LMFDB - Embedded newform 280.2.l.a.29.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(29,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1, 0]))

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

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

chi := DirichletCharacter("280.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.l (of order $2$, degree $1$, 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:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.19
Character	$\chi$	$=$	280.29
Dual form			280.2.l.a.29.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.139020 - 1.40736i) q^{2} +0.319826 q^{3} +(-1.96135 - 0.391304i) q^{4} +(1.20181 - 1.88564i) q^{5} +(0.0444622 - 0.450112i) q^{6} -1.00000i q^{7} +(-0.823373 + 2.70593i) q^{8} -2.89771 q^{9} +O(q^{10})$	\(q+(0.139020 - 1.40736i) q^{2} +0.319826 q^{3} +(-1.96135 - 0.391304i) q^{4} +(1.20181 - 1.88564i) q^{5} +(0.0444622 - 0.450112i) q^{6} -1.00000i q^{7} +(-0.823373 + 2.70593i) q^{8} -2.89771 q^{9} +(-2.48671 - 1.95353i) q^{10} -4.31560i q^{11} +(-0.627290 - 0.125149i) q^{12} +2.16506 q^{13} +(-1.40736 - 0.139020i) q^{14} +(0.384372 - 0.603077i) q^{15} +(3.69376 + 1.53496i) q^{16} +3.19581i q^{17} +(-0.402840 + 4.07813i) q^{18} -5.38650i q^{19} +(-3.09503 + 3.22812i) q^{20} -0.319826i q^{21} +(-6.07361 - 0.599954i) q^{22} +0.947361i q^{23} +(-0.263336 + 0.865427i) q^{24} +(-2.11128 - 4.53238i) q^{25} +(0.300986 - 3.04702i) q^{26} -1.88624 q^{27} +(-0.391304 + 1.96135i) q^{28} +7.55412i q^{29} +(-0.795314 - 0.624790i) q^{30} -1.97567 q^{31} +(2.67376 - 4.98508i) q^{32} -1.38024i q^{33} +(4.49767 + 0.444281i) q^{34} +(-1.88564 - 1.20181i) q^{35} +(5.68342 + 1.13388i) q^{36} +9.35534 q^{37} +(-7.58076 - 0.748831i) q^{38} +0.692441 q^{39} +(4.11287 + 4.80461i) q^{40} +8.13282 q^{41} +(-0.450112 - 0.0444622i) q^{42} +2.27658 q^{43} +(-1.68871 + 8.46438i) q^{44} +(-3.48251 + 5.46404i) q^{45} +(1.33328 + 0.131702i) q^{46} +6.88315i q^{47} +(1.18136 + 0.490922i) q^{48} -1.00000 q^{49} +(-6.67222 + 2.34125i) q^{50} +1.02210i q^{51} +(-4.24643 - 0.847194i) q^{52} +6.12756 q^{53} +(-0.262225 + 2.65463i) q^{54} +(-8.13766 - 5.18654i) q^{55} +(2.70593 + 0.823373i) q^{56} -1.72274i q^{57} +(10.6314 + 1.05017i) q^{58} -4.30565i q^{59} +(-0.989872 + 1.03244i) q^{60} -0.0705077i q^{61} +(-0.274657 + 2.78048i) q^{62} +2.89771i q^{63} +(-6.64411 - 4.45598i) q^{64} +(2.60200 - 4.08252i) q^{65} +(-1.94250 - 0.191881i) q^{66} +10.1964 q^{67} +(1.25053 - 6.26809i) q^{68} +0.302991i q^{69} +(-1.95353 + 2.48671i) q^{70} +5.61315 q^{71} +(2.38590 - 7.84100i) q^{72} +2.18227i q^{73} +(1.30058 - 13.1664i) q^{74} +(-0.675244 - 1.44957i) q^{75} +(-2.10775 + 10.5648i) q^{76} -4.31560 q^{77} +(0.0962632 - 0.974517i) q^{78} +10.0202 q^{79} +(7.33361 - 5.12037i) q^{80} +8.08986 q^{81} +(1.13063 - 11.4458i) q^{82} -16.4283 q^{83} +(-0.125149 + 0.627290i) q^{84} +(6.02615 + 3.84077i) q^{85} +(0.316490 - 3.20397i) q^{86} +2.41600i q^{87} +(11.6777 + 3.55334i) q^{88} -13.4992 q^{89} +(7.20576 + 5.66077i) q^{90} -2.16506i q^{91} +(0.370706 - 1.85810i) q^{92} -0.631870 q^{93} +(9.68710 + 0.956896i) q^{94} +(-10.1570 - 6.47357i) q^{95} +(0.855138 - 1.59436i) q^{96} +11.4733i q^{97} +(-0.139020 + 1.40736i) q^{98} +12.5053i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9}+O(q^{10}) $ 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9	$ 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9} - 8 q^{10} + 20 q^{16} - 24 q^{20} - 48 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{30} - 16 q^{31} + 12 q^{34} - 20 q^{36} - 32 q^{39} + 16 q^{40} - 8 q^{41} + 56 q^{44} - 36 q^{49} - 12 q^{50} - 52 q^{54} - 32 q^{55} + 12 q^{56} - 20 q^{60} - 20 q^{64} - 24 q^{65} - 28 q^{66} - 12 q^{70} + 56 q^{71} - 24 q^{74} + 48 q^{76} + 24 q^{79} + 64 q^{80} + 36 q^{81} + 24 q^{86} - 40 q^{89} - 52 q^{90} - 92 q^{94} + 40 q^{95} + 48 q^{96}+O(q^{100}) $ 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9 - 8 * q^10 + 20 * q^16 - 24 * q^20 - 48 * q^24 + 4 * q^25 - 4 * q^26 + 4 * q^30 - 16 * q^31 + 12 * q^34 - 20 * q^36 - 32 * q^39 + 16 * q^40 - 8 * q^41 + 56 * q^44 - 36 * q^49 - 12 * q^50 - 52 * q^54 - 32 * q^55 + 12 * q^56 - 20 * q^60 - 20 * q^64 - 24 * q^65 - 28 * q^66 - 12 * q^70 + 56 * q^71 - 24 * q^74 + 48 * q^76 + 24 * q^79 + 64 * q^80 + 36 * q^81 + 24 * q^86 - 40 * q^89 - 52 * q^90 - 92 * q^94 + 40 * q^95 + 48 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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 $

$2$	0.139020	−	1.40736i	0.0983020	−	0.995157i
$2$	0.139020	−	1.40736i	0.0983020	−	0.995157i
$3$	0.319826			0.184652			0.0923258	−	0.995729i	$-0.470570\pi$
$3$	0.319826			0.184652			0.0923258	+	0.995729i	$0.470570\pi$
$4$	−1.96135	−	0.391304i	−0.980673	−	0.195652i
$5$	1.20181	−	1.88564i	0.537468	−	0.843284i
$5$	1.20181	−	1.88564i	0.537468	−	0.843284i
$6$	0.0444622	−	0.450112i	0.0181516	−	0.183757i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−0.823373	+	2.70593i	−0.291106	+	0.956691i
$9$	−2.89771			−0.965904
$10$	−2.48671	−	1.95353i	−0.786366	−	0.617761i
$11$		−	4.31560i		−	1.30120i	−0.759420	−	0.650600i	$-0.774517\pi$
$11$		−	4.31560i		−	1.30120i	0.759420	−	0.650600i	$-0.225483\pi$
$12$	−0.627290	−	0.125149i	−0.181083	−	0.0361274i
$13$	2.16506			0.600478			0.300239	−	0.953864i	$-0.402933\pi$
$13$	2.16506			0.600478			0.300239	+	0.953864i	$0.402933\pi$
$14$	−1.40736	−	0.139020i	−0.376134	−	0.0371547i
$15$	0.384372	−	0.603077i	0.0992443	−	0.155714i
$16$	3.69376	+	1.53496i	0.923441	+	0.383741i
$17$			3.19581i			0.775097i	0.921849	+	0.387549i	$0.126678\pi$
$17$			3.19581i			0.775097i	−0.921849	+	0.387549i	$0.873322\pi$
$18$	−0.402840	+	4.07813i	−0.0949503	+	0.961226i
$19$		−	5.38650i		−	1.23575i	−0.786278	−	0.617873i	$-0.787994\pi$
$19$		−	5.38650i		−	1.23575i	0.786278	−	0.617873i	$-0.212006\pi$
$20$	−3.09503	+	3.22812i	−0.692070	+	0.721830i
$21$		−	0.319826i		−	0.0697918i
$22$	−6.07361	−	0.599954i	−1.29490	−	0.127911i
$23$			0.947361i			0.197538i	0.995110	+	0.0987692i	$0.0314906\pi$
$23$			0.947361i			0.197538i	−0.995110	+	0.0987692i	$0.968509\pi$
$24$	−0.263336	+	0.865427i	−0.0537533	+	0.176655i
$25$	−2.11128	−	4.53238i	−0.422257	−	0.906476i
$26$	0.300986	−	3.04702i	0.0590282	−	0.597570i
$27$	−1.88624			−0.363007
$28$	−0.391304	+	1.96135i	−0.0739494	+	0.370660i
$29$			7.55412i			1.40276i	0.712785	+	0.701382i	$0.247433\pi$
$29$			7.55412i			1.40276i	−0.712785	+	0.701382i	$0.752567\pi$
$30$	−0.795314	−	0.624790i	−0.145204	−	0.114071i
$31$	−1.97567			−0.354840			−0.177420	−	0.984135i	$-0.556775\pi$
$31$	−1.97567			−0.354840			−0.177420	+	0.984135i	$0.556775\pi$
$32$	2.67376	−	4.98508i	0.472659	−	0.881246i
$33$		−	1.38024i		−	0.240269i
$34$	4.49767	+	0.444281i	0.771343	+	0.0761936i
$35$	−1.88564	−	1.20181i	−0.318732	−	0.203144i
$36$	5.68342	+	1.13388i	0.947236	+	0.188981i
$37$	9.35534			1.53801			0.769004	−	0.639244i	$-0.220753\pi$
$37$	9.35534			1.53801			0.769004	+	0.639244i	$0.220753\pi$
$38$	−7.58076	−	0.748831i	−1.22976	−	0.121476i
$39$	0.692441			0.110879
$40$	4.11287	+	4.80461i	0.650302	+	0.759676i
$41$	8.13282			1.27013			0.635067	−	0.772457i	$-0.280973\pi$
$41$	8.13282			1.27013			0.635067	+	0.772457i	$0.280973\pi$
$42$	−0.450112	−	0.0444622i	−0.0694537	−	0.00686067i
$43$	2.27658			0.347175			0.173587	−	0.984818i	$-0.444464\pi$
$43$	2.27658			0.347175			0.173587	+	0.984818i	$0.444464\pi$
$44$	−1.68871	+	8.46438i	−0.254582	+	1.27605i
$45$	−3.48251	+	5.46404i	−0.519142	+	0.814532i
$46$	1.33328	+	0.131702i	0.196582	+	0.0194184i
$47$			6.88315i			1.00401i	0.864864	+	0.502006i	$0.167404\pi$
$47$			6.88315i			1.00401i	−0.864864	+	0.502006i	$0.832596\pi$
$48$	1.18136	+	0.490922i	0.170515	+	0.0708584i
$49$	−1.00000			−0.142857
$50$	−6.67222	+	2.34125i	−0.943595	+	0.331103i
$51$			1.02210i			0.143123i
$52$	−4.24643	−	0.847194i	−0.588873	−	0.117485i
$53$	6.12756			0.841685			0.420843	−	0.907134i	$-0.361734\pi$
$53$	6.12756			0.841685			0.420843	+	0.907134i	$0.361734\pi$
$54$	−0.262225	+	2.65463i	−0.0356844	+	0.361249i
$55$	−8.13766	−	5.18654i	−1.09728	−	0.699353i
$56$	2.70593	+	0.823373i	0.361595	+	0.110028i
$57$		−	1.72274i		−	0.228183i
$58$	10.6314	+	1.05017i	1.39597	+	0.137895i
$59$		−	4.30565i		−	0.560548i	−0.959920	−	0.280274i	$-0.909575\pi$
$59$		−	4.30565i		−	0.560548i	0.959920	−	0.280274i	$-0.0904253\pi$
$60$	−0.989872	+	1.03244i	−0.127792	+	0.133287i
$61$		−	0.0705077i		−	0.00902759i	−0.999990	−	0.00451380i	$-0.998563\pi$
$61$		−	0.0705077i		−	0.00902759i	0.999990	−	0.00451380i	$-0.00143679\pi$
$62$	−0.274657	+	2.78048i	−0.0348815	+	0.353121i
$63$			2.89771i			0.365077i
$64$	−6.64411	−	4.45598i	−0.830514	−	0.556997i
$65$	2.60200	−	4.08252i	0.322738	−	0.506374i
$66$	−1.94250	−	0.191881i	−0.239105	−	0.0236189i
$67$	10.1964			1.24569			0.622845	−	0.782346i	$-0.285977\pi$
$67$	10.1964			1.24569			0.622845	+	0.782346i	$0.285977\pi$
$68$	1.25053	−	6.26809i	0.151649	−	0.760117i
$69$			0.302991i			0.0364758i
$70$	−1.95353	+	2.48671i	−0.233492	+	0.297218i
$71$	5.61315			0.666159			0.333079	−	0.942899i	$-0.391912\pi$
$71$	5.61315			0.666159			0.333079	+	0.942899i	$0.391912\pi$
$72$	2.38590	−	7.84100i	0.281181	−	0.924071i
$73$			2.18227i			0.255415i	0.991812	+	0.127708i	$0.0407619\pi$
$73$			2.18227i			0.255415i	−0.991812	+	0.127708i	$0.959238\pi$
$74$	1.30058	−	13.1664i	0.151189	−	1.53056i
$75$	−0.675244	−	1.44957i	−0.0779704	−	0.167382i
$76$	−2.10775	+	10.5648i	−0.241776	+	1.21186i
$77$	−4.31560			−0.491808
$78$	0.0962632	−	0.974517i	0.0108997	−	0.110342i
$79$	10.0202			1.12737			0.563683	−	0.825991i	$-0.309384\pi$
$79$	10.0202			1.12737			0.563683	+	0.825991i	$0.309384\pi$
$80$	7.33361	−	5.12037i	0.819922	−	0.572475i
$81$	8.08986			0.898874
$82$	1.13063	−	11.4458i	0.124857	−	1.26398i
$83$	−16.4283			−1.80324			−0.901620	−	0.432530i	$-0.857621\pi$
$83$	−16.4283			−1.80324			−0.901620	+	0.432530i	$0.857621\pi$
$84$	−0.125149	+	0.627290i	−0.0136549	+	0.0684429i
$85$	6.02615	+	3.84077i	0.653627	+	0.416590i
$86$	0.316490	−	3.20397i	0.0341280	−	0.345493i
$87$			2.41600i			0.259023i
$88$	11.6777	+	3.55334i	1.24485	+	0.378788i
$89$	−13.4992			−1.43091			−0.715455	−	0.698659i	$-0.753781\pi$
$89$	−13.4992			−1.43091			−0.715455	+	0.698659i	$0.753781\pi$
$90$	7.20576	+	5.66077i	0.759554	+	0.596698i
$91$		−	2.16506i		−	0.226960i
$92$	0.370706	−	1.85810i	0.0386487	−	0.193721i
$93$	−0.631870			−0.0655218
$94$	9.68710	+	0.956896i	0.999148	+	0.0986963i
$95$	−10.1570	−	6.47357i	−1.04209	−	0.664174i
$96$	0.855138	−	1.59436i	0.0872772	−	0.162723i
$97$			11.4733i			1.16494i	0.812853	+	0.582469i	$0.197913\pi$
$97$			11.4733i			1.16494i	−0.812853	+	0.582469i	$0.802087\pi$
$98$	−0.139020	+	1.40736i	−0.0140431	+	0.142165i
$99$			12.5053i			1.25683i
$100$	2.36742	+	9.71572i	0.236742	+	0.971572i
$101$			10.0737i			1.00237i	0.865341	+	0.501184i	$0.167102\pi$
$101$			10.0737i			1.00237i	−0.865341	+	0.501184i	$0.832898\pi$
$102$	1.43847	+	0.142093i	0.142430	+	0.0140693i
$103$		−	9.84605i		−	0.970160i	−0.874470	−	0.485080i	$-0.838790\pi$
$103$		−	9.84605i		−	0.970160i	0.874470	−	0.485080i	$-0.161210\pi$
$104$	−1.78265	+	5.85849i	−0.174803	+	0.574472i
$105$	−0.603077	−	0.384372i	−0.0588543	−	0.0375108i
$106$	0.851854	−	8.62371i	0.0827393	−	0.837609i
$107$	−18.8737			−1.82459			−0.912297	−	0.409530i	$-0.865693\pi$
$107$	−18.8737			−1.82459			−0.912297	+	0.409530i	$0.865693\pi$
$108$	3.69957	+	0.738093i	0.355992	+	0.0710230i
$109$			2.69541i			0.258174i	0.991633	+	0.129087i	$0.0412046\pi$
$109$			2.69541i			0.258174i	−0.991633	+	0.129087i	$0.958795\pi$
$110$	−8.43065	+	10.7316i	−0.803831	+	1.02322i
$111$	2.99208			0.283996
$112$	1.53496	−	3.69376i	0.145040	−	0.349028i
$113$		−	5.00235i		−	0.470581i	−0.971925	−	0.235291i	$-0.924396\pi$
$113$		−	5.00235i		−	0.470581i	0.971925	−	0.235291i	$-0.0756042\pi$
$114$	−2.42452	−	0.239496i	−0.227078	−	0.0224308i
$115$	1.78638	+	1.13855i	0.166581	+	0.106171i
$116$	2.95595	−	14.8162i	0.274453	−	1.37565i
$117$	−6.27371			−0.580004
$118$	−6.05962	−	0.598572i	−0.557833	−	0.0551030i
$119$	3.19581			0.292959
$120$	1.31540	+	1.53664i	0.120079	+	0.140275i
$121$	−7.62436			−0.693124
$122$	−0.0992300	−	0.00980199i	−0.00898387	−	0.000887430i
$123$	2.60109			0.234532
$124$	3.87497	+	0.773085i	0.347982	+	0.0694251i
$125$	−11.0838	−	1.46596i	−0.991367	−	0.131119i
$126$	4.07813	+	0.402840i	0.363309	+	0.0358878i
$127$			6.20713i			0.550794i	0.961331	+	0.275397i	$0.0888093\pi$
$127$			6.20713i			0.550794i	−0.961331	+	0.275397i	$0.911191\pi$
$128$	−7.19485	+	8.73122i	−0.635941	+	0.771738i
$129$	0.728108			0.0641064
$130$	−5.38386	−	4.22951i	−0.472196	−	0.370952i
$131$		−	13.6430i		−	1.19199i	−0.802987	−	0.595997i	$-0.796757\pi$
$131$		−	13.6430i		−	1.19199i	0.802987	−	0.595997i	$-0.203243\pi$
$132$	−0.540093	+	2.70713i	−0.0470090	+	0.235625i
$133$	−5.38650			−0.467068
$134$	1.41750	−	14.3501i	0.122454	−	1.23966i
$135$	−2.26691	+	3.55677i	−0.195105	+	0.306118i
$136$	−8.64763	−	2.63134i	−0.741528	−	0.225636i
$137$			16.3488i			1.39677i	0.715723	+	0.698384i	$0.246097\pi$
$137$			16.3488i			1.39677i	−0.715723	+	0.698384i	$0.753903\pi$
$138$	0.426418	+	0.0421218i	0.0362991	+	0.00358564i
$139$			1.91419i			0.162359i	0.996699	+	0.0811796i	$0.0258687\pi$
$139$			1.91419i			0.162359i	−0.996699	+	0.0811796i	$0.974131\pi$
$140$	3.22812	+	3.09503i	0.272826	+	0.261578i
$141$			2.20141i			0.185392i
$142$	0.780341	−	7.89975i	0.0654848	−	0.662932i
$143$		−	9.34350i		−	0.781343i
$144$	−10.7035	−	4.44788i	−0.891955	−	0.370657i
$145$	14.2444	+	9.07865i	1.18293	+	0.753941i
$146$	3.07124	+	0.303379i	0.254178	+	0.0251078i
$147$	−0.319826			−0.0263788
$148$	−18.3491	−	3.66078i	−1.50828	−	0.300914i
$149$		−	14.9281i		−	1.22296i	−0.791260	−	0.611480i	$-0.790575\pi$
$149$		−	14.9281i		−	1.22296i	0.791260	−	0.611480i	$-0.209425\pi$
$150$	−2.13395	+	0.748794i	−0.174236	+	0.0611388i
$151$	0.106712			0.00868413			0.00434207	−	0.999991i	$-0.498618\pi$
$151$	0.106712			0.00868413			0.00434207	+	0.999991i	$0.498618\pi$
$152$	14.5755	+	4.43510i	1.18223	+	0.359734i
$153$		−	9.26053i		−	0.748669i
$154$	−0.599954	+	6.07361i	−0.0483457	+	0.489426i
$155$	−2.37438	+	3.72540i	−0.190715	+	0.299231i
$156$	−1.35812	−	0.270955i	−0.108736	−	0.0216937i
$157$	−10.7375			−0.856946			−0.428473	−	0.903555i	$-0.640948\pi$
$157$	−10.7375			−0.856946			−0.428473	+	0.903555i	$0.640948\pi$
$158$	1.39301	−	14.1021i	0.110822	−	1.12191i
$159$	1.95975			0.155419
$160$	−6.18670	−	11.0329i	−0.489102	−	0.872227i
$161$	0.947361			0.0746625
$162$	1.12465	−	11.3854i	0.0883611	−	0.894520i
$163$	−3.76600			−0.294976			−0.147488	−	0.989064i	$-0.547119\pi$
$163$	−3.76600			−0.294976			−0.147488	+	0.989064i	$0.547119\pi$
$164$	−15.9513	−	3.18240i	−1.24559	−	0.248504i
$165$	−2.60264	−	1.65879i	−0.202615	−	0.129137i
$166$	−2.28386	+	23.1206i	−0.177262	+	1.79451i
$167$			24.5491i			1.89967i	0.312754	+	0.949834i	$0.398748\pi$
$167$			24.5491i			1.89967i	−0.312754	+	0.949834i	$0.601252\pi$
$168$	0.865427	+	0.263336i	0.0667691	+	0.0203168i
$169$	−8.31253			−0.639426
$170$	6.24311	−	7.94704i	0.478825	−	0.609510i
$171$			15.6085i			1.19361i
$172$	−4.46515	−	0.890832i	−0.340465	−	0.0679253i
$173$	−18.9785			−1.44291			−0.721453	−	0.692464i	$-0.756525\pi$
$173$	−18.9785			−1.44291			−0.721453	+	0.692464i	$0.756525\pi$
$174$	3.40020	+	0.335873i	0.257768	+	0.0254625i
$175$	−4.53238	+	2.11128i	−0.342616	+	0.159598i
$176$	6.62428	−	15.9408i	0.499324	−	1.20158i
$177$		−	1.37706i		−	0.103506i
$178$	−1.87666	+	18.9983i	−0.140661	+	1.42398i
$179$		−	1.39807i		−	0.104497i	−0.998634	−	0.0522483i	$-0.983361\pi$
$179$		−	1.39807i		−	0.104497i	0.998634	−	0.0522483i	$-0.0166387\pi$
$180$	8.96851	−	9.35417i	0.668473	−	0.697218i
$181$		−	19.9912i		−	1.48593i	−0.669329	−	0.742966i	$-0.733418\pi$
$181$		−	19.9912i		−	1.48593i	0.669329	−	0.742966i	$-0.266582\pi$
$182$	−3.04702	−	0.300986i	−0.225860	−	0.0223106i
$183$		−	0.0225502i		−	0.00166696i
$184$	−2.56349	−	0.780031i	−0.188983	−	0.0575047i
$185$	11.2434	−	17.6408i	0.826630	−	1.29698i
$186$	−0.0878425	+	0.889270i	−0.00644093	+	0.0652045i
$187$	13.7918			1.00856
$188$	2.69340	−	13.5003i	0.196437	−	0.984607i
$189$			1.88624i			0.137204i
$190$	−10.5227	+	13.3946i	−0.763396	+	0.971749i
$191$	−16.1124			−1.16585			−0.582925	−	0.812526i	$-0.698092\pi$
$191$	−16.1124			−1.16585			−0.582925	+	0.812526i	$0.698092\pi$
$192$	−2.12496	−	1.42514i	−0.153356	−	0.102851i
$193$		−	12.9801i		−	0.934329i	−0.884170	−	0.467165i	$-0.845276\pi$
$193$		−	12.9801i		−	0.934329i	0.884170	−	0.467165i	$-0.154724\pi$
$194$	16.1471	+	1.59502i	1.15929	+	0.114516i
$195$	0.832186	−	1.30570i	0.0595941	−	0.0935028i
$196$	1.96135	+	0.391304i	0.140096	+	0.0279503i
$197$	16.5028			1.17577			0.587887	−	0.808943i	$-0.299960\pi$
$197$	16.5028			1.17577			0.587887	+	0.808943i	$0.299960\pi$
$198$	17.5996	+	1.73849i	1.25075	+	0.123549i
$199$	21.6505			1.53477			0.767383	−	0.641189i	$-0.221559\pi$
$199$	21.6505			1.53477			0.767383	+	0.641189i	$0.221559\pi$
$200$	14.0027	−	1.98115i	0.990139	−	0.140088i
$201$	3.26108			0.230019
$202$	14.1773	+	1.40044i	0.997513	+	0.0985348i
$203$	7.55412			0.530195
$204$	0.399952	−	2.00470i	0.0280023	−	0.140357i
$205$	9.77414	−	15.3356i	0.682656	−	1.07108i
$206$	−13.8570	−	1.36880i	−0.965461	−	0.0953687i
$207$		−	2.74518i		−	0.190803i
$208$	7.99720	+	3.32328i	0.554506	+	0.230428i
$209$	−23.2459			−1.60795
$210$	−0.624790	+	0.795314i	−0.0431146	+	0.0548819i
$211$			24.5315i			1.68882i	0.535698	+	0.844409i	$0.320048\pi$
$211$			24.5315i			1.68882i	−0.535698	+	0.844409i	$0.679952\pi$
$212$	−12.0183	−	2.39774i	−0.825418	−	0.164677i
$213$	1.79523			0.123007
$214$	−2.62383	+	26.5622i	−0.179361	+	1.81576i
$215$	2.73602	−	4.29280i	0.186595	−	0.292767i
$216$	1.55308	−	5.10404i	0.105674	−	0.347286i
$217$			1.97567i			0.134117i
$218$	3.79342	+	0.374716i	0.256923	+	0.0253790i
$219$			0.697946i			0.0471628i
$220$	13.9313	+	13.3569i	0.939246	+	0.900523i
$221$			6.91910i			0.465429i
$222$	0.415959	−	4.21095i	0.0279174	−	0.282620i
$223$		−	7.24853i		−	0.485398i	−0.970102	−	0.242699i	$-0.921967\pi$
$223$		−	7.24853i		−	0.485398i	0.970102	−	0.242699i	$-0.0780327\pi$
$224$	−4.98508	−	2.67376i	−0.333080	−	0.178648i
$225$	6.11789	+	13.1335i	0.407860	+	0.875569i
$226$	−7.04012	−	0.695426i	−0.468302	−	0.0462591i
$227$	24.2854			1.61188			0.805939	−	0.591998i	$-0.201661\pi$
$227$	24.2854			1.61188			0.805939	+	0.591998i	$0.201661\pi$
$228$	−0.674115	+	3.37889i	−0.0446444	+	0.223773i
$229$		−	6.92485i		−	0.457607i	−0.973473	−	0.228803i	$-0.926519\pi$
$229$		−	6.92485i		−	0.457607i	0.973473	−	0.228803i	$-0.0734813\pi$
$230$	1.85070	−	2.35581i	0.122032	−	0.155337i
$231$	−1.38024			−0.0908131
$232$	−20.4409	−	6.21986i	−1.34201	−	0.408354i
$233$			10.1782i			0.666796i	0.942786	+	0.333398i	$0.108195\pi$
$233$			10.1782i			0.666796i	−0.942786	+	0.333398i	$0.891805\pi$
$234$	−0.872171	+	8.82939i	−0.0570156	+	0.577195i
$235$	12.9792	+	8.27227i	0.846667	+	0.539624i
$236$	−1.68482	+	8.44488i	−0.109672	+	0.549715i
$237$	3.20473			0.208170
$238$	0.444281	−	4.49767i	0.0287985	−	0.291540i
$239$	0.483092			0.0312487			0.0156243	−	0.999878i	$-0.495026\pi$
$239$	0.483092			0.0312487			0.0156243	+	0.999878i	$0.495026\pi$
$240$	2.34548	−	1.63763i	0.151400	−	0.105708i
$241$	−14.0241			−0.903369			−0.451685	−	0.892178i	$-0.649177\pi$
$241$	−14.0241			−0.903369			−0.451685	+	0.892178i	$0.649177\pi$
$242$	−1.05994	+	10.7303i	−0.0681355	+	0.689767i
$243$	8.24607			0.528986
$244$	−0.0275899	+	0.138290i	−0.00176626	+	0.00885312i
$245$	−1.20181	+	1.88564i	−0.0767811	+	0.120469i
$246$	0.361603	−	3.66068i	0.0230550	−	0.233396i
$247$		−	11.6621i		−	0.742039i
$248$	1.62671	−	5.34601i	0.103296	−	0.339472i
$249$	−5.25420			−0.332971
$250$	−3.60401	+	15.3952i	−0.227937	+	0.973676i
$251$		−	4.58585i		−	0.289456i	−0.989471	−	0.144728i	$-0.953769\pi$
$251$		−	4.58585i		−	0.289456i	0.989471	−	0.144728i	$-0.0462308\pi$
$252$	1.13388	−	5.68342i	0.0714280	−	0.358022i
$253$	4.08843			0.257037
$254$	8.73569	+	0.862915i	0.548126	+	0.0541441i
$255$	1.92732	+	1.22838i	0.120693	+	0.0769240i
$256$	11.2878	+	11.3396i	0.705486	+	0.708724i
$257$		−	19.6305i		−	1.22452i	−0.790657	−	0.612260i	$-0.790261\pi$
$257$		−	19.6305i		−	1.22452i	0.790657	−	0.612260i	$-0.209739\pi$
$258$	0.101222	−	1.02471i	0.00630178	−	0.0637959i
$259$		−	9.35534i		−	0.581312i
$260$	−6.70092	+	6.98906i	−0.415573	+	0.433443i
$261$		−	21.8897i		−	1.35494i
$262$	−19.2006	−	1.89665i	−1.18622	−	0.117175i
$263$			13.7976i			0.850796i	0.905006	+	0.425398i	$0.139866\pi$
$263$			13.7976i			0.850796i	−0.905006	+	0.425398i	$0.860134\pi$
$264$	3.73483	+	1.13645i	0.229863	+	0.0699438i
$265$	7.36419	−	11.5544i	0.452379	−	0.709780i
$266$	−0.748831	+	7.58076i	−0.0459138	+	0.464806i
$267$	−4.31739			−0.264220
$268$	−19.9987	−	3.98989i	−1.22161	−	0.243721i
$269$			16.3189i			0.994981i	0.867469	+	0.497491i	$0.165745\pi$
$269$			16.3189i			0.994981i	−0.867469	+	0.497491i	$0.834255\pi$
$270$	4.69053	+	3.68483i	0.285457	+	0.224252i
$271$	−12.5470			−0.762176			−0.381088	−	0.924539i	$-0.624451\pi$
$271$	−12.5470			−0.762176			−0.381088	+	0.924539i	$0.624451\pi$
$272$	−4.90545	+	11.8046i	−0.297437	+	0.715756i
$273$		−	0.692441i		−	0.0419085i
$274$	23.0086	+	2.27280i	1.39000	+	0.137305i
$275$	−19.5599	+	9.11145i	−1.17951	+	0.549441i
$276$	0.118561	−	0.594270i	0.00713655	−	0.0357708i
$277$	−1.71783			−0.103214			−0.0516071	−	0.998667i	$-0.516434\pi$
$277$	−1.71783			−0.103214			−0.0516071	+	0.998667i	$0.516434\pi$
$278$	2.69396	+	0.266110i	0.161573	+	0.0159602i
$279$	5.72491			0.342741
$280$	4.80461	−	4.11287i	0.287130	−	0.245791i
$281$	20.0452			1.19579			0.597897	−	0.801573i	$-0.296003\pi$
$281$	20.0452			1.19579			0.597897	+	0.801573i	$0.296003\pi$
$282$	3.09819	+	0.306040i	0.184494	+	0.0182244i
$283$	16.3366			0.971108			0.485554	−	0.874207i	$-0.338618\pi$
$283$	16.3366			0.971108			0.485554	+	0.874207i	$0.338618\pi$
$284$	−11.0093	−	2.19645i	−0.653284	−	0.130335i
$285$	−3.24847	−	2.07042i	−0.192423	−	0.122641i
$286$	−13.1497	−	1.29893i	−0.777559	−	0.0768076i
$287$		−	8.13282i		−	0.480065i
$288$	−7.74779	+	14.4453i	−0.456543	+	0.851199i
$289$	6.78681			0.399224
$290$	14.7572	−	18.7849i	0.866573	−	1.10309i
$291$			3.66946i			0.215108i
$292$	0.853929	−	4.28018i	0.0499724	−	0.250479i
$293$	18.2850			1.06822			0.534109	−	0.845415i	$-0.320647\pi$
$293$	18.2850			1.06822			0.534109	+	0.845415i	$0.320647\pi$
$294$	−0.0444622	+	0.450112i	−0.00259309	+	0.0262510i
$295$	−8.11891	−	5.17459i	−0.472701	−	0.301277i
$296$	−7.70293	+	25.3149i	−0.447724	+	1.47140i
$297$			8.14026i			0.472346i
$298$	−21.0093	−	2.07531i	−1.21704	−	0.120219i
$299$			2.05109i			0.118618i
$300$	0.757164	+	3.10734i	0.0437149	+	0.179402i
$301$		−	2.27658i		−	0.131220i
$302$	0.0148352	−	0.150183i	0.000853668	−	0.00864207i
$303$			3.22182i			0.185089i
$304$	8.26808	−	19.8964i	0.474207	−	1.14114i
$305$	−0.132952	−	0.0847372i	−0.00761283	−	0.00485204i
$306$	−13.0329	−	1.28740i	−0.745043	−	0.0735957i
$307$	0.296292			0.0169103			0.00845513	−	0.999964i	$-0.497309\pi$
$307$	0.296292			0.0169103			0.00845513	+	0.999964i	$0.497309\pi$
$308$	8.46438	+	1.68871i	0.482303	+	0.0962231i
$309$		−	3.14902i		−	0.179142i
$310$	4.91290	+	3.85953i	0.279034	+	0.219206i
$311$	−25.9792			−1.47315			−0.736573	−	0.676358i	$-0.763557\pi$
$311$	−25.9792			−1.47315			−0.736573	+	0.676358i	$0.763557\pi$
$312$	−0.570138	+	1.87370i	−0.0322777	+	0.106077i
$313$			19.2606i			1.08867i	0.838867	+	0.544336i	$0.183218\pi$
$313$			19.2606i			1.08867i	−0.838867	+	0.544336i	$0.816782\pi$
$314$	−1.49273	+	15.1116i	−0.0842395	+	0.852796i
$315$	5.46404	+	3.48251i	0.307864	+	0.196217i
$316$	−19.6532	−	3.92096i	−1.10558	−	0.220571i
$317$	1.29196			0.0725638			0.0362819	−	0.999342i	$-0.488449\pi$
$317$	1.29196			0.0725638			0.0362819	+	0.999342i	$0.488449\pi$
$318$	0.272445	−	2.75809i	0.0152780	−	0.154666i
$319$	32.6005			1.82528
$320$	−16.3874	+	7.17315i	−0.916082	+	0.400991i
$321$	−6.03631			−0.336914
$322$	0.131702	−	1.33328i	0.00733947	−	0.0743009i
$323$	17.2142			0.957824
$324$	−15.8670	−	3.16559i	−0.881502	−	0.175866i
$325$	−4.57105	−	9.81286i	−0.253556	−	0.544319i
$326$	−0.523550	+	5.30013i	−0.0289967	+	0.293547i
$327$			0.862063i			0.0476722i
$328$	−6.69635	+	22.0068i	−0.369744	+	1.21512i
$329$	6.88315			0.379481
$330$	−2.69634	+	3.43225i	−0.148429	+	0.188939i
$331$			14.5727i			0.800986i	0.916300	+	0.400493i	$0.131161\pi$
$331$			14.5727i			0.800986i	−0.916300	+	0.400493i	$0.868839\pi$
$332$	32.2216	+	6.42845i	1.76839	+	0.352807i
$333$	−27.1091			−1.48557
$334$	34.5496	+	3.41282i	1.89047	+	0.186741i
$335$	12.2542	−	19.2268i	0.669518	−	1.05047i
$336$	0.490922	−	1.18136i	0.0267820	−	0.0644486i
$337$		−	14.6600i		−	0.798580i	−0.916825	−	0.399290i	$-0.869257\pi$
$337$		−	14.6600i		−	0.798580i	0.916825	−	0.399290i	$-0.130743\pi$
$338$	−1.15561	+	11.6988i	−0.0628568	+	0.636329i
$339$		−	1.59988i		−	0.0868936i
$340$	−10.3165	−	9.89113i	−0.559489	−	0.536422i
$341$			8.52618i			0.461718i
$342$	21.9669	+	2.16990i	1.18783	+	0.117335i
$343$			1.00000i			0.0539949i
$344$	−1.87447	+	6.16025i	−0.101065	+	0.332139i
$345$	0.571332	+	0.364139i	0.0307595	+	0.0196046i
$346$	−2.63839	+	26.7096i	−0.141841	+	1.43592i
$347$	−2.43803			−0.130880			−0.0654400	−	0.997857i	$-0.520845\pi$
$347$	−2.43803			−0.130880			−0.0654400	+	0.997857i	$0.520845\pi$
$348$	0.945391	−	4.73862i	0.0506783	−	0.254017i
$349$		−	22.0454i		−	1.18007i	−0.807379	−	0.590033i	$-0.799115\pi$
$349$		−	22.0454i		−	1.18007i	0.807379	−	0.590033i	$-0.200885\pi$
$350$	2.34125	+	6.67222i	0.125145	+	0.356645i
$351$	−4.08382			−0.217978
$352$	−21.5136	−	11.5389i	−1.14668	−	0.615024i
$353$			21.9292i			1.16717i	0.812050	+	0.583587i	$0.198351\pi$
$353$			21.9292i			1.16717i	−0.812050	+	0.583587i	$0.801649\pi$
$354$	−1.93802	−	0.191439i	−0.103005	−	0.0101749i
$355$	6.74597	−	10.5844i	0.358039	−	0.561761i
$356$	26.4766	+	5.28228i	1.40326	+	0.279960i
$357$	1.02210			0.0540954
$358$	−1.96759	−	0.194360i	−0.103991	−	0.0102722i
$359$	25.8696			1.36535			0.682674	−	0.730724i	$-0.260817\pi$
$359$	25.8696			1.36535			0.682674	+	0.730724i	$0.260817\pi$
$360$	−11.9179	−	13.9224i	−0.628129	−	0.733774i
$361$	−10.0143			−0.527070
$362$	−28.1349	−	2.77917i	−1.47874	−	0.146070i
$363$	−2.43847			−0.127986
$364$	−0.847194	+	4.24643i	−0.0444050	+	0.222573i
$365$	4.11497	+	2.62268i	0.215388	+	0.137277i
$366$	−0.0317364	−	0.00313493i	−0.00165889	−	0.000163865i
$367$			8.32030i			0.434316i	0.976136	+	0.217158i	$0.0696787\pi$
$367$			8.32030i			0.434316i	−0.976136	+	0.217158i	$0.930321\pi$
$368$	−1.45416	+	3.49933i	−0.0758036	+	0.182415i
$369$	−23.5666			−1.22683
$370$	−23.2640	−	18.2760i	−1.20944	−	0.950122i
$371$		−	6.12756i		−	0.318127i
$372$	1.23932	+	0.247253i	0.0642555	+	0.0128195i
$373$	31.1510			1.61294			0.806468	−	0.591277i	$-0.201376\pi$
$373$	31.1510			1.61294			0.806468	+	0.591277i	$0.201376\pi$
$374$	1.91734	−	19.4101i	0.0991432	−	1.00367i
$375$	−3.54489	−	0.468851i	−0.183057	−	0.0242114i
$376$	−18.6253	−	5.66740i	−0.960528	−	0.292274i
$377$			16.3551i			0.842330i
$378$	2.65463	+	0.262225i	0.136539	+	0.0134874i
$379$		−	6.70705i		−	0.344518i	−0.985052	−	0.172259i	$-0.944893\pi$
$379$		−	6.70705i		−	0.344518i	0.985052	−	0.172259i	$-0.0551066\pi$
$380$	17.3883	+	16.6714i	0.891999	+	0.855224i
$381$			1.98520i			0.101705i
$382$	−2.23994	+	22.6759i	−0.114605	+	1.16020i
$383$			9.09458i			0.464711i	0.972631	+	0.232356i	$0.0746433\pi$
$383$			9.09458i			0.464711i	−0.972631	+	0.232356i	$0.925357\pi$
$384$	−2.30110	+	2.79247i	−0.117428	+	0.142503i
$385$	−5.18654	+	8.13766i	−0.264331	+	0.414734i
$386$	−18.2677	−	1.80450i	−0.929804	−	0.0918464i
$387$	−6.59686			−0.335337
$388$	4.48954	−	22.5031i	0.227922	−	1.14242i
$389$			3.44036i			0.174433i	0.996189	+	0.0872167i	$0.0277973\pi$
$389$			3.44036i			0.174433i	−0.996189	+	0.0872167i	$0.972203\pi$
$390$	−1.72190	−	1.35271i	−0.0871917	−	0.0684969i
$391$	−3.02758			−0.153111
$392$	0.823373	−	2.70593i	0.0415866	−	0.136670i
$393$		−	4.36338i		−	0.220104i
$394$	2.29422	−	23.2254i	0.115581	−	1.17008i
$395$	12.0425	−	18.8946i	0.605922	−	0.950689i
$396$	4.89339	−	24.5273i	0.245902	−	1.23254i
$397$	−22.8353			−1.14607			−0.573035	−	0.819531i	$-0.694234\pi$
$397$	−22.8353			−1.14607			−0.573035	+	0.819531i	$0.694234\pi$
$398$	3.00986	−	30.4702i	0.150871	−	1.52733i
$399$	−1.72274			−0.0862449
$400$	−0.841543	−	19.9823i	−0.0420771	−	0.999114i
$401$	2.13911			0.106822			0.0534111	−	0.998573i	$-0.482991\pi$
$401$	2.13911			0.106822			0.0534111	+	0.998573i	$0.482991\pi$
$402$	0.453355	−	4.58952i	0.0226113	−	0.228904i
$403$	−4.27743			−0.213074
$404$	3.94187	−	19.7580i	0.196115	−	0.982996i
$405$	9.72252	−	15.2546i	0.483116	−	0.758006i
$406$	1.05017	−	10.6314i	0.0521192	−	0.527627i
$407$		−	40.3739i		−	2.00126i
$408$	−2.76574	−	0.841572i	−0.136924	−	0.0416640i
$409$	4.74000			0.234378			0.117189	−	0.993110i	$-0.462612\pi$
$409$	4.74000			0.234378			0.117189	+	0.993110i	$0.462612\pi$
$410$	−20.2239	−	15.8877i	−0.998790	−	0.784639i
$411$			5.22876i			0.257916i
$412$	−3.85279	+	19.3115i	−0.189814	+	0.951410i
$413$	−4.30565			−0.211867
$414$	−3.86346	−	0.381635i	−0.189879	−	0.0187563i
$415$	−19.7438	+	30.9779i	−0.969183	+	1.52064i
$416$	5.78884	−	10.7930i	0.283821	−	0.529169i
$417$			0.612207i			0.0299799i
$418$	−3.23165	+	32.7155i	−0.158065	+	1.60017i
$419$		−	1.06086i		−	0.0518265i	−0.999664	−	0.0259133i	$-0.991751\pi$
$419$		−	1.06086i		−	0.0518265i	0.999664	−	0.0259133i	$-0.00824937\pi$
$420$	1.03244	+	0.989872i	0.0503778	+	0.0483008i
$421$		−	11.4474i		−	0.557912i	−0.960304	−	0.278956i	$-0.910012\pi$
$421$		−	11.4474i		−	0.557912i	0.960304	−	0.278956i	$-0.0899884\pi$
$422$	34.5248	+	3.41037i	1.68064	+	0.166014i
$423$		−	19.9454i		−	0.969778i
$424$	−5.04527	+	16.5808i	−0.245020	+	0.805232i
$425$	14.4846	−	6.74726i	0.702607	−	0.327290i
$426$	0.249573	−	2.52655i	0.0120919	−	0.122412i
$427$	−0.0705077			−0.00341211
$428$	37.0180	+	7.38536i	1.78933	+	0.356985i
$429$		−	2.98830i		−	0.144276i
$430$	−5.66118	−	4.44736i	−0.273006	−	0.214471i
$431$	−2.17956			−0.104986			−0.0524929	−	0.998621i	$-0.516717\pi$
$431$	−2.17956			−0.104986			−0.0524929	+	0.998621i	$0.516717\pi$
$432$	−6.96733	−	2.89531i	−0.335216	−	0.139301i
$433$		−	19.2652i		−	0.925827i	−0.886403	−	0.462914i	$-0.846804\pi$
$433$		−	19.2652i		−	0.925827i	0.886403	−	0.462914i	$-0.153196\pi$
$434$	2.78048	+	0.274657i	0.133467	+	0.0131840i
$435$	4.55572	+	2.90359i	0.218430	+	0.139216i
$436$	1.05472	−	5.28664i	0.0505121	−	0.253184i
$437$	5.10295			0.244107
$438$	0.982264	+	0.0970285i	0.0469344	+	0.00463620i
$439$	−36.2154			−1.72847			−0.864233	−	0.503091i	$-0.832196\pi$
$439$	−36.2154			−1.72847			−0.864233	+	0.503091i	$0.832196\pi$
$440$	20.7348	−	17.7495i	0.988491	−	0.846174i
$441$	2.89771			0.137986
$442$	9.73770	+	0.961894i	0.463175	+	0.0457526i
$443$	−36.5965			−1.73875			−0.869377	−	0.494150i	$-0.835479\pi$
$443$	−36.5965			−1.73875			−0.869377	+	0.494150i	$0.835479\pi$
$444$	−5.86851	−	1.17081i	−0.278507	−	0.0555643i
$445$	−16.2235	+	25.4546i	−0.769068	+	1.20666i
$446$	−10.2013	−	1.00769i	−0.483047	−	0.0477156i
$447$		−	4.77440i		−	0.225821i
$448$	−4.45598	+	6.64411i	−0.210525	+	0.313905i
$449$	−30.2438			−1.42729			−0.713647	−	0.700506i	$-0.752958\pi$
$449$	−30.2438			−1.42729			−0.713647	+	0.700506i	$0.752958\pi$
$450$	19.3342	−	6.78428i	0.911421	−	0.319814i
$451$		−	35.0980i		−	1.65270i
$452$	−1.95744	+	9.81133i	−0.0920700	+	0.461486i
$453$	0.0341294			0.00160354
$454$	3.37616	−	34.1784i	0.158451	−	1.60407i
$455$	−4.08252	−	2.60200i	−0.191391	−	0.121983i
$456$	4.66162	+	1.41846i	0.218300	+	0.0664254i
$457$		−	19.8067i		−	0.926517i	−0.886223	−	0.463258i	$-0.846680\pi$
$457$		−	19.8067i		−	0.926517i	0.886223	−	0.463258i	$-0.153320\pi$
$458$	−9.74578	−	0.962693i	−0.455390	−	0.0449837i
$459$		−	6.02807i		−	0.281366i
$460$	−3.05820	−	2.93211i	−0.142589	−	0.136710i
$461$			24.5182i			1.14193i	0.820976	+	0.570963i	$0.193430\pi$
$461$			24.5182i			1.14193i	−0.820976	+	0.570963i	$0.806570\pi$
$462$	−0.191881	+	1.94250i	−0.00892711	+	0.0903733i
$463$			29.3342i			1.36328i	0.731689	+	0.681638i	$0.238732\pi$
$463$			29.3342i			1.36328i	−0.731689	+	0.681638i	$0.761268\pi$
$464$	−11.5953	+	27.9031i	−0.538298	+	1.29537i
$465$	−0.759390	+	1.19148i	−0.0352159	+	0.0552535i
$466$	14.3244	+	1.41497i	0.663566	+	0.0655473i
$467$	−34.1899			−1.58212			−0.791060	−	0.611738i	$-0.790470\pi$
$467$	−34.1899			−1.58212			−0.791060	+	0.611738i	$0.790470\pi$
$468$	12.3049	+	2.45492i	0.568795	+	0.113479i
$469$		−	10.1964i		−	0.470826i
$470$	13.4465	−	17.1164i	0.620239	−	0.789520i
$471$	−3.43413			−0.158237
$472$	11.6508	+	3.54516i	0.536271	+	0.163179i
$473$		−	9.82478i		−	0.451744i
$474$	0.445522	−	4.51023i	0.0204635	−	0.207162i
$475$	−24.4136	+	11.3724i	−1.12018	+	0.521803i
$476$	−6.26809	−	1.25053i	−0.287297	−	0.0573180i
$477$	−17.7559			−0.812987
$478$	0.0671595	−	0.679887i	0.00307181	−	0.0310973i
$479$	8.33951			0.381042			0.190521	−	0.981683i	$-0.438982\pi$
$479$	8.33951			0.381042			0.190521	+	0.981683i	$0.438982\pi$
$480$	−1.97867	−	3.52861i	−0.0903135	−	0.161058i
$481$	20.2548			0.923541
$482$	−1.94963	+	19.7370i	−0.0888030	+	0.898994i
$483$	0.302991			0.0137866
$484$	14.9540	+	2.98344i	0.679728	+	0.135611i
$485$	21.6345	+	13.7888i	0.982373	+	0.626116i
$486$	1.14637	−	11.6052i	0.0520004	−	0.526424i
$487$			11.4033i			0.516731i	0.966047	+	0.258366i	$0.0831840\pi$
$487$			11.4033i			0.516731i	−0.966047	+	0.258366i	$0.916816\pi$
$488$	0.190789	+	0.0580542i	0.00863661	+	0.00262799i
$489$	−1.20447			−0.0544678
$490$	2.48671	+	1.95353i	0.112338	+	0.0882516i
$491$		−	29.0913i		−	1.31287i	−0.754381	−	0.656437i	$-0.772063\pi$
$491$		−	29.0913i		−	1.31287i	0.754381	−	0.656437i	$-0.227937\pi$
$492$	−5.10164	−	1.01782i	−0.230000	−	0.0458867i
$493$	−24.1415			−1.08728
$494$	−16.4128	−	1.62126i	−0.738445	−	0.0729440i
$495$	23.5806	+	15.0291i	1.05987	+	0.675508i
$496$	−7.29764	−	3.03258i	−0.327674	−	0.136167i
$497$		−	5.61315i		−	0.251784i
$498$	−0.730438	+	7.39457i	−0.0327317	+	0.331358i
$499$			35.8988i			1.60705i	0.595270	+	0.803526i	$0.297045\pi$
$499$			35.8988i			1.60705i	−0.595270	+	0.803526i	$0.702955\pi$
$500$	21.1656	+	7.21238i	0.946553	+	0.322548i
$501$			7.85145i			0.350777i
$502$	−6.45396	−	0.637525i	−0.288055	−	0.0284542i
$503$			24.3630i			1.08629i	0.839639	+	0.543145i	$0.182767\pi$
$503$			24.3630i			1.08629i	−0.839639	+	0.543145i	$0.817233\pi$
$504$	−7.84100	−	2.38590i	−0.349266	−	0.106276i
$505$	18.9953	+	12.1067i	0.845281	+	0.538741i
$506$	0.568373	−	5.75390i	0.0252673	−	0.255792i
$507$	−2.65856			−0.118071
$508$	2.42887	−	12.1743i	0.107764	−	0.540149i
$509$			42.2864i			1.87431i	0.348911	+	0.937156i	$0.386551\pi$
$509$			42.2864i			1.87431i	−0.348911	+	0.937156i	$0.613449\pi$
$510$	1.99671	−	2.54167i	0.0884158	−	0.112547i
$511$	2.18227			0.0965378
$512$	17.5282	−	14.3096i	0.774642	−	0.632400i
$513$			10.1602i			0.448585i
$514$	−27.6273	−	2.72904i	−1.21859	−	0.120373i
$515$	−18.5661	−	11.8331i	−0.818121	−	0.521430i
$516$	−1.42807	−	0.284911i	−0.0628674	−	0.0125425i
$517$	29.7049			1.30642
$518$	−13.1664	−	1.30058i	−0.578497	−	0.0571442i
$519$	−6.06981			−0.266435
$520$	8.90460	+	10.4023i	0.390492	+	0.456169i
$521$	−4.28566			−0.187758			−0.0938790	−	0.995584i	$-0.529927\pi$
$521$	−4.28566			−0.187758			−0.0938790	+	0.995584i	$0.529927\pi$
$522$	−30.8067	−	3.04310i	−1.34837	−	0.133193i
$523$	4.71705			0.206262			0.103131	−	0.994668i	$-0.467114\pi$
$523$	4.71705			0.206262			0.103131	+	0.994668i	$0.467114\pi$
$524$	−5.33855	+	26.7586i	−0.233216	+	1.16896i
$525$	−1.44957	+	0.675244i	−0.0632646	+	0.0294701i
$526$	19.4182	+	1.91814i	0.846675	+	0.0836349i
$527$		−	6.31385i		−	0.275036i
$528$	2.11862	−	5.09828i	0.0922010	−	0.221874i
$529$	22.1025			0.960979
$530$	−15.2374	−	11.9704i	−0.661872	−	0.519960i
$531$			12.4765i			0.541436i
$532$	10.5648	+	2.10775i	0.458042	+	0.0913828i
$533$	17.6080			0.762688
$534$	−0.600204	+	6.07614i	−0.0259733	+	0.262940i
$535$	−22.6827	+	35.5891i	−0.980660	+	1.53865i
$536$	−8.39545	+	27.5908i	−0.362628	+	1.19174i
$537$		−	0.447139i		−	0.0192955i
$538$	22.9666	+	2.26866i	0.990162	+	0.0978087i
$539$			4.31560i			0.185886i
$540$	5.83798	−	6.08902i	0.251227	−	0.262030i
$541$			25.9673i			1.11642i	0.829700	+	0.558210i	$0.188512\pi$
$541$			25.9673i			1.11642i	−0.829700	+	0.558210i	$0.811488\pi$
$542$	−1.74429	+	17.6582i	−0.0749235	+	0.758485i
$543$		−	6.39370i		−	0.274380i
$544$	15.9314	+	8.54483i	0.683051	+	0.366356i
$545$	5.08258	+	3.23938i	0.217714	+	0.138760i
$546$	−0.974517	−	0.0962632i	−0.0417055	−	0.00411969i
$547$	−5.39594			−0.230714			−0.115357	−	0.993324i	$-0.536801\pi$
$547$	−5.39594			−0.230714			−0.115357	+	0.993324i	$0.536801\pi$
$548$	6.39733	−	32.0656i	0.273280	−	1.36977i
$549$			0.204311i			0.00871978i
$550$	10.1039	+	28.7946i	0.430832	+	1.22781i
$551$	40.6902			1.73346
$552$	−0.819872	−	0.249474i	−0.0348960	−	0.0106183i
$553$		−	10.0202i		−	0.426104i
$554$	−0.238812	+	2.41761i	−0.0101462	+	0.102714i
$555$	3.59593	−	5.64199i	0.152639	−	0.239489i
$556$	0.749028	−	3.75439i	0.0317659	−	0.159221i
$557$	−5.03653			−0.213405			−0.106702	−	0.994291i	$-0.534029\pi$
$557$	−5.03653			−0.213405			−0.106702	+	0.994291i	$0.534029\pi$
$558$	0.795877	−	8.05703i	0.0336922	−	0.341081i
$559$	4.92891			0.208471
$560$	−5.12037	−	7.33361i	−0.216375	−	0.309902i
$561$	4.41098			0.186232
$562$	2.78668	−	28.2108i	0.117549	−	1.19000i
$563$	−0.717513			−0.0302396			−0.0151198	−	0.999886i	$-0.504813\pi$
$563$	−0.717513			−0.0302396			−0.0151198	+	0.999886i	$0.504813\pi$
$564$	0.861420	−	4.31773i	0.0362723	−	0.181809i
$565$	−9.43263	−	6.01189i	−0.396834	−	0.252922i
$566$	2.27111	−	22.9915i	0.0954619	−	0.966405i
$567$		−	8.08986i		−	0.339742i
$568$	−4.62172	+	15.1888i	−0.193923	+	0.637308i
$569$	16.4900			0.691296			0.345648	−	0.938364i	$-0.387659\pi$
$569$	16.4900			0.691296			0.345648	+	0.938364i	$0.387659\pi$
$570$	−3.36543	+	4.28395i	−0.140962	+	0.179435i
$571$			1.12858i			0.0472298i	0.999721	+	0.0236149i	$0.00751755\pi$
$571$			1.12858i			0.0472298i	−0.999721	+	0.0236149i	$0.992482\pi$
$572$	−3.65615	+	18.3259i	−0.152871	+	0.766242i
$573$	−5.15315			−0.215276
$574$	−11.4458	−	1.13063i	−0.477740	−	0.0471914i
$575$	4.29380	−	2.00015i	0.179064	−	0.0834119i
$576$	19.2527	+	12.9121i	0.802197	+	0.538006i
$577$		−	36.2807i		−	1.51039i	−0.655503	−	0.755193i	$-0.727543\pi$
$577$		−	36.2807i		−	1.51039i	0.655503	−	0.755193i	$-0.272457\pi$
$578$	0.943503	−	9.55151i	0.0392445	−	0.397291i
$579$		−	4.15138i		−	0.172525i
$580$	−24.3856	−	23.3802i	−1.01256	−	0.970812i
$581$			16.4283i			0.681560i
$582$	5.16427	+	0.510128i	0.214066	+	0.0211455i
$583$		−	26.4441i		−	1.09520i
$584$	−5.90506	−	1.79682i	−0.244353	−	0.0743530i
$585$	−7.53983	+	11.8300i	−0.311734	+	0.489109i
$586$	2.54198	−	25.7336i	0.105008	−	1.06304i
$587$	−0.344317			−0.0142115			−0.00710573	−	0.999975i	$-0.502262\pi$
$587$	−0.344317			−0.0142115			−0.00710573	+	0.999975i	$0.502262\pi$
$588$	0.627290	+	0.125149i	0.0258690	+	0.00516106i
$589$			10.6419i			0.438493i
$590$	−8.41123	+	10.7069i	−0.346285	+	0.440796i
$591$	5.27802			0.217109
$592$	34.5564	+	14.3601i	1.42026	+	0.590197i
$593$			22.9480i			0.942362i	0.882036	+	0.471181i	$0.156172\pi$
$593$			22.9480i			0.942362i	−0.882036	+	0.471181i	$0.843828\pi$
$594$	11.4563	+	1.13166i	0.470058	+	0.0464325i
$595$	3.84077	−	6.02615i	0.157456	−	0.247048i
$596$	−5.84143	+	29.2792i	−0.239274	+	1.19932i
$597$	6.92440			0.283397
$598$	2.88663	+	0.285142i	0.118043	+	0.0116603i
$599$	3.90767			0.159663			0.0798315	−	0.996808i	$-0.474562\pi$
$599$	3.90767			0.159663			0.0798315	+	0.996808i	$0.474562\pi$
$600$	4.47842	−	0.633623i	0.182831	−	0.0258675i
$601$	−13.2081			−0.538769			−0.269384	−	0.963033i	$-0.586820\pi$
$601$	−13.2081			−0.538769			−0.269384	+	0.963033i	$0.586820\pi$
$602$	−3.20397	−	0.316490i	−0.130584	−	0.0128992i
$603$	−29.5462			−1.20322
$604$	−0.209300	−	0.0417569i	−0.00851630	−	0.00169907i
$605$	−9.16307	+	14.3768i	−0.372532	+	0.584500i
$606$	4.53428	+	0.447898i	0.184193	+	0.0181946i
$607$		−	31.9342i		−	1.29617i	−0.761568	−	0.648085i	$-0.775570\pi$
$607$		−	31.9342i		−	1.29617i	0.761568	−	0.648085i	$-0.224430\pi$
$608$	−26.8521	−	14.4022i	−1.08900	−	0.584086i
$609$	2.41600			0.0979014
$610$	−0.137739	+	0.175332i	−0.00557689	+	0.00709899i
$611$			14.9024i			0.602887i
$612$	−3.62368	+	18.1631i	−0.146479	+	0.734200i
$613$	−20.5483			−0.829937			−0.414969	−	0.909836i	$-0.636207\pi$
$613$	−20.5483			−0.829937			−0.414969	+	0.909836i	$0.636207\pi$
$614$	0.0411905	−	0.416990i	0.00166231	−	0.0168284i
$615$	3.12603	−	4.90472i	0.126054	−	0.197777i
$616$	3.55334	−	11.6777i	0.143168	−	0.470508i
$617$			0.543748i			0.0218905i	0.999940	+	0.0109452i	$0.00348405\pi$
$617$			0.543748i			0.0218905i	−0.999940	+	0.0109452i	$0.996516\pi$
$618$	−4.43182	−	0.437777i	−0.178274	−	0.0176100i
$619$		−	14.5163i		−	0.583460i	−0.956501	−	0.291730i	$-0.905769\pi$
$619$		−	14.5163i		−	0.583460i	0.956501	−	0.291730i	$-0.0942308\pi$
$620$	6.11475	−	6.37769i	0.245574	−	0.256134i
$621$		−	1.78695i		−	0.0717079i
$622$	−3.61163	+	36.5622i	−0.144813	+	1.46601i
$623$			13.4992i			0.540833i
$624$	2.55771	+	1.06287i	0.102391	+	0.0425490i
$625$	−16.0850	+	19.1383i	−0.643398	+	0.765532i
$626$	27.1066	+	2.67761i	1.08340	+	0.107019i
$627$	−7.43465			−0.296912
$628$	21.0600	+	4.20162i	0.840384	+	0.167663i
$629$			29.8979i			1.19211i
$630$	5.66077	−	7.20576i	0.225531	−	0.287084i
$631$	23.5413			0.937165			0.468582	−	0.883420i	$-0.344765\pi$
$631$	23.5413			0.937165			0.468582	+	0.883420i	$0.344765\pi$
$632$	−8.25040	+	27.1141i	−0.328183	+	1.07854i
$633$			7.84582i			0.311843i
$634$	0.179609	−	1.81826i	0.00713317	−	0.0722123i
$635$	11.7044	+	7.45982i	0.464476	+	0.296034i
$636$	−3.84376	−	0.766859i	−0.152415	−	0.0304079i
$637$	−2.16506			−0.0857826
$638$	4.53212	−	45.8808i	0.179429	−	1.81644i
$639$	−16.2653			−0.643445
$640$	7.81706	+	24.0602i	0.308997	+	0.951063i
$641$	−7.64593			−0.301996			−0.150998	−	0.988534i	$-0.548249\pi$
$641$	−7.64593			−0.301996			−0.150998	+	0.988534i	$0.548249\pi$
$642$	−0.839169	+	8.49529i	−0.0331193	+	0.335282i
$643$	26.9759			1.06383			0.531914	−	0.846799i	$-0.321473\pi$
$643$	26.9759			1.06383			0.531914	+	0.846799i	$0.321473\pi$
$644$	−1.85810	−	0.370706i	−0.0732195	−	0.0146078i
$645$	0.875051	−	1.37295i	0.0344551	−	0.0540599i
$646$	2.39312	−	24.2267i	0.0941560	−	0.953185i
$647$			10.6009i			0.416763i	0.978048	+	0.208382i	$0.0668196\pi$
$647$			10.6009i			0.416763i	−0.978048	+	0.208382i	$0.933180\pi$
$648$	−6.66098	+	21.8906i	−0.261668	+	0.859944i
$649$	−18.5815			−0.729386
$650$	−14.4457	+	5.06895i	−0.566608	+	0.198820i
$651$			0.631870i			0.0247649i
$652$	7.38643	+	1.47365i	0.289275	+	0.0577126i
$653$	13.6159			0.532831			0.266416	−	0.963858i	$-0.414161\pi$
$653$	13.6159			0.532831			0.266416	+	0.963858i	$0.414161\pi$
$654$	1.21324	+	0.119844i	0.0474413	+	0.00468627i
$655$	−25.7258	−	16.3963i	−1.00519	−	0.640658i
$656$	30.0407	+	12.4836i	1.17289	+	0.487402i
$657$		−	6.32358i		−	0.246706i
$658$	0.956896	−	9.68710i	0.0373037	−	0.377643i
$659$		−	15.6129i		−	0.608193i	−0.952641	−	0.304096i	$-0.901646\pi$
$659$		−	15.6129i		−	0.608193i	0.952641	−	0.304096i	$-0.0983545\pi$
$660$	4.45558	+	4.27189i	0.173433	+	0.166283i
$661$		−	5.45451i		−	0.212156i	−0.994358	−	0.106078i	$-0.966171\pi$
$661$		−	5.45451i		−	0.212156i	0.994358	−	0.106078i	$-0.0338293\pi$
$662$	20.5090	+	2.02589i	0.797106	+	0.0787385i
$663$			2.21291i			0.0859423i
$664$	13.5266	−	44.4538i	0.524934	−	1.72514i
$665$	−6.47357	+	10.1570i	−0.251034	+	0.393871i
$666$	−3.76870	+	38.1523i	−0.146034	+	1.47837i
$667$	−7.15648			−0.277100
$668$	9.60616	−	48.1493i	0.371673	−	1.86295i
$669$		−	2.31827i		−	0.0896295i
$670$	−25.3555	−	19.9190i	−0.979567	−	0.769538i
$671$	−0.304283			−0.0117467
$672$	−1.59436	−	0.855138i	−0.0615037	−	0.0329877i
$673$		−	1.98399i		−	0.0764773i	−0.999269	−	0.0382386i	$-0.987825\pi$
$673$		−	1.98399i		−	0.0764773i	0.999269	−	0.0382386i	$-0.0121747\pi$
$674$	−20.6319	−	2.03803i	−0.794712	−	0.0785020i
$675$	3.98239	+	8.54917i	0.153282	+	0.329058i
$676$	16.3038	+	3.25272i	0.627068	+	0.125105i
$677$	19.7354			0.758495			0.379247	−	0.925295i	$-0.376183\pi$
$677$	19.7354			0.758495			0.379247	+	0.925295i	$0.376183\pi$
$678$	−2.25161	−	0.222415i	−0.0864727	−	0.00854181i
$679$	11.4733			0.440305
$680$	−15.3546	+	13.1439i	−0.588823	+	0.504047i
$681$	7.76710			0.297636
$682$	11.9994	+	1.18531i	0.459482	+	0.0453878i
$683$	−2.75254			−0.105323			−0.0526615	−	0.998612i	$-0.516770\pi$
$683$	−2.75254			−0.105323			−0.0526615	+	0.998612i	$0.516770\pi$
$684$	6.10767	−	30.6137i	0.233532	−	1.17054i
$685$	30.8279	+	19.6482i	1.17787	+	0.750718i
$686$	1.40736	+	0.139020i	0.0537334	+	0.00530781i
$687$		−	2.21475i		−	0.0844979i
$688$	8.40913	+	3.49446i	0.320595	+	0.133225i
$689$	13.2665			0.505414
$690$	0.591902	−	0.753449i	0.0225333	−	0.0286833i
$691$		−	17.8656i		−	0.679640i	−0.940491	−	0.339820i	$-0.889634\pi$
$691$		−	17.8656i		−	0.679640i	0.940491	−	0.339820i	$-0.110366\pi$
$692$	37.2233	+	7.42634i	1.41502	+	0.282307i
$693$	12.5053			0.475039
$694$	−0.338934	+	3.43119i	−0.0128658	+	0.130246i
$695$	3.60947	+	2.30050i	0.136915	+	0.0872629i
$696$	−6.53754	−	1.98927i	−0.247805	−	0.0754032i
$697$			25.9909i			0.984477i
$698$	−31.0260	−	3.06476i	−1.17435	−	0.116003i
$699$			3.25525i			0.123125i
$700$	9.71572	−	2.36742i	0.367220	−	0.0894802i
$701$		−	21.3058i		−	0.804710i	−0.915484	−	0.402355i	$-0.868192\pi$
$701$		−	21.3058i		−	0.804710i	0.915484	−	0.402355i	$-0.131808\pi$
$702$	−0.567733	+	5.74742i	−0.0214277	+	0.216922i
$703$		−	50.3925i		−	1.90059i
$704$	−19.2302	+	28.6733i	−0.724766	+	1.08067i
$705$	4.15107	+	2.64569i	0.156338	+	0.0996424i
$706$	30.8624	+	3.04860i	1.16152	+	0.114736i
$707$	10.0737			0.378860
$708$	−0.538848	+	2.70089i	−0.0202512	+	0.101506i
$709$		−	3.57791i		−	0.134371i	−0.997740	−	0.0671857i	$-0.978598\pi$
$709$		−	3.57791i		−	0.134371i	0.997740	−	0.0671857i	$-0.0214020\pi$
$710$	−13.9583	−	10.9655i	−0.523845	−	0.411527i
$711$	−29.0358			−1.08893
$712$	11.1149	−	36.5278i	0.416547	−	1.36894i
$713$		−	1.87167i		−	0.0700945i
$714$	0.142093	−	1.43847i	0.00531769	−	0.0538334i
$715$	−17.6185	−	11.2292i	−0.658894	−	0.419947i
$716$	−0.547070	+	2.74210i	−0.0204450	+	0.102477i
$717$	0.154506			0.00577012
$718$	3.59640	−	36.4080i	0.134216	−	1.35873i
$719$	−31.1438			−1.16147			−0.580735	−	0.814093i	$-0.697235\pi$
$719$	−31.1438			−1.16147			−0.580735	+	0.814093i	$0.697235\pi$
$720$	−21.2507	+	14.8374i	−0.791966	+	0.552955i
$721$	−9.84605			−0.366686
$722$	−1.39219	+	14.0938i	−0.0518120	+	0.524517i
$723$	−4.48526			−0.166809
$724$	−7.82262	+	39.2096i	−0.290725	+	1.45721i
$725$	34.2381	−	15.9489i	1.27157	−	0.592327i
$726$	−0.338996	+	3.43181i	−0.0125813	+	0.127367i
$727$			5.71789i			0.212065i	0.994363	+	0.106032i	$0.0338147\pi$
$727$			5.71789i			0.212065i	−0.994363	+	0.106032i	$0.966185\pi$
$728$	5.85849	+	1.78265i	0.217130	+	0.0660694i
$729$	−21.6323			−0.801196
$730$	4.26313	−	5.42666i	0.157786	−	0.200850i
$731$			7.27550i			0.269094i
$732$	−0.00882398	+	0.0442288i	−0.000326144	+	0.00163474i
$733$	22.7095			0.838795			0.419398	−	0.907803i	$-0.362241\pi$
$733$	22.7095			0.838795			0.419398	+	0.907803i	$0.362241\pi$
$734$	11.7097	+	1.15669i	0.432213	+	0.0426941i
$735$	−0.384372	+	0.603077i	−0.0141778	+	0.0222448i
$736$	4.72267	+	2.53302i	0.174080	+	0.0933682i
$737$		−	44.0036i		−	1.62089i
$738$	−3.27623	+	33.1667i	−0.120600	+	1.22088i
$739$		−	28.1649i		−	1.03606i	−0.855362	−	0.518031i	$-0.826665\pi$
$739$		−	28.1649i		−	1.03606i	0.855362	−	0.518031i	$-0.173335\pi$
$740$	−28.9551	+	30.2002i	−1.06441	+	1.11018i
$741$		−	3.72983i		−	0.137019i
$742$	−8.62371	−	0.851854i	−0.316586	−	0.0312725i
$743$			41.3914i			1.51850i	0.650797	+	0.759252i	$0.274435\pi$
$743$			41.3914i			1.51850i	−0.650797	+	0.759252i	$0.725565\pi$
$744$	0.520264	−	1.70979i	0.0190738	−	0.0626841i
$745$	−28.1491	−	17.9408i	−1.03130	−	0.657301i
$746$	4.33061	−	43.8408i	0.158555	−	1.60512i
$747$	47.6044			1.74176
$748$	−27.0505	−	5.39679i	−0.989065	−	0.197326i
$749$			18.8737i			0.689631i
$750$	−1.15265	+	4.92378i	−0.0420890	+	0.179791i
$751$	46.0020			1.67864			0.839318	−	0.543641i	$-0.182955\pi$
$751$	46.0020			1.67864			0.839318	+	0.543641i	$0.182955\pi$
$752$	−10.5654	+	25.4247i	−0.385280	+	0.927145i
$753$		−	1.46668i		−	0.0534486i
$754$	23.0176	+	2.27368i	0.838250	+	0.0828027i
$755$	0.128248	−	0.201221i	0.00466744	−	0.00732319i
$756$	0.738093	−	3.69957i	0.0268442	−	0.134552i
$757$	−17.9355			−0.651877			−0.325938	−	0.945391i	$-0.605680\pi$
$757$	−17.9355			−0.651877			−0.325938	+	0.945391i	$0.605680\pi$
$758$	−9.43927	−	0.932415i	−0.342850	−	0.0338668i
$759$	1.30759			0.0474623
$760$	25.8800	−	22.1540i	0.938767	−	0.803609i
$761$	13.0061			0.471471			0.235736	−	0.971817i	$-0.424250\pi$
$761$	13.0061			0.471471			0.235736	+	0.971817i	$0.424250\pi$
$762$	2.79390	+	0.275983i	0.101212	+	0.00999780i
$763$	2.69541			0.0975804
$764$	31.6019	+	6.30482i	1.14332	+	0.228100i
$765$	−17.4620	−	11.1294i	−0.631341	−	0.402386i
$766$	12.7994	+	1.26433i	0.462461	+	0.0456821i
$767$		−	9.32198i		−	0.336597i
$768$	3.61012	+	3.62670i	0.130269	+	0.130867i
$769$	33.2033			1.19734			0.598671	−	0.800995i	$-0.295696\pi$
$769$	33.2033			1.19734			0.598671	+	0.800995i	$0.295696\pi$
$770$	10.7316	+	8.43065i	0.386741	+	0.303820i
$771$		−	6.27836i		−	0.226110i
$772$	−5.07917	+	25.4585i	−0.182803	+	0.916272i
$773$	3.75488			0.135053			0.0675267	−	0.997717i	$-0.478489\pi$
$773$	3.75488			0.135053			0.0675267	+	0.997717i	$0.478489\pi$
$774$	−0.917096	+	9.28418i	−0.0329643	+	0.333713i
$775$	4.17119	+	8.95447i	0.149834	+	0.321654i
$776$	−31.0459	−	9.44681i	−1.11448	−	0.339121i
$777$		−	2.99208i		−	0.107340i
$778$	4.84185	+	0.478280i	0.173589	+	0.0171472i
$779$		−	43.8074i		−	1.56956i
$780$	−2.14313	+	2.23528i	−0.0767363	+	0.0800360i
$781$		−	24.2241i		−	0.866807i
$782$	−0.420895	+	4.26091i	−0.0150512	+	0.152370i
$783$		−	14.2489i		−	0.509214i
$784$	−3.69376	−	1.53496i	−0.131920	−	0.0548201i
$785$	−12.9045	+	20.2471i	−0.460581	+	0.722649i
$786$	−6.14087	−	0.606598i	−0.219037	−	0.0216366i
$787$	−42.6751			−1.52120			−0.760602	−	0.649218i	$-0.775096\pi$
$787$	−42.6751			−1.52120			−0.760602	+	0.649218i	$0.775096\pi$
$788$	−32.3677	−	6.45760i	−1.15305	−	0.230042i
$789$			4.41283i			0.157101i
$790$	−24.9174	−	19.5749i	−0.886522	−	0.696442i
$791$	−5.00235			−0.177863
$792$	−33.8386	−	10.2966i	−1.20240	−	0.365873i
$793$		−	0.152653i		−	0.00542087i
$794$	−3.17456	+	32.1376i	−0.112661	+	1.14052i
$795$	2.35526	−	3.69539i	0.0835325	−	0.131062i
$796$	−42.4642	−	8.47193i	−1.50510	−	0.300280i
$797$	−6.50695			−0.230488			−0.115244	−	0.993337i	$-0.536765\pi$
$797$	−6.50695			−0.230488			−0.115244	+	0.993337i	$0.536765\pi$
$798$	−0.239496	+	2.42452i	−0.00847805	+	0.0858272i
$799$	−21.9972			−0.778206
$800$	−28.2393	−	1.59358i	−0.998412	−	0.0563416i
$801$	39.1167			1.38212
$802$	0.297379	−	3.01051i	0.0105008	−	0.106305i
$803$	9.41778			0.332346
$804$	−6.39610	−	1.27607i	−0.225573	−	0.0450035i
$805$	1.13855	−	1.78638i	0.0401287	−	0.0629617i
$806$	−0.594648	+	6.01990i	−0.0209456	+	0.212042i
$807$			5.21921i			0.183725i
$808$	−27.2587	−	8.29439i	−0.958956	−	0.291796i
$809$	31.1366			1.09470			0.547352	−	0.836903i	$-0.315636\pi$
$809$	31.1366			1.09470			0.547352	+	0.836903i	$0.315636\pi$
$810$	−20.1171	−	15.8038i	−0.706844	−	0.555289i
$811$		−	13.3805i		−	0.469854i	−0.972013	−	0.234927i	$-0.924515\pi$
$811$		−	13.3805i		−	0.469854i	0.972013	−	0.234927i	$-0.0754851\pi$
$812$	−14.8162	−	2.95595i	−0.519948	−	0.103734i
$813$	−4.01286			−0.140737
$814$	−56.8207	−	5.61277i	−1.99156	−	0.196728i
$815$	−4.52603	+	7.10133i	−0.158540	+	0.248749i
$816$	−1.56889	+	3.77541i	−0.0549222	+	0.132166i
$817$		−	12.2628i		−	0.429020i
$818$	0.658956	−	6.67091i	0.0230398	−	0.233243i
$819$			6.27371i			0.219221i
$820$	−25.1714	+	26.2537i	−0.879022	+	0.916821i
$821$		−	20.9626i		−	0.731600i	−0.930693	−	0.365800i	$-0.880795\pi$
$821$		−	20.9626i		−	0.731600i	0.930693	−	0.365800i	$-0.119205\pi$
$822$	7.35877	+	0.726902i	0.256666	+	0.0253536i
$823$			13.8301i			0.482086i	0.970514	+	0.241043i	$0.0774896\pi$
$823$			13.8301i			0.482086i	−0.970514	+	0.241043i	$0.922510\pi$
$824$	26.6427	+	8.10697i	0.928143	+	0.282420i
$825$	−6.25577	+	2.91408i	−0.217798	+	0.101455i
$826$	−0.598572	+	6.05962i	−0.0208270	+	0.210841i
$827$	−12.1584			−0.422790			−0.211395	−	0.977401i	$-0.567801\pi$
$827$	−12.1584			−0.422790			−0.211395	+	0.977401i	$0.567801\pi$
$828$	−1.07420	+	5.38425i	−0.0373310	+	0.187115i
$829$		−	35.0277i		−	1.21656i	−0.793722	−	0.608281i	$-0.791859\pi$
$829$		−	35.0277i		−	1.21656i	0.793722	−	0.608281i	$-0.208141\pi$
$830$	40.8523	+	32.0932i	1.41801	+	1.11397i
$831$	−0.549406			−0.0190587
$832$	−14.3849	−	9.64745i	−0.498706	−	0.334465i
$833$		−	3.19581i		−	0.110728i
$834$	0.861598	+	0.0851090i	0.0298347	+	0.00294708i
$835$	46.2908	+	29.5035i	1.60196	+	1.02101i
$836$	45.5933	+	9.09622i	1.57688	+	0.314599i
$837$	3.72658			0.128810
$838$	−1.49302	−	0.147481i	−0.0515755	−	0.00509465i
$839$	−54.0162			−1.86485			−0.932423	−	0.361367i	$-0.882310\pi$
$839$	−54.0162			−1.86485			−0.932423	+	0.361367i	$0.882310\pi$
$840$	1.53664	−	1.31540i	0.0530191	−	0.0453857i
$841$	−28.0647			−0.967748
$842$	−16.1107	−	1.59142i	−0.555210	−	0.0548439i
$843$	6.41097			0.220805
$844$	9.59927	−	48.1148i	0.330420	−	1.65618i
$845$	−9.99012	+	15.6745i	−0.343671	+	0.539218i
$846$	−28.0704	−	2.77281i	−0.965081	−	0.0953312i
$847$			7.62436i			0.261976i
$848$	22.6338	+	9.40559i	0.777246	+	0.322989i
$849$	5.22486			0.179317
$850$	−7.48220	−	21.3231i	−0.256637	−	0.731378i
$851$			8.86288i			0.303816i
$852$	−3.52108	−	0.702481i	−0.120630	−	0.0240666i
$853$	−32.8962			−1.12634			−0.563171	−	0.826340i	$-0.690419\pi$
$853$	−32.8962			−1.12634			−0.563171	+	0.826340i	$0.690419\pi$
$854$	−0.00980199	+	0.0992300i	−0.000335417	+	0.00339558i
$855$	29.4320	+	18.7585i	1.00655	+	0.641528i
$856$	15.5401	−	51.0710i	0.531151	−	1.74557i
$857$		−	10.8426i		−	0.370375i	−0.982703	−	0.185187i	$-0.940711\pi$
$857$		−	10.8426i		−	0.370375i	0.982703	−	0.185187i	$-0.0592892\pi$
$858$	−4.20562	−	0.415433i	−0.143578	−	0.0141827i
$859$			30.4434i			1.03872i	0.854557	+	0.519358i	$0.173829\pi$
$859$			30.4434i			1.03872i	−0.854557	+	0.519358i	$0.826171\pi$
$860$	−7.04608	+	7.34906i	−0.240269	+	0.250601i
$861$		−	2.60109i		−	0.0886449i
$862$	−0.303003	+	3.06744i	−0.0103203	+	0.104477i
$863$			6.17946i			0.210351i	0.994454	+	0.105176i	$0.0335405\pi$
$863$			6.17946i			0.210351i	−0.994454	+	0.105176i	$0.966460\pi$
$864$	−5.04336	+	9.40306i	−0.171579	+	0.319899i
$865$	−22.8086	+	35.7866i	−0.775515	+	1.21678i
$866$	−27.1132	−	2.67825i	−0.921343	−	0.0910107i
$867$	2.17060			0.0737174
$868$	0.773085	−	3.87497i	0.0262402	−	0.131525i
$869$		−	43.2433i		−	1.46693i
$870$	4.71974	−	6.00789i	0.160014	−	0.203687i
$871$	22.0758			0.748009
$872$	−7.29359	−	2.21933i	−0.246992	−	0.0751560i
$873$		−	33.2463i		−	1.12522i
$874$	0.709413	−	7.18171i	0.0239962	−	0.242925i
$875$	−1.46596	+	11.0838i	−0.0495583	+	0.374701i
$876$	0.273109	−	1.36891i	0.00922749	−	0.0462513i
$877$	5.84128			0.197246			0.0986229	−	0.995125i	$-0.468556\pi$
$877$	5.84128			0.197246			0.0986229	+	0.995125i	$0.468556\pi$
$878$	−5.03467	+	50.9682i	−0.169912	+	1.72010i
$879$	5.84801			0.197248
$880$	−22.0974	−	31.6489i	−0.744905	−	1.06688i
$881$	42.6160			1.43577			0.717886	−	0.696161i	$-0.245110\pi$
$881$	42.6160			1.43577			0.717886	+	0.696161i	$0.245110\pi$
$882$	0.402840	−	4.07813i	0.0135643	−	0.137318i
$883$	−34.4349			−1.15883			−0.579413	−	0.815034i	$-0.696718\pi$
$883$	−34.4349			−1.15883			−0.579413	+	0.815034i	$0.696718\pi$
$884$	2.70747	−	13.5708i	0.0910621	−	0.456434i
$885$	−2.59664	−	1.65497i	−0.0872851	−	0.0556312i
$886$	−5.08765	+	51.5046i	−0.170923	+	1.73033i
$887$		−	15.0372i		−	0.504899i	−0.967610	−	0.252450i	$-0.918764\pi$
$887$		−	15.0372i		−	0.504899i	0.967610	−	0.252450i	$-0.0812362\pi$
$888$	−2.46360	+	8.09636i	−0.0826730	+	0.271696i
$889$	6.20713			0.208180
$890$	33.5685	+	26.3711i	1.12522	+	0.883960i
$891$		−	34.9126i		−	1.16962i
$892$	−2.83638	+	14.2169i	−0.0949689	+	0.476017i
$893$	37.0761			1.24070
$894$	−6.71932	−	0.663738i	−0.224728	−	0.0221987i
$895$	−2.63626	−	1.68022i	−0.0881204	−	0.0561636i
$896$	8.73122	+	7.19485i	0.291689	+	0.240363i
$897$			0.655992i			0.0219029i
$898$	−4.20450	+	42.5641i	−0.140306	+	1.42038i
$899$		−	14.9244i		−	0.497757i
$900$	−6.86011	−	28.1534i	−0.228670	−	0.938445i
$901$			19.5825i			0.652388i
$902$	−49.3956	−	4.87932i	−1.64469	−	0.162464i
$903$		−	0.728108i		−	0.0242299i
$904$	13.5360	+	4.11880i	0.450201	+	0.136989i
$905$	−37.6962	−	24.0257i	−1.25306	−	0.798641i
$906$	0.00474467	−	0.0480325i	0.000157631	−	0.00159577i
$907$	24.7673			0.822384			0.411192	−	0.911549i	$-0.365113\pi$
$907$	24.7673			0.822384			0.411192	+	0.911549i	$0.365113\pi$
$908$	−47.6321	−	9.50296i	−1.58073	−	0.315367i
$909$		−	29.1906i		−	0.968191i
$910$	−4.22951	+	5.38386i	−0.140207	+	0.178473i
$911$	−17.6510			−0.584804			−0.292402	−	0.956295i	$-0.594455\pi$
$911$	−17.6510			−0.584804			−0.292402	+	0.956295i	$0.594455\pi$
$912$	2.64435	−	6.36340i	0.0875631	−	0.210713i
$913$			70.8979i			2.34638i
$914$	−27.8752	−	2.75352i	−0.922029	−	0.0910785i
$915$	−0.0425216	−	0.0271012i	−0.00140572	−	0.000895937i
$916$	−2.70972	+	13.5820i	−0.0895316	+	0.448763i
$917$	−13.6430			−0.450531
$918$	−8.48368	−	0.838022i	−0.280003	−	0.0276589i
$919$	21.1056			0.696211			0.348105	−	0.937455i	$-0.386825\pi$
$919$	21.1056			0.696211			0.348105	+	0.937455i	$0.386825\pi$
$920$	−4.55170	+	3.89637i	−0.150065	+	0.128460i
$921$	0.0947618			0.00312251
$922$	34.5060	+	3.40852i	1.13640	+	0.112254i
$923$	12.1528			0.400014
$924$	2.70713	+	0.540093i	0.0890580	+	0.0177677i
$925$	−19.7518	−	42.4020i	−0.649435	−	1.39417i
$926$	41.2839	+	4.07804i	1.35667	+	0.134013i
$927$			28.5310i			0.937081i
$928$	37.6579	+	20.1979i	1.23618	+	0.663029i
$929$	−29.7053			−0.974601			−0.487300	−	0.873234i	$-0.662018\pi$
$929$	−29.7053			−0.974601			−0.487300	+	0.873234i	$0.662018\pi$
$930$	1.57127	+	1.23438i	0.0515241	+	0.0404768i
$931$			5.38650i			0.176535i
$932$	3.98276	−	19.9630i	0.130460	−	0.653909i
$933$	−8.30883			−0.272019
$934$	−4.75308	+	48.1176i	−0.155526	+	1.57446i
$935$	16.5752	−	26.0064i	0.542067	−	0.850501i
$936$	5.16560	−	16.9762i	0.168843	−	0.554885i
$937$			53.4101i			1.74483i	0.488765	+	0.872415i	$0.337447\pi$
$937$			53.4101i			1.74483i	−0.488765	+	0.872415i	$0.662553\pi$
$938$	−14.3501	−	1.41750i	−0.468546	−	0.0462832i
$939$			6.16003i			0.201025i
$940$	−22.2197	−	21.3036i	−0.724725	−	0.694846i
$941$		−	5.54752i		−	0.180844i	−0.995904	−	0.0904220i	$-0.971178\pi$
$941$		−	5.54752i		−	0.180844i	0.995904	−	0.0904220i	$-0.0288216\pi$
$942$	−0.477413	+	4.83308i	−0.0155550	+	0.157470i
$943$			7.70472i			0.250900i
$944$	6.60902	−	15.9041i	0.215105	−	0.517633i
$945$	3.55677	+	2.26691i	0.115702	+	0.0737427i
$946$	−13.8270	−	1.36584i	−0.449556	−	0.0444073i
$947$	19.2133			0.624350			0.312175	−	0.950025i	$-0.398943\pi$
$947$	19.2133			0.624350			0.312175	+	0.950025i	$0.398943\pi$
$948$	−6.28560	−	1.25402i	−0.204147	−	0.0407288i
$949$			4.72473i			0.153371i
$950$	12.6112	+	35.9399i	0.409160	+	1.16604i
$951$	0.413203			0.0133990
$952$	−2.63134	+	8.64763i	−0.0852823	+	0.280271i
$953$		−	36.8866i		−	1.19488i	−0.801915	−	0.597438i	$-0.796186\pi$
$953$		−	36.8866i		−	1.19488i	0.801915	−	0.597438i	$-0.203814\pi$
$954$	−2.46843	+	24.9890i	−0.0799182	+	0.809049i
$955$	−19.3641	+	30.3821i	−0.626606	+	0.983142i
$956$	−0.947512	−	0.189036i	−0.0306447	−	0.00611386i
$957$	10.4265			0.337041
$958$	1.15936	−	11.7367i	0.0374572	−	0.379196i
$959$	16.3488			0.527929
$960$	−5.24111	+	2.29416i	−0.169156	+	0.0740437i
$961$	−27.0967			−0.874088
$962$	2.81583	−	28.5059i	0.0907859	−	0.919068i
$963$	54.6906			1.76238
$964$	27.5060	+	5.48767i	0.885910	+	0.176746i
$965$	−24.4758	−	15.5997i	−0.787905	−	0.502172i
$966$	0.0421218	−	0.426418i	0.00135525	−	0.0137198i
$967$		−	23.1225i		−	0.743569i	−0.928319	−	0.371785i	$-0.878746\pi$
$967$		−	23.1225i		−	0.743569i	0.928319	−	0.371785i	$-0.121254\pi$
$968$	6.27769	−	20.6310i	0.201773	−	0.663105i
$969$	5.50555			0.176864
$970$	22.4135	−	28.5307i	0.719653	−	0.916067i
$971$			34.1621i			1.09632i	0.836375	+	0.548158i	$0.184671\pi$
$971$			34.1621i			1.09632i	−0.836375	+	0.548158i	$0.815329\pi$
$972$	−16.1734	−	3.22672i	−0.518762	−	0.103497i
$973$	1.91419			0.0613660
$974$	16.0486	+	1.58528i	0.514229	+	0.0507957i
$975$	−1.46194	−	3.13841i	−0.0468196	−	0.100509i
$976$	0.108227	−	0.260439i	0.00346426	−	0.00833644i
$977$		−	41.5157i		−	1.32820i	−0.747642	−	0.664102i	$-0.768814\pi$
$977$		−	41.5157i		−	1.32820i	0.747642	−	0.664102i	$-0.231186\pi$
$978$	−0.167445	+	1.69512i	−0.00535429	+	0.0542040i
$979$			58.2570i			1.86190i
$980$	3.09503	−	3.22812i	0.0988672	−	0.103119i
$981$		−	7.81052i		−	0.249371i
$982$	−40.9421	−	4.04428i	−1.30652	−	0.129058i
$983$		−	27.0085i		−	0.861438i	−0.902486	−	0.430719i	$-0.858260\pi$
$983$		−	27.0085i		−	0.861438i	0.902486	−	0.430719i	$-0.141740\pi$
$984$	−2.14167	+	7.03836i	−0.0682738	+	0.224375i
$985$	19.8333	−	31.1183i	0.631941	−	0.991512i
$986$	−3.35615	+	33.9759i	−0.106882	+	1.08201i
$987$	2.20141			0.0700717
$988$	−4.56341	+	22.8734i	−0.145181	+	0.727698i
$989$			2.15674i			0.0685803i
$990$	24.4296	−	31.0971i	0.776424	−	0.988332i
$991$	13.7895			0.438037			0.219019	−	0.975721i	$-0.429714\pi$
$991$	13.7895			0.438037			0.219019	+	0.975721i	$0.429714\pi$
$992$	−5.28246	+	9.84885i	−0.167718	+	0.312701i
$993$			4.66072i			0.147903i
$994$	−7.89975	−	0.780341i	−0.250565	−	0.0247509i
$995$	26.0199	−	40.8251i	0.824887	−	1.29424i
$996$	10.3053	+	2.05599i	0.326536	+	0.0651464i
$997$	−21.0429			−0.666435			−0.333217	−	0.942850i	$-0.608134\pi$
$997$	−21.0429			−0.666435			−0.333217	+	0.942850i	$0.608134\pi$
$998$	50.5227	+	4.99066i	1.59927	+	0.157976i
$999$	−17.6464			−0.558308

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.l.a.29.19	yes	36
4.3	odd	2		1120.2.l.a.1009.18		36
5.4	even	2	inner	280.2.l.a.29.18	yes	36
8.3	odd	2		1120.2.l.a.1009.19		36
8.5	even	2	inner	280.2.l.a.29.17	✓	36
20.19	odd	2		1120.2.l.a.1009.20		36
40.19	odd	2		1120.2.l.a.1009.17		36
40.29	even	2	inner	280.2.l.a.29.20	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.l.a.29.17	✓	36	8.5	even	2	inner
280.2.l.a.29.18	yes	36	5.4	even	2	inner
280.2.l.a.29.19	yes	36	1.1	even	1	trivial
280.2.l.a.29.20	yes	36	40.29	even	2	inner
1120.2.l.a.1009.17		36	40.19	odd	2
1120.2.l.a.1009.18		36	4.3	odd	2
1120.2.l.a.1009.19		36	8.3	odd	2
1120.2.l.a.1009.20		36	20.19	odd	2

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.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.139020 - 1.40736i) q^{2} +0.319826 q^{3} +(-1.96135 - 0.391304i) q^{4} +(1.20181 - 1.88564i) q^{5} +(0.0444622 - 0.450112i) q^{6} -1.00000i q^{7} +(-0.823373 + 2.70593i) q^{8} -2.89771 q^{9} +O(q^{10})\)	\(q+(0.139020 - 1.40736i) q^{2} +0.319826 q^{3} +(-1.96135 - 0.391304i) q^{4} +(1.20181 - 1.88564i) q^{5} +(0.0444622 - 0.450112i) q^{6} -1.00000i q^{7} +(-0.823373 + 2.70593i) q^{8} -2.89771 q^{9} +(-2.48671 - 1.95353i) q^{10} -4.31560i q^{11} +(-0.627290 - 0.125149i) q^{12} +2.16506 q^{13} +(-1.40736 - 0.139020i) q^{14} +(0.384372 - 0.603077i) q^{15} +(3.69376 + 1.53496i) q^{16} +3.19581i q^{17} +(-0.402840 + 4.07813i) q^{18} -5.38650i q^{19} +(-3.09503 + 3.22812i) q^{20} -0.319826i q^{21} +(-6.07361 - 0.599954i) q^{22} +0.947361i q^{23} +(-0.263336 + 0.865427i) q^{24} +(-2.11128 - 4.53238i) q^{25} +(0.300986 - 3.04702i) q^{26} -1.88624 q^{27} +(-0.391304 + 1.96135i) q^{28} +7.55412i q^{29} +(-0.795314 - 0.624790i) q^{30} -1.97567 q^{31} +(2.67376 - 4.98508i) q^{32} -1.38024i q^{33} +(4.49767 + 0.444281i) q^{34} +(-1.88564 - 1.20181i) q^{35} +(5.68342 + 1.13388i) q^{36} +9.35534 q^{37} +(-7.58076 - 0.748831i) q^{38} +0.692441 q^{39} +(4.11287 + 4.80461i) q^{40} +8.13282 q^{41} +(-0.450112 - 0.0444622i) q^{42} +2.27658 q^{43} +(-1.68871 + 8.46438i) q^{44} +(-3.48251 + 5.46404i) q^{45} +(1.33328 + 0.131702i) q^{46} +6.88315i q^{47} +(1.18136 + 0.490922i) q^{48} -1.00000 q^{49} +(-6.67222 + 2.34125i) q^{50} +1.02210i q^{51} +(-4.24643 - 0.847194i) q^{52} +6.12756 q^{53} +(-0.262225 + 2.65463i) q^{54} +(-8.13766 - 5.18654i) q^{55} +(2.70593 + 0.823373i) q^{56} -1.72274i q^{57} +(10.6314 + 1.05017i) q^{58} -4.30565i q^{59} +(-0.989872 + 1.03244i) q^{60} -0.0705077i q^{61} +(-0.274657 + 2.78048i) q^{62} +2.89771i q^{63} +(-6.64411 - 4.45598i) q^{64} +(2.60200 - 4.08252i) q^{65} +(-1.94250 - 0.191881i) q^{66} +10.1964 q^{67} +(1.25053 - 6.26809i) q^{68} +0.302991i q^{69} +(-1.95353 + 2.48671i) q^{70} +5.61315 q^{71} +(2.38590 - 7.84100i) q^{72} +2.18227i q^{73} +(1.30058 - 13.1664i) q^{74} +(-0.675244 - 1.44957i) q^{75} +(-2.10775 + 10.5648i) q^{76} -4.31560 q^{77} +(0.0962632 - 0.974517i) q^{78} +10.0202 q^{79} +(7.33361 - 5.12037i) q^{80} +8.08986 q^{81} +(1.13063 - 11.4458i) q^{82} -16.4283 q^{83} +(-0.125149 + 0.627290i) q^{84} +(6.02615 + 3.84077i) q^{85} +(0.316490 - 3.20397i) q^{86} +2.41600i q^{87} +(11.6777 + 3.55334i) q^{88} -13.4992 q^{89} +(7.20576 + 5.66077i) q^{90} -2.16506i q^{91} +(0.370706 - 1.85810i) q^{92} -0.631870 q^{93} +(9.68710 + 0.956896i) q^{94} +(-10.1570 - 6.47357i) q^{95} +(0.855138 - 1.59436i) q^{96} +11.4733i q^{97} +(-0.139020 + 1.40736i) q^{98} +12.5053i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9}+O(q^{10}) \) 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9	\( 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9} - 8 q^{10} + 20 q^{16} - 24 q^{20} - 48 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{30} - 16 q^{31} + 12 q^{34} - 20 q^{36} - 32 q^{39} + 16 q^{40} - 8 q^{41} + 56 q^{44} - 36 q^{49} - 12 q^{50} - 52 q^{54} - 32 q^{55} + 12 q^{56} - 20 q^{60} - 20 q^{64} - 24 q^{65} - 28 q^{66} - 12 q^{70} + 56 q^{71} - 24 q^{74} + 48 q^{76} + 24 q^{79} + 64 q^{80} + 36 q^{81} + 24 q^{86} - 40 q^{89} - 52 q^{90} - 92 q^{94} + 40 q^{95} + 48 q^{96}+O(q^{100}) \) 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9 - 8 * q^10 + 20 * q^16 - 24 * q^20 - 48 * q^24 + 4 * q^25 - 4 * q^26 + 4 * q^30 - 16 * q^31 + 12 * q^34 - 20 * q^36 - 32 * q^39 + 16 * q^40 - 8 * q^41 + 56 * q^44 - 36 * q^49 - 12 * q^50 - 52 * q^54 - 32 * q^55 + 12 * q^56 - 20 * q^60 - 20 * q^64 - 24 * q^65 - 28 * q^66 - 12 * q^70 + 56 * q^71 - 24 * q^74 + 48 * q^76 + 24 * q^79 + 64 * q^80 + 36 * q^81 + 24 * q^86 - 40 * q^89 - 52 * q^90 - 92 * q^94 + 40 * q^95 + 48 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more