LMFDB - Embedded newform 169.2.g.a.27.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(14,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([18]))

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

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

chi := DirichletCharacter("169.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.g (of order $13$, 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:	$1.34947179416$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$13$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			27.5
Character	$\chi$	$=$	169.27
Dual form			169.2.g.a.144.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.235915 - 0.622057i) q^{2} +(1.17724 - 1.70553i) q^{3} +(1.16572 - 1.03274i) q^{4} +(0.100994 + 0.831764i) q^{5} +(-1.33867 - 0.329951i) q^{6} +(1.56980 + 0.823895i) q^{7} +(-2.09560 - 1.09986i) q^{8} +(-0.459118 - 1.21059i) q^{9} +O(q^{10})$	\(q+(-0.235915 - 0.622057i) q^{2} +(1.17724 - 1.70553i) q^{3} +(1.16572 - 1.03274i) q^{4} +(0.100994 + 0.831764i) q^{5} +(-1.33867 - 0.329951i) q^{6} +(1.56980 + 0.823895i) q^{7} +(-2.09560 - 1.09986i) q^{8} +(-0.459118 - 1.21059i) q^{9} +(0.493578 - 0.259050i) q^{10} +(-1.18451 + 3.12329i) q^{11} +(-0.389031 - 3.20396i) q^{12} +(-3.10393 + 1.83457i) q^{13} +(0.142170 - 1.17087i) q^{14} +(1.53749 + 0.806939i) q^{15} +(0.185655 - 1.52901i) q^{16} +(-2.49560 - 1.30979i) q^{17} +(-0.644745 + 0.571195i) q^{18} -0.972208 q^{19} +(0.976728 + 0.865305i) q^{20} +(3.25321 - 1.70742i) q^{21} +2.22231 q^{22} -4.18692 q^{23} +(-4.34287 + 2.27932i) q^{24} +(4.17308 - 1.02857i) q^{25} +(1.87347 + 1.49802i) q^{26} +(3.43127 + 0.845731i) q^{27} +(2.68082 - 0.660763i) q^{28} +(-0.356856 - 0.940952i) q^{29} +(0.139244 - 1.14678i) q^{30} +(4.99025 + 1.22999i) q^{31} +(-5.59078 + 1.37800i) q^{32} +(3.93241 + 5.69708i) q^{33} +(-0.226015 + 1.86140i) q^{34} +(-0.526745 + 1.38891i) q^{35} +(-1.78543 - 0.937067i) q^{36} +(-0.710919 - 0.175226i) q^{37} +(0.229358 + 0.604768i) q^{38} +(-0.525161 + 7.45357i) q^{39} +(0.703178 - 1.85413i) q^{40} +(-0.633254 + 0.917426i) q^{41} +(-1.82959 - 1.62088i) q^{42} +(-9.05816 + 2.23264i) q^{43} +(1.84474 + 4.86417i) q^{44} +(0.960560 - 0.504141i) q^{45} +(0.987757 + 2.60450i) q^{46} +(2.67405 + 2.36900i) q^{47} +(-2.38921 - 2.11666i) q^{48} +(-2.19098 - 3.17418i) q^{49} +(-1.62432 - 2.35324i) q^{50} +(-5.17181 + 2.71438i) q^{51} +(-1.72368 + 5.34415i) q^{52} +(7.65780 + 4.01912i) q^{53} +(-0.283394 - 2.33396i) q^{54} +(-2.71747 - 0.669795i) q^{55} +(-2.38351 - 3.45312i) q^{56} +(-1.14452 + 1.65813i) q^{57} +(-0.501138 + 0.443969i) q^{58} +(0.142756 + 1.17570i) q^{59} +(2.62565 - 0.647164i) q^{60} +(12.4958 - 6.55828i) q^{61} +(-0.412154 - 3.39439i) q^{62} +(0.276679 - 2.27866i) q^{63} +(0.426232 + 0.617504i) q^{64} +(-1.83941 - 2.39645i) q^{65} +(2.61619 - 3.79021i) q^{66} +(-1.97234 - 1.74734i) q^{67} +(-4.26185 + 1.05045i) q^{68} +(-4.92902 + 7.14091i) q^{69} +0.988250 q^{70} +(-0.244306 + 0.353939i) q^{71} +(-0.369352 + 3.04189i) q^{72} +(4.92621 - 12.9894i) q^{73} +(0.0587161 + 0.483570i) q^{74} +(3.15846 - 8.32818i) q^{75} +(-1.13332 + 1.00404i) q^{76} +(-4.43270 + 3.92703i) q^{77} +(4.76044 - 1.43173i) q^{78} +(0.723050 + 0.640566i) q^{79} +1.29053 q^{80} +(8.38921 - 7.43219i) q^{81} +(0.720085 + 0.177485i) q^{82} +(-10.1950 - 14.7700i) q^{83} +(2.02903 - 5.35010i) q^{84} +(0.837396 - 2.20803i) q^{85} +(3.52578 + 5.10798i) q^{86} +(-2.02493 - 0.499100i) q^{87} +(5.91743 - 5.24239i) q^{88} -0.552206 q^{89} +(-0.540215 - 0.478589i) q^{90} +(-6.38404 + 0.322598i) q^{91} +(-4.88079 + 4.32400i) q^{92} +(7.97251 - 7.06303i) q^{93} +(0.842804 - 2.22229i) q^{94} +(-0.0981876 - 0.808647i) q^{95} +(-4.23147 + 11.1575i) q^{96} +(-1.65086 + 13.5961i) q^{97} +(-1.45764 + 2.11175i) q^{98} +4.32486 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9}+O(q^{10}) $ 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9} + q^{10} - q^{11} + 11 q^{12} - 65 q^{13} + 9 q^{14} - 41 q^{15} + 3 q^{17} - 13 q^{18} - 6 q^{19} + 29 q^{20} + 19 q^{21} - 22 q^{22} - 82 q^{23} - 31 q^{24} + 2 q^{25} + 26 q^{26} + 21 q^{27} + 43 q^{28} + 13 q^{29} - 81 q^{30} - 33 q^{31} - 93 q^{32} + 35 q^{33} - 24 q^{34} + 27 q^{35} + 54 q^{36} + 25 q^{37} - 56 q^{38} - 13 q^{39} - 52 q^{40} + 29 q^{41} - 63 q^{42} + 21 q^{43} + 45 q^{44} + 33 q^{46} - 69 q^{47} + 54 q^{48} - 54 q^{49} + 80 q^{50} - 16 q^{51} + 13 q^{52} - 45 q^{53} + 29 q^{54} - 83 q^{55} + 91 q^{56} - 11 q^{57} + 25 q^{58} - 57 q^{59} + 51 q^{60} + 39 q^{61} + 4 q^{62} + 26 q^{63} + 86 q^{64} + 65 q^{65} - 138 q^{66} - 101 q^{67} + 36 q^{68} + 32 q^{69} - 90 q^{70} + 20 q^{71} + 13 q^{72} + 61 q^{73} - 4 q^{74} - 67 q^{75} - 107 q^{76} + 67 q^{77} + 13 q^{78} + 57 q^{79} + 160 q^{80} + 78 q^{81} - 31 q^{82} - 59 q^{83} - 36 q^{84} - 61 q^{85} + 41 q^{86} - 9 q^{87} - 45 q^{88} - 66 q^{89} + 191 q^{90} + 39 q^{91} + 79 q^{92} - 80 q^{93} - 21 q^{94} - 28 q^{95} + 70 q^{96} + 7 q^{97} + 158 q^{98} + 130 q^{99}+O(q^{100}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9 + q^10 - q^11 + 11 * q^12 - 65 * q^13 + 9 * q^14 - 41 * q^15 + 3 * q^17 - 13 * q^18 - 6 * q^19 + 29 * q^20 + 19 * q^21 - 22 * q^22 - 82 * q^23 - 31 * q^24 + 2 * q^25 + 26 * q^26 + 21 * q^27 + 43 * q^28 + 13 * q^29 - 81 * q^30 - 33 * q^31 - 93 * q^32 + 35 * q^33 - 24 * q^34 + 27 * q^35 + 54 * q^36 + 25 * q^37 - 56 * q^38 - 13 * q^39 - 52 * q^40 + 29 * q^41 - 63 * q^42 + 21 * q^43 + 45 * q^44 + 33 * q^46 - 69 * q^47 + 54 * q^48 - 54 * q^49 + 80 * q^50 - 16 * q^51 + 13 * q^52 - 45 * q^53 + 29 * q^54 - 83 * q^55 + 91 * q^56 - 11 * q^57 + 25 * q^58 - 57 * q^59 + 51 * q^60 + 39 * q^61 + 4 * q^62 + 26 * q^63 + 86 * q^64 + 65 * q^65 - 138 * q^66 - 101 * q^67 + 36 * q^68 + 32 * q^69 - 90 * q^70 + 20 * q^71 + 13 * q^72 + 61 * q^73 - 4 * q^74 - 67 * q^75 - 107 * q^76 + 67 * q^77 + 13 * q^78 + 57 * q^79 + 160 * q^80 + 78 * q^81 - 31 * q^82 - 59 * q^83 - 36 * q^84 - 61 * q^85 + 41 * q^86 - 9 * q^87 - 45 * q^88 - 66 * q^89 + 191 * q^90 + 39 * q^91 + 79 * q^92 - 80 * q^93 - 21 * q^94 - 28 * q^95 + 70 * q^96 + 7 * q^97 + 158 * q^98 + 130 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{13}\right)$

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 $

$2$	−0.235915	−	0.622057i	−0.166817	−	0.439861i	0.825374	−	0.564586i	$-0.190964\pi$
$2$	−0.235915	−	0.622057i	−0.166817	−	0.439861i	−0.992191	+	0.124726i	$0.960195\pi$
$3$	1.17724	−	1.70553i	0.679681	−	0.984688i	−0.319629	−	0.947543i	$-0.603558\pi$
$3$	1.17724	−	1.70553i	0.679681	−	0.984688i	0.999310	−	0.0371451i	$-0.0118264\pi$
$4$	1.16572	−	1.03274i	0.582861	−	0.516370i
$5$	0.100994	+	0.831764i	0.0451661	+	0.371976i	0.997713	+	0.0675858i	$0.0215296\pi$
$5$	0.100994	+	0.831764i	0.0451661	+	0.371976i	−0.952547	+	0.304390i	$0.901547\pi$
$6$	−1.33867	−	0.329951i	−0.546508	−	0.134702i
$7$	1.56980	+	0.823895i	0.593329	+	0.311403i	0.734528	−	0.678578i	$-0.237404\pi$
$7$	1.56980	+	0.823895i	0.593329	+	0.311403i	−0.141199	+	0.989981i	$0.545096\pi$
$8$	−2.09560	−	1.09986i	−0.740908	−	0.388859i
$9$	−0.459118	−	1.21059i	−0.153039	−	0.403531i
$10$	0.493578	−	0.259050i	0.156083	−	0.0819188i
$11$	−1.18451	+	3.12329i	−0.357142	+	0.941707i	0.629236	+	0.777214i	$0.283368\pi$
$11$	−1.18451	+	3.12329i	−0.357142	+	0.941707i	−0.986378	+	0.164492i	$0.947401\pi$
$12$	−0.389031	−	3.20396i	−0.112304	−	0.924903i
$13$	−3.10393	+	1.83457i	−0.860874	+	0.508818i
$13$	−3.10393	+	1.83457i	−0.860874	+	0.508818i
$14$	0.142170	−	1.17087i	0.0379965	−	0.312929i
$15$	1.53749	+	0.806939i	0.396979	+	0.208351i
$16$	0.185655	−	1.52901i	0.0464139	−	0.382253i
$17$	−2.49560	−	1.30979i	−0.605272	−	0.317671i	0.134101	−	0.990968i	$-0.457185\pi$
$17$	−2.49560	−	1.30979i	−0.605272	−	0.317671i	−0.739373	+	0.673297i	$0.764878\pi$
$18$	−0.644745	+	0.571195i	−0.151968	+	0.134632i
$19$	−0.972208			−0.223040			−0.111520	−	0.993762i	$-0.535572\pi$
$19$	−0.972208			−0.223040			−0.111520	+	0.993762i	$0.535572\pi$
$20$	0.976728	+	0.865305i	0.218403	+	0.193488i
$21$	3.25321	−	1.70742i	0.709909	−	0.372589i
$22$	2.22231			0.473797
$23$	−4.18692			−0.873033			−0.436516	−	0.899696i	$-0.643788\pi$
$23$	−4.18692			−0.873033			−0.436516	+	0.899696i	$0.643788\pi$
$24$	−4.34287	+	2.27932i	−0.886486	+	0.465263i
$25$	4.17308	−	1.02857i	0.834616	−	0.205714i
$26$	1.87347	+	1.49802i	0.367418	+	0.293785i
$27$	3.43127	+	0.845731i	0.660347	+	0.162761i
$28$	2.68082	−	0.660763i	0.506628	−	0.124873i
$29$	−0.356856	−	0.940952i	−0.0662665	−	0.174730i	0.897792	−	0.440419i	$-0.145170\pi$
$29$	−0.356856	−	0.940952i	−0.0662665	−	0.174730i	−0.964059	+	0.265688i	$0.914401\pi$
$30$	0.139244	−	1.14678i	0.0254224	−	0.209372i
$31$	4.99025	+	1.22999i	0.896275	+	0.220912i	0.660438	−	0.750881i	$-0.270371\pi$
$31$	4.99025	+	1.22999i	0.896275	+	0.220912i	0.235837	+	0.971793i	$0.424217\pi$
$32$	−5.59078	+	1.37800i	−0.988319	+	0.243599i
$33$	3.93241	+	5.69708i	0.684544	+	0.991734i
$34$	−0.226015	+	1.86140i	−0.0387613	+	0.319228i
$35$	−0.526745	+	1.38891i	−0.0890362	+	0.234769i
$36$	−1.78543	−	0.937067i	−0.297572	−	0.156178i
$37$	−0.710919	−	0.175226i	−0.116874	−	0.0288069i	0.180445	−	0.983585i	$-0.442246\pi$
$37$	−0.710919	−	0.175226i	−0.116874	−	0.0288069i	−0.297319	+	0.954778i	$0.596092\pi$
$38$	0.229358	+	0.604768i	0.0372068	+	0.0981064i
$39$	−0.525161	+	7.45357i	−0.0840931	+	1.19353i
$40$	0.703178	−	1.85413i	0.111182	−	0.293163i
$41$	−0.633254	+	0.917426i	−0.0988976	+	0.143278i	−0.869309	−	0.494269i	$-0.835436\pi$
$41$	−0.633254	+	0.917426i	−0.0988976	+	0.143278i	0.770411	+	0.637547i	$0.220051\pi$
$42$	−1.82959	−	1.62088i	−0.282312	−	0.250107i
$43$	−9.05816	+	2.23264i	−1.38136	+	0.340474i	−0.858879	−	0.512179i	$-0.828838\pi$
$43$	−9.05816	+	2.23264i	−1.38136	+	0.340474i	−0.522478	+	0.852653i	$0.674992\pi$
$44$	1.84474	+	4.86417i	0.278105	+	0.733302i
$45$	0.960560	−	0.504141i	0.143192	−	0.0751529i
$46$	0.987757	+	2.60450i	0.145637	+	0.384013i
$47$	2.67405	+	2.36900i	0.390050	+	0.345554i	0.835243	−	0.549880i	$-0.185327\pi$
$47$	2.67405	+	2.36900i	0.390050	+	0.345554i	−0.445194	+	0.895434i	$0.646865\pi$
$48$	−2.38921	−	2.11666i	−0.344853	−	0.305513i
$49$	−2.19098	−	3.17418i	−0.312997	−	0.453455i
$50$	−1.62432	−	2.35324i	−0.229714	−	0.332798i
$51$	−5.17181	+	2.71438i	−0.724199	+	0.380089i
$52$	−1.72368	+	5.34415i	−0.239032	+	0.741100i
$53$	7.65780	+	4.01912i	1.05188	+	0.552069i	0.899802	−	0.436299i	$-0.143711\pi$
$53$	7.65780	+	4.01912i	1.05188	+	0.552069i	0.152078	+	0.988368i	$0.451403\pi$
$54$	−0.283394	−	2.33396i	−0.0385651	−	0.317612i
$55$	−2.71747	−	0.669795i	−0.366423	−	0.0903152i
$56$	−2.38351	−	3.45312i	−0.318511	−	0.461442i
$57$	−1.14452	+	1.65813i	−0.151596	+	0.219625i
$58$	−0.501138	+	0.443969i	−0.0658026	+	0.0582960i
$59$	0.142756	+	1.17570i	0.0185852	+	0.153063i	0.999047	−	0.0436464i	$-0.0138975\pi$
$59$	0.142756	+	1.17570i	0.0185852	+	0.153063i	−0.980462	+	0.196710i	$0.936974\pi$
$60$	2.62565	−	0.647164i	0.338970	−	0.0835485i
$61$	12.4958	−	6.55828i	1.59992	−	0.839702i	0.600729	−	0.799452i	$-0.294877\pi$
$61$	12.4958	−	6.55828i	1.59992	−	0.839702i	0.999190	−	0.0402500i	$-0.0128154\pi$
$62$	−0.412154	−	3.39439i	−0.0523436	−	0.431088i
$63$	0.276679	−	2.27866i	0.0348583	−	0.287084i
$64$	0.426232	+	0.617504i	0.0532790	+	0.0771880i
$65$	−1.83941	−	2.39645i	−0.228150	−	0.297243i
$66$	2.61619	−	3.79021i	0.322031	−	0.466542i
$67$	−1.97234	−	1.74734i	−0.240960	−	0.213472i	0.533996	−	0.845487i	$-0.320690\pi$
$67$	−1.97234	−	1.74734i	−0.240960	−	0.213472i	−0.774956	+	0.632015i	$0.782228\pi$
$68$	−4.26185	+	1.05045i	−0.516825	+	0.127386i
$69$	−4.92902	+	7.14091i	−0.593384	+	0.859665i
$70$	0.988250			0.118118
$71$	−0.244306	+	0.353939i	−0.0289938	+	0.0420048i	−0.837213	−	0.546877i	$-0.815816\pi$
$71$	−0.244306	+	0.353939i	−0.0289938	+	0.0420048i	0.808219	+	0.588882i	$0.200432\pi$
$72$	−0.369352	+	3.04189i	−0.0435286	+	0.358490i
$73$	4.92621	−	12.9894i	0.576569	−	1.52029i	−0.256175	−	0.966631i	$-0.582462\pi$
$73$	4.92621	−	12.9894i	0.576569	−	1.52029i	0.832744	−	0.553658i	$-0.186769\pi$
$74$	0.0587161	+	0.483570i	0.00682561	+	0.0562139i
$75$	3.15846	−	8.32818i	0.364708	−	0.961656i
$76$	−1.13332	+	1.00404i	−0.130001	+	0.115171i
$77$	−4.43270	+	3.92703i	−0.505153	+	0.447527i
$78$	4.76044	−	1.43173i	0.539013	−	0.162111i
$79$	0.723050	+	0.640566i	0.0813495	+	0.0720693i	0.702818	−	0.711370i	$-0.251925\pi$
$79$	0.723050	+	0.640566i	0.0813495	+	0.0720693i	−0.621468	+	0.783439i	$0.713463\pi$
$80$	1.29053			0.144285
$81$	8.38921	−	7.43219i	0.932134	−	0.825799i
$82$	0.720085	+	0.177485i	0.0795201	+	0.0196000i
$83$	−10.1950	−	14.7700i	−1.11904	−	1.62122i	−0.701708	−	0.712465i	$-0.747579\pi$
$83$	−10.1950	−	14.7700i	−1.11904	−	1.62122i	−0.417337	−	0.908752i	$-0.637037\pi$
$84$	2.02903	−	5.35010i	0.221385	−	0.583744i
$85$	0.837396	−	2.20803i	0.0908284	−	0.239495i
$86$	3.52578	+	5.10798i	0.380195	+	0.550808i
$87$	−2.02493	−	0.499100i	−0.217095	−	0.0535091i
$88$	5.91743	−	5.24239i	0.630800	−	0.558840i
$89$	−0.552206			−0.0585337			−0.0292668	−	0.999572i	$-0.509317\pi$
$89$	−0.552206			−0.0585337			−0.0292668	+	0.999572i	$0.509317\pi$
$90$	−0.540215	−	0.478589i	−0.0569436	−	0.0504477i
$91$	−6.38404	+	0.322598i	−0.669229	+	0.0338175i
$92$	−4.88079	+	4.32400i	−0.508857	+	0.450808i
$93$	7.97251	−	7.06303i	0.826710	−	0.732402i
$94$	0.842804	−	2.22229i	0.0869286	−	0.229212i
$95$	−0.0981876	−	0.808647i	−0.0100738	−	0.0829655i
$96$	−4.23147	+	11.1575i	−0.431873	+	1.13876i
$97$	−1.65086	+	13.5961i	−0.167620	+	1.38047i	0.629664	+	0.776867i	$0.283192\pi$
$97$	−1.65086	+	13.5961i	−0.167620	+	1.38047i	−0.797284	+	0.603604i	$0.793731\pi$
$98$	−1.45764	+	2.11175i	−0.147244	+	0.213319i
$99$	4.32486			0.434665
$100$	3.80240	−	5.50873i	0.380240	−	0.550873i
$101$	−9.35193	+	2.30504i	−0.930552	+	0.229361i	−0.675325	−	0.737521i	$-0.735997\pi$
$101$	−9.35193	+	2.30504i	−0.930552	+	0.229361i	−0.255227	+	0.966881i	$0.582150\pi$
$102$	2.90861	+	2.57680i	0.287995	+	0.255141i
$103$	−1.16770	+	1.69170i	−0.115057	+	0.166688i	−0.876281	−	0.481800i	$-0.839983\pi$
$103$	−1.16770	+	1.69170i	−0.115057	+	0.166688i	0.761224	+	0.648488i	$0.224599\pi$
$104$	8.52237	−	0.430652i	0.835687	−	0.0422289i
$105$	1.74873	+	2.53347i	0.170658	+	0.247241i
$106$	0.693533	−	5.71176i	0.0673619	−	0.554775i
$107$	−0.145390	−	1.19740i	−0.0140554	−	0.115757i	0.983992	−	0.178210i	$-0.0570306\pi$
$107$	−0.145390	−	1.19740i	−0.0140554	−	0.115757i	−0.998048	+	0.0624533i	$0.980108\pi$
$108$	4.87332	−	2.55772i	0.468936	−	0.246116i
$109$	−8.32863	+	2.05282i	−0.797738	+	0.196625i	−0.617059	−	0.786917i	$-0.711676\pi$
$109$	−8.32863	+	2.05282i	−0.797738	+	0.196625i	−0.180680	+	0.983542i	$0.557830\pi$
$110$	0.224440	+	1.84843i	0.0213996	+	0.176241i
$111$	−1.13578	+	1.00621i	−0.107803	+	0.0955052i
$112$	1.55119	−	2.24728i	0.146573	−	0.212348i
$113$	−10.9076	−	15.8024i	−1.02610	−	1.48656i	−0.866372	−	0.499399i	$-0.833554\pi$
$113$	−10.9076	−	15.8024i	−1.02610	−	1.48656i	−0.159727	−	0.987161i	$-0.551061\pi$
$114$	1.30146	+	0.320781i	0.121893	+	0.0300439i
$115$	−0.422856	−	3.48253i	−0.0394315	−	0.324747i
$116$	−1.38775	−	0.728349i	−0.128850	−	0.0676255i
$117$	3.64598	+	2.91531i	0.337071	+	0.269521i
$118$	0.697674	−	0.366168i	0.0642261	−	0.0337085i
$119$	−2.83846	−	4.11223i	−0.260202	−	0.376967i
$120$	−2.33446	−	3.38205i	−0.213106	−	0.308737i
$121$	−0.118250	−	0.104761i	−0.0107500	−	0.00952369i
$122$	−7.02757	−	6.22588i	−0.636246	−	0.563665i
$123$	0.819205	+	2.16007i	0.0738652	+	0.194767i
$124$	7.08750	−	3.71981i	0.636476	−	0.334049i
$125$	2.76256	+	7.28426i	0.247090	+	0.651524i
$126$	−1.48273	+	0.365459i	−0.132092	+	0.0325577i
$127$	−3.97270	−	3.51951i	−0.352521	−	0.312306i	0.468215	−	0.883615i	$-0.344897\pi$
$127$	−3.97270	−	3.51951i	−0.352521	−	0.312306i	−0.820735	+	0.571309i	$0.806436\pi$
$128$	−6.25838	+	9.06682i	−0.553167	+	0.801401i
$129$	−6.85582	+	18.0773i	−0.603621	+	1.59162i
$130$	−1.05679	+	1.70958i	−0.0926863	+	0.149940i
$131$	3.96956	+	10.4669i	0.346822	+	0.914495i	0.988997	+	0.147937i	$0.0472631\pi$
$131$	3.96956	+	10.4669i	0.346822	+	0.914495i	−0.642175	+	0.766558i	$0.721968\pi$
$132$	10.4677	+	2.58006i	0.911096	+	0.224565i
$133$	−1.52617	−	0.800997i	−0.132336	−	0.0694553i
$134$	−0.621641	+	1.63913i	−0.0537016	+	0.141599i
$135$	−0.356910	+	2.93942i	−0.0307179	+	0.252985i
$136$	3.78921	+	5.48961i	0.324922	+	0.470730i
$137$	9.08614	−	2.23953i	0.776281	−	0.191336i	0.168779	−	0.985654i	$-0.446018\pi$
$137$	9.08614	−	2.23953i	0.776281	−	0.191336i	0.607502	+	0.794318i	$0.292172\pi$
$138$	5.60488	+	1.38148i	0.477119	+	0.117599i
$139$	−0.517147	+	4.25909i	−0.0438638	+	0.361251i	0.954206	+	0.299150i	$0.0967031\pi$
$139$	−0.517147	+	4.25909i	−0.0438638	+	0.361251i	−0.998070	+	0.0621009i	$0.980220\pi$
$140$	0.820347	+	2.16308i	0.0693320	+	0.182813i
$141$	7.18839	−	1.77178i	0.605372	−	0.149211i
$142$	0.277806	+	0.0684730i	0.0233129	+	0.00574612i
$143$	−2.05326	−	11.8675i	−0.171703	−	0.992411i
$144$	−1.93625	+	0.477242i	−0.161354	+	0.0397702i
$145$	0.746609	−	0.391851i	0.0620025	−	0.0325414i
$146$	−9.24228			−0.764897
$147$	−7.99298			−0.659250
$148$	−1.00970	+	0.529930i	−0.0829966	+	0.0435600i
$149$	16.3447	+	14.4801i	1.33901	+	1.18626i	0.966033	+	0.258417i	$0.0832008\pi$
$149$	16.3447	+	14.4801i	1.33901	+	1.18626i	0.372975	+	0.927841i	$0.378338\pi$
$150$	−5.92573			−0.483834
$151$	−4.05848	+	3.59550i	−0.330274	+	0.292597i	−0.811920	−	0.583768i	$-0.801578\pi$
$151$	−4.05848	+	3.59550i	−0.330274	+	0.292597i	0.481646	+	0.876366i	$0.340039\pi$
$152$	2.03736	+	1.06929i	0.165252	+	0.0867309i
$153$	−0.439852	+	3.62251i	−0.0355599	+	0.292862i
$154$	3.48858	+	1.83095i	0.281118	+	0.147542i
$155$	−0.519071	+	4.27493i	−0.0416928	+	0.343371i
$156$	7.08541	+	9.23115i	0.567287	+	0.739083i
$157$	2.73033	+	22.4863i	0.217904	+	1.79460i	0.533594	+	0.845741i	$0.320841\pi$
$157$	2.73033	+	22.4863i	0.217904	+	1.79460i	−0.315690	+	0.948863i	$0.602236\pi$
$158$	0.227890	−	0.600897i	0.0181300	−	0.0478048i
$159$	15.8698	−	8.32913i	1.25856	−	0.660543i
$160$	−1.71081	−	4.51104i	−0.135251	−	0.356629i
$161$	−6.57263	−	3.44958i	−0.517996	−	0.271865i
$162$	−6.60238	−	3.46520i	−0.518732	−	0.272252i
$163$	−22.1108	−	5.44981i	−1.73185	−	0.426862i	−0.757669	−	0.652639i	$-0.773662\pi$
$163$	−22.1108	−	5.44981i	−1.73185	−	0.426862i	−0.974179	+	0.225777i	$0.927508\pi$
$164$	0.209265	+	1.72345i	0.0163408	+	0.134579i
$165$	−4.34147	+	3.84621i	−0.337983	+	0.299427i
$166$	−6.78262	+	9.82632i	−0.526433	+	0.762671i
$167$	−7.45656	−	19.6613i	−0.577006	−	1.52144i	−0.832158	−	0.554538i	$-0.812895\pi$
$167$	−7.45656	−	19.6613i	−0.577006	−	1.52144i	0.255153	−	0.966901i	$-0.417874\pi$
$168$	−8.69537			−0.670862
$169$	6.26872	−	11.3887i	0.482209	−	0.876056i
$170$	−1.57108			−0.120496
$171$	0.446358	+	1.17695i	0.0341338	+	0.0900035i
$172$	−8.25357	+	11.9574i	−0.629329	+	0.911740i
$173$	12.5449	−	11.1138i	0.953773	−	0.844969i	−0.0342287	−	0.999414i	$-0.510897\pi$
$173$	12.5449	−	11.1138i	0.953773	−	0.844969i	0.988001	+	0.154445i	$0.0493590\pi$
$174$	0.167242	+	1.37736i	0.0126786	+	0.104418i
$175$	7.39834	+	1.82353i	0.559262	+	0.137846i
$176$	4.55563	+	2.39098i	0.343393	+	0.180227i
$177$	2.17325	+	1.14061i	0.163351	+	0.0857335i
$178$	0.130274	+	0.343503i	0.00976442	+	0.0257467i
$179$	−11.3083	+	5.93508i	−0.845225	+	0.443608i	−0.830988	−	0.556290i	$-0.812224\pi$
$179$	−11.3083	+	5.93508i	−0.845225	+	0.443608i	−0.0142371	+	0.999899i	$0.504532\pi$
$180$	0.599100	−	1.57970i	0.0446543	−	0.117744i
$181$	0.691941	+	5.69864i	0.0514316	+	0.423577i	0.995570	+	0.0940269i	$0.0299740\pi$
$181$	0.691941	+	5.69864i	0.0514316	+	0.423577i	−0.944138	+	0.329550i	$0.893103\pi$
$182$	1.70677	+	3.89513i	0.126514	+	0.288726i
$183$	3.52519	−	29.0326i	0.260590	−	2.14615i
$184$	8.77413	+	4.60502i	0.646837	+	0.339486i
$185$	0.0739476	−	0.609014i	0.00543674	−	0.0447756i
$186$	−6.27444	−	3.29308i	−0.460064	−	0.241460i
$187$	7.04691	−	6.24302i	0.515321	−	0.456535i
$188$	5.56375			0.405778
$189$	4.68961	+	4.15463i	0.341119	+	0.302205i
$190$	−0.479861	+	0.251850i	−0.0348128	+	0.0182711i
$191$	0.657915			0.0476051			0.0238025	−	0.999717i	$-0.492423\pi$
$191$	0.657915			0.0476051			0.0238025	+	0.999717i	$0.492423\pi$
$192$	1.55495			0.112219
$193$	−15.0285	+	7.88754i	−1.08177	+	0.567758i	−0.908827	−	0.417174i	$-0.863021\pi$
$193$	−15.0285	+	7.88754i	−1.08177	+	0.567758i	−0.172945	+	0.984932i	$0.555328\pi$
$194$	8.84699	−	2.18059i	0.635177	−	0.156557i
$195$	−6.25265	+	0.315959i	−0.447762	+	0.0226263i
$196$	−5.83218	−	1.43750i	−0.416585	−	0.102679i
$197$	8.23261	−	2.02916i	0.586549	−	0.144571i	0.0651369	−	0.997876i	$-0.479252\pi$
$197$	8.23261	−	2.02916i	0.586549	−	0.144571i	0.521412	+	0.853305i	$0.325405\pi$
$198$	−1.02030	−	2.69031i	−0.0725095	−	0.191192i
$199$	−0.466046	+	3.83824i	−0.0330371	+	0.272085i	0.966824	+	0.255442i	$0.0822210\pi$
$199$	−0.466046	+	3.83824i	−0.0330371	+	0.272085i	−0.999861	+	0.0166432i	$0.994702\pi$
$200$	−9.87640	−	2.43431i	−0.698367	−	0.172132i
$201$	−5.30206	+	1.30684i	−0.373979	+	0.0921775i
$202$	3.64013	+	5.27364i	0.256119	+	0.371052i
$203$	0.215053	−	1.77112i	0.0150937	−	0.124308i
$204$	−3.22565	+	8.50535i	−0.225841	+	0.595494i
$205$	−0.827037	−	0.434063i	−0.0577628	−	0.0303163i
$206$	1.32781	+	0.327276i	0.0925131	+	0.0228024i
$207$	1.92229	+	5.06866i	0.133608	+	0.352296i
$208$	2.22881	+	5.08653i	0.154540	+	0.352688i
$209$	1.15159	−	3.03648i	0.0796569	−	0.210038i
$210$	1.16341	−	1.68549i	0.0802829	−	0.116310i
$211$	4.08429	+	3.61837i	0.281174	+	0.249099i	0.791908	−	0.610640i	$-0.209088\pi$
$211$	4.08429	+	3.61837i	0.281174	+	0.249099i	−0.510734	+	0.859739i	$0.670626\pi$
$212$	13.0776	−	3.22334i	0.898172	−	0.221380i
$213$	0.316046	+	0.833344i	0.0216551	+	0.0570998i
$214$	−0.710549	+	0.372925i	−0.0485721	+	0.0254926i
$215$	−2.77185	−	7.30877i	−0.189039	−	0.498454i
$216$	−6.26039	−	5.54622i	−0.425966	−	0.377373i
$217$	6.82032	+	6.04227i	0.462993	+	0.410176i
$218$	3.24182	+	4.69659i	0.219564	+	0.318093i
$219$	−16.3544	−	23.6934i	−1.10513	−	1.60105i
$220$	−3.85954	+	2.02564i	−0.260210	+	0.136569i
$221$	10.1491	−	0.512852i	0.682700	−	0.0344982i
$222$	0.893867	+	0.469137i	0.0599924	+	0.0314864i
$223$	−0.334281	−	2.75305i	−0.0223851	−	0.184358i	0.977227	−	0.212195i	$-0.0680611\pi$
$223$	−0.334281	−	2.75305i	−0.0223851	−	0.184358i	−0.999612	+	0.0278370i	$0.991138\pi$
$224$	−9.91174	−	2.44302i	−0.662256	−	0.163231i
$225$	−3.16112	−	4.57967i	−0.210741	−	0.305311i
$226$	−7.25670	+	10.5131i	−0.482709	+	0.699324i
$227$	−12.5680	+	11.1343i	−0.834170	+	0.739010i	−0.967719	−	0.252032i	$-0.918901\pi$
$227$	−12.5680	+	11.1343i	−0.834170	+	0.739010i	0.133549	+	0.991042i	$0.457363\pi$
$228$	0.378219	+	3.11491i	0.0250482	+	0.206290i
$229$	7.95230	−	1.96007i	0.525503	−	0.129525i	0.0323652	−	0.999476i	$-0.489696\pi$
$229$	7.95230	−	1.96007i	0.525503	−	0.129525i	0.493138	+	0.869951i	$0.335850\pi$
$230$	−2.06657	+	1.08462i	−0.136266	+	0.0715178i
$231$	1.47930	+	12.1832i	0.0973311	+	0.801594i
$232$	−0.287085	+	2.36435i	−0.0188480	+	0.155227i
$233$	−4.93610	−	7.15118i	−0.323375	−	0.468489i	0.627256	−	0.778813i	$-0.284178\pi$
$233$	−4.93610	−	7.15118i	−0.323375	−	0.468489i	−0.950631	+	0.310324i	$0.899563\pi$
$234$	0.953346	−	2.95578i	0.0623222	−	0.193225i
$235$	−1.70038	+	2.46343i	−0.110921	+	0.160696i
$236$	1.38061	+	1.22311i	0.0898698	+	0.0796177i
$237$	1.94371	−	0.479081i	0.126258	−	0.0311197i
$238$	−1.88840	+	2.73582i	−0.122407	+	0.177337i
$239$	17.8074			1.15186			0.575932	−	0.817498i	$-0.304639\pi$
$239$	17.8074			1.15186			0.575932	+	0.817498i	$0.304639\pi$
$240$	1.51926	−	2.20103i	0.0980679	−	0.142076i
$241$	1.20366	−	9.91302i	0.0775345	−	0.638554i	−0.901197	−	0.433409i	$-0.857310\pi$
$241$	1.20366	−	9.91302i	0.0775345	−	0.638554i	0.978732	−	0.205145i	$-0.0657665\pi$
$242$	−0.0372700	+	0.0982730i	−0.00239581	+	0.00631723i
$243$	−1.52178	−	12.5330i	−0.0976220	−	0.803990i
$244$	7.79360	−	20.5500i	0.498934	−	1.31558i
$245$	2.41890	−	2.14295i	0.154538	−	0.136908i
$246$	1.15042	−	1.01918i	0.0733482	−	0.0649808i
$247$	3.01766	−	1.78358i	0.192009	−	0.113487i
$248$	−9.10478	−	8.06613i	−0.578154	−	0.512200i
$249$	−37.1926			−2.35699
$250$	3.87950	−	3.43693i	0.245361	−	0.217371i
$251$	22.1803	+	5.46696i	1.40001	+	0.345071i	0.865846	−	0.500310i	$-0.166781\pi$
$251$	22.1803	+	5.46696i	1.40001	+	0.345071i	0.534163	+	0.845382i	$0.320627\pi$
$252$	−2.03073	−	2.94202i	−0.127924	−	0.185330i
$253$	4.95943	−	13.0770i	0.311797	−	0.822141i
$254$	−1.25211	+	3.30155i	−0.0785646	+	0.207158i
$255$	−2.78005	−	4.02759i	−0.174093	−	0.252218i
$256$	8.57357	+	2.11319i	0.535848	+	0.132075i
$257$	17.1854	−	15.2249i	1.07199	−	0.949704i	0.0731291	−	0.997322i	$-0.476701\pi$
$257$	17.1854	−	15.2249i	1.07199	−	0.949704i	0.998866	+	0.0476181i	$0.0151630\pi$
$258$	12.8625			0.800785
$259$	−0.971634	−	0.860792i	−0.0603744	−	0.0534870i
$260$	−4.61915	−	0.893969i	−0.286468	−	0.0554416i
$261$	−0.975271	+	0.864015i	−0.0603678	+	0.0534812i
$262$	5.57451	−	4.93859i	0.344394	−	0.305107i
$263$	−0.752629	+	1.98452i	−0.0464091	+	0.122371i	−0.956217	−	0.292660i	$-0.905460\pi$
$263$	−0.752629	+	1.98452i	−0.0464091	+	0.122371i	0.909808	+	0.415030i	$0.136229\pi$
$264$	−1.97480	−	16.2639i	−0.121540	−	1.00097i
$265$	−2.56957	+	6.77539i	−0.157847	+	0.416209i
$266$	−0.138219	+	1.13833i	−0.00847473	+	0.0697957i
$267$	−0.650080	+	0.941803i	−0.0397842	+	0.0576374i
$268$	−4.10375			−0.250677
$269$	13.5237	−	19.5924i	0.824552	−	1.19457i	−0.153899	−	0.988087i	$-0.549183\pi$
$269$	13.5237	−	19.5924i	0.824552	−	1.19457i	0.978450	−	0.206483i	$-0.0662017\pi$
$270$	1.91269	−	0.471435i	0.116402	−	0.0286906i
$271$	3.77176	+	3.34149i	0.229118	+	0.202981i	0.769869	−	0.638202i	$-0.220321\pi$
$271$	3.77176	+	3.34149i	0.229118	+	0.202981i	−0.540751	+	0.841183i	$0.681860\pi$
$272$	−2.46601	+	3.57263i	−0.149524	+	0.216622i
$273$	−6.96536	+	11.2679i	−0.421563	+	0.681967i
$274$	−3.53667	−	5.12375i	−0.213658	−	0.309537i
$275$	−1.73051	+	14.2521i	−0.104354	+	0.859432i
$276$	1.62884	+	13.4147i	0.0980448	+	0.807471i
$277$	−6.05488	+	3.17785i	−0.363803	+	0.190938i	−0.636713	−	0.771101i	$-0.719706\pi$
$277$	−6.05488	+	3.17785i	−0.363803	+	0.190938i	0.272910	+	0.962040i	$0.412014\pi$
$278$	2.77140	−	0.683088i	0.166217	−	0.0409689i
$279$	−0.802098	−	6.60587i	−0.0480203	−	0.395483i
$280$	2.63146	−	2.33127i	0.157260	−	0.139320i
$281$	−11.4628	+	16.6068i	−0.683815	+	0.990678i	0.315315	+	0.948987i	$0.397890\pi$
$281$	−11.4628	+	16.6068i	−0.683815	+	0.990678i	−0.999131	+	0.0416906i	$0.986726\pi$
$282$	−2.79800	−	4.05360i	−0.166618	−	0.241388i
$283$	20.8986	+	5.15103i	1.24229	+	0.306197i	0.805082	−	0.593163i	$-0.202121\pi$
$283$	20.8986	+	5.15103i	1.24229	+	0.306197i	0.437209	+	0.899360i	$0.355967\pi$
$284$	0.0807334	+	0.664900i	0.00479065	+	0.0394545i
$285$	−1.49476	−	0.784512i	−0.0885421	−	0.0464705i
$286$	−6.89787	+	4.07697i	−0.407880	+	0.241076i
$287$	−1.74995	+	0.918442i	−0.103296	+	0.0542139i
$288$	4.23503	+	6.13549i	0.249551	+	0.361537i
$289$	−5.14464	−	7.45329i	−0.302626	−	0.438429i
$290$	−0.419890	−	0.371990i	−0.0246568	−	0.0218440i
$291$	21.2450	+	18.8215i	1.24541	+	1.10333i
$292$	−7.67203	−	20.2295i	−0.448972	−	1.18384i
$293$	21.6529	−	11.3643i	1.26498	−	0.663911i	0.307261	−	0.951625i	$-0.400588\pi$
$293$	21.6529	−	11.3643i	1.26498	−	0.663911i	0.957716	+	0.287714i	$0.0928952\pi$
$294$	1.88566	+	4.97209i	0.109974	+	0.289978i
$295$	−0.963488	+	0.237478i	−0.0560964	+	0.0138265i
$296$	1.29708	+	1.14911i	0.0753913	+	0.0667909i
$297$	−6.70582	+	9.71505i	−0.389111	+	0.563725i
$298$	5.15151	−	13.5834i	0.298419	−	0.786865i
$299$	12.9959	−	7.68119i	0.751572	−	0.444215i
$300$	−4.91896	−	12.9702i	−0.283996	−	0.748836i
$301$	−16.0590	−	3.95818i	−0.925624	−	0.228146i
$302$	3.19406	+	1.67637i	0.183797	+	0.0964644i
$303$	−7.07817	+	18.6636i	−0.406630	+	1.07220i
$304$	−0.180496	+	1.48652i	−0.0103521	+	0.0852575i
$305$	6.71695	+	9.73118i	0.384611	+	0.557206i
$306$	2.35717	−	0.580991i	0.134751	−	0.0332130i
$307$	−19.2746	−	4.75076i	−1.10006	−	0.271140i	−0.352818	−	0.935692i	$-0.614776\pi$
$307$	−19.2746	−	4.75076i	−1.10006	−	0.271140i	−0.747242	+	0.664552i	$0.768623\pi$
$308$	−1.11170	+	9.15566i	−0.0633449	+	0.521692i
$309$	1.51059	+	3.98309i	0.0859342	+	0.226590i
$310$	2.78171	−	0.685629i	0.157990	−	0.0389411i
$311$	1.19669	+	0.294958i	0.0678581	+	0.0167255i	0.273099	−	0.961986i	$-0.411951\pi$
$311$	1.19669	+	0.294958i	0.0678581	+	0.0167255i	−0.205240	+	0.978712i	$0.565798\pi$
$312$	9.29840	−	15.0421i	0.526418	−	0.851593i
$313$	24.4816	−	6.03418i	1.38378	−	0.341072i	0.523995	−	0.851722i	$-0.324441\pi$
$313$	24.4816	−	6.03418i	1.38378	−	0.341072i	0.859789	+	0.510650i	$0.170595\pi$
$314$	13.3436	−	7.00328i	0.753025	−	0.395218i
$315$	1.92325			0.108363
$316$	1.50441			0.0846299
$317$	−5.34365	+	2.80457i	−0.300129	+	0.157520i	−0.608065	−	0.793887i	$-0.708054\pi$
$317$	−5.34365	+	2.80457i	−0.300129	+	0.157520i	0.307936	+	0.951407i	$0.400362\pi$
$318$	−8.92512	−	7.90697i	−0.500496	−	0.443401i
$319$	3.36156			0.188211
$320$	−0.470571	+	0.416889i	−0.0263057	+	0.0233048i
$321$	−2.21335	−	1.16166i	−0.123537	−	0.0648374i
$322$	−0.595254	+	4.90236i	−0.0331722	+	0.273198i
$323$	2.42624	+	1.27339i	0.135000	+	0.0708533i
$324$	2.10397	−	17.3277i	0.116887	−	0.962652i
$325$	−11.0659	+	10.8484i	−0.613828	+	0.601761i
$326$	1.82617	+	15.0398i	0.101142	+	0.832980i
$327$	−6.30366	+	16.6214i	−0.348593	+	0.919165i
$328$	2.33609	−	1.22607i	0.128989	−	0.0676986i
$329$	2.24591	+	5.92199i	0.123821	+	0.326490i
$330$	3.41678	+	1.79326i	0.188088	+	0.0987159i
$331$	−26.4747	−	13.8950i	−1.45518	−	0.763739i	−0.462746	−	0.886491i	$-0.653136\pi$
$331$	−26.4747	−	13.8950i	−1.45518	−	0.763739i	−0.992437	+	0.122752i	$0.960828\pi$
$332$	−27.1381	−	6.68894i	−1.48940	−	0.367103i
$333$	0.114268	+	0.941083i	0.00626186	+	0.0515710i
$334$	−10.4713	+	9.27680i	−0.572967	+	0.507604i
$335$	1.25418	−	1.81699i	0.0685232	−	0.0992730i
$336$	−2.00668	−	5.29119i	−0.109474	−	0.288658i
$337$	23.1057			1.25865			0.629325	−	0.777142i	$-0.283332\pi$
$337$	23.1057			1.25865			0.629325	+	0.777142i	$0.283332\pi$
$338$	−8.56332	−	1.21272i	−0.465783	−	0.0659635i
$339$	−39.7922			−2.16122
$340$	−1.30415	−	3.43877i	−0.0707276	−	0.186493i
$341$	−9.75258	+	14.1291i	−0.528132	+	0.765131i
$342$	0.626826	−	0.555320i	0.0338949	−	0.0300282i
$343$	−2.32008	−	19.1076i	−0.125273	−	1.03171i
$344$	21.4379	+	5.28397i	1.15585	+	0.284893i
$345$	−6.43736	−	3.37859i	−0.346576	−	0.181897i
$346$	−9.87297	−	5.18173i	−0.530774	−	0.278572i
$347$	10.9297	+	28.8191i	0.586735	+	1.54709i	0.818612	+	0.574347i	$0.194744\pi$
$347$	10.9297	+	28.8191i	0.586735	+	1.54709i	−0.231877	+	0.972745i	$0.574487\pi$
$348$	−2.87594	+	1.50941i	−0.154167	+	0.0809130i
$349$	−10.5012	+	27.6894i	−0.562116	+	1.48218i	0.289068	+	0.957309i	$0.406655\pi$
$349$	−10.5012	+	27.6894i	−0.562116	+	1.48218i	−0.851183	+	0.524869i	$0.824114\pi$
$350$	−0.611042	−	5.03238i	−0.0326616	−	0.268992i
$351$	−12.2019	+	3.66981i	−0.651292	+	0.195880i
$352$	2.31841	−	19.0939i	0.123572	−	1.01771i
$353$	1.71045	+	0.897712i	0.0910379	+	0.0477804i	0.509628	−	0.860395i	$-0.329783\pi$
$353$	1.71045	+	0.897712i	0.0910379	+	0.0477804i	−0.418590	+	0.908175i	$0.637475\pi$
$354$	0.196822	−	1.62097i	0.0104610	−	0.0861537i
$355$	−0.319067	−	0.167459i	−0.0169343	−	0.00888782i
$356$	−0.643719	+	0.570285i	−0.0341170	+	0.0302251i
$357$	−10.3551			−0.548049
$358$	6.35976	+	5.63426i	0.336124	+	0.297780i
$359$	−11.7667	+	6.17563i	−0.621022	+	0.325937i	−0.745722	−	0.666257i	$-0.767895\pi$
$359$	−11.7667	+	6.17563i	−0.621022	+	0.325937i	0.124700	+	0.992194i	$0.460203\pi$
$360$	−2.56744			−0.135316
$361$	−18.0548			−0.950253
$362$	3.38164	−	1.77482i	0.177735	−	0.0932826i
$363$	−0.317882	+	0.0783508i	−0.0166845	+	0.00411235i
$364$	−7.10886	+	6.96911i	−0.372605	+	0.365281i
$365$	11.3016	+	2.78559i	0.591553	+	0.145805i
$366$	−18.8916	+	4.65635i	−0.987478	+	0.243392i
$367$	8.48261	+	22.3668i	0.442789	+	1.16754i	0.951784	+	0.306769i	$0.0992478\pi$
$367$	8.48261	+	22.3668i	0.442789	+	1.16754i	−0.508995	+	0.860769i	$0.669983\pi$
$368$	−0.777324	+	6.40184i	−0.0405208	+	0.333719i
$369$	1.40137	+	0.345406i	0.0729523	+	0.0179811i
$370$	−0.396286	+	0.0976758i	−0.0206020	+	0.00507793i
$371$	8.70989	+	12.6185i	0.452195	+	0.655117i
$372$	1.99946	−	16.4671i	0.103667	−	0.853777i
$373$	−6.13099	+	16.1661i	−0.317451	+	0.837049i	0.677392	+	0.735622i	$0.263110\pi$
$373$	−6.13099	+	16.1661i	−0.317451	+	0.837049i	−0.994843	+	0.101427i	$0.967659\pi$
$374$	−5.54598	−	2.91076i	−0.286776	−	0.150512i
$375$	15.6757	+	3.86372i	0.809491	+	0.199522i
$376$	−2.99818	−	7.90555i	−0.154619	−	0.407698i
$377$	2.83390	+	2.26597i	0.145953	+	0.116703i
$378$	1.47807	−	3.89734i	0.0760236	−	0.200458i
$379$	−19.7715	+	28.6439i	−1.01559	+	1.47134i	−0.138890	+	0.990308i	$0.544354\pi$
$379$	−19.7715	+	28.6439i	−1.01559	+	1.47134i	−0.876703	+	0.481033i	$0.840262\pi$
$380$	−0.949582	−	0.841256i	−0.0487125	−	0.0431555i
$381$	−10.6795	+	2.63225i	−0.547125	+	0.134854i
$382$	−0.155212	−	0.409261i	−0.00794134	−	0.0209396i
$383$	17.7452	−	9.31339i	0.906737	−	0.475892i	0.0541827	−	0.998531i	$-0.482745\pi$
$383$	17.7452	−	9.31339i	0.906737	−	0.475892i	0.852554	+	0.522639i	$0.175052\pi$
$384$	8.09611	+	21.3477i	0.413153	+	1.08939i
$385$	−3.71404	−	3.29035i	−0.189285	−	0.167692i
$386$	8.45194	+	7.48776i	0.430192	+	0.381117i
$387$	6.86158	+	9.94071i	0.348794	+	0.505315i
$388$	12.1168	+	17.5542i	0.615135	+	0.891177i
$389$	25.2576	−	13.2562i	1.28061	−	0.672116i	0.319318	−	0.947647i	$-0.396546\pi$
$389$	25.2576	−	13.2562i	1.28061	−	0.672116i	0.961292	+	0.275531i	$0.0888537\pi$
$390$	1.67164	+	3.81496i	0.0846467	+	0.193178i
$391$	10.4489	+	5.48399i	0.528422	+	0.277337i
$392$	1.10028	+	9.06160i	0.0555724	+	0.457680i
$393$	22.5247	+	5.55184i	1.13622	+	0.280053i
$394$	−3.20445	−	4.64244i	−0.161438	−	0.233883i
$395$	−0.459776	+	0.666101i	−0.0231338	+	0.0335152i
$396$	5.04159	−	4.46646i	0.253349	−	0.224448i
$397$	−1.63785	−	13.4889i	−0.0822011	−	0.676987i	−0.974317	−	0.225181i	$-0.927703\pi$
$397$	−1.63785	−	13.4889i	−0.0822011	−	0.676987i	0.892116	−	0.451807i	$-0.149220\pi$
$398$	2.49755	−	0.615590i	0.125191	−	0.0308568i
$399$	−3.16280	+	1.65996i	−0.158338	+	0.0831022i
$400$	−0.797941	−	6.57164i	−0.0398971	−	0.328582i
$401$	2.19503	−	18.0777i	0.109615	−	0.902757i	−0.829347	−	0.558734i	$-0.811287\pi$
$401$	2.19503	−	18.0777i	0.109615	−	0.902757i	0.938961	−	0.344023i	$-0.111790\pi$
$402$	2.06377	+	2.98988i	0.102931	+	0.149122i
$403$	−17.7459	+	5.33717i	−0.883984	+	0.265863i
$404$	−8.52125	+	12.3452i	−0.423948	+	0.614195i
$405$	7.02909	+	6.22723i	0.349278	+	0.309434i
$406$	−1.15247	+	0.284059i	−0.0571962	+	0.0140976i
$407$	1.38937	−	2.01285i	0.0688684	−	0.0997732i
$408$	13.8235			0.684366
$409$	−7.71205	+	11.1728i	−0.381336	+	0.552461i	−0.965910	−	0.258880i	$-0.916647\pi$
$409$	−7.71205	+	11.1728i	−0.381336	+	0.552461i	0.584573	+	0.811341i	$0.301262\pi$
$410$	−0.0749011	+	0.616866i	−0.00369910	+	0.0304649i
$411$	6.87699	−	18.1331i	0.339217	−	0.894442i
$412$	0.385877	+	3.17798i	0.0190108	+	0.156568i
$413$	−0.744556	+	1.96323i	−0.0366372	+	0.0966043i
$414$	2.69950	−	2.39155i	0.132673	−	0.117538i
$415$	11.2555	−	9.97151i	0.552511	−	0.489482i
$416$	14.8253	−	14.5339i	0.726871	−	0.712582i
$417$	6.65519	+	5.89598i	0.325906	+	0.288728i
$418$	−2.16054			−0.105676
$419$	−9.08066	+	8.04476i	−0.443619	+	0.393012i	−0.855148	−	0.518385i	$-0.826534\pi$
$419$	−9.08066	+	8.04476i	−0.443619	+	0.393012i	0.411528	+	0.911397i	$0.364995\pi$
$420$	4.65494	+	1.14734i	0.227138	+	0.0559845i
$421$	−8.40860	−	12.1820i	−0.409810	−	0.593713i	0.562675	−	0.826678i	$-0.309772\pi$
$421$	−8.40860	−	12.1820i	−0.409810	−	0.593713i	−0.972485	+	0.232966i	$0.925157\pi$
$422$	1.28729	−	3.39429i	0.0626641	−	0.165232i
$423$	1.64019	−	4.32483i	0.0797489	−	0.210280i
$424$	−11.6273	−	16.8450i	−0.564670	−	0.818065i
$425$	−11.7615	−	2.89896i	−0.570519	−	0.140620i
$426$	0.443827	−	0.393197i	0.0215035	−	0.0190504i
$427$	25.0192			1.21076
$428$	−1.40608	−	1.24568i	−0.0679656	−	0.0602123i
$429$	−22.6576	−	10.4690i	−1.09392	−	0.505450i
$430$	−3.89255	+	3.44850i	−0.187715	+	0.166301i
$431$	7.65943	−	6.78566i	0.368942	−	0.326854i	−0.458198	−	0.888850i	$-0.651505\pi$
$431$	7.65943	−	6.78566i	0.368942	−	0.326854i	0.827140	+	0.561996i	$0.189966\pi$
$432$	1.93016	−	5.08942i	0.0928651	−	0.244865i
$433$	−0.676258	−	5.56948i	−0.0324989	−	0.267652i	−0.999896	−	0.0143897i	$-0.995419\pi$
$433$	−0.676258	−	5.56948i	−0.0324989	−	0.267652i	0.967398	−	0.253262i	$-0.0815036\pi$
$434$	2.14962	−	5.66809i	0.103185	−	0.272077i
$435$	0.210627	−	1.73467i	0.0100988	−	0.0831710i
$436$	−7.58884	+	10.9943i	−0.363440	+	0.526533i
$437$	4.07055			0.194721
$438$	−10.8804	+	15.7630i	−0.519886	+	0.753185i
$439$	27.5372	−	6.78730i	1.31428	−	0.323940i	0.480964	−	0.876740i	$-0.340287\pi$
$439$	27.5372	−	6.78730i	1.31428	−	0.323940i	0.833314	+	0.552800i	$0.186441\pi$
$440$	4.95806	+	4.39245i	0.236366	+	0.209402i
$441$	−2.83673	+	4.10971i	−0.135082	+	0.195701i
$442$	−2.71334	−	6.19230i	−0.129060	−	0.294538i
$443$	−11.5337	−	16.7095i	−0.547983	−	0.793891i	0.446936	−	0.894566i	$-0.352515\pi$
$443$	−11.5337	−	16.7095i	−0.547983	−	0.793891i	−0.994919	+	0.100675i	$0.967900\pi$
$444$	−0.284847	+	2.34592i	−0.0135182	+	0.111333i
$445$	−0.0557697	−	0.459305i	−0.00264374	−	0.0217731i
$446$	−1.63369	+	0.857427i	−0.0773575	+	0.0406003i
$447$	43.9379	−	10.8297i	2.07819	−	0.512229i
$448$	0.160341	+	1.32053i	0.00757541	+	0.0623892i
$449$	21.7330	−	19.2538i	1.02565	−	0.908643i	0.0297870	−	0.999556i	$-0.490517\pi$
$449$	21.7330	−	19.2538i	1.02565	−	0.908643i	0.995859	+	0.0909134i	$0.0289786\pi$
$450$	−2.10306	+	3.04681i	−0.0991391	+	0.143628i
$451$	−2.11529	−	3.06453i	−0.0996053	−	0.144303i
$452$	−29.0349	−	7.15647i	−1.36569	−	0.336612i
$453$	1.35442	+	11.1546i	0.0636360	+	0.524090i
$454$	9.89116	+	5.19128i	0.464215	+	0.243639i
$455$	−0.913078	−	5.27743i	−0.0428058	−	0.247410i
$456$	4.22218	−	2.21597i	0.197721	−	0.103772i
$457$	−2.65318	−	3.84379i	−0.124110	−	0.179805i	0.756003	−	0.654568i	$-0.227149\pi$
$457$	−2.65318	−	3.84379i	−0.124110	−	0.179805i	−0.880114	+	0.474763i	$0.842534\pi$
$458$	−3.09534	−	4.48437i	−0.144636	−	0.209541i
$459$	−7.45533	−	6.60485i	−0.347985	−	0.308288i
$460$	−4.08948	−	3.62296i	−0.190673	−	0.168922i
$461$	−8.16012	−	21.5165i	−0.380055	−	1.00212i	−0.979453	−	0.201671i	$-0.935363\pi$
$461$	−8.16012	−	21.5165i	−0.380055	−	1.00212i	0.599399	−	0.800451i	$-0.295406\pi$
$462$	7.22963	−	3.79440i	0.336353	−	0.176532i
$463$	10.6549	+	28.0946i	0.495173	+	1.30567i	0.916963	+	0.398971i	$0.130633\pi$
$463$	10.6549	+	28.0946i	0.495173	+	1.30567i	−0.421790	+	0.906694i	$0.638598\pi$
$464$	−1.50498	+	0.370944i	−0.0698668	+	0.0172206i
$465$	6.67995	+	5.91792i	0.309775	+	0.274437i
$466$	−3.28394	+	4.75761i	−0.152126	+	0.220392i
$467$	0.244349	−	0.644294i	0.0113071	−	0.0298144i	−0.929244	−	0.369467i	$-0.879540\pi$
$467$	0.244349	−	0.644294i	0.0113071	−	0.0298144i	0.940551	+	0.339653i	$0.110310\pi$
$468$	7.26096	−	0.366911i	0.335638	−	0.0169605i
$469$	−1.65656	−	4.36798i	−0.0764927	−	0.201695i
$470$	1.93354	+	0.476575i	0.0891875	+	0.0219828i
$471$	41.5653	+	21.8152i	1.91523	+	1.00519i
$472$	0.993944	−	2.62081i	0.0457500	−	0.120633i
$473$	3.75629	−	30.9358i	0.172714	−	1.42243i
$474$	−0.756566	−	1.09608i	−0.0347502	−	0.0503444i
$475$	−4.05710	+	0.999985i	−0.186152	+	0.0458824i
$476$	−7.55572	−	1.86232i	−0.346316	−	0.0853592i
$477$	1.34969	−	11.1157i	0.0617983	−	0.508955i
$478$	−4.20103	−	11.0772i	−0.192150	−	0.506659i
$479$	21.9659	−	5.41412i	1.00365	−	0.247377i	0.296951	−	0.954893i	$-0.404030\pi$
$479$	21.9659	−	5.41412i	1.00365	−	0.247377i	0.706698	+	0.707515i	$0.250184\pi$
$480$	−9.70774	−	2.39274i	−0.443096	−	0.109213i
$481$	2.52810	−	0.760342i	0.115272	−	0.0346686i
$482$	−6.45043	+	1.58989i	−0.293809	+	0.0724174i
$483$	−13.6209	+	7.14882i	−0.619774	+	0.325283i
$484$	−0.246038			−0.0111835
$485$	−11.4754			−0.521073
$486$	−7.43720	+	3.90335i	−0.337358	+	0.177059i
$487$	−27.3338	−	24.2157i	−1.23861	−	1.09732i	−0.991739	−	0.128269i	$-0.959058\pi$
$487$	−27.3338	−	24.2157i	−1.23861	−	1.09732i	−0.246875	−	0.969047i	$-0.579404\pi$
$488$	−33.3994			−1.51192
$489$	−35.3245	+	31.2948i	−1.59743	+	1.41520i
$490$	−1.90369	−	0.999135i	−0.0860001	−	0.0451363i
$491$	−4.49586	+	37.0267i	−0.202895	+	1.67099i	0.434666	+	0.900592i	$0.356866\pi$
$491$	−4.49586	+	37.0267i	−0.202895	+	1.67099i	−0.637561	+	0.770400i	$0.720057\pi$
$492$	3.18575	+	1.67201i	0.143625	+	0.0753801i
$493$	−0.341881	+	2.81565i	−0.0153976	+	0.126810i
$494$	−1.82140	−	1.45638i	−0.0819487	−	0.0655258i
$495$	0.436787	+	3.59726i	0.0196321	+	0.161685i
$496$	2.80713	−	7.40179i	0.126044	−	0.332350i
$497$	−0.675121	+	0.354331i	−0.0302833	+	0.0158939i
$498$	8.77430	+	23.1359i	0.393186	+	1.03675i
$499$	25.6260	+	13.4496i	1.14718	+	0.602086i	0.927624	−	0.373515i	$-0.121847\pi$
$499$	25.6260	+	13.4496i	1.14718	+	0.602086i	0.219554	+	0.975600i	$0.429540\pi$
$500$	10.7431	+	5.63843i	0.480447	+	0.252158i
$501$	−42.3111	−	10.4288i	−1.89032	−	0.465923i
$502$	−1.83191	−	15.0872i	−0.0817622	−	0.673373i
$503$	−17.5098	+	15.5123i	−0.780723	+	0.691660i	−0.956165	−	0.292830i	$-0.905403\pi$
$503$	−17.5098	+	15.5123i	−0.780723	+	0.691660i	0.175442	+	0.984490i	$0.443865\pi$
$504$	−3.08601	+	4.47085i	−0.137462	+	0.199148i
$505$	−2.86175	−	7.54581i	−0.127346	−	0.335784i
$506$	−9.30461			−0.413641
$507$	−12.0440	−	24.0988i	−0.534894	−	1.07026i
$508$	−8.26581			−0.366736
$509$	−9.79810	−	25.8355i	−0.434293	−	1.14514i	−0.956349	−	0.292226i	$-0.905604\pi$
$509$	−9.79810	−	25.8355i	−0.434293	−	1.14514i	0.522056	−	0.852911i	$-0.325165\pi$
$510$	−1.84954	+	2.67952i	−0.0818989	+	0.118651i
$511$	18.4350	−	16.3320i	0.815518	−	0.722486i
$512$	1.94780	+	16.0416i	0.0860815	+	0.708945i
$513$	−3.33590	−	0.822226i	−0.147284	−	0.0363022i
$514$	−13.5251	−	7.09850i	−0.596565	−	0.313101i
$515$	−1.52503	−	0.800396i	−0.0672008	−	0.0352697i
$516$	10.6772	+	28.1534i	0.470037	+	1.23939i
$517$	−10.5665	+	5.54572i	−0.464713	+	0.243900i
$518$	−0.306239	+	0.807485i	−0.0134554	+	0.0354789i
$519$	−4.18656	−	34.4794i	−0.183769	−	1.51348i
$520$	1.21891	+	7.04511i	0.0534529	+	0.308948i
$521$	2.40188	−	19.7813i	0.105228	−	0.866633i	−0.840531	−	0.541764i	$-0.817757\pi$
$521$	2.40188	−	19.7813i	0.105228	−	0.866633i	0.945759	−	0.324869i	$-0.105320\pi$
$522$	0.767548	+	0.402840i	0.0335947	+	0.0176318i
$523$	4.46167	−	36.7452i	0.195095	−	1.60675i	−0.485595	−	0.874184i	$-0.661397\pi$
$523$	4.46167	−	36.7452i	0.195095	−	1.60675i	0.680691	−	0.732571i	$-0.261680\pi$
$524$	15.4370	+	8.10194i	0.674367	+	0.353935i
$525$	11.8197	−	10.4714i	0.515854	−	0.457007i
$526$	1.41204			0.0615679
$527$	−10.8426	−	9.60574i	−0.472313	−	0.418433i
$528$	9.44096	−	4.95500i	0.410865	−	0.215639i
$529$	−5.46971			−0.237813
$530$	4.82088			0.209406
$531$	1.35775	−	0.712604i	0.0589215	−	0.0309244i
$532$	−2.60632	+	0.642399i	−0.112998	+	0.0278515i
$533$	0.282491	−	4.00937i	0.0122360	−	0.173665i
$534$	0.739219	+	0.182201i	0.0319891	+	0.00788461i
$535$	0.981268	−	0.241861i	0.0424239	−	0.0104566i
$536$	2.21142	+	5.83103i	0.0955187	+	0.251862i
$537$	−3.19021	+	26.2737i	−0.137668	+	1.13380i
$538$	−15.3780	−	3.79034i	−0.662993	−	0.163413i
$539$	12.5091	−	3.08322i	0.538806	−	0.132804i
$540$	2.61960	+	3.79514i	0.112729	+	0.163317i
$541$	1.73477	−	14.2871i	0.0745835	−	0.614250i	−0.906713	−	0.421748i	$-0.861417\pi$
$541$	1.73477	−	14.2871i	0.0745835	−	0.614250i	0.981297	−	0.192502i	$-0.0616603\pi$
$542$	1.18878	−	3.13456i	0.0510625	−	0.134641i
$543$	10.5338	+	5.52856i	0.452048	+	0.237253i
$544$	15.7572	+	3.88381i	0.675586	+	0.166517i
$545$	−2.54861	−	6.72013i	−0.109170	−	0.287859i
$546$	8.65253	+	1.67457i	0.370294	+	0.0716651i
$547$	−10.7057	+	28.2285i	−0.457741	+	1.20696i	0.485319	+	0.874337i	$0.338704\pi$
$547$	−10.7057	+	28.2285i	−0.457741	+	1.20696i	−0.943059	+	0.332625i	$0.892066\pi$
$548$	8.27906	−	11.9943i	0.353664	−	0.512371i
$549$	−13.6764	−	12.1163i	−0.583696	−	0.517110i
$550$	9.27385	−	2.28580i	0.395438	−	0.0974668i
$551$	0.346938	+	0.914800i	0.0147801	+	0.0389718i
$552$	18.1833	−	9.54331i	0.773931	−	0.406190i
$553$	0.607285	+	1.60128i	0.0258244	+	0.0680933i
$554$	3.40524	+	3.01678i	0.144675	+	0.128171i
$555$	−0.951636	−	0.843076i	−0.0403947	−	0.0357866i
$556$	3.79568	+	5.49899i	0.160973	+	0.233209i
$557$	−10.7758	−	15.6114i	−0.456584	−	0.661476i	0.525310	−	0.850911i	$-0.323950\pi$
$557$	−10.7758	−	15.6114i	−0.456584	−	0.661476i	−0.981893	+	0.189436i	$0.939334\pi$
$558$	−3.92000	+	2.05737i	−0.165947	+	0.0870956i
$559$	24.0199	−	23.5478i	1.01594	−	0.995964i
$560$	2.02587	+	1.06326i	0.0856086	+	0.0449308i
$561$	−2.35173	−	19.3683i	−0.0992902	−	0.817729i
$562$	13.0346	+	3.21274i	0.549832	+	0.135521i
$563$	16.9492	+	24.5552i	0.714324	+	1.03488i	0.997131	+	0.0756999i	$0.0241191\pi$
$563$	16.9492	+	24.5552i	0.714324	+	1.03488i	−0.282807	+	0.959177i	$0.591266\pi$
$564$	6.54989	−	9.48915i	0.275800	−	0.399565i
$565$	12.0422	−	10.6685i	0.506620	−	0.448826i
$566$	−1.72605	−	14.2153i	−0.0725513	−	0.597514i
$567$	19.2927	−	4.75523i	0.810219	−	0.199701i
$568$	0.901252	−	0.473014i	0.0378157	−	0.0198472i
$569$	0.818835	+	6.74372i	0.0343274	+	0.282711i	0.999757	+	0.0220472i	$0.00701841\pi$
$569$	0.818835	+	6.74372i	0.0343274	+	0.282711i	−0.965430	+	0.260664i	$0.916059\pi$
$570$	−0.135374	+	1.11491i	−0.00567019	+	0.0466983i
$571$	4.95459	+	7.17796i	0.207343	+	0.300388i	0.912834	−	0.408331i	$-0.133889\pi$
$571$	4.95459	+	7.17796i	0.207343	+	0.300388i	−0.705491	+	0.708719i	$0.749274\pi$
$572$	−14.6496	−	11.7137i	−0.612530	−	0.489776i
$573$	0.774525	−	1.12209i	0.0323563	−	0.0468761i
$574$	0.984162	+	0.871891i	0.0410781	+	0.0363920i
$575$	−17.4723	+	4.30654i	−0.728647	+	0.179595i
$576$	0.551856	−	0.799501i	0.0229940	−	0.0333125i
$577$	3.23138			0.134524			0.0672621	−	0.997735i	$-0.478574\pi$
$577$	3.23138			0.134524			0.0672621	+	0.997735i	$0.478574\pi$
$578$	−3.42268	+	4.95860i	−0.142365	+	0.206251i
$579$	−4.23969	+	34.9170i	−0.176196	+	1.45110i
$580$	0.465659	−	1.22784i	0.0193355	−	0.0509834i
$581$	−3.83518	−	31.5855i	−0.159110	−	1.31039i
$582$	6.69599	−	17.6559i	0.277558	−	0.731860i
$583$	−21.6236	+	19.1568i	−0.895558	+	0.793395i
$584$	−24.6098	+	21.8024i	−1.01836	+	0.902190i
$585$	−2.05663	+	3.32703i	−0.0850310	+	0.137556i
$586$	−12.1775	−	10.7883i	−0.503048	−	0.445662i
$587$	29.0103			1.19738			0.598692	−	0.800979i	$-0.295687\pi$
$587$	29.0103			1.19738			0.598692	+	0.800979i	$0.295687\pi$
$588$	−9.31760	+	8.25467i	−0.384251	+	0.340417i
$589$	−4.85156	−	1.19580i	−0.199905	−	0.0492721i
$590$	0.375026	+	0.543319i	0.0154396	+	0.0223681i
$591$	6.23099	−	16.4298i	0.256309	−	0.675830i
$592$	−0.399908	+	1.05447i	−0.0164361	+	0.0433385i
$593$	12.7437	+	18.4624i	0.523319	+	0.758159i	0.992140	−	0.125134i	$-0.0399362\pi$
$593$	12.7437	+	18.4624i	0.523319	+	0.758159i	−0.468820	+	0.883294i	$0.655321\pi$
$594$	7.62532	+	1.87947i	0.312871	+	0.0771157i
$595$	3.13373	−	2.77624i	0.128470	−	0.113815i
$596$	34.0076			1.39300
$597$	5.99757	+	5.31339i	0.245464	+	0.217462i
$598$	−7.84406	−	6.27207i	−0.320768	−	0.256484i
$599$	−17.5046	+	15.5077i	−0.715219	+	0.633629i	−0.940156	−	0.340745i	$-0.889321\pi$
$599$	−17.5046	+	15.5077i	−0.715219	+	0.633629i	0.224937	+	0.974373i	$0.427782\pi$
$600$	−15.7787	+	13.9787i	−0.644163	+	0.570679i
$601$	−4.52169	+	11.9227i	−0.184443	+	0.486337i	−0.995064	−	0.0992342i	$-0.968361\pi$
$601$	−4.52169	+	11.9227i	−0.184443	+	0.486337i	0.810621	+	0.585572i	$0.199130\pi$
$602$	1.32634	+	10.9234i	0.0540576	+	0.445204i
$603$	−1.20978	+	3.18994i	−0.0492662	+	0.129904i
$604$	−1.01784	+	8.38271i	−0.0414155	+	0.341087i
$605$	0.0751935	−	0.108937i	0.00305705	−	0.00442890i
$606$	13.2797			0.539449
$607$	6.78844	−	9.83475i	0.275534	−	0.399180i	−0.660648	−	0.750696i	$-0.729718\pi$
$607$	6.78844	−	9.83475i	0.275534	−	0.399180i	0.936182	+	0.351516i	$0.114334\pi$
$608$	5.43540	−	1.33970i	0.220434	−	0.0543322i
$609$	−2.76753	−	2.45181i	−0.112146	−	0.0993525i
$610$	4.46872	−	6.47406i	0.180933	−	0.262127i
$611$	−12.6461	−	2.44747i	−0.511608	−	0.0990142i
$612$	3.22836	+	4.67709i	0.130499	+	0.189060i
$613$	−2.32413	+	19.1409i	−0.0938708	+	0.773095i	0.867423	+	0.497571i	$0.165775\pi$
$613$	−2.32413	+	19.1409i	−0.0938708	+	0.773095i	−0.961294	+	0.275524i	$0.911148\pi$
$614$	1.59192	+	13.1107i	0.0642449	+	0.529104i
$615$	−1.71393	+	0.899540i	−0.0691123	+	0.0362729i
$616$	13.6084	−	3.35416i	0.548297	−	0.135143i
$617$	3.30011	+	27.1789i	0.132857	+	1.09418i	0.894779	+	0.446510i	$0.147333\pi$
$617$	3.30011	+	27.1789i	0.132857	+	1.09418i	−0.761921	+	0.647670i	$0.775744\pi$
$618$	2.12134	−	1.87934i	0.0853327	−	0.0755981i
$619$	−16.7623	+	24.2844i	−0.673734	+	0.976073i	0.325796	+	0.945440i	$0.394368\pi$
$619$	−16.7623	+	24.2844i	−0.673734	+	0.976073i	−0.999531	+	0.0306328i	$0.990248\pi$
$620$	3.80980	+	5.51945i	0.153005	+	0.221666i
$621$	−14.3664	−	3.54101i	−0.576505	−	0.142096i
$622$	−0.0988369	−	0.813995i	−0.00396300	−	0.0326382i
$623$	−0.866853	−	0.454960i	−0.0347297	−	0.0182276i
$624$	11.2991	+	2.18677i	0.452325	+	0.0875410i
$625$	13.2485	−	6.95336i	0.529941	−	0.278135i
$626$	−9.52919	−	13.8054i	−0.380863	−	0.551775i
$627$	−3.82312	−	5.53874i	−0.152681	−	0.221196i
$628$	26.4053	+	23.3931i	1.05369	+	0.933486i
$629$	1.54466	+	1.36845i	0.0615896	+	0.0545636i
$630$	−0.453723	−	1.19637i	−0.0180768	−	0.0476645i
$631$	21.8910	−	11.4893i	0.871468	−	0.457382i	0.0311746	−	0.999514i	$-0.490075\pi$
$631$	21.8910	−	11.4893i	0.871468	−	0.457382i	0.840293	+	0.542132i	$0.182383\pi$
$632$	−0.810695	−	2.13763i	−0.0322477	−	0.0850302i
$633$	10.9794	−	2.70619i	0.436394	−	0.107561i
$634$	3.00525	+	2.66242i	0.119354	+	0.105738i
$635$	2.52618	−	3.65980i	0.100248	−	0.145235i
$636$	9.89799	−	26.0989i	0.392481	−	1.03489i
$637$	12.6239	+	5.83293i	0.500177	+	0.231109i
$638$	−0.793043	−	2.09108i	−0.0313969	−	0.0827867i
$639$	0.540642	+	0.133256i	0.0213875	+	0.00527153i
$640$	−8.17352	−	4.28979i	−0.323087	−	0.169569i
$641$	4.77373	−	12.5873i	0.188551	−	0.497168i	−0.807091	−	0.590427i	$-0.798959\pi$
$641$	4.77373	−	12.5873i	0.188551	−	0.497168i	0.995642	+	0.0932593i	$0.0297286\pi$
$642$	−0.200454	+	1.65089i	−0.00791128	+	0.0651552i
$643$	2.62792	+	3.80720i	0.103635	+	0.150141i	0.871370	−	0.490626i	$-0.163232\pi$
$643$	2.62792	+	3.80720i	0.103635	+	0.150141i	−0.767735	+	0.640767i	$0.778616\pi$
$644$	−11.2244	+	2.76656i	−0.442303	+	0.109018i
$645$	−15.7285	−	3.87672i	−0.619307	−	0.152646i
$646$	0.219734	−	1.80967i	0.00864532	−	0.0712006i
$647$	15.5969	+	41.1256i	0.613176	+	1.61681i	0.776412	+	0.630226i	$0.217038\pi$
$647$	15.5969	+	41.1256i	0.613176	+	1.61681i	−0.163235	+	0.986587i	$0.552193\pi$
$648$	−25.7548	+	6.34799i	−1.01174	+	0.249373i
$649$	−3.84115	−	0.946757i	−0.150778	−	0.0371635i
$650$	9.35895	+	4.32434i	0.367088	+	0.169615i
$651$	18.3344	−	4.51903i	0.718583	−	0.177115i
$652$	−31.4032	+	16.4817i	−1.22985	+	0.645473i
$653$	−44.5562			−1.74362			−0.871809	−	0.489846i	$-0.837053\pi$
$653$	−44.5562			−1.74362			−0.871809	+	0.489846i	$0.837053\pi$
$654$	11.8266			0.462456
$655$	−8.30506	+	4.35883i	−0.324506	+	0.170314i
$656$	1.28519	+	1.13858i	0.0501781	+	0.0444539i
$657$	−17.9865			−0.701722
$658$	3.15397	−	2.79417i	0.122955	−	0.108928i
$659$	−31.2980	−	16.4264i	−1.21920	−	0.639883i	−0.272544	−	0.962143i	$-0.587865\pi$
$659$	−31.2980	−	16.4264i	−1.21920	−	0.639883i	−0.946651	+	0.322260i	$0.895557\pi$
$660$	−1.08882	+	8.96723i	−0.0423822	+	0.349049i
$661$	23.7819	+	12.4817i	0.925008	+	0.485482i	0.858792	−	0.512324i	$-0.171215\pi$
$661$	23.7819	+	12.4817i	0.925008	+	0.485482i	0.0662155	+	0.997805i	$0.478908\pi$
$662$	−2.39770	+	19.7468i	−0.0931893	+	0.767483i
$663$	11.0732	−	17.9133i	0.430048	−	0.695694i
$664$	5.11977	+	42.1651i	0.198686	+	1.63632i
$665$	0.512106	−	1.35031i	0.0198586	−	0.0523628i
$666$	0.558450	−	0.293097i	0.0216395	−	0.0113573i
$667$	1.49413	+	3.93969i	0.0578528	+	0.152545i
$668$	−28.9973	−	15.2190i	−1.12194	−	0.588839i
$669$	−5.08893	−	2.67088i	−0.196750	−	0.103262i
$670$	−1.42615	−	0.351515i	−0.0550971	−	0.0135802i
$671$	5.68209	+	46.7962i	0.219355	+	1.80655i
$672$	−15.8352	+	14.0287i	−0.610855	+	0.541170i
$673$	4.43854	−	6.43034i	0.171093	−	0.247871i	−0.728052	−	0.685522i	$-0.759574\pi$
$673$	4.43854	−	6.43034i	0.171093	−	0.247871i	0.899145	+	0.437651i	$0.144189\pi$
$674$	−5.45099	−	14.3731i	−0.209964	−	0.553630i
$675$	15.1888			0.584618
$676$	−4.45402	−	19.7501i	−0.171308	−	0.759618i
$677$	−47.7975			−1.83701			−0.918504	−	0.395412i	$-0.870602\pi$
$677$	−47.7975			−1.83701			−0.918504	+	0.395412i	$0.870602\pi$
$678$	9.38759	+	24.7530i	0.360528	+	0.950635i
$679$	−13.7933	+	19.9830i	−0.529337	+	0.766877i
$680$	−4.18337	+	3.70614i	−0.160425	+	0.142124i
$681$	4.19427	+	34.5429i	0.160725	+	1.32369i
$682$	11.0899	+	2.73340i	0.424653	+	0.104667i
$683$	−32.0459	−	16.8190i	−1.22620	−	0.643560i	−0.277802	−	0.960638i	$-0.589606\pi$
$683$	−32.0459	−	16.8190i	−1.22620	−	0.643560i	−0.948400	+	0.317078i	$0.897298\pi$
$684$	1.73581	+	0.911024i	0.0663704	+	0.0348339i
$685$	2.78041	+	7.33134i	0.106234	+	0.280116i
$686$	−11.3387	+	5.95100i	−0.432913	+	0.227210i
$687$	6.01883	−	15.8704i	0.229633	−	0.605492i
$688$	1.73203	+	14.2645i	0.0660329	+	0.543830i
$689$	−31.1426	+	1.57370i	−1.18644	+	0.0599531i
$690$	−0.583003	+	4.80146i	−0.0221946	+	0.182789i
$691$	−20.9518	−	10.9964i	−0.797045	−	0.418322i	0.0164707	−	0.999864i	$-0.494757\pi$
$691$	−20.9518	−	10.9964i	−0.797045	−	0.418322i	−0.813516	+	0.581543i	$0.802449\pi$
$692$	3.14620	−	25.9113i	0.119601	−	0.984999i
$693$	6.78917	+	3.56323i	0.257899	+	0.135356i
$694$	15.3487	−	13.5977i	0.582628	−	0.516163i
$695$	−3.59478			−0.136358
$696$	3.69451	+	3.27305i	0.140040	+	0.124065i
$697$	2.78199	−	1.46010i	0.105375	−	0.0553052i
$698$	19.7017			0.745722
$699$	−18.0075			−0.681108
$700$	10.5076	−	5.51483i	0.397151	−	0.208441i
$701$	−19.9987	+	4.92923i	−0.755340	+	0.186175i	−0.598139	−	0.801392i	$-0.704093\pi$
$701$	−19.9987	+	4.92923i	−0.755340	+	0.186175i	−0.157201	+	0.987567i	$0.550247\pi$
$702$	5.16145	+	6.72454i	0.194806	+	0.253801i
$703$	0.691161	+	0.170356i	0.0260676	+	0.00642509i
$704$	−2.43352	+	0.599808i	−0.0917167	+	0.0226061i
$705$	2.19969	+	5.80011i	0.0828452	+	0.218445i
$706$	0.154908	−	1.27578i	0.00583003	−	0.0480146i
$707$	−16.5798	−	4.08655i	−0.623547	−	0.153691i
$708$	3.71136	−	0.914768i	0.139481	−	0.0343791i
$709$	19.2921	+	27.9494i	0.724530	+	1.04966i	0.996185	+	0.0872680i	$0.0278136\pi$
$709$	19.2921	+	27.9494i	0.724530	+	1.04966i	−0.271655	+	0.962395i	$0.587571\pi$
$710$	−0.0288965	+	0.237984i	−0.00108447	+	0.00893139i
$711$	0.443501	−	1.16941i	0.0166326	−	0.0438565i
$712$	1.15721	+	0.607348i	0.0433681	+	0.0227613i
$713$	−20.8938	−	5.14985i	−0.782478	−	0.192863i
$714$	2.44292	+	6.44145i	0.0914240	+	0.241065i
$715$	9.66360	−	2.90638i	0.361398	−	0.108693i
$716$	−7.05300	+	18.5972i	−0.263583	+	0.695011i
$717$	20.9636	−	30.3710i	0.782899	−	1.13423i
$718$	6.61753	+	5.86262i	0.246964	+	0.218791i
$719$	8.82279	−	2.17462i	0.329035	−	0.0810998i	−0.0713379	−	0.997452i	$-0.522727\pi$
$719$	8.82279	−	2.17462i	0.329035	−	0.0810998i	0.400373	+	0.916352i	$0.368881\pi$
$720$	−0.592503	−	1.56230i	−0.0220813	−	0.0582236i
$721$	−3.22684	+	1.69358i	−0.120174	+	0.0630720i
$722$	4.25940	+	11.2311i	0.158519	+	0.417979i
$723$	−15.4900	−	13.7229i	−0.576078	−	0.510360i
$724$	6.69183	+	5.92844i	0.248700	+	0.220329i
$725$	−2.45702	−	3.55961i	−0.0912516	−	0.132201i
$726$	0.123732	+	0.179256i	0.00459211	+	0.00665282i
$727$	4.99974	−	2.62407i	0.185430	−	0.0973212i	−0.369454	−	0.929249i	$-0.620455\pi$
$727$	4.99974	−	2.62407i	0.185430	−	0.0973212i	0.554884	+	0.831928i	$0.312763\pi$
$728$	13.7332	+	6.34550i	0.508988	+	0.235180i
$729$	6.60538	+	3.46677i	0.244644	+	0.128399i
$730$	−0.933419	−	7.68740i	−0.0345474	−	0.284523i
$731$	25.5298	+	6.29254i	0.944255	+	0.232738i
$732$	−25.8737	−	37.4846i	−0.956320	−	1.38547i
$733$	−10.9970	+	15.9319i	−0.406182	+	0.588457i	−0.971682	−	0.236292i	$-0.924068\pi$
$733$	−10.9970	+	15.9319i	−0.406182	+	0.588457i	0.565500	+	0.824748i	$0.308683\pi$
$734$	11.9123	−	10.5533i	0.439689	−	0.389531i
$735$	−0.807247	−	6.64827i	−0.0297757	−	0.245225i
$736$	23.4081	−	5.76959i	0.862835	−	0.212670i
$737$	7.79370	−	4.09045i	0.287085	−	0.150674i
$738$	−0.115742	−	0.953217i	−0.00426051	−	0.0350884i
$739$	3.04429	−	25.0720i	0.111986	−	0.922289i	−0.823107	−	0.567886i	$-0.807761\pi$
$739$	3.04429	−	25.0720i	0.111986	−	0.922289i	0.935093	−	0.354402i	$-0.115316\pi$
$740$	−0.542750	−	0.786310i	−0.0199519	−	0.0289053i
$741$	0.510566	−	7.24642i	0.0187561	−	0.266204i
$742$	5.79460	−	8.39493i	0.212727	−	0.308188i
$743$	34.4028	+	30.4783i	1.26212	+	1.11814i	0.987672	+	0.156536i	$0.0500328\pi$
$743$	34.4028	+	30.4783i	1.26212	+	1.11814i	0.274446	+	0.961603i	$0.411506\pi$
$744$	−24.4755	+	6.03268i	−0.897317	+	0.221169i
$745$	−10.3933	+	15.0573i	−0.380782	+	0.551658i
$746$	11.5026			0.421141
$747$	−13.1998	+	19.1231i	−0.482954	+	0.699679i
$748$	1.76733	−	14.5553i	0.0646199	−	0.532193i
$749$	0.758295	−	1.99946i	0.0277075	−	0.0730587i
$750$	−1.29469	−	10.6627i	−0.0472752	−	0.389347i
$751$	−3.50752	+	9.24856i	−0.127991	+	0.337485i	−0.983659	−	0.180040i	$-0.942377\pi$
$751$	−3.50752	+	9.24856i	−0.127991	+	0.337485i	0.855668	+	0.517525i	$0.173146\pi$
$752$	4.11867	−	3.64883i	0.150193	−	0.133059i
$753$	35.4357	−	31.3933i	1.29135	−	1.14403i
$754$	0.741003	−	2.29742i	0.0269857	−	0.0836671i
$755$	−3.40049	−	3.01257i	−0.123756	−	0.109639i
$756$	9.75744			0.354875
$757$	−27.2140	+	24.1095i	−0.989111	+	0.876276i	−0.992317	−	0.123719i	$-0.960518\pi$
$757$	−27.2140	+	24.1095i	−0.989111	+	0.876276i	0.00320619	+	0.999995i	$0.498979\pi$
$758$	22.4826	+	5.54145i	0.816603	+	0.201275i
$759$	−16.4647	−	23.8532i	−0.597630	−	0.865816i
$760$	−0.683635	+	1.80260i	−0.0247980	+	0.0653871i
$761$	16.7285	−	44.1093i	0.606406	−	1.59896i	−0.181653	−	0.983363i	$-0.558145\pi$
$761$	16.7285	−	44.1093i	0.606406	−	1.59896i	0.788059	−	0.615600i	$-0.211086\pi$
$762$	4.15686	+	6.02225i	0.150587	+	0.218163i
$763$	−14.7656	−	3.63939i	−0.534551	−	0.131755i
$764$	0.766947	−	0.679455i	0.0277472	−	0.0245818i
$765$	−3.05749			−0.110544
$766$	−9.97982	−	8.84135i	−0.360586	−	0.319451i
$767$	−2.60001	−	3.38739i	−0.0938808	−	0.122312i

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.g (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.235915 - 0.622057i) q^{2} +(1.17724 - 1.70553i) q^{3} +(1.16572 - 1.03274i) q^{4} +(0.100994 + 0.831764i) q^{5} +(-1.33867 - 0.329951i) q^{6} +(1.56980 + 0.823895i) q^{7} +(-2.09560 - 1.09986i) q^{8} +(-0.459118 - 1.21059i) q^{9} +O(q^{10})\)	\(q+(-0.235915 - 0.622057i) q^{2} +(1.17724 - 1.70553i) q^{3} +(1.16572 - 1.03274i) q^{4} +(0.100994 + 0.831764i) q^{5} +(-1.33867 - 0.329951i) q^{6} +(1.56980 + 0.823895i) q^{7} +(-2.09560 - 1.09986i) q^{8} +(-0.459118 - 1.21059i) q^{9} +(0.493578 - 0.259050i) q^{10} +(-1.18451 + 3.12329i) q^{11} +(-0.389031 - 3.20396i) q^{12} +(-3.10393 + 1.83457i) q^{13} +(0.142170 - 1.17087i) q^{14} +(1.53749 + 0.806939i) q^{15} +(0.185655 - 1.52901i) q^{16} +(-2.49560 - 1.30979i) q^{17} +(-0.644745 + 0.571195i) q^{18} -0.972208 q^{19} +(0.976728 + 0.865305i) q^{20} +(3.25321 - 1.70742i) q^{21} +2.22231 q^{22} -4.18692 q^{23} +(-4.34287 + 2.27932i) q^{24} +(4.17308 - 1.02857i) q^{25} +(1.87347 + 1.49802i) q^{26} +(3.43127 + 0.845731i) q^{27} +(2.68082 - 0.660763i) q^{28} +(-0.356856 - 0.940952i) q^{29} +(0.139244 - 1.14678i) q^{30} +(4.99025 + 1.22999i) q^{31} +(-5.59078 + 1.37800i) q^{32} +(3.93241 + 5.69708i) q^{33} +(-0.226015 + 1.86140i) q^{34} +(-0.526745 + 1.38891i) q^{35} +(-1.78543 - 0.937067i) q^{36} +(-0.710919 - 0.175226i) q^{37} +(0.229358 + 0.604768i) q^{38} +(-0.525161 + 7.45357i) q^{39} +(0.703178 - 1.85413i) q^{40} +(-0.633254 + 0.917426i) q^{41} +(-1.82959 - 1.62088i) q^{42} +(-9.05816 + 2.23264i) q^{43} +(1.84474 + 4.86417i) q^{44} +(0.960560 - 0.504141i) q^{45} +(0.987757 + 2.60450i) q^{46} +(2.67405 + 2.36900i) q^{47} +(-2.38921 - 2.11666i) q^{48} +(-2.19098 - 3.17418i) q^{49} +(-1.62432 - 2.35324i) q^{50} +(-5.17181 + 2.71438i) q^{51} +(-1.72368 + 5.34415i) q^{52} +(7.65780 + 4.01912i) q^{53} +(-0.283394 - 2.33396i) q^{54} +(-2.71747 - 0.669795i) q^{55} +(-2.38351 - 3.45312i) q^{56} +(-1.14452 + 1.65813i) q^{57} +(-0.501138 + 0.443969i) q^{58} +(0.142756 + 1.17570i) q^{59} +(2.62565 - 0.647164i) q^{60} +(12.4958 - 6.55828i) q^{61} +(-0.412154 - 3.39439i) q^{62} +(0.276679 - 2.27866i) q^{63} +(0.426232 + 0.617504i) q^{64} +(-1.83941 - 2.39645i) q^{65} +(2.61619 - 3.79021i) q^{66} +(-1.97234 - 1.74734i) q^{67} +(-4.26185 + 1.05045i) q^{68} +(-4.92902 + 7.14091i) q^{69} +0.988250 q^{70} +(-0.244306 + 0.353939i) q^{71} +(-0.369352 + 3.04189i) q^{72} +(4.92621 - 12.9894i) q^{73} +(0.0587161 + 0.483570i) q^{74} +(3.15846 - 8.32818i) q^{75} +(-1.13332 + 1.00404i) q^{76} +(-4.43270 + 3.92703i) q^{77} +(4.76044 - 1.43173i) q^{78} +(0.723050 + 0.640566i) q^{79} +1.29053 q^{80} +(8.38921 - 7.43219i) q^{81} +(0.720085 + 0.177485i) q^{82} +(-10.1950 - 14.7700i) q^{83} +(2.02903 - 5.35010i) q^{84} +(0.837396 - 2.20803i) q^{85} +(3.52578 + 5.10798i) q^{86} +(-2.02493 - 0.499100i) q^{87} +(5.91743 - 5.24239i) q^{88} -0.552206 q^{89} +(-0.540215 - 0.478589i) q^{90} +(-6.38404 + 0.322598i) q^{91} +(-4.88079 + 4.32400i) q^{92} +(7.97251 - 7.06303i) q^{93} +(0.842804 - 2.22229i) q^{94} +(-0.0981876 - 0.808647i) q^{95} +(-4.23147 + 11.1575i) q^{96} +(-1.65086 + 13.5961i) q^{97} +(-1.45764 + 2.11175i) q^{98} +4.32486 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9}+O(q^{10}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9} + q^{10} - q^{11} + 11 q^{12} - 65 q^{13} + 9 q^{14} - 41 q^{15} + 3 q^{17} - 13 q^{18} - 6 q^{19} + 29 q^{20} + 19 q^{21} - 22 q^{22} - 82 q^{23} - 31 q^{24} + 2 q^{25} + 26 q^{26} + 21 q^{27} + 43 q^{28} + 13 q^{29} - 81 q^{30} - 33 q^{31} - 93 q^{32} + 35 q^{33} - 24 q^{34} + 27 q^{35} + 54 q^{36} + 25 q^{37} - 56 q^{38} - 13 q^{39} - 52 q^{40} + 29 q^{41} - 63 q^{42} + 21 q^{43} + 45 q^{44} + 33 q^{46} - 69 q^{47} + 54 q^{48} - 54 q^{49} + 80 q^{50} - 16 q^{51} + 13 q^{52} - 45 q^{53} + 29 q^{54} - 83 q^{55} + 91 q^{56} - 11 q^{57} + 25 q^{58} - 57 q^{59} + 51 q^{60} + 39 q^{61} + 4 q^{62} + 26 q^{63} + 86 q^{64} + 65 q^{65} - 138 q^{66} - 101 q^{67} + 36 q^{68} + 32 q^{69} - 90 q^{70} + 20 q^{71} + 13 q^{72} + 61 q^{73} - 4 q^{74} - 67 q^{75} - 107 q^{76} + 67 q^{77} + 13 q^{78} + 57 q^{79} + 160 q^{80} + 78 q^{81} - 31 q^{82} - 59 q^{83} - 36 q^{84} - 61 q^{85} + 41 q^{86} - 9 q^{87} - 45 q^{88} - 66 q^{89} + 191 q^{90} + 39 q^{91} + 79 q^{92} - 80 q^{93} - 21 q^{94} - 28 q^{95} + 70 q^{96} + 7 q^{97} + 158 q^{98} + 130 q^{99}+O(q^{100}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9 + q^10 - q^11 + 11 * q^12 - 65 * q^13 + 9 * q^14 - 41 * q^15 + 3 * q^17 - 13 * q^18 - 6 * q^19 + 29 * q^20 + 19 * q^21 - 22 * q^22 - 82 * q^23 - 31 * q^24 + 2 * q^25 + 26 * q^26 + 21 * q^27 + 43 * q^28 + 13 * q^29 - 81 * q^30 - 33 * q^31 - 93 * q^32 + 35 * q^33 - 24 * q^34 + 27 * q^35 + 54 * q^36 + 25 * q^37 - 56 * q^38 - 13 * q^39 - 52 * q^40 + 29 * q^41 - 63 * q^42 + 21 * q^43 + 45 * q^44 + 33 * q^46 - 69 * q^47 + 54 * q^48 - 54 * q^49 + 80 * q^50 - 16 * q^51 + 13 * q^52 - 45 * q^53 + 29 * q^54 - 83 * q^55 + 91 * q^56 - 11 * q^57 + 25 * q^58 - 57 * q^59 + 51 * q^60 + 39 * q^61 + 4 * q^62 + 26 * q^63 + 86 * q^64 + 65 * q^65 - 138 * q^66 - 101 * q^67 + 36 * q^68 + 32 * q^69 - 90 * q^70 + 20 * q^71 + 13 * q^72 + 61 * q^73 - 4 * q^74 - 67 * q^75 - 107 * q^76 + 67 * q^77 + 13 * q^78 + 57 * q^79 + 160 * q^80 + 78 * q^81 - 31 * q^82 - 59 * q^83 - 36 * q^84 - 61 * q^85 + 41 * q^86 - 9 * q^87 - 45 * q^88 - 66 * q^89 + 191 * q^90 + 39 * q^91 + 79 * q^92 - 80 * q^93 - 21 * q^94 - 28 * q^95 + 70 * q^96 + 7 * q^97 + 158 * q^98 + 130 * q^99

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