LMFDB - Embedded newform 43.2.g.a.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,2,Mod(9,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("43.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	43.g (of order $21$, degree $12$, 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:	$0.343356728692$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			10.1
Character	$\chi$	$=$	43.10
Dual form			43.2.g.a.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.483758 - 2.11948i) q^{2} +(-0.240184 - 0.222858i) q^{3} +(-2.45624 + 1.18286i) q^{4} +(0.0260188 - 0.00392170i) q^{5} +(-0.356153 + 0.616875i) q^{6} +(1.56464 + 2.71003i) q^{7} +(0.984367 + 1.23436i) q^{8} +(-0.216168 - 2.88456i) q^{9} +O(q^{10})$	\(q+(-0.483758 - 2.11948i) q^{2} +(-0.240184 - 0.222858i) q^{3} +(-2.45624 + 1.18286i) q^{4} +(0.0260188 - 0.00392170i) q^{5} +(-0.356153 + 0.616875i) q^{6} +(1.56464 + 2.71003i) q^{7} +(0.984367 + 1.23436i) q^{8} +(-0.216168 - 2.88456i) q^{9} +(-0.0208988 - 0.0532492i) q^{10} +(3.36665 + 1.62129i) q^{11} +(0.853562 + 0.263289i) q^{12} +(-1.78860 + 4.55728i) q^{13} +(4.98695 - 4.62722i) q^{14} +(-0.00712328 - 0.00485657i) q^{15} +(-1.25954 + 1.57942i) q^{16} +(-5.84766 - 0.881392i) q^{17} +(-6.00919 + 1.85359i) q^{18} +(0.296638 - 3.95836i) q^{19} +(-0.0592696 + 0.0404093i) q^{20} +(0.228152 - 0.999599i) q^{21} +(1.80766 - 7.91985i) q^{22} +(0.284113 - 0.193705i) q^{23} +(0.0386574 - 0.515847i) q^{24} +(-4.77720 + 1.47357i) q^{25} +(10.5243 + 1.58629i) q^{26} +(-1.20379 + 1.50950i) q^{27} +(-7.04873 - 4.80574i) q^{28} +(0.971806 - 0.901704i) q^{29} +(-0.00684747 + 0.0174471i) q^{30} +(2.06955 + 0.638371i) q^{31} +(6.80176 + 3.27556i) q^{32} +(-0.447297 - 1.13969i) q^{33} +(0.960755 + 12.8204i) q^{34} +(0.0513379 + 0.0643757i) q^{35} +(3.94300 + 6.82948i) q^{36} +(5.01814 - 8.69167i) q^{37} +(-8.53318 + 1.28617i) q^{38} +(1.44522 - 0.695983i) q^{39} +(0.0304528 + 0.0282561i) q^{40} +(-0.431814 - 1.89190i) q^{41} -2.22900 q^{42} +(6.54856 + 0.341120i) q^{43} -10.1871 q^{44} +(-0.0169368 - 0.0742049i) q^{45} +(-0.547996 - 0.508466i) q^{46} +(-10.0138 + 4.82240i) q^{47} +(0.654509 - 0.0986513i) q^{48} +(-1.39618 + 2.41825i) q^{49} +(5.43422 + 9.41234i) q^{50} +(1.20809 + 1.51490i) q^{51} +(-0.997407 - 13.3095i) q^{52} +(-2.12587 - 5.41662i) q^{53} +(3.78170 + 1.82117i) q^{54} +(0.0939542 + 0.0289810i) q^{55} +(-1.80497 + 4.59898i) q^{56} +(-0.953402 + 0.884627i) q^{57} +(-2.38126 - 1.62352i) q^{58} +(0.107460 - 0.134751i) q^{59} +(0.0232412 + 0.00350304i) q^{60} +(5.31524 - 1.63953i) q^{61} +(0.351855 - 4.69519i) q^{62} +(7.47901 - 5.09911i) q^{63} +(2.75302 - 12.0618i) q^{64} +(-0.0286650 + 0.125589i) q^{65} +(-2.19918 + 1.49937i) q^{66} +(-0.0822742 + 1.09787i) q^{67} +(15.4058 - 4.75207i) q^{68} +(-0.111408 - 0.0167921i) q^{69} +(0.111608 - 0.139952i) q^{70} +(-4.37443 - 2.98244i) q^{71} +(3.34778 - 3.10629i) q^{72} +(-2.70214 + 6.88494i) q^{73} +(-20.8494 - 6.43119i) q^{74} +(1.47581 + 0.710711i) q^{75} +(3.95359 + 10.0736i) q^{76} +(0.873829 + 11.6604i) q^{77} +(-2.17426 - 2.72644i) q^{78} +(2.70765 + 4.68979i) q^{79} +(-0.0265778 + 0.0460341i) q^{80} +(-7.95548 + 1.19910i) q^{81} +(-3.80096 + 1.83044i) q^{82} +(-1.49132 - 1.38374i) q^{83} +(0.621993 + 2.72513i) q^{84} -0.155605 q^{85} +(-2.44492 - 14.0446i) q^{86} -0.434365 q^{87} +(1.31276 + 5.75159i) q^{88} +(2.93360 + 2.72198i) q^{89} +(-0.149083 + 0.0717944i) q^{90} +(-15.1489 + 2.28333i) q^{91} +(-0.468724 + 0.811854i) q^{92} +(-0.354806 - 0.614542i) q^{93} +(15.0652 + 18.8912i) q^{94} +(-0.00780535 - 0.104155i) q^{95} +(-0.903691 - 2.30257i) q^{96} +(-8.11049 - 3.90581i) q^{97} +(5.80084 + 1.78932i) q^{98} +(3.94895 - 10.0618i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9}+O(q^{10}) $ 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9} - 7 q^{10} - 4 q^{11} + 2 q^{12} + 18 q^{14} - 3 q^{15} - 10 q^{16} - 10 q^{17} + 11 q^{18} + 10 q^{19} - 3 q^{20} - 21 q^{21} - 3 q^{22} + 4 q^{23} + 31 q^{24} - 2 q^{25} - 15 q^{26} - 4 q^{27} + 20 q^{28} + 9 q^{29} + 88 q^{30} + 40 q^{31} + 48 q^{32} - 11 q^{33} - 42 q^{34} + 11 q^{35} - 47 q^{36} - 19 q^{37} - 21 q^{38} - q^{39} - 97 q^{40} - 28 q^{41} + 2 q^{42} - 8 q^{43} + 14 q^{44} - 46 q^{45} - 61 q^{46} - 30 q^{47} - 97 q^{48} + 6 q^{49} - 3 q^{50} + 57 q^{51} - 8 q^{52} - 24 q^{53} + 6 q^{54} + 14 q^{55} + 39 q^{56} + 52 q^{57} + 64 q^{58} - q^{59} + 111 q^{60} - 14 q^{61} + 33 q^{62} + 47 q^{63} + 48 q^{64} + 38 q^{65} + 79 q^{66} + 66 q^{67} + 66 q^{68} - 7 q^{69} + 47 q^{70} - 33 q^{71} + 26 q^{72} + 29 q^{73} - 40 q^{74} - 55 q^{75} - 39 q^{76} - 27 q^{77} - 126 q^{78} - 17 q^{79} + 8 q^{80} + 38 q^{81} - 54 q^{82} - 23 q^{83} - 155 q^{84} - 56 q^{85} - 45 q^{86} - 86 q^{87} - 17 q^{88} - 19 q^{89} - 127 q^{90} - 13 q^{91} - 18 q^{92} - 30 q^{93} + 44 q^{94} + q^{95} - 36 q^{96} - 31 q^{97} - 5 q^{98} - 31 q^{99}+O(q^{100}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9 - 7 * q^10 - 4 * q^11 + 2 * q^12 + 18 * q^14 - 3 * q^15 - 10 * q^16 - 10 * q^17 + 11 * q^18 + 10 * q^19 - 3 * q^20 - 21 * q^21 - 3 * q^22 + 4 * q^23 + 31 * q^24 - 2 * q^25 - 15 * q^26 - 4 * q^27 + 20 * q^28 + 9 * q^29 + 88 * q^30 + 40 * q^31 + 48 * q^32 - 11 * q^33 - 42 * q^34 + 11 * q^35 - 47 * q^36 - 19 * q^37 - 21 * q^38 - q^39 - 97 * q^40 - 28 * q^41 + 2 * q^42 - 8 * q^43 + 14 * q^44 - 46 * q^45 - 61 * q^46 - 30 * q^47 - 97 * q^48 + 6 * q^49 - 3 * q^50 + 57 * q^51 - 8 * q^52 - 24 * q^53 + 6 * q^54 + 14 * q^55 + 39 * q^56 + 52 * q^57 + 64 * q^58 - q^59 + 111 * q^60 - 14 * q^61 + 33 * q^62 + 47 * q^63 + 48 * q^64 + 38 * q^65 + 79 * q^66 + 66 * q^67 + 66 * q^68 - 7 * q^69 + 47 * q^70 - 33 * q^71 + 26 * q^72 + 29 * q^73 - 40 * q^74 - 55 * q^75 - 39 * q^76 - 27 * q^77 - 126 * q^78 - 17 * q^79 + 8 * q^80 + 38 * q^81 - 54 * q^82 - 23 * q^83 - 155 * q^84 - 56 * q^85 - 45 * q^86 - 86 * q^87 - 17 * q^88 - 19 * q^89 - 127 * q^90 - 13 * q^91 - 18 * q^92 - 30 * q^93 + 44 * q^94 + q^95 - 36 * q^96 - 31 * q^97 - 5 * q^98 - 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{21}\right)$

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 $

$2$	−0.483758	−	2.11948i	−0.342068	−	1.49870i	−0.794700	−	0.607002i	$-0.792372\pi$
$2$	−0.483758	−	2.11948i	−0.342068	−	1.49870i	0.452632	−	0.891698i	$-0.350485\pi$
$3$	−0.240184	−	0.222858i	−0.138670	−	0.128667i	0.607788	−	0.794099i	$-0.292057\pi$
$3$	−0.240184	−	0.222858i	−0.138670	−	0.128667i	−0.746459	+	0.665432i	$0.768247\pi$
$4$	−2.45624	+	1.18286i	−1.22812	+	0.591432i
$5$	0.0260188	−	0.00392170i	0.0116360	−	0.00175384i	−0.143222	−	0.989691i	$-0.545746\pi$
$5$	0.0260188	−	0.00392170i	0.0116360	−	0.00175384i	0.154858	+	0.987937i	$0.450508\pi$
$6$	−0.356153	+	0.616875i	−0.145399	+	0.251838i
$7$	1.56464	+	2.71003i	0.591377	+	1.02430i	0.994047	+	0.108950i	$0.0347489\pi$
$7$	1.56464	+	2.71003i	0.591377	+	1.02430i	−0.402670	+	0.915345i	$0.631918\pi$
$8$	0.984367	+	1.23436i	0.348026	+	0.436411i
$9$	−0.216168	−	2.88456i	−0.0720559	−	0.961519i
$10$	−0.0208988	−	0.0532492i	−0.00660877	−	0.0168389i
$11$	3.36665	+	1.62129i	1.01508	+	0.488838i	0.866030	−	0.499992i	$-0.166664\pi$
$11$	3.36665	+	1.62129i	1.01508	+	0.488838i	0.149052	+	0.988829i	$0.452378\pi$
$12$	0.853562	+	0.263289i	0.246402	+	0.0760050i
$13$	−1.78860	+	4.55728i	−0.496069	+	1.26396i	0.435431	+	0.900222i	$0.356596\pi$
$13$	−1.78860	+	4.55728i	−0.496069	+	1.26396i	−0.931500	+	0.363741i	$0.881499\pi$
$14$	4.98695	−	4.62722i	1.33282	−	1.23668i
$15$	−0.00712328	−	0.00485657i	−0.00183922	−	0.00125396i
$16$	−1.25954	+	1.57942i	−0.314886	+	0.394855i
$17$	−5.84766	−	0.881392i	−1.41827	−	0.213769i	−0.605261	−	0.796027i	$-0.706931\pi$
$17$	−5.84766	−	0.881392i	−1.41827	−	0.213769i	−0.813004	+	0.582258i	$0.802169\pi$
$18$	−6.00919	+	1.85359i	−1.41638	+	0.436896i
$19$	0.296638	−	3.95836i	0.0680535	−	0.908110i	−0.853807	−	0.520589i	$-0.825712\pi$
$19$	0.296638	−	3.95836i	0.0680535	−	0.908110i	0.921861	−	0.387521i	$-0.126669\pi$
$20$	−0.0592696	+	0.0404093i	−0.0132531	+	0.00903580i
$21$	0.228152	−	0.999599i	0.0497868	−	0.218130i
$22$	1.80766	−	7.91985i	0.385393	−	1.68852i
$23$	0.284113	−	0.193705i	0.0592417	−	0.0403903i	−0.533337	−	0.845903i	$-0.679062\pi$
$23$	0.284113	−	0.193705i	0.0592417	−	0.0403903i	0.592579	+	0.805512i	$0.298110\pi$
$24$	0.0386574	−	0.515847i	0.00789091	−	0.105297i
$25$	−4.77720	+	1.47357i	−0.955440	+	0.294714i
$26$	10.5243	+	1.58629i	2.06399	+	0.311097i
$27$	−1.20379	+	1.50950i	−0.231669	+	0.290503i
$28$	−7.04873	−	4.80574i	−1.33208	−	0.908199i
$29$	0.971806	−	0.901704i	0.180460	−	0.167442i	−0.584771	−	0.811199i	$-0.698815\pi$
$29$	0.971806	−	0.901704i	0.180460	−	0.167442i	0.765230	+	0.643756i	$0.222625\pi$
$30$	−0.00684747	+	0.0174471i	−0.00125017	+	0.00318538i
$31$	2.06955	+	0.638371i	0.371702	+	0.114655i	0.474977	−	0.879998i	$-0.342456\pi$
$31$	2.06955	+	0.638371i	0.371702	+	0.114655i	−0.103276	+	0.994653i	$0.532932\pi$
$32$	6.80176	+	3.27556i	1.20239	+	0.579042i
$33$	−0.447297	−	1.13969i	−0.0778643	−	0.198395i
$34$	0.960755	+	12.8204i	0.164768	+	2.19868i
$35$	0.0513379	+	0.0643757i	0.00867769	+	0.0108815i
$36$	3.94300	+	6.82948i	0.657167	+	1.13825i
$37$	5.01814	−	8.69167i	0.824977	−	1.42890i	−0.0769599	−	0.997034i	$-0.524521\pi$
$37$	5.01814	−	8.69167i	0.824977	−	1.42890i	0.901937	−	0.431868i	$-0.142145\pi$
$38$	−8.53318	+	1.28617i	−1.38426	+	0.208644i
$39$	1.44522	−	0.695983i	0.231421	−	0.111446i
$40$	0.0304528	+	0.0282561i	0.00481501	+	0.00446768i
$41$	−0.431814	−	1.89190i	−0.0674381	−	0.295465i	0.929951	−	0.367684i	$-0.119849\pi$
$41$	−0.431814	−	1.89190i	−0.0674381	−	0.295465i	−0.997389	+	0.0722186i	$0.976992\pi$
$42$	−2.22900			−0.343942
$43$	6.54856	+	0.341120i	0.998646	+	0.0520203i
$43$	6.54856	+	0.341120i	0.998646	+	0.0520203i
$44$	−10.1871			−1.53576
$45$	−0.0169368	−	0.0742049i	−0.00252479	−	0.0110618i
$46$	−0.547996	−	0.508466i	−0.0807976	−	0.0749693i
$47$	−10.0138	+	4.82240i	−1.46066	+	0.703419i	−0.984410	−	0.175888i	$-0.943720\pi$
$47$	−10.0138	+	4.82240i	−1.46066	+	0.703419i	−0.476255	+	0.879307i	$0.658006\pi$
$48$	0.654509	−	0.0986513i	0.0944702	−	0.0142391i
$49$	−1.39618	+	2.41825i	−0.199454	+	0.345464i
$50$	5.43422	+	9.41234i	0.768514	+	1.33111i
$51$	1.20809	+	1.51490i	0.169166	+	0.212128i
$52$	−0.997407	−	13.3095i	−0.138315	−	1.84569i
$53$	−2.12587	−	5.41662i	−0.292010	−	0.744030i	−0.999311	−	0.0371173i	$-0.988182\pi$
$53$	−2.12587	−	5.41662i	−0.292010	−	0.744030i	0.707301	−	0.706913i	$-0.249913\pi$
$54$	3.78170	+	1.82117i	0.514624	+	0.247830i
$55$	0.0939542	+	0.0289810i	0.0126688	+	0.00390780i
$56$	−1.80497	+	4.59898i	−0.241199	+	0.614565i
$57$	−0.953402	+	0.884627i	−0.126281	+	0.117172i
$58$	−2.38126	−	1.62352i	−0.312675	−	0.213178i
$59$	0.107460	−	0.134751i	0.0139901	−	0.0175431i	−0.774787	−	0.632222i	$-0.782143\pi$
$59$	0.107460	−	0.134751i	0.0139901	−	0.0175431i	0.788777	+	0.614679i	$0.210714\pi$
$60$	0.0232412	+	0.00350304i	0.00300042	+	0.000452241i
$61$	5.31524	−	1.63953i	0.680547	−	0.209921i	0.0648393	−	0.997896i	$-0.479347\pi$
$61$	5.31524	−	1.63953i	0.680547	−	0.209921i	0.615707	+	0.787975i	$0.288870\pi$
$62$	0.351855	−	4.69519i	0.0446857	−	0.596289i
$63$	7.47901	−	5.09911i	0.942267	−	0.642427i
$64$	2.75302	−	12.0618i	0.344128	−	1.50772i
$65$	−0.0286650	+	0.125589i	−0.00355545	+	0.0155774i
$66$	−2.19918	+	1.49937i	−0.270700	+	0.184560i
$67$	−0.0822742	+	1.09787i	−0.0100514	+	0.134126i	−0.999972	−	0.00749766i	$-0.997613\pi$
$67$	−0.0822742	+	1.09787i	−0.0100514	+	0.134126i	0.989921	+	0.141624i	$0.0452324\pi$
$68$	15.4058	−	4.75207i	1.86823	−	0.576273i
$69$	−0.111408	−	0.0167921i	−0.0134120	−	0.00202153i
$70$	0.111608	−	0.139952i	0.0133397	−	0.0167275i
$71$	−4.37443	−	2.98244i	−0.519150	−	0.353950i	0.275223	−	0.961380i	$-0.411248\pi$
$71$	−4.37443	−	2.98244i	−0.519150	−	0.353950i	−0.794373	+	0.607430i	$0.792201\pi$
$72$	3.34778	−	3.10629i	0.394540	−	0.366080i
$73$	−2.70214	+	6.88494i	−0.316261	+	0.805821i	0.681029	+	0.732256i	$0.261533\pi$
$73$	−2.70214	+	6.88494i	−0.316261	+	0.805821i	−0.997290	+	0.0735646i	$0.976562\pi$
$74$	−20.8494	−	6.43119i	−2.42369	−	0.747611i
$75$	1.47581	+	0.710711i	0.170411	+	0.0820658i
$76$	3.95359	+	10.0736i	0.453508	+	1.15552i
$77$	0.873829	+	11.6604i	0.0995821	+	1.32883i
$78$	−2.17426	−	2.72644i	−0.246186	−	0.308708i
$79$	2.70765	+	4.68979i	0.304635	+	0.527643i	0.977180	−	0.212413i	$-0.0681323\pi$
$79$	2.70765	+	4.68979i	0.304635	+	0.527643i	−0.672545	+	0.740056i	$0.734799\pi$
$80$	−0.0265778	+	0.0460341i	−0.00297149	+	0.00514677i
$81$	−7.95548	+	1.19910i	−0.883942	+	0.133233i
$82$	−3.80096	+	1.83044i	−0.419746	+	0.202139i
$83$	−1.49132	−	1.38374i	−0.163694	−	0.151885i	0.594073	−	0.804411i	$-0.297519\pi$
$83$	−1.49132	−	1.38374i	−0.163694	−	0.151885i	−0.757767	+	0.652526i	$0.773709\pi$
$84$	0.621993	+	2.72513i	0.0678650	+	0.297336i
$85$	−0.155605			−0.0168778
$86$	−2.44492	−	14.0446i	−0.263642	−	1.51447i
$87$	−0.434365			−0.0465688
$88$	1.31276	+	5.75159i	0.139941	+	0.613121i
$89$	2.93360	+	2.72198i	0.310961	+	0.288530i	0.820178	−	0.572109i	$-0.193874\pi$
$89$	2.93360	+	2.72198i	0.310961	+	0.288530i	−0.509217	+	0.860638i	$0.670065\pi$
$90$	−0.149083	+	0.0717944i	−0.0157147	+	0.00756780i
$91$	−15.1489	+	2.28333i	−1.58804	+	0.239358i
$92$	−0.468724	+	0.811854i	−0.0488679	+	0.0846416i
$93$	−0.354806	−	0.614542i	−0.0367917	−	0.0637251i
$94$	15.0652	+	18.8912i	1.55386	+	1.94848i
$95$	−0.00780535	−	0.104155i	−0.000800812	−	0.0106861i
$96$	−0.903691	−	2.30257i	−0.0922325	−	0.235005i
$97$	−8.11049	−	3.90581i	−0.823495	−	0.396574i	−0.0258237	−	0.999667i	$-0.508221\pi$
$97$	−8.11049	−	3.90581i	−0.823495	−	0.396574i	−0.797672	+	0.603092i	$0.793935\pi$
$98$	5.80084	+	1.78932i	0.585974	+	0.180749i
$99$	3.94895	−	10.0618i	0.396884	−	1.01124i
$100$	9.99093	−	9.27023i	0.999093	−	0.927023i
$101$	12.6400	+	8.61780i	1.25773	+	0.857503i	0.994242	−	0.107161i	$-0.0341759\pi$
$101$	12.6400	+	8.61780i	1.25773	+	0.857503i	0.263484	+	0.964664i	$0.415128\pi$
$102$	2.62637	−	3.29336i	0.260049	−	0.326092i
$103$	15.8309	+	2.38613i	1.55987	+	0.235112i	0.871554	−	0.490300i	$-0.163113\pi$
$103$	15.8309	+	2.38613i	1.55987	+	0.235112i	0.688315	+	0.725412i	$0.258351\pi$
$104$	−7.38596	+	2.27827i	−0.724253	+	0.223402i
$105$	0.00201611	−	0.0269031i	0.000196752	−	0.00262547i
$106$	−10.4520	+	7.12607i	−1.01519	+	0.692145i
$107$	−3.68337	+	16.1379i	−0.356085	+	1.56011i	0.406765	+	0.913533i	$0.366657\pi$
$107$	−3.68337	+	16.1379i	−0.356085	+	1.56011i	−0.762850	+	0.646576i	$0.776200\pi$
$108$	1.17126	−	5.13161i	0.112704	−	0.493790i
$109$	1.69999	−	1.15903i	0.162829	−	0.111015i	−0.479164	−	0.877725i	$-0.659060\pi$
$109$	1.69999	−	1.15903i	0.162829	−	0.111015i	0.641993	+	0.766710i	$0.278108\pi$
$110$	0.0159737	−	0.213154i	0.00152303	−	0.0203234i
$111$	−3.14229	+	0.969268i	−0.298253	+	0.0919988i
$112$	−6.25100	−	0.942187i	−0.590664	−	0.0890283i
$113$	7.27343	−	9.12059i	0.684226	−	0.857993i	−0.311509	−	0.950243i	$-0.600835\pi$
$113$	7.27343	−	9.12059i	0.684226	−	0.857993i	0.995736	+	0.0922502i	$0.0294060\pi$
$114$	2.33617	+	1.59277i	0.218802	+	0.149177i
$115$	0.00663263	−	0.00615418i	0.000618496	−	0.000573880i
$116$	−1.32040	+	3.36432i	−0.122596	+	0.312369i
$117$	13.5324	+	4.17419i	1.25107	+	0.385904i
$118$	−0.337586	−	0.162573i	−0.0310774	−	0.0149661i
$119$	−6.76086	−	17.2264i	−0.619767	−	1.57914i
$120$	−0.00101718	−	0.0135733i	−9.28554e−5	−	0.00123907i
$121$	1.84733	+	2.31648i	0.167939	+	0.210589i
$122$	−6.04625	−	10.4724i	−0.547402	−	0.948128i
$123$	−0.317911	+	0.550638i	−0.0286651	+	0.0496494i
$124$	−5.83842	+	0.880000i	−0.524305	+	0.0790263i
$125$	−0.237053	+	0.114159i	−0.0212026	+	0.0102106i
$126$	−14.4255	−	13.3849i	−1.28512	−	1.19242i
$127$	−1.67817	−	7.35255i	−0.148914	−	0.652433i	−0.993188	−	0.116522i	$-0.962825\pi$
$127$	−1.67817	−	7.35255i	−0.148914	−	0.652433i	0.844275	−	0.535911i	$-0.180032\pi$
$128$	−11.7978			−1.04278
$129$	−1.49684	−	1.54133i	−0.131789	−	0.135707i
$130$	0.280051			0.0245621
$131$	1.97245	+	8.64186i	0.172334	+	0.755043i	0.985034	+	0.172361i	$0.0551395\pi$
$131$	1.97245	+	8.64186i	0.172334	+	0.755043i	−0.812700	+	0.582682i	$0.802003\pi$
$132$	2.44677	+	2.27027i	0.212964	+	0.197602i
$133$	11.1914	−	5.38950i	0.970418	−	0.467329i
$134$	2.36672	−	0.356726i	0.204454	−	0.0308164i
$135$	−0.0254012	+	0.0439962i	−0.00218619	+	0.00378659i
$136$	−4.66829	−	8.08571i	−0.400302	−	0.693344i
$137$	−10.9540	−	13.7359i	−0.935863	−	1.17354i	−0.984617	−	0.174725i	$-0.944096\pi$
$137$	−10.9540	−	13.7359i	−0.935863	−	1.17354i	0.0487538	−	0.998811i	$-0.484475\pi$
$138$	0.0183041	+	0.244251i	0.00155815	+	0.0207920i
$139$	−5.64316	−	14.3785i	−0.478646	−	1.21957i	−0.942663	−	0.333745i	$-0.891688\pi$
$139$	−5.64316	−	14.3785i	−0.478646	−	1.21957i	0.464017	−	0.885826i	$-0.346408\pi$
$140$	−0.202246	−	0.0973965i	−0.0170929	−	0.00823151i
$141$	3.47987	+	1.07340i	0.293058	+	0.0903964i
$142$	−4.20506	+	10.7143i	−0.352880	+	0.899125i
$143$	−13.4103	+	12.4429i	−1.12142	+	1.04053i
$144$	4.82820	+	3.29181i	0.402350	+	0.274317i
$145$	0.0217490	−	0.0272724i	0.00180616	−	0.00226485i
$146$	15.8997	+	2.39649i	1.31587	+	0.198335i
$147$	0.874266	−	0.269675i	0.0721083	−	0.0222425i
$148$	−2.04470	+	27.2846i	−0.168073	+	2.24278i
$149$	−5.99816	+	4.08947i	−0.491388	+	0.335023i	−0.783532	−	0.621352i	$-0.786584\pi$
$149$	−5.99816	+	4.08947i	−0.491388	+	0.335023i	0.292144	+	0.956374i	$0.405631\pi$
$150$	0.792405	−	3.47176i	0.0646996	−	0.283468i
$151$	2.23243	−	9.78091i	0.181673	−	0.795960i	−0.799162	−	0.601116i	$-0.794723\pi$
$151$	2.23243	−	9.78091i	0.181673	−	0.795960i	0.980834	−	0.194844i	$-0.0624199\pi$
$152$	5.17803	−	3.53032i	0.419994	−	0.286347i
$153$	−1.27835	+	17.0584i	−0.103349	+	1.37909i
$154$	24.2914	−	7.49290i	1.95745	−	0.603795i
$155$	0.0563506	+	0.00849349i	0.00452619	+	0.000682213i
$156$	−2.72656	+	3.41900i	−0.218300	+	0.273739i
$157$	7.98170	+	5.44183i	0.637009	+	0.434305i	0.838287	−	0.545229i	$-0.183557\pi$
$157$	7.98170	+	5.44183i	0.637009	+	0.434305i	−0.201279	+	0.979534i	$0.564510\pi$
$158$	8.63008	−	8.00754i	0.686572	−	0.637046i
$159$	−0.696540	+	1.77475i	−0.0552392	+	0.140747i
$160$	0.189819	+	0.0585515i	0.0150065	+	0.00462890i
$161$	0.969481	+	0.466877i	0.0764058	+	0.0367951i
$162$	6.38998	+	16.2814i	0.502045	+	1.27919i
$163$	−0.507211	−	6.76827i	−0.0397279	−	0.530131i	−0.981194	−	0.193024i	$-0.938170\pi$
$163$	−0.507211	−	6.76827i	−0.0397279	−	0.530131i	0.941466	−	0.337107i	$-0.109449\pi$
$164$	3.29850	+	4.13619i	0.257570	+	0.322982i
$165$	−0.0161077	−	0.0278993i	−0.00125398	−	0.00217196i
$166$	−2.21138	+	3.83022i	−0.171636	+	0.297283i
$167$	13.8043	−	2.08066i	1.06821	−	0.161006i	0.408672	−	0.912681i	$-0.365992\pi$
$167$	13.8043	−	2.08066i	1.06821	−	0.161006i	0.659534	+	0.751675i	$0.270754\pi$
$168$	1.45845	−	0.702351i	0.112522	−	0.0541875i
$169$	−8.04007	−	7.46009i	−0.618467	−	0.573853i
$170$	0.0752754	+	0.329803i	0.00577336	+	0.0252947i
$171$	−11.4822			−0.878069
$172$	−16.4884	+	6.90818i	−1.25722	+	0.526744i
$173$	11.5110			0.875168			0.437584	−	0.899178i	$-0.355834\pi$
$173$	11.5110			0.875168			0.437584	+	0.899178i	$0.355834\pi$
$174$	0.210127	+	0.920628i	0.0159297	+	0.0697926i
$175$	−11.4680	−	10.6408i	−0.866900	−	0.804366i
$176$	−6.80113	+	3.27525i	−0.512655	+	0.246882i
$177$	−0.0558405	+	0.00841661i	−0.00419723	+	0.000632631i
$178$	4.35004	−	7.53449i	0.326049	−	0.564734i
$179$	−0.378359	−	0.655338i	−0.0282799	−	0.0489823i	0.851539	−	0.524291i	$-0.175670\pi$
$179$	−0.378359	−	0.655338i	−0.0282799	−	0.0489823i	−0.879819	+	0.475309i	$0.842336\pi$
$180$	0.129375	+	0.162231i	0.00964306	+	0.0120920i
$181$	−0.0777475	−	1.03747i	−0.00577892	−	0.0771144i	0.993569	−	0.113231i	$-0.0361201\pi$
$181$	−0.0777475	−	1.03747i	−0.00577892	−	0.0771144i	−0.999348	+	0.0361170i	$0.988501\pi$
$182$	12.1679	+	31.0032i	0.901942	+	2.29811i
$183$	−1.64202	−	0.790755i	−0.121382	−	0.0584543i
$184$	0.518773	+	0.160020i	0.0382444	+	0.0117968i
$185$	0.0964797	−	0.245826i	0.00709333	−	0.0180735i
$186$	−1.13087	+	1.04929i	−0.0829195	+	0.0769380i
$187$	−18.2580	−	12.4481i	−1.33516	−	0.910294i
$188$	18.8921	−	23.6900i	1.37785	−	1.72777i
$189$	−5.97428	−	0.900478i	−0.434565	−	0.0655001i
$190$	−0.216979	+	0.0669291i	−0.0157413	+	0.00485555i
$191$	−1.03588	+	13.8228i	−0.0749534	+	1.00018i	0.825265	+	0.564745i	$0.191026\pi$
$191$	−1.03588	+	13.8228i	−0.0749534	+	1.00018i	−0.900219	+	0.435438i	$0.856593\pi$
$192$	−3.34930	+	2.28352i	−0.241715	+	0.164799i
$193$	−3.28671	+	14.4000i	−0.236583	+	1.03654i	0.707470	+	0.706743i	$0.249836\pi$
$193$	−3.28671	+	14.4000i	−0.236583	+	1.03654i	−0.944053	+	0.329794i	$0.893021\pi$
$194$	−4.35477	+	19.0795i	−0.312654	+	1.36983i
$195$	0.0348735	−	0.0237764i	0.00249734	−	0.00170266i
$196$	0.568889	−	7.59129i	0.0406349	−	0.542235i
$197$	−7.25577	+	2.23811i	−0.516952	+	0.159459i	−0.542243	−	0.840221i	$-0.682425\pi$
$197$	−7.25577	+	2.23811i	−0.516952	+	0.159459i	0.0252911	+	0.999680i	$0.491949\pi$
$198$	−23.2360	−	3.50227i	−1.65131	−	0.248895i
$199$	−15.6429	+	19.6156i	−1.10890	+	1.39051i	−0.196844	+	0.980435i	$0.563069\pi$
$199$	−15.6429	+	19.6156i	−1.10890	+	1.39051i	−0.912051	+	0.410076i	$0.865502\pi$
$200$	−6.52143	−	4.44624i	−0.461135	−	0.314396i
$201$	0.264431	−	0.245356i	0.0186515	−	0.0173061i
$202$	12.1506	−	30.9592i	0.854911	−	2.17828i
$203$	3.96417	+	1.22278i	0.278230	+	0.0858226i
$204$	−4.75927	−	2.29195i	−0.333216	−	0.160468i
$205$	−0.0186548	−	0.0475315i	−0.00130290	−	0.00331975i
$206$	−2.60098	−	34.7077i	−0.181219	−	2.41820i
$207$	−0.620169	−	0.777668i	−0.0431048	−	0.0540517i
$208$	−4.94504	−	8.56505i	−0.342876	−	0.593879i
$209$	7.41633	−	12.8455i	0.512998	−	0.888539i
$210$	−0.0579959	+	0.00874147i	−0.00400210	+	0.000603219i
$211$	14.4636	−	6.96528i	0.995712	−	0.479510i	0.136231	−	0.990677i	$-0.456501\pi$
$211$	14.4636	−	6.96528i	0.995712	−	0.479510i	0.859481	+	0.511167i	$0.170787\pi$
$212$	11.6288	+	10.7899i	0.798668	+	0.741055i
$213$	0.386008	+	1.69121i	0.0264489	+	0.115880i
$214$	35.9858			2.45994
$215$	0.171723	−	0.0168060i	0.0117114	−	0.00114616i
$216$	−3.04823			−0.207406
$217$	1.50809	+	6.60736i	0.102376	+	0.448537i
$218$	−3.27893	−	3.04241i	−0.222077	−	0.206058i
$219$	2.18338	−	1.05146i	0.147539	−	0.0710510i
$220$	−0.265055	+	0.0399506i	−0.0178700	+	0.00269347i
$221$	14.4759	−	25.0730i	0.973754	−	1.68659i
$222$	3.57445	+	6.19113i	0.239901	+	0.415522i
$223$	−9.41103	−	11.8011i	−0.630209	−	0.790257i	0.359532	−	0.933133i	$-0.382937\pi$
$223$	−9.41103	−	11.8011i	−0.630209	−	0.790257i	−0.989741	+	0.142876i	$0.954365\pi$
$224$	1.76543	+	23.5580i	0.117958	+	1.57404i
$225$	5.28328	+	13.4616i	0.352219	+	0.897438i
$226$	−22.8495	−	11.0037i	−1.51993	−	0.731958i
$227$	19.2669	+	5.94305i	1.27879	+	0.394454i	0.858442	−	0.512910i	$-0.171433\pi$
$227$	19.2669	+	5.94305i	1.27879	+	0.394454i	0.420346	+	0.907364i	$0.361909\pi$
$228$	1.29539	−	3.30060i	0.0857894	−	0.218588i
$229$	−9.80918	+	9.10159i	−0.648209	+	0.601450i	−0.934186	−	0.356786i	$-0.883872\pi$
$229$	−9.80918	+	9.10159i	−0.648209	+	0.601450i	0.285977	+	0.958236i	$0.407682\pi$
$230$	−0.0162523	−	0.0110806i	−0.00107164	−	0.000730633i
$231$	2.38875	−	2.99539i	0.157168	−	0.197082i
$232$	2.06964	+	0.311948i	0.135878	+	0.0204804i
$233$	8.84939	−	2.72968i	0.579743	−	0.178827i	0.00900522	−	0.999959i	$-0.497134\pi$
$233$	8.84939	−	2.72968i	0.579743	−	0.178827i	0.570738	+	0.821132i	$0.306657\pi$
$234$	2.30072	−	30.7009i	0.150403	−	2.00698i
$235$	−0.241635	+	0.164744i	−0.0157625	+	0.0107467i
$236$	−0.104556	+	0.458091i	−0.00680604	+	0.0298192i
$237$	0.394824	−	1.72984i	0.0256466	−	0.112365i
$238$	−33.2404	+	22.6629i	−2.15465	+	1.46902i
$239$	−1.43677	+	19.1723i	−0.0929366	+	1.24015i	0.734506	+	0.678602i	$0.237414\pi$
$239$	−1.43677	+	19.1723i	−0.0929366	+	1.24015i	−0.827442	+	0.561550i	$0.810205\pi$
$240$	0.0166426	−	0.00513358i	0.00107428	−	0.000331371i
$241$	−5.72297	−	0.862599i	−0.368649	−	0.0555649i	−0.0378946	−	0.999282i	$-0.512065\pi$
$241$	−5.72297	−	0.862599i	−0.368649	−	0.0555649i	−0.330755	+	0.943717i	$0.607303\pi$
$242$	4.01607	−	5.03599i	0.258163	−	0.323726i
$243$	6.96372	+	4.74778i	0.446723	+	0.304571i
$244$	−11.1162	+	10.3143i	−0.711640	+	0.660305i
$245$	−0.0268432	+	0.0683953i	−0.00171495	+	0.00436961i
$246$	1.32086	+	0.407431i	0.0842149	+	0.0259769i
$247$	17.5088	+	8.43180i	1.11406	+	0.536503i
$248$	1.24922	+	3.18295i	0.0793253	+	0.202118i
$249$	0.0498128	+	0.664706i	0.00315676	+	0.0421240i
$250$	0.356633	+	0.447204i	0.0225554	+	0.0282836i
$251$	−3.71016	−	6.42619i	−0.234184	−	0.405618i	0.724852	−	0.688905i	$-0.241908\pi$
$251$	−3.71016	−	6.42619i	−0.234184	−	0.405618i	−0.959035	+	0.283287i	$0.908575\pi$
$252$	−12.3387	+	21.3713i	−0.777267	+	1.34627i
$253$	1.27056	−	0.191506i	0.0798795	−	0.0120399i
$254$	−14.7718	+	7.11370i	−0.926863	+	0.446353i
$255$	0.0373740	+	0.0346780i	0.00234045	+	0.00217162i
$256$	0.201207	+	0.881545i	0.0125754	+	0.0550966i
$257$	−22.5274			−1.40522			−0.702609	−	0.711576i	$-0.747982\pi$
$257$	−22.5274			−1.40522			−0.702609	+	0.711576i	$0.747982\pi$
$258$	−2.54272	+	3.91815i	−0.158303	+	0.243934i
$259$	31.4063			1.95149
$260$	−0.0781471	−	0.342385i	−0.00484648	−	0.0212338i
$261$	−2.81109	−	2.60831i	−0.174002	−	0.161450i
$262$	17.3621	−	8.36113i	1.07263	−	0.516552i
$263$	5.37090	−	0.809533i	0.331184	−	0.0499180i	0.0186545	−	0.999826i	$-0.494062\pi$
$263$	5.37090	−	0.809533i	0.331184	−	0.0499180i	0.312530	+	0.949908i	$0.398824\pi$
$264$	0.966484	−	1.67400i	0.0594830	−	0.103028i
$265$	−0.0765549	−	0.132597i	−0.00470273	−	0.00814536i
$266$	−16.8369	−	21.1128i	−1.03234	−	1.29451i
$267$	−0.0979876	−	1.30755i	−0.00599675	−	0.0800210i
$268$	−1.09655	−	2.79396i	−0.0669824	−	0.170668i
$269$	2.16753	+	1.04383i	0.132156	+	0.0636432i	0.498793	−	0.866721i	$-0.333777\pi$
$269$	2.16753	+	1.04383i	0.132156	+	0.0636432i	−0.366637	+	0.930364i	$0.619491\pi$
$270$	0.105537	+	0.0325539i	0.00642279	+	0.00198117i
$271$	−1.20518	+	3.07074i	−0.0732093	+	0.186534i	−0.962794	−	0.270236i	$-0.912898\pi$
$271$	−1.20518	+	3.07074i	−0.0732093	+	0.186534i	0.889585	+	0.456770i	$0.150994\pi$
$272$	8.75747	−	8.12574i	0.531000	−	0.492696i
$273$	4.14738	+	2.82764i	0.251011	+	0.171136i
$274$	−23.8139	+	29.8616i	−1.43865	+	1.80401i
$275$	−18.4722	−	2.78424i	−1.11392	−	0.167896i
$276$	0.293508	−	0.0905354i	0.0176671	−	0.00544959i
$277$	−1.03223	+	13.7742i	−0.0620207	+	0.827609i	0.876283	+	0.481797i	$0.160016\pi$
$277$	−1.03223	+	13.7742i	−0.0620207	+	0.827609i	−0.938304	+	0.345812i	$0.887603\pi$
$278$	−27.7451	+	18.9163i	−1.66404	+	1.13452i
$279$	1.39405	−	6.10772i	0.0834595	−	0.365660i
$280$	−0.0289272	+	0.126739i	−0.00172873	+	0.00757407i
$281$	14.8789	−	10.1443i	0.887603	−	0.605157i	−0.0313571	−	0.999508i	$-0.509983\pi$
$281$	14.8789	−	10.1443i	0.887603	−	0.605157i	0.918960	+	0.394351i	$0.129031\pi$
$282$	0.591632	−	7.89479i	0.0352312	−	0.470128i
$283$	−12.7020	+	3.91805i	−0.755057	+	0.232904i	−0.648304	−	0.761382i	$-0.724521\pi$
$283$	−12.7020	+	3.91805i	−0.755057	+	0.232904i	−0.106752	+	0.994286i	$0.534045\pi$
$284$	14.2725	+	2.15123i	0.846916	+	0.127652i
$285$	−0.0213371	+	0.0267559i	−0.00126390	+	0.00158488i
$286$	32.8599	+	22.4035i	1.94304	+	1.32475i
$287$	4.45148	−	4.13037i	0.262763	−	0.243808i
$288$	7.97821	−	20.3281i	0.470121	−	1.19785i
$289$	17.1735	+	5.29732i	1.01021	+	0.311607i
$290$	−0.0683246	−	0.0329034i	−0.00401216	−	0.00193215i
$291$	1.07757	+	2.74560i	0.0631682	+	0.160950i
$292$	−1.50684	−	20.1073i	−0.0881810	−	1.17669i
$293$	−2.31732	−	2.90583i	−0.135379	−	0.169760i	0.709521	−	0.704685i	$-0.248912\pi$
$293$	−2.31732	−	2.90583i	−0.135379	−	0.169760i	−0.844900	+	0.534924i	$0.820340\pi$
$294$	−0.994505	−	1.72253i	−0.0580007	−	0.100460i
$295$	0.00226753	−	0.00392748i	0.000132021	−	0.000228667i
$296$	15.6683	−	2.36162i	0.910702	−	0.137266i
$297$	−6.50006	+	3.13026i	−0.377172	+	0.181636i
$298$	11.5692	+	10.7347i	0.670187	+	0.621842i
$299$	0.374604	+	1.64125i	0.0216639	+	0.0949157i
$300$	−4.46561			−0.257822
$301$	9.32167	+	18.2805i	0.537292	+	1.05367i
$302$	−21.8104			−1.25505
$303$	−1.11538	−	4.88679i	−0.0640767	−	0.280738i
$304$	5.87828	+	5.45425i	0.337142	+	0.312823i
$305$	0.131866	−	0.0635035i	0.00755064	−	0.00363620i
$306$	36.7734	−	5.54270i	2.10220	−	0.316855i
$307$	−4.87728	+	8.44770i	−0.278361	+	0.482136i	−0.970978	−	0.239170i	$-0.923125\pi$
$307$	−4.87728	+	8.44770i	−0.278361	+	0.482136i	0.692617	+	0.721306i	$0.256458\pi$
$308$	−15.9391	−	27.6073i	−0.908212	−	1.57307i
$309$	−3.27057	−	4.10117i	−0.186056	−	0.233307i
$310$	−0.00925826	−	0.123543i	−0.000525834	−	0.00701676i
$311$	−1.43950	−	3.66777i	−0.0816263	−	0.207980i	0.884234	−	0.467044i	$-0.154681\pi$
$311$	−1.43950	−	3.66777i	−0.0816263	−	0.207980i	−0.965860	+	0.259064i	$0.916586\pi$
$312$	2.28172	+	1.09882i	0.129177	+	0.0622083i
$313$	−21.8743	−	6.74733i	−1.23641	−	0.381382i	−0.393444	−	0.919349i	$-0.628716\pi$
$313$	−21.8743	−	6.74733i	−1.23641	−	0.381382i	−0.842966	+	0.537967i	$0.819193\pi$
$314$	7.67265	−	19.5496i	0.432992	−	1.10325i
$315$	0.174598	−	0.162003i	0.00983747	−	0.00912783i
$316$	−12.1980	−	8.31648i	−0.686193	−	0.467839i
$317$	6.42280	−	8.05394i	0.360740	−	0.452354i	−0.568031	−	0.823007i	$-0.692295\pi$
$317$	6.42280	−	8.05394i	0.360740	−	0.452354i	0.928771	+	0.370653i	$0.120866\pi$
$318$	4.09851	+	0.617752i	0.229833	+	0.0346418i
$319$	4.73365	−	1.46014i	0.265034	−	0.0817520i
$320$	0.0243276	−	0.324630i	0.00135996	−	0.0181473i
$321$	4.48115	−	3.05520i	0.250113	−	0.170524i
$322$	0.520544	−	2.28065i	0.0290088	−	0.127096i
$323$	−5.22351	+	22.8857i	−0.290644	+	1.27339i
$324$	18.1222	−	12.3555i	1.00679	−	0.686418i
$325$	1.82903	−	24.4067i	0.101456	−	1.35384i
$326$	−14.0998	+	4.34923i	−0.780918	+	0.240881i
$327$	−0.666611	−	0.100475i	−0.0368637	−	0.00555630i
$328$	1.91022	−	2.39534i	0.105474	−	0.132260i
$329$	−28.7368	−	19.5924i	−1.58431	−	1.08017i
$330$	−0.0513398	+	0.0476364i	−0.00282616	+	0.00262230i
$331$	−4.35233	+	11.0896i	−0.239226	+	0.609537i	−0.999182	−	0.0404371i	$-0.987125\pi$
$331$	−4.35233	+	11.0896i	−0.239226	+	0.609537i	0.759956	+	0.649974i	$0.225220\pi$
$332$	5.29982	+	1.63478i	0.290865	+	0.0897201i
$333$	−26.1564	−	12.5963i	−1.43336	−	0.690270i
$334$	−11.0878	−	28.2514i	−0.606700	−	1.54585i
$335$	0.00216485	+	0.0288880i	0.000118279	+	0.00157832i
$336$	1.29142	+	1.61939i	0.0704526	+	0.0883447i
$337$	1.63994	+	2.84045i	0.0893330	+	0.154729i	0.907229	−	0.420636i	$-0.138193\pi$
$337$	1.63994	+	2.84045i	0.0893330	+	0.154729i	−0.817896	+	0.575366i	$0.804860\pi$
$338$	−11.9221	+	20.6497i	−0.648476	+	1.12319i
$339$	−3.77956	+	0.569677i	−0.205278	+	0.0309406i
$340$	0.382205	−	0.184060i	0.0207280	−	0.00998206i
$341$	5.93245	+	5.50451i	0.321260	+	0.298086i
$342$	5.55463	+	24.3364i	0.300360	+	1.31596i
$343$	13.1669			0.710945
$344$	6.02512	+	8.41905i	0.324853	+	0.453925i
$345$	−0.00296456			−0.000159607
$346$	−5.56856	−	24.3974i	−0.299367	−	1.31161i
$347$	9.18271	+	8.52031i	0.492954	+	0.457394i	0.887049	−	0.461675i	$-0.152752\pi$
$347$	9.18271	+	8.52031i	0.492954	+	0.457394i	−0.394095	+	0.919070i	$0.628942\pi$
$348$	1.06690	−	0.513794i	0.0571921	−	0.0275423i
$349$	−31.6460	+	4.76987i	−1.69397	+	0.255325i	−0.923900	−	0.382633i	$-0.875017\pi$
$349$	−31.6460	+	4.76987i	−1.69397	+	0.255325i	−0.770071	+	0.637958i	$0.779779\pi$
$350$	−17.0052	+	29.4538i	−0.908964	+	1.57437i
$351$	−4.72613	−	8.18589i	−0.252262	−	0.436930i
$352$	17.5885	+	22.0553i	0.937470	+	1.17555i
$353$	−0.179426	−	2.39427i	−0.00954988	−	0.127434i	0.990391	−	0.138295i	$-0.0441620\pi$
$353$	−0.179426	−	2.39427i	−0.00954988	−	0.127434i	−0.999941	+	0.0108603i	$0.996543\pi$
$354$	0.0448521	+	0.114281i	0.00238386	+	0.00607399i
$355$	−0.125514	−	0.0604442i	−0.00666157	−	0.00320805i
$356$	−10.4254	−	3.21580i	−0.552543	−	0.170437i
$357$	−2.21519	+	5.64422i	−0.117240	+	0.298724i
$358$	−1.20594	+	1.11895i	−0.0637360	+	0.0591384i
$359$	6.81331	+	4.64523i	0.359593	+	0.245166i	0.729617	−	0.683856i	$-0.239698\pi$
$359$	6.81331	+	4.64523i	0.359593	+	0.245166i	−0.370024	+	0.929022i	$0.620651\pi$
$360$	0.0749233	−	0.0939509i	0.00394881	−	0.00495165i
$361$	3.20715	+	0.483400i	0.168797	+	0.0254421i
$362$	−2.16128	+	0.666667i	−0.113595	+	0.0350393i
$363$	0.0725471	−	0.968074i	0.00380773	−	0.0508107i
$364$	34.5085	−	23.5275i	1.80874	−	1.23318i
$365$	−0.0433057	+	0.189735i	−0.00226672	+	0.00993117i
$366$	−0.881651	+	3.86276i	−0.0460846	+	0.201910i
$367$	8.55721	−	5.83421i	0.446683	−	0.304543i	−0.319008	−	0.947752i	$-0.603350\pi$
$367$	8.55721	−	5.83421i	0.446683	−	0.304543i	0.765691	+	0.643209i	$0.222397\pi$
$368$	−0.0519117	+	0.692714i	−0.00270608	+	0.0361102i
$369$	−5.36396	+	1.65456i	−0.279236	+	0.0861330i
$370$	−0.567697	−	0.0855666i	−0.0295132	−	0.00444840i
$371$	11.3530	−	14.2362i	0.589418	−	0.739107i
$372$	1.59841	+	1.08978i	0.0828737	+	0.0565023i
$373$	−8.47754	+	7.86601i	−0.438950	+	0.407286i	−0.868447	−	0.495782i	$-0.834882\pi$
$373$	−8.47754	+	7.86601i	−0.438950	+	0.407286i	0.429497	+	0.903068i	$0.358691\pi$
$374$	−17.5510	+	44.7193i	−0.907543	+	2.31238i
$375$	0.0823774	+	0.0254101i	0.00425395	+	0.00131217i
$376$	−15.8098	−	7.61361i	−0.815329	−	0.392642i
$377$	2.37115	+	6.04159i	0.122120	+	0.311158i
$378$	0.981558	+	13.0980i	0.0504859	+	0.673688i
$379$	7.24547	+	9.08554i	0.372175	+	0.466693i	0.932284	−	0.361726i	$-0.117812\pi$
$379$	7.24547	+	9.08554i	0.372175	+	0.466693i	−0.560110	+	0.828419i	$0.689241\pi$
$380$	0.142373	+	0.246598i	0.00730359	+	0.0126502i
$381$	−1.23551	+	2.13996i	−0.0632969	+	0.109633i
$382$	29.7983	−	4.49137i	1.52461	−	0.229799i
$383$	15.8309	−	7.62376i	0.808921	−	0.389556i	0.0167535	−	0.999860i	$-0.494667\pi$
$383$	15.8309	−	7.62376i	0.808921	−	0.389556i	0.792167	+	0.610304i	$0.208953\pi$
$384$	2.83363	+	2.62923i	0.144603	+	0.134172i
$385$	0.0684647	+	0.299964i	0.00348929	+	0.0152876i
$386$	32.1106			1.63439
$387$	−0.431607	−	18.9634i	−0.0219398	−	0.963966i
$388$	24.5414			1.24590
$389$	−1.45910	−	6.39272i	−0.0739792	−	0.324124i	0.924374	−	0.381487i	$-0.124588\pi$
$389$	−1.45910	−	6.39272i	−0.0739792	−	0.324124i	−0.998353	+	0.0573631i	$0.981731\pi$
$390$	−0.0672639	−	0.0624117i	−0.00340604	−	0.00316034i
$391$	−1.83213	+	0.882306i	−0.0926546	+	0.0446201i
$392$	−4.35933	+	0.657063i	−0.220179	+	0.0331867i
$393$	1.45216	−	2.51521i	0.0732517	−	0.126876i
$394$	8.25367	+	14.2958i	0.415814	+	0.720210i
$395$	0.0888418	+	0.111404i	0.00447012	+	0.00560535i
$396$	2.20211	+	29.3852i	0.110660	+	1.47666i
$397$	−10.7843	−	27.4779i	−0.541248	−	1.37908i	−0.895973	−	0.444108i	$-0.853521\pi$
$397$	−10.7843	−	27.4779i	−0.541248	−	1.37908i	0.354725	−	0.934971i	$-0.384575\pi$
$398$	49.1422	+	23.6656i	2.46328	+	1.18625i
$399$	−3.88909	−	1.19963i	−0.194698	−	0.0600565i
$400$	3.68971	−	9.40123i	0.184486	−	0.470061i
$401$	−18.2470	+	16.9307i	−0.911210	+	0.845479i	−0.988452	−	0.151533i	$-0.951579\pi$
$401$	−18.2470	+	16.9307i	−0.911210	+	0.845479i	0.0772425	+	0.997012i	$0.475388\pi$
$402$	−0.647948	−	0.441764i	−0.0323167	−	0.0220332i
$403$	−6.61084	+	8.28973i	−0.329309	+	0.412941i
$404$	−41.2406	−	6.21602i	−2.05180	−	0.309258i
$405$	−0.202289	+	0.0623980i	−0.0100518	+	0.00310058i
$406$	0.673971	−	8.99352i	0.0334486	−	0.446341i
$407$	30.9860	−	21.1259i	1.53592	−	1.04717i
$408$	−0.680719	+	2.98242i	−0.0337006	+	0.147652i
$409$	2.84836	−	12.4795i	0.140843	−	0.617072i	−0.854398	−	0.519620i	$-0.826074\pi$
$409$	2.84836	−	12.4795i	0.140843	−	0.617072i	0.995240	−	0.0974519i	$-0.0310692\pi$
$410$	−0.0917178	+	0.0625322i	−0.00452962	+	0.00308824i
$411$	−0.430178	+	5.74033i	−0.0212191	+	0.283150i
$412$	−41.7071	+	12.8649i	−2.05476	+	0.633810i
$413$	0.533315	+	0.0803843i	0.0262427	+	0.00395545i
$414$	−1.34824	+	1.69064i	−0.0662624	+	0.0830905i
$415$	−0.0442289	−	0.0301548i	−0.00217111	−	0.00148024i
$416$	−27.0933	+	25.1389i	−1.32836	+	1.23254i
$417$	−1.84898	+	4.71112i	−0.0905449	+	0.230705i
$418$	−30.8134	−	9.50468i	−1.50713	−	0.464889i
$419$	−25.2233	−	12.1469i	−1.23224	−	0.593415i	−0.299545	−	0.954082i	$-0.596835\pi$
$419$	−25.2233	−	12.1469i	−1.23224	−	0.593415i	−0.932695	+	0.360667i	$0.882549\pi$
$420$	0.0268706	+	0.0684653i	0.00131115	+	0.00334076i
$421$	1.03389	+	13.7963i	0.0503885	+	0.672388i	0.964017	+	0.265839i	$0.0856490\pi$
$421$	1.03389	+	13.7963i	0.0503885	+	0.672388i	−0.913629	+	0.406549i	$0.866732\pi$
$422$	−21.7596	−	27.2857i	−1.05924	−	1.32825i
$423$	16.0751	+	27.8430i	0.781600	+	1.35377i
$424$	4.59341	−	7.95602i	0.223076	−	0.386379i
$425$	29.2342	−	4.40635i	1.41807	−	0.213739i
$426$	3.39776	−	1.63628i	0.164622	−	0.0792778i
$427$	12.7596	+	11.8392i	0.617481	+	0.572938i
$428$	−10.0417	−	43.9955i	−0.485383	−	2.12660i
$429$	5.99394			0.289390
$430$	−0.118692	−	0.355834i	−0.00572386	−	0.0171599i
$431$	−32.0319			−1.54292			−0.771462	−	0.636276i	$-0.780474\pi$
$431$	−32.0319			−1.54292			−0.771462	+	0.636276i	$0.780474\pi$
$432$	−0.867910	−	3.80256i	−0.0417573	−	0.182951i
$433$	−0.278233	−	0.258163i	−0.0133710	−	0.0124065i	0.673459	−	0.739225i	$-0.264808\pi$
$433$	−0.278233	−	0.258163i	−0.0133710	−	0.0124065i	−0.686830	+	0.726818i	$0.740998\pi$
$434$	13.2746	−	6.39272i	0.637202	−	0.306860i
$435$	−0.0113016	+	0.00170345i	−0.000541872	+	8.16741e-5i
$436$	−2.80461	+	4.85772i	−0.134316	+	0.232643i
$437$	−0.682476	−	1.18208i	−0.0326473	−	0.0565467i
$438$	−3.28477	−	4.11897i	−0.156953	−	0.196812i
$439$	0.364516	+	4.86413i	0.0173974	+	0.232152i	0.999124	+	0.0418540i	$0.0133264\pi$
$439$	0.364516	+	4.86413i	0.0173974	+	0.232152i	−0.981726	+	0.190298i	$0.939055\pi$
$440$	0.0567125	+	0.144501i	0.00270366	+	0.00688882i
$441$	7.27738	+	3.50460i	0.346542	+	0.166886i
$442$	−60.1445	−	18.5521i	−2.86078	−	0.882435i
$443$	2.16832	−	5.52479i	0.103020	−	0.262491i	−0.870065	−	0.492937i	$-0.835923\pi$
$443$	2.16832	−	5.52479i	0.103020	−	0.262491i	0.973085	+	0.230446i	$0.0740186\pi$
$444$	6.57171	−	6.09766i	0.311880	−	0.289382i
$445$	0.0870035	+	0.0593180i	0.00412436	+	0.00281194i
$446$	−20.4595	+	25.6554i	−0.968784	+	1.21482i
$447$	2.35203	+	0.354512i	0.111247	+	0.0167679i
$448$	36.9953	−	11.4115i	1.74786	−	0.539144i
$449$	2.44448	−	32.6193i	0.115362	−	1.53940i	−0.576336	−	0.817213i	$-0.695518\pi$
$449$	2.44448	−	32.6193i	0.115362	−	1.53940i	0.691698	−	0.722187i	$-0.256863\pi$
$450$	25.9757	−	17.7100i	1.22451	−	0.834855i
$451$	1.61356	−	7.06946i	0.0759795	−	0.332888i
$452$	−7.07688	+	31.0059i	−0.332869	+	1.45839i
$453$	−2.71595	+	1.85170i	−0.127607	+	0.0870007i
$454$	3.27567	−	43.7108i	0.153735	−	2.05145i
$455$	−0.385201	+	0.118819i	−0.0180585	+	0.00557031i
$456$	−2.03044	−	0.306040i	−0.0950842	−	0.0143316i
$457$	18.1197	−	22.7213i	0.847602	−	1.06286i	−0.149647	−	0.988739i	$-0.547814\pi$
$457$	18.1197	−	22.7213i	0.847602	−	1.06286i	0.997249	−	0.0741197i	$-0.0236147\pi$
$458$	24.0359	+	16.3874i	1.12312	+	0.765734i
$459$	8.36979	−	7.76603i	0.390668	−	0.362487i
$460$	−0.00901178	+	0.0229616i	−0.000420177	+	0.00107059i
$461$	−13.8948	−	4.28598i	−0.647146	−	0.199618i	−0.0462305	−	0.998931i	$-0.514721\pi$
$461$	−13.8948	−	4.28598i	−0.647146	−	0.199618i	−0.600915	+	0.799313i	$0.705197\pi$
$462$	−7.50426	−	3.61386i	−0.349130	−	0.168132i
$463$	−2.25869	−	5.75504i	−0.104970	−	0.267459i	0.868733	−	0.495281i	$-0.164935\pi$
$463$	−2.25869	−	5.75504i	−0.104970	−	0.267459i	−0.973703	+	0.227822i	$0.926840\pi$
$464$	0.200136	+	2.67062i	0.00929106	+	0.123981i
$465$	−0.0116417	−	0.0145982i	−0.000539870	−	0.000676975i
$466$	−10.0665	−	17.4356i	−0.466320	−	0.807689i
$467$	7.90363	−	13.6895i	0.365736	−	0.633474i	−0.623158	−	0.782096i	$-0.714150\pi$
$467$	7.90363	−	13.6895i	0.365736	−	0.633474i	0.988894	+	0.148622i	$0.0474838\pi$
$468$	−38.1763	+	5.75416i	−1.76470	+	0.265986i
$469$	−3.10400	+	1.49481i	−0.143329	+	0.0690237i
$470$	0.466065	+	0.432445i	0.0214980	+	0.0199472i
$471$	−0.704320	−	3.08583i	−0.0324534	−	0.142187i
$472$	0.272111			0.0125249
$473$	21.4936	+	11.7656i	0.988278	+	0.540981i
$474$	−3.85736			−0.177174
$475$	4.41583	+	19.3470i	0.202612	+	0.887702i
$476$	36.9828	+	34.3150i	1.69510	+	1.57283i
$477$	−15.1650	+	7.30309i	−0.694358	+	0.334385i
$478$	41.3304	−	6.22955i	1.89041	−	0.284933i
$479$	−19.2621	+	33.3629i	−0.880107	+	1.52439i	−0.0288864	+	0.999583i	$0.509196\pi$
$479$	−19.2621	+	33.3629i	−0.880107	+	1.52439i	−0.851221	+	0.524808i	$0.824137\pi$
$480$	−0.0325429	−	0.0563660i	−0.00148537	−	0.00257274i
$481$	30.6350	+	38.4150i	1.39683	+	1.75157i
$482$	0.940270	+	12.5470i	0.0428281	+	0.571501i
$483$	−0.128806	−	0.328193i	−0.00586089	−	0.0149333i
$484$	−7.27757	−	3.50469i	−0.330798	−	0.159304i
$485$	−0.226342	−	0.0698174i	−0.0102777	−	0.00317024i
$486$	6.69409	−	17.0563i	0.303650	−	0.773688i
$487$	9.12024	−	8.46235i	0.413277	−	0.383465i	−0.445951	−	0.895057i	$-0.647134\pi$
$487$	9.12024	−	8.46235i	0.413277	−	0.383465i	0.859229	+	0.511592i	$0.170944\pi$
$488$	7.25591	+	4.94700i	0.328460	+	0.223940i
$489$	−1.38654	+	1.73867i	−0.0627015	+	0.0786252i
$490$	0.157948	+	0.0238068i	0.00713537	+	0.00107548i
$491$	−36.8246	+	11.3589i	−1.66187	+	0.512619i	−0.976489	−	0.215566i	$-0.930840\pi$
$491$	−36.8246	+	11.3589i	−1.66187	+	0.512619i	−0.685381	+	0.728185i	$0.740364\pi$
$492$	0.129537	−	1.72855i	0.00583996	−	0.0779289i
$493$	−6.47754	+	4.41631i	−0.291734	+	0.198901i
$494$	9.40102	−	41.1886i	0.422972	−	1.85316i
$495$	0.0632876	−	0.277281i	0.00284457	−	0.0124629i
$496$	−3.61494	+	2.46463i	−0.162316	+	0.110665i
$497$	1.23810	−	16.5213i	0.0555363	−	0.741081i
$498$	1.38473	−	0.427134i	0.0620514	−	0.0191403i
$499$	41.3979	+	6.23973i	1.85322	+	0.279329i	0.978645	−	0.205556i	$-0.0659002\pi$
$499$	41.3979	+	6.23973i	1.85322	+	0.279329i	0.874578	+	0.484884i	$0.161138\pi$
$500$	0.447225	−	0.560802i	0.0200005	−	0.0250798i
$501$	−3.77926	−	2.57665i	−0.168845	−	0.115116i
$502$	−11.8254	+	10.9723i	−0.527792	+	0.489720i
$503$	−5.36535	+	13.6707i	−0.239229	+	0.609546i	−0.999182	−	0.0404321i	$-0.987127\pi$
$503$	−5.36535	+	13.6707i	−0.239229	+	0.609546i	0.759953	+	0.649978i	$0.225222\pi$
$504$	13.6562	+	4.21238i	0.608296	+	0.187634i
$505$	0.362674	+	0.174654i	0.0161388	+	0.00777202i
$506$	−1.02054	−	2.60029i	−0.0453684	−	0.115597i
$507$	0.268553	+	3.58359i	0.0119269	+	0.159153i
$508$	12.8191	+	16.0746i	0.568754	+	0.713195i
$509$	11.0632	+	19.1620i	0.490368	+	0.849342i	0.999939	−	0.0110868i	$-0.00352910\pi$
$509$	11.0632	+	19.1620i	0.490368	+	0.849342i	−0.509571	+	0.860429i	$0.670196\pi$
$510$	0.0554194	−	0.0959892i	0.00245401	−	0.00425047i
$511$	−22.8863	+	3.44955i	−1.01243	+	0.152599i
$512$	−19.4877	+	9.38480i	−0.861244	+	0.414753i
$513$	5.61806	+	5.21280i	0.248043	+	0.230151i
$514$	10.8978	+	47.7463i	0.480681	+	2.10600i
$515$	0.421259			0.0185629
$516$	5.49979	+	2.01533i	0.242115	+	0.0887200i
$517$	−41.5315			−1.82655
$518$	−15.1930	−	66.5650i	−0.667543	−	2.92470i
$519$	−2.76477	−	2.56533i	−0.121360	−	0.112606i
$520$	−0.183239	+	0.0882432i	−0.00803556	+	0.00386972i
$521$	25.2437	−	3.80487i	1.10594	−	0.166694i	0.429413	−	0.903108i	$-0.358720\pi$
$521$	25.2437	−	3.80487i	1.10594	−	0.166694i	0.676531	+	0.736414i	$0.263482\pi$
$522$	−4.16838	+	7.21985i	−0.182445	+	0.316004i
$523$	−14.2828	−	24.7386i	−0.624544	−	1.08174i	−0.988629	−	0.150376i	$-0.951952\pi$
$523$	−14.2828	−	24.7386i	−0.624544	−	1.08174i	0.364085	−	0.931366i	$-0.381382\pi$
$524$	−15.0670	−	18.8934i	−0.658203	−	0.825360i
$525$	0.383053	+	5.11148i	0.0167178	+	0.223083i
$526$	−4.31401	−	10.9919i	−0.188100	−	0.479270i
$527$	−11.5393	−	5.55706i	−0.502662	−	0.242069i
$528$	2.36344	+	0.729025i	0.102856	+	0.0317268i
$529$	−8.35964	+	21.3000i	−0.363463	+	0.926088i
$530$	−0.244003	+	0.226401i	−0.0105988	+	0.00983425i
$531$	−0.411926	−	0.280846i	−0.0178761	−	0.0121877i
$532$	−21.1138	+	26.4758i	−0.915398	+	1.14787i
$533$	9.39428	+	1.41596i	0.406911	+	0.0613320i
$534$	−2.72393	+	0.840223i	−0.117876	+	0.0363600i
$535$	−0.0325488	+	0.434333i	−0.00140721	+	0.0187779i
$536$	−1.43615	+	0.979154i	−0.0620324	+	0.0422930i
$537$	−0.0551715	+	0.241722i	−0.00238083	+	0.0104311i
$538$	1.16381	−	5.09899i	0.0501755	−	0.219833i
$539$	−8.62112	+	5.87778i	−0.371338	+	0.253174i
$540$	0.0103500	−	0.138112i	0.000445395	−	0.00594338i
$541$	−1.66509	+	0.513613i	−0.0715879	+	0.0220819i	−0.330342	−	0.943861i	$-0.607164\pi$
$541$	−1.66509	+	0.513613i	−0.0715879	+	0.0220819i	0.258754	+	0.965943i	$0.416688\pi$
$542$	7.09139	+	1.06886i	0.304601	+	0.0459113i
$543$	−0.212535	+	0.266510i	−0.00912073	+	0.0114370i
$544$	−36.8873	−	25.1494i	−1.58153	−	1.07827i
$545$	0.0396863	−	0.0368235i	0.00169997	−	0.00157735i
$546$	3.98680	−	10.1582i	0.170619	−	0.434730i
$547$	10.3354	+	3.18805i	0.441909	+	0.136311i	0.507722	−	0.861521i	$-0.330488\pi$
$547$	10.3354	+	3.18805i	0.441909	+	0.136311i	−0.0658126	+	0.997832i	$0.520964\pi$
$548$	43.1534	+	20.7816i	1.84342	+	0.887745i
$549$	−5.87831	−	14.9777i	−0.250880	−	0.639233i
$550$	3.03494	+	40.4985i	0.129410	+	1.72686i
$551$	−3.28100	−	4.11424i	−0.139775	−	0.175273i
$552$	−0.0889391	−	0.154047i	−0.00378550	−	0.00655668i
$553$	−8.47299	+	14.6756i	−0.360308	+	0.624072i
$554$	29.6934	−	4.47556i	1.26155	−	0.190148i
$555$	−0.0779574	+	0.0375423i	−0.00330911	+	0.00159358i
$556$	30.8688	+	28.6421i	1.30913	+	1.21469i
$557$	−0.0339125	−	0.148580i	−0.00143692	−	0.00629554i	0.974204	−	0.225668i	$-0.0724563\pi$
$557$	−0.0339125	−	0.148580i	−0.00143692	−	0.00629554i	−0.975641	+	0.219372i	$0.929599\pi$
$558$	−13.6196			−0.576563
$559$	−13.2674	+	29.2335i	−0.561149	+	1.23645i
$560$	−0.166338			−0.00702908
$561$	1.61112	+	7.05878i	0.0680215	+	0.298022i
$562$	−28.6984	−	26.6283i	−1.21057	−	1.12324i
$563$	21.4601	−	10.3347i	0.904437	−	0.435554i	0.0769474	−	0.997035i	$-0.475483\pi$
$563$	21.4601	−	10.3347i	0.904437	−	0.435554i	0.827489	+	0.561481i	$0.189768\pi$
$564$	−9.81709	+	1.47969i	−0.413374	+	0.0623061i
$565$	0.153478	−	0.265831i	0.00645685	−	0.0111836i
$566$	14.4489	+	25.0263i	0.607334	+	1.05193i
$567$	−15.6970	−	19.6834i	−0.659213	−	0.826627i
$568$	−0.624654	−	8.33542i	−0.0262099	−	0.349747i
$569$	11.4363	+	29.1391i	0.479433	+	1.22158i	0.942187	+	0.335088i	$0.108766\pi$
$569$	11.4363	+	29.1391i	0.479433	+	1.22158i	−0.462754	+	0.886487i	$0.653139\pi$
$570$	0.0670306	+	0.0322802i	0.00280760	+	0.00135207i
$571$	−4.21255	−	1.29940i	−0.176290	−	0.0543782i	0.205354	−	0.978688i	$-0.434166\pi$
$571$	−4.21255	−	1.29940i	−0.176290	−	0.0543782i	−0.381643	+	0.924310i	$0.624642\pi$
$572$	18.2206	−	46.4254i	0.761842	−	1.94114i
$573$	3.32933	−	3.08917i	0.139085	−	0.129052i
$574$	−10.9077	−	7.43673i	−0.455278	−	0.310403i
$575$	−1.07183	+	1.34403i	−0.0446983	+	0.0560499i
$576$	−35.3880	−	5.33389i	−1.47450	−	0.222245i
$577$	24.4740	−	7.54924i	1.01887	−	0.314279i	0.260059	−	0.965593i	$-0.416258\pi$
$577$	24.4740	−	7.54924i	1.01887	−	0.314279i	0.758809	+	0.651314i	$0.225782\pi$
$578$	2.91976	−	38.9615i	0.121446	−	1.62059i
$579$	3.99858	−	2.72619i	0.166175	−	0.113297i
$580$	−0.0211613	+	0.0927137i	−0.000878675	+	0.00384973i
$581$	1.41661	−	6.20657i	0.0587709	−	0.257492i
$582$	5.29797	−	3.61209i	0.219608	−	0.149726i
$583$	1.62488	−	21.6825i	0.0672956	−	0.897997i
$584$	−11.1584	+	3.44190i	−0.461736	+	0.142427i
$585$	0.368466	+	0.0555373i	0.0152342	+	0.00229619i
$586$	−5.03783	+	6.31724i	−0.208111	+	0.260963i
$587$	21.8609	+	14.9045i	0.902298	+	0.615176i	0.923080	−	0.384608i	$-0.125663\pi$
$587$	21.8609	+	14.9045i	0.902298	+	0.615176i	−0.0207824	+	0.999784i	$0.506616\pi$
$588$	−1.82842	+	1.69653i	−0.0754028	+	0.0699636i
$589$	3.14081	−	8.00265i	0.129415	−	0.329744i
$590$	−0.00942115	−	0.00290604i	−0.000387863	−	0.000119640i
$591$	2.24150	+	1.07945i	0.0922031	+	0.0444027i
$592$	7.40722	+	18.8733i	0.304435	+	0.775687i
$593$	−2.82909	−	37.7516i	−0.116177	−	1.55027i	−0.685448	−	0.728121i	$-0.740394\pi$
$593$	−2.82909	−	37.7516i	−0.116177	−	1.55027i	0.569272	−	0.822149i	$-0.307225\pi$
$594$	9.77899	+	12.2625i	0.401237	+	0.503135i
$595$	−0.243466	−	0.421696i	−0.00998114	−	0.0172878i
$596$	9.89563	−	17.1397i	0.405341	−	0.702071i
$597$	8.12867	−	1.22520i	0.332684	−	0.0501441i
$598$	3.29737	−	1.58793i	0.134840	−	0.0649353i
$599$	5.30017	+	4.91784i	0.216559	+	0.200938i	0.780991	−	0.624542i	$-0.214714\pi$
$599$	5.30017	+	4.91784i	0.216559	+	0.200938i	−0.564432	+	0.825480i	$0.690905\pi$
$600$	0.575464	+	2.52127i	0.0234932	+	0.102930i
$601$	1.42190			0.0580006			0.0290003	−	0.999579i	$-0.490768\pi$
$601$	1.42190			0.0580006			0.0290003	+	0.999579i	$0.490768\pi$
$602$	34.2358	−	28.6005i	1.39535	−	1.16567i
$603$	3.18466			0.129689
$604$	6.08610	+	26.6650i	0.247640	+	1.08498i
$605$	0.0571498	+	0.0530272i	0.00232347	+	0.00215586i
$606$	−9.81788	+	4.72804i	−0.398824	+	0.192064i
$607$	−11.6641	+	1.75808i	−0.473432	+	0.0713583i	−0.381424	−	0.924400i	$-0.624566\pi$
$607$	−11.6641	+	1.75808i	−0.473432	+	0.0713583i	−0.0920071	+	0.995758i	$0.529328\pi$
$608$	14.9835	−	25.9522i	0.607661	−	1.05250i
$609$	−0.679623	−	1.17714i	−0.0275397	−	0.0477002i
$610$	−0.198386	−	0.248768i	−0.00803241	−	0.0100723i
$611$	−4.06631	−	54.2611i	−0.164505	−	2.19517i
$612$	−17.0379	−	43.4118i	−0.688715	−	1.75482i
$613$	21.6428	+	10.4226i	0.874145	+	0.420966i	0.816483	−	0.577370i	$-0.195921\pi$
$613$	21.6428	+	10.4226i	0.874145	+	0.420966i	0.0576626	+	0.998336i	$0.481635\pi$
$614$	20.2642	+	6.25067i	0.817795	+	0.252256i
$615$	−0.00611222	+	0.0155737i	−0.000246469	+	0.000627992i
$616$	−13.5330	+	12.5568i	−0.545259	+	0.505927i
$617$	1.32647	+	0.904369i	0.0534015	+	0.0364085i	0.589727	−	0.807603i	$-0.299236\pi$
$617$	1.32647	+	0.904369i	0.0534015	+	0.0364085i	−0.536325	+	0.844011i	$0.680188\pi$
$618$	−7.11018	+	8.91589i	−0.286013	+	0.358649i
$619$	−48.0499	−	7.24235i	−1.93129	−	0.291095i	−0.933557	−	0.358428i	$-0.883313\pi$
$619$	−48.0499	−	7.24235i	−1.93129	−	0.291095i	−0.997731	+	0.0673331i	$0.978551\pi$
$620$	−0.148457	+	0.0457931i	−0.00596219	+	0.00183909i
$621$	−0.0496137	+	0.662048i	−0.00199093	+	0.0265671i
$622$	−7.07741	+	4.82530i	−0.283778	+	0.193477i
$623$	−2.78664	+	12.2091i	−0.111644	+	0.489146i
$624$	−0.721074	+	3.15923i	−0.0288661	+	0.126470i
$625$	20.6474	−	14.0772i	0.825896	−	0.563086i
$626$	−3.71898	+	49.6263i	−0.148640	+	1.98347i
$627$	−4.64400	+	1.43249i	−0.185464	+	0.0572080i
$628$	−26.0419	−	3.92519i	−1.03919	−	0.156632i
$629$	−37.0051	+	46.4030i	−1.47549	+	1.85021i
$630$	−0.427825	−	0.291686i	−0.0170450	−	0.0116211i
$631$	14.5938	−	13.5411i	0.580971	−	0.539062i	−0.334005	−	0.942571i	$-0.608400\pi$
$631$	14.5938	−	13.5411i	0.580971	−	0.539062i	0.914975	+	0.403509i	$0.132210\pi$
$632$	−3.12355	+	7.95868i	−0.124248	+	0.316579i
$633$	−5.02619	−	1.55037i	−0.199773	−	0.0616218i
$634$	−20.1773	−	9.71685i	−0.801341	−	0.385905i
$635$	−0.0724985	−	0.184723i	−0.00287701	−	0.00733051i
$636$	−0.388422	−	5.18314i	−0.0154020	−	0.205525i
$637$	−8.52344	−	10.6881i	−0.337711	−	0.423476i
$638$	−5.38468	−	9.32653i	−0.213181	−	0.369241i
$639$	−7.65740	+	13.2630i	−0.302922	+	0.524677i
$640$	−0.306963	+	0.0462673i	−0.0121338	+	0.00182887i
$641$	−19.5056	+	9.39338i	−0.770423	+	0.371016i	−0.777438	−	0.628959i	$-0.783481\pi$
$641$	−19.5056	+	9.39338i	−0.770423	+	0.371016i	0.00701500	+	0.999975i	$0.497767\pi$
$642$	−8.64322	−	8.01974i	−0.341121	−	0.316514i
$643$	−0.473254	−	2.07346i	−0.0186633	−	0.0817694i	0.964739	−	0.263210i	$-0.0847812\pi$
$643$	−0.473254	−	2.07346i	−0.0186633	−	0.0817694i	−0.983402	+	0.181440i	$0.941924\pi$
$644$	−2.93353			−0.115597
$645$	−0.0449906	−	0.0342334i	−0.00177150	−	0.00134794i
$646$	51.0327			2.00785
$647$	0.593026	+	2.59822i	0.0233143	+	0.102146i	0.985246	−	0.171142i	$-0.0547457\pi$
$647$	0.593026	+	2.59822i	0.0233143	+	0.102146i	−0.961932	+	0.273289i	$0.911889\pi$
$648$	−9.31122	−	8.63955i	−0.365779	−	0.339393i
$649$	0.580250	−	0.279434i	0.0227768	−	0.0109687i
$650$	−52.6144	+	7.93034i	−2.06371	+	0.311054i
$651$	1.11029	−	1.92307i	0.0435155	−	0.0753711i
$652$	9.25177	+	16.0245i	0.362327	+	0.627569i
$653$	8.03489	+	10.0754i	0.314429	+	0.394282i	0.913783	−	0.406202i	$-0.133147\pi$
$653$	8.03489	+	10.0754i	0.314429	+	0.394282i	−0.599354	+	0.800484i	$0.704576\pi$
$654$	0.109522	+	1.46147i	0.00428266	+	0.0571482i
$655$	0.0852115	+	0.217115i	0.00332949	+	0.00848340i
$656$	3.53199	+	1.70092i	0.137901	+	0.0664097i
$657$	20.4441	+	6.30617i	0.797601	+	0.246027i
$658$	−27.6241	+	70.3852i	−1.07690	+	2.74390i
$659$	28.5593	−	26.4992i	1.11251	−	1.03226i	0.113261	−	0.993565i	$-0.463870\pi$
$659$	28.5593	−	26.4992i	1.11251	−	1.03226i	0.999251	−	0.0386951i	$-0.0123201\pi$
$660$	0.0725653	+	0.0494742i	0.00282460	+	0.00192578i
$661$	24.8200	−	31.1233i	0.965387	−	1.21056i	−0.0121787	−	0.999926i	$-0.503877\pi$
$661$	24.8200	−	31.1233i	0.965387	−	1.21056i	0.977566	−	0.210631i	$-0.0675519\pi$
$662$	25.6096	+	3.86002i	0.995344	+	0.150024i
$663$	−9.06460	+	2.79606i	−0.352040	+	0.108590i
$664$	0.240026	−	3.20293i	0.00931483	−	0.124298i
$665$	0.270051	−	0.184118i	0.0104721	−	0.00713977i
$666$	−14.0442	+	61.5315i	−0.544200	+	2.38430i
$667$	0.101438	−	0.444430i	0.00392770	−	0.0172084i
$668$	−31.4455	+	21.4392i	−1.21666	+	0.829507i
$669$	−0.369584	+	4.93175i	−0.0142889	+	0.190673i
$670$	0.0601803	−	0.0185631i	0.00232497	−	0.000717157i
$671$	20.5527	+	3.09782i	0.793428	+	0.119590i
$672$	4.82608	−	6.05171i	0.186170	−	0.233450i
$673$	−30.9218	−	21.0822i	−1.19195	−	0.812657i	−0.205813	−	0.978591i	$-0.565984\pi$
$673$	−30.9218	−	21.0822i	−1.19195	−	0.812657i	−0.986137	+	0.165934i	$0.946936\pi$
$674$	5.22696	−	4.84991i	0.201335	−	0.186811i
$675$	3.52637	−	8.98505i	0.135730	−	0.345835i
$676$	28.5726	+	8.81349i	1.09895	+	0.338980i
$677$	4.02286	+	1.93731i	0.154611	+	0.0744567i	0.509589	−	0.860418i	$-0.329797\pi$
$677$	4.02286	+	1.93731i	0.154611	+	0.0744567i	−0.354978	+	0.934875i	$0.615512\pi$
$678$	3.03581	+	7.73512i	0.116590	+	0.297066i
$679$	−2.10512	−	28.0908i	−0.0807870	−	1.07803i
$680$	−0.153173	−	0.192073i	−0.00587391	−	0.00736565i
$681$	−3.30314	−	5.72121i	−0.126577	−	0.219237i
$682$	8.79683	−	15.2366i	0.336848	−	0.583438i
$683$	−37.5870	+	5.66533i	−1.43823	+	0.216778i	−0.821414	−	0.570333i	$-0.806814\pi$
$683$	−37.5870	+	5.66533i	−1.43823	+	0.216778i	−0.616812	+	0.787110i	$0.711576\pi$
$684$	28.2032	−	13.5819i	1.07838	−	0.519318i
$685$	−0.338878	−	0.314433i	−0.0129479	−	0.0120139i
$686$	−6.36958	−	27.9070i	−0.243192	−	1.06549i
$687$	4.38437			0.167274
$688$	−8.78697	+	9.91326i	−0.335000	+	0.377939i
$689$	28.4874			1.08528
$690$	0.00143413	+	0.00628333i	5.45964e−5	+	0.000239202i
$691$	4.15300	+	3.85342i	0.157988	+	0.146591i	0.755206	−	0.655488i	$-0.227537\pi$
$691$	4.15300	+	3.85342i	0.157988	+	0.146591i	−0.597218	+	0.802079i	$0.703727\pi$
$692$	−28.2739	+	13.6160i	−1.07481	+	0.517602i
$693$	33.4463	−	5.04122i	1.27052	−	0.191500i
$694$	13.6164	−	23.5844i	0.516873	−	0.895250i
$695$	−0.203216	−	0.351981i	−0.00770844	−	0.0133514i
$696$	−0.427574	−	0.536161i	−0.0162072	−	0.0203231i
$697$	0.857594	+	11.4438i	0.0324837	+	0.433464i
$698$	25.4186	+	64.7656i	0.962110	+	2.45142i
$699$	−2.73381	−	1.31654i	−0.103402	−	0.0497959i
$700$	40.7548	+	12.5712i	1.54039	+	0.475146i
$701$	−9.33779	+	23.7923i	−0.352683	+	0.898623i	0.638916	+	0.769276i	$0.279383\pi$
$701$	−9.33779	+	23.7923i	−0.352683	+	0.898623i	−0.991600	+	0.129346i	$0.958712\pi$
$702$	−15.0635	+	13.9769i	−0.568537	+	0.527525i
$703$	−32.9162	−	22.4419i	−1.24146	−	0.846412i
$704$	28.8241	−	36.1443i	1.08635	−	1.36224i
$705$	0.0947515	+	0.0142815i	0.00356855	+	0.000537872i
$706$	−4.98782	+	1.53854i	−0.187719	+	0.0579036i
$707$	−3.57750	+	47.7385i	−0.134546	+	1.79539i
$708$	0.127202	−	0.0867250i	0.00478055	−	0.00325933i
$709$	7.82205	−	34.2706i	0.293763	−	1.28706i	−0.585480	−	0.810687i	$-0.699094\pi$
$709$	7.82205	−	34.2706i	0.293763	−	1.28706i	0.879243	−	0.476373i	$-0.158049\pi$
$710$	−0.0673921	+	0.295264i	−0.00252918	+	0.0110811i
$711$	12.9427	−	8.82416i	0.485388	−	0.330932i
$712$	−0.472160	+	6.30054i	−0.0176949	+	0.236123i
$713$	0.711641	−	0.219512i	0.0266512	−	0.00822080i
$714$	13.0344	+	1.96462i	0.487801	+	0.0735242i
$715$	−0.300122	+	0.376341i	−0.0112239	+	0.0140743i
$716$	1.70452	+	1.16212i	0.0637008	+	0.0434305i
$717$	4.61779	−	4.28469i	0.172455	−	0.160015i
$718$	6.54950	−	16.6878i	0.244425	−	0.622785i
$719$	4.82456	+	1.48818i	0.179926	+	0.0554998i	0.383409	−	0.923579i	$-0.374750\pi$
$719$	4.82456	+	1.48818i	0.179926	+	0.0554998i	−0.203483	+	0.979078i	$0.565226\pi$
$720$	0.138533	+	0.0667141i	0.00516283	+	0.00248629i
$721$	18.3032	+	46.6357i	0.681646	+	1.73681i
$722$	−0.526927	−	7.03135i	−0.0196102	−	0.261680i
$723$	1.18233	+	1.48259i	0.0439713	+	0.0551383i
$724$	1.41815	+	2.45631i	0.0527051	+	0.0912880i
$725$	−3.31379	+	5.73965i	−0.123071	+	0.213165i
$726$	−2.08691	+	0.314551i	−0.0774525	+	0.0116741i
$727$	14.8389	−	7.14602i	0.550343	−	0.265031i	−0.137981	−	0.990435i	$-0.544061\pi$
$727$	14.8389	−	7.14602i	0.550343	−	0.265031i	0.688324	+	0.725404i	$0.258347\pi$
$728$	−17.7305	−	16.4515i	−0.657136	−	0.609733i
$729$	4.75628	+	20.8386i	0.176158	+	0.771800i
$730$	0.423089			0.0156592
$731$	−37.9931	−	7.76660i	−1.40522	−	0.287258i
$732$	4.96856			0.183643
$733$	−2.52808	−	11.0763i	−0.0933769	−	0.409111i	0.906538	−	0.422123i	$-0.138715\pi$
$733$	−2.52808	−	11.0763i	−0.0933769	−	0.409111i	−0.999915	+	0.0130123i	$0.995858\pi$
$734$	−16.5051	−	15.3145i	−0.609215	−	0.565269i
$735$	0.0216898	−	0.0104452i	0.000800039	−	0.000385278i
$736$	2.56696	−	0.386907i	0.0946195	−	0.0142616i
$737$	−2.05696	+	3.56276i	−0.0757691	+	0.131236i
$738$	6.10167	+	10.5684i	0.224605	+	0.389028i
$739$	−18.4052	−	23.0794i	−0.677047	−	0.848990i	0.318032	−	0.948080i	$-0.396978\pi$
$739$	−18.4052	−	23.0794i	−0.677047	−	0.848990i	−0.995078	+	0.0990901i	$0.968407\pi$
$740$	0.0538015	+	0.717932i	0.00197778	+	0.0263917i
$741$	−2.32624	−	5.92717i	−0.0854566	−	0.217740i
$742$	−35.6655	−	17.1756i	−1.30932	−	0.630536i
$743$	−16.0390	−	4.94738i	−0.588414	−	0.181502i	−0.0137702	−	0.999905i	$-0.504383\pi$
$743$	−16.0390	−	4.94738i	−0.588414	−	0.181502i	−0.574644	+	0.818403i	$0.694860\pi$
$744$	0.409305	−	1.04289i	0.0150059	−	0.0382343i
$745$	−0.140027	+	0.129926i	−0.00513019	+	0.00476012i
$746$	20.7729	+	14.1627i	0.760551	+	0.518535i
$747$	−3.66911	+	4.60092i	−0.134246	+	0.168339i
$748$	59.5705	+	8.97880i	2.17811	+	0.328298i
$749$	−49.4973	+	15.2679i	−1.80859	+	0.557877i
$750$	0.0140055	−	0.186890i	0.000511407	−	0.00682425i
$751$	−44.5875	+	30.3993i	−1.62702	+	1.10928i	−0.715015	+	0.699110i	$0.753580\pi$
$751$	−44.5875	+	30.3993i	−1.62702	+	1.10928i	−0.912007	+	0.410175i	$0.865468\pi$
$752$	4.99625	−	21.8900i	0.182195	−	0.798247i
$753$	−0.541008	+	2.37031i	−0.0197154	+	0.0863789i
$754$	11.6580	−	7.94827i	0.424558	−	0.289459i
$755$	0.0197273	−	0.263242i	0.000717950	−	0.00958037i
$756$	15.7394	−	4.85497i	0.572437	−	0.176573i
$757$	−19.4613	−	2.93332i	−0.707332	−	0.106613i	−0.214483	−	0.976728i	$-0.568807\pi$
$757$	−19.4613	−	2.93332i	−0.707332	−	0.106613i	−0.492850	+	0.870115i	$0.664045\pi$
$758$	15.7516	−	19.7518i	0.572123	−	0.717419i
$759$	−0.347847	−	0.237158i	−0.0126261	−	0.00860830i
$760$	0.120881	−	0.112161i	0.00438482	−	0.00406852i
$761$	13.7137	−	34.9420i	0.497122	−	1.26665i	−0.433662	−	0.901076i	$-0.642779\pi$
$761$	13.7137	−	34.9420i	0.497122	−	1.26665i	0.930784	−	0.365571i	$-0.119126\pi$
$762$	5.13329	+	1.58341i	0.185959	+	0.0573609i
$763$	5.80088	+	2.79356i	0.210006	+	0.101134i
$764$	−13.8061	−	35.1775i	−0.499489	−	1.27268i
$765$	0.0336369	+	0.448853i	0.00121614	+	0.0162283i
$766$	−23.8167	−	29.8652i	−0.860533	−	1.07907i
$767$	0.421894	+	0.730742i	0.0152337	+	0.0263856i
$768$	0.148133	−	0.256574i	0.00534529	−	0.00925831i
$769$	30.4201	−	4.58509i	1.09698	−	0.165342i	0.424475	−	0.905439i	$-0.360459\pi$
$769$	30.4201	−	4.58509i	1.09698	−	0.165342i	0.672500	+	0.740097i	$0.265220\pi$
$770$	0.602647	−	0.290220i	0.0217179	−	0.0104588i
$771$	5.41072	+	5.02041i	0.194862	+	0.180806i
$772$	−8.96032	−	39.2577i	−0.322489	−	1.41292i
$773$	−41.3365			−1.48677			−0.743386	−	0.668863i	$-0.766781\pi$
$773$	−41.3365			−1.48677			−0.743386	+	0.668863i	$0.766781\pi$
$774$	−39.9839	+	10.0885i	−1.43719	+	0.362623i
$775$	−10.8273			−0.388929
$776$	−3.16254	−	13.8560i	−0.113528	−	0.497401i
$777$	−7.54328	−	6.99915i	−0.270614	−	0.251093i
$778$	−12.8434	+	6.18506i	−0.460459	+	0.221745i
$779$	−7.61692	+	1.14807i	−0.272905	+	0.0411338i
$780$	−0.0575336	+	0.0996511i	−0.00206003	+	0.00356808i
$781$	−9.89177	−	17.1330i	−0.353955	−	0.613068i
$782$	2.75634	+	3.45634i	0.0985664	+	0.123598i
$783$	0.191276	+	2.55240i	0.00683564	+	0.0912153i
$784$	−2.06088	−	5.25104i	−0.0736029	−	0.187537i
$785$	0.229015	+	0.110288i	0.00817391	+	0.00393635i
$786$	−6.03344	−	1.86107i	−0.215206	−	0.0663822i
$787$	3.59809	−	9.16779i	0.128258	−	0.326796i	−0.852292	−	0.523067i	$-0.824788\pi$
$787$	3.59809	−	9.16779i	0.128258	−	0.326796i	0.980550	+	0.196270i	$0.0628831\pi$
$788$	15.1746	−	14.0799i	0.540571	−	0.501577i
$789$	−1.47042	−	1.00251i	−0.0523482	−	0.0356904i
$790$	0.193141	−	0.242191i	0.00687165	−	0.00861677i
$791$	36.0973	+	5.44080i	1.28347	+	0.193453i
$792$	16.3070	−	5.03004i	0.579444	−	0.178735i
$793$	−2.03503	+	27.1555i	−0.0722659	+	0.964321i
$794$	−53.0220	+	36.1498i	−1.88168	+	1.28291i
$795$	−0.0111631	+	0.0489086i	−0.000395913	+	0.00173461i
$796$	15.2202	−	66.6840i	0.539465	−	2.36355i
$797$	−12.9391	+	8.82176i	−0.458328	+	0.312483i	−0.770383	−	0.637581i	$-0.779935\pi$
$797$	−12.9391	+	8.82176i	−0.458328	+	0.312483i	0.312055	+	0.950064i	$0.398983\pi$
$798$	−0.661207	+	8.82319i	−0.0234065	+	0.312338i
$799$	62.8078	−	19.3736i	2.22198	−	0.685390i
$800$	−37.3202	−	5.62511i	−1.31947	−	0.198878i
$801$	7.21757	−	9.05054i	0.255020	−	0.319785i
$802$	44.7114	+	30.4837i	1.57882	+	1.07642i
$803$	−20.2596	+	18.7982i	−0.714947	+	0.663374i
$804$	−0.359284	+	0.915440i	−0.0126710	+	0.0322851i
$805$	0.0270557	+	0.00834557i	0.000953587	+	0.000294143i
$806$	20.7680	+	10.0013i	0.731520	+	0.352282i
$807$	−0.287980	−	0.733762i	−0.0101374	−	0.0258296i
$808$	1.80495	+	24.0853i	0.0634978	+	0.847319i
$809$	32.3483	+	40.5635i	1.13731	+	1.42614i	0.889268	+	0.457387i	$0.151215\pi$
$809$	32.3483	+	40.5635i	1.13731	+	1.42614i	0.248039	+	0.968750i	$0.420214\pi$
$810$	0.230110	+	0.398563i	0.00808526	+	0.0140041i
$811$	−5.67356	+	9.82690i	−0.199226	+	0.345069i	−0.948278	−	0.317442i	$-0.897176\pi$
$811$	−5.67356	+	9.82690i	−0.199226	+	0.345069i	0.749052	+	0.662511i	$0.230509\pi$
$812$	−11.1833	+	1.68562i	−0.392459	+	0.0591536i
$813$	0.973804	−	0.468959i	0.0341528	−	0.0164471i
$814$	−59.7657	−	55.4545i	−2.09479	−	1.94368i
$815$	−0.0397401	−	0.174113i	−0.00139204	−	0.00609891i
$816$	−3.91429			−0.137028
$817$	3.29283	−	25.8204i	0.115202	−	0.903341i
$818$	−27.8280			−0.972983
$819$	9.86109	+	43.2043i	0.344574	+	1.50968i
$820$	0.102044	+	0.0946830i	0.00356353	+	0.00330647i
$821$	12.6582	−	6.09588i	0.441775	−	0.212748i	−0.199755	−	0.979846i	$-0.564014\pi$
$821$	12.6582	−	6.09588i	0.441775	−	0.212748i	0.641529	+	0.767098i	$0.278300\pi$
$822$	12.3746	−	1.86518i	0.431615	−	0.0650555i
$823$	4.75616	−	8.23791i	0.165789	−	0.287156i	−0.771146	−	0.636658i	$-0.780316\pi$
$823$	4.75616	−	8.23791i	0.165789	−	0.287156i	0.936935	+	0.349503i	$0.113649\pi$
$824$	12.6381	+	21.8898i	0.440269	+	0.762569i
$825$	3.81625	+	4.78542i	0.132865	+	0.166607i
$826$	−0.0876222	−	1.16924i	−0.00304877	−	0.0406830i
$827$	12.3551	+	31.4803i	0.429629	+	1.09468i	0.967773	+	0.251823i	$0.0810302\pi$
$827$	12.3551	+	31.4803i	0.429629	+	1.09468i	−0.538145	+	0.842852i	$0.680875\pi$
$828$	2.44316	+	1.17656i	0.0849058	+	0.0408885i
$829$	29.4594	+	9.08703i	1.02317	+	0.315606i	0.760540	−	0.649291i	$-0.224934\pi$
$829$	29.4594	+	9.08703i	1.02317	+	0.315606i	0.262628	+	0.964897i	$0.415411\pi$
$830$	−0.0425164	+	0.108330i	−0.00147577	+	0.00376019i
$831$	3.31761	−	3.07829i	0.115087	−	0.106785i
$832$	50.0449	+	34.1201i	1.73500	+	1.18290i
$833$	10.2958	−	12.9105i	0.356728	−	0.447323i
$834$	10.8796	+	1.63983i	0.376729	+	0.0567828i
$835$	0.351011	−	0.108272i	0.0121472	−	0.00374692i
$836$	−3.02187	+	40.3241i	−0.104514	+	1.39464i
$837$	−3.45491	+	2.35552i	−0.119419	+	0.0814187i
$838$	−13.5432	+	59.3365i	−0.467841	+	2.04975i
$839$	4.39393	−	19.2511i	0.151695	−	0.664621i	−0.840697	−	0.541506i	$-0.817854\pi$
$839$	4.39393	−	19.2511i	0.151695	−	0.664621i	0.992392	−	0.123115i	$-0.0392885\pi$
$840$	0.0351926	−	0.0239939i	0.00121426	−	0.000827868i
$841$	−2.03584	+	27.1663i	−0.0702013	+	0.936771i
$842$	28.7407	−	8.86535i	0.990472	−	0.305520i
$843$	−5.83442	−	0.879398i	−0.200948	−	0.0302881i
$844$	−27.2870	+	34.2168i	−0.939258	+	1.17779i
$845$	−0.238449	−	0.162572i	−0.00820290	−	0.00559264i
$846$	51.2362	−	47.5402i	1.76154	−	1.63447i
$847$	−3.38732	+	8.63076i	−0.116390	+	0.296557i
$848$	11.2327	+	3.46484i	0.385734	+	0.118983i
$849$	3.92399	+	1.88970i	0.134671	+	0.0648542i
$850$	−23.4815	−	59.8298i	−0.805408	−	2.05215i
$851$	−0.257902	−	3.44146i	−0.00884075	−	0.117972i
$852$	−2.94861	−	3.69743i	−0.101018	−	0.126672i
$853$	−26.3040	−	45.5599i	−0.900632	−	1.55994i	−0.826676	−	0.562678i	$-0.809771\pi$
$853$	−26.3040	−	45.5599i	−0.900632	−	1.55994i	−0.0739557	−	0.997262i	$-0.523562\pi$
$854$	18.9204	−	32.7710i	0.647442	−	1.12140i
$855$	−0.298754	+	0.0450299i	−0.0102172	+	0.00153999i
$856$	−23.5457	+	11.3390i	−0.804776	+	0.387559i
$857$	−29.8684	−	27.7139i	−1.02029	−	0.946687i	−0.0216959	−	0.999765i	$-0.506907\pi$
$857$	−29.8684	−	27.7139i	−1.02029	−	0.946687i	−0.998590	+	0.0530773i	$0.983097\pi$
$858$	−2.89962	−	12.7040i	−0.0989913	−	0.433709i
$859$	36.3447			1.24006			0.620032	−	0.784577i	$-0.287120\pi$
$859$	36.3447			1.24006			0.620032	+	0.784577i	$0.287120\pi$
$860$	−0.401915	+	0.244405i	−0.0137052	+	0.00833414i
$861$	−1.98966			−0.0678075
$862$	15.4957	+	67.8911i	0.527786	+	2.31238i
$863$	21.1458	+	19.6204i	0.719811	+	0.667887i	0.952456	−	0.304675i	$-0.0985478\pi$
$863$	21.1458	+	19.6204i	0.719811	+	0.667887i	−0.232646	+	0.972562i	$0.574738\pi$
$864$	−13.1323	+	6.32419i	−0.446771	+	0.215153i
$865$	0.299503	−	0.0451429i	0.0101834	−	0.00153490i
$866$	−0.412573	+	0.714598i	−0.0140198	+	0.0242830i
$867$	−2.94425	−	5.09959i	−0.0999920	−	0.173191i
$868$	−11.5198	−	14.4454i	−0.391008	−	0.490309i
$869$	1.51219	+	20.1788i	0.0512975	+	0.684518i
$870$	0.00907768	+	0.0231296i	0.000307762	+	0.000784166i
$871$	−4.85616	−	2.33860i	−0.164545	−	0.0792406i
$872$	3.10407	+	0.957480i	0.105117	+	0.0324244i
$873$	−9.51329	+	24.2395i	−0.321976	+	0.820382i
$874$	−2.17525	+	2.01834i	−0.0735789	+	0.0682713i
$875$	−0.680274	−	0.463803i	−0.0229975	−	0.0156794i
$876$	−4.11917	+	5.16528i	−0.139174	+	0.174518i
$877$	4.72066	+	0.711525i	0.159405	+	0.0240265i	0.228260	−	0.973600i	$-0.426696\pi$
$877$	4.72066	+	0.711525i	0.159405	+	0.0240265i	−0.0688546	+	0.997627i	$0.521934\pi$
$878$	10.1331	−	3.12564i	0.341975	−	0.105485i
$879$	−0.0910043	+	1.21437i	−0.00306950	+	0.0409596i
$880$	−0.164113	+	0.111890i	−0.00553224	+	0.00377182i
$881$	6.83266	−	29.9359i	0.230198	−	1.00856i	−0.719277	−	0.694723i	$-0.755527\pi$
$881$	6.83266	−	29.9359i	0.230198	−	1.00856i	0.949475	−	0.313841i	$-0.101616\pi$
$882$	3.90745	−	17.1197i	0.131571	−	0.576449i
$883$	−17.0934	+	11.6541i	−0.575238	+	0.392191i	−0.815706	−	0.578466i	$-0.803651\pi$
$883$	−17.0934	+	11.6541i	−0.575238	+	0.392191i	0.240468	+	0.970657i	$0.422699\pi$
$884$	−5.89837	+	78.7083i	−0.198384	+	2.64725i
$885$	−0.00141990		0.000437980i	−4.77293e−5		1.47225e-5i
$886$	−12.7586	−	1.92305i	−0.428635	−	0.0646063i
$887$	−1.55633	+	1.95158i	−0.0522565	+	0.0655276i	−0.807273	−	0.590178i	$-0.799057\pi$
$887$	−1.55633	+	1.95158i	−0.0522565	+	0.0655276i	0.755016	+	0.655706i	$0.227629\pi$
$888$	−4.28959	−	2.92459i	−0.143949	−	0.0981428i
$889$	17.2999	−	16.0520i	0.580220	−	0.538365i
$890$	0.0836348	−	0.213098i	0.00280344	−	0.00714306i
$891$	−28.7274	−	8.86121i	−0.962403	−	0.296862i
$892$	37.0748	+	17.8543i	1.24136	+	0.597806i
$893$	16.1183	+	41.0688i	0.539379	+	1.37432i
$894$	−0.386433	−	5.15659i	−0.0129243	−	0.172462i
$895$	−0.0124145	−	0.0155673i	−0.000414971	−	0.000520357i
$896$	−18.4592	−	31.9723i	−0.616678	−	1.06812i
$897$	0.275791	−	0.477685i	0.00920841	−	0.0159494i
$898$	−70.3185	+	10.5988i	−2.34656	+	0.353687i
$899$	2.58682	−	1.24575i	0.0862753	−	0.0415480i
$900$	−28.9002	−	26.8155i	−0.963341	−	0.893850i
$901$	7.65717	+	33.5483i	0.255097	+	1.11765i
$902$	−15.7642			−0.524889
$903$	1.83505	−	6.46810i	0.0610666	−	0.215245i
$904$	18.4178			0.612566
$905$	−0.00609153	−	0.0266887i	−0.000202489	−	0.000887164i
$906$	5.23852	+	4.86063i	0.174038	+	0.161484i
$907$	20.8618	−	10.0465i	0.692703	−	0.333588i	−0.0541915	−	0.998531i	$-0.517258\pi$
$907$	20.8618	−	10.0465i	0.692703	−	0.333588i	0.746895	+	0.664942i	$0.231544\pi$
$908$	−54.3539	+	8.19254i	−1.80380	+	0.271879i
$909$	22.1262	−	38.3237i	0.733879	−	1.27112i
$910$	0.438179	+	0.758947i	0.0145255	+	0.0251589i
$911$	10.8608	+	13.6190i	0.359834	+	0.451218i	0.928490	−	0.371358i	$-0.121108\pi$
$911$	10.8608	+	13.6190i	0.359834	+	0.451218i	−0.568655	+	0.822576i	$0.692536\pi$
$912$	−0.196345	−	2.62005i	−0.00650164	−	0.0867584i
$913$	−2.77729	−	7.07643i	−0.0919150	−	0.234196i
$914$	−56.9230	−	27.4127i	−1.88284	−	0.906730i
$915$	−0.0458245	−	0.0141350i	−0.00151491	−	0.000467288i
$916$	13.3278	−	33.9586i	0.440362	−	1.12203i
$917$	−20.3335	+	18.8668i	−0.671472	+	0.623035i
$918$	−20.5089	−	13.9827i	−0.676895	−	0.461499i
$919$	8.79901	−	11.0336i	0.290252	−	0.363965i	−0.615231	−	0.788347i	$-0.710937\pi$
$919$	8.79901	−	11.0336i	0.290252	−	0.363965i	0.905483	+	0.424382i	$0.139509\pi$
$920$	0.0141254	+	0.00212906i	0.000465700	+	7.01930e-5i
$921$	3.05408	−	0.942060i	0.100636	−	0.0310419i
$922$	−2.36233	+	31.5232i	−0.0777993	+	1.03816i
$923$	21.4159	−	14.6011i	0.704914	−	0.480602i
$924$	−2.32420	+	10.1830i	−0.0764605	+	0.334995i
$925$	−11.1649	+	48.9165i	−0.367098	+	1.60836i
$926$	−11.1050	+	7.57129i	−0.364934	+	0.248808i
$927$	3.46079	−	46.1810i	0.113667	−	1.51678i
$928$	9.56358	−	2.94997i	0.313940	−	0.0968376i
$929$	−22.8960	−	3.45101i	−0.751192	−	0.113224i	−0.237724	−	0.971333i	$-0.576401\pi$
$929$	−22.8960	−	3.45101i	−0.751192	−	0.113224i	−0.513468	+	0.858109i	$0.671640\pi$
$930$	−0.0253089	+	0.0317363i	−0.000829911	+	0.00104067i
$931$	9.15814	+	6.24392i	0.300146	+	0.204636i
$932$	−18.5074	+	17.1724i	−0.606231	+	0.562500i
$933$	−0.471650	+	1.20174i	−0.0154411	+	0.0393434i
$934$	−32.8381	−	10.1292i	−1.07449	−	0.331438i
$935$	−0.523868	−	0.252282i	−0.0171323	−	0.00825050i
$936$	8.16839	+	20.8127i	0.266992	+	0.680285i
$937$	2.99630	+	39.9829i	0.0978850	+	1.30618i	0.802525	+	0.596619i	$0.203490\pi$
$937$	2.99630	+	39.9829i	0.0978850	+	1.30618i	−0.704640	+	0.709565i	$0.748891\pi$
$938$	4.66980	+	5.85574i	0.152474	+	0.191197i
$939$	3.75016	+	6.49548i	0.122382	+	0.211972i
$940$	0.398645	−	0.690473i	0.0130024	−	0.0225208i
$941$	33.4023	−	5.03458i	1.08888	−	0.164123i	0.420025	−	0.907513i	$-0.362021\pi$
$941$	33.4023	−	5.03458i	1.08888	−	0.164123i	0.668858	+	0.743390i	$0.266783\pi$
$942$	−6.19963	+	2.98559i	−0.201995	+	0.0972757i
$943$	−0.489155	−	0.453870i	−0.0159291	−	0.0147800i
$944$	0.0774770	+	0.339449i	0.00252166	+	0.0110481i
$945$	−0.158975			−0.00517145
$946$	14.5392	−	51.2470i	0.472709	−	1.66618i
$947$	−6.10756			−0.198469			−0.0992345	−	0.995064i	$-0.531639\pi$
$947$	−6.10756			−0.198469			−0.0992345	+	0.995064i	$0.531639\pi$
$948$	1.07638	+	4.71592i	0.0349591	+	0.153166i
$949$	−26.5436	−	24.6288i	−0.861641	−	0.799486i
$950$	38.8694	−	18.7185i	1.26109	−	0.607310i
$951$	−3.33754	+	0.503053i	−0.108227	+	0.0163126i
$952$	14.6083	−	25.3024i	0.473459	−	0.820055i
$953$	−22.1509	−	38.3665i	−0.717538	−	1.24281i	−0.961973	−	0.273146i	$-0.911936\pi$
$953$	−22.1509	−	38.3665i	−0.717538	−	1.24281i	0.244435	−	0.969666i	$-0.421397\pi$
$954$	22.8149	+	28.6090i	0.738661	+	0.926252i
$955$	0.0272567	+	0.363715i	0.000882006	+	0.0117695i
$956$	−19.1492	−	48.7913i	−0.619329	−	1.57802i
$957$	−1.46235	−	0.704231i	−0.0472711	−	0.0227646i
$958$	80.0303	+	24.6861i	2.58566	+	0.797571i
$959$	20.0856	−	51.1773i	0.648599	−	1.65260i
$960$	−0.0781895	+	0.0725493i	−0.00252356	+	0.00234152i
$961$	−21.7379	−	14.8206i	−0.701222	−	0.478085i
$962$	66.6000	−	83.5138i	2.14727	−	2.69259i
$963$	47.3469	+	7.13640i	1.52573	+	0.229967i
$964$	15.0773	−	4.65075i	0.485609	−	0.149790i
$965$	−0.0290437	+	0.387561i	−0.000934949	+	0.0124760i
$966$	−0.633289	+	0.431769i	−0.0203757	+	0.0138919i
$967$	−11.5379	+	50.5507i	−0.371033	+	1.62560i	0.352851	+	0.935680i	$0.385212\pi$
$967$	−11.5379	+	50.5507i	−0.371033	+	1.62560i	−0.723884	+	0.689922i	$0.757645\pi$
$968$	−1.04091	+	4.56053i	−0.0334561	+	0.146581i
$969$	6.35487	−	4.33268i	0.204148	−	0.139186i
$970$	−0.0384818	+	0.513503i	−0.00123557	+	0.0164876i
$971$	39.1975	−	12.0908i	1.25791	−	0.388013i	0.407048	−	0.913407i	$-0.366558\pi$
$971$	39.1975	−	12.0908i	1.25791	−	0.388013i	0.850859	+	0.525394i	$0.176082\pi$
$972$	−22.7206	−	3.42458i	−0.728763	−	0.109843i
$973$	30.1368	−	37.7903i	0.966140	−	1.21150i
$974$	−22.3478	−	15.2365i	−0.716069	−	0.488207i
$975$	−5.87854	+	5.45449i	−0.188264	+	0.174683i
$976$	−4.10527	+	10.4601i	−0.131406	+	0.334818i
$977$	−38.3948	−	11.8432i	−1.22836	−	0.378899i	−0.388371	−	0.921503i	$-0.626962\pi$
$977$	−38.3948	−	11.8432i	−1.22836	−	0.378899i	−0.839988	+	0.542605i	$0.817438\pi$
$978$	4.35582	+	2.09765i	0.139284	+	0.0670755i
$979$	5.46326	+	13.9202i	0.174607	+	0.444891i
$980$	−0.0149690	−	0.199747i	−0.000478167	−	0.00638069i
$981$	−3.71078	−	4.65317i	−0.118476	−	0.148564i
$982$	41.8891	+	72.5541i	1.33674	+	2.31529i
$983$	−21.7405	+	37.6556i	−0.693414	+	1.20103i	0.277298	+	0.960784i	$0.410561\pi$
$983$	−21.7405	+	37.6556i	−0.693414	+	1.20103i	−0.970712	+	0.240245i	$0.922772\pi$
$984$	−0.992625	+	0.149614i	−0.0316437	+	0.00476953i
$985$	−0.180009	+	0.0866878i	−0.00573557	+	0.00276210i
$986$	12.4939	+	11.5926i	0.397886	+	0.369184i
$987$	2.53579	+	11.1100i	0.0807152	+	0.353636i
$988$	−52.9796			−1.68550
$989$	1.92661	−	1.17157i	0.0612626	−	0.0372538i
$990$	−0.618308			−0.0196511
$991$	−5.52848	−	24.2218i	−0.175618	−	0.769432i	−0.983620	−	0.180253i	$-0.942308\pi$
$991$	−5.52848	−	24.2218i	−0.175618	−	0.769432i	0.808002	−	0.589179i	$-0.200549\pi$
$992$	11.9856	+	11.1210i	0.380542	+	0.353091i
$993$	3.51676	−	1.69358i	0.111601	−	0.0537442i
$994$	−35.6155	+	5.36817i	−1.12965	+	0.170268i
$995$	−0.330083	+	0.571720i	−0.0104643	+	0.0181247i
$996$	−0.908609	−	1.57376i	−0.0287904	−	0.0498664i
$997$	17.7893	+	22.3071i	0.563394	+	0.706474i	0.979181	−	0.202988i	$-0.0650652\pi$
$997$	17.7893	+	22.3071i	0.563394	+	0.706474i	−0.415787	+	0.909462i	$0.636494\pi$
$998$	−6.80156	−	90.7606i	−0.215300	−	2.87298i
$999$	7.07931	+	18.0378i	0.223980	+	0.570690i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.2.g.a.10.1	✓	36
3.2	odd	2		387.2.y.c.10.3		36
4.3	odd	2		688.2.bg.c.225.2		36
43.13	even	21	inner	43.2.g.a.13.1	yes	36
43.20	odd	42		1849.2.a.o.1.3		18
43.23	even	21		1849.2.a.n.1.16		18
129.56	odd	42		387.2.y.c.271.3		36
172.99	odd	42		688.2.bg.c.529.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.10.1	✓	36	1.1	even	1	trivial
43.2.g.a.13.1	yes	36	43.13	even	21	inner
387.2.y.c.10.3		36	3.2	odd	2
387.2.y.c.271.3		36	129.56	odd	42
688.2.bg.c.225.2		36	4.3	odd	2
688.2.bg.c.529.2		36	172.99	odd	42
1849.2.a.n.1.16		18	43.23	even	21
1849.2.a.o.1.3		18	43.20	odd	42

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.483758 - 2.11948i) q^{2} +(-0.240184 - 0.222858i) q^{3} +(-2.45624 + 1.18286i) q^{4} +(0.0260188 - 0.00392170i) q^{5} +(-0.356153 + 0.616875i) q^{6} +(1.56464 + 2.71003i) q^{7} +(0.984367 + 1.23436i) q^{8} +(-0.216168 - 2.88456i) q^{9} +O(q^{10})\)	\(q+(-0.483758 - 2.11948i) q^{2} +(-0.240184 - 0.222858i) q^{3} +(-2.45624 + 1.18286i) q^{4} +(0.0260188 - 0.00392170i) q^{5} +(-0.356153 + 0.616875i) q^{6} +(1.56464 + 2.71003i) q^{7} +(0.984367 + 1.23436i) q^{8} +(-0.216168 - 2.88456i) q^{9} +(-0.0208988 - 0.0532492i) q^{10} +(3.36665 + 1.62129i) q^{11} +(0.853562 + 0.263289i) q^{12} +(-1.78860 + 4.55728i) q^{13} +(4.98695 - 4.62722i) q^{14} +(-0.00712328 - 0.00485657i) q^{15} +(-1.25954 + 1.57942i) q^{16} +(-5.84766 - 0.881392i) q^{17} +(-6.00919 + 1.85359i) q^{18} +(0.296638 - 3.95836i) q^{19} +(-0.0592696 + 0.0404093i) q^{20} +(0.228152 - 0.999599i) q^{21} +(1.80766 - 7.91985i) q^{22} +(0.284113 - 0.193705i) q^{23} +(0.0386574 - 0.515847i) q^{24} +(-4.77720 + 1.47357i) q^{25} +(10.5243 + 1.58629i) q^{26} +(-1.20379 + 1.50950i) q^{27} +(-7.04873 - 4.80574i) q^{28} +(0.971806 - 0.901704i) q^{29} +(-0.00684747 + 0.0174471i) q^{30} +(2.06955 + 0.638371i) q^{31} +(6.80176 + 3.27556i) q^{32} +(-0.447297 - 1.13969i) q^{33} +(0.960755 + 12.8204i) q^{34} +(0.0513379 + 0.0643757i) q^{35} +(3.94300 + 6.82948i) q^{36} +(5.01814 - 8.69167i) q^{37} +(-8.53318 + 1.28617i) q^{38} +(1.44522 - 0.695983i) q^{39} +(0.0304528 + 0.0282561i) q^{40} +(-0.431814 - 1.89190i) q^{41} -2.22900 q^{42} +(6.54856 + 0.341120i) q^{43} -10.1871 q^{44} +(-0.0169368 - 0.0742049i) q^{45} +(-0.547996 - 0.508466i) q^{46} +(-10.0138 + 4.82240i) q^{47} +(0.654509 - 0.0986513i) q^{48} +(-1.39618 + 2.41825i) q^{49} +(5.43422 + 9.41234i) q^{50} +(1.20809 + 1.51490i) q^{51} +(-0.997407 - 13.3095i) q^{52} +(-2.12587 - 5.41662i) q^{53} +(3.78170 + 1.82117i) q^{54} +(0.0939542 + 0.0289810i) q^{55} +(-1.80497 + 4.59898i) q^{56} +(-0.953402 + 0.884627i) q^{57} +(-2.38126 - 1.62352i) q^{58} +(0.107460 - 0.134751i) q^{59} +(0.0232412 + 0.00350304i) q^{60} +(5.31524 - 1.63953i) q^{61} +(0.351855 - 4.69519i) q^{62} +(7.47901 - 5.09911i) q^{63} +(2.75302 - 12.0618i) q^{64} +(-0.0286650 + 0.125589i) q^{65} +(-2.19918 + 1.49937i) q^{66} +(-0.0822742 + 1.09787i) q^{67} +(15.4058 - 4.75207i) q^{68} +(-0.111408 - 0.0167921i) q^{69} +(0.111608 - 0.139952i) q^{70} +(-4.37443 - 2.98244i) q^{71} +(3.34778 - 3.10629i) q^{72} +(-2.70214 + 6.88494i) q^{73} +(-20.8494 - 6.43119i) q^{74} +(1.47581 + 0.710711i) q^{75} +(3.95359 + 10.0736i) q^{76} +(0.873829 + 11.6604i) q^{77} +(-2.17426 - 2.72644i) q^{78} +(2.70765 + 4.68979i) q^{79} +(-0.0265778 + 0.0460341i) q^{80} +(-7.95548 + 1.19910i) q^{81} +(-3.80096 + 1.83044i) q^{82} +(-1.49132 - 1.38374i) q^{83} +(0.621993 + 2.72513i) q^{84} -0.155605 q^{85} +(-2.44492 - 14.0446i) q^{86} -0.434365 q^{87} +(1.31276 + 5.75159i) q^{88} +(2.93360 + 2.72198i) q^{89} +(-0.149083 + 0.0717944i) q^{90} +(-15.1489 + 2.28333i) q^{91} +(-0.468724 + 0.811854i) q^{92} +(-0.354806 - 0.614542i) q^{93} +(15.0652 + 18.8912i) q^{94} +(-0.00780535 - 0.104155i) q^{95} +(-0.903691 - 2.30257i) q^{96} +(-8.11049 - 3.90581i) q^{97} +(5.80084 + 1.78932i) q^{98} +(3.94895 - 10.0618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9}+O(q^{10}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9} - 7 q^{10} - 4 q^{11} + 2 q^{12} + 18 q^{14} - 3 q^{15} - 10 q^{16} - 10 q^{17} + 11 q^{18} + 10 q^{19} - 3 q^{20} - 21 q^{21} - 3 q^{22} + 4 q^{23} + 31 q^{24} - 2 q^{25} - 15 q^{26} - 4 q^{27} + 20 q^{28} + 9 q^{29} + 88 q^{30} + 40 q^{31} + 48 q^{32} - 11 q^{33} - 42 q^{34} + 11 q^{35} - 47 q^{36} - 19 q^{37} - 21 q^{38} - q^{39} - 97 q^{40} - 28 q^{41} + 2 q^{42} - 8 q^{43} + 14 q^{44} - 46 q^{45} - 61 q^{46} - 30 q^{47} - 97 q^{48} + 6 q^{49} - 3 q^{50} + 57 q^{51} - 8 q^{52} - 24 q^{53} + 6 q^{54} + 14 q^{55} + 39 q^{56} + 52 q^{57} + 64 q^{58} - q^{59} + 111 q^{60} - 14 q^{61} + 33 q^{62} + 47 q^{63} + 48 q^{64} + 38 q^{65} + 79 q^{66} + 66 q^{67} + 66 q^{68} - 7 q^{69} + 47 q^{70} - 33 q^{71} + 26 q^{72} + 29 q^{73} - 40 q^{74} - 55 q^{75} - 39 q^{76} - 27 q^{77} - 126 q^{78} - 17 q^{79} + 8 q^{80} + 38 q^{81} - 54 q^{82} - 23 q^{83} - 155 q^{84} - 56 q^{85} - 45 q^{86} - 86 q^{87} - 17 q^{88} - 19 q^{89} - 127 q^{90} - 13 q^{91} - 18 q^{92} - 30 q^{93} + 44 q^{94} + q^{95} - 36 q^{96} - 31 q^{97} - 5 q^{98} - 31 q^{99}+O(q^{100}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9 - 7 * q^10 - 4 * q^11 + 2 * q^12 + 18 * q^14 - 3 * q^15 - 10 * q^16 - 10 * q^17 + 11 * q^18 + 10 * q^19 - 3 * q^20 - 21 * q^21 - 3 * q^22 + 4 * q^23 + 31 * q^24 - 2 * q^25 - 15 * q^26 - 4 * q^27 + 20 * q^28 + 9 * q^29 + 88 * q^30 + 40 * q^31 + 48 * q^32 - 11 * q^33 - 42 * q^34 + 11 * q^35 - 47 * q^36 - 19 * q^37 - 21 * q^38 - q^39 - 97 * q^40 - 28 * q^41 + 2 * q^42 - 8 * q^43 + 14 * q^44 - 46 * q^45 - 61 * q^46 - 30 * q^47 - 97 * q^48 + 6 * q^49 - 3 * q^50 + 57 * q^51 - 8 * q^52 - 24 * q^53 + 6 * q^54 + 14 * q^55 + 39 * q^56 + 52 * q^57 + 64 * q^58 - q^59 + 111 * q^60 - 14 * q^61 + 33 * q^62 + 47 * q^63 + 48 * q^64 + 38 * q^65 + 79 * q^66 + 66 * q^67 + 66 * q^68 - 7 * q^69 + 47 * q^70 - 33 * q^71 + 26 * q^72 + 29 * q^73 - 40 * q^74 - 55 * q^75 - 39 * q^76 - 27 * q^77 - 126 * q^78 - 17 * q^79 + 8 * q^80 + 38 * q^81 - 54 * q^82 - 23 * q^83 - 155 * q^84 - 56 * q^85 - 45 * q^86 - 86 * q^87 - 17 * q^88 - 19 * q^89 - 127 * q^90 - 13 * q^91 - 18 * q^92 - 30 * q^93 + 44 * q^94 + q^95 - 36 * q^96 - 31 * q^97 - 5 * q^98 - 31 * q^99

Introduction

L-functions

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