LMFDB - Embedded newform 43.2.g.a.13.1

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			13.1
Character	$\chi$	$=$	43.13
Dual form			43.2.g.a.10.1

$q$-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 $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{16}{21}\right)$

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	0.452632	+	0.891698i	$0.350485\pi$
$2$	−0.483758	+	2.11948i	−0.342068	+	1.49870i	−0.794700	+	0.607002i	$0.792372\pi$
$3$	−0.240184	+	0.222858i	−0.138670	+	0.128667i	−0.746459	−	0.665432i	$-0.768247\pi$
$3$	−0.240184	+	0.222858i	−0.138670	+	0.128667i	0.607788	+	0.794099i	$0.292057\pi$
$4$	−2.45624	−	1.18286i	−1.22812	−	0.591432i
$5$	0.0260188	+	0.00392170i	0.0116360	+	0.00175384i	0.154858	−	0.987937i	$-0.450508\pi$
$5$	0.0260188	+	0.00392170i	0.0116360	+	0.00175384i	−0.143222	+	0.989691i	$0.545746\pi$
$6$	−0.356153	−	0.616875i	−0.145399	−	0.251838i
$7$	1.56464	−	2.71003i	0.591377	−	1.02430i	−0.402670	−	0.915345i	$-0.631918\pi$
$7$	1.56464	−	2.71003i	0.591377	−	1.02430i	0.994047	−	0.108950i	$-0.0347489\pi$
$8$	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	0.149052	−	0.988829i	$-0.452378\pi$
$11$	3.36665	−	1.62129i	1.01508	−	0.488838i	0.866030	+	0.499992i	$0.166664\pi$
$12$	0.853562	−	0.263289i	0.246402	−	0.0760050i
$13$	−1.78860	−	4.55728i	−0.496069	−	1.26396i	−0.931500	−	0.363741i	$-0.881499\pi$
$13$	−1.78860	−	4.55728i	−0.496069	−	1.26396i	0.435431	−	0.900222i	$-0.356596\pi$
$14$	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	−0.813004	−	0.582258i	$-0.802169\pi$
$17$	−5.84766	+	0.881392i	−1.41827	+	0.213769i	−0.605261	+	0.796027i	$0.706931\pi$
$18$	−6.00919	−	1.85359i	−1.41638	−	0.436896i
$19$	0.296638	+	3.95836i	0.0680535	+	0.908110i	0.921861	+	0.387521i	$0.126669\pi$
$19$	0.296638	+	3.95836i	0.0680535	+	0.908110i	−0.853807	+	0.520589i	$0.825712\pi$
$20$	−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	0.592579	−	0.805512i	$-0.298110\pi$
$23$	0.284113	+	0.193705i	0.0592417	+	0.0403903i	−0.533337	+	0.845903i	$0.679062\pi$
$24$	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	0.765230	−	0.643756i	$-0.222625\pi$
$29$	0.971806	+	0.901704i	0.180460	+	0.167442i	−0.584771	+	0.811199i	$0.698815\pi$
$30$	−0.00684747	−	0.0174471i	−0.00125017	−	0.00318538i
$31$	2.06955	−	0.638371i	0.371702	−	0.114655i	−0.103276	−	0.994653i	$-0.532932\pi$
$31$	2.06955	−	0.638371i	0.371702	−	0.114655i	0.474977	+	0.879998i	$0.342456\pi$
$32$	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	0.901937	+	0.431868i	$0.142145\pi$
$37$	5.01814	+	8.69167i	0.824977	+	1.42890i	−0.0769599	+	0.997034i	$0.524521\pi$
$38$	−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	−0.997389	−	0.0722186i	$-0.976992\pi$
$41$	−0.431814	+	1.89190i	−0.0674381	+	0.295465i	0.929951	+	0.367684i	$0.119849\pi$
$42$	−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	−0.476255	−	0.879307i	$-0.658006\pi$
$47$	−10.0138	−	4.82240i	−1.46066	−	0.703419i	−0.984410	+	0.175888i	$0.943720\pi$
$48$	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	0.707301	+	0.706913i	$0.249913\pi$
$53$	−2.12587	+	5.41662i	−0.292010	+	0.744030i	−0.999311	+	0.0371173i	$0.988182\pi$
$54$	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	0.788777	−	0.614679i	$-0.210714\pi$
$59$	0.107460	+	0.134751i	0.0139901	+	0.0175431i	−0.774787	+	0.632222i	$0.782143\pi$
$60$	0.0232412	−	0.00350304i	0.00300042	−	0.000452241i
$61$	5.31524	+	1.63953i	0.680547	+	0.209921i	0.615707	−	0.787975i	$-0.288870\pi$
$61$	5.31524	+	1.63953i	0.680547	+	0.209921i	0.0648393	+	0.997896i	$0.479347\pi$
$62$	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	0.989921	−	0.141624i	$-0.0452324\pi$
$67$	−0.0822742	−	1.09787i	−0.0100514	−	0.134126i	−0.999972	+	0.00749766i	$0.997613\pi$
$68$	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	−0.794373	−	0.607430i	$-0.792201\pi$
$71$	−4.37443	+	2.98244i	−0.519150	+	0.353950i	0.275223	+	0.961380i	$0.411248\pi$
$72$	3.34778	+	3.10629i	0.394540	+	0.366080i
$73$	−2.70214	−	6.88494i	−0.316261	−	0.805821i	−0.997290	−	0.0735646i	$-0.976562\pi$
$73$	−2.70214	−	6.88494i	−0.316261	−	0.805821i	0.681029	−	0.732256i	$-0.261533\pi$
$74$	−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	−0.672545	−	0.740056i	$-0.734799\pi$
$79$	2.70765	−	4.68979i	0.304635	−	0.527643i	0.977180	+	0.212413i	$0.0681323\pi$
$80$	−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	−0.757767	−	0.652526i	$-0.773709\pi$
$83$	−1.49132	+	1.38374i	−0.163694	+	0.151885i	0.594073	+	0.804411i	$0.297519\pi$
$84$	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	−0.509217	−	0.860638i	$-0.670065\pi$
$89$	2.93360	−	2.72198i	0.310961	−	0.288530i	0.820178	+	0.572109i	$0.193874\pi$
$90$	−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	−0.797672	−	0.603092i	$-0.793935\pi$
$97$	−8.11049	+	3.90581i	−0.823495	+	0.396574i	−0.0258237	+	0.999667i	$0.508221\pi$
$98$	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	0.263484	−	0.964664i	$-0.415128\pi$
$101$	12.6400	−	8.61780i	1.25773	−	0.857503i	0.994242	+	0.107161i	$0.0341759\pi$
$102$	2.62637	+	3.29336i	0.260049	+	0.326092i
$103$	15.8309	−	2.38613i	1.55987	−	0.235112i	0.688315	−	0.725412i	$-0.258351\pi$
$103$	15.8309	−	2.38613i	1.55987	−	0.235112i	0.871554	+	0.490300i	$0.163113\pi$
$104$	−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	−0.762850	−	0.646576i	$-0.776200\pi$
$107$	−3.68337	−	16.1379i	−0.356085	−	1.56011i	0.406765	−	0.913533i	$-0.366657\pi$
$108$	1.17126	+	5.13161i	0.112704	+	0.493790i
$109$	1.69999	+	1.15903i	0.162829	+	0.111015i	0.641993	−	0.766710i	$-0.278108\pi$
$109$	1.69999	+	1.15903i	0.162829	+	0.111015i	−0.479164	+	0.877725i	$0.659060\pi$
$110$	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	0.995736	−	0.0922502i	$-0.0294060\pi$
$113$	7.27343	+	9.12059i	0.684226	+	0.857993i	−0.311509	+	0.950243i	$0.600835\pi$
$114$	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	0.844275	+	0.535911i	$0.180032\pi$
$127$	−1.67817	+	7.35255i	−0.148914	+	0.652433i	−0.993188	+	0.116522i	$0.962825\pi$
$128$	−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	−0.812700	−	0.582682i	$-0.802003\pi$
$131$	1.97245	−	8.64186i	0.172334	−	0.755043i	0.985034	−	0.172361i	$-0.0551395\pi$
$132$	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	0.0487538	+	0.998811i	$0.484475\pi$
$137$	−10.9540	+	13.7359i	−0.935863	+	1.17354i	−0.984617	+	0.174725i	$0.944096\pi$
$138$	0.0183041	−	0.244251i	0.00155815	−	0.0207920i
$139$	−5.64316	+	14.3785i	−0.478646	+	1.21957i	0.464017	+	0.885826i	$0.346408\pi$
$139$	−5.64316	+	14.3785i	−0.478646	+	1.21957i	−0.942663	+	0.333745i	$0.891688\pi$
$140$	−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	0.292144	−	0.956374i	$-0.405631\pi$
$149$	−5.99816	−	4.08947i	−0.491388	−	0.335023i	−0.783532	+	0.621352i	$0.786584\pi$
$150$	0.792405	+	3.47176i	0.0646996	+	0.283468i
$151$	2.23243	+	9.78091i	0.181673	+	0.795960i	0.980834	+	0.194844i	$0.0624199\pi$
$151$	2.23243	+	9.78091i	0.181673	+	0.795960i	−0.799162	+	0.601116i	$0.794723\pi$
$152$	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	−0.201279	−	0.979534i	$-0.564510\pi$
$157$	7.98170	−	5.44183i	0.637009	−	0.434305i	0.838287	+	0.545229i	$0.183557\pi$
$158$	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	0.941466	+	0.337107i	$0.109449\pi$
$163$	−0.507211	+	6.76827i	−0.0397279	+	0.530131i	−0.981194	+	0.193024i	$0.938170\pi$
$164$	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	0.659534	−	0.751675i	$-0.270754\pi$
$167$	13.8043	+	2.08066i	1.06821	+	0.161006i	0.408672	+	0.912681i	$0.365992\pi$
$168$	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	−0.879819	−	0.475309i	$-0.842336\pi$
$179$	−0.378359	+	0.655338i	−0.0282799	+	0.0489823i	0.851539	+	0.524291i	$0.175670\pi$
$180$	0.129375	−	0.162231i	0.00964306	−	0.0120920i
$181$	−0.0777475	+	1.03747i	−0.00577892	+	0.0771144i	−0.999348	−	0.0361170i	$-0.988501\pi$
$181$	−0.0777475	+	1.03747i	−0.00577892	+	0.0771144i	0.993569	+	0.113231i	$0.0361201\pi$
$182$	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	−0.900219	−	0.435438i	$-0.856593\pi$
$191$	−1.03588	−	13.8228i	−0.0749534	−	1.00018i	0.825265	−	0.564745i	$-0.191026\pi$
$192$	−3.34930	−	2.28352i	−0.241715	−	0.164799i
$193$	−3.28671	−	14.4000i	−0.236583	−	1.03654i	−0.944053	−	0.329794i	$-0.893021\pi$
$193$	−3.28671	−	14.4000i	−0.236583	−	1.03654i	0.707470	−	0.706743i	$-0.249836\pi$
$194$	−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	0.0252911	−	0.999680i	$-0.491949\pi$
$197$	−7.25577	−	2.23811i	−0.516952	−	0.159459i	−0.542243	+	0.840221i	$0.682425\pi$
$198$	−23.2360	+	3.50227i	−1.65131	+	0.248895i
$199$	−15.6429	−	19.6156i	−1.10890	−	1.39051i	−0.912051	−	0.410076i	$-0.865502\pi$
$199$	−15.6429	−	19.6156i	−1.10890	−	1.39051i	−0.196844	−	0.980435i	$-0.563069\pi$
$200$	−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	0.859481	−	0.511167i	$-0.170787\pi$
$211$	14.4636	+	6.96528i	0.995712	+	0.479510i	0.136231	+	0.990677i	$0.456501\pi$
$212$	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	−0.989741	−	0.142876i	$-0.954365\pi$
$223$	−9.41103	+	11.8011i	−0.630209	+	0.790257i	0.359532	+	0.933133i	$0.382937\pi$
$224$	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	0.420346	−	0.907364i	$-0.361909\pi$
$227$	19.2669	−	5.94305i	1.27879	−	0.394454i	0.858442	+	0.512910i	$0.171433\pi$
$228$	1.29539	+	3.30060i	0.0857894	+	0.218588i
$229$	−9.80918	−	9.10159i	−0.648209	−	0.601450i	0.285977	−	0.958236i	$-0.407682\pi$
$229$	−9.80918	−	9.10159i	−0.648209	−	0.601450i	−0.934186	+	0.356786i	$0.883872\pi$
$230$	−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	0.570738	−	0.821132i	$-0.306657\pi$
$233$	8.84939	+	2.72968i	0.579743	+	0.178827i	0.00900522	+	0.999959i	$0.497134\pi$
$234$	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	−0.827442	−	0.561550i	$-0.810205\pi$
$239$	−1.43677	−	19.1723i	−0.0929366	−	1.24015i	0.734506	−	0.678602i	$-0.237414\pi$
$240$	0.0166426	+	0.00513358i	0.00107428	+	0.000331371i
$241$	−5.72297	+	0.862599i	−0.368649	+	0.0555649i	−0.330755	−	0.943717i	$-0.607303\pi$
$241$	−5.72297	+	0.862599i	−0.368649	+	0.0555649i	−0.0378946	+	0.999282i	$0.512065\pi$
$242$	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	−0.959035	−	0.283287i	$-0.908575\pi$
$251$	−3.71016	+	6.42619i	−0.234184	+	0.405618i	0.724852	+	0.688905i	$0.241908\pi$
$252$	−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	0.312530	−	0.949908i	$-0.398824\pi$
$263$	5.37090	+	0.809533i	0.331184	+	0.0499180i	0.0186545	+	0.999826i	$0.494062\pi$
$264$	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	−0.366637	−	0.930364i	$-0.619491\pi$
$269$	2.16753	−	1.04383i	0.132156	−	0.0636432i	0.498793	+	0.866721i	$0.333777\pi$
$270$	0.105537	−	0.0325539i	0.00642279	−	0.00198117i
$271$	−1.20518	−	3.07074i	−0.0732093	−	0.186534i	0.889585	−	0.456770i	$-0.150994\pi$
$271$	−1.20518	−	3.07074i	−0.0732093	−	0.186534i	−0.962794	+	0.270236i	$0.912898\pi$
$272$	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	−0.938304	−	0.345812i	$-0.887603\pi$
$277$	−1.03223	−	13.7742i	−0.0620207	−	0.827609i	0.876283	−	0.481797i	$-0.160016\pi$
$278$	−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	0.918960	−	0.394351i	$-0.129031\pi$
$281$	14.8789	+	10.1443i	0.887603	+	0.605157i	−0.0313571	+	0.999508i	$0.509983\pi$
$282$	0.591632	+	7.89479i	0.0352312	+	0.470128i
$283$	−12.7020	−	3.91805i	−0.755057	−	0.232904i	−0.106752	−	0.994286i	$-0.534045\pi$
$283$	−12.7020	−	3.91805i	−0.755057	−	0.232904i	−0.648304	+	0.761382i	$0.724521\pi$
$284$	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	−0.844900	−	0.534924i	$-0.820340\pi$
$293$	−2.31732	+	2.90583i	−0.135379	+	0.169760i	0.709521	+	0.704685i	$0.248912\pi$
$294$	−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	0.692617	−	0.721306i	$-0.256458\pi$
$307$	−4.87728	−	8.44770i	−0.278361	−	0.482136i	−0.970978	+	0.239170i	$0.923125\pi$
$308$	−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	−0.965860	−	0.259064i	$-0.916586\pi$
$311$	−1.43950	+	3.66777i	−0.0816263	+	0.207980i	0.884234	+	0.467044i	$0.154681\pi$
$312$	2.28172	−	1.09882i	0.129177	−	0.0622083i
$313$	−21.8743	+	6.74733i	−1.23641	+	0.381382i	−0.842966	−	0.537967i	$-0.819193\pi$
$313$	−21.8743	+	6.74733i	−1.23641	+	0.381382i	−0.393444	+	0.919349i	$0.628716\pi$
$314$	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	0.928771	−	0.370653i	$-0.120866\pi$
$317$	6.42280	+	8.05394i	0.360740	+	0.452354i	−0.568031	+	0.823007i	$0.692295\pi$
$318$	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	0.759956	−	0.649974i	$-0.225220\pi$
$331$	−4.35233	−	11.0896i	−0.239226	−	0.609537i	−0.999182	+	0.0404371i	$0.987125\pi$
$332$	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	−0.817896	−	0.575366i	$-0.804860\pi$
$337$	1.63994	−	2.84045i	0.0893330	−	0.154729i	0.907229	+	0.420636i	$0.138193\pi$
$338$	−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	−0.394095	−	0.919070i	$-0.628942\pi$
$347$	9.18271	−	8.52031i	0.492954	−	0.457394i	0.887049	+	0.461675i	$0.152752\pi$
$348$	1.06690	+	0.513794i	0.0571921	+	0.0275423i
$349$	−31.6460	−	4.76987i	−1.69397	−	0.255325i	−0.770071	−	0.637958i	$-0.779779\pi$
$349$	−31.6460	−	4.76987i	−1.69397	−	0.255325i	−0.923900	+	0.382633i	$0.875017\pi$
$350$	−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	−0.999941	−	0.0108603i	$-0.996543\pi$
$353$	−0.179426	+	2.39427i	−0.00954988	+	0.127434i	0.990391	+	0.138295i	$0.0441620\pi$
$354$	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	−0.370024	−	0.929022i	$-0.620651\pi$
$359$	6.81331	−	4.64523i	0.359593	−	0.245166i	0.729617	+	0.683856i	$0.239698\pi$
$360$	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	0.765691	−	0.643209i	$-0.222397\pi$
$367$	8.55721	+	5.83421i	0.446683	+	0.304543i	−0.319008	+	0.947752i	$0.603350\pi$
$368$	−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	0.429497	−	0.903068i	$-0.358691\pi$
$373$	−8.47754	−	7.86601i	−0.438950	−	0.407286i	−0.868447	+	0.495782i	$0.834882\pi$
$374$	−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	−0.560110	−	0.828419i	$-0.689241\pi$
$379$	7.24547	−	9.08554i	0.372175	−	0.466693i	0.932284	+	0.361726i	$0.117812\pi$
$380$	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	0.792167	−	0.610304i	$-0.208953\pi$
$383$	15.8309	+	7.62376i	0.808921	+	0.389556i	0.0167535	+	0.999860i	$0.494667\pi$
$384$	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	−0.998353	−	0.0573631i	$-0.981731\pi$
$389$	−1.45910	+	6.39272i	−0.0739792	+	0.324124i	0.924374	+	0.381487i	$0.124588\pi$
$390$	−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	0.354725	+	0.934971i	$0.384575\pi$
$397$	−10.7843	+	27.4779i	−0.541248	+	1.37908i	−0.895973	+	0.444108i	$0.853521\pi$
$398$	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	0.0772425	−	0.997012i	$-0.475388\pi$
$401$	−18.2470	−	16.9307i	−0.911210	−	0.845479i	−0.988452	+	0.151533i	$0.951579\pi$
$402$	−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	0.995240	+	0.0974519i	$0.0310692\pi$
$409$	2.84836	+	12.4795i	0.140843	+	0.617072i	−0.854398	+	0.519620i	$0.826074\pi$
$410$	−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	−0.932695	−	0.360667i	$-0.882549\pi$
$419$	−25.2233	+	12.1469i	−1.23224	+	0.593415i	−0.299545	+	0.954082i	$0.596835\pi$
$420$	0.0268706	−	0.0684653i	0.00131115	−	0.00334076i
$421$	1.03389	−	13.7963i	0.0503885	−	0.672388i	−0.913629	−	0.406549i	$-0.866732\pi$
$421$	1.03389	−	13.7963i	0.0503885	−	0.672388i	0.964017	−	0.265839i	$-0.0856490\pi$
$422$	−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	−0.686830	−	0.726818i	$-0.740998\pi$
$433$	−0.278233	+	0.258163i	−0.0133710	+	0.0124065i	0.673459	+	0.739225i	$0.264808\pi$
$434$	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	−0.981726	−	0.190298i	$-0.939055\pi$
$439$	0.364516	−	4.86413i	0.0173974	−	0.232152i	0.999124	−	0.0418540i	$-0.0133264\pi$
$440$	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	0.973085	−	0.230446i	$-0.0740186\pi$
$443$	2.16832	+	5.52479i	0.103020	+	0.262491i	−0.870065	+	0.492937i	$0.835923\pi$
$444$	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	0.691698	+	0.722187i	$0.256863\pi$
$449$	2.44448	+	32.6193i	0.115362	+	1.53940i	−0.576336	+	0.817213i	$0.695518\pi$
$450$	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	0.997249	+	0.0741197i	$0.0236147\pi$
$457$	18.1197	+	22.7213i	0.847602	+	1.06286i	−0.149647	+	0.988739i	$0.547814\pi$
$458$	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	−0.600915	−	0.799313i	$-0.705197\pi$
$461$	−13.8948	+	4.28598i	−0.647146	+	0.199618i	−0.0462305	+	0.998931i	$0.514721\pi$
$462$	−7.50426	+	3.61386i	−0.349130	+	0.168132i
$463$	−2.25869	+	5.75504i	−0.104970	+	0.267459i	−0.973703	−	0.227822i	$-0.926840\pi$
$463$	−2.25869	+	5.75504i	−0.104970	+	0.267459i	0.868733	+	0.495281i	$0.164935\pi$
$464$	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	0.988894	−	0.148622i	$-0.0474838\pi$
$467$	7.90363	+	13.6895i	0.365736	+	0.633474i	−0.623158	+	0.782096i	$0.714150\pi$
$468$	−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	−0.851221	−	0.524808i	$-0.824137\pi$
$479$	−19.2621	−	33.3629i	−0.880107	−	1.52439i	−0.0288864	−	0.999583i	$-0.509196\pi$
$480$	−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	0.859229	−	0.511592i	$-0.170944\pi$
$487$	9.12024	+	8.46235i	0.413277	+	0.383465i	−0.445951	+	0.895057i	$0.647134\pi$
$488$	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	−0.685381	−	0.728185i	$-0.740364\pi$
$491$	−36.8246	−	11.3589i	−1.66187	−	0.512619i	−0.976489	+	0.215566i	$0.930840\pi$
$492$	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	0.874578	−	0.484884i	$-0.161138\pi$
$499$	41.3979	−	6.23973i	1.85322	−	0.279329i	0.978645	+	0.205556i	$0.0659002\pi$
$500$	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	0.759953	−	0.649978i	$-0.225222\pi$
$503$	−5.36535	−	13.6707i	−0.239229	−	0.609546i	−0.999182	+	0.0404321i	$0.987127\pi$
$504$	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	−0.509571	−	0.860429i	$-0.670196\pi$
$509$	11.0632	−	19.1620i	0.490368	−	0.849342i	0.999939	+	0.0110868i	$0.00352910\pi$
$510$	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	0.676531	−	0.736414i	$-0.263482\pi$
$521$	25.2437	+	3.80487i	1.10594	+	0.166694i	0.429413	+	0.903108i	$0.358720\pi$
$522$	−4.16838	−	7.21985i	−0.182445	−	0.316004i
$523$	−14.2828	+	24.7386i	−0.624544	+	1.08174i	0.364085	+	0.931366i	$0.381382\pi$
$523$	−14.2828	+	24.7386i	−0.624544	+	1.08174i	−0.988629	+	0.150376i	$0.951952\pi$
$524$	−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	0.258754	−	0.965943i	$-0.416688\pi$
$541$	−1.66509	−	0.513613i	−0.0715879	−	0.0220819i	−0.330342	+	0.943861i	$0.607164\pi$
$542$	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	−0.0658126	−	0.997832i	$-0.520964\pi$
$547$	10.3354	−	3.18805i	0.441909	−	0.136311i	0.507722	+	0.861521i	$0.330488\pi$
$548$	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	−0.975641	−	0.219372i	$-0.929599\pi$
$557$	−0.0339125	+	0.148580i	−0.00143692	+	0.00629554i	0.974204	+	0.225668i	$0.0724563\pi$
$558$	−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	0.827489	−	0.561481i	$-0.189768\pi$
$563$	21.4601	+	10.3347i	0.904437	+	0.435554i	0.0769474	+	0.997035i	$0.475483\pi$
$564$	−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	−0.462754	−	0.886487i	$-0.653139\pi$
$569$	11.4363	−	29.1391i	0.479433	−	1.22158i	0.942187	−	0.335088i	$-0.108766\pi$
$570$	0.0670306	−	0.0322802i	0.00280760	−	0.00135207i
$571$	−4.21255	+	1.29940i	−0.176290	+	0.0543782i	−0.381643	−	0.924310i	$-0.624642\pi$
$571$	−4.21255	+	1.29940i	−0.176290	+	0.0543782i	0.205354	+	0.978688i	$0.434166\pi$
$572$	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	0.758809	−	0.651314i	$-0.225782\pi$
$577$	24.4740	+	7.54924i	1.01887	+	0.314279i	0.260059	+	0.965593i	$0.416258\pi$
$578$	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	−0.0207824	−	0.999784i	$-0.506616\pi$
$587$	21.8609	−	14.9045i	0.902298	−	0.615176i	0.923080	+	0.384608i	$0.125663\pi$
$588$	−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	0.569272	+	0.822149i	$0.307225\pi$
$593$	−2.82909	+	37.7516i	−0.116177	+	1.55027i	−0.685448	+	0.728121i	$0.740394\pi$
$594$	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	−0.564432	−	0.825480i	$-0.690905\pi$
$599$	5.30017	−	4.91784i	0.216559	−	0.200938i	0.780991	+	0.624542i	$0.214714\pi$
$600$	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	−0.0920071	−	0.995758i	$-0.529328\pi$
$607$	−11.6641	−	1.75808i	−0.473432	−	0.0713583i	−0.381424	+	0.924400i	$0.624566\pi$
$608$	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	0.0576626	−	0.998336i	$-0.481635\pi$
$613$	21.6428	−	10.4226i	0.874145	−	0.420966i	0.816483	+	0.577370i	$0.195921\pi$
$614$	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	−0.536325	−	0.844011i	$-0.680188\pi$
$617$	1.32647	−	0.904369i	0.0534015	−	0.0364085i	0.589727	+	0.807603i	$0.299236\pi$
$618$	−7.11018	−	8.91589i	−0.286013	−	0.358649i
$619$	−48.0499	+	7.24235i	−1.93129	+	0.291095i	−0.997731	−	0.0673331i	$-0.978551\pi$
$619$	−48.0499	+	7.24235i	−1.93129	+	0.291095i	−0.933557	+	0.358428i	$0.883313\pi$
$620$	−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	0.914975	−	0.403509i	$-0.132210\pi$
$631$	14.5938	+	13.5411i	0.580971	+	0.539062i	−0.334005	+	0.942571i	$0.608400\pi$
$632$	−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	0.00701500	−	0.999975i	$-0.497767\pi$
$641$	−19.5056	−	9.39338i	−0.770423	−	0.371016i	−0.777438	+	0.628959i	$0.783481\pi$
$642$	−8.64322	+	8.01974i	−0.341121	+	0.316514i
$643$	−0.473254	+	2.07346i	−0.0186633	+	0.0817694i	−0.983402	−	0.181440i	$-0.941924\pi$
$643$	−0.473254	+	2.07346i	−0.0186633	+	0.0817694i	0.964739	+	0.263210i	$0.0847812\pi$
$644$	−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	−0.961932	−	0.273289i	$-0.911889\pi$
$647$	0.593026	−	2.59822i	0.0233143	−	0.102146i	0.985246	+	0.171142i	$0.0547457\pi$
$648$	−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	−0.599354	−	0.800484i	$-0.704576\pi$
$653$	8.03489	−	10.0754i	0.314429	−	0.394282i	0.913783	+	0.406202i	$0.133147\pi$
$654$	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	0.999251	+	0.0386951i	$0.0123201\pi$
$659$	28.5593	+	26.4992i	1.11251	+	1.03226i	0.113261	+	0.993565i	$0.463870\pi$
$660$	0.0725653	−	0.0494742i	0.00282460	−	0.00192578i
$661$	24.8200	+	31.1233i	0.965387	+	1.21056i	0.977566	+	0.210631i	$0.0675519\pi$
$661$	24.8200	+	31.1233i	0.965387	+	1.21056i	−0.0121787	+	0.999926i	$0.503877\pi$
$662$	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	−0.986137	−	0.165934i	$-0.946936\pi$
$673$	−30.9218	+	21.0822i	−1.19195	+	0.812657i	−0.205813	+	0.978591i	$0.565984\pi$
$674$	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	−0.354978	−	0.934875i	$-0.615512\pi$
$677$	4.02286	−	1.93731i	0.154611	−	0.0744567i	0.509589	+	0.860418i	$0.329797\pi$
$678$	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	−0.616812	−	0.787110i	$-0.711576\pi$
$683$	−37.5870	−	5.66533i	−1.43823	−	0.216778i	−0.821414	+	0.570333i	$0.806814\pi$
$684$	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	−0.597218	−	0.802079i	$-0.703727\pi$
$691$	4.15300	−	3.85342i	0.157988	−	0.146591i	0.755206	+	0.655488i	$0.227537\pi$
$692$	−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	−0.991600	−	0.129346i	$-0.958712\pi$
$701$	−9.33779	−	23.7923i	−0.352683	−	0.898623i	0.638916	−	0.769276i	$-0.279383\pi$
$702$	−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	0.879243	+	0.476373i	$0.158049\pi$
$709$	7.82205	+	34.2706i	0.293763	+	1.28706i	−0.585480	+	0.810687i	$0.699094\pi$
$710$	−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	−0.203483	−	0.979078i	$-0.565226\pi$
$719$	4.82456	−	1.48818i	0.179926	−	0.0554998i	0.383409	+	0.923579i	$0.374750\pi$
$720$	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	0.688324	−	0.725404i	$-0.258347\pi$
$727$	14.8389	+	7.14602i	0.550343	+	0.265031i	−0.137981	+	0.990435i	$0.544061\pi$
$728$	−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	−0.999915	−	0.0130123i	$-0.995858\pi$
$733$	−2.52808	+	11.0763i	−0.0933769	+	0.409111i	0.906538	+	0.422123i	$0.138715\pi$
$734$	−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	−0.995078	−	0.0990901i	$-0.968407\pi$
$739$	−18.4052	+	23.0794i	−0.677047	+	0.848990i	0.318032	+	0.948080i	$0.396978\pi$
$740$	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	−0.574644	−	0.818403i	$-0.694860\pi$
$743$	−16.0390	+	4.94738i	−0.588414	+	0.181502i	−0.0137702	+	0.999905i	$0.504383\pi$
$744$	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	−0.912007	−	0.410175i	$-0.865468\pi$
$751$	−44.5875	−	30.3993i	−1.62702	−	1.10928i	−0.715015	−	0.699110i	$-0.753580\pi$
$752$	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	−0.492850	−	0.870115i	$-0.664045\pi$
$757$	−19.4613	+	2.93332i	−0.707332	+	0.106613i	−0.214483	+	0.976728i	$0.568807\pi$
$758$	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	0.930784	+	0.365571i	$0.119126\pi$
$761$	13.7137	+	34.9420i	0.497122	+	1.26665i	−0.433662	+	0.901076i	$0.642779\pi$
$762$	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	0.672500	−	0.740097i	$-0.265220\pi$
$769$	30.4201	+	4.58509i	1.09698	+	0.165342i	0.424475	+	0.905439i	$0.360459\pi$
$770$	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	0.980550	−	0.196270i	$-0.0628831\pi$
$787$	3.59809	+	9.16779i	0.128258	+	0.326796i	−0.852292	+	0.523067i	$0.824788\pi$
$788$	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	0.312055	−	0.950064i	$-0.398983\pi$
$797$	−12.9391	−	8.82176i	−0.458328	−	0.312483i	−0.770383	+	0.637581i	$0.779935\pi$
$798$	−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	0.248039	−	0.968750i	$-0.420214\pi$
$809$	32.3483	−	40.5635i	1.13731	−	1.42614i	0.889268	−	0.457387i	$-0.151215\pi$
$810$	0.230110	−	0.398563i	0.00808526	−	0.0140041i
$811$	−5.67356	−	9.82690i	−0.199226	−	0.345069i	0.749052	−	0.662511i	$-0.230509\pi$
$811$	−5.67356	−	9.82690i	−0.199226	−	0.345069i	−0.948278	+	0.317442i	$0.897176\pi$
$812$	−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	0.641529	−	0.767098i	$-0.278300\pi$
$821$	12.6582	+	6.09588i	0.441775	+	0.212748i	−0.199755	+	0.979846i	$0.564014\pi$
$822$	12.3746	+	1.86518i	0.431615	+	0.0650555i
$823$	4.75616	+	8.23791i	0.165789	+	0.287156i	0.936935	−	0.349503i	$-0.113649\pi$
$823$	4.75616	+	8.23791i	0.165789	+	0.287156i	−0.771146	+	0.636658i	$0.780316\pi$
$824$	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	−0.538145	−	0.842852i	$-0.680875\pi$
$827$	12.3551	−	31.4803i	0.429629	−	1.09468i	0.967773	−	0.251823i	$-0.0810302\pi$
$828$	2.44316	−	1.17656i	0.0849058	−	0.0408885i
$829$	29.4594	−	9.08703i	1.02317	−	0.315606i	0.262628	−	0.964897i	$-0.415411\pi$
$829$	29.4594	−	9.08703i	1.02317	−	0.315606i	0.760540	+	0.649291i	$0.224934\pi$
$830$	−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	0.992392	+	0.123115i	$0.0392885\pi$
$839$	4.39393	+	19.2511i	0.151695	+	0.664621i	−0.840697	+	0.541506i	$0.817854\pi$
$840$	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	−0.0739557	+	0.997262i	$0.523562\pi$
$853$	−26.3040	+	45.5599i	−0.900632	+	1.55994i	−0.826676	+	0.562678i	$0.809771\pi$
$854$	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	−0.998590	−	0.0530773i	$-0.983097\pi$
$857$	−29.8684	+	27.7139i	−1.02029	+	0.946687i	−0.0216959	+	0.999765i	$0.506907\pi$
$858$	−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	−0.232646	−	0.972562i	$-0.574738\pi$
$863$	21.1458	−	19.6204i	0.719811	−	0.667887i	0.952456	+	0.304675i	$0.0985478\pi$
$864$	−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	−0.0688546	−	0.997627i	$-0.521934\pi$
$877$	4.72066	−	0.711525i	0.159405	−	0.0240265i	0.228260	+	0.973600i	$0.426696\pi$
$878$	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	0.949475	+	0.313841i	$0.101616\pi$
$881$	6.83266	+	29.9359i	0.230198	+	1.00856i	−0.719277	+	0.694723i	$0.755527\pi$
$882$	3.90745	+	17.1197i	0.131571	+	0.576449i
$883$	−17.0934	−	11.6541i	−0.575238	−	0.392191i	0.240468	−	0.970657i	$-0.422699\pi$
$883$	−17.0934	−	11.6541i	−0.575238	−	0.392191i	−0.815706	+	0.578466i	$0.803651\pi$
$884$	−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	0.755016	−	0.655706i	$-0.227629\pi$
$887$	−1.55633	−	1.95158i	−0.0522565	−	0.0655276i	−0.807273	+	0.590178i	$0.799057\pi$
$888$	−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	0.746895	−	0.664942i	$-0.231544\pi$
$907$	20.8618	+	10.0465i	0.692703	+	0.333588i	−0.0541915	+	0.998531i	$0.517258\pi$
$908$	−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	−0.568655	−	0.822576i	$-0.692536\pi$
$911$	10.8608	−	13.6190i	0.359834	−	0.451218i	0.928490	+	0.371358i	$0.121108\pi$
$912$	−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	0.905483	−	0.424382i	$-0.139509\pi$
$919$	8.79901	+	11.0336i	0.290252	+	0.363965i	−0.615231	+	0.788347i	$0.710937\pi$
$920$	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	−0.513468	−	0.858109i	$-0.671640\pi$
$929$	−22.8960	+	3.45101i	−0.751192	+	0.113224i	−0.237724	+	0.971333i	$0.576401\pi$
$930$	−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	−0.704640	−	0.709565i	$-0.748891\pi$
$937$	2.99630	−	39.9829i	0.0978850	−	1.30618i	0.802525	−	0.596619i	$-0.203490\pi$
$938$	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	0.668858	−	0.743390i	$-0.266783\pi$
$941$	33.4023	+	5.03458i	1.08888	+	0.164123i	0.420025	+	0.907513i	$0.362021\pi$
$942$	−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	0.244435	+	0.969666i	$0.421397\pi$
$953$	−22.1509	+	38.3665i	−0.717538	+	1.24281i	−0.961973	+	0.273146i	$0.911936\pi$
$954$	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	−0.723884	−	0.689922i	$-0.757645\pi$
$967$	−11.5379	−	50.5507i	−0.371033	−	1.62560i	0.352851	−	0.935680i	$-0.385212\pi$
$968$	−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	0.850859	−	0.525394i	$-0.176082\pi$
$971$	39.1975	+	12.0908i	1.25791	+	0.388013i	0.407048	+	0.913407i	$0.366558\pi$
$972$	−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	−0.839988	−	0.542605i	$-0.817438\pi$
$977$	−38.3948	+	11.8432i	−1.22836	+	0.378899i	−0.388371	+	0.921503i	$0.626962\pi$
$978$	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	−0.970712	−	0.240245i	$-0.922772\pi$
$983$	−21.7405	−	37.6556i	−0.693414	−	1.20103i	0.277298	−	0.960784i	$-0.410561\pi$
$984$	−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	0.808002	+	0.589179i	$0.200549\pi$
$991$	−5.52848	+	24.2218i	−0.175618	+	0.769432i	−0.983620	+	0.180253i	$0.942308\pi$
$992$	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	−0.415787	−	0.909462i	$-0.636494\pi$
$997$	17.7893	−	22.3071i	0.563394	−	0.706474i	0.979181	+	0.202988i	$0.0650652\pi$
$998$	−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.13.1	yes	36
3.2	odd	2		387.2.y.c.271.3		36
4.3	odd	2		688.2.bg.c.529.2		36
43.10	even	21	inner	43.2.g.a.10.1	✓	36
43.15	even	21		1849.2.a.n.1.16		18
43.28	odd	42		1849.2.a.o.1.3		18
129.53	odd	42		387.2.y.c.10.3		36
172.139	odd	42		688.2.bg.c.225.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.10.1	✓	36	43.10	even	21	inner
43.2.g.a.13.1	yes	36	1.1	even	1	trivial
387.2.y.c.10.3		36	129.53	odd	42
387.2.y.c.271.3		36	3.2	odd	2
688.2.bg.c.225.2		36	172.139	odd	42
688.2.bg.c.529.2		36	4.3	odd	2
1849.2.a.n.1.16		18	43.15	even	21
1849.2.a.o.1.3		18	43.28	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

Modular forms

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