LMFDB - Embedded newform 175.2.x.a.33.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			33.4
Character	$\chi$	$=$	175.33
Dual form			175.2.x.a.122.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49982 + 0.973996i) q^{2} +(0.335932 - 0.128952i) q^{3} +(0.487325 - 1.09455i) q^{4} +(-1.15569 + 1.91426i) q^{5} +(-0.378240 + 0.520602i) q^{6} +(2.62695 + 0.314872i) q^{7} +(-0.224327 - 1.41635i) q^{8} +(-2.13321 + 1.92075i) q^{9} +O(q^{10})$	\(q+(-1.49982 + 0.973996i) q^{2} +(0.335932 - 0.128952i) q^{3} +(0.487325 - 1.09455i) q^{4} +(-1.15569 + 1.91426i) q^{5} +(-0.378240 + 0.520602i) q^{6} +(2.62695 + 0.314872i) q^{7} +(-0.224327 - 1.41635i) q^{8} +(-2.13321 + 1.92075i) q^{9} +(-0.131145 - 3.99668i) q^{10} +(-2.82518 + 3.13767i) q^{11} +(0.0225635 - 0.430536i) q^{12} +(-0.268631 - 0.527217i) q^{13} +(-4.24664 + 2.08638i) q^{14} +(-0.141386 + 0.792089i) q^{15} +(3.31938 + 3.68655i) q^{16} +(-0.675395 + 0.546924i) q^{17} +(1.32863 - 4.95853i) q^{18} +(-5.83214 + 2.59663i) q^{19} +(1.53205 + 2.19783i) q^{20} +(0.923080 - 0.232975i) q^{21} +(1.18118 - 7.45766i) q^{22} +(0.882537 + 1.35899i) q^{23} +(-0.258000 - 0.446869i) q^{24} +(-2.32875 - 4.42458i) q^{25} +(0.916406 + 0.529087i) q^{26} +(-0.959010 + 1.88216i) q^{27} +(1.62482 - 2.72188i) q^{28} +(-0.996818 - 1.37200i) q^{29} +(-0.559437 - 1.32570i) q^{30} +(8.94867 + 0.940543i) q^{31} +(-5.79889 - 1.55381i) q^{32} +(-0.544457 + 1.41836i) q^{33} +(0.480271 - 1.47812i) q^{34} +(-3.63869 + 4.66476i) q^{35} +(1.06279 + 3.27094i) q^{36} +(4.35142 + 0.228048i) q^{37} +(6.21806 - 9.57497i) q^{38} +(-0.158228 - 0.142469i) q^{39} +(2.97051 + 1.20744i) q^{40} +(5.70437 + 1.85346i) q^{41} +(-1.15754 + 1.24850i) q^{42} +(3.73281 + 3.73281i) q^{43} +(2.05756 + 4.62136i) q^{44} +(-1.21148 - 6.30331i) q^{45} +(-2.64730 - 1.17865i) q^{46} +(6.06621 - 7.49114i) q^{47} +(1.59048 + 0.810389i) q^{48} +(6.80171 + 1.65430i) q^{49} +(7.80224 + 4.36789i) q^{50} +(-0.156360 + 0.270823i) q^{51} +(-0.707976 + 0.0371035i) q^{52} +(3.03918 + 7.91735i) q^{53} +(-0.394875 - 3.75698i) q^{54} +(-2.74128 - 9.03429i) q^{55} +(-0.143329 - 3.79131i) q^{56} +(-1.62436 + 1.62436i) q^{57} +(2.83137 + 1.08686i) q^{58} +(6.62786 - 1.40879i) q^{59} +(0.798080 + 0.540760i) q^{60} +(0.256792 - 1.20811i) q^{61} +(-14.3375 + 7.30532i) q^{62} +(-6.20863 + 4.37403i) q^{63} +(0.774814 - 0.251752i) q^{64} +(1.31968 + 0.0950730i) q^{65} +(-0.564887 - 2.65758i) q^{66} +(-7.21376 - 8.90825i) q^{67} +(0.269499 + 1.00578i) q^{68} +(0.471717 + 0.342723i) q^{69} +(0.913931 - 10.5404i) q^{70} +(-11.3299 + 8.23164i) q^{71} +(3.19899 + 2.59049i) q^{72} +(-0.182500 - 3.48231i) q^{73} +(-6.74848 + 3.89623i) q^{74} +(-1.35286 - 1.18606i) q^{75} +7.64897i q^{76} +(-8.40955 + 7.35294i) q^{77} +(0.376077 + 0.0595648i) q^{78} +(-14.0514 + 1.47686i) q^{79} +(-10.8932 + 2.09364i) q^{80} +(0.820700 - 7.80844i) q^{81} +(-10.3608 + 2.77617i) q^{82} +(-3.01586 + 0.477665i) q^{83} +(0.194837 - 1.12389i) q^{84} +(-0.266404 - 1.92496i) q^{85} +(-9.23428 - 1.96281i) q^{86} +(-0.511786 - 0.332358i) q^{87} +(5.07780 + 3.29756i) q^{88} +(16.6785 + 3.54513i) q^{89} +(7.95640 + 8.27388i) q^{90} +(-0.539673 - 1.46956i) q^{91} +(1.91756 - 0.303712i) q^{92} +(3.12743 - 0.837993i) q^{93} +(-1.80189 + 17.1438i) q^{94} +(1.76953 - 14.1651i) q^{95} +(-2.14840 + 0.225806i) q^{96} +(11.5748 + 1.83327i) q^{97} +(-11.8126 + 4.14368i) q^{98} -12.1198i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{20}\right)$

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 $

$2$	−1.49982	+	0.973996i	−1.06053	+	0.688719i	−0.952225	−	0.305398i	$-0.901210\pi$
$2$	−1.49982	+	0.973996i	−1.06053	+	0.688719i	−0.108310	+	0.994117i	$0.534544\pi$
$3$	0.335932	−	0.128952i	0.193951	−	0.0744506i	−0.259454	−	0.965755i	$-0.583543\pi$
$3$	0.335932	−	0.128952i	0.193951	−	0.0744506i	0.453405	+	0.891305i	$0.350209\pi$
$4$	0.487325	−	1.09455i	0.243663	−	0.547275i
$5$	−1.15569	+	1.91426i	−0.516841	+	0.856081i
$5$	−1.15569	+	1.91426i	−0.516841	+	0.856081i
$6$	−0.378240	+	0.520602i	−0.154416	+	0.212535i
$7$	2.62695	+	0.314872i	0.992893	+	0.119010i
$7$	2.62695	+	0.314872i	0.992893	+	0.119010i
$8$	−0.224327	−	1.41635i	−0.0793117	−	0.500755i
$9$	−2.13321	+	1.92075i	−0.711071	+	0.640251i
$10$	−0.131145	−	3.99668i	−0.0414717	−	1.26386i
$11$	−2.82518	+	3.13767i	−0.851822	+	0.946045i	−0.999073	−	0.0430546i	$-0.986291\pi$
$11$	−2.82518	+	3.13767i	−0.851822	+	0.946045i	0.147250	+	0.989099i	$0.452958\pi$
$12$	0.0225635	−	0.430536i	0.00651351	−	0.124285i
$13$	−0.268631	−	0.527217i	−0.0745047	−	0.146224i	0.850749	−	0.525571i	$-0.176148\pi$
$13$	−0.268631	−	0.527217i	−0.0745047	−	0.146224i	−0.925254	+	0.379348i	$0.876148\pi$
$14$	−4.24664	+	2.08638i	−1.13496	+	0.557610i
$15$	−0.141386	+	0.792089i	−0.0365058	+	0.204517i
$16$	3.31938	+	3.68655i	0.829846	+	0.921638i
$17$	−0.675395	+	0.546924i	−0.163807	+	0.132649i	−0.707719	−	0.706494i	$-0.750276\pi$
$17$	−0.675395	+	0.546924i	−0.163807	+	0.132649i	0.543912	+	0.839142i	$0.316943\pi$
$18$	1.32863	−	4.95853i	0.313162	−	1.16874i
$19$	−5.83214	+	2.59663i	−1.33798	+	0.595709i	−0.945971	−	0.324251i	$-0.894888\pi$
$19$	−5.83214	+	2.59663i	−1.33798	+	0.595709i	−0.392013	+	0.919960i	$0.628221\pi$
$20$	1.53205	+	2.19783i	0.342577	+	0.491449i
$21$	0.923080	−	0.232975i	0.201433	−	0.0508394i
$22$	1.18118	−	7.45766i	0.251828	−	1.58998i
$23$	0.882537	+	1.35899i	0.184022	+	0.283369i	0.918627	−	0.395126i	$-0.129299\pi$
$23$	0.882537	+	1.35899i	0.184022	+	0.283369i	−0.734605	+	0.678495i	$0.762633\pi$
$24$	−0.258000	−	0.446869i	−0.0526640	−	0.0912168i
$25$	−2.32875	−	4.42458i	−0.465750	−	0.884916i
$26$	0.916406	+	0.529087i	0.179722	+	0.103762i
$27$	−0.959010	+	1.88216i	−0.184562	+	0.362223i
$28$	1.62482	−	2.72188i	0.307062	−	0.514387i
$29$	−0.996818	−	1.37200i	−0.185104	−	0.254774i	0.706373	−	0.707840i	$-0.250330\pi$
$29$	−0.996818	−	1.37200i	−0.185104	−	0.254774i	−0.891477	+	0.453066i	$0.850330\pi$
$30$	−0.559437	−	1.32570i	−0.102139	−	0.242039i
$31$	8.94867	+	0.940543i	1.60723	+	0.168927i	0.865195	−	0.501436i	$-0.167195\pi$
$31$	8.94867	+	0.940543i	1.60723	+	0.168927i	0.742034	+	0.670362i	$0.233861\pi$
$32$	−5.79889	−	1.55381i	−1.02511	−	0.274677i
$33$	−0.544457	+	1.41836i	−0.0947778	+	0.246905i
$34$	0.480271	−	1.47812i	0.0823657	−	0.253496i
$35$	−3.63869	+	4.66476i	−0.615050	+	0.788488i
$36$	1.06279	+	3.27094i	0.177132	+	0.545157i
$37$	4.35142	+	0.228048i	0.715369	+	0.0374909i	0.406548	−	0.913629i	$-0.366732\pi$
$37$	4.35142	+	0.228048i	0.715369	+	0.0374909i	0.308821	+	0.951120i	$0.400066\pi$
$38$	6.21806	−	9.57497i	1.00870	−	1.55326i
$39$	−0.158228	−	0.142469i	−0.0253367	−	0.0228133i
$40$	2.97051	+	1.20744i	0.469678	+	0.190913i
$41$	5.70437	+	1.85346i	0.890873	+	0.289462i	0.718465	−	0.695563i	$-0.244845\pi$
$41$	5.70437	+	1.85346i	0.890873	+	0.289462i	0.172408	+	0.985026i	$0.444845\pi$
$42$	−1.15754	+	1.24850i	−0.178612	+	0.192647i
$43$	3.73281	+	3.73281i	0.569248	+	0.569248i	0.931918	−	0.362670i	$-0.118135\pi$
$43$	3.73281	+	3.73281i	0.569248	+	0.569248i	−0.362670	+	0.931918i	$0.618135\pi$
$44$	2.05756	+	4.62136i	0.310189	+	0.696697i
$45$	−1.21148	−	6.30331i	−0.180596	−	0.939643i
$46$	−2.64730	−	1.17865i	−0.390323	−	0.173783i
$47$	6.06621	−	7.49114i	0.884847	−	1.09270i	−0.110261	−	0.993903i	$-0.535169\pi$
$47$	6.06621	−	7.49114i	0.884847	−	1.09270i	0.995108	−	0.0987925i	$-0.0314980\pi$
$48$	1.59048	+	0.810389i	0.229566	+	0.116970i
$49$	6.80171	+	1.65430i	0.971673	+	0.236329i
$50$	7.80224	+	4.36789i	1.10340	+	0.617713i
$51$	−0.156360	+	0.270823i	−0.0218948	+	0.0379228i
$52$	−0.707976	+	0.0371035i	−0.0981786	+	0.00514532i
$53$	3.03918	+	7.91735i	0.417464	+	1.08753i	0.967607	+	0.252461i	$0.0812399\pi$
$53$	3.03918	+	7.91735i	0.417464	+	1.08753i	−0.550143	+	0.835070i	$0.685427\pi$
$54$	−0.394875	−	3.75698i	−0.0537357	−	0.511261i
$55$	−2.74128	−	9.03429i	−0.369634	−	1.21818i
$56$	−0.143329	−	3.79131i	−0.0191531	−	0.506635i
$57$	−1.62436	+	1.62436i	−0.215152	+	0.215152i
$58$	2.83137	+	1.08686i	0.371778	+	0.142712i
$59$	6.62786	−	1.40879i	0.862874	−	0.183409i	0.244842	−	0.969563i	$-0.421264\pi$
$59$	6.62786	−	1.40879i	0.862874	−	0.183409i	0.618031	+	0.786153i	$0.287930\pi$
$60$	0.798080	+	0.540760i	0.103032	+	0.0698118i
$61$	0.256792	−	1.20811i	0.0328789	−	0.154683i	−0.958646	−	0.284602i	$-0.908138\pi$
$61$	0.256792	−	1.20811i	0.0328789	−	0.154683i	0.991525	+	0.129919i	$0.0414718\pi$
$62$	−14.3375	+	7.30532i	−1.82086	+	0.927777i
$63$	−6.20863	+	4.37403i	−0.782214	+	0.551076i
$64$	0.774814	−	0.251752i	0.0968517	−	0.0314690i
$65$	1.31968	+	0.0950730i	0.163687	+	0.0117923i
$66$	−0.564887	−	2.65758i	−0.0695328	−	0.327126i
$67$	−7.21376	−	8.90825i	−0.881301	−	1.08832i	−0.995491	−	0.0948576i	$-0.969760\pi$
$67$	−7.21376	−	8.90825i	−0.881301	−	1.08832i	0.114189	−	0.993459i	$-0.463573\pi$
$68$	0.269499	+	1.00578i	0.0326815	+	0.121969i
$69$	0.471717	+	0.342723i	0.0567881	+	0.0412590i
$70$	0.913931	−	10.5404i	0.109236	−	1.25982i
$71$	−11.3299	+	8.23164i	−1.34461	+	0.976915i	−0.345348	+	0.938475i	$0.612239\pi$
$71$	−11.3299	+	8.23164i	−1.34461	+	0.976915i	−0.999261	+	0.0384406i	$0.987761\pi$
$72$	3.19899	+	2.59049i	0.377005	+	0.305293i
$73$	−0.182500	−	3.48231i	−0.0213601	−	0.407574i	−0.988295	−	0.152552i	$-0.951251\pi$
$73$	−0.182500	−	3.48231i	−0.0213601	−	0.407574i	0.966935	−	0.255022i	$-0.0820826\pi$
$74$	−6.74848	+	3.89623i	−0.784494	+	0.452928i
$75$	−1.35286	−	1.18606i	−0.156215	−	0.136955i
$76$			7.64897i			0.877397i
$77$	−8.40955	+	7.35294i	−0.958358	+	0.837945i
$78$	0.376077	+	0.0595648i	0.0425823	+	0.00674438i
$79$	−14.0514	+	1.47686i	−1.58090	+	0.166159i	−0.853885	−	0.520462i	$-0.825760\pi$
$79$	−14.0514	+	1.47686i	−1.58090	+	0.166159i	−0.727016	+	0.686621i	$0.759093\pi$
$80$	−10.8932	+	2.09364i	−1.21790	+	0.234076i
$81$	0.820700	−	7.80844i	0.0911889	−	0.867605i
$82$	−10.3608	+	2.77617i	−1.14416	+	0.306577i
$83$	−3.01586	+	0.477665i	−0.331033	+	0.0524305i	−0.319739	−	0.947506i	$-0.603595\pi$
$83$	−3.01586	+	0.477665i	−0.331033	+	0.0524305i	−0.0112944	+	0.999936i	$0.503595\pi$
$84$	0.194837	−	1.12389i	0.0212584	−	0.122627i
$85$	−0.266404	−	1.92496i	−0.0288956	−	0.208791i
$86$	−9.23428	−	1.96281i	−0.995758	−	0.211655i
$87$	−0.511786	−	0.332358i	−0.0548692	−	0.0356325i
$88$	5.07780	+	3.29756i	0.541296	+	0.351522i
$89$	16.6785	+	3.54513i	1.76792	+	0.375783i	0.972977	−	0.230900i	$-0.0741671\pi$
$89$	16.6785	+	3.54513i	1.76792	+	0.375783i	0.794944	+	0.606683i	$0.207500\pi$
$90$	7.95640	+	8.27388i	0.838678	+	0.872143i
$91$	−0.539673	−	1.46956i	−0.0565731	−	0.154051i
$92$	1.91756	−	0.303712i	0.199920	−	0.0316642i
$93$	3.12743	−	0.837993i	0.324300	−	0.0868958i
$94$	−1.80189	+	17.1438i	−0.185851	+	1.76825i
$95$	1.76953	−	14.1651i	0.181550	−	1.45331i
$96$	−2.14840	+	0.225806i	−0.219270	+	0.0230462i
$97$	11.5748	+	1.83327i	1.17524	+	0.186140i	0.713358	−	0.700800i	$-0.247174\pi$
$97$	11.5748	+	1.83327i	1.17524	+	0.186140i	0.461884	+	0.886940i	$0.347174\pi$
$98$	−11.8126	+	4.14368i	−1.19326	+	0.418575i
$99$		−	12.1198i		−	1.21809i
$100$	−5.97778	+	0.392727i	−0.597778	+	0.0392727i
$101$	3.84878	−	2.22209i	0.382967	−	0.221106i	−0.296141	−	0.955144i	$-0.595700\pi$
$101$	3.84878	−	2.22209i	0.382967	−	0.221106i	0.679109	+	0.734038i	$0.262367\pi$
$102$	−0.0292687	−	0.558480i	−0.00289803	−	0.0552978i
$103$	−1.62888	−	1.31905i	−0.160499	−	0.129969i	0.545707	−	0.837976i	$-0.316261\pi$
$103$	−1.62888	−	1.31905i	−0.160499	−	0.129969i	−0.706206	+	0.708007i	$0.749595\pi$
$104$	−0.686462	+	0.498744i	−0.0673131	+	0.0489058i
$105$	−0.620821	+	2.03626i	−0.0605860	+	0.198719i
$106$	−12.2697	−	8.91446i	−1.19174	−	0.865849i
$107$	−1.06590	−	3.97800i	−0.103045	−	0.384568i	0.895071	−	0.445923i	$-0.147124\pi$
$107$	−1.06590	−	3.97800i	−0.103045	−	0.384568i	−0.998116	+	0.0613552i	$0.980458\pi$
$108$	1.59277	+	1.96691i	0.153265	+	0.189266i
$109$	2.48271	+	11.6802i	0.237801	+	1.11876i	0.921312	+	0.388824i	$0.127119\pi$
$109$	2.48271	+	11.6802i	0.237801	+	1.11876i	−0.683512	+	0.729940i	$0.739548\pi$
$110$	12.9108	+	10.8798i	1.23100	+	1.03735i
$111$	1.49119	−	0.484517i	0.141537	−	0.0459883i
$112$	7.55906	+	10.7296i	0.714264	+	1.01385i
$113$	−3.18186	+	1.62124i	−0.299324	+	0.152513i	−0.597202	−	0.802091i	$-0.703721\pi$
$113$	−3.18186	+	1.62124i	−0.299324	+	0.152513i	0.297878	+	0.954604i	$0.403721\pi$
$114$	0.854131	−	4.01837i	0.0799967	−	0.376355i
$115$	−3.62139	+	0.118831i	−0.337697	+	0.0110810i
$116$	−1.98750	+	0.422456i	−0.184535	+	0.0392241i
$117$	1.58570	+	0.608693i	0.146598	+	0.0562737i
$118$	−8.56845	+	8.56845i	−0.788789	+	0.788789i
$119$	−1.94644	+	1.22408i	−0.178430	+	0.112211i
$120$	1.15359	+	0.0225650i	0.105308	+	0.00205989i
$121$	−0.713576	−	6.78922i	−0.0648706	−	0.617202i
$122$	0.791555	+	2.06207i	0.0716640	+	0.186691i
$123$	2.15529	−	0.112954i	0.194336	−	0.0101847i
$124$	5.39038	−	9.33642i	0.484071	−	0.838435i
$125$	11.1611	+	0.655624i	0.998279	+	0.0586408i
$126$	5.05155	−	12.6074i	0.450028	−	1.12316i
$127$	−2.93160	−	1.49373i	−0.260138	−	0.132547i	0.319058	−	0.947735i	$-0.396633\pi$
$127$	−2.93160	−	1.49373i	−0.260138	−	0.132547i	−0.579196	+	0.815188i	$0.696633\pi$
$128$	6.63931	−	8.19887i	0.586838	−	0.724685i
$129$	1.73532	+	0.772616i	0.152787	+	0.0680250i
$130$	−2.07189	+	1.14277i	−0.181717	+	0.100228i
$131$	−1.50001	−	3.36908i	−0.131057	−	0.294358i	0.836083	−	0.548602i	$-0.184840\pi$
$131$	−1.50001	−	3.36908i	−0.131057	−	0.294358i	−0.967140	+	0.254244i	$0.918173\pi$
$132$	1.28714	+	1.28714i	0.112031	+	0.112031i
$133$	−16.1383	+	4.98485i	−1.39937	+	0.432241i
$134$	19.4960	+	6.33462i	1.68419	+	0.547228i
$135$	−2.49462	−	4.01099i	−0.214703	−	0.345211i
$136$	0.926145	+	0.833904i	0.0794162	+	0.0715067i
$137$	0.549457	−	0.846089i	0.0469433	−	0.0722863i	−0.814420	−	0.580276i	$-0.802945\pi$
$137$	0.549457	−	0.846089i	0.0469433	−	0.0722863i	0.861363	+	0.507990i	$0.169611\pi$
$138$	−1.04130	−	0.0545724i	−0.0886416	−	0.00464551i
$139$	−3.10037	−	9.54195i	−0.262970	−	0.809337i	−0.992154	−	0.125020i	$-0.960100\pi$
$139$	−3.10037	−	9.54195i	−0.262970	−	0.809337i	0.729185	−	0.684317i	$-0.239900\pi$
$140$	3.33259	+	6.25598i	0.281655	+	0.528727i
$141$	1.07183	−	3.29877i	0.0902647	−	0.277806i
$142$	8.97522	−	23.3812i	0.753183	−	1.96211i
$143$	2.41316	+	0.646606i	0.201799	+	0.0540719i
$144$	−14.1619	−	1.48848i	−1.18016	−	0.124040i
$145$	3.77838	−	0.322553i	0.313777	−	0.0267866i
$146$	3.66548	+	5.04510i	0.303357	+	0.417535i
$147$	2.49824	−	0.321362i	0.206051	−	0.0265055i
$148$	2.37017	−	4.65171i	0.194827	−	0.382369i
$149$	−6.19698	−	3.57783i	−0.507676	−	0.293107i	0.224202	−	0.974543i	$-0.428023\pi$
$149$	−6.19698	−	3.57783i	−0.507676	−	0.293107i	−0.731878	+	0.681436i	$0.761356\pi$
$150$	3.18427	+	0.461198i	0.259995	+	0.0376567i
$151$	12.2345	+	21.1907i	0.995627	+	1.72448i	0.578718	+	0.815527i	$0.303553\pi$
$151$	12.2345	+	21.1907i	0.995627	+	1.72448i	0.416908	+	0.908949i	$0.363114\pi$
$152$	4.98605	+	7.67784i	0.404422	+	0.622755i
$153$	0.390255	−	2.46397i	0.0315502	−	0.199200i
$154$	5.45110	−	19.2190i	0.439262	−	1.54871i
$155$	−12.1423	+	16.0431i	−0.975297	+	1.28861i
$156$	−0.233047	+	0.103759i	−0.0186587	+	0.00830740i
$157$	−5.19791	+	19.3989i	−0.414838	+	1.54820i	0.370321	+	0.928904i	$0.379248\pi$
$157$	−5.19791	+	19.3989i	−0.414838	+	1.54820i	−0.785159	+	0.619294i	$0.787419\pi$
$158$	19.6361	−	15.9010i	1.56216	−	1.26501i
$159$	2.04192	+	2.26778i	0.161935	+	0.179847i
$160$	9.67612	−	9.30484i	0.764964	−	0.735612i
$161$	1.89047	+	3.84788i	0.148990	+	0.303255i
$162$	6.37449	+	12.5106i	0.500827	+	0.982928i
$163$	−0.844482	+	16.1137i	−0.0661449	+	1.26212i	0.740894	+	0.671622i	$0.234402\pi$
$163$	−0.844482	+	16.1137i	−0.0661449	+	1.26212i	−0.807039	+	0.590498i	$0.798931\pi$
$164$	4.80859	−	5.34048i	0.375488	−	0.417021i
$165$	−2.08588	−	2.68142i	−0.162385	−	0.208748i
$166$	4.05801	−	3.65384i	0.314962	−	0.283593i
$167$	−1.58959	−	10.0363i	−0.123006	−	0.776630i	−0.969655	−	0.244478i	$-0.921383\pi$
$167$	−1.58959	−	10.0363i	−0.123006	−	0.776630i	0.846649	−	0.532152i	$-0.178617\pi$
$168$	−0.537046	−	1.25514i	−0.0414340	−	0.0968361i
$169$	7.43541	−	10.2340i	0.571955	−	0.787228i
$170$	2.27446	+	2.62761i	0.174443	+	0.201529i
$171$	7.45369	−	16.7413i	0.569998	−	1.28024i
$172$	5.90483	−	2.26665i	0.450239	−	0.172831i
$173$	2.81344	−	1.82707i	0.213902	−	0.138909i	−0.433241	−	0.901278i	$-0.642630\pi$
$173$	2.81344	−	1.82707i	0.213902	−	0.138909i	0.647143	+	0.762368i	$0.275964\pi$
$174$	1.09130			0.0827315
$175$	−4.72434	−	12.3564i	−0.357126	−	0.934056i
$176$	−20.9450			−1.57879
$177$	2.04484	−	1.32794i	0.153700	−	0.0998138i
$178$	−28.4678	+	10.9278i	−2.13375	+	0.819070i
$179$	1.18133	−	2.65332i	0.0882971	−	0.198319i	−0.863999	−	0.503493i	$-0.832048\pi$
$179$	1.18133	−	2.65332i	0.0882971	−	0.198319i	0.952297	+	0.305174i	$0.0987147\pi$
$180$	−7.48968	−	1.74574i	−0.558248	−	0.130120i
$181$	−4.64922	+	6.39910i	−0.345574	+	0.475641i	−0.946059	−	0.323994i	$-0.894974\pi$
$181$	−4.64922	+	6.39910i	−0.345574	+	0.475641i	0.600485	+	0.799636i	$0.294974\pi$
$182$	2.24076	+	1.67843i	0.166096	+	0.124414i
$183$	−0.0695242	−	0.438958i	−0.00513937	−	0.0324487i
$184$	1.72682	−	1.55484i	0.127303	−	0.114624i
$185$	−5.46544	+	8.06618i	−0.401827	+	0.593037i
$186$	−3.87439	+	4.30295i	−0.284084	+	0.315507i
$187$	0.192039	−	3.66433i	0.0140433	−	0.267962i
$188$	−5.24321	−	10.2904i	−0.382401	−	0.750504i
$189$	−3.11191	+	4.64238i	−0.226358	+	0.337684i
$190$	11.1428	+	22.9687i	0.808382	+	1.66632i
$191$	−9.73774	−	10.8149i	−0.704598	−	0.782536i	0.279503	−	0.960145i	$-0.409830\pi$
$191$	−9.73774	−	10.8149i	−0.704598	−	0.782536i	−0.984101	+	0.177609i	$0.943164\pi$
$192$	0.227821	−	0.184486i	0.0164416	−	0.0133141i
$193$	−0.160877	+	0.600403i	−0.0115802	+	0.0432179i	−0.971474	−	0.237145i	$-0.923788\pi$
$193$	−0.160877	+	0.600403i	−0.0115802	+	0.0432179i	0.959894	+	0.280363i	$0.0904549\pi$
$194$	−19.1457	+	8.52422i	−1.37458	+	0.612004i
$195$	0.455584	−	0.138238i	0.0326250	−	0.00989943i
$196$	5.12536	−	6.63863i	0.366097	−	0.474188i
$197$	3.81776	−	24.1044i	0.272004	−	1.71736i	−0.352048	−	0.935982i	$-0.614515\pi$
$197$	3.81776	−	24.1044i	0.272004	−	1.71736i	0.624052	−	0.781383i	$-0.285485\pi$
$198$	11.8046	+	18.1775i	0.838918	+	1.29182i
$199$	4.29215	+	7.43422i	0.304262	+	0.526998i	0.977097	−	0.212795i	$-0.0682568\pi$
$199$	4.29215	+	7.43422i	0.304262	+	0.526998i	−0.672835	+	0.739793i	$0.734923\pi$
$200$	−5.74434	+	4.29088i	−0.406186	+	0.303411i
$201$	−3.57207	−	2.06234i	−0.251955	−	0.145466i
$202$	−3.60817	+	7.08143i	−0.253870	+	0.498248i
$203$	−2.18658	−	3.91805i	−0.153468	−	0.274993i
$204$	0.220231	+	0.303123i	0.0154193	+	0.0212228i
$205$	−10.1405	+	8.77759i	−0.708243	+	0.613054i
$206$	3.72778	+	0.391806i	0.259727	+	0.0272984i
$207$	−4.49292	−	1.20387i	−0.312280	−	0.0836751i
$208$	1.05192	−	2.74036i	0.0729378	−	0.190010i
$209$	8.32941	−	25.6353i	0.576158	−	1.77323i
$210$	−1.05219	−	3.65870i	−0.0726077	−	0.252475i
$211$	1.28435	+	3.95282i	0.0884183	+	0.272123i	0.985483	−	0.169777i	$-0.0543046\pi$
$211$	1.28435	+	3.95282i	0.0884183	+	0.272123i	−0.897064	+	0.441900i	$0.854305\pi$
$212$	10.1470	+	0.531782i	0.696899	+	0.0365229i
$213$	−2.74458	+	4.22628i	−0.188056	+	0.289580i
$214$	5.47322	+	4.92811i	0.374141	+	0.336878i
$215$	−11.4595	+	2.83157i	−0.781533	+	0.193112i
$216$	2.88093	+	0.936071i	0.196023	+	0.0636916i
$217$	23.2115	+	5.28844i	1.57570	+	0.359003i
$218$	−15.1001	−	15.1001i	−1.02271	−	1.02271i
$219$	−0.510360	−	1.14629i	−0.0344869	−	0.0774589i
$220$	−11.2244	−	1.40217i	−0.756748	−	0.0945342i
$221$	0.469780	+	0.209159i	0.0316008	+	0.0140696i
$222$	−1.76460	+	2.17910i	−0.118432	+	0.146252i
$223$	−11.3328	−	5.77436i	−0.758902	−	0.386680i	0.0313132	−	0.999510i	$-0.490031\pi$
$223$	−11.3328	−	5.77436i	−0.758902	−	0.386680i	−0.790215	+	0.612830i	$0.790031\pi$
$224$	−14.7441	−	5.90768i	−0.985134	−	0.394723i
$225$	13.4663	+	4.96561i	0.897750	+	0.331041i
$226$	3.19314	−	5.53069i	0.212405	−	0.367896i
$227$	6.99268	−	0.366471i	0.464120	−	0.0243235i	0.181157	−	0.983454i	$-0.442016\pi$
$227$	6.99268	−	0.366471i	0.464120	−	0.0243235i	0.282963	+	0.959131i	$0.408682\pi$
$228$	0.986352	+	2.56954i	0.0653228	+	0.170172i
$229$	−1.54623	−	14.7114i	−0.102178	−	0.972159i	−0.918730	−	0.394887i	$-0.870784\pi$
$229$	−1.54623	−	14.7114i	−0.102178	−	0.972159i	0.816552	−	0.577272i	$-0.195883\pi$
$230$	5.31570	−	3.70545i	0.350507	−	0.244330i
$231$	−1.87686	+	3.55452i	−0.123488	+	0.233870i
$232$	−1.71962	+	1.71962i	−0.112899	+	0.112899i
$233$	−2.38168	−	0.914241i	−0.156029	−	0.0598939i	0.279100	−	0.960262i	$-0.409964\pi$
$233$	−2.38168	−	0.914241i	−0.156029	−	0.0598939i	−0.435129	+	0.900368i	$0.643297\pi$
$234$	−2.97113	+	0.631534i	−0.194229	+	0.0412847i
$235$	7.32930	+	20.2697i	0.478111	+	1.32225i
$236$	1.68793	−	7.94106i	0.109875	−	0.516919i
$237$	−4.52986	+	2.30808i	−0.294246	+	0.149926i
$238$	1.72706	−	3.73172i	0.111949	−	0.241892i
$239$	−0.945911	+	0.307345i	−0.0611859	+	0.0198805i	−0.339450	−	0.940624i	$-0.610241\pi$
$239$	−0.945911	+	0.307345i	−0.0611859	+	0.0198805i	0.278264	+	0.960505i	$0.410241\pi$
$240$	−3.38939	+	2.10802i	−0.218784	+	0.136072i
$241$	1.11500	+	5.24565i	0.0718234	+	0.337902i	0.999358	−	0.0358356i	$-0.0114093\pi$
$241$	1.11500	+	5.24565i	0.0718234	+	0.337902i	−0.927534	+	0.373738i	$0.878076\pi$
$242$	7.68291	+	9.48761i	0.493876	+	0.609886i
$243$	−2.37141	−	8.85021i	−0.152126	−	0.567741i
$244$	−1.19720	−	0.869816i	−0.0766428	−	0.0556843i
$245$	−11.0274	+	11.1084i	−0.704518	+	0.709687i
$246$	−3.12253	+	2.26865i	−0.199086	+	0.144644i
$247$	2.93568	+	2.37727i	0.186793	+	0.151262i
$248$	−0.675296	−	12.8854i	−0.0428814	−	0.818225i
$249$	−0.951527	+	0.549365i	−0.0603006	+	0.0348146i
$250$	−17.3782	+	9.88755i	−1.09910	+	0.625343i
$251$			15.5071i			0.978800i	0.872059	+	0.489400i	$0.162784\pi$
$251$			15.5071i			0.978800i	−0.872059	+	0.489400i	$0.837216\pi$
$252$	1.76197	+	8.92723i	0.110994	+	0.562363i
$253$	−6.75739	−	1.07026i	−0.424833	−	0.0672870i
$254$	5.85177	−	0.615046i	0.367173	−	0.0385914i
$255$	−0.337721	−	0.612301i	−0.0211489	−	0.0383438i
$256$	−2.14244	+	20.3840i	−0.133903	+	1.27400i
$257$	15.0766	−	4.03975i	0.940449	−	0.251993i	0.244145	−	0.969739i	$-0.421493\pi$
$257$	15.0766	−	4.03975i	0.940449	−	0.251993i	0.696305	+	0.717746i	$0.254826\pi$
$258$	−3.35520	+	0.531412i	−0.208886	+	0.0330842i
$259$	11.3591	+	1.96921i	0.705823	+	0.122361i
$260$	0.747177	−	1.39813i	0.0463379	−	0.0867082i
$261$	4.76170	+	1.01213i	0.294742	+	0.0626494i
$262$	5.53122	+	3.59202i	0.341720	+	0.221916i
$263$	3.44715	+	2.23861i	0.212561	+	0.138038i	0.646528	−	0.762890i	$-0.276220\pi$
$263$	3.44715	+	2.23861i	0.212561	+	0.138038i	−0.433968	+	0.900928i	$0.642887\pi$
$264$	2.13103	+	0.452964i	0.131156	+	0.0278780i
$265$	−18.6682	−	3.33224i	−1.14678	−	0.204698i
$266$	19.3494	−	23.1951i	1.18639	−	1.42218i
$267$	6.06001	−	0.959811i	0.370866	−	0.0587395i
$268$	−13.2660	+	3.55461i	−0.810349	+	0.217132i
$269$	−1.23301	+	11.7313i	−0.0751780	+	0.715271i	0.890404	+	0.455171i	$0.150422\pi$
$269$	−1.23301	+	11.7313i	−0.0751780	+	0.715271i	−0.965582	+	0.260099i	$0.916245\pi$
$270$	7.64818	+	3.58602i	0.465453	+	0.218238i
$271$	−6.69826	+	0.704015i	−0.406890	+	0.0427659i	−0.305763	−	0.952108i	$-0.598912\pi$
$271$	−6.69826	+	0.704015i	−0.406890	+	0.0427659i	−0.101127	+	0.994874i	$0.532245\pi$
$272$	−4.25816	−	0.674426i	−0.258189	−	0.0408931i
$273$	−0.370796	−	0.424079i	−0.0224416	−	0.0256664i
$274$			1.80415i			0.108993i
$275$	20.4620	+	5.19335i	1.23391	+	0.313171i
$276$	0.605007	−	0.349301i	0.0364171	−	0.0210254i
$277$	−1.59392	−	30.4139i	−0.0957696	−	1.82739i	−0.450899	−	0.892575i	$-0.648897\pi$
$277$	−1.59392	−	30.4139i	−0.0957696	−	1.82739i	0.355130	−	0.934817i	$-0.384437\pi$
$278$	13.9438	+	11.2915i	0.836294	+	0.677218i
$279$	−20.8960	+	15.1818i	−1.25101	+	0.908911i
$280$	7.42318	+	4.10721i	0.443620	+	0.245453i
$281$	3.78178	+	2.74762i	0.225602	+	0.163909i	0.694845	−	0.719160i	$-0.255473\pi$
$281$	3.78178	+	2.74762i	0.225602	+	0.163909i	−0.469243	+	0.883069i	$0.655473\pi$
$282$	1.60542	+	5.99152i	0.0956016	+	0.356790i
$283$	3.52471	+	4.35265i	0.209522	+	0.258738i	0.871064	−	0.491170i	$-0.163431\pi$
$283$	3.52471	+	4.35265i	0.209522	+	0.258738i	−0.661541	+	0.749909i	$0.730097\pi$
$284$	3.48861	+	16.4126i	0.207011	+	0.973908i
$285$	−1.23218	−	4.98670i	−0.0729881	−	0.295387i
$286$	−4.24911	+	1.38062i	−0.251255	+	0.0816377i
$287$	14.4015	+	6.66509i	0.850093	+	0.393428i
$288$	15.3547	−	7.82364i	0.904787	−	0.461012i
$289$	−3.37747	+	15.8897i	−0.198674	+	0.934690i
$290$	−5.35273	+	4.16390i	−0.314323	+	0.244512i
$291$	4.12475	−	0.876742i	0.241797	−	0.0513956i
$292$	−3.90050	−	1.49726i	−0.228260	−	0.0876207i
$293$	7.38400	−	7.38400i	0.431378	−	0.431378i	−0.457719	−	0.889097i	$-0.651333\pi$
$293$	7.38400	−	7.38400i	0.431378	−	0.431378i	0.889097	+	0.457719i	$0.151333\pi$
$294$	−3.43391	+	2.91526i	−0.200270	+	0.170022i
$295$	−4.96297	+	14.3155i	−0.288955	+	0.833483i
$296$	−0.653147	−	6.21428i	−0.0379634	−	0.361198i
$297$	−3.19625	−	8.32650i	−0.185465	−	0.483153i
$298$	12.7792	−	0.669727i	0.740277	−	0.0387962i
$299$	0.479406	−	0.830355i	0.0277247	−	0.0480207i
$300$	−1.95749	+	0.902779i	−0.113016	+	0.0521219i
$301$	8.63053	+	10.9812i	0.497456	+	0.632948i
$302$	−38.9892	−	19.8660i	−2.24358	−	1.14316i
$303$	1.00638	−	1.24278i	0.0578152	−	0.0713959i
$304$	−28.9317	−	12.8812i	−1.65935	−	0.738790i
$305$	2.01587	+	1.88777i	0.115428	+	0.108094i
$306$	1.81459	+	4.07563i	0.103733	+	0.232988i
$307$	−19.4310	−	19.4310i	−1.10899	−	1.10899i	−0.993284	−	0.115702i	$-0.963088\pi$
$307$	−19.4310	−	19.4310i	−1.10899	−	1.10899i	−0.115702	−	0.993284i	$-0.536912\pi$
$308$	3.94998	+	12.7880i	0.225071	+	0.728661i
$309$	−0.717289	−	0.233061i	−0.0408051	−	0.0132584i
$310$	2.58548	−	35.8884i	0.146845	−	2.03832i
$311$	−11.1492	−	10.0388i	−0.632212	−	0.569246i	0.289473	−	0.957186i	$-0.406520\pi$
$311$	−11.1492	−	10.0388i	−0.632212	−	0.569246i	−0.921685	+	0.387940i	$0.873187\pi$
$312$	−0.166290	+	0.256065i	−0.00941434	+	0.0144968i
$313$	−30.4559	−	1.59613i	−1.72147	−	0.0902185i	−0.834199	−	0.551464i	$-0.814069\pi$
$313$	−30.4559	−	1.59613i	−1.72147	−	0.0902185i	−0.887272	+	0.461246i	$0.847403\pi$
$314$	−11.0985	−	34.1576i	−0.626323	−	1.92762i
$315$	−1.19775	−	16.9399i	−0.0674856	−	0.954457i
$316$	−5.23108	+	16.0996i	−0.294271	+	0.905674i
$317$	−9.06260	+	23.6089i	−0.509006	+	1.32601i	0.402763	+	0.915304i	$0.368050\pi$
$317$	−9.06260	+	23.6089i	−0.509006	+	1.32601i	−0.911769	+	0.410703i	$0.865283\pi$
$318$	−5.27133	−	1.41245i	−0.295601	−	0.0792061i
$319$	7.12108	+	0.748456i	0.398704	+	0.0419055i
$320$	−0.413528	+	1.77414i	−0.0231169	+	0.0991774i
$321$	−0.871043	−	1.19889i	−0.0486169	−	0.0669154i
$322$	−6.58319	−	3.92982i	−0.366867	−	0.219000i
$323$	2.51883	−	4.94349i	0.140152	−	0.275063i
$324$	−8.14678	−	4.70355i	−0.452599	−	0.261308i
$325$	−1.70714	+	2.41634i	−0.0946951	+	0.134034i
$326$	−14.4281	−	24.9902i	−0.799097	−	1.38408i
$327$	2.34022	+	3.60362i	0.129414	+	0.199280i
$328$	1.34550	−	8.49516i	0.0742928	−	0.469066i
$329$	18.2944	−	17.7688i	1.00860	−	0.979623i
$330$	5.74013	+	1.99001i	0.315984	+	0.109546i
$331$	−6.04742	+	2.69249i	−0.332396	+	0.147992i	−0.566147	−	0.824304i	$-0.691567\pi$
$331$	−6.04742	+	2.69249i	−0.332396	+	0.147992i	0.233751	+	0.972297i	$0.424900\pi$
$332$	−0.946875	+	3.53378i	−0.0519665	+	0.193942i
$333$	−9.72053	+	7.87153i	−0.532682	+	0.431357i
$334$	12.1594	+	13.5044i	0.665332	+	0.738926i
$335$	25.3896	−	3.51379i	1.38718	−	0.191979i
$336$	3.92293	+	2.62965i	0.214014	+	0.143459i
$337$	2.24236	+	4.40088i	0.122149	+	0.239731i	0.943982	−	0.329998i	$-0.107048\pi$
$337$	2.24236	+	4.40088i	0.122149	+	0.239731i	−0.821833	+	0.569729i	$0.807048\pi$
$338$	−1.18395	+	22.5912i	−0.0643986	+	1.22880i
$339$	−0.859827	+	0.954934i	−0.0466994	+	0.0518649i
$340$	−2.23679	−	0.646486i	−0.121307	−	0.0350606i
$341$	−28.2327	+	25.4208i	−1.52889	+	1.37661i
$342$	5.12671	+	32.3688i	0.277221	+	1.75030i
$343$	17.3468	+	6.48744i	0.936642	+	0.350289i
$344$	4.44958	−	6.12432i	0.239905	−	0.330201i
$345$	−1.20122	+	0.506906i	−0.0646715	+	0.0272909i
$346$	−2.44010	+	5.48056i	−0.131181	+	0.294637i
$347$	−24.0377	+	9.22720i	−1.29041	+	0.495342i	−0.904216	−	0.427075i	$-0.859544\pi$
$347$	−24.0377	+	9.22720i	−1.29041	+	0.495342i	−0.386194	+	0.922417i	$0.626211\pi$
$348$	−0.613188	+	0.398209i	−0.0328704	+	0.0213463i
$349$	23.8148			1.27478			0.637389	−	0.770543i	$-0.280015\pi$
$349$	23.8148			1.27478			0.637389	+	0.770543i	$0.280015\pi$
$350$	19.1207	+	13.9309i	1.02205	+	0.744639i
$351$	1.24993			0.0667163
$352$	21.2582	−	13.8053i	1.13307	−	0.735823i
$353$	29.5626	−	11.3480i	1.57346	−	0.603995i	0.593792	−	0.804619i	$-0.297630\pi$
$353$	29.5626	−	11.3480i	1.57346	−	0.603995i	0.979668	+	0.200624i	$0.0642969\pi$
$354$	−1.77350	+	3.98334i	−0.0942603	+	0.211712i
$355$	−2.66361	−	31.2015i	−0.141370	−	1.65600i
$356$	12.0082	−	16.5279i	0.636433	−	0.875975i
$357$	−0.496024	+	0.662205i	−0.0262524	+	0.0350476i
$358$	0.812532	+	5.13013i	0.0429437	+	0.271136i
$359$	−9.42711	+	8.48821i	−0.497544	+	0.447990i	−0.879297	−	0.476274i	$-0.841987\pi$
$359$	−9.42711	+	8.48821i	−0.497544	+	0.447990i	0.381753	+	0.924264i	$0.375320\pi$
$360$	−8.65592	+	3.12988i	−0.456207	+	0.164959i
$361$	14.5578	−	16.1681i	0.766201	−	0.850953i
$362$	0.740304	−	14.1258i	0.0389095	−	0.742437i
$363$	−1.11520	−	2.18870i	−0.0585328	−	0.114877i
$364$	−1.87150	−	0.125453i	−0.0980932	−	0.00657552i
$365$	6.87696	+	3.67513i	0.359956	+	0.192365i
$366$	0.531817	+	0.590643i	0.0277985	+	0.0308734i
$367$	−6.10039	+	4.94000i	−0.318438	+	0.257866i	−0.775190	−	0.631728i	$-0.782346\pi$
$367$	−6.10039	+	4.94000i	−0.318438	+	0.257866i	0.456752	+	0.889594i	$0.349013\pi$
$368$	−2.08050	+	7.76452i	−0.108453	+	0.404754i
$369$	−15.7287	+	7.00286i	−0.818802	+	0.364554i
$370$	0.340769	−	17.4212i	0.0177157	−	0.905683i
$371$	5.49083	+	21.7554i	0.285070	+	1.12948i
$372$	0.606851	−	3.83151i	0.0314638	−	0.198654i
$373$	−1.98581	−	3.05789i	−0.102822	−	0.158331i	0.783515	−	0.621373i	$-0.213425\pi$
$373$	−1.98581	−	3.05789i	−0.102822	−	0.158331i	−0.886337	+	0.463042i	$0.846758\pi$
$374$	3.28101	+	5.68288i	0.169657	+	0.293855i
$375$	3.83392	−	1.21900i	0.197983	−	0.0629491i
$376$	−11.9709	−	6.91139i	−0.617351	−	0.356428i
$377$	−0.455567	+	0.894102i	−0.0234629	+	0.0460486i
$378$	0.145652	−	9.99373i	0.00749155	−	0.514022i
$379$	12.1944	+	16.7841i	0.626384	+	0.862143i	0.997798	−	0.0663239i	$-0.0211271\pi$
$379$	12.1944	+	16.7841i	0.626384	+	0.862143i	−0.371414	+	0.928467i	$0.621127\pi$
$380$	−14.6421	−	8.83985i	−0.751123	−	0.453475i
$381$	−1.17744	−	0.123754i	−0.0603221	−	0.00634010i
$382$	25.1385	+	6.73584i	1.28620	+	0.344636i
$383$	6.96275	−	18.1386i	0.355780	−	0.926838i	−0.632551	−	0.774518i	$-0.717992\pi$
$383$	6.96275	−	18.1386i	0.355780	−	0.926838i	0.988331	−	0.152320i	$-0.0486744\pi$
$384$	1.17310	−	3.61042i	0.0598643	−	0.184243i
$385$	−4.35656	−	24.5958i	−0.222031	−	1.25352i
$386$	−0.343502	−	1.05719i	−0.0174838	−	0.0538096i
$387$	−15.1327	−	0.793070i	−0.769237	−	0.0403140i
$388$	7.64729	−	11.7758i	0.388232	−	0.597825i
$389$	11.3701	+	10.2377i	0.576487	+	0.519072i	0.904991	−	0.425431i	$-0.139878\pi$
$389$	11.3701	+	10.2377i	0.576487	+	0.519072i	−0.328503	+	0.944503i	$0.606544\pi$
$390$	−0.548651	+	0.651069i	−0.0277820	+	0.0329682i
$391$	−1.33933	−	0.435173i	−0.0677326	−	0.0220077i
$392$	0.817259	−	10.0047i	0.0412778	−	0.505313i
$393$	−0.938353	−	0.938353i	−0.0473337	−	0.0473337i
$394$	17.7516	+	39.8707i	0.894312	+	2.00866i
$395$	13.4120	−	28.6047i	0.674829	−	1.43926i
$396$	−13.2657	−	5.90628i	−0.666628	−	0.296802i
$397$	−18.3983	+	22.7200i	−0.923382	+	1.14028i	0.0664145	+	0.997792i	$0.478844\pi$
$397$	−18.3983	+	22.7200i	−0.923382	+	1.14028i	−0.989796	+	0.142489i	$0.954489\pi$
$398$	−13.6784	−	6.96947i	−0.685634	−	0.349348i
$399$	−4.77858	+	3.75565i	−0.239228	+	0.188017i
$400$	8.58141	−	23.2719i	0.429071	−	1.16360i
$401$	10.9327	−	18.9359i	0.545952	−	0.945616i	−0.452595	−	0.891716i	$-0.649502\pi$
$401$	10.9327	−	18.9359i	0.545952	−	0.945616i	0.998546	−	0.0538996i	$-0.0171651\pi$
$402$	7.36619	−	0.386045i	0.367392	−	0.0192542i
$403$	−1.90802	−	4.97055i	−0.0950451	−	0.247601i
$404$	−0.556586	−	5.29556i	−0.0276912	−	0.263464i
$405$	13.9989	+	10.5952i	0.695610	+	0.526479i
$406$	7.09565	+	3.74665i	0.352151	+	0.185943i
$407$	−13.0091	+	13.0091i	−0.644836	+	0.644836i
$408$	0.418656	+	0.160707i	0.0207265	+	0.00795617i
$409$	30.0548	−	6.38835i	1.48611	−	0.315883i	0.607848	−	0.794054i	$-0.292033\pi$
$409$	30.0548	−	6.38835i	1.48611	−	0.315883i	0.878267	+	0.478170i	$0.158700\pi$
$410$	6.65960	−	23.0416i	0.328894	−	1.13795i
$411$	0.0754751	−	0.355082i	0.00372291	−	0.0175149i
$412$	−2.23756	+	1.14009i	−0.110237	+	0.0561683i
$413$	17.8546	−	1.61390i	0.878569	−	0.0794151i
$414$	7.91115	−	2.57049i	0.388812	−	0.126333i
$415$	2.57103	−	6.32516i	0.126207	−	0.310490i
$416$	0.738565	+	3.47468i	0.0362111	+	0.170360i
$417$	−2.27197	−	2.80565i	−0.111259	−	0.137393i
$418$	12.4760	+	46.5612i	0.610223	+	2.27738i
$419$	8.60424	+	6.25134i	0.420345	+	0.305398i	0.777776	−	0.628541i	$-0.216348\pi$
$419$	8.60424	+	6.25134i	0.420345	+	0.305398i	−0.357432	+	0.933939i	$0.616348\pi$
$420$	1.92625	+	1.67184i	0.0939912	+	0.0815774i
$421$	17.2687	−	12.5464i	0.841623	−	0.611475i	−0.0812007	−	0.996698i	$-0.525875\pi$
$421$	17.2687	−	12.5464i	0.841623	−	0.611475i	0.922824	+	0.385223i	$0.125875\pi$
$422$	−5.77633	−	4.67758i	−0.281187	−	0.227701i
$423$	1.44813	+	27.6319i	0.0704103	+	1.34351i
$424$	10.5319	−	6.08062i	0.511476	−	0.295301i
$425$	3.99274	+	1.71469i	0.193676	+	0.0831746i
$426$		−	9.01188i		−	0.436627i
$427$	1.05498	−	3.09280i	0.0510541	−	0.149671i
$428$	−4.87356	−	0.771896i	−0.235572	−	0.0373110i
$429$	0.894041	−	0.0939675i	0.0431647	−	0.00453679i
$430$	14.4293	−	15.4084i	0.695843	−	0.743058i
$431$	0.801158	−	7.62251i	0.0385904	−	0.367164i	−0.958136	−	0.286314i	$-0.907570\pi$
$431$	0.801158	−	7.62251i	0.0385904	−	0.367164i	0.996726	−	0.0808496i	$-0.0257634\pi$
$432$	−10.1220	+	2.71219i	−0.486996	+	0.130490i
$433$	−20.2759	+	3.21139i	−0.974399	+	0.154330i	−0.623278	−	0.782000i	$-0.714199\pi$
$433$	−20.2759	+	3.21139i	−0.974399	+	0.154330i	−0.351121	+	0.936330i	$0.614199\pi$
$434$	−39.9641	+	14.6762i	−1.91834	+	0.704481i
$435$	1.22768	−	0.595586i	0.0588630	−	0.0285562i
$436$	13.9945	+	2.97462i	0.670215	+	0.142458i
$437$	−8.67588	−	5.63418i	−0.415023	−	0.269519i
$438$	1.88193	+	1.22214i	0.0899220	+	0.0583961i
$439$	12.2397	+	2.60162i	0.584168	+	0.124169i	0.490510	−	0.871436i	$-0.336811\pi$
$439$	12.2397	+	2.60162i	0.584168	+	0.124169i	0.0936579	+	0.995604i	$0.470144\pi$
$440$	−12.1808	+	5.90925i	−0.580695	+	0.281712i
$441$	−17.6870	+	9.53543i	−0.842238	+	0.454068i
$442$	−0.908306	+	0.143862i	−0.0432037	+	0.00684280i
$443$	33.8090	−	9.05910i	1.60632	−	0.430411i	0.659373	−	0.751816i	$-0.270822\pi$
$443$	33.8090	−	9.05910i	1.60632	−	0.430411i	0.946942	+	0.321405i	$0.104155\pi$
$444$	0.196366	−	1.86830i	0.00931912	−	0.0886655i
$445$	−26.0615	+	27.8299i	−1.23544	+	1.31926i
$446$	22.6214	−	2.37761i	1.07115	−	0.112583i
$447$	−2.54313	−	0.402793i	−0.120286	−	0.0190514i
$448$	2.11466	−	0.417373i	0.0999085	−	0.0197190i
$449$			4.28525i			0.202233i	0.994875	+	0.101117i	$0.0322416\pi$
$449$			4.28525i			0.202233i	−0.994875	+	0.101117i	$0.967758\pi$
$450$	−25.0335	+	5.66854i	−1.18009	+	0.267217i
$451$	−21.9314	+	12.6621i	−1.03271	+	0.596235i
$452$	0.223927	+	4.27278i	0.0105326	+	0.200974i
$453$	6.84254	+	5.54098i	0.321491	+	0.260338i
$454$	−10.1308	+	7.36048i	−0.475464	+	0.345445i
$455$	3.43680	+	0.665283i	0.161120	+	0.0311889i
$456$	2.66505	+	1.93627i	0.124802	+	0.0906742i
$457$	−4.57736	−	17.0829i	−0.214120	−	0.799107i	−0.986474	−	0.163915i	$-0.947588\pi$
$457$	−4.57736	−	17.0829i	−0.214120	−	0.799107i	0.772355	−	0.635192i	$-0.219079\pi$
$458$	16.6479	+	20.5585i	0.777908	+	0.960636i
$459$	−0.381690	−	1.79571i	−0.0178158	−	0.0838166i
$460$	−1.63473	+	4.02171i	−0.0762197	+	0.187513i
$461$	23.7965	−	7.73195i	1.10831	−	0.360113i	0.303017	−	0.952985i	$-0.402006\pi$
$461$	23.7965	−	7.73195i	1.10831	−	0.360113i	0.805297	+	0.592872i	$0.202006\pi$
$462$	−0.647130	−	7.15920i	−0.0301072	−	0.333076i
$463$	24.3244	−	12.3939i	1.13045	−	0.575994i	0.214277	−	0.976773i	$-0.431260\pi$
$463$	24.3244	−	12.3939i	1.13045	−	0.575994i	0.916175	+	0.400779i	$0.131260\pi$
$464$	1.74913	−	8.22902i	0.0812015	−	0.382023i
$465$	−2.01022	+	6.95517i	−0.0932215	+	0.322538i
$466$	4.46256	−	0.948547i	0.206724	−	0.0439406i
$467$	−6.60852	−	2.53677i	−0.305806	−	0.117388i	0.200626	−	0.979668i	$-0.435702\pi$
$467$	−6.60852	−	2.53677i	−0.305806	−	0.117388i	−0.506432	+	0.862280i	$0.669036\pi$
$468$	1.43900	−	1.43900i	0.0665177	−	0.0665177i
$469$	−16.1452	−	25.6729i	−0.745517	−	1.18547i
$470$	−30.7353	−	23.2623i	−1.41771	−	1.07301i
$471$	0.755382	+	7.18698i	0.0348062	+	0.331159i
$472$	−3.48215	−	9.07132i	−0.160279	−	0.417541i
$473$	−22.2582	+	1.16650i	−1.02343	+	0.0536358i
$474$	4.54592	−	7.87377i	0.208801	−	0.361654i
$475$	25.0706	+	19.7578i	1.15032	+	0.906552i
$476$	0.391267	+	2.72700i	0.0179337	+	0.124992i
$477$	−21.6905	−	11.0519i	−0.993140	−	0.506030i
$478$	1.11935	−	1.38228i	0.0511977	−	0.0632239i
$479$	−34.5054	−	15.3628i	−1.57659	−	0.701943i	−0.582738	−	0.812660i	$-0.698019\pi$
$479$	−34.5054	−	15.3628i	−1.57659	−	0.701943i	−0.993852	+	0.110717i	$0.964685\pi$
$480$	2.05064	−	4.37355i	0.0935984	−	0.199624i
$481$	−1.04869	−	2.35540i	−0.0478163	−	0.107397i
$482$	−6.78154	−	6.78154i	−0.308891	−	0.308891i
$483$	1.13126	+	1.04885i	0.0514743	+	0.0477241i
$484$	−7.77889	−	2.52751i	−0.353586	−	0.114887i
$485$	−16.8862	+	20.0384i	−0.766764	+	0.909898i
$486$	12.1768	+	10.9640i	0.552349	+	0.497337i
$487$	7.15837	−	11.0229i	0.324377	−	0.499496i	−0.638433	−	0.769678i	$-0.720417\pi$
$487$	7.15837	−	11.0229i	0.324377	−	0.499496i	0.962809	+	0.270181i	$0.0870836\pi$
$488$	−1.76871	−	0.0926944i	−0.0800660	−	0.00419608i
$489$	1.79421	+	5.52200i	0.0811368	+	0.249713i
$490$	5.71971	−	27.4012i	0.258390	−	1.23786i
$491$	−7.21929	+	22.2187i	−0.325802	+	1.00272i	0.645275	+	0.763950i	$0.276743\pi$
$491$	−7.21929	+	22.2187i	−0.325802	+	1.00272i	−0.971077	+	0.238765i	$0.923257\pi$
$492$	0.926693	−	2.41412i	0.0417785	−	0.108837i
$493$	1.42363	+	0.381460i	0.0641170	+	0.0171801i
$494$	−6.71845	−	0.706137i	−0.302277	−	0.0317706i
$495$	23.2004	+	14.0067i	1.04278	+	0.629556i
$496$	26.2367	+	36.1118i	1.17806	+	1.62147i
$497$	−32.3549	+	18.0566i	−1.45132	+	0.809950i
$498$	0.892043	−	1.75073i	0.0399734	−	0.0784522i
$499$	7.78986	+	4.49748i	0.348722	+	0.201335i	0.664122	−	0.747624i	$-0.268805\pi$
$499$	7.78986	+	4.49748i	0.348722	+	0.201335i	−0.315400	+	0.948959i	$0.602139\pi$
$500$	6.15670	−	11.8969i	0.275336	−	0.532045i
$501$	−1.82819	−	3.16652i	−0.0816777	−	0.141470i
$502$	−15.1039	−	23.2579i	−0.674119	−	1.03805i
$503$	−5.63363	+	35.5693i	−0.251191	+	1.58596i	0.463228	+	0.886239i	$0.346691\pi$
$503$	−5.63363	+	35.5693i	−0.251191	+	1.58596i	−0.714419	+	0.699718i	$0.753309\pi$
$504$	7.58792	+	7.81236i	0.337993	+	0.347990i
$505$	−0.194347	+	9.93559i	−0.00864831	+	0.442128i
$506$	11.1773	−	4.97646i	0.496892	−	0.221231i
$507$	1.17810	−	4.39673i	0.0523213	−	0.195266i
$508$	−3.06360	+	2.48086i	−0.135925	+	0.110070i
$509$	−6.14407	−	6.82368i	−0.272331	−	0.302454i	0.591429	−	0.806357i	$-0.298564\pi$
$509$	−6.14407	−	6.82368i	−0.272331	−	0.302454i	−0.863761	+	0.503902i	$0.831897\pi$
$510$	1.10290	+	0.589403i	0.0488372	+	0.0260992i
$511$	0.617064	−	9.20532i	0.0272973	−	0.407220i
$512$	−7.06144	−	13.8588i	−0.312074	−	0.612480i
$513$	0.705788	−	13.4672i	0.0311613	−	0.594593i
$514$	−18.6774	+	20.7434i	−0.823827	+	0.914952i
$515$	4.40748	−	1.59369i	0.194217	−	0.0702265i
$516$	1.69133	−	1.52288i	0.0744568	−	0.0670412i
$517$	6.36667	+	40.1976i	0.280006	+	1.76789i
$518$	−18.9547	+	8.11030i	−0.832822	+	0.356346i
$519$	0.709520	−	0.976571i	0.0311445	−	0.0428667i
$520$	−0.161385	−	1.89046i	−0.00707719	−	0.0829021i
$521$	−4.96375	+	11.1488i	−0.217466	+	0.488437i	−0.989030	−	0.147715i	$-0.952808\pi$
$521$	−4.96375	+	11.1488i	−0.217466	+	0.488437i	0.771564	+	0.636152i	$0.219475\pi$
$522$	−8.12752	+	3.11986i	−0.355732	+	0.136553i
$523$	17.1195	−	11.1175i	0.748582	−	0.486135i	−0.113100	−	0.993584i	$-0.536078\pi$
$523$	17.1195	−	11.1175i	0.748582	−	0.486135i	0.861682	+	0.507449i	$0.169411\pi$
$524$	−4.41862			−0.193028
$525$	−3.18044	−	3.54170i	−0.138806	−	0.154572i
$526$	−7.35051			−0.320498
$527$	−6.55830	+	4.25901i	−0.285684	+	0.185525i
$528$	−7.03611	+	2.70091i	−0.306208	+	0.117542i
$529$	8.28697	−	18.6128i	0.360303	−	0.809253i
$530$	31.2445	−	13.1850i	1.35718	−	0.572719i
$531$	−11.4327	+	15.7357i	−0.496136	+	0.682873i
$532$	−2.40845	+	20.0934i	−0.104419	+	0.871162i
$533$	−0.555191	−	3.50534i	−0.0240480	−	0.151833i
$534$	−8.15408	+	7.34197i	−0.352862	+	0.317718i
$535$	8.84676	+	2.55693i	0.382479	+	0.110546i
$536$	−10.9989	+	12.2156i	−0.475082	+	0.527632i
$537$	0.0546965	−	1.04367i	0.00236033	−	0.0450378i
$538$	−9.57695	−	18.7958i	−0.412892	−	0.810346i
$539$	−24.4067	+	16.6679i	−1.05127	+	0.717936i
$540$	−5.60592	+	0.775832i	−0.241241	+	0.0333865i
$541$	−11.8063	−	13.1122i	−0.507591	−	0.563737i	0.433820	−	0.901000i	$-0.357165\pi$
$541$	−11.8063	−	13.1122i	−0.507591	−	0.563737i	−0.941410	+	0.337263i	$0.890499\pi$
$542$	9.36049	−	7.57997i	0.402067	−	0.325588i
$543$	−0.736644	+	2.74919i	−0.0316124	+	0.117979i
$544$	4.76636	−	2.12212i	0.204356	−	0.0909851i
$545$	−25.2282	−	8.74621i	−1.08066	−	0.374646i
$546$	0.969180	+	0.274890i	0.0414771	+	0.0117642i
$547$	0.468776	−	2.95974i	0.0200434	−	0.126549i	−0.975638	−	0.219388i	$-0.929594\pi$
$547$	0.468776	−	2.95974i	0.0200434	−	0.126549i	0.995681	+	0.0928385i	$0.0295940\pi$
$548$	−0.658323	−	1.01373i	−0.0281222	−	0.0433043i
$549$	1.77270	+	3.07040i	0.0756568	+	0.131041i
$550$	−35.7477	+	12.1408i	−1.52429	+	0.517687i
$551$	9.37617	+	5.41333i	0.399438	+	0.230616i
$552$	0.379595	−	0.744998i	0.0161567	−	0.0317092i
$553$	−37.3772	−	0.544749i	−1.58944	−	0.0231651i
$554$	32.0136	+	44.0629i	1.36013	+	1.87205i
$555$	−0.795866	+	3.41447i	−0.0337826	+	0.144936i
$556$	−11.9550	−	1.25652i	−0.507006	−	0.0532885i
$557$	30.2559	+	8.10705i	1.28198	+	0.343507i	0.834610	−	0.550841i	$-0.185693\pi$
$557$	30.2559	+	8.10705i	1.28198	+	0.343507i	0.447373	+	0.894347i	$0.352359\pi$
$558$	16.5532	−	43.1226i	0.700754	−	1.82553i
$559$	0.965254	−	2.97075i	0.0408259	−	0.125649i
$560$	−29.2751	+	2.06992i	−1.23710	+	0.0874699i
$561$	−0.408011	−	1.25573i	−0.0172262	−	0.0530169i
$562$	−8.34817	−	0.437509i	−0.352146	−	0.0184552i
$563$	−10.1341	+	15.6052i	−0.427103	+	0.657680i	−0.985064	−	0.172186i	$-0.944917\pi$
$563$	−10.1341	+	15.6052i	−0.427103	+	0.657680i	0.557962	+	0.829867i	$0.311584\pi$
$564$	−3.08833	−	2.78075i	−0.130042	−	0.117091i
$565$	0.573784	−	7.96455i	0.0241393	−	0.335071i
$566$	−9.52590	−	3.09515i	−0.400404	−	0.130099i
$567$	4.61460	−	20.2540i	0.193795	−	0.850586i
$568$	14.2005	+	14.2005i	0.595838	+	0.595838i
$569$	0.637171	+	1.43111i	0.0267116	+	0.0599952i	0.926409	−	0.376520i	$-0.122879\pi$
$569$	0.637171	+	1.43111i	0.0267116	+	0.0599952i	−0.899697	+	0.436515i	$0.856213\pi$
$570$	6.70508	+	6.27903i	0.280845	+	0.262999i
$571$	−12.0801	−	5.37840i	−0.505536	−	0.225079i	0.138090	−	0.990420i	$-0.455904\pi$
$571$	−12.0801	−	5.37840i	−0.505536	−	0.225079i	−0.643625	+	0.765341i	$0.722570\pi$
$572$	1.88374	−	2.32622i	0.0787630	−	0.0972643i
$573$	−4.66582	−	2.37736i	−0.194918	−	0.0993154i
$574$	−28.0914	+	4.03053i	−1.17251	+	0.168231i
$575$	3.95774	−	7.06961i	0.165049	−	0.294823i
$576$	−1.16929	+	2.02527i	−0.0487204	+	0.0843861i
$577$	9.27556	−	0.486112i	0.386147	−	0.0202371i	0.141725	−	0.989906i	$-0.454735\pi$
$577$	9.27556	−	0.486112i	0.386147	−	0.0202371i	0.244422	+	0.969669i	$0.421402\pi$
$578$	−10.4109	−	27.1214i	−0.433038	−	1.12810i
$579$	0.0233794	+	0.222440i	0.000971615	+	0.00924430i
$580$	1.48825	−	4.29281i	0.0617961	−	0.178249i
$581$	−8.07290	+	0.305192i	−0.334920	+	0.0126615i
$582$	−5.33245	+	5.33245i	−0.221037	+	0.221037i
$583$	−33.4283	−	12.8319i	−1.38446	−	0.531444i
$584$	−4.89123	+	1.03966i	−0.202400	+	0.0430216i
$585$	−2.99778	+	2.33197i	−0.123943	+	0.0964153i
$586$	−3.88270	+	18.2667i	−0.160393	+	0.754589i
$587$	−11.8830	+	6.05467i	−0.490462	+	0.249903i	−0.681688	−	0.731643i	$-0.738754\pi$
$587$	−11.8830	+	6.05467i	−0.490462	+	0.249903i	0.191226	+	0.981546i	$0.438754\pi$
$588$	0.865708	−	2.89106i	0.0357012	−	0.119225i
$589$	−54.6321	+	17.7511i	−2.25108	+	0.731419i
$590$	−6.49972	−	26.3047i	−0.267589	−	1.08295i
$591$	−1.82581	−	8.58974i	−0.0751036	−	0.353335i
$592$	13.6033	+	16.7987i	0.559093	+	0.690423i
$593$	−9.45404	−	35.2829i	−0.388231	−	1.44890i	−0.833011	−	0.553257i	$-0.813385\pi$
$593$	−9.45404	−	35.2829i	−0.388231	−	1.44890i	0.444780	−	0.895640i	$-0.353282\pi$
$594$	12.9038	+	9.37515i	0.529449	+	0.384667i
$595$	−0.0937160	−	5.14064i	−0.00384198	−	0.210746i
$596$	−6.93605	+	5.03934i	−0.284112	+	0.206419i
$597$	2.40053	+	1.94391i	0.0982471	+	0.0795589i
$598$	0.0897391	+	1.71232i	0.00366970	+	0.0700221i
$599$	−0.214739	+	0.123980i	−0.00877399	+	0.00506567i	−0.504381	−	0.863481i	$-0.668279\pi$
$599$	−0.214739	+	0.123980i	−0.00877399	+	0.00506567i	0.495607	+	0.868547i	$0.334946\pi$
$600$	−1.37639	+	2.18219i	−0.0561909	+	0.0890875i
$601$		−	19.3484i		−	0.789237i	−0.918845	−	0.394618i	$-0.870877\pi$
$601$		−	19.3484i		−	0.789237i	0.918845	−	0.394618i	$-0.129123\pi$
$602$	−23.6400	−	8.06381i	−0.963492	−	0.328656i
$603$	32.4991	+	5.14734i	1.32346	+	0.209616i
$604$	29.1565	−	3.06447i	1.18636	−	0.124691i
$605$	13.8210	+	6.48028i	0.561903	+	0.263461i
$606$	−0.298934	+	2.84416i	−0.0121433	+	0.115536i
$607$	34.8976	−	9.35079i	1.41645	−	0.379537i	0.532227	−	0.846601i	$-0.321355\pi$
$607$	34.8976	−	9.35079i	1.41645	−	0.379537i	0.884223	+	0.467065i	$0.154688\pi$
$608$	37.8546	−	5.99558i	1.53521	−	0.243153i
$609$	−1.23979	−	1.03423i	−0.0502386	−	0.0419093i
$610$	−4.86212	−	0.867880i	−0.196862	−	0.0351394i
$611$	−5.57903	−	1.18586i	−0.225703	−	0.0479747i
$612$	−2.50676	−	1.62791i	−0.101330	−	0.0658043i
$613$	−13.0930	−	8.50267i	−0.528820	−	0.343420i	0.252453	−	0.967609i	$-0.418763\pi$
$613$	−13.0930	−	8.50267i	−0.528820	−	0.343420i	−0.781273	+	0.624189i	$0.785429\pi$
$614$	48.0688	+	10.2173i	1.93990	+	0.412338i
$615$	−2.27463	+	4.25632i	−0.0917219	+	0.171631i
$616$	12.3008	+	10.2614i	0.495614	+	0.413443i
$617$	27.4606	−	4.34934i	1.10552	−	0.175098i	0.423120	−	0.906074i	$-0.360935\pi$
$617$	27.4606	−	4.34934i	1.10552	−	0.175098i	0.682403	+	0.730976i	$0.260935\pi$
$618$	1.30281	−	0.349086i	0.0524065	−	0.0140423i
$619$	3.75824	−	35.7573i	0.151056	−	1.43721i	−0.611992	−	0.790864i	$-0.709631\pi$
$619$	3.75824	−	35.7573i	0.151056	−	1.43721i	0.763048	−	0.646342i	$-0.223702\pi$
$620$	11.6427	+	21.1086i	0.467581	+	0.847742i
$621$	−3.40420	+	0.357796i	−0.136606	+	0.0143579i
$622$	26.4995	+	4.19711i	1.06253	+	0.168289i
$623$	42.6974	+	14.5645i	1.71063	+	0.583513i
$624$		−	1.05622i		−	0.0422827i
$625$	−14.1538	+	20.6075i	−0.566153	+	0.824300i
$626$	47.2331	−	27.2700i	1.88781	−	1.08993i
$627$	−0.507612	−	9.68582i	−0.0202721	−	0.386814i
$628$	18.7000	+	15.1429i	0.746209	+	0.604268i
$629$	−3.06365	+	2.22587i	−0.122156	+	0.0887514i
$630$	18.2958	+	24.2403i	0.728924	+	0.965756i
$631$	23.2118	+	16.8644i	0.924048	+	0.671360i	0.944528	−	0.328430i	$-0.106520\pi$
$631$	23.2118	+	16.8644i	0.924048	+	0.671360i	−0.0204802	+	0.999790i	$0.506520\pi$
$632$	5.24385	+	19.5703i	0.208589	+	0.778465i
$633$	0.941179	+	1.16226i	0.0374085	+	0.0461957i
$634$	−9.40266	−	44.2361i	−0.373427	−	1.75684i
$635$	6.24741	−	3.88555i	0.247921	−	0.154193i
$636$	3.47728	−	1.12984i	0.137883	−	0.0448009i
$637$	−0.954970	−	4.03038i	−0.0378373	−	0.159689i
$638$	−11.4094	+	5.81335i	−0.451701	+	0.230153i
$639$	8.35809	−	39.3217i	0.330641	−	1.55554i
$640$	8.02174	+	22.1847i	0.317087	+	0.876928i
$641$	−17.6000	+	3.74101i	−0.695160	+	0.147761i	−0.541922	−	0.840429i	$-0.682303\pi$
$641$	−17.6000	+	3.74101i	−0.695160	+	0.147761i	−0.153238	+	0.988189i	$0.548970\pi$
$642$	2.47412	+	0.949726i	0.0976457	+	0.0374827i
$643$	9.47610	−	9.47610i	0.373701	−	0.373701i	−0.495122	−	0.868823i	$-0.664877\pi$
$643$	9.47610	−	9.47610i	0.373701	−	0.373701i	0.868823	+	0.495122i	$0.164877\pi$
$644$	5.13297	−	0.194050i	0.202267	−	0.00764662i
$645$	−3.48448	+	2.42895i	−0.137201	+	0.0956397i
$646$	1.03714	+	9.86769i	0.0408056	+	0.388239i
$647$	4.96466	+	12.9334i	0.195181	+	0.508464i	0.995888	−	0.0905921i	$-0.0288760\pi$
$647$	4.96466	+	12.9334i	0.195181	+	0.508464i	−0.800707	+	0.599056i	$0.795543\pi$
$648$	−11.2436	+	0.589251i	−0.441689	+	0.0231480i
$649$	−14.3045	+	24.7762i	−0.561502	+	0.972549i
$650$	0.206906	−	5.28682i	0.00811554	−	0.207366i
$651$	8.47946	−	1.21662i	0.332336	−	0.0476832i
$652$	17.2257	+	8.77692i	0.674610	+	0.343731i
$653$	23.0993	−	28.5253i	0.903947	−	1.11628i	−0.0887994	−	0.996050i	$-0.528303\pi$
$653$	23.0993	−	28.5253i	0.903947	−	1.11628i	0.992746	−	0.120231i	$-0.0383637\pi$
$654$	−7.01981	−	3.12542i	−0.274496	−	0.122214i
$655$	8.18284	+	1.02221i	0.319730	+	0.0399412i
$656$	12.1021	+	27.1818i	0.472508	+	1.06127i
$657$	7.07798	+	7.07798i	0.276138	+	0.276138i
$658$	−10.1316	+	44.4686i	−0.394970	+	1.73357i
$659$	−17.1826	−	5.58297i	−0.669340	−	0.217482i	−0.0454175	−	0.998968i	$-0.514462\pi$
$659$	−17.1826	−	5.58297i	−0.669340	−	0.217482i	−0.623922	+	0.781486i	$0.714462\pi$
$660$	−3.95144	+	0.976376i	−0.153810	+	0.0380054i
$661$	−19.5718	−	17.6225i	−0.761253	−	0.685435i	0.194074	−	0.980987i	$-0.437830\pi$
$661$	−19.5718	−	17.6225i	−0.761253	−	0.685435i	−0.955327	+	0.295552i	$0.904497\pi$
$662$	6.44759	−	9.92841i	0.250593	−	0.385879i
$663$	0.184786	+	0.00968421i	0.00717648	+	0.000376103i
$664$	1.35308	+	4.16435i	0.0525097	+	0.161608i
$665$	9.10866	−	36.6538i	0.353219	−	1.42137i
$666$	6.91223	−	21.2737i	0.267843	−	0.824337i
$667$	0.984806	−	2.56551i	0.0381318	−	0.0993369i
$668$	−11.7598	−	3.15104i	−0.455002	−	0.121917i
$669$	−4.55167	−	0.478400i	−0.175978	−	0.0184960i
$670$	−34.6574	+	29.9994i	−1.33893	+	1.15898i
$671$	3.06518	+	4.21886i	0.118330	+	0.162867i
$672$	−5.71484	−	0.0832901i	−0.220455	−	0.00321299i
$673$	23.2205	−	45.5727i	0.895083	−	1.75670i	0.297896	−	0.954598i	$-0.403715\pi$
$673$	23.2205	−	45.5727i	0.895083	−	1.75670i	0.597187	−	0.802102i	$-0.296285\pi$
$674$	−7.64957	−	4.41648i	−0.294651	−	0.170117i
$675$	10.5611	−	0.139875i	0.406496	−	0.00538379i
$676$	−7.57813	−	13.1257i	−0.291466	−	0.504835i
$677$	21.5376	+	33.1651i	0.827759	+	1.27464i	0.959034	+	0.283291i	$0.0914261\pi$
$677$	21.5376	+	33.1651i	0.827759	+	1.27464i	−0.131275	+	0.991346i	$0.541907\pi$
$678$	0.359485	−	2.26970i	0.0138059	−	0.0871673i
$679$	29.8291	+	8.46047i	1.14474	+	0.324683i
$680$	−2.66664	+	0.809141i	−0.102261	+	0.0310292i
$681$	2.30181	−	1.02483i	0.0882055	−	0.0392716i
$682$	17.5842	−	65.6252i	0.673335	−	2.51292i
$683$	−8.47008	+	6.85894i	−0.324099	+	0.262450i	−0.777536	−	0.628838i	$-0.783531\pi$
$683$	−8.47008	+	6.85894i	−0.324099	+	0.262450i	0.453438	+	0.891288i	$0.350198\pi$
$684$	−14.6918	−	16.3169i	−0.561755	−	0.623892i
$685$	0.984629	+	2.02962i	0.0376207	+	0.0775478i
$686$	−32.3359	+	7.16576i	−1.23459	+	0.273590i
$687$	−2.41650	−	4.74265i	−0.0921953	−	0.180943i
$688$	−1.37056	+	26.1518i	−0.0522520	+	0.997028i
$689$	3.35774	−	3.72915i	0.127920	−	0.142069i
$690$	1.30789	−	1.93025i	0.0497905	−	0.0734834i
$691$	25.6649	−	23.1088i	0.976340	−	0.879101i	−0.0163408	−	0.999866i	$-0.505202\pi$
$691$	25.6649	−	23.1088i	0.976340	−	0.879101i	0.992681	+	0.120766i	$0.0385350\pi$
$692$	−0.628759	−	3.96983i	−0.0239018	−	0.150910i
$693$	3.81618	−	31.8381i	0.144965	−	1.20943i
$694$	27.0650	−	37.2518i	1.02737	−	1.41406i
$695$	21.8488	+	5.09266i	0.828772	+	0.193175i
$696$	−0.355927	+	0.799424i	−0.0134914	+	0.0303021i
$697$	−4.86641	+	1.86804i	−0.184328	+	0.0707570i
$698$	−35.7180	+	23.1955i	−1.35195	+	0.877963i
$699$	−0.917976			−0.0347211
$700$	−15.8270	−	0.850562i	−0.598204	−	0.0321482i
$701$	16.6461			0.628716			0.314358	−	0.949305i	$-0.398211\pi$
$701$	16.6461			0.628716			0.314358	+	0.949305i	$0.398211\pi$
$702$	−1.87467	+	1.21743i	−0.0707549	+	0.0459488i
$703$	−25.9702	+	9.96904i	−0.979486	+	0.375989i
$704$	−1.39907	+	3.14236i	−0.0527293	+	0.118432i
$705$	5.07597	+	5.86412i	0.191172	+	0.220856i
$706$	−33.2858	+	45.8139i	−1.25273	+	1.72423i
$707$	10.8102	−	4.62545i	0.406560	−	0.173958i
$708$	−0.456990	−	2.88532i	−0.0171747	−	0.108437i
$709$	−13.9859	+	12.5930i	−0.525253	+	0.472940i	−0.888580	−	0.458722i	$-0.848308\pi$
$709$	−13.9859	+	12.5930i	−0.525253	+	0.472940i	0.363327	+	0.931662i	$0.381641\pi$
$710$	34.3851	+	44.2024i	1.29045	+	1.65889i
$711$	27.1378	−	30.1396i	1.01775	−	1.13032i
$712$	1.27969	−	24.4179i	0.0479583	−	0.915099i
$713$	6.61935	+	12.9912i	0.247897	+	0.486525i
$714$	0.0989623	−	1.47631i	0.00370357	−	0.0552497i
$715$	−4.02664	+	3.87214i	−0.150588	+	0.144810i
$716$	−2.32850	−	2.58606i	−0.0870201	−	0.0966456i
$717$	−0.278129	+	0.225225i	−0.0103869	+	0.00841116i
$718$	5.87151	−	21.9128i	0.219123	−	0.817777i
$719$	−37.9155	+	16.8811i	−1.41401	+	0.629558i	−0.964588	−	0.263761i	$-0.915037\pi$
$719$	−37.9155	+	16.8811i	−1.41401	+	0.629558i	−0.449423	+	0.893319i	$0.648370\pi$
$720$	19.2161	−	25.3893i	0.716143	−	0.946203i
$721$	−3.86367	−	3.97795i	−0.143890	−	0.148147i
$722$	−6.08648	+	38.4285i	−0.226515	+	1.43016i
$723$	1.05100	+	1.61840i	0.0390872	+	0.0601890i
$724$	4.73846	+	8.20725i	0.176103	+	0.305020i
$725$	−3.74919	+	7.60556i	−0.139242	+	0.282463i
$726$	3.80439	+	2.19646i	0.141194	+	0.0815184i
$727$	9.01500	−	17.6929i	0.334348	−	0.656195i	−0.661225	−	0.750188i	$-0.729963\pi$
$727$	9.01500	−	17.6929i	0.334348	−	0.656195i	0.995573	+	0.0939929i	$0.0299631\pi$
$728$	−1.96034	+	1.09403i	−0.0726550	+	0.0405473i
$729$	11.9070	+	16.3886i	0.441001	+	0.606985i
$730$	−13.8938	+	1.18608i	−0.514232	+	0.0438990i
$731$	−4.56268	−	0.479557i	−0.168757	−	0.0177371i
$732$	−0.514343	−	0.137818i	−0.0190107	−	0.00509389i
$733$	3.55260	−	9.25483i	0.131218	−	0.341835i	−0.852192	−	0.523228i	$-0.824727\pi$
$733$	3.55260	−	9.25483i	0.131218	−	0.341835i	0.983411	+	0.181394i	$0.0580608\pi$
$734$	4.33796	−	13.3509i	0.160117	−	0.492790i
$735$	−2.27203	+	5.15367i	−0.0838049	+	0.190096i
$736$	−3.00613	−	9.25192i	−0.110807	−	0.341030i
$737$	48.3314	+	2.53294i	1.78031	+	0.0933020i
$738$	16.7695	−	25.8227i	0.617293	−	0.950547i
$739$	6.85463	+	6.17193i	0.252152	+	0.227038i	0.785507	−	0.618853i	$-0.212402\pi$
$739$	6.85463	+	6.17193i	0.252152	+	0.227038i	−0.533355	+	0.845891i	$0.679069\pi$
$740$	6.16539	+	9.91305i	0.226644	+	0.364411i
$741$	1.29274	+	0.420038i	0.0474901	+	0.0154305i
$742$	−29.4250	−	27.2812i	−1.08022	−	1.00152i
$743$	−31.8855	−	31.8855i	−1.16976	−	1.16976i	−0.982265	−	0.187500i	$-0.939962\pi$
$743$	−31.8855	−	31.8855i	−1.16976	−	1.16976i	−0.187500	−	0.982265i	$-0.560038\pi$
$744$	−1.88846	−	4.24155i	−0.0692342	−	0.155503i
$745$	14.0107	−	7.72774i	0.513311	−	0.283122i
$746$	5.95674	+	2.65211i	0.218092	+	0.0971006i
$747$	5.51599	−	6.81168i	0.201819	−	0.249226i
$748$	−3.91720	−	1.99592i	−0.143227	−	0.0729779i
$749$	−1.54751	−	10.7856i	−0.0565447	−	0.394098i
$750$	−4.56289	+	5.56251i	−0.166613	+	0.203114i
$751$	−4.83420	+	8.37308i	−0.176403	+	0.305538i	−0.940646	−	0.339390i	$-0.889779\pi$
$751$	−4.83420	+	8.37308i	−0.176403	+	0.305538i	0.764243	+	0.644928i	$0.223113\pi$
$752$	47.7525	−	2.50260i	1.74136	−	0.0912606i
$753$	1.99968	+	5.20934i	0.0728723	+	0.189839i
$754$	−0.187581	−	1.78471i	−0.00683130	−	0.0649955i
$755$	−54.7037	−	1.07004i	−1.99087	−	0.0389427i
$756$	3.56481	+	5.66849i	0.129651	+	0.206161i
$757$	−29.1640	+	29.1640i	−1.05998	+	1.05998i	−0.0619022	+	0.998082i	$0.519717\pi$
$757$	−29.1640	+	29.1640i	−1.05998	+	1.05998i	−0.998082	+	0.0619022i	$0.980283\pi$
$758$	−34.6371	−	13.2959i	−1.25808	−	0.482930i
$759$	−2.40804	+	0.511844i	−0.0874062	+	0.0185788i
$760$	−20.4597	+	0.671354i	−0.742151	+	0.0243526i
$761$	0.778111	−	3.66072i	0.0282065	−	0.132701i	−0.961791	−	0.273783i	$-0.911725\pi$
$761$	0.778111	−	3.66072i	0.0282065	−	0.132701i	0.989998	+	0.141082i	$0.0450582\pi$
$762$	1.88649	−	0.961213i	0.0683402	−	0.0348211i
$763$	2.84418	+	31.4651i	0.102966	+	1.13911i
$764$	−16.5829	+	5.38810i	−0.599947	+	0.194934i
$765$	4.26566	+	3.59464i	0.154225	+	0.129965i
$766$	7.22402	+	33.9863i	0.261014	+	1.22798i

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.49982 + 0.973996i) q^{2} +(0.335932 - 0.128952i) q^{3} +(0.487325 - 1.09455i) q^{4} +(-1.15569 + 1.91426i) q^{5} +(-0.378240 + 0.520602i) q^{6} +(2.62695 + 0.314872i) q^{7} +(-0.224327 - 1.41635i) q^{8} +(-2.13321 + 1.92075i) q^{9} +O(q^{10})\)	\(q+(-1.49982 + 0.973996i) q^{2} +(0.335932 - 0.128952i) q^{3} +(0.487325 - 1.09455i) q^{4} +(-1.15569 + 1.91426i) q^{5} +(-0.378240 + 0.520602i) q^{6} +(2.62695 + 0.314872i) q^{7} +(-0.224327 - 1.41635i) q^{8} +(-2.13321 + 1.92075i) q^{9} +(-0.131145 - 3.99668i) q^{10} +(-2.82518 + 3.13767i) q^{11} +(0.0225635 - 0.430536i) q^{12} +(-0.268631 - 0.527217i) q^{13} +(-4.24664 + 2.08638i) q^{14} +(-0.141386 + 0.792089i) q^{15} +(3.31938 + 3.68655i) q^{16} +(-0.675395 + 0.546924i) q^{17} +(1.32863 - 4.95853i) q^{18} +(-5.83214 + 2.59663i) q^{19} +(1.53205 + 2.19783i) q^{20} +(0.923080 - 0.232975i) q^{21} +(1.18118 - 7.45766i) q^{22} +(0.882537 + 1.35899i) q^{23} +(-0.258000 - 0.446869i) q^{24} +(-2.32875 - 4.42458i) q^{25} +(0.916406 + 0.529087i) q^{26} +(-0.959010 + 1.88216i) q^{27} +(1.62482 - 2.72188i) q^{28} +(-0.996818 - 1.37200i) q^{29} +(-0.559437 - 1.32570i) q^{30} +(8.94867 + 0.940543i) q^{31} +(-5.79889 - 1.55381i) q^{32} +(-0.544457 + 1.41836i) q^{33} +(0.480271 - 1.47812i) q^{34} +(-3.63869 + 4.66476i) q^{35} +(1.06279 + 3.27094i) q^{36} +(4.35142 + 0.228048i) q^{37} +(6.21806 - 9.57497i) q^{38} +(-0.158228 - 0.142469i) q^{39} +(2.97051 + 1.20744i) q^{40} +(5.70437 + 1.85346i) q^{41} +(-1.15754 + 1.24850i) q^{42} +(3.73281 + 3.73281i) q^{43} +(2.05756 + 4.62136i) q^{44} +(-1.21148 - 6.30331i) q^{45} +(-2.64730 - 1.17865i) q^{46} +(6.06621 - 7.49114i) q^{47} +(1.59048 + 0.810389i) q^{48} +(6.80171 + 1.65430i) q^{49} +(7.80224 + 4.36789i) q^{50} +(-0.156360 + 0.270823i) q^{51} +(-0.707976 + 0.0371035i) q^{52} +(3.03918 + 7.91735i) q^{53} +(-0.394875 - 3.75698i) q^{54} +(-2.74128 - 9.03429i) q^{55} +(-0.143329 - 3.79131i) q^{56} +(-1.62436 + 1.62436i) q^{57} +(2.83137 + 1.08686i) q^{58} +(6.62786 - 1.40879i) q^{59} +(0.798080 + 0.540760i) q^{60} +(0.256792 - 1.20811i) q^{61} +(-14.3375 + 7.30532i) q^{62} +(-6.20863 + 4.37403i) q^{63} +(0.774814 - 0.251752i) q^{64} +(1.31968 + 0.0950730i) q^{65} +(-0.564887 - 2.65758i) q^{66} +(-7.21376 - 8.90825i) q^{67} +(0.269499 + 1.00578i) q^{68} +(0.471717 + 0.342723i) q^{69} +(0.913931 - 10.5404i) q^{70} +(-11.3299 + 8.23164i) q^{71} +(3.19899 + 2.59049i) q^{72} +(-0.182500 - 3.48231i) q^{73} +(-6.74848 + 3.89623i) q^{74} +(-1.35286 - 1.18606i) q^{75} +7.64897i q^{76} +(-8.40955 + 7.35294i) q^{77} +(0.376077 + 0.0595648i) q^{78} +(-14.0514 + 1.47686i) q^{79} +(-10.8932 + 2.09364i) q^{80} +(0.820700 - 7.80844i) q^{81} +(-10.3608 + 2.77617i) q^{82} +(-3.01586 + 0.477665i) q^{83} +(0.194837 - 1.12389i) q^{84} +(-0.266404 - 1.92496i) q^{85} +(-9.23428 - 1.96281i) q^{86} +(-0.511786 - 0.332358i) q^{87} +(5.07780 + 3.29756i) q^{88} +(16.6785 + 3.54513i) q^{89} +(7.95640 + 8.27388i) q^{90} +(-0.539673 - 1.46956i) q^{91} +(1.91756 - 0.303712i) q^{92} +(3.12743 - 0.837993i) q^{93} +(-1.80189 + 17.1438i) q^{94} +(1.76953 - 14.1651i) q^{95} +(-2.14840 + 0.225806i) q^{96} +(11.5748 + 1.83327i) q^{97} +(-11.8126 + 4.14368i) q^{98} -12.1198i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

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