LMFDB - Embedded newform 43.2.g.a.17.1

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			17.1
Character	$\chi$	$=$	43.17
Dual form			43.2.g.a.38.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.515822 - 2.25996i) q^{2} +(1.28860 - 0.397480i) q^{3} +(-3.03942 + 1.46371i) q^{4} +(-1.48781 + 3.79089i) q^{5} +(-1.56298 - 2.70715i) q^{6} +(1.38920 - 2.40617i) q^{7} +(1.98513 + 2.48927i) q^{8} +(-0.976224 + 0.665578i) q^{9} +O(q^{10})$	\(q+(-0.515822 - 2.25996i) q^{2} +(1.28860 - 0.397480i) q^{3} +(-3.03942 + 1.46371i) q^{4} +(-1.48781 + 3.79089i) q^{5} +(-1.56298 - 2.70715i) q^{6} +(1.38920 - 2.40617i) q^{7} +(1.98513 + 2.48927i) q^{8} +(-0.976224 + 0.665578i) q^{9} +(9.33472 + 1.40698i) q^{10} +(-0.678323 - 0.326663i) q^{11} +(-3.33480 + 3.09424i) q^{12} +(1.70167 - 0.256486i) q^{13} +(-6.15444 - 1.89839i) q^{14} +(-0.410392 + 5.47630i) q^{15} +(0.394993 - 0.495306i) q^{16} +(-1.18750 - 3.02571i) q^{17} +(2.00774 + 1.86291i) q^{18} +(-0.0395049 - 0.0269340i) q^{19} +(-1.02666 - 13.6998i) q^{20} +(0.833720 - 3.65277i) q^{21} +(-0.388353 + 1.70148i) q^{22} +(0.152371 + 2.03326i) q^{23} +(3.54746 + 2.41862i) q^{24} +(-8.49199 - 7.87942i) q^{25} +(-1.45741 - 3.71341i) q^{26} +(-3.51575 + 4.40861i) q^{27} +(-0.700443 + 9.34676i) q^{28} +(0.714324 + 0.220340i) q^{29} +(12.5879 - 1.89733i) q^{30} +(2.52247 - 2.34051i) q^{31} +(4.41406 + 2.12570i) q^{32} +(-1.00393 - 0.151318i) q^{33} +(-6.22544 + 4.24444i) q^{34} +(7.05465 + 8.84626i) q^{35} +(1.99294 - 3.45188i) q^{36} +(3.91502 + 6.78101i) q^{37} +(-0.0404923 + 0.103173i) q^{38} +(2.09082 - 1.00689i) q^{39} +(-12.3900 + 3.82182i) q^{40} +(-1.86928 - 8.18985i) q^{41} -8.68517 q^{42} +(-4.39142 - 4.86985i) q^{43} +2.53985 q^{44} +(-1.07069 - 4.69101i) q^{45} +(4.51649 - 1.39315i) q^{46} +(7.05780 - 3.39886i) q^{47} +(0.312113 - 0.795251i) q^{48} +(-0.359777 - 0.623151i) q^{49} +(-13.4268 + 23.2560i) q^{50} +(-2.73287 - 3.42691i) q^{51} +(-4.79668 + 3.27032i) q^{52} +(-1.76849 - 0.266557i) q^{53} +(11.7768 + 5.67140i) q^{54} +(2.24756 - 2.08543i) q^{55} +(8.74735 - 1.31845i) q^{56} +(-0.0616116 - 0.0190047i) q^{57} +(0.129496 - 1.72800i) q^{58} +(3.60798 - 4.52427i) q^{59} +(-6.76836 - 17.2455i) q^{60} +(2.15836 + 2.00266i) q^{61} +(-6.59062 - 4.49341i) q^{62} +(0.245321 + 3.27359i) q^{63} +(2.80908 - 12.3074i) q^{64} +(-1.55946 + 6.83245i) q^{65} +(0.175875 + 2.34689i) q^{66} +(4.62708 + 3.15469i) q^{67} +(8.03807 + 7.45824i) q^{68} +(1.00452 + 2.55948i) q^{69} +(16.3533 - 20.5063i) q^{70} +(-0.543672 + 7.25480i) q^{71} +(-3.59473 - 1.10883i) q^{72} +(-10.0746 + 1.51850i) q^{73} +(13.3054 - 12.3456i) q^{74} +(-14.0747 - 6.77800i) q^{75} +(0.159495 + 0.0240401i) q^{76} +(-1.72834 + 1.17836i) q^{77} +(-3.35402 - 4.20580i) q^{78} +(-6.70519 + 11.6137i) q^{79} +(1.28997 + 2.23430i) q^{80} +(-1.48307 + 3.77880i) q^{81} +(-17.5445 + 8.44900i) q^{82} +(5.42706 - 1.67402i) q^{83} +(2.81256 + 12.3226i) q^{84} +13.2369 q^{85} +(-8.74049 + 12.4364i) q^{86} +1.00806 q^{87} +(-0.533404 - 2.33699i) q^{88} +(-11.7786 + 3.63323i) q^{89} +(-10.0492 + 4.83945i) q^{90} +(1.74682 - 4.45083i) q^{91} +(-3.43922 - 5.95690i) q^{92} +(2.32015 - 4.01861i) q^{93} +(-11.3219 - 14.1972i) q^{94} +(0.160880 - 0.109686i) q^{95} +(6.53287 + 0.984671i) q^{96} +(9.41101 + 4.53210i) q^{97} +(-1.22272 + 1.13452i) q^{98} +(0.879615 - 0.132581i) 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 $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{19}{21}\right)$

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 $

$2$	−0.515822	−	2.25996i	−0.364741	−	1.59803i	−0.740990	−	0.671516i	$-0.765643\pi$
$2$	−0.515822	−	2.25996i	−0.364741	−	1.59803i	0.376249	−	0.926519i	$-0.377214\pi$
$3$	1.28860	−	0.397480i	0.743972	−	0.229485i	0.100481	−	0.994939i	$-0.467962\pi$
$3$	1.28860	−	0.397480i	0.743972	−	0.229485i	0.643491	+	0.765454i	$0.277486\pi$
$4$	−3.03942	+	1.46371i	−1.51971	+	0.731854i
$5$	−1.48781	+	3.79089i	−0.665371	+	1.69534i	0.0520012	+	0.998647i	$0.483440\pi$
$5$	−1.48781	+	3.79089i	−0.665371	+	1.69534i	−0.717372	+	0.696690i	$0.754655\pi$
$6$	−1.56298	−	2.70715i	−0.638082	−	1.10519i
$7$	1.38920	−	2.40617i	0.525070	−	0.909448i	−0.474504	−	0.880253i	$-0.657373\pi$
$7$	1.38920	−	2.40617i	0.525070	−	0.909448i	0.999574	−	0.0291942i	$-0.00929413\pi$
$8$	1.98513	+	2.48927i	0.701848	+	0.880089i
$9$	−0.976224	+	0.665578i	−0.325408	+	0.221859i
$10$	9.33472	+	1.40698i	2.95190	+	0.444927i
$11$	−0.678323	−	0.326663i	−0.204522	−	0.0984926i	0.328819	−	0.944393i	$-0.393349\pi$
$11$	−0.678323	−	0.326663i	−0.204522	−	0.0984926i	−0.533341	+	0.845900i	$0.679064\pi$
$12$	−3.33480	+	3.09424i	−0.962673	+	0.893230i
$13$	1.70167	−	0.256486i	0.471959	−	0.0711364i	0.0912435	−	0.995829i	$-0.470916\pi$
$13$	1.70167	−	0.256486i	0.471959	−	0.0711364i	0.380715	+	0.924692i	$0.375678\pi$
$14$	−6.15444	−	1.89839i	−1.64484	−	0.507367i
$15$	−0.410392	+	5.47630i	−0.105963	+	1.41398i
$16$	0.394993	−	0.495306i	0.0987483	−	0.123826i
$17$	−1.18750	−	3.02571i	−0.288012	−	0.733842i	−0.999514	−	0.0311584i	$-0.990080\pi$
$17$	−1.18750	−	3.02571i	−0.288012	−	0.733842i	0.711503	−	0.702683i	$-0.248015\pi$
$18$	2.00774	+	1.86291i	0.473229	+	0.439092i
$19$	−0.0395049	−	0.0269340i	−0.00906304	−	0.00617908i	0.558780	−	0.829316i	$-0.311270\pi$
$19$	−0.0395049	−	0.0269340i	−0.00906304	−	0.00617908i	−0.567843	+	0.823137i	$0.692222\pi$
$20$	−1.02666	−	13.6998i	−0.229568	−	3.06338i
$21$	0.833720	−	3.65277i	0.181933	−	0.797099i
$22$	−0.388353	+	1.70148i	−0.0827971	+	0.362758i
$23$	0.152371	+	2.03326i	0.0317717	+	0.423963i	0.990298	+	0.138960i	$0.0443758\pi$
$23$	0.152371	+	2.03326i	0.0317717	+	0.423963i	−0.958526	+	0.285004i	$0.908005\pi$
$24$	3.54746	+	2.41862i	0.724122	+	0.493698i
$25$	−8.49199	−	7.87942i	−1.69840	−	1.57588i
$26$	−1.45741	−	3.71341i	−0.285821	−	0.728260i
$27$	−3.51575	+	4.40861i	−0.676606	+	0.848437i
$28$	−0.700443	+	9.34676i	−0.132371	+	1.76637i
$29$	0.714324	+	0.220340i	0.132647	+	0.0409161i	0.360368	−	0.932810i	$-0.382651\pi$
$29$	0.714324	+	0.220340i	0.132647	+	0.0409161i	−0.227721	+	0.973726i	$0.573127\pi$
$30$	12.5879	−	1.89733i	2.29823	−	0.346403i
$31$	2.52247	−	2.34051i	0.453050	−	0.420369i	−0.420358	−	0.907358i	$-0.638096\pi$
$31$	2.52247	−	2.34051i	0.453050	−	0.420369i	0.873408	+	0.486990i	$0.161905\pi$
$32$	4.41406	+	2.12570i	0.780303	+	0.375774i
$33$	−1.00393	−	0.151318i	−0.174761	−	0.0263410i
$34$	−6.22544	+	4.24444i	−1.06765	+	0.727915i
$35$	7.05465	+	8.84626i	1.19245	+	1.49529i
$36$	1.99294	−	3.45188i	0.332157	−	0.575313i
$37$	3.91502	+	6.78101i	0.643625	+	1.11479i	0.984617	+	0.174725i	$0.0559037\pi$
$37$	3.91502	+	6.78101i	0.643625	+	1.11479i	−0.340992	+	0.940066i	$0.610763\pi$
$38$	−0.0404923	+	0.103173i	−0.00656872	+	0.0167368i
$39$	2.09082	−	1.00689i	0.334799	−	0.161231i
$40$	−12.3900	+	3.82182i	−1.95904	+	0.604283i
$41$	−1.86928	−	8.18985i	−0.291932	−	1.27904i	−0.881832	−	0.471563i	$-0.843690\pi$
$41$	−1.86928	−	8.18985i	−0.291932	−	1.27904i	0.589900	−	0.807476i	$-0.299167\pi$
$42$	−8.68517			−1.34015
$43$	−4.39142	−	4.86985i	−0.669685	−	0.742645i
$43$	−4.39142	−	4.86985i	−0.669685	−	0.742645i
$44$	2.53985			0.382897
$45$	−1.07069	−	4.69101i	−0.159610	−	0.699295i
$46$	4.51649	−	1.39315i	0.665920	−	0.205409i
$47$	7.05780	−	3.39886i	1.02949	−	0.495775i	0.158644	−	0.987336i	$-0.449288\pi$
$47$	7.05780	−	3.39886i	1.02949	−	0.495775i	0.870843	+	0.491561i	$0.163574\pi$
$48$	0.312113	−	0.795251i	0.0450497	−	0.114785i
$49$	−0.359777	−	0.623151i	−0.0513966	−	0.0890216i
$50$	−13.4268	+	23.2560i	−1.89884	+	3.28889i
$51$	−2.73287	−	3.42691i	−0.382678	−	0.479863i
$52$	−4.79668	+	3.27032i	−0.665180	+	0.453512i
$53$	−1.76849	−	0.266557i	−0.242920	−	0.0366144i	0.0264535	−	0.999650i	$-0.491579\pi$
$53$	−1.76849	−	0.266557i	−0.242920	−	0.0366144i	−0.269374	+	0.963036i	$0.586817\pi$
$54$	11.7768	+	5.67140i	1.60262	+	0.771780i
$55$	2.24756	−	2.08543i	0.303061	−	0.281200i
$56$	8.74735	−	1.31845i	1.16891	−	0.176185i
$57$	−0.0616116	−	0.0190047i	−0.00816065	−	0.00251723i
$58$	0.129496	−	1.72800i	0.0170036	−	0.226898i
$59$	3.60798	−	4.52427i	0.469719	−	0.589009i	−0.489383	−	0.872069i	$-0.662778\pi$
$59$	3.60798	−	4.52427i	0.469719	−	0.589009i	0.959102	+	0.283060i	$0.0913494\pi$
$60$	−6.76836	−	17.2455i	−0.873791	−	2.22638i
$61$	2.15836	+	2.00266i	0.276349	+	0.256415i	0.806155	−	0.591704i	$-0.201545\pi$
$61$	2.15836	+	2.00266i	0.276349	+	0.256415i	−0.529806	+	0.848119i	$0.677735\pi$
$62$	−6.59062	−	4.49341i	−0.837010	−	0.570663i
$63$	0.245321	+	3.27359i	0.0309076	+	0.412433i
$64$	2.80908	−	12.3074i	0.351134	−	1.53842i
$65$	−1.55946	+	6.83245i	−0.193428	+	0.847462i
$66$	0.175875	+	2.34689i	0.0216487	+	0.288882i
$67$	4.62708	+	3.15469i	0.565288	+	0.385407i	0.811978	−	0.583688i	$-0.198391\pi$
$67$	4.62708	+	3.15469i	0.565288	+	0.385407i	−0.246691	+	0.969094i	$0.579343\pi$
$68$	8.03807	+	7.45824i	0.974759	+	0.904445i
$69$	1.00452	+	2.55948i	0.120930	+	0.308126i
$70$	16.3533	−	20.5063i	1.95459	−	2.45098i
$71$	−0.543672	+	7.25480i	−0.0645220	+	0.860987i	0.867234	+	0.497901i	$0.165896\pi$
$71$	−0.543672	+	7.25480i	−0.0645220	+	0.860987i	−0.931756	+	0.363086i	$0.881723\pi$
$72$	−3.59473	−	1.10883i	−0.423643	−	0.130677i
$73$	−10.0746	+	1.51850i	−1.17914	+	0.177727i	−0.709224	−	0.704983i	$-0.750955\pi$
$73$	−10.0746	+	1.51850i	−1.17914	+	0.177727i	−0.469918	+	0.882710i	$0.655716\pi$
$74$	13.3054	−	12.3456i	1.54672	−	1.43515i
$75$	−14.0747	−	6.77800i	−1.62520	−	0.782656i
$76$	0.159495	+	0.0240401i	0.0182954	+	0.00275759i
$77$	−1.72834	+	1.17836i	−0.196962	+	0.134287i
$78$	−3.35402	−	4.20580i	−0.379768	−	0.476214i
$79$	−6.70519	+	11.6137i	−0.754393	+	1.30665i	0.191283	+	0.981535i	$0.438735\pi$
$79$	−6.70519	+	11.6137i	−0.754393	+	1.30665i	−0.945676	+	0.325112i	$0.894598\pi$
$80$	1.28997	+	2.23430i	0.144223	+	0.249802i
$81$	−1.48307	+	3.77880i	−0.164785	+	0.419866i
$82$	−17.5445	+	8.44900i	−1.93747	+	0.933036i
$83$	5.42706	−	1.67402i	0.595697	−	0.183748i	0.0177773	−	0.999842i	$-0.494341\pi$
$83$	5.42706	−	1.67402i	0.595697	−	0.183748i	0.577919	+	0.816094i	$0.303865\pi$
$84$	2.81256	+	12.3226i	0.306875	+	1.34451i
$85$	13.2369			1.43574
$86$	−8.74049	+	12.4364i	−0.942511	+	1.34105i
$87$	1.00806			0.108075
$88$	−0.533404	−	2.33699i	−0.0568610	−	0.249124i
$89$	−11.7786	+	3.63323i	−1.24853	+	0.385121i	−0.847428	−	0.530911i	$-0.821850\pi$
$89$	−11.7786	+	3.63323i	−1.24853	+	0.385121i	−0.401105	+	0.916032i	$0.631374\pi$
$90$	−10.0492	+	4.83945i	−1.05928	+	0.510123i
$91$	1.74682	−	4.45083i	0.183117	−	0.466573i
$92$	−3.43922	−	5.95690i	−0.358563	−	0.621049i
$93$	2.32015	−	4.01861i	0.240588	−	0.416710i
$94$	−11.3219	−	14.1972i	−1.16776	−	1.46433i
$95$	0.160880	−	0.109686i	0.0165059	−	0.0112535i
$96$	6.53287	+	0.984671i	0.666758	+	0.100498i
$97$	9.41101	+	4.53210i	0.955543	+	0.460165i	0.845626	−	0.533775i	$-0.179227\pi$
$97$	9.41101	+	4.53210i	0.955543	+	0.460165i	0.109917	+	0.993941i	$0.464941\pi$
$98$	−1.22272	+	1.13452i	−0.123513	+	0.114603i
$99$	0.879615	−	0.132581i	0.0884046	−	0.0133249i
$100$	37.3439	+	11.5191i	3.73439	+	1.15191i
$101$	0.171298	−	2.28582i	0.0170448	−	0.227447i	−0.982175	−	0.187966i	$-0.939810\pi$
$101$	0.171298	−	2.28582i	0.0170448	−	0.227447i	0.999220	−	0.0394811i	$-0.0125705\pi$
$102$	−6.33501	+	7.94385i	−0.627260	+	0.786559i
$103$	−1.94001	−	4.94307i	−0.191155	−	0.487056i	0.802877	−	0.596145i	$-0.203302\pi$
$103$	−1.94001	−	4.94307i	−0.191155	−	0.487056i	−0.994032	+	0.109090i	$0.965206\pi$
$104$	4.01649	+	3.72676i	0.393850	+	0.365439i
$105$	12.6068	+	8.59518i	1.23030	+	0.838804i
$106$	0.309816	+	4.13421i	0.0300920	+	0.401550i
$107$	0.800089	−	3.50542i	0.0773475	−	0.338882i	−0.921417	−	0.388575i	$-0.872967\pi$
$107$	0.800089	−	3.50542i	0.0773475	−	0.338882i	0.998765	+	0.0496936i	$0.0158245\pi$
$108$	4.23292	−	18.5456i	0.407313	−	1.78456i
$109$	0.415847	+	5.54910i	0.0398310	+	0.531507i	0.981056	+	0.193726i	$0.0620573\pi$
$109$	0.415847	+	5.54910i	0.0398310	+	0.531507i	−0.941225	+	0.337781i	$0.890324\pi$
$110$	−5.87234	−	4.00369i	−0.559906	−	0.381737i
$111$	7.74019	+	7.18185i	0.734667	+	0.681671i
$112$	−0.643065	−	1.63850i	−0.0607639	−	0.154824i
$113$	0.0874119	−	0.109611i	0.00822302	−	0.0103113i	−0.777703	−	0.628632i	$-0.783615\pi$
$113$	0.0874119	−	0.109611i	0.00822302	−	0.0103113i	0.785926	+	0.618321i	$0.212187\pi$
$114$	−0.0111692	+	0.149043i	−0.00104609	+	0.0139591i
$115$	−7.93455	−	2.44748i	−0.739901	−	0.228229i
$116$	−2.49365	+	0.375857i	−0.231529	+	0.0348974i
$117$	−1.49050	+	1.38298i	−0.137797	+	0.127857i
$118$	−12.0857	−	5.82019i	−1.11258	−	0.535792i
$119$	−8.93005	−	1.34599i	−0.818617	−	0.123387i
$120$	−14.4467	+	9.84958i	−1.31879	+	0.899139i
$121$	−6.50497	−	8.15698i	−0.591361	−	0.741544i
$122$	3.41262	−	5.91082i	0.308964	−	0.535141i
$123$	−5.66405	−	9.81041i	−0.510710	−	0.884575i
$124$	−4.24103	+	10.8060i	−0.380856	+	0.970405i
$125$	24.1590	−	11.6344i	2.16084	−	1.04061i
$126$	7.27164	−	2.24300i	0.647809	−	0.199823i
$127$	−0.384858	−	1.68617i	−0.0341507	−	0.149624i	0.954978	−	0.296677i	$-0.0958784\pi$
$127$	−0.384858	−	1.68617i	−0.0341507	−	0.149624i	−0.989129	+	0.147053i	$0.953021\pi$
$128$	−19.4647			−1.72045
$129$	−7.59444	−	4.52977i	−0.668653	−	0.398824i
$130$	16.2455			1.42482
$131$	4.87229	+	21.3469i	0.425694	+	1.86509i	0.497180	+	0.867647i	$0.334369\pi$
$131$	4.87229	+	21.3469i	0.425694	+	1.86509i	−0.0714858	+	0.997442i	$0.522774\pi$
$132$	3.27284	−	1.00954i	0.284864	−	0.0878690i
$133$	−0.119688	+	0.0576388i	−0.0103783	+	0.00499791i
$134$	4.74273	−	12.0843i	0.409710	−	1.04392i
$135$	−11.4818	−	19.8870i	−0.988193	−	1.71160i
$136$	5.17445	−	8.96242i	0.443706	−	0.768521i
$137$	13.3197	+	16.7024i	1.13798	+	1.42698i	0.888665	+	0.458557i	$0.151634\pi$
$137$	13.3197	+	16.7024i	1.13798	+	1.42698i	0.249314	+	0.968423i	$0.419795\pi$
$138$	5.26618	−	3.59042i	0.448287	−	0.305637i
$139$	−12.0494	−	1.81616i	−1.02202	−	0.154044i	−0.383411	−	0.923578i	$-0.625251\pi$
$139$	−12.0494	−	1.81616i	−1.02202	−	0.154044i	−0.638606	+	0.769534i	$0.720489\pi$
$140$	−34.3904	−	16.5615i	−2.90652	−	1.39971i
$141$	7.74369	−	7.18509i	0.652136	−	0.605094i
$142$	16.6760	−	2.51351i	1.39942	−	0.210929i
$143$	−1.23807	−	0.381893i	−0.103532	−	0.0319355i
$144$	−0.0559371	+	0.746428i	−0.00466142	+	0.0622024i
$145$	−1.89807	+	2.38010i	−0.157626	+	0.197656i
$146$	8.62845	+	21.9849i	0.714095	+	1.81949i
$147$	−0.711297	−	0.659987i	−0.0586668	−	0.0544348i
$148$	−21.8248	−	14.8799i	−1.79399	−	1.22312i
$149$	−0.617820	−	8.24424i	−0.0506138	−	0.675395i	−0.963590	−	0.267383i	$-0.913841\pi$
$149$	−0.617820	−	8.24424i	−0.0506138	−	0.675395i	0.912977	−	0.408012i	$-0.133778\pi$
$150$	−8.05801	+	35.3044i	−0.657934	+	2.88260i
$151$	1.01707	−	4.45608i	0.0827681	−	0.362631i	−0.916535	−	0.399954i	$-0.869026\pi$
$151$	1.01707	−	4.45608i	0.0827681	−	0.362631i	0.999303	+	0.0373233i	$0.0118831\pi$
$152$	−0.0113763	−	0.151806i	−0.000922736	−	0.0123131i
$153$	3.17311	+	2.16339i	0.256531	+	0.174900i
$154$	3.55456	+	3.29815i	0.286435	+	0.265773i
$155$	5.11966	+	13.0447i	0.411221	+	1.04777i
$156$	−4.88110	+	6.12071i	−0.390801	+	0.490049i
$157$	−0.748623	+	9.98968i	−0.0597466	+	0.797263i	0.884188	+	0.467131i	$0.154712\pi$
$157$	−0.748623	+	9.98968i	−0.0597466	+	0.797263i	−0.943935	+	0.330132i	$0.892907\pi$
$158$	29.7053	+	9.16287i	2.36323	+	0.728959i
$159$	−2.38482	+	0.359453i	−0.189128	+	0.0285065i
$160$	−14.6256	+	13.5706i	−1.15625	+	1.07285i
$161$	5.10404	+	2.45798i	0.402255	+	0.193716i
$162$	9.30494	+	1.40249i	0.731065	+	0.110190i
$163$	17.6610	−	12.0410i	1.38331	−	0.943128i	0.383506	−	0.923538i	$-0.374716\pi$
$163$	17.6610	−	12.0410i	1.38331	−	0.943128i	0.999808	−	0.0195896i	$-0.00623595\pi$
$164$	17.6691	+	22.1563i	1.37972	+	1.73012i
$165$	2.06728	−	3.58064i	0.160938	−	0.278753i
$166$	−6.58263	−	11.4014i	−0.510911	−	0.884924i
$167$	8.02372	−	20.4441i	0.620894	−	1.58201i	−0.180302	−	0.983611i	$-0.557708\pi$
$167$	8.02372	−	20.4441i	0.620894	−	1.58201i	0.801197	−	0.598401i	$-0.204197\pi$
$168$	10.7478	−	5.17585i	0.829207	−	0.399325i
$169$	−9.59254	+	2.95891i	−0.737888	+	0.227608i
$170$	−6.82788	−	29.9149i	−0.523675	−	2.29437i
$171$	0.0564923			0.00432007
$172$	20.4754	+	8.37377i	1.56124	+	0.638494i
$173$	−15.5770			−1.18430			−0.592151	−	0.805827i	$-0.701721\pi$
$173$	−15.5770			−1.18430			−0.592151	+	0.805827i	$0.701721\pi$
$174$	−0.519977	−	2.27817i	−0.0394194	−	0.172708i
$175$	−30.7563	+	9.48708i	−2.32496	+	0.717155i
$176$	−0.429731	+	0.206948i	−0.0323922	+	0.0155993i
$177$	2.85093	−	7.26405i	0.214289	−	0.546000i
$178$	14.2866	+	24.7452i	1.07083	+	1.85473i
$179$	3.49011	−	6.04505i	0.260863	−	0.451828i	−0.705608	−	0.708602i	$-0.749326\pi$
$179$	3.49011	−	6.04505i	0.260863	−	0.451828i	0.966472	+	0.256774i	$0.0826596\pi$
$180$	10.1206	+	12.6908i	0.754342	+	0.945916i
$181$	−4.54803	+	3.10080i	−0.338053	+	0.230480i	−0.720433	−	0.693525i	$-0.756057\pi$
$181$	−4.54803	+	3.10080i	−0.338053	+	0.230480i	0.382380	+	0.924005i	$0.375104\pi$
$182$	−10.9598	−	1.65192i	−0.812391	−	0.122448i
$183$	3.57727	+	1.72272i	0.264439	+	0.127347i
$184$	−4.75884	+	4.41556i	−0.350827	+	0.325520i
$185$	−31.5309	+	4.75252i	−2.31820	+	0.349412i
$186$	−10.2787	−	3.17056i	−0.753670	−	0.232476i
$187$	−0.182877	+	2.44032i	−0.0133733	+	0.178454i
$188$	−16.4767	+	20.6611i	−1.20169	+	1.50687i
$189$	5.72378	+	14.5840i	0.416344	+	1.06083i
$190$	−0.330871	−	0.307004i	−0.0240039	−	0.0222724i
$191$	−15.7034	−	10.7064i	−1.13626	−	0.774689i	−0.159115	−	0.987260i	$-0.550864\pi$
$191$	−15.7034	−	10.7064i	−1.13626	−	0.774689i	−0.977146	+	0.212571i	$0.931816\pi$
$192$	−1.27216	−	16.9758i	−0.0918102	−	1.22512i
$193$	0.685255	−	3.00230i	0.0493257	−	0.216110i	−0.944258	−	0.329205i	$-0.893219\pi$
$193$	0.685255	−	3.00230i	0.0493257	−	0.216110i	0.993584	+	0.113095i	$0.0360764\pi$
$194$	5.38798	−	23.6063i	0.386835	−	1.69483i
$195$	0.706241	+	9.42413i	0.0505750	+	0.674876i
$196$	2.00562	+	1.36741i	0.143259	+	0.0976722i
$197$	−8.60862	−	7.98763i	−0.613339	−	0.569095i	0.311123	−	0.950370i	$-0.399295\pi$
$197$	−8.60862	−	7.98763i	−0.613339	−	0.569095i	−0.924462	+	0.381274i	$0.875485\pi$
$198$	−0.753352	−	1.91951i	−0.0535384	−	0.136414i
$199$	0.166901	−	0.209287i	0.0118313	−	0.0148360i	−0.775881	−	0.630880i	$-0.782694\pi$
$199$	0.166901	−	0.209287i	0.0118313	−	0.0148360i	0.787712	+	0.616044i	$0.211266\pi$
$200$	2.75632	−	36.7805i	0.194901	−	2.60077i
$201$	7.21637	+	2.22595i	0.509003	+	0.157007i
$202$	−5.25422	+	0.791947i	−0.369686	+	0.0557212i
$203$	1.52252	−	1.41269i	0.106860	−	0.0991514i
$204$	13.3223	+	6.41570i	0.932750	+	0.449189i
$205$	33.8280	+	5.09874i	2.36265	+	0.356112i
$206$	−10.1705	+	6.93410i	−0.708610	+	0.483122i
$207$	−1.50204	−	1.88350i	−0.104399	−	0.130912i
$208$	0.545110	−	0.944158i	0.0377966	−	0.0654656i
$209$	0.0179987	+	0.0311747i	0.00124500	+	0.00215640i
$210$	12.9219	−	32.9245i	0.891697	−	2.27201i
$211$	−14.7666	+	7.11124i	−1.01658	+	0.489558i	−0.866532	−	0.499122i	$-0.833656\pi$
$211$	−14.7666	+	7.11124i	−1.01658	+	0.489558i	−0.150045	+	0.988679i	$0.547942\pi$
$212$	5.76534	−	1.77837i	0.395965	−	0.122139i
$213$	2.18306	+	9.56462i	0.149581	+	0.655357i
$214$	−8.33482			−0.569757
$215$	24.9947	−	9.40196i	1.70462	−	0.641208i
$216$	−17.9534			−1.22157
$217$	−2.12745	−	9.32096i	−0.144421	−	0.632748i
$218$	12.3263	−	3.80215i	0.834839	−	0.257514i
$219$	−12.3785	+	5.96118i	−0.836463	+	0.402819i
$220$	−3.77882	+	9.62828i	−0.254768	+	0.649139i
$221$	−2.79679	−	4.84418i	−0.188132	−	0.325855i
$222$	12.2382	−	21.1971i	0.821371	−	1.42266i
$223$	3.03608	+	3.80712i	0.203311	+	0.254944i	0.873025	−	0.487675i	$-0.162155\pi$
$223$	3.03608	+	3.80712i	0.203311	+	0.254944i	−0.669714	+	0.742619i	$0.733583\pi$
$224$	11.2468	−	7.66796i	0.751460	−	0.512337i
$225$	13.5345	+	2.03999i	0.902297	+	0.135999i
$226$	−0.292806	−	0.141008i	−0.0194772	−	0.00937971i
$227$	14.1316	−	13.1122i	0.937947	−	0.870288i	−0.0537930	−	0.998552i	$-0.517131\pi$
$227$	14.1316	−	13.1122i	0.937947	−	0.870288i	0.991740	+	0.128265i	$0.0409406\pi$
$228$	0.215081	−	0.0324182i	0.0142441	−	0.00214695i
$229$	−6.90123	−	2.12875i	−0.456046	−	0.140672i	0.0582171	−	0.998304i	$-0.481458\pi$
$229$	−6.90123	−	2.12875i	−0.456046	−	0.140672i	−0.514263	+	0.857632i	$0.671935\pi$
$230$	−1.43841	+	19.1943i	−0.0948460	+	1.26563i
$231$	−1.75875	+	2.20541i	−0.115718	+	0.145105i
$232$	0.869538	+	2.21555i	0.0570880	+	0.145458i
$233$	−6.45459	−	5.98898i	−0.422854	−	0.392351i	0.439841	−	0.898076i	$-0.355035\pi$
$233$	−6.45459	−	5.98898i	−0.422854	−	0.392351i	−0.862695	+	0.505724i	$0.831225\pi$
$234$	3.89432	+	2.65511i	0.254580	+	0.173570i
$235$	2.38400	+	31.8122i	0.155515	+	2.07520i
$236$	−4.34397	+	19.0322i	−0.282768	+	1.23889i
$237$	−4.02407	+	17.6306i	−0.261391	+	1.14523i
$238$	1.56443	+	20.8759i	0.101407	+	1.35318i
$239$	4.97430	+	3.39142i	0.321761	+	0.219373i	0.713418	−	0.700738i	$-0.247146\pi$
$239$	4.97430	+	3.39142i	0.321761	+	0.219373i	−0.391658	+	0.920111i	$0.628098\pi$
$240$	2.55034	+	2.36637i	0.164624	+	0.152749i
$241$	−6.42983	−	16.3830i	−0.414182	−	1.05532i	−0.973969	−	0.226682i	$-0.927212\pi$
$241$	−6.42983	−	16.3830i	−0.414182	−	1.05532i	0.559787	−	0.828637i	$-0.310883\pi$
$242$	−15.0791	+	18.9085i	−0.969319	+	1.21549i
$243$	0.855086	−	11.4103i	0.0548538	−	0.731973i
$244$	−9.49147	−	2.92773i	−0.607629	−	0.187429i
$245$	2.89758	−	0.436740i	0.185119	−	0.0279023i
$246$	−19.2495	+	17.8610i	−1.22731	+	1.13877i
$247$	−0.0741325	−	0.0357003i	−0.00471694	−	0.00227156i
$248$	10.8336	+	1.63290i	0.687934	+	0.103689i
$249$	6.32790	−	4.31429i	0.401014	−	0.273407i
$250$	−38.7549	−	48.5971i	−2.45108	−	3.07355i
$251$	8.69184	−	15.0547i	0.548624	−	0.950245i	−0.449745	−	0.893157i	$-0.648485\pi$
$251$	8.69184	−	15.0547i	0.548624	−	0.950245i	0.998369	−	0.0570882i	$-0.0181816\pi$
$252$	−5.53721	−	9.59073i	−0.348812	−	0.604159i
$253$	0.560833	−	1.42898i	0.0352592	−	0.0898391i
$254$	−3.61217	+	1.73953i	−0.226648	+	0.109148i
$255$	17.0570	−	5.26140i	1.06815	−	0.329481i
$256$	4.42216	+	19.3748i	0.276385	+	1.21092i
$257$	−24.3517			−1.51902			−0.759508	−	0.650498i	$-0.774560\pi$
$257$	−24.3517			−1.51902			−0.759508	+	0.650498i	$0.774560\pi$
$258$	−6.31974	+	19.4997i	−0.393450	+	1.21400i
$259$	21.7550			1.35179
$260$	−5.26085	−	23.0493i	−0.326264	−	1.42946i
$261$	−0.843994	+	0.260338i	−0.0522419	+	0.0161145i
$262$	45.7300	−	22.0224i	2.82521	−	1.36055i
$263$	−7.49599	+	19.0995i	−0.462223	+	1.17772i	0.489838	+	0.871814i	$0.337056\pi$
$263$	−7.49599	+	19.0995i	−0.462223	+	1.17772i	−0.952060	+	0.305910i	$0.901039\pi$
$264$	−1.61625	−	2.79943i	−0.0994733	−	0.172293i
$265$	3.64167	−	6.30755i	0.223706	−	0.387470i
$266$	0.191999	+	0.240759i	0.0117722	+	0.0147619i
$267$	−13.7338	+	9.36353i	−0.840493	+	0.573039i
$268$	−18.6812	−	2.81574i	−1.14114	−	0.171999i
$269$	15.3360	+	7.38545i	0.935055	+	0.450299i	0.838422	−	0.545021i	$-0.183478\pi$
$269$	15.3360	+	7.38545i	0.935055	+	0.450299i	0.0966331	+	0.995320i	$0.469193\pi$
$270$	−39.0213	+	36.2065i	−2.37476	+	2.20346i
$271$	−3.41724	+	0.515067i	−0.207583	+	0.0312881i	−0.252010	−	0.967725i	$-0.581092\pi$
$271$	−3.41724	+	0.515067i	−0.207583	+	0.0312881i	0.0444275	+	0.999013i	$0.485854\pi$
$272$	−1.96771	−	0.606957i	−0.119310	−	0.0368022i
$273$	0.481835	−	6.42965i	0.0291620	−	0.389140i
$274$	30.8761	−	38.7175i	1.86530	−	2.33901i
$275$	3.18640	+	8.11881i	0.192147	+	0.489582i
$276$	−6.79951	−	6.30902i	−0.409282	−	0.379758i
$277$	19.9087	+	13.5735i	1.19619	+	0.815552i	0.986747	−	0.162268i	$-0.0518809\pi$
$277$	19.9087	+	13.5735i	1.19619	+	0.815552i	0.209448	+	0.977820i	$0.432833\pi$
$278$	2.11090	+	28.1680i	0.126603	+	1.68941i
$279$	−0.904705	+	3.96377i	−0.0541632	+	0.237305i
$280$	−8.01634	+	35.1219i	−0.479068	+	2.09893i
$281$	0.429939	+	5.73714i	0.0256480	+	0.342249i	0.995235	+	0.0975031i	$0.0310856\pi$
$281$	0.429939	+	5.73714i	0.0256480	+	0.342249i	−0.969587	+	0.244746i	$0.921295\pi$
$282$	−20.2324	−	13.7942i	−1.20482	−	0.821434i
$283$	11.6970	+	10.8533i	0.695317	+	0.645160i	0.946472	−	0.322787i	$-0.104620\pi$
$283$	11.6970	+	10.8533i	0.695317	+	0.645160i	−0.251154	+	0.967947i	$0.580810\pi$
$284$	−8.96647	−	22.8462i	−0.532062	−	1.35567i
$285$	0.163711	−	0.205287i	0.00969741	−	0.0121602i
$286$	−0.224442	+	2.99497i	−0.0132716	+	0.177097i
$287$	−22.3030	−	6.87956i	−1.31650	−	0.406088i
$288$	−5.72393	+	0.862744i	−0.337286	+	0.0508377i
$289$	4.71715	−	4.37687i	0.277479	−	0.257463i
$290$	6.35800	+	3.06185i	0.373355	+	0.179798i
$291$	13.9284	+	2.09937i	0.816498	+	0.123067i
$292$	28.3983	−	19.3616i	1.66188	−	1.13305i
$293$	−3.77347	−	4.73178i	−0.220449	−	0.276434i	0.659293	−	0.751886i	$-0.270856\pi$
$293$	−3.77347	−	4.73178i	−0.220449	−	0.276434i	−0.879741	+	0.475453i	$0.842284\pi$
$294$	−1.12464	+	1.94794i	−0.0655905	+	0.113606i
$295$	11.7830	+	20.4087i	0.686032	+	1.18824i
$296$	−9.10795	+	23.2067i	−0.529389	+	1.34886i
$297$	3.82494	−	1.84199i	0.221946	−	0.106883i
$298$	−18.3130	+	5.64881i	−1.06084	+	0.327227i
$299$	0.780788	+	3.42085i	0.0451541	+	0.197833i
$300$	52.6998			3.04263
$301$	−17.8183	+	3.80130i	−1.02703	+	0.219103i
$302$	−10.5952			−0.609686
$303$	−0.687831	−	3.01359i	−0.0395149	−	0.173126i
$304$	−0.0289447	+	0.00892826i	−0.00166009	+	0.000512071i
$305$	−10.8031	+	5.20250i	−0.618584	+	0.297894i
$306$	3.25242	−	8.28704i	0.185929	−	0.473739i
$307$	−11.7476	−	20.3475i	−0.670472	−	1.16129i	−0.977770	−	0.209679i	$-0.932758\pi$
$307$	−11.7476	−	20.3475i	−0.670472	−	1.16129i	0.307298	−	0.951613i	$-0.400575\pi$
$308$	3.52837	−	6.11131i	0.201047	−	0.348224i
$309$	−4.46467	−	5.59852i	−0.253986	−	0.318488i
$310$	26.8396	−	18.2990i	1.52439	−	1.03931i
$311$	1.16489	+	0.175579i	0.0660550	+	0.00995619i	0.181987	−	0.983301i	$-0.441747\pi$
$311$	1.16489	+	0.175579i	0.0660550	+	0.00995619i	−0.115932	+	0.993257i	$0.536985\pi$
$312$	6.65695	+	3.20582i	0.376876	+	0.181494i
$313$	21.8138	−	20.2403i	1.23299	−	1.14405i	0.248496	−	0.968633i	$-0.420064\pi$
$313$	21.8138	−	20.2403i	1.23299	−	1.14405i	0.984495	−	0.175415i	$-0.0561268\pi$
$314$	22.9625	−	3.46103i	1.29585	−	0.195317i
$315$	−12.7748	−	3.94050i	−0.719778	−	0.222022i
$316$	3.38079	−	45.1135i	0.190184	−	2.53783i
$317$	−16.7284	+	20.9767i	−0.939560	+	1.17817i	0.0442619	+	0.999020i	$0.485906\pi$
$317$	−16.7284	+	20.9767i	−0.939560	+	1.17817i	−0.983822	+	0.179151i	$0.942665\pi$
$318$	2.04249	+	5.20419i	0.114537	+	0.291836i
$319$	−0.412565	−	0.382805i	−0.0230992	−	0.0214330i
$320$	42.4765	+	28.9600i	2.37451	+	1.61891i
$321$	−0.362340	−	4.83509i	−0.0202239	−	0.269869i
$322$	2.92216	−	12.8028i	0.162846	−	0.713473i
$323$	−0.0345821	+	0.151514i	−0.00192420	+	0.00843048i
$324$	−1.02339	−	13.6561i	−0.0568548	−	0.758674i
$325$	−16.4715	−	11.2301i	−0.913677	−	0.622934i
$326$	−36.3222	−	33.7021i	−2.01170	−	1.86659i
$327$	2.74151	+	6.98526i	0.151606	+	0.386286i
$328$	16.6760	−	20.9110i	0.920777	−	1.15462i
$329$	1.62649	−	21.7040i	0.0896713	−	1.19658i
$330$	−9.15847	−	2.82501i	−0.504157	−	0.155512i
$331$	2.75598	−	0.415397i	0.151482	−	0.0228323i	−0.0728632	−	0.997342i	$-0.523214\pi$
$331$	2.75598	−	0.415397i	0.151482	−	0.0228323i	0.224346	+	0.974510i	$0.427976\pi$
$332$	−14.0448	+	13.0317i	−0.770810	+	0.715207i
$333$	−8.33523	−	4.01403i	−0.456768	−	0.219968i
$334$	−50.3417	−	7.58779i	−2.75458	−	0.415186i
$335$	−18.8433	+	12.8472i	−1.02952	+	0.701915i
$336$	−1.47992	−	1.85576i	−0.0807364	−	0.101240i
$337$	−4.52447	+	7.83661i	−0.246463	+	0.426887i	−0.962542	−	0.271132i	$-0.912602\pi$
$337$	−4.52447	+	7.83661i	−0.246463	+	0.426887i	0.716079	+	0.698020i	$0.245935\pi$
$338$	11.6351	+	20.1525i	0.632864	+	1.09615i
$339$	0.0690706	−	0.175989i	0.00375140	−	0.00955841i
$340$	−40.2325	+	19.3750i	−2.18191	+	1.05075i
$341$	−2.47561	+	0.763625i	−0.134062	+	0.0413526i
$342$	−0.0291399	−	0.127670i	−0.00157571	−	0.00690363i
$343$	17.4496			0.942192
$344$	3.40484	−	20.5987i	0.183577	−	1.11061i
$345$	−11.1973			−0.602840
$346$	8.03498	+	35.2036i	0.431963	+	1.89255i
$347$	10.0705	−	3.10634i	0.540613	−	0.166757i	−0.0124100	−	0.999923i	$-0.503950\pi$
$347$	10.0705	−	3.10634i	0.540613	−	0.166757i	0.553023	+	0.833166i	$0.313474\pi$
$348$	−3.06391	+	1.47550i	−0.164243	+	0.0790951i
$349$	−4.48874	+	11.4371i	−0.240277	+	0.612215i	−0.999242	−	0.0389157i	$-0.987610\pi$
$349$	−4.48874	+	11.4371i	−0.240277	+	0.612215i	0.758966	+	0.651130i	$0.225705\pi$
$350$	37.3052	+	64.6145i	1.99405	+	3.45379i
$351$	−4.85190	+	8.40374i	−0.258975	+	0.448559i
$352$	−2.29977	−	2.88382i	−0.122578	−	0.153708i
$353$	3.53890	−	2.41278i	0.188356	−	0.128419i	−0.465470	−	0.885063i	$-0.654115\pi$
$353$	3.53890	−	2.41278i	0.188356	−	0.128419i	0.653827	+	0.756644i	$0.273162\pi$
$354$	−17.8871	−	2.69604i	−0.950687	−	0.143293i
$355$	−26.6933	−	12.8548i	−1.41673	−	0.682262i
$356$	30.4822	−	28.2834i	1.61556	−	1.49902i
$357$	−12.0422	+	1.81508i	−0.637343	+	0.0960640i
$358$	−15.4619	−	4.76935i	−0.817184	−	0.252068i
$359$	−2.55838	+	34.1392i	−0.135026	+	1.80180i	0.360036	+	0.932938i	$0.382764\pi$
$359$	−2.55838	+	34.1392i	−0.135026	+	1.80180i	−0.495062	+	0.868858i	$0.664855\pi$
$360$	9.55173	−	11.9775i	0.503421	−	0.631269i
$361$	−6.94064	−	17.6845i	−0.365297	−	0.930762i
$362$	9.35366	+	8.67893i	0.491617	+	0.456154i
$363$	−11.6245	−	7.92547i	−0.610129	−	0.415979i
$364$	1.20539	+	16.0848i	0.0631795	+	0.843071i
$365$	9.23266	−	40.4509i	0.483259	−	2.11730i
$366$	2.04806	−	8.97312i	0.107054	−	0.469032i
$367$	−2.31138	−	30.8433i	−0.120653	−	1.61000i	−0.648873	−	0.760897i	$-0.724759\pi$
$367$	−2.31138	−	30.8433i	−0.120653	−	1.61000i	0.528219	−	0.849108i	$-0.322860\pi$
$368$	1.06727	+	0.727652i	0.0556353	+	0.0379315i
$369$	7.27582	+	6.75098i	0.378764	+	0.351442i
$370$	27.0048	+	68.8072i	1.40391	+	3.57711i
$371$	−3.09817	+	3.88498i	−0.160849	+	0.201698i
$372$	−1.16983	+	15.6103i	−0.0606528	+	0.809355i
$373$	7.58815	+	2.34063i	0.392900	+	0.121193i	0.484909	−	0.874565i	$-0.338853\pi$
$373$	7.58815	+	2.34063i	0.392900	+	0.121193i	−0.0920093	+	0.995758i	$0.529329\pi$
$374$	5.60936	−	0.845475i	0.290053	−	0.0437185i
$375$	26.5068	−	24.5947i	1.36880	−	1.27006i
$376$	22.4713	+	10.8216i	1.15887	+	0.558082i
$377$	1.27206	+	0.191732i	0.0655144	+	0.00987471i
$378$	30.0067	−	20.4582i	1.54338	−	1.05226i
$379$	13.9219	+	17.4576i	0.715122	+	0.896735i	0.998051	−	0.0624060i	$-0.0198774\pi$
$379$	13.9219	+	17.4576i	0.715122	+	0.896735i	−0.282929	+	0.959141i	$0.591306\pi$
$380$	−0.328433	+	0.568862i	−0.0168483	+	0.0291820i
$381$	−1.16615	−	2.01983i	−0.0597435	−	0.103479i
$382$	−16.0959	+	41.0118i	−0.823539	+	2.09834i
$383$	22.6340	−	10.8999i	1.15654	−	0.556961i	0.245549	−	0.969384i	$-0.421032\pi$
$383$	22.6340	−	10.8999i	1.15654	−	0.556961i	0.910992	+	0.412423i	$0.135318\pi$
$384$	−25.0822	+	7.73682i	−1.27997	+	0.394818i
$385$	−1.89559	−	8.30511i	−0.0966081	−	0.423268i
$386$	−7.13855			−0.363343
$387$	7.52828	+	1.83123i	0.382684	+	0.0930867i
$388$	−35.2377			−1.78892
$389$	3.91826	+	17.1670i	0.198664	+	0.870403i	0.971733	+	0.236081i	$0.0758632\pi$
$389$	3.91826	+	17.1670i	0.198664	+	0.870403i	−0.773070	+	0.634321i	$0.781280\pi$
$390$	20.9339	−	6.45725i	1.06003	−	0.326976i
$391$	5.97109	−	2.87553i	0.301971	−	0.145422i
$392$	0.836989	−	2.13261i	0.0422743	−	0.107713i
$393$	14.7634	+	25.5709i	0.744714	+	1.28988i
$394$	−13.6112	+	23.5753i	−0.685724	+	1.18771i
$395$	−34.0503	−	42.6977i	−1.71326	−	2.14836i
$396$	−2.47946	+	1.69047i	−0.124598	+	0.0849492i
$397$	−1.43147	−	0.215759i	−0.0718434	−	0.0108287i	0.113022	−	0.993592i	$-0.463947\pi$
$397$	−1.43147	−	0.215759i	−0.0718434	−	0.0108287i	−0.184866	+	0.982764i	$0.559185\pi$
$398$	−0.559072	−	0.269235i	−0.0280238	−	0.0134955i
$399$	−0.131320	+	0.121847i	−0.00657420	+	0.00609996i
$400$	−7.25700	+	1.09382i	−0.362850	+	0.0546908i
$401$	7.37812	+	2.27585i	0.368446	+	0.113650i	0.473448	−	0.880822i	$-0.343009\pi$
$401$	7.37812	+	2.27585i	0.368446	+	0.113650i	−0.105003	+	0.994472i	$0.533485\pi$
$402$	1.30821	−	17.4569i	0.0652478	−	0.870672i
$403$	3.69211	−	4.62976i	0.183917	−	0.230625i
$404$	2.82512	+	7.19829i	0.140555	+	0.358129i
$405$	−12.1185	−	11.2443i	−0.602172	−	0.558734i
$406$	−3.97797	−	2.71214i	−0.197424	−	0.134601i
$407$	−0.440541	−	5.87861i	−0.0218368	−	0.291392i
$408$	3.10541	−	13.6057i	0.153741	−	0.673582i
$409$	−7.12781	+	31.2290i	−0.352448	+	1.54417i	0.419063	+	0.907957i	$0.362359\pi$
$409$	−7.12781	+	31.2290i	−0.352448	+	1.54417i	−0.771511	+	0.636216i	$0.780499\pi$
$410$	−5.92622	−	79.0800i	−0.292675	−	3.90548i
$411$	23.8026	+	16.2283i	1.17409	+	0.800484i
$412$	13.1317	+	12.1845i	0.646954	+	0.600286i
$413$	−5.87394	−	14.9666i	−0.289038	−	0.736456i
$414$	−3.48185	+	4.36610i	−0.171124	+	0.214582i
$415$	−1.72841	+	23.0640i	−0.0848442	+	1.13217i
$416$	8.05649	+	2.48510i	0.395002	+	0.121842i
$417$	−16.2487	+	2.44910i	−0.795703	+	0.119933i
$418$	0.0611695	−	0.0567570i	0.00299190	−	0.00277608i
$419$	19.9028	+	9.58467i	0.972314	+	0.468242i	0.851455	−	0.524428i	$-0.175721\pi$
$419$	19.9028	+	9.58467i	0.972314	+	0.468242i	0.120859	+	0.992670i	$0.461435\pi$
$420$	−50.8983	−	7.67168i	−2.48358	−	0.374340i
$421$	−12.5748	+	8.57335i	−0.612858	+	0.417840i	−0.829575	−	0.558395i	$-0.811417\pi$
$421$	−12.5748	+	8.57335i	−0.612858	+	0.417840i	0.216717	+	0.976234i	$0.430465\pi$
$422$	23.6881	+	29.7039i	1.15312	+	1.44596i
$423$	−4.62779	+	8.01557i	−0.225011	+	0.389730i
$424$	−2.84714	−	4.93139i	−0.138269	−	0.239489i
$425$	−13.7565	+	35.0511i	−0.667290	+	1.70023i
$426$	20.4896	−	9.86727i	0.992725	−	0.478071i
$427$	7.81715	−	2.41127i	0.378298	−	0.116690i
$428$	2.69910	+	11.8255i	0.130466	+	0.571609i
$429$	−1.74716			−0.0843539
$430$	−34.1409	−	51.6373i	−1.64642	−	2.49017i
$431$	16.5109			0.795301			0.397651	−	0.917537i	$-0.369826\pi$
$431$	16.5109			0.795301			0.397651	+	0.917537i	$0.369826\pi$
$432$	0.794913	+	3.48274i	0.0382453	+	0.167563i
$433$	24.1153	−	7.43859i	1.15891	−	0.357476i	0.345075	−	0.938575i	$-0.387853\pi$
$433$	24.1153	−	7.43859i	1.15891	−	0.357476i	0.813833	+	0.581099i	$0.197377\pi$
$434$	−19.9676	+	9.61591i	−0.958477	+	0.461578i
$435$	−1.49980	+	3.82143i	−0.0719100	+	0.183224i
$436$	−9.38620	−	16.2574i	−0.449517	−	0.778587i
$437$	0.0487442	−	0.0844275i	0.00233175	−	0.00403872i
$438$	19.8571	+	24.9001i	0.948811	+	1.18977i
$439$	15.6707	−	10.6841i	0.747922	−	0.509924i	−0.128358	−	0.991728i	$-0.540971\pi$
$439$	15.6707	−	10.6841i	0.747922	−	0.509924i	0.876279	+	0.481804i	$0.160018\pi$
$440$	9.65289	+	1.45494i	0.460184	+	0.0693615i
$441$	0.765978	+	0.368876i	0.0364752	+	0.0175655i
$442$	−9.50503	+	8.81938i	−0.452108	+	0.419495i
$443$	−37.0756	+	5.58825i	−1.76152	+	0.265506i	−0.948510	−	0.316748i	$-0.897409\pi$
$443$	−37.0756	+	5.58825i	−1.76152	+	0.265506i	−0.813007	+	0.582254i	$0.802171\pi$
$444$	−34.0378	−	10.4993i	−1.61536	−	0.498274i
$445$	3.75126	−	50.0571i	0.177827	−	2.37293i
$446$	7.03788	−	8.82523i	0.333253	−	0.417887i
$447$	−4.07304	−	10.3779i	−0.192648	−	0.490859i
$448$	−25.7113	−	23.8566i	−1.21474	−	1.12712i
$449$	−14.9462	−	10.1902i	−0.705357	−	0.480904i	0.156745	−	0.987639i	$-0.449900\pi$
$449$	−14.9462	−	10.1902i	−0.705357	−	0.480904i	−0.862102	+	0.506735i	$0.830852\pi$
$450$	−2.37106	−	31.6396i	−0.111773	−	1.49151i
$451$	−1.40735	+	6.16599i	−0.0662693	+	0.290345i
$452$	−0.105243	+	0.461100i	−0.00495022	+	0.0216883i
$453$	−0.460606	−	6.14636i	−0.0216412	−	0.288781i
$454$	−36.9225	−	25.1733i	−1.73286	−	1.18144i
$455$	14.2736	+	13.2440i	0.669159	+	0.620889i
$456$	−0.0749990	−	0.191094i	−0.00351215	−	0.00894881i
$457$	4.42658	−	5.55075i	0.207067	−	0.259653i	−0.667444	−	0.744660i	$-0.732612\pi$
$457$	4.42658	−	5.55075i	0.207067	−	0.259653i	0.874510	+	0.485007i	$0.161183\pi$
$458$	−1.25109	+	16.6946i	−0.0584594	+	0.780087i
$459$	17.5141	+	5.40239i	0.817489	+	0.252162i
$460$	27.6988	−	4.17493i	1.29147	−	0.194657i
$461$	1.48177	−	1.37488i	0.0690130	−	0.0640347i	−0.644912	−	0.764257i	$-0.723106\pi$
$461$	1.48177	−	1.37488i	0.0690130	−	0.0640347i	0.713925	+	0.700222i	$0.246916\pi$
$462$	5.89135	+	2.83712i	0.274090	+	0.131995i
$463$	−23.5610	−	3.55125i	−1.09497	−	0.165041i	−0.423374	−	0.905955i	$-0.639154\pi$
$463$	−23.5610	−	3.55125i	−1.09497	−	0.165041i	−0.671600	+	0.740914i	$0.734392\pi$
$464$	0.391289	−	0.266776i	0.0181651	−	0.0123848i
$465$	11.7822	+	14.7744i	0.546385	+	0.685145i
$466$	−10.2055	+	17.6764i	−0.472759	+	0.818842i
$467$	−8.68583	−	15.0443i	−0.401932	−	0.696167i	0.592027	−	0.805918i	$-0.298328\pi$
$467$	−8.68583	−	15.0443i	−0.401932	−	0.696167i	−0.993959	+	0.109751i	$0.964995\pi$
$468$	2.50598	−	6.38513i	0.115839	−	0.295153i
$469$	14.0187	−	6.75104i	0.647323	−	0.311734i
$470$	70.6647	−	21.7972i	3.25952	−	1.00543i
$471$	3.00602	+	13.1702i	0.138510	+	0.606852i
$472$	18.4244			0.848052
$473$	1.38800	+	4.73784i	0.0638203	+	0.217846i
$474$	41.9202			1.92546
$475$	0.123251	+	0.539998i	0.00565515	+	0.0247768i
$476$	29.1123	−	8.97997i	1.33436	−	0.411596i
$477$	1.90385	−	0.916848i	0.0871715	−	0.0419796i
$478$	5.09863	−	12.9911i	0.233206	−	0.594199i
$479$	−3.86370	−	6.69213i	−0.176537	−	0.305771i	0.764155	−	0.645033i	$-0.223156\pi$
$479$	−3.86370	−	6.69213i	−0.176537	−	0.305771i	−0.940692	+	0.339261i	$0.889823\pi$
$480$	−13.4525	+	23.3004i	−0.614019	+	1.06351i
$481$	8.40131	+	10.5349i	0.383067	+	0.480350i
$482$	−33.7082	+	22.9819i	−1.53537	+	1.04680i
$483$	7.55405	+	1.13859i	0.343721	+	0.0518076i
$484$	31.7108	+	15.2711i	1.44140	+	0.694142i
$485$	−31.1825	+	28.9332i	−1.41593	+	1.31379i
$486$	−26.2280	+	3.95323i	−1.18973	+	0.179322i
$487$	16.7051	+	5.15285i	0.756982	+	0.233498i	0.649139	−	0.760670i	$-0.275129\pi$
$487$	16.7051	+	5.15285i	0.756982	+	0.233498i	0.107843	+	0.994168i	$0.465606\pi$
$488$	−0.700556	+	9.34827i	−0.0317127	+	0.423176i
$489$	17.9718	−	22.5359i	0.812713	−	1.01911i
$490$	−2.48165	−	6.32314i	−0.112109	−	0.285650i
$491$	15.9175	+	14.7693i	0.718346	+	0.666528i	0.952107	−	0.305766i	$-0.0989127\pi$
$491$	15.9175	+	14.7693i	0.718346	+	0.666528i	−0.233760	+	0.972294i	$0.575103\pi$
$492$	31.5750	+	21.5275i	1.42351	+	0.970534i
$493$	−0.181578	−	2.42299i	−0.00817786	−	0.109126i
$494$	−0.0424423	+	0.185952i	−0.00190957	+	0.00836636i
$495$	−0.806105	+	3.53178i	−0.0362317	+	0.158742i
$496$	−0.162910	−	2.17388i	−0.00731487	−	0.0976102i
$497$	16.7010	+	11.3866i	0.749144	+	0.510758i
$498$	−13.0142	−	12.0754i	−0.583180	−	0.541112i
$499$	−13.1125	−	33.4100i	−0.586995	−	1.49564i	−0.847837	−	0.530257i	$-0.822095\pi$
$499$	−13.1125	−	33.4100i	−0.586995	−	1.49564i	0.260842	−	0.965382i	$-0.416000\pi$
$500$	−56.4000	+	70.7234i	−2.52229	+	3.16285i
$501$	2.21323	−	29.5335i	0.0988797	−	1.31946i
$502$	−38.5065	−	11.8777i	−1.71863	−	0.530127i
$503$	0.0899578	−	0.0135590i	0.00401102	−	0.000604564i	−0.147036	−	0.989131i	$-0.546973\pi$
$503$	0.0899578	−	0.0135590i	0.00401102	−	0.000604564i	0.151047	+	0.988527i	$0.451735\pi$
$504$	−7.66184	+	7.10915i	−0.341286	+	0.316667i
$505$	8.41042	+	4.05025i	0.374259	+	0.180234i
$506$	−3.51873	−	0.530363i	−0.156426	−	0.0235775i
$507$	−11.1848	+	7.62568i	−0.496735	+	0.338668i
$508$	3.63781	+	4.56168i	0.161402	+	0.202392i
$509$	−11.3425	+	19.6459i	−0.502749	+	0.870787i	0.497246	+	0.867610i	$0.334345\pi$
$509$	−11.3425	+	19.6459i	−0.502749	+	0.870787i	−0.999995	+	0.00317746i	$0.998989\pi$
$510$	−20.6889	−	35.8343i	−0.916122	−	1.58677i
$511$	−10.3419	+	26.3507i	−0.457498	+	1.16569i
$512$	6.43101	−	3.09701i	0.284213	−	0.136870i
$513$	0.257630	−	0.0794685i	0.0113747	−	0.00350862i
$514$	12.5611	+	55.0339i	0.554048	+	2.42744i
$515$	21.6250			0.952913
$516$	29.7130	+	2.65185i	1.30804	+	0.116741i
$517$	−5.89775			−0.259383
$518$	−11.2217	−	49.1656i	−0.493054	−	2.16021i
$519$	−20.0725	+	6.19156i	−0.881087	+	0.271779i
$520$	−20.1035	+	9.68136i	−0.881599	+	0.424556i
$521$	1.72346	−	4.39129i	0.0755060	−	0.192386i	−0.888137	−	0.459578i	$-0.848001\pi$
$521$	1.72346	−	4.39129i	0.0755060	−	0.192386i	0.963643	+	0.267192i	$0.0860958\pi$
$522$	1.02370	+	1.77311i	0.0448063	+	0.0776068i
$523$	−0.853098	+	1.47761i	−0.0373034	+	0.0646113i	−0.884074	−	0.467346i	$-0.845210\pi$
$523$	−0.853098	+	1.47761i	−0.0373034	+	0.0646113i	0.846771	+	0.531958i	$0.178543\pi$
$524$	−46.0546	−	57.7507i	−2.01191	−	2.52285i
$525$	−35.8616	+	24.4500i	−1.56513	+	1.06709i
$526$	47.0307	+	7.08874i	2.05064	+	0.309084i
$527$	−10.0771	−	4.85290i	−0.438968	−	0.211396i
$528$	−0.471493	+	0.437481i	−0.0205191	+	0.0190389i
$529$	18.6322	−	2.80835i	0.810095	−	0.122102i
$530$	−16.1333	−	4.97646i	−0.700785	−	0.216164i
$531$	−0.510945	+	6.81809i	−0.0221731	+	0.295880i
$532$	0.279416	−	0.350377i	0.0121142	−	0.0151908i
$533$	−5.28148	−	13.4570i	−0.228766	−	0.582887i
$534$	28.2454	+	26.2079i	1.22230	+	1.13413i
$535$	12.0983	+	8.24846i	0.523054	+	0.356612i
$536$	1.33246	+	17.7805i	0.0575537	+	0.768001i
$537$	2.09456	−	9.17688i	0.0903870	−	0.396011i
$538$	8.78018	−	38.4685i	0.378540	−	1.65849i
$539$	0.0404841	+	0.540223i	0.00174378	+	0.0232691i
$540$	64.0067	+	43.6390i	2.75441	+	1.87792i
$541$	−8.33253	−	7.73145i	−0.358243	−	0.332401i	0.480433	−	0.877031i	$-0.340480\pi$
$541$	−8.33253	−	7.73145i	−0.358243	−	0.332401i	−0.838676	+	0.544630i	$0.816670\pi$
$542$	2.92672	+	7.45716i	0.125713	+	0.320313i
$543$	−4.62808	+	5.80343i	−0.198610	+	0.249049i
$544$	1.19004	−	15.8799i	0.0510224	−	0.680846i
$545$	−21.6547	−	6.67960i	−0.927586	−	0.286123i
$546$	−14.7793	+	2.22762i	−0.632496	+	0.0953334i
$547$	−17.1076	+	15.8735i	−0.731467	+	0.678703i	−0.955204	−	0.295947i	$-0.904365\pi$
$547$	−17.1076	+	15.8735i	−0.731467	+	0.678703i	0.223737	+	0.974650i	$0.428174\pi$
$548$	−64.9316	−	31.2694i	−2.77374	−	1.33576i
$549$	−3.43997	−	0.518492i	−0.146814	−	0.0221287i
$550$	16.7046	−	11.3890i	0.712286	−	0.485628i
$551$	−0.0222847	−	0.0279441i	−0.000949358	−	0.00119046i
$552$	−4.37714	+	7.58142i	−0.186303	+	0.322687i
$553$	18.6298	+	32.2677i	0.792218	+	1.37216i
$554$	20.4063	−	51.9943i	0.866979	−	2.20903i
$555$	−38.7416	+	18.6570i	−1.64449	+	0.791944i
$556$	39.2815	−	12.1167i	1.66591	−	0.513865i
$557$	−1.28534	−	5.63146i	−0.0544618	−	0.238613i	0.940369	−	0.340155i	$-0.110479\pi$
$557$	−1.28534	−	5.63146i	−0.0544618	−	0.238613i	−0.994831	+	0.101542i	$0.967622\pi$
$558$	9.42464			0.398977
$559$	−8.72180	−	7.16055i	−0.368893	−	0.302859i
$560$	7.16814			0.302909
$561$	0.734322	+	3.21728i	0.0310031	+	0.135834i
$562$	12.7440	−	3.93099i	0.537571	−	0.165819i
$563$	−3.42474	+	1.64927i	−0.144336	+	0.0695084i	−0.504657	−	0.863320i	$-0.668381\pi$
$563$	−3.42474	+	1.64927i	−0.144336	+	0.0695084i	0.360322	+	0.932828i	$0.382667\pi$
$564$	−13.0195	+	33.1730i	−0.548218	+	1.39684i
$565$	0.285471	+	0.494450i	0.0120098	+	0.0208017i
$566$	18.4944	−	32.0333i	0.777378	−	1.34646i
$567$	7.03215	+	8.81804i	0.295323	+	0.370323i
$568$	−19.1384	+	13.0483i	−0.803030	+	0.547497i
$569$	35.8718	+	5.40680i	1.50382	+	0.226665i	0.848707	−	0.528863i	$-0.177381\pi$
$569$	35.8718	+	5.40680i	1.50382	+	0.226665i	0.655116	+	0.755528i	$0.272620\pi$
$570$	−0.548387	−	0.264089i	−0.0229694	−	0.0110615i
$571$	−19.4633	+	18.0593i	−0.814514	+	0.755758i	−0.972803	−	0.231635i	$-0.925593\pi$
$571$	−19.4633	+	18.0593i	−0.814514	+	0.755758i	0.158289	+	0.987393i	$0.449402\pi$
$572$	4.32199	−	0.651435i	0.180711	−	0.0272379i
$573$	−24.4910	−	7.55446i	−1.02312	−	0.315592i
$574$	−4.04319	+	53.9526i	−0.168759	+	2.25194i
$575$	14.7269	−	18.4670i	0.614156	−	0.770127i
$576$	5.44923	+	13.8844i	0.227051	+	0.578517i
$577$	9.54816	+	8.85940i	0.397495	+	0.368821i	0.853444	−	0.521184i	$-0.174510\pi$
$577$	9.54816	+	8.85940i	0.397495	+	0.368821i	−0.455949	+	0.890006i	$0.650700\pi$
$578$	−12.3248	−	8.40289i	−0.512643	−	0.349514i
$579$	−0.310335	−	4.14113i	−0.0128971	−	0.172099i
$580$	2.28525	−	10.0123i	0.0948899	−	0.415740i
$581$	3.51130	−	15.3840i	0.145673	−	0.638236i
$582$	−2.44008	−	32.5606i	−0.101145	−	1.34968i
$583$	1.11253	+	0.758511i	0.0460763	+	0.0314143i
$584$	−23.7793	−	22.0639i	−0.983994	−	0.913013i
$585$	−3.02515	−	7.70795i	−0.125074	−	0.318685i
$586$	−8.74722	+	10.9687i	−0.361344	+	0.453111i
$587$	−0.430770	+	5.74822i	−0.0177798	+	0.237255i	0.981233	+	0.192827i	$0.0617655\pi$
$587$	−0.430770	+	5.74822i	−0.0177798	+	0.237255i	−0.999013	+	0.0444278i	$0.985854\pi$
$588$	3.12796	+	0.964848i	0.128995	+	0.0397896i
$589$	−0.162689	+	0.0245215i	−0.00670350	+	0.00101039i
$590$	40.0450	−	37.1564i	1.64863	−	1.52970i
$591$	−14.2680	−	6.87109i	−0.586905	−	0.282639i
$592$	4.90508	+	0.739322i	0.201598	+	0.0303859i
$593$	6.69370	−	4.56369i	0.274877	−	0.187408i	−0.418033	−	0.908432i	$-0.637280\pi$
$593$	6.69370	−	4.56369i	0.274877	−	0.187408i	0.692911	+	0.721024i	$0.256328\pi$
$594$	−6.13583	−	7.69408i	−0.251756	−	0.315692i
$595$	18.3888	−	31.8503i	0.753866	−	1.30573i
$596$	13.9450	+	24.1534i	0.571209	+	0.989362i
$597$	0.131881	−	0.336026i	0.00539752	−	0.0137526i
$598$	7.32826	−	3.52910i	0.299675	−	0.144316i
$599$	−8.12129	+	2.50509i	−0.331827	+	0.102355i	−0.456192	−	0.889882i	$-0.650787\pi$
$599$	−8.12129	+	2.50509i	−0.331827	+	0.102355i	0.124365	+	0.992237i	$0.460311\pi$
$600$	−11.0677	−	48.4908i	−0.451837	−	1.97963i
$601$	35.6791			1.45538			0.727691	−	0.685905i	$-0.240594\pi$
$601$	35.6791			1.45538			0.727691	+	0.685905i	$0.240594\pi$
$602$	17.7818	+	38.3078i	0.724734	+	1.56131i
$603$	−6.61676			−0.269455
$604$	3.43110	+	15.0326i	0.139609	+	0.611668i
$605$	40.6004	−	12.5236i	1.65064	−	0.509155i
$606$	−6.45579	+	3.10895i	−0.262249	+	0.126292i
$607$	12.0041	−	30.5861i	0.487233	−	1.24145i	−0.450088	−	0.892984i	$-0.648607\pi$
$607$	12.0041	−	30.5861i	0.487233	−	1.24145i	0.937321	−	0.348466i	$-0.113297\pi$
$608$	−0.117123	−	0.202864i	−0.00474998	−	0.00822721i
$609$	1.40040	−	2.42556i	0.0567469	−	0.0982886i
$610$	17.3299	+	21.7311i	0.701669	+	0.879865i
$611$	11.1383	−	7.59397i	0.450608	−	0.307219i
$612$	−12.8110	−	1.93095i	−0.517854	−	0.0780539i
$613$	2.01111	+	0.968499i	0.0812280	+	0.0391173i	0.474057	−	0.880494i	$-0.342789\pi$
$613$	2.01111	+	0.968499i	0.0812280	+	0.0391173i	−0.392829	+	0.919612i	$0.628503\pi$
$614$	−39.9249	+	37.0449i	−1.61124	+	1.49501i
$615$	45.6172	−	6.87569i	1.83946	−	0.277255i
$616$	−6.36422	−	1.96310i	−0.256422	−	0.0790956i
$617$	−0.983300	+	13.1212i	−0.0395862	+	0.528241i	0.941797	+	0.336182i	$0.109136\pi$
$617$	−0.983300	+	13.1212i	−0.0395862	+	0.528241i	−0.981383	+	0.192059i	$0.938483\pi$
$618$	−10.3495	+	12.9778i	−0.416316	+	0.522044i
$619$	−5.06713	−	12.9108i	−0.203665	−	0.518930i	0.792149	−	0.610327i	$-0.208962\pi$
$619$	−5.06713	−	12.9108i	−0.203665	−	0.518930i	−0.995815	+	0.0913968i	$0.970867\pi$
$620$	−34.6544	−	32.1546i	−1.39175	−	1.29136i
$621$	−9.49953	−	6.47667i	−0.381203	−	0.259900i
$622$	−0.204074	−	2.72318i	−0.00818263	−	0.109190i
$623$	−7.62076	+	33.3887i	−0.305319	+	1.33769i
$624$	0.327144	−	1.43331i	0.0130962	−	0.0573783i
$625$	3.83193	+	51.1336i	0.153277	+	2.04534i
$626$	−56.9943	−	38.8581i	−2.27795	−	1.55308i
$627$	0.0355844	+	0.0330175i	0.00142110	+	0.00131859i
$628$	−12.3466	−	31.4586i	−0.492683	−	1.25534i
$629$	15.8683	−	19.8982i	0.632709	−	0.793392i
$630$	−2.31587	+	30.9032i	−0.0922666	+	1.23121i
$631$	−5.11794	−	1.57867i	−0.203742	−	0.0628461i	0.191204	−	0.981550i	$-0.438761\pi$
$631$	−5.11794	−	1.57867i	−0.203742	−	0.0628461i	−0.394946	+	0.918704i	$0.629237\pi$
$632$	−42.2203	+	6.36369i	−1.67944	+	0.253134i
$633$	−16.2017	+	15.0330i	−0.643959	+	0.597506i
$634$	56.0355	+	26.9853i	2.22545	+	1.07172i
$635$	6.96470	+	1.04976i	0.276386	+	0.0416584i
$636$	6.72233	−	4.58321i	0.266558	−	0.181736i
$637$	−0.772051	−	0.968121i	−0.0305898	−	0.0383584i
$638$	−0.652314	+	1.12984i	−0.0258254	+	0.0447309i
$639$	−4.29789	−	7.44417i	−0.170022	−	0.294487i
$640$	28.9599	−	73.7885i	1.14474	−	2.91675i
$641$	−4.56273	+	2.19729i	−0.180217	+	0.0867879i	−0.521817	−	0.853058i	$-0.674746\pi$
$641$	−4.56273	+	2.19729i	−0.180217	+	0.0867879i	0.341600	+	0.939845i	$0.389031\pi$
$642$	−10.7402	+	3.31292i	−0.423883	+	0.130751i
$643$	−4.59652	−	20.1387i	−0.181269	−	0.794191i	−0.981027	−	0.193869i	$-0.937896\pi$
$643$	−4.59652	−	20.1387i	−0.181269	−	0.794191i	0.799758	−	0.600322i	$-0.204961\pi$
$644$	−19.1111			−0.753082
$645$	28.4710	−	22.0502i	1.12104	−	0.868226i
$646$	0.360255			0.0141740
$647$	−6.78518	−	29.7278i	−0.266753	−	1.16872i	−0.913766	−	0.406242i	$-0.866839\pi$
$647$	−6.78518	−	29.7278i	−0.266753	−	1.16872i	0.647013	−	0.762479i	$-0.276018\pi$
$648$	−12.3505	+	3.80963i	−0.485174	+	0.149656i
$649$	−3.92529	+	1.89032i	−0.154081	+	0.0742015i
$650$	−16.8832	+	43.0178i	−0.662215	+	1.68730i
$651$	−6.44631	−	11.1653i	−0.252651	−	0.437604i
$652$	−36.0546	+	62.4483i	−1.41201	+	2.44567i
$653$	25.9574	+	32.5496i	1.01579	+	1.27376i	0.961374	+	0.275244i	$0.0887587\pi$
$653$	25.9574	+	32.5496i	1.01579	+	1.27376i	0.0544173	+	0.998518i	$0.482670\pi$
$654$	14.3723	−	9.79887i	0.562001	−	0.383166i
$655$	−88.1729	−	13.2899i	−3.44520	−	0.519280i
$656$	−4.79483	−	2.30907i	−0.187207	−	0.0901540i
$657$	8.82438	−	8.18783i	0.344272	−	0.319438i
$658$	−49.8892	+	7.51959i	−1.94488	+	0.293144i
$659$	−20.9158	−	6.45166i	−0.814762	−	0.251321i	−0.140754	−	0.990045i	$-0.544953\pi$
$659$	−20.9158	−	6.45166i	−0.814762	−	0.251321i	−0.674008	+	0.738724i	$0.735429\pi$
$660$	−1.04233	+	13.9090i	−0.0405728	+	0.541406i
$661$	−3.40742	+	4.27277i	−0.132533	+	0.166191i	−0.843670	−	0.536863i	$-0.819609\pi$
$661$	−3.40742	+	4.27277i	−0.132533	+	0.166191i	0.711136	+	0.703054i	$0.248181\pi$
$662$	−2.36038	−	6.01414i	−0.0917386	−	0.233746i
$663$	−5.52940	−	5.13053i	−0.214744	−	0.199253i
$664$	14.9405	+	10.1862i	0.579803	+	0.395303i
$665$	−0.0404284	−	0.539480i	−0.00156775	−	0.0209201i
$666$	−4.77208	+	20.9078i	−0.184914	+	0.810162i
$667$	−0.339165	+	1.48598i	−0.0131325	+	0.0575373i
$668$	5.53674	+	73.8826i	0.214223	+	2.85861i
$669$	5.42554	+	3.69907i	0.209763	+	0.143014i
$670$	38.7539	+	35.9584i	1.49719	+	1.38919i
$671$	−0.809867	−	2.06351i	−0.0312646	−	0.0796608i
$672$	11.4448	−	14.3513i	0.441492	−	0.553613i
$673$	0.265593	−	3.54410i	0.0102379	−	0.136615i	−0.989743	−	0.142862i	$-0.954369\pi$
$673$	0.265593	−	3.54410i	0.0102379	−	0.136615i	0.999980	+	0.00624712i	$0.00198853\pi$
$674$	20.0443	+	6.18284i	0.772076	+	0.238154i
$675$	64.5930	−	9.73582i	2.48618	−	0.374732i
$676$	24.8248	−	23.0341i	0.954800	−	0.885925i
$677$	−8.78571	−	4.23097i	−0.337662	−	0.162610i	0.257367	−	0.966314i	$-0.417145\pi$
$677$	−8.78571	−	4.23097i	−0.337662	−	0.162610i	−0.595029	+	0.803704i	$0.702859\pi$
$678$	−0.433357	−	0.0653180i	−0.0166430	−	0.00250852i
$679$	23.9788	−	16.3485i	0.920223	−	0.627398i
$680$	26.2769	+	32.9502i	1.00767	+	1.26358i
$681$	12.9981	−	22.5134i	0.498088	−	0.862714i
$682$	3.00274	+	5.20089i	0.114981	+	0.199152i
$683$	−7.66440	+	19.5286i	−0.293270	+	0.747240i	0.705969	+	0.708242i	$0.250512\pi$
$683$	−7.66440	+	19.5286i	−0.293270	+	0.747240i	−0.999239	+	0.0389974i	$0.987584\pi$
$684$	−0.171704	+	0.0826882i	−0.00656526	+	0.00316166i
$685$	−83.1341	+	25.6435i	−3.17639	+	0.979787i
$686$	−9.00091	−	39.4356i	−0.343656	−	1.50566i
$687$	−9.73904			−0.371568
$688$	−4.14665	+	0.251538i	−0.158089	+	0.00958981i
$689$	−3.07775			−0.117253
$690$	5.77579	+	25.3054i	0.219881	+	0.963360i
$691$	8.48595	−	2.61757i	0.322821	−	0.0995770i	−0.129109	−	0.991630i	$-0.541212\pi$
$691$	8.48595	−	2.61757i	0.322821	−	0.0995770i	0.451930	+	0.892053i	$0.350736\pi$
$692$	47.3452	−	22.8003i	1.79980	−	0.866736i
$693$	0.902953	−	2.30069i	0.0343003	−	0.0873958i
$694$	−12.2148	−	21.1566i	−0.463667	−	0.803095i
$695$	24.8121	−	42.9758i	0.941177	−	1.63017i
$696$	2.00112	+	2.50932i	0.0758522	+	0.0951157i
$697$	−22.5603	+	15.3814i	−0.854532	+	0.582610i
$698$	28.1628	+	4.24486i	1.06598	+	0.160671i
$699$	−10.6979	−	5.15182i	−0.404630	−	0.194860i
$700$	79.5952	−	73.8535i	3.00842	−	2.79140i
$701$	24.8182	−	3.74074i	0.937370	−	0.141286i	0.337448	−	0.941344i	$-0.390436\pi$
$701$	24.8182	−	3.74074i	0.937370	−	0.141286i	0.599922	+	0.800058i	$0.295198\pi$
$702$	21.4949	+	6.63029i	0.811271	+	0.250244i
$703$	0.0279772	−	0.373330i	0.00105518	−	0.0140804i
$704$	−5.92582	+	7.43074i	−0.223338	+	0.280057i
$705$	15.7167	+	40.0456i	0.591926	+	1.50820i
$706$	−7.27823	−	6.75321i	−0.273920	−	0.254160i
$707$	−5.26210	−	3.58764i	−0.197902	−	0.134927i
$708$	1.96727	+	26.2515i	0.0739347	+	0.986590i
$709$	−11.1254	+	48.7436i	−0.417824	+	1.83060i	0.126806	+	0.991928i	$0.459528\pi$
$709$	−11.1254	+	48.7436i	−0.417824	+	1.83060i	−0.544629	+	0.838677i	$0.683330\pi$
$710$	−15.2824	+	66.9566i	−0.573538	+	2.51284i
$711$	−1.18408	−	15.8004i	−0.0444064	−	0.592563i
$712$	−32.4261	−	22.1078i	−1.21522	−	0.828524i
$713$	5.14322	+	4.77221i	0.192615	+	0.178721i
$714$	10.3137	+	26.2788i	0.385979	+	0.983458i
$715$	3.28973	−	4.12519i	0.123029	−	0.154273i
$716$	−1.75973	+	23.4820i	−0.0657642	+	0.877562i
$717$	7.75789	+	2.39299i	0.289724	+	0.0893679i
$718$	78.4729	−	11.8279i	2.92858	−	0.441413i
$719$	−8.04392	+	7.46367i	−0.299988	+	0.278348i	−0.815776	−	0.578368i	$-0.803690\pi$
$719$	−8.04392	+	7.46367i	−0.299988	+	0.278348i	0.515788	+	0.856716i	$0.327499\pi$
$720$	−2.74640	−	1.32260i	−0.102352	−	0.0492903i
$721$	−14.5890	−	2.19893i	−0.543321	−	0.0818925i
$722$	−36.3861	+	24.8076i	−1.35415	+	0.923245i
$723$	−14.7974	−	18.5553i	−0.550319	−	0.690079i
$724$	9.28473	−	16.0816i	0.345064	−	0.597669i
$725$	−4.32989	−	7.49958i	−0.160808	−	0.278527i
$726$	−11.9151	+	30.3591i	−0.442210	+	1.12673i
$727$	−21.2553	+	10.2360i	−0.788316	+	0.379633i	−0.784318	−	0.620359i	$-0.786987\pi$
$727$	−21.2553	+	10.2360i	−0.788316	+	0.379633i	−0.00399815	+	0.999992i	$0.501273\pi$
$728$	14.5470	−	4.48714i	0.539146	−	0.166305i
$729$	−6.14342	−	26.9161i	−0.227534	−	0.996892i
$730$	−96.1799			−3.55978
$731$	−9.51991	+	19.0701i	−0.352107	+	0.705333i
$732$	−13.3944			−0.495071
$733$	7.85287	+	34.4057i	0.290052	+	1.27080i	0.884451	+	0.466633i	$0.154533\pi$
$733$	7.85287	+	34.4057i	0.290052	+	1.27080i	−0.594399	+	0.804170i	$0.702610\pi$
$734$	−68.5124	+	21.1333i	−2.52884	+	0.780043i
$735$	3.56022	−	1.71451i	0.131321	−	0.0632406i
$736$	−3.64951	+	9.29881i	−0.134523	+	0.342759i
$737$	−2.10813	−	3.65139i	−0.0776541	−	0.134501i
$738$	11.5039	−	19.9254i	0.423465	−	0.733464i
$739$	−13.7042	−	17.1846i	−0.504119	−	0.632145i	0.463034	−	0.886340i	$-0.346761\pi$
$739$	−13.7042	−	17.1846i	−0.504119	−	0.632145i	−0.967153	+	0.254196i	$0.918189\pi$
$740$	88.8794	−	60.5969i	3.26727	−	2.22759i
$741$	−0.109717	−	0.0165372i	−0.00403056	−	0.000607509i
$742$	10.3780	+	4.99779i	0.380989	+	0.183475i
$743$	−1.34948	+	1.25213i	−0.0495075	+	0.0459362i	−0.704539	−	0.709666i	$-0.748846\pi$
$743$	−1.34948	+	1.25213i	−0.0495075	+	0.0459362i	0.655031	+	0.755602i	$0.272656\pi$
$744$	14.6092	−	2.20198i	0.535599	−	0.0807285i
$745$	32.1722	+	9.92381i	1.17870	+	0.363580i
$746$	1.37561	−	18.3563i	0.0503648	−	0.672071i
$747$	−4.18383	+	5.24635i	−0.153078	+	0.191954i
$748$	−3.01608	−	7.68483i	−0.110279	−	0.280985i
$749$	−7.32316	−	6.79490i	−0.267582	−	0.248280i
$750$	−69.2559	−	47.2178i	−2.52887	−	1.72415i
$751$	−2.39276	−	31.9291i	−0.0873129	−	1.16511i	−0.853005	−	0.521903i	$-0.825222\pi$
$751$	−2.39276	−	31.9291i	−0.0873129	−	1.16511i	0.765692	−	0.643207i	$-0.222397\pi$
$752$	1.10431	−	4.83830i	0.0402700	−	0.176435i
$753$	5.21634	−	22.8543i	0.190094	−	0.832857i
$754$	−0.222848	−	2.97371i	−0.00811566	−	0.108296i
$755$	15.3793	+	10.4854i	0.559710	+	0.381604i
$756$	−38.7436	−	35.9488i	−1.40909	−	1.30745i
$757$	6.22743	+	15.8672i	0.226340	+	0.576704i	0.998257	−	0.0590188i	$-0.0187972\pi$
$757$	6.22743	+	15.8672i	0.226340	+	0.576704i	−0.771917	+	0.635723i	$0.780702\pi$
$758$	32.2722	−	40.4681i	1.17218	−	1.46987i
$759$	0.154698	−	2.06430i	0.00561517	−	0.0749292i
$760$	0.592404	+	0.182732i	0.0214887	+	0.00662840i
$761$	−2.81970	+	0.425001i	−0.102214	+	0.0154063i	−0.199950	−	0.979806i	$-0.564078\pi$
$761$	−2.81970	+	0.425001i	−0.102214	+	0.0154063i	0.0977361	+	0.995212i	$0.468840\pi$
$762$	−3.96321	+	3.67732i	−0.143572	+	0.133215i
$763$	13.9298	+	6.70823i	0.504292	+	0.242854i
$764$	63.4004	+	9.55607i	2.29375	+	0.345727i
$765$	−12.9222	+	8.81019i	−0.467202	+	0.318533i
$766$	−36.3085	−	45.5295i	−1.31188	−	1.64505i
$767$	4.97919	−	8.62421i	0.179788	−	0.311402i
$768$	13.3995	+	23.2085i	0.483511	+	0.837466i
$769$	17.5058	−	44.6040i	0.631275	−	1.60846i	−0.153126	−	0.988207i	$-0.548934\pi$
$769$	17.5058	−	44.6040i	0.631275	−	1.60846i	0.784400	−	0.620255i	$-0.212971\pi$
$770$	−17.7915	+	8.56791i	−0.641160	+	0.308766i
$771$	−31.3795	+	9.67930i	−1.13011	+	0.348591i
$772$	2.31171	+	10.1283i	0.0832003	+	0.364524i
$773$	12.7995			0.460366			0.230183	−	0.973147i	$-0.426067\pi$
$773$	12.7995			0.460366			0.230183	+	0.973147i	$0.426067\pi$
$774$	0.255264	−	17.9582i	0.00917527	−	0.645495i
$775$	−39.8627			−1.43191
$776$	7.40041	+	32.4233i	0.265659	+	1.16393i
$777$	28.0335	−	8.64718i	1.00570	−	0.310216i
$778$	36.7757	−	17.7103i	1.31847	−	0.634943i
$779$	−0.146739	+	0.373886i	−0.00525749	+	0.0133959i
$780$	−15.9407	−	27.6102i	−0.570770	−	0.988603i
$781$	2.73866	−	4.74350i	0.0979970	−	0.169736i
$782$	−9.57861	−	12.0112i	−0.342530	−	0.429519i
$783$	−3.48278	+	2.37452i	−0.124464	+	0.0848583i
$784$	−0.450760	−	0.0679411i	−0.0160986	−	0.00242647i
$785$	−36.7559	−	17.7007i	−1.31188	−	0.631766i
$786$	50.1741	−	46.5548i	1.78965	−	1.66055i
$787$	−13.0915	+	1.97322i	−0.466660	+	0.0703377i	−0.378164	−	0.925739i	$-0.623444\pi$
$787$	−13.0915	+	1.97322i	−0.466660	+	0.0703377i	−0.0884966	+	0.996076i	$0.528206\pi$
$788$	37.8568	+	11.6773i	1.34859	+	0.415986i
$789$	−2.06766	+	27.5910i	−0.0736107	+	0.982267i
$790$	−78.9314	+	98.9768i	−2.80825	+	3.52144i
$791$	−0.142310	−	0.362600i	−0.00505997	−	0.0128926i
$792$	2.07617	+	1.92641i	0.0737736	+	0.0684519i
$793$	4.18647	+	2.85429i	0.148666	+	0.101359i
$794$	0.250775	+	3.34636i	0.00889968	+	0.118758i
$795$	2.18552	−	9.57538i	0.0775123	−	0.339604i
$796$	−0.200947	+	0.880406i	−0.00712238	+	0.0312052i
$797$	0.866491	+	11.5625i	0.0306927	+	0.409566i	0.991297	+	0.131645i	$0.0420260\pi$
$797$	0.866491	+	11.5625i	0.0306927	+	0.409566i	−0.960604	+	0.277920i	$0.910355\pi$
$798$	0.343106	+	0.233926i	0.0121458	+	0.00828089i
$799$	−18.6651	−	17.3187i	−0.660324	−	0.612691i
$800$	−20.7349	−	52.8316i	−0.733089	−	1.86788i
$801$	9.08039	−	11.3864i	0.320840	−	0.402320i
$802$	1.33754	−	17.8482i	0.0472301	−	0.630242i
$803$	7.32986	+	2.26096i	0.258665	+	0.0797876i
$804$	−25.1917	+	3.79704i	−0.888444	+	0.133911i
$805$	−16.9118	+	15.6918i	−0.596062	+	0.553065i
$806$	−12.3676	−	5.95591i	−0.435629	−	0.209788i
$807$	22.6976	+	3.42111i	0.798992	+	0.120429i
$808$	6.03006	−	4.11123i	0.212137	−	0.144632i
$809$	−15.0173	−	18.8311i	−0.527980	−	0.662066i	0.444302	−	0.895877i	$-0.353452\pi$
$809$	−15.0173	−	18.8311i	−0.527980	−	0.662066i	−0.972282	+	0.233811i	$0.924880\pi$
$810$	−19.1607	+	33.1873i	−0.673239	+	1.16608i
$811$	9.67307	+	16.7542i	0.339667	+	0.588321i	0.984370	−	0.176112i	$-0.0563522\pi$
$811$	9.67307	+	16.7542i	0.339667	+	0.588321i	−0.644703	+	0.764433i	$0.723019\pi$
$812$	−2.55981	+	6.52228i	−0.0898316	+	0.228887i
$813$	−4.19872	+	2.02200i	−0.147256	+	0.0709146i
$814$	−13.0582	+	4.02792i	−0.457689	+	0.141178i
$815$	19.3700	+	84.8657i	0.678503	+	2.97271i
$816$	−2.77683			−0.0972086
$817$	0.0423181	+	0.310661i	0.00148052	+	0.0108687i
$818$	74.2530			2.59620
$819$	1.25709	+	5.50765i	0.0439261	+	0.192453i
$820$	−110.280	+	34.0170i	−3.85116	+	1.18793i
$821$	4.68010	−	2.25382i	0.163336	−	0.0786587i	−0.350429	−	0.936589i	$-0.613964\pi$
$821$	4.68010	−	2.25382i	0.163336	−	0.0786587i	0.513766	+	0.857930i	$0.328250\pi$
$822$	24.3975	−	62.1638i	0.850961	−	2.16821i
$823$	27.1185	+	46.9706i	0.945290	+	1.63729i	0.755169	+	0.655530i	$0.227555\pi$
$823$	27.1185	+	46.9706i	0.945290	+	1.63729i	0.190122	+	0.981761i	$0.439112\pi$
$824$	8.45347	−	14.6418i	0.294491	−	0.510073i
$825$	7.33304	+	9.19534i	0.255304	+	0.320141i
$826$	−30.7939	+	20.9950i	−1.07146	+	0.730508i
$827$	−3.32662	−	0.501407i	−0.115678	−	0.0174356i	0.0909482	−	0.995856i	$-0.471010\pi$
$827$	−3.32662	−	0.501407i	−0.115678	−	0.0174356i	−0.206626	+	0.978420i	$0.566248\pi$
$828$	7.32223	+	3.52620i	0.254465	+	0.122544i
$829$	−29.6523	+	27.5133i	−1.02987	+	0.955578i	−0.999034	−	0.0439467i	$-0.986007\pi$
$829$	−29.6523	+	27.5133i	−1.02987	+	0.955578i	−0.0308341	+	0.999525i	$0.509816\pi$
$830$	53.0153	−	7.99078i	1.84019	−	0.277364i
$831$	31.0494	+	9.57747i	1.07709	+	0.332239i
$832$	1.62346	−	21.6636i	0.0562834	−	0.751050i
$833$	−1.45824	+	1.82857i	−0.0505249	+	0.0633562i
$834$	13.9163	+	35.4582i	0.481882	+	1.22782i
$835$	65.5635	+	60.8341i	2.26892	+	2.10525i
$836$	−0.100336	−	0.0684082i	−0.00347021	−	0.00236595i
$837$	1.45003	+	19.3493i	0.0501202	+	0.668808i
$838$	11.3947	−	49.9235i	0.393624	−	1.72458i
$839$	0.0182394	−	0.0799120i	0.000629694	−	0.00275887i	−0.974612	−	0.223900i	$-0.928121\pi$
$839$	0.0182394	−	0.0799120i	0.000629694	−	0.00275887i	0.975242	+	0.221141i	$0.0709782\pi$
$840$	3.63040	+	48.4443i	0.125261	+	1.67149i
$841$	−23.4992	−	16.0215i	−0.810318	−	0.552465i
$842$	25.8618	+	23.9962i	0.891257	+	0.826965i
$843$	2.83442	+	7.22197i	0.0976225	+	0.248738i
$844$	34.4733	−	43.2281i	1.18662	−	1.48797i
$845$	3.05503	−	40.7666i	0.105096	−	1.40241i
$846$	20.5020	+	6.32403i	0.704873	+	0.217425i
$847$	−28.6638	+	4.32038i	−0.984901	+	0.148450i
$848$	−0.830567	+	0.770654i	−0.0285218	+	0.0264644i
$849$	19.3867	+	9.33616i	0.665351	+	0.320416i
$850$	86.3101	+	13.0092i	2.96041	+	0.446210i
$851$	−13.1910	+	8.99347i	−0.452181	+	0.308292i
$852$	−20.6351	−	25.8755i	−0.706945	−	0.886481i
$853$	12.0750	−	20.9145i	0.413441	−	0.716101i	−0.581823	−	0.813316i	$-0.697660\pi$
$853$	12.0750	−	20.9145i	0.413441	−	0.716101i	0.995263	+	0.0972152i	$0.0309935\pi$
$854$	−9.48164	−	16.4227i	−0.324455	−	0.561973i
$855$	−0.0840500	+	0.214156i	−0.00287445	+	0.00732398i
$856$	10.3142	−	4.96706i	0.352532	−	0.169771i
$857$	40.2162	−	12.4051i	1.37376	−	0.423749i	0.481966	−	0.876190i	$-0.339923\pi$
$857$	40.2162	−	12.4051i	1.37376	−	0.423749i	0.891794	+	0.452441i	$0.149447\pi$
$858$	0.901225	+	3.94853i	0.0307673	+	0.134800i
$859$	−2.35350			−0.0803004			−0.0401502	−	0.999194i	$-0.512784\pi$
$859$	−2.35350			−0.0803004			−0.0401502	+	0.999194i	$0.512784\pi$
$860$	−62.2076	+	65.1614i	−2.12126	+	2.22199i
$861$	−31.4741			−1.07263
$862$	−8.51667	−	37.3140i	−0.290079	−	1.27092i
$863$	−29.2992	+	9.03761i	−0.997356	+	0.307644i	−0.750113	−	0.661310i	$-0.770001\pi$
$863$	−29.2992	+	9.03761i	−0.997356	+	0.307644i	−0.247243	+	0.968953i	$0.579525\pi$
$864$	−24.8901	+	11.9864i	−0.846778	+	0.407787i
$865$	23.1758	−	59.0509i	0.787999	−	2.00779i
$866$	−29.2501	−	50.6627i	−0.993960	−	1.72159i
$867$	4.33878	−	7.51499i	0.147353	−	0.255222i
$868$	20.1094	+	25.2164i	0.682557	+	0.855899i
$869$	8.34206	−	5.68752i	0.282985	−	0.192936i
$870$	9.40992	+	1.41832i	0.319026	+	0.0480855i
$871$	8.68290	+	4.18147i	0.294209	+	0.141684i
$872$	−12.9877	+	12.0508i	−0.439819	+	0.408092i
$873$	−12.2037	+	1.83942i	−0.413033	+	0.0622548i
$874$	−0.215946	−	0.0666106i	−0.00730449	−	0.00225314i
$875$	5.56750	−	74.2932i	0.188216	−	2.51157i
$876$	28.8981	−	36.2371i	0.976376	−	1.22434i
$877$	−16.8677	−	42.9782i	−0.569582	−	1.45127i	−0.867868	−	0.496794i	$-0.834510\pi$
$877$	−16.8677	−	42.9782i	−0.569582	−	1.45127i	0.298287	−	0.954476i	$-0.403585\pi$
$878$	−32.2290	−	29.9041i	−1.08767	−	1.00921i
$879$	−6.74327	−	4.59748i	−0.227445	−	0.155069i
$880$	−0.145155	−	1.93696i	−0.00489318	−	0.0652950i
$881$	−2.29329	+	10.0475i	−0.0772627	+	0.338510i	−0.998755	−	0.0498868i	$-0.984114\pi$
$881$	−2.29329	+	10.0475i	−0.0772627	+	0.338510i	0.921492	+	0.388397i	$0.126971\pi$
$882$	0.438537	−	1.92136i	0.0147663	−	0.0646955i
$883$	0.882701	+	11.7788i	0.0297053	+	0.396389i	0.992162	+	0.124955i	$0.0398787\pi$
$883$	0.882701	+	11.7788i	0.0297053	+	0.396389i	−0.962457	+	0.271434i	$0.912502\pi$
$884$	15.5911	+	10.6298i	0.524385	+	0.357520i
$885$	23.2956	+	21.6151i	0.783072	+	0.726585i
$886$	31.7537	+	80.9070i	1.06679	+	2.71812i
$887$	−13.8680	+	17.3899i	−0.465640	+	0.583895i	−0.958098	−	0.286442i	$-0.907527\pi$
$887$	−13.8680	+	17.3899i	−0.465640	+	0.583895i	0.492457	+	0.870337i	$0.336099\pi$
$888$	−2.51230	+	33.5243i	−0.0843072	+	1.12500i
$889$	−4.59187	−	1.41641i	−0.154006	−	0.0475047i
$890$	−115.062	+	17.3428i	−3.85689	+	0.581333i
$891$	2.24039	−	2.07878i	0.0750560	−	0.0696418i
$892$	−14.8005	−	7.12752i	−0.495556	−	0.238647i
$893$	−0.370362	−	0.0558232i	−0.0123937	−	0.00186805i
$894$	−21.3528	+	14.5581i	−0.714144	+	0.486895i
$895$	17.7235	+	22.2245i	0.592430	+	0.742884i
$896$	−27.0404	+	46.8354i	−0.903358	+	1.56466i
$897$	2.36584	+	4.09776i	0.0789931	+	0.136820i
$898$	−15.3198	+	39.0343i	−0.511229	+	1.30259i
$899$	2.31757	−	1.11608i	0.0772954	−	0.0372235i
$900$	−44.1229	+	13.6101i	−1.47076	+	0.453670i
$901$	1.29356	+	5.66746i	0.0430947	+	0.188810i
$902$	14.6608			0.488152
$903$	−21.4496	+	11.9807i	−0.713799	+	0.398694i
$904$	0.446375			0.0148462
$905$	−4.98815	−	21.8545i	−0.165812	−	0.726468i
$906$	−13.6530	+	4.21138i	−0.453589	+	0.139914i
$907$	−31.5843	+	15.2102i	−1.04874	+	0.505046i	−0.877197	−	0.480131i	$-0.840589\pi$
$907$	−31.5843	+	15.2102i	−1.04874	+	0.505046i	−0.171541	+	0.985177i	$0.554875\pi$
$908$	−23.7594	+	60.5381i	−0.788485	+	2.00903i
$909$	1.35416	+	2.34548i	0.0449148	+	0.0777947i
$910$	22.5683	−	39.0895i	0.748132	−	1.29580i
$911$	34.7823	+	43.6156i	1.15239	+	1.44505i	0.874890	+	0.484322i	$0.160934\pi$
$911$	34.7823	+	43.6156i	1.15239	+	1.44505i	0.277498	+	0.960726i	$0.410495\pi$
$912$	−0.0337493	+	0.0230099i	−0.00111755	+	0.000761933i
$913$	−4.22814	−	0.637289i	−0.139931	−	0.0210912i
$914$	−14.8278	−	7.14070i	−0.490461	−	0.236193i
$915$	−11.8530	+	10.9979i	−0.391847	+	0.363581i
$916$	24.0916	−	3.63123i	0.796010	−	0.119979i
$917$	58.1330	+	17.9316i	1.91972	+	0.592155i
$918$	3.17504	−	42.3679i	0.104792	−	1.39835i
$919$	27.4108	−	34.3720i	0.904198	−	1.13383i	−0.0862951	−	0.996270i	$-0.527503\pi$
$919$	27.4108	−	34.3720i	0.904198	−	1.13383i	0.990494	−	0.137559i	$-0.0439258\pi$
$920$	−9.65863	−	24.6098i	−0.318436	−	0.811361i
$921$	−23.2257	−	21.5503i	−0.765312	−	0.710105i
$922$	−3.87151	−	2.63955i	−0.127502	−	0.0869291i
$923$	0.935602	+	12.4847i	0.0307957	+	0.410940i
$924$	2.11752	−	9.27747i	0.0696614	−	0.305206i
$925$	20.1841	−	88.4323i	0.663649	−	2.90764i
$926$	4.12759	+	55.0789i	0.135641	+	1.81000i
$927$	5.18389	+	3.53432i	0.170261	+	0.116082i
$928$	2.68469	+	2.49103i	0.0881294	+	0.0817721i
$929$	−2.10522	−	5.36400i	−0.0690699	−	0.175987i	0.892171	−	0.451699i	$-0.149182\pi$
$929$	−2.10522	−	5.36400i	−0.0690699	−	0.175987i	−0.961240	+	0.275711i	$0.911087\pi$
$930$	27.3120	−	34.2482i	0.895596	−	1.12304i
$931$	−0.00257101	+	0.0343077i	−8.42614e−5	+	0.00112439i
$932$	28.3843	+	8.75541i	0.929760	+	0.286793i
$933$	1.57087	−	0.236770i	0.0514278	−	0.00775150i
$934$	−29.5192	+	27.3898i	−0.965898	+	0.896222i
$935$	−8.97889	−	4.32401i	−0.293641	−	0.141410i
$936$	−6.40145	−	0.964863i	−0.209238	−	0.0315375i
$937$	−18.1263	+	12.3583i	−0.592161	+	0.403729i	−0.821990	−	0.569503i	$-0.807136\pi$
$937$	−18.1263	+	12.3583i	−0.592161	+	0.403729i	0.229828	+	0.973231i	$0.426184\pi$
$938$	−22.4882	−	28.1994i	−0.734267	−	0.920742i
$939$	20.0641	−	34.7521i	0.654769	−	1.13409i
$940$	−53.8098	−	93.2013i	−1.75508	−	3.03989i
$941$	−6.91668	+	17.6234i	−0.225477	+	0.574507i	−0.998183	−	0.0602578i	$-0.980808\pi$
$941$	−6.91668	+	17.6234i	−0.225477	+	0.574507i	0.772706	+	0.634765i	$0.218903\pi$
$942$	28.2137	−	13.5870i	0.919251	−	0.442688i
$943$	16.3672	−	5.04862i	0.532991	−	0.164406i
$944$	−0.815767	−	3.57411i	−0.0265510	−	0.116327i
$945$	−63.8021			−2.07548
$946$	9.99139	−	5.58071i	0.324848	−	0.181445i
$947$	40.2434			1.30774			0.653868	−	0.756609i	$-0.273145\pi$
$947$	40.2434			1.30774			0.653868	+	0.756609i	$0.273145\pi$
$948$	−13.5752	−	59.4769i	−0.440902	−	1.93172i
$949$	−16.7542	+	5.16798i	−0.543864	+	0.167760i
$950$	1.15680	−	0.557086i	0.0375316	−	0.0180743i
$951$	−13.2183	+	33.6797i	−0.428634	+	1.09214i
$952$	−14.3767	−	24.9013i	−0.465953	−	0.807054i
$953$	−18.3255	+	31.7407i	−0.593621	+	1.02818i	0.400119	+	0.916463i	$0.368969\pi$
$953$	−18.3255	+	31.7407i	−0.593621	+	1.02818i	−0.993740	+	0.111718i	$0.964365\pi$
$954$	−3.05409	−	3.82971i	−0.0988798	−	0.123991i
$955$	63.9506	−	43.6008i	2.06939	−	1.41089i
$956$	−20.0830	−	3.02703i	−0.649532	−	0.0979012i
$957$	−0.683788	−	0.329295i	−0.0221037	−	0.0106446i
$958$	−13.1310	+	12.1838i	−0.424243	+	0.393640i
$959$	58.6926	−	8.84648i	1.89528	−	0.285668i
$960$	66.2461	+	20.4342i	2.13808	+	0.659511i
$961$	−1.43176	+	19.1056i	−0.0461859	+	0.616308i
$962$	19.4749	−	24.4208i	0.627897	−	0.787358i
$963$	1.55207	+	3.95460i	0.0500146	+	0.127435i
$964$	43.5228	+	40.3833i	1.40178	+	1.30066i
$965$	10.3619	+	7.06459i	0.333560	+	0.227417i
$966$	−1.32337	−	17.6592i	−0.0425788	−	0.568175i
$967$	1.90500	−	8.34635i	0.0612607	−	0.268400i	−0.935017	−	0.354603i	$-0.884616\pi$
$967$	1.90500	−	8.34635i	0.0612607	−	0.268400i	0.996278	+	0.0862025i	$0.0274732\pi$
$968$	7.39172	−	32.3853i	0.237579	−	1.04090i
$969$	0.0156614	+	0.208987i	0.000503116	+	0.00671362i
$970$	81.4725	+	55.5470i	2.61592	+	1.78351i
$971$	36.2742	+	33.6575i	1.16409	+	1.08012i	0.995531	+	0.0944301i	$0.0301029\pi$
$971$	36.2742	+	33.6575i	1.16409	+	1.08012i	0.168562	+	0.985691i	$0.446088\pi$
$972$	14.1024	+	35.9324i	0.452335	+	1.15253i
$973$	−21.1091	+	26.4699i	−0.676725	+	0.848587i
$974$	3.02838	−	40.4109i	0.0970356	−	1.29485i
$975$	−25.6889	−	7.92398i	−0.822704	−	0.253770i
$976$	1.84447	−	0.278009i	0.0590400	−	0.00889884i
$977$	−13.4546	+	12.4840i	−0.430450	+	0.399399i	−0.865421	−	0.501045i	$-0.832949\pi$
$977$	−13.4546	+	12.4840i	−0.430450	+	0.399399i	0.434971	+	0.900444i	$0.356759\pi$
$978$	−60.2006	−	28.9911i	−1.92500	−	0.927033i
$979$	9.17655	+	1.38314i	0.293284	+	0.0442054i
$980$	−8.16770	+	5.56865i	−0.260908	+	0.177884i
$981$	−4.09932	−	5.14038i	−0.130881	−	0.164120i
$982$	25.1674	−	43.5912i	0.803124	−	1.39105i
$983$	2.35817	+	4.08447i	0.0752140	+	0.130274i	0.901179	−	0.433446i	$-0.142703\pi$
$983$	2.35817	+	4.08447i	0.0752140	+	0.130274i	−0.825965	+	0.563721i	$0.809369\pi$
$984$	13.1769	−	33.5742i	0.420065	−	1.07031i
$985$	43.0882	−	20.7502i	1.37291	−	0.661157i
$986$	−5.38220	+	1.66019i	−0.171404	+	0.0528712i
$987$	−6.53101	−	28.6142i	−0.207884	−	0.910800i
$988$	0.277575			0.00883083
$989$	9.23252	−	9.67091i	0.293577	−	0.307517i
$990$	8.39749			0.266890
$991$	−10.0778	−	44.1536i	−0.320131	−	1.40259i	−0.837319	−	0.546714i	$-0.815878\pi$
$991$	−10.0778	−	44.1536i	−0.320131	−	1.40259i	0.517188	−	0.855872i	$-0.326979\pi$
$992$	16.1096	−	4.96915i	0.511480	−	0.157771i
$993$	3.38623	−	1.63072i	0.107459	−	0.0517495i
$994$	17.1185	−	43.6172i	0.542965	−	1.38345i
$995$	0.545067	+	0.944083i	0.0172798	+	0.0299295i
$996$	−12.9183	+	22.3751i	−0.409332	+	0.708983i
$997$	−18.2570	−	22.8935i	−0.578204	−	0.725045i	0.403601	−	0.914935i	$-0.367758\pi$
$997$	−18.2570	−	22.8935i	−0.578204	−	0.725045i	−0.981805	+	0.189890i	$0.939187\pi$
$998$	−68.7418	+	46.8673i	−2.17598	+	1.48356i
$999$	−43.6590	−	6.58054i	−1.38131	−	0.208199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.2.g.a.17.1	✓	36
3.2	odd	2		387.2.y.c.361.3		36
4.3	odd	2		688.2.bg.c.17.1		36
43.9	even	21		1849.2.a.n.1.18		18
43.34	odd	42		1849.2.a.o.1.1		18
43.38	even	21	inner	43.2.g.a.38.1	yes	36
129.38	odd	42		387.2.y.c.253.3		36
172.167	odd	42		688.2.bg.c.81.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.17.1	✓	36	1.1	even	1	trivial
43.2.g.a.38.1	yes	36	43.38	even	21	inner
387.2.y.c.253.3		36	129.38	odd	42
387.2.y.c.361.3		36	3.2	odd	2
688.2.bg.c.17.1		36	4.3	odd	2
688.2.bg.c.81.1		36	172.167	odd	42
1849.2.a.n.1.18		18	43.9	even	21
1849.2.a.o.1.1		18	43.34	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)

\(f(q)\)	\(=\)	\(q+(-0.515822 - 2.25996i) q^{2} +(1.28860 - 0.397480i) q^{3} +(-3.03942 + 1.46371i) q^{4} +(-1.48781 + 3.79089i) q^{5} +(-1.56298 - 2.70715i) q^{6} +(1.38920 - 2.40617i) q^{7} +(1.98513 + 2.48927i) q^{8} +(-0.976224 + 0.665578i) q^{9} +O(q^{10})\)	\(q+(-0.515822 - 2.25996i) q^{2} +(1.28860 - 0.397480i) q^{3} +(-3.03942 + 1.46371i) q^{4} +(-1.48781 + 3.79089i) q^{5} +(-1.56298 - 2.70715i) q^{6} +(1.38920 - 2.40617i) q^{7} +(1.98513 + 2.48927i) q^{8} +(-0.976224 + 0.665578i) q^{9} +(9.33472 + 1.40698i) q^{10} +(-0.678323 - 0.326663i) q^{11} +(-3.33480 + 3.09424i) q^{12} +(1.70167 - 0.256486i) q^{13} +(-6.15444 - 1.89839i) q^{14} +(-0.410392 + 5.47630i) q^{15} +(0.394993 - 0.495306i) q^{16} +(-1.18750 - 3.02571i) q^{17} +(2.00774 + 1.86291i) q^{18} +(-0.0395049 - 0.0269340i) q^{19} +(-1.02666 - 13.6998i) q^{20} +(0.833720 - 3.65277i) q^{21} +(-0.388353 + 1.70148i) q^{22} +(0.152371 + 2.03326i) q^{23} +(3.54746 + 2.41862i) q^{24} +(-8.49199 - 7.87942i) q^{25} +(-1.45741 - 3.71341i) q^{26} +(-3.51575 + 4.40861i) q^{27} +(-0.700443 + 9.34676i) q^{28} +(0.714324 + 0.220340i) q^{29} +(12.5879 - 1.89733i) q^{30} +(2.52247 - 2.34051i) q^{31} +(4.41406 + 2.12570i) q^{32} +(-1.00393 - 0.151318i) q^{33} +(-6.22544 + 4.24444i) q^{34} +(7.05465 + 8.84626i) q^{35} +(1.99294 - 3.45188i) q^{36} +(3.91502 + 6.78101i) q^{37} +(-0.0404923 + 0.103173i) q^{38} +(2.09082 - 1.00689i) q^{39} +(-12.3900 + 3.82182i) q^{40} +(-1.86928 - 8.18985i) q^{41} -8.68517 q^{42} +(-4.39142 - 4.86985i) q^{43} +2.53985 q^{44} +(-1.07069 - 4.69101i) q^{45} +(4.51649 - 1.39315i) q^{46} +(7.05780 - 3.39886i) q^{47} +(0.312113 - 0.795251i) q^{48} +(-0.359777 - 0.623151i) q^{49} +(-13.4268 + 23.2560i) q^{50} +(-2.73287 - 3.42691i) q^{51} +(-4.79668 + 3.27032i) q^{52} +(-1.76849 - 0.266557i) q^{53} +(11.7768 + 5.67140i) q^{54} +(2.24756 - 2.08543i) q^{55} +(8.74735 - 1.31845i) q^{56} +(-0.0616116 - 0.0190047i) q^{57} +(0.129496 - 1.72800i) q^{58} +(3.60798 - 4.52427i) q^{59} +(-6.76836 - 17.2455i) q^{60} +(2.15836 + 2.00266i) q^{61} +(-6.59062 - 4.49341i) q^{62} +(0.245321 + 3.27359i) q^{63} +(2.80908 - 12.3074i) q^{64} +(-1.55946 + 6.83245i) q^{65} +(0.175875 + 2.34689i) q^{66} +(4.62708 + 3.15469i) q^{67} +(8.03807 + 7.45824i) q^{68} +(1.00452 + 2.55948i) q^{69} +(16.3533 - 20.5063i) q^{70} +(-0.543672 + 7.25480i) q^{71} +(-3.59473 - 1.10883i) q^{72} +(-10.0746 + 1.51850i) q^{73} +(13.3054 - 12.3456i) q^{74} +(-14.0747 - 6.77800i) q^{75} +(0.159495 + 0.0240401i) q^{76} +(-1.72834 + 1.17836i) q^{77} +(-3.35402 - 4.20580i) q^{78} +(-6.70519 + 11.6137i) q^{79} +(1.28997 + 2.23430i) q^{80} +(-1.48307 + 3.77880i) q^{81} +(-17.5445 + 8.44900i) q^{82} +(5.42706 - 1.67402i) q^{83} +(2.81256 + 12.3226i) q^{84} +13.2369 q^{85} +(-8.74049 + 12.4364i) q^{86} +1.00806 q^{87} +(-0.533404 - 2.33699i) q^{88} +(-11.7786 + 3.63323i) q^{89} +(-10.0492 + 4.83945i) q^{90} +(1.74682 - 4.45083i) q^{91} +(-3.43922 - 5.95690i) q^{92} +(2.32015 - 4.01861i) q^{93} +(-11.3219 - 14.1972i) q^{94} +(0.160880 - 0.109686i) q^{95} +(6.53287 + 0.984671i) q^{96} +(9.41101 + 4.53210i) q^{97} +(-1.22272 + 1.13452i) q^{98} +(0.879615 - 0.132581i) 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

Varieties

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Groups

Database

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