i	−0.00363873	+	0.00170236i
$835$	4.09089	−	20.3682i	0.141571	−	0.704870i
$836$	−6.64487	+	38.2497i	−0.229817	+	1.32289i
$837$	−0.203468	−	0.0545192i	−0.00703290	−	0.00188446i
$838$	−7.04595	+	5.92744i	−0.243398	+	0.204760i
$839$	11.5236			0.397840			0.198920	−	0.980016i	$-0.436257\pi$
$839$	11.5236			0.397840			0.198920	+	0.980016i	$0.436257\pi$
$840$	−0.253209	−	0.532409i	−0.00873655	−	0.0183699i
$841$	−28.3378			−0.977167
$842$	−42.2947	+	35.5806i	−1.45757	+	1.22619i
$843$	0.964600	+	0.258464i	0.0332226	+	0.00890197i
$844$	−11.2479	−	1.95402i	−0.387168	−	0.0672601i
$845$	−15.4643	−	23.2375i	−0.531989	−	0.799394i
$846$	−14.0505	+	6.57349i	−0.483067	+	0.226001i
$847$	−4.22977	−	5.70061i	−0.145337	−	0.195875i
$848$	−23.9406	+	34.5611i	−0.822125	+	1.18683i
$849$	−0.268122	−	0.154801i	−0.00920193	−	0.00531274i
$850$	42.9622	−	1.76998i	1.47359	−	0.0607098i
$851$	21.2433	−	12.2648i	0.728209	−	0.420432i
$852$	0.114405	−	0.246968i	0.00391944	−	0.00846100i
$853$	−14.1873	+	14.1873i	−0.485763	+	0.485763i	−0.906966	−	0.421203i	$-0.861608\pi$
$853$	−14.1873	+	14.1873i	−0.485763	+	0.485763i	0.421203	+	0.906966i	$0.361608\pi$
$854$	3.85818	−	16.2544i	0.132024	−	0.556214i
$855$	−31.5299	−	15.6218i	−1.07830	−	0.534254i
$856$	−33.2955	−	33.0441i	−1.13802	−	1.12942i
$857$	39.0140	+	10.4538i	1.33269	+	0.357094i	0.853719	−	0.520734i	$-0.174342\pi$
$857$	39.0140	+	10.4538i	1.33269	+	0.357094i	0.478975	+	0.877828i	$0.341008\pi$
$858$	0.130481	−	0.0231773i	0.00445456	−	0.000791262i
$859$	−43.2960	−	24.9969i	−1.47724	−	0.852884i	−0.477570	−	0.878594i	$-0.658482\pi$
$859$	−43.2960	−	24.9969i	−1.47724	−	0.852884i	−0.999669	+	0.0257096i	$0.991815\pi$
$860$	2.13861	−	5.51028i	0.0729259	−	0.187899i
$861$	0.213018	+	0.168988i	0.00725963	+	0.00575910i
$862$	16.4861	−	45.4739i	0.561519	−	1.54885i
$863$	−4.63089	−	17.2827i	−0.157637	−	0.588310i	−0.998865	−	0.0476292i	$-0.984833\pi$
$863$	−4.63089	−	17.2827i	−0.157637	−	0.588310i	0.841228	−	0.540681i	$-0.181833\pi$
$864$	−0.498424	+	1.08674i	−0.0169567	+	0.0369716i
$865$	17.9179	+	15.7727i	0.609229	+	0.536288i
$866$	1.01617	−	11.7864i	0.0345310	−	0.400517i
$867$	−0.497706	−	0.497706i	−0.0169030	−	0.0169030i
$868$	−5.26519	−	0.301782i	−0.178712	−	0.0102431i
$869$	−14.8590			−0.504057
$870$	0.0774798	+	0.0470793i	0.00262681	+	0.00159614i
$871$	−6.45337	+	3.72586i	−0.218664	+	0.126246i
$872$	−0.606820	−	0.347288i	−0.0205495	−	0.0117607i
$873$	18.6030	−	4.98467i	0.629617	−	0.168705i
$874$	−48.3867	+	22.6375i	−1.63670	+	0.765726i
$875$	28.8798	+	6.39982i	0.976315	+	0.216353i
$876$	−0.649558	−	0.542254i	−0.0219465	−	0.0183210i
$877$	−0.162594	−	0.606807i	−0.00549039	−	0.0204904i	0.963126	−	0.269050i	$-0.0867096\pi$
$877$	−0.162594	−	0.606807i	−0.00549039	−	0.0204904i	−0.968617	+	0.248559i	$0.920043\pi$
$878$	−26.3967	+	4.68884i	−0.890847	+	0.158241i
$879$	−0.481039	+	0.277728i	−0.0162251	+	0.00936754i
$880$	−23.8265	+	22.9551i	−0.803190	+	0.773816i
$881$			0.193658i			0.00652452i	0.999995	+	0.00326226i	$0.00103841\pi$
$881$			0.193658i			0.00652452i	−0.999995	+	0.00326226i	$0.998962\pi$
$882$	17.7736	−	23.7775i	0.598467	−	0.800631i
$883$	−36.0517	−	36.0517i	−1.21324	−	1.21324i	−0.969956	−	0.243279i	$-0.921777\pi$
$883$	−36.0517	−	36.0517i	−1.21324	−	1.21324i	−0.243279	−	0.969956i	$-0.578223\pi$
$884$	3.01160	+	8.20972i	0.101291	+	0.276123i
$885$	−0.555431	+	0.630975i	−0.0186706	+	0.0212100i
$886$	−3.41836	−	2.38713i	−0.114842	−	0.0801972i
$887$	−9.41889	−	35.1518i	−0.316255	−	1.18028i	−0.922815	−	0.385243i	$-0.874118\pi$
$887$	−9.41889	−	35.1518i	−0.316255	−	1.18028i	0.606560	−	0.795038i	$-0.292549\pi$
$888$	0.170908	+	0.293447i	0.00573528	+	0.00984744i
$889$	25.4310	−	10.0559i	0.852929	−	0.337266i
$890$	−24.0761	+	23.0203i	−0.807034	+	0.771643i
$891$	−28.7954	−	16.6251i	−0.964684	−	0.556960i
$892$	43.0692	−	30.3198i	1.44206	−	1.01518i
$893$	4.96795	−	18.5406i	0.166246	−	0.620439i
$894$	1.12331	+	0.0968471i	0.0375690	+	0.00323905i
$895$	23.1291	+	11.4596i	0.773120	+	0.383051i
$896$	−6.69205	+	29.1756i	−0.223566	+	0.974689i
$897$	0.128944	+	0.128944i	0.00430531	+	0.00430531i
$898$	−3.17697	+	2.67264i	−0.106017	+	0.0891871i
$899$	0.702356	−	0.405505i	0.0234249	−	0.0135244i
$900$	−13.8149	−	26.6158i	−0.460498	−	0.887195i
$901$	−31.9576	+	55.3522i	−1.06466	+	1.84405i
$902$	5.20084	−	14.3456i	0.173169	−	0.477655i
$903$	−0.122392	+	0.0141069i	−0.00407297	+	0.000469447i
$904$	−11.0587	+	41.9060i	−0.367806	+	1.39377i
$905$	31.4174	−	20.9080i	1.04435	−	0.695006i
$906$	−0.181430	+	0.259807i	−0.00602761	+	0.00863151i
$907$	35.7866	+	9.58898i	1.18827	+	0.318397i	0.798203	−	0.602388i	$-0.205784\pi$
$907$	35.7866	+	9.58898i	1.18827	+	0.318397i	0.390070	+	0.920785i	$0.372451\pi$
$908$	15.9040	+	7.36731i	0.527793	+	0.244493i
$909$			33.0028i			1.09464i
$910$	0.554703	+	5.99017i	0.0183882	+	0.198572i
$911$	−44.0611			−1.45981			−0.729904	−	0.683549i	$-0.760435\pi$
$911$	−44.0611			−1.45981			−0.729904	+	0.683549i	$0.760435\pi$
$912$	−0.315931	−	0.668675i	−0.0104615	−	0.0221420i
$913$	−10.0850	+	37.6376i	−0.333764	+	1.24562i
$914$	15.0823	+	10.5324i	0.498879	+	0.348381i
$915$	−0.0692655	+	0.344866i	−0.00228985	+	0.0114009i
$916$	−12.7696	+	15.2966i	−0.421921	+	0.505413i
$917$	26.5573	+	35.7923i	0.877000	+	1.18196i
$918$	−0.619487	+	1.70874i	−0.0204461	+	0.0563968i
$919$	−31.8965	−	18.4154i	−1.05217	−	0.607469i	−0.128912	−	0.991656i	$-0.541148\pi$
$919$	−31.8965	−	18.4154i	−1.05217	−	0.607469i	−0.923255	+	0.384187i	$0.874482\pi$
$920$	−44.6680	−	8.79550i	−1.47266	−	0.289979i
$921$	0.356359	+	0.617232i	0.0117424	+	0.0203385i
$922$	−8.47288	−	10.0717i	−0.279040	−	0.331695i
$923$	−1.96386	+	1.96386i	−0.0646411	+	0.0646411i
$924$	0.654823	+	0.216314i	0.0215421	+	0.00711619i
$925$	−16.8844	−	2.28682i	−0.555156	−	0.0751903i
$926$	−4.72307	−	0.407204i	−0.155210	−	0.0133816i
$927$	−2.90038	−	0.777155i	−0.0952611	−	0.0255251i
$928$	−1.60165	−	4.31551i	−0.0525769	−	0.141664i
$929$	−27.3398	+	47.3540i	−0.896991	+	1.55363i	−0.0656694	+	0.997841i	$0.520918\pi$
$929$	−27.3398	+	47.3540i	−0.896991	+	1.55363i	−0.831321	+	0.555792i	$0.812415\pi$
$930$	0.111015	+	0.00248872i	0.00364033	+	8.16083e-5i
$931$	8.35674	+	35.7703i	0.273881	+	1.17232i
$932$	36.3444	−	3.27226i	1.19050	−	0.107186i
$933$	0.872310	−	0.233735i	0.0285581	−	0.00765213i
$934$	−44.0442	−	30.7572i	−1.44117	−	1.00641i
$935$	−33.2336	+	37.7537i	−1.08685	+	1.23468i
$936$	4.29599	−	4.32867i	0.140419	−	0.141487i
$937$	0.243229	−	0.243229i	0.00794595	−	0.00794595i	−0.703123	−	0.711069i	$-0.748212\pi$
$937$	0.243229	−	0.243229i	0.00794595	−	0.00794595i	0.711069	+	0.703123i	$0.248212\pi$
$938$	−38.7612	+	1.11467i	−1.26560	+	0.0363954i
$939$	−0.0958687			−0.00312856
$940$	12.7506	−	10.2474i	0.415878	−	0.334233i
$941$	−7.27191	−	12.5953i	−0.237058	−	0.410596i	0.722811	−	0.691046i	$-0.242850\pi$
$941$	−7.27191	−	12.5953i	−0.237058	−	0.410596i	−0.959869	+	0.280450i	$0.909516\pi$
$942$	−0.935840	+	0.166233i	−0.0304913	+	0.00541616i
$943$	20.2814	−	5.43438i	0.660453	−	0.176968i
$944$	41.9939	−	7.62361i	1.36678	−	0.248127i
$945$	−0.713279	+	1.02697i	−0.0232030	+	0.0334074i
$946$	2.92991	+	6.26255i	0.0952596	+	0.203613i
$947$	−4.24477	−	15.8417i	−0.137936	−	0.514786i	−0.999969	−	0.00793216i	$-0.997475\pi$
$947$	−4.24477	−	15.8417i	−0.137936	−	0.514786i	0.862032	−	0.506854i	$-0.169192\pi$
$948$	0.231456	−	0.162940i	0.00751735	−	0.00529205i
$949$	4.31703	+	7.47731i	0.140137	+	0.242724i
$950$	36.2070	+	8.12032i	1.17471	+	0.263458i
$951$		−	0.936563i		−	0.0303701i
$952$	−6.49671	+	45.0393i	−0.210560	+	1.45973i
$953$	−1.53674	+	1.53674i	−0.0497797	+	0.0497797i	−0.731558	−	0.681779i	$-0.761207\pi$
$953$	−1.53674	+	1.53674i	−0.0497797	+	0.0497797i	0.681779	+	0.731558i	$0.261207\pi$
$954$	44.4103	+	3.82888i	1.43784	+	0.123965i
$955$	−1.31309	−	20.6217i	−0.0424907	−	0.667303i
$956$	25.4653	+	4.42392i	0.823607	+	0.143080i
$957$	−0.102437	+	0.0274480i	−0.00331133	+	0.000887268i
$958$	18.2780	−	50.4164i	0.590535	−	1.62888i
$959$	−25.2497	−	20.0307i	−0.815357	−	0.646827i
$960$	0.119421	−	0.618843i	0.00385430	−	0.0199731i
$961$	−15.0033	+	25.9865i	−0.483979	+	0.838275i
$962$	−0.606027	−	3.41175i	−0.0195391	−	0.109999i
$963$	−12.8722	+	48.0398i	−0.414801	+	1.54806i
$964$	1.91327	+	5.21564i	0.0616223	+	0.167984i
$965$	21.6390	−	7.30057i	0.696583	−	0.235014i
$966$	0.271849	+	0.909161i	0.00874659	+	0.0292518i
$967$	−1.90308	−	1.90308i	−0.0611988	−	0.0611988i	0.675845	−	0.737044i	$-0.263779\pi$
$967$	−1.90308	−	1.90308i	−0.0611988	−	0.0611988i	−0.737044	+	0.675845i	$0.763779\pi$
$968$	−0.0287547	−	7.58851i	−0.000924210	−	0.243904i
$969$	−0.562145	−	0.973664i	−0.0180587	−	0.0312786i
$970$	−17.8117	+	9.75798i	−0.571898	+	0.313310i
$971$	5.91779	−	10.2499i	0.189911	−	0.328935i	−0.755310	−	0.655368i	$-0.772513\pi$
$971$	5.91779	−	10.2499i	0.189911	−	0.328935i	0.945220	+	0.326433i	$0.105847\pi$
$972$	1.89385	−	0.170512i	0.0607453	−	0.00546919i
$973$	5.65257	+	2.44903i	0.181213	+	0.0785124i
$974$	34.3734	−	16.0815i	1.10140	−	0.515284i
$975$	−0.0160658	−	0.125643i	−0.000514517	−	0.00402379i
$976$	13.6230	−	11.5488i	0.436061	−	0.369669i
$977$	11.2127	−	41.8465i	0.358727	−	1.33879i	−0.517001	−	0.855985i	$-0.672952\pi$
$977$	11.2127	−	41.8465i	0.358727	−	1.33879i	0.875728	−	0.482804i	$-0.160382\pi$
$978$	−0.0702781	−	0.0835397i	−0.00224725	−	0.00267130i
$979$		−	38.9648i		−	1.24532i
$980$	−12.2631	+	28.8031i	−0.391729	+	0.920081i
$981$			0.741276i			0.0236671i
$982$	−1.13747	+	0.956905i	−0.0362982	+	0.0305361i
$983$	12.1478	−	45.3362i	0.387455	−	1.44600i	−0.446806	−	0.894631i	$-0.647439\pi$
$983$	12.1478	−	45.3362i	0.387455	−	1.44600i	0.834261	−	0.551370i	$-0.185895\pi$
$984$	0.0762972	+	0.280489i	0.00243227	+	0.00894168i
$985$	2.04509	−	10.1823i	0.0651618	−	0.324435i
$986$	−2.96542	−	6.33846i	−0.0944383	−	0.201858i
$987$	−0.312863	−	0.135551i	−0.00995855	−	0.00431464i
$988$	0.676698	+	7.51597i	0.0215286	+	0.239115i
$989$	−4.75690	+	8.23918i	−0.151260	+	0.261991i
$990$	33.6705	+	9.83589i	1.07012	+	0.312605i
$991$	0.804688	+	1.39376i	0.0255617	+	0.0442742i	0.878523	−	0.477700i	$-0.158529\pi$
$991$	0.804688	+	1.39376i	0.0255617	+	0.0442742i	−0.852962	+	0.521974i	$0.825196\pi$
$992$	−4.34173	−	3.59666i	−0.137850	−	0.114194i
$993$	0.0327838	+	0.0327838i	0.00104036	+	0.00104036i
$994$	−13.8468	+	4.14035i	−0.439194	+	0.131324i
$995$	48.3312	+	23.9462i	1.53220	+	0.759146i
$996$	−0.255633	−	0.696864i	−0.00810005	−	0.0220810i
$997$	14.9485	−	55.7885i	0.473423	−	1.76684i	−0.153907	−	0.988085i	$-0.549186\pi$
$997$	14.9485	−	55.7885i	0.473423	−	1.76684i	0.627330	−	0.778754i	$-0.284148\pi$
$998$	56.4113	−	10.0203i	1.78567	−	0.317188i
$999$	0.360114	−	0.623735i	0.0113935	−	0.0197341i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bv.e.117.10	✓	160
5.3	odd	4	inner	280.2.bv.e.173.11	yes	160
7.3	odd	6	inner	280.2.bv.e.157.38	yes	160
8.5	even	2	inner	280.2.bv.e.117.18	yes	160
35.3	even	12	inner	280.2.bv.e.213.18	yes	160
40.13	odd	4	inner	280.2.bv.e.173.38	yes	160
56.45	odd	6	inner	280.2.bv.e.157.11	yes	160
280.213	even	12	inner	280.2.bv.e.213.10	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bv.e.117.10	✓	160	1.1	even	1	trivial
280.2.bv.e.117.18	yes	160	8.5	even	2	inner
280.2.bv.e.157.11	yes	160	56.45	odd	6	inner
280.2.bv.e.157.38	yes	160	7.3	odd	6	inner
280.2.bv.e.173.11	yes	160	5.3	odd	4	inner
280.2.bv.e.173.38	yes	160	40.13	odd	4	inner
280.2.bv.e.213.10	yes	160	280.213	even	12	inner
280.2.bv.e.213.18	yes	160	35.3	even	12	inner

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.910407 - 1.08220i) q^{2} +(-0.0340321 - 0.00911887i) q^{3} +(-0.342320 + 1.97049i) q^{4} +(-1.86153 + 1.23883i) q^{5} +(0.0211146 + 0.0451315i) q^{6} +(1.05182 - 2.42769i) q^{7} +(2.44411 - 1.42349i) q^{8} +(-2.59700 - 1.49938i) q^{9} +O(q^{10})\)	\(q+(-0.910407 - 1.08220i) q^{2} +(-0.0340321 - 0.00911887i) q^{3} +(-0.342320 + 1.97049i) q^{4} +(-1.86153 + 1.23883i) q^{5} +(0.0211146 + 0.0451315i) q^{6} +(1.05182 - 2.42769i) q^{7} +(2.44411 - 1.42349i) q^{8} +(-2.59700 - 1.49938i) q^{9} +(3.03542 + 0.886711i) q^{10} +(-3.20347 + 1.84952i) q^{11} +(0.0296185 - 0.0639382i) q^{12} +(-0.508427 + 0.508427i) q^{13} +(-3.58483 + 1.07190i) q^{14} +(0.0746485 - 0.0251850i) q^{15} +(-3.76563 - 1.34907i) q^{16} +(-5.87372 - 1.57386i) q^{17} +(0.741697 + 4.17552i) q^{18} +(-4.54459 - 2.62382i) q^{19} +(-1.80386 - 4.09220i) q^{20} +(-0.0579334 + 0.0730279i) q^{21} +(4.91802 + 1.78298i) q^{22} +(1.86304 + 6.95298i) q^{23} +(-0.0961589 + 0.0261566i) q^{24} +(1.93059 - 4.61225i) q^{25} +(1.01310 + 0.0873452i) q^{26} +(0.149448 + 0.149448i) q^{27} +(4.42367 + 2.90364i) q^{28} -0.813729 q^{29} +(-0.0952157 - 0.0578562i) q^{30} +(-0.863133 + 0.498330i) q^{31} +(1.96829 + 5.30338i) q^{32} +(0.125886 - 0.0337312i) q^{33} +(3.64424 + 7.78940i) q^{34} +(1.04950 + 5.82225i) q^{35} +(3.84351 - 4.60409i) q^{36} +(-0.881982 - 3.29160i) q^{37} +(1.29792 + 7.30691i) q^{38} +(0.0219391 - 0.0126666i) q^{39} +(-2.78633 + 5.67771i) q^{40} -2.91694i q^{41} +(0.131774 - 0.00378949i) q^{42} +(0.934569 + 0.934569i) q^{43} +(-2.54785 - 6.94552i) q^{44} +(6.69188 - 0.426106i) q^{45} +(5.82839 - 8.34623i) q^{46} +(0.946701 + 3.53314i) q^{47} +(0.115850 + 0.0802501i) q^{48} +(-4.78735 - 5.10698i) q^{49} +(-6.74900 + 2.10973i) q^{50} +(0.185543 + 0.107123i) q^{51} +(-0.827805 - 1.17589i) q^{52} +(2.72039 - 10.1526i) q^{53} +(0.0256745 - 0.297792i) q^{54} +(3.67211 - 7.41151i) q^{55} +(-0.885012 - 7.43080i) q^{56} +(0.130736 + 0.130736i) q^{57} +(0.740824 + 0.880619i) q^{58} +(-9.24055 + 5.33503i) q^{59} +(0.0240730 + 0.155715i) q^{60} +(-2.23243 + 3.86669i) q^{61} +(1.32509 + 0.480401i) q^{62} +(-6.37160 + 4.72763i) q^{63} +(3.94738 - 6.95832i) q^{64} +(0.316597 - 1.57631i) q^{65} +(-0.151112 - 0.105525i) q^{66} +(10.0105 + 2.68231i) q^{67} +(5.11196 - 11.0353i) q^{68} -0.253613i q^{69} +(5.34537 - 6.43638i) q^{70} +3.86261 q^{71} +(-8.48171 + 0.0321392i) q^{72} +(3.10790 - 11.5988i) q^{73} +(-2.75921 + 3.95118i) q^{74} +(-0.107761 + 0.139360i) q^{75} +(6.72591 - 8.05687i) q^{76} +(1.12060 + 9.72240i) q^{77} +(-0.0336813 - 0.0122108i) q^{78} +(3.47881 + 2.00849i) q^{79} +(8.68112 - 2.15365i) q^{80} +(4.49441 + 7.78455i) q^{81} +(-3.15671 + 2.65560i) q^{82} +(7.44858 - 7.44858i) q^{83} +(-0.124069 - 0.139156i) q^{84} +(12.8839 - 4.34676i) q^{85} +(0.160554 - 1.86223i) q^{86} +(0.0276929 + 0.00742029i) q^{87} +(-5.19687 + 9.08054i) q^{88} +(-5.26687 + 9.12248i) q^{89} +(-6.55346 - 6.85403i) q^{90} +(0.699530 + 1.76908i) q^{91} +(-14.3385 + 1.29096i) q^{92} +(0.0339184 - 0.00908841i) q^{93} +(2.96168 - 4.24111i) q^{94} +(11.7104 - 0.745660i) q^{95} +(-0.0186242 - 0.198434i) q^{96} +(-4.54133 + 4.54133i) q^{97} +(-1.16835 + 9.83031i) q^{98} +11.0926 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 2 q^{2} + 12 q^{7} + 4 q^{8}+O(q^{10}) \) 160 * q - 2 * q^2 + 12 * q^7 + 4 * q^8	\( 160 q - 2 q^{2} + 12 q^{7} + 4 q^{8} - 6 q^{10} + 6 q^{12} - 8 q^{15} + 4 q^{16} - 12 q^{17} - 28 q^{18} - 24 q^{22} - 16 q^{23} + 20 q^{25} - 12 q^{26} - 46 q^{28} + 32 q^{30} + 48 q^{31} + 18 q^{32} - 12 q^{33} - 32 q^{36} - 48 q^{38} + 54 q^{40} + 6 q^{42} - 64 q^{46} - 132 q^{47} - 12 q^{50} - 20 q^{56} - 88 q^{57} + 6 q^{58} + 34 q^{60} - 32 q^{63} - 28 q^{65} - 180 q^{66} + 60 q^{68} - 108 q^{70} - 160 q^{71} + 52 q^{72} + 84 q^{73} + 48 q^{78} - 48 q^{80} + 16 q^{81} - 90 q^{82} - 84 q^{86} - 12 q^{87} + 44 q^{88} + 36 q^{92} - 20 q^{95} - 48 q^{96} - 94 q^{98}+O(q^{100}) \) 160 * q - 2 * q^2 + 12 * q^7 + 4 * q^8 - 6 * q^10 + 6 * q^12 - 8 * q^15 + 4 * q^16 - 12 * q^17 - 28 * q^18 - 24 * q^22 - 16 * q^23 + 20 * q^25 - 12 * q^26 - 46 * q^28 + 32 * q^30 + 48 * q^31 + 18 * q^32 - 12 * q^33 - 32 * q^36 - 48 * q^38 + 54 * q^40 + 6 * q^42 - 64 * q^46 - 132 * q^47 - 12 * q^50 - 20 * q^56 - 88 * q^57 + 6 * q^58 + 34 * q^60 - 32 * q^63 - 28 * q^65 - 180 * q^66 + 60 * q^68 - 108 * q^70 - 160 * q^71 + 52 * q^72 + 84 * q^73 + 48 * q^78 - 48 * q^80 + 16 * q^81 - 90 * q^82 - 84 * q^86 - 12 * q^87 + 44 * q^88 + 36 * q^92 - 20 * q^95 - 48 * q^96 - 94 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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